TSTP Solution File: ALG139+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG139+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 15:36:15 EDT 2022
% Result : Unsatisfiable 4.62s 1.54s
% Output : Proof 10.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10 % Problem : ALG139+1 : TPTP v8.1.0. Released v2.7.0.
% 0.10/0.11 % Command : ePrincess-casc -timeout=%d %s
% 0.10/0.31 % Computer : n032.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 600
% 0.10/0.31 % DateTime : Thu Jun 9 06:46:52 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.16/0.54 ____ _
% 0.16/0.54 ___ / __ \_____(_)___ ________ __________
% 0.16/0.54 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.16/0.54 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.16/0.54 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.16/0.54
% 0.16/0.54 A Theorem Prover for First-Order Logic
% 0.16/0.54 (ePrincess v.1.0)
% 0.16/0.54
% 0.16/0.54 (c) Philipp Rümmer, 2009-2015
% 0.16/0.54 (c) Peter Backeman, 2014-2015
% 0.16/0.54 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.16/0.54 Free software under GNU Lesser General Public License (LGPL).
% 0.16/0.54 Bug reports to peter@backeman.se
% 0.16/0.54
% 0.16/0.54 For more information, visit http://user.uu.se/~petba168/breu/
% 0.16/0.54
% 0.16/0.54 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.59 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.92/0.99 Prover 0: Preprocessing ...
% 3.21/1.26 Prover 0: Constructing countermodel ...
% 4.62/1.54 Prover 0: proved (948ms)
% 4.62/1.54
% 4.62/1.54 No countermodel exists, formula is valid
% 4.62/1.54 % SZS status Unsatisfiable for theBenchmark
% 4.62/1.54
% 4.62/1.54 Generating proof ... found it (size 1274)
% 8.99/2.53
% 8.99/2.53 % SZS output start Proof for theBenchmark
% 8.99/2.53 Assumed formulas after preprocessing and simplification:
% 8.99/2.53 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ( ~ (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(v15, v15) = v19 & op(v15, e3) = v18 & op(v10, v10) = v17 & op(v10, e2) = v16 & op(v5, v5) = v21 & op(v5, e1) = v20 & op(v0, v0) = v23 & op(v0, e0) = v22 & op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & ! [v24] : ! [v25] : ! [v26] : ! [v27] : (v25 = v24 | ~ (op(v27, v26) = v25) | ~ (op(v27, v26) = v24)) & ( ~ (v23 = e3) | ~ (v22 = e2) | ~ (v0 = e1)) & ( ~ (v23 = e3) | ~ (v22 = e1) | ~ (v0 = e2)) & ( ~ (v23 = e2) | ~ (v22 = e3) | ~ (v0 = e1)) & ( ~ (v23 = e2) | ~ (v22 = e1) | ~ (v0 = e3)) & ( ~ (v23 = e1) | ~ (v22 = e3) | ~ (v0 = e2)) & ( ~ (v23 = e1) | ~ (v22 = e2) | ~ (v0 = e3)) & ( ~ (v21 = e3) | ~ (v20 = e2) | ~ (v5 = e0)) & ( ~ (v21 = e3) | ~ (v20 = e0) | ~ (v5 = e2)) & ( ~ (v21 = e2) | ~ (v20 = e3) | ~ (v5 = e0)) & ( ~ (v21 = e2) | ~ (v20 = e0) | ~ (v5 = e3)) & ( ~ (v21 = e0) | ~ (v20 = e3) | ~ (v5 = e2)) & ( ~ (v21 = e0) | ~ (v20 = e2) | ~ (v5 = e3)) & ( ~ (v19 = e2) | ~ (v18 = e1) | ~ (v15 = e0)) & ( ~ (v19 = e2) | ~ (v18 = e0) | ~ (v15 = e1)) & ( ~ (v19 = e1) | ~ (v18 = e2) | ~ (v15 = e0)) & ( ~ (v19 = e1) | ~ (v18 = e0) | ~ (v15 = e2)) & ( ~ (v19 = e0) | ~ (v18 = e2) | ~ (v15 = e1)) & ( ~ (v19 = e0) | ~ (v18 = e1) | ~ (v15 = e2)) & ( ~ (v17 = e3) | ~ (v16 = e1) | ~ (v10 = e0)) & ( ~ (v17 = e3) | ~ (v16 = e0) | ~ (v10 = e1)) & ( ~ (v17 = e1) | ~ (v16 = e3) | ~ (v10 = e0)) & ( ~ (v17 = e1) | ~ (v16 = e0) | ~ (v10 = e3)) & ( ~ (v17 = e0) | ~ (v16 = e3) | ~ (v10 = e1)) & ( ~ (v17 = e0) | ~ (v16 = e1) | ~ (v10 = 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) & ((v15 = e2 & ~ (v10 = e3)) | (v5 = e2 & ~ (v10 = e1)) | (v0 = e2 & ~ (v10 = e0))) & ((v15 = e1 & ~ (v5 = e3)) | (v10 = e1 & ~ (v5 = e2)) | (v0 = e1 & ~ (v5 = e0))) & ((v15 = e0 & ~ (v0 = e3)) | (v10 = e0 & ~ (v0 = e2)) | (v5 = e0 & ~ (v0 = e1))) & ((v10 = e3 & ~ (v15 = e2)) | (v5 = e3 & ~ (v15 = e1)) | (v0 = e3 & ~ (v15 = e0))))
% 8.99/2.58 | 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, all_0_19_19, all_0_20_20, all_0_21_21, all_0_22_22, all_0_23_23 yields:
% 8.99/2.58 | (1) ~ (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_8_8 = all_0_16_16) & ~ (all_0_8_8 = all_0_20_20) & ~ (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_9_9 = all_0_17_17) & ~ (all_0_9_9 = all_0_21_21) & ~ (all_0_10_10 = all_0_11_11) & ~ (all_0_10_10 = all_0_14_14) & ~ (all_0_10_10 = all_0_18_18) & ~ (all_0_10_10 = all_0_22_22) & ~ (all_0_11_11 = all_0_15_15) & ~ (all_0_11_11 = all_0_19_19) & ~ (all_0_11_11 = all_0_23_23) & ~ (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 = all_0_20_20) & ~ (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 = all_0_21_21) & ~ (all_0_14_14 = all_0_15_15) & ~ (all_0_14_14 = all_0_18_18) & ~ (all_0_14_14 = all_0_22_22) & ~ (all_0_15_15 = all_0_19_19) & ~ (all_0_15_15 = all_0_23_23) & ~ (all_0_16_16 = all_0_17_17) & ~ (all_0_16_16 = all_0_18_18) & ~ (all_0_16_16 = all_0_19_19) & ~ (all_0_16_16 = all_0_20_20) & ~ (all_0_17_17 = all_0_18_18) & ~ (all_0_17_17 = all_0_19_19) & ~ (all_0_17_17 = all_0_21_21) & ~ (all_0_18_18 = all_0_19_19) & ~ (all_0_18_18 = all_0_22_22) & ~ (all_0_19_19 = all_0_23_23) & ~ (all_0_20_20 = all_0_21_21) & ~ (all_0_20_20 = all_0_22_22) & ~ (all_0_20_20 = all_0_23_23) & ~ (all_0_21_21 = all_0_22_22) & ~ (all_0_21_21 = all_0_23_23) & ~ (all_0_22_22 = all_0_23_23) & ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ (e1 = e0) & op(all_0_8_8, all_0_8_8) = all_0_4_4 & op(all_0_8_8, e3) = all_0_5_5 & op(all_0_13_13, all_0_13_13) = all_0_6_6 & op(all_0_13_13, e2) = all_0_7_7 & op(all_0_18_18, all_0_18_18) = all_0_2_2 & op(all_0_18_18, e1) = all_0_3_3 & op(all_0_23_23, all_0_23_23) = all_0_0_0 & op(all_0_23_23, e0) = all_0_1_1 & op(e3, e3) = all_0_8_8 & op(e3, e2) = all_0_9_9 & op(e3, e1) = all_0_10_10 & op(e3, e0) = all_0_11_11 & op(e2, e3) = all_0_12_12 & op(e2, e2) = all_0_13_13 & op(e2, e1) = all_0_14_14 & op(e2, e0) = all_0_15_15 & op(e1, e3) = all_0_16_16 & op(e1, e2) = all_0_17_17 & op(e1, e1) = all_0_18_18 & op(e1, e0) = all_0_19_19 & op(e0, e3) = all_0_20_20 & op(e0, e2) = all_0_21_21 & op(e0, e1) = all_0_22_22 & op(e0, e0) = all_0_23_23 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) & ( ~ (all_0_0_0 = e3) | ~ (all_0_1_1 = e2) | ~ (all_0_23_23 = e1)) & ( ~ (all_0_0_0 = e3) | ~ (all_0_1_1 = e1) | ~ (all_0_23_23 = e2)) & ( ~ (all_0_0_0 = e2) | ~ (all_0_1_1 = e3) | ~ (all_0_23_23 = e1)) & ( ~ (all_0_0_0 = e2) | ~ (all_0_1_1 = e1) | ~ (all_0_23_23 = e3)) & ( ~ (all_0_0_0 = e1) | ~ (all_0_1_1 = e3) | ~ (all_0_23_23 = e2)) & ( ~ (all_0_0_0 = e1) | ~ (all_0_1_1 = e2) | ~ (all_0_23_23 = e3)) & ( ~ (all_0_2_2 = e3) | ~ (all_0_3_3 = e2) | ~ (all_0_18_18 = e0)) & ( ~ (all_0_2_2 = e3) | ~ (all_0_3_3 = e0) | ~ (all_0_18_18 = e2)) & ( ~ (all_0_2_2 = e2) | ~ (all_0_3_3 = e3) | ~ (all_0_18_18 = e0)) & ( ~ (all_0_2_2 = e2) | ~ (all_0_3_3 = e0) | ~ (all_0_18_18 = e3)) & ( ~ (all_0_2_2 = e0) | ~ (all_0_3_3 = e3) | ~ (all_0_18_18 = e2)) & ( ~ (all_0_2_2 = e0) | ~ (all_0_3_3 = e2) | ~ (all_0_18_18 = e3)) & ( ~ (all_0_4_4 = e2) | ~ (all_0_5_5 = e1) | ~ (all_0_8_8 = e0)) & ( ~ (all_0_4_4 = e2) | ~ (all_0_5_5 = e0) | ~ (all_0_8_8 = e1)) & ( ~ (all_0_4_4 = e1) | ~ (all_0_5_5 = e2) | ~ (all_0_8_8 = e0)) & ( ~ (all_0_4_4 = e1) | ~ (all_0_5_5 = e0) | ~ (all_0_8_8 = e2)) & ( ~ (all_0_4_4 = e0) | ~ (all_0_5_5 = e2) | ~ (all_0_8_8 = e1)) & ( ~ (all_0_4_4 = e0) | ~ (all_0_5_5 = e1) | ~ (all_0_8_8 = e2)) & ( ~ (all_0_6_6 = e3) | ~ (all_0_7_7 = e1) | ~ (all_0_13_13 = e0)) & ( ~ (all_0_6_6 = e3) | ~ (all_0_7_7 = e0) | ~ (all_0_13_13 = e1)) & ( ~ (all_0_6_6 = e1) | ~ (all_0_7_7 = e3) | ~ (all_0_13_13 = e0)) & ( ~ (all_0_6_6 = e1) | ~ (all_0_7_7 = e0) | ~ (all_0_13_13 = e3)) & ( ~ (all_0_6_6 = e0) | ~ (all_0_7_7 = e3) | ~ (all_0_13_13 = e1)) & ( ~ (all_0_6_6 = e0) | ~ (all_0_7_7 = e1) | ~ (all_0_13_13 = e3)) & (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 = e3 | all_0_12_12 = e3 | all_0_16_16 = e3 | all_0_20_20 = 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 = e2 | all_0_12_12 = e2 | all_0_16_16 = e2 | all_0_20_20 = 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 = e1 | all_0_12_12 = e1 | all_0_16_16 = e1 | all_0_20_20 = e1) & (all_0_8_8 = e0 | all_0_9_9 = e0 | all_0_10_10 = e0 | all_0_11_11 = e0) & (all_0_8_8 = e0 | all_0_12_12 = e0 | all_0_16_16 = e0 | all_0_20_20 = e0) & (all_0_9_9 = e3 | all_0_9_9 = e2 | all_0_9_9 = e1 | all_0_9_9 = e0) & (all_0_9_9 = e3 | all_0_13_13 = e3 | all_0_17_17 = e3 | all_0_21_21 = e3) & (all_0_9_9 = e2 | all_0_13_13 = e2 | all_0_17_17 = e2 | all_0_21_21 = e2) & (all_0_9_9 = e1 | all_0_13_13 = e1 | all_0_17_17 = e1 | all_0_21_21 = e1) & (all_0_9_9 = e0 | all_0_13_13 = e0 | all_0_17_17 = e0 | all_0_21_21 = e0) & (all_0_10_10 = e3 | all_0_10_10 = e2 | all_0_10_10 = e1 | all_0_10_10 = e0) & (all_0_10_10 = e3 | all_0_14_14 = e3 | all_0_18_18 = e3 | all_0_22_22 = e3) & (all_0_10_10 = e2 | all_0_14_14 = e2 | all_0_18_18 = e2 | all_0_22_22 = e2) & (all_0_10_10 = e1 | all_0_14_14 = e1 | all_0_18_18 = e1 | all_0_22_22 = e1) & (all_0_10_10 = e0 | all_0_14_14 = e0 | all_0_18_18 = e0 | all_0_22_22 = e0) & (all_0_11_11 = e3 | all_0_11_11 = e2 | all_0_11_11 = e1 | all_0_11_11 = e0) & (all_0_11_11 = e3 | all_0_15_15 = e3 | all_0_19_19 = e3 | all_0_23_23 = e3) & (all_0_11_11 = e2 | all_0_15_15 = e2 | all_0_19_19 = e2 | all_0_23_23 = e2) & (all_0_11_11 = e1 | all_0_15_15 = e1 | all_0_19_19 = e1 | all_0_23_23 = e1) & (all_0_11_11 = e0 | all_0_15_15 = e0 | all_0_19_19 = e0 | all_0_23_23 = 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) & (all_0_16_16 = e3 | all_0_16_16 = e2 | all_0_16_16 = e1 | all_0_16_16 = e0) & (all_0_16_16 = e3 | all_0_17_17 = e3 | all_0_18_18 = e3 | all_0_19_19 = e3) & (all_0_16_16 = e2 | all_0_17_17 = e2 | all_0_18_18 = e2 | all_0_19_19 = e2) & (all_0_16_16 = e1 | all_0_17_17 = e1 | all_0_18_18 = e1 | all_0_19_19 = e1) & (all_0_16_16 = e0 | all_0_17_17 = e0 | all_0_18_18 = e0 | all_0_19_19 = e0) & (all_0_17_17 = e3 | all_0_17_17 = e2 | all_0_17_17 = e1 | all_0_17_17 = e0) & (all_0_18_18 = e3 | all_0_18_18 = e2 | all_0_18_18 = e1 | all_0_18_18 = e0) & (all_0_19_19 = e3 | all_0_19_19 = e2 | all_0_19_19 = e1 | all_0_19_19 = e0) & (all_0_20_20 = e3 | all_0_20_20 = e2 | all_0_20_20 = e1 | all_0_20_20 = e0) & (all_0_20_20 = e3 | all_0_21_21 = e3 | all_0_22_22 = e3 | all_0_23_23 = e3) & (all_0_20_20 = e2 | all_0_21_21 = e2 | all_0_22_22 = e2 | all_0_23_23 = e2) & (all_0_20_20 = e1 | all_0_21_21 = e1 | all_0_22_22 = e1 | all_0_23_23 = e1) & (all_0_20_20 = e0 | all_0_21_21 = e0 | all_0_22_22 = e0 | all_0_23_23 = e0) & (all_0_21_21 = e3 | all_0_21_21 = e2 | all_0_21_21 = e1 | all_0_21_21 = e0) & (all_0_22_22 = e3 | all_0_22_22 = e2 | all_0_22_22 = e1 | all_0_22_22 = e0) & (all_0_23_23 = e3 | all_0_23_23 = e2 | all_0_23_23 = e1 | all_0_23_23 = e0) & ((all_0_8_8 = e2 & ~ (all_0_13_13 = e3)) | (all_0_18_18 = e2 & ~ (all_0_13_13 = e1)) | (all_0_23_23 = e2 & ~ (all_0_13_13 = e0))) & ((all_0_8_8 = e1 & ~ (all_0_18_18 = e3)) | (all_0_13_13 = e1 & ~ (all_0_18_18 = e2)) | (all_0_23_23 = e1 & ~ (all_0_18_18 = e0))) & ((all_0_8_8 = e0 & ~ (all_0_23_23 = e3)) | (all_0_13_13 = e0 & ~ (all_0_23_23 = e2)) | (all_0_18_18 = e0 & ~ (all_0_23_23 = e1))) & ((all_0_13_13 = e3 & ~ (all_0_8_8 = e2)) | (all_0_18_18 = e3 & ~ (all_0_8_8 = e1)) | (all_0_23_23 = e3 & ~ (all_0_8_8 = e0)))
% 9.43/2.60 |
% 9.43/2.60 | Applying alpha-rule on (1) yields:
% 9.43/2.60 | (2) ~ (all_0_18_18 = all_0_19_19)
% 9.43/2.60 | (3) ~ (all_0_11_11 = all_0_23_23)
% 9.43/2.60 | (4) all_0_11_11 = e1 | all_0_15_15 = e1 | all_0_19_19 = e1 | all_0_23_23 = e1
% 9.43/2.60 | (5) op(e1, e2) = all_0_17_17
% 9.43/2.60 | (6) ~ (all_0_6_6 = e1) | ~ (all_0_7_7 = e0) | ~ (all_0_13_13 = e3)
% 9.43/2.60 | (7) all_0_20_20 = e1 | all_0_21_21 = e1 | all_0_22_22 = e1 | all_0_23_23 = e1
% 9.43/2.60 | (8) ~ (all_0_22_22 = all_0_23_23)
% 9.43/2.60 | (9) ~ (all_0_8_8 = all_0_20_20)
% 9.43/2.60 | (10) ~ (all_0_16_16 = all_0_19_19)
% 9.43/2.60 | (11) op(e1, e1) = all_0_18_18
% 9.43/2.60 | (12) ~ (all_0_14_14 = all_0_15_15)
% 9.43/2.60 | (13) all_0_10_10 = e0 | all_0_14_14 = e0 | all_0_18_18 = e0 | all_0_22_22 = e0
% 9.43/2.60 | (14) op(all_0_13_13, e2) = all_0_7_7
% 9.43/2.60 | (15) all_0_9_9 = e1 | all_0_13_13 = e1 | all_0_17_17 = e1 | all_0_21_21 = e1
% 9.43/2.60 | (16) all_0_8_8 = e2 | all_0_12_12 = e2 | all_0_16_16 = e2 | all_0_20_20 = e2
% 9.43/2.60 | (17) all_0_8_8 = e3 | all_0_9_9 = e3 | all_0_10_10 = e3 | all_0_11_11 = e3
% 9.43/2.60 | (18) all_0_8_8 = e2 | all_0_9_9 = e2 | all_0_10_10 = e2 | all_0_11_11 = e2
% 9.43/2.60 | (19) ~ (all_0_8_8 = all_0_11_11)
% 9.43/2.60 | (20) all_0_20_20 = e2 | all_0_21_21 = e2 | all_0_22_22 = e2 | all_0_23_23 = e2
% 9.43/2.60 | (21) all_0_9_9 = e3 | all_0_9_9 = e2 | all_0_9_9 = e1 | all_0_9_9 = e0
% 9.43/2.60 | (22) op(e3, e2) = all_0_9_9
% 9.43/2.60 | (23) ~ (all_0_12_12 = all_0_20_20)
% 9.43/2.60 | (24) ~ (e2 = e1)
% 9.43/2.60 | (25) ~ (all_0_12_12 = all_0_16_16)
% 9.43/2.60 | (26) ~ (all_0_14_14 = all_0_18_18)
% 9.43/2.60 | (27) ~ (all_0_20_20 = all_0_22_22)
% 9.43/2.60 | (28) all_0_19_19 = e3 | all_0_19_19 = e2 | all_0_19_19 = e1 | all_0_19_19 = e0
% 9.43/2.60 | (29) all_0_10_10 = e3 | all_0_14_14 = e3 | all_0_18_18 = e3 | all_0_22_22 = e3
% 9.43/2.60 | (30) all_0_13_13 = e3 | all_0_13_13 = e2 | all_0_13_13 = e1 | all_0_13_13 = e0
% 9.43/2.60 | (31) ~ (all_0_17_17 = all_0_21_21)
% 9.43/2.60 | (32) all_0_9_9 = e3 | all_0_13_13 = e3 | all_0_17_17 = e3 | all_0_21_21 = e3
% 9.43/2.60 | (33) op(e1, e0) = all_0_19_19
% 9.43/2.60 | (34) all_0_16_16 = e0 | all_0_17_17 = e0 | all_0_18_18 = e0 | all_0_19_19 = e0
% 9.43/2.60 | (35) ~ (all_0_13_13 = all_0_15_15)
% 9.43/2.60 | (36) ~ (all_0_0_0 = e1) | ~ (all_0_1_1 = e2) | ~ (all_0_23_23 = e3)
% 9.43/2.60 | (37) op(e3, e3) = all_0_8_8
% 9.43/2.60 | (38) ~ (all_0_19_19 = all_0_23_23)
% 9.43/2.60 | (39) all_0_12_12 = e0 | all_0_13_13 = e0 | all_0_14_14 = e0 | all_0_15_15 = e0
% 9.43/2.60 | (40) ~ (e3 = e0)
% 9.43/2.60 | (41) ~ (all_0_2_2 = e2) | ~ (all_0_3_3 = e0) | ~ (all_0_18_18 = e3)
% 9.43/2.60 | (42) ~ (all_0_18_18 = all_0_22_22)
% 9.43/2.60 | (43) op(e0, e2) = all_0_21_21
% 9.43/2.60 | (44) ~ (all_0_6_6 = e3) | ~ (all_0_7_7 = e0) | ~ (all_0_13_13 = e1)
% 9.43/2.60 | (45) ~ (all_0_17_17 = all_0_18_18)
% 9.43/2.60 | (46) all_0_14_14 = e3 | all_0_14_14 = e2 | all_0_14_14 = e1 | all_0_14_14 = e0
% 9.43/2.60 | (47) op(all_0_13_13, all_0_13_13) = all_0_6_6
% 9.43/2.60 | (48) ~ (all_0_14_14 = all_0_22_22)
% 9.43/2.60 | (49) op(e1, e3) = all_0_16_16
% 9.43/2.60 | (50) all_0_11_11 = e0 | all_0_15_15 = e0 | all_0_19_19 = e0 | all_0_23_23 = e0
% 9.43/2.60 | (51) ~ (all_0_15_15 = all_0_19_19)
% 9.43/2.60 | (52) op(all_0_8_8, all_0_8_8) = all_0_4_4
% 9.43/2.60 | (53) ~ (all_0_4_4 = e2) | ~ (all_0_5_5 = e0) | ~ (all_0_8_8 = e1)
% 9.43/2.60 | (54) ~ (all_0_2_2 = e3) | ~ (all_0_3_3 = e2) | ~ (all_0_18_18 = e0)
% 9.43/2.60 | (55) op(all_0_23_23, e0) = all_0_1_1
% 9.43/2.60 | (56) all_0_11_11 = e3 | all_0_15_15 = e3 | all_0_19_19 = e3 | all_0_23_23 = e3
% 9.43/2.60 | (57) ~ (all_0_10_10 = all_0_22_22)
% 9.43/2.60 | (58) all_0_22_22 = e3 | all_0_22_22 = e2 | all_0_22_22 = e1 | all_0_22_22 = e0
% 9.43/2.60 | (59) ~ (all_0_17_17 = all_0_19_19)
% 9.43/2.61 | (60) op(e2, e0) = all_0_15_15
% 9.43/2.61 | (61) ~ (all_0_13_13 = all_0_21_21)
% 9.43/2.61 | (62) all_0_18_18 = e3 | all_0_18_18 = e2 | all_0_18_18 = e1 | all_0_18_18 = e0
% 9.43/2.61 | (63) op(all_0_8_8, e3) = all_0_5_5
% 9.43/2.61 | (64) all_0_8_8 = e0 | all_0_9_9 = e0 | all_0_10_10 = e0 | all_0_11_11 = e0
% 9.43/2.61 | (65) all_0_23_23 = e3 | all_0_23_23 = e2 | all_0_23_23 = e1 | all_0_23_23 = e0
% 9.43/2.61 | (66) ~ (all_0_12_12 = all_0_13_13)
% 9.43/2.61 | (67) all_0_17_17 = e3 | all_0_17_17 = e2 | all_0_17_17 = e1 | all_0_17_17 = e0
% 9.43/2.61 | (68) ~ (all_0_16_16 = all_0_20_20)
% 9.43/2.61 | (69) (all_0_13_13 = e3 & ~ (all_0_8_8 = e2)) | (all_0_18_18 = e3 & ~ (all_0_8_8 = e1)) | (all_0_23_23 = e3 & ~ (all_0_8_8 = e0))
% 9.43/2.61 | (70) ~ (all_0_2_2 = e0) | ~ (all_0_3_3 = e3) | ~ (all_0_18_18 = e2)
% 9.43/2.61 | (71) all_0_10_10 = e1 | all_0_14_14 = e1 | all_0_18_18 = e1 | all_0_22_22 = e1
% 9.43/2.61 | (72) ~ (all_0_21_21 = all_0_22_22)
% 9.43/2.61 | (73) ~ (all_0_4_4 = e0) | ~ (all_0_5_5 = e2) | ~ (all_0_8_8 = e1)
% 9.43/2.61 | (74) all_0_9_9 = e2 | all_0_13_13 = e2 | all_0_17_17 = e2 | all_0_21_21 = e2
% 9.43/2.61 | (75) ~ (all_0_12_12 = all_0_14_14)
% 9.43/2.61 | (76) ~ (all_0_10_10 = all_0_18_18)
% 9.43/2.61 | (77) all_0_16_16 = e2 | all_0_17_17 = e2 | all_0_18_18 = e2 | all_0_19_19 = e2
% 9.43/2.61 | (78) ~ (all_0_16_16 = all_0_17_17)
% 9.43/2.61 | (79) op(e2, e2) = all_0_13_13
% 9.43/2.61 | (80) all_0_11_11 = e3 | all_0_11_11 = e2 | all_0_11_11 = e1 | all_0_11_11 = e0
% 9.43/2.61 | (81) all_0_12_12 = e3 | all_0_13_13 = e3 | all_0_14_14 = e3 | all_0_15_15 = e3
% 9.43/2.61 | (82) op(e3, e0) = all_0_11_11
% 9.43/2.61 | (83) all_0_11_11 = e2 | all_0_15_15 = e2 | all_0_19_19 = e2 | all_0_23_23 = e2
% 9.43/2.61 | (84) ~ (all_0_4_4 = e2) | ~ (all_0_5_5 = e1) | ~ (all_0_8_8 = e0)
% 9.43/2.61 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 9.43/2.61 | (86) ~ (all_0_13_13 = all_0_14_14)
% 9.43/2.61 | (87) op(e0, e1) = all_0_22_22
% 9.43/2.61 | (88) ~ (e1 = e0)
% 9.43/2.61 | (89) all_0_12_12 = e2 | all_0_13_13 = e2 | all_0_14_14 = e2 | all_0_15_15 = e2
% 9.43/2.61 | (90) all_0_15_15 = e3 | all_0_15_15 = e2 | all_0_15_15 = e1 | all_0_15_15 = e0
% 9.43/2.61 | (91) ~ (all_0_8_8 = all_0_12_12)
% 9.43/2.61 | (92) ~ (all_0_4_4 = e1) | ~ (all_0_5_5 = e2) | ~ (all_0_8_8 = e0)
% 9.43/2.61 | (93) ~ (all_0_0_0 = e2) | ~ (all_0_1_1 = e3) | ~ (all_0_23_23 = e1)
% 9.43/2.61 | (94) op(all_0_18_18, e1) = all_0_3_3
% 9.43/2.61 | (95) op(all_0_18_18, all_0_18_18) = all_0_2_2
% 9.43/2.61 | (96) ~ (all_0_0_0 = e3) | ~ (all_0_1_1 = e1) | ~ (all_0_23_23 = e2)
% 9.43/2.61 | (97) ~ (all_0_0_0 = e2) | ~ (all_0_1_1 = e1) | ~ (all_0_23_23 = e3)
% 9.43/2.61 | (98) ~ (all_0_8_8 = all_0_16_16)
% 9.43/2.61 | (99) ~ (all_0_2_2 = e2) | ~ (all_0_3_3 = e3) | ~ (all_0_18_18 = e0)
% 9.43/2.61 | (100) ~ (all_0_16_16 = all_0_18_18)
% 9.43/2.61 | (101) ~ (all_0_4_4 = e1) | ~ (all_0_5_5 = e0) | ~ (all_0_8_8 = e2)
% 9.43/2.61 | (102) all_0_16_16 = e1 | all_0_17_17 = e1 | all_0_18_18 = e1 | all_0_19_19 = e1
% 9.43/2.61 | (103) op(all_0_23_23, all_0_23_23) = all_0_0_0
% 9.43/2.61 | (104) ~ (all_0_9_9 = all_0_21_21)
% 9.43/2.61 | (105) ~ (all_0_11_11 = all_0_19_19)
% 9.43/2.61 | (106) ~ (all_0_13_13 = all_0_17_17)
% 9.43/2.61 | (107) all_0_20_20 = e0 | all_0_21_21 = e0 | all_0_22_22 = e0 | all_0_23_23 = e0
% 9.43/2.61 | (108) ~ (all_0_21_21 = all_0_23_23)
% 9.43/2.61 | (109) ~ (all_0_15_15 = all_0_23_23)
% 9.43/2.61 | (110) ~ (all_0_6_6 = e1) | ~ (all_0_7_7 = e3) | ~ (all_0_13_13 = e0)
% 9.43/2.61 | (111) ~ (all_0_6_6 = e0) | ~ (all_0_7_7 = e3) | ~ (all_0_13_13 = e1)
% 9.43/2.61 | (112) ~ (all_0_6_6 = e0) | ~ (all_0_7_7 = e1) | ~ (all_0_13_13 = e3)
% 9.43/2.61 | (113) all_0_8_8 = e3 | all_0_12_12 = e3 | all_0_16_16 = e3 | all_0_20_20 = e3
% 9.43/2.61 | (114) all_0_8_8 = e3 | all_0_8_8 = e2 | all_0_8_8 = e1 | all_0_8_8 = e0
% 9.43/2.61 | (115) ~ (all_0_4_4 = e0) | ~ (all_0_5_5 = e1) | ~ (all_0_8_8 = e2)
% 9.43/2.61 | (116) all_0_20_20 = e3 | all_0_21_21 = e3 | all_0_22_22 = e3 | all_0_23_23 = e3
% 9.43/2.61 | (117) op(e3, e1) = all_0_10_10
% 9.43/2.61 | (118) op(e0, e3) = all_0_20_20
% 9.43/2.61 | (119) ~ (e2 = e0)
% 9.43/2.61 | (120) (all_0_8_8 = e0 & ~ (all_0_23_23 = e3)) | (all_0_13_13 = e0 & ~ (all_0_23_23 = e2)) | (all_0_18_18 = e0 & ~ (all_0_23_23 = e1))
% 9.43/2.62 | (121) ~ (all_0_2_2 = e3) | ~ (all_0_3_3 = e0) | ~ (all_0_18_18 = e2)
% 9.43/2.62 | (122) ~ (all_0_10_10 = all_0_11_11)
% 9.43/2.62 | (123) ~ (all_0_6_6 = e3) | ~ (all_0_7_7 = e1) | ~ (all_0_13_13 = e0)
% 9.43/2.62 | (124) all_0_8_8 = e1 | all_0_9_9 = e1 | all_0_10_10 = e1 | all_0_11_11 = e1
% 9.43/2.62 | (125) ~ (all_0_0_0 = e1) | ~ (all_0_1_1 = e3) | ~ (all_0_23_23 = e2)
% 9.43/2.62 | (126) ~ (e3 = e2)
% 9.43/2.62 | (127) all_0_8_8 = e1 | all_0_12_12 = e1 | all_0_16_16 = e1 | all_0_20_20 = e1
% 9.43/2.62 | (128) ~ (all_0_11_11 = all_0_15_15)
% 9.43/2.62 | (129) ~ (all_0_2_2 = e0) | ~ (all_0_3_3 = e2) | ~ (all_0_18_18 = e3)
% 9.43/2.62 | (130) all_0_12_12 = e1 | all_0_13_13 = e1 | all_0_14_14 = e1 | all_0_15_15 = e1
% 9.43/2.62 | (131) ~ (all_0_20_20 = all_0_21_21)
% 9.43/2.62 | (132) (all_0_8_8 = e2 & ~ (all_0_13_13 = e3)) | (all_0_18_18 = e2 & ~ (all_0_13_13 = e1)) | (all_0_23_23 = e2 & ~ (all_0_13_13 = e0))
% 9.43/2.62 | (133) ~ (all_0_10_10 = all_0_14_14)
% 9.43/2.62 | (134) ~ (all_0_9_9 = all_0_10_10)
% 9.43/2.62 | (135) ~ (all_0_9_9 = all_0_11_11)
% 9.43/2.62 | (136) op(e2, e3) = all_0_12_12
% 9.43/2.62 | (137) all_0_21_21 = e3 | all_0_21_21 = e2 | all_0_21_21 = e1 | all_0_21_21 = e0
% 9.43/2.62 | (138) ~ (all_0_12_12 = all_0_15_15)
% 9.43/2.62 | (139) ~ (all_0_8_8 = all_0_10_10)
% 9.43/2.62 | (140) ~ (all_0_8_8 = all_0_9_9)
% 9.43/2.62 | (141) all_0_16_16 = e3 | all_0_17_17 = e3 | all_0_18_18 = e3 | all_0_19_19 = e3
% 9.43/2.62 | (142) all_0_8_8 = e0 | all_0_12_12 = e0 | all_0_16_16 = e0 | all_0_20_20 = e0
% 9.43/2.62 | (143) all_0_12_12 = e3 | all_0_12_12 = e2 | all_0_12_12 = e1 | all_0_12_12 = e0
% 9.43/2.62 | (144) op(e0, e0) = all_0_23_23
% 9.43/2.62 | (145) ~ (all_0_9_9 = all_0_17_17)
% 9.43/2.62 | (146) ~ (all_0_0_0 = e3) | ~ (all_0_1_1 = e2) | ~ (all_0_23_23 = e1)
% 9.43/2.62 | (147) all_0_10_10 = e3 | all_0_10_10 = e2 | all_0_10_10 = e1 | all_0_10_10 = e0
% 9.43/2.62 | (148) all_0_20_20 = e3 | all_0_20_20 = e2 | all_0_20_20 = e1 | all_0_20_20 = e0
% 9.43/2.62 | (149) ~ (all_0_20_20 = all_0_23_23)
% 9.43/2.62 | (150) all_0_10_10 = e2 | all_0_14_14 = e2 | all_0_18_18 = e2 | all_0_22_22 = e2
% 9.43/2.62 | (151) all_0_9_9 = e0 | all_0_13_13 = e0 | all_0_17_17 = e0 | all_0_21_21 = e0
% 9.43/2.62 | (152) ~ (all_0_9_9 = all_0_13_13)
% 9.43/2.62 | (153) op(e2, e1) = all_0_14_14
% 9.43/2.62 | (154) all_0_16_16 = e3 | all_0_16_16 = e2 | all_0_16_16 = e1 | all_0_16_16 = e0
% 9.43/2.62 | (155) ~ (e3 = e1)
% 9.43/2.62 | (156) (all_0_8_8 = e1 & ~ (all_0_18_18 = e3)) | (all_0_13_13 = e1 & ~ (all_0_18_18 = e2)) | (all_0_23_23 = e1 & ~ (all_0_18_18 = e0))
% 9.43/2.62 |
% 9.43/2.62 +-Applying beta-rule and splitting (120), into two cases.
