TSTP Solution File: ALG056+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG056+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 15:33:56 EDT 2022
% Result : Theorem 8.31s 2.54s
% Output : Proof 31.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ALG056+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.32 % Computer : n024.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Wed Jun 8 08:25:19 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.51/0.57 ____ _
% 0.51/0.57 ___ / __ \_____(_)___ ________ __________
% 0.51/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.57
% 0.51/0.57 A Theorem Prover for First-Order Logic
% 0.51/0.58 (ePrincess v.1.0)
% 0.51/0.58
% 0.51/0.58 (c) Philipp Rümmer, 2009-2015
% 0.51/0.58 (c) Peter Backeman, 2014-2015
% 0.51/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.58 Bug reports to peter@backeman.se
% 0.51/0.58
% 0.51/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.58
% 0.51/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.51/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.70/1.20 Prover 0: Preprocessing ...
% 4.62/1.61 Prover 0: Constructing countermodel ...
% 8.31/2.54 Prover 0: proved (1912ms)
% 8.31/2.54
% 8.31/2.54 No countermodel exists, formula is valid
% 8.31/2.54 % SZS status Theorem for theBenchmark
% 8.31/2.54
% 8.31/2.54 Generating proof ... found it (size 16572)
% 26.14/7.26
% 26.14/7.26 % SZS output start Proof for theBenchmark
% 26.14/7.26 Assumed formulas after preprocessing and simplification:
% 26.14/7.26 | (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] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : ? [v31] : ? [v32] : ? [v33] : ? [v34] : ? [v35] : ? [v36] : ? [v37] : ? [v38] : ? [v39] : ? [v40] : ? [v41] : ? [v42] : ? [v43] : ? [v44] : ? [v45] : ? [v46] : ? [v47] : ? [v48] : ? [v49] : ? [v50] : ? [v51] : ? [v52] : ? [v53] : ? [v54] : ? [v55] : ? [v56] : ? [v57] : ? [v58] : ? [v59] : ( ~ (v20 = v19) & ~ (v20 = v18) & ~ (v20 = v17) & ~ (v20 = v16) & ~ (v20 = v12) & ~ (v20 = v8) & ~ (v20 = v3) & ~ (v20 = e0) & ~ (v19 = v18) & ~ (v19 = v17) & ~ (v19 = v15) & ~ (v19 = v7) & ~ (v19 = v2) & ~ (v19 = e4) & ~ (v19 = e0) & ~ (v18 = v17) & ~ (v18 = v14) & ~ (v18 = v11) & ~ (v18 = v6) & ~ (v18 = v1) & ~ (v18 = e0) & ~ (v17 = v13) & ~ (v17 = v10) & ~ (v17 = v5) & ~ (v17 = v0) & ~ (v17 = e0) & ~ (v16 = v15) & ~ (v16 = v14) & ~ (v16 = v13) & ~ (v16 = v12) & ~ (v16 = v8) & ~ (v16 = v3) & ~ (v16 = e1) & ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = v7) & ~ (v15 = v2) & ~ (v15 = e4) & ~ (v15 = e1) & ~ (v14 = v13) & ~ (v14 = v11) & ~ (v14 = v6) & ~ (v14 = v1) & ~ (v14 = e1) & ~ (v13 = v10) & ~ (v13 = v5) & ~ (v13 = v0) & ~ (v13 = e1) & ~ (v12 = v11) & ~ (v12 = v10) & ~ (v12 = v8) & ~ (v12 = v3) & ~ (v12 = e4) & ~ (v12 = e3) & ~ (v11 = v10) & ~ (v11 = v6) & ~ (v11 = v1) & ~ (v11 = e4) & ~ (v11 = e3) & ~ (v10 = v5) & ~ (v10 = v0) & ~ (v10 = e4) & ~ (v10 = e3) & ~ (v9 = v8) & ~ (v9 = v7) & ~ (v9 = v6) & ~ (v9 = v5) & ~ (v9 = v4) & ~ (v9 = e3) & ~ (v9 = e1) & ~ (v9 = e0) & ~ (v8 = v7) & ~ (v8 = v6) & ~ (v8 = v5) & ~ (v8 = v3) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v2) & ~ (v7 = e4) & ~ (v6 = v5) & ~ (v6 = v1) & ~ (v5 = v0) & ~ (v4 = v3) & ~ (v4 = v2) & ~ (v4 = v1) & ~ (v4 = v0) & ~ (v4 = e3) & ~ (v4 = e1) & ~ (v4 = e0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = v0) & ~ (v2 = e4) & ~ (v1 = v0) & ~ (e4 = e3) & ~ (e4 = e2) & ~ (e4 = e1) & ~ (e4 = e0) & ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ (e1 = e0) & op(unit, e4) = e4 & op(unit, e3) = e3 & op(unit, e2) = e2 & op(unit, e1) = e1 & op(unit, e0) = e0 & op(e4, v20) = v54 & op(e4, v19) = v45 & op(e4, v18) = v37 & op(e4, v17) = v28 & op(e4, v9) = v59 & op(e4, v4) = v57 & op(e4, unit) = e4 & op(e4, e4) = e0 & op(e4, e3) = v20 & op(e4, e2) = v19 & op(e4, e1) = v18 & op(e4, e0) = v17 & op(e3, v20) = v55 & op(e3, v16) = v53 & op(e3, v15) = v43 & op(e3, v14) = v35 & op(e3, v13) = v26 & op(e3, v12) = v52 & op(e3, v8) = v50 & op(e3, v3) = v48 & op(e3, unit) = e3 & op(e3, e4) = e1 & op(e3, e3) = v16 & op(e3, e2) = v15 & op(e3, e1) = v14 & op(e3, e0) = v13 & op(e2, v19) = v46 & op(e2, v15) = v44 & op(e2, v12) = v51 & op(e2, v11) = v33 & op(e2, v10) = v24 & op(e2, v7) = v42 & op(e2, v2) = v40 & op(e2, unit) = e2 & op(e2, e4) = e3 & op(e2, e3) = v12 & op(e2, e2) = e4 & op(e2, e1) = v11 & op(e2, e0) = v10 & op(e1, v18) = v38 & op(e1, v14) = v36 & op(e1, v11) = v34 & op(e1, v9) = v58 & op(e1, v8) = v49 & op(e1, v7) = v41 & op(e1, v6) = v32 & op(e1, v5) = v22 & op(e1, v1) = v31 & op(e1, unit) = e1 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = v7 & op(e1, e1) = v6 & op(e1, e0) = v5 & op(e0, v17) = v29 & op(e0, v13) = v27 & op(e0, v10) = v25 & op(e0, v5) = v23 & op(e0, v4) = v56 & op(e0, v3) = v47 & op(e0, v2) = v39 & op(e0, v1) = v30 & op(e0, v0) = v21 & op(e0, unit) = e0 & op(e0, e4) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & ! [v60] : ! [v61] : ! [v62] : ! [v63] : (v61 = v60 | ~ (op(v63, v62) = v61) | ~ (op(v63, v62) = v60)) & (v20 = e4 | v20 = e3 | v20 = e2 | v20 = e1) & (v20 = e4 | v18 = e4 | v17 = e4) & (v20 = e4 | v16 = e4 | v8 = e4 | v3 = e4) & (v20 = e3 | v19 = e3 | v18 = e3 | v17 = e3) & (v20 = e3 | v16 = e3 | v8 = e3 | v3 = e3) & (v20 = e2 | v19 = e2 | v18 = e2 | v17 = e2) & (v20 = e2 | v16 = e2 | v12 = e2 | v8 = e2 | v3 = e2) & (v20 = e2 | (v59 = e1 & ~ (v58 = e4)) | (v57 = e0 & ~ (v56 = e4)) | (v18 = e3 & ~ (v14 = e4))) & (v20 = e1 | v19 = e1 | v18 = e1 | v17 = e1) & (v20 = e1 | v12 = e1 | v8 = e1 | v3 = e1) & (v19 = e3 | v19 = e2 | v19 = e1) & (v19 = e3 | v15 = e3 | v7 = e3 | v2 = e3) & (v19 = e2 | v15 = e2 | v7 = e2 | v2 = e2) & (v19 = e1 | v7 = e1 | v2 = e1) & (v18 = e4 | v18 = e3 | v18 = e2 | v18 = e1) & (v18 = e4 | v14 = e4 | v6 = e4 | v1 = e4) & (v18 = e3 | v14 = e3 | v6 = e3 | v1 = e3) & (v18 = e2 | v14 = e2 | v11 = e2 | v6 = e2 | v1 = e2) & (v18 = e1 | v11 = e1 | v6 = e1 | v1 = e1) & (v17 = e4 | v17 = e3 | v17 = e2 | v17 = e1) & (v17 = e4 | v13 = e4 | v5 = e4 | v0 = e4) & (v17 = e3 | v13 = e3 | v5 = e3 | v0 = e3) & (v17 = e2 | v13 = e2 | v10 = e2 | v5 = e2 | v0 = e2) & (v17 = e1 | v10 = e1 | v5 = e1 | v0 = e1) & (v16 = e4 | v16 = e3 | v16 = e2 | v16 = e0) & (v16 = e4 | v14 = e4 | v13 = e4) & (v16 = e3 | v15 = e3 | v14 = e3 | v13 = e3) & (v16 = e2 | v15 = e2 | v14 = e2 | v13 = e2) & (v16 = e0 | v15 = e0 | v14 = e0 | v13 = e0) & (v16 = e0 | v12 = e0 | v8 = e0 | v3 = e0) & (v15 = e3 | v15 = e2 | v15 = e0) & (v15 = e0 | v7 = e0 | v2 = e0) & (v14 = e4 | v14 = e3 | v14 = e2 | v14 = e0) & (v14 = e0 | v11 = e0 | v6 = e0 | v1 = e0) & (v13 = e4 | v13 = e3 | v13 = e2 | v13 = e0) & (v13 = e0 | v10 = e0 | v5 = e0 | v0 = e0) & (v12 = e2 | v12 = e1 | v12 = e0) & (v12 = e2 | v11 = e2 | v10 = e2) & (v12 = e1 | v11 = e1 | v10 = e1) & (v12 = e0 | v11 = e0 | v10 = e0) & (v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e4 | v9 = e2) & (v9 = e4 | v8 = e4 | v6 = e4 | v5 = e4) & (v9 = e4 | v4 = e4) & (v9 = e2 | v8 = e2 | v7 = e2 | v6 = e2 | v5 = e2) & (v9 = e2 | v4 = e2) & (v8 = e4 | v8 = e3 | v8 = e2 | v8 = e1 | v8 = e0) & (v8 = e3 | v7 = e3 | v6 = e3 | v5 = e3) & (v8 = e1 | v7 = e1 | v6 = e1 | v5 = e1) & (v8 = e0 | v7 = e0 | v6 = e0 | v5 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e4 | v6 = e3 | v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e4 | v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & (v4 = e4 | v4 = e2) & (v4 = e4 | v3 = e4 | v1 = e4 | v0 = e4) & (v4 = e2 | v3 = e2 | v2 = e2 | v1 = e2 | v0 = e2) & (v3 = e4 | v3 = e3 | v3 = e2 | v3 = e1 | v3 = e0) & (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & (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 = e4 | v1 = e3 | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e4 | v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0) & (v0 = e4 | (v16 = e0 & v0 = e3 & ~ (v13 = e3)) | (v16 = e0 & v0 = e3 & ~ (v3 = e0)) | (v6 = e0 & v0 = e1 & ~ (v5 = e1)) | (v6 = e0 & v0 = e1 & ~ (v1 = e0))) & (unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0) & ((v55 = e4 & ~ (v54 = e3)) | (v52 = e2 & ~ (v51 = e3)) | (v50 = e1 & ~ (v49 = e3)) | (v48 = e0 & ~ (v47 = e3))) & ((v46 = e4 & ~ (v45 = e2)) | (v44 = e3 & ~ (v43 = e2)) | (v42 = e1 & ~ (v41 = e2)) | (v40 = e0 & ~ (v39 = e2))) & ((v38 = e4 & ~ (v37 = e1)) | (v36 = e3 & ~ (v35 = e1)) | (v34 = e2 & ~ (v33 = e1)) | (v31 = e0 & ~ (v30 = e1))) & ((v29 = e4 & ~ (v28 = e0)) | (v27 = e3 & ~ (v26 = e0)) | (v25 = e2 & ~ (v24 = e0)) | (v23 = e1 & ~ (v22 = e0))))
% 26.36/7.32 | 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, all_0_24_24, all_0_25_25, all_0_26_26, all_0_27_27, all_0_28_28, all_0_29_29, all_0_30_30, all_0_31_31, all_0_32_32, all_0_33_33, all_0_34_34, all_0_35_35, all_0_36_36, all_0_37_37, all_0_38_38, all_0_39_39, all_0_40_40, all_0_41_41, all_0_42_42, all_0_43_43, all_0_44_44, all_0_45_45, all_0_46_46, all_0_47_47, all_0_48_48, all_0_49_49, all_0_50_50, all_0_51_51, all_0_52_52, all_0_53_53, all_0_54_54, all_0_55_55, all_0_56_56, all_0_57_57, all_0_58_58, all_0_59_59 yields:
% 26.36/7.32 | (1) ~ (all_0_39_39 = all_0_40_40) & ~ (all_0_39_39 = all_0_41_41) & ~ (all_0_39_39 = all_0_42_42) & ~ (all_0_39_39 = all_0_43_43) & ~ (all_0_39_39 = all_0_47_47) & ~ (all_0_39_39 = all_0_51_51) & ~ (all_0_39_39 = all_0_56_56) & ~ (all_0_39_39 = e0) & ~ (all_0_40_40 = all_0_41_41) & ~ (all_0_40_40 = all_0_42_42) & ~ (all_0_40_40 = all_0_44_44) & ~ (all_0_40_40 = all_0_52_52) & ~ (all_0_40_40 = all_0_57_57) & ~ (all_0_40_40 = e4) & ~ (all_0_40_40 = e0) & ~ (all_0_41_41 = all_0_42_42) & ~ (all_0_41_41 = all_0_45_45) & ~ (all_0_41_41 = all_0_48_48) & ~ (all_0_41_41 = all_0_53_53) & ~ (all_0_41_41 = all_0_58_58) & ~ (all_0_41_41 = e0) & ~ (all_0_42_42 = all_0_46_46) & ~ (all_0_42_42 = all_0_49_49) & ~ (all_0_42_42 = all_0_54_54) & ~ (all_0_42_42 = all_0_59_59) & ~ (all_0_42_42 = e0) & ~ (all_0_43_43 = all_0_44_44) & ~ (all_0_43_43 = all_0_45_45) & ~ (all_0_43_43 = all_0_46_46) & ~ (all_0_43_43 = all_0_47_47) & ~ (all_0_43_43 = all_0_51_51) & ~ (all_0_43_43 = all_0_56_56) & ~ (all_0_43_43 = e1) & ~ (all_0_44_44 = all_0_45_45) & ~ (all_0_44_44 = all_0_46_46) & ~ (all_0_44_44 = all_0_52_52) & ~ (all_0_44_44 = all_0_57_57) & ~ (all_0_44_44 = e4) & ~ (all_0_44_44 = e1) & ~ (all_0_45_45 = all_0_46_46) & ~ (all_0_45_45 = all_0_48_48) & ~ (all_0_45_45 = all_0_53_53) & ~ (all_0_45_45 = all_0_58_58) & ~ (all_0_45_45 = e1) & ~ (all_0_46_46 = all_0_49_49) & ~ (all_0_46_46 = all_0_54_54) & ~ (all_0_46_46 = all_0_59_59) & ~ (all_0_46_46 = e1) & ~ (all_0_47_47 = all_0_48_48) & ~ (all_0_47_47 = all_0_49_49) & ~ (all_0_47_47 = all_0_51_51) & ~ (all_0_47_47 = all_0_56_56) & ~ (all_0_47_47 = e4) & ~ (all_0_47_47 = e3) & ~ (all_0_48_48 = all_0_49_49) & ~ (all_0_48_48 = all_0_53_53) & ~ (all_0_48_48 = all_0_58_58) & ~ (all_0_48_48 = e4) & ~ (all_0_48_48 = e3) & ~ (all_0_49_49 = all_0_54_54) & ~ (all_0_49_49 = all_0_59_59) & ~ (all_0_49_49 = e4) & ~ (all_0_49_49 = e3) & ~ (all_0_50_50 = all_0_51_51) & ~ (all_0_50_50 = all_0_52_52) & ~ (all_0_50_50 = all_0_53_53) & ~ (all_0_50_50 = all_0_54_54) & ~ (all_0_50_50 = all_0_55_55) & ~ (all_0_50_50 = e3) & ~ (all_0_50_50 = e1) & ~ (all_0_50_50 = e0) & ~ (all_0_51_51 = all_0_52_52) & ~ (all_0_51_51 = all_0_53_53) & ~ (all_0_51_51 = all_0_54_54) & ~ (all_0_51_51 = all_0_56_56) & ~ (all_0_52_52 = all_0_53_53) & ~ (all_0_52_52 = all_0_54_54) & ~ (all_0_52_52 = all_0_57_57) & ~ (all_0_52_52 = e4) & ~ (all_0_53_53 = all_0_54_54) & ~ (all_0_53_53 = all_0_58_58) & ~ (all_0_54_54 = all_0_59_59) & ~ (all_0_55_55 = all_0_56_56) & ~ (all_0_55_55 = all_0_57_57) & ~ (all_0_55_55 = all_0_58_58) & ~ (all_0_55_55 = all_0_59_59) & ~ (all_0_55_55 = e3) & ~ (all_0_55_55 = e1) & ~ (all_0_55_55 = e0) & ~ (all_0_56_56 = all_0_57_57) & ~ (all_0_56_56 = all_0_58_58) & ~ (all_0_56_56 = all_0_59_59) & ~ (all_0_57_57 = all_0_58_58) & ~ (all_0_57_57 = all_0_59_59) & ~ (all_0_57_57 = e4) & ~ (all_0_58_58 = all_0_59_59) & ~ (e4 = e3) & ~ (e4 = e2) & ~ (e4 = e1) & ~ (e4 = e0) & ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ (e1 = e0) & op(unit, e4) = e4 & op(unit, e3) = e3 & op(unit, e2) = e2 & op(unit, e1) = e1 & op(unit, e0) = e0 & op(e4, all_0_39_39) = all_0_5_5 & op(e4, all_0_40_40) = all_0_14_14 & op(e4, all_0_41_41) = all_0_22_22 & op(e4, all_0_42_42) = all_0_31_31 & op(e4, all_0_50_50) = all_0_0_0 & op(e4, all_0_55_55) = all_0_2_2 & op(e4, unit) = e4 & op(e4, e4) = e0 & op(e4, e3) = all_0_39_39 & op(e4, e2) = all_0_40_40 & op(e4, e1) = all_0_41_41 & op(e4, e0) = all_0_42_42 & op(e3, all_0_39_39) = all_0_4_4 & op(e3, all_0_43_43) = all_0_6_6 & op(e3, all_0_44_44) = all_0_16_16 & op(e3, all_0_45_45) = all_0_24_24 & op(e3, all_0_46_46) = all_0_33_33 & op(e3, all_0_47_47) = all_0_7_7 & op(e3, all_0_51_51) = all_0_9_9 & op(e3, all_0_56_56) = all_0_11_11 & op(e3, unit) = e3 & op(e3, e4) = e1 & op(e3, e3) = all_0_43_43 & op(e3, e2) = all_0_44_44 & op(e3, e1) = all_0_45_45 & op(e3, e0) = all_0_46_46 & op(e2, all_0_40_40) = all_0_13_13 & op(e2, all_0_44_44) = all_0_15_15 & op(e2, all_0_47_47) = all_0_8_8 & op(e2, all_0_48_48) = all_0_26_26 & op(e2, all_0_49_49) = all_0_35_35 & op(e2, all_0_52_52) = all_0_17_17 & op(e2, all_0_57_57) = all_0_19_19 & op(e2, unit) = e2 & op(e2, e4) = e3 & op(e2, e3) = all_0_47_47 & op(e2, e2) = e4 & op(e2, e1) = all_0_48_48 & op(e2, e0) = all_0_49_49 & op(e1, all_0_41_41) = all_0_21_21 & op(e1, all_0_45_45) = all_0_23_23 & op(e1, all_0_48_48) = all_0_25_25 & op(e1, all_0_50_50) = all_0_1_1 & op(e1, all_0_51_51) = all_0_10_10 & op(e1, all_0_52_52) = all_0_18_18 & op(e1, all_0_53_53) = all_0_27_27 & op(e1, all_0_54_54) = all_0_37_37 & op(e1, all_0_58_58) = all_0_28_28 & op(e1, unit) = e1 & op(e1, e4) = all_0_50_50 & op(e1, e3) = all_0_51_51 & op(e1, e2) = all_0_52_52 & op(e1, e1) = all_0_53_53 & op(e1, e0) = all_0_54_54 & op(e0, all_0_42_42) = all_0_30_30 & op(e0, all_0_46_46) = all_0_32_32 & op(e0, all_0_49_49) = all_0_34_34 & op(e0, all_0_54_54) = all_0_36_36 & op(e0, all_0_55_55) = all_0_3_3 & op(e0, all_0_56_56) = all_0_12_12 & op(e0, all_0_57_57) = all_0_20_20 & op(e0, all_0_58_58) = all_0_29_29 & op(e0, all_0_59_59) = all_0_38_38 & op(e0, unit) = e0 & op(e0, e4) = all_0_55_55 & op(e0, e3) = all_0_56_56 & op(e0, e2) = all_0_57_57 & op(e0, e1) = all_0_58_58 & op(e0, e0) = all_0_59_59 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) & (all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e2 | all_0_39_39 = e1) & (all_0_39_39 = e4 | all_0_41_41 = e4 | all_0_42_42 = e4) & (all_0_39_39 = e4 | all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4) & (all_0_39_39 = e3 | all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3) & (all_0_39_39 = e3 | all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3) & (all_0_39_39 = e2 | all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2) & (all_0_39_39 = e2 | all_0_43_43 = e2 | all_0_47_47 = e2 | all_0_51_51 = e2 | all_0_56_56 = e2) & (all_0_39_39 = e2 | (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))) & (all_0_39_39 = e1 | all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1) & (all_0_39_39 = e1 | all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1) & (all_0_40_40 = e3 | all_0_40_40 = e2 | all_0_40_40 = e1) & (all_0_40_40 = e3 | all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3) & (all_0_40_40 = e2 | all_0_44_44 = e2 | all_0_52_52 = e2 | all_0_57_57 = e2) & (all_0_40_40 = e1 | all_0_52_52 = e1 | all_0_57_57 = e1) & (all_0_41_41 = e4 | all_0_41_41 = e3 | all_0_41_41 = e2 | all_0_41_41 = e1) & (all_0_41_41 = e4 | all_0_45_45 = e4 | all_0_53_53 = e4 | all_0_58_58 = e4) & (all_0_41_41 = e3 | all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3) & (all_0_41_41 = e2 | all_0_45_45 = e2 | all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2) & (all_0_41_41 = e1 | all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1) & (all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e2 | all_0_42_42 = e1) & (all_0_42_42 = e4 | all_0_46_46 = e4 | all_0_54_54 = e4 | all_0_59_59 = e4) & (all_0_42_42 = e3 | all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3) & (all_0_42_42 = e2 | all_0_46_46 = e2 | all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2) & (all_0_42_42 = e1 | all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1) & (all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e2 | all_0_43_43 = e0) & (all_0_43_43 = e4 | all_0_45_45 = e4 | all_0_46_46 = e4) & (all_0_43_43 = e3 | all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3) & (all_0_43_43 = e2 | all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2) & (all_0_43_43 = e0 | all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0) & (all_0_43_43 = e0 | all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0) & (all_0_44_44 = e3 | all_0_44_44 = e2 | all_0_44_44 = e0) & (all_0_44_44 = e0 | all_0_52_52 = e0 | all_0_57_57 = e0) & (all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e2 | all_0_45_45 = e0) & (all_0_45_45 = e0 | all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0) & (all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e2 | all_0_46_46 = e0) & (all_0_46_46 = e0 | all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0) & (all_0_47_47 = e2 | all_0_47_47 = e1 | all_0_47_47 = e0) & (all_0_47_47 = e2 | all_0_48_48 = e2 | all_0_49_49 = e2) & (all_0_47_47 = e1 | all_0_48_48 = e1 | all_0_49_49 = e1) & (all_0_47_47 = e0 | all_0_48_48 = e0 | all_0_49_49 = e0) & (all_0_48_48 = e2 | all_0_48_48 = e1 | all_0_48_48 = e0) & (all_0_49_49 = e2 | all_0_49_49 = e1 | all_0_49_49 = e0) & (all_0_50_50 = e4 | all_0_50_50 = e2) & (all_0_50_50 = e4 | all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4) & (all_0_50_50 = e4 | all_0_55_55 = e4) & (all_0_50_50 = e2 | all_0_51_51 = e2 | all_0_52_52 = e2 | all_0_53_53 = e2 | all_0_54_54 = e2) & (all_0_50_50 = e2 | all_0_55_55 = e2) & (all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e2 | all_0_51_51 = e1 | all_0_51_51 = e0) & (all_0_51_51 = e3 | all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3) & (all_0_51_51 = e1 | all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1) & (all_0_51_51 = e0 | all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0) & (all_0_52_52 = e3 | all_0_52_52 = e2 | all_0_52_52 = e1 | all_0_52_52 = e0) & (all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e2 | all_0_53_53 = e1 | all_0_53_53 = e0) & (all_0_54_54 = e4 | all_0_54_54 = e3 | all_0_54_54 = e2 | all_0_54_54 = e1 | all_0_54_54 = e0) & (all_0_55_55 = e4 | all_0_55_55 = e2) & (all_0_55_55 = e4 | all_0_56_56 = e4 | all_0_58_58 = e4 | all_0_59_59 = e4) & (all_0_55_55 = e2 | all_0_56_56 = e2 | all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2) & (all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e2 | all_0_56_56 = e1 | all_0_56_56 = e0) & (all_0_56_56 = e3 | all_0_57_57 = e3 | all_0_58_58 = e3 | all_0_59_59 = e3) & (all_0_56_56 = e1 | all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1) & (all_0_56_56 = e0 | all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0) & (all_0_57_57 = e3 | all_0_57_57 = e2 | all_0_57_57 = e1 | all_0_57_57 = e0) & (all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e2 | all_0_58_58 = e1 | all_0_58_58 = e0) & (all_0_59_59 = e4 | all_0_59_59 = e3 | all_0_59_59 = e2 | all_0_59_59 = e1 | all_0_59_59 = e0) & (all_0_59_59 = e4 | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))) & (unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0) & ((all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3)) | (all_0_9_9 = e1 & ~ (all_0_10_10 = e3)) | (all_0_11_11 = e0 & ~ (all_0_12_12 = e3))) & ((all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e0 & ~ (all_0_20_20 = e2))) & ((all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1)) | (all_0_28_28 = e0 & ~ (all_0_29_29 = e1))) & ((all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0)) | (all_0_34_34 = e2 & ~ (all_0_35_35 = e0)) | (all_0_36_36 = e1 & ~ (all_0_37_37 = e0)))
% 26.36/7.34 |
% 26.36/7.34 | Applying alpha-rule on (1) yields:
% 26.36/7.34 | (2) op(unit, e4) = e4
% 26.36/7.34 | (3) ~ (all_0_47_47 = all_0_51_51)
% 26.36/7.34 | (4) ~ (all_0_48_48 = all_0_49_49)
% 26.36/7.34 | (5) op(e3, all_0_44_44) = all_0_16_16
% 26.36/7.34 | (6) ~ (e4 = e0)
% 26.36/7.34 | (7) op(e3, all_0_51_51) = all_0_9_9
% 26.36/7.34 | (8) all_0_40_40 = e1 | all_0_52_52 = e1 | all_0_57_57 = e1
% 26.36/7.34 | (9) all_0_44_44 = e0 | all_0_52_52 = e0 | all_0_57_57 = e0
% 26.36/7.34 | (10) ~ (all_0_44_44 = all_0_57_57)
% 26.36/7.34 | (11) ~ (all_0_55_55 = all_0_57_57)
% 26.36/7.34 | (12) ~ (all_0_51_51 = all_0_53_53)
% 26.36/7.34 | (13) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e2 | all_0_53_53 = e1 | all_0_53_53 = e0
% 26.36/7.34 | (14) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1)) | (all_0_28_28 = e0 & ~ (all_0_29_29 = e1))
% 26.36/7.34 | (15) ~ (all_0_40_40 = all_0_44_44)
% 26.36/7.34 | (16) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e2 | all_0_42_42 = e1
% 26.36/7.34 | (17) ~ (all_0_42_42 = all_0_59_59)
% 26.36/7.34 | (18) ~ (all_0_42_42 = all_0_46_46)
% 26.36/7.34 | (19) ~ (all_0_50_50 = all_0_54_54)
% 26.36/7.34 | (20) all_0_40_40 = e2 | all_0_44_44 = e2 | all_0_52_52 = e2 | all_0_57_57 = e2
% 26.36/7.34 | (21) all_0_51_51 = e3 | all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 26.36/7.34 | (22) all_0_43_43 = e3 | all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 26.36/7.34 | (23) op(e1, e4) = all_0_50_50
% 26.36/7.34 | (24) op(e4, all_0_40_40) = all_0_14_14
% 26.36/7.34 | (25) op(e4, e4) = e0
% 26.36/7.34 | (26) ~ (all_0_45_45 = e1)
% 26.36/7.34 | (27) op(e2, all_0_52_52) = all_0_17_17
% 26.36/7.34 | (28) op(e4, all_0_55_55) = all_0_2_2
% 26.36/7.34 | (29) op(e1, all_0_54_54) = all_0_37_37
% 26.36/7.34 | (30) op(e2, all_0_57_57) = all_0_19_19
% 26.36/7.34 | (31) op(e4, e2) = all_0_40_40
% 26.36/7.34 | (32) ~ (all_0_39_39 = all_0_51_51)
% 26.36/7.34 | (33) all_0_57_57 = e3 | all_0_57_57 = e2 | all_0_57_57 = e1 | all_0_57_57 = e0
% 26.36/7.34 | (34) ~ (e4 = e3)
% 26.36/7.34 | (35) op(e4, e3) = all_0_39_39
% 26.36/7.34 | (36) op(e1, all_0_53_53) = all_0_27_27
% 26.36/7.34 | (37) ~ (all_0_57_57 = all_0_58_58)
% 26.36/7.34 | (38) ~ (all_0_45_45 = all_0_46_46)
% 26.36/7.34 | (39) op(e0, unit) = e0
% 26.36/7.34 | (40) op(e2, e3) = all_0_47_47
% 26.36/7.34 | (41) ~ (all_0_50_50 = all_0_51_51)
% 26.36/7.34 | (42) op(e2, all_0_47_47) = all_0_8_8
% 26.36/7.34 | (43) ~ (all_0_55_55 = all_0_56_56)
% 26.36/7.34 | (44) all_0_43_43 = e4 | all_0_45_45 = e4 | all_0_46_46 = e4
% 26.36/7.35 | (45) ~ (all_0_44_44 = e4)
% 26.36/7.35 | (46) all_0_55_55 = e4 | all_0_55_55 = e2
% 26.36/7.35 | (47) all_0_43_43 = e2 | all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2
% 26.36/7.35 | (48) ~ (all_0_48_48 = all_0_53_53)
% 26.36/7.35 | (49) op(unit, e2) = e2
% 26.36/7.35 | (50) ~ (all_0_51_51 = all_0_54_54)
% 26.36/7.35 | (51) ~ (all_0_41_41 = all_0_45_45)
% 26.36/7.35 | (52) all_0_41_41 = e1 | all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 26.36/7.35 | (53) op(e1, e0) = all_0_54_54
% 26.36/7.35 | (54) ~ (all_0_50_50 = all_0_55_55)
% 26.36/7.35 | (55) ~ (all_0_50_50 = e3)
% 26.36/7.35 | (56) op(e2, e1) = all_0_48_48
% 26.36/7.35 | (57) ~ (e2 = e0)
% 26.36/7.35 | (58) all_0_50_50 = e2 | all_0_51_51 = e2 | all_0_52_52 = e2 | all_0_53_53 = e2 | all_0_54_54 = e2
% 26.36/7.35 | (59) ~ (all_0_48_48 = all_0_58_58)
% 26.36/7.35 | (60) ~ (all_0_51_51 = all_0_56_56)
% 26.36/7.35 | (61) op(e0, all_0_58_58) = all_0_29_29
% 26.36/7.35 | (62) unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0
% 26.36/7.35 | (63) op(e1, all_0_58_58) = all_0_28_28
% 26.36/7.35 | (64) all_0_51_51 = e0 | all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 26.36/7.35 | (65) ~ (all_0_45_45 = all_0_48_48)
% 26.36/7.35 | (66) ~ (e3 = e0)
% 26.36/7.35 | (67) ~ (all_0_50_50 = e0)
% 26.36/7.35 | (68) op(e2, all_0_40_40) = all_0_13_13
% 26.36/7.35 | (69) op(e3, all_0_43_43) = all_0_6_6
% 26.36/7.35 | (70) ~ (all_0_53_53 = all_0_58_58)
% 26.36/7.35 | (71) op(unit, e0) = e0
% 26.36/7.35 | (72) ~ (all_0_54_54 = all_0_59_59)
% 26.36/7.35 | (73) ~ (all_0_55_55 = all_0_58_58)
% 26.36/7.35 | (74) op(e3, all_0_46_46) = all_0_33_33
% 26.36/7.35 | (75) all_0_43_43 = e0 | all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 26.36/7.35 | (76) op(e1, all_0_48_48) = all_0_25_25
% 26.36/7.35 | (77) all_0_47_47 = e0 | all_0_48_48 = e0 | all_0_49_49 = e0
% 26.36/7.35 | (78) all_0_39_39 = e3 | all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 26.36/7.35 | (79) op(e0, all_0_59_59) = all_0_38_38
% 26.36/7.35 | (80) ~ (all_0_47_47 = all_0_49_49)
% 26.36/7.35 | (81) ~ (all_0_56_56 = all_0_58_58)
% 26.36/7.35 | (82) all_0_50_50 = e4 | all_0_50_50 = e2
% 26.36/7.35 | (83) all_0_47_47 = e1 | all_0_48_48 = e1 | all_0_49_49 = e1
% 26.36/7.35 | (84) ~ (all_0_43_43 = all_0_45_45)
% 26.36/7.35 | (85) op(unit, e3) = e3
% 26.36/7.35 | (86) ~ (all_0_50_50 = e1)
% 26.36/7.35 | (87) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e0 & ~ (all_0_20_20 = e2))
% 26.36/7.35 | (88) op(e0, all_0_49_49) = all_0_34_34
% 26.36/7.35 | (89) op(e0, all_0_46_46) = all_0_32_32
% 26.36/7.35 | (90) all_0_52_52 = e3 | all_0_52_52 = e2 | all_0_52_52 = e1 | all_0_52_52 = e0
% 26.36/7.35 | (91) op(e3, all_0_45_45) = all_0_24_24
% 26.36/7.35 | (92) op(e4, all_0_39_39) = all_0_5_5
% 26.36/7.35 | (93) all_0_59_59 = e4 | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 26.36/7.35 | (94) ~ (all_0_41_41 = all_0_42_42)
% 26.36/7.35 | (95) all_0_42_42 = e3 | all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 26.36/7.35 | (96) all_0_39_39 = e2 | all_0_43_43 = e2 | all_0_47_47 = e2 | all_0_51_51 = e2 | all_0_56_56 = e2
% 26.36/7.35 | (97) op(e4, all_0_42_42) = all_0_31_31
% 26.36/7.35 | (98) ~ (all_0_55_55 = e3)
% 26.36/7.35 | (99) all_0_39_39 = e1 | all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 26.36/7.36 | (100) ~ (all_0_39_39 = all_0_47_47)
% 26.36/7.36 | (101) ~ (all_0_39_39 = e0)
% 26.36/7.36 | (102) op(unit, e1) = e1
% 26.36/7.36 | (103) ~ (all_0_43_43 = all_0_46_46)
% 26.36/7.36 | (104) ~ (all_0_56_56 = all_0_57_57)
% 26.36/7.36 | (105) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e2 | all_0_45_45 = e0
% 26.36/7.36 | (106) ~ (all_0_46_46 = e1)
% 26.36/7.36 | (107) op(e3, e4) = e1
% 26.36/7.36 | (108) ~ (all_0_45_45 = all_0_58_58)
% 26.36/7.36 | (109) all_0_59_59 = e4 | all_0_59_59 = e3 | all_0_59_59 = e2 | all_0_59_59 = e1 | all_0_59_59 = e0
% 26.64/7.36 | (110) all_0_54_54 = e4 | all_0_54_54 = e3 | all_0_54_54 = e2 | all_0_54_54 = e1 | all_0_54_54 = e0
% 26.64/7.36 | (111) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0)) | (all_0_34_34 = e2 & ~ (all_0_35_35 = e0)) | (all_0_36_36 = e1 & ~ (all_0_37_37 = e0))
% 26.64/7.36 | (112) op(e1, all_0_41_41) = all_0_21_21
% 26.64/7.36 | (113) ~ (all_0_49_49 = all_0_59_59)
% 26.64/7.36 | (114) ~ (all_0_39_39 = all_0_40_40)
% 26.64/7.36 | (115) op(e2, e2) = e4
% 26.64/7.36 | (116) all_0_43_43 = e0 | all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 26.64/7.36 | (117) all_0_49_49 = e2 | all_0_49_49 = e1 | all_0_49_49 = e0
% 26.64/7.36 | (118) ~ (all_0_52_52 = all_0_54_54)
% 26.64/7.36 | (119) op(e0, all_0_55_55) = all_0_3_3
% 26.64/7.36 | (120) op(e0, all_0_57_57) = all_0_20_20
% 26.64/7.36 | (121) ~ (all_0_48_48 = e3)
% 26.64/7.36 | (122) ~ (all_0_44_44 = all_0_52_52)
% 26.64/7.36 | (123) ~ (all_0_50_50 = all_0_52_52)
% 26.64/7.36 | (124) all_0_47_47 = e2 | all_0_48_48 = e2 | all_0_49_49 = e2
% 26.64/7.36 | (125) all_0_40_40 = e3 | all_0_40_40 = e2 | all_0_40_40 = e1
% 26.64/7.36 | (126) ~ (all_0_50_50 = all_0_53_53)
% 26.65/7.36 | (127) all_0_42_42 = e1 | all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 26.65/7.36 | (128) ~ (all_0_45_45 = all_0_53_53)
% 26.65/7.36 | (129) all_0_48_48 = e2 | all_0_48_48 = e1 | all_0_48_48 = e0
% 26.65/7.36 | (130) all_0_50_50 = e4 | all_0_55_55 = e4
% 26.65/7.36 | (131) ~ (all_0_44_44 = e1)
% 26.65/7.36 | (132) ~ (e1 = e0)
% 26.65/7.36 | (133) all_0_40_40 = e3 | all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 26.65/7.36 | (134) op(e2, e0) = all_0_49_49
% 26.65/7.36 | (135) all_0_51_51 = e1 | all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 26.65/7.36 | (136) ~ (e3 = e1)
% 26.65/7.36 | (137) ~ (all_0_40_40 = all_0_52_52)
% 26.65/7.36 | (138) op(e0, all_0_54_54) = all_0_36_36
% 26.65/7.36 | (139) all_0_50_50 = e2 | all_0_55_55 = e2
% 26.65/7.36 | (140) ~ (all_0_57_57 = all_0_59_59)
% 26.65/7.36 | (141) ~ (e2 = e1)
% 26.65/7.36 | (142) op(e1, all_0_45_45) = all_0_23_23
% 26.65/7.36 | (143) ~ (all_0_57_57 = e4)
% 26.65/7.36 | (144) ~ (all_0_55_55 = all_0_59_59)
% 26.65/7.36 | (145) ~ (all_0_40_40 = all_0_42_42)
% 26.65/7.36 | (146) ~ (all_0_55_55 = e1)
% 26.65/7.36 | (147) ~ (all_0_40_40 = all_0_41_41)
% 26.65/7.36 | (148) op(e3, e2) = all_0_44_44
% 26.65/7.36 | (149) ~ (all_0_40_40 = all_0_57_57)
% 26.65/7.36 | (150) ~ (all_0_49_49 = e3)
% 26.65/7.36 | (151) op(e4, all_0_50_50) = all_0_0_0
% 26.65/7.37 | (152) op(e4, unit) = e4
% 26.65/7.37 | (153) op(e2, all_0_49_49) = all_0_35_35
% 26.65/7.37 | (154) ~ (all_0_51_51 = all_0_52_52)
% 26.65/7.37 | (155) all_0_47_47 = e2 | all_0_47_47 = e1 | all_0_47_47 = e0
% 26.65/7.37 | (156) ~ (all_0_58_58 = all_0_59_59)
% 26.65/7.37 | (157) ~ (all_0_41_41 = all_0_58_58)
% 26.65/7.37 | (158) all_0_41_41 = e4 | all_0_45_45 = e4 | all_0_53_53 = e4 | all_0_58_58 = e4
% 26.65/7.37 | (159) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e2 | all_0_43_43 = e0
% 26.65/7.37 | (160) op(e4, e1) = all_0_41_41
% 26.65/7.37 | (161) op(e0, e0) = all_0_59_59
% 26.65/7.37 | (162) ~ (all_0_49_49 = all_0_54_54)
% 26.65/7.37 | (163) all_0_55_55 = e4 | all_0_56_56 = e4 | all_0_58_58 = e4 | all_0_59_59 = e4
% 26.65/7.37 | (164) all_0_39_39 = e2 | all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 26.65/7.37 | (165) op(e2, all_0_44_44) = all_0_15_15
% 26.65/7.37 | (166) all_0_39_39 = e4 | all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 26.65/7.37 | (167) ~ (all_0_39_39 = all_0_43_43)
% 26.65/7.37 | (168) all_0_55_55 = e2 | all_0_56_56 = e2 | all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 26.65/7.37 | (169) ~ (all_0_42_42 = all_0_49_49)
% 26.65/7.37 | (170) ~ (all_0_43_43 = all_0_47_47)
% 26.65/7.37 | (171) op(e1, e3) = all_0_51_51
% 26.65/7.37 | (172) ~ (all_0_47_47 = e4)
% 26.65/7.37 | (173) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e2 | all_0_51_51 = e1 | all_0_51_51 = e0
% 26.65/7.37 | (174) ~ (all_0_44_44 = all_0_46_46)
% 26.65/7.37 | (175) ~ (all_0_55_55 = e0)
% 26.65/7.37 | (176) all_0_56_56 = e0 | all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 26.65/7.37 | (177) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e2 | all_0_39_39 = e1
% 26.65/7.37 | (178) all_0_39_39 = e3 | all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 26.65/7.37 | (179) all_0_42_42 = e4 | all_0_46_46 = e4 | all_0_54_54 = e4 | all_0_59_59 = e4
% 26.65/7.37 | (180) op(e2, e4) = e3
% 26.65/7.37 | (181) op(e0, e4) = all_0_55_55
% 26.65/7.37 | (182) all_0_45_45 = e0 | all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 26.65/7.37 | (183) op(e2, all_0_48_48) = all_0_26_26
% 26.65/7.37 | (184) ~ (all_0_39_39 = all_0_42_42)
% 26.65/7.37 | (185) ~ (all_0_56_56 = all_0_59_59)
% 26.65/7.37 | (186) all_0_39_39 = e2 | (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 26.65/7.37 | (187) all_0_41_41 = e2 | all_0_45_45 = e2 | all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 26.65/7.37 | (188) ~ (all_0_43_43 = all_0_56_56)
% 26.65/7.37 | (189) all_0_50_50 = e4 | all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 26.65/7.37 | (190) ~ (all_0_41_41 = all_0_48_48)
% 26.65/7.37 | (191) ~ (all_0_42_42 = all_0_54_54)
% 26.65/7.37 | (192) ~ (all_0_48_48 = e4)
% 26.65/7.37 | (193) all_0_44_44 = e3 | all_0_44_44 = e2 | all_0_44_44 = e0
% 26.65/7.37 | (194) all_0_56_56 = e1 | all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 26.65/7.37 | (195) op(e1, all_0_52_52) = all_0_18_18
% 26.65/7.37 | (196) op(e4, all_0_41_41) = all_0_22_22
% 26.65/7.37 | (197) op(e3, e1) = all_0_45_45
% 26.65/7.38 | (198) ~ (all_0_46_46 = all_0_49_49)
% 26.65/7.38 | (199) ~ (all_0_42_42 = e0)
% 26.65/7.38 | (200) op(e3, all_0_39_39) = all_0_4_4
% 26.65/7.38 | (201) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 26.65/7.38 | (202) ~ (all_0_49_49 = e4)
% 26.65/7.38 | (203) op(e1, e2) = all_0_52_52
% 26.65/7.38 | (204) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e2 | all_0_58_58 = e1 | all_0_58_58 = e0
% 26.65/7.38 | (205) op(e0, all_0_56_56) = all_0_12_12
% 26.65/7.38 | (206) ~ (all_0_46_46 = all_0_59_59)
% 26.65/7.38 | (207) op(e0, e2) = all_0_57_57
% 26.65/7.38 | (208) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e2 | all_0_56_56 = e1 | all_0_56_56 = e0
% 26.65/7.38 | (209) all_0_42_42 = e2 | all_0_46_46 = e2 | all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 26.65/7.38 | (210) all_0_39_39 = e1 | all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1
% 26.65/7.38 | (211) op(e1, all_0_50_50) = all_0_1_1
% 26.65/7.38 | (212) ~ (all_0_39_39 = all_0_56_56)
% 26.65/7.38 | (213) ~ (all_0_52_52 = all_0_53_53)
% 26.65/7.38 | (214) ~ (all_0_41_41 = all_0_53_53)
% 26.65/7.38 | (215) ~ (all_0_46_46 = all_0_54_54)
% 26.65/7.38 | (216) op(e1, all_0_51_51) = all_0_10_10
% 26.65/7.38 | (217) all_0_41_41 = e4 | all_0_41_41 = e3 | all_0_41_41 = e2 | all_0_41_41 = e1
% 26.65/7.38 | (218) ~ (all_0_47_47 = all_0_56_56)
% 26.65/7.38 | (219) all_0_41_41 = e3 | all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 26.65/7.38 | (220) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e2 | all_0_46_46 = e0
% 26.65/7.38 | (221) all_0_46_46 = e0 | all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 26.65/7.38 | (222) all_0_39_39 = e4 | all_0_41_41 = e4 | all_0_42_42 = e4
% 26.65/7.38 | (223) ~ (e3 = e2)
% 26.65/7.38 | (224) op(e4, e0) = all_0_42_42
% 26.65/7.38 | (225) ~ (all_0_47_47 = all_0_48_48)
% 26.65/7.38 | (226) ~ (all_0_39_39 = all_0_41_41)
% 26.65/7.38 | (227) op(e1, e1) = all_0_53_53
% 26.65/7.38 | (228) op(e0, e1) = all_0_58_58
% 26.65/7.38 | (229) ~ (all_0_44_44 = all_0_45_45)
% 26.65/7.38 | (230) ~ (all_0_52_52 = e4)
% 26.65/7.38 | (231) ~ (e4 = e2)
% 26.65/7.38 | (232) ~ (all_0_41_41 = e0)
% 26.65/7.38 | (233) ~ (all_0_40_40 = e4)
% 26.65/7.38 | (234) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3)) | (all_0_9_9 = e1 & ~ (all_0_10_10 = e3)) | (all_0_11_11 = e0 & ~ (all_0_12_12 = e3))
% 26.65/7.38 | (235) ~ (all_0_52_52 = all_0_57_57)
% 26.65/7.38 | (236) all_0_56_56 = e3 | all_0_57_57 = e3 | all_0_58_58 = e3 | all_0_59_59 = e3
% 26.65/7.38 | (237) op(e3, all_0_47_47) = all_0_7_7
% 26.65/7.38 | (238) ~ (all_0_40_40 = e0)
% 26.65/7.38 | (239) op(e3, all_0_56_56) = all_0_11_11
% 26.65/7.38 | (240) ~ (all_0_43_43 = all_0_51_51)
% 26.65/7.38 | (241) ~ (all_0_43_43 = all_0_44_44)
% 26.65/7.38 | (242) op(e3, e0) = all_0_46_46
% 26.65/7.38 | (243) op(e0, all_0_42_42) = all_0_30_30
% 26.65/7.39 | (244) op(e2, unit) = e2
% 26.65/7.39 | (245) op(e0, e3) = all_0_56_56
% 26.65/7.39 | (246) op(e1, unit) = e1
% 26.65/7.39 | (247) ~ (all_0_47_47 = e3)
% 26.65/7.39 | (248) op(e3, e3) = all_0_43_43
% 26.65/7.39 | (249) ~ (all_0_43_43 = e1)
% 26.65/7.39 | (250) op(e3, unit) = e3
% 26.65/7.39 | (251) ~ (e4 = e1)
% 26.65/7.39 | (252) ~ (all_0_53_53 = all_0_54_54)
% 26.65/7.39 |
% 26.65/7.39 +-Applying beta-rule and splitting (139), into two cases.
% 26.65/7.39 |-Branch one:
% 26.65/7.39 | (253) all_0_50_50 = e2
% 26.65/7.39 |
% 26.65/7.39 | Equations (253) can reduce 41 to:
% 26.65/7.39 | (254) ~ (all_0_51_51 = e2)
% 26.65/7.39 |
% 26.65/7.39 | Simplifying 254 yields:
% 26.65/7.39 | (255) ~ (all_0_51_51 = e2)
% 26.65/7.39 |
% 26.65/7.39 | Equations (253) can reduce 123 to:
% 26.65/7.39 | (256) ~ (all_0_52_52 = e2)
% 26.65/7.39 |
% 26.65/7.39 | Simplifying 256 yields:
% 26.65/7.39 | (257) ~ (all_0_52_52 = e2)
% 26.65/7.39 |
% 26.65/7.39 | Equations (253) can reduce 126 to:
% 26.65/7.39 | (258) ~ (all_0_53_53 = e2)
% 26.65/7.39 |
% 26.65/7.39 | Simplifying 258 yields:
% 26.65/7.39 | (259) ~ (all_0_53_53 = e2)
% 26.65/7.39 |
% 26.65/7.39 | Equations (253) can reduce 19 to:
% 26.65/7.39 | (260) ~ (all_0_54_54 = e2)
% 26.65/7.39 |
% 26.65/7.39 | Simplifying 260 yields:
% 26.65/7.39 | (261) ~ (all_0_54_54 = e2)
% 26.65/7.39 |
% 26.65/7.39 | Equations (253) can reduce 86 to:
% 26.65/7.39 | (141) ~ (e2 = e1)
% 26.65/7.39 |
% 26.65/7.39 | Equations (253) can reduce 67 to:
% 26.65/7.39 | (57) ~ (e2 = e0)
% 26.65/7.39 |
% 26.65/7.39 | From (253) and (151) follows:
% 26.65/7.39 | (264) op(e4, e2) = all_0_0_0
% 26.65/7.39 |
% 26.65/7.39 | From (253) and (211) follows:
% 26.65/7.39 | (265) op(e1, e2) = all_0_1_1
% 26.65/7.39 |
% 26.65/7.39 | From (253) and (23) follows:
% 26.65/7.39 | (266) op(e1, e4) = e2
% 26.65/7.39 |
% 26.65/7.39 +-Applying beta-rule and splitting (130), into two cases.
% 26.65/7.39 |-Branch one:
% 26.65/7.39 | (267) all_0_50_50 = e4
% 26.65/7.39 |
% 26.65/7.39 | Combining equations (267,253) yields a new equation:
% 26.65/7.39 | (268) e4 = e2
% 26.65/7.39 |
% 26.65/7.39 | Simplifying 268 yields:
% 26.65/7.39 | (269) e4 = e2
% 26.65/7.39 |
% 26.65/7.39 | Equations (269) can reduce 231 to:
% 26.65/7.39 | (270) $false
% 26.65/7.39 |
% 26.65/7.39 |-The branch is then unsatisfiable
% 26.65/7.39 |-Branch two:
% 26.65/7.39 | (271) ~ (all_0_50_50 = e4)
% 26.65/7.40 | (272) all_0_55_55 = e4
% 26.65/7.40 |
% 26.65/7.40 | Equations (272) can reduce 43 to:
% 26.65/7.40 | (273) ~ (all_0_56_56 = e4)
% 26.65/7.40 |
% 26.65/7.40 | Simplifying 273 yields:
% 26.65/7.40 | (274) ~ (all_0_56_56 = e4)
% 26.65/7.40 |
% 26.65/7.40 | Equations (272) can reduce 11 to:
% 26.65/7.40 | (275) ~ (all_0_57_57 = e4)
% 26.65/7.40 |
% 26.65/7.40 | Simplifying 275 yields:
% 26.65/7.40 | (143) ~ (all_0_57_57 = e4)
% 26.65/7.40 |
% 26.65/7.40 | Equations (272) can reduce 73 to:
% 26.65/7.40 | (277) ~ (all_0_58_58 = e4)
% 26.65/7.40 |
% 26.65/7.40 | Simplifying 277 yields:
% 26.65/7.40 | (278) ~ (all_0_58_58 = e4)
% 26.65/7.40 |
% 26.65/7.40 | Equations (272) can reduce 144 to:
% 26.65/7.40 | (279) ~ (all_0_59_59 = e4)
% 26.65/7.40 |
% 26.65/7.40 | Simplifying 279 yields:
% 26.65/7.40 | (280) ~ (all_0_59_59 = e4)
% 26.65/7.40 |
% 26.65/7.40 | Equations (272) can reduce 98 to:
% 26.65/7.40 | (34) ~ (e4 = e3)
% 26.65/7.40 |
% 26.65/7.40 | Equations (272) can reduce 146 to:
% 26.65/7.40 | (251) ~ (e4 = e1)
% 26.65/7.40 |
% 26.65/7.40 | From (272) and (119) follows:
% 26.65/7.40 | (283) op(e0, e4) = all_0_3_3
% 26.65/7.40 |
% 26.65/7.40 | From (272) and (181) follows:
% 26.65/7.40 | (284) op(e0, e4) = e4
% 26.65/7.40 |
% 26.85/7.40 | Instantiating formula (201) with e4, e2, all_0_0_0, all_0_40_40 and discharging atoms op(e4, e2) = all_0_0_0, op(e4, e2) = all_0_40_40, yields:
% 26.85/7.40 | (285) all_0_0_0 = all_0_40_40
% 26.85/7.40 |
% 26.85/7.40 | Instantiating formula (201) with e1, e2, all_0_1_1, all_0_52_52 and discharging atoms op(e1, e2) = all_0_1_1, op(e1, e2) = all_0_52_52, yields:
% 26.85/7.40 | (286) all_0_1_1 = all_0_52_52
% 26.85/7.40 |
% 26.85/7.40 | Instantiating formula (201) with e0, e4, e4, all_0_3_3 and discharging atoms op(e0, e4) = all_0_3_3, op(e0, e4) = e4, yields:
% 26.85/7.40 | (287) all_0_3_3 = e4
% 26.85/7.40 |
% 26.85/7.40 | From (286) and (265) follows:
% 26.85/7.40 | (203) op(e1, e2) = all_0_52_52
% 26.85/7.40 |
% 26.85/7.40 | From (287) and (283) follows:
% 26.85/7.40 | (284) op(e0, e4) = e4
% 26.85/7.41 |
% 26.85/7.41 +-Applying beta-rule and splitting (124), into two cases.
% 26.85/7.41 |-Branch one:
% 26.85/7.41 | (290) all_0_47_47 = e2
% 26.85/7.41 |
% 26.85/7.41 | Equations (290) can reduce 100 to:
% 26.85/7.41 | (291) ~ (all_0_39_39 = e2)
% 26.85/7.41 |
% 26.85/7.41 | Equations (290) can reduce 170 to:
% 26.85/7.41 | (292) ~ (all_0_43_43 = e2)
% 26.85/7.41 |
% 26.85/7.41 | Equations (290) can reduce 225 to:
% 26.85/7.41 | (293) ~ (all_0_48_48 = e2)
% 26.85/7.41 |
% 26.85/7.41 | Simplifying 293 yields:
% 26.85/7.41 | (294) ~ (all_0_48_48 = e2)
% 26.85/7.41 |
% 26.85/7.41 | Equations (290) can reduce 80 to:
% 26.85/7.41 | (295) ~ (all_0_49_49 = e2)
% 26.85/7.41 |
% 26.85/7.41 | Simplifying 295 yields:
% 26.85/7.41 | (296) ~ (all_0_49_49 = e2)
% 26.85/7.41 |
% 26.85/7.41 | Equations (290) can reduce 3 to:
% 26.85/7.41 | (254) ~ (all_0_51_51 = e2)
% 26.85/7.41 |
% 26.85/7.41 | Simplifying 254 yields:
% 26.85/7.41 | (255) ~ (all_0_51_51 = e2)
% 26.85/7.41 |
% 26.85/7.41 | Equations (290) can reduce 218 to:
% 26.85/7.41 | (299) ~ (all_0_56_56 = e2)
% 26.85/7.41 |
% 26.85/7.41 | Simplifying 299 yields:
% 26.85/7.41 | (300) ~ (all_0_56_56 = e2)
% 26.85/7.41 |
% 26.85/7.41 | Equations (290) can reduce 247 to:
% 26.85/7.41 | (301) ~ (e3 = e2)
% 26.85/7.41 |
% 26.85/7.41 | Simplifying 301 yields:
% 26.85/7.41 | (223) ~ (e3 = e2)
% 26.85/7.41 |
% 26.85/7.41 | From (290) and (42) follows:
% 26.85/7.41 | (303) op(e2, e2) = all_0_8_8
% 26.85/7.41 |
% 26.85/7.41 | From (290) and (40) follows:
% 26.85/7.41 | (304) op(e2, e3) = e2
% 26.85/7.41 |
% 26.85/7.41 | Instantiating formula (201) with e2, e2, all_0_8_8, e4 and discharging atoms op(e2, e2) = all_0_8_8, op(e2, e2) = e4, yields:
% 26.85/7.41 | (305) all_0_8_8 = e4
% 26.85/7.41 |
% 26.85/7.41 | From (305) and (303) follows:
% 26.85/7.41 | (115) op(e2, e2) = e4
% 26.85/7.41 |
% 26.85/7.41 +-Applying beta-rule and splitting (117), into two cases.
% 26.85/7.41 |-Branch one:
% 26.85/7.41 | (307) all_0_49_49 = e2
% 26.85/7.41 |
% 26.85/7.41 | Equations (307) can reduce 296 to:
% 26.85/7.41 | (270) $false
% 26.85/7.41 |
% 26.85/7.41 |-The branch is then unsatisfiable
% 26.85/7.41 |-Branch two:
% 26.85/7.41 | (296) ~ (all_0_49_49 = e2)
% 26.85/7.41 | (310) all_0_49_49 = e1 | all_0_49_49 = e0
% 26.85/7.41 |
% 26.85/7.41 +-Applying beta-rule and splitting (129), into two cases.
% 26.85/7.41 |-Branch one:
% 26.85/7.41 | (311) all_0_48_48 = e2
% 26.85/7.41 |
% 26.85/7.41 | Equations (311) can reduce 294 to:
% 26.85/7.41 | (270) $false
% 26.85/7.41 |
% 26.85/7.41 |-The branch is then unsatisfiable
% 26.85/7.41 |-Branch two:
% 26.85/7.41 | (294) ~ (all_0_48_48 = e2)
% 26.85/7.41 | (314) all_0_48_48 = e1 | all_0_48_48 = e0
% 26.85/7.41 |
% 26.85/7.41 +-Applying beta-rule and splitting (77), into two cases.
% 26.85/7.41 |-Branch one:
% 26.85/7.41 | (315) all_0_47_47 = e0
% 26.85/7.41 |
% 26.85/7.42 | Combining equations (315,290) yields a new equation:
% 26.85/7.42 | (316) e2 = e0
% 26.85/7.42 |
% 26.85/7.42 | Equations (316) can reduce 57 to:
% 26.85/7.42 | (270) $false
% 26.85/7.42 |
% 26.85/7.42 |-The branch is then unsatisfiable
% 26.85/7.42 |-Branch two:
% 26.85/7.42 | (318) ~ (all_0_47_47 = e0)
% 26.85/7.42 | (319) all_0_48_48 = e0 | all_0_49_49 = e0
% 26.85/7.42 |
% 26.85/7.42 | Equations (290) can reduce 318 to:
% 26.85/7.42 | (57) ~ (e2 = e0)
% 26.85/7.42 |
% 26.85/7.42 +-Applying beta-rule and splitting (83), into two cases.
% 26.85/7.42 |-Branch one:
% 26.85/7.42 | (321) all_0_47_47 = e1
% 26.85/7.42 |
% 26.85/7.42 | Combining equations (321,290) yields a new equation:
% 26.85/7.42 | (322) e2 = e1
% 26.85/7.42 |
% 26.85/7.42 | Equations (322) can reduce 141 to:
% 26.85/7.42 | (270) $false
% 26.85/7.42 |
% 26.85/7.42 |-The branch is then unsatisfiable
% 26.85/7.42 |-Branch two:
% 26.85/7.42 | (324) ~ (all_0_47_47 = e1)
% 26.85/7.42 | (325) all_0_48_48 = e1 | all_0_49_49 = e1
% 26.85/7.42 |
% 26.85/7.42 | Equations (290) can reduce 324 to:
% 26.85/7.42 | (141) ~ (e2 = e1)
% 26.85/7.42 |
% 26.85/7.42 +-Applying beta-rule and splitting (125), into two cases.
% 26.85/7.42 |-Branch one:
% 26.85/7.42 | (327) all_0_40_40 = e2
% 26.85/7.42 |
% 26.85/7.42 | Combining equations (327,285) yields a new equation:
% 26.85/7.42 | (328) all_0_0_0 = e2
% 26.85/7.42 |
% 26.85/7.42 | Equations (327) can reduce 114 to:
% 26.85/7.42 | (291) ~ (all_0_39_39 = e2)
% 26.85/7.42 |
% 26.85/7.42 | Equations (327) can reduce 147 to:
% 26.85/7.42 | (330) ~ (all_0_41_41 = e2)
% 26.85/7.42 |
% 26.85/7.42 | Simplifying 330 yields:
% 26.85/7.42 | (331) ~ (all_0_41_41 = e2)
% 26.85/7.42 |
% 26.85/7.42 | Equations (327) can reduce 15 to:
% 26.85/7.42 | (332) ~ (all_0_44_44 = e2)
% 26.85/7.42 |
% 26.85/7.42 | Simplifying 332 yields:
% 26.85/7.42 | (333) ~ (all_0_44_44 = e2)
% 26.85/7.42 |
% 26.85/7.42 | Equations (327) can reduce 149 to:
% 26.85/7.42 | (334) ~ (all_0_57_57 = e2)
% 26.85/7.42 |
% 26.85/7.42 | Simplifying 334 yields:
% 26.85/7.42 | (335) ~ (all_0_57_57 = e2)
% 26.85/7.42 |
% 26.85/7.42 +-Applying beta-rule and splitting (186), into two cases.
% 26.85/7.42 |-Branch one:
% 26.85/7.42 | (336) all_0_39_39 = e2
% 26.85/7.42 |
% 26.85/7.42 | Equations (336) can reduce 291 to:
% 26.85/7.42 | (270) $false
% 26.85/7.42 |
% 26.85/7.42 |-The branch is then unsatisfiable
% 26.85/7.42 |-Branch two:
% 26.85/7.42 | (291) ~ (all_0_39_39 = e2)
% 26.85/7.42 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 26.85/7.42 |
% 26.85/7.42 +-Applying beta-rule and splitting (339), into two cases.
% 26.85/7.42 |-Branch one:
% 26.85/7.42 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 26.85/7.42 |
% 26.85/7.42 +-Applying beta-rule and splitting (340), into two cases.
% 26.85/7.42 |-Branch one:
% 26.85/7.42 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 26.85/7.42 |
% 26.85/7.42 | Applying alpha-rule on (341) yields:
% 26.85/7.42 | (342) all_0_0_0 = e1
% 26.85/7.42 | (343) ~ (all_0_1_1 = e4)
% 26.85/7.42 |
% 26.85/7.42 | Combining equations (342,328) yields a new equation:
% 26.85/7.42 | (322) e2 = e1
% 26.85/7.42 |
% 26.85/7.42 | Equations (322) can reduce 141 to:
% 26.85/7.42 | (270) $false
% 26.85/7.42 |
% 26.85/7.42 |-The branch is then unsatisfiable
% 26.85/7.42 |-Branch two:
% 26.85/7.42 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 26.85/7.42 |
% 26.85/7.42 | Applying alpha-rule on (346) yields:
% 26.85/7.42 | (347) all_0_2_2 = e0
% 26.85/7.42 | (348) ~ (all_0_3_3 = e4)
% 26.85/7.42 |
% 26.85/7.42 | Equations (287) can reduce 348 to:
% 26.85/7.42 | (270) $false
% 26.85/7.42 |
% 26.85/7.42 |-The branch is then unsatisfiable
% 26.85/7.42 |-Branch two:
% 26.85/7.42 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 26.85/7.42 |
% 26.85/7.42 | Applying alpha-rule on (350) yields:
% 26.85/7.42 | (351) all_0_41_41 = e3
% 26.85/7.42 | (352) ~ (all_0_45_45 = e4)
% 26.85/7.42 |
% 26.85/7.42 | Equations (351) can reduce 51 to:
% 26.85/7.42 | (353) ~ (all_0_45_45 = e3)
% 26.85/7.42 |
% 26.85/7.42 | Simplifying 353 yields:
% 26.85/7.42 | (354) ~ (all_0_45_45 = e3)
% 26.85/7.42 |
% 26.85/7.42 | Equations (351) can reduce 214 to:
% 26.85/7.42 | (355) ~ (all_0_53_53 = e3)
% 26.85/7.42 |
% 26.85/7.42 | Simplifying 355 yields:
% 26.85/7.42 | (356) ~ (all_0_53_53 = e3)
% 26.85/7.42 |
% 26.85/7.42 | Equations (351) can reduce 331 to:
% 26.85/7.42 | (223) ~ (e3 = e2)
% 26.85/7.42 |
% 26.85/7.42 +-Applying beta-rule and splitting (158), into two cases.
% 26.85/7.42 |-Branch one:
% 26.85/7.42 | (358) all_0_41_41 = e4
% 26.85/7.42 |
% 26.85/7.42 | Combining equations (351,358) yields a new equation:
% 26.85/7.42 | (359) e4 = e3
% 26.85/7.42 |
% 26.85/7.42 | Equations (359) can reduce 34 to:
% 26.85/7.42 | (270) $false
% 26.85/7.42 |
% 26.85/7.42 |-The branch is then unsatisfiable
% 26.85/7.42 |-Branch two:
% 26.85/7.42 | (361) ~ (all_0_41_41 = e4)
% 26.85/7.43 | (362) all_0_45_45 = e4 | all_0_53_53 = e4 | all_0_58_58 = e4
% 26.85/7.43 |
% 26.85/7.43 +-Applying beta-rule and splitting (362), into two cases.
% 26.85/7.43 |-Branch one:
% 26.85/7.43 | (363) all_0_45_45 = e4
% 26.85/7.43 |
% 26.85/7.43 | Equations (363) can reduce 352 to:
% 26.85/7.43 | (270) $false
% 26.85/7.43 |
% 26.85/7.43 |-The branch is then unsatisfiable
% 26.85/7.43 |-Branch two:
% 26.85/7.43 | (352) ~ (all_0_45_45 = e4)
% 26.85/7.43 | (366) all_0_53_53 = e4 | all_0_58_58 = e4
% 26.85/7.43 |
% 26.85/7.43 +-Applying beta-rule and splitting (366), into two cases.
% 26.85/7.43 |-Branch one:
% 26.85/7.43 | (367) all_0_53_53 = e4
% 26.85/7.43 |
% 26.85/7.43 | Equations (367) can reduce 128 to:
% 26.85/7.43 | (352) ~ (all_0_45_45 = e4)
% 26.85/7.43 |
% 26.85/7.43 | Equations (367) can reduce 356 to:
% 26.85/7.43 | (34) ~ (e4 = e3)
% 26.85/7.43 |
% 26.85/7.43 +-Applying beta-rule and splitting (193), into two cases.
% 26.85/7.43 |-Branch one:
% 26.85/7.43 | (370) all_0_44_44 = e2
% 26.85/7.43 |
% 26.85/7.43 | Equations (370) can reduce 333 to:
% 26.85/7.43 | (270) $false
% 26.85/7.43 |
% 26.85/7.43 |-The branch is then unsatisfiable
% 26.85/7.43 |-Branch two:
% 26.85/7.43 | (333) ~ (all_0_44_44 = e2)
% 26.85/7.43 | (373) all_0_44_44 = e3 | all_0_44_44 = e0
% 26.85/7.43 |
% 26.85/7.43 +-Applying beta-rule and splitting (105), into two cases.
% 26.85/7.43 |-Branch one:
% 26.85/7.43 | (374) all_0_45_45 = e2
% 26.85/7.43 |
% 26.85/7.43 | Equations (374) can reduce 108 to:
% 26.85/7.43 | (375) ~ (all_0_58_58 = e2)
% 26.85/7.43 |
% 26.85/7.43 | Simplifying 375 yields:
% 26.85/7.43 | (376) ~ (all_0_58_58 = e2)
% 26.85/7.43 |
% 26.85/7.43 | Equations (374) can reduce 352 to:
% 26.85/7.43 | (377) ~ (e4 = e2)
% 26.85/7.43 |
% 26.85/7.43 | Simplifying 377 yields:
% 26.85/7.43 | (231) ~ (e4 = e2)
% 26.85/7.43 |
% 26.85/7.43 | Equations (374) can reduce 354 to:
% 26.85/7.43 | (301) ~ (e3 = e2)
% 26.85/7.43 |
% 26.85/7.43 | Simplifying 301 yields:
% 26.85/7.43 | (223) ~ (e3 = e2)
% 26.85/7.43 |
% 26.85/7.43 | Equations (374) can reduce 26 to:
% 26.85/7.43 | (141) ~ (e2 = e1)
% 26.85/7.43 |
% 26.85/7.43 +-Applying beta-rule and splitting (168), into two cases.
% 26.85/7.43 |-Branch one:
% 26.85/7.43 | (382) all_0_55_55 = e2
% 26.85/7.43 |
% 26.85/7.43 | Combining equations (272,382) yields a new equation:
% 26.85/7.43 | (268) e4 = e2
% 26.85/7.43 |
% 26.85/7.43 | Simplifying 268 yields:
% 26.85/7.43 | (269) e4 = e2
% 26.85/7.43 |
% 26.85/7.43 | Equations (269) can reduce 231 to:
% 26.85/7.43 | (270) $false
% 26.85/7.43 |
% 26.85/7.43 |-The branch is then unsatisfiable
% 26.85/7.43 |-Branch two:
% 26.85/7.43 | (386) ~ (all_0_55_55 = e2)
% 26.85/7.43 | (387) all_0_56_56 = e2 | all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 26.85/7.43 |
% 26.85/7.43 +-Applying beta-rule and splitting (387), into two cases.
% 26.85/7.43 |-Branch one:
% 26.85/7.43 | (388) all_0_56_56 = e2
% 26.85/7.43 |
% 26.85/7.43 | Equations (388) can reduce 300 to:
% 26.85/7.43 | (270) $false
% 26.85/7.43 |
% 26.85/7.43 |-The branch is then unsatisfiable
% 26.85/7.43 |-Branch two:
% 26.85/7.43 | (300) ~ (all_0_56_56 = e2)
% 26.85/7.43 | (391) all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 26.85/7.43 |
% 26.85/7.43 +-Applying beta-rule and splitting (391), into two cases.
% 26.85/7.43 |-Branch one:
% 26.85/7.43 | (392) all_0_57_57 = e2
% 26.85/7.43 |
% 26.85/7.43 | Equations (392) can reduce 335 to:
% 26.85/7.43 | (270) $false
% 26.85/7.43 |
% 26.85/7.43 |-The branch is then unsatisfiable
% 26.85/7.43 |-Branch two:
% 26.85/7.43 | (335) ~ (all_0_57_57 = e2)
% 26.85/7.43 | (395) all_0_58_58 = e2 | all_0_59_59 = e2
% 26.85/7.43 |
% 26.85/7.43 +-Applying beta-rule and splitting (395), into two cases.
% 26.85/7.43 |-Branch one:
% 26.85/7.43 | (396) all_0_58_58 = e2
% 26.85/7.43 |
% 26.85/7.43 | Equations (396) can reduce 376 to:
% 26.85/7.43 | (270) $false
% 26.85/7.43 |
% 26.85/7.43 |-The branch is then unsatisfiable
% 26.85/7.43 |-Branch two:
% 26.85/7.43 | (376) ~ (all_0_58_58 = e2)
% 26.85/7.43 | (399) all_0_59_59 = e2
% 26.85/7.43 |
% 26.85/7.43 | Equations (399) can reduce 280 to:
% 26.85/7.43 | (377) ~ (e4 = e2)
% 26.85/7.43 |
% 26.85/7.43 | Simplifying 377 yields:
% 26.85/7.43 | (231) ~ (e4 = e2)
% 26.85/7.43 |
% 26.85/7.43 +-Applying beta-rule and splitting (93), into two cases.
% 26.85/7.43 |-Branch one:
% 26.85/7.43 | (402) all_0_59_59 = e4
% 26.85/7.43 |
% 26.85/7.43 | Combining equations (402,399) yields a new equation:
% 26.85/7.43 | (268) e4 = e2
% 26.85/7.43 |
% 26.85/7.43 | Simplifying 268 yields:
% 26.85/7.43 | (269) e4 = e2
% 26.85/7.43 |
% 26.85/7.43 | Equations (269) can reduce 231 to:
% 26.85/7.43 | (270) $false
% 26.85/7.43 |
% 26.85/7.43 |-The branch is then unsatisfiable
% 26.85/7.43 |-Branch two:
% 26.85/7.43 | (280) ~ (all_0_59_59 = e4)
% 26.85/7.43 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 26.85/7.43 |
% 26.85/7.43 +-Applying beta-rule and splitting (407), into two cases.
% 26.85/7.43 |-Branch one:
% 26.85/7.43 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 26.85/7.43 |
% 26.85/7.43 +-Applying beta-rule and splitting (408), into two cases.
% 26.85/7.43 |-Branch one:
% 26.85/7.43 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 26.85/7.43 |
% 26.85/7.43 +-Applying beta-rule and splitting (409), into two cases.
% 26.85/7.43 |-Branch one:
% 26.85/7.43 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 26.85/7.43 |
% 26.85/7.43 | Applying alpha-rule on (410) yields:
% 26.85/7.43 | (411) all_0_43_43 = e0
% 26.85/7.43 | (412) all_0_59_59 = e3
% 26.85/7.43 | (413) ~ (all_0_46_46 = e3)
% 26.85/7.43 |
% 26.85/7.43 | Combining equations (399,412) yields a new equation:
% 26.85/7.43 | (414) e3 = e2
% 26.85/7.43 |
% 26.85/7.43 | Equations (414) can reduce 223 to:
% 26.85/7.43 | (270) $false
% 26.85/7.43 |
% 26.85/7.43 |-The branch is then unsatisfiable
% 26.85/7.43 |-Branch two:
% 26.85/7.43 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 26.85/7.43 |
% 26.85/7.43 | Applying alpha-rule on (416) yields:
% 26.85/7.43 | (411) all_0_43_43 = e0
% 26.85/7.43 | (412) all_0_59_59 = e3
% 26.85/7.43 | (419) ~ (all_0_56_56 = e0)
% 26.85/7.43 |
% 26.85/7.43 | Combining equations (399,412) yields a new equation:
% 26.85/7.43 | (414) e3 = e2
% 26.85/7.43 |
% 26.85/7.43 | Equations (414) can reduce 223 to:
% 26.85/7.43 | (270) $false
% 26.85/7.43 |
% 26.85/7.43 |-The branch is then unsatisfiable
% 26.85/7.43 |-Branch two:
% 26.85/7.43 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 26.85/7.43 |
% 26.85/7.43 | Applying alpha-rule on (422) yields:
% 26.85/7.43 | (423) all_0_53_53 = e0
% 26.85/7.43 | (424) all_0_59_59 = e1
% 26.85/7.43 | (425) ~ (all_0_54_54 = e1)
% 26.85/7.43 |
% 26.85/7.43 | Combining equations (424,399) yields a new equation:
% 26.85/7.43 | (322) e2 = e1
% 26.85/7.43 |
% 26.85/7.43 | Equations (322) can reduce 141 to:
% 26.85/7.43 | (270) $false
% 26.85/7.43 |
% 26.85/7.43 |-The branch is then unsatisfiable
% 26.85/7.43 |-Branch two:
% 26.85/7.43 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 26.85/7.43 |
% 26.85/7.43 | Applying alpha-rule on (428) yields:
% 26.85/7.43 | (423) all_0_53_53 = e0
% 26.85/7.43 | (424) all_0_59_59 = e1
% 26.85/7.43 | (431) ~ (all_0_58_58 = e0)
% 26.85/7.43 |
% 26.85/7.43 | Combining equations (424,399) yields a new equation:
% 26.85/7.43 | (322) e2 = e1
% 26.85/7.43 |
% 26.85/7.43 | Equations (322) can reduce 141 to:
% 26.85/7.43 | (270) $false
% 26.85/7.43 |
% 26.85/7.43 |-The branch is then unsatisfiable
% 26.85/7.43 |-Branch two:
% 26.85/7.43 | (434) ~ (all_0_45_45 = e2)
% 26.85/7.43 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 26.85/7.43 |
% 26.85/7.43 +-Applying beta-rule and splitting (187), into two cases.
% 26.85/7.43 |-Branch one:
% 26.85/7.43 | (436) all_0_41_41 = e2
% 26.85/7.43 |
% 26.85/7.43 | Combining equations (351,436) yields a new equation:
% 26.85/7.43 | (437) e3 = e2
% 26.85/7.43 |
% 26.85/7.43 | Simplifying 437 yields:
% 26.85/7.43 | (414) e3 = e2
% 26.85/7.43 |
% 26.85/7.43 | Equations (414) can reduce 223 to:
% 26.85/7.43 | (270) $false
% 26.85/7.43 |
% 26.85/7.43 |-The branch is then unsatisfiable
% 26.85/7.43 |-Branch two:
% 26.85/7.43 | (331) ~ (all_0_41_41 = e2)
% 26.85/7.43 | (441) all_0_45_45 = e2 | all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 26.85/7.43 |
% 26.85/7.43 +-Applying beta-rule and splitting (441), into two cases.
% 26.85/7.43 |-Branch one:
% 26.85/7.43 | (374) all_0_45_45 = e2
% 26.85/7.43 |
% 26.85/7.43 | Equations (374) can reduce 434 to:
% 26.85/7.43 | (270) $false
% 26.85/7.43 |
% 26.85/7.43 |-The branch is then unsatisfiable
% 26.85/7.43 |-Branch two:
% 26.85/7.43 | (434) ~ (all_0_45_45 = e2)
% 26.85/7.43 | (445) all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 26.85/7.43 |
% 26.85/7.43 +-Applying beta-rule and splitting (445), into two cases.
% 26.85/7.43 |-Branch one:
% 26.85/7.43 | (311) all_0_48_48 = e2
% 26.85/7.43 |
% 26.85/7.43 | Equations (311) can reduce 294 to:
% 26.85/7.43 | (270) $false
% 26.85/7.43 |
% 26.85/7.43 |-The branch is then unsatisfiable
% 26.85/7.43 |-Branch two:
% 26.85/7.43 | (294) ~ (all_0_48_48 = e2)
% 26.85/7.43 | (449) all_0_53_53 = e2 | all_0_58_58 = e2
% 26.85/7.43 |
% 26.85/7.43 +-Applying beta-rule and splitting (47), into two cases.
% 26.85/7.43 |-Branch one:
% 26.85/7.43 | (450) all_0_43_43 = e2
% 26.85/7.43 |
% 26.85/7.43 | Equations (450) can reduce 292 to:
% 26.85/7.43 | (270) $false
% 26.85/7.43 |
% 26.85/7.43 |-The branch is then unsatisfiable
% 26.85/7.43 |-Branch two:
% 26.85/7.43 | (292) ~ (all_0_43_43 = e2)
% 26.85/7.43 | (453) all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2
% 26.85/7.43 |
% 26.85/7.43 +-Applying beta-rule and splitting (435), into two cases.
% 26.85/7.43 |-Branch one:
% 26.85/7.43 | (454) all_0_45_45 = e0
% 26.85/7.43 |
% 26.85/7.43 | Equations (454) can reduce 84 to:
% 26.85/7.43 | (455) ~ (all_0_43_43 = e0)
% 26.85/7.43 |
% 26.85/7.43 | Equations (454) can reduce 352 to:
% 26.85/7.43 | (456) ~ (e4 = e0)
% 26.85/7.43 |
% 26.85/7.43 | Simplifying 456 yields:
% 26.85/7.43 | (6) ~ (e4 = e0)
% 26.85/7.43 |
% 26.85/7.43 +-Applying beta-rule and splitting (93), into two cases.
% 26.85/7.43 |-Branch one:
% 26.85/7.43 | (402) all_0_59_59 = e4
% 26.85/7.43 |
% 26.85/7.43 | Equations (402) can reduce 280 to:
% 26.85/7.43 | (270) $false
% 26.85/7.43 |
% 26.85/7.43 |-The branch is then unsatisfiable
% 26.85/7.43 |-Branch two:
% 26.85/7.43 | (280) ~ (all_0_59_59 = e4)
% 26.85/7.43 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 26.85/7.43 |
% 26.85/7.43 +-Applying beta-rule and splitting (407), into two cases.
% 26.85/7.43 |-Branch one:
% 26.85/7.43 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 26.85/7.43 |
% 26.85/7.43 +-Applying beta-rule and splitting (408), into two cases.
% 26.85/7.43 |-Branch one:
% 26.85/7.43 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 26.85/7.43 |
% 26.85/7.43 +-Applying beta-rule and splitting (409), into two cases.
% 26.85/7.43 |-Branch one:
% 26.85/7.43 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 26.85/7.43 |
% 26.85/7.43 | Applying alpha-rule on (410) yields:
% 26.85/7.43 | (411) all_0_43_43 = e0
% 26.85/7.43 | (412) all_0_59_59 = e3
% 26.85/7.43 | (413) ~ (all_0_46_46 = e3)
% 26.85/7.43 |
% 26.85/7.43 | Equations (411) can reduce 455 to:
% 26.85/7.43 | (270) $false
% 26.85/7.43 |
% 26.85/7.43 |-The branch is then unsatisfiable
% 26.85/7.43 |-Branch two:
% 26.85/7.43 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 26.85/7.43 |
% 26.85/7.43 | Applying alpha-rule on (416) yields:
% 26.85/7.43 | (411) all_0_43_43 = e0
% 26.85/7.43 | (412) all_0_59_59 = e3
% 26.85/7.43 | (419) ~ (all_0_56_56 = e0)
% 26.85/7.43 |
% 26.85/7.43 | Equations (411) can reduce 455 to:
% 26.85/7.43 | (270) $false
% 26.85/7.43 |
% 26.85/7.43 |-The branch is then unsatisfiable
% 26.85/7.43 |-Branch two:
% 26.85/7.43 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 26.85/7.43 |
% 26.85/7.43 | Applying alpha-rule on (422) yields:
% 26.85/7.43 | (423) all_0_53_53 = e0
% 26.85/7.43 | (424) all_0_59_59 = e1
% 26.85/7.43 | (425) ~ (all_0_54_54 = e1)
% 26.85/7.43 |
% 26.85/7.43 | Combining equations (367,423) yields a new equation:
% 26.85/7.43 | (478) e4 = e0
% 26.85/7.43 |
% 26.85/7.43 | Simplifying 478 yields:
% 26.85/7.43 | (479) e4 = e0
% 26.85/7.43 |
% 26.85/7.43 | Equations (479) can reduce 6 to:
% 26.85/7.43 | (270) $false
% 26.85/7.43 |
% 26.85/7.43 |-The branch is then unsatisfiable
% 26.85/7.43 |-Branch two:
% 26.85/7.43 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 26.85/7.43 |
% 26.85/7.43 | Applying alpha-rule on (428) yields:
% 26.85/7.43 | (423) all_0_53_53 = e0
% 26.85/7.43 | (424) all_0_59_59 = e1
% 26.85/7.43 | (431) ~ (all_0_58_58 = e0)
% 26.85/7.43 |
% 26.85/7.43 | Combining equations (367,423) yields a new equation:
% 26.85/7.43 | (478) e4 = e0
% 26.85/7.43 |
% 26.85/7.43 | Simplifying 478 yields:
% 26.85/7.43 | (479) e4 = e0
% 26.85/7.43 |
% 26.85/7.43 | Equations (479) can reduce 6 to:
% 26.85/7.43 | (270) $false
% 26.85/7.43 |
% 26.85/7.43 |-The branch is then unsatisfiable
% 26.85/7.43 |-Branch two:
% 26.85/7.44 | (488) ~ (all_0_45_45 = e0)
% 26.85/7.44 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 26.85/7.44 |
% 26.85/7.44 +-Applying beta-rule and splitting (453), into two cases.
% 26.85/7.44 |-Branch one:
% 26.85/7.44 | (370) all_0_44_44 = e2
% 26.85/7.44 |
% 26.85/7.44 | Equations (370) can reduce 333 to:
% 26.85/7.44 | (270) $false
% 26.85/7.44 |
% 26.85/7.44 |-The branch is then unsatisfiable
% 26.85/7.44 |-Branch two:
% 26.85/7.44 | (333) ~ (all_0_44_44 = e2)
% 26.85/7.44 | (493) all_0_45_45 = e2 | all_0_46_46 = e2
% 26.85/7.44 |
% 26.85/7.44 +-Applying beta-rule and splitting (493), into two cases.
% 26.85/7.44 |-Branch one:
% 26.85/7.44 | (374) all_0_45_45 = e2
% 26.85/7.44 |
% 26.85/7.44 | Equations (374) can reduce 434 to:
% 26.85/7.44 | (270) $false
% 26.85/7.44 |
% 26.85/7.44 |-The branch is then unsatisfiable
% 26.85/7.44 |-Branch two:
% 26.85/7.44 | (434) ~ (all_0_45_45 = e2)
% 26.85/7.44 | (497) all_0_46_46 = e2
% 26.85/7.44 |
% 26.85/7.44 | Equations (497) can reduce 18 to:
% 26.85/7.44 | (498) ~ (all_0_42_42 = e2)
% 26.85/7.44 |
% 26.85/7.44 | Equations (497) can reduce 198 to:
% 26.85/7.44 | (295) ~ (all_0_49_49 = e2)
% 26.85/7.44 |
% 26.85/7.44 | Simplifying 295 yields:
% 26.85/7.44 | (296) ~ (all_0_49_49 = e2)
% 26.85/7.44 |
% 26.85/7.44 | Equations (497) can reduce 106 to:
% 26.85/7.44 | (141) ~ (e2 = e1)
% 26.85/7.44 |
% 26.85/7.44 +-Applying beta-rule and splitting (44), into two cases.
% 26.85/7.44 |-Branch one:
% 26.85/7.44 | (502) all_0_43_43 = e4
% 26.85/7.44 |
% 26.85/7.44 | Equations (502) can reduce 84 to:
% 26.85/7.44 | (503) ~ (all_0_45_45 = e4)
% 26.85/7.44 |
% 26.85/7.44 | Simplifying 503 yields:
% 26.85/7.44 | (352) ~ (all_0_45_45 = e4)
% 26.85/7.44 |
% 26.85/7.44 +-Applying beta-rule and splitting (489), into two cases.
% 26.85/7.44 |-Branch one:
% 26.85/7.44 | (505) all_0_45_45 = e3
% 26.85/7.44 |
% 26.85/7.44 | Equations (505) can reduce 354 to:
% 26.85/7.44 | (270) $false
% 26.85/7.44 |
% 26.85/7.44 |-The branch is then unsatisfiable
% 26.85/7.44 |-Branch two:
% 26.85/7.44 | (354) ~ (all_0_45_45 = e3)
% 26.85/7.44 | (363) all_0_45_45 = e4
% 26.85/7.44 |
% 26.85/7.44 | Equations (363) can reduce 352 to:
% 26.85/7.44 | (270) $false
% 26.85/7.44 |
% 26.85/7.44 |-The branch is then unsatisfiable
% 26.85/7.44 |-Branch two:
% 26.85/7.44 | (510) ~ (all_0_43_43 = e4)
% 26.85/7.44 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 26.85/7.44 |
% 26.85/7.44 +-Applying beta-rule and splitting (179), into two cases.
% 26.85/7.44 |-Branch one:
% 26.85/7.44 | (512) all_0_42_42 = e4
% 26.85/7.44 |
% 26.85/7.44 | Equations (512) can reduce 498 to:
% 26.85/7.44 | (231) ~ (e4 = e2)
% 26.85/7.44 |
% 26.85/7.44 +-Applying beta-rule and splitting (511), into two cases.
% 26.85/7.44 |-Branch one:
% 26.85/7.44 | (363) all_0_45_45 = e4
% 27.02/7.44 |
% 27.02/7.44 | Equations (363) can reduce 352 to:
% 27.02/7.44 | (270) $false
% 27.02/7.44 |
% 27.02/7.44 |-The branch is then unsatisfiable
% 27.02/7.44 |-Branch two:
% 27.02/7.44 | (352) ~ (all_0_45_45 = e4)
% 27.02/7.44 | (517) all_0_46_46 = e4
% 27.02/7.44 |
% 27.02/7.44 | Combining equations (497,517) yields a new equation:
% 27.02/7.44 | (269) e4 = e2
% 27.02/7.44 |
% 27.02/7.44 | Equations (269) can reduce 231 to:
% 27.02/7.44 | (270) $false
% 27.02/7.44 |
% 27.02/7.44 |-The branch is then unsatisfiable
% 27.02/7.44 |-Branch two:
% 27.02/7.44 | (520) ~ (all_0_42_42 = e4)
% 27.02/7.44 | (521) all_0_46_46 = e4 | all_0_54_54 = e4 | all_0_59_59 = e4
% 27.02/7.44 |
% 27.02/7.44 +-Applying beta-rule and splitting (222), into two cases.
% 27.02/7.44 |-Branch one:
% 27.02/7.44 | (522) all_0_39_39 = e4
% 27.02/7.44 |
% 27.02/7.44 | Equations (522) can reduce 291 to:
% 27.02/7.44 | (231) ~ (e4 = e2)
% 27.02/7.44 |
% 27.02/7.44 +-Applying beta-rule and splitting (210), into two cases.
% 27.02/7.44 |-Branch one:
% 27.02/7.44 | (524) all_0_39_39 = e1
% 27.02/7.44 |
% 27.02/7.44 | Combining equations (522,524) yields a new equation:
% 27.02/7.44 | (525) e4 = e1
% 27.02/7.44 |
% 27.02/7.44 | Simplifying 525 yields:
% 27.02/7.44 | (526) e4 = e1
% 27.02/7.44 |
% 27.02/7.44 | Equations (526) can reduce 251 to:
% 27.02/7.44 | (270) $false
% 27.02/7.44 |
% 27.02/7.44 |-The branch is then unsatisfiable
% 27.02/7.44 |-Branch two:
% 27.02/7.44 | (528) ~ (all_0_39_39 = e1)
% 27.02/7.44 | (529) all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1
% 27.02/7.44 |
% 27.02/7.44 +-Applying beta-rule and splitting (529), into two cases.
% 27.02/7.44 |-Branch one:
% 27.02/7.44 | (530) all_0_40_40 = e1
% 27.02/7.44 |
% 27.02/7.44 | Combining equations (327,530) yields a new equation:
% 27.02/7.44 | (531) e2 = e1
% 27.02/7.44 |
% 27.02/7.44 | Simplifying 531 yields:
% 27.02/7.44 | (322) e2 = e1
% 27.02/7.44 |
% 27.02/7.44 | Equations (322) can reduce 141 to:
% 27.02/7.44 | (270) $false
% 27.02/7.44 |
% 27.02/7.44 |-The branch is then unsatisfiable
% 27.02/7.44 |-Branch two:
% 27.02/7.44 | (534) ~ (all_0_40_40 = e1)
% 27.02/7.44 | (535) all_0_41_41 = e1 | all_0_42_42 = e1
% 27.02/7.44 |
% 27.02/7.44 +-Applying beta-rule and splitting (535), into two cases.
% 27.02/7.44 |-Branch one:
% 27.02/7.44 | (536) all_0_41_41 = e1
% 27.02/7.44 |
% 27.02/7.44 | Combining equations (351,536) yields a new equation:
% 27.02/7.44 | (537) e3 = e1
% 27.02/7.44 |
% 27.02/7.44 | Simplifying 537 yields:
% 27.02/7.44 | (538) e3 = e1
% 27.02/7.44 |
% 27.02/7.44 | Equations (538) can reduce 136 to:
% 27.02/7.44 | (270) $false
% 27.02/7.44 |
% 27.02/7.44 |-The branch is then unsatisfiable
% 27.02/7.44 |-Branch two:
% 27.02/7.44 | (540) ~ (all_0_41_41 = e1)
% 27.02/7.44 | (541) all_0_42_42 = e1
% 27.02/7.44 |
% 27.02/7.44 | Equations (541) can reduce 169 to:
% 27.02/7.44 | (542) ~ (all_0_49_49 = e1)
% 27.02/7.44 |
% 27.02/7.44 | Simplifying 542 yields:
% 27.02/7.44 | (543) ~ (all_0_49_49 = e1)
% 27.02/7.44 |
% 27.02/7.44 | Equations (541) can reduce 199 to:
% 27.02/7.44 | (132) ~ (e1 = e0)
% 27.02/7.44 |
% 27.02/7.44 +-Applying beta-rule and splitting (168), into two cases.
% 27.02/7.44 |-Branch one:
% 27.02/7.44 | (382) all_0_55_55 = e2
% 27.02/7.44 |
% 27.02/7.44 | Combining equations (272,382) yields a new equation:
% 27.02/7.44 | (268) e4 = e2
% 27.02/7.44 |
% 27.02/7.44 | Simplifying 268 yields:
% 27.02/7.44 | (269) e4 = e2
% 27.02/7.44 |
% 27.02/7.44 | Equations (269) can reduce 231 to:
% 27.02/7.44 | (270) $false
% 27.02/7.44 |
% 27.02/7.44 |-The branch is then unsatisfiable
% 27.02/7.44 |-Branch two:
% 27.02/7.44 | (386) ~ (all_0_55_55 = e2)
% 27.02/7.44 | (387) all_0_56_56 = e2 | all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 27.02/7.44 |
% 27.02/7.44 | Equations (272) can reduce 386 to:
% 27.02/7.44 | (231) ~ (e4 = e2)
% 27.02/7.44 |
% 27.02/7.44 +-Applying beta-rule and splitting (325), into two cases.
% 27.02/7.44 |-Branch one:
% 27.02/7.44 | (552) all_0_48_48 = e1
% 27.02/7.44 |
% 27.02/7.44 | Equations (552) can reduce 4 to:
% 27.02/7.44 | (542) ~ (all_0_49_49 = e1)
% 27.02/7.44 |
% 27.02/7.44 | Simplifying 542 yields:
% 27.02/7.44 | (543) ~ (all_0_49_49 = e1)
% 27.02/7.44 |
% 27.02/7.44 +-Applying beta-rule and splitting (182), into two cases.
% 27.02/7.44 |-Branch one:
% 27.02/7.44 | (454) all_0_45_45 = e0
% 27.02/7.44 |
% 27.02/7.44 | Equations (454) can reduce 488 to:
% 27.02/7.44 | (270) $false
% 27.02/7.44 |
% 27.02/7.44 |-The branch is then unsatisfiable
% 27.02/7.44 |-Branch two:
% 27.02/7.44 | (488) ~ (all_0_45_45 = e0)
% 27.02/7.44 | (558) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 27.02/7.44 |
% 27.02/7.44 +-Applying beta-rule and splitting (319), into two cases.
% 27.02/7.44 |-Branch one:
% 27.02/7.44 | (559) all_0_48_48 = e0
% 27.02/7.44 |
% 27.02/7.44 | Combining equations (559,552) yields a new equation:
% 27.02/7.44 | (560) e1 = e0
% 27.02/7.44 |
% 27.02/7.44 | Equations (560) can reduce 132 to:
% 27.02/7.44 | (270) $false
% 27.02/7.44 |
% 27.02/7.44 |-The branch is then unsatisfiable
% 27.02/7.44 |-Branch two:
% 27.02/7.44 | (562) ~ (all_0_48_48 = e0)
% 27.02/7.44 | (563) all_0_49_49 = e0
% 27.02/7.44 |
% 27.02/7.44 | Equations (563) can reduce 202 to:
% 27.02/7.44 | (456) ~ (e4 = e0)
% 27.02/7.44 |
% 27.02/7.44 | Simplifying 456 yields:
% 27.02/7.44 | (6) ~ (e4 = e0)
% 27.02/7.44 |
% 27.02/7.44 | Equations (563) can reduce 296 to:
% 27.02/7.44 | (566) ~ (e2 = e0)
% 27.02/7.44 |
% 27.02/7.44 | Simplifying 566 yields:
% 27.02/7.44 | (57) ~ (e2 = e0)
% 27.02/7.44 |
% 27.02/7.44 | Equations (563) can reduce 543 to:
% 27.02/7.44 | (568) ~ (e1 = e0)
% 27.02/7.44 |
% 27.02/7.44 | Simplifying 568 yields:
% 27.02/7.44 | (132) ~ (e1 = e0)
% 27.02/7.44 |
% 27.02/7.44 +-Applying beta-rule and splitting (558), into two cases.
% 27.02/7.44 |-Branch one:
% 27.02/7.44 | (559) all_0_48_48 = e0
% 27.02/7.44 |
% 27.02/7.44 | Combining equations (552,559) yields a new equation:
% 27.02/7.44 | (571) e1 = e0
% 27.02/7.44 |
% 27.02/7.44 | Simplifying 571 yields:
% 27.02/7.44 | (560) e1 = e0
% 27.02/7.44 |
% 27.02/7.44 | Equations (560) can reduce 132 to:
% 27.02/7.44 | (270) $false
% 27.02/7.44 |
% 27.02/7.44 |-The branch is then unsatisfiable
% 27.02/7.44 |-Branch two:
% 27.02/7.44 | (562) ~ (all_0_48_48 = e0)
% 27.02/7.44 | (575) all_0_53_53 = e0 | all_0_58_58 = e0
% 27.02/7.44 |
% 27.02/7.44 +-Applying beta-rule and splitting (449), into two cases.
% 27.02/7.44 |-Branch one:
% 27.02/7.44 | (576) all_0_53_53 = e2
% 27.02/7.44 |
% 27.02/7.44 | Combining equations (576,367) yields a new equation:
% 27.02/7.44 | (269) e4 = e2
% 27.02/7.44 |
% 27.02/7.44 | Equations (269) can reduce 231 to:
% 27.02/7.44 | (270) $false
% 27.02/7.44 |
% 27.02/7.44 |-The branch is then unsatisfiable
% 27.02/7.44 |-Branch two:
% 27.02/7.44 | (259) ~ (all_0_53_53 = e2)
% 27.02/7.44 | (396) all_0_58_58 = e2
% 27.02/7.44 |
% 27.02/7.44 +-Applying beta-rule and splitting (575), into two cases.
% 27.02/7.44 |-Branch one:
% 27.02/7.44 | (423) all_0_53_53 = e0
% 27.02/7.44 |
% 27.02/7.44 | Combining equations (423,367) yields a new equation:
% 27.02/7.44 | (479) e4 = e0
% 27.02/7.44 |
% 27.02/7.44 | Equations (479) can reduce 6 to:
% 27.02/7.44 | (270) $false
% 27.02/7.44 |
% 27.02/7.44 |-The branch is then unsatisfiable
% 27.02/7.44 |-Branch two:
% 27.02/7.44 | (584) ~ (all_0_53_53 = e0)
% 27.02/7.44 | (585) all_0_58_58 = e0
% 27.02/7.44 |
% 27.02/7.44 | Combining equations (585,396) yields a new equation:
% 27.02/7.44 | (316) e2 = e0
% 27.02/7.44 |
% 27.02/7.44 | Equations (316) can reduce 57 to:
% 27.02/7.44 | (270) $false
% 27.02/7.44 |
% 27.02/7.44 |-The branch is then unsatisfiable
% 27.02/7.44 |-Branch two:
% 27.02/7.44 | (588) ~ (all_0_48_48 = e1)
% 27.02/7.44 | (589) all_0_49_49 = e1
% 27.02/7.44 |
% 27.02/7.44 | Equations (589) can reduce 543 to:
% 27.02/7.44 | (270) $false
% 27.02/7.44 |
% 27.02/7.44 |-The branch is then unsatisfiable
% 27.02/7.44 |-Branch two:
% 27.02/7.44 | (591) ~ (all_0_39_39 = e4)
% 27.02/7.44 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 27.02/7.44 |
% 27.02/7.44 +-Applying beta-rule and splitting (592), into two cases.
% 27.02/7.44 |-Branch one:
% 27.02/7.44 | (358) all_0_41_41 = e4
% 27.02/7.44 |
% 27.02/7.44 | Combining equations (351,358) yields a new equation:
% 27.02/7.44 | (359) e4 = e3
% 27.02/7.44 |
% 27.02/7.44 | Equations (359) can reduce 34 to:
% 27.02/7.44 | (270) $false
% 27.02/7.44 |
% 27.02/7.44 |-The branch is then unsatisfiable
% 27.02/7.44 |-Branch two:
% 27.02/7.44 | (361) ~ (all_0_41_41 = e4)
% 27.02/7.44 | (512) all_0_42_42 = e4
% 27.02/7.44 |
% 27.02/7.44 | Equations (512) can reduce 520 to:
% 27.02/7.44 | (270) $false
% 27.02/7.44 |
% 27.02/7.44 |-The branch is then unsatisfiable
% 27.02/7.44 |-Branch two:
% 27.02/7.44 | (599) ~ (all_0_53_53 = e4)
% 27.02/7.44 | (600) all_0_58_58 = e4
% 27.02/7.44 |
% 27.02/7.44 | Equations (600) can reduce 278 to:
% 27.02/7.44 | (270) $false
% 27.02/7.44 |
% 27.02/7.44 |-The branch is then unsatisfiable
% 27.02/7.44 |-Branch two:
% 27.02/7.44 | (602) ~ (all_0_40_40 = e2)
% 27.02/7.44 | (603) all_0_40_40 = e3 | all_0_40_40 = e1
% 27.02/7.44 |
% 27.02/7.44 +-Applying beta-rule and splitting (20), into two cases.
% 27.02/7.44 |-Branch one:
% 27.02/7.44 | (327) all_0_40_40 = e2
% 27.02/7.44 |
% 27.02/7.44 | Equations (327) can reduce 602 to:
% 27.02/7.44 | (270) $false
% 27.02/7.44 |
% 27.02/7.44 |-The branch is then unsatisfiable
% 27.02/7.44 |-Branch two:
% 27.02/7.44 | (602) ~ (all_0_40_40 = e2)
% 27.02/7.44 | (607) all_0_44_44 = e2 | all_0_52_52 = e2 | all_0_57_57 = e2
% 27.02/7.44 |
% 27.02/7.44 +-Applying beta-rule and splitting (193), into two cases.
% 27.02/7.44 |-Branch one:
% 27.02/7.44 | (370) all_0_44_44 = e2
% 27.02/7.44 |
% 27.02/7.44 | Equations (370) can reduce 15 to:
% 27.02/7.44 | (602) ~ (all_0_40_40 = e2)
% 27.02/7.44 |
% 27.02/7.44 | Equations (370) can reduce 241 to:
% 27.02/7.44 | (292) ~ (all_0_43_43 = e2)
% 27.02/7.44 |
% 27.02/7.44 | Equations (370) can reduce 229 to:
% 27.02/7.44 | (611) ~ (all_0_45_45 = e2)
% 27.02/7.44 |
% 27.02/7.44 | Simplifying 611 yields:
% 27.02/7.44 | (434) ~ (all_0_45_45 = e2)
% 27.02/7.44 |
% 27.02/7.44 | Equations (370) can reduce 122 to:
% 27.02/7.44 | (256) ~ (all_0_52_52 = e2)
% 27.02/7.44 |
% 27.02/7.44 | Simplifying 256 yields:
% 27.02/7.44 | (257) ~ (all_0_52_52 = e2)
% 27.02/7.44 |
% 27.02/7.44 | Equations (370) can reduce 10 to:
% 27.02/7.44 | (334) ~ (all_0_57_57 = e2)
% 27.02/7.44 |
% 27.02/7.44 | Simplifying 334 yields:
% 27.02/7.44 | (335) ~ (all_0_57_57 = e2)
% 27.02/7.44 |
% 27.02/7.44 | Equations (370) can reduce 45 to:
% 27.02/7.44 | (377) ~ (e4 = e2)
% 27.02/7.44 |
% 27.02/7.44 | Simplifying 377 yields:
% 27.02/7.44 | (231) ~ (e4 = e2)
% 27.02/7.44 |
% 27.02/7.44 | From (370) and (165) follows:
% 27.02/7.44 | (619) op(e2, e2) = all_0_15_15
% 27.02/7.44 |
% 27.02/7.44 | Instantiating formula (201) with e2, e2, all_0_15_15, e4 and discharging atoms op(e2, e2) = all_0_15_15, op(e2, e2) = e4, yields:
% 27.02/7.44 | (620) all_0_15_15 = e4
% 27.02/7.44 |
% 27.02/7.44 +-Applying beta-rule and splitting (9), into two cases.
% 27.02/7.44 |-Branch one:
% 27.02/7.44 | (621) all_0_44_44 = e0
% 27.02/7.44 |
% 27.02/7.44 | Combining equations (370,621) yields a new equation:
% 27.02/7.44 | (622) e2 = e0
% 27.02/7.44 |
% 27.02/7.44 | Simplifying 622 yields:
% 27.02/7.44 | (316) e2 = e0
% 27.02/7.44 |
% 27.02/7.44 | Equations (316) can reduce 57 to:
% 27.02/7.44 | (270) $false
% 27.02/7.44 |
% 27.02/7.44 |-The branch is then unsatisfiable
% 27.02/7.44 |-Branch two:
% 27.02/7.44 | (625) ~ (all_0_44_44 = e0)
% 27.02/7.44 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 27.02/7.44 |
% 27.02/7.44 +-Applying beta-rule and splitting (164), into two cases.
% 27.02/7.44 |-Branch one:
% 27.02/7.44 | (336) all_0_39_39 = e2
% 27.02/7.44 |
% 27.02/7.44 | Equations (336) can reduce 291 to:
% 27.02/7.44 | (270) $false
% 27.02/7.44 |
% 27.02/7.44 |-The branch is then unsatisfiable
% 27.02/7.44 |-Branch two:
% 27.02/7.44 | (291) ~ (all_0_39_39 = e2)
% 27.02/7.45 | (630) all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (186), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (336) all_0_39_39 = e2
% 27.02/7.45 |
% 27.02/7.45 | Equations (336) can reduce 291 to:
% 27.02/7.45 | (270) $false
% 27.02/7.45 |
% 27.02/7.45 |-The branch is then unsatisfiable
% 27.02/7.45 |-Branch two:
% 27.02/7.45 | (291) ~ (all_0_39_39 = e2)
% 27.02/7.45 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (8), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (530) all_0_40_40 = e1
% 27.02/7.45 |
% 27.02/7.45 | Equations (530) can reduce 114 to:
% 27.02/7.45 | (528) ~ (all_0_39_39 = e1)
% 27.02/7.45 |
% 27.02/7.45 | Equations (530) can reduce 147 to:
% 27.02/7.45 | (637) ~ (all_0_41_41 = e1)
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 637 yields:
% 27.02/7.45 | (540) ~ (all_0_41_41 = e1)
% 27.02/7.45 |
% 27.02/7.45 | Equations (530) can reduce 145 to:
% 27.02/7.45 | (639) ~ (all_0_42_42 = e1)
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 639 yields:
% 27.02/7.45 | (640) ~ (all_0_42_42 = e1)
% 27.02/7.45 |
% 27.02/7.45 | Equations (530) can reduce 137 to:
% 27.02/7.45 | (641) ~ (all_0_52_52 = e1)
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 641 yields:
% 27.02/7.45 | (642) ~ (all_0_52_52 = e1)
% 27.02/7.45 |
% 27.02/7.45 | Equations (530) can reduce 149 to:
% 27.02/7.45 | (643) ~ (all_0_57_57 = e1)
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 643 yields:
% 27.02/7.45 | (644) ~ (all_0_57_57 = e1)
% 27.02/7.45 |
% 27.02/7.45 | Equations (530) can reduce 602 to:
% 27.02/7.45 | (645) ~ (e2 = e1)
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 645 yields:
% 27.02/7.45 | (141) ~ (e2 = e1)
% 27.02/7.45 |
% 27.02/7.45 | Equations (530) can reduce 238 to:
% 27.02/7.45 | (132) ~ (e1 = e0)
% 27.02/7.45 |
% 27.02/7.45 | From (530) and (68) follows:
% 27.02/7.45 | (648) op(e2, e1) = all_0_13_13
% 27.02/7.45 |
% 27.02/7.45 | Instantiating formula (201) with e2, e1, all_0_13_13, all_0_48_48 and discharging atoms op(e2, e1) = all_0_13_13, op(e2, e1) = all_0_48_48, yields:
% 27.02/7.45 | (649) all_0_13_13 = all_0_48_48
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (87), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (650) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (650), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (651) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (651), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (652) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 27.02/7.45 |
% 27.02/7.45 | Applying alpha-rule on (652) yields:
% 27.02/7.45 | (653) all_0_13_13 = e4
% 27.02/7.45 | (654) ~ (all_0_14_14 = e2)
% 27.02/7.45 |
% 27.02/7.45 | Combining equations (653,649) yields a new equation:
% 27.02/7.45 | (655) all_0_48_48 = e4
% 27.02/7.45 |
% 27.02/7.45 | Equations (655) can reduce 192 to:
% 27.02/7.45 | (270) $false
% 27.02/7.45 |
% 27.02/7.45 |-The branch is then unsatisfiable
% 27.02/7.45 |-Branch two:
% 27.02/7.45 | (657) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 27.02/7.45 |
% 27.02/7.45 | Applying alpha-rule on (657) yields:
% 27.02/7.45 | (658) all_0_15_15 = e3
% 27.02/7.45 | (659) ~ (all_0_16_16 = e2)
% 27.02/7.45 |
% 27.02/7.45 | Combining equations (620,658) yields a new equation:
% 27.02/7.45 | (660) e4 = e3
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 660 yields:
% 27.02/7.45 | (359) e4 = e3
% 27.02/7.45 |
% 27.02/7.45 | Equations (359) can reduce 34 to:
% 27.02/7.45 | (270) $false
% 27.02/7.45 |
% 27.02/7.45 |-The branch is then unsatisfiable
% 27.02/7.45 |-Branch two:
% 27.02/7.45 | (663) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 27.02/7.45 |
% 27.02/7.45 | Applying alpha-rule on (663) yields:
% 27.02/7.45 | (664) all_0_17_17 = e1
% 27.02/7.45 | (665) ~ (all_0_18_18 = e2)
% 27.02/7.45 |
% 27.02/7.45 | From (664) and (27) follows:
% 27.02/7.45 | (666) op(e2, all_0_52_52) = e1
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (33), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (392) all_0_57_57 = e2
% 27.02/7.45 |
% 27.02/7.45 | Equations (392) can reduce 335 to:
% 27.02/7.45 | (270) $false
% 27.02/7.45 |
% 27.02/7.45 |-The branch is then unsatisfiable
% 27.02/7.45 |-Branch two:
% 27.02/7.45 | (335) ~ (all_0_57_57 = e2)
% 27.02/7.45 | (670) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (133), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (671) all_0_40_40 = e3
% 27.02/7.45 |
% 27.02/7.45 | Combining equations (671,530) yields a new equation:
% 27.02/7.45 | (537) e3 = e1
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 537 yields:
% 27.02/7.45 | (538) e3 = e1
% 27.02/7.45 |
% 27.02/7.45 | Equations (538) can reduce 136 to:
% 27.02/7.45 | (270) $false
% 27.02/7.45 |
% 27.02/7.45 |-The branch is then unsatisfiable
% 27.02/7.45 |-Branch two:
% 27.02/7.45 | (675) ~ (all_0_40_40 = e3)
% 27.02/7.45 | (676) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (99), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (524) all_0_39_39 = e1
% 27.02/7.45 |
% 27.02/7.45 | Equations (524) can reduce 528 to:
% 27.02/7.45 | (270) $false
% 27.02/7.45 |
% 27.02/7.45 |-The branch is then unsatisfiable
% 27.02/7.45 |-Branch two:
% 27.02/7.45 | (528) ~ (all_0_39_39 = e1)
% 27.02/7.45 | (680) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (177), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (336) all_0_39_39 = e2
% 27.02/7.45 |
% 27.02/7.45 | Equations (336) can reduce 291 to:
% 27.02/7.45 | (270) $false
% 27.02/7.45 |
% 27.02/7.45 |-The branch is then unsatisfiable
% 27.02/7.45 |-Branch two:
% 27.02/7.45 | (291) ~ (all_0_39_39 = e2)
% 27.02/7.45 | (684) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (90), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (685) all_0_52_52 = e2
% 27.02/7.45 |
% 27.02/7.45 | Equations (685) can reduce 257 to:
% 27.02/7.45 | (270) $false
% 27.02/7.45 |
% 27.02/7.45 |-The branch is then unsatisfiable
% 27.02/7.45 |-Branch two:
% 27.02/7.45 | (257) ~ (all_0_52_52 = e2)
% 27.02/7.45 | (688) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (222), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (522) all_0_39_39 = e4
% 27.02/7.45 |
% 27.02/7.45 | Equations (522) can reduce 226 to:
% 27.02/7.45 | (690) ~ (all_0_41_41 = e4)
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 690 yields:
% 27.02/7.45 | (361) ~ (all_0_41_41 = e4)
% 27.02/7.45 |
% 27.02/7.45 | Equations (522) can reduce 184 to:
% 27.02/7.45 | (692) ~ (all_0_42_42 = e4)
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 692 yields:
% 27.02/7.45 | (520) ~ (all_0_42_42 = e4)
% 27.02/7.45 |
% 27.02/7.45 | Equations (522) can reduce 167 to:
% 27.02/7.45 | (694) ~ (all_0_43_43 = e4)
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 694 yields:
% 27.02/7.45 | (510) ~ (all_0_43_43 = e4)
% 27.02/7.45 |
% 27.02/7.45 | Equations (522) can reduce 32 to:
% 27.02/7.45 | (696) ~ (all_0_51_51 = e4)
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 696 yields:
% 27.02/7.45 | (697) ~ (all_0_51_51 = e4)
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (16), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (698) all_0_42_42 = e2
% 27.02/7.45 |
% 27.02/7.45 | Equations (698) can reduce 94 to:
% 27.02/7.45 | (331) ~ (all_0_41_41 = e2)
% 27.02/7.45 |
% 27.02/7.45 | Equations (698) can reduce 17 to:
% 27.02/7.45 | (700) ~ (all_0_59_59 = e2)
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 700 yields:
% 27.02/7.45 | (701) ~ (all_0_59_59 = e2)
% 27.02/7.45 |
% 27.02/7.45 | Equations (698) can reduce 520 to:
% 27.02/7.45 | (377) ~ (e4 = e2)
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 377 yields:
% 27.02/7.45 | (231) ~ (e4 = e2)
% 27.02/7.45 |
% 27.02/7.45 | Equations (698) can reduce 640 to:
% 27.02/7.45 | (141) ~ (e2 = e1)
% 27.02/7.45 |
% 27.02/7.45 | Equations (698) can reduce 199 to:
% 27.02/7.45 | (57) ~ (e2 = e0)
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (217), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (436) all_0_41_41 = e2
% 27.02/7.45 |
% 27.02/7.45 | Equations (436) can reduce 331 to:
% 27.02/7.45 | (270) $false
% 27.02/7.45 |
% 27.02/7.45 |-The branch is then unsatisfiable
% 27.02/7.45 |-Branch two:
% 27.02/7.45 | (331) ~ (all_0_41_41 = e2)
% 27.02/7.45 | (709) all_0_41_41 = e4 | all_0_41_41 = e3 | all_0_41_41 = e1
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (709), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (351) all_0_41_41 = e3
% 27.02/7.45 |
% 27.02/7.45 | Equations (351) can reduce 51 to:
% 27.02/7.45 | (353) ~ (all_0_45_45 = e3)
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 353 yields:
% 27.02/7.45 | (354) ~ (all_0_45_45 = e3)
% 27.02/7.45 |
% 27.02/7.45 | Equations (351) can reduce 190 to:
% 27.02/7.45 | (713) ~ (all_0_48_48 = e3)
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 713 yields:
% 27.02/7.45 | (121) ~ (all_0_48_48 = e3)
% 27.02/7.45 |
% 27.02/7.45 | Equations (351) can reduce 214 to:
% 27.02/7.45 | (355) ~ (all_0_53_53 = e3)
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 355 yields:
% 27.02/7.45 | (356) ~ (all_0_53_53 = e3)
% 27.02/7.45 |
% 27.02/7.45 | Equations (351) can reduce 157 to:
% 27.02/7.45 | (717) ~ (all_0_58_58 = e3)
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 717 yields:
% 27.02/7.45 | (718) ~ (all_0_58_58 = e3)
% 27.02/7.45 |
% 27.02/7.45 | Equations (351) can reduce 361 to:
% 27.02/7.45 | (719) ~ (e4 = e3)
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 719 yields:
% 27.02/7.45 | (34) ~ (e4 = e3)
% 27.02/7.45 |
% 27.02/7.45 | Equations (351) can reduce 540 to:
% 27.02/7.45 | (136) ~ (e3 = e1)
% 27.02/7.45 |
% 27.02/7.45 | Equations (351) can reduce 232 to:
% 27.02/7.45 | (66) ~ (e3 = e0)
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (168), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (382) all_0_55_55 = e2
% 27.02/7.45 |
% 27.02/7.45 | Combining equations (382,272) yields a new equation:
% 27.02/7.45 | (269) e4 = e2
% 27.02/7.45 |
% 27.02/7.45 | Equations (269) can reduce 231 to:
% 27.02/7.45 | (270) $false
% 27.02/7.45 |
% 27.02/7.45 |-The branch is then unsatisfiable
% 27.02/7.45 |-Branch two:
% 27.02/7.45 | (386) ~ (all_0_55_55 = e2)
% 27.02/7.45 | (387) all_0_56_56 = e2 | all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (387), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (388) all_0_56_56 = e2
% 27.02/7.45 |
% 27.02/7.45 | Equations (388) can reduce 300 to:
% 27.02/7.45 | (270) $false
% 27.02/7.45 |
% 27.02/7.45 |-The branch is then unsatisfiable
% 27.02/7.45 |-Branch two:
% 27.02/7.45 | (300) ~ (all_0_56_56 = e2)
% 27.02/7.45 | (391) all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (391), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (392) all_0_57_57 = e2
% 27.02/7.45 |
% 27.02/7.45 | Equations (392) can reduce 335 to:
% 27.02/7.45 | (270) $false
% 27.02/7.45 |
% 27.02/7.45 |-The branch is then unsatisfiable
% 27.02/7.45 |-Branch two:
% 27.02/7.45 | (335) ~ (all_0_57_57 = e2)
% 27.02/7.45 | (395) all_0_58_58 = e2 | all_0_59_59 = e2
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (395), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (396) all_0_58_58 = e2
% 27.02/7.45 |
% 27.02/7.45 | Equations (396) can reduce 108 to:
% 27.02/7.45 | (434) ~ (all_0_45_45 = e2)
% 27.02/7.45 |
% 27.02/7.45 | Equations (396) can reduce 70 to:
% 27.02/7.45 | (259) ~ (all_0_53_53 = e2)
% 27.02/7.45 |
% 27.02/7.45 | Equations (396) can reduce 156 to:
% 27.02/7.45 | (700) ~ (all_0_59_59 = e2)
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 700 yields:
% 27.02/7.45 | (701) ~ (all_0_59_59 = e2)
% 27.02/7.45 |
% 27.02/7.45 | Equations (396) can reduce 718 to:
% 27.02/7.45 | (301) ~ (e3 = e2)
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 301 yields:
% 27.02/7.45 | (223) ~ (e3 = e2)
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (44), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (502) all_0_43_43 = e4
% 27.02/7.45 |
% 27.02/7.45 | Equations (502) can reduce 510 to:
% 27.02/7.45 | (270) $false
% 27.02/7.45 |
% 27.02/7.45 |-The branch is then unsatisfiable
% 27.02/7.45 |-Branch two:
% 27.02/7.45 | (510) ~ (all_0_43_43 = e4)
% 27.02/7.45 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (194), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (747) all_0_56_56 = e1
% 27.02/7.45 |
% 27.02/7.45 | Equations (747) can reduce 60 to:
% 27.02/7.45 | (748) ~ (all_0_51_51 = e1)
% 27.02/7.45 |
% 27.02/7.45 | Equations (747) can reduce 185 to:
% 27.02/7.45 | (749) ~ (all_0_59_59 = e1)
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 749 yields:
% 27.02/7.45 | (750) ~ (all_0_59_59 = e1)
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (178), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (751) all_0_39_39 = e3
% 27.02/7.45 |
% 27.02/7.45 | Combining equations (522,751) yields a new equation:
% 27.02/7.45 | (660) e4 = e3
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 660 yields:
% 27.02/7.45 | (359) e4 = e3
% 27.02/7.45 |
% 27.02/7.45 | Equations (359) can reduce 34 to:
% 27.02/7.45 | (270) $false
% 27.02/7.45 |
% 27.02/7.45 |-The branch is then unsatisfiable
% 27.02/7.45 |-Branch two:
% 27.02/7.45 | (755) ~ (all_0_39_39 = e3)
% 27.02/7.45 | (756) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (52), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (536) all_0_41_41 = e1
% 27.02/7.45 |
% 27.02/7.45 | Combining equations (351,536) yields a new equation:
% 27.02/7.45 | (537) e3 = e1
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 537 yields:
% 27.02/7.45 | (538) e3 = e1
% 27.02/7.45 |
% 27.02/7.45 | Equations (538) can reduce 136 to:
% 27.02/7.45 | (270) $false
% 27.02/7.45 |
% 27.02/7.45 |-The branch is then unsatisfiable
% 27.02/7.45 |-Branch two:
% 27.02/7.45 | (540) ~ (all_0_41_41 = e1)
% 27.02/7.45 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 27.02/7.45 |
% 27.02/7.45 | Equations (351) can reduce 540 to:
% 27.02/7.45 | (136) ~ (e3 = e1)
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (236), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (764) all_0_56_56 = e3
% 27.02/7.45 |
% 27.02/7.45 | Combining equations (747,764) yields a new equation:
% 27.02/7.45 | (538) e3 = e1
% 27.02/7.45 |
% 27.02/7.45 | Equations (538) can reduce 136 to:
% 27.02/7.45 | (270) $false
% 27.02/7.45 |
% 27.02/7.45 |-The branch is then unsatisfiable
% 27.02/7.45 |-Branch two:
% 27.02/7.45 | (767) ~ (all_0_56_56 = e3)
% 27.02/7.45 | (768) all_0_57_57 = e3 | all_0_58_58 = e3 | all_0_59_59 = e3
% 27.02/7.45 |
% 27.02/7.45 | Equations (747) can reduce 767 to:
% 27.02/7.45 | (769) ~ (e3 = e1)
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 769 yields:
% 27.02/7.45 | (136) ~ (e3 = e1)
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (159), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (450) all_0_43_43 = e2
% 27.02/7.45 |
% 27.02/7.45 | Equations (450) can reduce 292 to:
% 27.02/7.45 | (270) $false
% 27.02/7.45 |
% 27.02/7.45 |-The branch is then unsatisfiable
% 27.02/7.45 |-Branch two:
% 27.02/7.45 | (292) ~ (all_0_43_43 = e2)
% 27.02/7.45 | (774) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (75), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.45 | (411) all_0_43_43 = e0
% 27.02/7.45 |
% 27.02/7.45 | Equations (411) can reduce 84 to:
% 27.02/7.45 | (776) ~ (all_0_45_45 = e0)
% 27.02/7.45 |
% 27.02/7.45 | Simplifying 776 yields:
% 27.02/7.45 | (488) ~ (all_0_45_45 = e0)
% 27.02/7.45 |
% 27.02/7.45 +-Applying beta-rule and splitting (105), into two cases.
% 27.02/7.45 |-Branch one:
% 27.02/7.46 | (374) all_0_45_45 = e2
% 27.02/7.46 |
% 27.02/7.46 | Equations (374) can reduce 434 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (434) ~ (all_0_45_45 = e2)
% 27.02/7.46 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (22), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (782) all_0_43_43 = e3
% 27.02/7.46 |
% 27.02/7.46 | Combining equations (782,411) yields a new equation:
% 27.02/7.46 | (783) e3 = e0
% 27.02/7.46 |
% 27.02/7.46 | Simplifying 783 yields:
% 27.02/7.46 | (784) e3 = e0
% 27.02/7.46 |
% 27.02/7.46 | Equations (784) can reduce 66 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (786) ~ (all_0_43_43 = e3)
% 27.02/7.46 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 27.02/7.46 |
% 27.02/7.46 | Equations (411) can reduce 786 to:
% 27.02/7.46 | (788) ~ (e3 = e0)
% 27.02/7.46 |
% 27.02/7.46 | Simplifying 788 yields:
% 27.02/7.46 | (66) ~ (e3 = e0)
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (435), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (454) all_0_45_45 = e0
% 27.02/7.46 |
% 27.02/7.46 | Equations (454) can reduce 488 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (488) ~ (all_0_45_45 = e0)
% 27.02/7.46 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (756), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (782) all_0_43_43 = e3
% 27.02/7.46 |
% 27.02/7.46 | Combining equations (782,411) yields a new equation:
% 27.02/7.46 | (783) e3 = e0
% 27.02/7.46 |
% 27.02/7.46 | Simplifying 783 yields:
% 27.02/7.46 | (784) e3 = e0
% 27.02/7.46 |
% 27.02/7.46 | Equations (784) can reduce 66 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (786) ~ (all_0_43_43 = e3)
% 27.02/7.46 | (799) all_0_51_51 = e3 | all_0_56_56 = e3
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (489), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (505) all_0_45_45 = e3
% 27.02/7.46 |
% 27.02/7.46 | Equations (505) can reduce 354 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (354) ~ (all_0_45_45 = e3)
% 27.02/7.46 | (363) all_0_45_45 = e4
% 27.02/7.46 |
% 27.02/7.46 | Equations (363) can reduce 38 to:
% 27.02/7.46 | (804) ~ (all_0_46_46 = e4)
% 27.02/7.46 |
% 27.02/7.46 | Simplifying 804 yields:
% 27.02/7.46 | (805) ~ (all_0_46_46 = e4)
% 27.02/7.46 |
% 27.02/7.46 | Equations (363) can reduce 434 to:
% 27.02/7.46 | (231) ~ (e4 = e2)
% 27.02/7.46 |
% 27.02/7.46 | Equations (363) can reduce 26 to:
% 27.02/7.46 | (251) ~ (e4 = e1)
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (179), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (512) all_0_42_42 = e4
% 27.02/7.46 |
% 27.02/7.46 | Combining equations (698,512) yields a new equation:
% 27.02/7.46 | (269) e4 = e2
% 27.02/7.46 |
% 27.02/7.46 | Equations (269) can reduce 231 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (520) ~ (all_0_42_42 = e4)
% 27.02/7.46 | (521) all_0_46_46 = e4 | all_0_54_54 = e4 | all_0_59_59 = e4
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (521), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (517) all_0_46_46 = e4
% 27.02/7.46 |
% 27.02/7.46 | Equations (517) can reduce 805 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (805) ~ (all_0_46_46 = e4)
% 27.02/7.46 | (816) all_0_54_54 = e4 | all_0_59_59 = e4
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (816), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (817) all_0_54_54 = e4
% 27.02/7.46 |
% 27.02/7.46 | Equations (817) can reduce 72 to:
% 27.02/7.46 | (279) ~ (all_0_59_59 = e4)
% 27.02/7.46 |
% 27.02/7.46 | Simplifying 279 yields:
% 27.02/7.46 | (280) ~ (all_0_59_59 = e4)
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (135), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (820) all_0_51_51 = e1
% 27.02/7.46 |
% 27.02/7.46 | Equations (820) can reduce 748 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (748) ~ (all_0_51_51 = e1)
% 27.02/7.46 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (799), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (824) all_0_51_51 = e3
% 27.02/7.46 |
% 27.02/7.46 | Equations (824) can reduce 154 to:
% 27.02/7.46 | (825) ~ (all_0_52_52 = e3)
% 27.02/7.46 |
% 27.02/7.46 | Simplifying 825 yields:
% 27.02/7.46 | (826) ~ (all_0_52_52 = e3)
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (688), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (827) all_0_52_52 = e0
% 27.02/7.46 |
% 27.02/7.46 | Equations (827) can reduce 642 to:
% 27.02/7.46 | (568) ~ (e1 = e0)
% 27.02/7.46 |
% 27.02/7.46 | Simplifying 568 yields:
% 27.02/7.46 | (132) ~ (e1 = e0)
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (176), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (830) all_0_56_56 = e0
% 27.02/7.46 |
% 27.02/7.46 | Combining equations (830,747) yields a new equation:
% 27.02/7.46 | (560) e1 = e0
% 27.02/7.46 |
% 27.02/7.46 | Equations (560) can reduce 132 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (419) ~ (all_0_56_56 = e0)
% 27.02/7.46 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 27.02/7.46 |
% 27.02/7.46 | Equations (747) can reduce 419 to:
% 27.02/7.46 | (132) ~ (e1 = e0)
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (93), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (402) all_0_59_59 = e4
% 27.02/7.46 |
% 27.02/7.46 | Equations (402) can reduce 280 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (280) ~ (all_0_59_59 = e4)
% 27.02/7.46 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (407), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (408), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (409), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.02/7.46 |
% 27.02/7.46 | Applying alpha-rule on (410) yields:
% 27.02/7.46 | (411) all_0_43_43 = e0
% 27.02/7.46 | (412) all_0_59_59 = e3
% 27.02/7.46 | (413) ~ (all_0_46_46 = e3)
% 27.02/7.46 |
% 27.02/7.46 | Equations (412) can reduce 140 to:
% 27.02/7.46 | (846) ~ (all_0_57_57 = e3)
% 27.02/7.46 |
% 27.02/7.46 | Equations (412) can reduce 701 to:
% 27.02/7.46 | (223) ~ (e3 = e2)
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (823), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (848) all_0_52_52 = e1
% 27.02/7.46 |
% 27.02/7.46 | Combining equations (827,848) yields a new equation:
% 27.02/7.46 | (560) e1 = e0
% 27.02/7.46 |
% 27.02/7.46 | Equations (560) can reduce 132 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (642) ~ (all_0_52_52 = e1)
% 27.02/7.46 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (852), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (853) all_0_53_53 = e1
% 27.02/7.46 |
% 27.02/7.46 | Equations (853) can reduce 48 to:
% 27.02/7.46 | (588) ~ (all_0_48_48 = e1)
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (314), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (559) all_0_48_48 = e0
% 27.02/7.46 |
% 27.02/7.46 | Equations (559) can reduce 121 to:
% 27.02/7.46 | (788) ~ (e3 = e0)
% 27.02/7.46 |
% 27.02/7.46 | Simplifying 788 yields:
% 27.02/7.46 | (66) ~ (e3 = e0)
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (676), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (858) all_0_44_44 = e3
% 27.02/7.46 |
% 27.02/7.46 | Combining equations (858,370) yields a new equation:
% 27.02/7.46 | (437) e3 = e2
% 27.02/7.46 |
% 27.02/7.46 | Simplifying 437 yields:
% 27.02/7.46 | (414) e3 = e2
% 27.02/7.46 |
% 27.02/7.46 | Equations (414) can reduce 223 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (862) ~ (all_0_44_44 = e3)
% 27.02/7.46 | (863) all_0_52_52 = e3 | all_0_57_57 = e3
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (863), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (864) all_0_52_52 = e3
% 27.02/7.46 |
% 27.02/7.46 | Combining equations (864,827) yields a new equation:
% 27.02/7.46 | (783) e3 = e0
% 27.02/7.46 |
% 27.02/7.46 | Simplifying 783 yields:
% 27.02/7.46 | (784) e3 = e0
% 27.02/7.46 |
% 27.02/7.46 | Equations (784) can reduce 66 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (826) ~ (all_0_52_52 = e3)
% 27.02/7.46 | (869) all_0_57_57 = e3
% 27.02/7.46 |
% 27.02/7.46 | Equations (869) can reduce 846 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (562) ~ (all_0_48_48 = e0)
% 27.02/7.46 | (552) all_0_48_48 = e1
% 27.02/7.46 |
% 27.02/7.46 | Equations (552) can reduce 588 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (874) ~ (all_0_53_53 = e1)
% 27.02/7.46 | (875) all_0_54_54 = e1
% 27.02/7.46 |
% 27.02/7.46 | Combining equations (875,817) yields a new equation:
% 27.02/7.46 | (526) e4 = e1
% 27.02/7.46 |
% 27.02/7.46 | Equations (526) can reduce 251 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.02/7.46 |
% 27.02/7.46 | Applying alpha-rule on (416) yields:
% 27.02/7.46 | (411) all_0_43_43 = e0
% 27.02/7.46 | (412) all_0_59_59 = e3
% 27.02/7.46 | (419) ~ (all_0_56_56 = e0)
% 27.02/7.46 |
% 27.02/7.46 | Equations (747) can reduce 419 to:
% 27.02/7.46 | (132) ~ (e1 = e0)
% 27.02/7.46 |
% 27.02/7.46 | Equations (412) can reduce 140 to:
% 27.02/7.46 | (846) ~ (all_0_57_57 = e3)
% 27.02/7.46 |
% 27.02/7.46 | Equations (412) can reduce 701 to:
% 27.02/7.46 | (223) ~ (e3 = e2)
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (823), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (848) all_0_52_52 = e1
% 27.02/7.46 |
% 27.02/7.46 | Combining equations (827,848) yields a new equation:
% 27.02/7.46 | (560) e1 = e0
% 27.02/7.46 |
% 27.02/7.46 | Equations (560) can reduce 132 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (642) ~ (all_0_52_52 = e1)
% 27.02/7.46 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (852), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (853) all_0_53_53 = e1
% 27.02/7.46 |
% 27.02/7.46 | Equations (853) can reduce 48 to:
% 27.02/7.46 | (588) ~ (all_0_48_48 = e1)
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (314), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (559) all_0_48_48 = e0
% 27.02/7.46 |
% 27.02/7.46 | Equations (559) can reduce 121 to:
% 27.02/7.46 | (788) ~ (e3 = e0)
% 27.02/7.46 |
% 27.02/7.46 | Simplifying 788 yields:
% 27.02/7.46 | (66) ~ (e3 = e0)
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (676), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (858) all_0_44_44 = e3
% 27.02/7.46 |
% 27.02/7.46 | Combining equations (858,370) yields a new equation:
% 27.02/7.46 | (437) e3 = e2
% 27.02/7.46 |
% 27.02/7.46 | Simplifying 437 yields:
% 27.02/7.46 | (414) e3 = e2
% 27.02/7.46 |
% 27.02/7.46 | Equations (414) can reduce 223 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (862) ~ (all_0_44_44 = e3)
% 27.02/7.46 | (863) all_0_52_52 = e3 | all_0_57_57 = e3
% 27.02/7.46 |
% 27.02/7.46 +-Applying beta-rule and splitting (863), into two cases.
% 27.02/7.46 |-Branch one:
% 27.02/7.46 | (864) all_0_52_52 = e3
% 27.02/7.46 |
% 27.02/7.46 | Combining equations (864,827) yields a new equation:
% 27.02/7.46 | (783) e3 = e0
% 27.02/7.46 |
% 27.02/7.46 | Simplifying 783 yields:
% 27.02/7.46 | (784) e3 = e0
% 27.02/7.46 |
% 27.02/7.46 | Equations (784) can reduce 66 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (826) ~ (all_0_52_52 = e3)
% 27.02/7.46 | (869) all_0_57_57 = e3
% 27.02/7.46 |
% 27.02/7.46 | Equations (869) can reduce 846 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (562) ~ (all_0_48_48 = e0)
% 27.02/7.46 | (552) all_0_48_48 = e1
% 27.02/7.46 |
% 27.02/7.46 | Equations (552) can reduce 588 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (874) ~ (all_0_53_53 = e1)
% 27.02/7.46 | (875) all_0_54_54 = e1
% 27.02/7.46 |
% 27.02/7.46 | Combining equations (875,817) yields a new equation:
% 27.02/7.46 | (526) e4 = e1
% 27.02/7.46 |
% 27.02/7.46 | Equations (526) can reduce 251 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.02/7.46 |
% 27.02/7.46 | Applying alpha-rule on (422) yields:
% 27.02/7.46 | (423) all_0_53_53 = e0
% 27.02/7.46 | (424) all_0_59_59 = e1
% 27.02/7.46 | (425) ~ (all_0_54_54 = e1)
% 27.02/7.46 |
% 27.02/7.46 | Equations (424) can reduce 750 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.02/7.46 |
% 27.02/7.46 | Applying alpha-rule on (428) yields:
% 27.02/7.46 | (423) all_0_53_53 = e0
% 27.02/7.46 | (424) all_0_59_59 = e1
% 27.02/7.46 | (431) ~ (all_0_58_58 = e0)
% 27.02/7.46 |
% 27.02/7.46 | Equations (424) can reduce 750 to:
% 27.02/7.46 | (270) $false
% 27.02/7.46 |
% 27.02/7.46 |-The branch is then unsatisfiable
% 27.02/7.46 |-Branch two:
% 27.02/7.46 | (925) ~ (all_0_52_52 = e0)
% 27.02/7.47 | (926) all_0_52_52 = e3 | all_0_52_52 = e1
% 27.02/7.47 |
% 27.02/7.47 +-Applying beta-rule and splitting (926), into two cases.
% 27.02/7.47 |-Branch one:
% 27.02/7.47 | (864) all_0_52_52 = e3
% 27.02/7.47 |
% 27.02/7.47 | Equations (864) can reduce 826 to:
% 27.02/7.47 | (270) $false
% 27.02/7.47 |
% 27.02/7.47 |-The branch is then unsatisfiable
% 27.02/7.47 |-Branch two:
% 27.02/7.47 | (826) ~ (all_0_52_52 = e3)
% 27.02/7.47 | (848) all_0_52_52 = e1
% 27.02/7.47 |
% 27.02/7.47 | Equations (848) can reduce 642 to:
% 27.02/7.47 | (270) $false
% 27.02/7.47 |
% 27.02/7.47 |-The branch is then unsatisfiable
% 27.02/7.47 |-Branch two:
% 27.02/7.47 | (932) ~ (all_0_51_51 = e3)
% 27.02/7.47 | (764) all_0_56_56 = e3
% 27.02/7.47 |
% 27.02/7.47 | Combining equations (747,764) yields a new equation:
% 27.02/7.47 | (538) e3 = e1
% 27.02/7.47 |
% 27.02/7.47 | Equations (538) can reduce 136 to:
% 27.02/7.47 | (270) $false
% 27.02/7.47 |
% 27.02/7.47 |-The branch is then unsatisfiable
% 27.02/7.47 |-Branch two:
% 27.02/7.47 | (936) ~ (all_0_54_54 = e4)
% 27.02/7.47 | (402) all_0_59_59 = e4
% 27.02/7.47 |
% 27.02/7.47 | Equations (402) can reduce 280 to:
% 27.02/7.47 | (270) $false
% 27.02/7.47 |
% 27.02/7.47 |-The branch is then unsatisfiable
% 27.02/7.47 |-Branch two:
% 27.02/7.47 | (455) ~ (all_0_43_43 = e0)
% 27.02/7.47 | (940) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 27.02/7.47 |
% 27.02/7.47 +-Applying beta-rule and splitting (774), into two cases.
% 27.02/7.47 |-Branch one:
% 27.02/7.47 | (411) all_0_43_43 = e0
% 27.02/7.47 |
% 27.02/7.47 | Equations (411) can reduce 455 to:
% 27.02/7.47 | (270) $false
% 27.02/7.47 |
% 27.02/7.47 |-The branch is then unsatisfiable
% 27.02/7.47 |-Branch two:
% 27.02/7.47 | (455) ~ (all_0_43_43 = e0)
% 27.02/7.47 | (944) all_0_43_43 = e4 | all_0_43_43 = e3
% 27.02/7.47 |
% 27.02/7.47 +-Applying beta-rule and splitting (940), into two cases.
% 27.02/7.47 |-Branch one:
% 27.02/7.47 | (315) all_0_47_47 = e0
% 27.02/7.47 |
% 27.02/7.47 | Combining equations (290,315) yields a new equation:
% 27.02/7.47 | (622) e2 = e0
% 27.02/7.47 |
% 27.02/7.47 | Simplifying 622 yields:
% 27.02/7.47 | (316) e2 = e0
% 27.02/7.47 |
% 27.02/7.47 | Equations (316) can reduce 57 to:
% 27.02/7.47 | (270) $false
% 27.02/7.47 |
% 27.02/7.47 |-The branch is then unsatisfiable
% 27.02/7.47 |-Branch two:
% 27.02/7.47 | (318) ~ (all_0_47_47 = e0)
% 27.02/7.47 | (950) all_0_51_51 = e0 | all_0_56_56 = e0
% 27.02/7.47 |
% 27.02/7.47 +-Applying beta-rule and splitting (944), into two cases.
% 27.02/7.47 |-Branch one:
% 27.02/7.47 | (782) all_0_43_43 = e3
% 27.02/7.47 |
% 27.02/7.47 | Equations (782) can reduce 240 to:
% 27.02/7.47 | (952) ~ (all_0_51_51 = e3)
% 27.02/7.47 |
% 27.02/7.47 | Simplifying 952 yields:
% 27.02/7.47 | (932) ~ (all_0_51_51 = e3)
% 27.02/7.47 |
% 27.02/7.47 +-Applying beta-rule and splitting (950), into two cases.
% 27.02/7.47 |-Branch one:
% 27.02/7.47 | (954) all_0_51_51 = e0
% 27.02/7.47 |
% 27.02/7.47 | Equations (954) can reduce 932 to:
% 27.02/7.47 | (788) ~ (e3 = e0)
% 27.02/7.47 |
% 27.02/7.47 | Simplifying 788 yields:
% 27.02/7.47 | (66) ~ (e3 = e0)
% 27.02/7.47 |
% 27.02/7.47 +-Applying beta-rule and splitting (93), into two cases.
% 27.02/7.47 |-Branch one:
% 27.02/7.47 | (402) all_0_59_59 = e4
% 27.02/7.47 |
% 27.02/7.47 | Equations (402) can reduce 280 to:
% 27.02/7.47 | (270) $false
% 27.02/7.47 |
% 27.02/7.47 |-The branch is then unsatisfiable
% 27.02/7.47 |-Branch two:
% 27.02/7.47 | (280) ~ (all_0_59_59 = e4)
% 27.02/7.47 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.02/7.47 |
% 27.02/7.47 +-Applying beta-rule and splitting (407), into two cases.
% 27.02/7.47 |-Branch one:
% 27.02/7.47 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.02/7.47 |
% 27.02/7.47 +-Applying beta-rule and splitting (408), into two cases.
% 27.02/7.47 |-Branch one:
% 27.02/7.47 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.02/7.47 |
% 27.02/7.47 +-Applying beta-rule and splitting (409), into two cases.
% 27.02/7.47 |-Branch one:
% 27.02/7.47 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.02/7.47 |
% 27.02/7.47 | Applying alpha-rule on (410) yields:
% 27.02/7.47 | (411) all_0_43_43 = e0
% 27.02/7.47 | (412) all_0_59_59 = e3
% 27.02/7.47 | (413) ~ (all_0_46_46 = e3)
% 27.02/7.47 |
% 27.02/7.47 | Combining equations (782,411) yields a new equation:
% 27.02/7.47 | (783) e3 = e0
% 27.02/7.47 |
% 27.02/7.47 | Simplifying 783 yields:
% 27.02/7.47 | (784) e3 = e0
% 27.02/7.47 |
% 27.02/7.47 | Equations (784) can reduce 66 to:
% 27.02/7.47 | (270) $false
% 27.02/7.47 |
% 27.02/7.47 |-The branch is then unsatisfiable
% 27.02/7.47 |-Branch two:
% 27.02/7.47 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.02/7.47 |
% 27.02/7.47 | Applying alpha-rule on (416) yields:
% 27.02/7.47 | (411) all_0_43_43 = e0
% 27.02/7.47 | (412) all_0_59_59 = e3
% 27.02/7.47 | (419) ~ (all_0_56_56 = e0)
% 27.02/7.47 |
% 27.02/7.47 | Combining equations (782,411) yields a new equation:
% 27.02/7.47 | (783) e3 = e0
% 27.02/7.47 |
% 27.02/7.47 | Simplifying 783 yields:
% 27.02/7.47 | (784) e3 = e0
% 27.02/7.47 |
% 27.02/7.47 | Equations (784) can reduce 66 to:
% 27.02/7.47 | (270) $false
% 27.02/7.47 |
% 27.02/7.47 |-The branch is then unsatisfiable
% 27.02/7.47 |-Branch two:
% 27.02/7.47 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.02/7.47 |
% 27.02/7.47 | Applying alpha-rule on (422) yields:
% 27.02/7.47 | (423) all_0_53_53 = e0
% 27.02/7.47 | (424) all_0_59_59 = e1
% 27.02/7.47 | (425) ~ (all_0_54_54 = e1)
% 27.02/7.47 |
% 27.02/7.47 | Equations (424) can reduce 750 to:
% 27.02/7.47 | (270) $false
% 27.02/7.47 |
% 27.02/7.47 |-The branch is then unsatisfiable
% 27.02/7.47 |-Branch two:
% 27.02/7.47 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.02/7.47 |
% 27.02/7.47 | Applying alpha-rule on (428) yields:
% 27.02/7.47 | (423) all_0_53_53 = e0
% 27.02/7.47 | (424) all_0_59_59 = e1
% 27.02/7.47 | (431) ~ (all_0_58_58 = e0)
% 27.02/7.47 |
% 27.02/7.47 | Equations (424) can reduce 750 to:
% 27.02/7.47 | (270) $false
% 27.02/7.47 |
% 27.02/7.47 |-The branch is then unsatisfiable
% 27.02/7.47 |-Branch two:
% 27.02/7.47 | (987) ~ (all_0_51_51 = e0)
% 27.02/7.47 | (830) all_0_56_56 = e0
% 27.02/7.47 |
% 27.02/7.47 | Combining equations (747,830) yields a new equation:
% 27.02/7.47 | (571) e1 = e0
% 27.02/7.47 |
% 27.02/7.47 | Simplifying 571 yields:
% 27.02/7.47 | (560) e1 = e0
% 27.02/7.47 |
% 27.02/7.47 | Equations (560) can reduce 132 to:
% 27.02/7.47 | (270) $false
% 27.02/7.47 |
% 27.02/7.47 |-The branch is then unsatisfiable
% 27.02/7.47 |-Branch two:
% 27.02/7.47 | (786) ~ (all_0_43_43 = e3)
% 27.02/7.47 | (502) all_0_43_43 = e4
% 27.02/7.47 |
% 27.02/7.47 | Equations (502) can reduce 510 to:
% 27.02/7.47 | (270) $false
% 27.02/7.47 |
% 27.02/7.47 |-The branch is then unsatisfiable
% 27.02/7.47 |-Branch two:
% 27.02/7.47 | (995) ~ (all_0_56_56 = e1)
% 27.02/7.47 | (996) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 27.02/7.47 |
% 27.02/7.47 +-Applying beta-rule and splitting (996), into two cases.
% 27.02/7.47 |-Branch one:
% 27.02/7.47 | (997) all_0_57_57 = e1
% 27.02/7.47 |
% 27.02/7.47 | Equations (997) can reduce 644 to:
% 27.02/7.47 | (270) $false
% 27.02/7.47 |
% 27.02/7.47 |-The branch is then unsatisfiable
% 27.02/7.47 |-Branch two:
% 27.02/7.47 | (644) ~ (all_0_57_57 = e1)
% 27.02/7.47 | (1000) all_0_58_58 = e1 | all_0_59_59 = e1
% 27.02/7.47 |
% 27.02/7.47 +-Applying beta-rule and splitting (1000), into two cases.
% 27.02/7.47 |-Branch one:
% 27.02/7.47 | (1001) all_0_58_58 = e1
% 27.02/7.47 |
% 27.02/7.47 | Combining equations (1001,396) yields a new equation:
% 27.02/7.47 | (322) e2 = e1
% 27.02/7.47 |
% 27.02/7.47 | Equations (322) can reduce 141 to:
% 27.02/7.47 | (270) $false
% 27.02/7.47 |
% 27.02/7.47 |-The branch is then unsatisfiable
% 27.02/7.47 |-Branch two:
% 27.02/7.47 | (1004) ~ (all_0_58_58 = e1)
% 27.02/7.47 | (424) all_0_59_59 = e1
% 27.02/7.47 |
% 27.02/7.47 | Equations (424) can reduce 206 to:
% 27.02/7.47 | (106) ~ (all_0_46_46 = e1)
% 27.02/7.47 |
% 27.02/7.47 | Equations (424) can reduce 113 to:
% 27.02/7.47 | (543) ~ (all_0_49_49 = e1)
% 27.02/7.47 |
% 27.02/7.47 | Equations (424) can reduce 72 to:
% 27.02/7.47 | (425) ~ (all_0_54_54 = e1)
% 27.02/7.47 |
% 27.02/7.47 +-Applying beta-rule and splitting (310), into two cases.
% 27.02/7.47 |-Branch one:
% 27.02/7.47 | (563) all_0_49_49 = e0
% 27.02/7.47 |
% 27.02/7.47 | Equations (563) can reduce 198 to:
% 27.02/7.47 | (1010) ~ (all_0_46_46 = e0)
% 27.02/7.47 |
% 27.02/7.47 | Equations (563) can reduce 4 to:
% 27.02/7.47 | (562) ~ (all_0_48_48 = e0)
% 27.02/7.47 |
% 27.02/7.47 +-Applying beta-rule and splitting (314), into two cases.
% 27.02/7.47 |-Branch one:
% 27.02/7.47 | (559) all_0_48_48 = e0
% 27.02/7.47 |
% 27.02/7.47 | Equations (559) can reduce 562 to:
% 27.02/7.47 | (270) $false
% 27.02/7.47 |
% 27.02/7.47 |-The branch is then unsatisfiable
% 27.02/7.47 |-Branch two:
% 27.02/7.47 | (562) ~ (all_0_48_48 = e0)
% 27.02/7.47 | (552) all_0_48_48 = e1
% 27.02/7.47 |
% 27.02/7.47 | Equations (552) can reduce 48 to:
% 27.02/7.47 | (1016) ~ (all_0_53_53 = e1)
% 27.02/7.47 |
% 27.02/7.47 | Simplifying 1016 yields:
% 27.02/7.47 | (874) ~ (all_0_53_53 = e1)
% 27.02/7.47 |
% 27.02/7.47 | Equations (552) can reduce 121 to:
% 27.02/7.47 | (769) ~ (e3 = e1)
% 27.02/7.47 |
% 27.02/7.47 | Simplifying 769 yields:
% 27.02/7.47 | (136) ~ (e3 = e1)
% 27.02/7.47 |
% 27.02/7.47 +-Applying beta-rule and splitting (135), into two cases.
% 27.02/7.47 |-Branch one:
% 27.02/7.47 | (820) all_0_51_51 = e1
% 27.02/7.47 |
% 27.02/7.47 | Equations (820) can reduce 697 to:
% 27.02/7.47 | (1021) ~ (e4 = e1)
% 27.02/7.47 |
% 27.02/7.47 | Simplifying 1021 yields:
% 27.02/7.47 | (251) ~ (e4 = e1)
% 27.02/7.47 |
% 27.02/7.47 | Equations (820) can reduce 255 to:
% 27.02/7.47 | (645) ~ (e2 = e1)
% 27.02/7.47 |
% 27.02/7.47 | Simplifying 645 yields:
% 27.02/7.47 | (141) ~ (e2 = e1)
% 27.02/7.47 |
% 27.02/7.47 +-Applying beta-rule and splitting (93), into two cases.
% 27.02/7.47 |-Branch one:
% 27.02/7.47 | (402) all_0_59_59 = e4
% 27.02/7.47 |
% 27.02/7.47 | Combining equations (402,424) yields a new equation:
% 27.02/7.47 | (525) e4 = e1
% 27.02/7.47 |
% 27.02/7.47 | Simplifying 525 yields:
% 27.02/7.47 | (526) e4 = e1
% 27.02/7.47 |
% 27.02/7.47 | Equations (526) can reduce 251 to:
% 27.02/7.47 | (270) $false
% 27.02/7.47 |
% 27.02/7.47 |-The branch is then unsatisfiable
% 27.02/7.47 |-Branch two:
% 27.02/7.47 | (280) ~ (all_0_59_59 = e4)
% 27.02/7.47 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.02/7.47 |
% 27.02/7.47 +-Applying beta-rule and splitting (407), into two cases.
% 27.02/7.47 |-Branch one:
% 27.02/7.47 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.02/7.47 |
% 27.02/7.47 +-Applying beta-rule and splitting (408), into two cases.
% 27.02/7.47 |-Branch one:
% 27.02/7.47 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.02/7.47 |
% 27.02/7.47 +-Applying beta-rule and splitting (409), into two cases.
% 27.02/7.47 |-Branch one:
% 27.02/7.47 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.02/7.47 |
% 27.02/7.47 | Applying alpha-rule on (410) yields:
% 27.02/7.47 | (411) all_0_43_43 = e0
% 27.02/7.47 | (412) all_0_59_59 = e3
% 27.02/7.47 | (413) ~ (all_0_46_46 = e3)
% 27.02/7.47 |
% 27.02/7.47 | Combining equations (412,424) yields a new equation:
% 27.02/7.47 | (537) e3 = e1
% 27.02/7.47 |
% 27.02/7.47 | Simplifying 537 yields:
% 27.02/7.47 | (538) e3 = e1
% 27.02/7.47 |
% 27.02/7.47 | Equations (538) can reduce 136 to:
% 27.02/7.47 | (270) $false
% 27.02/7.47 |
% 27.02/7.47 |-The branch is then unsatisfiable
% 27.02/7.47 |-Branch two:
% 27.02/7.47 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.02/7.47 |
% 27.02/7.47 | Applying alpha-rule on (416) yields:
% 27.02/7.47 | (411) all_0_43_43 = e0
% 27.02/7.47 | (412) all_0_59_59 = e3
% 27.02/7.47 | (419) ~ (all_0_56_56 = e0)
% 27.02/7.47 |
% 27.02/7.47 | Combining equations (412,424) yields a new equation:
% 27.02/7.47 | (537) e3 = e1
% 27.02/7.47 |
% 27.02/7.47 | Simplifying 537 yields:
% 27.02/7.47 | (538) e3 = e1
% 27.02/7.47 |
% 27.02/7.47 | Equations (538) can reduce 136 to:
% 27.02/7.47 | (270) $false
% 27.02/7.47 |
% 27.02/7.47 |-The branch is then unsatisfiable
% 27.02/7.47 |-Branch two:
% 27.02/7.47 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.02/7.47 |
% 27.02/7.47 | Applying alpha-rule on (422) yields:
% 27.02/7.47 | (423) all_0_53_53 = e0
% 27.02/7.47 | (424) all_0_59_59 = e1
% 27.02/7.47 | (425) ~ (all_0_54_54 = e1)
% 27.02/7.47 |
% 27.02/7.47 | Equations (423) can reduce 128 to:
% 27.02/7.47 | (488) ~ (all_0_45_45 = e0)
% 27.02/7.47 |
% 27.02/7.47 | Equations (423) can reduce 356 to:
% 27.02/7.47 | (788) ~ (e3 = e0)
% 27.02/7.47 |
% 27.02/7.47 | Simplifying 788 yields:
% 27.02/7.47 | (66) ~ (e3 = e0)
% 27.02/7.47 |
% 27.02/7.47 | Equations (423) can reduce 259 to:
% 27.02/7.47 | (566) ~ (e2 = e0)
% 27.02/7.47 |
% 27.02/7.47 | Simplifying 566 yields:
% 27.02/7.47 | (57) ~ (e2 = e0)
% 27.02/7.47 |
% 27.02/7.47 +-Applying beta-rule and splitting (116), into two cases.
% 27.02/7.47 |-Branch one:
% 27.02/7.47 | (411) all_0_43_43 = e0
% 27.02/7.47 |
% 27.02/7.47 | Equations (411) can reduce 103 to:
% 27.02/7.47 | (1057) ~ (all_0_46_46 = e0)
% 27.02/7.47 |
% 27.02/7.47 | Simplifying 1057 yields:
% 27.02/7.47 | (1010) ~ (all_0_46_46 = e0)
% 27.02/7.47 |
% 27.02/7.47 +-Applying beta-rule and splitting (22), into two cases.
% 27.02/7.47 |-Branch one:
% 27.02/7.47 | (782) all_0_43_43 = e3
% 27.02/7.47 |
% 27.02/7.47 | Combining equations (411,782) yields a new equation:
% 27.02/7.47 | (784) e3 = e0
% 27.02/7.47 |
% 27.02/7.47 | Equations (784) can reduce 66 to:
% 27.02/7.47 | (270) $false
% 27.02/7.47 |
% 27.02/7.47 |-The branch is then unsatisfiable
% 27.02/7.47 |-Branch two:
% 27.02/7.47 | (786) ~ (all_0_43_43 = e3)
% 27.02/7.47 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 27.02/7.47 |
% 27.02/7.47 | Equations (411) can reduce 786 to:
% 27.02/7.47 | (788) ~ (e3 = e0)
% 27.02/7.47 |
% 27.02/7.47 | Simplifying 788 yields:
% 27.02/7.47 | (66) ~ (e3 = e0)
% 27.02/7.47 |
% 27.02/7.47 +-Applying beta-rule and splitting (787), into two cases.
% 27.02/7.47 |-Branch one:
% 27.02/7.47 | (858) all_0_44_44 = e3
% 27.02/7.47 |
% 27.02/7.47 | Combining equations (370,858) yields a new equation:
% 27.02/7.47 | (414) e3 = e2
% 27.02/7.47 |
% 27.02/7.47 | Equations (414) can reduce 223 to:
% 27.02/7.47 | (270) $false
% 27.02/7.47 |
% 27.02/7.47 |-The branch is then unsatisfiable
% 27.02/7.47 |-Branch two:
% 27.02/7.47 | (862) ~ (all_0_44_44 = e3)
% 27.02/7.47 | (1070) all_0_45_45 = e3 | all_0_46_46 = e3
% 27.02/7.48 |
% 27.02/7.48 +-Applying beta-rule and splitting (178), into two cases.
% 27.02/7.48 |-Branch one:
% 27.02/7.48 | (751) all_0_39_39 = e3
% 27.02/7.48 |
% 27.02/7.48 | Combining equations (522,751) yields a new equation:
% 27.02/7.48 | (660) e4 = e3
% 27.02/7.48 |
% 27.02/7.48 | Simplifying 660 yields:
% 27.02/7.48 | (359) e4 = e3
% 27.02/7.48 |
% 27.02/7.48 | Equations (359) can reduce 34 to:
% 27.02/7.48 | (270) $false
% 27.02/7.48 |
% 27.02/7.48 |-The branch is then unsatisfiable
% 27.02/7.48 |-Branch two:
% 27.02/7.48 | (755) ~ (all_0_39_39 = e3)
% 27.02/7.48 | (756) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 27.02/7.48 |
% 27.02/7.48 +-Applying beta-rule and splitting (756), into two cases.
% 27.02/7.48 |-Branch one:
% 27.02/7.48 | (782) all_0_43_43 = e3
% 27.02/7.48 |
% 27.02/7.48 | Combining equations (411,782) yields a new equation:
% 27.02/7.48 | (784) e3 = e0
% 27.02/7.48 |
% 27.02/7.48 | Equations (784) can reduce 66 to:
% 27.02/7.48 | (270) $false
% 27.02/7.48 |
% 27.02/7.48 |-The branch is then unsatisfiable
% 27.02/7.48 |-Branch two:
% 27.02/7.48 | (786) ~ (all_0_43_43 = e3)
% 27.02/7.48 | (799) all_0_51_51 = e3 | all_0_56_56 = e3
% 27.02/7.48 |
% 27.02/7.48 +-Applying beta-rule and splitting (799), into two cases.
% 27.02/7.48 |-Branch one:
% 27.02/7.48 | (824) all_0_51_51 = e3
% 27.02/7.48 |
% 27.02/7.48 | Combining equations (824,820) yields a new equation:
% 27.02/7.48 | (537) e3 = e1
% 27.02/7.48 |
% 27.02/7.48 | Simplifying 537 yields:
% 27.02/7.48 | (538) e3 = e1
% 27.02/7.48 |
% 27.02/7.48 | Equations (538) can reduce 136 to:
% 27.02/7.48 | (270) $false
% 27.02/7.48 |
% 27.02/7.48 |-The branch is then unsatisfiable
% 27.02/7.48 |-Branch two:
% 27.02/7.48 | (932) ~ (all_0_51_51 = e3)
% 27.02/7.48 | (764) all_0_56_56 = e3
% 27.02/7.48 |
% 27.02/7.48 +-Applying beta-rule and splitting (1070), into two cases.
% 27.02/7.48 |-Branch one:
% 27.02/7.48 | (505) all_0_45_45 = e3
% 27.02/7.48 |
% 27.02/7.48 | Equations (505) can reduce 354 to:
% 27.02/7.48 | (270) $false
% 27.02/7.48 |
% 27.02/7.48 |-The branch is then unsatisfiable
% 27.02/7.48 |-Branch two:
% 27.02/7.48 | (354) ~ (all_0_45_45 = e3)
% 27.02/7.48 | (1091) all_0_46_46 = e3
% 27.02/7.48 |
% 27.02/7.48 | Equations (1091) can reduce 215 to:
% 27.02/7.48 | (1092) ~ (all_0_54_54 = e3)
% 27.02/7.48 |
% 27.02/7.48 | Simplifying 1092 yields:
% 27.02/7.48 | (1093) ~ (all_0_54_54 = e3)
% 27.02/7.48 |
% 27.02/7.48 | Equations (1091) can reduce 106 to:
% 27.02/7.48 | (136) ~ (e3 = e1)
% 27.02/7.48 |
% 27.02/7.48 | Equations (1091) can reduce 1010 to:
% 27.02/7.48 | (66) ~ (e3 = e0)
% 27.02/7.48 |
% 27.02/7.48 +-Applying beta-rule and splitting (21), into two cases.
% 27.02/7.48 |-Branch one:
% 27.02/7.48 | (824) all_0_51_51 = e3
% 27.02/7.48 |
% 27.02/7.48 | Combining equations (824,820) yields a new equation:
% 27.02/7.48 | (537) e3 = e1
% 27.02/7.48 |
% 27.02/7.48 | Simplifying 537 yields:
% 27.02/7.48 | (538) e3 = e1
% 27.02/7.48 |
% 27.02/7.48 | Equations (538) can reduce 136 to:
% 27.02/7.48 | (270) $false
% 27.02/7.48 |
% 27.02/7.48 |-The branch is then unsatisfiable
% 27.02/7.48 |-Branch two:
% 27.02/7.48 | (932) ~ (all_0_51_51 = e3)
% 27.02/7.48 | (1101) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 27.02/7.48 |
% 27.02/7.48 +-Applying beta-rule and splitting (1101), into two cases.
% 27.02/7.48 |-Branch one:
% 27.02/7.48 | (864) all_0_52_52 = e3
% 27.02/7.48 |
% 27.02/7.48 | From (864) and (666) follows:
% 27.02/7.48 | (1103) op(e2, e3) = e1
% 27.02/7.48 |
% 27.02/7.48 | Instantiating formula (201) with e2, e3, e1, e2 and discharging atoms op(e2, e3) = e2, op(e2, e3) = e1, yields:
% 27.02/7.48 | (322) e2 = e1
% 27.02/7.48 |
% 27.02/7.48 | Equations (322) can reduce 141 to:
% 27.02/7.48 | (270) $false
% 27.02/7.48 |
% 27.02/7.48 |-The branch is then unsatisfiable
% 27.02/7.48 |-Branch two:
% 27.02/7.48 | (826) ~ (all_0_52_52 = e3)
% 27.02/7.48 | (1107) all_0_53_53 = e3 | all_0_54_54 = e3
% 27.02/7.48 |
% 27.02/7.48 +-Applying beta-rule and splitting (176), into two cases.
% 27.02/7.48 |-Branch one:
% 27.02/7.48 | (830) all_0_56_56 = e0
% 27.02/7.48 |
% 27.02/7.48 | Combining equations (830,764) yields a new equation:
% 27.02/7.48 | (784) e3 = e0
% 27.02/7.48 |
% 27.02/7.48 | Equations (784) can reduce 66 to:
% 27.02/7.48 | (270) $false
% 27.02/7.48 |
% 27.02/7.48 |-The branch is then unsatisfiable
% 27.02/7.48 |-Branch two:
% 27.02/7.48 | (419) ~ (all_0_56_56 = e0)
% 27.02/7.48 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 27.02/7.48 |
% 27.02/7.48 | Equations (764) can reduce 419 to:
% 27.02/7.48 | (66) ~ (e3 = e0)
% 27.02/7.48 |
% 27.02/7.48 +-Applying beta-rule and splitting (1107), into two cases.
% 27.02/7.48 |-Branch one:
% 27.02/7.48 | (1114) all_0_53_53 = e3
% 27.02/7.48 |
% 27.02/7.48 | Combining equations (1114,423) yields a new equation:
% 27.02/7.48 | (783) e3 = e0
% 27.02/7.48 |
% 27.02/7.48 | Simplifying 783 yields:
% 27.02/7.48 | (784) e3 = e0
% 27.02/7.48 |
% 27.02/7.48 | Equations (784) can reduce 66 to:
% 27.02/7.48 | (270) $false
% 27.02/7.48 |
% 27.02/7.48 |-The branch is then unsatisfiable
% 27.02/7.48 |-Branch two:
% 27.02/7.48 | (356) ~ (all_0_53_53 = e3)
% 27.02/7.48 | (1119) all_0_54_54 = e3
% 27.02/7.48 |
% 27.02/7.48 | Equations (1119) can reduce 1093 to:
% 27.02/7.48 | (270) $false
% 27.02/7.48 |
% 27.02/7.48 |-The branch is then unsatisfiable
% 27.02/7.48 |-Branch two:
% 27.02/7.48 | (455) ~ (all_0_43_43 = e0)
% 27.02/7.48 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 27.02/7.48 |
% 27.02/7.48 +-Applying beta-rule and splitting (1122), into two cases.
% 27.02/7.48 |-Branch one:
% 27.02/7.48 | (621) all_0_44_44 = e0
% 27.02/7.48 |
% 27.02/7.48 | Combining equations (370,621) yields a new equation:
% 27.02/7.48 | (622) e2 = e0
% 27.02/7.48 |
% 27.02/7.48 | Simplifying 622 yields:
% 27.02/7.48 | (316) e2 = e0
% 27.02/7.48 |
% 27.02/7.48 | Equations (316) can reduce 57 to:
% 27.02/7.48 | (270) $false
% 27.02/7.48 |
% 27.02/7.48 |-The branch is then unsatisfiable
% 27.02/7.48 |-Branch two:
% 27.02/7.48 | (625) ~ (all_0_44_44 = e0)
% 27.02/7.48 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 27.02/7.48 |
% 27.02/7.48 +-Applying beta-rule and splitting (1128), into two cases.
% 27.02/7.48 |-Branch one:
% 27.02/7.48 | (454) all_0_45_45 = e0
% 27.02/7.48 |
% 27.02/7.48 | Equations (454) can reduce 488 to:
% 27.02/7.48 | (270) $false
% 27.02/7.48 |
% 27.02/7.48 |-The branch is then unsatisfiable
% 27.02/7.48 |-Branch two:
% 27.02/7.48 | (488) ~ (all_0_45_45 = e0)
% 27.02/7.48 | (1132) all_0_46_46 = e0
% 27.02/7.48 |
% 27.02/7.48 | Equations (1132) can reduce 1010 to:
% 27.02/7.48 | (270) $false
% 27.02/7.48 |
% 27.02/7.48 |-The branch is then unsatisfiable
% 27.02/7.48 |-Branch two:
% 27.02/7.48 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.02/7.48 |
% 27.02/7.48 | Applying alpha-rule on (428) yields:
% 27.02/7.48 | (423) all_0_53_53 = e0
% 27.02/7.48 | (424) all_0_59_59 = e1
% 27.02/7.48 | (431) ~ (all_0_58_58 = e0)
% 27.02/7.48 |
% 27.02/7.48 | Equations (423) can reduce 128 to:
% 27.02/7.48 | (488) ~ (all_0_45_45 = e0)
% 27.02/7.48 |
% 27.02/7.48 | Equations (423) can reduce 356 to:
% 27.02/7.48 | (788) ~ (e3 = e0)
% 27.02/7.48 |
% 27.02/7.48 | Simplifying 788 yields:
% 27.02/7.48 | (66) ~ (e3 = e0)
% 27.02/7.48 |
% 27.02/7.48 | Equations (396) can reduce 431 to:
% 27.02/7.48 | (57) ~ (e2 = e0)
% 27.02/7.48 |
% 27.02/7.48 +-Applying beta-rule and splitting (116), into two cases.
% 27.02/7.48 |-Branch one:
% 27.02/7.48 | (411) all_0_43_43 = e0
% 27.02/7.48 |
% 27.02/7.48 | Equations (411) can reduce 103 to:
% 27.02/7.48 | (1057) ~ (all_0_46_46 = e0)
% 27.02/7.48 |
% 27.02/7.48 | Simplifying 1057 yields:
% 27.02/7.48 | (1010) ~ (all_0_46_46 = e0)
% 27.02/7.48 |
% 27.02/7.48 +-Applying beta-rule and splitting (22), into two cases.
% 27.02/7.48 |-Branch one:
% 27.02/7.48 | (782) all_0_43_43 = e3
% 27.02/7.48 |
% 27.02/7.48 | Combining equations (411,782) yields a new equation:
% 27.02/7.48 | (784) e3 = e0
% 27.02/7.48 |
% 27.02/7.48 | Equations (784) can reduce 66 to:
% 27.02/7.48 | (270) $false
% 27.02/7.48 |
% 27.02/7.48 |-The branch is then unsatisfiable
% 27.02/7.48 |-Branch two:
% 27.02/7.48 | (786) ~ (all_0_43_43 = e3)
% 27.02/7.48 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 27.02/7.48 |
% 27.02/7.48 | Equations (411) can reduce 786 to:
% 27.02/7.48 | (788) ~ (e3 = e0)
% 27.02/7.48 |
% 27.02/7.48 | Simplifying 788 yields:
% 27.02/7.48 | (66) ~ (e3 = e0)
% 27.02/7.48 |
% 27.02/7.48 +-Applying beta-rule and splitting (787), into two cases.
% 27.02/7.48 |-Branch one:
% 27.02/7.48 | (858) all_0_44_44 = e3
% 27.02/7.48 |
% 27.02/7.48 | Combining equations (370,858) yields a new equation:
% 27.02/7.48 | (414) e3 = e2
% 27.02/7.48 |
% 27.02/7.48 | Equations (414) can reduce 223 to:
% 27.02/7.48 | (270) $false
% 27.02/7.48 |
% 27.02/7.48 |-The branch is then unsatisfiable
% 27.02/7.48 |-Branch two:
% 27.02/7.48 | (862) ~ (all_0_44_44 = e3)
% 27.02/7.48 | (1070) all_0_45_45 = e3 | all_0_46_46 = e3
% 27.02/7.48 |
% 27.02/7.48 +-Applying beta-rule and splitting (178), into two cases.
% 27.02/7.48 |-Branch one:
% 27.02/7.48 | (751) all_0_39_39 = e3
% 27.02/7.48 |
% 27.02/7.48 | Combining equations (522,751) yields a new equation:
% 27.02/7.48 | (660) e4 = e3
% 27.02/7.48 |
% 27.02/7.48 | Simplifying 660 yields:
% 27.02/7.48 | (359) e4 = e3
% 27.02/7.48 |
% 27.02/7.48 | Equations (359) can reduce 34 to:
% 27.02/7.48 | (270) $false
% 27.02/7.48 |
% 27.02/7.48 |-The branch is then unsatisfiable
% 27.02/7.48 |-Branch two:
% 27.02/7.48 | (755) ~ (all_0_39_39 = e3)
% 27.02/7.48 | (756) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 27.02/7.48 |
% 27.02/7.48 +-Applying beta-rule and splitting (756), into two cases.
% 27.02/7.48 |-Branch one:
% 27.02/7.48 | (782) all_0_43_43 = e3
% 27.02/7.48 |
% 27.02/7.48 | Combining equations (411,782) yields a new equation:
% 27.02/7.48 | (784) e3 = e0
% 27.02/7.48 |
% 27.02/7.48 | Equations (784) can reduce 66 to:
% 27.02/7.48 | (270) $false
% 27.02/7.48 |
% 27.02/7.48 |-The branch is then unsatisfiable
% 27.02/7.48 |-Branch two:
% 27.02/7.48 | (786) ~ (all_0_43_43 = e3)
% 27.02/7.48 | (799) all_0_51_51 = e3 | all_0_56_56 = e3
% 27.02/7.48 |
% 27.02/7.48 +-Applying beta-rule and splitting (799), into two cases.
% 27.02/7.48 |-Branch one:
% 27.02/7.48 | (824) all_0_51_51 = e3
% 27.02/7.48 |
% 27.02/7.48 | Combining equations (824,820) yields a new equation:
% 27.02/7.48 | (537) e3 = e1
% 27.02/7.48 |
% 27.02/7.48 | Simplifying 537 yields:
% 27.02/7.48 | (538) e3 = e1
% 27.02/7.48 |
% 27.02/7.48 | Equations (538) can reduce 136 to:
% 27.02/7.48 | (270) $false
% 27.02/7.48 |
% 27.02/7.48 |-The branch is then unsatisfiable
% 27.02/7.48 |-Branch two:
% 27.02/7.48 | (932) ~ (all_0_51_51 = e3)
% 27.02/7.48 | (764) all_0_56_56 = e3
% 27.02/7.48 |
% 27.02/7.48 +-Applying beta-rule and splitting (1070), into two cases.
% 27.02/7.48 |-Branch one:
% 27.02/7.48 | (505) all_0_45_45 = e3
% 27.02/7.48 |
% 27.02/7.48 | Equations (505) can reduce 354 to:
% 27.02/7.48 | (270) $false
% 27.02/7.48 |
% 27.02/7.48 |-The branch is then unsatisfiable
% 27.02/7.48 |-Branch two:
% 27.02/7.48 | (354) ~ (all_0_45_45 = e3)
% 27.02/7.48 | (1091) all_0_46_46 = e3
% 27.02/7.48 |
% 27.02/7.48 | Equations (1091) can reduce 215 to:
% 27.02/7.48 | (1092) ~ (all_0_54_54 = e3)
% 27.02/7.48 |
% 27.02/7.48 | Simplifying 1092 yields:
% 27.02/7.48 | (1093) ~ (all_0_54_54 = e3)
% 27.02/7.48 |
% 27.02/7.48 | Equations (1091) can reduce 106 to:
% 27.02/7.48 | (136) ~ (e3 = e1)
% 27.02/7.48 |
% 27.02/7.48 | Equations (1091) can reduce 1010 to:
% 27.02/7.48 | (66) ~ (e3 = e0)
% 27.02/7.48 |
% 27.02/7.48 +-Applying beta-rule and splitting (21), into two cases.
% 27.02/7.48 |-Branch one:
% 27.02/7.48 | (824) all_0_51_51 = e3
% 27.02/7.48 |
% 27.02/7.48 | Combining equations (824,820) yields a new equation:
% 27.02/7.48 | (537) e3 = e1
% 27.02/7.48 |
% 27.02/7.48 | Simplifying 537 yields:
% 27.02/7.48 | (538) e3 = e1
% 27.02/7.48 |
% 27.02/7.48 | Equations (538) can reduce 136 to:
% 27.02/7.48 | (270) $false
% 27.02/7.48 |
% 27.02/7.48 |-The branch is then unsatisfiable
% 27.02/7.48 |-Branch two:
% 27.02/7.48 | (932) ~ (all_0_51_51 = e3)
% 27.02/7.48 | (1101) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 27.02/7.48 |
% 27.02/7.48 +-Applying beta-rule and splitting (1101), into two cases.
% 27.02/7.48 |-Branch one:
% 27.02/7.48 | (864) all_0_52_52 = e3
% 27.02/7.48 |
% 27.02/7.48 | From (864) and (666) follows:
% 27.02/7.48 | (1103) op(e2, e3) = e1
% 27.02/7.48 |
% 27.02/7.48 | Instantiating formula (201) with e2, e3, e1, e2 and discharging atoms op(e2, e3) = e2, op(e2, e3) = e1, yields:
% 27.02/7.48 | (322) e2 = e1
% 27.02/7.48 |
% 27.02/7.48 | Equations (322) can reduce 141 to:
% 27.02/7.48 | (270) $false
% 27.02/7.48 |
% 27.02/7.48 |-The branch is then unsatisfiable
% 27.02/7.48 |-Branch two:
% 27.02/7.48 | (826) ~ (all_0_52_52 = e3)
% 27.02/7.48 | (1107) all_0_53_53 = e3 | all_0_54_54 = e3
% 27.02/7.48 |
% 27.02/7.48 +-Applying beta-rule and splitting (176), into two cases.
% 27.02/7.48 |-Branch one:
% 27.02/7.49 | (830) all_0_56_56 = e0
% 27.02/7.49 |
% 27.02/7.49 | Combining equations (830,764) yields a new equation:
% 27.02/7.49 | (784) e3 = e0
% 27.02/7.49 |
% 27.02/7.49 | Equations (784) can reduce 66 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (419) ~ (all_0_56_56 = e0)
% 27.02/7.49 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 27.02/7.49 |
% 27.02/7.49 | Equations (764) can reduce 419 to:
% 27.02/7.49 | (66) ~ (e3 = e0)
% 27.02/7.49 |
% 27.02/7.49 +-Applying beta-rule and splitting (1107), into two cases.
% 27.02/7.49 |-Branch one:
% 27.02/7.49 | (1114) all_0_53_53 = e3
% 27.02/7.49 |
% 27.02/7.49 | Combining equations (1114,423) yields a new equation:
% 27.02/7.49 | (783) e3 = e0
% 27.02/7.49 |
% 27.02/7.49 | Simplifying 783 yields:
% 27.02/7.49 | (784) e3 = e0
% 27.02/7.49 |
% 27.02/7.49 | Equations (784) can reduce 66 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (356) ~ (all_0_53_53 = e3)
% 27.02/7.49 | (1119) all_0_54_54 = e3
% 27.02/7.49 |
% 27.02/7.49 | Equations (1119) can reduce 1093 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (455) ~ (all_0_43_43 = e0)
% 27.02/7.49 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 27.02/7.49 |
% 27.02/7.49 +-Applying beta-rule and splitting (1122), into two cases.
% 27.02/7.49 |-Branch one:
% 27.02/7.49 | (621) all_0_44_44 = e0
% 27.02/7.49 |
% 27.02/7.49 | Combining equations (370,621) yields a new equation:
% 27.02/7.49 | (622) e2 = e0
% 27.02/7.49 |
% 27.02/7.49 | Simplifying 622 yields:
% 27.02/7.49 | (316) e2 = e0
% 27.02/7.49 |
% 27.02/7.49 | Equations (316) can reduce 57 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (625) ~ (all_0_44_44 = e0)
% 27.02/7.49 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 27.02/7.49 |
% 27.02/7.49 +-Applying beta-rule and splitting (1128), into two cases.
% 27.02/7.49 |-Branch one:
% 27.02/7.49 | (454) all_0_45_45 = e0
% 27.02/7.49 |
% 27.02/7.49 | Equations (454) can reduce 488 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (488) ~ (all_0_45_45 = e0)
% 27.02/7.49 | (1132) all_0_46_46 = e0
% 27.02/7.49 |
% 27.02/7.49 | Equations (1132) can reduce 1010 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (748) ~ (all_0_51_51 = e1)
% 27.02/7.49 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 27.02/7.49 |
% 27.02/7.49 +-Applying beta-rule and splitting (823), into two cases.
% 27.02/7.49 |-Branch one:
% 27.02/7.49 | (848) all_0_52_52 = e1
% 27.02/7.49 |
% 27.02/7.49 | Equations (848) can reduce 642 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (642) ~ (all_0_52_52 = e1)
% 27.02/7.49 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 27.02/7.49 |
% 27.02/7.49 +-Applying beta-rule and splitting (852), into two cases.
% 27.02/7.49 |-Branch one:
% 27.02/7.49 | (853) all_0_53_53 = e1
% 27.02/7.49 |
% 27.02/7.49 | Equations (853) can reduce 874 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (874) ~ (all_0_53_53 = e1)
% 27.02/7.49 | (875) all_0_54_54 = e1
% 27.02/7.49 |
% 27.02/7.49 | Equations (875) can reduce 425 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (1231) ~ (all_0_49_49 = e0)
% 27.02/7.49 | (589) all_0_49_49 = e1
% 27.02/7.49 |
% 27.02/7.49 | Equations (589) can reduce 543 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (376) ~ (all_0_58_58 = e2)
% 27.02/7.49 | (399) all_0_59_59 = e2
% 27.02/7.49 |
% 27.02/7.49 | Equations (399) can reduce 701 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (1237) ~ (all_0_41_41 = e3)
% 27.02/7.49 | (1238) all_0_41_41 = e4 | all_0_41_41 = e1
% 27.02/7.49 |
% 27.02/7.49 +-Applying beta-rule and splitting (1238), into two cases.
% 27.02/7.49 |-Branch one:
% 27.02/7.49 | (536) all_0_41_41 = e1
% 27.02/7.49 |
% 27.02/7.49 | Equations (536) can reduce 540 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (540) ~ (all_0_41_41 = e1)
% 27.02/7.49 | (358) all_0_41_41 = e4
% 27.02/7.49 |
% 27.02/7.49 | Equations (358) can reduce 361 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (498) ~ (all_0_42_42 = e2)
% 27.02/7.49 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 27.02/7.49 |
% 27.02/7.49 +-Applying beta-rule and splitting (630), into two cases.
% 27.02/7.49 |-Branch one:
% 27.02/7.49 | (327) all_0_40_40 = e2
% 27.02/7.49 |
% 27.02/7.49 | Combining equations (327,530) yields a new equation:
% 27.02/7.49 | (531) e2 = e1
% 27.02/7.49 |
% 27.02/7.49 | Simplifying 531 yields:
% 27.02/7.49 | (322) e2 = e1
% 27.02/7.49 |
% 27.02/7.49 | Equations (322) can reduce 141 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (602) ~ (all_0_40_40 = e2)
% 27.02/7.49 | (1251) all_0_41_41 = e2 | all_0_42_42 = e2
% 27.02/7.49 |
% 27.02/7.49 +-Applying beta-rule and splitting (1251), into two cases.
% 27.02/7.49 |-Branch one:
% 27.02/7.49 | (436) all_0_41_41 = e2
% 27.02/7.49 |
% 27.02/7.49 | Equations (436) can reduce 157 to:
% 27.02/7.49 | (375) ~ (all_0_58_58 = e2)
% 27.02/7.49 |
% 27.02/7.49 | Simplifying 375 yields:
% 27.02/7.49 | (376) ~ (all_0_58_58 = e2)
% 27.02/7.49 |
% 27.02/7.49 | Equations (436) can reduce 361 to:
% 27.02/7.49 | (377) ~ (e4 = e2)
% 27.02/7.49 |
% 27.02/7.49 | Simplifying 377 yields:
% 27.02/7.49 | (231) ~ (e4 = e2)
% 27.02/7.49 |
% 27.02/7.49 | Equations (436) can reduce 540 to:
% 27.02/7.49 | (141) ~ (e2 = e1)
% 27.02/7.49 |
% 27.02/7.49 +-Applying beta-rule and splitting (1245), into two cases.
% 27.02/7.49 |-Branch one:
% 27.02/7.49 | (1258) all_0_42_42 = e3
% 27.02/7.49 |
% 27.02/7.49 | Equations (1258) can reduce 17 to:
% 27.02/7.49 | (1259) ~ (all_0_59_59 = e3)
% 27.02/7.49 |
% 27.02/7.49 | Simplifying 1259 yields:
% 27.02/7.49 | (1260) ~ (all_0_59_59 = e3)
% 27.02/7.49 |
% 27.02/7.49 +-Applying beta-rule and splitting (168), into two cases.
% 27.02/7.49 |-Branch one:
% 27.02/7.49 | (382) all_0_55_55 = e2
% 27.02/7.49 |
% 27.02/7.49 | Combining equations (382,272) yields a new equation:
% 27.02/7.49 | (269) e4 = e2
% 27.02/7.49 |
% 27.02/7.49 | Equations (269) can reduce 231 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (386) ~ (all_0_55_55 = e2)
% 27.02/7.49 | (387) all_0_56_56 = e2 | all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 27.02/7.49 |
% 27.02/7.49 +-Applying beta-rule and splitting (387), into two cases.
% 27.02/7.49 |-Branch one:
% 27.02/7.49 | (388) all_0_56_56 = e2
% 27.02/7.49 |
% 27.02/7.49 | Equations (388) can reduce 300 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (300) ~ (all_0_56_56 = e2)
% 27.02/7.49 | (391) all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 27.02/7.49 |
% 27.02/7.49 +-Applying beta-rule and splitting (391), into two cases.
% 27.02/7.49 |-Branch one:
% 27.02/7.49 | (392) all_0_57_57 = e2
% 27.02/7.49 |
% 27.02/7.49 | Equations (392) can reduce 335 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (335) ~ (all_0_57_57 = e2)
% 27.02/7.49 | (395) all_0_58_58 = e2 | all_0_59_59 = e2
% 27.02/7.49 |
% 27.02/7.49 +-Applying beta-rule and splitting (395), into two cases.
% 27.02/7.49 |-Branch one:
% 27.02/7.49 | (396) all_0_58_58 = e2
% 27.02/7.49 |
% 27.02/7.49 | Equations (396) can reduce 376 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (376) ~ (all_0_58_58 = e2)
% 27.02/7.49 | (399) all_0_59_59 = e2
% 27.02/7.49 |
% 27.02/7.49 | Equations (399) can reduce 280 to:
% 27.02/7.49 | (377) ~ (e4 = e2)
% 27.02/7.49 |
% 27.02/7.49 | Simplifying 377 yields:
% 27.02/7.49 | (231) ~ (e4 = e2)
% 27.02/7.49 |
% 27.02/7.49 | Equations (399) can reduce 1260 to:
% 27.02/7.49 | (301) ~ (e3 = e2)
% 27.02/7.49 |
% 27.02/7.49 | Simplifying 301 yields:
% 27.02/7.49 | (223) ~ (e3 = e2)
% 27.02/7.49 |
% 27.02/7.49 +-Applying beta-rule and splitting (93), into two cases.
% 27.02/7.49 |-Branch one:
% 27.02/7.49 | (402) all_0_59_59 = e4
% 27.02/7.49 |
% 27.02/7.49 | Combining equations (402,399) yields a new equation:
% 27.02/7.49 | (268) e4 = e2
% 27.02/7.49 |
% 27.02/7.49 | Simplifying 268 yields:
% 27.02/7.49 | (269) e4 = e2
% 27.02/7.49 |
% 27.02/7.49 | Equations (269) can reduce 231 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (280) ~ (all_0_59_59 = e4)
% 27.02/7.49 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.02/7.49 |
% 27.02/7.49 +-Applying beta-rule and splitting (407), into two cases.
% 27.02/7.49 |-Branch one:
% 27.02/7.49 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.02/7.49 |
% 27.02/7.49 +-Applying beta-rule and splitting (408), into two cases.
% 27.02/7.49 |-Branch one:
% 27.02/7.49 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.02/7.49 |
% 27.02/7.49 +-Applying beta-rule and splitting (409), into two cases.
% 27.02/7.49 |-Branch one:
% 27.02/7.49 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.02/7.49 |
% 27.02/7.49 | Applying alpha-rule on (410) yields:
% 27.02/7.49 | (411) all_0_43_43 = e0
% 27.02/7.49 | (412) all_0_59_59 = e3
% 27.02/7.49 | (413) ~ (all_0_46_46 = e3)
% 27.02/7.49 |
% 27.02/7.49 | Combining equations (412,399) yields a new equation:
% 27.02/7.49 | (437) e3 = e2
% 27.02/7.49 |
% 27.02/7.49 | Simplifying 437 yields:
% 27.02/7.49 | (414) e3 = e2
% 27.02/7.49 |
% 27.02/7.49 | Equations (414) can reduce 223 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.02/7.49 |
% 27.02/7.49 | Applying alpha-rule on (416) yields:
% 27.02/7.49 | (411) all_0_43_43 = e0
% 27.02/7.49 | (412) all_0_59_59 = e3
% 27.02/7.49 | (419) ~ (all_0_56_56 = e0)
% 27.02/7.49 |
% 27.02/7.49 | Combining equations (412,399) yields a new equation:
% 27.02/7.49 | (437) e3 = e2
% 27.02/7.49 |
% 27.02/7.49 | Simplifying 437 yields:
% 27.02/7.49 | (414) e3 = e2
% 27.02/7.49 |
% 27.02/7.49 | Equations (414) can reduce 223 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.02/7.49 |
% 27.02/7.49 | Applying alpha-rule on (422) yields:
% 27.02/7.49 | (423) all_0_53_53 = e0
% 27.02/7.49 | (424) all_0_59_59 = e1
% 27.02/7.49 | (425) ~ (all_0_54_54 = e1)
% 27.02/7.49 |
% 27.02/7.49 | Combining equations (424,399) yields a new equation:
% 27.02/7.49 | (322) e2 = e1
% 27.02/7.49 |
% 27.02/7.49 | Equations (322) can reduce 141 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.02/7.49 |
% 27.02/7.49 | Applying alpha-rule on (428) yields:
% 27.02/7.49 | (423) all_0_53_53 = e0
% 27.02/7.49 | (424) all_0_59_59 = e1
% 27.02/7.49 | (431) ~ (all_0_58_58 = e0)
% 27.02/7.49 |
% 27.02/7.49 | Combining equations (424,399) yields a new equation:
% 27.02/7.49 | (322) e2 = e1
% 27.02/7.49 |
% 27.02/7.49 | Equations (322) can reduce 141 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (1316) ~ (all_0_42_42 = e3)
% 27.02/7.49 | (1317) all_0_42_42 = e4 | all_0_42_42 = e1
% 27.02/7.49 |
% 27.02/7.49 +-Applying beta-rule and splitting (1317), into two cases.
% 27.02/7.49 |-Branch one:
% 27.02/7.49 | (541) all_0_42_42 = e1
% 27.02/7.49 |
% 27.02/7.49 | Equations (541) can reduce 640 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (640) ~ (all_0_42_42 = e1)
% 27.02/7.49 | (512) all_0_42_42 = e4
% 27.02/7.49 |
% 27.02/7.49 | Equations (512) can reduce 520 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (331) ~ (all_0_41_41 = e2)
% 27.02/7.49 | (698) all_0_42_42 = e2
% 27.02/7.49 |
% 27.02/7.49 | Equations (698) can reduce 498 to:
% 27.02/7.49 | (270) $false
% 27.02/7.49 |
% 27.02/7.49 |-The branch is then unsatisfiable
% 27.02/7.49 |-Branch two:
% 27.02/7.49 | (591) ~ (all_0_39_39 = e4)
% 27.02/7.49 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 27.02/7.49 |
% 27.02/7.49 +-Applying beta-rule and splitting (684), into two cases.
% 27.02/7.49 |-Branch one:
% 27.02/7.49 | (751) all_0_39_39 = e3
% 27.02/7.49 |
% 27.02/7.49 | Equations (751) can reduce 226 to:
% 27.02/7.49 | (1329) ~ (all_0_41_41 = e3)
% 27.02/7.49 |
% 27.02/7.49 | Simplifying 1329 yields:
% 27.02/7.49 | (1237) ~ (all_0_41_41 = e3)
% 27.02/7.49 |
% 27.02/7.50 | Equations (751) can reduce 184 to:
% 27.02/7.50 | (1331) ~ (all_0_42_42 = e3)
% 27.02/7.50 |
% 27.02/7.50 | Simplifying 1331 yields:
% 27.02/7.50 | (1316) ~ (all_0_42_42 = e3)
% 27.02/7.50 |
% 27.02/7.50 | Equations (751) can reduce 167 to:
% 27.02/7.50 | (1333) ~ (all_0_43_43 = e3)
% 27.02/7.50 |
% 27.02/7.50 | Simplifying 1333 yields:
% 27.02/7.50 | (786) ~ (all_0_43_43 = e3)
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (217), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (436) all_0_41_41 = e2
% 27.02/7.50 |
% 27.02/7.50 | Equations (436) can reduce 94 to:
% 27.02/7.50 | (1336) ~ (all_0_42_42 = e2)
% 27.02/7.50 |
% 27.02/7.50 | Simplifying 1336 yields:
% 27.02/7.50 | (498) ~ (all_0_42_42 = e2)
% 27.02/7.50 |
% 27.02/7.50 | Equations (436) can reduce 157 to:
% 27.02/7.50 | (375) ~ (all_0_58_58 = e2)
% 27.02/7.50 |
% 27.02/7.50 | Simplifying 375 yields:
% 27.02/7.50 | (376) ~ (all_0_58_58 = e2)
% 27.02/7.50 |
% 27.02/7.50 | Equations (436) can reduce 1237 to:
% 27.02/7.50 | (301) ~ (e3 = e2)
% 27.02/7.50 |
% 27.02/7.50 | Simplifying 301 yields:
% 27.02/7.50 | (223) ~ (e3 = e2)
% 27.02/7.50 |
% 27.02/7.50 | Equations (436) can reduce 540 to:
% 27.02/7.50 | (141) ~ (e2 = e1)
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (16), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (698) all_0_42_42 = e2
% 27.02/7.50 |
% 27.02/7.50 | Equations (698) can reduce 498 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (498) ~ (all_0_42_42 = e2)
% 27.02/7.50 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (168), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (382) all_0_55_55 = e2
% 27.02/7.50 |
% 27.02/7.50 | Combining equations (272,382) yields a new equation:
% 27.02/7.50 | (268) e4 = e2
% 27.02/7.50 |
% 27.02/7.50 | Simplifying 268 yields:
% 27.02/7.50 | (269) e4 = e2
% 27.02/7.50 |
% 27.02/7.50 | Equations (269) can reduce 231 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (386) ~ (all_0_55_55 = e2)
% 27.02/7.50 | (387) all_0_56_56 = e2 | all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (1245), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (1258) all_0_42_42 = e3
% 27.02/7.50 |
% 27.02/7.50 | Equations (1258) can reduce 1316 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (1316) ~ (all_0_42_42 = e3)
% 27.02/7.50 | (1317) all_0_42_42 = e4 | all_0_42_42 = e1
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (387), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (388) all_0_56_56 = e2
% 27.02/7.50 |
% 27.02/7.50 | Equations (388) can reduce 300 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (300) ~ (all_0_56_56 = e2)
% 27.02/7.50 | (391) all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (391), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (392) all_0_57_57 = e2
% 27.02/7.50 |
% 27.02/7.50 | Equations (392) can reduce 335 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (335) ~ (all_0_57_57 = e2)
% 27.02/7.50 | (395) all_0_58_58 = e2 | all_0_59_59 = e2
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (395), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (396) all_0_58_58 = e2
% 27.02/7.50 |
% 27.02/7.50 | Equations (396) can reduce 376 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (376) ~ (all_0_58_58 = e2)
% 27.02/7.50 | (399) all_0_59_59 = e2
% 27.02/7.50 |
% 27.02/7.50 | Equations (399) can reduce 17 to:
% 27.02/7.50 | (498) ~ (all_0_42_42 = e2)
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (1317), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (541) all_0_42_42 = e1
% 27.02/7.50 |
% 27.02/7.50 | Equations (541) can reduce 640 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (640) ~ (all_0_42_42 = e1)
% 27.02/7.50 | (512) all_0_42_42 = e4
% 27.02/7.50 |
% 27.02/7.50 | Equations (512) can reduce 498 to:
% 27.02/7.50 | (231) ~ (e4 = e2)
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (93), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (402) all_0_59_59 = e4
% 27.02/7.50 |
% 27.02/7.50 | Combining equations (402,399) yields a new equation:
% 27.02/7.50 | (268) e4 = e2
% 27.02/7.50 |
% 27.02/7.50 | Simplifying 268 yields:
% 27.02/7.50 | (269) e4 = e2
% 27.02/7.50 |
% 27.02/7.50 | Equations (269) can reduce 231 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (280) ~ (all_0_59_59 = e4)
% 27.02/7.50 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (407), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (408), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (409), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.02/7.50 |
% 27.02/7.50 | Applying alpha-rule on (410) yields:
% 27.02/7.50 | (411) all_0_43_43 = e0
% 27.02/7.50 | (412) all_0_59_59 = e3
% 27.02/7.50 | (413) ~ (all_0_46_46 = e3)
% 27.02/7.50 |
% 27.02/7.50 | Combining equations (412,399) yields a new equation:
% 27.02/7.50 | (437) e3 = e2
% 27.02/7.50 |
% 27.02/7.50 | Simplifying 437 yields:
% 27.02/7.50 | (414) e3 = e2
% 27.02/7.50 |
% 27.02/7.50 | Equations (414) can reduce 223 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.02/7.50 |
% 27.02/7.50 | Applying alpha-rule on (416) yields:
% 27.02/7.50 | (411) all_0_43_43 = e0
% 27.02/7.50 | (412) all_0_59_59 = e3
% 27.02/7.50 | (419) ~ (all_0_56_56 = e0)
% 27.02/7.50 |
% 27.02/7.50 | Combining equations (412,399) yields a new equation:
% 27.02/7.50 | (437) e3 = e2
% 27.02/7.50 |
% 27.02/7.50 | Simplifying 437 yields:
% 27.02/7.50 | (414) e3 = e2
% 27.02/7.50 |
% 27.02/7.50 | Equations (414) can reduce 223 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.02/7.50 |
% 27.02/7.50 | Applying alpha-rule on (422) yields:
% 27.02/7.50 | (423) all_0_53_53 = e0
% 27.02/7.50 | (424) all_0_59_59 = e1
% 27.02/7.50 | (425) ~ (all_0_54_54 = e1)
% 27.02/7.50 |
% 27.02/7.50 | Combining equations (424,399) yields a new equation:
% 27.02/7.50 | (322) e2 = e1
% 27.02/7.50 |
% 27.02/7.50 | Equations (322) can reduce 141 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.02/7.50 |
% 27.02/7.50 | Applying alpha-rule on (428) yields:
% 27.02/7.50 | (423) all_0_53_53 = e0
% 27.02/7.50 | (424) all_0_59_59 = e1
% 27.02/7.50 | (431) ~ (all_0_58_58 = e0)
% 27.02/7.50 |
% 27.02/7.50 | Combining equations (424,399) yields a new equation:
% 27.02/7.50 | (322) e2 = e1
% 27.02/7.50 |
% 27.02/7.50 | Equations (322) can reduce 141 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (331) ~ (all_0_41_41 = e2)
% 27.02/7.50 | (709) all_0_41_41 = e4 | all_0_41_41 = e3 | all_0_41_41 = e1
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (709), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (351) all_0_41_41 = e3
% 27.02/7.50 |
% 27.02/7.50 | Equations (351) can reduce 1237 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (1237) ~ (all_0_41_41 = e3)
% 27.02/7.50 | (1238) all_0_41_41 = e4 | all_0_41_41 = e1
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (187), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (436) all_0_41_41 = e2
% 27.02/7.50 |
% 27.02/7.50 | Equations (436) can reduce 331 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (331) ~ (all_0_41_41 = e2)
% 27.02/7.50 | (441) all_0_45_45 = e2 | all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (441), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (374) all_0_45_45 = e2
% 27.02/7.50 |
% 27.02/7.50 | Equations (374) can reduce 434 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (434) ~ (all_0_45_45 = e2)
% 27.02/7.50 | (445) all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (445), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (311) all_0_48_48 = e2
% 27.02/7.50 |
% 27.02/7.50 | Equations (311) can reduce 294 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (294) ~ (all_0_48_48 = e2)
% 27.02/7.50 | (449) all_0_53_53 = e2 | all_0_58_58 = e2
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (449), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (576) all_0_53_53 = e2
% 27.02/7.50 |
% 27.02/7.50 | Equations (576) can reduce 259 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (259) ~ (all_0_53_53 = e2)
% 27.02/7.50 | (396) all_0_58_58 = e2
% 27.02/7.50 |
% 27.02/7.50 | Equations (396) can reduce 157 to:
% 27.02/7.50 | (331) ~ (all_0_41_41 = e2)
% 27.02/7.50 |
% 27.02/7.50 | Equations (396) can reduce 108 to:
% 27.02/7.50 | (434) ~ (all_0_45_45 = e2)
% 27.02/7.50 |
% 27.02/7.50 | Equations (396) can reduce 81 to:
% 27.02/7.50 | (300) ~ (all_0_56_56 = e2)
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (209), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (698) all_0_42_42 = e2
% 27.02/7.50 |
% 27.02/7.50 | Equations (698) can reduce 18 to:
% 27.02/7.50 | (1435) ~ (all_0_46_46 = e2)
% 27.02/7.50 |
% 27.02/7.50 | Simplifying 1435 yields:
% 27.02/7.50 | (1436) ~ (all_0_46_46 = e2)
% 27.02/7.50 |
% 27.02/7.50 | Equations (698) can reduce 640 to:
% 27.02/7.50 | (141) ~ (e2 = e1)
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (1238), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (536) all_0_41_41 = e1
% 27.02/7.50 |
% 27.02/7.50 | Equations (536) can reduce 540 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (540) ~ (all_0_41_41 = e1)
% 27.02/7.50 | (358) all_0_41_41 = e4
% 27.02/7.50 |
% 27.02/7.50 | Equations (358) can reduce 51 to:
% 27.02/7.50 | (503) ~ (all_0_45_45 = e4)
% 27.02/7.50 |
% 27.02/7.50 | Simplifying 503 yields:
% 27.02/7.50 | (352) ~ (all_0_45_45 = e4)
% 27.02/7.50 |
% 27.02/7.50 | Equations (358) can reduce 214 to:
% 27.02/7.50 | (1444) ~ (all_0_53_53 = e4)
% 27.02/7.50 |
% 27.02/7.50 | Simplifying 1444 yields:
% 27.02/7.50 | (599) ~ (all_0_53_53 = e4)
% 27.02/7.50 |
% 27.02/7.50 | Equations (358) can reduce 232 to:
% 27.02/7.50 | (6) ~ (e4 = e0)
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (44), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (502) all_0_43_43 = e4
% 27.02/7.50 |
% 27.02/7.50 | Equations (502) can reduce 84 to:
% 27.02/7.50 | (503) ~ (all_0_45_45 = e4)
% 27.02/7.50 |
% 27.02/7.50 | Simplifying 503 yields:
% 27.02/7.50 | (352) ~ (all_0_45_45 = e4)
% 27.02/7.50 |
% 27.02/7.50 | Equations (502) can reduce 240 to:
% 27.02/7.50 | (696) ~ (all_0_51_51 = e4)
% 27.02/7.50 |
% 27.02/7.50 | Simplifying 696 yields:
% 27.02/7.50 | (697) ~ (all_0_51_51 = e4)
% 27.02/7.50 |
% 27.02/7.50 | Equations (502) can reduce 786 to:
% 27.02/7.50 | (34) ~ (e4 = e3)
% 27.02/7.50 |
% 27.02/7.50 | Equations (502) can reduce 292 to:
% 27.02/7.50 | (231) ~ (e4 = e2)
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (179), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (512) all_0_42_42 = e4
% 27.02/7.50 |
% 27.02/7.50 | Combining equations (512,698) yields a new equation:
% 27.02/7.50 | (268) e4 = e2
% 27.02/7.50 |
% 27.02/7.50 | Simplifying 268 yields:
% 27.02/7.50 | (269) e4 = e2
% 27.02/7.50 |
% 27.02/7.50 | Equations (269) can reduce 231 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (520) ~ (all_0_42_42 = e4)
% 27.02/7.50 | (521) all_0_46_46 = e4 | all_0_54_54 = e4 | all_0_59_59 = e4
% 27.02/7.50 |
% 27.02/7.50 | Equations (698) can reduce 520 to:
% 27.02/7.50 | (377) ~ (e4 = e2)
% 27.02/7.50 |
% 27.02/7.50 | Simplifying 377 yields:
% 27.02/7.50 | (231) ~ (e4 = e2)
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (189), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (267) all_0_50_50 = e4
% 27.02/7.50 |
% 27.02/7.50 | Combining equations (253,267) yields a new equation:
% 27.02/7.50 | (269) e4 = e2
% 27.02/7.50 |
% 27.02/7.50 | Equations (269) can reduce 231 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (271) ~ (all_0_50_50 = e4)
% 27.02/7.50 | (1466) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (1466), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (1467) all_0_51_51 = e4
% 27.02/7.50 |
% 27.02/7.50 | Equations (1467) can reduce 697 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (697) ~ (all_0_51_51 = e4)
% 27.02/7.50 | (1470) all_0_53_53 = e4 | all_0_54_54 = e4
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (1470), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (367) all_0_53_53 = e4
% 27.02/7.50 |
% 27.02/7.50 | Equations (367) can reduce 599 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (599) ~ (all_0_53_53 = e4)
% 27.02/7.50 | (817) all_0_54_54 = e4
% 27.02/7.50 |
% 27.02/7.50 | Equations (817) can reduce 215 to:
% 27.02/7.50 | (805) ~ (all_0_46_46 = e4)
% 27.02/7.50 |
% 27.02/7.50 | Equations (817) can reduce 72 to:
% 27.02/7.50 | (279) ~ (all_0_59_59 = e4)
% 27.02/7.50 |
% 27.02/7.50 | Simplifying 279 yields:
% 27.02/7.50 | (280) ~ (all_0_59_59 = e4)
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (93), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (402) all_0_59_59 = e4
% 27.02/7.50 |
% 27.02/7.50 | Equations (402) can reduce 280 to:
% 27.02/7.50 | (270) $false
% 27.02/7.50 |
% 27.02/7.50 |-The branch is then unsatisfiable
% 27.02/7.50 |-Branch two:
% 27.02/7.50 | (280) ~ (all_0_59_59 = e4)
% 27.02/7.50 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (407), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (408), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.02/7.50 |
% 27.02/7.50 +-Applying beta-rule and splitting (409), into two cases.
% 27.02/7.50 |-Branch one:
% 27.02/7.50 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.02/7.50 |
% 27.02/7.50 | Applying alpha-rule on (410) yields:
% 27.02/7.50 | (411) all_0_43_43 = e0
% 27.02/7.50 | (412) all_0_59_59 = e3
% 27.02/7.51 | (413) ~ (all_0_46_46 = e3)
% 27.02/7.51 |
% 27.02/7.51 | Combining equations (502,411) yields a new equation:
% 27.02/7.51 | (478) e4 = e0
% 27.02/7.51 |
% 27.02/7.51 | Simplifying 478 yields:
% 27.02/7.51 | (479) e4 = e0
% 27.02/7.51 |
% 27.02/7.51 | Equations (479) can reduce 6 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.02/7.51 |
% 27.02/7.51 | Applying alpha-rule on (416) yields:
% 27.02/7.51 | (411) all_0_43_43 = e0
% 27.02/7.51 | (412) all_0_59_59 = e3
% 27.02/7.51 | (419) ~ (all_0_56_56 = e0)
% 27.02/7.51 |
% 27.02/7.51 | Combining equations (502,411) yields a new equation:
% 27.02/7.51 | (478) e4 = e0
% 27.02/7.51 |
% 27.02/7.51 | Simplifying 478 yields:
% 27.02/7.51 | (479) e4 = e0
% 27.02/7.51 |
% 27.02/7.51 | Equations (479) can reduce 6 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.02/7.51 |
% 27.02/7.51 | Applying alpha-rule on (422) yields:
% 27.02/7.51 | (423) all_0_53_53 = e0
% 27.02/7.51 | (424) all_0_59_59 = e1
% 27.02/7.51 | (425) ~ (all_0_54_54 = e1)
% 27.02/7.51 |
% 27.02/7.51 | Equations (423) can reduce 128 to:
% 27.02/7.51 | (488) ~ (all_0_45_45 = e0)
% 27.02/7.51 |
% 27.02/7.51 | Equations (424) can reduce 113 to:
% 27.02/7.51 | (543) ~ (all_0_49_49 = e1)
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (219), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (351) all_0_41_41 = e3
% 27.02/7.51 |
% 27.02/7.51 | Combining equations (351,358) yields a new equation:
% 27.02/7.51 | (359) e4 = e3
% 27.02/7.51 |
% 27.02/7.51 | Equations (359) can reduce 34 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (1237) ~ (all_0_41_41 = e3)
% 27.02/7.51 | (1508) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (105), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (374) all_0_45_45 = e2
% 27.02/7.51 |
% 27.02/7.51 | Equations (374) can reduce 434 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (434) ~ (all_0_45_45 = e2)
% 27.02/7.51 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (435), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (454) all_0_45_45 = e0
% 27.02/7.51 |
% 27.02/7.51 | Equations (454) can reduce 488 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (488) ~ (all_0_45_45 = e0)
% 27.02/7.51 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (1508), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (505) all_0_45_45 = e3
% 27.02/7.51 |
% 27.02/7.51 | Equations (505) can reduce 38 to:
% 27.02/7.51 | (1518) ~ (all_0_46_46 = e3)
% 27.02/7.51 |
% 27.02/7.51 | Simplifying 1518 yields:
% 27.02/7.51 | (413) ~ (all_0_46_46 = e3)
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (220), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (497) all_0_46_46 = e2
% 27.02/7.51 |
% 27.02/7.51 | Equations (497) can reduce 1436 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (1436) ~ (all_0_46_46 = e2)
% 27.02/7.51 | (1523) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e0
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (310), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (563) all_0_49_49 = e0
% 27.02/7.51 |
% 27.02/7.51 | Equations (563) can reduce 198 to:
% 27.02/7.51 | (1010) ~ (all_0_46_46 = e0)
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (1523), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (1132) all_0_46_46 = e0
% 27.02/7.51 |
% 27.02/7.51 | Equations (1132) can reduce 1010 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (1010) ~ (all_0_46_46 = e0)
% 27.02/7.51 | (1529) all_0_46_46 = e4 | all_0_46_46 = e3
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (1529), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (1091) all_0_46_46 = e3
% 27.02/7.51 |
% 27.02/7.51 | Equations (1091) can reduce 413 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (413) ~ (all_0_46_46 = e3)
% 27.02/7.51 | (517) all_0_46_46 = e4
% 27.02/7.51 |
% 27.02/7.51 | Equations (517) can reduce 805 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (1231) ~ (all_0_49_49 = e0)
% 27.02/7.51 | (589) all_0_49_49 = e1
% 27.02/7.51 |
% 27.02/7.51 | Equations (589) can reduce 543 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (354) ~ (all_0_45_45 = e3)
% 27.02/7.51 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (489), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (505) all_0_45_45 = e3
% 27.02/7.51 |
% 27.02/7.51 | Equations (505) can reduce 354 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (354) ~ (all_0_45_45 = e3)
% 27.02/7.51 | (363) all_0_45_45 = e4
% 27.02/7.51 |
% 27.02/7.51 | Equations (363) can reduce 352 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.02/7.51 |
% 27.02/7.51 | Applying alpha-rule on (428) yields:
% 27.02/7.51 | (423) all_0_53_53 = e0
% 27.02/7.51 | (424) all_0_59_59 = e1
% 27.02/7.51 | (431) ~ (all_0_58_58 = e0)
% 27.02/7.51 |
% 27.02/7.51 | Equations (423) can reduce 128 to:
% 27.02/7.51 | (488) ~ (all_0_45_45 = e0)
% 27.02/7.51 |
% 27.02/7.51 | Equations (424) can reduce 113 to:
% 27.02/7.51 | (543) ~ (all_0_49_49 = e1)
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (219), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (351) all_0_41_41 = e3
% 27.02/7.51 |
% 27.02/7.51 | Combining equations (351,358) yields a new equation:
% 27.02/7.51 | (359) e4 = e3
% 27.02/7.51 |
% 27.02/7.51 | Equations (359) can reduce 34 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (1237) ~ (all_0_41_41 = e3)
% 27.02/7.51 | (1508) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (105), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (374) all_0_45_45 = e2
% 27.02/7.51 |
% 27.02/7.51 | Equations (374) can reduce 434 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (434) ~ (all_0_45_45 = e2)
% 27.02/7.51 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (435), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (454) all_0_45_45 = e0
% 27.02/7.51 |
% 27.02/7.51 | Equations (454) can reduce 488 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (488) ~ (all_0_45_45 = e0)
% 27.02/7.51 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (1508), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (505) all_0_45_45 = e3
% 27.02/7.51 |
% 27.02/7.51 | Equations (505) can reduce 38 to:
% 27.02/7.51 | (1518) ~ (all_0_46_46 = e3)
% 27.02/7.51 |
% 27.02/7.51 | Simplifying 1518 yields:
% 27.02/7.51 | (413) ~ (all_0_46_46 = e3)
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (220), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (497) all_0_46_46 = e2
% 27.02/7.51 |
% 27.02/7.51 | Equations (497) can reduce 1436 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (1436) ~ (all_0_46_46 = e2)
% 27.02/7.51 | (1523) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e0
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (310), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (563) all_0_49_49 = e0
% 27.02/7.51 |
% 27.02/7.51 | Equations (563) can reduce 198 to:
% 27.02/7.51 | (1010) ~ (all_0_46_46 = e0)
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (1523), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (1132) all_0_46_46 = e0
% 27.02/7.51 |
% 27.02/7.51 | Equations (1132) can reduce 1010 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (1010) ~ (all_0_46_46 = e0)
% 27.02/7.51 | (1529) all_0_46_46 = e4 | all_0_46_46 = e3
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (1529), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (1091) all_0_46_46 = e3
% 27.02/7.51 |
% 27.02/7.51 | Equations (1091) can reduce 413 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (413) ~ (all_0_46_46 = e3)
% 27.02/7.51 | (517) all_0_46_46 = e4
% 27.02/7.51 |
% 27.02/7.51 | Equations (517) can reduce 805 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (1231) ~ (all_0_49_49 = e0)
% 27.02/7.51 | (589) all_0_49_49 = e1
% 27.02/7.51 |
% 27.02/7.51 | Equations (589) can reduce 543 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (354) ~ (all_0_45_45 = e3)
% 27.02/7.51 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (489), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (505) all_0_45_45 = e3
% 27.02/7.51 |
% 27.02/7.51 | Equations (505) can reduce 354 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (354) ~ (all_0_45_45 = e3)
% 27.02/7.51 | (363) all_0_45_45 = e4
% 27.02/7.51 |
% 27.02/7.51 | Equations (363) can reduce 352 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (510) ~ (all_0_43_43 = e4)
% 27.02/7.51 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (511), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (363) all_0_45_45 = e4
% 27.02/7.51 |
% 27.02/7.51 | Equations (363) can reduce 352 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (352) ~ (all_0_45_45 = e4)
% 27.02/7.51 | (517) all_0_46_46 = e4
% 27.02/7.51 |
% 27.02/7.51 | Equations (517) can reduce 38 to:
% 27.02/7.51 | (352) ~ (all_0_45_45 = e4)
% 27.02/7.51 |
% 27.02/7.51 | Equations (517) can reduce 215 to:
% 27.02/7.51 | (1599) ~ (all_0_54_54 = e4)
% 27.02/7.51 |
% 27.02/7.51 | Simplifying 1599 yields:
% 27.02/7.51 | (936) ~ (all_0_54_54 = e4)
% 27.02/7.51 |
% 27.02/7.51 | Equations (517) can reduce 206 to:
% 27.02/7.51 | (279) ~ (all_0_59_59 = e4)
% 27.02/7.51 |
% 27.02/7.51 | Simplifying 279 yields:
% 27.02/7.51 | (280) ~ (all_0_59_59 = e4)
% 27.02/7.51 |
% 27.02/7.51 | Equations (517) can reduce 1436 to:
% 27.02/7.51 | (231) ~ (e4 = e2)
% 27.02/7.51 |
% 27.02/7.51 | Equations (517) can reduce 106 to:
% 27.02/7.51 | (251) ~ (e4 = e1)
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (22), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (782) all_0_43_43 = e3
% 27.02/7.51 |
% 27.02/7.51 | Equations (782) can reduce 786 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (786) ~ (all_0_43_43 = e3)
% 27.02/7.51 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (189), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (267) all_0_50_50 = e4
% 27.02/7.51 |
% 27.02/7.51 | Combining equations (253,267) yields a new equation:
% 27.02/7.51 | (269) e4 = e2
% 27.02/7.51 |
% 27.02/7.51 | Equations (269) can reduce 231 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (271) ~ (all_0_50_50 = e4)
% 27.02/7.51 | (1466) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (1466), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (1467) all_0_51_51 = e4
% 27.02/7.51 |
% 27.02/7.51 | Equations (1467) can reduce 240 to:
% 27.02/7.51 | (510) ~ (all_0_43_43 = e4)
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (159), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (450) all_0_43_43 = e2
% 27.02/7.51 |
% 27.02/7.51 | Equations (450) can reduce 292 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (292) ~ (all_0_43_43 = e2)
% 27.02/7.51 | (774) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (680), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (321) all_0_47_47 = e1
% 27.02/7.51 |
% 27.02/7.51 | Combining equations (290,321) yields a new equation:
% 27.02/7.51 | (531) e2 = e1
% 27.02/7.51 |
% 27.02/7.51 | Simplifying 531 yields:
% 27.02/7.51 | (322) e2 = e1
% 27.02/7.51 |
% 27.02/7.51 | Equations (322) can reduce 141 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (324) ~ (all_0_47_47 = e1)
% 27.02/7.51 | (1625) all_0_51_51 = e1 | all_0_56_56 = e1
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (1625), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (820) all_0_51_51 = e1
% 27.02/7.51 |
% 27.02/7.51 | Combining equations (1467,820) yields a new equation:
% 27.02/7.51 | (525) e4 = e1
% 27.02/7.51 |
% 27.02/7.51 | Simplifying 525 yields:
% 27.02/7.51 | (526) e4 = e1
% 27.02/7.51 |
% 27.02/7.51 | Equations (526) can reduce 251 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (748) ~ (all_0_51_51 = e1)
% 27.02/7.51 | (747) all_0_56_56 = e1
% 27.02/7.51 |
% 27.02/7.51 | Equations (747) can reduce 185 to:
% 27.02/7.51 | (749) ~ (all_0_59_59 = e1)
% 27.02/7.51 |
% 27.02/7.51 | Simplifying 749 yields:
% 27.02/7.51 | (750) ~ (all_0_59_59 = e1)
% 27.02/7.51 |
% 27.02/7.51 | Equations (747) can reduce 300 to:
% 27.02/7.51 | (645) ~ (e2 = e1)
% 27.02/7.51 |
% 27.02/7.51 | Simplifying 645 yields:
% 27.02/7.51 | (141) ~ (e2 = e1)
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (774), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (411) all_0_43_43 = e0
% 27.02/7.51 |
% 27.02/7.51 | Equations (411) can reduce 84 to:
% 27.02/7.51 | (776) ~ (all_0_45_45 = e0)
% 27.02/7.51 |
% 27.02/7.51 | Simplifying 776 yields:
% 27.02/7.51 | (488) ~ (all_0_45_45 = e0)
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (105), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.51 | (374) all_0_45_45 = e2
% 27.02/7.51 |
% 27.02/7.51 | Equations (374) can reduce 434 to:
% 27.02/7.51 | (270) $false
% 27.02/7.51 |
% 27.02/7.51 |-The branch is then unsatisfiable
% 27.02/7.51 |-Branch two:
% 27.02/7.51 | (434) ~ (all_0_45_45 = e2)
% 27.02/7.51 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 27.02/7.51 |
% 27.02/7.51 +-Applying beta-rule and splitting (435), into two cases.
% 27.02/7.51 |-Branch one:
% 27.02/7.52 | (454) all_0_45_45 = e0
% 27.02/7.52 |
% 27.02/7.52 | Equations (454) can reduce 488 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (488) ~ (all_0_45_45 = e0)
% 27.02/7.52 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 27.02/7.52 |
% 27.02/7.52 +-Applying beta-rule and splitting (489), into two cases.
% 27.02/7.52 |-Branch one:
% 27.02/7.52 | (505) all_0_45_45 = e3
% 27.02/7.52 |
% 27.02/7.52 | Equations (505) can reduce 128 to:
% 27.02/7.52 | (355) ~ (all_0_53_53 = e3)
% 27.02/7.52 |
% 27.02/7.52 | Simplifying 355 yields:
% 27.02/7.52 | (356) ~ (all_0_53_53 = e3)
% 27.02/7.52 |
% 27.02/7.52 +-Applying beta-rule and splitting (93), into two cases.
% 27.02/7.52 |-Branch one:
% 27.02/7.52 | (402) all_0_59_59 = e4
% 27.02/7.52 |
% 27.02/7.52 | Equations (402) can reduce 280 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (280) ~ (all_0_59_59 = e4)
% 27.02/7.52 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.02/7.52 |
% 27.02/7.52 +-Applying beta-rule and splitting (407), into two cases.
% 27.02/7.52 |-Branch one:
% 27.02/7.52 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.02/7.52 |
% 27.02/7.52 +-Applying beta-rule and splitting (408), into two cases.
% 27.02/7.52 |-Branch one:
% 27.02/7.52 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.02/7.52 |
% 27.02/7.52 +-Applying beta-rule and splitting (409), into two cases.
% 27.02/7.52 |-Branch one:
% 27.02/7.52 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.02/7.52 |
% 27.02/7.52 | Applying alpha-rule on (410) yields:
% 27.02/7.52 | (411) all_0_43_43 = e0
% 27.02/7.52 | (412) all_0_59_59 = e3
% 27.02/7.52 | (413) ~ (all_0_46_46 = e3)
% 27.02/7.52 |
% 27.02/7.52 | Equations (412) can reduce 72 to:
% 27.02/7.52 | (1093) ~ (all_0_54_54 = e3)
% 27.02/7.52 |
% 27.02/7.52 | Equations (412) can reduce 280 to:
% 27.02/7.52 | (719) ~ (e4 = e3)
% 27.02/7.52 |
% 27.02/7.52 | Simplifying 719 yields:
% 27.02/7.52 | (34) ~ (e4 = e3)
% 27.02/7.52 |
% 27.02/7.52 +-Applying beta-rule and splitting (21), into two cases.
% 27.02/7.52 |-Branch one:
% 27.02/7.52 | (824) all_0_51_51 = e3
% 27.02/7.52 |
% 27.02/7.52 | Combining equations (1467,824) yields a new equation:
% 27.02/7.52 | (660) e4 = e3
% 27.02/7.52 |
% 27.02/7.52 | Simplifying 660 yields:
% 27.02/7.52 | (359) e4 = e3
% 27.02/7.52 |
% 27.02/7.52 | Equations (359) can reduce 34 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (932) ~ (all_0_51_51 = e3)
% 27.02/7.52 | (1101) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 27.02/7.52 |
% 27.02/7.52 +-Applying beta-rule and splitting (1101), into two cases.
% 27.02/7.52 |-Branch one:
% 27.02/7.52 | (864) all_0_52_52 = e3
% 27.02/7.52 |
% 27.02/7.52 | From (864) and (666) follows:
% 27.02/7.52 | (1103) op(e2, e3) = e1
% 27.02/7.52 |
% 27.02/7.52 | Instantiating formula (201) with e2, e3, e1, e2 and discharging atoms op(e2, e3) = e2, op(e2, e3) = e1, yields:
% 27.02/7.52 | (322) e2 = e1
% 27.02/7.52 |
% 27.02/7.52 | Equations (322) can reduce 141 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (826) ~ (all_0_52_52 = e3)
% 27.02/7.52 | (1107) all_0_53_53 = e3 | all_0_54_54 = e3
% 27.02/7.52 |
% 27.02/7.52 +-Applying beta-rule and splitting (1107), into two cases.
% 27.02/7.52 |-Branch one:
% 27.02/7.52 | (1114) all_0_53_53 = e3
% 27.02/7.52 |
% 27.02/7.52 | Equations (1114) can reduce 356 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (356) ~ (all_0_53_53 = e3)
% 27.02/7.52 | (1119) all_0_54_54 = e3
% 27.02/7.52 |
% 27.02/7.52 | Equations (1119) can reduce 1093 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.02/7.52 |
% 27.02/7.52 | Applying alpha-rule on (416) yields:
% 27.02/7.52 | (411) all_0_43_43 = e0
% 27.02/7.52 | (412) all_0_59_59 = e3
% 27.02/7.52 | (419) ~ (all_0_56_56 = e0)
% 27.02/7.52 |
% 27.02/7.52 | Equations (412) can reduce 72 to:
% 27.02/7.52 | (1093) ~ (all_0_54_54 = e3)
% 27.02/7.52 |
% 27.02/7.52 | Equations (412) can reduce 280 to:
% 27.02/7.52 | (719) ~ (e4 = e3)
% 27.02/7.52 |
% 27.02/7.52 | Simplifying 719 yields:
% 27.02/7.52 | (34) ~ (e4 = e3)
% 27.02/7.52 |
% 27.02/7.52 +-Applying beta-rule and splitting (21), into two cases.
% 27.02/7.52 |-Branch one:
% 27.02/7.52 | (824) all_0_51_51 = e3
% 27.02/7.52 |
% 27.02/7.52 | Combining equations (1467,824) yields a new equation:
% 27.02/7.52 | (660) e4 = e3
% 27.02/7.52 |
% 27.02/7.52 | Simplifying 660 yields:
% 27.02/7.52 | (359) e4 = e3
% 27.02/7.52 |
% 27.02/7.52 | Equations (359) can reduce 34 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (932) ~ (all_0_51_51 = e3)
% 27.02/7.52 | (1101) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 27.02/7.52 |
% 27.02/7.52 +-Applying beta-rule and splitting (1101), into two cases.
% 27.02/7.52 |-Branch one:
% 27.02/7.52 | (864) all_0_52_52 = e3
% 27.02/7.52 |
% 27.02/7.52 | From (864) and (666) follows:
% 27.02/7.52 | (1103) op(e2, e3) = e1
% 27.02/7.52 |
% 27.02/7.52 | Instantiating formula (201) with e2, e3, e1, e2 and discharging atoms op(e2, e3) = e2, op(e2, e3) = e1, yields:
% 27.02/7.52 | (322) e2 = e1
% 27.02/7.52 |
% 27.02/7.52 | Equations (322) can reduce 141 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (826) ~ (all_0_52_52 = e3)
% 27.02/7.52 | (1107) all_0_53_53 = e3 | all_0_54_54 = e3
% 27.02/7.52 |
% 27.02/7.52 +-Applying beta-rule and splitting (1107), into two cases.
% 27.02/7.52 |-Branch one:
% 27.02/7.52 | (1114) all_0_53_53 = e3
% 27.02/7.52 |
% 27.02/7.52 | Equations (1114) can reduce 356 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (356) ~ (all_0_53_53 = e3)
% 27.02/7.52 | (1119) all_0_54_54 = e3
% 27.02/7.52 |
% 27.02/7.52 | Equations (1119) can reduce 1093 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.02/7.52 |
% 27.02/7.52 | Applying alpha-rule on (422) yields:
% 27.02/7.52 | (423) all_0_53_53 = e0
% 27.02/7.52 | (424) all_0_59_59 = e1
% 27.02/7.52 | (425) ~ (all_0_54_54 = e1)
% 27.02/7.52 |
% 27.02/7.52 | Equations (424) can reduce 750 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.02/7.52 |
% 27.02/7.52 | Applying alpha-rule on (428) yields:
% 27.02/7.52 | (423) all_0_53_53 = e0
% 27.02/7.52 | (424) all_0_59_59 = e1
% 27.02/7.52 | (431) ~ (all_0_58_58 = e0)
% 27.02/7.52 |
% 27.02/7.52 | Equations (424) can reduce 750 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (354) ~ (all_0_45_45 = e3)
% 27.02/7.52 | (363) all_0_45_45 = e4
% 27.02/7.52 |
% 27.02/7.52 | Equations (363) can reduce 352 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (455) ~ (all_0_43_43 = e0)
% 27.02/7.52 | (944) all_0_43_43 = e4 | all_0_43_43 = e3
% 27.02/7.52 |
% 27.02/7.52 +-Applying beta-rule and splitting (944), into two cases.
% 27.02/7.52 |-Branch one:
% 27.02/7.52 | (782) all_0_43_43 = e3
% 27.02/7.52 |
% 27.02/7.52 | Equations (782) can reduce 786 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (786) ~ (all_0_43_43 = e3)
% 27.02/7.52 | (502) all_0_43_43 = e4
% 27.02/7.52 |
% 27.02/7.52 | Equations (502) can reduce 510 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (697) ~ (all_0_51_51 = e4)
% 27.02/7.52 | (1470) all_0_53_53 = e4 | all_0_54_54 = e4
% 27.02/7.52 |
% 27.02/7.52 +-Applying beta-rule and splitting (1470), into two cases.
% 27.02/7.52 |-Branch one:
% 27.02/7.52 | (367) all_0_53_53 = e4
% 27.02/7.52 |
% 27.02/7.52 | Equations (367) can reduce 599 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (599) ~ (all_0_53_53 = e4)
% 27.02/7.52 | (817) all_0_54_54 = e4
% 27.02/7.52 |
% 27.02/7.52 | Equations (817) can reduce 936 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (498) ~ (all_0_42_42 = e2)
% 27.02/7.52 | (1732) all_0_46_46 = e2 | all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 27.02/7.52 |
% 27.02/7.52 +-Applying beta-rule and splitting (16), into two cases.
% 27.02/7.52 |-Branch one:
% 27.02/7.52 | (698) all_0_42_42 = e2
% 27.02/7.52 |
% 27.02/7.52 | Equations (698) can reduce 498 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (498) ~ (all_0_42_42 = e2)
% 27.02/7.52 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 27.02/7.52 |
% 27.02/7.52 +-Applying beta-rule and splitting (1238), into two cases.
% 27.02/7.52 |-Branch one:
% 27.02/7.52 | (536) all_0_41_41 = e1
% 27.02/7.52 |
% 27.02/7.52 | Equations (536) can reduce 540 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (540) ~ (all_0_41_41 = e1)
% 27.02/7.52 | (358) all_0_41_41 = e4
% 27.02/7.52 |
% 27.02/7.52 | Equations (358) can reduce 331 to:
% 27.02/7.52 | (231) ~ (e4 = e2)
% 27.02/7.52 |
% 27.02/7.52 +-Applying beta-rule and splitting (630), into two cases.
% 27.02/7.52 |-Branch one:
% 27.02/7.52 | (327) all_0_40_40 = e2
% 27.02/7.52 |
% 27.02/7.52 | Combining equations (327,530) yields a new equation:
% 27.02/7.52 | (531) e2 = e1
% 27.02/7.52 |
% 27.02/7.52 | Simplifying 531 yields:
% 27.02/7.52 | (322) e2 = e1
% 27.02/7.52 |
% 27.02/7.52 | Equations (322) can reduce 141 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (602) ~ (all_0_40_40 = e2)
% 27.02/7.52 | (1251) all_0_41_41 = e2 | all_0_42_42 = e2
% 27.02/7.52 |
% 27.02/7.52 +-Applying beta-rule and splitting (1251), into two cases.
% 27.02/7.52 |-Branch one:
% 27.02/7.52 | (436) all_0_41_41 = e2
% 27.02/7.52 |
% 27.02/7.52 | Combining equations (358,436) yields a new equation:
% 27.02/7.52 | (268) e4 = e2
% 27.02/7.52 |
% 27.02/7.52 | Simplifying 268 yields:
% 27.02/7.52 | (269) e4 = e2
% 27.02/7.52 |
% 27.02/7.52 | Equations (269) can reduce 231 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (331) ~ (all_0_41_41 = e2)
% 27.02/7.52 | (698) all_0_42_42 = e2
% 27.02/7.52 |
% 27.02/7.52 | Equations (698) can reduce 498 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (755) ~ (all_0_39_39 = e3)
% 27.02/7.52 | (1756) all_0_39_39 = e4 | all_0_39_39 = e1
% 27.02/7.52 |
% 27.02/7.52 +-Applying beta-rule and splitting (1756), into two cases.
% 27.02/7.52 |-Branch one:
% 27.02/7.52 | (524) all_0_39_39 = e1
% 27.02/7.52 |
% 27.02/7.52 | Equations (524) can reduce 528 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (528) ~ (all_0_39_39 = e1)
% 27.02/7.52 | (522) all_0_39_39 = e4
% 27.02/7.52 |
% 27.02/7.52 | Equations (522) can reduce 591 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (1762) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 27.02/7.52 |
% 27.02/7.52 | Applying alpha-rule on (1762) yields:
% 27.02/7.52 | (1763) all_0_19_19 = e0
% 27.02/7.52 | (1764) ~ (all_0_20_20 = e2)
% 27.02/7.52 |
% 27.02/7.52 | From (1763) and (30) follows:
% 27.02/7.52 | (1765) op(e2, all_0_57_57) = e0
% 27.02/7.52 |
% 27.02/7.52 +-Applying beta-rule and splitting (33), into two cases.
% 27.02/7.52 |-Branch one:
% 27.02/7.52 | (392) all_0_57_57 = e2
% 27.02/7.52 |
% 27.02/7.52 | Equations (392) can reduce 335 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (335) ~ (all_0_57_57 = e2)
% 27.02/7.52 | (670) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 27.02/7.52 |
% 27.02/7.52 +-Applying beta-rule and splitting (133), into two cases.