% 9.43/2.62 |-Branch one:
% 9.43/2.62 | (157) (all_0_8_8 = e0 & ~ (all_0_23_23 = e3)) | (all_0_13_13 = e0 & ~ (all_0_23_23 = e2))
% 9.43/2.62 |
% 9.43/2.62 +-Applying beta-rule and splitting (157), into two cases.
% 9.43/2.62 |-Branch one:
% 9.43/2.62 | (158) all_0_8_8 = e0 & ~ (all_0_23_23 = e3)
% 9.43/2.62 |
% 9.43/2.62 | Applying alpha-rule on (158) yields:
% 9.43/2.62 | (159) all_0_8_8 = e0
% 9.43/2.62 | (160) ~ (all_0_23_23 = e3)
% 9.43/2.62 |
% 9.43/2.62 | Equations (159) can reduce 140 to:
% 9.43/2.62 | (161) ~ (all_0_9_9 = e0)
% 9.43/2.62 |
% 9.43/2.62 | Simplifying 161 yields:
% 9.43/2.62 | (162) ~ (all_0_9_9 = e0)
% 9.43/2.62 |
% 9.43/2.62 | Equations (159) can reduce 91 to:
% 9.43/2.62 | (163) ~ (all_0_12_12 = e0)
% 9.43/2.62 |
% 9.43/2.62 | Simplifying 163 yields:
% 9.43/2.62 | (164) ~ (all_0_12_12 = e0)
% 9.43/2.62 |
% 9.43/2.62 | Equations (159) can reduce 9 to:
% 9.43/2.62 | (165) ~ (all_0_20_20 = e0)
% 9.43/2.62 |
% 9.43/2.62 | Simplifying 165 yields:
% 9.43/2.62 | (166) ~ (all_0_20_20 = e0)
% 9.43/2.62 |
% 9.43/2.62 | From (159)(159) and (52) follows:
% 9.43/2.62 | (167) op(e0, e0) = all_0_4_4
% 9.43/2.63 |
% 9.43/2.63 | From (159) and (63) follows:
% 9.43/2.63 | (168) op(e0, e3) = all_0_5_5
% 9.43/2.63 |
% 9.43/2.63 | Instantiating formula (85) with e0, e3, all_0_5_5, all_0_20_20 and discharging atoms op(e0, e3) = all_0_5_5, op(e0, e3) = all_0_20_20, yields:
% 9.43/2.63 | (169) all_0_5_5 = all_0_20_20
% 9.43/2.63 |
% 9.43/2.63 | Instantiating formula (85) with e0, e0, all_0_4_4, all_0_23_23 and discharging atoms op(e0, e0) = all_0_4_4, op(e0, e0) = all_0_23_23, yields:
% 9.43/2.63 | (170) all_0_4_4 = all_0_23_23
% 9.43/2.63 |
% 9.43/2.63 +-Applying beta-rule and splitting (84), into two cases.
% 9.43/2.63 |-Branch one:
% 9.43/2.63 | (171) ~ (all_0_4_4 = e2)
% 9.43/2.63 |
% 9.43/2.63 | Equations (170) can reduce 171 to:
% 9.43/2.63 | (172) ~ (all_0_23_23 = e2)
% 9.43/2.63 |
% 9.43/2.63 +-Applying beta-rule and splitting (132), into two cases.
% 9.43/2.63 |-Branch one:
% 9.43/2.63 | (173) (all_0_8_8 = e2 & ~ (all_0_13_13 = e3)) | (all_0_18_18 = e2 & ~ (all_0_13_13 = e1))
% 9.43/2.63 |
% 9.43/2.63 +-Applying beta-rule and splitting (173), into two cases.
% 9.43/2.63 |-Branch one:
% 9.43/2.63 | (174) all_0_8_8 = e2 & ~ (all_0_13_13 = e3)
% 9.43/2.63 |
% 9.43/2.63 | Applying alpha-rule on (174) yields:
% 9.43/2.63 | (175) all_0_8_8 = e2
% 9.43/2.63 | (176) ~ (all_0_13_13 = e3)
% 9.43/2.63 |
% 9.43/2.63 | Combining equations (175,159) yields a new equation:
% 9.43/2.63 | (177) e2 = e0
% 9.43/2.63 |
% 9.43/2.63 | Simplifying 177 yields:
% 9.43/2.63 | (178) e2 = e0
% 9.43/2.63 |
% 9.43/2.63 | Equations (178) can reduce 119 to:
% 9.43/2.63 | (179) $false
% 9.43/2.63 |
% 9.43/2.63 |-The branch is then unsatisfiable
% 9.43/2.63 |-Branch two:
% 9.43/2.63 | (180) all_0_18_18 = e2 & ~ (all_0_13_13 = e1)
% 9.43/2.63 |
% 9.43/2.63 | Applying alpha-rule on (180) yields:
% 9.43/2.63 | (181) all_0_18_18 = e2
% 9.43/2.63 | (182) ~ (all_0_13_13 = e1)
% 9.43/2.63 |
% 9.43/2.63 | Equations (181) can reduce 100 to:
% 9.43/2.63 | (183) ~ (all_0_16_16 = e2)
% 9.43/2.63 |
% 9.43/2.63 | Equations (181) can reduce 2 to:
% 9.43/2.63 | (184) ~ (all_0_19_19 = e2)
% 9.43/2.63 |
% 9.43/2.63 | Simplifying 184 yields:
% 9.43/2.63 | (185) ~ (all_0_19_19 = e2)
% 9.43/2.63 |
% 9.43/2.63 | Equations (181) can reduce 42 to:
% 9.43/2.63 | (186) ~ (all_0_22_22 = e2)
% 9.43/2.63 |
% 9.43/2.63 | Simplifying 186 yields:
% 9.43/2.63 | (187) ~ (all_0_22_22 = e2)
% 9.43/2.63 |
% 9.43/2.63 | From (181) and (11) follows:
% 9.43/2.63 | (188) op(e1, e1) = e2
% 9.43/2.63 |
% 9.43/2.63 +-Applying beta-rule and splitting (69), into two cases.
% 9.43/2.63 |-Branch one:
% 9.43/2.63 | (189) (all_0_13_13 = e3 & ~ (all_0_8_8 = e2)) | (all_0_18_18 = e3 & ~ (all_0_8_8 = e1))
% 9.43/2.63 |
% 9.43/2.63 +-Applying beta-rule and splitting (189), into two cases.
% 9.43/2.63 |-Branch one:
% 9.43/2.63 | (190) all_0_13_13 = e3 & ~ (all_0_8_8 = e2)
% 9.43/2.63 |
% 9.43/2.63 | Applying alpha-rule on (190) yields:
% 9.43/2.63 | (191) all_0_13_13 = e3
% 9.43/2.63 | (192) ~ (all_0_8_8 = e2)
% 9.43/2.63 |
% 9.43/2.63 | Equations (191) can reduce 152 to:
% 9.43/2.63 | (193) ~ (all_0_9_9 = e3)
% 9.43/2.63 |
% 9.43/2.63 | Equations (191) can reduce 106 to:
% 9.43/2.63 | (194) ~ (all_0_17_17 = e3)
% 9.43/2.63 |
% 9.43/2.63 | Simplifying 194 yields:
% 9.43/2.63 | (195) ~ (all_0_17_17 = e3)
% 9.43/2.63 |
% 9.43/2.63 | Equations (191) can reduce 182 to:
% 9.43/2.64 | (155) ~ (e3 = e1)
% 9.43/2.64 |
% 9.43/2.64 +-Applying beta-rule and splitting (156), into two cases.
% 9.43/2.64 |-Branch one:
% 9.43/2.64 | (197) (all_0_8_8 = e1 & ~ (all_0_18_18 = e3)) | (all_0_13_13 = e1 & ~ (all_0_18_18 = e2))
% 9.43/2.64 |
% 9.43/2.64 +-Applying beta-rule and splitting (197), into two cases.
% 9.43/2.64 |-Branch one:
% 9.43/2.64 | (198) all_0_8_8 = e1 & ~ (all_0_18_18 = e3)
% 9.43/2.64 |
% 9.43/2.64 | Applying alpha-rule on (198) yields:
% 9.43/2.64 | (199) all_0_8_8 = e1
% 9.43/2.64 | (200) ~ (all_0_18_18 = e3)
% 9.43/2.64 |
% 9.43/2.64 | Combining equations (159,199) yields a new equation:
% 9.43/2.64 | (201) e1 = e0
% 9.43/2.64 |
% 9.43/2.64 | Equations (201) can reduce 88 to:
% 9.43/2.64 | (179) $false
% 9.43/2.64 |
% 9.43/2.64 |-The branch is then unsatisfiable
% 9.43/2.64 |-Branch two:
% 9.43/2.64 | (203) all_0_13_13 = e1 & ~ (all_0_18_18 = e2)
% 9.43/2.64 |
% 9.43/2.64 | Applying alpha-rule on (203) yields:
% 9.43/2.64 | (204) all_0_13_13 = e1
% 9.43/2.64 | (205) ~ (all_0_18_18 = e2)
% 9.43/2.64 |
% 9.43/2.64 | Combining equations (204,191) yields a new equation:
% 9.43/2.64 | (206) e3 = e1
% 9.43/2.64 |
% 9.43/2.64 | Equations (206) can reduce 155 to:
% 9.43/2.64 | (179) $false
% 9.43/2.64 |
% 9.43/2.64 |-The branch is then unsatisfiable
% 9.43/2.64 |-Branch two:
% 9.43/2.64 | (208) all_0_23_23 = e1 & ~ (all_0_18_18 = e0)
% 9.43/2.64 |
% 9.43/2.64 | Applying alpha-rule on (208) yields:
% 9.43/2.64 | (209) all_0_23_23 = e1
% 9.43/2.64 | (210) ~ (all_0_18_18 = e0)
% 9.43/2.64 |
% 9.43/2.64 | Combining equations (209,170) yields a new equation:
% 9.43/2.64 | (211) all_0_4_4 = e1
% 9.43/2.64 |
% 9.43/2.64 | Equations (209) can reduce 3 to:
% 9.43/2.64 | (212) ~ (all_0_11_11 = e1)
% 9.43/2.64 |
% 9.43/2.64 | Equations (181) can reduce 210 to:
% 9.43/2.64 | (119) ~ (e2 = e0)
% 9.43/2.64 |
% 9.43/2.64 | Equations (209) can reduce 149 to:
% 9.43/2.64 | (214) ~ (all_0_20_20 = e1)
% 9.43/2.64 |
% 9.43/2.64 | Equations (209) can reduce 108 to:
% 9.43/2.64 | (215) ~ (all_0_21_21 = e1)
% 9.43/2.64 |
% 9.43/2.64 | Equations (209) can reduce 160 to:
% 9.43/2.64 | (216) ~ (e3 = e1)
% 9.43/2.64 |
% 9.43/2.64 | Simplifying 216 yields:
% 9.43/2.64 | (155) ~ (e3 = e1)
% 9.43/2.64 |
% 9.43/2.64 | Equations (209) can reduce 172 to:
% 9.43/2.64 | (218) ~ (e2 = e1)
% 9.43/2.64 |
% 9.43/2.64 | Simplifying 218 yields:
% 9.43/2.64 | (24) ~ (e2 = e1)
% 9.43/2.64 |
% 9.43/2.64 | From (209)(209) and (103) follows:
% 9.43/2.64 | (220) op(e1, e1) = all_0_0_0
% 9.43/2.64 |
% 9.43/2.64 | From (209) and (55) follows:
% 9.43/2.64 | (221) op(e1, e0) = all_0_1_1
% 9.43/2.64 |
% 9.43/2.64 +-Applying beta-rule and splitting (92), into two cases.
% 9.43/2.64 |-Branch one:
% 9.43/2.64 | (222) ~ (all_0_4_4 = e1)
% 9.43/2.64 |
% 9.43/2.64 | Equations (211) can reduce 222 to:
% 9.43/2.64 | (179) $false
% 9.43/2.64 |
% 9.43/2.64 |-The branch is then unsatisfiable
% 9.43/2.64 |-Branch two:
% 9.43/2.64 | (211) all_0_4_4 = e1
% 9.43/2.64 | (225) ~ (all_0_5_5 = e2) | ~ (all_0_8_8 = e0)
% 9.43/2.64 |
% 9.43/2.64 +-Applying beta-rule and splitting (225), into two cases.
% 9.43/2.64 |-Branch one:
% 9.43/2.64 | (226) ~ (all_0_5_5 = e2)
% 9.43/2.65 |
% 9.43/2.65 | Equations (169) can reduce 226 to:
% 9.43/2.65 | (227) ~ (all_0_20_20 = e2)
% 9.43/2.65 |
% 9.43/2.65 +-Applying beta-rule and splitting (16), into two cases.
% 9.43/2.65 |-Branch one:
% 9.43/2.65 | (175) all_0_8_8 = e2
% 9.43/2.65 |
% 9.43/2.65 | Combining equations (159,175) yields a new equation:
% 9.43/2.65 | (178) e2 = e0
% 9.43/2.65 |
% 9.43/2.65 | Equations (178) can reduce 119 to:
% 9.43/2.65 | (179) $false
% 9.43/2.65 |
% 9.43/2.65 |-The branch is then unsatisfiable
% 9.43/2.65 |-Branch two:
% 9.43/2.65 | (192) ~ (all_0_8_8 = e2)
% 9.43/2.65 | (232) all_0_12_12 = e2 | all_0_16_16 = e2 | all_0_20_20 = e2
% 9.43/2.65 |
% 9.43/2.65 +-Applying beta-rule and splitting (232), into two cases.
% 9.43/2.65 |-Branch one:
% 9.43/2.65 | (233) all_0_12_12 = e2
% 9.43/2.65 |
% 9.43/2.65 | Equations (233) can reduce 138 to:
% 9.43/2.65 | (234) ~ (all_0_15_15 = e2)
% 9.43/2.65 |
% 9.43/2.65 | Simplifying 234 yields:
% 9.43/2.65 | (235) ~ (all_0_15_15 = e2)
% 9.43/2.65 |
% 9.43/2.65 | Equations (233) can reduce 25 to:
% 9.43/2.65 | (236) ~ (all_0_16_16 = e2)
% 9.43/2.65 |
% 9.43/2.65 | Simplifying 236 yields:
% 9.43/2.65 | (183) ~ (all_0_16_16 = e2)
% 9.43/2.65 |
% 9.43/2.65 | Equations (233) can reduce 23 to:
% 9.43/2.65 | (238) ~ (all_0_20_20 = e2)
% 9.43/2.65 |
% 9.43/2.65 | Simplifying 238 yields:
% 9.43/2.65 | (227) ~ (all_0_20_20 = e2)
% 9.43/2.65 |
% 9.43/2.65 +-Applying beta-rule and splitting (130), into two cases.
% 9.43/2.65 |-Branch one:
% 9.43/2.65 | (240) all_0_12_12 = e1
% 9.43/2.65 |
% 9.43/2.65 | Combining equations (233,240) yields a new equation:
% 9.43/2.65 | (241) e2 = e1
% 9.43/2.65 |
% 9.43/2.65 | Simplifying 241 yields:
% 9.43/2.65 | (242) e2 = e1
% 9.43/2.65 |
% 9.43/2.65 | Equations (242) can reduce 24 to:
% 9.43/2.65 | (179) $false
% 9.43/2.65 |
% 9.43/2.65 |-The branch is then unsatisfiable
% 9.43/2.65 |-Branch two:
% 9.43/2.65 | (244) ~ (all_0_12_12 = e1)
% 9.43/2.65 | (245) all_0_13_13 = e1 | all_0_14_14 = e1 | all_0_15_15 = e1
% 9.43/2.65 |
% 9.43/2.65 | Equations (233) can reduce 244 to:
% 9.43/2.65 | (24) ~ (e2 = e1)
% 9.43/2.65 |
% 9.43/2.65 +-Applying beta-rule and splitting (20), into two cases.
% 9.43/2.65 |-Branch one:
% 9.43/2.65 | (247) all_0_20_20 = e2
% 9.43/2.65 |
% 9.43/2.65 | Equations (247) can reduce 227 to:
% 9.43/2.65 | (179) $false
% 9.43/2.65 |
% 9.43/2.65 |-The branch is then unsatisfiable
% 9.43/2.65 |-Branch two:
% 9.43/2.65 | (227) ~ (all_0_20_20 = e2)
% 9.43/2.65 | (250) all_0_21_21 = e2 | all_0_22_22 = e2 | all_0_23_23 = e2
% 9.43/2.65 |
% 9.43/2.65 +-Applying beta-rule and splitting (250), into two cases.
% 9.43/2.65 |-Branch one:
% 9.43/2.65 | (251) all_0_21_21 = e2
% 9.43/2.65 |
% 9.43/2.65 | Equations (251) can reduce 131 to:
% 9.43/2.65 | (227) ~ (all_0_20_20 = e2)
% 9.43/2.65 |
% 9.43/2.65 | Equations (251) can reduce 215 to:
% 9.43/2.65 | (24) ~ (e2 = e1)
% 9.43/2.65 |
% 9.43/2.65 +-Applying beta-rule and splitting (83), into two cases.
% 9.43/2.65 |-Branch one:
% 9.43/2.65 | (254) all_0_11_11 = e2
% 9.43/2.65 |
% 9.43/2.65 | Equations (254) can reduce 212 to:
% 9.43/2.65 | (24) ~ (e2 = e1)
% 9.43/2.65 |
% 9.43/2.65 +-Applying beta-rule and splitting (17), into two cases.
% 9.43/2.65 |-Branch one:
% 9.43/2.65 | (256) all_0_8_8 = e3
% 9.43/2.65 |
% 9.43/2.65 | Combining equations (159,256) yields a new equation:
% 9.43/2.65 | (257) e3 = e0
% 9.43/2.65 |
% 9.43/2.65 | Equations (257) can reduce 40 to:
% 9.43/2.65 | (179) $false
% 9.43/2.65 |
% 9.43/2.65 |-The branch is then unsatisfiable
% 9.43/2.65 |-Branch two:
% 9.43/2.65 | (259) ~ (all_0_8_8 = e3)
% 9.43/2.65 | (260) all_0_9_9 = e3 | all_0_10_10 = e3 | all_0_11_11 = e3
% 9.43/2.65 |
% 9.43/2.66 +-Applying beta-rule and splitting (260), into two cases.
% 9.43/2.66 |-Branch one:
% 9.43/2.66 | (261) all_0_9_9 = e3
% 9.43/2.66 |
% 9.43/2.66 | Equations (261) can reduce 193 to:
% 9.43/2.66 | (179) $false
% 9.43/2.66 |
% 9.43/2.66 |-The branch is then unsatisfiable
% 9.43/2.66 |-Branch two:
% 9.43/2.66 | (193) ~ (all_0_9_9 = e3)
% 9.43/2.66 | (264) all_0_10_10 = e3 | all_0_11_11 = e3
% 9.43/2.66 |
% 9.43/2.66 +-Applying beta-rule and splitting (127), into two cases.
% 9.43/2.66 |-Branch one:
% 9.43/2.66 | (199) all_0_8_8 = e1
% 9.43/2.66 |
% 9.43/2.66 | Combining equations (159,199) yields a new equation:
% 9.43/2.66 | (201) e1 = e0
% 9.43/2.66 |
% 9.43/2.66 | Equations (201) can reduce 88 to:
% 9.43/2.66 | (179) $false
% 9.43/2.66 |
% 9.43/2.66 |-The branch is then unsatisfiable
% 9.43/2.66 |-Branch two:
% 9.43/2.66 | (268) ~ (all_0_8_8 = e1)
% 9.43/2.66 | (269) all_0_12_12 = e1 | all_0_16_16 = e1 | all_0_20_20 = e1
% 9.43/2.66 |
% 9.43/2.66 +-Applying beta-rule and splitting (269), into two cases.
% 9.43/2.66 |-Branch one:
% 9.43/2.66 | (240) all_0_12_12 = e1
% 9.43/2.66 |
% 9.43/2.66 | Combining equations (233,240) yields a new equation:
% 9.43/2.66 | (241) e2 = e1
% 9.43/2.66 |
% 9.43/2.66 | Simplifying 241 yields:
% 9.43/2.66 | (242) e2 = e1
% 9.43/2.66 |
% 9.43/2.66 | Equations (242) can reduce 24 to:
% 9.43/2.66 | (179) $false
% 9.43/2.66 |
% 9.43/2.66 |-The branch is then unsatisfiable
% 9.43/2.66 |-Branch two:
% 9.43/2.66 | (244) ~ (all_0_12_12 = e1)
% 9.43/2.66 | (275) all_0_16_16 = e1 | all_0_20_20 = e1
% 9.43/2.66 |
% 9.43/2.66 +-Applying beta-rule and splitting (275), into two cases.
% 9.43/2.66 |-Branch one:
% 9.43/2.66 | (276) all_0_16_16 = e1
% 9.43/2.66 |
% 9.43/2.66 | Equations (276) can reduce 78 to:
% 9.43/2.66 | (277) ~ (all_0_17_17 = e1)
% 9.43/2.66 |
% 9.43/2.66 | Simplifying 277 yields:
% 9.43/2.66 | (278) ~ (all_0_17_17 = e1)
% 9.43/2.66 |
% 9.43/2.66 | Equations (276) can reduce 68 to:
% 9.43/2.66 | (279) ~ (all_0_20_20 = e1)
% 9.43/2.66 |
% 9.43/2.66 | Simplifying 279 yields:
% 9.43/2.66 | (214) ~ (all_0_20_20 = e1)
% 9.43/2.66 |
% 9.43/2.66 | Equations (276) can reduce 183 to:
% 9.43/2.66 | (218) ~ (e2 = e1)
% 9.43/2.66 |
% 9.43/2.66 | Simplifying 218 yields:
% 9.43/2.66 | (24) ~ (e2 = e1)
% 9.43/2.66 |
% 9.43/2.66 +-Applying beta-rule and splitting (15), into two cases.
% 9.43/2.66 |-Branch one:
% 9.43/2.66 | (283) all_0_9_9 = e1
% 9.43/2.66 |
% 9.43/2.66 | Equations (283) can reduce 193 to:
% 9.43/2.66 | (216) ~ (e3 = e1)
% 9.43/2.66 |
% 9.43/2.66 | Simplifying 216 yields:
% 9.43/2.66 | (155) ~ (e3 = e1)
% 9.43/2.66 |
% 9.43/2.66 +-Applying beta-rule and splitting (141), into two cases.
% 9.43/2.66 |-Branch one:
% 9.43/2.66 | (286) all_0_16_16 = e3
% 9.43/2.66 |
% 9.43/2.66 | Combining equations (276,286) yields a new equation:
% 9.43/2.66 | (206) e3 = e1
% 9.43/2.66 |
% 9.43/2.66 | Equations (206) can reduce 155 to:
% 9.43/2.66 | (179) $false
% 9.43/2.66 |
% 9.43/2.66 |-The branch is then unsatisfiable
% 9.43/2.66 |-Branch two:
% 9.43/2.66 | (289) ~ (all_0_16_16 = e3)
% 9.43/2.66 | (290) all_0_17_17 = e3 | all_0_18_18 = e3 | all_0_19_19 = e3
% 9.43/2.66 |
% 9.43/2.66 +-Applying beta-rule and splitting (148), into two cases.
% 9.43/2.66 |-Branch one:
% 9.43/2.66 | (291) all_0_20_20 = e3
% 9.43/2.66 |
% 9.43/2.66 | Equations (291) can reduce 227 to:
% 9.43/2.67 | (126) ~ (e3 = e2)
% 9.43/2.67 |
% 9.43/2.67 +-Applying beta-rule and splitting (290), into two cases.
% 9.43/2.67 |-Branch one:
% 9.43/2.67 | (293) all_0_17_17 = e3
% 9.43/2.67 |
% 9.43/2.67 | Equations (293) can reduce 195 to:
% 9.43/2.67 | (179) $false
% 9.43/2.67 |
% 9.43/2.67 |-The branch is then unsatisfiable
% 9.43/2.67 |-Branch two:
% 9.43/2.67 | (195) ~ (all_0_17_17 = e3)
% 9.43/2.67 | (296) all_0_18_18 = e3 | all_0_19_19 = e3
% 9.43/2.67 |
% 9.43/2.67 +-Applying beta-rule and splitting (296), into two cases.
% 9.43/2.67 |-Branch one:
% 9.43/2.67 | (297) all_0_18_18 = e3
% 9.43/2.67 |
% 9.43/2.67 | Combining equations (181,297) yields a new equation:
% 9.43/2.67 | (298) e3 = e2
% 9.43/2.67 |
% 9.43/2.67 | Equations (298) can reduce 126 to:
% 9.43/2.67 | (179) $false
% 9.43/2.67 |
% 9.43/2.67 |-The branch is then unsatisfiable
% 9.43/2.67 |-Branch two:
% 9.43/2.67 | (200) ~ (all_0_18_18 = e3)
% 9.43/2.67 | (301) all_0_19_19 = e3
% 9.43/2.67 |
% 9.43/2.67 | From (301) and (33) follows:
% 9.43/2.67 | (302) op(e1, e0) = e3
% 9.43/2.67 |
% 9.43/2.67 | Instantiating formula (85) with e1, e1, e2, all_0_0_0 and discharging atoms op(e1, e1) = all_0_0_0, op(e1, e1) = e2, yields:
% 9.43/2.67 | (303) all_0_0_0 = e2
% 9.43/2.67 |
% 9.43/2.67 | Instantiating formula (85) with e1, e0, e3, all_0_1_1 and discharging atoms op(e1, e0) = all_0_1_1, op(e1, e0) = e3, yields:
% 9.43/2.67 | (304) all_0_1_1 = e3
% 9.43/2.67 |
% 9.43/2.67 +-Applying beta-rule and splitting (93), into two cases.
% 9.43/2.67 |-Branch one:
% 9.43/2.67 | (305) ~ (all_0_0_0 = e2)
% 9.43/2.67 |
% 9.43/2.67 | Equations (303) can reduce 305 to:
% 9.43/2.67 | (179) $false
% 9.43/2.67 |
% 9.43/2.67 |-The branch is then unsatisfiable
% 9.43/2.67 |-Branch two:
% 9.43/2.67 | (303) all_0_0_0 = e2
% 9.43/2.67 | (308) ~ (all_0_1_1 = e3) | ~ (all_0_23_23 = e1)
% 9.43/2.67 |
% 9.43/2.67 +-Applying beta-rule and splitting (308), into two cases.
% 9.43/2.67 |-Branch one:
% 9.43/2.67 | (309) ~ (all_0_1_1 = e3)
% 9.43/2.67 |
% 9.43/2.67 | Equations (304) can reduce 309 to:
% 9.43/2.67 | (179) $false
% 9.43/2.67 |
% 9.43/2.67 |-The branch is then unsatisfiable
% 9.43/2.67 |-Branch two:
% 9.43/2.67 | (304) all_0_1_1 = e3
% 9.43/2.67 | (312) ~ (all_0_23_23 = e1)
% 9.43/2.67 |
% 9.43/2.67 | Equations (209) can reduce 312 to:
% 9.43/2.67 | (179) $false
% 9.43/2.67 |
% 9.43/2.67 |-The branch is then unsatisfiable
% 9.43/2.67 |-Branch two:
% 9.43/2.67 | (314) ~ (all_0_20_20 = e3)
% 9.43/2.67 | (315) all_0_20_20 = e2 | all_0_20_20 = e1 | all_0_20_20 = e0
% 9.43/2.67 |
% 9.43/2.67 +-Applying beta-rule and splitting (315), into two cases.
% 9.43/2.67 |-Branch one:
% 9.43/2.67 | (247) all_0_20_20 = e2
% 9.43/2.67 |
% 9.43/2.67 | Equations (247) can reduce 227 to:
% 9.43/2.67 | (179) $false
% 9.43/2.67 |
% 9.43/2.67 |-The branch is then unsatisfiable
% 9.43/2.67 |-Branch two:
% 9.43/2.67 | (227) ~ (all_0_20_20 = e2)
% 9.43/2.68 | (319) all_0_20_20 = e1 | all_0_20_20 = e0
% 9.43/2.68 |
% 9.43/2.68 +-Applying beta-rule and splitting (319), into two cases.
% 9.43/2.68 |-Branch one:
% 9.43/2.68 | (320) all_0_20_20 = e1
% 9.43/2.68 |
% 9.43/2.68 | Equations (320) can reduce 214 to:
% 9.43/2.68 | (179) $false
% 9.43/2.68 |
% 9.43/2.68 |-The branch is then unsatisfiable
% 9.43/2.68 |-Branch two:
% 9.43/2.68 | (214) ~ (all_0_20_20 = e1)
% 9.43/2.68 | (323) all_0_20_20 = e0
% 9.43/2.68 |
% 9.43/2.68 | Equations (323) can reduce 166 to:
% 9.43/2.68 | (179) $false
% 9.43/2.68 |
% 9.43/2.68 |-The branch is then unsatisfiable
% 9.43/2.68 |-Branch two:
% 9.43/2.68 | (325) ~ (all_0_9_9 = e1)
% 9.43/2.68 | (326) all_0_13_13 = e1 | all_0_17_17 = e1 | all_0_21_21 = e1
% 9.43/2.68 |
% 9.43/2.68 +-Applying beta-rule and splitting (326), into two cases.
% 9.43/2.68 |-Branch one:
% 9.43/2.68 | (204) all_0_13_13 = e1
% 9.43/2.68 |
% 9.43/2.68 | Combining equations (191,204) yields a new equation:
% 9.43/2.68 | (328) e3 = e1
% 9.43/2.68 |
% 9.43/2.68 | Simplifying 328 yields:
% 9.43/2.68 | (206) e3 = e1
% 9.43/2.68 |
% 9.43/2.68 | Equations (206) can reduce 155 to:
% 9.43/2.68 | (179) $false
% 9.43/2.68 |
% 9.43/2.68 |-The branch is then unsatisfiable
% 9.43/2.68 |-Branch two:
% 9.43/2.68 | (182) ~ (all_0_13_13 = e1)
% 9.43/2.68 | (332) all_0_17_17 = e1 | all_0_21_21 = e1
% 9.43/2.68 |
% 9.43/2.68 +-Applying beta-rule and splitting (332), into two cases.
% 9.43/2.68 |-Branch one:
% 9.43/2.68 | (333) all_0_17_17 = e1
% 9.43/2.68 |
% 9.43/2.68 | Equations (333) can reduce 278 to:
% 9.43/2.68 | (179) $false
% 9.43/2.68 |
% 9.43/2.68 |-The branch is then unsatisfiable
% 9.43/2.68 |-Branch two:
% 9.43/2.68 | (278) ~ (all_0_17_17 = e1)
% 9.43/2.68 | (336) all_0_21_21 = e1
% 9.43/2.68 |
% 9.43/2.68 | Combining equations (251,336) yields a new equation:
% 9.43/2.68 | (241) e2 = e1
% 9.43/2.68 |
% 9.43/2.68 | Simplifying 241 yields:
% 9.43/2.68 | (242) e2 = e1
% 9.43/2.68 |
% 9.43/2.68 | Equations (242) can reduce 24 to:
% 9.43/2.68 | (179) $false
% 9.43/2.68 |
% 9.43/2.68 |-The branch is then unsatisfiable
% 9.43/2.68 |-Branch two:
% 9.43/2.68 | (340) ~ (all_0_16_16 = e1)
% 9.43/2.68 | (320) all_0_20_20 = e1
% 9.43/2.68 |
% 9.43/2.68 | Equations (320) can reduce 214 to:
% 9.43/2.68 | (179) $false
% 9.43/2.68 |
% 9.43/2.68 |-The branch is then unsatisfiable
% 9.43/2.68 |-Branch two:
% 9.43/2.68 | (343) ~ (all_0_11_11 = e2)
% 9.43/2.68 | (344) all_0_15_15 = e2 | all_0_19_19 = e2 | all_0_23_23 = e2
% 9.43/2.68 |
% 9.43/2.68 +-Applying beta-rule and splitting (344), into two cases.
% 9.43/2.68 |-Branch one:
% 9.43/2.68 | (345) all_0_15_15 = e2
% 9.43/2.68 |
% 9.43/2.68 | Equations (345) can reduce 235 to:
% 9.43/2.68 | (179) $false
% 9.43/2.68 |
% 9.43/2.68 |-The branch is then unsatisfiable
% 9.43/2.68 |-Branch two:
% 9.43/2.68 | (235) ~ (all_0_15_15 = e2)
% 9.43/2.68 | (348) all_0_19_19 = e2 | all_0_23_23 = e2
% 9.43/2.68 |
% 9.43/2.68 +-Applying beta-rule and splitting (348), into two cases.
% 9.43/2.68 |-Branch one:
% 9.43/2.68 | (349) all_0_19_19 = e2
% 9.43/2.68 |
% 9.43/2.68 | Equations (349) can reduce 185 to:
% 9.43/2.68 | (179) $false
% 9.43/2.68 |
% 9.43/2.68 |-The branch is then unsatisfiable
% 9.43/2.68 |-Branch two:
% 9.43/2.68 | (185) ~ (all_0_19_19 = e2)
% 9.43/2.68 | (352) all_0_23_23 = e2
% 9.43/2.68 |
% 9.43/2.68 | Combining equations (352,209) yields a new equation:
% 9.43/2.68 | (241) e2 = e1
% 9.43/2.68 |
% 9.43/2.68 | Simplifying 241 yields:
% 9.43/2.68 | (242) e2 = e1
% 9.43/2.68 |
% 9.43/2.68 | Equations (242) can reduce 24 to:
% 9.43/2.68 | (179) $false
% 9.43/2.68 |
% 9.43/2.68 |-The branch is then unsatisfiable
% 9.43/2.68 |-Branch two:
% 9.43/2.68 | (356) ~ (all_0_21_21 = e2)
% 9.43/2.68 | (357) all_0_22_22 = e2 | all_0_23_23 = e2
% 9.43/2.68 |
% 9.43/2.68 +-Applying beta-rule and splitting (357), into two cases.
% 9.43/2.68 |-Branch one:
% 9.43/2.68 | (358) all_0_22_22 = e2
% 9.43/2.68 |
% 9.43/2.68 | Equations (358) can reduce 187 to:
% 9.43/2.68 | (179) $false
% 9.43/2.68 |
% 9.43/2.68 |-The branch is then unsatisfiable
% 9.43/2.68 |-Branch two:
% 9.43/2.68 | (187) ~ (all_0_22_22 = e2)
% 9.43/2.69 | (352) all_0_23_23 = e2
% 9.43/2.69 |
% 9.43/2.69 | Combining equations (352,209) yields a new equation:
% 9.43/2.69 | (241) e2 = e1
% 9.43/2.69 |
% 9.43/2.69 | Simplifying 241 yields:
% 9.43/2.69 | (242) e2 = e1
% 9.43/2.69 |
% 9.43/2.69 | Equations (242) can reduce 24 to:
% 9.43/2.69 | (179) $false
% 9.43/2.69 |
% 9.43/2.69 |-The branch is then unsatisfiable
% 9.43/2.69 |-Branch two:
% 9.43/2.69 | (365) ~ (all_0_12_12 = e2)
% 9.43/2.69 | (366) all_0_16_16 = e2 | all_0_20_20 = e2
% 9.43/2.69 |
% 9.43/2.69 +-Applying beta-rule and splitting (20), into two cases.
% 9.43/2.69 |-Branch one:
% 9.43/2.69 | (247) all_0_20_20 = e2
% 9.43/2.69 |
% 9.43/2.69 | Equations (247) can reduce 227 to:
% 9.43/2.69 | (179) $false
% 9.43/2.69 |
% 9.43/2.69 |-The branch is then unsatisfiable
% 9.43/2.69 |-Branch two:
% 9.43/2.69 | (227) ~ (all_0_20_20 = e2)
% 9.43/2.69 | (250) all_0_21_21 = e2 | all_0_22_22 = e2 | all_0_23_23 = e2
% 9.43/2.69 |
% 9.43/2.69 +-Applying beta-rule and splitting (366), into two cases.
% 9.43/2.69 |-Branch one:
% 9.43/2.69 | (371) all_0_16_16 = e2
% 9.43/2.69 |
% 9.43/2.69 | Equations (371) can reduce 183 to:
% 9.43/2.69 | (179) $false
% 9.43/2.69 |
% 9.43/2.69 |-The branch is then unsatisfiable
% 9.43/2.69 |-Branch two:
% 9.43/2.69 | (183) ~ (all_0_16_16 = e2)
% 9.43/2.69 | (247) all_0_20_20 = e2
% 9.43/2.69 |
% 9.43/2.69 | Equations (247) can reduce 227 to:
% 9.43/2.69 | (179) $false
% 9.43/2.69 |
% 9.43/2.69 |-The branch is then unsatisfiable
% 9.43/2.69 |-Branch two:
% 9.43/2.69 | (376) all_0_5_5 = e2
% 9.43/2.69 | (377) ~ (all_0_8_8 = e0)
% 9.43/2.69 |
% 9.43/2.69 | Equations (159) can reduce 377 to:
% 9.43/2.69 | (179) $false
% 9.43/2.69 |
% 9.43/2.69 |-The branch is then unsatisfiable
% 9.43/2.69 |-Branch two:
% 9.43/2.69 | (379) all_0_18_18 = e3 & ~ (all_0_8_8 = e1)
% 9.43/2.69 |
% 9.90/2.69 | Applying alpha-rule on (379) yields:
% 9.90/2.69 | (297) all_0_18_18 = e3
% 9.90/2.69 | (268) ~ (all_0_8_8 = e1)
% 9.90/2.69 |
% 9.90/2.69 | Combining equations (297,181) yields a new equation:
% 9.90/2.69 | (382) e3 = e2
% 9.90/2.69 |
% 9.90/2.69 | Simplifying 382 yields:
% 9.90/2.69 | (298) e3 = e2
% 9.90/2.69 |
% 9.90/2.69 | Equations (298) can reduce 126 to:
% 9.90/2.69 | (179) $false
% 9.90/2.69 |
% 9.90/2.69 |-The branch is then unsatisfiable
% 9.90/2.69 |-Branch two:
% 9.90/2.69 | (385) all_0_23_23 = e3 & ~ (all_0_8_8 = e0)
% 9.90/2.69 |
% 9.90/2.69 | Applying alpha-rule on (385) yields:
% 9.90/2.69 | (386) all_0_23_23 = e3
% 9.90/2.69 | (377) ~ (all_0_8_8 = e0)
% 9.90/2.69 |
% 9.90/2.69 | Equations (386) can reduce 160 to:
% 9.90/2.69 | (179) $false
% 9.90/2.69 |
% 9.90/2.69 |-The branch is then unsatisfiable
% 9.90/2.69 |-Branch two:
% 9.90/2.69 | (389) all_0_23_23 = e2 & ~ (all_0_13_13 = e0)
% 9.90/2.69 |
% 9.90/2.69 | Applying alpha-rule on (389) yields:
% 9.90/2.69 | (352) all_0_23_23 = e2
% 9.90/2.69 | (391) ~ (all_0_13_13 = e0)
% 9.90/2.69 |
% 9.90/2.69 | Equations (352) can reduce 172 to:
% 9.90/2.69 | (179) $false
% 9.90/2.69 |
% 9.90/2.69 |-The branch is then unsatisfiable
% 9.90/2.69 |-Branch two:
% 9.90/2.69 | (393) all_0_4_4 = e2
% 9.90/2.69 | (394) ~ (all_0_5_5 = e1) | ~ (all_0_8_8 = e0)
% 9.90/2.69 |
% 9.90/2.69 | Combining equations (393,170) yields a new equation:
% 9.90/2.69 | (352) all_0_23_23 = e2
% 9.90/2.69 |
% 9.90/2.69 | Equations (352) can reduce 3 to:
% 9.90/2.69 | (343) ~ (all_0_11_11 = e2)
% 9.90/2.69 |
% 9.90/2.69 | Equations (352) can reduce 149 to:
% 9.90/2.69 | (227) ~ (all_0_20_20 = e2)
% 9.90/2.69 |
% 9.90/2.69 | Equations (352) can reduce 160 to:
% 9.90/2.69 | (398) ~ (e3 = e2)
% 9.90/2.69 |
% 9.90/2.69 | Simplifying 398 yields:
% 9.90/2.69 | (126) ~ (e3 = e2)
% 9.90/2.69 |
% 9.90/2.69 | From (352)(352) and (103) follows:
% 9.90/2.69 | (400) op(e2, e2) = all_0_0_0
% 9.90/2.69 |
% 9.90/2.69 | From (352) and (55) follows:
% 9.90/2.69 | (401) op(e2, e0) = all_0_1_1
% 9.90/2.70 |
% 9.90/2.70 +-Applying beta-rule and splitting (156), into two cases.
% 9.90/2.70 |-Branch one:
% 9.90/2.70 | (197) (all_0_8_8 = e1 & ~ (all_0_18_18 = e3)) | (all_0_13_13 = e1 & ~ (all_0_18_18 = e2))
% 9.90/2.70 |
% 9.90/2.70 +-Applying beta-rule and splitting (197), into two cases.
% 9.90/2.70 |-Branch one:
% 9.90/2.70 | (198) all_0_8_8 = e1 & ~ (all_0_18_18 = e3)
% 9.90/2.70 |
% 9.90/2.70 | Applying alpha-rule on (198) yields:
% 9.90/2.70 | (199) all_0_8_8 = e1
% 9.90/2.70 | (200) ~ (all_0_18_18 = e3)
% 9.90/2.70 |
% 9.90/2.70 | Combining equations (159,199) yields a new equation:
% 9.90/2.70 | (201) e1 = e0
% 9.90/2.70 |
% 9.90/2.70 | Equations (201) can reduce 88 to:
% 9.90/2.70 | (179) $false
% 9.90/2.70 |
% 9.90/2.70 |-The branch is then unsatisfiable
% 9.90/2.70 |-Branch two:
% 9.90/2.70 | (203) all_0_13_13 = e1 & ~ (all_0_18_18 = e2)
% 9.90/2.70 |
% 9.90/2.70 | Applying alpha-rule on (203) yields:
% 9.90/2.70 | (204) all_0_13_13 = e1
% 9.90/2.70 | (205) ~ (all_0_18_18 = e2)
% 9.90/2.70 |
% 9.90/2.70 | Equations (204) can reduce 152 to:
% 9.90/2.70 | (325) ~ (all_0_9_9 = e1)
% 9.90/2.70 |
% 9.90/2.70 | Equations (204) can reduce 66 to:
% 9.90/2.70 | (244) ~ (all_0_12_12 = e1)
% 9.90/2.70 |
% 9.90/2.70 | From (204) and (79) follows:
% 9.90/2.70 | (413) op(e2, e2) = e1
% 9.90/2.70 |
% 9.90/2.70 +-Applying beta-rule and splitting (69), into two cases.
% 9.90/2.70 |-Branch one:
% 9.90/2.70 | (189) (all_0_13_13 = e3 & ~ (all_0_8_8 = e2)) | (all_0_18_18 = e3 & ~ (all_0_8_8 = e1))
% 9.90/2.70 |
% 9.90/2.70 +-Applying beta-rule and splitting (189), into two cases.
% 9.90/2.70 |-Branch one:
% 9.90/2.70 | (190) all_0_13_13 = e3 & ~ (all_0_8_8 = e2)
% 9.90/2.70 |
% 9.90/2.70 | Applying alpha-rule on (190) yields:
% 9.90/2.70 | (191) all_0_13_13 = e3
% 9.90/2.70 | (192) ~ (all_0_8_8 = e2)
% 9.90/2.70 |
% 9.90/2.70 | Combining equations (191,204) yields a new equation:
% 9.90/2.70 | (328) e3 = e1
% 9.90/2.70 |
% 9.90/2.70 | Simplifying 328 yields:
% 9.90/2.70 | (206) e3 = e1
% 9.90/2.70 |
% 9.90/2.70 | Equations (206) can reduce 155 to:
% 9.90/2.70 | (179) $false
% 9.90/2.70 |
% 9.90/2.70 |-The branch is then unsatisfiable
% 9.90/2.70 |-Branch two:
% 9.90/2.70 | (379) all_0_18_18 = e3 & ~ (all_0_8_8 = e1)
% 9.90/2.70 |
% 9.90/2.70 | Applying alpha-rule on (379) yields:
% 9.90/2.70 | (297) all_0_18_18 = e3
% 9.90/2.70 | (268) ~ (all_0_8_8 = e1)
% 9.90/2.70 |
% 9.90/2.70 | Equations (159) can reduce 268 to:
% 9.90/2.70 | (424) ~ (e1 = e0)
% 9.90/2.70 |
% 9.90/2.70 | Simplifying 424 yields:
% 9.90/2.70 | (88) ~ (e1 = e0)
% 9.90/2.70 |
% 9.90/2.70 | Equations (297) can reduce 76 to:
% 9.90/2.70 | (426) ~ (all_0_10_10 = e3)
% 9.90/2.70 |
% 9.90/2.70 | Equations (297) can reduce 26 to:
% 9.90/2.70 | (427) ~ (all_0_14_14 = e3)
% 9.90/2.70 |
% 9.90/2.70 +-Applying beta-rule and splitting (394), into two cases.
% 9.90/2.70 |-Branch one:
% 9.90/2.70 | (428) ~ (all_0_5_5 = e1)
% 9.90/2.70 |
% 9.90/2.70 | Equations (169) can reduce 428 to:
% 9.90/2.70 | (214) ~ (all_0_20_20 = e1)
% 9.90/2.70 |
% 9.90/2.70 +-Applying beta-rule and splitting (148), into two cases.
% 9.90/2.70 |-Branch one:
% 9.90/2.70 | (291) all_0_20_20 = e3
% 9.90/2.70 |
% 9.90/2.70 | Equations (291) can reduce 23 to:
% 9.90/2.70 | (431) ~ (all_0_12_12 = e3)
% 9.90/2.70 |
% 9.90/2.70 | Equations (291) can reduce 214 to:
% 9.90/2.70 | (155) ~ (e3 = e1)
% 9.90/2.70 |
% 9.90/2.70 | Equations (291) can reduce 166 to:
% 9.90/2.70 | (40) ~ (e3 = e0)
% 9.90/2.70 |
% 9.90/2.70 +-Applying beta-rule and splitting (143), into two cases.
% 9.90/2.70 |-Branch one:
% 9.90/2.70 | (434) all_0_12_12 = e3
% 9.90/2.70 |
% 9.90/2.70 | Equations (434) can reduce 431 to:
% 9.90/2.70 | (179) $false
% 9.90/2.70 |
% 9.90/2.70 |-The branch is then unsatisfiable
% 9.90/2.70 |-Branch two:
% 9.90/2.70 | (431) ~ (all_0_12_12 = e3)
% 9.90/2.70 | (437) all_0_12_12 = e2 | all_0_12_12 = e1 | all_0_12_12 = e0
% 9.90/2.70 |
% 9.90/2.70 +-Applying beta-rule and splitting (437), into two cases.
% 9.90/2.70 |-Branch one:
% 9.90/2.70 | (233) all_0_12_12 = e2
% 9.90/2.70 |
% 9.90/2.70 | Equations (233) can reduce 138 to:
% 9.90/2.70 | (234) ~ (all_0_15_15 = e2)
% 9.90/2.70 |
% 9.90/2.70 | Simplifying 234 yields:
% 9.90/2.70 | (235) ~ (all_0_15_15 = e2)
% 9.90/2.70 |
% 9.90/2.70 | Equations (233) can reduce 431 to:
% 9.90/2.70 | (398) ~ (e3 = e2)
% 9.90/2.70 |
% 9.90/2.70 | Simplifying 398 yields:
% 9.90/2.70 | (126) ~ (e3 = e2)
% 9.90/2.70 |
% 9.90/2.70 | Equations (233) can reduce 164 to:
% 9.90/2.70 | (119) ~ (e2 = e0)
% 9.90/2.70 |
% 9.90/2.70 +-Applying beta-rule and splitting (7), into two cases.
% 9.90/2.70 |-Branch one:
% 9.90/2.70 | (320) all_0_20_20 = e1
% 9.90/2.70 |
% 9.90/2.70 | Combining equations (291,320) yields a new equation:
% 9.90/2.70 | (328) e3 = e1
% 9.90/2.70 |
% 9.90/2.70 | Simplifying 328 yields:
% 9.90/2.70 | (206) e3 = e1
% 9.90/2.70 |
% 9.90/2.70 | Equations (206) can reduce 155 to:
% 9.90/2.70 | (179) $false
% 9.90/2.70 |
% 9.90/2.70 |-The branch is then unsatisfiable
% 9.90/2.70 |-Branch two:
% 9.90/2.70 | (214) ~ (all_0_20_20 = e1)
% 9.90/2.70 | (449) all_0_21_21 = e1 | all_0_22_22 = e1 | all_0_23_23 = e1
% 9.90/2.70 |
% 9.90/2.70 | Equations (291) can reduce 214 to:
% 9.90/2.70 | (155) ~ (e3 = e1)
% 9.90/2.70 |
% 9.90/2.70 +-Applying beta-rule and splitting (46), into two cases.
% 9.90/2.70 |-Branch one:
% 9.90/2.70 | (451) all_0_14_14 = e3
% 9.90/2.70 |
% 9.90/2.70 | Equations (451) can reduce 427 to:
% 9.90/2.70 | (179) $false
% 9.90/2.70 |
% 9.90/2.70 |-The branch is then unsatisfiable
% 9.90/2.70 |-Branch two:
% 9.90/2.70 | (427) ~ (all_0_14_14 = e3)
% 9.90/2.70 | (454) all_0_14_14 = e2 | all_0_14_14 = e1 | all_0_14_14 = e0
% 9.90/2.70 |
% 9.90/2.70 +-Applying beta-rule and splitting (127), into two cases.
% 9.90/2.70 |-Branch one:
% 9.90/2.70 | (199) all_0_8_8 = e1
% 9.90/2.70 |
% 9.90/2.71 | Combining equations (159,199) yields a new equation:
% 9.90/2.71 | (201) e1 = e0
% 9.90/2.71 |
% 9.90/2.71 | Equations (201) can reduce 88 to:
% 9.90/2.71 | (179) $false
% 9.90/2.71 |
% 9.90/2.71 |-The branch is then unsatisfiable
% 9.90/2.71 |-Branch two:
% 9.90/2.71 | (268) ~ (all_0_8_8 = e1)
% 9.90/2.71 | (269) all_0_12_12 = e1 | all_0_16_16 = e1 | all_0_20_20 = e1
% 9.90/2.71 |
% 9.90/2.71 | Equations (159) can reduce 268 to:
% 9.90/2.71 | (424) ~ (e1 = e0)
% 9.90/2.71 |
% 9.90/2.71 | Simplifying 424 yields:
% 9.90/2.71 | (88) ~ (e1 = e0)
% 9.90/2.71 |
% 9.90/2.71 +-Applying beta-rule and splitting (150), into two cases.
% 9.90/2.71 |-Branch one:
% 9.90/2.71 | (462) all_0_10_10 = e2
% 9.90/2.71 |
% 9.90/2.71 | Equations (462) can reduce 426 to:
% 9.90/2.71 | (398) ~ (e3 = e2)
% 9.90/2.71 |
% 9.90/2.71 | Simplifying 398 yields:
% 9.90/2.71 | (126) ~ (e3 = e2)
% 9.90/2.71 |
% 9.90/2.71 +-Applying beta-rule and splitting (81), into two cases.
% 9.90/2.71 |-Branch one:
% 9.90/2.71 | (434) all_0_12_12 = e3
% 9.90/2.71 |
% 9.90/2.71 | Combining equations (233,434) yields a new equation:
% 9.90/2.71 | (298) e3 = e2
% 9.90/2.71 |
% 9.90/2.71 | Equations (298) can reduce 126 to:
% 9.90/2.71 | (179) $false
% 9.90/2.71 |
% 9.90/2.71 |-The branch is then unsatisfiable
% 9.90/2.71 |-Branch two:
% 9.90/2.71 | (431) ~ (all_0_12_12 = e3)
% 9.90/2.71 | (469) all_0_13_13 = e3 | all_0_14_14 = e3 | all_0_15_15 = e3
% 9.90/2.71 |
% 9.90/2.71 +-Applying beta-rule and splitting (469), into two cases.
% 9.90/2.71 |-Branch one:
% 9.90/2.71 | (191) all_0_13_13 = e3
% 9.90/2.71 |
% 9.90/2.71 | Combining equations (204,191) yields a new equation:
% 9.90/2.71 | (206) e3 = e1
% 9.90/2.71 |
% 9.90/2.71 | Equations (206) can reduce 155 to:
% 9.90/2.71 | (179) $false
% 9.90/2.71 |
% 9.90/2.71 |-The branch is then unsatisfiable
% 9.90/2.71 |-Branch two:
% 9.90/2.71 | (176) ~ (all_0_13_13 = e3)
% 9.90/2.71 | (474) all_0_14_14 = e3 | all_0_15_15 = e3
% 9.90/2.71 |
% 9.90/2.71 +-Applying beta-rule and splitting (474), into two cases.
% 9.90/2.71 |-Branch one:
% 9.90/2.71 | (451) all_0_14_14 = e3
% 9.90/2.71 |
% 9.90/2.71 | Equations (451) can reduce 427 to:
% 9.90/2.71 | (179) $false
% 9.90/2.71 |
% 9.90/2.71 |-The branch is then unsatisfiable
% 9.90/2.71 |-Branch two:
% 9.90/2.71 | (427) ~ (all_0_14_14 = e3)
% 9.90/2.71 | (478) all_0_15_15 = e3
% 9.90/2.71 |
% 9.90/2.71 | From (478) and (60) follows:
% 9.90/2.71 | (479) op(e2, e0) = e3
% 9.90/2.71 |
% 9.90/2.71 | Instantiating formula (85) with e2, e2, e1, all_0_0_0 and discharging atoms op(e2, e2) = all_0_0_0, op(e2, e2) = e1, yields:
% 9.90/2.71 | (480) all_0_0_0 = e1
% 9.90/2.71 |
% 9.90/2.71 | Instantiating formula (85) with e2, e0, e3, all_0_1_1 and discharging atoms op(e2, e0) = all_0_1_1, op(e2, e0) = e3, yields:
% 9.90/2.71 | (304) all_0_1_1 = e3
% 9.90/2.71 |
% 9.90/2.71 +-Applying beta-rule and splitting (125), into two cases.
% 9.90/2.71 |-Branch one:
% 9.90/2.71 | (482) ~ (all_0_0_0 = e1)
% 9.90/2.71 |
% 9.90/2.71 | Equations (480) can reduce 482 to:
% 9.90/2.71 | (179) $false
% 9.90/2.71 |
% 9.90/2.71 |-The branch is then unsatisfiable
% 9.90/2.71 |-Branch two:
% 9.90/2.71 | (480) all_0_0_0 = e1
% 9.90/2.71 | (485) ~ (all_0_1_1 = e3) | ~ (all_0_23_23 = e2)
% 9.90/2.71 |
% 9.90/2.71 +-Applying beta-rule and splitting (485), into two cases.
% 9.90/2.71 |-Branch one:
% 9.90/2.71 | (309) ~ (all_0_1_1 = e3)
% 9.90/2.71 |
% 9.90/2.71 | Equations (304) can reduce 309 to:
% 9.90/2.71 | (179) $false
% 9.90/2.71 |
% 9.90/2.71 |-The branch is then unsatisfiable
% 9.90/2.71 |-Branch two:
% 9.90/2.71 | (304) all_0_1_1 = e3
% 9.90/2.71 | (172) ~ (all_0_23_23 = e2)
% 9.90/2.71 |
% 9.90/2.71 | Equations (352) can reduce 172 to:
% 9.90/2.71 | (179) $false
% 9.90/2.71 |
% 9.90/2.71 |-The branch is then unsatisfiable
% 9.90/2.71 |-Branch two:
% 9.90/2.71 | (491) ~ (all_0_10_10 = e2)
% 9.90/2.71 | (492) all_0_14_14 = e2 | all_0_18_18 = e2 | all_0_22_22 = e2
% 9.90/2.71 |
% 9.90/2.71 +-Applying beta-rule and splitting (81), into two cases.
% 9.90/2.71 |-Branch one:
% 9.90/2.71 | (434) all_0_12_12 = e3
% 9.90/2.71 |
% 9.90/2.71 | Combining equations (233,434) yields a new equation:
% 9.90/2.71 | (298) e3 = e2
% 9.90/2.71 |
% 9.90/2.71 | Equations (298) can reduce 126 to:
% 9.90/2.71 | (179) $false
% 9.90/2.71 |
% 9.90/2.71 |-The branch is then unsatisfiable
% 9.90/2.71 |-Branch two:
% 9.90/2.71 | (431) ~ (all_0_12_12 = e3)
% 9.90/2.71 | (469) all_0_13_13 = e3 | all_0_14_14 = e3 | all_0_15_15 = e3
% 9.90/2.71 |
% 9.90/2.71 +-Applying beta-rule and splitting (469), into two cases.
% 9.90/2.71 |-Branch one:
% 9.90/2.71 | (191) all_0_13_13 = e3
% 9.90/2.71 |
% 9.90/2.71 | Combining equations (204,191) yields a new equation:
% 9.90/2.71 | (206) e3 = e1
% 9.90/2.71 |
% 9.90/2.71 | Equations (206) can reduce 155 to:
% 9.90/2.71 | (179) $false
% 9.90/2.71 |
% 9.90/2.71 |-The branch is then unsatisfiable
% 9.90/2.71 |-Branch two:
% 9.90/2.71 | (176) ~ (all_0_13_13 = e3)
% 9.90/2.71 | (474) all_0_14_14 = e3 | all_0_15_15 = e3
% 9.90/2.71 |
% 9.90/2.71 +-Applying beta-rule and splitting (474), into two cases.
% 9.90/2.71 |-Branch one:
% 9.90/2.71 | (451) all_0_14_14 = e3
% 9.90/2.71 |
% 9.90/2.72 | Equations (451) can reduce 427 to:
% 9.90/2.72 | (179) $false
% 9.90/2.72 |
% 9.90/2.72 |-The branch is then unsatisfiable
% 9.90/2.72 |-Branch two:
% 9.90/2.72 | (427) ~ (all_0_14_14 = e3)
% 9.90/2.72 | (478) all_0_15_15 = e3
% 9.90/2.72 |
% 9.90/2.72 | Equations (478) can reduce 128 to:
% 9.90/2.72 | (507) ~ (all_0_11_11 = e3)
% 9.90/2.72 |
% 9.90/2.72 | Equations (478) can reduce 12 to:
% 9.90/2.72 | (427) ~ (all_0_14_14 = e3)
% 9.90/2.72 |
% 9.90/2.72 | Equations (478) can reduce 235 to:
% 9.90/2.72 | (126) ~ (e3 = e2)
% 9.90/2.72 |
% 9.90/2.72 +-Applying beta-rule and splitting (18), into two cases.
% 9.90/2.72 |-Branch one:
% 9.90/2.72 | (175) all_0_8_8 = e2
% 9.90/2.72 |
% 9.90/2.72 | Combining equations (159,175) yields a new equation:
% 9.90/2.72 | (178) e2 = e0
% 9.90/2.72 |
% 9.90/2.72 | Equations (178) can reduce 119 to:
% 9.90/2.72 | (179) $false
% 9.90/2.72 |
% 9.90/2.72 |-The branch is then unsatisfiable
% 9.90/2.72 |-Branch two:
% 9.90/2.72 | (192) ~ (all_0_8_8 = e2)
% 9.90/2.72 | (514) all_0_9_9 = e2 | all_0_10_10 = e2 | all_0_11_11 = e2
% 9.90/2.72 |
% 9.90/2.72 | Equations (159) can reduce 192 to:
% 9.90/2.72 | (515) ~ (e2 = e0)
% 9.90/2.72 |
% 9.90/2.72 | Simplifying 515 yields:
% 9.90/2.72 | (119) ~ (e2 = e0)
% 9.90/2.72 |
% 9.90/2.72 +-Applying beta-rule and splitting (32), into two cases.
% 9.90/2.72 |-Branch one:
% 9.90/2.72 | (261) all_0_9_9 = e3
% 9.90/2.72 |
% 9.90/2.72 +-Applying beta-rule and splitting (514), into two cases.
% 9.90/2.72 |-Branch one:
% 9.90/2.72 | (518) all_0_9_9 = e2
% 9.90/2.72 |
% 9.90/2.72 | Combining equations (518,261) yields a new equation:
% 9.90/2.72 | (298) e3 = e2
% 9.90/2.72 |
% 9.90/2.72 | Equations (298) can reduce 126 to:
% 9.90/2.72 | (179) $false
% 9.90/2.72 |
% 9.90/2.72 |-The branch is then unsatisfiable
% 9.90/2.72 |-Branch two:
% 9.90/2.72 | (521) ~ (all_0_9_9 = e2)
% 9.90/2.72 | (522) all_0_10_10 = e2 | all_0_11_11 = e2
% 9.90/2.72 |
% 9.90/2.72 +-Applying beta-rule and splitting (522), into two cases.
% 9.90/2.72 |-Branch one:
% 9.90/2.72 | (462) all_0_10_10 = e2
% 9.90/2.72 |
% 9.90/2.72 | Equations (462) can reduce 491 to:
% 9.90/2.72 | (179) $false
% 9.90/2.72 |
% 9.90/2.72 |-The branch is then unsatisfiable
% 9.90/2.72 |-Branch two:
% 9.90/2.72 | (491) ~ (all_0_10_10 = e2)
% 9.90/2.72 | (254) all_0_11_11 = e2
% 9.90/2.72 |
% 9.90/2.72 | Equations (254) can reduce 343 to:
% 9.90/2.72 | (179) $false
% 9.90/2.72 |
% 9.90/2.72 |-The branch is then unsatisfiable
% 9.90/2.72 |-Branch two:
% 9.90/2.72 | (193) ~ (all_0_9_9 = e3)
% 9.90/2.72 | (529) all_0_13_13 = e3 | all_0_17_17 = e3 | all_0_21_21 = e3
% 9.90/2.72 |
% 9.90/2.72 +-Applying beta-rule and splitting (39), into two cases.
% 9.90/2.72 |-Branch one:
% 9.90/2.72 | (530) all_0_12_12 = e0
% 9.90/2.72 |
% 9.90/2.72 | Combining equations (530,233) yields a new equation:
% 9.90/2.72 | (178) e2 = e0
% 9.90/2.72 |
% 9.90/2.72 | Equations (178) can reduce 119 to:
% 9.90/2.72 | (179) $false
% 9.90/2.72 |
% 9.90/2.72 |-The branch is then unsatisfiable
% 9.90/2.72 |-Branch two:
% 9.90/2.72 | (164) ~ (all_0_12_12 = e0)
% 9.90/2.72 | (534) all_0_13_13 = e0 | all_0_14_14 = e0 | all_0_15_15 = e0
% 9.90/2.72 |
% 9.90/2.72 +-Applying beta-rule and splitting (21), into two cases.
% 9.90/2.72 |-Branch one:
% 9.90/2.72 | (261) all_0_9_9 = e3
% 9.90/2.72 |
% 9.90/2.72 | Equations (261) can reduce 193 to:
% 9.90/2.72 | (179) $false
% 9.90/2.72 |
% 9.90/2.72 |-The branch is then unsatisfiable
% 9.90/2.72 |-Branch two:
% 9.90/2.72 | (193) ~ (all_0_9_9 = e3)
% 9.90/2.72 | (538) all_0_9_9 = e2 | all_0_9_9 = e1 | all_0_9_9 = e0
% 9.90/2.72 |
% 9.90/2.72 +-Applying beta-rule and splitting (534), into two cases.
% 9.90/2.72 |-Branch one:
% 9.90/2.72 | (539) all_0_13_13 = e0
% 9.90/2.72 |
% 9.90/2.72 | Combining equations (204,539) yields a new equation:
% 9.90/2.72 | (540) e1 = e0
% 9.90/2.72 |
% 9.90/2.72 | Simplifying 540 yields:
% 9.90/2.72 | (201) e1 = e0
% 9.90/2.72 |
% 9.90/2.72 | Equations (201) can reduce 88 to:
% 9.90/2.72 | (179) $false
% 9.90/2.72 |
% 9.90/2.72 |-The branch is then unsatisfiable
% 9.90/2.72 |-Branch two:
% 9.90/2.72 | (391) ~ (all_0_13_13 = e0)
% 9.90/2.72 | (544) all_0_14_14 = e0 | all_0_15_15 = e0
% 9.90/2.72 |
% 9.90/2.72 +-Applying beta-rule and splitting (544), into two cases.
% 9.90/2.72 |-Branch one:
% 9.90/2.72 | (545) all_0_14_14 = e0
% 9.90/2.72 |
% 9.90/2.72 | Equations (545) can reduce 427 to:
% 9.90/2.72 | (546) ~ (e3 = e0)
% 9.90/2.72 |
% 9.90/2.72 | Simplifying 546 yields:
% 9.90/2.72 | (40) ~ (e3 = e0)
% 9.90/2.72 |
% 9.90/2.72 +-Applying beta-rule and splitting (538), into two cases.
% 9.90/2.72 |-Branch one:
% 9.90/2.72 | (518) all_0_9_9 = e2
% 9.90/2.72 |
% 9.90/2.72 | Equations (518) can reduce 193 to:
% 9.90/2.72 | (398) ~ (e3 = e2)
% 9.90/2.72 |
% 9.90/2.72 | Simplifying 398 yields:
% 9.90/2.72 | (126) ~ (e3 = e2)
% 9.90/2.72 |
% 9.90/2.72 +-Applying beta-rule and splitting (17), into two cases.
% 9.90/2.72 |-Branch one:
% 9.90/2.72 | (256) all_0_8_8 = e3
% 9.90/2.72 |
% 9.90/2.72 | Combining equations (256,159) yields a new equation:
% 9.90/2.72 | (552) e3 = e0
% 9.90/2.72 |
% 9.90/2.73 | Simplifying 552 yields:
% 9.90/2.73 | (257) e3 = e0
% 9.90/2.73 |
% 9.90/2.73 | Equations (257) can reduce 40 to:
% 9.90/2.73 | (179) $false
% 9.90/2.73 |
% 9.90/2.73 |-The branch is then unsatisfiable
% 9.90/2.73 |-Branch two:
% 9.90/2.73 | (259) ~ (all_0_8_8 = e3)
% 9.90/2.73 | (260) all_0_9_9 = e3 | all_0_10_10 = e3 | all_0_11_11 = e3
% 9.90/2.73 |
% 9.90/2.73 +-Applying beta-rule and splitting (260), into two cases.
% 9.90/2.73 |-Branch one:
% 9.90/2.73 | (261) all_0_9_9 = e3
% 9.90/2.73 |
% 9.90/2.73 | Combining equations (261,518) yields a new equation:
% 9.90/2.73 | (382) e3 = e2
% 9.90/2.73 |
% 9.90/2.73 | Simplifying 382 yields:
% 9.90/2.73 | (298) e3 = e2
% 9.90/2.73 |
% 9.90/2.73 | Equations (298) can reduce 126 to:
% 9.90/2.73 | (179) $false
% 9.90/2.73 |
% 9.90/2.73 |-The branch is then unsatisfiable
% 9.90/2.73 |-Branch two:
% 9.90/2.73 | (193) ~ (all_0_9_9 = e3)
% 9.90/2.73 | (264) all_0_10_10 = e3 | all_0_11_11 = e3
% 9.90/2.73 |
% 9.90/2.73 +-Applying beta-rule and splitting (264), into two cases.
% 9.90/2.73 |-Branch one:
% 9.90/2.73 | (563) all_0_10_10 = e3
% 9.90/2.73 |
% 9.90/2.73 | Equations (563) can reduce 426 to:
% 9.90/2.73 | (179) $false
% 9.90/2.73 |
% 9.90/2.73 |-The branch is then unsatisfiable
% 9.90/2.73 |-Branch two:
% 9.90/2.73 | (426) ~ (all_0_10_10 = e3)
% 9.90/2.73 | (566) all_0_11_11 = e3
% 9.90/2.73 |
% 9.90/2.73 | Equations (566) can reduce 507 to:
% 9.90/2.73 | (179) $false
% 9.90/2.73 |
% 9.90/2.73 |-The branch is then unsatisfiable
% 9.90/2.73 |-Branch two:
% 9.90/2.73 | (521) ~ (all_0_9_9 = e2)
% 9.90/2.73 | (569) all_0_9_9 = e1 | all_0_9_9 = e0
% 9.90/2.73 |
% 9.90/2.73 +-Applying beta-rule and splitting (569), into two cases.