% 27.02/7.52 |-Branch one:
% 27.02/7.52 | (671) all_0_40_40 = e3
% 27.02/7.52 |
% 27.02/7.52 | Combining equations (671,530) yields a new equation:
% 27.02/7.52 | (537) e3 = e1
% 27.02/7.52 |
% 27.02/7.52 | Simplifying 537 yields:
% 27.02/7.52 | (538) e3 = e1
% 27.02/7.52 |
% 27.02/7.52 | Equations (538) can reduce 136 to:
% 27.02/7.52 | (270) $false
% 27.02/7.52 |
% 27.02/7.52 |-The branch is then unsatisfiable
% 27.02/7.52 |-Branch two:
% 27.02/7.52 | (675) ~ (all_0_40_40 = e3)
% 27.02/7.52 | (676) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (99), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (524) all_0_39_39 = e1
% 27.02/7.53 |
% 27.02/7.53 | Equations (524) can reduce 528 to:
% 27.02/7.53 | (270) $false
% 27.02/7.53 |
% 27.02/7.53 |-The branch is then unsatisfiable
% 27.02/7.53 |-Branch two:
% 27.02/7.53 | (528) ~ (all_0_39_39 = e1)
% 27.02/7.53 | (680) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (177), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (336) all_0_39_39 = e2
% 27.02/7.53 |
% 27.02/7.53 | Equations (336) can reduce 291 to:
% 27.02/7.53 | (270) $false
% 27.02/7.53 |
% 27.02/7.53 |-The branch is then unsatisfiable
% 27.02/7.53 |-Branch two:
% 27.02/7.53 | (291) ~ (all_0_39_39 = e2)
% 27.02/7.53 | (684) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (90), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (685) all_0_52_52 = e2
% 27.02/7.53 |
% 27.02/7.53 | Equations (685) can reduce 257 to:
% 27.02/7.53 | (270) $false
% 27.02/7.53 |
% 27.02/7.53 |-The branch is then unsatisfiable
% 27.02/7.53 |-Branch two:
% 27.02/7.53 | (257) ~ (all_0_52_52 = e2)
% 27.02/7.53 | (688) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (222), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (522) all_0_39_39 = e4
% 27.02/7.53 |
% 27.02/7.53 | Equations (522) can reduce 226 to:
% 27.02/7.53 | (690) ~ (all_0_41_41 = e4)
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 690 yields:
% 27.02/7.53 | (361) ~ (all_0_41_41 = e4)
% 27.02/7.53 |
% 27.02/7.53 | Equations (522) can reduce 184 to:
% 27.02/7.53 | (692) ~ (all_0_42_42 = e4)
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 692 yields:
% 27.02/7.53 | (520) ~ (all_0_42_42 = e4)
% 27.02/7.53 |
% 27.02/7.53 | Equations (522) can reduce 167 to:
% 27.02/7.53 | (694) ~ (all_0_43_43 = e4)
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 694 yields:
% 27.02/7.53 | (510) ~ (all_0_43_43 = e4)
% 27.02/7.53 |
% 27.02/7.53 | Equations (522) can reduce 32 to:
% 27.02/7.53 | (696) ~ (all_0_51_51 = e4)
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 696 yields:
% 27.02/7.53 | (697) ~ (all_0_51_51 = e4)
% 27.02/7.53 |
% 27.02/7.53 | Equations (522) can reduce 212 to:
% 27.02/7.53 | (273) ~ (all_0_56_56 = e4)
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 273 yields:
% 27.02/7.53 | (274) ~ (all_0_56_56 = e4)
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (16), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (698) all_0_42_42 = e2
% 27.02/7.53 |
% 27.02/7.53 | Equations (698) can reduce 94 to:
% 27.02/7.53 | (331) ~ (all_0_41_41 = e2)
% 27.02/7.53 |
% 27.02/7.53 | Equations (698) can reduce 17 to:
% 27.02/7.53 | (700) ~ (all_0_59_59 = e2)
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 700 yields:
% 27.02/7.53 | (701) ~ (all_0_59_59 = e2)
% 27.02/7.53 |
% 27.02/7.53 | Equations (698) can reduce 520 to:
% 27.02/7.53 | (377) ~ (e4 = e2)
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 377 yields:
% 27.02/7.53 | (231) ~ (e4 = e2)
% 27.02/7.53 |
% 27.02/7.53 | Equations (698) can reduce 640 to:
% 27.02/7.53 | (141) ~ (e2 = e1)
% 27.02/7.53 |
% 27.02/7.53 | Equations (698) can reduce 199 to:
% 27.02/7.53 | (57) ~ (e2 = e0)
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (217), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (436) all_0_41_41 = e2
% 27.02/7.53 |
% 27.02/7.53 | Equations (436) can reduce 331 to:
% 27.02/7.53 | (270) $false
% 27.02/7.53 |
% 27.02/7.53 |-The branch is then unsatisfiable
% 27.02/7.53 |-Branch two:
% 27.02/7.53 | (331) ~ (all_0_41_41 = e2)
% 27.02/7.53 | (709) all_0_41_41 = e4 | all_0_41_41 = e3 | all_0_41_41 = e1
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (709), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (351) all_0_41_41 = e3
% 27.02/7.53 |
% 27.02/7.53 | Equations (351) can reduce 51 to:
% 27.02/7.53 | (353) ~ (all_0_45_45 = e3)
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 353 yields:
% 27.02/7.53 | (354) ~ (all_0_45_45 = e3)
% 27.02/7.53 |
% 27.02/7.53 | Equations (351) can reduce 190 to:
% 27.02/7.53 | (713) ~ (all_0_48_48 = e3)
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 713 yields:
% 27.02/7.53 | (121) ~ (all_0_48_48 = e3)
% 27.02/7.53 |
% 27.02/7.53 | Equations (351) can reduce 214 to:
% 27.02/7.53 | (355) ~ (all_0_53_53 = e3)
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 355 yields:
% 27.02/7.53 | (356) ~ (all_0_53_53 = e3)
% 27.02/7.53 |
% 27.02/7.53 | Equations (351) can reduce 157 to:
% 27.02/7.53 | (717) ~ (all_0_58_58 = e3)
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 717 yields:
% 27.02/7.53 | (718) ~ (all_0_58_58 = e3)
% 27.02/7.53 |
% 27.02/7.53 | Equations (351) can reduce 361 to:
% 27.02/7.53 | (719) ~ (e4 = e3)
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 719 yields:
% 27.02/7.53 | (34) ~ (e4 = e3)
% 27.02/7.53 |
% 27.02/7.53 | Equations (351) can reduce 540 to:
% 27.02/7.53 | (136) ~ (e3 = e1)
% 27.02/7.53 |
% 27.02/7.53 | Equations (351) can reduce 232 to:
% 27.02/7.53 | (66) ~ (e3 = e0)
% 27.02/7.53 |
% 27.02/7.53 | From (351) and (112) follows:
% 27.02/7.53 | (1824) op(e1, e3) = all_0_21_21
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (168), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (382) all_0_55_55 = e2
% 27.02/7.53 |
% 27.02/7.53 | Combining equations (382,272) yields a new equation:
% 27.02/7.53 | (269) e4 = e2
% 27.02/7.53 |
% 27.02/7.53 | Equations (269) can reduce 231 to:
% 27.02/7.53 | (270) $false
% 27.02/7.53 |
% 27.02/7.53 |-The branch is then unsatisfiable
% 27.02/7.53 |-Branch two:
% 27.02/7.53 | (386) ~ (all_0_55_55 = e2)
% 27.02/7.53 | (387) all_0_56_56 = e2 | all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (387), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (388) all_0_56_56 = e2
% 27.02/7.53 |
% 27.02/7.53 | Equations (388) can reduce 300 to:
% 27.02/7.53 | (270) $false
% 27.02/7.53 |
% 27.02/7.53 |-The branch is then unsatisfiable
% 27.02/7.53 |-Branch two:
% 27.02/7.53 | (300) ~ (all_0_56_56 = e2)
% 27.02/7.53 | (391) all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (391), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (392) all_0_57_57 = e2
% 27.02/7.53 |
% 27.02/7.53 | Equations (392) can reduce 335 to:
% 27.02/7.53 | (270) $false
% 27.02/7.53 |
% 27.02/7.53 |-The branch is then unsatisfiable
% 27.02/7.53 |-Branch two:
% 27.02/7.53 | (335) ~ (all_0_57_57 = e2)
% 27.02/7.53 | (395) all_0_58_58 = e2 | all_0_59_59 = e2
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (395), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (396) all_0_58_58 = e2
% 27.02/7.53 |
% 27.02/7.53 | Equations (396) can reduce 108 to:
% 27.02/7.53 | (434) ~ (all_0_45_45 = e2)
% 27.02/7.53 |
% 27.02/7.53 | Equations (396) can reduce 70 to:
% 27.02/7.53 | (259) ~ (all_0_53_53 = e2)
% 27.02/7.53 |
% 27.02/7.53 | Equations (396) can reduce 37 to:
% 27.02/7.53 | (335) ~ (all_0_57_57 = e2)
% 27.02/7.53 |
% 27.02/7.53 | Equations (396) can reduce 156 to:
% 27.02/7.53 | (700) ~ (all_0_59_59 = e2)
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 700 yields:
% 27.02/7.53 | (701) ~ (all_0_59_59 = e2)
% 27.02/7.53 |
% 27.02/7.53 | Equations (396) can reduce 718 to:
% 27.02/7.53 | (301) ~ (e3 = e2)
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 301 yields:
% 27.02/7.53 | (223) ~ (e3 = e2)
% 27.02/7.53 |
% 27.02/7.53 | From (396) and (63) follows:
% 27.02/7.53 | (1846) op(e1, e2) = all_0_28_28
% 27.02/7.53 |
% 27.02/7.53 | Instantiating formula (201) with e1, e3, all_0_21_21, all_0_51_51 and discharging atoms op(e1, e3) = all_0_21_21, op(e1, e3) = all_0_51_51, yields:
% 27.02/7.53 | (1847) all_0_21_21 = all_0_51_51
% 27.02/7.53 |
% 27.02/7.53 | Instantiating formula (201) with e1, e2, all_0_28_28, all_0_52_52 and discharging atoms op(e1, e2) = all_0_28_28, op(e1, e2) = all_0_52_52, yields:
% 27.02/7.53 | (1848) all_0_28_28 = all_0_52_52
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (44), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (502) all_0_43_43 = e4
% 27.02/7.53 |
% 27.02/7.53 | Equations (502) can reduce 510 to:
% 27.02/7.53 | (270) $false
% 27.02/7.53 |
% 27.02/7.53 |-The branch is then unsatisfiable
% 27.02/7.53 |-Branch two:
% 27.02/7.53 | (510) ~ (all_0_43_43 = e4)
% 27.02/7.53 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (194), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (747) all_0_56_56 = e1
% 27.02/7.53 |
% 27.02/7.53 | Equations (747) can reduce 60 to:
% 27.02/7.53 | (748) ~ (all_0_51_51 = e1)
% 27.02/7.53 |
% 27.02/7.53 | Equations (747) can reduce 185 to:
% 27.02/7.53 | (749) ~ (all_0_59_59 = e1)
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 749 yields:
% 27.02/7.53 | (750) ~ (all_0_59_59 = e1)
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (178), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (751) all_0_39_39 = e3
% 27.02/7.53 |
% 27.02/7.53 | Combining equations (522,751) yields a new equation:
% 27.02/7.53 | (660) e4 = e3
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 660 yields:
% 27.02/7.53 | (359) e4 = e3
% 27.02/7.53 |
% 27.02/7.53 | Equations (359) can reduce 34 to:
% 27.02/7.53 | (270) $false
% 27.02/7.53 |
% 27.02/7.53 |-The branch is then unsatisfiable
% 27.02/7.53 |-Branch two:
% 27.02/7.53 | (755) ~ (all_0_39_39 = e3)
% 27.02/7.53 | (756) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (52), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (536) all_0_41_41 = e1
% 27.02/7.53 |
% 27.02/7.53 | Combining equations (351,536) yields a new equation:
% 27.02/7.53 | (537) e3 = e1
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 537 yields:
% 27.02/7.53 | (538) e3 = e1
% 27.02/7.53 |
% 27.02/7.53 | Equations (538) can reduce 136 to:
% 27.02/7.53 | (270) $false
% 27.02/7.53 |
% 27.02/7.53 |-The branch is then unsatisfiable
% 27.02/7.53 |-Branch two:
% 27.02/7.53 | (540) ~ (all_0_41_41 = e1)
% 27.02/7.53 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 27.02/7.53 |
% 27.02/7.53 | Equations (351) can reduce 540 to:
% 27.02/7.53 | (136) ~ (e3 = e1)
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (236), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (764) all_0_56_56 = e3
% 27.02/7.53 |
% 27.02/7.53 | Combining equations (747,764) yields a new equation:
% 27.02/7.53 | (538) e3 = e1
% 27.02/7.53 |
% 27.02/7.53 | Equations (538) can reduce 136 to:
% 27.02/7.53 | (270) $false
% 27.02/7.53 |
% 27.02/7.53 |-The branch is then unsatisfiable
% 27.02/7.53 |-Branch two:
% 27.02/7.53 | (767) ~ (all_0_56_56 = e3)
% 27.02/7.53 | (768) all_0_57_57 = e3 | all_0_58_58 = e3 | all_0_59_59 = e3
% 27.02/7.53 |
% 27.02/7.53 | Equations (747) can reduce 767 to:
% 27.02/7.53 | (769) ~ (e3 = e1)
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 769 yields:
% 27.02/7.53 | (136) ~ (e3 = e1)
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (159), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (450) all_0_43_43 = e2
% 27.02/7.53 |
% 27.02/7.53 | Equations (450) can reduce 292 to:
% 27.02/7.53 | (270) $false
% 27.02/7.53 |
% 27.02/7.53 |-The branch is then unsatisfiable
% 27.02/7.53 |-Branch two:
% 27.02/7.53 | (292) ~ (all_0_43_43 = e2)
% 27.02/7.53 | (774) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (75), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (411) all_0_43_43 = e0
% 27.02/7.53 |
% 27.02/7.53 | Equations (411) can reduce 84 to:
% 27.02/7.53 | (776) ~ (all_0_45_45 = e0)
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 776 yields:
% 27.02/7.53 | (488) ~ (all_0_45_45 = e0)
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (105), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (374) all_0_45_45 = e2
% 27.02/7.53 |
% 27.02/7.53 | Equations (374) can reduce 434 to:
% 27.02/7.53 | (270) $false
% 27.02/7.53 |
% 27.02/7.53 |-The branch is then unsatisfiable
% 27.02/7.53 |-Branch two:
% 27.02/7.53 | (434) ~ (all_0_45_45 = e2)
% 27.02/7.53 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (22), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (782) all_0_43_43 = e3
% 27.02/7.53 |
% 27.02/7.53 | Combining equations (782,411) yields a new equation:
% 27.02/7.53 | (783) e3 = e0
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 783 yields:
% 27.02/7.53 | (784) e3 = e0
% 27.02/7.53 |
% 27.02/7.53 | Equations (784) can reduce 66 to:
% 27.02/7.53 | (270) $false
% 27.02/7.53 |
% 27.02/7.53 |-The branch is then unsatisfiable
% 27.02/7.53 |-Branch two:
% 27.02/7.53 | (786) ~ (all_0_43_43 = e3)
% 27.02/7.53 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 27.02/7.53 |
% 27.02/7.53 | Equations (411) can reduce 786 to:
% 27.02/7.53 | (788) ~ (e3 = e0)
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 788 yields:
% 27.02/7.53 | (66) ~ (e3 = e0)
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (435), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (454) all_0_45_45 = e0
% 27.02/7.53 |
% 27.02/7.53 | Equations (454) can reduce 488 to:
% 27.02/7.53 | (270) $false
% 27.02/7.53 |
% 27.02/7.53 |-The branch is then unsatisfiable
% 27.02/7.53 |-Branch two:
% 27.02/7.53 | (488) ~ (all_0_45_45 = e0)
% 27.02/7.53 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (756), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (782) all_0_43_43 = e3
% 27.02/7.53 |
% 27.02/7.53 | Combining equations (782,411) yields a new equation:
% 27.02/7.53 | (783) e3 = e0
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 783 yields:
% 27.02/7.53 | (784) e3 = e0
% 27.02/7.53 |
% 27.02/7.53 | Equations (784) can reduce 66 to:
% 27.02/7.53 | (270) $false
% 27.02/7.53 |
% 27.02/7.53 |-The branch is then unsatisfiable
% 27.02/7.53 |-Branch two:
% 27.02/7.53 | (786) ~ (all_0_43_43 = e3)
% 27.02/7.53 | (799) all_0_51_51 = e3 | all_0_56_56 = e3
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (489), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (505) all_0_45_45 = e3
% 27.02/7.53 |
% 27.02/7.53 | Equations (505) can reduce 354 to:
% 27.02/7.53 | (270) $false
% 27.02/7.53 |
% 27.02/7.53 |-The branch is then unsatisfiable
% 27.02/7.53 |-Branch two:
% 27.02/7.53 | (354) ~ (all_0_45_45 = e3)
% 27.02/7.53 | (363) all_0_45_45 = e4
% 27.02/7.53 |
% 27.02/7.53 | Equations (363) can reduce 38 to:
% 27.02/7.53 | (804) ~ (all_0_46_46 = e4)
% 27.02/7.53 |
% 27.02/7.53 | Simplifying 804 yields:
% 27.02/7.53 | (805) ~ (all_0_46_46 = e4)
% 27.02/7.53 |
% 27.02/7.53 | Equations (363) can reduce 434 to:
% 27.02/7.53 | (231) ~ (e4 = e2)
% 27.02/7.53 |
% 27.02/7.53 | Equations (363) can reduce 26 to:
% 27.02/7.53 | (251) ~ (e4 = e1)
% 27.02/7.53 |
% 27.02/7.53 +-Applying beta-rule and splitting (179), into two cases.
% 27.02/7.53 |-Branch one:
% 27.02/7.53 | (512) all_0_42_42 = e4
% 27.02/7.53 |
% 27.02/7.53 | Combining equations (698,512) yields a new equation:
% 27.02/7.53 | (269) e4 = e2
% 27.02/7.53 |
% 27.02/7.53 | Equations (269) can reduce 231 to:
% 27.02/7.53 | (270) $false
% 27.45/7.53 |
% 27.45/7.53 |-The branch is then unsatisfiable
% 27.45/7.53 |-Branch two:
% 27.45/7.53 | (520) ~ (all_0_42_42 = e4)
% 27.45/7.53 | (521) all_0_46_46 = e4 | all_0_54_54 = e4 | all_0_59_59 = e4
% 27.45/7.53 |
% 27.45/7.53 +-Applying beta-rule and splitting (521), into two cases.
% 27.45/7.53 |-Branch one:
% 27.45/7.53 | (517) all_0_46_46 = e4
% 27.45/7.53 |
% 27.45/7.53 | Equations (517) can reduce 805 to:
% 27.45/7.53 | (270) $false
% 27.45/7.53 |
% 27.45/7.53 |-The branch is then unsatisfiable
% 27.45/7.53 |-Branch two:
% 27.45/7.53 | (805) ~ (all_0_46_46 = e4)
% 27.45/7.53 | (816) all_0_54_54 = e4 | all_0_59_59 = e4
% 27.45/7.53 |
% 27.45/7.53 +-Applying beta-rule and splitting (816), into two cases.
% 27.45/7.53 |-Branch one:
% 27.45/7.53 | (817) all_0_54_54 = e4
% 27.45/7.53 |
% 27.45/7.53 | Equations (817) can reduce 72 to:
% 27.45/7.53 | (279) ~ (all_0_59_59 = e4)
% 27.45/7.53 |
% 27.45/7.53 | Simplifying 279 yields:
% 27.45/7.53 | (280) ~ (all_0_59_59 = e4)
% 27.45/7.53 |
% 27.45/7.53 +-Applying beta-rule and splitting (135), into two cases.
% 27.45/7.53 |-Branch one:
% 27.45/7.53 | (820) all_0_51_51 = e1
% 27.45/7.53 |
% 27.45/7.53 | Equations (820) can reduce 748 to:
% 27.45/7.53 | (270) $false
% 27.45/7.53 |
% 27.45/7.53 |-The branch is then unsatisfiable
% 27.45/7.53 |-Branch two:
% 27.45/7.53 | (748) ~ (all_0_51_51 = e1)
% 27.45/7.53 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 27.45/7.53 |
% 27.45/7.53 +-Applying beta-rule and splitting (799), into two cases.
% 27.45/7.53 |-Branch one:
% 27.45/7.53 | (824) all_0_51_51 = e3
% 27.45/7.53 |
% 27.45/7.53 | Equations (824) can reduce 154 to:
% 27.45/7.53 | (825) ~ (all_0_52_52 = e3)
% 27.45/7.53 |
% 27.45/7.53 | Simplifying 825 yields:
% 27.45/7.53 | (826) ~ (all_0_52_52 = e3)
% 27.45/7.53 |
% 27.45/7.53 +-Applying beta-rule and splitting (688), into two cases.
% 27.45/7.53 |-Branch one:
% 27.45/7.53 | (827) all_0_52_52 = e0
% 27.45/7.53 |
% 27.45/7.53 | Equations (827) can reduce 642 to:
% 27.45/7.53 | (568) ~ (e1 = e0)
% 27.45/7.53 |
% 27.45/7.53 | Simplifying 568 yields:
% 27.45/7.53 | (132) ~ (e1 = e0)
% 27.45/7.53 |
% 27.45/7.53 +-Applying beta-rule and splitting (176), into two cases.
% 27.45/7.53 |-Branch one:
% 27.45/7.53 | (830) all_0_56_56 = e0
% 27.45/7.53 |
% 27.45/7.53 | Combining equations (830,747) yields a new equation:
% 27.45/7.53 | (560) e1 = e0
% 27.45/7.53 |
% 27.45/7.53 | Equations (560) can reduce 132 to:
% 27.45/7.53 | (270) $false
% 27.45/7.53 |
% 27.45/7.53 |-The branch is then unsatisfiable
% 27.45/7.53 |-Branch two:
% 27.45/7.53 | (419) ~ (all_0_56_56 = e0)
% 27.45/7.53 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 27.45/7.53 |
% 27.45/7.53 | Equations (747) can reduce 419 to:
% 27.45/7.53 | (132) ~ (e1 = e0)
% 27.45/7.53 |
% 27.45/7.53 +-Applying beta-rule and splitting (93), into two cases.
% 27.45/7.53 |-Branch one:
% 27.45/7.53 | (402) all_0_59_59 = e4
% 27.45/7.53 |
% 27.45/7.53 | Equations (402) can reduce 280 to:
% 27.45/7.53 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (280) ~ (all_0_59_59 = e4)
% 27.45/7.54 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.45/7.54 |
% 27.45/7.54 +-Applying beta-rule and splitting (407), into two cases.
% 27.45/7.54 |-Branch one:
% 27.45/7.54 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.45/7.54 |
% 27.45/7.54 +-Applying beta-rule and splitting (408), into two cases.
% 27.45/7.54 |-Branch one:
% 27.45/7.54 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.45/7.54 |
% 27.45/7.54 +-Applying beta-rule and splitting (409), into two cases.
% 27.45/7.54 |-Branch one:
% 27.45/7.54 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.45/7.54 |
% 27.45/7.54 | Applying alpha-rule on (410) yields:
% 27.45/7.54 | (411) all_0_43_43 = e0
% 27.45/7.54 | (412) all_0_59_59 = e3
% 27.45/7.54 | (413) ~ (all_0_46_46 = e3)
% 27.45/7.54 |
% 27.45/7.54 | Equations (412) can reduce 140 to:
% 27.45/7.54 | (846) ~ (all_0_57_57 = e3)
% 27.45/7.54 |
% 27.45/7.54 | Equations (412) can reduce 701 to:
% 27.45/7.54 | (223) ~ (e3 = e2)
% 27.45/7.54 |
% 27.45/7.54 +-Applying beta-rule and splitting (823), into two cases.
% 27.45/7.54 |-Branch one:
% 27.45/7.54 | (848) all_0_52_52 = e1
% 27.45/7.54 |
% 27.45/7.54 | Combining equations (827,848) yields a new equation:
% 27.45/7.54 | (560) e1 = e0
% 27.45/7.54 |
% 27.45/7.54 | Equations (560) can reduce 132 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (642) ~ (all_0_52_52 = e1)
% 27.45/7.54 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 27.45/7.54 |
% 27.45/7.54 +-Applying beta-rule and splitting (852), into two cases.
% 27.45/7.54 |-Branch one:
% 27.45/7.54 | (853) all_0_53_53 = e1
% 27.45/7.54 |
% 27.45/7.54 | Equations (853) can reduce 48 to:
% 27.45/7.54 | (588) ~ (all_0_48_48 = e1)
% 27.45/7.54 |
% 27.45/7.54 +-Applying beta-rule and splitting (314), into two cases.
% 27.45/7.54 |-Branch one:
% 27.45/7.54 | (559) all_0_48_48 = e0
% 27.45/7.54 |
% 27.45/7.54 | Equations (559) can reduce 121 to:
% 27.45/7.54 | (788) ~ (e3 = e0)
% 27.45/7.54 |
% 27.45/7.54 | Simplifying 788 yields:
% 27.45/7.54 | (66) ~ (e3 = e0)
% 27.45/7.54 |
% 27.45/7.54 +-Applying beta-rule and splitting (676), into two cases.
% 27.45/7.54 |-Branch one:
% 27.45/7.54 | (858) all_0_44_44 = e3
% 27.45/7.54 |
% 27.45/7.54 | Combining equations (858,370) yields a new equation:
% 27.45/7.54 | (437) e3 = e2
% 27.45/7.54 |
% 27.45/7.54 | Simplifying 437 yields:
% 27.45/7.54 | (414) e3 = e2
% 27.45/7.54 |
% 27.45/7.54 | Equations (414) can reduce 223 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (862) ~ (all_0_44_44 = e3)
% 27.45/7.54 | (863) all_0_52_52 = e3 | all_0_57_57 = e3
% 27.45/7.54 |
% 27.45/7.54 +-Applying beta-rule and splitting (863), into two cases.
% 27.45/7.54 |-Branch one:
% 27.45/7.54 | (864) all_0_52_52 = e3
% 27.45/7.54 |
% 27.45/7.54 | Combining equations (864,827) yields a new equation:
% 27.45/7.54 | (783) e3 = e0
% 27.45/7.54 |
% 27.45/7.54 | Simplifying 783 yields:
% 27.45/7.54 | (784) e3 = e0
% 27.45/7.54 |
% 27.45/7.54 | Equations (784) can reduce 66 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (826) ~ (all_0_52_52 = e3)
% 27.45/7.54 | (869) all_0_57_57 = e3
% 27.45/7.54 |
% 27.45/7.54 | Equations (869) can reduce 846 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (562) ~ (all_0_48_48 = e0)
% 27.45/7.54 | (552) all_0_48_48 = e1
% 27.45/7.54 |
% 27.45/7.54 | Equations (552) can reduce 588 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (874) ~ (all_0_53_53 = e1)
% 27.45/7.54 | (875) all_0_54_54 = e1
% 27.45/7.54 |
% 27.45/7.54 | Combining equations (875,817) yields a new equation:
% 27.45/7.54 | (526) e4 = e1
% 27.45/7.54 |
% 27.45/7.54 | Equations (526) can reduce 251 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.45/7.54 |
% 27.45/7.54 | Applying alpha-rule on (416) yields:
% 27.45/7.54 | (411) all_0_43_43 = e0
% 27.45/7.54 | (412) all_0_59_59 = e3
% 27.45/7.54 | (419) ~ (all_0_56_56 = e0)
% 27.45/7.54 |
% 27.45/7.54 | Equations (747) can reduce 419 to:
% 27.45/7.54 | (132) ~ (e1 = e0)
% 27.45/7.54 |
% 27.45/7.54 | Equations (412) can reduce 140 to:
% 27.45/7.54 | (846) ~ (all_0_57_57 = e3)
% 27.45/7.54 |
% 27.45/7.54 | Equations (412) can reduce 701 to:
% 27.45/7.54 | (223) ~ (e3 = e2)
% 27.45/7.54 |
% 27.45/7.54 +-Applying beta-rule and splitting (823), into two cases.
% 27.45/7.54 |-Branch one:
% 27.45/7.54 | (848) all_0_52_52 = e1
% 27.45/7.54 |
% 27.45/7.54 | Combining equations (827,848) yields a new equation:
% 27.45/7.54 | (560) e1 = e0
% 27.45/7.54 |
% 27.45/7.54 | Equations (560) can reduce 132 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (642) ~ (all_0_52_52 = e1)
% 27.45/7.54 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 27.45/7.54 |
% 27.45/7.54 +-Applying beta-rule and splitting (852), into two cases.
% 27.45/7.54 |-Branch one:
% 27.45/7.54 | (853) all_0_53_53 = e1
% 27.45/7.54 |
% 27.45/7.54 | Equations (853) can reduce 48 to:
% 27.45/7.54 | (588) ~ (all_0_48_48 = e1)
% 27.45/7.54 |
% 27.45/7.54 +-Applying beta-rule and splitting (314), into two cases.
% 27.45/7.54 |-Branch one:
% 27.45/7.54 | (559) all_0_48_48 = e0
% 27.45/7.54 |
% 27.45/7.54 | Equations (559) can reduce 121 to:
% 27.45/7.54 | (788) ~ (e3 = e0)
% 27.45/7.54 |
% 27.45/7.54 | Simplifying 788 yields:
% 27.45/7.54 | (66) ~ (e3 = e0)
% 27.45/7.54 |
% 27.45/7.54 +-Applying beta-rule and splitting (676), into two cases.
% 27.45/7.54 |-Branch one:
% 27.45/7.54 | (858) all_0_44_44 = e3
% 27.45/7.54 |
% 27.45/7.54 | Combining equations (858,370) yields a new equation:
% 27.45/7.54 | (437) e3 = e2
% 27.45/7.54 |
% 27.45/7.54 | Simplifying 437 yields:
% 27.45/7.54 | (414) e3 = e2
% 27.45/7.54 |
% 27.45/7.54 | Equations (414) can reduce 223 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (862) ~ (all_0_44_44 = e3)
% 27.45/7.54 | (863) all_0_52_52 = e3 | all_0_57_57 = e3
% 27.45/7.54 |
% 27.45/7.54 +-Applying beta-rule and splitting (863), into two cases.
% 27.45/7.54 |-Branch one:
% 27.45/7.54 | (864) all_0_52_52 = e3
% 27.45/7.54 |
% 27.45/7.54 | Combining equations (864,827) yields a new equation:
% 27.45/7.54 | (783) e3 = e0
% 27.45/7.54 |
% 27.45/7.54 | Simplifying 783 yields:
% 27.45/7.54 | (784) e3 = e0
% 27.45/7.54 |
% 27.45/7.54 | Equations (784) can reduce 66 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (826) ~ (all_0_52_52 = e3)
% 27.45/7.54 | (869) all_0_57_57 = e3
% 27.45/7.54 |
% 27.45/7.54 | Equations (869) can reduce 846 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (562) ~ (all_0_48_48 = e0)
% 27.45/7.54 | (552) all_0_48_48 = e1
% 27.45/7.54 |
% 27.45/7.54 | Equations (552) can reduce 588 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (874) ~ (all_0_53_53 = e1)
% 27.45/7.54 | (875) all_0_54_54 = e1
% 27.45/7.54 |
% 27.45/7.54 | Combining equations (875,817) yields a new equation:
% 27.45/7.54 | (526) e4 = e1
% 27.45/7.54 |
% 27.45/7.54 | Equations (526) can reduce 251 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.45/7.54 |
% 27.45/7.54 | Applying alpha-rule on (422) yields:
% 27.45/7.54 | (423) all_0_53_53 = e0
% 27.45/7.54 | (424) all_0_59_59 = e1
% 27.45/7.54 | (425) ~ (all_0_54_54 = e1)
% 27.45/7.54 |
% 27.45/7.54 | Equations (424) can reduce 750 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.45/7.54 |
% 27.45/7.54 | Applying alpha-rule on (428) yields:
% 27.45/7.54 | (423) all_0_53_53 = e0
% 27.45/7.54 | (424) all_0_59_59 = e1
% 27.45/7.54 | (431) ~ (all_0_58_58 = e0)
% 27.45/7.54 |
% 27.45/7.54 | Equations (424) can reduce 750 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (925) ~ (all_0_52_52 = e0)
% 27.45/7.54 | (926) all_0_52_52 = e3 | all_0_52_52 = e1
% 27.45/7.54 |
% 27.45/7.54 +-Applying beta-rule and splitting (926), into two cases.
% 27.45/7.54 |-Branch one:
% 27.45/7.54 | (864) all_0_52_52 = e3
% 27.45/7.54 |
% 27.45/7.54 | Equations (864) can reduce 826 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (826) ~ (all_0_52_52 = e3)
% 27.45/7.54 | (848) all_0_52_52 = e1
% 27.45/7.54 |
% 27.45/7.54 | Equations (848) can reduce 642 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (932) ~ (all_0_51_51 = e3)
% 27.45/7.54 | (764) all_0_56_56 = e3
% 27.45/7.54 |
% 27.45/7.54 | Combining equations (747,764) yields a new equation:
% 27.45/7.54 | (538) e3 = e1
% 27.45/7.54 |
% 27.45/7.54 | Equations (538) can reduce 136 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (936) ~ (all_0_54_54 = e4)
% 27.45/7.54 | (402) all_0_59_59 = e4
% 27.45/7.54 |
% 27.45/7.54 | Equations (402) can reduce 280 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (455) ~ (all_0_43_43 = e0)
% 27.45/7.54 | (940) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 27.45/7.54 |
% 27.45/7.54 +-Applying beta-rule and splitting (774), into two cases.
% 27.45/7.54 |-Branch one:
% 27.45/7.54 | (411) all_0_43_43 = e0
% 27.45/7.54 |
% 27.45/7.54 | Equations (411) can reduce 455 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (455) ~ (all_0_43_43 = e0)
% 27.45/7.54 | (944) all_0_43_43 = e4 | all_0_43_43 = e3
% 27.45/7.54 |
% 27.45/7.54 +-Applying beta-rule and splitting (940), into two cases.
% 27.45/7.54 |-Branch one:
% 27.45/7.54 | (315) all_0_47_47 = e0
% 27.45/7.54 |
% 27.45/7.54 | Combining equations (290,315) yields a new equation:
% 27.45/7.54 | (622) e2 = e0
% 27.45/7.54 |
% 27.45/7.54 | Simplifying 622 yields:
% 27.45/7.54 | (316) e2 = e0
% 27.45/7.54 |
% 27.45/7.54 | Equations (316) can reduce 57 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (318) ~ (all_0_47_47 = e0)
% 27.45/7.54 | (950) all_0_51_51 = e0 | all_0_56_56 = e0
% 27.45/7.54 |
% 27.45/7.54 +-Applying beta-rule and splitting (944), into two cases.
% 27.45/7.54 |-Branch one:
% 27.45/7.54 | (782) all_0_43_43 = e3
% 27.45/7.54 |
% 27.45/7.54 | Equations (782) can reduce 240 to:
% 27.45/7.54 | (952) ~ (all_0_51_51 = e3)
% 27.45/7.54 |
% 27.45/7.54 | Simplifying 952 yields:
% 27.45/7.54 | (932) ~ (all_0_51_51 = e3)
% 27.45/7.54 |
% 27.45/7.54 +-Applying beta-rule and splitting (950), into two cases.
% 27.45/7.54 |-Branch one:
% 27.45/7.54 | (954) all_0_51_51 = e0
% 27.45/7.54 |
% 27.45/7.54 | Equations (954) can reduce 932 to:
% 27.45/7.54 | (788) ~ (e3 = e0)
% 27.45/7.54 |
% 27.45/7.54 | Simplifying 788 yields:
% 27.45/7.54 | (66) ~ (e3 = e0)
% 27.45/7.54 |
% 27.45/7.54 +-Applying beta-rule and splitting (93), into two cases.
% 27.45/7.54 |-Branch one:
% 27.45/7.54 | (402) all_0_59_59 = e4
% 27.45/7.54 |
% 27.45/7.54 | Equations (402) can reduce 280 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (280) ~ (all_0_59_59 = e4)
% 27.45/7.54 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.45/7.54 |
% 27.45/7.54 +-Applying beta-rule and splitting (407), into two cases.
% 27.45/7.54 |-Branch one:
% 27.45/7.54 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.45/7.54 |
% 27.45/7.54 +-Applying beta-rule and splitting (408), into two cases.
% 27.45/7.54 |-Branch one:
% 27.45/7.54 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.45/7.54 |
% 27.45/7.54 +-Applying beta-rule and splitting (409), into two cases.
% 27.45/7.54 |-Branch one:
% 27.45/7.54 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.45/7.54 |
% 27.45/7.54 | Applying alpha-rule on (410) yields:
% 27.45/7.54 | (411) all_0_43_43 = e0
% 27.45/7.54 | (412) all_0_59_59 = e3
% 27.45/7.54 | (413) ~ (all_0_46_46 = e3)
% 27.45/7.54 |
% 27.45/7.54 | Combining equations (782,411) yields a new equation:
% 27.45/7.54 | (783) e3 = e0
% 27.45/7.54 |
% 27.45/7.54 | Simplifying 783 yields:
% 27.45/7.54 | (784) e3 = e0
% 27.45/7.54 |
% 27.45/7.54 | Equations (784) can reduce 66 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.45/7.54 |
% 27.45/7.54 | Applying alpha-rule on (416) yields:
% 27.45/7.54 | (411) all_0_43_43 = e0
% 27.45/7.54 | (412) all_0_59_59 = e3
% 27.45/7.54 | (419) ~ (all_0_56_56 = e0)
% 27.45/7.54 |
% 27.45/7.54 | Combining equations (782,411) yields a new equation:
% 27.45/7.54 | (783) e3 = e0
% 27.45/7.54 |
% 27.45/7.54 | Simplifying 783 yields:
% 27.45/7.54 | (784) e3 = e0
% 27.45/7.54 |
% 27.45/7.54 | Equations (784) can reduce 66 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.45/7.54 |
% 27.45/7.54 | Applying alpha-rule on (422) yields:
% 27.45/7.54 | (423) all_0_53_53 = e0
% 27.45/7.54 | (424) all_0_59_59 = e1
% 27.45/7.54 | (425) ~ (all_0_54_54 = e1)
% 27.45/7.54 |
% 27.45/7.54 | Equations (424) can reduce 750 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.45/7.54 |
% 27.45/7.54 | Applying alpha-rule on (428) yields:
% 27.45/7.54 | (423) all_0_53_53 = e0
% 27.45/7.54 | (424) all_0_59_59 = e1
% 27.45/7.54 | (431) ~ (all_0_58_58 = e0)
% 27.45/7.54 |
% 27.45/7.54 | Equations (424) can reduce 750 to:
% 27.45/7.54 | (270) $false
% 27.45/7.54 |
% 27.45/7.54 |-The branch is then unsatisfiable
% 27.45/7.54 |-Branch two:
% 27.45/7.54 | (987) ~ (all_0_51_51 = e0)
% 27.45/7.54 | (830) all_0_56_56 = e0
% 27.45/7.54 |
% 27.45/7.55 | Combining equations (747,830) yields a new equation:
% 27.45/7.55 | (571) e1 = e0
% 27.45/7.55 |
% 27.45/7.55 | Simplifying 571 yields:
% 27.45/7.55 | (560) e1 = e0
% 27.45/7.55 |
% 27.45/7.55 | Equations (560) can reduce 132 to:
% 27.45/7.55 | (270) $false
% 27.45/7.55 |
% 27.45/7.55 |-The branch is then unsatisfiable
% 27.45/7.55 |-Branch two:
% 27.45/7.55 | (786) ~ (all_0_43_43 = e3)
% 27.45/7.55 | (502) all_0_43_43 = e4
% 27.45/7.55 |
% 27.45/7.55 | Equations (502) can reduce 510 to:
% 27.45/7.55 | (270) $false
% 27.45/7.55 |
% 27.45/7.55 |-The branch is then unsatisfiable
% 27.45/7.55 |-Branch two:
% 27.45/7.55 | (995) ~ (all_0_56_56 = e1)
% 27.45/7.55 | (996) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (996), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (997) all_0_57_57 = e1
% 27.45/7.55 |
% 27.45/7.55 | Equations (997) can reduce 644 to:
% 27.45/7.55 | (270) $false
% 27.45/7.55 |
% 27.45/7.55 |-The branch is then unsatisfiable
% 27.45/7.55 |-Branch two:
% 27.45/7.55 | (644) ~ (all_0_57_57 = e1)
% 27.45/7.55 | (1000) all_0_58_58 = e1 | all_0_59_59 = e1
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (1000), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (1001) all_0_58_58 = e1
% 27.45/7.55 |
% 27.45/7.55 | Combining equations (1001,396) yields a new equation:
% 27.45/7.55 | (322) e2 = e1
% 27.45/7.55 |
% 27.45/7.55 | Equations (322) can reduce 141 to:
% 27.45/7.55 | (270) $false
% 27.45/7.55 |
% 27.45/7.55 |-The branch is then unsatisfiable
% 27.45/7.55 |-Branch two:
% 27.45/7.55 | (1004) ~ (all_0_58_58 = e1)
% 27.45/7.55 | (424) all_0_59_59 = e1
% 27.45/7.55 |
% 27.45/7.55 | Equations (424) can reduce 206 to:
% 27.45/7.55 | (106) ~ (all_0_46_46 = e1)
% 27.45/7.55 |
% 27.45/7.55 | Equations (424) can reduce 113 to:
% 27.45/7.55 | (543) ~ (all_0_49_49 = e1)
% 27.45/7.55 |
% 27.45/7.55 | Equations (424) can reduce 72 to:
% 27.45/7.55 | (425) ~ (all_0_54_54 = e1)
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (310), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (563) all_0_49_49 = e0
% 27.45/7.55 |
% 27.45/7.55 | Equations (563) can reduce 198 to:
% 27.45/7.55 | (1010) ~ (all_0_46_46 = e0)
% 27.45/7.55 |
% 27.45/7.55 | Equations (563) can reduce 4 to:
% 27.45/7.55 | (562) ~ (all_0_48_48 = e0)
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (314), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (559) all_0_48_48 = e0
% 27.45/7.55 |
% 27.45/7.55 | Equations (559) can reduce 562 to:
% 27.45/7.55 | (270) $false
% 27.45/7.55 |
% 27.45/7.55 |-The branch is then unsatisfiable
% 27.45/7.55 |-Branch two:
% 27.45/7.55 | (562) ~ (all_0_48_48 = e0)
% 27.45/7.55 | (552) all_0_48_48 = e1
% 27.45/7.55 |
% 27.45/7.55 | Equations (552) can reduce 65 to:
% 27.45/7.55 | (26) ~ (all_0_45_45 = e1)
% 27.45/7.55 |
% 27.45/7.55 | Equations (552) can reduce 48 to:
% 27.45/7.55 | (1016) ~ (all_0_53_53 = e1)
% 27.45/7.55 |
% 27.45/7.55 | Simplifying 1016 yields:
% 27.45/7.55 | (874) ~ (all_0_53_53 = e1)
% 27.45/7.55 |
% 27.45/7.55 | Equations (552) can reduce 121 to:
% 27.45/7.55 | (769) ~ (e3 = e1)
% 27.45/7.55 |
% 27.45/7.55 | Simplifying 769 yields:
% 27.45/7.55 | (136) ~ (e3 = e1)
% 27.45/7.55 |
% 27.45/7.55 | From (552) and (76) follows:
% 27.45/7.55 | (2127) op(e1, e1) = all_0_25_25
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (135), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (820) all_0_51_51 = e1
% 27.45/7.55 |
% 27.45/7.55 | Combining equations (820,1847) yields a new equation:
% 27.45/7.55 | (2129) all_0_21_21 = e1
% 27.45/7.55 |
% 27.45/7.55 | Equations (820) can reduce 240 to:
% 27.45/7.55 | (249) ~ (all_0_43_43 = e1)
% 27.45/7.55 |
% 27.45/7.55 | Equations (820) can reduce 50 to:
% 27.45/7.55 | (2131) ~ (all_0_54_54 = e1)
% 27.45/7.55 |
% 27.45/7.55 | Simplifying 2131 yields:
% 27.45/7.55 | (425) ~ (all_0_54_54 = e1)
% 27.45/7.55 |
% 27.45/7.55 | Equations (820) can reduce 697 to:
% 27.45/7.55 | (1021) ~ (e4 = e1)
% 27.45/7.55 |
% 27.45/7.55 | Simplifying 1021 yields:
% 27.45/7.55 | (251) ~ (e4 = e1)
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (93), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (402) all_0_59_59 = e4
% 27.45/7.55 |
% 27.45/7.55 | Combining equations (402,424) yields a new equation:
% 27.45/7.55 | (525) e4 = e1
% 27.45/7.55 |
% 27.45/7.55 | Simplifying 525 yields:
% 27.45/7.55 | (526) e4 = e1
% 27.45/7.55 |
% 27.45/7.55 | Equations (526) can reduce 251 to:
% 27.45/7.55 | (270) $false
% 27.45/7.55 |
% 27.45/7.55 |-The branch is then unsatisfiable
% 27.45/7.55 |-Branch two:
% 27.45/7.55 | (280) ~ (all_0_59_59 = e4)
% 27.45/7.55 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (407), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (408), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (409), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.45/7.55 |
% 27.45/7.55 | Applying alpha-rule on (410) yields:
% 27.45/7.55 | (411) all_0_43_43 = e0
% 27.45/7.55 | (412) all_0_59_59 = e3
% 27.45/7.55 | (413) ~ (all_0_46_46 = e3)
% 27.45/7.55 |
% 27.45/7.55 | Combining equations (412,424) yields a new equation:
% 27.45/7.55 | (537) e3 = e1
% 27.45/7.55 |
% 27.45/7.55 | Simplifying 537 yields:
% 27.45/7.55 | (538) e3 = e1
% 27.45/7.55 |
% 27.45/7.55 | Equations (538) can reduce 136 to:
% 27.45/7.55 | (270) $false
% 27.45/7.55 |
% 27.45/7.55 |-The branch is then unsatisfiable
% 27.45/7.55 |-Branch two:
% 27.45/7.55 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.45/7.55 |
% 27.45/7.55 | Applying alpha-rule on (416) yields:
% 27.45/7.55 | (411) all_0_43_43 = e0
% 27.45/7.55 | (412) all_0_59_59 = e3
% 27.45/7.55 | (419) ~ (all_0_56_56 = e0)
% 27.45/7.55 |
% 27.45/7.55 | Combining equations (412,424) yields a new equation:
% 27.45/7.55 | (537) e3 = e1
% 27.45/7.55 |
% 27.45/7.55 | Simplifying 537 yields:
% 27.45/7.55 | (538) e3 = e1
% 27.45/7.55 |
% 27.45/7.55 | Equations (538) can reduce 136 to:
% 27.45/7.55 | (270) $false
% 27.45/7.55 |
% 27.45/7.55 |-The branch is then unsatisfiable
% 27.45/7.55 |-Branch two:
% 27.45/7.55 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.45/7.55 |
% 27.45/7.55 | Applying alpha-rule on (422) yields:
% 27.45/7.55 | (423) all_0_53_53 = e0
% 27.45/7.55 | (424) all_0_59_59 = e1
% 27.45/7.55 | (425) ~ (all_0_54_54 = e1)
% 27.45/7.55 |
% 27.45/7.55 | Equations (423) can reduce 128 to:
% 27.45/7.55 | (488) ~ (all_0_45_45 = e0)
% 27.45/7.55 |
% 27.45/7.55 | Equations (423) can reduce 213 to:
% 27.45/7.55 | (925) ~ (all_0_52_52 = e0)
% 27.45/7.55 |
% 27.45/7.55 | Equations (423) can reduce 356 to:
% 27.45/7.55 | (788) ~ (e3 = e0)
% 27.45/7.55 |
% 27.45/7.55 | Simplifying 788 yields:
% 27.45/7.55 | (66) ~ (e3 = e0)
% 27.45/7.55 |
% 27.45/7.55 | Equations (423) can reduce 259 to:
% 27.45/7.55 | (566) ~ (e2 = e0)
% 27.45/7.55 |
% 27.45/7.55 | Simplifying 566 yields:
% 27.45/7.55 | (57) ~ (e2 = e0)
% 27.45/7.55 |
% 27.45/7.55 | From (423) and (227) follows:
% 27.45/7.55 | (2167) op(e1, e1) = e0
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (116), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (411) all_0_43_43 = e0
% 27.45/7.55 |
% 27.45/7.55 | Equations (411) can reduce 103 to:
% 27.45/7.55 | (1057) ~ (all_0_46_46 = e0)
% 27.45/7.55 |
% 27.45/7.55 | Simplifying 1057 yields:
% 27.45/7.55 | (1010) ~ (all_0_46_46 = e0)
% 27.45/7.55 |
% 27.45/7.55 | Equations (411) can reduce 292 to:
% 27.45/7.55 | (566) ~ (e2 = e0)
% 27.45/7.55 |
% 27.45/7.55 | Simplifying 566 yields:
% 27.45/7.55 | (57) ~ (e2 = e0)
% 27.45/7.55 |
% 27.45/7.55 | Equations (411) can reduce 249 to:
% 27.45/7.55 | (568) ~ (e1 = e0)
% 27.45/7.55 |
% 27.45/7.55 | Simplifying 568 yields:
% 27.45/7.55 | (132) ~ (e1 = e0)
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (22), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (782) all_0_43_43 = e3
% 27.45/7.55 |
% 27.45/7.55 | Combining equations (411,782) yields a new equation:
% 27.45/7.55 | (784) e3 = e0
% 27.45/7.55 |
% 27.45/7.55 | Equations (784) can reduce 66 to:
% 27.45/7.55 | (270) $false
% 27.45/7.55 |
% 27.45/7.55 |-The branch is then unsatisfiable
% 27.45/7.55 |-Branch two:
% 27.45/7.55 | (786) ~ (all_0_43_43 = e3)
% 27.45/7.55 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 27.45/7.55 |
% 27.45/7.55 | Equations (411) can reduce 786 to:
% 27.45/7.55 | (788) ~ (e3 = e0)
% 27.45/7.55 |
% 27.45/7.55 | Simplifying 788 yields:
% 27.45/7.55 | (66) ~ (e3 = e0)
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (787), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (858) all_0_44_44 = e3
% 27.45/7.55 |
% 27.45/7.55 | Combining equations (370,858) yields a new equation:
% 27.45/7.55 | (414) e3 = e2
% 27.45/7.55 |
% 27.45/7.55 | Equations (414) can reduce 223 to:
% 27.45/7.55 | (270) $false
% 27.45/7.55 |
% 27.45/7.55 |-The branch is then unsatisfiable
% 27.45/7.55 |-Branch two:
% 27.45/7.55 | (862) ~ (all_0_44_44 = e3)
% 27.45/7.55 | (1070) all_0_45_45 = e3 | all_0_46_46 = e3
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (178), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (751) all_0_39_39 = e3
% 27.45/7.55 |
% 27.45/7.55 | Combining equations (522,751) yields a new equation:
% 27.45/7.55 | (660) e4 = e3
% 27.45/7.55 |
% 27.45/7.55 | Simplifying 660 yields:
% 27.45/7.55 | (359) e4 = e3
% 27.45/7.55 |
% 27.45/7.55 | Equations (359) can reduce 34 to:
% 27.45/7.55 | (270) $false
% 27.45/7.55 |
% 27.45/7.55 |-The branch is then unsatisfiable
% 27.45/7.55 |-Branch two:
% 27.45/7.55 | (755) ~ (all_0_39_39 = e3)
% 27.45/7.55 | (756) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (756), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (782) all_0_43_43 = e3
% 27.45/7.55 |
% 27.45/7.55 | Combining equations (411,782) yields a new equation:
% 27.45/7.55 | (784) e3 = e0
% 27.45/7.55 |
% 27.45/7.55 | Equations (784) can reduce 66 to:
% 27.45/7.55 | (270) $false
% 27.45/7.55 |
% 27.45/7.55 |-The branch is then unsatisfiable
% 27.45/7.55 |-Branch two:
% 27.45/7.55 | (786) ~ (all_0_43_43 = e3)
% 27.45/7.55 | (799) all_0_51_51 = e3 | all_0_56_56 = e3
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (799), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (824) all_0_51_51 = e3
% 27.45/7.55 |
% 27.45/7.55 | Combining equations (824,820) yields a new equation:
% 27.45/7.55 | (537) e3 = e1
% 27.45/7.55 |
% 27.45/7.55 | Simplifying 537 yields:
% 27.45/7.55 | (538) e3 = e1
% 27.45/7.55 |
% 27.45/7.55 | Equations (538) can reduce 136 to:
% 27.45/7.55 | (270) $false
% 27.45/7.55 |
% 27.45/7.55 |-The branch is then unsatisfiable
% 27.45/7.55 |-Branch two:
% 27.45/7.55 | (932) ~ (all_0_51_51 = e3)
% 27.45/7.55 | (764) all_0_56_56 = e3
% 27.45/7.55 |
% 27.45/7.55 | Equations (764) can reduce 274 to:
% 27.45/7.55 | (719) ~ (e4 = e3)
% 27.45/7.55 |
% 27.45/7.55 | Simplifying 719 yields:
% 27.45/7.55 | (34) ~ (e4 = e3)
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (105), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (374) all_0_45_45 = e2
% 27.45/7.55 |
% 27.45/7.55 | Equations (374) can reduce 434 to:
% 27.45/7.55 | (270) $false
% 27.45/7.55 |
% 27.45/7.55 |-The branch is then unsatisfiable
% 27.45/7.55 |-Branch two:
% 27.45/7.55 | (434) ~ (all_0_45_45 = e2)
% 27.45/7.55 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (1070), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (505) all_0_45_45 = e3
% 27.45/7.55 |
% 27.45/7.55 | Equations (505) can reduce 354 to:
% 27.45/7.55 | (270) $false
% 27.45/7.55 |
% 27.45/7.55 |-The branch is then unsatisfiable
% 27.45/7.55 |-Branch two:
% 27.45/7.55 | (354) ~ (all_0_45_45 = e3)
% 27.45/7.55 | (1091) all_0_46_46 = e3
% 27.45/7.55 |
% 27.45/7.55 | Equations (1091) can reduce 215 to:
% 27.45/7.55 | (1092) ~ (all_0_54_54 = e3)
% 27.45/7.55 |
% 27.45/7.55 | Simplifying 1092 yields:
% 27.45/7.55 | (1093) ~ (all_0_54_54 = e3)
% 27.45/7.55 |
% 27.45/7.55 | Equations (1091) can reduce 106 to:
% 27.45/7.55 | (136) ~ (e3 = e1)
% 27.45/7.55 |
% 27.45/7.55 | Equations (1091) can reduce 1010 to:
% 27.45/7.55 | (66) ~ (e3 = e0)
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (511), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (363) all_0_45_45 = e4
% 27.45/7.55 |
% 27.45/7.55 | Equations (363) can reduce 434 to:
% 27.45/7.55 | (231) ~ (e4 = e2)
% 27.45/7.55 |
% 27.45/7.55 | Equations (363) can reduce 26 to:
% 27.45/7.55 | (251) ~ (e4 = e1)
% 27.45/7.55 |
% 27.45/7.55 | From (363) and (142) follows:
% 27.45/7.55 | (2221) op(e1, e4) = all_0_23_23
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (179), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (512) all_0_42_42 = e4
% 27.45/7.55 |
% 27.45/7.55 | Combining equations (512,698) yields a new equation:
% 27.45/7.55 | (268) e4 = e2
% 27.45/7.55 |
% 27.45/7.55 | Simplifying 268 yields:
% 27.45/7.55 | (269) e4 = e2
% 27.45/7.55 |
% 27.45/7.55 | Equations (269) can reduce 231 to:
% 27.45/7.55 | (270) $false
% 27.45/7.55 |
% 27.45/7.55 |-The branch is then unsatisfiable
% 27.45/7.55 |-Branch two:
% 27.45/7.55 | (520) ~ (all_0_42_42 = e4)
% 27.45/7.55 | (521) all_0_46_46 = e4 | all_0_54_54 = e4 | all_0_59_59 = e4
% 27.45/7.55 |
% 27.45/7.55 | Equations (698) can reduce 520 to:
% 27.45/7.55 | (377) ~ (e4 = e2)
% 27.45/7.55 |
% 27.45/7.55 | Simplifying 377 yields:
% 27.45/7.55 | (231) ~ (e4 = e2)
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (21), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (824) all_0_51_51 = e3
% 27.45/7.55 |
% 27.45/7.55 | Combining equations (824,820) yields a new equation:
% 27.45/7.55 | (537) e3 = e1
% 27.45/7.55 |
% 27.45/7.55 | Simplifying 537 yields:
% 27.45/7.55 | (538) e3 = e1
% 27.45/7.55 |
% 27.45/7.55 | Equations (538) can reduce 136 to:
% 27.45/7.55 | (270) $false
% 27.45/7.55 |
% 27.45/7.55 |-The branch is then unsatisfiable
% 27.45/7.55 |-Branch two:
% 27.45/7.55 | (932) ~ (all_0_51_51 = e3)
% 27.45/7.55 | (1101) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (1101), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (864) all_0_52_52 = e3
% 27.45/7.55 |
% 27.45/7.55 | Combining equations (864,1848) yields a new equation:
% 27.45/7.55 | (2237) all_0_28_28 = e3
% 27.45/7.55 |
% 27.45/7.55 | Equations (864) can reduce 235 to:
% 27.45/7.55 | (2238) ~ (all_0_57_57 = e3)
% 27.45/7.55 |
% 27.45/7.55 | Simplifying 2238 yields:
% 27.45/7.55 | (846) ~ (all_0_57_57 = e3)
% 27.45/7.55 |
% 27.45/7.55 | Equations (864) can reduce 257 to:
% 27.45/7.55 | (223) ~ (e3 = e2)
% 27.45/7.55 |
% 27.45/7.55 | Equations (864) can reduce 925 to:
% 27.45/7.55 | (66) ~ (e3 = e0)
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (176), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (830) all_0_56_56 = e0
% 27.45/7.55 |
% 27.45/7.55 | Combining equations (830,764) yields a new equation:
% 27.45/7.55 | (784) e3 = e0
% 27.45/7.55 |
% 27.45/7.55 | Equations (784) can reduce 66 to:
% 27.45/7.55 | (270) $false
% 27.45/7.55 |
% 27.45/7.55 |-The branch is then unsatisfiable
% 27.45/7.55 |-Branch two:
% 27.45/7.55 | (419) ~ (all_0_56_56 = e0)
% 27.45/7.55 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 27.45/7.55 |
% 27.45/7.55 +-Applying beta-rule and splitting (189), into two cases.
% 27.45/7.55 |-Branch one:
% 27.45/7.55 | (267) all_0_50_50 = e4
% 27.45/7.55 |
% 27.45/7.55 | Combining equations (253,267) yields a new equation:
% 27.45/7.55 | (269) e4 = e2
% 27.45/7.55 |
% 27.45/7.55 | Equations (269) can reduce 231 to:
% 27.45/7.55 | (270) $false
% 27.45/7.55 |
% 27.45/7.56 |-The branch is then unsatisfiable
% 27.45/7.56 |-Branch two:
% 27.45/7.56 | (271) ~ (all_0_50_50 = e4)
% 27.45/7.56 | (1466) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 27.45/7.56 |
% 27.45/7.56 +-Applying beta-rule and splitting (1466), into two cases.
% 27.45/7.56 |-Branch one:
% 27.45/7.56 | (1467) all_0_51_51 = e4
% 27.45/7.56 |
% 27.45/7.56 | Combining equations (1467,820) yields a new equation:
% 27.45/7.56 | (525) e4 = e1
% 27.45/7.56 |
% 27.45/7.56 | Simplifying 525 yields:
% 27.45/7.56 | (526) e4 = e1
% 27.45/7.56 |
% 27.45/7.56 | Equations (526) can reduce 251 to:
% 27.45/7.56 | (270) $false
% 27.45/7.56 |
% 27.45/7.56 |-The branch is then unsatisfiable
% 27.45/7.56 |-Branch two:
% 27.45/7.56 | (697) ~ (all_0_51_51 = e4)
% 27.45/7.56 | (1470) all_0_53_53 = e4 | all_0_54_54 = e4
% 27.45/7.56 |
% 27.45/7.56 +-Applying beta-rule and splitting (834), into two cases.
% 27.45/7.56 |-Branch one:
% 27.45/7.56 | (2258) all_0_57_57 = e0
% 27.45/7.56 |
% 27.45/7.56 | Equations (2258) can reduce 143 to:
% 27.45/7.56 | (456) ~ (e4 = e0)
% 27.45/7.56 |
% 27.45/7.56 | Simplifying 456 yields:
% 27.45/7.56 | (6) ~ (e4 = e0)
% 27.45/7.56 |
% 27.45/7.56 | Equations (2258) can reduce 846 to:
% 27.45/7.56 | (788) ~ (e3 = e0)
% 27.45/7.56 |
% 27.45/7.56 | Simplifying 788 yields:
% 27.45/7.56 | (66) ~ (e3 = e0)
% 27.45/7.56 |
% 27.45/7.56 | Equations (2258) can reduce 335 to:
% 27.45/7.56 | (566) ~ (e2 = e0)
% 27.45/7.56 |
% 27.45/7.56 | Simplifying 566 yields:
% 27.45/7.56 | (57) ~ (e2 = e0)
% 27.45/7.56 |
% 27.45/7.56 +-Applying beta-rule and splitting (1470), into two cases.
% 27.45/7.56 |-Branch one:
% 27.45/7.56 | (367) all_0_53_53 = e4
% 27.45/7.56 |
% 27.45/7.56 | Combining equations (423,367) yields a new equation:
% 27.45/7.56 | (479) e4 = e0
% 27.45/7.56 |
% 27.45/7.56 | Equations (479) can reduce 6 to:
% 27.45/7.56 | (270) $false
% 27.45/7.56 |
% 27.45/7.56 |-The branch is then unsatisfiable
% 27.45/7.56 |-Branch two:
% 27.45/7.56 | (599) ~ (all_0_53_53 = e4)
% 27.45/7.56 | (817) all_0_54_54 = e4
% 27.45/7.56 |
% 27.45/7.56 | Equations (817) can reduce 425 to:
% 27.45/7.56 | (251) ~ (e4 = e1)
% 27.45/7.56 |
% 27.45/7.56 | From (817) and (29) follows:
% 27.45/7.56 | (2271) op(e1, e4) = all_0_37_37
% 27.45/7.56 |
% 27.45/7.56 | Instantiating formula (201) with e1, e4, all_0_23_23, e2 and discharging atoms op(e1, e4) = all_0_23_23, op(e1, e4) = e2, yields:
% 27.45/7.56 | (2272) all_0_23_23 = e2
% 27.45/7.56 |
% 27.45/7.56 | Instantiating formula (201) with e1, e4, all_0_37_37, all_0_23_23 and discharging atoms op(e1, e4) = all_0_23_23, op(e1, e4) = all_0_37_37, yields:
% 27.45/7.56 | (2273) all_0_23_23 = all_0_37_37
% 27.45/7.56 |
% 27.45/7.56 | Instantiating formula (201) with e1, e1, e0, all_0_25_25 and discharging atoms op(e1, e1) = all_0_25_25, op(e1, e1) = e0, yields:
% 27.45/7.56 | (2274) all_0_25_25 = e0
% 27.45/7.56 |
% 27.45/7.56 | Combining equations (2272,2273) yields a new equation:
% 27.45/7.56 | (2275) all_0_37_37 = e2
% 27.45/7.56 |
% 27.45/7.56 | Combining equations (2275,2273) yields a new equation:
% 27.45/7.56 | (2272) all_0_23_23 = e2
% 27.45/7.56 |
% 27.45/7.56 +-Applying beta-rule and splitting (14), into two cases.
% 27.45/7.56 |-Branch one:
% 27.45/7.56 | (2277) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1))
% 27.45/7.56 |
% 27.45/7.56 +-Applying beta-rule and splitting (2277), into two cases.
% 27.45/7.56 |-Branch one:
% 27.45/7.56 | (2278) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1))
% 27.45/7.56 |
% 27.45/7.56 +-Applying beta-rule and splitting (2278), into two cases.
% 27.45/7.56 |-Branch one:
% 27.45/7.56 | (2279) all_0_21_21 = e4 & ~ (all_0_22_22 = e1)
% 27.45/7.56 |
% 27.45/7.56 | Applying alpha-rule on (2279) yields:
% 27.45/7.56 | (2280) all_0_21_21 = e4
% 27.45/7.56 | (2281) ~ (all_0_22_22 = e1)
% 27.45/7.56 |
% 27.45/7.56 | Combining equations (2280,2129) yields a new equation:
% 27.45/7.56 | (525) e4 = e1
% 27.45/7.56 |
% 27.45/7.56 | Simplifying 525 yields:
% 27.45/7.56 | (526) e4 = e1
% 27.45/7.56 |
% 27.45/7.56 | Equations (526) can reduce 251 to:
% 27.45/7.56 | (270) $false
% 27.45/7.56 |
% 27.45/7.56 |-The branch is then unsatisfiable
% 27.45/7.56 |-Branch two:
% 27.45/7.56 | (2285) all_0_23_23 = e3 & ~ (all_0_24_24 = e1)
% 27.45/7.56 |
% 27.45/7.56 | Applying alpha-rule on (2285) yields:
% 27.45/7.56 | (2286) all_0_23_23 = e3
% 27.45/7.56 | (2287) ~ (all_0_24_24 = e1)
% 27.45/7.56 |
% 27.45/7.56 | Combining equations (2286,2272) yields a new equation:
% 27.45/7.56 | (437) e3 = e2
% 27.45/7.56 |
% 27.45/7.56 | Simplifying 437 yields:
% 27.45/7.56 | (414) e3 = e2
% 27.45/7.56 |
% 27.45/7.56 | Equations (414) can reduce 223 to:
% 27.45/7.56 | (270) $false
% 27.45/7.56 |
% 27.45/7.56 |-The branch is then unsatisfiable
% 27.45/7.56 |-Branch two:
% 27.45/7.56 | (2291) all_0_25_25 = e2 & ~ (all_0_26_26 = e1)
% 27.45/7.56 |
% 27.45/7.56 | Applying alpha-rule on (2291) yields:
% 27.45/7.56 | (2292) all_0_25_25 = e2
% 27.45/7.56 | (2293) ~ (all_0_26_26 = e1)
% 27.45/7.56 |
% 27.45/7.56 | Combining equations (2274,2292) yields a new equation:
% 27.45/7.56 | (316) e2 = e0
% 27.45/7.56 |
% 27.45/7.56 | Equations (316) can reduce 57 to:
% 27.45/7.56 | (270) $false
% 27.45/7.56 |
% 27.45/7.56 |-The branch is then unsatisfiable
% 27.45/7.56 |-Branch two:
% 27.45/7.56 | (2296) all_0_28_28 = e0 & ~ (all_0_29_29 = e1)
% 27.45/7.56 |
% 27.45/7.56 | Applying alpha-rule on (2296) yields:
% 27.45/7.56 | (2297) all_0_28_28 = e0
% 27.45/7.56 | (2298) ~ (all_0_29_29 = e1)
% 27.45/7.56 |
% 27.45/7.56 | Combining equations (2297,2237) yields a new equation:
% 27.45/7.56 | (784) e3 = e0
% 27.45/7.56 |
% 27.45/7.56 | Equations (784) can reduce 66 to:
% 27.45/7.56 | (270) $false
% 27.45/7.56 |
% 27.45/7.56 |-The branch is then unsatisfiable
% 27.45/7.56 |-Branch two:
% 27.45/7.56 | (2301) ~ (all_0_57_57 = e0)
% 27.45/7.56 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 27.45/7.56 |
% 27.45/7.56 +-Applying beta-rule and splitting (2302), into two cases.
% 27.45/7.56 |-Branch one:
% 27.45/7.56 | (585) all_0_58_58 = e0
% 27.45/7.56 |
% 27.45/7.56 | Combining equations (396,585) yields a new equation:
% 27.45/7.56 | (622) e2 = e0
% 27.45/7.56 |
% 27.45/7.56 | Simplifying 622 yields:
% 27.45/7.56 | (316) e2 = e0
% 27.45/7.56 |
% 27.45/7.56 | Equations (316) can reduce 57 to:
% 27.45/7.56 | (270) $false
% 27.45/7.56 |
% 27.45/7.56 |-The branch is then unsatisfiable
% 27.45/7.56 |-Branch two:
% 27.45/7.56 | (431) ~ (all_0_58_58 = e0)
% 27.45/7.56 | (2308) all_0_59_59 = e0
% 27.45/7.56 |
% 27.45/7.56 | Combining equations (2308,424) yields a new equation:
% 27.45/7.56 | (560) e1 = e0
% 27.45/7.56 |
% 27.45/7.56 | Equations (560) can reduce 132 to:
% 27.45/7.56 | (270) $false
% 27.45/7.56 |
% 27.45/7.56 |-The branch is then unsatisfiable
% 27.45/7.56 |-Branch two:
% 27.45/7.56 | (826) ~ (all_0_52_52 = e3)
% 27.45/7.56 | (1107) all_0_53_53 = e3 | all_0_54_54 = e3
% 27.45/7.56 |
% 27.45/7.56 +-Applying beta-rule and splitting (176), into two cases.
% 27.45/7.56 |-Branch one:
% 27.45/7.56 | (830) all_0_56_56 = e0
% 27.45/7.56 |
% 27.45/7.56 | Combining equations (830,764) yields a new equation:
% 27.45/7.56 | (784) e3 = e0
% 27.45/7.56 |
% 27.45/7.56 | Equations (784) can reduce 66 to:
% 27.45/7.56 | (270) $false
% 27.45/7.56 |
% 27.45/7.56 |-The branch is then unsatisfiable
% 27.45/7.56 |-Branch two:
% 27.45/7.56 | (419) ~ (all_0_56_56 = e0)
% 27.45/7.56 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 27.45/7.56 |
% 27.45/7.56 | Equations (764) can reduce 419 to:
% 27.45/7.56 | (66) ~ (e3 = e0)
% 27.45/7.56 |
% 27.45/7.56 +-Applying beta-rule and splitting (1107), into two cases.
% 27.45/7.56 |-Branch one:
% 27.45/7.56 | (1114) all_0_53_53 = e3
% 27.45/7.56 |
% 27.45/7.56 | Combining equations (1114,423) yields a new equation:
% 27.45/7.56 | (783) e3 = e0
% 27.45/7.56 |
% 27.45/7.56 | Simplifying 783 yields:
% 27.45/7.56 | (784) e3 = e0
% 27.45/7.56 |
% 27.45/7.56 | Equations (784) can reduce 66 to:
% 27.45/7.56 | (270) $false
% 27.45/7.56 |
% 27.45/7.56 |-The branch is then unsatisfiable
% 27.45/7.56 |-Branch two:
% 27.45/7.56 | (356) ~ (all_0_53_53 = e3)
% 27.45/7.56 | (1119) all_0_54_54 = e3
% 27.45/7.56 |
% 27.45/7.56 | Equations (1119) can reduce 1093 to:
% 27.45/7.56 | (270) $false
% 27.45/7.56 |
% 27.45/7.56 |-The branch is then unsatisfiable
% 27.45/7.56 |-Branch two:
% 27.45/7.56 | (352) ~ (all_0_45_45 = e4)
% 27.45/7.56 | (517) all_0_46_46 = e4
% 27.45/7.56 |
% 27.45/7.56 | Combining equations (1091,517) yields a new equation:
% 27.45/7.56 | (359) e4 = e3
% 27.45/7.56 |
% 27.45/7.56 | Equations (359) can reduce 34 to:
% 27.45/7.56 | (270) $false
% 27.45/7.56 |
% 27.45/7.56 |-The branch is then unsatisfiable
% 27.45/7.56 |-Branch two:
% 27.45/7.56 | (455) ~ (all_0_43_43 = e0)
% 27.45/7.56 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 27.45/7.56 |
% 27.45/7.56 +-Applying beta-rule and splitting (1122), into two cases.
% 27.45/7.56 |-Branch one:
% 27.45/7.56 | (621) all_0_44_44 = e0
% 27.45/7.56 |
% 27.45/7.56 | Combining equations (370,621) yields a new equation:
% 27.45/7.56 | (622) e2 = e0
% 27.45/7.56 |
% 27.45/7.56 | Simplifying 622 yields:
% 27.45/7.56 | (316) e2 = e0
% 27.45/7.56 |
% 27.45/7.56 | Equations (316) can reduce 57 to:
% 27.45/7.56 | (270) $false
% 27.45/7.56 |
% 27.45/7.56 |-The branch is then unsatisfiable
% 27.45/7.56 |-Branch two:
% 27.45/7.56 | (625) ~ (all_0_44_44 = e0)
% 27.45/7.56 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 27.45/7.56 |
% 27.45/7.56 +-Applying beta-rule and splitting (1128), into two cases.
% 27.45/7.56 |-Branch one:
% 27.45/7.56 | (454) all_0_45_45 = e0
% 27.45/7.56 |
% 27.45/7.56 | Equations (454) can reduce 488 to:
% 27.45/7.56 | (270) $false
% 27.45/7.56 |
% 27.45/7.56 |-The branch is then unsatisfiable
% 27.45/7.56 |-Branch two:
% 27.45/7.56 | (488) ~ (all_0_45_45 = e0)
% 27.45/7.56 | (1132) all_0_46_46 = e0
% 27.45/7.56 |
% 27.45/7.56 | Equations (1132) can reduce 1010 to:
% 27.45/7.56 | (270) $false
% 27.45/7.56 |
% 27.45/7.56 |-The branch is then unsatisfiable
% 27.45/7.56 |-Branch two:
% 27.45/7.56 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.45/7.56 |
% 27.45/7.56 | Applying alpha-rule on (428) yields:
% 27.45/7.56 | (423) all_0_53_53 = e0
% 27.45/7.56 | (424) all_0_59_59 = e1
% 27.45/7.56 | (431) ~ (all_0_58_58 = e0)
% 27.45/7.56 |
% 27.45/7.56 | Equations (423) can reduce 128 to:
% 27.45/7.56 | (488) ~ (all_0_45_45 = e0)
% 27.45/7.56 |
% 27.45/7.56 | Equations (423) can reduce 213 to:
% 27.45/7.56 | (925) ~ (all_0_52_52 = e0)
% 27.45/7.56 |
% 27.45/7.56 | Equations (423) can reduce 356 to:
% 27.45/7.56 | (788) ~ (e3 = e0)
% 27.45/7.56 |
% 27.45/7.56 | Simplifying 788 yields:
% 27.45/7.56 | (66) ~ (e3 = e0)
% 27.45/7.56 |
% 27.45/7.56 | Equations (396) can reduce 431 to:
% 27.45/7.56 | (57) ~ (e2 = e0)
% 27.45/7.56 |
% 27.45/7.56 | From (423) and (227) follows:
% 27.45/7.56 | (2167) op(e1, e1) = e0
% 27.45/7.56 |
% 27.45/7.56 +-Applying beta-rule and splitting (116), into two cases.
% 27.45/7.56 |-Branch one:
% 27.45/7.56 | (411) all_0_43_43 = e0
% 27.45/7.56 |
% 27.45/7.56 | Equations (411) can reduce 103 to:
% 27.45/7.56 | (1057) ~ (all_0_46_46 = e0)
% 27.45/7.56 |
% 27.45/7.56 | Simplifying 1057 yields:
% 27.45/7.56 | (1010) ~ (all_0_46_46 = e0)
% 27.45/7.56 |
% 27.45/7.56 | Equations (411) can reduce 292 to:
% 27.45/7.56 | (566) ~ (e2 = e0)
% 27.45/7.56 |
% 27.45/7.56 | Simplifying 566 yields:
% 27.45/7.56 | (57) ~ (e2 = e0)
% 27.45/7.56 |
% 27.45/7.56 | Equations (411) can reduce 249 to:
% 27.45/7.56 | (568) ~ (e1 = e0)
% 27.45/7.56 |
% 27.45/7.56 | Simplifying 568 yields:
% 27.45/7.56 | (132) ~ (e1 = e0)
% 27.45/7.56 |
% 27.45/7.56 +-Applying beta-rule and splitting (22), into two cases.
% 27.45/7.56 |-Branch one:
% 27.45/7.56 | (782) all_0_43_43 = e3
% 27.45/7.56 |
% 27.45/7.56 | Combining equations (411,782) yields a new equation:
% 27.45/7.56 | (784) e3 = e0
% 27.45/7.56 |
% 27.45/7.56 | Equations (784) can reduce 66 to:
% 27.45/7.56 | (270) $false
% 27.45/7.56 |
% 27.45/7.56 |-The branch is then unsatisfiable
% 27.45/7.56 |-Branch two:
% 27.45/7.56 | (786) ~ (all_0_43_43 = e3)
% 27.45/7.56 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 27.45/7.56 |
% 27.45/7.56 | Equations (411) can reduce 786 to:
% 27.45/7.56 | (788) ~ (e3 = e0)
% 27.45/7.56 |
% 27.45/7.56 | Simplifying 788 yields:
% 27.45/7.56 | (66) ~ (e3 = e0)
% 27.45/7.56 |
% 27.45/7.56 +-Applying beta-rule and splitting (787), into two cases.
% 27.45/7.56 |-Branch one:
% 27.45/7.56 | (858) all_0_44_44 = e3
% 27.45/7.56 |
% 27.45/7.57 | Combining equations (370,858) yields a new equation:
% 27.45/7.57 | (414) e3 = e2
% 27.45/7.57 |
% 27.45/7.57 | Equations (414) can reduce 223 to:
% 27.45/7.57 | (270) $false
% 27.45/7.57 |
% 27.45/7.57 |-The branch is then unsatisfiable
% 27.45/7.57 |-Branch two:
% 27.45/7.57 | (862) ~ (all_0_44_44 = e3)
% 27.45/7.57 | (1070) all_0_45_45 = e3 | all_0_46_46 = e3
% 27.45/7.57 |
% 27.45/7.57 +-Applying beta-rule and splitting (178), into two cases.
% 27.45/7.57 |-Branch one:
% 27.45/7.57 | (751) all_0_39_39 = e3
% 27.45/7.57 |
% 27.45/7.57 | Combining equations (522,751) yields a new equation:
% 27.45/7.57 | (660) e4 = e3
% 27.45/7.57 |
% 27.45/7.57 | Simplifying 660 yields:
% 27.45/7.57 | (359) e4 = e3
% 27.45/7.57 |
% 27.45/7.57 | Equations (359) can reduce 34 to:
% 27.45/7.57 | (270) $false
% 27.45/7.57 |
% 27.45/7.57 |-The branch is then unsatisfiable
% 27.45/7.57 |-Branch two:
% 27.45/7.57 | (755) ~ (all_0_39_39 = e3)
% 27.45/7.57 | (756) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 27.45/7.57 |
% 27.45/7.57 +-Applying beta-rule and splitting (756), into two cases.
% 27.45/7.57 |-Branch one:
% 27.45/7.57 | (782) all_0_43_43 = e3
% 27.45/7.57 |
% 27.45/7.57 | Combining equations (411,782) yields a new equation:
% 27.45/7.57 | (784) e3 = e0
% 27.45/7.57 |
% 27.45/7.57 | Equations (784) can reduce 66 to:
% 27.45/7.57 | (270) $false
% 27.45/7.57 |
% 27.45/7.57 |-The branch is then unsatisfiable
% 27.45/7.57 |-Branch two:
% 27.45/7.57 | (786) ~ (all_0_43_43 = e3)
% 27.45/7.57 | (799) all_0_51_51 = e3 | all_0_56_56 = e3
% 27.45/7.57 |
% 27.45/7.57 +-Applying beta-rule and splitting (799), into two cases.
% 27.45/7.57 |-Branch one:
% 27.45/7.57 | (824) all_0_51_51 = e3
% 27.45/7.57 |
% 27.45/7.57 | Combining equations (824,820) yields a new equation:
% 27.45/7.57 | (537) e3 = e1
% 27.45/7.57 |
% 27.45/7.57 | Simplifying 537 yields:
% 27.45/7.57 | (538) e3 = e1
% 27.45/7.57 |
% 27.45/7.57 | Equations (538) can reduce 136 to:
% 27.45/7.57 | (270) $false
% 27.45/7.57 |
% 27.45/7.57 |-The branch is then unsatisfiable
% 27.45/7.57 |-Branch two:
% 27.45/7.57 | (932) ~ (all_0_51_51 = e3)
% 27.45/7.57 | (764) all_0_56_56 = e3
% 27.45/7.57 |
% 27.45/7.57 | Equations (764) can reduce 274 to:
% 27.45/7.57 | (719) ~ (e4 = e3)
% 27.45/7.57 |
% 27.45/7.57 | Simplifying 719 yields:
% 27.45/7.57 | (34) ~ (e4 = e3)
% 27.45/7.57 |
% 27.45/7.57 +-Applying beta-rule and splitting (105), into two cases.
% 27.45/7.57 |-Branch one:
% 27.45/7.57 | (374) all_0_45_45 = e2
% 27.45/7.57 |
% 27.45/7.57 | Equations (374) can reduce 434 to:
% 27.45/7.57 | (270) $false
% 27.45/7.57 |
% 27.45/7.57 |-The branch is then unsatisfiable
% 27.45/7.57 |-Branch two:
% 27.45/7.57 | (434) ~ (all_0_45_45 = e2)
% 27.45/7.57 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 27.45/7.57 |
% 27.45/7.57 +-Applying beta-rule and splitting (1070), into two cases.
% 27.45/7.57 |-Branch one:
% 27.45/7.57 | (505) all_0_45_45 = e3
% 27.45/7.57 |
% 27.45/7.57 | Equations (505) can reduce 354 to:
% 27.45/7.57 | (270) $false
% 27.45/7.57 |
% 27.45/7.57 |-The branch is then unsatisfiable
% 27.45/7.57 |-Branch two:
% 27.45/7.57 | (354) ~ (all_0_45_45 = e3)
% 27.45/7.57 | (1091) all_0_46_46 = e3
% 27.45/7.57 |
% 27.45/7.57 | Equations (1091) can reduce 215 to:
% 27.45/7.57 | (1092) ~ (all_0_54_54 = e3)
% 27.45/7.57 |
% 27.45/7.57 | Simplifying 1092 yields:
% 27.45/7.57 | (1093) ~ (all_0_54_54 = e3)
% 27.45/7.57 |
% 27.45/7.57 | Equations (1091) can reduce 106 to:
% 27.45/7.57 | (136) ~ (e3 = e1)
% 27.45/7.57 |
% 27.45/7.57 | Equations (1091) can reduce 1010 to:
% 27.45/7.57 | (66) ~ (e3 = e0)
% 27.45/7.57 |
% 27.45/7.57 +-Applying beta-rule and splitting (511), into two cases.
% 27.45/7.57 |-Branch one:
% 27.45/7.57 | (363) all_0_45_45 = e4
% 27.45/7.57 |
% 27.45/7.57 | Equations (363) can reduce 434 to:
% 27.45/7.57 | (231) ~ (e4 = e2)
% 27.45/7.57 |
% 27.45/7.57 | Equations (363) can reduce 26 to:
% 27.45/7.57 | (251) ~ (e4 = e1)
% 27.45/7.57 |
% 27.45/7.57 | From (363) and (142) follows:
% 27.45/7.57 | (2221) op(e1, e4) = all_0_23_23
% 27.45/7.57 |
% 27.45/7.57 +-Applying beta-rule and splitting (179), into two cases.
% 27.45/7.57 |-Branch one:
% 27.45/7.57 | (512) all_0_42_42 = e4
% 27.45/7.57 |
% 27.45/7.57 | Combining equations (512,698) yields a new equation:
% 27.45/7.57 | (268) e4 = e2
% 27.45/7.57 |
% 27.45/7.57 | Simplifying 268 yields:
% 27.45/7.57 | (269) e4 = e2
% 27.45/7.57 |
% 27.45/7.57 | Equations (269) can reduce 231 to:
% 27.45/7.57 | (270) $false
% 27.45/7.57 |
% 27.45/7.57 |-The branch is then unsatisfiable
% 27.45/7.57 |-Branch two:
% 27.45/7.57 | (520) ~ (all_0_42_42 = e4)
% 27.45/7.57 | (521) all_0_46_46 = e4 | all_0_54_54 = e4 | all_0_59_59 = e4
% 27.45/7.57 |
% 27.45/7.57 | Equations (698) can reduce 520 to:
% 27.45/7.57 | (377) ~ (e4 = e2)
% 27.45/7.57 |
% 27.45/7.57 | Simplifying 377 yields:
% 27.45/7.57 | (231) ~ (e4 = e2)
% 27.45/7.57 |
% 27.45/7.57 +-Applying beta-rule and splitting (21), into two cases.
% 27.45/7.57 |-Branch one:
% 27.45/7.57 | (824) all_0_51_51 = e3
% 27.45/7.57 |
% 27.45/7.57 | Combining equations (824,820) yields a new equation:
% 27.45/7.57 | (537) e3 = e1
% 27.45/7.57 |
% 27.45/7.57 | Simplifying 537 yields:
% 27.45/7.57 | (538) e3 = e1
% 27.45/7.57 |
% 27.45/7.57 | Equations (538) can reduce 136 to:
% 27.45/7.57 | (270) $false
% 27.45/7.57 |
% 27.45/7.57 |-The branch is then unsatisfiable
% 27.45/7.57 |-Branch two:
% 27.45/7.57 | (932) ~ (all_0_51_51 = e3)
% 27.45/7.57 | (1101) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 27.45/7.57 |
% 27.45/7.57 +-Applying beta-rule and splitting (1101), into two cases.
% 27.45/7.57 |-Branch one:
% 27.45/7.57 | (864) all_0_52_52 = e3
% 27.45/7.57 |
% 27.45/7.57 | Combining equations (864,1848) yields a new equation:
% 27.45/7.57 | (2237) all_0_28_28 = e3
% 27.45/7.57 |
% 27.45/7.57 | Equations (864) can reduce 235 to:
% 27.45/7.57 | (2238) ~ (all_0_57_57 = e3)
% 27.45/7.57 |
% 27.45/7.57 | Simplifying 2238 yields:
% 27.45/7.57 | (846) ~ (all_0_57_57 = e3)
% 27.45/7.57 |
% 27.45/7.57 | Equations (864) can reduce 257 to:
% 27.45/7.57 | (223) ~ (e3 = e2)
% 27.45/7.57 |
% 27.45/7.57 | Equations (864) can reduce 925 to:
% 27.45/7.57 | (66) ~ (e3 = e0)
% 27.45/7.57 |
% 27.45/7.57 +-Applying beta-rule and splitting (176), into two cases.
% 27.45/7.57 |-Branch one:
% 27.45/7.57 | (830) all_0_56_56 = e0
% 27.45/7.57 |
% 27.45/7.57 | Combining equations (830,764) yields a new equation:
% 27.45/7.57 | (784) e3 = e0
% 27.45/7.57 |
% 27.45/7.57 | Equations (784) can reduce 66 to:
% 27.45/7.57 | (270) $false
% 27.45/7.57 |
% 27.45/7.57 |-The branch is then unsatisfiable
% 27.45/7.57 |-Branch two:
% 27.45/7.57 | (419) ~ (all_0_56_56 = e0)
% 27.45/7.57 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 27.45/7.57 |
% 27.45/7.57 +-Applying beta-rule and splitting (189), into two cases.
% 27.45/7.57 |-Branch one:
% 27.45/7.57 | (267) all_0_50_50 = e4
% 27.45/7.57 |
% 27.45/7.57 | Combining equations (253,267) yields a new equation:
% 27.45/7.57 | (269) e4 = e2
% 27.45/7.57 |
% 27.45/7.57 | Equations (269) can reduce 231 to:
% 27.45/7.57 | (270) $false
% 27.45/7.57 |
% 27.45/7.57 |-The branch is then unsatisfiable
% 27.45/7.57 |-Branch two:
% 27.45/7.57 | (271) ~ (all_0_50_50 = e4)
% 27.45/7.57 | (1466) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 27.45/7.57 |
% 27.45/7.57 +-Applying beta-rule and splitting (1466), into two cases.
% 27.45/7.57 |-Branch one:
% 27.45/7.57 | (1467) all_0_51_51 = e4
% 27.45/7.57 |
% 27.45/7.57 | Combining equations (1467,820) yields a new equation:
% 27.45/7.57 | (525) e4 = e1
% 27.45/7.57 |
% 27.45/7.57 | Simplifying 525 yields:
% 27.45/7.57 | (526) e4 = e1
% 27.45/7.57 |
% 27.45/7.57 | Equations (526) can reduce 251 to:
% 27.45/7.57 | (270) $false
% 27.45/7.57 |
% 27.45/7.57 |-The branch is then unsatisfiable
% 27.45/7.57 |-Branch two:
% 27.45/7.57 | (697) ~ (all_0_51_51 = e4)
% 27.45/7.57 | (1470) all_0_53_53 = e4 | all_0_54_54 = e4
% 27.45/7.57 |
% 27.45/7.57 +-Applying beta-rule and splitting (834), into two cases.
% 27.45/7.57 |-Branch one:
% 27.45/7.57 | (2258) all_0_57_57 = e0
% 27.45/7.57 |
% 27.45/7.57 | Equations (2258) can reduce 143 to:
% 27.45/7.57 | (456) ~ (e4 = e0)
% 27.45/7.57 |
% 27.45/7.57 | Simplifying 456 yields:
% 27.45/7.57 | (6) ~ (e4 = e0)
% 27.45/7.57 |
% 27.45/7.57 | Equations (2258) can reduce 846 to:
% 27.45/7.57 | (788) ~ (e3 = e0)
% 27.45/7.57 |
% 27.45/7.57 | Simplifying 788 yields:
% 27.45/7.57 | (66) ~ (e3 = e0)
% 27.45/7.57 |
% 27.45/7.57 | Equations (2258) can reduce 335 to:
% 27.45/7.57 | (566) ~ (e2 = e0)
% 27.45/7.57 |
% 27.45/7.57 | Simplifying 566 yields:
% 27.45/7.57 | (57) ~ (e2 = e0)
% 27.45/7.57 |
% 27.45/7.57 +-Applying beta-rule and splitting (1470), into two cases.
% 27.45/7.57 |-Branch one:
% 27.45/7.57 | (367) all_0_53_53 = e4
% 27.45/7.57 |
% 27.45/7.57 | Combining equations (423,367) yields a new equation:
% 27.45/7.57 | (479) e4 = e0
% 27.45/7.57 |
% 27.45/7.57 | Equations (479) can reduce 6 to:
% 27.45/7.57 | (270) $false
% 27.45/7.57 |
% 27.45/7.57 |-The branch is then unsatisfiable
% 27.45/7.57 |-Branch two:
% 27.45/7.57 | (599) ~ (all_0_53_53 = e4)
% 27.45/7.57 | (817) all_0_54_54 = e4
% 27.45/7.57 |
% 27.45/7.57 | Equations (817) can reduce 425 to:
% 27.45/7.57 | (251) ~ (e4 = e1)
% 27.45/7.57 |
% 27.45/7.57 | From (817) and (29) follows:
% 27.45/7.57 | (2271) op(e1, e4) = all_0_37_37
% 27.45/7.57 |
% 27.45/7.57 | Instantiating formula (201) with e1, e4, all_0_23_23, e2 and discharging atoms op(e1, e4) = all_0_23_23, op(e1, e4) = e2, yields:
% 27.45/7.57 | (2272) all_0_23_23 = e2
% 27.45/7.57 |
% 27.45/7.57 | Instantiating formula (201) with e1, e4, all_0_37_37, all_0_23_23 and discharging atoms op(e1, e4) = all_0_23_23, op(e1, e4) = all_0_37_37, yields:
% 27.45/7.57 | (2273) all_0_23_23 = all_0_37_37
% 27.45/7.57 |
% 27.45/7.57 | Instantiating formula (201) with e1, e1, e0, all_0_25_25 and discharging atoms op(e1, e1) = all_0_25_25, op(e1, e1) = e0, yields:
% 27.45/7.57 | (2274) all_0_25_25 = e0
% 27.45/7.57 |
% 27.45/7.57 | Combining equations (2272,2273) yields a new equation:
% 27.45/7.57 | (2275) all_0_37_37 = e2
% 27.45/7.57 |
% 27.45/7.57 | Combining equations (2275,2273) yields a new equation:
% 27.45/7.57 | (2272) all_0_23_23 = e2
% 27.45/7.57 |
% 27.45/7.57 +-Applying beta-rule and splitting (14), into two cases.
% 27.45/7.57 |-Branch one:
% 27.45/7.57 | (2277) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1))
% 27.45/7.57 |
% 27.45/7.57 +-Applying beta-rule and splitting (2277), into two cases.
% 27.45/7.57 |-Branch one:
% 27.45/7.57 | (2278) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1))
% 27.45/7.57 |
% 27.45/7.57 +-Applying beta-rule and splitting (2278), into two cases.
% 27.45/7.57 |-Branch one:
% 27.45/7.57 | (2279) all_0_21_21 = e4 & ~ (all_0_22_22 = e1)
% 27.45/7.57 |
% 27.45/7.57 | Applying alpha-rule on (2279) yields:
% 27.45/7.57 | (2280) all_0_21_21 = e4
% 27.45/7.57 | (2281) ~ (all_0_22_22 = e1)
% 27.45/7.57 |
% 27.45/7.57 | Combining equations (2280,2129) yields a new equation:
% 27.45/7.57 | (525) e4 = e1
% 27.45/7.57 |
% 27.45/7.57 | Simplifying 525 yields:
% 27.45/7.57 | (526) e4 = e1
% 27.45/7.57 |
% 27.45/7.57 | Equations (526) can reduce 251 to:
% 27.45/7.57 | (270) $false
% 27.45/7.57 |
% 27.45/7.57 |-The branch is then unsatisfiable
% 27.45/7.57 |-Branch two:
% 27.45/7.57 | (2285) all_0_23_23 = e3 & ~ (all_0_24_24 = e1)
% 27.45/7.57 |
% 27.45/7.57 | Applying alpha-rule on (2285) yields:
% 27.45/7.57 | (2286) all_0_23_23 = e3
% 27.45/7.57 | (2287) ~ (all_0_24_24 = e1)
% 27.45/7.57 |
% 27.45/7.57 | Combining equations (2286,2272) yields a new equation:
% 27.45/7.57 | (437) e3 = e2
% 27.45/7.57 |
% 27.45/7.57 | Simplifying 437 yields:
% 27.45/7.57 | (414) e3 = e2
% 27.45/7.57 |
% 27.45/7.57 | Equations (414) can reduce 223 to:
% 27.45/7.57 | (270) $false
% 27.45/7.57 |
% 27.45/7.57 |-The branch is then unsatisfiable
% 27.45/7.57 |-Branch two:
% 27.45/7.57 | (2291) all_0_25_25 = e2 & ~ (all_0_26_26 = e1)
% 27.45/7.57 |
% 27.45/7.57 | Applying alpha-rule on (2291) yields:
% 27.45/7.57 | (2292) all_0_25_25 = e2
% 27.45/7.57 | (2293) ~ (all_0_26_26 = e1)
% 27.45/7.57 |
% 27.45/7.57 | Combining equations (2274,2292) yields a new equation:
% 27.45/7.57 | (316) e2 = e0
% 27.45/7.57 |
% 27.45/7.57 | Equations (316) can reduce 57 to:
% 27.45/7.57 | (270) $false
% 27.45/7.57 |
% 27.45/7.57 |-The branch is then unsatisfiable
% 27.45/7.57 |-Branch two:
% 27.45/7.57 | (2296) all_0_28_28 = e0 & ~ (all_0_29_29 = e1)
% 27.45/7.57 |
% 27.45/7.57 | Applying alpha-rule on (2296) yields:
% 27.45/7.57 | (2297) all_0_28_28 = e0
% 27.45/7.57 | (2298) ~ (all_0_29_29 = e1)
% 27.45/7.57 |
% 27.45/7.57 | Combining equations (2297,2237) yields a new equation:
% 27.45/7.57 | (784) e3 = e0
% 27.45/7.57 |
% 27.45/7.57 | Equations (784) can reduce 66 to:
% 27.45/7.57 | (270) $false
% 27.45/7.57 |
% 27.45/7.57 |-The branch is then unsatisfiable
% 27.45/7.57 |-Branch two:
% 27.45/7.57 | (2301) ~ (all_0_57_57 = e0)
% 27.45/7.57 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 27.45/7.57 |
% 27.45/7.57 +-Applying beta-rule and splitting (2302), into two cases.
% 27.45/7.57 |-Branch one:
% 27.45/7.57 | (585) all_0_58_58 = e0
% 27.45/7.57 |
% 27.45/7.57 | Combining equations (396,585) yields a new equation:
% 27.45/7.57 | (622) e2 = e0
% 27.45/7.57 |
% 27.45/7.57 | Simplifying 622 yields:
% 27.45/7.57 | (316) e2 = e0
% 27.45/7.57 |
% 27.45/7.57 | Equations (316) can reduce 57 to:
% 27.45/7.57 | (270) $false
% 27.45/7.57 |
% 27.45/7.57 |-The branch is then unsatisfiable
% 27.45/7.57 |-Branch two:
% 27.45/7.57 | (431) ~ (all_0_58_58 = e0)
% 27.45/7.57 | (2308) all_0_59_59 = e0
% 27.45/7.57 |
% 27.45/7.57 | Combining equations (2308,424) yields a new equation:
% 27.45/7.57 | (560) e1 = e0
% 27.45/7.58 |
% 27.45/7.58 | Equations (560) can reduce 132 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (826) ~ (all_0_52_52 = e3)
% 27.45/7.58 | (1107) all_0_53_53 = e3 | all_0_54_54 = e3
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (176), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (830) all_0_56_56 = e0
% 27.45/7.58 |
% 27.45/7.58 | Combining equations (830,764) yields a new equation:
% 27.45/7.58 | (784) e3 = e0
% 27.45/7.58 |
% 27.45/7.58 | Equations (784) can reduce 66 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (419) ~ (all_0_56_56 = e0)
% 27.45/7.58 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 27.45/7.58 |
% 27.45/7.58 | Equations (764) can reduce 419 to:
% 27.45/7.58 | (66) ~ (e3 = e0)
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (1107), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (1114) all_0_53_53 = e3
% 27.45/7.58 |
% 27.45/7.58 | Combining equations (1114,423) yields a new equation:
% 27.45/7.58 | (783) e3 = e0
% 27.45/7.58 |
% 27.45/7.58 | Simplifying 783 yields:
% 27.45/7.58 | (784) e3 = e0
% 27.45/7.58 |
% 27.45/7.58 | Equations (784) can reduce 66 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (356) ~ (all_0_53_53 = e3)
% 27.45/7.58 | (1119) all_0_54_54 = e3
% 27.45/7.58 |
% 27.45/7.58 | Equations (1119) can reduce 1093 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (352) ~ (all_0_45_45 = e4)
% 27.45/7.58 | (517) all_0_46_46 = e4
% 27.45/7.58 |
% 27.45/7.58 | Combining equations (1091,517) yields a new equation:
% 27.45/7.58 | (359) e4 = e3
% 27.45/7.58 |
% 27.45/7.58 | Equations (359) can reduce 34 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (455) ~ (all_0_43_43 = e0)
% 27.45/7.58 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (1122), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (621) all_0_44_44 = e0
% 27.45/7.58 |
% 27.45/7.58 | Combining equations (370,621) yields a new equation:
% 27.45/7.58 | (622) e2 = e0
% 27.45/7.58 |
% 27.45/7.58 | Simplifying 622 yields:
% 27.45/7.58 | (316) e2 = e0
% 27.45/7.58 |
% 27.45/7.58 | Equations (316) can reduce 57 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (625) ~ (all_0_44_44 = e0)
% 27.45/7.58 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (1128), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (454) all_0_45_45 = e0
% 27.45/7.58 |
% 27.45/7.58 | Equations (454) can reduce 488 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (488) ~ (all_0_45_45 = e0)
% 27.45/7.58 | (1132) all_0_46_46 = e0
% 27.45/7.58 |
% 27.45/7.58 | Equations (1132) can reduce 1010 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (748) ~ (all_0_51_51 = e1)
% 27.45/7.58 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (823), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (848) all_0_52_52 = e1
% 27.45/7.58 |
% 27.45/7.58 | Equations (848) can reduce 642 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (642) ~ (all_0_52_52 = e1)
% 27.45/7.58 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (852), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (853) all_0_53_53 = e1
% 27.45/7.58 |
% 27.45/7.58 | Equations (853) can reduce 874 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (874) ~ (all_0_53_53 = e1)
% 27.45/7.58 | (875) all_0_54_54 = e1
% 27.45/7.58 |
% 27.45/7.58 | Equations (875) can reduce 425 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (1231) ~ (all_0_49_49 = e0)
% 27.45/7.58 | (589) all_0_49_49 = e1
% 27.45/7.58 |
% 27.45/7.58 | Equations (589) can reduce 543 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (376) ~ (all_0_58_58 = e2)
% 27.45/7.58 | (399) all_0_59_59 = e2
% 27.45/7.58 |
% 27.45/7.58 | Equations (399) can reduce 701 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (1237) ~ (all_0_41_41 = e3)
% 27.45/7.58 | (1238) all_0_41_41 = e4 | all_0_41_41 = e1
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (1238), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (536) all_0_41_41 = e1
% 27.45/7.58 |
% 27.45/7.58 | Equations (536) can reduce 540 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (540) ~ (all_0_41_41 = e1)
% 27.45/7.58 | (358) all_0_41_41 = e4
% 27.45/7.58 |
% 27.45/7.58 | Equations (358) can reduce 361 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (498) ~ (all_0_42_42 = e2)
% 27.45/7.58 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (630), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (327) all_0_40_40 = e2
% 27.45/7.58 |
% 27.45/7.58 | Combining equations (327,530) yields a new equation:
% 27.45/7.58 | (531) e2 = e1
% 27.45/7.58 |
% 27.45/7.58 | Simplifying 531 yields:
% 27.45/7.58 | (322) e2 = e1
% 27.45/7.58 |
% 27.45/7.58 | Equations (322) can reduce 141 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (602) ~ (all_0_40_40 = e2)
% 27.45/7.58 | (1251) all_0_41_41 = e2 | all_0_42_42 = e2
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (1251), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (436) all_0_41_41 = e2
% 27.45/7.58 |
% 27.45/7.58 | Equations (436) can reduce 157 to:
% 27.45/7.58 | (375) ~ (all_0_58_58 = e2)
% 27.45/7.58 |
% 27.45/7.58 | Simplifying 375 yields:
% 27.45/7.58 | (376) ~ (all_0_58_58 = e2)
% 27.45/7.58 |
% 27.45/7.58 | Equations (436) can reduce 361 to:
% 27.45/7.58 | (377) ~ (e4 = e2)
% 27.45/7.58 |
% 27.45/7.58 | Simplifying 377 yields:
% 27.45/7.58 | (231) ~ (e4 = e2)
% 27.45/7.58 |
% 27.45/7.58 | Equations (436) can reduce 540 to:
% 27.45/7.58 | (141) ~ (e2 = e1)
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (1245), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (1258) all_0_42_42 = e3
% 27.45/7.58 |
% 27.45/7.58 | Equations (1258) can reduce 17 to:
% 27.45/7.58 | (1259) ~ (all_0_59_59 = e3)
% 27.45/7.58 |
% 27.45/7.58 | Simplifying 1259 yields:
% 27.45/7.58 | (1260) ~ (all_0_59_59 = e3)
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (168), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (382) all_0_55_55 = e2
% 27.45/7.58 |
% 27.45/7.58 | Combining equations (382,272) yields a new equation:
% 27.45/7.58 | (269) e4 = e2
% 27.45/7.58 |
% 27.45/7.58 | Equations (269) can reduce 231 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (386) ~ (all_0_55_55 = e2)
% 27.45/7.58 | (387) all_0_56_56 = e2 | all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (387), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (388) all_0_56_56 = e2
% 27.45/7.58 |
% 27.45/7.58 | Equations (388) can reduce 300 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (300) ~ (all_0_56_56 = e2)
% 27.45/7.58 | (391) all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (391), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (392) all_0_57_57 = e2
% 27.45/7.58 |
% 27.45/7.58 | Equations (392) can reduce 335 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (335) ~ (all_0_57_57 = e2)
% 27.45/7.58 | (395) all_0_58_58 = e2 | all_0_59_59 = e2
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (395), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (396) all_0_58_58 = e2
% 27.45/7.58 |
% 27.45/7.58 | Equations (396) can reduce 376 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (376) ~ (all_0_58_58 = e2)
% 27.45/7.58 | (399) all_0_59_59 = e2
% 27.45/7.58 |
% 27.45/7.58 | Equations (399) can reduce 280 to:
% 27.45/7.58 | (377) ~ (e4 = e2)
% 27.45/7.58 |
% 27.45/7.58 | Simplifying 377 yields:
% 27.45/7.58 | (231) ~ (e4 = e2)
% 27.45/7.58 |
% 27.45/7.58 | Equations (399) can reduce 1260 to:
% 27.45/7.58 | (301) ~ (e3 = e2)
% 27.45/7.58 |
% 27.45/7.58 | Simplifying 301 yields:
% 27.45/7.58 | (223) ~ (e3 = e2)
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (93), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (402) all_0_59_59 = e4
% 27.45/7.58 |
% 27.45/7.58 | Combining equations (402,399) yields a new equation:
% 27.45/7.58 | (268) e4 = e2
% 27.45/7.58 |
% 27.45/7.58 | Simplifying 268 yields:
% 27.45/7.58 | (269) e4 = e2
% 27.45/7.58 |
% 27.45/7.58 | Equations (269) can reduce 231 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (280) ~ (all_0_59_59 = e4)
% 27.45/7.58 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (407), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (408), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (409), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.45/7.58 |
% 27.45/7.58 | Applying alpha-rule on (410) yields:
% 27.45/7.58 | (411) all_0_43_43 = e0
% 27.45/7.58 | (412) all_0_59_59 = e3
% 27.45/7.58 | (413) ~ (all_0_46_46 = e3)
% 27.45/7.58 |
% 27.45/7.58 | Combining equations (412,399) yields a new equation:
% 27.45/7.58 | (437) e3 = e2
% 27.45/7.58 |
% 27.45/7.58 | Simplifying 437 yields:
% 27.45/7.58 | (414) e3 = e2
% 27.45/7.58 |
% 27.45/7.58 | Equations (414) can reduce 223 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.45/7.58 |
% 27.45/7.58 | Applying alpha-rule on (416) yields:
% 27.45/7.58 | (411) all_0_43_43 = e0
% 27.45/7.58 | (412) all_0_59_59 = e3
% 27.45/7.58 | (419) ~ (all_0_56_56 = e0)
% 27.45/7.58 |
% 27.45/7.58 | Combining equations (412,399) yields a new equation:
% 27.45/7.58 | (437) e3 = e2
% 27.45/7.58 |
% 27.45/7.58 | Simplifying 437 yields:
% 27.45/7.58 | (414) e3 = e2
% 27.45/7.58 |
% 27.45/7.58 | Equations (414) can reduce 223 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.45/7.58 |
% 27.45/7.58 | Applying alpha-rule on (422) yields:
% 27.45/7.58 | (423) all_0_53_53 = e0
% 27.45/7.58 | (424) all_0_59_59 = e1
% 27.45/7.58 | (425) ~ (all_0_54_54 = e1)
% 27.45/7.58 |
% 27.45/7.58 | Combining equations (424,399) yields a new equation:
% 27.45/7.58 | (322) e2 = e1
% 27.45/7.58 |
% 27.45/7.58 | Equations (322) can reduce 141 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.45/7.58 |
% 27.45/7.58 | Applying alpha-rule on (428) yields:
% 27.45/7.58 | (423) all_0_53_53 = e0
% 27.45/7.58 | (424) all_0_59_59 = e1
% 27.45/7.58 | (431) ~ (all_0_58_58 = e0)
% 27.45/7.58 |
% 27.45/7.58 | Combining equations (424,399) yields a new equation:
% 27.45/7.58 | (322) e2 = e1
% 27.45/7.58 |
% 27.45/7.58 | Equations (322) can reduce 141 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (1316) ~ (all_0_42_42 = e3)
% 27.45/7.58 | (1317) all_0_42_42 = e4 | all_0_42_42 = e1
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (1317), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (541) all_0_42_42 = e1
% 27.45/7.58 |
% 27.45/7.58 | Equations (541) can reduce 640 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (640) ~ (all_0_42_42 = e1)
% 27.45/7.58 | (512) all_0_42_42 = e4
% 27.45/7.58 |
% 27.45/7.58 | Equations (512) can reduce 520 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (331) ~ (all_0_41_41 = e2)
% 27.45/7.58 | (698) all_0_42_42 = e2
% 27.45/7.58 |
% 27.45/7.58 | Equations (698) can reduce 498 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (591) ~ (all_0_39_39 = e4)
% 27.45/7.58 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (684), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (751) all_0_39_39 = e3
% 27.45/7.58 |
% 27.45/7.58 | Equations (751) can reduce 226 to:
% 27.45/7.58 | (1329) ~ (all_0_41_41 = e3)
% 27.45/7.58 |
% 27.45/7.58 | Simplifying 1329 yields:
% 27.45/7.58 | (1237) ~ (all_0_41_41 = e3)
% 27.45/7.58 |
% 27.45/7.58 | Equations (751) can reduce 184 to:
% 27.45/7.58 | (1331) ~ (all_0_42_42 = e3)
% 27.45/7.58 |
% 27.45/7.58 | Simplifying 1331 yields:
% 27.45/7.58 | (1316) ~ (all_0_42_42 = e3)
% 27.45/7.58 |
% 27.45/7.58 | Equations (751) can reduce 167 to:
% 27.45/7.58 | (1333) ~ (all_0_43_43 = e3)
% 27.45/7.58 |
% 27.45/7.58 | Simplifying 1333 yields:
% 27.45/7.58 | (786) ~ (all_0_43_43 = e3)
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (217), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (436) all_0_41_41 = e2
% 27.45/7.58 |
% 27.45/7.58 | Equations (436) can reduce 94 to:
% 27.45/7.58 | (1336) ~ (all_0_42_42 = e2)
% 27.45/7.58 |
% 27.45/7.58 | Simplifying 1336 yields:
% 27.45/7.58 | (498) ~ (all_0_42_42 = e2)
% 27.45/7.58 |
% 27.45/7.58 | Equations (436) can reduce 157 to:
% 27.45/7.58 | (375) ~ (all_0_58_58 = e2)
% 27.45/7.58 |
% 27.45/7.58 | Simplifying 375 yields:
% 27.45/7.58 | (376) ~ (all_0_58_58 = e2)
% 27.45/7.58 |
% 27.45/7.58 | Equations (436) can reduce 1237 to:
% 27.45/7.58 | (301) ~ (e3 = e2)
% 27.45/7.58 |
% 27.45/7.58 | Simplifying 301 yields:
% 27.45/7.58 | (223) ~ (e3 = e2)
% 27.45/7.58 |
% 27.45/7.58 | Equations (436) can reduce 540 to:
% 27.45/7.58 | (141) ~ (e2 = e1)
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (16), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (698) all_0_42_42 = e2
% 27.45/7.58 |
% 27.45/7.58 | Equations (698) can reduce 498 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (498) ~ (all_0_42_42 = e2)
% 27.45/7.58 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 27.45/7.58 |
% 27.45/7.58 +-Applying beta-rule and splitting (168), into two cases.
% 27.45/7.58 |-Branch one:
% 27.45/7.58 | (382) all_0_55_55 = e2
% 27.45/7.58 |
% 27.45/7.58 | Combining equations (272,382) yields a new equation:
% 27.45/7.58 | (268) e4 = e2
% 27.45/7.58 |
% 27.45/7.58 | Simplifying 268 yields:
% 27.45/7.58 | (269) e4 = e2
% 27.45/7.58 |
% 27.45/7.58 | Equations (269) can reduce 231 to:
% 27.45/7.58 | (270) $false
% 27.45/7.58 |
% 27.45/7.58 |-The branch is then unsatisfiable
% 27.45/7.58 |-Branch two:
% 27.45/7.58 | (386) ~ (all_0_55_55 = e2)
% 27.45/7.58 | (387) all_0_56_56 = e2 | all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 27.45/7.58 |
% 27.45/7.59 +-Applying beta-rule and splitting (1245), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (1258) all_0_42_42 = e3
% 27.45/7.59 |
% 27.45/7.59 | Equations (1258) can reduce 1316 to:
% 27.45/7.59 | (270) $false
% 27.45/7.59 |
% 27.45/7.59 |-The branch is then unsatisfiable
% 27.45/7.59 |-Branch two:
% 27.45/7.59 | (1316) ~ (all_0_42_42 = e3)
% 27.45/7.59 | (1317) all_0_42_42 = e4 | all_0_42_42 = e1
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (387), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (388) all_0_56_56 = e2
% 27.45/7.59 |
% 27.45/7.59 | Equations (388) can reduce 300 to:
% 27.45/7.59 | (270) $false
% 27.45/7.59 |
% 27.45/7.59 |-The branch is then unsatisfiable
% 27.45/7.59 |-Branch two:
% 27.45/7.59 | (300) ~ (all_0_56_56 = e2)
% 27.45/7.59 | (391) all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (391), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (392) all_0_57_57 = e2
% 27.45/7.59 |
% 27.45/7.59 | Equations (392) can reduce 335 to:
% 27.45/7.59 | (270) $false
% 27.45/7.59 |
% 27.45/7.59 |-The branch is then unsatisfiable
% 27.45/7.59 |-Branch two:
% 27.45/7.59 | (335) ~ (all_0_57_57 = e2)
% 27.45/7.59 | (395) all_0_58_58 = e2 | all_0_59_59 = e2
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (395), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (396) all_0_58_58 = e2
% 27.45/7.59 |
% 27.45/7.59 | Equations (396) can reduce 376 to:
% 27.45/7.59 | (270) $false
% 27.45/7.59 |
% 27.45/7.59 |-The branch is then unsatisfiable
% 27.45/7.59 |-Branch two:
% 27.45/7.59 | (376) ~ (all_0_58_58 = e2)
% 27.45/7.59 | (399) all_0_59_59 = e2
% 27.45/7.59 |
% 27.45/7.59 | Equations (399) can reduce 17 to:
% 27.45/7.59 | (498) ~ (all_0_42_42 = e2)
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (1317), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (541) all_0_42_42 = e1
% 27.45/7.59 |
% 27.45/7.59 | Equations (541) can reduce 640 to:
% 27.45/7.59 | (270) $false
% 27.45/7.59 |
% 27.45/7.59 |-The branch is then unsatisfiable
% 27.45/7.59 |-Branch two:
% 27.45/7.59 | (640) ~ (all_0_42_42 = e1)
% 27.45/7.59 | (512) all_0_42_42 = e4
% 27.45/7.59 |
% 27.45/7.59 | Equations (512) can reduce 498 to:
% 27.45/7.59 | (231) ~ (e4 = e2)
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (93), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (402) all_0_59_59 = e4
% 27.45/7.59 |
% 27.45/7.59 | Combining equations (402,399) yields a new equation:
% 27.45/7.59 | (268) e4 = e2
% 27.45/7.59 |
% 27.45/7.59 | Simplifying 268 yields:
% 27.45/7.59 | (269) e4 = e2
% 27.45/7.59 |
% 27.45/7.59 | Equations (269) can reduce 231 to:
% 27.45/7.59 | (270) $false
% 27.45/7.59 |
% 27.45/7.59 |-The branch is then unsatisfiable
% 27.45/7.59 |-Branch two:
% 27.45/7.59 | (280) ~ (all_0_59_59 = e4)
% 27.45/7.59 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (407), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (408), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (409), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.45/7.59 |
% 27.45/7.59 | Applying alpha-rule on (410) yields:
% 27.45/7.59 | (411) all_0_43_43 = e0
% 27.45/7.59 | (412) all_0_59_59 = e3
% 27.45/7.59 | (413) ~ (all_0_46_46 = e3)
% 27.45/7.59 |
% 27.45/7.59 | Combining equations (412,399) yields a new equation:
% 27.45/7.59 | (437) e3 = e2
% 27.45/7.59 |
% 27.45/7.59 | Simplifying 437 yields:
% 27.45/7.59 | (414) e3 = e2
% 27.45/7.59 |
% 27.45/7.59 | Equations (414) can reduce 223 to:
% 27.45/7.59 | (270) $false
% 27.45/7.59 |
% 27.45/7.59 |-The branch is then unsatisfiable
% 27.45/7.59 |-Branch two:
% 27.45/7.59 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.45/7.59 |
% 27.45/7.59 | Applying alpha-rule on (416) yields:
% 27.45/7.59 | (411) all_0_43_43 = e0
% 27.45/7.59 | (412) all_0_59_59 = e3
% 27.45/7.59 | (419) ~ (all_0_56_56 = e0)
% 27.45/7.59 |
% 27.45/7.59 | Combining equations (412,399) yields a new equation:
% 27.45/7.59 | (437) e3 = e2
% 27.45/7.59 |
% 27.45/7.59 | Simplifying 437 yields:
% 27.45/7.59 | (414) e3 = e2
% 27.45/7.59 |
% 27.45/7.59 | Equations (414) can reduce 223 to:
% 27.45/7.59 | (270) $false
% 27.45/7.59 |
% 27.45/7.59 |-The branch is then unsatisfiable
% 27.45/7.59 |-Branch two:
% 27.45/7.59 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.45/7.59 |
% 27.45/7.59 | Applying alpha-rule on (422) yields:
% 27.45/7.59 | (423) all_0_53_53 = e0
% 27.45/7.59 | (424) all_0_59_59 = e1
% 27.45/7.59 | (425) ~ (all_0_54_54 = e1)
% 27.45/7.59 |
% 27.45/7.59 | Combining equations (424,399) yields a new equation:
% 27.45/7.59 | (322) e2 = e1
% 27.45/7.59 |
% 27.45/7.59 | Equations (322) can reduce 141 to:
% 27.45/7.59 | (270) $false
% 27.45/7.59 |
% 27.45/7.59 |-The branch is then unsatisfiable
% 27.45/7.59 |-Branch two:
% 27.45/7.59 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.45/7.59 |
% 27.45/7.59 | Applying alpha-rule on (428) yields:
% 27.45/7.59 | (423) all_0_53_53 = e0
% 27.45/7.59 | (424) all_0_59_59 = e1
% 27.45/7.59 | (431) ~ (all_0_58_58 = e0)
% 27.45/7.59 |
% 27.45/7.59 | Combining equations (424,399) yields a new equation:
% 27.45/7.59 | (322) e2 = e1
% 27.45/7.59 |
% 27.45/7.59 | Equations (322) can reduce 141 to:
% 27.45/7.59 | (270) $false
% 27.45/7.59 |
% 27.45/7.59 |-The branch is then unsatisfiable
% 27.45/7.59 |-Branch two:
% 27.45/7.59 | (331) ~ (all_0_41_41 = e2)
% 27.45/7.59 | (709) all_0_41_41 = e4 | all_0_41_41 = e3 | all_0_41_41 = e1
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (709), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (351) all_0_41_41 = e3
% 27.45/7.59 |
% 27.45/7.59 | Equations (351) can reduce 1237 to:
% 27.45/7.59 | (270) $false
% 27.45/7.59 |
% 27.45/7.59 |-The branch is then unsatisfiable
% 27.45/7.59 |-Branch two:
% 27.45/7.59 | (1237) ~ (all_0_41_41 = e3)
% 27.45/7.59 | (1238) all_0_41_41 = e4 | all_0_41_41 = e1
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (187), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (436) all_0_41_41 = e2
% 27.45/7.59 |
% 27.45/7.59 | Equations (436) can reduce 331 to:
% 27.45/7.59 | (270) $false
% 27.45/7.59 |
% 27.45/7.59 |-The branch is then unsatisfiable
% 27.45/7.59 |-Branch two:
% 27.45/7.59 | (331) ~ (all_0_41_41 = e2)
% 27.45/7.59 | (441) all_0_45_45 = e2 | all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (441), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (374) all_0_45_45 = e2
% 27.45/7.59 |
% 27.45/7.59 | Equations (374) can reduce 434 to:
% 27.45/7.59 | (270) $false
% 27.45/7.59 |
% 27.45/7.59 |-The branch is then unsatisfiable
% 27.45/7.59 |-Branch two:
% 27.45/7.59 | (434) ~ (all_0_45_45 = e2)
% 27.45/7.59 | (445) all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (445), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (311) all_0_48_48 = e2
% 27.45/7.59 |
% 27.45/7.59 | Equations (311) can reduce 294 to:
% 27.45/7.59 | (270) $false
% 27.45/7.59 |
% 27.45/7.59 |-The branch is then unsatisfiable
% 27.45/7.59 |-Branch two:
% 27.45/7.59 | (294) ~ (all_0_48_48 = e2)
% 27.45/7.59 | (449) all_0_53_53 = e2 | all_0_58_58 = e2
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (449), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (576) all_0_53_53 = e2
% 27.45/7.59 |
% 27.45/7.59 | Equations (576) can reduce 259 to:
% 27.45/7.59 | (270) $false
% 27.45/7.59 |
% 27.45/7.59 |-The branch is then unsatisfiable
% 27.45/7.59 |-Branch two:
% 27.45/7.59 | (259) ~ (all_0_53_53 = e2)
% 27.45/7.59 | (396) all_0_58_58 = e2
% 27.45/7.59 |
% 27.45/7.59 | Equations (396) can reduce 157 to:
% 27.45/7.59 | (331) ~ (all_0_41_41 = e2)
% 27.45/7.59 |
% 27.45/7.59 | Equations (396) can reduce 108 to:
% 27.45/7.59 | (434) ~ (all_0_45_45 = e2)
% 27.45/7.59 |
% 27.45/7.59 | Equations (396) can reduce 59 to:
% 27.45/7.59 | (294) ~ (all_0_48_48 = e2)
% 27.45/7.59 |
% 27.45/7.59 | Equations (396) can reduce 70 to:
% 27.45/7.59 | (259) ~ (all_0_53_53 = e2)
% 27.45/7.59 |
% 27.45/7.59 | From (396) and (63) follows:
% 27.45/7.59 | (1846) op(e1, e2) = all_0_28_28
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (209), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (698) all_0_42_42 = e2
% 27.45/7.59 |
% 27.45/7.59 | Equations (698) can reduce 18 to:
% 27.45/7.59 | (1435) ~ (all_0_46_46 = e2)
% 27.45/7.59 |
% 27.45/7.59 | Simplifying 1435 yields:
% 27.45/7.59 | (1436) ~ (all_0_46_46 = e2)
% 27.45/7.59 |
% 27.45/7.59 | Equations (698) can reduce 640 to:
% 27.45/7.59 | (141) ~ (e2 = e1)
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (1238), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (536) all_0_41_41 = e1
% 27.45/7.59 |
% 27.45/7.59 | Equations (536) can reduce 540 to:
% 27.45/7.59 | (270) $false
% 27.45/7.59 |
% 27.45/7.59 |-The branch is then unsatisfiable
% 27.45/7.59 |-Branch two:
% 27.45/7.59 | (540) ~ (all_0_41_41 = e1)
% 27.45/7.59 | (358) all_0_41_41 = e4
% 27.45/7.59 |
% 27.45/7.59 | Equations (358) can reduce 51 to:
% 27.45/7.59 | (503) ~ (all_0_45_45 = e4)
% 27.45/7.59 |
% 27.45/7.59 | Simplifying 503 yields:
% 27.45/7.59 | (352) ~ (all_0_45_45 = e4)
% 27.45/7.59 |
% 27.45/7.59 | Equations (358) can reduce 190 to:
% 27.45/7.59 | (2754) ~ (all_0_48_48 = e4)
% 27.45/7.59 |
% 27.45/7.59 | Simplifying 2754 yields:
% 27.45/7.59 | (192) ~ (all_0_48_48 = e4)
% 27.45/7.59 |
% 27.45/7.59 | Equations (358) can reduce 214 to:
% 27.45/7.59 | (1444) ~ (all_0_53_53 = e4)
% 27.45/7.59 |
% 27.45/7.59 | Simplifying 1444 yields:
% 27.45/7.59 | (599) ~ (all_0_53_53 = e4)
% 27.45/7.59 |
% 27.45/7.59 | Equations (358) can reduce 232 to:
% 27.45/7.59 | (6) ~ (e4 = e0)
% 27.45/7.59 |
% 27.45/7.59 | From (358) and (112) follows:
% 27.45/7.59 | (2759) op(e1, e4) = all_0_21_21
% 27.45/7.59 |
% 27.45/7.59 | Instantiating formula (201) with e1, e4, all_0_21_21, e2 and discharging atoms op(e1, e4) = all_0_21_21, op(e1, e4) = e2, yields:
% 27.45/7.59 | (2760) all_0_21_21 = e2
% 27.45/7.59 |
% 27.45/7.59 | Instantiating formula (201) with e1, e2, all_0_28_28, all_0_52_52 and discharging atoms op(e1, e2) = all_0_28_28, op(e1, e2) = all_0_52_52, yields:
% 27.45/7.59 | (1848) all_0_28_28 = all_0_52_52
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (44), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (502) all_0_43_43 = e4
% 27.45/7.59 |
% 27.45/7.59 | Equations (502) can reduce 84 to:
% 27.45/7.59 | (503) ~ (all_0_45_45 = e4)
% 27.45/7.59 |
% 27.45/7.59 | Simplifying 503 yields:
% 27.45/7.59 | (352) ~ (all_0_45_45 = e4)
% 27.45/7.59 |
% 27.45/7.59 | Equations (502) can reduce 240 to:
% 27.45/7.59 | (696) ~ (all_0_51_51 = e4)
% 27.45/7.59 |
% 27.45/7.59 | Simplifying 696 yields:
% 27.45/7.59 | (697) ~ (all_0_51_51 = e4)
% 27.45/7.59 |
% 27.45/7.59 | Equations (502) can reduce 786 to:
% 27.45/7.59 | (34) ~ (e4 = e3)
% 27.45/7.59 |
% 27.45/7.59 | Equations (502) can reduce 292 to:
% 27.45/7.59 | (231) ~ (e4 = e2)
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (179), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (512) all_0_42_42 = e4
% 27.45/7.59 |
% 27.45/7.59 | Combining equations (512,698) yields a new equation:
% 27.45/7.59 | (268) e4 = e2
% 27.45/7.59 |
% 27.45/7.59 | Simplifying 268 yields:
% 27.45/7.59 | (269) e4 = e2
% 27.45/7.59 |
% 27.45/7.59 | Equations (269) can reduce 231 to:
% 27.45/7.59 | (270) $false
% 27.45/7.59 |
% 27.45/7.59 |-The branch is then unsatisfiable
% 27.45/7.59 |-Branch two:
% 27.45/7.59 | (520) ~ (all_0_42_42 = e4)
% 27.45/7.59 | (521) all_0_46_46 = e4 | all_0_54_54 = e4 | all_0_59_59 = e4
% 27.45/7.59 |
% 27.45/7.59 | Equations (698) can reduce 520 to:
% 27.45/7.59 | (377) ~ (e4 = e2)
% 27.45/7.59 |
% 27.45/7.59 | Simplifying 377 yields:
% 27.45/7.59 | (231) ~ (e4 = e2)
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (189), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (267) all_0_50_50 = e4
% 27.45/7.59 |
% 27.45/7.59 | Combining equations (253,267) yields a new equation:
% 27.45/7.59 | (269) e4 = e2
% 27.45/7.59 |
% 27.45/7.59 | Equations (269) can reduce 231 to:
% 27.45/7.59 | (270) $false
% 27.45/7.59 |
% 27.45/7.59 |-The branch is then unsatisfiable
% 27.45/7.59 |-Branch two:
% 27.45/7.59 | (271) ~ (all_0_50_50 = e4)
% 27.45/7.59 | (1466) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (1466), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (1467) all_0_51_51 = e4
% 27.45/7.59 |
% 27.45/7.59 | Equations (1467) can reduce 697 to:
% 27.45/7.59 | (270) $false
% 27.45/7.59 |
% 27.45/7.59 |-The branch is then unsatisfiable
% 27.45/7.59 |-Branch two:
% 27.45/7.59 | (697) ~ (all_0_51_51 = e4)
% 27.45/7.59 | (1470) all_0_53_53 = e4 | all_0_54_54 = e4
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (1470), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (367) all_0_53_53 = e4
% 27.45/7.59 |
% 27.45/7.59 | Equations (367) can reduce 599 to:
% 27.45/7.59 | (270) $false
% 27.45/7.59 |
% 27.45/7.59 |-The branch is then unsatisfiable
% 27.45/7.59 |-Branch two:
% 27.45/7.59 | (599) ~ (all_0_53_53 = e4)
% 27.45/7.59 | (817) all_0_54_54 = e4
% 27.45/7.59 |
% 27.45/7.59 | Equations (817) can reduce 215 to:
% 27.45/7.59 | (805) ~ (all_0_46_46 = e4)
% 27.45/7.59 |
% 27.45/7.59 | Equations (817) can reduce 72 to:
% 27.45/7.59 | (279) ~ (all_0_59_59 = e4)
% 27.45/7.59 |
% 27.45/7.59 | Simplifying 279 yields:
% 27.45/7.59 | (280) ~ (all_0_59_59 = e4)
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (93), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (402) all_0_59_59 = e4
% 27.45/7.59 |
% 27.45/7.59 | Equations (402) can reduce 280 to:
% 27.45/7.59 | (270) $false
% 27.45/7.59 |
% 27.45/7.59 |-The branch is then unsatisfiable
% 27.45/7.59 |-Branch two:
% 27.45/7.59 | (280) ~ (all_0_59_59 = e4)
% 27.45/7.59 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (407), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (408), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.45/7.59 |
% 27.45/7.59 +-Applying beta-rule and splitting (409), into two cases.
% 27.45/7.59 |-Branch one:
% 27.45/7.59 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.45/7.59 |
% 27.45/7.59 | Applying alpha-rule on (410) yields:
% 27.45/7.59 | (411) all_0_43_43 = e0
% 27.67/7.59 | (412) all_0_59_59 = e3
% 27.67/7.59 | (413) ~ (all_0_46_46 = e3)
% 27.67/7.59 |
% 27.67/7.59 | Combining equations (502,411) yields a new equation:
% 27.67/7.59 | (478) e4 = e0
% 27.67/7.59 |
% 27.67/7.59 | Simplifying 478 yields:
% 27.67/7.59 | (479) e4 = e0
% 27.67/7.59 |
% 27.67/7.59 | Equations (479) can reduce 6 to:
% 27.67/7.59 | (270) $false
% 27.67/7.59 |
% 27.67/7.59 |-The branch is then unsatisfiable
% 27.67/7.59 |-Branch two:
% 27.67/7.59 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.67/7.59 |
% 27.67/7.59 | Applying alpha-rule on (416) yields:
% 27.67/7.59 | (411) all_0_43_43 = e0
% 27.67/7.59 | (412) all_0_59_59 = e3
% 27.67/7.59 | (419) ~ (all_0_56_56 = e0)
% 27.67/7.59 |
% 27.67/7.59 | Combining equations (502,411) yields a new equation:
% 27.67/7.59 | (478) e4 = e0
% 27.67/7.59 |
% 27.67/7.59 | Simplifying 478 yields:
% 27.67/7.59 | (479) e4 = e0
% 27.67/7.59 |
% 27.67/7.59 | Equations (479) can reduce 6 to:
% 27.67/7.59 | (270) $false
% 27.67/7.59 |
% 27.67/7.59 |-The branch is then unsatisfiable
% 27.67/7.59 |-Branch two:
% 27.67/7.59 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.67/7.59 |
% 27.67/7.59 | Applying alpha-rule on (422) yields:
% 27.67/7.59 | (423) all_0_53_53 = e0
% 27.67/7.59 | (424) all_0_59_59 = e1
% 27.67/7.59 | (425) ~ (all_0_54_54 = e1)
% 27.67/7.59 |
% 27.67/7.59 | Equations (423) can reduce 128 to:
% 27.67/7.59 | (488) ~ (all_0_45_45 = e0)
% 27.67/7.59 |
% 27.67/7.59 | Equations (424) can reduce 113 to:
% 27.67/7.59 | (543) ~ (all_0_49_49 = e1)
% 27.67/7.59 |
% 27.67/7.59 +-Applying beta-rule and splitting (219), into two cases.
% 27.67/7.59 |-Branch one:
% 27.67/7.59 | (351) all_0_41_41 = e3
% 27.67/7.59 |
% 27.67/7.59 | Combining equations (351,358) yields a new equation:
% 27.67/7.59 | (359) e4 = e3
% 27.67/7.59 |
% 27.67/7.59 | Equations (359) can reduce 34 to:
% 27.67/7.59 | (270) $false
% 27.67/7.59 |
% 27.67/7.59 |-The branch is then unsatisfiable
% 27.67/7.59 |-Branch two:
% 27.67/7.59 | (1237) ~ (all_0_41_41 = e3)
% 27.67/7.59 | (1508) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 27.67/7.59 |
% 27.67/7.59 +-Applying beta-rule and splitting (105), into two cases.
% 27.67/7.59 |-Branch one:
% 27.67/7.59 | (374) all_0_45_45 = e2
% 27.67/7.59 |
% 27.67/7.59 | Equations (374) can reduce 434 to:
% 27.67/7.59 | (270) $false
% 27.67/7.59 |
% 27.67/7.59 |-The branch is then unsatisfiable
% 27.67/7.59 |-Branch two:
% 27.67/7.59 | (434) ~ (all_0_45_45 = e2)
% 27.67/7.59 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 27.67/7.59 |
% 27.67/7.59 +-Applying beta-rule and splitting (435), into two cases.
% 27.67/7.59 |-Branch one:
% 27.67/7.59 | (454) all_0_45_45 = e0
% 27.67/7.59 |
% 27.67/7.59 | Equations (454) can reduce 488 to:
% 27.67/7.59 | (270) $false
% 27.67/7.59 |
% 27.67/7.59 |-The branch is then unsatisfiable
% 27.67/7.59 |-Branch two:
% 27.67/7.59 | (488) ~ (all_0_45_45 = e0)
% 27.67/7.59 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 27.67/7.59 |
% 27.67/7.59 +-Applying beta-rule and splitting (1508), into two cases.
% 27.67/7.59 |-Branch one:
% 27.67/7.59 | (505) all_0_45_45 = e3
% 27.67/7.59 |
% 27.67/7.59 | Equations (505) can reduce 38 to:
% 27.67/7.59 | (1518) ~ (all_0_46_46 = e3)
% 27.67/7.59 |
% 27.67/7.59 | Simplifying 1518 yields:
% 27.67/7.59 | (413) ~ (all_0_46_46 = e3)
% 27.67/7.59 |
% 27.67/7.59 +-Applying beta-rule and splitting (220), into two cases.
% 27.67/7.59 |-Branch one:
% 27.67/7.59 | (497) all_0_46_46 = e2
% 27.67/7.59 |
% 27.67/7.60 | Equations (497) can reduce 1436 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (1436) ~ (all_0_46_46 = e2)
% 27.67/7.60 | (1523) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e0
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (310), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (563) all_0_49_49 = e0
% 27.67/7.60 |
% 27.67/7.60 | Equations (563) can reduce 198 to:
% 27.67/7.60 | (1010) ~ (all_0_46_46 = e0)
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (1523), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (1132) all_0_46_46 = e0
% 27.67/7.60 |
% 27.67/7.60 | Equations (1132) can reduce 1010 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (1010) ~ (all_0_46_46 = e0)
% 27.67/7.60 | (1529) all_0_46_46 = e4 | all_0_46_46 = e3
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (1529), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (1091) all_0_46_46 = e3
% 27.67/7.60 |
% 27.67/7.60 | Equations (1091) can reduce 413 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (413) ~ (all_0_46_46 = e3)
% 27.67/7.60 | (517) all_0_46_46 = e4
% 27.67/7.60 |
% 27.67/7.60 | Equations (517) can reduce 805 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (1231) ~ (all_0_49_49 = e0)
% 27.67/7.60 | (589) all_0_49_49 = e1
% 27.67/7.60 |
% 27.67/7.60 | Equations (589) can reduce 543 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (354) ~ (all_0_45_45 = e3)
% 27.67/7.60 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (489), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (505) all_0_45_45 = e3
% 27.67/7.60 |
% 27.67/7.60 | Equations (505) can reduce 354 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (354) ~ (all_0_45_45 = e3)
% 27.67/7.60 | (363) all_0_45_45 = e4
% 27.67/7.60 |
% 27.67/7.60 | Equations (363) can reduce 352 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.67/7.60 |
% 27.67/7.60 | Applying alpha-rule on (428) yields:
% 27.67/7.60 | (423) all_0_53_53 = e0
% 27.67/7.60 | (424) all_0_59_59 = e1
% 27.67/7.60 | (431) ~ (all_0_58_58 = e0)
% 27.67/7.60 |
% 27.67/7.60 | Equations (423) can reduce 128 to:
% 27.67/7.60 | (488) ~ (all_0_45_45 = e0)
% 27.67/7.60 |
% 27.67/7.60 | Equations (424) can reduce 113 to:
% 27.67/7.60 | (543) ~ (all_0_49_49 = e1)
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (219), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (351) all_0_41_41 = e3
% 27.67/7.60 |
% 27.67/7.60 | Combining equations (351,358) yields a new equation:
% 27.67/7.60 | (359) e4 = e3
% 27.67/7.60 |
% 27.67/7.60 | Equations (359) can reduce 34 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (1237) ~ (all_0_41_41 = e3)
% 27.67/7.60 | (1508) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (105), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (374) all_0_45_45 = e2
% 27.67/7.60 |
% 27.67/7.60 | Equations (374) can reduce 434 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (434) ~ (all_0_45_45 = e2)
% 27.67/7.60 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (435), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (454) all_0_45_45 = e0
% 27.67/7.60 |
% 27.67/7.60 | Equations (454) can reduce 488 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (488) ~ (all_0_45_45 = e0)
% 27.67/7.60 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (1508), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (505) all_0_45_45 = e3
% 27.67/7.60 |
% 27.67/7.60 | Equations (505) can reduce 38 to:
% 27.67/7.60 | (1518) ~ (all_0_46_46 = e3)
% 27.67/7.60 |
% 27.67/7.60 | Simplifying 1518 yields:
% 27.67/7.60 | (413) ~ (all_0_46_46 = e3)
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (220), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (497) all_0_46_46 = e2
% 27.67/7.60 |
% 27.67/7.60 | Equations (497) can reduce 1436 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (1436) ~ (all_0_46_46 = e2)
% 27.67/7.60 | (1523) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e0
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (310), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (563) all_0_49_49 = e0
% 27.67/7.60 |
% 27.67/7.60 | Equations (563) can reduce 198 to:
% 27.67/7.60 | (1010) ~ (all_0_46_46 = e0)
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (1523), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (1132) all_0_46_46 = e0
% 27.67/7.60 |
% 27.67/7.60 | Equations (1132) can reduce 1010 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (1010) ~ (all_0_46_46 = e0)
% 27.67/7.60 | (1529) all_0_46_46 = e4 | all_0_46_46 = e3
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (1529), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (1091) all_0_46_46 = e3
% 27.67/7.60 |
% 27.67/7.60 | Equations (1091) can reduce 413 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (413) ~ (all_0_46_46 = e3)
% 27.67/7.60 | (517) all_0_46_46 = e4
% 27.67/7.60 |
% 27.67/7.60 | Equations (517) can reduce 805 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (1231) ~ (all_0_49_49 = e0)
% 27.67/7.60 | (589) all_0_49_49 = e1
% 27.67/7.60 |
% 27.67/7.60 | Equations (589) can reduce 543 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (354) ~ (all_0_45_45 = e3)
% 27.67/7.60 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (489), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (505) all_0_45_45 = e3
% 27.67/7.60 |
% 27.67/7.60 | Equations (505) can reduce 354 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (354) ~ (all_0_45_45 = e3)
% 27.67/7.60 | (363) all_0_45_45 = e4
% 27.67/7.60 |
% 27.67/7.60 | Equations (363) can reduce 352 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (510) ~ (all_0_43_43 = e4)
% 27.67/7.60 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (511), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (363) all_0_45_45 = e4
% 27.67/7.60 |
% 27.67/7.60 | Equations (363) can reduce 352 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (352) ~ (all_0_45_45 = e4)
% 27.67/7.60 | (517) all_0_46_46 = e4
% 27.67/7.60 |
% 27.67/7.60 | Equations (517) can reduce 38 to:
% 27.67/7.60 | (352) ~ (all_0_45_45 = e4)
% 27.67/7.60 |
% 27.67/7.60 | Equations (517) can reduce 198 to:
% 27.67/7.60 | (2914) ~ (all_0_49_49 = e4)
% 27.67/7.60 |
% 27.67/7.60 | Simplifying 2914 yields:
% 27.67/7.60 | (202) ~ (all_0_49_49 = e4)
% 27.67/7.60 |
% 27.67/7.60 | Equations (517) can reduce 215 to:
% 27.67/7.60 | (1599) ~ (all_0_54_54 = e4)
% 27.67/7.60 |
% 27.67/7.60 | Simplifying 1599 yields:
% 27.67/7.60 | (936) ~ (all_0_54_54 = e4)
% 27.67/7.60 |
% 27.67/7.60 | Equations (517) can reduce 206 to:
% 27.67/7.60 | (279) ~ (all_0_59_59 = e4)
% 27.67/7.60 |
% 27.67/7.60 | Simplifying 279 yields:
% 27.67/7.60 | (280) ~ (all_0_59_59 = e4)
% 27.67/7.60 |
% 27.67/7.60 | Equations (517) can reduce 1436 to:
% 27.67/7.60 | (231) ~ (e4 = e2)
% 27.67/7.60 |
% 27.67/7.60 | Equations (517) can reduce 106 to:
% 27.67/7.60 | (251) ~ (e4 = e1)
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (22), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (782) all_0_43_43 = e3
% 27.67/7.60 |
% 27.67/7.60 | Equations (782) can reduce 786 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (786) ~ (all_0_43_43 = e3)
% 27.67/7.60 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (189), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (267) all_0_50_50 = e4
% 27.67/7.60 |
% 27.67/7.60 | Combining equations (253,267) yields a new equation:
% 27.67/7.60 | (269) e4 = e2
% 27.67/7.60 |
% 27.67/7.60 | Equations (269) can reduce 231 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (271) ~ (all_0_50_50 = e4)
% 27.67/7.60 | (1466) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (1466), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (1467) all_0_51_51 = e4
% 27.67/7.60 |
% 27.67/7.60 | Equations (1467) can reduce 240 to:
% 27.67/7.60 | (510) ~ (all_0_43_43 = e4)
% 27.67/7.60 |
% 27.67/7.60 | Equations (1467) can reduce 154 to:
% 27.67/7.60 | (2933) ~ (all_0_52_52 = e4)
% 27.67/7.60 |
% 27.67/7.60 | Simplifying 2933 yields:
% 27.67/7.60 | (230) ~ (all_0_52_52 = e4)
% 27.67/7.60 |
% 27.67/7.60 | Equations (1467) can reduce 255 to:
% 27.67/7.60 | (231) ~ (e4 = e2)
% 27.67/7.60 |
% 27.67/7.60 | From (1467) and (171) follows:
% 27.67/7.60 | (2936) op(e1, e3) = e4
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (159), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (450) all_0_43_43 = e2
% 27.67/7.60 |
% 27.67/7.60 | Equations (450) can reduce 292 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (292) ~ (all_0_43_43 = e2)
% 27.67/7.60 | (774) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (680), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (321) all_0_47_47 = e1
% 27.67/7.60 |
% 27.67/7.60 | Combining equations (290,321) yields a new equation:
% 27.67/7.60 | (531) e2 = e1
% 27.67/7.60 |
% 27.67/7.60 | Simplifying 531 yields:
% 27.67/7.60 | (322) e2 = e1
% 27.67/7.60 |
% 27.67/7.60 | Equations (322) can reduce 141 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (324) ~ (all_0_47_47 = e1)
% 27.67/7.60 | (1625) all_0_51_51 = e1 | all_0_56_56 = e1
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (1625), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (820) all_0_51_51 = e1
% 27.67/7.60 |
% 27.67/7.60 | Combining equations (1467,820) yields a new equation:
% 27.67/7.60 | (525) e4 = e1
% 27.67/7.60 |
% 27.67/7.60 | Simplifying 525 yields:
% 27.67/7.60 | (526) e4 = e1
% 27.67/7.60 |
% 27.67/7.60 | Equations (526) can reduce 251 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (748) ~ (all_0_51_51 = e1)
% 27.67/7.60 | (747) all_0_56_56 = e1
% 27.67/7.60 |
% 27.67/7.60 | Equations (747) can reduce 188 to:
% 27.67/7.60 | (249) ~ (all_0_43_43 = e1)
% 27.67/7.60 |
% 27.67/7.60 | Equations (747) can reduce 185 to:
% 27.67/7.60 | (749) ~ (all_0_59_59 = e1)
% 27.67/7.60 |
% 27.67/7.60 | Simplifying 749 yields:
% 27.67/7.60 | (750) ~ (all_0_59_59 = e1)
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (774), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (411) all_0_43_43 = e0
% 27.67/7.60 |
% 27.67/7.60 | Equations (411) can reduce 84 to:
% 27.67/7.60 | (776) ~ (all_0_45_45 = e0)
% 27.67/7.60 |
% 27.67/7.60 | Simplifying 776 yields:
% 27.67/7.60 | (488) ~ (all_0_45_45 = e0)
% 27.67/7.60 |
% 27.67/7.60 | Equations (411) can reduce 249 to:
% 27.67/7.60 | (568) ~ (e1 = e0)
% 27.67/7.60 |
% 27.67/7.60 | Simplifying 568 yields:
% 27.67/7.60 | (132) ~ (e1 = e0)
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (105), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (374) all_0_45_45 = e2
% 27.67/7.60 |
% 27.67/7.60 | Equations (374) can reduce 434 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (434) ~ (all_0_45_45 = e2)
% 27.67/7.60 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (435), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (454) all_0_45_45 = e0
% 27.67/7.60 |
% 27.67/7.60 | Equations (454) can reduce 488 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (488) ~ (all_0_45_45 = e0)
% 27.67/7.60 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (489), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (505) all_0_45_45 = e3
% 27.67/7.60 |
% 27.67/7.60 | Equations (505) can reduce 65 to:
% 27.67/7.60 | (713) ~ (all_0_48_48 = e3)
% 27.67/7.60 |
% 27.67/7.60 | Simplifying 713 yields:
% 27.67/7.60 | (121) ~ (all_0_48_48 = e3)
% 27.67/7.60 |
% 27.67/7.60 | Equations (505) can reduce 128 to:
% 27.67/7.60 | (355) ~ (all_0_53_53 = e3)
% 27.67/7.60 |
% 27.67/7.60 | Simplifying 355 yields:
% 27.67/7.60 | (356) ~ (all_0_53_53 = e3)
% 27.67/7.60 |
% 27.67/7.60 | Equations (505) can reduce 488 to:
% 27.67/7.60 | (66) ~ (e3 = e0)
% 27.67/7.60 |
% 27.67/7.60 | From (505) and (142) follows:
% 27.67/7.60 | (2975) op(e1, e3) = all_0_23_23
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (93), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (402) all_0_59_59 = e4
% 27.67/7.60 |
% 27.67/7.60 | Equations (402) can reduce 280 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (280) ~ (all_0_59_59 = e4)
% 27.67/7.60 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (407), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (408), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (409), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.67/7.60 |
% 27.67/7.60 | Applying alpha-rule on (410) yields:
% 27.67/7.60 | (411) all_0_43_43 = e0
% 27.67/7.60 | (412) all_0_59_59 = e3
% 27.67/7.60 | (413) ~ (all_0_46_46 = e3)
% 27.67/7.60 |
% 27.67/7.60 | Equations (412) can reduce 113 to:
% 27.67/7.60 | (150) ~ (all_0_49_49 = e3)
% 27.67/7.60 |
% 27.67/7.60 | Equations (412) can reduce 72 to:
% 27.67/7.60 | (1093) ~ (all_0_54_54 = e3)
% 27.67/7.60 |
% 27.67/7.60 | Equations (412) can reduce 280 to:
% 27.67/7.60 | (719) ~ (e4 = e3)
% 27.67/7.60 |
% 27.67/7.60 | Simplifying 719 yields:
% 27.67/7.60 | (34) ~ (e4 = e3)
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (176), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (830) all_0_56_56 = e0
% 27.67/7.60 |
% 27.67/7.60 | Combining equations (830,747) yields a new equation:
% 27.67/7.60 | (560) e1 = e0
% 27.67/7.60 |
% 27.67/7.60 | Equations (560) can reduce 132 to:
% 27.67/7.60 | (270) $false
% 27.67/7.60 |
% 27.67/7.60 |-The branch is then unsatisfiable
% 27.67/7.60 |-Branch two:
% 27.67/7.60 | (419) ~ (all_0_56_56 = e0)
% 27.67/7.60 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (834), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.60 | (2258) all_0_57_57 = e0
% 27.67/7.60 |
% 27.67/7.60 | From (2258) and (1765) follows:
% 27.67/7.60 | (2996) op(e2, e0) = e0
% 27.67/7.60 |
% 27.67/7.60 +-Applying beta-rule and splitting (21), into two cases.
% 27.67/7.60 |-Branch one:
% 27.67/7.61 | (824) all_0_51_51 = e3
% 27.67/7.61 |
% 27.67/7.61 | Combining equations (1467,824) yields a new equation:
% 27.67/7.61 | (660) e4 = e3
% 27.67/7.61 |
% 27.67/7.61 | Simplifying 660 yields:
% 27.67/7.61 | (359) e4 = e3
% 27.67/7.61 |
% 27.67/7.61 | Equations (359) can reduce 34 to:
% 27.67/7.61 | (270) $false
% 27.67/7.61 |
% 27.67/7.61 |-The branch is then unsatisfiable
% 27.67/7.61 |-Branch two:
% 27.67/7.61 | (932) ~ (all_0_51_51 = e3)
% 27.67/7.61 | (1101) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 27.67/7.61 |
% 27.67/7.61 +-Applying beta-rule and splitting (1101), into two cases.
% 27.67/7.61 |-Branch one:
% 27.67/7.61 | (864) all_0_52_52 = e3
% 27.67/7.61 |
% 27.67/7.61 | Combining equations (864,1848) yields a new equation:
% 27.67/7.61 | (2237) all_0_28_28 = e3
% 27.67/7.61 |
% 27.67/7.61 | Equations (864) can reduce 230 to:
% 27.67/7.61 | (719) ~ (e4 = e3)
% 27.67/7.61 |
% 27.67/7.61 | Simplifying 719 yields:
% 27.67/7.61 | (34) ~ (e4 = e3)
% 27.67/7.61 |
% 27.67/7.61 | Instantiating formula (201) with e2, e0, e0, all_0_49_49 and discharging atoms op(e2, e0) = all_0_49_49, op(e2, e0) = e0, yields:
% 27.67/7.61 | (563) all_0_49_49 = e0
% 27.67/7.61 |
% 27.67/7.61 | Instantiating formula (201) with e1, e3, e4, all_0_23_23 and discharging atoms op(e1, e3) = all_0_23_23, op(e1, e3) = e4, yields:
% 27.67/7.61 | (3008) all_0_23_23 = e4
% 27.67/7.61 |
% 27.67/7.61 | Equations (563) can reduce 4 to:
% 27.67/7.61 | (562) ~ (all_0_48_48 = e0)
% 27.67/7.61 |
% 27.67/7.61 | Equations (563) can reduce 162 to:
% 27.67/7.61 | (3010) ~ (all_0_54_54 = e0)
% 27.67/7.61 |
% 27.67/7.61 | Simplifying 3010 yields:
% 27.67/7.61 | (3011) ~ (all_0_54_54 = e0)
% 27.67/7.61 |
% 27.67/7.61 | Equations (563) can reduce 202 to:
% 27.67/7.61 | (456) ~ (e4 = e0)
% 27.67/7.61 |
% 27.67/7.61 | Simplifying 456 yields:
% 27.67/7.61 | (6) ~ (e4 = e0)
% 27.67/7.61 |
% 27.67/7.61 | Equations (563) can reduce 150 to:
% 27.67/7.61 | (788) ~ (e3 = e0)
% 27.67/7.61 |
% 27.67/7.61 | Simplifying 788 yields:
% 27.67/7.61 | (66) ~ (e3 = e0)
% 27.67/7.61 |
% 27.67/7.61 +-Applying beta-rule and splitting (14), into two cases.
% 27.67/7.61 |-Branch one:
% 27.67/7.61 | (2277) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1))
% 27.67/7.61 |
% 27.67/7.61 +-Applying beta-rule and splitting (2277), into two cases.
% 27.67/7.61 |-Branch one:
% 27.67/7.61 | (2278) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1))
% 27.67/7.61 |
% 27.67/7.61 +-Applying beta-rule and splitting (2278), into two cases.
% 27.67/7.61 |-Branch one:
% 27.67/7.61 | (2279) all_0_21_21 = e4 & ~ (all_0_22_22 = e1)
% 27.67/7.61 |
% 27.67/7.61 | Applying alpha-rule on (2279) yields:
% 27.67/7.61 | (2280) all_0_21_21 = e4
% 27.67/7.61 | (2281) ~ (all_0_22_22 = e1)
% 27.67/7.61 |
% 27.67/7.61 | Combining equations (2280,2760) yields a new equation:
% 27.67/7.61 | (268) e4 = e2
% 27.67/7.61 |
% 27.67/7.61 | Simplifying 268 yields:
% 27.67/7.61 | (269) e4 = e2
% 27.67/7.61 |
% 27.67/7.61 | Equations (269) can reduce 231 to:
% 27.67/7.61 | (270) $false
% 27.67/7.61 |
% 27.67/7.61 |-The branch is then unsatisfiable
% 27.67/7.61 |-Branch two:
% 27.67/7.61 | (2285) all_0_23_23 = e3 & ~ (all_0_24_24 = e1)
% 27.67/7.61 |
% 27.67/7.61 | Applying alpha-rule on (2285) yields:
% 27.67/7.61 | (2286) all_0_23_23 = e3
% 27.67/7.61 | (2287) ~ (all_0_24_24 = e1)
% 27.67/7.61 |
% 27.67/7.61 | Combining equations (2286,3008) yields a new equation:
% 27.67/7.61 | (359) e4 = e3
% 27.67/7.61 |
% 27.67/7.61 | Equations (359) can reduce 34 to:
% 27.67/7.61 | (270) $false
% 27.67/7.61 |
% 27.67/7.61 |-The branch is then unsatisfiable
% 27.67/7.61 |-Branch two:
% 27.67/7.61 | (2291) all_0_25_25 = e2 & ~ (all_0_26_26 = e1)
% 27.67/7.61 |
% 27.67/7.61 | Applying alpha-rule on (2291) yields:
% 27.67/7.61 | (2292) all_0_25_25 = e2
% 27.67/7.61 | (2293) ~ (all_0_26_26 = e1)
% 27.67/7.61 |
% 27.67/7.61 | From (2292) and (76) follows:
% 27.67/7.61 | (3032) op(e1, all_0_48_48) = e2
% 27.67/7.61 |
% 27.67/7.61 +-Applying beta-rule and splitting (314), into two cases.
% 27.67/7.61 |-Branch one:
% 27.67/7.61 | (559) all_0_48_48 = e0
% 27.67/7.61 |
% 27.67/7.61 | Equations (559) can reduce 562 to:
% 27.67/7.61 | (270) $false
% 27.67/7.61 |
% 27.67/7.61 |-The branch is then unsatisfiable
% 27.67/7.61 |-Branch two:
% 27.67/7.61 | (562) ~ (all_0_48_48 = e0)
% 27.67/7.61 | (552) all_0_48_48 = e1
% 27.67/7.61 |
% 27.67/7.61 | Equations (552) can reduce 48 to:
% 27.67/7.61 | (1016) ~ (all_0_53_53 = e1)
% 27.67/7.61 |
% 27.67/7.61 | Simplifying 1016 yields:
% 27.67/7.61 | (874) ~ (all_0_53_53 = e1)
% 27.67/7.61 |
% 27.67/7.61 | Equations (552) can reduce 192 to:
% 27.67/7.61 | (1021) ~ (e4 = e1)
% 27.67/7.61 |
% 27.67/7.61 | Simplifying 1021 yields:
% 27.67/7.61 | (251) ~ (e4 = e1)
% 27.67/7.61 |
% 27.67/7.61 | Equations (552) can reduce 121 to:
% 27.67/7.61 | (769) ~ (e3 = e1)
% 27.67/7.61 |
% 27.67/7.61 | Simplifying 769 yields:
% 27.67/7.61 | (136) ~ (e3 = e1)
% 27.67/7.61 |
% 27.67/7.61 | From (552) and (3032) follows:
% 27.67/7.61 | (3043) op(e1, e1) = e2
% 27.67/7.61 |
% 27.67/7.61 +-Applying beta-rule and splitting (135), into two cases.
% 27.67/7.61 |-Branch one:
% 27.67/7.61 | (820) all_0_51_51 = e1
% 27.67/7.61 |
% 27.67/7.61 | Combining equations (1467,820) yields a new equation:
% 27.67/7.61 | (525) e4 = e1
% 27.67/7.61 |
% 27.67/7.61 | Simplifying 525 yields:
% 27.67/7.61 | (526) e4 = e1
% 27.67/7.61 |
% 27.67/7.61 | Equations (526) can reduce 251 to:
% 27.67/7.61 | (270) $false
% 27.67/7.61 |
% 27.67/7.61 |-The branch is then unsatisfiable
% 27.67/7.61 |-Branch two:
% 27.67/7.61 | (748) ~ (all_0_51_51 = e1)
% 27.67/7.61 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 27.67/7.61 |
% 27.67/7.61 +-Applying beta-rule and splitting (823), into two cases.
% 27.67/7.61 |-Branch one:
% 27.67/7.61 | (848) all_0_52_52 = e1
% 27.67/7.61 |
% 27.67/7.61 | Combining equations (864,848) yields a new equation:
% 27.67/7.61 | (537) e3 = e1
% 27.67/7.61 |
% 27.67/7.61 | Simplifying 537 yields:
% 27.67/7.61 | (538) e3 = e1
% 27.67/7.61 |
% 27.67/7.61 | Equations (538) can reduce 136 to:
% 27.67/7.61 | (270) $false
% 27.67/7.61 |
% 27.67/7.61 |-The branch is then unsatisfiable
% 27.67/7.61 |-Branch two:
% 27.67/7.61 | (642) ~ (all_0_52_52 = e1)
% 27.67/7.61 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 27.67/7.61 |
% 27.67/7.61 +-Applying beta-rule and splitting (852), into two cases.
% 27.67/7.61 |-Branch one:
% 27.67/7.61 | (853) all_0_53_53 = e1
% 27.67/7.61 |
% 27.67/7.61 | Equations (853) can reduce 874 to:
% 27.67/7.61 | (270) $false
% 27.67/7.61 |
% 27.67/7.61 |-The branch is then unsatisfiable
% 27.67/7.61 |-Branch two:
% 27.67/7.61 | (874) ~ (all_0_53_53 = e1)
% 27.67/7.61 | (875) all_0_54_54 = e1
% 27.67/7.61 |
% 27.67/7.61 | Equations (875) can reduce 3011 to:
% 27.67/7.61 | (132) ~ (e1 = e0)
% 27.67/7.61 |
% 27.67/7.61 | From (875) and (29) follows:
% 27.67/7.61 | (3061) op(e1, e1) = all_0_37_37
% 27.67/7.61 |
% 27.67/7.61 +-Applying beta-rule and splitting (64), into two cases.
% 27.67/7.61 |-Branch one:
% 27.67/7.61 | (954) all_0_51_51 = e0
% 27.67/7.61 |
% 27.67/7.61 | Combining equations (1467,954) yields a new equation:
% 27.67/7.61 | (478) e4 = e0
% 27.67/7.61 |
% 27.67/7.61 | Simplifying 478 yields:
% 27.67/7.61 | (479) e4 = e0
% 27.67/7.61 |
% 27.67/7.61 | Equations (479) can reduce 6 to:
% 27.67/7.61 | (270) $false
% 27.67/7.61 |
% 27.67/7.61 |-The branch is then unsatisfiable
% 27.67/7.61 |-Branch two:
% 27.67/7.61 | (987) ~ (all_0_51_51 = e0)
% 27.67/7.61 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 27.67/7.61 |
% 27.67/7.61 +-Applying beta-rule and splitting (3067), into two cases.
% 27.67/7.61 |-Branch one:
% 27.67/7.61 | (827) all_0_52_52 = e0
% 27.67/7.61 |
% 27.67/7.61 | Combining equations (864,827) yields a new equation:
% 27.67/7.61 | (783) e3 = e0
% 27.67/7.61 |
% 27.67/7.61 | Simplifying 783 yields:
% 27.67/7.61 | (784) e3 = e0
% 27.67/7.61 |
% 27.67/7.61 | Equations (784) can reduce 66 to:
% 27.67/7.61 | (270) $false
% 27.67/7.61 |
% 27.67/7.61 |-The branch is then unsatisfiable
% 27.67/7.61 |-Branch two:
% 27.67/7.61 | (925) ~ (all_0_52_52 = e0)
% 27.67/7.61 | (3073) all_0_53_53 = e0 | all_0_54_54 = e0
% 27.67/7.61 |
% 27.67/7.61 +-Applying beta-rule and splitting (3073), into two cases.
% 27.67/7.61 |-Branch one:
% 27.67/7.61 | (423) all_0_53_53 = e0
% 27.67/7.61 |
% 27.67/7.61 | Equations (423) can reduce 259 to:
% 27.67/7.61 | (566) ~ (e2 = e0)
% 27.67/7.61 |
% 27.67/7.61 | Simplifying 566 yields:
% 27.67/7.61 | (57) ~ (e2 = e0)
% 27.67/7.61 |
% 27.67/7.61 | From (423) and (227) follows:
% 27.67/7.61 | (2167) op(e1, e1) = e0
% 27.67/7.61 |
% 27.67/7.61 | Instantiating formula (201) with e1, e1, e2, all_0_37_37 and discharging atoms op(e1, e1) = all_0_37_37, op(e1, e1) = e2, yields:
% 27.67/7.61 | (2275) all_0_37_37 = e2
% 27.67/7.61 |
% 27.67/7.61 | Instantiating formula (201) with e1, e1, e0, all_0_37_37 and discharging atoms op(e1, e1) = all_0_37_37, op(e1, e1) = e0, yields:
% 27.67/7.61 | (3079) all_0_37_37 = e0
% 27.67/7.61 |
% 27.67/7.61 | Combining equations (2275,3079) yields a new equation:
% 27.67/7.61 | (622) e2 = e0
% 27.67/7.61 |
% 27.67/7.61 | Simplifying 622 yields:
% 27.67/7.61 | (316) e2 = e0
% 27.67/7.61 |
% 27.67/7.61 | Equations (316) can reduce 57 to:
% 27.67/7.61 | (270) $false
% 27.67/7.61 |
% 27.67/7.61 |-The branch is then unsatisfiable
% 27.67/7.61 |-Branch two:
% 27.67/7.61 | (584) ~ (all_0_53_53 = e0)
% 27.67/7.61 | (3084) all_0_54_54 = e0
% 27.67/7.61 |
% 27.67/7.61 | Combining equations (875,3084) yields a new equation:
% 27.67/7.61 | (571) e1 = e0
% 27.67/7.61 |
% 27.67/7.61 | Simplifying 571 yields:
% 27.67/7.61 | (560) e1 = e0
% 27.67/7.61 |
% 27.67/7.61 | Equations (560) can reduce 132 to:
% 27.67/7.61 | (270) $false
% 27.67/7.61 |
% 27.67/7.61 |-The branch is then unsatisfiable
% 27.67/7.61 |-Branch two:
% 27.67/7.61 | (2296) all_0_28_28 = e0 & ~ (all_0_29_29 = e1)
% 27.67/7.61 |
% 27.67/7.61 | Applying alpha-rule on (2296) yields:
% 27.67/7.61 | (2297) all_0_28_28 = e0
% 27.67/7.61 | (2298) ~ (all_0_29_29 = e1)
% 27.67/7.61 |
% 27.67/7.61 | Combining equations (2297,2237) yields a new equation:
% 27.67/7.61 | (784) e3 = e0
% 27.67/7.61 |
% 27.67/7.61 | Equations (784) can reduce 66 to:
% 27.67/7.61 | (270) $false
% 27.67/7.61 |
% 27.67/7.61 |-The branch is then unsatisfiable
% 27.67/7.61 |-Branch two:
% 27.67/7.61 | (826) ~ (all_0_52_52 = e3)
% 27.67/7.61 | (1107) all_0_53_53 = e3 | all_0_54_54 = e3
% 27.67/7.61 |
% 27.67/7.61 +-Applying beta-rule and splitting (1107), into two cases.
% 27.67/7.61 |-Branch one:
% 27.67/7.61 | (1114) all_0_53_53 = e3
% 27.67/7.61 |
% 27.67/7.61 | Equations (1114) can reduce 356 to:
% 27.67/7.61 | (270) $false
% 27.67/7.61 |
% 27.67/7.61 |-The branch is then unsatisfiable
% 27.67/7.61 |-Branch two:
% 27.67/7.61 | (356) ~ (all_0_53_53 = e3)
% 27.67/7.61 | (1119) all_0_54_54 = e3
% 27.67/7.61 |
% 27.67/7.61 | Equations (1119) can reduce 1093 to:
% 27.67/7.61 | (270) $false
% 27.67/7.61 |
% 27.67/7.61 |-The branch is then unsatisfiable
% 27.67/7.61 |-Branch two:
% 27.67/7.61 | (2301) ~ (all_0_57_57 = e0)
% 27.67/7.61 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 27.67/7.61 |
% 27.67/7.61 +-Applying beta-rule and splitting (626), into two cases.
% 27.67/7.61 |-Branch one:
% 27.67/7.61 | (827) all_0_52_52 = e0
% 27.67/7.61 |
% 27.67/7.61 | Equations (827) can reduce 213 to:
% 27.67/7.61 | (3103) ~ (all_0_53_53 = e0)
% 27.67/7.61 |
% 27.67/7.62 | Simplifying 3103 yields:
% 27.67/7.62 | (584) ~ (all_0_53_53 = e0)
% 27.67/7.62 |
% 27.67/7.62 | Equations (827) can reduce 257 to:
% 27.67/7.62 | (566) ~ (e2 = e0)
% 27.67/7.62 |
% 27.67/7.62 | Simplifying 566 yields:
% 27.67/7.62 | (57) ~ (e2 = e0)
% 27.67/7.62 |
% 27.67/7.62 +-Applying beta-rule and splitting (182), into two cases.
% 27.67/7.62 |-Branch one:
% 27.67/7.62 | (454) all_0_45_45 = e0
% 27.67/7.62 |
% 27.67/7.62 | Combining equations (505,454) yields a new equation:
% 27.67/7.62 | (783) e3 = e0
% 27.67/7.62 |
% 27.67/7.62 | Simplifying 783 yields:
% 27.67/7.62 | (784) e3 = e0
% 27.67/7.62 |
% 27.67/7.62 | Equations (784) can reduce 66 to:
% 27.67/7.62 | (270) $false
% 27.67/7.62 |
% 27.67/7.62 |-The branch is then unsatisfiable
% 27.67/7.62 |-Branch two:
% 27.67/7.62 | (488) ~ (all_0_45_45 = e0)
% 27.67/7.62 | (558) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 27.67/7.62 |
% 27.67/7.62 +-Applying beta-rule and splitting (558), into two cases.
% 27.67/7.62 |-Branch one:
% 27.67/7.62 | (559) all_0_48_48 = e0
% 27.67/7.62 |
% 27.67/7.62 | Equations (559) can reduce 121 to:
% 27.67/7.62 | (788) ~ (e3 = e0)
% 27.67/7.62 |
% 27.67/7.62 | Simplifying 788 yields:
% 27.67/7.62 | (66) ~ (e3 = e0)
% 27.67/7.62 |
% 27.67/7.62 | Equations (559) can reduce 294 to:
% 27.67/7.62 | (566) ~ (e2 = e0)
% 27.67/7.62 |
% 27.67/7.62 | Simplifying 566 yields:
% 27.67/7.62 | (57) ~ (e2 = e0)
% 27.67/7.62 |
% 27.67/7.62 +-Applying beta-rule and splitting (2302), into two cases.
% 27.67/7.62 |-Branch one:
% 27.67/7.62 | (585) all_0_58_58 = e0
% 27.67/7.62 |
% 27.67/7.62 | Combining equations (585,396) yields a new equation:
% 27.67/7.62 | (316) e2 = e0
% 27.67/7.62 |
% 27.67/7.62 | Equations (316) can reduce 57 to:
% 27.67/7.62 | (270) $false
% 27.67/7.62 |
% 27.67/7.62 |-The branch is then unsatisfiable
% 27.67/7.62 |-Branch two:
% 27.67/7.62 | (431) ~ (all_0_58_58 = e0)
% 27.67/7.62 | (2308) all_0_59_59 = e0
% 27.67/7.62 |
% 27.67/7.62 | Combining equations (412,2308) yields a new equation:
% 27.67/7.62 | (783) e3 = e0
% 27.67/7.62 |
% 27.67/7.62 | Simplifying 783 yields:
% 27.67/7.62 | (784) e3 = e0
% 27.67/7.62 |
% 27.67/7.62 | Equations (784) can reduce 66 to:
% 27.67/7.62 | (270) $false
% 27.67/7.62 |
% 27.67/7.62 |-The branch is then unsatisfiable
% 27.67/7.62 |-Branch two:
% 27.67/7.62 | (562) ~ (all_0_48_48 = e0)
% 27.67/7.62 | (575) all_0_53_53 = e0 | all_0_58_58 = e0
% 27.67/7.62 |
% 27.67/7.62 +-Applying beta-rule and splitting (575), into two cases.
% 27.67/7.62 |-Branch one:
% 27.67/7.62 | (423) all_0_53_53 = e0
% 27.67/7.62 |
% 27.67/7.62 | Equations (423) can reduce 584 to:
% 27.67/7.62 | (270) $false
% 27.67/7.62 |
% 27.67/7.62 |-The branch is then unsatisfiable
% 27.67/7.62 |-Branch two:
% 27.67/7.62 | (584) ~ (all_0_53_53 = e0)
% 27.67/7.62 | (585) all_0_58_58 = e0
% 27.67/7.62 |
% 27.67/7.62 | Combining equations (585,396) yields a new equation:
% 27.67/7.62 | (316) e2 = e0
% 27.67/7.62 |
% 27.67/7.62 | Equations (316) can reduce 57 to:
% 27.67/7.62 | (270) $false
% 27.67/7.62 |
% 27.67/7.62 |-The branch is then unsatisfiable
% 27.67/7.62 |-Branch two:
% 27.67/7.62 | (925) ~ (all_0_52_52 = e0)
% 27.67/7.62 | (2258) all_0_57_57 = e0
% 27.67/7.62 |
% 27.67/7.62 | Equations (2258) can reduce 2301 to:
% 27.67/7.62 | (270) $false
% 27.67/7.62 |
% 27.67/7.62 |-The branch is then unsatisfiable
% 27.67/7.62 |-Branch two:
% 27.67/7.62 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.67/7.62 |
% 27.67/7.62 | Applying alpha-rule on (416) yields:
% 27.67/7.62 | (411) all_0_43_43 = e0
% 27.67/7.62 | (412) all_0_59_59 = e3
% 27.67/7.62 | (419) ~ (all_0_56_56 = e0)
% 27.67/7.62 |
% 27.67/7.62 | Equations (412) can reduce 113 to:
% 27.67/7.62 | (150) ~ (all_0_49_49 = e3)
% 27.67/7.62 |
% 27.67/7.62 | Equations (412) can reduce 72 to:
% 27.67/7.62 | (1093) ~ (all_0_54_54 = e3)
% 27.67/7.62 |
% 27.67/7.62 | Equations (747) can reduce 419 to:
% 27.67/7.62 | (132) ~ (e1 = e0)
% 27.67/7.62 |
% 27.67/7.62 | Equations (412) can reduce 280 to:
% 27.67/7.62 | (719) ~ (e4 = e3)
% 27.67/7.62 |
% 27.67/7.62 | Simplifying 719 yields:
% 27.67/7.62 | (34) ~ (e4 = e3)
% 27.67/7.62 |
% 27.67/7.62 +-Applying beta-rule and splitting (176), into two cases.
% 27.67/7.62 |-Branch one:
% 27.67/7.62 | (830) all_0_56_56 = e0
% 27.67/7.62 |
% 27.67/7.62 | Combining equations (830,747) yields a new equation:
% 27.67/7.62 | (560) e1 = e0
% 27.67/7.62 |
% 27.67/7.62 | Equations (560) can reduce 132 to:
% 27.67/7.62 | (270) $false
% 27.67/7.62 |
% 27.67/7.62 |-The branch is then unsatisfiable
% 27.67/7.62 |-Branch two:
% 27.67/7.62 | (419) ~ (all_0_56_56 = e0)
% 27.67/7.62 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 27.67/7.62 |
% 27.67/7.62 +-Applying beta-rule and splitting (834), into two cases.
% 27.67/7.62 |-Branch one:
% 27.67/7.62 | (2258) all_0_57_57 = e0
% 27.67/7.62 |
% 27.67/7.62 | From (2258) and (1765) follows:
% 27.67/7.62 | (2996) op(e2, e0) = e0
% 27.67/7.62 |
% 27.67/7.62 +-Applying beta-rule and splitting (21), into two cases.
% 27.67/7.62 |-Branch one:
% 27.67/7.62 | (824) all_0_51_51 = e3
% 27.67/7.62 |
% 27.67/7.62 | Combining equations (1467,824) yields a new equation:
% 27.67/7.62 | (660) e4 = e3
% 27.67/7.62 |
% 27.67/7.62 | Simplifying 660 yields:
% 27.67/7.62 | (359) e4 = e3
% 27.67/7.62 |
% 27.67/7.62 | Equations (359) can reduce 34 to:
% 27.67/7.62 | (270) $false
% 27.67/7.62 |
% 27.67/7.62 |-The branch is then unsatisfiable
% 27.67/7.62 |-Branch two:
% 27.67/7.62 | (932) ~ (all_0_51_51 = e3)
% 27.67/7.62 | (1101) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 27.67/7.62 |
% 27.67/7.62 +-Applying beta-rule and splitting (1101), into two cases.
% 27.67/7.62 |-Branch one:
% 27.67/7.62 | (864) all_0_52_52 = e3
% 27.67/7.62 |
% 27.67/7.62 | Combining equations (864,1848) yields a new equation:
% 27.67/7.62 | (2237) all_0_28_28 = e3
% 27.67/7.62 |
% 27.67/7.62 | Equations (864) can reduce 230 to:
% 27.67/7.62 | (719) ~ (e4 = e3)
% 27.67/7.62 |
% 27.67/7.62 | Simplifying 719 yields:
% 27.67/7.62 | (34) ~ (e4 = e3)
% 27.67/7.62 |
% 27.67/7.62 | Instantiating formula (201) with e2, e0, e0, all_0_49_49 and discharging atoms op(e2, e0) = all_0_49_49, op(e2, e0) = e0, yields:
% 27.67/7.62 | (563) all_0_49_49 = e0
% 27.67/7.62 |
% 27.67/7.62 | Instantiating formula (201) with e1, e3, e4, all_0_23_23 and discharging atoms op(e1, e3) = all_0_23_23, op(e1, e3) = e4, yields:
% 27.67/7.62 | (3008) all_0_23_23 = e4
% 27.67/7.62 |
% 27.67/7.62 | Equations (563) can reduce 4 to:
% 27.67/7.62 | (562) ~ (all_0_48_48 = e0)
% 27.67/7.62 |
% 27.67/7.62 | Equations (563) can reduce 162 to:
% 27.67/7.62 | (3010) ~ (all_0_54_54 = e0)
% 27.67/7.62 |
% 27.67/7.62 | Simplifying 3010 yields:
% 27.67/7.62 | (3011) ~ (all_0_54_54 = e0)
% 27.67/7.62 |
% 27.67/7.62 | Equations (563) can reduce 202 to:
% 27.67/7.62 | (456) ~ (e4 = e0)
% 27.67/7.62 |
% 27.67/7.62 | Simplifying 456 yields:
% 27.67/7.62 | (6) ~ (e4 = e0)
% 27.67/7.62 |
% 27.67/7.62 | Equations (563) can reduce 150 to:
% 27.67/7.62 | (788) ~ (e3 = e0)
% 27.67/7.62 |
% 27.67/7.62 | Simplifying 788 yields:
% 27.67/7.62 | (66) ~ (e3 = e0)
% 27.67/7.62 |
% 27.67/7.62 +-Applying beta-rule and splitting (14), into two cases.
% 27.67/7.62 |-Branch one:
% 27.67/7.62 | (2277) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1))
% 27.67/7.62 |
% 27.67/7.62 +-Applying beta-rule and splitting (2277), into two cases.
% 27.67/7.62 |-Branch one:
% 27.67/7.62 | (2278) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1))
% 27.67/7.62 |
% 27.67/7.62 +-Applying beta-rule and splitting (2278), into two cases.
% 27.67/7.62 |-Branch one:
% 27.67/7.62 | (2279) all_0_21_21 = e4 & ~ (all_0_22_22 = e1)
% 27.67/7.62 |
% 27.67/7.62 | Applying alpha-rule on (2279) yields:
% 27.67/7.62 | (2280) all_0_21_21 = e4
% 27.67/7.62 | (2281) ~ (all_0_22_22 = e1)
% 27.67/7.62 |
% 27.67/7.62 | Combining equations (2280,2760) yields a new equation:
% 27.67/7.62 | (268) e4 = e2
% 27.67/7.62 |
% 27.67/7.62 | Simplifying 268 yields:
% 27.67/7.62 | (269) e4 = e2
% 27.67/7.62 |
% 27.67/7.62 | Equations (269) can reduce 231 to:
% 27.67/7.62 | (270) $false
% 27.67/7.62 |
% 27.67/7.62 |-The branch is then unsatisfiable
% 27.67/7.62 |-Branch two:
% 27.67/7.62 | (2285) all_0_23_23 = e3 & ~ (all_0_24_24 = e1)
% 27.67/7.62 |
% 27.67/7.62 | Applying alpha-rule on (2285) yields:
% 27.67/7.62 | (2286) all_0_23_23 = e3
% 27.67/7.62 | (2287) ~ (all_0_24_24 = e1)
% 27.67/7.62 |
% 27.67/7.62 | Combining equations (2286,3008) yields a new equation:
% 27.67/7.62 | (359) e4 = e3
% 27.67/7.62 |
% 27.67/7.62 | Equations (359) can reduce 34 to:
% 27.67/7.62 | (270) $false
% 27.67/7.62 |
% 27.67/7.62 |-The branch is then unsatisfiable
% 27.67/7.62 |-Branch two:
% 27.67/7.62 | (2291) all_0_25_25 = e2 & ~ (all_0_26_26 = e1)
% 27.67/7.62 |
% 27.67/7.62 | Applying alpha-rule on (2291) yields:
% 27.67/7.62 | (2292) all_0_25_25 = e2
% 27.67/7.62 | (2293) ~ (all_0_26_26 = e1)
% 27.67/7.62 |
% 27.67/7.62 | From (2292) and (76) follows:
% 27.67/7.62 | (3032) op(e1, all_0_48_48) = e2
% 27.67/7.62 |
% 27.67/7.62 +-Applying beta-rule and splitting (314), into two cases.
% 27.67/7.62 |-Branch one:
% 27.67/7.62 | (559) all_0_48_48 = e0
% 27.67/7.62 |
% 27.67/7.62 | Equations (559) can reduce 562 to:
% 27.67/7.62 | (270) $false
% 27.67/7.62 |
% 27.67/7.62 |-The branch is then unsatisfiable
% 27.67/7.62 |-Branch two:
% 27.67/7.62 | (562) ~ (all_0_48_48 = e0)
% 27.67/7.62 | (552) all_0_48_48 = e1
% 27.67/7.62 |
% 27.67/7.62 | Equations (552) can reduce 48 to:
% 27.67/7.62 | (1016) ~ (all_0_53_53 = e1)
% 27.67/7.62 |
% 27.67/7.62 | Simplifying 1016 yields:
% 27.67/7.62 | (874) ~ (all_0_53_53 = e1)
% 27.67/7.62 |
% 27.67/7.62 | Equations (552) can reduce 192 to:
% 27.67/7.62 | (1021) ~ (e4 = e1)
% 27.67/7.62 |
% 27.67/7.62 | Simplifying 1021 yields:
% 27.67/7.62 | (251) ~ (e4 = e1)
% 27.67/7.62 |
% 27.67/7.62 | Equations (552) can reduce 121 to:
% 27.67/7.62 | (769) ~ (e3 = e1)
% 27.67/7.62 |
% 27.67/7.62 | Simplifying 769 yields:
% 27.67/7.62 | (136) ~ (e3 = e1)
% 27.67/7.62 |
% 27.67/7.62 | From (552) and (3032) follows:
% 27.67/7.62 | (3043) op(e1, e1) = e2
% 27.67/7.62 |
% 27.67/7.62 +-Applying beta-rule and splitting (135), into two cases.
% 27.67/7.62 |-Branch one:
% 27.67/7.62 | (820) all_0_51_51 = e1
% 27.67/7.62 |
% 27.67/7.62 | Combining equations (1467,820) yields a new equation:
% 27.67/7.62 | (525) e4 = e1
% 27.67/7.62 |
% 27.67/7.62 | Simplifying 525 yields:
% 27.67/7.62 | (526) e4 = e1
% 27.67/7.62 |
% 27.67/7.62 | Equations (526) can reduce 251 to:
% 27.67/7.62 | (270) $false
% 27.67/7.62 |
% 27.67/7.62 |-The branch is then unsatisfiable
% 27.67/7.62 |-Branch two:
% 27.67/7.62 | (748) ~ (all_0_51_51 = e1)
% 27.67/7.62 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 27.67/7.62 |
% 27.67/7.62 +-Applying beta-rule and splitting (823), into two cases.
% 27.67/7.62 |-Branch one:
% 27.67/7.62 | (848) all_0_52_52 = e1
% 27.67/7.62 |
% 27.67/7.62 | Combining equations (864,848) yields a new equation:
% 27.67/7.62 | (537) e3 = e1
% 27.67/7.62 |
% 27.67/7.62 | Simplifying 537 yields:
% 27.67/7.62 | (538) e3 = e1
% 27.67/7.62 |
% 27.67/7.62 | Equations (538) can reduce 136 to:
% 27.67/7.62 | (270) $false
% 27.67/7.62 |
% 27.67/7.62 |-The branch is then unsatisfiable
% 27.67/7.62 |-Branch two:
% 27.67/7.62 | (642) ~ (all_0_52_52 = e1)
% 27.67/7.62 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 27.67/7.62 |
% 27.67/7.62 +-Applying beta-rule and splitting (852), into two cases.
% 27.67/7.62 |-Branch one:
% 27.67/7.62 | (853) all_0_53_53 = e1
% 27.67/7.62 |
% 27.67/7.62 | Equations (853) can reduce 874 to:
% 27.67/7.62 | (270) $false
% 27.67/7.62 |
% 27.67/7.62 |-The branch is then unsatisfiable
% 27.67/7.62 |-Branch two:
% 27.67/7.62 | (874) ~ (all_0_53_53 = e1)
% 27.67/7.62 | (875) all_0_54_54 = e1
% 27.67/7.62 |
% 27.67/7.62 | Equations (875) can reduce 3011 to:
% 27.67/7.62 | (132) ~ (e1 = e0)
% 27.67/7.62 |
% 27.67/7.62 | From (875) and (29) follows:
% 27.67/7.62 | (3061) op(e1, e1) = all_0_37_37
% 27.67/7.62 |
% 27.67/7.62 +-Applying beta-rule and splitting (64), into two cases.
% 27.67/7.62 |-Branch one:
% 27.67/7.62 | (954) all_0_51_51 = e0
% 27.67/7.62 |
% 27.67/7.62 | Combining equations (1467,954) yields a new equation:
% 27.67/7.62 | (478) e4 = e0
% 27.67/7.62 |
% 27.67/7.62 | Simplifying 478 yields:
% 27.67/7.62 | (479) e4 = e0
% 27.67/7.62 |
% 27.67/7.62 | Equations (479) can reduce 6 to:
% 27.67/7.62 | (270) $false
% 27.67/7.62 |
% 27.67/7.62 |-The branch is then unsatisfiable
% 27.67/7.62 |-Branch two:
% 27.67/7.62 | (987) ~ (all_0_51_51 = e0)
% 27.67/7.62 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 27.67/7.62 |
% 27.67/7.62 +-Applying beta-rule and splitting (3067), into two cases.
% 27.67/7.62 |-Branch one:
% 27.67/7.62 | (827) all_0_52_52 = e0
% 27.67/7.62 |
% 27.67/7.62 | Combining equations (864,827) yields a new equation:
% 27.67/7.62 | (783) e3 = e0
% 27.67/7.62 |
% 27.67/7.62 | Simplifying 783 yields:
% 27.67/7.62 | (784) e3 = e0
% 27.67/7.62 |
% 27.67/7.62 | Equations (784) can reduce 66 to:
% 27.67/7.62 | (270) $false
% 27.67/7.62 |
% 27.67/7.62 |-The branch is then unsatisfiable
% 27.67/7.62 |-Branch two:
% 27.67/7.62 | (925) ~ (all_0_52_52 = e0)
% 27.67/7.62 | (3073) all_0_53_53 = e0 | all_0_54_54 = e0
% 27.67/7.63 |
% 27.67/7.63 +-Applying beta-rule and splitting (3073), into two cases.
% 27.67/7.63 |-Branch one:
% 27.67/7.63 | (423) all_0_53_53 = e0
% 27.67/7.63 |
% 27.67/7.63 | Equations (423) can reduce 259 to:
% 27.67/7.63 | (566) ~ (e2 = e0)
% 27.67/7.63 |
% 27.67/7.63 | Simplifying 566 yields:
% 27.67/7.63 | (57) ~ (e2 = e0)
% 27.67/7.63 |
% 27.67/7.63 | From (423) and (227) follows:
% 27.67/7.63 | (2167) op(e1, e1) = e0
% 27.67/7.63 |
% 27.67/7.63 | Instantiating formula (201) with e1, e1, e2, all_0_37_37 and discharging atoms op(e1, e1) = all_0_37_37, op(e1, e1) = e2, yields:
% 27.67/7.63 | (2275) all_0_37_37 = e2
% 27.67/7.63 |
% 27.67/7.63 | Instantiating formula (201) with e1, e1, e0, all_0_37_37 and discharging atoms op(e1, e1) = all_0_37_37, op(e1, e1) = e0, yields:
% 27.67/7.63 | (3079) all_0_37_37 = e0
% 27.67/7.63 |
% 27.67/7.63 | Combining equations (2275,3079) yields a new equation:
% 27.67/7.63 | (622) e2 = e0
% 27.67/7.63 |
% 27.67/7.63 | Simplifying 622 yields:
% 27.67/7.63 | (316) e2 = e0
% 27.67/7.63 |
% 27.67/7.63 | Equations (316) can reduce 57 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (584) ~ (all_0_53_53 = e0)
% 27.67/7.63 | (3084) all_0_54_54 = e0
% 27.67/7.63 |
% 27.67/7.63 | Combining equations (875,3084) yields a new equation:
% 27.67/7.63 | (571) e1 = e0
% 27.67/7.63 |
% 27.67/7.63 | Simplifying 571 yields:
% 27.67/7.63 | (560) e1 = e0
% 27.67/7.63 |
% 27.67/7.63 | Equations (560) can reduce 132 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (2296) all_0_28_28 = e0 & ~ (all_0_29_29 = e1)
% 27.67/7.63 |
% 27.67/7.63 | Applying alpha-rule on (2296) yields:
% 27.67/7.63 | (2297) all_0_28_28 = e0
% 27.67/7.63 | (2298) ~ (all_0_29_29 = e1)
% 27.67/7.63 |
% 27.67/7.63 | Combining equations (2297,2237) yields a new equation:
% 27.67/7.63 | (784) e3 = e0
% 27.67/7.63 |
% 27.67/7.63 | Equations (784) can reduce 66 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (826) ~ (all_0_52_52 = e3)
% 27.67/7.63 | (1107) all_0_53_53 = e3 | all_0_54_54 = e3
% 27.67/7.63 |
% 27.67/7.63 +-Applying beta-rule and splitting (1107), into two cases.
% 27.67/7.63 |-Branch one:
% 27.67/7.63 | (1114) all_0_53_53 = e3
% 27.67/7.63 |
% 27.67/7.63 | Equations (1114) can reduce 356 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (356) ~ (all_0_53_53 = e3)
% 27.67/7.63 | (1119) all_0_54_54 = e3
% 27.67/7.63 |
% 27.67/7.63 | Equations (1119) can reduce 1093 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (2301) ~ (all_0_57_57 = e0)
% 27.67/7.63 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 27.67/7.63 |
% 27.67/7.63 +-Applying beta-rule and splitting (626), into two cases.
% 27.67/7.63 |-Branch one:
% 27.67/7.63 | (827) all_0_52_52 = e0
% 27.67/7.63 |
% 27.67/7.63 | Equations (827) can reduce 213 to:
% 27.67/7.63 | (3103) ~ (all_0_53_53 = e0)
% 27.67/7.63 |
% 27.67/7.63 | Simplifying 3103 yields:
% 27.67/7.63 | (584) ~ (all_0_53_53 = e0)
% 27.67/7.63 |
% 27.67/7.63 | Equations (827) can reduce 257 to:
% 27.67/7.63 | (566) ~ (e2 = e0)
% 27.67/7.63 |
% 27.67/7.63 | Simplifying 566 yields:
% 27.67/7.63 | (57) ~ (e2 = e0)
% 27.67/7.63 |
% 27.67/7.63 +-Applying beta-rule and splitting (182), into two cases.
% 27.67/7.63 |-Branch one:
% 27.67/7.63 | (454) all_0_45_45 = e0
% 27.67/7.63 |
% 27.67/7.63 | Combining equations (505,454) yields a new equation:
% 27.67/7.63 | (783) e3 = e0
% 27.67/7.63 |
% 27.67/7.63 | Simplifying 783 yields:
% 27.67/7.63 | (784) e3 = e0
% 27.67/7.63 |
% 27.67/7.63 | Equations (784) can reduce 66 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (488) ~ (all_0_45_45 = e0)
% 27.67/7.63 | (558) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 27.67/7.63 |
% 27.67/7.63 +-Applying beta-rule and splitting (558), into two cases.
% 27.67/7.63 |-Branch one:
% 27.67/7.63 | (559) all_0_48_48 = e0
% 27.67/7.63 |
% 27.67/7.63 | Equations (559) can reduce 121 to:
% 27.67/7.63 | (788) ~ (e3 = e0)
% 27.67/7.63 |
% 27.67/7.63 | Simplifying 788 yields:
% 27.67/7.63 | (66) ~ (e3 = e0)
% 27.67/7.63 |
% 27.67/7.63 | Equations (559) can reduce 294 to:
% 27.67/7.63 | (566) ~ (e2 = e0)
% 27.67/7.63 |
% 27.67/7.63 | Simplifying 566 yields:
% 27.67/7.63 | (57) ~ (e2 = e0)
% 27.67/7.63 |
% 27.67/7.63 +-Applying beta-rule and splitting (2302), into two cases.
% 27.67/7.63 |-Branch one:
% 27.67/7.63 | (585) all_0_58_58 = e0
% 27.67/7.63 |
% 27.67/7.63 | Combining equations (585,396) yields a new equation:
% 27.67/7.63 | (316) e2 = e0
% 27.67/7.63 |
% 27.67/7.63 | Equations (316) can reduce 57 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (431) ~ (all_0_58_58 = e0)
% 27.67/7.63 | (2308) all_0_59_59 = e0
% 27.67/7.63 |
% 27.67/7.63 | Combining equations (412,2308) yields a new equation:
% 27.67/7.63 | (783) e3 = e0
% 27.67/7.63 |
% 27.67/7.63 | Simplifying 783 yields:
% 27.67/7.63 | (784) e3 = e0
% 27.67/7.63 |
% 27.67/7.63 | Equations (784) can reduce 66 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (562) ~ (all_0_48_48 = e0)
% 27.67/7.63 | (575) all_0_53_53 = e0 | all_0_58_58 = e0
% 27.67/7.63 |
% 27.67/7.63 +-Applying beta-rule and splitting (575), into two cases.
% 27.67/7.63 |-Branch one:
% 27.67/7.63 | (423) all_0_53_53 = e0
% 27.67/7.63 |
% 27.67/7.63 | Equations (423) can reduce 584 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (584) ~ (all_0_53_53 = e0)
% 27.67/7.63 | (585) all_0_58_58 = e0
% 27.67/7.63 |
% 27.67/7.63 | Combining equations (585,396) yields a new equation:
% 27.67/7.63 | (316) e2 = e0
% 27.67/7.63 |
% 27.67/7.63 | Equations (316) can reduce 57 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (925) ~ (all_0_52_52 = e0)
% 27.67/7.63 | (2258) all_0_57_57 = e0
% 27.67/7.63 |
% 27.67/7.63 | Equations (2258) can reduce 2301 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.67/7.63 |
% 27.67/7.63 | Applying alpha-rule on (422) yields:
% 27.67/7.63 | (423) all_0_53_53 = e0
% 27.67/7.63 | (424) all_0_59_59 = e1
% 27.67/7.63 | (425) ~ (all_0_54_54 = e1)
% 27.67/7.63 |
% 27.67/7.63 | Equations (424) can reduce 750 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.67/7.63 |
% 27.67/7.63 | Applying alpha-rule on (428) yields:
% 27.67/7.63 | (423) all_0_53_53 = e0
% 27.67/7.63 | (424) all_0_59_59 = e1
% 27.67/7.63 | (431) ~ (all_0_58_58 = e0)
% 27.67/7.63 |
% 27.67/7.63 | Equations (424) can reduce 750 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (354) ~ (all_0_45_45 = e3)
% 27.67/7.63 | (363) all_0_45_45 = e4
% 27.67/7.63 |
% 27.67/7.63 | Equations (363) can reduce 352 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (455) ~ (all_0_43_43 = e0)
% 27.67/7.63 | (944) all_0_43_43 = e4 | all_0_43_43 = e3
% 27.67/7.63 |
% 27.67/7.63 +-Applying beta-rule and splitting (944), into two cases.
% 27.67/7.63 |-Branch one:
% 27.67/7.63 | (782) all_0_43_43 = e3
% 27.67/7.63 |
% 27.67/7.63 | Equations (782) can reduce 786 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (786) ~ (all_0_43_43 = e3)
% 27.67/7.63 | (502) all_0_43_43 = e4
% 27.67/7.63 |
% 27.67/7.63 | Equations (502) can reduce 510 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (697) ~ (all_0_51_51 = e4)
% 27.67/7.63 | (1470) all_0_53_53 = e4 | all_0_54_54 = e4
% 27.67/7.63 |
% 27.67/7.63 +-Applying beta-rule and splitting (1470), into two cases.
% 27.67/7.63 |-Branch one:
% 27.67/7.63 | (367) all_0_53_53 = e4
% 27.67/7.63 |
% 27.67/7.63 | Equations (367) can reduce 599 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (599) ~ (all_0_53_53 = e4)
% 27.67/7.63 | (817) all_0_54_54 = e4
% 27.67/7.63 |
% 27.67/7.63 | Equations (817) can reduce 936 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (498) ~ (all_0_42_42 = e2)
% 27.67/7.63 | (1732) all_0_46_46 = e2 | all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 27.67/7.63 |
% 27.67/7.63 +-Applying beta-rule and splitting (16), into two cases.
% 27.67/7.63 |-Branch one:
% 27.67/7.63 | (698) all_0_42_42 = e2
% 27.67/7.63 |
% 27.67/7.63 | Equations (698) can reduce 498 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (498) ~ (all_0_42_42 = e2)
% 27.67/7.63 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 27.67/7.63 |
% 27.67/7.63 +-Applying beta-rule and splitting (1238), into two cases.
% 27.67/7.63 |-Branch one:
% 27.67/7.63 | (536) all_0_41_41 = e1
% 27.67/7.63 |
% 27.67/7.63 | Equations (536) can reduce 540 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (540) ~ (all_0_41_41 = e1)
% 27.67/7.63 | (358) all_0_41_41 = e4
% 27.67/7.63 |
% 27.67/7.63 | Equations (358) can reduce 331 to:
% 27.67/7.63 | (231) ~ (e4 = e2)
% 27.67/7.63 |
% 27.67/7.63 +-Applying beta-rule and splitting (630), into two cases.
% 27.67/7.63 |-Branch one:
% 27.67/7.63 | (327) all_0_40_40 = e2
% 27.67/7.63 |
% 27.67/7.63 | Combining equations (327,530) yields a new equation:
% 27.67/7.63 | (531) e2 = e1
% 27.67/7.63 |
% 27.67/7.63 | Simplifying 531 yields:
% 27.67/7.63 | (322) e2 = e1
% 27.67/7.63 |
% 27.67/7.63 | Equations (322) can reduce 141 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (602) ~ (all_0_40_40 = e2)
% 27.67/7.63 | (1251) all_0_41_41 = e2 | all_0_42_42 = e2
% 27.67/7.63 |
% 27.67/7.63 +-Applying beta-rule and splitting (1251), into two cases.
% 27.67/7.63 |-Branch one:
% 27.67/7.63 | (436) all_0_41_41 = e2
% 27.67/7.63 |
% 27.67/7.63 | Combining equations (358,436) yields a new equation:
% 27.67/7.63 | (268) e4 = e2
% 27.67/7.63 |
% 27.67/7.63 | Simplifying 268 yields:
% 27.67/7.63 | (269) e4 = e2
% 27.67/7.63 |
% 27.67/7.63 | Equations (269) can reduce 231 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (331) ~ (all_0_41_41 = e2)
% 27.67/7.63 | (698) all_0_42_42 = e2
% 27.67/7.63 |
% 27.67/7.63 | Equations (698) can reduce 498 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (755) ~ (all_0_39_39 = e3)
% 27.67/7.63 | (1756) all_0_39_39 = e4 | all_0_39_39 = e1
% 27.67/7.63 |
% 27.67/7.63 +-Applying beta-rule and splitting (1756), into two cases.
% 27.67/7.63 |-Branch one:
% 27.67/7.63 | (524) all_0_39_39 = e1
% 27.67/7.63 |
% 27.67/7.63 | Equations (524) can reduce 528 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (528) ~ (all_0_39_39 = e1)
% 27.67/7.63 | (522) all_0_39_39 = e4
% 27.67/7.63 |
% 27.67/7.63 | Equations (522) can reduce 591 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (534) ~ (all_0_40_40 = e1)
% 27.67/7.63 | (3352) all_0_52_52 = e1 | all_0_57_57 = e1
% 27.67/7.63 |
% 27.67/7.63 +-Applying beta-rule and splitting (339), into two cases.
% 27.67/7.63 |-Branch one:
% 27.67/7.63 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 27.67/7.63 |
% 27.67/7.63 +-Applying beta-rule and splitting (340), into two cases.
% 27.67/7.63 |-Branch one:
% 27.67/7.63 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 27.67/7.63 |
% 27.67/7.63 | Applying alpha-rule on (341) yields:
% 27.67/7.63 | (342) all_0_0_0 = e1
% 27.67/7.63 | (343) ~ (all_0_1_1 = e4)
% 27.67/7.63 |
% 27.67/7.63 | Combining equations (342,285) yields a new equation:
% 27.67/7.63 | (530) all_0_40_40 = e1
% 27.67/7.63 |
% 27.67/7.63 | Equations (530) can reduce 534 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 27.67/7.63 |
% 27.67/7.63 | Applying alpha-rule on (346) yields:
% 27.67/7.63 | (347) all_0_2_2 = e0
% 27.67/7.63 | (348) ~ (all_0_3_3 = e4)
% 27.67/7.63 |
% 27.67/7.63 | Equations (287) can reduce 348 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 27.67/7.63 |
% 27.67/7.63 | Applying alpha-rule on (350) yields:
% 27.67/7.63 | (351) all_0_41_41 = e3
% 27.67/7.63 | (352) ~ (all_0_45_45 = e4)
% 27.67/7.63 |
% 27.67/7.63 | Equations (351) can reduce 147 to:
% 27.67/7.63 | (675) ~ (all_0_40_40 = e3)
% 27.67/7.63 |
% 27.67/7.63 +-Applying beta-rule and splitting (603), into two cases.
% 27.67/7.63 |-Branch one:
% 27.67/7.63 | (671) all_0_40_40 = e3
% 27.67/7.63 |
% 27.67/7.63 | Equations (671) can reduce 675 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (675) ~ (all_0_40_40 = e3)
% 27.67/7.63 | (530) all_0_40_40 = e1
% 27.67/7.63 |
% 27.67/7.63 | Equations (530) can reduce 534 to:
% 27.67/7.63 | (270) $false
% 27.67/7.63 |
% 27.67/7.63 |-The branch is then unsatisfiable
% 27.67/7.63 |-Branch two:
% 27.67/7.63 | (333) ~ (all_0_44_44 = e2)
% 27.67/7.63 | (373) all_0_44_44 = e3 | all_0_44_44 = e0
% 27.67/7.63 |
% 27.67/7.63 +-Applying beta-rule and splitting (607), into two cases.
% 27.67/7.63 |-Branch one:
% 27.67/7.64 | (370) all_0_44_44 = e2
% 27.67/7.64 |
% 27.67/7.64 | Equations (370) can reduce 333 to:
% 27.67/7.64 | (270) $false
% 27.67/7.64 |
% 27.67/7.64 |-The branch is then unsatisfiable
% 27.67/7.64 |-Branch two:
% 27.67/7.64 | (333) ~ (all_0_44_44 = e2)
% 27.67/7.64 | (3377) all_0_52_52 = e2 | all_0_57_57 = e2
% 27.67/7.64 |
% 27.67/7.64 +-Applying beta-rule and splitting (3377), into two cases.
% 27.67/7.64 |-Branch one:
% 27.67/7.64 | (685) all_0_52_52 = e2
% 27.67/7.64 |
% 27.67/7.64 | Equations (685) can reduce 257 to:
% 27.67/7.64 | (270) $false
% 27.67/7.64 |
% 27.67/7.64 |-The branch is then unsatisfiable
% 27.67/7.64 |-Branch two:
% 27.67/7.64 | (257) ~ (all_0_52_52 = e2)
% 27.67/7.64 | (392) all_0_57_57 = e2
% 27.67/7.64 |
% 27.67/7.64 | Equations (392) can reduce 149 to:
% 27.67/7.64 | (602) ~ (all_0_40_40 = e2)
% 27.67/7.64 |
% 27.67/7.64 | Equations (392) can reduce 10 to:
% 27.67/7.64 | (333) ~ (all_0_44_44 = e2)
% 27.67/7.64 |
% 27.67/7.64 | Equations (392) can reduce 37 to:
% 27.67/7.64 | (375) ~ (all_0_58_58 = e2)
% 27.67/7.64 |
% 27.67/7.64 | Simplifying 375 yields:
% 27.67/7.64 | (376) ~ (all_0_58_58 = e2)
% 27.67/7.64 |
% 27.67/7.64 | Equations (392) can reduce 140 to:
% 27.67/7.64 | (700) ~ (all_0_59_59 = e2)
% 27.67/7.64 |
% 27.67/7.64 | Simplifying 700 yields:
% 27.67/7.64 | (701) ~ (all_0_59_59 = e2)
% 27.67/7.64 |
% 27.67/7.64 | Equations (392) can reduce 143 to:
% 27.67/7.64 | (377) ~ (e4 = e2)
% 27.67/7.64 |
% 27.67/7.64 | Simplifying 377 yields:
% 27.67/7.64 | (231) ~ (e4 = e2)
% 27.67/7.64 |
% 27.67/7.64 | From (392) and (30) follows:
% 27.67/7.64 | (3390) op(e2, e2) = all_0_19_19
% 27.67/7.64 |
% 27.67/7.64 | Instantiating formula (201) with e2, e2, all_0_19_19, e4 and discharging atoms op(e2, e2) = all_0_19_19, op(e2, e2) = e4, yields:
% 27.67/7.64 | (3391) all_0_19_19 = e4
% 27.67/7.64 |
% 27.67/7.64 +-Applying beta-rule and splitting (9), into two cases.
% 27.67/7.64 |-Branch one:
% 27.67/7.64 | (621) all_0_44_44 = e0
% 27.67/7.64 |
% 27.67/7.64 | Equations (621) can reduce 45 to:
% 27.67/7.64 | (456) ~ (e4 = e0)
% 27.67/7.64 |
% 27.67/7.64 | Simplifying 456 yields:
% 27.67/7.64 | (6) ~ (e4 = e0)
% 27.67/7.64 |
% 27.67/7.64 | From (621) and (165) follows:
% 27.67/7.64 | (3395) op(e2, e0) = all_0_15_15
% 27.67/7.64 |
% 27.67/7.64 | Instantiating formula (201) with e2, e0, all_0_15_15, all_0_49_49 and discharging atoms op(e2, e0) = all_0_15_15, op(e2, e0) = all_0_49_49, yields:
% 27.67/7.64 | (3396) all_0_15_15 = all_0_49_49
% 27.67/7.64 |
% 27.67/7.64 +-Applying beta-rule and splitting (8), into two cases.
% 27.67/7.64 |-Branch one:
% 27.67/7.64 | (530) all_0_40_40 = e1
% 27.67/7.64 |
% 27.67/7.64 | Equations (530) can reduce 602 to:
% 27.67/7.64 | (645) ~ (e2 = e1)
% 27.67/7.64 |
% 27.67/7.64 | Simplifying 645 yields:
% 27.67/7.64 | (141) ~ (e2 = e1)
% 27.67/7.64 |
% 27.67/7.64 | From (530) and (68) follows:
% 27.67/7.64 | (648) op(e2, e1) = all_0_13_13
% 27.67/7.64 |
% 27.67/7.64 +-Applying beta-rule and splitting (133), into two cases.
% 27.67/7.64 |-Branch one:
% 27.67/7.64 | (671) all_0_40_40 = e3
% 27.67/7.64 |
% 27.67/7.64 | Combining equations (530,671) yields a new equation:
% 27.67/7.64 | (538) e3 = e1
% 27.67/7.64 |
% 27.67/7.64 | Equations (538) can reduce 136 to:
% 27.67/7.64 | (270) $false
% 27.67/7.64 |
% 27.67/7.64 |-The branch is then unsatisfiable
% 27.67/7.64 |-Branch two:
% 27.67/7.64 | (675) ~ (all_0_40_40 = e3)
% 27.67/7.64 | (676) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 27.67/7.64 |
% 27.67/7.64 +-Applying beta-rule and splitting (676), into two cases.
% 27.67/7.64 |-Branch one:
% 27.67/7.64 | (858) all_0_44_44 = e3
% 27.67/7.64 |
% 27.67/7.64 | Combining equations (621,858) yields a new equation:
% 27.67/7.64 | (784) e3 = e0
% 27.67/7.64 |
% 27.67/7.64 | Equations (784) can reduce 66 to:
% 27.67/7.64 | (270) $false
% 27.67/7.64 |
% 27.67/7.64 |-The branch is then unsatisfiable
% 27.67/7.64 |-Branch two:
% 27.67/7.64 | (862) ~ (all_0_44_44 = e3)
% 27.67/7.64 | (863) all_0_52_52 = e3 | all_0_57_57 = e3
% 27.67/7.64 |
% 27.67/7.64 +-Applying beta-rule and splitting (863), into two cases.
% 27.67/7.64 |-Branch one:
% 27.67/7.64 | (864) all_0_52_52 = e3
% 27.67/7.64 |
% 27.67/7.64 | From (864) and (27) follows:
% 27.67/7.64 | (3412) op(e2, e3) = all_0_17_17
% 27.67/7.64 |
% 27.67/7.64 | Instantiating formula (201) with e2, e3, all_0_17_17, e2 and discharging atoms op(e2, e3) = all_0_17_17, op(e2, e3) = e2, yields:
% 27.67/7.64 | (3413) all_0_17_17 = e2
% 27.67/7.64 |
% 27.67/7.64 | Instantiating formula (201) with e2, e1, all_0_13_13, all_0_48_48 and discharging atoms op(e2, e1) = all_0_13_13, op(e2, e1) = all_0_48_48, yields:
% 27.67/7.64 | (649) all_0_13_13 = all_0_48_48
% 27.67/7.64 |
% 27.67/7.64 +-Applying beta-rule and splitting (87), into two cases.
% 27.67/7.64 |-Branch one:
% 27.67/7.64 | (650) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 27.67/7.64 |
% 27.67/7.64 +-Applying beta-rule and splitting (650), into two cases.
% 27.67/7.64 |-Branch one:
% 27.67/7.64 | (651) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 27.67/7.64 |
% 27.67/7.64 +-Applying beta-rule and splitting (651), into two cases.
% 27.67/7.64 |-Branch one:
% 27.67/7.64 | (652) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 27.67/7.64 |
% 27.67/7.64 | Applying alpha-rule on (652) yields:
% 27.67/7.64 | (653) all_0_13_13 = e4
% 27.67/7.64 | (654) ~ (all_0_14_14 = e2)
% 27.67/7.64 |
% 27.67/7.64 | Combining equations (649,653) yields a new equation:
% 27.67/7.64 | (3420) all_0_48_48 = e4
% 27.67/7.64 |
% 27.67/7.64 | Simplifying 3420 yields:
% 27.67/7.64 | (655) all_0_48_48 = e4
% 27.67/7.64 |
% 27.67/7.64 | Equations (655) can reduce 192 to:
% 27.67/7.64 | (270) $false
% 27.67/7.64 |
% 27.67/7.64 |-The branch is then unsatisfiable
% 27.67/7.64 |-Branch two:
% 27.67/7.64 | (657) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 27.67/7.64 |
% 27.67/7.64 | Applying alpha-rule on (657) yields:
% 27.67/7.64 | (658) all_0_15_15 = e3
% 27.67/7.64 | (659) ~ (all_0_16_16 = e2)
% 27.67/7.64 |
% 27.67/7.64 | Combining equations (658,3396) yields a new equation:
% 27.67/7.64 | (3426) all_0_49_49 = e3
% 27.67/7.64 |
% 27.67/7.64 | Equations (3426) can reduce 150 to:
% 27.67/7.64 | (270) $false
% 27.67/7.64 |
% 27.67/7.64 |-The branch is then unsatisfiable
% 27.67/7.64 |-Branch two:
% 27.67/7.64 | (663) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 27.67/7.64 |
% 27.67/7.64 | Applying alpha-rule on (663) yields:
% 27.67/7.64 | (664) all_0_17_17 = e1
% 27.67/7.64 | (665) ~ (all_0_18_18 = e2)
% 27.67/7.64 |
% 27.67/7.64 | Combining equations (3413,664) yields a new equation:
% 27.67/7.64 | (531) e2 = e1
% 27.67/7.64 |
% 27.67/7.64 | Simplifying 531 yields:
% 27.67/7.64 | (322) e2 = e1
% 27.67/7.64 |
% 27.67/7.64 | Equations (322) can reduce 141 to:
% 27.67/7.64 | (270) $false
% 27.67/7.64 |
% 27.67/7.64 |-The branch is then unsatisfiable
% 27.67/7.64 |-Branch two:
% 27.67/7.64 | (1762) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 27.67/7.64 |
% 27.67/7.64 | Applying alpha-rule on (1762) yields:
% 27.67/7.64 | (1763) all_0_19_19 = e0
% 27.67/7.64 | (1764) ~ (all_0_20_20 = e2)
% 27.67/7.64 |
% 27.67/7.64 | Combining equations (3391,1763) yields a new equation:
% 27.67/7.64 | (478) e4 = e0
% 27.67/7.64 |
% 27.67/7.64 | Simplifying 478 yields:
% 27.67/7.64 | (479) e4 = e0
% 27.67/7.64 |
% 27.67/7.64 | Equations (479) can reduce 6 to:
% 27.67/7.64 | (270) $false
% 27.67/7.64 |
% 27.67/7.64 |-The branch is then unsatisfiable
% 27.67/7.64 |-Branch two:
% 27.67/7.64 | (826) ~ (all_0_52_52 = e3)
% 27.67/7.64 | (869) all_0_57_57 = e3
% 27.67/7.64 |
% 27.67/7.64 | Combining equations (869,392) yields a new equation:
% 27.67/7.64 | (437) e3 = e2
% 27.67/7.64 |
% 27.67/7.64 | Simplifying 437 yields:
% 27.67/7.64 | (414) e3 = e2
% 27.67/7.64 |
% 27.67/7.64 | Equations (414) can reduce 223 to:
% 27.67/7.64 | (270) $false
% 27.67/7.64 |
% 27.67/7.64 |-The branch is then unsatisfiable
% 27.67/7.64 |-Branch two:
% 27.67/7.64 | (534) ~ (all_0_40_40 = e1)
% 27.67/7.64 | (3352) all_0_52_52 = e1 | all_0_57_57 = e1
% 27.67/7.64 |
% 27.67/7.64 +-Applying beta-rule and splitting (186), into two cases.
% 27.67/7.64 |-Branch one:
% 27.67/7.64 | (336) all_0_39_39 = e2
% 27.67/7.64 |
% 27.67/7.64 | Equations (336) can reduce 291 to:
% 27.67/7.64 | (270) $false
% 27.67/7.64 |
% 27.67/7.64 |-The branch is then unsatisfiable
% 27.67/7.64 |-Branch two:
% 27.67/7.64 | (291) ~ (all_0_39_39 = e2)
% 27.67/7.64 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 27.67/7.64 |
% 27.67/7.64 +-Applying beta-rule and splitting (603), into two cases.
% 27.67/7.64 |-Branch one:
% 27.67/7.64 | (671) all_0_40_40 = e3
% 27.67/7.64 |
% 27.67/7.64 | Combining equations (671,285) yields a new equation:
% 27.67/7.64 | (3452) all_0_0_0 = e3
% 27.67/7.64 |
% 27.67/7.64 | Equations (671) can reduce 147 to:
% 27.67/7.64 | (1329) ~ (all_0_41_41 = e3)
% 27.67/7.64 |
% 27.67/7.64 | Simplifying 1329 yields:
% 27.67/7.64 | (1237) ~ (all_0_41_41 = e3)
% 27.67/7.64 |
% 27.67/7.64 | Equations (671) can reduce 534 to:
% 27.67/7.64 | (136) ~ (e3 = e1)
% 27.67/7.64 |
% 27.67/7.64 +-Applying beta-rule and splitting (339), into two cases.
% 27.67/7.64 |-Branch one:
% 27.67/7.64 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 27.67/7.64 |
% 27.67/7.64 +-Applying beta-rule and splitting (340), into two cases.
% 27.67/7.64 |-Branch one:
% 27.67/7.64 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 27.67/7.64 |
% 27.67/7.64 | Applying alpha-rule on (341) yields:
% 27.67/7.64 | (342) all_0_0_0 = e1
% 27.67/7.64 | (343) ~ (all_0_1_1 = e4)
% 27.67/7.64 |
% 27.67/7.64 | Combining equations (342,3452) yields a new equation:
% 27.67/7.64 | (538) e3 = e1
% 27.67/7.64 |
% 27.67/7.64 | Equations (538) can reduce 136 to:
% 27.67/7.64 | (270) $false
% 27.67/7.64 |
% 27.67/7.64 |-The branch is then unsatisfiable
% 27.67/7.64 |-Branch two:
% 27.67/7.64 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 27.67/7.64 |
% 27.67/7.64 | Applying alpha-rule on (346) yields:
% 27.67/7.64 | (347) all_0_2_2 = e0
% 27.67/7.64 | (348) ~ (all_0_3_3 = e4)
% 27.67/7.64 |
% 27.67/7.64 | Equations (287) can reduce 348 to:
% 27.67/7.64 | (270) $false
% 27.67/7.64 |
% 27.67/7.64 |-The branch is then unsatisfiable
% 27.67/7.64 |-Branch two:
% 27.67/7.64 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 27.67/7.64 |
% 27.67/7.64 | Applying alpha-rule on (350) yields:
% 27.67/7.64 | (351) all_0_41_41 = e3
% 27.67/7.64 | (352) ~ (all_0_45_45 = e4)
% 27.67/7.64 |
% 27.67/7.64 | Equations (351) can reduce 1237 to:
% 27.67/7.64 | (270) $false
% 27.67/7.64 |
% 27.67/7.64 |-The branch is then unsatisfiable
% 27.67/7.64 |-Branch two:
% 27.67/7.64 | (675) ~ (all_0_40_40 = e3)
% 27.67/7.64 | (530) all_0_40_40 = e1
% 27.67/7.64 |
% 27.67/7.64 | Equations (530) can reduce 534 to:
% 27.67/7.64 | (270) $false
% 27.67/7.64 |
% 27.67/7.64 |-The branch is then unsatisfiable
% 27.67/7.64 |-Branch two:
% 27.67/7.64 | (625) ~ (all_0_44_44 = e0)
% 27.67/7.64 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 27.67/7.64 |
% 27.67/7.64 +-Applying beta-rule and splitting (626), into two cases.
% 27.67/7.64 |-Branch one:
% 27.67/7.64 | (827) all_0_52_52 = e0
% 27.67/7.64 |
% 27.67/7.64 | Equations (827) can reduce 137 to:
% 27.67/7.64 | (238) ~ (all_0_40_40 = e0)
% 27.67/7.64 |
% 27.67/7.64 | Equations (827) can reduce 122 to:
% 27.67/7.64 | (625) ~ (all_0_44_44 = e0)
% 27.67/7.64 |
% 27.67/7.64 | Equations (827) can reduce 118 to:
% 27.67/7.64 | (3010) ~ (all_0_54_54 = e0)
% 27.67/7.64 |
% 27.67/7.64 | Simplifying 3010 yields:
% 27.67/7.64 | (3011) ~ (all_0_54_54 = e0)
% 27.67/7.64 |
% 27.67/7.64 | Equations (827) can reduce 230 to:
% 27.67/7.64 | (456) ~ (e4 = e0)
% 27.67/7.64 |
% 27.67/7.64 | Simplifying 456 yields:
% 27.67/7.64 | (6) ~ (e4 = e0)
% 27.67/7.64 |
% 27.67/7.64 | From (827) and (27) follows:
% 27.67/7.64 | (3482) op(e2, e0) = all_0_17_17
% 27.67/7.64 |
% 27.67/7.64 | From (827) and (195) follows:
% 27.67/7.64 | (3483) op(e1, e0) = all_0_18_18
% 27.67/7.64 |
% 27.67/7.64 +-Applying beta-rule and splitting (8), into two cases.
% 27.67/7.64 |-Branch one:
% 27.67/7.64 | (530) all_0_40_40 = e1
% 27.67/7.64 |
% 27.67/7.64 | Equations (530) can reduce 147 to:
% 27.67/7.64 | (637) ~ (all_0_41_41 = e1)
% 27.67/7.64 |
% 27.67/7.64 | Simplifying 637 yields:
% 27.67/7.64 | (540) ~ (all_0_41_41 = e1)
% 27.67/7.64 |
% 27.67/7.64 | Equations (530) can reduce 238 to:
% 27.67/7.64 | (132) ~ (e1 = e0)
% 27.67/7.64 |
% 27.67/7.64 | From (530) and (68) follows:
% 27.67/7.64 | (648) op(e2, e1) = all_0_13_13
% 27.67/7.64 |
% 27.67/7.64 +-Applying beta-rule and splitting (373), into two cases.
% 27.67/7.64 |-Branch one:
% 27.67/7.64 | (621) all_0_44_44 = e0
% 27.67/7.64 |
% 27.67/7.64 | Equations (621) can reduce 625 to:
% 27.67/7.64 | (270) $false
% 27.67/7.64 |
% 27.67/7.64 |-The branch is then unsatisfiable
% 27.67/7.64 |-Branch two:
% 27.67/7.64 | (625) ~ (all_0_44_44 = e0)
% 27.67/7.64 | (858) all_0_44_44 = e3
% 27.67/7.64 |
% 27.67/7.64 | Equations (858) can reduce 241 to:
% 27.67/7.64 | (786) ~ (all_0_43_43 = e3)
% 27.67/7.64 |
% 27.67/7.64 | Equations (858) can reduce 229 to:
% 27.67/7.64 | (353) ~ (all_0_45_45 = e3)
% 27.67/7.64 |
% 27.67/7.64 | Simplifying 353 yields:
% 27.67/7.64 | (354) ~ (all_0_45_45 = e3)
% 27.67/7.64 |
% 27.67/7.64 | Equations (858) can reduce 174 to:
% 27.67/7.64 | (1518) ~ (all_0_46_46 = e3)
% 27.67/7.64 |
% 27.67/7.64 | Simplifying 1518 yields:
% 27.67/7.64 | (413) ~ (all_0_46_46 = e3)
% 27.67/7.64 |
% 27.67/7.64 | Equations (858) can reduce 333 to:
% 27.67/7.64 | (223) ~ (e3 = e2)
% 27.67/7.64 |
% 27.67/7.64 | From (858) and (165) follows:
% 27.67/7.64 | (3499) op(e2, e3) = all_0_15_15
% 27.67/7.64 |
% 27.67/7.64 | Instantiating formula (201) with e2, e3, all_0_15_15, e2 and discharging atoms op(e2, e3) = all_0_15_15, op(e2, e3) = e2, yields:
% 27.67/7.64 | (3500) all_0_15_15 = e2
% 27.67/7.64 |
% 27.67/7.64 | Instantiating formula (201) with e2, e1, all_0_13_13, all_0_48_48 and discharging atoms op(e2, e1) = all_0_13_13, op(e2, e1) = all_0_48_48, yields:
% 27.67/7.64 | (649) all_0_13_13 = all_0_48_48
% 27.67/7.64 |
% 27.67/7.64 | Instantiating formula (201) with e2, e0, all_0_17_17, all_0_49_49 and discharging atoms op(e2, e0) = all_0_17_17, op(e2, e0) = all_0_49_49, yields:
% 27.67/7.64 | (3502) all_0_17_17 = all_0_49_49
% 27.67/7.64 |
% 27.67/7.64 | Instantiating formula (201) with e1, e0, all_0_18_18, all_0_54_54 and discharging atoms op(e1, e0) = all_0_18_18, op(e1, e0) = all_0_54_54, yields:
% 27.67/7.64 | (3503) all_0_18_18 = all_0_54_54
% 27.67/7.64 |
% 27.67/7.64 +-Applying beta-rule and splitting (87), into two cases.
% 27.67/7.64 |-Branch one:
% 27.67/7.64 | (650) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 27.67/7.64 |
% 27.67/7.64 +-Applying beta-rule and splitting (650), into two cases.
% 27.67/7.64 |-Branch one:
% 27.67/7.64 | (651) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 27.67/7.64 |
% 27.67/7.64 +-Applying beta-rule and splitting (651), into two cases.
% 27.67/7.64 |-Branch one:
% 27.67/7.64 | (652) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 27.67/7.64 |
% 27.67/7.64 | Applying alpha-rule on (652) yields:
% 27.67/7.64 | (653) all_0_13_13 = e4
% 27.67/7.64 | (654) ~ (all_0_14_14 = e2)
% 27.67/7.64 |
% 27.67/7.64 | Combining equations (649,653) yields a new equation:
% 27.67/7.64 | (3420) all_0_48_48 = e4
% 27.67/7.64 |
% 27.67/7.65 | Simplifying 3420 yields:
% 27.67/7.65 | (655) all_0_48_48 = e4
% 27.67/7.65 |
% 27.67/7.65 | Equations (655) can reduce 192 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (657) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 27.67/7.65 |
% 27.67/7.65 | Applying alpha-rule on (657) yields:
% 27.67/7.65 | (658) all_0_15_15 = e3
% 27.67/7.65 | (659) ~ (all_0_16_16 = e2)
% 27.67/7.65 |
% 27.67/7.65 | Combining equations (658,3500) yields a new equation:
% 27.67/7.65 | (437) e3 = e2
% 27.67/7.65 |
% 27.67/7.65 | Simplifying 437 yields:
% 27.67/7.65 | (414) e3 = e2
% 27.67/7.65 |
% 27.67/7.65 | Equations (414) can reduce 223 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (663) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 27.67/7.65 |
% 27.67/7.65 | Applying alpha-rule on (663) yields:
% 27.67/7.65 | (664) all_0_17_17 = e1
% 27.67/7.65 | (665) ~ (all_0_18_18 = e2)
% 27.67/7.65 |
% 27.67/7.65 | Combining equations (3502,664) yields a new equation:
% 27.67/7.65 | (3521) all_0_49_49 = e1
% 27.67/7.65 |
% 27.67/7.65 | Simplifying 3521 yields:
% 27.67/7.65 | (589) all_0_49_49 = e1
% 27.67/7.65 |
% 27.67/7.65 | Equations (3503) can reduce 665 to:
% 27.67/7.65 | (261) ~ (all_0_54_54 = e2)
% 27.67/7.65 |
% 27.67/7.65 | Equations (589) can reduce 4 to:
% 27.67/7.65 | (588) ~ (all_0_48_48 = e1)
% 27.67/7.65 |
% 27.67/7.65 | Equations (589) can reduce 113 to:
% 27.67/7.65 | (749) ~ (all_0_59_59 = e1)
% 27.67/7.65 |
% 27.67/7.65 | Simplifying 749 yields:
% 27.67/7.65 | (750) ~ (all_0_59_59 = e1)
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (319), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (559) all_0_48_48 = e0
% 27.67/7.65 |
% 27.67/7.65 | Equations (559) can reduce 190 to:
% 27.67/7.65 | (232) ~ (all_0_41_41 = e0)
% 27.67/7.65 |
% 27.67/7.65 | Equations (559) can reduce 65 to:
% 27.67/7.65 | (488) ~ (all_0_45_45 = e0)
% 27.67/7.65 |
% 27.67/7.65 | Equations (559) can reduce 59 to:
% 27.67/7.65 | (3530) ~ (all_0_58_58 = e0)
% 27.67/7.65 |
% 27.67/7.65 | Simplifying 3530 yields:
% 27.67/7.65 | (431) ~ (all_0_58_58 = e0)
% 27.67/7.65 |
% 27.67/7.65 | Equations (559) can reduce 588 to:
% 27.67/7.65 | (568) ~ (e1 = e0)
% 27.67/7.65 |
% 27.67/7.65 | Simplifying 568 yields:
% 27.67/7.65 | (132) ~ (e1 = e0)
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (47), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (450) all_0_43_43 = e2
% 27.67/7.65 |
% 27.67/7.65 | Equations (450) can reduce 292 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (292) ~ (all_0_43_43 = e2)
% 27.67/7.65 | (453) all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (105), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (374) all_0_45_45 = e2
% 27.67/7.65 |
% 27.67/7.65 | Equations (374) can reduce 51 to:
% 27.67/7.65 | (331) ~ (all_0_41_41 = e2)
% 27.67/7.65 |
% 27.67/7.65 | Equations (374) can reduce 84 to:
% 27.67/7.65 | (292) ~ (all_0_43_43 = e2)
% 27.67/7.65 |
% 27.67/7.65 | Equations (374) can reduce 354 to:
% 27.67/7.65 | (301) ~ (e3 = e2)
% 27.67/7.65 |
% 27.67/7.65 | Simplifying 301 yields:
% 27.67/7.65 | (223) ~ (e3 = e2)
% 27.67/7.65 |
% 27.67/7.65 | Equations (374) can reduce 26 to:
% 27.67/7.65 | (141) ~ (e2 = e1)
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (164), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (336) all_0_39_39 = e2
% 27.67/7.65 |
% 27.67/7.65 | Equations (336) can reduce 291 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (291) ~ (all_0_39_39 = e2)
% 27.67/7.65 | (630) all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (209), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (698) all_0_42_42 = e2
% 27.67/7.65 |
% 27.67/7.65 | Equations (698) can reduce 94 to:
% 27.67/7.65 | (331) ~ (all_0_41_41 = e2)
% 27.67/7.65 |
% 27.67/7.65 | Equations (698) can reduce 191 to:
% 27.67/7.65 | (260) ~ (all_0_54_54 = e2)
% 27.67/7.65 |
% 27.67/7.65 | Simplifying 260 yields:
% 27.67/7.65 | (261) ~ (all_0_54_54 = e2)
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (44), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (502) all_0_43_43 = e4
% 27.67/7.65 |
% 27.67/7.65 | Equations (502) can reduce 167 to:
% 27.67/7.65 | (591) ~ (all_0_39_39 = e4)
% 27.67/7.65 |
% 27.67/7.65 | Equations (502) can reduce 103 to:
% 27.67/7.65 | (804) ~ (all_0_46_46 = e4)
% 27.67/7.65 |
% 27.67/7.65 | Simplifying 804 yields:
% 27.67/7.65 | (805) ~ (all_0_46_46 = e4)
% 27.67/7.65 |
% 27.67/7.65 | Equations (502) can reduce 292 to:
% 27.67/7.65 | (231) ~ (e4 = e2)
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (222), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (522) all_0_39_39 = e4
% 27.67/7.65 |
% 27.67/7.65 | Equations (522) can reduce 591 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (591) ~ (all_0_39_39 = e4)
% 27.67/7.65 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (592), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (358) all_0_41_41 = e4
% 27.67/7.65 |
% 27.67/7.65 | Equations (358) can reduce 331 to:
% 27.67/7.65 | (231) ~ (e4 = e2)
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (179), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (512) all_0_42_42 = e4
% 27.67/7.65 |
% 27.67/7.65 | Combining equations (698,512) yields a new equation:
% 27.67/7.65 | (269) e4 = e2
% 27.67/7.65 |
% 27.67/7.65 | Equations (269) can reduce 231 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (520) ~ (all_0_42_42 = e4)
% 27.67/7.65 | (521) all_0_46_46 = e4 | all_0_54_54 = e4 | all_0_59_59 = e4
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (521), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (517) all_0_46_46 = e4
% 27.67/7.65 |
% 27.67/7.65 | Equations (517) can reduce 805 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (805) ~ (all_0_46_46 = e4)
% 27.67/7.65 | (816) all_0_54_54 = e4 | all_0_59_59 = e4
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (816), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (817) all_0_54_54 = e4
% 27.67/7.65 |
% 27.67/7.65 | Equations (817) can reduce 72 to:
% 27.67/7.65 | (279) ~ (all_0_59_59 = e4)
% 27.67/7.65 |
% 27.67/7.65 | Simplifying 279 yields:
% 27.67/7.65 | (280) ~ (all_0_59_59 = e4)
% 27.67/7.65 |
% 27.67/7.65 | Equations (817) can reduce 3011 to:
% 27.67/7.65 | (6) ~ (e4 = e0)
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (93), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (402) all_0_59_59 = e4
% 27.67/7.65 |
% 27.67/7.65 | Equations (402) can reduce 280 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (280) ~ (all_0_59_59 = e4)
% 27.67/7.65 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (407), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (408), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (409), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.67/7.65 |
% 27.67/7.65 | Applying alpha-rule on (410) yields:
% 27.67/7.65 | (411) all_0_43_43 = e0
% 27.67/7.65 | (412) all_0_59_59 = e3
% 27.67/7.65 | (413) ~ (all_0_46_46 = e3)
% 27.67/7.65 |
% 27.67/7.65 | Combining equations (502,411) yields a new equation:
% 27.67/7.65 | (478) e4 = e0
% 27.67/7.65 |
% 27.67/7.65 | Simplifying 478 yields:
% 27.67/7.65 | (479) e4 = e0
% 27.67/7.65 |
% 27.67/7.65 | Equations (479) can reduce 6 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.67/7.65 |
% 27.67/7.65 | Applying alpha-rule on (416) yields:
% 27.67/7.65 | (411) all_0_43_43 = e0
% 27.67/7.65 | (412) all_0_59_59 = e3
% 27.67/7.65 | (419) ~ (all_0_56_56 = e0)
% 27.67/7.65 |
% 27.67/7.65 | Combining equations (502,411) yields a new equation:
% 27.67/7.65 | (478) e4 = e0
% 27.67/7.65 |
% 27.67/7.65 | Simplifying 478 yields:
% 27.67/7.65 | (479) e4 = e0
% 27.67/7.65 |
% 27.67/7.65 | Equations (479) can reduce 6 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.67/7.65 |
% 27.67/7.65 | Applying alpha-rule on (422) yields:
% 27.67/7.65 | (423) all_0_53_53 = e0
% 27.67/7.65 | (424) all_0_59_59 = e1
% 27.67/7.65 | (425) ~ (all_0_54_54 = e1)
% 27.67/7.65 |
% 27.67/7.65 | Equations (424) can reduce 750 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.67/7.65 |
% 27.67/7.65 | Applying alpha-rule on (428) yields:
% 27.67/7.65 | (423) all_0_53_53 = e0
% 27.67/7.65 | (424) all_0_59_59 = e1
% 27.67/7.65 | (431) ~ (all_0_58_58 = e0)
% 27.67/7.65 |
% 27.67/7.65 | Equations (424) can reduce 750 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (936) ~ (all_0_54_54 = e4)
% 27.67/7.65 | (402) all_0_59_59 = e4
% 27.67/7.65 |
% 27.67/7.65 | Equations (402) can reduce 280 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (361) ~ (all_0_41_41 = e4)
% 27.67/7.65 | (512) all_0_42_42 = e4
% 27.67/7.65 |
% 27.67/7.65 | Combining equations (698,512) yields a new equation:
% 27.67/7.65 | (269) e4 = e2
% 27.67/7.65 |
% 27.67/7.65 | Equations (269) can reduce 231 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (510) ~ (all_0_43_43 = e4)
% 27.67/7.65 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (159), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (450) all_0_43_43 = e2
% 27.67/7.65 |
% 27.67/7.65 | Equations (450) can reduce 292 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (292) ~ (all_0_43_43 = e2)
% 27.67/7.65 | (774) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (774), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (411) all_0_43_43 = e0
% 27.67/7.65 |
% 27.67/7.65 | Equations (411) can reduce 103 to:
% 27.67/7.65 | (1057) ~ (all_0_46_46 = e0)
% 27.67/7.65 |
% 27.67/7.65 | Simplifying 1057 yields:
% 27.67/7.65 | (1010) ~ (all_0_46_46 = e0)
% 27.67/7.65 |
% 27.67/7.65 | Equations (411) can reduce 786 to:
% 27.67/7.65 | (788) ~ (e3 = e0)
% 27.67/7.65 |
% 27.67/7.65 | Simplifying 788 yields:
% 27.67/7.65 | (66) ~ (e3 = e0)
% 27.67/7.65 |
% 27.67/7.65 | Equations (411) can reduce 249 to:
% 27.67/7.65 | (568) ~ (e1 = e0)
% 27.67/7.65 |
% 27.67/7.65 | Simplifying 568 yields:
% 27.67/7.65 | (132) ~ (e1 = e0)
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (221), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (1132) all_0_46_46 = e0
% 27.67/7.65 |
% 27.67/7.65 | Equations (1132) can reduce 1010 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (1010) ~ (all_0_46_46 = e0)
% 27.67/7.65 | (3629) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (93), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (402) all_0_59_59 = e4
% 27.67/7.65 |
% 27.67/7.65 | Equations (402) can reduce 280 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (280) ~ (all_0_59_59 = e4)
% 27.67/7.65 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (3629), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (563) all_0_49_49 = e0
% 27.67/7.65 |
% 27.67/7.65 | Combining equations (563,589) yields a new equation:
% 27.67/7.65 | (560) e1 = e0
% 27.67/7.65 |
% 27.67/7.65 | Equations (560) can reduce 132 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (1231) ~ (all_0_49_49 = e0)
% 27.67/7.65 | (3638) all_0_54_54 = e0 | all_0_59_59 = e0
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (3638), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (3084) all_0_54_54 = e0
% 27.67/7.65 |
% 27.67/7.65 | Equations (3084) can reduce 3011 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (3011) ~ (all_0_54_54 = e0)
% 27.67/7.65 | (2308) all_0_59_59 = e0
% 27.67/7.65 |
% 27.67/7.65 | Equations (2308) can reduce 72 to:
% 27.67/7.65 | (3011) ~ (all_0_54_54 = e0)
% 27.67/7.65 |
% 27.67/7.65 | Equations (2308) can reduce 750 to:
% 27.67/7.65 | (568) ~ (e1 = e0)
% 27.67/7.65 |
% 27.67/7.65 | Simplifying 568 yields:
% 27.67/7.65 | (132) ~ (e1 = e0)
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (511), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (363) all_0_45_45 = e4
% 27.67/7.65 |
% 27.67/7.65 | Combining equations (374,363) yields a new equation:
% 27.67/7.65 | (269) e4 = e2
% 27.67/7.65 |
% 27.67/7.65 | Equations (269) can reduce 231 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (352) ~ (all_0_45_45 = e4)
% 27.67/7.65 | (517) all_0_46_46 = e4
% 27.67/7.65 |
% 27.67/7.65 | Equations (517) can reduce 413 to:
% 27.67/7.65 | (34) ~ (e4 = e3)
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (95), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (1258) all_0_42_42 = e3
% 27.67/7.65 |
% 27.67/7.65 | Combining equations (698,1258) yields a new equation:
% 27.67/7.65 | (414) e3 = e2
% 27.67/7.65 |
% 27.67/7.65 | Equations (414) can reduce 223 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (1316) ~ (all_0_42_42 = e3)
% 27.67/7.65 | (3656) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (110), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (3657) all_0_54_54 = e2
% 27.67/7.65 |
% 27.67/7.65 | Equations (3657) can reduce 261 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (261) ~ (all_0_54_54 = e2)
% 27.67/7.65 | (3660) all_0_54_54 = e4 | all_0_54_54 = e3 | all_0_54_54 = e1 | all_0_54_54 = e0
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (3660), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (3084) all_0_54_54 = e0
% 27.67/7.65 |
% 27.67/7.65 | Equations (3084) can reduce 3011 to:
% 27.67/7.65 | (270) $false
% 27.67/7.65 |
% 27.67/7.65 |-The branch is then unsatisfiable
% 27.67/7.65 |-Branch two:
% 27.67/7.65 | (3011) ~ (all_0_54_54 = e0)
% 27.67/7.65 | (3664) all_0_54_54 = e4 | all_0_54_54 = e3 | all_0_54_54 = e1
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (3664), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (1119) all_0_54_54 = e3
% 27.67/7.65 |
% 27.67/7.65 | Equations (1119) can reduce 3011 to:
% 27.67/7.65 | (66) ~ (e3 = e0)
% 27.67/7.65 |
% 27.67/7.65 +-Applying beta-rule and splitting (407), into two cases.
% 27.67/7.65 |-Branch one:
% 27.67/7.65 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.67/7.66 |
% 27.67/7.66 +-Applying beta-rule and splitting (408), into two cases.
% 27.67/7.66 |-Branch one:
% 27.67/7.66 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.67/7.66 |
% 27.67/7.66 +-Applying beta-rule and splitting (409), into two cases.
% 27.67/7.66 |-Branch one:
% 27.67/7.66 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.67/7.66 |
% 27.67/7.66 | Applying alpha-rule on (410) yields:
% 27.67/7.66 | (411) all_0_43_43 = e0
% 27.67/7.66 | (412) all_0_59_59 = e3
% 27.67/7.66 | (413) ~ (all_0_46_46 = e3)
% 27.67/7.66 |
% 27.67/7.66 | Combining equations (2308,412) yields a new equation:
% 27.67/7.66 | (784) e3 = e0
% 27.67/7.66 |
% 27.67/7.66 | Equations (784) can reduce 66 to:
% 27.67/7.66 | (270) $false
% 27.67/7.66 |
% 27.67/7.66 |-The branch is then unsatisfiable
% 27.67/7.66 |-Branch two:
% 27.67/7.66 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.67/7.66 |
% 27.67/7.66 | Applying alpha-rule on (416) yields:
% 27.67/7.66 | (411) all_0_43_43 = e0
% 27.67/7.66 | (412) all_0_59_59 = e3
% 27.67/7.66 | (419) ~ (all_0_56_56 = e0)
% 27.67/7.66 |
% 27.67/7.66 | Combining equations (2308,412) yields a new equation:
% 27.67/7.66 | (784) e3 = e0
% 27.67/7.66 |
% 27.67/7.66 | Equations (784) can reduce 66 to:
% 27.67/7.66 | (270) $false
% 27.67/7.66 |
% 27.67/7.66 |-The branch is then unsatisfiable
% 27.67/7.66 |-Branch two:
% 27.67/7.66 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.67/7.66 |
% 27.67/7.66 | Applying alpha-rule on (422) yields:
% 27.67/7.66 | (423) all_0_53_53 = e0
% 27.67/7.66 | (424) all_0_59_59 = e1
% 27.67/7.66 | (425) ~ (all_0_54_54 = e1)
% 27.67/7.66 |
% 27.67/7.66 | Combining equations (2308,424) yields a new equation:
% 27.67/7.66 | (560) e1 = e0
% 27.67/7.66 |
% 27.67/7.66 | Equations (560) can reduce 132 to:
% 27.67/7.66 | (270) $false
% 27.67/7.66 |
% 27.67/7.66 |-The branch is then unsatisfiable
% 27.67/7.66 |-Branch two:
% 27.67/7.66 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.67/7.66 |
% 27.67/7.66 | Applying alpha-rule on (428) yields:
% 27.67/7.66 | (423) all_0_53_53 = e0
% 27.67/7.66 | (424) all_0_59_59 = e1
% 27.67/7.66 | (431) ~ (all_0_58_58 = e0)
% 27.67/7.66 |
% 27.67/7.66 | Combining equations (2308,424) yields a new equation:
% 27.67/7.66 | (560) e1 = e0
% 27.67/7.66 |
% 27.67/7.66 | Equations (560) can reduce 132 to:
% 27.67/7.66 | (270) $false
% 27.67/7.66 |
% 27.67/7.66 |-The branch is then unsatisfiable
% 27.67/7.66 |-Branch two:
% 27.67/7.66 | (1093) ~ (all_0_54_54 = e3)
% 27.67/7.66 | (3694) all_0_54_54 = e4 | all_0_54_54 = e1
% 27.67/7.66 |
% 27.67/7.66 +-Applying beta-rule and splitting (3656), into two cases.
% 27.67/7.66 |-Branch one:
% 27.67/7.66 | (1091) all_0_46_46 = e3
% 27.67/7.66 |
% 27.67/7.66 | Combining equations (517,1091) yields a new equation:
% 27.67/7.66 | (660) e4 = e3
% 27.67/7.66 |
% 27.67/7.66 | Simplifying 660 yields:
% 27.67/7.66 | (359) e4 = e3
% 27.67/7.66 |
% 27.67/7.66 | Equations (359) can reduce 34 to:
% 27.67/7.66 | (270) $false
% 27.67/7.66 |
% 27.67/7.66 |-The branch is then unsatisfiable
% 27.67/7.66 |-Branch two:
% 27.67/7.66 | (413) ~ (all_0_46_46 = e3)
% 27.67/7.66 | (3700) all_0_54_54 = e3 | all_0_59_59 = e3
% 27.86/7.66 |
% 27.86/7.66 +-Applying beta-rule and splitting (3700), into two cases.
% 27.86/7.66 |-Branch one:
% 27.86/7.66 | (1119) all_0_54_54 = e3
% 27.86/7.66 |
% 27.86/7.66 | Equations (1119) can reduce 1093 to:
% 27.86/7.66 | (270) $false
% 27.86/7.66 |
% 27.86/7.66 |-The branch is then unsatisfiable
% 27.86/7.66 |-Branch two:
% 27.86/7.66 | (1093) ~ (all_0_54_54 = e3)
% 27.86/7.66 | (412) all_0_59_59 = e3
% 27.86/7.66 |
% 27.86/7.66 | Combining equations (412,2308) yields a new equation:
% 27.86/7.66 | (783) e3 = e0
% 27.86/7.66 |
% 27.86/7.66 | Simplifying 783 yields:
% 27.86/7.66 | (784) e3 = e0
% 27.86/7.66 |
% 27.86/7.66 | Equations (784) can reduce 66 to:
% 27.86/7.66 | (270) $false
% 27.86/7.66 |
% 27.86/7.66 |-The branch is then unsatisfiable
% 27.86/7.66 |-Branch two:
% 27.86/7.66 | (455) ~ (all_0_43_43 = e0)
% 27.86/7.66 | (944) all_0_43_43 = e4 | all_0_43_43 = e3
% 27.86/7.66 |
% 27.86/7.66 +-Applying beta-rule and splitting (511), into two cases.
% 27.86/7.66 |-Branch one:
% 27.86/7.66 | (363) all_0_45_45 = e4
% 27.86/7.66 |
% 27.86/7.66 | Combining equations (374,363) yields a new equation:
% 27.86/7.66 | (269) e4 = e2
% 27.86/7.66 |
% 27.86/7.66 | Equations (269) can reduce 231 to:
% 27.86/7.66 | (270) $false
% 27.86/7.66 |
% 27.86/7.66 |-The branch is then unsatisfiable
% 27.86/7.66 |-Branch two:
% 27.86/7.66 | (352) ~ (all_0_45_45 = e4)
% 27.86/7.66 | (517) all_0_46_46 = e4
% 27.86/7.66 |
% 27.86/7.66 | Equations (517) can reduce 103 to:
% 27.86/7.66 | (510) ~ (all_0_43_43 = e4)
% 27.86/7.66 |
% 27.86/7.66 +-Applying beta-rule and splitting (944), into two cases.
% 27.86/7.66 |-Branch one:
% 27.86/7.66 | (782) all_0_43_43 = e3
% 27.86/7.66 |
% 27.86/7.66 | Equations (782) can reduce 786 to:
% 27.86/7.66 | (270) $false
% 27.86/7.66 |
% 27.86/7.66 |-The branch is then unsatisfiable
% 27.86/7.66 |-Branch two:
% 27.86/7.66 | (786) ~ (all_0_43_43 = e3)
% 27.86/7.66 | (502) all_0_43_43 = e4
% 27.86/7.66 |
% 27.86/7.66 | Equations (502) can reduce 510 to:
% 27.86/7.66 | (270) $false
% 27.86/7.66 |
% 27.86/7.66 |-The branch is then unsatisfiable
% 27.86/7.66 |-Branch two:
% 27.86/7.66 | (498) ~ (all_0_42_42 = e2)
% 27.86/7.66 | (1732) all_0_46_46 = e2 | all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 27.86/7.66 |
% 27.86/7.66 +-Applying beta-rule and splitting (630), into two cases.
% 27.86/7.66 |-Branch one:
% 27.86/7.66 | (327) all_0_40_40 = e2
% 27.86/7.66 |
% 27.86/7.66 | Combining equations (530,327) yields a new equation:
% 27.86/7.66 | (322) e2 = e1
% 27.86/7.66 |
% 27.86/7.66 | Equations (322) can reduce 141 to:
% 27.86/7.66 | (270) $false
% 27.86/7.66 |
% 27.86/7.66 |-The branch is then unsatisfiable
% 27.86/7.66 |-Branch two:
% 27.86/7.66 | (602) ~ (all_0_40_40 = e2)
% 27.86/7.66 | (1251) all_0_41_41 = e2 | all_0_42_42 = e2
% 27.86/7.66 |
% 27.86/7.66 +-Applying beta-rule and splitting (1251), into two cases.
% 27.86/7.66 |-Branch one:
% 27.86/7.66 | (436) all_0_41_41 = e2
% 27.86/7.66 |
% 27.86/7.66 | Equations (436) can reduce 331 to:
% 27.86/7.66 | (270) $false
% 27.86/7.66 |
% 27.86/7.66 |-The branch is then unsatisfiable
% 27.86/7.66 |-Branch two:
% 27.86/7.66 | (331) ~ (all_0_41_41 = e2)
% 27.86/7.66 | (698) all_0_42_42 = e2
% 27.86/7.66 |
% 27.86/7.66 | Equations (698) can reduce 498 to:
% 27.86/7.66 | (270) $false
% 27.86/7.66 |
% 27.86/7.66 |-The branch is then unsatisfiable
% 27.86/7.66 |-Branch two:
% 27.86/7.66 | (434) ~ (all_0_45_45 = e2)
% 27.86/7.66 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 27.86/7.66 |
% 27.86/7.66 +-Applying beta-rule and splitting (187), into two cases.
% 27.86/7.66 |-Branch one:
% 27.86/7.66 | (436) all_0_41_41 = e2
% 27.86/7.66 |
% 27.86/7.66 | Equations (436) can reduce 94 to:
% 27.86/7.66 | (1336) ~ (all_0_42_42 = e2)
% 27.86/7.66 |
% 27.86/7.66 | Simplifying 1336 yields:
% 27.86/7.66 | (498) ~ (all_0_42_42 = e2)
% 27.86/7.66 |
% 27.86/7.66 | Equations (436) can reduce 540 to:
% 27.86/7.66 | (141) ~ (e2 = e1)
% 27.86/7.66 |
% 27.86/7.66 | Equations (436) can reduce 232 to:
% 27.86/7.66 | (57) ~ (e2 = e0)
% 27.86/7.66 |
% 27.86/7.66 +-Applying beta-rule and splitting (435), into two cases.
% 27.86/7.66 |-Branch one:
% 27.86/7.66 | (454) all_0_45_45 = e0
% 27.86/7.66 |
% 27.86/7.66 | Equations (454) can reduce 488 to:
% 27.86/7.66 | (270) $false
% 27.86/7.66 |
% 27.86/7.66 |-The branch is then unsatisfiable
% 27.86/7.66 |-Branch two:
% 27.86/7.66 | (488) ~ (all_0_45_45 = e0)
% 27.86/7.66 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 27.86/7.66 |
% 27.86/7.66 +-Applying beta-rule and splitting (489), into two cases.
% 27.86/7.66 |-Branch one:
% 27.86/7.66 | (505) all_0_45_45 = e3
% 27.86/7.66 |
% 27.86/7.66 | Equations (505) can reduce 354 to:
% 27.86/7.66 | (270) $false
% 27.86/7.66 |
% 27.86/7.66 |-The branch is then unsatisfiable
% 27.86/7.66 |-Branch two:
% 27.86/7.66 | (354) ~ (all_0_45_45 = e3)
% 27.86/7.66 | (363) all_0_45_45 = e4
% 27.86/7.66 |
% 27.86/7.66 | Equations (363) can reduce 84 to:
% 27.86/7.66 | (510) ~ (all_0_43_43 = e4)
% 27.86/7.66 |
% 27.86/7.66 +-Applying beta-rule and splitting (209), into two cases.
% 27.86/7.66 |-Branch one:
% 27.86/7.66 | (698) all_0_42_42 = e2
% 27.86/7.66 |
% 27.86/7.66 | Equations (698) can reduce 498 to:
% 27.86/7.66 | (270) $false
% 27.86/7.66 |
% 27.86/7.66 |-The branch is then unsatisfiable
% 27.86/7.66 |-Branch two:
% 27.86/7.66 | (498) ~ (all_0_42_42 = e2)
% 27.86/7.66 | (1732) all_0_46_46 = e2 | all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 27.86/7.66 |
% 27.86/7.66 +-Applying beta-rule and splitting (1732), into two cases.
% 27.86/7.66 |-Branch one:
% 27.86/7.66 | (497) all_0_46_46 = e2
% 27.86/7.66 |
% 27.86/7.66 | Equations (497) can reduce 103 to:
% 27.86/7.66 | (292) ~ (all_0_43_43 = e2)
% 27.86/7.66 |
% 27.86/7.66 +-Applying beta-rule and splitting (221), into two cases.
% 27.86/7.66 |-Branch one:
% 27.86/7.66 | (1132) all_0_46_46 = e0
% 27.86/7.66 |
% 27.86/7.66 | Combining equations (497,1132) yields a new equation:
% 27.86/7.66 | (622) e2 = e0
% 27.86/7.66 |
% 27.86/7.66 | Simplifying 622 yields:
% 27.86/7.66 | (316) e2 = e0
% 27.86/7.66 |
% 27.86/7.66 | Equations (316) can reduce 57 to:
% 27.86/7.66 | (270) $false
% 27.86/7.66 |
% 27.86/7.66 |-The branch is then unsatisfiable
% 27.86/7.66 |-Branch two:
% 27.86/7.66 | (1010) ~ (all_0_46_46 = e0)
% 27.86/7.66 | (3629) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 27.86/7.66 |
% 27.86/7.66 +-Applying beta-rule and splitting (3629), into two cases.
% 27.86/7.66 |-Branch one:
% 27.86/7.66 | (563) all_0_49_49 = e0
% 27.86/7.66 |
% 27.86/7.66 | Combining equations (589,563) yields a new equation:
% 27.86/7.66 | (571) e1 = e0
% 27.86/7.66 |
% 27.86/7.66 | Simplifying 571 yields:
% 27.86/7.66 | (560) e1 = e0
% 27.86/7.66 |
% 27.86/7.66 | Equations (560) can reduce 132 to:
% 27.86/7.66 | (270) $false
% 27.86/7.66 |
% 27.86/7.66 |-The branch is then unsatisfiable
% 27.86/7.66 |-Branch two:
% 27.86/7.66 | (1231) ~ (all_0_49_49 = e0)
% 27.86/7.66 | (3638) all_0_54_54 = e0 | all_0_59_59 = e0
% 27.86/7.66 |
% 27.86/7.66 +-Applying beta-rule and splitting (3638), into two cases.
% 27.86/7.66 |-Branch one:
% 27.86/7.66 | (3084) all_0_54_54 = e0
% 27.86/7.66 |
% 27.86/7.66 | Equations (3084) can reduce 3011 to:
% 27.86/7.66 | (270) $false
% 27.86/7.66 |
% 27.86/7.66 |-The branch is then unsatisfiable
% 27.86/7.66 |-Branch two:
% 27.86/7.66 | (3011) ~ (all_0_54_54 = e0)
% 27.86/7.66 | (2308) all_0_59_59 = e0
% 27.86/7.66 |
% 27.86/7.66 +-Applying beta-rule and splitting (159), into two cases.
% 27.86/7.66 |-Branch one:
% 27.86/7.66 | (450) all_0_43_43 = e2
% 27.86/7.66 |
% 27.86/7.66 | Equations (450) can reduce 292 to:
% 27.86/7.66 | (270) $false
% 27.86/7.66 |
% 27.86/7.66 |-The branch is then unsatisfiable
% 27.86/7.66 |-Branch two:
% 27.86/7.66 | (292) ~ (all_0_43_43 = e2)
% 27.86/7.66 | (774) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 27.86/7.66 |
% 27.86/7.66 +-Applying beta-rule and splitting (774), into two cases.
% 27.86/7.66 |-Branch one:
% 27.86/7.66 | (411) all_0_43_43 = e0
% 27.86/7.66 |
% 27.86/7.66 | Equations (411) can reduce 510 to:
% 27.86/7.66 | (456) ~ (e4 = e0)
% 27.86/7.66 |
% 27.86/7.66 | Simplifying 456 yields:
% 27.86/7.66 | (6) ~ (e4 = e0)
% 27.86/7.66 |
% 27.86/7.66 | Equations (411) can reduce 786 to:
% 27.86/7.66 | (788) ~ (e3 = e0)
% 27.86/7.66 |
% 27.86/7.66 | Simplifying 788 yields:
% 27.86/7.66 | (66) ~ (e3 = e0)
% 27.86/7.66 |
% 27.86/7.66 | Equations (411) can reduce 249 to:
% 27.86/7.66 | (568) ~ (e1 = e0)
% 27.86/7.66 |
% 27.86/7.66 | Simplifying 568 yields:
% 27.86/7.66 | (132) ~ (e1 = e0)
% 27.86/7.66 |
% 27.86/7.66 +-Applying beta-rule and splitting (93), into two cases.
% 27.86/7.66 |-Branch one:
% 27.86/7.66 | (402) all_0_59_59 = e4
% 27.86/7.66 |
% 27.86/7.66 | Combining equations (402,2308) yields a new equation:
% 27.86/7.66 | (478) e4 = e0
% 27.86/7.66 |
% 27.86/7.66 | Simplifying 478 yields:
% 27.86/7.66 | (479) e4 = e0
% 27.86/7.66 |
% 27.86/7.66 | Equations (479) can reduce 6 to:
% 27.86/7.66 | (270) $false
% 27.86/7.66 |
% 27.86/7.66 |-The branch is then unsatisfiable
% 27.86/7.66 |-Branch two:
% 27.86/7.66 | (280) ~ (all_0_59_59 = e4)
% 27.86/7.66 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.86/7.66 |
% 27.86/7.66 +-Applying beta-rule and splitting (407), into two cases.
% 27.86/7.66 |-Branch one:
% 27.86/7.66 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.86/7.66 |
% 27.86/7.66 +-Applying beta-rule and splitting (408), into two cases.
% 27.86/7.66 |-Branch one:
% 27.86/7.66 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.86/7.66 |
% 27.86/7.66 +-Applying beta-rule and splitting (409), into two cases.
% 27.86/7.66 |-Branch one:
% 27.86/7.66 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.86/7.66 |
% 27.86/7.66 | Applying alpha-rule on (410) yields:
% 27.86/7.66 | (411) all_0_43_43 = e0
% 27.86/7.66 | (412) all_0_59_59 = e3
% 27.86/7.66 | (413) ~ (all_0_46_46 = e3)
% 27.86/7.66 |
% 27.86/7.66 | Combining equations (412,2308) yields a new equation:
% 27.86/7.66 | (783) e3 = e0
% 27.86/7.66 |
% 27.86/7.66 | Simplifying 783 yields:
% 27.86/7.66 | (784) e3 = e0
% 27.86/7.66 |
% 27.86/7.66 | Equations (784) can reduce 66 to:
% 27.86/7.66 | (270) $false
% 27.86/7.66 |
% 27.86/7.66 |-The branch is then unsatisfiable
% 27.86/7.66 |-Branch two:
% 27.86/7.66 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.86/7.66 |
% 27.86/7.66 | Applying alpha-rule on (416) yields:
% 27.86/7.66 | (411) all_0_43_43 = e0
% 27.86/7.66 | (412) all_0_59_59 = e3
% 27.86/7.66 | (419) ~ (all_0_56_56 = e0)
% 27.86/7.66 |
% 27.86/7.66 | Combining equations (412,2308) yields a new equation:
% 27.86/7.66 | (783) e3 = e0
% 27.86/7.66 |
% 27.86/7.66 | Simplifying 783 yields:
% 27.86/7.66 | (784) e3 = e0
% 27.86/7.66 |
% 27.86/7.66 | Equations (784) can reduce 66 to:
% 27.86/7.66 | (270) $false
% 27.86/7.66 |
% 27.86/7.66 |-The branch is then unsatisfiable
% 27.86/7.66 |-Branch two:
% 27.86/7.66 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.86/7.66 |
% 27.86/7.66 | Applying alpha-rule on (422) yields:
% 27.86/7.66 | (423) all_0_53_53 = e0
% 27.86/7.66 | (424) all_0_59_59 = e1
% 27.86/7.66 | (425) ~ (all_0_54_54 = e1)
% 27.86/7.66 |
% 27.86/7.66 | Combining equations (2308,424) yields a new equation:
% 27.86/7.66 | (560) e1 = e0
% 27.86/7.66 |
% 27.86/7.66 | Equations (560) can reduce 132 to:
% 27.86/7.66 | (270) $false
% 27.86/7.66 |
% 27.86/7.66 |-The branch is then unsatisfiable
% 27.86/7.66 |-Branch two:
% 27.86/7.66 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.86/7.66 |
% 27.86/7.66 | Applying alpha-rule on (428) yields:
% 27.86/7.66 | (423) all_0_53_53 = e0
% 27.86/7.66 | (424) all_0_59_59 = e1
% 27.86/7.66 | (431) ~ (all_0_58_58 = e0)
% 27.86/7.66 |
% 27.86/7.66 | Combining equations (2308,424) yields a new equation:
% 27.86/7.66 | (560) e1 = e0
% 27.86/7.66 |
% 27.86/7.66 | Equations (560) can reduce 132 to:
% 27.86/7.66 | (270) $false
% 27.86/7.66 |
% 27.86/7.66 |-The branch is then unsatisfiable
% 27.86/7.66 |-Branch two:
% 27.86/7.66 | (455) ~ (all_0_43_43 = e0)
% 27.86/7.66 | (944) all_0_43_43 = e4 | all_0_43_43 = e3
% 27.86/7.66 |
% 27.86/7.66 +-Applying beta-rule and splitting (944), into two cases.
% 27.86/7.66 |-Branch one:
% 27.86/7.66 | (782) all_0_43_43 = e3
% 27.86/7.66 |
% 27.86/7.66 | Equations (782) can reduce 786 to:
% 27.86/7.66 | (270) $false
% 27.86/7.66 |
% 27.86/7.66 |-The branch is then unsatisfiable
% 27.86/7.66 |-Branch two:
% 27.86/7.66 | (786) ~ (all_0_43_43 = e3)
% 27.86/7.66 | (502) all_0_43_43 = e4
% 27.86/7.66 |
% 27.86/7.66 | Equations (502) can reduce 510 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (1436) ~ (all_0_46_46 = e2)
% 27.86/7.67 | (3824) all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 27.86/7.67 |
% 27.86/7.67 +-Applying beta-rule and splitting (3824), into two cases.
% 27.86/7.67 |-Branch one:
% 27.86/7.67 | (307) all_0_49_49 = e2
% 27.86/7.67 |
% 27.86/7.67 | Combining equations (589,307) yields a new equation:
% 27.86/7.67 | (322) e2 = e1
% 27.86/7.67 |
% 27.86/7.67 | Equations (322) can reduce 141 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (296) ~ (all_0_49_49 = e2)
% 27.86/7.67 | (3829) all_0_54_54 = e2 | all_0_59_59 = e2
% 27.86/7.67 |
% 27.86/7.67 +-Applying beta-rule and splitting (3829), into two cases.
% 27.86/7.67 |-Branch one:
% 27.86/7.67 | (3657) all_0_54_54 = e2
% 27.86/7.67 |
% 27.86/7.67 | Equations (3657) can reduce 261 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (261) ~ (all_0_54_54 = e2)
% 27.86/7.67 | (399) all_0_59_59 = e2
% 27.86/7.67 |
% 27.86/7.67 | Equations (399) can reduce 701 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (331) ~ (all_0_41_41 = e2)
% 27.86/7.67 | (441) all_0_45_45 = e2 | all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 27.86/7.67 |
% 27.86/7.67 +-Applying beta-rule and splitting (453), into two cases.
% 27.86/7.67 |-Branch one:
% 27.86/7.67 | (370) all_0_44_44 = e2
% 27.86/7.67 |
% 27.86/7.67 | Combining equations (858,370) yields a new equation:
% 27.86/7.67 | (437) e3 = e2
% 27.86/7.67 |
% 27.86/7.67 | Simplifying 437 yields:
% 27.86/7.67 | (414) e3 = e2
% 27.86/7.67 |
% 27.86/7.67 | Equations (414) can reduce 223 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (333) ~ (all_0_44_44 = e2)
% 27.86/7.67 | (493) all_0_45_45 = e2 | all_0_46_46 = e2
% 27.86/7.67 |
% 27.86/7.67 +-Applying beta-rule and splitting (493), into two cases.
% 27.86/7.67 |-Branch one:
% 27.86/7.67 | (374) all_0_45_45 = e2
% 27.86/7.67 |
% 27.86/7.67 | Equations (374) can reduce 434 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (434) ~ (all_0_45_45 = e2)
% 27.86/7.67 | (497) all_0_46_46 = e2
% 27.86/7.67 |
% 27.86/7.67 | Equations (497) can reduce 103 to:
% 27.86/7.67 | (292) ~ (all_0_43_43 = e2)
% 27.86/7.67 |
% 27.86/7.67 | Equations (497) can reduce 38 to:
% 27.86/7.67 | (434) ~ (all_0_45_45 = e2)
% 27.86/7.67 |
% 27.86/7.67 | Equations (497) can reduce 206 to:
% 27.86/7.67 | (700) ~ (all_0_59_59 = e2)
% 27.86/7.67 |
% 27.86/7.67 | Simplifying 700 yields:
% 27.86/7.67 | (701) ~ (all_0_59_59 = e2)
% 27.86/7.67 |
% 27.86/7.67 +-Applying beta-rule and splitting (116), into two cases.
% 27.86/7.67 |-Branch one:
% 27.86/7.67 | (411) all_0_43_43 = e0
% 27.86/7.67 |
% 27.86/7.67 | Equations (411) can reduce 188 to:
% 27.86/7.67 | (3852) ~ (all_0_56_56 = e0)
% 27.86/7.67 |
% 27.86/7.67 | Simplifying 3852 yields:
% 27.86/7.67 | (419) ~ (all_0_56_56 = e0)
% 27.86/7.67 |
% 27.86/7.67 | Equations (411) can reduce 292 to:
% 27.86/7.67 | (566) ~ (e2 = e0)
% 27.86/7.67 |
% 27.86/7.67 | Simplifying 566 yields:
% 27.86/7.67 | (57) ~ (e2 = e0)
% 27.86/7.67 |
% 27.86/7.67 +-Applying beta-rule and splitting (176), into two cases.
% 27.86/7.67 |-Branch one:
% 27.86/7.67 | (830) all_0_56_56 = e0
% 27.86/7.67 |
% 27.86/7.67 | Equations (830) can reduce 419 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (419) ~ (all_0_56_56 = e0)
% 27.86/7.67 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 27.86/7.67 |
% 27.86/7.67 +-Applying beta-rule and splitting (221), into two cases.
% 27.86/7.67 |-Branch one:
% 27.86/7.67 | (1132) all_0_46_46 = e0
% 27.86/7.67 |
% 27.86/7.67 | Combining equations (497,1132) yields a new equation:
% 27.86/7.67 | (622) e2 = e0
% 27.86/7.67 |
% 27.86/7.67 | Simplifying 622 yields:
% 27.86/7.67 | (316) e2 = e0
% 27.86/7.67 |
% 27.86/7.67 | Equations (316) can reduce 57 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (1010) ~ (all_0_46_46 = e0)
% 27.86/7.67 | (3629) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 27.86/7.67 |
% 27.86/7.67 | Equations (497) can reduce 1010 to:
% 27.86/7.67 | (57) ~ (e2 = e0)
% 27.86/7.67 |
% 27.86/7.67 +-Applying beta-rule and splitting (441), into two cases.
% 27.86/7.67 |-Branch one:
% 27.86/7.67 | (374) all_0_45_45 = e2
% 27.86/7.67 |
% 27.86/7.67 | Equations (374) can reduce 434 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (434) ~ (all_0_45_45 = e2)
% 27.86/7.67 | (445) all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 27.86/7.67 |
% 27.86/7.67 +-Applying beta-rule and splitting (834), into two cases.
% 27.86/7.67 |-Branch one:
% 27.86/7.67 | (2258) all_0_57_57 = e0
% 27.86/7.67 |
% 27.86/7.67 | Combining equations (2258,392) yields a new equation:
% 27.86/7.67 | (316) e2 = e0
% 27.86/7.67 |
% 27.86/7.67 | Equations (316) can reduce 57 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (2301) ~ (all_0_57_57 = e0)
% 27.86/7.67 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 27.86/7.67 |
% 27.86/7.67 +-Applying beta-rule and splitting (2302), into two cases.
% 27.86/7.67 |-Branch one:
% 27.86/7.67 | (585) all_0_58_58 = e0
% 27.86/7.67 |
% 27.86/7.67 | Equations (585) can reduce 431 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (431) ~ (all_0_58_58 = e0)
% 27.86/7.67 | (2308) all_0_59_59 = e0
% 27.86/7.67 |
% 27.86/7.67 | Equations (2308) can reduce 701 to:
% 27.86/7.67 | (566) ~ (e2 = e0)
% 27.86/7.67 |
% 27.86/7.67 | Simplifying 566 yields:
% 27.86/7.67 | (57) ~ (e2 = e0)
% 27.86/7.67 |
% 27.86/7.67 +-Applying beta-rule and splitting (445), into two cases.
% 27.86/7.67 |-Branch one:
% 27.86/7.67 | (311) all_0_48_48 = e2
% 27.86/7.67 |
% 27.86/7.67 | Combining equations (559,311) yields a new equation:
% 27.86/7.67 | (316) e2 = e0
% 27.86/7.67 |
% 27.86/7.67 | Equations (316) can reduce 57 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (294) ~ (all_0_48_48 = e2)
% 27.86/7.67 | (449) all_0_53_53 = e2 | all_0_58_58 = e2
% 27.86/7.67 |
% 27.86/7.67 +-Applying beta-rule and splitting (204), into two cases.
% 27.86/7.67 |-Branch one:
% 27.86/7.67 | (396) all_0_58_58 = e2
% 27.86/7.67 |
% 27.86/7.67 | Equations (396) can reduce 376 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (376) ~ (all_0_58_58 = e2)
% 27.86/7.67 | (3890) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1 | all_0_58_58 = e0
% 27.86/7.67 |
% 27.86/7.67 +-Applying beta-rule and splitting (449), into two cases.
% 27.86/7.67 |-Branch one:
% 27.86/7.67 | (576) all_0_53_53 = e2
% 27.86/7.67 |
% 27.86/7.67 | Equations (576) can reduce 259 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (259) ~ (all_0_53_53 = e2)
% 27.86/7.67 | (396) all_0_58_58 = e2
% 27.86/7.67 |
% 27.86/7.67 | Equations (396) can reduce 376 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (455) ~ (all_0_43_43 = e0)
% 27.86/7.67 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 27.86/7.67 |
% 27.86/7.67 +-Applying beta-rule and splitting (75), into two cases.
% 27.86/7.67 |-Branch one:
% 27.86/7.67 | (411) all_0_43_43 = e0
% 27.86/7.67 |
% 27.86/7.67 | Equations (411) can reduce 455 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (455) ~ (all_0_43_43 = e0)
% 27.86/7.67 | (940) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 27.86/7.67 |
% 27.86/7.67 +-Applying beta-rule and splitting (435), into two cases.
% 27.86/7.67 |-Branch one:
% 27.86/7.67 | (454) all_0_45_45 = e0
% 27.86/7.67 |
% 27.86/7.67 | Equations (454) can reduce 488 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (488) ~ (all_0_45_45 = e0)
% 27.86/7.67 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 27.86/7.67 |
% 27.86/7.67 +-Applying beta-rule and splitting (159), into two cases.
% 27.86/7.67 |-Branch one:
% 27.86/7.67 | (450) all_0_43_43 = e2
% 27.86/7.67 |
% 27.86/7.67 | Equations (450) can reduce 292 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (292) ~ (all_0_43_43 = e2)
% 27.86/7.67 | (774) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 27.86/7.67 |
% 27.86/7.67 +-Applying beta-rule and splitting (774), into two cases.
% 27.86/7.67 |-Branch one:
% 27.86/7.67 | (411) all_0_43_43 = e0
% 27.86/7.67 |
% 27.86/7.67 | Equations (411) can reduce 455 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (455) ~ (all_0_43_43 = e0)
% 27.86/7.67 | (944) all_0_43_43 = e4 | all_0_43_43 = e3
% 27.86/7.67 |
% 27.86/7.67 +-Applying beta-rule and splitting (944), into two cases.
% 27.86/7.67 |-Branch one:
% 27.86/7.67 | (782) all_0_43_43 = e3
% 27.86/7.67 |
% 27.86/7.67 | Equations (782) can reduce 786 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (786) ~ (all_0_43_43 = e3)
% 27.86/7.67 | (502) all_0_43_43 = e4
% 27.86/7.67 |
% 27.86/7.67 | Equations (502) can reduce 84 to:
% 27.86/7.67 | (503) ~ (all_0_45_45 = e4)
% 27.86/7.67 |
% 27.86/7.67 | Simplifying 503 yields:
% 27.86/7.67 | (352) ~ (all_0_45_45 = e4)
% 27.86/7.67 |
% 27.86/7.67 +-Applying beta-rule and splitting (489), into two cases.
% 27.86/7.67 |-Branch one:
% 27.86/7.67 | (505) all_0_45_45 = e3
% 27.86/7.67 |
% 27.86/7.67 | Equations (505) can reduce 354 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (354) ~ (all_0_45_45 = e3)
% 27.86/7.67 | (363) all_0_45_45 = e4
% 27.86/7.67 |
% 27.86/7.67 | Equations (363) can reduce 352 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (562) ~ (all_0_48_48 = e0)
% 27.86/7.67 | (563) all_0_49_49 = e0
% 27.86/7.67 |
% 27.86/7.67 | Combining equations (563,589) yields a new equation:
% 27.86/7.67 | (560) e1 = e0
% 27.86/7.67 |
% 27.86/7.67 | Equations (560) can reduce 132 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (1762) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 27.86/7.67 |
% 27.86/7.67 | Applying alpha-rule on (1762) yields:
% 27.86/7.67 | (1763) all_0_19_19 = e0
% 27.86/7.67 | (1764) ~ (all_0_20_20 = e2)
% 27.86/7.67 |
% 27.86/7.67 | Combining equations (3391,1763) yields a new equation:
% 27.86/7.67 | (478) e4 = e0
% 27.86/7.67 |
% 27.86/7.67 | Simplifying 478 yields:
% 27.86/7.67 | (479) e4 = e0
% 27.86/7.67 |
% 27.86/7.67 | Equations (479) can reduce 6 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (534) ~ (all_0_40_40 = e1)
% 27.86/7.67 | (3352) all_0_52_52 = e1 | all_0_57_57 = e1
% 27.86/7.67 |
% 27.86/7.67 +-Applying beta-rule and splitting (3352), into two cases.
% 27.86/7.67 |-Branch one:
% 27.86/7.67 | (848) all_0_52_52 = e1
% 27.86/7.67 |
% 27.86/7.67 | Combining equations (848,827) yields a new equation:
% 27.86/7.67 | (571) e1 = e0
% 27.86/7.67 |
% 27.86/7.67 | Simplifying 571 yields:
% 27.86/7.67 | (560) e1 = e0
% 27.86/7.67 |
% 27.86/7.67 | Equations (560) can reduce 132 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (642) ~ (all_0_52_52 = e1)
% 27.86/7.67 | (997) all_0_57_57 = e1
% 27.86/7.67 |
% 27.86/7.67 | Combining equations (392,997) yields a new equation:
% 27.86/7.67 | (531) e2 = e1
% 27.86/7.67 |
% 27.86/7.67 | Simplifying 531 yields:
% 27.86/7.67 | (322) e2 = e1
% 27.86/7.67 |
% 27.86/7.67 | Equations (322) can reduce 141 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (925) ~ (all_0_52_52 = e0)
% 27.86/7.67 | (2258) all_0_57_57 = e0
% 27.86/7.67 |
% 27.86/7.67 | Combining equations (392,2258) yields a new equation:
% 27.86/7.67 | (622) e2 = e0
% 27.86/7.67 |
% 27.86/7.67 | Simplifying 622 yields:
% 27.86/7.67 | (316) e2 = e0
% 27.86/7.67 |
% 27.86/7.67 | Equations (316) can reduce 57 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (3951) ~ (all_0_47_47 = e2)
% 27.86/7.67 | (3952) all_0_48_48 = e2 | all_0_49_49 = e2
% 27.86/7.67 |
% 27.86/7.67 +-Applying beta-rule and splitting (155), into two cases.
% 27.86/7.67 |-Branch one:
% 27.86/7.67 | (290) all_0_47_47 = e2
% 27.86/7.67 |
% 27.86/7.67 | Equations (290) can reduce 3951 to:
% 27.86/7.67 | (270) $false
% 27.86/7.67 |
% 27.86/7.67 |-The branch is then unsatisfiable
% 27.86/7.67 |-Branch two:
% 27.86/7.67 | (3951) ~ (all_0_47_47 = e2)
% 27.86/7.67 | (3956) all_0_47_47 = e1 | all_0_47_47 = e0
% 27.86/7.67 |
% 27.86/7.67 +-Applying beta-rule and splitting (129), into two cases.
% 27.86/7.67 |-Branch one:
% 27.86/7.67 | (311) all_0_48_48 = e2
% 27.86/7.67 |
% 27.86/7.67 | Equations (311) can reduce 190 to:
% 27.86/7.67 | (331) ~ (all_0_41_41 = e2)
% 27.86/7.67 |
% 27.86/7.67 | Equations (311) can reduce 65 to:
% 27.86/7.67 | (434) ~ (all_0_45_45 = e2)
% 27.86/7.67 |
% 27.86/7.67 | Equations (311) can reduce 225 to:
% 27.86/7.67 | (3951) ~ (all_0_47_47 = e2)
% 27.86/7.67 |
% 27.86/7.67 | Equations (311) can reduce 4 to:
% 27.86/7.67 | (295) ~ (all_0_49_49 = e2)
% 27.86/7.67 |
% 27.86/7.67 | Simplifying 295 yields:
% 27.86/7.67 | (296) ~ (all_0_49_49 = e2)
% 27.86/7.67 |
% 27.86/7.67 | Equations (311) can reduce 48 to:
% 27.86/7.67 | (258) ~ (all_0_53_53 = e2)
% 27.86/7.67 |
% 27.86/7.67 | Simplifying 258 yields:
% 27.86/7.67 | (259) ~ (all_0_53_53 = e2)
% 27.86/7.67 |
% 27.86/7.67 | Equations (311) can reduce 59 to:
% 27.86/7.67 | (375) ~ (all_0_58_58 = e2)
% 27.86/7.67 |
% 27.86/7.67 | Simplifying 375 yields:
% 27.86/7.67 | (376) ~ (all_0_58_58 = e2)
% 27.86/7.67 |
% 27.86/7.67 | Equations (311) can reduce 121 to:
% 27.86/7.67 | (301) ~ (e3 = e2)
% 27.86/7.67 |
% 27.86/7.67 | Simplifying 301 yields:
% 27.86/7.67 | (223) ~ (e3 = e2)
% 27.86/7.67 |
% 27.86/7.67 | From (311) and (183) follows:
% 27.86/7.68 | (3969) op(e2, e2) = all_0_26_26
% 27.86/7.68 |
% 27.86/7.68 | From (311) and (56) follows:
% 27.86/7.68 | (3970) op(e2, e1) = e2
% 27.86/7.68 |
% 27.86/7.68 | From (311) and (76) follows:
% 27.86/7.68 | (3971) op(e1, e2) = all_0_25_25
% 27.86/7.68 |
% 27.86/7.68 | Instantiating formula (201) with e2, e2, all_0_26_26, e4 and discharging atoms op(e2, e2) = all_0_26_26, op(e2, e2) = e4, yields:
% 27.86/7.68 | (3972) all_0_26_26 = e4
% 27.86/7.68 |
% 27.86/7.68 | Instantiating formula (201) with e1, e2, all_0_25_25, all_0_52_52 and discharging atoms op(e1, e2) = all_0_25_25, op(e1, e2) = all_0_52_52, yields:
% 27.86/7.68 | (3973) all_0_25_25 = all_0_52_52
% 27.86/7.68 |
% 27.86/7.68 | From (3972) and (3969) follows:
% 27.86/7.68 | (115) op(e2, e2) = e4
% 27.86/7.68 |
% 27.86/7.68 +-Applying beta-rule and splitting (117), into two cases.
% 27.86/7.68 |-Branch one:
% 27.86/7.68 | (307) all_0_49_49 = e2
% 27.86/7.68 |
% 27.86/7.68 | Equations (307) can reduce 296 to:
% 27.86/7.68 | (270) $false
% 27.86/7.68 |
% 27.86/7.68 |-The branch is then unsatisfiable
% 27.86/7.68 |-Branch two:
% 27.86/7.68 | (296) ~ (all_0_49_49 = e2)
% 27.86/7.68 | (310) all_0_49_49 = e1 | all_0_49_49 = e0
% 27.86/7.68 |
% 27.86/7.68 +-Applying beta-rule and splitting (83), into two cases.
% 27.86/7.68 |-Branch one:
% 27.86/7.68 | (321) all_0_47_47 = e1
% 27.86/7.68 |
% 27.86/7.68 | Equations (321) can reduce 100 to:
% 27.86/7.68 | (528) ~ (all_0_39_39 = e1)
% 27.86/7.68 |
% 27.86/7.68 | Equations (321) can reduce 170 to:
% 27.86/7.68 | (249) ~ (all_0_43_43 = e1)
% 27.86/7.68 |
% 27.86/7.68 | Equations (321) can reduce 80 to:
% 27.86/7.68 | (542) ~ (all_0_49_49 = e1)
% 27.86/7.68 |
% 27.86/7.68 | Simplifying 542 yields:
% 27.86/7.68 | (543) ~ (all_0_49_49 = e1)
% 27.86/7.68 |
% 27.86/7.68 | Equations (321) can reduce 3 to:
% 27.86/7.68 | (3984) ~ (all_0_51_51 = e1)
% 27.86/7.68 |
% 27.89/7.68 | Simplifying 3984 yields:
% 27.89/7.68 | (748) ~ (all_0_51_51 = e1)
% 27.89/7.68 |
% 27.89/7.68 | Equations (321) can reduce 218 to:
% 27.89/7.68 | (3986) ~ (all_0_56_56 = e1)
% 27.89/7.68 |
% 27.89/7.68 | Simplifying 3986 yields:
% 27.89/7.68 | (995) ~ (all_0_56_56 = e1)
% 27.89/7.68 |
% 27.89/7.68 | Equations (321) can reduce 247 to:
% 27.89/7.68 | (769) ~ (e3 = e1)
% 27.89/7.68 |
% 27.89/7.68 | Simplifying 769 yields:
% 27.89/7.68 | (136) ~ (e3 = e1)
% 27.89/7.68 |
% 27.89/7.68 | Equations (321) can reduce 3951 to:
% 27.89/7.68 | (645) ~ (e2 = e1)
% 27.89/7.68 |
% 27.89/7.68 | Simplifying 645 yields:
% 27.89/7.68 | (141) ~ (e2 = e1)
% 27.89/7.68 |
% 27.89/7.68 | From (321) and (237) follows:
% 27.89/7.68 | (3992) op(e3, e1) = all_0_7_7
% 27.89/7.68 |
% 27.89/7.68 | From (321) and (42) follows:
% 27.89/7.68 | (3993) op(e2, e1) = all_0_8_8
% 27.89/7.68 |
% 27.89/7.68 | From (321) and (40) follows:
% 27.89/7.68 | (1103) op(e2, e3) = e1
% 27.89/7.68 |
% 27.89/7.68 +-Applying beta-rule and splitting (310), into two cases.
% 27.89/7.68 |-Branch one:
% 27.89/7.68 | (563) all_0_49_49 = e0
% 27.89/7.68 |
% 27.89/7.68 | Equations (563) can reduce 169 to:
% 27.89/7.68 | (199) ~ (all_0_42_42 = e0)
% 27.89/7.68 |
% 27.89/7.68 | Equations (563) can reduce 198 to:
% 27.89/7.68 | (1010) ~ (all_0_46_46 = e0)
% 27.89/7.68 |
% 27.89/7.68 | Equations (563) can reduce 162 to:
% 27.89/7.68 | (3010) ~ (all_0_54_54 = e0)
% 27.89/7.68 |
% 27.89/7.68 | Simplifying 3010 yields:
% 27.89/7.68 | (3011) ~ (all_0_54_54 = e0)
% 27.89/7.68 |
% 27.89/7.68 | Equations (563) can reduce 113 to:
% 27.89/7.68 | (4000) ~ (all_0_59_59 = e0)
% 27.89/7.68 |
% 27.89/7.68 | Simplifying 4000 yields:
% 27.89/7.68 | (4001) ~ (all_0_59_59 = e0)
% 27.89/7.68 |
% 27.89/7.68 | Equations (563) can reduce 150 to:
% 27.89/7.68 | (788) ~ (e3 = e0)
% 27.89/7.68 |
% 27.89/7.68 | Simplifying 788 yields:
% 27.89/7.68 | (66) ~ (e3 = e0)
% 27.89/7.68 |
% 27.89/7.68 | Equations (563) can reduce 296 to:
% 27.89/7.68 | (566) ~ (e2 = e0)
% 27.89/7.68 |
% 27.89/7.68 | Simplifying 566 yields:
% 27.89/7.68 | (57) ~ (e2 = e0)
% 27.89/7.68 |
% 27.89/7.68 | Equations (563) can reduce 543 to:
% 27.89/7.68 | (568) ~ (e1 = e0)
% 27.89/7.68 |
% 27.89/7.68 | Simplifying 568 yields:
% 27.89/7.68 | (132) ~ (e1 = e0)
% 27.89/7.68 |
% 27.89/7.68 | From (563) and (153) follows:
% 27.89/7.68 | (4008) op(e2, e0) = all_0_35_35
% 27.89/7.68 |
% 27.89/7.68 | From (563) and (134) follows:
% 27.89/7.68 | (2996) op(e2, e0) = e0
% 27.89/7.68 |
% 27.89/7.68 | From (563) and (88) follows:
% 27.89/7.68 | (4010) op(e0, e0) = all_0_34_34
% 27.89/7.68 |
% 27.89/7.68 | Instantiating formula (201) with e3, e1, all_0_7_7, all_0_45_45 and discharging atoms op(e3, e1) = all_0_7_7, op(e3, e1) = all_0_45_45, yields:
% 27.89/7.68 | (4011) all_0_7_7 = all_0_45_45
% 27.89/7.68 |
% 27.89/7.68 | Instantiating formula (201) with e2, e1, all_0_8_8, e2 and discharging atoms op(e2, e1) = all_0_8_8, op(e2, e1) = e2, yields:
% 27.89/7.68 | (4012) all_0_8_8 = e2
% 27.89/7.68 |
% 27.89/7.68 | Instantiating formula (201) with e2, e0, e0, all_0_35_35 and discharging atoms op(e2, e0) = all_0_35_35, op(e2, e0) = e0, yields:
% 27.89/7.68 | (4013) all_0_35_35 = e0
% 27.89/7.68 |
% 27.89/7.68 | Instantiating formula (201) with e0, e0, all_0_34_34, all_0_59_59 and discharging atoms op(e0, e0) = all_0_34_34, op(e0, e0) = all_0_59_59, yields:
% 27.89/7.68 | (4014) all_0_34_34 = all_0_59_59
% 27.89/7.68 |
% 27.89/7.68 | From (4012) and (3993) follows:
% 27.89/7.68 | (3970) op(e2, e1) = e2
% 27.89/7.68 |
% 27.89/7.68 | From (4013) and (4008) follows:
% 27.89/7.68 | (2996) op(e2, e0) = e0
% 27.89/7.68 |
% 27.89/7.68 +-Applying beta-rule and splitting (125), into two cases.
% 27.89/7.68 |-Branch one:
% 27.89/7.68 | (327) all_0_40_40 = e2
% 27.89/7.68 |
% 27.89/7.68 | Combining equations (327,285) yields a new equation:
% 27.89/7.68 | (328) all_0_0_0 = e2
% 27.89/7.68 |
% 27.89/7.68 | Equations (327) can reduce 114 to:
% 27.89/7.68 | (291) ~ (all_0_39_39 = e2)
% 27.89/7.68 |
% 27.89/7.68 +-Applying beta-rule and splitting (186), into two cases.
% 27.89/7.68 |-Branch one:
% 27.89/7.68 | (336) all_0_39_39 = e2
% 27.89/7.68 |
% 27.89/7.68 | Equations (336) can reduce 291 to:
% 27.89/7.68 | (270) $false
% 27.89/7.68 |
% 27.89/7.68 |-The branch is then unsatisfiable
% 27.89/7.68 |-Branch two:
% 27.89/7.68 | (291) ~ (all_0_39_39 = e2)
% 27.89/7.68 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 27.89/7.68 |
% 27.89/7.68 +-Applying beta-rule and splitting (339), into two cases.
% 27.89/7.68 |-Branch one:
% 27.89/7.68 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 27.89/7.68 |
% 27.89/7.68 +-Applying beta-rule and splitting (340), into two cases.
% 27.89/7.68 |-Branch one:
% 27.89/7.68 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 27.89/7.68 |
% 27.89/7.68 | Applying alpha-rule on (341) yields:
% 27.89/7.68 | (342) all_0_0_0 = e1
% 27.89/7.68 | (343) ~ (all_0_1_1 = e4)
% 27.89/7.68 |
% 27.89/7.68 | Combining equations (342,328) yields a new equation:
% 27.89/7.68 | (322) e2 = e1
% 27.89/7.68 |
% 27.89/7.68 | Equations (322) can reduce 141 to:
% 27.89/7.68 | (270) $false
% 27.89/7.68 |
% 27.89/7.68 |-The branch is then unsatisfiable
% 27.89/7.68 |-Branch two:
% 27.89/7.68 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 27.89/7.68 |
% 27.89/7.68 | Applying alpha-rule on (346) yields:
% 27.89/7.68 | (347) all_0_2_2 = e0
% 27.89/7.68 | (348) ~ (all_0_3_3 = e4)
% 27.89/7.68 |
% 27.89/7.68 | Equations (287) can reduce 348 to:
% 27.89/7.68 | (270) $false
% 27.89/7.68 |
% 27.89/7.68 |-The branch is then unsatisfiable
% 27.89/7.68 |-Branch two:
% 27.89/7.68 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 27.89/7.68 |
% 27.89/7.68 | Applying alpha-rule on (350) yields:
% 27.89/7.68 | (351) all_0_41_41 = e3
% 27.89/7.68 | (352) ~ (all_0_45_45 = e4)
% 27.89/7.68 |
% 27.89/7.68 | Equations (351) can reduce 51 to:
% 27.89/7.68 | (353) ~ (all_0_45_45 = e3)
% 27.89/7.68 |
% 27.89/7.68 | Simplifying 353 yields:
% 27.89/7.68 | (354) ~ (all_0_45_45 = e3)
% 27.89/7.68 |
% 27.89/7.68 +-Applying beta-rule and splitting (158), into two cases.
% 27.89/7.68 |-Branch one:
% 27.89/7.68 | (358) all_0_41_41 = e4
% 27.89/7.68 |
% 27.89/7.68 | Combining equations (351,358) yields a new equation:
% 27.89/7.68 | (359) e4 = e3
% 27.89/7.68 |
% 27.89/7.68 | Equations (359) can reduce 34 to:
% 27.89/7.68 | (270) $false
% 27.89/7.68 |
% 27.89/7.68 |-The branch is then unsatisfiable
% 27.89/7.68 |-Branch two:
% 27.89/7.68 | (361) ~ (all_0_41_41 = e4)
% 27.89/7.68 | (362) all_0_45_45 = e4 | all_0_53_53 = e4 | all_0_58_58 = e4
% 27.89/7.68 |
% 27.89/7.68 +-Applying beta-rule and splitting (105), into two cases.
% 27.89/7.68 |-Branch one:
% 27.89/7.68 | (374) all_0_45_45 = e2
% 27.89/7.68 |
% 27.89/7.68 | Equations (374) can reduce 434 to:
% 27.89/7.68 | (270) $false
% 27.89/7.68 |
% 27.89/7.68 |-The branch is then unsatisfiable
% 27.89/7.68 |-Branch two:
% 27.89/7.68 | (434) ~ (all_0_45_45 = e2)
% 27.89/7.68 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 27.89/7.68 |
% 27.89/7.68 +-Applying beta-rule and splitting (435), into two cases.
% 27.89/7.68 |-Branch one:
% 27.89/7.68 | (454) all_0_45_45 = e0
% 27.89/7.68 |
% 27.89/7.68 | Equations (454) can reduce 84 to:
% 27.89/7.68 | (455) ~ (all_0_43_43 = e0)
% 27.89/7.68 |
% 27.89/7.68 | Equations (454) can reduce 128 to:
% 27.89/7.68 | (3103) ~ (all_0_53_53 = e0)
% 27.89/7.68 |
% 27.89/7.68 | Simplifying 3103 yields:
% 27.89/7.68 | (584) ~ (all_0_53_53 = e0)
% 27.89/7.68 |
% 27.89/7.68 | Equations (454) can reduce 352 to:
% 27.89/7.68 | (456) ~ (e4 = e0)
% 27.89/7.68 |
% 27.89/7.68 | Simplifying 456 yields:
% 27.89/7.68 | (6) ~ (e4 = e0)
% 27.89/7.68 |
% 27.89/7.68 +-Applying beta-rule and splitting (362), into two cases.
% 27.89/7.68 |-Branch one:
% 27.89/7.68 | (363) all_0_45_45 = e4
% 27.89/7.68 |
% 27.89/7.68 | Combining equations (454,363) yields a new equation:
% 27.89/7.68 | (479) e4 = e0
% 27.89/7.68 |
% 27.89/7.68 | Equations (479) can reduce 6 to:
% 27.89/7.68 | (270) $false
% 27.89/7.68 |
% 27.89/7.68 |-The branch is then unsatisfiable
% 27.89/7.68 |-Branch two:
% 27.89/7.68 | (352) ~ (all_0_45_45 = e4)
% 27.89/7.68 | (366) all_0_53_53 = e4 | all_0_58_58 = e4
% 27.89/7.68 |
% 27.89/7.68 +-Applying beta-rule and splitting (366), into two cases.
% 27.89/7.68 |-Branch one:
% 27.89/7.68 | (367) all_0_53_53 = e4
% 27.89/7.68 |
% 27.89/7.68 | Equations (367) can reduce 584 to:
% 27.89/7.68 | (6) ~ (e4 = e0)
% 27.89/7.68 |
% 27.89/7.68 +-Applying beta-rule and splitting (93), into two cases.
% 27.89/7.68 |-Branch one:
% 27.89/7.68 | (402) all_0_59_59 = e4
% 27.89/7.68 |
% 27.89/7.68 | Equations (402) can reduce 280 to:
% 27.89/7.68 | (270) $false
% 27.89/7.68 |
% 27.89/7.68 |-The branch is then unsatisfiable
% 27.89/7.68 |-Branch two:
% 27.89/7.68 | (280) ~ (all_0_59_59 = e4)
% 27.89/7.68 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.89/7.68 |
% 27.89/7.68 +-Applying beta-rule and splitting (407), into two cases.
% 27.89/7.68 |-Branch one:
% 27.89/7.68 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.89/7.68 |
% 27.89/7.68 +-Applying beta-rule and splitting (408), into two cases.
% 27.89/7.68 |-Branch one:
% 27.89/7.68 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.89/7.68 |
% 27.89/7.68 +-Applying beta-rule and splitting (409), into two cases.
% 27.89/7.68 |-Branch one:
% 27.89/7.68 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.89/7.68 |
% 27.89/7.68 | Applying alpha-rule on (410) yields:
% 27.89/7.68 | (411) all_0_43_43 = e0
% 27.89/7.68 | (412) all_0_59_59 = e3
% 27.89/7.68 | (413) ~ (all_0_46_46 = e3)
% 27.89/7.68 |
% 27.89/7.68 | Equations (411) can reduce 455 to:
% 27.89/7.68 | (270) $false
% 27.89/7.68 |
% 27.89/7.68 |-The branch is then unsatisfiable
% 27.89/7.68 |-Branch two:
% 27.89/7.68 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.89/7.68 |
% 27.89/7.68 | Applying alpha-rule on (416) yields:
% 27.89/7.68 | (411) all_0_43_43 = e0
% 27.89/7.68 | (412) all_0_59_59 = e3
% 27.89/7.68 | (419) ~ (all_0_56_56 = e0)
% 27.89/7.68 |
% 27.89/7.68 | Equations (411) can reduce 455 to:
% 27.89/7.68 | (270) $false
% 27.89/7.68 |
% 27.89/7.68 |-The branch is then unsatisfiable
% 27.89/7.68 |-Branch two:
% 27.89/7.68 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.89/7.68 |
% 27.89/7.68 | Applying alpha-rule on (422) yields:
% 27.89/7.68 | (423) all_0_53_53 = e0
% 27.89/7.68 | (424) all_0_59_59 = e1
% 27.89/7.68 | (425) ~ (all_0_54_54 = e1)
% 27.89/7.68 |
% 27.89/7.68 | Combining equations (423,367) yields a new equation:
% 27.89/7.68 | (479) e4 = e0
% 27.89/7.68 |
% 27.89/7.68 | Equations (479) can reduce 6 to:
% 27.89/7.68 | (270) $false
% 27.89/7.68 |
% 27.89/7.68 |-The branch is then unsatisfiable
% 27.89/7.68 |-Branch two:
% 27.89/7.68 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.89/7.68 |
% 27.89/7.68 | Applying alpha-rule on (428) yields:
% 27.89/7.68 | (423) all_0_53_53 = e0
% 27.89/7.68 | (424) all_0_59_59 = e1
% 27.89/7.68 | (431) ~ (all_0_58_58 = e0)
% 27.89/7.68 |
% 27.89/7.68 | Combining equations (423,367) yields a new equation:
% 27.89/7.68 | (479) e4 = e0
% 27.89/7.68 |
% 27.89/7.68 | Equations (479) can reduce 6 to:
% 27.89/7.68 | (270) $false
% 27.89/7.68 |
% 27.89/7.68 |-The branch is then unsatisfiable
% 27.89/7.68 |-Branch two:
% 27.89/7.68 | (599) ~ (all_0_53_53 = e4)
% 27.89/7.68 | (600) all_0_58_58 = e4
% 27.89/7.68 |
% 27.89/7.68 | Equations (600) can reduce 278 to:
% 27.89/7.68 | (270) $false
% 27.89/7.68 |
% 27.89/7.68 |-The branch is then unsatisfiable
% 27.89/7.68 |-Branch two:
% 27.89/7.68 | (488) ~ (all_0_45_45 = e0)
% 27.89/7.69 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 27.89/7.69 |
% 27.89/7.69 +-Applying beta-rule and splitting (489), into two cases.
% 27.89/7.69 |-Branch one:
% 27.89/7.69 | (505) all_0_45_45 = e3
% 27.89/7.69 |
% 27.89/7.69 | Equations (505) can reduce 354 to:
% 27.89/7.69 | (270) $false
% 27.89/7.69 |
% 27.89/7.69 |-The branch is then unsatisfiable
% 27.89/7.69 |-Branch two:
% 27.89/7.69 | (354) ~ (all_0_45_45 = e3)
% 27.89/7.69 | (363) all_0_45_45 = e4
% 27.89/7.69 |
% 27.89/7.69 | Equations (363) can reduce 352 to:
% 27.89/7.69 | (270) $false
% 27.89/7.69 |
% 27.89/7.69 |-The branch is then unsatisfiable
% 27.89/7.69 |-Branch two:
% 27.89/7.69 | (602) ~ (all_0_40_40 = e2)
% 27.89/7.69 | (603) all_0_40_40 = e3 | all_0_40_40 = e1
% 27.89/7.69 |
% 27.89/7.69 +-Applying beta-rule and splitting (20), into two cases.
% 27.89/7.69 |-Branch one:
% 27.89/7.69 | (327) all_0_40_40 = e2
% 27.89/7.69 |
% 27.89/7.69 | Equations (327) can reduce 602 to:
% 27.89/7.69 | (270) $false
% 27.89/7.69 |
% 27.89/7.69 |-The branch is then unsatisfiable
% 27.89/7.69 |-Branch two:
% 27.89/7.69 | (602) ~ (all_0_40_40 = e2)
% 27.89/7.69 | (607) all_0_44_44 = e2 | all_0_52_52 = e2 | all_0_57_57 = e2
% 27.89/7.69 |
% 27.89/7.69 +-Applying beta-rule and splitting (193), into two cases.
% 27.89/7.69 |-Branch one:
% 27.89/7.69 | (370) all_0_44_44 = e2
% 27.89/7.69 |
% 27.89/7.69 | Equations (370) can reduce 15 to:
% 27.89/7.69 | (602) ~ (all_0_40_40 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Equations (370) can reduce 241 to:
% 27.89/7.69 | (292) ~ (all_0_43_43 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Equations (370) can reduce 229 to:
% 27.89/7.69 | (611) ~ (all_0_45_45 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Simplifying 611 yields:
% 27.89/7.69 | (434) ~ (all_0_45_45 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Equations (370) can reduce 122 to:
% 27.89/7.69 | (256) ~ (all_0_52_52 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Simplifying 256 yields:
% 27.89/7.69 | (257) ~ (all_0_52_52 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Equations (370) can reduce 10 to:
% 27.89/7.69 | (334) ~ (all_0_57_57 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Simplifying 334 yields:
% 27.89/7.69 | (335) ~ (all_0_57_57 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Equations (370) can reduce 45 to:
% 27.89/7.69 | (377) ~ (e4 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Simplifying 377 yields:
% 27.89/7.69 | (231) ~ (e4 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Equations (370) can reduce 131 to:
% 27.89/7.69 | (141) ~ (e2 = e1)
% 27.89/7.69 |
% 27.89/7.69 | From (370) and (5) follows:
% 27.89/7.69 | (4117) op(e3, e2) = all_0_16_16
% 27.89/7.69 |
% 27.89/7.69 | From (370) and (148) follows:
% 27.89/7.69 | (4118) op(e3, e2) = e2
% 27.89/7.69 |
% 27.89/7.69 | Instantiating formula (201) with e3, e2, e2, all_0_16_16 and discharging atoms op(e3, e2) = all_0_16_16, op(e3, e2) = e2, yields:
% 27.89/7.69 | (4119) all_0_16_16 = e2
% 27.89/7.69 |
% 27.89/7.69 | From (4119) and (4117) follows:
% 27.89/7.69 | (4118) op(e3, e2) = e2
% 27.89/7.69 |
% 27.89/7.69 +-Applying beta-rule and splitting (9), into two cases.
% 27.89/7.69 |-Branch one:
% 27.89/7.69 | (621) all_0_44_44 = e0
% 27.89/7.69 |
% 27.89/7.69 | Combining equations (370,621) yields a new equation:
% 27.89/7.69 | (622) e2 = e0
% 27.89/7.69 |
% 27.89/7.69 | Simplifying 622 yields:
% 27.89/7.69 | (316) e2 = e0
% 27.89/7.69 |
% 27.89/7.69 | Equations (316) can reduce 57 to:
% 27.89/7.69 | (270) $false
% 27.89/7.69 |
% 27.89/7.69 |-The branch is then unsatisfiable
% 27.89/7.69 |-Branch two:
% 27.89/7.69 | (625) ~ (all_0_44_44 = e0)
% 27.89/7.69 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 27.89/7.69 |
% 27.89/7.69 +-Applying beta-rule and splitting (164), into two cases.
% 27.89/7.69 |-Branch one:
% 27.89/7.69 | (336) all_0_39_39 = e2
% 27.89/7.69 |
% 27.89/7.69 | Equations (336) can reduce 212 to:
% 27.89/7.69 | (299) ~ (all_0_56_56 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Simplifying 299 yields:
% 27.89/7.69 | (300) ~ (all_0_56_56 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Equations (336) can reduce 528 to:
% 27.89/7.69 | (141) ~ (e2 = e1)
% 27.89/7.69 |
% 27.89/7.69 +-Applying beta-rule and splitting (168), into two cases.
% 27.89/7.69 |-Branch one:
% 27.89/7.69 | (382) all_0_55_55 = e2
% 27.89/7.69 |
% 27.89/7.69 | Combining equations (382,272) yields a new equation:
% 27.89/7.69 | (269) e4 = e2
% 27.89/7.69 |
% 27.89/7.69 | Equations (269) can reduce 231 to:
% 27.89/7.69 | (270) $false
% 27.89/7.69 |
% 27.89/7.69 |-The branch is then unsatisfiable
% 27.89/7.69 |-Branch two:
% 27.89/7.69 | (386) ~ (all_0_55_55 = e2)
% 27.89/7.69 | (387) all_0_56_56 = e2 | all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 27.89/7.69 |
% 27.89/7.69 +-Applying beta-rule and splitting (387), into two cases.
% 27.89/7.69 |-Branch one:
% 27.89/7.69 | (388) all_0_56_56 = e2
% 27.89/7.69 |
% 27.89/7.69 | Equations (388) can reduce 300 to:
% 27.89/7.69 | (270) $false
% 27.89/7.69 |
% 27.89/7.69 |-The branch is then unsatisfiable
% 27.89/7.69 |-Branch two:
% 27.89/7.69 | (300) ~ (all_0_56_56 = e2)
% 27.89/7.69 | (391) all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 27.89/7.69 |
% 27.89/7.69 +-Applying beta-rule and splitting (391), into two cases.
% 27.89/7.69 |-Branch one:
% 27.89/7.69 | (392) all_0_57_57 = e2
% 27.89/7.69 |
% 27.89/7.69 | Equations (392) can reduce 335 to:
% 27.89/7.69 | (270) $false
% 27.89/7.69 |
% 27.89/7.69 |-The branch is then unsatisfiable
% 27.89/7.69 |-Branch two:
% 27.89/7.69 | (335) ~ (all_0_57_57 = e2)
% 27.89/7.69 | (395) all_0_58_58 = e2 | all_0_59_59 = e2
% 27.89/7.69 |
% 27.89/7.69 +-Applying beta-rule and splitting (395), into two cases.
% 27.89/7.69 |-Branch one:
% 27.89/7.69 | (396) all_0_58_58 = e2
% 27.89/7.69 |
% 27.89/7.69 | Equations (396) can reduce 376 to:
% 27.89/7.69 | (270) $false
% 27.89/7.69 |
% 27.89/7.69 |-The branch is then unsatisfiable
% 27.89/7.69 |-Branch two:
% 27.89/7.69 | (376) ~ (all_0_58_58 = e2)
% 27.89/7.69 | (399) all_0_59_59 = e2
% 27.89/7.69 |
% 27.89/7.69 | Equations (399) can reduce 280 to:
% 27.89/7.69 | (377) ~ (e4 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Simplifying 377 yields:
% 27.89/7.69 | (231) ~ (e4 = e2)
% 27.89/7.69 |
% 27.89/7.69 +-Applying beta-rule and splitting (93), into two cases.
% 27.89/7.69 |-Branch one:
% 27.89/7.69 | (402) all_0_59_59 = e4
% 27.89/7.69 |
% 27.89/7.69 | Combining equations (399,402) yields a new equation:
% 27.89/7.69 | (269) e4 = e2
% 27.89/7.69 |
% 27.89/7.69 | Equations (269) can reduce 231 to:
% 27.89/7.69 | (270) $false
% 27.89/7.69 |
% 27.89/7.69 |-The branch is then unsatisfiable
% 27.89/7.69 |-Branch two:
% 27.89/7.69 | (280) ~ (all_0_59_59 = e4)
% 27.89/7.69 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.89/7.69 |
% 27.89/7.69 +-Applying beta-rule and splitting (407), into two cases.
% 27.89/7.69 |-Branch one:
% 27.89/7.69 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.89/7.69 |
% 27.89/7.69 +-Applying beta-rule and splitting (408), into two cases.
% 27.89/7.69 |-Branch one:
% 27.89/7.69 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.89/7.69 |
% 27.89/7.69 +-Applying beta-rule and splitting (409), into two cases.
% 27.89/7.69 |-Branch one:
% 27.89/7.69 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.89/7.69 |
% 27.89/7.69 | Applying alpha-rule on (410) yields:
% 27.89/7.69 | (411) all_0_43_43 = e0
% 27.89/7.69 | (412) all_0_59_59 = e3
% 27.89/7.69 | (413) ~ (all_0_46_46 = e3)
% 27.89/7.69 |
% 27.89/7.69 | Combining equations (412,399) yields a new equation:
% 27.89/7.69 | (437) e3 = e2
% 27.89/7.69 |
% 27.89/7.69 | Simplifying 437 yields:
% 27.89/7.69 | (414) e3 = e2
% 27.89/7.69 |
% 27.89/7.69 | Equations (414) can reduce 223 to:
% 27.89/7.69 | (270) $false
% 27.89/7.69 |
% 27.89/7.69 |-The branch is then unsatisfiable
% 27.89/7.69 |-Branch two:
% 27.89/7.69 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.89/7.69 |
% 27.89/7.69 | Applying alpha-rule on (416) yields:
% 27.89/7.69 | (411) all_0_43_43 = e0
% 27.89/7.69 | (412) all_0_59_59 = e3
% 27.89/7.69 | (419) ~ (all_0_56_56 = e0)
% 27.89/7.69 |
% 27.89/7.69 | Combining equations (412,399) yields a new equation:
% 27.89/7.69 | (437) e3 = e2
% 27.89/7.69 |
% 27.89/7.69 | Simplifying 437 yields:
% 27.89/7.69 | (414) e3 = e2
% 27.89/7.69 |
% 27.89/7.69 | Equations (414) can reduce 223 to:
% 27.89/7.69 | (270) $false
% 27.89/7.69 |
% 27.89/7.69 |-The branch is then unsatisfiable
% 27.89/7.69 |-Branch two:
% 27.89/7.69 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.89/7.69 |
% 27.89/7.69 | Applying alpha-rule on (422) yields:
% 27.89/7.69 | (423) all_0_53_53 = e0
% 27.89/7.69 | (424) all_0_59_59 = e1
% 27.89/7.69 | (425) ~ (all_0_54_54 = e1)
% 27.89/7.69 |
% 27.89/7.69 | Combining equations (399,424) yields a new equation:
% 27.89/7.69 | (531) e2 = e1
% 27.89/7.69 |
% 27.89/7.69 | Simplifying 531 yields:
% 27.89/7.69 | (322) e2 = e1
% 27.89/7.69 |
% 27.89/7.69 | Equations (322) can reduce 141 to:
% 27.89/7.69 | (270) $false
% 27.89/7.69 |
% 27.89/7.69 |-The branch is then unsatisfiable
% 27.89/7.69 |-Branch two:
% 27.89/7.69 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.89/7.69 |
% 27.89/7.69 | Applying alpha-rule on (428) yields:
% 27.89/7.69 | (423) all_0_53_53 = e0
% 27.89/7.69 | (424) all_0_59_59 = e1
% 27.89/7.69 | (431) ~ (all_0_58_58 = e0)
% 27.89/7.69 |
% 27.89/7.69 | Combining equations (399,424) yields a new equation:
% 27.89/7.69 | (531) e2 = e1
% 27.89/7.69 |
% 27.89/7.69 | Simplifying 531 yields:
% 27.89/7.69 | (322) e2 = e1
% 27.89/7.69 |
% 27.89/7.69 | Equations (322) can reduce 141 to:
% 27.89/7.69 | (270) $false
% 27.89/7.69 |
% 27.89/7.69 |-The branch is then unsatisfiable
% 27.89/7.69 |-Branch two:
% 27.89/7.69 | (291) ~ (all_0_39_39 = e2)
% 27.89/7.69 | (630) all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 27.89/7.69 |
% 27.89/7.69 +-Applying beta-rule and splitting (630), into two cases.
% 27.89/7.69 |-Branch one:
% 27.89/7.69 | (327) all_0_40_40 = e2
% 27.89/7.69 |
% 27.89/7.69 | Equations (327) can reduce 602 to:
% 27.89/7.69 | (270) $false
% 27.89/7.69 |
% 27.89/7.69 |-The branch is then unsatisfiable
% 27.89/7.69 |-Branch two:
% 27.89/7.69 | (602) ~ (all_0_40_40 = e2)
% 27.89/7.69 | (1251) all_0_41_41 = e2 | all_0_42_42 = e2
% 27.89/7.69 |
% 27.89/7.69 +-Applying beta-rule and splitting (1251), into two cases.
% 27.89/7.69 |-Branch one:
% 27.89/7.69 | (436) all_0_41_41 = e2
% 27.89/7.69 |
% 27.89/7.69 | Equations (436) can reduce 331 to:
% 27.89/7.69 | (270) $false
% 27.89/7.69 |
% 27.89/7.69 |-The branch is then unsatisfiable
% 27.89/7.69 |-Branch two:
% 27.89/7.69 | (331) ~ (all_0_41_41 = e2)
% 27.89/7.69 | (698) all_0_42_42 = e2
% 27.89/7.69 |
% 27.89/7.69 | Equations (698) can reduce 184 to:
% 27.89/7.69 | (291) ~ (all_0_39_39 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Equations (698) can reduce 145 to:
% 27.89/7.69 | (602) ~ (all_0_40_40 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Equations (698) can reduce 94 to:
% 27.89/7.69 | (331) ~ (all_0_41_41 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Equations (698) can reduce 18 to:
% 27.89/7.69 | (1435) ~ (all_0_46_46 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Simplifying 1435 yields:
% 27.89/7.69 | (1436) ~ (all_0_46_46 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Equations (698) can reduce 199 to:
% 27.89/7.69 | (57) ~ (e2 = e0)
% 27.89/7.69 |
% 27.89/7.69 | From (698) and (243) follows:
% 27.89/7.69 | (4201) op(e0, e2) = all_0_30_30
% 27.89/7.69 |
% 27.89/7.69 +-Applying beta-rule and splitting (96), into two cases.
% 27.89/7.69 |-Branch one:
% 27.89/7.69 | (336) all_0_39_39 = e2
% 27.89/7.69 |
% 27.89/7.69 | Equations (336) can reduce 291 to:
% 27.89/7.69 | (270) $false
% 27.89/7.69 |
% 27.89/7.69 |-The branch is then unsatisfiable
% 27.89/7.69 |-Branch two:
% 27.89/7.69 | (291) ~ (all_0_39_39 = e2)
% 27.89/7.69 | (4205) all_0_43_43 = e2 | all_0_47_47 = e2 | all_0_51_51 = e2 | all_0_56_56 = e2
% 27.89/7.69 |
% 27.89/7.69 +-Applying beta-rule and splitting (4205), into two cases.
% 27.89/7.69 |-Branch one:
% 27.89/7.69 | (450) all_0_43_43 = e2
% 27.89/7.69 |
% 27.89/7.69 | Equations (450) can reduce 292 to:
% 27.89/7.69 | (270) $false
% 27.89/7.69 |
% 27.89/7.69 |-The branch is then unsatisfiable
% 27.89/7.69 |-Branch two:
% 27.89/7.69 | (292) ~ (all_0_43_43 = e2)
% 27.89/7.69 | (4209) all_0_47_47 = e2 | all_0_51_51 = e2 | all_0_56_56 = e2
% 27.89/7.69 |
% 27.89/7.69 +-Applying beta-rule and splitting (4209), into two cases.
% 27.89/7.69 |-Branch one:
% 27.89/7.69 | (290) all_0_47_47 = e2
% 27.89/7.69 |
% 27.89/7.69 | Combining equations (321,290) yields a new equation:
% 27.89/7.69 | (322) e2 = e1
% 27.89/7.69 |
% 27.89/7.69 | Equations (322) can reduce 141 to:
% 27.89/7.69 | (270) $false
% 27.89/7.69 |
% 27.89/7.69 |-The branch is then unsatisfiable
% 27.89/7.69 |-Branch two:
% 27.89/7.69 | (3951) ~ (all_0_47_47 = e2)
% 27.89/7.69 | (4214) all_0_51_51 = e2 | all_0_56_56 = e2
% 27.89/7.69 |
% 27.89/7.69 +-Applying beta-rule and splitting (4214), into two cases.
% 27.89/7.69 |-Branch one:
% 27.89/7.69 | (4215) all_0_51_51 = e2
% 27.89/7.69 |
% 27.89/7.69 | Equations (4215) can reduce 255 to:
% 27.89/7.69 | (270) $false
% 27.89/7.69 |
% 27.89/7.69 |-The branch is then unsatisfiable
% 27.89/7.69 |-Branch two:
% 27.89/7.69 | (255) ~ (all_0_51_51 = e2)
% 27.89/7.69 | (388) all_0_56_56 = e2
% 27.89/7.69 |
% 27.89/7.69 | Equations (388) can reduce 212 to:
% 27.89/7.69 | (291) ~ (all_0_39_39 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Equations (388) can reduce 188 to:
% 27.89/7.69 | (292) ~ (all_0_43_43 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Equations (388) can reduce 104 to:
% 27.89/7.69 | (334) ~ (all_0_57_57 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Simplifying 334 yields:
% 27.89/7.69 | (335) ~ (all_0_57_57 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Equations (388) can reduce 81 to:
% 27.89/7.69 | (375) ~ (all_0_58_58 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Simplifying 375 yields:
% 27.89/7.69 | (376) ~ (all_0_58_58 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Equations (388) can reduce 185 to:
% 27.89/7.69 | (700) ~ (all_0_59_59 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Simplifying 700 yields:
% 27.89/7.69 | (701) ~ (all_0_59_59 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Equations (388) can reduce 274 to:
% 27.89/7.69 | (377) ~ (e4 = e2)
% 27.89/7.69 |
% 27.89/7.69 | Simplifying 377 yields:
% 27.89/7.69 | (231) ~ (e4 = e2)
% 27.89/7.69 |
% 27.89/7.69 | From (388) and (239) follows:
% 27.89/7.69 | (4229) op(e3, e2) = all_0_11_11
% 27.89/7.69 |
% 27.89/7.69 | From (388) and (205) follows:
% 27.89/7.69 | (4230) op(e0, e2) = all_0_12_12
% 27.89/7.69 |
% 27.89/7.69 | Instantiating formula (201) with e3, e2, all_0_11_11, e2 and discharging atoms op(e3, e2) = all_0_11_11, op(e3, e2) = e2, yields:
% 27.89/7.69 | (4231) all_0_11_11 = e2
% 27.89/7.69 |
% 27.89/7.69 | Instantiating formula (201) with e0, e2, all_0_12_12, all_0_57_57 and discharging atoms op(e0, e2) = all_0_12_12, op(e0, e2) = all_0_57_57, yields:
% 27.89/7.69 | (4232) all_0_12_12 = all_0_57_57
% 27.89/7.69 |
% 27.89/7.69 | Instantiating formula (201) with e0, e2, all_0_30_30, all_0_12_12 and discharging atoms op(e0, e2) = all_0_12_12, op(e0, e2) = all_0_30_30, yields:
% 27.89/7.69 | (4233) all_0_12_12 = all_0_30_30
% 27.89/7.69 |
% 27.89/7.69 | Combining equations (4232,4233) yields a new equation:
% 27.89/7.69 | (4234) all_0_30_30 = all_0_57_57
% 27.89/7.69 |
% 27.89/7.69 +-Applying beta-rule and splitting (222), into two cases.
% 27.89/7.69 |-Branch one:
% 27.89/7.69 | (522) all_0_39_39 = e4
% 27.89/7.69 |
% 27.89/7.69 | Equations (522) can reduce 528 to:
% 27.89/7.69 | (251) ~ (e4 = e1)
% 27.89/7.69 |
% 27.89/7.69 | From (522) and (200) follows:
% 27.89/7.69 | (4237) op(e3, e4) = all_0_4_4
% 27.89/7.69 |
% 27.89/7.69 | Instantiating formula (201) with e3, e4, all_0_4_4, e1 and discharging atoms op(e3, e4) = all_0_4_4, op(e3, e4) = e1, yields:
% 27.89/7.69 | (4238) all_0_4_4 = e1
% 27.89/7.69 |
% 27.89/7.69 +-Applying beta-rule and splitting (234), into two cases.
% 27.89/7.69 |-Branch one:
% 27.89/7.69 | (4239) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3)) | (all_0_9_9 = e1 & ~ (all_0_10_10 = e3))
% 27.89/7.69 |
% 27.89/7.69 +-Applying beta-rule and splitting (4239), into two cases.
% 27.89/7.69 |-Branch one:
% 27.89/7.69 | (4240) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3))
% 27.89/7.70 |
% 27.89/7.70 +-Applying beta-rule and splitting (4240), into two cases.
% 27.89/7.70 |-Branch one:
% 27.89/7.70 | (4241) all_0_4_4 = e4 & ~ (all_0_5_5 = e3)
% 27.89/7.70 |
% 27.89/7.70 | Applying alpha-rule on (4241) yields:
% 27.89/7.70 | (4242) all_0_4_4 = e4
% 27.89/7.70 | (4243) ~ (all_0_5_5 = e3)
% 27.89/7.70 |
% 27.89/7.70 | Combining equations (4242,4238) yields a new equation:
% 27.89/7.70 | (525) e4 = e1
% 27.89/7.70 |
% 27.89/7.70 | Simplifying 525 yields:
% 27.89/7.70 | (526) e4 = e1
% 27.89/7.70 |
% 27.89/7.70 | Equations (526) can reduce 251 to:
% 27.89/7.70 | (270) $false
% 27.89/7.70 |
% 27.89/7.70 |-The branch is then unsatisfiable
% 27.89/7.70 |-Branch two:
% 27.89/7.70 | (4247) all_0_7_7 = e2 & ~ (all_0_8_8 = e3)
% 27.89/7.70 |
% 27.89/7.70 | Applying alpha-rule on (4247) yields:
% 27.89/7.70 | (4248) all_0_7_7 = e2
% 27.89/7.70 | (4249) ~ (all_0_8_8 = e3)
% 27.89/7.70 |
% 27.89/7.70 | Combining equations (4011,4248) yields a new equation:
% 27.89/7.70 | (4250) all_0_45_45 = e2
% 27.89/7.70 |
% 27.89/7.70 | Simplifying 4250 yields:
% 27.89/7.70 | (374) all_0_45_45 = e2
% 27.89/7.70 |
% 27.89/7.70 | Equations (374) can reduce 434 to:
% 27.89/7.70 | (270) $false
% 27.89/7.70 |
% 27.89/7.70 |-The branch is then unsatisfiable
% 27.89/7.70 |-Branch two:
% 27.89/7.70 | (4253) all_0_9_9 = e1 & ~ (all_0_10_10 = e3)
% 27.89/7.70 |
% 27.89/7.70 | Applying alpha-rule on (4253) yields:
% 27.89/7.70 | (4254) all_0_9_9 = e1
% 27.89/7.70 | (4255) ~ (all_0_10_10 = e3)
% 27.89/7.70 |
% 27.89/7.70 | From (4254) and (7) follows:
% 27.89/7.70 | (4256) op(e3, all_0_51_51) = e1
% 27.89/7.70 |
% 27.89/7.70 +-Applying beta-rule and splitting (78), into two cases.
% 27.89/7.70 |-Branch one:
% 27.89/7.70 | (751) all_0_39_39 = e3
% 27.89/7.70 |
% 27.89/7.70 | Combining equations (522,751) yields a new equation:
% 27.89/7.70 | (660) e4 = e3
% 27.89/7.70 |
% 27.89/7.70 | Simplifying 660 yields:
% 27.89/7.70 | (359) e4 = e3
% 27.89/7.70 |
% 27.89/7.70 | Equations (359) can reduce 34 to:
% 27.89/7.70 | (270) $false
% 27.89/7.70 |
% 27.89/7.70 |-The branch is then unsatisfiable
% 27.89/7.70 |-Branch two:
% 27.89/7.70 | (755) ~ (all_0_39_39 = e3)
% 27.89/7.70 | (4262) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 27.89/7.70 |
% 27.89/7.70 | Equations (522) can reduce 755 to:
% 27.89/7.70 | (34) ~ (e4 = e3)
% 27.89/7.70 |
% 27.89/7.70 +-Applying beta-rule and splitting (75), into two cases.
% 27.89/7.70 |-Branch one:
% 27.89/7.70 | (411) all_0_43_43 = e0
% 27.89/7.70 |
% 27.89/7.70 | Equations (411) can reduce 249 to:
% 27.89/7.70 | (568) ~ (e1 = e0)
% 27.89/7.70 |
% 27.89/7.70 | Simplifying 568 yields:
% 27.89/7.70 | (132) ~ (e1 = e0)
% 27.89/7.70 |
% 27.89/7.70 | From (411) and (248) follows:
% 27.89/7.70 | (4267) op(e3, e3) = e0
% 27.89/7.70 |
% 27.89/7.70 +-Applying beta-rule and splitting (178), into two cases.
% 27.89/7.70 |-Branch one:
% 27.89/7.70 | (751) all_0_39_39 = e3
% 27.89/7.70 |
% 27.89/7.70 | Combining equations (522,751) yields a new equation:
% 27.89/7.70 | (660) e4 = e3
% 27.89/7.70 |
% 27.89/7.70 | Simplifying 660 yields:
% 27.89/7.70 | (359) e4 = e3
% 27.89/7.70 |
% 27.89/7.70 | Equations (359) can reduce 34 to:
% 27.89/7.70 | (270) $false
% 27.89/7.70 |
% 27.89/7.70 |-The branch is then unsatisfiable
% 27.89/7.70 |-Branch two:
% 27.89/7.70 | (755) ~ (all_0_39_39 = e3)
% 27.89/7.70 | (756) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 27.89/7.70 |
% 27.89/7.70 +-Applying beta-rule and splitting (756), into two cases.
% 27.89/7.70 |-Branch one:
% 27.89/7.70 | (782) all_0_43_43 = e3
% 27.89/7.70 |
% 27.89/7.70 | Combining equations (411,782) yields a new equation:
% 27.89/7.70 | (784) e3 = e0
% 27.89/7.70 |
% 27.89/7.70 | Equations (784) can reduce 66 to:
% 27.89/7.70 | (270) $false
% 27.89/7.70 |
% 27.89/7.70 |-The branch is then unsatisfiable
% 27.89/7.70 |-Branch two:
% 27.89/7.70 | (786) ~ (all_0_43_43 = e3)
% 27.89/7.70 | (799) all_0_51_51 = e3 | all_0_56_56 = e3
% 27.89/7.70 |
% 27.89/7.70 +-Applying beta-rule and splitting (799), into two cases.
% 27.89/7.70 |-Branch one:
% 27.89/7.70 | (824) all_0_51_51 = e3
% 27.89/7.70 |
% 27.89/7.70 | From (824) and (4256) follows:
% 27.89/7.70 | (4280) op(e3, e3) = e1
% 27.89/7.70 |
% 27.89/7.70 | Instantiating formula (201) with e3, e3, e0, e1 and discharging atoms op(e3, e3) = e1, op(e3, e3) = e0, yields:
% 27.89/7.70 | (560) e1 = e0
% 27.89/7.70 |
% 27.89/7.70 | Equations (560) can reduce 132 to:
% 27.89/7.70 | (270) $false
% 27.89/7.70 |
% 27.89/7.70 |-The branch is then unsatisfiable
% 27.89/7.70 |-Branch two:
% 27.89/7.70 | (932) ~ (all_0_51_51 = e3)
% 27.89/7.70 | (764) all_0_56_56 = e3
% 27.89/7.70 |
% 27.89/7.70 | Combining equations (764,388) yields a new equation:
% 27.89/7.70 | (437) e3 = e2
% 27.89/7.70 |
% 27.89/7.70 | Simplifying 437 yields:
% 27.89/7.70 | (414) e3 = e2
% 27.89/7.70 |
% 27.89/7.70 | Equations (414) can reduce 223 to:
% 27.89/7.70 | (270) $false
% 27.89/7.70 |
% 27.89/7.70 |-The branch is then unsatisfiable
% 27.89/7.70 |-Branch two:
% 27.89/7.70 | (455) ~ (all_0_43_43 = e0)
% 27.89/7.70 | (940) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 27.89/7.70 |
% 27.89/7.70 +-Applying beta-rule and splitting (940), into two cases.
% 27.89/7.70 |-Branch one:
% 27.89/7.70 | (315) all_0_47_47 = e0
% 27.89/7.70 |
% 27.89/7.70 | Combining equations (321,315) yields a new equation:
% 27.89/7.70 | (571) e1 = e0
% 27.89/7.70 |
% 27.89/7.70 | Simplifying 571 yields:
% 27.89/7.70 | (560) e1 = e0
% 27.89/7.70 |
% 27.89/7.70 | Equations (560) can reduce 132 to:
% 27.89/7.70 | (270) $false
% 27.89/7.70 |
% 27.89/7.70 |-The branch is then unsatisfiable
% 27.89/7.70 |-Branch two:
% 27.89/7.70 | (318) ~ (all_0_47_47 = e0)
% 27.89/7.70 | (950) all_0_51_51 = e0 | all_0_56_56 = e0
% 27.89/7.70 |
% 27.89/7.70 +-Applying beta-rule and splitting (950), into two cases.
% 27.89/7.70 |-Branch one:
% 27.89/7.70 | (954) all_0_51_51 = e0
% 27.89/7.70 |
% 27.89/7.70 | Equations (954) can reduce 154 to:
% 27.89/7.70 | (4297) ~ (all_0_52_52 = e0)
% 27.89/7.70 |
% 27.89/7.70 | Simplifying 4297 yields:
% 27.89/7.70 | (925) ~ (all_0_52_52 = e0)
% 27.89/7.70 |
% 27.89/7.70 | Equations (954) can reduce 12 to:
% 27.89/7.70 | (3103) ~ (all_0_53_53 = e0)
% 27.89/7.70 |
% 27.89/7.70 | Simplifying 3103 yields:
% 27.89/7.70 | (584) ~ (all_0_53_53 = e0)
% 27.89/7.70 |
% 27.89/7.70 +-Applying beta-rule and splitting (178), into two cases.
% 27.89/7.70 |-Branch one:
% 27.89/7.70 | (751) all_0_39_39 = e3
% 27.89/7.70 |
% 27.89/7.70 | Combining equations (522,751) yields a new equation:
% 27.89/7.70 | (660) e4 = e3
% 27.89/7.70 |
% 27.89/7.70 | Simplifying 660 yields:
% 27.89/7.70 | (359) e4 = e3
% 27.89/7.70 |
% 27.89/7.70 | Equations (359) can reduce 34 to:
% 27.89/7.70 | (270) $false
% 27.89/7.70 |
% 27.89/7.70 |-The branch is then unsatisfiable
% 27.89/7.70 |-Branch two:
% 27.89/7.70 | (755) ~ (all_0_39_39 = e3)
% 27.89/7.70 | (756) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 27.89/7.70 |
% 27.89/7.70 +-Applying beta-rule and splitting (626), into two cases.
% 27.89/7.70 |-Branch one:
% 27.89/7.70 | (827) all_0_52_52 = e0
% 27.89/7.70 |
% 27.89/7.70 | Equations (827) can reduce 925 to:
% 27.89/7.70 | (270) $false
% 27.89/7.70 |
% 27.89/7.70 |-The branch is then unsatisfiable
% 27.89/7.70 |-Branch two:
% 27.89/7.70 | (925) ~ (all_0_52_52 = e0)
% 27.89/7.70 | (2258) all_0_57_57 = e0
% 27.89/7.70 |
% 27.89/7.70 | Equations (2258) can reduce 37 to:
% 27.89/7.70 | (3530) ~ (all_0_58_58 = e0)
% 27.89/7.70 |
% 27.89/7.70 | Simplifying 3530 yields:
% 27.89/7.70 | (431) ~ (all_0_58_58 = e0)
% 27.89/7.70 |
% 27.89/7.70 | Equations (2258) can reduce 335 to:
% 27.89/7.70 | (566) ~ (e2 = e0)
% 27.89/7.70 |
% 27.89/7.70 | Simplifying 566 yields:
% 27.89/7.70 | (57) ~ (e2 = e0)
% 27.89/7.70 |
% 27.89/7.70 +-Applying beta-rule and splitting (756), into two cases.
% 27.89/7.70 |-Branch one:
% 27.89/7.70 | (782) all_0_43_43 = e3
% 27.89/7.70 |
% 27.89/7.70 | Equations (782) can reduce 84 to:
% 27.89/7.70 | (353) ~ (all_0_45_45 = e3)
% 27.89/7.70 |
% 27.89/7.70 | Simplifying 353 yields:
% 27.89/7.70 | (354) ~ (all_0_45_45 = e3)
% 27.89/7.70 |
% 27.89/7.70 +-Applying beta-rule and splitting (182), into two cases.
% 27.89/7.70 |-Branch one:
% 27.89/7.70 | (454) all_0_45_45 = e0
% 27.89/7.70 |
% 27.89/7.70 | Equations (454) can reduce 128 to:
% 27.89/7.70 | (3103) ~ (all_0_53_53 = e0)
% 27.89/7.70 |
% 27.89/7.70 | Simplifying 3103 yields:
% 27.89/7.70 | (584) ~ (all_0_53_53 = e0)
% 27.89/7.70 |
% 27.89/7.70 | Equations (454) can reduce 354 to:
% 27.89/7.70 | (788) ~ (e3 = e0)
% 27.89/7.70 |
% 27.89/7.70 | Simplifying 788 yields:
% 27.89/7.70 | (66) ~ (e3 = e0)
% 27.89/7.70 |
% 27.89/7.70 +-Applying beta-rule and splitting (93), into two cases.
% 27.89/7.70 |-Branch one:
% 27.89/7.70 | (402) all_0_59_59 = e4
% 27.89/7.70 |
% 27.89/7.70 | Equations (402) can reduce 280 to:
% 27.89/7.70 | (270) $false
% 27.89/7.70 |
% 27.89/7.70 |-The branch is then unsatisfiable
% 27.89/7.70 |-Branch two:
% 27.89/7.70 | (280) ~ (all_0_59_59 = e4)
% 27.89/7.70 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.89/7.70 |
% 27.89/7.70 +-Applying beta-rule and splitting (407), into two cases.
% 27.89/7.70 |-Branch one:
% 27.89/7.70 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.89/7.70 |
% 27.89/7.70 +-Applying beta-rule and splitting (408), into two cases.
% 27.89/7.70 |-Branch one:
% 27.89/7.70 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.89/7.70 |
% 27.89/7.70 +-Applying beta-rule and splitting (409), into two cases.
% 27.89/7.70 |-Branch one:
% 27.89/7.70 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.89/7.70 |
% 27.89/7.70 | Applying alpha-rule on (410) yields:
% 27.89/7.70 | (411) all_0_43_43 = e0
% 27.89/7.70 | (412) all_0_59_59 = e3
% 27.89/7.70 | (413) ~ (all_0_46_46 = e3)
% 27.89/7.70 |
% 27.89/7.70 | Combining equations (411,782) yields a new equation:
% 27.89/7.70 | (784) e3 = e0
% 27.89/7.70 |
% 27.89/7.70 | Equations (784) can reduce 66 to:
% 27.89/7.70 | (270) $false
% 27.89/7.70 |
% 27.89/7.70 |-The branch is then unsatisfiable
% 27.89/7.70 |-Branch two:
% 27.89/7.70 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.89/7.70 |
% 27.89/7.70 | Applying alpha-rule on (416) yields:
% 27.89/7.70 | (411) all_0_43_43 = e0
% 27.89/7.70 | (412) all_0_59_59 = e3
% 27.89/7.70 | (419) ~ (all_0_56_56 = e0)
% 27.89/7.70 |
% 27.89/7.70 | Combining equations (411,782) yields a new equation:
% 27.89/7.70 | (784) e3 = e0
% 27.89/7.70 |
% 27.89/7.70 | Equations (784) can reduce 66 to:
% 27.89/7.70 | (270) $false
% 27.89/7.70 |
% 27.89/7.70 |-The branch is then unsatisfiable
% 27.89/7.70 |-Branch two:
% 27.89/7.70 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.89/7.70 |
% 27.89/7.70 | Applying alpha-rule on (422) yields:
% 27.89/7.70 | (423) all_0_53_53 = e0
% 27.89/7.70 | (424) all_0_59_59 = e1
% 27.89/7.70 | (425) ~ (all_0_54_54 = e1)
% 27.89/7.70 |
% 27.89/7.70 | Equations (423) can reduce 584 to:
% 27.89/7.70 | (270) $false
% 27.89/7.70 |
% 27.89/7.70 |-The branch is then unsatisfiable
% 27.89/7.70 |-Branch two:
% 27.89/7.70 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.89/7.70 |
% 27.89/7.70 | Applying alpha-rule on (428) yields:
% 27.89/7.70 | (423) all_0_53_53 = e0
% 27.89/7.70 | (424) all_0_59_59 = e1
% 27.89/7.70 | (431) ~ (all_0_58_58 = e0)
% 27.89/7.70 |
% 27.89/7.70 | Equations (423) can reduce 584 to:
% 27.89/7.70 | (270) $false
% 27.89/7.70 |
% 27.89/7.70 |-The branch is then unsatisfiable
% 27.89/7.70 |-Branch two:
% 27.89/7.70 | (488) ~ (all_0_45_45 = e0)
% 27.89/7.70 | (558) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 27.89/7.70 |
% 27.89/7.70 +-Applying beta-rule and splitting (558), into two cases.
% 27.89/7.70 |-Branch one:
% 27.89/7.70 | (559) all_0_48_48 = e0
% 27.89/7.70 |
% 27.89/7.70 | Combining equations (311,559) yields a new equation:
% 27.89/7.70 | (622) e2 = e0
% 27.89/7.70 |
% 27.89/7.70 | Simplifying 622 yields:
% 27.89/7.70 | (316) e2 = e0
% 27.89/7.70 |
% 27.89/7.70 | Equations (316) can reduce 57 to:
% 27.89/7.70 | (270) $false
% 27.89/7.70 |
% 27.89/7.70 |-The branch is then unsatisfiable
% 27.89/7.70 |-Branch two:
% 27.89/7.70 | (562) ~ (all_0_48_48 = e0)
% 27.89/7.70 | (575) all_0_53_53 = e0 | all_0_58_58 = e0
% 27.89/7.70 |
% 27.89/7.70 +-Applying beta-rule and splitting (575), into two cases.
% 27.89/7.70 |-Branch one:
% 27.89/7.70 | (423) all_0_53_53 = e0
% 27.89/7.70 |
% 27.89/7.70 | Equations (423) can reduce 584 to:
% 27.89/7.70 | (270) $false
% 27.89/7.70 |
% 27.89/7.70 |-The branch is then unsatisfiable
% 27.89/7.70 |-Branch two:
% 27.89/7.70 | (584) ~ (all_0_53_53 = e0)
% 27.89/7.70 | (585) all_0_58_58 = e0
% 27.89/7.70 |
% 27.89/7.70 | Equations (585) can reduce 431 to:
% 27.89/7.70 | (270) $false
% 27.89/7.70 |
% 27.89/7.70 |-The branch is then unsatisfiable
% 27.89/7.70 |-Branch two:
% 27.89/7.70 | (786) ~ (all_0_43_43 = e3)
% 27.89/7.70 | (799) all_0_51_51 = e3 | all_0_56_56 = e3
% 27.89/7.70 |
% 27.89/7.70 +-Applying beta-rule and splitting (799), into two cases.
% 27.89/7.70 |-Branch one:
% 27.89/7.70 | (824) all_0_51_51 = e3
% 27.89/7.70 |
% 27.89/7.70 | Combining equations (954,824) yields a new equation:
% 27.89/7.70 | (784) e3 = e0
% 27.89/7.70 |
% 27.89/7.70 | Equations (784) can reduce 66 to:
% 27.89/7.70 | (270) $false
% 27.89/7.70 |
% 27.89/7.70 |-The branch is then unsatisfiable
% 27.89/7.70 |-Branch two:
% 27.89/7.70 | (932) ~ (all_0_51_51 = e3)
% 27.89/7.70 | (764) all_0_56_56 = e3
% 27.89/7.70 |
% 27.89/7.70 | Combining equations (764,388) yields a new equation:
% 27.89/7.70 | (437) e3 = e2
% 27.89/7.70 |
% 27.89/7.70 | Simplifying 437 yields:
% 27.89/7.70 | (414) e3 = e2
% 27.89/7.70 |
% 27.89/7.70 | Equations (414) can reduce 223 to:
% 27.89/7.70 | (270) $false
% 27.89/7.70 |
% 27.89/7.70 |-The branch is then unsatisfiable
% 27.89/7.70 |-Branch two:
% 27.89/7.70 | (987) ~ (all_0_51_51 = e0)
% 27.89/7.70 | (830) all_0_56_56 = e0
% 27.89/7.70 |
% 27.89/7.70 | Combining equations (830,388) yields a new equation:
% 27.89/7.70 | (316) e2 = e0
% 27.89/7.70 |
% 27.89/7.71 | Equations (316) can reduce 57 to:
% 27.89/7.71 | (270) $false
% 27.89/7.71 |
% 27.89/7.71 |-The branch is then unsatisfiable
% 27.89/7.71 |-Branch two:
% 27.89/7.71 | (4378) all_0_11_11 = e0 & ~ (all_0_12_12 = e3)
% 27.89/7.71 |
% 27.89/7.71 | Applying alpha-rule on (4378) yields:
% 27.89/7.71 | (4379) all_0_11_11 = e0
% 27.89/7.71 | (4380) ~ (all_0_12_12 = e3)
% 27.89/7.71 |
% 27.89/7.71 | Combining equations (4379,4231) yields a new equation:
% 27.89/7.71 | (316) e2 = e0
% 27.89/7.71 |
% 27.89/7.71 | Equations (316) can reduce 57 to:
% 27.89/7.71 | (270) $false
% 27.89/7.71 |
% 27.89/7.71 |-The branch is then unsatisfiable
% 27.89/7.71 |-Branch two:
% 27.89/7.71 | (591) ~ (all_0_39_39 = e4)
% 27.89/7.71 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (177), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (336) all_0_39_39 = e2
% 27.89/7.71 |
% 27.89/7.71 | Equations (336) can reduce 291 to:
% 27.89/7.71 | (270) $false
% 27.89/7.71 |
% 27.89/7.71 |-The branch is then unsatisfiable
% 27.89/7.71 |-Branch two:
% 27.89/7.71 | (291) ~ (all_0_39_39 = e2)
% 27.89/7.71 | (684) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (592), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (358) all_0_41_41 = e4
% 27.89/7.71 |
% 27.89/7.71 | Equations (358) can reduce 226 to:
% 27.89/7.71 | (591) ~ (all_0_39_39 = e4)
% 27.89/7.71 |
% 27.89/7.71 | Equations (358) can reduce 51 to:
% 27.89/7.71 | (503) ~ (all_0_45_45 = e4)
% 27.89/7.71 |
% 27.89/7.71 | Simplifying 503 yields:
% 27.89/7.71 | (352) ~ (all_0_45_45 = e4)
% 27.89/7.71 |
% 27.89/7.71 | Equations (358) can reduce 157 to:
% 27.89/7.71 | (277) ~ (all_0_58_58 = e4)
% 27.89/7.71 |
% 27.89/7.71 | Simplifying 277 yields:
% 27.89/7.71 | (278) ~ (all_0_58_58 = e4)
% 27.89/7.71 |
% 27.89/7.71 | Equations (358) can reduce 331 to:
% 27.89/7.71 | (231) ~ (e4 = e2)
% 27.89/7.71 |
% 27.89/7.71 | Equations (358) can reduce 232 to:
% 27.89/7.71 | (6) ~ (e4 = e0)
% 27.89/7.71 |
% 27.89/7.71 | From (358) and (112) follows:
% 27.89/7.71 | (2759) op(e1, e4) = all_0_21_21
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (684), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (751) all_0_39_39 = e3
% 27.89/7.71 |
% 27.89/7.71 | Equations (751) can reduce 167 to:
% 27.89/7.71 | (1333) ~ (all_0_43_43 = e3)
% 27.89/7.71 |
% 27.89/7.71 | Simplifying 1333 yields:
% 27.89/7.71 | (786) ~ (all_0_43_43 = e3)
% 27.89/7.71 |
% 27.89/7.71 | Equations (751) can reduce 591 to:
% 27.89/7.71 | (719) ~ (e4 = e3)
% 27.89/7.71 |
% 27.89/7.71 | Simplifying 719 yields:
% 27.89/7.71 | (34) ~ (e4 = e3)
% 27.89/7.71 |
% 27.89/7.71 | Equations (751) can reduce 291 to:
% 27.89/7.71 | (223) ~ (e3 = e2)
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (186), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (336) all_0_39_39 = e2
% 27.89/7.71 |
% 27.89/7.71 | Combining equations (336,751) yields a new equation:
% 27.89/7.71 | (414) e3 = e2
% 27.89/7.71 |
% 27.89/7.71 | Equations (414) can reduce 223 to:
% 27.89/7.71 | (270) $false
% 27.89/7.71 |
% 27.89/7.71 |-The branch is then unsatisfiable
% 27.89/7.71 |-Branch two:
% 27.89/7.71 | (291) ~ (all_0_39_39 = e2)
% 27.89/7.71 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (339), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (340), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 27.89/7.71 |
% 27.89/7.71 | Applying alpha-rule on (341) yields:
% 27.89/7.71 | (342) all_0_0_0 = e1
% 27.89/7.71 | (343) ~ (all_0_1_1 = e4)
% 27.89/7.71 |
% 27.89/7.71 | Combining equations (342,285) yields a new equation:
% 27.89/7.71 | (530) all_0_40_40 = e1
% 27.89/7.71 |
% 27.89/7.71 | Equations (530) can reduce 602 to:
% 27.89/7.71 | (645) ~ (e2 = e1)
% 27.89/7.71 |
% 27.89/7.71 | Simplifying 645 yields:
% 27.89/7.71 | (141) ~ (e2 = e1)
% 27.89/7.71 |
% 27.89/7.71 | Instantiating formula (201) with e1, e4, all_0_21_21, e2 and discharging atoms op(e1, e4) = all_0_21_21, op(e1, e4) = e2, yields:
% 27.89/7.71 | (2760) all_0_21_21 = e2
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (44), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (502) all_0_43_43 = e4
% 27.89/7.71 |
% 27.89/7.71 | Equations (502) can reduce 240 to:
% 27.89/7.71 | (696) ~ (all_0_51_51 = e4)
% 27.89/7.71 |
% 27.89/7.71 | Simplifying 696 yields:
% 27.89/7.71 | (697) ~ (all_0_51_51 = e4)
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (75), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (411) all_0_43_43 = e0
% 27.89/7.71 |
% 27.89/7.71 | Combining equations (502,411) yields a new equation:
% 27.89/7.71 | (478) e4 = e0
% 27.89/7.71 |
% 27.89/7.71 | Simplifying 478 yields:
% 27.89/7.71 | (479) e4 = e0
% 27.89/7.71 |
% 27.89/7.71 | Equations (479) can reduce 6 to:
% 27.89/7.71 | (270) $false
% 27.89/7.71 |
% 27.89/7.71 |-The branch is then unsatisfiable
% 27.89/7.71 |-Branch two:
% 27.89/7.71 | (455) ~ (all_0_43_43 = e0)
% 27.89/7.71 | (940) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 27.89/7.71 |
% 27.89/7.71 | Equations (502) can reduce 455 to:
% 27.89/7.71 | (6) ~ (e4 = e0)
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (116), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (411) all_0_43_43 = e0
% 27.89/7.71 |
% 27.89/7.71 | Combining equations (502,411) yields a new equation:
% 27.89/7.71 | (478) e4 = e0
% 27.89/7.71 |
% 27.89/7.71 | Simplifying 478 yields:
% 27.89/7.71 | (479) e4 = e0
% 27.89/7.71 |
% 27.89/7.71 | Equations (479) can reduce 6 to:
% 27.89/7.71 | (270) $false
% 27.89/7.71 |
% 27.89/7.71 |-The branch is then unsatisfiable
% 27.89/7.71 |-Branch two:
% 27.89/7.71 | (455) ~ (all_0_43_43 = e0)
% 27.89/7.71 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (1122), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (621) all_0_44_44 = e0
% 27.89/7.71 |
% 27.89/7.71 | Combining equations (621,370) yields a new equation:
% 27.89/7.71 | (316) e2 = e0
% 27.89/7.71 |
% 27.89/7.71 | Equations (316) can reduce 57 to:
% 27.89/7.71 | (270) $false
% 27.89/7.71 |
% 27.89/7.71 |-The branch is then unsatisfiable
% 27.89/7.71 |-Branch two:
% 27.89/7.71 | (625) ~ (all_0_44_44 = e0)
% 27.89/7.71 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (1128), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (454) all_0_45_45 = e0
% 27.89/7.71 |
% 27.89/7.71 | Equations (454) can reduce 128 to:
% 27.89/7.71 | (3103) ~ (all_0_53_53 = e0)
% 27.89/7.71 |
% 27.89/7.71 | Simplifying 3103 yields:
% 27.89/7.71 | (584) ~ (all_0_53_53 = e0)
% 27.89/7.71 |
% 27.89/7.71 | Equations (454) can reduce 108 to:
% 27.89/7.71 | (3530) ~ (all_0_58_58 = e0)
% 27.89/7.71 |
% 27.89/7.71 | Simplifying 3530 yields:
% 27.89/7.71 | (431) ~ (all_0_58_58 = e0)
% 27.89/7.71 |
% 27.89/7.71 | Equations (454) can reduce 434 to:
% 27.89/7.71 | (566) ~ (e2 = e0)
% 27.89/7.71 |
% 27.89/7.71 | Simplifying 566 yields:
% 27.89/7.71 | (57) ~ (e2 = e0)
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (176), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (830) all_0_56_56 = e0
% 27.89/7.71 |
% 27.89/7.71 | Combining equations (388,830) yields a new equation:
% 27.89/7.71 | (622) e2 = e0
% 27.89/7.71 |
% 27.89/7.71 | Simplifying 622 yields:
% 27.89/7.71 | (316) e2 = e0
% 27.89/7.71 |
% 27.89/7.71 | Equations (316) can reduce 57 to:
% 27.89/7.71 | (270) $false
% 27.89/7.71 |
% 27.89/7.71 |-The branch is then unsatisfiable
% 27.89/7.71 |-Branch two:
% 27.89/7.71 | (419) ~ (all_0_56_56 = e0)
% 27.89/7.71 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (834), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (2258) all_0_57_57 = e0
% 27.89/7.71 |
% 27.89/7.71 | Equations (2258) can reduce 235 to:
% 27.89/7.71 | (925) ~ (all_0_52_52 = e0)
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (64), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (954) all_0_51_51 = e0
% 27.89/7.71 |
% 27.89/7.71 | Equations (954) can reduce 12 to:
% 27.89/7.71 | (3103) ~ (all_0_53_53 = e0)
% 27.89/7.71 |
% 27.89/7.71 | Simplifying 3103 yields:
% 27.89/7.71 | (584) ~ (all_0_53_53 = e0)
% 27.89/7.71 |
% 27.89/7.71 | Equations (954) can reduce 697 to:
% 27.89/7.71 | (456) ~ (e4 = e0)
% 27.89/7.71 |
% 27.89/7.71 | Simplifying 456 yields:
% 27.89/7.71 | (6) ~ (e4 = e0)
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (93), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (402) all_0_59_59 = e4
% 27.89/7.71 |
% 27.89/7.71 | Equations (402) can reduce 280 to:
% 27.89/7.71 | (270) $false
% 27.89/7.71 |
% 27.89/7.71 |-The branch is then unsatisfiable
% 27.89/7.71 |-Branch two:
% 27.89/7.71 | (280) ~ (all_0_59_59 = e4)
% 27.89/7.71 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (407), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (408), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (409), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.89/7.71 |
% 27.89/7.71 | Applying alpha-rule on (410) yields:
% 27.89/7.71 | (411) all_0_43_43 = e0
% 27.89/7.71 | (412) all_0_59_59 = e3
% 27.89/7.71 | (413) ~ (all_0_46_46 = e3)
% 27.89/7.71 |
% 27.89/7.71 | Combining equations (411,502) yields a new equation:
% 27.89/7.71 | (479) e4 = e0
% 27.89/7.71 |
% 27.89/7.71 | Equations (479) can reduce 6 to:
% 27.89/7.71 | (270) $false
% 27.89/7.71 |
% 27.89/7.71 |-The branch is then unsatisfiable
% 27.89/7.71 |-Branch two:
% 27.89/7.71 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.89/7.71 |
% 27.89/7.71 | Applying alpha-rule on (416) yields:
% 27.89/7.71 | (411) all_0_43_43 = e0
% 27.89/7.71 | (412) all_0_59_59 = e3
% 27.89/7.71 | (419) ~ (all_0_56_56 = e0)
% 27.89/7.71 |
% 27.89/7.71 | Combining equations (411,502) yields a new equation:
% 27.89/7.71 | (479) e4 = e0
% 27.89/7.71 |
% 27.89/7.71 | Equations (479) can reduce 6 to:
% 27.89/7.71 | (270) $false
% 27.89/7.71 |
% 27.89/7.71 |-The branch is then unsatisfiable
% 27.89/7.71 |-Branch two:
% 27.89/7.71 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.89/7.71 |
% 27.89/7.71 | Applying alpha-rule on (422) yields:
% 27.89/7.71 | (423) all_0_53_53 = e0
% 27.89/7.71 | (424) all_0_59_59 = e1
% 27.89/7.71 | (425) ~ (all_0_54_54 = e1)
% 27.89/7.71 |
% 27.89/7.71 | Equations (423) can reduce 584 to:
% 27.89/7.71 | (270) $false
% 27.89/7.71 |
% 27.89/7.71 |-The branch is then unsatisfiable
% 27.89/7.71 |-Branch two:
% 27.89/7.71 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.89/7.71 |
% 27.89/7.71 | Applying alpha-rule on (428) yields:
% 27.89/7.71 | (423) all_0_53_53 = e0
% 27.89/7.71 | (424) all_0_59_59 = e1
% 27.89/7.71 | (431) ~ (all_0_58_58 = e0)
% 27.89/7.71 |
% 27.89/7.71 | Equations (423) can reduce 584 to:
% 27.89/7.71 | (270) $false
% 27.89/7.71 |
% 27.89/7.71 |-The branch is then unsatisfiable
% 27.89/7.71 |-Branch two:
% 27.89/7.71 | (987) ~ (all_0_51_51 = e0)
% 27.89/7.71 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (3067), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (827) all_0_52_52 = e0
% 27.89/7.71 |
% 27.89/7.71 | Equations (827) can reduce 925 to:
% 27.89/7.71 | (270) $false
% 27.89/7.71 |
% 27.89/7.71 |-The branch is then unsatisfiable
% 27.89/7.71 |-Branch two:
% 27.89/7.71 | (925) ~ (all_0_52_52 = e0)
% 27.89/7.71 | (3073) all_0_53_53 = e0 | all_0_54_54 = e0
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (3073), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (423) all_0_53_53 = e0
% 27.89/7.71 |
% 27.89/7.71 | Equations (423) can reduce 584 to:
% 27.89/7.71 | (270) $false
% 27.89/7.71 |
% 27.89/7.71 |-The branch is then unsatisfiable
% 27.89/7.71 |-Branch two:
% 27.89/7.71 | (584) ~ (all_0_53_53 = e0)
% 27.89/7.71 | (3084) all_0_54_54 = e0
% 27.89/7.71 |
% 27.89/7.71 | Equations (3084) can reduce 3011 to:
% 27.89/7.71 | (270) $false
% 27.89/7.71 |
% 27.89/7.71 |-The branch is then unsatisfiable
% 27.89/7.71 |-Branch two:
% 27.89/7.71 | (2301) ~ (all_0_57_57 = e0)
% 27.89/7.71 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (2302), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (585) all_0_58_58 = e0
% 27.89/7.71 |
% 27.89/7.71 | Equations (585) can reduce 431 to:
% 27.89/7.71 | (270) $false
% 27.89/7.71 |
% 27.89/7.71 |-The branch is then unsatisfiable
% 27.89/7.71 |-Branch two:
% 27.89/7.71 | (431) ~ (all_0_58_58 = e0)
% 27.89/7.71 | (2308) all_0_59_59 = e0
% 27.89/7.71 |
% 27.89/7.71 | Equations (2308) can reduce 4001 to:
% 27.89/7.71 | (270) $false
% 27.89/7.71 |
% 27.89/7.71 |-The branch is then unsatisfiable
% 27.89/7.71 |-Branch two:
% 27.89/7.71 | (488) ~ (all_0_45_45 = e0)
% 27.89/7.71 | (1132) all_0_46_46 = e0
% 27.89/7.71 |
% 27.89/7.71 | Equations (1132) can reduce 1010 to:
% 27.89/7.71 | (270) $false
% 27.89/7.71 |
% 27.89/7.71 |-The branch is then unsatisfiable
% 27.89/7.71 |-Branch two:
% 27.89/7.71 | (510) ~ (all_0_43_43 = e4)
% 27.89/7.71 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (159), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (450) all_0_43_43 = e2
% 27.89/7.71 |
% 27.89/7.71 | Equations (450) can reduce 292 to:
% 27.89/7.71 | (270) $false
% 27.89/7.71 |
% 27.89/7.71 |-The branch is then unsatisfiable
% 27.89/7.71 |-Branch two:
% 27.89/7.71 | (292) ~ (all_0_43_43 = e2)
% 27.89/7.71 | (774) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (774), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (411) all_0_43_43 = e0
% 27.89/7.71 |
% 27.89/7.71 | Equations (411) can reduce 84 to:
% 27.89/7.71 | (776) ~ (all_0_45_45 = e0)
% 27.89/7.71 |
% 27.89/7.71 | Simplifying 776 yields:
% 27.89/7.71 | (488) ~ (all_0_45_45 = e0)
% 27.89/7.71 |
% 27.89/7.71 | Equations (411) can reduce 510 to:
% 27.89/7.71 | (456) ~ (e4 = e0)
% 27.89/7.71 |
% 27.89/7.71 | Simplifying 456 yields:
% 27.89/7.71 | (6) ~ (e4 = e0)
% 27.89/7.71 |
% 27.89/7.71 +-Applying beta-rule and splitting (166), into two cases.
% 27.89/7.71 |-Branch one:
% 27.89/7.71 | (522) all_0_39_39 = e4
% 27.89/7.71 |
% 27.89/7.71 | Combining equations (751,522) yields a new equation:
% 27.89/7.71 | (359) e4 = e3
% 27.89/7.71 |
% 27.89/7.71 | Equations (359) can reduce 34 to:
% 27.89/7.71 | (270) $false
% 27.89/7.71 |
% 27.89/7.71 |-The branch is then unsatisfiable
% 27.89/7.71 |-Branch two:
% 27.89/7.71 | (591) ~ (all_0_39_39 = e4)
% 27.89/7.71 | (4522) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 27.89/7.72 |
% 27.89/7.72 +-Applying beta-rule and splitting (4522), into two cases.
% 27.89/7.72 |-Branch one:
% 27.89/7.72 | (502) all_0_43_43 = e4
% 27.89/7.72 |
% 27.89/7.72 | Combining equations (411,502) yields a new equation:
% 27.89/7.72 | (479) e4 = e0
% 27.89/7.72 |
% 27.89/7.72 | Equations (479) can reduce 6 to:
% 27.89/7.72 | (270) $false
% 27.89/7.72 |
% 27.89/7.72 |-The branch is then unsatisfiable
% 27.89/7.72 |-Branch two:
% 27.89/7.72 | (510) ~ (all_0_43_43 = e4)
% 27.89/7.72 | (4527) all_0_51_51 = e4 | all_0_56_56 = e4
% 27.89/7.72 |
% 27.89/7.72 +-Applying beta-rule and splitting (4527), into two cases.
% 27.89/7.72 |-Branch one:
% 27.89/7.72 | (1467) all_0_51_51 = e4
% 27.89/7.72 |
% 27.89/7.72 | From (1467) and (171) follows:
% 27.89/7.72 | (2936) op(e1, e3) = e4
% 27.89/7.72 |
% 27.89/7.72 +-Applying beta-rule and splitting (105), into two cases.
% 27.89/7.72 |-Branch one:
% 27.89/7.72 | (374) all_0_45_45 = e2
% 27.89/7.72 |
% 27.89/7.72 | Equations (374) can reduce 434 to:
% 27.89/7.72 | (270) $false
% 27.89/7.72 |
% 27.89/7.72 |-The branch is then unsatisfiable
% 27.89/7.72 |-Branch two:
% 27.89/7.72 | (434) ~ (all_0_45_45 = e2)
% 27.89/7.72 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 27.89/7.72 |
% 27.89/7.72 +-Applying beta-rule and splitting (435), into two cases.
% 27.89/7.72 |-Branch one:
% 27.89/7.72 | (454) all_0_45_45 = e0
% 27.89/7.72 |
% 27.89/7.72 | Equations (454) can reduce 488 to:
% 27.89/7.72 | (270) $false
% 27.89/7.72 |
% 27.89/7.72 |-The branch is then unsatisfiable
% 27.89/7.72 |-Branch two:
% 27.89/7.72 | (488) ~ (all_0_45_45 = e0)
% 27.89/7.72 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 27.89/7.72 |
% 27.89/7.72 +-Applying beta-rule and splitting (511), into two cases.
% 27.89/7.72 |-Branch one:
% 27.89/7.72 | (363) all_0_45_45 = e4
% 27.89/7.72 |
% 27.89/7.72 | Equations (363) can reduce 352 to:
% 27.89/7.72 | (270) $false
% 27.89/7.72 |
% 27.89/7.72 |-The branch is then unsatisfiable
% 27.89/7.72 |-Branch two:
% 27.89/7.72 | (352) ~ (all_0_45_45 = e4)
% 27.89/7.72 | (517) all_0_46_46 = e4
% 27.89/7.72 |
% 27.89/7.72 | Equations (517) can reduce 38 to:
% 27.89/7.72 | (352) ~ (all_0_45_45 = e4)
% 27.89/7.72 |
% 27.89/7.72 | Equations (517) can reduce 206 to:
% 27.89/7.72 | (279) ~ (all_0_59_59 = e4)
% 27.89/7.72 |
% 27.89/7.72 | Simplifying 279 yields:
% 27.89/7.72 | (280) ~ (all_0_59_59 = e4)
% 27.89/7.72 |
% 27.89/7.72 | Equations (517) can reduce 1436 to:
% 27.89/7.72 | (231) ~ (e4 = e2)
% 27.89/7.72 |
% 27.89/7.72 | From (517) and (89) follows:
% 27.99/7.72 | (4546) op(e0, e4) = all_0_32_32
% 27.99/7.72 |
% 27.99/7.72 +-Applying beta-rule and splitting (489), into two cases.
% 27.99/7.72 |-Branch one:
% 27.99/7.72 | (505) all_0_45_45 = e3
% 27.99/7.72 |
% 27.99/7.72 | Equations (505) can reduce 108 to:
% 27.99/7.72 | (717) ~ (all_0_58_58 = e3)
% 27.99/7.72 |
% 27.99/7.72 | Simplifying 717 yields:
% 27.99/7.72 | (718) ~ (all_0_58_58 = e3)
% 27.99/7.72 |
% 27.99/7.72 | Equations (505) can reduce 352 to:
% 27.99/7.72 | (719) ~ (e4 = e3)
% 27.99/7.72 |
% 27.99/7.72 | Simplifying 719 yields:
% 27.99/7.72 | (34) ~ (e4 = e3)
% 27.99/7.72 |
% 27.99/7.72 | Equations (505) can reduce 26 to:
% 27.99/7.72 | (136) ~ (e3 = e1)
% 27.99/7.72 |
% 27.99/7.72 | Equations (505) can reduce 488 to:
% 27.99/7.72 | (66) ~ (e3 = e0)
% 27.99/7.72 |
% 27.99/7.72 | From (505) and (142) follows:
% 27.99/7.72 | (2975) op(e1, e3) = all_0_23_23
% 27.99/7.72 |
% 27.99/7.72 | Instantiating formula (201) with e1, e3, e4, all_0_23_23 and discharging atoms op(e1, e3) = all_0_23_23, op(e1, e3) = e4, yields:
% 27.99/7.72 | (3008) all_0_23_23 = e4
% 27.99/7.72 |
% 27.99/7.72 | Instantiating formula (201) with e0, e4, all_0_32_32, e4 and discharging atoms op(e0, e4) = all_0_32_32, op(e0, e4) = e4, yields:
% 27.99/7.72 | (4556) all_0_32_32 = e4
% 27.99/7.72 |
% 27.99/7.72 +-Applying beta-rule and splitting (111), into two cases.
% 27.99/7.72 |-Branch one:
% 27.99/7.72 | (4557) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0)) | (all_0_34_34 = e2 & ~ (all_0_35_35 = e0))
% 27.99/7.72 |
% 27.99/7.72 +-Applying beta-rule and splitting (4557), into two cases.
% 27.99/7.72 |-Branch one:
% 27.99/7.72 | (4558) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0))
% 27.99/7.72 |
% 27.99/7.72 +-Applying beta-rule and splitting (4558), into two cases.
% 27.99/7.72 |-Branch one:
% 27.99/7.72 | (4559) all_0_30_30 = e4 & ~ (all_0_31_31 = e0)
% 27.99/7.72 |
% 27.99/7.72 | Applying alpha-rule on (4559) yields:
% 27.99/7.72 | (4560) all_0_30_30 = e4
% 27.99/7.72 | (4561) ~ (all_0_31_31 = e0)
% 27.99/7.72 |
% 27.99/7.72 | Combining equations (4234,4560) yields a new equation:
% 27.99/7.72 | (4562) all_0_57_57 = e4
% 27.99/7.72 |
% 27.99/7.72 | Simplifying 4562 yields:
% 27.99/7.72 | (4563) all_0_57_57 = e4
% 27.99/7.72 |
% 27.99/7.72 | Equations (4563) can reduce 143 to:
% 27.99/7.72 | (270) $false
% 27.99/7.72 |
% 27.99/7.72 |-The branch is then unsatisfiable
% 27.99/7.72 |-Branch two:
% 27.99/7.72 | (4565) all_0_32_32 = e3 & ~ (all_0_33_33 = e0)
% 27.99/7.72 |
% 27.99/7.72 | Applying alpha-rule on (4565) yields:
% 27.99/7.72 | (4566) all_0_32_32 = e3
% 27.99/7.72 | (4567) ~ (all_0_33_33 = e0)
% 27.99/7.72 |
% 27.99/7.72 | Combining equations (4556,4566) yields a new equation:
% 27.99/7.72 | (660) e4 = e3
% 27.99/7.72 |
% 27.99/7.72 | Simplifying 660 yields:
% 27.99/7.72 | (359) e4 = e3
% 27.99/7.72 |
% 27.99/7.72 | Equations (359) can reduce 34 to:
% 27.99/7.72 | (270) $false
% 27.99/7.72 |
% 27.99/7.72 |-The branch is then unsatisfiable
% 27.99/7.72 |-Branch two:
% 27.99/7.72 | (4571) all_0_34_34 = e2 & ~ (all_0_35_35 = e0)
% 27.99/7.72 |
% 27.99/7.72 | Applying alpha-rule on (4571) yields:
% 27.99/7.72 | (4572) all_0_34_34 = e2
% 27.99/7.72 | (4573) ~ (all_0_35_35 = e0)
% 27.99/7.72 |
% 27.99/7.72 | Combining equations (4014,4572) yields a new equation:
% 27.99/7.72 | (4574) all_0_59_59 = e2
% 27.99/7.72 |
% 27.99/7.72 | Simplifying 4574 yields:
% 27.99/7.72 | (399) all_0_59_59 = e2
% 27.99/7.72 |
% 27.99/7.72 | Equations (399) can reduce 701 to:
% 27.99/7.72 | (270) $false
% 27.99/7.72 |
% 27.99/7.72 |-The branch is then unsatisfiable
% 27.99/7.72 |-Branch two:
% 27.99/7.72 | (4577) all_0_36_36 = e1 & ~ (all_0_37_37 = e0)
% 27.99/7.72 |
% 27.99/7.72 | Applying alpha-rule on (4577) yields:
% 27.99/7.72 | (4578) all_0_36_36 = e1
% 27.99/7.72 | (4579) ~ (all_0_37_37 = e0)
% 27.99/7.72 |
% 27.99/7.72 +-Applying beta-rule and splitting (14), into two cases.
% 27.99/7.72 |-Branch one:
% 27.99/7.72 | (2277) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1))
% 27.99/7.72 |
% 27.99/7.72 +-Applying beta-rule and splitting (2277), into two cases.
% 27.99/7.72 |-Branch one:
% 27.99/7.72 | (2278) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1))
% 27.99/7.72 |
% 27.99/7.72 +-Applying beta-rule and splitting (2278), into two cases.
% 27.99/7.72 |-Branch one:
% 27.99/7.72 | (2279) all_0_21_21 = e4 & ~ (all_0_22_22 = e1)
% 27.99/7.72 |
% 27.99/7.72 | Applying alpha-rule on (2279) yields:
% 27.99/7.72 | (2280) all_0_21_21 = e4
% 27.99/7.72 | (2281) ~ (all_0_22_22 = e1)
% 27.99/7.72 |
% 27.99/7.72 | Combining equations (2760,2280) yields a new equation:
% 27.99/7.72 | (269) e4 = e2
% 27.99/7.72 |
% 27.99/7.72 | Equations (269) can reduce 231 to:
% 27.99/7.72 | (270) $false
% 27.99/7.72 |
% 27.99/7.72 |-The branch is then unsatisfiable
% 27.99/7.72 |-Branch two:
% 27.99/7.72 | (2285) all_0_23_23 = e3 & ~ (all_0_24_24 = e1)
% 27.99/7.72 |
% 27.99/7.72 | Applying alpha-rule on (2285) yields:
% 27.99/7.72 | (2286) all_0_23_23 = e3
% 27.99/7.72 | (2287) ~ (all_0_24_24 = e1)
% 27.99/7.72 |
% 27.99/7.72 | Combining equations (2286,3008) yields a new equation:
% 27.99/7.72 | (359) e4 = e3
% 27.99/7.72 |
% 27.99/7.72 | Equations (359) can reduce 34 to:
% 27.99/7.72 | (270) $false
% 27.99/7.72 |
% 27.99/7.72 |-The branch is then unsatisfiable
% 27.99/7.72 |-Branch two:
% 27.99/7.72 | (2291) all_0_25_25 = e2 & ~ (all_0_26_26 = e1)
% 27.99/7.72 |
% 27.99/7.72 | Applying alpha-rule on (2291) yields:
% 27.99/7.72 | (2292) all_0_25_25 = e2
% 27.99/7.72 | (2293) ~ (all_0_26_26 = e1)
% 27.99/7.72 |
% 27.99/7.72 | Combining equations (3973,2292) yields a new equation:
% 27.99/7.72 | (4595) all_0_52_52 = e2
% 27.99/7.72 |
% 27.99/7.72 | Simplifying 4595 yields:
% 27.99/7.72 | (685) all_0_52_52 = e2
% 27.99/7.72 |
% 27.99/7.72 | Equations (685) can reduce 257 to:
% 27.99/7.72 | (270) $false
% 27.99/7.72 |
% 27.99/7.72 |-The branch is then unsatisfiable
% 27.99/7.72 |-Branch two:
% 27.99/7.72 | (2296) all_0_28_28 = e0 & ~ (all_0_29_29 = e1)
% 27.99/7.72 |
% 27.99/7.73 | Applying alpha-rule on (2296) yields:
% 27.99/7.73 | (2297) all_0_28_28 = e0
% 27.99/7.73 | (2298) ~ (all_0_29_29 = e1)
% 27.99/7.73 |
% 27.99/7.73 | From (2297) and (63) follows:
% 27.99/7.73 | (4601) op(e1, all_0_58_58) = e0
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (182), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (454) all_0_45_45 = e0
% 27.99/7.73 |
% 27.99/7.73 | Combining equations (505,454) yields a new equation:
% 27.99/7.73 | (783) e3 = e0
% 27.99/7.73 |
% 27.99/7.73 | Simplifying 783 yields:
% 27.99/7.73 | (784) e3 = e0
% 27.99/7.73 |
% 27.99/7.73 | Equations (784) can reduce 66 to:
% 27.99/7.73 | (270) $false
% 27.99/7.73 |
% 27.99/7.73 |-The branch is then unsatisfiable
% 27.99/7.73 |-Branch two:
% 27.99/7.73 | (488) ~ (all_0_45_45 = e0)
% 27.99/7.73 | (558) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (33), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (392) all_0_57_57 = e2
% 27.99/7.73 |
% 27.99/7.73 | Equations (392) can reduce 335 to:
% 27.99/7.73 | (270) $false
% 27.99/7.73 |
% 27.99/7.73 |-The branch is then unsatisfiable
% 27.99/7.73 |-Branch two:
% 27.99/7.73 | (335) ~ (all_0_57_57 = e2)
% 27.99/7.73 | (670) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (194), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (747) all_0_56_56 = e1
% 27.99/7.73 |
% 27.99/7.73 | Combining equations (747,388) yields a new equation:
% 27.99/7.73 | (322) e2 = e1
% 27.99/7.73 |
% 27.99/7.73 | Equations (322) can reduce 141 to:
% 27.99/7.73 | (270) $false
% 27.99/7.73 |
% 27.99/7.73 |-The branch is then unsatisfiable
% 27.99/7.73 |-Branch two:
% 27.99/7.73 | (995) ~ (all_0_56_56 = e1)
% 27.99/7.73 | (996) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 27.99/7.73 |
% 27.99/7.73 | Equations (388) can reduce 995 to:
% 27.99/7.73 | (141) ~ (e2 = e1)
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (133), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (671) all_0_40_40 = e3
% 27.99/7.73 |
% 27.99/7.73 | Combining equations (671,530) yields a new equation:
% 27.99/7.73 | (537) e3 = e1
% 27.99/7.73 |
% 27.99/7.73 | Simplifying 537 yields:
% 27.99/7.73 | (538) e3 = e1
% 27.99/7.73 |
% 27.99/7.73 | Equations (538) can reduce 136 to:
% 27.99/7.73 | (270) $false
% 27.99/7.73 |
% 27.99/7.73 |-The branch is then unsatisfiable
% 27.99/7.73 |-Branch two:
% 27.99/7.73 | (675) ~ (all_0_40_40 = e3)
% 27.99/7.73 | (676) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (127), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (541) all_0_42_42 = e1
% 27.99/7.73 |
% 27.99/7.73 | Combining equations (541,698) yields a new equation:
% 27.99/7.73 | (322) e2 = e1
% 27.99/7.73 |
% 27.99/7.73 | Equations (322) can reduce 141 to:
% 27.99/7.73 | (270) $false
% 27.99/7.73 |
% 27.99/7.73 |-The branch is then unsatisfiable
% 27.99/7.73 |-Branch two:
% 27.99/7.73 | (640) ~ (all_0_42_42 = e1)
% 27.99/7.73 | (4628) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (204), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (396) all_0_58_58 = e2
% 27.99/7.73 |
% 27.99/7.73 | Equations (396) can reduce 376 to:
% 27.99/7.73 | (270) $false
% 27.99/7.73 |
% 27.99/7.73 |-The branch is then unsatisfiable
% 27.99/7.73 |-Branch two:
% 27.99/7.73 | (376) ~ (all_0_58_58 = e2)
% 27.99/7.73 | (3890) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1 | all_0_58_58 = e0
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (109), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (399) all_0_59_59 = e2
% 27.99/7.73 |
% 27.99/7.73 | Equations (399) can reduce 701 to:
% 27.99/7.73 | (270) $false
% 27.99/7.73 |
% 27.99/7.73 |-The branch is then unsatisfiable
% 27.99/7.73 |-Branch two:
% 27.99/7.73 | (701) ~ (all_0_59_59 = e2)
% 27.99/7.73 | (4636) all_0_59_59 = e4 | all_0_59_59 = e3 | all_0_59_59 = e1 | all_0_59_59 = e0
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (93), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (402) all_0_59_59 = e4
% 27.99/7.73 |
% 27.99/7.73 | Equations (402) can reduce 280 to:
% 27.99/7.73 | (270) $false
% 27.99/7.73 |
% 27.99/7.73 |-The branch is then unsatisfiable
% 27.99/7.73 |-Branch two:
% 27.99/7.73 | (280) ~ (all_0_59_59 = e4)
% 27.99/7.73 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (626), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (827) all_0_52_52 = e0
% 27.99/7.73 |
% 27.99/7.73 | Equations (827) can reduce 213 to:
% 27.99/7.73 | (3103) ~ (all_0_53_53 = e0)
% 27.99/7.73 |
% 27.99/7.73 | Simplifying 3103 yields:
% 27.99/7.73 | (584) ~ (all_0_53_53 = e0)
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (407), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (408), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (409), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.99/7.73 |
% 27.99/7.73 | Applying alpha-rule on (410) yields:
% 27.99/7.73 | (411) all_0_43_43 = e0
% 27.99/7.73 | (412) all_0_59_59 = e3
% 27.99/7.73 | (413) ~ (all_0_46_46 = e3)
% 27.99/7.73 |
% 27.99/7.73 | Equations (412) can reduce 140 to:
% 27.99/7.73 | (846) ~ (all_0_57_57 = e3)
% 27.99/7.73 |
% 27.99/7.73 | Equations (412) can reduce 701 to:
% 27.99/7.73 | (223) ~ (e3 = e2)
% 27.99/7.73 |
% 27.99/7.73 | Equations (412) can reduce 4001 to:
% 27.99/7.73 | (66) ~ (e3 = e0)
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (676), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (858) all_0_44_44 = e3
% 27.99/7.73 |
% 27.99/7.73 | Combining equations (858,370) yields a new equation:
% 27.99/7.73 | (437) e3 = e2
% 27.99/7.73 |
% 27.99/7.73 | Simplifying 437 yields:
% 27.99/7.73 | (414) e3 = e2
% 27.99/7.73 |
% 27.99/7.73 | Equations (414) can reduce 223 to:
% 27.99/7.73 | (270) $false
% 27.99/7.73 |
% 27.99/7.73 |-The branch is then unsatisfiable
% 27.99/7.73 |-Branch two:
% 27.99/7.73 | (862) ~ (all_0_44_44 = e3)
% 27.99/7.73 | (863) all_0_52_52 = e3 | all_0_57_57 = e3
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (863), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (864) all_0_52_52 = e3
% 27.99/7.73 |
% 27.99/7.73 | Combining equations (827,864) yields a new equation:
% 27.99/7.73 | (784) e3 = e0
% 27.99/7.73 |
% 27.99/7.73 | Equations (784) can reduce 66 to:
% 27.99/7.73 | (270) $false
% 27.99/7.73 |
% 27.99/7.73 |-The branch is then unsatisfiable
% 27.99/7.73 |-Branch two:
% 27.99/7.73 | (826) ~ (all_0_52_52 = e3)
% 27.99/7.73 | (869) all_0_57_57 = e3
% 27.99/7.73 |
% 27.99/7.73 | Equations (869) can reduce 846 to:
% 27.99/7.73 | (270) $false
% 27.99/7.73 |
% 27.99/7.73 |-The branch is then unsatisfiable
% 27.99/7.73 |-Branch two:
% 27.99/7.73 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.99/7.73 |
% 27.99/7.73 | Applying alpha-rule on (416) yields:
% 27.99/7.73 | (411) all_0_43_43 = e0
% 27.99/7.73 | (412) all_0_59_59 = e3
% 27.99/7.73 | (419) ~ (all_0_56_56 = e0)
% 27.99/7.73 |
% 27.99/7.73 | Equations (412) can reduce 140 to:
% 27.99/7.73 | (846) ~ (all_0_57_57 = e3)
% 27.99/7.73 |
% 27.99/7.73 | Equations (412) can reduce 701 to:
% 27.99/7.73 | (223) ~ (e3 = e2)
% 27.99/7.73 |
% 27.99/7.73 | Equations (412) can reduce 4001 to:
% 27.99/7.73 | (66) ~ (e3 = e0)
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (676), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (858) all_0_44_44 = e3
% 27.99/7.73 |
% 27.99/7.73 | Combining equations (858,370) yields a new equation:
% 27.99/7.73 | (437) e3 = e2
% 27.99/7.73 |
% 27.99/7.73 | Simplifying 437 yields:
% 27.99/7.73 | (414) e3 = e2
% 27.99/7.73 |
% 27.99/7.73 | Equations (414) can reduce 223 to:
% 27.99/7.73 | (270) $false
% 27.99/7.73 |
% 27.99/7.73 |-The branch is then unsatisfiable
% 27.99/7.73 |-Branch two:
% 27.99/7.73 | (862) ~ (all_0_44_44 = e3)
% 27.99/7.73 | (863) all_0_52_52 = e3 | all_0_57_57 = e3
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (863), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (864) all_0_52_52 = e3
% 27.99/7.73 |
% 27.99/7.73 | Combining equations (827,864) yields a new equation:
% 27.99/7.73 | (784) e3 = e0
% 27.99/7.73 |
% 27.99/7.73 | Equations (784) can reduce 66 to:
% 27.99/7.73 | (270) $false
% 27.99/7.73 |
% 27.99/7.73 |-The branch is then unsatisfiable
% 27.99/7.73 |-Branch two:
% 27.99/7.73 | (826) ~ (all_0_52_52 = e3)
% 27.99/7.73 | (869) all_0_57_57 = e3
% 27.99/7.73 |
% 27.99/7.73 | Equations (869) can reduce 846 to:
% 27.99/7.73 | (270) $false
% 27.99/7.73 |
% 27.99/7.73 |-The branch is then unsatisfiable
% 27.99/7.73 |-Branch two:
% 27.99/7.73 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.99/7.73 |
% 27.99/7.73 | Applying alpha-rule on (422) yields:
% 27.99/7.73 | (423) all_0_53_53 = e0
% 27.99/7.73 | (424) all_0_59_59 = e1
% 27.99/7.73 | (425) ~ (all_0_54_54 = e1)
% 27.99/7.73 |
% 27.99/7.73 | Equations (423) can reduce 584 to:
% 27.99/7.73 | (270) $false
% 27.99/7.73 |
% 27.99/7.73 |-The branch is then unsatisfiable
% 27.99/7.73 |-Branch two:
% 27.99/7.73 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.99/7.73 |
% 27.99/7.73 | Applying alpha-rule on (428) yields:
% 27.99/7.73 | (423) all_0_53_53 = e0
% 27.99/7.73 | (424) all_0_59_59 = e1
% 27.99/7.73 | (431) ~ (all_0_58_58 = e0)
% 27.99/7.73 |
% 27.99/7.73 | Equations (423) can reduce 584 to:
% 27.99/7.73 | (270) $false
% 27.99/7.73 |
% 27.99/7.73 |-The branch is then unsatisfiable
% 27.99/7.73 |-Branch two:
% 27.99/7.73 | (925) ~ (all_0_52_52 = e0)
% 27.99/7.73 | (2258) all_0_57_57 = e0
% 27.99/7.73 |
% 27.99/7.73 | Equations (2258) can reduce 37 to:
% 27.99/7.73 | (3530) ~ (all_0_58_58 = e0)
% 27.99/7.73 |
% 27.99/7.73 | Simplifying 3530 yields:
% 27.99/7.73 | (431) ~ (all_0_58_58 = e0)
% 27.99/7.73 |
% 27.99/7.73 | Equations (2258) can reduce 335 to:
% 27.99/7.73 | (566) ~ (e2 = e0)
% 27.99/7.73 |
% 27.99/7.73 | Simplifying 566 yields:
% 27.99/7.73 | (57) ~ (e2 = e0)
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (558), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (559) all_0_48_48 = e0
% 27.99/7.73 |
% 27.99/7.73 | Combining equations (311,559) yields a new equation:
% 27.99/7.73 | (622) e2 = e0
% 27.99/7.73 |
% 27.99/7.73 | Simplifying 622 yields:
% 27.99/7.73 | (316) e2 = e0
% 27.99/7.73 |
% 27.99/7.73 | Equations (316) can reduce 57 to:
% 27.99/7.73 | (270) $false
% 27.99/7.73 |
% 27.99/7.73 |-The branch is then unsatisfiable
% 27.99/7.73 |-Branch two:
% 27.99/7.73 | (562) ~ (all_0_48_48 = e0)
% 27.99/7.73 | (575) all_0_53_53 = e0 | all_0_58_58 = e0
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (3890), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (585) all_0_58_58 = e0
% 27.99/7.73 |
% 27.99/7.73 | Equations (585) can reduce 431 to:
% 27.99/7.73 | (270) $false
% 27.99/7.73 |
% 27.99/7.73 |-The branch is then unsatisfiable
% 27.99/7.73 |-Branch two:
% 27.99/7.73 | (431) ~ (all_0_58_58 = e0)
% 27.99/7.73 | (4709) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (575), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (423) all_0_53_53 = e0
% 27.99/7.73 |
% 27.99/7.73 | Equations (423) can reduce 70 to:
% 27.99/7.73 | (3530) ~ (all_0_58_58 = e0)
% 27.99/7.73 |
% 27.99/7.73 | Simplifying 3530 yields:
% 27.99/7.73 | (431) ~ (all_0_58_58 = e0)
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (4709), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (4713) all_0_58_58 = e3
% 27.99/7.73 |
% 27.99/7.73 | Equations (4713) can reduce 718 to:
% 27.99/7.73 | (270) $false
% 27.99/7.73 |
% 27.99/7.73 |-The branch is then unsatisfiable
% 27.99/7.73 |-Branch two:
% 27.99/7.73 | (718) ~ (all_0_58_58 = e3)
% 27.99/7.73 | (4716) all_0_58_58 = e4 | all_0_58_58 = e1
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (4716), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (1001) all_0_58_58 = e1
% 27.99/7.73 |
% 27.99/7.73 | Equations (1001) can reduce 156 to:
% 27.99/7.73 | (749) ~ (all_0_59_59 = e1)
% 27.99/7.73 |
% 27.99/7.73 | Simplifying 749 yields:
% 27.99/7.73 | (750) ~ (all_0_59_59 = e1)
% 27.99/7.73 |
% 27.99/7.73 | Equations (1001) can reduce 431 to:
% 27.99/7.73 | (132) ~ (e1 = e0)
% 27.99/7.73 |
% 27.99/7.73 | From (1001) and (4601) follows:
% 27.99/7.73 | (2167) op(e1, e1) = e0
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (4628), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (589) all_0_49_49 = e1
% 27.99/7.73 |
% 27.99/7.73 | Combining equations (563,589) yields a new equation:
% 27.99/7.73 | (560) e1 = e0
% 27.99/7.73 |
% 27.99/7.73 | Equations (560) can reduce 132 to:
% 27.99/7.73 | (270) $false
% 27.99/7.73 |
% 27.99/7.73 |-The branch is then unsatisfiable
% 27.99/7.73 |-Branch two:
% 27.99/7.73 | (543) ~ (all_0_49_49 = e1)
% 27.99/7.73 | (4726) all_0_54_54 = e1 | all_0_59_59 = e1
% 27.99/7.73 |
% 27.99/7.73 +-Applying beta-rule and splitting (4726), into two cases.
% 27.99/7.73 |-Branch one:
% 27.99/7.73 | (875) all_0_54_54 = e1
% 27.99/7.73 |
% 27.99/7.73 | From (875) and (29) follows:
% 27.99/7.73 | (3061) op(e1, e1) = all_0_37_37
% 27.99/7.73 |
% 27.99/7.73 | Instantiating formula (201) with e1, e1, e0, all_0_37_37 and discharging atoms op(e1, e1) = all_0_37_37, op(e1, e1) = e0, yields:
% 27.99/7.73 | (3079) all_0_37_37 = e0
% 27.99/7.73 |
% 27.99/7.73 | Equations (3079) can reduce 4579 to:
% 27.99/7.73 | (270) $false
% 27.99/7.73 |
% 27.99/7.73 |-The branch is then unsatisfiable
% 27.99/7.73 |-Branch two:
% 27.99/7.73 | (425) ~ (all_0_54_54 = e1)
% 27.99/7.73 | (424) all_0_59_59 = e1
% 27.99/7.73 |
% 27.99/7.73 | Equations (424) can reduce 750 to:
% 27.99/7.73 | (270) $false
% 27.99/7.73 |
% 27.99/7.73 |-The branch is then unsatisfiable
% 27.99/7.74 |-Branch two:
% 27.99/7.74 | (1004) ~ (all_0_58_58 = e1)
% 27.99/7.74 | (600) all_0_58_58 = e4
% 27.99/7.74 |
% 27.99/7.74 | Equations (600) can reduce 278 to:
% 27.99/7.74 | (270) $false
% 27.99/7.74 |
% 27.99/7.74 |-The branch is then unsatisfiable
% 27.99/7.74 |-Branch two:
% 27.99/7.74 | (584) ~ (all_0_53_53 = e0)
% 27.99/7.74 | (585) all_0_58_58 = e0
% 27.99/7.74 |
% 27.99/7.74 | Equations (585) can reduce 431 to:
% 27.99/7.74 | (270) $false
% 27.99/7.74 |
% 27.99/7.74 |-The branch is then unsatisfiable
% 27.99/7.74 |-Branch two:
% 27.99/7.74 | (354) ~ (all_0_45_45 = e3)
% 27.99/7.74 | (363) all_0_45_45 = e4
% 27.99/7.74 |
% 27.99/7.74 | Equations (363) can reduce 352 to:
% 27.99/7.74 | (270) $false
% 27.99/7.74 |
% 27.99/7.74 |-The branch is then unsatisfiable
% 27.99/7.74 |-Branch two:
% 27.99/7.74 | (697) ~ (all_0_51_51 = e4)
% 27.99/7.74 | (4744) all_0_56_56 = e4
% 27.99/7.74 |
% 27.99/7.74 | Combining equations (4744,388) yields a new equation:
% 27.99/7.74 | (268) e4 = e2
% 27.99/7.74 |
% 27.99/7.74 | Simplifying 268 yields:
% 27.99/7.74 | (269) e4 = e2
% 27.99/7.74 |
% 27.99/7.74 | Equations (269) can reduce 231 to:
% 27.99/7.74 | (270) $false
% 27.99/7.74 |
% 27.99/7.74 |-The branch is then unsatisfiable
% 27.99/7.74 |-Branch two:
% 27.99/7.74 | (455) ~ (all_0_43_43 = e0)
% 27.99/7.74 | (944) all_0_43_43 = e4 | all_0_43_43 = e3
% 27.99/7.74 |
% 27.99/7.74 +-Applying beta-rule and splitting (944), into two cases.
% 27.99/7.74 |-Branch one:
% 27.99/7.74 | (782) all_0_43_43 = e3
% 27.99/7.74 |
% 27.99/7.74 | Equations (782) can reduce 786 to:
% 27.99/7.74 | (270) $false
% 27.99/7.74 |
% 27.99/7.74 |-The branch is then unsatisfiable
% 27.99/7.74 |-Branch two:
% 27.99/7.74 | (786) ~ (all_0_43_43 = e3)
% 27.99/7.74 | (502) all_0_43_43 = e4
% 27.99/7.74 |
% 27.99/7.74 | Equations (502) can reduce 510 to:
% 27.99/7.74 | (270) $false
% 27.99/7.74 |
% 27.99/7.74 |-The branch is then unsatisfiable
% 27.99/7.74 |-Branch two:
% 27.99/7.74 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 27.99/7.74 |
% 27.99/7.74 | Applying alpha-rule on (346) yields:
% 27.99/7.74 | (347) all_0_2_2 = e0
% 27.99/7.74 | (348) ~ (all_0_3_3 = e4)
% 27.99/7.74 |
% 27.99/7.74 | Equations (287) can reduce 348 to:
% 27.99/7.74 | (270) $false
% 27.99/7.74 |
% 27.99/7.74 |-The branch is then unsatisfiable
% 27.99/7.74 |-Branch two:
% 27.99/7.74 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 27.99/7.74 |
% 27.99/7.74 | Applying alpha-rule on (350) yields:
% 27.99/7.74 | (351) all_0_41_41 = e3
% 27.99/7.74 | (352) ~ (all_0_45_45 = e4)
% 27.99/7.74 |
% 27.99/7.74 | Combining equations (358,351) yields a new equation:
% 27.99/7.74 | (660) e4 = e3
% 27.99/7.74 |
% 27.99/7.74 | Simplifying 660 yields:
% 27.99/7.74 | (359) e4 = e3
% 27.99/7.74 |
% 27.99/7.74 | Equations (359) can reduce 34 to:
% 27.99/7.74 | (270) $false
% 27.99/7.74 |
% 27.99/7.74 |-The branch is then unsatisfiable
% 27.99/7.74 |-Branch two:
% 27.99/7.74 | (755) ~ (all_0_39_39 = e3)
% 27.99/7.74 | (1756) all_0_39_39 = e4 | all_0_39_39 = e1
% 27.99/7.74 |
% 27.99/7.74 +-Applying beta-rule and splitting (186), into two cases.
% 27.99/7.74 |-Branch one:
% 27.99/7.74 | (336) all_0_39_39 = e2
% 27.99/7.74 |
% 27.99/7.74 | Equations (336) can reduce 291 to:
% 27.99/7.74 | (270) $false
% 27.99/7.74 |
% 27.99/7.74 |-The branch is then unsatisfiable
% 27.99/7.74 |-Branch two:
% 27.99/7.74 | (291) ~ (all_0_39_39 = e2)
% 27.99/7.74 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 27.99/7.74 |
% 27.99/7.74 +-Applying beta-rule and splitting (339), into two cases.
% 27.99/7.74 |-Branch one:
% 27.99/7.74 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 27.99/7.74 |
% 27.99/7.74 +-Applying beta-rule and splitting (340), into two cases.
% 27.99/7.74 |-Branch one:
% 27.99/7.74 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 27.99/7.74 |
% 27.99/7.74 | Applying alpha-rule on (341) yields:
% 27.99/7.74 | (342) all_0_0_0 = e1
% 27.99/7.74 | (343) ~ (all_0_1_1 = e4)
% 27.99/7.74 |
% 27.99/7.74 | Combining equations (342,285) yields a new equation:
% 27.99/7.74 | (530) all_0_40_40 = e1
% 27.99/7.74 |
% 27.99/7.74 | Equations (530) can reduce 114 to:
% 27.99/7.74 | (528) ~ (all_0_39_39 = e1)
% 27.99/7.74 |
% 27.99/7.74 +-Applying beta-rule and splitting (1756), into two cases.
% 27.99/7.74 |-Branch one:
% 27.99/7.74 | (524) all_0_39_39 = e1
% 27.99/7.74 |
% 27.99/7.74 | Equations (524) can reduce 528 to:
% 27.99/7.74 | (270) $false
% 27.99/7.74 |
% 27.99/7.74 |-The branch is then unsatisfiable
% 27.99/7.74 |-Branch two:
% 27.99/7.74 | (528) ~ (all_0_39_39 = e1)
% 27.99/7.74 | (522) all_0_39_39 = e4
% 27.99/7.74 |
% 27.99/7.74 | Equations (522) can reduce 591 to:
% 27.99/7.74 | (270) $false
% 27.99/7.74 |
% 27.99/7.74 |-The branch is then unsatisfiable
% 27.99/7.74 |-Branch two:
% 27.99/7.74 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 27.99/7.74 |
% 27.99/7.74 | Applying alpha-rule on (346) yields:
% 27.99/7.74 | (347) all_0_2_2 = e0
% 27.99/7.74 | (348) ~ (all_0_3_3 = e4)
% 27.99/7.74 |
% 27.99/7.74 | Equations (287) can reduce 348 to:
% 27.99/7.74 | (270) $false
% 27.99/7.74 |
% 27.99/7.74 |-The branch is then unsatisfiable
% 27.99/7.74 |-Branch two:
% 27.99/7.74 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 27.99/7.74 |
% 27.99/7.74 | Applying alpha-rule on (350) yields:
% 27.99/7.74 | (351) all_0_41_41 = e3
% 27.99/7.74 | (352) ~ (all_0_45_45 = e4)
% 27.99/7.74 |
% 27.99/7.74 | Combining equations (358,351) yields a new equation:
% 27.99/7.74 | (660) e4 = e3
% 27.99/7.74 |
% 27.99/7.74 | Simplifying 660 yields:
% 27.99/7.74 | (359) e4 = e3
% 27.99/7.74 |
% 27.99/7.74 | Equations (359) can reduce 34 to:
% 27.99/7.74 | (270) $false
% 27.99/7.74 |
% 27.99/7.74 |-The branch is then unsatisfiable
% 27.99/7.74 |-Branch two:
% 27.99/7.74 | (361) ~ (all_0_41_41 = e4)
% 27.99/7.74 | (512) all_0_42_42 = e4
% 27.99/7.74 |
% 27.99/7.74 | Combining equations (698,512) yields a new equation:
% 27.99/7.74 | (269) e4 = e2
% 27.99/7.74 |
% 27.99/7.74 | Equations (269) can reduce 231 to:
% 27.99/7.74 | (270) $false
% 27.99/7.74 |
% 27.99/7.74 |-The branch is then unsatisfiable
% 27.99/7.74 |-Branch two:
% 27.99/7.74 | (333) ~ (all_0_44_44 = e2)
% 27.99/7.74 | (373) all_0_44_44 = e3 | all_0_44_44 = e0
% 27.99/7.74 |
% 27.99/7.74 +-Applying beta-rule and splitting (607), into two cases.
% 27.99/7.74 |-Branch one:
% 27.99/7.74 | (370) all_0_44_44 = e2
% 27.99/7.74 |
% 27.99/7.74 | Equations (370) can reduce 333 to:
% 27.99/7.74 | (270) $false
% 27.99/7.74 |
% 27.99/7.74 |-The branch is then unsatisfiable
% 27.99/7.74 |-Branch two:
% 27.99/7.74 | (333) ~ (all_0_44_44 = e2)
% 27.99/7.74 | (3377) all_0_52_52 = e2 | all_0_57_57 = e2
% 27.99/7.74 |
% 27.99/7.74 +-Applying beta-rule and splitting (3377), into two cases.
% 27.99/7.74 |-Branch one:
% 27.99/7.74 | (685) all_0_52_52 = e2
% 27.99/7.74 |
% 27.99/7.74 | Equations (685) can reduce 257 to:
% 27.99/7.74 | (270) $false
% 27.99/7.74 |
% 27.99/7.74 |-The branch is then unsatisfiable
% 27.99/7.74 |-Branch two:
% 27.99/7.74 | (257) ~ (all_0_52_52 = e2)
% 27.99/7.74 | (392) all_0_57_57 = e2
% 27.99/7.74 |
% 27.99/7.74 | Equations (392) can reduce 149 to:
% 27.99/7.74 | (602) ~ (all_0_40_40 = e2)
% 27.99/7.74 |
% 27.99/7.74 | Equations (392) can reduce 10 to:
% 27.99/7.74 | (333) ~ (all_0_44_44 = e2)
% 27.99/7.74 |
% 27.99/7.74 | Equations (392) can reduce 235 to:
% 27.99/7.74 | (257) ~ (all_0_52_52 = e2)
% 27.99/7.74 |
% 27.99/7.74 | Equations (392) can reduce 37 to:
% 27.99/7.74 | (375) ~ (all_0_58_58 = e2)
% 27.99/7.74 |
% 27.99/7.74 | Simplifying 375 yields:
% 27.99/7.74 | (376) ~ (all_0_58_58 = e2)
% 27.99/7.74 |
% 27.99/7.74 | Equations (392) can reduce 140 to:
% 27.99/7.74 | (700) ~ (all_0_59_59 = e2)
% 27.99/7.74 |
% 27.99/7.74 | Simplifying 700 yields:
% 27.99/7.74 | (701) ~ (all_0_59_59 = e2)
% 27.99/7.74 |
% 27.99/7.74 | Equations (392) can reduce 143 to:
% 27.99/7.74 | (377) ~ (e4 = e2)
% 27.99/7.74 |
% 27.99/7.74 | Simplifying 377 yields:
% 27.99/7.74 | (231) ~ (e4 = e2)
% 27.99/7.74 |
% 27.99/7.74 | From (392) and (30) follows:
% 27.99/7.74 | (3390) op(e2, e2) = all_0_19_19
% 27.99/7.74 |
% 27.99/7.74 | Instantiating formula (201) with e2, e2, all_0_19_19, e4 and discharging atoms op(e2, e2) = all_0_19_19, op(e2, e2) = e4, yields:
% 27.99/7.74 | (3391) all_0_19_19 = e4
% 27.99/7.74 |
% 27.99/7.74 +-Applying beta-rule and splitting (8), into two cases.
% 27.99/7.74 |-Branch one:
% 27.99/7.74 | (530) all_0_40_40 = e1
% 27.99/7.74 |
% 27.99/7.74 | Equations (530) can reduce 147 to:
% 27.99/7.74 | (637) ~ (all_0_41_41 = e1)
% 27.99/7.74 |
% 27.99/7.74 | Simplifying 637 yields:
% 27.99/7.74 | (540) ~ (all_0_41_41 = e1)
% 27.99/7.74 |
% 27.99/7.74 | Equations (530) can reduce 145 to:
% 27.99/7.74 | (639) ~ (all_0_42_42 = e1)
% 27.99/7.74 |
% 27.99/7.74 | Simplifying 639 yields:
% 27.99/7.74 | (640) ~ (all_0_42_42 = e1)
% 27.99/7.74 |
% 27.99/7.74 | Equations (530) can reduce 15 to:
% 27.99/7.74 | (4822) ~ (all_0_44_44 = e1)
% 27.99/7.74 |
% 27.99/7.74 | Simplifying 4822 yields:
% 27.99/7.74 | (131) ~ (all_0_44_44 = e1)
% 27.99/7.74 |
% 27.99/7.74 | Equations (530) can reduce 137 to:
% 27.99/7.74 | (641) ~ (all_0_52_52 = e1)
% 27.99/7.74 |
% 27.99/7.74 | Simplifying 641 yields:
% 27.99/7.74 | (642) ~ (all_0_52_52 = e1)
% 27.99/7.74 |
% 27.99/7.74 | Equations (530) can reduce 602 to:
% 27.99/7.74 | (645) ~ (e2 = e1)
% 27.99/7.74 |
% 27.99/7.74 | Simplifying 645 yields:
% 27.99/7.74 | (141) ~ (e2 = e1)
% 27.99/7.74 |
% 27.99/7.74 | From (530) and (68) follows:
% 27.99/7.74 | (648) op(e2, e1) = all_0_13_13
% 27.99/7.74 |
% 27.99/7.74 | Instantiating formula (201) with e2, e1, all_0_13_13, e2 and discharging atoms op(e2, e1) = all_0_13_13, op(e2, e1) = e2, yields:
% 27.99/7.74 | (4829) all_0_13_13 = e2
% 27.99/7.74 |
% 27.99/7.74 +-Applying beta-rule and splitting (9), into two cases.
% 27.99/7.74 |-Branch one:
% 27.99/7.74 | (621) all_0_44_44 = e0
% 27.99/7.74 |
% 27.99/7.74 | Equations (621) can reduce 241 to:
% 27.99/7.74 | (455) ~ (all_0_43_43 = e0)
% 27.99/7.74 |
% 27.99/7.74 | Equations (621) can reduce 229 to:
% 27.99/7.74 | (776) ~ (all_0_45_45 = e0)
% 27.99/7.74 |
% 27.99/7.74 | Simplifying 776 yields:
% 27.99/7.74 | (488) ~ (all_0_45_45 = e0)
% 27.99/7.74 |
% 27.99/7.74 | Equations (621) can reduce 174 to:
% 27.99/7.74 | (1057) ~ (all_0_46_46 = e0)
% 27.99/7.74 |
% 27.99/7.74 | Simplifying 1057 yields:
% 27.99/7.74 | (1010) ~ (all_0_46_46 = e0)
% 27.99/7.74 |
% 27.99/7.74 | Equations (621) can reduce 122 to:
% 27.99/7.74 | (4297) ~ (all_0_52_52 = e0)
% 27.99/7.74 |
% 27.99/7.74 | Simplifying 4297 yields:
% 27.99/7.74 | (925) ~ (all_0_52_52 = e0)
% 27.99/7.74 |
% 27.99/7.74 | Equations (621) can reduce 333 to:
% 27.99/7.74 | (566) ~ (e2 = e0)
% 27.99/7.74 |
% 27.99/7.74 | Simplifying 566 yields:
% 27.99/7.74 | (57) ~ (e2 = e0)
% 27.99/7.74 |
% 27.99/7.74 +-Applying beta-rule and splitting (133), into two cases.
% 27.99/7.74 |-Branch one:
% 27.99/7.74 | (671) all_0_40_40 = e3
% 27.99/7.74 |
% 27.99/7.74 | Combining equations (530,671) yields a new equation:
% 27.99/7.74 | (538) e3 = e1
% 27.99/7.74 |
% 27.99/7.74 | Equations (538) can reduce 136 to:
% 27.99/7.74 | (270) $false
% 27.99/7.74 |
% 27.99/7.74 |-The branch is then unsatisfiable
% 27.99/7.74 |-Branch two:
% 27.99/7.74 | (675) ~ (all_0_40_40 = e3)
% 27.99/7.74 | (676) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 27.99/7.74 |
% 27.99/7.74 +-Applying beta-rule and splitting (676), into two cases.
% 27.99/7.74 |-Branch one:
% 27.99/7.74 | (858) all_0_44_44 = e3
% 27.99/7.74 |
% 27.99/7.74 | Combining equations (621,858) yields a new equation:
% 27.99/7.74 | (784) e3 = e0
% 27.99/7.74 |
% 27.99/7.74 | Equations (784) can reduce 66 to:
% 27.99/7.74 | (270) $false
% 27.99/7.74 |
% 27.99/7.74 |-The branch is then unsatisfiable
% 27.99/7.74 |-Branch two:
% 27.99/7.74 | (862) ~ (all_0_44_44 = e3)
% 27.99/7.74 | (863) all_0_52_52 = e3 | all_0_57_57 = e3
% 27.99/7.74 |
% 27.99/7.74 +-Applying beta-rule and splitting (863), into two cases.
% 27.99/7.74 |-Branch one:
% 27.99/7.74 | (864) all_0_52_52 = e3
% 27.99/7.74 |
% 27.99/7.74 | Equations (864) can reduce 154 to:
% 27.99/7.74 | (932) ~ (all_0_51_51 = e3)
% 27.99/7.74 |
% 27.99/7.74 | Equations (864) can reduce 213 to:
% 27.99/7.74 | (355) ~ (all_0_53_53 = e3)
% 27.99/7.74 |
% 27.99/7.74 | Simplifying 355 yields:
% 27.99/7.74 | (356) ~ (all_0_53_53 = e3)
% 27.99/7.74 |
% 27.99/7.74 | Equations (864) can reduce 118 to:
% 27.99/7.74 | (1092) ~ (all_0_54_54 = e3)
% 27.99/7.74 |
% 27.99/7.74 | Simplifying 1092 yields:
% 27.99/7.74 | (1093) ~ (all_0_54_54 = e3)
% 27.99/7.74 |
% 27.99/7.74 | Equations (864) can reduce 230 to:
% 27.99/7.74 | (719) ~ (e4 = e3)
% 27.99/7.74 |
% 27.99/7.74 | Simplifying 719 yields:
% 27.99/7.74 | (34) ~ (e4 = e3)
% 27.99/7.74 |
% 27.99/7.74 | Equations (864) can reduce 257 to:
% 27.99/7.74 | (223) ~ (e3 = e2)
% 27.99/7.74 |
% 27.99/7.74 | Equations (864) can reduce 642 to:
% 27.99/7.74 | (136) ~ (e3 = e1)
% 27.99/7.74 |
% 27.99/7.74 | Equations (864) can reduce 925 to:
% 27.99/7.74 | (66) ~ (e3 = e0)
% 27.99/7.74 |
% 27.99/7.74 +-Applying beta-rule and splitting (47), into two cases.
% 27.99/7.74 |-Branch one:
% 27.99/7.74 | (450) all_0_43_43 = e2
% 27.99/7.74 |
% 27.99/7.74 | Equations (450) can reduce 167 to:
% 27.99/7.74 | (291) ~ (all_0_39_39 = e2)
% 27.99/7.74 |
% 27.99/7.74 | Equations (450) can reduce 84 to:
% 27.99/7.74 | (611) ~ (all_0_45_45 = e2)
% 27.99/7.74 |
% 27.99/7.74 | Simplifying 611 yields:
% 27.99/7.74 | (434) ~ (all_0_45_45 = e2)
% 27.99/7.74 |
% 27.99/7.74 | Equations (450) can reduce 240 to:
% 27.99/7.74 | (254) ~ (all_0_51_51 = e2)
% 27.99/7.74 |
% 27.99/7.74 | Simplifying 254 yields:
% 27.99/7.74 | (255) ~ (all_0_51_51 = e2)
% 27.99/7.74 |
% 27.99/7.74 | Equations (450) can reduce 188 to:
% 27.99/7.74 | (299) ~ (all_0_56_56 = e2)
% 27.99/7.74 |
% 27.99/7.74 | Simplifying 299 yields:
% 27.99/7.74 | (300) ~ (all_0_56_56 = e2)
% 27.99/7.74 |
% 27.99/7.74 | Equations (450) can reduce 249 to:
% 27.99/7.74 | (141) ~ (e2 = e1)
% 27.99/7.74 |
% 27.99/7.74 +-Applying beta-rule and splitting (164), into two cases.
% 27.99/7.74 |-Branch one:
% 27.99/7.74 | (336) all_0_39_39 = e2
% 27.99/7.74 |
% 27.99/7.74 | Equations (336) can reduce 291 to:
% 27.99/7.74 | (270) $false
% 27.99/7.74 |
% 27.99/7.74 |-The branch is then unsatisfiable
% 27.99/7.74 |-Branch two:
% 27.99/7.74 | (291) ~ (all_0_39_39 = e2)
% 27.99/7.74 | (630) all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 27.99/7.74 |
% 27.99/7.74 +-Applying beta-rule and splitting (209), into two cases.
% 27.99/7.74 |-Branch one:
% 27.99/7.74 | (698) all_0_42_42 = e2
% 27.99/7.74 |
% 27.99/7.74 | Equations (698) can reduce 184 to:
% 27.99/7.74 | (291) ~ (all_0_39_39 = e2)
% 27.99/7.74 |
% 27.99/7.75 | Equations (698) can reduce 94 to:
% 27.99/7.75 | (331) ~ (all_0_41_41 = e2)
% 27.99/7.75 |
% 27.99/7.75 | Equations (698) can reduce 191 to:
% 27.99/7.75 | (260) ~ (all_0_54_54 = e2)
% 27.99/7.75 |
% 27.99/7.75 | Simplifying 260 yields:
% 27.99/7.75 | (261) ~ (all_0_54_54 = e2)
% 27.99/7.75 |
% 27.99/7.75 | Equations (698) can reduce 640 to:
% 27.99/7.75 | (141) ~ (e2 = e1)
% 27.99/7.75 |
% 27.99/7.75 | Equations (698) can reduce 199 to:
% 27.99/7.75 | (57) ~ (e2 = e0)
% 27.99/7.75 |
% 27.99/7.75 +-Applying beta-rule and splitting (222), into two cases.
% 27.99/7.75 |-Branch one:
% 27.99/7.75 | (522) all_0_39_39 = e4
% 27.99/7.75 |
% 27.99/7.75 | Equations (522) can reduce 32 to:
% 27.99/7.75 | (696) ~ (all_0_51_51 = e4)
% 27.99/7.75 |
% 27.99/7.75 | Simplifying 696 yields:
% 27.99/7.75 | (697) ~ (all_0_51_51 = e4)
% 27.99/7.75 |
% 27.99/7.75 | Equations (522) can reduce 291 to:
% 27.99/7.75 | (231) ~ (e4 = e2)
% 27.99/7.75 |
% 27.99/7.75 +-Applying beta-rule and splitting (173), into two cases.
% 27.99/7.75 |-Branch one:
% 27.99/7.75 | (4215) all_0_51_51 = e2
% 27.99/7.75 |
% 27.99/7.75 | Equations (4215) can reduce 255 to:
% 27.99/7.75 | (270) $false
% 27.99/7.75 |
% 27.99/7.75 |-The branch is then unsatisfiable
% 27.99/7.75 |-Branch two:
% 27.99/7.75 | (255) ~ (all_0_51_51 = e2)
% 27.99/7.75 | (4888) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1 | all_0_51_51 = e0
% 27.99/7.75 |
% 27.99/7.75 +-Applying beta-rule and splitting (4888), into two cases.
% 27.99/7.75 |-Branch one:
% 27.99/7.75 | (954) all_0_51_51 = e0
% 27.99/7.75 |
% 27.99/7.75 | Equations (954) can reduce 12 to:
% 27.99/7.75 | (3103) ~ (all_0_53_53 = e0)
% 27.99/7.75 |
% 27.99/7.75 | Simplifying 3103 yields:
% 27.99/7.75 | (584) ~ (all_0_53_53 = e0)
% 27.99/7.75 |
% 27.99/7.75 | Equations (954) can reduce 255 to:
% 27.99/7.75 | (566) ~ (e2 = e0)
% 27.99/7.75 |
% 27.99/7.75 | Simplifying 566 yields:
% 27.99/7.75 | (57) ~ (e2 = e0)
% 27.99/7.75 |
% 27.99/7.75 | Equations (954) can reduce 748 to:
% 27.99/7.75 | (568) ~ (e1 = e0)
% 27.99/7.75 |
% 27.99/7.75 | Simplifying 568 yields:
% 27.99/7.75 | (132) ~ (e1 = e0)
% 27.99/7.75 |
% 27.99/7.75 +-Applying beta-rule and splitting (182), into two cases.
% 27.99/7.75 |-Branch one:
% 27.99/7.75 | (454) all_0_45_45 = e0
% 27.99/7.75 |
% 27.99/7.75 | Equations (454) can reduce 488 to:
% 27.99/7.75 | (270) $false
% 27.99/7.75 |
% 27.99/7.75 |-The branch is then unsatisfiable
% 27.99/7.75 |-Branch two:
% 27.99/7.75 | (488) ~ (all_0_45_45 = e0)
% 27.99/7.75 | (558) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 27.99/7.75 |
% 27.99/7.75 +-Applying beta-rule and splitting (558), into two cases.
% 27.99/7.75 |-Branch one:
% 27.99/7.75 | (559) all_0_48_48 = e0
% 27.99/7.75 |
% 27.99/7.75 | Combining equations (559,311) yields a new equation:
% 27.99/7.75 | (316) e2 = e0
% 27.99/7.75 |
% 27.99/7.75 | Equations (316) can reduce 57 to:
% 27.99/7.75 | (270) $false
% 27.99/7.75 |
% 27.99/7.75 |-The branch is then unsatisfiable
% 27.99/7.75 |-Branch two:
% 27.99/7.75 | (562) ~ (all_0_48_48 = e0)
% 27.99/7.75 | (575) all_0_53_53 = e0 | all_0_58_58 = e0
% 27.99/7.75 |
% 27.99/7.75 +-Applying beta-rule and splitting (575), into two cases.
% 27.99/7.75 |-Branch one:
% 27.99/7.75 | (423) all_0_53_53 = e0
% 27.99/7.75 |
% 27.99/7.75 | Equations (423) can reduce 584 to:
% 27.99/7.75 | (270) $false
% 27.99/7.75 |
% 27.99/7.75 |-The branch is then unsatisfiable
% 27.99/7.75 |-Branch two:
% 27.99/7.75 | (584) ~ (all_0_53_53 = e0)
% 27.99/7.75 | (585) all_0_58_58 = e0
% 27.99/7.75 |
% 27.99/7.75 | Equations (585) can reduce 70 to:
% 27.99/7.75 | (584) ~ (all_0_53_53 = e0)
% 27.99/7.75 |
% 27.99/7.75 | Equations (585) can reduce 156 to:
% 27.99/7.75 | (4000) ~ (all_0_59_59 = e0)
% 27.99/7.75 |
% 27.99/7.75 | Simplifying 4000 yields:
% 27.99/7.75 | (4001) ~ (all_0_59_59 = e0)
% 27.99/7.75 |
% 27.99/7.75 | Equations (585) can reduce 278 to:
% 27.99/7.75 | (456) ~ (e4 = e0)
% 27.99/7.75 |
% 27.99/7.75 | Simplifying 456 yields:
% 27.99/7.75 | (6) ~ (e4 = e0)
% 27.99/7.75 |
% 27.99/7.75 | Equations (585) can reduce 376 to:
% 27.99/7.75 | (566) ~ (e2 = e0)
% 27.99/7.75 |
% 27.99/7.75 | Simplifying 566 yields:
% 27.99/7.75 | (57) ~ (e2 = e0)
% 27.99/7.75 |
% 27.99/7.75 +-Applying beta-rule and splitting (52), into two cases.
% 27.99/7.75 |-Branch one:
% 27.99/7.75 | (536) all_0_41_41 = e1
% 27.99/7.75 |
% 27.99/7.75 | Equations (536) can reduce 540 to:
% 27.99/7.75 | (270) $false
% 27.99/7.75 |
% 27.99/7.75 |-The branch is then unsatisfiable
% 27.99/7.75 |-Branch two:
% 27.99/7.75 | (540) ~ (all_0_41_41 = e1)
% 27.99/7.75 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 27.99/7.75 |
% 27.99/7.75 +-Applying beta-rule and splitting (762), into two cases.
% 27.99/7.75 |-Branch one:
% 27.99/7.75 | (552) all_0_48_48 = e1
% 27.99/7.75 |
% 27.99/7.75 | Combining equations (311,552) yields a new equation:
% 27.99/7.75 | (531) e2 = e1
% 27.99/7.75 |
% 27.99/7.75 | Simplifying 531 yields:
% 27.99/7.75 | (322) e2 = e1
% 27.99/7.75 |
% 27.99/7.75 | Equations (322) can reduce 141 to:
% 27.99/7.75 | (270) $false
% 27.99/7.75 |
% 27.99/7.75 |-The branch is then unsatisfiable
% 27.99/7.75 |-Branch two:
% 27.99/7.75 | (588) ~ (all_0_48_48 = e1)
% 27.99/7.75 | (4925) all_0_53_53 = e1 | all_0_58_58 = e1
% 27.99/7.75 |
% 27.99/7.75 +-Applying beta-rule and splitting (4925), into two cases.
% 27.99/7.75 |-Branch one:
% 27.99/7.75 | (853) all_0_53_53 = e1
% 27.99/7.75 |
% 27.99/7.75 | Equations (853) can reduce 252 to:
% 27.99/7.75 | (2131) ~ (all_0_54_54 = e1)
% 27.99/7.75 |
% 27.99/7.75 | Simplifying 2131 yields:
% 27.99/7.75 | (425) ~ (all_0_54_54 = e1)
% 27.99/7.75 |
% 27.99/7.75 | Equations (853) can reduce 259 to:
% 27.99/7.75 | (645) ~ (e2 = e1)
% 27.99/7.75 |
% 27.99/7.75 | Simplifying 645 yields:
% 27.99/7.75 | (141) ~ (e2 = e1)
% 27.99/7.75 |
% 27.99/7.75 | Equations (853) can reduce 584 to:
% 27.99/7.75 | (132) ~ (e1 = e0)
% 27.99/7.75 |
% 27.99/7.75 +-Applying beta-rule and splitting (127), into two cases.
% 27.99/7.75 |-Branch one:
% 27.99/7.75 | (541) all_0_42_42 = e1
% 27.99/7.75 |
% 27.99/7.75 | Combining equations (541,698) yields a new equation:
% 27.99/7.75 | (322) e2 = e1
% 27.99/7.75 |
% 27.99/7.75 | Equations (322) can reduce 141 to:
% 27.99/7.75 | (270) $false
% 27.99/7.75 |
% 27.99/7.75 |-The branch is then unsatisfiable
% 27.99/7.75 |-Branch two:
% 27.99/7.75 | (640) ~ (all_0_42_42 = e1)
% 27.99/7.75 | (4628) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 27.99/7.75 |
% 27.99/7.75 +-Applying beta-rule and splitting (4628), into two cases.
% 27.99/7.75 |-Branch one:
% 27.99/7.75 | (589) all_0_49_49 = e1
% 27.99/7.75 |
% 27.99/7.75 | Combining equations (563,589) yields a new equation:
% 27.99/7.75 | (560) e1 = e0
% 27.99/7.75 |
% 27.99/7.75 | Equations (560) can reduce 132 to:
% 27.99/7.75 | (270) $false
% 27.99/7.75 |
% 27.99/7.75 |-The branch is then unsatisfiable
% 27.99/7.75 |-Branch two:
% 27.99/7.75 | (543) ~ (all_0_49_49 = e1)
% 27.99/7.75 | (4726) all_0_54_54 = e1 | all_0_59_59 = e1
% 27.99/7.75 |
% 27.99/7.75 +-Applying beta-rule and splitting (4726), into two cases.
% 27.99/7.75 |-Branch one:
% 27.99/7.75 | (875) all_0_54_54 = e1
% 27.99/7.75 |
% 27.99/7.75 | Equations (875) can reduce 425 to:
% 27.99/7.75 | (270) $false
% 27.99/7.75 |
% 27.99/7.75 |-The branch is then unsatisfiable
% 27.99/7.75 |-Branch two:
% 27.99/7.75 | (425) ~ (all_0_54_54 = e1)
% 27.99/7.75 | (424) all_0_59_59 = e1
% 27.99/7.75 |
% 27.99/7.75 | Equations (424) can reduce 72 to:
% 27.99/7.75 | (425) ~ (all_0_54_54 = e1)
% 27.99/7.75 |
% 27.99/7.75 | Equations (424) can reduce 280 to:
% 27.99/7.75 | (1021) ~ (e4 = e1)
% 27.99/7.75 |
% 27.99/7.75 | Simplifying 1021 yields:
% 27.99/7.75 | (251) ~ (e4 = e1)
% 27.99/7.75 |
% 27.99/7.75 | Equations (424) can reduce 4001 to:
% 27.99/7.75 | (132) ~ (e1 = e0)
% 27.99/7.75 |
% 27.99/7.75 +-Applying beta-rule and splitting (189), into two cases.
% 27.99/7.75 |-Branch one:
% 27.99/7.75 | (267) all_0_50_50 = e4
% 27.99/7.75 |
% 27.99/7.75 | Combining equations (253,267) yields a new equation:
% 27.99/7.75 | (269) e4 = e2
% 27.99/7.75 |
% 27.99/7.75 | Equations (269) can reduce 231 to:
% 27.99/7.75 | (270) $false
% 27.99/7.75 |
% 27.99/7.75 |-The branch is then unsatisfiable
% 27.99/7.75 |-Branch two:
% 27.99/7.75 | (271) ~ (all_0_50_50 = e4)
% 27.99/7.75 | (1466) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 27.99/7.75 |
% 27.99/7.75 +-Applying beta-rule and splitting (1466), into two cases.
% 27.99/7.75 |-Branch one:
% 27.99/7.75 | (1467) all_0_51_51 = e4
% 27.99/7.75 |
% 27.99/7.75 | Combining equations (954,1467) yields a new equation:
% 27.99/7.75 | (479) e4 = e0
% 27.99/7.75 |
% 27.99/7.75 | Equations (479) can reduce 6 to:
% 27.99/7.75 | (270) $false
% 27.99/7.75 |
% 27.99/7.75 |-The branch is then unsatisfiable
% 27.99/7.75 |-Branch two:
% 27.99/7.75 | (697) ~ (all_0_51_51 = e4)
% 27.99/7.75 | (1470) all_0_53_53 = e4 | all_0_54_54 = e4
% 27.99/7.75 |
% 27.99/7.75 +-Applying beta-rule and splitting (1470), into two cases.
% 27.99/7.75 |-Branch one:
% 27.99/7.75 | (367) all_0_53_53 = e4
% 27.99/7.75 |
% 27.99/7.75 | Combining equations (853,367) yields a new equation:
% 27.99/7.75 | (526) e4 = e1
% 27.99/7.75 |
% 27.99/7.75 | Equations (526) can reduce 251 to:
% 27.99/7.75 | (270) $false
% 27.99/7.75 |
% 27.99/7.75 |-The branch is then unsatisfiable
% 27.99/7.75 |-Branch two:
% 27.99/7.75 | (599) ~ (all_0_53_53 = e4)
% 27.99/7.75 | (817) all_0_54_54 = e4
% 27.99/7.75 |
% 27.99/7.75 | Equations (817) can reduce 425 to:
% 27.99/7.75 | (251) ~ (e4 = e1)
% 27.99/7.75 |
% 27.99/7.75 +-Applying beta-rule and splitting (93), into two cases.
% 27.99/7.75 |-Branch one:
% 27.99/7.75 | (402) all_0_59_59 = e4
% 27.99/7.75 |
% 27.99/7.75 | Combining equations (402,424) yields a new equation:
% 27.99/7.75 | (525) e4 = e1
% 27.99/7.75 |
% 27.99/7.75 | Simplifying 525 yields:
% 27.99/7.75 | (526) e4 = e1
% 27.99/7.75 |
% 27.99/7.75 | Equations (526) can reduce 251 to:
% 27.99/7.75 | (270) $false
% 27.99/7.75 |
% 27.99/7.75 |-The branch is then unsatisfiable
% 27.99/7.75 |-Branch two:
% 27.99/7.75 | (280) ~ (all_0_59_59 = e4)
% 27.99/7.75 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 27.99/7.75 |
% 27.99/7.75 +-Applying beta-rule and splitting (407), into two cases.
% 27.99/7.75 |-Branch one:
% 27.99/7.75 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 27.99/7.75 |
% 27.99/7.75 +-Applying beta-rule and splitting (408), into two cases.
% 27.99/7.75 |-Branch one:
% 27.99/7.75 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 27.99/7.75 |
% 27.99/7.75 +-Applying beta-rule and splitting (409), into two cases.
% 27.99/7.75 |-Branch one:
% 27.99/7.75 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 27.99/7.75 |
% 27.99/7.75 | Applying alpha-rule on (410) yields:
% 27.99/7.75 | (411) all_0_43_43 = e0
% 27.99/7.75 | (412) all_0_59_59 = e3
% 27.99/7.75 | (413) ~ (all_0_46_46 = e3)
% 27.99/7.75 |
% 27.99/7.75 | Combining equations (411,450) yields a new equation:
% 27.99/7.75 | (316) e2 = e0
% 27.99/7.75 |
% 27.99/7.75 | Equations (316) can reduce 57 to:
% 27.99/7.75 | (270) $false
% 27.99/7.75 |
% 27.99/7.75 |-The branch is then unsatisfiable
% 27.99/7.75 |-Branch two:
% 27.99/7.75 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 27.99/7.75 |
% 27.99/7.75 | Applying alpha-rule on (416) yields:
% 27.99/7.75 | (411) all_0_43_43 = e0
% 27.99/7.75 | (412) all_0_59_59 = e3
% 27.99/7.75 | (419) ~ (all_0_56_56 = e0)
% 27.99/7.75 |
% 27.99/7.75 | Combining equations (411,450) yields a new equation:
% 27.99/7.75 | (316) e2 = e0
% 27.99/7.75 |
% 27.99/7.75 | Equations (316) can reduce 57 to:
% 27.99/7.75 | (270) $false
% 27.99/7.75 |
% 27.99/7.75 |-The branch is then unsatisfiable
% 27.99/7.75 |-Branch two:
% 27.99/7.75 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 27.99/7.75 |
% 27.99/7.75 | Applying alpha-rule on (422) yields:
% 27.99/7.75 | (423) all_0_53_53 = e0
% 27.99/7.75 | (424) all_0_59_59 = e1
% 27.99/7.75 | (425) ~ (all_0_54_54 = e1)
% 27.99/7.75 |
% 27.99/7.75 | Combining equations (423,853) yields a new equation:
% 27.99/7.75 | (560) e1 = e0
% 27.99/7.75 |
% 27.99/7.75 | Equations (560) can reduce 132 to:
% 27.99/7.75 | (270) $false
% 27.99/7.75 |
% 27.99/7.75 |-The branch is then unsatisfiable
% 27.99/7.75 |-Branch two:
% 27.99/7.75 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 27.99/7.75 |
% 27.99/7.75 | Applying alpha-rule on (428) yields:
% 27.99/7.75 | (423) all_0_53_53 = e0
% 27.99/7.75 | (424) all_0_59_59 = e1
% 27.99/7.75 | (431) ~ (all_0_58_58 = e0)
% 27.99/7.75 |
% 27.99/7.75 | Combining equations (423,853) yields a new equation:
% 27.99/7.75 | (560) e1 = e0
% 27.99/7.75 |
% 27.99/7.75 | Equations (560) can reduce 132 to:
% 27.99/7.75 | (270) $false
% 27.99/7.75 |
% 27.99/7.75 |-The branch is then unsatisfiable
% 28.11/7.75 |-Branch two:
% 28.11/7.75 | (874) ~ (all_0_53_53 = e1)
% 28.11/7.75 | (1001) all_0_58_58 = e1
% 28.11/7.75 |
% 28.11/7.75 | Combining equations (585,1001) yields a new equation:
% 28.11/7.75 | (560) e1 = e0
% 28.11/7.75 |
% 28.11/7.75 | Equations (560) can reduce 132 to:
% 28.11/7.75 | (270) $false
% 28.11/7.75 |
% 28.11/7.75 |-The branch is then unsatisfiable
% 28.11/7.75 |-Branch two:
% 28.11/7.75 | (987) ~ (all_0_51_51 = e0)
% 28.11/7.75 | (5003) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1
% 28.11/7.75 |
% 28.11/7.75 +-Applying beta-rule and splitting (5003), into two cases.
% 28.11/7.75 |-Branch one:
% 28.11/7.75 | (824) all_0_51_51 = e3
% 28.11/7.75 |
% 28.11/7.75 | Equations (824) can reduce 932 to:
% 28.11/7.75 | (270) $false
% 28.11/7.75 |
% 28.11/7.75 |-The branch is then unsatisfiable
% 28.11/7.75 |-Branch two:
% 28.11/7.75 | (932) ~ (all_0_51_51 = e3)
% 28.11/7.75 | (5007) all_0_51_51 = e4 | all_0_51_51 = e1
% 28.11/7.75 |
% 28.11/7.75 +-Applying beta-rule and splitting (5007), into two cases.
% 28.11/7.75 |-Branch one:
% 28.11/7.75 | (820) all_0_51_51 = e1
% 28.11/7.75 |
% 28.11/7.75 | Equations (820) can reduce 748 to:
% 28.11/7.75 | (270) $false
% 28.11/7.75 |
% 28.11/7.75 |-The branch is then unsatisfiable
% 28.11/7.75 |-Branch two:
% 28.11/7.75 | (748) ~ (all_0_51_51 = e1)
% 28.11/7.75 | (1467) all_0_51_51 = e4
% 28.11/7.75 |
% 28.11/7.75 | Equations (1467) can reduce 697 to:
% 28.11/7.75 | (270) $false
% 28.11/7.75 |
% 28.11/7.75 |-The branch is then unsatisfiable
% 28.11/7.76 |-Branch two:
% 28.11/7.76 | (591) ~ (all_0_39_39 = e4)
% 28.11/7.76 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (166), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (522) all_0_39_39 = e4
% 28.11/7.76 |
% 28.11/7.76 | Equations (522) can reduce 591 to:
% 28.11/7.76 | (270) $false
% 28.11/7.76 |
% 28.11/7.76 |-The branch is then unsatisfiable
% 28.11/7.76 |-Branch two:
% 28.11/7.76 | (591) ~ (all_0_39_39 = e4)
% 28.11/7.76 | (4522) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (4522), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (502) all_0_43_43 = e4
% 28.11/7.76 |
% 28.11/7.76 | Combining equations (450,502) yields a new equation:
% 28.11/7.76 | (269) e4 = e2
% 28.11/7.76 |
% 28.11/7.76 | Equations (269) can reduce 231 to:
% 28.11/7.76 | (270) $false
% 28.11/7.76 |
% 28.11/7.76 |-The branch is then unsatisfiable
% 28.11/7.76 |-Branch two:
% 28.11/7.76 | (510) ~ (all_0_43_43 = e4)
% 28.11/7.76 | (4527) all_0_51_51 = e4 | all_0_56_56 = e4
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (4527), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (1467) all_0_51_51 = e4
% 28.11/7.76 |
% 28.11/7.76 | Equations (1467) can reduce 255 to:
% 28.11/7.76 | (231) ~ (e4 = e2)
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (75), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (411) all_0_43_43 = e0
% 28.11/7.76 |
% 28.11/7.76 | Combining equations (450,411) yields a new equation:
% 28.11/7.76 | (622) e2 = e0
% 28.11/7.76 |
% 28.11/7.76 | Simplifying 622 yields:
% 28.11/7.76 | (316) e2 = e0
% 28.11/7.76 |
% 28.11/7.76 | Equations (316) can reduce 57 to:
% 28.11/7.76 | (270) $false
% 28.11/7.76 |
% 28.11/7.76 |-The branch is then unsatisfiable
% 28.11/7.76 |-Branch two:
% 28.11/7.76 | (455) ~ (all_0_43_43 = e0)
% 28.11/7.76 | (940) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 28.11/7.76 |
% 28.11/7.76 | Equations (450) can reduce 455 to:
% 28.11/7.76 | (57) ~ (e2 = e0)
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (110), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (3657) all_0_54_54 = e2
% 28.11/7.76 |
% 28.11/7.76 | Equations (3657) can reduce 261 to:
% 28.11/7.76 | (270) $false
% 28.11/7.76 |
% 28.11/7.76 |-The branch is then unsatisfiable
% 28.11/7.76 |-Branch two:
% 28.11/7.76 | (261) ~ (all_0_54_54 = e2)
% 28.11/7.76 | (3660) all_0_54_54 = e4 | all_0_54_54 = e3 | all_0_54_54 = e1 | all_0_54_54 = e0
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (179), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (512) all_0_42_42 = e4
% 28.11/7.76 |
% 28.11/7.76 | Combining equations (698,512) yields a new equation:
% 28.11/7.76 | (269) e4 = e2
% 28.11/7.76 |
% 28.11/7.76 | Equations (269) can reduce 231 to:
% 28.11/7.76 | (270) $false
% 28.11/7.76 |
% 28.11/7.76 |-The branch is then unsatisfiable
% 28.11/7.76 |-Branch two:
% 28.11/7.76 | (520) ~ (all_0_42_42 = e4)
% 28.11/7.76 | (521) all_0_46_46 = e4 | all_0_54_54 = e4 | all_0_59_59 = e4
% 28.11/7.76 |
% 28.11/7.76 | Equations (698) can reduce 520 to:
% 28.11/7.76 | (377) ~ (e4 = e2)
% 28.11/7.76 |
% 28.11/7.76 | Simplifying 377 yields:
% 28.11/7.76 | (231) ~ (e4 = e2)
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (592), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (358) all_0_41_41 = e4
% 28.11/7.76 |
% 28.11/7.76 | Equations (358) can reduce 51 to:
% 28.11/7.76 | (503) ~ (all_0_45_45 = e4)
% 28.11/7.76 |
% 28.11/7.76 | Simplifying 503 yields:
% 28.11/7.76 | (352) ~ (all_0_45_45 = e4)
% 28.11/7.76 |
% 28.11/7.76 | Equations (358) can reduce 331 to:
% 28.11/7.76 | (231) ~ (e4 = e2)
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (44), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (502) all_0_43_43 = e4
% 28.11/7.76 |
% 28.11/7.76 | Combining equations (450,502) yields a new equation:
% 28.11/7.76 | (269) e4 = e2
% 28.11/7.76 |
% 28.11/7.76 | Equations (269) can reduce 231 to:
% 28.11/7.76 | (270) $false
% 28.11/7.76 |
% 28.11/7.76 |-The branch is then unsatisfiable
% 28.11/7.76 |-Branch two:
% 28.11/7.76 | (510) ~ (all_0_43_43 = e4)
% 28.11/7.76 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (3660), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (3084) all_0_54_54 = e0
% 28.11/7.76 |
% 28.11/7.76 | Equations (3084) can reduce 3011 to:
% 28.11/7.76 | (270) $false
% 28.11/7.76 |
% 28.11/7.76 |-The branch is then unsatisfiable
% 28.11/7.76 |-Branch two:
% 28.11/7.76 | (3011) ~ (all_0_54_54 = e0)
% 28.11/7.76 | (3664) all_0_54_54 = e4 | all_0_54_54 = e3 | all_0_54_54 = e1
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (105), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (374) all_0_45_45 = e2
% 28.11/7.76 |
% 28.11/7.76 | Equations (374) can reduce 434 to:
% 28.11/7.76 | (270) $false
% 28.11/7.76 |
% 28.11/7.76 |-The branch is then unsatisfiable
% 28.11/7.76 |-Branch two:
% 28.11/7.76 | (434) ~ (all_0_45_45 = e2)
% 28.11/7.76 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (435), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (454) all_0_45_45 = e0
% 28.11/7.76 |
% 28.11/7.76 | Equations (454) can reduce 488 to:
% 28.11/7.76 | (270) $false
% 28.11/7.76 |
% 28.11/7.76 |-The branch is then unsatisfiable
% 28.11/7.76 |-Branch two:
% 28.11/7.76 | (488) ~ (all_0_45_45 = e0)
% 28.11/7.76 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (78), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (751) all_0_39_39 = e3
% 28.11/7.76 |
% 28.11/7.76 | Equations (751) can reduce 212 to:
% 28.11/7.76 | (5066) ~ (all_0_56_56 = e3)
% 28.11/7.76 |
% 28.11/7.76 | Simplifying 5066 yields:
% 28.11/7.76 | (767) ~ (all_0_56_56 = e3)
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (489), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (505) all_0_45_45 = e3
% 28.11/7.76 |
% 28.11/7.76 | Equations (505) can reduce 108 to:
% 28.11/7.76 | (717) ~ (all_0_58_58 = e3)
% 28.11/7.76 |
% 28.11/7.76 | Simplifying 717 yields:
% 28.11/7.76 | (718) ~ (all_0_58_58 = e3)
% 28.11/7.76 |
% 28.11/7.76 | Equations (505) can reduce 434 to:
% 28.11/7.76 | (223) ~ (e3 = e2)
% 28.11/7.76 |
% 28.11/7.76 | Equations (505) can reduce 488 to:
% 28.11/7.76 | (66) ~ (e3 = e0)
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (208), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (388) all_0_56_56 = e2
% 28.11/7.76 |
% 28.11/7.76 | Equations (388) can reduce 300 to:
% 28.11/7.76 | (270) $false
% 28.11/7.76 |
% 28.11/7.76 |-The branch is then unsatisfiable
% 28.11/7.76 |-Branch two:
% 28.11/7.76 | (300) ~ (all_0_56_56 = e2)
% 28.11/7.76 | (5076) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1 | all_0_56_56 = e0
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (3664), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (1119) all_0_54_54 = e3
% 28.11/7.76 |
% 28.11/7.76 | Equations (1119) can reduce 1093 to:
% 28.11/7.76 | (270) $false
% 28.11/7.76 |
% 28.11/7.76 |-The branch is then unsatisfiable
% 28.11/7.76 |-Branch two:
% 28.11/7.76 | (1093) ~ (all_0_54_54 = e3)
% 28.11/7.76 | (3694) all_0_54_54 = e4 | all_0_54_54 = e1
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (95), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (1258) all_0_42_42 = e3
% 28.11/7.76 |
% 28.11/7.76 | Combining equations (698,1258) yields a new equation:
% 28.11/7.76 | (414) e3 = e2
% 28.11/7.76 |
% 28.11/7.76 | Equations (414) can reduce 223 to:
% 28.11/7.76 | (270) $false
% 28.11/7.76 |
% 28.11/7.76 |-The branch is then unsatisfiable
% 28.11/7.76 |-Branch two:
% 28.11/7.76 | (1316) ~ (all_0_42_42 = e3)
% 28.11/7.76 | (3656) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 28.11/7.76 |
% 28.11/7.76 | Equations (698) can reduce 1316 to:
% 28.11/7.76 | (301) ~ (e3 = e2)
% 28.11/7.76 |
% 28.11/7.76 | Simplifying 301 yields:
% 28.11/7.76 | (223) ~ (e3 = e2)
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (521), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (517) all_0_46_46 = e4
% 28.11/7.76 |
% 28.11/7.76 | Equations (517) can reduce 215 to:
% 28.11/7.76 | (1599) ~ (all_0_54_54 = e4)
% 28.11/7.76 |
% 28.11/7.76 | Simplifying 1599 yields:
% 28.11/7.76 | (936) ~ (all_0_54_54 = e4)
% 28.11/7.76 |
% 28.11/7.76 | Equations (517) can reduce 206 to:
% 28.11/7.76 | (279) ~ (all_0_59_59 = e4)
% 28.11/7.76 |
% 28.11/7.76 | Simplifying 279 yields:
% 28.11/7.76 | (280) ~ (all_0_59_59 = e4)
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (3694), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (875) all_0_54_54 = e1
% 28.11/7.76 |
% 28.11/7.76 | Equations (875) can reduce 252 to:
% 28.11/7.76 | (874) ~ (all_0_53_53 = e1)
% 28.11/7.76 |
% 28.11/7.76 | Equations (875) can reduce 936 to:
% 28.11/7.76 | (1021) ~ (e4 = e1)
% 28.11/7.76 |
% 28.11/7.76 | Simplifying 1021 yields:
% 28.11/7.76 | (251) ~ (e4 = e1)
% 28.11/7.76 |
% 28.11/7.76 | Equations (875) can reduce 261 to:
% 28.11/7.76 | (645) ~ (e2 = e1)
% 28.11/7.76 |
% 28.11/7.76 | Simplifying 645 yields:
% 28.11/7.76 | (141) ~ (e2 = e1)
% 28.11/7.76 |
% 28.11/7.76 | Equations (875) can reduce 3011 to:
% 28.11/7.76 | (132) ~ (e1 = e0)
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (194), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (747) all_0_56_56 = e1
% 28.11/7.76 |
% 28.11/7.76 | Equations (747) can reduce 995 to:
% 28.11/7.76 | (270) $false
% 28.11/7.76 |
% 28.11/7.76 |-The branch is then unsatisfiable
% 28.11/7.76 |-Branch two:
% 28.11/7.76 | (995) ~ (all_0_56_56 = e1)
% 28.11/7.76 | (996) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (996), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (997) all_0_57_57 = e1
% 28.11/7.76 |
% 28.11/7.76 | Combining equations (392,997) yields a new equation:
% 28.11/7.76 | (531) e2 = e1
% 28.11/7.76 |
% 28.11/7.76 | Simplifying 531 yields:
% 28.11/7.76 | (322) e2 = e1
% 28.11/7.76 |
% 28.11/7.76 | Equations (322) can reduce 141 to:
% 28.11/7.76 | (270) $false
% 28.11/7.76 |
% 28.11/7.76 |-The branch is then unsatisfiable
% 28.11/7.76 |-Branch two:
% 28.11/7.76 | (644) ~ (all_0_57_57 = e1)
% 28.11/7.76 | (1000) all_0_58_58 = e1 | all_0_59_59 = e1
% 28.11/7.76 |
% 28.11/7.76 | Equations (392) can reduce 644 to:
% 28.11/7.76 | (141) ~ (e2 = e1)
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (52), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (536) all_0_41_41 = e1
% 28.11/7.76 |
% 28.11/7.76 | Combining equations (536,358) yields a new equation:
% 28.11/7.76 | (526) e4 = e1
% 28.11/7.76 |
% 28.11/7.76 | Equations (526) can reduce 251 to:
% 28.11/7.76 | (270) $false
% 28.11/7.76 |
% 28.11/7.76 |-The branch is then unsatisfiable
% 28.11/7.76 |-Branch two:
% 28.11/7.76 | (540) ~ (all_0_41_41 = e1)
% 28.11/7.76 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (762), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (552) all_0_48_48 = e1
% 28.11/7.76 |
% 28.11/7.76 | Combining equations (311,552) yields a new equation:
% 28.11/7.76 | (531) e2 = e1
% 28.11/7.76 |
% 28.11/7.76 | Simplifying 531 yields:
% 28.11/7.76 | (322) e2 = e1
% 28.11/7.76 |
% 28.11/7.76 | Equations (322) can reduce 141 to:
% 28.11/7.76 | (270) $false
% 28.11/7.76 |
% 28.11/7.76 |-The branch is then unsatisfiable
% 28.11/7.76 |-Branch two:
% 28.11/7.76 | (588) ~ (all_0_48_48 = e1)
% 28.11/7.76 | (4925) all_0_53_53 = e1 | all_0_58_58 = e1
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (4925), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (853) all_0_53_53 = e1
% 28.11/7.76 |
% 28.11/7.76 | Equations (853) can reduce 874 to:
% 28.11/7.76 | (270) $false
% 28.11/7.76 |
% 28.11/7.76 |-The branch is then unsatisfiable
% 28.11/7.76 |-Branch two:
% 28.11/7.76 | (874) ~ (all_0_53_53 = e1)
% 28.11/7.76 | (1001) all_0_58_58 = e1
% 28.11/7.76 |
% 28.11/7.76 | Equations (1001) can reduce 70 to:
% 28.11/7.76 | (874) ~ (all_0_53_53 = e1)
% 28.11/7.76 |
% 28.11/7.76 | Equations (1001) can reduce 81 to:
% 28.11/7.76 | (995) ~ (all_0_56_56 = e1)
% 28.11/7.76 |
% 28.11/7.76 | Equations (1001) can reduce 156 to:
% 28.11/7.76 | (749) ~ (all_0_59_59 = e1)
% 28.11/7.76 |
% 28.11/7.76 | Simplifying 749 yields:
% 28.11/7.76 | (750) ~ (all_0_59_59 = e1)
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (182), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (454) all_0_45_45 = e0
% 28.11/7.76 |
% 28.11/7.76 | Combining equations (505,454) yields a new equation:
% 28.11/7.76 | (783) e3 = e0
% 28.11/7.76 |
% 28.11/7.76 | Simplifying 783 yields:
% 28.11/7.76 | (784) e3 = e0
% 28.11/7.76 |
% 28.11/7.76 | Equations (784) can reduce 66 to:
% 28.11/7.76 | (270) $false
% 28.11/7.76 |
% 28.11/7.76 |-The branch is then unsatisfiable
% 28.11/7.76 |-Branch two:
% 28.11/7.76 | (488) ~ (all_0_45_45 = e0)
% 28.11/7.76 | (558) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (176), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (830) all_0_56_56 = e0
% 28.11/7.76 |
% 28.11/7.76 | Equations (830) can reduce 300 to:
% 28.11/7.76 | (566) ~ (e2 = e0)
% 28.11/7.76 |
% 28.11/7.76 | Simplifying 566 yields:
% 28.11/7.76 | (57) ~ (e2 = e0)
% 28.11/7.76 |
% 28.11/7.76 | Equations (830) can reduce 995 to:
% 28.11/7.76 | (568) ~ (e1 = e0)
% 28.11/7.76 |
% 28.11/7.76 | Simplifying 568 yields:
% 28.11/7.76 | (132) ~ (e1 = e0)
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (558), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (559) all_0_48_48 = e0
% 28.11/7.76 |
% 28.11/7.76 | Combining equations (311,559) yields a new equation:
% 28.11/7.76 | (622) e2 = e0
% 28.11/7.76 |
% 28.11/7.76 | Simplifying 622 yields:
% 28.11/7.76 | (316) e2 = e0
% 28.11/7.76 |
% 28.11/7.76 | Equations (316) can reduce 57 to:
% 28.11/7.76 | (270) $false
% 28.11/7.76 |
% 28.11/7.76 |-The branch is then unsatisfiable
% 28.11/7.76 |-Branch two:
% 28.11/7.76 | (562) ~ (all_0_48_48 = e0)
% 28.11/7.76 | (575) all_0_53_53 = e0 | all_0_58_58 = e0
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (575), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (423) all_0_53_53 = e0
% 28.11/7.76 |
% 28.11/7.76 | Equations (423) can reduce 259 to:
% 28.11/7.76 | (566) ~ (e2 = e0)
% 28.11/7.76 |
% 28.11/7.76 | Simplifying 566 yields:
% 28.11/7.76 | (57) ~ (e2 = e0)
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (93), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (402) all_0_59_59 = e4
% 28.11/7.76 |
% 28.11/7.76 | Equations (402) can reduce 280 to:
% 28.11/7.76 | (270) $false
% 28.11/7.76 |
% 28.11/7.76 |-The branch is then unsatisfiable
% 28.11/7.76 |-Branch two:
% 28.11/7.76 | (280) ~ (all_0_59_59 = e4)
% 28.11/7.76 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (407), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (408), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 28.11/7.76 |
% 28.11/7.76 +-Applying beta-rule and splitting (409), into two cases.
% 28.11/7.76 |-Branch one:
% 28.11/7.76 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 28.11/7.77 |
% 28.11/7.77 | Applying alpha-rule on (410) yields:
% 28.11/7.77 | (411) all_0_43_43 = e0
% 28.11/7.77 | (412) all_0_59_59 = e3
% 28.11/7.77 | (413) ~ (all_0_46_46 = e3)
% 28.11/7.77 |
% 28.11/7.77 | Combining equations (411,450) yields a new equation:
% 28.11/7.77 | (316) e2 = e0
% 28.11/7.77 |
% 28.11/7.77 | Equations (316) can reduce 57 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 28.11/7.77 |
% 28.11/7.77 | Applying alpha-rule on (416) yields:
% 28.11/7.77 | (411) all_0_43_43 = e0
% 28.11/7.77 | (412) all_0_59_59 = e3
% 28.11/7.77 | (419) ~ (all_0_56_56 = e0)
% 28.11/7.77 |
% 28.11/7.77 | Combining equations (411,450) yields a new equation:
% 28.11/7.77 | (316) e2 = e0
% 28.11/7.77 |
% 28.11/7.77 | Equations (316) can reduce 57 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 28.11/7.77 |
% 28.11/7.77 | Applying alpha-rule on (422) yields:
% 28.11/7.77 | (423) all_0_53_53 = e0
% 28.11/7.77 | (424) all_0_59_59 = e1
% 28.11/7.77 | (425) ~ (all_0_54_54 = e1)
% 28.11/7.77 |
% 28.11/7.77 | Equations (424) can reduce 750 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 28.11/7.77 |
% 28.11/7.77 | Applying alpha-rule on (428) yields:
% 28.11/7.77 | (423) all_0_53_53 = e0
% 28.11/7.77 | (424) all_0_59_59 = e1
% 28.11/7.77 | (431) ~ (all_0_58_58 = e0)
% 28.11/7.77 |
% 28.11/7.77 | Equations (424) can reduce 750 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (584) ~ (all_0_53_53 = e0)
% 28.11/7.77 | (585) all_0_58_58 = e0
% 28.11/7.77 |
% 28.11/7.77 | Combining equations (1001,585) yields a new equation:
% 28.11/7.77 | (571) e1 = e0
% 28.11/7.77 |
% 28.11/7.77 | Simplifying 571 yields:
% 28.11/7.77 | (560) e1 = e0
% 28.11/7.77 |
% 28.11/7.77 | Equations (560) can reduce 132 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (419) ~ (all_0_56_56 = e0)
% 28.11/7.77 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 28.11/7.77 |
% 28.11/7.77 +-Applying beta-rule and splitting (558), into two cases.
% 28.11/7.77 |-Branch one:
% 28.11/7.77 | (559) all_0_48_48 = e0
% 28.11/7.77 |
% 28.11/7.77 | Combining equations (311,559) yields a new equation:
% 28.11/7.77 | (622) e2 = e0
% 28.11/7.77 |
% 28.11/7.77 | Simplifying 622 yields:
% 28.11/7.77 | (316) e2 = e0
% 28.11/7.77 |
% 28.11/7.77 | Equations (316) can reduce 57 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (562) ~ (all_0_48_48 = e0)
% 28.11/7.77 | (575) all_0_53_53 = e0 | all_0_58_58 = e0
% 28.11/7.77 |
% 28.11/7.77 | Equations (311) can reduce 562 to:
% 28.11/7.77 | (57) ~ (e2 = e0)
% 28.11/7.77 |
% 28.11/7.77 +-Applying beta-rule and splitting (834), into two cases.
% 28.11/7.77 |-Branch one:
% 28.11/7.77 | (2258) all_0_57_57 = e0
% 28.11/7.77 |
% 28.11/7.77 | Combining equations (392,2258) yields a new equation:
% 28.11/7.77 | (622) e2 = e0
% 28.11/7.77 |
% 28.11/7.77 | Simplifying 622 yields:
% 28.11/7.77 | (316) e2 = e0
% 28.11/7.77 |
% 28.11/7.77 | Equations (316) can reduce 57 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (2301) ~ (all_0_57_57 = e0)
% 28.11/7.77 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 28.11/7.77 |
% 28.11/7.77 +-Applying beta-rule and splitting (575), into two cases.
% 28.11/7.77 |-Branch one:
% 28.11/7.77 | (423) all_0_53_53 = e0
% 28.11/7.77 |
% 28.11/7.77 | Equations (423) can reduce 874 to:
% 28.11/7.77 | (568) ~ (e1 = e0)
% 28.11/7.77 |
% 28.11/7.77 | Simplifying 568 yields:
% 28.11/7.77 | (132) ~ (e1 = e0)
% 28.11/7.77 |
% 28.11/7.77 +-Applying beta-rule and splitting (2302), into two cases.
% 28.11/7.77 |-Branch one:
% 28.11/7.77 | (585) all_0_58_58 = e0
% 28.11/7.77 |
% 28.11/7.77 | Combining equations (1001,585) yields a new equation:
% 28.11/7.77 | (571) e1 = e0
% 28.11/7.77 |
% 28.11/7.77 | Simplifying 571 yields:
% 28.11/7.77 | (560) e1 = e0
% 28.11/7.77 |
% 28.11/7.77 | Equations (560) can reduce 132 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (431) ~ (all_0_58_58 = e0)
% 28.11/7.77 | (2308) all_0_59_59 = e0
% 28.11/7.77 |
% 28.11/7.77 | Equations (2308) can reduce 4001 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (584) ~ (all_0_53_53 = e0)
% 28.11/7.77 | (585) all_0_58_58 = e0
% 28.11/7.77 |
% 28.11/7.77 | Combining equations (585,1001) yields a new equation:
% 28.11/7.77 | (560) e1 = e0
% 28.11/7.77 |
% 28.11/7.77 | Equations (560) can reduce 132 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (425) ~ (all_0_54_54 = e1)
% 28.11/7.77 | (817) all_0_54_54 = e4
% 28.11/7.77 |
% 28.11/7.77 | Equations (817) can reduce 936 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (805) ~ (all_0_46_46 = e4)
% 28.11/7.77 | (816) all_0_54_54 = e4 | all_0_59_59 = e4
% 28.11/7.77 |
% 28.11/7.77 +-Applying beta-rule and splitting (236), into two cases.
% 28.11/7.77 |-Branch one:
% 28.11/7.77 | (764) all_0_56_56 = e3
% 28.11/7.77 |
% 28.11/7.77 | Equations (764) can reduce 767 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (767) ~ (all_0_56_56 = e3)
% 28.11/7.77 | (768) all_0_57_57 = e3 | all_0_58_58 = e3 | all_0_59_59 = e3
% 28.11/7.77 |
% 28.11/7.77 +-Applying beta-rule and splitting (768), into two cases.
% 28.11/7.77 |-Branch one:
% 28.11/7.77 | (869) all_0_57_57 = e3
% 28.11/7.77 |
% 28.11/7.77 | Combining equations (392,869) yields a new equation:
% 28.11/7.77 | (414) e3 = e2
% 28.11/7.77 |
% 28.11/7.77 | Equations (414) can reduce 223 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (846) ~ (all_0_57_57 = e3)
% 28.11/7.77 | (5225) all_0_58_58 = e3 | all_0_59_59 = e3
% 28.11/7.77 |
% 28.11/7.77 +-Applying beta-rule and splitting (5225), into two cases.
% 28.11/7.77 |-Branch one:
% 28.11/7.77 | (4713) all_0_58_58 = e3
% 28.11/7.77 |
% 28.11/7.77 | Equations (4713) can reduce 718 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (718) ~ (all_0_58_58 = e3)
% 28.11/7.77 | (412) all_0_59_59 = e3
% 28.11/7.77 |
% 28.11/7.77 | Equations (412) can reduce 280 to:
% 28.11/7.77 | (719) ~ (e4 = e3)
% 28.11/7.77 |
% 28.11/7.77 | Simplifying 719 yields:
% 28.11/7.77 | (34) ~ (e4 = e3)
% 28.11/7.77 |
% 28.11/7.77 +-Applying beta-rule and splitting (511), into two cases.
% 28.11/7.77 |-Branch one:
% 28.11/7.77 | (363) all_0_45_45 = e4
% 28.11/7.77 |
% 28.11/7.77 | Combining equations (363,505) yields a new equation:
% 28.11/7.77 | (660) e4 = e3
% 28.11/7.77 |
% 28.11/7.77 | Simplifying 660 yields:
% 28.11/7.77 | (359) e4 = e3
% 28.11/7.77 |
% 28.11/7.77 | Equations (359) can reduce 34 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (352) ~ (all_0_45_45 = e4)
% 28.11/7.77 | (517) all_0_46_46 = e4
% 28.11/7.77 |
% 28.11/7.77 | Equations (517) can reduce 805 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (354) ~ (all_0_45_45 = e3)
% 28.11/7.77 | (363) all_0_45_45 = e4
% 28.11/7.77 |
% 28.11/7.77 | Equations (363) can reduce 352 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (755) ~ (all_0_39_39 = e3)
% 28.11/7.77 | (4262) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 28.11/7.77 |
% 28.11/7.77 +-Applying beta-rule and splitting (489), into two cases.
% 28.11/7.77 |-Branch one:
% 28.11/7.77 | (505) all_0_45_45 = e3
% 28.11/7.77 |
% 28.11/7.77 | Equations (505) can reduce 352 to:
% 28.11/7.77 | (719) ~ (e4 = e3)
% 28.11/7.77 |
% 28.11/7.77 | Simplifying 719 yields:
% 28.11/7.77 | (34) ~ (e4 = e3)
% 28.11/7.77 |
% 28.11/7.77 | Equations (505) can reduce 434 to:
% 28.11/7.77 | (223) ~ (e3 = e2)
% 28.11/7.77 |
% 28.11/7.77 | Equations (505) can reduce 26 to:
% 28.11/7.77 | (136) ~ (e3 = e1)
% 28.11/7.77 |
% 28.11/7.77 +-Applying beta-rule and splitting (4262), into two cases.
% 28.11/7.77 |-Branch one:
% 28.11/7.77 | (671) all_0_40_40 = e3
% 28.11/7.77 |
% 28.11/7.77 | Combining equations (671,530) yields a new equation:
% 28.11/7.77 | (537) e3 = e1
% 28.11/7.77 |
% 28.11/7.77 | Simplifying 537 yields:
% 28.11/7.77 | (538) e3 = e1
% 28.11/7.77 |
% 28.11/7.77 | Equations (538) can reduce 136 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (675) ~ (all_0_40_40 = e3)
% 28.11/7.77 | (5254) all_0_41_41 = e3 | all_0_42_42 = e3
% 28.11/7.77 |
% 28.11/7.77 +-Applying beta-rule and splitting (95), into two cases.
% 28.11/7.77 |-Branch one:
% 28.11/7.77 | (1258) all_0_42_42 = e3
% 28.11/7.77 |
% 28.11/7.77 | Combining equations (698,1258) yields a new equation:
% 28.11/7.77 | (414) e3 = e2
% 28.11/7.77 |
% 28.11/7.77 | Equations (414) can reduce 223 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (1316) ~ (all_0_42_42 = e3)
% 28.11/7.77 | (3656) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 28.11/7.77 |
% 28.11/7.77 | Equations (698) can reduce 1316 to:
% 28.11/7.77 | (301) ~ (e3 = e2)
% 28.11/7.77 |
% 28.11/7.77 | Simplifying 301 yields:
% 28.11/7.77 | (223) ~ (e3 = e2)
% 28.11/7.77 |
% 28.11/7.77 +-Applying beta-rule and splitting (5254), into two cases.
% 28.11/7.77 |-Branch one:
% 28.11/7.77 | (351) all_0_41_41 = e3
% 28.11/7.77 |
% 28.11/7.77 | Combining equations (351,358) yields a new equation:
% 28.11/7.77 | (359) e4 = e3
% 28.11/7.77 |
% 28.11/7.77 | Equations (359) can reduce 34 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (1237) ~ (all_0_41_41 = e3)
% 28.11/7.77 | (1258) all_0_42_42 = e3
% 28.11/7.77 |
% 28.11/7.77 | Combining equations (698,1258) yields a new equation:
% 28.11/7.77 | (414) e3 = e2
% 28.11/7.77 |
% 28.11/7.77 | Equations (414) can reduce 223 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (354) ~ (all_0_45_45 = e3)
% 28.11/7.77 | (363) all_0_45_45 = e4
% 28.11/7.77 |
% 28.11/7.77 | Equations (363) can reduce 352 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (361) ~ (all_0_41_41 = e4)
% 28.11/7.77 | (512) all_0_42_42 = e4
% 28.11/7.77 |
% 28.11/7.77 | Combining equations (698,512) yields a new equation:
% 28.11/7.77 | (269) e4 = e2
% 28.11/7.77 |
% 28.11/7.77 | Equations (269) can reduce 231 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (697) ~ (all_0_51_51 = e4)
% 28.11/7.77 | (4744) all_0_56_56 = e4
% 28.11/7.77 |
% 28.11/7.77 | Equations (4744) can reduce 274 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (498) ~ (all_0_42_42 = e2)
% 28.11/7.77 | (1732) all_0_46_46 = e2 | all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 28.11/7.77 |
% 28.11/7.77 +-Applying beta-rule and splitting (630), into two cases.
% 28.11/7.77 |-Branch one:
% 28.11/7.77 | (327) all_0_40_40 = e2
% 28.11/7.77 |
% 28.11/7.77 | Combining equations (530,327) yields a new equation:
% 28.11/7.77 | (322) e2 = e1
% 28.11/7.77 |
% 28.11/7.77 | Equations (322) can reduce 141 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (602) ~ (all_0_40_40 = e2)
% 28.11/7.77 | (1251) all_0_41_41 = e2 | all_0_42_42 = e2
% 28.11/7.77 |
% 28.11/7.77 +-Applying beta-rule and splitting (1251), into two cases.
% 28.11/7.77 |-Branch one:
% 28.11/7.77 | (436) all_0_41_41 = e2
% 28.11/7.77 |
% 28.11/7.77 | Equations (436) can reduce 331 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (331) ~ (all_0_41_41 = e2)
% 28.11/7.77 | (698) all_0_42_42 = e2
% 28.11/7.77 |
% 28.11/7.77 | Equations (698) can reduce 498 to:
% 28.11/7.77 | (270) $false
% 28.11/7.77 |
% 28.11/7.77 |-The branch is then unsatisfiable
% 28.11/7.77 |-Branch two:
% 28.11/7.77 | (292) ~ (all_0_43_43 = e2)
% 28.11/7.77 | (453) all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2
% 28.11/7.77 |
% 28.11/7.77 +-Applying beta-rule and splitting (96), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (336) all_0_39_39 = e2
% 28.11/7.78 |
% 28.11/7.78 | Equations (336) can reduce 226 to:
% 28.11/7.78 | (330) ~ (all_0_41_41 = e2)
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 330 yields:
% 28.11/7.78 | (331) ~ (all_0_41_41 = e2)
% 28.11/7.78 |
% 28.11/7.78 | Equations (336) can reduce 184 to:
% 28.11/7.78 | (1336) ~ (all_0_42_42 = e2)
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 1336 yields:
% 28.11/7.78 | (498) ~ (all_0_42_42 = e2)
% 28.11/7.78 |
% 28.11/7.78 | Equations (336) can reduce 32 to:
% 28.11/7.78 | (254) ~ (all_0_51_51 = e2)
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 254 yields:
% 28.11/7.78 | (255) ~ (all_0_51_51 = e2)
% 28.11/7.78 |
% 28.11/7.78 | Equations (336) can reduce 212 to:
% 28.11/7.78 | (299) ~ (all_0_56_56 = e2)
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 299 yields:
% 28.11/7.78 | (300) ~ (all_0_56_56 = e2)
% 28.11/7.78 |
% 28.11/7.78 | Equations (336) can reduce 101 to:
% 28.11/7.78 | (57) ~ (e2 = e0)
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (209), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (698) all_0_42_42 = e2
% 28.11/7.78 |
% 28.11/7.78 | Equations (698) can reduce 498 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (498) ~ (all_0_42_42 = e2)
% 28.11/7.78 | (1732) all_0_46_46 = e2 | all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (453), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (370) all_0_44_44 = e2
% 28.11/7.78 |
% 28.11/7.78 | Combining equations (621,370) yields a new equation:
% 28.11/7.78 | (316) e2 = e0
% 28.11/7.78 |
% 28.11/7.78 | Equations (316) can reduce 57 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (333) ~ (all_0_44_44 = e2)
% 28.11/7.78 | (493) all_0_45_45 = e2 | all_0_46_46 = e2
% 28.11/7.78 |
% 28.11/7.78 | Equations (621) can reduce 333 to:
% 28.11/7.78 | (566) ~ (e2 = e0)
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 566 yields:
% 28.11/7.78 | (57) ~ (e2 = e0)
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (1732), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (497) all_0_46_46 = e2
% 28.11/7.78 |
% 28.11/7.78 | Equations (497) can reduce 18 to:
% 28.11/7.78 | (498) ~ (all_0_42_42 = e2)
% 28.11/7.78 |
% 28.11/7.78 | Equations (497) can reduce 103 to:
% 28.11/7.78 | (292) ~ (all_0_43_43 = e2)
% 28.11/7.78 |
% 28.11/7.78 | Equations (497) can reduce 206 to:
% 28.11/7.78 | (700) ~ (all_0_59_59 = e2)
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 700 yields:
% 28.11/7.78 | (701) ~ (all_0_59_59 = e2)
% 28.11/7.78 |
% 28.11/7.78 | Equations (497) can reduce 106 to:
% 28.11/7.78 | (141) ~ (e2 = e1)
% 28.11/7.78 |
% 28.11/7.78 | Equations (497) can reduce 1010 to:
% 28.11/7.78 | (57) ~ (e2 = e0)
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (222), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (522) all_0_39_39 = e4
% 28.11/7.78 |
% 28.11/7.78 | Combining equations (336,522) yields a new equation:
% 28.11/7.78 | (269) e4 = e2
% 28.11/7.78 |
% 28.11/7.78 | Equations (269) can reduce 231 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (591) ~ (all_0_39_39 = e4)
% 28.11/7.78 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 28.11/7.78 |
% 28.11/7.78 | Equations (336) can reduce 591 to:
% 28.11/7.78 | (377) ~ (e4 = e2)
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 377 yields:
% 28.11/7.78 | (231) ~ (e4 = e2)
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (44), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (502) all_0_43_43 = e4
% 28.11/7.78 |
% 28.11/7.78 | Equations (502) can reduce 240 to:
% 28.11/7.78 | (696) ~ (all_0_51_51 = e4)
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 696 yields:
% 28.11/7.78 | (697) ~ (all_0_51_51 = e4)
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (22), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (782) all_0_43_43 = e3
% 28.11/7.78 |
% 28.11/7.78 | Combining equations (502,782) yields a new equation:
% 28.11/7.78 | (660) e4 = e3
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 660 yields:
% 28.11/7.78 | (359) e4 = e3
% 28.11/7.78 |
% 28.11/7.78 | Equations (359) can reduce 34 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (786) ~ (all_0_43_43 = e3)
% 28.11/7.78 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (178), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (751) all_0_39_39 = e3
% 28.11/7.78 |
% 28.11/7.78 | Combining equations (336,751) yields a new equation:
% 28.11/7.78 | (414) e3 = e2
% 28.11/7.78 |
% 28.11/7.78 | Equations (414) can reduce 223 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (755) ~ (all_0_39_39 = e3)
% 28.11/7.78 | (756) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 28.11/7.78 |
% 28.11/7.78 | Equations (336) can reduce 755 to:
% 28.11/7.78 | (301) ~ (e3 = e2)
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 301 yields:
% 28.11/7.78 | (223) ~ (e3 = e2)
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (787), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (858) all_0_44_44 = e3
% 28.11/7.78 |
% 28.11/7.78 | Combining equations (621,858) yields a new equation:
% 28.11/7.78 | (784) e3 = e0
% 28.11/7.78 |
% 28.11/7.78 | Equations (784) can reduce 66 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (862) ~ (all_0_44_44 = e3)
% 28.11/7.78 | (1070) all_0_45_45 = e3 | all_0_46_46 = e3
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (173), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (4215) all_0_51_51 = e2
% 28.11/7.78 |
% 28.11/7.78 | Equations (4215) can reduce 255 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (255) ~ (all_0_51_51 = e2)
% 28.11/7.78 | (4888) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1 | all_0_51_51 = e0
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (4888), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (954) all_0_51_51 = e0
% 28.11/7.78 |
% 28.11/7.78 | Equations (954) can reduce 60 to:
% 28.11/7.78 | (3852) ~ (all_0_56_56 = e0)
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 3852 yields:
% 28.11/7.78 | (419) ~ (all_0_56_56 = e0)
% 28.11/7.78 |
% 28.11/7.78 | Equations (954) can reduce 255 to:
% 28.11/7.78 | (566) ~ (e2 = e0)
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 566 yields:
% 28.11/7.78 | (57) ~ (e2 = e0)
% 28.11/7.78 |
% 28.11/7.78 | Equations (954) can reduce 748 to:
% 28.11/7.78 | (568) ~ (e1 = e0)
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 568 yields:
% 28.11/7.78 | (132) ~ (e1 = e0)
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (93), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (402) all_0_59_59 = e4
% 28.11/7.78 |
% 28.11/7.78 | Equations (402) can reduce 280 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (280) ~ (all_0_59_59 = e4)
% 28.11/7.78 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (176), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (830) all_0_56_56 = e0
% 28.11/7.78 |
% 28.11/7.78 | Equations (830) can reduce 419 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (419) ~ (all_0_56_56 = e0)
% 28.11/7.78 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (834), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (2258) all_0_57_57 = e0
% 28.11/7.78 |
% 28.11/7.78 | Combining equations (392,2258) yields a new equation:
% 28.11/7.78 | (622) e2 = e0
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 622 yields:
% 28.11/7.78 | (316) e2 = e0
% 28.11/7.78 |
% 28.11/7.78 | Equations (316) can reduce 57 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (2301) ~ (all_0_57_57 = e0)
% 28.11/7.78 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (2302), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (585) all_0_58_58 = e0
% 28.11/7.78 |
% 28.11/7.78 | Equations (585) can reduce 70 to:
% 28.11/7.78 | (584) ~ (all_0_53_53 = e0)
% 28.11/7.78 |
% 28.11/7.78 | Equations (585) can reduce 156 to:
% 28.11/7.78 | (4000) ~ (all_0_59_59 = e0)
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 4000 yields:
% 28.11/7.78 | (4001) ~ (all_0_59_59 = e0)
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (194), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (747) all_0_56_56 = e1
% 28.11/7.78 |
% 28.11/7.78 | Equations (747) can reduce 995 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (995) ~ (all_0_56_56 = e1)
% 28.11/7.78 | (996) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (52), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (536) all_0_41_41 = e1
% 28.11/7.78 |
% 28.11/7.78 | Equations (536) can reduce 540 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (540) ~ (all_0_41_41 = e1)
% 28.11/7.78 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (996), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (997) all_0_57_57 = e1
% 28.11/7.78 |
% 28.11/7.78 | Combining equations (392,997) yields a new equation:
% 28.11/7.78 | (531) e2 = e1
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 531 yields:
% 28.11/7.78 | (322) e2 = e1
% 28.11/7.78 |
% 28.11/7.78 | Equations (322) can reduce 141 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (644) ~ (all_0_57_57 = e1)
% 28.11/7.78 | (1000) all_0_58_58 = e1 | all_0_59_59 = e1
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (1000), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (1001) all_0_58_58 = e1
% 28.11/7.78 |
% 28.11/7.78 | Combining equations (1001,585) yields a new equation:
% 28.11/7.78 | (571) e1 = e0
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 571 yields:
% 28.11/7.78 | (560) e1 = e0
% 28.11/7.78 |
% 28.11/7.78 | Equations (560) can reduce 132 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (1004) ~ (all_0_58_58 = e1)
% 28.11/7.78 | (424) all_0_59_59 = e1
% 28.11/7.78 |
% 28.11/7.78 | Equations (424) can reduce 701 to:
% 28.11/7.78 | (645) ~ (e2 = e1)
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 645 yields:
% 28.11/7.78 | (141) ~ (e2 = e1)
% 28.11/7.78 |
% 28.11/7.78 | Equations (424) can reduce 4001 to:
% 28.11/7.78 | (132) ~ (e1 = e0)
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (95), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (1258) all_0_42_42 = e3
% 28.11/7.78 |
% 28.11/7.78 | Equations (1258) can reduce 498 to:
% 28.11/7.78 | (223) ~ (e3 = e2)
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (135), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (820) all_0_51_51 = e1
% 28.11/7.78 |
% 28.11/7.78 | Combining equations (954,820) yields a new equation:
% 28.11/7.78 | (560) e1 = e0
% 28.11/7.78 |
% 28.11/7.78 | Equations (560) can reduce 132 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (748) ~ (all_0_51_51 = e1)
% 28.11/7.78 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 28.11/7.78 |
% 28.11/7.78 | Equations (954) can reduce 748 to:
% 28.11/7.78 | (568) ~ (e1 = e0)
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 568 yields:
% 28.11/7.78 | (132) ~ (e1 = e0)
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (762), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (552) all_0_48_48 = e1
% 28.11/7.78 |
% 28.11/7.78 | Combining equations (311,552) yields a new equation:
% 28.11/7.78 | (531) e2 = e1
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 531 yields:
% 28.11/7.78 | (322) e2 = e1
% 28.11/7.78 |
% 28.11/7.78 | Equations (322) can reduce 141 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (588) ~ (all_0_48_48 = e1)
% 28.11/7.78 | (4925) all_0_53_53 = e1 | all_0_58_58 = e1
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (4925), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (853) all_0_53_53 = e1
% 28.11/7.78 |
% 28.11/7.78 | Equations (853) can reduce 128 to:
% 28.11/7.78 | (26) ~ (all_0_45_45 = e1)
% 28.11/7.78 |
% 28.11/7.78 | Equations (853) can reduce 584 to:
% 28.11/7.78 | (132) ~ (e1 = e0)
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (1070), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (505) all_0_45_45 = e3
% 28.11/7.78 |
% 28.11/7.78 | Equations (505) can reduce 26 to:
% 28.11/7.78 | (136) ~ (e3 = e1)
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (407), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (408), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (409), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 28.11/7.78 |
% 28.11/7.78 | Applying alpha-rule on (410) yields:
% 28.11/7.78 | (411) all_0_43_43 = e0
% 28.11/7.78 | (412) all_0_59_59 = e3
% 28.11/7.78 | (413) ~ (all_0_46_46 = e3)
% 28.11/7.78 |
% 28.11/7.78 | Combining equations (424,412) yields a new equation:
% 28.11/7.78 | (538) e3 = e1
% 28.11/7.78 |
% 28.11/7.78 | Equations (538) can reduce 136 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 28.11/7.78 |
% 28.11/7.78 | Applying alpha-rule on (416) yields:
% 28.11/7.78 | (411) all_0_43_43 = e0
% 28.11/7.78 | (412) all_0_59_59 = e3
% 28.11/7.78 | (419) ~ (all_0_56_56 = e0)
% 28.11/7.78 |
% 28.11/7.78 | Combining equations (424,412) yields a new equation:
% 28.11/7.78 | (538) e3 = e1
% 28.11/7.78 |
% 28.11/7.78 | Equations (538) can reduce 136 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 28.11/7.78 |
% 28.11/7.78 | Applying alpha-rule on (422) yields:
% 28.11/7.78 | (423) all_0_53_53 = e0
% 28.11/7.78 | (424) all_0_59_59 = e1
% 28.11/7.78 | (425) ~ (all_0_54_54 = e1)
% 28.11/7.78 |
% 28.11/7.78 | Combining equations (853,423) yields a new equation:
% 28.11/7.78 | (571) e1 = e0
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 571 yields:
% 28.11/7.78 | (560) e1 = e0
% 28.11/7.78 |
% 28.11/7.78 | Equations (560) can reduce 132 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 28.11/7.78 |
% 28.11/7.78 | Applying alpha-rule on (428) yields:
% 28.11/7.78 | (423) all_0_53_53 = e0
% 28.11/7.78 | (424) all_0_59_59 = e1
% 28.11/7.78 | (431) ~ (all_0_58_58 = e0)
% 28.11/7.78 |
% 28.11/7.78 | Combining equations (853,423) yields a new equation:
% 28.11/7.78 | (571) e1 = e0
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 571 yields:
% 28.11/7.78 | (560) e1 = e0
% 28.11/7.78 |
% 28.11/7.78 | Equations (560) can reduce 132 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (354) ~ (all_0_45_45 = e3)
% 28.11/7.78 | (1091) all_0_46_46 = e3
% 28.11/7.78 |
% 28.11/7.78 | Combining equations (497,1091) yields a new equation:
% 28.11/7.78 | (414) e3 = e2
% 28.11/7.78 |
% 28.11/7.78 | Equations (414) can reduce 223 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (874) ~ (all_0_53_53 = e1)
% 28.11/7.78 | (1001) all_0_58_58 = e1
% 28.11/7.78 |
% 28.11/7.78 | Combining equations (585,1001) yields a new equation:
% 28.11/7.78 | (560) e1 = e0
% 28.11/7.78 |
% 28.11/7.78 | Equations (560) can reduce 132 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (1316) ~ (all_0_42_42 = e3)
% 28.11/7.78 | (3656) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 28.11/7.78 |
% 28.11/7.78 +-Applying beta-rule and splitting (78), into two cases.
% 28.11/7.78 |-Branch one:
% 28.11/7.78 | (751) all_0_39_39 = e3
% 28.11/7.78 |
% 28.11/7.78 | Combining equations (751,336) yields a new equation:
% 28.11/7.78 | (437) e3 = e2
% 28.11/7.78 |
% 28.11/7.78 | Simplifying 437 yields:
% 28.11/7.78 | (414) e3 = e2
% 28.11/7.78 |
% 28.11/7.78 | Equations (414) can reduce 223 to:
% 28.11/7.78 | (270) $false
% 28.11/7.78 |
% 28.11/7.78 |-The branch is then unsatisfiable
% 28.11/7.78 |-Branch two:
% 28.11/7.78 | (755) ~ (all_0_39_39 = e3)
% 28.11/7.79 | (4262) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 28.11/7.79 |
% 28.11/7.79 | Equations (336) can reduce 755 to:
% 28.11/7.79 | (301) ~ (e3 = e2)
% 28.11/7.79 |
% 28.11/7.79 | Simplifying 301 yields:
% 28.11/7.79 | (223) ~ (e3 = e2)
% 28.11/7.79 |
% 28.11/7.79 +-Applying beta-rule and splitting (3656), into two cases.
% 28.11/7.79 |-Branch one:
% 28.11/7.79 | (1091) all_0_46_46 = e3
% 28.11/7.79 |
% 28.11/7.79 | Combining equations (497,1091) yields a new equation:
% 28.11/7.79 | (414) e3 = e2
% 28.11/7.79 |
% 28.11/7.79 | Equations (414) can reduce 223 to:
% 28.11/7.79 | (270) $false
% 28.11/7.79 |
% 28.11/7.79 |-The branch is then unsatisfiable
% 28.11/7.79 |-Branch two:
% 28.11/7.79 | (413) ~ (all_0_46_46 = e3)
% 28.11/7.79 | (3700) all_0_54_54 = e3 | all_0_59_59 = e3
% 28.11/7.79 |
% 28.11/7.79 +-Applying beta-rule and splitting (4262), into two cases.
% 28.11/7.79 |-Branch one:
% 28.11/7.79 | (671) all_0_40_40 = e3
% 28.11/7.79 |
% 28.11/7.79 | Combining equations (530,671) yields a new equation:
% 28.11/7.79 | (538) e3 = e1
% 28.11/7.79 |
% 28.11/7.79 | Equations (538) can reduce 136 to:
% 28.11/7.79 | (270) $false
% 28.11/7.79 |
% 28.11/7.79 |-The branch is then unsatisfiable
% 28.11/7.79 |-Branch two:
% 28.11/7.79 | (675) ~ (all_0_40_40 = e3)
% 28.11/7.79 | (5254) all_0_41_41 = e3 | all_0_42_42 = e3
% 28.11/7.79 |
% 28.11/7.79 | Equations (530) can reduce 675 to:
% 28.11/7.79 | (769) ~ (e3 = e1)
% 28.11/7.79 |
% 28.11/7.79 | Simplifying 769 yields:
% 28.11/7.79 | (136) ~ (e3 = e1)
% 28.11/7.79 |
% 28.11/7.79 +-Applying beta-rule and splitting (3700), into two cases.
% 28.11/7.79 |-Branch one:
% 28.11/7.79 | (1119) all_0_54_54 = e3
% 28.11/7.79 |
% 28.11/7.79 | Equations (1119) can reduce 1093 to:
% 28.11/7.79 | (270) $false
% 28.11/7.79 |
% 28.11/7.79 |-The branch is then unsatisfiable
% 28.11/7.79 |-Branch two:
% 28.11/7.79 | (1093) ~ (all_0_54_54 = e3)
% 28.11/7.79 | (412) all_0_59_59 = e3
% 28.11/7.79 |
% 28.11/7.79 | Combining equations (424,412) yields a new equation:
% 28.11/7.79 | (538) e3 = e1
% 28.11/7.79 |
% 28.11/7.79 | Equations (538) can reduce 136 to:
% 28.11/7.79 | (270) $false
% 28.11/7.79 |
% 28.11/7.79 |-The branch is then unsatisfiable
% 28.11/7.79 |-Branch two:
% 28.11/7.79 | (431) ~ (all_0_58_58 = e0)
% 28.11/7.79 | (2308) all_0_59_59 = e0
% 28.11/7.79 |
% 28.11/7.79 | Equations (2308) can reduce 4001 to:
% 28.11/7.79 | (270) $false
% 28.11/7.79 |
% 28.11/7.79 |-The branch is then unsatisfiable
% 28.11/7.79 |-Branch two:
% 28.11/7.79 | (987) ~ (all_0_51_51 = e0)
% 28.11/7.79 | (5003) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1
% 28.11/7.79 |
% 28.11/7.79 +-Applying beta-rule and splitting (5003), into two cases.
% 28.11/7.79 |-Branch one:
% 28.11/7.79 | (824) all_0_51_51 = e3
% 28.11/7.79 |
% 28.11/7.79 | Equations (824) can reduce 932 to:
% 28.11/7.79 | (270) $false
% 28.11/7.79 |
% 28.11/7.79 |-The branch is then unsatisfiable
% 28.11/7.79 |-Branch two:
% 28.11/7.79 | (932) ~ (all_0_51_51 = e3)
% 28.11/7.79 | (5007) all_0_51_51 = e4 | all_0_51_51 = e1
% 28.11/7.79 |
% 28.11/7.79 +-Applying beta-rule and splitting (5007), into two cases.
% 28.11/7.79 |-Branch one:
% 28.11/7.79 | (820) all_0_51_51 = e1
% 28.11/7.79 |
% 28.11/7.79 | Equations (820) can reduce 748 to:
% 28.11/7.79 | (270) $false
% 28.11/7.79 |
% 28.11/7.79 |-The branch is then unsatisfiable
% 28.11/7.79 |-Branch two:
% 28.11/7.79 | (748) ~ (all_0_51_51 = e1)
% 28.11/7.79 | (1467) all_0_51_51 = e4
% 28.11/7.79 |
% 28.11/7.79 | Equations (1467) can reduce 697 to:
% 28.11/7.79 | (270) $false
% 28.11/7.79 |
% 28.11/7.79 |-The branch is then unsatisfiable
% 28.11/7.79 |-Branch two:
% 28.11/7.79 | (510) ~ (all_0_43_43 = e4)
% 28.11/7.79 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 28.11/7.79 |
% 28.11/7.79 +-Applying beta-rule and splitting (159), into two cases.
% 28.11/7.79 |-Branch one:
% 28.11/7.79 | (450) all_0_43_43 = e2
% 28.11/7.79 |
% 28.11/7.79 | Equations (450) can reduce 292 to:
% 28.11/7.79 | (270) $false
% 28.11/7.79 |
% 28.11/7.79 |-The branch is then unsatisfiable
% 28.11/7.79 |-Branch two:
% 28.11/7.79 | (292) ~ (all_0_43_43 = e2)
% 28.11/7.79 | (774) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 28.11/7.79 |
% 28.11/7.79 +-Applying beta-rule and splitting (166), into two cases.
% 28.11/7.79 |-Branch one:
% 28.11/7.79 | (522) all_0_39_39 = e4
% 28.11/7.79 |
% 28.11/7.79 | Combining equations (336,522) yields a new equation:
% 28.11/7.79 | (269) e4 = e2
% 28.11/7.79 |
% 28.11/7.79 | Equations (269) can reduce 231 to:
% 28.11/7.79 | (270) $false
% 28.11/7.79 |
% 28.11/7.79 |-The branch is then unsatisfiable
% 28.11/7.79 |-Branch two:
% 28.11/7.79 | (591) ~ (all_0_39_39 = e4)
% 28.11/7.79 | (4522) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 28.11/7.79 |
% 28.11/7.79 | Equations (336) can reduce 591 to:
% 28.11/7.79 | (377) ~ (e4 = e2)
% 28.11/7.79 |
% 28.11/7.79 | Simplifying 377 yields:
% 28.11/7.79 | (231) ~ (e4 = e2)
% 28.11/7.79 |
% 28.11/7.79 +-Applying beta-rule and splitting (511), into two cases.
% 28.11/7.79 |-Branch one:
% 28.11/7.79 | (363) all_0_45_45 = e4
% 28.11/7.79 |
% 28.11/7.79 | Equations (363) can reduce 51 to:
% 28.11/7.79 | (361) ~ (all_0_41_41 = e4)
% 28.11/7.79 |
% 28.11/7.79 | Equations (363) can reduce 84 to:
% 28.11/7.79 | (510) ~ (all_0_43_43 = e4)
% 28.11/7.79 |
% 28.11/7.79 | Equations (363) can reduce 128 to:
% 28.11/7.79 | (1444) ~ (all_0_53_53 = e4)
% 28.11/7.79 |
% 28.11/7.79 | Simplifying 1444 yields:
% 28.11/7.79 | (599) ~ (all_0_53_53 = e4)
% 28.11/7.79 |
% 28.11/7.79 +-Applying beta-rule and splitting (22), into two cases.
% 28.11/7.79 |-Branch one:
% 28.11/7.79 | (782) all_0_43_43 = e3
% 28.11/7.79 |
% 28.11/7.79 | Equations (782) can reduce 240 to:
% 28.11/7.79 | (952) ~ (all_0_51_51 = e3)
% 28.11/7.79 |
% 28.11/7.79 | Simplifying 952 yields:
% 28.11/7.79 | (932) ~ (all_0_51_51 = e3)
% 28.11/7.79 |
% 28.11/7.79 | Equations (782) can reduce 510 to:
% 28.11/7.79 | (719) ~ (e4 = e3)
% 28.11/7.79 |
% 28.11/7.79 | Simplifying 719 yields:
% 28.11/7.79 | (34) ~ (e4 = e3)
% 28.11/7.79 |
% 28.11/7.79 | Equations (782) can reduce 292 to:
% 28.11/7.79 | (223) ~ (e3 = e2)
% 28.11/7.79 |
% 28.11/7.79 | Equations (782) can reduce 455 to:
% 28.11/7.79 | (66) ~ (e3 = e0)
% 28.11/7.79 |
% 28.11/7.79 +-Applying beta-rule and splitting (208), into two cases.
% 28.11/7.79 |-Branch one:
% 28.11/7.79 | (388) all_0_56_56 = e2
% 28.11/7.79 |
% 28.11/7.79 | Equations (388) can reduce 300 to:
% 28.11/7.79 | (270) $false
% 28.11/7.79 |
% 28.11/7.79 |-The branch is then unsatisfiable
% 28.11/7.79 |-Branch two:
% 28.11/7.79 | (300) ~ (all_0_56_56 = e2)
% 28.11/7.79 | (5076) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1 | all_0_56_56 = e0
% 28.11/7.79 |
% 28.11/7.79 +-Applying beta-rule and splitting (5076), into two cases.