% 9.90/2.73 |-Branch one:
% 9.90/2.73 | (283) all_0_9_9 = e1
% 9.90/2.73 |
% 9.90/2.73 | Equations (283) can reduce 325 to:
% 9.90/2.73 | (179) $false
% 9.90/2.73 |
% 9.90/2.73 |-The branch is then unsatisfiable
% 9.90/2.73 |-Branch two:
% 9.90/2.73 | (325) ~ (all_0_9_9 = e1)
% 9.90/2.73 | (573) all_0_9_9 = e0
% 9.90/2.73 |
% 9.90/2.73 | Equations (573) can reduce 162 to:
% 9.90/2.73 | (179) $false
% 9.90/2.73 |
% 9.90/2.73 |-The branch is then unsatisfiable
% 9.90/2.73 |-Branch two:
% 9.90/2.73 | (575) ~ (all_0_14_14 = e0)
% 9.90/2.73 | (576) all_0_15_15 = e0
% 9.90/2.73 |
% 9.90/2.73 | Combining equations (478,576) yields a new equation:
% 9.90/2.73 | (552) e3 = e0
% 9.90/2.73 |
% 9.90/2.73 | Simplifying 552 yields:
% 9.90/2.73 | (257) e3 = e0
% 9.90/2.73 |
% 9.90/2.73 | Equations (257) can reduce 40 to:
% 9.90/2.73 | (179) $false
% 9.90/2.73 |
% 9.90/2.73 |-The branch is then unsatisfiable
% 9.90/2.73 |-Branch two:
% 9.90/2.73 | (365) ~ (all_0_12_12 = e2)
% 9.90/2.73 | (581) all_0_12_12 = e1 | all_0_12_12 = e0
% 9.90/2.73 |
% 9.90/2.73 +-Applying beta-rule and splitting (581), into two cases.
% 9.90/2.73 |-Branch one:
% 9.90/2.73 | (240) all_0_12_12 = e1
% 9.90/2.73 |
% 9.90/2.73 | Equations (240) can reduce 244 to:
% 9.90/2.73 | (179) $false
% 9.90/2.73 |
% 9.90/2.73 |-The branch is then unsatisfiable
% 9.90/2.73 |-Branch two:
% 9.90/2.73 | (244) ~ (all_0_12_12 = e1)
% 9.90/2.73 | (530) all_0_12_12 = e0
% 9.90/2.73 |
% 9.90/2.73 | Equations (530) can reduce 164 to:
% 9.90/2.73 | (179) $false
% 9.90/2.73 |
% 9.90/2.73 |-The branch is then unsatisfiable
% 9.90/2.74 |-Branch two:
% 9.90/2.74 | (314) ~ (all_0_20_20 = e3)
% 9.90/2.74 | (315) all_0_20_20 = e2 | all_0_20_20 = e1 | all_0_20_20 = e0
% 9.90/2.74 |
% 9.90/2.74 +-Applying beta-rule and splitting (315), into two cases.
% 9.90/2.74 |-Branch one:
% 9.90/2.74 | (247) all_0_20_20 = e2
% 9.90/2.74 |
% 9.90/2.74 | Equations (247) can reduce 227 to:
% 9.90/2.74 | (179) $false
% 9.90/2.74 |
% 9.90/2.74 |-The branch is then unsatisfiable
% 9.90/2.74 |-Branch two:
% 9.90/2.74 | (227) ~ (all_0_20_20 = e2)
% 9.90/2.74 | (319) all_0_20_20 = e1 | all_0_20_20 = e0
% 9.90/2.74 |
% 9.90/2.74 +-Applying beta-rule and splitting (319), into two cases.
% 9.90/2.74 |-Branch one:
% 9.90/2.74 | (320) all_0_20_20 = e1
% 9.90/2.74 |
% 9.90/2.74 | Equations (320) can reduce 214 to:
% 9.90/2.74 | (179) $false
% 9.90/2.74 |
% 9.90/2.74 |-The branch is then unsatisfiable
% 9.90/2.74 |-Branch two:
% 9.90/2.74 | (214) ~ (all_0_20_20 = e1)
% 9.90/2.74 | (323) all_0_20_20 = e0
% 9.90/2.74 |
% 9.90/2.74 | Equations (323) can reduce 166 to:
% 9.90/2.74 | (179) $false
% 9.90/2.74 |
% 9.90/2.74 |-The branch is then unsatisfiable
% 9.90/2.74 |-Branch two:
% 9.90/2.74 | (598) all_0_5_5 = e1
% 9.90/2.74 | (377) ~ (all_0_8_8 = e0)
% 9.90/2.74 |
% 9.90/2.74 | Equations (159) can reduce 377 to:
% 9.90/2.74 | (179) $false
% 9.90/2.74 |
% 9.90/2.74 |-The branch is then unsatisfiable
% 9.90/2.74 |-Branch two:
% 9.90/2.74 | (385) all_0_23_23 = e3 & ~ (all_0_8_8 = e0)
% 9.90/2.74 |
% 9.90/2.74 | Applying alpha-rule on (385) yields:
% 9.90/2.74 | (386) all_0_23_23 = e3
% 9.90/2.74 | (377) ~ (all_0_8_8 = e0)
% 9.90/2.74 |
% 9.90/2.74 | Combining equations (386,352) yields a new equation:
% 9.90/2.74 | (382) e3 = e2
% 9.90/2.74 |
% 9.90/2.74 | Simplifying 382 yields:
% 9.90/2.74 | (298) e3 = e2
% 9.90/2.74 |
% 9.90/2.74 | Equations (298) can reduce 126 to:
% 9.90/2.74 | (179) $false
% 9.90/2.74 |
% 9.90/2.74 |-The branch is then unsatisfiable
% 9.90/2.74 |-Branch two:
% 9.90/2.74 | (208) all_0_23_23 = e1 & ~ (all_0_18_18 = e0)
% 9.90/2.74 |
% 9.90/2.74 | Applying alpha-rule on (208) yields:
% 9.90/2.74 | (209) all_0_23_23 = e1
% 9.90/2.74 | (210) ~ (all_0_18_18 = e0)
% 9.90/2.74 |
% 9.90/2.74 | Combining equations (209,352) yields a new equation:
% 9.90/2.74 | (242) e2 = e1
% 9.90/2.74 |
% 9.90/2.74 | Equations (242) can reduce 24 to:
% 9.90/2.74 | (179) $false
% 9.90/2.74 |
% 9.90/2.74 |-The branch is then unsatisfiable
% 9.90/2.74 |-Branch two:
% 9.90/2.74 | (612) all_0_13_13 = e0 & ~ (all_0_23_23 = e2)
% 9.90/2.74 |
% 9.90/2.74 | Applying alpha-rule on (612) yields:
% 9.90/2.74 | (539) all_0_13_13 = e0
% 9.90/2.74 | (172) ~ (all_0_23_23 = e2)
% 9.90/2.74 |
% 9.90/2.74 | Equations (539) can reduce 152 to:
% 9.90/2.74 | (162) ~ (all_0_9_9 = e0)
% 9.90/2.74 |
% 9.90/2.74 | Equations (539) can reduce 66 to:
% 9.90/2.74 | (164) ~ (all_0_12_12 = e0)
% 9.90/2.74 |
% 9.90/2.74 | Equations (539) can reduce 106 to:
% 9.90/2.74 | (617) ~ (all_0_17_17 = e0)
% 9.90/2.74 |
% 9.90/2.74 | Simplifying 617 yields:
% 9.90/2.74 | (618) ~ (all_0_17_17 = e0)
% 9.90/2.74 |
% 9.90/2.74 | Equations (539) can reduce 61 to:
% 9.90/2.74 | (619) ~ (all_0_21_21 = e0)
% 9.90/2.74 |
% 9.90/2.74 | Simplifying 619 yields:
% 9.90/2.74 | (620) ~ (all_0_21_21 = e0)
% 9.90/2.74 |
% 9.90/2.74 | From (539)(539) and (47) follows:
% 9.90/2.74 | (621) op(e0, e0) = all_0_6_6
% 9.90/2.74 |
% 9.90/2.74 | From (539) and (14) follows:
% 9.90/2.74 | (622) op(e0, e2) = all_0_7_7
% 9.90/2.74 |
% 9.90/2.74 | Instantiating formula (85) with e0, e2, all_0_7_7, all_0_21_21 and discharging atoms op(e0, e2) = all_0_7_7, op(e0, e2) = all_0_21_21, yields:
% 9.90/2.74 | (623) all_0_7_7 = all_0_21_21
% 9.90/2.75 |
% 9.90/2.75 | Instantiating formula (85) with e0, e0, all_0_6_6, all_0_23_23 and discharging atoms op(e0, e0) = all_0_6_6, op(e0, e0) = all_0_23_23, yields:
% 9.90/2.75 | (624) all_0_6_6 = all_0_23_23
% 9.90/2.75 |
% 9.90/2.75 +-Applying beta-rule and splitting (123), into two cases.
% 9.90/2.75 |-Branch one:
% 9.90/2.75 | (625) ~ (all_0_6_6 = e3)
% 9.90/2.75 |
% 9.90/2.75 | Equations (624) can reduce 625 to:
% 9.90/2.75 | (160) ~ (all_0_23_23 = e3)
% 9.90/2.75 |
% 9.90/2.75 +-Applying beta-rule and splitting (69), into two cases.
% 9.90/2.75 |-Branch one:
% 9.90/2.75 | (189) (all_0_13_13 = e3 & ~ (all_0_8_8 = e2)) | (all_0_18_18 = e3 & ~ (all_0_8_8 = e1))
% 9.90/2.75 |
% 9.90/2.75 +-Applying beta-rule and splitting (189), into two cases.
% 9.90/2.75 |-Branch one:
% 9.90/2.75 | (190) all_0_13_13 = e3 & ~ (all_0_8_8 = e2)
% 9.90/2.75 |
% 9.90/2.75 | Applying alpha-rule on (190) yields:
% 9.90/2.75 | (191) all_0_13_13 = e3
% 9.90/2.75 | (192) ~ (all_0_8_8 = e2)
% 9.90/2.75 |
% 9.90/2.75 | Combining equations (191,539) yields a new equation:
% 9.90/2.75 | (552) e3 = e0
% 9.90/2.75 |
% 9.90/2.75 | Simplifying 552 yields:
% 9.90/2.75 | (257) e3 = e0
% 9.90/2.75 |
% 9.90/2.75 | Equations (257) can reduce 40 to:
% 9.90/2.75 | (179) $false
% 9.90/2.75 |
% 9.90/2.75 |-The branch is then unsatisfiable
% 9.90/2.75 |-Branch two:
% 9.90/2.75 | (379) all_0_18_18 = e3 & ~ (all_0_8_8 = e1)
% 9.90/2.75 |
% 9.90/2.75 | Applying alpha-rule on (379) yields:
% 9.90/2.75 | (297) all_0_18_18 = e3
% 9.90/2.75 | (268) ~ (all_0_8_8 = e1)
% 9.90/2.75 |
% 9.90/2.75 | Equations (297) can reduce 26 to:
% 9.90/2.75 | (427) ~ (all_0_14_14 = e3)
% 9.90/2.75 |
% 9.90/2.75 | Equations (297) can reduce 42 to:
% 9.90/2.75 | (638) ~ (all_0_22_22 = e3)
% 9.90/2.75 |
% 9.90/2.75 | Simplifying 638 yields:
% 9.90/2.75 | (639) ~ (all_0_22_22 = e3)
% 9.90/2.75 |
% 9.90/2.75 | From (297) and (11) follows:
% 9.90/2.75 | (640) op(e1, e1) = e3
% 9.90/2.75 |
% 9.90/2.75 +-Applying beta-rule and splitting (132), into two cases.
% 9.90/2.75 |-Branch one:
% 9.90/2.75 | (173) (all_0_8_8 = e2 & ~ (all_0_13_13 = e3)) | (all_0_18_18 = e2 & ~ (all_0_13_13 = e1))
% 9.90/2.75 |
% 9.90/2.75 +-Applying beta-rule and splitting (173), into two cases.
% 9.90/2.75 |-Branch one:
% 9.90/2.75 | (174) all_0_8_8 = e2 & ~ (all_0_13_13 = e3)
% 9.90/2.75 |
% 9.90/2.75 | Applying alpha-rule on (174) yields:
% 9.90/2.75 | (175) all_0_8_8 = e2
% 9.90/2.75 | (176) ~ (all_0_13_13 = e3)
% 9.90/2.75 |
% 9.90/2.75 | Equations (175) can reduce 139 to:
% 9.90/2.75 | (645) ~ (all_0_10_10 = e2)
% 9.90/2.75 |
% 9.90/2.75 | Simplifying 645 yields:
% 9.90/2.75 | (491) ~ (all_0_10_10 = e2)
% 9.90/2.75 |
% 9.90/2.75 | Equations (175) can reduce 19 to:
% 9.90/2.75 | (647) ~ (all_0_11_11 = e2)
% 9.90/2.75 |
% 9.90/2.75 | Simplifying 647 yields:
% 9.90/2.75 | (343) ~ (all_0_11_11 = e2)
% 9.90/2.75 |
% 9.90/2.75 | Equations (175) can reduce 91 to:
% 9.90/2.75 | (649) ~ (all_0_12_12 = e2)
% 9.90/2.75 |
% 9.90/2.75 | Simplifying 649 yields:
% 9.90/2.75 | (365) ~ (all_0_12_12 = e2)
% 9.90/2.75 |
% 9.90/2.75 | Equations (175) can reduce 98 to:
% 9.90/2.75 | (236) ~ (all_0_16_16 = e2)
% 9.90/2.75 |
% 9.90/2.75 | Simplifying 236 yields:
% 9.90/2.75 | (183) ~ (all_0_16_16 = e2)
% 9.90/2.75 |
% 9.90/2.75 | Equations (175) can reduce 9 to:
% 9.90/2.75 | (238) ~ (all_0_20_20 = e2)
% 9.90/2.75 |
% 9.90/2.75 | Simplifying 238 yields:
% 9.90/2.75 | (227) ~ (all_0_20_20 = e2)
% 9.90/2.75 |
% 9.90/2.75 | Equations (175) can reduce 268 to:
% 9.90/2.75 | (24) ~ (e2 = e1)
% 9.90/2.75 |
% 9.90/2.75 +-Applying beta-rule and splitting (156), into two cases.
% 9.90/2.75 |-Branch one:
% 9.90/2.75 | (197) (all_0_8_8 = e1 & ~ (all_0_18_18 = e3)) | (all_0_13_13 = e1 & ~ (all_0_18_18 = e2))
% 9.90/2.75 |
% 9.90/2.75 +-Applying beta-rule and splitting (197), into two cases.
% 9.90/2.75 |-Branch one:
% 9.90/2.75 | (198) all_0_8_8 = e1 & ~ (all_0_18_18 = e3)
% 9.90/2.75 |
% 9.90/2.75 | Applying alpha-rule on (198) yields:
% 9.90/2.75 | (199) all_0_8_8 = e1
% 9.90/2.75 | (200) ~ (all_0_18_18 = e3)
% 9.90/2.75 |
% 9.90/2.75 | Combining equations (175,199) yields a new equation:
% 9.90/2.75 | (241) e2 = e1
% 9.90/2.75 |
% 9.90/2.75 | Simplifying 241 yields:
% 9.90/2.75 | (242) e2 = e1
% 9.90/2.75 |
% 9.90/2.75 | Equations (242) can reduce 24 to:
% 9.90/2.75 | (179) $false
% 9.90/2.75 |
% 9.90/2.75 |-The branch is then unsatisfiable
% 9.90/2.75 |-Branch two:
% 9.90/2.75 | (203) all_0_13_13 = e1 & ~ (all_0_18_18 = e2)
% 9.90/2.75 |
% 9.90/2.75 | Applying alpha-rule on (203) yields:
% 9.90/2.75 | (204) all_0_13_13 = e1
% 9.90/2.75 | (205) ~ (all_0_18_18 = e2)
% 9.90/2.75 |
% 9.90/2.75 | Combining equations (204,539) yields a new equation:
% 9.90/2.75 | (540) e1 = e0
% 9.90/2.75 |
% 9.90/2.75 | Simplifying 540 yields:
% 9.90/2.75 | (201) e1 = e0
% 9.90/2.75 |
% 9.90/2.75 | Equations (201) can reduce 88 to:
% 9.90/2.75 | (179) $false
% 9.90/2.75 |
% 9.90/2.75 |-The branch is then unsatisfiable
% 9.90/2.75 |-Branch two:
% 9.90/2.75 | (208) all_0_23_23 = e1 & ~ (all_0_18_18 = e0)
% 9.90/2.75 |
% 9.90/2.75 | Applying alpha-rule on (208) yields:
% 9.90/2.75 | (209) all_0_23_23 = e1
% 9.90/2.75 | (210) ~ (all_0_18_18 = e0)
% 9.90/2.75 |
% 9.90/2.75 | Combining equations (209,624) yields a new equation:
% 9.90/2.76 | (672) all_0_6_6 = e1
% 9.90/2.76 |
% 9.90/2.76 | Equations (209) can reduce 3 to:
% 9.90/2.76 | (212) ~ (all_0_11_11 = e1)
% 9.90/2.76 |
% 9.90/2.76 | Equations (209) can reduce 38 to:
% 9.90/2.76 | (674) ~ (all_0_19_19 = e1)
% 9.90/2.76 |
% 9.90/2.76 | Equations (209) can reduce 149 to:
% 9.90/2.76 | (214) ~ (all_0_20_20 = e1)
% 9.90/2.76 |
% 9.90/2.76 | Equations (209) can reduce 108 to:
% 9.90/2.76 | (215) ~ (all_0_21_21 = e1)
% 9.90/2.76 |
% 9.90/2.76 | Equations (209) can reduce 8 to:
% 9.90/2.76 | (677) ~ (all_0_22_22 = e1)
% 9.90/2.76 |
% 9.90/2.76 | Equations (209) can reduce 160 to:
% 9.90/2.76 | (216) ~ (e3 = e1)
% 9.90/2.76 |
% 9.90/2.76 | Simplifying 216 yields:
% 9.90/2.76 | (155) ~ (e3 = e1)
% 9.90/2.76 |
% 9.90/2.76 | From (209)(209) and (103) follows:
% 9.90/2.76 | (220) op(e1, e1) = all_0_0_0
% 9.90/2.76 |
% 9.90/2.76 | From (209) and (55) follows:
% 9.90/2.76 | (221) op(e1, e0) = all_0_1_1
% 9.90/2.76 |
% 9.90/2.76 +-Applying beta-rule and splitting (110), into two cases.
% 9.90/2.76 |-Branch one:
% 9.90/2.76 | (682) ~ (all_0_6_6 = e1)
% 9.90/2.76 |
% 9.90/2.76 | Equations (672) can reduce 682 to:
% 9.90/2.76 | (179) $false
% 9.90/2.76 |
% 9.90/2.76 |-The branch is then unsatisfiable
% 9.90/2.76 |-Branch two:
% 9.90/2.76 | (672) all_0_6_6 = e1
% 9.90/2.76 | (685) ~ (all_0_7_7 = e3) | ~ (all_0_13_13 = e0)
% 9.90/2.76 |
% 9.90/2.76 +-Applying beta-rule and splitting (685), into two cases.
% 9.90/2.76 |-Branch one:
% 9.90/2.76 | (686) ~ (all_0_7_7 = e3)
% 9.90/2.76 |
% 9.90/2.76 | Equations (623) can reduce 686 to:
% 9.90/2.76 | (687) ~ (all_0_21_21 = e3)
% 9.90/2.76 |
% 9.90/2.76 +-Applying beta-rule and splitting (116), into two cases.
% 9.90/2.76 |-Branch one:
% 9.90/2.76 | (291) all_0_20_20 = e3
% 9.90/2.76 |
% 9.90/2.76 | Equations (291) can reduce 23 to:
% 9.90/2.76 | (431) ~ (all_0_12_12 = e3)
% 9.90/2.76 |
% 9.90/2.76 | Equations (291) can reduce 68 to:
% 9.90/2.76 | (289) ~ (all_0_16_16 = e3)
% 9.90/2.76 |
% 9.90/2.76 | Equations (291) can reduce 131 to:
% 9.90/2.76 | (691) ~ (all_0_21_21 = e3)
% 9.90/2.76 |
% 9.90/2.76 | Simplifying 691 yields:
% 9.90/2.76 | (687) ~ (all_0_21_21 = e3)
% 9.90/2.76 |
% 9.90/2.76 | Equations (291) can reduce 27 to:
% 9.90/2.76 | (638) ~ (all_0_22_22 = e3)
% 9.90/2.76 |
% 9.90/2.76 | Simplifying 638 yields:
% 9.90/2.76 | (639) ~ (all_0_22_22 = e3)
% 9.90/2.76 |
% 9.90/2.76 +-Applying beta-rule and splitting (81), into two cases.
% 9.90/2.76 |-Branch one:
% 9.90/2.76 | (434) all_0_12_12 = e3
% 9.90/2.76 |
% 9.90/2.76 | Equations (434) can reduce 431 to:
% 9.90/2.76 | (179) $false
% 9.90/2.76 |
% 9.90/2.76 |-The branch is then unsatisfiable
% 9.90/2.76 |-Branch two:
% 9.90/2.76 | (431) ~ (all_0_12_12 = e3)
% 9.90/2.76 | (469) all_0_13_13 = e3 | all_0_14_14 = e3 | all_0_15_15 = e3
% 9.90/2.76 |
% 9.90/2.76 +-Applying beta-rule and splitting (143), into two cases.
% 9.90/2.76 |-Branch one:
% 9.90/2.76 | (434) all_0_12_12 = e3
% 9.90/2.76 |
% 9.90/2.76 | Equations (434) can reduce 431 to:
% 9.90/2.76 | (179) $false
% 9.90/2.76 |
% 9.90/2.76 |-The branch is then unsatisfiable
% 9.90/2.76 |-Branch two:
% 9.90/2.76 | (431) ~ (all_0_12_12 = e3)
% 9.90/2.76 | (437) all_0_12_12 = e2 | all_0_12_12 = e1 | all_0_12_12 = e0
% 9.90/2.76 |
% 9.90/2.76 +-Applying beta-rule and splitting (437), into two cases.
% 9.90/2.76 |-Branch one:
% 9.90/2.76 | (233) all_0_12_12 = e2
% 9.90/2.76 |
% 9.90/2.76 | Equations (233) can reduce 365 to:
% 9.90/2.76 | (179) $false
% 9.90/2.76 |
% 9.90/2.76 |-The branch is then unsatisfiable
% 9.90/2.76 |-Branch two:
% 9.90/2.76 | (365) ~ (all_0_12_12 = e2)
% 9.90/2.76 | (581) all_0_12_12 = e1 | all_0_12_12 = e0
% 9.90/2.76 |
% 9.90/2.76 +-Applying beta-rule and splitting (581), into two cases.
% 9.90/2.76 |-Branch one:
% 9.90/2.76 | (240) all_0_12_12 = e1
% 9.90/2.76 |
% 9.90/2.76 | Equations (240) can reduce 75 to:
% 9.90/2.76 | (708) ~ (all_0_14_14 = e1)
% 9.90/2.76 |
% 9.90/2.76 | Simplifying 708 yields:
% 9.90/2.76 | (709) ~ (all_0_14_14 = e1)
% 9.90/2.76 |
% 9.90/2.76 | Equations (240) can reduce 138 to:
% 9.90/2.76 | (710) ~ (all_0_15_15 = e1)
% 9.90/2.76 |
% 9.90/2.76 | Simplifying 710 yields:
% 9.90/2.76 | (711) ~ (all_0_15_15 = e1)
% 9.90/2.76 |
% 9.90/2.76 | Equations (240) can reduce 25 to:
% 9.90/2.76 | (712) ~ (all_0_16_16 = e1)
% 9.90/2.76 |
% 9.90/2.76 | Simplifying 712 yields:
% 9.90/2.76 | (340) ~ (all_0_16_16 = e1)
% 9.90/2.76 |
% 9.90/2.77 | Equations (240) can reduce 431 to:
% 9.90/2.77 | (216) ~ (e3 = e1)
% 9.90/2.77 |
% 9.90/2.77 | Simplifying 216 yields:
% 9.90/2.77 | (155) ~ (e3 = e1)
% 9.90/2.77 |
% 9.90/2.77 +-Applying beta-rule and splitting (137), into two cases.
% 9.90/2.77 |-Branch one:
% 9.90/2.77 | (716) all_0_21_21 = e3
% 9.90/2.77 |
% 9.90/2.77 | Equations (716) can reduce 687 to:
% 9.90/2.77 | (179) $false
% 9.90/2.77 |
% 9.90/2.77 |-The branch is then unsatisfiable
% 9.90/2.77 |-Branch two:
% 9.90/2.77 | (687) ~ (all_0_21_21 = e3)
% 9.90/2.77 | (719) all_0_21_21 = e2 | all_0_21_21 = e1 | all_0_21_21 = e0
% 9.90/2.77 |
% 9.90/2.77 +-Applying beta-rule and splitting (154), into two cases.
% 9.90/2.77 |-Branch one:
% 9.90/2.77 | (286) all_0_16_16 = e3
% 9.90/2.77 |
% 9.90/2.77 | Equations (286) can reduce 289 to:
% 9.90/2.77 | (179) $false
% 9.90/2.77 |
% 9.90/2.77 |-The branch is then unsatisfiable
% 9.90/2.77 |-Branch two:
% 9.90/2.77 | (289) ~ (all_0_16_16 = e3)
% 9.90/2.77 | (723) all_0_16_16 = e2 | all_0_16_16 = e1 | all_0_16_16 = e0
% 9.90/2.77 |
% 9.90/2.77 +-Applying beta-rule and splitting (719), into two cases.
% 9.90/2.77 |-Branch one:
% 9.90/2.77 | (251) all_0_21_21 = e2
% 9.90/2.77 |
% 9.90/2.77 | Equations (251) can reduce 104 to:
% 9.90/2.77 | (521) ~ (all_0_9_9 = e2)
% 9.90/2.77 |
% 9.90/2.77 | Equations (251) can reduce 72 to:
% 9.90/2.77 | (186) ~ (all_0_22_22 = e2)
% 9.90/2.77 |
% 9.90/2.77 | Simplifying 186 yields:
% 9.90/2.77 | (187) ~ (all_0_22_22 = e2)
% 9.90/2.77 |
% 9.90/2.77 +-Applying beta-rule and splitting (58), into two cases.
% 9.90/2.77 |-Branch one:
% 9.90/2.77 | (728) all_0_22_22 = e3
% 9.90/2.77 |
% 9.90/2.77 | Equations (728) can reduce 639 to:
% 9.90/2.77 | (179) $false
% 9.90/2.77 |
% 9.90/2.77 |-The branch is then unsatisfiable
% 9.90/2.77 |-Branch two:
% 9.90/2.77 | (639) ~ (all_0_22_22 = e3)
% 9.90/2.77 | (731) all_0_22_22 = e2 | all_0_22_22 = e1 | all_0_22_22 = e0
% 9.90/2.77 |
% 9.90/2.77 +-Applying beta-rule and splitting (731), into two cases.
% 9.90/2.77 |-Branch one:
% 9.90/2.77 | (358) all_0_22_22 = e2
% 9.90/2.77 |
% 9.90/2.77 | Equations (358) can reduce 187 to:
% 9.90/2.77 | (179) $false
% 9.90/2.77 |
% 9.90/2.77 |-The branch is then unsatisfiable
% 9.90/2.77 |-Branch two:
% 9.90/2.77 | (187) ~ (all_0_22_22 = e2)
% 9.90/2.77 | (735) all_0_22_22 = e1 | all_0_22_22 = e0
% 9.90/2.77 |
% 9.90/2.77 +-Applying beta-rule and splitting (735), into two cases.
% 9.90/2.77 |-Branch one:
% 9.90/2.77 | (736) all_0_22_22 = e1
% 9.90/2.77 |
% 9.90/2.77 | Equations (736) can reduce 677 to:
% 9.90/2.77 | (179) $false
% 9.90/2.77 |
% 9.90/2.77 |-The branch is then unsatisfiable
% 9.90/2.77 |-Branch two:
% 9.90/2.77 | (677) ~ (all_0_22_22 = e1)
% 9.90/2.77 | (739) all_0_22_22 = e0
% 9.90/2.77 |
% 9.90/2.77 | Equations (739) can reduce 57 to:
% 9.90/2.77 | (740) ~ (all_0_10_10 = e0)
% 9.90/2.77 |
% 9.90/2.77 | Equations (739) can reduce 48 to:
% 9.90/2.77 | (575) ~ (all_0_14_14 = e0)
% 9.90/2.77 |
% 9.90/2.77 +-Applying beta-rule and splitting (723), into two cases.
% 9.90/2.77 |-Branch one:
% 9.90/2.77 | (371) all_0_16_16 = e2
% 9.90/2.77 |
% 9.90/2.77 | Equations (371) can reduce 183 to:
% 9.90/2.77 | (179) $false
% 9.90/2.77 |
% 9.90/2.77 |-The branch is then unsatisfiable
% 9.90/2.77 |-Branch two:
% 9.90/2.77 | (183) ~ (all_0_16_16 = e2)
% 9.90/2.77 | (745) all_0_16_16 = e1 | all_0_16_16 = e0
% 9.90/2.77 |
% 9.90/2.77 +-Applying beta-rule and splitting (102), into two cases.
% 9.90/2.77 |-Branch one:
% 9.90/2.77 | (276) all_0_16_16 = e1
% 9.90/2.77 |
% 9.90/2.77 | Equations (276) can reduce 340 to:
% 9.90/2.77 | (179) $false
% 9.90/2.77 |
% 9.90/2.77 |-The branch is then unsatisfiable
% 9.90/2.77 |-Branch two:
% 9.90/2.77 | (340) ~ (all_0_16_16 = e1)
% 9.90/2.77 | (749) all_0_17_17 = e1 | all_0_18_18 = e1 | all_0_19_19 = e1
% 9.90/2.77 |
% 9.90/2.77 +-Applying beta-rule and splitting (749), into two cases.
% 9.90/2.77 |-Branch one:
% 9.90/2.77 | (333) all_0_17_17 = e1
% 9.90/2.77 |
% 9.90/2.77 | Equations (333) can reduce 145 to:
% 9.90/2.77 | (325) ~ (all_0_9_9 = e1)
% 9.90/2.77 |
% 9.90/2.77 | Equations (333) can reduce 78 to:
% 9.90/2.77 | (340) ~ (all_0_16_16 = e1)
% 9.90/2.77 |
% 9.90/2.77 +-Applying beta-rule and splitting (745), into two cases.
% 9.90/2.77 |-Branch one:
% 9.90/2.77 | (276) all_0_16_16 = e1
% 9.90/2.77 |
% 9.90/2.77 | Equations (276) can reduce 340 to:
% 9.90/2.77 | (179) $false
% 9.90/2.77 |
% 9.90/2.77 |-The branch is then unsatisfiable
% 9.90/2.77 |-Branch two:
% 9.90/2.77 | (340) ~ (all_0_16_16 = e1)
% 9.90/2.77 | (756) all_0_16_16 = e0
% 9.90/2.77 |
% 9.90/2.77 | Equations (756) can reduce 183 to:
% 9.90/2.77 | (515) ~ (e2 = e0)
% 9.90/2.77 |
% 9.90/2.78 | Simplifying 515 yields:
% 9.90/2.78 | (119) ~ (e2 = e0)
% 9.90/2.78 |
% 9.90/2.78 | Equations (756) can reduce 340 to:
% 9.90/2.78 | (424) ~ (e1 = e0)
% 9.90/2.78 |
% 9.90/2.78 | Simplifying 424 yields:
% 9.90/2.78 | (88) ~ (e1 = e0)
% 9.90/2.78 |
% 9.90/2.78 +-Applying beta-rule and splitting (71), into two cases.
% 9.90/2.78 |-Branch one:
% 9.90/2.78 | (761) all_0_10_10 = e1
% 9.90/2.78 |
% 9.90/2.78 | Equations (761) can reduce 133 to:
% 9.90/2.78 | (708) ~ (all_0_14_14 = e1)
% 9.90/2.78 |
% 9.90/2.78 | Simplifying 708 yields:
% 9.90/2.78 | (709) ~ (all_0_14_14 = e1)
% 9.90/2.78 |
% 9.90/2.78 | Equations (761) can reduce 740 to:
% 9.90/2.78 | (88) ~ (e1 = e0)
% 9.90/2.78 |
% 9.90/2.78 +-Applying beta-rule and splitting (64), into two cases.
% 9.90/2.78 |-Branch one:
% 9.90/2.78 | (159) all_0_8_8 = e0
% 9.90/2.78 |
% 9.90/2.78 | Combining equations (159,175) yields a new equation:
% 9.90/2.78 | (178) e2 = e0
% 9.90/2.78 |
% 9.90/2.78 | Equations (178) can reduce 119 to:
% 9.90/2.78 | (179) $false
% 9.90/2.78 |
% 9.90/2.78 |-The branch is then unsatisfiable
% 9.90/2.78 |-Branch two:
% 9.90/2.78 | (377) ~ (all_0_8_8 = e0)
% 9.90/2.78 | (769) all_0_9_9 = e0 | all_0_10_10 = e0 | all_0_11_11 = e0
% 9.90/2.78 |
% 9.90/2.78 +-Applying beta-rule and splitting (769), into two cases.
% 9.90/2.78 |-Branch one:
% 9.90/2.78 | (573) all_0_9_9 = e0
% 9.90/2.78 |
% 9.90/2.78 | Equations (573) can reduce 162 to:
% 9.90/2.78 | (179) $false
% 9.90/2.78 |
% 9.90/2.78 |-The branch is then unsatisfiable
% 9.90/2.78 |-Branch two:
% 9.90/2.78 | (162) ~ (all_0_9_9 = e0)
% 9.90/2.78 | (773) all_0_10_10 = e0 | all_0_11_11 = e0
% 9.90/2.78 |
% 9.90/2.78 +-Applying beta-rule and splitting (773), into two cases.
% 9.90/2.78 |-Branch one:
% 9.90/2.78 | (774) all_0_10_10 = e0
% 9.90/2.78 |
% 9.90/2.78 | Combining equations (774,761) yields a new equation:
% 9.90/2.78 | (201) e1 = e0
% 9.90/2.78 |
% 9.90/2.78 | Equations (201) can reduce 88 to:
% 9.90/2.78 | (179) $false
% 9.90/2.78 |
% 9.90/2.78 |-The branch is then unsatisfiable
% 9.90/2.78 |-Branch two:
% 9.90/2.78 | (740) ~ (all_0_10_10 = e0)
% 9.90/2.78 | (778) all_0_11_11 = e0
% 9.90/2.78 |
% 9.90/2.78 +-Applying beta-rule and splitting (46), into two cases.
% 9.90/2.78 |-Branch one:
% 9.90/2.78 | (451) all_0_14_14 = e3
% 9.90/2.78 |
% 9.90/2.78 | Equations (451) can reduce 427 to:
% 9.90/2.78 | (179) $false
% 9.90/2.78 |
% 9.90/2.78 |-The branch is then unsatisfiable
% 9.90/2.78 |-Branch two:
% 9.90/2.78 | (427) ~ (all_0_14_14 = e3)
% 9.90/2.78 | (454) all_0_14_14 = e2 | all_0_14_14 = e1 | all_0_14_14 = e0
% 9.90/2.78 |
% 9.90/2.78 +-Applying beta-rule and splitting (454), into two cases.