% 28.11/7.79 |-Branch one:
% 28.11/7.79 | (830) all_0_56_56 = e0
% 28.11/7.79 |
% 28.11/7.79 | Equations (830) can reduce 185 to:
% 28.11/7.79 | (4000) ~ (all_0_59_59 = e0)
% 28.11/7.79 |
% 28.11/7.79 | Simplifying 4000 yields:
% 28.11/7.79 | (4001) ~ (all_0_59_59 = e0)
% 28.11/7.79 |
% 28.11/7.79 | Equations (830) can reduce 274 to:
% 28.11/7.79 | (456) ~ (e4 = e0)
% 28.11/7.79 |
% 28.11/7.79 | Simplifying 456 yields:
% 28.11/7.79 | (6) ~ (e4 = e0)
% 28.11/7.79 |
% 28.11/7.79 | Equations (830) can reduce 995 to:
% 28.11/7.79 | (568) ~ (e1 = e0)
% 28.11/7.79 |
% 28.11/7.79 | Simplifying 568 yields:
% 28.11/7.79 | (132) ~ (e1 = e0)
% 28.11/7.79 |
% 28.11/7.79 +-Applying beta-rule and splitting (4522), into two cases.
% 28.11/7.79 |-Branch one:
% 28.11/7.79 | (502) all_0_43_43 = e4
% 28.11/7.79 |
% 28.11/7.79 | Combining equations (782,502) yields a new equation:
% 28.11/7.79 | (359) e4 = e3
% 28.11/7.79 |
% 28.11/7.79 | Equations (359) can reduce 34 to:
% 28.11/7.79 | (270) $false
% 28.11/7.79 |
% 28.11/7.79 |-The branch is then unsatisfiable
% 28.11/7.79 |-Branch two:
% 28.11/7.79 | (510) ~ (all_0_43_43 = e4)
% 28.11/7.79 | (4527) all_0_51_51 = e4 | all_0_56_56 = e4
% 28.11/7.79 |
% 28.11/7.79 +-Applying beta-rule and splitting (4527), into two cases.
% 28.11/7.79 |-Branch one:
% 28.11/7.79 | (1467) all_0_51_51 = e4
% 28.11/7.79 |
% 28.11/7.79 | Equations (1467) can reduce 932 to:
% 28.11/7.79 | (34) ~ (e4 = e3)
% 28.11/7.79 |
% 28.11/7.79 +-Applying beta-rule and splitting (592), into two cases.
% 28.11/7.79 |-Branch one:
% 28.11/7.79 | (358) all_0_41_41 = e4
% 28.11/7.79 |
% 28.11/7.79 | Equations (358) can reduce 361 to:
% 28.11/7.79 | (270) $false
% 28.11/7.79 |
% 28.11/7.79 |-The branch is then unsatisfiable
% 28.11/7.79 |-Branch two:
% 28.11/7.79 | (361) ~ (all_0_41_41 = e4)
% 28.11/7.79 | (512) all_0_42_42 = e4
% 28.11/7.79 |
% 28.11/7.79 | Equations (512) can reduce 94 to:
% 28.11/7.79 | (361) ~ (all_0_41_41 = e4)
% 28.11/7.79 |
% 28.11/7.79 | Equations (512) can reduce 17 to:
% 28.11/7.79 | (279) ~ (all_0_59_59 = e4)
% 28.11/7.79 |
% 28.11/7.79 | Simplifying 279 yields:
% 28.11/7.79 | (280) ~ (all_0_59_59 = e4)
% 28.11/7.79 |
% 28.11/7.79 | Equations (512) can reduce 640 to:
% 28.11/7.79 | (251) ~ (e4 = e1)
% 28.11/7.79 |
% 28.11/7.79 +-Applying beta-rule and splitting (95), into two cases.
% 28.11/7.79 |-Branch one:
% 28.11/7.79 | (1258) all_0_42_42 = e3
% 28.11/7.79 |
% 28.11/7.79 | Combining equations (512,1258) yields a new equation:
% 28.11/7.79 | (660) e4 = e3
% 28.11/7.79 |
% 28.11/7.79 | Simplifying 660 yields:
% 28.11/7.79 | (359) e4 = e3
% 28.11/7.79 |
% 28.11/7.79 | Equations (359) can reduce 34 to:
% 28.11/7.79 | (270) $false
% 28.11/7.79 |
% 28.11/7.79 |-The branch is then unsatisfiable
% 28.11/7.79 |-Branch two:
% 28.11/7.79 | (1316) ~ (all_0_42_42 = e3)
% 28.11/7.79 | (3656) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 28.11/7.79 |
% 28.11/7.79 +-Applying beta-rule and splitting (78), into two cases.
% 28.11/7.79 |-Branch one:
% 28.11/7.79 | (751) all_0_39_39 = e3
% 28.11/7.79 |
% 28.11/7.79 | Combining equations (751,336) yields a new equation:
% 28.11/7.79 | (437) e3 = e2
% 28.11/7.79 |
% 28.11/7.79 | Simplifying 437 yields:
% 28.11/7.79 | (414) e3 = e2
% 28.11/7.79 |
% 28.11/7.79 | Equations (414) can reduce 223 to:
% 28.11/7.79 | (270) $false
% 28.11/7.79 |
% 28.11/7.79 |-The branch is then unsatisfiable
% 28.11/7.79 |-Branch two:
% 28.11/7.79 | (755) ~ (all_0_39_39 = e3)
% 28.11/7.79 | (4262) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 28.11/7.79 |
% 28.11/7.79 | Equations (336) can reduce 755 to:
% 28.11/7.79 | (301) ~ (e3 = e2)
% 28.11/7.79 |
% 28.11/7.79 | Simplifying 301 yields:
% 28.11/7.79 | (223) ~ (e3 = e2)
% 28.11/7.79 |
% 28.11/7.79 +-Applying beta-rule and splitting (217), into two cases.
% 28.11/7.79 |-Branch one:
% 28.11/7.79 | (436) all_0_41_41 = e2
% 28.11/7.79 |
% 28.11/7.79 | Equations (436) can reduce 331 to:
% 28.11/7.79 | (270) $false
% 28.11/7.79 |
% 28.11/7.79 |-The branch is then unsatisfiable
% 28.11/7.79 |-Branch two:
% 28.11/7.79 | (331) ~ (all_0_41_41 = e2)
% 28.11/7.79 | (709) all_0_41_41 = e4 | all_0_41_41 = e3 | all_0_41_41 = e1
% 28.11/7.79 |
% 28.11/7.79 +-Applying beta-rule and splitting (135), into two cases.
% 28.11/7.79 |-Branch one:
% 28.11/7.79 | (820) all_0_51_51 = e1
% 28.11/7.79 |
% 28.11/7.79 | Combining equations (1467,820) yields a new equation:
% 28.11/7.79 | (525) e4 = e1
% 28.11/7.79 |
% 28.11/7.79 | Simplifying 525 yields:
% 28.11/7.79 | (526) e4 = e1
% 28.11/7.79 |
% 28.11/7.79 | Equations (526) can reduce 251 to:
% 28.11/7.79 | (270) $false
% 28.11/7.79 |
% 28.11/7.79 |-The branch is then unsatisfiable
% 28.11/7.79 |-Branch two:
% 28.11/7.79 | (748) ~ (all_0_51_51 = e1)
% 28.11/7.79 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 28.11/7.79 |
% 28.11/7.79 | Equations (1467) can reduce 748 to:
% 28.11/7.79 | (251) ~ (e4 = e1)
% 28.11/7.79 |
% 28.11/7.79 +-Applying beta-rule and splitting (3656), into two cases.
% 28.11/7.79 |-Branch one:
% 28.11/7.79 | (1091) all_0_46_46 = e3
% 28.11/7.79 |
% 28.11/7.79 | Combining equations (497,1091) yields a new equation:
% 28.11/7.79 | (414) e3 = e2
% 28.11/7.79 |
% 28.11/7.79 | Equations (414) can reduce 223 to:
% 28.11/7.79 | (270) $false
% 28.11/7.79 |
% 28.11/7.79 |-The branch is then unsatisfiable
% 28.11/7.79 |-Branch two:
% 28.11/7.79 | (413) ~ (all_0_46_46 = e3)
% 28.11/7.79 | (3700) all_0_54_54 = e3 | all_0_59_59 = e3
% 28.11/7.79 |
% 28.11/7.79 +-Applying beta-rule and splitting (52), into two cases.
% 28.11/7.79 |-Branch one:
% 28.11/7.79 | (536) all_0_41_41 = e1
% 28.11/7.79 |
% 28.11/7.79 | Equations (536) can reduce 540 to:
% 28.11/7.79 | (270) $false
% 28.11/7.79 |
% 28.11/7.79 |-The branch is then unsatisfiable
% 28.11/7.79 |-Branch two:
% 28.11/7.79 | (540) ~ (all_0_41_41 = e1)
% 28.11/7.79 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 28.11/7.79 |
% 28.11/7.79 +-Applying beta-rule and splitting (709), into two cases.
% 28.11/7.79 |-Branch one:
% 28.11/7.79 | (351) all_0_41_41 = e3
% 28.11/7.79 |
% 28.11/7.79 | Equations (351) can reduce 540 to:
% 28.11/7.79 | (136) ~ (e3 = e1)
% 28.11/7.79 |
% 28.11/7.79 +-Applying beta-rule and splitting (3700), into two cases.
% 28.11/7.79 |-Branch one:
% 28.11/7.79 | (1119) all_0_54_54 = e3
% 28.11/7.79 |
% 28.11/7.79 | Equations (1119) can reduce 1093 to:
% 28.11/7.79 | (270) $false
% 28.11/7.79 |
% 28.11/7.79 |-The branch is then unsatisfiable
% 28.11/7.79 |-Branch two:
% 28.11/7.79 | (1093) ~ (all_0_54_54 = e3)
% 28.11/7.79 | (412) all_0_59_59 = e3
% 28.11/7.80 |
% 28.11/7.80 | Equations (412) can reduce 72 to:
% 28.11/7.80 | (1093) ~ (all_0_54_54 = e3)
% 28.11/7.80 |
% 28.11/7.80 | Equations (412) can reduce 280 to:
% 28.11/7.80 | (719) ~ (e4 = e3)
% 28.11/7.80 |
% 28.11/7.80 | Simplifying 719 yields:
% 28.11/7.80 | (34) ~ (e4 = e3)
% 28.11/7.80 |
% 28.11/7.80 | Equations (412) can reduce 4001 to:
% 28.11/7.80 | (66) ~ (e3 = e0)
% 28.11/7.80 |
% 28.11/7.80 +-Applying beta-rule and splitting (127), into two cases.
% 28.11/7.80 |-Branch one:
% 28.11/7.80 | (541) all_0_42_42 = e1
% 28.11/7.80 |
% 28.11/7.80 | Combining equations (512,541) yields a new equation:
% 28.11/7.80 | (525) e4 = e1
% 28.11/7.80 |
% 28.11/7.80 | Simplifying 525 yields:
% 28.11/7.80 | (526) e4 = e1
% 28.11/7.80 |
% 28.11/7.80 | Equations (526) can reduce 251 to:
% 28.11/7.80 | (270) $false
% 28.11/7.80 |
% 28.11/7.80 |-The branch is then unsatisfiable
% 28.11/7.80 |-Branch two:
% 28.11/7.80 | (640) ~ (all_0_42_42 = e1)
% 28.11/7.80 | (4628) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 28.11/7.80 |
% 28.11/7.80 +-Applying beta-rule and splitting (194), into two cases.
% 28.11/7.80 |-Branch one:
% 28.11/7.80 | (747) all_0_56_56 = e1
% 28.11/7.80 |
% 28.11/7.80 | Combining equations (747,830) yields a new equation:
% 28.11/7.80 | (571) e1 = e0
% 28.11/7.80 |
% 28.11/7.80 | Simplifying 571 yields:
% 28.11/7.80 | (560) e1 = e0
% 28.11/7.80 |
% 28.11/7.80 | Equations (560) can reduce 132 to:
% 28.11/7.80 | (270) $false
% 28.11/7.80 |
% 28.11/7.80 |-The branch is then unsatisfiable
% 28.11/7.80 |-Branch two:
% 28.11/7.80 | (995) ~ (all_0_56_56 = e1)
% 28.11/7.80 | (996) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 28.11/7.80 |
% 28.11/7.80 | Equations (830) can reduce 995 to:
% 28.11/7.80 | (568) ~ (e1 = e0)
% 28.11/7.80 |
% 28.11/7.80 | Simplifying 568 yields:
% 28.11/7.80 | (132) ~ (e1 = e0)
% 28.11/7.80 |
% 28.11/7.80 +-Applying beta-rule and splitting (4628), into two cases.
% 28.11/7.80 |-Branch one:
% 28.11/7.80 | (589) all_0_49_49 = e1
% 28.11/7.80 |
% 28.11/7.80 | Combining equations (563,589) yields a new equation:
% 28.11/7.80 | (560) e1 = e0
% 28.11/7.80 |
% 28.11/7.80 | Equations (560) can reduce 132 to:
% 28.11/7.80 | (270) $false
% 28.11/7.80 |
% 28.11/7.80 |-The branch is then unsatisfiable
% 28.11/7.80 |-Branch two:
% 28.11/7.80 | (543) ~ (all_0_49_49 = e1)
% 28.11/7.80 | (4726) all_0_54_54 = e1 | all_0_59_59 = e1
% 28.11/7.80 |
% 28.11/7.80 +-Applying beta-rule and splitting (4726), into two cases.
% 28.11/7.80 |-Branch one:
% 28.11/7.80 | (875) all_0_54_54 = e1
% 28.11/7.80 |
% 28.11/7.80 | Equations (875) can reduce 1093 to:
% 28.11/7.80 | (769) ~ (e3 = e1)
% 28.11/7.80 |
% 28.11/7.80 | Simplifying 769 yields:
% 28.11/7.80 | (136) ~ (e3 = e1)
% 28.11/7.80 |
% 28.11/7.80 +-Applying beta-rule and splitting (93), into two cases.
% 28.11/7.80 |-Branch one:
% 28.11/7.80 | (402) all_0_59_59 = e4
% 28.11/7.80 |
% 28.11/7.80 | Combining equations (402,412) yields a new equation:
% 28.11/7.80 | (660) e4 = e3
% 28.11/7.80 |
% 28.11/7.80 | Simplifying 660 yields:
% 28.11/7.80 | (359) e4 = e3
% 28.11/7.80 |
% 28.11/7.80 | Equations (359) can reduce 34 to:
% 28.11/7.80 | (270) $false
% 28.11/7.80 |
% 28.11/7.80 |-The branch is then unsatisfiable
% 28.11/7.80 |-Branch two:
% 28.11/7.80 | (280) ~ (all_0_59_59 = e4)
% 28.11/7.80 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 28.11/7.80 |
% 28.11/7.80 +-Applying beta-rule and splitting (407), into two cases.
% 28.11/7.80 |-Branch one:
% 28.11/7.80 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 28.11/7.80 |
% 28.11/7.80 +-Applying beta-rule and splitting (408), into two cases.
% 28.11/7.80 |-Branch one:
% 28.11/7.80 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 28.11/7.80 |
% 28.11/7.80 +-Applying beta-rule and splitting (409), into two cases.
% 28.11/7.80 |-Branch one:
% 28.11/7.80 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 28.11/7.80 |
% 28.11/7.80 | Applying alpha-rule on (410) yields:
% 28.11/7.80 | (411) all_0_43_43 = e0
% 28.11/7.80 | (412) all_0_59_59 = e3
% 28.11/7.80 | (413) ~ (all_0_46_46 = e3)
% 28.11/7.80 |
% 28.11/7.80 | Combining equations (782,411) yields a new equation:
% 28.11/7.80 | (783) e3 = e0
% 28.11/7.80 |
% 28.11/7.80 | Simplifying 783 yields:
% 28.11/7.80 | (784) e3 = e0
% 28.11/7.80 |
% 28.11/7.80 | Equations (784) can reduce 66 to:
% 28.11/7.80 | (270) $false
% 28.11/7.80 |
% 28.11/7.80 |-The branch is then unsatisfiable
% 28.11/7.80 |-Branch two:
% 28.11/7.80 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 28.11/7.80 |
% 28.11/7.80 | Applying alpha-rule on (416) yields:
% 28.11/7.80 | (411) all_0_43_43 = e0
% 28.11/7.80 | (412) all_0_59_59 = e3
% 28.11/7.80 | (419) ~ (all_0_56_56 = e0)
% 28.11/7.80 |
% 28.11/7.80 | Combining equations (782,411) yields a new equation:
% 28.11/7.80 | (783) e3 = e0
% 28.11/7.80 |
% 28.11/7.80 | Simplifying 783 yields:
% 28.11/7.80 | (784) e3 = e0
% 28.11/7.80 |
% 28.11/7.80 | Equations (784) can reduce 66 to:
% 28.11/7.80 | (270) $false
% 28.11/7.80 |
% 28.11/7.80 |-The branch is then unsatisfiable
% 28.11/7.80 |-Branch two:
% 28.11/7.80 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 28.11/7.80 |
% 28.11/7.80 | Applying alpha-rule on (422) yields:
% 28.11/7.80 | (423) all_0_53_53 = e0
% 28.11/7.80 | (424) all_0_59_59 = e1
% 28.11/7.80 | (425) ~ (all_0_54_54 = e1)
% 28.11/7.80 |
% 28.11/7.80 | Combining equations (424,412) yields a new equation:
% 28.11/7.80 | (538) e3 = e1
% 28.11/7.80 |
% 28.11/7.80 | Equations (538) can reduce 136 to:
% 28.11/7.80 | (270) $false
% 28.11/7.80 |
% 28.11/7.80 |-The branch is then unsatisfiable
% 28.11/7.80 |-Branch two:
% 28.11/7.80 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 28.11/7.80 |
% 28.11/7.80 | Applying alpha-rule on (428) yields:
% 28.11/7.80 | (423) all_0_53_53 = e0
% 28.11/7.80 | (424) all_0_59_59 = e1
% 28.11/7.80 | (431) ~ (all_0_58_58 = e0)
% 28.11/7.80 |
% 28.11/7.80 | Combining equations (424,412) yields a new equation:
% 28.11/7.80 | (538) e3 = e1
% 28.11/7.80 |
% 28.11/7.80 | Equations (538) can reduce 136 to:
% 28.11/7.80 | (270) $false
% 28.11/7.80 |
% 28.11/7.80 |-The branch is then unsatisfiable
% 28.11/7.80 |-Branch two:
% 28.11/7.80 | (425) ~ (all_0_54_54 = e1)
% 28.11/7.80 | (424) all_0_59_59 = e1
% 28.11/7.80 |
% 28.11/7.80 | Combining equations (412,424) yields a new equation:
% 28.11/7.80 | (537) e3 = e1
% 28.11/7.80 |
% 28.11/7.80 | Simplifying 537 yields:
% 28.11/7.80 | (538) e3 = e1
% 28.11/7.80 |
% 28.11/7.80 | Equations (538) can reduce 136 to:
% 28.11/7.80 | (270) $false
% 28.11/7.80 |
% 28.11/7.80 |-The branch is then unsatisfiable
% 28.11/7.80 |-Branch two:
% 28.11/7.80 | (1237) ~ (all_0_41_41 = e3)
% 28.11/7.80 | (1238) all_0_41_41 = e4 | all_0_41_41 = e1
% 28.11/7.80 |
% 28.11/7.80 +-Applying beta-rule and splitting (1238), into two cases.
% 28.11/7.80 |-Branch one:
% 28.11/7.80 | (536) all_0_41_41 = e1
% 28.11/7.80 |
% 28.11/7.80 | Equations (536) can reduce 540 to:
% 28.11/7.80 | (270) $false
% 28.11/7.80 |
% 28.11/7.80 |-The branch is then unsatisfiable
% 28.11/7.80 |-Branch two:
% 28.11/7.80 | (540) ~ (all_0_41_41 = e1)
% 28.11/7.80 | (358) all_0_41_41 = e4
% 28.11/7.80 |
% 28.11/7.80 | Equations (358) can reduce 361 to:
% 28.11/7.80 | (270) $false
% 28.11/7.80 |
% 28.11/7.80 |-The branch is then unsatisfiable
% 28.11/7.80 |-Branch two:
% 28.11/7.80 | (697) ~ (all_0_51_51 = e4)
% 28.11/7.80 | (4744) all_0_56_56 = e4
% 28.11/7.80 |
% 28.11/7.80 | Combining equations (830,4744) yields a new equation:
% 28.11/7.80 | (479) e4 = e0
% 28.11/7.80 |
% 28.11/7.80 | Equations (479) can reduce 6 to:
% 28.11/7.80 | (270) $false
% 28.11/7.80 |
% 28.11/7.80 |-The branch is then unsatisfiable
% 28.11/7.80 |-Branch two:
% 28.11/7.80 | (419) ~ (all_0_56_56 = e0)
% 28.11/7.80 | (5667) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1
% 28.11/7.80 |
% 28.11/7.80 +-Applying beta-rule and splitting (75), into two cases.
% 28.11/7.80 |-Branch one:
% 28.11/7.80 | (411) all_0_43_43 = e0
% 28.11/7.80 |
% 28.11/7.80 | Combining equations (782,411) yields a new equation:
% 28.11/7.80 | (783) e3 = e0
% 28.11/7.80 |
% 28.11/7.80 | Simplifying 783 yields:
% 28.11/7.80 | (784) e3 = e0
% 28.11/7.80 |
% 28.11/7.80 | Equations (784) can reduce 66 to:
% 28.11/7.80 | (270) $false
% 28.11/7.80 |
% 28.11/7.80 |-The branch is then unsatisfiable
% 28.11/7.80 |-Branch two:
% 28.11/7.80 | (455) ~ (all_0_43_43 = e0)
% 28.11/7.80 | (940) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 28.11/7.80 |
% 28.11/7.80 | Equations (782) can reduce 455 to:
% 28.11/7.80 | (66) ~ (e3 = e0)
% 28.11/7.80 |
% 28.11/7.80 +-Applying beta-rule and splitting (592), into two cases.
% 28.11/7.80 |-Branch one:
% 28.11/7.80 | (358) all_0_41_41 = e4
% 28.11/7.80 |
% 28.11/7.80 | Equations (358) can reduce 361 to:
% 28.11/7.80 | (270) $false
% 28.11/7.80 |
% 28.11/7.80 |-The branch is then unsatisfiable
% 28.11/7.80 |-Branch two:
% 28.11/7.80 | (361) ~ (all_0_41_41 = e4)
% 28.11/7.80 | (512) all_0_42_42 = e4
% 28.11/7.80 |
% 28.11/7.80 +-Applying beta-rule and splitting (95), into two cases.
% 28.11/7.80 |-Branch one:
% 28.11/7.80 | (1258) all_0_42_42 = e3
% 28.11/7.80 |
% 28.11/7.80 | Combining equations (512,1258) yields a new equation:
% 28.11/7.80 | (660) e4 = e3
% 28.11/7.80 |
% 28.11/7.80 | Simplifying 660 yields:
% 28.11/7.80 | (359) e4 = e3
% 28.11/7.80 |
% 28.11/7.80 | Equations (359) can reduce 34 to:
% 28.11/7.80 | (270) $false
% 28.11/7.80 |
% 28.11/7.80 |-The branch is then unsatisfiable
% 28.11/7.80 |-Branch two:
% 28.11/7.80 | (1316) ~ (all_0_42_42 = e3)
% 28.11/7.80 | (3656) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 28.11/7.80 |
% 28.11/7.80 +-Applying beta-rule and splitting (78), into two cases.
% 28.11/7.80 |-Branch one:
% 28.11/7.80 | (751) all_0_39_39 = e3
% 28.11/7.80 |
% 28.11/7.80 | Combining equations (751,336) yields a new equation:
% 28.11/7.80 | (437) e3 = e2
% 28.11/7.80 |
% 28.11/7.80 | Simplifying 437 yields:
% 28.11/7.80 | (414) e3 = e2
% 28.11/7.80 |
% 28.11/7.80 | Equations (414) can reduce 223 to:
% 28.11/7.80 | (270) $false
% 28.11/7.80 |
% 28.11/7.80 |-The branch is then unsatisfiable
% 28.11/7.80 |-Branch two:
% 28.11/7.80 | (755) ~ (all_0_39_39 = e3)
% 28.11/7.80 | (4262) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 28.11/7.80 |
% 28.11/7.80 | Equations (336) can reduce 755 to:
% 28.11/7.80 | (301) ~ (e3 = e2)
% 28.11/7.80 |
% 28.11/7.80 | Simplifying 301 yields:
% 28.11/7.80 | (223) ~ (e3 = e2)
% 28.11/7.80 |
% 28.11/7.80 +-Applying beta-rule and splitting (176), into two cases.
% 28.11/7.80 |-Branch one:
% 28.11/7.80 | (830) all_0_56_56 = e0
% 28.11/7.80 |
% 28.11/7.80 | Equations (830) can reduce 419 to:
% 28.11/7.80 | (270) $false
% 28.11/7.80 |
% 28.11/7.80 |-The branch is then unsatisfiable
% 28.11/7.80 |-Branch two:
% 28.11/7.80 | (419) ~ (all_0_56_56 = e0)
% 28.11/7.80 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 28.11/7.80 |
% 28.11/7.80 +-Applying beta-rule and splitting (3656), into two cases.
% 28.11/7.80 |-Branch one:
% 28.11/7.80 | (1091) all_0_46_46 = e3
% 28.11/7.80 |
% 28.11/7.80 | Combining equations (497,1091) yields a new equation:
% 28.11/7.80 | (414) e3 = e2
% 28.11/7.80 |
% 28.11/7.80 | Equations (414) can reduce 223 to:
% 28.11/7.80 | (270) $false
% 28.11/7.80 |
% 28.11/7.80 |-The branch is then unsatisfiable
% 28.11/7.80 |-Branch two:
% 28.11/7.80 | (413) ~ (all_0_46_46 = e3)
% 28.11/7.80 | (3700) all_0_54_54 = e3 | all_0_59_59 = e3
% 28.11/7.80 |
% 28.11/7.80 +-Applying beta-rule and splitting (834), into two cases.
% 28.11/7.80 |-Branch one:
% 28.11/7.80 | (2258) all_0_57_57 = e0
% 28.11/7.80 |
% 28.11/7.80 | Combining equations (2258,392) yields a new equation:
% 28.11/7.80 | (316) e2 = e0
% 28.11/7.80 |
% 28.11/7.80 | Equations (316) can reduce 57 to:
% 28.11/7.80 | (270) $false
% 28.11/7.80 |
% 28.11/7.80 |-The branch is then unsatisfiable
% 28.11/7.80 |-Branch two:
% 28.11/7.80 | (2301) ~ (all_0_57_57 = e0)
% 28.11/7.80 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 28.11/7.80 |
% 28.11/7.80 +-Applying beta-rule and splitting (2302), into two cases.
% 28.11/7.80 |-Branch one:
% 28.11/7.80 | (585) all_0_58_58 = e0
% 28.11/7.80 |
% 28.11/7.80 | Equations (585) can reduce 70 to:
% 28.11/7.80 | (584) ~ (all_0_53_53 = e0)
% 28.11/7.80 |
% 28.11/7.80 +-Applying beta-rule and splitting (64), into two cases.
% 28.11/7.80 |-Branch one:
% 28.11/7.80 | (954) all_0_51_51 = e0
% 28.11/7.80 |
% 28.11/7.80 | Equations (954) can reduce 12 to:
% 28.11/7.80 | (3103) ~ (all_0_53_53 = e0)
% 28.11/7.80 |
% 28.11/7.80 | Simplifying 3103 yields:
% 28.11/7.80 | (584) ~ (all_0_53_53 = e0)
% 28.11/7.80 |
% 28.11/7.80 +-Applying beta-rule and splitting (13), into two cases.
% 28.11/7.80 |-Branch one:
% 28.11/7.80 | (576) all_0_53_53 = e2
% 28.11/7.80 |
% 28.11/7.80 | Equations (576) can reduce 259 to:
% 28.11/7.80 | (270) $false
% 28.11/7.80 |
% 28.11/7.80 |-The branch is then unsatisfiable
% 28.11/7.80 |-Branch two:
% 28.11/7.80 | (259) ~ (all_0_53_53 = e2)
% 28.11/7.80 | (5715) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 28.11/7.80 |
% 28.11/7.80 +-Applying beta-rule and splitting (5715), into two cases.
% 28.11/7.80 |-Branch one:
% 28.11/7.80 | (423) all_0_53_53 = e0
% 28.11/7.80 |
% 28.11/7.80 | Equations (423) can reduce 584 to:
% 28.11/7.80 | (270) $false
% 28.11/7.80 |
% 28.11/7.80 |-The branch is then unsatisfiable
% 28.11/7.80 |-Branch two:
% 28.11/7.80 | (584) ~ (all_0_53_53 = e0)
% 28.11/7.80 | (5719) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1
% 28.11/7.80 |
% 28.11/7.80 +-Applying beta-rule and splitting (5719), into two cases.
% 28.11/7.80 |-Branch one:
% 28.11/7.80 | (1114) all_0_53_53 = e3
% 28.11/7.80 |
% 28.11/7.80 | Equations (1114) can reduce 356 to:
% 28.11/7.80 | (270) $false
% 28.11/7.80 |
% 28.11/7.80 |-The branch is then unsatisfiable
% 28.11/7.80 |-Branch two:
% 28.11/7.80 | (356) ~ (all_0_53_53 = e3)
% 28.11/7.80 | (5723) all_0_53_53 = e4 | all_0_53_53 = e1
% 28.11/7.80 |
% 28.11/7.80 +-Applying beta-rule and splitting (5723), into two cases.
% 28.11/7.80 |-Branch one:
% 28.11/7.80 | (853) all_0_53_53 = e1
% 28.11/7.80 |
% 28.11/7.81 | Equations (853) can reduce 252 to:
% 28.11/7.81 | (2131) ~ (all_0_54_54 = e1)
% 28.11/7.81 |
% 28.11/7.81 | Simplifying 2131 yields:
% 28.11/7.81 | (425) ~ (all_0_54_54 = e1)
% 28.11/7.81 |
% 28.11/7.81 | Equations (853) can reduce 599 to:
% 28.11/7.81 | (1021) ~ (e4 = e1)
% 28.11/7.81 |
% 28.11/7.81 | Simplifying 1021 yields:
% 28.11/7.81 | (251) ~ (e4 = e1)
% 28.11/7.81 |
% 28.11/7.81 | Equations (853) can reduce 356 to:
% 28.11/7.81 | (769) ~ (e3 = e1)
% 28.11/7.81 |
% 28.11/7.81 | Simplifying 769 yields:
% 28.11/7.81 | (136) ~ (e3 = e1)
% 28.11/7.81 |
% 28.11/7.81 | Equations (853) can reduce 584 to:
% 28.11/7.81 | (132) ~ (e1 = e0)
% 28.11/7.81 |
% 28.11/7.81 +-Applying beta-rule and splitting (127), into two cases.
% 28.11/7.81 |-Branch one:
% 28.11/7.81 | (541) all_0_42_42 = e1
% 28.11/7.81 |
% 28.11/7.81 | Combining equations (512,541) yields a new equation:
% 28.11/7.81 | (525) e4 = e1
% 28.11/7.81 |
% 28.11/7.81 | Simplifying 525 yields:
% 28.11/7.81 | (526) e4 = e1
% 28.11/7.81 |
% 28.11/7.81 | Equations (526) can reduce 251 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (640) ~ (all_0_42_42 = e1)
% 28.11/7.81 | (4628) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 28.11/7.81 |
% 28.11/7.81 +-Applying beta-rule and splitting (4628), into two cases.
% 28.11/7.81 |-Branch one:
% 28.11/7.81 | (589) all_0_49_49 = e1
% 28.11/7.81 |
% 28.11/7.81 | Combining equations (563,589) yields a new equation:
% 28.11/7.81 | (560) e1 = e0
% 28.11/7.81 |
% 28.11/7.81 | Equations (560) can reduce 132 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (543) ~ (all_0_49_49 = e1)
% 28.11/7.81 | (4726) all_0_54_54 = e1 | all_0_59_59 = e1
% 28.11/7.81 |
% 28.11/7.81 +-Applying beta-rule and splitting (4726), into two cases.
% 28.11/7.81 |-Branch one:
% 28.11/7.81 | (875) all_0_54_54 = e1
% 28.11/7.81 |
% 28.11/7.81 | Equations (875) can reduce 425 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (425) ~ (all_0_54_54 = e1)
% 28.11/7.81 | (424) all_0_59_59 = e1
% 28.11/7.81 |
% 28.11/7.81 +-Applying beta-rule and splitting (3700), into two cases.
% 28.11/7.81 |-Branch one:
% 28.11/7.81 | (1119) all_0_54_54 = e3
% 28.11/7.81 |
% 28.11/7.81 | Equations (1119) can reduce 1093 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (1093) ~ (all_0_54_54 = e3)
% 28.11/7.81 | (412) all_0_59_59 = e3
% 28.11/7.81 |
% 28.11/7.81 | Combining equations (424,412) yields a new equation:
% 28.11/7.81 | (538) e3 = e1
% 28.11/7.81 |
% 28.11/7.81 | Equations (538) can reduce 136 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (874) ~ (all_0_53_53 = e1)
% 28.11/7.81 | (367) all_0_53_53 = e4
% 28.11/7.81 |
% 28.11/7.81 | Equations (367) can reduce 599 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (987) ~ (all_0_51_51 = e0)
% 28.11/7.81 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 28.11/7.81 |
% 28.11/7.81 +-Applying beta-rule and splitting (3067), into two cases.
% 28.11/7.81 |-Branch one:
% 28.11/7.81 | (827) all_0_52_52 = e0
% 28.11/7.81 |
% 28.11/7.81 | Combining equations (827,864) yields a new equation:
% 28.11/7.81 | (784) e3 = e0
% 28.11/7.81 |
% 28.11/7.81 | Equations (784) can reduce 66 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (925) ~ (all_0_52_52 = e0)
% 28.11/7.81 | (3073) all_0_53_53 = e0 | all_0_54_54 = e0
% 28.11/7.81 |
% 28.11/7.81 +-Applying beta-rule and splitting (3073), into two cases.
% 28.11/7.81 |-Branch one:
% 28.11/7.81 | (423) all_0_53_53 = e0
% 28.11/7.81 |
% 28.11/7.81 | Equations (423) can reduce 584 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (584) ~ (all_0_53_53 = e0)
% 28.11/7.81 | (3084) all_0_54_54 = e0
% 28.11/7.81 |
% 28.11/7.81 | Equations (3084) can reduce 3011 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (431) ~ (all_0_58_58 = e0)
% 28.11/7.81 | (2308) all_0_59_59 = e0
% 28.11/7.81 |
% 28.11/7.81 | Equations (2308) can reduce 4001 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (786) ~ (all_0_43_43 = e3)
% 28.11/7.81 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 28.11/7.81 |
% 28.11/7.81 +-Applying beta-rule and splitting (219), into two cases.
% 28.11/7.81 |-Branch one:
% 28.11/7.81 | (351) all_0_41_41 = e3
% 28.11/7.81 |
% 28.11/7.81 | Equations (351) can reduce 361 to:
% 28.11/7.81 | (719) ~ (e4 = e3)
% 28.11/7.81 |
% 28.11/7.81 | Simplifying 719 yields:
% 28.11/7.81 | (34) ~ (e4 = e3)
% 28.11/7.81 |
% 28.11/7.81 | Equations (351) can reduce 331 to:
% 28.11/7.81 | (223) ~ (e3 = e2)
% 28.11/7.81 |
% 28.11/7.81 | Equations (351) can reduce 232 to:
% 28.11/7.81 | (66) ~ (e3 = e0)
% 28.11/7.81 |
% 28.11/7.81 +-Applying beta-rule and splitting (787), into two cases.
% 28.11/7.81 |-Branch one:
% 28.11/7.81 | (858) all_0_44_44 = e3
% 28.11/7.81 |
% 28.11/7.81 | Combining equations (621,858) yields a new equation:
% 28.11/7.81 | (784) e3 = e0
% 28.11/7.81 |
% 28.11/7.81 | Equations (784) can reduce 66 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (862) ~ (all_0_44_44 = e3)
% 28.11/7.81 | (1070) all_0_45_45 = e3 | all_0_46_46 = e3
% 28.11/7.81 |
% 28.11/7.81 +-Applying beta-rule and splitting (1070), into two cases.
% 28.11/7.81 |-Branch one:
% 28.11/7.81 | (505) all_0_45_45 = e3
% 28.11/7.81 |
% 28.11/7.81 | Combining equations (363,505) yields a new equation:
% 28.11/7.81 | (660) e4 = e3
% 28.11/7.81 |
% 28.11/7.81 | Simplifying 660 yields:
% 28.11/7.81 | (359) e4 = e3
% 28.11/7.81 |
% 28.11/7.81 | Equations (359) can reduce 34 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (354) ~ (all_0_45_45 = e3)
% 28.11/7.81 | (1091) all_0_46_46 = e3
% 28.11/7.81 |
% 28.11/7.81 | Combining equations (497,1091) yields a new equation:
% 28.11/7.81 | (414) e3 = e2
% 28.11/7.81 |
% 28.11/7.81 | Equations (414) can reduce 223 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (1237) ~ (all_0_41_41 = e3)
% 28.11/7.81 | (1508) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 28.11/7.81 |
% 28.11/7.81 +-Applying beta-rule and splitting (592), into two cases.
% 28.11/7.81 |-Branch one:
% 28.11/7.81 | (358) all_0_41_41 = e4
% 28.11/7.81 |
% 28.11/7.81 | Equations (358) can reduce 361 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (361) ~ (all_0_41_41 = e4)
% 28.11/7.81 | (512) all_0_42_42 = e4
% 28.11/7.81 |
% 28.11/7.81 | Equations (512) can reduce 94 to:
% 28.11/7.81 | (361) ~ (all_0_41_41 = e4)
% 28.11/7.81 |
% 28.11/7.81 +-Applying beta-rule and splitting (217), into two cases.
% 28.11/7.81 |-Branch one:
% 28.11/7.81 | (436) all_0_41_41 = e2
% 28.11/7.81 |
% 28.11/7.81 | Equations (436) can reduce 331 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (331) ~ (all_0_41_41 = e2)
% 28.11/7.81 | (709) all_0_41_41 = e4 | all_0_41_41 = e3 | all_0_41_41 = e1
% 28.11/7.81 |
% 28.11/7.81 +-Applying beta-rule and splitting (709), into two cases.
% 28.11/7.81 |-Branch one:
% 28.11/7.81 | (351) all_0_41_41 = e3
% 28.11/7.81 |
% 28.11/7.81 | Equations (351) can reduce 1237 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (1237) ~ (all_0_41_41 = e3)
% 28.11/7.81 | (1238) all_0_41_41 = e4 | all_0_41_41 = e1
% 28.11/7.81 |
% 28.11/7.81 +-Applying beta-rule and splitting (1238), into two cases.
% 28.11/7.81 |-Branch one:
% 28.11/7.81 | (536) all_0_41_41 = e1
% 28.11/7.81 |
% 28.11/7.81 | Equations (536) can reduce 540 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (540) ~ (all_0_41_41 = e1)
% 28.11/7.81 | (358) all_0_41_41 = e4
% 28.11/7.81 |
% 28.11/7.81 | Equations (358) can reduce 361 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (352) ~ (all_0_45_45 = e4)
% 28.11/7.81 | (517) all_0_46_46 = e4
% 28.11/7.81 |
% 28.11/7.81 | Combining equations (497,517) yields a new equation:
% 28.11/7.81 | (269) e4 = e2
% 28.11/7.81 |
% 28.11/7.81 | Equations (269) can reduce 231 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (1436) ~ (all_0_46_46 = e2)
% 28.11/7.81 | (3824) all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 28.11/7.81 |
% 28.11/7.81 +-Applying beta-rule and splitting (3824), into two cases.
% 28.11/7.81 |-Branch one:
% 28.11/7.81 | (307) all_0_49_49 = e2
% 28.11/7.81 |
% 28.11/7.81 | Combining equations (563,307) yields a new equation:
% 28.11/7.81 | (316) e2 = e0
% 28.11/7.81 |
% 28.11/7.81 | Equations (316) can reduce 57 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (296) ~ (all_0_49_49 = e2)
% 28.11/7.81 | (3829) all_0_54_54 = e2 | all_0_59_59 = e2
% 28.11/7.81 |
% 28.11/7.81 +-Applying beta-rule and splitting (3829), into two cases.
% 28.11/7.81 |-Branch one:
% 28.11/7.81 | (3657) all_0_54_54 = e2
% 28.11/7.81 |
% 28.11/7.81 | Equations (3657) can reduce 261 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (261) ~ (all_0_54_54 = e2)
% 28.11/7.81 | (399) all_0_59_59 = e2
% 28.11/7.81 |
% 28.11/7.81 | Equations (399) can reduce 701 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (291) ~ (all_0_39_39 = e2)
% 28.11/7.81 | (4205) all_0_43_43 = e2 | all_0_47_47 = e2 | all_0_51_51 = e2 | all_0_56_56 = e2
% 28.11/7.81 |
% 28.11/7.81 +-Applying beta-rule and splitting (164), into two cases.
% 28.11/7.81 |-Branch one:
% 28.11/7.81 | (336) all_0_39_39 = e2
% 28.11/7.81 |
% 28.11/7.81 | Equations (336) can reduce 291 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (291) ~ (all_0_39_39 = e2)
% 28.11/7.81 | (630) all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 28.11/7.81 |
% 28.11/7.81 +-Applying beta-rule and splitting (630), into two cases.
% 28.11/7.81 |-Branch one:
% 28.11/7.81 | (327) all_0_40_40 = e2
% 28.11/7.81 |
% 28.11/7.81 | Combining equations (530,327) yields a new equation:
% 28.11/7.81 | (322) e2 = e1
% 28.11/7.81 |
% 28.11/7.81 | Equations (322) can reduce 141 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (602) ~ (all_0_40_40 = e2)
% 28.11/7.81 | (1251) all_0_41_41 = e2 | all_0_42_42 = e2
% 28.11/7.81 |
% 28.11/7.81 +-Applying beta-rule and splitting (453), into two cases.
% 28.11/7.81 |-Branch one:
% 28.11/7.81 | (370) all_0_44_44 = e2
% 28.11/7.81 |
% 28.11/7.81 | Combining equations (621,370) yields a new equation:
% 28.11/7.81 | (316) e2 = e0
% 28.11/7.81 |
% 28.11/7.81 | Equations (316) can reduce 57 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (333) ~ (all_0_44_44 = e2)
% 28.11/7.81 | (493) all_0_45_45 = e2 | all_0_46_46 = e2
% 28.11/7.81 |
% 28.11/7.81 +-Applying beta-rule and splitting (1251), into two cases.
% 28.11/7.81 |-Branch one:
% 28.11/7.81 | (436) all_0_41_41 = e2
% 28.11/7.81 |
% 28.11/7.81 | Equations (436) can reduce 331 to:
% 28.11/7.81 | (270) $false
% 28.11/7.81 |
% 28.11/7.81 |-The branch is then unsatisfiable
% 28.11/7.81 |-Branch two:
% 28.11/7.81 | (331) ~ (all_0_41_41 = e2)
% 28.11/7.81 | (698) all_0_42_42 = e2
% 28.11/7.81 |
% 28.11/7.81 | Equations (698) can reduce 18 to:
% 28.11/7.81 | (1435) ~ (all_0_46_46 = e2)
% 28.11/7.81 |
% 28.11/7.81 | Simplifying 1435 yields:
% 28.11/7.81 | (1436) ~ (all_0_46_46 = e2)
% 28.11/7.82 |
% 28.11/7.82 +-Applying beta-rule and splitting (493), into two cases.
% 28.11/7.82 |-Branch one:
% 28.11/7.82 | (374) all_0_45_45 = e2
% 28.11/7.82 |
% 28.11/7.82 | Equations (374) can reduce 434 to:
% 28.11/7.82 | (270) $false
% 28.11/7.82 |
% 28.11/7.82 |-The branch is then unsatisfiable
% 28.11/7.82 |-Branch two:
% 28.11/7.82 | (434) ~ (all_0_45_45 = e2)
% 28.11/7.82 | (497) all_0_46_46 = e2
% 28.11/7.82 |
% 28.11/7.82 | Equations (497) can reduce 1436 to:
% 28.11/7.82 | (270) $false
% 28.11/7.82 |
% 28.11/7.82 |-The branch is then unsatisfiable
% 28.11/7.82 |-Branch two:
% 28.11/7.82 | (826) ~ (all_0_52_52 = e3)
% 28.11/7.82 | (869) all_0_57_57 = e3
% 28.11/7.82 |
% 28.11/7.82 | Combining equations (869,392) yields a new equation:
% 28.11/7.82 | (437) e3 = e2
% 28.11/7.82 |
% 28.11/7.82 | Simplifying 437 yields:
% 28.11/7.82 | (414) e3 = e2
% 28.11/7.82 |
% 28.11/7.82 | Equations (414) can reduce 223 to:
% 28.11/7.82 | (270) $false
% 28.11/7.82 |
% 28.11/7.82 |-The branch is then unsatisfiable
% 28.11/7.82 |-Branch two:
% 28.11/7.82 | (625) ~ (all_0_44_44 = e0)
% 28.11/7.82 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 28.11/7.82 |
% 28.11/7.82 +-Applying beta-rule and splitting (373), into two cases.
% 28.11/7.82 |-Branch one:
% 28.11/7.82 | (621) all_0_44_44 = e0
% 28.11/7.82 |
% 28.11/7.82 | Equations (621) can reduce 625 to:
% 28.11/7.82 | (270) $false
% 28.11/7.82 |
% 28.11/7.82 |-The branch is then unsatisfiable
% 28.11/7.82 |-Branch two:
% 28.11/7.82 | (625) ~ (all_0_44_44 = e0)
% 28.11/7.82 | (858) all_0_44_44 = e3
% 28.11/7.82 |
% 28.11/7.82 | Equations (858) can reduce 122 to:
% 28.11/7.82 | (825) ~ (all_0_52_52 = e3)
% 28.11/7.82 |
% 28.11/7.82 | Simplifying 825 yields:
% 28.11/7.82 | (826) ~ (all_0_52_52 = e3)
% 28.11/7.82 |
% 28.11/7.82 | Equations (858) can reduce 131 to:
% 28.11/7.82 | (136) ~ (e3 = e1)
% 28.11/7.82 |
% 28.11/7.82 | From (858) and (165) follows:
% 28.11/7.82 | (3499) op(e2, e3) = all_0_15_15
% 28.11/7.82 |
% 28.11/7.82 +-Applying beta-rule and splitting (90), into two cases.
% 28.11/7.82 |-Branch one:
% 28.11/7.82 | (685) all_0_52_52 = e2
% 28.11/7.82 |
% 28.11/7.82 | Equations (685) can reduce 257 to:
% 28.11/7.82 | (270) $false
% 28.11/7.82 |
% 28.11/7.82 |-The branch is then unsatisfiable
% 28.11/7.82 |-Branch two:
% 28.11/7.82 | (257) ~ (all_0_52_52 = e2)
% 28.11/7.82 | (688) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 28.11/7.82 |
% 28.11/7.82 +-Applying beta-rule and splitting (688), into two cases.
% 28.11/7.82 |-Branch one:
% 28.11/7.82 | (827) all_0_52_52 = e0
% 28.11/7.82 |
% 28.11/7.82 | Equations (827) can reduce 230 to:
% 28.11/7.82 | (456) ~ (e4 = e0)
% 28.11/7.82 |
% 28.11/7.82 | Simplifying 456 yields:
% 28.11/7.82 | (6) ~ (e4 = e0)
% 28.11/7.82 |
% 28.11/7.82 | Equations (827) can reduce 642 to:
% 28.11/7.82 | (568) ~ (e1 = e0)
% 28.11/7.82 |
% 28.11/7.82 | Simplifying 568 yields:
% 28.11/7.82 | (132) ~ (e1 = e0)
% 28.11/7.82 |
% 28.11/7.82 | From (827) and (27) follows:
% 28.11/7.82 | (3482) op(e2, e0) = all_0_17_17
% 28.11/7.82 |
% 28.11/7.82 | Instantiating formula (201) with e2, e3, all_0_15_15, e1 and discharging atoms op(e2, e3) = all_0_15_15, op(e2, e3) = e1, yields:
% 28.11/7.82 | (5879) all_0_15_15 = e1
% 28.11/7.82 |
% 28.11/7.82 | Instantiating formula (201) with e2, e0, all_0_17_17, e0 and discharging atoms op(e2, e0) = all_0_17_17, op(e2, e0) = e0, yields:
% 28.11/7.82 | (5880) all_0_17_17 = e0
% 28.11/7.82 |
% 28.11/7.82 +-Applying beta-rule and splitting (87), into two cases.
% 28.11/7.82 |-Branch one:
% 28.11/7.82 | (650) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 28.11/7.82 |
% 28.11/7.82 +-Applying beta-rule and splitting (650), into two cases.
% 28.11/7.82 |-Branch one:
% 28.11/7.82 | (651) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 28.11/7.82 |
% 28.11/7.82 +-Applying beta-rule and splitting (651), into two cases.
% 28.11/7.82 |-Branch one:
% 28.11/7.82 | (652) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 28.11/7.82 |
% 28.11/7.82 | Applying alpha-rule on (652) yields:
% 28.11/7.82 | (653) all_0_13_13 = e4
% 28.11/7.82 | (654) ~ (all_0_14_14 = e2)
% 28.11/7.82 |
% 28.11/7.82 | Combining equations (4829,653) yields a new equation:
% 28.11/7.82 | (269) e4 = e2
% 28.11/7.82 |
% 28.11/7.82 | Equations (269) can reduce 231 to:
% 28.11/7.82 | (270) $false
% 28.11/7.82 |
% 28.11/7.82 |-The branch is then unsatisfiable
% 28.11/7.82 |-Branch two:
% 28.11/7.82 | (657) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 28.11/7.82 |
% 28.11/7.82 | Applying alpha-rule on (657) yields:
% 28.11/7.82 | (658) all_0_15_15 = e3
% 28.11/7.82 | (659) ~ (all_0_16_16 = e2)
% 28.11/7.82 |
% 28.11/7.82 | Combining equations (658,5879) yields a new equation:
% 28.11/7.82 | (537) e3 = e1
% 28.11/7.82 |
% 28.11/7.82 | Simplifying 537 yields:
% 28.11/7.82 | (538) e3 = e1
% 28.11/7.82 |
% 28.11/7.82 | Equations (538) can reduce 136 to:
% 28.11/7.82 | (270) $false
% 28.11/7.82 |
% 28.11/7.82 |-The branch is then unsatisfiable
% 28.11/7.82 |-Branch two:
% 28.11/7.82 | (663) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 28.11/7.82 |
% 28.11/7.82 | Applying alpha-rule on (663) yields:
% 28.11/7.82 | (664) all_0_17_17 = e1
% 28.11/7.82 | (665) ~ (all_0_18_18 = e2)
% 28.11/7.82 |
% 28.11/7.82 | Combining equations (5880,664) yields a new equation:
% 28.11/7.82 | (560) e1 = e0
% 28.11/7.82 |
% 28.11/7.82 | Equations (560) can reduce 132 to:
% 28.11/7.82 | (270) $false
% 28.11/7.82 |
% 28.11/7.82 |-The branch is then unsatisfiable
% 28.11/7.82 |-Branch two:
% 28.11/7.82 | (1762) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 28.11/7.82 |
% 28.11/7.82 | Applying alpha-rule on (1762) yields:
% 28.11/7.82 | (1763) all_0_19_19 = e0
% 28.11/7.82 | (1764) ~ (all_0_20_20 = e2)
% 28.11/7.82 |
% 28.11/7.82 | Combining equations (1763,3391) yields a new equation:
% 28.11/7.82 | (479) e4 = e0
% 28.11/7.82 |
% 28.11/7.82 | Equations (479) can reduce 6 to:
% 28.11/7.82 | (270) $false
% 28.11/7.82 |
% 28.11/7.82 |-The branch is then unsatisfiable
% 28.11/7.82 |-Branch two:
% 28.11/7.82 | (925) ~ (all_0_52_52 = e0)
% 28.11/7.82 | (926) all_0_52_52 = e3 | all_0_52_52 = e1
% 28.11/7.82 |
% 28.11/7.82 +-Applying beta-rule and splitting (926), into two cases.
% 28.11/7.82 |-Branch one:
% 28.11/7.82 | (864) all_0_52_52 = e3
% 28.11/7.82 |
% 28.11/7.82 | Equations (864) can reduce 826 to:
% 28.11/7.82 | (270) $false
% 28.11/7.82 |
% 28.11/7.82 |-The branch is then unsatisfiable
% 28.11/7.82 |-Branch two:
% 28.11/7.82 | (826) ~ (all_0_52_52 = e3)
% 28.11/7.82 | (848) all_0_52_52 = e1
% 28.11/7.82 |
% 28.11/7.82 | Equations (848) can reduce 642 to:
% 28.11/7.82 | (270) $false
% 28.11/7.82 |
% 28.11/7.82 |-The branch is then unsatisfiable
% 28.11/7.82 |-Branch two:
% 28.11/7.82 | (534) ~ (all_0_40_40 = e1)
% 28.11/7.82 | (3352) all_0_52_52 = e1 | all_0_57_57 = e1
% 28.11/7.82 |
% 28.11/7.82 +-Applying beta-rule and splitting (603), into two cases.
% 28.11/7.82 |-Branch one:
% 28.11/7.82 | (671) all_0_40_40 = e3
% 28.11/7.82 |
% 28.11/7.82 | Combining equations (671,285) yields a new equation:
% 28.11/7.82 | (3452) all_0_0_0 = e3
% 28.11/7.82 |
% 28.11/7.82 | Equations (671) can reduce 147 to:
% 28.11/7.82 | (1329) ~ (all_0_41_41 = e3)
% 28.11/7.82 |
% 28.11/7.82 | Simplifying 1329 yields:
% 28.11/7.82 | (1237) ~ (all_0_41_41 = e3)
% 28.11/7.82 |
% 28.11/7.82 | Equations (671) can reduce 15 to:
% 28.11/7.82 | (5917) ~ (all_0_44_44 = e3)
% 28.11/7.82 |
% 28.11/7.82 | Simplifying 5917 yields:
% 28.11/7.82 | (862) ~ (all_0_44_44 = e3)
% 28.11/7.82 |
% 28.11/7.82 | Equations (671) can reduce 137 to:
% 28.11/7.82 | (825) ~ (all_0_52_52 = e3)
% 28.11/7.82 |
% 28.11/7.82 | Simplifying 825 yields:
% 28.11/7.82 | (826) ~ (all_0_52_52 = e3)
% 28.11/7.82 |
% 28.11/7.82 | From (671) and (68) follows:
% 28.11/7.82 | (5921) op(e2, e3) = all_0_13_13
% 28.11/7.82 |
% 28.11/7.82 +-Applying beta-rule and splitting (373), into two cases.
% 28.11/7.82 |-Branch one:
% 28.11/7.82 | (621) all_0_44_44 = e0
% 28.11/7.82 |
% 28.11/7.82 | Equations (621) can reduce 45 to:
% 28.11/7.82 | (456) ~ (e4 = e0)
% 28.11/7.82 |
% 28.11/7.82 | Simplifying 456 yields:
% 28.11/7.82 | (6) ~ (e4 = e0)
% 28.11/7.82 |
% 28.11/7.82 | Equations (621) can reduce 862 to:
% 28.11/7.82 | (788) ~ (e3 = e0)
% 28.11/7.82 |
% 28.11/7.82 | Simplifying 788 yields:
% 28.11/7.82 | (66) ~ (e3 = e0)
% 28.11/7.82 |
% 28.11/7.82 | From (621) and (165) follows:
% 28.11/7.82 | (3395) op(e2, e0) = all_0_15_15
% 28.11/7.82 |
% 28.11/7.82 +-Applying beta-rule and splitting (3352), into two cases.
% 28.11/7.82 |-Branch one:
% 28.11/7.82 | (848) all_0_52_52 = e1
% 28.11/7.82 |
% 28.11/7.82 | Equations (848) can reduce 230 to:
% 28.11/7.82 | (1021) ~ (e4 = e1)
% 28.11/7.82 |
% 28.11/7.82 | Simplifying 1021 yields:
% 28.11/7.82 | (251) ~ (e4 = e1)
% 28.11/7.82 |
% 28.11/7.82 | Equations (848) can reduce 826 to:
% 28.11/7.82 | (769) ~ (e3 = e1)
% 28.11/7.82 |
% 28.11/7.82 | Simplifying 769 yields:
% 28.11/7.82 | (136) ~ (e3 = e1)
% 28.11/7.82 |
% 28.11/7.82 | From (848) and (27) follows:
% 28.11/7.82 | (5933) op(e2, e1) = all_0_17_17
% 28.11/7.82 |
% 28.11/7.82 +-Applying beta-rule and splitting (186), into two cases.
% 28.11/7.82 |-Branch one:
% 28.11/7.82 | (336) all_0_39_39 = e2
% 28.11/7.82 |
% 28.11/7.82 | Equations (336) can reduce 184 to:
% 28.11/7.82 | (1336) ~ (all_0_42_42 = e2)
% 28.11/7.82 |
% 28.11/7.82 | Simplifying 1336 yields:
% 28.11/7.82 | (498) ~ (all_0_42_42 = e2)
% 28.11/7.82 |
% 28.11/7.82 | Equations (336) can reduce 167 to:
% 28.11/7.82 | (5937) ~ (all_0_43_43 = e2)
% 28.11/7.82 |
% 28.11/7.82 | Simplifying 5937 yields:
% 28.11/7.82 | (292) ~ (all_0_43_43 = e2)
% 28.11/7.82 |
% 28.11/7.82 | Equations (336) can reduce 101 to:
% 28.11/7.82 | (57) ~ (e2 = e0)
% 28.11/7.82 |
% 28.11/7.82 +-Applying beta-rule and splitting (47), into two cases.
% 28.11/7.82 |-Branch one:
% 28.11/7.82 | (450) all_0_43_43 = e2
% 28.11/7.82 |
% 28.11/7.82 | Equations (450) can reduce 292 to:
% 28.11/7.82 | (270) $false
% 28.11/7.82 |
% 28.11/7.82 |-The branch is then unsatisfiable
% 28.11/7.82 |-Branch two:
% 28.11/7.82 | (292) ~ (all_0_43_43 = e2)
% 28.11/7.82 | (453) all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2
% 28.11/7.82 |
% 28.11/7.82 +-Applying beta-rule and splitting (209), into two cases.
% 28.11/7.82 |-Branch one:
% 28.11/7.82 | (698) all_0_42_42 = e2
% 28.11/7.82 |
% 28.11/7.82 | Equations (698) can reduce 498 to:
% 28.11/7.82 | (270) $false
% 28.11/7.82 |
% 28.11/7.82 |-The branch is then unsatisfiable
% 28.11/7.82 |-Branch two:
% 28.11/7.82 | (498) ~ (all_0_42_42 = e2)
% 28.11/7.82 | (1732) all_0_46_46 = e2 | all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 28.11/7.82 |
% 28.11/7.82 +-Applying beta-rule and splitting (453), into two cases.
% 28.11/7.82 |-Branch one:
% 28.11/7.82 | (370) all_0_44_44 = e2
% 28.11/7.82 |
% 28.11/7.82 | Combining equations (621,370) yields a new equation:
% 28.11/7.82 | (316) e2 = e0
% 28.11/7.82 |
% 28.11/7.82 | Equations (316) can reduce 57 to:
% 28.11/7.82 | (270) $false
% 28.11/7.82 |
% 28.11/7.82 |-The branch is then unsatisfiable
% 28.11/7.82 |-Branch two:
% 28.11/7.82 | (333) ~ (all_0_44_44 = e2)
% 28.11/7.82 | (493) all_0_45_45 = e2 | all_0_46_46 = e2
% 28.11/7.82 |
% 28.11/7.82 | Equations (621) can reduce 333 to:
% 28.11/7.82 | (566) ~ (e2 = e0)
% 28.11/7.82 |
% 28.11/7.82 | Simplifying 566 yields:
% 28.11/7.82 | (57) ~ (e2 = e0)
% 28.11/7.82 |
% 28.11/7.82 +-Applying beta-rule and splitting (1732), into two cases.
% 28.11/7.82 |-Branch one:
% 28.11/7.82 | (497) all_0_46_46 = e2
% 28.11/7.82 |
% 28.11/7.82 | Equations (497) can reduce 106 to:
% 28.11/7.82 | (141) ~ (e2 = e1)
% 28.11/7.82 |
% 28.11/7.82 | Instantiating formula (201) with e2, e3, all_0_13_13, e1 and discharging atoms op(e2, e3) = all_0_13_13, op(e2, e3) = e1, yields:
% 28.11/7.82 | (5957) all_0_13_13 = e1
% 28.11/7.82 |
% 28.11/7.82 | Instantiating formula (201) with e2, e1, all_0_17_17, e2 and discharging atoms op(e2, e1) = all_0_17_17, op(e2, e1) = e2, yields:
% 28.11/7.82 | (3413) all_0_17_17 = e2
% 28.11/7.82 |
% 28.11/7.82 | Instantiating formula (201) with e2, e0, all_0_15_15, e0 and discharging atoms op(e2, e0) = all_0_15_15, op(e2, e0) = e0, yields:
% 28.11/7.82 | (5959) all_0_15_15 = e0
% 28.11/7.82 |
% 28.11/7.82 +-Applying beta-rule and splitting (87), into two cases.
% 28.11/7.82 |-Branch one:
% 28.11/7.82 | (650) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 28.11/7.82 |
% 28.11/7.82 +-Applying beta-rule and splitting (650), into two cases.
% 28.11/7.82 |-Branch one:
% 28.11/7.82 | (651) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 28.11/7.82 |
% 28.11/7.82 +-Applying beta-rule and splitting (651), into two cases.
% 28.11/7.82 |-Branch one:
% 28.11/7.82 | (652) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 28.11/7.82 |
% 28.11/7.82 | Applying alpha-rule on (652) yields:
% 28.11/7.82 | (653) all_0_13_13 = e4
% 28.11/7.82 | (654) ~ (all_0_14_14 = e2)
% 28.11/7.82 |
% 28.11/7.82 | Combining equations (5957,653) yields a new equation:
% 28.11/7.82 | (526) e4 = e1
% 28.11/7.82 |
% 28.11/7.83 | Equations (526) can reduce 251 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (657) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 28.11/7.83 |
% 28.11/7.83 | Applying alpha-rule on (657) yields:
% 28.11/7.83 | (658) all_0_15_15 = e3
% 28.11/7.83 | (659) ~ (all_0_16_16 = e2)
% 28.11/7.83 |
% 28.11/7.83 | Combining equations (5959,658) yields a new equation:
% 28.11/7.83 | (784) e3 = e0
% 28.11/7.83 |
% 28.11/7.83 | Equations (784) can reduce 66 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (663) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 28.11/7.83 |
% 28.11/7.83 | Applying alpha-rule on (663) yields:
% 28.11/7.83 | (664) all_0_17_17 = e1
% 28.11/7.83 | (665) ~ (all_0_18_18 = e2)
% 28.11/7.83 |
% 28.11/7.83 | Combining equations (3413,664) yields a new equation:
% 28.11/7.83 | (531) e2 = e1
% 28.11/7.83 |
% 28.11/7.83 | Simplifying 531 yields:
% 28.11/7.83 | (322) e2 = e1
% 28.11/7.83 |
% 28.11/7.83 | Equations (322) can reduce 141 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (1762) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 28.11/7.83 |
% 28.11/7.83 | Applying alpha-rule on (1762) yields:
% 28.11/7.83 | (1763) all_0_19_19 = e0
% 28.11/7.83 | (1764) ~ (all_0_20_20 = e2)
% 28.11/7.83 |
% 28.11/7.83 | Combining equations (3391,1763) yields a new equation:
% 28.11/7.83 | (478) e4 = e0
% 28.11/7.83 |
% 28.11/7.83 | Simplifying 478 yields:
% 28.11/7.83 | (479) e4 = e0
% 28.11/7.83 |
% 28.11/7.83 | Equations (479) can reduce 6 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (1436) ~ (all_0_46_46 = e2)
% 28.11/7.83 | (3824) all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 28.11/7.83 |
% 28.11/7.83 +-Applying beta-rule and splitting (3824), into two cases.
% 28.11/7.83 |-Branch one:
% 28.11/7.83 | (307) all_0_49_49 = e2
% 28.11/7.83 |
% 28.11/7.83 | Combining equations (307,563) yields a new equation:
% 28.11/7.83 | (622) e2 = e0
% 28.11/7.83 |
% 28.11/7.83 | Simplifying 622 yields:
% 28.11/7.83 | (316) e2 = e0
% 28.11/7.83 |
% 28.11/7.83 | Equations (316) can reduce 57 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (296) ~ (all_0_49_49 = e2)
% 28.11/7.83 | (3829) all_0_54_54 = e2 | all_0_59_59 = e2
% 28.11/7.83 |
% 28.11/7.83 +-Applying beta-rule and splitting (3829), into two cases.
% 28.11/7.83 |-Branch one:
% 28.11/7.83 | (3657) all_0_54_54 = e2
% 28.11/7.83 |
% 28.11/7.83 | Equations (3657) can reduce 261 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (261) ~ (all_0_54_54 = e2)
% 28.11/7.83 | (399) all_0_59_59 = e2
% 28.11/7.83 |
% 28.11/7.83 | Equations (399) can reduce 701 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (291) ~ (all_0_39_39 = e2)
% 28.11/7.83 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 28.11/7.83 |
% 28.11/7.83 +-Applying beta-rule and splitting (339), into two cases.
% 28.11/7.83 |-Branch one:
% 28.11/7.83 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 28.11/7.83 |
% 28.11/7.83 +-Applying beta-rule and splitting (340), into two cases.
% 28.11/7.83 |-Branch one:
% 28.11/7.83 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 28.11/7.83 |
% 28.11/7.83 | Applying alpha-rule on (341) yields:
% 28.11/7.83 | (342) all_0_0_0 = e1
% 28.11/7.83 | (343) ~ (all_0_1_1 = e4)
% 28.11/7.83 |
% 28.11/7.83 | Combining equations (342,3452) yields a new equation:
% 28.11/7.83 | (538) e3 = e1
% 28.11/7.83 |
% 28.11/7.83 | Equations (538) can reduce 136 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 28.11/7.83 |
% 28.11/7.83 | Applying alpha-rule on (346) yields:
% 28.11/7.83 | (347) all_0_2_2 = e0
% 28.11/7.83 | (348) ~ (all_0_3_3 = e4)
% 28.11/7.83 |
% 28.11/7.83 | Equations (287) can reduce 348 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 28.11/7.83 |
% 28.11/7.83 | Applying alpha-rule on (350) yields:
% 28.11/7.83 | (351) all_0_41_41 = e3
% 28.11/7.83 | (352) ~ (all_0_45_45 = e4)
% 28.11/7.83 |
% 28.11/7.83 | Equations (351) can reduce 1237 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (642) ~ (all_0_52_52 = e1)
% 28.11/7.83 | (997) all_0_57_57 = e1
% 28.11/7.83 |
% 28.11/7.83 | Combining equations (997,392) yields a new equation:
% 28.11/7.83 | (322) e2 = e1
% 28.11/7.83 |
% 28.11/7.83 | Equations (322) can reduce 141 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (625) ~ (all_0_44_44 = e0)
% 28.11/7.83 | (858) all_0_44_44 = e3
% 28.11/7.83 |
% 28.11/7.83 | Equations (858) can reduce 862 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (675) ~ (all_0_40_40 = e3)
% 28.11/7.83 | (530) all_0_40_40 = e1
% 28.11/7.83 |
% 28.11/7.83 | Equations (530) can reduce 534 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (1231) ~ (all_0_49_49 = e0)
% 28.11/7.83 | (589) all_0_49_49 = e1
% 28.11/7.83 |
% 28.11/7.83 | Equations (589) can reduce 543 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (324) ~ (all_0_47_47 = e1)
% 28.11/7.83 | (325) all_0_48_48 = e1 | all_0_49_49 = e1
% 28.11/7.83 |
% 28.11/7.83 +-Applying beta-rule and splitting (325), into two cases.
% 28.11/7.83 |-Branch one:
% 28.11/7.83 | (552) all_0_48_48 = e1
% 28.11/7.83 |
% 28.11/7.83 | Combining equations (552,311) yields a new equation:
% 28.11/7.83 | (322) e2 = e1
% 28.11/7.83 |
% 28.11/7.83 | Equations (322) can reduce 141 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (588) ~ (all_0_48_48 = e1)
% 28.11/7.83 | (589) all_0_49_49 = e1
% 28.11/7.83 |
% 28.11/7.83 | Equations (589) can reduce 113 to:
% 28.11/7.83 | (749) ~ (all_0_59_59 = e1)
% 28.11/7.83 |
% 28.11/7.83 | Simplifying 749 yields:
% 28.11/7.83 | (750) ~ (all_0_59_59 = e1)
% 28.11/7.83 |
% 28.11/7.83 +-Applying beta-rule and splitting (77), into two cases.
% 28.11/7.83 |-Branch one:
% 28.11/7.83 | (315) all_0_47_47 = e0
% 28.11/7.83 |
% 28.11/7.83 | Equations (315) can reduce 170 to:
% 28.11/7.83 | (455) ~ (all_0_43_43 = e0)
% 28.11/7.83 |
% 28.11/7.83 +-Applying beta-rule and splitting (93), into two cases.
% 28.11/7.83 |-Branch one:
% 28.11/7.83 | (402) all_0_59_59 = e4
% 28.11/7.83 |
% 28.11/7.83 | Equations (402) can reduce 280 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (280) ~ (all_0_59_59 = e4)
% 28.11/7.83 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 28.11/7.83 |
% 28.11/7.83 +-Applying beta-rule and splitting (407), into two cases.
% 28.11/7.83 |-Branch one:
% 28.11/7.83 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 28.11/7.83 |
% 28.11/7.83 +-Applying beta-rule and splitting (408), into two cases.
% 28.11/7.83 |-Branch one:
% 28.11/7.83 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 28.11/7.83 |
% 28.11/7.83 +-Applying beta-rule and splitting (409), into two cases.
% 28.11/7.83 |-Branch one:
% 28.11/7.83 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 28.11/7.83 |
% 28.11/7.83 | Applying alpha-rule on (410) yields:
% 28.11/7.83 | (411) all_0_43_43 = e0
% 28.11/7.83 | (412) all_0_59_59 = e3
% 28.11/7.83 | (413) ~ (all_0_46_46 = e3)
% 28.11/7.83 |
% 28.11/7.83 | Equations (411) can reduce 455 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 28.11/7.83 |
% 28.11/7.83 | Applying alpha-rule on (416) yields:
% 28.11/7.83 | (411) all_0_43_43 = e0
% 28.11/7.83 | (412) all_0_59_59 = e3
% 28.11/7.83 | (419) ~ (all_0_56_56 = e0)
% 28.11/7.83 |
% 28.11/7.83 | Equations (411) can reduce 455 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 28.11/7.83 |
% 28.11/7.83 | Applying alpha-rule on (422) yields:
% 28.11/7.83 | (423) all_0_53_53 = e0
% 28.11/7.83 | (424) all_0_59_59 = e1
% 28.11/7.83 | (425) ~ (all_0_54_54 = e1)
% 28.11/7.83 |
% 28.11/7.83 | Equations (424) can reduce 750 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 28.11/7.83 |
% 28.11/7.83 | Applying alpha-rule on (428) yields:
% 28.11/7.83 | (423) all_0_53_53 = e0
% 28.11/7.83 | (424) all_0_59_59 = e1
% 28.11/7.83 | (431) ~ (all_0_58_58 = e0)
% 28.11/7.83 |
% 28.11/7.83 | Equations (424) can reduce 750 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (318) ~ (all_0_47_47 = e0)
% 28.11/7.83 | (319) all_0_48_48 = e0 | all_0_49_49 = e0
% 28.11/7.83 |
% 28.11/7.83 +-Applying beta-rule and splitting (319), into two cases.
% 28.11/7.83 |-Branch one:
% 28.11/7.83 | (559) all_0_48_48 = e0
% 28.11/7.83 |
% 28.11/7.83 | Combining equations (311,559) yields a new equation:
% 28.11/7.83 | (622) e2 = e0
% 28.11/7.83 |
% 28.11/7.83 | Simplifying 622 yields:
% 28.11/7.83 | (316) e2 = e0
% 28.11/7.83 |
% 28.11/7.83 | Equations (316) can reduce 57 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (562) ~ (all_0_48_48 = e0)
% 28.11/7.83 | (563) all_0_49_49 = e0
% 28.11/7.83 |
% 28.11/7.83 | Combining equations (563,589) yields a new equation:
% 28.11/7.83 | (560) e1 = e0
% 28.11/7.83 |
% 28.11/7.83 | Equations (560) can reduce 132 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (294) ~ (all_0_48_48 = e2)
% 28.11/7.83 | (314) all_0_48_48 = e1 | all_0_48_48 = e0
% 28.11/7.83 |
% 28.11/7.83 +-Applying beta-rule and splitting (3952), into two cases.
% 28.11/7.83 |-Branch one:
% 28.11/7.83 | (311) all_0_48_48 = e2
% 28.11/7.83 |
% 28.11/7.83 | Equations (311) can reduce 294 to:
% 28.11/7.83 | (270) $false
% 28.11/7.83 |
% 28.11/7.83 |-The branch is then unsatisfiable
% 28.11/7.83 |-Branch two:
% 28.11/7.83 | (294) ~ (all_0_48_48 = e2)
% 28.11/7.83 | (307) all_0_49_49 = e2
% 28.11/7.83 |
% 28.11/7.83 | Equations (307) can reduce 169 to:
% 28.11/7.83 | (498) ~ (all_0_42_42 = e2)
% 28.11/7.83 |
% 28.11/7.83 | Equations (307) can reduce 198 to:
% 28.11/7.83 | (1436) ~ (all_0_46_46 = e2)
% 28.11/7.83 |
% 28.11/7.83 | Equations (307) can reduce 80 to:
% 28.11/7.83 | (3951) ~ (all_0_47_47 = e2)
% 28.11/7.83 |
% 28.11/7.83 | Equations (307) can reduce 4 to:
% 28.11/7.83 | (294) ~ (all_0_48_48 = e2)
% 28.11/7.83 |
% 28.11/7.83 | Equations (307) can reduce 162 to:
% 28.11/7.83 | (260) ~ (all_0_54_54 = e2)
% 28.11/7.83 |
% 28.11/7.83 | Simplifying 260 yields:
% 28.11/7.83 | (261) ~ (all_0_54_54 = e2)
% 28.11/7.83 |
% 28.11/7.83 | Equations (307) can reduce 113 to:
% 28.11/7.83 | (700) ~ (all_0_59_59 = e2)
% 28.11/7.83 |
% 28.11/7.83 | Simplifying 700 yields:
% 28.11/7.83 | (701) ~ (all_0_59_59 = e2)
% 28.11/7.83 |
% 28.11/7.83 | Equations (307) can reduce 202 to:
% 28.11/7.83 | (377) ~ (e4 = e2)
% 28.11/7.83 |
% 28.11/7.83 | Simplifying 377 yields:
% 28.11/7.83 | (231) ~ (e4 = e2)
% 28.11/7.83 |
% 28.11/7.83 | Equations (307) can reduce 150 to:
% 28.11/7.83 | (301) ~ (e3 = e2)
% 28.11/7.83 |
% 28.11/7.83 | Simplifying 301 yields:
% 28.11/7.83 | (223) ~ (e3 = e2)
% 28.11/7.83 |
% 28.11/7.83 | From (307) and (153) follows:
% 28.11/7.83 | (6091) op(e2, e2) = all_0_35_35
% 28.11/7.83 |
% 28.11/7.83 | From (307) and (134) follows:
% 28.41/7.83 | (6092) op(e2, e0) = e2
% 28.41/7.83 |
% 28.41/7.83 | From (307) and (88) follows:
% 28.41/7.83 | (6093) op(e0, e2) = all_0_34_34
% 28.41/7.83 |
% 28.41/7.83 | Instantiating formula (201) with e2, e2, all_0_35_35, e4 and discharging atoms op(e2, e2) = all_0_35_35, op(e2, e2) = e4, yields:
% 28.41/7.83 | (6094) all_0_35_35 = e4
% 28.41/7.83 |
% 28.41/7.83 | Instantiating formula (201) with e0, e2, all_0_34_34, all_0_57_57 and discharging atoms op(e0, e2) = all_0_34_34, op(e0, e2) = all_0_57_57, yields:
% 28.41/7.83 | (6095) all_0_34_34 = all_0_57_57
% 28.41/7.83 |
% 28.41/7.83 | From (6094) and (6091) follows:
% 28.41/7.83 | (115) op(e2, e2) = e4
% 28.41/7.83 |
% 28.41/7.83 | From (6095) and (6093) follows:
% 28.41/7.83 | (207) op(e0, e2) = all_0_57_57
% 28.41/7.83 |
% 28.41/7.83 +-Applying beta-rule and splitting (83), into two cases.
% 28.41/7.83 |-Branch one:
% 28.41/7.83 | (321) all_0_47_47 = e1
% 28.41/7.83 |
% 28.41/7.83 | Equations (321) can reduce 100 to:
% 28.41/7.83 | (528) ~ (all_0_39_39 = e1)
% 28.41/7.83 |
% 28.41/7.83 | Equations (321) can reduce 225 to:
% 28.41/7.84 | (6100) ~ (all_0_48_48 = e1)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 6100 yields:
% 28.41/7.84 | (588) ~ (all_0_48_48 = e1)
% 28.41/7.84 |
% 28.41/7.84 | Equations (321) can reduce 3 to:
% 28.41/7.84 | (3984) ~ (all_0_51_51 = e1)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 3984 yields:
% 28.41/7.84 | (748) ~ (all_0_51_51 = e1)
% 28.41/7.84 |
% 28.41/7.84 | Equations (321) can reduce 218 to:
% 28.41/7.84 | (3986) ~ (all_0_56_56 = e1)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 3986 yields:
% 28.41/7.84 | (995) ~ (all_0_56_56 = e1)
% 28.41/7.84 |
% 28.41/7.84 | Equations (321) can reduce 172 to:
% 28.41/7.84 | (1021) ~ (e4 = e1)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 1021 yields:
% 28.41/7.84 | (251) ~ (e4 = e1)
% 28.41/7.84 |
% 28.41/7.84 | Equations (321) can reduce 247 to:
% 28.41/7.84 | (769) ~ (e3 = e1)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 769 yields:
% 28.41/7.84 | (136) ~ (e3 = e1)
% 28.41/7.84 |
% 28.41/7.84 | Equations (321) can reduce 3951 to:
% 28.41/7.84 | (645) ~ (e2 = e1)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 645 yields:
% 28.41/7.84 | (141) ~ (e2 = e1)
% 28.41/7.84 |
% 28.41/7.84 | From (321) and (42) follows:
% 28.41/7.84 | (3993) op(e2, e1) = all_0_8_8
% 28.41/7.84 |
% 28.41/7.84 | From (321) and (40) follows:
% 28.41/7.84 | (1103) op(e2, e3) = e1
% 28.41/7.84 |
% 28.41/7.84 +-Applying beta-rule and splitting (314), into two cases.
% 28.41/7.84 |-Branch one:
% 28.41/7.84 | (559) all_0_48_48 = e0
% 28.41/7.84 |
% 28.41/7.84 | Equations (559) can reduce 190 to:
% 28.41/7.84 | (232) ~ (all_0_41_41 = e0)
% 28.41/7.84 |
% 28.41/7.84 | Equations (559) can reduce 65 to:
% 28.41/7.84 | (488) ~ (all_0_45_45 = e0)
% 28.41/7.84 |
% 28.41/7.84 | Equations (559) can reduce 48 to:
% 28.41/7.84 | (3103) ~ (all_0_53_53 = e0)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 3103 yields:
% 28.41/7.84 | (584) ~ (all_0_53_53 = e0)
% 28.41/7.84 |
% 28.41/7.84 | Equations (559) can reduce 59 to:
% 28.41/7.84 | (3530) ~ (all_0_58_58 = e0)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 3530 yields:
% 28.41/7.84 | (431) ~ (all_0_58_58 = e0)
% 28.41/7.84 |
% 28.41/7.84 | Equations (559) can reduce 294 to:
% 28.41/7.84 | (566) ~ (e2 = e0)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 566 yields:
% 28.41/7.84 | (57) ~ (e2 = e0)
% 28.41/7.84 |
% 28.41/7.84 | Equations (559) can reduce 588 to:
% 28.41/7.84 | (568) ~ (e1 = e0)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 568 yields:
% 28.41/7.84 | (132) ~ (e1 = e0)
% 28.41/7.84 |
% 28.41/7.84 | From (559) and (183) follows:
% 28.41/7.84 | (6125) op(e2, e0) = all_0_26_26
% 28.41/7.84 |
% 28.41/7.84 | From (559) and (56) follows:
% 28.41/7.84 | (6126) op(e2, e1) = e0
% 28.41/7.84 |
% 28.41/7.84 | From (559) and (76) follows:
% 28.41/7.84 | (6127) op(e1, e0) = all_0_25_25
% 28.41/7.84 |
% 28.41/7.84 | Instantiating formula (201) with e2, e1, e0, all_0_8_8 and discharging atoms op(e2, e1) = all_0_8_8, op(e2, e1) = e0, yields:
% 28.41/7.84 | (6128) all_0_8_8 = e0
% 28.41/7.84 |
% 28.41/7.84 | Instantiating formula (201) with e2, e0, all_0_26_26, e2 and discharging atoms op(e2, e0) = all_0_26_26, op(e2, e0) = e2, yields:
% 28.41/7.84 | (6129) all_0_26_26 = e2
% 28.41/7.84 |
% 28.41/7.84 | Instantiating formula (201) with e1, e0, all_0_25_25, all_0_54_54 and discharging atoms op(e1, e0) = all_0_25_25, op(e1, e0) = all_0_54_54, yields:
% 28.41/7.84 | (6130) all_0_25_25 = all_0_54_54
% 28.41/7.84 |
% 28.41/7.84 | From (6128) and (3993) follows:
% 28.41/7.84 | (6126) op(e2, e1) = e0
% 28.41/7.84 |
% 28.41/7.84 | From (6129) and (6125) follows:
% 28.41/7.84 | (6092) op(e2, e0) = e2
% 28.41/7.84 |
% 28.41/7.84 +-Applying beta-rule and splitting (125), into two cases.
% 28.41/7.84 |-Branch one:
% 28.41/7.84 | (327) all_0_40_40 = e2
% 28.41/7.84 |
% 28.41/7.84 | Combining equations (327,285) yields a new equation:
% 28.41/7.84 | (328) all_0_0_0 = e2
% 28.41/7.84 |
% 28.41/7.84 | Equations (327) can reduce 114 to:
% 28.41/7.84 | (291) ~ (all_0_39_39 = e2)
% 28.41/7.84 |
% 28.41/7.84 | Equations (327) can reduce 149 to:
% 28.41/7.84 | (334) ~ (all_0_57_57 = e2)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 334 yields:
% 28.41/7.84 | (335) ~ (all_0_57_57 = e2)
% 28.41/7.84 |
% 28.41/7.84 +-Applying beta-rule and splitting (186), into two cases.
% 28.41/7.84 |-Branch one:
% 28.41/7.84 | (336) all_0_39_39 = e2
% 28.41/7.84 |
% 28.41/7.84 | Equations (336) can reduce 291 to:
% 28.41/7.84 | (270) $false
% 28.41/7.84 |
% 28.41/7.84 |-The branch is then unsatisfiable
% 28.41/7.84 |-Branch two:
% 28.41/7.84 | (291) ~ (all_0_39_39 = e2)
% 28.41/7.84 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 28.41/7.84 |
% 28.41/7.84 +-Applying beta-rule and splitting (339), into two cases.
% 28.41/7.84 |-Branch one:
% 28.41/7.84 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 28.41/7.84 |
% 28.41/7.84 +-Applying beta-rule and splitting (340), into two cases.
% 28.41/7.84 |-Branch one:
% 28.41/7.84 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 28.41/7.84 |
% 28.41/7.84 | Applying alpha-rule on (341) yields:
% 28.41/7.84 | (342) all_0_0_0 = e1
% 28.41/7.84 | (343) ~ (all_0_1_1 = e4)
% 28.41/7.84 |
% 28.41/7.84 | Combining equations (342,328) yields a new equation:
% 28.41/7.84 | (322) e2 = e1
% 28.41/7.84 |
% 28.41/7.84 | Equations (322) can reduce 141 to:
% 28.41/7.84 | (270) $false
% 28.41/7.84 |
% 28.41/7.84 |-The branch is then unsatisfiable
% 28.41/7.84 |-Branch two:
% 28.41/7.84 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 28.41/7.84 |
% 28.41/7.84 | Applying alpha-rule on (346) yields:
% 28.41/7.84 | (347) all_0_2_2 = e0
% 28.41/7.84 | (348) ~ (all_0_3_3 = e4)
% 28.41/7.84 |
% 28.41/7.84 | Equations (287) can reduce 348 to:
% 28.41/7.84 | (270) $false
% 28.41/7.84 |
% 28.41/7.84 |-The branch is then unsatisfiable
% 28.41/7.84 |-Branch two:
% 28.41/7.84 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 28.41/7.84 |
% 28.41/7.84 | Applying alpha-rule on (350) yields:
% 28.41/7.84 | (351) all_0_41_41 = e3
% 28.41/7.84 | (352) ~ (all_0_45_45 = e4)
% 28.41/7.84 |
% 28.41/7.84 | Equations (351) can reduce 51 to:
% 28.41/7.84 | (353) ~ (all_0_45_45 = e3)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 353 yields:
% 28.41/7.84 | (354) ~ (all_0_45_45 = e3)
% 28.41/7.84 |
% 28.41/7.84 +-Applying beta-rule and splitting (105), into two cases.
% 28.41/7.84 |-Branch one:
% 28.41/7.84 | (374) all_0_45_45 = e2
% 28.41/7.84 |
% 28.41/7.84 | Equations (374) can reduce 229 to:
% 28.41/7.84 | (333) ~ (all_0_44_44 = e2)
% 28.41/7.84 |
% 28.41/7.84 | Equations (374) can reduce 128 to:
% 28.41/7.84 | (258) ~ (all_0_53_53 = e2)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 258 yields:
% 28.41/7.84 | (259) ~ (all_0_53_53 = e2)
% 28.41/7.84 |
% 28.41/7.84 | Equations (374) can reduce 108 to:
% 28.41/7.84 | (375) ~ (all_0_58_58 = e2)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 375 yields:
% 28.41/7.84 | (376) ~ (all_0_58_58 = e2)
% 28.41/7.84 |
% 28.41/7.84 | Equations (374) can reduce 352 to:
% 28.41/7.84 | (377) ~ (e4 = e2)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 377 yields:
% 28.41/7.84 | (231) ~ (e4 = e2)
% 28.41/7.84 |
% 28.41/7.84 +-Applying beta-rule and splitting (168), into two cases.
% 28.41/7.84 |-Branch one:
% 28.41/7.84 | (382) all_0_55_55 = e2
% 28.41/7.84 |
% 28.41/7.84 | Combining equations (382,272) yields a new equation:
% 28.41/7.84 | (269) e4 = e2
% 28.41/7.84 |
% 28.41/7.84 | Equations (269) can reduce 231 to:
% 28.41/7.84 | (270) $false
% 28.41/7.84 |
% 28.41/7.84 |-The branch is then unsatisfiable
% 28.41/7.84 |-Branch two:
% 28.41/7.84 | (386) ~ (all_0_55_55 = e2)
% 28.41/7.84 | (387) all_0_56_56 = e2 | all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 28.41/7.84 |
% 28.41/7.84 +-Applying beta-rule and splitting (387), into two cases.
% 28.41/7.84 |-Branch one:
% 28.41/7.84 | (388) all_0_56_56 = e2
% 28.41/7.84 |
% 28.41/7.84 | Equations (388) can reduce 188 to:
% 28.41/7.84 | (292) ~ (all_0_43_43 = e2)
% 28.41/7.84 |
% 28.41/7.84 | Equations (388) can reduce 60 to:
% 28.41/7.84 | (255) ~ (all_0_51_51 = e2)
% 28.41/7.84 |
% 28.41/7.84 | Equations (388) can reduce 81 to:
% 28.41/7.84 | (375) ~ (all_0_58_58 = e2)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 375 yields:
% 28.41/7.84 | (376) ~ (all_0_58_58 = e2)
% 28.41/7.84 |
% 28.41/7.84 | Equations (388) can reduce 274 to:
% 28.41/7.84 | (377) ~ (e4 = e2)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 377 yields:
% 28.41/7.84 | (231) ~ (e4 = e2)
% 28.41/7.84 |
% 28.41/7.84 | Equations (388) can reduce 995 to:
% 28.41/7.84 | (141) ~ (e2 = e1)
% 28.41/7.84 |
% 28.41/7.84 +-Applying beta-rule and splitting (158), into two cases.
% 28.41/7.84 |-Branch one:
% 28.41/7.84 | (358) all_0_41_41 = e4
% 28.41/7.84 |
% 28.41/7.84 | Combining equations (351,358) yields a new equation:
% 28.41/7.84 | (359) e4 = e3
% 28.41/7.84 |
% 28.41/7.84 | Equations (359) can reduce 34 to:
% 28.41/7.84 | (270) $false
% 28.41/7.84 |
% 28.41/7.84 |-The branch is then unsatisfiable
% 28.41/7.84 |-Branch two:
% 28.41/7.84 | (361) ~ (all_0_41_41 = e4)
% 28.41/7.84 | (362) all_0_45_45 = e4 | all_0_53_53 = e4 | all_0_58_58 = e4
% 28.41/7.84 |
% 28.41/7.84 | Equations (351) can reduce 361 to:
% 28.41/7.84 | (719) ~ (e4 = e3)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 719 yields:
% 28.41/7.84 | (34) ~ (e4 = e3)
% 28.41/7.84 |
% 28.41/7.84 +-Applying beta-rule and splitting (210), into two cases.
% 28.41/7.84 |-Branch one:
% 28.41/7.84 | (524) all_0_39_39 = e1
% 28.41/7.84 |
% 28.41/7.84 | Equations (524) can reduce 528 to:
% 28.41/7.84 | (270) $false
% 28.41/7.84 |
% 28.41/7.84 |-The branch is then unsatisfiable
% 28.41/7.84 |-Branch two:
% 28.41/7.84 | (528) ~ (all_0_39_39 = e1)
% 28.41/7.84 | (529) all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1
% 28.41/7.84 |
% 28.41/7.84 +-Applying beta-rule and splitting (529), into two cases.
% 28.41/7.84 |-Branch one:
% 28.41/7.84 | (530) all_0_40_40 = e1
% 28.41/7.84 |
% 28.41/7.84 | Combining equations (327,530) yields a new equation:
% 28.41/7.84 | (531) e2 = e1
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 531 yields:
% 28.41/7.84 | (322) e2 = e1
% 28.41/7.84 |
% 28.41/7.84 | Equations (322) can reduce 141 to:
% 28.41/7.84 | (270) $false
% 28.41/7.84 |
% 28.41/7.84 |-The branch is then unsatisfiable
% 28.41/7.84 |-Branch two:
% 28.41/7.84 | (534) ~ (all_0_40_40 = e1)
% 28.41/7.84 | (535) all_0_41_41 = e1 | all_0_42_42 = e1
% 28.41/7.84 |
% 28.41/7.84 +-Applying beta-rule and splitting (535), into two cases.
% 28.41/7.84 |-Branch one:
% 28.41/7.84 | (536) all_0_41_41 = e1
% 28.41/7.84 |
% 28.41/7.84 | Combining equations (351,536) yields a new equation:
% 28.41/7.84 | (537) e3 = e1
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 537 yields:
% 28.41/7.84 | (538) e3 = e1
% 28.41/7.84 |
% 28.41/7.84 | Equations (538) can reduce 136 to:
% 28.41/7.84 | (270) $false
% 28.41/7.84 |
% 28.41/7.84 |-The branch is then unsatisfiable
% 28.41/7.84 |-Branch two:
% 28.41/7.84 | (540) ~ (all_0_41_41 = e1)
% 28.41/7.84 | (541) all_0_42_42 = e1
% 28.41/7.84 |
% 28.41/7.84 | Equations (541) can reduce 18 to:
% 28.41/7.84 | (6201) ~ (all_0_46_46 = e1)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 6201 yields:
% 28.41/7.84 | (106) ~ (all_0_46_46 = e1)
% 28.41/7.84 |
% 28.41/7.84 | Equations (541) can reduce 191 to:
% 28.41/7.84 | (2131) ~ (all_0_54_54 = e1)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 2131 yields:
% 28.41/7.84 | (425) ~ (all_0_54_54 = e1)
% 28.41/7.84 |
% 28.41/7.84 | From (541) and (243) follows:
% 28.41/7.84 | (6205) op(e0, e1) = all_0_30_30
% 28.41/7.84 |
% 28.41/7.84 +-Applying beta-rule and splitting (362), into two cases.
% 28.41/7.84 |-Branch one:
% 28.41/7.84 | (363) all_0_45_45 = e4
% 28.41/7.84 |
% 28.41/7.84 | Combining equations (374,363) yields a new equation:
% 28.41/7.84 | (269) e4 = e2
% 28.41/7.84 |
% 28.41/7.84 | Equations (269) can reduce 231 to:
% 28.41/7.84 | (270) $false
% 28.41/7.84 |
% 28.41/7.84 |-The branch is then unsatisfiable
% 28.41/7.84 |-Branch two:
% 28.41/7.84 | (352) ~ (all_0_45_45 = e4)
% 28.41/7.84 | (366) all_0_53_53 = e4 | all_0_58_58 = e4
% 28.41/7.84 |
% 28.41/7.84 +-Applying beta-rule and splitting (222), into two cases.
% 28.41/7.84 |-Branch one:
% 28.41/7.84 | (522) all_0_39_39 = e4
% 28.41/7.84 |
% 28.41/7.84 | Equations (522) can reduce 167 to:
% 28.41/7.84 | (694) ~ (all_0_43_43 = e4)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 694 yields:
% 28.41/7.84 | (510) ~ (all_0_43_43 = e4)
% 28.41/7.84 |
% 28.41/7.84 +-Applying beta-rule and splitting (366), into two cases.
% 28.41/7.84 |-Branch one:
% 28.41/7.84 | (367) all_0_53_53 = e4
% 28.41/7.84 |
% 28.41/7.84 | Equations (367) can reduce 12 to:
% 28.41/7.84 | (697) ~ (all_0_51_51 = e4)
% 28.41/7.84 |
% 28.41/7.84 | Equations (367) can reduce 70 to:
% 28.41/7.84 | (277) ~ (all_0_58_58 = e4)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 277 yields:
% 28.41/7.84 | (278) ~ (all_0_58_58 = e4)
% 28.41/7.84 |
% 28.41/7.84 | Equations (367) can reduce 259 to:
% 28.41/7.84 | (231) ~ (e4 = e2)
% 28.41/7.84 |
% 28.41/7.84 | Equations (367) can reduce 584 to:
% 28.41/7.84 | (6) ~ (e4 = e0)
% 28.41/7.84 |
% 28.41/7.84 +-Applying beta-rule and splitting (44), into two cases.
% 28.41/7.84 |-Branch one:
% 28.41/7.84 | (502) all_0_43_43 = e4
% 28.41/7.84 |
% 28.41/7.84 | Equations (502) can reduce 510 to:
% 28.41/7.84 | (270) $false
% 28.41/7.84 |
% 28.41/7.84 |-The branch is then unsatisfiable
% 28.41/7.84 |-Branch two:
% 28.41/7.84 | (510) ~ (all_0_43_43 = e4)
% 28.41/7.84 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 28.41/7.84 |
% 28.41/7.84 +-Applying beta-rule and splitting (511), into two cases.
% 28.41/7.84 |-Branch one:
% 28.41/7.84 | (363) all_0_45_45 = e4
% 28.41/7.84 |
% 28.41/7.84 | Combining equations (374,363) yields a new equation:
% 28.41/7.84 | (269) e4 = e2
% 28.41/7.84 |
% 28.41/7.84 | Equations (269) can reduce 231 to:
% 28.41/7.84 | (270) $false
% 28.41/7.84 |
% 28.41/7.84 |-The branch is then unsatisfiable
% 28.41/7.84 |-Branch two:
% 28.41/7.84 | (352) ~ (all_0_45_45 = e4)
% 28.41/7.84 | (517) all_0_46_46 = e4
% 28.41/7.84 |
% 28.41/7.84 | Equations (517) can reduce 206 to:
% 28.41/7.84 | (279) ~ (all_0_59_59 = e4)
% 28.41/7.84 |
% 28.41/7.84 | Simplifying 279 yields:
% 28.41/7.84 | (280) ~ (all_0_59_59 = e4)
% 28.41/7.84 |
% 28.41/7.85 | Equations (517) can reduce 106 to:
% 28.41/7.85 | (251) ~ (e4 = e1)
% 28.41/7.85 |
% 28.41/7.85 | From (517) and (89) follows:
% 28.41/7.85 | (4546) op(e0, e4) = all_0_32_32
% 28.41/7.85 |
% 28.41/7.85 +-Applying beta-rule and splitting (93), into two cases.
% 28.41/7.85 |-Branch one:
% 28.41/7.85 | (402) all_0_59_59 = e4
% 28.41/7.85 |
% 28.41/7.85 | Equations (402) can reduce 280 to:
% 28.41/7.85 | (270) $false
% 28.41/7.85 |
% 28.41/7.85 |-The branch is then unsatisfiable
% 28.41/7.85 |-Branch two:
% 28.41/7.85 | (280) ~ (all_0_59_59 = e4)
% 28.41/7.85 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 28.41/7.85 |
% 28.41/7.85 +-Applying beta-rule and splitting (135), into two cases.
% 28.41/7.85 |-Branch one:
% 28.41/7.85 | (820) all_0_51_51 = e1
% 28.41/7.85 |
% 28.41/7.85 | Equations (820) can reduce 748 to:
% 28.41/7.85 | (270) $false
% 28.41/7.85 |
% 28.41/7.85 |-The branch is then unsatisfiable
% 28.41/7.85 |-Branch two:
% 28.41/7.85 | (748) ~ (all_0_51_51 = e1)
% 28.41/7.85 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 28.41/7.85 |
% 28.41/7.85 +-Applying beta-rule and splitting (823), into two cases.
% 28.41/7.85 |-Branch one:
% 28.41/7.85 | (848) all_0_52_52 = e1
% 28.41/7.85 |
% 28.41/7.85 | Equations (848) can reduce 154 to:
% 28.41/7.85 | (748) ~ (all_0_51_51 = e1)
% 28.41/7.85 |
% 28.41/7.85 | Equations (848) can reduce 235 to:
% 28.41/7.85 | (643) ~ (all_0_57_57 = e1)
% 28.41/7.85 |
% 28.41/7.85 | Simplifying 643 yields:
% 28.41/7.85 | (644) ~ (all_0_57_57 = e1)
% 28.41/7.85 |
% 28.41/7.85 +-Applying beta-rule and splitting (407), into two cases.
% 28.41/7.85 |-Branch one:
% 28.41/7.85 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 28.41/7.85 |
% 28.41/7.85 +-Applying beta-rule and splitting (408), into two cases.
% 28.41/7.85 |-Branch one:
% 28.41/7.85 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 28.41/7.85 |
% 28.41/7.85 +-Applying beta-rule and splitting (409), into two cases.
% 28.41/7.85 |-Branch one:
% 28.41/7.85 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 28.41/7.85 |
% 28.41/7.85 | Applying alpha-rule on (410) yields:
% 28.41/7.85 | (411) all_0_43_43 = e0
% 28.41/7.85 | (412) all_0_59_59 = e3
% 28.41/7.85 | (413) ~ (all_0_46_46 = e3)
% 28.41/7.85 |
% 28.41/7.85 | Equations (411) can reduce 241 to:
% 28.41/7.85 | (6251) ~ (all_0_44_44 = e0)
% 28.41/7.85 |
% 28.41/7.85 | Simplifying 6251 yields:
% 28.41/7.85 | (625) ~ (all_0_44_44 = e0)
% 28.41/7.85 |
% 28.41/7.85 | Equations (411) can reduce 240 to:
% 28.41/7.85 | (6253) ~ (all_0_51_51 = e0)
% 28.41/7.85 |
% 28.41/7.85 | Simplifying 6253 yields:
% 28.41/7.85 | (987) ~ (all_0_51_51 = e0)
% 28.41/7.85 |
% 28.41/7.85 | Equations (411) can reduce 292 to:
% 28.41/7.85 | (566) ~ (e2 = e0)
% 28.41/7.85 |
% 28.41/7.85 | Simplifying 566 yields:
% 28.41/7.85 | (57) ~ (e2 = e0)
% 28.41/7.85 |
% 28.41/7.85 | Equations (412) can reduce 156 to:
% 28.41/7.85 | (718) ~ (all_0_58_58 = e3)
% 28.41/7.85 |
% 28.41/7.85 | From (412) and (161) follows:
% 28.41/7.85 | (6258) op(e0, e0) = e3
% 28.41/7.85 |
% 28.41/7.85 +-Applying beta-rule and splitting (193), into two cases.
% 28.41/7.85 |-Branch one:
% 28.41/7.85 | (370) all_0_44_44 = e2
% 28.41/7.85 |
% 28.41/7.85 | Equations (370) can reduce 333 to:
% 28.41/7.85 | (270) $false
% 28.41/7.85 |
% 28.41/7.85 |-The branch is then unsatisfiable
% 28.41/7.85 |-Branch two:
% 28.41/7.85 | (333) ~ (all_0_44_44 = e2)
% 28.41/7.85 | (373) all_0_44_44 = e3 | all_0_44_44 = e0
% 28.41/7.85 |
% 28.41/7.85 +-Applying beta-rule and splitting (373), into two cases.
% 28.41/7.85 |-Branch one:
% 28.41/7.85 | (621) all_0_44_44 = e0
% 28.41/7.85 |
% 28.41/7.85 | Equations (621) can reduce 625 to:
% 28.41/7.85 | (270) $false
% 28.41/7.85 |
% 28.41/7.85 |-The branch is then unsatisfiable
% 28.41/7.85 |-Branch two:
% 28.41/7.85 | (625) ~ (all_0_44_44 = e0)
% 28.41/7.85 | (858) all_0_44_44 = e3
% 28.41/7.85 |
% 28.41/7.85 | Equations (858) can reduce 625 to:
% 28.41/7.85 | (66) ~ (e3 = e0)
% 28.41/7.85 |
% 28.41/7.85 +-Applying beta-rule and splitting (176), into two cases.
% 28.41/7.85 |-Branch one:
% 28.41/7.85 | (830) all_0_56_56 = e0
% 28.41/7.85 |
% 28.41/7.85 | Combining equations (830,388) yields a new equation:
% 28.41/7.85 | (316) e2 = e0
% 28.41/7.85 |
% 28.41/7.85 | Equations (316) can reduce 57 to:
% 28.41/7.85 | (270) $false
% 28.41/7.85 |
% 28.41/7.85 |-The branch is then unsatisfiable
% 28.41/7.85 |-Branch two:
% 28.41/7.85 | (419) ~ (all_0_56_56 = e0)
% 28.41/7.85 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 28.41/7.85 |
% 28.41/7.85 +-Applying beta-rule and splitting (173), into two cases.
% 28.41/7.85 |-Branch one:
% 28.41/7.85 | (4215) all_0_51_51 = e2
% 28.41/7.85 |
% 28.41/7.85 | Equations (4215) can reduce 255 to:
% 28.41/7.85 | (270) $false
% 28.41/7.85 |
% 28.41/7.85 |-The branch is then unsatisfiable
% 28.41/7.85 |-Branch two:
% 28.41/7.85 | (255) ~ (all_0_51_51 = e2)
% 28.41/7.85 | (4888) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1 | all_0_51_51 = e0
% 28.41/7.85 |
% 28.41/7.85 +-Applying beta-rule and splitting (834), into two cases.
% 28.41/7.85 |-Branch one:
% 28.41/7.85 | (2258) all_0_57_57 = e0
% 28.41/7.85 |
% 28.41/7.85 | Combining equations (2258,6095) yields a new equation:
% 28.41/7.85 | (6278) all_0_34_34 = e0
% 28.41/7.85 |
% 28.41/7.85 | Equations (2258) can reduce 37 to:
% 28.41/7.85 | (3530) ~ (all_0_58_58 = e0)
% 28.41/7.85 |
% 28.41/7.85 | Simplifying 3530 yields:
% 28.41/7.85 | (431) ~ (all_0_58_58 = e0)
% 28.41/7.85 |
% 28.41/7.85 | Equations (2258) can reduce 143 to:
% 28.41/7.85 | (456) ~ (e4 = e0)
% 28.41/7.85 |
% 28.41/7.85 | Simplifying 456 yields:
% 28.41/7.85 | (6) ~ (e4 = e0)
% 28.41/7.85 |
% 28.41/7.85 | Equations (2258) can reduce 644 to:
% 28.41/7.85 | (568) ~ (e1 = e0)
% 28.41/7.85 |
% 28.41/7.85 | Simplifying 568 yields:
% 28.41/7.85 | (132) ~ (e1 = e0)
% 28.41/7.85 |
% 28.41/7.85 | From (2258) and (120) follows:
% 28.41/7.85 | (6285) op(e0, e0) = all_0_20_20
% 28.41/7.85 |
% 28.41/7.85 +-Applying beta-rule and splitting (4888), into two cases.
% 28.41/7.85 |-Branch one:
% 28.41/7.85 | (954) all_0_51_51 = e0
% 28.41/7.85 |
% 28.41/7.85 | Equations (954) can reduce 987 to:
% 28.41/7.85 | (270) $false
% 28.41/7.85 |
% 28.41/7.85 |-The branch is then unsatisfiable
% 28.41/7.85 |-Branch two:
% 28.41/7.85 | (987) ~ (all_0_51_51 = e0)
% 28.41/7.85 | (5003) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1
% 28.41/7.85 |
% 28.41/7.85 +-Applying beta-rule and splitting (5003), into two cases.
% 28.41/7.85 |-Branch one:
% 28.41/7.85 | (824) all_0_51_51 = e3
% 28.41/7.85 |
% 28.41/7.85 | Equations (824) can reduce 697 to:
% 28.41/7.85 | (719) ~ (e4 = e3)
% 28.41/7.85 |
% 28.41/7.85 | Simplifying 719 yields:
% 28.41/7.85 | (34) ~ (e4 = e3)
% 28.41/7.85 |
% 28.41/7.85 | Equations (824) can reduce 987 to:
% 28.41/7.85 | (66) ~ (e3 = e0)
% 28.41/7.85 |
% 28.41/7.85 +-Applying beta-rule and splitting (64), into two cases.
% 28.41/7.85 |-Branch one:
% 28.41/7.85 | (954) all_0_51_51 = e0
% 28.41/7.85 |
% 28.41/7.85 | Combining equations (954,824) yields a new equation:
% 28.41/7.85 | (784) e3 = e0
% 28.41/7.85 |
% 28.41/7.85 | Equations (784) can reduce 66 to:
% 28.41/7.85 | (270) $false
% 28.41/7.85 |
% 28.41/7.85 |-The branch is then unsatisfiable
% 28.41/7.85 |-Branch two:
% 28.41/7.85 | (987) ~ (all_0_51_51 = e0)
% 28.41/7.85 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 28.41/7.85 |
% 28.41/7.85 +-Applying beta-rule and splitting (221), into two cases.
% 28.41/7.85 |-Branch one:
% 28.41/7.85 | (1132) all_0_46_46 = e0
% 28.41/7.85 |
% 28.41/7.85 | Combining equations (517,1132) yields a new equation:
% 28.41/7.85 | (478) e4 = e0
% 28.41/7.85 |
% 28.41/7.85 | Simplifying 478 yields:
% 28.41/7.85 | (479) e4 = e0
% 28.41/7.85 |
% 28.41/7.85 | Equations (479) can reduce 6 to:
% 28.41/7.85 | (270) $false
% 28.41/7.85 |
% 28.41/7.85 |-The branch is then unsatisfiable
% 28.41/7.85 |-Branch two:
% 28.41/7.85 | (1010) ~ (all_0_46_46 = e0)
% 28.41/7.85 | (3629) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 28.41/7.85 |
% 28.41/7.85 | Equations (517) can reduce 1010 to:
% 28.41/7.85 | (6) ~ (e4 = e0)
% 28.41/7.85 |
% 28.41/7.85 +-Applying beta-rule and splitting (3067), into two cases.
% 28.41/7.85 |-Branch one:
% 28.41/7.85 | (827) all_0_52_52 = e0
% 28.41/7.85 |
% 28.41/7.85 | Combining equations (848,827) yields a new equation:
% 28.41/7.85 | (571) e1 = e0
% 28.41/7.85 |
% 28.41/7.85 | Simplifying 571 yields:
% 28.41/7.85 | (560) e1 = e0
% 28.41/7.85 |
% 28.41/7.85 | Equations (560) can reduce 132 to:
% 28.41/7.85 | (270) $false
% 28.41/7.85 |
% 28.41/7.85 |-The branch is then unsatisfiable
% 28.41/7.85 |-Branch two:
% 28.41/7.85 | (925) ~ (all_0_52_52 = e0)
% 28.41/7.85 | (3073) all_0_53_53 = e0 | all_0_54_54 = e0
% 28.41/7.85 |
% 28.41/7.85 +-Applying beta-rule and splitting (3073), into two cases.
% 28.41/7.85 |-Branch one:
% 28.41/7.85 | (423) all_0_53_53 = e0
% 28.41/7.85 |
% 28.41/7.85 | Combining equations (367,423) yields a new equation:
% 28.41/7.85 | (478) e4 = e0
% 28.41/7.85 |
% 28.41/7.85 | Simplifying 478 yields:
% 28.41/7.85 | (479) e4 = e0
% 28.41/7.85 |
% 28.41/7.85 | Equations (479) can reduce 6 to:
% 28.41/7.85 | (270) $false
% 28.41/7.85 |
% 28.41/7.85 |-The branch is then unsatisfiable
% 28.41/7.85 |-Branch two:
% 28.41/7.85 | (584) ~ (all_0_53_53 = e0)
% 28.41/7.85 | (3084) all_0_54_54 = e0
% 28.41/7.85 |
% 28.41/7.85 | Equations (3084) can reduce 261 to:
% 28.41/7.85 | (566) ~ (e2 = e0)
% 28.41/7.85 |
% 28.41/7.85 | Simplifying 566 yields:
% 28.41/7.85 | (57) ~ (e2 = e0)
% 28.41/7.85 |
% 28.41/7.85 | From (3084) and (138) follows:
% 28.41/7.85 | (6320) op(e0, e0) = all_0_36_36
% 28.41/7.85 |
% 28.41/7.85 +-Applying beta-rule and splitting (204), into two cases.
% 28.41/7.85 |-Branch one:
% 28.41/7.85 | (396) all_0_58_58 = e2
% 28.41/7.85 |
% 28.41/7.85 | Equations (396) can reduce 376 to:
% 28.41/7.85 | (270) $false
% 28.41/7.85 |
% 28.41/7.85 |-The branch is then unsatisfiable
% 28.41/7.85 |-Branch two:
% 28.41/7.85 | (376) ~ (all_0_58_58 = e2)
% 28.41/7.85 | (3890) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1 | all_0_58_58 = e0
% 28.41/7.85 |
% 28.41/7.85 +-Applying beta-rule and splitting (3890), into two cases.
% 28.41/7.85 |-Branch one:
% 28.41/7.85 | (585) all_0_58_58 = e0
% 28.41/7.85 |
% 28.41/7.85 | Equations (585) can reduce 431 to:
% 28.41/7.85 | (270) $false
% 28.41/7.85 |
% 28.41/7.85 |-The branch is then unsatisfiable
% 28.41/7.85 |-Branch two:
% 28.41/7.85 | (431) ~ (all_0_58_58 = e0)
% 28.41/7.85 | (4709) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1
% 28.41/7.85 |
% 28.41/7.85 +-Applying beta-rule and splitting (4709), into two cases.
% 28.41/7.85 |-Branch one:
% 28.41/7.85 | (4713) all_0_58_58 = e3
% 28.41/7.85 |
% 28.41/7.85 | Equations (4713) can reduce 718 to:
% 28.41/7.85 | (270) $false
% 28.41/7.85 |
% 28.41/7.85 |-The branch is then unsatisfiable
% 28.41/7.85 |-Branch two:
% 28.41/7.85 | (718) ~ (all_0_58_58 = e3)
% 28.41/7.85 | (4716) all_0_58_58 = e4 | all_0_58_58 = e1
% 28.41/7.85 |
% 28.41/7.85 +-Applying beta-rule and splitting (4716), into two cases.
% 28.41/7.85 |-Branch one:
% 28.41/7.85 | (1001) all_0_58_58 = e1
% 28.41/7.85 |
% 28.41/7.85 | Equations (1001) can reduce 278 to:
% 28.41/7.85 | (1021) ~ (e4 = e1)
% 28.41/7.85 |
% 28.41/7.85 | Simplifying 1021 yields:
% 28.41/7.85 | (251) ~ (e4 = e1)
% 28.41/7.85 |
% 28.41/7.85 | Equations (1001) can reduce 718 to:
% 28.41/7.85 | (769) ~ (e3 = e1)
% 28.41/7.85 |
% 28.41/7.85 | Simplifying 769 yields:
% 28.41/7.85 | (136) ~ (e3 = e1)
% 28.41/7.85 |
% 28.41/7.85 | From (1001) and (61) follows:
% 28.41/7.85 | (6338) op(e0, e1) = all_0_29_29
% 28.41/7.85 |
% 28.41/7.85 | From (1001) and (228) follows:
% 28.41/7.85 | (6339) op(e0, e1) = e1
% 28.41/7.86 |
% 28.41/7.86 | Instantiating formula (201) with e0, e4, all_0_32_32, e4 and discharging atoms op(e0, e4) = all_0_32_32, op(e0, e4) = e4, yields:
% 28.41/7.86 | (4556) all_0_32_32 = e4
% 28.41/7.86 |
% 28.41/7.86 | Instantiating formula (201) with e0, e1, all_0_30_30, all_0_29_29 and discharging atoms op(e0, e1) = all_0_29_29, op(e0, e1) = all_0_30_30, yields:
% 28.41/7.86 | (6341) all_0_29_29 = all_0_30_30
% 28.41/7.86 |
% 28.41/7.86 | Instantiating formula (201) with e0, e1, e1, all_0_29_29 and discharging atoms op(e0, e1) = all_0_29_29, op(e0, e1) = e1, yields:
% 28.41/7.86 | (6342) all_0_29_29 = e1
% 28.41/7.86 |
% 28.41/7.86 | Instantiating formula (201) with e0, e0, all_0_36_36, all_0_20_20 and discharging atoms op(e0, e0) = all_0_20_20, op(e0, e0) = all_0_36_36, yields:
% 28.41/7.86 | (6343) all_0_20_20 = all_0_36_36
% 28.41/7.86 |
% 28.41/7.86 | Instantiating formula (201) with e0, e0, e3, all_0_20_20 and discharging atoms op(e0, e0) = all_0_20_20, op(e0, e0) = e3, yields:
% 28.41/7.86 | (6344) all_0_20_20 = e3
% 28.41/7.86 |
% 28.41/7.86 | Combining equations (6343,6344) yields a new equation:
% 28.41/7.86 | (6345) all_0_36_36 = e3
% 28.41/7.86 |
% 28.41/7.86 | Simplifying 6345 yields:
% 28.41/7.86 | (6346) all_0_36_36 = e3
% 28.41/7.86 |
% 28.41/7.86 | Combining equations (6341,6342) yields a new equation:
% 28.41/7.86 | (6347) all_0_30_30 = e1
% 28.41/7.86 |
% 28.41/7.86 | Simplifying 6347 yields:
% 28.41/7.86 | (6348) all_0_30_30 = e1
% 28.41/7.86 |
% 28.41/7.86 +-Applying beta-rule and splitting (111), into two cases.
% 28.41/7.86 |-Branch one:
% 28.41/7.86 | (4557) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0)) | (all_0_34_34 = e2 & ~ (all_0_35_35 = e0))
% 28.41/7.86 |
% 28.41/7.86 +-Applying beta-rule and splitting (4557), into two cases.
% 28.41/7.86 |-Branch one:
% 28.41/7.86 | (4558) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0))
% 28.41/7.86 |
% 28.41/7.86 +-Applying beta-rule and splitting (4558), into two cases.
% 28.41/7.86 |-Branch one:
% 28.41/7.86 | (4559) all_0_30_30 = e4 & ~ (all_0_31_31 = e0)
% 28.41/7.86 |
% 28.41/7.86 | Applying alpha-rule on (4559) yields:
% 28.41/7.86 | (4560) all_0_30_30 = e4
% 28.41/7.86 | (4561) ~ (all_0_31_31 = e0)
% 28.41/7.86 |
% 28.41/7.86 | Combining equations (6348,4560) yields a new equation:
% 28.41/7.86 | (526) e4 = e1
% 28.41/7.86 |
% 28.41/7.86 | Equations (526) can reduce 251 to:
% 28.41/7.86 | (270) $false
% 28.41/7.86 |
% 28.41/7.86 |-The branch is then unsatisfiable
% 28.41/7.86 |-Branch two:
% 28.41/7.86 | (4565) all_0_32_32 = e3 & ~ (all_0_33_33 = e0)
% 28.41/7.86 |
% 28.41/7.86 | Applying alpha-rule on (4565) yields:
% 28.41/7.86 | (4566) all_0_32_32 = e3
% 28.41/7.86 | (4567) ~ (all_0_33_33 = e0)
% 28.41/7.86 |
% 28.41/7.86 | Combining equations (4556,4566) yields a new equation:
% 28.41/7.86 | (660) e4 = e3
% 28.41/7.86 |
% 28.41/7.86 | Simplifying 660 yields:
% 28.41/7.86 | (359) e4 = e3
% 28.41/7.86 |
% 28.41/7.86 | Equations (359) can reduce 34 to:
% 28.41/7.86 | (270) $false
% 28.41/7.86 |
% 28.41/7.86 |-The branch is then unsatisfiable
% 28.41/7.86 |-Branch two:
% 28.41/7.86 | (4571) all_0_34_34 = e2 & ~ (all_0_35_35 = e0)
% 28.41/7.86 |
% 28.41/7.86 | Applying alpha-rule on (4571) yields:
% 28.41/7.86 | (4572) all_0_34_34 = e2
% 28.41/7.86 | (4573) ~ (all_0_35_35 = e0)
% 28.41/7.86 |
% 28.41/7.86 | Combining equations (6278,4572) yields a new equation:
% 28.41/7.86 | (316) e2 = e0
% 28.41/7.86 |
% 28.41/7.86 | Equations (316) can reduce 57 to:
% 28.41/7.86 | (270) $false
% 28.41/7.86 |
% 28.41/7.86 |-The branch is then unsatisfiable
% 28.41/7.86 |-Branch two:
% 28.41/7.86 | (4577) all_0_36_36 = e1 & ~ (all_0_37_37 = e0)
% 28.41/7.86 |
% 28.41/7.86 | Applying alpha-rule on (4577) yields:
% 28.41/7.86 | (4578) all_0_36_36 = e1
% 28.41/7.86 | (4579) ~ (all_0_37_37 = e0)
% 28.41/7.86 |
% 28.41/7.86 | Combining equations (6346,4578) yields a new equation:
% 28.41/7.86 | (537) e3 = e1
% 28.41/7.86 |
% 28.41/7.86 | Simplifying 537 yields:
% 28.41/7.86 | (538) e3 = e1
% 28.41/7.86 |
% 28.41/7.86 | Equations (538) can reduce 136 to:
% 28.41/7.86 | (270) $false
% 28.41/7.86 |
% 28.41/7.86 |-The branch is then unsatisfiable
% 28.41/7.86 |-Branch two:
% 28.41/7.86 | (1004) ~ (all_0_58_58 = e1)
% 28.41/7.86 | (600) all_0_58_58 = e4
% 28.41/7.86 |
% 28.41/7.86 | Equations (600) can reduce 278 to:
% 28.41/7.86 | (270) $false
% 28.41/7.86 |
% 28.41/7.86 |-The branch is then unsatisfiable
% 28.41/7.86 |-Branch two:
% 28.41/7.86 | (932) ~ (all_0_51_51 = e3)
% 28.41/7.86 | (5007) all_0_51_51 = e4 | all_0_51_51 = e1
% 28.41/7.86 |
% 28.41/7.86 +-Applying beta-rule and splitting (5007), into two cases.
% 28.41/7.86 |-Branch one:
% 28.41/7.86 | (820) all_0_51_51 = e1
% 28.41/7.86 |
% 28.41/7.86 | Equations (820) can reduce 748 to:
% 28.41/7.86 | (270) $false
% 28.41/7.86 |
% 28.41/7.86 |-The branch is then unsatisfiable
% 28.41/7.86 |-Branch two:
% 28.41/7.86 | (748) ~ (all_0_51_51 = e1)
% 28.41/7.86 | (1467) all_0_51_51 = e4
% 28.41/7.86 |
% 28.41/7.86 | Equations (1467) can reduce 697 to:
% 28.41/7.86 | (270) $false
% 28.41/7.86 |
% 28.41/7.86 |-The branch is then unsatisfiable
% 28.41/7.86 |-Branch two:
% 28.41/7.86 | (2301) ~ (all_0_57_57 = e0)
% 28.41/7.86 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 28.41/7.86 |
% 28.41/7.86 +-Applying beta-rule and splitting (2302), into two cases.
% 28.41/7.86 |-Branch one:
% 28.41/7.86 | (585) all_0_58_58 = e0
% 28.41/7.86 |
% 28.41/7.86 | Equations (585) can reduce 431 to:
% 28.41/7.86 | (270) $false
% 28.41/7.86 |
% 28.41/7.86 |-The branch is then unsatisfiable
% 28.41/7.86 |-Branch two:
% 28.41/7.86 | (431) ~ (all_0_58_58 = e0)
% 28.41/7.87 | (2308) all_0_59_59 = e0
% 28.41/7.87 |
% 28.41/7.87 | Combining equations (412,2308) yields a new equation:
% 28.41/7.87 | (783) e3 = e0
% 28.41/7.87 |
% 28.41/7.87 | Simplifying 783 yields:
% 28.41/7.87 | (784) e3 = e0
% 28.41/7.87 |
% 28.41/7.87 | Equations (784) can reduce 66 to:
% 28.41/7.87 | (270) $false
% 28.41/7.87 |
% 28.41/7.87 |-The branch is then unsatisfiable
% 28.41/7.87 |-Branch two:
% 28.41/7.87 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 28.41/7.87 |
% 28.41/7.87 | Applying alpha-rule on (416) yields:
% 28.41/7.87 | (411) all_0_43_43 = e0
% 28.41/7.87 | (412) all_0_59_59 = e3
% 28.41/7.87 | (419) ~ (all_0_56_56 = e0)
% 28.41/7.87 |
% 28.41/7.87 | Equations (411) can reduce 241 to:
% 28.41/7.87 | (6251) ~ (all_0_44_44 = e0)
% 28.41/7.87 |
% 28.41/7.87 | Simplifying 6251 yields:
% 28.41/7.87 | (625) ~ (all_0_44_44 = e0)
% 28.41/7.87 |
% 28.41/7.87 | Equations (411) can reduce 240 to:
% 28.41/7.87 | (6253) ~ (all_0_51_51 = e0)
% 28.41/7.87 |
% 28.41/7.87 | Simplifying 6253 yields:
% 28.41/7.87 | (987) ~ (all_0_51_51 = e0)
% 28.41/7.87 |
% 28.41/7.87 | Equations (388) can reduce 419 to:
% 28.41/7.87 | (57) ~ (e2 = e0)
% 28.41/7.87 |
% 28.41/7.87 | Equations (412) can reduce 156 to:
% 28.41/7.87 | (718) ~ (all_0_58_58 = e3)
% 28.41/7.87 |
% 28.41/7.87 | From (412) and (161) follows:
% 28.41/7.87 | (6258) op(e0, e0) = e3
% 28.41/7.87 |
% 28.41/7.87 +-Applying beta-rule and splitting (193), into two cases.
% 28.41/7.87 |-Branch one:
% 28.41/7.87 | (370) all_0_44_44 = e2
% 28.41/7.87 |
% 28.41/7.87 | Equations (370) can reduce 333 to:
% 28.41/7.87 | (270) $false
% 28.41/7.87 |
% 28.41/7.87 |-The branch is then unsatisfiable
% 28.41/7.87 |-Branch two:
% 28.41/7.87 | (333) ~ (all_0_44_44 = e2)
% 28.41/7.87 | (373) all_0_44_44 = e3 | all_0_44_44 = e0
% 28.41/7.87 |
% 28.41/7.87 +-Applying beta-rule and splitting (373), into two cases.
% 28.41/7.87 |-Branch one:
% 28.41/7.87 | (621) all_0_44_44 = e0
% 28.41/7.87 |
% 28.41/7.87 | Equations (621) can reduce 625 to:
% 28.41/7.87 | (270) $false
% 28.41/7.87 |
% 28.41/7.87 |-The branch is then unsatisfiable
% 28.41/7.87 |-Branch two:
% 28.41/7.87 | (625) ~ (all_0_44_44 = e0)
% 28.41/7.87 | (858) all_0_44_44 = e3
% 28.41/7.87 |
% 28.41/7.87 | Equations (858) can reduce 625 to:
% 28.41/7.87 | (66) ~ (e3 = e0)
% 28.41/7.87 |
% 28.41/7.87 +-Applying beta-rule and splitting (176), into two cases.
% 28.41/7.87 |-Branch one:
% 28.41/7.87 | (830) all_0_56_56 = e0
% 28.41/7.87 |
% 28.41/7.87 | Combining equations (830,388) yields a new equation:
% 28.41/7.87 | (316) e2 = e0
% 28.41/7.87 |
% 28.41/7.87 | Equations (316) can reduce 57 to:
% 28.41/7.87 | (270) $false
% 28.41/7.87 |
% 28.41/7.87 |-The branch is then unsatisfiable
% 28.41/7.87 |-Branch two:
% 28.41/7.87 | (419) ~ (all_0_56_56 = e0)
% 28.41/7.87 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 28.41/7.87 |
% 28.41/7.87 +-Applying beta-rule and splitting (173), into two cases.
% 28.41/7.87 |-Branch one:
% 28.41/7.87 | (4215) all_0_51_51 = e2
% 28.41/7.87 |
% 28.41/7.87 | Equations (4215) can reduce 255 to:
% 28.41/7.87 | (270) $false
% 28.41/7.87 |
% 28.41/7.87 |-The branch is then unsatisfiable
% 28.41/7.87 |-Branch two:
% 28.41/7.87 | (255) ~ (all_0_51_51 = e2)
% 28.41/7.87 | (4888) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1 | all_0_51_51 = e0
% 28.41/7.87 |
% 28.41/7.87 +-Applying beta-rule and splitting (834), into two cases.
% 28.41/7.87 |-Branch one:
% 28.41/7.87 | (2258) all_0_57_57 = e0
% 28.41/7.87 |
% 28.41/7.87 | Combining equations (2258,6095) yields a new equation:
% 28.41/7.87 | (6278) all_0_34_34 = e0
% 28.41/7.87 |
% 28.41/7.87 | Equations (2258) can reduce 37 to:
% 28.41/7.87 | (3530) ~ (all_0_58_58 = e0)
% 28.41/7.87 |
% 28.41/7.87 | Simplifying 3530 yields:
% 28.41/7.87 | (431) ~ (all_0_58_58 = e0)
% 28.41/7.87 |
% 28.41/7.87 | Equations (2258) can reduce 143 to:
% 28.41/7.87 | (456) ~ (e4 = e0)
% 28.41/7.87 |
% 28.41/7.87 | Simplifying 456 yields:
% 28.41/7.87 | (6) ~ (e4 = e0)
% 28.41/7.87 |
% 28.41/7.87 | Equations (2258) can reduce 644 to:
% 28.41/7.87 | (568) ~ (e1 = e0)
% 28.41/7.87 |
% 28.41/7.87 | Simplifying 568 yields:
% 28.41/7.87 | (132) ~ (e1 = e0)
% 28.41/7.87 |
% 28.41/7.87 | From (2258) and (120) follows:
% 28.41/7.87 | (6285) op(e0, e0) = all_0_20_20
% 28.41/7.87 |
% 28.41/7.87 +-Applying beta-rule and splitting (4888), into two cases.
% 28.41/7.87 |-Branch one:
% 28.41/7.87 | (954) all_0_51_51 = e0
% 28.41/7.87 |
% 28.41/7.87 | Equations (954) can reduce 987 to:
% 28.41/7.87 | (270) $false
% 28.41/7.87 |
% 28.41/7.87 |-The branch is then unsatisfiable
% 28.41/7.87 |-Branch two:
% 28.41/7.87 | (987) ~ (all_0_51_51 = e0)
% 28.41/7.87 | (5003) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1
% 28.41/7.87 |
% 28.41/7.87 +-Applying beta-rule and splitting (5003), into two cases.
% 28.41/7.87 |-Branch one:
% 28.41/7.87 | (824) all_0_51_51 = e3
% 28.41/7.87 |
% 28.41/7.87 | Equations (824) can reduce 697 to:
% 28.41/7.87 | (719) ~ (e4 = e3)
% 28.41/7.87 |
% 28.41/7.87 | Simplifying 719 yields:
% 28.41/7.87 | (34) ~ (e4 = e3)
% 28.41/7.87 |
% 28.41/7.87 | Equations (824) can reduce 987 to:
% 28.41/7.87 | (66) ~ (e3 = e0)
% 28.41/7.87 |
% 28.41/7.87 +-Applying beta-rule and splitting (64), into two cases.
% 28.41/7.87 |-Branch one:
% 28.41/7.87 | (954) all_0_51_51 = e0
% 28.41/7.87 |
% 28.41/7.87 | Combining equations (954,824) yields a new equation:
% 28.41/7.87 | (784) e3 = e0
% 28.41/7.87 |
% 28.41/7.87 | Equations (784) can reduce 66 to:
% 28.41/7.87 | (270) $false
% 28.41/7.87 |
% 28.41/7.87 |-The branch is then unsatisfiable
% 28.41/7.87 |-Branch two:
% 28.41/7.87 | (987) ~ (all_0_51_51 = e0)
% 28.41/7.87 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 28.41/7.87 |
% 28.41/7.87 +-Applying beta-rule and splitting (221), into two cases.
% 28.41/7.87 |-Branch one:
% 28.41/7.87 | (1132) all_0_46_46 = e0
% 28.41/7.87 |
% 28.41/7.87 | Combining equations (517,1132) yields a new equation:
% 28.41/7.87 | (478) e4 = e0
% 28.41/7.87 |
% 28.41/7.87 | Simplifying 478 yields:
% 28.41/7.87 | (479) e4 = e0
% 28.41/7.87 |
% 28.41/7.87 | Equations (479) can reduce 6 to:
% 28.41/7.87 | (270) $false
% 28.41/7.87 |
% 28.41/7.87 |-The branch is then unsatisfiable
% 28.41/7.87 |-Branch two:
% 28.41/7.87 | (1010) ~ (all_0_46_46 = e0)
% 28.41/7.87 | (3629) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 28.41/7.87 |
% 28.41/7.87 | Equations (517) can reduce 1010 to:
% 28.41/7.87 | (6) ~ (e4 = e0)
% 28.41/7.87 |
% 28.41/7.87 +-Applying beta-rule and splitting (3067), into two cases.
% 28.41/7.87 |-Branch one:
% 28.41/7.87 | (827) all_0_52_52 = e0
% 28.41/7.87 |
% 28.41/7.87 | Combining equations (848,827) yields a new equation:
% 28.41/7.87 | (571) e1 = e0
% 28.41/7.87 |
% 28.41/7.87 | Simplifying 571 yields:
% 28.41/7.87 | (560) e1 = e0
% 28.41/7.87 |
% 28.41/7.87 | Equations (560) can reduce 132 to:
% 28.41/7.87 | (270) $false
% 28.41/7.87 |
% 28.41/7.87 |-The branch is then unsatisfiable
% 28.41/7.87 |-Branch two:
% 28.41/7.87 | (925) ~ (all_0_52_52 = e0)
% 28.41/7.87 | (3073) all_0_53_53 = e0 | all_0_54_54 = e0
% 28.41/7.87 |
% 28.41/7.87 +-Applying beta-rule and splitting (3073), into two cases.
% 28.41/7.87 |-Branch one:
% 28.41/7.87 | (423) all_0_53_53 = e0
% 28.41/7.87 |
% 28.41/7.87 | Combining equations (367,423) yields a new equation:
% 28.41/7.87 | (478) e4 = e0
% 28.41/7.87 |
% 28.41/7.87 | Simplifying 478 yields:
% 28.41/7.87 | (479) e4 = e0
% 28.41/7.87 |
% 28.41/7.87 | Equations (479) can reduce 6 to:
% 28.41/7.87 | (270) $false
% 28.41/7.87 |
% 28.41/7.87 |-The branch is then unsatisfiable
% 28.41/7.87 |-Branch two:
% 28.41/7.87 | (584) ~ (all_0_53_53 = e0)
% 28.41/7.87 | (3084) all_0_54_54 = e0
% 28.41/7.87 |
% 28.41/7.87 | Equations (3084) can reduce 261 to:
% 28.41/7.87 | (566) ~ (e2 = e0)
% 28.41/7.87 |
% 28.41/7.87 | Simplifying 566 yields:
% 28.41/7.87 | (57) ~ (e2 = e0)
% 28.41/7.87 |
% 28.41/7.87 | From (3084) and (138) follows:
% 28.41/7.87 | (6320) op(e0, e0) = all_0_36_36
% 28.41/7.87 |
% 28.41/7.87 +-Applying beta-rule and splitting (204), into two cases.
% 28.41/7.87 |-Branch one:
% 28.41/7.87 | (396) all_0_58_58 = e2
% 28.41/7.87 |
% 28.41/7.87 | Equations (396) can reduce 376 to:
% 28.41/7.87 | (270) $false
% 28.41/7.87 |
% 28.41/7.87 |-The branch is then unsatisfiable
% 28.41/7.87 |-Branch two:
% 28.41/7.87 | (376) ~ (all_0_58_58 = e2)
% 28.41/7.87 | (3890) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1 | all_0_58_58 = e0
% 28.41/7.87 |
% 28.41/7.87 +-Applying beta-rule and splitting (3890), into two cases.
% 28.41/7.87 |-Branch one:
% 28.41/7.87 | (585) all_0_58_58 = e0
% 28.41/7.87 |
% 28.41/7.87 | Equations (585) can reduce 431 to:
% 28.41/7.87 | (270) $false
% 28.41/7.87 |
% 28.41/7.87 |-The branch is then unsatisfiable
% 28.41/7.87 |-Branch two:
% 28.41/7.87 | (431) ~ (all_0_58_58 = e0)
% 28.41/7.87 | (4709) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1
% 28.41/7.87 |
% 28.41/7.87 +-Applying beta-rule and splitting (4709), into two cases.
% 28.41/7.87 |-Branch one:
% 28.41/7.87 | (4713) all_0_58_58 = e3
% 28.41/7.87 |
% 28.41/7.87 | Equations (4713) can reduce 718 to:
% 28.41/7.87 | (270) $false
% 28.41/7.87 |
% 28.41/7.87 |-The branch is then unsatisfiable
% 28.41/7.87 |-Branch two:
% 28.41/7.87 | (718) ~ (all_0_58_58 = e3)
% 28.41/7.87 | (4716) all_0_58_58 = e4 | all_0_58_58 = e1
% 28.41/7.87 |
% 28.41/7.87 +-Applying beta-rule and splitting (4716), into two cases.
% 28.41/7.87 |-Branch one:
% 28.41/7.87 | (1001) all_0_58_58 = e1
% 28.41/7.87 |
% 28.41/7.87 | Equations (1001) can reduce 278 to:
% 28.41/7.87 | (1021) ~ (e4 = e1)
% 28.41/7.87 |
% 28.41/7.87 | Simplifying 1021 yields:
% 28.41/7.87 | (251) ~ (e4 = e1)
% 28.41/7.87 |
% 28.41/7.87 | Equations (1001) can reduce 718 to:
% 28.41/7.87 | (769) ~ (e3 = e1)
% 28.41/7.87 |
% 28.41/7.87 | Simplifying 769 yields:
% 28.41/7.87 | (136) ~ (e3 = e1)
% 28.41/7.87 |
% 28.41/7.87 | From (1001) and (61) follows:
% 28.41/7.87 | (6338) op(e0, e1) = all_0_29_29
% 28.41/7.87 |
% 28.41/7.87 | From (1001) and (228) follows:
% 28.41/7.87 | (6339) op(e0, e1) = e1
% 28.41/7.87 |
% 28.41/7.87 | Instantiating formula (201) with e0, e4, all_0_32_32, e4 and discharging atoms op(e0, e4) = all_0_32_32, op(e0, e4) = e4, yields:
% 28.41/7.87 | (4556) all_0_32_32 = e4
% 28.41/7.87 |
% 28.41/7.87 | Instantiating formula (201) with e0, e1, all_0_30_30, all_0_29_29 and discharging atoms op(e0, e1) = all_0_29_29, op(e0, e1) = all_0_30_30, yields:
% 28.41/7.87 | (6341) all_0_29_29 = all_0_30_30
% 28.41/7.87 |
% 28.41/7.87 | Instantiating formula (201) with e0, e1, e1, all_0_29_29 and discharging atoms op(e0, e1) = all_0_29_29, op(e0, e1) = e1, yields:
% 28.41/7.88 | (6342) all_0_29_29 = e1
% 28.41/7.88 |
% 28.41/7.88 | Instantiating formula (201) with e0, e0, all_0_36_36, all_0_20_20 and discharging atoms op(e0, e0) = all_0_20_20, op(e0, e0) = all_0_36_36, yields:
% 28.41/7.88 | (6343) all_0_20_20 = all_0_36_36
% 28.41/7.88 |
% 28.41/7.88 | Instantiating formula (201) with e0, e0, e3, all_0_20_20 and discharging atoms op(e0, e0) = all_0_20_20, op(e0, e0) = e3, yields:
% 28.41/7.88 | (6344) all_0_20_20 = e3
% 28.41/7.88 |
% 28.41/7.88 | Combining equations (6343,6344) yields a new equation:
% 28.41/7.88 | (6345) all_0_36_36 = e3
% 28.41/7.88 |
% 28.41/7.88 | Simplifying 6345 yields:
% 28.41/7.88 | (6346) all_0_36_36 = e3
% 28.41/7.88 |
% 28.41/7.88 | Combining equations (6341,6342) yields a new equation:
% 28.41/7.88 | (6347) all_0_30_30 = e1
% 28.41/7.88 |
% 28.41/7.88 | Simplifying 6347 yields:
% 28.58/7.88 | (6348) all_0_30_30 = e1
% 28.58/7.88 |
% 28.58/7.88 +-Applying beta-rule and splitting (111), into two cases.
% 28.58/7.88 |-Branch one:
% 28.58/7.88 | (4557) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0)) | (all_0_34_34 = e2 & ~ (all_0_35_35 = e0))
% 28.58/7.88 |
% 28.58/7.88 +-Applying beta-rule and splitting (4557), into two cases.
% 28.58/7.88 |-Branch one:
% 28.58/7.88 | (4558) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0))
% 28.58/7.88 |
% 28.58/7.88 +-Applying beta-rule and splitting (4558), into two cases.
% 28.58/7.88 |-Branch one:
% 28.58/7.88 | (4559) all_0_30_30 = e4 & ~ (all_0_31_31 = e0)
% 28.58/7.88 |
% 28.58/7.88 | Applying alpha-rule on (4559) yields:
% 28.58/7.88 | (4560) all_0_30_30 = e4
% 28.58/7.88 | (4561) ~ (all_0_31_31 = e0)
% 28.58/7.88 |
% 28.58/7.88 | Combining equations (6348,4560) yields a new equation:
% 28.58/7.88 | (526) e4 = e1
% 28.58/7.88 |
% 28.58/7.88 | Equations (526) can reduce 251 to:
% 28.58/7.88 | (270) $false
% 28.58/7.88 |
% 28.58/7.88 |-The branch is then unsatisfiable
% 28.58/7.88 |-Branch two:
% 28.58/7.88 | (4565) all_0_32_32 = e3 & ~ (all_0_33_33 = e0)
% 28.58/7.88 |
% 28.58/7.88 | Applying alpha-rule on (4565) yields:
% 28.58/7.88 | (4566) all_0_32_32 = e3
% 28.58/7.88 | (4567) ~ (all_0_33_33 = e0)
% 28.58/7.88 |
% 28.58/7.88 | Combining equations (4556,4566) yields a new equation:
% 28.58/7.88 | (660) e4 = e3
% 28.58/7.88 |
% 28.58/7.88 | Simplifying 660 yields:
% 28.58/7.88 | (359) e4 = e3
% 28.58/7.88 |
% 28.58/7.88 | Equations (359) can reduce 34 to:
% 28.58/7.88 | (270) $false
% 28.58/7.88 |
% 28.58/7.88 |-The branch is then unsatisfiable
% 28.58/7.88 |-Branch two:
% 28.58/7.88 | (4571) all_0_34_34 = e2 & ~ (all_0_35_35 = e0)
% 28.58/7.88 |
% 28.58/7.88 | Applying alpha-rule on (4571) yields:
% 28.58/7.88 | (4572) all_0_34_34 = e2
% 28.58/7.88 | (4573) ~ (all_0_35_35 = e0)
% 28.58/7.88 |
% 28.58/7.88 | Combining equations (6278,4572) yields a new equation:
% 28.58/7.88 | (316) e2 = e0
% 28.58/7.88 |
% 28.58/7.88 | Equations (316) can reduce 57 to:
% 28.58/7.88 | (270) $false
% 28.58/7.88 |
% 28.58/7.88 |-The branch is then unsatisfiable
% 28.58/7.88 |-Branch two:
% 28.58/7.88 | (4577) all_0_36_36 = e1 & ~ (all_0_37_37 = e0)
% 28.58/7.88 |
% 28.58/7.88 | Applying alpha-rule on (4577) yields:
% 28.58/7.88 | (4578) all_0_36_36 = e1
% 28.58/7.88 | (4579) ~ (all_0_37_37 = e0)
% 28.58/7.88 |
% 28.58/7.88 | Combining equations (6346,4578) yields a new equation:
% 28.58/7.88 | (537) e3 = e1
% 28.58/7.88 |
% 28.58/7.88 | Simplifying 537 yields:
% 28.58/7.88 | (538) e3 = e1
% 28.58/7.88 |
% 28.58/7.88 | Equations (538) can reduce 136 to:
% 28.58/7.88 | (270) $false
% 28.58/7.88 |
% 28.58/7.88 |-The branch is then unsatisfiable
% 28.58/7.88 |-Branch two:
% 28.58/7.88 | (1004) ~ (all_0_58_58 = e1)
% 28.58/7.88 | (600) all_0_58_58 = e4
% 28.58/7.88 |
% 28.58/7.88 | Equations (600) can reduce 278 to:
% 28.58/7.88 | (270) $false
% 28.58/7.88 |
% 28.58/7.88 |-The branch is then unsatisfiable
% 28.58/7.88 |-Branch two:
% 28.58/7.88 | (932) ~ (all_0_51_51 = e3)
% 28.58/7.88 | (5007) all_0_51_51 = e4 | all_0_51_51 = e1
% 28.58/7.88 |
% 28.58/7.88 +-Applying beta-rule and splitting (5007), into two cases.
% 28.58/7.88 |-Branch one:
% 28.58/7.88 | (820) all_0_51_51 = e1
% 28.58/7.88 |
% 28.58/7.88 | Equations (820) can reduce 748 to:
% 28.58/7.88 | (270) $false
% 28.58/7.88 |
% 28.58/7.88 |-The branch is then unsatisfiable
% 28.58/7.88 |-Branch two:
% 28.58/7.88 | (748) ~ (all_0_51_51 = e1)
% 28.58/7.88 | (1467) all_0_51_51 = e4
% 28.58/7.88 |
% 28.58/7.88 | Equations (1467) can reduce 697 to:
% 28.58/7.88 | (270) $false
% 28.58/7.88 |
% 28.58/7.88 |-The branch is then unsatisfiable
% 28.58/7.88 |-Branch two:
% 28.58/7.88 | (2301) ~ (all_0_57_57 = e0)
% 28.58/7.88 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 28.58/7.88 |
% 28.58/7.88 +-Applying beta-rule and splitting (2302), into two cases.
% 28.58/7.88 |-Branch one:
% 28.58/7.88 | (585) all_0_58_58 = e0
% 28.58/7.88 |
% 28.58/7.88 | Equations (585) can reduce 431 to:
% 28.58/7.88 | (270) $false
% 28.58/7.88 |
% 28.58/7.88 |-The branch is then unsatisfiable
% 28.58/7.88 |-Branch two:
% 28.58/7.88 | (431) ~ (all_0_58_58 = e0)
% 28.58/7.88 | (2308) all_0_59_59 = e0
% 28.58/7.88 |
% 28.58/7.88 | Combining equations (412,2308) yields a new equation:
% 28.58/7.88 | (783) e3 = e0
% 28.58/7.88 |
% 28.58/7.88 | Simplifying 783 yields:
% 28.58/7.88 | (784) e3 = e0
% 28.58/7.88 |
% 28.58/7.88 | Equations (784) can reduce 66 to:
% 28.58/7.88 | (270) $false
% 28.58/7.88 |
% 28.58/7.88 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 28.58/7.89 |
% 28.58/7.89 | Applying alpha-rule on (422) yields:
% 28.58/7.89 | (423) all_0_53_53 = e0
% 28.58/7.89 | (424) all_0_59_59 = e1
% 28.58/7.89 | (425) ~ (all_0_54_54 = e1)
% 28.58/7.89 |
% 28.58/7.89 | Combining equations (367,423) yields a new equation:
% 28.58/7.89 | (478) e4 = e0
% 28.58/7.89 |
% 28.58/7.89 | Simplifying 478 yields:
% 28.58/7.89 | (479) e4 = e0
% 28.58/7.89 |
% 28.58/7.89 | Equations (479) can reduce 6 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 28.58/7.89 |
% 28.58/7.89 | Applying alpha-rule on (428) yields:
% 28.58/7.89 | (423) all_0_53_53 = e0
% 28.58/7.89 | (424) all_0_59_59 = e1
% 28.58/7.89 | (431) ~ (all_0_58_58 = e0)
% 28.58/7.89 |
% 28.58/7.89 | Combining equations (367,423) yields a new equation:
% 28.58/7.89 | (478) e4 = e0
% 28.58/7.89 |
% 28.58/7.89 | Simplifying 478 yields:
% 28.58/7.89 | (479) e4 = e0
% 28.58/7.89 |
% 28.58/7.89 | Equations (479) can reduce 6 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (642) ~ (all_0_52_52 = e1)
% 28.58/7.89 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (852), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (853) all_0_53_53 = e1
% 28.58/7.89 |
% 28.58/7.89 | Combining equations (853,367) yields a new equation:
% 28.58/7.89 | (526) e4 = e1
% 28.58/7.89 |
% 28.58/7.89 | Equations (526) can reduce 251 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (874) ~ (all_0_53_53 = e1)
% 28.58/7.89 | (875) all_0_54_54 = e1
% 28.58/7.89 |
% 28.58/7.89 | Equations (875) can reduce 425 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (599) ~ (all_0_53_53 = e4)
% 28.58/7.89 | (600) all_0_58_58 = e4
% 28.58/7.89 |
% 28.58/7.89 | Equations (600) can reduce 278 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (591) ~ (all_0_39_39 = e4)
% 28.58/7.89 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (592), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (358) all_0_41_41 = e4
% 28.58/7.89 |
% 28.58/7.89 | Combining equations (351,358) yields a new equation:
% 28.58/7.89 | (359) e4 = e3
% 28.58/7.89 |
% 28.58/7.89 | Equations (359) can reduce 34 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (361) ~ (all_0_41_41 = e4)
% 28.58/7.89 | (512) all_0_42_42 = e4
% 28.58/7.89 |
% 28.58/7.89 | Combining equations (541,512) yields a new equation:
% 28.58/7.89 | (526) e4 = e1
% 28.58/7.89 |
% 28.58/7.89 | Equations (526) can reduce 251 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (300) ~ (all_0_56_56 = e2)
% 28.58/7.89 | (391) all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (391), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (392) all_0_57_57 = e2
% 28.58/7.89 |
% 28.58/7.89 | Equations (392) can reduce 335 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (335) ~ (all_0_57_57 = e2)
% 28.58/7.89 | (395) all_0_58_58 = e2 | all_0_59_59 = e2
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (395), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (396) all_0_58_58 = e2
% 28.58/7.89 |
% 28.58/7.89 | Equations (396) can reduce 376 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (376) ~ (all_0_58_58 = e2)
% 28.58/7.89 | (399) all_0_59_59 = e2
% 28.58/7.89 |
% 28.58/7.89 | Equations (399) can reduce 701 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (434) ~ (all_0_45_45 = e2)
% 28.58/7.89 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (435), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (454) all_0_45_45 = e0
% 28.58/7.89 |
% 28.58/7.89 | Equations (454) can reduce 488 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (488) ~ (all_0_45_45 = e0)
% 28.58/7.89 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (489), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (505) all_0_45_45 = e3
% 28.58/7.89 |
% 28.58/7.89 | Equations (505) can reduce 354 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (354) ~ (all_0_45_45 = e3)
% 28.58/7.89 | (363) all_0_45_45 = e4
% 28.58/7.89 |
% 28.58/7.89 | Equations (363) can reduce 352 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (602) ~ (all_0_40_40 = e2)
% 28.58/7.89 | (603) all_0_40_40 = e3 | all_0_40_40 = e1
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (20), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (327) all_0_40_40 = e2
% 28.58/7.89 |
% 28.58/7.89 | Equations (327) can reduce 602 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (602) ~ (all_0_40_40 = e2)
% 28.58/7.89 | (607) all_0_44_44 = e2 | all_0_52_52 = e2 | all_0_57_57 = e2
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (193), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (370) all_0_44_44 = e2
% 28.58/7.89 |
% 28.58/7.89 | Equations (370) can reduce 15 to:
% 28.58/7.89 | (602) ~ (all_0_40_40 = e2)
% 28.58/7.89 |
% 28.58/7.89 | Equations (370) can reduce 241 to:
% 28.58/7.89 | (292) ~ (all_0_43_43 = e2)
% 28.58/7.89 |
% 28.58/7.89 | Equations (370) can reduce 229 to:
% 28.58/7.89 | (611) ~ (all_0_45_45 = e2)
% 28.58/7.89 |
% 28.58/7.89 | Simplifying 611 yields:
% 28.58/7.89 | (434) ~ (all_0_45_45 = e2)
% 28.58/7.89 |
% 28.58/7.89 | Equations (370) can reduce 131 to:
% 28.58/7.89 | (141) ~ (e2 = e1)
% 28.58/7.89 |
% 28.58/7.89 | From (370) and (165) follows:
% 28.58/7.89 | (619) op(e2, e2) = all_0_15_15
% 28.58/7.89 |
% 28.58/7.89 | Instantiating formula (201) with e2, e2, all_0_15_15, e4 and discharging atoms op(e2, e2) = all_0_15_15, op(e2, e2) = e4, yields:
% 28.58/7.89 | (620) all_0_15_15 = e4
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (9), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (621) all_0_44_44 = e0
% 28.58/7.89 |
% 28.58/7.89 | Combining equations (370,621) yields a new equation:
% 28.58/7.89 | (622) e2 = e0
% 28.58/7.89 |
% 28.58/7.89 | Simplifying 622 yields:
% 28.58/7.89 | (316) e2 = e0
% 28.58/7.89 |
% 28.58/7.89 | Equations (316) can reduce 57 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (625) ~ (all_0_44_44 = e0)
% 28.58/7.89 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (164), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (336) all_0_39_39 = e2
% 28.58/7.89 |
% 28.58/7.89 | Equations (336) can reduce 114 to:
% 28.58/7.89 | (6613) ~ (all_0_40_40 = e2)
% 28.58/7.89 |
% 28.58/7.89 | Simplifying 6613 yields:
% 28.58/7.89 | (602) ~ (all_0_40_40 = e2)
% 28.58/7.89 |
% 28.58/7.89 | Equations (336) can reduce 226 to:
% 28.58/7.89 | (330) ~ (all_0_41_41 = e2)
% 28.58/7.89 |
% 28.58/7.89 | Simplifying 330 yields:
% 28.58/7.89 | (331) ~ (all_0_41_41 = e2)
% 28.58/7.89 |
% 28.58/7.89 | Equations (336) can reduce 184 to:
% 28.58/7.89 | (1336) ~ (all_0_42_42 = e2)
% 28.58/7.89 |
% 28.58/7.89 | Simplifying 1336 yields:
% 28.58/7.89 | (498) ~ (all_0_42_42 = e2)
% 28.58/7.89 |
% 28.58/7.89 | Equations (336) can reduce 528 to:
% 28.58/7.89 | (141) ~ (e2 = e1)
% 28.58/7.89 |
% 28.58/7.89 | Equations (336) can reduce 101 to:
% 28.58/7.89 | (57) ~ (e2 = e0)
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (187), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (436) all_0_41_41 = e2
% 28.58/7.89 |
% 28.58/7.89 | Equations (436) can reduce 331 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (331) ~ (all_0_41_41 = e2)
% 28.58/7.89 | (441) all_0_45_45 = e2 | all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (441), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (374) all_0_45_45 = e2
% 28.58/7.89 |
% 28.58/7.89 | Equations (374) can reduce 434 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (434) ~ (all_0_45_45 = e2)
% 28.58/7.89 | (445) all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (445), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (311) all_0_48_48 = e2
% 28.58/7.89 |
% 28.58/7.89 | Combining equations (311,559) yields a new equation:
% 28.58/7.89 | (622) e2 = e0
% 28.58/7.89 |
% 28.58/7.89 | Simplifying 622 yields:
% 28.58/7.89 | (316) e2 = e0
% 28.58/7.89 |
% 28.58/7.89 | Equations (316) can reduce 57 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (294) ~ (all_0_48_48 = e2)
% 28.58/7.89 | (449) all_0_53_53 = e2 | all_0_58_58 = e2
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (449), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (576) all_0_53_53 = e2
% 28.58/7.89 |
% 28.58/7.89 | Equations (576) can reduce 259 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (259) ~ (all_0_53_53 = e2)
% 28.58/7.89 | (396) all_0_58_58 = e2
% 28.58/7.89 |
% 28.58/7.89 | Equations (396) can reduce 157 to:
% 28.58/7.89 | (331) ~ (all_0_41_41 = e2)
% 28.58/7.89 |
% 28.58/7.89 | Equations (396) can reduce 108 to:
% 28.58/7.89 | (434) ~ (all_0_45_45 = e2)
% 28.58/7.89 |
% 28.58/7.89 | Equations (396) can reduce 70 to:
% 28.58/7.89 | (259) ~ (all_0_53_53 = e2)
% 28.58/7.89 |
% 28.58/7.89 | Equations (396) can reduce 37 to:
% 28.58/7.89 | (335) ~ (all_0_57_57 = e2)
% 28.58/7.89 |
% 28.58/7.89 | From (396) and (63) follows:
% 28.58/7.89 | (1846) op(e1, e2) = all_0_28_28
% 28.58/7.89 |
% 28.58/7.89 | From (396) and (61) follows:
% 28.58/7.89 | (6644) op(e0, e2) = all_0_29_29
% 28.58/7.89 |
% 28.58/7.89 | From (396) and (228) follows:
% 28.58/7.89 | (6645) op(e0, e1) = e2
% 28.58/7.89 |
% 28.58/7.89 | Instantiating formula (201) with e1, e2, all_0_28_28, all_0_52_52 and discharging atoms op(e1, e2) = all_0_28_28, op(e1, e2) = all_0_52_52, yields:
% 28.58/7.89 | (1848) all_0_28_28 = all_0_52_52
% 28.58/7.89 |
% 28.58/7.89 | Instantiating formula (201) with e0, e2, all_0_29_29, all_0_57_57 and discharging atoms op(e0, e2) = all_0_29_29, op(e0, e2) = all_0_57_57, yields:
% 28.58/7.89 | (6647) all_0_29_29 = all_0_57_57
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (52), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (536) all_0_41_41 = e1
% 28.58/7.89 |
% 28.58/7.89 | Equations (536) can reduce 147 to:
% 28.58/7.89 | (534) ~ (all_0_40_40 = e1)
% 28.58/7.89 |
% 28.58/7.89 | Equations (536) can reduce 94 to:
% 28.58/7.89 | (639) ~ (all_0_42_42 = e1)
% 28.58/7.89 |
% 28.58/7.89 | Simplifying 639 yields:
% 28.58/7.89 | (640) ~ (all_0_42_42 = e1)
% 28.58/7.89 |
% 28.58/7.89 | Equations (536) can reduce 214 to:
% 28.58/7.89 | (1016) ~ (all_0_53_53 = e1)
% 28.58/7.89 |
% 28.58/7.89 | Simplifying 1016 yields:
% 28.58/7.89 | (874) ~ (all_0_53_53 = e1)
% 28.58/7.89 |
% 28.58/7.89 | Equations (536) can reduce 232 to:
% 28.58/7.89 | (132) ~ (e1 = e0)
% 28.58/7.89 |
% 28.58/7.89 | From (536) and (112) follows:
% 28.58/7.89 | (6655) op(e1, e1) = all_0_21_21
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (603), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (671) all_0_40_40 = e3
% 28.58/7.89 |
% 28.58/7.89 | Equations (671) can reduce 145 to:
% 28.58/7.89 | (1331) ~ (all_0_42_42 = e3)
% 28.58/7.89 |
% 28.58/7.89 | Simplifying 1331 yields:
% 28.58/7.89 | (1316) ~ (all_0_42_42 = e3)
% 28.58/7.89 |
% 28.58/7.89 | Equations (671) can reduce 137 to:
% 28.58/7.89 | (825) ~ (all_0_52_52 = e3)
% 28.58/7.89 |
% 28.58/7.89 | Simplifying 825 yields:
% 28.58/7.89 | (826) ~ (all_0_52_52 = e3)
% 28.58/7.89 |
% 28.58/7.89 | Equations (671) can reduce 534 to:
% 28.58/7.89 | (136) ~ (e3 = e1)
% 28.58/7.89 |
% 28.58/7.89 | Equations (671) can reduce 238 to:
% 28.58/7.89 | (66) ~ (e3 = e0)
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (16), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (698) all_0_42_42 = e2
% 28.58/7.89 |
% 28.58/7.89 | Equations (698) can reduce 498 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (498) ~ (all_0_42_42 = e2)
% 28.58/7.89 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (1245), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (1258) all_0_42_42 = e3
% 28.58/7.89 |
% 28.58/7.89 | Equations (1258) can reduce 1316 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (1316) ~ (all_0_42_42 = e3)
% 28.58/7.89 | (1317) all_0_42_42 = e4 | all_0_42_42 = e1
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (1317), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (541) all_0_42_42 = e1
% 28.58/7.89 |
% 28.58/7.89 | Equations (541) can reduce 640 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (640) ~ (all_0_42_42 = e1)
% 28.58/7.89 | (512) all_0_42_42 = e4
% 28.58/7.89 |
% 28.58/7.89 | Equations (512) can reduce 18 to:
% 28.58/7.89 | (804) ~ (all_0_46_46 = e4)
% 28.58/7.89 |
% 28.58/7.89 | Simplifying 804 yields:
% 28.58/7.89 | (805) ~ (all_0_46_46 = e4)
% 28.58/7.89 |
% 28.58/7.89 | Equations (512) can reduce 17 to:
% 28.58/7.89 | (279) ~ (all_0_59_59 = e4)
% 28.58/7.89 |
% 28.58/7.89 | Simplifying 279 yields:
% 28.58/7.89 | (280) ~ (all_0_59_59 = e4)
% 28.58/7.89 |
% 28.58/7.89 | Equations (512) can reduce 1316 to:
% 28.58/7.89 | (34) ~ (e4 = e3)
% 28.58/7.89 |
% 28.58/7.89 | Instantiating formula (201) with e1, e1, all_0_21_21, all_0_53_53 and discharging atoms op(e1, e1) = all_0_21_21, op(e1, e1) = all_0_53_53, yields:
% 28.58/7.89 | (6680) all_0_21_21 = all_0_53_53
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (8), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (530) all_0_40_40 = e1
% 28.58/7.89 |
% 28.58/7.89 | Combining equations (530,671) yields a new equation:
% 28.58/7.89 | (538) e3 = e1
% 28.58/7.89 |
% 28.58/7.89 | Equations (538) can reduce 136 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (534) ~ (all_0_40_40 = e1)
% 28.58/7.89 | (3352) all_0_52_52 = e1 | all_0_57_57 = e1
% 28.58/7.89 |
% 28.58/7.89 | Equations (671) can reduce 534 to:
% 28.58/7.89 | (136) ~ (e3 = e1)
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (44), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (502) all_0_43_43 = e4
% 28.58/7.89 |
% 28.58/7.89 | Equations (502) can reduce 84 to:
% 28.58/7.89 | (503) ~ (all_0_45_45 = e4)
% 28.58/7.89 |
% 28.58/7.89 | Simplifying 503 yields:
% 28.58/7.89 | (352) ~ (all_0_45_45 = e4)
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (105), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (374) all_0_45_45 = e2
% 28.58/7.89 |
% 28.58/7.89 | Equations (374) can reduce 434 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (434) ~ (all_0_45_45 = e2)
% 28.58/7.89 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (435), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (454) all_0_45_45 = e0
% 28.58/7.89 |
% 28.58/7.89 | Equations (454) can reduce 488 to:
% 28.58/7.89 | (270) $false
% 28.58/7.89 |
% 28.58/7.89 |-The branch is then unsatisfiable
% 28.58/7.89 |-Branch two:
% 28.58/7.89 | (488) ~ (all_0_45_45 = e0)
% 28.58/7.89 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 28.58/7.89 |
% 28.58/7.89 +-Applying beta-rule and splitting (489), into two cases.
% 28.58/7.89 |-Branch one:
% 28.58/7.89 | (505) all_0_45_45 = e3
% 28.58/7.89 |
% 28.58/7.90 | Equations (505) can reduce 128 to:
% 28.58/7.90 | (355) ~ (all_0_53_53 = e3)
% 28.58/7.90 |
% 28.58/7.90 | Simplifying 355 yields:
% 28.58/7.90 | (356) ~ (all_0_53_53 = e3)
% 28.58/7.90 |
% 28.58/7.90 +-Applying beta-rule and splitting (13), into two cases.
% 28.58/7.90 |-Branch one:
% 28.58/7.90 | (576) all_0_53_53 = e2
% 28.58/7.90 |
% 28.58/7.90 | Equations (576) can reduce 259 to:
% 28.58/7.90 | (270) $false
% 28.58/7.90 |
% 28.58/7.90 |-The branch is then unsatisfiable
% 28.58/7.90 |-Branch two:
% 28.58/7.90 | (259) ~ (all_0_53_53 = e2)
% 28.58/7.90 | (5715) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 28.58/7.90 |
% 28.58/7.90 +-Applying beta-rule and splitting (5715), into two cases.
% 28.58/7.90 |-Branch one:
% 28.58/7.90 | (423) all_0_53_53 = e0
% 28.58/7.90 |
% 28.58/7.90 | Equations (423) can reduce 584 to:
% 28.58/7.90 | (270) $false
% 28.58/7.90 |
% 28.58/7.90 |-The branch is then unsatisfiable
% 28.58/7.90 |-Branch two:
% 28.58/7.90 | (584) ~ (all_0_53_53 = e0)
% 28.58/7.90 | (5719) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1
% 28.58/7.90 |
% 28.58/7.90 +-Applying beta-rule and splitting (5719), into two cases.
% 28.58/7.90 |-Branch one:
% 28.58/7.90 | (1114) all_0_53_53 = e3
% 28.58/7.90 |
% 28.58/7.90 | Equations (1114) can reduce 356 to:
% 28.58/7.90 | (270) $false
% 28.58/7.90 |
% 28.58/7.90 |-The branch is then unsatisfiable
% 28.58/7.90 |-Branch two:
% 28.58/7.90 | (356) ~ (all_0_53_53 = e3)
% 28.58/7.90 | (5723) all_0_53_53 = e4 | all_0_53_53 = e1
% 28.58/7.90 |
% 28.58/7.90 +-Applying beta-rule and splitting (5723), into two cases.
% 28.58/7.90 |-Branch one:
% 28.58/7.90 | (853) all_0_53_53 = e1
% 28.58/7.90 |
% 28.58/7.90 | Equations (853) can reduce 874 to:
% 28.58/7.90 | (270) $false
% 28.58/7.90 |
% 28.58/7.90 |-The branch is then unsatisfiable
% 28.58/7.90 |-Branch two:
% 28.58/7.90 | (874) ~ (all_0_53_53 = e1)
% 28.58/7.90 | (367) all_0_53_53 = e4
% 28.58/7.90 |
% 28.58/7.90 | Equations (367) can reduce 584 to:
% 28.58/7.90 | (6) ~ (e4 = e0)
% 28.58/7.90 |
% 28.58/7.90 +-Applying beta-rule and splitting (93), into two cases.
% 28.58/7.90 |-Branch one:
% 28.58/7.90 | (402) all_0_59_59 = e4
% 28.58/7.90 |
% 28.58/7.90 | Equations (402) can reduce 280 to:
% 28.58/7.90 | (270) $false
% 28.58/7.90 |
% 28.58/7.90 |-The branch is then unsatisfiable
% 28.58/7.90 |-Branch two:
% 28.58/7.90 | (280) ~ (all_0_59_59 = e4)
% 28.58/7.90 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 28.58/7.90 |
% 28.58/7.90 +-Applying beta-rule and splitting (407), into two cases.
% 28.58/7.90 |-Branch one:
% 28.58/7.90 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 28.58/7.90 |
% 28.58/7.90 +-Applying beta-rule and splitting (408), into two cases.
% 28.58/7.90 |-Branch one:
% 28.58/7.90 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 28.58/7.90 |
% 28.58/7.90 +-Applying beta-rule and splitting (409), into two cases.
% 28.58/7.90 |-Branch one:
% 28.58/7.90 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 28.58/7.90 |
% 28.58/7.90 | Applying alpha-rule on (410) yields:
% 28.58/7.90 | (411) all_0_43_43 = e0
% 28.58/7.90 | (412) all_0_59_59 = e3
% 28.58/7.90 | (413) ~ (all_0_46_46 = e3)
% 28.58/7.90 |
% 28.58/7.90 | Combining equations (411,502) yields a new equation:
% 28.58/7.90 | (479) e4 = e0
% 28.58/7.90 |
% 28.58/7.90 | Equations (479) can reduce 6 to:
% 28.58/7.90 | (270) $false
% 28.58/7.90 |
% 28.58/7.90 |-The branch is then unsatisfiable
% 28.58/7.90 |-Branch two:
% 28.58/7.90 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 28.58/7.90 |
% 28.58/7.90 | Applying alpha-rule on (416) yields:
% 28.58/7.90 | (411) all_0_43_43 = e0
% 28.58/7.90 | (412) all_0_59_59 = e3
% 28.58/7.90 | (419) ~ (all_0_56_56 = e0)
% 28.58/7.90 |
% 28.58/7.90 | Combining equations (411,502) yields a new equation:
% 28.58/7.90 | (479) e4 = e0
% 28.58/7.90 |
% 28.58/7.90 | Equations (479) can reduce 6 to:
% 28.58/7.90 | (270) $false
% 28.58/7.90 |
% 28.58/7.90 |-The branch is then unsatisfiable
% 28.58/7.90 |-Branch two:
% 28.58/7.90 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 28.58/7.90 |
% 28.58/7.90 | Applying alpha-rule on (422) yields:
% 28.58/7.90 | (423) all_0_53_53 = e0
% 28.58/7.90 | (424) all_0_59_59 = e1
% 28.58/7.90 | (425) ~ (all_0_54_54 = e1)
% 28.58/7.90 |
% 28.58/7.90 | Combining equations (423,367) yields a new equation:
% 28.58/7.90 | (479) e4 = e0
% 28.58/7.90 |
% 28.58/7.90 | Equations (479) can reduce 6 to:
% 28.58/7.90 | (270) $false
% 28.58/7.90 |
% 28.58/7.90 |-The branch is then unsatisfiable
% 28.58/7.90 |-Branch two:
% 28.58/7.90 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 28.58/7.90 |
% 28.58/7.90 | Applying alpha-rule on (428) yields:
% 28.58/7.90 | (423) all_0_53_53 = e0
% 28.58/7.90 | (424) all_0_59_59 = e1
% 28.58/7.90 | (431) ~ (all_0_58_58 = e0)
% 28.58/7.90 |
% 28.58/7.90 | Combining equations (423,367) yields a new equation:
% 28.58/7.90 | (479) e4 = e0
% 28.58/7.90 |
% 28.58/7.90 | Equations (479) can reduce 6 to:
% 28.58/7.90 | (270) $false
% 28.58/7.90 |
% 28.58/7.90 |-The branch is then unsatisfiable
% 28.58/7.90 |-Branch two:
% 28.58/7.90 | (354) ~ (all_0_45_45 = e3)
% 28.58/7.90 | (363) all_0_45_45 = e4
% 28.58/7.90 |
% 28.58/7.90 | Equations (363) can reduce 352 to:
% 28.58/7.90 | (270) $false
% 28.58/7.90 |
% 28.58/7.90 |-The branch is then unsatisfiable
% 28.58/7.90 |-Branch two:
% 28.58/7.90 | (510) ~ (all_0_43_43 = e4)
% 28.58/7.90 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 28.58/7.90 |
% 28.58/7.90 +-Applying beta-rule and splitting (511), into two cases.
% 28.58/7.90 |-Branch one:
% 28.58/7.90 | (363) all_0_45_45 = e4
% 28.58/7.90 |
% 28.58/7.90 | Equations (363) can reduce 84 to:
% 28.58/7.90 | (510) ~ (all_0_43_43 = e4)
% 28.58/7.90 |
% 28.58/7.90 | Equations (363) can reduce 434 to:
% 28.58/7.90 | (231) ~ (e4 = e2)
% 28.58/7.90 |
% 28.58/7.90 | Equations (363) can reduce 488 to:
% 28.58/7.90 | (6) ~ (e4 = e0)
% 28.58/7.90 |
% 28.58/7.90 | From (363) and (142) follows:
% 28.58/7.90 | (2221) op(e1, e4) = all_0_23_23
% 28.58/7.90 |
% 28.58/7.90 +-Applying beta-rule and splitting (219), into two cases.
% 28.58/7.90 |-Branch one:
% 28.58/7.90 | (351) all_0_41_41 = e3
% 28.58/7.90 |
% 28.58/7.90 | Combining equations (351,536) yields a new equation:
% 28.58/7.90 | (537) e3 = e1
% 28.58/7.90 |
% 28.58/7.90 | Simplifying 537 yields:
% 28.58/7.90 | (538) e3 = e1
% 28.58/7.90 |
% 28.58/7.90 | Equations (538) can reduce 136 to:
% 28.58/7.90 | (270) $false
% 28.58/7.90 |
% 28.58/7.90 |-The branch is then unsatisfiable
% 28.58/7.90 |-Branch two:
% 28.58/7.90 | (1237) ~ (all_0_41_41 = e3)
% 28.58/7.90 | (1508) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 28.58/7.90 |
% 28.58/7.90 | Equations (536) can reduce 1237 to:
% 28.58/7.90 | (769) ~ (e3 = e1)
% 28.58/7.90 |
% 28.58/7.90 | Simplifying 769 yields:
% 28.58/7.90 | (136) ~ (e3 = e1)
% 28.58/7.90 |
% 28.58/7.90 +-Applying beta-rule and splitting (166), into two cases.
% 28.58/7.90 |-Branch one:
% 28.58/7.90 | (522) all_0_39_39 = e4
% 28.58/7.90 |
% 28.58/7.90 | Combining equations (522,336) yields a new equation:
% 28.58/7.90 | (268) e4 = e2
% 28.58/7.90 |
% 28.58/7.90 | Simplifying 268 yields:
% 28.58/7.90 | (269) e4 = e2
% 28.58/7.90 |
% 28.58/7.90 | Equations (269) can reduce 231 to:
% 28.58/7.90 | (270) $false
% 28.58/7.90 |
% 28.58/7.90 |-The branch is then unsatisfiable
% 28.58/7.90 |-Branch two:
% 28.58/7.90 | (591) ~ (all_0_39_39 = e4)
% 28.58/7.90 | (4522) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 28.58/7.90 |
% 28.58/7.90 +-Applying beta-rule and splitting (4522), into two cases.
% 28.58/7.90 |-Branch one:
% 28.58/7.90 | (502) all_0_43_43 = e4
% 28.58/7.90 |
% 28.58/7.90 | Equations (502) can reduce 510 to:
% 28.58/7.90 | (270) $false
% 28.58/7.90 |
% 28.58/7.90 |-The branch is then unsatisfiable
% 28.58/7.90 |-Branch two:
% 28.58/7.90 | (510) ~ (all_0_43_43 = e4)
% 28.58/7.90 | (4527) all_0_51_51 = e4 | all_0_56_56 = e4
% 28.58/7.90 |
% 28.58/7.90 +-Applying beta-rule and splitting (4527), into two cases.
% 28.58/7.90 |-Branch one:
% 28.58/7.90 | (1467) all_0_51_51 = e4
% 28.58/7.90 |
% 28.58/7.90 | Equations (1467) can reduce 12 to:
% 28.58/7.90 | (1444) ~ (all_0_53_53 = e4)
% 28.58/7.90 |
% 28.58/7.90 | Simplifying 1444 yields:
% 28.58/7.90 | (599) ~ (all_0_53_53 = e4)
% 28.58/7.90 |
% 28.58/7.90 | Equations (1467) can reduce 748 to:
% 28.58/7.90 | (251) ~ (e4 = e1)
% 28.58/7.90 |
% 28.58/7.90 | From (1467) and (216) follows:
% 28.58/7.90 | (6780) op(e1, e4) = all_0_10_10
% 28.58/7.90 |
% 28.58/7.90 +-Applying beta-rule and splitting (1508), into two cases.
% 28.58/7.90 |-Branch one:
% 28.58/7.90 | (505) all_0_45_45 = e3
% 28.58/7.90 |
% 28.58/7.90 | Combining equations (363,505) yields a new equation:
% 28.58/7.90 | (660) e4 = e3
% 28.58/7.90 |
% 28.58/7.90 | Simplifying 660 yields:
% 28.58/7.90 | (359) e4 = e3
% 28.58/7.90 |
% 28.58/7.90 | Equations (359) can reduce 34 to:
% 28.58/7.90 | (270) $false
% 28.58/7.90 |
% 28.58/7.90 |-The branch is then unsatisfiable
% 28.58/7.90 |-Branch two:
% 28.58/7.90 | (354) ~ (all_0_45_45 = e3)
% 28.58/7.90 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 28.58/7.90 |
% 28.58/7.90 | Equations (363) can reduce 354 to:
% 28.58/7.90 | (34) ~ (e4 = e3)
% 28.58/7.90 |
% 28.58/7.90 +-Applying beta-rule and splitting (13), into two cases.
% 28.58/7.90 |-Branch one:
% 28.58/7.90 | (576) all_0_53_53 = e2
% 28.58/7.90 |
% 28.58/7.90 | Equations (576) can reduce 259 to:
% 28.58/7.90 | (270) $false
% 28.58/7.90 |
% 28.58/7.90 |-The branch is then unsatisfiable
% 28.58/7.90 |-Branch two:
% 28.58/7.90 | (259) ~ (all_0_53_53 = e2)
% 28.58/7.90 | (5715) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 28.58/7.90 |
% 28.58/7.90 +-Applying beta-rule and splitting (5715), into two cases.
% 28.58/7.90 |-Branch one:
% 28.58/7.90 | (423) all_0_53_53 = e0
% 28.58/7.90 |
% 28.58/7.90 | Equations (423) can reduce 584 to:
% 28.58/7.90 | (270) $false
% 28.58/7.90 |
% 28.58/7.90 |-The branch is then unsatisfiable
% 28.58/7.90 |-Branch two:
% 28.58/7.90 | (584) ~ (all_0_53_53 = e0)
% 28.58/7.90 | (5719) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1
% 28.58/7.90 |
% 28.58/7.90 +-Applying beta-rule and splitting (5719), into two cases.
% 28.58/7.90 |-Branch one:
% 28.58/7.90 | (1114) all_0_53_53 = e3
% 28.58/7.90 |
% 28.58/7.90 | Combining equations (1114,6680) yields a new equation:
% 28.58/7.90 | (6797) all_0_21_21 = e3
% 28.58/7.90 |
% 28.58/7.90 | Equations (1114) can reduce 599 to:
% 28.58/7.90 | (719) ~ (e4 = e3)
% 28.58/7.90 |
% 28.58/7.90 | Simplifying 719 yields:
% 28.58/7.90 | (34) ~ (e4 = e3)
% 28.58/7.90 |
% 28.58/7.90 | Equations (1114) can reduce 259 to:
% 28.58/7.90 | (223) ~ (e3 = e2)
% 28.58/7.90 |
% 28.58/7.90 | Instantiating formula (201) with e1, e4, all_0_10_10, e2 and discharging atoms op(e1, e4) = all_0_10_10, op(e1, e4) = e2, yields:
% 28.58/7.90 | (6801) all_0_10_10 = e2
% 28.58/7.90 |
% 28.58/7.90 | Instantiating formula (201) with e1, e4, all_0_23_23, all_0_10_10 and discharging atoms op(e1, e4) = all_0_10_10, op(e1, e4) = all_0_23_23, yields:
% 28.58/7.90 | (6802) all_0_10_10 = all_0_23_23
% 28.58/7.90 |
% 28.58/7.90 | Combining equations (6801,6802) yields a new equation:
% 28.58/7.90 | (2272) all_0_23_23 = e2
% 28.58/7.90 |
% 28.58/7.90 +-Applying beta-rule and splitting (14), into two cases.
% 28.58/7.90 |-Branch one:
% 28.58/7.90 | (2277) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1))
% 28.58/7.90 |
% 28.58/7.90 +-Applying beta-rule and splitting (2277), into two cases.
% 28.58/7.90 |-Branch one:
% 28.58/7.90 | (2278) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1))
% 28.58/7.90 |
% 28.58/7.90 +-Applying beta-rule and splitting (2278), into two cases.
% 28.58/7.90 |-Branch one:
% 28.58/7.90 | (2279) all_0_21_21 = e4 & ~ (all_0_22_22 = e1)
% 28.58/7.90 |
% 28.58/7.90 | Applying alpha-rule on (2279) yields:
% 28.58/7.90 | (2280) all_0_21_21 = e4
% 28.58/7.90 | (2281) ~ (all_0_22_22 = e1)
% 28.58/7.90 |
% 28.58/7.90 | Combining equations (6797,2280) yields a new equation:
% 28.58/7.90 | (359) e4 = e3
% 28.58/7.90 |
% 28.58/7.90 | Equations (359) can reduce 34 to:
% 28.58/7.90 | (270) $false
% 28.58/7.90 |
% 28.58/7.90 |-The branch is then unsatisfiable
% 28.58/7.90 |-Branch two:
% 28.58/7.90 | (2285) all_0_23_23 = e3 & ~ (all_0_24_24 = e1)
% 28.58/7.90 |
% 28.58/7.90 | Applying alpha-rule on (2285) yields:
% 28.58/7.90 | (2286) all_0_23_23 = e3
% 28.58/7.91 | (2287) ~ (all_0_24_24 = e1)
% 28.58/7.91 |
% 28.58/7.91 | Combining equations (2272,2286) yields a new equation:
% 28.58/7.91 | (414) e3 = e2
% 28.58/7.91 |
% 28.58/7.91 | Equations (414) can reduce 223 to:
% 28.58/7.91 | (270) $false
% 28.58/7.91 |
% 28.58/7.91 |-The branch is then unsatisfiable
% 28.58/7.91 |-Branch two:
% 28.58/7.91 | (2291) all_0_25_25 = e2 & ~ (all_0_26_26 = e1)
% 28.58/7.91 |
% 28.58/7.91 | Applying alpha-rule on (2291) yields:
% 28.58/7.91 | (2292) all_0_25_25 = e2
% 28.58/7.91 | (2293) ~ (all_0_26_26 = e1)
% 28.58/7.91 |
% 28.58/7.91 | Combining equations (6130,2292) yields a new equation:
% 28.58/7.91 | (6819) all_0_54_54 = e2
% 28.58/7.91 |
% 28.58/7.91 | Simplifying 6819 yields:
% 28.58/7.91 | (3657) all_0_54_54 = e2
% 28.58/7.91 |
% 28.58/7.91 | Equations (3657) can reduce 261 to:
% 28.58/7.91 | (270) $false
% 28.58/7.91 |
% 28.58/7.91 |-The branch is then unsatisfiable
% 28.58/7.91 |-Branch two:
% 28.58/7.91 | (2296) all_0_28_28 = e0 & ~ (all_0_29_29 = e1)
% 28.58/7.91 |
% 28.58/7.91 | Applying alpha-rule on (2296) yields:
% 28.58/7.91 | (2297) all_0_28_28 = e0
% 28.58/7.91 | (2298) ~ (all_0_29_29 = e1)
% 28.58/7.91 |
% 28.58/7.91 | Combining equations (1848,2297) yields a new equation:
% 28.58/7.91 | (6825) all_0_52_52 = e0
% 28.58/7.91 |
% 28.58/7.91 | Simplifying 6825 yields:
% 28.58/7.91 | (827) all_0_52_52 = e0
% 28.58/7.91 |
% 28.58/7.91 | Equations (6647) can reduce 2298 to:
% 28.58/7.91 | (644) ~ (all_0_57_57 = e1)
% 28.58/7.91 |
% 28.58/7.91 +-Applying beta-rule and splitting (3352), into two cases.
% 28.58/7.91 |-Branch one:
% 28.58/7.91 | (848) all_0_52_52 = e1
% 28.58/7.91 |
% 28.58/7.91 | Combining equations (827,848) yields a new equation:
% 28.58/7.91 | (560) e1 = e0
% 28.58/7.91 |
% 28.58/7.91 | Equations (560) can reduce 132 to:
% 28.58/7.91 | (270) $false
% 28.58/7.91 |
% 28.58/7.91 |-The branch is then unsatisfiable
% 28.58/7.91 |-Branch two:
% 28.58/7.91 | (642) ~ (all_0_52_52 = e1)
% 28.58/7.91 | (997) all_0_57_57 = e1
% 28.58/7.91 |
% 28.58/7.91 | Equations (997) can reduce 644 to:
% 28.58/7.91 | (270) $false
% 28.58/7.91 |
% 28.58/7.91 |-The branch is then unsatisfiable
% 28.58/7.91 |-Branch two:
% 28.58/7.91 | (356) ~ (all_0_53_53 = e3)
% 28.58/7.91 | (5723) all_0_53_53 = e4 | all_0_53_53 = e1
% 28.58/7.91 |
% 28.58/7.91 +-Applying beta-rule and splitting (21), into two cases.
% 28.58/7.91 |-Branch one:
% 28.58/7.91 | (824) all_0_51_51 = e3
% 28.58/7.91 |
% 28.58/7.91 | Combining equations (824,1467) yields a new equation:
% 28.58/7.91 | (359) e4 = e3
% 28.58/7.91 |
% 28.58/7.91 | Equations (359) can reduce 34 to:
% 28.58/7.91 | (270) $false
% 28.58/7.91 |
% 28.58/7.91 |-The branch is then unsatisfiable
% 28.58/7.91 |-Branch two:
% 28.58/7.91 | (932) ~ (all_0_51_51 = e3)
% 28.58/7.91 | (1101) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 28.58/7.91 |
% 28.58/7.91 +-Applying beta-rule and splitting (1101), into two cases.
% 28.58/7.91 |-Branch one:
% 28.58/7.91 | (864) all_0_52_52 = e3
% 28.58/7.91 |
% 28.58/7.91 | Equations (864) can reduce 826 to:
% 28.58/7.91 | (270) $false
% 28.58/7.91 |
% 28.58/7.91 |-The branch is then unsatisfiable
% 28.58/7.91 |-Branch two:
% 28.58/7.91 | (826) ~ (all_0_52_52 = e3)
% 28.58/7.91 | (1107) all_0_53_53 = e3 | all_0_54_54 = e3
% 28.58/7.91 |
% 28.58/7.91 +-Applying beta-rule and splitting (1107), into two cases.
% 28.58/7.91 |-Branch one:
% 28.58/7.91 | (1114) all_0_53_53 = e3
% 28.58/7.91 |
% 28.58/7.91 | Equations (1114) can reduce 356 to:
% 28.58/7.91 | (270) $false
% 28.58/7.91 |
% 28.58/7.91 |-The branch is then unsatisfiable
% 28.58/7.91 |-Branch two:
% 28.58/7.91 | (356) ~ (all_0_53_53 = e3)
% 28.58/7.91 | (1119) all_0_54_54 = e3
% 28.58/7.91 |
% 28.58/7.91 +-Applying beta-rule and splitting (127), into two cases.
% 28.58/7.91 |-Branch one:
% 28.58/7.91 | (541) all_0_42_42 = e1
% 28.58/7.91 |
% 28.58/7.91 | Combining equations (512,541) yields a new equation:
% 28.58/7.91 | (525) e4 = e1
% 28.58/7.91 |
% 28.58/7.91 | Simplifying 525 yields:
% 28.58/7.91 | (526) e4 = e1
% 28.58/7.91 |
% 28.58/7.91 | Equations (526) can reduce 251 to:
% 28.58/7.91 | (270) $false
% 28.58/7.91 |
% 28.58/7.91 |-The branch is then unsatisfiable
% 28.58/7.91 |-Branch two:
% 28.58/7.91 | (640) ~ (all_0_42_42 = e1)
% 28.58/7.91 | (4628) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 28.58/7.91 |
% 28.58/7.91 | Equations (512) can reduce 640 to:
% 28.58/7.91 | (251) ~ (e4 = e1)
% 28.58/7.91 |
% 28.58/7.91 +-Applying beta-rule and splitting (135), into two cases.
% 28.58/7.91 |-Branch one:
% 28.58/7.91 | (820) all_0_51_51 = e1
% 28.58/7.91 |
% 28.58/7.91 | Combining equations (1467,820) yields a new equation:
% 28.58/7.91 | (525) e4 = e1
% 28.58/7.91 |
% 28.58/7.91 | Simplifying 525 yields:
% 28.58/7.91 | (526) e4 = e1
% 28.58/7.91 |
% 28.58/7.91 | Equations (526) can reduce 251 to:
% 28.58/7.91 | (270) $false
% 28.58/7.91 |
% 28.58/7.91 |-The branch is then unsatisfiable
% 28.58/7.91 |-Branch two:
% 28.58/7.91 | (748) ~ (all_0_51_51 = e1)
% 28.58/7.91 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 28.58/7.91 |
% 28.58/7.91 +-Applying beta-rule and splitting (64), into two cases.
% 28.58/7.91 |-Branch one:
% 28.58/7.91 | (954) all_0_51_51 = e0
% 28.58/7.91 |
% 28.58/7.91 | Combining equations (1467,954) yields a new equation:
% 28.58/7.91 | (478) e4 = e0
% 28.58/7.91 |
% 28.58/7.91 | Simplifying 478 yields:
% 28.58/7.91 | (479) e4 = e0
% 28.58/7.91 |
% 28.58/7.91 | Equations (479) can reduce 6 to:
% 28.58/7.91 | (270) $false
% 28.58/7.91 |
% 28.58/7.91 |-The branch is then unsatisfiable
% 28.58/7.91 |-Branch two:
% 28.58/7.91 | (987) ~ (all_0_51_51 = e0)
% 28.58/7.91 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 28.58/7.91 |
% 28.58/7.91 +-Applying beta-rule and splitting (3067), into two cases.
% 28.58/7.91 |-Branch one:
% 28.58/7.91 | (827) all_0_52_52 = e0
% 28.58/7.91 |
% 28.58/7.91 +-Applying beta-rule and splitting (823), into two cases.
% 28.58/7.91 |-Branch one:
% 28.58/7.91 | (848) all_0_52_52 = e1
% 28.58/7.91 |
% 28.58/7.91 | Combining equations (827,848) yields a new equation:
% 28.58/7.91 | (560) e1 = e0
% 28.58/7.91 |
% 28.58/7.91 | Equations (560) can reduce 132 to:
% 28.58/7.91 | (270) $false
% 28.58/7.91 |
% 28.58/7.91 |-The branch is then unsatisfiable
% 28.58/7.91 |-Branch two:
% 28.58/7.91 | (642) ~ (all_0_52_52 = e1)
% 28.58/7.91 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 28.58/7.91 |
% 28.58/7.91 +-Applying beta-rule and splitting (852), into two cases.
% 28.58/7.91 |-Branch one:
% 28.58/7.91 | (853) all_0_53_53 = e1
% 28.58/7.91 |
% 28.58/7.91 | Equations (853) can reduce 874 to:
% 28.58/7.91 | (270) $false
% 28.58/7.91 |
% 28.58/7.91 |-The branch is then unsatisfiable
% 28.58/7.91 |-Branch two:
% 28.58/7.91 | (874) ~ (all_0_53_53 = e1)
% 28.58/7.91 | (875) all_0_54_54 = e1
% 28.58/7.91 |
% 28.58/7.91 | Combining equations (1119,875) yields a new equation:
% 28.58/7.91 | (537) e3 = e1
% 28.58/7.91 |
% 28.58/7.91 | Simplifying 537 yields:
% 28.58/7.91 | (538) e3 = e1
% 28.58/7.91 |
% 28.58/7.91 | Equations (538) can reduce 136 to:
% 28.58/7.91 | (270) $false
% 28.58/7.91 |
% 28.58/7.91 |-The branch is then unsatisfiable
% 28.58/7.91 |-Branch two:
% 28.58/7.91 | (925) ~ (all_0_52_52 = e0)
% 28.58/7.91 | (3073) all_0_53_53 = e0 | all_0_54_54 = e0
% 28.58/7.91 |
% 28.58/7.91 +-Applying beta-rule and splitting (3073), into two cases.
% 28.58/7.91 |-Branch one:
% 28.58/7.91 | (423) all_0_53_53 = e0
% 28.58/7.91 |
% 28.58/7.91 | Equations (423) can reduce 584 to:
% 28.58/7.91 | (270) $false
% 28.58/7.91 |
% 28.58/7.91 |-The branch is then unsatisfiable
% 28.58/7.91 |-Branch two:
% 28.58/7.91 | (584) ~ (all_0_53_53 = e0)
% 28.58/7.91 | (3084) all_0_54_54 = e0
% 28.58/7.91 |
% 28.58/7.91 | Combining equations (1119,3084) yields a new equation:
% 28.58/7.91 | (783) e3 = e0
% 28.58/7.91 |
% 28.58/7.91 | Simplifying 783 yields:
% 28.58/7.91 | (784) e3 = e0
% 28.58/7.91 |
% 28.58/7.91 | Equations (784) can reduce 66 to:
% 28.58/7.91 | (270) $false
% 28.58/7.91 |
% 28.58/7.91 |-The branch is then unsatisfiable
% 28.58/7.91 |-Branch two:
% 28.58/7.91 | (697) ~ (all_0_51_51 = e4)
% 28.58/7.91 | (4744) all_0_56_56 = e4
% 28.58/7.91 |
% 28.58/7.91 | Equations (4744) can reduce 274 to:
% 28.58/7.91 | (270) $false
% 28.58/7.91 |
% 28.58/7.91 |-The branch is then unsatisfiable
% 28.58/7.91 |-Branch two:
% 28.58/7.91 | (352) ~ (all_0_45_45 = e4)
% 28.58/7.91 | (517) all_0_46_46 = e4
% 28.58/7.91 |
% 28.58/7.91 | Equations (517) can reduce 805 to:
% 28.58/7.91 | (270) $false
% 28.58/7.91 |
% 28.58/7.91 |-The branch is then unsatisfiable
% 28.58/7.91 |-Branch two:
% 28.58/7.91 | (675) ~ (all_0_40_40 = e3)
% 28.58/7.91 | (530) all_0_40_40 = e1
% 28.58/7.91 |
% 28.58/7.91 | Equations (530) can reduce 534 to:
% 28.58/7.91 | (270) $false
% 28.58/7.91 |
% 28.58/7.91 |-The branch is then unsatisfiable
% 28.58/7.91 |-Branch two:
% 28.58/7.91 | (540) ~ (all_0_41_41 = e1)
% 28.58/7.91 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 28.58/7.91 |
% 28.58/7.91 +-Applying beta-rule and splitting (762), into two cases.
% 28.58/7.91 |-Branch one:
% 28.58/7.91 | (552) all_0_48_48 = e1
% 28.58/7.91 |
% 28.58/7.91 | Combining equations (552,559) yields a new equation:
% 28.58/7.91 | (571) e1 = e0
% 28.58/7.91 |
% 28.58/7.91 | Simplifying 571 yields:
% 28.58/7.91 | (560) e1 = e0
% 28.58/7.91 |
% 28.58/7.91 | Equations (560) can reduce 132 to:
% 28.58/7.91 | (270) $false
% 28.58/7.91 |
% 28.58/7.91 |-The branch is then unsatisfiable
% 28.58/7.91 |-Branch two:
% 28.58/7.91 | (588) ~ (all_0_48_48 = e1)
% 28.58/7.91 | (4925) all_0_53_53 = e1 | all_0_58_58 = e1
% 28.58/7.91 |
% 28.58/7.91 +-Applying beta-rule and splitting (4925), into two cases.
% 28.58/7.91 |-Branch one:
% 28.58/7.91 | (853) all_0_53_53 = e1
% 28.58/7.91 |
% 28.58/7.91 | Equations (853) can reduce 214 to:
% 28.58/7.91 | (540) ~ (all_0_41_41 = e1)
% 28.58/7.91 |
% 28.58/7.91 | Equations (853) can reduce 213 to:
% 28.58/7.91 | (642) ~ (all_0_52_52 = e1)
% 28.58/7.91 |
% 28.58/7.91 | Equations (853) can reduce 252 to:
% 28.58/7.91 | (2131) ~ (all_0_54_54 = e1)
% 28.58/7.91 |
% 28.58/7.91 | Simplifying 2131 yields:
% 28.58/7.91 | (425) ~ (all_0_54_54 = e1)
% 28.58/7.91 |
% 28.58/7.91 +-Applying beta-rule and splitting (8), into two cases.
% 28.58/7.91 |-Branch one:
% 28.58/7.91 | (530) all_0_40_40 = e1
% 28.58/7.91 |
% 28.58/7.91 | Equations (530) can reduce 145 to:
% 28.58/7.91 | (639) ~ (all_0_42_42 = e1)
% 28.58/7.91 |
% 28.58/7.91 | Simplifying 639 yields:
% 28.58/7.91 | (640) ~ (all_0_42_42 = e1)
% 28.58/7.91 |
% 28.58/7.91 | Equations (530) can reduce 602 to:
% 28.58/7.92 | (645) ~ (e2 = e1)
% 28.58/7.92 |
% 28.58/7.92 | Simplifying 645 yields:
% 28.58/7.92 | (141) ~ (e2 = e1)
% 28.58/7.92 |
% 28.58/7.92 | Equations (530) can reduce 238 to:
% 28.58/7.92 | (132) ~ (e1 = e0)
% 28.58/7.92 |
% 28.58/7.92 +-Applying beta-rule and splitting (127), into two cases.
% 28.58/7.92 |-Branch one:
% 28.58/7.92 | (541) all_0_42_42 = e1
% 28.58/7.92 |
% 28.58/7.92 | Equations (541) can reduce 640 to:
% 28.58/7.92 | (270) $false
% 28.58/7.92 |
% 28.58/7.92 |-The branch is then unsatisfiable
% 28.58/7.92 |-Branch two:
% 28.58/7.92 | (640) ~ (all_0_42_42 = e1)
% 28.58/7.92 | (4628) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 28.58/7.92 |
% 28.58/7.92 +-Applying beta-rule and splitting (4628), into two cases.
% 28.58/7.92 |-Branch one:
% 28.58/7.92 | (589) all_0_49_49 = e1
% 28.58/7.92 |
% 28.58/7.92 | Combining equations (307,589) yields a new equation:
% 28.58/7.92 | (531) e2 = e1
% 28.58/7.92 |
% 28.58/7.92 | Simplifying 531 yields:
% 28.58/7.92 | (322) e2 = e1
% 28.58/7.92 |
% 28.58/7.92 | Equations (322) can reduce 141 to:
% 28.58/7.92 | (270) $false
% 28.58/7.92 |
% 28.58/7.92 |-The branch is then unsatisfiable
% 28.58/7.92 |-Branch two:
% 28.58/7.92 | (543) ~ (all_0_49_49 = e1)
% 28.58/7.92 | (4726) all_0_54_54 = e1 | all_0_59_59 = e1
% 28.58/7.92 |
% 28.58/7.92 +-Applying beta-rule and splitting (4726), into two cases.
% 28.58/7.92 |-Branch one:
% 28.58/7.92 | (875) all_0_54_54 = e1
% 28.58/7.92 |
% 28.58/7.92 | Equations (875) can reduce 425 to:
% 28.58/7.92 | (270) $false
% 28.58/7.92 |
% 28.58/7.92 |-The branch is then unsatisfiable
% 28.58/7.92 |-Branch two:
% 28.58/7.92 | (425) ~ (all_0_54_54 = e1)
% 28.58/7.92 | (424) all_0_59_59 = e1
% 28.58/7.92 |
% 28.58/7.92 | Equations (424) can reduce 280 to:
% 28.58/7.92 | (1021) ~ (e4 = e1)
% 28.58/7.92 |
% 28.58/7.92 | Simplifying 1021 yields:
% 28.58/7.92 | (251) ~ (e4 = e1)
% 28.58/7.92 |
% 28.58/7.92 +-Applying beta-rule and splitting (93), into two cases.
% 28.58/7.92 |-Branch one:
% 28.58/7.92 | (402) all_0_59_59 = e4
% 28.58/7.92 |
% 28.58/7.92 | Combining equations (424,402) yields a new equation:
% 28.58/7.92 | (526) e4 = e1
% 28.58/7.92 |
% 28.58/7.92 | Equations (526) can reduce 251 to:
% 28.58/7.92 | (270) $false
% 28.58/7.92 |
% 28.58/7.92 |-The branch is then unsatisfiable
% 28.58/7.92 |-Branch two:
% 28.58/7.92 | (280) ~ (all_0_59_59 = e4)
% 28.58/7.92 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 28.58/7.92 |
% 28.58/7.92 +-Applying beta-rule and splitting (407), into two cases.
% 28.58/7.92 |-Branch one:
% 28.58/7.92 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 28.58/7.92 |
% 28.58/7.92 +-Applying beta-rule and splitting (408), into two cases.
% 28.58/7.92 |-Branch one:
% 28.58/7.92 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 28.58/7.92 |
% 28.58/7.92 +-Applying beta-rule and splitting (409), into two cases.
% 28.58/7.92 |-Branch one:
% 28.58/7.92 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 28.58/7.92 |
% 28.58/7.92 | Applying alpha-rule on (410) yields:
% 28.58/7.92 | (411) all_0_43_43 = e0
% 28.58/7.92 | (412) all_0_59_59 = e3
% 28.58/7.92 | (413) ~ (all_0_46_46 = e3)
% 28.58/7.92 |
% 28.58/7.92 | Combining equations (412,424) yields a new equation:
% 28.58/7.92 | (537) e3 = e1
% 28.58/7.92 |
% 28.58/7.92 | Simplifying 537 yields:
% 28.58/7.92 | (538) e3 = e1
% 28.58/7.92 |
% 28.58/7.92 | Equations (538) can reduce 136 to:
% 28.58/7.92 | (270) $false
% 28.58/7.92 |
% 28.58/7.92 |-The branch is then unsatisfiable
% 28.58/7.92 |-Branch two:
% 28.58/7.92 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 28.58/7.92 |
% 28.58/7.92 | Applying alpha-rule on (416) yields:
% 28.58/7.92 | (411) all_0_43_43 = e0
% 28.58/7.92 | (412) all_0_59_59 = e3
% 28.58/7.92 | (419) ~ (all_0_56_56 = e0)
% 28.58/7.92 |
% 28.58/7.92 | Combining equations (412,424) yields a new equation:
% 28.58/7.92 | (537) e3 = e1
% 28.58/7.92 |
% 28.58/7.92 | Simplifying 537 yields:
% 28.58/7.92 | (538) e3 = e1
% 28.58/7.92 |
% 28.58/7.92 | Equations (538) can reduce 136 to:
% 28.58/7.92 | (270) $false
% 28.58/7.92 |
% 28.58/7.92 |-The branch is then unsatisfiable
% 28.58/7.92 |-Branch two:
% 28.58/7.92 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 28.58/7.92 |
% 28.58/7.92 | Applying alpha-rule on (422) yields:
% 28.58/7.92 | (423) all_0_53_53 = e0
% 28.58/7.92 | (424) all_0_59_59 = e1
% 28.58/7.92 | (425) ~ (all_0_54_54 = e1)
% 28.58/7.92 |
% 28.58/7.92 | Combining equations (423,853) yields a new equation:
% 28.58/7.92 | (560) e1 = e0
% 28.58/7.92 |
% 28.58/7.92 | Equations (560) can reduce 132 to:
% 28.58/7.92 | (270) $false
% 28.58/7.92 |
% 28.58/7.92 |-The branch is then unsatisfiable
% 28.58/7.92 |-Branch two:
% 28.58/7.92 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 28.58/7.92 |
% 28.58/7.92 | Applying alpha-rule on (428) yields:
% 28.58/7.92 | (423) all_0_53_53 = e0
% 28.58/7.92 | (424) all_0_59_59 = e1
% 28.58/7.92 | (431) ~ (all_0_58_58 = e0)
% 28.58/7.92 |
% 28.58/7.92 | Combining equations (423,853) yields a new equation:
% 28.58/7.92 | (560) e1 = e0
% 28.58/7.92 |
% 28.58/7.92 | Equations (560) can reduce 132 to:
% 28.58/7.92 | (270) $false
% 28.58/7.92 |
% 28.58/7.92 |-The branch is then unsatisfiable
% 28.58/7.92 |-Branch two:
% 28.58/7.92 | (534) ~ (all_0_40_40 = e1)
% 28.58/7.92 | (3352) all_0_52_52 = e1 | all_0_57_57 = e1
% 28.58/7.92 |
% 28.58/7.92 +-Applying beta-rule and splitting (3352), into two cases.
% 28.58/7.92 |-Branch one:
% 28.58/7.92 | (848) all_0_52_52 = e1
% 28.58/7.92 |
% 28.58/7.92 | Equations (848) can reduce 642 to:
% 28.58/7.92 | (270) $false
% 28.58/7.92 |
% 28.58/7.92 |-The branch is then unsatisfiable
% 28.58/7.92 |-Branch two:
% 28.58/7.92 | (642) ~ (all_0_52_52 = e1)
% 28.58/7.92 | (997) all_0_57_57 = e1
% 28.58/7.92 |
% 28.58/7.92 | Equations (997) can reduce 149 to:
% 28.58/7.92 | (534) ~ (all_0_40_40 = e1)
% 28.58/7.92 |
% 28.58/7.92 | Equations (997) can reduce 335 to:
% 28.58/7.92 | (645) ~ (e2 = e1)
% 28.58/7.92 |
% 28.58/7.92 | Simplifying 645 yields:
% 28.58/7.92 | (141) ~ (e2 = e1)
% 28.58/7.92 |
% 28.58/7.92 | From (997) and (120) follows:
% 28.58/7.92 | (6976) op(e0, e1) = all_0_20_20
% 28.58/7.92 |
% 28.58/7.92 +-Applying beta-rule and splitting (210), into two cases.
% 28.58/7.92 |-Branch one:
% 28.58/7.92 | (524) all_0_39_39 = e1
% 28.58/7.92 |
% 28.58/7.92 | Combining equations (336,524) yields a new equation:
% 28.58/7.92 | (531) e2 = e1
% 28.58/7.92 |
% 28.58/7.92 | Simplifying 531 yields:
% 28.58/7.92 | (322) e2 = e1
% 28.58/7.92 |
% 28.58/7.92 | Equations (322) can reduce 141 to:
% 28.58/7.92 | (270) $false
% 28.58/7.92 |
% 28.58/7.92 |-The branch is then unsatisfiable
% 28.58/7.92 |-Branch two:
% 28.58/7.92 | (528) ~ (all_0_39_39 = e1)
% 28.58/7.92 | (529) all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1
% 28.58/7.92 |
% 28.58/7.92 +-Applying beta-rule and splitting (529), into two cases.
% 28.58/7.92 |-Branch one:
% 28.58/7.92 | (530) all_0_40_40 = e1
% 28.58/7.92 |
% 28.58/7.92 | Equations (530) can reduce 534 to:
% 28.58/7.92 | (270) $false
% 28.58/7.92 |
% 28.58/7.92 |-The branch is then unsatisfiable
% 28.58/7.92 |-Branch two:
% 28.58/7.92 | (534) ~ (all_0_40_40 = e1)
% 28.58/7.92 | (535) all_0_41_41 = e1 | all_0_42_42 = e1
% 28.58/7.92 |
% 28.58/7.92 +-Applying beta-rule and splitting (127), into two cases.
% 28.58/7.92 |-Branch one:
% 28.58/7.92 | (541) all_0_42_42 = e1
% 28.58/7.92 |
% 28.58/7.92 | Equations (541) can reduce 145 to:
% 28.58/7.92 | (534) ~ (all_0_40_40 = e1)
% 28.58/7.92 |
% 28.58/7.92 | Equations (541) can reduce 94 to:
% 28.58/7.92 | (540) ~ (all_0_41_41 = e1)
% 28.58/7.92 |
% 28.58/7.92 | Equations (541) can reduce 498 to:
% 28.58/7.92 | (645) ~ (e2 = e1)
% 28.58/7.92 |
% 28.58/7.92 | Simplifying 645 yields:
% 28.58/7.92 | (141) ~ (e2 = e1)
% 28.58/7.92 |
% 28.58/7.92 | Equations (541) can reduce 199 to:
% 28.58/7.92 | (132) ~ (e1 = e0)
% 28.58/7.92 |
% 28.58/7.92 +-Applying beta-rule and splitting (603), into two cases.
% 28.58/7.92 |-Branch one:
% 28.58/7.92 | (671) all_0_40_40 = e3
% 28.58/7.92 |
% 28.58/7.92 | Equations (671) can reduce 147 to:
% 28.58/7.92 | (1329) ~ (all_0_41_41 = e3)
% 28.58/7.92 |
% 28.58/7.92 | Simplifying 1329 yields:
% 28.58/7.92 | (1237) ~ (all_0_41_41 = e3)
% 28.58/7.92 |
% 28.58/7.92 | Equations (671) can reduce 602 to:
% 28.58/7.92 | (223) ~ (e3 = e2)
% 28.58/7.92 |
% 28.58/7.92 | Equations (671) can reduce 534 to:
% 28.58/7.92 | (136) ~ (e3 = e1)
% 28.58/7.92 |
% 28.58/7.92 | From (671) and (68) follows:
% 28.58/7.92 | (5921) op(e2, e3) = all_0_13_13
% 28.58/7.92 |
% 28.58/7.92 +-Applying beta-rule and splitting (217), into two cases.
% 28.58/7.92 |-Branch one:
% 28.58/7.92 | (436) all_0_41_41 = e2
% 28.58/7.92 |
% 28.58/7.92 | Equations (436) can reduce 331 to:
% 28.58/7.92 | (270) $false
% 28.58/7.92 |
% 28.58/7.92 |-The branch is then unsatisfiable
% 28.58/7.92 |-Branch two:
% 28.58/7.92 | (331) ~ (all_0_41_41 = e2)
% 28.58/7.92 | (709) all_0_41_41 = e4 | all_0_41_41 = e3 | all_0_41_41 = e1
% 28.58/7.92 |
% 28.58/7.92 +-Applying beta-rule and splitting (219), into two cases.
% 28.58/7.92 |-Branch one:
% 28.58/7.92 | (351) all_0_41_41 = e3
% 28.58/7.92 |
% 28.58/7.92 | Equations (351) can reduce 1237 to:
% 28.58/7.92 | (270) $false
% 28.58/7.92 |
% 28.58/7.92 |-The branch is then unsatisfiable
% 28.58/7.92 |-Branch two:
% 28.58/7.92 | (1237) ~ (all_0_41_41 = e3)
% 28.58/7.92 | (1508) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 28.58/7.92 |
% 28.58/7.92 +-Applying beta-rule and splitting (626), into two cases.
% 28.58/7.92 |-Branch one:
% 28.58/7.92 | (827) all_0_52_52 = e0
% 28.58/7.92 |
% 28.58/7.92 | From (827) and (27) follows:
% 28.58/7.92 | (3482) op(e2, e0) = all_0_17_17
% 28.58/7.92 |
% 28.58/7.92 +-Applying beta-rule and splitting (709), into two cases.
% 28.58/7.92 |-Branch one:
% 28.58/7.92 | (351) all_0_41_41 = e3
% 28.58/7.92 |
% 28.58/7.92 | Equations (351) can reduce 1237 to:
% 28.58/7.92 | (270) $false
% 28.58/7.92 |
% 28.58/7.92 |-The branch is then unsatisfiable
% 28.58/7.92 |-Branch two:
% 28.58/7.92 | (1237) ~ (all_0_41_41 = e3)
% 28.58/7.92 | (1238) all_0_41_41 = e4 | all_0_41_41 = e1
% 28.58/7.92 |
% 28.58/7.92 +-Applying beta-rule and splitting (1238), into two cases.
% 28.58/7.92 |-Branch one:
% 28.58/7.92 | (536) all_0_41_41 = e1
% 28.58/7.92 |
% 28.58/7.92 | Equations (536) can reduce 540 to:
% 28.58/7.92 | (270) $false
% 28.58/7.92 |
% 28.58/7.92 |-The branch is then unsatisfiable
% 28.58/7.92 |-Branch two:
% 28.58/7.92 | (540) ~ (all_0_41_41 = e1)
% 28.58/7.92 | (358) all_0_41_41 = e4
% 28.58/7.92 |
% 28.58/7.92 | Equations (358) can reduce 51 to:
% 28.58/7.92 | (503) ~ (all_0_45_45 = e4)
% 28.58/7.92 |
% 28.58/7.92 | Simplifying 503 yields:
% 28.58/7.92 | (352) ~ (all_0_45_45 = e4)
% 28.58/7.92 |
% 28.58/7.92 | Equations (358) can reduce 540 to:
% 28.58/7.92 | (251) ~ (e4 = e1)
% 28.58/7.92 |
% 28.58/7.92 +-Applying beta-rule and splitting (1508), into two cases.
% 28.58/7.92 |-Branch one:
% 28.58/7.92 | (505) all_0_45_45 = e3
% 28.58/7.92 |
% 28.58/7.92 | Equations (505) can reduce 352 to:
% 28.58/7.92 | (719) ~ (e4 = e3)
% 28.58/7.92 |
% 28.58/7.92 | Simplifying 719 yields:
% 28.58/7.92 | (34) ~ (e4 = e3)
% 28.58/7.92 |
% 28.58/7.92 | Instantiating formula (201) with e2, e3, all_0_13_13, e1 and discharging atoms op(e2, e3) = all_0_13_13, op(e2, e3) = e1, yields:
% 28.58/7.92 | (5957) all_0_13_13 = e1
% 28.58/7.92 |
% 28.58/7.92 | Instantiating formula (201) with e2, e0, all_0_17_17, e2 and discharging atoms op(e2, e0) = all_0_17_17, op(e2, e0) = e2, yields:
% 28.58/7.92 | (3413) all_0_17_17 = e2
% 28.58/7.92 |
% 28.58/7.92 | Instantiating formula (201) with e0, e1, all_0_20_20, e2 and discharging atoms op(e0, e1) = all_0_20_20, op(e0, e1) = e2, yields:
% 28.58/7.92 | (7025) all_0_20_20 = e2
% 28.58/7.92 |
% 28.58/7.92 +-Applying beta-rule and splitting (87), into two cases.
% 28.58/7.92 |-Branch one:
% 28.58/7.92 | (650) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 28.58/7.92 |
% 28.58/7.92 +-Applying beta-rule and splitting (650), into two cases.
% 28.58/7.92 |-Branch one:
% 28.58/7.92 | (651) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 28.58/7.92 |
% 28.58/7.92 +-Applying beta-rule and splitting (651), into two cases.
% 28.58/7.92 |-Branch one:
% 28.58/7.92 | (652) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 28.58/7.92 |
% 28.58/7.92 | Applying alpha-rule on (652) yields:
% 28.58/7.92 | (653) all_0_13_13 = e4
% 28.58/7.92 | (654) ~ (all_0_14_14 = e2)
% 28.58/7.92 |
% 28.58/7.92 | Combining equations (5957,653) yields a new equation:
% 28.58/7.92 | (526) e4 = e1
% 28.58/7.92 |
% 28.58/7.92 | Equations (526) can reduce 251 to:
% 28.58/7.92 | (270) $false
% 28.58/7.92 |
% 28.58/7.92 |-The branch is then unsatisfiable
% 28.58/7.92 |-Branch two:
% 28.58/7.92 | (657) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 28.58/7.92 |
% 28.58/7.92 | Applying alpha-rule on (657) yields:
% 28.58/7.92 | (658) all_0_15_15 = e3
% 28.58/7.92 | (659) ~ (all_0_16_16 = e2)
% 28.58/7.92 |
% 28.58/7.92 | Combining equations (620,658) yields a new equation:
% 28.58/7.92 | (660) e4 = e3
% 28.58/7.92 |
% 28.58/7.92 | Simplifying 660 yields:
% 28.58/7.92 | (359) e4 = e3
% 28.58/7.92 |
% 28.58/7.92 | Equations (359) can reduce 34 to:
% 28.58/7.92 | (270) $false
% 28.58/7.92 |
% 28.58/7.92 |-The branch is then unsatisfiable
% 28.58/7.92 |-Branch two:
% 28.58/7.92 | (663) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 28.58/7.92 |
% 28.58/7.92 | Applying alpha-rule on (663) yields:
% 28.58/7.92 | (664) all_0_17_17 = e1
% 28.58/7.92 | (665) ~ (all_0_18_18 = e2)
% 28.58/7.92 |
% 28.58/7.92 | Combining equations (664,3413) yields a new equation:
% 28.58/7.92 | (322) e2 = e1
% 28.58/7.92 |
% 28.58/7.92 | Equations (322) can reduce 141 to:
% 28.58/7.92 | (270) $false
% 28.58/7.92 |
% 28.58/7.92 |-The branch is then unsatisfiable
% 28.58/7.92 |-Branch two:
% 28.58/7.92 | (1762) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 28.58/7.92 |
% 28.58/7.92 | Applying alpha-rule on (1762) yields:
% 28.58/7.92 | (1763) all_0_19_19 = e0
% 28.58/7.92 | (1764) ~ (all_0_20_20 = e2)
% 28.58/7.92 |
% 28.58/7.92 | Equations (7025) can reduce 1764 to:
% 28.58/7.92 | (270) $false
% 28.58/7.92 |
% 28.58/7.92 |-The branch is then unsatisfiable
% 28.58/7.92 |-Branch two:
% 28.58/7.92 | (354) ~ (all_0_45_45 = e3)
% 28.58/7.92 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 28.58/7.92 |
% 28.58/7.92 +-Applying beta-rule and splitting (1539), into two cases.
% 28.58/7.92 |-Branch one:
% 28.58/7.92 | (1114) all_0_53_53 = e3
% 28.58/7.92 |
% 28.58/7.92 | Combining equations (1114,853) yields a new equation:
% 28.58/7.92 | (537) e3 = e1
% 28.58/7.92 |
% 28.58/7.92 | Simplifying 537 yields:
% 28.58/7.92 | (538) e3 = e1
% 28.58/7.92 |
% 28.58/7.92 | Equations (538) can reduce 136 to:
% 28.58/7.92 | (270) $false
% 28.58/7.92 |
% 28.58/7.92 |-The branch is then unsatisfiable
% 28.58/7.92 |-Branch two:
% 28.58/7.92 | (356) ~ (all_0_53_53 = e3)
% 28.58/7.92 | (4713) all_0_58_58 = e3
% 28.58/7.92 |
% 28.58/7.93 | Combining equations (396,4713) yields a new equation:
% 28.58/7.93 | (414) e3 = e2
% 28.58/7.93 |
% 28.58/7.93 | Equations (414) can reduce 223 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (925) ~ (all_0_52_52 = e0)
% 28.58/7.93 | (2258) all_0_57_57 = e0
% 28.58/7.93 |
% 28.58/7.93 | Combining equations (2258,997) yields a new equation:
% 28.58/7.93 | (560) e1 = e0
% 28.58/7.93 |
% 28.58/7.93 | Equations (560) can reduce 132 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (675) ~ (all_0_40_40 = e3)
% 28.58/7.93 | (530) all_0_40_40 = e1
% 28.58/7.93 |
% 28.58/7.93 | Equations (530) can reduce 534 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (640) ~ (all_0_42_42 = e1)
% 28.58/7.93 | (4628) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (535), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (536) all_0_41_41 = e1
% 28.58/7.93 |
% 28.58/7.93 | Equations (536) can reduce 540 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (540) ~ (all_0_41_41 = e1)
% 28.58/7.93 | (541) all_0_42_42 = e1
% 28.58/7.93 |
% 28.58/7.93 | Equations (541) can reduce 640 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (874) ~ (all_0_53_53 = e1)
% 28.58/7.93 | (1001) all_0_58_58 = e1
% 28.58/7.93 |
% 28.58/7.93 | Combining equations (1001,396) yields a new equation:
% 28.58/7.93 | (322) e2 = e1
% 28.58/7.93 |
% 28.58/7.93 | Equations (322) can reduce 141 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (291) ~ (all_0_39_39 = e2)
% 28.58/7.93 | (630) all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (630), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (327) all_0_40_40 = e2
% 28.58/7.93 |
% 28.58/7.93 | Equations (327) can reduce 602 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (602) ~ (all_0_40_40 = e2)
% 28.58/7.93 | (1251) all_0_41_41 = e2 | all_0_42_42 = e2
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (96), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (336) all_0_39_39 = e2
% 28.58/7.93 |
% 28.58/7.93 | Equations (336) can reduce 291 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (291) ~ (all_0_39_39 = e2)
% 28.58/7.93 | (4205) all_0_43_43 = e2 | all_0_47_47 = e2 | all_0_51_51 = e2 | all_0_56_56 = e2
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (4205), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (450) all_0_43_43 = e2
% 28.58/7.93 |
% 28.58/7.93 | Equations (450) can reduce 292 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (292) ~ (all_0_43_43 = e2)
% 28.58/7.93 | (4209) all_0_47_47 = e2 | all_0_51_51 = e2 | all_0_56_56 = e2
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (4209), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (290) all_0_47_47 = e2
% 28.58/7.93 |
% 28.58/7.93 | Combining equations (321,290) yields a new equation:
% 28.58/7.93 | (322) e2 = e1
% 28.58/7.93 |
% 28.58/7.93 | Equations (322) can reduce 141 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (3951) ~ (all_0_47_47 = e2)
% 28.58/7.93 | (4214) all_0_51_51 = e2 | all_0_56_56 = e2
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (1251), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (436) all_0_41_41 = e2
% 28.58/7.93 |
% 28.58/7.93 | Equations (436) can reduce 226 to:
% 28.58/7.93 | (291) ~ (all_0_39_39 = e2)
% 28.58/7.93 |
% 28.58/7.93 | Equations (436) can reduce 51 to:
% 28.58/7.93 | (611) ~ (all_0_45_45 = e2)
% 28.58/7.93 |
% 28.58/7.93 | Simplifying 611 yields:
% 28.58/7.93 | (434) ~ (all_0_45_45 = e2)
% 28.58/7.93 |
% 28.58/7.93 | Equations (436) can reduce 214 to:
% 28.58/7.93 | (258) ~ (all_0_53_53 = e2)
% 28.58/7.93 |
% 28.58/7.93 | Simplifying 258 yields:
% 28.58/7.93 | (259) ~ (all_0_53_53 = e2)
% 28.58/7.93 |
% 28.58/7.93 | Equations (436) can reduce 232 to:
% 28.58/7.93 | (57) ~ (e2 = e0)
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (186), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (336) all_0_39_39 = e2
% 28.58/7.93 |
% 28.58/7.93 | Equations (336) can reduce 291 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (291) ~ (all_0_39_39 = e2)
% 28.58/7.93 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (339), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (340), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 28.58/7.93 |
% 28.58/7.93 | Applying alpha-rule on (341) yields:
% 28.58/7.93 | (342) all_0_0_0 = e1
% 28.58/7.93 | (343) ~ (all_0_1_1 = e4)
% 28.58/7.93 |
% 28.58/7.93 | Combining equations (342,285) yields a new equation:
% 28.58/7.93 | (530) all_0_40_40 = e1
% 28.58/7.93 |
% 28.58/7.93 | Equations (530) can reduce 114 to:
% 28.58/7.93 | (528) ~ (all_0_39_39 = e1)
% 28.58/7.93 |
% 28.58/7.93 | Equations (530) can reduce 137 to:
% 28.58/7.93 | (641) ~ (all_0_52_52 = e1)
% 28.58/7.93 |
% 28.58/7.93 | Simplifying 641 yields:
% 28.58/7.93 | (642) ~ (all_0_52_52 = e1)
% 28.58/7.93 |
% 28.58/7.93 | Equations (530) can reduce 149 to:
% 28.58/7.93 | (643) ~ (all_0_57_57 = e1)
% 28.58/7.93 |
% 28.58/7.93 | Simplifying 643 yields:
% 28.58/7.93 | (644) ~ (all_0_57_57 = e1)
% 28.58/7.93 |
% 28.58/7.93 | Equations (530) can reduce 238 to:
% 28.58/7.93 | (132) ~ (e1 = e0)
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (4214), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (4215) all_0_51_51 = e2
% 28.58/7.93 |
% 28.58/7.93 | Equations (4215) can reduce 255 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (255) ~ (all_0_51_51 = e2)
% 28.58/7.93 | (388) all_0_56_56 = e2
% 28.58/7.93 |
% 28.58/7.93 | Equations (388) can reduce 188 to:
% 28.58/7.93 | (292) ~ (all_0_43_43 = e2)
% 28.58/7.93 |
% 28.58/7.93 | Equations (388) can reduce 60 to:
% 28.58/7.93 | (255) ~ (all_0_51_51 = e2)
% 28.58/7.93 |
% 28.58/7.93 | Equations (388) can reduce 185 to:
% 28.58/7.93 | (700) ~ (all_0_59_59 = e2)
% 28.58/7.93 |
% 28.58/7.93 | Simplifying 700 yields:
% 28.58/7.93 | (701) ~ (all_0_59_59 = e2)
% 28.58/7.93 |
% 28.58/7.93 | Equations (388) can reduce 274 to:
% 28.58/7.93 | (377) ~ (e4 = e2)
% 28.58/7.93 |
% 28.58/7.93 | Simplifying 377 yields:
% 28.58/7.93 | (231) ~ (e4 = e2)
% 28.58/7.93 |
% 28.58/7.93 | Equations (388) can reduce 995 to:
% 28.58/7.93 | (141) ~ (e2 = e1)
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (222), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (522) all_0_39_39 = e4
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (78), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (751) all_0_39_39 = e3
% 28.58/7.93 |
% 28.58/7.93 | Combining equations (522,751) yields a new equation:
% 28.58/7.93 | (660) e4 = e3
% 28.58/7.93 |
% 28.58/7.93 | Simplifying 660 yields:
% 28.58/7.93 | (359) e4 = e3
% 28.58/7.93 |
% 28.58/7.93 | Equations (359) can reduce 34 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (755) ~ (all_0_39_39 = e3)
% 28.58/7.93 | (4262) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (4262), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (671) all_0_40_40 = e3
% 28.58/7.93 |
% 28.58/7.93 | Combining equations (530,671) yields a new equation:
% 28.58/7.93 | (538) e3 = e1
% 28.58/7.93 |
% 28.58/7.93 | Equations (538) can reduce 136 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (675) ~ (all_0_40_40 = e3)
% 28.58/7.93 | (5254) all_0_41_41 = e3 | all_0_42_42 = e3
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (5254), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (351) all_0_41_41 = e3
% 28.58/7.93 |
% 28.58/7.93 | Combining equations (436,351) yields a new equation:
% 28.58/7.93 | (414) e3 = e2
% 28.58/7.93 |
% 28.58/7.93 | Equations (414) can reduce 223 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (1237) ~ (all_0_41_41 = e3)
% 28.58/7.93 | (1258) all_0_42_42 = e3
% 28.58/7.93 |
% 28.58/7.93 | Equations (1258) can reduce 17 to:
% 28.58/7.93 | (1259) ~ (all_0_59_59 = e3)
% 28.58/7.93 |
% 28.58/7.93 | Simplifying 1259 yields:
% 28.58/7.93 | (1260) ~ (all_0_59_59 = e3)
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (93), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (402) all_0_59_59 = e4
% 28.58/7.93 |
% 28.58/7.93 | Equations (402) can reduce 280 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (280) ~ (all_0_59_59 = e4)
% 28.58/7.93 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (407), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (408), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (409), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 28.58/7.93 |
% 28.58/7.93 | Applying alpha-rule on (410) yields:
% 28.58/7.93 | (411) all_0_43_43 = e0
% 28.58/7.93 | (412) all_0_59_59 = e3
% 28.58/7.93 | (413) ~ (all_0_46_46 = e3)
% 28.58/7.93 |
% 28.58/7.93 | Equations (412) can reduce 1260 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 28.58/7.93 |
% 28.58/7.93 | Applying alpha-rule on (416) yields:
% 28.58/7.93 | (411) all_0_43_43 = e0
% 28.58/7.93 | (412) all_0_59_59 = e3
% 28.58/7.93 | (419) ~ (all_0_56_56 = e0)
% 28.58/7.93 |
% 28.58/7.93 | Equations (412) can reduce 1260 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 28.58/7.93 |
% 28.58/7.93 | Applying alpha-rule on (422) yields:
% 28.58/7.93 | (423) all_0_53_53 = e0
% 28.58/7.93 | (424) all_0_59_59 = e1
% 28.58/7.93 | (425) ~ (all_0_54_54 = e1)
% 28.58/7.93 |
% 28.58/7.93 | Equations (423) can reduce 584 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 28.58/7.93 |
% 28.58/7.93 | Applying alpha-rule on (428) yields:
% 28.58/7.93 | (423) all_0_53_53 = e0
% 28.58/7.93 | (424) all_0_59_59 = e1
% 28.58/7.93 | (431) ~ (all_0_58_58 = e0)
% 28.58/7.93 |
% 28.58/7.93 | Equations (423) can reduce 584 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (591) ~ (all_0_39_39 = e4)
% 28.58/7.93 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (592), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (358) all_0_41_41 = e4
% 28.58/7.93 |
% 28.58/7.93 | Combining equations (436,358) yields a new equation:
% 28.58/7.93 | (269) e4 = e2
% 28.58/7.93 |
% 28.58/7.93 | Equations (269) can reduce 231 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (361) ~ (all_0_41_41 = e4)
% 28.58/7.93 | (512) all_0_42_42 = e4
% 28.58/7.93 |
% 28.58/7.93 | Equations (512) can reduce 184 to:
% 28.58/7.93 | (591) ~ (all_0_39_39 = e4)
% 28.58/7.93 |
% 28.58/7.93 | Equations (512) can reduce 18 to:
% 28.58/7.93 | (804) ~ (all_0_46_46 = e4)
% 28.58/7.93 |
% 28.58/7.93 | Simplifying 804 yields:
% 28.58/7.93 | (805) ~ (all_0_46_46 = e4)
% 28.58/7.93 |
% 28.58/7.93 | Equations (512) can reduce 17 to:
% 28.58/7.93 | (279) ~ (all_0_59_59 = e4)
% 28.58/7.93 |
% 28.58/7.93 | Simplifying 279 yields:
% 28.58/7.93 | (280) ~ (all_0_59_59 = e4)
% 28.58/7.93 |
% 28.58/7.93 | Equations (512) can reduce 199 to:
% 28.58/7.93 | (6) ~ (e4 = e0)
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (78), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (751) all_0_39_39 = e3
% 28.58/7.93 |
% 28.58/7.93 | Equations (751) can reduce 167 to:
% 28.58/7.93 | (1333) ~ (all_0_43_43 = e3)
% 28.58/7.93 |
% 28.58/7.93 | Simplifying 1333 yields:
% 28.58/7.93 | (786) ~ (all_0_43_43 = e3)
% 28.58/7.93 |
% 28.58/7.93 | Equations (751) can reduce 591 to:
% 28.58/7.93 | (719) ~ (e4 = e3)
% 28.58/7.93 |
% 28.58/7.93 | Simplifying 719 yields:
% 28.58/7.93 | (34) ~ (e4 = e3)
% 28.58/7.93 |
% 28.58/7.93 | Equations (751) can reduce 528 to:
% 28.58/7.93 | (136) ~ (e3 = e1)
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (44), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (502) all_0_43_43 = e4
% 28.58/7.93 |
% 28.58/7.93 | Equations (502) can reduce 103 to:
% 28.58/7.93 | (804) ~ (all_0_46_46 = e4)
% 28.58/7.93 |
% 28.58/7.93 | Simplifying 804 yields:
% 28.58/7.93 | (805) ~ (all_0_46_46 = e4)
% 28.58/7.93 |
% 28.58/7.93 | Equations (502) can reduce 240 to:
% 28.58/7.93 | (696) ~ (all_0_51_51 = e4)
% 28.58/7.93 |
% 28.58/7.93 | Simplifying 696 yields:
% 28.58/7.93 | (697) ~ (all_0_51_51 = e4)
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (75), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (411) all_0_43_43 = e0
% 28.58/7.93 |
% 28.58/7.93 | Combining equations (502,411) yields a new equation:
% 28.58/7.93 | (478) e4 = e0
% 28.58/7.93 |
% 28.58/7.93 | Simplifying 478 yields:
% 28.58/7.93 | (479) e4 = e0
% 28.58/7.93 |
% 28.58/7.93 | Equations (479) can reduce 6 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (455) ~ (all_0_43_43 = e0)
% 28.58/7.93 | (940) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 28.58/7.93 |
% 28.58/7.93 +-Applying beta-rule and splitting (940), into two cases.
% 28.58/7.93 |-Branch one:
% 28.58/7.93 | (315) all_0_47_47 = e0
% 28.58/7.93 |
% 28.58/7.93 | Combining equations (321,315) yields a new equation:
% 28.58/7.93 | (571) e1 = e0
% 28.58/7.93 |
% 28.58/7.93 | Simplifying 571 yields:
% 28.58/7.93 | (560) e1 = e0
% 28.58/7.93 |
% 28.58/7.93 | Equations (560) can reduce 132 to:
% 28.58/7.93 | (270) $false
% 28.58/7.93 |
% 28.58/7.93 |-The branch is then unsatisfiable
% 28.58/7.93 |-Branch two:
% 28.58/7.93 | (318) ~ (all_0_47_47 = e0)
% 28.58/7.93 | (950) all_0_51_51 = e0 | all_0_56_56 = e0
% 28.58/7.94 |
% 28.58/7.94 +-Applying beta-rule and splitting (950), into two cases.
% 28.58/7.94 |-Branch one:
% 28.58/7.94 | (954) all_0_51_51 = e0
% 28.58/7.94 |
% 28.58/7.94 | Equations (954) can reduce 12 to:
% 28.58/7.94 | (3103) ~ (all_0_53_53 = e0)
% 28.58/7.94 |
% 28.58/7.94 | Simplifying 3103 yields:
% 28.58/7.94 | (584) ~ (all_0_53_53 = e0)
% 28.58/7.94 |
% 28.58/7.94 | Equations (954) can reduce 697 to:
% 28.58/7.94 | (456) ~ (e4 = e0)
% 28.58/7.94 |
% 28.58/7.94 | Simplifying 456 yields:
% 28.58/7.94 | (6) ~ (e4 = e0)
% 28.58/7.94 |
% 28.58/7.94 | Equations (954) can reduce 255 to:
% 28.58/7.94 | (566) ~ (e2 = e0)
% 28.58/7.94 |
% 28.58/7.94 | Simplifying 566 yields:
% 28.58/7.94 | (57) ~ (e2 = e0)
% 28.58/7.94 |
% 28.58/7.94 +-Applying beta-rule and splitting (93), into two cases.
% 28.58/7.94 |-Branch one:
% 28.58/7.94 | (402) all_0_59_59 = e4
% 28.58/7.94 |
% 28.58/7.94 | Equations (402) can reduce 280 to:
% 28.58/7.94 | (270) $false
% 28.58/7.94 |
% 28.58/7.94 |-The branch is then unsatisfiable
% 28.58/7.94 |-Branch two:
% 28.58/7.94 | (280) ~ (all_0_59_59 = e4)
% 28.58/7.94 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 28.58/7.94 |
% 28.58/7.94 +-Applying beta-rule and splitting (116), into two cases.
% 28.58/7.94 |-Branch one:
% 28.58/7.94 | (411) all_0_43_43 = e0
% 28.58/7.94 |
% 28.58/7.94 | Combining equations (502,411) yields a new equation:
% 28.58/7.94 | (478) e4 = e0
% 28.58/7.94 |
% 28.58/7.94 | Simplifying 478 yields:
% 28.58/7.94 | (479) e4 = e0
% 28.58/7.94 |
% 28.58/7.94 | Equations (479) can reduce 6 to:
% 28.58/7.94 | (270) $false
% 28.58/7.94 |
% 28.58/7.94 |-The branch is then unsatisfiable
% 28.58/7.94 |-Branch two:
% 28.58/7.94 | (455) ~ (all_0_43_43 = e0)
% 28.58/7.94 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 28.58/7.94 |
% 28.58/7.94 +-Applying beta-rule and splitting (1122), into two cases.
% 28.58/7.94 |-Branch one:
% 28.58/7.94 | (621) all_0_44_44 = e0
% 28.58/7.94 |
% 28.58/7.94 | Combining equations (370,621) yields a new equation:
% 28.58/7.94 | (622) e2 = e0
% 28.58/7.94 |
% 28.58/7.94 | Simplifying 622 yields:
% 28.58/7.94 | (316) e2 = e0
% 28.58/7.94 |
% 28.58/7.94 | Equations (316) can reduce 57 to:
% 28.58/7.94 | (270) $false
% 28.58/7.94 |
% 28.58/7.94 |-The branch is then unsatisfiable
% 28.58/7.94 |-Branch two:
% 28.58/7.94 | (625) ~ (all_0_44_44 = e0)
% 28.58/7.94 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 28.58/7.94 |
% 28.58/7.94 +-Applying beta-rule and splitting (1128), into two cases.
% 28.58/7.94 |-Branch one:
% 28.58/7.94 | (454) all_0_45_45 = e0
% 28.58/7.94 |
% 28.58/7.94 | Equations (454) can reduce 488 to:
% 28.58/7.94 | (270) $false
% 28.58/7.94 |
% 28.58/7.94 |-The branch is then unsatisfiable
% 28.58/7.94 |-Branch two:
% 28.58/7.94 | (488) ~ (all_0_45_45 = e0)
% 28.58/7.94 | (1132) all_0_46_46 = e0
% 28.58/7.94 |
% 28.58/7.94 | Equations (1132) can reduce 805 to:
% 28.58/7.94 | (456) ~ (e4 = e0)
% 28.58/7.94 |
% 28.58/7.94 | Simplifying 456 yields:
% 28.58/7.94 | (6) ~ (e4 = e0)
% 28.58/7.94 |
% 28.58/7.94 +-Applying beta-rule and splitting (407), into two cases.
% 28.58/7.94 |-Branch one:
% 28.58/7.94 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 28.58/7.94 |
% 28.58/7.94 +-Applying beta-rule and splitting (408), into two cases.
% 28.58/7.94 |-Branch one:
% 28.58/7.94 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 28.58/7.94 |
% 28.58/7.94 +-Applying beta-rule and splitting (409), into two cases.
% 28.58/7.94 |-Branch one:
% 28.58/7.94 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 28.58/7.94 |
% 28.58/7.94 | Applying alpha-rule on (410) yields:
% 28.58/7.94 | (411) all_0_43_43 = e0
% 28.58/7.94 | (412) all_0_59_59 = e3
% 28.58/7.94 | (413) ~ (all_0_46_46 = e3)
% 28.58/7.94 |
% 28.58/7.94 | Combining equations (411,502) yields a new equation:
% 28.58/7.94 | (479) e4 = e0
% 28.58/7.94 |
% 28.58/7.94 | Equations (479) can reduce 6 to:
% 28.58/7.94 | (270) $false
% 28.58/7.94 |
% 28.58/7.94 |-The branch is then unsatisfiable
% 28.58/7.94 |-Branch two:
% 28.58/7.94 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 28.58/7.94 |
% 28.58/7.94 | Applying alpha-rule on (416) yields:
% 28.58/7.94 | (411) all_0_43_43 = e0
% 28.58/7.94 | (412) all_0_59_59 = e3
% 28.58/7.94 | (419) ~ (all_0_56_56 = e0)
% 28.58/7.94 |
% 28.58/7.94 | Combining equations (411,502) yields a new equation:
% 28.58/7.94 | (479) e4 = e0
% 28.58/7.94 |
% 28.58/7.94 | Equations (479) can reduce 6 to:
% 28.58/7.94 | (270) $false
% 28.58/7.94 |
% 28.58/7.94 |-The branch is then unsatisfiable
% 28.58/7.94 |-Branch two:
% 28.58/7.94 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 28.58/7.94 |
% 28.58/7.94 | Applying alpha-rule on (422) yields:
% 28.58/7.94 | (423) all_0_53_53 = e0
% 28.58/7.94 | (424) all_0_59_59 = e1
% 28.58/7.94 | (425) ~ (all_0_54_54 = e1)
% 28.58/7.94 |
% 28.58/7.94 | Equations (423) can reduce 584 to:
% 28.58/7.94 | (270) $false
% 28.58/7.94 |
% 28.58/7.94 |-The branch is then unsatisfiable
% 28.58/7.94 |-Branch two:
% 28.58/7.94 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 28.58/7.94 |
% 28.58/7.94 | Applying alpha-rule on (428) yields:
% 28.58/7.94 | (423) all_0_53_53 = e0
% 28.58/7.94 | (424) all_0_59_59 = e1
% 28.58/7.94 | (431) ~ (all_0_58_58 = e0)
% 28.58/7.94 |
% 28.58/7.94 | Equations (423) can reduce 584 to:
% 28.58/7.94 | (270) $false
% 28.58/7.94 |
% 28.58/7.94 |-The branch is then unsatisfiable
% 28.58/7.94 |-Branch two:
% 28.58/7.94 | (987) ~ (all_0_51_51 = e0)
% 28.58/7.94 | (830) all_0_56_56 = e0
% 28.58/7.94 |
% 28.58/7.94 | Combining equations (830,388) yields a new equation:
% 28.58/7.94 | (316) e2 = e0
% 28.58/7.94 |
% 28.58/7.94 | Equations (316) can reduce 57 to:
% 28.58/7.94 | (270) $false
% 28.58/7.94 |
% 28.58/7.94 |-The branch is then unsatisfiable
% 28.58/7.94 |-Branch two:
% 28.58/7.94 | (510) ~ (all_0_43_43 = e4)
% 28.58/7.94 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 28.58/7.94 |
% 28.58/7.94 +-Applying beta-rule and splitting (159), into two cases.
% 28.58/7.94 |-Branch one:
% 28.58/7.94 | (450) all_0_43_43 = e2
% 28.58/7.94 |
% 28.58/7.94 | Equations (450) can reduce 292 to:
% 28.58/7.94 | (270) $false
% 28.58/7.94 |
% 28.58/7.94 |-The branch is then unsatisfiable
% 28.58/7.94 |-Branch two:
% 28.58/7.94 | (292) ~ (all_0_43_43 = e2)
% 28.58/7.94 | (774) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 28.58/7.94 |
% 28.58/7.94 +-Applying beta-rule and splitting (166), into two cases.
% 28.58/7.94 |-Branch one:
% 28.58/7.94 | (522) all_0_39_39 = e4
% 28.58/7.94 |
% 28.58/7.94 | Combining equations (751,522) yields a new equation:
% 28.58/7.94 | (359) e4 = e3
% 28.58/7.94 |
% 28.58/7.94 | Equations (359) can reduce 34 to:
% 28.58/7.94 | (270) $false
% 28.58/7.94 |
% 28.58/7.94 |-The branch is then unsatisfiable
% 28.58/7.94 |-Branch two:
% 28.58/7.94 | (591) ~ (all_0_39_39 = e4)
% 28.58/7.94 | (4522) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 28.58/7.94 |
% 28.58/7.94 +-Applying beta-rule and splitting (774), into two cases.
% 28.58/7.94 |-Branch one:
% 28.58/7.94 | (411) all_0_43_43 = e0
% 28.58/7.94 |
% 28.58/7.94 | Equations (411) can reduce 510 to:
% 28.58/7.94 | (456) ~ (e4 = e0)
% 28.58/7.94 |
% 28.58/7.94 | Simplifying 456 yields:
% 28.58/7.94 | (6) ~ (e4 = e0)
% 28.58/7.94 |
% 28.58/7.94 | Equations (411) can reduce 786 to:
% 28.58/7.94 | (788) ~ (e3 = e0)
% 28.58/7.94 |
% 28.58/7.94 | Simplifying 788 yields:
% 28.58/7.94 | (66) ~ (e3 = e0)
% 28.58/7.94 |
% 28.58/7.94 +-Applying beta-rule and splitting (4522), into two cases.
% 28.58/7.94 |-Branch one:
% 28.58/7.94 | (502) all_0_43_43 = e4
% 28.58/7.94 |
% 28.58/7.94 | Combining equations (411,502) yields a new equation:
% 28.58/7.94 | (479) e4 = e0
% 28.58/7.94 |
% 28.58/7.94 | Equations (479) can reduce 6 to:
% 28.58/7.94 | (270) $false
% 28.58/7.94 |
% 28.58/7.94 |-The branch is then unsatisfiable
% 28.58/7.94 |-Branch two:
% 28.58/7.94 | (510) ~ (all_0_43_43 = e4)
% 28.58/7.94 | (4527) all_0_51_51 = e4 | all_0_56_56 = e4
% 28.58/7.94 |
% 28.58/7.94 +-Applying beta-rule and splitting (93), into two cases.
% 28.58/7.94 |-Branch one:
% 28.58/7.94 | (402) all_0_59_59 = e4
% 28.58/7.94 |
% 28.58/7.94 | Equations (402) can reduce 280 to:
% 28.58/7.94 | (270) $false
% 28.58/7.94 |
% 28.58/7.94 |-The branch is then unsatisfiable
% 28.58/7.94 |-Branch two:
% 28.58/7.94 | (280) ~ (all_0_59_59 = e4)
% 28.58/7.94 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 28.58/7.94 |
% 28.58/7.94 +-Applying beta-rule and splitting (407), into two cases.
% 28.58/7.94 |-Branch one:
% 28.58/7.94 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 28.58/7.94 |
% 28.58/7.94 +-Applying beta-rule and splitting (408), into two cases.
% 28.58/7.94 |-Branch one:
% 28.58/7.94 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 28.58/7.94 |
% 28.58/7.94 +-Applying beta-rule and splitting (409), into two cases.
% 28.58/7.94 |-Branch one:
% 28.58/7.94 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 28.58/7.94 |
% 28.58/7.94 | Applying alpha-rule on (410) yields:
% 28.58/7.94 | (411) all_0_43_43 = e0
% 28.58/7.94 | (412) all_0_59_59 = e3
% 28.58/7.94 | (413) ~ (all_0_46_46 = e3)
% 28.58/7.94 |
% 28.58/7.94 | Equations (412) can reduce 140 to:
% 28.58/7.94 | (846) ~ (all_0_57_57 = e3)
% 28.58/7.94 |
% 28.58/7.94 | Equations (412) can reduce 701 to:
% 28.58/7.94 | (223) ~ (e3 = e2)
% 28.58/7.94 |
% 28.58/7.94 +-Applying beta-rule and splitting (22), into two cases.
% 28.58/7.94 |-Branch one:
% 28.58/7.94 | (782) all_0_43_43 = e3
% 28.58/7.94 |
% 28.58/7.94 | Combining equations (411,782) yields a new equation:
% 28.58/7.94 | (784) e3 = e0
% 28.58/7.94 |
% 28.58/7.94 | Equations (784) can reduce 66 to:
% 28.58/7.94 | (270) $false
% 28.58/7.94 |
% 28.58/7.94 |-The branch is then unsatisfiable
% 28.58/7.94 |-Branch two:
% 28.58/7.94 | (786) ~ (all_0_43_43 = e3)
% 28.58/7.94 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 28.58/7.94 |
% 28.58/7.94 | Equations (411) can reduce 786 to:
% 28.58/7.94 | (788) ~ (e3 = e0)
% 28.58/7.94 |
% 28.58/7.94 | Simplifying 788 yields:
% 28.58/7.94 | (66) ~ (e3 = e0)
% 28.58/7.94 |
% 28.58/7.94 +-Applying beta-rule and splitting (194), into two cases.
% 28.58/7.94 |-Branch one:
% 28.58/7.94 | (747) all_0_56_56 = e1
% 28.58/7.94 |
% 28.58/7.94 | Combining equations (388,747) yields a new equation:
% 28.58/7.94 | (531) e2 = e1
% 28.58/7.94 |
% 28.58/7.94 | Simplifying 531 yields:
% 28.58/7.94 | (322) e2 = e1
% 28.58/7.94 |
% 28.58/7.94 | Equations (322) can reduce 141 to:
% 28.58/7.94 | (270) $false
% 28.58/7.94 |
% 28.58/7.94 |-The branch is then unsatisfiable
% 28.58/7.94 |-Branch two:
% 28.58/7.94 | (995) ~ (all_0_56_56 = e1)
% 28.58/7.94 | (996) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 28.84/7.94 |
% 28.84/7.94 +-Applying beta-rule and splitting (133), into two cases.
% 28.84/7.94 |-Branch one:
% 28.84/7.94 | (671) all_0_40_40 = e3
% 28.84/7.94 |
% 28.84/7.94 | Combining equations (530,671) yields a new equation:
% 28.84/7.94 | (538) e3 = e1
% 28.84/7.94 |
% 28.84/7.94 | Equations (538) can reduce 136 to:
% 28.84/7.94 | (270) $false
% 28.84/7.94 |
% 28.84/7.94 |-The branch is then unsatisfiable
% 28.84/7.94 |-Branch two:
% 28.84/7.94 | (675) ~ (all_0_40_40 = e3)
% 28.84/7.94 | (676) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 28.84/7.94 |
% 28.84/7.94 +-Applying beta-rule and splitting (676), into two cases.
% 28.84/7.94 |-Branch one:
% 28.84/7.94 | (858) all_0_44_44 = e3
% 28.84/7.94 |
% 28.84/7.94 | Combining equations (370,858) yields a new equation:
% 28.84/7.94 | (414) e3 = e2
% 28.84/7.94 |
% 28.84/7.94 | Equations (414) can reduce 223 to:
% 28.84/7.94 | (270) $false
% 28.84/7.94 |
% 28.84/7.94 |-The branch is then unsatisfiable
% 28.84/7.94 |-Branch two:
% 28.84/7.94 | (862) ~ (all_0_44_44 = e3)
% 28.84/7.94 | (863) all_0_52_52 = e3 | all_0_57_57 = e3
% 28.84/7.94 |
% 28.84/7.94 +-Applying beta-rule and splitting (863), into two cases.
% 28.84/7.94 |-Branch one:
% 28.84/7.94 | (864) all_0_52_52 = e3
% 28.84/7.94 |
% 28.84/7.94 | Equations (864) can reduce 213 to:
% 28.84/7.94 | (355) ~ (all_0_53_53 = e3)
% 28.84/7.94 |
% 28.84/7.94 | Simplifying 355 yields:
% 28.84/7.94 | (356) ~ (all_0_53_53 = e3)
% 28.84/7.94 |
% 28.84/7.94 | Equations (864) can reduce 642 to:
% 28.84/7.94 | (136) ~ (e3 = e1)
% 28.84/7.94 |
% 28.84/7.94 +-Applying beta-rule and splitting (626), into two cases.
% 28.84/7.94 |-Branch one:
% 28.84/7.94 | (827) all_0_52_52 = e0
% 28.84/7.94 |
% 28.84/7.94 | Combining equations (864,827) yields a new equation:
% 28.84/7.94 | (783) e3 = e0
% 28.84/7.94 |
% 28.84/7.94 | Simplifying 783 yields:
% 28.84/7.94 | (784) e3 = e0
% 28.84/7.94 |
% 28.84/7.94 | Equations (784) can reduce 66 to:
% 28.84/7.94 | (270) $false
% 28.84/7.94 |
% 28.84/7.94 |-The branch is then unsatisfiable
% 28.84/7.94 |-Branch two:
% 28.84/7.94 | (925) ~ (all_0_52_52 = e0)
% 28.84/7.94 | (2258) all_0_57_57 = e0
% 28.84/7.94 |
% 28.84/7.94 | Equations (2258) can reduce 644 to:
% 28.84/7.94 | (568) ~ (e1 = e0)
% 28.84/7.94 |
% 28.84/7.94 | Simplifying 568 yields:
% 28.84/7.94 | (132) ~ (e1 = e0)
% 28.84/7.94 |
% 28.84/7.94 +-Applying beta-rule and splitting (996), into two cases.
% 28.84/7.94 |-Branch one:
% 28.84/7.94 | (997) all_0_57_57 = e1
% 28.84/7.94 |
% 28.84/7.94 | Combining equations (997,2258) yields a new equation:
% 28.84/7.94 | (571) e1 = e0
% 28.84/7.94 |
% 28.84/7.94 | Simplifying 571 yields:
% 28.84/7.94 | (560) e1 = e0
% 28.84/7.94 |
% 28.84/7.94 | Equations (560) can reduce 132 to:
% 28.84/7.94 | (270) $false
% 28.84/7.94 |
% 28.84/7.94 |-The branch is then unsatisfiable
% 28.84/7.94 |-Branch two:
% 28.84/7.94 | (644) ~ (all_0_57_57 = e1)
% 28.84/7.94 | (1000) all_0_58_58 = e1 | all_0_59_59 = e1
% 28.84/7.94 |
% 28.84/7.94 +-Applying beta-rule and splitting (511), into two cases.
% 28.84/7.94 |-Branch one:
% 28.84/7.94 | (363) all_0_45_45 = e4
% 28.84/7.94 |
% 28.84/7.94 | Equations (363) can reduce 434 to:
% 28.84/7.94 | (231) ~ (e4 = e2)
% 28.84/7.94 |
% 28.84/7.94 +-Applying beta-rule and splitting (189), into two cases.
% 28.84/7.94 |-Branch one:
% 28.84/7.94 | (267) all_0_50_50 = e4
% 28.84/7.94 |
% 28.84/7.94 | Combining equations (253,267) yields a new equation:
% 28.84/7.94 | (269) e4 = e2
% 28.84/7.94 |
% 28.84/7.94 | Equations (269) can reduce 231 to:
% 28.84/7.94 | (270) $false
% 28.84/7.94 |
% 28.84/7.94 |-The branch is then unsatisfiable
% 28.84/7.94 |-Branch two:
% 28.84/7.94 | (271) ~ (all_0_50_50 = e4)
% 28.84/7.94 | (1466) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 28.84/7.94 |
% 28.84/7.94 | Equations (253) can reduce 271 to:
% 28.84/7.94 | (377) ~ (e4 = e2)
% 28.84/7.94 |
% 28.84/7.94 | Simplifying 377 yields:
% 28.84/7.94 | (231) ~ (e4 = e2)
% 28.84/7.94 |
% 28.84/7.94 +-Applying beta-rule and splitting (4527), into two cases.
% 28.84/7.94 |-Branch one:
% 28.84/7.94 | (1467) all_0_51_51 = e4
% 28.84/7.94 |
% 28.84/7.94 | Equations (1467) can reduce 12 to:
% 28.84/7.94 | (1444) ~ (all_0_53_53 = e4)
% 28.84/7.94 |
% 28.84/7.94 | Simplifying 1444 yields:
% 28.84/7.94 | (599) ~ (all_0_53_53 = e4)
% 28.84/7.94 |
% 28.84/7.94 +-Applying beta-rule and splitting (13), into two cases.
% 28.84/7.94 |-Branch one:
% 28.84/7.94 | (576) all_0_53_53 = e2
% 28.84/7.94 |
% 28.84/7.94 | Equations (576) can reduce 259 to:
% 28.84/7.94 | (270) $false
% 28.84/7.94 |
% 28.84/7.94 |-The branch is then unsatisfiable
% 28.84/7.94 |-Branch two:
% 28.84/7.94 | (259) ~ (all_0_53_53 = e2)
% 28.84/7.94 | (5715) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 28.84/7.94 |
% 28.84/7.94 +-Applying beta-rule and splitting (5715), into two cases.
% 28.84/7.94 |-Branch one:
% 28.84/7.94 | (423) all_0_53_53 = e0
% 28.84/7.94 |
% 28.84/7.94 | Equations (423) can reduce 584 to:
% 28.84/7.94 | (270) $false
% 28.84/7.94 |
% 28.84/7.94 |-The branch is then unsatisfiable
% 28.84/7.94 |-Branch two:
% 28.84/7.94 | (584) ~ (all_0_53_53 = e0)
% 28.84/7.94 | (5719) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1
% 28.84/7.94 |
% 28.84/7.94 +-Applying beta-rule and splitting (5719), into two cases.
% 28.84/7.94 |-Branch one:
% 28.84/7.94 | (1114) all_0_53_53 = e3
% 28.84/7.94 |
% 28.84/7.94 | Equations (1114) can reduce 356 to:
% 28.84/7.94 | (270) $false
% 28.84/7.94 |
% 28.84/7.94 |-The branch is then unsatisfiable
% 28.84/7.94 |-Branch two:
% 28.84/7.94 | (356) ~ (all_0_53_53 = e3)
% 28.84/7.94 | (5723) all_0_53_53 = e4 | all_0_53_53 = e1
% 28.84/7.94 |
% 28.84/7.94 +-Applying beta-rule and splitting (1000), into two cases.
% 28.84/7.94 |-Branch one:
% 28.84/7.94 | (1001) all_0_58_58 = e1
% 28.84/7.94 |
% 28.84/7.94 | Equations (1001) can reduce 70 to:
% 28.84/7.94 | (874) ~ (all_0_53_53 = e1)
% 28.84/7.94 |
% 28.84/7.95 +-Applying beta-rule and splitting (5723), into two cases.
% 28.84/7.95 |-Branch one:
% 28.84/7.95 | (853) all_0_53_53 = e1
% 28.84/7.95 |
% 28.84/7.95 | Equations (853) can reduce 874 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (874) ~ (all_0_53_53 = e1)
% 28.84/7.95 | (367) all_0_53_53 = e4
% 28.84/7.95 |
% 28.84/7.95 | Equations (367) can reduce 599 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (1004) ~ (all_0_58_58 = e1)
% 28.84/7.95 | (424) all_0_59_59 = e1
% 28.84/7.95 |
% 28.84/7.95 | Combining equations (424,412) yields a new equation:
% 28.84/7.95 | (538) e3 = e1
% 28.84/7.95 |
% 28.84/7.95 | Equations (538) can reduce 136 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (697) ~ (all_0_51_51 = e4)
% 28.84/7.95 | (4744) all_0_56_56 = e4
% 28.84/7.95 |
% 28.84/7.95 | Combining equations (4744,388) yields a new equation:
% 28.84/7.95 | (268) e4 = e2
% 28.84/7.95 |
% 28.84/7.95 | Simplifying 268 yields:
% 28.84/7.95 | (269) e4 = e2
% 28.84/7.95 |
% 28.84/7.95 | Equations (269) can reduce 231 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (352) ~ (all_0_45_45 = e4)
% 28.84/7.95 | (517) all_0_46_46 = e4
% 28.84/7.95 |
% 28.84/7.95 | Equations (517) can reduce 805 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (826) ~ (all_0_52_52 = e3)
% 28.84/7.95 | (869) all_0_57_57 = e3
% 28.84/7.95 |
% 28.84/7.95 | Equations (869) can reduce 846 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 28.84/7.95 |
% 28.84/7.95 | Applying alpha-rule on (416) yields:
% 28.84/7.95 | (411) all_0_43_43 = e0
% 28.84/7.95 | (412) all_0_59_59 = e3
% 28.84/7.95 | (419) ~ (all_0_56_56 = e0)
% 28.84/7.95 |
% 28.84/7.95 | Equations (412) can reduce 140 to:
% 28.84/7.95 | (846) ~ (all_0_57_57 = e3)
% 28.84/7.95 |
% 28.84/7.95 | Equations (412) can reduce 701 to:
% 28.84/7.95 | (223) ~ (e3 = e2)
% 28.84/7.95 |
% 28.84/7.95 +-Applying beta-rule and splitting (22), into two cases.
% 28.84/7.95 |-Branch one:
% 28.84/7.95 | (782) all_0_43_43 = e3
% 28.84/7.95 |
% 28.84/7.95 | Combining equations (411,782) yields a new equation:
% 28.84/7.95 | (784) e3 = e0
% 28.84/7.95 |
% 28.84/7.95 | Equations (784) can reduce 66 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (786) ~ (all_0_43_43 = e3)
% 28.84/7.95 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 28.84/7.95 |
% 28.84/7.95 | Equations (411) can reduce 786 to:
% 28.84/7.95 | (788) ~ (e3 = e0)
% 28.84/7.95 |
% 28.84/7.95 | Simplifying 788 yields:
% 28.84/7.95 | (66) ~ (e3 = e0)
% 28.84/7.95 |
% 28.84/7.95 +-Applying beta-rule and splitting (194), into two cases.
% 28.84/7.95 |-Branch one:
% 28.84/7.95 | (747) all_0_56_56 = e1
% 28.84/7.95 |
% 28.84/7.95 | Combining equations (388,747) yields a new equation:
% 28.84/7.95 | (531) e2 = e1
% 28.84/7.95 |
% 28.84/7.95 | Simplifying 531 yields:
% 28.84/7.95 | (322) e2 = e1
% 28.84/7.95 |
% 28.84/7.95 | Equations (322) can reduce 141 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (995) ~ (all_0_56_56 = e1)
% 28.84/7.95 | (996) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 28.84/7.95 |
% 28.84/7.95 +-Applying beta-rule and splitting (133), into two cases.
% 28.84/7.95 |-Branch one:
% 28.84/7.95 | (671) all_0_40_40 = e3
% 28.84/7.95 |
% 28.84/7.95 | Combining equations (530,671) yields a new equation:
% 28.84/7.95 | (538) e3 = e1
% 28.84/7.95 |
% 28.84/7.95 | Equations (538) can reduce 136 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (675) ~ (all_0_40_40 = e3)
% 28.84/7.95 | (676) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 28.84/7.95 |
% 28.84/7.95 +-Applying beta-rule and splitting (676), into two cases.
% 28.84/7.95 |-Branch one:
% 28.84/7.95 | (858) all_0_44_44 = e3
% 28.84/7.95 |
% 28.84/7.95 | Combining equations (370,858) yields a new equation:
% 28.84/7.95 | (414) e3 = e2
% 28.84/7.95 |
% 28.84/7.95 | Equations (414) can reduce 223 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (862) ~ (all_0_44_44 = e3)
% 28.84/7.95 | (863) all_0_52_52 = e3 | all_0_57_57 = e3
% 28.84/7.95 |
% 28.84/7.95 +-Applying beta-rule and splitting (863), into two cases.
% 28.84/7.95 |-Branch one:
% 28.84/7.95 | (864) all_0_52_52 = e3
% 28.84/7.95 |
% 28.84/7.95 | Equations (864) can reduce 213 to:
% 28.84/7.95 | (355) ~ (all_0_53_53 = e3)
% 28.84/7.95 |
% 28.84/7.95 | Simplifying 355 yields:
% 28.84/7.95 | (356) ~ (all_0_53_53 = e3)
% 28.84/7.95 |
% 28.84/7.95 | Equations (864) can reduce 642 to:
% 28.84/7.95 | (136) ~ (e3 = e1)
% 28.84/7.95 |
% 28.84/7.95 +-Applying beta-rule and splitting (626), into two cases.
% 28.84/7.95 |-Branch one:
% 28.84/7.95 | (827) all_0_52_52 = e0
% 28.84/7.95 |
% 28.84/7.95 | Combining equations (864,827) yields a new equation:
% 28.84/7.95 | (783) e3 = e0
% 28.84/7.95 |
% 28.84/7.95 | Simplifying 783 yields:
% 28.84/7.95 | (784) e3 = e0
% 28.84/7.95 |
% 28.84/7.95 | Equations (784) can reduce 66 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (925) ~ (all_0_52_52 = e0)
% 28.84/7.95 | (2258) all_0_57_57 = e0
% 28.84/7.95 |
% 28.84/7.95 | Equations (2258) can reduce 644 to:
% 28.84/7.95 | (568) ~ (e1 = e0)
% 28.84/7.95 |
% 28.84/7.95 | Simplifying 568 yields:
% 28.84/7.95 | (132) ~ (e1 = e0)
% 28.84/7.95 |
% 28.84/7.95 +-Applying beta-rule and splitting (996), into two cases.
% 28.84/7.95 |-Branch one:
% 28.84/7.95 | (997) all_0_57_57 = e1
% 28.84/7.95 |
% 28.84/7.95 | Combining equations (997,2258) yields a new equation:
% 28.84/7.95 | (571) e1 = e0
% 28.84/7.95 |
% 28.84/7.95 | Simplifying 571 yields:
% 28.84/7.95 | (560) e1 = e0
% 28.84/7.95 |
% 28.84/7.95 | Equations (560) can reduce 132 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (644) ~ (all_0_57_57 = e1)
% 28.84/7.95 | (1000) all_0_58_58 = e1 | all_0_59_59 = e1
% 28.84/7.95 |
% 28.84/7.95 +-Applying beta-rule and splitting (511), into two cases.
% 28.84/7.95 |-Branch one:
% 28.84/7.95 | (363) all_0_45_45 = e4
% 28.84/7.95 |
% 28.84/7.95 | Equations (363) can reduce 434 to:
% 28.84/7.95 | (231) ~ (e4 = e2)
% 28.84/7.95 |
% 28.84/7.95 +-Applying beta-rule and splitting (189), into two cases.
% 28.84/7.95 |-Branch one:
% 28.84/7.95 | (267) all_0_50_50 = e4
% 28.84/7.95 |
% 28.84/7.95 | Combining equations (253,267) yields a new equation:
% 28.84/7.95 | (269) e4 = e2
% 28.84/7.95 |
% 28.84/7.95 | Equations (269) can reduce 231 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (271) ~ (all_0_50_50 = e4)
% 28.84/7.95 | (1466) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 28.84/7.95 |
% 28.84/7.95 | Equations (253) can reduce 271 to:
% 28.84/7.95 | (377) ~ (e4 = e2)
% 28.84/7.95 |
% 28.84/7.95 | Simplifying 377 yields:
% 28.84/7.95 | (231) ~ (e4 = e2)
% 28.84/7.95 |
% 28.84/7.95 +-Applying beta-rule and splitting (4527), into two cases.
% 28.84/7.95 |-Branch one:
% 28.84/7.95 | (1467) all_0_51_51 = e4
% 28.84/7.95 |
% 28.84/7.95 | Equations (1467) can reduce 12 to:
% 28.84/7.95 | (1444) ~ (all_0_53_53 = e4)
% 28.84/7.95 |
% 28.84/7.95 | Simplifying 1444 yields:
% 28.84/7.95 | (599) ~ (all_0_53_53 = e4)
% 28.84/7.95 |
% 28.84/7.95 +-Applying beta-rule and splitting (13), into two cases.
% 28.84/7.95 |-Branch one:
% 28.84/7.95 | (576) all_0_53_53 = e2
% 28.84/7.95 |
% 28.84/7.95 | Equations (576) can reduce 259 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (259) ~ (all_0_53_53 = e2)
% 28.84/7.95 | (5715) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 28.84/7.95 |
% 28.84/7.95 +-Applying beta-rule and splitting (5715), into two cases.
% 28.84/7.95 |-Branch one:
% 28.84/7.95 | (423) all_0_53_53 = e0
% 28.84/7.95 |
% 28.84/7.95 | Equations (423) can reduce 584 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (584) ~ (all_0_53_53 = e0)
% 28.84/7.95 | (5719) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1
% 28.84/7.95 |
% 28.84/7.95 +-Applying beta-rule and splitting (5719), into two cases.
% 28.84/7.95 |-Branch one:
% 28.84/7.95 | (1114) all_0_53_53 = e3
% 28.84/7.95 |
% 28.84/7.95 | Equations (1114) can reduce 356 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (356) ~ (all_0_53_53 = e3)
% 28.84/7.95 | (5723) all_0_53_53 = e4 | all_0_53_53 = e1
% 28.84/7.95 |
% 28.84/7.95 +-Applying beta-rule and splitting (1000), into two cases.
% 28.84/7.95 |-Branch one:
% 28.84/7.95 | (1001) all_0_58_58 = e1
% 28.84/7.95 |
% 28.84/7.95 | Equations (1001) can reduce 70 to:
% 28.84/7.95 | (874) ~ (all_0_53_53 = e1)
% 28.84/7.95 |
% 28.84/7.95 +-Applying beta-rule and splitting (5723), into two cases.
% 28.84/7.95 |-Branch one:
% 28.84/7.95 | (853) all_0_53_53 = e1
% 28.84/7.95 |
% 28.84/7.95 | Equations (853) can reduce 874 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (874) ~ (all_0_53_53 = e1)
% 28.84/7.95 | (367) all_0_53_53 = e4
% 28.84/7.95 |
% 28.84/7.95 | Equations (367) can reduce 599 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (1004) ~ (all_0_58_58 = e1)
% 28.84/7.95 | (424) all_0_59_59 = e1
% 28.84/7.95 |
% 28.84/7.95 | Combining equations (424,412) yields a new equation:
% 28.84/7.95 | (538) e3 = e1
% 28.84/7.95 |
% 28.84/7.95 | Equations (538) can reduce 136 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (697) ~ (all_0_51_51 = e4)
% 28.84/7.95 | (4744) all_0_56_56 = e4
% 28.84/7.95 |
% 28.84/7.95 | Combining equations (4744,388) yields a new equation:
% 28.84/7.95 | (268) e4 = e2
% 28.84/7.95 |
% 28.84/7.95 | Simplifying 268 yields:
% 28.84/7.95 | (269) e4 = e2
% 28.84/7.95 |
% 28.84/7.95 | Equations (269) can reduce 231 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (352) ~ (all_0_45_45 = e4)
% 28.84/7.95 | (517) all_0_46_46 = e4
% 28.84/7.95 |
% 28.84/7.95 | Equations (517) can reduce 805 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (826) ~ (all_0_52_52 = e3)
% 28.84/7.95 | (869) all_0_57_57 = e3
% 28.84/7.95 |
% 28.84/7.95 | Equations (869) can reduce 846 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 28.84/7.95 |
% 28.84/7.95 | Applying alpha-rule on (422) yields:
% 28.84/7.95 | (423) all_0_53_53 = e0
% 28.84/7.95 | (424) all_0_59_59 = e1
% 28.84/7.95 | (425) ~ (all_0_54_54 = e1)
% 28.84/7.95 |
% 28.84/7.95 | Equations (423) can reduce 584 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 28.84/7.95 |
% 28.84/7.95 | Applying alpha-rule on (428) yields:
% 28.84/7.95 | (423) all_0_53_53 = e0
% 28.84/7.95 | (424) all_0_59_59 = e1
% 28.84/7.95 | (431) ~ (all_0_58_58 = e0)
% 28.84/7.95 |
% 28.84/7.95 | Equations (423) can reduce 584 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (455) ~ (all_0_43_43 = e0)
% 28.84/7.95 | (944) all_0_43_43 = e4 | all_0_43_43 = e3
% 28.84/7.95 |
% 28.84/7.95 +-Applying beta-rule and splitting (75), into two cases.
% 28.84/7.95 |-Branch one:
% 28.84/7.95 | (411) all_0_43_43 = e0
% 28.84/7.95 |
% 28.84/7.95 | Equations (411) can reduce 455 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (455) ~ (all_0_43_43 = e0)
% 28.84/7.95 | (940) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 28.84/7.95 |
% 28.84/7.95 +-Applying beta-rule and splitting (940), into two cases.
% 28.84/7.95 |-Branch one:
% 28.84/7.95 | (315) all_0_47_47 = e0
% 28.84/7.95 |
% 28.84/7.95 | Combining equations (321,315) yields a new equation:
% 28.84/7.95 | (571) e1 = e0
% 28.84/7.95 |
% 28.84/7.95 | Simplifying 571 yields:
% 28.84/7.95 | (560) e1 = e0
% 28.84/7.95 |
% 28.84/7.95 | Equations (560) can reduce 132 to:
% 28.84/7.95 | (270) $false
% 28.84/7.95 |
% 28.84/7.95 |-The branch is then unsatisfiable
% 28.84/7.95 |-Branch two:
% 28.84/7.95 | (318) ~ (all_0_47_47 = e0)
% 28.84/7.95 | (950) all_0_51_51 = e0 | all_0_56_56 = e0
% 28.84/7.96 |
% 28.84/7.96 +-Applying beta-rule and splitting (950), into two cases.
% 28.84/7.96 |-Branch one:
% 28.84/7.96 | (954) all_0_51_51 = e0
% 28.84/7.96 |
% 28.84/7.96 | Equations (954) can reduce 240 to:
% 28.84/7.96 | (455) ~ (all_0_43_43 = e0)
% 28.84/7.96 |
% 28.84/7.96 | Equations (954) can reduce 12 to:
% 28.84/7.96 | (3103) ~ (all_0_53_53 = e0)
% 28.84/7.96 |
% 28.84/7.96 | Simplifying 3103 yields:
% 28.84/7.96 | (584) ~ (all_0_53_53 = e0)
% 28.84/7.96 |
% 28.84/7.96 +-Applying beta-rule and splitting (93), into two cases.
% 28.84/7.96 |-Branch one:
% 28.84/7.96 | (402) all_0_59_59 = e4
% 28.84/7.96 |
% 28.84/7.96 | Equations (402) can reduce 280 to:
% 28.84/7.96 | (270) $false
% 28.84/7.96 |
% 28.84/7.96 |-The branch is then unsatisfiable
% 28.84/7.96 |-Branch two:
% 28.84/7.96 | (280) ~ (all_0_59_59 = e4)
% 28.84/7.96 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 28.84/7.96 |
% 28.84/7.96 +-Applying beta-rule and splitting (116), into two cases.
% 28.84/7.96 |-Branch one:
% 28.84/7.96 | (411) all_0_43_43 = e0
% 28.84/7.96 |
% 28.84/7.96 | Equations (411) can reduce 455 to:
% 28.84/7.96 | (270) $false
% 28.84/7.96 |
% 28.84/7.96 |-The branch is then unsatisfiable
% 28.84/7.96 |-Branch two:
% 28.84/7.96 | (455) ~ (all_0_43_43 = e0)
% 28.84/7.96 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 28.84/7.96 |
% 28.84/7.96 +-Applying beta-rule and splitting (407), into two cases.
% 28.84/7.96 |-Branch one:
% 28.84/7.96 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 28.84/7.96 |
% 28.84/7.96 +-Applying beta-rule and splitting (408), into two cases.
% 28.84/7.96 |-Branch one:
% 28.84/7.96 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 28.84/7.96 |
% 28.84/7.96 +-Applying beta-rule and splitting (409), into two cases.
% 28.84/7.96 |-Branch one:
% 28.84/7.96 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 28.84/7.96 |
% 28.84/7.96 | Applying alpha-rule on (410) yields:
% 28.84/7.96 | (411) all_0_43_43 = e0
% 28.84/7.96 | (412) all_0_59_59 = e3
% 28.84/7.96 | (413) ~ (all_0_46_46 = e3)
% 28.84/7.96 |
% 28.84/7.96 | Equations (411) can reduce 455 to:
% 28.84/7.96 | (270) $false
% 28.84/7.96 |
% 28.84/7.96 |-The branch is then unsatisfiable
% 28.84/7.96 |-Branch two:
% 28.84/7.96 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 28.84/7.96 |
% 28.84/7.96 | Applying alpha-rule on (416) yields:
% 28.84/7.96 | (411) all_0_43_43 = e0
% 28.84/7.96 | (412) all_0_59_59 = e3
% 28.84/7.96 | (419) ~ (all_0_56_56 = e0)
% 28.84/7.96 |
% 28.84/7.96 | Equations (411) can reduce 455 to:
% 28.84/7.96 | (270) $false
% 28.84/7.96 |
% 28.84/7.96 |-The branch is then unsatisfiable
% 28.84/7.96 |-Branch two:
% 28.84/7.96 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 28.84/7.96 |
% 28.84/7.96 | Applying alpha-rule on (422) yields:
% 28.84/7.96 | (423) all_0_53_53 = e0
% 28.84/7.96 | (424) all_0_59_59 = e1
% 28.84/7.96 | (425) ~ (all_0_54_54 = e1)
% 28.84/7.96 |
% 28.84/7.96 | Equations (423) can reduce 584 to:
% 28.84/7.96 | (270) $false
% 28.84/7.96 |
% 28.84/7.96 |-The branch is then unsatisfiable
% 28.84/7.96 |-Branch two:
% 28.84/7.96 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 28.84/7.96 |
% 28.84/7.96 | Applying alpha-rule on (428) yields:
% 28.84/7.96 | (423) all_0_53_53 = e0
% 28.84/7.96 | (424) all_0_59_59 = e1
% 28.84/7.96 | (431) ~ (all_0_58_58 = e0)
% 28.84/7.96 |
% 28.84/7.96 | Equations (423) can reduce 584 to:
% 28.84/7.96 | (270) $false
% 28.84/7.96 |
% 28.84/7.96 |-The branch is then unsatisfiable
% 28.84/7.96 |-Branch two:
% 28.84/7.96 | (987) ~ (all_0_51_51 = e0)
% 28.84/7.96 | (830) all_0_56_56 = e0
% 28.84/7.96 |
% 28.84/7.96 | Combining equations (830,388) yields a new equation:
% 28.84/7.96 | (316) e2 = e0
% 28.84/7.96 |
% 28.84/7.96 | Equations (316) can reduce 57 to:
% 28.84/7.96 | (270) $false
% 28.84/7.96 |
% 28.84/7.96 |-The branch is then unsatisfiable
% 28.84/7.96 |-Branch two:
% 28.84/7.96 | (755) ~ (all_0_39_39 = e3)
% 28.84/7.96 | (4262) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 28.84/7.96 |
% 28.84/7.96 +-Applying beta-rule and splitting (4262), into two cases.
% 28.84/7.96 |-Branch one:
% 28.84/7.96 | (671) all_0_40_40 = e3
% 28.84/7.96 |
% 28.84/7.96 | Combining equations (530,671) yields a new equation:
% 28.84/7.96 | (538) e3 = e1
% 28.84/7.96 |
% 28.84/7.96 | Equations (538) can reduce 136 to:
% 28.84/7.96 | (270) $false
% 28.84/7.96 |
% 28.84/7.96 |-The branch is then unsatisfiable
% 28.84/7.96 |-Branch two:
% 28.84/7.96 | (675) ~ (all_0_40_40 = e3)
% 28.84/7.96 | (5254) all_0_41_41 = e3 | all_0_42_42 = e3
% 28.84/7.96 |
% 28.84/7.96 +-Applying beta-rule and splitting (5254), into two cases.
% 28.84/7.96 |-Branch one:
% 28.84/7.96 | (351) all_0_41_41 = e3
% 28.84/7.96 |
% 28.84/7.96 | Combining equations (436,351) yields a new equation:
% 28.84/7.96 | (414) e3 = e2
% 28.84/7.96 |
% 28.84/7.96 | Equations (414) can reduce 223 to:
% 28.84/7.96 | (270) $false
% 28.84/7.96 |
% 28.84/7.96 |-The branch is then unsatisfiable
% 28.84/7.96 |-Branch two:
% 28.84/7.96 | (1237) ~ (all_0_41_41 = e3)
% 28.84/7.96 | (1258) all_0_42_42 = e3
% 28.84/7.96 |
% 28.84/7.96 | Combining equations (512,1258) yields a new equation:
% 28.84/7.96 | (660) e4 = e3
% 28.84/7.96 |
% 28.84/7.96 | Simplifying 660 yields:
% 28.84/7.96 | (359) e4 = e3
% 28.84/7.96 |
% 28.84/7.96 | Equations (359) can reduce 34 to:
% 28.84/7.96 | (270) $false
% 28.84/7.96 |
% 28.84/7.96 |-The branch is then unsatisfiable
% 28.84/7.96 |-Branch two:
% 28.84/7.96 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 28.84/7.96 |
% 28.84/7.96 | Applying alpha-rule on (346) yields:
% 28.84/7.96 | (347) all_0_2_2 = e0
% 28.84/7.96 | (348) ~ (all_0_3_3 = e4)
% 28.84/7.96 |
% 28.84/7.96 | Equations (287) can reduce 348 to:
% 28.84/7.96 | (270) $false
% 28.84/7.96 |
% 28.84/7.96 |-The branch is then unsatisfiable
% 28.84/7.96 |-Branch two:
% 28.84/7.96 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 28.84/7.96 |
% 28.84/7.96 | Applying alpha-rule on (350) yields:
% 28.84/7.96 | (351) all_0_41_41 = e3
% 28.84/7.96 | (352) ~ (all_0_45_45 = e4)
% 28.84/7.96 |
% 28.84/7.96 | Combining equations (436,351) yields a new equation:
% 28.84/7.96 | (414) e3 = e2
% 28.84/7.96 |
% 28.84/7.96 | Equations (414) can reduce 223 to:
% 28.84/7.96 | (270) $false
% 28.84/7.96 |
% 28.84/7.96 |-The branch is then unsatisfiable
% 28.84/7.96 |-Branch two:
% 28.84/7.96 | (331) ~ (all_0_41_41 = e2)
% 28.84/7.96 | (698) all_0_42_42 = e2
% 28.84/7.96 |
% 28.84/7.96 | Equations (698) can reduce 498 to:
% 28.84/7.96 | (270) $false
% 28.84/7.96 |
% 28.84/7.96 |-The branch is then unsatisfiable
% 28.84/7.96 |-Branch two:
% 28.84/7.96 | (333) ~ (all_0_44_44 = e2)
% 28.84/7.96 | (373) all_0_44_44 = e3 | all_0_44_44 = e0
% 28.84/7.96 |
% 28.84/7.96 +-Applying beta-rule and splitting (607), into two cases.
% 28.84/7.96 |-Branch one:
% 28.84/7.96 | (370) all_0_44_44 = e2
% 28.84/7.96 |
% 28.84/7.96 | Equations (370) can reduce 333 to:
% 28.84/7.96 | (270) $false
% 28.84/7.96 |
% 28.84/7.96 |-The branch is then unsatisfiable
% 28.84/7.96 |-Branch two:
% 28.84/7.96 | (333) ~ (all_0_44_44 = e2)
% 28.84/7.96 | (3377) all_0_52_52 = e2 | all_0_57_57 = e2
% 28.84/7.96 |
% 28.84/7.96 +-Applying beta-rule and splitting (3377), into two cases.
% 28.84/7.96 |-Branch one:
% 28.84/7.96 | (685) all_0_52_52 = e2
% 28.84/7.96 |
% 28.84/7.96 | Equations (685) can reduce 257 to:
% 28.84/7.96 | (270) $false
% 28.84/7.96 |
% 28.84/7.96 |-The branch is then unsatisfiable
% 28.84/7.96 |-Branch two:
% 28.84/7.96 | (257) ~ (all_0_52_52 = e2)
% 28.84/7.96 | (392) all_0_57_57 = e2
% 28.84/7.96 |
% 28.84/7.96 | Equations (392) can reduce 149 to:
% 28.84/7.96 | (602) ~ (all_0_40_40 = e2)
% 28.84/7.96 |
% 28.84/7.96 | From (392) and (30) follows:
% 28.84/7.96 | (3390) op(e2, e2) = all_0_19_19
% 28.84/7.96 |
% 28.84/7.96 | Instantiating formula (201) with e2, e2, all_0_19_19, e4 and discharging atoms op(e2, e2) = all_0_19_19, op(e2, e2) = e4, yields:
% 28.84/7.96 | (3391) all_0_19_19 = e4
% 28.84/7.96 |
% 28.84/7.96 +-Applying beta-rule and splitting (8), into two cases.
% 28.84/7.96 |-Branch one:
% 28.84/7.96 | (530) all_0_40_40 = e1
% 28.92/7.96 |
% 28.92/7.96 | Equations (530) can reduce 15 to:
% 28.92/7.96 | (4822) ~ (all_0_44_44 = e1)
% 28.92/7.96 |
% 28.92/7.96 | Simplifying 4822 yields:
% 28.92/7.96 | (131) ~ (all_0_44_44 = e1)
% 28.92/7.96 |
% 28.92/7.96 | Equations (530) can reduce 602 to:
% 28.92/7.96 | (645) ~ (e2 = e1)
% 28.92/7.96 |
% 28.92/7.96 | Simplifying 645 yields:
% 28.92/7.96 | (141) ~ (e2 = e1)
% 28.92/7.96 |
% 28.92/7.96 | From (530) and (68) follows:
% 28.92/7.96 | (648) op(e2, e1) = all_0_13_13
% 28.92/7.96 |
% 28.92/7.96 | Instantiating formula (201) with e2, e1, all_0_13_13, e0 and discharging atoms op(e2, e1) = all_0_13_13, op(e2, e1) = e0, yields:
% 28.92/7.96 | (7585) all_0_13_13 = e0
% 28.92/7.96 |
% 28.92/7.96 +-Applying beta-rule and splitting (9), into two cases.
% 28.92/7.96 |-Branch one:
% 28.92/7.96 | (621) all_0_44_44 = e0
% 28.92/7.96 |
% 28.92/7.96 | Equations (621) can reduce 241 to:
% 28.92/7.96 | (455) ~ (all_0_43_43 = e0)
% 28.92/7.96 |
% 28.92/7.96 +-Applying beta-rule and splitting (93), into two cases.
% 28.92/7.96 |-Branch one:
% 28.92/7.96 | (402) all_0_59_59 = e4
% 28.92/7.96 |
% 28.92/7.96 | Equations (402) can reduce 280 to:
% 28.92/7.96 | (270) $false
% 28.92/7.96 |
% 28.92/7.96 |-The branch is then unsatisfiable
% 28.92/7.96 |-Branch two:
% 28.92/7.96 | (280) ~ (all_0_59_59 = e4)
% 28.92/7.96 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 28.92/7.96 |
% 28.92/7.96 +-Applying beta-rule and splitting (407), into two cases.
% 28.92/7.96 |-Branch one:
% 28.92/7.96 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 28.92/7.96 |
% 28.92/7.96 +-Applying beta-rule and splitting (408), into two cases.
% 28.92/7.96 |-Branch one:
% 28.92/7.96 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 28.92/7.96 |
% 28.92/7.96 +-Applying beta-rule and splitting (409), into two cases.
% 28.92/7.96 |-Branch one:
% 28.92/7.96 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 28.92/7.96 |
% 28.92/7.96 | Applying alpha-rule on (410) yields:
% 28.92/7.96 | (411) all_0_43_43 = e0
% 28.92/7.96 | (412) all_0_59_59 = e3
% 28.92/7.96 | (413) ~ (all_0_46_46 = e3)
% 28.92/7.96 |
% 28.92/7.96 | Equations (411) can reduce 455 to:
% 28.92/7.96 | (270) $false
% 28.92/7.96 |
% 28.92/7.96 |-The branch is then unsatisfiable
% 28.92/7.96 |-Branch two:
% 28.92/7.96 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 28.92/7.96 |
% 28.92/7.96 | Applying alpha-rule on (416) yields:
% 28.92/7.96 | (411) all_0_43_43 = e0
% 28.92/7.96 | (412) all_0_59_59 = e3
% 28.92/7.96 | (419) ~ (all_0_56_56 = e0)
% 28.92/7.96 |
% 28.92/7.96 | Equations (411) can reduce 455 to:
% 28.92/7.96 | (270) $false
% 28.92/7.96 |
% 28.92/7.96 |-The branch is then unsatisfiable
% 28.92/7.96 |-Branch two:
% 28.92/7.96 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 28.92/7.96 |
% 28.92/7.96 | Applying alpha-rule on (422) yields:
% 28.92/7.96 | (423) all_0_53_53 = e0
% 28.92/7.96 | (424) all_0_59_59 = e1
% 28.92/7.96 | (425) ~ (all_0_54_54 = e1)
% 28.92/7.96 |
% 28.92/7.96 | Equations (423) can reduce 584 to:
% 28.92/7.96 | (270) $false
% 28.92/7.96 |
% 28.92/7.96 |-The branch is then unsatisfiable
% 28.92/7.96 |-Branch two:
% 28.92/7.96 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 28.92/7.96 |
% 28.92/7.96 | Applying alpha-rule on (428) yields:
% 28.92/7.96 | (423) all_0_53_53 = e0
% 28.92/7.96 | (424) all_0_59_59 = e1
% 28.92/7.96 | (431) ~ (all_0_58_58 = e0)
% 28.92/7.96 |
% 28.92/7.96 | Equations (423) can reduce 584 to:
% 28.92/7.96 | (270) $false
% 28.92/7.96 |
% 28.92/7.96 |-The branch is then unsatisfiable
% 28.92/7.96 |-Branch two:
% 28.92/7.96 | (625) ~ (all_0_44_44 = e0)
% 28.92/7.96 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 28.92/7.96 |
% 28.92/7.96 +-Applying beta-rule and splitting (373), into two cases.
% 28.92/7.96 |-Branch one:
% 28.92/7.96 | (621) all_0_44_44 = e0
% 28.92/7.96 |
% 28.92/7.96 | Equations (621) can reduce 625 to:
% 28.92/7.96 | (270) $false
% 28.92/7.96 |
% 28.92/7.96 |-The branch is then unsatisfiable
% 28.92/7.96 |-Branch two:
% 28.92/7.96 | (625) ~ (all_0_44_44 = e0)
% 28.92/7.96 | (858) all_0_44_44 = e3
% 28.92/7.96 |
% 28.92/7.96 | Equations (858) can reduce 131 to:
% 28.92/7.96 | (136) ~ (e3 = e1)
% 28.92/7.96 |
% 28.92/7.96 | From (858) and (165) follows:
% 28.92/7.96 | (3499) op(e2, e3) = all_0_15_15
% 28.92/7.96 |
% 28.92/7.96 +-Applying beta-rule and splitting (626), into two cases.
% 28.92/7.96 |-Branch one:
% 28.92/7.96 | (827) all_0_52_52 = e0
% 28.92/7.96 |
% 28.92/7.96 | Equations (827) can reduce 230 to:
% 28.92/7.96 | (456) ~ (e4 = e0)
% 28.92/7.96 |
% 28.92/7.96 | Simplifying 456 yields:
% 28.92/7.96 | (6) ~ (e4 = e0)
% 28.92/7.96 |
% 28.92/7.96 | From (827) and (27) follows:
% 28.92/7.96 | (3482) op(e2, e0) = all_0_17_17
% 28.92/7.96 |
% 28.92/7.96 | Instantiating formula (201) with e2, e3, all_0_15_15, e1 and discharging atoms op(e2, e3) = all_0_15_15, op(e2, e3) = e1, yields:
% 28.92/7.96 | (5879) all_0_15_15 = e1
% 28.92/7.96 |
% 28.92/7.96 | Instantiating formula (201) with e2, e0, all_0_17_17, e2 and discharging atoms op(e2, e0) = all_0_17_17, op(e2, e0) = e2, yields:
% 28.92/7.96 | (3413) all_0_17_17 = e2
% 28.92/7.96 |
% 28.92/7.96 +-Applying beta-rule and splitting (87), into two cases.
% 28.92/7.96 |-Branch one:
% 28.92/7.96 | (650) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 28.92/7.96 |
% 28.92/7.96 +-Applying beta-rule and splitting (650), into two cases.
% 28.92/7.96 |-Branch one:
% 28.92/7.96 | (651) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 28.92/7.96 |
% 28.92/7.96 +-Applying beta-rule and splitting (651), into two cases.
% 28.92/7.96 |-Branch one:
% 28.92/7.96 | (652) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 28.92/7.96 |
% 28.92/7.96 | Applying alpha-rule on (652) yields:
% 28.92/7.96 | (653) all_0_13_13 = e4
% 28.92/7.96 | (654) ~ (all_0_14_14 = e2)
% 28.92/7.96 |
% 28.92/7.97 | Combining equations (7585,653) yields a new equation:
% 28.92/7.97 | (479) e4 = e0
% 28.92/7.97 |
% 28.92/7.97 | Equations (479) can reduce 6 to:
% 28.92/7.97 | (270) $false
% 28.92/7.97 |
% 28.92/7.97 |-The branch is then unsatisfiable
% 28.92/7.97 |-Branch two:
% 28.92/7.97 | (657) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 28.92/7.97 |
% 28.92/7.97 | Applying alpha-rule on (657) yields:
% 28.92/7.97 | (658) all_0_15_15 = e3
% 28.92/7.97 | (659) ~ (all_0_16_16 = e2)
% 28.92/7.97 |
% 28.92/7.97 | Combining equations (658,5879) yields a new equation:
% 28.92/7.97 | (537) e3 = e1
% 28.92/7.97 |
% 28.92/7.97 | Simplifying 537 yields:
% 28.92/7.97 | (538) e3 = e1
% 28.92/7.97 |
% 28.92/7.97 | Equations (538) can reduce 136 to:
% 28.92/7.97 | (270) $false
% 28.92/7.97 |
% 28.92/7.97 |-The branch is then unsatisfiable
% 28.92/7.97 |-Branch two:
% 28.92/7.97 | (663) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 28.92/7.97 |
% 28.92/7.97 | Applying alpha-rule on (663) yields:
% 28.92/7.97 | (664) all_0_17_17 = e1
% 28.92/7.97 | (665) ~ (all_0_18_18 = e2)
% 28.92/7.97 |
% 28.92/7.97 | Combining equations (3413,664) yields a new equation:
% 28.92/7.97 | (531) e2 = e1
% 28.92/7.97 |
% 28.92/7.97 | Simplifying 531 yields:
% 28.92/7.97 | (322) e2 = e1
% 28.92/7.97 |
% 28.92/7.97 | Equations (322) can reduce 141 to:
% 28.92/7.97 | (270) $false
% 28.92/7.97 |
% 28.92/7.97 |-The branch is then unsatisfiable
% 28.92/7.97 |-Branch two:
% 28.92/7.97 | (1762) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 28.92/7.97 |
% 28.92/7.97 | Applying alpha-rule on (1762) yields:
% 28.92/7.97 | (1763) all_0_19_19 = e0
% 28.92/7.97 | (1764) ~ (all_0_20_20 = e2)
% 28.92/7.97 |
% 28.92/7.97 | Combining equations (1763,3391) yields a new equation:
% 28.92/7.97 | (479) e4 = e0
% 28.92/7.97 |
% 28.92/7.97 | Equations (479) can reduce 6 to:
% 28.92/7.97 | (270) $false
% 28.92/7.97 |
% 28.92/7.97 |-The branch is then unsatisfiable
% 28.92/7.97 |-Branch two:
% 28.92/7.97 | (925) ~ (all_0_52_52 = e0)
% 28.92/7.97 | (2258) all_0_57_57 = e0
% 28.92/7.97 |
% 28.92/7.97 | Combining equations (2258,392) yields a new equation:
% 28.92/7.97 | (316) e2 = e0
% 28.92/7.97 |
% 28.92/7.97 | Equations (316) can reduce 57 to:
% 28.92/7.97 | (270) $false
% 28.92/7.97 |
% 28.92/7.97 |-The branch is then unsatisfiable
% 28.92/7.97 |-Branch two:
% 28.92/7.97 | (534) ~ (all_0_40_40 = e1)
% 28.92/7.97 | (3352) all_0_52_52 = e1 | all_0_57_57 = e1
% 28.92/7.97 |
% 28.92/7.97 +-Applying beta-rule and splitting (3352), into two cases.
% 28.92/7.97 |-Branch one:
% 28.92/7.97 | (848) all_0_52_52 = e1
% 28.92/7.97 |
% 28.92/7.97 +-Applying beta-rule and splitting (9), into two cases.
% 28.92/7.97 |-Branch one:
% 28.92/7.97 | (621) all_0_44_44 = e0
% 28.92/7.97 |
% 28.92/7.97 | Equations (621) can reduce 241 to:
% 28.92/7.97 | (455) ~ (all_0_43_43 = e0)
% 28.92/7.97 |
% 28.92/7.97 +-Applying beta-rule and splitting (93), into two cases.
% 28.92/7.97 |-Branch one:
% 28.92/7.97 | (402) all_0_59_59 = e4
% 28.92/7.97 |
% 28.92/7.97 | Equations (402) can reduce 280 to:
% 28.92/7.97 | (270) $false
% 28.92/7.97 |
% 28.92/7.97 |-The branch is then unsatisfiable
% 28.92/7.97 |-Branch two:
% 28.92/7.97 | (280) ~ (all_0_59_59 = e4)
% 28.92/7.97 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 28.92/7.97 |
% 28.92/7.97 +-Applying beta-rule and splitting (407), into two cases.
% 28.92/7.97 |-Branch one:
% 28.92/7.97 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 28.92/7.97 |
% 28.92/7.97 +-Applying beta-rule and splitting (408), into two cases.
% 28.92/7.97 |-Branch one:
% 28.92/7.97 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 28.92/7.97 |
% 28.92/7.97 +-Applying beta-rule and splitting (409), into two cases.
% 28.92/7.97 |-Branch one:
% 28.92/7.97 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 28.92/7.97 |
% 28.92/7.97 | Applying alpha-rule on (410) yields:
% 28.92/7.97 | (411) all_0_43_43 = e0
% 28.92/7.97 | (412) all_0_59_59 = e3
% 28.92/7.97 | (413) ~ (all_0_46_46 = e3)
% 28.92/7.97 |
% 28.92/7.97 | Equations (411) can reduce 455 to:
% 28.92/7.97 | (270) $false
% 28.92/7.97 |
% 28.92/7.97 |-The branch is then unsatisfiable
% 28.92/7.97 |-Branch two:
% 28.92/7.97 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 28.92/7.97 |
% 28.92/7.97 | Applying alpha-rule on (416) yields:
% 28.92/7.97 | (411) all_0_43_43 = e0
% 28.92/7.97 | (412) all_0_59_59 = e3
% 28.92/7.97 | (419) ~ (all_0_56_56 = e0)
% 28.92/7.97 |
% 28.92/7.97 | Equations (411) can reduce 455 to:
% 28.92/7.97 | (270) $false
% 28.92/7.97 |
% 28.92/7.97 |-The branch is then unsatisfiable
% 28.92/7.97 |-Branch two:
% 28.92/7.97 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 28.92/7.97 |
% 28.92/7.97 | Applying alpha-rule on (422) yields:
% 28.92/7.97 | (423) all_0_53_53 = e0
% 28.92/7.97 | (424) all_0_59_59 = e1
% 28.92/7.97 | (425) ~ (all_0_54_54 = e1)
% 28.92/7.97 |
% 28.92/7.97 | Equations (423) can reduce 584 to:
% 28.92/7.97 | (270) $false
% 28.92/7.97 |
% 28.92/7.97 |-The branch is then unsatisfiable
% 28.92/7.97 |-Branch two:
% 28.92/7.97 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 28.92/7.97 |
% 28.92/7.97 | Applying alpha-rule on (428) yields:
% 28.92/7.97 | (423) all_0_53_53 = e0
% 28.92/7.97 | (424) all_0_59_59 = e1
% 28.92/7.97 | (431) ~ (all_0_58_58 = e0)
% 28.92/7.97 |
% 28.92/7.97 | Equations (423) can reduce 584 to:
% 28.92/7.97 | (270) $false
% 28.92/7.97 |
% 28.92/7.97 |-The branch is then unsatisfiable
% 28.92/7.97 |-Branch two:
% 28.92/7.97 | (625) ~ (all_0_44_44 = e0)
% 28.92/7.97 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 28.92/7.97 |
% 28.92/7.97 +-Applying beta-rule and splitting (626), into two cases.
% 28.92/7.97 |-Branch one:
% 28.92/7.97 | (827) all_0_52_52 = e0
% 28.92/7.97 |
% 28.92/7.97 | Combining equations (848,827) yields a new equation:
% 28.92/7.97 | (571) e1 = e0
% 28.92/7.97 |
% 28.92/7.97 | Simplifying 571 yields:
% 28.92/7.97 | (560) e1 = e0
% 28.92/7.97 |
% 28.92/7.97 | Equations (560) can reduce 132 to:
% 28.92/7.97 | (270) $false
% 28.92/7.97 |
% 28.92/7.97 |-The branch is then unsatisfiable
% 28.92/7.97 |-Branch two:
% 28.92/7.97 | (925) ~ (all_0_52_52 = e0)
% 28.92/7.97 | (2258) all_0_57_57 = e0
% 28.92/7.97 |
% 28.92/7.97 | Combining equations (2258,392) yields a new equation:
% 28.92/7.97 | (316) e2 = e0
% 28.92/7.97 |
% 28.92/7.97 | Equations (316) can reduce 57 to:
% 28.92/7.97 | (270) $false
% 28.92/7.97 |
% 28.92/7.97 |-The branch is then unsatisfiable
% 28.92/7.97 |-Branch two:
% 28.92/7.97 | (642) ~ (all_0_52_52 = e1)
% 28.92/7.97 | (997) all_0_57_57 = e1
% 28.92/7.97 |
% 28.92/7.97 | Combining equations (997,392) yields a new equation:
% 28.92/7.97 | (322) e2 = e1
% 28.92/7.97 |
% 28.92/7.97 | Equations (322) can reduce 141 to:
% 28.92/7.97 | (270) $false
% 28.92/7.97 |
% 28.92/7.97 |-The branch is then unsatisfiable
% 28.92/7.97 |-Branch two:
% 28.92/7.97 | (562) ~ (all_0_48_48 = e0)
% 28.92/7.97 | (552) all_0_48_48 = e1
% 28.92/7.97 |
% 28.92/7.97 | Equations (552) can reduce 588 to:
% 28.92/7.97 | (270) $false
% 28.92/7.97 |
% 28.92/7.97 |-The branch is then unsatisfiable
% 28.92/7.97 |-Branch two:
% 28.92/7.97 | (324) ~ (all_0_47_47 = e1)
% 28.92/7.97 | (325) all_0_48_48 = e1 | all_0_49_49 = e1
% 28.92/7.97 |
% 28.92/7.97 +-Applying beta-rule and splitting (3956), into two cases.
% 28.92/7.97 |-Branch one:
% 28.92/7.97 | (315) all_0_47_47 = e0
% 28.92/7.97 |
% 28.92/7.97 | Equations (315) can reduce 100 to:
% 28.92/7.97 | (101) ~ (all_0_39_39 = e0)
% 28.92/7.97 |
% 28.92/7.97 | Equations (315) can reduce 170 to:
% 28.92/7.97 | (455) ~ (all_0_43_43 = e0)
% 28.92/7.97 |
% 28.92/7.97 | Equations (315) can reduce 225 to:
% 28.92/7.97 | (7709) ~ (all_0_48_48 = e0)
% 28.92/7.97 |
% 28.92/7.97 | Simplifying 7709 yields:
% 28.92/7.97 | (562) ~ (all_0_48_48 = e0)
% 28.92/7.97 |
% 28.92/7.97 | Equations (315) can reduce 218 to:
% 28.92/7.97 | (3852) ~ (all_0_56_56 = e0)
% 28.92/7.97 |
% 28.92/7.97 | Simplifying 3852 yields:
% 28.92/7.97 | (419) ~ (all_0_56_56 = e0)
% 28.92/7.97 |
% 28.92/7.97 | Equations (315) can reduce 172 to:
% 28.92/7.97 | (456) ~ (e4 = e0)
% 28.92/7.97 |
% 28.92/7.97 | Simplifying 456 yields:
% 28.92/7.97 | (6) ~ (e4 = e0)
% 28.92/7.97 |
% 28.92/7.97 | Equations (315) can reduce 247 to:
% 28.92/7.97 | (788) ~ (e3 = e0)
% 28.92/7.97 |
% 28.92/7.97 | Simplifying 788 yields:
% 28.92/7.97 | (66) ~ (e3 = e0)
% 28.92/7.97 |
% 28.92/7.97 | From (315) and (42) follows:
% 28.92/7.97 | (7717) op(e2, e0) = all_0_8_8
% 28.92/7.97 |
% 28.92/7.97 | From (315) and (40) follows:
% 28.92/7.97 | (7718) op(e2, e3) = e0
% 28.92/7.97 |
% 28.92/7.97 +-Applying beta-rule and splitting (314), into two cases.
% 28.92/7.97 |-Branch one:
% 28.92/7.97 | (559) all_0_48_48 = e0
% 28.92/7.97 |
% 28.92/7.97 | Equations (559) can reduce 562 to:
% 28.92/7.97 | (270) $false
% 28.92/7.97 |
% 28.92/7.97 |-The branch is then unsatisfiable
% 28.92/7.97 |-Branch two:
% 28.92/7.97 | (562) ~ (all_0_48_48 = e0)
% 28.92/7.97 | (552) all_0_48_48 = e1
% 28.92/7.97 |
% 28.92/7.97 | Equations (552) can reduce 190 to:
% 28.92/7.97 | (540) ~ (all_0_41_41 = e1)
% 28.92/7.97 |
% 28.92/7.97 | Equations (552) can reduce 65 to:
% 28.92/7.97 | (26) ~ (all_0_45_45 = e1)
% 28.92/7.97 |
% 28.92/7.97 | Equations (552) can reduce 59 to:
% 28.92/7.97 | (7725) ~ (all_0_58_58 = e1)
% 28.92/7.97 |
% 28.92/7.97 | Simplifying 7725 yields:
% 28.92/7.97 | (1004) ~ (all_0_58_58 = e1)
% 28.92/7.97 |
% 28.92/7.97 | Equations (552) can reduce 121 to:
% 28.92/7.97 | (769) ~ (e3 = e1)
% 28.92/7.97 |
% 28.92/7.97 | Simplifying 769 yields:
% 28.92/7.97 | (136) ~ (e3 = e1)
% 28.92/7.97 |
% 28.92/7.97 | Equations (552) can reduce 294 to:
% 28.92/7.97 | (645) ~ (e2 = e1)
% 28.92/7.97 |
% 28.92/7.97 | Simplifying 645 yields:
% 28.92/7.97 | (141) ~ (e2 = e1)
% 28.92/7.97 |
% 28.92/7.97 | From (552) and (183) follows:
% 28.92/7.97 | (7731) op(e2, e1) = all_0_26_26
% 28.92/7.97 |
% 28.92/7.97 | From (552) and (56) follows:
% 28.92/7.97 | (7732) op(e2, e1) = e1
% 28.92/7.97 |
% 28.92/7.97 | From (552) and (76) follows:
% 28.92/7.97 | (2127) op(e1, e1) = all_0_25_25
% 28.92/7.97 |
% 28.92/7.97 | Instantiating formula (201) with e2, e1, e1, all_0_26_26 and discharging atoms op(e2, e1) = all_0_26_26, op(e2, e1) = e1, yields:
% 28.92/7.97 | (7734) all_0_26_26 = e1
% 28.92/7.97 |
% 28.92/7.97 | Instantiating formula (201) with e2, e0, all_0_8_8, e2 and discharging atoms op(e2, e0) = all_0_8_8, op(e2, e0) = e2, yields:
% 28.92/7.97 | (4012) all_0_8_8 = e2
% 28.92/7.97 |
% 28.92/7.97 | Instantiating formula (201) with e1, e1, all_0_25_25, all_0_53_53 and discharging atoms op(e1, e1) = all_0_25_25, op(e1, e1) = all_0_53_53, yields:
% 28.92/7.97 | (7736) all_0_25_25 = all_0_53_53
% 28.92/7.97 |
% 28.92/7.97 | From (7734) and (7731) follows:
% 28.92/7.97 | (7732) op(e2, e1) = e1
% 28.92/7.97 |
% 28.92/7.97 | From (4012) and (7717) follows:
% 28.92/7.98 | (6092) op(e2, e0) = e2
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (125), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (327) all_0_40_40 = e2
% 28.92/7.98 |
% 28.92/7.98 | Combining equations (327,285) yields a new equation:
% 28.92/7.98 | (328) all_0_0_0 = e2
% 28.92/7.98 |
% 28.92/7.98 | Equations (327) can reduce 114 to:
% 28.92/7.98 | (291) ~ (all_0_39_39 = e2)
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (186), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (336) all_0_39_39 = e2
% 28.92/7.98 |
% 28.92/7.98 | Equations (336) can reduce 291 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (291) ~ (all_0_39_39 = e2)
% 28.92/7.98 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (339), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (340), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 28.92/7.98 |
% 28.92/7.98 | Applying alpha-rule on (341) yields:
% 28.92/7.98 | (342) all_0_0_0 = e1
% 28.92/7.98 | (343) ~ (all_0_1_1 = e4)
% 28.92/7.98 |
% 28.92/7.98 | Combining equations (342,328) yields a new equation:
% 28.92/7.98 | (322) e2 = e1
% 28.92/7.98 |
% 28.92/7.98 | Equations (322) can reduce 141 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 28.92/7.98 |
% 28.92/7.98 | Applying alpha-rule on (346) yields:
% 28.92/7.98 | (347) all_0_2_2 = e0
% 28.92/7.98 | (348) ~ (all_0_3_3 = e4)
% 28.92/7.98 |
% 28.92/7.98 | Equations (287) can reduce 348 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 28.92/7.98 |
% 28.92/7.98 | Applying alpha-rule on (350) yields:
% 28.92/7.98 | (351) all_0_41_41 = e3
% 28.92/7.98 | (352) ~ (all_0_45_45 = e4)
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (158), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (358) all_0_41_41 = e4
% 28.92/7.98 |
% 28.92/7.98 | Combining equations (351,358) yields a new equation:
% 28.92/7.98 | (359) e4 = e3
% 28.92/7.98 |
% 28.92/7.98 | Equations (359) can reduce 34 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (361) ~ (all_0_41_41 = e4)
% 28.92/7.98 | (362) all_0_45_45 = e4 | all_0_53_53 = e4 | all_0_58_58 = e4
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (362), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (363) all_0_45_45 = e4
% 28.92/7.98 |
% 28.92/7.98 | Equations (363) can reduce 352 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (352) ~ (all_0_45_45 = e4)
% 28.92/7.98 | (366) all_0_53_53 = e4 | all_0_58_58 = e4
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (366), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (367) all_0_53_53 = e4
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (93), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (402) all_0_59_59 = e4
% 28.92/7.98 |
% 28.92/7.98 | Equations (402) can reduce 280 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (280) ~ (all_0_59_59 = e4)
% 28.92/7.98 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (407), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (408), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (409), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 28.92/7.98 |
% 28.92/7.98 | Applying alpha-rule on (410) yields:
% 28.92/7.98 | (411) all_0_43_43 = e0
% 28.92/7.98 | (412) all_0_59_59 = e3
% 28.92/7.98 | (413) ~ (all_0_46_46 = e3)
% 28.92/7.98 |
% 28.92/7.98 | Equations (411) can reduce 455 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 28.92/7.98 |
% 28.92/7.98 | Applying alpha-rule on (416) yields:
% 28.92/7.98 | (411) all_0_43_43 = e0
% 28.92/7.98 | (412) all_0_59_59 = e3
% 28.92/7.98 | (419) ~ (all_0_56_56 = e0)
% 28.92/7.98 |
% 28.92/7.98 | Equations (411) can reduce 455 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 28.92/7.98 |
% 28.92/7.98 | Applying alpha-rule on (422) yields:
% 28.92/7.98 | (423) all_0_53_53 = e0
% 28.92/7.98 | (424) all_0_59_59 = e1
% 28.92/7.98 | (425) ~ (all_0_54_54 = e1)
% 28.92/7.98 |
% 28.92/7.98 | Combining equations (367,423) yields a new equation:
% 28.92/7.98 | (478) e4 = e0
% 28.92/7.98 |
% 28.92/7.98 | Simplifying 478 yields:
% 28.92/7.98 | (479) e4 = e0
% 28.92/7.98 |
% 28.92/7.98 | Equations (479) can reduce 6 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 28.92/7.98 |
% 28.92/7.98 | Applying alpha-rule on (428) yields:
% 28.92/7.98 | (423) all_0_53_53 = e0
% 28.92/7.98 | (424) all_0_59_59 = e1
% 28.92/7.98 | (431) ~ (all_0_58_58 = e0)
% 28.92/7.98 |
% 28.92/7.98 | Combining equations (367,423) yields a new equation:
% 28.92/7.98 | (478) e4 = e0
% 28.92/7.98 |
% 28.92/7.98 | Simplifying 478 yields:
% 28.92/7.98 | (479) e4 = e0
% 28.92/7.98 |
% 28.92/7.98 | Equations (479) can reduce 6 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (599) ~ (all_0_53_53 = e4)
% 28.92/7.98 | (600) all_0_58_58 = e4
% 28.92/7.98 |
% 28.92/7.98 | Equations (600) can reduce 278 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (602) ~ (all_0_40_40 = e2)
% 28.92/7.98 | (603) all_0_40_40 = e3 | all_0_40_40 = e1
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (164), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (336) all_0_39_39 = e2
% 28.92/7.98 |
% 28.92/7.98 | Equations (336) can reduce 114 to:
% 28.92/7.98 | (6613) ~ (all_0_40_40 = e2)
% 28.92/7.98 |
% 28.92/7.98 | Simplifying 6613 yields:
% 28.92/7.98 | (602) ~ (all_0_40_40 = e2)
% 28.92/7.98 |
% 28.92/7.98 | Equations (336) can reduce 226 to:
% 28.92/7.98 | (330) ~ (all_0_41_41 = e2)
% 28.92/7.98 |
% 28.92/7.98 | Simplifying 330 yields:
% 28.92/7.98 | (331) ~ (all_0_41_41 = e2)
% 28.92/7.98 |
% 28.92/7.98 | Equations (336) can reduce 167 to:
% 28.92/7.98 | (5937) ~ (all_0_43_43 = e2)
% 28.92/7.98 |
% 28.92/7.98 | Simplifying 5937 yields:
% 28.92/7.98 | (292) ~ (all_0_43_43 = e2)
% 28.92/7.98 |
% 28.92/7.98 | Equations (336) can reduce 101 to:
% 28.92/7.98 | (57) ~ (e2 = e0)
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (20), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (327) all_0_40_40 = e2
% 28.92/7.98 |
% 28.92/7.98 | Equations (327) can reduce 602 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (602) ~ (all_0_40_40 = e2)
% 28.92/7.98 | (607) all_0_44_44 = e2 | all_0_52_52 = e2 | all_0_57_57 = e2
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (47), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (450) all_0_43_43 = e2
% 28.92/7.98 |
% 28.92/7.98 | Equations (450) can reduce 292 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (292) ~ (all_0_43_43 = e2)
% 28.92/7.98 | (453) all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (193), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (370) all_0_44_44 = e2
% 28.92/7.98 |
% 28.92/7.98 | Equations (370) can reduce 229 to:
% 28.92/7.98 | (611) ~ (all_0_45_45 = e2)
% 28.92/7.98 |
% 28.92/7.98 | Simplifying 611 yields:
% 28.92/7.98 | (434) ~ (all_0_45_45 = e2)
% 28.92/7.98 |
% 28.92/7.98 | Equations (370) can reduce 174 to:
% 28.92/7.98 | (1435) ~ (all_0_46_46 = e2)
% 28.92/7.98 |
% 28.92/7.98 | Simplifying 1435 yields:
% 28.92/7.98 | (1436) ~ (all_0_46_46 = e2)
% 28.92/7.98 |
% 28.92/7.98 | Equations (370) can reduce 122 to:
% 28.92/7.98 | (256) ~ (all_0_52_52 = e2)
% 28.92/7.98 |
% 28.92/7.98 | Simplifying 256 yields:
% 28.92/7.98 | (257) ~ (all_0_52_52 = e2)
% 28.92/7.98 |
% 28.92/7.98 | Equations (370) can reduce 131 to:
% 28.92/7.98 | (141) ~ (e2 = e1)
% 28.92/7.98 |
% 28.92/7.98 | From (370) and (165) follows:
% 28.92/7.98 | (619) op(e2, e2) = all_0_15_15
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (187), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (436) all_0_41_41 = e2
% 28.92/7.98 |
% 28.92/7.98 | Equations (436) can reduce 331 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (331) ~ (all_0_41_41 = e2)
% 28.92/7.98 | (441) all_0_45_45 = e2 | all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (441), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (374) all_0_45_45 = e2
% 28.92/7.98 |
% 28.92/7.98 | Equations (374) can reduce 434 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (434) ~ (all_0_45_45 = e2)
% 28.92/7.98 | (445) all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (445), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (311) all_0_48_48 = e2
% 28.92/7.98 |
% 28.92/7.98 | Combining equations (552,311) yields a new equation:
% 28.92/7.98 | (322) e2 = e1
% 28.92/7.98 |
% 28.92/7.98 | Equations (322) can reduce 141 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (294) ~ (all_0_48_48 = e2)
% 28.92/7.98 | (449) all_0_53_53 = e2 | all_0_58_58 = e2
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (449), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (576) all_0_53_53 = e2
% 28.92/7.98 |
% 28.92/7.98 | Equations (576) can reduce 259 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (259) ~ (all_0_53_53 = e2)
% 28.92/7.98 | (396) all_0_58_58 = e2
% 28.92/7.98 |
% 28.92/7.98 | Equations (396) can reduce 1004 to:
% 28.92/7.98 | (141) ~ (e2 = e1)
% 28.92/7.98 |
% 28.92/7.98 | Instantiating formula (201) with e2, e2, all_0_15_15, e4 and discharging atoms op(e2, e2) = all_0_15_15, op(e2, e2) = e4, yields:
% 28.92/7.98 | (620) all_0_15_15 = e4
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (9), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (621) all_0_44_44 = e0
% 28.92/7.98 |
% 28.92/7.98 | Combining equations (370,621) yields a new equation:
% 28.92/7.98 | (622) e2 = e0
% 28.92/7.98 |
% 28.92/7.98 | Simplifying 622 yields:
% 28.92/7.98 | (316) e2 = e0
% 28.92/7.98 |
% 28.92/7.98 | Equations (316) can reduce 57 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (625) ~ (all_0_44_44 = e0)
% 28.92/7.98 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 28.92/7.98 |
% 28.92/7.98 | Equations (370) can reduce 625 to:
% 28.92/7.98 | (57) ~ (e2 = e0)
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (99), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (524) all_0_39_39 = e1
% 28.92/7.98 |
% 28.92/7.98 | Combining equations (336,524) yields a new equation:
% 28.92/7.98 | (531) e2 = e1
% 28.92/7.98 |
% 28.92/7.98 | Simplifying 531 yields:
% 28.92/7.98 | (322) e2 = e1
% 28.92/7.98 |
% 28.92/7.98 | Equations (322) can reduce 141 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (528) ~ (all_0_39_39 = e1)
% 28.92/7.98 | (680) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 28.92/7.98 |
% 28.92/7.98 | Equations (336) can reduce 528 to:
% 28.92/7.98 | (141) ~ (e2 = e1)
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (8), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (530) all_0_40_40 = e1
% 28.92/7.98 |
% 28.92/7.98 | Equations (530) can reduce 137 to:
% 28.92/7.98 | (641) ~ (all_0_52_52 = e1)
% 28.92/7.98 |
% 28.92/7.98 | Simplifying 641 yields:
% 28.92/7.98 | (642) ~ (all_0_52_52 = e1)
% 28.92/7.98 |
% 28.92/7.98 | Equations (530) can reduce 233 to:
% 28.92/7.98 | (1021) ~ (e4 = e1)
% 28.92/7.98 |
% 28.92/7.98 | Simplifying 1021 yields:
% 28.92/7.98 | (251) ~ (e4 = e1)
% 28.92/7.98 |
% 28.92/7.98 | Equations (530) can reduce 238 to:
% 28.92/7.98 | (132) ~ (e1 = e0)
% 28.92/7.98 |
% 28.92/7.98 | From (530) and (68) follows:
% 28.92/7.98 | (648) op(e2, e1) = all_0_13_13
% 28.92/7.98 |
% 28.92/7.98 | Instantiating formula (201) with e2, e1, all_0_13_13, e1 and discharging atoms op(e2, e1) = all_0_13_13, op(e2, e1) = e1, yields:
% 28.92/7.98 | (5957) all_0_13_13 = e1
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (87), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (650) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (650), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (651) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (651), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (652) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 28.92/7.98 |
% 28.92/7.98 | Applying alpha-rule on (652) yields:
% 28.92/7.98 | (653) all_0_13_13 = e4
% 28.92/7.98 | (654) ~ (all_0_14_14 = e2)
% 28.92/7.98 |
% 28.92/7.98 | Combining equations (653,5957) yields a new equation:
% 28.92/7.98 | (525) e4 = e1
% 28.92/7.98 |
% 28.92/7.98 | Simplifying 525 yields:
% 28.92/7.98 | (526) e4 = e1
% 28.92/7.98 |
% 28.92/7.98 | Equations (526) can reduce 251 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (657) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 28.92/7.98 |
% 28.92/7.98 | Applying alpha-rule on (657) yields:
% 28.92/7.98 | (658) all_0_15_15 = e3
% 28.92/7.98 | (659) ~ (all_0_16_16 = e2)
% 28.92/7.98 |
% 28.92/7.98 | Combining equations (620,658) yields a new equation:
% 28.92/7.98 | (660) e4 = e3
% 28.92/7.98 |
% 28.92/7.98 | Simplifying 660 yields:
% 28.92/7.98 | (359) e4 = e3
% 28.92/7.98 |
% 28.92/7.98 | Equations (359) can reduce 34 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (663) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 28.92/7.98 |
% 28.92/7.98 | Applying alpha-rule on (663) yields:
% 28.92/7.98 | (664) all_0_17_17 = e1
% 28.92/7.98 | (665) ~ (all_0_18_18 = e2)
% 28.92/7.98 |
% 28.92/7.98 | From (664) and (27) follows:
% 28.92/7.98 | (666) op(e2, all_0_52_52) = e1
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (90), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (685) all_0_52_52 = e2
% 28.92/7.98 |
% 28.92/7.98 | Equations (685) can reduce 257 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (257) ~ (all_0_52_52 = e2)
% 28.92/7.98 | (688) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (182), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (454) all_0_45_45 = e0
% 28.92/7.98 |
% 28.92/7.98 | Equations (454) can reduce 84 to:
% 28.92/7.98 | (455) ~ (all_0_43_43 = e0)
% 28.92/7.98 |
% 28.92/7.98 | Equations (454) can reduce 128 to:
% 28.92/7.98 | (3103) ~ (all_0_53_53 = e0)
% 28.92/7.98 |
% 28.92/7.98 | Simplifying 3103 yields:
% 28.92/7.98 | (584) ~ (all_0_53_53 = e0)
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (93), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (402) all_0_59_59 = e4
% 28.92/7.98 |
% 28.92/7.98 | Equations (402) can reduce 280 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (280) ~ (all_0_59_59 = e4)
% 28.92/7.98 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (407), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (408), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 28.92/7.98 |
% 28.92/7.98 +-Applying beta-rule and splitting (409), into two cases.
% 28.92/7.98 |-Branch one:
% 28.92/7.98 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 28.92/7.98 |
% 28.92/7.98 | Applying alpha-rule on (410) yields:
% 28.92/7.98 | (411) all_0_43_43 = e0
% 28.92/7.98 | (412) all_0_59_59 = e3
% 28.92/7.98 | (413) ~ (all_0_46_46 = e3)
% 28.92/7.98 |
% 28.92/7.98 | Equations (411) can reduce 455 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 28.92/7.98 |
% 28.92/7.98 | Applying alpha-rule on (416) yields:
% 28.92/7.98 | (411) all_0_43_43 = e0
% 28.92/7.98 | (412) all_0_59_59 = e3
% 28.92/7.98 | (419) ~ (all_0_56_56 = e0)
% 28.92/7.98 |
% 28.92/7.98 | Equations (411) can reduce 455 to:
% 28.92/7.98 | (270) $false
% 28.92/7.98 |
% 28.92/7.98 |-The branch is then unsatisfiable
% 28.92/7.98 |-Branch two:
% 28.92/7.98 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 28.92/7.99 |
% 28.92/7.99 | Applying alpha-rule on (422) yields:
% 28.92/7.99 | (423) all_0_53_53 = e0
% 28.92/7.99 | (424) all_0_59_59 = e1
% 28.92/7.99 | (425) ~ (all_0_54_54 = e1)
% 28.92/7.99 |
% 28.92/7.99 | Equations (423) can reduce 584 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 28.92/7.99 |
% 28.92/7.99 | Applying alpha-rule on (428) yields:
% 28.92/7.99 | (423) all_0_53_53 = e0
% 28.92/7.99 | (424) all_0_59_59 = e1
% 28.92/7.99 | (431) ~ (all_0_58_58 = e0)
% 28.92/7.99 |
% 28.92/7.99 | Equations (423) can reduce 584 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (488) ~ (all_0_45_45 = e0)
% 28.92/7.99 | (558) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (116), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (411) all_0_43_43 = e0
% 28.92/7.99 |
% 28.92/7.99 | Equations (411) can reduce 455 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (455) ~ (all_0_43_43 = e0)
% 28.92/7.99 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (558), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (559) all_0_48_48 = e0
% 28.92/7.99 |
% 28.92/7.99 | Combining equations (552,559) yields a new equation:
% 28.92/7.99 | (571) e1 = e0
% 28.92/7.99 |
% 28.92/7.99 | Simplifying 571 yields:
% 28.92/7.99 | (560) e1 = e0
% 28.92/7.99 |
% 28.92/7.99 | Equations (560) can reduce 132 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (562) ~ (all_0_48_48 = e0)
% 28.92/7.99 | (575) all_0_53_53 = e0 | all_0_58_58 = e0
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (1122), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (621) all_0_44_44 = e0
% 28.92/7.99 |
% 28.92/7.99 | Combining equations (621,370) yields a new equation:
% 28.92/7.99 | (316) e2 = e0
% 28.92/7.99 |
% 28.92/7.99 | Equations (316) can reduce 57 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (625) ~ (all_0_44_44 = e0)
% 28.92/7.99 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 28.92/7.99 |
% 28.92/7.99 | Equations (370) can reduce 625 to:
% 28.92/7.99 | (57) ~ (e2 = e0)
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (575), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (423) all_0_53_53 = e0
% 28.92/7.99 |
% 28.92/7.99 | Equations (423) can reduce 128 to:
% 28.92/7.99 | (488) ~ (all_0_45_45 = e0)
% 28.92/7.99 |
% 28.92/7.99 | Equations (423) can reduce 12 to:
% 28.92/7.99 | (987) ~ (all_0_51_51 = e0)
% 28.92/7.99 |
% 28.92/7.99 | Equations (423) can reduce 213 to:
% 28.92/7.99 | (925) ~ (all_0_52_52 = e0)
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (626), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (827) all_0_52_52 = e0
% 28.92/7.99 |
% 28.92/7.99 | Equations (827) can reduce 925 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (925) ~ (all_0_52_52 = e0)
% 28.92/7.99 | (2258) all_0_57_57 = e0
% 28.92/7.99 |
% 28.92/7.99 | Equations (2258) can reduce 235 to:
% 28.92/7.99 | (925) ~ (all_0_52_52 = e0)
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (1128), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (454) all_0_45_45 = e0
% 28.92/7.99 |
% 28.92/7.99 | Equations (454) can reduce 488 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (488) ~ (all_0_45_45 = e0)
% 28.92/7.99 | (1132) all_0_46_46 = e0
% 28.92/7.99 |
% 28.92/7.99 | Equations (1132) can reduce 103 to:
% 28.92/7.99 | (455) ~ (all_0_43_43 = e0)
% 28.92/7.99 |
% 28.92/7.99 | Equations (1132) can reduce 206 to:
% 28.92/7.99 | (4000) ~ (all_0_59_59 = e0)
% 28.92/7.99 |
% 28.92/7.99 | Simplifying 4000 yields:
% 28.92/7.99 | (4001) ~ (all_0_59_59 = e0)
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (688), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (827) all_0_52_52 = e0
% 28.92/7.99 |
% 28.92/7.99 | Equations (827) can reduce 925 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (925) ~ (all_0_52_52 = e0)
% 28.92/7.99 | (926) all_0_52_52 = e3 | all_0_52_52 = e1
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (93), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (402) all_0_59_59 = e4
% 28.92/7.99 |
% 28.92/7.99 | Equations (402) can reduce 280 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (280) ~ (all_0_59_59 = e4)
% 28.92/7.99 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (926), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (864) all_0_52_52 = e3
% 28.92/7.99 |
% 28.92/7.99 | Equations (864) can reduce 642 to:
% 28.92/7.99 | (136) ~ (e3 = e1)
% 28.92/7.99 |
% 28.92/7.99 | From (864) and (666) follows:
% 28.92/7.99 | (1103) op(e2, e3) = e1
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (407), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (408), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (409), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 28.92/7.99 |
% 28.92/7.99 | Applying alpha-rule on (410) yields:
% 28.92/7.99 | (411) all_0_43_43 = e0
% 28.92/7.99 | (412) all_0_59_59 = e3
% 28.92/7.99 | (413) ~ (all_0_46_46 = e3)
% 28.92/7.99 |
% 28.92/7.99 | Equations (411) can reduce 455 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 28.92/7.99 |
% 28.92/7.99 | Applying alpha-rule on (416) yields:
% 28.92/7.99 | (411) all_0_43_43 = e0
% 28.92/7.99 | (412) all_0_59_59 = e3
% 28.92/7.99 | (419) ~ (all_0_56_56 = e0)
% 28.92/7.99 |
% 28.92/7.99 | Equations (411) can reduce 455 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 28.92/7.99 |
% 28.92/7.99 | Applying alpha-rule on (422) yields:
% 28.92/7.99 | (423) all_0_53_53 = e0
% 28.92/7.99 | (424) all_0_59_59 = e1
% 28.92/7.99 | (425) ~ (all_0_54_54 = e1)
% 28.92/7.99 |
% 28.92/7.99 | Equations (424) can reduce 72 to:
% 28.92/7.99 | (425) ~ (all_0_54_54 = e1)
% 28.92/7.99 |
% 28.92/7.99 | Equations (424) can reduce 4001 to:
% 28.92/7.99 | (132) ~ (e1 = e0)
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (135), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (820) all_0_51_51 = e1
% 28.92/7.99 |
% 28.92/7.99 | Equations (820) can reduce 987 to:
% 28.92/7.99 | (132) ~ (e1 = e0)
% 28.92/7.99 |
% 28.92/7.99 | Instantiating formula (201) with e2, e3, e1, e0 and discharging atoms op(e2, e3) = e1, op(e2, e3) = e0, yields:
% 28.92/7.99 | (560) e1 = e0
% 28.92/7.99 |
% 28.92/7.99 | Equations (560) can reduce 132 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (748) ~ (all_0_51_51 = e1)
% 28.92/7.99 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (823), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (848) all_0_52_52 = e1
% 28.92/7.99 |
% 28.92/7.99 | Combining equations (864,848) yields a new equation:
% 28.92/7.99 | (537) e3 = e1
% 28.92/7.99 |
% 28.92/7.99 | Simplifying 537 yields:
% 28.92/7.99 | (538) e3 = e1
% 28.92/7.99 |
% 28.92/7.99 | Equations (538) can reduce 136 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (642) ~ (all_0_52_52 = e1)
% 28.92/7.99 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (852), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (853) all_0_53_53 = e1
% 28.92/7.99 |
% 28.92/7.99 | Combining equations (853,423) yields a new equation:
% 28.92/7.99 | (571) e1 = e0
% 28.92/7.99 |
% 28.92/7.99 | Simplifying 571 yields:
% 28.92/7.99 | (560) e1 = e0
% 28.92/7.99 |
% 28.92/7.99 | Equations (560) can reduce 132 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (874) ~ (all_0_53_53 = e1)
% 28.92/7.99 | (875) all_0_54_54 = e1
% 28.92/7.99 |
% 28.92/7.99 | Equations (875) can reduce 425 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 28.92/7.99 |
% 28.92/7.99 | Applying alpha-rule on (428) yields:
% 28.92/7.99 | (423) all_0_53_53 = e0
% 28.92/7.99 | (424) all_0_59_59 = e1
% 28.92/7.99 | (431) ~ (all_0_58_58 = e0)
% 28.92/7.99 |
% 28.92/7.99 | Equations (424) can reduce 72 to:
% 28.92/7.99 | (425) ~ (all_0_54_54 = e1)
% 28.92/7.99 |
% 28.92/7.99 | Equations (424) can reduce 4001 to:
% 28.92/7.99 | (132) ~ (e1 = e0)
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (135), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (820) all_0_51_51 = e1
% 28.92/7.99 |
% 28.92/7.99 | Equations (820) can reduce 987 to:
% 28.92/7.99 | (132) ~ (e1 = e0)
% 28.92/7.99 |
% 28.92/7.99 | Instantiating formula (201) with e2, e3, e1, e0 and discharging atoms op(e2, e3) = e1, op(e2, e3) = e0, yields:
% 28.92/7.99 | (560) e1 = e0
% 28.92/7.99 |
% 28.92/7.99 | Equations (560) can reduce 132 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (748) ~ (all_0_51_51 = e1)
% 28.92/7.99 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (823), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (848) all_0_52_52 = e1
% 28.92/7.99 |
% 28.92/7.99 | Combining equations (864,848) yields a new equation:
% 28.92/7.99 | (537) e3 = e1
% 28.92/7.99 |
% 28.92/7.99 | Simplifying 537 yields:
% 28.92/7.99 | (538) e3 = e1
% 28.92/7.99 |
% 28.92/7.99 | Equations (538) can reduce 136 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (642) ~ (all_0_52_52 = e1)
% 28.92/7.99 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (852), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (853) all_0_53_53 = e1
% 28.92/7.99 |
% 28.92/7.99 | Combining equations (853,423) yields a new equation:
% 28.92/7.99 | (571) e1 = e0
% 28.92/7.99 |
% 28.92/7.99 | Simplifying 571 yields:
% 28.92/7.99 | (560) e1 = e0
% 28.92/7.99 |
% 28.92/7.99 | Equations (560) can reduce 132 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (874) ~ (all_0_53_53 = e1)
% 28.92/7.99 | (875) all_0_54_54 = e1
% 28.92/7.99 |
% 28.92/7.99 | Equations (875) can reduce 425 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (826) ~ (all_0_52_52 = e3)
% 28.92/7.99 | (848) all_0_52_52 = e1
% 28.92/7.99 |
% 28.92/7.99 | Equations (848) can reduce 642 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (584) ~ (all_0_53_53 = e0)
% 28.92/7.99 | (585) all_0_58_58 = e0
% 28.92/7.99 |
% 28.92/7.99 | Combining equations (396,585) yields a new equation:
% 28.92/7.99 | (622) e2 = e0
% 28.92/7.99 |
% 28.92/7.99 | Simplifying 622 yields:
% 28.92/7.99 | (316) e2 = e0
% 28.92/7.99 |
% 28.92/7.99 | Equations (316) can reduce 57 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (1762) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 28.92/7.99 |
% 28.92/7.99 | Applying alpha-rule on (1762) yields:
% 28.92/7.99 | (1763) all_0_19_19 = e0
% 28.92/7.99 | (1764) ~ (all_0_20_20 = e2)
% 28.92/7.99 |
% 28.92/7.99 | From (1763) and (30) follows:
% 28.92/7.99 | (1765) op(e2, all_0_57_57) = e0
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (182), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (454) all_0_45_45 = e0
% 28.92/7.99 |
% 28.92/7.99 | Equations (454) can reduce 84 to:
% 28.92/7.99 | (455) ~ (all_0_43_43 = e0)
% 28.92/7.99 |
% 28.92/7.99 | Equations (454) can reduce 128 to:
% 28.92/7.99 | (3103) ~ (all_0_53_53 = e0)
% 28.92/7.99 |
% 28.92/7.99 | Simplifying 3103 yields:
% 28.92/7.99 | (584) ~ (all_0_53_53 = e0)
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (93), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (402) all_0_59_59 = e4
% 28.92/7.99 |
% 28.92/7.99 | Equations (402) can reduce 280 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (280) ~ (all_0_59_59 = e4)
% 28.92/7.99 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (407), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (408), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (409), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 28.92/7.99 |
% 28.92/7.99 | Applying alpha-rule on (410) yields:
% 28.92/7.99 | (411) all_0_43_43 = e0
% 28.92/7.99 | (412) all_0_59_59 = e3
% 28.92/7.99 | (413) ~ (all_0_46_46 = e3)
% 28.92/7.99 |
% 28.92/7.99 | Equations (411) can reduce 455 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 28.92/7.99 |
% 28.92/7.99 | Applying alpha-rule on (416) yields:
% 28.92/7.99 | (411) all_0_43_43 = e0
% 28.92/7.99 | (412) all_0_59_59 = e3
% 28.92/7.99 | (419) ~ (all_0_56_56 = e0)
% 28.92/7.99 |
% 28.92/7.99 | Equations (411) can reduce 455 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 28.92/7.99 |
% 28.92/7.99 | Applying alpha-rule on (422) yields:
% 28.92/7.99 | (423) all_0_53_53 = e0
% 28.92/7.99 | (424) all_0_59_59 = e1
% 28.92/7.99 | (425) ~ (all_0_54_54 = e1)
% 28.92/7.99 |
% 28.92/7.99 | Equations (423) can reduce 584 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 28.92/7.99 |
% 28.92/7.99 | Applying alpha-rule on (428) yields:
% 28.92/7.99 | (423) all_0_53_53 = e0
% 28.92/7.99 | (424) all_0_59_59 = e1
% 28.92/7.99 | (431) ~ (all_0_58_58 = e0)
% 28.92/7.99 |
% 28.92/7.99 | Equations (423) can reduce 584 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (488) ~ (all_0_45_45 = e0)
% 28.92/7.99 | (558) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (116), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (411) all_0_43_43 = e0
% 28.92/7.99 |
% 28.92/7.99 | Equations (411) can reduce 455 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (455) ~ (all_0_43_43 = e0)
% 28.92/7.99 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (558), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/7.99 | (559) all_0_48_48 = e0
% 28.92/7.99 |
% 28.92/7.99 | Combining equations (552,559) yields a new equation:
% 28.92/7.99 | (571) e1 = e0
% 28.92/7.99 |
% 28.92/7.99 | Simplifying 571 yields:
% 28.92/7.99 | (560) e1 = e0
% 28.92/7.99 |
% 28.92/7.99 | Equations (560) can reduce 132 to:
% 28.92/7.99 | (270) $false
% 28.92/7.99 |
% 28.92/7.99 |-The branch is then unsatisfiable
% 28.92/7.99 |-Branch two:
% 28.92/7.99 | (562) ~ (all_0_48_48 = e0)
% 28.92/7.99 | (575) all_0_53_53 = e0 | all_0_58_58 = e0
% 28.92/7.99 |
% 28.92/7.99 +-Applying beta-rule and splitting (1122), into two cases.
% 28.92/7.99 |-Branch one:
% 28.92/8.00 | (621) all_0_44_44 = e0
% 28.92/8.00 |
% 28.92/8.00 | Combining equations (621,370) yields a new equation:
% 28.92/8.00 | (316) e2 = e0
% 28.92/8.00 |
% 28.92/8.00 | Equations (316) can reduce 57 to:
% 28.92/8.00 | (270) $false
% 28.92/8.00 |
% 28.92/8.00 |-The branch is then unsatisfiable
% 28.92/8.00 |-Branch two:
% 28.92/8.00 | (625) ~ (all_0_44_44 = e0)
% 28.92/8.00 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 28.92/8.00 |
% 28.92/8.00 | Equations (370) can reduce 625 to:
% 28.92/8.00 | (57) ~ (e2 = e0)
% 28.92/8.00 |
% 28.92/8.00 +-Applying beta-rule and splitting (575), into two cases.
% 28.92/8.00 |-Branch one:
% 28.92/8.00 | (423) all_0_53_53 = e0
% 28.92/8.00 |
% 28.92/8.00 | Equations (423) can reduce 128 to:
% 28.92/8.00 | (488) ~ (all_0_45_45 = e0)
% 28.92/8.00 |
% 28.92/8.00 | Equations (423) can reduce 213 to:
% 28.92/8.00 | (925) ~ (all_0_52_52 = e0)
% 28.92/8.00 |
% 28.92/8.00 +-Applying beta-rule and splitting (626), into two cases.
% 28.92/8.00 |-Branch one:
% 28.92/8.00 | (827) all_0_52_52 = e0
% 28.92/8.00 |
% 28.92/8.00 | Equations (827) can reduce 925 to:
% 28.92/8.00 | (270) $false
% 28.92/8.00 |
% 28.92/8.00 |-The branch is then unsatisfiable
% 28.92/8.00 |-Branch two:
% 28.92/8.00 | (925) ~ (all_0_52_52 = e0)
% 28.92/8.00 | (2258) all_0_57_57 = e0
% 28.92/8.00 |
% 28.92/8.00 | From (2258) and (1765) follows:
% 28.92/8.00 | (2996) op(e2, e0) = e0
% 28.92/8.00 |
% 28.92/8.00 +-Applying beta-rule and splitting (1128), into two cases.
% 28.92/8.00 |-Branch one:
% 28.92/8.00 | (454) all_0_45_45 = e0
% 28.92/8.00 |
% 28.92/8.00 | Equations (454) can reduce 488 to:
% 28.92/8.00 | (270) $false
% 28.92/8.00 |
% 28.92/8.00 |-The branch is then unsatisfiable
% 28.92/8.00 |-Branch two:
% 28.92/8.00 | (488) ~ (all_0_45_45 = e0)
% 28.92/8.00 | (1132) all_0_46_46 = e0
% 28.92/8.00 |
% 28.92/8.00 | Equations (1132) can reduce 1436 to:
% 28.92/8.00 | (566) ~ (e2 = e0)
% 28.92/8.00 |
% 28.92/8.00 | Simplifying 566 yields:
% 28.92/8.00 | (57) ~ (e2 = e0)
% 28.92/8.00 |
% 28.92/8.00 | Instantiating formula (201) with e2, e0, e0, e2 and discharging atoms op(e2, e0) = e2, op(e2, e0) = e0, yields:
% 28.92/8.00 | (316) e2 = e0
% 28.92/8.00 |
% 28.92/8.00 | Equations (316) can reduce 57 to:
% 28.92/8.00 | (270) $false
% 28.92/8.00 |
% 28.92/8.00 |-The branch is then unsatisfiable
% 28.92/8.00 |-Branch two:
% 28.92/8.00 | (584) ~ (all_0_53_53 = e0)
% 28.92/8.00 | (585) all_0_58_58 = e0
% 28.92/8.00 |
% 28.92/8.00 | Combining equations (396,585) yields a new equation:
% 28.92/8.00 | (622) e2 = e0
% 28.92/8.00 |
% 28.92/8.00 | Simplifying 622 yields:
% 28.92/8.00 | (316) e2 = e0
% 28.92/8.00 |
% 28.92/8.00 | Equations (316) can reduce 57 to:
% 28.92/8.00 | (270) $false
% 28.92/8.00 |
% 28.92/8.00 |-The branch is then unsatisfiable
% 28.92/8.00 |-Branch two:
% 28.92/8.00 | (534) ~ (all_0_40_40 = e1)
% 28.92/8.00 | (3352) all_0_52_52 = e1 | all_0_57_57 = e1
% 28.92/8.00 |
% 28.92/8.00 +-Applying beta-rule and splitting (210), into two cases.
% 28.92/8.00 |-Branch one:
% 28.92/8.00 | (524) all_0_39_39 = e1
% 28.92/8.00 |
% 28.92/8.00 | Combining equations (336,524) yields a new equation:
% 28.92/8.00 | (531) e2 = e1
% 28.92/8.00 |
% 28.92/8.00 | Simplifying 531 yields:
% 28.92/8.00 | (322) e2 = e1
% 28.92/8.00 |
% 28.92/8.00 | Equations (322) can reduce 141 to:
% 28.92/8.00 | (270) $false
% 28.92/8.00 |
% 28.92/8.00 |-The branch is then unsatisfiable
% 28.92/8.00 |-Branch two:
% 28.92/8.00 | (528) ~ (all_0_39_39 = e1)
% 28.92/8.00 | (529) all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1
% 28.92/8.00 |
% 28.92/8.00 +-Applying beta-rule and splitting (529), into two cases.
% 28.92/8.00 |-Branch one:
% 28.92/8.00 | (530) all_0_40_40 = e1
% 28.92/8.00 |
% 28.92/8.00 | Equations (530) can reduce 534 to:
% 28.92/8.00 | (270) $false
% 28.92/8.00 |
% 28.92/8.00 |-The branch is then unsatisfiable
% 28.92/8.00 |-Branch two:
% 28.92/8.00 | (534) ~ (all_0_40_40 = e1)
% 28.92/8.00 | (535) all_0_41_41 = e1 | all_0_42_42 = e1
% 28.92/8.00 |
% 28.92/8.00 +-Applying beta-rule and splitting (535), into two cases.
% 28.92/8.00 |-Branch one:
% 28.92/8.00 | (536) all_0_41_41 = e1
% 28.92/8.00 |
% 28.92/8.00 | Equations (536) can reduce 540 to:
% 28.92/8.00 | (270) $false
% 28.92/8.00 |
% 28.92/8.00 |-The branch is then unsatisfiable
% 28.92/8.00 |-Branch two:
% 28.92/8.00 | (540) ~ (all_0_41_41 = e1)
% 28.92/8.00 | (541) all_0_42_42 = e1
% 28.92/8.00 |
% 28.92/8.00 | Equations (541) can reduce 17 to:
% 28.92/8.00 | (749) ~ (all_0_59_59 = e1)
% 28.92/8.00 |
% 28.92/8.00 | Simplifying 749 yields:
% 28.92/8.00 | (750) ~ (all_0_59_59 = e1)
% 28.92/8.00 |
% 28.92/8.00 +-Applying beta-rule and splitting (93), into two cases.
% 28.92/8.00 |-Branch one:
% 28.92/8.00 | (402) all_0_59_59 = e4
% 28.92/8.00 |
% 28.92/8.00 | Equations (402) can reduce 280 to:
% 28.92/8.00 | (270) $false
% 28.92/8.00 |
% 28.92/8.00 |-The branch is then unsatisfiable
% 28.92/8.00 |-Branch two:
% 28.92/8.00 | (280) ~ (all_0_59_59 = e4)
% 28.92/8.00 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 28.92/8.00 |
% 28.92/8.00 +-Applying beta-rule and splitting (407), into two cases.
% 28.92/8.00 |-Branch one:
% 28.92/8.00 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 28.92/8.00 |
% 28.92/8.00 +-Applying beta-rule and splitting (408), into two cases.
% 28.92/8.00 |-Branch one:
% 28.92/8.00 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 28.92/8.00 |
% 28.92/8.00 +-Applying beta-rule and splitting (409), into two cases.
% 28.92/8.00 |-Branch one:
% 28.92/8.00 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 28.92/8.00 |
% 28.92/8.00 | Applying alpha-rule on (410) yields:
% 28.92/8.00 | (411) all_0_43_43 = e0
% 28.92/8.00 | (412) all_0_59_59 = e3
% 28.92/8.00 | (413) ~ (all_0_46_46 = e3)
% 28.92/8.00 |
% 28.92/8.00 | Equations (411) can reduce 455 to:
% 28.92/8.00 | (270) $false
% 28.92/8.00 |
% 28.92/8.00 |-The branch is then unsatisfiable
% 28.92/8.00 |-Branch two:
% 28.92/8.00 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 28.92/8.00 |
% 28.92/8.00 | Applying alpha-rule on (416) yields:
% 28.92/8.00 | (411) all_0_43_43 = e0
% 28.92/8.00 | (412) all_0_59_59 = e3
% 28.92/8.00 | (419) ~ (all_0_56_56 = e0)
% 28.92/8.00 |
% 28.92/8.00 | Equations (411) can reduce 455 to:
% 28.92/8.00 | (270) $false
% 28.92/8.00 |
% 28.92/8.00 |-The branch is then unsatisfiable
% 28.92/8.00 |-Branch two:
% 28.92/8.00 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 28.92/8.00 |
% 28.92/8.00 | Applying alpha-rule on (422) yields:
% 28.92/8.00 | (423) all_0_53_53 = e0
% 28.92/8.00 | (424) all_0_59_59 = e1
% 28.92/8.00 | (425) ~ (all_0_54_54 = e1)
% 28.92/8.00 |
% 28.92/8.00 | Equations (424) can reduce 750 to:
% 28.92/8.00 | (270) $false
% 28.92/8.00 |
% 28.92/8.00 |-The branch is then unsatisfiable
% 28.92/8.00 |-Branch two:
% 28.92/8.00 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 28.92/8.00 |
% 28.92/8.00 | Applying alpha-rule on (428) yields:
% 28.92/8.00 | (423) all_0_53_53 = e0
% 28.92/8.00 | (424) all_0_59_59 = e1
% 28.92/8.00 | (431) ~ (all_0_58_58 = e0)
% 28.92/8.00 |
% 28.92/8.00 | Equations (424) can reduce 750 to:
% 28.92/8.00 | (270) $false
% 28.92/8.00 |
% 28.92/8.00 |-The branch is then unsatisfiable
% 28.92/8.00 |-Branch two:
% 28.92/8.00 | (333) ~ (all_0_44_44 = e2)
% 28.92/8.00 | (373) all_0_44_44 = e3 | all_0_44_44 = e0
% 28.92/8.00 |
% 28.92/8.00 +-Applying beta-rule and splitting (607), into two cases.
% 28.92/8.00 |-Branch one:
% 28.92/8.00 | (370) all_0_44_44 = e2
% 28.92/8.00 |
% 28.92/8.00 | Equations (370) can reduce 333 to:
% 28.92/8.00 | (270) $false
% 28.92/8.00 |
% 28.92/8.00 |-The branch is then unsatisfiable
% 28.92/8.00 |-Branch two:
% 28.92/8.00 | (333) ~ (all_0_44_44 = e2)
% 28.92/8.00 | (3377) all_0_52_52 = e2 | all_0_57_57 = e2
% 28.92/8.00 |
% 28.92/8.00 +-Applying beta-rule and splitting (3377), into two cases.
% 28.92/8.00 |-Branch one:
% 28.92/8.00 | (685) all_0_52_52 = e2
% 28.92/8.00 |
% 28.92/8.00 | Equations (685) can reduce 257 to:
% 28.92/8.00 | (270) $false
% 28.92/8.00 |
% 28.92/8.00 |-The branch is then unsatisfiable
% 28.92/8.00 |-Branch two:
% 28.92/8.00 | (257) ~ (all_0_52_52 = e2)
% 28.92/8.00 | (392) all_0_57_57 = e2
% 28.92/8.00 |
% 28.92/8.00 | Equations (392) can reduce 10 to:
% 28.92/8.00 | (333) ~ (all_0_44_44 = e2)
% 28.92/8.00 |
% 28.92/8.00 | Equations (392) can reduce 235 to:
% 28.92/8.00 | (257) ~ (all_0_52_52 = e2)
% 28.92/8.00 |
% 28.92/8.00 | From (392) and (30) follows:
% 28.92/8.00 | (3390) op(e2, e2) = all_0_19_19
% 28.92/8.00 |
% 28.92/8.00 +-Applying beta-rule and splitting (453), into two cases.
% 28.92/8.00 |-Branch one:
% 28.92/8.00 | (370) all_0_44_44 = e2
% 28.92/8.00 |
% 28.92/8.00 | Equations (370) can reduce 333 to:
% 28.92/8.00 | (270) $false
% 28.92/8.00 |
% 28.92/8.00 |-The branch is then unsatisfiable
% 28.92/8.00 |-Branch two:
% 28.92/8.00 | (333) ~ (all_0_44_44 = e2)
% 28.92/8.00 | (493) all_0_45_45 = e2 | all_0_46_46 = e2
% 28.92/8.00 |
% 28.92/8.00 +-Applying beta-rule and splitting (493), into two cases.
% 28.92/8.00 |-Branch one:
% 28.92/8.00 | (374) all_0_45_45 = e2
% 28.92/8.00 |
% 28.92/8.00 | Equations (374) can reduce 38 to:
% 28.92/8.00 | (1435) ~ (all_0_46_46 = e2)
% 28.92/8.00 |
% 28.92/8.00 | Simplifying 1435 yields:
% 28.92/8.00 | (1436) ~ (all_0_46_46 = e2)
% 28.92/8.00 |
% 28.92/8.00 | Equations (374) can reduce 26 to:
% 28.92/8.00 | (141) ~ (e2 = e1)
% 28.92/8.00 |
% 28.92/8.00 | Instantiating formula (201) with e2, e2, all_0_19_19, e4 and discharging atoms op(e2, e2) = all_0_19_19, op(e2, e2) = e4, yields:
% 28.92/8.00 | (3391) all_0_19_19 = e4
% 28.92/8.00 |
% 28.92/8.00 +-Applying beta-rule and splitting (9), into two cases.
% 28.92/8.00 |-Branch one:
% 28.92/8.00 | (621) all_0_44_44 = e0
% 28.92/8.00 |
% 28.92/8.00 | Equations (621) can reduce 15 to:
% 28.92/8.00 | (238) ~ (all_0_40_40 = e0)
% 28.92/8.00 |
% 28.92/8.00 | Equations (621) can reduce 241 to:
% 28.92/8.00 | (455) ~ (all_0_43_43 = e0)
% 28.92/8.00 |
% 28.92/8.00 | Equations (621) can reduce 122 to:
% 28.92/8.00 | (4297) ~ (all_0_52_52 = e0)
% 28.92/8.00 |
% 28.92/8.00 | Simplifying 4297 yields:
% 28.92/8.00 | (925) ~ (all_0_52_52 = e0)
% 28.92/8.00 |
% 28.92/8.00 | Equations (621) can reduce 45 to:
% 28.92/8.00 | (456) ~ (e4 = e0)
% 28.92/8.00 |
% 28.92/8.00 | Simplifying 456 yields:
% 28.92/8.00 | (6) ~ (e4 = e0)
% 28.92/8.00 |
% 28.92/8.00 | From (621) and (165) follows:
% 28.92/8.00 | (3395) op(e2, e0) = all_0_15_15
% 28.92/8.00 |
% 28.92/8.00 | Instantiating formula (201) with e2, e0, all_0_15_15, e2 and discharging atoms op(e2, e0) = all_0_15_15, op(e2, e0) = e2, yields:
% 28.92/8.00 | (3500) all_0_15_15 = e2
% 28.92/8.00 |
% 28.92/8.00 +-Applying beta-rule and splitting (8), into two cases.
% 28.92/8.00 |-Branch one:
% 28.92/8.00 | (530) all_0_40_40 = e1
% 28.92/8.00 |
% 28.92/8.00 | Equations (530) can reduce 137 to:
% 28.92/8.00 | (641) ~ (all_0_52_52 = e1)
% 28.92/8.00 |
% 28.92/8.00 | Simplifying 641 yields:
% 28.92/8.00 | (642) ~ (all_0_52_52 = e1)
% 28.92/8.00 |
% 28.92/8.00 | Equations (530) can reduce 233 to:
% 28.92/8.00 | (1021) ~ (e4 = e1)
% 28.92/8.00 |
% 28.92/8.00 | Simplifying 1021 yields:
% 28.92/8.00 | (251) ~ (e4 = e1)
% 28.92/8.00 |
% 28.92/8.00 | Equations (530) can reduce 238 to:
% 28.92/8.00 | (132) ~ (e1 = e0)
% 28.92/8.00 |
% 28.92/8.00 | From (530) and (68) follows:
% 28.92/8.00 | (648) op(e2, e1) = all_0_13_13
% 28.92/8.00 |
% 28.92/8.00 +-Applying beta-rule and splitting (90), into two cases.
% 28.92/8.00 |-Branch one:
% 28.92/8.00 | (685) all_0_52_52 = e2
% 28.92/8.00 |
% 28.92/8.00 | Equations (685) can reduce 257 to:
% 28.92/8.00 | (270) $false
% 28.92/8.00 |
% 28.92/8.00 |-The branch is then unsatisfiable
% 28.92/8.00 |-Branch two:
% 28.92/8.00 | (257) ~ (all_0_52_52 = e2)
% 28.92/8.00 | (688) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 28.92/8.00 |
% 28.92/8.00 +-Applying beta-rule and splitting (688), into two cases.
% 28.92/8.00 |-Branch one:
% 28.92/8.00 | (827) all_0_52_52 = e0
% 28.92/8.00 |
% 28.92/8.00 | Equations (827) can reduce 925 to:
% 28.92/8.00 | (270) $false
% 28.92/8.00 |
% 28.92/8.00 |-The branch is then unsatisfiable
% 28.92/8.00 |-Branch two:
% 28.92/8.00 | (925) ~ (all_0_52_52 = e0)
% 28.92/8.00 | (926) all_0_52_52 = e3 | all_0_52_52 = e1
% 28.92/8.00 |
% 28.92/8.00 +-Applying beta-rule and splitting (926), into two cases.
% 28.92/8.00 |-Branch one:
% 28.92/8.00 | (864) all_0_52_52 = e3
% 28.92/8.00 |
% 28.92/8.00 | Equations (864) can reduce 257 to:
% 28.92/8.00 | (223) ~ (e3 = e2)
% 28.92/8.00 |
% 28.92/8.00 | From (864) and (27) follows:
% 28.92/8.00 | (3412) op(e2, e3) = all_0_17_17
% 28.92/8.00 |
% 28.92/8.00 | Instantiating formula (201) with e2, e3, all_0_17_17, e0 and discharging atoms op(e2, e3) = all_0_17_17, op(e2, e3) = e0, yields:
% 28.92/8.00 | (5880) all_0_17_17 = e0
% 28.92/8.00 |
% 28.92/8.00 | Instantiating formula (201) with e2, e1, all_0_13_13, e1 and discharging atoms op(e2, e1) = all_0_13_13, op(e2, e1) = e1, yields:
% 28.92/8.00 | (5957) all_0_13_13 = e1
% 28.92/8.00 |
% 28.92/8.00 +-Applying beta-rule and splitting (87), into two cases.
% 28.92/8.00 |-Branch one:
% 28.92/8.00 | (650) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 28.92/8.00 |
% 28.92/8.00 +-Applying beta-rule and splitting (650), into two cases.
% 28.92/8.00 |-Branch one:
% 28.92/8.00 | (651) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 28.92/8.00 |
% 28.92/8.00 +-Applying beta-rule and splitting (651), into two cases.
% 28.92/8.00 |-Branch one:
% 28.92/8.00 | (652) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 28.92/8.00 |
% 28.92/8.00 | Applying alpha-rule on (652) yields:
% 28.92/8.00 | (653) all_0_13_13 = e4
% 28.92/8.00 | (654) ~ (all_0_14_14 = e2)
% 28.92/8.00 |
% 28.92/8.00 | Combining equations (653,5957) yields a new equation:
% 28.92/8.00 | (525) e4 = e1
% 28.92/8.00 |
% 28.92/8.00 | Simplifying 525 yields:
% 28.92/8.00 | (526) e4 = e1
% 28.92/8.00 |
% 28.92/8.00 | Equations (526) can reduce 251 to:
% 28.92/8.00 | (270) $false
% 28.92/8.00 |
% 28.92/8.00 |-The branch is then unsatisfiable
% 28.92/8.00 |-Branch two:
% 28.92/8.00 | (657) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 28.92/8.00 |
% 28.92/8.00 | Applying alpha-rule on (657) yields:
% 28.92/8.00 | (658) all_0_15_15 = e3
% 28.92/8.00 | (659) ~ (all_0_16_16 = e2)
% 28.92/8.00 |
% 28.92/8.00 | Combining equations (3500,658) yields a new equation:
% 28.92/8.00 | (414) e3 = e2
% 28.92/8.00 |
% 28.92/8.00 | Equations (414) can reduce 223 to:
% 28.92/8.00 | (270) $false
% 28.92/8.00 |
% 28.92/8.00 |-The branch is then unsatisfiable
% 28.92/8.00 |-Branch two:
% 28.92/8.00 | (663) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 28.92/8.00 |
% 28.92/8.00 | Applying alpha-rule on (663) yields:
% 28.92/8.00 | (664) all_0_17_17 = e1
% 28.92/8.00 | (665) ~ (all_0_18_18 = e2)
% 28.92/8.00 |
% 28.92/8.00 | Combining equations (664,5880) yields a new equation:
% 28.92/8.00 | (571) e1 = e0
% 28.92/8.00 |
% 28.92/8.00 | Simplifying 571 yields:
% 28.92/8.00 | (560) e1 = e0
% 28.92/8.00 |
% 28.92/8.00 | Equations (560) can reduce 132 to:
% 28.92/8.00 | (270) $false
% 28.92/8.00 |
% 28.92/8.00 |-The branch is then unsatisfiable
% 28.92/8.00 |-Branch two:
% 28.92/8.00 | (1762) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 28.92/8.00 |
% 28.92/8.00 | Applying alpha-rule on (1762) yields:
% 28.92/8.00 | (1763) all_0_19_19 = e0
% 28.92/8.00 | (1764) ~ (all_0_20_20 = e2)
% 28.92/8.00 |
% 28.92/8.00 | Combining equations (1763,3391) yields a new equation:
% 28.92/8.00 | (479) e4 = e0
% 28.92/8.00 |
% 28.92/8.00 | Equations (479) can reduce 6 to:
% 28.92/8.00 | (270) $false
% 28.92/8.00 |
% 28.92/8.00 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (826) ~ (all_0_52_52 = e3)
% 28.92/8.01 | (848) all_0_52_52 = e1
% 28.92/8.01 |
% 28.92/8.01 | Equations (848) can reduce 642 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (534) ~ (all_0_40_40 = e1)
% 28.92/8.01 | (3352) all_0_52_52 = e1 | all_0_57_57 = e1
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (3352), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (848) all_0_52_52 = e1
% 28.92/8.01 |
% 28.92/8.01 | Equations (848) can reduce 154 to:
% 28.92/8.01 | (748) ~ (all_0_51_51 = e1)
% 28.92/8.01 |
% 28.92/8.01 | Equations (848) can reduce 257 to:
% 28.92/8.01 | (645) ~ (e2 = e1)
% 28.92/8.01 |
% 28.92/8.01 | Simplifying 645 yields:
% 28.92/8.01 | (141) ~ (e2 = e1)
% 28.92/8.01 |
% 28.92/8.01 | Equations (848) can reduce 925 to:
% 28.92/8.01 | (132) ~ (e1 = e0)
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (99), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (524) all_0_39_39 = e1
% 28.92/8.01 |
% 28.92/8.01 | Combining equations (336,524) yields a new equation:
% 28.92/8.01 | (531) e2 = e1
% 28.92/8.01 |
% 28.92/8.01 | Simplifying 531 yields:
% 28.92/8.01 | (322) e2 = e1
% 28.92/8.01 |
% 28.92/8.01 | Equations (322) can reduce 141 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (528) ~ (all_0_39_39 = e1)
% 28.92/8.01 | (680) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (680), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (321) all_0_47_47 = e1
% 28.92/8.01 |
% 28.92/8.01 | Combining equations (321,315) yields a new equation:
% 28.92/8.01 | (571) e1 = e0
% 28.92/8.01 |
% 28.92/8.01 | Simplifying 571 yields:
% 28.92/8.01 | (560) e1 = e0
% 28.92/8.01 |
% 28.92/8.01 | Equations (560) can reduce 132 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (324) ~ (all_0_47_47 = e1)
% 28.92/8.01 | (1625) all_0_51_51 = e1 | all_0_56_56 = e1
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (1625), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (820) all_0_51_51 = e1
% 28.92/8.01 |
% 28.92/8.01 | Equations (820) can reduce 748 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (748) ~ (all_0_51_51 = e1)
% 28.92/8.01 | (747) all_0_56_56 = e1
% 28.92/8.01 |
% 28.92/8.01 | Equations (747) can reduce 185 to:
% 28.92/8.01 | (749) ~ (all_0_59_59 = e1)
% 28.92/8.01 |
% 28.92/8.01 | Simplifying 749 yields:
% 28.92/8.01 | (750) ~ (all_0_59_59 = e1)
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (93), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (402) all_0_59_59 = e4
% 28.92/8.01 |
% 28.92/8.01 | Equations (402) can reduce 280 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (280) ~ (all_0_59_59 = e4)
% 28.92/8.01 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (407), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (408), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (409), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 28.92/8.01 |
% 28.92/8.01 | Applying alpha-rule on (410) yields:
% 28.92/8.01 | (411) all_0_43_43 = e0
% 28.92/8.01 | (412) all_0_59_59 = e3
% 28.92/8.01 | (413) ~ (all_0_46_46 = e3)
% 28.92/8.01 |
% 28.92/8.01 | Equations (411) can reduce 455 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 28.92/8.01 |
% 28.92/8.01 | Applying alpha-rule on (416) yields:
% 28.92/8.01 | (411) all_0_43_43 = e0
% 28.92/8.01 | (412) all_0_59_59 = e3
% 28.92/8.01 | (419) ~ (all_0_56_56 = e0)
% 28.92/8.01 |
% 28.92/8.01 | Equations (411) can reduce 455 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 28.92/8.01 |
% 28.92/8.01 | Applying alpha-rule on (422) yields:
% 28.92/8.01 | (423) all_0_53_53 = e0
% 28.92/8.01 | (424) all_0_59_59 = e1
% 28.92/8.01 | (425) ~ (all_0_54_54 = e1)
% 28.92/8.01 |
% 28.92/8.01 | Equations (424) can reduce 750 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 28.92/8.01 |
% 28.92/8.01 | Applying alpha-rule on (428) yields:
% 28.92/8.01 | (423) all_0_53_53 = e0
% 28.92/8.01 | (424) all_0_59_59 = e1
% 28.92/8.01 | (431) ~ (all_0_58_58 = e0)
% 28.92/8.01 |
% 28.92/8.01 | Equations (424) can reduce 750 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (642) ~ (all_0_52_52 = e1)
% 28.92/8.01 | (997) all_0_57_57 = e1
% 28.92/8.01 |
% 28.92/8.01 | Combining equations (392,997) yields a new equation:
% 28.92/8.01 | (531) e2 = e1
% 28.92/8.01 |
% 28.92/8.01 | Simplifying 531 yields:
% 28.92/8.01 | (322) e2 = e1
% 28.92/8.01 |
% 28.92/8.01 | Equations (322) can reduce 141 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (625) ~ (all_0_44_44 = e0)
% 28.92/8.01 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (626), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (827) all_0_52_52 = e0
% 28.92/8.01 |
% 28.92/8.01 | Equations (827) can reduce 122 to:
% 28.92/8.01 | (625) ~ (all_0_44_44 = e0)
% 28.92/8.01 |
% 28.92/8.01 | Equations (827) can reduce 257 to:
% 28.92/8.01 | (566) ~ (e2 = e0)
% 28.92/8.01 |
% 28.92/8.01 | Simplifying 566 yields:
% 28.92/8.01 | (57) ~ (e2 = e0)
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (116), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (411) all_0_43_43 = e0
% 28.92/8.01 |
% 28.92/8.01 | Equations (411) can reduce 455 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (455) ~ (all_0_43_43 = e0)
% 28.92/8.01 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (1122), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (621) all_0_44_44 = e0
% 28.92/8.01 |
% 28.92/8.01 | Equations (621) can reduce 625 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (625) ~ (all_0_44_44 = e0)
% 28.92/8.01 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (1128), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (454) all_0_45_45 = e0
% 28.92/8.01 |
% 28.92/8.01 | Combining equations (374,454) yields a new equation:
% 28.92/8.01 | (622) e2 = e0
% 28.92/8.01 |
% 28.92/8.01 | Simplifying 622 yields:
% 28.92/8.01 | (316) e2 = e0
% 28.92/8.01 |
% 28.92/8.01 | Equations (316) can reduce 57 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (488) ~ (all_0_45_45 = e0)
% 28.92/8.01 | (1132) all_0_46_46 = e0
% 28.92/8.01 |
% 28.92/8.01 | Equations (1132) can reduce 103 to:
% 28.92/8.01 | (455) ~ (all_0_43_43 = e0)
% 28.92/8.01 |
% 28.92/8.01 | Equations (1132) can reduce 206 to:
% 28.92/8.01 | (4000) ~ (all_0_59_59 = e0)
% 28.92/8.01 |
% 28.92/8.01 | Simplifying 4000 yields:
% 28.92/8.01 | (4001) ~ (all_0_59_59 = e0)
% 28.92/8.01 |
% 28.92/8.01 | Equations (1132) can reduce 1436 to:
% 28.92/8.01 | (566) ~ (e2 = e0)
% 28.92/8.01 |
% 28.92/8.01 | Simplifying 566 yields:
% 28.92/8.01 | (57) ~ (e2 = e0)
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (176), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (830) all_0_56_56 = e0
% 28.92/8.01 |
% 28.92/8.01 | Equations (830) can reduce 419 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (419) ~ (all_0_56_56 = e0)
% 28.92/8.01 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (834), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (2258) all_0_57_57 = e0
% 28.92/8.01 |
% 28.92/8.01 | Combining equations (392,2258) yields a new equation:
% 28.92/8.01 | (622) e2 = e0
% 28.92/8.01 |
% 28.92/8.01 | Simplifying 622 yields:
% 28.92/8.01 | (316) e2 = e0
% 28.92/8.01 |
% 28.92/8.01 | Equations (316) can reduce 57 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (2301) ~ (all_0_57_57 = e0)
% 28.92/8.01 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (2302), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (585) all_0_58_58 = e0
% 28.92/8.01 |
% 28.92/8.01 | Equations (585) can reduce 70 to:
% 28.92/8.01 | (584) ~ (all_0_53_53 = e0)
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (93), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (402) all_0_59_59 = e4
% 28.92/8.01 |
% 28.92/8.01 | Equations (402) can reduce 280 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (280) ~ (all_0_59_59 = e4)
% 28.92/8.01 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (407), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (408), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (409), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 28.92/8.01 |
% 28.92/8.01 | Applying alpha-rule on (410) yields:
% 28.92/8.01 | (411) all_0_43_43 = e0
% 28.92/8.01 | (412) all_0_59_59 = e3
% 28.92/8.01 | (413) ~ (all_0_46_46 = e3)
% 28.92/8.01 |
% 28.92/8.01 | Equations (411) can reduce 455 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 28.92/8.01 |
% 28.92/8.01 | Applying alpha-rule on (416) yields:
% 28.92/8.01 | (411) all_0_43_43 = e0
% 28.92/8.01 | (412) all_0_59_59 = e3
% 28.92/8.01 | (419) ~ (all_0_56_56 = e0)
% 28.92/8.01 |
% 28.92/8.01 | Equations (411) can reduce 455 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 28.92/8.01 |
% 28.92/8.01 | Applying alpha-rule on (422) yields:
% 28.92/8.01 | (423) all_0_53_53 = e0
% 28.92/8.01 | (424) all_0_59_59 = e1
% 28.92/8.01 | (425) ~ (all_0_54_54 = e1)
% 28.92/8.01 |
% 28.92/8.01 | Equations (423) can reduce 584 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 28.92/8.01 |
% 28.92/8.01 | Applying alpha-rule on (428) yields:
% 28.92/8.01 | (423) all_0_53_53 = e0
% 28.92/8.01 | (424) all_0_59_59 = e1
% 28.92/8.01 | (431) ~ (all_0_58_58 = e0)
% 28.92/8.01 |
% 28.92/8.01 | Equations (585) can reduce 431 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (431) ~ (all_0_58_58 = e0)
% 28.92/8.01 | (2308) all_0_59_59 = e0
% 28.92/8.01 |
% 28.92/8.01 | Equations (2308) can reduce 4001 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (925) ~ (all_0_52_52 = e0)
% 28.92/8.01 | (2258) all_0_57_57 = e0
% 28.92/8.01 |
% 28.92/8.01 | Combining equations (2258,392) yields a new equation:
% 28.92/8.01 | (316) e2 = e0
% 28.92/8.01 |
% 28.92/8.01 | Equations (316) can reduce 57 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (434) ~ (all_0_45_45 = e2)
% 28.92/8.01 | (497) all_0_46_46 = e2
% 28.92/8.01 |
% 28.92/8.01 | Equations (497) can reduce 1436 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (291) ~ (all_0_39_39 = e2)
% 28.92/8.01 | (630) all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (630), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (327) all_0_40_40 = e2
% 28.92/8.01 |
% 28.92/8.01 | Equations (327) can reduce 602 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (602) ~ (all_0_40_40 = e2)
% 28.92/8.01 | (1251) all_0_41_41 = e2 | all_0_42_42 = e2
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (1251), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (436) all_0_41_41 = e2
% 28.92/8.01 |
% 28.92/8.01 | Equations (436) can reduce 226 to:
% 28.92/8.01 | (291) ~ (all_0_39_39 = e2)
% 28.92/8.01 |
% 28.92/8.01 | Equations (436) can reduce 94 to:
% 28.92/8.01 | (1336) ~ (all_0_42_42 = e2)
% 28.92/8.01 |
% 28.92/8.01 | Simplifying 1336 yields:
% 28.92/8.01 | (498) ~ (all_0_42_42 = e2)
% 28.92/8.01 |
% 28.92/8.01 | Equations (436) can reduce 51 to:
% 28.92/8.01 | (611) ~ (all_0_45_45 = e2)
% 28.92/8.01 |
% 28.92/8.01 | Simplifying 611 yields:
% 28.92/8.01 | (434) ~ (all_0_45_45 = e2)
% 28.92/8.01 |
% 28.92/8.01 | Equations (436) can reduce 214 to:
% 28.92/8.01 | (258) ~ (all_0_53_53 = e2)
% 28.92/8.01 |
% 28.92/8.01 | Simplifying 258 yields:
% 28.92/8.01 | (259) ~ (all_0_53_53 = e2)
% 28.92/8.01 |
% 28.92/8.01 | Equations (436) can reduce 157 to:
% 28.92/8.01 | (375) ~ (all_0_58_58 = e2)
% 28.92/8.01 |
% 28.92/8.01 | Simplifying 375 yields:
% 28.92/8.01 | (376) ~ (all_0_58_58 = e2)
% 28.92/8.01 |
% 28.92/8.01 | From (436) and (112) follows:
% 28.92/8.01 | (8377) op(e1, e2) = all_0_21_21
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (186), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (336) all_0_39_39 = e2
% 28.92/8.01 |
% 28.92/8.01 | Equations (336) can reduce 291 to:
% 28.92/8.01 | (270) $false
% 28.92/8.01 |
% 28.92/8.01 |-The branch is then unsatisfiable
% 28.92/8.01 |-Branch two:
% 28.92/8.01 | (291) ~ (all_0_39_39 = e2)
% 28.92/8.01 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (339), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 28.92/8.01 |
% 28.92/8.01 +-Applying beta-rule and splitting (340), into two cases.
% 28.92/8.01 |-Branch one:
% 28.92/8.01 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 28.92/8.01 |
% 28.92/8.01 | Applying alpha-rule on (341) yields:
% 28.92/8.01 | (342) all_0_0_0 = e1
% 28.92/8.01 | (343) ~ (all_0_1_1 = e4)
% 28.92/8.02 |
% 28.92/8.02 | Combining equations (342,285) yields a new equation:
% 28.92/8.02 | (530) all_0_40_40 = e1
% 28.92/8.02 |
% 28.92/8.02 | Equations (530) can reduce 114 to:
% 28.92/8.02 | (528) ~ (all_0_39_39 = e1)
% 28.92/8.02 |
% 28.92/8.02 | Equations (530) can reduce 15 to:
% 28.92/8.02 | (4822) ~ (all_0_44_44 = e1)
% 28.92/8.02 |
% 28.92/8.02 | Simplifying 4822 yields:
% 28.92/8.02 | (131) ~ (all_0_44_44 = e1)
% 28.92/8.02 |
% 28.92/8.02 | Equations (530) can reduce 149 to:
% 28.92/8.02 | (643) ~ (all_0_57_57 = e1)
% 28.92/8.02 |
% 28.92/8.02 | Simplifying 643 yields:
% 28.92/8.02 | (644) ~ (all_0_57_57 = e1)
% 28.92/8.02 |
% 28.92/8.02 | Equations (530) can reduce 233 to:
% 28.92/8.02 | (1021) ~ (e4 = e1)
% 28.92/8.02 |
% 28.92/8.02 | Simplifying 1021 yields:
% 28.92/8.02 | (251) ~ (e4 = e1)
% 28.92/8.02 |
% 28.92/8.02 | Equations (530) can reduce 238 to:
% 28.92/8.02 | (132) ~ (e1 = e0)
% 28.92/8.02 |
% 28.92/8.02 | From (530) and (68) follows:
% 28.92/8.02 | (648) op(e2, e1) = all_0_13_13
% 28.92/8.02 |
% 28.92/8.02 | Instantiating formula (201) with e2, e1, all_0_13_13, e1 and discharging atoms op(e2, e1) = all_0_13_13, op(e2, e1) = e1, yields:
% 28.92/8.02 | (5957) all_0_13_13 = e1
% 28.92/8.02 |
% 28.92/8.02 | Instantiating formula (201) with e1, e2, all_0_21_21, all_0_52_52 and discharging atoms op(e1, e2) = all_0_21_21, op(e1, e2) = all_0_52_52, yields:
% 28.92/8.02 | (8397) all_0_21_21 = all_0_52_52
% 28.92/8.02 |
% 28.92/8.02 +-Applying beta-rule and splitting (47), into two cases.
% 28.92/8.02 |-Branch one:
% 28.92/8.02 | (450) all_0_43_43 = e2
% 28.92/8.02 |
% 28.92/8.02 | Equations (450) can reduce 188 to:
% 28.92/8.02 | (299) ~ (all_0_56_56 = e2)
% 28.92/8.02 |
% 28.92/8.02 | Simplifying 299 yields:
% 28.92/8.02 | (300) ~ (all_0_56_56 = e2)
% 28.92/8.02 |
% 29.14/8.02 | Equations (450) can reduce 455 to:
% 29.14/8.02 | (57) ~ (e2 = e0)
% 29.14/8.02 |
% 29.14/8.02 +-Applying beta-rule and splitting (168), into two cases.
% 29.14/8.02 |-Branch one:
% 29.14/8.02 | (382) all_0_55_55 = e2
% 29.14/8.02 |
% 29.14/8.02 | Combining equations (382,272) yields a new equation:
% 29.14/8.02 | (269) e4 = e2
% 29.14/8.02 |
% 29.14/8.02 | Equations (269) can reduce 231 to:
% 29.14/8.02 | (270) $false
% 29.14/8.02 |
% 29.14/8.02 |-The branch is then unsatisfiable
% 29.14/8.02 |-Branch two:
% 29.14/8.02 | (386) ~ (all_0_55_55 = e2)
% 29.14/8.02 | (387) all_0_56_56 = e2 | all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 29.14/8.02 |
% 29.14/8.02 +-Applying beta-rule and splitting (387), into two cases.
% 29.14/8.02 |-Branch one:
% 29.14/8.02 | (388) all_0_56_56 = e2
% 29.14/8.02 |
% 29.14/8.02 | Equations (388) can reduce 300 to:
% 29.14/8.02 | (270) $false
% 29.14/8.02 |
% 29.14/8.02 |-The branch is then unsatisfiable
% 29.14/8.02 |-Branch two:
% 29.14/8.02 | (300) ~ (all_0_56_56 = e2)
% 29.14/8.02 | (391) all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 29.14/8.02 |
% 29.14/8.02 +-Applying beta-rule and splitting (391), into two cases.
% 29.14/8.02 |-Branch one:
% 29.14/8.02 | (392) all_0_57_57 = e2
% 29.14/8.02 |
% 29.14/8.02 | Equations (392) can reduce 235 to:
% 29.14/8.02 | (257) ~ (all_0_52_52 = e2)
% 29.14/8.02 |
% 29.14/8.02 | From (392) and (30) follows:
% 29.14/8.02 | (3390) op(e2, e2) = all_0_19_19
% 29.14/8.02 |
% 29.14/8.02 | Instantiating formula (201) with e2, e2, all_0_19_19, e4 and discharging atoms op(e2, e2) = all_0_19_19, op(e2, e2) = e4, yields:
% 29.14/8.02 | (3391) all_0_19_19 = e4
% 29.14/8.02 |
% 29.14/8.02 +-Applying beta-rule and splitting (9), into two cases.
% 29.14/8.02 |-Branch one:
% 29.14/8.02 | (621) all_0_44_44 = e0
% 29.14/8.02 |
% 29.14/8.02 | Equations (621) can reduce 45 to:
% 29.14/8.02 | (456) ~ (e4 = e0)
% 29.14/8.02 |
% 29.14/8.02 | Simplifying 456 yields:
% 29.14/8.02 | (6) ~ (e4 = e0)
% 29.14/8.02 |
% 29.14/8.02 | Equations (621) can reduce 131 to:
% 29.14/8.02 | (568) ~ (e1 = e0)
% 29.14/8.02 |
% 29.14/8.02 | Simplifying 568 yields:
% 29.14/8.02 | (132) ~ (e1 = e0)
% 29.14/8.02 |
% 29.14/8.02 | From (621) and (165) follows:
% 29.14/8.02 | (3395) op(e2, e0) = all_0_15_15
% 29.14/8.02 |
% 29.14/8.02 +-Applying beta-rule and splitting (90), into two cases.
% 29.14/8.02 |-Branch one:
% 29.14/8.02 | (685) all_0_52_52 = e2
% 29.14/8.02 |
% 29.14/8.02 | Equations (685) can reduce 257 to:
% 29.14/8.02 | (270) $false
% 29.14/8.02 |
% 29.14/8.02 |-The branch is then unsatisfiable
% 29.14/8.02 |-Branch two:
% 29.14/8.02 | (257) ~ (all_0_52_52 = e2)
% 29.14/8.02 | (688) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 29.14/8.02 |
% 29.14/8.02 +-Applying beta-rule and splitting (133), into two cases.
% 29.14/8.02 |-Branch one:
% 29.14/8.02 | (671) all_0_40_40 = e3
% 29.14/8.02 |
% 29.14/8.02 | Combining equations (530,671) yields a new equation:
% 29.14/8.02 | (538) e3 = e1
% 29.14/8.02 |
% 29.14/8.02 | Equations (538) can reduce 136 to:
% 29.14/8.02 | (270) $false
% 29.14/8.02 |
% 29.14/8.02 |-The branch is then unsatisfiable
% 29.14/8.02 |-Branch two:
% 29.14/8.02 | (675) ~ (all_0_40_40 = e3)
% 29.14/8.02 | (676) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 29.14/8.02 |
% 29.14/8.02 +-Applying beta-rule and splitting (676), into two cases.
% 29.14/8.02 |-Branch one:
% 29.14/8.02 | (858) all_0_44_44 = e3
% 29.14/8.02 |
% 29.14/8.02 | Combining equations (621,858) yields a new equation:
% 29.14/8.02 | (784) e3 = e0
% 29.14/8.02 |
% 29.14/8.02 | Equations (784) can reduce 66 to:
% 29.14/8.02 | (270) $false
% 29.14/8.02 |
% 29.14/8.02 |-The branch is then unsatisfiable
% 29.14/8.02 |-Branch two:
% 29.14/8.02 | (862) ~ (all_0_44_44 = e3)
% 29.14/8.02 | (863) all_0_52_52 = e3 | all_0_57_57 = e3
% 29.14/8.02 |
% 29.14/8.02 +-Applying beta-rule and splitting (863), into two cases.
% 29.14/8.02 |-Branch one:
% 29.14/8.02 | (864) all_0_52_52 = e3
% 29.14/8.02 |
% 29.14/8.02 | Equations (864) can reduce 257 to:
% 29.14/8.02 | (223) ~ (e3 = e2)
% 29.14/8.02 |
% 29.14/8.02 | From (864) and (27) follows:
% 29.14/8.02 | (3412) op(e2, e3) = all_0_17_17
% 29.14/8.02 |
% 29.14/8.02 | Instantiating formula (201) with e2, e3, all_0_17_17, e0 and discharging atoms op(e2, e3) = all_0_17_17, op(e2, e3) = e0, yields:
% 29.14/8.02 | (5880) all_0_17_17 = e0
% 29.14/8.02 |
% 29.14/8.02 | Instantiating formula (201) with e2, e0, all_0_15_15, e2 and discharging atoms op(e2, e0) = all_0_15_15, op(e2, e0) = e2, yields:
% 29.14/8.02 | (3500) all_0_15_15 = e2
% 29.14/8.02 |
% 29.14/8.02 +-Applying beta-rule and splitting (87), into two cases.
% 29.14/8.02 |-Branch one:
% 29.14/8.02 | (650) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 29.14/8.02 |
% 29.14/8.02 +-Applying beta-rule and splitting (650), into two cases.
% 29.14/8.02 |-Branch one:
% 29.14/8.02 | (651) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 29.14/8.02 |
% 29.14/8.02 +-Applying beta-rule and splitting (651), into two cases.
% 29.14/8.02 |-Branch one:
% 29.14/8.02 | (652) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 29.14/8.02 |
% 29.14/8.02 | Applying alpha-rule on (652) yields:
% 29.14/8.02 | (653) all_0_13_13 = e4
% 29.14/8.02 | (654) ~ (all_0_14_14 = e2)
% 29.14/8.02 |
% 29.14/8.02 | Combining equations (653,5957) yields a new equation:
% 29.14/8.02 | (525) e4 = e1
% 29.14/8.02 |
% 29.14/8.02 | Simplifying 525 yields:
% 29.14/8.02 | (526) e4 = e1
% 29.14/8.02 |
% 29.14/8.02 | Equations (526) can reduce 251 to:
% 29.14/8.02 | (270) $false
% 29.14/8.02 |
% 29.14/8.02 |-The branch is then unsatisfiable
% 29.14/8.02 |-Branch two:
% 29.14/8.02 | (657) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 29.14/8.02 |
% 29.14/8.02 | Applying alpha-rule on (657) yields:
% 29.14/8.02 | (658) all_0_15_15 = e3
% 29.14/8.02 | (659) ~ (all_0_16_16 = e2)
% 29.14/8.02 |
% 29.14/8.02 | Combining equations (658,3500) yields a new equation:
% 29.14/8.02 | (437) e3 = e2
% 29.14/8.02 |
% 29.14/8.02 | Simplifying 437 yields:
% 29.14/8.02 | (414) e3 = e2
% 29.14/8.02 |
% 29.14/8.02 | Equations (414) can reduce 223 to:
% 29.14/8.02 | (270) $false
% 29.14/8.02 |
% 29.14/8.02 |-The branch is then unsatisfiable
% 29.14/8.02 |-Branch two:
% 29.14/8.02 | (663) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 29.14/8.02 |
% 29.14/8.02 | Applying alpha-rule on (663) yields:
% 29.14/8.02 | (664) all_0_17_17 = e1
% 29.14/8.02 | (665) ~ (all_0_18_18 = e2)
% 29.14/8.02 |
% 29.14/8.02 | Combining equations (5880,664) yields a new equation:
% 29.14/8.02 | (560) e1 = e0
% 29.14/8.02 |
% 29.14/8.02 | Equations (560) can reduce 132 to:
% 29.14/8.02 | (270) $false
% 29.14/8.02 |
% 29.14/8.02 |-The branch is then unsatisfiable
% 29.14/8.02 |-Branch two:
% 29.14/8.02 | (1762) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 29.14/8.02 |
% 29.14/8.02 | Applying alpha-rule on (1762) yields:
% 29.14/8.02 | (1763) all_0_19_19 = e0
% 29.14/8.02 | (1764) ~ (all_0_20_20 = e2)
% 29.14/8.02 |
% 29.14/8.02 | Combining equations (1763,3391) yields a new equation:
% 29.14/8.02 | (479) e4 = e0
% 29.14/8.02 |
% 29.14/8.02 | Equations (479) can reduce 6 to:
% 29.14/8.02 | (270) $false
% 29.14/8.02 |
% 29.14/8.02 |-The branch is then unsatisfiable
% 29.14/8.02 |-Branch two:
% 29.14/8.02 | (826) ~ (all_0_52_52 = e3)
% 29.14/8.02 | (869) all_0_57_57 = e3
% 29.14/8.02 |
% 29.14/8.02 | Combining equations (869,392) yields a new equation:
% 29.14/8.02 | (437) e3 = e2
% 29.14/8.02 |
% 29.14/8.02 | Simplifying 437 yields:
% 29.14/8.02 | (414) e3 = e2
% 29.14/8.02 |
% 29.14/8.02 | Equations (414) can reduce 223 to:
% 29.14/8.02 | (270) $false
% 29.14/8.02 |
% 29.14/8.02 |-The branch is then unsatisfiable
% 29.14/8.02 |-Branch two:
% 29.14/8.02 | (625) ~ (all_0_44_44 = e0)
% 29.14/8.02 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 29.14/8.02 |
% 29.14/8.02 +-Applying beta-rule and splitting (90), into two cases.
% 29.14/8.02 |-Branch one:
% 29.14/8.02 | (685) all_0_52_52 = e2
% 29.14/8.02 |
% 29.14/8.02 | Equations (685) can reduce 257 to:
% 29.14/8.02 | (270) $false
% 29.14/8.02 |
% 29.14/8.02 |-The branch is then unsatisfiable
% 29.14/8.02 |-Branch two:
% 29.14/8.02 | (257) ~ (all_0_52_52 = e2)
% 29.14/8.02 | (688) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 29.14/8.02 |
% 29.14/8.02 +-Applying beta-rule and splitting (626), into two cases.
% 29.14/8.02 |-Branch one:
% 29.14/8.02 | (827) all_0_52_52 = e0
% 29.14/8.02 |
% 29.14/8.02 | Equations (827) can reduce 213 to:
% 29.14/8.02 | (3103) ~ (all_0_53_53 = e0)
% 29.14/8.02 |
% 29.14/8.02 | Simplifying 3103 yields:
% 29.14/8.02 | (584) ~ (all_0_53_53 = e0)
% 29.14/8.02 |
% 29.14/8.02 | Equations (827) can reduce 257 to:
% 29.14/8.02 | (566) ~ (e2 = e0)
% 29.14/8.02 |
% 29.14/8.02 | Simplifying 566 yields:
% 29.14/8.02 | (57) ~ (e2 = e0)
% 29.14/8.02 |
% 29.14/8.02 +-Applying beta-rule and splitting (93), into two cases.
% 29.14/8.02 |-Branch one:
% 29.14/8.02 | (402) all_0_59_59 = e4
% 29.14/8.02 |
% 29.14/8.02 | Equations (402) can reduce 280 to:
% 29.14/8.02 | (270) $false
% 29.14/8.02 |
% 29.14/8.02 |-The branch is then unsatisfiable
% 29.14/8.02 |-Branch two:
% 29.14/8.02 | (280) ~ (all_0_59_59 = e4)
% 29.14/8.02 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 29.14/8.02 |
% 29.14/8.02 +-Applying beta-rule and splitting (407), into two cases.
% 29.14/8.02 |-Branch one:
% 29.14/8.02 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 29.14/8.02 |
% 29.14/8.02 +-Applying beta-rule and splitting (408), into two cases.
% 29.14/8.02 |-Branch one:
% 29.14/8.02 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 29.14/8.02 |
% 29.14/8.02 +-Applying beta-rule and splitting (409), into two cases.
% 29.14/8.02 |-Branch one:
% 29.14/8.02 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 29.14/8.02 |
% 29.14/8.02 | Applying alpha-rule on (410) yields:
% 29.14/8.02 | (411) all_0_43_43 = e0
% 29.14/8.02 | (412) all_0_59_59 = e3
% 29.14/8.02 | (413) ~ (all_0_46_46 = e3)
% 29.14/8.02 |
% 29.14/8.02 | Combining equations (411,450) yields a new equation:
% 29.14/8.02 | (316) e2 = e0
% 29.14/8.02 |
% 29.14/8.02 | Equations (316) can reduce 57 to:
% 29.14/8.02 | (270) $false
% 29.14/8.02 |
% 29.14/8.02 |-The branch is then unsatisfiable
% 29.14/8.02 |-Branch two:
% 29.14/8.02 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 29.14/8.02 |
% 29.14/8.02 | Applying alpha-rule on (416) yields:
% 29.14/8.02 | (411) all_0_43_43 = e0
% 29.14/8.02 | (412) all_0_59_59 = e3
% 29.14/8.02 | (419) ~ (all_0_56_56 = e0)
% 29.14/8.02 |
% 29.14/8.02 | Combining equations (411,450) yields a new equation:
% 29.14/8.02 | (316) e2 = e0
% 29.14/8.02 |
% 29.14/8.02 | Equations (316) can reduce 57 to:
% 29.14/8.02 | (270) $false
% 29.14/8.02 |
% 29.14/8.02 |-The branch is then unsatisfiable
% 29.14/8.02 |-Branch two:
% 29.14/8.02 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 29.14/8.02 |
% 29.14/8.02 | Applying alpha-rule on (422) yields:
% 29.14/8.02 | (423) all_0_53_53 = e0
% 29.14/8.02 | (424) all_0_59_59 = e1
% 29.14/8.02 | (425) ~ (all_0_54_54 = e1)
% 29.14/8.02 |
% 29.14/8.02 | Equations (423) can reduce 584 to:
% 29.14/8.02 | (270) $false
% 29.14/8.02 |
% 29.14/8.02 |-The branch is then unsatisfiable
% 29.14/8.02 |-Branch two:
% 29.14/8.02 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 29.14/8.02 |
% 29.14/8.02 | Applying alpha-rule on (428) yields:
% 29.14/8.02 | (423) all_0_53_53 = e0
% 29.14/8.02 | (424) all_0_59_59 = e1
% 29.14/8.02 | (431) ~ (all_0_58_58 = e0)
% 29.14/8.02 |
% 29.14/8.02 | Equations (423) can reduce 584 to:
% 29.14/8.02 | (270) $false
% 29.14/8.02 |
% 29.14/8.02 |-The branch is then unsatisfiable
% 29.14/8.02 |-Branch two:
% 29.14/8.02 | (925) ~ (all_0_52_52 = e0)
% 29.14/8.02 | (2258) all_0_57_57 = e0
% 29.14/8.02 |
% 29.14/8.02 | Combining equations (2258,392) yields a new equation:
% 29.14/8.02 | (316) e2 = e0
% 29.14/8.02 |
% 29.14/8.02 | Equations (316) can reduce 57 to:
% 29.14/8.02 | (270) $false
% 29.14/8.02 |
% 29.14/8.02 |-The branch is then unsatisfiable
% 29.14/8.02 |-Branch two:
% 29.14/8.02 | (335) ~ (all_0_57_57 = e2)
% 29.14/8.02 | (395) all_0_58_58 = e2 | all_0_59_59 = e2
% 29.14/8.02 |
% 29.14/8.02 +-Applying beta-rule and splitting (395), into two cases.
% 29.14/8.02 |-Branch one:
% 29.14/8.02 | (396) all_0_58_58 = e2
% 29.14/8.02 |
% 29.14/8.02 | Equations (396) can reduce 376 to:
% 29.14/8.02 | (270) $false
% 29.14/8.02 |
% 29.14/8.02 |-The branch is then unsatisfiable
% 29.14/8.02 |-Branch two:
% 29.14/8.02 | (376) ~ (all_0_58_58 = e2)
% 29.14/8.02 | (399) all_0_59_59 = e2
% 29.14/8.02 |
% 29.14/8.02 | Equations (399) can reduce 701 to:
% 29.14/8.02 | (270) $false
% 29.14/8.02 |
% 29.14/8.02 |-The branch is then unsatisfiable
% 29.14/8.02 |-Branch two:
% 29.14/8.02 | (292) ~ (all_0_43_43 = e2)
% 29.14/8.02 | (453) all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2
% 29.14/8.02 |
% 29.14/8.02 +-Applying beta-rule and splitting (453), into two cases.
% 29.14/8.02 |-Branch one:
% 29.14/8.02 | (370) all_0_44_44 = e2
% 29.14/8.02 |
% 29.14/8.02 | Equations (370) can reduce 174 to:
% 29.14/8.02 | (1435) ~ (all_0_46_46 = e2)
% 29.14/8.02 |
% 29.14/8.02 | Simplifying 1435 yields:
% 29.14/8.02 | (1436) ~ (all_0_46_46 = e2)
% 29.14/8.02 |
% 29.14/8.02 | Equations (370) can reduce 122 to:
% 29.14/8.02 | (256) ~ (all_0_52_52 = e2)
% 29.14/8.02 |
% 29.14/8.02 | Simplifying 256 yields:
% 29.14/8.02 | (257) ~ (all_0_52_52 = e2)
% 29.14/8.02 |
% 29.14/8.02 | Equations (370) can reduce 10 to:
% 29.14/8.02 | (334) ~ (all_0_57_57 = e2)
% 29.14/8.02 |
% 29.14/8.02 | Simplifying 334 yields:
% 29.14/8.02 | (335) ~ (all_0_57_57 = e2)
% 29.14/8.02 |
% 29.14/8.02 | Equations (370) can reduce 45 to:
% 29.14/8.02 | (377) ~ (e4 = e2)
% 29.14/8.02 |
% 29.14/8.03 | Simplifying 377 yields:
% 29.14/8.03 | (231) ~ (e4 = e2)
% 29.14/8.03 |
% 29.14/8.03 | Equations (370) can reduce 131 to:
% 29.14/8.03 | (141) ~ (e2 = e1)
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (168), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (382) all_0_55_55 = e2
% 29.14/8.03 |
% 29.14/8.03 | Combining equations (382,272) yields a new equation:
% 29.14/8.03 | (269) e4 = e2
% 29.14/8.03 |
% 29.14/8.03 | Equations (269) can reduce 231 to:
% 29.14/8.03 | (270) $false
% 29.14/8.03 |
% 29.14/8.03 |-The branch is then unsatisfiable
% 29.14/8.03 |-Branch two:
% 29.14/8.03 | (386) ~ (all_0_55_55 = e2)
% 29.14/8.03 | (387) all_0_56_56 = e2 | all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (387), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (388) all_0_56_56 = e2
% 29.14/8.03 |
% 29.14/8.03 | Equations (388) can reduce 104 to:
% 29.14/8.03 | (334) ~ (all_0_57_57 = e2)
% 29.14/8.03 |
% 29.14/8.03 | Simplifying 334 yields:
% 29.14/8.03 | (335) ~ (all_0_57_57 = e2)
% 29.14/8.03 |
% 29.14/8.03 | Equations (388) can reduce 81 to:
% 29.14/8.03 | (375) ~ (all_0_58_58 = e2)
% 29.14/8.03 |
% 29.14/8.03 | Simplifying 375 yields:
% 29.14/8.03 | (376) ~ (all_0_58_58 = e2)
% 29.14/8.03 |
% 29.14/8.03 | Equations (388) can reduce 185 to:
% 29.14/8.03 | (700) ~ (all_0_59_59 = e2)
% 29.14/8.03 |
% 29.14/8.03 | Simplifying 700 yields:
% 29.14/8.03 | (701) ~ (all_0_59_59 = e2)
% 29.14/8.03 |
% 29.14/8.03 | Equations (388) can reduce 274 to:
% 29.14/8.03 | (377) ~ (e4 = e2)
% 29.14/8.03 |
% 29.14/8.03 | Simplifying 377 yields:
% 29.14/8.03 | (231) ~ (e4 = e2)
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (194), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (747) all_0_56_56 = e1
% 29.14/8.03 |
% 29.14/8.03 | Combining equations (747,388) yields a new equation:
% 29.14/8.03 | (322) e2 = e1
% 29.14/8.03 |
% 29.14/8.03 | Equations (322) can reduce 141 to:
% 29.14/8.03 | (270) $false
% 29.14/8.03 |
% 29.14/8.03 |-The branch is then unsatisfiable
% 29.14/8.03 |-Branch two:
% 29.14/8.03 | (995) ~ (all_0_56_56 = e1)
% 29.14/8.03 | (996) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (99), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (524) all_0_39_39 = e1
% 29.14/8.03 |
% 29.14/8.03 | Equations (524) can reduce 528 to:
% 29.14/8.03 | (270) $false
% 29.14/8.03 |
% 29.14/8.03 |-The branch is then unsatisfiable
% 29.14/8.03 |-Branch two:
% 29.14/8.03 | (528) ~ (all_0_39_39 = e1)
% 29.14/8.03 | (680) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (996), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (997) all_0_57_57 = e1
% 29.14/8.03 |
% 29.14/8.03 | Equations (997) can reduce 644 to:
% 29.14/8.03 | (270) $false
% 29.14/8.03 |
% 29.14/8.03 |-The branch is then unsatisfiable
% 29.14/8.03 |-Branch two:
% 29.14/8.03 | (644) ~ (all_0_57_57 = e1)
% 29.14/8.03 | (1000) all_0_58_58 = e1 | all_0_59_59 = e1
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (1000), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (1001) all_0_58_58 = e1
% 29.14/8.03 |
% 29.14/8.03 | Equations (1001) can reduce 1004 to:
% 29.14/8.03 | (270) $false
% 29.14/8.03 |
% 29.14/8.03 |-The branch is then unsatisfiable
% 29.14/8.03 |-Branch two:
% 29.14/8.03 | (1004) ~ (all_0_58_58 = e1)
% 29.14/8.03 | (424) all_0_59_59 = e1
% 29.14/8.03 |
% 29.14/8.03 | Equations (424) can reduce 206 to:
% 29.14/8.03 | (106) ~ (all_0_46_46 = e1)
% 29.14/8.03 |
% 29.14/8.03 | Equations (424) can reduce 140 to:
% 29.14/8.03 | (644) ~ (all_0_57_57 = e1)
% 29.14/8.03 |
% 29.14/8.03 | Equations (424) can reduce 156 to:
% 29.14/8.03 | (1004) ~ (all_0_58_58 = e1)
% 29.14/8.03 |
% 29.14/8.03 | Equations (424) can reduce 280 to:
% 29.14/8.03 | (1021) ~ (e4 = e1)
% 29.14/8.03 |
% 29.14/8.03 | Simplifying 1021 yields:
% 29.14/8.03 | (251) ~ (e4 = e1)
% 29.14/8.03 |
% 29.14/8.03 | Equations (424) can reduce 701 to:
% 29.14/8.03 | (645) ~ (e2 = e1)
% 29.14/8.03 |
% 29.14/8.03 | Simplifying 645 yields:
% 29.14/8.03 | (141) ~ (e2 = e1)
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (680), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (321) all_0_47_47 = e1
% 29.14/8.03 |
% 29.14/8.03 | Combining equations (315,321) yields a new equation:
% 29.14/8.03 | (560) e1 = e0
% 29.14/8.03 |
% 29.14/8.03 | Equations (560) can reduce 132 to:
% 29.14/8.03 | (270) $false
% 29.14/8.03 |
% 29.14/8.03 |-The branch is then unsatisfiable
% 29.14/8.03 |-Branch two:
% 29.14/8.03 | (324) ~ (all_0_47_47 = e1)
% 29.14/8.03 | (1625) all_0_51_51 = e1 | all_0_56_56 = e1
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (1625), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (820) all_0_51_51 = e1
% 29.14/8.03 |
% 29.14/8.03 | Equations (820) can reduce 154 to:
% 29.14/8.03 | (641) ~ (all_0_52_52 = e1)
% 29.14/8.03 |
% 29.14/8.03 | Simplifying 641 yields:
% 29.14/8.03 | (642) ~ (all_0_52_52 = e1)
% 29.14/8.03 |
% 29.14/8.03 | From (820) and (171) follows:
% 29.14/8.03 | (8577) op(e1, e3) = e1
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (93), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (402) all_0_59_59 = e4
% 29.14/8.03 |
% 29.14/8.03 | Combining equations (424,402) yields a new equation:
% 29.14/8.03 | (526) e4 = e1
% 29.14/8.03 |
% 29.14/8.03 | Equations (526) can reduce 251 to:
% 29.14/8.03 | (270) $false
% 29.14/8.03 |
% 29.14/8.03 |-The branch is then unsatisfiable
% 29.14/8.03 |-Branch two:
% 29.14/8.03 | (280) ~ (all_0_59_59 = e4)
% 29.14/8.03 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 29.14/8.03 |
% 29.14/8.03 | Equations (424) can reduce 280 to:
% 29.14/8.03 | (1021) ~ (e4 = e1)
% 29.14/8.03 |
% 29.14/8.03 | Simplifying 1021 yields:
% 29.14/8.03 | (251) ~ (e4 = e1)
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (407), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (408), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (409), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 29.14/8.03 |
% 29.14/8.03 | Applying alpha-rule on (410) yields:
% 29.14/8.03 | (411) all_0_43_43 = e0
% 29.14/8.03 | (412) all_0_59_59 = e3
% 29.14/8.03 | (413) ~ (all_0_46_46 = e3)
% 29.14/8.03 |
% 29.14/8.03 | Combining equations (424,412) yields a new equation:
% 29.14/8.03 | (538) e3 = e1
% 29.14/8.03 |
% 29.14/8.03 | Equations (538) can reduce 136 to:
% 29.14/8.03 | (270) $false
% 29.14/8.03 |
% 29.14/8.03 |-The branch is then unsatisfiable
% 29.14/8.03 |-Branch two:
% 29.14/8.03 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 29.14/8.03 |
% 29.14/8.03 | Applying alpha-rule on (416) yields:
% 29.14/8.03 | (411) all_0_43_43 = e0
% 29.14/8.03 | (412) all_0_59_59 = e3
% 29.14/8.03 | (419) ~ (all_0_56_56 = e0)
% 29.14/8.03 |
% 29.14/8.03 | Combining equations (424,412) yields a new equation:
% 29.14/8.03 | (538) e3 = e1
% 29.14/8.03 |
% 29.14/8.03 | Equations (538) can reduce 136 to:
% 29.14/8.03 | (270) $false
% 29.14/8.03 |
% 29.14/8.03 |-The branch is then unsatisfiable
% 29.14/8.03 |-Branch two:
% 29.14/8.03 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 29.14/8.03 |
% 29.14/8.03 | Applying alpha-rule on (422) yields:
% 29.14/8.03 | (423) all_0_53_53 = e0
% 29.14/8.03 | (424) all_0_59_59 = e1
% 29.14/8.03 | (425) ~ (all_0_54_54 = e1)
% 29.14/8.03 |
% 29.14/8.03 | Combining equations (423,7736) yields a new equation:
% 29.14/8.03 | (2274) all_0_25_25 = e0
% 29.14/8.03 |
% 29.14/8.03 | Equations (423) can reduce 213 to:
% 29.14/8.03 | (925) ~ (all_0_52_52 = e0)
% 29.14/8.03 |
% 29.14/8.03 | Equations (423) can reduce 252 to:
% 29.14/8.03 | (3010) ~ (all_0_54_54 = e0)
% 29.14/8.03 |
% 29.14/8.03 | Simplifying 3010 yields:
% 29.14/8.03 | (3011) ~ (all_0_54_54 = e0)
% 29.14/8.03 |
% 29.14/8.03 | Equations (423) can reduce 259 to:
% 29.14/8.03 | (566) ~ (e2 = e0)
% 29.14/8.03 |
% 29.14/8.03 | Simplifying 566 yields:
% 29.14/8.03 | (57) ~ (e2 = e0)
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (9), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (621) all_0_44_44 = e0
% 29.14/8.03 |
% 29.14/8.03 | Combining equations (370,621) yields a new equation:
% 29.14/8.03 | (622) e2 = e0
% 29.14/8.03 |
% 29.14/8.03 | Simplifying 622 yields:
% 29.14/8.03 | (316) e2 = e0
% 29.14/8.03 |
% 29.14/8.03 | Equations (316) can reduce 57 to:
% 29.14/8.03 | (270) $false
% 29.14/8.03 |
% 29.14/8.03 |-The branch is then unsatisfiable
% 29.14/8.03 |-Branch two:
% 29.14/8.03 | (625) ~ (all_0_44_44 = e0)
% 29.14/8.03 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (626), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (827) all_0_52_52 = e0
% 29.14/8.03 |
% 29.14/8.03 | Equations (827) can reduce 925 to:
% 29.14/8.03 | (270) $false
% 29.14/8.03 |
% 29.14/8.03 |-The branch is then unsatisfiable
% 29.14/8.03 |-Branch two:
% 29.14/8.03 | (925) ~ (all_0_52_52 = e0)
% 29.14/8.03 | (2258) all_0_57_57 = e0
% 29.14/8.03 |
% 29.14/8.03 | Equations (2258) can reduce 235 to:
% 29.14/8.03 | (925) ~ (all_0_52_52 = e0)
% 29.14/8.03 |
% 29.14/8.03 | Equations (2258) can reduce 37 to:
% 29.14/8.03 | (3530) ~ (all_0_58_58 = e0)
% 29.14/8.03 |
% 29.14/8.03 | Simplifying 3530 yields:
% 29.14/8.03 | (431) ~ (all_0_58_58 = e0)
% 29.14/8.03 |
% 29.14/8.03 | Equations (2258) can reduce 143 to:
% 29.14/8.03 | (456) ~ (e4 = e0)
% 29.14/8.03 |
% 29.14/8.03 | Simplifying 456 yields:
% 29.14/8.03 | (6) ~ (e4 = e0)
% 29.14/8.03 |
% 29.14/8.03 | Equations (2258) can reduce 335 to:
% 29.14/8.03 | (566) ~ (e2 = e0)
% 29.14/8.03 |
% 29.14/8.03 | Simplifying 566 yields:
% 29.14/8.03 | (57) ~ (e2 = e0)
% 29.14/8.03 |
% 29.14/8.03 | Equations (2258) can reduce 644 to:
% 29.14/8.03 | (568) ~ (e1 = e0)
% 29.14/8.03 |
% 29.14/8.03 | Simplifying 568 yields:
% 29.14/8.03 | (132) ~ (e1 = e0)
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (221), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (1132) all_0_46_46 = e0
% 29.14/8.03 |
% 29.14/8.03 | Equations (1132) can reduce 1436 to:
% 29.14/8.03 | (566) ~ (e2 = e0)
% 29.14/8.03 |
% 29.14/8.03 | Simplifying 566 yields:
% 29.14/8.03 | (57) ~ (e2 = e0)
% 29.14/8.03 |
% 29.14/8.03 | Equations (1132) can reduce 106 to:
% 29.14/8.03 | (568) ~ (e1 = e0)
% 29.14/8.03 |
% 29.14/8.03 | Simplifying 568 yields:
% 29.14/8.03 | (132) ~ (e1 = e0)
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (204), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (396) all_0_58_58 = e2
% 29.14/8.03 |
% 29.14/8.03 | Equations (396) can reduce 376 to:
% 29.14/8.03 | (270) $false
% 29.14/8.03 |
% 29.14/8.03 |-The branch is then unsatisfiable
% 29.14/8.03 |-Branch two:
% 29.14/8.03 | (376) ~ (all_0_58_58 = e2)
% 29.14/8.03 | (3890) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1 | all_0_58_58 = e0
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (3890), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (585) all_0_58_58 = e0
% 29.14/8.03 |
% 29.14/8.03 | Equations (585) can reduce 431 to:
% 29.14/8.03 | (270) $false
% 29.14/8.03 |
% 29.14/8.03 |-The branch is then unsatisfiable
% 29.14/8.03 |-Branch two:
% 29.14/8.03 | (431) ~ (all_0_58_58 = e0)
% 29.14/8.03 | (4709) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (189), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (267) all_0_50_50 = e4
% 29.14/8.03 |
% 29.14/8.03 | Combining equations (253,267) yields a new equation:
% 29.14/8.03 | (269) e4 = e2
% 29.14/8.03 |
% 29.14/8.03 | Equations (269) can reduce 231 to:
% 29.14/8.03 | (270) $false
% 29.14/8.03 |
% 29.14/8.03 |-The branch is then unsatisfiable
% 29.14/8.03 |-Branch two:
% 29.14/8.03 | (271) ~ (all_0_50_50 = e4)
% 29.14/8.03 | (1466) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (1466), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (1467) all_0_51_51 = e4
% 29.14/8.03 |
% 29.14/8.03 | Combining equations (820,1467) yields a new equation:
% 29.14/8.03 | (526) e4 = e1
% 29.14/8.03 |
% 29.14/8.03 | Equations (526) can reduce 251 to:
% 29.14/8.03 | (270) $false
% 29.14/8.03 |
% 29.14/8.03 |-The branch is then unsatisfiable
% 29.14/8.03 |-Branch two:
% 29.14/8.03 | (697) ~ (all_0_51_51 = e4)
% 29.14/8.03 | (1470) all_0_53_53 = e4 | all_0_54_54 = e4
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (1470), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (367) all_0_53_53 = e4
% 29.14/8.03 |
% 29.14/8.03 | Combining equations (423,367) yields a new equation:
% 29.14/8.03 | (479) e4 = e0
% 29.14/8.03 |
% 29.14/8.03 | Equations (479) can reduce 6 to:
% 29.14/8.03 | (270) $false
% 29.14/8.03 |
% 29.14/8.03 |-The branch is then unsatisfiable
% 29.14/8.03 |-Branch two:
% 29.14/8.03 | (599) ~ (all_0_53_53 = e4)
% 29.14/8.03 | (817) all_0_54_54 = e4
% 29.14/8.03 |
% 29.14/8.03 | Equations (817) can reduce 191 to:
% 29.14/8.03 | (520) ~ (all_0_42_42 = e4)
% 29.14/8.03 |
% 29.14/8.03 | Equations (817) can reduce 261 to:
% 29.14/8.03 | (231) ~ (e4 = e2)
% 29.14/8.03 |
% 29.14/8.03 | From (817) and (29) follows:
% 29.14/8.03 | (2271) op(e1, e4) = all_0_37_37
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (222), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (522) all_0_39_39 = e4
% 29.14/8.03 |
% 29.14/8.03 | Equations (522) can reduce 184 to:
% 29.14/8.03 | (692) ~ (all_0_42_42 = e4)
% 29.14/8.03 |
% 29.14/8.03 | Simplifying 692 yields:
% 29.14/8.03 | (520) ~ (all_0_42_42 = e4)
% 29.14/8.03 |
% 29.14/8.03 | Equations (522) can reduce 167 to:
% 29.14/8.03 | (694) ~ (all_0_43_43 = e4)
% 29.14/8.03 |
% 29.14/8.03 | Simplifying 694 yields:
% 29.14/8.03 | (510) ~ (all_0_43_43 = e4)
% 29.14/8.03 |
% 29.14/8.03 | Equations (522) can reduce 101 to:
% 29.14/8.03 | (6) ~ (e4 = e0)
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (16), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (698) all_0_42_42 = e2
% 29.14/8.03 |
% 29.14/8.03 | Equations (698) can reduce 498 to:
% 29.14/8.03 | (270) $false
% 29.14/8.03 |
% 29.14/8.03 |-The branch is then unsatisfiable
% 29.14/8.03 |-Branch two:
% 29.14/8.03 | (498) ~ (all_0_42_42 = e2)
% 29.14/8.03 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (90), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (685) all_0_52_52 = e2
% 29.14/8.03 |
% 29.14/8.03 | Equations (685) can reduce 257 to:
% 29.14/8.03 | (270) $false
% 29.14/8.03 |
% 29.14/8.03 |-The branch is then unsatisfiable
% 29.14/8.03 |-Branch two:
% 29.14/8.03 | (257) ~ (all_0_52_52 = e2)
% 29.14/8.03 | (688) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (4709), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (4713) all_0_58_58 = e3
% 29.14/8.03 |
% 29.14/8.03 | Equations (4713) can reduce 278 to:
% 29.14/8.03 | (719) ~ (e4 = e3)
% 29.14/8.03 |
% 29.14/8.03 | Simplifying 719 yields:
% 29.14/8.03 | (34) ~ (e4 = e3)
% 29.14/8.03 |
% 29.14/8.03 | From (4713) and (63) follows:
% 29.14/8.03 | (8676) op(e1, e3) = all_0_28_28
% 29.14/8.03 |
% 29.14/8.03 +-Applying beta-rule and splitting (178), into two cases.
% 29.14/8.03 |-Branch one:
% 29.14/8.03 | (751) all_0_39_39 = e3
% 29.14/8.03 |
% 29.14/8.03 | Combining equations (751,522) yields a new equation:
% 29.14/8.03 | (359) e4 = e3
% 29.14/8.03 |
% 29.14/8.03 | Equations (359) can reduce 34 to:
% 29.14/8.03 | (270) $false
% 29.14/8.03 |
% 29.14/8.03 |-The branch is then unsatisfiable
% 29.14/8.03 |-Branch two:
% 29.14/8.03 | (755) ~ (all_0_39_39 = e3)
% 29.14/8.04 | (756) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 29.14/8.04 |
% 29.14/8.04 | Equations (522) can reduce 755 to:
% 29.14/8.04 | (34) ~ (e4 = e3)
% 29.14/8.04 |
% 29.14/8.04 +-Applying beta-rule and splitting (78), into two cases.
% 29.14/8.04 |-Branch one:
% 29.14/8.04 | (751) all_0_39_39 = e3
% 29.14/8.04 |
% 29.14/8.04 | Combining equations (751,522) yields a new equation:
% 29.14/8.04 | (359) e4 = e3
% 29.14/8.04 |
% 29.14/8.04 | Equations (359) can reduce 34 to:
% 29.14/8.04 | (270) $false
% 29.14/8.04 |
% 29.14/8.04 |-The branch is then unsatisfiable
% 29.14/8.04 |-Branch two:
% 29.14/8.04 | (755) ~ (all_0_39_39 = e3)
% 29.14/8.04 | (4262) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 29.14/8.04 |
% 29.14/8.04 +-Applying beta-rule and splitting (44), into two cases.
% 29.14/8.04 |-Branch one:
% 29.14/8.04 | (502) all_0_43_43 = e4
% 29.14/8.04 |
% 29.14/8.04 | Equations (502) can reduce 510 to:
% 29.14/8.04 | (270) $false
% 29.14/8.04 |
% 29.14/8.04 |-The branch is then unsatisfiable
% 29.14/8.04 |-Branch two:
% 29.14/8.04 | (510) ~ (all_0_43_43 = e4)
% 29.14/8.04 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 29.14/8.04 |
% 29.14/8.04 +-Applying beta-rule and splitting (688), into two cases.
% 29.14/8.04 |-Branch one:
% 29.14/8.04 | (827) all_0_52_52 = e0
% 29.14/8.04 |
% 29.14/8.04 | Equations (827) can reduce 925 to:
% 29.14/8.04 | (270) $false
% 29.14/8.04 |
% 29.14/8.04 |-The branch is then unsatisfiable
% 29.14/8.04 |-Branch two:
% 29.14/8.04 | (925) ~ (all_0_52_52 = e0)
% 29.14/8.04 | (926) all_0_52_52 = e3 | all_0_52_52 = e1
% 29.14/8.04 |
% 29.14/8.04 +-Applying beta-rule and splitting (511), into two cases.
% 29.14/8.04 |-Branch one:
% 29.14/8.04 | (363) all_0_45_45 = e4
% 29.14/8.04 |
% 29.14/8.04 | From (363) and (142) follows:
% 29.14/8.04 | (2221) op(e1, e4) = all_0_23_23
% 29.14/8.04 |
% 29.14/8.04 +-Applying beta-rule and splitting (926), into two cases.
% 29.14/8.04 |-Branch one:
% 29.14/8.04 | (864) all_0_52_52 = e3
% 29.14/8.04 |
% 29.14/8.04 | Combining equations (864,8397) yields a new equation:
% 29.14/8.04 | (6797) all_0_21_21 = e3
% 29.14/8.04 |
% 29.14/8.04 | Equations (864) can reduce 257 to:
% 29.14/8.04 | (223) ~ (e3 = e2)
% 29.14/8.04 |
% 29.14/8.04 | Equations (864) can reduce 642 to:
% 29.14/8.04 | (136) ~ (e3 = e1)
% 29.14/8.04 |
% 29.14/8.04 | From (864) and (195) follows:
% 29.14/8.04 | (8702) op(e1, e3) = all_0_18_18
% 29.14/8.04 |
% 29.14/8.04 +-Applying beta-rule and splitting (95), into two cases.
% 29.14/8.04 |-Branch one:
% 29.14/8.04 | (1258) all_0_42_42 = e3
% 29.14/8.04 |
% 29.14/8.04 | Equations (1258) can reduce 520 to:
% 29.14/8.04 | (719) ~ (e4 = e3)
% 29.14/8.04 |
% 29.14/8.04 | Simplifying 719 yields:
% 29.14/8.04 | (34) ~ (e4 = e3)
% 29.14/8.04 |
% 29.14/8.04 | Equations (1258) can reduce 498 to:
% 29.14/8.04 | (223) ~ (e3 = e2)
% 29.14/8.04 |
% 29.14/8.04 | Instantiating formula (201) with e1, e4, all_0_23_23, e2 and discharging atoms op(e1, e4) = all_0_23_23, op(e1, e4) = e2, yields:
% 29.14/8.04 | (2272) all_0_23_23 = e2
% 29.14/8.04 |
% 29.14/8.04 | Instantiating formula (201) with e1, e4, all_0_37_37, all_0_23_23 and discharging atoms op(e1, e4) = all_0_23_23, op(e1, e4) = all_0_37_37, yields:
% 29.14/8.04 | (2273) all_0_23_23 = all_0_37_37
% 29.14/8.04 |
% 29.14/8.04 | Instantiating formula (201) with e1, e3, all_0_28_28, all_0_18_18 and discharging atoms op(e1, e3) = all_0_18_18, op(e1, e3) = all_0_28_28, yields:
% 29.14/8.04 | (8709) all_0_18_18 = all_0_28_28
% 29.14/8.04 |
% 29.14/8.04 | Instantiating formula (201) with e1, e3, e1, all_0_18_18 and discharging atoms op(e1, e3) = all_0_18_18, op(e1, e3) = e1, yields:
% 29.14/8.04 | (8710) all_0_18_18 = e1
% 29.14/8.04 |
% 29.14/8.04 | Combining equations (8709,8710) yields a new equation:
% 29.14/8.04 | (8711) all_0_28_28 = e1
% 29.14/8.04 |
% 29.14/8.04 | Simplifying 8711 yields:
% 29.14/8.04 | (8712) all_0_28_28 = e1
% 29.14/8.04 |
% 29.14/8.04 | Combining equations (2272,2273) yields a new equation:
% 29.14/8.04 | (2275) all_0_37_37 = e2
% 29.14/8.04 |
% 29.14/8.04 | Combining equations (2275,2273) yields a new equation:
% 29.14/8.04 | (2272) all_0_23_23 = e2
% 29.14/8.04 |
% 29.14/8.04 +-Applying beta-rule and splitting (14), into two cases.
% 29.14/8.04 |-Branch one:
% 29.14/8.04 | (2277) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1))
% 29.14/8.04 |
% 29.14/8.04 +-Applying beta-rule and splitting (2277), into two cases.
% 29.14/8.04 |-Branch one:
% 29.14/8.04 | (2278) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1))
% 29.14/8.04 |
% 29.14/8.04 +-Applying beta-rule and splitting (2278), into two cases.
% 29.14/8.04 |-Branch one:
% 29.14/8.04 | (2279) all_0_21_21 = e4 & ~ (all_0_22_22 = e1)
% 29.14/8.04 |
% 29.14/8.04 | Applying alpha-rule on (2279) yields:
% 29.14/8.04 | (2280) all_0_21_21 = e4
% 29.14/8.04 | (2281) ~ (all_0_22_22 = e1)
% 29.14/8.04 |
% 29.14/8.04 | Combining equations (2280,6797) yields a new equation:
% 29.14/8.04 | (660) e4 = e3
% 29.14/8.04 |
% 29.14/8.04 | Simplifying 660 yields:
% 29.14/8.04 | (359) e4 = e3
% 29.14/8.04 |
% 29.14/8.04 | Equations (359) can reduce 34 to:
% 29.14/8.04 | (270) $false
% 29.14/8.04 |
% 29.14/8.04 |-The branch is then unsatisfiable
% 29.14/8.04 |-Branch two:
% 29.14/8.04 | (2285) all_0_23_23 = e3 & ~ (all_0_24_24 = e1)
% 29.14/8.04 |
% 29.14/8.04 | Applying alpha-rule on (2285) yields:
% 29.14/8.04 | (2286) all_0_23_23 = e3
% 29.14/8.04 | (2287) ~ (all_0_24_24 = e1)
% 29.14/8.04 |
% 29.14/8.04 | Combining equations (2286,2272) yields a new equation:
% 29.14/8.04 | (437) e3 = e2
% 29.14/8.04 |
% 29.14/8.04 | Simplifying 437 yields:
% 29.14/8.04 | (414) e3 = e2
% 29.14/8.04 |
% 29.14/8.04 | Equations (414) can reduce 223 to:
% 29.14/8.04 | (270) $false
% 29.14/8.04 |
% 29.14/8.04 |-The branch is then unsatisfiable
% 29.14/8.04 |-Branch two:
% 29.14/8.04 | (2291) all_0_25_25 = e2 & ~ (all_0_26_26 = e1)
% 29.14/8.04 |
% 29.14/8.04 | Applying alpha-rule on (2291) yields:
% 29.14/8.04 | (2292) all_0_25_25 = e2
% 29.14/8.04 | (2293) ~ (all_0_26_26 = e1)
% 29.14/8.04 |
% 29.14/8.04 | Combining equations (2292,2274) yields a new equation:
% 29.14/8.04 | (622) e2 = e0
% 29.14/8.04 |
% 29.14/8.04 | Simplifying 622 yields:
% 29.14/8.04 | (316) e2 = e0
% 29.14/8.04 |
% 29.14/8.04 | Equations (316) can reduce 57 to:
% 29.14/8.04 | (270) $false
% 29.14/8.04 |
% 29.14/8.04 |-The branch is then unsatisfiable
% 29.14/8.04 |-Branch two:
% 29.14/8.04 | (2296) all_0_28_28 = e0 & ~ (all_0_29_29 = e1)
% 29.14/8.04 |
% 29.14/8.04 | Applying alpha-rule on (2296) yields:
% 29.14/8.04 | (2297) all_0_28_28 = e0
% 29.14/8.04 | (2298) ~ (all_0_29_29 = e1)
% 29.14/8.04 |
% 29.14/8.04 | Combining equations (2297,8712) yields a new equation:
% 29.14/8.04 | (560) e1 = e0
% 29.14/8.04 |
% 29.14/8.04 | Equations (560) can reduce 132 to:
% 29.14/8.04 | (270) $false
% 29.14/8.04 |
% 29.14/8.04 |-The branch is then unsatisfiable
% 29.14/8.04 |-Branch two:
% 29.14/8.04 | (1316) ~ (all_0_42_42 = e3)
% 29.14/8.04 | (3656) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 29.14/8.04 |
% 29.14/8.04 +-Applying beta-rule and splitting (1245), into two cases.
% 29.14/8.04 |-Branch one:
% 29.14/8.04 | (1258) all_0_42_42 = e3
% 29.14/8.04 |
% 29.14/8.04 | Equations (1258) can reduce 1316 to:
% 29.14/8.04 | (270) $false
% 29.14/8.04 |
% 29.14/8.04 |-The branch is then unsatisfiable
% 29.14/8.04 |-Branch two:
% 29.14/8.04 | (1316) ~ (all_0_42_42 = e3)
% 29.14/8.04 | (1317) all_0_42_42 = e4 | all_0_42_42 = e1
% 29.14/8.04 |
% 29.14/8.04 +-Applying beta-rule and splitting (4262), into two cases.
% 29.14/8.04 |-Branch one:
% 29.14/8.04 | (671) all_0_40_40 = e3
% 29.14/8.04 |
% 29.14/8.04 | Combining equations (671,530) yields a new equation:
% 29.14/8.04 | (537) e3 = e1
% 29.14/8.04 |
% 29.14/8.04 | Simplifying 537 yields:
% 29.14/8.04 | (538) e3 = e1
% 29.14/8.04 |
% 29.14/8.04 | Equations (538) can reduce 136 to:
% 29.14/8.04 | (270) $false
% 29.14/8.04 |
% 29.14/8.04 |-The branch is then unsatisfiable
% 29.14/8.04 |-Branch two:
% 29.14/8.04 | (675) ~ (all_0_40_40 = e3)
% 29.14/8.04 | (5254) all_0_41_41 = e3 | all_0_42_42 = e3
% 29.14/8.04 |
% 29.14/8.04 +-Applying beta-rule and splitting (5254), into two cases.
% 29.14/8.04 |-Branch one:
% 29.14/8.04 | (351) all_0_41_41 = e3
% 29.14/8.04 |
% 29.14/8.04 | Combining equations (351,436) yields a new equation:
% 29.14/8.04 | (437) e3 = e2
% 29.14/8.04 |
% 29.14/8.04 | Simplifying 437 yields:
% 29.14/8.04 | (414) e3 = e2
% 29.14/8.04 |
% 29.14/8.04 | Equations (414) can reduce 223 to:
% 29.14/8.04 | (270) $false
% 29.14/8.04 |
% 29.14/8.04 |-The branch is then unsatisfiable
% 29.14/8.04 |-Branch two:
% 29.14/8.04 | (1237) ~ (all_0_41_41 = e3)
% 29.14/8.04 | (1258) all_0_42_42 = e3
% 29.14/8.04 |
% 29.14/8.04 | Equations (1258) can reduce 1316 to:
% 29.14/8.04 | (270) $false
% 29.14/8.04 |
% 29.14/8.04 |-The branch is then unsatisfiable
% 29.14/8.04 |-Branch two:
% 29.14/8.04 | (826) ~ (all_0_52_52 = e3)
% 29.14/8.04 | (848) all_0_52_52 = e1
% 29.14/8.04 |
% 29.14/8.04 | Equations (848) can reduce 642 to:
% 29.14/8.04 | (270) $false
% 29.14/8.04 |
% 29.14/8.04 |-The branch is then unsatisfiable
% 29.14/8.04 |-Branch two:
% 29.14/8.04 | (352) ~ (all_0_45_45 = e4)
% 29.14/8.04 | (517) all_0_46_46 = e4
% 29.14/8.04 |
% 29.14/8.04 | Combining equations (1132,517) yields a new equation:
% 29.14/8.04 | (479) e4 = e0
% 29.14/8.04 |
% 29.14/8.04 | Equations (479) can reduce 6 to:
% 29.14/8.04 | (270) $false
% 29.14/8.04 |
% 29.14/8.04 |-The branch is then unsatisfiable
% 29.14/8.04 |-Branch two:
% 29.14/8.04 | (718) ~ (all_0_58_58 = e3)
% 29.14/8.04 | (4716) all_0_58_58 = e4 | all_0_58_58 = e1
% 29.14/8.05 |
% 29.14/8.05 +-Applying beta-rule and splitting (4716), into two cases.
% 29.14/8.05 |-Branch one:
% 29.14/8.05 | (1001) all_0_58_58 = e1
% 29.14/8.05 |
% 29.14/8.05 | Equations (1001) can reduce 1004 to:
% 29.14/8.05 | (270) $false
% 29.14/8.05 |
% 29.14/8.05 |-The branch is then unsatisfiable
% 29.14/8.05 |-Branch two:
% 29.14/8.05 | (1004) ~ (all_0_58_58 = e1)
% 29.14/8.05 | (600) all_0_58_58 = e4
% 29.14/8.05 |
% 29.14/8.05 | Equations (600) can reduce 278 to:
% 29.14/8.05 | (270) $false
% 29.14/8.05 |
% 29.14/8.05 |-The branch is then unsatisfiable
% 29.14/8.05 |-Branch two:
% 29.14/8.05 | (591) ~ (all_0_39_39 = e4)
% 29.14/8.05 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 29.14/8.05 |
% 29.14/8.05 +-Applying beta-rule and splitting (592), into two cases.
% 29.14/8.05 |-Branch one:
% 29.14/8.05 | (358) all_0_41_41 = e4
% 29.14/8.05 |
% 29.14/8.05 | Combining equations (358,436) yields a new equation:
% 29.14/8.05 | (268) e4 = e2
% 29.14/8.05 |
% 29.14/8.05 | Simplifying 268 yields:
% 29.14/8.05 | (269) e4 = e2
% 29.14/8.05 |
% 29.14/8.05 | Equations (269) can reduce 231 to:
% 29.14/8.05 | (270) $false
% 29.14/8.05 |
% 29.14/8.05 |-The branch is then unsatisfiable
% 29.14/8.05 |-Branch two:
% 29.14/8.05 | (361) ~ (all_0_41_41 = e4)
% 29.14/8.05 | (512) all_0_42_42 = e4
% 29.14/8.05 |
% 29.14/8.05 | Equations (512) can reduce 520 to:
% 29.14/8.05 | (270) $false
% 29.14/8.05 |
% 29.14/8.05 |-The branch is then unsatisfiable
% 29.14/8.05 |-Branch two:
% 29.14/8.05 | (1010) ~ (all_0_46_46 = e0)
% 29.14/8.05 | (3629) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 29.14/8.05 |
% 29.14/8.05 +-Applying beta-rule and splitting (3629), into two cases.
% 29.14/8.05 |-Branch one:
% 29.14/8.05 | (563) all_0_49_49 = e0
% 29.14/8.05 |
% 29.14/8.05 | Combining equations (307,563) yields a new equation:
% 29.14/8.05 | (622) e2 = e0
% 29.14/8.05 |
% 29.14/8.05 | Simplifying 622 yields:
% 29.14/8.05 | (316) e2 = e0
% 29.14/8.05 |
% 29.14/8.05 | Equations (316) can reduce 57 to:
% 29.14/8.05 | (270) $false
% 29.14/8.05 |
% 29.14/8.05 |-The branch is then unsatisfiable
% 29.14/8.05 |-Branch two:
% 29.14/8.05 | (1231) ~ (all_0_49_49 = e0)
% 29.14/8.05 | (3638) all_0_54_54 = e0 | all_0_59_59 = e0
% 29.14/8.05 |
% 29.14/8.05 +-Applying beta-rule and splitting (3638), into two cases.
% 29.14/8.05 |-Branch one:
% 29.14/8.05 | (3084) all_0_54_54 = e0
% 29.14/8.05 |
% 29.14/8.05 | Equations (3084) can reduce 3011 to:
% 29.14/8.05 | (270) $false
% 29.14/8.05 |
% 29.14/8.05 |-The branch is then unsatisfiable
% 29.14/8.05 |-Branch two:
% 29.14/8.05 | (3011) ~ (all_0_54_54 = e0)
% 29.14/8.05 | (2308) all_0_59_59 = e0
% 29.14/8.05 |
% 29.14/8.05 | Combining equations (2308,424) yields a new equation:
% 29.14/8.05 | (560) e1 = e0
% 29.14/8.05 |
% 29.14/8.05 | Equations (560) can reduce 132 to:
% 29.14/8.05 | (270) $false
% 29.14/8.05 |
% 29.14/8.05 |-The branch is then unsatisfiable
% 29.14/8.05 |-Branch two:
% 29.14/8.05 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 29.14/8.05 |
% 29.14/8.05 | Applying alpha-rule on (428) yields:
% 29.14/8.05 | (423) all_0_53_53 = e0
% 29.14/8.05 | (424) all_0_59_59 = e1
% 29.14/8.05 | (431) ~ (all_0_58_58 = e0)
% 29.14/8.05 |
% 29.14/8.05 | Combining equations (423,7736) yields a new equation:
% 29.14/8.05 | (2274) all_0_25_25 = e0
% 29.14/8.05 |
% 29.14/8.05 | Equations (423) can reduce 213 to:
% 29.14/8.05 | (925) ~ (all_0_52_52 = e0)
% 29.14/8.05 |
% 29.14/8.05 | Equations (423) can reduce 252 to:
% 29.14/8.05 | (3010) ~ (all_0_54_54 = e0)
% 29.14/8.05 |
% 29.14/8.05 | Simplifying 3010 yields:
% 29.14/8.05 | (3011) ~ (all_0_54_54 = e0)
% 29.14/8.05 |
% 29.14/8.05 | Equations (423) can reduce 259 to:
% 29.14/8.05 | (566) ~ (e2 = e0)
% 29.14/8.05 |
% 29.14/8.05 | Simplifying 566 yields:
% 29.14/8.05 | (57) ~ (e2 = e0)
% 29.14/8.05 |
% 29.14/8.05 +-Applying beta-rule and splitting (9), into two cases.
% 29.14/8.05 |-Branch one:
% 29.14/8.05 | (621) all_0_44_44 = e0
% 29.14/8.05 |
% 29.14/8.05 | Combining equations (370,621) yields a new equation:
% 29.14/8.05 | (622) e2 = e0
% 29.14/8.05 |
% 29.14/8.05 | Simplifying 622 yields:
% 29.14/8.05 | (316) e2 = e0
% 29.14/8.05 |
% 29.14/8.05 | Equations (316) can reduce 57 to:
% 29.14/8.05 | (270) $false
% 29.14/8.05 |
% 29.14/8.05 |-The branch is then unsatisfiable
% 29.14/8.05 |-Branch two:
% 29.14/8.05 | (625) ~ (all_0_44_44 = e0)
% 29.14/8.05 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 29.14/8.05 |
% 29.14/8.05 +-Applying beta-rule and splitting (626), into two cases.
% 29.14/8.05 |-Branch one:
% 29.14/8.05 | (827) all_0_52_52 = e0
% 29.14/8.05 |
% 29.14/8.05 | Equations (827) can reduce 925 to:
% 29.14/8.05 | (270) $false
% 29.14/8.05 |
% 29.14/8.05 |-The branch is then unsatisfiable
% 29.14/8.05 |-Branch two:
% 29.14/8.05 | (925) ~ (all_0_52_52 = e0)
% 29.14/8.05 | (2258) all_0_57_57 = e0
% 29.14/8.05 |
% 29.14/8.05 | Equations (2258) can reduce 235 to:
% 29.14/8.05 | (925) ~ (all_0_52_52 = e0)
% 29.14/8.05 |
% 29.14/8.05 | Equations (2258) can reduce 37 to:
% 29.14/8.05 | (3530) ~ (all_0_58_58 = e0)
% 29.14/8.05 |
% 29.14/8.05 | Simplifying 3530 yields:
% 29.14/8.05 | (431) ~ (all_0_58_58 = e0)
% 29.14/8.05 |
% 29.14/8.05 | Equations (2258) can reduce 143 to:
% 29.14/8.05 | (456) ~ (e4 = e0)
% 29.14/8.05 |
% 29.14/8.05 | Simplifying 456 yields:
% 29.14/8.05 | (6) ~ (e4 = e0)
% 29.14/8.05 |
% 29.14/8.05 | Equations (2258) can reduce 335 to:
% 29.14/8.05 | (566) ~ (e2 = e0)
% 29.14/8.05 |
% 29.14/8.05 | Simplifying 566 yields:
% 29.14/8.05 | (57) ~ (e2 = e0)
% 29.14/8.05 |
% 29.14/8.05 | Equations (2258) can reduce 644 to:
% 29.14/8.05 | (568) ~ (e1 = e0)
% 29.14/8.05 |
% 29.14/8.05 | Simplifying 568 yields:
% 29.14/8.05 | (132) ~ (e1 = e0)
% 29.14/8.05 |
% 29.14/8.05 +-Applying beta-rule and splitting (221), into two cases.
% 29.14/8.05 |-Branch one:
% 29.14/8.05 | (1132) all_0_46_46 = e0
% 29.14/8.05 |
% 29.14/8.05 | Equations (1132) can reduce 1436 to:
% 29.14/8.05 | (566) ~ (e2 = e0)
% 29.14/8.05 |
% 29.14/8.05 | Simplifying 566 yields:
% 29.14/8.05 | (57) ~ (e2 = e0)
% 29.14/8.05 |
% 29.14/8.05 | Equations (1132) can reduce 106 to:
% 29.14/8.05 | (568) ~ (e1 = e0)
% 29.14/8.05 |
% 29.14/8.05 | Simplifying 568 yields:
% 29.14/8.05 | (132) ~ (e1 = e0)
% 29.14/8.05 |
% 29.14/8.05 +-Applying beta-rule and splitting (204), into two cases.
% 29.14/8.05 |-Branch one:
% 29.14/8.05 | (396) all_0_58_58 = e2
% 29.14/8.05 |
% 29.14/8.05 | Equations (396) can reduce 376 to:
% 29.14/8.05 | (270) $false
% 29.14/8.05 |
% 29.14/8.05 |-The branch is then unsatisfiable
% 29.14/8.05 |-Branch two:
% 29.14/8.05 | (376) ~ (all_0_58_58 = e2)
% 29.14/8.05 | (3890) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1 | all_0_58_58 = e0
% 29.14/8.05 |
% 29.14/8.05 +-Applying beta-rule and splitting (3890), into two cases.
% 29.14/8.05 |-Branch one:
% 29.14/8.05 | (585) all_0_58_58 = e0
% 29.14/8.05 |
% 29.14/8.05 | Equations (585) can reduce 431 to:
% 29.14/8.05 | (270) $false
% 29.14/8.05 |
% 29.14/8.05 |-The branch is then unsatisfiable
% 29.14/8.05 |-Branch two:
% 29.14/8.05 | (431) ~ (all_0_58_58 = e0)
% 29.14/8.05 | (4709) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1
% 29.14/8.05 |
% 29.14/8.05 +-Applying beta-rule and splitting (189), into two cases.
% 29.14/8.05 |-Branch one:
% 29.14/8.05 | (267) all_0_50_50 = e4
% 29.14/8.05 |
% 29.14/8.05 | Combining equations (253,267) yields a new equation:
% 29.14/8.05 | (269) e4 = e2
% 29.14/8.05 |
% 29.14/8.05 | Equations (269) can reduce 231 to:
% 29.14/8.05 | (270) $false
% 29.14/8.05 |
% 29.14/8.05 |-The branch is then unsatisfiable
% 29.14/8.05 |-Branch two:
% 29.14/8.05 | (271) ~ (all_0_50_50 = e4)
% 29.14/8.05 | (1466) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 29.14/8.05 |
% 29.14/8.05 +-Applying beta-rule and splitting (1466), into two cases.
% 29.14/8.05 |-Branch one:
% 29.14/8.05 | (1467) all_0_51_51 = e4
% 29.14/8.05 |
% 29.14/8.05 | Combining equations (820,1467) yields a new equation:
% 29.14/8.05 | (526) e4 = e1
% 29.14/8.05 |
% 29.14/8.05 | Equations (526) can reduce 251 to:
% 29.14/8.05 | (270) $false
% 29.14/8.05 |
% 29.14/8.05 |-The branch is then unsatisfiable
% 29.14/8.05 |-Branch two:
% 29.14/8.05 | (697) ~ (all_0_51_51 = e4)
% 29.14/8.05 | (1470) all_0_53_53 = e4 | all_0_54_54 = e4
% 29.14/8.05 |
% 29.14/8.05 +-Applying beta-rule and splitting (1470), into two cases.
% 29.14/8.05 |-Branch one:
% 29.14/8.05 | (367) all_0_53_53 = e4
% 29.14/8.05 |
% 29.14/8.05 | Combining equations (423,367) yields a new equation:
% 29.14/8.05 | (479) e4 = e0
% 29.14/8.05 |
% 29.14/8.05 | Equations (479) can reduce 6 to:
% 29.14/8.05 | (270) $false
% 29.14/8.05 |
% 29.14/8.05 |-The branch is then unsatisfiable
% 29.14/8.05 |-Branch two:
% 29.14/8.05 | (599) ~ (all_0_53_53 = e4)
% 29.14/8.05 | (817) all_0_54_54 = e4
% 29.14/8.05 |
% 29.14/8.05 | Equations (817) can reduce 191 to:
% 29.14/8.05 | (520) ~ (all_0_42_42 = e4)
% 29.14/8.05 |
% 29.14/8.05 | Equations (817) can reduce 261 to:
% 29.14/8.05 | (231) ~ (e4 = e2)
% 29.14/8.05 |
% 29.14/8.05 | From (817) and (29) follows:
% 29.14/8.05 | (2271) op(e1, e4) = all_0_37_37
% 29.14/8.05 |
% 29.14/8.05 +-Applying beta-rule and splitting (222), into two cases.
% 29.14/8.05 |-Branch one:
% 29.14/8.05 | (522) all_0_39_39 = e4
% 29.14/8.05 |
% 29.14/8.05 | Equations (522) can reduce 184 to:
% 29.14/8.05 | (692) ~ (all_0_42_42 = e4)
% 29.14/8.05 |
% 29.14/8.05 | Simplifying 692 yields:
% 29.14/8.05 | (520) ~ (all_0_42_42 = e4)
% 29.14/8.05 |
% 29.14/8.05 | Equations (522) can reduce 167 to:
% 29.14/8.05 | (694) ~ (all_0_43_43 = e4)
% 29.14/8.05 |
% 29.14/8.05 | Simplifying 694 yields:
% 29.14/8.05 | (510) ~ (all_0_43_43 = e4)
% 29.14/8.05 |
% 29.14/8.05 | Equations (522) can reduce 101 to:
% 29.14/8.05 | (6) ~ (e4 = e0)
% 29.14/8.05 |
% 29.29/8.05 +-Applying beta-rule and splitting (16), into two cases.
% 29.29/8.05 |-Branch one:
% 29.29/8.05 | (698) all_0_42_42 = e2
% 29.29/8.05 |
% 29.29/8.05 | Equations (698) can reduce 498 to:
% 29.29/8.05 | (270) $false
% 29.29/8.05 |
% 29.29/8.05 |-The branch is then unsatisfiable
% 29.29/8.05 |-Branch two:
% 29.29/8.05 | (498) ~ (all_0_42_42 = e2)
% 29.29/8.05 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 29.29/8.05 |
% 29.29/8.05 +-Applying beta-rule and splitting (90), into two cases.
% 29.29/8.05 |-Branch one:
% 29.29/8.05 | (685) all_0_52_52 = e2
% 29.29/8.05 |
% 29.29/8.05 | Equations (685) can reduce 257 to:
% 29.29/8.05 | (270) $false
% 29.29/8.05 |
% 29.29/8.05 |-The branch is then unsatisfiable
% 29.29/8.05 |-Branch two:
% 29.29/8.05 | (257) ~ (all_0_52_52 = e2)
% 29.29/8.05 | (688) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 29.29/8.05 |
% 29.29/8.05 +-Applying beta-rule and splitting (4709), into two cases.
% 29.29/8.05 |-Branch one:
% 29.29/8.05 | (4713) all_0_58_58 = e3
% 29.29/8.05 |
% 29.29/8.05 | Equations (4713) can reduce 278 to:
% 29.29/8.05 | (719) ~ (e4 = e3)
% 29.29/8.05 |
% 29.29/8.05 | Simplifying 719 yields:
% 29.29/8.05 | (34) ~ (e4 = e3)
% 29.29/8.05 |
% 29.29/8.05 | From (4713) and (63) follows:
% 29.29/8.05 | (8676) op(e1, e3) = all_0_28_28
% 29.29/8.05 |
% 29.29/8.05 +-Applying beta-rule and splitting (178), into two cases.
% 29.29/8.05 |-Branch one:
% 29.29/8.05 | (751) all_0_39_39 = e3
% 29.29/8.05 |
% 29.29/8.05 | Combining equations (751,522) yields a new equation:
% 29.29/8.05 | (359) e4 = e3
% 29.29/8.05 |
% 29.29/8.05 | Equations (359) can reduce 34 to:
% 29.29/8.05 | (270) $false
% 29.29/8.05 |
% 29.29/8.05 |-The branch is then unsatisfiable
% 29.29/8.05 |-Branch two:
% 29.29/8.05 | (755) ~ (all_0_39_39 = e3)
% 29.29/8.05 | (756) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 29.29/8.05 |
% 29.29/8.05 | Equations (522) can reduce 755 to:
% 29.29/8.05 | (34) ~ (e4 = e3)
% 29.29/8.05 |
% 29.29/8.05 +-Applying beta-rule and splitting (78), into two cases.
% 29.29/8.05 |-Branch one:
% 29.29/8.05 | (751) all_0_39_39 = e3
% 29.29/8.05 |
% 29.29/8.05 | Combining equations (751,522) yields a new equation:
% 29.29/8.05 | (359) e4 = e3
% 29.29/8.05 |
% 29.29/8.05 | Equations (359) can reduce 34 to:
% 29.29/8.05 | (270) $false
% 29.29/8.05 |
% 29.29/8.05 |-The branch is then unsatisfiable
% 29.29/8.05 |-Branch two:
% 29.29/8.05 | (755) ~ (all_0_39_39 = e3)
% 29.29/8.05 | (4262) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 29.29/8.05 |
% 29.29/8.05 +-Applying beta-rule and splitting (44), into two cases.
% 29.29/8.05 |-Branch one:
% 29.29/8.05 | (502) all_0_43_43 = e4
% 29.29/8.05 |
% 29.29/8.05 | Equations (502) can reduce 510 to:
% 29.29/8.05 | (270) $false
% 29.29/8.05 |
% 29.29/8.05 |-The branch is then unsatisfiable
% 29.29/8.05 |-Branch two:
% 29.29/8.05 | (510) ~ (all_0_43_43 = e4)
% 29.29/8.05 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 29.29/8.05 |
% 29.29/8.05 +-Applying beta-rule and splitting (688), into two cases.
% 29.29/8.05 |-Branch one:
% 29.29/8.05 | (827) all_0_52_52 = e0
% 29.29/8.05 |
% 29.29/8.05 | Equations (827) can reduce 925 to:
% 29.29/8.05 | (270) $false
% 29.29/8.05 |
% 29.29/8.05 |-The branch is then unsatisfiable
% 29.29/8.05 |-Branch two:
% 29.29/8.05 | (925) ~ (all_0_52_52 = e0)
% 29.29/8.05 | (926) all_0_52_52 = e3 | all_0_52_52 = e1
% 29.29/8.05 |
% 29.29/8.05 +-Applying beta-rule and splitting (511), into two cases.
% 29.29/8.05 |-Branch one:
% 29.29/8.05 | (363) all_0_45_45 = e4
% 29.29/8.05 |
% 29.29/8.05 | From (363) and (142) follows:
% 29.29/8.06 | (2221) op(e1, e4) = all_0_23_23
% 29.29/8.06 |
% 29.29/8.06 +-Applying beta-rule and splitting (926), into two cases.
% 29.29/8.06 |-Branch one:
% 29.29/8.06 | (864) all_0_52_52 = e3
% 29.29/8.06 |
% 29.29/8.06 | Combining equations (864,8397) yields a new equation:
% 29.29/8.06 | (6797) all_0_21_21 = e3
% 29.29/8.06 |
% 29.29/8.06 | Equations (864) can reduce 257 to:
% 29.29/8.06 | (223) ~ (e3 = e2)
% 29.29/8.06 |
% 29.29/8.06 | Equations (864) can reduce 642 to:
% 29.29/8.06 | (136) ~ (e3 = e1)
% 29.29/8.06 |
% 29.29/8.06 | From (864) and (195) follows:
% 29.29/8.06 | (8702) op(e1, e3) = all_0_18_18
% 29.29/8.06 |
% 29.29/8.06 +-Applying beta-rule and splitting (95), into two cases.
% 29.29/8.06 |-Branch one:
% 29.29/8.06 | (1258) all_0_42_42 = e3
% 29.29/8.06 |
% 29.29/8.06 | Equations (1258) can reduce 520 to:
% 29.29/8.06 | (719) ~ (e4 = e3)
% 29.29/8.06 |
% 29.29/8.06 | Simplifying 719 yields:
% 29.29/8.06 | (34) ~ (e4 = e3)
% 29.29/8.06 |
% 29.29/8.06 | Equations (1258) can reduce 498 to:
% 29.29/8.06 | (223) ~ (e3 = e2)
% 29.29/8.06 |
% 29.29/8.06 | Instantiating formula (201) with e1, e4, all_0_23_23, e2 and discharging atoms op(e1, e4) = all_0_23_23, op(e1, e4) = e2, yields:
% 29.29/8.06 | (2272) all_0_23_23 = e2
% 29.29/8.06 |
% 29.29/8.06 | Instantiating formula (201) with e1, e4, all_0_37_37, all_0_23_23 and discharging atoms op(e1, e4) = all_0_23_23, op(e1, e4) = all_0_37_37, yields:
% 29.29/8.06 | (2273) all_0_23_23 = all_0_37_37
% 29.29/8.06 |
% 29.29/8.06 | Instantiating formula (201) with e1, e3, all_0_28_28, all_0_18_18 and discharging atoms op(e1, e3) = all_0_18_18, op(e1, e3) = all_0_28_28, yields:
% 29.29/8.06 | (8709) all_0_18_18 = all_0_28_28
% 29.29/8.06 |
% 29.29/8.06 | Instantiating formula (201) with e1, e3, e1, all_0_18_18 and discharging atoms op(e1, e3) = all_0_18_18, op(e1, e3) = e1, yields:
% 29.29/8.06 | (8710) all_0_18_18 = e1
% 29.29/8.06 |
% 29.29/8.06 | Combining equations (8709,8710) yields a new equation:
% 29.29/8.06 | (8711) all_0_28_28 = e1
% 29.29/8.06 |
% 29.29/8.06 | Simplifying 8711 yields:
% 29.29/8.06 | (8712) all_0_28_28 = e1
% 29.29/8.06 |
% 29.29/8.06 | Combining equations (2272,2273) yields a new equation:
% 29.29/8.06 | (2275) all_0_37_37 = e2
% 29.29/8.06 |
% 29.29/8.06 | Combining equations (2275,2273) yields a new equation:
% 29.29/8.06 | (2272) all_0_23_23 = e2
% 29.29/8.06 |
% 29.29/8.06 +-Applying beta-rule and splitting (14), into two cases.
% 29.29/8.06 |-Branch one:
% 29.29/8.06 | (2277) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1))
% 29.29/8.06 |
% 29.29/8.06 +-Applying beta-rule and splitting (2277), into two cases.
% 29.29/8.06 |-Branch one:
% 29.29/8.06 | (2278) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1))
% 29.29/8.06 |
% 29.29/8.06 +-Applying beta-rule and splitting (2278), into two cases.
% 29.29/8.06 |-Branch one:
% 29.29/8.06 | (2279) all_0_21_21 = e4 & ~ (all_0_22_22 = e1)
% 29.29/8.06 |
% 29.29/8.06 | Applying alpha-rule on (2279) yields:
% 29.29/8.06 | (2280) all_0_21_21 = e4
% 29.29/8.06 | (2281) ~ (all_0_22_22 = e1)
% 29.29/8.06 |
% 29.29/8.06 | Combining equations (2280,6797) yields a new equation:
% 29.29/8.06 | (660) e4 = e3
% 29.29/8.06 |
% 29.29/8.06 | Simplifying 660 yields:
% 29.29/8.06 | (359) e4 = e3
% 29.29/8.06 |
% 29.29/8.06 | Equations (359) can reduce 34 to:
% 29.29/8.06 | (270) $false
% 29.29/8.06 |
% 29.29/8.06 |-The branch is then unsatisfiable
% 29.29/8.06 |-Branch two:
% 29.29/8.06 | (2285) all_0_23_23 = e3 & ~ (all_0_24_24 = e1)
% 29.29/8.06 |
% 29.29/8.06 | Applying alpha-rule on (2285) yields:
% 29.29/8.06 | (2286) all_0_23_23 = e3
% 29.29/8.06 | (2287) ~ (all_0_24_24 = e1)
% 29.29/8.06 |
% 29.29/8.06 | Combining equations (2286,2272) yields a new equation:
% 29.29/8.06 | (437) e3 = e2
% 29.29/8.06 |
% 29.29/8.06 | Simplifying 437 yields:
% 29.29/8.06 | (414) e3 = e2
% 29.29/8.06 |
% 29.29/8.06 | Equations (414) can reduce 223 to:
% 29.29/8.06 | (270) $false
% 29.29/8.06 |
% 29.29/8.06 |-The branch is then unsatisfiable
% 29.29/8.06 |-Branch two:
% 29.29/8.06 | (2291) all_0_25_25 = e2 & ~ (all_0_26_26 = e1)
% 29.29/8.06 |
% 29.29/8.06 | Applying alpha-rule on (2291) yields:
% 29.29/8.06 | (2292) all_0_25_25 = e2
% 29.29/8.06 | (2293) ~ (all_0_26_26 = e1)
% 29.29/8.06 |
% 29.29/8.06 | Combining equations (2292,2274) yields a new equation:
% 29.29/8.06 | (622) e2 = e0
% 29.29/8.06 |
% 29.29/8.06 | Simplifying 622 yields:
% 29.29/8.06 | (316) e2 = e0
% 29.29/8.06 |
% 29.29/8.06 | Equations (316) can reduce 57 to:
% 29.29/8.06 | (270) $false
% 29.29/8.06 |
% 29.29/8.06 |-The branch is then unsatisfiable
% 29.29/8.06 |-Branch two:
% 29.29/8.06 | (2296) all_0_28_28 = e0 & ~ (all_0_29_29 = e1)
% 29.29/8.06 |
% 29.29/8.06 | Applying alpha-rule on (2296) yields:
% 29.29/8.06 | (2297) all_0_28_28 = e0
% 29.29/8.06 | (2298) ~ (all_0_29_29 = e1)
% 29.29/8.06 |
% 29.29/8.06 | Combining equations (2297,8712) yields a new equation:
% 29.29/8.06 | (560) e1 = e0
% 29.29/8.06 |
% 29.29/8.06 | Equations (560) can reduce 132 to:
% 29.29/8.06 | (270) $false
% 29.29/8.06 |
% 29.29/8.06 |-The branch is then unsatisfiable
% 29.29/8.06 |-Branch two:
% 29.29/8.06 | (1316) ~ (all_0_42_42 = e3)
% 29.29/8.06 | (3656) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 29.29/8.06 |
% 29.29/8.06 +-Applying beta-rule and splitting (1245), into two cases.
% 29.29/8.06 |-Branch one:
% 29.29/8.06 | (1258) all_0_42_42 = e3
% 29.29/8.06 |
% 29.29/8.06 | Equations (1258) can reduce 1316 to:
% 29.29/8.06 | (270) $false
% 29.29/8.06 |
% 29.29/8.06 |-The branch is then unsatisfiable
% 29.29/8.06 |-Branch two:
% 29.29/8.06 | (1316) ~ (all_0_42_42 = e3)
% 29.29/8.06 | (1317) all_0_42_42 = e4 | all_0_42_42 = e1
% 29.29/8.06 |
% 29.29/8.06 +-Applying beta-rule and splitting (4262), into two cases.
% 29.29/8.06 |-Branch one:
% 29.29/8.06 | (671) all_0_40_40 = e3
% 29.29/8.06 |
% 29.29/8.06 | Combining equations (671,530) yields a new equation:
% 29.29/8.06 | (537) e3 = e1
% 29.29/8.06 |
% 29.29/8.06 | Simplifying 537 yields:
% 29.29/8.06 | (538) e3 = e1
% 29.29/8.06 |
% 29.29/8.06 | Equations (538) can reduce 136 to:
% 29.29/8.06 | (270) $false
% 29.29/8.06 |
% 29.29/8.06 |-The branch is then unsatisfiable
% 29.29/8.06 |-Branch two:
% 29.29/8.06 | (675) ~ (all_0_40_40 = e3)
% 29.29/8.06 | (5254) all_0_41_41 = e3 | all_0_42_42 = e3
% 29.29/8.06 |
% 29.29/8.06 +-Applying beta-rule and splitting (5254), into two cases.
% 29.29/8.06 |-Branch one:
% 29.29/8.06 | (351) all_0_41_41 = e3
% 29.29/8.06 |
% 29.29/8.06 | Combining equations (351,436) yields a new equation:
% 29.29/8.06 | (437) e3 = e2
% 29.29/8.06 |
% 29.29/8.06 | Simplifying 437 yields:
% 29.29/8.06 | (414) e3 = e2
% 29.29/8.06 |
% 29.29/8.06 | Equations (414) can reduce 223 to:
% 29.29/8.06 | (270) $false
% 29.29/8.06 |
% 29.29/8.06 |-The branch is then unsatisfiable
% 29.29/8.06 |-Branch two:
% 29.29/8.06 | (1237) ~ (all_0_41_41 = e3)
% 29.29/8.06 | (1258) all_0_42_42 = e3
% 29.29/8.06 |
% 29.29/8.06 | Equations (1258) can reduce 1316 to:
% 29.29/8.06 | (270) $false
% 29.29/8.06 |
% 29.29/8.06 |-The branch is then unsatisfiable
% 29.29/8.06 |-Branch two:
% 29.29/8.06 | (826) ~ (all_0_52_52 = e3)
% 29.29/8.06 | (848) all_0_52_52 = e1
% 29.29/8.06 |
% 29.29/8.06 | Equations (848) can reduce 642 to:
% 29.29/8.06 | (270) $false
% 29.29/8.06 |
% 29.29/8.06 |-The branch is then unsatisfiable
% 29.29/8.06 |-Branch two:
% 29.29/8.06 | (352) ~ (all_0_45_45 = e4)
% 29.29/8.06 | (517) all_0_46_46 = e4
% 29.29/8.06 |
% 29.29/8.06 | Combining equations (1132,517) yields a new equation:
% 29.29/8.06 | (479) e4 = e0
% 29.29/8.06 |
% 29.29/8.06 | Equations (479) can reduce 6 to:
% 29.29/8.06 | (270) $false
% 29.29/8.06 |
% 29.29/8.06 |-The branch is then unsatisfiable
% 29.29/8.06 |-Branch two:
% 29.29/8.06 | (718) ~ (all_0_58_58 = e3)
% 29.29/8.06 | (4716) all_0_58_58 = e4 | all_0_58_58 = e1
% 29.29/8.06 |
% 29.29/8.06 +-Applying beta-rule and splitting (4716), into two cases.
% 29.29/8.06 |-Branch one:
% 29.29/8.06 | (1001) all_0_58_58 = e1
% 29.29/8.06 |
% 29.29/8.06 | Equations (1001) can reduce 1004 to:
% 29.29/8.06 | (270) $false
% 29.29/8.06 |
% 29.29/8.06 |-The branch is then unsatisfiable
% 29.29/8.06 |-Branch two:
% 29.29/8.06 | (1004) ~ (all_0_58_58 = e1)
% 29.29/8.06 | (600) all_0_58_58 = e4
% 29.29/8.06 |
% 29.29/8.06 | Equations (600) can reduce 278 to:
% 29.29/8.06 | (270) $false
% 29.29/8.06 |
% 29.29/8.06 |-The branch is then unsatisfiable
% 29.29/8.07 |-Branch two:
% 29.29/8.07 | (591) ~ (all_0_39_39 = e4)
% 29.29/8.07 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 29.29/8.07 |
% 29.29/8.07 +-Applying beta-rule and splitting (592), into two cases.
% 29.29/8.07 |-Branch one:
% 29.29/8.07 | (358) all_0_41_41 = e4
% 29.29/8.07 |
% 29.29/8.07 | Combining equations (358,436) yields a new equation:
% 29.29/8.07 | (268) e4 = e2
% 29.29/8.07 |
% 29.29/8.07 | Simplifying 268 yields:
% 29.29/8.07 | (269) e4 = e2
% 29.29/8.07 |
% 29.29/8.07 | Equations (269) can reduce 231 to:
% 29.29/8.07 | (270) $false
% 29.29/8.07 |
% 29.29/8.07 |-The branch is then unsatisfiable
% 29.29/8.07 |-Branch two:
% 29.29/8.07 | (361) ~ (all_0_41_41 = e4)
% 29.29/8.07 | (512) all_0_42_42 = e4
% 29.29/8.07 |
% 29.29/8.07 | Equations (512) can reduce 520 to:
% 29.29/8.07 | (270) $false
% 29.29/8.07 |
% 29.29/8.07 |-The branch is then unsatisfiable
% 29.29/8.07 |-Branch two:
% 29.29/8.07 | (1010) ~ (all_0_46_46 = e0)
% 29.29/8.07 | (3629) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 29.29/8.07 |
% 29.29/8.07 +-Applying beta-rule and splitting (3629), into two cases.
% 29.29/8.07 |-Branch one:
% 29.29/8.07 | (563) all_0_49_49 = e0
% 29.29/8.07 |
% 29.29/8.07 | Combining equations (307,563) yields a new equation:
% 29.29/8.07 | (622) e2 = e0
% 29.29/8.07 |
% 29.29/8.07 | Simplifying 622 yields:
% 29.29/8.07 | (316) e2 = e0
% 29.29/8.07 |
% 29.29/8.07 | Equations (316) can reduce 57 to:
% 29.29/8.07 | (270) $false
% 29.29/8.07 |
% 29.29/8.07 |-The branch is then unsatisfiable
% 29.29/8.07 |-Branch two:
% 29.29/8.07 | (1231) ~ (all_0_49_49 = e0)
% 29.29/8.07 | (3638) all_0_54_54 = e0 | all_0_59_59 = e0
% 29.29/8.07 |
% 29.29/8.07 +-Applying beta-rule and splitting (3638), into two cases.
% 29.29/8.07 |-Branch one:
% 29.29/8.07 | (3084) all_0_54_54 = e0
% 29.29/8.07 |
% 29.29/8.07 | Equations (3084) can reduce 3011 to:
% 29.29/8.07 | (270) $false
% 29.29/8.07 |
% 29.29/8.07 |-The branch is then unsatisfiable
% 29.29/8.07 |-Branch two:
% 29.29/8.07 | (3011) ~ (all_0_54_54 = e0)
% 29.29/8.07 | (2308) all_0_59_59 = e0
% 29.29/8.07 |
% 29.29/8.07 | Combining equations (2308,424) yields a new equation:
% 29.29/8.07 | (560) e1 = e0
% 29.29/8.07 |
% 29.29/8.07 | Equations (560) can reduce 132 to:
% 29.29/8.07 | (270) $false
% 29.29/8.07 |
% 29.29/8.07 |-The branch is then unsatisfiable
% 29.29/8.07 |-Branch two:
% 29.29/8.07 | (748) ~ (all_0_51_51 = e1)
% 29.29/8.07 | (747) all_0_56_56 = e1
% 29.29/8.07 |
% 29.29/8.07 | Combining equations (388,747) yields a new equation:
% 29.29/8.07 | (531) e2 = e1
% 29.29/8.07 |
% 29.29/8.07 | Simplifying 531 yields:
% 29.29/8.07 | (322) e2 = e1
% 29.29/8.07 |
% 29.29/8.07 | Equations (322) can reduce 141 to:
% 29.29/8.07 | (270) $false
% 29.29/8.07 |
% 29.29/8.07 |-The branch is then unsatisfiable
% 29.29/8.07 |-Branch two:
% 29.29/8.07 | (300) ~ (all_0_56_56 = e2)
% 29.29/8.07 | (391) all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 29.29/8.07 |
% 29.29/8.07 +-Applying beta-rule and splitting (391), into two cases.
% 29.29/8.07 |-Branch one:
% 29.29/8.07 | (392) all_0_57_57 = e2
% 29.29/8.07 |
% 29.29/8.07 | Equations (392) can reduce 335 to:
% 29.29/8.07 | (270) $false
% 29.29/8.07 |
% 29.29/8.07 |-The branch is then unsatisfiable
% 29.29/8.07 |-Branch two:
% 29.29/8.07 | (335) ~ (all_0_57_57 = e2)
% 29.29/8.07 | (395) all_0_58_58 = e2 | all_0_59_59 = e2
% 29.29/8.07 |
% 29.29/8.07 +-Applying beta-rule and splitting (395), into two cases.
% 29.29/8.07 |-Branch one:
% 29.29/8.07 | (396) all_0_58_58 = e2
% 29.29/8.07 |
% 29.29/8.07 | Equations (396) can reduce 376 to:
% 29.29/8.07 | (270) $false
% 29.29/8.07 |
% 29.29/8.07 |-The branch is then unsatisfiable
% 29.29/8.07 |-Branch two:
% 29.29/8.07 | (376) ~ (all_0_58_58 = e2)
% 29.29/8.07 | (399) all_0_59_59 = e2
% 29.29/8.07 |
% 29.29/8.07 | Equations (399) can reduce 701 to:
% 29.29/8.07 | (270) $false
% 29.29/8.07 |
% 29.29/8.07 |-The branch is then unsatisfiable
% 29.29/8.07 |-Branch two:
% 29.29/8.07 | (333) ~ (all_0_44_44 = e2)
% 29.29/8.07 | (493) all_0_45_45 = e2 | all_0_46_46 = e2
% 29.29/8.07 |
% 29.29/8.07 +-Applying beta-rule and splitting (493), into two cases.
% 29.29/8.07 |-Branch one:
% 29.29/8.07 | (374) all_0_45_45 = e2
% 29.29/8.07 |
% 29.29/8.07 | Equations (374) can reduce 434 to:
% 29.29/8.07 | (270) $false
% 29.29/8.07 |
% 29.29/8.07 |-The branch is then unsatisfiable
% 29.29/8.07 |-Branch two:
% 29.29/8.07 | (434) ~ (all_0_45_45 = e2)
% 29.29/8.07 | (497) all_0_46_46 = e2
% 29.29/8.07 |
% 29.29/8.07 | Equations (497) can reduce 1436 to:
% 29.29/8.07 | (270) $false
% 29.29/8.07 |
% 29.29/8.07 |-The branch is then unsatisfiable
% 29.29/8.07 |-Branch two:
% 29.29/8.07 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 29.29/8.07 |
% 29.29/8.07 | Applying alpha-rule on (346) yields:
% 29.29/8.07 | (347) all_0_2_2 = e0
% 29.29/8.07 | (348) ~ (all_0_3_3 = e4)
% 29.29/8.07 |
% 29.29/8.07 | Equations (287) can reduce 348 to:
% 29.29/8.07 | (270) $false
% 29.29/8.07 |
% 29.29/8.07 |-The branch is then unsatisfiable
% 29.29/8.07 |-Branch two:
% 29.29/8.07 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 29.29/8.07 |
% 29.29/8.07 | Applying alpha-rule on (350) yields:
% 29.29/8.07 | (351) all_0_41_41 = e3
% 29.29/8.07 | (352) ~ (all_0_45_45 = e4)
% 29.29/8.07 |
% 29.29/8.07 | Combining equations (351,436) yields a new equation:
% 29.29/8.07 | (437) e3 = e2
% 29.29/8.07 |
% 29.29/8.07 | Simplifying 437 yields:
% 29.29/8.07 | (414) e3 = e2
% 29.29/8.07 |
% 29.29/8.07 | Equations (414) can reduce 223 to:
% 29.29/8.07 | (270) $false
% 29.29/8.07 |
% 29.29/8.07 |-The branch is then unsatisfiable
% 29.29/8.07 |-Branch two:
% 29.29/8.07 | (331) ~ (all_0_41_41 = e2)
% 29.29/8.07 | (698) all_0_42_42 = e2
% 29.29/8.07 |
% 29.29/8.07 | Equations (698) can reduce 498 to:
% 29.29/8.07 | (270) $false
% 29.29/8.07 |
% 29.29/8.07 |-The branch is then unsatisfiable
% 29.29/8.07 |-Branch two:
% 29.29/8.07 | (318) ~ (all_0_47_47 = e0)
% 29.29/8.07 | (321) all_0_47_47 = e1
% 29.29/8.07 |
% 29.29/8.07 | Equations (321) can reduce 324 to:
% 29.29/8.07 | (270) $false
% 29.29/8.07 |
% 29.29/8.07 |-The branch is then unsatisfiable
% 29.29/8.07 |-Branch two:
% 29.29/8.07 | (9032) ~ (all_0_50_50 = e2)
% 29.29/8.07 | (382) all_0_55_55 = e2
% 29.29/8.07 |
% 29.29/8.07 | Equations (382) can reduce 54 to:
% 29.29/8.07 | (9032) ~ (all_0_50_50 = e2)
% 29.29/8.07 |
% 29.29/8.07 | Equations (382) can reduce 43 to:
% 29.29/8.07 | (299) ~ (all_0_56_56 = e2)
% 29.29/8.07 |
% 29.29/8.07 | Simplifying 299 yields:
% 29.29/8.07 | (300) ~ (all_0_56_56 = e2)
% 29.29/8.07 |
% 29.29/8.07 | Equations (382) can reduce 11 to:
% 29.29/8.07 | (334) ~ (all_0_57_57 = e2)
% 29.29/8.07 |
% 29.29/8.07 | Simplifying 334 yields:
% 29.29/8.07 | (335) ~ (all_0_57_57 = e2)
% 29.29/8.07 |
% 29.29/8.07 | Equations (382) can reduce 73 to:
% 29.29/8.07 | (375) ~ (all_0_58_58 = e2)
% 29.29/8.07 |
% 29.29/8.07 | Simplifying 375 yields:
% 29.29/8.07 | (376) ~ (all_0_58_58 = e2)
% 29.29/8.07 |
% 29.29/8.07 | Equations (382) can reduce 144 to:
% 29.29/8.07 | (700) ~ (all_0_59_59 = e2)
% 29.29/8.07 |
% 29.29/8.07 | Simplifying 700 yields:
% 29.29/8.07 | (701) ~ (all_0_59_59 = e2)
% 29.29/8.07 |
% 29.29/8.07 | Equations (382) can reduce 146 to:
% 29.29/8.07 | (141) ~ (e2 = e1)
% 29.29/8.07 |
% 29.29/8.07 | Equations (382) can reduce 175 to:
% 29.29/8.07 | (57) ~ (e2 = e0)
% 29.29/8.07 |
% 29.29/8.07 | From (382) and (28) follows:
% 29.29/8.07 | (9045) op(e4, e2) = all_0_2_2
% 29.29/8.07 |
% 29.29/8.07 | From (382) and (119) follows:
% 29.29/8.07 | (9046) op(e0, e2) = all_0_3_3
% 29.29/8.07 |
% 29.29/8.07 | From (382) and (181) follows:
% 29.29/8.07 | (9047) op(e0, e4) = e2
% 29.29/8.07 |
% 29.29/8.07 +-Applying beta-rule and splitting (82), into two cases.
% 29.29/8.07 |-Branch one:
% 29.29/8.07 | (253) all_0_50_50 = e2
% 29.29/8.07 |
% 29.29/8.07 | Equations (253) can reduce 9032 to:
% 29.29/8.07 | (270) $false
% 29.29/8.07 |
% 29.29/8.07 |-The branch is then unsatisfiable
% 29.29/8.07 |-Branch two:
% 29.29/8.07 | (9032) ~ (all_0_50_50 = e2)
% 29.29/8.07 | (267) all_0_50_50 = e4
% 29.29/8.07 |
% 29.29/8.07 | Equations (267) can reduce 41 to:
% 29.29/8.07 | (696) ~ (all_0_51_51 = e4)
% 29.29/8.07 |
% 29.29/8.07 | Simplifying 696 yields:
% 29.29/8.07 | (697) ~ (all_0_51_51 = e4)
% 29.29/8.07 |
% 29.29/8.07 | Equations (267) can reduce 123 to:
% 29.29/8.07 | (2933) ~ (all_0_52_52 = e4)
% 29.29/8.07 |
% 29.29/8.07 | Simplifying 2933 yields:
% 29.29/8.07 | (230) ~ (all_0_52_52 = e4)
% 29.29/8.07 |
% 29.29/8.07 | Equations (267) can reduce 126 to:
% 29.29/8.07 | (1444) ~ (all_0_53_53 = e4)
% 29.29/8.07 |
% 29.29/8.07 | Simplifying 1444 yields:
% 29.29/8.07 | (599) ~ (all_0_53_53 = e4)
% 29.29/8.07 |
% 29.29/8.07 | Equations (267) can reduce 19 to:
% 29.29/8.07 | (1599) ~ (all_0_54_54 = e4)
% 29.29/8.07 |
% 29.29/8.07 | Simplifying 1599 yields:
% 29.29/8.07 | (936) ~ (all_0_54_54 = e4)
% 29.29/8.07 |
% 29.29/8.07 | Equations (267) can reduce 55 to:
% 29.29/8.07 | (34) ~ (e4 = e3)
% 29.29/8.07 |
% 29.29/8.07 | From (267) and (151) follows:
% 29.29/8.07 | (9061) op(e4, e4) = all_0_0_0
% 29.29/8.07 |
% 29.29/8.07 | From (267) and (211) follows:
% 29.29/8.07 | (9062) op(e1, e4) = all_0_1_1
% 29.29/8.07 |
% 29.29/8.07 | From (267) and (23) follows:
% 29.29/8.07 | (9063) op(e1, e4) = e4
% 29.29/8.07 |
% 29.29/8.07 | Instantiating formula (201) with e4, e4, all_0_0_0, e0 and discharging atoms op(e4, e4) = all_0_0_0, op(e4, e4) = e0, yields:
% 29.29/8.07 | (9064) all_0_0_0 = e0
% 29.29/8.07 |
% 29.29/8.07 | Instantiating formula (201) with e4, e2, all_0_2_2, all_0_40_40 and discharging atoms op(e4, e2) = all_0_2_2, op(e4, e2) = all_0_40_40, yields:
% 29.29/8.07 | (9065) all_0_2_2 = all_0_40_40
% 29.29/8.07 |
% 29.29/8.07 | Instantiating formula (201) with e1, e4, e4, all_0_1_1 and discharging atoms op(e1, e4) = all_0_1_1, op(e1, e4) = e4, yields:
% 29.29/8.07 | (9066) all_0_1_1 = e4
% 29.29/8.07 |
% 29.29/8.07 | Instantiating formula (201) with e0, e2, all_0_3_3, all_0_57_57 and discharging atoms op(e0, e2) = all_0_3_3, op(e0, e2) = all_0_57_57, yields:
% 29.29/8.07 | (9067) all_0_3_3 = all_0_57_57
% 29.29/8.07 |
% 29.29/8.07 | From (9066) and (9062) follows:
% 29.29/8.08 | (9063) op(e1, e4) = e4
% 29.29/8.08 |
% 29.29/8.08 | From (9067) and (9046) follows:
% 29.29/8.08 | (207) op(e0, e2) = all_0_57_57
% 29.29/8.08 |
% 29.29/8.08 +-Applying beta-rule and splitting (125), into two cases.
% 29.29/8.08 |-Branch one:
% 29.29/8.08 | (327) all_0_40_40 = e2
% 29.29/8.08 |
% 29.29/8.08 | Combining equations (327,9065) yields a new equation:
% 29.29/8.08 | (9071) all_0_2_2 = e2
% 29.29/8.08 |
% 29.29/8.08 | Equations (327) can reduce 114 to:
% 29.29/8.08 | (291) ~ (all_0_39_39 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Equations (327) can reduce 145 to:
% 29.29/8.08 | (1336) ~ (all_0_42_42 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 1336 yields:
% 29.29/8.08 | (498) ~ (all_0_42_42 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Equations (327) can reduce 15 to:
% 29.29/8.08 | (332) ~ (all_0_44_44 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 332 yields:
% 29.29/8.08 | (333) ~ (all_0_44_44 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Equations (327) can reduce 137 to:
% 29.29/8.08 | (256) ~ (all_0_52_52 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 256 yields:
% 29.29/8.08 | (257) ~ (all_0_52_52 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Equations (327) can reduce 149 to:
% 29.29/8.08 | (334) ~ (all_0_57_57 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 334 yields:
% 29.29/8.08 | (335) ~ (all_0_57_57 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Equations (327) can reduce 238 to:
% 29.29/8.08 | (57) ~ (e2 = e0)
% 29.29/8.08 |
% 29.29/8.08 +-Applying beta-rule and splitting (186), into two cases.
% 29.29/8.08 |-Branch one:
% 29.29/8.08 | (336) all_0_39_39 = e2
% 29.29/8.08 |
% 29.29/8.08 | Equations (336) can reduce 291 to:
% 29.29/8.08 | (270) $false
% 29.29/8.08 |
% 29.29/8.08 |-The branch is then unsatisfiable
% 29.29/8.08 |-Branch two:
% 29.29/8.08 | (291) ~ (all_0_39_39 = e2)
% 29.29/8.08 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 29.29/8.08 |
% 29.29/8.08 +-Applying beta-rule and splitting (339), into two cases.
% 29.29/8.08 |-Branch one:
% 29.29/8.08 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 29.29/8.08 |
% 29.29/8.08 +-Applying beta-rule and splitting (340), into two cases.
% 29.29/8.08 |-Branch one:
% 29.29/8.08 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Applying alpha-rule on (341) yields:
% 29.29/8.08 | (342) all_0_0_0 = e1
% 29.29/8.08 | (343) ~ (all_0_1_1 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Combining equations (342,9064) yields a new equation:
% 29.29/8.08 | (571) e1 = e0
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 571 yields:
% 29.29/8.08 | (560) e1 = e0
% 29.29/8.08 |
% 29.29/8.08 | Equations (560) can reduce 132 to:
% 29.29/8.08 | (270) $false
% 29.29/8.08 |
% 29.29/8.08 |-The branch is then unsatisfiable
% 29.29/8.08 |-Branch two:
% 29.29/8.08 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Applying alpha-rule on (346) yields:
% 29.29/8.08 | (347) all_0_2_2 = e0
% 29.29/8.08 | (348) ~ (all_0_3_3 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Combining equations (9071,347) yields a new equation:
% 29.29/8.08 | (622) e2 = e0
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 622 yields:
% 29.29/8.08 | (316) e2 = e0
% 29.29/8.08 |
% 29.29/8.08 | Equations (316) can reduce 57 to:
% 29.29/8.08 | (270) $false
% 29.29/8.08 |
% 29.29/8.08 |-The branch is then unsatisfiable
% 29.29/8.08 |-Branch two:
% 29.29/8.08 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Applying alpha-rule on (350) yields:
% 29.29/8.08 | (351) all_0_41_41 = e3
% 29.29/8.08 | (352) ~ (all_0_45_45 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Equations (351) can reduce 226 to:
% 29.29/8.08 | (755) ~ (all_0_39_39 = e3)
% 29.29/8.08 |
% 29.29/8.08 | Equations (351) can reduce 94 to:
% 29.29/8.08 | (1331) ~ (all_0_42_42 = e3)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 1331 yields:
% 29.29/8.08 | (1316) ~ (all_0_42_42 = e3)
% 29.29/8.08 |
% 29.29/8.08 | Equations (351) can reduce 51 to:
% 29.29/8.08 | (353) ~ (all_0_45_45 = e3)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 353 yields:
% 29.29/8.08 | (354) ~ (all_0_45_45 = e3)
% 29.29/8.08 |
% 29.29/8.08 | Equations (351) can reduce 190 to:
% 29.29/8.08 | (713) ~ (all_0_48_48 = e3)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 713 yields:
% 29.29/8.08 | (121) ~ (all_0_48_48 = e3)
% 29.29/8.08 |
% 29.29/8.08 | Equations (351) can reduce 214 to:
% 29.29/8.08 | (355) ~ (all_0_53_53 = e3)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 355 yields:
% 29.29/8.08 | (356) ~ (all_0_53_53 = e3)
% 29.29/8.08 |
% 29.29/8.08 | Equations (351) can reduce 157 to:
% 29.29/8.08 | (717) ~ (all_0_58_58 = e3)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 717 yields:
% 29.29/8.08 | (718) ~ (all_0_58_58 = e3)
% 29.29/8.08 |
% 29.29/8.08 | From (351) and (112) follows:
% 29.29/8.08 | (1824) op(e1, e3) = all_0_21_21
% 29.29/8.08 |
% 29.29/8.08 +-Applying beta-rule and splitting (158), into two cases.
% 29.29/8.08 |-Branch one:
% 29.29/8.08 | (358) all_0_41_41 = e4
% 29.29/8.08 |
% 29.29/8.08 | Combining equations (351,358) yields a new equation:
% 29.29/8.08 | (359) e4 = e3
% 29.29/8.08 |
% 29.29/8.08 | Equations (359) can reduce 34 to:
% 29.29/8.08 | (270) $false
% 29.29/8.08 |
% 29.29/8.08 |-The branch is then unsatisfiable
% 29.29/8.08 |-Branch two:
% 29.29/8.08 | (361) ~ (all_0_41_41 = e4)
% 29.29/8.08 | (362) all_0_45_45 = e4 | all_0_53_53 = e4 | all_0_58_58 = e4
% 29.29/8.08 |
% 29.29/8.08 +-Applying beta-rule and splitting (362), into two cases.