% 9.90/2.78 |-Branch one:
% 9.90/2.78 | (783) all_0_14_14 = e2
% 9.90/2.78 |
% 9.90/2.78 | Equations (783) can reduce 12 to:
% 9.90/2.78 | (234) ~ (all_0_15_15 = e2)
% 9.90/2.78 |
% 9.90/2.78 | Simplifying 234 yields:
% 9.90/2.78 | (235) ~ (all_0_15_15 = e2)
% 9.90/2.78 |
% 9.90/2.78 | Equations (783) can reduce 709 to:
% 9.90/2.78 | (24) ~ (e2 = e1)
% 9.90/2.78 |
% 9.90/2.78 | Equations (783) can reduce 575 to:
% 9.90/2.78 | (119) ~ (e2 = e0)
% 9.90/2.78 |
% 9.90/2.78 +-Applying beta-rule and splitting (83), into two cases.
% 9.90/2.78 |-Branch one:
% 9.90/2.78 | (254) all_0_11_11 = e2
% 9.90/2.78 |
% 9.90/2.78 | Combining equations (778,254) yields a new equation:
% 9.90/2.78 | (178) e2 = e0
% 9.90/2.78 |
% 9.90/2.78 | Equations (178) can reduce 119 to:
% 9.90/2.78 | (179) $false
% 9.90/2.78 |
% 9.90/2.78 |-The branch is then unsatisfiable
% 9.90/2.78 |-Branch two:
% 9.90/2.78 | (343) ~ (all_0_11_11 = e2)
% 9.90/2.78 | (344) all_0_15_15 = e2 | all_0_19_19 = e2 | all_0_23_23 = e2
% 9.90/2.78 |
% 9.90/2.78 +-Applying beta-rule and splitting (344), into two cases.
% 9.90/2.78 |-Branch one:
% 9.90/2.78 | (345) all_0_15_15 = e2
% 9.90/2.78 |
% 9.90/2.78 | Equations (345) can reduce 235 to:
% 9.90/2.78 | (179) $false
% 9.90/2.78 |
% 9.90/2.78 |-The branch is then unsatisfiable
% 9.90/2.78 |-Branch two:
% 9.90/2.78 | (235) ~ (all_0_15_15 = e2)
% 9.90/2.78 | (348) all_0_19_19 = e2 | all_0_23_23 = e2
% 9.90/2.78 |
% 9.90/2.78 +-Applying beta-rule and splitting (348), into two cases.
% 9.90/2.78 |-Branch one:
% 9.90/2.78 | (349) all_0_19_19 = e2
% 9.90/2.78 |
% 9.90/2.78 | From (349) and (33) follows:
% 9.90/2.78 | (798) op(e1, e0) = e2
% 9.90/2.78 |
% 9.90/2.78 | Instantiating formula (85) with e1, e1, e3, all_0_0_0 and discharging atoms op(e1, e1) = all_0_0_0, op(e1, e1) = e3, yields:
% 9.90/2.78 | (799) all_0_0_0 = e3
% 9.90/2.78 |
% 9.90/2.78 | Instantiating formula (85) with e1, e0, e2, all_0_1_1 and discharging atoms op(e1, e0) = all_0_1_1, op(e1, e0) = e2, yields:
% 9.90/2.79 | (800) all_0_1_1 = e2
% 9.90/2.79 |
% 9.90/2.79 +-Applying beta-rule and splitting (146), into two cases.
% 9.90/2.79 |-Branch one:
% 9.90/2.79 | (801) ~ (all_0_0_0 = e3)
% 9.90/2.79 |
% 9.90/2.79 | Equations (799) can reduce 801 to:
% 9.90/2.79 | (179) $false
% 9.90/2.79 |
% 9.90/2.79 |-The branch is then unsatisfiable
% 9.90/2.79 |-Branch two:
% 9.90/2.79 | (799) all_0_0_0 = e3
% 9.90/2.79 | (804) ~ (all_0_1_1 = e2) | ~ (all_0_23_23 = e1)
% 9.90/2.79 |
% 9.90/2.79 +-Applying beta-rule and splitting (804), into two cases.
% 9.90/2.79 |-Branch one:
% 9.90/2.79 | (805) ~ (all_0_1_1 = e2)
% 9.90/2.79 |
% 9.90/2.79 | Equations (800) can reduce 805 to:
% 9.90/2.79 | (179) $false
% 9.90/2.79 |
% 9.90/2.79 |-The branch is then unsatisfiable
% 9.90/2.79 |-Branch two:
% 9.90/2.79 | (800) all_0_1_1 = e2
% 9.90/2.79 | (312) ~ (all_0_23_23 = e1)
% 9.90/2.79 |
% 9.90/2.79 | Equations (209) can reduce 312 to:
% 9.90/2.79 | (179) $false
% 9.90/2.79 |
% 9.90/2.79 |-The branch is then unsatisfiable
% 9.90/2.79 |-Branch two:
% 9.90/2.79 | (185) ~ (all_0_19_19 = e2)
% 9.90/2.79 | (352) all_0_23_23 = e2
% 9.90/2.79 |
% 9.90/2.79 | Combining equations (352,209) yields a new equation:
% 9.90/2.79 | (241) e2 = e1
% 9.90/2.79 |
% 9.90/2.79 | Simplifying 241 yields:
% 9.90/2.79 | (242) e2 = e1
% 9.90/2.79 |
% 9.90/2.79 | Equations (242) can reduce 24 to:
% 9.90/2.79 | (179) $false
% 9.90/2.79 |
% 9.90/2.79 |-The branch is then unsatisfiable
% 10.31/2.79 |-Branch two:
% 10.31/2.79 | (815) ~ (all_0_14_14 = e2)
% 10.31/2.79 | (816) all_0_14_14 = e1 | all_0_14_14 = e0
% 10.31/2.79 |
% 10.31/2.79 +-Applying beta-rule and splitting (816), into two cases.
% 10.31/2.79 |-Branch one:
% 10.31/2.79 | (817) all_0_14_14 = e1
% 10.31/2.79 |
% 10.31/2.79 | Equations (817) can reduce 709 to:
% 10.31/2.79 | (179) $false
% 10.31/2.79 |
% 10.31/2.79 |-The branch is then unsatisfiable
% 10.31/2.79 |-Branch two:
% 10.31/2.79 | (709) ~ (all_0_14_14 = e1)
% 10.31/2.79 | (545) all_0_14_14 = e0
% 10.31/2.79 |
% 10.31/2.79 | Equations (545) can reduce 575 to:
% 10.31/2.79 | (179) $false
% 10.31/2.79 |
% 10.31/2.79 |-The branch is then unsatisfiable
% 10.31/2.79 |-Branch two:
% 10.31/2.79 | (822) ~ (all_0_10_10 = e1)
% 10.31/2.79 | (823) all_0_14_14 = e1 | all_0_18_18 = e1 | all_0_22_22 = e1
% 10.31/2.79 |
% 10.31/2.79 +-Applying beta-rule and splitting (50), into two cases.
% 10.31/2.79 |-Branch one:
% 10.31/2.79 | (778) all_0_11_11 = e0
% 10.31/2.79 |
% 10.31/2.79 | Equations (778) can reduce 135 to:
% 10.31/2.79 | (162) ~ (all_0_9_9 = e0)
% 10.31/2.79 |
% 10.31/2.79 | Equations (778) can reduce 128 to:
% 10.31/2.79 | (826) ~ (all_0_15_15 = e0)
% 10.31/2.80 |
% 10.31/2.80 | Simplifying 826 yields:
% 10.31/2.80 | (827) ~ (all_0_15_15 = e0)
% 10.31/2.80 |
% 10.31/2.80 | Equations (778) can reduce 343 to:
% 10.31/2.80 | (515) ~ (e2 = e0)
% 10.31/2.80 |
% 10.31/2.80 | Simplifying 515 yields:
% 10.31/2.80 | (119) ~ (e2 = e0)
% 10.31/2.80 |
% 10.34/2.80 | Equations (778) can reduce 212 to:
% 10.34/2.80 | (424) ~ (e1 = e0)
% 10.34/2.80 |
% 10.34/2.80 | Simplifying 424 yields:
% 10.34/2.80 | (88) ~ (e1 = e0)
% 10.34/2.80 |
% 10.34/2.80 +-Applying beta-rule and splitting (21), into two cases.
% 10.34/2.80 |-Branch one:
% 10.34/2.80 | (261) all_0_9_9 = e3
% 10.34/2.80 |
% 10.34/2.80 | Equations (261) can reduce 521 to:
% 10.34/2.80 | (126) ~ (e3 = e2)
% 10.34/2.80 |
% 10.34/2.80 +-Applying beta-rule and splitting (150), into two cases.
% 10.34/2.80 |-Branch one:
% 10.34/2.80 | (462) all_0_10_10 = e2
% 10.34/2.80 |
% 10.34/2.80 | Equations (462) can reduce 491 to:
% 10.34/2.80 | (179) $false
% 10.34/2.80 |
% 10.34/2.80 |-The branch is then unsatisfiable
% 10.34/2.80 |-Branch two:
% 10.34/2.80 | (491) ~ (all_0_10_10 = e2)
% 10.34/2.80 | (492) all_0_14_14 = e2 | all_0_18_18 = e2 | all_0_22_22 = e2
% 10.34/2.80 |
% 10.34/2.80 +-Applying beta-rule and splitting (492), into two cases.
% 10.34/2.80 |-Branch one:
% 10.34/2.80 | (783) all_0_14_14 = e2
% 10.34/2.80 |
% 10.34/2.80 | Equations (783) can reduce 12 to:
% 10.34/2.80 | (234) ~ (all_0_15_15 = e2)
% 10.34/2.80 |
% 10.34/2.80 | Simplifying 234 yields:
% 10.34/2.80 | (235) ~ (all_0_15_15 = e2)
% 10.34/2.80 |
% 10.34/2.80 | Equations (783) can reduce 709 to:
% 10.34/2.80 | (24) ~ (e2 = e1)
% 10.34/2.80 |
% 10.34/2.80 +-Applying beta-rule and splitting (90), into two cases.
% 10.34/2.80 |-Branch one:
% 10.34/2.80 | (478) all_0_15_15 = e3
% 10.34/2.80 |
% 10.34/2.80 | Equations (478) can reduce 711 to:
% 10.34/2.80 | (155) ~ (e3 = e1)
% 10.34/2.80 |
% 10.34/2.80 +-Applying beta-rule and splitting (823), into two cases.
% 10.34/2.80 |-Branch one:
% 10.34/2.80 | (817) all_0_14_14 = e1
% 10.34/2.80 |
% 10.34/2.80 | Combining equations (783,817) yields a new equation:
% 10.34/2.80 | (241) e2 = e1
% 10.34/2.80 |
% 10.34/2.80 | Simplifying 241 yields:
% 10.34/2.80 | (242) e2 = e1
% 10.34/2.80 |
% 10.34/2.80 | Equations (242) can reduce 24 to:
% 10.34/2.80 | (179) $false
% 10.34/2.80 |
% 10.34/2.80 |-The branch is then unsatisfiable
% 10.34/2.80 |-Branch two:
% 10.34/2.80 | (709) ~ (all_0_14_14 = e1)
% 10.34/2.80 | (849) all_0_18_18 = e1 | all_0_22_22 = e1
% 10.34/2.80 |
% 10.34/2.80 +-Applying beta-rule and splitting (849), into two cases.
% 10.34/2.80 |-Branch one:
% 10.34/2.80 | (850) all_0_18_18 = e1
% 10.34/2.80 |
% 10.34/2.80 | Combining equations (297,850) yields a new equation:
% 10.34/2.80 | (328) e3 = e1
% 10.34/2.80 |
% 10.34/2.80 | Simplifying 328 yields:
% 10.34/2.80 | (206) e3 = e1
% 10.34/2.80 |
% 10.34/2.80 | Equations (206) can reduce 155 to:
% 10.34/2.80 | (179) $false
% 10.34/2.80 |
% 10.34/2.80 |-The branch is then unsatisfiable
% 10.34/2.80 |-Branch two:
% 10.34/2.80 | (854) ~ (all_0_18_18 = e1)
% 10.36/2.80 | (736) all_0_22_22 = e1
% 10.36/2.80 |
% 10.36/2.80 | Combining equations (739,736) yields a new equation:
% 10.36/2.80 | (201) e1 = e0
% 10.36/2.80 |
% 10.36/2.80 | Equations (201) can reduce 88 to:
% 10.36/2.80 | (179) $false
% 10.36/2.80 |
% 10.36/2.80 |-The branch is then unsatisfiable
% 10.36/2.80 |-Branch two:
% 10.36/2.80 | (858) ~ (all_0_15_15 = e3)
% 10.36/2.81 | (859) all_0_15_15 = e2 | all_0_15_15 = e1 | all_0_15_15 = e0
% 10.36/2.81 |
% 10.36/2.81 +-Applying beta-rule and splitting (859), into two cases.
% 10.36/2.81 |-Branch one:
% 10.36/2.81 | (345) all_0_15_15 = e2
% 10.36/2.81 |
% 10.36/2.81 | Equations (345) can reduce 235 to:
% 10.36/2.81 | (179) $false
% 10.36/2.81 |
% 10.36/2.81 |-The branch is then unsatisfiable
% 10.36/2.81 |-Branch two:
% 10.36/2.81 | (235) ~ (all_0_15_15 = e2)
% 10.36/2.81 | (863) all_0_15_15 = e1 | all_0_15_15 = e0
% 10.36/2.81 |
% 10.36/2.81 +-Applying beta-rule and splitting (863), into two cases.
% 10.36/2.81 |-Branch one:
% 10.36/2.81 | (864) all_0_15_15 = e1
% 10.36/2.81 |
% 10.36/2.81 | Equations (864) can reduce 711 to:
% 10.36/2.81 | (179) $false
% 10.36/2.81 |
% 10.36/2.81 |-The branch is then unsatisfiable
% 10.36/2.81 |-Branch two:
% 10.36/2.81 | (711) ~ (all_0_15_15 = e1)
% 10.36/2.81 | (576) all_0_15_15 = e0
% 10.36/2.81 |
% 10.36/2.81 | Equations (576) can reduce 827 to:
% 10.36/2.81 | (179) $false
% 10.36/2.81 |
% 10.36/2.81 |-The branch is then unsatisfiable
% 10.36/2.81 |-Branch two:
% 10.36/2.81 | (815) ~ (all_0_14_14 = e2)
% 10.36/2.81 | (870) all_0_18_18 = e2 | all_0_22_22 = e2
% 10.36/2.81 |
% 10.36/2.81 +-Applying beta-rule and splitting (870), into two cases.
% 10.36/2.81 |-Branch one:
% 10.36/2.81 | (181) all_0_18_18 = e2
% 10.36/2.81 |
% 10.36/2.81 | Combining equations (297,181) yields a new equation:
% 10.36/2.81 | (382) e3 = e2
% 10.36/2.81 |
% 10.36/2.81 | Simplifying 382 yields:
% 10.36/2.81 | (298) e3 = e2
% 10.36/2.81 |
% 10.36/2.81 | Equations (298) can reduce 126 to:
% 10.36/2.81 | (179) $false
% 10.36/2.81 |
% 10.36/2.81 |-The branch is then unsatisfiable
% 10.36/2.81 |-Branch two:
% 10.36/2.81 | (205) ~ (all_0_18_18 = e2)
% 10.36/2.81 | (358) all_0_22_22 = e2
% 10.36/2.81 |
% 10.36/2.81 | Combining equations (739,358) yields a new equation:
% 10.36/2.81 | (178) e2 = e0
% 10.36/2.81 |
% 10.36/2.81 | Equations (178) can reduce 119 to:
% 10.36/2.81 | (179) $false
% 10.36/2.81 |
% 10.36/2.81 |-The branch is then unsatisfiable
% 10.36/2.81 |-Branch two:
% 10.36/2.81 | (193) ~ (all_0_9_9 = e3)
% 10.36/2.81 | (538) all_0_9_9 = e2 | all_0_9_9 = e1 | all_0_9_9 = e0
% 10.36/2.81 |
% 10.36/2.81 +-Applying beta-rule and splitting (538), into two cases.
% 10.36/2.81 |-Branch one:
% 10.36/2.81 | (518) all_0_9_9 = e2
% 10.36/2.81 |
% 10.36/2.81 | Equations (518) can reduce 521 to:
% 10.36/2.81 | (179) $false
% 10.36/2.81 |
% 10.36/2.81 |-The branch is then unsatisfiable
% 10.36/2.81 |-Branch two:
% 10.36/2.81 | (521) ~ (all_0_9_9 = e2)
% 10.36/2.81 | (569) all_0_9_9 = e1 | all_0_9_9 = e0
% 10.36/2.81 |
% 10.36/2.81 +-Applying beta-rule and splitting (569), into two cases.
% 10.36/2.81 |-Branch one:
% 10.36/2.81 | (283) all_0_9_9 = e1
% 10.36/2.81 |
% 10.36/2.81 | Equations (283) can reduce 325 to:
% 10.36/2.81 | (179) $false
% 10.36/2.81 |
% 10.36/2.81 |-The branch is then unsatisfiable
% 10.36/2.81 |-Branch two:
% 10.36/2.81 | (325) ~ (all_0_9_9 = e1)
% 10.36/2.81 | (573) all_0_9_9 = e0
% 10.36/2.81 |
% 10.36/2.81 | Equations (573) can reduce 162 to:
% 10.36/2.81 | (179) $false
% 10.36/2.81 |
% 10.36/2.81 |-The branch is then unsatisfiable
% 10.36/2.81 |-Branch two:
% 10.36/2.81 | (890) ~ (all_0_11_11 = e0)
% 10.36/2.81 | (891) all_0_15_15 = e0 | all_0_19_19 = e0 | all_0_23_23 = e0
% 10.36/2.81 |
% 10.36/2.82 +-Applying beta-rule and splitting (823), into two cases.
% 10.36/2.82 |-Branch one:
% 10.36/2.82 | (817) all_0_14_14 = e1
% 10.36/2.82 |
% 10.36/2.82 | Equations (817) can reduce 709 to:
% 10.36/2.82 | (179) $false
% 10.36/2.82 |
% 10.36/2.82 |-The branch is then unsatisfiable
% 10.36/2.82 |-Branch two:
% 10.36/2.82 | (709) ~ (all_0_14_14 = e1)
% 10.36/2.82 | (849) all_0_18_18 = e1 | all_0_22_22 = e1
% 10.36/2.82 |
% 10.36/2.82 +-Applying beta-rule and splitting (80), into two cases.
% 10.36/2.82 |-Branch one:
% 10.36/2.82 | (566) all_0_11_11 = e3
% 10.36/2.82 |
% 10.36/2.82 | Equations (566) can reduce 212 to:
% 10.36/2.82 | (155) ~ (e3 = e1)
% 10.36/2.82 |
% 10.36/2.82 +-Applying beta-rule and splitting (849), into two cases.
% 10.36/2.82 |-Branch one:
% 10.36/2.82 | (850) all_0_18_18 = e1
% 10.36/2.82 |
% 10.36/2.82 | Combining equations (297,850) yields a new equation:
% 10.36/2.82 | (328) e3 = e1
% 10.36/2.82 |
% 10.36/2.82 | Simplifying 328 yields:
% 10.36/2.82 | (206) e3 = e1
% 10.36/2.82 |
% 10.36/2.82 | Equations (206) can reduce 155 to:
% 10.36/2.82 | (179) $false
% 10.36/2.82 |
% 10.36/2.82 |-The branch is then unsatisfiable
% 10.36/2.82 |-Branch two:
% 10.36/2.82 | (854) ~ (all_0_18_18 = e1)
% 10.36/2.82 | (736) all_0_22_22 = e1
% 10.36/2.82 |
% 10.36/2.82 | Combining equations (739,736) yields a new equation:
% 10.36/2.82 | (201) e1 = e0
% 10.36/2.82 |
% 10.36/2.82 | Equations (201) can reduce 88 to:
% 10.36/2.82 | (179) $false
% 10.36/2.82 |
% 10.36/2.82 |-The branch is then unsatisfiable
% 10.36/2.82 |-Branch two:
% 10.36/2.82 | (507) ~ (all_0_11_11 = e3)
% 10.36/2.82 | (907) all_0_11_11 = e2 | all_0_11_11 = e1 | all_0_11_11 = e0
% 10.36/2.82 |
% 10.36/2.82 +-Applying beta-rule and splitting (907), into two cases.
% 10.36/2.82 |-Branch one:
% 10.36/2.82 | (254) all_0_11_11 = e2
% 10.36/2.82 |
% 10.36/2.82 | Equations (254) can reduce 343 to:
% 10.36/2.82 | (179) $false
% 10.36/2.82 |
% 10.36/2.82 |-The branch is then unsatisfiable
% 10.36/2.82 |-Branch two:
% 10.36/2.82 | (343) ~ (all_0_11_11 = e2)
% 10.36/2.82 | (911) all_0_11_11 = e1 | all_0_11_11 = e0
% 10.36/2.82 |
% 10.36/2.82 +-Applying beta-rule and splitting (911), into two cases.
% 10.36/2.82 |-Branch one:
% 10.36/2.82 | (912) all_0_11_11 = e1
% 10.36/2.82 |
% 10.36/2.82 | Equations (912) can reduce 212 to:
% 10.36/2.82 | (179) $false
% 10.36/2.82 |
% 10.36/2.82 |-The branch is then unsatisfiable
% 10.36/2.82 |-Branch two:
% 10.36/2.82 | (212) ~ (all_0_11_11 = e1)
% 10.36/2.82 | (778) all_0_11_11 = e0
% 10.36/2.82 |
% 10.36/2.82 | Equations (778) can reduce 890 to:
% 10.36/2.82 | (179) $false
% 10.36/2.82 |
% 10.36/2.82 |-The branch is then unsatisfiable
% 10.36/2.82 |-Branch two:
% 10.36/2.82 | (278) ~ (all_0_17_17 = e1)
% 10.36/2.83 | (918) all_0_18_18 = e1 | all_0_19_19 = e1
% 10.36/2.83 |
% 10.36/2.83 +-Applying beta-rule and splitting (918), into two cases.
% 10.36/2.83 |-Branch one:
% 10.36/2.83 | (850) all_0_18_18 = e1
% 10.36/2.83 |
% 10.36/2.83 | Combining equations (297,850) yields a new equation:
% 10.36/2.83 | (328) e3 = e1
% 10.36/2.83 |
% 10.36/2.83 | Simplifying 328 yields:
% 10.36/2.83 | (206) e3 = e1
% 10.36/2.83 |
% 10.36/2.83 | Equations (206) can reduce 155 to:
% 10.36/2.83 | (179) $false
% 10.36/2.83 |
% 10.36/2.83 |-The branch is then unsatisfiable
% 10.36/2.83 |-Branch two:
% 10.36/2.83 | (854) ~ (all_0_18_18 = e1)
% 10.36/2.83 | (924) all_0_19_19 = e1
% 10.36/2.83 |
% 10.36/2.83 | Equations (924) can reduce 674 to:
% 10.36/2.83 | (179) $false
% 10.36/2.83 |
% 10.36/2.83 |-The branch is then unsatisfiable
% 10.36/2.83 |-Branch two:
% 10.36/2.83 | (356) ~ (all_0_21_21 = e2)
% 10.36/2.83 | (927) all_0_21_21 = e1 | all_0_21_21 = e0
% 10.36/2.83 |
% 10.36/2.83 +-Applying beta-rule and splitting (927), into two cases.
% 10.36/2.83 |-Branch one:
% 10.36/2.83 | (336) all_0_21_21 = e1
% 10.36/2.83 |
% 10.36/2.83 | Equations (336) can reduce 215 to:
% 10.36/2.83 | (179) $false
% 10.36/2.83 |
% 10.36/2.83 |-The branch is then unsatisfiable
% 10.36/2.83 |-Branch two:
% 10.36/2.83 | (215) ~ (all_0_21_21 = e1)
% 10.36/2.83 | (931) all_0_21_21 = e0
% 10.36/2.83 |
% 10.36/2.83 | Equations (931) can reduce 620 to:
% 10.36/2.83 | (179) $false
% 10.36/2.83 |
% 10.36/2.83 |-The branch is then unsatisfiable
% 10.36/2.83 |-Branch two:
% 10.36/2.83 | (244) ~ (all_0_12_12 = e1)
% 10.36/2.83 | (530) all_0_12_12 = e0
% 10.36/2.83 |
% 10.36/2.83 | Equations (530) can reduce 164 to:
% 10.36/2.83 | (179) $false
% 10.36/2.83 |
% 10.36/2.83 |-The branch is then unsatisfiable
% 10.36/2.83 |-Branch two:
% 10.36/2.83 | (314) ~ (all_0_20_20 = e3)
% 10.36/2.83 | (937) all_0_21_21 = e3 | all_0_22_22 = e3 | all_0_23_23 = e3
% 10.36/2.83 |
% 10.36/2.83 +-Applying beta-rule and splitting (137), into two cases.
% 10.36/2.83 |-Branch one:
% 10.36/2.83 | (716) all_0_21_21 = e3
% 10.36/2.83 |
% 10.36/2.83 | Equations (716) can reduce 687 to:
% 10.36/2.83 | (179) $false
% 10.36/2.83 |
% 10.36/2.83 |-The branch is then unsatisfiable
% 10.36/2.83 |-Branch two:
% 10.36/2.83 | (687) ~ (all_0_21_21 = e3)
% 10.36/2.83 | (719) all_0_21_21 = e2 | all_0_21_21 = e1 | all_0_21_21 = e0
% 10.36/2.83 |
% 10.36/2.84 +-Applying beta-rule and splitting (937), into two cases.
% 10.36/2.84 |-Branch one:
% 10.36/2.84 | (716) all_0_21_21 = e3
% 10.36/2.84 |
% 10.36/2.84 | Equations (716) can reduce 687 to:
% 10.36/2.84 | (179) $false
% 10.36/2.84 |
% 10.36/2.84 |-The branch is then unsatisfiable
% 10.36/2.84 |-Branch two:
% 10.36/2.84 | (687) ~ (all_0_21_21 = e3)
% 10.36/2.84 | (945) all_0_22_22 = e3 | all_0_23_23 = e3
% 10.36/2.84 |
% 10.36/2.84 +-Applying beta-rule and splitting (148), into two cases.
% 10.36/2.84 |-Branch one:
% 10.36/2.84 | (291) all_0_20_20 = e3
% 10.36/2.84 |
% 10.36/2.84 | Equations (291) can reduce 314 to:
% 10.36/2.84 | (179) $false
% 10.36/2.84 |
% 10.36/2.84 |-The branch is then unsatisfiable
% 10.36/2.84 |-Branch two:
% 10.36/2.84 | (314) ~ (all_0_20_20 = e3)
% 10.36/2.84 | (315) all_0_20_20 = e2 | all_0_20_20 = e1 | all_0_20_20 = e0
% 10.36/2.84 |
% 10.36/2.84 +-Applying beta-rule and splitting (315), into two cases.
% 10.36/2.84 |-Branch one:
% 10.36/2.84 | (247) all_0_20_20 = e2
% 10.36/2.84 |
% 10.36/2.84 | Equations (247) can reduce 227 to:
% 10.36/2.84 | (179) $false
% 10.36/2.84 |
% 10.36/2.84 |-The branch is then unsatisfiable
% 10.36/2.84 |-Branch two:
% 10.36/2.84 | (227) ~ (all_0_20_20 = e2)
% 10.36/2.84 | (319) all_0_20_20 = e1 | all_0_20_20 = e0
% 10.36/2.84 |
% 10.36/2.84 +-Applying beta-rule and splitting (319), into two cases.
% 10.36/2.84 |-Branch one:
% 10.36/2.84 | (320) all_0_20_20 = e1
% 10.36/2.84 |
% 10.36/2.84 | Equations (320) can reduce 214 to:
% 10.36/2.84 | (179) $false
% 10.36/2.84 |
% 10.36/2.84 |-The branch is then unsatisfiable
% 10.36/2.84 |-Branch two:
% 10.36/2.84 | (214) ~ (all_0_20_20 = e1)
% 10.36/2.84 | (323) all_0_20_20 = e0
% 10.36/2.84 |
% 10.36/2.84 | Equations (323) can reduce 27 to:
% 10.36/2.84 | (958) ~ (all_0_22_22 = e0)
% 10.36/2.84 |
% 10.36/2.84 | Simplifying 958 yields:
% 10.36/2.84 | (959) ~ (all_0_22_22 = e0)
% 10.36/2.84 |
% 10.36/2.84 +-Applying beta-rule and splitting (58), into two cases.
% 10.36/2.84 |-Branch one:
% 10.36/2.84 | (728) all_0_22_22 = e3
% 10.36/2.84 |
% 10.36/2.84 | Equations (728) can reduce 639 to:
% 10.36/2.84 | (179) $false
% 10.36/2.84 |
% 10.36/2.84 |-The branch is then unsatisfiable
% 10.36/2.84 |-Branch two:
% 10.36/2.84 | (639) ~ (all_0_22_22 = e3)
% 10.36/2.84 | (731) all_0_22_22 = e2 | all_0_22_22 = e1 | all_0_22_22 = e0
% 10.36/2.84 |
% 10.36/2.84 +-Applying beta-rule and splitting (731), into two cases.
% 10.36/2.84 |-Branch one:
% 10.36/2.84 | (358) all_0_22_22 = e2
% 10.36/2.84 |
% 10.36/2.84 | Equations (358) can reduce 639 to:
% 10.36/2.84 | (398) ~ (e3 = e2)
% 10.36/2.84 |
% 10.36/2.84 | Simplifying 398 yields:
% 10.36/2.84 | (126) ~ (e3 = e2)
% 10.36/2.84 |
% 10.36/2.84 +-Applying beta-rule and splitting (945), into two cases.
% 10.36/2.84 |-Branch one:
% 10.36/2.84 | (728) all_0_22_22 = e3
% 10.36/2.84 |
% 10.36/2.84 | Combining equations (358,728) yields a new equation:
% 10.36/2.84 | (298) e3 = e2
% 10.36/2.84 |
% 10.36/2.84 | Equations (298) can reduce 126 to:
% 10.36/2.84 | (179) $false
% 10.36/2.84 |
% 10.36/2.84 |-The branch is then unsatisfiable
% 10.36/2.84 |-Branch two:
% 10.36/2.84 | (639) ~ (all_0_22_22 = e3)
% 10.36/2.84 | (386) all_0_23_23 = e3
% 10.36/2.84 |
% 10.36/2.84 | Combining equations (386,209) yields a new equation:
% 10.36/2.84 | (328) e3 = e1
% 10.36/2.84 |
% 10.36/2.84 | Simplifying 328 yields:
% 10.36/2.84 | (206) e3 = e1
% 10.36/2.84 |
% 10.36/2.84 | Equations (206) can reduce 155 to:
% 10.36/2.84 | (179) $false
% 10.36/2.84 |
% 10.36/2.84 |-The branch is then unsatisfiable
% 10.36/2.84 |-Branch two:
% 10.36/2.84 | (187) ~ (all_0_22_22 = e2)
% 10.36/2.84 | (735) all_0_22_22 = e1 | all_0_22_22 = e0
% 10.36/2.84 |
% 10.36/2.84 +-Applying beta-rule and splitting (735), into two cases.
% 10.36/2.84 |-Branch one:
% 10.36/2.84 | (736) all_0_22_22 = e1
% 10.36/2.84 |
% 10.36/2.84 | Equations (736) can reduce 677 to:
% 10.36/2.84 | (179) $false
% 10.36/2.84 |
% 10.36/2.84 |-The branch is then unsatisfiable
% 10.36/2.84 |-Branch two:
% 10.36/2.84 | (677) ~ (all_0_22_22 = e1)
% 10.36/2.84 | (739) all_0_22_22 = e0
% 10.36/2.84 |
% 10.36/2.84 | Equations (739) can reduce 959 to:
% 10.36/2.84 | (179) $false
% 10.36/2.84 |
% 10.36/2.84 |-The branch is then unsatisfiable
% 10.36/2.85 |-Branch two:
% 10.36/2.85 | (982) all_0_7_7 = e3
% 10.36/2.85 | (391) ~ (all_0_13_13 = e0)
% 10.36/2.85 |
% 10.36/2.85 | Equations (539) can reduce 391 to:
% 10.36/2.85 | (179) $false
% 10.36/2.85 |
% 10.36/2.85 |-The branch is then unsatisfiable
% 10.36/2.85 |-Branch two:
% 10.36/2.85 | (180) all_0_18_18 = e2 & ~ (all_0_13_13 = e1)
% 10.36/2.85 |
% 10.36/2.85 | Applying alpha-rule on (180) yields:
% 10.36/2.85 | (181) all_0_18_18 = e2
% 10.36/2.85 | (182) ~ (all_0_13_13 = e1)
% 10.36/2.85 |
% 10.36/2.85 | Combining equations (181,297) yields a new equation:
% 10.36/2.85 | (298) e3 = e2
% 10.36/2.85 |
% 10.36/2.85 | Equations (298) can reduce 126 to:
% 10.36/2.85 | (179) $false
% 10.36/2.85 |
% 10.36/2.85 |-The branch is then unsatisfiable
% 10.36/2.85 |-Branch two:
% 10.36/2.85 | (389) all_0_23_23 = e2 & ~ (all_0_13_13 = e0)
% 10.36/2.85 |
% 10.36/2.85 | Applying alpha-rule on (389) yields:
% 10.36/2.85 | (352) all_0_23_23 = e2
% 10.36/2.85 | (391) ~ (all_0_13_13 = e0)
% 10.36/2.85 |
% 10.36/2.85 | Equations (352) can reduce 172 to:
% 10.36/2.85 | (179) $false
% 10.36/2.85 |
% 10.36/2.85 |-The branch is then unsatisfiable
% 10.36/2.85 |-Branch two:
% 10.36/2.85 | (385) all_0_23_23 = e3 & ~ (all_0_8_8 = e0)
% 10.36/2.85 |
% 10.36/2.85 | Applying alpha-rule on (385) yields:
% 10.36/2.85 | (386) all_0_23_23 = e3
% 10.36/2.85 | (377) ~ (all_0_8_8 = e0)
% 10.36/2.85 |
% 10.36/2.85 | Equations (386) can reduce 160 to:
% 10.36/2.85 | (179) $false
% 10.36/2.85 |
% 10.36/2.85 |-The branch is then unsatisfiable
% 10.36/2.85 |-Branch two:
% 10.36/2.85 | (998) all_0_6_6 = e3
% 10.36/2.85 | (999) ~ (all_0_7_7 = e1) | ~ (all_0_13_13 = e0)
% 10.36/2.85 |
% 10.36/2.85 | Combining equations (998,624) yields a new equation:
% 10.36/2.85 | (386) all_0_23_23 = e3
% 10.36/2.85 |
% 10.36/2.85 | Equations (386) can reduce 3 to:
% 10.36/2.85 | (507) ~ (all_0_11_11 = e3)
% 10.36/2.85 |
% 10.36/2.85 | Equations (386) can reduce 109 to:
% 10.36/2.85 | (858) ~ (all_0_15_15 = e3)
% 10.36/2.85 |
% 10.36/2.85 | Equations (386) can reduce 38 to:
% 10.36/2.85 | (1003) ~ (all_0_19_19 = e3)
% 10.36/2.85 |
% 10.36/2.85 | Equations (386) can reduce 149 to:
% 10.36/2.85 | (314) ~ (all_0_20_20 = e3)
% 10.36/2.85 |
% 10.36/2.85 | Equations (386) can reduce 172 to:
% 10.36/2.85 | (126) ~ (e3 = e2)
% 10.36/2.85 |
% 10.36/2.85 | From (386)(386) and (103) follows:
% 10.36/2.85 | (1006) op(e3, e3) = all_0_0_0
% 10.36/2.85 |
% 10.36/2.85 | From (386) and (55) follows:
% 10.36/2.85 | (1007) op(e3, e0) = all_0_1_1
% 10.36/2.86 |
% 10.36/2.86 +-Applying beta-rule and splitting (156), into two cases.