% 29.29/8.08 |-Branch one:
% 29.29/8.08 | (363) all_0_45_45 = e4
% 29.29/8.08 |
% 29.29/8.08 | Equations (363) can reduce 352 to:
% 29.29/8.08 | (270) $false
% 29.29/8.08 |
% 29.29/8.08 |-The branch is then unsatisfiable
% 29.29/8.08 |-Branch two:
% 29.29/8.08 | (352) ~ (all_0_45_45 = e4)
% 29.29/8.08 | (366) all_0_53_53 = e4 | all_0_58_58 = e4
% 29.29/8.08 |
% 29.29/8.08 +-Applying beta-rule and splitting (366), into two cases.
% 29.29/8.08 |-Branch one:
% 29.29/8.08 | (367) all_0_53_53 = e4
% 29.29/8.08 |
% 29.29/8.08 | Equations (367) can reduce 599 to:
% 29.29/8.08 | (270) $false
% 29.29/8.08 |
% 29.29/8.08 |-The branch is then unsatisfiable
% 29.29/8.08 |-Branch two:
% 29.29/8.08 | (599) ~ (all_0_53_53 = e4)
% 29.29/8.08 | (600) all_0_58_58 = e4
% 29.29/8.08 |
% 29.29/8.08 | Equations (600) can reduce 108 to:
% 29.29/8.08 | (352) ~ (all_0_45_45 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Equations (600) can reduce 70 to:
% 29.29/8.08 | (599) ~ (all_0_53_53 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Equations (600) can reduce 81 to:
% 29.29/8.08 | (274) ~ (all_0_56_56 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Equations (600) can reduce 37 to:
% 29.29/8.08 | (143) ~ (all_0_57_57 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Equations (600) can reduce 156 to:
% 29.29/8.08 | (279) ~ (all_0_59_59 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 279 yields:
% 29.29/8.08 | (280) ~ (all_0_59_59 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Equations (600) can reduce 718 to:
% 29.29/8.08 | (34) ~ (e4 = e3)
% 29.29/8.08 |
% 29.29/8.08 | From (600) and (63) follows:
% 29.29/8.08 | (9134) op(e1, e4) = all_0_28_28
% 29.29/8.08 |
% 29.29/8.08 | Instantiating formula (201) with e1, e4, all_0_28_28, e4 and discharging atoms op(e1, e4) = all_0_28_28, op(e1, e4) = e4, yields:
% 29.29/8.08 | (9135) all_0_28_28 = e4
% 29.29/8.08 |
% 29.29/8.08 | Instantiating formula (201) with e1, e3, all_0_21_21, all_0_51_51 and discharging atoms op(e1, e3) = all_0_21_21, op(e1, e3) = all_0_51_51, yields:
% 29.29/8.08 | (1847) all_0_21_21 = all_0_51_51
% 29.29/8.08 |
% 29.29/8.08 +-Applying beta-rule and splitting (193), into two cases.
% 29.29/8.08 |-Branch one:
% 29.29/8.08 | (370) all_0_44_44 = e2
% 29.29/8.08 |
% 29.29/8.08 | Equations (370) can reduce 333 to:
% 29.29/8.08 | (270) $false
% 29.29/8.08 |
% 29.29/8.08 |-The branch is then unsatisfiable
% 29.29/8.08 |-Branch two:
% 29.29/8.08 | (333) ~ (all_0_44_44 = e2)
% 29.29/8.08 | (373) all_0_44_44 = e3 | all_0_44_44 = e0
% 29.29/8.08 |
% 29.29/8.08 +-Applying beta-rule and splitting (8), into two cases.
% 29.29/8.08 |-Branch one:
% 29.29/8.08 | (530) all_0_40_40 = e1
% 29.29/8.08 |
% 29.29/8.08 | Combining equations (327,530) yields a new equation:
% 29.29/8.08 | (531) e2 = e1
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 531 yields:
% 29.29/8.08 | (322) e2 = e1
% 29.29/8.08 |
% 29.29/8.08 | Equations (322) can reduce 141 to:
% 29.29/8.08 | (270) $false
% 29.29/8.08 |
% 29.29/8.08 |-The branch is then unsatisfiable
% 29.29/8.08 |-Branch two:
% 29.29/8.08 | (534) ~ (all_0_40_40 = e1)
% 29.29/8.08 | (3352) all_0_52_52 = e1 | all_0_57_57 = e1
% 29.29/8.08 |
% 29.29/8.08 | Equations (327) can reduce 534 to:
% 29.29/8.08 | (141) ~ (e2 = e1)
% 29.29/8.08 |
% 29.29/8.08 +-Applying beta-rule and splitting (155), into two cases.
% 29.29/8.08 |-Branch one:
% 29.29/8.08 | (290) all_0_47_47 = e2
% 29.29/8.08 |
% 29.29/8.08 | Equations (290) can reduce 100 to:
% 29.29/8.08 | (291) ~ (all_0_39_39 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Equations (290) can reduce 170 to:
% 29.29/8.08 | (292) ~ (all_0_43_43 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Equations (290) can reduce 225 to:
% 29.29/8.08 | (293) ~ (all_0_48_48 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 293 yields:
% 29.29/8.08 | (294) ~ (all_0_48_48 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Equations (290) can reduce 80 to:
% 29.29/8.08 | (295) ~ (all_0_49_49 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 295 yields:
% 29.29/8.08 | (296) ~ (all_0_49_49 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Equations (290) can reduce 3 to:
% 29.29/8.08 | (254) ~ (all_0_51_51 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 254 yields:
% 29.29/8.08 | (255) ~ (all_0_51_51 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Equations (290) can reduce 218 to:
% 29.29/8.08 | (299) ~ (all_0_56_56 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 299 yields:
% 29.29/8.08 | (300) ~ (all_0_56_56 = e2)
% 29.29/8.08 |
% 29.29/8.08 +-Applying beta-rule and splitting (129), into two cases.
% 29.29/8.08 |-Branch one:
% 29.29/8.08 | (311) all_0_48_48 = e2
% 29.29/8.08 |
% 29.29/8.08 | Equations (311) can reduce 294 to:
% 29.29/8.08 | (270) $false
% 29.29/8.08 |
% 29.29/8.08 |-The branch is then unsatisfiable
% 29.29/8.08 |-Branch two:
% 29.29/8.08 | (294) ~ (all_0_48_48 = e2)
% 29.29/8.08 | (314) all_0_48_48 = e1 | all_0_48_48 = e0
% 29.29/8.08 |
% 29.29/8.08 +-Applying beta-rule and splitting (117), into two cases.
% 29.29/8.08 |-Branch one:
% 29.29/8.08 | (307) all_0_49_49 = e2
% 29.29/8.08 |
% 29.29/8.08 | Equations (307) can reduce 296 to:
% 29.29/8.08 | (270) $false
% 29.29/8.08 |
% 29.29/8.08 |-The branch is then unsatisfiable
% 29.29/8.08 |-Branch two:
% 29.29/8.08 | (296) ~ (all_0_49_49 = e2)
% 29.29/8.08 | (310) all_0_49_49 = e1 | all_0_49_49 = e0
% 29.29/8.08 |
% 29.29/8.08 +-Applying beta-rule and splitting (83), into two cases.
% 29.29/8.08 |-Branch one:
% 29.29/8.08 | (321) all_0_47_47 = e1
% 29.29/8.08 |
% 29.29/8.08 | Combining equations (290,321) yields a new equation:
% 29.29/8.08 | (531) e2 = e1
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 531 yields:
% 29.29/8.08 | (322) e2 = e1
% 29.29/8.08 |
% 29.29/8.08 | Equations (322) can reduce 141 to:
% 29.29/8.08 | (270) $false
% 29.29/8.08 |
% 29.29/8.08 |-The branch is then unsatisfiable
% 29.29/8.08 |-Branch two:
% 29.29/8.08 | (324) ~ (all_0_47_47 = e1)
% 29.29/8.08 | (325) all_0_48_48 = e1 | all_0_49_49 = e1
% 29.29/8.08 |
% 29.29/8.08 +-Applying beta-rule and splitting (77), into two cases.
% 29.29/8.08 |-Branch one:
% 29.29/8.08 | (315) all_0_47_47 = e0
% 29.29/8.08 |
% 29.29/8.08 | Combining equations (290,315) yields a new equation:
% 29.29/8.08 | (622) e2 = e0
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 622 yields:
% 29.29/8.08 | (316) e2 = e0
% 29.29/8.08 |
% 29.29/8.08 | Equations (316) can reduce 57 to:
% 29.29/8.08 | (270) $false
% 29.29/8.08 |
% 29.29/8.08 |-The branch is then unsatisfiable
% 29.29/8.08 |-Branch two:
% 29.29/8.08 | (318) ~ (all_0_47_47 = e0)
% 29.29/8.08 | (319) all_0_48_48 = e0 | all_0_49_49 = e0
% 29.29/8.08 |
% 29.29/8.08 +-Applying beta-rule and splitting (47), into two cases.
% 29.29/8.08 |-Branch one:
% 29.29/8.08 | (450) all_0_43_43 = e2
% 29.29/8.08 |
% 29.29/8.08 | Equations (450) can reduce 292 to:
% 29.29/8.08 | (270) $false
% 29.29/8.08 |
% 29.29/8.08 |-The branch is then unsatisfiable
% 29.29/8.08 |-Branch two:
% 29.29/8.08 | (292) ~ (all_0_43_43 = e2)
% 29.29/8.08 | (453) all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2
% 29.29/8.08 |
% 29.29/8.08 +-Applying beta-rule and splitting (44), into two cases.
% 29.29/8.08 |-Branch one:
% 29.29/8.08 | (502) all_0_43_43 = e4
% 29.29/8.08 |
% 29.29/8.08 | Equations (502) can reduce 167 to:
% 29.29/8.08 | (591) ~ (all_0_39_39 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Equations (502) can reduce 241 to:
% 29.29/8.08 | (9185) ~ (all_0_44_44 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 9185 yields:
% 29.29/8.08 | (45) ~ (all_0_44_44 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Equations (502) can reduce 84 to:
% 29.29/8.08 | (503) ~ (all_0_45_45 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 503 yields:
% 29.29/8.08 | (352) ~ (all_0_45_45 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Equations (502) can reduce 240 to:
% 29.29/8.08 | (696) ~ (all_0_51_51 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 696 yields:
% 29.29/8.08 | (697) ~ (all_0_51_51 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Equations (502) can reduce 188 to:
% 29.29/8.08 | (273) ~ (all_0_56_56 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 273 yields:
% 29.29/8.08 | (274) ~ (all_0_56_56 = e4)
% 29.29/8.08 |
% 29.29/8.08 +-Applying beta-rule and splitting (177), into two cases.
% 29.29/8.08 |-Branch one:
% 29.29/8.08 | (336) all_0_39_39 = e2
% 29.29/8.08 |
% 29.29/8.08 | Equations (336) can reduce 291 to:
% 29.29/8.08 | (270) $false
% 29.29/8.08 |
% 29.29/8.08 |-The branch is then unsatisfiable
% 29.29/8.08 |-Branch two:
% 29.29/8.08 | (291) ~ (all_0_39_39 = e2)
% 29.29/8.08 | (684) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 29.29/8.08 |
% 29.29/8.08 +-Applying beta-rule and splitting (684), into two cases.
% 29.29/8.08 |-Branch one:
% 29.29/8.08 | (751) all_0_39_39 = e3
% 29.29/8.08 |
% 29.29/8.08 | Equations (751) can reduce 755 to:
% 29.29/8.08 | (270) $false
% 29.29/8.08 |
% 29.29/8.08 |-The branch is then unsatisfiable
% 29.29/8.08 |-Branch two:
% 29.29/8.08 | (755) ~ (all_0_39_39 = e3)
% 29.29/8.08 | (1756) all_0_39_39 = e4 | all_0_39_39 = e1
% 29.29/8.08 |
% 29.29/8.08 +-Applying beta-rule and splitting (179), into two cases.
% 29.29/8.08 |-Branch one:
% 29.29/8.08 | (512) all_0_42_42 = e4
% 29.29/8.08 |
% 29.29/8.08 | Equations (512) can reduce 184 to:
% 29.29/8.08 | (591) ~ (all_0_39_39 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Equations (512) can reduce 18 to:
% 29.29/8.08 | (804) ~ (all_0_46_46 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 804 yields:
% 29.29/8.08 | (805) ~ (all_0_46_46 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Equations (512) can reduce 169 to:
% 29.29/8.08 | (2914) ~ (all_0_49_49 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 2914 yields:
% 29.29/8.08 | (202) ~ (all_0_49_49 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Equations (512) can reduce 17 to:
% 29.29/8.08 | (279) ~ (all_0_59_59 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 279 yields:
% 29.29/8.08 | (280) ~ (all_0_59_59 = e4)
% 29.29/8.08 |
% 29.29/8.08 | Equations (512) can reduce 1316 to:
% 29.29/8.08 | (34) ~ (e4 = e3)
% 29.29/8.08 |
% 29.29/8.08 | Equations (512) can reduce 199 to:
% 29.29/8.08 | (6) ~ (e4 = e0)
% 29.29/8.08 |
% 29.29/8.08 +-Applying beta-rule and splitting (1756), into two cases.
% 29.29/8.08 |-Branch one:
% 29.29/8.08 | (524) all_0_39_39 = e1
% 29.29/8.08 |
% 29.29/8.08 | Equations (524) can reduce 32 to:
% 29.29/8.08 | (3984) ~ (all_0_51_51 = e1)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 3984 yields:
% 29.29/8.08 | (748) ~ (all_0_51_51 = e1)
% 29.29/8.08 |
% 29.29/8.08 | Equations (524) can reduce 755 to:
% 29.29/8.08 | (769) ~ (e3 = e1)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 769 yields:
% 29.29/8.08 | (136) ~ (e3 = e1)
% 29.29/8.08 |
% 29.29/8.08 +-Applying beta-rule and splitting (105), into two cases.
% 29.29/8.08 |-Branch one:
% 29.29/8.08 | (374) all_0_45_45 = e2
% 29.29/8.08 |
% 29.29/8.08 | Equations (374) can reduce 229 to:
% 29.29/8.08 | (333) ~ (all_0_44_44 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Equations (374) can reduce 38 to:
% 29.29/8.08 | (1435) ~ (all_0_46_46 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 1435 yields:
% 29.29/8.08 | (1436) ~ (all_0_46_46 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Equations (374) can reduce 65 to:
% 29.29/8.08 | (293) ~ (all_0_48_48 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 293 yields:
% 29.29/8.08 | (294) ~ (all_0_48_48 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Equations (374) can reduce 352 to:
% 29.29/8.08 | (377) ~ (e4 = e2)
% 29.29/8.08 |
% 29.29/8.08 | Simplifying 377 yields:
% 29.29/8.08 | (231) ~ (e4 = e2)
% 29.29/8.08 |
% 29.29/8.08 | From (374) and (142) follows:
% 29.29/8.09 | (9224) op(e1, e2) = all_0_23_23
% 29.29/8.09 |
% 29.29/8.09 +-Applying beta-rule and splitting (209), into two cases.
% 29.29/8.09 |-Branch one:
% 29.29/8.09 | (698) all_0_42_42 = e2
% 29.29/8.09 |
% 29.29/8.09 | Combining equations (698,512) yields a new equation:
% 29.29/8.09 | (269) e4 = e2
% 29.29/8.09 |
% 29.29/8.09 | Equations (269) can reduce 231 to:
% 29.29/8.09 | (270) $false
% 29.29/8.09 |
% 29.29/8.09 |-The branch is then unsatisfiable
% 29.29/8.09 |-Branch two:
% 29.29/8.09 | (498) ~ (all_0_42_42 = e2)
% 29.29/8.09 | (1732) all_0_46_46 = e2 | all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 29.29/8.09 |
% 29.29/8.09 +-Applying beta-rule and splitting (1732), into two cases.
% 29.29/8.09 |-Branch one:
% 29.29/8.09 | (497) all_0_46_46 = e2
% 29.29/8.09 |
% 29.29/8.09 | Equations (497) can reduce 1436 to:
% 29.29/8.09 | (270) $false
% 29.29/8.09 |
% 29.29/8.09 |-The branch is then unsatisfiable
% 29.29/8.09 |-Branch two:
% 29.29/8.09 | (1436) ~ (all_0_46_46 = e2)
% 29.29/8.09 | (3824) all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 29.29/8.09 |
% 29.29/8.09 +-Applying beta-rule and splitting (3824), into two cases.
% 29.29/8.09 |-Branch one:
% 29.29/8.09 | (307) all_0_49_49 = e2
% 29.29/8.09 |
% 29.29/8.09 | Equations (307) can reduce 296 to:
% 29.29/8.09 | (270) $false
% 29.29/8.09 |
% 29.29/8.09 |-The branch is then unsatisfiable
% 29.29/8.09 |-Branch two:
% 29.29/8.09 | (296) ~ (all_0_49_49 = e2)
% 29.29/8.09 | (3829) all_0_54_54 = e2 | all_0_59_59 = e2
% 29.29/8.09 |
% 29.29/8.09 +-Applying beta-rule and splitting (3829), into two cases.
% 29.29/8.09 |-Branch one:
% 29.29/8.09 | (3657) all_0_54_54 = e2
% 29.29/8.09 |
% 29.29/8.09 | Equations (3657) can reduce 162 to:
% 29.29/8.09 | (296) ~ (all_0_49_49 = e2)
% 29.29/8.09 |
% 29.29/8.09 | Equations (3657) can reduce 50 to:
% 29.29/8.09 | (255) ~ (all_0_51_51 = e2)
% 29.29/8.09 |
% 29.29/8.09 | Equations (3657) can reduce 118 to:
% 29.29/8.09 | (257) ~ (all_0_52_52 = e2)
% 29.29/8.09 |
% 29.29/8.09 | Equations (3657) can reduce 72 to:
% 29.29/8.09 | (700) ~ (all_0_59_59 = e2)
% 29.29/8.09 |
% 29.29/8.09 | Simplifying 700 yields:
% 29.29/8.09 | (701) ~ (all_0_59_59 = e2)
% 29.29/8.09 |
% 29.29/8.09 +-Applying beta-rule and splitting (93), into two cases.
% 29.29/8.09 |-Branch one:
% 29.29/8.09 | (402) all_0_59_59 = e4
% 29.29/8.09 |
% 29.29/8.09 | Equations (402) can reduce 280 to:
% 29.29/8.09 | (270) $false
% 29.29/8.09 |
% 29.29/8.09 |-The branch is then unsatisfiable
% 29.29/8.09 |-Branch two:
% 29.29/8.09 | (280) ~ (all_0_59_59 = e4)
% 29.29/8.09 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 29.29/8.09 |
% 29.29/8.09 +-Applying beta-rule and splitting (407), into two cases.
% 29.29/8.09 |-Branch one:
% 29.29/8.09 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 29.29/8.09 |
% 29.29/8.09 +-Applying beta-rule and splitting (408), into two cases.
% 29.29/8.09 |-Branch one:
% 29.29/8.09 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 29.29/8.09 |
% 29.29/8.09 +-Applying beta-rule and splitting (409), into two cases.
% 29.29/8.09 |-Branch one:
% 29.29/8.09 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 29.29/8.09 |
% 29.29/8.09 | Applying alpha-rule on (410) yields:
% 29.29/8.09 | (411) all_0_43_43 = e0
% 29.29/8.09 | (412) all_0_59_59 = e3
% 29.29/8.09 | (413) ~ (all_0_46_46 = e3)
% 29.29/8.09 |
% 29.29/8.09 | Combining equations (411,502) yields a new equation:
% 29.29/8.09 | (479) e4 = e0
% 29.29/8.09 |
% 29.29/8.09 | Equations (479) can reduce 6 to:
% 29.29/8.09 | (270) $false
% 29.29/8.09 |
% 29.29/8.09 |-The branch is then unsatisfiable
% 29.29/8.09 |-Branch two:
% 29.29/8.09 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 29.29/8.09 |
% 29.29/8.09 | Applying alpha-rule on (416) yields:
% 29.29/8.09 | (411) all_0_43_43 = e0
% 29.29/8.09 | (412) all_0_59_59 = e3
% 29.29/8.09 | (419) ~ (all_0_56_56 = e0)
% 29.29/8.09 |
% 29.29/8.09 | Combining equations (411,502) yields a new equation:
% 29.29/8.09 | (479) e4 = e0
% 29.29/8.09 |
% 29.29/8.09 | Equations (479) can reduce 6 to:
% 29.29/8.09 | (270) $false
% 29.29/8.09 |
% 29.29/8.09 |-The branch is then unsatisfiable
% 29.29/8.09 |-Branch two:
% 29.29/8.09 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 29.29/8.09 |
% 29.29/8.09 | Applying alpha-rule on (422) yields:
% 29.29/8.09 | (423) all_0_53_53 = e0
% 29.29/8.09 | (424) all_0_59_59 = e1
% 29.29/8.09 | (425) ~ (all_0_54_54 = e1)
% 29.29/8.09 |
% 29.29/8.09 | Equations (424) can reduce 113 to:
% 29.29/8.09 | (543) ~ (all_0_49_49 = e1)
% 29.29/8.09 |
% 29.29/8.09 | Equations (423) can reduce 12 to:
% 29.29/8.09 | (987) ~ (all_0_51_51 = e0)
% 29.29/8.09 |
% 29.29/8.09 | Equations (423) can reduce 213 to:
% 29.29/8.09 | (925) ~ (all_0_52_52 = e0)
% 29.29/8.09 |
% 29.29/8.09 | Equations (424) can reduce 185 to:
% 29.29/8.09 | (995) ~ (all_0_56_56 = e1)
% 29.29/8.09 |
% 29.29/8.09 | Equations (424) can reduce 701 to:
% 29.29/8.09 | (645) ~ (e2 = e1)
% 29.29/8.09 |
% 29.29/8.09 | Simplifying 645 yields:
% 29.29/8.09 | (141) ~ (e2 = e1)
% 29.29/8.09 |
% 29.29/8.09 | From (423) and (227) follows:
% 29.29/8.09 | (2167) op(e1, e1) = e0
% 29.29/8.09 |
% 29.29/8.09 +-Applying beta-rule and splitting (52), into two cases.
% 29.29/8.09 |-Branch one:
% 29.29/8.09 | (536) all_0_41_41 = e1
% 29.29/8.09 |
% 29.29/8.09 | Combining equations (351,536) yields a new equation:
% 29.29/8.09 | (537) e3 = e1
% 29.29/8.09 |
% 29.29/8.09 | Simplifying 537 yields:
% 29.29/8.09 | (538) e3 = e1
% 29.29/8.09 |
% 29.29/8.09 | Equations (538) can reduce 136 to:
% 29.29/8.09 | (270) $false
% 29.29/8.09 |
% 29.29/8.09 |-The branch is then unsatisfiable
% 29.29/8.09 |-Branch two:
% 29.29/8.09 | (540) ~ (all_0_41_41 = e1)
% 29.29/8.09 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 29.29/8.09 |
% 29.29/8.09 +-Applying beta-rule and splitting (310), into two cases.
% 29.29/8.09 |-Branch one:
% 29.29/8.09 | (563) all_0_49_49 = e0
% 29.29/8.09 |
% 29.29/8.09 | Equations (563) can reduce 198 to:
% 29.29/8.09 | (1010) ~ (all_0_46_46 = e0)
% 29.29/8.09 |
% 29.29/8.09 | Equations (563) can reduce 4 to:
% 29.29/8.09 | (562) ~ (all_0_48_48 = e0)
% 29.29/8.09 |
% 29.29/8.09 | Equations (563) can reduce 202 to:
% 29.29/8.09 | (456) ~ (e4 = e0)
% 29.29/8.09 |
% 29.29/8.09 | Simplifying 456 yields:
% 29.29/8.09 | (6) ~ (e4 = e0)
% 29.29/8.09 |
% 29.29/8.09 | Equations (563) can reduce 296 to:
% 29.29/8.09 | (566) ~ (e2 = e0)
% 29.29/8.09 |
% 29.29/8.09 | Simplifying 566 yields:
% 29.29/8.09 | (57) ~ (e2 = e0)
% 29.29/8.09 |
% 29.29/8.09 +-Applying beta-rule and splitting (95), into two cases.
% 29.29/8.09 |-Branch one:
% 29.29/8.09 | (1258) all_0_42_42 = e3
% 29.29/8.09 |
% 29.29/8.09 | Combining equations (512,1258) yields a new equation:
% 29.29/8.09 | (660) e4 = e3
% 29.29/8.09 |
% 29.29/8.09 | Simplifying 660 yields:
% 29.29/8.09 | (359) e4 = e3
% 29.29/8.09 |
% 29.29/8.09 | Equations (359) can reduce 34 to:
% 29.29/8.09 | (270) $false
% 29.29/8.09 |
% 29.29/8.09 |-The branch is then unsatisfiable
% 29.29/8.09 |-Branch two:
% 29.29/8.09 | (1316) ~ (all_0_42_42 = e3)
% 29.29/8.09 | (3656) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 29.29/8.09 |
% 29.29/8.09 +-Applying beta-rule and splitting (173), into two cases.
% 29.29/8.09 |-Branch one:
% 29.29/8.09 | (4215) all_0_51_51 = e2
% 29.29/8.09 |
% 29.29/8.09 | Equations (4215) can reduce 255 to:
% 29.29/8.09 | (270) $false
% 29.29/8.09 |
% 29.29/8.09 |-The branch is then unsatisfiable
% 29.29/8.09 |-Branch two:
% 29.29/8.09 | (255) ~ (all_0_51_51 = e2)
% 29.29/8.09 | (4888) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1 | all_0_51_51 = e0
% 29.29/8.09 |
% 29.29/8.09 +-Applying beta-rule and splitting (4888), into two cases.
% 29.29/8.09 |-Branch one:
% 29.29/8.09 | (954) all_0_51_51 = e0
% 29.29/8.09 |
% 29.29/8.09 | Equations (954) can reduce 987 to:
% 29.29/8.09 | (270) $false
% 29.29/8.09 |
% 29.29/8.09 |-The branch is then unsatisfiable
% 29.29/8.09 |-Branch two:
% 29.29/8.09 | (987) ~ (all_0_51_51 = e0)
% 29.29/8.09 | (5003) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1
% 29.29/8.09 |
% 29.29/8.09 +-Applying beta-rule and splitting (762), into two cases.
% 29.29/8.09 |-Branch one:
% 29.29/8.09 | (552) all_0_48_48 = e1
% 29.29/8.09 |
% 29.29/8.09 | Equations (552) can reduce 294 to:
% 29.29/8.09 | (645) ~ (e2 = e1)
% 29.29/8.09 |
% 29.29/8.09 | Simplifying 645 yields:
% 29.29/8.09 | (141) ~ (e2 = e1)
% 29.29/8.09 |
% 29.29/8.09 | Equations (552) can reduce 562 to:
% 29.29/8.09 | (132) ~ (e1 = e0)
% 29.29/8.09 |
% 29.29/8.09 | From (552) and (76) follows:
% 29.29/8.09 | (2127) op(e1, e1) = all_0_25_25
% 29.29/8.09 |
% 29.29/8.09 +-Applying beta-rule and splitting (5003), into two cases.
% 29.29/8.09 |-Branch one:
% 29.29/8.09 | (824) all_0_51_51 = e3
% 29.29/8.09 |
% 29.29/8.09 | Combining equations (824,1847) yields a new equation:
% 29.29/8.09 | (6797) all_0_21_21 = e3
% 29.29/8.09 |
% 29.29/8.09 | Equations (824) can reduce 154 to:
% 29.29/8.09 | (825) ~ (all_0_52_52 = e3)
% 29.29/8.09 |
% 29.29/8.09 | Simplifying 825 yields:
% 29.29/8.09 | (826) ~ (all_0_52_52 = e3)
% 29.29/8.09 |
% 29.29/8.09 | Equations (824) can reduce 255 to:
% 29.29/8.09 | (223) ~ (e3 = e2)
% 29.29/8.09 |
% 29.29/8.09 | Equations (824) can reduce 748 to:
% 29.29/8.09 | (136) ~ (e3 = e1)
% 29.29/8.09 |
% 29.29/8.09 +-Applying beta-rule and splitting (135), into two cases.
% 29.29/8.09 |-Branch one:
% 29.29/8.09 | (820) all_0_51_51 = e1
% 29.29/8.09 |
% 29.29/8.09 | Combining equations (824,820) yields a new equation:
% 29.29/8.09 | (537) e3 = e1
% 29.29/8.09 |
% 29.29/8.09 | Simplifying 537 yields:
% 29.29/8.09 | (538) e3 = e1
% 29.29/8.09 |
% 29.29/8.09 | Equations (538) can reduce 136 to:
% 29.29/8.09 | (270) $false
% 29.29/8.09 |
% 29.29/8.09 |-The branch is then unsatisfiable
% 29.29/8.09 |-Branch two:
% 29.29/8.09 | (748) ~ (all_0_51_51 = e1)
% 29.29/8.09 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 29.29/8.09 |
% 29.29/8.09 +-Applying beta-rule and splitting (116), into two cases.
% 29.29/8.09 |-Branch one:
% 29.29/8.09 | (411) all_0_43_43 = e0
% 29.29/8.09 |
% 29.29/8.09 | Combining equations (502,411) yields a new equation:
% 29.29/8.09 | (478) e4 = e0
% 29.29/8.09 |
% 29.29/8.09 | Simplifying 478 yields:
% 29.29/8.09 | (479) e4 = e0
% 29.29/8.09 |
% 29.29/8.09 | Equations (479) can reduce 6 to:
% 29.29/8.09 | (270) $false
% 29.29/8.09 |
% 29.29/8.09 |-The branch is then unsatisfiable
% 29.29/8.09 |-Branch two:
% 29.29/8.09 | (455) ~ (all_0_43_43 = e0)
% 29.29/8.09 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 29.29/8.09 |
% 29.29/8.09 +-Applying beta-rule and splitting (1122), into two cases.
% 29.29/8.09 |-Branch one:
% 29.29/8.09 | (621) all_0_44_44 = e0
% 29.29/8.09 |
% 29.29/8.09 | Equations (621) can reduce 122 to:
% 29.29/8.09 | (4297) ~ (all_0_52_52 = e0)
% 29.29/8.09 |
% 29.29/8.09 | Simplifying 4297 yields:
% 29.29/8.09 | (925) ~ (all_0_52_52 = e0)
% 29.29/8.09 |
% 29.29/8.09 | Equations (621) can reduce 10 to:
% 29.29/8.09 | (9326) ~ (all_0_57_57 = e0)
% 29.29/8.09 |
% 29.29/8.09 | Simplifying 9326 yields:
% 29.29/8.09 | (2301) ~ (all_0_57_57 = e0)
% 29.29/8.09 |
% 29.29/8.09 | Equations (621) can reduce 45 to:
% 29.29/8.09 | (456) ~ (e4 = e0)
% 29.29/8.09 |
% 29.29/8.09 | Simplifying 456 yields:
% 29.29/8.09 | (6) ~ (e4 = e0)
% 29.29/8.09 |
% 29.29/8.09 | Equations (621) can reduce 131 to:
% 29.29/8.09 | (568) ~ (e1 = e0)
% 29.29/8.09 |
% 29.29/8.09 | Simplifying 568 yields:
% 29.29/8.09 | (132) ~ (e1 = e0)
% 29.29/8.09 |
% 29.29/8.09 +-Applying beta-rule and splitting (33), into two cases.
% 29.29/8.09 |-Branch one:
% 29.29/8.09 | (392) all_0_57_57 = e2
% 29.29/8.09 |
% 29.29/8.09 | Equations (392) can reduce 335 to:
% 29.29/8.09 | (270) $false
% 29.29/8.09 |
% 29.29/8.09 |-The branch is then unsatisfiable
% 29.29/8.09 |-Branch two:
% 29.29/8.09 | (335) ~ (all_0_57_57 = e2)
% 29.29/8.09 | (670) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 29.29/8.09 |
% 29.29/8.09 +-Applying beta-rule and splitting (823), into two cases.
% 29.29/8.09 |-Branch one:
% 29.29/8.09 | (848) all_0_52_52 = e1
% 29.29/8.09 |
% 29.29/8.09 | Equations (848) can reduce 235 to:
% 29.29/8.09 | (643) ~ (all_0_57_57 = e1)
% 29.29/8.09 |
% 29.29/8.09 | Simplifying 643 yields:
% 29.29/8.09 | (644) ~ (all_0_57_57 = e1)
% 29.29/8.09 |
% 29.29/8.09 | Equations (848) can reduce 925 to:
% 29.29/8.09 | (132) ~ (e1 = e0)
% 29.29/8.09 |
% 29.29/8.09 | From (848) and (195) follows:
% 29.29/8.09 | (9340) op(e1, e1) = all_0_18_18
% 29.29/8.09 |
% 29.29/8.09 | From (848) and (203) follows:
% 29.29/8.09 | (9341) op(e1, e2) = e1
% 29.29/8.09 |
% 29.29/8.09 +-Applying beta-rule and splitting (670), into two cases.
% 29.29/8.09 |-Branch one:
% 29.29/8.09 | (2258) all_0_57_57 = e0
% 29.29/8.09 |
% 29.29/8.09 | Equations (2258) can reduce 2301 to:
% 29.29/8.09 | (270) $false
% 29.29/8.09 |
% 29.29/8.09 |-The branch is then unsatisfiable
% 29.29/8.09 |-Branch two:
% 29.29/8.09 | (2301) ~ (all_0_57_57 = e0)
% 29.29/8.09 | (9345) all_0_57_57 = e3 | all_0_57_57 = e1
% 29.29/8.09 |
% 29.29/8.10 +-Applying beta-rule and splitting (9345), into two cases.
% 29.29/8.10 |-Branch one:
% 29.29/8.10 | (869) all_0_57_57 = e3
% 29.29/8.10 |
% 29.29/8.10 | Equations (869) can reduce 143 to:
% 29.29/8.10 | (719) ~ (e4 = e3)
% 29.29/8.10 |
% 29.29/8.10 | Simplifying 719 yields:
% 29.29/8.10 | (34) ~ (e4 = e3)
% 29.29/8.10 |
% 29.29/8.10 | Equations (869) can reduce 644 to:
% 29.29/8.10 | (136) ~ (e3 = e1)
% 29.29/8.10 |
% 29.29/8.10 | Equations (869) can reduce 2301 to:
% 29.29/8.10 | (66) ~ (e3 = e0)
% 29.29/8.10 |
% 29.29/8.10 +-Applying beta-rule and splitting (176), into two cases.
% 29.29/8.10 |-Branch one:
% 29.29/8.10 | (830) all_0_56_56 = e0
% 29.29/8.10 |
% 29.29/8.10 | Equations (830) can reduce 274 to:
% 29.29/8.10 | (456) ~ (e4 = e0)
% 29.29/8.10 |
% 29.29/8.10 | Simplifying 456 yields:
% 29.29/8.10 | (6) ~ (e4 = e0)
% 29.29/8.10 |
% 29.29/8.10 | Equations (830) can reduce 300 to:
% 29.29/8.10 | (566) ~ (e2 = e0)
% 29.29/8.10 |
% 29.29/8.10 | Simplifying 566 yields:
% 29.29/8.10 | (57) ~ (e2 = e0)
% 29.29/8.10 |
% 29.29/8.10 | Instantiating formula (201) with e1, e2, e1, all_0_23_23 and discharging atoms op(e1, e2) = all_0_23_23, op(e1, e2) = e1, yields:
% 29.29/8.10 | (9356) all_0_23_23 = e1
% 29.29/8.10 |
% 29.29/8.10 | Instantiating formula (201) with e1, e1, all_0_25_25, all_0_18_18 and discharging atoms op(e1, e1) = all_0_18_18, op(e1, e1) = all_0_25_25, yields:
% 29.29/8.10 | (9357) all_0_18_18 = all_0_25_25
% 29.29/8.10 |
% 29.29/8.10 | Instantiating formula (201) with e1, e1, e0, all_0_18_18 and discharging atoms op(e1, e1) = all_0_18_18, op(e1, e1) = e0, yields:
% 29.29/8.10 | (9358) all_0_18_18 = e0
% 29.29/8.10 |
% 29.29/8.10 | Combining equations (9357,9358) yields a new equation:
% 29.29/8.10 | (9359) all_0_25_25 = e0
% 29.29/8.10 |
% 29.29/8.10 | Simplifying 9359 yields:
% 29.29/8.10 | (2274) all_0_25_25 = e0
% 29.29/8.10 |
% 29.29/8.10 +-Applying beta-rule and splitting (14), into two cases.
% 29.29/8.10 |-Branch one:
% 29.29/8.10 | (2277) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1))
% 29.29/8.10 |
% 29.29/8.10 +-Applying beta-rule and splitting (2277), into two cases.
% 29.29/8.10 |-Branch one:
% 29.29/8.10 | (2278) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1))
% 29.29/8.10 |
% 29.29/8.10 +-Applying beta-rule and splitting (2278), into two cases.
% 29.29/8.10 |-Branch one:
% 29.29/8.10 | (2279) all_0_21_21 = e4 & ~ (all_0_22_22 = e1)
% 29.29/8.10 |
% 29.29/8.10 | Applying alpha-rule on (2279) yields:
% 29.29/8.10 | (2280) all_0_21_21 = e4
% 29.29/8.10 | (2281) ~ (all_0_22_22 = e1)
% 29.29/8.10 |
% 29.29/8.10 | Combining equations (2280,6797) yields a new equation:
% 29.29/8.10 | (660) e4 = e3
% 29.29/8.10 |
% 29.29/8.10 | Simplifying 660 yields:
% 29.29/8.10 | (359) e4 = e3
% 29.29/8.10 |
% 29.29/8.10 | Equations (359) can reduce 34 to:
% 29.29/8.10 | (270) $false
% 29.29/8.10 |
% 29.29/8.10 |-The branch is then unsatisfiable
% 29.29/8.10 |-Branch two:
% 29.29/8.10 | (2285) all_0_23_23 = e3 & ~ (all_0_24_24 = e1)
% 29.29/8.10 |
% 29.29/8.10 | Applying alpha-rule on (2285) yields:
% 29.29/8.10 | (2286) all_0_23_23 = e3
% 29.29/8.10 | (2287) ~ (all_0_24_24 = e1)
% 29.29/8.10 |
% 29.29/8.10 | Combining equations (2286,9356) yields a new equation:
% 29.29/8.10 | (537) e3 = e1
% 29.29/8.10 |
% 29.29/8.10 | Simplifying 537 yields:
% 29.29/8.10 | (538) e3 = e1
% 29.29/8.10 |
% 29.29/8.10 | Equations (538) can reduce 136 to:
% 29.29/8.10 | (270) $false
% 29.29/8.10 |
% 29.29/8.10 |-The branch is then unsatisfiable
% 29.29/8.10 |-Branch two:
% 29.29/8.10 | (2291) all_0_25_25 = e2 & ~ (all_0_26_26 = e1)
% 29.29/8.10 |
% 29.29/8.10 | Applying alpha-rule on (2291) yields:
% 29.29/8.10 | (2292) all_0_25_25 = e2
% 29.29/8.10 | (2293) ~ (all_0_26_26 = e1)
% 29.29/8.10 |
% 29.29/8.10 | Combining equations (2292,2274) yields a new equation:
% 29.29/8.10 | (622) e2 = e0
% 29.29/8.10 |
% 29.29/8.10 | Simplifying 622 yields:
% 29.29/8.10 | (316) e2 = e0
% 29.29/8.10 |
% 29.29/8.10 | Equations (316) can reduce 57 to:
% 29.29/8.10 | (270) $false
% 29.29/8.10 |
% 29.29/8.10 |-The branch is then unsatisfiable
% 29.29/8.10 |-Branch two:
% 29.29/8.10 | (2296) all_0_28_28 = e0 & ~ (all_0_29_29 = e1)
% 29.29/8.10 |
% 29.29/8.10 | Applying alpha-rule on (2296) yields:
% 29.29/8.10 | (2297) all_0_28_28 = e0
% 29.29/8.10 | (2298) ~ (all_0_29_29 = e1)
% 29.29/8.10 |
% 29.29/8.10 | Combining equations (2297,9135) yields a new equation:
% 29.29/8.10 | (479) e4 = e0
% 29.29/8.10 |
% 29.29/8.10 | Equations (479) can reduce 6 to:
% 29.29/8.10 | (270) $false
% 29.29/8.10 |
% 29.29/8.10 |-The branch is then unsatisfiable
% 29.29/8.10 |-Branch two:
% 29.29/8.10 | (419) ~ (all_0_56_56 = e0)
% 29.29/8.10 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 29.29/8.10 |
% 29.29/8.10 +-Applying beta-rule and splitting (834), into two cases.
% 29.29/8.10 |-Branch one:
% 29.29/8.10 | (2258) all_0_57_57 = e0
% 29.29/8.10 |
% 29.29/8.10 | Combining equations (869,2258) yields a new equation:
% 29.29/8.10 | (783) e3 = e0
% 29.29/8.10 |
% 29.29/8.10 | Simplifying 783 yields:
% 29.29/8.10 | (784) e3 = e0
% 29.29/8.10 |
% 29.29/8.10 | Equations (784) can reduce 66 to:
% 29.29/8.10 | (270) $false
% 29.29/8.10 |
% 29.29/8.10 |-The branch is then unsatisfiable
% 29.29/8.10 |-Branch two:
% 29.29/8.10 | (2301) ~ (all_0_57_57 = e0)
% 29.29/8.10 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 29.29/8.10 |
% 29.29/8.10 +-Applying beta-rule and splitting (2302), into two cases.
% 29.29/8.10 |-Branch one:
% 29.29/8.10 | (585) all_0_58_58 = e0
% 29.29/8.10 |
% 29.29/8.10 | Combining equations (585,600) yields a new equation:
% 29.29/8.10 | (479) e4 = e0
% 29.29/8.10 |
% 29.29/8.10 | Equations (479) can reduce 6 to:
% 29.29/8.10 | (270) $false
% 29.29/8.10 |
% 29.29/8.10 |-The branch is then unsatisfiable
% 29.29/8.10 |-Branch two:
% 29.29/8.10 | (431) ~ (all_0_58_58 = e0)
% 29.29/8.10 | (2308) all_0_59_59 = e0
% 29.29/8.10 |
% 29.29/8.10 | Combining equations (424,2308) yields a new equation:
% 29.29/8.10 | (571) e1 = e0
% 29.29/8.10 |
% 29.29/8.10 | Simplifying 571 yields:
% 29.29/8.10 | (560) e1 = e0
% 29.29/8.10 |
% 29.29/8.10 | Equations (560) can reduce 132 to:
% 29.29/8.10 | (270) $false
% 29.29/8.10 |
% 29.29/8.10 |-The branch is then unsatisfiable
% 29.29/8.10 |-Branch two:
% 29.29/8.10 | (846) ~ (all_0_57_57 = e3)
% 29.29/8.10 | (997) all_0_57_57 = e1
% 29.29/8.10 |
% 29.29/8.10 | Equations (997) can reduce 644 to:
% 29.29/8.10 | (270) $false
% 29.29/8.10 |
% 29.29/8.10 |-The branch is then unsatisfiable
% 29.29/8.10 |-Branch two:
% 29.29/8.10 | (642) ~ (all_0_52_52 = e1)
% 29.29/8.10 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 29.29/8.10 |
% 29.29/8.10 +-Applying beta-rule and splitting (852), into two cases.
% 29.29/8.10 |-Branch one:
% 29.29/8.10 | (853) all_0_53_53 = e1
% 29.29/8.10 |
% 29.29/8.10 | Combining equations (423,853) yields a new equation:
% 29.29/8.10 | (560) e1 = e0
% 29.29/8.10 |
% 29.29/8.10 | Equations (560) can reduce 132 to:
% 29.29/8.10 | (270) $false
% 29.29/8.10 |
% 29.29/8.10 |-The branch is then unsatisfiable
% 29.29/8.10 |-Branch two:
% 29.29/8.10 | (874) ~ (all_0_53_53 = e1)
% 29.29/8.10 | (875) all_0_54_54 = e1
% 29.29/8.10 |
% 29.29/8.10 | Combining equations (875,3657) yields a new equation:
% 29.29/8.10 | (322) e2 = e1
% 29.29/8.10 |
% 29.29/8.10 | Equations (322) can reduce 141 to:
% 29.29/8.10 | (270) $false
% 29.29/8.10 |
% 29.29/8.10 |-The branch is then unsatisfiable
% 29.29/8.10 |-Branch two:
% 29.29/8.10 | (625) ~ (all_0_44_44 = e0)
% 29.29/8.10 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 29.29/8.10 |
% 29.29/8.10 +-Applying beta-rule and splitting (90), into two cases.
% 29.29/8.10 |-Branch one:
% 29.29/8.10 | (685) all_0_52_52 = e2
% 29.29/8.10 |
% 29.29/8.10 | Equations (685) can reduce 257 to:
% 29.29/8.10 | (270) $false
% 29.29/8.10 |
% 29.29/8.10 |-The branch is then unsatisfiable
% 29.29/8.10 |-Branch two:
% 29.29/8.10 | (257) ~ (all_0_52_52 = e2)
% 29.29/8.10 | (688) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 29.29/8.10 |
% 29.29/8.10 +-Applying beta-rule and splitting (688), into two cases.
% 29.29/8.10 |-Branch one:
% 29.29/8.10 | (827) all_0_52_52 = e0
% 29.29/8.10 |
% 29.29/8.10 | Equations (827) can reduce 925 to:
% 29.29/8.10 | (270) $false
% 29.29/8.10 |
% 29.29/8.10 |-The branch is then unsatisfiable
% 29.29/8.10 |-Branch two:
% 29.29/8.10 | (925) ~ (all_0_52_52 = e0)
% 29.29/8.10 | (926) all_0_52_52 = e3 | all_0_52_52 = e1
% 29.29/8.10 |
% 29.29/8.10 +-Applying beta-rule and splitting (926), into two cases.
% 29.29/8.10 |-Branch one:
% 29.29/8.10 | (864) all_0_52_52 = e3
% 29.29/8.10 |
% 29.29/8.10 | Equations (864) can reduce 826 to:
% 29.29/8.10 | (270) $false
% 29.29/8.10 |
% 29.29/8.10 |-The branch is then unsatisfiable
% 29.29/8.10 |-Branch two:
% 29.29/8.10 | (826) ~ (all_0_52_52 = e3)
% 29.29/8.10 | (848) all_0_52_52 = e1
% 29.29/8.10 |
% 29.29/8.10 | Equations (848) can reduce 826 to:
% 29.29/8.10 | (769) ~ (e3 = e1)
% 29.29/8.10 |
% 29.29/8.10 | Simplifying 769 yields:
% 29.29/8.10 | (136) ~ (e3 = e1)
% 29.29/8.10 |
% 29.29/8.10 +-Applying beta-rule and splitting (3656), into two cases.
% 29.29/8.10 |-Branch one:
% 29.29/8.10 | (1091) all_0_46_46 = e3
% 29.29/8.10 |
% 29.29/8.10 | Equations (1091) can reduce 174 to:
% 29.29/8.10 | (862) ~ (all_0_44_44 = e3)
% 29.29/8.10 |
% 29.29/8.10 +-Applying beta-rule and splitting (373), into two cases.
% 29.29/8.10 |-Branch one:
% 29.29/8.10 | (621) all_0_44_44 = e0
% 29.29/8.10 |
% 29.29/8.10 | Equations (621) can reduce 625 to:
% 29.29/8.10 | (270) $false
% 29.29/8.10 |
% 29.29/8.10 |-The branch is then unsatisfiable
% 29.29/8.10 |-Branch two:
% 29.29/8.10 | (625) ~ (all_0_44_44 = e0)
% 29.29/8.10 | (858) all_0_44_44 = e3
% 29.29/8.10 |
% 29.29/8.10 | Equations (858) can reduce 862 to:
% 29.29/8.10 | (270) $false
% 29.29/8.10 |
% 29.29/8.10 |-The branch is then unsatisfiable
% 29.29/8.10 |-Branch two:
% 29.29/8.10 | (413) ~ (all_0_46_46 = e3)
% 29.29/8.10 | (3700) all_0_54_54 = e3 | all_0_59_59 = e3
% 29.29/8.10 |
% 29.29/8.10 +-Applying beta-rule and splitting (3700), into two cases.
% 29.29/8.10 |-Branch one:
% 29.29/8.10 | (1119) all_0_54_54 = e3
% 29.29/8.10 |
% 29.29/8.10 | Combining equations (3657,1119) yields a new equation:
% 29.29/8.10 | (414) e3 = e2
% 29.29/8.10 |
% 29.29/8.10 | Equations (414) can reduce 223 to:
% 29.29/8.10 | (270) $false
% 29.29/8.10 |
% 29.29/8.10 |-The branch is then unsatisfiable
% 29.29/8.10 |-Branch two:
% 29.29/8.10 | (1093) ~ (all_0_54_54 = e3)
% 29.29/8.10 | (412) all_0_59_59 = e3
% 29.29/8.10 |
% 29.29/8.11 | Combining equations (412,424) yields a new equation:
% 29.29/8.11 | (537) e3 = e1
% 29.29/8.11 |
% 29.29/8.11 | Simplifying 537 yields:
% 29.29/8.11 | (538) e3 = e1
% 29.29/8.11 |
% 29.29/8.11 | Equations (538) can reduce 136 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (932) ~ (all_0_51_51 = e3)
% 29.29/8.11 | (5007) all_0_51_51 = e4 | all_0_51_51 = e1
% 29.29/8.11 |
% 29.29/8.11 +-Applying beta-rule and splitting (135), into two cases.
% 29.29/8.11 |-Branch one:
% 29.29/8.11 | (820) all_0_51_51 = e1
% 29.29/8.11 |
% 29.29/8.11 | Equations (820) can reduce 748 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (748) ~ (all_0_51_51 = e1)
% 29.29/8.11 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 29.29/8.11 |
% 29.29/8.11 +-Applying beta-rule and splitting (823), into two cases.
% 29.29/8.11 |-Branch one:
% 29.29/8.11 | (848) all_0_52_52 = e1
% 29.29/8.11 |
% 29.29/8.11 | Equations (848) can reduce 154 to:
% 29.29/8.11 | (748) ~ (all_0_51_51 = e1)
% 29.29/8.11 |
% 29.29/8.11 +-Applying beta-rule and splitting (5007), into two cases.
% 29.29/8.11 |-Branch one:
% 29.29/8.11 | (820) all_0_51_51 = e1
% 29.29/8.11 |
% 29.29/8.11 | Equations (820) can reduce 748 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (748) ~ (all_0_51_51 = e1)
% 29.29/8.11 | (1467) all_0_51_51 = e4
% 29.29/8.11 |
% 29.29/8.11 | Equations (1467) can reduce 697 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (642) ~ (all_0_52_52 = e1)
% 29.29/8.11 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 29.29/8.11 |
% 29.29/8.11 +-Applying beta-rule and splitting (852), into two cases.
% 29.29/8.11 |-Branch one:
% 29.29/8.11 | (853) all_0_53_53 = e1
% 29.29/8.11 |
% 29.29/8.11 | Combining equations (853,423) yields a new equation:
% 29.29/8.11 | (571) e1 = e0
% 29.29/8.11 |
% 29.29/8.11 | Simplifying 571 yields:
% 29.29/8.11 | (560) e1 = e0
% 29.29/8.11 |
% 29.29/8.11 | Equations (560) can reduce 132 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (874) ~ (all_0_53_53 = e1)
% 29.29/8.11 | (875) all_0_54_54 = e1
% 29.29/8.11 |
% 29.29/8.11 | Combining equations (875,3657) yields a new equation:
% 29.29/8.11 | (322) e2 = e1
% 29.29/8.11 |
% 29.29/8.11 | Equations (322) can reduce 141 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (588) ~ (all_0_48_48 = e1)
% 29.29/8.11 | (4925) all_0_53_53 = e1 | all_0_58_58 = e1
% 29.29/8.11 |
% 29.29/8.11 +-Applying beta-rule and splitting (135), into two cases.
% 29.29/8.11 |-Branch one:
% 29.29/8.11 | (820) all_0_51_51 = e1
% 29.29/8.11 |
% 29.29/8.11 | Equations (820) can reduce 748 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (748) ~ (all_0_51_51 = e1)
% 29.29/8.11 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 29.29/8.11 |
% 29.29/8.11 +-Applying beta-rule and splitting (116), into two cases.
% 29.29/8.11 |-Branch one:
% 29.29/8.11 | (411) all_0_43_43 = e0
% 29.29/8.11 |
% 29.29/8.11 | Combining equations (411,502) yields a new equation:
% 29.29/8.11 | (479) e4 = e0
% 29.29/8.11 |
% 29.29/8.11 | Equations (479) can reduce 6 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (455) ~ (all_0_43_43 = e0)
% 29.29/8.11 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 29.29/8.11 |
% 29.29/8.11 | Equations (502) can reduce 455 to:
% 29.29/8.11 | (6) ~ (e4 = e0)
% 29.29/8.11 |
% 29.29/8.11 +-Applying beta-rule and splitting (75), into two cases.
% 29.29/8.11 |-Branch one:
% 29.29/8.11 | (411) all_0_43_43 = e0
% 29.29/8.11 |
% 29.29/8.11 | Combining equations (411,502) yields a new equation:
% 29.29/8.11 | (479) e4 = e0
% 29.29/8.11 |
% 29.29/8.11 | Equations (479) can reduce 6 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (455) ~ (all_0_43_43 = e0)
% 29.29/8.11 | (940) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 29.29/8.11 |
% 29.29/8.11 +-Applying beta-rule and splitting (1122), into two cases.
% 29.29/8.11 |-Branch one:
% 29.29/8.11 | (621) all_0_44_44 = e0
% 29.29/8.11 |
% 29.29/8.11 | Equations (621) can reduce 122 to:
% 29.29/8.11 | (4297) ~ (all_0_52_52 = e0)
% 29.29/8.11 |
% 29.29/8.11 | Simplifying 4297 yields:
% 29.29/8.11 | (925) ~ (all_0_52_52 = e0)
% 29.29/8.11 |
% 29.29/8.11 | Equations (621) can reduce 333 to:
% 29.29/8.11 | (566) ~ (e2 = e0)
% 29.29/8.11 |
% 29.29/8.11 | Simplifying 566 yields:
% 29.29/8.11 | (57) ~ (e2 = e0)
% 29.29/8.11 |
% 29.29/8.11 +-Applying beta-rule and splitting (940), into two cases.
% 29.29/8.11 |-Branch one:
% 29.29/8.11 | (315) all_0_47_47 = e0
% 29.29/8.11 |
% 29.29/8.11 | Combining equations (290,315) yields a new equation:
% 29.29/8.11 | (622) e2 = e0
% 29.29/8.11 |
% 29.29/8.11 | Simplifying 622 yields:
% 29.29/8.11 | (316) e2 = e0
% 29.29/8.11 |
% 29.29/8.11 | Equations (316) can reduce 57 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (318) ~ (all_0_47_47 = e0)
% 29.29/8.11 | (950) all_0_51_51 = e0 | all_0_56_56 = e0
% 29.29/8.11 |
% 29.29/8.11 +-Applying beta-rule and splitting (950), into two cases.
% 29.29/8.11 |-Branch one:
% 29.29/8.11 | (954) all_0_51_51 = e0
% 29.29/8.11 |
% 29.29/8.11 | Equations (954) can reduce 987 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (987) ~ (all_0_51_51 = e0)
% 29.29/8.11 | (830) all_0_56_56 = e0
% 29.29/8.11 |
% 29.29/8.11 | Equations (830) can reduce 995 to:
% 29.29/8.11 | (568) ~ (e1 = e0)
% 29.29/8.11 |
% 29.29/8.11 | Simplifying 568 yields:
% 29.29/8.11 | (132) ~ (e1 = e0)
% 29.29/8.11 |
% 29.29/8.11 +-Applying beta-rule and splitting (823), into two cases.
% 29.29/8.11 |-Branch one:
% 29.29/8.11 | (848) all_0_52_52 = e1
% 29.29/8.11 |
% 29.29/8.11 | Equations (848) can reduce 230 to:
% 29.29/8.11 | (1021) ~ (e4 = e1)
% 29.29/8.11 |
% 29.29/8.11 | Simplifying 1021 yields:
% 29.29/8.11 | (251) ~ (e4 = e1)
% 29.29/8.11 |
% 29.29/8.11 | Equations (848) can reduce 925 to:
% 29.29/8.11 | (132) ~ (e1 = e0)
% 29.29/8.11 |
% 29.29/8.11 +-Applying beta-rule and splitting (4925), into two cases.
% 29.29/8.11 |-Branch one:
% 29.29/8.11 | (853) all_0_53_53 = e1
% 29.29/8.11 |
% 29.29/8.11 | Combining equations (423,853) yields a new equation:
% 29.29/8.11 | (560) e1 = e0
% 29.29/8.11 |
% 29.29/8.11 | Equations (560) can reduce 132 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (874) ~ (all_0_53_53 = e1)
% 29.29/8.11 | (1001) all_0_58_58 = e1
% 29.29/8.11 |
% 29.29/8.11 | Combining equations (600,1001) yields a new equation:
% 29.29/8.11 | (525) e4 = e1
% 29.29/8.11 |
% 29.29/8.11 | Simplifying 525 yields:
% 29.29/8.11 | (526) e4 = e1
% 29.29/8.11 |
% 29.29/8.11 | Equations (526) can reduce 251 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (642) ~ (all_0_52_52 = e1)
% 29.29/8.11 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 29.29/8.11 |
% 29.29/8.11 +-Applying beta-rule and splitting (852), into two cases.
% 29.29/8.11 |-Branch one:
% 29.29/8.11 | (853) all_0_53_53 = e1
% 29.29/8.11 |
% 29.29/8.11 | Combining equations (853,423) yields a new equation:
% 29.29/8.11 | (571) e1 = e0
% 29.29/8.11 |
% 29.29/8.11 | Simplifying 571 yields:
% 29.29/8.11 | (560) e1 = e0
% 29.29/8.11 |
% 29.29/8.11 | Equations (560) can reduce 132 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (874) ~ (all_0_53_53 = e1)
% 29.29/8.11 | (875) all_0_54_54 = e1
% 29.29/8.11 |
% 29.29/8.11 | Combining equations (3657,875) yields a new equation:
% 29.29/8.11 | (531) e2 = e1
% 29.29/8.11 |
% 29.29/8.11 | Simplifying 531 yields:
% 29.29/8.11 | (322) e2 = e1
% 29.29/8.11 |
% 29.29/8.11 | Equations (322) can reduce 141 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (625) ~ (all_0_44_44 = e0)
% 29.29/8.11 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 29.29/8.11 |
% 29.29/8.11 +-Applying beta-rule and splitting (940), into two cases.
% 29.29/8.11 |-Branch one:
% 29.29/8.11 | (315) all_0_47_47 = e0
% 29.29/8.11 |
% 29.29/8.11 | Combining equations (290,315) yields a new equation:
% 29.29/8.11 | (622) e2 = e0
% 29.29/8.11 |
% 29.29/8.11 | Simplifying 622 yields:
% 29.29/8.11 | (316) e2 = e0
% 29.29/8.11 |
% 29.29/8.11 | Equations (316) can reduce 57 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (318) ~ (all_0_47_47 = e0)
% 29.29/8.11 | (950) all_0_51_51 = e0 | all_0_56_56 = e0
% 29.29/8.11 |
% 29.29/8.11 | Equations (290) can reduce 318 to:
% 29.29/8.11 | (57) ~ (e2 = e0)
% 29.29/8.11 |
% 29.29/8.11 +-Applying beta-rule and splitting (1128), into two cases.
% 29.29/8.11 |-Branch one:
% 29.29/8.11 | (454) all_0_45_45 = e0
% 29.29/8.11 |
% 29.29/8.11 | Combining equations (374,454) yields a new equation:
% 29.29/8.11 | (622) e2 = e0
% 29.29/8.11 |
% 29.29/8.11 | Simplifying 622 yields:
% 29.29/8.11 | (316) e2 = e0
% 29.29/8.11 |
% 29.29/8.11 | Equations (316) can reduce 57 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (488) ~ (all_0_45_45 = e0)
% 29.29/8.11 | (1132) all_0_46_46 = e0
% 29.29/8.11 |
% 29.29/8.11 | Equations (1132) can reduce 1010 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (1231) ~ (all_0_49_49 = e0)
% 29.29/8.11 | (589) all_0_49_49 = e1
% 29.29/8.11 |
% 29.29/8.11 | Equations (589) can reduce 543 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 29.29/8.11 |
% 29.29/8.11 | Applying alpha-rule on (428) yields:
% 29.29/8.11 | (423) all_0_53_53 = e0
% 29.29/8.11 | (424) all_0_59_59 = e1
% 29.29/8.11 | (431) ~ (all_0_58_58 = e0)
% 29.29/8.11 |
% 29.29/8.11 | Equations (424) can reduce 113 to:
% 29.29/8.11 | (543) ~ (all_0_49_49 = e1)
% 29.29/8.11 |
% 29.29/8.11 | Equations (423) can reduce 12 to:
% 29.29/8.11 | (987) ~ (all_0_51_51 = e0)
% 29.29/8.11 |
% 29.29/8.11 | Equations (423) can reduce 213 to:
% 29.29/8.11 | (925) ~ (all_0_52_52 = e0)
% 29.29/8.11 |
% 29.29/8.11 | Equations (424) can reduce 185 to:
% 29.29/8.11 | (995) ~ (all_0_56_56 = e1)
% 29.29/8.11 |
% 29.29/8.11 | Equations (424) can reduce 701 to:
% 29.29/8.11 | (645) ~ (e2 = e1)
% 29.29/8.11 |
% 29.29/8.11 | Simplifying 645 yields:
% 29.29/8.11 | (141) ~ (e2 = e1)
% 29.29/8.11 |
% 29.29/8.11 | From (423) and (227) follows:
% 29.29/8.11 | (2167) op(e1, e1) = e0
% 29.29/8.11 |
% 29.29/8.11 +-Applying beta-rule and splitting (52), into two cases.
% 29.29/8.11 |-Branch one:
% 29.29/8.11 | (536) all_0_41_41 = e1
% 29.29/8.11 |
% 29.29/8.11 | Combining equations (351,536) yields a new equation:
% 29.29/8.11 | (537) e3 = e1
% 29.29/8.11 |
% 29.29/8.11 | Simplifying 537 yields:
% 29.29/8.11 | (538) e3 = e1
% 29.29/8.11 |
% 29.29/8.11 | Equations (538) can reduce 136 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (540) ~ (all_0_41_41 = e1)
% 29.29/8.11 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 29.29/8.11 |
% 29.29/8.11 +-Applying beta-rule and splitting (310), into two cases.
% 29.29/8.11 |-Branch one:
% 29.29/8.11 | (563) all_0_49_49 = e0
% 29.29/8.11 |
% 29.29/8.11 | Equations (563) can reduce 198 to:
% 29.29/8.11 | (1010) ~ (all_0_46_46 = e0)
% 29.29/8.11 |
% 29.29/8.11 | Equations (563) can reduce 4 to:
% 29.29/8.11 | (562) ~ (all_0_48_48 = e0)
% 29.29/8.11 |
% 29.29/8.11 | Equations (563) can reduce 202 to:
% 29.29/8.11 | (456) ~ (e4 = e0)
% 29.29/8.11 |
% 29.29/8.11 | Simplifying 456 yields:
% 29.29/8.11 | (6) ~ (e4 = e0)
% 29.29/8.11 |
% 29.29/8.11 | Equations (563) can reduce 296 to:
% 29.29/8.11 | (566) ~ (e2 = e0)
% 29.29/8.11 |
% 29.29/8.11 | Simplifying 566 yields:
% 29.29/8.11 | (57) ~ (e2 = e0)
% 29.29/8.11 |
% 29.29/8.11 +-Applying beta-rule and splitting (95), into two cases.
% 29.29/8.11 |-Branch one:
% 29.29/8.11 | (1258) all_0_42_42 = e3
% 29.29/8.11 |
% 29.29/8.11 | Combining equations (512,1258) yields a new equation:
% 29.29/8.11 | (660) e4 = e3
% 29.29/8.11 |
% 29.29/8.11 | Simplifying 660 yields:
% 29.29/8.11 | (359) e4 = e3
% 29.29/8.11 |
% 29.29/8.11 | Equations (359) can reduce 34 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (1316) ~ (all_0_42_42 = e3)
% 29.29/8.11 | (3656) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 29.29/8.11 |
% 29.29/8.11 +-Applying beta-rule and splitting (173), into two cases.
% 29.29/8.11 |-Branch one:
% 29.29/8.11 | (4215) all_0_51_51 = e2
% 29.29/8.11 |
% 29.29/8.11 | Equations (4215) can reduce 255 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (255) ~ (all_0_51_51 = e2)
% 29.29/8.11 | (4888) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1 | all_0_51_51 = e0
% 29.29/8.11 |
% 29.29/8.11 +-Applying beta-rule and splitting (4888), into two cases.
% 29.29/8.11 |-Branch one:
% 29.29/8.11 | (954) all_0_51_51 = e0
% 29.29/8.11 |
% 29.29/8.11 | Equations (954) can reduce 987 to:
% 29.29/8.11 | (270) $false
% 29.29/8.11 |
% 29.29/8.11 |-The branch is then unsatisfiable
% 29.29/8.11 |-Branch two:
% 29.29/8.11 | (987) ~ (all_0_51_51 = e0)
% 29.29/8.11 | (5003) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1
% 29.29/8.11 |
% 29.29/8.11 +-Applying beta-rule and splitting (762), into two cases.
% 29.29/8.11 |-Branch one:
% 29.29/8.11 | (552) all_0_48_48 = e1
% 29.29/8.11 |
% 29.29/8.11 | Equations (552) can reduce 294 to:
% 29.29/8.11 | (645) ~ (e2 = e1)
% 29.29/8.12 |
% 29.29/8.12 | Simplifying 645 yields:
% 29.29/8.12 | (141) ~ (e2 = e1)
% 29.29/8.12 |
% 29.29/8.12 | Equations (552) can reduce 562 to:
% 29.29/8.12 | (132) ~ (e1 = e0)
% 29.29/8.12 |
% 29.29/8.12 | From (552) and (76) follows:
% 29.29/8.12 | (2127) op(e1, e1) = all_0_25_25
% 29.29/8.12 |
% 29.29/8.12 +-Applying beta-rule and splitting (5003), into two cases.
% 29.29/8.12 |-Branch one:
% 29.29/8.12 | (824) all_0_51_51 = e3
% 29.29/8.12 |
% 29.29/8.12 | Combining equations (824,1847) yields a new equation:
% 29.29/8.12 | (6797) all_0_21_21 = e3
% 29.29/8.12 |
% 29.29/8.12 | Equations (824) can reduce 154 to:
% 29.29/8.12 | (825) ~ (all_0_52_52 = e3)
% 29.29/8.12 |
% 29.29/8.12 | Simplifying 825 yields:
% 29.29/8.12 | (826) ~ (all_0_52_52 = e3)
% 29.29/8.12 |
% 29.29/8.12 | Equations (824) can reduce 255 to:
% 29.29/8.12 | (223) ~ (e3 = e2)
% 29.29/8.12 |
% 29.29/8.12 | Equations (824) can reduce 748 to:
% 29.29/8.12 | (136) ~ (e3 = e1)
% 29.29/8.12 |
% 29.29/8.12 +-Applying beta-rule and splitting (135), into two cases.
% 29.29/8.12 |-Branch one:
% 29.29/8.12 | (820) all_0_51_51 = e1
% 29.29/8.12 |
% 29.29/8.12 | Combining equations (824,820) yields a new equation:
% 29.29/8.12 | (537) e3 = e1
% 29.29/8.12 |
% 29.29/8.12 | Simplifying 537 yields:
% 29.29/8.12 | (538) e3 = e1
% 29.29/8.12 |
% 29.29/8.12 | Equations (538) can reduce 136 to:
% 29.29/8.12 | (270) $false
% 29.29/8.12 |
% 29.29/8.12 |-The branch is then unsatisfiable
% 29.29/8.12 |-Branch two:
% 29.29/8.12 | (748) ~ (all_0_51_51 = e1)
% 29.29/8.12 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 29.29/8.12 |
% 29.29/8.12 +-Applying beta-rule and splitting (116), into two cases.
% 29.29/8.12 |-Branch one:
% 29.29/8.12 | (411) all_0_43_43 = e0
% 29.29/8.12 |
% 29.29/8.12 | Combining equations (502,411) yields a new equation:
% 29.29/8.12 | (478) e4 = e0
% 29.29/8.12 |
% 29.29/8.12 | Simplifying 478 yields:
% 29.29/8.12 | (479) e4 = e0
% 29.29/8.12 |
% 29.29/8.12 | Equations (479) can reduce 6 to:
% 29.29/8.12 | (270) $false
% 29.29/8.12 |
% 29.29/8.12 |-The branch is then unsatisfiable
% 29.29/8.12 |-Branch two:
% 29.29/8.12 | (455) ~ (all_0_43_43 = e0)
% 29.29/8.12 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 29.29/8.12 |
% 29.29/8.12 +-Applying beta-rule and splitting (1122), into two cases.
% 29.29/8.12 |-Branch one:
% 29.29/8.12 | (621) all_0_44_44 = e0
% 29.29/8.12 |
% 29.29/8.12 | Equations (621) can reduce 122 to:
% 29.29/8.12 | (4297) ~ (all_0_52_52 = e0)
% 29.29/8.12 |
% 29.29/8.12 | Simplifying 4297 yields:
% 29.29/8.12 | (925) ~ (all_0_52_52 = e0)
% 29.29/8.12 |
% 29.29/8.12 | Equations (621) can reduce 10 to:
% 29.29/8.12 | (9326) ~ (all_0_57_57 = e0)
% 29.29/8.12 |
% 29.29/8.12 | Simplifying 9326 yields:
% 29.29/8.12 | (2301) ~ (all_0_57_57 = e0)
% 29.29/8.12 |
% 29.29/8.12 | Equations (621) can reduce 45 to:
% 29.29/8.12 | (456) ~ (e4 = e0)
% 29.29/8.12 |
% 29.29/8.12 | Simplifying 456 yields:
% 29.29/8.12 | (6) ~ (e4 = e0)
% 29.29/8.12 |
% 29.29/8.12 | Equations (621) can reduce 131 to:
% 29.29/8.12 | (568) ~ (e1 = e0)
% 29.29/8.12 |
% 29.29/8.12 | Simplifying 568 yields:
% 29.29/8.12 | (132) ~ (e1 = e0)
% 29.29/8.12 |
% 29.29/8.12 +-Applying beta-rule and splitting (33), into two cases.
% 29.29/8.12 |-Branch one:
% 29.29/8.12 | (392) all_0_57_57 = e2
% 29.29/8.12 |
% 29.29/8.12 | Equations (392) can reduce 335 to:
% 29.29/8.12 | (270) $false
% 29.29/8.12 |
% 29.29/8.12 |-The branch is then unsatisfiable
% 29.29/8.12 |-Branch two:
% 29.29/8.12 | (335) ~ (all_0_57_57 = e2)
% 29.29/8.12 | (670) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 29.29/8.12 |
% 29.29/8.12 +-Applying beta-rule and splitting (823), into two cases.
% 29.29/8.12 |-Branch one:
% 29.29/8.12 | (848) all_0_52_52 = e1
% 29.29/8.12 |
% 29.29/8.12 | Equations (848) can reduce 235 to:
% 29.29/8.12 | (643) ~ (all_0_57_57 = e1)
% 29.29/8.12 |
% 29.29/8.12 | Simplifying 643 yields:
% 29.29/8.12 | (644) ~ (all_0_57_57 = e1)
% 29.29/8.12 |
% 29.29/8.12 | Equations (848) can reduce 925 to:
% 29.29/8.12 | (132) ~ (e1 = e0)
% 29.29/8.12 |
% 29.29/8.12 | From (848) and (195) follows:
% 29.29/8.12 | (9340) op(e1, e1) = all_0_18_18
% 29.29/8.12 |
% 29.29/8.12 | From (848) and (203) follows:
% 29.29/8.12 | (9341) op(e1, e2) = e1
% 29.29/8.12 |
% 29.29/8.12 +-Applying beta-rule and splitting (670), into two cases.
% 29.29/8.12 |-Branch one:
% 29.29/8.12 | (2258) all_0_57_57 = e0
% 29.29/8.12 |
% 29.29/8.12 | Equations (2258) can reduce 2301 to:
% 29.29/8.12 | (270) $false
% 29.29/8.12 |
% 29.29/8.12 |-The branch is then unsatisfiable
% 29.29/8.12 |-Branch two:
% 29.29/8.12 | (2301) ~ (all_0_57_57 = e0)
% 29.29/8.12 | (9345) all_0_57_57 = e3 | all_0_57_57 = e1
% 29.29/8.12 |
% 29.29/8.12 +-Applying beta-rule and splitting (9345), into two cases.
% 29.29/8.12 |-Branch one:
% 29.29/8.12 | (869) all_0_57_57 = e3
% 29.29/8.12 |
% 29.29/8.12 | Equations (869) can reduce 143 to:
% 29.29/8.12 | (719) ~ (e4 = e3)
% 29.29/8.12 |
% 29.29/8.12 | Simplifying 719 yields:
% 29.29/8.12 | (34) ~ (e4 = e3)
% 29.29/8.12 |
% 29.29/8.12 | Equations (869) can reduce 644 to:
% 29.29/8.12 | (136) ~ (e3 = e1)
% 29.29/8.12 |
% 29.29/8.12 | Equations (869) can reduce 2301 to:
% 29.29/8.12 | (66) ~ (e3 = e0)
% 29.29/8.12 |
% 29.29/8.12 +-Applying beta-rule and splitting (176), into two cases.
% 29.29/8.12 |-Branch one:
% 29.29/8.12 | (830) all_0_56_56 = e0
% 29.29/8.12 |
% 29.29/8.12 | Equations (830) can reduce 274 to:
% 29.29/8.12 | (456) ~ (e4 = e0)
% 29.29/8.12 |
% 29.29/8.12 | Simplifying 456 yields:
% 29.29/8.12 | (6) ~ (e4 = e0)
% 29.29/8.12 |
% 29.29/8.12 | Equations (830) can reduce 300 to:
% 29.29/8.12 | (566) ~ (e2 = e0)
% 29.29/8.12 |
% 29.29/8.12 | Simplifying 566 yields:
% 29.29/8.12 | (57) ~ (e2 = e0)
% 29.29/8.12 |
% 29.29/8.12 | Instantiating formula (201) with e1, e2, e1, all_0_23_23 and discharging atoms op(e1, e2) = all_0_23_23, op(e1, e2) = e1, yields:
% 29.29/8.12 | (9356) all_0_23_23 = e1
% 29.29/8.12 |
% 29.29/8.12 | Instantiating formula (201) with e1, e1, all_0_25_25, all_0_18_18 and discharging atoms op(e1, e1) = all_0_18_18, op(e1, e1) = all_0_25_25, yields:
% 29.29/8.12 | (9357) all_0_18_18 = all_0_25_25
% 29.29/8.12 |
% 29.29/8.12 | Instantiating formula (201) with e1, e1, e0, all_0_18_18 and discharging atoms op(e1, e1) = all_0_18_18, op(e1, e1) = e0, yields:
% 29.29/8.12 | (9358) all_0_18_18 = e0
% 29.29/8.12 |
% 29.29/8.12 | Combining equations (9357,9358) yields a new equation:
% 29.29/8.12 | (9359) all_0_25_25 = e0
% 29.29/8.12 |
% 29.29/8.12 | Simplifying 9359 yields:
% 29.29/8.12 | (2274) all_0_25_25 = e0
% 29.29/8.12 |
% 29.29/8.12 +-Applying beta-rule and splitting (14), into two cases.
% 29.29/8.12 |-Branch one:
% 29.29/8.12 | (2277) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1))
% 29.29/8.12 |
% 29.29/8.12 +-Applying beta-rule and splitting (2277), into two cases.
% 29.29/8.12 |-Branch one:
% 29.29/8.12 | (2278) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1))
% 29.29/8.12 |
% 29.29/8.12 +-Applying beta-rule and splitting (2278), into two cases.
% 29.29/8.12 |-Branch one:
% 29.29/8.12 | (2279) all_0_21_21 = e4 & ~ (all_0_22_22 = e1)
% 29.29/8.12 |
% 29.29/8.12 | Applying alpha-rule on (2279) yields:
% 29.29/8.12 | (2280) all_0_21_21 = e4
% 29.29/8.12 | (2281) ~ (all_0_22_22 = e1)
% 29.29/8.12 |
% 29.29/8.12 | Combining equations (2280,6797) yields a new equation:
% 29.29/8.12 | (660) e4 = e3
% 29.29/8.12 |
% 29.29/8.12 | Simplifying 660 yields:
% 29.29/8.12 | (359) e4 = e3
% 29.29/8.12 |
% 29.29/8.12 | Equations (359) can reduce 34 to:
% 29.29/8.12 | (270) $false
% 29.29/8.12 |
% 29.29/8.12 |-The branch is then unsatisfiable
% 29.29/8.12 |-Branch two:
% 29.29/8.12 | (2285) all_0_23_23 = e3 & ~ (all_0_24_24 = e1)
% 29.29/8.12 |
% 29.29/8.12 | Applying alpha-rule on (2285) yields:
% 29.29/8.12 | (2286) all_0_23_23 = e3
% 29.29/8.12 | (2287) ~ (all_0_24_24 = e1)
% 29.29/8.12 |
% 29.29/8.12 | Combining equations (2286,9356) yields a new equation:
% 29.29/8.12 | (537) e3 = e1
% 29.29/8.12 |
% 29.29/8.12 | Simplifying 537 yields:
% 29.29/8.12 | (538) e3 = e1
% 29.29/8.12 |
% 29.29/8.12 | Equations (538) can reduce 136 to:
% 29.29/8.12 | (270) $false
% 29.29/8.12 |
% 29.29/8.12 |-The branch is then unsatisfiable
% 29.29/8.12 |-Branch two:
% 29.29/8.12 | (2291) all_0_25_25 = e2 & ~ (all_0_26_26 = e1)
% 29.29/8.12 |
% 29.29/8.12 | Applying alpha-rule on (2291) yields:
% 29.29/8.12 | (2292) all_0_25_25 = e2
% 29.29/8.12 | (2293) ~ (all_0_26_26 = e1)
% 29.29/8.12 |
% 29.29/8.12 | Combining equations (2292,2274) yields a new equation:
% 29.29/8.12 | (622) e2 = e0
% 29.29/8.12 |
% 29.29/8.12 | Simplifying 622 yields:
% 29.29/8.12 | (316) e2 = e0
% 29.29/8.12 |
% 29.29/8.12 | Equations (316) can reduce 57 to:
% 29.29/8.12 | (270) $false
% 29.29/8.12 |
% 29.29/8.12 |-The branch is then unsatisfiable
% 29.29/8.12 |-Branch two:
% 29.29/8.12 | (2296) all_0_28_28 = e0 & ~ (all_0_29_29 = e1)
% 29.29/8.12 |
% 29.29/8.12 | Applying alpha-rule on (2296) yields:
% 29.29/8.12 | (2297) all_0_28_28 = e0
% 29.29/8.12 | (2298) ~ (all_0_29_29 = e1)
% 29.29/8.12 |
% 29.29/8.13 | Combining equations (2297,9135) yields a new equation:
% 29.29/8.13 | (479) e4 = e0
% 29.29/8.13 |
% 29.29/8.13 | Equations (479) can reduce 6 to:
% 29.29/8.13 | (270) $false
% 29.29/8.13 |
% 29.29/8.13 |-The branch is then unsatisfiable
% 29.29/8.13 |-Branch two:
% 29.29/8.13 | (419) ~ (all_0_56_56 = e0)
% 29.29/8.13 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 29.29/8.13 |
% 29.29/8.13 +-Applying beta-rule and splitting (834), into two cases.
% 29.29/8.13 |-Branch one:
% 29.29/8.13 | (2258) all_0_57_57 = e0
% 29.29/8.13 |
% 29.29/8.13 | Combining equations (869,2258) yields a new equation:
% 29.29/8.13 | (783) e3 = e0
% 29.29/8.13 |
% 29.29/8.13 | Simplifying 783 yields:
% 29.29/8.13 | (784) e3 = e0
% 29.29/8.13 |
% 29.29/8.13 | Equations (784) can reduce 66 to:
% 29.29/8.13 | (270) $false
% 29.29/8.13 |
% 29.29/8.13 |-The branch is then unsatisfiable
% 29.29/8.13 |-Branch two:
% 29.29/8.13 | (2301) ~ (all_0_57_57 = e0)
% 29.29/8.13 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 29.29/8.13 |
% 29.29/8.13 +-Applying beta-rule and splitting (2302), into two cases.
% 29.29/8.13 |-Branch one:
% 29.29/8.13 | (585) all_0_58_58 = e0
% 29.29/8.13 |
% 29.29/8.13 | Combining equations (585,600) yields a new equation:
% 29.29/8.13 | (479) e4 = e0
% 29.29/8.13 |
% 29.29/8.13 | Equations (479) can reduce 6 to:
% 29.29/8.13 | (270) $false
% 29.29/8.13 |
% 29.29/8.13 |-The branch is then unsatisfiable
% 29.29/8.13 |-Branch two:
% 29.29/8.13 | (431) ~ (all_0_58_58 = e0)
% 29.29/8.13 | (2308) all_0_59_59 = e0
% 29.29/8.13 |
% 29.29/8.13 | Combining equations (424,2308) yields a new equation:
% 29.29/8.13 | (571) e1 = e0
% 29.29/8.13 |
% 29.29/8.13 | Simplifying 571 yields:
% 29.29/8.13 | (560) e1 = e0
% 29.29/8.13 |
% 29.29/8.13 | Equations (560) can reduce 132 to:
% 29.29/8.13 | (270) $false
% 29.29/8.13 |
% 29.29/8.13 |-The branch is then unsatisfiable
% 29.29/8.13 |-Branch two:
% 29.29/8.13 | (846) ~ (all_0_57_57 = e3)
% 29.29/8.13 | (997) all_0_57_57 = e1
% 29.29/8.13 |
% 29.29/8.13 | Equations (997) can reduce 644 to:
% 29.29/8.13 | (270) $false
% 29.29/8.13 |
% 29.29/8.13 |-The branch is then unsatisfiable
% 29.29/8.13 |-Branch two:
% 29.29/8.13 | (642) ~ (all_0_52_52 = e1)
% 29.29/8.13 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 29.29/8.13 |
% 29.29/8.13 +-Applying beta-rule and splitting (852), into two cases.
% 29.29/8.13 |-Branch one:
% 29.29/8.13 | (853) all_0_53_53 = e1
% 29.29/8.13 |
% 29.29/8.13 | Combining equations (423,853) yields a new equation:
% 29.29/8.13 | (560) e1 = e0
% 29.29/8.13 |
% 29.29/8.13 | Equations (560) can reduce 132 to:
% 29.29/8.13 | (270) $false
% 29.29/8.13 |
% 29.29/8.13 |-The branch is then unsatisfiable
% 29.29/8.13 |-Branch two:
% 29.29/8.13 | (874) ~ (all_0_53_53 = e1)
% 29.29/8.13 | (875) all_0_54_54 = e1
% 29.29/8.13 |
% 29.29/8.13 | Combining equations (875,3657) yields a new equation:
% 29.29/8.13 | (322) e2 = e1
% 29.29/8.13 |
% 29.29/8.13 | Equations (322) can reduce 141 to:
% 29.29/8.13 | (270) $false
% 29.29/8.13 |
% 29.29/8.13 |-The branch is then unsatisfiable
% 29.29/8.13 |-Branch two:
% 29.29/8.13 | (625) ~ (all_0_44_44 = e0)
% 29.29/8.13 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 29.29/8.13 |
% 29.29/8.13 +-Applying beta-rule and splitting (90), into two cases.
% 29.29/8.13 |-Branch one:
% 29.29/8.13 | (685) all_0_52_52 = e2
% 29.29/8.13 |
% 29.29/8.13 | Equations (685) can reduce 257 to:
% 29.29/8.13 | (270) $false
% 29.29/8.13 |
% 29.29/8.13 |-The branch is then unsatisfiable
% 29.29/8.13 |-Branch two:
% 29.29/8.13 | (257) ~ (all_0_52_52 = e2)
% 29.29/8.13 | (688) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 29.29/8.13 |
% 29.29/8.13 +-Applying beta-rule and splitting (688), into two cases.
% 29.29/8.13 |-Branch one:
% 29.29/8.13 | (827) all_0_52_52 = e0
% 29.29/8.13 |
% 29.29/8.13 | Equations (827) can reduce 925 to:
% 29.29/8.13 | (270) $false
% 29.29/8.13 |
% 29.29/8.13 |-The branch is then unsatisfiable
% 29.29/8.13 |-Branch two:
% 29.29/8.13 | (925) ~ (all_0_52_52 = e0)
% 29.29/8.13 | (926) all_0_52_52 = e3 | all_0_52_52 = e1
% 29.29/8.13 |
% 29.29/8.13 +-Applying beta-rule and splitting (926), into two cases.
% 29.29/8.13 |-Branch one:
% 29.29/8.13 | (864) all_0_52_52 = e3
% 29.29/8.13 |
% 29.29/8.13 | Equations (864) can reduce 826 to:
% 29.29/8.13 | (270) $false
% 29.29/8.13 |
% 29.29/8.13 |-The branch is then unsatisfiable
% 29.29/8.13 |-Branch two:
% 29.29/8.13 | (826) ~ (all_0_52_52 = e3)
% 29.29/8.13 | (848) all_0_52_52 = e1
% 29.29/8.13 |
% 29.29/8.13 | Equations (848) can reduce 826 to:
% 29.29/8.13 | (769) ~ (e3 = e1)
% 29.29/8.13 |
% 29.29/8.13 | Simplifying 769 yields:
% 29.29/8.13 | (136) ~ (e3 = e1)
% 29.29/8.13 |
% 29.29/8.13 +-Applying beta-rule and splitting (3656), into two cases.
% 29.29/8.13 |-Branch one:
% 29.29/8.13 | (1091) all_0_46_46 = e3
% 29.29/8.13 |
% 29.29/8.13 | Equations (1091) can reduce 174 to:
% 29.29/8.13 | (862) ~ (all_0_44_44 = e3)
% 29.29/8.13 |
% 29.29/8.13 +-Applying beta-rule and splitting (373), into two cases.
% 29.29/8.13 |-Branch one:
% 29.29/8.13 | (621) all_0_44_44 = e0
% 29.29/8.13 |
% 29.29/8.13 | Equations (621) can reduce 625 to:
% 29.29/8.13 | (270) $false
% 29.29/8.13 |
% 29.29/8.13 |-The branch is then unsatisfiable
% 29.29/8.13 |-Branch two:
% 29.29/8.13 | (625) ~ (all_0_44_44 = e0)
% 29.29/8.13 | (858) all_0_44_44 = e3
% 29.29/8.13 |
% 29.29/8.13 | Equations (858) can reduce 862 to:
% 29.29/8.13 | (270) $false
% 29.29/8.13 |
% 29.29/8.13 |-The branch is then unsatisfiable
% 29.29/8.13 |-Branch two:
% 29.29/8.13 | (413) ~ (all_0_46_46 = e3)
% 29.29/8.13 | (3700) all_0_54_54 = e3 | all_0_59_59 = e3
% 29.29/8.13 |
% 29.29/8.13 +-Applying beta-rule and splitting (3700), into two cases.
% 29.29/8.13 |-Branch one:
% 29.29/8.13 | (1119) all_0_54_54 = e3
% 29.29/8.13 |
% 29.29/8.13 | Combining equations (3657,1119) yields a new equation:
% 29.29/8.13 | (414) e3 = e2
% 29.29/8.13 |
% 29.29/8.13 | Equations (414) can reduce 223 to:
% 29.29/8.13 | (270) $false
% 29.29/8.13 |
% 29.29/8.13 |-The branch is then unsatisfiable
% 29.29/8.13 |-Branch two:
% 29.29/8.13 | (1093) ~ (all_0_54_54 = e3)
% 29.29/8.13 | (412) all_0_59_59 = e3
% 29.29/8.13 |
% 29.29/8.13 | Combining equations (412,424) yields a new equation:
% 29.29/8.13 | (537) e3 = e1
% 29.29/8.13 |
% 29.29/8.13 | Simplifying 537 yields:
% 29.29/8.13 | (538) e3 = e1
% 29.29/8.13 |
% 29.29/8.13 | Equations (538) can reduce 136 to:
% 29.29/8.13 | (270) $false
% 29.29/8.13 |
% 29.29/8.13 |-The branch is then unsatisfiable
% 29.29/8.13 |-Branch two:
% 29.29/8.13 | (932) ~ (all_0_51_51 = e3)
% 29.29/8.13 | (5007) all_0_51_51 = e4 | all_0_51_51 = e1
% 29.29/8.13 |
% 29.29/8.13 +-Applying beta-rule and splitting (135), into two cases.
% 29.29/8.13 |-Branch one:
% 29.29/8.13 | (820) all_0_51_51 = e1
% 29.29/8.13 |
% 29.29/8.13 | Equations (820) can reduce 748 to:
% 29.29/8.13 | (270) $false
% 29.29/8.13 |
% 29.29/8.13 |-The branch is then unsatisfiable
% 29.29/8.13 |-Branch two:
% 29.29/8.13 | (748) ~ (all_0_51_51 = e1)
% 29.29/8.13 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 29.29/8.13 |
% 29.29/8.13 +-Applying beta-rule and splitting (823), into two cases.
% 29.29/8.13 |-Branch one:
% 29.29/8.13 | (848) all_0_52_52 = e1
% 29.29/8.13 |
% 29.29/8.13 | Equations (848) can reduce 154 to:
% 29.29/8.13 | (748) ~ (all_0_51_51 = e1)
% 29.29/8.13 |
% 29.29/8.13 +-Applying beta-rule and splitting (5007), into two cases.
% 29.29/8.13 |-Branch one:
% 29.29/8.13 | (820) all_0_51_51 = e1
% 29.29/8.13 |
% 29.29/8.13 | Equations (820) can reduce 748 to:
% 29.29/8.13 | (270) $false
% 29.29/8.13 |
% 29.29/8.13 |-The branch is then unsatisfiable
% 29.29/8.13 |-Branch two:
% 29.29/8.13 | (748) ~ (all_0_51_51 = e1)
% 29.29/8.13 | (1467) all_0_51_51 = e4
% 29.29/8.13 |
% 29.29/8.13 | Equations (1467) can reduce 697 to:
% 29.29/8.13 | (270) $false
% 29.29/8.13 |
% 29.29/8.13 |-The branch is then unsatisfiable
% 29.29/8.13 |-Branch two:
% 29.29/8.13 | (642) ~ (all_0_52_52 = e1)
% 29.29/8.13 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 29.29/8.13 |
% 29.29/8.13 +-Applying beta-rule and splitting (852), into two cases.
% 29.29/8.13 |-Branch one:
% 29.29/8.13 | (853) all_0_53_53 = e1
% 29.29/8.13 |
% 29.29/8.13 | Combining equations (853,423) yields a new equation:
% 29.29/8.13 | (571) e1 = e0
% 29.29/8.13 |
% 29.29/8.13 | Simplifying 571 yields:
% 29.29/8.13 | (560) e1 = e0
% 29.29/8.13 |
% 29.29/8.13 | Equations (560) can reduce 132 to:
% 29.29/8.13 | (270) $false
% 29.29/8.13 |
% 29.29/8.13 |-The branch is then unsatisfiable
% 29.29/8.13 |-Branch two:
% 29.29/8.13 | (874) ~ (all_0_53_53 = e1)
% 29.29/8.13 | (875) all_0_54_54 = e1
% 29.29/8.13 |
% 29.29/8.13 | Combining equations (875,3657) yields a new equation:
% 29.29/8.13 | (322) e2 = e1
% 29.29/8.13 |
% 29.29/8.13 | Equations (322) can reduce 141 to:
% 29.29/8.13 | (270) $false
% 29.29/8.13 |
% 29.29/8.13 |-The branch is then unsatisfiable
% 29.29/8.13 |-Branch two:
% 29.29/8.13 | (588) ~ (all_0_48_48 = e1)
% 29.29/8.13 | (4925) all_0_53_53 = e1 | all_0_58_58 = e1
% 29.29/8.13 |
% 29.29/8.13 +-Applying beta-rule and splitting (135), into two cases.
% 29.29/8.13 |-Branch one:
% 29.29/8.13 | (820) all_0_51_51 = e1
% 29.29/8.13 |
% 29.29/8.13 | Equations (820) can reduce 748 to:
% 29.29/8.13 | (270) $false
% 29.29/8.13 |
% 29.29/8.13 |-The branch is then unsatisfiable
% 29.29/8.13 |-Branch two:
% 29.29/8.13 | (748) ~ (all_0_51_51 = e1)
% 29.29/8.13 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 29.29/8.13 |
% 29.29/8.13 +-Applying beta-rule and splitting (116), into two cases.
% 29.29/8.13 |-Branch one:
% 29.29/8.13 | (411) all_0_43_43 = e0
% 29.29/8.13 |
% 29.29/8.13 | Combining equations (411,502) yields a new equation:
% 29.29/8.13 | (479) e4 = e0
% 29.29/8.13 |
% 29.29/8.13 | Equations (479) can reduce 6 to:
% 29.29/8.13 | (270) $false
% 29.29/8.13 |
% 29.29/8.13 |-The branch is then unsatisfiable
% 29.29/8.13 |-Branch two:
% 29.29/8.13 | (455) ~ (all_0_43_43 = e0)
% 29.29/8.13 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 29.29/8.13 |
% 29.29/8.13 | Equations (502) can reduce 455 to:
% 29.29/8.13 | (6) ~ (e4 = e0)
% 29.29/8.13 |
% 29.29/8.13 +-Applying beta-rule and splitting (75), into two cases.
% 29.29/8.13 |-Branch one:
% 29.29/8.13 | (411) all_0_43_43 = e0
% 29.29/8.13 |
% 29.29/8.13 | Combining equations (411,502) yields a new equation:
% 29.29/8.13 | (479) e4 = e0
% 29.29/8.13 |
% 29.29/8.13 | Equations (479) can reduce 6 to:
% 29.29/8.13 | (270) $false
% 29.29/8.13 |
% 29.29/8.13 |-The branch is then unsatisfiable
% 29.29/8.13 |-Branch two:
% 29.29/8.13 | (455) ~ (all_0_43_43 = e0)
% 29.29/8.13 | (940) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 29.29/8.13 |
% 29.29/8.13 +-Applying beta-rule and splitting (1122), into two cases.
% 29.29/8.13 |-Branch one:
% 29.29/8.13 | (621) all_0_44_44 = e0
% 29.29/8.13 |
% 29.29/8.13 | Equations (621) can reduce 122 to:
% 29.29/8.13 | (4297) ~ (all_0_52_52 = e0)
% 29.29/8.13 |
% 29.29/8.13 | Simplifying 4297 yields:
% 29.29/8.13 | (925) ~ (all_0_52_52 = e0)
% 29.29/8.13 |
% 29.29/8.13 | Equations (621) can reduce 333 to:
% 29.29/8.13 | (566) ~ (e2 = e0)
% 29.29/8.13 |
% 29.29/8.13 | Simplifying 566 yields:
% 29.29/8.13 | (57) ~ (e2 = e0)
% 29.29/8.13 |
% 29.29/8.13 +-Applying beta-rule and splitting (940), into two cases.
% 29.29/8.13 |-Branch one:
% 29.29/8.13 | (315) all_0_47_47 = e0
% 29.29/8.13 |
% 29.29/8.13 | Combining equations (290,315) yields a new equation:
% 29.29/8.13 | (622) e2 = e0
% 29.61/8.13 |
% 29.61/8.13 | Simplifying 622 yields:
% 29.61/8.13 | (316) e2 = e0
% 29.61/8.13 |
% 29.61/8.13 | Equations (316) can reduce 57 to:
% 29.61/8.13 | (270) $false
% 29.61/8.13 |
% 29.61/8.13 |-The branch is then unsatisfiable
% 29.61/8.13 |-Branch two:
% 29.61/8.13 | (318) ~ (all_0_47_47 = e0)
% 29.61/8.13 | (950) all_0_51_51 = e0 | all_0_56_56 = e0
% 29.61/8.13 |
% 29.61/8.13 +-Applying beta-rule and splitting (950), into two cases.
% 29.61/8.13 |-Branch one:
% 29.61/8.13 | (954) all_0_51_51 = e0
% 29.61/8.13 |
% 29.61/8.13 | Equations (954) can reduce 987 to:
% 29.61/8.13 | (270) $false
% 29.61/8.13 |
% 29.61/8.13 |-The branch is then unsatisfiable
% 29.61/8.13 |-Branch two:
% 29.61/8.13 | (987) ~ (all_0_51_51 = e0)
% 29.61/8.13 | (830) all_0_56_56 = e0
% 29.61/8.13 |
% 29.61/8.13 | Equations (830) can reduce 995 to:
% 29.61/8.13 | (568) ~ (e1 = e0)
% 29.61/8.13 |
% 29.61/8.13 | Simplifying 568 yields:
% 29.61/8.13 | (132) ~ (e1 = e0)
% 29.61/8.13 |
% 29.61/8.13 +-Applying beta-rule and splitting (823), into two cases.
% 29.61/8.13 |-Branch one:
% 29.61/8.13 | (848) all_0_52_52 = e1
% 29.61/8.13 |
% 29.61/8.13 | Equations (848) can reduce 230 to:
% 29.61/8.13 | (1021) ~ (e4 = e1)
% 29.61/8.13 |
% 29.61/8.13 | Simplifying 1021 yields:
% 29.61/8.13 | (251) ~ (e4 = e1)
% 29.61/8.13 |
% 29.61/8.13 | Equations (848) can reduce 925 to:
% 29.61/8.13 | (132) ~ (e1 = e0)
% 29.61/8.13 |
% 29.61/8.13 +-Applying beta-rule and splitting (4925), into two cases.
% 29.61/8.13 |-Branch one:
% 29.61/8.13 | (853) all_0_53_53 = e1
% 29.61/8.13 |
% 29.61/8.13 | Combining equations (423,853) yields a new equation:
% 29.61/8.13 | (560) e1 = e0
% 29.61/8.13 |
% 29.61/8.13 | Equations (560) can reduce 132 to:
% 29.61/8.13 | (270) $false
% 29.61/8.13 |
% 29.61/8.13 |-The branch is then unsatisfiable
% 29.61/8.13 |-Branch two:
% 29.61/8.13 | (874) ~ (all_0_53_53 = e1)
% 29.61/8.13 | (1001) all_0_58_58 = e1
% 29.61/8.13 |
% 29.61/8.13 | Combining equations (600,1001) yields a new equation:
% 29.61/8.13 | (525) e4 = e1
% 29.61/8.13 |
% 29.61/8.13 | Simplifying 525 yields:
% 29.61/8.13 | (526) e4 = e1
% 29.61/8.13 |
% 29.61/8.13 | Equations (526) can reduce 251 to:
% 29.61/8.13 | (270) $false
% 29.61/8.13 |
% 29.61/8.13 |-The branch is then unsatisfiable
% 29.61/8.13 |-Branch two:
% 29.61/8.13 | (642) ~ (all_0_52_52 = e1)
% 29.61/8.13 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 29.61/8.13 |
% 29.61/8.13 +-Applying beta-rule and splitting (852), into two cases.
% 29.61/8.13 |-Branch one:
% 29.61/8.13 | (853) all_0_53_53 = e1
% 29.61/8.13 |
% 29.61/8.13 | Combining equations (853,423) yields a new equation:
% 29.61/8.13 | (571) e1 = e0
% 29.61/8.13 |
% 29.61/8.13 | Simplifying 571 yields:
% 29.61/8.13 | (560) e1 = e0
% 29.61/8.13 |
% 29.61/8.13 | Equations (560) can reduce 132 to:
% 29.61/8.13 | (270) $false
% 29.61/8.13 |
% 29.61/8.13 |-The branch is then unsatisfiable
% 29.61/8.13 |-Branch two:
% 29.61/8.13 | (874) ~ (all_0_53_53 = e1)
% 29.61/8.13 | (875) all_0_54_54 = e1
% 29.61/8.13 |
% 29.61/8.13 | Combining equations (3657,875) yields a new equation:
% 29.61/8.13 | (531) e2 = e1
% 29.61/8.13 |
% 29.61/8.13 | Simplifying 531 yields:
% 29.61/8.13 | (322) e2 = e1
% 29.61/8.13 |
% 29.61/8.13 | Equations (322) can reduce 141 to:
% 29.61/8.13 | (270) $false
% 29.61/8.13 |
% 29.61/8.13 |-The branch is then unsatisfiable
% 29.61/8.13 |-Branch two:
% 29.61/8.13 | (625) ~ (all_0_44_44 = e0)
% 29.61/8.14 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 29.61/8.14 |
% 29.61/8.14 +-Applying beta-rule and splitting (940), into two cases.
% 29.61/8.14 |-Branch one:
% 29.61/8.14 | (315) all_0_47_47 = e0
% 29.61/8.14 |
% 29.61/8.14 | Combining equations (290,315) yields a new equation:
% 29.61/8.14 | (622) e2 = e0
% 29.61/8.14 |
% 29.61/8.14 | Simplifying 622 yields:
% 29.61/8.14 | (316) e2 = e0
% 29.61/8.14 |
% 29.61/8.14 | Equations (316) can reduce 57 to:
% 29.61/8.14 | (270) $false
% 29.61/8.14 |
% 29.61/8.14 |-The branch is then unsatisfiable
% 29.61/8.14 |-Branch two:
% 29.61/8.14 | (318) ~ (all_0_47_47 = e0)
% 29.61/8.14 | (950) all_0_51_51 = e0 | all_0_56_56 = e0
% 29.61/8.14 |
% 29.61/8.14 | Equations (290) can reduce 318 to:
% 29.61/8.14 | (57) ~ (e2 = e0)
% 29.61/8.14 |
% 29.61/8.14 +-Applying beta-rule and splitting (1128), into two cases.
% 29.61/8.14 |-Branch one:
% 29.61/8.14 | (454) all_0_45_45 = e0
% 29.61/8.14 |
% 29.61/8.14 | Combining equations (374,454) yields a new equation:
% 29.61/8.14 | (622) e2 = e0
% 29.61/8.14 |
% 29.61/8.14 | Simplifying 622 yields:
% 29.61/8.14 | (316) e2 = e0
% 29.61/8.14 |
% 29.61/8.14 | Equations (316) can reduce 57 to:
% 29.61/8.14 | (270) $false
% 29.61/8.14 |
% 29.61/8.14 |-The branch is then unsatisfiable
% 29.61/8.14 |-Branch two:
% 29.61/8.14 | (488) ~ (all_0_45_45 = e0)
% 29.61/8.14 | (1132) all_0_46_46 = e0
% 29.61/8.14 |
% 29.61/8.14 | Equations (1132) can reduce 1010 to:
% 29.61/8.14 | (270) $false
% 29.61/8.14 |
% 29.61/8.14 |-The branch is then unsatisfiable
% 29.61/8.14 |-Branch two:
% 29.61/8.14 | (1231) ~ (all_0_49_49 = e0)
% 29.61/8.14 | (589) all_0_49_49 = e1
% 29.61/8.14 |
% 29.61/8.14 | Equations (589) can reduce 543 to:
% 29.61/8.14 | (270) $false
% 29.61/8.14 |
% 29.61/8.14 |-The branch is then unsatisfiable
% 29.61/8.14 |-Branch two:
% 29.61/8.14 | (261) ~ (all_0_54_54 = e2)
% 29.61/8.14 | (399) all_0_59_59 = e2
% 29.61/8.14 |
% 29.61/8.14 | Equations (399) can reduce 701 to:
% 29.61/8.14 | (270) $false
% 29.61/8.14 |
% 29.61/8.14 |-The branch is then unsatisfiable
% 29.61/8.14 |-Branch two:
% 29.61/8.14 | (434) ~ (all_0_45_45 = e2)
% 29.61/8.14 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 29.61/8.14 |
% 29.61/8.14 +-Applying beta-rule and splitting (453), into two cases.
% 29.61/8.14 |-Branch one:
% 29.61/8.14 | (370) all_0_44_44 = e2
% 29.61/8.14 |
% 29.61/8.14 | Equations (370) can reduce 333 to:
% 29.61/8.14 | (270) $false
% 29.61/8.14 |
% 29.61/8.14 |-The branch is then unsatisfiable
% 29.61/8.14 |-Branch two:
% 29.61/8.14 | (333) ~ (all_0_44_44 = e2)
% 29.61/8.14 | (493) all_0_45_45 = e2 | all_0_46_46 = e2
% 29.61/8.14 |
% 29.61/8.14 +-Applying beta-rule and splitting (435), into two cases.
% 29.61/8.14 |-Branch one:
% 29.61/8.14 | (454) all_0_45_45 = e0
% 29.61/8.14 |
% 29.61/8.14 | Equations (454) can reduce 65 to:
% 29.61/8.14 | (7709) ~ (all_0_48_48 = e0)
% 29.61/8.14 |
% 29.61/8.14 | Simplifying 7709 yields:
% 29.61/8.14 | (562) ~ (all_0_48_48 = e0)
% 29.61/8.14 |
% 29.61/8.14 +-Applying beta-rule and splitting (314), into two cases.
% 29.61/8.14 |-Branch one:
% 29.61/8.14 | (559) all_0_48_48 = e0
% 29.61/8.14 |
% 29.61/8.14 | Equations (559) can reduce 562 to:
% 29.61/8.14 | (270) $false
% 29.61/8.14 |
% 29.61/8.14 |-The branch is then unsatisfiable
% 29.61/8.14 |-Branch two:
% 29.61/8.14 | (562) ~ (all_0_48_48 = e0)
% 29.61/8.14 | (552) all_0_48_48 = e1
% 29.61/8.14 |
% 29.61/8.14 | Equations (552) can reduce 4 to:
% 29.61/8.14 | (542) ~ (all_0_49_49 = e1)
% 29.61/8.14 |
% 29.61/8.14 | Simplifying 542 yields:
% 29.61/8.14 | (543) ~ (all_0_49_49 = e1)
% 29.61/8.14 |
% 29.61/8.14 +-Applying beta-rule and splitting (220), into two cases.
% 29.61/8.14 |-Branch one:
% 29.61/8.14 | (497) all_0_46_46 = e2
% 29.61/8.14 |
% 29.61/8.14 | Equations (497) can reduce 198 to:
% 29.61/8.14 | (295) ~ (all_0_49_49 = e2)
% 29.61/8.14 |
% 29.61/8.14 | Simplifying 295 yields:
% 29.61/8.14 | (296) ~ (all_0_49_49 = e2)
% 29.61/8.14 |
% 29.61/8.14 | Equations (497) can reduce 215 to:
% 29.61/8.14 | (260) ~ (all_0_54_54 = e2)
% 29.61/8.14 |
% 29.61/8.14 | Simplifying 260 yields:
% 29.61/8.14 | (261) ~ (all_0_54_54 = e2)
% 29.61/8.14 |
% 29.61/8.14 | Equations (497) can reduce 805 to:
% 29.61/8.14 | (377) ~ (e4 = e2)
% 29.61/8.14 |
% 29.61/8.14 | Simplifying 377 yields:
% 29.61/8.14 | (231) ~ (e4 = e2)
% 29.61/8.14 |
% 29.61/8.14 +-Applying beta-rule and splitting (58), into two cases.
% 29.61/8.14 |-Branch one:
% 29.61/8.14 | (253) all_0_50_50 = e2
% 29.61/8.14 |
% 29.61/8.14 | Combining equations (267,253) yields a new equation:
% 29.61/8.14 | (268) e4 = e2
% 29.61/8.14 |
% 29.61/8.14 | Simplifying 268 yields:
% 29.61/8.14 | (269) e4 = e2
% 29.61/8.14 |
% 29.61/8.14 | Equations (269) can reduce 231 to:
% 29.61/8.14 | (270) $false
% 29.61/8.14 |
% 29.61/8.14 |-The branch is then unsatisfiable
% 29.61/8.14 |-Branch two:
% 29.61/8.14 | (9032) ~ (all_0_50_50 = e2)
% 29.61/8.14 | (9860) all_0_51_51 = e2 | all_0_52_52 = e2 | all_0_53_53 = e2 | all_0_54_54 = e2
% 29.61/8.14 |
% 29.61/8.14 +-Applying beta-rule and splitting (9860), into two cases.
% 29.61/8.14 |-Branch one:
% 29.61/8.14 | (4215) all_0_51_51 = e2
% 29.61/8.14 |
% 29.61/8.14 | Equations (4215) can reduce 255 to:
% 29.61/8.14 | (270) $false
% 29.61/8.14 |
% 29.61/8.14 |-The branch is then unsatisfiable
% 29.61/8.14 |-Branch two:
% 29.61/8.14 | (255) ~ (all_0_51_51 = e2)
% 29.61/8.14 | (9864) all_0_52_52 = e2 | all_0_53_53 = e2 | all_0_54_54 = e2
% 29.61/8.14 |
% 29.61/8.14 +-Applying beta-rule and splitting (9864), into two cases.
% 29.61/8.14 |-Branch one:
% 29.61/8.14 | (685) all_0_52_52 = e2
% 29.61/8.14 |
% 29.61/8.14 | Equations (685) can reduce 257 to:
% 29.61/8.14 | (270) $false
% 29.61/8.14 |
% 29.61/8.14 |-The branch is then unsatisfiable
% 29.61/8.14 |-Branch two:
% 29.61/8.14 | (257) ~ (all_0_52_52 = e2)
% 29.61/8.14 | (9868) all_0_53_53 = e2 | all_0_54_54 = e2
% 29.61/8.14 |
% 29.61/8.14 +-Applying beta-rule and splitting (9868), into two cases.
% 29.61/8.14 |-Branch one:
% 29.61/8.14 | (576) all_0_53_53 = e2
% 29.61/8.14 |
% 29.61/8.14 +-Applying beta-rule and splitting (93), into two cases.
% 29.61/8.14 |-Branch one:
% 29.61/8.14 | (402) all_0_59_59 = e4
% 29.61/8.14 |
% 29.61/8.14 | Equations (402) can reduce 280 to:
% 29.61/8.14 | (270) $false
% 29.61/8.14 |
% 29.61/8.14 |-The branch is then unsatisfiable
% 29.61/8.14 |-Branch two:
% 29.61/8.14 | (280) ~ (all_0_59_59 = e4)
% 29.61/8.14 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 29.61/8.14 |
% 29.61/8.14 +-Applying beta-rule and splitting (310), into two cases.
% 29.61/8.14 |-Branch one:
% 29.61/8.14 | (563) all_0_49_49 = e0
% 29.61/8.14 |
% 29.61/8.14 | Equations (563) can reduce 202 to:
% 29.61/8.14 | (456) ~ (e4 = e0)
% 29.61/8.14 |
% 29.61/8.14 | Simplifying 456 yields:
% 29.61/8.14 | (6) ~ (e4 = e0)
% 29.61/8.14 |
% 29.61/8.14 | Equations (563) can reduce 296 to:
% 29.61/8.14 | (566) ~ (e2 = e0)
% 29.61/8.14 |
% 29.61/8.14 | Simplifying 566 yields:
% 29.61/8.14 | (57) ~ (e2 = e0)
% 29.61/8.14 |
% 29.61/8.14 +-Applying beta-rule and splitting (407), into two cases.
% 29.61/8.14 |-Branch one:
% 29.61/8.14 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 29.61/8.14 |
% 29.61/8.14 +-Applying beta-rule and splitting (408), into two cases.
% 29.61/8.14 |-Branch one:
% 29.61/8.14 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 29.61/8.14 |
% 29.61/8.14 +-Applying beta-rule and splitting (409), into two cases.
% 29.61/8.14 |-Branch one:
% 29.61/8.14 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 29.61/8.14 |
% 29.61/8.14 | Applying alpha-rule on (410) yields:
% 29.61/8.14 | (411) all_0_43_43 = e0
% 29.61/8.14 | (412) all_0_59_59 = e3
% 29.61/8.14 | (413) ~ (all_0_46_46 = e3)
% 29.61/8.14 |
% 29.61/8.14 | Combining equations (411,502) yields a new equation:
% 29.61/8.14 | (479) e4 = e0
% 29.61/8.14 |
% 29.61/8.14 | Equations (479) can reduce 6 to:
% 29.61/8.14 | (270) $false
% 29.61/8.14 |
% 29.61/8.14 |-The branch is then unsatisfiable
% 29.61/8.14 |-Branch two:
% 29.61/8.14 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 29.61/8.14 |
% 29.61/8.14 | Applying alpha-rule on (416) yields:
% 29.61/8.14 | (411) all_0_43_43 = e0
% 29.61/8.14 | (412) all_0_59_59 = e3
% 29.61/8.14 | (419) ~ (all_0_56_56 = e0)
% 29.61/8.14 |
% 29.61/8.14 | Combining equations (411,502) yields a new equation:
% 29.61/8.14 | (479) e4 = e0
% 29.61/8.14 |
% 29.61/8.14 | Equations (479) can reduce 6 to:
% 29.61/8.14 | (270) $false
% 29.61/8.14 |
% 29.61/8.14 |-The branch is then unsatisfiable
% 29.61/8.14 |-Branch two:
% 29.61/8.14 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 29.61/8.14 |
% 29.61/8.14 | Applying alpha-rule on (422) yields:
% 29.61/8.14 | (423) all_0_53_53 = e0
% 29.61/8.14 | (424) all_0_59_59 = e1
% 29.61/8.14 | (425) ~ (all_0_54_54 = e1)
% 29.61/8.14 |
% 29.61/8.14 | Combining equations (423,576) yields a new equation:
% 29.61/8.14 | (316) e2 = e0
% 29.61/8.14 |
% 29.61/8.14 | Equations (316) can reduce 57 to:
% 29.61/8.14 | (270) $false
% 29.61/8.14 |
% 29.61/8.14 |-The branch is then unsatisfiable
% 29.61/8.14 |-Branch two:
% 29.61/8.14 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 29.61/8.14 |
% 29.61/8.14 | Applying alpha-rule on (428) yields:
% 29.61/8.14 | (423) all_0_53_53 = e0
% 29.61/8.14 | (424) all_0_59_59 = e1
% 29.61/8.14 | (431) ~ (all_0_58_58 = e0)
% 29.61/8.14 |
% 29.61/8.14 | Combining equations (423,576) yields a new equation:
% 29.61/8.14 | (316) e2 = e0
% 29.61/8.14 |
% 29.61/8.14 | Equations (316) can reduce 57 to:
% 29.61/8.14 | (270) $false
% 29.61/8.14 |
% 29.61/8.14 |-The branch is then unsatisfiable
% 29.61/8.14 |-Branch two:
% 29.61/8.14 | (1231) ~ (all_0_49_49 = e0)
% 29.61/8.14 | (589) all_0_49_49 = e1
% 29.61/8.14 |
% 29.61/8.14 | Equations (589) can reduce 543 to:
% 29.61/8.14 | (270) $false
% 29.61/8.14 |
% 29.61/8.14 |-The branch is then unsatisfiable
% 29.61/8.14 |-Branch two:
% 29.61/8.14 | (259) ~ (all_0_53_53 = e2)
% 29.61/8.14 | (3657) all_0_54_54 = e2
% 29.61/8.14 |
% 29.61/8.14 | Equations (3657) can reduce 261 to:
% 29.61/8.14 | (270) $false
% 29.61/8.14 |
% 29.61/8.14 |-The branch is then unsatisfiable
% 29.61/8.14 |-Branch two:
% 29.61/8.14 | (1436) ~ (all_0_46_46 = e2)
% 29.61/8.14 | (1523) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e0
% 29.61/8.14 |
% 29.61/8.14 +-Applying beta-rule and splitting (310), into two cases.
% 29.61/8.14 |-Branch one:
% 29.61/8.14 | (563) all_0_49_49 = e0
% 29.61/8.14 |
% 29.61/8.14 | Equations (563) can reduce 296 to:
% 29.61/8.14 | (566) ~ (e2 = e0)
% 29.61/8.14 |
% 29.61/8.14 | Simplifying 566 yields:
% 29.61/8.14 | (57) ~ (e2 = e0)
% 29.61/8.14 |
% 29.61/8.14 +-Applying beta-rule and splitting (493), into two cases.
% 29.61/8.14 |-Branch one:
% 29.61/8.14 | (374) all_0_45_45 = e2
% 29.61/8.14 |
% 29.61/8.14 | Combining equations (454,374) yields a new equation:
% 29.61/8.14 | (316) e2 = e0
% 29.61/8.14 |
% 29.61/8.14 | Equations (316) can reduce 57 to:
% 29.61/8.14 | (270) $false
% 29.61/8.14 |
% 29.61/8.14 |-The branch is then unsatisfiable
% 29.61/8.14 |-Branch two:
% 29.61/8.14 | (434) ~ (all_0_45_45 = e2)
% 29.61/8.14 | (497) all_0_46_46 = e2
% 29.61/8.14 |
% 29.61/8.14 | Equations (497) can reduce 1436 to:
% 29.61/8.14 | (270) $false
% 29.61/8.14 |
% 29.61/8.14 |-The branch is then unsatisfiable
% 29.61/8.14 |-Branch two:
% 29.61/8.14 | (1231) ~ (all_0_49_49 = e0)
% 29.61/8.14 | (589) all_0_49_49 = e1
% 29.61/8.14 |
% 29.61/8.14 | Equations (589) can reduce 543 to:
% 29.61/8.14 | (270) $false
% 29.61/8.14 |
% 29.61/8.14 |-The branch is then unsatisfiable
% 29.61/8.14 |-Branch two:
% 29.61/8.14 | (488) ~ (all_0_45_45 = e0)
% 29.61/8.14 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 29.61/8.14 |
% 29.61/8.14 +-Applying beta-rule and splitting (489), into two cases.
% 29.61/8.14 |-Branch one:
% 29.61/8.14 | (505) all_0_45_45 = e3
% 29.61/8.14 |
% 29.61/8.14 | Equations (505) can reduce 354 to:
% 29.61/8.14 | (270) $false
% 29.61/8.14 |
% 29.61/8.14 |-The branch is then unsatisfiable
% 29.61/8.14 |-Branch two:
% 29.61/8.14 | (354) ~ (all_0_45_45 = e3)
% 29.61/8.14 | (363) all_0_45_45 = e4
% 29.61/8.14 |
% 29.61/8.14 | Equations (363) can reduce 352 to:
% 29.61/8.14 | (270) $false
% 29.61/8.15 |
% 29.61/8.15 |-The branch is then unsatisfiable
% 29.61/8.15 |-Branch two:
% 29.61/8.15 | (528) ~ (all_0_39_39 = e1)
% 29.61/8.15 | (522) all_0_39_39 = e4
% 29.61/8.15 |
% 29.61/8.15 | Equations (522) can reduce 591 to:
% 29.61/8.15 | (270) $false
% 29.61/8.15 |
% 29.61/8.15 |-The branch is then unsatisfiable
% 29.61/8.15 |-Branch two:
% 29.61/8.15 | (520) ~ (all_0_42_42 = e4)
% 29.61/8.15 | (521) all_0_46_46 = e4 | all_0_54_54 = e4 | all_0_59_59 = e4
% 29.61/8.15 |
% 29.61/8.15 +-Applying beta-rule and splitting (222), into two cases.
% 29.61/8.15 |-Branch one:
% 29.61/8.15 | (522) all_0_39_39 = e4
% 29.61/8.15 |
% 29.61/8.15 | Equations (522) can reduce 591 to:
% 29.61/8.15 | (270) $false
% 29.61/8.15 |
% 29.61/8.15 |-The branch is then unsatisfiable
% 29.61/8.15 |-Branch two:
% 29.61/8.15 | (591) ~ (all_0_39_39 = e4)
% 29.61/8.15 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 29.61/8.15 |
% 29.61/8.15 +-Applying beta-rule and splitting (592), into two cases.
% 29.61/8.15 |-Branch one:
% 29.61/8.15 | (358) all_0_41_41 = e4
% 29.61/8.15 |
% 29.61/8.15 | Combining equations (351,358) yields a new equation:
% 29.61/8.15 | (359) e4 = e3
% 29.61/8.15 |
% 29.61/8.15 | Equations (359) can reduce 34 to:
% 29.61/8.15 | (270) $false
% 29.61/8.15 |
% 29.61/8.15 |-The branch is then unsatisfiable
% 29.61/8.15 |-Branch two:
% 29.61/8.15 | (361) ~ (all_0_41_41 = e4)
% 29.61/8.15 | (512) all_0_42_42 = e4
% 29.61/8.15 |
% 29.61/8.15 | Equations (512) can reduce 520 to:
% 29.61/8.15 | (270) $false
% 29.61/8.15 |
% 29.61/8.15 |-The branch is then unsatisfiable
% 29.61/8.15 |-Branch two:
% 29.61/8.15 | (510) ~ (all_0_43_43 = e4)
% 29.61/8.15 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 29.61/8.15 |
% 29.61/8.15 +-Applying beta-rule and splitting (511), into two cases.
% 29.61/8.15 |-Branch one:
% 29.61/8.15 | (363) all_0_45_45 = e4
% 29.61/8.15 |
% 29.61/8.15 | Equations (363) can reduce 352 to:
% 29.61/8.15 | (270) $false
% 29.61/8.15 |
% 29.61/8.15 |-The branch is then unsatisfiable
% 29.61/8.15 |-Branch two:
% 29.61/8.15 | (352) ~ (all_0_45_45 = e4)
% 29.61/8.15 | (517) all_0_46_46 = e4
% 29.61/8.15 |
% 29.61/8.15 | Equations (517) can reduce 103 to:
% 29.61/8.15 | (510) ~ (all_0_43_43 = e4)
% 29.61/8.15 |
% 29.61/8.15 | Equations (517) can reduce 174 to:
% 29.61/8.15 | (45) ~ (all_0_44_44 = e4)
% 29.61/8.15 |
% 29.61/8.15 | Equations (517) can reduce 38 to:
% 29.61/8.15 | (352) ~ (all_0_45_45 = e4)
% 29.61/8.15 |
% 29.61/8.15 | Equations (517) can reduce 206 to:
% 29.61/8.15 | (279) ~ (all_0_59_59 = e4)
% 29.61/8.15 |
% 29.61/8.15 | Simplifying 279 yields:
% 29.61/8.15 | (280) ~ (all_0_59_59 = e4)
% 29.61/8.15 |
% 29.61/8.15 +-Applying beta-rule and splitting (222), into two cases.
% 29.61/8.15 |-Branch one:
% 29.61/8.15 | (522) all_0_39_39 = e4
% 29.61/8.15 |
% 29.61/8.15 | Equations (522) can reduce 184 to:
% 29.61/8.15 | (692) ~ (all_0_42_42 = e4)
% 29.61/8.15 |
% 29.61/8.15 | Simplifying 692 yields:
% 29.61/8.15 | (520) ~ (all_0_42_42 = e4)
% 29.61/8.15 |
% 29.61/8.15 | Equations (522) can reduce 32 to:
% 29.61/8.15 | (696) ~ (all_0_51_51 = e4)
% 29.61/8.15 |
% 29.61/8.15 | Simplifying 696 yields:
% 29.61/8.15 | (697) ~ (all_0_51_51 = e4)
% 29.61/8.15 |
% 29.61/8.15 | Equations (522) can reduce 212 to:
% 29.61/8.15 | (273) ~ (all_0_56_56 = e4)
% 29.61/8.15 |
% 29.61/8.15 | Simplifying 273 yields:
% 29.61/8.15 | (274) ~ (all_0_56_56 = e4)
% 29.61/8.15 |
% 29.61/8.15 | Equations (522) can reduce 755 to:
% 29.61/8.15 | (34) ~ (e4 = e3)
% 29.61/8.15 |
% 29.61/8.15 | Equations (522) can reduce 291 to:
% 29.61/8.15 | (231) ~ (e4 = e2)
% 29.61/8.15 |
% 29.61/8.15 +-Applying beta-rule and splitting (453), into two cases.
% 29.61/8.15 |-Branch one:
% 29.61/8.15 | (370) all_0_44_44 = e2
% 29.61/8.15 |
% 29.61/8.15 | Equations (370) can reduce 333 to:
% 29.61/8.15 | (270) $false
% 29.61/8.15 |
% 29.61/8.15 |-The branch is then unsatisfiable
% 29.61/8.15 |-Branch two:
% 29.61/8.15 | (333) ~ (all_0_44_44 = e2)
% 29.61/8.15 | (493) all_0_45_45 = e2 | all_0_46_46 = e2
% 29.61/8.15 |
% 29.61/8.15 +-Applying beta-rule and splitting (16), into two cases.
% 29.61/8.15 |-Branch one:
% 29.61/8.15 | (698) all_0_42_42 = e2
% 29.61/8.15 |
% 29.61/8.15 | Equations (698) can reduce 498 to:
% 29.61/8.15 | (270) $false
% 29.61/8.15 |
% 29.61/8.15 |-The branch is then unsatisfiable
% 29.61/8.15 |-Branch two:
% 29.61/8.15 | (498) ~ (all_0_42_42 = e2)
% 29.61/8.15 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 29.61/8.15 |
% 29.61/8.15 +-Applying beta-rule and splitting (493), into two cases.
% 29.61/8.15 |-Branch one:
% 29.61/8.15 | (374) all_0_45_45 = e2
% 29.61/8.15 |
% 29.61/8.15 | Equations (374) can reduce 128 to:
% 29.61/8.15 | (258) ~ (all_0_53_53 = e2)
% 29.61/8.15 |
% 29.61/8.15 | Simplifying 258 yields:
% 29.61/8.15 | (259) ~ (all_0_53_53 = e2)
% 29.61/8.15 |
% 29.61/8.15 | Equations (374) can reduce 352 to:
% 29.61/8.15 | (377) ~ (e4 = e2)
% 29.61/8.15 |
% 29.61/8.15 | Simplifying 377 yields:
% 29.61/8.15 | (231) ~ (e4 = e2)
% 29.61/8.15 |
% 29.61/8.15 | Equations (374) can reduce 354 to:
% 29.61/8.15 | (301) ~ (e3 = e2)
% 29.61/8.15 |
% 29.61/8.15 | Simplifying 301 yields:
% 29.61/8.15 | (223) ~ (e3 = e2)
% 29.61/8.15 |
% 29.61/8.15 | From (374) and (142) follows:
% 29.61/8.15 | (9224) op(e1, e2) = all_0_23_23
% 29.61/8.15 |
% 29.61/8.15 +-Applying beta-rule and splitting (1245), into two cases.
% 29.61/8.15 |-Branch one:
% 29.61/8.15 | (1258) all_0_42_42 = e3
% 29.61/8.15 |
% 29.61/8.15 | Equations (1258) can reduce 1316 to:
% 29.61/8.15 | (270) $false
% 29.61/8.15 |
% 29.61/8.15 |-The branch is then unsatisfiable
% 29.61/8.15 |-Branch two:
% 29.61/8.15 | (1316) ~ (all_0_42_42 = e3)
% 29.61/8.15 | (1317) all_0_42_42 = e4 | all_0_42_42 = e1
% 29.61/8.15 |
% 29.61/8.15 +-Applying beta-rule and splitting (1317), into two cases.
% 29.61/8.15 |-Branch one:
% 29.61/8.15 | (541) all_0_42_42 = e1
% 29.61/8.15 |
% 29.61/8.15 | Equations (541) can reduce 169 to:
% 29.61/8.15 | (542) ~ (all_0_49_49 = e1)
% 29.61/8.15 |
% 29.61/8.15 | Simplifying 542 yields:
% 29.61/8.15 | (543) ~ (all_0_49_49 = e1)
% 29.61/8.15 |
% 29.61/8.15 | Equations (541) can reduce 191 to:
% 29.61/8.15 | (2131) ~ (all_0_54_54 = e1)
% 29.61/8.15 |
% 29.61/8.15 | Simplifying 2131 yields:
% 29.61/8.15 | (425) ~ (all_0_54_54 = e1)
% 29.61/8.15 |
% 29.61/8.15 | Equations (541) can reduce 17 to:
% 29.61/8.15 | (749) ~ (all_0_59_59 = e1)
% 29.61/8.15 |
% 29.61/8.15 | Simplifying 749 yields:
% 29.61/8.15 | (750) ~ (all_0_59_59 = e1)
% 29.61/8.15 |
% 29.61/8.15 | Equations (541) can reduce 199 to:
% 29.61/8.15 | (132) ~ (e1 = e0)
% 29.61/8.15 |
% 29.61/8.15 +-Applying beta-rule and splitting (58), into two cases.
% 29.61/8.15 |-Branch one:
% 29.61/8.15 | (253) all_0_50_50 = e2
% 29.61/8.15 |
% 29.61/8.15 | Combining equations (267,253) yields a new equation:
% 29.61/8.15 | (268) e4 = e2
% 29.61/8.15 |
% 29.61/8.15 | Simplifying 268 yields:
% 29.61/8.15 | (269) e4 = e2
% 29.61/8.15 |
% 29.61/8.15 | Equations (269) can reduce 231 to:
% 29.61/8.15 | (270) $false
% 29.61/8.15 |
% 29.61/8.15 |-The branch is then unsatisfiable
% 29.61/8.15 |-Branch two:
% 29.61/8.15 | (9032) ~ (all_0_50_50 = e2)
% 29.61/8.15 | (9860) all_0_51_51 = e2 | all_0_52_52 = e2 | all_0_53_53 = e2 | all_0_54_54 = e2
% 29.61/8.15 |
% 29.61/8.15 +-Applying beta-rule and splitting (325), into two cases.
% 29.61/8.15 |-Branch one:
% 29.61/8.15 | (552) all_0_48_48 = e1
% 29.61/8.15 |
% 29.61/8.15 | Equations (552) can reduce 48 to:
% 29.61/8.15 | (1016) ~ (all_0_53_53 = e1)
% 29.61/8.15 |
% 29.61/8.15 | Simplifying 1016 yields:
% 29.61/8.15 | (874) ~ (all_0_53_53 = e1)
% 29.61/8.15 |
% 29.61/8.15 | Equations (552) can reduce 121 to:
% 29.61/8.15 | (769) ~ (e3 = e1)
% 29.61/8.15 |
% 29.61/8.15 | Simplifying 769 yields:
% 29.61/8.15 | (136) ~ (e3 = e1)
% 29.61/8.15 |
% 29.61/8.15 | From (552) and (76) follows:
% 29.61/8.15 | (2127) op(e1, e1) = all_0_25_25
% 29.61/8.15 |
% 29.61/8.15 +-Applying beta-rule and splitting (9860), into two cases.
% 29.61/8.15 |-Branch one:
% 29.61/8.15 | (4215) all_0_51_51 = e2
% 29.61/8.15 |
% 29.61/8.15 | Equations (4215) can reduce 255 to:
% 29.61/8.15 | (270) $false
% 29.61/8.15 |
% 29.61/8.15 |-The branch is then unsatisfiable
% 29.61/8.15 |-Branch two:
% 29.61/8.15 | (255) ~ (all_0_51_51 = e2)
% 29.61/8.15 | (9864) all_0_52_52 = e2 | all_0_53_53 = e2 | all_0_54_54 = e2
% 29.61/8.15 |
% 29.61/8.15 +-Applying beta-rule and splitting (9864), into two cases.
% 29.61/8.15 |-Branch one:
% 29.61/8.15 | (685) all_0_52_52 = e2
% 29.61/8.15 |
% 29.61/8.15 | Equations (685) can reduce 257 to:
% 29.61/8.15 | (270) $false
% 29.61/8.15 |
% 29.61/8.15 |-The branch is then unsatisfiable
% 29.61/8.15 |-Branch two:
% 29.61/8.15 | (257) ~ (all_0_52_52 = e2)
% 29.61/8.15 | (9868) all_0_53_53 = e2 | all_0_54_54 = e2
% 29.61/8.15 |
% 29.61/8.15 +-Applying beta-rule and splitting (9868), into two cases.
% 29.61/8.15 |-Branch one:
% 29.61/8.15 | (576) all_0_53_53 = e2
% 29.61/8.15 |
% 29.61/8.15 | Equations (576) can reduce 259 to:
% 29.61/8.15 | (270) $false
% 29.61/8.15 |
% 29.61/8.15 |-The branch is then unsatisfiable
% 29.61/8.15 |-Branch two:
% 29.61/8.15 | (259) ~ (all_0_53_53 = e2)
% 29.61/8.15 | (3657) all_0_54_54 = e2
% 29.61/8.15 |
% 29.61/8.15 | Equations (3657) can reduce 252 to:
% 29.61/8.15 | (259) ~ (all_0_53_53 = e2)
% 29.61/8.15 |
% 29.61/8.15 | Equations (3657) can reduce 72 to:
% 29.61/8.15 | (700) ~ (all_0_59_59 = e2)
% 29.61/8.15 |
% 29.61/8.15 | Simplifying 700 yields:
% 29.61/8.15 | (701) ~ (all_0_59_59 = e2)
% 29.61/8.15 |
% 29.61/8.15 | Equations (3657) can reduce 425 to:
% 29.61/8.15 | (141) ~ (e2 = e1)
% 29.61/8.15 |
% 29.61/8.15 +-Applying beta-rule and splitting (13), into two cases.
% 29.61/8.15 |-Branch one:
% 29.61/8.15 | (576) all_0_53_53 = e2
% 29.61/8.15 |
% 29.61/8.15 | Equations (576) can reduce 259 to:
% 29.61/8.15 | (270) $false
% 29.61/8.15 |
% 29.61/8.15 |-The branch is then unsatisfiable
% 29.61/8.15 |-Branch two:
% 29.61/8.15 | (259) ~ (all_0_53_53 = e2)
% 29.61/8.15 | (5715) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 29.61/8.15 |
% 29.61/8.15 +-Applying beta-rule and splitting (319), into two cases.
% 29.61/8.15 |-Branch one:
% 29.61/8.15 | (559) all_0_48_48 = e0
% 29.61/8.15 |
% 29.61/8.15 | Combining equations (559,552) yields a new equation:
% 29.61/8.15 | (560) e1 = e0
% 29.61/8.15 |
% 29.61/8.15 | Equations (560) can reduce 132 to:
% 29.61/8.15 | (270) $false
% 29.61/8.15 |
% 29.61/8.15 |-The branch is then unsatisfiable
% 29.61/8.15 |-Branch two:
% 29.61/8.15 | (562) ~ (all_0_48_48 = e0)
% 29.61/8.15 | (563) all_0_49_49 = e0
% 29.61/8.15 |
% 29.61/8.15 | Equations (563) can reduce 113 to:
% 29.61/8.15 | (4000) ~ (all_0_59_59 = e0)
% 29.61/8.15 |
% 29.61/8.15 | Simplifying 4000 yields:
% 29.61/8.15 | (4001) ~ (all_0_59_59 = e0)
% 29.61/8.15 |
% 29.61/8.15 +-Applying beta-rule and splitting (5715), into two cases.
% 29.61/8.15 |-Branch one:
% 29.61/8.15 | (423) all_0_53_53 = e0
% 29.61/8.15 |
% 29.61/8.15 | From (423) and (227) follows:
% 29.61/8.15 | (2167) op(e1, e1) = e0
% 29.61/8.15 |
% 29.61/8.15 +-Applying beta-rule and splitting (95), into two cases.
% 29.61/8.15 |-Branch one:
% 29.61/8.15 | (1258) all_0_42_42 = e3
% 29.61/8.15 |
% 29.61/8.15 | Combining equations (541,1258) yields a new equation:
% 29.61/8.15 | (538) e3 = e1
% 29.61/8.15 |
% 29.61/8.15 | Equations (538) can reduce 136 to:
% 29.61/8.15 | (270) $false
% 29.61/8.15 |
% 29.61/8.15 |-The branch is then unsatisfiable
% 29.61/8.15 |-Branch two:
% 29.61/8.15 | (1316) ~ (all_0_42_42 = e3)
% 29.61/8.15 | (3656) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 29.61/8.15 |
% 29.61/8.15 +-Applying beta-rule and splitting (3656), into two cases.
% 29.61/8.15 |-Branch one:
% 29.61/8.15 | (1091) all_0_46_46 = e3
% 29.61/8.15 |
% 29.61/8.15 | Combining equations (517,1091) yields a new equation:
% 29.61/8.15 | (660) e4 = e3
% 29.61/8.15 |
% 29.61/8.15 | Simplifying 660 yields:
% 29.61/8.15 | (359) e4 = e3
% 29.61/8.15 |
% 29.61/8.15 | Equations (359) can reduce 34 to:
% 29.61/8.15 | (270) $false
% 29.61/8.15 |
% 29.61/8.15 |-The branch is then unsatisfiable
% 29.61/8.15 |-Branch two:
% 29.61/8.15 | (413) ~ (all_0_46_46 = e3)
% 29.61/8.15 | (3700) all_0_54_54 = e3 | all_0_59_59 = e3
% 29.61/8.15 |
% 29.61/8.15 +-Applying beta-rule and splitting (3700), into two cases.
% 29.61/8.15 |-Branch one:
% 29.61/8.15 | (1119) all_0_54_54 = e3
% 29.61/8.15 |
% 29.61/8.15 | Combining equations (1119,3657) yields a new equation:
% 29.61/8.15 | (437) e3 = e2
% 29.61/8.15 |
% 29.61/8.15 | Simplifying 437 yields:
% 29.61/8.15 | (414) e3 = e2
% 29.61/8.15 |
% 29.61/8.15 | Equations (414) can reduce 223 to:
% 29.61/8.15 | (270) $false
% 29.61/8.15 |
% 29.61/8.15 |-The branch is then unsatisfiable
% 29.61/8.15 |-Branch two:
% 29.61/8.15 | (1093) ~ (all_0_54_54 = e3)
% 29.61/8.15 | (412) all_0_59_59 = e3
% 29.61/8.15 |
% 29.61/8.15 | Equations (412) can reduce 185 to:
% 29.61/8.15 | (767) ~ (all_0_56_56 = e3)
% 29.61/8.15 |
% 29.61/8.15 | Equations (412) can reduce 280 to:
% 29.61/8.15 | (719) ~ (e4 = e3)
% 29.61/8.15 |
% 29.61/8.15 | Simplifying 719 yields:
% 29.61/8.15 | (34) ~ (e4 = e3)
% 29.61/8.15 |
% 29.61/8.15 | Equations (412) can reduce 701 to:
% 29.61/8.15 | (223) ~ (e3 = e2)
% 29.61/8.15 |
% 29.61/8.15 | Equations (412) can reduce 750 to:
% 29.61/8.15 | (136) ~ (e3 = e1)
% 29.61/8.15 |
% 29.61/8.15 | Equations (412) can reduce 4001 to:
% 29.61/8.15 | (66) ~ (e3 = e0)
% 29.61/8.15 |
% 29.61/8.15 +-Applying beta-rule and splitting (93), into two cases.
% 29.61/8.15 |-Branch one:
% 29.61/8.15 | (402) all_0_59_59 = e4
% 29.61/8.15 |
% 29.61/8.15 | Combining equations (412,402) yields a new equation:
% 29.61/8.15 | (359) e4 = e3
% 29.61/8.15 |
% 29.61/8.15 | Equations (359) can reduce 34 to:
% 29.61/8.15 | (270) $false
% 29.61/8.15 |
% 29.61/8.15 |-The branch is then unsatisfiable
% 29.61/8.15 |-Branch two:
% 29.61/8.15 | (280) ~ (all_0_59_59 = e4)
% 29.61/8.15 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 29.61/8.15 |
% 29.61/8.15 | Equations (412) can reduce 280 to:
% 29.61/8.15 | (719) ~ (e4 = e3)
% 29.61/8.15 |
% 29.61/8.16 | Simplifying 719 yields:
% 29.61/8.16 | (34) ~ (e4 = e3)
% 29.61/8.16 |
% 29.61/8.16 +-Applying beta-rule and splitting (407), into two cases.
% 29.61/8.16 |-Branch one:
% 29.61/8.16 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 29.61/8.16 |
% 29.61/8.16 +-Applying beta-rule and splitting (408), into two cases.
% 29.61/8.16 |-Branch one:
% 29.61/8.16 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 29.61/8.16 |
% 29.61/8.16 +-Applying beta-rule and splitting (409), into two cases.
% 29.61/8.16 |-Branch one:
% 29.61/8.16 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 29.61/8.16 |
% 29.61/8.16 | Applying alpha-rule on (410) yields:
% 29.61/8.16 | (411) all_0_43_43 = e0
% 29.61/8.16 | (412) all_0_59_59 = e3
% 29.61/8.16 | (413) ~ (all_0_46_46 = e3)
% 29.61/8.16 |
% 29.61/8.16 | Equations (411) can reduce 241 to:
% 29.61/8.16 | (6251) ~ (all_0_44_44 = e0)
% 29.61/8.16 |
% 29.61/8.16 | Simplifying 6251 yields:
% 29.61/8.16 | (625) ~ (all_0_44_44 = e0)
% 29.61/8.16 |
% 29.61/8.16 | Equations (411) can reduce 188 to:
% 29.61/8.16 | (3852) ~ (all_0_56_56 = e0)
% 29.61/8.16 |
% 29.61/8.16 | Simplifying 3852 yields:
% 29.61/8.16 | (419) ~ (all_0_56_56 = e0)
% 29.61/8.16 |
% 29.61/8.16 | Equations (411) can reduce 249 to:
% 29.61/8.16 | (568) ~ (e1 = e0)
% 29.61/8.16 |
% 29.61/8.16 | Simplifying 568 yields:
% 29.61/8.16 | (132) ~ (e1 = e0)
% 29.61/8.16 |
% 29.61/8.16 | Equations (517) can reduce 413 to:
% 29.61/8.16 | (34) ~ (e4 = e3)
% 29.61/8.16 |
% 29.61/8.16 +-Applying beta-rule and splitting (22), into two cases.
% 29.61/8.16 |-Branch one:
% 29.61/8.16 | (782) all_0_43_43 = e3
% 29.61/8.16 |
% 29.61/8.16 | Combining equations (411,782) yields a new equation:
% 29.61/8.16 | (784) e3 = e0
% 29.61/8.16 |
% 29.61/8.16 | Equations (784) can reduce 66 to:
% 29.61/8.16 | (270) $false
% 29.61/8.16 |
% 29.61/8.16 |-The branch is then unsatisfiable
% 29.61/8.16 |-Branch two:
% 29.61/8.16 | (786) ~ (all_0_43_43 = e3)
% 29.61/8.16 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 29.61/8.16 |
% 29.61/8.16 +-Applying beta-rule and splitting (787), into two cases.
% 29.61/8.16 |-Branch one:
% 29.61/8.16 | (858) all_0_44_44 = e3
% 29.61/8.16 |
% 29.61/8.16 | Equations (858) can reduce 45 to:
% 29.61/8.16 | (719) ~ (e4 = e3)
% 29.61/8.16 |
% 29.61/8.16 | Simplifying 719 yields:
% 29.61/8.16 | (34) ~ (e4 = e3)
% 29.61/8.16 |
% 29.61/8.16 | Equations (858) can reduce 131 to:
% 29.61/8.16 | (136) ~ (e3 = e1)
% 29.61/8.16 |
% 29.61/8.16 | Equations (858) can reduce 625 to:
% 29.61/8.16 | (66) ~ (e3 = e0)
% 29.61/8.16 |
% 29.61/8.16 +-Applying beta-rule and splitting (9), into two cases.
% 29.61/8.16 |-Branch one:
% 29.61/8.16 | (621) all_0_44_44 = e0
% 29.61/8.16 |
% 29.61/8.16 | Combining equations (858,621) yields a new equation:
% 29.61/8.16 | (783) e3 = e0
% 29.61/8.16 |
% 29.61/8.16 | Simplifying 783 yields:
% 29.61/8.16 | (784) e3 = e0
% 29.61/8.16 |
% 29.61/8.16 | Equations (784) can reduce 66 to:
% 29.61/8.16 | (270) $false
% 29.61/8.16 |
% 29.61/8.16 |-The branch is then unsatisfiable
% 29.61/8.16 |-Branch two:
% 29.61/8.16 | (625) ~ (all_0_44_44 = e0)
% 29.61/8.16 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 29.61/8.16 |
% 29.61/8.16 | Equations (858) can reduce 625 to:
% 29.61/8.16 | (66) ~ (e3 = e0)
% 29.61/8.16 |
% 29.61/8.16 +-Applying beta-rule and splitting (178), into two cases.
% 29.61/8.16 |-Branch one:
% 29.61/8.16 | (751) all_0_39_39 = e3
% 29.61/8.16 |
% 29.61/8.16 | Combining equations (751,522) yields a new equation:
% 29.61/8.16 | (359) e4 = e3
% 29.61/8.16 |
% 29.61/8.16 | Equations (359) can reduce 34 to:
% 29.61/8.16 | (270) $false
% 29.61/8.16 |
% 29.61/8.16 |-The branch is then unsatisfiable
% 29.61/8.16 |-Branch two:
% 29.61/8.16 | (755) ~ (all_0_39_39 = e3)
% 29.61/8.16 | (756) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 29.61/8.16 |
% 29.61/8.16 +-Applying beta-rule and splitting (756), into two cases.
% 29.61/8.16 |-Branch one:
% 29.61/8.16 | (782) all_0_43_43 = e3
% 29.61/8.16 |
% 29.61/8.16 | Combining equations (411,782) yields a new equation:
% 29.61/8.16 | (784) e3 = e0
% 29.61/8.16 |
% 29.61/8.16 | Equations (784) can reduce 66 to:
% 29.61/8.16 | (270) $false
% 29.61/8.16 |
% 29.61/8.16 |-The branch is then unsatisfiable
% 29.61/8.16 |-Branch two:
% 29.61/8.16 | (786) ~ (all_0_43_43 = e3)
% 29.61/8.16 | (799) all_0_51_51 = e3 | all_0_56_56 = e3
% 29.61/8.16 |
% 29.61/8.16 +-Applying beta-rule and splitting (799), into two cases.
% 29.61/8.16 |-Branch one:
% 29.61/8.16 | (824) all_0_51_51 = e3
% 29.61/8.16 |
% 29.61/8.16 | Combining equations (824,1847) yields a new equation:
% 29.61/8.16 | (6797) all_0_21_21 = e3
% 29.61/8.16 |
% 29.61/8.16 | Equations (824) can reduce 60 to:
% 29.61/8.16 | (5066) ~ (all_0_56_56 = e3)
% 29.61/8.16 |
% 29.61/8.16 | Simplifying 5066 yields:
% 29.61/8.16 | (767) ~ (all_0_56_56 = e3)
% 29.61/8.16 |
% 29.61/8.16 | Equations (824) can reduce 697 to:
% 29.61/8.16 | (719) ~ (e4 = e3)
% 29.61/8.16 |
% 29.61/8.16 | Simplifying 719 yields:
% 29.61/8.16 | (34) ~ (e4 = e3)
% 29.61/8.16 |
% 29.61/8.16 +-Applying beta-rule and splitting (135), into two cases.
% 29.61/8.16 |-Branch one:
% 29.61/8.16 | (820) all_0_51_51 = e1
% 29.61/8.16 |
% 29.61/8.16 | Combining equations (824,820) yields a new equation:
% 29.61/8.16 | (537) e3 = e1
% 29.61/8.16 |
% 29.61/8.16 | Simplifying 537 yields:
% 29.61/8.16 | (538) e3 = e1
% 29.61/8.16 |
% 29.61/8.16 | Equations (538) can reduce 136 to:
% 29.61/8.16 | (270) $false
% 29.61/8.16 |
% 29.61/8.16 |-The branch is then unsatisfiable
% 29.61/8.16 |-Branch two:
% 29.61/8.16 | (748) ~ (all_0_51_51 = e1)
% 29.61/8.16 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 29.61/8.16 |
% 29.61/8.16 +-Applying beta-rule and splitting (823), into two cases.
% 29.61/8.16 |-Branch one:
% 29.61/8.16 | (848) all_0_52_52 = e1
% 29.61/8.16 |
% 29.61/8.16 | From (848) and (195) follows:
% 29.61/8.16 | (9340) op(e1, e1) = all_0_18_18
% 29.61/8.16 |
% 29.61/8.16 | From (848) and (203) follows:
% 29.61/8.16 | (9341) op(e1, e2) = e1
% 29.61/8.16 |
% 29.61/8.16 +-Applying beta-rule and splitting (176), into two cases.
% 29.61/8.16 |-Branch one:
% 29.61/8.16 | (830) all_0_56_56 = e0
% 29.61/8.16 |
% 29.61/8.16 | Equations (830) can reduce 419 to:
% 29.61/8.16 | (270) $false
% 29.61/8.16 |
% 29.61/8.16 |-The branch is then unsatisfiable
% 29.61/8.16 |-Branch two:
% 29.61/8.16 | (419) ~ (all_0_56_56 = e0)
% 29.61/8.16 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 29.61/8.16 |
% 29.61/8.16 +-Applying beta-rule and splitting (208), into two cases.
% 29.61/8.16 |-Branch one:
% 29.61/8.16 | (388) all_0_56_56 = e2
% 29.61/8.16 |
% 29.61/8.16 | Equations (388) can reduce 300 to:
% 29.61/8.16 | (270) $false
% 29.61/8.16 |
% 29.61/8.16 |-The branch is then unsatisfiable
% 29.61/8.16 |-Branch two:
% 29.61/8.16 | (300) ~ (all_0_56_56 = e2)
% 29.61/8.16 | (5076) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1 | all_0_56_56 = e0
% 29.61/8.16 |
% 29.61/8.16 +-Applying beta-rule and splitting (5076), into two cases.
% 29.61/8.16 |-Branch one:
% 29.61/8.16 | (830) all_0_56_56 = e0
% 29.61/8.16 |
% 29.61/8.16 | Equations (830) can reduce 419 to:
% 29.61/8.16 | (270) $false
% 29.61/8.16 |
% 29.61/8.16 |-The branch is then unsatisfiable
% 29.61/8.16 |-Branch two:
% 29.61/8.16 | (419) ~ (all_0_56_56 = e0)
% 29.61/8.16 | (5667) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1
% 29.61/8.16 |
% 29.61/8.16 +-Applying beta-rule and splitting (5667), into two cases.
% 29.61/8.16 |-Branch one:
% 29.61/8.16 | (764) all_0_56_56 = e3
% 29.61/8.16 |
% 29.61/8.16 | Equations (764) can reduce 767 to:
% 29.61/8.16 | (270) $false
% 29.61/8.16 |
% 29.61/8.16 |-The branch is then unsatisfiable
% 29.61/8.16 |-Branch two:
% 29.61/8.16 | (767) ~ (all_0_56_56 = e3)
% 29.61/8.16 | (10136) all_0_56_56 = e4 | all_0_56_56 = e1
% 29.61/8.16 |
% 29.61/8.16 +-Applying beta-rule and splitting (10136), into two cases.
% 29.61/8.16 |-Branch one:
% 29.61/8.16 | (747) all_0_56_56 = e1
% 29.61/8.16 |
% 29.61/8.16 | Equations (747) can reduce 767 to:
% 29.61/8.16 | (769) ~ (e3 = e1)
% 29.61/8.16 |
% 29.61/8.16 | Simplifying 769 yields:
% 29.61/8.16 | (136) ~ (e3 = e1)
% 29.61/8.16 |
% 29.61/8.16 | Equations (747) can reduce 419 to:
% 29.61/8.16 | (132) ~ (e1 = e0)
% 29.61/8.16 |
% 29.61/8.16 +-Applying beta-rule and splitting (626), into two cases.
% 29.61/8.16 |-Branch one:
% 29.61/8.16 | (827) all_0_52_52 = e0
% 29.61/8.16 |
% 29.61/8.16 | Combining equations (827,848) yields a new equation:
% 29.61/8.16 | (560) e1 = e0
% 29.61/8.16 |
% 29.61/8.16 | Equations (560) can reduce 132 to:
% 29.61/8.16 | (270) $false
% 29.61/8.16 |
% 29.61/8.16 |-The branch is then unsatisfiable
% 29.61/8.16 |-Branch two:
% 29.61/8.16 | (925) ~ (all_0_52_52 = e0)
% 29.61/8.16 | (2258) all_0_57_57 = e0
% 29.61/8.16 |
% 29.61/8.16 | Equations (2258) can reduce 143 to:
% 29.61/8.16 | (456) ~ (e4 = e0)
% 29.61/8.16 |
% 29.61/8.16 | Simplifying 456 yields:
% 29.61/8.16 | (6) ~ (e4 = e0)
% 29.61/8.16 |
% 29.61/8.16 | Equations (2258) can reduce 335 to:
% 29.61/8.16 | (566) ~ (e2 = e0)
% 29.61/8.16 |
% 29.61/8.16 | Simplifying 566 yields:
% 29.61/8.16 | (57) ~ (e2 = e0)
% 29.61/8.16 |
% 29.61/8.16 | Instantiating formula (201) with e1, e2, e1, all_0_23_23 and discharging atoms op(e1, e2) = all_0_23_23, op(e1, e2) = e1, yields:
% 29.61/8.16 | (9356) all_0_23_23 = e1
% 29.61/8.16 |
% 29.61/8.16 | Instantiating formula (201) with e1, e1, all_0_25_25, all_0_18_18 and discharging atoms op(e1, e1) = all_0_18_18, op(e1, e1) = all_0_25_25, yields:
% 29.61/8.16 | (9357) all_0_18_18 = all_0_25_25
% 29.61/8.16 |
% 29.61/8.16 | Instantiating formula (201) with e1, e1, e0, all_0_18_18 and discharging atoms op(e1, e1) = all_0_18_18, op(e1, e1) = e0, yields:
% 29.61/8.16 | (9358) all_0_18_18 = e0
% 29.61/8.16 |
% 29.61/8.16 | Combining equations (9357,9358) yields a new equation:
% 29.61/8.16 | (9359) all_0_25_25 = e0
% 29.61/8.16 |
% 29.61/8.16 | Simplifying 9359 yields:
% 29.61/8.16 | (2274) all_0_25_25 = e0
% 29.61/8.16 |
% 29.61/8.16 +-Applying beta-rule and splitting (14), into two cases.
% 29.61/8.16 |-Branch one:
% 29.61/8.16 | (2277) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1))
% 29.61/8.16 |
% 29.61/8.16 +-Applying beta-rule and splitting (2277), into two cases.
% 29.61/8.16 |-Branch one:
% 29.61/8.16 | (2278) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1))
% 29.61/8.16 |
% 29.61/8.16 +-Applying beta-rule and splitting (2278), into two cases.
% 29.61/8.16 |-Branch one:
% 29.61/8.16 | (2279) all_0_21_21 = e4 & ~ (all_0_22_22 = e1)
% 29.61/8.16 |
% 29.61/8.16 | Applying alpha-rule on (2279) yields:
% 29.61/8.16 | (2280) all_0_21_21 = e4
% 29.61/8.16 | (2281) ~ (all_0_22_22 = e1)
% 29.61/8.16 |
% 29.61/8.16 | Combining equations (2280,6797) yields a new equation:
% 29.61/8.16 | (660) e4 = e3
% 29.61/8.16 |
% 29.61/8.17 | Simplifying 660 yields:
% 29.61/8.17 | (359) e4 = e3
% 29.61/8.17 |
% 29.61/8.17 | Equations (359) can reduce 34 to:
% 29.61/8.17 | (270) $false
% 29.61/8.17 |
% 29.61/8.17 |-The branch is then unsatisfiable
% 29.61/8.17 |-Branch two:
% 29.61/8.17 | (2285) all_0_23_23 = e3 & ~ (all_0_24_24 = e1)
% 29.61/8.17 |
% 29.61/8.17 | Applying alpha-rule on (2285) yields:
% 29.61/8.17 | (2286) all_0_23_23 = e3
% 29.61/8.17 | (2287) ~ (all_0_24_24 = e1)
% 29.61/8.17 |
% 29.61/8.17 | Combining equations (2286,9356) yields a new equation:
% 29.61/8.17 | (537) e3 = e1
% 29.61/8.17 |
% 29.61/8.17 | Simplifying 537 yields:
% 29.61/8.17 | (538) e3 = e1
% 29.61/8.17 |
% 29.61/8.17 | Equations (538) can reduce 136 to:
% 29.61/8.17 | (270) $false
% 29.61/8.17 |
% 29.61/8.17 |-The branch is then unsatisfiable
% 29.61/8.17 |-Branch two:
% 29.61/8.17 | (2291) all_0_25_25 = e2 & ~ (all_0_26_26 = e1)
% 29.61/8.17 |
% 29.61/8.17 | Applying alpha-rule on (2291) yields:
% 29.61/8.17 | (2292) all_0_25_25 = e2
% 29.61/8.17 | (2293) ~ (all_0_26_26 = e1)
% 29.61/8.17 |
% 29.61/8.17 | Combining equations (2292,2274) yields a new equation:
% 29.61/8.17 | (622) e2 = e0
% 29.61/8.17 |
% 29.61/8.17 | Simplifying 622 yields:
% 29.61/8.17 | (316) e2 = e0
% 29.61/8.17 |
% 29.61/8.17 | Equations (316) can reduce 57 to:
% 29.61/8.17 | (270) $false
% 29.61/8.17 |
% 29.61/8.17 |-The branch is then unsatisfiable
% 29.61/8.17 |-Branch two:
% 29.61/8.17 | (2296) all_0_28_28 = e0 & ~ (all_0_29_29 = e1)
% 29.61/8.17 |
% 29.61/8.17 | Applying alpha-rule on (2296) yields:
% 29.61/8.17 | (2297) all_0_28_28 = e0
% 29.61/8.17 | (2298) ~ (all_0_29_29 = e1)
% 29.61/8.17 |
% 29.61/8.17 | Combining equations (2297,9135) yields a new equation:
% 29.61/8.17 | (479) e4 = e0
% 29.61/8.17 |
% 29.61/8.17 | Equations (479) can reduce 6 to:
% 29.61/8.17 | (270) $false
% 29.61/8.17 |
% 29.61/8.17 |-The branch is then unsatisfiable
% 29.61/8.17 |-Branch two:
% 29.61/8.17 | (995) ~ (all_0_56_56 = e1)
% 29.61/8.17 | (4744) all_0_56_56 = e4
% 29.61/8.17 |
% 29.61/8.17 | Equations (4744) can reduce 274 to:
% 29.61/8.17 | (270) $false
% 29.61/8.17 |
% 29.61/8.17 |-The branch is then unsatisfiable
% 29.61/8.17 |-Branch two:
% 29.61/8.17 | (642) ~ (all_0_52_52 = e1)
% 29.61/8.17 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 29.61/8.17 |
% 29.61/8.17 +-Applying beta-rule and splitting (852), into two cases.
% 29.61/8.17 |-Branch one:
% 29.61/8.17 | (853) all_0_53_53 = e1
% 29.61/8.17 |
% 29.61/8.17 | Combining equations (423,853) yields a new equation:
% 29.61/8.17 | (560) e1 = e0
% 29.61/8.17 |
% 29.61/8.17 | Equations (560) can reduce 132 to:
% 29.61/8.17 | (270) $false
% 29.61/8.17 |
% 29.61/8.17 |-The branch is then unsatisfiable
% 29.61/8.17 |-Branch two:
% 29.61/8.17 | (874) ~ (all_0_53_53 = e1)
% 29.61/8.17 | (875) all_0_54_54 = e1
% 29.61/8.17 |
% 29.61/8.17 | Combining equations (3657,875) yields a new equation:
% 29.61/8.17 | (531) e2 = e1
% 29.61/8.17 |
% 29.61/8.17 | Simplifying 531 yields:
% 29.61/8.17 | (322) e2 = e1
% 29.61/8.17 |
% 29.61/8.17 | Equations (322) can reduce 141 to:
% 29.61/8.17 | (270) $false
% 29.61/8.17 |
% 29.61/8.17 |-The branch is then unsatisfiable
% 29.61/8.17 |-Branch two:
% 29.61/8.17 | (932) ~ (all_0_51_51 = e3)
% 29.61/8.17 | (764) all_0_56_56 = e3
% 29.61/8.17 |
% 29.61/8.17 | Equations (764) can reduce 767 to:
% 29.61/8.17 | (270) $false
% 29.61/8.17 |
% 29.61/8.17 |-The branch is then unsatisfiable
% 29.61/8.17 |-Branch two:
% 29.61/8.17 | (862) ~ (all_0_44_44 = e3)
% 29.61/8.17 | (1070) all_0_45_45 = e3 | all_0_46_46 = e3
% 29.61/8.17 |
% 29.61/8.17 +-Applying beta-rule and splitting (1070), into two cases.
% 29.61/8.17 |-Branch one:
% 29.61/8.17 | (505) all_0_45_45 = e3
% 29.61/8.17 |
% 29.61/8.17 | Combining equations (374,505) yields a new equation:
% 29.61/8.17 | (414) e3 = e2
% 29.61/8.17 |
% 29.61/8.17 | Equations (414) can reduce 223 to:
% 29.61/8.17 | (270) $false
% 29.61/8.17 |
% 29.61/8.17 |-The branch is then unsatisfiable
% 29.61/8.17 |-Branch two:
% 29.61/8.17 | (354) ~ (all_0_45_45 = e3)
% 29.61/8.17 | (1091) all_0_46_46 = e3
% 29.61/8.17 |
% 29.61/8.17 | Combining equations (1091,517) yields a new equation:
% 29.61/8.17 | (359) e4 = e3
% 29.61/8.17 |
% 29.61/8.17 | Equations (359) can reduce 34 to:
% 29.61/8.17 | (270) $false
% 29.61/8.17 |
% 29.61/8.17 |-The branch is then unsatisfiable
% 29.61/8.17 |-Branch two:
% 29.61/8.17 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 29.61/8.17 |
% 29.61/8.17 | Applying alpha-rule on (416) yields:
% 29.61/8.17 | (411) all_0_43_43 = e0
% 29.61/8.17 | (412) all_0_59_59 = e3
% 29.61/8.17 | (419) ~ (all_0_56_56 = e0)
% 29.61/8.17 |
% 29.61/8.17 | Equations (411) can reduce 241 to:
% 29.61/8.17 | (6251) ~ (all_0_44_44 = e0)
% 29.61/8.17 |
% 29.61/8.17 | Simplifying 6251 yields:
% 29.61/8.17 | (625) ~ (all_0_44_44 = e0)
% 29.61/8.17 |
% 29.61/8.17 | Equations (411) can reduce 188 to:
% 29.61/8.17 | (3852) ~ (all_0_56_56 = e0)
% 29.61/8.17 |
% 29.61/8.17 | Simplifying 3852 yields:
% 29.61/8.17 | (419) ~ (all_0_56_56 = e0)
% 29.61/8.17 |
% 29.61/8.17 | Equations (411) can reduce 249 to:
% 29.61/8.17 | (568) ~ (e1 = e0)
% 29.61/8.17 |
% 29.61/8.17 | Simplifying 568 yields:
% 29.61/8.17 | (132) ~ (e1 = e0)
% 29.61/8.17 |
% 29.61/8.17 +-Applying beta-rule and splitting (22), into two cases.
% 29.61/8.17 |-Branch one:
% 29.61/8.17 | (782) all_0_43_43 = e3
% 29.61/8.17 |
% 29.61/8.17 | Combining equations (411,782) yields a new equation:
% 29.61/8.17 | (784) e3 = e0
% 29.61/8.17 |
% 29.61/8.17 | Equations (784) can reduce 66 to:
% 29.61/8.17 | (270) $false
% 29.61/8.17 |
% 29.61/8.17 |-The branch is then unsatisfiable
% 29.61/8.17 |-Branch two:
% 29.61/8.17 | (786) ~ (all_0_43_43 = e3)
% 29.61/8.17 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 29.61/8.17 |
% 29.61/8.17 +-Applying beta-rule and splitting (787), into two cases.
% 29.61/8.17 |-Branch one:
% 29.61/8.17 | (858) all_0_44_44 = e3
% 29.61/8.17 |
% 29.61/8.17 | Equations (858) can reduce 45 to:
% 29.61/8.17 | (719) ~ (e4 = e3)
% 29.61/8.17 |
% 29.61/8.17 | Simplifying 719 yields:
% 29.61/8.17 | (34) ~ (e4 = e3)
% 29.61/8.17 |
% 29.61/8.17 | Equations (858) can reduce 131 to:
% 29.61/8.17 | (136) ~ (e3 = e1)
% 29.61/8.17 |
% 29.61/8.17 | Equations (858) can reduce 625 to:
% 29.61/8.17 | (66) ~ (e3 = e0)
% 29.61/8.17 |
% 29.61/8.17 +-Applying beta-rule and splitting (9), into two cases.
% 29.61/8.17 |-Branch one:
% 29.61/8.17 | (621) all_0_44_44 = e0
% 29.61/8.17 |
% 29.61/8.17 | Combining equations (858,621) yields a new equation:
% 29.61/8.17 | (783) e3 = e0
% 29.61/8.17 |
% 29.61/8.17 | Simplifying 783 yields:
% 29.61/8.17 | (784) e3 = e0
% 29.61/8.17 |
% 29.61/8.17 | Equations (784) can reduce 66 to:
% 29.61/8.17 | (270) $false
% 29.61/8.17 |
% 29.61/8.17 |-The branch is then unsatisfiable
% 29.61/8.17 |-Branch two:
% 29.61/8.17 | (625) ~ (all_0_44_44 = e0)
% 29.61/8.17 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 29.61/8.17 |
% 29.61/8.17 | Equations (858) can reduce 625 to:
% 29.61/8.17 | (66) ~ (e3 = e0)
% 29.61/8.17 |
% 29.61/8.17 +-Applying beta-rule and splitting (178), into two cases.
% 29.61/8.17 |-Branch one:
% 29.61/8.17 | (751) all_0_39_39 = e3
% 29.61/8.17 |
% 29.61/8.17 | Combining equations (751,522) yields a new equation:
% 29.61/8.17 | (359) e4 = e3
% 29.61/8.17 |
% 29.61/8.17 | Equations (359) can reduce 34 to:
% 29.61/8.17 | (270) $false
% 29.61/8.17 |
% 29.61/8.17 |-The branch is then unsatisfiable
% 29.61/8.17 |-Branch two:
% 29.61/8.17 | (755) ~ (all_0_39_39 = e3)
% 29.61/8.17 | (756) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 29.61/8.17 |
% 29.61/8.17 +-Applying beta-rule and splitting (756), into two cases.
% 29.61/8.17 |-Branch one:
% 29.61/8.17 | (782) all_0_43_43 = e3
% 29.61/8.17 |
% 29.61/8.17 | Combining equations (411,782) yields a new equation:
% 29.61/8.17 | (784) e3 = e0
% 29.61/8.17 |
% 29.61/8.17 | Equations (784) can reduce 66 to:
% 29.61/8.17 | (270) $false
% 29.61/8.17 |
% 29.61/8.17 |-The branch is then unsatisfiable
% 29.61/8.17 |-Branch two:
% 29.61/8.17 | (786) ~ (all_0_43_43 = e3)
% 29.61/8.17 | (799) all_0_51_51 = e3 | all_0_56_56 = e3
% 29.61/8.17 |
% 29.61/8.17 +-Applying beta-rule and splitting (799), into two cases.
% 29.61/8.17 |-Branch one:
% 29.61/8.17 | (824) all_0_51_51 = e3
% 29.61/8.17 |
% 29.61/8.17 | Combining equations (824,1847) yields a new equation:
% 29.61/8.17 | (6797) all_0_21_21 = e3
% 29.61/8.17 |
% 29.61/8.17 | Equations (824) can reduce 60 to:
% 29.61/8.17 | (5066) ~ (all_0_56_56 = e3)
% 29.61/8.17 |
% 29.61/8.17 | Simplifying 5066 yields:
% 29.61/8.17 | (767) ~ (all_0_56_56 = e3)
% 29.61/8.17 |
% 29.61/8.17 | Equations (824) can reduce 697 to:
% 29.61/8.17 | (719) ~ (e4 = e3)
% 29.61/8.17 |
% 29.61/8.17 | Simplifying 719 yields:
% 29.61/8.17 | (34) ~ (e4 = e3)
% 29.61/8.17 |
% 29.61/8.17 +-Applying beta-rule and splitting (135), into two cases.
% 29.61/8.17 |-Branch one:
% 29.61/8.17 | (820) all_0_51_51 = e1
% 29.61/8.17 |
% 29.61/8.17 | Combining equations (824,820) yields a new equation:
% 29.61/8.17 | (537) e3 = e1
% 29.61/8.17 |
% 29.61/8.17 | Simplifying 537 yields:
% 29.61/8.17 | (538) e3 = e1
% 29.61/8.17 |
% 29.61/8.17 | Equations (538) can reduce 136 to:
% 29.61/8.17 | (270) $false
% 29.61/8.17 |
% 29.61/8.17 |-The branch is then unsatisfiable
% 29.61/8.17 |-Branch two:
% 29.61/8.17 | (748) ~ (all_0_51_51 = e1)
% 29.61/8.17 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 29.61/8.17 |
% 29.61/8.17 +-Applying beta-rule and splitting (823), into two cases.
% 29.61/8.17 |-Branch one:
% 29.61/8.17 | (848) all_0_52_52 = e1
% 29.61/8.17 |
% 29.61/8.17 | From (848) and (195) follows:
% 29.61/8.17 | (9340) op(e1, e1) = all_0_18_18
% 29.61/8.17 |
% 29.61/8.17 | From (848) and (203) follows:
% 29.61/8.17 | (9341) op(e1, e2) = e1
% 29.61/8.17 |
% 29.61/8.17 +-Applying beta-rule and splitting (176), into two cases.
% 29.61/8.17 |-Branch one:
% 29.61/8.17 | (830) all_0_56_56 = e0
% 29.61/8.17 |
% 29.61/8.17 | Equations (830) can reduce 419 to:
% 29.61/8.17 | (270) $false
% 29.61/8.17 |
% 29.61/8.17 |-The branch is then unsatisfiable
% 29.61/8.17 |-Branch two:
% 29.61/8.17 | (419) ~ (all_0_56_56 = e0)
% 29.61/8.17 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 29.61/8.17 |
% 29.61/8.17 +-Applying beta-rule and splitting (208), into two cases.
% 29.61/8.17 |-Branch one:
% 29.61/8.17 | (388) all_0_56_56 = e2
% 29.61/8.17 |
% 29.61/8.17 | Equations (388) can reduce 300 to:
% 29.61/8.17 | (270) $false
% 29.61/8.17 |
% 29.61/8.17 |-The branch is then unsatisfiable
% 29.61/8.17 |-Branch two:
% 29.61/8.17 | (300) ~ (all_0_56_56 = e2)
% 29.61/8.17 | (5076) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1 | all_0_56_56 = e0
% 29.61/8.17 |
% 29.61/8.17 +-Applying beta-rule and splitting (5076), into two cases.
% 29.61/8.17 |-Branch one:
% 29.61/8.17 | (830) all_0_56_56 = e0
% 29.61/8.17 |
% 29.61/8.17 | Equations (830) can reduce 419 to:
% 29.61/8.17 | (270) $false
% 29.61/8.17 |
% 29.61/8.17 |-The branch is then unsatisfiable
% 29.61/8.17 |-Branch two:
% 29.61/8.17 | (419) ~ (all_0_56_56 = e0)
% 29.61/8.17 | (5667) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1
% 29.61/8.17 |
% 29.61/8.17 +-Applying beta-rule and splitting (5667), into two cases.
% 29.61/8.17 |-Branch one:
% 29.61/8.17 | (764) all_0_56_56 = e3
% 29.61/8.17 |
% 29.61/8.17 | Equations (764) can reduce 767 to:
% 29.61/8.17 | (270) $false
% 29.61/8.17 |
% 29.61/8.17 |-The branch is then unsatisfiable
% 29.61/8.17 |-Branch two:
% 29.61/8.17 | (767) ~ (all_0_56_56 = e3)
% 29.61/8.18 | (10136) all_0_56_56 = e4 | all_0_56_56 = e1
% 29.61/8.18 |
% 29.61/8.18 +-Applying beta-rule and splitting (10136), into two cases.
% 29.61/8.18 |-Branch one:
% 29.61/8.18 | (747) all_0_56_56 = e1
% 29.61/8.18 |
% 29.61/8.18 | Equations (747) can reduce 767 to:
% 29.61/8.18 | (769) ~ (e3 = e1)
% 29.61/8.18 |
% 29.61/8.18 | Simplifying 769 yields:
% 29.61/8.18 | (136) ~ (e3 = e1)
% 29.61/8.18 |
% 29.61/8.18 | Equations (747) can reduce 419 to:
% 29.61/8.18 | (132) ~ (e1 = e0)
% 29.61/8.18 |
% 29.61/8.18 +-Applying beta-rule and splitting (626), into two cases.
% 29.61/8.18 |-Branch one:
% 29.61/8.18 | (827) all_0_52_52 = e0
% 29.61/8.18 |
% 29.61/8.18 | Combining equations (827,848) yields a new equation:
% 29.61/8.18 | (560) e1 = e0
% 29.61/8.18 |
% 29.61/8.18 | Equations (560) can reduce 132 to:
% 29.61/8.18 | (270) $false
% 29.61/8.18 |
% 29.61/8.18 |-The branch is then unsatisfiable
% 29.61/8.18 |-Branch two:
% 29.61/8.18 | (925) ~ (all_0_52_52 = e0)
% 29.61/8.18 | (2258) all_0_57_57 = e0
% 29.61/8.18 |
% 29.61/8.18 | Equations (2258) can reduce 143 to:
% 29.61/8.18 | (456) ~ (e4 = e0)
% 29.61/8.18 |
% 29.61/8.18 | Simplifying 456 yields:
% 29.61/8.18 | (6) ~ (e4 = e0)
% 29.61/8.18 |
% 29.61/8.18 | Equations (2258) can reduce 335 to:
% 29.61/8.18 | (566) ~ (e2 = e0)
% 29.61/8.18 |
% 29.61/8.18 | Simplifying 566 yields:
% 29.61/8.18 | (57) ~ (e2 = e0)
% 29.61/8.18 |
% 29.61/8.18 | Instantiating formula (201) with e1, e2, e1, all_0_23_23 and discharging atoms op(e1, e2) = all_0_23_23, op(e1, e2) = e1, yields:
% 29.61/8.18 | (9356) all_0_23_23 = e1
% 29.61/8.18 |
% 29.61/8.18 | Instantiating formula (201) with e1, e1, all_0_25_25, all_0_18_18 and discharging atoms op(e1, e1) = all_0_18_18, op(e1, e1) = all_0_25_25, yields:
% 29.61/8.18 | (9357) all_0_18_18 = all_0_25_25
% 29.61/8.18 |
% 29.61/8.18 | Instantiating formula (201) with e1, e1, e0, all_0_18_18 and discharging atoms op(e1, e1) = all_0_18_18, op(e1, e1) = e0, yields:
% 29.79/8.18 | (9358) all_0_18_18 = e0
% 29.79/8.18 |
% 29.79/8.18 | Combining equations (9357,9358) yields a new equation:
% 29.79/8.18 | (9359) all_0_25_25 = e0
% 29.79/8.18 |
% 29.79/8.18 | Simplifying 9359 yields:
% 29.79/8.18 | (2274) all_0_25_25 = e0
% 29.79/8.18 |
% 29.79/8.18 +-Applying beta-rule and splitting (14), into two cases.
% 29.79/8.18 |-Branch one:
% 29.79/8.18 | (2277) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1))
% 29.79/8.18 |
% 29.79/8.18 +-Applying beta-rule and splitting (2277), into two cases.
% 29.79/8.18 |-Branch one:
% 29.79/8.18 | (2278) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1))
% 29.79/8.18 |
% 29.79/8.18 +-Applying beta-rule and splitting (2278), into two cases.
% 29.79/8.18 |-Branch one:
% 29.79/8.18 | (2279) all_0_21_21 = e4 & ~ (all_0_22_22 = e1)
% 29.79/8.18 |
% 29.79/8.18 | Applying alpha-rule on (2279) yields:
% 29.79/8.18 | (2280) all_0_21_21 = e4
% 29.79/8.18 | (2281) ~ (all_0_22_22 = e1)
% 29.79/8.18 |
% 29.79/8.18 | Combining equations (2280,6797) yields a new equation:
% 29.79/8.18 | (660) e4 = e3
% 29.79/8.18 |
% 29.79/8.18 | Simplifying 660 yields:
% 29.79/8.18 | (359) e4 = e3
% 29.79/8.18 |
% 29.79/8.18 | Equations (359) can reduce 34 to:
% 29.79/8.18 | (270) $false
% 29.79/8.18 |
% 29.79/8.18 |-The branch is then unsatisfiable
% 29.79/8.18 |-Branch two:
% 29.79/8.18 | (2285) all_0_23_23 = e3 & ~ (all_0_24_24 = e1)
% 29.79/8.18 |
% 29.79/8.18 | Applying alpha-rule on (2285) yields:
% 29.79/8.18 | (2286) all_0_23_23 = e3
% 29.79/8.18 | (2287) ~ (all_0_24_24 = e1)
% 29.79/8.18 |
% 29.79/8.18 | Combining equations (2286,9356) yields a new equation:
% 29.79/8.18 | (537) e3 = e1
% 29.79/8.18 |
% 29.79/8.18 | Simplifying 537 yields:
% 29.79/8.18 | (538) e3 = e1
% 29.79/8.18 |
% 29.79/8.18 | Equations (538) can reduce 136 to:
% 29.79/8.18 | (270) $false
% 29.79/8.18 |
% 29.79/8.18 |-The branch is then unsatisfiable
% 29.79/8.18 |-Branch two:
% 29.79/8.18 | (2291) all_0_25_25 = e2 & ~ (all_0_26_26 = e1)
% 29.79/8.18 |
% 29.79/8.18 | Applying alpha-rule on (2291) yields:
% 29.79/8.18 | (2292) all_0_25_25 = e2
% 29.79/8.18 | (2293) ~ (all_0_26_26 = e1)
% 29.79/8.18 |
% 29.79/8.18 | Combining equations (2292,2274) yields a new equation:
% 29.79/8.18 | (622) e2 = e0
% 29.79/8.18 |
% 29.79/8.18 | Simplifying 622 yields:
% 29.79/8.18 | (316) e2 = e0
% 29.79/8.18 |
% 29.79/8.18 | Equations (316) can reduce 57 to:
% 29.79/8.18 | (270) $false
% 29.79/8.18 |
% 29.79/8.18 |-The branch is then unsatisfiable
% 29.79/8.18 |-Branch two:
% 29.79/8.18 | (2296) all_0_28_28 = e0 & ~ (all_0_29_29 = e1)
% 29.79/8.18 |
% 29.79/8.18 | Applying alpha-rule on (2296) yields:
% 29.79/8.18 | (2297) all_0_28_28 = e0
% 29.79/8.18 | (2298) ~ (all_0_29_29 = e1)
% 29.79/8.18 |
% 29.79/8.18 | Combining equations (2297,9135) yields a new equation:
% 29.79/8.18 | (479) e4 = e0
% 29.79/8.18 |
% 29.79/8.18 | Equations (479) can reduce 6 to:
% 29.79/8.18 | (270) $false
% 29.79/8.18 |
% 29.79/8.18 |-The branch is then unsatisfiable
% 29.79/8.18 |-Branch two:
% 29.79/8.18 | (995) ~ (all_0_56_56 = e1)
% 29.79/8.18 | (4744) all_0_56_56 = e4
% 29.79/8.18 |
% 29.79/8.18 | Equations (4744) can reduce 274 to:
% 29.79/8.18 | (270) $false
% 29.79/8.18 |
% 29.79/8.18 |-The branch is then unsatisfiable
% 29.79/8.18 |-Branch two:
% 29.79/8.18 | (642) ~ (all_0_52_52 = e1)
% 29.79/8.18 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 29.79/8.18 |
% 29.79/8.18 +-Applying beta-rule and splitting (852), into two cases.
% 29.79/8.18 |-Branch one:
% 29.79/8.18 | (853) all_0_53_53 = e1
% 29.79/8.18 |
% 29.79/8.18 | Combining equations (423,853) yields a new equation:
% 29.79/8.18 | (560) e1 = e0
% 29.79/8.18 |
% 29.79/8.18 | Equations (560) can reduce 132 to:
% 29.79/8.18 | (270) $false
% 29.79/8.18 |
% 29.79/8.18 |-The branch is then unsatisfiable
% 29.79/8.18 |-Branch two:
% 29.79/8.18 | (874) ~ (all_0_53_53 = e1)
% 29.79/8.18 | (875) all_0_54_54 = e1
% 29.79/8.18 |
% 29.79/8.18 | Combining equations (3657,875) yields a new equation:
% 29.79/8.18 | (531) e2 = e1
% 29.79/8.18 |
% 29.79/8.18 | Simplifying 531 yields:
% 29.79/8.18 | (322) e2 = e1
% 29.79/8.18 |
% 29.79/8.18 | Equations (322) can reduce 141 to:
% 29.79/8.18 | (270) $false
% 29.79/8.18 |
% 29.79/8.18 |-The branch is then unsatisfiable
% 29.79/8.18 |-Branch two:
% 29.79/8.18 | (932) ~ (all_0_51_51 = e3)
% 29.79/8.18 | (764) all_0_56_56 = e3
% 29.79/8.18 |
% 29.79/8.18 | Equations (764) can reduce 767 to:
% 29.79/8.18 | (270) $false
% 29.79/8.18 |
% 29.79/8.18 |-The branch is then unsatisfiable
% 29.79/8.18 |-Branch two:
% 29.79/8.18 | (862) ~ (all_0_44_44 = e3)
% 29.79/8.18 | (1070) all_0_45_45 = e3 | all_0_46_46 = e3
% 29.79/8.18 |
% 29.79/8.18 +-Applying beta-rule and splitting (1070), into two cases.
% 29.79/8.18 |-Branch one:
% 29.79/8.18 | (505) all_0_45_45 = e3
% 29.79/8.18 |
% 29.79/8.18 | Combining equations (374,505) yields a new equation:
% 29.79/8.18 | (414) e3 = e2
% 29.79/8.18 |
% 29.79/8.18 | Equations (414) can reduce 223 to:
% 29.79/8.18 | (270) $false
% 29.79/8.18 |
% 29.79/8.18 |-The branch is then unsatisfiable
% 29.79/8.18 |-Branch two:
% 29.79/8.18 | (354) ~ (all_0_45_45 = e3)
% 29.79/8.18 | (1091) all_0_46_46 = e3
% 29.79/8.18 |
% 29.79/8.18 | Combining equations (1091,517) yields a new equation:
% 29.79/8.18 | (359) e4 = e3
% 29.79/8.18 |
% 29.79/8.18 | Equations (359) can reduce 34 to:
% 29.79/8.18 | (270) $false
% 29.79/8.18 |
% 29.79/8.18 |-The branch is then unsatisfiable
% 29.79/8.18 |-Branch two:
% 29.79/8.18 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 29.79/8.18 |
% 29.79/8.18 | Applying alpha-rule on (422) yields:
% 29.79/8.18 | (423) all_0_53_53 = e0
% 29.79/8.18 | (424) all_0_59_59 = e1
% 29.79/8.18 | (425) ~ (all_0_54_54 = e1)
% 29.79/8.18 |
% 29.79/8.18 | Combining equations (424,412) yields a new equation:
% 29.79/8.18 | (538) e3 = e1
% 29.79/8.18 |
% 29.79/8.18 | Equations (538) can reduce 136 to:
% 29.79/8.18 | (270) $false
% 29.79/8.18 |
% 29.79/8.18 |-The branch is then unsatisfiable
% 29.79/8.18 |-Branch two:
% 29.79/8.18 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 29.79/8.18 |
% 29.79/8.18 | Applying alpha-rule on (428) yields:
% 29.79/8.18 | (423) all_0_53_53 = e0
% 29.79/8.18 | (424) all_0_59_59 = e1
% 29.79/8.18 | (431) ~ (all_0_58_58 = e0)
% 29.79/8.18 |
% 29.79/8.18 | Combining equations (424,412) yields a new equation:
% 29.79/8.18 | (538) e3 = e1
% 29.79/8.18 |
% 29.79/8.18 | Equations (538) can reduce 136 to:
% 29.79/8.18 | (270) $false
% 29.79/8.18 |
% 29.79/8.18 |-The branch is then unsatisfiable
% 29.79/8.18 |-Branch two:
% 29.79/8.18 | (584) ~ (all_0_53_53 = e0)
% 29.79/8.19 | (5719) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1
% 29.79/8.19 |
% 29.79/8.19 +-Applying beta-rule and splitting (5719), into two cases.
% 29.79/8.19 |-Branch one:
% 29.79/8.19 | (1114) all_0_53_53 = e3
% 29.79/8.19 |
% 29.79/8.19 | Equations (1114) can reduce 356 to:
% 29.79/8.19 | (270) $false
% 29.79/8.19 |
% 29.79/8.19 |-The branch is then unsatisfiable
% 29.79/8.19 |-Branch two:
% 29.79/8.19 | (356) ~ (all_0_53_53 = e3)
% 29.79/8.19 | (5723) all_0_53_53 = e4 | all_0_53_53 = e1
% 29.79/8.19 |
% 29.79/8.19 +-Applying beta-rule and splitting (5723), into two cases.
% 29.79/8.19 |-Branch one:
% 29.79/8.19 | (853) all_0_53_53 = e1
% 29.79/8.19 |
% 29.79/8.19 | Equations (853) can reduce 874 to:
% 29.79/8.19 | (270) $false
% 29.79/8.19 |
% 29.79/8.19 |-The branch is then unsatisfiable
% 29.79/8.19 |-Branch two:
% 29.79/8.19 | (874) ~ (all_0_53_53 = e1)
% 29.79/8.19 | (367) all_0_53_53 = e4
% 29.79/8.19 |
% 29.79/8.19 | Equations (367) can reduce 599 to:
% 29.79/8.19 | (270) $false
% 29.79/8.19 |
% 29.79/8.19 |-The branch is then unsatisfiable
% 29.79/8.19 |-Branch two:
% 29.79/8.19 | (588) ~ (all_0_48_48 = e1)
% 29.79/8.19 | (589) all_0_49_49 = e1
% 29.79/8.19 |
% 29.79/8.19 | Equations (589) can reduce 543 to:
% 29.79/8.19 | (270) $false
% 29.79/8.19 |
% 29.79/8.19 |-The branch is then unsatisfiable
% 29.79/8.19 |-Branch two:
% 29.79/8.19 | (640) ~ (all_0_42_42 = e1)
% 29.79/8.19 | (512) all_0_42_42 = e4
% 29.79/8.19 |
% 29.79/8.19 | Equations (512) can reduce 520 to:
% 29.79/8.19 | (270) $false
% 29.79/8.19 |
% 29.79/8.19 |-The branch is then unsatisfiable
% 29.79/8.19 |-Branch two:
% 29.79/8.19 | (434) ~ (all_0_45_45 = e2)
% 29.79/8.19 | (497) all_0_46_46 = e2
% 29.79/8.19 |
% 29.79/8.19 | Combining equations (517,497) yields a new equation:
% 29.79/8.19 | (268) e4 = e2
% 29.79/8.19 |
% 29.79/8.19 | Simplifying 268 yields:
% 29.79/8.19 | (269) e4 = e2
% 29.79/8.19 |
% 29.79/8.19 | Equations (269) can reduce 231 to:
% 29.79/8.19 | (270) $false
% 29.79/8.19 |
% 29.79/8.19 |-The branch is then unsatisfiable
% 29.79/8.19 |-Branch two:
% 29.79/8.19 | (591) ~ (all_0_39_39 = e4)
% 29.79/8.19 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 29.79/8.19 |
% 29.79/8.19 +-Applying beta-rule and splitting (166), into two cases.
% 29.79/8.19 |-Branch one:
% 29.79/8.19 | (522) all_0_39_39 = e4
% 29.79/8.19 |
% 29.79/8.19 | Equations (522) can reduce 591 to:
% 29.79/8.19 | (270) $false
% 29.79/8.19 |
% 29.79/8.19 |-The branch is then unsatisfiable
% 29.79/8.19 |-Branch two:
% 29.79/8.19 | (591) ~ (all_0_39_39 = e4)
% 29.79/8.19 | (4522) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 29.79/8.19 |
% 29.79/8.19 +-Applying beta-rule and splitting (4522), into two cases.
% 29.79/8.19 |-Branch one:
% 29.79/8.19 | (502) all_0_43_43 = e4
% 29.79/8.19 |
% 29.79/8.19 | Equations (502) can reduce 510 to:
% 29.79/8.19 | (270) $false
% 29.79/8.19 |
% 29.79/8.19 |-The branch is then unsatisfiable
% 29.79/8.19 |-Branch two:
% 29.79/8.19 | (510) ~ (all_0_43_43 = e4)
% 29.79/8.19 | (4527) all_0_51_51 = e4 | all_0_56_56 = e4
% 29.79/8.19 |
% 29.79/8.19 +-Applying beta-rule and splitting (4527), into two cases.
% 29.79/8.19 |-Branch one:
% 29.79/8.19 | (1467) all_0_51_51 = e4
% 29.79/8.19 |
% 29.79/8.19 | Equations (1467) can reduce 697 to:
% 29.79/8.19 | (270) $false
% 29.79/8.19 |
% 29.79/8.19 |-The branch is then unsatisfiable
% 29.79/8.19 |-Branch two:
% 29.79/8.19 | (697) ~ (all_0_51_51 = e4)
% 29.79/8.19 | (4744) all_0_56_56 = e4
% 29.79/8.19 |
% 29.79/8.19 | Equations (4744) can reduce 274 to:
% 29.79/8.19 | (270) $false
% 29.79/8.19 |
% 29.79/8.19 |-The branch is then unsatisfiable
% 29.79/8.19 |-Branch two:
% 29.79/8.19 | (3951) ~ (all_0_47_47 = e2)
% 29.79/8.19 | (3956) all_0_47_47 = e1 | all_0_47_47 = e0
% 29.79/8.19 |
% 29.79/8.19 +-Applying beta-rule and splitting (124), into two cases.
% 29.79/8.19 |-Branch one:
% 29.79/8.19 | (290) all_0_47_47 = e2
% 29.79/8.19 |
% 29.79/8.19 | Equations (290) can reduce 3951 to:
% 29.79/8.19 | (270) $false
% 29.79/8.19 |
% 29.79/8.19 |-The branch is then unsatisfiable
% 29.79/8.19 |-Branch two:
% 29.79/8.19 | (3951) ~ (all_0_47_47 = e2)
% 29.79/8.19 | (3952) all_0_48_48 = e2 | all_0_49_49 = e2
% 29.79/8.19 |
% 29.79/8.19 +-Applying beta-rule and splitting (105), into two cases.
% 29.79/8.19 |-Branch one:
% 29.79/8.19 | (374) all_0_45_45 = e2
% 29.79/8.19 |
% 29.79/8.19 | Equations (374) can reduce 229 to:
% 29.79/8.19 | (333) ~ (all_0_44_44 = e2)
% 29.79/8.19 |
% 29.79/8.19 | Equations (374) can reduce 65 to:
% 29.79/8.19 | (293) ~ (all_0_48_48 = e2)
% 29.79/8.19 |
% 29.79/8.19 | Simplifying 293 yields:
% 29.79/8.19 | (294) ~ (all_0_48_48 = e2)
% 29.79/8.19 |
% 29.79/8.19 | Equations (374) can reduce 128 to:
% 29.79/8.19 | (258) ~ (all_0_53_53 = e2)
% 29.79/8.19 |
% 29.79/8.19 | Simplifying 258 yields:
% 29.79/8.19 | (259) ~ (all_0_53_53 = e2)
% 29.79/8.19 |
% 29.79/8.19 | Equations (374) can reduce 26 to:
% 29.79/8.19 | (141) ~ (e2 = e1)
% 29.79/8.19 |
% 29.79/8.19 | From (374) and (91) follows:
% 29.79/8.19 | (10403) op(e3, e2) = all_0_24_24
% 29.79/8.19 |
% 29.79/8.19 | From (374) and (142) follows:
% 29.79/8.19 | (9224) op(e1, e2) = all_0_23_23
% 29.79/8.19 |
% 29.79/8.19 +-Applying beta-rule and splitting (3952), into two cases.
% 29.79/8.19 |-Branch one:
% 29.79/8.19 | (311) all_0_48_48 = e2
% 29.79/8.19 |
% 29.79/8.19 | Equations (311) can reduce 294 to:
% 29.79/8.19 | (270) $false
% 29.79/8.19 |
% 29.79/8.19 |-The branch is then unsatisfiable
% 29.79/8.19 |-Branch two:
% 29.79/8.19 | (294) ~ (all_0_48_48 = e2)
% 29.79/8.19 | (307) all_0_49_49 = e2
% 29.79/8.19 |
% 29.79/8.19 | Equations (307) can reduce 169 to:
% 29.79/8.19 | (498) ~ (all_0_42_42 = e2)
% 29.79/8.19 |
% 29.79/8.19 | Equations (307) can reduce 198 to:
% 29.79/8.19 | (1436) ~ (all_0_46_46 = e2)
% 29.79/8.19 |
% 29.79/8.19 | Equations (307) can reduce 162 to:
% 29.79/8.19 | (260) ~ (all_0_54_54 = e2)
% 29.79/8.19 |
% 29.79/8.19 | Simplifying 260 yields:
% 29.79/8.19 | (261) ~ (all_0_54_54 = e2)
% 29.79/8.19 |
% 29.79/8.19 | Equations (307) can reduce 202 to:
% 29.79/8.19 | (377) ~ (e4 = e2)
% 29.79/8.19 |
% 29.79/8.19 | Simplifying 377 yields:
% 29.79/8.19 | (231) ~ (e4 = e2)
% 29.79/8.19 |
% 29.79/8.19 +-Applying beta-rule and splitting (58), into two cases.
% 29.79/8.19 |-Branch one:
% 29.79/8.19 | (253) all_0_50_50 = e2
% 29.79/8.19 |
% 29.79/8.19 | Combining equations (253,267) yields a new equation:
% 29.79/8.19 | (269) e4 = e2
% 29.79/8.19 |
% 29.79/8.19 | Equations (269) can reduce 231 to:
% 29.79/8.19 | (270) $false
% 29.79/8.19 |
% 29.79/8.19 |-The branch is then unsatisfiable
% 29.79/8.19 |-Branch two:
% 29.79/8.19 | (9032) ~ (all_0_50_50 = e2)
% 29.79/8.19 | (9860) all_0_51_51 = e2 | all_0_52_52 = e2 | all_0_53_53 = e2 | all_0_54_54 = e2
% 29.79/8.19 |
% 29.79/8.19 +-Applying beta-rule and splitting (9860), into two cases.
% 29.79/8.19 |-Branch one:
% 29.79/8.19 | (4215) all_0_51_51 = e2
% 29.79/8.19 |
% 29.79/8.19 | Combining equations (4215,1847) yields a new equation:
% 29.79/8.19 | (2760) all_0_21_21 = e2
% 29.79/8.19 |
% 29.79/8.19 | Equations (4215) can reduce 32 to:
% 29.79/8.19 | (291) ~ (all_0_39_39 = e2)
% 29.79/8.19 |
% 29.79/8.19 | Equations (4215) can reduce 3 to:
% 29.79/8.19 | (3951) ~ (all_0_47_47 = e2)
% 29.79/8.19 |
% 29.79/8.19 | Equations (4215) can reduce 154 to:
% 29.79/8.19 | (256) ~ (all_0_52_52 = e2)
% 29.79/8.19 |
% 29.79/8.19 | Simplifying 256 yields:
% 29.79/8.19 | (257) ~ (all_0_52_52 = e2)
% 29.79/8.19 |
% 29.79/8.19 | Equations (4215) can reduce 12 to:
% 29.79/8.19 | (258) ~ (all_0_53_53 = e2)
% 29.79/8.19 |
% 29.79/8.19 | Simplifying 258 yields:
% 29.79/8.19 | (259) ~ (all_0_53_53 = e2)
% 29.79/8.19 |
% 29.79/8.19 | Equations (4215) can reduce 50 to:
% 29.79/8.19 | (260) ~ (all_0_54_54 = e2)
% 29.79/8.19 |
% 29.79/8.19 | Simplifying 260 yields:
% 29.79/8.19 | (261) ~ (all_0_54_54 = e2)
% 29.79/8.19 |
% 29.79/8.19 | Equations (4215) can reduce 60 to:
% 29.79/8.19 | (299) ~ (all_0_56_56 = e2)
% 29.79/8.19 |
% 29.79/8.19 | Simplifying 299 yields:
% 29.79/8.19 | (300) ~ (all_0_56_56 = e2)
% 29.79/8.19 |
% 29.79/8.19 | Equations (4215) can reduce 697 to:
% 29.79/8.19 | (377) ~ (e4 = e2)
% 29.79/8.19 |
% 29.79/8.19 | Simplifying 377 yields:
% 29.79/8.19 | (231) ~ (e4 = e2)
% 29.79/8.19 |
% 29.79/8.19 | From (4215) and (7) follows:
% 29.79/8.19 | (10434) op(e3, e2) = all_0_9_9
% 29.79/8.19 |
% 29.79/8.19 | From (4215) and (216) follows:
% 29.79/8.20 | (10435) op(e1, e2) = all_0_10_10
% 29.79/8.20 |
% 29.79/8.20 | Instantiating formula (201) with e3, e2, all_0_9_9, all_0_44_44 and discharging atoms op(e3, e2) = all_0_9_9, op(e3, e2) = all_0_44_44, yields:
% 29.79/8.20 | (10436) all_0_9_9 = all_0_44_44
% 29.79/8.20 |
% 29.79/8.20 | Instantiating formula (201) with e3, e2, all_0_24_24, all_0_9_9 and discharging atoms op(e3, e2) = all_0_9_9, op(e3, e2) = all_0_24_24, yields:
% 29.79/8.20 | (10437) all_0_9_9 = all_0_24_24
% 29.79/8.20 |
% 29.79/8.20 | Instantiating formula (201) with e1, e2, all_0_10_10, all_0_52_52 and discharging atoms op(e1, e2) = all_0_10_10, op(e1, e2) = all_0_52_52, yields:
% 29.79/8.20 | (10438) all_0_10_10 = all_0_52_52
% 29.79/8.20 |
% 29.79/8.20 | Instantiating formula (201) with e1, e2, all_0_23_23, all_0_10_10 and discharging atoms op(e1, e2) = all_0_10_10, op(e1, e2) = all_0_23_23, yields:
% 29.79/8.20 | (6802) all_0_10_10 = all_0_23_23
% 29.79/8.20 |
% 29.79/8.20 | Combining equations (10436,10437) yields a new equation:
% 29.79/8.20 | (10440) all_0_24_24 = all_0_44_44
% 29.79/8.20 |
% 29.79/8.20 | Combining equations (10438,6802) yields a new equation:
% 29.79/8.20 | (10441) all_0_23_23 = all_0_52_52
% 29.79/8.20 |
% 29.79/8.20 +-Applying beta-rule and splitting (77), into two cases.
% 29.79/8.20 |-Branch one:
% 29.79/8.20 | (315) all_0_47_47 = e0
% 29.79/8.20 |
% 29.79/8.20 | Equations (315) can reduce 170 to:
% 29.79/8.20 | (455) ~ (all_0_43_43 = e0)
% 29.79/8.20 |
% 29.79/8.20 | Equations (315) can reduce 225 to:
% 29.79/8.20 | (7709) ~ (all_0_48_48 = e0)
% 29.79/8.20 |
% 29.79/8.20 | Simplifying 7709 yields:
% 29.79/8.20 | (562) ~ (all_0_48_48 = e0)
% 29.79/8.20 |
% 29.79/8.20 | Equations (315) can reduce 218 to:
% 29.79/8.20 | (3852) ~ (all_0_56_56 = e0)
% 29.79/8.20 |
% 29.79/8.20 | Simplifying 3852 yields:
% 29.79/8.20 | (419) ~ (all_0_56_56 = e0)
% 29.79/8.20 |
% 29.79/8.20 | Equations (315) can reduce 172 to:
% 29.79/8.20 | (456) ~ (e4 = e0)
% 29.79/8.20 |
% 29.79/8.20 | Simplifying 456 yields:
% 29.79/8.20 | (6) ~ (e4 = e0)
% 29.79/8.20 |
% 29.79/8.20 | Equations (315) can reduce 3951 to:
% 29.79/8.20 | (566) ~ (e2 = e0)
% 29.79/8.20 |
% 29.79/8.20 | Simplifying 566 yields:
% 29.79/8.20 | (57) ~ (e2 = e0)
% 29.79/8.20 |
% 29.79/8.20 +-Applying beta-rule and splitting (83), into two cases.
% 29.79/8.20 |-Branch one:
% 29.79/8.20 | (321) all_0_47_47 = e1
% 29.79/8.20 |
% 29.79/8.20 | Combining equations (321,315) yields a new equation:
% 29.79/8.20 | (571) e1 = e0
% 29.79/8.20 |
% 29.79/8.20 | Simplifying 571 yields:
% 29.79/8.20 | (560) e1 = e0
% 29.79/8.20 |
% 29.79/8.20 | Equations (560) can reduce 132 to:
% 29.79/8.20 | (270) $false
% 29.79/8.20 |
% 29.79/8.20 |-The branch is then unsatisfiable
% 29.79/8.20 |-Branch two:
% 29.79/8.20 | (324) ~ (all_0_47_47 = e1)
% 29.79/8.20 | (325) all_0_48_48 = e1 | all_0_49_49 = e1
% 29.79/8.20 |
% 29.79/8.20 +-Applying beta-rule and splitting (182), into two cases.
% 29.79/8.20 |-Branch one:
% 29.79/8.20 | (454) all_0_45_45 = e0
% 29.79/8.20 |
% 29.79/8.20 | Combining equations (374,454) yields a new equation:
% 29.79/8.20 | (622) e2 = e0
% 29.79/8.20 |
% 29.79/8.20 | Simplifying 622 yields:
% 29.79/8.20 | (316) e2 = e0
% 29.79/8.20 |
% 29.79/8.20 | Equations (316) can reduce 57 to:
% 29.79/8.20 | (270) $false
% 29.79/8.20 |
% 29.79/8.20 |-The branch is then unsatisfiable
% 29.79/8.20 |-Branch two:
% 29.79/8.20 | (488) ~ (all_0_45_45 = e0)
% 29.79/8.20 | (558) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 29.79/8.20 |
% 29.79/8.20 +-Applying beta-rule and splitting (325), into two cases.
% 29.79/8.20 |-Branch one:
% 29.79/8.20 | (552) all_0_48_48 = e1
% 29.79/8.20 |
% 29.79/8.20 | Equations (552) can reduce 562 to:
% 29.79/8.20 | (132) ~ (e1 = e0)
% 29.79/8.20 |
% 29.79/8.20 | From (552) and (76) follows:
% 29.79/8.20 | (2127) op(e1, e1) = all_0_25_25
% 29.79/8.20 |
% 29.79/8.20 +-Applying beta-rule and splitting (13), into two cases.
% 29.79/8.20 |-Branch one:
% 29.79/8.20 | (576) all_0_53_53 = e2
% 29.79/8.20 |
% 29.79/8.20 | Equations (576) can reduce 259 to:
% 29.79/8.20 | (270) $false
% 29.79/8.20 |
% 29.79/8.20 |-The branch is then unsatisfiable
% 29.79/8.20 |-Branch two:
% 29.79/8.20 | (259) ~ (all_0_53_53 = e2)
% 29.79/8.20 | (5715) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 29.79/8.20 |
% 29.79/8.20 +-Applying beta-rule and splitting (5715), into two cases.
% 29.79/8.20 |-Branch one:
% 29.79/8.20 | (423) all_0_53_53 = e0
% 29.79/8.20 |
% 29.79/8.20 | Equations (423) can reduce 213 to:
% 29.79/8.20 | (925) ~ (all_0_52_52 = e0)
% 29.79/8.20 |
% 29.79/8.20 | Equations (423) can reduce 252 to:
% 29.79/8.20 | (3010) ~ (all_0_54_54 = e0)
% 29.79/8.20 |
% 29.79/8.20 | Simplifying 3010 yields:
% 29.79/8.20 | (3011) ~ (all_0_54_54 = e0)
% 29.79/8.20 |
% 29.79/8.20 | From (423) and (227) follows:
% 29.79/8.20 | (2167) op(e1, e1) = e0
% 29.79/8.20 |
% 29.79/8.20 +-Applying beta-rule and splitting (93), into two cases.
% 29.79/8.20 |-Branch one:
% 29.79/8.20 | (402) all_0_59_59 = e4
% 29.79/8.20 |
% 29.79/8.20 | Equations (402) can reduce 280 to:
% 29.79/8.20 | (270) $false
% 29.79/8.20 |
% 29.79/8.20 |-The branch is then unsatisfiable
% 29.79/8.20 |-Branch two:
% 29.79/8.20 | (280) ~ (all_0_59_59 = e4)
% 29.79/8.20 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 29.79/8.20 |
% 29.79/8.20 +-Applying beta-rule and splitting (407), into two cases.
% 29.79/8.20 |-Branch one:
% 29.79/8.20 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 29.79/8.20 |
% 29.79/8.20 +-Applying beta-rule and splitting (408), into two cases.
% 29.79/8.20 |-Branch one:
% 29.79/8.20 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 29.79/8.20 |
% 29.79/8.20 +-Applying beta-rule and splitting (409), into two cases.
% 29.79/8.20 |-Branch one:
% 29.79/8.20 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 29.79/8.20 |
% 29.79/8.20 | Applying alpha-rule on (410) yields:
% 29.79/8.20 | (411) all_0_43_43 = e0
% 29.79/8.20 | (412) all_0_59_59 = e3
% 29.79/8.20 | (413) ~ (all_0_46_46 = e3)
% 29.79/8.20 |
% 29.79/8.20 | Equations (411) can reduce 455 to:
% 29.79/8.20 | (270) $false
% 29.79/8.20 |
% 29.79/8.20 |-The branch is then unsatisfiable
% 29.79/8.20 |-Branch two:
% 29.79/8.20 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 29.79/8.20 |
% 29.79/8.20 | Applying alpha-rule on (416) yields:
% 29.79/8.20 | (411) all_0_43_43 = e0
% 29.79/8.20 | (412) all_0_59_59 = e3
% 29.79/8.20 | (419) ~ (all_0_56_56 = e0)
% 29.79/8.20 |
% 29.79/8.20 | Equations (411) can reduce 455 to:
% 29.79/8.20 | (270) $false
% 29.79/8.20 |
% 29.79/8.20 |-The branch is then unsatisfiable
% 29.79/8.20 |-Branch two:
% 29.79/8.20 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 29.79/8.20 |
% 29.79/8.20 | Applying alpha-rule on (422) yields:
% 29.79/8.20 | (423) all_0_53_53 = e0
% 29.79/8.20 | (424) all_0_59_59 = e1
% 29.79/8.20 | (425) ~ (all_0_54_54 = e1)
% 29.79/8.20 |
% 29.79/8.20 | Equations (424) can reduce 17 to:
% 29.79/8.20 | (640) ~ (all_0_42_42 = e1)
% 29.79/8.20 |
% 29.79/8.20 | Equations (424) can reduce 206 to:
% 29.79/8.20 | (106) ~ (all_0_46_46 = e1)
% 29.79/8.20 |
% 29.79/8.20 | Equations (424) can reduce 72 to:
% 29.79/8.20 | (425) ~ (all_0_54_54 = e1)
% 29.79/8.20 |
% 29.79/8.20 | Equations (424) can reduce 140 to:
% 29.79/8.20 | (644) ~ (all_0_57_57 = e1)
% 29.79/8.20 |
% 29.79/8.20 | Equations (424) can reduce 280 to:
% 29.79/8.20 | (1021) ~ (e4 = e1)
% 29.79/8.20 |
% 29.79/8.20 | Simplifying 1021 yields:
% 29.79/8.20 | (251) ~ (e4 = e1)
% 29.79/8.20 |
% 29.79/8.20 +-Applying beta-rule and splitting (16), into two cases.
% 29.79/8.20 |-Branch one:
% 29.79/8.20 | (698) all_0_42_42 = e2
% 29.79/8.20 |
% 29.79/8.20 | Equations (698) can reduce 498 to:
% 29.79/8.20 | (270) $false
% 29.79/8.20 |
% 29.79/8.20 |-The branch is then unsatisfiable
% 29.79/8.20 |-Branch two:
% 29.79/8.20 | (498) ~ (all_0_42_42 = e2)
% 29.79/8.20 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 29.79/8.20 |
% 29.79/8.20 +-Applying beta-rule and splitting (1245), into two cases.
% 29.79/8.20 |-Branch one:
% 29.79/8.20 | (1258) all_0_42_42 = e3
% 29.79/8.20 |
% 29.79/8.20 | Equations (1258) can reduce 1316 to:
% 29.79/8.20 | (270) $false
% 29.79/8.20 |
% 29.79/8.20 |-The branch is then unsatisfiable
% 29.79/8.20 |-Branch two:
% 29.79/8.20 | (1316) ~ (all_0_42_42 = e3)
% 29.79/8.20 | (1317) all_0_42_42 = e4 | all_0_42_42 = e1
% 29.79/8.20 |
% 29.79/8.20 +-Applying beta-rule and splitting (99), into two cases.
% 29.79/8.20 |-Branch one:
% 29.79/8.20 | (524) all_0_39_39 = e1
% 29.79/8.20 |
% 29.79/8.20 +-Applying beta-rule and splitting (176), into two cases.
% 29.79/8.20 |-Branch one:
% 29.79/8.20 | (830) all_0_56_56 = e0
% 29.79/8.20 |
% 29.79/8.20 | Equations (830) can reduce 419 to:
% 29.79/8.20 | (270) $false
% 29.79/8.20 |
% 29.79/8.20 |-The branch is then unsatisfiable
% 29.79/8.20 |-Branch two:
% 29.79/8.20 | (419) ~ (all_0_56_56 = e0)
% 29.79/8.20 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 29.79/8.20 |
% 29.79/8.20 +-Applying beta-rule and splitting (834), into two cases.
% 29.79/8.20 |-Branch one:
% 29.79/8.20 | (2258) all_0_57_57 = e0
% 29.79/8.20 |
% 29.79/8.20 | Equations (2258) can reduce 10 to:
% 29.79/8.20 | (625) ~ (all_0_44_44 = e0)
% 29.79/8.20 |
% 29.79/8.20 | Equations (2258) can reduce 235 to:
% 29.79/8.20 | (925) ~ (all_0_52_52 = e0)
% 29.79/8.20 |
% 29.79/8.20 | Equations (2258) can reduce 143 to:
% 29.79/8.20 | (456) ~ (e4 = e0)
% 29.79/8.20 |
% 29.79/8.20 | Simplifying 456 yields:
% 29.79/8.20 | (6) ~ (e4 = e0)
% 29.79/8.20 |
% 29.79/8.20 | Equations (2258) can reduce 335 to:
% 29.79/8.20 | (566) ~ (e2 = e0)
% 29.79/8.20 |
% 29.79/8.20 | Simplifying 566 yields:
% 29.79/8.20 | (57) ~ (e2 = e0)
% 29.79/8.20 |
% 29.79/8.20 | Equations (2258) can reduce 644 to:
% 29.79/8.20 | (568) ~ (e1 = e0)
% 29.79/8.20 |
% 29.79/8.20 | Simplifying 568 yields:
% 29.79/8.20 | (132) ~ (e1 = e0)
% 29.79/8.20 |
% 29.79/8.20 +-Applying beta-rule and splitting (373), into two cases.
% 29.79/8.20 |-Branch one:
% 29.79/8.20 | (621) all_0_44_44 = e0
% 29.79/8.20 |
% 29.79/8.20 | Equations (621) can reduce 625 to:
% 29.79/8.20 | (270) $false
% 29.79/8.20 |
% 29.79/8.20 |-The branch is then unsatisfiable
% 29.79/8.20 |-Branch two:
% 29.79/8.20 | (625) ~ (all_0_44_44 = e0)
% 29.79/8.20 | (858) all_0_44_44 = e3
% 29.79/8.20 |
% 29.79/8.20 | Equations (858) can reduce 122 to:
% 29.79/8.20 | (825) ~ (all_0_52_52 = e3)
% 29.79/8.20 |
% 29.79/8.20 | Simplifying 825 yields:
% 29.79/8.20 | (826) ~ (all_0_52_52 = e3)
% 29.79/8.20 |
% 29.79/8.20 +-Applying beta-rule and splitting (14), into two cases.
% 29.79/8.20 |-Branch one:
% 29.79/8.20 | (2277) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1))
% 29.79/8.20 |
% 29.79/8.20 +-Applying beta-rule and splitting (2277), into two cases.
% 29.79/8.20 |-Branch one:
% 29.79/8.20 | (2278) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1))
% 29.79/8.20 |
% 29.79/8.20 +-Applying beta-rule and splitting (2278), into two cases.
% 29.79/8.20 |-Branch one:
% 29.79/8.20 | (2279) all_0_21_21 = e4 & ~ (all_0_22_22 = e1)
% 29.79/8.20 |
% 29.79/8.20 | Applying alpha-rule on (2279) yields:
% 29.79/8.20 | (2280) all_0_21_21 = e4
% 29.79/8.20 | (2281) ~ (all_0_22_22 = e1)
% 29.79/8.20 |
% 29.79/8.20 | Combining equations (2280,2760) yields a new equation:
% 29.79/8.20 | (268) e4 = e2
% 29.79/8.20 |
% 29.79/8.20 | Simplifying 268 yields:
% 29.79/8.20 | (269) e4 = e2
% 29.79/8.20 |
% 29.79/8.20 | Equations (269) can reduce 231 to:
% 29.79/8.20 | (270) $false
% 29.79/8.20 |
% 29.79/8.20 |-The branch is then unsatisfiable
% 29.79/8.20 |-Branch two:
% 29.79/8.20 | (2285) all_0_23_23 = e3 & ~ (all_0_24_24 = e1)
% 29.79/8.20 |
% 29.79/8.20 | Applying alpha-rule on (2285) yields:
% 29.79/8.20 | (2286) all_0_23_23 = e3
% 29.79/8.20 | (2287) ~ (all_0_24_24 = e1)
% 29.79/8.20 |
% 29.79/8.21 | Combining equations (10441,2286) yields a new equation:
% 29.79/8.21 | (10541) all_0_52_52 = e3
% 29.79/8.21 |
% 29.79/8.21 | Simplifying 10541 yields:
% 29.79/8.21 | (864) all_0_52_52 = e3
% 29.79/8.21 |
% 29.79/8.21 | Equations (864) can reduce 826 to:
% 29.79/8.21 | (270) $false
% 29.79/8.21 |
% 29.79/8.21 |-The branch is then unsatisfiable
% 29.79/8.21 |-Branch two:
% 29.79/8.21 | (2291) all_0_25_25 = e2 & ~ (all_0_26_26 = e1)
% 29.79/8.21 |
% 29.79/8.21 | Applying alpha-rule on (2291) yields:
% 29.79/8.21 | (2292) all_0_25_25 = e2
% 29.79/8.21 | (2293) ~ (all_0_26_26 = e1)
% 29.79/8.21 |
% 29.79/8.21 | From (2292) and (2127) follows:
% 29.79/8.21 | (3043) op(e1, e1) = e2
% 29.79/8.21 |
% 29.79/8.21 +-Applying beta-rule and splitting (221), into two cases.
% 29.79/8.21 |-Branch one:
% 29.79/8.21 | (1132) all_0_46_46 = e0
% 29.79/8.21 |
% 29.79/8.21 | Equations (1132) can reduce 1436 to:
% 29.79/8.21 | (566) ~ (e2 = e0)
% 29.79/8.21 |
% 29.79/8.21 | Simplifying 566 yields:
% 29.79/8.21 | (57) ~ (e2 = e0)
% 29.79/8.21 |
% 29.79/8.21 | Equations (1132) can reduce 106 to:
% 29.79/8.21 | (568) ~ (e1 = e0)
% 29.79/8.21 |
% 29.79/8.21 | Simplifying 568 yields:
% 29.79/8.21 | (132) ~ (e1 = e0)
% 29.79/8.21 |
% 29.79/8.21 +-Applying beta-rule and splitting (3352), into two cases.
% 29.79/8.21 |-Branch one:
% 29.79/8.21 | (848) all_0_52_52 = e1
% 29.79/8.21 |
% 29.79/8.21 | From (848) and (195) follows:
% 29.79/8.21 | (9340) op(e1, e1) = all_0_18_18
% 29.79/8.21 |
% 29.79/8.21 | Instantiating formula (201) with e1, e1, e2, all_0_18_18 and discharging atoms op(e1, e1) = all_0_18_18, op(e1, e1) = e2, yields:
% 29.79/8.21 | (10555) all_0_18_18 = e2
% 29.79/8.21 |
% 29.79/8.21 | Instantiating formula (201) with e1, e1, e0, all_0_18_18 and discharging atoms op(e1, e1) = all_0_18_18, op(e1, e1) = e0, yields:
% 29.79/8.21 | (9358) all_0_18_18 = e0
% 29.79/8.21 |
% 29.79/8.21 | Combining equations (9358,10555) yields a new equation:
% 29.79/8.21 | (316) e2 = e0
% 29.79/8.21 |
% 29.79/8.21 | Equations (316) can reduce 57 to:
% 29.79/8.21 | (270) $false
% 29.79/8.21 |
% 29.79/8.21 |-The branch is then unsatisfiable
% 29.79/8.21 |-Branch two:
% 29.79/8.21 | (642) ~ (all_0_52_52 = e1)
% 29.79/8.21 | (997) all_0_57_57 = e1
% 29.79/8.21 |
% 29.79/8.21 | Combining equations (2258,997) yields a new equation:
% 29.79/8.21 | (560) e1 = e0
% 29.79/8.21 |
% 29.79/8.21 | Equations (560) can reduce 132 to:
% 29.79/8.21 | (270) $false
% 29.79/8.21 |
% 29.79/8.21 |-The branch is then unsatisfiable
% 29.79/8.21 |-Branch two:
% 29.79/8.21 | (1010) ~ (all_0_46_46 = e0)
% 29.79/8.21 | (3629) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 29.79/8.21 |
% 29.79/8.21 +-Applying beta-rule and splitting (3352), into two cases.
% 29.79/8.21 |-Branch one:
% 29.79/8.21 | (848) all_0_52_52 = e1
% 29.79/8.21 |
% 29.79/8.21 | Equations (848) can reduce 925 to:
% 29.79/8.21 | (132) ~ (e1 = e0)
% 29.79/8.21 |
% 29.79/8.21 +-Applying beta-rule and splitting (3629), into two cases.
% 29.79/8.21 |-Branch one:
% 29.79/8.21 | (563) all_0_49_49 = e0
% 29.79/8.21 |
% 29.79/8.21 | Combining equations (307,563) yields a new equation:
% 29.79/8.21 | (622) e2 = e0
% 29.79/8.21 |
% 29.79/8.21 | Simplifying 622 yields:
% 29.79/8.21 | (316) e2 = e0
% 29.79/8.21 |
% 29.79/8.21 | Equations (316) can reduce 57 to:
% 29.79/8.21 | (270) $false
% 29.79/8.21 |
% 29.79/8.21 |-The branch is then unsatisfiable
% 29.79/8.21 |-Branch two:
% 29.79/8.21 | (1231) ~ (all_0_49_49 = e0)
% 29.79/8.21 | (3638) all_0_54_54 = e0 | all_0_59_59 = e0
% 29.79/8.21 |
% 29.79/8.21 +-Applying beta-rule and splitting (3638), into two cases.
% 29.79/8.21 |-Branch one:
% 29.79/8.21 | (3084) all_0_54_54 = e0
% 29.79/8.21 |
% 29.79/8.21 | Equations (3084) can reduce 3011 to:
% 29.79/8.21 | (270) $false
% 29.79/8.21 |
% 29.79/8.21 |-The branch is then unsatisfiable
% 29.79/8.21 |-Branch two:
% 29.79/8.21 | (3011) ~ (all_0_54_54 = e0)
% 29.79/8.21 | (2308) all_0_59_59 = e0
% 29.79/8.21 |
% 29.79/8.21 | Combining equations (2308,424) yields a new equation:
% 29.79/8.21 | (560) e1 = e0
% 29.79/8.21 |
% 29.79/8.21 | Equations (560) can reduce 132 to:
% 29.79/8.21 | (270) $false
% 29.79/8.21 |
% 29.79/8.21 |-The branch is then unsatisfiable
% 29.79/8.21 |-Branch two:
% 29.79/8.21 | (642) ~ (all_0_52_52 = e1)
% 29.79/8.21 | (997) all_0_57_57 = e1
% 29.79/8.21 |
% 29.79/8.21 | Combining equations (997,2258) yields a new equation:
% 29.79/8.21 | (571) e1 = e0
% 29.79/8.21 |
% 29.79/8.21 | Simplifying 571 yields:
% 29.79/8.21 | (560) e1 = e0
% 29.79/8.21 |
% 29.79/8.21 | Equations (560) can reduce 132 to:
% 29.79/8.21 | (270) $false
% 29.79/8.21 |
% 29.79/8.21 |-The branch is then unsatisfiable
% 29.79/8.21 |-Branch two:
% 29.79/8.21 | (2296) all_0_28_28 = e0 & ~ (all_0_29_29 = e1)
% 29.79/8.21 |
% 29.79/8.21 | Applying alpha-rule on (2296) yields:
% 29.79/8.21 | (2297) all_0_28_28 = e0
% 29.79/8.21 | (2298) ~ (all_0_29_29 = e1)
% 29.79/8.21 |
% 29.79/8.21 | Combining equations (2297,9135) yields a new equation:
% 29.79/8.21 | (479) e4 = e0
% 29.79/8.21 |
% 29.79/8.21 | Equations (479) can reduce 6 to:
% 29.79/8.21 | (270) $false
% 29.79/8.21 |
% 29.79/8.21 |-The branch is then unsatisfiable
% 29.79/8.21 |-Branch two:
% 29.79/8.21 | (2301) ~ (all_0_57_57 = e0)
% 29.79/8.21 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 29.79/8.21 |
% 29.79/8.21 +-Applying beta-rule and splitting (9), into two cases.
% 29.79/8.21 |-Branch one:
% 29.79/8.21 | (621) all_0_44_44 = e0
% 29.79/8.21 |
% 29.79/8.21 | Equations (621) can reduce 241 to:
% 29.79/8.21 | (455) ~ (all_0_43_43 = e0)
% 29.79/8.21 |
% 29.79/8.21 | Equations (621) can reduce 131 to:
% 29.79/8.21 | (568) ~ (e1 = e0)
% 29.79/8.21 |
% 29.79/8.21 | Simplifying 568 yields:
% 29.79/8.21 | (132) ~ (e1 = e0)
% 29.79/8.21 |
% 29.79/8.21 +-Applying beta-rule and splitting (222), into two cases.
% 29.79/8.21 |-Branch one:
% 29.79/8.21 | (522) all_0_39_39 = e4
% 29.79/8.21 |
% 29.79/8.21 | Combining equations (524,522) yields a new equation:
% 29.79/8.21 | (526) e4 = e1
% 29.79/8.21 |
% 29.79/8.21 | Equations (526) can reduce 251 to:
% 29.79/8.21 | (270) $false
% 29.79/8.21 |
% 29.79/8.21 |-The branch is then unsatisfiable
% 29.79/8.21 |-Branch two:
% 29.79/8.21 | (591) ~ (all_0_39_39 = e4)
% 29.79/8.21 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 29.79/8.21 |
% 29.79/8.21 +-Applying beta-rule and splitting (110), into two cases.
% 29.79/8.21 |-Branch one:
% 29.79/8.21 | (3657) all_0_54_54 = e2
% 29.79/8.21 |
% 29.79/8.21 | Equations (3657) can reduce 261 to:
% 29.79/8.21 | (270) $false
% 29.79/8.21 |
% 29.79/8.21 |-The branch is then unsatisfiable
% 29.79/8.21 |-Branch two:
% 29.79/8.21 | (261) ~ (all_0_54_54 = e2)
% 29.79/8.21 | (3660) all_0_54_54 = e4 | all_0_54_54 = e3 | all_0_54_54 = e1 | all_0_54_54 = e0
% 29.79/8.21 |
% 29.79/8.21 +-Applying beta-rule and splitting (3660), into two cases.
% 29.79/8.21 |-Branch one:
% 29.79/8.21 | (3084) all_0_54_54 = e0
% 29.79/8.21 |
% 29.79/8.21 | Equations (3084) can reduce 3011 to:
% 29.79/8.21 | (270) $false
% 29.79/8.21 |
% 29.79/8.21 |-The branch is then unsatisfiable
% 29.79/8.21 |-Branch two:
% 29.79/8.21 | (3011) ~ (all_0_54_54 = e0)
% 29.79/8.21 | (3664) all_0_54_54 = e4 | all_0_54_54 = e3 | all_0_54_54 = e1
% 29.79/8.21 |
% 29.79/8.21 +-Applying beta-rule and splitting (3664), into two cases.
% 29.79/8.21 |-Branch one:
% 29.79/8.21 | (1119) all_0_54_54 = e3
% 29.79/8.21 |
% 29.79/8.21 | Equations (1119) can reduce 936 to:
% 29.79/8.21 | (719) ~ (e4 = e3)
% 29.79/8.21 |
% 29.79/8.21 | Simplifying 719 yields:
% 29.79/8.21 | (34) ~ (e4 = e3)
% 29.79/8.21 |
% 29.79/8.21 +-Applying beta-rule and splitting (592), into two cases.
% 29.79/8.21 |-Branch one:
% 29.79/8.21 | (358) all_0_41_41 = e4
% 29.79/8.21 |
% 29.79/8.21 | Combining equations (351,358) yields a new equation:
% 29.79/8.21 | (359) e4 = e3
% 29.79/8.21 |
% 29.79/8.21 | Equations (359) can reduce 34 to:
% 29.79/8.21 | (270) $false
% 29.79/8.21 |
% 29.79/8.21 |-The branch is then unsatisfiable
% 29.79/8.21 |-Branch two:
% 29.79/8.21 | (361) ~ (all_0_41_41 = e4)
% 29.79/8.21 | (512) all_0_42_42 = e4
% 29.79/8.21 |
% 29.79/8.21 | Equations (512) can reduce 18 to:
% 29.79/8.21 | (804) ~ (all_0_46_46 = e4)
% 29.79/8.21 |
% 29.79/8.21 | Simplifying 804 yields:
% 29.79/8.21 | (805) ~ (all_0_46_46 = e4)
% 29.79/8.21 |
% 29.79/8.21 | Equations (512) can reduce 498 to:
% 29.79/8.21 | (231) ~ (e4 = e2)
% 29.79/8.21 |
% 29.79/8.21 +-Applying beta-rule and splitting (44), into two cases.
% 29.79/8.21 |-Branch one:
% 29.79/8.21 | (502) all_0_43_43 = e4
% 29.79/8.21 |
% 29.79/8.21 | Equations (502) can reduce 455 to:
% 29.79/8.21 | (6) ~ (e4 = e0)
% 29.79/8.21 |
% 29.79/8.21 +-Applying beta-rule and splitting (2302), into two cases.
% 29.79/8.21 |-Branch one:
% 29.79/8.21 | (585) all_0_58_58 = e0
% 29.79/8.21 |
% 29.79/8.21 | Combining equations (585,600) yields a new equation:
% 29.79/8.21 | (479) e4 = e0
% 29.79/8.21 |
% 29.79/8.21 | Equations (479) can reduce 6 to:
% 29.79/8.21 | (270) $false
% 29.79/8.21 |
% 29.79/8.21 |-The branch is then unsatisfiable
% 29.79/8.21 |-Branch two:
% 29.79/8.21 | (431) ~ (all_0_58_58 = e0)
% 29.79/8.21 | (2308) all_0_59_59 = e0
% 29.79/8.21 |
% 29.79/8.21 | Combining equations (424,2308) yields a new equation:
% 29.79/8.21 | (571) e1 = e0
% 29.79/8.21 |
% 29.79/8.21 | Simplifying 571 yields:
% 29.79/8.21 | (560) e1 = e0
% 29.79/8.21 |
% 29.79/8.21 | Equations (560) can reduce 132 to:
% 29.79/8.21 | (270) $false
% 29.79/8.21 |
% 29.79/8.21 |-The branch is then unsatisfiable
% 29.79/8.21 |-Branch two:
% 29.79/8.21 | (510) ~ (all_0_43_43 = e4)
% 29.79/8.21 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 29.79/8.21 |
% 29.79/8.21 +-Applying beta-rule and splitting (511), into two cases.
% 29.79/8.21 |-Branch one:
% 29.79/8.21 | (363) all_0_45_45 = e4
% 29.79/8.21 |
% 29.79/8.21 | Combining equations (374,363) yields a new equation:
% 29.79/8.21 | (269) e4 = e2
% 29.79/8.21 |
% 29.79/8.22 | Equations (269) can reduce 231 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (352) ~ (all_0_45_45 = e4)
% 29.79/8.22 | (517) all_0_46_46 = e4
% 29.79/8.22 |
% 29.79/8.22 | Equations (517) can reduce 805 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (1093) ~ (all_0_54_54 = e3)
% 29.79/8.22 | (3694) all_0_54_54 = e4 | all_0_54_54 = e1
% 29.79/8.22 |
% 29.79/8.22 +-Applying beta-rule and splitting (3694), into two cases.
% 29.79/8.22 |-Branch one:
% 29.79/8.22 | (875) all_0_54_54 = e1
% 29.79/8.22 |
% 29.79/8.22 | Equations (875) can reduce 425 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (425) ~ (all_0_54_54 = e1)
% 29.79/8.22 | (817) all_0_54_54 = e4
% 29.79/8.22 |
% 29.79/8.22 | Equations (817) can reduce 936 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (625) ~ (all_0_44_44 = e0)
% 29.79/8.22 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 29.79/8.22 |
% 29.79/8.22 +-Applying beta-rule and splitting (373), into two cases.
% 29.79/8.22 |-Branch one:
% 29.79/8.22 | (621) all_0_44_44 = e0
% 29.79/8.22 |
% 29.79/8.22 | Equations (621) can reduce 625 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (625) ~ (all_0_44_44 = e0)
% 29.79/8.22 | (858) all_0_44_44 = e3
% 29.79/8.22 |
% 29.79/8.22 | Equations (858) can reduce 122 to:
% 29.79/8.22 | (825) ~ (all_0_52_52 = e3)
% 29.79/8.22 |
% 29.79/8.22 | Simplifying 825 yields:
% 29.79/8.22 | (826) ~ (all_0_52_52 = e3)
% 29.79/8.22 |
% 29.79/8.22 +-Applying beta-rule and splitting (90), into two cases.
% 29.79/8.22 |-Branch one:
% 29.79/8.22 | (685) all_0_52_52 = e2
% 29.79/8.22 |
% 29.79/8.22 | Equations (685) can reduce 257 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (257) ~ (all_0_52_52 = e2)
% 29.79/8.22 | (688) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 29.79/8.22 |
% 29.79/8.22 +-Applying beta-rule and splitting (688), into two cases.
% 29.79/8.22 |-Branch one:
% 29.79/8.22 | (827) all_0_52_52 = e0
% 29.79/8.22 |
% 29.79/8.22 | Equations (827) can reduce 925 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (925) ~ (all_0_52_52 = e0)
% 29.79/8.22 | (926) all_0_52_52 = e3 | all_0_52_52 = e1
% 29.79/8.22 |
% 29.79/8.22 +-Applying beta-rule and splitting (926), into two cases.
% 29.79/8.22 |-Branch one:
% 29.79/8.22 | (864) all_0_52_52 = e3
% 29.79/8.22 |
% 29.79/8.22 | Equations (864) can reduce 826 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (826) ~ (all_0_52_52 = e3)
% 29.79/8.22 | (848) all_0_52_52 = e1
% 29.79/8.22 |
% 29.79/8.22 | Equations (848) can reduce 925 to:
% 29.79/8.22 | (132) ~ (e1 = e0)
% 29.79/8.22 |
% 29.79/8.22 +-Applying beta-rule and splitting (626), into two cases.
% 29.79/8.22 |-Branch one:
% 29.79/8.22 | (827) all_0_52_52 = e0
% 29.79/8.22 |
% 29.79/8.22 | Combining equations (827,848) yields a new equation:
% 29.79/8.22 | (560) e1 = e0
% 29.79/8.22 |
% 29.79/8.22 | Equations (560) can reduce 132 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (925) ~ (all_0_52_52 = e0)
% 29.79/8.22 | (2258) all_0_57_57 = e0
% 29.79/8.22 |
% 29.79/8.22 | Equations (2258) can reduce 2301 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (528) ~ (all_0_39_39 = e1)
% 29.79/8.22 | (680) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 29.79/8.22 |
% 29.79/8.22 +-Applying beta-rule and splitting (1317), into two cases.
% 29.79/8.22 |-Branch one:
% 29.79/8.22 | (541) all_0_42_42 = e1
% 29.79/8.22 |
% 29.79/8.22 | Equations (541) can reduce 640 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (640) ~ (all_0_42_42 = e1)
% 29.79/8.22 | (512) all_0_42_42 = e4
% 29.79/8.22 |
% 29.79/8.22 | Equations (512) can reduce 184 to:
% 29.79/8.22 | (591) ~ (all_0_39_39 = e4)
% 29.79/8.22 |
% 29.79/8.22 +-Applying beta-rule and splitting (210), into two cases.
% 29.79/8.22 |-Branch one:
% 29.79/8.22 | (524) all_0_39_39 = e1
% 29.79/8.22 |
% 29.79/8.22 | Equations (524) can reduce 528 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (528) ~ (all_0_39_39 = e1)
% 29.79/8.22 | (529) all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1
% 29.79/8.22 |
% 29.79/8.22 +-Applying beta-rule and splitting (166), into two cases.
% 29.79/8.22 |-Branch one:
% 29.79/8.22 | (522) all_0_39_39 = e4
% 29.79/8.22 |
% 29.79/8.22 | Equations (522) can reduce 591 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (591) ~ (all_0_39_39 = e4)
% 29.79/8.22 | (4522) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 29.79/8.22 |
% 29.79/8.22 +-Applying beta-rule and splitting (177), into two cases.
% 29.79/8.22 |-Branch one:
% 29.79/8.22 | (336) all_0_39_39 = e2
% 29.79/8.22 |
% 29.79/8.22 | Equations (336) can reduce 291 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (291) ~ (all_0_39_39 = e2)
% 29.79/8.22 | (684) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 29.79/8.22 |
% 29.79/8.22 +-Applying beta-rule and splitting (684), into two cases.
% 29.79/8.22 |-Branch one:
% 29.79/8.22 | (751) all_0_39_39 = e3
% 29.79/8.22 |
% 29.79/8.22 | Equations (751) can reduce 755 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (755) ~ (all_0_39_39 = e3)
% 29.79/8.22 | (1756) all_0_39_39 = e4 | all_0_39_39 = e1
% 29.79/8.22 |
% 29.79/8.22 +-Applying beta-rule and splitting (1756), into two cases.
% 29.79/8.22 |-Branch one:
% 29.79/8.22 | (524) all_0_39_39 = e1
% 29.79/8.22 |
% 29.79/8.22 | Equations (524) can reduce 528 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (528) ~ (all_0_39_39 = e1)
% 29.79/8.22 | (522) all_0_39_39 = e4
% 29.79/8.22 |
% 29.79/8.22 | Equations (522) can reduce 591 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 29.79/8.22 |
% 29.79/8.22 | Applying alpha-rule on (428) yields:
% 29.79/8.22 | (423) all_0_53_53 = e0
% 29.79/8.22 | (424) all_0_59_59 = e1
% 29.79/8.22 | (431) ~ (all_0_58_58 = e0)
% 29.79/8.22 |
% 29.79/8.22 | Equations (424) can reduce 17 to:
% 29.79/8.22 | (640) ~ (all_0_42_42 = e1)
% 29.79/8.22 |
% 29.79/8.22 | Equations (424) can reduce 206 to:
% 29.79/8.22 | (106) ~ (all_0_46_46 = e1)
% 29.79/8.22 |
% 29.79/8.22 | Equations (424) can reduce 72 to:
% 29.79/8.22 | (425) ~ (all_0_54_54 = e1)
% 29.79/8.22 |
% 29.79/8.22 | Equations (424) can reduce 140 to:
% 29.79/8.22 | (644) ~ (all_0_57_57 = e1)
% 29.79/8.22 |
% 29.79/8.22 | Equations (424) can reduce 280 to:
% 29.79/8.22 | (1021) ~ (e4 = e1)
% 29.79/8.22 |
% 29.79/8.22 | Simplifying 1021 yields:
% 29.79/8.22 | (251) ~ (e4 = e1)
% 29.79/8.22 |
% 29.79/8.22 +-Applying beta-rule and splitting (16), into two cases.
% 29.79/8.22 |-Branch one:
% 29.79/8.22 | (698) all_0_42_42 = e2
% 29.79/8.22 |
% 29.79/8.22 | Equations (698) can reduce 498 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (498) ~ (all_0_42_42 = e2)
% 29.79/8.22 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 29.79/8.22 |
% 29.79/8.22 +-Applying beta-rule and splitting (1245), into two cases.
% 29.79/8.22 |-Branch one:
% 29.79/8.22 | (1258) all_0_42_42 = e3
% 29.79/8.22 |
% 29.79/8.22 | Equations (1258) can reduce 1316 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (1316) ~ (all_0_42_42 = e3)
% 29.79/8.22 | (1317) all_0_42_42 = e4 | all_0_42_42 = e1
% 29.79/8.22 |
% 29.79/8.22 +-Applying beta-rule and splitting (99), into two cases.
% 29.79/8.22 |-Branch one:
% 29.79/8.22 | (524) all_0_39_39 = e1
% 29.79/8.22 |
% 29.79/8.22 +-Applying beta-rule and splitting (176), into two cases.
% 29.79/8.22 |-Branch one:
% 29.79/8.22 | (830) all_0_56_56 = e0
% 29.79/8.22 |
% 29.79/8.22 | Equations (830) can reduce 419 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (419) ~ (all_0_56_56 = e0)
% 29.79/8.22 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 29.79/8.22 |
% 29.79/8.22 +-Applying beta-rule and splitting (834), into two cases.
% 29.79/8.22 |-Branch one:
% 29.79/8.22 | (2258) all_0_57_57 = e0
% 29.79/8.22 |
% 29.79/8.22 | Equations (2258) can reduce 10 to:
% 29.79/8.22 | (625) ~ (all_0_44_44 = e0)
% 29.79/8.22 |
% 29.79/8.22 | Equations (2258) can reduce 235 to:
% 29.79/8.22 | (925) ~ (all_0_52_52 = e0)
% 29.79/8.22 |
% 29.79/8.22 | Equations (2258) can reduce 143 to:
% 29.79/8.22 | (456) ~ (e4 = e0)
% 29.79/8.22 |
% 29.79/8.22 | Simplifying 456 yields:
% 29.79/8.22 | (6) ~ (e4 = e0)
% 29.79/8.22 |
% 29.79/8.22 | Equations (2258) can reduce 335 to:
% 29.79/8.22 | (566) ~ (e2 = e0)
% 29.79/8.22 |
% 29.79/8.22 | Simplifying 566 yields:
% 29.79/8.22 | (57) ~ (e2 = e0)
% 29.79/8.22 |
% 29.79/8.22 | Equations (2258) can reduce 644 to:
% 29.79/8.22 | (568) ~ (e1 = e0)
% 29.79/8.22 |
% 29.79/8.22 | Simplifying 568 yields:
% 29.79/8.22 | (132) ~ (e1 = e0)
% 29.79/8.22 |
% 29.79/8.22 +-Applying beta-rule and splitting (373), into two cases.
% 29.79/8.22 |-Branch one:
% 29.79/8.22 | (621) all_0_44_44 = e0
% 29.79/8.22 |
% 29.79/8.22 | Equations (621) can reduce 625 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (625) ~ (all_0_44_44 = e0)
% 29.79/8.22 | (858) all_0_44_44 = e3
% 29.79/8.22 |
% 29.79/8.22 | Equations (858) can reduce 122 to:
% 29.79/8.22 | (825) ~ (all_0_52_52 = e3)
% 29.79/8.22 |
% 29.79/8.22 | Simplifying 825 yields:
% 29.79/8.22 | (826) ~ (all_0_52_52 = e3)
% 29.79/8.22 |
% 29.79/8.22 +-Applying beta-rule and splitting (14), into two cases.
% 29.79/8.22 |-Branch one:
% 29.79/8.22 | (2277) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1))
% 29.79/8.22 |
% 29.79/8.22 +-Applying beta-rule and splitting (2277), into two cases.
% 29.79/8.22 |-Branch one:
% 29.79/8.22 | (2278) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1))
% 29.79/8.22 |
% 29.79/8.22 +-Applying beta-rule and splitting (2278), into two cases.
% 29.79/8.22 |-Branch one:
% 29.79/8.22 | (2279) all_0_21_21 = e4 & ~ (all_0_22_22 = e1)
% 29.79/8.22 |
% 29.79/8.22 | Applying alpha-rule on (2279) yields:
% 29.79/8.22 | (2280) all_0_21_21 = e4
% 29.79/8.22 | (2281) ~ (all_0_22_22 = e1)
% 29.79/8.22 |
% 29.79/8.22 | Combining equations (2280,2760) yields a new equation:
% 29.79/8.22 | (268) e4 = e2
% 29.79/8.22 |
% 29.79/8.22 | Simplifying 268 yields:
% 29.79/8.22 | (269) e4 = e2
% 29.79/8.22 |
% 29.79/8.22 | Equations (269) can reduce 231 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (2285) all_0_23_23 = e3 & ~ (all_0_24_24 = e1)
% 29.79/8.22 |
% 29.79/8.22 | Applying alpha-rule on (2285) yields:
% 29.79/8.22 | (2286) all_0_23_23 = e3
% 29.79/8.22 | (2287) ~ (all_0_24_24 = e1)
% 29.79/8.22 |
% 29.79/8.22 | Combining equations (10441,2286) yields a new equation:
% 29.79/8.22 | (10541) all_0_52_52 = e3
% 29.79/8.22 |
% 29.79/8.22 | Simplifying 10541 yields:
% 29.79/8.22 | (864) all_0_52_52 = e3
% 29.79/8.22 |
% 29.79/8.22 | Equations (864) can reduce 826 to:
% 29.79/8.22 | (270) $false
% 29.79/8.22 |
% 29.79/8.22 |-The branch is then unsatisfiable
% 29.79/8.22 |-Branch two:
% 29.79/8.22 | (2291) all_0_25_25 = e2 & ~ (all_0_26_26 = e1)
% 29.79/8.22 |
% 29.79/8.22 | Applying alpha-rule on (2291) yields:
% 29.79/8.22 | (2292) all_0_25_25 = e2
% 29.79/8.22 | (2293) ~ (all_0_26_26 = e1)
% 29.79/8.22 |
% 29.79/8.22 | From (2292) and (2127) follows:
% 29.79/8.22 | (3043) op(e1, e1) = e2
% 29.79/8.22 |
% 29.79/8.22 +-Applying beta-rule and splitting (221), into two cases.
% 29.79/8.22 |-Branch one:
% 29.79/8.22 | (1132) all_0_46_46 = e0
% 29.79/8.22 |
% 29.79/8.22 | Equations (1132) can reduce 1436 to:
% 29.79/8.22 | (566) ~ (e2 = e0)
% 29.79/8.22 |
% 29.79/8.22 | Simplifying 566 yields:
% 29.79/8.22 | (57) ~ (e2 = e0)
% 29.79/8.22 |
% 29.79/8.22 | Equations (1132) can reduce 106 to:
% 29.79/8.22 | (568) ~ (e1 = e0)
% 29.79/8.22 |
% 29.79/8.22 | Simplifying 568 yields:
% 29.79/8.22 | (132) ~ (e1 = e0)
% 29.79/8.22 |
% 29.79/8.23 +-Applying beta-rule and splitting (3352), into two cases.
% 29.79/8.23 |-Branch one:
% 29.79/8.23 | (848) all_0_52_52 = e1
% 29.79/8.23 |
% 29.79/8.23 | From (848) and (195) follows:
% 29.79/8.23 | (9340) op(e1, e1) = all_0_18_18
% 29.79/8.23 |
% 29.79/8.23 | Instantiating formula (201) with e1, e1, e2, all_0_18_18 and discharging atoms op(e1, e1) = all_0_18_18, op(e1, e1) = e2, yields:
% 29.79/8.23 | (10555) all_0_18_18 = e2
% 29.79/8.23 |
% 29.79/8.23 | Instantiating formula (201) with e1, e1, e0, all_0_18_18 and discharging atoms op(e1, e1) = all_0_18_18, op(e1, e1) = e0, yields:
% 29.79/8.23 | (9358) all_0_18_18 = e0
% 29.79/8.23 |
% 29.79/8.23 | Combining equations (9358,10555) yields a new equation:
% 29.79/8.23 | (316) e2 = e0
% 29.79/8.23 |
% 29.79/8.23 | Equations (316) can reduce 57 to:
% 29.79/8.23 | (270) $false
% 29.79/8.23 |
% 29.79/8.23 |-The branch is then unsatisfiable
% 29.79/8.23 |-Branch two:
% 29.79/8.23 | (642) ~ (all_0_52_52 = e1)
% 29.79/8.23 | (997) all_0_57_57 = e1
% 29.79/8.23 |
% 29.79/8.23 | Combining equations (2258,997) yields a new equation:
% 29.79/8.23 | (560) e1 = e0
% 29.79/8.23 |
% 29.79/8.23 | Equations (560) can reduce 132 to:
% 29.79/8.23 | (270) $false
% 29.79/8.23 |
% 29.79/8.23 |-The branch is then unsatisfiable
% 29.79/8.23 |-Branch two:
% 29.79/8.23 | (1010) ~ (all_0_46_46 = e0)
% 29.79/8.23 | (3629) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 29.79/8.23 |
% 29.79/8.23 +-Applying beta-rule and splitting (3352), into two cases.
% 29.79/8.23 |-Branch one:
% 29.79/8.23 | (848) all_0_52_52 = e1
% 29.79/8.23 |
% 29.79/8.23 | Equations (848) can reduce 925 to:
% 29.79/8.23 | (132) ~ (e1 = e0)
% 29.79/8.23 |
% 29.79/8.23 +-Applying beta-rule and splitting (3629), into two cases.
% 29.79/8.23 |-Branch one:
% 29.79/8.23 | (563) all_0_49_49 = e0
% 29.79/8.23 |
% 29.79/8.23 | Combining equations (307,563) yields a new equation:
% 29.79/8.23 | (622) e2 = e0
% 29.79/8.23 |
% 29.79/8.23 | Simplifying 622 yields:
% 29.79/8.23 | (316) e2 = e0
% 29.79/8.23 |
% 29.79/8.23 | Equations (316) can reduce 57 to:
% 29.79/8.23 | (270) $false
% 29.79/8.23 |
% 29.79/8.23 |-The branch is then unsatisfiable
% 29.79/8.23 |-Branch two:
% 29.79/8.23 | (1231) ~ (all_0_49_49 = e0)
% 29.79/8.23 | (3638) all_0_54_54 = e0 | all_0_59_59 = e0
% 29.79/8.23 |
% 29.79/8.23 +-Applying beta-rule and splitting (3638), into two cases.
% 29.79/8.23 |-Branch one:
% 29.79/8.23 | (3084) all_0_54_54 = e0
% 29.79/8.23 |
% 29.79/8.23 | Equations (3084) can reduce 3011 to:
% 29.79/8.23 | (270) $false
% 29.79/8.23 |
% 29.79/8.23 |-The branch is then unsatisfiable
% 29.79/8.23 |-Branch two:
% 29.79/8.23 | (3011) ~ (all_0_54_54 = e0)
% 29.79/8.23 | (2308) all_0_59_59 = e0
% 29.79/8.23 |
% 29.79/8.23 | Combining equations (2308,424) yields a new equation:
% 29.79/8.23 | (560) e1 = e0
% 29.79/8.23 |
% 29.79/8.23 | Equations (560) can reduce 132 to:
% 29.79/8.23 | (270) $false
% 29.79/8.23 |
% 29.79/8.23 |-The branch is then unsatisfiable
% 29.79/8.23 |-Branch two:
% 29.79/8.23 | (642) ~ (all_0_52_52 = e1)
% 29.79/8.23 | (997) all_0_57_57 = e1
% 29.79/8.23 |
% 29.79/8.23 | Combining equations (997,2258) yields a new equation:
% 29.79/8.23 | (571) e1 = e0
% 29.79/8.23 |
% 29.79/8.23 | Simplifying 571 yields:
% 29.79/8.23 | (560) e1 = e0
% 29.79/8.23 |
% 29.79/8.23 | Equations (560) can reduce 132 to:
% 29.79/8.23 | (270) $false
% 29.79/8.23 |
% 29.79/8.23 |-The branch is then unsatisfiable
% 29.79/8.23 |-Branch two:
% 29.79/8.23 | (2296) all_0_28_28 = e0 & ~ (all_0_29_29 = e1)
% 29.79/8.23 |
% 29.79/8.23 | Applying alpha-rule on (2296) yields:
% 29.79/8.23 | (2297) all_0_28_28 = e0
% 29.79/8.23 | (2298) ~ (all_0_29_29 = e1)
% 29.79/8.23 |
% 29.79/8.23 | Combining equations (2297,9135) yields a new equation:
% 29.79/8.23 | (479) e4 = e0
% 29.79/8.23 |
% 29.79/8.23 | Equations (479) can reduce 6 to:
% 29.79/8.23 | (270) $false
% 29.79/8.23 |
% 29.79/8.23 |-The branch is then unsatisfiable
% 29.79/8.23 |-Branch two:
% 29.79/8.23 | (2301) ~ (all_0_57_57 = e0)
% 29.79/8.23 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 29.79/8.23 |
% 29.79/8.23 +-Applying beta-rule and splitting (9), into two cases.
% 29.79/8.23 |-Branch one:
% 29.79/8.23 | (621) all_0_44_44 = e0
% 29.79/8.23 |
% 29.79/8.23 | Equations (621) can reduce 241 to:
% 29.79/8.23 | (455) ~ (all_0_43_43 = e0)
% 29.79/8.23 |
% 29.79/8.23 | Equations (621) can reduce 131 to:
% 29.79/8.23 | (568) ~ (e1 = e0)
% 29.79/8.23 |
% 29.79/8.23 | Simplifying 568 yields:
% 29.79/8.23 | (132) ~ (e1 = e0)
% 29.79/8.23 |
% 29.79/8.23 +-Applying beta-rule and splitting (222), into two cases.
% 29.79/8.23 |-Branch one:
% 29.79/8.23 | (522) all_0_39_39 = e4
% 29.79/8.23 |
% 29.79/8.23 | Combining equations (524,522) yields a new equation:
% 29.79/8.23 | (526) e4 = e1
% 29.79/8.23 |
% 29.79/8.23 | Equations (526) can reduce 251 to:
% 29.79/8.23 | (270) $false
% 29.79/8.23 |
% 29.79/8.23 |-The branch is then unsatisfiable
% 29.79/8.23 |-Branch two:
% 29.79/8.23 | (591) ~ (all_0_39_39 = e4)
% 29.79/8.23 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 29.79/8.23 |
% 29.79/8.23 +-Applying beta-rule and splitting (110), into two cases.
% 29.79/8.23 |-Branch one:
% 29.79/8.23 | (3657) all_0_54_54 = e2
% 29.79/8.23 |
% 29.79/8.23 | Equations (3657) can reduce 261 to:
% 29.79/8.23 | (270) $false
% 29.79/8.23 |
% 29.79/8.23 |-The branch is then unsatisfiable
% 29.79/8.23 |-Branch two:
% 29.79/8.23 | (261) ~ (all_0_54_54 = e2)
% 29.79/8.23 | (3660) all_0_54_54 = e4 | all_0_54_54 = e3 | all_0_54_54 = e1 | all_0_54_54 = e0
% 29.79/8.23 |
% 29.79/8.23 +-Applying beta-rule and splitting (3660), into two cases.
% 29.79/8.23 |-Branch one:
% 29.79/8.23 | (3084) all_0_54_54 = e0
% 29.79/8.23 |
% 29.79/8.23 | Equations (3084) can reduce 3011 to:
% 29.79/8.23 | (270) $false
% 29.79/8.23 |
% 29.79/8.23 |-The branch is then unsatisfiable
% 29.79/8.23 |-Branch two:
% 29.79/8.23 | (3011) ~ (all_0_54_54 = e0)
% 29.79/8.23 | (3664) all_0_54_54 = e4 | all_0_54_54 = e3 | all_0_54_54 = e1
% 29.79/8.23 |
% 29.79/8.23 +-Applying beta-rule and splitting (3664), into two cases.
% 29.79/8.23 |-Branch one:
% 29.79/8.23 | (1119) all_0_54_54 = e3
% 29.79/8.23 |
% 29.79/8.23 | Equations (1119) can reduce 936 to:
% 29.79/8.23 | (719) ~ (e4 = e3)
% 29.79/8.23 |
% 29.79/8.23 | Simplifying 719 yields:
% 29.79/8.23 | (34) ~ (e4 = e3)
% 29.79/8.23 |
% 29.79/8.23 +-Applying beta-rule and splitting (592), into two cases.
% 29.79/8.23 |-Branch one:
% 29.79/8.23 | (358) all_0_41_41 = e4
% 29.79/8.23 |
% 29.79/8.23 | Combining equations (351,358) yields a new equation:
% 29.79/8.23 | (359) e4 = e3
% 29.79/8.23 |
% 29.79/8.23 | Equations (359) can reduce 34 to:
% 29.79/8.23 | (270) $false
% 29.79/8.23 |
% 29.79/8.23 |-The branch is then unsatisfiable
% 29.79/8.23 |-Branch two:
% 29.79/8.23 | (361) ~ (all_0_41_41 = e4)
% 29.79/8.23 | (512) all_0_42_42 = e4
% 29.79/8.23 |
% 29.79/8.23 | Equations (512) can reduce 18 to:
% 29.79/8.23 | (804) ~ (all_0_46_46 = e4)
% 29.79/8.23 |
% 29.79/8.23 | Simplifying 804 yields:
% 29.79/8.23 | (805) ~ (all_0_46_46 = e4)
% 29.79/8.23 |
% 29.79/8.23 | Equations (512) can reduce 498 to:
% 29.79/8.23 | (231) ~ (e4 = e2)
% 29.79/8.23 |
% 29.79/8.23 +-Applying beta-rule and splitting (44), into two cases.
% 29.79/8.23 |-Branch one:
% 29.79/8.23 | (502) all_0_43_43 = e4
% 29.79/8.23 |
% 29.79/8.23 | Equations (502) can reduce 455 to:
% 29.79/8.23 | (6) ~ (e4 = e0)
% 29.79/8.23 |
% 29.79/8.23 +-Applying beta-rule and splitting (2302), into two cases.
% 29.79/8.23 |-Branch one:
% 29.79/8.23 | (585) all_0_58_58 = e0
% 29.79/8.23 |
% 29.79/8.23 | Combining equations (585,600) yields a new equation:
% 29.79/8.23 | (479) e4 = e0
% 29.79/8.23 |
% 29.79/8.23 | Equations (479) can reduce 6 to:
% 29.79/8.23 | (270) $false
% 29.79/8.23 |
% 29.79/8.23 |-The branch is then unsatisfiable
% 29.79/8.23 |-Branch two:
% 29.79/8.23 | (431) ~ (all_0_58_58 = e0)
% 29.79/8.23 | (2308) all_0_59_59 = e0
% 29.79/8.23 |
% 29.79/8.23 | Combining equations (424,2308) yields a new equation:
% 29.79/8.23 | (571) e1 = e0
% 29.79/8.23 |
% 29.79/8.23 | Simplifying 571 yields:
% 29.79/8.23 | (560) e1 = e0
% 29.79/8.23 |
% 29.79/8.23 | Equations (560) can reduce 132 to:
% 29.79/8.23 | (270) $false
% 29.79/8.23 |
% 29.79/8.23 |-The branch is then unsatisfiable
% 29.79/8.23 |-Branch two:
% 29.79/8.23 | (510) ~ (all_0_43_43 = e4)
% 29.79/8.23 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 29.79/8.23 |
% 29.79/8.23 +-Applying beta-rule and splitting (511), into two cases.
% 29.79/8.23 |-Branch one:
% 29.79/8.23 | (363) all_0_45_45 = e4
% 29.79/8.23 |
% 29.79/8.23 | Combining equations (374,363) yields a new equation:
% 29.79/8.23 | (269) e4 = e2
% 29.79/8.23 |
% 29.79/8.23 | Equations (269) can reduce 231 to:
% 29.79/8.23 | (270) $false
% 29.79/8.23 |
% 29.79/8.23 |-The branch is then unsatisfiable
% 29.79/8.23 |-Branch two:
% 29.79/8.23 | (352) ~ (all_0_45_45 = e4)
% 29.79/8.23 | (517) all_0_46_46 = e4
% 29.79/8.23 |
% 29.79/8.23 | Equations (517) can reduce 805 to:
% 29.79/8.23 | (270) $false
% 29.79/8.23 |
% 29.79/8.23 |-The branch is then unsatisfiable
% 29.79/8.23 |-Branch two:
% 29.79/8.23 | (1093) ~ (all_0_54_54 = e3)
% 29.79/8.23 | (3694) all_0_54_54 = e4 | all_0_54_54 = e1
% 29.79/8.23 |
% 29.79/8.23 +-Applying beta-rule and splitting (3694), into two cases.
% 29.79/8.23 |-Branch one:
% 29.79/8.23 | (875) all_0_54_54 = e1
% 29.79/8.24 |
% 29.79/8.24 | Equations (875) can reduce 425 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (425) ~ (all_0_54_54 = e1)
% 29.79/8.24 | (817) all_0_54_54 = e4
% 29.79/8.24 |
% 29.79/8.24 | Equations (817) can reduce 936 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (625) ~ (all_0_44_44 = e0)
% 29.79/8.24 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 29.79/8.24 |
% 29.79/8.24 +-Applying beta-rule and splitting (373), into two cases.
% 29.79/8.24 |-Branch one:
% 29.79/8.24 | (621) all_0_44_44 = e0
% 29.79/8.24 |
% 29.79/8.24 | Equations (621) can reduce 625 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (625) ~ (all_0_44_44 = e0)
% 29.79/8.24 | (858) all_0_44_44 = e3
% 29.79/8.24 |
% 29.79/8.24 | Equations (858) can reduce 122 to:
% 29.79/8.24 | (825) ~ (all_0_52_52 = e3)
% 29.79/8.24 |
% 29.79/8.24 | Simplifying 825 yields:
% 29.79/8.24 | (826) ~ (all_0_52_52 = e3)
% 29.79/8.24 |
% 29.79/8.24 +-Applying beta-rule and splitting (90), into two cases.
% 29.79/8.24 |-Branch one:
% 29.79/8.24 | (685) all_0_52_52 = e2
% 29.79/8.24 |
% 29.79/8.24 | Equations (685) can reduce 257 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (257) ~ (all_0_52_52 = e2)
% 29.79/8.24 | (688) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 29.79/8.24 |
% 29.79/8.24 +-Applying beta-rule and splitting (688), into two cases.
% 29.79/8.24 |-Branch one:
% 29.79/8.24 | (827) all_0_52_52 = e0
% 29.79/8.24 |
% 29.79/8.24 | Equations (827) can reduce 925 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (925) ~ (all_0_52_52 = e0)
% 29.79/8.24 | (926) all_0_52_52 = e3 | all_0_52_52 = e1
% 29.79/8.24 |
% 29.79/8.24 +-Applying beta-rule and splitting (926), into two cases.
% 29.79/8.24 |-Branch one:
% 29.79/8.24 | (864) all_0_52_52 = e3
% 29.79/8.24 |
% 29.79/8.24 | Equations (864) can reduce 826 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (826) ~ (all_0_52_52 = e3)
% 29.79/8.24 | (848) all_0_52_52 = e1
% 29.79/8.24 |
% 29.79/8.24 | Equations (848) can reduce 925 to:
% 29.79/8.24 | (132) ~ (e1 = e0)
% 29.79/8.24 |
% 29.79/8.24 +-Applying beta-rule and splitting (626), into two cases.
% 29.79/8.24 |-Branch one:
% 29.79/8.24 | (827) all_0_52_52 = e0
% 29.79/8.24 |
% 29.79/8.24 | Combining equations (827,848) yields a new equation:
% 29.79/8.24 | (560) e1 = e0
% 29.79/8.24 |
% 29.79/8.24 | Equations (560) can reduce 132 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (925) ~ (all_0_52_52 = e0)
% 29.79/8.24 | (2258) all_0_57_57 = e0
% 29.79/8.24 |
% 29.79/8.24 | Equations (2258) can reduce 2301 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (528) ~ (all_0_39_39 = e1)
% 29.79/8.24 | (680) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 29.79/8.24 |
% 29.79/8.24 +-Applying beta-rule and splitting (1317), into two cases.
% 29.79/8.24 |-Branch one:
% 29.79/8.24 | (541) all_0_42_42 = e1
% 29.79/8.24 |
% 29.79/8.24 | Equations (541) can reduce 640 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (640) ~ (all_0_42_42 = e1)
% 29.79/8.24 | (512) all_0_42_42 = e4
% 29.79/8.24 |
% 29.79/8.24 | Equations (512) can reduce 184 to:
% 29.79/8.24 | (591) ~ (all_0_39_39 = e4)
% 29.79/8.24 |
% 29.79/8.24 +-Applying beta-rule and splitting (210), into two cases.
% 29.79/8.24 |-Branch one:
% 29.79/8.24 | (524) all_0_39_39 = e1
% 29.79/8.24 |
% 29.79/8.24 | Equations (524) can reduce 528 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (528) ~ (all_0_39_39 = e1)
% 29.79/8.24 | (529) all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1
% 29.79/8.24 |
% 29.79/8.24 +-Applying beta-rule and splitting (166), into two cases.
% 29.79/8.24 |-Branch one:
% 29.79/8.24 | (522) all_0_39_39 = e4
% 29.79/8.24 |
% 29.79/8.24 | Equations (522) can reduce 591 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (591) ~ (all_0_39_39 = e4)
% 29.79/8.24 | (4522) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 29.79/8.24 |
% 29.79/8.24 +-Applying beta-rule and splitting (177), into two cases.
% 29.79/8.24 |-Branch one:
% 29.79/8.24 | (336) all_0_39_39 = e2
% 29.79/8.24 |
% 29.79/8.24 | Equations (336) can reduce 291 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (291) ~ (all_0_39_39 = e2)
% 29.79/8.24 | (684) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 29.79/8.24 |
% 29.79/8.24 +-Applying beta-rule and splitting (684), into two cases.
% 29.79/8.24 |-Branch one:
% 29.79/8.24 | (751) all_0_39_39 = e3
% 29.79/8.24 |
% 29.79/8.24 | Equations (751) can reduce 755 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (755) ~ (all_0_39_39 = e3)
% 29.79/8.24 | (1756) all_0_39_39 = e4 | all_0_39_39 = e1
% 29.79/8.24 |
% 29.79/8.24 +-Applying beta-rule and splitting (1756), into two cases.
% 29.79/8.24 |-Branch one:
% 29.79/8.24 | (524) all_0_39_39 = e1
% 29.79/8.24 |
% 29.79/8.24 | Equations (524) can reduce 528 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (528) ~ (all_0_39_39 = e1)
% 29.79/8.24 | (522) all_0_39_39 = e4
% 29.79/8.24 |
% 29.79/8.24 | Equations (522) can reduce 591 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (584) ~ (all_0_53_53 = e0)
% 29.79/8.24 | (5719) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1
% 29.79/8.24 |
% 29.79/8.24 +-Applying beta-rule and splitting (558), into two cases.
% 29.79/8.24 |-Branch one:
% 29.79/8.24 | (559) all_0_48_48 = e0
% 29.79/8.24 |
% 29.79/8.24 | Combining equations (552,559) yields a new equation:
% 29.79/8.24 | (571) e1 = e0
% 29.79/8.24 |
% 29.79/8.24 | Simplifying 571 yields:
% 29.79/8.24 | (560) e1 = e0
% 29.79/8.24 |
% 29.79/8.24 | Equations (560) can reduce 132 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (562) ~ (all_0_48_48 = e0)
% 29.79/8.24 | (575) all_0_53_53 = e0 | all_0_58_58 = e0
% 29.79/8.24 |
% 29.79/8.24 +-Applying beta-rule and splitting (575), into two cases.
% 29.79/8.24 |-Branch one:
% 29.79/8.24 | (423) all_0_53_53 = e0
% 29.79/8.24 |
% 29.79/8.24 | Equations (423) can reduce 584 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (584) ~ (all_0_53_53 = e0)
% 29.79/8.24 | (585) all_0_58_58 = e0
% 29.79/8.24 |
% 29.79/8.24 | Combining equations (600,585) yields a new equation:
% 29.79/8.24 | (478) e4 = e0
% 29.79/8.24 |
% 29.79/8.24 | Simplifying 478 yields:
% 29.79/8.24 | (479) e4 = e0
% 29.79/8.24 |
% 29.79/8.24 | Equations (479) can reduce 6 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (588) ~ (all_0_48_48 = e1)
% 29.79/8.24 | (589) all_0_49_49 = e1
% 29.79/8.24 |
% 29.79/8.24 | Combining equations (589,307) yields a new equation:
% 29.79/8.24 | (322) e2 = e1
% 29.79/8.24 |
% 29.79/8.24 | Equations (322) can reduce 141 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (318) ~ (all_0_47_47 = e0)
% 29.79/8.24 | (319) all_0_48_48 = e0 | all_0_49_49 = e0
% 29.79/8.24 |
% 29.79/8.24 +-Applying beta-rule and splitting (319), into two cases.
% 29.79/8.24 |-Branch one:
% 29.79/8.24 | (559) all_0_48_48 = e0
% 29.79/8.24 |
% 29.79/8.24 | Equations (559) can reduce 48 to:
% 29.79/8.24 | (3103) ~ (all_0_53_53 = e0)
% 29.79/8.24 |
% 29.79/8.24 | Simplifying 3103 yields:
% 29.79/8.24 | (584) ~ (all_0_53_53 = e0)
% 29.79/8.24 |
% 29.79/8.24 | From (559) and (76) follows:
% 29.79/8.24 | (6127) op(e1, e0) = all_0_25_25
% 29.79/8.24 |
% 29.79/8.24 +-Applying beta-rule and splitting (83), into two cases.
% 29.79/8.24 |-Branch one:
% 29.79/8.24 | (321) all_0_47_47 = e1
% 29.79/8.24 |
% 29.79/8.24 | Equations (321) can reduce 100 to:
% 29.79/8.24 | (528) ~ (all_0_39_39 = e1)
% 29.79/8.24 |
% 29.79/8.24 | Equations (321) can reduce 218 to:
% 29.79/8.24 | (3986) ~ (all_0_56_56 = e1)
% 29.79/8.24 |
% 29.79/8.24 | Simplifying 3986 yields:
% 29.79/8.24 | (995) ~ (all_0_56_56 = e1)
% 29.79/8.24 |
% 29.79/8.24 | Equations (321) can reduce 172 to:
% 29.79/8.24 | (1021) ~ (e4 = e1)
% 29.79/8.24 |
% 29.79/8.24 | Simplifying 1021 yields:
% 29.79/8.24 | (251) ~ (e4 = e1)
% 29.79/8.24 |
% 29.79/8.24 | Equations (321) can reduce 247 to:
% 29.79/8.24 | (769) ~ (e3 = e1)
% 29.79/8.24 |
% 29.79/8.24 | Simplifying 769 yields:
% 29.79/8.24 | (136) ~ (e3 = e1)
% 29.79/8.24 |
% 29.79/8.24 | Equations (321) can reduce 3951 to:
% 29.79/8.24 | (645) ~ (e2 = e1)
% 29.79/8.24 |
% 29.79/8.24 | Simplifying 645 yields:
% 29.79/8.24 | (141) ~ (e2 = e1)
% 29.79/8.24 |
% 29.79/8.24 +-Applying beta-rule and splitting (52), into two cases.
% 29.79/8.24 |-Branch one:
% 29.79/8.24 | (536) all_0_41_41 = e1
% 29.79/8.24 |
% 29.79/8.24 | Combining equations (351,536) yields a new equation:
% 29.79/8.24 | (537) e3 = e1
% 29.79/8.24 |
% 29.79/8.24 | Simplifying 537 yields:
% 29.79/8.24 | (538) e3 = e1
% 29.79/8.24 |
% 29.79/8.24 | Equations (538) can reduce 136 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (540) ~ (all_0_41_41 = e1)
% 29.79/8.24 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 29.79/8.24 |
% 29.79/8.24 | Equations (351) can reduce 540 to:
% 29.79/8.24 | (136) ~ (e3 = e1)
% 29.79/8.24 |
% 29.79/8.24 +-Applying beta-rule and splitting (210), into two cases.
% 29.79/8.24 |-Branch one:
% 29.79/8.24 | (524) all_0_39_39 = e1
% 29.79/8.24 |
% 29.79/8.24 | Equations (524) can reduce 528 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (528) ~ (all_0_39_39 = e1)
% 29.79/8.24 | (529) all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1
% 29.79/8.24 |
% 29.79/8.24 +-Applying beta-rule and splitting (529), into two cases.
% 29.79/8.24 |-Branch one:
% 29.79/8.24 | (530) all_0_40_40 = e1
% 29.79/8.24 |
% 29.79/8.24 | Combining equations (327,530) yields a new equation:
% 29.79/8.24 | (531) e2 = e1
% 29.79/8.24 |
% 29.79/8.24 | Simplifying 531 yields:
% 29.79/8.24 | (322) e2 = e1
% 29.79/8.24 |
% 29.79/8.24 | Equations (322) can reduce 141 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (534) ~ (all_0_40_40 = e1)
% 29.79/8.24 | (535) all_0_41_41 = e1 | all_0_42_42 = e1
% 29.79/8.24 |
% 29.79/8.24 +-Applying beta-rule and splitting (535), into two cases.
% 29.79/8.24 |-Branch one:
% 29.79/8.24 | (536) all_0_41_41 = e1
% 29.79/8.24 |
% 29.79/8.24 | Combining equations (351,536) yields a new equation:
% 29.79/8.24 | (537) e3 = e1
% 29.79/8.24 |
% 29.79/8.24 | Simplifying 537 yields:
% 29.79/8.24 | (538) e3 = e1
% 29.79/8.24 |
% 29.79/8.24 | Equations (538) can reduce 136 to:
% 29.79/8.24 | (270) $false
% 29.79/8.24 |
% 29.79/8.24 |-The branch is then unsatisfiable
% 29.79/8.24 |-Branch two:
% 29.79/8.24 | (540) ~ (all_0_41_41 = e1)
% 29.79/8.24 | (541) all_0_42_42 = e1
% 29.79/8.24 |
% 29.79/8.24 | Equations (541) can reduce 18 to:
% 29.79/8.24 | (6201) ~ (all_0_46_46 = e1)
% 29.79/8.24 |
% 29.79/8.24 | Simplifying 6201 yields:
% 29.79/8.24 | (106) ~ (all_0_46_46 = e1)
% 29.79/8.24 |
% 29.79/8.24 | Equations (541) can reduce 17 to:
% 29.79/8.24 | (749) ~ (all_0_59_59 = e1)
% 29.79/8.24 |
% 29.79/8.24 | Simplifying 749 yields:
% 29.79/8.24 | (750) ~ (all_0_59_59 = e1)
% 29.79/8.24 |
% 29.79/8.24 | Equations (541) can reduce 199 to:
% 29.79/8.24 | (132) ~ (e1 = e0)
% 29.79/8.24 |
% 29.79/8.24 +-Applying beta-rule and splitting (222), into two cases.
% 29.79/8.24 |-Branch one:
% 29.79/8.24 | (522) all_0_39_39 = e4
% 29.79/8.24 |
% 29.79/8.24 | Equations (522) can reduce 167 to:
% 29.79/8.24 | (694) ~ (all_0_43_43 = e4)
% 29.79/8.24 |
% 29.79/8.24 | Simplifying 694 yields:
% 29.79/8.24 | (510) ~ (all_0_43_43 = e4)
% 29.79/8.24 |
% 29.79/8.24 | Equations (522) can reduce 212 to:
% 29.79/8.24 | (273) ~ (all_0_56_56 = e4)
% 29.79/8.24 |
% 29.79/8.24 | Simplifying 273 yields:
% 29.79/8.24 | (274) ~ (all_0_56_56 = e4)
% 29.79/8.24 |
% 29.79/8.24 | Equations (522) can reduce 291 to:
% 29.79/8.25 | (231) ~ (e4 = e2)
% 29.79/8.25 |
% 29.79/8.25 | Equations (522) can reduce 101 to:
% 29.79/8.25 | (6) ~ (e4 = e0)
% 29.79/8.25 |
% 29.79/8.25 +-Applying beta-rule and splitting (44), into two cases.
% 29.79/8.25 |-Branch one:
% 29.79/8.25 | (502) all_0_43_43 = e4
% 29.79/8.25 |
% 29.79/8.25 | Equations (502) can reduce 510 to:
% 29.79/8.25 | (270) $false
% 29.79/8.25 |
% 29.79/8.25 |-The branch is then unsatisfiable
% 29.79/8.25 |-Branch two:
% 29.79/8.25 | (510) ~ (all_0_43_43 = e4)
% 29.79/8.25 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 29.79/8.25 |
% 29.79/8.25 +-Applying beta-rule and splitting (194), into two cases.
% 29.79/8.25 |-Branch one:
% 29.79/8.25 | (747) all_0_56_56 = e1
% 29.79/8.25 |
% 29.79/8.25 | Equations (747) can reduce 995 to:
% 29.79/8.25 | (270) $false
% 29.79/8.25 |
% 29.79/8.25 |-The branch is then unsatisfiable
% 29.79/8.25 |-Branch two:
% 29.79/8.25 | (995) ~ (all_0_56_56 = e1)
% 29.79/8.25 | (996) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 29.79/8.25 |
% 29.79/8.25 +-Applying beta-rule and splitting (511), into two cases.
% 29.79/8.25 |-Branch one:
% 29.79/8.25 | (363) all_0_45_45 = e4
% 29.79/8.25 |
% 29.79/8.25 | Combining equations (363,374) yields a new equation:
% 29.79/8.25 | (268) e4 = e2
% 29.79/8.25 |
% 29.79/8.25 | Simplifying 268 yields:
% 29.79/8.25 | (269) e4 = e2
% 29.79/8.25 |
% 29.79/8.25 | Equations (269) can reduce 231 to:
% 29.79/8.25 | (270) $false
% 29.79/8.25 |
% 29.79/8.25 |-The branch is then unsatisfiable
% 29.79/8.25 |-Branch two:
% 29.79/8.25 | (352) ~ (all_0_45_45 = e4)
% 29.79/8.25 | (517) all_0_46_46 = e4
% 29.79/8.25 |
% 29.79/8.25 | Equations (517) can reduce 215 to:
% 29.79/8.25 | (1599) ~ (all_0_54_54 = e4)
% 29.79/8.25 |
% 29.79/8.25 | Simplifying 1599 yields:
% 29.79/8.25 | (936) ~ (all_0_54_54 = e4)
% 29.79/8.25 |
% 29.79/8.25 | Equations (517) can reduce 206 to:
% 29.79/8.25 | (279) ~ (all_0_59_59 = e4)
% 29.79/8.25 |
% 29.79/8.25 | Simplifying 279 yields:
% 29.79/8.25 | (280) ~ (all_0_59_59 = e4)
% 29.79/8.25 |
% 29.79/8.25 | Equations (517) can reduce 1436 to:
% 29.79/8.25 | (231) ~ (e4 = e2)
% 29.79/8.25 |
% 29.79/8.25 | Equations (517) can reduce 106 to:
% 29.79/8.25 | (251) ~ (e4 = e1)
% 29.79/8.25 |
% 29.79/8.25 +-Applying beta-rule and splitting (996), into two cases.
% 29.79/8.25 |-Branch one:
% 29.79/8.25 | (997) all_0_57_57 = e1
% 29.79/8.25 |
% 29.79/8.25 | Equations (997) can reduce 104 to:
% 29.79/8.25 | (995) ~ (all_0_56_56 = e1)
% 29.79/8.25 |
% 29.79/8.25 | Equations (997) can reduce 143 to:
% 29.79/8.25 | (1021) ~ (e4 = e1)
% 29.79/8.25 |
% 29.79/8.25 | Simplifying 1021 yields:
% 29.79/8.25 | (251) ~ (e4 = e1)
% 29.79/8.25 |
% 29.79/8.25 +-Applying beta-rule and splitting (762), into two cases.
% 29.79/8.25 |-Branch one:
% 29.79/8.25 | (552) all_0_48_48 = e1
% 29.79/8.25 |
% 29.79/8.25 | Combining equations (559,552) yields a new equation:
% 29.79/8.25 | (560) e1 = e0
% 29.79/8.25 |
% 29.79/8.25 | Equations (560) can reduce 132 to:
% 29.79/8.25 | (270) $false
% 29.79/8.25 |
% 29.79/8.25 |-The branch is then unsatisfiable
% 29.79/8.25 |-Branch two:
% 29.79/8.25 | (588) ~ (all_0_48_48 = e1)
% 29.79/8.25 | (4925) all_0_53_53 = e1 | all_0_58_58 = e1
% 29.79/8.25 |
% 29.79/8.25 +-Applying beta-rule and splitting (4925), into two cases.
% 29.79/8.25 |-Branch one:
% 29.79/8.25 | (853) all_0_53_53 = e1
% 29.79/8.25 |
% 29.79/8.25 | Equations (853) can reduce 252 to:
% 29.79/8.25 | (2131) ~ (all_0_54_54 = e1)
% 29.79/8.25 |
% 29.79/8.25 | Simplifying 2131 yields:
% 29.79/8.25 | (425) ~ (all_0_54_54 = e1)
% 29.79/8.25 |
% 29.79/8.25 | Instantiating formula (201) with e1, e0, all_0_25_25, all_0_54_54 and discharging atoms op(e1, e0) = all_0_25_25, op(e1, e0) = all_0_54_54, yields:
% 29.79/8.25 | (6130) all_0_25_25 = all_0_54_54
% 29.79/8.25 |
% 29.79/8.25 +-Applying beta-rule and splitting (14), into two cases.
% 29.79/8.25 |-Branch one:
% 29.79/8.25 | (2277) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1))
% 29.79/8.25 |
% 29.79/8.25 +-Applying beta-rule and splitting (2277), into two cases.
% 29.79/8.25 |-Branch one:
% 29.79/8.25 | (2278) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1))
% 29.79/8.25 |
% 29.79/8.25 +-Applying beta-rule and splitting (2278), into two cases.
% 29.79/8.25 |-Branch one:
% 29.79/8.25 | (2279) all_0_21_21 = e4 & ~ (all_0_22_22 = e1)
% 29.79/8.25 |
% 29.79/8.25 | Applying alpha-rule on (2279) yields:
% 29.79/8.25 | (2280) all_0_21_21 = e4
% 29.79/8.25 | (2281) ~ (all_0_22_22 = e1)
% 29.79/8.25 |
% 29.79/8.25 | Combining equations (2760,2280) yields a new equation:
% 29.79/8.25 | (269) e4 = e2
% 29.79/8.25 |
% 29.79/8.25 | Equations (269) can reduce 231 to:
% 29.79/8.25 | (270) $false
% 29.79/8.25 |
% 29.79/8.25 |-The branch is then unsatisfiable
% 29.79/8.25 |-Branch two:
% 29.79/8.25 | (2285) all_0_23_23 = e3 & ~ (all_0_24_24 = e1)
% 29.79/8.25 |
% 29.79/8.25 | Applying alpha-rule on (2285) yields:
% 29.79/8.25 | (2286) all_0_23_23 = e3
% 29.79/8.25 | (2287) ~ (all_0_24_24 = e1)
% 29.79/8.25 |
% 29.79/8.25 | Combining equations (10441,2286) yields a new equation:
% 29.79/8.25 | (10541) all_0_52_52 = e3
% 29.79/8.25 |
% 29.79/8.25 | Simplifying 10541 yields:
% 29.79/8.25 | (864) all_0_52_52 = e3
% 29.79/8.25 |
% 29.79/8.25 | Equations (10440) can reduce 2287 to:
% 29.79/8.25 | (131) ~ (all_0_44_44 = e1)
% 29.79/8.25 |
% 29.79/8.25 | Equations (864) can reduce 122 to:
% 29.79/8.25 | (862) ~ (all_0_44_44 = e3)
% 29.79/8.25 |
% 29.79/8.25 | Equations (864) can reduce 118 to:
% 29.79/8.25 | (1092) ~ (all_0_54_54 = e3)
% 29.79/8.25 |
% 29.79/8.25 | Simplifying 1092 yields:
% 29.79/8.25 | (1093) ~ (all_0_54_54 = e3)
% 29.79/8.25 |
% 29.79/8.25 | Equations (864) can reduce 230 to:
% 29.79/8.25 | (719) ~ (e4 = e3)
% 29.79/8.25 |
% 29.79/8.25 | Simplifying 719 yields:
% 29.79/8.25 | (34) ~ (e4 = e3)
% 29.79/8.25 |
% 29.79/8.25 | Equations (864) can reduce 257 to:
% 29.79/8.25 | (223) ~ (e3 = e2)
% 29.79/8.25 |
% 29.79/8.25 +-Applying beta-rule and splitting (9), into two cases.
% 29.79/8.25 |-Branch one:
% 29.79/8.25 | (621) all_0_44_44 = e0
% 29.79/8.25 |
% 29.79/8.25 | Equations (621) can reduce 862 to:
% 29.79/8.25 | (788) ~ (e3 = e0)
% 29.79/8.25 |
% 29.79/8.25 | Simplifying 788 yields:
% 29.79/8.25 | (66) ~ (e3 = e0)
% 29.79/8.25 |
% 29.79/8.25 | Equations (621) can reduce 333 to:
% 29.79/8.25 | (566) ~ (e2 = e0)
% 29.79/8.25 |
% 29.79/8.25 | Simplifying 566 yields:
% 29.79/8.25 | (57) ~ (e2 = e0)
% 29.79/8.25 |
% 29.79/8.25 | Equations (621) can reduce 131 to:
% 29.79/8.25 | (568) ~ (e1 = e0)
% 29.79/8.25 |
% 29.79/8.25 | Simplifying 568 yields:
% 29.79/8.25 | (132) ~ (e1 = e0)
% 29.79/8.25 |
% 29.79/8.25 +-Applying beta-rule and splitting (110), into two cases.
% 29.79/8.25 |-Branch one:
% 29.79/8.25 | (3657) all_0_54_54 = e2
% 29.79/8.25 |
% 29.79/8.25 | Equations (3657) can reduce 261 to:
% 29.79/8.25 | (270) $false
% 29.79/8.25 |
% 29.79/8.25 |-The branch is then unsatisfiable
% 29.79/8.25 |-Branch two:
% 29.79/8.25 | (261) ~ (all_0_54_54 = e2)
% 29.79/8.25 | (3660) all_0_54_54 = e4 | all_0_54_54 = e3 | all_0_54_54 = e1 | all_0_54_54 = e0
% 29.79/8.25 |
% 29.79/8.25 +-Applying beta-rule and splitting (22), into two cases.
% 29.79/8.25 |-Branch one:
% 29.79/8.25 | (782) all_0_43_43 = e3
% 29.79/8.25 |
% 29.79/8.25 | Equations (782) can reduce 188 to:
% 29.79/8.25 | (5066) ~ (all_0_56_56 = e3)
% 29.79/8.25 |
% 29.79/8.25 | Simplifying 5066 yields:
% 29.79/8.25 | (767) ~ (all_0_56_56 = e3)
% 29.79/8.25 |
% 29.79/8.25 +-Applying beta-rule and splitting (208), into two cases.
% 29.79/8.25 |-Branch one:
% 29.79/8.25 | (388) all_0_56_56 = e2
% 29.79/8.25 |
% 29.79/8.25 | Equations (388) can reduce 300 to:
% 29.79/8.25 | (270) $false
% 29.79/8.25 |
% 29.79/8.25 |-The branch is then unsatisfiable
% 29.79/8.25 |-Branch two:
% 29.79/8.25 | (300) ~ (all_0_56_56 = e2)
% 29.79/8.25 | (5076) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1 | all_0_56_56 = e0
% 29.79/8.25 |
% 29.79/8.25 +-Applying beta-rule and splitting (236), into two cases.
% 29.79/8.25 |-Branch one:
% 29.79/8.25 | (764) all_0_56_56 = e3
% 29.79/8.25 |
% 29.79/8.25 | Equations (764) can reduce 767 to:
% 29.79/8.25 | (270) $false
% 29.79/8.25 |
% 29.79/8.25 |-The branch is then unsatisfiable
% 29.79/8.25 |-Branch two:
% 29.79/8.25 | (767) ~ (all_0_56_56 = e3)
% 29.79/8.25 | (768) all_0_57_57 = e3 | all_0_58_58 = e3 | all_0_59_59 = e3
% 29.79/8.25 |
% 29.79/8.25 +-Applying beta-rule and splitting (5076), into two cases.
% 29.79/8.25 |-Branch one:
% 29.79/8.25 | (830) all_0_56_56 = e0
% 29.79/8.25 |
% 29.79/8.25 | Equations (830) can reduce 767 to:
% 29.79/8.25 | (788) ~ (e3 = e0)
% 29.79/8.25 |
% 29.79/8.25 | Simplifying 788 yields:
% 29.79/8.25 | (66) ~ (e3 = e0)
% 29.79/8.25 |
% 29.79/8.25 | Equations (830) can reduce 995 to:
% 29.79/8.25 | (568) ~ (e1 = e0)
% 29.79/8.25 |
% 29.79/8.25 | Simplifying 568 yields:
% 29.79/8.25 | (132) ~ (e1 = e0)
% 29.79/8.25 |
% 29.79/8.25 +-Applying beta-rule and splitting (93), into two cases.
% 29.79/8.25 |-Branch one:
% 29.79/8.25 | (402) all_0_59_59 = e4
% 29.79/8.25 |
% 29.79/8.25 | Equations (402) can reduce 280 to:
% 29.79/8.25 | (270) $false
% 29.79/8.25 |
% 29.79/8.25 |-The branch is then unsatisfiable
% 29.79/8.25 |-Branch two:
% 29.79/8.25 | (280) ~ (all_0_59_59 = e4)
% 29.79/8.25 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 29.79/8.25 |
% 29.79/8.25 +-Applying beta-rule and splitting (407), into two cases.
% 29.79/8.25 |-Branch one:
% 29.79/8.25 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 29.79/8.25 |
% 29.79/8.25 +-Applying beta-rule and splitting (408), into two cases.
% 29.79/8.25 |-Branch one:
% 29.79/8.25 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 29.79/8.25 |
% 29.79/8.25 +-Applying beta-rule and splitting (409), into two cases.
% 29.79/8.25 |-Branch one:
% 29.79/8.25 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 29.79/8.25 |
% 29.79/8.25 | Applying alpha-rule on (410) yields:
% 29.79/8.25 | (411) all_0_43_43 = e0
% 29.79/8.25 | (412) all_0_59_59 = e3
% 29.79/8.25 | (413) ~ (all_0_46_46 = e3)
% 29.79/8.25 |
% 29.79/8.25 | Combining equations (782,411) yields a new equation:
% 29.79/8.25 | (783) e3 = e0
% 29.79/8.25 |
% 29.79/8.25 | Simplifying 783 yields:
% 29.79/8.25 | (784) e3 = e0
% 29.79/8.25 |
% 29.79/8.25 | Equations (784) can reduce 66 to:
% 29.79/8.25 | (270) $false
% 29.79/8.25 |
% 29.79/8.25 |-The branch is then unsatisfiable
% 29.79/8.25 |-Branch two:
% 29.79/8.25 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 29.79/8.25 |
% 29.79/8.25 | Applying alpha-rule on (416) yields:
% 29.79/8.25 | (411) all_0_43_43 = e0
% 29.79/8.25 | (412) all_0_59_59 = e3
% 29.79/8.25 | (419) ~ (all_0_56_56 = e0)
% 29.79/8.25 |
% 29.79/8.25 | Combining equations (782,411) yields a new equation:
% 29.79/8.25 | (783) e3 = e0
% 29.79/8.25 |
% 29.79/8.25 | Simplifying 783 yields:
% 29.79/8.25 | (784) e3 = e0
% 29.79/8.25 |
% 29.79/8.25 | Equations (784) can reduce 66 to:
% 29.79/8.25 | (270) $false
% 29.79/8.25 |
% 29.79/8.25 |-The branch is then unsatisfiable
% 29.79/8.25 |-Branch two:
% 29.79/8.25 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 29.79/8.25 |
% 29.79/8.25 | Applying alpha-rule on (422) yields:
% 29.79/8.25 | (423) all_0_53_53 = e0
% 29.79/8.25 | (424) all_0_59_59 = e1
% 29.79/8.25 | (425) ~ (all_0_54_54 = e1)
% 29.79/8.25 |
% 29.79/8.25 | Combining equations (423,853) yields a new equation:
% 29.79/8.25 | (560) e1 = e0
% 29.79/8.26 |
% 29.79/8.26 | Equations (560) can reduce 132 to:
% 29.79/8.26 | (270) $false
% 29.79/8.26 |
% 29.79/8.26 |-The branch is then unsatisfiable
% 29.79/8.26 |-Branch two:
% 29.79/8.26 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 29.79/8.26 |
% 29.79/8.26 | Applying alpha-rule on (428) yields:
% 29.79/8.26 | (423) all_0_53_53 = e0
% 29.79/8.26 | (424) all_0_59_59 = e1
% 29.79/8.26 | (431) ~ (all_0_58_58 = e0)
% 29.79/8.26 |
% 29.79/8.26 | Combining equations (423,853) yields a new equation:
% 29.79/8.26 | (560) e1 = e0
% 29.79/8.26 |
% 29.79/8.26 | Equations (560) can reduce 132 to:
% 29.79/8.26 | (270) $false
% 29.79/8.26 |
% 29.79/8.26 |-The branch is then unsatisfiable
% 29.79/8.26 |-Branch two:
% 29.79/8.26 | (419) ~ (all_0_56_56 = e0)
% 29.79/8.26 | (5667) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1
% 29.79/8.26 |
% 29.79/8.26 +-Applying beta-rule and splitting (5667), into two cases.
% 29.79/8.26 |-Branch one:
% 29.79/8.26 | (764) all_0_56_56 = e3
% 29.79/8.26 |
% 29.79/8.26 | Equations (764) can reduce 767 to:
% 29.79/8.26 | (270) $false
% 29.79/8.26 |
% 29.79/8.26 |-The branch is then unsatisfiable
% 29.79/8.26 |-Branch two:
% 29.79/8.26 | (767) ~ (all_0_56_56 = e3)
% 29.79/8.26 | (10136) all_0_56_56 = e4 | all_0_56_56 = e1
% 29.79/8.26 |
% 29.79/8.26 +-Applying beta-rule and splitting (10136), into two cases.
% 29.79/8.26 |-Branch one:
% 29.79/8.26 | (747) all_0_56_56 = e1
% 29.79/8.26 |
% 29.79/8.26 | Equations (747) can reduce 995 to:
% 29.79/8.26 | (270) $false
% 29.79/8.26 |
% 29.79/8.26 |-The branch is then unsatisfiable
% 29.79/8.26 |-Branch two:
% 29.79/8.26 | (995) ~ (all_0_56_56 = e1)
% 29.79/8.26 | (4744) all_0_56_56 = e4
% 29.79/8.26 |
% 29.79/8.26 | Equations (4744) can reduce 274 to:
% 29.79/8.26 | (270) $false
% 29.79/8.26 |
% 29.79/8.26 |-The branch is then unsatisfiable
% 30.11/8.26 |-Branch two:
% 30.11/8.26 | (786) ~ (all_0_43_43 = e3)
% 30.11/8.26 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 30.11/8.26 |
% 30.11/8.26 +-Applying beta-rule and splitting (64), into two cases.
% 30.11/8.26 |-Branch one:
% 30.11/8.26 | (954) all_0_51_51 = e0
% 30.11/8.26 |
% 30.11/8.26 | Combining equations (954,4215) yields a new equation:
% 30.11/8.26 | (316) e2 = e0
% 30.11/8.26 |
% 30.11/8.26 | Equations (316) can reduce 57 to:
% 30.11/8.26 | (270) $false
% 30.11/8.26 |
% 30.11/8.26 |-The branch is then unsatisfiable
% 30.11/8.26 |-Branch two:
% 30.11/8.26 | (987) ~ (all_0_51_51 = e0)
% 30.11/8.26 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 30.11/8.26 |
% 30.11/8.26 +-Applying beta-rule and splitting (178), into two cases.
% 30.11/8.26 |-Branch one:
% 30.11/8.26 | (751) all_0_39_39 = e3
% 30.11/8.26 |
% 30.11/8.26 | Combining equations (522,751) yields a new equation:
% 30.11/8.26 | (660) e4 = e3
% 30.11/8.26 |
% 30.11/8.26 | Simplifying 660 yields:
% 30.11/8.26 | (359) e4 = e3
% 30.11/8.26 |
% 30.11/8.26 | Equations (359) can reduce 34 to:
% 30.11/8.26 | (270) $false
% 30.11/8.26 |
% 30.11/8.26 |-The branch is then unsatisfiable
% 30.11/8.26 |-Branch two:
% 30.11/8.26 | (755) ~ (all_0_39_39 = e3)
% 30.11/8.26 | (756) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 30.11/8.26 |
% 30.11/8.26 | Equations (522) can reduce 755 to:
% 30.11/8.26 | (34) ~ (e4 = e3)
% 30.11/8.26 |
% 30.11/8.26 +-Applying beta-rule and splitting (3067), into two cases.
% 30.11/8.26 |-Branch one:
% 30.11/8.26 | (827) all_0_52_52 = e0
% 30.11/8.26 |
% 30.11/8.26 | Combining equations (864,827) yields a new equation:
% 30.11/8.26 | (783) e3 = e0
% 30.11/8.26 |
% 30.11/8.26 | Simplifying 783 yields:
% 30.11/8.26 | (784) e3 = e0
% 30.11/8.26 |
% 30.11/8.26 | Equations (784) can reduce 66 to:
% 30.11/8.26 | (270) $false
% 30.11/8.26 |
% 30.11/8.26 |-The branch is then unsatisfiable
% 30.11/8.26 |-Branch two:
% 30.11/8.26 | (925) ~ (all_0_52_52 = e0)
% 30.11/8.26 | (3073) all_0_53_53 = e0 | all_0_54_54 = e0
% 30.11/8.26 |
% 30.11/8.26 +-Applying beta-rule and splitting (3660), into two cases.
% 30.11/8.26 |-Branch one:
% 30.11/8.26 | (3084) all_0_54_54 = e0
% 30.11/8.26 |
% 30.11/8.26 | Equations (3084) can reduce 72 to:
% 30.11/8.26 | (4000) ~ (all_0_59_59 = e0)
% 30.11/8.26 |
% 30.11/8.26 | Simplifying 4000 yields:
% 30.11/8.26 | (4001) ~ (all_0_59_59 = e0)
% 30.11/8.26 |
% 30.11/8.26 | Equations (3084) can reduce 936 to:
% 30.11/8.26 | (456) ~ (e4 = e0)
% 30.11/8.26 |
% 30.11/8.26 | Simplifying 456 yields:
% 30.11/8.26 | (6) ~ (e4 = e0)
% 30.11/8.26 |
% 30.11/8.26 | Equations (3084) can reduce 1093 to:
% 30.11/8.26 | (788) ~ (e3 = e0)
% 30.11/8.26 |
% 30.11/8.26 | Simplifying 788 yields:
% 30.11/8.26 | (66) ~ (e3 = e0)
% 30.11/8.26 |
% 30.11/8.26 | Equations (3084) can reduce 425 to:
% 30.11/8.26 | (568) ~ (e1 = e0)
% 30.11/8.26 |
% 30.11/8.26 | Simplifying 568 yields:
% 30.11/8.26 | (132) ~ (e1 = e0)
% 30.11/8.26 |
% 30.11/8.26 +-Applying beta-rule and splitting (176), into two cases.
% 30.11/8.26 |-Branch one:
% 30.11/8.26 | (830) all_0_56_56 = e0
% 30.11/8.26 |
% 30.11/8.26 +-Applying beta-rule and splitting (236), into two cases.
% 30.11/8.26 |-Branch one:
% 30.11/8.26 | (764) all_0_56_56 = e3
% 30.11/8.26 |
% 30.11/8.26 | Combining equations (830,764) yields a new equation:
% 30.11/8.26 | (784) e3 = e0
% 30.11/8.26 |
% 30.11/8.26 | Equations (784) can reduce 66 to:
% 30.11/8.26 | (270) $false
% 30.11/8.26 |
% 30.11/8.26 |-The branch is then unsatisfiable
% 30.11/8.26 |-Branch two:
% 30.11/8.26 | (767) ~ (all_0_56_56 = e3)
% 30.11/8.26 | (768) all_0_57_57 = e3 | all_0_58_58 = e3 | all_0_59_59 = e3
% 30.11/8.26 |
% 30.11/8.26 | Equations (830) can reduce 767 to:
% 30.11/8.26 | (788) ~ (e3 = e0)
% 30.11/8.26 |
% 30.11/8.26 | Simplifying 788 yields:
% 30.11/8.26 | (66) ~ (e3 = e0)
% 30.11/8.26 |
% 30.11/8.26 +-Applying beta-rule and splitting (787), into two cases.
% 30.11/8.26 |-Branch one:
% 30.11/8.26 | (858) all_0_44_44 = e3
% 30.11/8.26 |
% 30.11/8.26 | Combining equations (621,858) yields a new equation:
% 30.11/8.26 | (784) e3 = e0
% 30.11/8.26 |
% 30.11/8.26 | Equations (784) can reduce 66 to:
% 30.11/8.26 | (270) $false
% 30.11/8.26 |
% 30.11/8.26 |-The branch is then unsatisfiable
% 30.11/8.26 |-Branch two:
% 30.11/8.26 | (862) ~ (all_0_44_44 = e3)
% 30.11/8.26 | (1070) all_0_45_45 = e3 | all_0_46_46 = e3
% 30.11/8.26 |
% 30.11/8.26 +-Applying beta-rule and splitting (1070), into two cases.
% 30.11/8.26 |-Branch one:
% 30.11/8.26 | (505) all_0_45_45 = e3
% 30.11/8.26 |
% 30.11/8.26 | Combining equations (374,505) yields a new equation:
% 30.11/8.26 | (414) e3 = e2
% 30.11/8.26 |
% 30.11/8.26 | Equations (414) can reduce 223 to:
% 30.11/8.26 | (270) $false
% 30.11/8.26 |
% 30.11/8.26 |-The branch is then unsatisfiable
% 30.11/8.26 |-Branch two:
% 30.11/8.26 | (354) ~ (all_0_45_45 = e3)
% 30.11/8.26 | (1091) all_0_46_46 = e3
% 30.11/8.26 |
% 30.11/8.26 | Combining equations (517,1091) yields a new equation:
% 30.11/8.26 | (660) e4 = e3
% 30.11/8.26 |
% 30.11/8.26 | Simplifying 660 yields:
% 30.11/8.26 | (359) e4 = e3
% 30.11/8.26 |
% 30.11/8.26 | Equations (359) can reduce 34 to:
% 30.11/8.26 | (270) $false
% 30.11/8.26 |
% 30.11/8.26 |-The branch is then unsatisfiable
% 30.11/8.26 |-Branch two:
% 30.11/8.26 | (419) ~ (all_0_56_56 = e0)
% 30.11/8.26 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 30.11/8.26 |
% 30.11/8.26 +-Applying beta-rule and splitting (834), into two cases.
% 30.11/8.26 |-Branch one:
% 30.11/8.26 | (2258) all_0_57_57 = e0
% 30.11/8.26 |
% 30.11/8.26 | Combining equations (997,2258) yields a new equation:
% 30.11/8.26 | (571) e1 = e0
% 30.11/8.26 |
% 30.11/8.26 | Simplifying 571 yields:
% 30.11/8.26 | (560) e1 = e0
% 30.11/8.26 |
% 30.11/8.26 | Equations (560) can reduce 132 to:
% 30.11/8.26 | (270) $false
% 30.11/8.26 |
% 30.11/8.26 |-The branch is then unsatisfiable
% 30.11/8.26 |-Branch two:
% 30.11/8.26 | (2301) ~ (all_0_57_57 = e0)
% 30.11/8.26 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 30.11/8.26 |
% 30.11/8.26 +-Applying beta-rule and splitting (2302), into two cases.
% 30.11/8.26 |-Branch one:
% 30.11/8.26 | (585) all_0_58_58 = e0
% 30.11/8.26 |
% 30.11/8.26 | Combining equations (585,600) yields a new equation:
% 30.11/8.26 | (479) e4 = e0
% 30.11/8.26 |
% 30.11/8.26 | Equations (479) can reduce 6 to:
% 30.11/8.26 | (270) $false
% 30.11/8.26 |
% 30.11/8.26 |-The branch is then unsatisfiable
% 30.11/8.26 |-Branch two:
% 30.11/8.26 | (431) ~ (all_0_58_58 = e0)
% 30.11/8.26 | (2308) all_0_59_59 = e0
% 30.11/8.26 |
% 30.11/8.26 | Equations (2308) can reduce 4001 to:
% 30.11/8.26 | (270) $false
% 30.11/8.26 |
% 30.11/8.26 |-The branch is then unsatisfiable
% 30.11/8.26 |-Branch two:
% 30.11/8.26 | (3011) ~ (all_0_54_54 = e0)
% 30.11/8.26 | (3664) all_0_54_54 = e4 | all_0_54_54 = e3 | all_0_54_54 = e1
% 30.11/8.26 |
% 30.11/8.26 +-Applying beta-rule and splitting (3073), into two cases.
% 30.11/8.26 |-Branch one:
% 30.11/8.26 | (423) all_0_53_53 = e0
% 30.11/8.26 |
% 30.11/8.26 | Combining equations (853,423) yields a new equation:
% 30.11/8.26 | (571) e1 = e0
% 30.11/8.26 |
% 30.11/8.26 | Simplifying 571 yields:
% 30.11/8.26 | (560) e1 = e0
% 30.11/8.26 |
% 30.11/8.26 | Equations (560) can reduce 132 to:
% 30.11/8.26 | (270) $false
% 30.11/8.26 |
% 30.11/8.26 |-The branch is then unsatisfiable
% 30.11/8.26 |-Branch two:
% 30.11/8.26 | (584) ~ (all_0_53_53 = e0)
% 30.11/8.26 | (3084) all_0_54_54 = e0
% 30.11/8.26 |
% 30.11/8.26 | Equations (3084) can reduce 3011 to:
% 30.11/8.26 | (270) $false
% 30.11/8.26 |
% 30.11/8.26 |-The branch is then unsatisfiable
% 30.11/8.26 |-Branch two:
% 30.11/8.26 | (625) ~ (all_0_44_44 = e0)
% 30.11/8.26 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 30.11/8.26 |
% 30.11/8.26 +-Applying beta-rule and splitting (373), into two cases.
% 30.11/8.26 |-Branch one:
% 30.11/8.26 | (621) all_0_44_44 = e0
% 30.11/8.26 |
% 30.11/8.26 | Equations (621) can reduce 625 to:
% 30.11/8.26 | (270) $false
% 30.11/8.26 |
% 30.11/8.26 |-The branch is then unsatisfiable
% 30.11/8.26 |-Branch two:
% 30.11/8.26 | (625) ~ (all_0_44_44 = e0)
% 30.11/8.26 | (858) all_0_44_44 = e3
% 30.11/8.26 |
% 30.11/8.26 | Equations (858) can reduce 862 to:
% 30.11/8.26 | (270) $false
% 30.11/8.26 |
% 30.11/8.26 |-The branch is then unsatisfiable
% 30.11/8.26 |-Branch two:
% 30.11/8.26 | (2291) all_0_25_25 = e2 & ~ (all_0_26_26 = e1)
% 30.11/8.26 |
% 30.11/8.27 | Applying alpha-rule on (2291) yields:
% 30.11/8.27 | (2292) all_0_25_25 = e2
% 30.11/8.27 | (2293) ~ (all_0_26_26 = e1)
% 30.11/8.27 |
% 30.11/8.27 | Combining equations (6130,2292) yields a new equation:
% 30.11/8.27 | (6819) all_0_54_54 = e2
% 30.11/8.27 |
% 30.11/8.27 | Simplifying 6819 yields:
% 30.11/8.27 | (3657) all_0_54_54 = e2
% 30.11/8.27 |
% 30.11/8.27 | Equations (3657) can reduce 261 to:
% 30.11/8.27 | (270) $false
% 30.11/8.27 |
% 30.11/8.27 |-The branch is then unsatisfiable
% 30.11/8.27 |-Branch two:
% 30.11/8.27 | (2296) all_0_28_28 = e0 & ~ (all_0_29_29 = e1)
% 30.11/8.27 |
% 30.11/8.27 | Applying alpha-rule on (2296) yields:
% 30.11/8.27 | (2297) all_0_28_28 = e0
% 30.11/8.27 | (2298) ~ (all_0_29_29 = e1)
% 30.11/8.27 |
% 30.11/8.27 | Combining equations (2297,9135) yields a new equation:
% 30.11/8.27 | (479) e4 = e0
% 30.11/8.27 |
% 30.11/8.27 | Equations (479) can reduce 6 to:
% 30.11/8.27 | (270) $false
% 30.11/8.27 |
% 30.11/8.27 |-The branch is then unsatisfiable
% 30.11/8.27 |-Branch two:
% 30.11/8.27 | (874) ~ (all_0_53_53 = e1)
% 30.11/8.27 | (1001) all_0_58_58 = e1
% 30.11/8.27 |
% 30.11/8.27 | Combining equations (600,1001) yields a new equation:
% 30.11/8.27 | (525) e4 = e1
% 30.11/8.27 |
% 30.11/8.27 | Simplifying 525 yields:
% 30.11/8.27 | (526) e4 = e1
% 30.11/8.27 |
% 30.11/8.27 | Equations (526) can reduce 251 to:
% 30.11/8.27 | (270) $false
% 30.11/8.27 |
% 30.11/8.27 |-The branch is then unsatisfiable
% 30.11/8.27 |-Branch two:
% 30.11/8.27 | (644) ~ (all_0_57_57 = e1)
% 30.11/8.27 | (1000) all_0_58_58 = e1 | all_0_59_59 = e1
% 30.11/8.27 |
% 30.11/8.27 +-Applying beta-rule and splitting (1000), into two cases.
% 30.11/8.27 |-Branch one:
% 30.11/8.27 | (1001) all_0_58_58 = e1
% 30.11/8.27 |
% 30.11/8.27 | Combining equations (1001,600) yields a new equation:
% 30.11/8.27 | (526) e4 = e1
% 30.11/8.27 |
% 30.11/8.27 | Equations (526) can reduce 251 to:
% 30.11/8.27 | (270) $false
% 30.11/8.27 |
% 30.11/8.27 |-The branch is then unsatisfiable
% 30.11/8.27 |-Branch two:
% 30.11/8.27 | (1004) ~ (all_0_58_58 = e1)
% 30.11/8.27 | (424) all_0_59_59 = e1
% 30.11/8.27 |
% 30.11/8.27 | Equations (424) can reduce 750 to:
% 30.11/8.27 | (270) $false
% 30.11/8.27 |
% 30.11/8.27 |-The branch is then unsatisfiable
% 30.11/8.27 |-Branch two:
% 30.11/8.27 | (591) ~ (all_0_39_39 = e4)
% 30.11/8.27 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 30.11/8.27 |
% 30.11/8.27 +-Applying beta-rule and splitting (592), into two cases.
% 30.11/8.27 |-Branch one:
% 30.11/8.27 | (358) all_0_41_41 = e4
% 30.11/8.27 |
% 30.11/8.27 | Combining equations (351,358) yields a new equation:
% 30.11/8.27 | (359) e4 = e3
% 30.11/8.27 |
% 30.11/8.27 | Equations (359) can reduce 34 to:
% 30.11/8.27 | (270) $false
% 30.11/8.27 |
% 30.11/8.27 |-The branch is then unsatisfiable
% 30.11/8.27 |-Branch two:
% 30.11/8.27 | (361) ~ (all_0_41_41 = e4)
% 30.11/8.27 | (512) all_0_42_42 = e4
% 30.11/8.27 |
% 30.11/8.27 | Combining equations (541,512) yields a new equation:
% 30.11/8.27 | (526) e4 = e1
% 30.11/8.27 |
% 30.11/8.27 | Equations (526) can reduce 251 to:
% 30.11/8.27 | (270) $false
% 30.11/8.27 |
% 30.11/8.27 |-The branch is then unsatisfiable
% 30.11/8.27 |-Branch two:
% 30.11/8.27 | (324) ~ (all_0_47_47 = e1)
% 30.11/8.27 | (325) all_0_48_48 = e1 | all_0_49_49 = e1
% 30.11/8.27 |
% 30.11/8.27 +-Applying beta-rule and splitting (13), into two cases.
% 30.11/8.27 |-Branch one:
% 30.11/8.27 | (576) all_0_53_53 = e2
% 30.11/8.27 |
% 30.11/8.27 | Equations (576) can reduce 259 to:
% 30.11/8.27 | (270) $false
% 30.11/8.27 |
% 30.11/8.27 |-The branch is then unsatisfiable
% 30.11/8.27 |-Branch two:
% 30.11/8.27 | (259) ~ (all_0_53_53 = e2)
% 30.11/8.27 | (5715) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 30.11/8.27 |
% 30.11/8.27 +-Applying beta-rule and splitting (5715), into two cases.
% 30.11/8.27 |-Branch one:
% 30.11/8.27 | (423) all_0_53_53 = e0
% 30.11/8.27 |
% 30.11/8.27 | Equations (423) can reduce 584 to:
% 30.11/8.27 | (270) $false
% 30.11/8.27 |
% 30.11/8.27 |-The branch is then unsatisfiable
% 30.11/8.27 |-Branch two:
% 30.11/8.27 | (584) ~ (all_0_53_53 = e0)
% 30.11/8.27 | (5719) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1
% 30.11/8.27 |
% 30.11/8.27 +-Applying beta-rule and splitting (5719), into two cases.
% 30.11/8.27 |-Branch one:
% 30.11/8.27 | (1114) all_0_53_53 = e3
% 30.11/8.27 |
% 30.11/8.27 | Equations (1114) can reduce 356 to:
% 30.11/8.27 | (270) $false
% 30.11/8.27 |
% 30.11/8.27 |-The branch is then unsatisfiable
% 30.11/8.27 |-Branch two:
% 30.11/8.27 | (356) ~ (all_0_53_53 = e3)
% 30.11/8.27 | (5723) all_0_53_53 = e4 | all_0_53_53 = e1
% 30.11/8.27 |
% 30.11/8.27 +-Applying beta-rule and splitting (5723), into two cases.
% 30.11/8.27 |-Branch one:
% 30.11/8.27 | (853) all_0_53_53 = e1
% 30.11/8.27 |
% 30.11/8.27 | Equations (853) can reduce 213 to:
% 30.11/8.27 | (642) ~ (all_0_52_52 = e1)
% 30.11/8.27 |
% 30.11/8.27 | Equations (853) can reduce 252 to:
% 30.11/8.27 | (2131) ~ (all_0_54_54 = e1)
% 30.11/8.27 |
% 30.11/8.27 | Simplifying 2131 yields:
% 30.11/8.27 | (425) ~ (all_0_54_54 = e1)
% 30.11/8.27 |
% 30.11/8.27 +-Applying beta-rule and splitting (3352), into two cases.
% 30.11/8.27 |-Branch one:
% 30.11/8.27 | (848) all_0_52_52 = e1
% 30.11/8.27 |
% 30.11/8.27 | Equations (848) can reduce 642 to:
% 30.11/8.27 | (270) $false
% 30.11/8.27 |
% 30.11/8.27 |-The branch is then unsatisfiable
% 30.11/8.27 |-Branch two:
% 30.11/8.27 | (642) ~ (all_0_52_52 = e1)
% 30.11/8.27 | (997) all_0_57_57 = e1
% 30.11/8.27 |
% 30.11/8.27 | Equations (997) can reduce 140 to:
% 30.11/8.27 | (749) ~ (all_0_59_59 = e1)
% 30.11/8.27 |
% 30.11/8.27 | Simplifying 749 yields:
% 30.11/8.27 | (750) ~ (all_0_59_59 = e1)
% 30.11/8.27 |
% 30.11/8.27 | Equations (997) can reduce 335 to:
% 30.11/8.27 | (645) ~ (e2 = e1)
% 30.11/8.27 |
% 30.11/8.27 | Simplifying 645 yields:
% 30.11/8.27 | (141) ~ (e2 = e1)
% 30.11/8.27 |
% 30.11/8.27 +-Applying beta-rule and splitting (127), into two cases.
% 30.11/8.27 |-Branch one:
% 30.11/8.27 | (541) all_0_42_42 = e1
% 30.11/8.27 |
% 30.11/8.27 | Equations (541) can reduce 498 to:
% 30.11/8.27 | (645) ~ (e2 = e1)
% 30.11/8.27 |
% 30.11/8.27 | Simplifying 645 yields:
% 30.11/8.27 | (141) ~ (e2 = e1)
% 30.11/8.27 |
% 30.11/8.27 | Equations (541) can reduce 199 to:
% 30.11/8.27 | (132) ~ (e1 = e0)
% 30.11/8.27 |
% 30.11/8.27 +-Applying beta-rule and splitting (325), into two cases.
% 30.11/8.27 |-Branch one:
% 30.11/8.27 | (552) all_0_48_48 = e1
% 30.11/8.27 |
% 30.11/8.27 | Combining equations (559,552) yields a new equation:
% 30.11/8.27 | (560) e1 = e0
% 30.11/8.27 |
% 30.11/8.27 | Equations (560) can reduce 132 to:
% 30.11/8.27 | (270) $false
% 30.11/8.27 |
% 30.11/8.27 |-The branch is then unsatisfiable
% 30.11/8.27 |-Branch two:
% 30.11/8.27 | (588) ~ (all_0_48_48 = e1)
% 30.11/8.27 | (589) all_0_49_49 = e1
% 30.11/8.27 |
% 30.11/8.27 | Combining equations (307,589) yields a new equation:
% 30.11/8.27 | (531) e2 = e1
% 30.11/8.27 |
% 30.11/8.27 | Simplifying 531 yields:
% 30.11/8.27 | (322) e2 = e1
% 30.11/8.27 |
% 30.11/8.27 | Equations (322) can reduce 141 to:
% 30.11/8.27 | (270) $false
% 30.11/8.27 |
% 30.11/8.27 |-The branch is then unsatisfiable
% 30.11/8.27 |-Branch two:
% 30.11/8.27 | (640) ~ (all_0_42_42 = e1)
% 30.11/8.27 | (4628) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 30.11/8.27 |
% 30.11/8.27 +-Applying beta-rule and splitting (4628), into two cases.
% 30.11/8.27 |-Branch one:
% 30.11/8.27 | (589) all_0_49_49 = e1
% 30.11/8.27 |
% 30.11/8.27 | Combining equations (307,589) yields a new equation:
% 30.11/8.27 | (531) e2 = e1
% 30.11/8.27 |
% 30.11/8.27 | Simplifying 531 yields:
% 30.11/8.27 | (322) e2 = e1
% 30.11/8.27 |
% 30.11/8.27 | Equations (322) can reduce 141 to:
% 30.11/8.27 | (270) $false
% 30.11/8.27 |
% 30.11/8.27 |-The branch is then unsatisfiable
% 30.11/8.27 |-Branch two:
% 30.11/8.27 | (543) ~ (all_0_49_49 = e1)
% 30.11/8.27 | (4726) all_0_54_54 = e1 | all_0_59_59 = e1
% 30.11/8.27 |
% 30.11/8.27 +-Applying beta-rule and splitting (4726), into two cases.
% 30.11/8.27 |-Branch one:
% 30.11/8.27 | (875) all_0_54_54 = e1
% 30.11/8.27 |
% 30.11/8.27 | Equations (875) can reduce 425 to:
% 30.11/8.27 | (270) $false
% 30.11/8.27 |
% 30.11/8.27 |-The branch is then unsatisfiable
% 30.11/8.27 |-Branch two:
% 30.11/8.27 | (425) ~ (all_0_54_54 = e1)
% 30.11/8.27 | (424) all_0_59_59 = e1
% 30.11/8.27 |
% 30.11/8.27 | Equations (424) can reduce 750 to:
% 30.11/8.27 | (270) $false
% 30.11/8.27 |
% 30.11/8.27 |-The branch is then unsatisfiable
% 30.11/8.27 |-Branch two:
% 30.11/8.27 | (874) ~ (all_0_53_53 = e1)
% 30.11/8.27 | (367) all_0_53_53 = e4
% 30.11/8.27 |
% 30.11/8.27 | Equations (367) can reduce 599 to:
% 30.11/8.27 | (270) $false
% 30.11/8.27 |
% 30.11/8.27 |-The branch is then unsatisfiable
% 30.11/8.27 |-Branch two:
% 30.11/8.27 | (562) ~ (all_0_48_48 = e0)
% 30.11/8.27 | (563) all_0_49_49 = e0
% 30.11/8.27 |
% 30.11/8.27 | Combining equations (307,563) yields a new equation:
% 30.11/8.27 | (622) e2 = e0
% 30.11/8.27 |
% 30.11/8.27 | Simplifying 622 yields:
% 30.11/8.27 | (316) e2 = e0
% 30.11/8.27 |
% 30.11/8.27 | Equations (316) can reduce 57 to:
% 30.11/8.27 | (270) $false
% 30.11/8.27 |
% 30.11/8.27 |-The branch is then unsatisfiable
% 30.11/8.27 |-Branch two:
% 30.11/8.27 | (255) ~ (all_0_51_51 = e2)
% 30.11/8.27 | (9864) all_0_52_52 = e2 | all_0_53_53 = e2 | all_0_54_54 = e2
% 30.11/8.27 |
% 30.11/8.27 +-Applying beta-rule and splitting (9864), into two cases.
% 30.11/8.27 |-Branch one:
% 30.11/8.27 | (685) all_0_52_52 = e2
% 30.11/8.27 |
% 30.11/8.27 | Equations (685) can reduce 257 to:
% 30.11/8.27 | (270) $false
% 30.11/8.27 |
% 30.11/8.27 |-The branch is then unsatisfiable
% 30.11/8.27 |-Branch two:
% 30.11/8.27 | (257) ~ (all_0_52_52 = e2)
% 30.11/8.27 | (9868) all_0_53_53 = e2 | all_0_54_54 = e2
% 30.11/8.27 |
% 30.11/8.27 +-Applying beta-rule and splitting (9868), into two cases.
% 30.11/8.27 |-Branch one:
% 30.11/8.27 | (576) all_0_53_53 = e2
% 30.11/8.27 |
% 30.11/8.27 | Equations (576) can reduce 259 to:
% 30.11/8.27 | (270) $false
% 30.11/8.27 |
% 30.11/8.27 |-The branch is then unsatisfiable
% 30.11/8.27 |-Branch two:
% 30.11/8.27 | (259) ~ (all_0_53_53 = e2)
% 30.11/8.27 | (3657) all_0_54_54 = e2
% 30.11/8.27 |
% 30.11/8.27 | Equations (3657) can reduce 261 to:
% 30.11/8.27 | (270) $false
% 30.11/8.27 |
% 30.11/8.27 |-The branch is then unsatisfiable
% 30.11/8.28 |-Branch two:
% 30.11/8.28 | (434) ~ (all_0_45_45 = e2)
% 30.11/8.28 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 30.11/8.28 |
% 30.11/8.28 +-Applying beta-rule and splitting (435), into two cases.
% 30.11/8.28 |-Branch one:
% 30.11/8.28 | (454) all_0_45_45 = e0
% 30.11/8.28 |
% 30.11/8.28 | Equations (454) can reduce 84 to:
% 30.11/8.28 | (455) ~ (all_0_43_43 = e0)
% 30.11/8.28 |
% 30.11/8.28 | Equations (454) can reduce 128 to:
% 30.11/8.28 | (3103) ~ (all_0_53_53 = e0)
% 30.11/8.28 |
% 30.11/8.28 | Simplifying 3103 yields:
% 30.11/8.28 | (584) ~ (all_0_53_53 = e0)
% 30.11/8.28 |
% 30.11/8.28 +-Applying beta-rule and splitting (93), into two cases.
% 30.11/8.28 |-Branch one:
% 30.11/8.28 | (402) all_0_59_59 = e4
% 30.11/8.28 |
% 30.11/8.28 | Equations (402) can reduce 280 to:
% 30.11/8.28 | (270) $false
% 30.11/8.28 |
% 30.11/8.28 |-The branch is then unsatisfiable
% 30.11/8.28 |-Branch two:
% 30.11/8.28 | (280) ~ (all_0_59_59 = e4)
% 30.11/8.28 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 30.11/8.28 |
% 30.11/8.28 +-Applying beta-rule and splitting (407), into two cases.
% 30.11/8.28 |-Branch one:
% 30.11/8.28 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 30.11/8.28 |
% 30.11/8.28 +-Applying beta-rule and splitting (408), into two cases.
% 30.11/8.28 |-Branch one:
% 30.11/8.28 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 30.11/8.28 |
% 30.11/8.28 +-Applying beta-rule and splitting (409), into two cases.
% 30.11/8.28 |-Branch one:
% 30.11/8.28 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 30.11/8.28 |
% 30.11/8.28 | Applying alpha-rule on (410) yields:
% 30.11/8.28 | (411) all_0_43_43 = e0
% 30.11/8.28 | (412) all_0_59_59 = e3
% 30.11/8.28 | (413) ~ (all_0_46_46 = e3)
% 30.11/8.28 |
% 30.11/8.28 | Equations (411) can reduce 455 to:
% 30.11/8.28 | (270) $false
% 30.11/8.28 |
% 30.11/8.28 |-The branch is then unsatisfiable
% 30.11/8.28 |-Branch two:
% 30.11/8.28 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 30.11/8.28 |
% 30.11/8.28 | Applying alpha-rule on (416) yields:
% 30.11/8.28 | (411) all_0_43_43 = e0
% 30.11/8.28 | (412) all_0_59_59 = e3
% 30.11/8.28 | (419) ~ (all_0_56_56 = e0)
% 30.11/8.28 |
% 30.17/8.28 | Equations (411) can reduce 455 to:
% 30.17/8.28 | (270) $false
% 30.17/8.28 |
% 30.17/8.28 |-The branch is then unsatisfiable
% 30.17/8.28 |-Branch two:
% 30.17/8.28 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 30.17/8.28 |
% 30.17/8.28 | Applying alpha-rule on (422) yields:
% 30.17/8.28 | (423) all_0_53_53 = e0
% 30.17/8.28 | (424) all_0_59_59 = e1
% 30.17/8.28 | (425) ~ (all_0_54_54 = e1)
% 30.17/8.28 |
% 30.17/8.28 | Equations (423) can reduce 584 to:
% 30.17/8.28 | (270) $false
% 30.17/8.28 |
% 30.17/8.28 |-The branch is then unsatisfiable
% 30.17/8.28 |-Branch two:
% 30.17/8.28 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 30.17/8.28 |
% 30.17/8.28 | Applying alpha-rule on (428) yields:
% 30.17/8.28 | (423) all_0_53_53 = e0
% 30.17/8.28 | (424) all_0_59_59 = e1
% 30.17/8.28 | (431) ~ (all_0_58_58 = e0)
% 30.17/8.28 |
% 30.17/8.28 | Equations (423) can reduce 584 to:
% 30.17/8.28 | (270) $false
% 30.17/8.28 |
% 30.17/8.28 |-The branch is then unsatisfiable
% 30.17/8.28 |-Branch two:
% 30.17/8.28 | (488) ~ (all_0_45_45 = e0)
% 30.17/8.28 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 30.17/8.28 |
% 30.17/8.28 +-Applying beta-rule and splitting (489), into two cases.
% 30.17/8.28 |-Branch one:
% 30.17/8.28 | (505) all_0_45_45 = e3
% 30.17/8.28 |
% 30.17/8.28 | Equations (505) can reduce 354 to:
% 30.17/8.28 | (270) $false
% 30.17/8.28 |
% 30.17/8.28 |-The branch is then unsatisfiable
% 30.17/8.28 |-Branch two:
% 30.17/8.28 | (354) ~ (all_0_45_45 = e3)
% 30.17/8.28 | (363) all_0_45_45 = e4
% 30.17/8.28 |
% 30.17/8.28 | Equations (363) can reduce 352 to:
% 30.17/8.28 | (270) $false
% 30.17/8.28 |
% 30.17/8.28 |-The branch is then unsatisfiable
% 30.17/8.28 |-Branch two:
% 30.17/8.28 | (602) ~ (all_0_40_40 = e2)
% 30.17/8.28 | (603) all_0_40_40 = e3 | all_0_40_40 = e1
% 30.17/8.28 |
% 30.17/8.28 +-Applying beta-rule and splitting (20), into two cases.
% 30.17/8.28 |-Branch one:
% 30.17/8.28 | (327) all_0_40_40 = e2
% 30.17/8.28 |
% 30.17/8.28 | Equations (327) can reduce 602 to:
% 30.17/8.28 | (270) $false
% 30.17/8.28 |
% 30.17/8.28 |-The branch is then unsatisfiable
% 30.17/8.28 |-Branch two:
% 30.17/8.28 | (602) ~ (all_0_40_40 = e2)
% 30.17/8.28 | (607) all_0_44_44 = e2 | all_0_52_52 = e2 | all_0_57_57 = e2
% 30.17/8.28 |
% 30.17/8.28 +-Applying beta-rule and splitting (129), into two cases.
% 30.17/8.28 |-Branch one:
% 30.17/8.28 | (311) all_0_48_48 = e2
% 30.17/8.28 |
% 30.17/8.28 | Equations (311) can reduce 190 to:
% 30.17/8.28 | (331) ~ (all_0_41_41 = e2)
% 30.17/8.28 |
% 30.17/8.28 | Equations (311) can reduce 65 to:
% 30.17/8.28 | (434) ~ (all_0_45_45 = e2)
% 30.17/8.28 |
% 30.17/8.28 | Equations (311) can reduce 225 to:
% 30.17/8.28 | (3951) ~ (all_0_47_47 = e2)
% 30.17/8.28 |
% 30.17/8.28 | Equations (311) can reduce 4 to:
% 30.17/8.28 | (295) ~ (all_0_49_49 = e2)
% 30.17/8.28 |
% 30.17/8.28 | Simplifying 295 yields:
% 30.17/8.28 | (296) ~ (all_0_49_49 = e2)
% 30.17/8.28 |
% 30.17/8.28 | Equations (311) can reduce 48 to:
% 30.17/8.28 | (258) ~ (all_0_53_53 = e2)
% 30.17/8.28 |
% 30.17/8.28 | Simplifying 258 yields:
% 30.17/8.28 | (259) ~ (all_0_53_53 = e2)
% 30.17/8.28 |
% 30.17/8.28 | Equations (311) can reduce 59 to:
% 30.17/8.28 | (375) ~ (all_0_58_58 = e2)
% 30.17/8.28 |
% 30.17/8.28 | Simplifying 375 yields:
% 30.17/8.28 | (376) ~ (all_0_58_58 = e2)
% 30.17/8.28 |
% 30.17/8.28 | Equations (311) can reduce 121 to:
% 30.17/8.28 | (301) ~ (e3 = e2)
% 30.17/8.28 |
% 30.17/8.28 | Simplifying 301 yields:
% 30.17/8.28 | (223) ~ (e3 = e2)
% 30.17/8.28 |
% 30.17/8.28 | From (311) and (183) follows:
% 30.17/8.28 | (3969) op(e2, e2) = all_0_26_26
% 30.17/8.28 |
% 30.17/8.28 | From (311) and (56) follows:
% 30.17/8.28 | (3970) op(e2, e1) = e2
% 30.17/8.28 |
% 30.17/8.28 | Instantiating formula (201) with e2, e2, all_0_26_26, e4 and discharging atoms op(e2, e2) = all_0_26_26, op(e2, e2) = e4, yields:
% 30.17/8.28 | (3972) all_0_26_26 = e4
% 30.17/8.28 |
% 30.17/8.28 | From (3972) and (3969) follows:
% 30.17/8.28 | (115) op(e2, e2) = e4
% 30.17/8.28 |
% 30.17/8.28 +-Applying beta-rule and splitting (155), into two cases.
% 30.17/8.28 |-Branch one:
% 30.17/8.28 | (290) all_0_47_47 = e2
% 30.17/8.28 |
% 30.17/8.28 | Equations (290) can reduce 3951 to:
% 30.17/8.28 | (270) $false
% 30.17/8.28 |
% 30.17/8.28 |-The branch is then unsatisfiable
% 30.17/8.28 |-Branch two:
% 30.17/8.28 | (3951) ~ (all_0_47_47 = e2)
% 30.17/8.28 | (3956) all_0_47_47 = e1 | all_0_47_47 = e0
% 30.17/8.28 |
% 30.17/8.28 +-Applying beta-rule and splitting (117), into two cases.
% 30.17/8.28 |-Branch one:
% 30.17/8.28 | (307) all_0_49_49 = e2
% 30.17/8.28 |
% 30.17/8.28 | Equations (307) can reduce 296 to:
% 30.17/8.28 | (270) $false
% 30.17/8.28 |
% 30.17/8.28 |-The branch is then unsatisfiable
% 30.17/8.28 |-Branch two:
% 30.17/8.28 | (296) ~ (all_0_49_49 = e2)
% 30.17/8.28 | (310) all_0_49_49 = e1 | all_0_49_49 = e0
% 30.17/8.28 |
% 30.17/8.28 +-Applying beta-rule and splitting (77), into two cases.
% 30.17/8.28 |-Branch one:
% 30.17/8.28 | (315) all_0_47_47 = e0
% 30.17/8.28 |
% 30.17/8.28 | Equations (315) can reduce 100 to:
% 30.17/8.28 | (101) ~ (all_0_39_39 = e0)
% 30.17/8.28 |
% 30.17/8.28 | Equations (315) can reduce 170 to:
% 30.17/8.28 | (455) ~ (all_0_43_43 = e0)
% 30.17/8.28 |
% 30.17/8.28 | Equations (315) can reduce 80 to:
% 30.17/8.28 | (11353) ~ (all_0_49_49 = e0)
% 30.17/8.28 |
% 30.17/8.28 | Simplifying 11353 yields:
% 30.17/8.28 | (1231) ~ (all_0_49_49 = e0)
% 30.17/8.28 |
% 30.17/8.28 | Equations (315) can reduce 3 to:
% 30.17/8.28 | (6253) ~ (all_0_51_51 = e0)
% 30.17/8.28 |
% 30.17/8.28 | Simplifying 6253 yields:
% 30.17/8.28 | (987) ~ (all_0_51_51 = e0)
% 30.17/8.28 |
% 30.17/8.28 | Equations (315) can reduce 218 to:
% 30.17/8.28 | (3852) ~ (all_0_56_56 = e0)
% 30.17/8.28 |
% 30.17/8.28 | Simplifying 3852 yields:
% 30.17/8.28 | (419) ~ (all_0_56_56 = e0)
% 30.17/8.28 |
% 30.17/8.28 | Equations (315) can reduce 247 to:
% 30.17/8.28 | (788) ~ (e3 = e0)
% 30.17/8.28 |
% 30.17/8.28 | Simplifying 788 yields:
% 30.17/8.28 | (66) ~ (e3 = e0)
% 30.17/8.28 |
% 30.17/8.28 | Equations (315) can reduce 3951 to:
% 30.17/8.28 | (566) ~ (e2 = e0)
% 30.17/8.28 |
% 30.17/8.28 | Simplifying 566 yields:
% 30.17/8.28 | (57) ~ (e2 = e0)
% 30.17/8.28 |
% 30.17/8.28 | From (315) and (237) follows:
% 30.17/8.28 | (11363) op(e3, e0) = all_0_7_7
% 30.17/8.28 |
% 30.17/8.28 | From (315) and (42) follows:
% 30.17/8.28 | (7717) op(e2, e0) = all_0_8_8
% 30.17/8.28 |
% 30.17/8.28 | From (315) and (40) follows:
% 30.17/8.28 | (7718) op(e2, e3) = e0
% 30.17/8.28 |
% 30.17/8.28 +-Applying beta-rule and splitting (310), into two cases.
% 30.17/8.28 |-Branch one:
% 30.17/8.28 | (563) all_0_49_49 = e0
% 30.17/8.28 |
% 30.17/8.28 | Equations (563) can reduce 1231 to:
% 30.17/8.28 | (270) $false
% 30.17/8.28 |
% 30.17/8.28 |-The branch is then unsatisfiable
% 30.17/8.28 |-Branch two:
% 30.17/8.28 | (1231) ~ (all_0_49_49 = e0)
% 30.17/8.28 | (589) all_0_49_49 = e1
% 30.17/8.28 |
% 30.17/8.28 | Equations (589) can reduce 169 to:
% 30.17/8.28 | (640) ~ (all_0_42_42 = e1)
% 30.17/8.28 |
% 30.17/8.28 | Equations (589) can reduce 198 to:
% 30.17/8.28 | (106) ~ (all_0_46_46 = e1)
% 30.17/8.28 |
% 30.17/8.28 | Equations (589) can reduce 162 to:
% 30.17/8.28 | (2131) ~ (all_0_54_54 = e1)
% 30.17/8.28 |
% 30.17/8.28 | Simplifying 2131 yields:
% 30.17/8.28 | (425) ~ (all_0_54_54 = e1)
% 30.17/8.28 |
% 30.17/8.28 | Equations (589) can reduce 113 to:
% 30.17/8.28 | (749) ~ (all_0_59_59 = e1)
% 30.17/8.28 |
% 30.17/8.28 | Simplifying 749 yields:
% 30.17/8.28 | (750) ~ (all_0_59_59 = e1)
% 30.17/8.28 |
% 30.17/8.28 | Equations (589) can reduce 150 to:
% 30.17/8.28 | (769) ~ (e3 = e1)
% 30.17/8.28 |
% 30.17/8.28 | Simplifying 769 yields:
% 30.17/8.28 | (136) ~ (e3 = e1)
% 30.17/8.28 |
% 30.17/8.28 | Equations (589) can reduce 296 to:
% 30.17/8.28 | (645) ~ (e2 = e1)
% 30.17/8.28 |
% 30.17/8.28 | Simplifying 645 yields:
% 30.17/8.28 | (141) ~ (e2 = e1)
% 30.17/8.28 |
% 30.17/8.28 | Equations (589) can reduce 1231 to:
% 30.17/8.28 | (132) ~ (e1 = e0)
% 30.17/8.28 |
% 30.17/8.28 | From (589) and (153) follows:
% 30.17/8.29 | (11381) op(e2, e1) = all_0_35_35
% 30.17/8.29 |
% 30.17/8.29 | From (589) and (134) follows:
% 30.17/8.29 | (11382) op(e2, e0) = e1
% 30.17/8.29 |
% 30.17/8.29 | From (589) and (88) follows:
% 30.17/8.29 | (11383) op(e0, e1) = all_0_34_34
% 30.17/8.29 |
% 30.17/8.29 +-Applying beta-rule and splitting (93), into two cases.
% 30.17/8.29 |-Branch one:
% 30.17/8.29 | (402) all_0_59_59 = e4
% 30.17/8.29 |
% 30.17/8.29 | Equations (402) can reduce 17 to:
% 30.17/8.29 | (520) ~ (all_0_42_42 = e4)
% 30.17/8.29 |
% 30.17/8.29 | Equations (402) can reduce 206 to:
% 30.17/8.29 | (805) ~ (all_0_46_46 = e4)
% 30.17/8.29 |
% 30.17/8.29 | Equations (402) can reduce 72 to:
% 30.17/8.29 | (936) ~ (all_0_54_54 = e4)
% 30.17/8.29 |
% 30.17/8.29 | Equations (402) can reduce 185 to:
% 30.17/8.29 | (274) ~ (all_0_56_56 = e4)
% 30.17/8.29 |
% 30.17/8.29 | From (402) and (161) follows:
% 30.17/8.29 | (11389) op(e0, e0) = e4
% 30.17/8.29 |
% 30.17/8.29 | Instantiating formula (201) with e3, e0, all_0_7_7, all_0_46_46 and discharging atoms op(e3, e0) = all_0_7_7, op(e3, e0) = all_0_46_46, yields:
% 30.17/8.29 | (11390) all_0_7_7 = all_0_46_46
% 30.17/8.29 |
% 30.17/8.29 | Instantiating formula (201) with e2, e1, all_0_35_35, e2 and discharging atoms op(e2, e1) = all_0_35_35, op(e2, e1) = e2, yields:
% 30.17/8.29 | (11391) all_0_35_35 = e2
% 30.17/8.29 |
% 30.17/8.29 | Instantiating formula (201) with e2, e0, e1, all_0_8_8 and discharging atoms op(e2, e0) = all_0_8_8, op(e2, e0) = e1, yields:
% 30.17/8.29 | (11392) all_0_8_8 = e1
% 30.17/8.29 |
% 30.17/8.29 | Instantiating formula (201) with e0, e1, all_0_34_34, all_0_58_58 and discharging atoms op(e0, e1) = all_0_34_34, op(e0, e1) = all_0_58_58, yields:
% 30.17/8.29 | (11393) all_0_34_34 = all_0_58_58
% 30.17/8.29 |
% 30.17/8.29 | From (11391) and (11381) follows:
% 30.17/8.29 | (3970) op(e2, e1) = e2
% 30.17/8.29 |
% 30.17/8.29 | From (11392) and (7717) follows:
% 30.17/8.29 | (11382) op(e2, e0) = e1
% 30.17/8.29 |
% 30.17/8.29 +-Applying beta-rule and splitting (193), into two cases.
% 30.17/8.29 |-Branch one:
% 30.17/8.29 | (370) all_0_44_44 = e2
% 30.17/8.29 |
% 30.17/8.29 | Equations (370) can reduce 15 to:
% 30.17/8.29 | (602) ~ (all_0_40_40 = e2)
% 30.17/8.29 |
% 30.17/8.29 | Equations (370) can reduce 229 to:
% 30.17/8.29 | (611) ~ (all_0_45_45 = e2)
% 30.17/8.29 |
% 30.17/8.29 | Simplifying 611 yields:
% 30.17/8.29 | (434) ~ (all_0_45_45 = e2)
% 30.17/8.29 |
% 30.17/8.29 | Equations (370) can reduce 122 to:
% 30.17/8.29 | (256) ~ (all_0_52_52 = e2)
% 30.17/8.29 |
% 30.17/8.29 | Simplifying 256 yields:
% 30.17/8.29 | (257) ~ (all_0_52_52 = e2)
% 30.17/8.29 |
% 30.17/8.29 | Equations (370) can reduce 10 to:
% 30.17/8.29 | (334) ~ (all_0_57_57 = e2)
% 30.17/8.29 |
% 30.17/8.29 | Simplifying 334 yields:
% 30.17/8.29 | (335) ~ (all_0_57_57 = e2)
% 30.17/8.29 |
% 30.17/8.29 +-Applying beta-rule and splitting (222), into two cases.
% 30.17/8.29 |-Branch one:
% 30.17/8.29 | (522) all_0_39_39 = e4
% 30.17/8.29 |
% 30.17/8.29 | Equations (522) can reduce 184 to:
% 30.17/8.29 | (692) ~ (all_0_42_42 = e4)
% 30.17/8.29 |
% 30.17/8.29 | Simplifying 692 yields:
% 30.17/8.29 | (520) ~ (all_0_42_42 = e4)
% 30.17/8.29 |
% 30.17/8.29 | Equations (522) can reduce 167 to:
% 30.17/8.29 | (694) ~ (all_0_43_43 = e4)
% 30.17/8.29 |
% 30.17/8.29 | Simplifying 694 yields:
% 30.17/8.29 | (510) ~ (all_0_43_43 = e4)
% 30.17/8.29 |
% 30.17/8.29 | Equations (522) can reduce 101 to:
% 30.17/8.29 | (6) ~ (e4 = e0)
% 30.17/8.29 |
% 30.17/8.29 +-Applying beta-rule and splitting (44), into two cases.
% 30.17/8.29 |-Branch one:
% 30.17/8.29 | (502) all_0_43_43 = e4
% 30.17/8.29 |
% 30.17/8.29 | Equations (502) can reduce 510 to:
% 30.17/8.29 | (270) $false
% 30.17/8.29 |
% 30.17/8.29 |-The branch is then unsatisfiable
% 30.17/8.29 |-Branch two:
% 30.17/8.29 | (510) ~ (all_0_43_43 = e4)
% 30.17/8.29 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 30.17/8.29 |
% 30.17/8.29 +-Applying beta-rule and splitting (511), into two cases.
% 30.17/8.29 |-Branch one:
% 30.17/8.29 | (363) all_0_45_45 = e4
% 30.17/8.29 |
% 30.17/8.29 | Equations (363) can reduce 434 to:
% 30.17/8.29 | (231) ~ (e4 = e2)
% 30.17/8.29 |
% 30.17/8.29 +-Applying beta-rule and splitting (164), into two cases.
% 30.17/8.29 |-Branch one:
% 30.17/8.29 | (336) all_0_39_39 = e2
% 30.17/8.29 |
% 30.17/8.29 | Combining equations (522,336) yields a new equation:
% 30.17/8.29 | (268) e4 = e2
% 30.17/8.29 |
% 30.17/8.29 | Simplifying 268 yields:
% 30.17/8.29 | (269) e4 = e2
% 30.17/8.29 |
% 30.17/8.29 | Equations (269) can reduce 231 to:
% 30.17/8.29 | (270) $false
% 30.17/8.29 |
% 30.17/8.29 |-The branch is then unsatisfiable
% 30.17/8.29 |-Branch two:
% 30.17/8.29 | (291) ~ (all_0_39_39 = e2)
% 30.17/8.29 | (630) all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 30.17/8.29 |
% 30.17/8.29 +-Applying beta-rule and splitting (630), into two cases.
% 30.17/8.29 |-Branch one:
% 30.17/8.29 | (327) all_0_40_40 = e2
% 30.17/8.29 |
% 30.17/8.29 | Equations (327) can reduce 602 to:
% 30.17/8.29 | (270) $false
% 30.17/8.29 |
% 30.17/8.29 |-The branch is then unsatisfiable
% 30.17/8.29 |-Branch two:
% 30.17/8.29 | (602) ~ (all_0_40_40 = e2)
% 30.17/8.29 | (1251) all_0_41_41 = e2 | all_0_42_42 = e2
% 30.17/8.29 |
% 30.17/8.29 +-Applying beta-rule and splitting (1251), into two cases.
% 30.17/8.29 |-Branch one:
% 30.17/8.29 | (436) all_0_41_41 = e2
% 30.17/8.29 |
% 30.17/8.29 | Equations (436) can reduce 331 to:
% 30.17/8.29 | (270) $false
% 30.17/8.29 |
% 30.17/8.29 |-The branch is then unsatisfiable
% 30.17/8.29 |-Branch two:
% 30.17/8.29 | (331) ~ (all_0_41_41 = e2)
% 30.17/8.29 | (698) all_0_42_42 = e2
% 30.17/8.29 |
% 30.17/8.29 | Equations (698) can reduce 520 to:
% 30.17/8.29 | (377) ~ (e4 = e2)
% 30.17/8.29 |
% 30.17/8.29 | Simplifying 377 yields:
% 30.17/8.29 | (231) ~ (e4 = e2)
% 30.17/8.29 |
% 30.17/8.29 | Equations (698) can reduce 199 to:
% 30.17/8.29 | (57) ~ (e2 = e0)
% 30.17/8.29 |
% 30.17/8.29 +-Applying beta-rule and splitting (186), into two cases.
% 30.17/8.29 |-Branch one:
% 30.17/8.29 | (336) all_0_39_39 = e2
% 30.17/8.29 |
% 30.17/8.29 | Combining equations (522,336) yields a new equation:
% 30.17/8.29 | (268) e4 = e2
% 30.17/8.29 |
% 30.17/8.29 | Simplifying 268 yields:
% 30.17/8.29 | (269) e4 = e2
% 30.17/8.29 |
% 30.17/8.29 | Equations (269) can reduce 231 to:
% 30.17/8.29 | (270) $false
% 30.17/8.29 |
% 30.17/8.29 |-The branch is then unsatisfiable
% 30.17/8.29 |-Branch two:
% 30.17/8.29 | (291) ~ (all_0_39_39 = e2)
% 30.17/8.29 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 30.17/8.29 |
% 30.17/8.29 +-Applying beta-rule and splitting (116), into two cases.
% 30.17/8.29 |-Branch one:
% 30.17/8.29 | (411) all_0_43_43 = e0
% 30.17/8.29 |
% 30.17/8.29 | Equations (411) can reduce 455 to:
% 30.17/8.29 | (270) $false
% 30.17/8.29 |
% 30.17/8.29 |-The branch is then unsatisfiable
% 30.17/8.29 |-Branch two:
% 30.17/8.29 | (455) ~ (all_0_43_43 = e0)
% 30.17/8.29 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 30.17/8.29 |
% 30.17/8.29 +-Applying beta-rule and splitting (1122), into two cases.
% 30.17/8.29 |-Branch one:
% 30.17/8.29 | (621) all_0_44_44 = e0
% 30.17/8.29 |
% 30.17/8.29 | Combining equations (370,621) yields a new equation:
% 30.17/8.29 | (622) e2 = e0
% 30.17/8.29 |
% 30.17/8.29 | Simplifying 622 yields:
% 30.17/8.29 | (316) e2 = e0
% 30.17/8.29 |
% 30.17/8.29 | Equations (316) can reduce 57 to:
% 30.17/8.29 | (270) $false
% 30.17/8.29 |
% 30.17/8.29 |-The branch is then unsatisfiable
% 30.17/8.29 |-Branch two:
% 30.17/8.29 | (625) ~ (all_0_44_44 = e0)
% 30.17/8.29 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 30.17/8.29 |
% 30.17/8.29 +-Applying beta-rule and splitting (1128), into two cases.
% 30.17/8.29 |-Branch one:
% 30.17/8.29 | (454) all_0_45_45 = e0
% 30.17/8.29 |
% 30.17/8.29 | Combining equations (363,454) yields a new equation:
% 30.17/8.29 | (478) e4 = e0
% 30.17/8.29 |
% 30.17/8.29 | Simplifying 478 yields:
% 30.17/8.29 | (479) e4 = e0
% 30.17/8.29 |
% 30.17/8.29 | Equations (479) can reduce 6 to:
% 30.17/8.29 | (270) $false
% 30.17/8.29 |
% 30.17/8.29 |-The branch is then unsatisfiable
% 30.17/8.29 |-Branch two:
% 30.17/8.29 | (488) ~ (all_0_45_45 = e0)
% 30.17/8.29 | (1132) all_0_46_46 = e0
% 30.17/8.29 |
% 30.17/8.29 | Equations (1132) can reduce 106 to:
% 30.17/8.29 | (568) ~ (e1 = e0)
% 30.17/8.29 |
% 30.17/8.29 | Simplifying 568 yields:
% 30.17/8.29 | (132) ~ (e1 = e0)
% 30.17/8.29 |
% 30.17/8.29 +-Applying beta-rule and splitting (339), into two cases.
% 30.17/8.29 |-Branch one:
% 30.17/8.29 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 30.17/8.29 |
% 30.17/8.29 +-Applying beta-rule and splitting (340), into two cases.
% 30.17/8.29 |-Branch one:
% 30.17/8.29 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 30.17/8.29 |
% 30.17/8.29 | Applying alpha-rule on (341) yields:
% 30.17/8.29 | (342) all_0_0_0 = e1
% 30.17/8.29 | (343) ~ (all_0_1_1 = e4)
% 30.17/8.29 |
% 30.17/8.29 | Combining equations (342,9064) yields a new equation:
% 30.17/8.29 | (571) e1 = e0
% 30.17/8.29 |
% 30.17/8.29 | Simplifying 571 yields:
% 30.17/8.29 | (560) e1 = e0
% 30.17/8.29 |
% 30.17/8.29 | Equations (560) can reduce 132 to:
% 30.17/8.29 | (270) $false
% 30.17/8.29 |
% 30.17/8.29 |-The branch is then unsatisfiable
% 30.17/8.29 |-Branch two:
% 30.17/8.29 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 30.17/8.29 |
% 30.17/8.29 | Applying alpha-rule on (346) yields:
% 30.17/8.29 | (347) all_0_2_2 = e0
% 30.17/8.29 | (348) ~ (all_0_3_3 = e4)
% 30.17/8.29 |
% 30.17/8.29 | Combining equations (347,9065) yields a new equation:
% 30.17/8.29 | (11467) all_0_40_40 = e0
% 30.17/8.29 |
% 30.17/8.29 | Equations (11467) can reduce 238 to:
% 30.17/8.29 | (270) $false
% 30.17/8.29 |
% 30.17/8.29 |-The branch is then unsatisfiable
% 30.17/8.29 |-Branch two:
% 30.17/8.29 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 30.17/8.29 |
% 30.17/8.29 | Applying alpha-rule on (350) yields:
% 30.17/8.29 | (351) all_0_41_41 = e3
% 30.17/8.29 | (352) ~ (all_0_45_45 = e4)
% 30.17/8.29 |
% 30.17/8.29 | Equations (363) can reduce 352 to:
% 30.17/8.29 | (270) $false
% 30.17/8.29 |
% 30.17/8.29 |-The branch is then unsatisfiable
% 30.17/8.29 |-Branch two:
% 30.17/8.29 | (352) ~ (all_0_45_45 = e4)
% 30.17/8.29 | (517) all_0_46_46 = e4
% 30.17/8.29 |
% 30.17/8.29 | Equations (517) can reduce 805 to:
% 30.17/8.29 | (270) $false
% 30.17/8.29 |
% 30.17/8.29 |-The branch is then unsatisfiable
% 30.17/8.29 |-Branch two:
% 30.17/8.29 | (591) ~ (all_0_39_39 = e4)
% 30.17/8.29 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 30.17/8.29 |
% 30.17/8.29 +-Applying beta-rule and splitting (592), into two cases.
% 30.17/8.29 |-Branch one:
% 30.17/8.29 | (358) all_0_41_41 = e4
% 30.17/8.29 |
% 30.17/8.29 | Equations (358) can reduce 94 to:
% 30.17/8.29 | (692) ~ (all_0_42_42 = e4)
% 30.17/8.29 |
% 30.17/8.29 | Simplifying 692 yields:
% 30.17/8.29 | (520) ~ (all_0_42_42 = e4)
% 30.17/8.29 |
% 30.17/8.29 | Equations (358) can reduce 51 to:
% 30.17/8.29 | (503) ~ (all_0_45_45 = e4)
% 30.17/8.29 |
% 30.17/8.29 | Simplifying 503 yields:
% 30.17/8.29 | (352) ~ (all_0_45_45 = e4)
% 30.17/8.29 |
% 30.17/8.29 +-Applying beta-rule and splitting (44), into two cases.
% 30.17/8.29 |-Branch one:
% 30.17/8.29 | (502) all_0_43_43 = e4
% 30.17/8.29 |
% 30.17/8.29 | Equations (502) can reduce 167 to:
% 30.17/8.29 | (591) ~ (all_0_39_39 = e4)
% 30.17/8.29 |
% 30.17/8.29 | Equations (502) can reduce 84 to:
% 30.17/8.29 | (503) ~ (all_0_45_45 = e4)
% 30.17/8.30 |
% 30.17/8.30 | Simplifying 503 yields:
% 30.17/8.30 | (352) ~ (all_0_45_45 = e4)
% 30.17/8.30 |
% 30.17/8.30 | Equations (502) can reduce 188 to:
% 30.17/8.30 | (273) ~ (all_0_56_56 = e4)
% 30.17/8.30 |
% 30.17/8.30 | Simplifying 273 yields:
% 30.17/8.30 | (274) ~ (all_0_56_56 = e4)
% 30.17/8.30 |
% 30.17/8.30 | Equations (502) can reduce 249 to:
% 30.17/8.30 | (251) ~ (e4 = e1)
% 30.17/8.30 |
% 30.17/8.30 | Equations (502) can reduce 455 to:
% 30.17/8.30 | (6) ~ (e4 = e0)
% 30.17/8.30 |
% 30.17/8.30 +-Applying beta-rule and splitting (186), into two cases.
% 30.17/8.30 |-Branch one:
% 30.17/8.30 | (336) all_0_39_39 = e2
% 30.17/8.30 |
% 30.17/8.30 | Equations (336) can reduce 32 to:
% 30.17/8.30 | (254) ~ (all_0_51_51 = e2)
% 30.17/8.30 |
% 30.17/8.30 | Simplifying 254 yields:
% 30.17/8.30 | (255) ~ (all_0_51_51 = e2)
% 30.17/8.30 |
% 30.17/8.30 | Equations (336) can reduce 591 to:
% 30.17/8.30 | (377) ~ (e4 = e2)
% 30.17/8.30 |
% 30.17/8.30 | Simplifying 377 yields:
% 30.17/8.30 | (231) ~ (e4 = e2)
% 30.17/8.30 |
% 30.17/8.30 | Equations (336) can reduce 101 to:
% 30.17/8.30 | (57) ~ (e2 = e0)
% 30.17/8.30 |
% 30.17/8.30 +-Applying beta-rule and splitting (58), into two cases.
% 30.17/8.30 |-Branch one:
% 30.17/8.30 | (253) all_0_50_50 = e2
% 30.17/8.30 |
% 30.17/8.30 | Combining equations (253,267) yields a new equation:
% 30.17/8.30 | (269) e4 = e2
% 30.17/8.30 |
% 30.17/8.30 | Equations (269) can reduce 231 to:
% 30.17/8.30 | (270) $false
% 30.17/8.30 |
% 30.17/8.30 |-The branch is then unsatisfiable
% 30.17/8.30 |-Branch two:
% 30.17/8.30 | (9032) ~ (all_0_50_50 = e2)
% 30.17/8.30 | (9860) all_0_51_51 = e2 | all_0_52_52 = e2 | all_0_53_53 = e2 | all_0_54_54 = e2
% 30.17/8.30 |
% 30.17/8.30 +-Applying beta-rule and splitting (9860), into two cases.
% 30.17/8.30 |-Branch one:
% 30.17/8.30 | (4215) all_0_51_51 = e2
% 30.17/8.30 |
% 30.17/8.30 | Equations (4215) can reduce 255 to:
% 30.17/8.30 | (270) $false
% 30.17/8.30 |
% 30.17/8.30 |-The branch is then unsatisfiable
% 30.17/8.30 |-Branch two:
% 30.17/8.30 | (255) ~ (all_0_51_51 = e2)
% 30.17/8.30 | (9864) all_0_52_52 = e2 | all_0_53_53 = e2 | all_0_54_54 = e2
% 30.17/8.30 |
% 30.17/8.30 +-Applying beta-rule and splitting (9864), into two cases.
% 30.17/8.30 |-Branch one:
% 30.17/8.30 | (685) all_0_52_52 = e2
% 30.17/8.30 |
% 30.17/8.30 | Equations (685) can reduce 257 to:
% 30.17/8.30 | (270) $false
% 30.17/8.30 |
% 30.17/8.30 |-The branch is then unsatisfiable
% 30.17/8.30 |-Branch two:
% 30.17/8.30 | (257) ~ (all_0_52_52 = e2)
% 30.17/8.30 | (9868) all_0_53_53 = e2 | all_0_54_54 = e2
% 30.17/8.30 |
% 30.17/8.30 +-Applying beta-rule and splitting (9868), into two cases.
% 30.17/8.30 |-Branch one:
% 30.17/8.30 | (576) all_0_53_53 = e2
% 30.17/8.30 |
% 30.17/8.30 | Equations (576) can reduce 259 to:
% 30.17/8.30 | (270) $false
% 30.17/8.30 |
% 30.17/8.30 |-The branch is then unsatisfiable
% 30.17/8.30 |-Branch two:
% 30.17/8.30 | (259) ~ (all_0_53_53 = e2)
% 30.17/8.30 | (3657) all_0_54_54 = e2
% 30.17/8.30 |
% 30.17/8.30 | Equations (3657) can reduce 191 to:
% 30.17/8.30 | (498) ~ (all_0_42_42 = e2)
% 30.17/8.30 |
% 30.17/8.30 | Equations (3657) can reduce 425 to:
% 30.17/8.30 | (141) ~ (e2 = e1)
% 30.17/8.30 |
% 30.17/8.30 | From (3657) and (138) follows:
% 30.17/8.30 | (11516) op(e0, e2) = all_0_36_36
% 30.17/8.30 |
% 30.17/8.30 +-Applying beta-rule and splitting (16), into two cases.
% 30.17/8.30 |-Branch one:
% 30.17/8.30 | (698) all_0_42_42 = e2
% 30.17/8.30 |
% 30.17/8.30 | Equations (698) can reduce 498 to:
% 30.17/8.30 | (270) $false
% 30.17/8.30 |
% 30.17/8.30 |-The branch is then unsatisfiable
% 30.17/8.30 |-Branch two:
% 30.17/8.30 | (498) ~ (all_0_42_42 = e2)
% 30.17/8.30 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 30.17/8.30 |
% 30.17/8.30 +-Applying beta-rule and splitting (210), into two cases.
% 30.17/8.30 |-Branch one:
% 30.17/8.30 | (524) all_0_39_39 = e1
% 30.17/8.30 |
% 30.17/8.30 | Combining equations (336,524) yields a new equation:
% 30.17/8.30 | (531) e2 = e1
% 30.17/8.30 |
% 30.17/8.30 | Simplifying 531 yields:
% 30.17/8.30 | (322) e2 = e1
% 30.17/8.30 |
% 30.17/8.30 | Equations (322) can reduce 141 to:
% 30.17/8.30 | (270) $false
% 30.17/8.30 |
% 30.17/8.30 |-The branch is then unsatisfiable
% 30.17/8.30 |-Branch two:
% 30.17/8.30 | (528) ~ (all_0_39_39 = e1)
% 30.17/8.30 | (529) all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1
% 30.17/8.30 |
% 30.17/8.30 +-Applying beta-rule and splitting (221), into two cases.
% 30.17/8.30 |-Branch one:
% 30.17/8.30 | (1132) all_0_46_46 = e0
% 30.17/8.30 |
% 30.17/8.30 | Equations (1132) can reduce 18 to:
% 30.17/8.30 | (199) ~ (all_0_42_42 = e0)
% 30.17/8.30 |
% 30.17/8.30 | Equations (1132) can reduce 38 to:
% 30.17/8.30 | (488) ~ (all_0_45_45 = e0)
% 30.17/8.30 |
% 30.17/8.30 | From (1132) and (89) follows:
% 30.17/8.30 | (11530) op(e0, e0) = all_0_32_32
% 30.17/8.30 |
% 30.17/8.30 +-Applying beta-rule and splitting (1245), into two cases.
% 30.17/8.30 |-Branch one:
% 30.17/8.30 | (1258) all_0_42_42 = e3
% 30.17/8.30 |
% 30.17/8.30 | Equations (1258) can reduce 520 to:
% 30.17/8.30 | (719) ~ (e4 = e3)
% 30.17/8.30 |
% 30.17/8.30 | Simplifying 719 yields:
% 30.17/8.30 | (34) ~ (e4 = e3)
% 30.17/8.30 |
% 30.17/8.30 | Equations (1258) can reduce 498 to:
% 30.17/8.30 | (223) ~ (e3 = e2)
% 30.17/8.30 |
% 30.17/8.30 | Equations (1258) can reduce 199 to:
% 30.17/8.30 | (66) ~ (e3 = e0)
% 30.17/8.30 |
% 30.17/8.30 | From (1258) and (243) follows:
% 30.17/8.30 | (11536) op(e0, e3) = all_0_30_30
% 30.17/8.30 |
% 30.17/8.30 +-Applying beta-rule and splitting (22), into two cases.
% 30.17/8.30 |-Branch one:
% 30.17/8.30 | (782) all_0_43_43 = e3
% 30.17/8.30 |
% 30.17/8.30 | Combining equations (502,782) yields a new equation:
% 30.17/8.30 | (660) e4 = e3
% 30.17/8.30 |
% 30.17/8.30 | Simplifying 660 yields:
% 30.17/8.30 | (359) e4 = e3
% 30.17/8.30 |
% 30.17/8.30 | Equations (359) can reduce 34 to:
% 30.17/8.30 | (270) $false
% 30.17/8.30 |
% 30.17/8.30 |-The branch is then unsatisfiable
% 30.17/8.30 |-Branch two:
% 30.17/8.30 | (786) ~ (all_0_43_43 = e3)
% 30.17/8.30 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 30.17/8.30 |
% 30.17/8.30 +-Applying beta-rule and splitting (787), into two cases.
% 30.17/8.30 |-Branch one:
% 30.17/8.30 | (858) all_0_44_44 = e3
% 30.17/8.30 |
% 30.17/8.30 | Combining equations (370,858) yields a new equation:
% 30.17/8.30 | (414) e3 = e2
% 30.17/8.30 |
% 30.17/8.30 | Equations (414) can reduce 223 to:
% 30.17/8.30 | (270) $false
% 30.17/8.30 |
% 30.17/8.30 |-The branch is then unsatisfiable
% 30.17/8.30 |-Branch two:
% 30.17/8.30 | (862) ~ (all_0_44_44 = e3)
% 30.17/8.30 | (1070) all_0_45_45 = e3 | all_0_46_46 = e3
% 30.17/8.30 |
% 30.17/8.30 +-Applying beta-rule and splitting (529), into two cases.
% 30.17/8.30 |-Branch one:
% 30.17/8.30 | (530) all_0_40_40 = e1
% 30.17/8.30 |
% 30.17/8.30 | Equations (530) can reduce 149 to:
% 30.17/8.30 | (643) ~ (all_0_57_57 = e1)
% 30.17/8.30 |
% 30.17/8.30 | Simplifying 643 yields:
% 30.17/8.30 | (644) ~ (all_0_57_57 = e1)
% 30.17/8.30 |
% 30.17/8.30 +-Applying beta-rule and splitting (105), into two cases.
% 30.17/8.30 |-Branch one:
% 30.17/8.30 | (374) all_0_45_45 = e2
% 30.17/8.30 |
% 30.17/8.30 | Equations (374) can reduce 434 to:
% 30.17/8.30 | (270) $false
% 30.17/8.30 |
% 30.17/8.30 |-The branch is then unsatisfiable
% 30.17/8.30 |-Branch two:
% 30.17/8.30 | (434) ~ (all_0_45_45 = e2)
% 30.17/8.30 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 30.17/8.30 |
% 30.17/8.30 +-Applying beta-rule and splitting (435), into two cases.
% 30.17/8.30 |-Branch one:
% 30.17/8.30 | (454) all_0_45_45 = e0
% 30.17/8.30 |
% 30.17/8.30 | Equations (454) can reduce 488 to:
% 30.17/8.30 | (270) $false
% 30.17/8.30 |
% 30.17/8.30 |-The branch is then unsatisfiable
% 30.17/8.30 |-Branch two:
% 30.17/8.30 | (488) ~ (all_0_45_45 = e0)
% 30.17/8.30 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 30.17/8.30 |
% 30.17/8.30 +-Applying beta-rule and splitting (489), into two cases.
% 30.17/8.30 |-Branch one:
% 30.17/8.30 | (505) all_0_45_45 = e3
% 30.17/8.30 |
% 30.17/8.30 | Equations (505) can reduce 352 to:
% 30.17/8.30 | (719) ~ (e4 = e3)
% 30.17/8.30 |
% 30.17/8.30 | Simplifying 719 yields:
% 30.17/8.30 | (34) ~ (e4 = e3)
% 30.17/8.30 |
% 30.17/8.30 | Instantiating formula (201) with e0, e3, all_0_30_30, all_0_56_56 and discharging atoms op(e0, e3) = all_0_30_30, op(e0, e3) = all_0_56_56, yields:
% 30.17/8.30 | (11562) all_0_30_30 = all_0_56_56
% 30.17/8.30 |
% 30.17/8.30 | Instantiating formula (201) with e0, e2, all_0_36_36, all_0_57_57 and discharging atoms op(e0, e2) = all_0_36_36, op(e0, e2) = all_0_57_57, yields:
% 30.17/8.30 | (11563) all_0_36_36 = all_0_57_57
% 30.17/8.30 |
% 30.17/8.30 | Instantiating formula (201) with e0, e0, all_0_32_32, e4 and discharging atoms op(e0, e0) = all_0_32_32, op(e0, e0) = e4, yields:
% 30.17/8.30 | (4556) all_0_32_32 = e4
% 30.17/8.30 |
% 30.17/8.30 +-Applying beta-rule and splitting (111), into two cases.
% 30.17/8.30 |-Branch one:
% 30.17/8.30 | (4557) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0)) | (all_0_34_34 = e2 & ~ (all_0_35_35 = e0))
% 30.17/8.30 |
% 30.17/8.30 +-Applying beta-rule and splitting (4557), into two cases.
% 30.17/8.30 |-Branch one:
% 30.17/8.30 | (4558) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0))
% 30.17/8.30 |
% 30.17/8.30 +-Applying beta-rule and splitting (4558), into two cases.
% 30.17/8.30 |-Branch one:
% 30.17/8.30 | (4559) all_0_30_30 = e4 & ~ (all_0_31_31 = e0)
% 30.17/8.30 |
% 30.17/8.30 | Applying alpha-rule on (4559) yields:
% 30.17/8.30 | (4560) all_0_30_30 = e4
% 30.17/8.30 | (4561) ~ (all_0_31_31 = e0)
% 30.17/8.30 |
% 30.17/8.31 | Combining equations (4560,11562) yields a new equation:
% 30.17/8.31 | (4744) all_0_56_56 = e4
% 30.17/8.31 |
% 30.17/8.31 | Equations (4744) can reduce 274 to:
% 30.17/8.31 | (270) $false
% 30.17/8.31 |
% 30.17/8.31 |-The branch is then unsatisfiable
% 30.17/8.31 |-Branch two:
% 30.17/8.31 | (4565) all_0_32_32 = e3 & ~ (all_0_33_33 = e0)
% 30.17/8.31 |
% 30.17/8.31 | Applying alpha-rule on (4565) yields:
% 30.17/8.31 | (4566) all_0_32_32 = e3
% 30.17/8.31 | (4567) ~ (all_0_33_33 = e0)
% 30.17/8.31 |
% 30.17/8.31 | Combining equations (4556,4566) yields a new equation:
% 30.17/8.31 | (660) e4 = e3
% 30.17/8.31 |
% 30.17/8.31 | Simplifying 660 yields:
% 30.17/8.31 | (359) e4 = e3
% 30.17/8.31 |
% 30.17/8.31 | Equations (359) can reduce 34 to:
% 30.17/8.31 | (270) $false
% 30.17/8.31 |
% 30.17/8.31 |-The branch is then unsatisfiable
% 30.17/8.31 |-Branch two:
% 30.17/8.31 | (4571) all_0_34_34 = e2 & ~ (all_0_35_35 = e0)
% 30.17/8.31 |
% 30.17/8.31 | Applying alpha-rule on (4571) yields:
% 30.17/8.31 | (4572) all_0_34_34 = e2
% 30.17/8.31 | (4573) ~ (all_0_35_35 = e0)
% 30.17/8.31 |
% 30.17/8.31 | Combining equations (11393,4572) yields a new equation:
% 30.17/8.31 | (11581) all_0_58_58 = e2
% 30.17/8.31 |
% 30.17/8.31 | Simplifying 11581 yields:
% 30.17/8.31 | (396) all_0_58_58 = e2
% 30.17/8.31 |
% 30.17/8.31 | Equations (396) can reduce 376 to:
% 30.17/8.31 | (270) $false
% 30.17/8.31 |
% 30.17/8.31 |-The branch is then unsatisfiable
% 30.17/8.31 |-Branch two:
% 30.17/8.31 | (4577) all_0_36_36 = e1 & ~ (all_0_37_37 = e0)
% 30.17/8.31 |
% 30.17/8.31 | Applying alpha-rule on (4577) yields:
% 30.17/8.31 | (4578) all_0_36_36 = e1
% 30.17/8.31 | (4579) ~ (all_0_37_37 = e0)
% 30.17/8.31 |
% 30.17/8.31 | Combining equations (11563,4578) yields a new equation:
% 30.17/8.31 | (11587) all_0_57_57 = e1
% 30.17/8.31 |
% 30.17/8.31 | Simplifying 11587 yields:
% 30.17/8.31 | (997) all_0_57_57 = e1
% 30.17/8.31 |
% 30.17/8.31 | Equations (997) can reduce 644 to:
% 30.17/8.31 | (270) $false
% 30.17/8.31 |
% 30.17/8.31 |-The branch is then unsatisfiable
% 30.17/8.31 |-Branch two:
% 30.17/8.31 | (354) ~ (all_0_45_45 = e3)
% 30.17/8.31 | (363) all_0_45_45 = e4
% 30.17/8.31 |
% 30.17/8.31 | Equations (363) can reduce 352 to:
% 30.17/8.31 | (270) $false
% 30.17/8.31 |
% 30.17/8.31 |-The branch is then unsatisfiable
% 30.17/8.31 |-Branch two:
% 30.17/8.31 | (534) ~ (all_0_40_40 = e1)
% 30.17/8.31 | (535) all_0_41_41 = e1 | all_0_42_42 = e1
% 30.17/8.31 |
% 30.17/8.31 +-Applying beta-rule and splitting (1070), into two cases.
% 30.17/8.31 |-Branch one:
% 30.17/8.31 | (505) all_0_45_45 = e3
% 30.17/8.31 |
% 30.17/8.31 | Equations (505) can reduce 26 to:
% 30.17/8.31 | (136) ~ (e3 = e1)
% 30.17/8.31 |
% 30.17/8.31 +-Applying beta-rule and splitting (535), into two cases.
% 30.17/8.31 |-Branch one:
% 30.17/8.31 | (536) all_0_41_41 = e1
% 30.17/8.31 |
% 30.17/8.31 | Combining equations (358,536) yields a new equation:
% 30.17/8.31 | (525) e4 = e1
% 30.17/8.31 |
% 30.17/8.31 | Simplifying 525 yields:
% 30.17/8.31 | (526) e4 = e1
% 30.17/8.31 |
% 30.17/8.31 | Equations (526) can reduce 251 to:
% 30.17/8.31 | (270) $false
% 30.17/8.31 |
% 30.17/8.31 |-The branch is then unsatisfiable
% 30.17/8.31 |-Branch two:
% 30.17/8.31 | (540) ~ (all_0_41_41 = e1)
% 30.17/8.31 | (541) all_0_42_42 = e1
% 30.17/8.31 |
% 30.17/8.31 | Combining equations (1258,541) yields a new equation:
% 30.17/8.31 | (537) e3 = e1
% 30.17/8.31 |
% 30.17/8.31 | Simplifying 537 yields:
% 30.17/8.31 | (538) e3 = e1
% 30.17/8.31 |
% 30.17/8.31 | Equations (538) can reduce 136 to:
% 30.17/8.31 | (270) $false
% 30.17/8.31 |
% 30.17/8.31 |-The branch is then unsatisfiable
% 30.17/8.31 |-Branch two:
% 30.17/8.31 | (354) ~ (all_0_45_45 = e3)
% 30.17/8.31 | (1091) all_0_46_46 = e3
% 30.17/8.31 |
% 30.17/8.31 | Combining equations (1132,1091) yields a new equation:
% 30.17/8.31 | (784) e3 = e0
% 30.17/8.31 |
% 30.17/8.31 | Equations (784) can reduce 66 to:
% 30.17/8.31 | (270) $false
% 30.17/8.31 |
% 30.17/8.31 |-The branch is then unsatisfiable
% 30.17/8.31 |-Branch two:
% 30.17/8.31 | (1316) ~ (all_0_42_42 = e3)
% 30.17/8.31 | (1317) all_0_42_42 = e4 | all_0_42_42 = e1
% 30.17/8.31 |
% 30.17/8.31 +-Applying beta-rule and splitting (1317), into two cases.
% 30.17/8.31 |-Branch one:
% 30.17/8.31 | (541) all_0_42_42 = e1
% 30.17/8.31 |
% 30.17/8.31 | Equations (541) can reduce 640 to:
% 30.17/8.31 | (270) $false
% 30.17/8.31 |
% 30.17/8.31 |-The branch is then unsatisfiable
% 30.17/8.31 |-Branch two:
% 30.17/8.31 | (640) ~ (all_0_42_42 = e1)
% 30.17/8.31 | (512) all_0_42_42 = e4
% 30.17/8.31 |
% 30.17/8.31 | Equations (512) can reduce 520 to:
% 30.17/8.31 | (270) $false
% 30.17/8.31 |
% 30.17/8.31 |-The branch is then unsatisfiable
% 30.17/8.31 |-Branch two:
% 30.17/8.31 | (1010) ~ (all_0_46_46 = e0)
% 30.17/8.31 | (3629) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 30.17/8.31 |
% 30.17/8.31 +-Applying beta-rule and splitting (116), into two cases.
% 30.17/8.31 |-Branch one:
% 30.17/8.31 | (411) all_0_43_43 = e0
% 30.17/8.31 |
% 30.17/8.31 | Combining equations (502,411) yields a new equation:
% 30.17/8.31 | (478) e4 = e0
% 30.17/8.31 |
% 30.17/8.31 | Simplifying 478 yields:
% 30.17/8.31 | (479) e4 = e0
% 30.17/8.31 |
% 30.17/8.31 | Equations (479) can reduce 6 to:
% 30.17/8.31 | (270) $false
% 30.17/8.31 |
% 30.17/8.31 |-The branch is then unsatisfiable
% 30.17/8.31 |-Branch two:
% 30.17/8.31 | (455) ~ (all_0_43_43 = e0)
% 30.17/8.31 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 30.17/8.31 |
% 30.17/8.31 +-Applying beta-rule and splitting (1122), into two cases.
% 30.17/8.31 |-Branch one:
% 30.17/8.31 | (621) all_0_44_44 = e0
% 30.17/8.31 |
% 30.17/8.31 | Combining equations (370,621) yields a new equation:
% 30.17/8.31 | (622) e2 = e0
% 30.17/8.31 |
% 30.17/8.31 | Simplifying 622 yields:
% 30.17/8.31 | (316) e2 = e0
% 30.17/8.31 |
% 30.17/8.31 | Equations (316) can reduce 57 to:
% 30.17/8.31 | (270) $false
% 30.17/8.31 |
% 30.17/8.31 |-The branch is then unsatisfiable
% 30.17/8.31 |-Branch two:
% 30.17/8.31 | (625) ~ (all_0_44_44 = e0)
% 30.17/8.31 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 30.17/8.31 |
% 30.17/8.31 +-Applying beta-rule and splitting (1128), into two cases.
% 30.17/8.31 |-Branch one:
% 30.17/8.31 | (454) all_0_45_45 = e0
% 30.17/8.31 |
% 30.17/8.31 | Equations (454) can reduce 128 to:
% 30.17/8.31 | (3103) ~ (all_0_53_53 = e0)
% 30.17/8.31 |
% 30.17/8.31 | Simplifying 3103 yields:
% 30.17/8.31 | (584) ~ (all_0_53_53 = e0)
% 30.17/8.31 |
% 30.17/8.31 | Equations (454) can reduce 108 to:
% 30.17/8.31 | (3530) ~ (all_0_58_58 = e0)
% 30.17/8.31 |
% 30.17/8.31 | Simplifying 3530 yields:
% 30.17/8.31 | (431) ~ (all_0_58_58 = e0)
% 30.17/8.31 |
% 30.17/8.31 | Equations (454) can reduce 434 to:
% 30.17/8.31 | (566) ~ (e2 = e0)
% 30.17/8.31 |
% 30.17/8.31 | Simplifying 566 yields:
% 30.17/8.31 | (57) ~ (e2 = e0)
% 30.17/8.31 |
% 30.17/8.31 +-Applying beta-rule and splitting (176), into two cases.
% 30.17/8.31 |-Branch one:
% 30.17/8.31 | (830) all_0_56_56 = e0
% 30.17/8.31 |
% 30.17/8.31 | Equations (830) can reduce 419 to:
% 30.17/8.31 | (270) $false
% 30.17/8.31 |
% 30.17/8.31 |-The branch is then unsatisfiable
% 30.17/8.31 |-Branch two:
% 30.17/8.31 | (419) ~ (all_0_56_56 = e0)
% 30.17/8.31 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 30.17/8.31 |
% 30.17/8.31 +-Applying beta-rule and splitting (834), into two cases.
% 30.17/8.31 |-Branch one:
% 30.17/8.31 | (2258) all_0_57_57 = e0
% 30.17/8.31 |
% 30.17/8.31 | Equations (2258) can reduce 235 to:
% 30.17/8.31 | (925) ~ (all_0_52_52 = e0)
% 30.17/8.31 |
% 30.17/8.31 | Equations (2258) can reduce 335 to:
% 30.17/8.31 | (566) ~ (e2 = e0)
% 30.17/8.31 |
% 30.17/8.31 | Simplifying 566 yields:
% 30.17/8.31 | (57) ~ (e2 = e0)
% 30.17/8.31 |
% 30.17/8.31 +-Applying beta-rule and splitting (64), into two cases.
% 30.17/8.31 |-Branch one:
% 30.17/8.31 | (954) all_0_51_51 = e0
% 30.17/8.31 |
% 30.17/8.31 | Equations (954) can reduce 987 to:
% 30.17/8.31 | (270) $false
% 30.17/8.31 |
% 30.17/8.31 |-The branch is then unsatisfiable
% 30.17/8.31 |-Branch two:
% 30.17/8.31 | (987) ~ (all_0_51_51 = e0)
% 30.17/8.31 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 30.17/8.31 |
% 30.17/8.31 +-Applying beta-rule and splitting (3067), into two cases.
% 30.17/8.31 |-Branch one:
% 30.17/8.31 | (827) all_0_52_52 = e0
% 30.17/8.31 |
% 30.17/8.31 | Equations (827) can reduce 925 to:
% 30.17/8.31 | (270) $false
% 30.17/8.31 |
% 30.17/8.31 |-The branch is then unsatisfiable
% 30.17/8.31 |-Branch two:
% 30.17/8.31 | (925) ~ (all_0_52_52 = e0)
% 30.17/8.31 | (3073) all_0_53_53 = e0 | all_0_54_54 = e0
% 30.17/8.31 |
% 30.17/8.31 +-Applying beta-rule and splitting (3073), into two cases.
% 30.17/8.31 |-Branch one:
% 30.17/8.31 | (423) all_0_53_53 = e0
% 30.17/8.31 |
% 30.17/8.31 | Equations (423) can reduce 584 to:
% 30.17/8.31 | (270) $false
% 30.17/8.31 |
% 30.17/8.31 |-The branch is then unsatisfiable
% 30.17/8.31 |-Branch two:
% 30.17/8.31 | (584) ~ (all_0_53_53 = e0)
% 30.17/8.32 | (3084) all_0_54_54 = e0
% 30.17/8.32 |
% 30.17/8.32 | Combining equations (3084,3657) yields a new equation:
% 30.17/8.32 | (316) e2 = e0
% 30.17/8.32 |
% 30.17/8.32 | Equations (316) can reduce 57 to:
% 30.17/8.32 | (270) $false
% 30.17/8.32 |
% 30.17/8.32 |-The branch is then unsatisfiable
% 30.17/8.32 |-Branch two:
% 30.17/8.32 | (2301) ~ (all_0_57_57 = e0)
% 30.17/8.32 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 30.17/8.32 |
% 30.17/8.32 +-Applying beta-rule and splitting (64), into two cases.
% 30.17/8.32 |-Branch one:
% 30.17/8.32 | (954) all_0_51_51 = e0
% 30.17/8.32 |
% 30.17/8.32 | Equations (954) can reduce 987 to:
% 30.17/8.32 | (270) $false
% 30.17/8.32 |
% 30.17/8.32 |-The branch is then unsatisfiable
% 30.17/8.32 |-Branch two:
% 30.17/8.32 | (987) ~ (all_0_51_51 = e0)
% 30.17/8.32 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 30.17/8.32 |
% 30.17/8.32 +-Applying beta-rule and splitting (3067), into two cases.
% 30.17/8.32 |-Branch one:
% 30.17/8.32 | (827) all_0_52_52 = e0
% 30.17/8.32 |
% 30.17/8.32 | Equations (827) can reduce 230 to:
% 30.17/8.32 | (456) ~ (e4 = e0)
% 30.17/8.32 |
% 30.17/8.32 | Simplifying 456 yields:
% 30.17/8.32 | (6) ~ (e4 = e0)
% 30.17/8.32 |
% 30.17/8.32 +-Applying beta-rule and splitting (2302), into two cases.
% 30.17/8.32 |-Branch one:
% 30.17/8.32 | (585) all_0_58_58 = e0
% 30.17/8.32 |
% 30.17/8.32 | Equations (585) can reduce 431 to:
% 30.17/8.32 | (270) $false
% 30.17/8.32 |
% 30.17/8.32 |-The branch is then unsatisfiable
% 30.17/8.32 |-Branch two:
% 30.17/8.32 | (431) ~ (all_0_58_58 = e0)
% 30.17/8.32 | (2308) all_0_59_59 = e0
% 30.17/8.32 |
% 30.17/8.32 | Combining equations (2308,402) yields a new equation:
% 30.17/8.32 | (479) e4 = e0
% 30.17/8.32 |
% 30.17/8.32 | Equations (479) can reduce 6 to:
% 30.17/8.32 | (270) $false
% 30.17/8.32 |
% 30.17/8.32 |-The branch is then unsatisfiable
% 30.17/8.32 |-Branch two:
% 30.17/8.32 | (925) ~ (all_0_52_52 = e0)
% 30.17/8.32 | (3073) all_0_53_53 = e0 | all_0_54_54 = e0
% 30.17/8.32 |
% 30.17/8.32 +-Applying beta-rule and splitting (3073), into two cases.
% 30.17/8.32 |-Branch one:
% 30.17/8.32 | (423) all_0_53_53 = e0
% 30.17/8.32 |
% 30.17/8.32 | Equations (423) can reduce 584 to:
% 30.17/8.32 | (270) $false
% 30.17/8.32 |
% 30.17/8.32 |-The branch is then unsatisfiable
% 30.17/8.32 |-Branch two:
% 30.17/8.32 | (584) ~ (all_0_53_53 = e0)
% 30.17/8.32 | (3084) all_0_54_54 = e0
% 30.17/8.32 |
% 30.17/8.32 | Combining equations (3084,3657) yields a new equation:
% 30.17/8.32 | (316) e2 = e0
% 30.17/8.32 |
% 30.17/8.32 | Equations (316) can reduce 57 to:
% 30.17/8.32 | (270) $false
% 30.17/8.32 |
% 30.17/8.32 |-The branch is then unsatisfiable
% 30.17/8.32 |-Branch two:
% 30.17/8.32 | (488) ~ (all_0_45_45 = e0)
% 30.17/8.32 | (1132) all_0_46_46 = e0
% 30.17/8.32 |
% 30.17/8.32 | Equations (1132) can reduce 1010 to:
% 30.17/8.32 | (270) $false
% 30.17/8.32 |
% 30.17/8.32 |-The branch is then unsatisfiable
% 30.17/8.32 |-Branch two:
% 30.17/8.32 | (291) ~ (all_0_39_39 = e2)
% 30.17/8.32 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 30.17/8.32 |
% 30.17/8.32 +-Applying beta-rule and splitting (339), into two cases.
% 30.17/8.32 |-Branch one:
% 30.17/8.32 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 30.17/8.32 |
% 30.17/8.32 +-Applying beta-rule and splitting (340), into two cases.
% 30.17/8.32 |-Branch one:
% 30.17/8.32 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 30.17/8.32 |
% 30.17/8.32 | Applying alpha-rule on (341) yields:
% 30.17/8.32 | (342) all_0_0_0 = e1
% 30.17/8.32 | (343) ~ (all_0_1_1 = e4)
% 30.17/8.32 |
% 30.17/8.32 | Combining equations (342,9064) yields a new equation:
% 30.17/8.32 | (571) e1 = e0
% 30.17/8.32 |
% 30.17/8.32 | Simplifying 571 yields:
% 30.17/8.32 | (560) e1 = e0
% 30.17/8.32 |
% 30.17/8.32 | Equations (560) can reduce 132 to:
% 30.17/8.32 | (270) $false
% 30.17/8.32 |
% 30.17/8.32 |-The branch is then unsatisfiable
% 30.17/8.32 |-Branch two:
% 30.17/8.32 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 30.17/8.32 |
% 30.17/8.32 | Applying alpha-rule on (346) yields:
% 30.17/8.32 | (347) all_0_2_2 = e0
% 30.17/8.32 | (348) ~ (all_0_3_3 = e4)
% 30.17/8.32 |
% 30.17/8.32 | Combining equations (9065,347) yields a new equation:
% 30.17/8.32 | (11698) all_0_40_40 = e0
% 30.17/8.32 |
% 30.17/8.32 | Simplifying 11698 yields:
% 30.17/8.32 | (11467) all_0_40_40 = e0
% 30.17/8.32 |
% 30.17/8.32 | Equations (11467) can reduce 238 to:
% 30.17/8.32 | (270) $false
% 30.17/8.32 |
% 30.17/8.32 |-The branch is then unsatisfiable
% 30.17/8.32 |-Branch two:
% 30.17/8.32 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 30.17/8.32 |
% 30.17/8.32 | Applying alpha-rule on (350) yields:
% 30.17/8.32 | (351) all_0_41_41 = e3
% 30.17/8.32 | (352) ~ (all_0_45_45 = e4)
% 30.17/8.32 |
% 30.17/8.32 | Combining equations (358,351) yields a new equation:
% 30.17/8.32 | (660) e4 = e3
% 30.17/8.32 |
% 30.17/8.32 | Simplifying 660 yields:
% 30.17/8.32 | (359) e4 = e3
% 30.17/8.32 |
% 30.17/8.32 | Equations (359) can reduce 34 to:
% 30.17/8.32 | (270) $false
% 30.17/8.32 |
% 30.17/8.32 |-The branch is then unsatisfiable
% 30.17/8.32 |-Branch two:
% 30.17/8.32 | (510) ~ (all_0_43_43 = e4)
% 30.17/8.32 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 30.17/8.32 |
% 30.17/8.32 +-Applying beta-rule and splitting (511), into two cases.
% 30.17/8.32 |-Branch one:
% 30.17/8.32 | (363) all_0_45_45 = e4
% 30.17/8.32 |
% 30.17/8.32 | Equations (363) can reduce 352 to:
% 30.17/8.32 | (270) $false
% 30.17/8.32 |
% 30.17/8.32 |-The branch is then unsatisfiable
% 30.17/8.32 |-Branch two:
% 30.17/8.32 | (352) ~ (all_0_45_45 = e4)
% 30.17/8.32 | (517) all_0_46_46 = e4
% 30.17/8.32 |
% 30.17/8.32 | Equations (517) can reduce 805 to:
% 30.17/8.32 | (270) $false
% 30.17/8.32 |
% 30.17/8.32 |-The branch is then unsatisfiable
% 30.17/8.32 |-Branch two:
% 30.17/8.32 | (361) ~ (all_0_41_41 = e4)
% 30.17/8.32 | (512) all_0_42_42 = e4
% 30.17/8.32 |
% 30.17/8.32 | Equations (512) can reduce 520 to:
% 30.17/8.32 | (270) $false
% 30.17/8.32 |
% 30.17/8.32 |-The branch is then unsatisfiable
% 30.17/8.32 |-Branch two:
% 30.17/8.32 | (333) ~ (all_0_44_44 = e2)
% 30.17/8.32 | (373) all_0_44_44 = e3 | all_0_44_44 = e0
% 30.17/8.32 |
% 30.17/8.32 +-Applying beta-rule and splitting (607), into two cases.
% 30.17/8.32 |-Branch one:
% 30.17/8.32 | (370) all_0_44_44 = e2
% 30.17/8.32 |
% 30.17/8.32 | Equations (370) can reduce 333 to:
% 30.17/8.32 | (270) $false
% 30.17/8.32 |
% 30.17/8.32 |-The branch is then unsatisfiable
% 30.17/8.32 |-Branch two:
% 30.17/8.32 | (333) ~ (all_0_44_44 = e2)
% 30.17/8.32 | (3377) all_0_52_52 = e2 | all_0_57_57 = e2
% 30.17/8.32 |
% 30.17/8.32 +-Applying beta-rule and splitting (3377), into two cases.
% 30.17/8.32 |-Branch one:
% 30.17/8.32 | (685) all_0_52_52 = e2
% 30.17/8.32 |
% 30.17/8.32 | Equations (685) can reduce 137 to:
% 30.17/8.32 | (602) ~ (all_0_40_40 = e2)
% 30.17/8.32 |
% 30.17/8.32 | Equations (685) can reduce 154 to:
% 30.17/8.32 | (255) ~ (all_0_51_51 = e2)
% 30.17/8.32 |
% 30.17/8.32 | Equations (685) can reduce 213 to:
% 30.17/8.32 | (258) ~ (all_0_53_53 = e2)
% 30.17/8.32 |
% 30.17/8.32 | Simplifying 258 yields:
% 30.17/8.32 | (259) ~ (all_0_53_53 = e2)
% 30.17/8.32 |
% 30.17/8.32 | Equations (685) can reduce 118 to:
% 30.17/8.32 | (260) ~ (all_0_54_54 = e2)
% 30.17/8.32 |
% 30.17/8.32 | Simplifying 260 yields:
% 30.17/8.32 | (261) ~ (all_0_54_54 = e2)
% 30.17/8.32 |
% 30.17/8.32 | Equations (685) can reduce 235 to:
% 30.17/8.32 | (334) ~ (all_0_57_57 = e2)
% 30.17/8.32 |
% 30.17/8.32 | Simplifying 334 yields:
% 30.17/8.32 | (335) ~ (all_0_57_57 = e2)
% 30.17/8.32 |
% 30.17/8.32 | Equations (685) can reduce 230 to:
% 30.17/8.32 | (377) ~ (e4 = e2)
% 30.17/8.32 |
% 30.17/8.32 | Simplifying 377 yields:
% 30.17/8.32 | (231) ~ (e4 = e2)
% 30.17/8.32 |
% 30.17/8.32 | From (685) and (27) follows:
% 30.17/8.32 | (11734) op(e2, e2) = all_0_17_17
% 30.17/8.32 |
% 30.17/8.32 | Instantiating formula (201) with e2, e2, all_0_17_17, e4 and discharging atoms op(e2, e2) = all_0_17_17, op(e2, e2) = e4, yields:
% 30.17/8.32 | (11735) all_0_17_17 = e4
% 30.17/8.32 |
% 30.17/8.32 +-Applying beta-rule and splitting (8), into two cases.
% 30.17/8.32 |-Branch one:
% 30.17/8.32 | (530) all_0_40_40 = e1
% 30.17/8.32 |
% 30.17/8.32 | Combining equations (530,9065) yields a new equation:
% 30.17/8.32 | (11737) all_0_2_2 = e1
% 30.17/8.32 |
% 30.17/8.32 | Equations (530) can reduce 147 to:
% 30.17/8.32 | (637) ~ (all_0_41_41 = e1)
% 30.17/8.32 |
% 30.17/8.32 | Simplifying 637 yields:
% 30.17/8.32 | (540) ~ (all_0_41_41 = e1)
% 30.17/8.33 |
% 30.17/8.33 | Equations (530) can reduce 145 to:
% 30.17/8.33 | (639) ~ (all_0_42_42 = e1)
% 30.17/8.33 |
% 30.17/8.33 | Simplifying 639 yields:
% 30.17/8.33 | (640) ~ (all_0_42_42 = e1)
% 30.17/8.33 |
% 30.17/8.33 | Equations (530) can reduce 15 to:
% 30.17/8.33 | (4822) ~ (all_0_44_44 = e1)
% 30.17/8.33 |
% 30.17/8.33 | Simplifying 4822 yields:
% 30.17/8.33 | (131) ~ (all_0_44_44 = e1)
% 30.17/8.33 |
% 30.17/8.33 | Equations (530) can reduce 149 to:
% 30.17/8.33 | (643) ~ (all_0_57_57 = e1)
% 30.17/8.33 |
% 30.17/8.33 | Simplifying 643 yields:
% 30.17/8.33 | (644) ~ (all_0_57_57 = e1)
% 30.17/8.33 |
% 30.17/8.33 | Equations (530) can reduce 233 to:
% 30.17/8.33 | (1021) ~ (e4 = e1)
% 30.17/8.33 |
% 30.17/8.33 | Simplifying 1021 yields:
% 30.17/8.33 | (251) ~ (e4 = e1)
% 30.17/8.33 |
% 30.17/8.33 | Equations (530) can reduce 602 to:
% 30.17/8.33 | (645) ~ (e2 = e1)
% 30.17/8.33 |
% 30.17/8.33 | Simplifying 645 yields:
% 30.17/8.33 | (141) ~ (e2 = e1)
% 30.17/8.33 |
% 30.17/8.33 | From (530) and (68) follows:
% 30.17/8.33 | (648) op(e2, e1) = all_0_13_13
% 30.17/8.33 |
% 30.17/8.33 | Instantiating formula (201) with e2, e1, all_0_13_13, e2 and discharging atoms op(e2, e1) = all_0_13_13, op(e2, e1) = e2, yields:
% 30.17/8.33 | (4829) all_0_13_13 = e2
% 30.17/8.33 |
% 30.17/8.33 +-Applying beta-rule and splitting (9), into two cases.
% 30.17/8.33 |-Branch one:
% 30.17/8.33 | (621) all_0_44_44 = e0
% 30.17/8.33 |
% 30.17/8.33 | Equations (621) can reduce 241 to:
% 30.17/8.33 | (455) ~ (all_0_43_43 = e0)
% 30.17/8.33 |
% 30.17/8.33 | Equations (621) can reduce 174 to:
% 30.17/8.33 | (1057) ~ (all_0_46_46 = e0)
% 30.17/8.33 |
% 30.17/8.33 | Simplifying 1057 yields:
% 30.17/8.33 | (1010) ~ (all_0_46_46 = e0)
% 30.17/8.33 |
% 30.17/8.33 | Equations (621) can reduce 10 to:
% 30.17/8.33 | (9326) ~ (all_0_57_57 = e0)
% 30.17/8.33 |
% 30.17/8.33 | Simplifying 9326 yields:
% 30.17/8.33 | (2301) ~ (all_0_57_57 = e0)
% 30.17/8.33 |
% 30.17/8.33 | Equations (621) can reduce 45 to:
% 30.17/8.33 | (456) ~ (e4 = e0)
% 30.17/8.33 |
% 30.17/8.33 | Simplifying 456 yields:
% 30.17/8.33 | (6) ~ (e4 = e0)
% 30.17/8.33 |
% 30.17/8.33 | Equations (621) can reduce 131 to:
% 30.17/8.33 | (568) ~ (e1 = e0)
% 30.17/8.33 |
% 30.17/8.33 | Simplifying 568 yields:
% 30.17/8.33 | (132) ~ (e1 = e0)
% 30.17/8.33 |
% 30.17/8.33 | From (621) and (148) follows:
% 30.17/8.33 | (11762) op(e3, e2) = e0
% 30.17/8.33 |
% 30.17/8.33 +-Applying beta-rule and splitting (33), into two cases.
% 30.17/8.33 |-Branch one:
% 30.17/8.33 | (392) all_0_57_57 = e2
% 30.17/8.33 |
% 30.17/8.33 | Equations (392) can reduce 335 to:
% 30.17/8.33 | (270) $false
% 30.17/8.33 |
% 30.17/8.33 |-The branch is then unsatisfiable
% 30.17/8.33 |-Branch two:
% 30.17/8.33 | (335) ~ (all_0_57_57 = e2)
% 30.17/8.33 | (670) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 30.17/8.33 |
% 30.17/8.33 +-Applying beta-rule and splitting (221), into two cases.
% 30.17/8.33 |-Branch one:
% 30.17/8.33 | (1132) all_0_46_46 = e0
% 30.17/8.33 |
% 30.17/8.33 | Equations (1132) can reduce 1010 to:
% 30.17/8.33 | (270) $false
% 30.17/8.33 |
% 30.17/8.33 |-The branch is then unsatisfiable
% 30.17/8.33 |-Branch two:
% 30.17/8.33 | (1010) ~ (all_0_46_46 = e0)
% 30.17/8.33 | (3629) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 30.17/8.33 |
% 30.17/8.33 +-Applying beta-rule and splitting (3629), into two cases.
% 30.17/8.33 |-Branch one:
% 30.17/8.33 | (563) all_0_49_49 = e0
% 30.17/8.33 |
% 30.17/8.33 | Combining equations (563,589) yields a new equation:
% 30.17/8.33 | (560) e1 = e0
% 30.17/8.33 |
% 30.17/8.33 | Equations (560) can reduce 132 to:
% 30.17/8.33 | (270) $false
% 30.17/8.33 |
% 30.17/8.33 |-The branch is then unsatisfiable
% 30.17/8.33 |-Branch two:
% 30.17/8.33 | (1231) ~ (all_0_49_49 = e0)
% 30.17/8.33 | (3638) all_0_54_54 = e0 | all_0_59_59 = e0
% 30.17/8.33 |
% 30.17/8.33 +-Applying beta-rule and splitting (670), into two cases.
% 30.17/8.33 |-Branch one:
% 30.17/8.33 | (2258) all_0_57_57 = e0
% 30.17/8.33 |
% 30.17/8.33 | Equations (2258) can reduce 2301 to:
% 30.17/8.33 | (270) $false
% 30.17/8.33 |
% 30.17/8.33 |-The branch is then unsatisfiable
% 30.17/8.33 |-Branch two:
% 30.17/8.33 | (2301) ~ (all_0_57_57 = e0)
% 30.17/8.33 | (9345) all_0_57_57 = e3 | all_0_57_57 = e1
% 30.17/8.33 |
% 30.17/8.33 +-Applying beta-rule and splitting (3638), into two cases.
% 30.17/8.33 |-Branch one:
% 30.17/8.33 | (3084) all_0_54_54 = e0
% 30.17/8.33 |
% 30.17/8.33 | Equations (3084) can reduce 50 to:
% 30.17/8.33 | (987) ~ (all_0_51_51 = e0)
% 30.17/8.33 |
% 30.17/8.33 | Equations (3084) can reduce 936 to:
% 30.17/8.33 | (456) ~ (e4 = e0)
% 30.17/8.33 |
% 30.17/8.33 | Simplifying 456 yields:
% 30.17/8.33 | (6) ~ (e4 = e0)
% 30.17/8.33 |
% 30.17/8.33 | From (3084) and (138) follows:
% 30.17/8.33 | (6320) op(e0, e0) = all_0_36_36
% 30.17/8.33 |
% 30.17/8.33 +-Applying beta-rule and splitting (133), into two cases.
% 30.17/8.33 |-Branch one:
% 30.17/8.33 | (671) all_0_40_40 = e3
% 30.17/8.33 |
% 30.17/8.33 | Combining equations (530,671) yields a new equation:
% 30.17/8.33 | (538) e3 = e1
% 30.17/8.33 |
% 30.17/8.33 | Equations (538) can reduce 136 to:
% 30.17/8.33 | (270) $false
% 30.17/8.33 |
% 30.17/8.33 |-The branch is then unsatisfiable
% 30.17/8.33 |-Branch two:
% 30.17/8.33 | (675) ~ (all_0_40_40 = e3)
% 30.17/8.33 | (676) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 30.17/8.33 |
% 30.17/8.33 +-Applying beta-rule and splitting (676), into two cases.
% 30.17/8.33 |-Branch one:
% 30.17/8.33 | (858) all_0_44_44 = e3
% 30.17/8.33 |
% 30.17/8.33 | Combining equations (621,858) yields a new equation:
% 30.17/8.33 | (784) e3 = e0
% 30.17/8.33 |
% 30.17/8.33 | Equations (784) can reduce 66 to:
% 30.17/8.33 | (270) $false
% 30.17/8.33 |
% 30.17/8.33 |-The branch is then unsatisfiable
% 30.17/8.33 |-Branch two:
% 30.17/8.33 | (862) ~ (all_0_44_44 = e3)
% 30.17/8.33 | (863) all_0_52_52 = e3 | all_0_57_57 = e3
% 30.17/8.33 |
% 30.17/8.33 +-Applying beta-rule and splitting (863), into two cases.
% 30.17/8.33 |-Branch one:
% 30.17/8.33 | (864) all_0_52_52 = e3
% 30.17/8.33 |
% 30.17/8.33 | Combining equations (685,864) yields a new equation:
% 30.17/8.33 | (414) e3 = e2
% 30.17/8.33 |
% 30.17/8.33 | Equations (414) can reduce 223 to:
% 30.17/8.33 | (270) $false
% 30.17/8.33 |
% 30.17/8.33 |-The branch is then unsatisfiable
% 30.17/8.33 |-Branch two:
% 30.17/8.33 | (826) ~ (all_0_52_52 = e3)
% 30.17/8.33 | (869) all_0_57_57 = e3
% 30.17/8.33 |
% 30.17/8.33 | Equations (869) can reduce 104 to:
% 30.17/8.33 | (767) ~ (all_0_56_56 = e3)
% 30.17/8.33 |
% 30.17/8.33 | Equations (869) can reduce 2301 to:
% 30.17/8.33 | (66) ~ (e3 = e0)
% 30.17/8.33 |
% 30.17/8.33 | From (869) and (120) follows:
% 30.17/8.33 | (11802) op(e0, e3) = all_0_20_20
% 30.17/8.33 |
% 30.17/8.33 +-Applying beta-rule and splitting (176), into two cases.
% 30.17/8.33 |-Branch one:
% 30.17/8.33 | (830) all_0_56_56 = e0
% 30.17/8.33 |
% 30.17/8.33 | Equations (830) can reduce 419 to:
% 30.17/8.33 | (270) $false
% 30.17/8.33 |
% 30.17/8.33 |-The branch is then unsatisfiable
% 30.17/8.33 |-Branch two:
% 30.17/8.33 | (419) ~ (all_0_56_56 = e0)
% 30.17/8.33 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 30.17/8.33 |
% 30.17/8.33 +-Applying beta-rule and splitting (834), into two cases.
% 30.17/8.33 |-Branch one:
% 30.17/8.33 | (2258) all_0_57_57 = e0
% 30.17/8.33 |
% 30.17/8.33 | Combining equations (2258,869) yields a new equation:
% 30.17/8.33 | (784) e3 = e0
% 30.17/8.33 |
% 30.17/8.33 | Equations (784) can reduce 66 to:
% 30.17/8.33 | (270) $false
% 30.17/8.33 |
% 30.17/8.33 |-The branch is then unsatisfiable
% 30.17/8.33 |-Branch two:
% 30.17/8.33 | (2301) ~ (all_0_57_57 = e0)
% 30.17/8.33 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 30.17/8.33 |
% 30.17/8.33 +-Applying beta-rule and splitting (2302), into two cases.
% 30.17/8.33 |-Branch one:
% 30.17/8.33 | (585) all_0_58_58 = e0
% 30.17/8.33 |
% 30.17/8.33 | Combining equations (585,11393) yields a new equation:
% 30.17/8.33 | (6278) all_0_34_34 = e0
% 30.17/8.33 |
% 30.17/8.33 | Equations (585) can reduce 157 to:
% 30.17/8.33 | (232) ~ (all_0_41_41 = e0)
% 30.17/8.33 |
% 30.17/8.33 | Equations (585) can reduce 108 to:
% 30.17/8.33 | (488) ~ (all_0_45_45 = e0)
% 30.17/8.33 |
% 30.17/8.33 | Equations (585) can reduce 70 to:
% 30.17/8.33 | (584) ~ (all_0_53_53 = e0)
% 30.17/8.33 |
% 30.17/8.33 | Equations (585) can reduce 81 to:
% 30.34/8.33 | (419) ~ (all_0_56_56 = e0)
% 30.34/8.33 |
% 30.34/8.33 +-Applying beta-rule and splitting (52), into two cases.
% 30.34/8.33 |-Branch one:
% 30.34/8.33 | (536) all_0_41_41 = e1
% 30.34/8.33 |
% 30.34/8.33 | Equations (536) can reduce 540 to:
% 30.34/8.33 | (270) $false
% 30.34/8.33 |
% 30.34/8.33 |-The branch is then unsatisfiable
% 30.34/8.33 |-Branch two:
% 30.34/8.33 | (540) ~ (all_0_41_41 = e1)
% 30.34/8.33 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 30.34/8.33 |
% 30.34/8.33 +-Applying beta-rule and splitting (762), into two cases.
% 30.34/8.33 |-Branch one:
% 30.34/8.33 | (552) all_0_48_48 = e1
% 30.34/8.33 |
% 30.34/8.33 | Combining equations (311,552) yields a new equation:
% 30.34/8.33 | (531) e2 = e1
% 30.34/8.33 |
% 30.34/8.33 | Simplifying 531 yields:
% 30.34/8.33 | (322) e2 = e1
% 30.34/8.33 |
% 30.34/8.33 | Equations (322) can reduce 141 to:
% 30.34/8.33 | (270) $false
% 30.34/8.33 |
% 30.34/8.33 |-The branch is then unsatisfiable
% 30.34/8.33 |-Branch two:
% 30.34/8.33 | (588) ~ (all_0_48_48 = e1)
% 30.34/8.33 | (4925) all_0_53_53 = e1 | all_0_58_58 = e1
% 30.34/8.33 |
% 30.34/8.33 +-Applying beta-rule and splitting (194), into two cases.
% 30.34/8.33 |-Branch one:
% 30.34/8.33 | (747) all_0_56_56 = e1
% 30.34/8.33 |
% 30.34/8.33 | Equations (747) can reduce 212 to:
% 30.34/8.33 | (528) ~ (all_0_39_39 = e1)
% 30.34/8.33 |
% 30.34/8.33 | Equations (747) can reduce 188 to:
% 30.34/8.33 | (249) ~ (all_0_43_43 = e1)
% 30.34/8.33 |
% 30.34/8.33 | Equations (747) can reduce 419 to:
% 30.34/8.33 | (132) ~ (e1 = e0)
% 30.34/8.33 |
% 30.34/8.33 | From (747) and (239) follows:
% 30.34/8.33 | (11832) op(e3, e1) = all_0_11_11
% 30.34/8.33 |
% 30.34/8.33 | From (747) and (245) follows:
% 30.34/8.33 | (11833) op(e0, e3) = e1
% 30.34/8.33 |
% 30.34/8.33 +-Applying beta-rule and splitting (4925), into two cases.
% 30.34/8.33 |-Branch one:
% 30.34/8.33 | (853) all_0_53_53 = e1
% 30.34/8.33 |
% 30.34/8.33 | Equations (853) can reduce 214 to:
% 30.34/8.33 | (540) ~ (all_0_41_41 = e1)
% 30.34/8.34 |
% 30.34/8.34 | Equations (853) can reduce 12 to:
% 30.34/8.34 | (748) ~ (all_0_51_51 = e1)
% 30.34/8.34 |
% 30.34/8.34 | Equations (853) can reduce 259 to:
% 30.34/8.34 | (645) ~ (e2 = e1)
% 30.34/8.34 |
% 30.34/8.34 | Simplifying 645 yields:
% 30.34/8.34 | (141) ~ (e2 = e1)
% 30.34/8.34 |
% 30.34/8.34 | Equations (853) can reduce 584 to:
% 30.34/8.34 | (132) ~ (e1 = e0)
% 30.34/8.34 |
% 30.34/8.34 +-Applying beta-rule and splitting (21), into two cases.
% 30.34/8.34 |-Branch one:
% 30.34/8.34 | (824) all_0_51_51 = e3
% 30.34/8.34 |
% 30.34/8.34 | Equations (824) can reduce 32 to:
% 30.34/8.34 | (755) ~ (all_0_39_39 = e3)
% 30.34/8.34 |
% 30.34/8.34 | Equations (824) can reduce 240 to:
% 30.34/8.34 | (786) ~ (all_0_43_43 = e3)
% 30.34/8.34 |
% 30.34/8.34 | Equations (824) can reduce 697 to:
% 30.34/8.34 | (719) ~ (e4 = e3)
% 30.34/8.34 |
% 30.34/8.34 | Simplifying 719 yields:
% 30.34/8.34 | (34) ~ (e4 = e3)
% 30.34/8.34 |
% 30.34/8.34 | Equations (824) can reduce 987 to:
% 30.34/8.34 | (66) ~ (e3 = e0)
% 30.34/8.34 |
% 30.34/8.34 | From (824) and (7) follows:
% 30.34/8.34 | (11846) op(e3, e3) = all_0_9_9
% 30.34/8.34 |
% 30.34/8.34 | Instantiating formula (201) with e3, e3, all_0_9_9, all_0_43_43 and discharging atoms op(e3, e3) = all_0_9_9, op(e3, e3) = all_0_43_43, yields:
% 30.34/8.34 | (11847) all_0_9_9 = all_0_43_43
% 30.34/8.34 |
% 30.34/8.34 | Instantiating formula (201) with e3, e1, all_0_11_11, all_0_45_45 and discharging atoms op(e3, e1) = all_0_11_11, op(e3, e1) = all_0_45_45, yields:
% 30.34/8.34 | (11848) all_0_11_11 = all_0_45_45
% 30.34/8.34 |
% 30.34/8.34 | Instantiating formula (201) with e0, e3, e1, all_0_20_20 and discharging atoms op(e0, e3) = all_0_20_20, op(e0, e3) = e1, yields:
% 30.34/8.34 | (11849) all_0_20_20 = e1
% 30.34/8.34 |
% 30.34/8.34 | Instantiating formula (201) with e0, e0, all_0_36_36, e4 and discharging atoms op(e0, e0) = all_0_36_36, op(e0, e0) = e4, yields:
% 30.34/8.34 | (11850) all_0_36_36 = e4
% 30.34/8.34 |
% 30.34/8.34 | From (11849) and (11802) follows:
% 30.34/8.34 | (11833) op(e0, e3) = e1
% 30.34/8.34 |
% 30.34/8.34 +-Applying beta-rule and splitting (234), into two cases.
% 30.34/8.34 |-Branch one:
% 30.34/8.34 | (4239) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3)) | (all_0_9_9 = e1 & ~ (all_0_10_10 = e3))
% 30.34/8.34 |
% 30.34/8.34 +-Applying beta-rule and splitting (4239), into two cases.
% 30.34/8.34 |-Branch one:
% 30.34/8.34 | (4240) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3))
% 30.34/8.34 |
% 30.34/8.34 +-Applying beta-rule and splitting (4240), into two cases.
% 30.34/8.34 |-Branch one:
% 30.34/8.34 | (4241) all_0_4_4 = e4 & ~ (all_0_5_5 = e3)
% 30.34/8.34 |
% 30.34/8.34 | Applying alpha-rule on (4241) yields:
% 30.34/8.34 | (4242) all_0_4_4 = e4
% 30.34/8.34 | (4243) ~ (all_0_5_5 = e3)
% 30.34/8.34 |
% 30.34/8.34 | From (4242) and (200) follows:
% 30.34/8.34 | (11857) op(e3, all_0_39_39) = e4
% 30.34/8.34 |
% 30.34/8.34 +-Applying beta-rule and splitting (44), into two cases.
% 30.34/8.34 |-Branch one:
% 30.34/8.34 | (502) all_0_43_43 = e4
% 30.34/8.34 |
% 30.34/8.34 | Equations (502) can reduce 167 to:
% 30.34/8.34 | (591) ~ (all_0_39_39 = e4)
% 30.34/8.34 |
% 30.34/8.34 | Equations (502) can reduce 84 to:
% 30.34/8.34 | (503) ~ (all_0_45_45 = e4)
% 30.34/8.34 |
% 30.34/8.34 | Simplifying 503 yields:
% 30.34/8.34 | (352) ~ (all_0_45_45 = e4)
% 30.34/8.34 |
% 30.34/8.34 +-Applying beta-rule and splitting (47), into two cases.
% 30.34/8.34 |-Branch one:
% 30.34/8.34 | (450) all_0_43_43 = e2
% 30.34/8.34 |
% 30.34/8.34 | Combining equations (502,450) yields a new equation:
% 30.34/8.34 | (268) e4 = e2
% 30.34/8.34 |
% 30.34/8.34 | Simplifying 268 yields:
% 30.34/8.34 | (269) e4 = e2
% 30.34/8.34 |
% 30.34/8.34 | Equations (269) can reduce 231 to:
% 30.34/8.34 | (270) $false
% 30.34/8.34 |
% 30.34/8.34 |-The branch is then unsatisfiable
% 30.34/8.34 |-Branch two:
% 30.34/8.34 | (292) ~ (all_0_43_43 = e2)
% 30.34/8.34 | (453) all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2
% 30.34/8.34 |
% 30.34/8.34 +-Applying beta-rule and splitting (96), into two cases.
% 30.34/8.34 |-Branch one:
% 30.34/8.34 | (336) all_0_39_39 = e2
% 30.34/8.34 |
% 30.34/8.34 | Equations (336) can reduce 184 to:
% 30.34/8.34 | (1336) ~ (all_0_42_42 = e2)
% 30.34/8.34 |
% 30.34/8.34 | Simplifying 1336 yields:
% 30.34/8.34 | (498) ~ (all_0_42_42 = e2)
% 30.34/8.34 |
% 30.34/8.34 | Equations (336) can reduce 591 to:
% 30.34/8.34 | (377) ~ (e4 = e2)
% 30.34/8.34 |
% 30.34/8.34 | Simplifying 377 yields:
% 30.34/8.34 | (231) ~ (e4 = e2)
% 30.34/8.34 |
% 30.34/8.34 | Equations (336) can reduce 101 to:
% 30.34/8.34 | (57) ~ (e2 = e0)
% 30.34/8.34 |
% 30.34/8.34 | From (336) and (11857) follows:
% 30.34/8.34 | (11874) op(e3, e2) = e4
% 30.34/8.34 |
% 30.34/8.34 +-Applying beta-rule and splitting (16), into two cases.
% 30.34/8.34 |-Branch one:
% 30.34/8.34 | (698) all_0_42_42 = e2
% 30.34/8.34 |
% 30.34/8.34 | Equations (698) can reduce 498 to:
% 30.34/8.34 | (270) $false
% 30.34/8.34 |
% 30.34/8.34 |-The branch is then unsatisfiable
% 30.34/8.34 |-Branch two:
% 30.34/8.34 | (498) ~ (all_0_42_42 = e2)
% 30.34/8.34 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 30.34/8.34 |
% 30.34/8.34 +-Applying beta-rule and splitting (222), into two cases.
% 30.34/8.34 |-Branch one:
% 30.34/8.34 | (522) all_0_39_39 = e4
% 30.34/8.34 |
% 30.34/8.34 | Combining equations (522,336) yields a new equation:
% 30.34/8.34 | (268) e4 = e2
% 30.34/8.34 |
% 30.34/8.34 | Simplifying 268 yields:
% 30.34/8.34 | (269) e4 = e2
% 30.34/8.34 |
% 30.34/8.34 | Equations (269) can reduce 231 to:
% 30.34/8.34 | (270) $false
% 30.34/8.34 |
% 30.34/8.34 |-The branch is then unsatisfiable
% 30.34/8.34 |-Branch two:
% 30.34/8.34 | (591) ~ (all_0_39_39 = e4)
% 30.34/8.34 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 30.34/8.34 |
% 30.34/8.34 +-Applying beta-rule and splitting (592), into two cases.
% 30.34/8.34 |-Branch one:
% 30.34/8.34 | (358) all_0_41_41 = e4
% 30.34/8.34 |
% 30.34/8.34 | Equations (358) can reduce 94 to:
% 30.34/8.34 | (692) ~ (all_0_42_42 = e4)
% 30.34/8.34 |
% 30.34/8.34 | Simplifying 692 yields:
% 30.34/8.34 | (520) ~ (all_0_42_42 = e4)
% 30.34/8.34 |
% 30.34/8.34 | Equations (358) can reduce 232 to:
% 30.34/8.34 | (6) ~ (e4 = e0)
% 30.34/8.34 |
% 30.34/8.34 +-Applying beta-rule and splitting (105), into two cases.
% 30.34/8.34 |-Branch one:
% 30.34/8.34 | (374) all_0_45_45 = e2
% 30.34/8.34 |
% 30.34/8.34 | Equations (374) can reduce 434 to:
% 30.34/8.34 | (270) $false
% 30.34/8.34 |
% 30.34/8.34 |-The branch is then unsatisfiable
% 30.34/8.34 |-Branch two:
% 30.34/8.34 | (434) ~ (all_0_45_45 = e2)
% 30.34/8.34 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 30.34/8.34 |
% 30.34/8.34 +-Applying beta-rule and splitting (1245), into two cases.
% 30.34/8.34 |-Branch one:
% 30.34/8.34 | (1258) all_0_42_42 = e3
% 30.34/8.34 |
% 30.34/8.34 | Equations (1258) can reduce 498 to:
% 30.34/8.34 | (223) ~ (e3 = e2)
% 30.34/8.34 |
% 30.34/8.34 +-Applying beta-rule and splitting (220), into two cases.
% 30.34/8.34 |-Branch one:
% 30.34/8.34 | (497) all_0_46_46 = e2
% 30.34/8.34 |
% 30.34/8.34 | From (497) and (74) follows:
% 30.34/8.34 | (11896) op(e3, e2) = all_0_33_33
% 30.34/8.34 |
% 30.34/8.34 | Instantiating formula (201) with e3, e2, all_0_33_33, e0 and discharging atoms op(e3, e2) = all_0_33_33, op(e3, e2) = e0, yields:
% 30.34/8.34 | (11897) all_0_33_33 = e0
% 30.34/8.34 |
% 30.34/8.34 | Instantiating formula (201) with e3, e2, e4, all_0_33_33 and discharging atoms op(e3, e2) = all_0_33_33, op(e3, e2) = e4, yields:
% 30.34/8.34 | (11898) all_0_33_33 = e4
% 30.34/8.34 |
% 30.34/8.35 | Combining equations (11897,11898) yields a new equation:
% 30.34/8.35 | (479) e4 = e0
% 30.34/8.35 |
% 30.34/8.35 | Equations (479) can reduce 6 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (1436) ~ (all_0_46_46 = e2)
% 30.34/8.35 | (1523) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e0
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (209), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (698) all_0_42_42 = e2
% 30.34/8.35 |
% 30.34/8.35 | Combining equations (1258,698) yields a new equation:
% 30.34/8.35 | (437) e3 = e2
% 30.34/8.35 |
% 30.34/8.35 | Simplifying 437 yields:
% 30.34/8.35 | (414) e3 = e2
% 30.34/8.35 |
% 30.34/8.35 | Equations (414) can reduce 223 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (498) ~ (all_0_42_42 = e2)
% 30.34/8.35 | (1732) all_0_46_46 = e2 | all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (453), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (370) all_0_44_44 = e2
% 30.34/8.35 |
% 30.34/8.35 | Combining equations (621,370) yields a new equation:
% 30.34/8.35 | (316) e2 = e0
% 30.34/8.35 |
% 30.34/8.35 | Equations (316) can reduce 57 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (333) ~ (all_0_44_44 = e2)
% 30.34/8.35 | (493) all_0_45_45 = e2 | all_0_46_46 = e2
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (1732), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (497) all_0_46_46 = e2
% 30.34/8.35 |
% 30.34/8.35 | Equations (497) can reduce 1436 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (1436) ~ (all_0_46_46 = e2)
% 30.34/8.35 | (3824) all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (493), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (374) all_0_45_45 = e2
% 30.34/8.35 |
% 30.34/8.35 | Equations (374) can reduce 434 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (434) ~ (all_0_45_45 = e2)
% 30.34/8.35 | (497) all_0_46_46 = e2
% 30.34/8.35 |
% 30.34/8.35 | Equations (497) can reduce 1436 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (1316) ~ (all_0_42_42 = e3)
% 30.34/8.35 | (1317) all_0_42_42 = e4 | all_0_42_42 = e1
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (1317), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (541) all_0_42_42 = e1
% 30.34/8.35 |
% 30.34/8.35 | Equations (541) can reduce 640 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (640) ~ (all_0_42_42 = e1)
% 30.34/8.35 | (512) all_0_42_42 = e4
% 30.34/8.35 |
% 30.34/8.35 | Equations (512) can reduce 520 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (361) ~ (all_0_41_41 = e4)
% 30.34/8.35 | (512) all_0_42_42 = e4
% 30.34/8.35 |
% 30.34/8.35 | Equations (512) can reduce 520 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (291) ~ (all_0_39_39 = e2)
% 30.34/8.35 | (4205) all_0_43_43 = e2 | all_0_47_47 = e2 | all_0_51_51 = e2 | all_0_56_56 = e2
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (105), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (374) all_0_45_45 = e2
% 30.34/8.35 |
% 30.34/8.35 | Equations (374) can reduce 434 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (434) ~ (all_0_45_45 = e2)
% 30.34/8.35 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (177), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (336) all_0_39_39 = e2
% 30.34/8.35 |
% 30.34/8.35 | Equations (336) can reduce 291 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (291) ~ (all_0_39_39 = e2)
% 30.34/8.35 | (684) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (186), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (336) all_0_39_39 = e2
% 30.34/8.35 |
% 30.34/8.35 | Equations (336) can reduce 291 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (291) ~ (all_0_39_39 = e2)
% 30.34/8.35 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (164), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (336) all_0_39_39 = e2
% 30.34/8.35 |
% 30.34/8.35 | Equations (336) can reduce 291 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (291) ~ (all_0_39_39 = e2)
% 30.34/8.35 | (630) all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (630), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (327) all_0_40_40 = e2
% 30.34/8.35 |
% 30.34/8.35 | Combining equations (327,530) yields a new equation:
% 30.34/8.35 | (531) e2 = e1
% 30.34/8.35 |
% 30.34/8.35 | Simplifying 531 yields:
% 30.34/8.35 | (322) e2 = e1
% 30.34/8.35 |
% 30.34/8.35 | Equations (322) can reduce 141 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (602) ~ (all_0_40_40 = e2)
% 30.34/8.35 | (1251) all_0_41_41 = e2 | all_0_42_42 = e2
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (1251), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (436) all_0_41_41 = e2
% 30.34/8.35 |
% 30.34/8.35 | Equations (436) can reduce 331 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (331) ~ (all_0_41_41 = e2)
% 30.34/8.35 | (698) all_0_42_42 = e2
% 30.34/8.35 |
% 30.34/8.35 | Equations (698) can reduce 94 to:
% 30.34/8.35 | (331) ~ (all_0_41_41 = e2)
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (78), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (751) all_0_39_39 = e3
% 30.34/8.35 |
% 30.34/8.35 | Equations (751) can reduce 755 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (755) ~ (all_0_39_39 = e3)
% 30.34/8.35 | (4262) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (219), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (351) all_0_41_41 = e3
% 30.34/8.35 |
% 30.34/8.35 | Equations (351) can reduce 51 to:
% 30.34/8.35 | (353) ~ (all_0_45_45 = e3)
% 30.34/8.35 |
% 30.34/8.35 | Simplifying 353 yields:
% 30.34/8.35 | (354) ~ (all_0_45_45 = e3)
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (435), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (454) all_0_45_45 = e0
% 30.34/8.35 |
% 30.34/8.35 | Equations (454) can reduce 488 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (488) ~ (all_0_45_45 = e0)
% 30.34/8.35 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (489), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (505) all_0_45_45 = e3
% 30.34/8.35 |
% 30.34/8.35 | Equations (505) can reduce 354 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (354) ~ (all_0_45_45 = e3)
% 30.34/8.35 | (363) all_0_45_45 = e4
% 30.34/8.35 |
% 30.34/8.35 | Equations (363) can reduce 352 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (1237) ~ (all_0_41_41 = e3)
% 30.34/8.35 | (1508) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (158), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (358) all_0_41_41 = e4
% 30.34/8.35 |
% 30.34/8.35 | Equations (358) can reduce 226 to:
% 30.34/8.35 | (591) ~ (all_0_39_39 = e4)
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (684), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (751) all_0_39_39 = e3
% 30.34/8.35 |
% 30.34/8.35 | Equations (751) can reduce 755 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (755) ~ (all_0_39_39 = e3)
% 30.34/8.35 | (1756) all_0_39_39 = e4 | all_0_39_39 = e1
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (1756), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (524) all_0_39_39 = e1
% 30.34/8.35 |
% 30.34/8.35 | Equations (524) can reduce 528 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (528) ~ (all_0_39_39 = e1)
% 30.34/8.35 | (522) all_0_39_39 = e4
% 30.34/8.35 |
% 30.34/8.35 | Equations (522) can reduce 591 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (361) ~ (all_0_41_41 = e4)
% 30.34/8.35 | (362) all_0_45_45 = e4 | all_0_53_53 = e4 | all_0_58_58 = e4
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (217), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (436) all_0_41_41 = e2
% 30.34/8.35 |
% 30.34/8.35 | Equations (436) can reduce 331 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (331) ~ (all_0_41_41 = e2)
% 30.34/8.35 | (709) all_0_41_41 = e4 | all_0_41_41 = e3 | all_0_41_41 = e1
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (709), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (351) all_0_41_41 = e3
% 30.34/8.35 |
% 30.34/8.35 | Equations (351) can reduce 1237 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (1237) ~ (all_0_41_41 = e3)
% 30.34/8.35 | (1238) all_0_41_41 = e4 | all_0_41_41 = e1
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (1238), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (536) all_0_41_41 = e1
% 30.34/8.35 |
% 30.34/8.35 | Equations (536) can reduce 540 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (540) ~ (all_0_41_41 = e1)
% 30.34/8.35 | (358) all_0_41_41 = e4
% 30.34/8.35 |
% 30.34/8.35 | Equations (358) can reduce 361 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (510) ~ (all_0_43_43 = e4)
% 30.34/8.35 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (159), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (450) all_0_43_43 = e2
% 30.34/8.35 |
% 30.34/8.35 | Equations (450) can reduce 167 to:
% 30.34/8.35 | (291) ~ (all_0_39_39 = e2)
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (186), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (336) all_0_39_39 = e2
% 30.34/8.35 |
% 30.34/8.35 | Equations (336) can reduce 291 to:
% 30.34/8.35 | (270) $false
% 30.34/8.35 |
% 30.34/8.35 |-The branch is then unsatisfiable
% 30.34/8.35 |-Branch two:
% 30.34/8.35 | (291) ~ (all_0_39_39 = e2)
% 30.34/8.35 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (511), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (363) all_0_45_45 = e4
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (339), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 30.34/8.35 |
% 30.34/8.35 +-Applying beta-rule and splitting (340), into two cases.
% 30.34/8.35 |-Branch one:
% 30.34/8.35 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 30.34/8.35 |
% 30.34/8.35 | Applying alpha-rule on (341) yields:
% 30.34/8.35 | (342) all_0_0_0 = e1
% 30.34/8.35 | (343) ~ (all_0_1_1 = e4)
% 30.34/8.35 |
% 30.40/8.35 | Combining equations (342,9064) yields a new equation:
% 30.40/8.35 | (571) e1 = e0
% 30.40/8.35 |
% 30.40/8.35 | Simplifying 571 yields:
% 30.40/8.35 | (560) e1 = e0
% 30.40/8.35 |
% 30.40/8.35 | Equations (560) can reduce 132 to:
% 30.40/8.35 | (270) $false
% 30.40/8.35 |
% 30.40/8.35 |-The branch is then unsatisfiable
% 30.40/8.35 |-Branch two:
% 30.40/8.35 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 30.40/8.35 |
% 30.40/8.35 | Applying alpha-rule on (346) yields:
% 30.40/8.35 | (347) all_0_2_2 = e0
% 30.40/8.35 | (348) ~ (all_0_3_3 = e4)
% 30.40/8.35 |
% 30.40/8.35 | Combining equations (347,11737) yields a new equation:
% 30.40/8.35 | (560) e1 = e0
% 30.40/8.35 |
% 30.40/8.35 | Equations (560) can reduce 132 to:
% 30.40/8.35 | (270) $false
% 30.40/8.35 |
% 30.40/8.35 |-The branch is then unsatisfiable
% 30.40/8.35 |-Branch two:
% 30.40/8.35 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 30.40/8.35 |
% 30.40/8.35 | Applying alpha-rule on (350) yields:
% 30.40/8.35 | (351) all_0_41_41 = e3
% 30.40/8.35 | (352) ~ (all_0_45_45 = e4)
% 30.40/8.35 |
% 30.40/8.35 | Equations (363) can reduce 352 to:
% 30.40/8.35 | (270) $false
% 30.40/8.35 |
% 30.40/8.35 |-The branch is then unsatisfiable
% 30.40/8.35 |-Branch two:
% 30.40/8.35 | (352) ~ (all_0_45_45 = e4)
% 30.40/8.35 | (517) all_0_46_46 = e4
% 30.40/8.35 |
% 30.40/8.35 | Equations (517) can reduce 805 to:
% 30.40/8.35 | (270) $false
% 30.40/8.35 |
% 30.40/8.35 |-The branch is then unsatisfiable
% 30.40/8.35 |-Branch two:
% 30.40/8.35 | (292) ~ (all_0_43_43 = e2)
% 30.40/8.35 | (774) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 30.40/8.35 |
% 30.40/8.35 +-Applying beta-rule and splitting (774), into two cases.
% 30.40/8.35 |-Branch one:
% 30.40/8.35 | (411) all_0_43_43 = e0
% 30.40/8.35 |
% 30.40/8.35 | Equations (411) can reduce 455 to:
% 30.40/8.35 | (270) $false
% 30.40/8.35 |
% 30.40/8.35 |-The branch is then unsatisfiable
% 30.40/8.35 |-Branch two:
% 30.40/8.35 | (455) ~ (all_0_43_43 = e0)
% 30.40/8.35 | (944) all_0_43_43 = e4 | all_0_43_43 = e3
% 30.40/8.35 |
% 30.40/8.35 +-Applying beta-rule and splitting (944), into two cases.
% 30.40/8.35 |-Branch one:
% 30.40/8.35 | (782) all_0_43_43 = e3
% 30.40/8.35 |
% 30.40/8.35 | Equations (782) can reduce 786 to:
% 30.40/8.35 | (270) $false
% 30.40/8.35 |
% 30.40/8.35 |-The branch is then unsatisfiable
% 30.40/8.35 |-Branch two:
% 30.40/8.35 | (786) ~ (all_0_43_43 = e3)
% 30.40/8.35 | (502) all_0_43_43 = e4
% 30.40/8.35 |
% 30.40/8.35 | Equations (502) can reduce 510 to:
% 30.40/8.35 | (270) $false
% 30.40/8.35 |
% 30.40/8.35 |-The branch is then unsatisfiable
% 30.40/8.35 |-Branch two:
% 30.40/8.35 | (4247) all_0_7_7 = e2 & ~ (all_0_8_8 = e3)
% 30.40/8.35 |
% 30.40/8.35 | Applying alpha-rule on (4247) yields:
% 30.40/8.35 | (4248) all_0_7_7 = e2
% 30.40/8.35 | (4249) ~ (all_0_8_8 = e3)
% 30.40/8.35 |
% 30.40/8.36 | Combining equations (4248,11390) yields a new equation:
% 30.40/8.36 | (497) all_0_46_46 = e2
% 30.40/8.36 |
% 30.40/8.36 | Equations (497) can reduce 38 to:
% 30.40/8.36 | (434) ~ (all_0_45_45 = e2)
% 30.40/8.36 |
% 30.40/8.36 | From (497) and (74) follows:
% 30.40/8.36 | (11896) op(e3, e2) = all_0_33_33
% 30.40/8.36 |
% 30.40/8.36 +-Applying beta-rule and splitting (164), into two cases.
% 30.40/8.36 |-Branch one:
% 30.40/8.36 | (336) all_0_39_39 = e2
% 30.40/8.36 |
% 30.40/8.36 | Equations (336) can reduce 167 to:
% 30.40/8.36 | (5937) ~ (all_0_43_43 = e2)
% 30.40/8.36 |
% 30.40/8.36 | Simplifying 5937 yields:
% 30.40/8.36 | (292) ~ (all_0_43_43 = e2)
% 30.40/8.36 |
% 30.40/8.36 | Equations (336) can reduce 755 to:
% 30.40/8.36 | (301) ~ (e3 = e2)
% 30.40/8.36 |
% 30.40/8.36 | Simplifying 301 yields:
% 30.40/8.36 | (223) ~ (e3 = e2)
% 30.40/8.36 |
% 30.40/8.36 | Equations (336) can reduce 101 to:
% 30.40/8.36 | (57) ~ (e2 = e0)
% 30.40/8.36 |
% 30.40/8.36 | From (336) and (200) follows:
% 30.40/8.36 | (12057) op(e3, e2) = all_0_4_4
% 30.40/8.36 |
% 30.40/8.36 +-Applying beta-rule and splitting (159), into two cases.
% 30.40/8.36 |-Branch one:
% 30.40/8.36 | (450) all_0_43_43 = e2
% 30.40/8.36 |
% 30.40/8.36 | Equations (450) can reduce 292 to:
% 30.40/8.36 | (270) $false
% 30.40/8.36 |
% 30.40/8.36 |-The branch is then unsatisfiable
% 30.40/8.36 |-Branch two:
% 30.40/8.36 | (292) ~ (all_0_43_43 = e2)
% 30.40/8.36 | (774) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 30.40/8.36 |
% 30.40/8.36 +-Applying beta-rule and splitting (774), into two cases.
% 30.40/8.36 |-Branch one:
% 30.40/8.36 | (411) all_0_43_43 = e0
% 30.40/8.36 |
% 30.40/8.36 | Equations (411) can reduce 455 to:
% 30.40/8.36 | (270) $false
% 30.40/8.36 |
% 30.40/8.36 |-The branch is then unsatisfiable
% 30.40/8.36 |-Branch two:
% 30.40/8.36 | (455) ~ (all_0_43_43 = e0)
% 30.40/8.36 | (944) all_0_43_43 = e4 | all_0_43_43 = e3
% 30.40/8.36 |
% 30.40/8.36 +-Applying beta-rule and splitting (944), into two cases.
% 30.40/8.36 |-Branch one:
% 30.40/8.36 | (782) all_0_43_43 = e3
% 30.40/8.36 |
% 30.40/8.36 | Equations (782) can reduce 786 to:
% 30.40/8.36 | (270) $false
% 30.40/8.36 |
% 30.40/8.36 |-The branch is then unsatisfiable
% 30.40/8.36 |-Branch two:
% 30.40/8.36 | (786) ~ (all_0_43_43 = e3)
% 30.40/8.36 | (502) all_0_43_43 = e4
% 30.40/8.36 |
% 30.40/8.36 | Equations (502) can reduce 84 to:
% 30.40/8.36 | (503) ~ (all_0_45_45 = e4)
% 30.40/8.36 |
% 30.40/8.36 | Simplifying 503 yields:
% 30.40/8.36 | (352) ~ (all_0_45_45 = e4)
% 30.40/8.36 |
% 30.40/8.36 | Equations (502) can reduce 786 to:
% 30.40/8.36 | (34) ~ (e4 = e3)
% 30.40/8.36 |
% 30.40/8.36 | Equations (502) can reduce 249 to:
% 30.40/8.36 | (251) ~ (e4 = e1)
% 30.40/8.36 |
% 30.40/8.36 | Equations (502) can reduce 455 to:
% 30.40/8.36 | (6) ~ (e4 = e0)
% 30.40/8.36 |
% 30.40/8.36 +-Applying beta-rule and splitting (105), into two cases.
% 30.40/8.36 |-Branch one:
% 30.40/8.36 | (374) all_0_45_45 = e2
% 30.40/8.36 |
% 30.40/8.36 | Equations (374) can reduce 434 to:
% 30.40/8.36 | (270) $false
% 30.40/8.36 |
% 30.40/8.36 |-The branch is then unsatisfiable
% 30.40/8.36 |-Branch two:
% 30.40/8.36 | (434) ~ (all_0_45_45 = e2)
% 30.40/8.36 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 30.40/8.36 |
% 30.40/8.36 +-Applying beta-rule and splitting (22), into two cases.
% 30.40/8.36 |-Branch one:
% 30.40/8.36 | (782) all_0_43_43 = e3
% 30.40/8.36 |
% 30.40/8.36 | Combining equations (502,782) yields a new equation:
% 30.40/8.36 | (660) e4 = e3
% 30.40/8.36 |
% 30.40/8.36 | Simplifying 660 yields:
% 30.40/8.36 | (359) e4 = e3
% 30.40/8.36 |
% 30.40/8.36 | Equations (359) can reduce 34 to:
% 30.40/8.36 | (270) $false
% 30.40/8.36 |
% 30.40/8.36 |-The branch is then unsatisfiable
% 30.40/8.36 |-Branch two:
% 30.40/8.36 | (786) ~ (all_0_43_43 = e3)
% 30.40/8.36 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 30.40/8.36 |
% 30.40/8.36 | Equations (502) can reduce 786 to:
% 30.40/8.36 | (34) ~ (e4 = e3)
% 30.40/8.36 |
% 30.40/8.36 +-Applying beta-rule and splitting (95), into two cases.
% 30.40/8.36 |-Branch one:
% 30.40/8.36 | (1258) all_0_42_42 = e3
% 30.40/8.36 |
% 30.40/8.36 | From (1258) and (243) follows:
% 30.40/8.36 | (11536) op(e0, e3) = all_0_30_30
% 30.40/8.36 |
% 30.40/8.36 +-Applying beta-rule and splitting (435), into two cases.
% 30.40/8.36 |-Branch one:
% 30.40/8.36 | (454) all_0_45_45 = e0
% 30.40/8.36 |
% 30.40/8.36 | Equations (454) can reduce 488 to:
% 30.40/8.36 | (270) $false
% 30.40/8.36 |
% 30.40/8.36 |-The branch is then unsatisfiable
% 30.40/8.36 |-Branch two:
% 30.40/8.36 | (488) ~ (all_0_45_45 = e0)
% 30.40/8.36 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 30.40/8.36 |
% 30.40/8.36 +-Applying beta-rule and splitting (489), into two cases.
% 30.40/8.36 |-Branch one:
% 30.40/8.36 | (505) all_0_45_45 = e3
% 30.40/8.36 |
% 30.40/8.36 | Equations (505) can reduce 352 to:
% 30.40/8.36 | (719) ~ (e4 = e3)
% 30.40/8.36 |
% 30.40/8.36 | Simplifying 719 yields:
% 30.40/8.36 | (34) ~ (e4 = e3)
% 30.40/8.36 |
% 30.40/8.36 +-Applying beta-rule and splitting (158), into two cases.
% 30.40/8.36 |-Branch one:
% 30.40/8.36 | (358) all_0_41_41 = e4
% 30.40/8.36 |
% 30.40/8.36 | Equations (358) can reduce 540 to:
% 30.40/8.36 | (251) ~ (e4 = e1)
% 30.40/8.36 |
% 30.40/8.36 | Instantiating formula (201) with e3, e2, all_0_4_4, e0 and discharging atoms op(e3, e2) = all_0_4_4, op(e3, e2) = e0, yields:
% 30.40/8.36 | (12097) all_0_4_4 = e0
% 30.40/8.36 |
% 30.40/8.36 | Instantiating formula (201) with e3, e2, all_0_33_33, all_0_4_4 and discharging atoms op(e3, e2) = all_0_4_4, op(e3, e2) = all_0_33_33, yields:
% 30.40/8.36 | (12098) all_0_4_4 = all_0_33_33
% 30.40/8.36 |
% 30.40/8.36 | Instantiating formula (201) with e0, e3, all_0_30_30, e1 and discharging atoms op(e0, e3) = all_0_30_30, op(e0, e3) = e1, yields:
% 30.40/8.36 | (6348) all_0_30_30 = e1
% 30.40/8.36 |
% 30.40/8.36 | Combining equations (12098,12097) yields a new equation:
% 30.40/8.36 | (12100) all_0_33_33 = e0
% 30.40/8.36 |
% 30.40/8.36 | Simplifying 12100 yields:
% 30.40/8.36 | (11897) all_0_33_33 = e0
% 30.40/8.36 |
% 30.40/8.36 +-Applying beta-rule and splitting (111), into two cases.
% 30.40/8.36 |-Branch one:
% 30.40/8.36 | (4557) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0)) | (all_0_34_34 = e2 & ~ (all_0_35_35 = e0))
% 30.40/8.36 |
% 30.40/8.36 +-Applying beta-rule and splitting (4557), into two cases.
% 30.40/8.36 |-Branch one:
% 30.40/8.36 | (4558) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0))
% 30.40/8.36 |
% 30.40/8.36 +-Applying beta-rule and splitting (4558), into two cases.
% 30.40/8.36 |-Branch one:
% 30.40/8.36 | (4559) all_0_30_30 = e4 & ~ (all_0_31_31 = e0)
% 30.40/8.36 |
% 30.40/8.36 | Applying alpha-rule on (4559) yields:
% 30.40/8.36 | (4560) all_0_30_30 = e4
% 30.40/8.36 | (4561) ~ (all_0_31_31 = e0)
% 30.40/8.36 |
% 30.40/8.36 | Combining equations (6348,4560) yields a new equation:
% 30.40/8.36 | (526) e4 = e1
% 30.40/8.36 |
% 30.40/8.36 | Equations (526) can reduce 251 to:
% 30.40/8.36 | (270) $false
% 30.40/8.36 |
% 30.40/8.36 |-The branch is then unsatisfiable
% 30.40/8.36 |-Branch two:
% 30.40/8.36 | (4565) all_0_32_32 = e3 & ~ (all_0_33_33 = e0)
% 30.40/8.36 |
% 30.40/8.36 | Applying alpha-rule on (4565) yields:
% 30.40/8.36 | (4566) all_0_32_32 = e3
% 30.40/8.36 | (4567) ~ (all_0_33_33 = e0)
% 30.40/8.36 |
% 30.40/8.36 | Equations (11897) can reduce 4567 to:
% 30.40/8.36 | (270) $false
% 30.40/8.36 |
% 30.40/8.36 |-The branch is then unsatisfiable
% 30.40/8.36 |-Branch two:
% 30.40/8.36 | (4571) all_0_34_34 = e2 & ~ (all_0_35_35 = e0)
% 30.40/8.36 |
% 30.40/8.36 | Applying alpha-rule on (4571) yields:
% 30.40/8.36 | (4572) all_0_34_34 = e2
% 30.40/8.36 | (4573) ~ (all_0_35_35 = e0)
% 30.40/8.36 |
% 30.40/8.37 | Combining equations (4572,6278) yields a new equation:
% 30.40/8.37 | (622) e2 = e0
% 30.40/8.37 |
% 30.40/8.37 | Simplifying 622 yields:
% 30.40/8.37 | (316) e2 = e0
% 30.40/8.37 |
% 30.40/8.37 | Equations (316) can reduce 57 to:
% 30.40/8.37 | (270) $false
% 30.40/8.37 |
% 30.40/8.37 |-The branch is then unsatisfiable
% 30.40/8.37 |-Branch two:
% 30.40/8.37 | (4577) all_0_36_36 = e1 & ~ (all_0_37_37 = e0)
% 30.40/8.37 |
% 30.40/8.37 | Applying alpha-rule on (4577) yields:
% 30.40/8.37 | (4578) all_0_36_36 = e1
% 30.40/8.37 | (4579) ~ (all_0_37_37 = e0)
% 30.40/8.37 |
% 30.40/8.37 | Combining equations (11850,4578) yields a new equation:
% 30.40/8.37 | (525) e4 = e1
% 30.40/8.37 |
% 30.40/8.37 | Simplifying 525 yields:
% 30.40/8.37 | (526) e4 = e1
% 30.40/8.37 |
% 30.40/8.37 | Equations (526) can reduce 251 to:
% 30.40/8.37 | (270) $false
% 30.40/8.37 |
% 30.40/8.37 |-The branch is then unsatisfiable
% 30.40/8.37 |-Branch two:
% 30.40/8.37 | (361) ~ (all_0_41_41 = e4)
% 30.40/8.37 | (362) all_0_45_45 = e4 | all_0_53_53 = e4 | all_0_58_58 = e4
% 30.40/8.37 |
% 30.40/8.37 +-Applying beta-rule and splitting (362), into two cases.
% 30.40/8.37 |-Branch one:
% 30.40/8.37 | (363) all_0_45_45 = e4
% 30.40/8.37 |
% 30.40/8.37 | Combining equations (505,363) yields a new equation:
% 30.40/8.37 | (359) e4 = e3
% 30.40/8.37 |
% 30.40/8.37 | Equations (359) can reduce 34 to:
% 30.40/8.37 | (270) $false
% 30.40/8.37 |
% 30.40/8.37 |-The branch is then unsatisfiable
% 30.40/8.37 |-Branch two:
% 30.40/8.37 | (352) ~ (all_0_45_45 = e4)
% 30.40/8.37 | (366) all_0_53_53 = e4 | all_0_58_58 = e4
% 30.40/8.37 |
% 30.40/8.37 +-Applying beta-rule and splitting (366), into two cases.
% 30.40/8.37 |-Branch one:
% 30.40/8.37 | (367) all_0_53_53 = e4
% 30.40/8.37 |
% 30.40/8.37 | Combining equations (853,367) yields a new equation:
% 30.40/8.37 | (526) e4 = e1
% 30.40/8.37 |
% 30.40/8.37 | Equations (526) can reduce 251 to:
% 30.40/8.37 | (270) $false
% 30.40/8.37 |
% 30.40/8.37 |-The branch is then unsatisfiable
% 30.40/8.37 |-Branch two:
% 30.40/8.37 | (599) ~ (all_0_53_53 = e4)
% 30.40/8.37 | (600) all_0_58_58 = e4
% 30.40/8.37 |
% 30.40/8.37 | Combining equations (585,600) yields a new equation:
% 30.40/8.37 | (479) e4 = e0
% 30.40/8.37 |
% 30.40/8.37 | Equations (479) can reduce 6 to:
% 30.40/8.37 | (270) $false
% 30.40/8.37 |
% 30.40/8.37 |-The branch is then unsatisfiable
% 30.40/8.37 |-Branch two:
% 30.40/8.37 | (354) ~ (all_0_45_45 = e3)
% 30.40/8.37 | (363) all_0_45_45 = e4
% 30.40/8.37 |
% 30.40/8.37 | Equations (363) can reduce 352 to:
% 30.40/8.37 | (270) $false
% 30.40/8.37 |
% 30.40/8.37 |-The branch is then unsatisfiable
% 30.40/8.37 |-Branch two:
% 30.40/8.37 | (1316) ~ (all_0_42_42 = e3)
% 30.40/8.37 | (3656) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 30.40/8.37 |
% 30.40/8.37 +-Applying beta-rule and splitting (78), into two cases.
% 30.40/8.37 |-Branch one:
% 30.40/8.37 | (751) all_0_39_39 = e3
% 30.40/8.37 |
% 30.40/8.37 | Combining equations (336,751) yields a new equation:
% 30.40/8.37 | (414) e3 = e2
% 30.40/8.37 |
% 30.40/8.37 | Equations (414) can reduce 223 to:
% 30.40/8.37 | (270) $false
% 30.40/8.37 |
% 30.40/8.37 |-The branch is then unsatisfiable
% 30.40/8.37 |-Branch two:
% 30.40/8.37 | (755) ~ (all_0_39_39 = e3)
% 30.40/8.37 | (4262) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 30.40/8.37 |
% 30.40/8.37 | Equations (336) can reduce 755 to:
% 30.40/8.37 | (301) ~ (e3 = e2)
% 30.40/8.37 |
% 30.40/8.37 | Simplifying 301 yields:
% 30.40/8.37 | (223) ~ (e3 = e2)
% 30.40/8.37 |
% 30.40/8.37 +-Applying beta-rule and splitting (3656), into two cases.
% 30.40/8.37 |-Branch one:
% 30.40/8.37 | (1091) all_0_46_46 = e3
% 30.40/8.37 |
% 30.40/8.37 | Combining equations (1091,497) yields a new equation:
% 30.40/8.37 | (437) e3 = e2
% 30.40/8.37 |
% 30.40/8.37 | Simplifying 437 yields:
% 30.40/8.37 | (414) e3 = e2
% 30.40/8.37 |
% 30.40/8.37 | Equations (414) can reduce 223 to:
% 30.40/8.37 | (270) $false
% 30.40/8.37 |
% 30.40/8.37 |-The branch is then unsatisfiable
% 30.40/8.37 |-Branch two:
% 30.40/8.37 | (413) ~ (all_0_46_46 = e3)
% 30.40/8.37 | (3700) all_0_54_54 = e3 | all_0_59_59 = e3
% 30.40/8.37 |
% 30.40/8.37 +-Applying beta-rule and splitting (787), into two cases.
% 30.40/8.37 |-Branch one:
% 30.40/8.37 | (858) all_0_44_44 = e3
% 30.40/8.37 |
% 30.40/8.37 | Combining equations (621,858) yields a new equation:
% 30.40/8.37 | (784) e3 = e0
% 30.40/8.37 |
% 30.40/8.37 | Equations (784) can reduce 66 to:
% 30.40/8.37 | (270) $false
% 30.40/8.37 |
% 30.40/8.37 |-The branch is then unsatisfiable
% 30.40/8.37 |-Branch two:
% 30.40/8.37 | (862) ~ (all_0_44_44 = e3)
% 30.40/8.37 | (1070) all_0_45_45 = e3 | all_0_46_46 = e3
% 30.40/8.37 |
% 30.40/8.37 | Equations (621) can reduce 862 to:
% 30.40/8.37 | (788) ~ (e3 = e0)
% 30.40/8.37 |
% 30.40/8.37 | Simplifying 788 yields:
% 30.40/8.37 | (66) ~ (e3 = e0)
% 30.40/8.37 |
% 30.40/8.37 +-Applying beta-rule and splitting (3700), into two cases.
% 30.40/8.37 |-Branch one:
% 30.40/8.37 | (1119) all_0_54_54 = e3
% 30.40/8.37 |
% 30.40/8.37 | Combining equations (1119,3084) yields a new equation:
% 30.40/8.37 | (783) e3 = e0
% 30.40/8.37 |
% 30.40/8.37 | Simplifying 783 yields:
% 30.40/8.37 | (784) e3 = e0
% 30.40/8.37 |
% 30.40/8.37 | Equations (784) can reduce 66 to:
% 30.40/8.37 | (270) $false
% 30.40/8.37 |
% 30.40/8.37 |-The branch is then unsatisfiable
% 30.40/8.37 |-Branch two:
% 30.40/8.37 | (1093) ~ (all_0_54_54 = e3)
% 30.40/8.37 | (412) all_0_59_59 = e3
% 30.40/8.37 |
% 30.40/8.37 | Combining equations (402,412) yields a new equation:
% 30.40/8.37 | (660) e4 = e3
% 30.40/8.37 |
% 30.40/8.37 | Simplifying 660 yields:
% 30.40/8.37 | (359) e4 = e3
% 30.40/8.37 |
% 30.40/8.37 | Equations (359) can reduce 34 to:
% 30.40/8.37 | (270) $false
% 30.40/8.37 |
% 30.40/8.37 |-The branch is then unsatisfiable
% 30.40/8.37 |-Branch two:
% 30.40/8.37 | (291) ~ (all_0_39_39 = e2)
% 30.40/8.37 | (630) all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 30.40/8.37 |
% 30.40/8.37 +-Applying beta-rule and splitting (186), into two cases.
% 30.40/8.37 |-Branch one:
% 30.40/8.37 | (336) all_0_39_39 = e2
% 30.40/8.37 |
% 30.40/8.37 | Equations (336) can reduce 291 to:
% 30.40/8.37 | (270) $false
% 30.40/8.37 |
% 30.40/8.37 |-The branch is then unsatisfiable
% 30.40/8.37 |-Branch two:
% 30.40/8.37 | (291) ~ (all_0_39_39 = e2)
% 30.40/8.37 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 30.40/8.37 |
% 30.40/8.37 +-Applying beta-rule and splitting (177), into two cases.
% 30.40/8.37 |-Branch one:
% 30.40/8.37 | (336) all_0_39_39 = e2
% 30.40/8.37 |
% 30.40/8.37 | Equations (336) can reduce 291 to:
% 30.40/8.37 | (270) $false
% 30.40/8.37 |
% 30.40/8.37 |-The branch is then unsatisfiable
% 30.40/8.37 |-Branch two:
% 30.40/8.37 | (291) ~ (all_0_39_39 = e2)
% 30.40/8.37 | (684) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 30.40/8.37 |
% 30.40/8.37 +-Applying beta-rule and splitting (339), into two cases.
% 30.40/8.37 |-Branch one:
% 30.40/8.37 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 30.40/8.37 |
% 30.40/8.37 +-Applying beta-rule and splitting (340), into two cases.
% 30.40/8.37 |-Branch one:
% 30.40/8.37 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 30.40/8.37 |
% 30.40/8.37 | Applying alpha-rule on (341) yields:
% 30.40/8.37 | (342) all_0_0_0 = e1
% 30.40/8.37 | (343) ~ (all_0_1_1 = e4)
% 30.40/8.37 |
% 30.40/8.37 | Combining equations (342,9064) yields a new equation:
% 30.40/8.37 | (571) e1 = e0
% 30.40/8.37 |
% 30.40/8.37 | Simplifying 571 yields:
% 30.40/8.37 | (560) e1 = e0
% 30.40/8.37 |
% 30.40/8.37 | Equations (560) can reduce 132 to:
% 30.40/8.37 | (270) $false
% 30.40/8.37 |
% 30.40/8.37 |-The branch is then unsatisfiable
% 30.40/8.37 |-Branch two:
% 30.40/8.37 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 30.40/8.37 |
% 30.40/8.37 | Applying alpha-rule on (346) yields:
% 30.40/8.37 | (347) all_0_2_2 = e0
% 30.40/8.37 | (348) ~ (all_0_3_3 = e4)
% 30.40/8.37 |
% 30.40/8.37 | Combining equations (347,11737) yields a new equation:
% 30.40/8.37 | (560) e1 = e0
% 30.40/8.37 |
% 30.40/8.37 | Equations (560) can reduce 132 to:
% 30.40/8.37 | (270) $false
% 30.40/8.37 |
% 30.40/8.37 |-The branch is then unsatisfiable
% 30.40/8.37 |-Branch two:
% 30.40/8.37 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 30.40/8.37 |
% 30.40/8.37 | Applying alpha-rule on (350) yields:
% 30.40/8.37 | (351) all_0_41_41 = e3
% 30.40/8.37 | (352) ~ (all_0_45_45 = e4)
% 30.40/8.37 |
% 30.40/8.37 +-Applying beta-rule and splitting (222), into two cases.
% 30.40/8.37 |-Branch one:
% 30.40/8.37 | (522) all_0_39_39 = e4
% 30.40/8.37 |
% 30.40/8.37 | Equations (522) can reduce 167 to:
% 30.40/8.37 | (694) ~ (all_0_43_43 = e4)
% 30.40/8.37 |
% 30.40/8.37 | Simplifying 694 yields:
% 30.40/8.37 | (510) ~ (all_0_43_43 = e4)
% 30.40/8.37 |
% 30.40/8.37 | Equations (522) can reduce 291 to:
% 30.40/8.37 | (231) ~ (e4 = e2)
% 30.40/8.37 |
% 30.40/8.37 +-Applying beta-rule and splitting (44), into two cases.
% 30.40/8.37 |-Branch one:
% 30.40/8.37 | (502) all_0_43_43 = e4
% 30.40/8.37 |
% 30.40/8.37 | Equations (502) can reduce 510 to:
% 30.40/8.37 | (270) $false
% 30.40/8.37 |
% 30.40/8.37 |-The branch is then unsatisfiable
% 30.40/8.37 |-Branch two:
% 30.40/8.37 | (510) ~ (all_0_43_43 = e4)
% 30.40/8.37 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 30.40/8.37 |
% 30.40/8.37 +-Applying beta-rule and splitting (511), into two cases.
% 30.40/8.37 |-Branch one:
% 30.40/8.37 | (363) all_0_45_45 = e4
% 30.40/8.37 |
% 30.40/8.37 | Equations (363) can reduce 352 to:
% 30.40/8.37 | (270) $false
% 30.40/8.37 |
% 30.40/8.37 |-The branch is then unsatisfiable
% 30.40/8.37 |-Branch two:
% 30.40/8.37 | (352) ~ (all_0_45_45 = e4)
% 30.40/8.37 | (517) all_0_46_46 = e4
% 30.40/8.37 |
% 30.40/8.37 | Combining equations (517,497) yields a new equation:
% 30.40/8.37 | (268) e4 = e2
% 30.40/8.37 |
% 30.40/8.37 | Simplifying 268 yields:
% 30.40/8.37 | (269) e4 = e2
% 30.40/8.37 |
% 30.40/8.37 | Equations (269) can reduce 231 to:
% 30.40/8.37 | (270) $false
% 30.40/8.37 |
% 30.40/8.37 |-The branch is then unsatisfiable
% 30.40/8.37 |-Branch two:
% 30.40/8.37 | (591) ~ (all_0_39_39 = e4)
% 30.40/8.37 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 30.40/8.37 |
% 30.40/8.37 +-Applying beta-rule and splitting (592), into two cases.
% 30.40/8.37 |-Branch one:
% 30.40/8.37 | (358) all_0_41_41 = e4
% 30.40/8.37 |
% 30.40/8.37 | Combining equations (351,358) yields a new equation:
% 30.40/8.37 | (359) e4 = e3
% 30.40/8.37 |
% 30.40/8.37 | Equations (359) can reduce 34 to:
% 30.40/8.37 | (270) $false
% 30.40/8.37 |
% 30.40/8.37 |-The branch is then unsatisfiable
% 30.40/8.37 |-Branch two:
% 30.40/8.37 | (361) ~ (all_0_41_41 = e4)
% 30.40/8.37 | (512) all_0_42_42 = e4
% 30.40/8.37 |
% 30.40/8.37 | Equations (512) can reduce 520 to:
% 30.40/8.37 | (270) $false
% 30.40/8.37 |
% 30.40/8.37 |-The branch is then unsatisfiable
% 30.40/8.37 |-Branch two:
% 30.40/8.37 | (4253) all_0_9_9 = e1 & ~ (all_0_10_10 = e3)
% 30.40/8.37 |
% 30.40/8.37 | Applying alpha-rule on (4253) yields:
% 30.40/8.37 | (4254) all_0_9_9 = e1
% 30.40/8.37 | (4255) ~ (all_0_10_10 = e3)
% 30.40/8.37 |
% 30.40/8.37 | Combining equations (11847,4254) yields a new equation:
% 30.40/8.37 | (12224) all_0_43_43 = e1
% 30.40/8.37 |
% 30.40/8.37 | Simplifying 12224 yields:
% 30.40/8.37 | (12225) all_0_43_43 = e1
% 30.40/8.37 |
% 30.40/8.38 | Equations (12225) can reduce 249 to:
% 30.40/8.38 | (270) $false
% 30.40/8.38 |
% 30.40/8.38 |-The branch is then unsatisfiable
% 30.40/8.38 |-Branch two:
% 30.40/8.38 | (4378) all_0_11_11 = e0 & ~ (all_0_12_12 = e3)
% 30.40/8.38 |
% 30.40/8.38 | Applying alpha-rule on (4378) yields:
% 30.40/8.38 | (4379) all_0_11_11 = e0
% 30.40/8.38 | (4380) ~ (all_0_12_12 = e3)
% 30.40/8.38 |
% 30.40/8.38 | Combining equations (4379,11848) yields a new equation:
% 30.40/8.38 | (454) all_0_45_45 = e0
% 30.40/8.38 |
% 30.40/8.38 | Equations (454) can reduce 488 to:
% 30.40/8.38 | (270) $false
% 30.40/8.38 |
% 30.40/8.38 |-The branch is then unsatisfiable
% 30.40/8.38 |-Branch two:
% 30.40/8.38 | (932) ~ (all_0_51_51 = e3)
% 30.40/8.38 | (1101) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 30.40/8.38 |
% 30.40/8.38 +-Applying beta-rule and splitting (173), into two cases.
% 30.40/8.38 |-Branch one:
% 30.40/8.38 | (4215) all_0_51_51 = e2
% 30.40/8.38 |
% 30.40/8.38 | Equations (4215) can reduce 255 to:
% 30.40/8.38 | (270) $false
% 30.40/8.38 |
% 30.40/8.38 |-The branch is then unsatisfiable
% 30.40/8.38 |-Branch two:
% 30.40/8.38 | (255) ~ (all_0_51_51 = e2)
% 30.40/8.38 | (4888) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1 | all_0_51_51 = e0
% 30.40/8.38 |
% 30.40/8.38 +-Applying beta-rule and splitting (4888), into two cases.
% 30.40/8.38 |-Branch one:
% 30.40/8.38 | (954) all_0_51_51 = e0
% 30.40/8.38 |
% 30.40/8.38 | Equations (954) can reduce 987 to:
% 30.40/8.38 | (270) $false
% 30.40/8.38 |
% 30.40/8.38 |-The branch is then unsatisfiable
% 30.40/8.38 |-Branch two:
% 30.40/8.38 | (987) ~ (all_0_51_51 = e0)
% 30.40/8.38 | (5003) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1
% 30.40/8.38 |
% 30.40/8.38 +-Applying beta-rule and splitting (5003), into two cases.
% 30.40/8.38 |-Branch one:
% 30.40/8.38 | (824) all_0_51_51 = e3
% 30.40/8.38 |
% 30.40/8.38 | Equations (824) can reduce 932 to:
% 30.40/8.38 | (270) $false
% 30.40/8.38 |
% 30.40/8.38 |-The branch is then unsatisfiable
% 30.40/8.38 |-Branch two:
% 30.40/8.38 | (932) ~ (all_0_51_51 = e3)
% 30.40/8.38 | (5007) all_0_51_51 = e4 | all_0_51_51 = e1
% 30.40/8.38 |
% 30.40/8.38 +-Applying beta-rule and splitting (5007), into two cases.
% 30.40/8.38 |-Branch one:
% 30.40/8.38 | (820) all_0_51_51 = e1
% 30.40/8.38 |
% 30.40/8.38 | Equations (820) can reduce 748 to:
% 30.40/8.38 | (270) $false
% 30.40/8.38 |
% 30.40/8.38 |-The branch is then unsatisfiable
% 30.40/8.38 |-Branch two:
% 30.40/8.38 | (748) ~ (all_0_51_51 = e1)
% 30.40/8.38 | (1467) all_0_51_51 = e4
% 30.40/8.38 |
% 30.40/8.38 | Equations (1467) can reduce 697 to:
% 30.40/8.38 | (270) $false
% 30.40/8.38 |
% 30.40/8.38 |-The branch is then unsatisfiable
% 30.40/8.38 |-Branch two:
% 30.40/8.38 | (874) ~ (all_0_53_53 = e1)
% 30.40/8.38 | (1001) all_0_58_58 = e1
% 30.40/8.38 |
% 30.40/8.38 | Combining equations (585,1001) yields a new equation:
% 30.40/8.38 | (560) e1 = e0
% 30.40/8.38 |
% 30.40/8.38 | Equations (560) can reduce 132 to:
% 30.40/8.38 | (270) $false
% 30.40/8.38 |
% 30.40/8.38 |-The branch is then unsatisfiable
% 30.40/8.38 |-Branch two:
% 30.40/8.38 | (995) ~ (all_0_56_56 = e1)
% 30.40/8.38 | (996) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 30.40/8.38 |
% 30.40/8.38 +-Applying beta-rule and splitting (208), into two cases.
% 30.40/8.38 |-Branch one:
% 30.40/8.38 | (388) all_0_56_56 = e2
% 30.40/8.38 |
% 30.40/8.38 | Equations (388) can reduce 300 to:
% 30.40/8.38 | (270) $false
% 30.40/8.38 |
% 30.40/8.38 |-The branch is then unsatisfiable
% 30.40/8.38 |-Branch two:
% 30.40/8.38 | (300) ~ (all_0_56_56 = e2)
% 30.40/8.38 | (5076) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1 | all_0_56_56 = e0
% 30.40/8.38 |
% 30.40/8.38 +-Applying beta-rule and splitting (5076), into two cases.
% 30.40/8.38 |-Branch one:
% 30.40/8.38 | (830) all_0_56_56 = e0
% 30.40/8.38 |
% 30.40/8.38 | Equations (830) can reduce 419 to:
% 30.40/8.38 | (270) $false
% 30.40/8.38 |
% 30.40/8.38 |-The branch is then unsatisfiable
% 30.40/8.38 |-Branch two:
% 30.40/8.38 | (419) ~ (all_0_56_56 = e0)
% 30.40/8.38 | (5667) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1
% 30.40/8.38 |
% 30.40/8.38 +-Applying beta-rule and splitting (5667), into two cases.
% 30.40/8.38 |-Branch one:
% 30.40/8.38 | (764) all_0_56_56 = e3
% 30.40/8.38 |
% 30.40/8.38 | Equations (764) can reduce 767 to:
% 30.40/8.38 | (270) $false
% 30.40/8.38 |
% 30.40/8.38 |-The branch is then unsatisfiable
% 30.40/8.38 |-Branch two:
% 30.40/8.38 | (767) ~ (all_0_56_56 = e3)
% 30.40/8.38 | (10136) all_0_56_56 = e4 | all_0_56_56 = e1
% 30.40/8.38 |
% 30.40/8.38 +-Applying beta-rule and splitting (10136), into two cases.
% 30.40/8.38 |-Branch one:
% 30.40/8.38 | (747) all_0_56_56 = e1
% 30.40/8.38 |
% 30.40/8.38 | Equations (747) can reduce 995 to:
% 30.40/8.38 | (270) $false
% 30.40/8.38 |
% 30.40/8.38 |-The branch is then unsatisfiable
% 30.40/8.38 |-Branch two:
% 30.40/8.38 | (995) ~ (all_0_56_56 = e1)
% 30.40/8.38 | (4744) all_0_56_56 = e4
% 30.40/8.38 |
% 30.40/8.38 | Equations (4744) can reduce 274 to:
% 30.40/8.38 | (270) $false
% 30.40/8.38 |
% 30.40/8.38 |-The branch is then unsatisfiable
% 30.40/8.38 |-Branch two:
% 30.40/8.38 | (431) ~ (all_0_58_58 = e0)
% 30.40/8.38 | (2308) all_0_59_59 = e0
% 30.40/8.38 |
% 30.40/8.38 | Combining equations (402,2308) yields a new equation:
% 30.40/8.38 | (478) e4 = e0
% 30.40/8.38 |
% 30.40/8.38 | Simplifying 478 yields:
% 30.40/8.38 | (479) e4 = e0
% 30.40/8.38 |
% 30.40/8.38 | Equations (479) can reduce 6 to:
% 30.40/8.38 | (270) $false
% 30.40/8.38 |
% 30.40/8.38 |-The branch is then unsatisfiable
% 30.40/8.38 |-Branch two:
% 30.40/8.38 | (3011) ~ (all_0_54_54 = e0)
% 30.40/8.38 | (2308) all_0_59_59 = e0
% 30.40/8.38 |
% 30.40/8.38 | Combining equations (2308,402) yields a new equation:
% 30.40/8.38 | (479) e4 = e0
% 30.40/8.38 |
% 30.40/8.38 | Equations (479) can reduce 6 to:
% 30.40/8.38 | (270) $false
% 30.40/8.38 |
% 30.40/8.38 |-The branch is then unsatisfiable
% 30.40/8.38 |-Branch two:
% 30.40/8.38 | (625) ~ (all_0_44_44 = e0)
% 30.40/8.38 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 30.40/8.38 |
% 30.40/8.38 +-Applying beta-rule and splitting (626), into two cases.
% 30.40/8.38 |-Branch one:
% 30.40/8.38 | (827) all_0_52_52 = e0
% 30.40/8.38 |
% 30.40/8.38 | Combining equations (827,685) yields a new equation:
% 30.40/8.38 | (316) e2 = e0
% 30.40/8.38 |
% 30.40/8.38 | Equations (316) can reduce 57 to:
% 30.40/8.38 | (270) $false
% 30.40/8.38 |
% 30.40/8.38 |-The branch is then unsatisfiable
% 30.40/8.38 |-Branch two:
% 30.40/8.38 | (925) ~ (all_0_52_52 = e0)
% 30.40/8.38 | (2258) all_0_57_57 = e0
% 30.40/8.38 |
% 30.40/8.38 | Equations (2258) can reduce 10 to:
% 30.40/8.38 | (625) ~ (all_0_44_44 = e0)
% 30.40/8.38 |
% 30.40/8.38 | Equations (2258) can reduce 644 to:
% 30.40/8.38 | (568) ~ (e1 = e0)
% 30.40/8.38 |
% 30.40/8.38 | Simplifying 568 yields:
% 30.40/8.38 | (132) ~ (e1 = e0)
% 30.40/8.38 |
% 30.40/8.38 | From (2258) and (30) follows:
% 30.40/8.38 | (12293) op(e2, e0) = all_0_19_19
% 30.40/8.38 |
% 30.40/8.38 +-Applying beta-rule and splitting (373), into two cases.
% 30.40/8.38 |-Branch one:
% 30.40/8.38 | (621) all_0_44_44 = e0
% 30.40/8.38 |
% 30.40/8.38 | Equations (621) can reduce 625 to:
% 30.40/8.38 | (270) $false
% 30.40/8.38 |
% 30.40/8.38 |-The branch is then unsatisfiable
% 30.40/8.38 |-Branch two:
% 30.40/8.38 | (625) ~ (all_0_44_44 = e0)
% 30.40/8.38 | (858) all_0_44_44 = e3
% 30.40/8.38 |
% 30.40/8.38 | Equations (858) can reduce 625 to:
% 30.40/8.38 | (66) ~ (e3 = e0)
% 30.40/8.38 |
% 30.40/8.38 | From (858) and (165) follows:
% 30.40/8.38 | (3499) op(e2, e3) = all_0_15_15
% 30.40/8.39 |
% 30.40/8.39 | Instantiating formula (201) with e2, e3, all_0_15_15, e0 and discharging atoms op(e2, e3) = all_0_15_15, op(e2, e3) = e0, yields:
% 30.40/8.39 | (5959) all_0_15_15 = e0
% 30.40/8.39 |
% 30.40/8.39 | Instantiating formula (201) with e2, e0, all_0_19_19, e1 and discharging atoms op(e2, e0) = all_0_19_19, op(e2, e0) = e1, yields:
% 30.40/8.39 | (12301) all_0_19_19 = e1
% 30.40/8.39 |
% 30.40/8.39 +-Applying beta-rule and splitting (87), into two cases.
% 30.40/8.39 |-Branch one:
% 30.40/8.39 | (650) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 30.40/8.39 |
% 30.40/8.39 +-Applying beta-rule and splitting (650), into two cases.
% 30.40/8.39 |-Branch one:
% 30.40/8.39 | (651) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 30.40/8.39 |
% 30.40/8.39 +-Applying beta-rule and splitting (651), into two cases.
% 30.40/8.39 |-Branch one:
% 30.40/8.39 | (652) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 30.40/8.39 |
% 30.40/8.39 | Applying alpha-rule on (652) yields:
% 30.40/8.39 | (653) all_0_13_13 = e4
% 30.40/8.39 | (654) ~ (all_0_14_14 = e2)
% 30.40/8.39 |
% 30.40/8.39 | Combining equations (4829,653) yields a new equation:
% 30.40/8.39 | (269) e4 = e2
% 30.40/8.39 |
% 30.40/8.39 | Equations (269) can reduce 231 to:
% 30.40/8.39 | (270) $false
% 30.40/8.39 |
% 30.40/8.39 |-The branch is then unsatisfiable
% 30.40/8.39 |-Branch two:
% 30.40/8.39 | (657) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 30.40/8.39 |
% 30.40/8.39 | Applying alpha-rule on (657) yields:
% 30.40/8.39 | (658) all_0_15_15 = e3
% 30.40/8.39 | (659) ~ (all_0_16_16 = e2)
% 30.40/8.39 |
% 30.40/8.39 | Combining equations (658,5959) yields a new equation:
% 30.40/8.39 | (783) e3 = e0
% 30.40/8.39 |
% 30.40/8.39 | Simplifying 783 yields:
% 30.40/8.39 | (784) e3 = e0
% 30.40/8.39 |
% 30.40/8.39 | Equations (784) can reduce 66 to:
% 30.40/8.39 | (270) $false
% 30.40/8.39 |
% 30.40/8.39 |-The branch is then unsatisfiable
% 30.40/8.39 |-Branch two:
% 30.40/8.39 | (663) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 30.40/8.39 |
% 30.40/8.39 | Applying alpha-rule on (663) yields:
% 30.40/8.39 | (664) all_0_17_17 = e1
% 30.40/8.39 | (665) ~ (all_0_18_18 = e2)
% 30.40/8.39 |
% 30.40/8.39 | Combining equations (664,11735) yields a new equation:
% 30.40/8.39 | (526) e4 = e1
% 30.40/8.39 |
% 30.40/8.39 | Equations (526) can reduce 251 to:
% 30.40/8.39 | (270) $false
% 30.40/8.39 |
% 30.40/8.39 |-The branch is then unsatisfiable
% 30.40/8.39 |-Branch two:
% 30.40/8.39 | (1762) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 30.40/8.39 |
% 30.40/8.39 | Applying alpha-rule on (1762) yields:
% 30.40/8.39 | (1763) all_0_19_19 = e0
% 30.40/8.39 | (1764) ~ (all_0_20_20 = e2)
% 30.40/8.39 |
% 30.40/8.39 | Combining equations (12301,1763) yields a new equation:
% 30.40/8.39 | (571) e1 = e0
% 30.40/8.39 |
% 30.40/8.39 | Simplifying 571 yields:
% 30.40/8.39 | (560) e1 = e0
% 30.40/8.39 |
% 30.40/8.39 | Equations (560) can reduce 132 to:
% 30.40/8.39 | (270) $false
% 30.40/8.39 |
% 30.40/8.39 |-The branch is then unsatisfiable
% 30.40/8.39 |-Branch two:
% 30.40/8.39 | (534) ~ (all_0_40_40 = e1)
% 30.40/8.39 | (3352) all_0_52_52 = e1 | all_0_57_57 = e1
% 30.40/8.39 |
% 30.40/8.39 +-Applying beta-rule and splitting (3352), into two cases.
% 30.40/8.39 |-Branch one:
% 30.40/8.39 | (848) all_0_52_52 = e1
% 30.40/8.39 |
% 30.40/8.39 | Combining equations (685,848) yields a new equation:
% 30.40/8.39 | (531) e2 = e1
% 30.40/8.39 |
% 30.40/8.39 | Simplifying 531 yields:
% 30.40/8.39 | (322) e2 = e1
% 30.40/8.39 |
% 30.40/8.39 | Equations (322) can reduce 141 to:
% 30.40/8.39 | (270) $false
% 30.40/8.39 |
% 30.40/8.39 |-The branch is then unsatisfiable
% 30.40/8.39 |-Branch two:
% 30.40/8.39 | (642) ~ (all_0_52_52 = e1)
% 30.40/8.39 | (997) all_0_57_57 = e1
% 30.40/8.39 |
% 30.40/8.39 | Equations (997) can reduce 10 to:
% 30.40/8.39 | (131) ~ (all_0_44_44 = e1)
% 30.40/8.39 |
% 30.40/8.39 | Equations (997) can reduce 104 to:
% 30.40/8.39 | (995) ~ (all_0_56_56 = e1)
% 30.40/8.39 |
% 30.40/8.39 +-Applying beta-rule and splitting (9), into two cases.
% 30.40/8.39 |-Branch one:
% 30.40/8.39 | (621) all_0_44_44 = e0
% 30.40/8.39 |
% 30.40/8.39 | Equations (621) can reduce 15 to:
% 30.40/8.39 | (238) ~ (all_0_40_40 = e0)
% 30.40/8.39 |
% 30.40/8.39 | Equations (621) can reduce 174 to:
% 30.40/8.39 | (1057) ~ (all_0_46_46 = e0)
% 30.40/8.39 |
% 30.40/8.39 | Simplifying 1057 yields:
% 30.40/8.39 | (1010) ~ (all_0_46_46 = e0)
% 30.40/8.39 |
% 30.40/8.39 | Equations (621) can reduce 45 to:
% 30.40/8.39 | (456) ~ (e4 = e0)
% 30.40/8.39 |
% 30.40/8.39 | Simplifying 456 yields:
% 30.40/8.39 | (6) ~ (e4 = e0)
% 30.40/8.39 |
% 30.40/8.39 | Equations (621) can reduce 131 to:
% 30.40/8.39 | (568) ~ (e1 = e0)
% 30.40/8.39 |
% 30.40/8.39 | Simplifying 568 yields:
% 30.40/8.39 | (132) ~ (e1 = e0)
% 30.40/8.39 |
% 30.40/8.39 +-Applying beta-rule and splitting (221), into two cases.
% 30.40/8.39 |-Branch one:
% 30.40/8.39 | (1132) all_0_46_46 = e0
% 30.40/8.39 |
% 30.40/8.39 | Equations (1132) can reduce 1010 to:
% 30.40/8.39 | (270) $false
% 30.40/8.39 |
% 30.40/8.39 |-The branch is then unsatisfiable
% 30.40/8.39 |-Branch two:
% 30.40/8.39 | (1010) ~ (all_0_46_46 = e0)
% 30.40/8.39 | (3629) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 30.40/8.39 |
% 30.40/8.39 +-Applying beta-rule and splitting (176), into two cases.
% 30.40/8.39 |-Branch one:
% 30.40/8.39 | (830) all_0_56_56 = e0
% 30.40/8.39 |
% 30.40/8.39 | Equations (830) can reduce 419 to:
% 30.40/8.39 | (270) $false
% 30.40/8.39 |
% 30.40/8.39 |-The branch is then unsatisfiable
% 30.40/8.39 |-Branch two:
% 30.40/8.39 | (419) ~ (all_0_56_56 = e0)
% 30.40/8.39 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 30.40/8.39 |
% 30.40/8.39 +-Applying beta-rule and splitting (133), into two cases.
% 30.40/8.39 |-Branch one:
% 30.40/8.39 | (671) all_0_40_40 = e3
% 30.40/8.39 |
% 30.40/8.39 | Combining equations (671,9065) yields a new equation:
% 30.40/8.39 | (12353) all_0_2_2 = e3
% 30.40/8.39 |
% 30.40/8.39 | Equations (671) can reduce 145 to:
% 30.40/8.39 | (1331) ~ (all_0_42_42 = e3)
% 30.40/8.39 |
% 30.40/8.39 | Simplifying 1331 yields:
% 30.40/8.39 | (1316) ~ (all_0_42_42 = e3)
% 30.40/8.39 |
% 30.40/8.39 | Equations (671) can reduce 238 to:
% 30.40/8.39 | (66) ~ (e3 = e0)
% 30.40/8.39 |
% 30.40/8.39 +-Applying beta-rule and splitting (186), into two cases.
% 30.40/8.39 |-Branch one:
% 30.40/8.39 | (336) all_0_39_39 = e2
% 30.40/8.39 |
% 30.40/8.39 | Equations (336) can reduce 184 to:
% 30.40/8.39 | (1336) ~ (all_0_42_42 = e2)
% 30.40/8.39 |
% 30.40/8.39 | Simplifying 1336 yields:
% 30.40/8.39 | (498) ~ (all_0_42_42 = e2)
% 30.40/8.39 |
% 30.40/8.39 | Equations (336) can reduce 167 to:
% 30.40/8.39 | (5937) ~ (all_0_43_43 = e2)
% 30.40/8.39 |
% 30.40/8.39 | Simplifying 5937 yields:
% 30.40/8.39 | (292) ~ (all_0_43_43 = e2)
% 30.40/8.39 |
% 30.40/8.39 | Equations (336) can reduce 32 to:
% 30.40/8.39 | (254) ~ (all_0_51_51 = e2)
% 30.40/8.39 |
% 30.40/8.39 | Simplifying 254 yields:
% 30.40/8.39 | (255) ~ (all_0_51_51 = e2)
% 30.40/8.39 |
% 30.40/8.39 | Equations (336) can reduce 212 to:
% 30.40/8.39 | (299) ~ (all_0_56_56 = e2)
% 30.40/8.39 |
% 30.40/8.39 | Simplifying 299 yields:
% 30.40/8.39 | (300) ~ (all_0_56_56 = e2)
% 30.40/8.39 |
% 30.40/8.39 +-Applying beta-rule and splitting (47), into two cases.