% 10.36/2.86 |-Branch one:
% 10.36/2.86 | (197) (all_0_8_8 = e1 & ~ (all_0_18_18 = e3)) | (all_0_13_13 = e1 & ~ (all_0_18_18 = e2))
% 10.36/2.86 |
% 10.36/2.86 +-Applying beta-rule and splitting (197), into two cases.
% 10.36/2.86 |-Branch one:
% 10.36/2.86 | (198) all_0_8_8 = e1 & ~ (all_0_18_18 = e3)
% 10.36/2.86 |
% 10.36/2.86 | Applying alpha-rule on (198) yields:
% 10.36/2.86 | (199) all_0_8_8 = e1
% 10.36/2.86 | (200) ~ (all_0_18_18 = e3)
% 10.36/2.86 |
% 10.36/2.86 | Equations (199) can reduce 91 to:
% 10.36/2.86 | (1012) ~ (all_0_12_12 = e1)
% 10.36/2.86 |
% 10.36/2.86 | Simplifying 1012 yields:
% 10.36/2.86 | (244) ~ (all_0_12_12 = e1)
% 10.36/2.86 |
% 10.36/2.86 | Equations (199) can reduce 98 to:
% 10.36/2.86 | (712) ~ (all_0_16_16 = e1)
% 10.36/2.86 |
% 10.36/2.86 | Simplifying 712 yields:
% 10.36/2.86 | (340) ~ (all_0_16_16 = e1)
% 10.36/2.86 |
% 10.36/2.86 | Equations (199) can reduce 9 to:
% 10.36/2.86 | (279) ~ (all_0_20_20 = e1)
% 10.36/2.86 |
% 10.36/2.86 | Simplifying 279 yields:
% 10.36/2.86 | (214) ~ (all_0_20_20 = e1)
% 10.36/2.86 |
% 10.36/2.86 | From (199) and (37) follows:
% 10.36/2.86 | (1018) op(e3, e3) = e1
% 10.36/2.86 |
% 10.36/2.86 +-Applying beta-rule and splitting (999), into two cases.
% 10.36/2.86 |-Branch one:
% 10.36/2.86 | (1019) ~ (all_0_7_7 = e1)
% 10.36/2.86 |
% 10.36/2.86 | Equations (623) can reduce 1019 to:
% 10.36/2.86 | (215) ~ (all_0_21_21 = e1)
% 10.36/2.86 |
% 10.36/2.86 +-Applying beta-rule and splitting (132), into two cases.
% 10.36/2.86 |-Branch one:
% 10.36/2.86 | (173) (all_0_8_8 = e2 & ~ (all_0_13_13 = e3)) | (all_0_18_18 = e2 & ~ (all_0_13_13 = e1))
% 10.36/2.86 |
% 10.36/2.86 +-Applying beta-rule and splitting (173), into two cases.
% 10.36/2.86 |-Branch one:
% 10.36/2.86 | (174) all_0_8_8 = e2 & ~ (all_0_13_13 = e3)
% 10.36/2.86 |
% 10.36/2.86 | Applying alpha-rule on (174) yields:
% 10.36/2.86 | (175) all_0_8_8 = e2
% 10.36/2.86 | (176) ~ (all_0_13_13 = e3)
% 10.36/2.86 |
% 10.36/2.86 | Combining equations (199,175) yields a new equation:
% 10.36/2.86 | (242) e2 = e1
% 10.36/2.86 |
% 10.36/2.86 | Equations (242) can reduce 24 to:
% 10.36/2.86 | (179) $false
% 10.36/2.86 |
% 10.36/2.86 |-The branch is then unsatisfiable
% 10.36/2.86 |-Branch two:
% 10.36/2.86 | (180) all_0_18_18 = e2 & ~ (all_0_13_13 = e1)
% 10.36/2.86 |
% 10.36/2.86 | Applying alpha-rule on (180) yields:
% 10.36/2.86 | (181) all_0_18_18 = e2
% 10.36/2.86 | (182) ~ (all_0_13_13 = e1)
% 10.36/2.86 |
% 10.36/2.86 | Equations (181) can reduce 76 to:
% 10.36/2.86 | (491) ~ (all_0_10_10 = e2)
% 10.36/2.86 |
% 10.36/2.86 | Equations (539) can reduce 182 to:
% 10.36/2.86 | (424) ~ (e1 = e0)
% 10.36/2.86 |
% 10.36/2.86 | Simplifying 424 yields:
% 10.36/2.86 | (88) ~ (e1 = e0)
% 10.36/2.86 |
% 10.36/2.86 | Equations (181) can reduce 26 to:
% 10.36/2.86 | (815) ~ (all_0_14_14 = e2)
% 10.36/2.86 |
% 10.36/2.86 | Equations (181) can reduce 2 to:
% 10.36/2.86 | (184) ~ (all_0_19_19 = e2)
% 10.36/2.86 |
% 10.36/2.86 | Simplifying 184 yields:
% 10.36/2.86 | (185) ~ (all_0_19_19 = e2)
% 10.36/2.86 |
% 10.36/2.86 | Equations (181) can reduce 42 to:
% 10.36/2.86 | (186) ~ (all_0_22_22 = e2)
% 10.36/2.86 |
% 10.36/2.86 | Simplifying 186 yields:
% 10.36/2.86 | (187) ~ (all_0_22_22 = e2)
% 10.36/2.86 |
% 10.36/2.86 | Equations (181) can reduce 200 to:
% 10.36/2.86 | (398) ~ (e3 = e2)
% 10.36/2.86 |
% 10.36/2.86 | Simplifying 398 yields:
% 10.36/2.86 | (126) ~ (e3 = e2)
% 10.36/2.86 |
% 10.36/2.86 +-Applying beta-rule and splitting (7), into two cases.
% 10.36/2.86 |-Branch one:
% 10.36/2.86 | (320) all_0_20_20 = e1
% 10.36/2.86 |
% 10.36/2.86 | Equations (320) can reduce 214 to:
% 10.36/2.86 | (179) $false
% 10.36/2.86 |
% 10.36/2.86 |-The branch is then unsatisfiable
% 10.36/2.86 |-Branch two:
% 10.36/2.86 | (214) ~ (all_0_20_20 = e1)
% 10.36/2.86 | (449) all_0_21_21 = e1 | all_0_22_22 = e1 | all_0_23_23 = e1
% 10.36/2.86 |
% 10.36/2.86 +-Applying beta-rule and splitting (449), into two cases.
% 10.36/2.86 |-Branch one:
% 10.36/2.86 | (336) all_0_21_21 = e1
% 10.36/2.86 |
% 10.36/2.86 | Equations (336) can reduce 215 to:
% 10.36/2.86 | (179) $false
% 10.36/2.86 |
% 10.36/2.86 |-The branch is then unsatisfiable
% 10.36/2.86 |-Branch two:
% 10.36/2.86 | (215) ~ (all_0_21_21 = e1)
% 10.36/2.86 | (1047) all_0_22_22 = e1 | all_0_23_23 = e1
% 10.36/2.86 |
% 10.36/2.86 +-Applying beta-rule and splitting (1047), into two cases.
% 10.36/2.86 |-Branch one:
% 10.36/2.86 | (736) all_0_22_22 = e1
% 10.36/2.86 |
% 10.36/2.86 | Equations (736) can reduce 48 to:
% 10.36/2.86 | (709) ~ (all_0_14_14 = e1)
% 10.36/2.86 |
% 10.36/2.86 | Equations (736) can reduce 72 to:
% 10.36/2.86 | (215) ~ (all_0_21_21 = e1)
% 10.36/2.86 |
% 10.36/2.86 | Equations (736) can reduce 187 to:
% 10.36/2.86 | (218) ~ (e2 = e1)
% 10.36/2.87 |
% 10.36/2.87 | Simplifying 218 yields:
% 10.36/2.87 | (24) ~ (e2 = e1)
% 10.36/2.87 |
% 10.36/2.87 +-Applying beta-rule and splitting (130), into two cases.
% 10.36/2.87 |-Branch one:
% 10.36/2.87 | (240) all_0_12_12 = e1
% 10.36/2.87 |
% 10.36/2.87 | Equations (240) can reduce 244 to:
% 10.36/2.87 | (179) $false
% 10.36/2.87 |
% 10.36/2.87 |-The branch is then unsatisfiable
% 10.36/2.87 |-Branch two:
% 10.36/2.87 | (244) ~ (all_0_12_12 = e1)
% 10.36/2.87 | (245) all_0_13_13 = e1 | all_0_14_14 = e1 | all_0_15_15 = e1
% 10.36/2.87 |
% 10.36/2.87 +-Applying beta-rule and splitting (245), into two cases.
% 10.36/2.87 |-Branch one:
% 10.36/2.87 | (204) all_0_13_13 = e1
% 10.36/2.87 |
% 10.36/2.87 | Combining equations (539,204) yields a new equation:
% 10.36/2.87 | (201) e1 = e0
% 10.36/2.87 |
% 10.36/2.87 | Equations (201) can reduce 88 to:
% 10.36/2.87 | (179) $false
% 10.36/2.87 |
% 10.36/2.87 |-The branch is then unsatisfiable
% 10.36/2.87 |-Branch two:
% 10.36/2.87 | (182) ~ (all_0_13_13 = e1)
% 10.36/2.87 | (1061) all_0_14_14 = e1 | all_0_15_15 = e1
% 10.36/2.87 |
% 10.36/2.87 +-Applying beta-rule and splitting (1061), into two cases.
% 10.36/2.87 |-Branch one:
% 10.36/2.87 | (817) all_0_14_14 = e1
% 10.36/2.87 |
% 10.36/2.87 | Equations (817) can reduce 709 to:
% 10.36/2.87 | (179) $false
% 10.36/2.87 |
% 10.36/2.87 |-The branch is then unsatisfiable
% 10.36/2.87 |-Branch two:
% 10.36/2.87 | (709) ~ (all_0_14_14 = e1)
% 10.36/2.87 | (864) all_0_15_15 = e1
% 10.36/2.87 |
% 10.36/2.87 | Equations (864) can reduce 138 to:
% 10.36/2.87 | (244) ~ (all_0_12_12 = e1)
% 10.36/2.87 |
% 10.36/2.87 | Equations (864) can reduce 12 to:
% 10.36/2.87 | (709) ~ (all_0_14_14 = e1)
% 10.36/2.87 |
% 10.36/2.87 | Equations (864) can reduce 51 to:
% 10.36/2.87 | (1068) ~ (all_0_19_19 = e1)
% 10.36/2.87 |
% 10.36/2.87 | Simplifying 1068 yields:
% 10.36/2.87 | (674) ~ (all_0_19_19 = e1)
% 10.36/2.87 |
% 10.36/2.87 | Equations (864) can reduce 858 to:
% 10.36/2.87 | (216) ~ (e3 = e1)
% 10.36/2.87 |
% 10.36/2.87 | Simplifying 216 yields:
% 10.36/2.87 | (155) ~ (e3 = e1)
% 10.36/2.87 |
% 10.36/2.87 +-Applying beta-rule and splitting (89), into two cases.
% 10.36/2.87 |-Branch one:
% 10.36/2.87 | (233) all_0_12_12 = e2
% 10.36/2.87 |
% 10.36/2.87 | Equations (233) can reduce 25 to:
% 10.36/2.87 | (236) ~ (all_0_16_16 = e2)
% 10.36/2.87 |
% 10.36/2.87 | Simplifying 236 yields:
% 10.36/2.87 | (183) ~ (all_0_16_16 = e2)
% 10.36/2.87 |
% 10.36/2.87 | Equations (233) can reduce 23 to:
% 10.36/2.87 | (238) ~ (all_0_20_20 = e2)
% 10.36/2.87 |
% 10.36/2.87 | Simplifying 238 yields:
% 10.36/2.87 | (227) ~ (all_0_20_20 = e2)
% 10.36/2.87 |
% 10.36/2.87 | Equations (233) can reduce 244 to:
% 10.36/2.87 | (24) ~ (e2 = e1)
% 10.36/2.87 |
% 10.36/2.87 +-Applying beta-rule and splitting (81), into two cases.
% 10.36/2.87 |-Branch one:
% 10.36/2.87 | (434) all_0_12_12 = e3
% 10.36/2.87 |
% 10.36/2.87 | Combining equations (434,233) yields a new equation:
% 10.36/2.87 | (382) e3 = e2
% 10.36/2.87 |
% 10.36/2.87 | Simplifying 382 yields:
% 10.36/2.87 | (298) e3 = e2
% 10.36/2.87 |
% 10.36/2.87 | Equations (298) can reduce 126 to:
% 10.36/2.87 | (179) $false
% 10.36/2.87 |
% 10.36/2.87 |-The branch is then unsatisfiable
% 10.36/2.87 |-Branch two:
% 10.36/2.87 | (431) ~ (all_0_12_12 = e3)
% 10.36/2.87 | (469) all_0_13_13 = e3 | all_0_14_14 = e3 | all_0_15_15 = e3
% 10.36/2.87 |
% 10.36/2.87 | Equations (233) can reduce 431 to:
% 10.36/2.87 | (398) ~ (e3 = e2)
% 10.36/2.87 |
% 10.36/2.87 | Simplifying 398 yields:
% 10.36/2.87 | (126) ~ (e3 = e2)
% 10.36/2.87 |
% 10.36/2.87 +-Applying beta-rule and splitting (469), into two cases.
% 10.36/2.87 |-Branch one:
% 10.36/2.87 | (191) all_0_13_13 = e3
% 10.36/2.87 |
% 10.36/2.87 | Combining equations (539,191) yields a new equation:
% 10.36/2.87 | (257) e3 = e0
% 10.36/2.87 |
% 10.36/2.87 | Equations (257) can reduce 40 to:
% 10.36/2.87 | (179) $false
% 10.36/2.87 |
% 10.36/2.87 |-The branch is then unsatisfiable
% 10.36/2.87 |-Branch two:
% 10.36/2.87 | (176) ~ (all_0_13_13 = e3)
% 10.36/2.87 | (474) all_0_14_14 = e3 | all_0_15_15 = e3
% 10.36/2.87 |
% 10.36/2.87 +-Applying beta-rule and splitting (20), into two cases.
% 10.36/2.87 |-Branch one:
% 10.36/2.87 | (247) all_0_20_20 = e2
% 10.36/2.87 |
% 10.36/2.87 | Equations (247) can reduce 227 to:
% 10.36/2.87 | (179) $false
% 10.36/2.87 |
% 10.36/2.87 |-The branch is then unsatisfiable
% 10.36/2.87 |-Branch two:
% 10.36/2.87 | (227) ~ (all_0_20_20 = e2)
% 10.36/2.87 | (250) all_0_21_21 = e2 | all_0_22_22 = e2 | all_0_23_23 = e2
% 10.36/2.87 |
% 10.36/2.87 +-Applying beta-rule and splitting (250), into two cases.
% 10.36/2.87 |-Branch one:
% 10.36/2.87 | (251) all_0_21_21 = e2
% 10.36/2.87 |
% 10.36/2.87 | Equations (251) can reduce 104 to:
% 10.36/2.87 | (521) ~ (all_0_9_9 = e2)
% 10.36/2.87 |
% 10.36/2.87 | Equations (251) can reduce 215 to:
% 10.36/2.87 | (24) ~ (e2 = e1)
% 10.36/2.87 |
% 10.36/2.87 | Equations (251) can reduce 620 to:
% 10.36/2.87 | (119) ~ (e2 = e0)
% 10.36/2.87 |
% 10.36/2.87 +-Applying beta-rule and splitting (474), into two cases.
% 10.36/2.87 |-Branch one:
% 10.36/2.87 | (451) all_0_14_14 = e3
% 10.36/2.87 |
% 10.36/2.87 | Equations (451) can reduce 133 to:
% 10.36/2.87 | (426) ~ (all_0_10_10 = e3)
% 10.36/2.87 |
% 10.36/2.88 | Equations (451) can reduce 709 to:
% 10.36/2.88 | (155) ~ (e3 = e1)
% 10.36/2.88 |
% 10.36/2.88 +-Applying beta-rule and splitting (102), into two cases.
% 10.36/2.88 |-Branch one:
% 10.36/2.88 | (276) all_0_16_16 = e1
% 10.36/2.88 |
% 10.36/2.88 | Equations (276) can reduce 340 to:
% 10.36/2.88 | (179) $false
% 10.36/2.88 |
% 10.36/2.88 |-The branch is then unsatisfiable
% 10.36/2.88 |-Branch two:
% 10.36/2.88 | (340) ~ (all_0_16_16 = e1)
% 10.36/2.88 | (749) all_0_17_17 = e1 | all_0_18_18 = e1 | all_0_19_19 = e1
% 10.36/2.88 |
% 10.36/2.88 +-Applying beta-rule and splitting (18), into two cases.
% 10.36/2.88 |-Branch one:
% 10.36/2.88 | (175) all_0_8_8 = e2
% 10.36/2.88 |
% 10.36/2.88 | Combining equations (175,199) yields a new equation:
% 10.36/2.88 | (241) e2 = e1
% 10.36/2.88 |
% 10.36/2.88 | Simplifying 241 yields:
% 10.36/2.88 | (242) e2 = e1
% 10.36/2.88 |
% 10.36/2.88 | Equations (242) can reduce 24 to:
% 10.36/2.88 | (179) $false
% 10.36/2.88 |
% 10.36/2.88 |-The branch is then unsatisfiable
% 10.36/2.88 |-Branch two:
% 10.36/2.88 | (192) ~ (all_0_8_8 = e2)
% 10.36/2.88 | (514) all_0_9_9 = e2 | all_0_10_10 = e2 | all_0_11_11 = e2
% 10.36/2.88 |
% 10.36/2.88 | Equations (199) can reduce 192 to:
% 10.36/2.88 | (218) ~ (e2 = e1)
% 10.36/2.88 |
% 10.36/2.88 | Simplifying 218 yields:
% 10.36/2.88 | (24) ~ (e2 = e1)
% 10.36/2.88 |
% 10.36/2.88 +-Applying beta-rule and splitting (21), into two cases.
% 10.36/2.88 |-Branch one:
% 10.36/2.88 | (261) all_0_9_9 = e3
% 10.36/2.88 |
% 10.36/2.88 | Equations (261) can reduce 145 to:
% 10.36/2.88 | (194) ~ (all_0_17_17 = e3)
% 10.36/2.88 |
% 10.36/2.88 | Simplifying 194 yields:
% 10.36/2.88 | (195) ~ (all_0_17_17 = e3)
% 10.36/2.88 |
% 10.36/2.88 | Equations (261) can reduce 521 to:
% 10.36/2.88 | (126) ~ (e3 = e2)
% 10.36/2.88 |
% 10.36/2.88 +-Applying beta-rule and splitting (141), into two cases.
% 10.36/2.88 |-Branch one:
% 10.36/2.88 | (286) all_0_16_16 = e3
% 10.36/2.88 |
% 10.36/2.88 | Equations (286) can reduce 183 to:
% 10.36/2.88 | (126) ~ (e3 = e2)
% 10.36/2.88 |
% 10.36/2.88 +-Applying beta-rule and splitting (514), into two cases.
% 10.36/2.88 |-Branch one:
% 10.36/2.88 | (518) all_0_9_9 = e2
% 10.36/2.88 |
% 10.36/2.88 | Combining equations (518,261) yields a new equation:
% 10.36/2.88 | (298) e3 = e2
% 10.36/2.88 |
% 10.36/2.88 | Equations (298) can reduce 126 to:
% 10.36/2.88 | (179) $false
% 10.36/2.88 |
% 10.36/2.88 |-The branch is then unsatisfiable
% 10.36/2.88 |-Branch two:
% 10.36/2.88 | (521) ~ (all_0_9_9 = e2)
% 10.36/2.88 | (522) all_0_10_10 = e2 | all_0_11_11 = e2
% 10.36/2.88 |
% 10.36/2.88 | Equations (261) can reduce 521 to:
% 10.36/2.88 | (126) ~ (e3 = e2)
% 10.36/2.88 |
% 10.36/2.88 +-Applying beta-rule and splitting (83), into two cases.
% 10.36/2.88 |-Branch one:
% 10.36/2.88 | (254) all_0_11_11 = e2
% 10.36/2.88 |
% 10.36/2.88 | From (254) and (82) follows:
% 10.36/2.88 | (1127) op(e3, e0) = e2
% 10.36/2.88 |
% 10.36/2.88 | Instantiating formula (85) with e3, e3, e1, all_0_0_0 and discharging atoms op(e3, e3) = all_0_0_0, op(e3, e3) = e1, yields:
% 10.36/2.88 | (480) all_0_0_0 = e1
% 10.36/2.88 |
% 10.36/2.88 | Instantiating formula (85) with e3, e0, e2, all_0_1_1 and discharging atoms op(e3, e0) = all_0_1_1, op(e3, e0) = e2, yields:
% 10.36/2.88 | (800) all_0_1_1 = e2
% 10.36/2.88 |
% 10.36/2.88 +-Applying beta-rule and splitting (36), into two cases.
% 10.36/2.88 |-Branch one:
% 10.36/2.88 | (482) ~ (all_0_0_0 = e1)
% 10.36/2.88 |
% 10.36/2.88 | Equations (480) can reduce 482 to:
% 10.36/2.88 | (179) $false
% 10.36/2.88 |
% 10.36/2.88 |-The branch is then unsatisfiable
% 10.36/2.88 |-Branch two:
% 10.36/2.88 | (480) all_0_0_0 = e1
% 10.36/2.88 | (1133) ~ (all_0_1_1 = e2) | ~ (all_0_23_23 = e3)
% 10.36/2.88 |
% 10.36/2.88 +-Applying beta-rule and splitting (1133), into two cases.
% 10.36/2.88 |-Branch one:
% 10.36/2.88 | (805) ~ (all_0_1_1 = e2)
% 10.36/2.88 |
% 10.36/2.88 | Equations (800) can reduce 805 to:
% 10.36/2.88 | (179) $false
% 10.36/2.88 |
% 10.36/2.88 |-The branch is then unsatisfiable
% 10.36/2.88 |-Branch two:
% 10.36/2.88 | (800) all_0_1_1 = e2
% 10.36/2.88 | (160) ~ (all_0_23_23 = e3)
% 10.36/2.88 |
% 10.36/2.88 | Equations (386) can reduce 160 to:
% 10.36/2.88 | (179) $false
% 10.36/2.88 |
% 10.36/2.88 |-The branch is then unsatisfiable
% 10.36/2.88 |-Branch two:
% 10.36/2.88 | (343) ~ (all_0_11_11 = e2)
% 10.36/2.88 | (344) all_0_15_15 = e2 | all_0_19_19 = e2 | all_0_23_23 = e2
% 10.36/2.88 |
% 10.36/2.88 +-Applying beta-rule and splitting (344), into two cases.
% 10.36/2.88 |-Branch one:
% 10.36/2.88 | (345) all_0_15_15 = e2
% 10.36/2.88 |
% 10.36/2.88 | Combining equations (345,864) yields a new equation:
% 10.36/2.89 | (241) e2 = e1
% 10.36/2.89 |
% 10.36/2.89 | Simplifying 241 yields:
% 10.36/2.89 | (242) e2 = e1
% 10.36/2.89 |
% 10.36/2.89 | Equations (242) can reduce 24 to:
% 10.36/2.89 | (179) $false
% 10.36/2.89 |
% 10.36/2.89 |-The branch is then unsatisfiable
% 10.36/2.89 |-Branch two:
% 10.36/2.89 | (235) ~ (all_0_15_15 = e2)
% 10.36/2.89 | (348) all_0_19_19 = e2 | all_0_23_23 = e2
% 10.36/2.89 |
% 10.36/2.89 +-Applying beta-rule and splitting (348), into two cases.
% 10.36/2.89 |-Branch one:
% 10.36/2.89 | (349) all_0_19_19 = e2
% 10.36/2.89 |
% 10.36/2.89 | Equations (349) can reduce 185 to:
% 10.36/2.89 | (179) $false
% 10.36/2.89 |
% 10.36/2.89 |-The branch is then unsatisfiable
% 10.36/2.89 |-Branch two:
% 10.36/2.89 | (185) ~ (all_0_19_19 = e2)
% 10.36/2.89 | (352) all_0_23_23 = e2
% 10.36/2.89 |
% 10.36/2.89 | Combining equations (352,386) yields a new equation:
% 10.36/2.89 | (298) e3 = e2
% 10.36/2.89 |
% 10.36/2.89 | Equations (298) can reduce 126 to:
% 10.36/2.89 | (179) $false
% 10.36/2.89 |
% 10.36/2.89 |-The branch is then unsatisfiable
% 10.36/2.89 |-Branch two:
% 10.36/2.89 | (289) ~ (all_0_16_16 = e3)
% 10.36/2.89 | (290) all_0_17_17 = e3 | all_0_18_18 = e3 | all_0_19_19 = e3
% 10.36/2.89 |
% 10.36/2.89 +-Applying beta-rule and splitting (28), into two cases.
% 10.36/2.89 |-Branch one:
% 10.36/2.89 | (301) all_0_19_19 = e3
% 10.36/2.89 |
% 10.36/2.89 | Equations (301) can reduce 1003 to:
% 10.36/2.89 | (179) $false
% 10.36/2.89 |
% 10.36/2.89 |-The branch is then unsatisfiable
% 10.36/2.89 |-Branch two:
% 10.36/2.89 | (1003) ~ (all_0_19_19 = e3)
% 10.36/2.89 | (1158) all_0_19_19 = e2 | all_0_19_19 = e1 | all_0_19_19 = e0
% 10.36/2.89 |
% 10.36/2.89 +-Applying beta-rule and splitting (1158), into two cases.
% 10.36/2.89 |-Branch one:
% 10.36/2.89 | (349) all_0_19_19 = e2
% 10.36/2.89 |
% 10.36/2.89 | Equations (349) can reduce 185 to:
% 10.36/2.89 | (179) $false
% 10.36/2.89 |
% 10.36/2.89 |-The branch is then unsatisfiable
% 10.36/2.89 |-Branch two:
% 10.36/2.89 | (185) ~ (all_0_19_19 = e2)
% 10.36/2.89 | (1162) all_0_19_19 = e1 | all_0_19_19 = e0
% 10.36/2.89 |
% 10.36/2.89 +-Applying beta-rule and splitting (1162), into two cases.
% 10.36/2.89 |-Branch one:
% 10.36/2.89 | (924) all_0_19_19 = e1
% 10.36/2.89 |
% 10.36/2.89 | Equations (924) can reduce 674 to:
% 10.36/2.89 | (179) $false
% 10.36/2.89 |
% 10.36/2.89 |-The branch is then unsatisfiable
% 10.36/2.89 |-Branch two:
% 10.36/2.89 | (674) ~ (all_0_19_19 = e1)
% 10.36/2.89 | (1166) all_0_19_19 = e0
% 10.36/2.89 |
% 10.36/2.89 | Equations (1166) can reduce 1003 to:
% 10.36/2.89 | (546) ~ (e3 = e0)
% 10.36/2.89 |
% 10.36/2.89 | Simplifying 546 yields:
% 10.36/2.89 | (40) ~ (e3 = e0)
% 10.36/2.89 |
% 10.36/2.89 +-Applying beta-rule and splitting (290), into two cases.
% 10.36/2.89 |-Branch one:
% 10.36/2.89 | (293) all_0_17_17 = e3
% 10.36/2.89 |
% 10.36/2.89 | Equations (293) can reduce 195 to:
% 10.36/2.89 | (179) $false
% 10.36/2.89 |
% 10.36/2.89 |-The branch is then unsatisfiable
% 10.36/2.89 |-Branch two:
% 10.36/2.89 | (195) ~ (all_0_17_17 = e3)
% 10.36/2.89 | (296) all_0_18_18 = e3 | all_0_19_19 = e3
% 10.36/2.89 |
% 10.36/2.89 +-Applying beta-rule and splitting (296), into two cases.
% 10.36/2.89 |-Branch one:
% 10.36/2.89 | (297) all_0_18_18 = e3
% 10.36/2.89 |
% 10.36/2.89 | Combining equations (297,181) yields a new equation:
% 10.36/2.89 | (382) e3 = e2
% 10.36/2.89 |
% 10.36/2.89 | Simplifying 382 yields:
% 10.36/2.89 | (298) e3 = e2
% 10.36/2.89 |
% 10.36/2.89 | Equations (298) can reduce 126 to:
% 10.36/2.89 | (179) $false
% 10.36/2.89 |
% 10.36/2.89 |-The branch is then unsatisfiable
% 10.36/2.89 |-Branch two:
% 10.36/2.89 | (200) ~ (all_0_18_18 = e3)
% 10.36/2.89 | (301) all_0_19_19 = e3
% 10.36/2.89 |
% 10.36/2.89 | Combining equations (1166,301) yields a new equation:
% 10.36/2.89 | (257) e3 = e0
% 10.36/2.89 |
% 10.36/2.89 | Equations (257) can reduce 40 to:
% 10.36/2.89 | (179) $false
% 10.36/2.89 |
% 10.36/2.89 |-The branch is then unsatisfiable
% 10.36/2.89 |-Branch two:
% 10.36/2.90 | (193) ~ (all_0_9_9 = e3)
% 10.36/2.90 | (538) all_0_9_9 = e2 | all_0_9_9 = e1 | all_0_9_9 = e0
% 10.36/2.90 |
% 10.36/2.90 +-Applying beta-rule and splitting (749), into two cases.
% 10.36/2.90 |-Branch one:
% 10.36/2.90 | (333) all_0_17_17 = e1
% 10.36/2.90 |
% 10.36/2.90 | Equations (333) can reduce 78 to:
% 10.36/2.90 | (340) ~ (all_0_16_16 = e1)
% 10.36/2.90 |
% 10.36/2.90 | Equations (333) can reduce 618 to:
% 10.36/2.90 | (88) ~ (e1 = e0)
% 10.36/2.90 |
% 10.36/2.90 +-Applying beta-rule and splitting (514), into two cases.
% 10.36/2.90 |-Branch one:
% 10.36/2.90 | (518) all_0_9_9 = e2
% 10.36/2.90 |
% 10.36/2.90 | Equations (518) can reduce 521 to:
% 10.36/2.90 | (179) $false
% 10.36/2.90 |
% 10.36/2.90 |-The branch is then unsatisfiable
% 10.36/2.90 |-Branch two:
% 10.36/2.90 | (521) ~ (all_0_9_9 = e2)
% 10.36/2.90 | (522) all_0_10_10 = e2 | all_0_11_11 = e2
% 10.36/2.90 |
% 10.36/2.90 +-Applying beta-rule and splitting (522), into two cases.
% 10.36/2.90 |-Branch one:
% 10.36/2.90 | (462) all_0_10_10 = e2
% 10.36/2.90 |
% 10.36/2.90 | Equations (462) can reduce 491 to:
% 10.36/2.90 | (179) $false
% 10.36/2.90 |
% 10.36/2.90 |-The branch is then unsatisfiable
% 10.36/2.90 |-Branch two:
% 10.36/2.90 | (491) ~ (all_0_10_10 = e2)
% 10.36/2.90 | (254) all_0_11_11 = e2
% 10.36/2.90 |
% 10.36/2.90 | Equations (254) can reduce 507 to:
% 10.36/2.90 | (398) ~ (e3 = e2)
% 10.36/2.90 |
% 10.36/2.90 | Simplifying 398 yields:
% 10.36/2.90 | (126) ~ (e3 = e2)
% 10.36/2.90 |
% 10.36/2.90 +-Applying beta-rule and splitting (64), into two cases.
% 10.36/2.90 |-Branch one:
% 10.36/2.90 | (159) all_0_8_8 = e0
% 10.36/2.90 |
% 10.36/2.90 | Combining equations (159,199) yields a new equation:
% 10.36/2.90 | (201) e1 = e0
% 10.36/2.90 |
% 10.36/2.90 | Equations (201) can reduce 88 to:
% 10.36/2.90 | (179) $false
% 10.36/2.90 |
% 10.36/2.90 |-The branch is then unsatisfiable
% 10.36/2.90 |-Branch two:
% 10.36/2.90 | (377) ~ (all_0_8_8 = e0)
% 10.36/2.90 | (769) all_0_9_9 = e0 | all_0_10_10 = e0 | all_0_11_11 = e0
% 10.36/2.90 |
% 10.36/2.90 +-Applying beta-rule and splitting (769), into two cases.
% 10.36/2.90 |-Branch one:
% 10.36/2.90 | (573) all_0_9_9 = e0
% 10.36/2.90 |
% 10.36/2.90 | Equations (573) can reduce 162 to:
% 10.36/2.90 | (179) $false
% 10.36/2.90 |
% 10.36/2.90 |-The branch is then unsatisfiable
% 10.36/2.90 |-Branch two:
% 10.36/2.90 | (162) ~ (all_0_9_9 = e0)
% 10.36/2.90 | (773) all_0_10_10 = e0 | all_0_11_11 = e0
% 10.36/2.90 |
% 10.36/2.90 +-Applying beta-rule and splitting (773), into two cases.
% 10.36/2.90 |-Branch one:
% 10.36/2.90 | (774) all_0_10_10 = e0
% 10.36/2.90 |
% 10.36/2.90 | Equations (774) can reduce 426 to:
% 10.36/2.90 | (546) ~ (e3 = e0)
% 10.36/2.90 |
% 10.36/2.90 | Simplifying 546 yields:
% 10.36/2.90 | (40) ~ (e3 = e0)
% 10.36/2.90 |
% 10.36/2.90 +-Applying beta-rule and splitting (113), into two cases.
% 10.36/2.90 |-Branch one:
% 10.36/2.90 | (256) all_0_8_8 = e3
% 10.36/2.90 |
% 10.36/2.90 | Combining equations (256,199) yields a new equation:
% 10.36/2.90 | (328) e3 = e1
% 10.36/2.90 |
% 10.36/2.90 | Simplifying 328 yields:
% 10.36/2.90 | (206) e3 = e1
% 10.36/2.90 |
% 10.36/2.90 | Equations (206) can reduce 155 to:
% 10.36/2.90 | (179) $false
% 10.36/2.90 |
% 10.36/2.90 |-The branch is then unsatisfiable
% 10.36/2.90 |-Branch two:
% 10.36/2.90 | (259) ~ (all_0_8_8 = e3)
% 10.36/2.90 | (1213) all_0_12_12 = e3 | all_0_16_16 = e3 | all_0_20_20 = e3
% 10.36/2.90 |
% 10.36/2.90 +-Applying beta-rule and splitting (1213), into two cases.
% 10.36/2.90 |-Branch one:
% 10.36/2.90 | (434) all_0_12_12 = e3
% 10.36/2.90 |
% 10.36/2.90 | Combining equations (434,233) yields a new equation:
% 10.36/2.90 | (382) e3 = e2
% 10.36/2.90 |
% 10.36/2.90 | Simplifying 382 yields:
% 10.36/2.90 | (298) e3 = e2
% 10.36/2.90 |
% 10.36/2.90 | Equations (298) can reduce 126 to:
% 10.36/2.90 | (179) $false
% 10.36/2.90 |
% 10.36/2.90 |-The branch is then unsatisfiable
% 10.36/2.90 |-Branch two:
% 10.36/2.90 | (431) ~ (all_0_12_12 = e3)
% 10.36/2.90 | (1219) all_0_16_16 = e3 | all_0_20_20 = e3
% 10.36/2.90 |
% 10.36/2.90 +-Applying beta-rule and splitting (1219), into two cases.
% 10.36/2.90 |-Branch one:
% 10.36/2.90 | (286) all_0_16_16 = e3
% 10.36/2.90 |
% 10.36/2.90 | Equations (286) can reduce 183 to:
% 10.36/2.90 | (126) ~ (e3 = e2)
% 10.36/2.90 |
% 10.36/2.90 | Equations (286) can reduce 340 to:
% 10.80/2.90 | (155) ~ (e3 = e1)
% 10.80/2.90 |
% 10.80/2.90 +-Applying beta-rule and splitting (17), into two cases.
% 10.80/2.90 |-Branch one:
% 10.80/2.90 | (256) all_0_8_8 = e3
% 10.80/2.90 |
% 10.80/2.90 | Combining equations (199,256) yields a new equation:
% 10.80/2.90 | (206) e3 = e1
% 10.80/2.90 |
% 10.80/2.90 | Equations (206) can reduce 155 to:
% 10.80/2.90 | (179) $false
% 10.80/2.90 |
% 10.80/2.90 |-The branch is then unsatisfiable
% 10.80/2.90 |-Branch two:
% 10.80/2.90 | (259) ~ (all_0_8_8 = e3)
% 10.80/2.90 | (260) all_0_9_9 = e3 | all_0_10_10 = e3 | all_0_11_11 = e3
% 10.80/2.90 |
% 10.80/2.90 +-Applying beta-rule and splitting (260), into two cases.
% 10.80/2.90 |-Branch one:
% 10.80/2.90 | (261) all_0_9_9 = e3
% 10.80/2.90 |
% 10.80/2.90 | Equations (261) can reduce 193 to:
% 10.80/2.90 | (179) $false
% 10.80/2.90 |
% 10.80/2.90 |-The branch is then unsatisfiable
% 10.80/2.90 |-Branch two:
% 10.80/2.91 | (193) ~ (all_0_9_9 = e3)
% 10.80/2.91 | (264) all_0_10_10 = e3 | all_0_11_11 = e3
% 10.80/2.91 |
% 10.80/2.91 +-Applying beta-rule and splitting (264), into two cases.
% 10.80/2.91 |-Branch one:
% 10.80/2.91 | (563) all_0_10_10 = e3
% 10.80/2.91 |
% 10.80/2.91 | Combining equations (563,774) yields a new equation:
% 10.80/2.91 | (552) e3 = e0
% 10.80/2.91 |
% 10.80/2.91 | Simplifying 552 yields:
% 10.80/2.91 | (257) e3 = e0
% 10.80/2.91 |
% 10.80/2.91 | Equations (257) can reduce 40 to:
% 10.80/2.91 | (179) $false
% 10.80/2.91 |
% 10.80/2.91 |-The branch is then unsatisfiable
% 10.80/2.91 |-Branch two:
% 10.80/2.91 | (426) ~ (all_0_10_10 = e3)
% 10.80/2.91 | (566) all_0_11_11 = e3
% 10.80/2.91 |
% 10.80/2.91 | Combining equations (254,566) yields a new equation:
% 10.80/2.91 | (298) e3 = e2
% 10.80/2.91 |
% 10.80/2.91 | Equations (298) can reduce 126 to:
% 10.80/2.91 | (179) $false
% 10.80/2.91 |
% 10.80/2.91 |-The branch is then unsatisfiable
% 10.80/2.91 |-Branch two:
% 10.80/2.91 | (289) ~ (all_0_16_16 = e3)
% 10.80/2.91 | (291) all_0_20_20 = e3
% 10.80/2.91 |
% 10.80/2.91 | Equations (291) can reduce 314 to:
% 10.80/2.91 | (179) $false
% 10.80/2.91 |
% 10.80/2.91 |-The branch is then unsatisfiable
% 10.80/2.91 |-Branch two:
% 10.80/2.91 | (740) ~ (all_0_10_10 = e0)
% 10.80/2.91 | (778) all_0_11_11 = e0
% 10.80/2.91 |
% 10.80/2.91 | Combining equations (778,254) yields a new equation:
% 10.80/2.91 | (178) e2 = e0
% 10.80/2.91 |
% 10.80/2.91 | Equations (178) can reduce 119 to:
% 10.80/2.91 | (179) $false
% 10.80/2.91 |
% 10.80/2.91 |-The branch is then unsatisfiable
% 10.80/2.91 |-Branch two:
% 10.80/2.91 | (278) ~ (all_0_17_17 = e1)
% 10.80/2.91 | (918) all_0_18_18 = e1 | all_0_19_19 = e1
% 10.80/2.91 |
% 10.80/2.91 +-Applying beta-rule and splitting (918), into two cases.
% 10.80/2.91 |-Branch one:
% 10.80/2.91 | (850) all_0_18_18 = e1
% 10.80/2.91 |
% 10.80/2.91 | Combining equations (181,850) yields a new equation:
% 10.80/2.91 | (241) e2 = e1
% 10.80/2.91 |
% 10.80/2.91 | Simplifying 241 yields:
% 10.80/2.91 | (242) e2 = e1
% 10.80/2.91 |
% 10.80/2.91 | Equations (242) can reduce 24 to:
% 10.80/2.91 | (179) $false
% 10.80/2.91 |
% 10.80/2.91 |-The branch is then unsatisfiable
% 10.80/2.91 |-Branch two:
% 10.80/2.91 | (854) ~ (all_0_18_18 = e1)
% 10.80/2.91 | (924) all_0_19_19 = e1
% 10.80/2.91 |
% 10.80/2.91 | Equations (924) can reduce 674 to:
% 10.80/2.91 | (179) $false
% 10.80/2.91 |
% 10.80/2.91 |-The branch is then unsatisfiable
% 10.80/2.91 |-Branch two:
% 10.80/2.91 | (427) ~ (all_0_14_14 = e3)
% 10.80/2.91 | (478) all_0_15_15 = e3
% 10.80/2.91 |
% 10.80/2.92 | Combining equations (864,478) yields a new equation:
% 10.80/2.92 | (206) e3 = e1
% 10.80/2.92 |
% 10.80/2.92 | Equations (206) can reduce 155 to:
% 10.80/2.92 | (179) $false
% 10.80/2.92 |
% 10.80/2.92 |-The branch is then unsatisfiable
% 10.80/2.92 |-Branch two:
% 10.80/2.92 | (356) ~ (all_0_21_21 = e2)
% 10.80/2.92 | (357) all_0_22_22 = e2 | all_0_23_23 = e2
% 10.80/2.92 |
% 10.80/2.92 +-Applying beta-rule and splitting (357), into two cases.
% 10.80/2.92 |-Branch one:
% 10.80/2.92 | (358) all_0_22_22 = e2
% 10.80/2.92 |
% 10.80/2.92 | Combining equations (736,358) yields a new equation:
% 10.80/2.92 | (242) e2 = e1
% 10.80/2.92 |
% 10.80/2.92 | Equations (242) can reduce 24 to:
% 10.80/2.92 | (179) $false
% 10.80/2.92 |
% 10.80/2.92 |-The branch is then unsatisfiable
% 10.80/2.92 |-Branch two:
% 10.80/2.92 | (187) ~ (all_0_22_22 = e2)
% 10.80/2.92 | (352) all_0_23_23 = e2
% 10.80/2.92 |
% 10.80/2.92 | Combining equations (352,386) yields a new equation:
% 10.80/2.92 | (298) e3 = e2
% 10.80/2.92 |
% 10.80/2.92 | Equations (298) can reduce 126 to:
% 10.80/2.92 | (179) $false
% 10.80/2.92 |
% 10.80/2.92 |-The branch is then unsatisfiable
% 10.80/2.92 |-Branch two:
% 10.80/2.92 | (365) ~ (all_0_12_12 = e2)
% 10.80/2.92 | (1270) all_0_13_13 = e2 | all_0_14_14 = e2 | all_0_15_15 = e2
% 10.80/2.92 |
% 10.80/2.92 +-Applying beta-rule and splitting (1270), into two cases.
% 10.80/2.92 |-Branch one:
% 10.80/2.92 | (1271) all_0_13_13 = e2
% 10.80/2.92 |
% 10.80/2.92 | Combining equations (539,1271) yields a new equation:
% 10.80/2.92 | (178) e2 = e0
% 10.80/2.92 |
% 10.80/2.92 | Equations (178) can reduce 119 to:
% 10.80/2.92 | (179) $false
% 10.80/2.92 |
% 10.80/2.92 |-The branch is then unsatisfiable
% 10.80/2.92 |-Branch two:
% 10.80/2.92 | (1274) ~ (all_0_13_13 = e2)
% 10.80/2.92 | (1275) all_0_14_14 = e2 | all_0_15_15 = e2
% 10.80/2.92 |
% 10.80/2.92 +-Applying beta-rule and splitting (1275), into two cases.
% 10.80/2.92 |-Branch one:
% 10.80/2.92 | (783) all_0_14_14 = e2
% 10.80/2.92 |
% 10.80/2.92 | Equations (783) can reduce 815 to:
% 10.80/2.92 | (179) $false
% 10.80/2.92 |
% 10.80/2.92 |-The branch is then unsatisfiable
% 10.80/2.92 |-Branch two:
% 10.80/2.92 | (815) ~ (all_0_14_14 = e2)
% 10.80/2.92 | (345) all_0_15_15 = e2
% 10.80/2.92 |
% 10.80/2.92 | Combining equations (864,345) yields a new equation:
% 10.80/2.92 | (242) e2 = e1
% 10.80/2.92 |
% 10.80/2.92 | Equations (242) can reduce 24 to:
% 10.80/2.92 | (179) $false
% 10.80/2.92 |
% 10.80/2.92 |-The branch is then unsatisfiable
% 10.80/2.92 |-Branch two:
% 10.80/2.92 | (677) ~ (all_0_22_22 = e1)
% 10.80/2.92 | (209) all_0_23_23 = e1
% 10.80/2.92 |
% 10.80/2.92 | Combining equations (209,386) yields a new equation:
% 10.80/2.92 | (206) e3 = e1
% 10.80/2.92 |
% 10.80/2.92 | Equations (206) can reduce 155 to:
% 10.80/2.92 | (179) $false
% 10.80/2.92 |
% 10.80/2.92 |-The branch is then unsatisfiable
% 10.80/2.93 |-Branch two:
% 10.80/2.93 | (389) all_0_23_23 = e2 & ~ (all_0_13_13 = e0)
% 10.80/2.93 |
% 10.80/2.93 | Applying alpha-rule on (389) yields:
% 10.80/2.93 | (352) all_0_23_23 = e2
% 10.80/2.93 | (391) ~ (all_0_13_13 = e0)
% 10.80/2.93 |
% 10.80/2.93 | Combining equations (352,386) yields a new equation:
% 10.80/2.93 | (298) e3 = e2
% 10.80/2.93 |
% 10.80/2.93 | Equations (298) can reduce 126 to:
% 10.80/2.93 | (179) $false
% 10.80/2.93 |
% 10.80/2.93 |-The branch is then unsatisfiable
% 10.80/2.93 |-Branch two:
% 10.80/2.93 | (1291) all_0_7_7 = e1
% 10.80/2.93 | (391) ~ (all_0_13_13 = e0)
% 10.80/2.93 |
% 10.80/2.93 | Equations (539) can reduce 391 to:
% 10.80/2.93 | (179) $false
% 10.80/2.93 |
% 10.80/2.93 |-The branch is then unsatisfiable
% 10.80/2.93 |-Branch two:
% 10.80/2.93 | (203) all_0_13_13 = e1 & ~ (all_0_18_18 = e2)
% 10.80/2.93 |
% 10.80/2.93 | Applying alpha-rule on (203) yields:
% 10.80/2.93 | (204) all_0_13_13 = e1
% 10.80/2.93 | (205) ~ (all_0_18_18 = e2)
% 10.80/2.93 |
% 10.80/2.93 | Combining equations (539,204) yields a new equation:
% 10.80/2.93 | (201) e1 = e0
% 10.80/2.93 |
% 10.80/2.93 | Equations (201) can reduce 88 to:
% 10.80/2.93 | (179) $false
% 10.80/2.93 |
% 10.80/2.93 |-The branch is then unsatisfiable
% 10.80/2.93 |-Branch two:
% 10.80/2.93 | (208) all_0_23_23 = e1 & ~ (all_0_18_18 = e0)
% 10.80/2.93 |
% 10.80/2.93 | Applying alpha-rule on (208) yields:
% 10.80/2.93 | (209) all_0_23_23 = e1
% 10.80/2.93 | (210) ~ (all_0_18_18 = e0)
% 10.80/2.93 |
% 10.80/2.93 | Combining equations (209,386) yields a new equation:
% 10.80/2.93 | (206) e3 = e1
% 10.80/2.93 |
% 10.80/2.93 | Equations (206) can reduce 155 to:
% 10.80/2.93 | (179) $false
% 10.80/2.93 |
% 10.80/2.93 |-The branch is then unsatisfiable
% 10.80/2.93 |-Branch two:
% 10.80/2.93 | (1304) all_0_18_18 = e0 & ~ (all_0_23_23 = e1)
% 10.80/2.93 |
% 10.80/2.93 | Applying alpha-rule on (1304) yields:
% 10.80/2.93 | (1305) all_0_18_18 = e0
% 10.80/2.93 | (312) ~ (all_0_23_23 = e1)
% 10.80/2.93 |
% 10.80/2.93 | Equations (1305) can reduce 76 to:
% 10.80/2.93 | (740) ~ (all_0_10_10 = e0)
% 10.80/2.93 |
% 10.80/2.93 | Equations (1305) can reduce 26 to:
% 10.80/2.93 | (575) ~ (all_0_14_14 = e0)
% 10.80/2.93 |
% 10.80/2.93 | Equations (1305) can reduce 100 to:
% 10.80/2.93 | (1309) ~ (all_0_16_16 = e0)
% 10.80/2.93 |
% 10.80/2.93 | Equations (1305) can reduce 45 to:
% 10.80/2.93 | (618) ~ (all_0_17_17 = e0)
% 10.80/2.93 |
% 10.80/2.93 | Equations (1305) can reduce 42 to:
% 10.80/2.93 | (958) ~ (all_0_22_22 = e0)
% 10.80/2.93 |
% 10.80/2.93 | Simplifying 958 yields:
% 10.80/2.93 | (959) ~ (all_0_22_22 = e0)
% 10.80/2.93 |
% 10.80/2.93 | From (1305)(1305) and (95) follows:
% 10.80/2.93 | (1313) op(e0, e0) = all_0_2_2
% 10.80/2.93 |
% 10.80/2.93 | From (1305) and (94) follows:
% 10.80/2.94 | (1314) op(e0, e1) = all_0_3_3
% 10.80/2.94 |
% 10.80/2.94 | From (1305) and (11) follows:
% 10.80/2.94 | (1315) op(e1, e1) = e0
% 10.80/2.94 |
% 10.80/2.94 | Instantiating formula (85) with e0, e1, all_0_3_3, all_0_22_22 and discharging atoms op(e0, e1) = all_0_3_3, op(e0, e1) = all_0_22_22, yields:
% 10.80/2.94 | (1316) all_0_3_3 = all_0_22_22
% 10.80/2.94 |
% 10.80/2.94 | Instantiating formula (85) with e0, e0, all_0_2_2, all_0_23_23 and discharging atoms op(e0, e0) = all_0_2_2, op(e0, e0) = all_0_23_23, yields:
% 10.80/2.94 | (1317) all_0_2_2 = all_0_23_23
% 10.80/2.94 |
% 10.80/2.94 +-Applying beta-rule and splitting (99), into two cases.
% 10.80/2.94 |-Branch one:
% 10.80/2.94 | (1318) ~ (all_0_2_2 = e2)
% 10.80/2.94 |
% 10.80/2.94 | Equations (1317) can reduce 1318 to:
% 10.80/2.94 | (172) ~ (all_0_23_23 = e2)
% 10.80/2.94 |
% 10.80/2.94 +-Applying beta-rule and splitting (132), into two cases.
% 10.80/2.94 |-Branch one:
% 10.80/2.94 | (173) (all_0_8_8 = e2 & ~ (all_0_13_13 = e3)) | (all_0_18_18 = e2 & ~ (all_0_13_13 = e1))
% 10.80/2.94 |
% 10.80/2.94 +-Applying beta-rule and splitting (173), into two cases.
% 10.80/2.94 |-Branch one:
% 10.80/2.94 | (174) all_0_8_8 = e2 & ~ (all_0_13_13 = e3)
% 10.80/2.94 |
% 10.80/2.94 | Applying alpha-rule on (174) yields:
% 10.80/2.94 | (175) all_0_8_8 = e2
% 10.80/2.94 | (176) ~ (all_0_13_13 = e3)
% 10.80/2.94 |
% 10.80/2.94 | Equations (175) can reduce 139 to:
% 10.80/2.94 | (645) ~ (all_0_10_10 = e2)
% 10.80/2.94 |
% 10.80/2.94 | Simplifying 645 yields:
% 10.80/2.94 | (491) ~ (all_0_10_10 = e2)
% 10.80/2.94 |
% 10.80/2.94 | Equations (175) can reduce 19 to:
% 10.80/2.94 | (647) ~ (all_0_11_11 = e2)
% 10.80/2.94 |
% 10.80/2.94 | Simplifying 647 yields:
% 10.80/2.94 | (343) ~ (all_0_11_11 = e2)
% 10.80/2.94 |
% 10.80/2.94 +-Applying beta-rule and splitting (69), into two cases.
% 10.80/2.94 |-Branch one:
% 10.80/2.94 | (189) (all_0_13_13 = e3 & ~ (all_0_8_8 = e2)) | (all_0_18_18 = e3 & ~ (all_0_8_8 = e1))
% 10.80/2.94 |
% 10.80/2.94 +-Applying beta-rule and splitting (189), into two cases.
% 10.80/2.94 |-Branch one:
% 10.80/2.94 | (190) all_0_13_13 = e3 & ~ (all_0_8_8 = e2)
% 10.80/2.94 |
% 10.80/2.94 | Applying alpha-rule on (190) yields:
% 10.80/2.94 | (191) all_0_13_13 = e3
% 10.80/2.94 | (192) ~ (all_0_8_8 = e2)
% 10.80/2.94 |
% 10.80/2.94 | Equations (191) can reduce 176 to:
% 10.80/2.94 | (179) $false
% 10.80/2.94 |
% 10.80/2.94 |-The branch is then unsatisfiable
% 10.80/2.94 |-Branch two:
% 10.80/2.94 | (379) all_0_18_18 = e3 & ~ (all_0_8_8 = e1)
% 10.80/2.94 |
% 10.80/2.94 | Applying alpha-rule on (379) yields:
% 10.80/2.94 | (297) all_0_18_18 = e3
% 10.80/2.94 | (268) ~ (all_0_8_8 = e1)
% 10.80/2.94 |
% 10.80/2.94 | Combining equations (297,1305) yields a new equation:
% 10.80/2.94 | (552) e3 = e0
% 10.80/2.94 |
% 10.80/2.94 | Simplifying 552 yields:
% 10.80/2.94 | (257) e3 = e0
% 10.80/2.94 |
% 10.80/2.94 | Equations (257) can reduce 40 to:
% 10.80/2.94 | (179) $false
% 10.80/2.94 |
% 10.80/2.94 |-The branch is then unsatisfiable
% 10.80/2.94 |-Branch two:
% 10.80/2.94 | (385) all_0_23_23 = e3 & ~ (all_0_8_8 = e0)
% 10.80/2.94 |
% 10.80/2.94 | Applying alpha-rule on (385) yields:
% 10.80/2.94 | (386) all_0_23_23 = e3
% 10.80/2.94 | (377) ~ (all_0_8_8 = e0)
% 10.80/2.94 |
% 10.80/2.94 | Combining equations (386,1317) yields a new equation:
% 10.80/2.94 | (1342) all_0_2_2 = e3
% 10.80/2.94 |
% 10.80/2.94 | Equations (386) can reduce 109 to:
% 10.80/2.94 | (858) ~ (all_0_15_15 = e3)
% 10.80/2.94 |
% 10.80/2.94 | Equations (386) can reduce 108 to:
% 10.80/2.94 | (687) ~ (all_0_21_21 = e3)
% 10.80/2.94 |
% 10.80/2.94 | Equations (386) can reduce 8 to:
% 10.80/2.94 | (639) ~ (all_0_22_22 = e3)
% 10.80/2.94 |
% 10.80/2.94 +-Applying beta-rule and splitting (54), into two cases.
% 10.80/2.94 |-Branch one:
% 10.80/2.94 | (1346) ~ (all_0_2_2 = e3)
% 10.80/2.94 |
% 10.80/2.95 | Equations (1342) can reduce 1346 to:
% 10.80/2.95 | (179) $false
% 10.80/2.95 |
% 10.80/2.95 |-The branch is then unsatisfiable
% 10.80/2.95 |-Branch two:
% 10.80/2.95 | (1342) all_0_2_2 = e3
% 10.80/2.95 | (1349) ~ (all_0_3_3 = e2) | ~ (all_0_18_18 = e0)
% 10.80/2.95 |
% 10.80/2.95 +-Applying beta-rule and splitting (1349), into two cases.
% 10.80/2.95 |-Branch one:
% 10.80/2.95 | (1350) ~ (all_0_3_3 = e2)
% 10.80/2.95 |
% 10.80/2.95 | Equations (1316) can reduce 1350 to:
% 10.80/2.95 | (187) ~ (all_0_22_22 = e2)
% 10.80/2.95 |
% 10.80/2.95 +-Applying beta-rule and splitting (58), into two cases.
% 10.80/2.95 |-Branch one:
% 10.80/2.95 | (728) all_0_22_22 = e3
% 10.80/2.95 |
% 10.80/2.95 | Equations (728) can reduce 639 to:
% 10.80/2.95 | (179) $false
% 10.80/2.95 |
% 10.80/2.95 |-The branch is then unsatisfiable
% 10.80/2.95 |-Branch two:
% 10.80/2.95 | (639) ~ (all_0_22_22 = e3)
% 10.80/2.95 | (731) all_0_22_22 = e2 | all_0_22_22 = e1 | all_0_22_22 = e0
% 10.80/2.95 |
% 10.80/2.95 +-Applying beta-rule and splitting (731), into two cases.
% 10.80/2.95 |-Branch one:
% 10.80/2.95 | (358) all_0_22_22 = e2
% 10.80/2.95 |
% 10.80/2.95 | Equations (358) can reduce 187 to:
% 10.80/2.95 | (179) $false
% 10.80/2.95 |
% 10.80/2.95 |-The branch is then unsatisfiable
% 10.80/2.95 |-Branch two:
% 10.80/2.95 | (187) ~ (all_0_22_22 = e2)
% 10.80/2.95 | (735) all_0_22_22 = e1 | all_0_22_22 = e0
% 10.80/2.95 |
% 10.80/2.95 +-Applying beta-rule and splitting (735), into two cases.
% 10.80/2.95 |-Branch one:
% 10.80/2.95 | (736) all_0_22_22 = e1
% 10.80/2.95 |
% 10.80/2.95 | Equations (736) can reduce 57 to:
% 10.80/2.95 | (822) ~ (all_0_10_10 = e1)
% 10.80/2.95 |
% 10.80/2.95 | Equations (736) can reduce 27 to:
% 10.80/2.95 | (214) ~ (all_0_20_20 = e1)
% 10.80/2.95 |
% 10.80/2.95 | Equations (736) can reduce 639 to:
% 10.80/2.95 | (216) ~ (e3 = e1)
% 10.80/2.95 |
% 10.80/2.95 | Simplifying 216 yields:
% 10.80/2.95 | (155) ~ (e3 = e1)
% 10.80/2.95 |
% 10.80/2.95 | Equations (736) can reduce 187 to:
% 10.80/2.95 | (218) ~ (e2 = e1)
% 10.80/2.95 |
% 10.80/2.95 | Simplifying 218 yields:
% 10.80/2.95 | (24) ~ (e2 = e1)
% 10.80/2.95 |
% 10.80/2.95 +-Applying beta-rule and splitting (156), into two cases.
% 10.80/2.95 |-Branch one:
% 10.80/2.95 | (197) (all_0_8_8 = e1 & ~ (all_0_18_18 = e3)) | (all_0_13_13 = e1 & ~ (all_0_18_18 = e2))
% 10.80/2.95 |
% 10.80/2.95 +-Applying beta-rule and splitting (197), into two cases.
% 10.80/2.95 |-Branch one:
% 10.80/2.95 | (198) all_0_8_8 = e1 & ~ (all_0_18_18 = e3)
% 10.80/2.95 |
% 10.80/2.95 | Applying alpha-rule on (198) yields:
% 10.80/2.95 | (199) all_0_8_8 = e1
% 10.80/2.95 | (200) ~ (all_0_18_18 = e3)
% 10.80/2.95 |
% 10.80/2.95 | Combining equations (175,199) yields a new equation:
% 10.80/2.95 | (241) e2 = e1
% 10.80/2.95 |
% 10.80/2.95 | Simplifying 241 yields:
% 10.80/2.95 | (242) e2 = e1
% 10.80/2.95 |
% 10.80/2.95 | Equations (242) can reduce 24 to:
% 10.80/2.95 | (179) $false
% 10.80/2.95 |
% 10.80/2.95 |-The branch is then unsatisfiable
% 10.80/2.95 |-Branch two:
% 10.80/2.95 | (203) all_0_13_13 = e1 & ~ (all_0_18_18 = e2)
% 10.80/2.95 |
% 10.80/2.95 | Applying alpha-rule on (203) yields:
% 10.80/2.95 | (204) all_0_13_13 = e1
% 10.80/2.95 | (205) ~ (all_0_18_18 = e2)
% 10.80/2.95 |
% 10.80/2.95 | Equations (204) can reduce 66 to:
% 10.80/2.95 | (244) ~ (all_0_12_12 = e1)
% 10.80/2.95 |
% 10.80/2.95 | Equations (204) can reduce 86 to:
% 10.80/2.95 | (708) ~ (all_0_14_14 = e1)
% 10.80/2.95 |
% 10.80/2.95 | Simplifying 708 yields:
% 10.80/2.95 | (709) ~ (all_0_14_14 = e1)
% 10.80/2.95 |
% 10.80/2.95 | Equations (204) can reduce 106 to:
% 10.80/2.95 | (277) ~ (all_0_17_17 = e1)
% 10.80/2.95 |
% 10.80/2.95 | Simplifying 277 yields:
% 10.80/2.95 | (278) ~ (all_0_17_17 = e1)
% 10.80/2.95 |
% 10.80/2.95 | From (204)(204) and (47) follows:
% 10.80/2.95 | (1382) op(e1, e1) = all_0_6_6
% 10.80/2.95 |
% 10.80/2.95 | From (204) and (14) follows:
% 10.80/2.96 | (1383) op(e1, e2) = all_0_7_7
% 10.80/2.96 |
% 10.80/2.96 +-Applying beta-rule and splitting (147), into two cases.
% 10.80/2.96 |-Branch one:
% 10.80/2.96 | (563) all_0_10_10 = e3
% 10.80/2.96 |
% 10.80/2.96 | Equations (563) can reduce 134 to:
% 10.80/2.96 | (193) ~ (all_0_9_9 = e3)
% 10.80/2.96 |
% 10.80/2.96 | Equations (563) can reduce 133 to:
% 10.80/2.96 | (1386) ~ (all_0_14_14 = e3)
% 10.80/2.96 |
% 10.80/2.96 | Simplifying 1386 yields:
% 10.80/2.96 | (427) ~ (all_0_14_14 = e3)
% 10.80/2.96 |
% 10.80/2.96 | Equations (563) can reduce 822 to:
% 10.80/2.96 | (155) ~ (e3 = e1)
% 10.80/2.96 |
% 10.80/2.96 +-Applying beta-rule and splitting (81), into two cases.
% 10.80/2.96 |-Branch one:
% 10.80/2.96 | (434) all_0_12_12 = e3
% 10.80/2.96 |
% 10.80/2.96 | Equations (434) can reduce 75 to:
% 10.80/2.96 | (1386) ~ (all_0_14_14 = e3)
% 10.80/2.96 |
% 10.80/2.96 | Simplifying 1386 yields:
% 10.80/2.96 | (427) ~ (all_0_14_14 = e3)
% 10.80/2.96 |
% 10.80/2.96 +-Applying beta-rule and splitting (46), into two cases.
% 10.80/2.96 |-Branch one:
% 10.80/2.96 | (451) all_0_14_14 = e3
% 10.80/2.96 |
% 10.80/2.96 | Equations (451) can reduce 427 to:
% 10.80/2.96 | (179) $false
% 10.80/2.96 |
% 10.80/2.96 |-The branch is then unsatisfiable
% 10.80/2.96 |-Branch two:
% 10.80/2.96 | (427) ~ (all_0_14_14 = e3)
% 10.80/2.96 | (454) all_0_14_14 = e2 | all_0_14_14 = e1 | all_0_14_14 = e0
% 10.80/2.96 |
% 10.80/2.96 +-Applying beta-rule and splitting (454), into two cases.
% 10.80/2.96 |-Branch one:
% 10.80/2.96 | (783) all_0_14_14 = e2
% 10.80/2.96 |
% 10.80/2.96 | Equations (783) can reduce 12 to:
% 10.80/2.96 | (234) ~ (all_0_15_15 = e2)
% 10.80/2.96 |
% 10.80/2.96 | Simplifying 234 yields:
% 10.80/2.96 | (235) ~ (all_0_15_15 = e2)
% 10.80/2.96 |
% 10.80/2.96 | Equations (783) can reduce 427 to:
% 10.80/2.96 | (398) ~ (e3 = e2)
% 10.80/2.96 |
% 10.80/2.96 | Simplifying 398 yields:
% 10.80/2.96 | (126) ~ (e3 = e2)
% 10.80/2.96 |
% 10.80/2.96 +-Applying beta-rule and splitting (83), into two cases.
% 10.80/2.96 |-Branch one:
% 10.80/2.96 | (254) all_0_11_11 = e2
% 10.80/2.96 |
% 10.80/2.96 | Equations (254) can reduce 343 to:
% 10.80/2.96 | (179) $false
% 10.80/2.96 |
% 10.80/2.96 |-The branch is then unsatisfiable
% 10.80/2.96 |-Branch two:
% 10.80/2.96 | (343) ~ (all_0_11_11 = e2)
% 10.80/2.96 | (344) all_0_15_15 = e2 | all_0_19_19 = e2 | all_0_23_23 = e2
% 10.80/2.96 |
% 10.80/2.96 +-Applying beta-rule and splitting (344), into two cases.
% 10.80/2.96 |-Branch one:
% 10.80/2.96 | (345) all_0_15_15 = e2
% 10.80/2.96 |
% 10.80/2.96 | Equations (345) can reduce 235 to:
% 10.80/2.96 | (179) $false
% 10.80/2.96 |
% 10.80/2.96 |-The branch is then unsatisfiable
% 10.80/2.96 |-Branch two:
% 10.80/2.96 | (235) ~ (all_0_15_15 = e2)
% 10.80/2.96 | (348) all_0_19_19 = e2 | all_0_23_23 = e2
% 10.80/2.96 |
% 10.80/2.96 +-Applying beta-rule and splitting (348), into two cases.
% 10.80/2.96 |-Branch one:
% 10.80/2.96 | (349) all_0_19_19 = e2
% 10.80/2.96 |
% 10.80/2.96 | Equations (349) can reduce 59 to:
% 10.80/2.96 | (1410) ~ (all_0_17_17 = e2)
% 10.80/2.96 |
% 10.80/2.96 +-Applying beta-rule and splitting (67), into two cases.
% 10.80/2.96 |-Branch one:
% 10.80/2.96 | (293) all_0_17_17 = e3
% 10.80/2.96 |
% 10.80/2.96 | From (293) and (5) follows:
% 10.80/2.96 | (1412) op(e1, e2) = e3
% 10.80/2.96 |
% 10.80/2.96 | Instantiating formula (85) with e1, e2, e3, all_0_7_7 and discharging atoms op(e1, e2) = all_0_7_7, op(e1, e2) = e3, yields:
% 10.80/2.96 | (982) all_0_7_7 = e3
% 10.80/2.96 |
% 10.80/2.96 | Instantiating formula (85) with e1, e1, all_0_6_6, e0 and discharging atoms op(e1, e1) = all_0_6_6, op(e1, e1) = e0, yields:
% 10.80/2.96 | (1414) all_0_6_6 = e0
% 10.80/2.96 |
% 10.80/2.96 +-Applying beta-rule and splitting (111), into two cases.
% 10.80/2.96 |-Branch one:
% 10.80/2.96 | (1415) ~ (all_0_6_6 = e0)
% 10.80/2.96 |
% 10.80/2.97 | Equations (1414) can reduce 1415 to:
% 10.80/2.97 | (179) $false
% 10.80/2.97 |
% 10.80/2.97 |-The branch is then unsatisfiable
% 10.80/2.97 |-Branch two:
% 10.80/2.97 | (1414) all_0_6_6 = e0
% 10.80/2.97 | (1418) ~ (all_0_7_7 = e3) | ~ (all_0_13_13 = e1)
% 10.80/2.97 |
% 10.80/2.97 +-Applying beta-rule and splitting (1418), into two cases.
% 10.80/2.97 |-Branch one:
% 10.80/2.97 | (686) ~ (all_0_7_7 = e3)
% 10.80/2.97 |
% 10.80/2.97 | Equations (982) can reduce 686 to:
% 10.80/2.97 | (179) $false
% 10.80/2.97 |
% 10.80/2.97 |-The branch is then unsatisfiable
% 10.80/2.97 |-Branch two:
% 10.80/2.97 | (982) all_0_7_7 = e3
% 10.80/2.97 | (182) ~ (all_0_13_13 = e1)
% 10.80/2.97 |
% 10.80/2.97 | Equations (204) can reduce 182 to:
% 10.80/2.97 | (179) $false
% 10.80/2.97 |
% 10.80/2.97 |-The branch is then unsatisfiable
% 10.80/2.97 |-Branch two:
% 10.80/2.97 | (195) ~ (all_0_17_17 = e3)
% 10.80/2.97 | (1425) all_0_17_17 = e2 | all_0_17_17 = e1 | all_0_17_17 = e0
% 10.80/2.97 |
% 10.80/2.97 +-Applying beta-rule and splitting (1425), into two cases.
% 10.80/2.97 |-Branch one:
% 10.80/2.97 | (1426) all_0_17_17 = e2
% 10.80/2.97 |
% 10.80/2.97 | Equations (1426) can reduce 1410 to:
% 10.80/2.97 | (179) $false
% 10.80/2.97 |
% 10.80/2.97 |-The branch is then unsatisfiable
% 10.80/2.97 |-Branch two:
% 10.80/2.97 | (1410) ~ (all_0_17_17 = e2)
% 10.80/2.97 | (1429) all_0_17_17 = e1 | all_0_17_17 = e0
% 10.80/2.97 |
% 10.80/2.97 +-Applying beta-rule and splitting (1429), into two cases.
% 10.80/2.97 |-Branch one:
% 10.80/2.97 | (333) all_0_17_17 = e1
% 10.80/2.97 |
% 10.80/2.97 | Equations (333) can reduce 278 to:
% 10.80/2.97 | (179) $false
% 10.80/2.97 |
% 10.80/2.97 |-The branch is then unsatisfiable
% 10.80/2.97 |-Branch two:
% 10.80/2.97 | (278) ~ (all_0_17_17 = e1)
% 10.80/2.97 | (1433) all_0_17_17 = e0
% 10.80/2.97 |
% 10.80/2.97 | Equations (1433) can reduce 618 to:
% 10.80/2.97 | (179) $false
% 10.80/2.97 |
% 10.80/2.97 |-The branch is then unsatisfiable
% 10.80/2.97 |-Branch two:
% 10.80/2.97 | (185) ~ (all_0_19_19 = e2)
% 10.80/2.97 | (352) all_0_23_23 = e2
% 10.80/2.97 |
% 10.80/2.97 | Combining equations (352,386) yields a new equation:
% 10.80/2.97 | (298) e3 = e2
% 10.80/2.97 |
% 10.80/2.97 | Equations (298) can reduce 126 to:
% 10.80/2.97 | (179) $false
% 10.80/2.97 |
% 10.80/2.97 |-The branch is then unsatisfiable
% 10.80/2.97 |-Branch two:
% 10.80/2.97 | (815) ~ (all_0_14_14 = e2)
% 10.80/2.97 | (816) all_0_14_14 = e1 | all_0_14_14 = e0
% 10.80/2.97 |
% 10.80/2.97 +-Applying beta-rule and splitting (816), into two cases.
% 10.80/2.97 |-Branch one:
% 10.80/2.97 | (817) all_0_14_14 = e1
% 10.80/2.97 |
% 10.80/2.97 | Equations (817) can reduce 709 to:
% 10.80/2.97 | (179) $false
% 10.80/2.97 |
% 10.80/2.97 |-The branch is then unsatisfiable
% 10.80/2.97 |-Branch two:
% 10.80/2.97 | (709) ~ (all_0_14_14 = e1)
% 10.80/2.97 | (545) all_0_14_14 = e0
% 10.80/2.97 |
% 10.80/2.97 | Equations (545) can reduce 575 to:
% 10.80/2.97 | (179) $false
% 10.80/2.97 |
% 10.80/2.97 |-The branch is then unsatisfiable
% 10.80/2.97 |-Branch two:
% 10.80/2.97 | (431) ~ (all_0_12_12 = e3)
% 10.80/2.97 | (469) all_0_13_13 = e3 | all_0_14_14 = e3 | all_0_15_15 = e3
% 10.80/2.97 |
% 10.80/2.97 +-Applying beta-rule and splitting (127), into two cases.
% 10.80/2.97 |-Branch one:
% 10.80/2.97 | (199) all_0_8_8 = e1
% 10.80/2.97 |
% 10.80/2.97 | Combining equations (175,199) yields a new equation:
% 10.80/2.97 | (241) e2 = e1
% 10.80/2.97 |
% 10.80/2.97 | Simplifying 241 yields:
% 10.80/2.97 | (242) e2 = e1
% 10.80/2.97 |
% 10.80/2.97 | Equations (242) can reduce 24 to:
% 10.80/2.97 | (179) $false
% 10.80/2.97 |
% 10.80/2.97 |-The branch is then unsatisfiable
% 10.80/2.97 |-Branch two:
% 10.80/2.97 | (268) ~ (all_0_8_8 = e1)
% 10.80/2.97 | (269) all_0_12_12 = e1 | all_0_16_16 = e1 | all_0_20_20 = e1
% 10.80/2.97 |
% 10.80/2.97 +-Applying beta-rule and splitting (269), into two cases.
% 10.80/2.97 |-Branch one:
% 10.80/2.97 | (240) all_0_12_12 = e1
% 10.80/2.97 |
% 10.80/2.97 | Equations (240) can reduce 244 to:
% 10.80/2.97 | (179) $false
% 10.80/2.97 |
% 10.80/2.97 |-The branch is then unsatisfiable
% 10.80/2.97 |-Branch two:
% 10.80/2.97 | (244) ~ (all_0_12_12 = e1)
% 10.80/2.97 | (275) all_0_16_16 = e1 | all_0_20_20 = e1
% 10.80/2.97 |
% 10.80/2.97 +-Applying beta-rule and splitting (32), into two cases.
% 10.80/2.97 |-Branch one:
% 10.80/2.97 | (261) all_0_9_9 = e3
% 10.80/2.97 |
% 10.80/2.97 | Equations (261) can reduce 193 to:
% 10.80/2.97 | (179) $false
% 10.80/2.97 |
% 10.80/2.97 |-The branch is then unsatisfiable
% 10.80/2.97 |-Branch two:
% 10.80/2.97 | (193) ~ (all_0_9_9 = e3)
% 10.80/2.97 | (529) all_0_13_13 = e3 | all_0_17_17 = e3 | all_0_21_21 = e3
% 10.80/2.97 |
% 10.80/2.97 +-Applying beta-rule and splitting (529), into two cases.
% 10.80/2.97 |-Branch one:
% 10.80/2.97 | (191) all_0_13_13 = e3
% 10.80/2.97 |
% 10.80/2.97 | Combining equations (204,191) yields a new equation:
% 10.80/2.97 | (206) e3 = e1
% 10.80/2.97 |
% 10.80/2.97 | Equations (206) can reduce 155 to:
% 10.80/2.97 | (179) $false
% 10.80/2.97 |
% 10.80/2.97 |-The branch is then unsatisfiable
% 10.80/2.97 |-Branch two:
% 10.80/2.97 | (176) ~ (all_0_13_13 = e3)
% 10.80/2.97 | (1466) all_0_17_17 = e3 | all_0_21_21 = e3
% 10.80/2.97 |
% 10.80/2.97 +-Applying beta-rule and splitting (275), into two cases.
% 10.80/2.97 |-Branch one:
% 10.80/2.97 | (276) all_0_16_16 = e1
% 10.80/2.97 |
% 10.80/2.97 | Equations (276) can reduce 78 to:
% 10.80/2.97 | (277) ~ (all_0_17_17 = e1)
% 10.80/2.97 |
% 10.80/2.97 | Simplifying 277 yields:
% 10.80/2.97 | (278) ~ (all_0_17_17 = e1)
% 10.80/2.97 |
% 10.80/2.97 +-Applying beta-rule and splitting (1466), into two cases.
% 10.80/2.97 |-Branch one:
% 10.80/2.97 | (293) all_0_17_17 = e3
% 10.80/2.97 |
% 10.80/2.97 | Equations (293) can reduce 278 to:
% 10.80/2.97 | (155) ~ (e3 = e1)
% 10.80/2.97 |
% 10.80/2.97 +-Applying beta-rule and splitting (469), into two cases.
% 10.80/2.97 |-Branch one:
% 10.80/2.97 | (191) all_0_13_13 = e3
% 10.80/2.97 |
% 10.80/2.97 | Combining equations (204,191) yields a new equation:
% 10.80/2.97 | (206) e3 = e1
% 10.80/2.97 |
% 10.80/2.97 | Equations (206) can reduce 155 to:
% 10.80/2.97 | (179) $false
% 10.80/2.97 |
% 10.80/2.97 |-The branch is then unsatisfiable
% 10.80/2.97 |-Branch two:
% 10.80/2.97 | (176) ~ (all_0_13_13 = e3)
% 10.80/2.97 | (474) all_0_14_14 = e3 | all_0_15_15 = e3
% 10.80/2.97 |
% 10.80/2.97 +-Applying beta-rule and splitting (474), into two cases.
% 10.80/2.97 |-Branch one:
% 10.80/2.97 | (451) all_0_14_14 = e3
% 10.80/2.97 |
% 10.80/2.97 | Equations (451) can reduce 427 to:
% 10.80/2.97 | (179) $false
% 10.80/2.97 |
% 10.80/2.97 |-The branch is then unsatisfiable
% 10.80/2.97 |-Branch two:
% 10.80/2.97 | (427) ~ (all_0_14_14 = e3)
% 10.80/2.97 | (478) all_0_15_15 = e3
% 10.80/2.97 |
% 10.80/2.97 | Equations (478) can reduce 858 to:
% 10.80/2.97 | (179) $false
% 10.80/2.97 |
% 10.80/2.97 |-The branch is then unsatisfiable
% 10.80/2.97 |-Branch two:
% 10.80/2.97 | (195) ~ (all_0_17_17 = e3)
% 10.80/2.97 | (716) all_0_21_21 = e3
% 10.80/2.97 |
% 10.80/2.97 | Equations (716) can reduce 687 to:
% 10.80/2.97 | (179) $false
% 10.80/2.97 |
% 10.80/2.97 |-The branch is then unsatisfiable
% 10.80/2.97 |-Branch two:
% 10.80/2.97 | (340) ~ (all_0_16_16 = e1)
% 10.80/2.97 | (320) all_0_20_20 = e1
% 10.80/2.97 |
% 10.80/2.97 | Equations (320) can reduce 214 to:
% 10.80/2.97 | (179) $false
% 10.80/2.97 |
% 10.80/2.97 |-The branch is then unsatisfiable
% 10.80/2.97 |-Branch two:
% 10.80/2.97 | (426) ~ (all_0_10_10 = e3)
% 10.80/2.97 | (1489) all_0_10_10 = e2 | all_0_10_10 = e1 | all_0_10_10 = e0
% 10.80/2.97 |
% 10.80/2.97 +-Applying beta-rule and splitting (1489), into two cases.
% 10.80/2.97 |-Branch one:
% 10.80/2.97 | (462) all_0_10_10 = e2
% 10.80/2.97 |
% 10.80/2.97 | Equations (462) can reduce 491 to:
% 10.80/2.97 | (179) $false
% 10.80/2.97 |
% 10.80/2.97 |-The branch is then unsatisfiable
% 10.80/2.97 |-Branch two:
% 10.80/2.97 | (491) ~ (all_0_10_10 = e2)
% 10.80/2.97 | (1493) all_0_10_10 = e1 | all_0_10_10 = e0
% 10.80/2.97 |
% 10.80/2.97 +-Applying beta-rule and splitting (1493), into two cases.
% 10.80/2.97 |-Branch one:
% 10.80/2.97 | (761) all_0_10_10 = e1
% 10.80/2.97 |
% 10.80/2.98 | Equations (761) can reduce 822 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (822) ~ (all_0_10_10 = e1)
% 10.80/2.98 | (774) all_0_10_10 = e0
% 10.80/2.98 |
% 10.80/2.98 | Equations (774) can reduce 740 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (208) all_0_23_23 = e1 & ~ (all_0_18_18 = e0)
% 10.80/2.98 |
% 10.80/2.98 | Applying alpha-rule on (208) yields:
% 10.80/2.98 | (209) all_0_23_23 = e1
% 10.80/2.98 | (210) ~ (all_0_18_18 = e0)
% 10.80/2.98 |
% 10.80/2.98 | Combining equations (209,386) yields a new equation:
% 10.80/2.98 | (206) e3 = e1
% 10.80/2.98 |
% 10.80/2.98 | Equations (206) can reduce 155 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (677) ~ (all_0_22_22 = e1)
% 10.80/2.98 | (739) all_0_22_22 = e0
% 10.80/2.98 |
% 10.80/2.98 | Equations (739) can reduce 959 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (1507) all_0_3_3 = e2
% 10.80/2.98 | (210) ~ (all_0_18_18 = e0)
% 10.80/2.98 |
% 10.80/2.98 | Equations (1305) can reduce 210 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (180) all_0_18_18 = e2 & ~ (all_0_13_13 = e1)
% 10.80/2.98 |
% 10.80/2.98 | Applying alpha-rule on (180) yields:
% 10.80/2.98 | (181) all_0_18_18 = e2
% 10.80/2.98 | (182) ~ (all_0_13_13 = e1)
% 10.80/2.98 |
% 10.80/2.98 | Combining equations (181,1305) yields a new equation:
% 10.80/2.98 | (177) e2 = e0
% 10.80/2.98 |
% 10.80/2.98 | Simplifying 177 yields:
% 10.80/2.98 | (178) e2 = e0
% 10.80/2.98 |
% 10.80/2.98 | Equations (178) can reduce 119 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (389) all_0_23_23 = e2 & ~ (all_0_13_13 = e0)
% 10.80/2.98 |
% 10.80/2.98 | Applying alpha-rule on (389) yields:
% 10.80/2.98 | (352) all_0_23_23 = e2
% 10.80/2.98 | (391) ~ (all_0_13_13 = e0)
% 10.80/2.98 |
% 10.80/2.98 | Equations (352) can reduce 172 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (1520) all_0_2_2 = e2
% 10.80/2.98 | (1521) ~ (all_0_3_3 = e3) | ~ (all_0_18_18 = e0)
% 10.80/2.98 |
% 10.80/2.98 | Combining equations (1520,1317) yields a new equation:
% 10.80/2.98 | (352) all_0_23_23 = e2
% 10.80/2.98 |
% 10.80/2.98 | Equations (352) can reduce 3 to:
% 10.80/2.98 | (343) ~ (all_0_11_11 = e2)
% 10.80/2.98 |
% 10.80/2.98 | Equations (352) can reduce 108 to:
% 10.80/2.98 | (356) ~ (all_0_21_21 = e2)
% 10.80/2.98 |
% 10.80/2.98 | Equations (352) can reduce 312 to:
% 10.80/2.98 | (24) ~ (e2 = e1)
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (1521), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (1526) ~ (all_0_3_3 = e3)
% 10.80/2.98 |
% 10.80/2.98 | Equations (1316) can reduce 1526 to:
% 10.80/2.98 | (639) ~ (all_0_22_22 = e3)
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (69), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (189) (all_0_13_13 = e3 & ~ (all_0_8_8 = e2)) | (all_0_18_18 = e3 & ~ (all_0_8_8 = e1))
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (189), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (190) all_0_13_13 = e3 & ~ (all_0_8_8 = e2)
% 10.80/2.98 |
% 10.80/2.98 | Applying alpha-rule on (190) yields:
% 10.80/2.98 | (191) all_0_13_13 = e3
% 10.80/2.98 | (192) ~ (all_0_8_8 = e2)
% 10.80/2.98 |
% 10.80/2.98 | Equations (191) can reduce 86 to:
% 10.80/2.98 | (1386) ~ (all_0_14_14 = e3)
% 10.80/2.98 |
% 10.80/2.98 | Simplifying 1386 yields:
% 10.80/2.98 | (427) ~ (all_0_14_14 = e3)
% 10.80/2.98 |
% 10.80/2.98 | Equations (191) can reduce 35 to:
% 10.80/2.98 | (1534) ~ (all_0_15_15 = e3)
% 10.80/2.98 |
% 10.80/2.98 | Simplifying 1534 yields:
% 10.80/2.98 | (858) ~ (all_0_15_15 = e3)
% 10.80/2.98 |
% 10.80/2.98 | Equations (191) can reduce 106 to:
% 10.80/2.98 | (194) ~ (all_0_17_17 = e3)
% 10.80/2.98 |
% 10.80/2.98 | Simplifying 194 yields:
% 10.80/2.98 | (195) ~ (all_0_17_17 = e3)
% 10.80/2.98 |
% 10.80/2.98 | Equations (191) can reduce 61 to:
% 10.80/2.98 | (691) ~ (all_0_21_21 = e3)
% 10.80/2.98 |
% 10.80/2.98 | Simplifying 691 yields:
% 10.80/2.98 | (687) ~ (all_0_21_21 = e3)
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (29), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (563) all_0_10_10 = e3
% 10.80/2.98 |
% 10.80/2.98 | Equations (563) can reduce 134 to:
% 10.80/2.98 | (193) ~ (all_0_9_9 = e3)
% 10.80/2.98 |
% 10.80/2.98 | Equations (563) can reduce 122 to:
% 10.80/2.98 | (1542) ~ (all_0_11_11 = e3)
% 10.80/2.98 |
% 10.80/2.98 | Simplifying 1542 yields:
% 10.80/2.98 | (507) ~ (all_0_11_11 = e3)
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (18), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (175) all_0_8_8 = e2
% 10.80/2.98 |
% 10.80/2.98 | Equations (175) can reduce 192 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (192) ~ (all_0_8_8 = e2)
% 10.80/2.98 | (514) all_0_9_9 = e2 | all_0_10_10 = e2 | all_0_11_11 = e2
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (156), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (197) (all_0_8_8 = e1 & ~ (all_0_18_18 = e3)) | (all_0_13_13 = e1 & ~ (all_0_18_18 = e2))
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (197), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (198) all_0_8_8 = e1 & ~ (all_0_18_18 = e3)
% 10.80/2.98 |
% 10.80/2.98 | Applying alpha-rule on (198) yields:
% 10.80/2.98 | (199) all_0_8_8 = e1
% 10.80/2.98 | (200) ~ (all_0_18_18 = e3)
% 10.80/2.98 |
% 10.80/2.98 | Equations (199) can reduce 98 to:
% 10.80/2.98 | (712) ~ (all_0_16_16 = e1)
% 10.80/2.98 |
% 10.80/2.98 | Simplifying 712 yields:
% 10.80/2.98 | (340) ~ (all_0_16_16 = e1)
% 10.80/2.98 |
% 10.80/2.98 | From (199)(199) and (52) follows:
% 10.80/2.98 | (1554) op(e1, e1) = all_0_4_4
% 10.80/2.98 |
% 10.80/2.98 | From (199) and (63) follows:
% 10.80/2.98 | (1555) op(e1, e3) = all_0_5_5
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (514), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (518) all_0_9_9 = e2
% 10.80/2.98 |
% 10.80/2.98 | Equations (518) can reduce 193 to:
% 10.80/2.98 | (398) ~ (e3 = e2)
% 10.80/2.98 |
% 10.80/2.98 | Simplifying 398 yields:
% 10.80/2.98 | (126) ~ (e3 = e2)
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (56), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (566) all_0_11_11 = e3
% 10.80/2.98 |
% 10.80/2.98 | Equations (566) can reduce 507 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (507) ~ (all_0_11_11 = e3)
% 10.80/2.98 | (1562) all_0_15_15 = e3 | all_0_19_19 = e3 | all_0_23_23 = e3
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (1562), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (478) all_0_15_15 = e3
% 10.80/2.98 |
% 10.80/2.98 | Equations (478) can reduce 858 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (858) ~ (all_0_15_15 = e3)
% 10.80/2.98 | (1566) all_0_19_19 = e3 | all_0_23_23 = e3
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (1566), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (301) all_0_19_19 = e3
% 10.80/2.98 |
% 10.80/2.98 | Equations (301) can reduce 10 to:
% 10.80/2.98 | (289) ~ (all_0_16_16 = e3)
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (154), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (286) all_0_16_16 = e3
% 10.80/2.98 |
% 10.80/2.98 | Equations (286) can reduce 289 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (289) ~ (all_0_16_16 = e3)
% 10.80/2.98 | (723) all_0_16_16 = e2 | all_0_16_16 = e1 | all_0_16_16 = e0
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (723), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (371) all_0_16_16 = e2
% 10.80/2.98 |
% 10.80/2.98 | From (371) and (49) follows:
% 10.80/2.98 | (1574) op(e1, e3) = e2
% 10.80/2.98 |
% 10.80/2.98 | Instantiating formula (85) with e1, e3, e2, all_0_5_5 and discharging atoms op(e1, e3) = all_0_5_5, op(e1, e3) = e2, yields:
% 10.80/2.98 | (376) all_0_5_5 = e2
% 10.80/2.98 |
% 10.80/2.98 | Instantiating formula (85) with e1, e1, all_0_4_4, e0 and discharging atoms op(e1, e1) = all_0_4_4, op(e1, e1) = e0, yields:
% 10.80/2.98 | (1576) all_0_4_4 = e0
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (73), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (1577) ~ (all_0_4_4 = e0)
% 10.80/2.98 |
% 10.80/2.98 | Equations (1576) can reduce 1577 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (1576) all_0_4_4 = e0
% 10.80/2.98 | (1580) ~ (all_0_5_5 = e2) | ~ (all_0_8_8 = e1)
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (1580), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (226) ~ (all_0_5_5 = e2)
% 10.80/2.98 |
% 10.80/2.98 | Equations (376) can reduce 226 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (376) all_0_5_5 = e2
% 10.80/2.98 | (268) ~ (all_0_8_8 = e1)
% 10.80/2.98 |
% 10.80/2.98 | Equations (199) can reduce 268 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (183) ~ (all_0_16_16 = e2)
% 10.80/2.98 | (745) all_0_16_16 = e1 | all_0_16_16 = e0
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (745), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (276) all_0_16_16 = e1
% 10.80/2.98 |
% 10.80/2.98 | Equations (276) can reduce 340 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (340) ~ (all_0_16_16 = e1)
% 10.80/2.98 | (756) all_0_16_16 = e0
% 10.80/2.98 |
% 10.80/2.98 | Equations (756) can reduce 1309 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (1003) ~ (all_0_19_19 = e3)
% 10.80/2.98 | (386) all_0_23_23 = e3
% 10.80/2.98 |
% 10.80/2.98 | Combining equations (386,352) yields a new equation:
% 10.80/2.98 | (382) e3 = e2
% 10.80/2.98 |
% 10.80/2.98 | Simplifying 382 yields:
% 10.80/2.98 | (298) e3 = e2
% 10.80/2.98 |
% 10.80/2.98 | Equations (298) can reduce 126 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (521) ~ (all_0_9_9 = e2)
% 10.80/2.98 | (522) all_0_10_10 = e2 | all_0_11_11 = e2
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (74), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (518) all_0_9_9 = e2
% 10.80/2.98 |
% 10.80/2.98 | Equations (518) can reduce 521 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (521) ~ (all_0_9_9 = e2)
% 10.80/2.98 | (1603) all_0_13_13 = e2 | all_0_17_17 = e2 | all_0_21_21 = e2
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (1603), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (1271) all_0_13_13 = e2
% 10.80/2.98 |
% 10.80/2.98 | Combining equations (1271,191) yields a new equation:
% 10.80/2.98 | (298) e3 = e2
% 10.80/2.98 |
% 10.80/2.98 | Equations (298) can reduce 126 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (1274) ~ (all_0_13_13 = e2)
% 10.80/2.98 | (1608) all_0_17_17 = e2 | all_0_21_21 = e2
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (1608), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (1426) all_0_17_17 = e2
% 10.80/2.98 |
% 10.80/2.98 | Equations (1426) can reduce 195 to:
% 10.80/2.98 | (398) ~ (e3 = e2)
% 10.80/2.98 |
% 10.80/2.98 | Simplifying 398 yields:
% 10.80/2.98 | (126) ~ (e3 = e2)
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (522), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (462) all_0_10_10 = e2
% 10.80/2.98 |
% 10.80/2.98 | Combining equations (563,462) yields a new equation:
% 10.80/2.98 | (382) e3 = e2
% 10.80/2.98 |
% 10.80/2.98 | Simplifying 382 yields:
% 10.80/2.98 | (298) e3 = e2
% 10.80/2.98 |
% 10.80/2.98 | Equations (298) can reduce 126 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (491) ~ (all_0_10_10 = e2)
% 10.80/2.98 | (254) all_0_11_11 = e2
% 10.80/2.98 |
% 10.80/2.98 | Equations (254) can reduce 343 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (1410) ~ (all_0_17_17 = e2)
% 10.80/2.98 | (251) all_0_21_21 = e2
% 10.80/2.98 |
% 10.80/2.98 | Equations (251) can reduce 356 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (203) all_0_13_13 = e1 & ~ (all_0_18_18 = e2)
% 10.80/2.98 |
% 10.80/2.98 | Applying alpha-rule on (203) yields:
% 10.80/2.98 | (204) all_0_13_13 = e1
% 10.80/2.98 | (205) ~ (all_0_18_18 = e2)
% 10.80/2.98 |
% 10.80/2.98 | Combining equations (191,204) yields a new equation:
% 10.80/2.98 | (328) e3 = e1
% 10.80/2.98 |
% 10.80/2.98 | Simplifying 328 yields:
% 10.80/2.98 | (206) e3 = e1
% 10.80/2.98 |
% 10.80/2.98 | Equations (206) can reduce 155 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (208) all_0_23_23 = e1 & ~ (all_0_18_18 = e0)
% 10.80/2.98 |
% 10.80/2.98 | Applying alpha-rule on (208) yields:
% 10.80/2.98 | (209) all_0_23_23 = e1
% 10.80/2.98 | (210) ~ (all_0_18_18 = e0)
% 10.80/2.98 |
% 10.80/2.98 | Combining equations (209,352) yields a new equation:
% 10.80/2.98 | (242) e2 = e1
% 10.80/2.98 |
% 10.80/2.98 | Equations (242) can reduce 24 to:
% 10.80/2.98 | (179) $false
% 10.80/2.98 |
% 10.80/2.98 |-The branch is then unsatisfiable
% 10.80/2.98 |-Branch two:
% 10.80/2.98 | (426) ~ (all_0_10_10 = e3)
% 10.80/2.98 | (1634) all_0_14_14 = e3 | all_0_18_18 = e3 | all_0_22_22 = e3
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (116), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (291) all_0_20_20 = e3
% 10.80/2.98 |
% 10.80/2.98 | Equations (291) can reduce 27 to:
% 10.80/2.98 | (638) ~ (all_0_22_22 = e3)
% 10.80/2.98 |
% 10.80/2.98 | Simplifying 638 yields:
% 10.80/2.98 | (639) ~ (all_0_22_22 = e3)
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (156), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (197) (all_0_8_8 = e1 & ~ (all_0_18_18 = e3)) | (all_0_13_13 = e1 & ~ (all_0_18_18 = e2))
% 10.80/2.98 |
% 10.80/2.98 +-Applying beta-rule and splitting (197), into two cases.
% 10.80/2.98 |-Branch one:
% 10.80/2.98 | (198) all_0_8_8 = e1 & ~ (all_0_18_18 = e3)
% 10.80/2.99 |
% 10.80/2.99 | Applying alpha-rule on (198) yields:
% 10.80/2.99 | (199) all_0_8_8 = e1
% 10.80/2.99 | (200) ~ (all_0_18_18 = e3)
% 10.80/2.99 |
% 10.80/2.99 | Equations (1305) can reduce 200 to:
% 10.80/2.99 | (546) ~ (e3 = e0)
% 10.80/2.99 |
% 10.80/2.99 | Simplifying 546 yields:
% 10.80/2.99 | (40) ~ (e3 = e0)
% 10.80/2.99 |
% 10.80/2.99 +-Applying beta-rule and splitting (1634), into two cases.
% 10.80/2.99 |-Branch one:
% 10.80/2.99 | (451) all_0_14_14 = e3
% 10.80/2.99 |
% 10.80/2.99 | Equations (451) can reduce 427 to:
% 10.80/2.99 | (179) $false
% 10.80/2.99 |
% 10.80/2.99 |-The branch is then unsatisfiable
% 10.80/2.99 |-Branch two:
% 10.80/2.99 | (427) ~ (all_0_14_14 = e3)
% 10.80/2.99 | (1647) all_0_18_18 = e3 | all_0_22_22 = e3
% 10.80/2.99 |
% 10.80/2.99 +-Applying beta-rule and splitting (1647), into two cases.
% 10.80/2.99 |-Branch one:
% 10.80/2.99 | (297) all_0_18_18 = e3
% 10.80/2.99 |
% 10.80/2.99 | Combining equations (297,1305) yields a new equation:
% 10.80/2.99 | (552) e3 = e0
% 10.80/2.99 |
% 10.80/2.99 | Simplifying 552 yields:
% 10.80/2.99 | (257) e3 = e0
% 10.80/2.99 |
% 10.80/2.99 | Equations (257) can reduce 40 to:
% 10.80/2.99 | (179) $false
% 10.80/2.99 |
% 10.80/2.99 |-The branch is then unsatisfiable
% 10.80/2.99 |-Branch two:
% 10.80/2.99 | (200) ~ (all_0_18_18 = e3)
% 10.80/2.99 | (728) all_0_22_22 = e3
% 10.80/2.99 |
% 10.80/2.99 | Equations (728) can reduce 639 to:
% 10.80/2.99 | (179) $false
% 10.80/2.99 |
% 10.80/2.99 |-The branch is then unsatisfiable
% 10.80/2.99 |-Branch two:
% 10.80/2.99 | (203) all_0_13_13 = e1 & ~ (all_0_18_18 = e2)
% 10.80/2.99 |
% 10.80/2.99 | Applying alpha-rule on (203) yields:
% 10.80/2.99 | (204) all_0_13_13 = e1
% 10.80/2.99 | (205) ~ (all_0_18_18 = e2)
% 10.80/2.99 |
% 10.80/2.99 | Combining equations (191,204) yields a new equation:
% 10.80/2.99 | (328) e3 = e1
% 10.80/2.99 |
% 10.80/2.99 | Simplifying 328 yields:
% 10.80/2.99 | (206) e3 = e1
% 10.80/2.99 |
% 10.80/2.99 | Equations (206) can reduce 155 to:
% 10.80/2.99 | (179) $false
% 10.80/2.99 |
% 10.80/2.99 |-The branch is then unsatisfiable
% 10.80/2.99 |-Branch two:
% 10.80/2.99 | (208) all_0_23_23 = e1 & ~ (all_0_18_18 = e0)
% 10.80/2.99 |
% 10.80/2.99 | Applying alpha-rule on (208) yields:
% 10.80/2.99 | (209) all_0_23_23 = e1
% 10.80/2.99 | (210) ~ (all_0_18_18 = e0)
% 10.80/2.99 |
% 10.80/2.99 | Combining equations (209,352) yields a new equation:
% 10.80/2.99 | (242) e2 = e1
% 10.80/2.99 |
% 10.80/2.99 | Equations (242) can reduce 24 to:
% 10.80/2.99 | (179) $false
% 10.80/2.99 |
% 10.80/2.99 |-The branch is then unsatisfiable
% 10.80/2.99 |-Branch two:
% 10.80/2.99 | (314) ~ (all_0_20_20 = e3)
% 10.80/2.99 | (937) all_0_21_21 = e3 | all_0_22_22 = e3 | all_0_23_23 = e3
% 10.80/2.99 |
% 10.80/2.99 +-Applying beta-rule and splitting (937), into two cases.
% 10.80/2.99 |-Branch one:
% 10.80/2.99 | (716) all_0_21_21 = e3
% 10.80/2.99 |
% 10.80/2.99 | Equations (716) can reduce 687 to:
% 10.80/2.99 | (179) $false
% 10.80/2.99 |
% 10.80/2.99 |-The branch is then unsatisfiable
% 10.80/2.99 |-Branch two:
% 10.80/2.99 | (687) ~ (all_0_21_21 = e3)
% 10.80/2.99 | (945) all_0_22_22 = e3 | all_0_23_23 = e3
% 10.80/2.99 |
% 10.80/2.99 +-Applying beta-rule and splitting (945), into two cases.
% 10.80/2.99 |-Branch one:
% 10.80/2.99 | (728) all_0_22_22 = e3
% 10.80/2.99 |
% 10.80/2.99 | Equations (728) can reduce 639 to:
% 10.80/2.99 | (179) $false
% 10.80/2.99 |
% 10.80/2.99 |-The branch is then unsatisfiable
% 10.80/2.99 |-Branch two:
% 10.80/2.99 | (639) ~ (all_0_22_22 = e3)
% 10.80/2.99 | (386) all_0_23_23 = e3
% 10.80/2.99 |
% 10.80/2.99 | Combining equations (386,352) yields a new equation:
% 10.80/2.99 | (382) e3 = e2
% 10.80/2.99 |
% 10.80/2.99 | Simplifying 382 yields:
% 10.80/2.99 | (298) e3 = e2
% 10.80/2.99 |
% 10.80/2.99 | Equations (298) can reduce 126 to:
% 10.80/2.99 | (179) $false
% 10.80/2.99 |
% 10.80/2.99 |-The branch is then unsatisfiable
% 10.80/2.99 |-Branch two:
% 10.80/2.99 | (379) all_0_18_18 = e3 & ~ (all_0_8_8 = e1)
% 10.80/2.99 |
% 10.80/2.99 | Applying alpha-rule on (379) yields:
% 10.80/2.99 | (297) all_0_18_18 = e3
% 10.80/2.99 | (268) ~ (all_0_8_8 = e1)
% 10.80/2.99 |
% 10.80/2.99 | Combining equations (1305,297) yields a new equation:
% 10.80/2.99 | (257) e3 = e0
% 10.80/2.99 |
% 10.80/2.99 | Equations (257) can reduce 40 to:
% 10.80/2.99 | (179) $false
% 10.80/2.99 |
% 10.80/2.99 |-The branch is then unsatisfiable
% 10.80/2.99 |-Branch two:
% 10.80/2.99 | (385) all_0_23_23 = e3 & ~ (all_0_8_8 = e0)
% 10.80/2.99 |
% 10.80/2.99 | Applying alpha-rule on (385) yields:
% 10.80/2.99 | (386) all_0_23_23 = e3
% 10.80/2.99 | (377) ~ (all_0_8_8 = e0)
% 10.80/2.99 |
% 10.80/2.99 | Combining equations (386,352) yields a new equation:
% 10.80/2.99 | (382) e3 = e2
% 10.80/2.99 |
% 10.80/2.99 | Simplifying 382 yields:
% 10.80/2.99 | (298) e3 = e2
% 10.80/2.99 |
% 10.80/2.99 | Equations (298) can reduce 126 to:
% 10.80/2.99 | (179) $false
% 10.80/2.99 |
% 10.80/2.99 |-The branch is then unsatisfiable
% 10.80/2.99 |-Branch two:
% 10.80/2.99 | (1690) all_0_3_3 = e3
% 10.80/2.99 | (210) ~ (all_0_18_18 = e0)
% 10.80/2.99 |
% 10.80/2.99 | Equations (1305) can reduce 210 to:
% 10.80/2.99 | (179) $false
% 10.80/2.99 |
% 10.80/2.99 |-The branch is then unsatisfiable
% 10.80/2.99 % SZS output end Proof for theBenchmark
% 10.80/2.99
% 10.80/2.99 2435ms
%------------------------------------------------------------------------------