% 30.40/8.39 |-Branch one:
% 30.40/8.39 | (450) all_0_43_43 = e2
% 30.40/8.39 |
% 30.40/8.39 | Equations (450) can reduce 292 to:
% 30.40/8.39 | (270) $false
% 30.40/8.39 |
% 30.40/8.39 |-The branch is then unsatisfiable
% 30.40/8.39 |-Branch two:
% 30.40/8.39 | (292) ~ (all_0_43_43 = e2)
% 30.40/8.39 | (453) all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2
% 30.40/8.39 |
% 30.40/8.39 +-Applying beta-rule and splitting (16), into two cases.
% 30.40/8.39 |-Branch one:
% 30.40/8.39 | (698) all_0_42_42 = e2
% 30.40/8.39 |
% 30.40/8.39 | Equations (698) can reduce 498 to:
% 30.40/8.39 | (270) $false
% 30.40/8.39 |
% 30.40/8.39 |-The branch is then unsatisfiable
% 30.40/8.39 |-Branch two:
% 30.40/8.39 | (498) ~ (all_0_42_42 = e2)
% 30.40/8.39 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 30.40/8.39 |
% 30.40/8.39 +-Applying beta-rule and splitting (208), into two cases.
% 30.40/8.39 |-Branch one:
% 30.40/8.39 | (388) all_0_56_56 = e2
% 30.40/8.39 |
% 30.40/8.39 | Equations (388) can reduce 300 to:
% 30.40/8.39 | (270) $false
% 30.40/8.39 |
% 30.40/8.39 |-The branch is then unsatisfiable
% 30.40/8.39 |-Branch two:
% 30.40/8.39 | (300) ~ (all_0_56_56 = e2)
% 30.40/8.39 | (5076) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1 | all_0_56_56 = e0
% 30.40/8.39 |
% 30.40/8.39 +-Applying beta-rule and splitting (3629), into two cases.
% 30.40/8.39 |-Branch one:
% 30.40/8.39 | (563) all_0_49_49 = e0
% 30.40/8.39 |
% 30.40/8.39 | Combining equations (563,589) yields a new equation:
% 30.40/8.39 | (560) e1 = e0
% 30.40/8.39 |
% 30.40/8.39 | Equations (560) can reduce 132 to:
% 30.40/8.39 | (270) $false
% 30.40/8.39 |
% 30.40/8.39 |-The branch is then unsatisfiable
% 30.40/8.39 |-Branch two:
% 30.40/8.39 | (1231) ~ (all_0_49_49 = e0)
% 30.40/8.39 | (3638) all_0_54_54 = e0 | all_0_59_59 = e0
% 30.40/8.39 |
% 30.40/8.39 +-Applying beta-rule and splitting (5076), into two cases.
% 30.40/8.39 |-Branch one:
% 30.40/8.39 | (830) all_0_56_56 = e0
% 30.40/8.39 |
% 30.40/8.39 | Equations (830) can reduce 419 to:
% 30.40/8.39 | (270) $false
% 30.40/8.39 |
% 30.40/8.39 |-The branch is then unsatisfiable
% 30.40/8.39 |-Branch two:
% 30.40/8.39 | (419) ~ (all_0_56_56 = e0)
% 30.40/8.39 | (5667) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1
% 30.40/8.39 |
% 30.40/8.39 +-Applying beta-rule and splitting (3638), into two cases.
% 30.40/8.39 |-Branch one:
% 30.40/8.39 | (3084) all_0_54_54 = e0
% 30.40/8.39 |
% 30.40/8.39 | Equations (3084) can reduce 50 to:
% 30.40/8.39 | (987) ~ (all_0_51_51 = e0)
% 30.40/8.39 |
% 30.40/8.39 | Equations (3084) can reduce 252 to:
% 30.40/8.39 | (584) ~ (all_0_53_53 = e0)
% 30.40/8.39 |
% 30.40/8.39 | Equations (3084) can reduce 261 to:
% 30.40/8.39 | (566) ~ (e2 = e0)
% 30.40/8.39 |
% 30.40/8.39 | Simplifying 566 yields:
% 30.40/8.39 | (57) ~ (e2 = e0)
% 30.40/8.39 |
% 30.40/8.39 +-Applying beta-rule and splitting (5667), into two cases.
% 30.40/8.39 |-Branch one:
% 30.40/8.39 | (764) all_0_56_56 = e3
% 30.40/8.39 |
% 30.40/8.39 | Equations (764) can reduce 60 to:
% 30.40/8.39 | (932) ~ (all_0_51_51 = e3)
% 30.40/8.39 |
% 30.40/8.39 | Equations (764) can reduce 300 to:
% 30.40/8.39 | (223) ~ (e3 = e2)
% 30.40/8.39 |
% 30.40/8.39 | Equations (764) can reduce 419 to:
% 30.40/8.39 | (66) ~ (e3 = e0)
% 30.40/8.39 |
% 30.40/8.39 +-Applying beta-rule and splitting (173), into two cases.
% 30.40/8.39 |-Branch one:
% 30.40/8.39 | (4215) all_0_51_51 = e2
% 30.40/8.39 |
% 30.40/8.39 | Equations (4215) can reduce 255 to:
% 30.40/8.39 | (270) $false
% 30.40/8.39 |
% 30.40/8.39 |-The branch is then unsatisfiable
% 30.40/8.39 |-Branch two:
% 30.40/8.39 | (255) ~ (all_0_51_51 = e2)
% 30.40/8.39 | (4888) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1 | all_0_51_51 = e0
% 30.40/8.39 |
% 30.40/8.39 +-Applying beta-rule and splitting (4888), into two cases.
% 30.40/8.39 |-Branch one:
% 30.40/8.39 | (954) all_0_51_51 = e0
% 30.40/8.39 |
% 30.40/8.40 | Equations (954) can reduce 987 to:
% 30.40/8.40 | (270) $false
% 30.40/8.40 |
% 30.40/8.40 |-The branch is then unsatisfiable
% 30.40/8.40 |-Branch two:
% 30.40/8.40 | (987) ~ (all_0_51_51 = e0)
% 30.40/8.40 | (5003) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1
% 30.40/8.40 |
% 30.40/8.40 +-Applying beta-rule and splitting (5003), into two cases.
% 30.40/8.40 |-Branch one:
% 30.40/8.40 | (824) all_0_51_51 = e3
% 30.40/8.40 |
% 30.40/8.40 | Equations (824) can reduce 932 to:
% 30.40/8.40 | (270) $false
% 30.40/8.40 |
% 30.40/8.40 |-The branch is then unsatisfiable
% 30.40/8.40 |-Branch two:
% 30.40/8.40 | (932) ~ (all_0_51_51 = e3)
% 30.40/8.40 | (5007) all_0_51_51 = e4 | all_0_51_51 = e1
% 30.40/8.40 |
% 30.40/8.40 +-Applying beta-rule and splitting (5007), into two cases.
% 30.40/8.40 |-Branch one:
% 30.40/8.40 | (820) all_0_51_51 = e1
% 30.40/8.40 |
% 30.40/8.40 | Equations (820) can reduce 932 to:
% 30.40/8.40 | (769) ~ (e3 = e1)
% 30.40/8.40 |
% 30.40/8.40 | Simplifying 769 yields:
% 30.40/8.40 | (136) ~ (e3 = e1)
% 30.40/8.40 |
% 30.40/8.40 +-Applying beta-rule and splitting (1245), into two cases.
% 30.40/8.40 |-Branch one:
% 30.40/8.40 | (1258) all_0_42_42 = e3
% 30.40/8.40 |
% 30.40/8.40 | Equations (1258) can reduce 1316 to:
% 30.40/8.40 | (270) $false
% 30.40/8.40 |
% 30.40/8.40 |-The branch is then unsatisfiable
% 30.40/8.40 |-Branch two:
% 30.40/8.40 | (1316) ~ (all_0_42_42 = e3)
% 30.40/8.40 | (1317) all_0_42_42 = e4 | all_0_42_42 = e1
% 30.40/8.40 |
% 30.40/8.40 +-Applying beta-rule and splitting (95), into two cases.
% 30.40/8.40 |-Branch one:
% 30.40/8.40 | (1258) all_0_42_42 = e3
% 30.40/8.40 |
% 30.40/8.40 | Equations (1258) can reduce 1316 to:
% 30.40/8.40 | (270) $false
% 30.40/8.40 |
% 30.40/8.40 |-The branch is then unsatisfiable
% 30.40/8.40 |-Branch two:
% 30.40/8.40 | (1316) ~ (all_0_42_42 = e3)
% 30.40/8.40 | (3656) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 30.40/8.40 |
% 30.40/8.40 +-Applying beta-rule and splitting (21), into two cases.
% 30.40/8.40 |-Branch one:
% 30.40/8.40 | (824) all_0_51_51 = e3
% 30.40/8.40 |
% 30.40/8.40 | Combining equations (824,820) yields a new equation:
% 30.40/8.40 | (537) e3 = e1
% 30.40/8.40 |
% 30.40/8.40 | Simplifying 537 yields:
% 30.40/8.40 | (538) e3 = e1
% 30.40/8.40 |
% 30.40/8.40 | Equations (538) can reduce 136 to:
% 30.40/8.40 | (270) $false
% 30.40/8.40 |
% 30.40/8.40 |-The branch is then unsatisfiable
% 30.40/8.40 |-Branch two:
% 30.40/8.40 | (932) ~ (all_0_51_51 = e3)
% 30.40/8.40 | (1101) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 30.40/8.40 |
% 30.40/8.40 +-Applying beta-rule and splitting (1101), into two cases.
% 30.40/8.40 |-Branch one:
% 30.40/8.40 | (864) all_0_52_52 = e3
% 30.40/8.40 |
% 30.40/8.40 | Combining equations (864,685) yields a new equation:
% 30.40/8.40 | (437) e3 = e2
% 30.40/8.40 |
% 30.40/8.40 | Simplifying 437 yields:
% 30.40/8.40 | (414) e3 = e2
% 30.40/8.40 |
% 30.40/8.40 | Equations (414) can reduce 223 to:
% 30.40/8.40 | (270) $false
% 30.40/8.40 |
% 30.40/8.40 |-The branch is then unsatisfiable
% 30.40/8.40 |-Branch two:
% 30.40/8.40 | (826) ~ (all_0_52_52 = e3)
% 30.40/8.40 | (1107) all_0_53_53 = e3 | all_0_54_54 = e3
% 30.40/8.40 |
% 30.40/8.40 +-Applying beta-rule and splitting (1107), into two cases.
% 30.40/8.40 |-Branch one:
% 30.40/8.40 | (1114) all_0_53_53 = e3
% 30.40/8.40 |
% 30.40/8.40 | Equations (1114) can reduce 599 to:
% 30.40/8.40 | (719) ~ (e4 = e3)
% 30.40/8.40 |
% 30.40/8.40 | Simplifying 719 yields:
% 30.40/8.40 | (34) ~ (e4 = e3)
% 30.40/8.40 |
% 30.40/8.40 | Equations (1114) can reduce 259 to:
% 30.40/8.40 | (223) ~ (e3 = e2)
% 30.40/8.40 |
% 30.40/8.40 | Equations (1114) can reduce 584 to:
% 30.40/8.40 | (66) ~ (e3 = e0)
% 30.40/8.40 |
% 30.40/8.40 +-Applying beta-rule and splitting (453), into two cases.
% 30.40/8.40 |-Branch one:
% 30.40/8.40 | (370) all_0_44_44 = e2
% 30.40/8.40 |
% 30.40/8.40 | Combining equations (621,370) yields a new equation:
% 30.40/8.40 | (316) e2 = e0
% 30.40/8.40 |
% 30.40/8.40 | Equations (316) can reduce 57 to:
% 30.40/8.40 | (270) $false
% 30.40/8.40 |
% 30.40/8.40 |-The branch is then unsatisfiable
% 30.40/8.40 |-Branch two:
% 30.40/8.40 | (333) ~ (all_0_44_44 = e2)
% 30.40/8.40 | (493) all_0_45_45 = e2 | all_0_46_46 = e2
% 30.40/8.40 |
% 30.40/8.40 +-Applying beta-rule and splitting (3656), into two cases.
% 30.40/8.40 |-Branch one:
% 30.40/8.40 | (1091) all_0_46_46 = e3
% 30.40/8.40 |
% 30.40/8.40 +-Applying beta-rule and splitting (493), into two cases.
% 30.40/8.40 |-Branch one:
% 30.40/8.40 | (374) all_0_45_45 = e2
% 30.40/8.40 |
% 30.40/8.40 | Equations (374) can reduce 434 to:
% 30.40/8.40 | (270) $false
% 30.40/8.40 |
% 30.40/8.40 |-The branch is then unsatisfiable
% 30.40/8.40 |-Branch two:
% 30.40/8.40 | (434) ~ (all_0_45_45 = e2)
% 30.40/8.40 | (497) all_0_46_46 = e2
% 30.40/8.40 |
% 30.40/8.40 | Combining equations (1091,497) yields a new equation:
% 30.40/8.40 | (437) e3 = e2
% 30.40/8.40 |
% 30.40/8.40 | Simplifying 437 yields:
% 30.40/8.40 | (414) e3 = e2
% 30.40/8.40 |
% 30.40/8.40 | Equations (414) can reduce 223 to:
% 30.40/8.40 | (270) $false
% 30.40/8.40 |
% 30.40/8.40 |-The branch is then unsatisfiable
% 30.40/8.40 |-Branch two:
% 30.40/8.40 | (413) ~ (all_0_46_46 = e3)
% 30.40/8.40 | (3700) all_0_54_54 = e3 | all_0_59_59 = e3
% 30.40/8.40 |
% 30.40/8.40 +-Applying beta-rule and splitting (3700), into two cases.
% 30.40/8.40 |-Branch one:
% 30.40/8.40 | (1119) all_0_54_54 = e3
% 30.40/8.40 |
% 30.40/8.40 | Combining equations (3084,1119) yields a new equation:
% 30.40/8.40 | (784) e3 = e0
% 30.40/8.40 |
% 30.40/8.40 | Equations (784) can reduce 66 to:
% 30.40/8.40 | (270) $false
% 30.40/8.40 |
% 30.40/8.40 |-The branch is then unsatisfiable
% 30.40/8.40 |-Branch two:
% 30.40/8.40 | (1093) ~ (all_0_54_54 = e3)
% 30.40/8.40 | (412) all_0_59_59 = e3
% 30.40/8.40 |
% 30.40/8.40 | Combining equations (402,412) yields a new equation:
% 30.40/8.40 | (660) e4 = e3
% 30.40/8.40 |
% 30.40/8.40 | Simplifying 660 yields:
% 30.40/8.40 | (359) e4 = e3
% 30.40/8.40 |
% 30.40/8.40 | Equations (359) can reduce 34 to:
% 30.40/8.40 | (270) $false
% 30.40/8.40 |
% 30.40/8.40 |-The branch is then unsatisfiable
% 30.40/8.40 |-Branch two:
% 30.40/8.40 | (356) ~ (all_0_53_53 = e3)
% 30.40/8.40 | (1119) all_0_54_54 = e3
% 30.40/8.40 |
% 30.40/8.40 | Combining equations (1119,3084) yields a new equation:
% 30.40/8.40 | (783) e3 = e0
% 30.40/8.40 |
% 30.40/8.40 | Simplifying 783 yields:
% 30.40/8.40 | (784) e3 = e0
% 30.40/8.40 |
% 30.40/8.40 | Equations (784) can reduce 66 to:
% 30.40/8.40 | (270) $false
% 30.40/8.40 |
% 30.40/8.40 |-The branch is then unsatisfiable
% 30.40/8.40 |-Branch two:
% 30.40/8.40 | (748) ~ (all_0_51_51 = e1)
% 30.40/8.40 | (1467) all_0_51_51 = e4
% 30.40/8.40 |
% 30.40/8.40 | Equations (1467) can reduce 697 to:
% 30.40/8.40 | (270) $false
% 30.40/8.40 |
% 30.40/8.40 |-The branch is then unsatisfiable
% 30.40/8.40 |-Branch two:
% 30.40/8.40 | (767) ~ (all_0_56_56 = e3)
% 30.40/8.40 | (10136) all_0_56_56 = e4 | all_0_56_56 = e1
% 30.40/8.40 |
% 30.40/8.40 +-Applying beta-rule and splitting (10136), into two cases.
% 30.40/8.40 |-Branch one:
% 30.40/8.40 | (747) all_0_56_56 = e1
% 30.40/8.40 |
% 30.40/8.40 | Equations (747) can reduce 995 to:
% 30.40/8.40 | (270) $false
% 30.40/8.40 |
% 30.40/8.40 |-The branch is then unsatisfiable
% 30.40/8.40 |-Branch two:
% 30.40/8.40 | (995) ~ (all_0_56_56 = e1)
% 30.40/8.40 | (4744) all_0_56_56 = e4
% 30.40/8.40 |
% 30.40/8.40 | Equations (4744) can reduce 274 to:
% 30.40/8.40 | (270) $false
% 30.40/8.40 |
% 30.40/8.40 |-The branch is then unsatisfiable
% 30.40/8.40 |-Branch two:
% 30.40/8.40 | (3011) ~ (all_0_54_54 = e0)
% 30.40/8.40 | (2308) all_0_59_59 = e0
% 30.40/8.40 |
% 30.40/8.40 | Combining equations (2308,402) yields a new equation:
% 30.40/8.40 | (479) e4 = e0
% 30.40/8.40 |
% 30.40/8.40 | Equations (479) can reduce 6 to:
% 30.40/8.40 | (270) $false
% 30.40/8.40 |
% 30.40/8.40 |-The branch is then unsatisfiable
% 30.40/8.40 |-Branch two:
% 30.40/8.40 | (291) ~ (all_0_39_39 = e2)
% 30.40/8.40 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 30.40/8.40 |
% 30.40/8.40 +-Applying beta-rule and splitting (16), into two cases.
% 30.40/8.40 |-Branch one:
% 30.40/8.40 | (698) all_0_42_42 = e2
% 30.40/8.40 |
% 30.40/8.40 | Equations (698) can reduce 18 to:
% 30.40/8.40 | (1435) ~ (all_0_46_46 = e2)
% 30.40/8.40 |
% 30.40/8.40 | Simplifying 1435 yields:
% 30.40/8.40 | (1436) ~ (all_0_46_46 = e2)
% 30.40/8.40 |
% 30.40/8.40 | Equations (698) can reduce 520 to:
% 30.40/8.40 | (377) ~ (e4 = e2)
% 30.40/8.40 |
% 30.40/8.40 | Simplifying 377 yields:
% 30.40/8.40 | (231) ~ (e4 = e2)
% 30.40/8.40 |
% 30.40/8.40 | Equations (698) can reduce 199 to:
% 30.40/8.40 | (57) ~ (e2 = e0)
% 30.40/8.40 |
% 30.40/8.40 +-Applying beta-rule and splitting (47), into two cases.
% 30.40/8.40 |-Branch one:
% 30.40/8.40 | (450) all_0_43_43 = e2
% 30.40/8.40 |
% 30.40/8.40 +-Applying beta-rule and splitting (44), into two cases.
% 30.40/8.40 |-Branch one:
% 30.40/8.40 | (502) all_0_43_43 = e4
% 30.40/8.40 |
% 30.40/8.40 | Combining equations (450,502) yields a new equation:
% 30.40/8.40 | (269) e4 = e2
% 30.40/8.40 |
% 30.40/8.40 | Equations (269) can reduce 231 to:
% 30.40/8.40 | (270) $false
% 30.40/8.40 |
% 30.40/8.40 |-The branch is then unsatisfiable
% 30.40/8.40 |-Branch two:
% 30.40/8.40 | (510) ~ (all_0_43_43 = e4)
% 30.40/8.40 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 30.40/8.40 |
% 30.40/8.40 +-Applying beta-rule and splitting (511), into two cases.
% 30.40/8.40 |-Branch one:
% 30.40/8.40 | (363) all_0_45_45 = e4
% 30.40/8.40 |
% 30.40/8.40 +-Applying beta-rule and splitting (3629), into two cases.
% 30.40/8.40 |-Branch one:
% 30.40/8.40 | (563) all_0_49_49 = e0
% 30.40/8.40 |
% 30.40/8.40 | Combining equations (563,589) yields a new equation:
% 30.40/8.40 | (560) e1 = e0
% 30.40/8.40 |
% 30.40/8.40 | Equations (560) can reduce 132 to:
% 30.40/8.40 | (270) $false
% 30.40/8.40 |
% 30.40/8.40 |-The branch is then unsatisfiable
% 30.40/8.40 |-Branch two:
% 30.40/8.40 | (1231) ~ (all_0_49_49 = e0)
% 30.40/8.40 | (3638) all_0_54_54 = e0 | all_0_59_59 = e0
% 30.40/8.40 |
% 30.40/8.40 | Equations (589) can reduce 1231 to:
% 30.40/8.40 | (132) ~ (e1 = e0)
% 30.40/8.40 |
% 30.40/8.40 +-Applying beta-rule and splitting (339), into two cases.
% 30.40/8.40 |-Branch one:
% 30.40/8.40 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 30.40/8.40 |
% 30.40/8.40 +-Applying beta-rule and splitting (340), into two cases.
% 30.40/8.40 |-Branch one:
% 30.40/8.40 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 30.40/8.40 |
% 30.40/8.40 | Applying alpha-rule on (341) yields:
% 30.40/8.40 | (342) all_0_0_0 = e1
% 30.40/8.40 | (343) ~ (all_0_1_1 = e4)
% 30.40/8.40 |
% 30.40/8.40 | Combining equations (342,9064) yields a new equation:
% 30.40/8.40 | (571) e1 = e0
% 30.40/8.40 |
% 30.40/8.40 | Simplifying 571 yields:
% 30.40/8.40 | (560) e1 = e0
% 30.40/8.40 |
% 30.40/8.40 | Equations (560) can reduce 132 to:
% 30.40/8.40 | (270) $false
% 30.40/8.40 |
% 30.40/8.40 |-The branch is then unsatisfiable
% 30.40/8.40 |-Branch two:
% 30.40/8.40 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 30.40/8.40 |
% 30.40/8.40 | Applying alpha-rule on (346) yields:
% 30.40/8.40 | (347) all_0_2_2 = e0
% 30.40/8.40 | (348) ~ (all_0_3_3 = e4)
% 30.40/8.40 |
% 30.40/8.40 | Combining equations (12353,347) yields a new equation:
% 30.40/8.40 | (783) e3 = e0
% 30.40/8.40 |
% 30.40/8.40 | Simplifying 783 yields:
% 30.40/8.40 | (784) e3 = e0
% 30.40/8.40 |
% 30.40/8.40 | Equations (784) can reduce 66 to:
% 30.40/8.40 | (270) $false
% 30.40/8.40 |
% 30.40/8.40 |-The branch is then unsatisfiable
% 30.40/8.40 |-Branch two:
% 30.40/8.40 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 30.40/8.40 |
% 30.40/8.40 | Applying alpha-rule on (350) yields:
% 30.40/8.40 | (351) all_0_41_41 = e3
% 30.40/8.40 | (352) ~ (all_0_45_45 = e4)
% 30.40/8.41 |
% 30.40/8.41 | Equations (363) can reduce 352 to:
% 30.40/8.41 | (270) $false
% 30.40/8.41 |
% 30.40/8.41 |-The branch is then unsatisfiable
% 30.40/8.41 |-Branch two:
% 30.40/8.41 | (352) ~ (all_0_45_45 = e4)
% 30.40/8.41 | (517) all_0_46_46 = e4
% 30.40/8.41 |
% 30.40/8.41 | Equations (517) can reduce 805 to:
% 30.40/8.41 | (270) $false
% 30.40/8.41 |
% 30.40/8.41 |-The branch is then unsatisfiable
% 30.40/8.41 |-Branch two:
% 30.40/8.41 | (292) ~ (all_0_43_43 = e2)
% 30.40/8.41 | (453) all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2
% 30.40/8.41 |
% 30.40/8.41 +-Applying beta-rule and splitting (453), into two cases.
% 30.40/8.41 |-Branch one:
% 30.40/8.41 | (370) all_0_44_44 = e2
% 30.40/8.41 |
% 30.40/8.41 | Combining equations (621,370) yields a new equation:
% 30.40/8.41 | (316) e2 = e0
% 30.40/8.41 |
% 30.40/8.41 | Equations (316) can reduce 57 to:
% 30.40/8.41 | (270) $false
% 30.40/8.41 |
% 30.40/8.41 |-The branch is then unsatisfiable
% 30.40/8.41 |-Branch two:
% 30.40/8.41 | (333) ~ (all_0_44_44 = e2)
% 30.40/8.41 | (493) all_0_45_45 = e2 | all_0_46_46 = e2
% 30.40/8.41 |
% 30.40/8.41 +-Applying beta-rule and splitting (493), into two cases.
% 30.40/8.41 |-Branch one:
% 30.40/8.41 | (374) all_0_45_45 = e2
% 30.40/8.41 |
% 30.40/8.41 | Equations (374) can reduce 434 to:
% 30.40/8.41 | (270) $false
% 30.40/8.41 |
% 30.40/8.41 |-The branch is then unsatisfiable
% 30.40/8.41 |-Branch two:
% 30.40/8.41 | (434) ~ (all_0_45_45 = e2)
% 30.40/8.41 | (497) all_0_46_46 = e2
% 30.40/8.41 |
% 30.40/8.41 | Equations (497) can reduce 1436 to:
% 30.40/8.41 | (270) $false
% 30.40/8.41 |
% 30.40/8.41 |-The branch is then unsatisfiable
% 30.40/8.41 |-Branch two:
% 30.40/8.41 | (498) ~ (all_0_42_42 = e2)
% 30.40/8.41 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 30.40/8.41 |
% 30.40/8.41 +-Applying beta-rule and splitting (1245), into two cases.
% 30.40/8.41 |-Branch one:
% 30.40/8.41 | (1258) all_0_42_42 = e3
% 30.40/8.41 |
% 30.40/8.41 | Equations (1258) can reduce 1316 to:
% 30.40/8.41 | (270) $false
% 30.40/8.41 |
% 30.40/8.41 |-The branch is then unsatisfiable
% 30.40/8.41 |-Branch two:
% 30.40/8.41 | (1316) ~ (all_0_42_42 = e3)
% 30.40/8.41 | (1317) all_0_42_42 = e4 | all_0_42_42 = e1
% 30.40/8.41 |
% 30.40/8.41 +-Applying beta-rule and splitting (1317), into two cases.
% 30.40/8.41 |-Branch one:
% 30.40/8.41 | (541) all_0_42_42 = e1
% 30.40/8.41 |
% 30.40/8.41 | Equations (541) can reduce 640 to:
% 30.40/8.41 | (270) $false
% 30.40/8.41 |
% 30.40/8.41 |-The branch is then unsatisfiable
% 30.40/8.41 |-Branch two:
% 30.40/8.41 | (640) ~ (all_0_42_42 = e1)
% 30.40/8.41 | (512) all_0_42_42 = e4
% 30.40/8.41 |
% 30.40/8.41 | Equations (512) can reduce 520 to:
% 30.40/8.41 | (270) $false
% 30.40/8.41 |
% 30.40/8.41 |-The branch is then unsatisfiable
% 30.40/8.41 |-Branch two:
% 30.40/8.41 | (675) ~ (all_0_40_40 = e3)
% 30.40/8.41 | (676) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 30.40/8.41 |
% 30.40/8.41 +-Applying beta-rule and splitting (676), into two cases.
% 30.40/8.41 |-Branch one:
% 30.40/8.41 | (858) all_0_44_44 = e3
% 30.40/8.41 |
% 30.40/8.41 | Combining equations (621,858) yields a new equation:
% 30.40/8.41 | (784) e3 = e0
% 30.40/8.41 |
% 30.40/8.41 | Equations (784) can reduce 66 to:
% 30.40/8.41 | (270) $false
% 30.40/8.41 |
% 30.40/8.41 |-The branch is then unsatisfiable
% 30.40/8.41 |-Branch two:
% 30.40/8.41 | (862) ~ (all_0_44_44 = e3)
% 30.40/8.41 | (863) all_0_52_52 = e3 | all_0_57_57 = e3
% 30.40/8.41 |
% 30.40/8.41 +-Applying beta-rule and splitting (863), into two cases.
% 30.40/8.41 |-Branch one:
% 30.40/8.41 | (864) all_0_52_52 = e3
% 30.40/8.41 |
% 30.40/8.41 | Combining equations (864,685) yields a new equation:
% 30.40/8.41 | (437) e3 = e2
% 30.40/8.41 |
% 30.40/8.41 | Simplifying 437 yields:
% 30.40/8.41 | (414) e3 = e2
% 30.40/8.41 |
% 30.40/8.41 | Equations (414) can reduce 223 to:
% 30.40/8.41 | (270) $false
% 30.40/8.41 |
% 30.40/8.41 |-The branch is then unsatisfiable
% 30.40/8.41 |-Branch two:
% 30.40/8.41 | (826) ~ (all_0_52_52 = e3)
% 30.40/8.41 | (869) all_0_57_57 = e3
% 30.40/8.41 |
% 30.40/8.41 | Combining equations (997,869) yields a new equation:
% 30.40/8.41 | (538) e3 = e1
% 30.40/8.41 |
% 30.40/8.41 | Equations (538) can reduce 136 to:
% 30.40/8.41 | (270) $false
% 30.40/8.41 |
% 30.40/8.41 |-The branch is then unsatisfiable
% 30.40/8.41 |-Branch two:
% 30.40/8.41 | (625) ~ (all_0_44_44 = e0)
% 30.40/8.41 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 30.40/8.41 |
% 30.40/8.41 +-Applying beta-rule and splitting (626), into two cases.
% 30.40/8.41 |-Branch one:
% 30.40/8.41 | (827) all_0_52_52 = e0
% 30.40/8.41 |
% 30.40/8.41 | Combining equations (685,827) yields a new equation:
% 30.40/8.41 | (622) e2 = e0
% 30.40/8.41 |
% 30.40/8.41 | Simplifying 622 yields:
% 30.40/8.41 | (316) e2 = e0
% 30.40/8.41 |
% 30.40/8.41 | Equations (316) can reduce 57 to:
% 30.40/8.41 | (270) $false
% 30.40/8.41 |
% 30.40/8.41 |-The branch is then unsatisfiable
% 30.40/8.41 |-Branch two:
% 30.40/8.41 | (925) ~ (all_0_52_52 = e0)
% 30.40/8.41 | (2258) all_0_57_57 = e0
% 30.40/8.41 |
% 30.40/8.41 | Combining equations (997,2258) yields a new equation:
% 30.40/8.41 | (571) e1 = e0
% 30.40/8.41 |
% 30.40/8.41 | Simplifying 571 yields:
% 30.40/8.41 | (560) e1 = e0
% 30.40/8.41 |
% 30.40/8.41 | Equations (560) can reduce 132 to:
% 30.40/8.41 | (270) $false
% 30.40/8.41 |
% 30.40/8.41 |-The branch is then unsatisfiable
% 30.40/8.41 |-Branch two:
% 30.40/8.41 | (257) ~ (all_0_52_52 = e2)
% 30.40/8.41 | (392) all_0_57_57 = e2
% 30.40/8.41 |
% 30.40/8.41 | Equations (392) can reduce 335 to:
% 30.40/8.41 | (270) $false
% 30.40/8.41 |
% 30.40/8.41 |-The branch is then unsatisfiable
% 30.40/8.41 |-Branch two:
% 30.40/8.41 | (280) ~ (all_0_59_59 = e4)
% 30.40/8.41 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 30.40/8.41 |
% 30.40/8.41 +-Applying beta-rule and splitting (407), into two cases.
% 30.40/8.41 |-Branch one:
% 30.40/8.41 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 30.40/8.41 |
% 30.40/8.41 +-Applying beta-rule and splitting (408), into two cases.
% 30.40/8.41 |-Branch one:
% 30.40/8.41 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 30.40/8.41 |
% 30.40/8.41 +-Applying beta-rule and splitting (409), into two cases.
% 30.40/8.41 |-Branch one:
% 30.40/8.41 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 30.40/8.41 |
% 30.40/8.41 | Applying alpha-rule on (410) yields:
% 30.40/8.41 | (411) all_0_43_43 = e0
% 30.40/8.41 | (412) all_0_59_59 = e3
% 30.40/8.41 | (413) ~ (all_0_46_46 = e3)
% 30.40/8.41 |
% 30.40/8.41 | Equations (411) can reduce 455 to:
% 30.40/8.41 | (270) $false
% 30.40/8.41 |
% 30.40/8.41 |-The branch is then unsatisfiable
% 30.40/8.41 |-Branch two:
% 30.40/8.41 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 30.40/8.41 |
% 30.40/8.41 | Applying alpha-rule on (416) yields:
% 30.40/8.41 | (411) all_0_43_43 = e0
% 30.40/8.41 | (412) all_0_59_59 = e3
% 30.40/8.41 | (419) ~ (all_0_56_56 = e0)
% 30.40/8.41 |
% 30.40/8.41 | Equations (411) can reduce 455 to:
% 30.40/8.41 | (270) $false
% 30.40/8.41 |
% 30.40/8.41 |-The branch is then unsatisfiable
% 30.40/8.41 |-Branch two:
% 30.40/8.41 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 30.40/8.41 |
% 30.40/8.41 | Applying alpha-rule on (422) yields:
% 30.40/8.41 | (423) all_0_53_53 = e0
% 30.40/8.41 | (424) all_0_59_59 = e1
% 30.40/8.41 | (425) ~ (all_0_54_54 = e1)
% 30.40/8.41 |
% 30.40/8.41 | Equations (424) can reduce 750 to:
% 30.40/8.41 | (270) $false
% 30.40/8.41 |
% 30.40/8.41 |-The branch is then unsatisfiable
% 30.40/8.41 |-Branch two:
% 30.40/8.41 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 30.40/8.41 |
% 30.40/8.41 | Applying alpha-rule on (428) yields:
% 30.40/8.41 | (423) all_0_53_53 = e0
% 30.40/8.41 | (424) all_0_59_59 = e1
% 30.40/8.41 | (431) ~ (all_0_58_58 = e0)
% 30.40/8.41 |
% 30.40/8.41 | Equations (424) can reduce 750 to:
% 30.40/8.41 | (270) $false
% 30.40/8.41 |
% 30.40/8.41 |-The branch is then unsatisfiable
% 30.40/8.41 |-Branch two:
% 30.40/8.41 | (318) ~ (all_0_47_47 = e0)
% 30.40/8.41 | (319) all_0_48_48 = e0 | all_0_49_49 = e0
% 30.40/8.41 |
% 30.40/8.41 +-Applying beta-rule and splitting (319), into two cases.
% 30.40/8.41 |-Branch one:
% 30.40/8.41 | (559) all_0_48_48 = e0
% 30.40/8.41 |
% 30.40/8.41 | Combining equations (559,311) yields a new equation:
% 30.40/8.41 | (316) e2 = e0
% 30.40/8.41 |
% 30.40/8.41 | Equations (316) can reduce 57 to:
% 30.40/8.41 | (270) $false
% 30.40/8.41 |
% 30.40/8.41 |-The branch is then unsatisfiable
% 30.40/8.41 |-Branch two:
% 30.40/8.41 | (562) ~ (all_0_48_48 = e0)
% 30.40/8.41 | (563) all_0_49_49 = e0
% 30.40/8.41 |
% 30.40/8.41 | Equations (563) can reduce 169 to:
% 30.40/8.41 | (199) ~ (all_0_42_42 = e0)
% 30.40/8.41 |
% 30.40/8.41 | Equations (563) can reduce 198 to:
% 30.40/8.41 | (1010) ~ (all_0_46_46 = e0)
% 30.40/8.41 |
% 30.40/8.41 | Equations (563) can reduce 80 to:
% 30.40/8.41 | (318) ~ (all_0_47_47 = e0)
% 30.40/8.41 |
% 30.40/8.41 | Equations (563) can reduce 162 to:
% 30.40/8.41 | (3010) ~ (all_0_54_54 = e0)
% 30.40/8.41 |
% 30.40/8.41 | Simplifying 3010 yields:
% 30.40/8.41 | (3011) ~ (all_0_54_54 = e0)
% 30.40/8.41 |
% 30.40/8.41 | Equations (563) can reduce 113 to:
% 30.40/8.41 | (4000) ~ (all_0_59_59 = e0)
% 30.40/8.41 |
% 30.40/8.41 | Simplifying 4000 yields:
% 30.40/8.41 | (4001) ~ (all_0_59_59 = e0)
% 30.40/8.41 |
% 30.40/8.41 | Equations (563) can reduce 202 to:
% 30.40/8.41 | (456) ~ (e4 = e0)
% 30.40/8.41 |
% 30.40/8.41 | Simplifying 456 yields:
% 30.40/8.41 | (6) ~ (e4 = e0)
% 30.40/8.41 |
% 30.40/8.41 | Equations (563) can reduce 150 to:
% 30.40/8.41 | (788) ~ (e3 = e0)
% 30.40/8.41 |
% 30.40/8.41 | Simplifying 788 yields:
% 30.40/8.41 | (66) ~ (e3 = e0)
% 30.40/8.41 |
% 30.40/8.41 | Equations (563) can reduce 296 to:
% 30.40/8.41 | (566) ~ (e2 = e0)
% 30.40/8.41 |
% 30.40/8.41 | Simplifying 566 yields:
% 30.40/8.41 | (57) ~ (e2 = e0)
% 30.40/8.41 |
% 30.40/8.41 | From (563) and (153) follows:
% 30.40/8.41 | (4008) op(e2, e0) = all_0_35_35
% 30.40/8.41 |
% 30.40/8.41 | From (563) and (134) follows:
% 30.40/8.41 | (2996) op(e2, e0) = e0
% 30.40/8.41 |
% 30.40/8.41 | From (563) and (88) follows:
% 30.40/8.41 | (4010) op(e0, e0) = all_0_34_34
% 30.40/8.41 |
% 30.40/8.41 +-Applying beta-rule and splitting (83), into two cases.
% 30.40/8.41 |-Branch one:
% 30.40/8.41 | (321) all_0_47_47 = e1
% 30.40/8.41 |
% 30.40/8.41 | Equations (321) can reduce 100 to:
% 30.40/8.41 | (528) ~ (all_0_39_39 = e1)
% 30.40/8.41 |
% 30.40/8.41 | Equations (321) can reduce 170 to:
% 30.40/8.41 | (249) ~ (all_0_43_43 = e1)
% 30.40/8.41 |
% 30.40/8.41 | Equations (321) can reduce 3 to:
% 30.40/8.41 | (3984) ~ (all_0_51_51 = e1)
% 30.40/8.41 |
% 30.40/8.41 | Simplifying 3984 yields:
% 30.40/8.41 | (748) ~ (all_0_51_51 = e1)
% 30.40/8.41 |
% 30.40/8.41 | Equations (321) can reduce 218 to:
% 30.40/8.41 | (3986) ~ (all_0_56_56 = e1)
% 30.40/8.41 |
% 30.40/8.41 | Simplifying 3986 yields:
% 30.40/8.41 | (995) ~ (all_0_56_56 = e1)
% 30.40/8.41 |
% 30.40/8.41 | Equations (321) can reduce 172 to:
% 30.40/8.41 | (1021) ~ (e4 = e1)
% 30.40/8.41 |
% 30.40/8.41 | Simplifying 1021 yields:
% 30.40/8.41 | (251) ~ (e4 = e1)
% 30.40/8.41 |
% 30.40/8.41 | Equations (321) can reduce 247 to:
% 30.40/8.41 | (769) ~ (e3 = e1)
% 30.40/8.41 |
% 30.40/8.41 | Simplifying 769 yields:
% 30.40/8.41 | (136) ~ (e3 = e1)
% 30.40/8.41 |
% 30.40/8.41 | Equations (321) can reduce 3951 to:
% 30.40/8.41 | (645) ~ (e2 = e1)
% 30.40/8.41 |
% 30.40/8.41 | Simplifying 645 yields:
% 30.40/8.41 | (141) ~ (e2 = e1)
% 30.40/8.41 |
% 30.40/8.41 | Equations (321) can reduce 318 to:
% 30.40/8.41 | (132) ~ (e1 = e0)
% 30.40/8.41 |
% 30.40/8.41 | From (321) and (237) follows:
% 30.40/8.41 | (3992) op(e3, e1) = all_0_7_7
% 30.40/8.41 |
% 30.40/8.41 | From (321) and (42) follows:
% 30.40/8.41 | (3993) op(e2, e1) = all_0_8_8
% 30.40/8.41 |
% 30.40/8.41 | From (321) and (40) follows:
% 30.40/8.41 | (1103) op(e2, e3) = e1
% 30.40/8.41 |
% 30.40/8.41 | Instantiating formula (201) with e3, e1, all_0_7_7, all_0_45_45 and discharging atoms op(e3, e1) = all_0_7_7, op(e3, e1) = all_0_45_45, yields:
% 30.40/8.41 | (4011) all_0_7_7 = all_0_45_45
% 30.40/8.41 |
% 30.40/8.41 | Instantiating formula (201) with e2, e1, all_0_8_8, e2 and discharging atoms op(e2, e1) = all_0_8_8, op(e2, e1) = e2, yields:
% 30.40/8.41 | (4012) all_0_8_8 = e2
% 30.40/8.41 |
% 30.40/8.41 | Instantiating formula (201) with e2, e0, e0, all_0_35_35 and discharging atoms op(e2, e0) = all_0_35_35, op(e2, e0) = e0, yields:
% 30.40/8.41 | (4013) all_0_35_35 = e0
% 30.40/8.41 |
% 30.40/8.41 | Instantiating formula (201) with e0, e0, all_0_34_34, all_0_59_59 and discharging atoms op(e0, e0) = all_0_34_34, op(e0, e0) = all_0_59_59, yields:
% 30.40/8.41 | (4014) all_0_34_34 = all_0_59_59
% 30.40/8.41 |
% 30.40/8.41 | From (4012) and (3993) follows:
% 30.40/8.41 | (3970) op(e2, e1) = e2
% 30.40/8.41 |
% 30.40/8.41 | From (4013) and (4008) follows:
% 30.40/8.41 | (2996) op(e2, e0) = e0
% 30.40/8.41 |
% 30.40/8.41 | From (4014) and (4010) follows:
% 30.40/8.41 | (161) op(e0, e0) = all_0_59_59
% 30.40/8.41 |
% 30.40/8.42 +-Applying beta-rule and splitting (193), into two cases.
% 30.40/8.42 |-Branch one:
% 30.40/8.42 | (370) all_0_44_44 = e2
% 30.40/8.42 |
% 30.40/8.42 | Equations (370) can reduce 241 to:
% 30.40/8.42 | (292) ~ (all_0_43_43 = e2)
% 30.40/8.42 |
% 30.40/8.42 | Equations (370) can reduce 229 to:
% 30.40/8.42 | (611) ~ (all_0_45_45 = e2)
% 30.40/8.42 |
% 30.40/8.42 | Simplifying 611 yields:
% 30.40/8.42 | (434) ~ (all_0_45_45 = e2)
% 30.40/8.42 |
% 30.40/8.42 | Equations (370) can reduce 174 to:
% 30.40/8.42 | (1435) ~ (all_0_46_46 = e2)
% 30.40/8.42 |
% 30.40/8.42 | Simplifying 1435 yields:
% 30.40/8.42 | (1436) ~ (all_0_46_46 = e2)
% 30.40/8.42 |
% 30.40/8.42 | Equations (370) can reduce 10 to:
% 30.40/8.42 | (334) ~ (all_0_57_57 = e2)
% 30.40/8.42 |
% 30.40/8.42 | Simplifying 334 yields:
% 30.40/8.42 | (335) ~ (all_0_57_57 = e2)
% 30.40/8.42 |
% 30.40/8.42 | Equations (370) can reduce 131 to:
% 30.40/8.42 | (141) ~ (e2 = e1)
% 30.40/8.42 |
% 30.40/8.42 | From (370) and (5) follows:
% 30.40/8.42 | (4117) op(e3, e2) = all_0_16_16
% 30.40/8.42 |
% 30.40/8.42 | From (370) and (148) follows:
% 30.40/8.42 | (4118) op(e3, e2) = e2
% 30.40/8.42 |
% 30.40/8.42 | From (370) and (165) follows:
% 30.40/8.42 | (619) op(e2, e2) = all_0_15_15
% 30.40/8.42 |
% 30.40/8.42 | Instantiating formula (201) with e3, e2, e2, all_0_16_16 and discharging atoms op(e3, e2) = all_0_16_16, op(e3, e2) = e2, yields:
% 30.40/8.42 | (4119) all_0_16_16 = e2
% 30.40/8.42 |
% 30.40/8.42 | Instantiating formula (201) with e2, e2, all_0_15_15, e4 and discharging atoms op(e2, e2) = all_0_15_15, op(e2, e2) = e4, yields:
% 30.40/8.42 | (620) all_0_15_15 = e4
% 30.40/8.42 |
% 30.40/8.42 | From (4119) and (4117) follows:
% 30.40/8.42 | (4118) op(e3, e2) = e2
% 30.54/8.42 |
% 30.54/8.42 +-Applying beta-rule and splitting (9), into two cases.
% 30.54/8.42 |-Branch one:
% 30.54/8.42 | (621) all_0_44_44 = e0
% 30.54/8.42 |
% 30.54/8.42 | Combining equations (370,621) yields a new equation:
% 30.54/8.42 | (622) e2 = e0
% 30.54/8.42 |
% 30.54/8.42 | Simplifying 622 yields:
% 30.54/8.42 | (316) e2 = e0
% 30.54/8.42 |
% 30.54/8.42 | Equations (316) can reduce 57 to:
% 30.54/8.42 | (270) $false
% 30.54/8.42 |
% 30.54/8.42 |-The branch is then unsatisfiable
% 30.54/8.42 |-Branch two:
% 30.54/8.42 | (625) ~ (all_0_44_44 = e0)
% 30.54/8.42 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 30.54/8.42 |
% 30.54/8.42 | Equations (370) can reduce 625 to:
% 30.54/8.42 | (57) ~ (e2 = e0)
% 30.54/8.42 |
% 30.54/8.42 +-Applying beta-rule and splitting (186), into two cases.
% 30.54/8.42 |-Branch one:
% 30.54/8.42 | (336) all_0_39_39 = e2
% 30.54/8.42 |
% 30.54/8.42 | Equations (336) can reduce 114 to:
% 30.54/8.42 | (6613) ~ (all_0_40_40 = e2)
% 30.54/8.42 |
% 30.54/8.42 | Simplifying 6613 yields:
% 30.54/8.42 | (602) ~ (all_0_40_40 = e2)
% 30.54/8.42 |
% 30.54/8.42 | Equations (336) can reduce 226 to:
% 30.54/8.42 | (330) ~ (all_0_41_41 = e2)
% 30.54/8.42 |
% 30.54/8.42 | Simplifying 330 yields:
% 30.54/8.42 | (331) ~ (all_0_41_41 = e2)
% 30.54/8.42 |
% 30.54/8.42 | Equations (336) can reduce 184 to:
% 30.54/8.42 | (1336) ~ (all_0_42_42 = e2)
% 30.54/8.42 |
% 30.54/8.42 | Simplifying 1336 yields:
% 30.54/8.42 | (498) ~ (all_0_42_42 = e2)
% 30.54/8.42 |
% 30.54/8.42 | Equations (336) can reduce 212 to:
% 30.54/8.42 | (299) ~ (all_0_56_56 = e2)
% 30.54/8.42 |
% 30.54/8.42 | Simplifying 299 yields:
% 30.54/8.42 | (300) ~ (all_0_56_56 = e2)
% 30.54/8.42 |
% 30.54/8.42 | Equations (336) can reduce 528 to:
% 30.54/8.42 | (141) ~ (e2 = e1)
% 30.54/8.42 |
% 30.54/8.42 | Equations (336) can reduce 101 to:
% 30.54/8.42 | (57) ~ (e2 = e0)
% 30.54/8.42 |
% 30.54/8.42 | From (336) and (200) follows:
% 30.54/8.42 | (12057) op(e3, e2) = all_0_4_4
% 30.54/8.42 |
% 30.54/8.42 +-Applying beta-rule and splitting (209), into two cases.
% 30.54/8.42 |-Branch one:
% 30.54/8.42 | (698) all_0_42_42 = e2
% 30.54/8.42 |
% 30.54/8.42 | Equations (698) can reduce 498 to:
% 30.54/8.42 | (270) $false
% 30.54/8.42 |
% 30.54/8.42 |-The branch is then unsatisfiable
% 30.54/8.42 |-Branch two:
% 30.54/8.42 | (498) ~ (all_0_42_42 = e2)
% 30.54/8.42 | (1732) all_0_46_46 = e2 | all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 30.54/8.42 |
% 30.54/8.42 +-Applying beta-rule and splitting (1732), into two cases.
% 30.54/8.42 |-Branch one:
% 30.54/8.42 | (497) all_0_46_46 = e2
% 30.54/8.42 |
% 30.54/8.42 | Equations (497) can reduce 1436 to:
% 30.54/8.42 | (270) $false
% 30.54/8.42 |
% 30.54/8.42 |-The branch is then unsatisfiable
% 30.54/8.42 |-Branch two:
% 30.54/8.42 | (1436) ~ (all_0_46_46 = e2)
% 30.54/8.42 | (3824) all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 30.54/8.42 |
% 30.54/8.42 +-Applying beta-rule and splitting (3824), into two cases.
% 30.54/8.42 |-Branch one:
% 30.54/8.42 | (307) all_0_49_49 = e2
% 30.54/8.42 |
% 30.54/8.42 | Combining equations (307,563) yields a new equation:
% 30.54/8.42 | (622) e2 = e0
% 30.54/8.42 |
% 30.54/8.42 | Simplifying 622 yields:
% 30.54/8.42 | (316) e2 = e0
% 30.54/8.42 |
% 30.54/8.42 | Equations (316) can reduce 57 to:
% 30.54/8.42 | (270) $false
% 30.54/8.42 |
% 30.54/8.42 |-The branch is then unsatisfiable
% 30.54/8.42 |-Branch two:
% 30.54/8.42 | (296) ~ (all_0_49_49 = e2)
% 30.54/8.42 | (3829) all_0_54_54 = e2 | all_0_59_59 = e2
% 30.54/8.42 |
% 30.54/8.42 +-Applying beta-rule and splitting (3829), into two cases.
% 30.54/8.42 |-Branch one:
% 30.54/8.42 | (3657) all_0_54_54 = e2
% 30.54/8.42 |
% 30.54/8.42 | Equations (3657) can reduce 191 to:
% 30.54/8.42 | (498) ~ (all_0_42_42 = e2)
% 30.54/8.42 |
% 30.54/8.42 | Equations (3657) can reduce 215 to:
% 30.54/8.42 | (1436) ~ (all_0_46_46 = e2)
% 30.54/8.42 |
% 30.54/8.42 | Equations (3657) can reduce 50 to:
% 30.54/8.42 | (255) ~ (all_0_51_51 = e2)
% 30.54/8.42 |
% 30.54/8.42 | Equations (3657) can reduce 118 to:
% 30.54/8.42 | (257) ~ (all_0_52_52 = e2)
% 30.54/8.42 |
% 30.54/8.42 | Equations (3657) can reduce 252 to:
% 30.54/8.42 | (259) ~ (all_0_53_53 = e2)
% 30.54/8.42 |
% 30.54/8.42 | Equations (3657) can reduce 72 to:
% 30.54/8.42 | (700) ~ (all_0_59_59 = e2)
% 30.54/8.42 |
% 30.54/8.42 | Simplifying 700 yields:
% 30.54/8.42 | (701) ~ (all_0_59_59 = e2)
% 30.54/8.42 |
% 30.54/8.42 | Equations (3657) can reduce 936 to:
% 30.54/8.42 | (377) ~ (e4 = e2)
% 30.54/8.42 |
% 30.54/8.42 | Simplifying 377 yields:
% 30.54/8.42 | (231) ~ (e4 = e2)
% 30.54/8.42 |
% 30.54/8.42 | Equations (3657) can reduce 3011 to:
% 30.54/8.42 | (57) ~ (e2 = e0)
% 30.54/8.42 |
% 30.54/8.42 | Instantiating formula (201) with e3, e2, all_0_4_4, e2 and discharging atoms op(e3, e2) = all_0_4_4, op(e3, e2) = e2, yields:
% 30.54/8.42 | (12701) all_0_4_4 = e2
% 30.54/8.42 |
% 30.54/8.42 +-Applying beta-rule and splitting (222), into two cases.
% 30.54/8.42 |-Branch one:
% 30.54/8.42 | (522) all_0_39_39 = e4
% 30.54/8.42 |
% 30.54/8.42 | Combining equations (336,522) yields a new equation:
% 30.54/8.42 | (269) e4 = e2
% 30.54/8.42 |
% 30.54/8.42 | Equations (269) can reduce 231 to:
% 30.54/8.42 | (270) $false
% 30.54/8.42 |
% 30.54/8.42 |-The branch is then unsatisfiable
% 30.54/8.42 |-Branch two:
% 30.54/8.42 | (591) ~ (all_0_39_39 = e4)
% 30.54/8.42 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 30.54/8.42 |
% 30.54/8.42 | Equations (336) can reduce 591 to:
% 30.54/8.42 | (377) ~ (e4 = e2)
% 30.54/8.42 |
% 30.54/8.42 | Simplifying 377 yields:
% 30.54/8.42 | (231) ~ (e4 = e2)
% 30.54/8.42 |
% 30.54/8.42 +-Applying beta-rule and splitting (8), into two cases.
% 30.54/8.42 |-Branch one:
% 30.54/8.42 | (530) all_0_40_40 = e1
% 30.54/8.42 |
% 30.54/8.42 | Equations (530) can reduce 147 to:
% 30.54/8.42 | (637) ~ (all_0_41_41 = e1)
% 30.54/8.42 |
% 30.54/8.42 | Simplifying 637 yields:
% 30.54/8.42 | (540) ~ (all_0_41_41 = e1)
% 30.54/8.42 |
% 30.54/8.42 | Equations (530) can reduce 145 to:
% 30.54/8.42 | (639) ~ (all_0_42_42 = e1)
% 30.54/8.42 |
% 30.54/8.42 | Simplifying 639 yields:
% 30.54/8.42 | (640) ~ (all_0_42_42 = e1)
% 30.54/8.42 |
% 30.54/8.42 | Equations (530) can reduce 233 to:
% 30.54/8.42 | (1021) ~ (e4 = e1)
% 30.54/8.42 |
% 30.54/8.42 | Simplifying 1021 yields:
% 30.54/8.42 | (251) ~ (e4 = e1)
% 30.54/8.42 |
% 30.54/8.42 | Equations (530) can reduce 602 to:
% 30.54/8.42 | (645) ~ (e2 = e1)
% 30.54/8.42 |
% 30.54/8.42 | Simplifying 645 yields:
% 30.54/8.42 | (141) ~ (e2 = e1)
% 30.54/8.42 |
% 30.54/8.42 | Equations (530) can reduce 238 to:
% 30.54/8.42 | (132) ~ (e1 = e0)
% 30.54/8.42 |
% 30.54/8.42 +-Applying beta-rule and splitting (127), into two cases.
% 30.54/8.42 |-Branch one:
% 30.54/8.42 | (541) all_0_42_42 = e1
% 30.54/8.42 |
% 30.54/8.42 | Equations (541) can reduce 640 to:
% 30.54/8.42 | (270) $false
% 30.54/8.42 |
% 30.54/8.42 |-The branch is then unsatisfiable
% 30.54/8.42 |-Branch two:
% 30.54/8.42 | (640) ~ (all_0_42_42 = e1)
% 30.54/8.42 | (4628) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 30.54/8.42 |
% 30.54/8.42 +-Applying beta-rule and splitting (4628), into two cases.
% 30.54/8.42 |-Branch one:
% 30.54/8.42 | (589) all_0_49_49 = e1
% 30.54/8.42 |
% 30.54/8.42 | Combining equations (563,589) yields a new equation:
% 30.54/8.42 | (560) e1 = e0
% 30.54/8.42 |
% 30.54/8.42 | Equations (560) can reduce 132 to:
% 30.54/8.42 | (270) $false
% 30.54/8.42 |
% 30.54/8.42 |-The branch is then unsatisfiable
% 30.54/8.42 |-Branch two:
% 30.54/8.42 | (543) ~ (all_0_49_49 = e1)
% 30.54/8.42 | (4726) all_0_54_54 = e1 | all_0_59_59 = e1
% 30.54/8.42 |
% 30.54/8.42 +-Applying beta-rule and splitting (4726), into two cases.
% 30.54/8.42 |-Branch one:
% 30.54/8.42 | (875) all_0_54_54 = e1
% 30.54/8.42 |
% 30.54/8.42 | Combining equations (3657,875) yields a new equation:
% 30.54/8.42 | (531) e2 = e1
% 30.54/8.42 |
% 30.54/8.42 | Simplifying 531 yields:
% 30.54/8.42 | (322) e2 = e1
% 30.54/8.42 |
% 30.54/8.42 | Equations (322) can reduce 141 to:
% 30.54/8.42 | (270) $false
% 30.54/8.42 |
% 30.54/8.42 |-The branch is then unsatisfiable
% 30.54/8.42 |-Branch two:
% 30.54/8.42 | (425) ~ (all_0_54_54 = e1)
% 30.54/8.42 | (424) all_0_59_59 = e1
% 30.54/8.42 |
% 30.54/8.42 | Equations (424) can reduce 140 to:
% 30.54/8.42 | (644) ~ (all_0_57_57 = e1)
% 30.54/8.42 |
% 30.54/8.42 | Equations (424) can reduce 156 to:
% 30.54/8.42 | (1004) ~ (all_0_58_58 = e1)
% 30.54/8.42 |
% 30.54/8.42 | Equations (424) can reduce 701 to:
% 30.54/8.42 | (645) ~ (e2 = e1)
% 30.54/8.42 |
% 30.54/8.42 | Simplifying 645 yields:
% 30.54/8.42 | (141) ~ (e2 = e1)
% 30.54/8.42 |
% 30.54/8.42 +-Applying beta-rule and splitting (52), into two cases.
% 30.54/8.42 |-Branch one:
% 30.54/8.42 | (536) all_0_41_41 = e1
% 30.54/8.42 |
% 30.54/8.42 | Equations (536) can reduce 540 to:
% 30.54/8.42 | (270) $false
% 30.54/8.42 |
% 30.54/8.42 |-The branch is then unsatisfiable
% 30.54/8.42 |-Branch two:
% 30.54/8.42 | (540) ~ (all_0_41_41 = e1)
% 30.54/8.42 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 30.54/8.42 |
% 30.54/8.42 +-Applying beta-rule and splitting (93), into two cases.
% 30.54/8.42 |-Branch one:
% 30.54/8.42 | (402) all_0_59_59 = e4
% 30.54/8.42 |
% 30.54/8.42 | Combining equations (424,402) yields a new equation:
% 30.54/8.42 | (526) e4 = e1
% 30.54/8.42 |
% 30.54/8.42 | Equations (526) can reduce 251 to:
% 30.54/8.42 | (270) $false
% 30.54/8.42 |
% 30.54/8.42 |-The branch is then unsatisfiable
% 30.54/8.42 |-Branch two:
% 30.54/8.42 | (280) ~ (all_0_59_59 = e4)
% 30.54/8.42 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 30.54/8.42 |
% 30.54/8.42 +-Applying beta-rule and splitting (762), into two cases.
% 30.54/8.42 |-Branch one:
% 30.54/8.42 | (552) all_0_48_48 = e1
% 30.54/8.42 |
% 30.54/8.42 | Combining equations (311,552) yields a new equation:
% 30.54/8.42 | (531) e2 = e1
% 30.54/8.42 |
% 30.54/8.42 | Simplifying 531 yields:
% 30.54/8.42 | (322) e2 = e1
% 30.54/8.42 |
% 30.54/8.42 | Equations (322) can reduce 141 to:
% 30.54/8.42 | (270) $false
% 30.54/8.42 |
% 30.54/8.42 |-The branch is then unsatisfiable
% 30.54/8.42 |-Branch two:
% 30.54/8.42 | (588) ~ (all_0_48_48 = e1)
% 30.54/8.42 | (4925) all_0_53_53 = e1 | all_0_58_58 = e1
% 30.54/8.42 |
% 30.54/8.42 +-Applying beta-rule and splitting (407), into two cases.
% 30.54/8.42 |-Branch one:
% 30.54/8.42 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 30.54/8.42 |
% 30.54/8.42 +-Applying beta-rule and splitting (408), into two cases.
% 30.54/8.42 |-Branch one:
% 30.54/8.42 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 30.54/8.42 |
% 30.54/8.42 +-Applying beta-rule and splitting (409), into two cases.
% 30.54/8.42 |-Branch one:
% 30.54/8.42 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 30.54/8.42 |
% 30.54/8.42 | Applying alpha-rule on (410) yields:
% 30.54/8.42 | (411) all_0_43_43 = e0
% 30.54/8.42 | (412) all_0_59_59 = e3
% 30.54/8.42 | (413) ~ (all_0_46_46 = e3)
% 30.54/8.42 |
% 30.54/8.42 | Combining equations (412,424) yields a new equation:
% 30.54/8.42 | (537) e3 = e1
% 30.54/8.42 |
% 30.54/8.42 | Simplifying 537 yields:
% 30.54/8.42 | (538) e3 = e1
% 30.54/8.42 |
% 30.54/8.42 | Equations (538) can reduce 136 to:
% 30.54/8.42 | (270) $false
% 30.54/8.42 |
% 30.54/8.42 |-The branch is then unsatisfiable
% 30.54/8.42 |-Branch two:
% 30.54/8.42 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 30.54/8.42 |
% 30.54/8.42 | Applying alpha-rule on (416) yields:
% 30.54/8.42 | (411) all_0_43_43 = e0
% 30.54/8.43 | (412) all_0_59_59 = e3
% 30.54/8.43 | (419) ~ (all_0_56_56 = e0)
% 30.54/8.43 |
% 30.54/8.43 | Combining equations (412,424) yields a new equation:
% 30.54/8.43 | (537) e3 = e1
% 30.54/8.43 |
% 30.54/8.43 | Simplifying 537 yields:
% 30.54/8.43 | (538) e3 = e1
% 30.54/8.43 |
% 30.54/8.43 | Equations (538) can reduce 136 to:
% 30.54/8.43 | (270) $false
% 30.54/8.43 |
% 30.54/8.43 |-The branch is then unsatisfiable
% 30.54/8.43 |-Branch two:
% 30.54/8.43 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 30.54/8.43 |
% 30.54/8.43 | Applying alpha-rule on (422) yields:
% 30.54/8.43 | (423) all_0_53_53 = e0
% 30.54/8.43 | (424) all_0_59_59 = e1
% 30.54/8.43 | (425) ~ (all_0_54_54 = e1)
% 30.54/8.43 |
% 30.54/8.43 | Equations (423) can reduce 213 to:
% 30.54/8.43 | (925) ~ (all_0_52_52 = e0)
% 30.54/8.43 |
% 30.54/8.43 +-Applying beta-rule and splitting (90), into two cases.
% 30.54/8.43 |-Branch one:
% 30.54/8.43 | (685) all_0_52_52 = e2
% 30.54/8.43 |
% 30.54/8.43 | Equations (685) can reduce 257 to:
% 30.54/8.43 | (270) $false
% 30.54/8.43 |
% 30.54/8.43 |-The branch is then unsatisfiable
% 30.54/8.43 |-Branch two:
% 30.54/8.43 | (257) ~ (all_0_52_52 = e2)
% 30.54/8.43 | (688) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 30.54/8.43 |
% 30.54/8.43 +-Applying beta-rule and splitting (688), into two cases.
% 30.54/8.43 |-Branch one:
% 30.54/8.43 | (827) all_0_52_52 = e0
% 30.54/8.43 |
% 30.54/8.43 | Equations (827) can reduce 925 to:
% 30.54/8.43 | (270) $false
% 30.54/8.43 |
% 30.54/8.43 |-The branch is then unsatisfiable
% 30.54/8.43 |-Branch two:
% 30.54/8.43 | (925) ~ (all_0_52_52 = e0)
% 30.54/8.43 | (926) all_0_52_52 = e3 | all_0_52_52 = e1
% 30.54/8.43 |
% 30.54/8.43 +-Applying beta-rule and splitting (626), into two cases.
% 30.54/8.43 |-Branch one:
% 30.54/8.43 | (827) all_0_52_52 = e0
% 30.54/8.43 |
% 30.54/8.43 | Equations (827) can reduce 925 to:
% 30.54/8.43 | (270) $false
% 30.54/8.43 |
% 30.54/8.43 |-The branch is then unsatisfiable
% 30.54/8.43 |-Branch two:
% 30.54/8.43 | (925) ~ (all_0_52_52 = e0)
% 30.54/8.43 | (2258) all_0_57_57 = e0
% 30.54/8.43 |
% 30.54/8.43 | Equations (2258) can reduce 644 to:
% 30.54/8.43 | (568) ~ (e1 = e0)
% 30.54/8.43 |
% 30.54/8.43 | Simplifying 568 yields:
% 30.54/8.43 | (132) ~ (e1 = e0)
% 30.54/8.43 |
% 30.54/8.43 +-Applying beta-rule and splitting (4925), into two cases.
% 30.54/8.43 |-Branch one:
% 30.54/8.43 | (853) all_0_53_53 = e1
% 30.54/8.43 |
% 30.54/8.43 | Combining equations (423,853) yields a new equation:
% 30.54/8.43 | (560) e1 = e0
% 30.54/8.43 |
% 30.54/8.43 | Equations (560) can reduce 132 to:
% 30.54/8.43 | (270) $false
% 30.54/8.43 |
% 30.54/8.43 |-The branch is then unsatisfiable
% 30.54/8.43 |-Branch two:
% 30.54/8.43 | (874) ~ (all_0_53_53 = e1)
% 30.54/8.43 | (1001) all_0_58_58 = e1
% 30.54/8.43 |
% 30.54/8.43 | Equations (1001) can reduce 1004 to:
% 30.54/8.43 | (270) $false
% 30.54/8.43 |
% 30.54/8.43 |-The branch is then unsatisfiable
% 30.54/8.43 |-Branch two:
% 30.54/8.43 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 30.54/8.43 |
% 30.54/8.43 | Applying alpha-rule on (428) yields:
% 30.54/8.43 | (423) all_0_53_53 = e0
% 30.54/8.43 | (424) all_0_59_59 = e1
% 30.54/8.43 | (431) ~ (all_0_58_58 = e0)
% 30.54/8.43 |
% 30.54/8.43 | Equations (423) can reduce 213 to:
% 30.54/8.43 | (925) ~ (all_0_52_52 = e0)
% 30.54/8.43 |
% 30.54/8.43 +-Applying beta-rule and splitting (90), into two cases.
% 30.54/8.43 |-Branch one:
% 30.54/8.43 | (685) all_0_52_52 = e2
% 30.54/8.43 |
% 30.54/8.43 | Equations (685) can reduce 257 to:
% 30.54/8.43 | (270) $false
% 30.54/8.43 |
% 30.54/8.43 |-The branch is then unsatisfiable
% 30.54/8.43 |-Branch two:
% 30.54/8.43 | (257) ~ (all_0_52_52 = e2)
% 30.54/8.43 | (688) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 30.54/8.43 |
% 30.54/8.43 +-Applying beta-rule and splitting (688), into two cases.
% 30.54/8.43 |-Branch one:
% 30.54/8.43 | (827) all_0_52_52 = e0
% 30.54/8.43 |
% 30.54/8.43 | Equations (827) can reduce 925 to:
% 30.54/8.43 | (270) $false
% 30.54/8.43 |
% 30.54/8.43 |-The branch is then unsatisfiable
% 30.54/8.43 |-Branch two:
% 30.54/8.43 | (925) ~ (all_0_52_52 = e0)
% 30.54/8.43 | (926) all_0_52_52 = e3 | all_0_52_52 = e1
% 30.54/8.43 |
% 30.54/8.43 +-Applying beta-rule and splitting (626), into two cases.
% 30.54/8.43 |-Branch one:
% 30.54/8.43 | (827) all_0_52_52 = e0
% 30.54/8.43 |
% 30.54/8.43 | Equations (827) can reduce 925 to:
% 30.54/8.43 | (270) $false
% 30.54/8.43 |
% 30.54/8.43 |-The branch is then unsatisfiable
% 30.54/8.43 |-Branch two:
% 30.54/8.43 | (925) ~ (all_0_52_52 = e0)
% 30.54/8.43 | (2258) all_0_57_57 = e0
% 30.54/8.43 |
% 30.54/8.43 | Equations (2258) can reduce 644 to:
% 30.54/8.43 | (568) ~ (e1 = e0)
% 30.54/8.43 |
% 30.54/8.43 | Simplifying 568 yields:
% 30.54/8.43 | (132) ~ (e1 = e0)
% 30.54/8.43 |
% 30.54/8.43 +-Applying beta-rule and splitting (4925), into two cases.
% 30.54/8.43 |-Branch one:
% 30.54/8.43 | (853) all_0_53_53 = e1
% 30.54/8.43 |
% 30.54/8.43 | Combining equations (423,853) yields a new equation:
% 30.54/8.43 | (560) e1 = e0
% 30.54/8.43 |
% 30.54/8.43 | Equations (560) can reduce 132 to:
% 30.54/8.43 | (270) $false
% 30.54/8.43 |
% 30.54/8.43 |-The branch is then unsatisfiable
% 30.54/8.43 |-Branch two:
% 30.54/8.43 | (874) ~ (all_0_53_53 = e1)
% 30.54/8.43 | (1001) all_0_58_58 = e1
% 30.54/8.43 |
% 30.54/8.43 | Equations (1001) can reduce 1004 to:
% 30.54/8.43 | (270) $false
% 30.54/8.43 |
% 30.54/8.43 |-The branch is then unsatisfiable
% 30.54/8.43 |-Branch two:
% 30.54/8.43 | (534) ~ (all_0_40_40 = e1)
% 30.54/8.43 | (3352) all_0_52_52 = e1 | all_0_57_57 = e1
% 30.54/8.43 |
% 30.54/8.43 +-Applying beta-rule and splitting (603), into two cases.
% 30.54/8.43 |-Branch one:
% 30.54/8.43 | (671) all_0_40_40 = e3
% 30.54/8.43 |
% 30.54/8.43 | Equations (671) can reduce 147 to:
% 30.54/8.43 | (1329) ~ (all_0_41_41 = e3)
% 30.54/8.43 |
% 30.54/8.43 | Simplifying 1329 yields:
% 30.54/8.43 | (1237) ~ (all_0_41_41 = e3)
% 30.54/8.43 |
% 30.54/8.43 | Equations (671) can reduce 145 to:
% 30.54/8.43 | (1331) ~ (all_0_42_42 = e3)
% 30.54/8.43 |
% 30.54/8.43 | Simplifying 1331 yields:
% 30.54/8.43 | (1316) ~ (all_0_42_42 = e3)
% 30.54/8.43 |
% 30.54/8.43 | Equations (671) can reduce 137 to:
% 30.54/8.43 | (825) ~ (all_0_52_52 = e3)
% 30.54/8.43 |
% 30.54/8.43 | Simplifying 825 yields:
% 30.54/8.43 | (826) ~ (all_0_52_52 = e3)
% 30.54/8.43 |
% 30.54/8.43 | Equations (671) can reduce 149 to:
% 30.54/8.43 | (2238) ~ (all_0_57_57 = e3)
% 30.54/8.43 |
% 30.54/8.43 | Simplifying 2238 yields:
% 30.54/8.43 | (846) ~ (all_0_57_57 = e3)
% 30.54/8.43 |
% 30.54/8.43 | Equations (671) can reduce 233 to:
% 30.54/8.43 | (719) ~ (e4 = e3)
% 30.54/8.43 |
% 30.54/8.43 | Simplifying 719 yields:
% 30.54/8.43 | (34) ~ (e4 = e3)
% 30.54/8.43 |
% 30.54/8.43 | Equations (671) can reduce 602 to:
% 30.54/8.43 | (223) ~ (e3 = e2)
% 30.54/8.43 |
% 30.54/8.43 | Equations (671) can reduce 238 to:
% 30.54/8.43 | (66) ~ (e3 = e0)
% 30.54/8.43 |
% 30.54/8.43 | From (671) and (68) follows:
% 30.54/8.43 | (5921) op(e2, e3) = all_0_13_13
% 30.54/8.43 |
% 30.54/8.43 | Instantiating formula (201) with e2, e3, all_0_13_13, e1 and discharging atoms op(e2, e3) = all_0_13_13, op(e2, e3) = e1, yields:
% 30.54/8.43 | (5957) all_0_13_13 = e1
% 30.54/8.43 |
% 30.54/8.43 +-Applying beta-rule and splitting (87), into two cases.
% 30.54/8.43 |-Branch one:
% 30.54/8.43 | (650) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 30.54/8.43 |
% 30.54/8.43 +-Applying beta-rule and splitting (650), into two cases.
% 30.54/8.43 |-Branch one:
% 30.54/8.43 | (651) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 30.54/8.43 |
% 30.54/8.43 +-Applying beta-rule and splitting (651), into two cases.
% 30.54/8.43 |-Branch one:
% 30.54/8.43 | (652) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 30.54/8.43 |
% 30.54/8.43 | Applying alpha-rule on (652) yields:
% 30.54/8.43 | (653) all_0_13_13 = e4
% 30.54/8.43 | (654) ~ (all_0_14_14 = e2)
% 30.54/8.43 |
% 30.54/8.43 | Combining equations (653,5957) yields a new equation:
% 30.54/8.43 | (525) e4 = e1
% 30.54/8.43 |
% 30.54/8.43 | Simplifying 525 yields:
% 30.54/8.43 | (526) e4 = e1
% 30.54/8.43 |
% 30.54/8.43 | Equations (526) can reduce 251 to:
% 30.54/8.43 | (270) $false
% 30.54/8.43 |
% 30.54/8.43 |-The branch is then unsatisfiable
% 30.54/8.43 |-Branch two:
% 30.54/8.43 | (657) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 30.54/8.43 |
% 30.54/8.43 | Applying alpha-rule on (657) yields:
% 30.54/8.43 | (658) all_0_15_15 = e3
% 30.54/8.43 | (659) ~ (all_0_16_16 = e2)
% 30.54/8.43 |
% 30.54/8.43 | Combining equations (620,658) yields a new equation:
% 30.54/8.43 | (660) e4 = e3
% 30.54/8.43 |
% 30.54/8.43 | Simplifying 660 yields:
% 30.54/8.43 | (359) e4 = e3
% 30.54/8.43 |
% 30.54/8.43 | Equations (359) can reduce 34 to:
% 30.54/8.43 | (270) $false
% 30.54/8.43 |
% 30.54/8.43 |-The branch is then unsatisfiable
% 30.54/8.43 |-Branch two:
% 30.54/8.43 | (663) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 30.54/8.43 |
% 30.54/8.43 | Applying alpha-rule on (663) yields:
% 30.54/8.43 | (664) all_0_17_17 = e1
% 30.54/8.43 | (665) ~ (all_0_18_18 = e2)
% 30.54/8.43 |
% 30.54/8.43 | From (664) and (27) follows:
% 30.54/8.43 | (666) op(e2, all_0_52_52) = e1
% 30.54/8.43 |
% 30.54/8.43 +-Applying beta-rule and splitting (16), into two cases.
% 30.54/8.43 |-Branch one:
% 30.54/8.43 | (698) all_0_42_42 = e2
% 30.54/8.43 |
% 30.54/8.43 | Equations (698) can reduce 498 to:
% 30.54/8.43 | (270) $false
% 30.54/8.43 |
% 30.54/8.43 |-The branch is then unsatisfiable
% 30.54/8.43 |-Branch two:
% 30.54/8.43 | (498) ~ (all_0_42_42 = e2)
% 30.54/8.43 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 30.54/8.43 |
% 30.54/8.43 +-Applying beta-rule and splitting (210), into two cases.
% 30.54/8.43 |-Branch one:
% 30.54/8.43 | (524) all_0_39_39 = e1
% 30.54/8.43 |
% 30.54/8.43 | Combining equations (336,524) yields a new equation:
% 30.54/8.43 | (531) e2 = e1
% 30.54/8.43 |
% 30.54/8.43 | Simplifying 531 yields:
% 30.54/8.43 | (322) e2 = e1
% 30.54/8.43 |
% 30.54/8.43 | Equations (322) can reduce 141 to:
% 30.54/8.43 | (270) $false
% 30.54/8.43 |
% 30.54/8.43 |-The branch is then unsatisfiable
% 30.54/8.43 |-Branch two:
% 30.54/8.43 | (528) ~ (all_0_39_39 = e1)
% 30.54/8.43 | (529) all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1
% 30.54/8.43 |
% 30.54/8.43 | Equations (336) can reduce 528 to:
% 30.54/8.43 | (141) ~ (e2 = e1)
% 30.54/8.43 |
% 30.54/8.43 +-Applying beta-rule and splitting (21), into two cases.
% 30.54/8.43 |-Branch one:
% 30.54/8.43 | (824) all_0_51_51 = e3
% 30.54/8.43 |
% 30.54/8.43 | Equations (824) can reduce 240 to:
% 30.54/8.43 | (786) ~ (all_0_43_43 = e3)
% 30.54/8.43 |
% 30.54/8.43 | Equations (824) can reduce 154 to:
% 30.54/8.43 | (825) ~ (all_0_52_52 = e3)
% 30.54/8.43 |
% 30.54/8.43 | Simplifying 825 yields:
% 30.54/8.43 | (826) ~ (all_0_52_52 = e3)
% 30.54/8.43 |
% 30.54/8.43 | Equations (824) can reduce 12 to:
% 30.54/8.43 | (355) ~ (all_0_53_53 = e3)
% 30.54/8.43 |
% 30.54/8.43 | Simplifying 355 yields:
% 30.54/8.43 | (356) ~ (all_0_53_53 = e3)
% 30.54/8.43 |
% 30.54/8.43 | Equations (824) can reduce 697 to:
% 30.54/8.43 | (719) ~ (e4 = e3)
% 30.54/8.43 |
% 30.54/8.43 | Simplifying 719 yields:
% 30.54/8.43 | (34) ~ (e4 = e3)
% 30.54/8.43 |
% 30.54/8.43 | Equations (824) can reduce 255 to:
% 30.54/8.43 | (223) ~ (e3 = e2)
% 30.54/8.43 |
% 30.54/8.43 | Equations (824) can reduce 748 to:
% 30.54/8.43 | (136) ~ (e3 = e1)
% 30.54/8.43 |
% 30.54/8.43 | From (824) and (7) follows:
% 30.54/8.43 | (11846) op(e3, e3) = all_0_9_9
% 30.54/8.43 |
% 30.54/8.43 | Instantiating formula (201) with e3, e3, all_0_9_9, all_0_43_43 and discharging atoms op(e3, e3) = all_0_9_9, op(e3, e3) = all_0_43_43, yields:
% 30.54/8.43 | (11847) all_0_9_9 = all_0_43_43
% 30.54/8.43 |
% 30.54/8.43 +-Applying beta-rule and splitting (234), into two cases.
% 30.54/8.43 |-Branch one:
% 30.54/8.43 | (4239) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3)) | (all_0_9_9 = e1 & ~ (all_0_10_10 = e3))
% 30.54/8.43 |
% 30.54/8.43 +-Applying beta-rule and splitting (4239), into two cases.
% 30.54/8.43 |-Branch one:
% 30.54/8.43 | (4240) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3))
% 30.54/8.43 |
% 30.54/8.43 +-Applying beta-rule and splitting (4240), into two cases.
% 30.54/8.43 |-Branch one:
% 30.54/8.43 | (4241) all_0_4_4 = e4 & ~ (all_0_5_5 = e3)
% 30.54/8.43 |
% 30.54/8.43 | Applying alpha-rule on (4241) yields:
% 30.54/8.44 | (4242) all_0_4_4 = e4
% 30.54/8.44 | (4243) ~ (all_0_5_5 = e3)
% 30.54/8.44 |
% 30.54/8.44 | Combining equations (4242,12701) yields a new equation:
% 30.54/8.44 | (268) e4 = e2
% 30.54/8.44 |
% 30.54/8.44 | Simplifying 268 yields:
% 30.54/8.44 | (269) e4 = e2
% 30.54/8.44 |
% 30.54/8.44 | Equations (269) can reduce 231 to:
% 30.54/8.44 | (270) $false
% 30.54/8.44 |
% 30.54/8.44 |-The branch is then unsatisfiable
% 30.54/8.44 |-Branch two:
% 30.54/8.44 | (4247) all_0_7_7 = e2 & ~ (all_0_8_8 = e3)
% 30.54/8.44 |
% 30.54/8.44 | Applying alpha-rule on (4247) yields:
% 30.54/8.44 | (4248) all_0_7_7 = e2
% 30.54/8.44 | (4249) ~ (all_0_8_8 = e3)
% 30.54/8.44 |
% 30.54/8.44 | Combining equations (4011,4248) yields a new equation:
% 30.54/8.44 | (4250) all_0_45_45 = e2
% 30.54/8.44 |
% 30.54/8.44 | Simplifying 4250 yields:
% 30.54/8.44 | (374) all_0_45_45 = e2
% 30.54/8.44 |
% 30.54/8.44 | Equations (374) can reduce 434 to:
% 30.54/8.44 | (270) $false
% 30.54/8.44 |
% 30.54/8.44 |-The branch is then unsatisfiable
% 30.54/8.44 |-Branch two:
% 30.54/8.44 | (4253) all_0_9_9 = e1 & ~ (all_0_10_10 = e3)
% 30.54/8.44 |
% 30.54/8.44 | Applying alpha-rule on (4253) yields:
% 30.54/8.44 | (4254) all_0_9_9 = e1
% 30.54/8.44 | (4255) ~ (all_0_10_10 = e3)
% 30.54/8.44 |
% 30.54/8.44 | Combining equations (4254,11847) yields a new equation:
% 30.54/8.44 | (12225) all_0_43_43 = e1
% 30.54/8.44 |
% 30.54/8.44 | Equations (12225) can reduce 249 to:
% 30.54/8.44 | (270) $false
% 30.54/8.44 |
% 30.54/8.44 |-The branch is then unsatisfiable
% 30.54/8.44 |-Branch two:
% 30.54/8.44 | (4378) all_0_11_11 = e0 & ~ (all_0_12_12 = e3)
% 30.54/8.44 |
% 30.54/8.44 | Applying alpha-rule on (4378) yields:
% 30.54/8.44 | (4379) all_0_11_11 = e0
% 30.54/8.44 | (4380) ~ (all_0_12_12 = e3)
% 30.54/8.44 |
% 30.54/8.44 | From (4379) and (239) follows:
% 30.54/8.44 | (12899) op(e3, all_0_56_56) = e0
% 30.54/8.44 |
% 30.54/8.44 +-Applying beta-rule and splitting (64), into two cases.
% 30.54/8.44 |-Branch one:
% 30.54/8.44 | (954) all_0_51_51 = e0
% 30.54/8.44 |
% 30.54/8.44 | Combining equations (954,824) yields a new equation:
% 30.54/8.44 | (784) e3 = e0
% 30.54/8.44 |
% 30.54/8.44 | Equations (784) can reduce 66 to:
% 30.54/8.44 | (270) $false
% 30.54/8.44 |
% 30.54/8.44 |-The branch is then unsatisfiable
% 30.54/8.44 |-Branch two:
% 30.54/8.44 | (987) ~ (all_0_51_51 = e0)
% 30.54/8.44 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 30.54/8.44 |
% 30.54/8.44 | Equations (824) can reduce 987 to:
% 30.54/8.44 | (66) ~ (e3 = e0)
% 30.54/8.44 |
% 30.54/8.44 +-Applying beta-rule and splitting (75), into two cases.
% 30.54/8.44 |-Branch one:
% 30.54/8.44 | (411) all_0_43_43 = e0
% 30.54/8.44 |
% 30.54/8.44 | Equations (411) can reduce 249 to:
% 30.54/8.44 | (568) ~ (e1 = e0)
% 30.54/8.44 |
% 30.54/8.44 | Simplifying 568 yields:
% 30.54/8.44 | (132) ~ (e1 = e0)
% 30.54/8.44 |
% 30.54/8.44 +-Applying beta-rule and splitting (166), into two cases.
% 30.54/8.44 |-Branch one:
% 30.54/8.44 | (522) all_0_39_39 = e4
% 30.54/8.44 |
% 30.54/8.44 | Combining equations (336,522) yields a new equation:
% 30.54/8.44 | (269) e4 = e2
% 30.54/8.44 |
% 30.54/8.44 | Equations (269) can reduce 231 to:
% 30.54/8.44 | (270) $false
% 30.54/8.44 |
% 30.54/8.44 |-The branch is then unsatisfiable
% 30.54/8.44 |-Branch two:
% 30.54/8.44 | (591) ~ (all_0_39_39 = e4)
% 30.54/8.44 | (4522) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 30.54/8.44 |
% 30.54/8.44 +-Applying beta-rule and splitting (4522), into two cases.
% 30.54/8.44 |-Branch one:
% 30.54/8.44 | (502) all_0_43_43 = e4
% 30.54/8.44 |
% 30.54/8.44 | Combining equations (411,502) yields a new equation:
% 30.54/8.44 | (479) e4 = e0
% 30.54/8.44 |
% 30.54/8.44 | Equations (479) can reduce 6 to:
% 30.54/8.44 | (270) $false
% 30.54/8.44 |
% 30.54/8.44 |-The branch is then unsatisfiable
% 30.54/8.44 |-Branch two:
% 30.54/8.44 | (510) ~ (all_0_43_43 = e4)
% 30.54/8.44 | (4527) all_0_51_51 = e4 | all_0_56_56 = e4
% 30.54/8.44 |
% 30.54/8.44 +-Applying beta-rule and splitting (4527), into two cases.
% 30.54/8.44 |-Branch one:
% 30.54/8.44 | (1467) all_0_51_51 = e4
% 30.54/8.44 |
% 30.54/8.44 | Combining equations (824,1467) yields a new equation:
% 30.54/8.44 | (359) e4 = e3
% 30.54/8.44 |
% 30.54/8.44 | Equations (359) can reduce 34 to:
% 30.54/8.44 | (270) $false
% 30.54/8.44 |
% 30.54/8.44 |-The branch is then unsatisfiable
% 30.54/8.44 |-Branch two:
% 30.54/8.44 | (697) ~ (all_0_51_51 = e4)
% 30.54/8.44 | (4744) all_0_56_56 = e4
% 30.54/8.44 |
% 30.54/8.44 | From (4744) and (12899) follows:
% 30.54/8.44 | (12924) op(e3, e4) = e0
% 30.54/8.44 |
% 30.54/8.44 | Instantiating formula (201) with e3, e4, e0, e1 and discharging atoms op(e3, e4) = e1, op(e3, e4) = e0, yields:
% 30.54/8.44 | (560) e1 = e0
% 30.54/8.44 |
% 30.54/8.44 | Equations (560) can reduce 132 to:
% 30.54/8.44 | (270) $false
% 30.54/8.44 |
% 30.54/8.44 |-The branch is then unsatisfiable
% 30.54/8.44 |-Branch two:
% 30.54/8.44 | (455) ~ (all_0_43_43 = e0)
% 30.54/8.44 | (940) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 30.54/8.44 |
% 30.54/8.44 +-Applying beta-rule and splitting (940), into two cases.
% 30.54/8.44 |-Branch one:
% 30.54/8.44 | (315) all_0_47_47 = e0
% 30.54/8.44 |
% 30.54/8.44 | Combining equations (321,315) yields a new equation:
% 30.54/8.44 | (571) e1 = e0
% 30.54/8.44 |
% 30.54/8.44 | Simplifying 571 yields:
% 30.54/8.44 | (560) e1 = e0
% 30.54/8.44 |
% 30.54/8.44 | Equations (560) can reduce 132 to:
% 30.54/8.44 | (270) $false
% 30.54/8.44 |
% 30.54/8.44 |-The branch is then unsatisfiable
% 30.54/8.44 |-Branch two:
% 30.54/8.44 | (318) ~ (all_0_47_47 = e0)
% 30.54/8.44 | (950) all_0_51_51 = e0 | all_0_56_56 = e0
% 30.54/8.44 |
% 30.54/8.44 +-Applying beta-rule and splitting (116), into two cases.
% 30.54/8.44 |-Branch one:
% 30.54/8.44 | (411) all_0_43_43 = e0
% 30.54/8.44 |
% 30.54/8.44 | Equations (411) can reduce 455 to:
% 30.54/8.44 | (270) $false
% 30.54/8.44 |
% 30.54/8.44 |-The branch is then unsatisfiable
% 30.54/8.44 |-Branch two:
% 30.54/8.44 | (455) ~ (all_0_43_43 = e0)
% 30.54/8.44 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 30.54/8.44 |
% 30.54/8.44 +-Applying beta-rule and splitting (1122), into two cases.
% 30.54/8.44 |-Branch one:
% 30.54/8.44 | (621) all_0_44_44 = e0
% 30.54/8.44 |
% 30.54/8.44 | Combining equations (370,621) yields a new equation:
% 30.54/8.44 | (622) e2 = e0
% 30.54/8.44 |
% 30.54/8.44 | Simplifying 622 yields:
% 30.54/8.44 | (316) e2 = e0
% 30.54/8.44 |
% 30.54/8.44 | Equations (316) can reduce 57 to:
% 30.54/8.44 | (270) $false
% 30.54/8.44 |
% 30.54/8.44 |-The branch is then unsatisfiable
% 30.54/8.44 |-Branch two:
% 30.54/8.44 | (625) ~ (all_0_44_44 = e0)
% 30.54/8.44 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 30.54/8.44 |
% 30.54/8.44 +-Applying beta-rule and splitting (1128), into two cases.
% 30.54/8.44 |-Branch one:
% 30.54/8.44 | (454) all_0_45_45 = e0
% 30.54/8.44 |
% 30.54/8.44 | Equations (454) can reduce 128 to:
% 30.54/8.44 | (3103) ~ (all_0_53_53 = e0)
% 30.54/8.44 |
% 30.54/8.44 | Simplifying 3103 yields:
% 30.54/8.44 | (584) ~ (all_0_53_53 = e0)
% 30.54/8.44 |
% 30.54/8.44 | Equations (454) can reduce 108 to:
% 30.54/8.44 | (3530) ~ (all_0_58_58 = e0)
% 30.54/8.44 |
% 30.54/8.44 | Simplifying 3530 yields:
% 30.54/8.44 | (431) ~ (all_0_58_58 = e0)
% 30.54/8.44 |
% 30.54/8.44 | Equations (454) can reduce 434 to:
% 30.54/8.44 | (566) ~ (e2 = e0)
% 30.54/8.44 |
% 30.54/8.44 | Simplifying 566 yields:
% 30.54/8.44 | (57) ~ (e2 = e0)
% 30.54/8.44 |
% 30.54/8.44 | Equations (454) can reduce 26 to:
% 30.54/8.44 | (568) ~ (e1 = e0)
% 30.54/8.44 |
% 30.54/8.44 | Simplifying 568 yields:
% 30.54/8.44 | (132) ~ (e1 = e0)
% 30.54/8.44 |
% 30.54/8.44 +-Applying beta-rule and splitting (22), into two cases.
% 30.54/8.44 |-Branch one:
% 30.54/8.44 | (782) all_0_43_43 = e3
% 30.54/8.44 |
% 30.54/8.44 | Equations (782) can reduce 786 to:
% 30.54/8.44 | (270) $false
% 30.54/8.44 |
% 30.54/8.44 |-The branch is then unsatisfiable
% 30.54/8.44 |-Branch two:
% 30.54/8.44 | (786) ~ (all_0_43_43 = e3)
% 30.54/8.44 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 30.54/8.44 |
% 30.54/8.44 +-Applying beta-rule and splitting (219), into two cases.
% 30.54/8.44 |-Branch one:
% 30.54/8.44 | (351) all_0_41_41 = e3
% 30.54/8.44 |
% 30.54/8.44 | Equations (351) can reduce 1237 to:
% 30.54/8.44 | (270) $false
% 30.54/8.44 |
% 30.54/8.44 |-The branch is then unsatisfiable
% 30.54/8.44 |-Branch two:
% 30.54/8.44 | (1237) ~ (all_0_41_41 = e3)
% 30.54/8.44 | (1508) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 30.54/8.45 |
% 30.54/8.45 +-Applying beta-rule and splitting (93), into two cases.
% 30.54/8.45 |-Branch one:
% 30.54/8.45 | (402) all_0_59_59 = e4
% 30.54/8.45 |
% 30.54/8.45 | Equations (402) can reduce 17 to:
% 30.54/8.45 | (520) ~ (all_0_42_42 = e4)
% 30.54/8.45 |
% 30.54/8.45 | Equations (402) can reduce 206 to:
% 30.54/8.45 | (805) ~ (all_0_46_46 = e4)
% 30.54/8.45 |
% 30.54/8.45 | Equations (402) can reduce 4001 to:
% 30.54/8.45 | (6) ~ (e4 = e0)
% 30.54/8.45 |
% 30.54/8.45 +-Applying beta-rule and splitting (44), into two cases.
% 30.54/8.45 |-Branch one:
% 30.54/8.45 | (502) all_0_43_43 = e4
% 30.54/8.45 |
% 30.54/8.45 | Equations (502) can reduce 249 to:
% 30.54/8.45 | (251) ~ (e4 = e1)
% 30.54/8.45 |
% 30.54/8.45 +-Applying beta-rule and splitting (127), into two cases.
% 30.54/8.45 |-Branch one:
% 30.54/8.45 | (541) all_0_42_42 = e1
% 30.54/8.45 |
% 30.54/8.45 | Equations (541) can reduce 94 to:
% 30.54/8.45 | (540) ~ (all_0_41_41 = e1)
% 30.54/8.45 |
% 30.54/8.45 | Equations (541) can reduce 1316 to:
% 30.54/8.45 | (769) ~ (e3 = e1)
% 30.54/8.45 |
% 30.54/8.45 | Simplifying 769 yields:
% 30.54/8.45 | (136) ~ (e3 = e1)
% 30.54/8.45 |
% 30.54/8.45 | Equations (541) can reduce 498 to:
% 30.54/8.45 | (645) ~ (e2 = e1)
% 30.54/8.45 |
% 30.54/8.45 | Simplifying 645 yields:
% 30.54/8.45 | (141) ~ (e2 = e1)
% 30.54/8.45 |
% 30.54/8.45 +-Applying beta-rule and splitting (95), into two cases.
% 30.54/8.45 |-Branch one:
% 30.54/8.45 | (1258) all_0_42_42 = e3
% 30.54/8.45 |
% 30.54/8.45 | Combining equations (1258,541) yields a new equation:
% 30.54/8.45 | (537) e3 = e1
% 30.54/8.45 |
% 30.54/8.45 | Simplifying 537 yields:
% 30.54/8.45 | (538) e3 = e1
% 30.54/8.45 |
% 30.54/8.45 | Equations (538) can reduce 136 to:
% 30.54/8.45 | (270) $false
% 30.54/8.45 |
% 30.54/8.45 |-The branch is then unsatisfiable
% 30.54/8.45 |-Branch two:
% 30.54/8.45 | (1316) ~ (all_0_42_42 = e3)
% 30.54/8.45 | (3656) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 30.54/8.45 |
% 30.54/8.45 | Equations (541) can reduce 1316 to:
% 30.54/8.45 | (769) ~ (e3 = e1)
% 30.54/8.45 |
% 30.54/8.45 | Simplifying 769 yields:
% 30.54/8.45 | (136) ~ (e3 = e1)
% 30.54/8.45 |
% 30.54/8.45 +-Applying beta-rule and splitting (3067), into two cases.
% 30.54/8.45 |-Branch one:
% 30.54/8.45 | (827) all_0_52_52 = e0
% 30.54/8.45 |
% 30.54/8.45 | Equations (827) can reduce 213 to:
% 30.54/8.45 | (3103) ~ (all_0_53_53 = e0)
% 30.54/8.45 |
% 30.54/8.45 | Simplifying 3103 yields:
% 30.54/8.45 | (584) ~ (all_0_53_53 = e0)
% 30.54/8.45 |
% 30.54/8.45 | Equations (827) can reduce 826 to:
% 30.54/8.45 | (788) ~ (e3 = e0)
% 30.54/8.45 |
% 30.54/8.45 | Simplifying 788 yields:
% 30.54/8.45 | (66) ~ (e3 = e0)
% 30.54/8.45 |
% 30.54/8.45 | From (827) and (666) follows:
% 30.54/8.45 | (11382) op(e2, e0) = e1
% 30.54/8.45 |
% 30.54/8.45 +-Applying beta-rule and splitting (33), into two cases.
% 30.54/8.45 |-Branch one:
% 30.54/8.45 | (392) all_0_57_57 = e2
% 30.54/8.45 |
% 30.54/8.45 | Equations (392) can reduce 335 to:
% 30.54/8.45 | (270) $false
% 30.54/8.45 |
% 30.54/8.45 |-The branch is then unsatisfiable
% 30.54/8.45 |-Branch two:
% 30.54/8.45 | (335) ~ (all_0_57_57 = e2)
% 30.54/8.45 | (670) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 30.54/8.45 |
% 30.54/8.45 +-Applying beta-rule and splitting (1508), into two cases.
% 30.54/8.45 |-Branch one:
% 30.54/8.45 | (505) all_0_45_45 = e3
% 30.54/8.45 |
% 30.54/8.45 | Combining equations (454,505) yields a new equation:
% 30.54/8.45 | (784) e3 = e0
% 30.54/8.45 |
% 30.54/8.45 | Equations (784) can reduce 66 to:
% 30.54/8.45 | (270) $false
% 30.54/8.45 |
% 30.54/8.45 |-The branch is then unsatisfiable
% 30.54/8.45 |-Branch two:
% 30.54/8.45 | (354) ~ (all_0_45_45 = e3)
% 30.54/8.45 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 30.54/8.45 |
% 30.54/8.45 | Equations (454) can reduce 354 to:
% 30.54/8.45 | (788) ~ (e3 = e0)
% 30.54/8.45 |
% 30.54/8.45 | Simplifying 788 yields:
% 30.54/8.45 | (66) ~ (e3 = e0)
% 30.54/8.45 |
% 30.54/8.45 +-Applying beta-rule and splitting (176), into two cases.
% 30.54/8.45 |-Branch one:
% 30.54/8.45 | (830) all_0_56_56 = e0
% 30.54/8.45 |
% 30.54/8.45 | Equations (830) can reduce 995 to:
% 30.54/8.45 | (568) ~ (e1 = e0)
% 30.54/8.45 |
% 30.54/8.45 | Simplifying 568 yields:
% 30.54/8.45 | (132) ~ (e1 = e0)
% 30.54/8.45 |
% 30.54/8.45 +-Applying beta-rule and splitting (3352), into two cases.
% 30.54/8.45 |-Branch one:
% 30.54/8.45 | (848) all_0_52_52 = e1
% 30.54/8.45 |
% 30.54/8.45 | Combining equations (827,848) yields a new equation:
% 30.54/8.45 | (560) e1 = e0
% 30.54/8.45 |
% 30.54/8.45 | Equations (560) can reduce 132 to:
% 30.54/8.45 | (270) $false
% 30.54/8.45 |
% 30.54/8.45 |-The branch is then unsatisfiable
% 30.54/8.45 |-Branch two:
% 30.54/8.45 | (642) ~ (all_0_52_52 = e1)
% 30.54/8.45 | (997) all_0_57_57 = e1
% 30.54/8.45 |
% 30.54/8.45 | Equations (997) can reduce 37 to:
% 30.54/8.45 | (7725) ~ (all_0_58_58 = e1)
% 30.54/8.45 |
% 30.54/8.45 | Simplifying 7725 yields:
% 30.54/8.45 | (1004) ~ (all_0_58_58 = e1)
% 30.54/8.45 |
% 30.54/8.45 | Equations (997) can reduce 335 to:
% 30.54/8.45 | (645) ~ (e2 = e1)
% 30.54/8.45 |
% 30.54/8.45 | Simplifying 645 yields:
% 30.54/8.45 | (141) ~ (e2 = e1)
% 30.54/8.45 |
% 30.54/8.45 +-Applying beta-rule and splitting (52), into two cases.
% 30.54/8.45 |-Branch one:
% 30.54/8.45 | (536) all_0_41_41 = e1
% 30.54/8.45 |
% 30.54/8.45 | Equations (536) can reduce 540 to:
% 30.54/8.45 | (270) $false
% 30.54/8.45 |
% 30.54/8.45 |-The branch is then unsatisfiable
% 30.54/8.45 |-Branch two:
% 30.54/8.45 | (540) ~ (all_0_41_41 = e1)
% 30.54/8.45 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 30.54/8.45 |
% 30.54/8.45 +-Applying beta-rule and splitting (762), into two cases.
% 30.54/8.45 |-Branch one:
% 30.54/8.45 | (552) all_0_48_48 = e1
% 30.54/8.45 |
% 30.54/8.45 | Combining equations (311,552) yields a new equation:
% 30.54/8.45 | (531) e2 = e1
% 30.54/8.45 |
% 30.54/8.45 | Simplifying 531 yields:
% 30.54/8.45 | (322) e2 = e1
% 30.54/8.45 |
% 30.54/8.45 | Equations (322) can reduce 141 to:
% 30.54/8.45 | (270) $false
% 30.54/8.45 |
% 30.54/8.45 |-The branch is then unsatisfiable
% 30.54/8.45 |-Branch two:
% 30.54/8.45 | (588) ~ (all_0_48_48 = e1)
% 30.54/8.45 | (4925) all_0_53_53 = e1 | all_0_58_58 = e1
% 30.54/8.45 |
% 30.54/8.45 +-Applying beta-rule and splitting (4925), into two cases.
% 30.54/8.45 |-Branch one:
% 30.54/8.45 | (853) all_0_53_53 = e1
% 30.54/8.45 |
% 30.54/8.45 | Equations (853) can reduce 584 to:
% 30.54/8.45 | (132) ~ (e1 = e0)
% 30.54/8.45 |
% 30.54/8.45 | Instantiating formula (201) with e2, e0, e1, e0 and discharging atoms op(e2, e0) = e1, op(e2, e0) = e0, yields:
% 30.54/8.45 | (560) e1 = e0
% 30.54/8.45 |
% 30.54/8.45 | Equations (560) can reduce 132 to:
% 30.54/8.45 | (270) $false
% 30.54/8.45 |
% 30.54/8.45 |-The branch is then unsatisfiable
% 30.54/8.45 |-Branch two:
% 30.54/8.45 | (874) ~ (all_0_53_53 = e1)
% 30.54/8.45 | (1001) all_0_58_58 = e1
% 30.54/8.45 |
% 30.54/8.45 | Equations (1001) can reduce 1004 to:
% 30.54/8.45 | (270) $false
% 30.54/8.45 |
% 30.54/8.45 |-The branch is then unsatisfiable
% 30.54/8.45 |-Branch two:
% 30.54/8.45 | (419) ~ (all_0_56_56 = e0)
% 30.54/8.45 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 30.54/8.45 |
% 30.54/8.45 +-Applying beta-rule and splitting (950), into two cases.
% 30.54/8.45 |-Branch one:
% 30.54/8.45 | (954) all_0_51_51 = e0
% 30.54/8.45 |
% 30.54/8.45 | Combining equations (824,954) yields a new equation:
% 30.54/8.45 | (783) e3 = e0
% 30.54/8.45 |
% 30.54/8.45 | Simplifying 783 yields:
% 30.54/8.45 | (784) e3 = e0
% 30.54/8.45 |
% 30.54/8.45 | Equations (784) can reduce 66 to:
% 30.54/8.45 | (270) $false
% 30.54/8.45 |
% 30.54/8.45 |-The branch is then unsatisfiable
% 30.54/8.45 |-Branch two:
% 30.54/8.45 | (987) ~ (all_0_51_51 = e0)
% 30.54/8.45 | (830) all_0_56_56 = e0
% 30.54/8.45 |
% 30.54/8.45 | Equations (830) can reduce 419 to:
% 30.54/8.45 | (270) $false
% 30.54/8.45 |
% 30.54/8.45 |-The branch is then unsatisfiable
% 30.54/8.45 |-Branch two:
% 30.54/8.45 | (925) ~ (all_0_52_52 = e0)
% 30.54/8.45 | (3073) all_0_53_53 = e0 | all_0_54_54 = e0
% 30.54/8.45 |
% 30.54/8.45 +-Applying beta-rule and splitting (1508), into two cases.
% 30.54/8.45 |-Branch one:
% 30.54/8.45 | (505) all_0_45_45 = e3
% 30.54/8.45 |
% 30.54/8.45 | Combining equations (454,505) yields a new equation:
% 30.54/8.45 | (784) e3 = e0
% 30.54/8.45 |
% 30.54/8.45 | Equations (784) can reduce 66 to:
% 30.54/8.45 | (270) $false
% 30.54/8.45 |
% 30.54/8.45 |-The branch is then unsatisfiable
% 30.54/8.45 |-Branch two:
% 30.54/8.45 | (354) ~ (all_0_45_45 = e3)
% 30.54/8.45 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 30.54/8.45 |
% 30.54/8.45 +-Applying beta-rule and splitting (1539), into two cases.
% 30.54/8.45 |-Branch one:
% 30.54/8.45 | (1114) all_0_53_53 = e3
% 30.54/8.45 |
% 30.54/8.45 | Equations (1114) can reduce 356 to:
% 30.54/8.45 | (270) $false
% 30.54/8.45 |
% 30.54/8.45 |-The branch is then unsatisfiable
% 30.54/8.45 |-Branch two:
% 30.54/8.45 | (356) ~ (all_0_53_53 = e3)
% 30.54/8.45 | (4713) all_0_58_58 = e3
% 30.54/8.45 |
% 30.54/8.45 | Equations (4713) can reduce 70 to:
% 30.54/8.45 | (356) ~ (all_0_53_53 = e3)
% 30.54/8.45 |
% 30.54/8.45 +-Applying beta-rule and splitting (52), into two cases.
% 30.54/8.45 |-Branch one:
% 30.54/8.45 | (536) all_0_41_41 = e1
% 30.54/8.45 |
% 30.54/8.45 | Equations (536) can reduce 540 to:
% 30.54/8.45 | (270) $false
% 30.54/8.45 |
% 30.54/8.45 |-The branch is then unsatisfiable
% 30.54/8.45 |-Branch two:
% 30.54/8.45 | (540) ~ (all_0_41_41 = e1)
% 30.54/8.45 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 30.54/8.45 |
% 30.54/8.45 +-Applying beta-rule and splitting (626), into two cases.
% 30.54/8.45 |-Branch one:
% 30.54/8.45 | (827) all_0_52_52 = e0
% 30.54/8.45 |
% 30.54/8.45 | Equations (827) can reduce 925 to:
% 30.54/8.45 | (270) $false
% 30.54/8.45 |
% 30.54/8.45 |-The branch is then unsatisfiable
% 30.54/8.45 |-Branch two:
% 30.54/8.45 | (925) ~ (all_0_52_52 = e0)
% 30.54/8.45 | (2258) all_0_57_57 = e0
% 30.54/8.45 |
% 30.54/8.45 +-Applying beta-rule and splitting (762), into two cases.
% 30.54/8.45 |-Branch one:
% 30.54/8.45 | (552) all_0_48_48 = e1
% 30.54/8.45 |
% 30.54/8.45 | Combining equations (311,552) yields a new equation:
% 30.54/8.45 | (531) e2 = e1
% 30.54/8.45 |
% 30.54/8.45 | Simplifying 531 yields:
% 30.54/8.45 | (322) e2 = e1
% 30.54/8.45 |
% 30.54/8.45 | Equations (322) can reduce 141 to:
% 30.54/8.45 | (270) $false
% 30.54/8.45 |
% 30.54/8.45 |-The branch is then unsatisfiable
% 30.54/8.45 |-Branch two:
% 30.54/8.45 | (588) ~ (all_0_48_48 = e1)
% 30.54/8.45 | (4925) all_0_53_53 = e1 | all_0_58_58 = e1
% 30.54/8.45 |
% 30.54/8.45 +-Applying beta-rule and splitting (4925), into two cases.
% 30.54/8.45 |-Branch one:
% 30.54/8.45 | (853) all_0_53_53 = e1
% 30.54/8.45 |
% 30.54/8.45 | Equations (853) can reduce 599 to:
% 30.54/8.45 | (1021) ~ (e4 = e1)
% 30.54/8.45 |
% 30.54/8.45 | Simplifying 1021 yields:
% 30.54/8.45 | (251) ~ (e4 = e1)
% 30.54/8.45 |
% 30.54/8.45 | Equations (853) can reduce 356 to:
% 30.54/8.45 | (769) ~ (e3 = e1)
% 30.54/8.45 |
% 30.54/8.45 | Simplifying 769 yields:
% 30.54/8.45 | (136) ~ (e3 = e1)
% 30.54/8.45 |
% 30.54/8.45 | Equations (853) can reduce 584 to:
% 30.54/8.45 | (132) ~ (e1 = e0)
% 30.54/8.45 |
% 30.54/8.45 +-Applying beta-rule and splitting (194), into two cases.
% 30.54/8.45 |-Branch one:
% 30.54/8.45 | (747) all_0_56_56 = e1
% 30.54/8.45 |
% 30.54/8.45 | Equations (747) can reduce 995 to:
% 30.54/8.45 | (270) $false
% 30.54/8.45 |
% 30.54/8.45 |-The branch is then unsatisfiable
% 30.54/8.45 |-Branch two:
% 30.54/8.45 | (995) ~ (all_0_56_56 = e1)
% 30.54/8.45 | (996) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 30.54/8.45 |
% 30.54/8.45 +-Applying beta-rule and splitting (996), into two cases.
% 30.54/8.45 |-Branch one:
% 30.54/8.45 | (997) all_0_57_57 = e1
% 30.54/8.45 |
% 30.54/8.45 | Combining equations (997,2258) yields a new equation:
% 30.54/8.45 | (571) e1 = e0
% 30.54/8.45 |
% 30.54/8.45 | Simplifying 571 yields:
% 30.54/8.45 | (560) e1 = e0
% 30.54/8.45 |
% 30.54/8.45 | Equations (560) can reduce 132 to:
% 30.54/8.45 | (270) $false
% 30.54/8.45 |
% 30.54/8.45 |-The branch is then unsatisfiable
% 30.54/8.45 |-Branch two:
% 30.54/8.45 | (644) ~ (all_0_57_57 = e1)
% 30.54/8.45 | (1000) all_0_58_58 = e1 | all_0_59_59 = e1
% 30.54/8.45 |
% 30.54/8.45 +-Applying beta-rule and splitting (1000), into two cases.
% 30.54/8.45 |-Branch one:
% 30.54/8.45 | (1001) all_0_58_58 = e1
% 30.54/8.45 |
% 30.54/8.45 | Combining equations (1001,4713) yields a new equation:
% 30.54/8.45 | (538) e3 = e1
% 30.54/8.45 |
% 30.54/8.45 | Equations (538) can reduce 136 to:
% 30.54/8.45 | (270) $false
% 30.54/8.45 |
% 30.54/8.45 |-The branch is then unsatisfiable
% 30.54/8.45 |-Branch two:
% 30.54/8.45 | (1004) ~ (all_0_58_58 = e1)
% 30.54/8.45 | (424) all_0_59_59 = e1
% 30.54/8.45 |
% 30.54/8.45 | Combining equations (402,424) yields a new equation:
% 30.54/8.45 | (525) e4 = e1
% 30.54/8.45 |
% 30.54/8.45 | Simplifying 525 yields:
% 30.54/8.45 | (526) e4 = e1
% 30.54/8.45 |
% 30.54/8.45 | Equations (526) can reduce 251 to:
% 30.54/8.45 | (270) $false
% 30.54/8.45 |
% 30.54/8.45 |-The branch is then unsatisfiable
% 30.54/8.45 |-Branch two:
% 30.54/8.45 | (874) ~ (all_0_53_53 = e1)
% 30.54/8.45 | (1001) all_0_58_58 = e1
% 30.54/8.45 |
% 30.54/8.45 | Combining equations (1001,4713) yields a new equation:
% 30.54/8.45 | (538) e3 = e1
% 30.54/8.45 |
% 30.54/8.45 | Equations (538) can reduce 136 to:
% 30.54/8.45 | (270) $false
% 30.54/8.45 |
% 30.54/8.45 |-The branch is then unsatisfiable
% 30.54/8.46 |-Branch two:
% 30.54/8.46 | (640) ~ (all_0_42_42 = e1)
% 30.54/8.46 | (4628) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 30.54/8.46 |
% 30.54/8.46 +-Applying beta-rule and splitting (1508), into two cases.
% 30.54/8.46 |-Branch one:
% 30.54/8.46 | (505) all_0_45_45 = e3
% 30.54/8.46 |
% 30.54/8.46 | Combining equations (454,505) yields a new equation:
% 30.54/8.46 | (784) e3 = e0
% 30.54/8.46 |
% 30.54/8.46 | Equations (784) can reduce 66 to:
% 30.54/8.46 | (270) $false
% 30.54/8.46 |
% 30.54/8.46 |-The branch is then unsatisfiable
% 30.54/8.46 |-Branch two:
% 30.54/8.46 | (354) ~ (all_0_45_45 = e3)
% 30.54/8.46 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 30.54/8.46 |
% 30.54/8.46 +-Applying beta-rule and splitting (1539), into two cases.
% 30.54/8.46 |-Branch one:
% 30.54/8.46 | (1114) all_0_53_53 = e3
% 30.54/8.46 |
% 30.54/8.46 | Equations (1114) can reduce 356 to:
% 30.54/8.46 | (270) $false
% 30.54/8.46 |
% 30.54/8.46 |-The branch is then unsatisfiable
% 30.54/8.46 |-Branch two:
% 30.54/8.46 | (356) ~ (all_0_53_53 = e3)
% 30.54/8.46 | (4713) all_0_58_58 = e3
% 30.54/8.46 |
% 30.54/8.46 | Equations (4713) can reduce 157 to:
% 30.54/8.46 | (1237) ~ (all_0_41_41 = e3)
% 30.54/8.46 |
% 30.54/8.46 | Equations (4713) can reduce 70 to:
% 30.54/8.46 | (356) ~ (all_0_53_53 = e3)
% 30.54/8.46 |
% 30.54/8.46 | Equations (4713) can reduce 376 to:
% 30.54/8.46 | (223) ~ (e3 = e2)
% 30.54/8.46 |
% 30.54/8.46 | Equations (4713) can reduce 431 to:
% 30.54/8.46 | (66) ~ (e3 = e0)
% 30.54/8.46 |
% 30.54/8.46 +-Applying beta-rule and splitting (1245), into two cases.
% 30.54/8.46 |-Branch one:
% 30.54/8.46 | (1258) all_0_42_42 = e3
% 30.54/8.46 |
% 30.54/8.46 | Equations (1258) can reduce 1316 to:
% 30.54/8.46 | (270) $false
% 30.54/8.46 |
% 30.54/8.46 |-The branch is then unsatisfiable
% 30.54/8.46 |-Branch two:
% 30.54/8.46 | (1316) ~ (all_0_42_42 = e3)
% 30.54/8.46 | (1317) all_0_42_42 = e4 | all_0_42_42 = e1
% 30.54/8.46 |
% 30.54/8.46 +-Applying beta-rule and splitting (13), into two cases.
% 30.54/8.46 |-Branch one:
% 30.54/8.46 | (576) all_0_53_53 = e2
% 30.54/8.46 |
% 30.54/8.46 | Equations (576) can reduce 259 to:
% 30.54/8.46 | (270) $false
% 30.54/8.46 |
% 30.54/8.46 |-The branch is then unsatisfiable
% 30.54/8.46 |-Branch two:
% 30.54/8.46 | (259) ~ (all_0_53_53 = e2)
% 30.54/8.46 | (5715) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 30.54/8.46 |
% 30.54/8.46 +-Applying beta-rule and splitting (592), into two cases.
% 30.54/8.46 |-Branch one:
% 30.54/8.46 | (358) all_0_41_41 = e4
% 30.54/8.46 |
% 30.54/8.46 | Equations (358) can reduce 214 to:
% 30.54/8.46 | (1444) ~ (all_0_53_53 = e4)
% 30.54/8.46 |
% 30.54/8.46 | Simplifying 1444 yields:
% 30.54/8.46 | (599) ~ (all_0_53_53 = e4)
% 30.54/8.46 |
% 30.54/8.46 | Equations (358) can reduce 1237 to:
% 30.54/8.46 | (34) ~ (e4 = e3)
% 30.54/8.46 |
% 30.54/8.46 +-Applying beta-rule and splitting (95), into two cases.
% 30.54/8.46 |-Branch one:
% 30.54/8.46 | (1258) all_0_42_42 = e3
% 30.54/8.46 |
% 30.54/8.46 | Equations (1258) can reduce 1316 to:
% 30.54/8.46 | (270) $false
% 30.54/8.46 |
% 30.54/8.46 |-The branch is then unsatisfiable
% 30.54/8.46 |-Branch two:
% 30.54/8.46 | (1316) ~ (all_0_42_42 = e3)
% 30.54/8.46 | (3656) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 30.54/8.46 |
% 30.54/8.46 +-Applying beta-rule and splitting (950), into two cases.
% 30.54/8.46 |-Branch one:
% 30.54/8.46 | (954) all_0_51_51 = e0
% 30.54/8.46 |
% 30.54/8.46 | Combining equations (824,954) yields a new equation:
% 30.54/8.46 | (783) e3 = e0
% 30.54/8.46 |
% 30.54/8.46 | Simplifying 783 yields:
% 30.54/8.46 | (784) e3 = e0
% 30.54/8.46 |
% 30.54/8.46 | Equations (784) can reduce 66 to:
% 30.54/8.46 | (270) $false
% 30.54/8.46 |
% 30.54/8.46 |-The branch is then unsatisfiable
% 30.54/8.46 |-Branch two:
% 30.54/8.46 | (987) ~ (all_0_51_51 = e0)
% 30.54/8.46 | (830) all_0_56_56 = e0
% 30.54/8.46 |
% 30.54/8.46 | Equations (830) can reduce 104 to:
% 30.54/8.46 | (9326) ~ (all_0_57_57 = e0)
% 30.54/8.46 |
% 30.54/8.46 | Simplifying 9326 yields:
% 30.54/8.46 | (2301) ~ (all_0_57_57 = e0)
% 30.54/8.46 |
% 30.54/8.46 | Equations (830) can reduce 995 to:
% 30.54/8.46 | (568) ~ (e1 = e0)
% 30.54/8.46 |
% 30.54/8.46 | Simplifying 568 yields:
% 30.54/8.46 | (132) ~ (e1 = e0)
% 30.54/8.46 |
% 30.54/8.46 +-Applying beta-rule and splitting (52), into two cases.
% 30.54/8.46 |-Branch one:
% 30.54/8.46 | (536) all_0_41_41 = e1
% 30.54/8.46 |
% 30.54/8.46 | Combining equations (536,358) yields a new equation:
% 30.54/8.46 | (526) e4 = e1
% 30.54/8.46 |
% 30.54/8.46 | Equations (526) can reduce 251 to:
% 30.54/8.46 | (270) $false
% 30.54/8.46 |
% 30.54/8.46 |-The branch is then unsatisfiable
% 30.54/8.46 |-Branch two:
% 30.54/8.46 | (540) ~ (all_0_41_41 = e1)
% 30.54/8.46 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 30.54/8.46 |
% 30.54/8.46 | Equations (358) can reduce 540 to:
% 30.54/8.46 | (251) ~ (e4 = e1)
% 30.54/8.46 |
% 30.54/8.46 +-Applying beta-rule and splitting (529), into two cases.
% 30.54/8.46 |-Branch one:
% 30.54/8.46 | (530) all_0_40_40 = e1
% 30.54/8.46 |
% 30.54/8.46 | Combining equations (530,671) yields a new equation:
% 30.54/8.46 | (538) e3 = e1
% 30.54/8.46 |
% 30.54/8.46 | Equations (538) can reduce 136 to:
% 30.54/8.46 | (270) $false
% 30.54/8.46 |
% 30.54/8.46 |-The branch is then unsatisfiable
% 30.54/8.46 |-Branch two:
% 30.54/8.46 | (534) ~ (all_0_40_40 = e1)
% 30.54/8.46 | (535) all_0_41_41 = e1 | all_0_42_42 = e1
% 30.54/8.46 |
% 30.54/8.46 | Equations (671) can reduce 534 to:
% 30.54/8.46 | (136) ~ (e3 = e1)
% 30.54/8.46 |
% 30.54/8.46 +-Applying beta-rule and splitting (626), into two cases.
% 30.54/8.46 |-Branch one:
% 30.54/8.46 | (827) all_0_52_52 = e0
% 30.54/8.46 |
% 30.54/8.46 | Equations (827) can reduce 213 to:
% 30.54/8.46 | (3103) ~ (all_0_53_53 = e0)
% 30.54/8.46 |
% 30.54/8.46 | Simplifying 3103 yields:
% 30.54/8.46 | (584) ~ (all_0_53_53 = e0)
% 30.54/8.46 |
% 30.54/8.46 | Equations (827) can reduce 235 to:
% 30.66/8.46 | (9326) ~ (all_0_57_57 = e0)
% 30.66/8.46 |
% 30.66/8.46 | Simplifying 9326 yields:
% 30.66/8.46 | (2301) ~ (all_0_57_57 = e0)
% 30.66/8.46 |
% 30.66/8.46 +-Applying beta-rule and splitting (135), into two cases.
% 30.66/8.46 |-Branch one:
% 30.66/8.46 | (820) all_0_51_51 = e1
% 30.66/8.46 |
% 30.66/8.46 | Combining equations (824,820) yields a new equation:
% 30.66/8.46 | (537) e3 = e1
% 30.66/8.46 |
% 30.66/8.46 | Simplifying 537 yields:
% 30.66/8.46 | (538) e3 = e1
% 30.66/8.46 |
% 30.66/8.46 | Equations (538) can reduce 136 to:
% 30.66/8.46 | (270) $false
% 30.66/8.46 |
% 30.66/8.46 |-The branch is then unsatisfiable
% 30.66/8.46 |-Branch two:
% 30.66/8.46 | (748) ~ (all_0_51_51 = e1)
% 30.66/8.46 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 30.66/8.46 |
% 30.66/8.46 +-Applying beta-rule and splitting (5715), into two cases.
% 30.66/8.46 |-Branch one:
% 30.66/8.46 | (423) all_0_53_53 = e0
% 30.66/8.46 |
% 30.66/8.46 | Equations (423) can reduce 584 to:
% 30.66/8.46 | (270) $false
% 30.66/8.46 |
% 30.66/8.46 |-The branch is then unsatisfiable
% 30.66/8.46 |-Branch two:
% 30.66/8.46 | (584) ~ (all_0_53_53 = e0)
% 30.66/8.46 | (5719) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1
% 30.66/8.46 |
% 30.66/8.46 +-Applying beta-rule and splitting (823), into two cases.
% 30.66/8.46 |-Branch one:
% 30.66/8.46 | (848) all_0_52_52 = e1
% 30.66/8.46 |
% 30.66/8.46 | Combining equations (848,827) yields a new equation:
% 30.66/8.46 | (571) e1 = e0
% 30.66/8.46 |
% 30.66/8.46 | Simplifying 571 yields:
% 30.66/8.46 | (560) e1 = e0
% 30.66/8.46 |
% 30.66/8.46 | Equations (560) can reduce 132 to:
% 30.66/8.46 | (270) $false
% 30.66/8.46 |
% 30.66/8.46 |-The branch is then unsatisfiable
% 30.66/8.46 |-Branch two:
% 30.66/8.46 | (642) ~ (all_0_52_52 = e1)
% 30.66/8.46 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 30.66/8.46 |
% 30.66/8.46 | Equations (827) can reduce 642 to:
% 30.66/8.46 | (568) ~ (e1 = e0)
% 30.66/8.46 |
% 30.66/8.46 | Simplifying 568 yields:
% 30.66/8.46 | (132) ~ (e1 = e0)
% 30.66/8.46 |
% 30.66/8.46 +-Applying beta-rule and splitting (194), into two cases.
% 30.66/8.46 |-Branch one:
% 30.66/8.46 | (747) all_0_56_56 = e1
% 30.66/8.46 |
% 30.66/8.46 | Combining equations (747,830) yields a new equation:
% 30.66/8.46 | (571) e1 = e0
% 30.66/8.46 |
% 30.66/8.46 | Simplifying 571 yields:
% 30.66/8.46 | (560) e1 = e0
% 30.66/8.46 |
% 30.66/8.46 | Equations (560) can reduce 132 to:
% 30.66/8.46 | (270) $false
% 30.66/8.46 |
% 30.66/8.46 |-The branch is then unsatisfiable
% 30.66/8.46 |-Branch two:
% 30.66/8.46 | (995) ~ (all_0_56_56 = e1)
% 30.66/8.46 | (996) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 30.66/8.46 |
% 30.66/8.46 +-Applying beta-rule and splitting (3656), into two cases.
% 30.66/8.46 |-Branch one:
% 30.66/8.46 | (1091) all_0_46_46 = e3
% 30.66/8.46 |
% 30.66/8.46 | Equations (1091) can reduce 106 to:
% 30.66/8.46 | (136) ~ (e3 = e1)
% 30.66/8.46 |
% 30.66/8.46 +-Applying beta-rule and splitting (996), into two cases.
% 30.66/8.46 |-Branch one:
% 30.66/8.46 | (997) all_0_57_57 = e1
% 30.66/8.46 |
% 30.66/8.46 | Equations (997) can reduce 2301 to:
% 30.66/8.46 | (132) ~ (e1 = e0)
% 30.66/8.46 |
% 30.66/8.46 +-Applying beta-rule and splitting (4628), into two cases.
% 30.66/8.46 |-Branch one:
% 30.66/8.46 | (589) all_0_49_49 = e1
% 30.66/8.46 |
% 30.66/8.46 | Combining equations (563,589) yields a new equation:
% 30.66/8.46 | (560) e1 = e0
% 30.66/8.46 |
% 30.66/8.46 | Equations (560) can reduce 132 to:
% 30.66/8.46 | (270) $false
% 30.66/8.46 |
% 30.66/8.46 |-The branch is then unsatisfiable
% 30.66/8.46 |-Branch two:
% 30.66/8.46 | (543) ~ (all_0_49_49 = e1)
% 30.66/8.46 | (4726) all_0_54_54 = e1 | all_0_59_59 = e1
% 30.66/8.46 |
% 30.66/8.46 +-Applying beta-rule and splitting (5719), into two cases.
% 30.66/8.46 |-Branch one:
% 30.66/8.46 | (1114) all_0_53_53 = e3
% 30.66/8.46 |
% 30.66/8.46 | Equations (1114) can reduce 356 to:
% 30.66/8.46 | (270) $false
% 30.66/8.46 |
% 30.66/8.46 |-The branch is then unsatisfiable
% 30.66/8.46 |-Branch two:
% 30.66/8.46 | (356) ~ (all_0_53_53 = e3)
% 30.66/8.46 | (5723) all_0_53_53 = e4 | all_0_53_53 = e1
% 30.66/8.46 |
% 30.66/8.46 +-Applying beta-rule and splitting (5723), into two cases.
% 30.66/8.46 |-Branch one:
% 30.66/8.46 | (853) all_0_53_53 = e1
% 30.66/8.46 |
% 30.66/8.46 | Equations (853) can reduce 599 to:
% 30.66/8.46 | (1021) ~ (e4 = e1)
% 30.66/8.46 |
% 30.66/8.46 | Simplifying 1021 yields:
% 30.66/8.46 | (251) ~ (e4 = e1)
% 30.66/8.46 |
% 30.66/8.46 | Equations (853) can reduce 259 to:
% 30.66/8.46 | (645) ~ (e2 = e1)
% 30.66/8.46 |
% 30.66/8.46 | Simplifying 645 yields:
% 30.66/8.46 | (141) ~ (e2 = e1)
% 30.66/8.46 |
% 30.66/8.46 +-Applying beta-rule and splitting (4726), into two cases.
% 30.66/8.46 |-Branch one:
% 30.66/8.46 | (875) all_0_54_54 = e1
% 30.66/8.46 |
% 30.66/8.46 | Combining equations (3657,875) yields a new equation:
% 30.66/8.46 | (531) e2 = e1
% 30.66/8.46 |
% 30.66/8.46 | Simplifying 531 yields:
% 30.66/8.46 | (322) e2 = e1
% 30.66/8.46 |
% 30.66/8.46 | Equations (322) can reduce 141 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (425) ~ (all_0_54_54 = e1)
% 30.66/8.47 | (424) all_0_59_59 = e1
% 30.66/8.47 |
% 30.66/8.47 | Combining equations (424,402) yields a new equation:
% 30.66/8.47 | (526) e4 = e1
% 30.66/8.47 |
% 30.66/8.47 | Equations (526) can reduce 251 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (874) ~ (all_0_53_53 = e1)
% 30.66/8.47 | (367) all_0_53_53 = e4
% 30.66/8.47 |
% 30.66/8.47 | Equations (367) can reduce 599 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (644) ~ (all_0_57_57 = e1)
% 30.66/8.47 | (1000) all_0_58_58 = e1 | all_0_59_59 = e1
% 30.66/8.47 |
% 30.66/8.47 +-Applying beta-rule and splitting (1000), into two cases.
% 30.66/8.47 |-Branch one:
% 30.66/8.47 | (1001) all_0_58_58 = e1
% 30.66/8.47 |
% 30.66/8.47 | Combining equations (4713,1001) yields a new equation:
% 30.66/8.47 | (537) e3 = e1
% 30.66/8.47 |
% 30.66/8.47 | Simplifying 537 yields:
% 30.66/8.47 | (538) e3 = e1
% 30.66/8.47 |
% 30.66/8.47 | Equations (538) can reduce 136 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (1004) ~ (all_0_58_58 = e1)
% 30.66/8.47 | (424) all_0_59_59 = e1
% 30.66/8.47 |
% 30.66/8.47 | Combining equations (424,402) yields a new equation:
% 30.66/8.47 | (526) e4 = e1
% 30.66/8.47 |
% 30.66/8.47 | Equations (526) can reduce 251 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (413) ~ (all_0_46_46 = e3)
% 30.66/8.47 | (3700) all_0_54_54 = e3 | all_0_59_59 = e3
% 30.66/8.47 |
% 30.66/8.47 +-Applying beta-rule and splitting (3700), into two cases.
% 30.66/8.47 |-Branch one:
% 30.66/8.47 | (1119) all_0_54_54 = e3
% 30.66/8.47 |
% 30.66/8.47 | Combining equations (1119,3657) yields a new equation:
% 30.66/8.47 | (437) e3 = e2
% 30.66/8.47 |
% 30.66/8.47 | Simplifying 437 yields:
% 30.66/8.47 | (414) e3 = e2
% 30.66/8.47 |
% 30.66/8.47 | Equations (414) can reduce 223 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (1093) ~ (all_0_54_54 = e3)
% 30.66/8.47 | (412) all_0_59_59 = e3
% 30.66/8.47 |
% 30.66/8.47 | Combining equations (402,412) yields a new equation:
% 30.66/8.47 | (660) e4 = e3
% 30.66/8.47 |
% 30.66/8.47 | Simplifying 660 yields:
% 30.66/8.47 | (359) e4 = e3
% 30.66/8.47 |
% 30.66/8.47 | Equations (359) can reduce 34 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (925) ~ (all_0_52_52 = e0)
% 30.66/8.47 | (2258) all_0_57_57 = e0
% 30.66/8.47 |
% 30.66/8.47 | Equations (2258) can reduce 2301 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (361) ~ (all_0_41_41 = e4)
% 30.66/8.47 | (512) all_0_42_42 = e4
% 30.66/8.47 |
% 30.66/8.47 | Equations (512) can reduce 520 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (510) ~ (all_0_43_43 = e4)
% 30.66/8.47 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 30.66/8.47 |
% 30.66/8.47 +-Applying beta-rule and splitting (511), into two cases.
% 30.66/8.47 |-Branch one:
% 30.66/8.47 | (363) all_0_45_45 = e4
% 30.66/8.47 |
% 30.66/8.47 | Combining equations (454,363) yields a new equation:
% 30.66/8.47 | (479) e4 = e0
% 30.66/8.47 |
% 30.66/8.47 | Equations (479) can reduce 6 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (352) ~ (all_0_45_45 = e4)
% 30.66/8.47 | (517) all_0_46_46 = e4
% 30.66/8.47 |
% 30.66/8.47 | Equations (517) can reduce 805 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (280) ~ (all_0_59_59 = e4)
% 30.66/8.47 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 30.66/8.47 |
% 30.66/8.47 +-Applying beta-rule and splitting (1508), into two cases.
% 30.66/8.47 |-Branch one:
% 30.66/8.47 | (505) all_0_45_45 = e3
% 30.66/8.47 |
% 30.66/8.47 | Combining equations (454,505) yields a new equation:
% 30.66/8.47 | (784) e3 = e0
% 30.66/8.47 |
% 30.66/8.47 | Equations (784) can reduce 66 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (354) ~ (all_0_45_45 = e3)
% 30.66/8.47 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 30.66/8.47 |
% 30.66/8.47 | Equations (454) can reduce 354 to:
% 30.66/8.47 | (788) ~ (e3 = e0)
% 30.66/8.47 |
% 30.66/8.47 | Simplifying 788 yields:
% 30.66/8.47 | (66) ~ (e3 = e0)
% 30.66/8.47 |
% 30.66/8.47 +-Applying beta-rule and splitting (787), into two cases.
% 30.66/8.47 |-Branch one:
% 30.66/8.47 | (858) all_0_44_44 = e3
% 30.66/8.47 |
% 30.66/8.47 | Combining equations (370,858) yields a new equation:
% 30.66/8.47 | (414) e3 = e2
% 30.66/8.47 |
% 30.66/8.47 | Equations (414) can reduce 223 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (862) ~ (all_0_44_44 = e3)
% 30.66/8.47 | (1070) all_0_45_45 = e3 | all_0_46_46 = e3
% 30.66/8.47 |
% 30.66/8.47 +-Applying beta-rule and splitting (1070), into two cases.
% 30.66/8.47 |-Branch one:
% 30.66/8.47 | (505) all_0_45_45 = e3
% 30.66/8.47 |
% 30.66/8.47 | Combining equations (454,505) yields a new equation:
% 30.66/8.47 | (784) e3 = e0
% 30.66/8.47 |
% 30.66/8.47 | Equations (784) can reduce 66 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (354) ~ (all_0_45_45 = e3)
% 30.66/8.47 | (1091) all_0_46_46 = e3
% 30.66/8.47 |
% 30.66/8.47 | Equations (1091) can reduce 106 to:
% 30.66/8.47 | (136) ~ (e3 = e1)
% 30.66/8.47 |
% 30.66/8.47 +-Applying beta-rule and splitting (44), into two cases.
% 30.66/8.47 |-Branch one:
% 30.66/8.47 | (502) all_0_43_43 = e4
% 30.66/8.47 |
% 30.66/8.47 +-Applying beta-rule and splitting (3067), into two cases.
% 30.66/8.47 |-Branch one:
% 30.66/8.47 | (827) all_0_52_52 = e0
% 30.66/8.47 |
% 30.66/8.47 | Equations (827) can reduce 213 to:
% 30.66/8.47 | (3103) ~ (all_0_53_53 = e0)
% 30.66/8.47 |
% 30.66/8.47 | Simplifying 3103 yields:
% 30.66/8.47 | (584) ~ (all_0_53_53 = e0)
% 30.66/8.47 |
% 30.66/8.47 | Equations (827) can reduce 230 to:
% 30.66/8.47 | (456) ~ (e4 = e0)
% 30.66/8.47 |
% 30.66/8.47 | Simplifying 456 yields:
% 30.66/8.47 | (6) ~ (e4 = e0)
% 30.66/8.47 |
% 30.66/8.47 +-Applying beta-rule and splitting (135), into two cases.
% 30.66/8.47 |-Branch one:
% 30.66/8.47 | (820) all_0_51_51 = e1
% 30.66/8.47 |
% 30.66/8.47 | Combining equations (820,824) yields a new equation:
% 30.66/8.47 | (538) e3 = e1
% 30.66/8.47 |
% 30.66/8.47 | Equations (538) can reduce 136 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (748) ~ (all_0_51_51 = e1)
% 30.66/8.47 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 30.66/8.47 |
% 30.66/8.47 +-Applying beta-rule and splitting (823), into two cases.
% 30.66/8.47 |-Branch one:
% 30.66/8.47 | (848) all_0_52_52 = e1
% 30.66/8.47 |
% 30.66/8.47 | Combining equations (848,827) yields a new equation:
% 30.66/8.47 | (571) e1 = e0
% 30.66/8.47 |
% 30.66/8.47 | Simplifying 571 yields:
% 30.66/8.47 | (560) e1 = e0
% 30.66/8.47 |
% 30.66/8.47 | Equations (560) can reduce 132 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (642) ~ (all_0_52_52 = e1)
% 30.66/8.47 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 30.66/8.47 |
% 30.66/8.47 +-Applying beta-rule and splitting (852), into two cases.
% 30.66/8.47 |-Branch one:
% 30.66/8.47 | (853) all_0_53_53 = e1
% 30.66/8.47 |
% 30.66/8.47 | Equations (853) can reduce 584 to:
% 30.66/8.47 | (132) ~ (e1 = e0)
% 30.66/8.47 |
% 30.66/8.47 +-Applying beta-rule and splitting (407), into two cases.
% 30.66/8.47 |-Branch one:
% 30.66/8.47 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 30.66/8.47 |
% 30.66/8.47 +-Applying beta-rule and splitting (408), into two cases.
% 30.66/8.47 |-Branch one:
% 30.66/8.47 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 30.66/8.47 |
% 30.66/8.47 +-Applying beta-rule and splitting (409), into two cases.
% 30.66/8.47 |-Branch one:
% 30.66/8.47 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 30.66/8.47 |
% 30.66/8.47 | Applying alpha-rule on (410) yields:
% 30.66/8.47 | (411) all_0_43_43 = e0
% 30.66/8.47 | (412) all_0_59_59 = e3
% 30.66/8.47 | (413) ~ (all_0_46_46 = e3)
% 30.66/8.47 |
% 30.66/8.47 | Combining equations (411,502) yields a new equation:
% 30.66/8.47 | (479) e4 = e0
% 30.66/8.47 |
% 30.66/8.47 | Equations (479) can reduce 6 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 30.66/8.47 |
% 30.66/8.47 | Applying alpha-rule on (416) yields:
% 30.66/8.47 | (411) all_0_43_43 = e0
% 30.66/8.47 | (412) all_0_59_59 = e3
% 30.66/8.47 | (419) ~ (all_0_56_56 = e0)
% 30.66/8.47 |
% 30.66/8.47 | Combining equations (411,502) yields a new equation:
% 30.66/8.47 | (479) e4 = e0
% 30.66/8.47 |
% 30.66/8.47 | Equations (479) can reduce 6 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 30.66/8.47 |
% 30.66/8.47 | Applying alpha-rule on (422) yields:
% 30.66/8.47 | (423) all_0_53_53 = e0
% 30.66/8.47 | (424) all_0_59_59 = e1
% 30.66/8.47 | (425) ~ (all_0_54_54 = e1)
% 30.66/8.47 |
% 30.66/8.47 | Combining equations (423,853) yields a new equation:
% 30.66/8.47 | (560) e1 = e0
% 30.66/8.47 |
% 30.66/8.47 | Equations (560) can reduce 132 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 30.66/8.47 |
% 30.66/8.47 | Applying alpha-rule on (428) yields:
% 30.66/8.47 | (423) all_0_53_53 = e0
% 30.66/8.47 | (424) all_0_59_59 = e1
% 30.66/8.47 | (431) ~ (all_0_58_58 = e0)
% 30.66/8.47 |
% 30.66/8.47 | Combining equations (423,853) yields a new equation:
% 30.66/8.47 | (560) e1 = e0
% 30.66/8.47 |
% 30.66/8.47 | Equations (560) can reduce 132 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (874) ~ (all_0_53_53 = e1)
% 30.66/8.47 | (875) all_0_54_54 = e1
% 30.66/8.47 |
% 30.66/8.47 | Combining equations (3657,875) yields a new equation:
% 30.66/8.47 | (531) e2 = e1
% 30.66/8.47 |
% 30.66/8.47 | Simplifying 531 yields:
% 30.66/8.47 | (322) e2 = e1
% 30.66/8.47 |
% 30.66/8.47 | Equations (322) can reduce 141 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (925) ~ (all_0_52_52 = e0)
% 30.66/8.47 | (3073) all_0_53_53 = e0 | all_0_54_54 = e0
% 30.66/8.47 |
% 30.66/8.47 +-Applying beta-rule and splitting (3073), into two cases.
% 30.66/8.47 |-Branch one:
% 30.66/8.47 | (423) all_0_53_53 = e0
% 30.66/8.47 |
% 30.66/8.47 | Equations (423) can reduce 584 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (584) ~ (all_0_53_53 = e0)
% 30.66/8.47 | (3084) all_0_54_54 = e0
% 30.66/8.47 |
% 30.66/8.47 | Combining equations (3084,3657) yields a new equation:
% 30.66/8.47 | (316) e2 = e0
% 30.66/8.47 |
% 30.66/8.47 | Equations (316) can reduce 57 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (510) ~ (all_0_43_43 = e4)
% 30.66/8.47 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 30.66/8.47 |
% 30.66/8.47 +-Applying beta-rule and splitting (511), into two cases.
% 30.66/8.47 |-Branch one:
% 30.66/8.47 | (363) all_0_45_45 = e4
% 30.66/8.47 |
% 30.66/8.47 | Combining equations (454,363) yields a new equation:
% 30.66/8.47 | (479) e4 = e0
% 30.66/8.47 |
% 30.66/8.47 | Equations (479) can reduce 6 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (352) ~ (all_0_45_45 = e4)
% 30.66/8.47 | (517) all_0_46_46 = e4
% 30.66/8.47 |
% 30.66/8.47 | Combining equations (1091,517) yields a new equation:
% 30.66/8.47 | (359) e4 = e3
% 30.66/8.47 |
% 30.66/8.47 | Equations (359) can reduce 34 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (488) ~ (all_0_45_45 = e0)
% 30.66/8.47 | (1132) all_0_46_46 = e0
% 30.66/8.47 |
% 30.66/8.47 | Equations (1132) can reduce 1010 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.47 | (932) ~ (all_0_51_51 = e3)
% 30.66/8.47 | (1101) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 30.66/8.47 |
% 30.66/8.47 +-Applying beta-rule and splitting (1101), into two cases.
% 30.66/8.47 |-Branch one:
% 30.66/8.47 | (864) all_0_52_52 = e3
% 30.66/8.47 |
% 30.66/8.47 | Equations (864) can reduce 826 to:
% 30.66/8.47 | (270) $false
% 30.66/8.47 |
% 30.66/8.47 |-The branch is then unsatisfiable
% 30.66/8.47 |-Branch two:
% 30.66/8.48 | (826) ~ (all_0_52_52 = e3)
% 30.66/8.48 | (1107) all_0_53_53 = e3 | all_0_54_54 = e3
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (1107), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (1114) all_0_53_53 = e3
% 30.66/8.48 |
% 30.66/8.48 | Equations (1114) can reduce 12 to:
% 30.66/8.48 | (932) ~ (all_0_51_51 = e3)
% 30.66/8.48 |
% 30.66/8.48 | Equations (1114) can reduce 213 to:
% 30.66/8.48 | (826) ~ (all_0_52_52 = e3)
% 30.66/8.48 |
% 30.66/8.48 | Equations (1114) can reduce 599 to:
% 30.66/8.48 | (719) ~ (e4 = e3)
% 30.66/8.48 |
% 30.66/8.48 | Simplifying 719 yields:
% 30.66/8.48 | (34) ~ (e4 = e3)
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (135), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (820) all_0_51_51 = e1
% 30.66/8.48 |
% 30.66/8.48 | Equations (820) can reduce 748 to:
% 30.66/8.48 | (270) $false
% 30.66/8.48 |
% 30.66/8.48 |-The branch is then unsatisfiable
% 30.66/8.48 |-Branch two:
% 30.66/8.48 | (748) ~ (all_0_51_51 = e1)
% 30.66/8.48 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (823), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (848) all_0_52_52 = e1
% 30.66/8.48 |
% 30.66/8.48 | Equations (848) can reduce 230 to:
% 30.66/8.48 | (1021) ~ (e4 = e1)
% 30.66/8.48 |
% 30.66/8.48 | Simplifying 1021 yields:
% 30.66/8.48 | (251) ~ (e4 = e1)
% 30.66/8.48 |
% 30.66/8.48 | Equations (848) can reduce 826 to:
% 30.66/8.48 | (769) ~ (e3 = e1)
% 30.66/8.48 |
% 30.66/8.48 | Simplifying 769 yields:
% 30.66/8.48 | (136) ~ (e3 = e1)
% 30.66/8.48 |
% 30.66/8.48 | Equations (848) can reduce 257 to:
% 30.66/8.48 | (645) ~ (e2 = e1)
% 30.66/8.48 |
% 30.66/8.48 | Simplifying 645 yields:
% 30.66/8.48 | (141) ~ (e2 = e1)
% 30.66/8.48 |
% 30.66/8.48 | From (848) and (666) follows:
% 30.66/8.48 | (7732) op(e2, e1) = e1
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (626), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (827) all_0_52_52 = e0
% 30.66/8.48 |
% 30.66/8.48 | Combining equations (848,827) yields a new equation:
% 30.66/8.48 | (571) e1 = e0
% 30.66/8.48 |
% 30.66/8.48 | Simplifying 571 yields:
% 30.66/8.48 | (560) e1 = e0
% 30.66/8.48 |
% 30.66/8.48 | Equations (560) can reduce 132 to:
% 30.66/8.48 | (270) $false
% 30.66/8.48 |
% 30.66/8.48 |-The branch is then unsatisfiable
% 30.66/8.48 |-Branch two:
% 30.66/8.48 | (925) ~ (all_0_52_52 = e0)
% 30.66/8.48 | (2258) all_0_57_57 = e0
% 30.66/8.48 |
% 30.66/8.48 | Equations (2258) can reduce 104 to:
% 30.66/8.48 | (419) ~ (all_0_56_56 = e0)
% 30.66/8.48 |
% 30.66/8.48 | Equations (2258) can reduce 37 to:
% 30.66/8.48 | (3530) ~ (all_0_58_58 = e0)
% 30.66/8.48 |
% 30.66/8.48 | Simplifying 3530 yields:
% 30.66/8.48 | (431) ~ (all_0_58_58 = e0)
% 30.66/8.48 |
% 30.66/8.48 | Equations (2258) can reduce 140 to:
% 30.66/8.48 | (4000) ~ (all_0_59_59 = e0)
% 30.66/8.48 |
% 30.66/8.48 | Simplifying 4000 yields:
% 30.66/8.48 | (4001) ~ (all_0_59_59 = e0)
% 30.66/8.48 |
% 30.66/8.48 | Equations (2258) can reduce 846 to:
% 30.66/8.48 | (788) ~ (e3 = e0)
% 30.66/8.48 |
% 30.66/8.48 | Simplifying 788 yields:
% 30.66/8.48 | (66) ~ (e3 = e0)
% 30.66/8.48 |
% 30.66/8.48 | Equations (2258) can reduce 335 to:
% 30.66/8.48 | (566) ~ (e2 = e0)
% 30.66/8.48 |
% 30.66/8.48 | Simplifying 566 yields:
% 30.66/8.48 | (57) ~ (e2 = e0)
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (64), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (954) all_0_51_51 = e0
% 30.66/8.48 |
% 30.66/8.48 | Equations (954) can reduce 240 to:
% 30.66/8.48 | (455) ~ (all_0_43_43 = e0)
% 30.66/8.48 |
% 30.66/8.48 | Equations (954) can reduce 932 to:
% 30.66/8.48 | (788) ~ (e3 = e0)
% 30.66/8.48 |
% 30.66/8.48 | Simplifying 788 yields:
% 30.66/8.48 | (66) ~ (e3 = e0)
% 30.66/8.48 |
% 30.66/8.48 | Equations (954) can reduce 255 to:
% 30.66/8.48 | (566) ~ (e2 = e0)
% 30.66/8.48 |
% 30.66/8.48 | Simplifying 566 yields:
% 30.66/8.48 | (57) ~ (e2 = e0)
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (93), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (402) all_0_59_59 = e4
% 30.66/8.48 |
% 30.66/8.48 | Equations (402) can reduce 17 to:
% 30.66/8.48 | (520) ~ (all_0_42_42 = e4)
% 30.66/8.48 |
% 30.66/8.48 | Equations (402) can reduce 206 to:
% 30.66/8.48 | (805) ~ (all_0_46_46 = e4)
% 30.66/8.48 |
% 30.66/8.48 | Equations (402) can reduce 156 to:
% 30.66/8.48 | (278) ~ (all_0_58_58 = e4)
% 30.66/8.48 |
% 30.66/8.48 | Equations (402) can reduce 4001 to:
% 30.66/8.48 | (6) ~ (e4 = e0)
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (220), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (497) all_0_46_46 = e2
% 30.66/8.48 |
% 30.66/8.48 | Equations (497) can reduce 1436 to:
% 30.66/8.48 | (270) $false
% 30.66/8.48 |
% 30.66/8.48 |-The branch is then unsatisfiable
% 30.66/8.48 |-Branch two:
% 30.66/8.48 | (1436) ~ (all_0_46_46 = e2)
% 30.66/8.48 | (1523) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e0
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (127), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (541) all_0_42_42 = e1
% 30.66/8.48 |
% 30.66/8.48 | Equations (541) can reduce 94 to:
% 30.66/8.48 | (540) ~ (all_0_41_41 = e1)
% 30.66/8.48 |
% 30.66/8.48 | Equations (541) can reduce 18 to:
% 30.66/8.48 | (6201) ~ (all_0_46_46 = e1)
% 30.66/8.48 |
% 30.66/8.48 | Simplifying 6201 yields:
% 30.66/8.48 | (106) ~ (all_0_46_46 = e1)
% 30.66/8.48 |
% 30.66/8.48 | Equations (541) can reduce 498 to:
% 30.66/8.48 | (645) ~ (e2 = e1)
% 30.66/8.48 |
% 30.66/8.48 | Simplifying 645 yields:
% 30.66/8.48 | (141) ~ (e2 = e1)
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (52), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (536) all_0_41_41 = e1
% 30.66/8.48 |
% 30.66/8.48 | Equations (536) can reduce 540 to:
% 30.66/8.48 | (270) $false
% 30.66/8.48 |
% 30.66/8.48 |-The branch is then unsatisfiable
% 30.66/8.48 |-Branch two:
% 30.66/8.48 | (540) ~ (all_0_41_41 = e1)
% 30.66/8.48 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (116), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (411) all_0_43_43 = e0
% 30.66/8.48 |
% 30.66/8.48 | Equations (411) can reduce 455 to:
% 30.66/8.48 | (270) $false
% 30.66/8.48 |
% 30.66/8.48 |-The branch is then unsatisfiable
% 30.66/8.48 |-Branch two:
% 30.66/8.48 | (455) ~ (all_0_43_43 = e0)
% 30.66/8.48 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (1122), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (621) all_0_44_44 = e0
% 30.66/8.48 |
% 30.66/8.48 | Combining equations (370,621) yields a new equation:
% 30.66/8.48 | (622) e2 = e0
% 30.66/8.48 |
% 30.66/8.48 | Simplifying 622 yields:
% 30.66/8.48 | (316) e2 = e0
% 30.66/8.48 |
% 30.66/8.48 | Equations (316) can reduce 57 to:
% 30.66/8.48 | (270) $false
% 30.66/8.48 |
% 30.66/8.48 |-The branch is then unsatisfiable
% 30.66/8.48 |-Branch two:
% 30.66/8.48 | (625) ~ (all_0_44_44 = e0)
% 30.66/8.48 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (1128), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (454) all_0_45_45 = e0
% 30.66/8.48 |
% 30.66/8.48 | Equations (454) can reduce 51 to:
% 30.66/8.48 | (232) ~ (all_0_41_41 = e0)
% 30.66/8.48 |
% 30.66/8.48 | Equations (454) can reduce 38 to:
% 30.66/8.48 | (1057) ~ (all_0_46_46 = e0)
% 30.66/8.48 |
% 30.66/8.48 | Simplifying 1057 yields:
% 30.66/8.48 | (1010) ~ (all_0_46_46 = e0)
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (158), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (358) all_0_41_41 = e4
% 30.66/8.48 |
% 30.66/8.48 | Equations (358) can reduce 232 to:
% 30.66/8.48 | (6) ~ (e4 = e0)
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (44), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (502) all_0_43_43 = e4
% 30.66/8.48 |
% 30.66/8.48 | Equations (502) can reduce 103 to:
% 30.66/8.48 | (804) ~ (all_0_46_46 = e4)
% 30.66/8.48 |
% 30.66/8.48 | Simplifying 804 yields:
% 30.66/8.48 | (805) ~ (all_0_46_46 = e4)
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (1523), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (1132) all_0_46_46 = e0
% 30.66/8.48 |
% 30.66/8.48 | Equations (1132) can reduce 1010 to:
% 30.66/8.48 | (270) $false
% 30.66/8.48 |
% 30.66/8.48 |-The branch is then unsatisfiable
% 30.66/8.48 |-Branch two:
% 30.66/8.48 | (1010) ~ (all_0_46_46 = e0)
% 30.66/8.48 | (1529) all_0_46_46 = e4 | all_0_46_46 = e3
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (1529), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (1091) all_0_46_46 = e3
% 30.66/8.48 |
% 30.66/8.48 | Equations (1091) can reduce 106 to:
% 30.66/8.48 | (136) ~ (e3 = e1)
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (204), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (396) all_0_58_58 = e2
% 30.66/8.48 |
% 30.66/8.48 | Equations (396) can reduce 376 to:
% 30.66/8.48 | (270) $false
% 30.66/8.48 |
% 30.66/8.48 |-The branch is then unsatisfiable
% 30.66/8.48 |-Branch two:
% 30.66/8.48 | (376) ~ (all_0_58_58 = e2)
% 30.66/8.48 | (3890) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1 | all_0_58_58 = e0
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (762), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (552) all_0_48_48 = e1
% 30.66/8.48 |
% 30.66/8.48 | Combining equations (311,552) yields a new equation:
% 30.66/8.48 | (531) e2 = e1
% 30.66/8.48 |
% 30.66/8.48 | Simplifying 531 yields:
% 30.66/8.48 | (322) e2 = e1
% 30.66/8.48 |
% 30.66/8.48 | Equations (322) can reduce 141 to:
% 30.66/8.48 | (270) $false
% 30.66/8.48 |
% 30.66/8.48 |-The branch is then unsatisfiable
% 30.66/8.48 |-Branch two:
% 30.66/8.48 | (588) ~ (all_0_48_48 = e1)
% 30.66/8.48 | (4925) all_0_53_53 = e1 | all_0_58_58 = e1
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (4925), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (853) all_0_53_53 = e1
% 30.66/8.48 |
% 30.66/8.48 | Combining equations (853,1114) yields a new equation:
% 30.66/8.48 | (538) e3 = e1
% 30.66/8.48 |
% 30.66/8.48 | Equations (538) can reduce 136 to:
% 30.66/8.48 | (270) $false
% 30.66/8.48 |
% 30.66/8.48 |-The branch is then unsatisfiable
% 30.66/8.48 |-Branch two:
% 30.66/8.48 | (874) ~ (all_0_53_53 = e1)
% 30.66/8.48 | (1001) all_0_58_58 = e1
% 30.66/8.48 |
% 30.66/8.48 | Equations (1001) can reduce 376 to:
% 30.66/8.48 | (645) ~ (e2 = e1)
% 30.66/8.48 |
% 30.66/8.48 | Simplifying 645 yields:
% 30.66/8.48 | (141) ~ (e2 = e1)
% 30.66/8.48 |
% 30.66/8.48 | Instantiating formula (201) with e2, e1, e1, e2 and discharging atoms op(e2, e1) = e2, op(e2, e1) = e1, yields:
% 30.66/8.48 | (322) e2 = e1
% 30.66/8.48 |
% 30.66/8.48 | Equations (322) can reduce 141 to:
% 30.66/8.48 | (270) $false
% 30.66/8.48 |
% 30.66/8.48 |-The branch is then unsatisfiable
% 30.66/8.48 |-Branch two:
% 30.66/8.48 | (413) ~ (all_0_46_46 = e3)
% 30.66/8.48 | (517) all_0_46_46 = e4
% 30.66/8.48 |
% 30.66/8.48 | Equations (517) can reduce 805 to:
% 30.66/8.48 | (270) $false
% 30.66/8.48 |
% 30.66/8.48 |-The branch is then unsatisfiable
% 30.66/8.48 |-Branch two:
% 30.66/8.48 | (510) ~ (all_0_43_43 = e4)
% 30.66/8.48 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (1523), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (1132) all_0_46_46 = e0
% 30.66/8.48 |
% 30.66/8.48 | Equations (1132) can reduce 1010 to:
% 30.66/8.48 | (270) $false
% 30.66/8.48 |
% 30.66/8.48 |-The branch is then unsatisfiable
% 30.66/8.48 |-Branch two:
% 30.66/8.48 | (1010) ~ (all_0_46_46 = e0)
% 30.66/8.48 | (1529) all_0_46_46 = e4 | all_0_46_46 = e3
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (1529), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (1091) all_0_46_46 = e3
% 30.66/8.48 |
% 30.66/8.48 | Equations (1091) can reduce 805 to:
% 30.66/8.48 | (719) ~ (e4 = e3)
% 30.66/8.48 |
% 30.66/8.48 | Simplifying 719 yields:
% 30.66/8.48 | (34) ~ (e4 = e3)
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (511), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (363) all_0_45_45 = e4
% 30.66/8.48 |
% 30.66/8.48 | Combining equations (454,363) yields a new equation:
% 30.66/8.48 | (479) e4 = e0
% 30.66/8.48 |
% 30.66/8.48 | Equations (479) can reduce 6 to:
% 30.66/8.48 | (270) $false
% 30.66/8.48 |
% 30.66/8.48 |-The branch is then unsatisfiable
% 30.66/8.48 |-Branch two:
% 30.66/8.48 | (352) ~ (all_0_45_45 = e4)
% 30.66/8.48 | (517) all_0_46_46 = e4
% 30.66/8.48 |
% 30.66/8.48 | Combining equations (1091,517) yields a new equation:
% 30.66/8.48 | (359) e4 = e3
% 30.66/8.48 |
% 30.66/8.48 | Equations (359) can reduce 34 to:
% 30.66/8.48 | (270) $false
% 30.66/8.48 |
% 30.66/8.48 |-The branch is then unsatisfiable
% 30.66/8.48 |-Branch two:
% 30.66/8.48 | (413) ~ (all_0_46_46 = e3)
% 30.66/8.48 | (517) all_0_46_46 = e4
% 30.66/8.48 |
% 30.66/8.48 | Equations (517) can reduce 805 to:
% 30.66/8.48 | (270) $false
% 30.66/8.48 |
% 30.66/8.48 |-The branch is then unsatisfiable
% 30.66/8.48 |-Branch two:
% 30.66/8.48 | (361) ~ (all_0_41_41 = e4)
% 30.66/8.48 | (362) all_0_45_45 = e4 | all_0_53_53 = e4 | all_0_58_58 = e4
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (362), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (363) all_0_45_45 = e4
% 30.66/8.48 |
% 30.66/8.48 | Combining equations (454,363) yields a new equation:
% 30.66/8.48 | (479) e4 = e0
% 30.66/8.48 |
% 30.66/8.48 | Equations (479) can reduce 6 to:
% 30.66/8.48 | (270) $false
% 30.66/8.48 |
% 30.66/8.48 |-The branch is then unsatisfiable
% 30.66/8.48 |-Branch two:
% 30.66/8.48 | (352) ~ (all_0_45_45 = e4)
% 30.66/8.48 | (366) all_0_53_53 = e4 | all_0_58_58 = e4
% 30.66/8.48 |
% 30.66/8.48 +-Applying beta-rule and splitting (366), into two cases.
% 30.66/8.48 |-Branch one:
% 30.66/8.48 | (367) all_0_53_53 = e4
% 30.66/8.48 |
% 30.66/8.48 | Combining equations (1114,367) yields a new equation:
% 30.66/8.48 | (359) e4 = e3
% 30.66/8.48 |
% 30.66/8.48 | Equations (359) can reduce 34 to:
% 30.66/8.48 | (270) $false
% 30.66/8.48 |
% 30.66/8.48 |-The branch is then unsatisfiable
% 30.66/8.48 |-Branch two:
% 30.66/8.48 | (599) ~ (all_0_53_53 = e4)
% 30.66/8.48 | (600) all_0_58_58 = e4
% 30.66/8.48 |
% 30.66/8.48 | Equations (600) can reduce 278 to:
% 30.66/8.48 | (270) $false
% 30.66/8.48 |
% 30.66/8.48 |-The branch is then unsatisfiable
% 30.66/8.48 |-Branch two:
% 30.66/8.48 | (488) ~ (all_0_45_45 = e0)
% 30.66/8.48 | (1132) all_0_46_46 = e0
% 30.66/8.48 |
% 30.66/8.48 | Equations (1132) can reduce 1010 to:
% 30.66/8.48 | (270) $false
% 30.66/8.48 |
% 30.66/8.48 |-The branch is then unsatisfiable
% 30.66/8.48 |-Branch two:
% 30.66/8.48 | (640) ~ (all_0_42_42 = e1)
% 30.66/8.48 | (4628) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 30.66/8.49 |
% 30.66/8.49 +-Applying beta-rule and splitting (592), into two cases.
% 30.66/8.49 |-Branch one:
% 30.66/8.49 | (358) all_0_41_41 = e4
% 30.66/8.49 |
% 30.66/8.49 | Equations (358) can reduce 157 to:
% 30.66/8.49 | (277) ~ (all_0_58_58 = e4)
% 30.66/8.49 |
% 30.66/8.49 | Simplifying 277 yields:
% 30.66/8.49 | (278) ~ (all_0_58_58 = e4)
% 30.66/8.49 |
% 30.66/8.49 +-Applying beta-rule and splitting (52), into two cases.
% 30.66/8.49 |-Branch one:
% 30.66/8.49 | (536) all_0_41_41 = e1
% 30.66/8.49 |
% 30.66/8.49 | Combining equations (358,536) yields a new equation:
% 30.66/8.49 | (525) e4 = e1
% 30.66/8.49 |
% 30.66/8.49 | Simplifying 525 yields:
% 30.66/8.49 | (526) e4 = e1
% 30.66/8.49 |
% 30.66/8.49 | Equations (526) can reduce 251 to:
% 30.66/8.49 | (270) $false
% 30.66/8.49 |
% 30.66/8.49 |-The branch is then unsatisfiable
% 30.66/8.49 |-Branch two:
% 30.66/8.49 | (540) ~ (all_0_41_41 = e1)
% 30.66/8.49 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 30.66/8.49 |
% 30.66/8.49 +-Applying beta-rule and splitting (762), into two cases.
% 30.66/8.49 |-Branch one:
% 30.66/8.49 | (552) all_0_48_48 = e1
% 30.66/8.49 |
% 30.66/8.49 | Combining equations (311,552) yields a new equation:
% 30.66/8.49 | (531) e2 = e1
% 30.66/8.49 |
% 30.66/8.49 | Simplifying 531 yields:
% 30.66/8.49 | (322) e2 = e1
% 30.66/8.49 |
% 30.66/8.49 | Equations (322) can reduce 141 to:
% 30.66/8.49 | (270) $false
% 30.66/8.49 |
% 30.66/8.49 |-The branch is then unsatisfiable
% 30.66/8.49 |-Branch two:
% 30.66/8.49 | (588) ~ (all_0_48_48 = e1)
% 30.66/8.49 | (4925) all_0_53_53 = e1 | all_0_58_58 = e1
% 30.66/8.49 |
% 30.66/8.49 +-Applying beta-rule and splitting (4925), into two cases.
% 30.66/8.49 |-Branch one:
% 30.66/8.49 | (853) all_0_53_53 = e1
% 30.66/8.49 |
% 30.66/8.49 | Combining equations (1114,853) yields a new equation:
% 30.66/8.49 | (537) e3 = e1
% 30.66/8.49 |
% 30.66/8.49 | Simplifying 537 yields:
% 30.66/8.49 | (538) e3 = e1
% 30.66/8.49 |
% 30.66/8.49 | Equations (538) can reduce 136 to:
% 30.66/8.49 | (270) $false
% 30.66/8.49 |
% 30.66/8.49 |-The branch is then unsatisfiable
% 30.66/8.49 |-Branch two:
% 30.66/8.49 | (874) ~ (all_0_53_53 = e1)
% 30.66/8.49 | (1001) all_0_58_58 = e1
% 30.66/8.49 |
% 30.66/8.49 | Equations (1001) can reduce 278 to:
% 30.66/8.49 | (1021) ~ (e4 = e1)
% 30.66/8.49 |
% 30.66/8.49 | Simplifying 1021 yields:
% 30.66/8.49 | (251) ~ (e4 = e1)
% 30.66/8.49 |
% 30.66/8.49 | Equations (1001) can reduce 376 to:
% 30.66/8.49 | (645) ~ (e2 = e1)
% 30.66/8.49 |
% 30.66/8.49 | Simplifying 645 yields:
% 30.66/8.49 | (141) ~ (e2 = e1)
% 30.66/8.49 |
% 30.66/8.49 | Equations (1001) can reduce 431 to:
% 30.66/8.49 | (132) ~ (e1 = e0)
% 30.66/8.49 |
% 30.66/8.49 +-Applying beta-rule and splitting (4628), into two cases.
% 30.66/8.49 |-Branch one:
% 30.66/8.49 | (589) all_0_49_49 = e1
% 30.66/8.49 |
% 30.66/8.49 | Combining equations (589,563) yields a new equation:
% 30.66/8.49 | (571) e1 = e0
% 30.66/8.49 |
% 30.66/8.49 | Simplifying 571 yields:
% 30.66/8.49 | (560) e1 = e0
% 30.66/8.49 |
% 30.66/8.49 | Equations (560) can reduce 132 to:
% 30.66/8.49 | (270) $false
% 30.66/8.49 |
% 30.66/8.49 |-The branch is then unsatisfiable
% 30.66/8.49 |-Branch two:
% 30.66/8.49 | (543) ~ (all_0_49_49 = e1)
% 30.66/8.49 | (4726) all_0_54_54 = e1 | all_0_59_59 = e1
% 30.66/8.49 |
% 30.66/8.49 +-Applying beta-rule and splitting (4726), into two cases.
% 30.66/8.49 |-Branch one:
% 30.66/8.49 | (875) all_0_54_54 = e1
% 30.66/8.49 |
% 30.66/8.49 | Combining equations (3657,875) yields a new equation:
% 30.66/8.49 | (531) e2 = e1
% 30.66/8.49 |
% 30.66/8.49 | Simplifying 531 yields:
% 30.66/8.49 | (322) e2 = e1
% 30.66/8.49 |
% 30.66/8.49 | Equations (322) can reduce 141 to:
% 30.66/8.49 | (270) $false
% 30.66/8.49 |
% 30.66/8.49 |-The branch is then unsatisfiable
% 30.66/8.49 |-Branch two:
% 30.66/8.49 | (425) ~ (all_0_54_54 = e1)
% 30.66/8.49 | (424) all_0_59_59 = e1
% 30.66/8.49 |
% 30.66/8.49 | Combining equations (424,402) yields a new equation:
% 30.66/8.49 | (526) e4 = e1
% 30.66/8.49 |
% 30.66/8.49 | Equations (526) can reduce 251 to:
% 30.66/8.49 | (270) $false
% 30.66/8.49 |
% 30.66/8.49 |-The branch is then unsatisfiable
% 30.66/8.49 |-Branch two:
% 30.66/8.49 | (361) ~ (all_0_41_41 = e4)
% 30.66/8.49 | (512) all_0_42_42 = e4
% 30.66/8.49 |
% 30.66/8.49 | Equations (512) can reduce 520 to:
% 30.66/8.49 | (270) $false
% 30.66/8.49 |
% 30.66/8.49 |-The branch is then unsatisfiable
% 30.66/8.49 |-Branch two:
% 30.66/8.49 | (280) ~ (all_0_59_59 = e4)
% 30.66/8.49 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 30.66/8.49 |
% 30.66/8.49 +-Applying beta-rule and splitting (407), into two cases.
% 30.66/8.49 |-Branch one:
% 30.66/8.49 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 30.66/8.49 |
% 30.66/8.49 +-Applying beta-rule and splitting (408), into two cases.
% 30.66/8.49 |-Branch one:
% 30.66/8.49 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 30.66/8.49 |
% 30.66/8.49 +-Applying beta-rule and splitting (409), into two cases.
% 30.66/8.49 |-Branch one:
% 30.66/8.49 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 30.66/8.49 |
% 30.66/8.49 | Applying alpha-rule on (410) yields:
% 30.66/8.49 | (411) all_0_43_43 = e0
% 30.66/8.49 | (412) all_0_59_59 = e3
% 30.66/8.49 | (413) ~ (all_0_46_46 = e3)
% 30.66/8.49 |
% 30.66/8.49 | Equations (411) can reduce 455 to:
% 30.66/8.49 | (270) $false
% 30.66/8.49 |
% 30.66/8.49 |-The branch is then unsatisfiable
% 30.66/8.49 |-Branch two:
% 30.66/8.49 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 30.66/8.49 |
% 30.66/8.49 | Applying alpha-rule on (416) yields:
% 30.66/8.49 | (411) all_0_43_43 = e0
% 30.66/8.49 | (412) all_0_59_59 = e3
% 30.66/8.49 | (419) ~ (all_0_56_56 = e0)
% 30.66/8.49 |
% 30.66/8.49 | Equations (411) can reduce 455 to:
% 30.66/8.49 | (270) $false
% 30.66/8.49 |
% 30.66/8.49 |-The branch is then unsatisfiable
% 30.66/8.49 |-Branch two:
% 30.66/8.49 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 30.66/8.49 |
% 30.66/8.49 | Applying alpha-rule on (422) yields:
% 30.66/8.49 | (423) all_0_53_53 = e0
% 30.66/8.49 | (424) all_0_59_59 = e1
% 30.66/8.49 | (425) ~ (all_0_54_54 = e1)
% 30.66/8.49 |
% 30.66/8.49 | Combining equations (423,1114) yields a new equation:
% 30.66/8.49 | (784) e3 = e0
% 30.66/8.49 |
% 30.66/8.49 | Equations (784) can reduce 66 to:
% 30.66/8.49 | (270) $false
% 30.66/8.49 |
% 30.66/8.49 |-The branch is then unsatisfiable
% 30.66/8.49 |-Branch two:
% 30.66/8.49 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 30.66/8.49 |
% 30.66/8.49 | Applying alpha-rule on (428) yields:
% 30.66/8.49 | (423) all_0_53_53 = e0
% 30.66/8.49 | (424) all_0_59_59 = e1
% 30.66/8.49 | (431) ~ (all_0_58_58 = e0)
% 30.66/8.49 |
% 30.66/8.49 | Combining equations (423,1114) yields a new equation:
% 30.66/8.49 | (784) e3 = e0
% 30.66/8.49 |
% 30.66/8.49 | Equations (784) can reduce 66 to:
% 30.66/8.49 | (270) $false
% 30.66/8.49 |
% 30.66/8.49 |-The branch is then unsatisfiable
% 30.66/8.49 |-Branch two:
% 30.66/8.49 | (987) ~ (all_0_51_51 = e0)
% 30.66/8.49 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 30.66/8.49 |
% 30.66/8.49 +-Applying beta-rule and splitting (182), into two cases.
% 30.66/8.49 |-Branch one:
% 30.66/8.49 | (454) all_0_45_45 = e0
% 30.66/8.49 |
% 30.66/8.49 | Equations (454) can reduce 84 to:
% 30.66/8.49 | (455) ~ (all_0_43_43 = e0)
% 30.66/8.49 |
% 30.66/8.49 | Equations (454) can reduce 26 to:
% 30.66/8.49 | (568) ~ (e1 = e0)
% 30.66/8.49 |
% 30.66/8.49 | Simplifying 568 yields:
% 30.66/8.49 | (132) ~ (e1 = e0)
% 30.66/8.49 |
% 30.66/8.49 +-Applying beta-rule and splitting (75), into two cases.
% 30.66/8.49 |-Branch one:
% 30.66/8.49 | (411) all_0_43_43 = e0
% 30.66/8.49 |
% 30.66/8.49 | Equations (411) can reduce 455 to:
% 30.66/8.49 | (270) $false
% 30.66/8.49 |
% 30.66/8.49 |-The branch is then unsatisfiable
% 30.66/8.49 |-Branch two:
% 30.66/8.49 | (455) ~ (all_0_43_43 = e0)
% 30.66/8.49 | (940) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 30.66/8.49 |
% 30.66/8.49 +-Applying beta-rule and splitting (3067), into two cases.
% 30.66/8.49 |-Branch one:
% 30.66/8.49 | (827) all_0_52_52 = e0
% 30.66/8.49 |
% 30.66/8.49 | Combining equations (827,848) yields a new equation:
% 30.66/8.49 | (560) e1 = e0
% 30.66/8.49 |
% 30.66/8.49 | Equations (560) can reduce 132 to:
% 30.66/8.49 | (270) $false
% 30.66/8.49 |
% 30.66/8.49 |-The branch is then unsatisfiable
% 30.66/8.49 |-Branch two:
% 30.66/8.49 | (925) ~ (all_0_52_52 = e0)
% 30.66/8.49 | (3073) all_0_53_53 = e0 | all_0_54_54 = e0
% 30.66/8.49 |
% 30.66/8.49 | Equations (848) can reduce 925 to:
% 30.66/8.49 | (132) ~ (e1 = e0)
% 30.66/8.49 |
% 30.66/8.49 +-Applying beta-rule and splitting (940), into two cases.
% 30.66/8.49 |-Branch one:
% 30.66/8.49 | (315) all_0_47_47 = e0
% 30.66/8.49 |
% 30.66/8.49 | Combining equations (321,315) yields a new equation:
% 30.66/8.49 | (571) e1 = e0
% 30.66/8.49 |
% 30.66/8.49 | Simplifying 571 yields:
% 30.66/8.49 | (560) e1 = e0
% 30.66/8.49 |
% 30.66/8.49 | Equations (560) can reduce 132 to:
% 30.66/8.49 | (270) $false
% 30.66/8.49 |
% 30.66/8.49 |-The branch is then unsatisfiable
% 30.66/8.49 |-Branch two:
% 30.66/8.49 | (318) ~ (all_0_47_47 = e0)
% 30.66/8.49 | (950) all_0_51_51 = e0 | all_0_56_56 = e0
% 30.66/8.49 |
% 30.66/8.49 +-Applying beta-rule and splitting (173), into two cases.
% 30.66/8.49 |-Branch one:
% 30.66/8.49 | (4215) all_0_51_51 = e2
% 30.66/8.49 |
% 30.66/8.49 | Equations (4215) can reduce 255 to:
% 30.66/8.49 | (270) $false
% 30.66/8.49 |
% 30.66/8.49 |-The branch is then unsatisfiable
% 30.66/8.49 |-Branch two:
% 30.66/8.49 | (255) ~ (all_0_51_51 = e2)
% 30.66/8.49 | (4888) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1 | all_0_51_51 = e0
% 30.66/8.49 |
% 30.66/8.49 +-Applying beta-rule and splitting (4888), into two cases.
% 30.66/8.49 |-Branch one:
% 30.66/8.49 | (954) all_0_51_51 = e0
% 30.66/8.49 |
% 30.66/8.49 | Equations (954) can reduce 987 to:
% 30.66/8.49 | (270) $false
% 30.66/8.49 |
% 30.66/8.49 |-The branch is then unsatisfiable
% 30.66/8.49 |-Branch two:
% 30.66/8.49 | (987) ~ (all_0_51_51 = e0)
% 30.66/8.49 | (5003) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1
% 30.66/8.49 |
% 30.66/8.49 +-Applying beta-rule and splitting (950), into two cases.
% 30.66/8.49 |-Branch one:
% 30.66/8.49 | (954) all_0_51_51 = e0
% 30.66/8.49 |
% 30.66/8.49 | Equations (954) can reduce 987 to:
% 30.66/8.49 | (270) $false
% 30.66/8.49 |
% 30.66/8.49 |-The branch is then unsatisfiable
% 30.66/8.49 |-Branch two:
% 30.66/8.49 | (987) ~ (all_0_51_51 = e0)
% 30.66/8.49 | (830) all_0_56_56 = e0
% 30.66/8.49 |
% 30.66/8.49 | Equations (830) can reduce 419 to:
% 30.66/8.49 | (270) $false
% 30.66/8.49 |
% 30.66/8.49 |-The branch is then unsatisfiable
% 30.66/8.49 |-Branch two:
% 30.66/8.49 | (488) ~ (all_0_45_45 = e0)
% 30.66/8.49 | (558) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 30.66/8.49 |
% 30.66/8.49 +-Applying beta-rule and splitting (558), into two cases.
% 30.66/8.49 |-Branch one:
% 30.66/8.49 | (559) all_0_48_48 = e0
% 30.66/8.49 |
% 30.66/8.49 | Combining equations (311,559) yields a new equation:
% 30.66/8.49 | (622) e2 = e0
% 30.66/8.49 |
% 30.66/8.49 | Simplifying 622 yields:
% 30.66/8.49 | (316) e2 = e0
% 30.66/8.49 |
% 30.66/8.49 | Equations (316) can reduce 57 to:
% 30.66/8.49 | (270) $false
% 30.66/8.49 |
% 30.66/8.49 |-The branch is then unsatisfiable
% 30.66/8.49 |-Branch two:
% 30.66/8.49 | (562) ~ (all_0_48_48 = e0)
% 30.66/8.49 | (575) all_0_53_53 = e0 | all_0_58_58 = e0
% 30.66/8.49 |
% 30.66/8.49 +-Applying beta-rule and splitting (575), into two cases.
% 30.66/8.49 |-Branch one:
% 30.66/8.49 | (423) all_0_53_53 = e0
% 30.66/8.49 |
% 30.66/8.49 | Combining equations (423,1114) yields a new equation:
% 30.66/8.49 | (784) e3 = e0
% 30.66/8.49 |
% 30.66/8.49 | Equations (784) can reduce 66 to:
% 30.66/8.49 | (270) $false
% 30.66/8.49 |
% 30.66/8.49 |-The branch is then unsatisfiable
% 30.66/8.49 |-Branch two:
% 30.66/8.49 | (584) ~ (all_0_53_53 = e0)
% 30.66/8.49 | (585) all_0_58_58 = e0
% 30.66/8.49 |
% 30.66/8.49 | Equations (585) can reduce 431 to:
% 30.66/8.49 | (270) $false
% 30.66/8.49 |
% 30.66/8.49 |-The branch is then unsatisfiable
% 30.66/8.49 |-Branch two:
% 30.66/8.49 | (642) ~ (all_0_52_52 = e1)
% 30.66/8.49 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 30.66/8.49 |
% 30.66/8.49 +-Applying beta-rule and splitting (3352), into two cases.
% 30.66/8.49 |-Branch one:
% 30.66/8.49 | (848) all_0_52_52 = e1
% 30.66/8.49 |
% 30.66/8.49 | Equations (848) can reduce 642 to:
% 30.66/8.49 | (270) $false
% 30.66/8.49 |
% 30.66/8.49 |-The branch is then unsatisfiable
% 30.66/8.49 |-Branch two:
% 30.66/8.49 | (642) ~ (all_0_52_52 = e1)
% 30.66/8.49 | (997) all_0_57_57 = e1
% 30.66/8.49 |
% 30.66/8.49 | Equations (997) can reduce 37 to:
% 30.66/8.49 | (7725) ~ (all_0_58_58 = e1)
% 30.66/8.49 |
% 30.66/8.49 | Simplifying 7725 yields:
% 30.66/8.49 | (1004) ~ (all_0_58_58 = e1)
% 30.66/8.49 |
% 30.66/8.49 | Equations (997) can reduce 140 to:
% 30.66/8.49 | (749) ~ (all_0_59_59 = e1)
% 30.66/8.49 |
% 30.66/8.49 | Simplifying 749 yields:
% 30.66/8.49 | (750) ~ (all_0_59_59 = e1)
% 30.66/8.49 |
% 30.66/8.49 | Equations (997) can reduce 143 to:
% 30.66/8.49 | (1021) ~ (e4 = e1)
% 30.66/8.49 |
% 30.66/8.49 | Simplifying 1021 yields:
% 30.66/8.49 | (251) ~ (e4 = e1)
% 30.66/8.49 |
% 30.66/8.49 | Equations (997) can reduce 846 to:
% 30.66/8.49 | (769) ~ (e3 = e1)
% 30.66/8.49 |
% 30.66/8.49 | Simplifying 769 yields:
% 30.66/8.49 | (136) ~ (e3 = e1)
% 30.66/8.49 |
% 30.66/8.49 | Equations (997) can reduce 335 to:
% 30.66/8.49 | (645) ~ (e2 = e1)
% 30.66/8.49 |
% 30.66/8.49 | Simplifying 645 yields:
% 30.66/8.49 | (141) ~ (e2 = e1)
% 30.66/8.49 |
% 30.66/8.49 +-Applying beta-rule and splitting (52), into two cases.
% 30.66/8.49 |-Branch one:
% 30.66/8.49 | (536) all_0_41_41 = e1
% 30.66/8.49 |
% 30.66/8.49 | Equations (536) can reduce 94 to:
% 30.66/8.49 | (639) ~ (all_0_42_42 = e1)
% 30.66/8.49 |
% 30.66/8.49 | Simplifying 639 yields:
% 30.66/8.49 | (640) ~ (all_0_42_42 = e1)
% 30.66/8.50 |
% 30.66/8.50 | Equations (536) can reduce 331 to:
% 30.66/8.50 | (645) ~ (e2 = e1)
% 30.66/8.50 |
% 30.66/8.50 | Simplifying 645 yields:
% 30.66/8.50 | (141) ~ (e2 = e1)
% 30.66/8.50 |
% 30.66/8.50 | Equations (536) can reduce 232 to:
% 30.66/8.50 | (132) ~ (e1 = e0)
% 30.66/8.50 |
% 30.66/8.50 +-Applying beta-rule and splitting (592), into two cases.
% 30.66/8.50 |-Branch one:
% 30.66/8.50 | (358) all_0_41_41 = e4
% 30.66/8.50 |
% 30.66/8.50 | Combining equations (536,358) yields a new equation:
% 30.66/8.50 | (526) e4 = e1
% 30.66/8.50 |
% 30.66/8.50 | Equations (526) can reduce 251 to:
% 30.66/8.50 | (270) $false
% 30.66/8.50 |
% 30.66/8.50 |-The branch is then unsatisfiable
% 30.66/8.50 |-Branch two:
% 30.66/8.50 | (361) ~ (all_0_41_41 = e4)
% 30.66/8.50 | (512) all_0_42_42 = e4
% 30.66/8.50 |
% 30.66/8.50 | Equations (512) can reduce 640 to:
% 30.66/8.50 | (251) ~ (e4 = e1)
% 30.66/8.50 |
% 30.66/8.50 +-Applying beta-rule and splitting (127), into two cases.
% 30.66/8.50 |-Branch one:
% 30.66/8.50 | (541) all_0_42_42 = e1
% 30.66/8.50 |
% 30.66/8.50 | Combining equations (512,541) yields a new equation:
% 30.66/8.50 | (525) e4 = e1
% 30.66/8.50 |
% 30.66/8.50 | Simplifying 525 yields:
% 30.66/8.50 | (526) e4 = e1
% 30.66/8.50 |
% 30.66/8.50 | Equations (526) can reduce 251 to:
% 30.66/8.50 | (270) $false
% 30.66/8.50 |
% 30.66/8.50 |-The branch is then unsatisfiable
% 30.66/8.50 |-Branch two:
% 30.66/8.50 | (640) ~ (all_0_42_42 = e1)
% 30.66/8.50 | (4628) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 30.66/8.50 |
% 30.66/8.50 +-Applying beta-rule and splitting (4628), into two cases.
% 30.66/8.50 |-Branch one:
% 30.66/8.50 | (589) all_0_49_49 = e1
% 30.66/8.50 |
% 30.66/8.50 | Combining equations (589,563) yields a new equation:
% 30.66/8.50 | (571) e1 = e0
% 30.66/8.50 |
% 30.66/8.50 | Simplifying 571 yields:
% 30.66/8.50 | (560) e1 = e0
% 30.66/8.50 |
% 30.66/8.50 | Equations (560) can reduce 132 to:
% 30.66/8.50 | (270) $false
% 30.66/8.50 |
% 30.66/8.50 |-The branch is then unsatisfiable
% 30.66/8.50 |-Branch two:
% 30.66/8.50 | (543) ~ (all_0_49_49 = e1)
% 30.66/8.50 | (4726) all_0_54_54 = e1 | all_0_59_59 = e1
% 30.66/8.50 |
% 30.66/8.50 +-Applying beta-rule and splitting (4726), into two cases.
% 30.66/8.50 |-Branch one:
% 30.66/8.50 | (875) all_0_54_54 = e1
% 30.66/8.50 |
% 30.66/8.50 | Combining equations (875,3657) yields a new equation:
% 30.66/8.50 | (322) e2 = e1
% 30.66/8.50 |
% 30.66/8.50 | Equations (322) can reduce 141 to:
% 30.66/8.50 | (270) $false
% 30.66/8.50 |
% 30.66/8.50 |-The branch is then unsatisfiable
% 30.66/8.50 |-Branch two:
% 30.66/8.50 | (425) ~ (all_0_54_54 = e1)
% 30.66/8.50 | (424) all_0_59_59 = e1
% 30.66/8.50 |
% 30.66/8.50 | Equations (424) can reduce 750 to:
% 30.66/8.50 | (270) $false
% 30.66/8.50 |
% 30.66/8.50 |-The branch is then unsatisfiable
% 30.66/8.50 |-Branch two:
% 30.66/8.50 | (540) ~ (all_0_41_41 = e1)
% 30.66/8.50 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 30.66/8.50 |
% 30.66/8.50 +-Applying beta-rule and splitting (762), into two cases.
% 30.66/8.50 |-Branch one:
% 30.66/8.50 | (552) all_0_48_48 = e1
% 30.66/8.50 |
% 30.66/8.50 | Combining equations (552,311) yields a new equation:
% 30.66/8.50 | (322) e2 = e1
% 30.66/8.50 |
% 30.66/8.50 | Equations (322) can reduce 141 to:
% 30.66/8.50 | (270) $false
% 30.66/8.50 |
% 30.66/8.50 |-The branch is then unsatisfiable
% 30.66/8.50 |-Branch two:
% 30.66/8.50 | (588) ~ (all_0_48_48 = e1)
% 30.66/8.50 | (4925) all_0_53_53 = e1 | all_0_58_58 = e1
% 30.66/8.50 |
% 30.66/8.50 +-Applying beta-rule and splitting (4925), into two cases.
% 30.66/8.50 |-Branch one:
% 30.66/8.50 | (853) all_0_53_53 = e1
% 30.66/8.50 |
% 30.66/8.50 | Combining equations (1114,853) yields a new equation:
% 30.66/8.50 | (537) e3 = e1
% 30.66/8.50 |
% 30.66/8.50 | Simplifying 537 yields:
% 30.66/8.50 | (538) e3 = e1
% 30.66/8.50 |
% 30.66/8.50 | Equations (538) can reduce 136 to:
% 30.66/8.50 | (270) $false
% 30.66/8.50 |
% 30.66/8.50 |-The branch is then unsatisfiable
% 30.66/8.50 |-Branch two:
% 30.66/8.50 | (874) ~ (all_0_53_53 = e1)
% 30.66/8.50 | (1001) all_0_58_58 = e1
% 30.66/8.50 |
% 30.66/8.50 | Equations (1001) can reduce 1004 to:
% 30.66/8.50 | (270) $false
% 30.66/8.50 |
% 30.66/8.50 |-The branch is then unsatisfiable
% 30.66/8.50 |-Branch two:
% 30.66/8.50 | (356) ~ (all_0_53_53 = e3)
% 30.66/8.50 | (1119) all_0_54_54 = e3
% 30.66/8.50 |
% 30.66/8.50 | Combining equations (1119,3657) yields a new equation:
% 30.66/8.50 | (437) e3 = e2
% 30.66/8.50 |
% 30.66/8.50 | Simplifying 437 yields:
% 30.66/8.50 | (414) e3 = e2
% 30.66/8.50 |
% 30.66/8.50 | Equations (414) can reduce 223 to:
% 30.66/8.50 | (270) $false
% 30.66/8.50 |
% 30.66/8.50 |-The branch is then unsatisfiable
% 30.66/8.50 |-Branch two:
% 30.66/8.50 | (1762) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 30.66/8.50 |
% 30.66/8.50 | Applying alpha-rule on (1762) yields:
% 30.66/8.50 | (1763) all_0_19_19 = e0
% 30.66/8.50 | (1764) ~ (all_0_20_20 = e2)
% 30.66/8.50 |
% 30.66/8.50 | From (1763) and (30) follows:
% 30.66/8.50 | (1765) op(e2, all_0_57_57) = e0
% 30.66/8.50 |
% 30.66/8.50 +-Applying beta-rule and splitting (16), into two cases.
% 30.66/8.50 |-Branch one:
% 30.66/8.50 | (698) all_0_42_42 = e2
% 30.66/8.50 |
% 30.66/8.50 | Equations (698) can reduce 498 to:
% 30.66/8.50 | (270) $false
% 30.66/8.50 |
% 30.66/8.50 |-The branch is then unsatisfiable
% 30.66/8.50 |-Branch two:
% 30.66/8.50 | (498) ~ (all_0_42_42 = e2)
% 30.66/8.50 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 30.66/8.50 |
% 30.66/8.50 +-Applying beta-rule and splitting (210), into two cases.
% 30.66/8.50 |-Branch one:
% 30.66/8.50 | (524) all_0_39_39 = e1
% 30.66/8.50 |
% 30.66/8.50 | Combining equations (336,524) yields a new equation:
% 30.66/8.50 | (531) e2 = e1
% 30.66/8.50 |
% 30.66/8.50 | Simplifying 531 yields:
% 30.66/8.50 | (322) e2 = e1
% 30.66/8.50 |
% 30.66/8.50 | Equations (322) can reduce 141 to:
% 30.66/8.50 | (270) $false
% 30.66/8.50 |
% 30.66/8.50 |-The branch is then unsatisfiable
% 30.66/8.50 |-Branch two:
% 30.66/8.50 | (528) ~ (all_0_39_39 = e1)
% 30.66/8.50 | (529) all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1
% 30.66/8.50 |
% 30.66/8.50 | Equations (336) can reduce 528 to:
% 30.66/8.50 | (141) ~ (e2 = e1)
% 30.66/8.50 |
% 30.66/8.50 +-Applying beta-rule and splitting (21), into two cases.
% 30.66/8.50 |-Branch one:
% 30.66/8.50 | (824) all_0_51_51 = e3
% 30.66/8.50 |
% 30.66/8.50 | Equations (824) can reduce 240 to:
% 30.66/8.50 | (786) ~ (all_0_43_43 = e3)
% 30.66/8.50 |
% 30.66/8.50 | Equations (824) can reduce 154 to:
% 30.66/8.50 | (825) ~ (all_0_52_52 = e3)
% 30.66/8.50 |
% 30.66/8.50 | Simplifying 825 yields:
% 30.66/8.50 | (826) ~ (all_0_52_52 = e3)
% 30.66/8.50 |
% 30.66/8.50 | Equations (824) can reduce 12 to:
% 30.66/8.50 | (355) ~ (all_0_53_53 = e3)
% 30.66/8.50 |
% 30.66/8.50 | Simplifying 355 yields:
% 30.66/8.50 | (356) ~ (all_0_53_53 = e3)
% 30.66/8.50 |
% 30.66/8.50 | Equations (824) can reduce 697 to:
% 30.66/8.50 | (719) ~ (e4 = e3)
% 30.66/8.50 |
% 30.66/8.50 | Simplifying 719 yields:
% 30.66/8.50 | (34) ~ (e4 = e3)
% 30.66/8.50 |
% 30.66/8.50 | Equations (824) can reduce 255 to:
% 30.66/8.50 | (223) ~ (e3 = e2)
% 30.66/8.50 |
% 30.66/8.50 | Equations (824) can reduce 748 to:
% 30.66/8.50 | (136) ~ (e3 = e1)
% 30.66/8.50 |
% 30.66/8.50 | From (824) and (7) follows:
% 30.66/8.50 | (11846) op(e3, e3) = all_0_9_9
% 30.66/8.50 |
% 30.66/8.50 | Instantiating formula (201) with e3, e3, all_0_9_9, all_0_43_43 and discharging atoms op(e3, e3) = all_0_9_9, op(e3, e3) = all_0_43_43, yields:
% 30.66/8.50 | (11847) all_0_9_9 = all_0_43_43
% 30.66/8.50 |
% 30.66/8.50 +-Applying beta-rule and splitting (234), into two cases.
% 30.66/8.50 |-Branch one:
% 30.66/8.50 | (4239) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3)) | (all_0_9_9 = e1 & ~ (all_0_10_10 = e3))
% 30.66/8.50 |
% 30.66/8.50 +-Applying beta-rule and splitting (4239), into two cases.
% 30.66/8.50 |-Branch one:
% 30.66/8.50 | (4240) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3))
% 30.66/8.50 |
% 30.66/8.50 +-Applying beta-rule and splitting (4240), into two cases.
% 30.66/8.50 |-Branch one:
% 30.66/8.50 | (4241) all_0_4_4 = e4 & ~ (all_0_5_5 = e3)
% 30.66/8.50 |
% 30.66/8.50 | Applying alpha-rule on (4241) yields:
% 30.66/8.50 | (4242) all_0_4_4 = e4
% 30.66/8.50 | (4243) ~ (all_0_5_5 = e3)
% 30.66/8.50 |
% 30.66/8.50 | Combining equations (4242,12701) yields a new equation:
% 30.66/8.50 | (268) e4 = e2
% 30.66/8.50 |
% 30.66/8.50 | Simplifying 268 yields:
% 30.66/8.50 | (269) e4 = e2
% 30.66/8.50 |
% 30.66/8.50 | Equations (269) can reduce 231 to:
% 30.66/8.50 | (270) $false
% 30.66/8.50 |
% 30.66/8.50 |-The branch is then unsatisfiable
% 30.66/8.50 |-Branch two:
% 30.66/8.50 | (4247) all_0_7_7 = e2 & ~ (all_0_8_8 = e3)
% 30.66/8.50 |
% 30.66/8.50 | Applying alpha-rule on (4247) yields:
% 30.66/8.50 | (4248) all_0_7_7 = e2
% 30.66/8.50 | (4249) ~ (all_0_8_8 = e3)
% 30.66/8.50 |
% 30.66/8.50 | Combining equations (4011,4248) yields a new equation:
% 30.66/8.50 | (4250) all_0_45_45 = e2
% 30.66/8.50 |
% 30.66/8.50 | Simplifying 4250 yields:
% 30.66/8.50 | (374) all_0_45_45 = e2
% 30.66/8.50 |
% 30.66/8.50 | Equations (374) can reduce 434 to:
% 30.66/8.50 | (270) $false
% 30.66/8.50 |
% 30.66/8.50 |-The branch is then unsatisfiable
% 30.66/8.50 |-Branch two:
% 30.66/8.50 | (4253) all_0_9_9 = e1 & ~ (all_0_10_10 = e3)
% 30.66/8.50 |
% 30.66/8.50 | Applying alpha-rule on (4253) yields:
% 30.66/8.50 | (4254) all_0_9_9 = e1
% 30.66/8.50 | (4255) ~ (all_0_10_10 = e3)
% 30.66/8.50 |
% 30.66/8.51 | Combining equations (4254,11847) yields a new equation:
% 30.66/8.51 | (12225) all_0_43_43 = e1
% 30.66/8.51 |
% 30.66/8.51 | Equations (12225) can reduce 249 to:
% 30.66/8.51 | (270) $false
% 30.66/8.51 |
% 30.66/8.51 |-The branch is then unsatisfiable
% 30.66/8.51 |-Branch two:
% 30.66/8.51 | (4378) all_0_11_11 = e0 & ~ (all_0_12_12 = e3)
% 30.66/8.51 |
% 30.66/8.51 | Applying alpha-rule on (4378) yields:
% 30.66/8.51 | (4379) all_0_11_11 = e0
% 30.66/8.51 | (4380) ~ (all_0_12_12 = e3)
% 30.66/8.51 |
% 30.66/8.51 | From (4379) and (239) follows:
% 30.66/8.51 | (12899) op(e3, all_0_56_56) = e0
% 30.66/8.51 |
% 30.66/8.51 +-Applying beta-rule and splitting (64), into two cases.
% 30.66/8.51 |-Branch one:
% 30.66/8.51 | (954) all_0_51_51 = e0
% 30.66/8.51 |
% 30.66/8.51 | Combining equations (954,824) yields a new equation:
% 30.66/8.51 | (784) e3 = e0
% 30.66/8.51 |
% 30.66/8.51 | Equations (784) can reduce 66 to:
% 30.66/8.51 | (270) $false
% 30.66/8.51 |
% 30.66/8.51 |-The branch is then unsatisfiable
% 30.66/8.51 |-Branch two:
% 30.66/8.51 | (987) ~ (all_0_51_51 = e0)
% 30.66/8.51 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 30.66/8.51 |
% 30.66/8.51 | Equations (824) can reduce 987 to:
% 30.66/8.51 | (66) ~ (e3 = e0)
% 30.66/8.51 |
% 30.66/8.51 +-Applying beta-rule and splitting (75), into two cases.
% 30.66/8.51 |-Branch one:
% 30.66/8.51 | (411) all_0_43_43 = e0
% 30.66/8.51 |
% 30.66/8.51 | Equations (411) can reduce 249 to:
% 30.66/8.51 | (568) ~ (e1 = e0)
% 30.66/8.51 |
% 30.66/8.51 | Simplifying 568 yields:
% 30.66/8.51 | (132) ~ (e1 = e0)
% 30.66/8.51 |
% 30.66/8.51 +-Applying beta-rule and splitting (166), into two cases.
% 30.66/8.51 |-Branch one:
% 30.66/8.51 | (522) all_0_39_39 = e4
% 30.66/8.51 |
% 30.66/8.51 | Combining equations (336,522) yields a new equation:
% 30.66/8.51 | (269) e4 = e2
% 30.66/8.51 |
% 30.66/8.51 | Equations (269) can reduce 231 to:
% 30.66/8.51 | (270) $false
% 30.66/8.51 |
% 30.66/8.51 |-The branch is then unsatisfiable
% 30.66/8.51 |-Branch two:
% 30.66/8.51 | (591) ~ (all_0_39_39 = e4)
% 30.66/8.51 | (4522) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 30.66/8.51 |
% 30.66/8.51 +-Applying beta-rule and splitting (4522), into two cases.
% 30.66/8.51 |-Branch one:
% 30.66/8.51 | (502) all_0_43_43 = e4
% 30.66/8.51 |
% 30.66/8.51 | Combining equations (411,502) yields a new equation:
% 30.66/8.51 | (479) e4 = e0
% 30.66/8.51 |
% 30.66/8.51 | Equations (479) can reduce 6 to:
% 30.66/8.51 | (270) $false
% 30.66/8.51 |
% 30.66/8.51 |-The branch is then unsatisfiable
% 30.66/8.51 |-Branch two:
% 30.66/8.51 | (510) ~ (all_0_43_43 = e4)
% 30.66/8.51 | (4527) all_0_51_51 = e4 | all_0_56_56 = e4
% 30.66/8.51 |
% 30.66/8.51 +-Applying beta-rule and splitting (4527), into two cases.
% 30.66/8.51 |-Branch one:
% 30.66/8.51 | (1467) all_0_51_51 = e4
% 30.66/8.51 |
% 30.66/8.51 | Combining equations (824,1467) yields a new equation:
% 30.66/8.51 | (359) e4 = e3
% 30.66/8.51 |
% 30.66/8.51 | Equations (359) can reduce 34 to:
% 30.66/8.51 | (270) $false
% 30.66/8.51 |
% 30.66/8.51 |-The branch is then unsatisfiable
% 30.66/8.51 |-Branch two:
% 30.66/8.51 | (697) ~ (all_0_51_51 = e4)
% 30.66/8.51 | (4744) all_0_56_56 = e4
% 30.66/8.51 |
% 30.66/8.51 | From (4744) and (12899) follows:
% 30.66/8.51 | (12924) op(e3, e4) = e0
% 30.66/8.51 |
% 30.66/8.51 | Instantiating formula (201) with e3, e4, e0, e1 and discharging atoms op(e3, e4) = e1, op(e3, e4) = e0, yields:
% 30.66/8.51 | (560) e1 = e0
% 30.66/8.51 |
% 30.66/8.51 | Equations (560) can reduce 132 to:
% 30.66/8.51 | (270) $false
% 30.66/8.51 |
% 30.66/8.51 |-The branch is then unsatisfiable
% 30.66/8.51 |-Branch two:
% 30.66/8.51 | (455) ~ (all_0_43_43 = e0)
% 30.66/8.51 | (940) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 30.66/8.51 |
% 30.66/8.51 +-Applying beta-rule and splitting (940), into two cases.
% 30.66/8.51 |-Branch one:
% 30.66/8.51 | (315) all_0_47_47 = e0
% 30.66/8.51 |
% 30.66/8.51 | Combining equations (321,315) yields a new equation:
% 30.66/8.51 | (571) e1 = e0
% 30.66/8.51 |
% 30.66/8.51 | Simplifying 571 yields:
% 30.66/8.51 | (560) e1 = e0
% 30.66/8.51 |
% 30.66/8.51 | Equations (560) can reduce 132 to:
% 30.66/8.51 | (270) $false
% 30.66/8.51 |
% 30.66/8.51 |-The branch is then unsatisfiable
% 30.66/8.51 |-Branch two:
% 30.66/8.51 | (318) ~ (all_0_47_47 = e0)
% 30.66/8.51 | (950) all_0_51_51 = e0 | all_0_56_56 = e0
% 30.66/8.51 |
% 30.66/8.51 +-Applying beta-rule and splitting (116), into two cases.
% 30.66/8.51 |-Branch one:
% 30.66/8.51 | (411) all_0_43_43 = e0
% 30.66/8.51 |
% 30.66/8.51 | Equations (411) can reduce 455 to:
% 30.66/8.51 | (270) $false
% 30.66/8.51 |
% 30.66/8.51 |-The branch is then unsatisfiable
% 30.66/8.51 |-Branch two:
% 30.66/8.51 | (455) ~ (all_0_43_43 = e0)
% 30.66/8.51 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 30.66/8.51 |
% 30.66/8.51 +-Applying beta-rule and splitting (1122), into two cases.
% 30.66/8.51 |-Branch one:
% 30.66/8.51 | (621) all_0_44_44 = e0
% 30.66/8.51 |
% 30.66/8.51 | Combining equations (370,621) yields a new equation:
% 30.66/8.51 | (622) e2 = e0
% 30.66/8.51 |
% 30.66/8.51 | Simplifying 622 yields:
% 30.66/8.51 | (316) e2 = e0
% 30.66/8.51 |
% 30.66/8.51 | Equations (316) can reduce 57 to:
% 30.66/8.51 | (270) $false
% 30.66/8.51 |
% 30.66/8.51 |-The branch is then unsatisfiable
% 30.66/8.51 |-Branch two:
% 30.66/8.51 | (625) ~ (all_0_44_44 = e0)
% 30.66/8.51 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 30.66/8.51 |
% 30.66/8.51 +-Applying beta-rule and splitting (1128), into two cases.
% 30.66/8.51 |-Branch one:
% 30.66/8.51 | (454) all_0_45_45 = e0
% 30.66/8.51 |
% 30.66/8.51 | Equations (454) can reduce 128 to:
% 30.66/8.51 | (3103) ~ (all_0_53_53 = e0)
% 30.66/8.51 |
% 30.66/8.51 | Simplifying 3103 yields:
% 30.66/8.51 | (584) ~ (all_0_53_53 = e0)
% 30.66/8.51 |
% 30.66/8.51 | Equations (454) can reduce 108 to:
% 30.66/8.51 | (3530) ~ (all_0_58_58 = e0)
% 30.66/8.51 |
% 30.66/8.51 | Simplifying 3530 yields:
% 30.66/8.51 | (431) ~ (all_0_58_58 = e0)
% 30.66/8.51 |
% 30.66/8.51 | Equations (454) can reduce 434 to:
% 30.66/8.51 | (566) ~ (e2 = e0)
% 30.66/8.51 |
% 30.66/8.51 | Simplifying 566 yields:
% 30.66/8.51 | (57) ~ (e2 = e0)
% 30.66/8.51 |
% 30.66/8.51 | Equations (454) can reduce 26 to:
% 30.66/8.51 | (568) ~ (e1 = e0)
% 30.66/8.51 |
% 30.66/8.51 | Simplifying 568 yields:
% 30.66/8.51 | (132) ~ (e1 = e0)
% 30.66/8.51 |
% 30.66/8.51 +-Applying beta-rule and splitting (22), into two cases.
% 30.66/8.51 |-Branch one:
% 30.66/8.51 | (782) all_0_43_43 = e3
% 30.66/8.51 |
% 30.66/8.51 | Equations (782) can reduce 786 to:
% 30.66/8.51 | (270) $false
% 30.66/8.51 |
% 30.66/8.51 |-The branch is then unsatisfiable
% 30.66/8.51 |-Branch two:
% 30.66/8.51 | (786) ~ (all_0_43_43 = e3)
% 30.66/8.51 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 30.66/8.51 |
% 30.66/8.51 +-Applying beta-rule and splitting (219), into two cases.
% 30.66/8.51 |-Branch one:
% 30.66/8.51 | (351) all_0_41_41 = e3
% 30.66/8.51 |
% 30.66/8.51 | Equations (351) can reduce 1237 to:
% 30.66/8.51 | (270) $false
% 30.66/8.51 |
% 30.66/8.51 |-The branch is then unsatisfiable
% 30.66/8.51 |-Branch two:
% 30.66/8.51 | (1237) ~ (all_0_41_41 = e3)
% 30.66/8.51 | (1508) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 30.66/8.51 |
% 30.66/8.51 +-Applying beta-rule and splitting (93), into two cases.
% 30.66/8.51 |-Branch one:
% 30.66/8.51 | (402) all_0_59_59 = e4
% 30.66/8.51 |
% 30.66/8.51 | Equations (402) can reduce 17 to:
% 30.66/8.51 | (520) ~ (all_0_42_42 = e4)
% 30.66/8.51 |
% 30.66/8.51 | Equations (402) can reduce 206 to:
% 30.66/8.51 | (805) ~ (all_0_46_46 = e4)
% 30.66/8.51 |
% 30.66/8.51 | Equations (402) can reduce 4001 to:
% 30.66/8.51 | (6) ~ (e4 = e0)
% 30.66/8.51 |
% 30.66/8.51 +-Applying beta-rule and splitting (44), into two cases.
% 30.66/8.51 |-Branch one:
% 30.66/8.51 | (502) all_0_43_43 = e4
% 30.66/8.51 |
% 30.66/8.51 | Equations (502) can reduce 249 to:
% 30.66/8.51 | (251) ~ (e4 = e1)
% 30.66/8.51 |
% 30.66/8.51 +-Applying beta-rule and splitting (127), into two cases.
% 30.66/8.51 |-Branch one:
% 30.66/8.51 | (541) all_0_42_42 = e1
% 30.66/8.51 |
% 30.66/8.51 | Equations (541) can reduce 94 to:
% 30.66/8.51 | (540) ~ (all_0_41_41 = e1)
% 30.66/8.51 |
% 30.66/8.51 | Equations (541) can reduce 1316 to:
% 30.66/8.51 | (769) ~ (e3 = e1)
% 30.66/8.51 |
% 30.66/8.51 | Simplifying 769 yields:
% 30.66/8.51 | (136) ~ (e3 = e1)
% 30.66/8.51 |
% 30.66/8.51 | Equations (541) can reduce 498 to:
% 30.66/8.51 | (645) ~ (e2 = e1)
% 30.66/8.51 |
% 30.66/8.51 | Simplifying 645 yields:
% 30.66/8.51 | (141) ~ (e2 = e1)
% 30.66/8.51 |
% 30.66/8.51 +-Applying beta-rule and splitting (95), into two cases.
% 30.66/8.51 |-Branch one:
% 30.66/8.51 | (1258) all_0_42_42 = e3
% 30.66/8.51 |
% 30.66/8.51 | Combining equations (1258,541) yields a new equation:
% 30.66/8.51 | (537) e3 = e1
% 30.66/8.51 |
% 30.66/8.51 | Simplifying 537 yields:
% 30.66/8.51 | (538) e3 = e1
% 30.66/8.51 |
% 30.66/8.51 | Equations (538) can reduce 136 to:
% 30.66/8.51 | (270) $false
% 30.66/8.51 |
% 30.66/8.51 |-The branch is then unsatisfiable
% 30.66/8.51 |-Branch two:
% 30.66/8.51 | (1316) ~ (all_0_42_42 = e3)
% 30.66/8.51 | (3656) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 30.66/8.51 |
% 30.66/8.51 | Equations (541) can reduce 1316 to:
% 30.66/8.51 | (769) ~ (e3 = e1)
% 30.66/8.51 |
% 30.66/8.51 | Simplifying 769 yields:
% 30.66/8.51 | (136) ~ (e3 = e1)
% 30.66/8.51 |
% 30.66/8.51 +-Applying beta-rule and splitting (3067), into two cases.
% 30.66/8.51 |-Branch one:
% 30.66/8.51 | (827) all_0_52_52 = e0
% 30.66/8.51 |
% 30.66/8.51 | Equations (827) can reduce 826 to:
% 30.66/8.51 | (788) ~ (e3 = e0)
% 30.66/8.51 |
% 30.66/8.51 | Simplifying 788 yields:
% 30.66/8.51 | (66) ~ (e3 = e0)
% 30.66/8.51 |
% 30.66/8.51 +-Applying beta-rule and splitting (208), into two cases.
% 30.66/8.51 |-Branch one:
% 30.66/8.51 | (388) all_0_56_56 = e2
% 30.66/8.51 |
% 30.66/8.51 | Equations (388) can reduce 300 to:
% 30.66/8.51 | (270) $false
% 30.66/8.51 |
% 30.66/8.51 |-The branch is then unsatisfiable
% 30.66/8.51 |-Branch two:
% 30.66/8.51 | (300) ~ (all_0_56_56 = e2)
% 30.66/8.51 | (5076) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1 | all_0_56_56 = e0
% 30.66/8.51 |
% 30.66/8.51 +-Applying beta-rule and splitting (1508), into two cases.
% 30.66/8.51 |-Branch one:
% 30.66/8.51 | (505) all_0_45_45 = e3
% 30.66/8.51 |
% 30.66/8.51 | Combining equations (454,505) yields a new equation:
% 30.66/8.51 | (784) e3 = e0
% 30.66/8.51 |
% 30.66/8.51 | Equations (784) can reduce 66 to:
% 30.66/8.51 | (270) $false
% 30.66/8.51 |
% 30.66/8.51 |-The branch is then unsatisfiable
% 30.66/8.51 |-Branch two:
% 30.66/8.51 | (354) ~ (all_0_45_45 = e3)
% 30.66/8.51 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 30.66/8.51 |
% 30.66/8.51 | Equations (454) can reduce 354 to:
% 30.66/8.51 | (788) ~ (e3 = e0)
% 30.66/8.51 |
% 30.66/8.51 | Simplifying 788 yields:
% 30.66/8.51 | (66) ~ (e3 = e0)
% 30.66/8.51 |
% 30.66/8.51 +-Applying beta-rule and splitting (176), into two cases.
% 30.66/8.51 |-Branch one:
% 30.66/8.51 | (830) all_0_56_56 = e0
% 30.66/8.51 |
% 30.66/8.51 | Equations (830) can reduce 300 to:
% 30.66/8.51 | (566) ~ (e2 = e0)
% 30.66/8.51 |
% 30.66/8.51 | Simplifying 566 yields:
% 30.66/8.51 | (57) ~ (e2 = e0)
% 30.66/8.51 |
% 30.66/8.51 | Equations (830) can reduce 995 to:
% 30.66/8.51 | (568) ~ (e1 = e0)
% 30.66/8.51 |
% 30.66/8.51 | Simplifying 568 yields:
% 30.66/8.51 | (132) ~ (e1 = e0)
% 30.66/8.51 |
% 30.66/8.51 +-Applying beta-rule and splitting (3352), into two cases.
% 30.66/8.51 |-Branch one:
% 30.66/8.51 | (848) all_0_52_52 = e1
% 30.66/8.51 |
% 30.66/8.51 | Combining equations (827,848) yields a new equation:
% 30.66/8.51 | (560) e1 = e0
% 30.66/8.51 |
% 30.66/8.51 | Equations (560) can reduce 132 to:
% 30.66/8.51 | (270) $false
% 30.66/8.51 |
% 30.66/8.51 |-The branch is then unsatisfiable
% 30.66/8.51 |-Branch two:
% 30.66/8.52 | (642) ~ (all_0_52_52 = e1)
% 30.66/8.52 | (997) all_0_57_57 = e1
% 30.66/8.52 |
% 30.66/8.52 | From (997) and (1765) follows:
% 30.66/8.52 | (6126) op(e2, e1) = e0
% 30.66/8.52 |
% 30.66/8.52 | Instantiating formula (201) with e2, e1, e0, e2 and discharging atoms op(e2, e1) = e2, op(e2, e1) = e0, yields:
% 30.66/8.52 | (316) e2 = e0
% 30.66/8.52 |
% 30.66/8.52 | Equations (316) can reduce 57 to:
% 30.66/8.52 | (270) $false
% 30.66/8.52 |
% 30.66/8.52 |-The branch is then unsatisfiable
% 30.66/8.52 |-Branch two:
% 30.66/8.52 | (419) ~ (all_0_56_56 = e0)
% 30.66/8.52 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 30.66/8.52 |
% 30.66/8.52 +-Applying beta-rule and splitting (950), into two cases.
% 30.66/8.52 |-Branch one:
% 30.66/8.52 | (954) all_0_51_51 = e0
% 30.66/8.52 |
% 30.66/8.52 | Combining equations (824,954) yields a new equation:
% 30.66/8.52 | (783) e3 = e0
% 30.66/8.52 |
% 30.66/8.52 | Simplifying 783 yields:
% 30.66/8.52 | (784) e3 = e0
% 30.66/8.52 |
% 30.66/8.52 | Equations (784) can reduce 66 to:
% 30.66/8.52 | (270) $false
% 30.66/8.52 |
% 30.66/8.52 |-The branch is then unsatisfiable
% 30.66/8.52 |-Branch two:
% 30.66/8.52 | (987) ~ (all_0_51_51 = e0)
% 30.66/8.52 | (830) all_0_56_56 = e0
% 30.66/8.52 |
% 30.66/8.52 | Equations (830) can reduce 419 to:
% 30.66/8.52 | (270) $false
% 30.66/8.52 |
% 30.66/8.52 |-The branch is then unsatisfiable
% 30.66/8.52 |-Branch two:
% 30.66/8.52 | (925) ~ (all_0_52_52 = e0)
% 30.66/8.52 | (3073) all_0_53_53 = e0 | all_0_54_54 = e0
% 30.66/8.52 |
% 30.66/8.52 +-Applying beta-rule and splitting (1508), into two cases.
% 30.66/8.52 |-Branch one:
% 30.66/8.52 | (505) all_0_45_45 = e3
% 30.66/8.52 |
% 30.66/8.52 | Combining equations (454,505) yields a new equation:
% 30.66/8.52 | (784) e3 = e0
% 30.66/8.52 |
% 30.66/8.52 | Equations (784) can reduce 66 to:
% 30.66/8.52 | (270) $false
% 30.66/8.52 |
% 30.66/8.52 |-The branch is then unsatisfiable
% 30.66/8.52 |-Branch two:
% 30.66/8.52 | (354) ~ (all_0_45_45 = e3)
% 30.66/8.52 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 30.66/8.52 |
% 30.66/8.52 +-Applying beta-rule and splitting (1539), into two cases.
% 30.66/8.52 |-Branch one:
% 30.66/8.52 | (1114) all_0_53_53 = e3
% 30.66/8.52 |
% 30.66/8.52 | Equations (1114) can reduce 356 to:
% 30.66/8.52 | (270) $false
% 30.66/8.52 |
% 30.66/8.52 |-The branch is then unsatisfiable
% 30.66/8.52 |-Branch two:
% 30.66/8.52 | (356) ~ (all_0_53_53 = e3)
% 30.66/8.52 | (4713) all_0_58_58 = e3
% 30.66/8.52 |
% 30.66/8.52 | Equations (4713) can reduce 70 to:
% 30.66/8.52 | (356) ~ (all_0_53_53 = e3)
% 30.66/8.52 |
% 30.66/8.52 +-Applying beta-rule and splitting (52), into two cases.
% 30.66/8.52 |-Branch one:
% 30.66/8.52 | (536) all_0_41_41 = e1
% 30.66/8.52 |
% 30.66/8.52 | Equations (536) can reduce 540 to:
% 30.66/8.52 | (270) $false
% 30.66/8.52 |
% 30.66/8.52 |-The branch is then unsatisfiable
% 30.66/8.52 |-Branch two:
% 30.66/8.52 | (540) ~ (all_0_41_41 = e1)
% 30.66/8.52 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 30.66/8.52 |
% 30.66/8.52 +-Applying beta-rule and splitting (626), into two cases.
% 30.66/8.52 |-Branch one:
% 30.66/8.52 | (827) all_0_52_52 = e0
% 30.66/8.52 |
% 30.66/8.52 | Equations (827) can reduce 925 to:
% 30.66/8.52 | (270) $false
% 30.66/8.52 |
% 30.66/8.52 |-The branch is then unsatisfiable
% 30.66/8.52 |-Branch two:
% 30.66/8.52 | (925) ~ (all_0_52_52 = e0)
% 30.66/8.52 | (2258) all_0_57_57 = e0
% 30.66/8.52 |
% 30.66/8.52 +-Applying beta-rule and splitting (762), into two cases.
% 30.66/8.52 |-Branch one:
% 30.66/8.52 | (552) all_0_48_48 = e1
% 30.66/8.52 |
% 30.66/8.52 | Combining equations (311,552) yields a new equation:
% 30.66/8.52 | (531) e2 = e1
% 30.66/8.52 |
% 30.66/8.52 | Simplifying 531 yields:
% 30.66/8.52 | (322) e2 = e1
% 30.66/8.52 |
% 30.66/8.52 | Equations (322) can reduce 141 to:
% 30.66/8.52 | (270) $false
% 30.66/8.52 |
% 30.66/8.52 |-The branch is then unsatisfiable
% 30.66/8.52 |-Branch two:
% 30.66/8.52 | (588) ~ (all_0_48_48 = e1)
% 30.66/8.52 | (4925) all_0_53_53 = e1 | all_0_58_58 = e1
% 30.66/8.52 |
% 30.66/8.52 +-Applying beta-rule and splitting (4925), into two cases.
% 30.66/8.52 |-Branch one:
% 30.66/8.52 | (853) all_0_53_53 = e1
% 30.66/8.52 |
% 30.66/8.52 | Equations (853) can reduce 599 to:
% 30.66/8.52 | (1021) ~ (e4 = e1)
% 30.66/8.52 |
% 30.66/8.52 | Simplifying 1021 yields:
% 30.66/8.52 | (251) ~ (e4 = e1)
% 30.66/8.52 |
% 30.66/8.52 | Equations (853) can reduce 356 to:
% 30.66/8.52 | (769) ~ (e3 = e1)
% 30.66/8.52 |
% 30.66/8.52 | Simplifying 769 yields:
% 30.66/8.52 | (136) ~ (e3 = e1)
% 30.66/8.52 |
% 30.66/8.52 | Equations (853) can reduce 584 to:
% 30.66/8.52 | (132) ~ (e1 = e0)
% 30.66/8.52 |
% 30.66/8.52 +-Applying beta-rule and splitting (194), into two cases.
% 30.66/8.52 |-Branch one:
% 30.66/8.52 | (747) all_0_56_56 = e1
% 30.66/8.52 |
% 30.66/8.52 | Equations (747) can reduce 995 to:
% 30.66/8.52 | (270) $false
% 30.66/8.52 |
% 30.66/8.52 |-The branch is then unsatisfiable
% 30.66/8.52 |-Branch two:
% 30.66/8.52 | (995) ~ (all_0_56_56 = e1)
% 30.66/8.52 | (996) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 30.66/8.52 |
% 30.66/8.52 +-Applying beta-rule and splitting (996), into two cases.
% 30.66/8.52 |-Branch one:
% 30.66/8.52 | (997) all_0_57_57 = e1
% 30.66/8.52 |
% 30.66/8.52 | Combining equations (997,2258) yields a new equation:
% 30.66/8.52 | (571) e1 = e0
% 30.66/8.52 |
% 30.66/8.52 | Simplifying 571 yields:
% 30.66/8.52 | (560) e1 = e0
% 30.66/8.52 |
% 30.66/8.52 | Equations (560) can reduce 132 to:
% 30.66/8.52 | (270) $false
% 30.66/8.52 |
% 30.66/8.52 |-The branch is then unsatisfiable
% 30.66/8.52 |-Branch two:
% 30.66/8.52 | (644) ~ (all_0_57_57 = e1)
% 30.66/8.52 | (1000) all_0_58_58 = e1 | all_0_59_59 = e1
% 30.66/8.52 |
% 30.66/8.52 +-Applying beta-rule and splitting (1000), into two cases.
% 30.66/8.52 |-Branch one:
% 30.66/8.52 | (1001) all_0_58_58 = e1
% 30.66/8.52 |
% 30.66/8.52 | Combining equations (1001,4713) yields a new equation:
% 30.66/8.52 | (538) e3 = e1
% 30.66/8.52 |
% 30.66/8.52 | Equations (538) can reduce 136 to:
% 30.66/8.52 | (270) $false
% 30.66/8.52 |
% 30.66/8.52 |-The branch is then unsatisfiable
% 30.66/8.52 |-Branch two:
% 30.66/8.52 | (1004) ~ (all_0_58_58 = e1)
% 30.66/8.52 | (424) all_0_59_59 = e1
% 30.66/8.52 |
% 30.66/8.52 | Combining equations (402,424) yields a new equation:
% 30.66/8.52 | (525) e4 = e1
% 30.66/8.52 |
% 30.66/8.52 | Simplifying 525 yields:
% 30.66/8.52 | (526) e4 = e1
% 30.66/8.52 |
% 30.66/8.52 | Equations (526) can reduce 251 to:
% 30.66/8.52 | (270) $false
% 30.66/8.52 |
% 30.66/8.52 |-The branch is then unsatisfiable
% 30.66/8.52 |-Branch two:
% 30.66/8.52 | (874) ~ (all_0_53_53 = e1)
% 30.66/8.52 | (1001) all_0_58_58 = e1
% 30.66/8.52 |
% 30.66/8.52 | Combining equations (1001,4713) yields a new equation:
% 30.66/8.52 | (538) e3 = e1
% 30.66/8.52 |
% 30.66/8.52 | Equations (538) can reduce 136 to:
% 30.66/8.52 | (270) $false
% 30.66/8.52 |
% 30.66/8.52 |-The branch is then unsatisfiable
% 30.66/8.52 |-Branch two:
% 30.66/8.52 | (640) ~ (all_0_42_42 = e1)
% 30.66/8.52 | (4628) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 30.66/8.52 |
% 30.66/8.52 +-Applying beta-rule and splitting (1508), into two cases.
% 30.66/8.52 |-Branch one:
% 30.66/8.52 | (505) all_0_45_45 = e3
% 30.66/8.52 |
% 30.66/8.52 | Combining equations (454,505) yields a new equation:
% 30.66/8.52 | (784) e3 = e0
% 30.66/8.52 |
% 30.66/8.52 | Equations (784) can reduce 66 to:
% 30.66/8.52 | (270) $false
% 30.66/8.52 |
% 30.66/8.52 |-The branch is then unsatisfiable
% 30.66/8.52 |-Branch two:
% 30.66/8.52 | (354) ~ (all_0_45_45 = e3)
% 30.66/8.52 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 30.66/8.52 |
% 30.66/8.52 +-Applying beta-rule and splitting (1539), into two cases.
% 30.66/8.52 |-Branch one:
% 30.66/8.52 | (1114) all_0_53_53 = e3
% 30.66/8.52 |
% 30.66/8.52 | Equations (1114) can reduce 356 to:
% 30.66/8.52 | (270) $false
% 30.66/8.52 |
% 30.66/8.52 |-The branch is then unsatisfiable
% 30.66/8.52 |-Branch two:
% 30.66/8.52 | (356) ~ (all_0_53_53 = e3)
% 30.66/8.52 | (4713) all_0_58_58 = e3
% 30.66/8.52 |
% 30.66/8.52 | Equations (4713) can reduce 157 to:
% 30.66/8.52 | (1237) ~ (all_0_41_41 = e3)
% 30.66/8.52 |
% 30.66/8.52 | Equations (4713) can reduce 70 to:
% 30.66/8.52 | (356) ~ (all_0_53_53 = e3)
% 30.66/8.52 |
% 30.66/8.52 | Equations (4713) can reduce 376 to:
% 30.66/8.52 | (223) ~ (e3 = e2)
% 30.66/8.52 |
% 30.66/8.52 | Equations (4713) can reduce 431 to:
% 30.66/8.52 | (66) ~ (e3 = e0)
% 30.66/8.52 |
% 30.66/8.52 +-Applying beta-rule and splitting (1245), into two cases.
% 30.66/8.52 |-Branch one:
% 30.66/8.52 | (1258) all_0_42_42 = e3
% 30.66/8.52 |
% 30.66/8.52 | Equations (1258) can reduce 1316 to:
% 30.66/8.52 | (270) $false
% 30.66/8.52 |
% 30.66/8.52 |-The branch is then unsatisfiable
% 30.66/8.52 |-Branch two:
% 30.66/8.52 | (1316) ~ (all_0_42_42 = e3)
% 30.66/8.52 | (1317) all_0_42_42 = e4 | all_0_42_42 = e1
% 30.66/8.52 |
% 30.66/8.52 +-Applying beta-rule and splitting (13), into two cases.
% 30.66/8.52 |-Branch one:
% 30.66/8.52 | (576) all_0_53_53 = e2
% 30.66/8.52 |
% 30.66/8.52 | Equations (576) can reduce 259 to:
% 30.66/8.52 | (270) $false
% 30.66/8.52 |
% 30.66/8.52 |-The branch is then unsatisfiable
% 30.66/8.52 |-Branch two:
% 30.66/8.52 | (259) ~ (all_0_53_53 = e2)
% 30.66/8.52 | (5715) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 30.66/8.52 |
% 30.66/8.52 +-Applying beta-rule and splitting (592), into two cases.
% 30.66/8.52 |-Branch one:
% 30.66/8.52 | (358) all_0_41_41 = e4
% 30.66/8.52 |
% 30.66/8.52 | Equations (358) can reduce 214 to:
% 30.66/8.52 | (1444) ~ (all_0_53_53 = e4)
% 30.66/8.52 |
% 30.66/8.52 | Simplifying 1444 yields:
% 30.66/8.52 | (599) ~ (all_0_53_53 = e4)
% 30.66/8.52 |
% 30.66/8.52 | Equations (358) can reduce 1237 to:
% 30.66/8.52 | (34) ~ (e4 = e3)
% 30.66/8.52 |
% 30.66/8.52 +-Applying beta-rule and splitting (95), into two cases.
% 30.66/8.52 |-Branch one:
% 30.66/8.52 | (1258) all_0_42_42 = e3
% 30.66/8.52 |
% 30.66/8.52 | Equations (1258) can reduce 1316 to:
% 30.66/8.52 | (270) $false
% 30.66/8.52 |
% 30.66/8.52 |-The branch is then unsatisfiable
% 30.66/8.52 |-Branch two:
% 30.66/8.52 | (1316) ~ (all_0_42_42 = e3)
% 30.66/8.52 | (3656) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 30.66/8.52 |
% 30.66/8.52 +-Applying beta-rule and splitting (950), into two cases.
% 30.66/8.52 |-Branch one:
% 30.66/8.52 | (954) all_0_51_51 = e0
% 30.66/8.52 |
% 30.66/8.52 | Combining equations (824,954) yields a new equation:
% 30.66/8.52 | (783) e3 = e0
% 30.66/8.52 |
% 30.66/8.52 | Simplifying 783 yields:
% 30.66/8.52 | (784) e3 = e0
% 30.66/8.52 |
% 30.66/8.52 | Equations (784) can reduce 66 to:
% 30.66/8.52 | (270) $false
% 30.66/8.52 |
% 30.66/8.52 |-The branch is then unsatisfiable
% 30.66/8.52 |-Branch two:
% 30.66/8.52 | (987) ~ (all_0_51_51 = e0)
% 30.66/8.52 | (830) all_0_56_56 = e0
% 30.66/8.52 |
% 30.66/8.52 | Equations (830) can reduce 104 to:
% 30.66/8.52 | (9326) ~ (all_0_57_57 = e0)
% 30.66/8.52 |
% 30.66/8.52 | Simplifying 9326 yields:
% 30.66/8.52 | (2301) ~ (all_0_57_57 = e0)
% 30.66/8.52 |
% 30.66/8.52 | Equations (830) can reduce 995 to:
% 30.66/8.52 | (568) ~ (e1 = e0)
% 30.66/8.52 |
% 30.66/8.52 | Simplifying 568 yields:
% 30.66/8.52 | (132) ~ (e1 = e0)
% 30.66/8.52 |
% 30.66/8.52 +-Applying beta-rule and splitting (52), into two cases.
% 30.66/8.52 |-Branch one:
% 30.66/8.52 | (536) all_0_41_41 = e1
% 30.66/8.52 |
% 30.66/8.52 | Combining equations (536,358) yields a new equation:
% 30.66/8.52 | (526) e4 = e1
% 30.66/8.52 |
% 30.66/8.52 | Equations (526) can reduce 251 to:
% 30.66/8.52 | (270) $false
% 30.66/8.52 |
% 30.66/8.52 |-The branch is then unsatisfiable
% 30.66/8.52 |-Branch two:
% 30.66/8.52 | (540) ~ (all_0_41_41 = e1)
% 30.66/8.52 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 30.66/8.52 |
% 30.66/8.52 | Equations (358) can reduce 540 to:
% 30.66/8.52 | (251) ~ (e4 = e1)
% 30.66/8.52 |
% 30.66/8.52 +-Applying beta-rule and splitting (529), into two cases.
% 30.66/8.52 |-Branch one:
% 30.66/8.52 | (530) all_0_40_40 = e1
% 30.66/8.52 |
% 30.66/8.52 | Combining equations (530,671) yields a new equation:
% 30.66/8.52 | (538) e3 = e1
% 30.66/8.52 |
% 30.66/8.52 | Equations (538) can reduce 136 to:
% 30.66/8.52 | (270) $false
% 30.66/8.52 |
% 30.66/8.52 |-The branch is then unsatisfiable
% 30.66/8.52 |-Branch two:
% 30.66/8.52 | (534) ~ (all_0_40_40 = e1)
% 30.66/8.52 | (535) all_0_41_41 = e1 | all_0_42_42 = e1
% 30.66/8.52 |
% 30.66/8.52 | Equations (671) can reduce 534 to:
% 30.66/8.52 | (136) ~ (e3 = e1)
% 30.66/8.52 |
% 30.66/8.52 +-Applying beta-rule and splitting (626), into two cases.
% 30.66/8.52 |-Branch one:
% 30.66/8.52 | (827) all_0_52_52 = e0
% 30.66/8.52 |
% 30.66/8.52 | Equations (827) can reduce 213 to:
% 30.66/8.53 | (3103) ~ (all_0_53_53 = e0)
% 30.66/8.53 |
% 30.66/8.53 | Simplifying 3103 yields:
% 30.66/8.53 | (584) ~ (all_0_53_53 = e0)
% 30.66/8.53 |
% 30.66/8.53 | Equations (827) can reduce 235 to:
% 30.66/8.53 | (9326) ~ (all_0_57_57 = e0)
% 30.66/8.53 |
% 30.66/8.53 | Simplifying 9326 yields:
% 30.66/8.53 | (2301) ~ (all_0_57_57 = e0)
% 30.66/8.53 |
% 30.66/8.53 +-Applying beta-rule and splitting (135), into two cases.
% 30.66/8.53 |-Branch one:
% 30.66/8.53 | (820) all_0_51_51 = e1
% 30.66/8.53 |
% 30.66/8.53 | Combining equations (824,820) yields a new equation:
% 30.66/8.53 | (537) e3 = e1
% 30.66/8.53 |
% 30.66/8.53 | Simplifying 537 yields:
% 30.66/8.53 | (538) e3 = e1
% 30.66/8.53 |
% 30.66/8.53 | Equations (538) can reduce 136 to:
% 30.66/8.53 | (270) $false
% 30.66/8.53 |
% 30.66/8.53 |-The branch is then unsatisfiable
% 30.66/8.53 |-Branch two:
% 30.66/8.53 | (748) ~ (all_0_51_51 = e1)
% 30.66/8.53 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 30.66/8.53 |
% 30.66/8.53 +-Applying beta-rule and splitting (5715), into two cases.
% 30.66/8.53 |-Branch one:
% 30.66/8.53 | (423) all_0_53_53 = e0
% 30.66/8.53 |
% 30.66/8.53 | Equations (423) can reduce 584 to:
% 30.66/8.53 | (270) $false
% 30.66/8.53 |
% 30.66/8.53 |-The branch is then unsatisfiable
% 30.66/8.53 |-Branch two:
% 30.66/8.53 | (584) ~ (all_0_53_53 = e0)
% 30.66/8.53 | (5719) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1
% 30.66/8.53 |
% 30.66/8.53 +-Applying beta-rule and splitting (823), into two cases.
% 30.66/8.53 |-Branch one:
% 30.66/8.53 | (848) all_0_52_52 = e1
% 30.66/8.53 |
% 30.66/8.53 | Combining equations (848,827) yields a new equation:
% 30.66/8.53 | (571) e1 = e0
% 30.66/8.53 |
% 30.66/8.53 | Simplifying 571 yields:
% 30.66/8.53 | (560) e1 = e0
% 30.66/8.53 |
% 30.66/8.53 | Equations (560) can reduce 132 to:
% 30.66/8.53 | (270) $false
% 30.66/8.53 |
% 30.66/8.53 |-The branch is then unsatisfiable
% 30.66/8.53 |-Branch two:
% 30.66/8.53 | (642) ~ (all_0_52_52 = e1)
% 30.66/8.53 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 30.66/8.53 |
% 30.66/8.53 | Equations (827) can reduce 642 to:
% 30.66/8.53 | (568) ~ (e1 = e0)
% 30.66/8.53 |
% 30.66/8.53 | Simplifying 568 yields:
% 30.66/8.53 | (132) ~ (e1 = e0)
% 30.66/8.53 |
% 30.66/8.53 +-Applying beta-rule and splitting (194), into two cases.
% 30.66/8.53 |-Branch one:
% 30.66/8.53 | (747) all_0_56_56 = e1
% 30.66/8.53 |
% 30.66/8.53 | Combining equations (747,830) yields a new equation:
% 30.66/8.53 | (571) e1 = e0
% 30.66/8.53 |
% 30.66/8.53 | Simplifying 571 yields:
% 30.66/8.53 | (560) e1 = e0
% 30.66/8.53 |
% 30.66/8.53 | Equations (560) can reduce 132 to:
% 30.66/8.53 | (270) $false
% 30.66/8.53 |
% 30.66/8.53 |-The branch is then unsatisfiable
% 30.66/8.53 |-Branch two:
% 30.66/8.53 | (995) ~ (all_0_56_56 = e1)
% 30.66/8.53 | (996) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 30.66/8.53 |
% 30.66/8.53 +-Applying beta-rule and splitting (3656), into two cases.
% 30.66/8.53 |-Branch one:
% 30.66/8.53 | (1091) all_0_46_46 = e3
% 30.66/8.53 |
% 30.66/8.53 | Equations (1091) can reduce 106 to:
% 30.66/8.53 | (136) ~ (e3 = e1)
% 30.66/8.53 |
% 30.66/8.53 +-Applying beta-rule and splitting (996), into two cases.
% 30.66/8.53 |-Branch one:
% 30.66/8.53 | (997) all_0_57_57 = e1
% 30.66/8.53 |
% 30.66/8.53 | Equations (997) can reduce 2301 to:
% 30.66/8.53 | (132) ~ (e1 = e0)
% 30.66/8.53 |
% 30.66/8.53 +-Applying beta-rule and splitting (4628), into two cases.
% 30.66/8.53 |-Branch one:
% 30.66/8.53 | (589) all_0_49_49 = e1
% 30.66/8.53 |
% 30.66/8.53 | Combining equations (563,589) yields a new equation:
% 30.66/8.53 | (560) e1 = e0
% 30.66/8.53 |
% 30.66/8.53 | Equations (560) can reduce 132 to:
% 30.66/8.53 | (270) $false
% 30.66/8.53 |
% 30.66/8.53 |-The branch is then unsatisfiable
% 30.66/8.53 |-Branch two:
% 30.66/8.53 | (543) ~ (all_0_49_49 = e1)
% 30.66/8.53 | (4726) all_0_54_54 = e1 | all_0_59_59 = e1
% 30.66/8.53 |
% 30.66/8.53 +-Applying beta-rule and splitting (5719), into two cases.
% 30.66/8.53 |-Branch one:
% 30.66/8.53 | (1114) all_0_53_53 = e3
% 30.66/8.53 |
% 30.66/8.53 | Equations (1114) can reduce 356 to:
% 30.66/8.53 | (270) $false
% 30.66/8.53 |
% 30.66/8.53 |-The branch is then unsatisfiable
% 30.66/8.53 |-Branch two:
% 30.66/8.53 | (356) ~ (all_0_53_53 = e3)
% 30.66/8.53 | (5723) all_0_53_53 = e4 | all_0_53_53 = e1
% 30.66/8.53 |
% 30.66/8.53 +-Applying beta-rule and splitting (5723), into two cases.
% 30.66/8.53 |-Branch one:
% 30.66/8.53 | (853) all_0_53_53 = e1
% 30.66/8.53 |
% 30.66/8.53 | Equations (853) can reduce 599 to:
% 30.66/8.53 | (1021) ~ (e4 = e1)
% 30.66/8.53 |
% 30.66/8.53 | Simplifying 1021 yields:
% 30.66/8.53 | (251) ~ (e4 = e1)
% 30.66/8.53 |
% 30.66/8.53 | Equations (853) can reduce 259 to:
% 30.66/8.53 | (645) ~ (e2 = e1)
% 30.66/8.53 |
% 30.66/8.53 | Simplifying 645 yields:
% 30.66/8.53 | (141) ~ (e2 = e1)
% 30.66/8.53 |
% 30.66/8.53 +-Applying beta-rule and splitting (4726), into two cases.
% 30.66/8.53 |-Branch one:
% 30.66/8.53 | (875) all_0_54_54 = e1
% 30.66/8.53 |
% 30.66/8.53 | Combining equations (3657,875) yields a new equation:
% 30.66/8.53 | (531) e2 = e1
% 30.66/8.53 |
% 30.66/8.53 | Simplifying 531 yields:
% 30.66/8.53 | (322) e2 = e1
% 30.66/8.53 |
% 30.66/8.53 | Equations (322) can reduce 141 to:
% 30.66/8.53 | (270) $false
% 30.66/8.53 |
% 30.66/8.53 |-The branch is then unsatisfiable
% 30.66/8.53 |-Branch two:
% 30.66/8.53 | (425) ~ (all_0_54_54 = e1)
% 30.66/8.53 | (424) all_0_59_59 = e1
% 30.66/8.53 |
% 30.66/8.53 | Combining equations (424,402) yields a new equation:
% 30.66/8.53 | (526) e4 = e1
% 30.66/8.53 |
% 30.66/8.53 | Equations (526) can reduce 251 to:
% 30.66/8.53 | (270) $false
% 30.66/8.53 |
% 30.66/8.53 |-The branch is then unsatisfiable
% 30.66/8.53 |-Branch two:
% 30.66/8.53 | (874) ~ (all_0_53_53 = e1)
% 30.66/8.53 | (367) all_0_53_53 = e4
% 30.66/8.53 |
% 30.66/8.53 | Equations (367) can reduce 599 to:
% 30.66/8.53 | (270) $false
% 30.66/8.53 |
% 30.66/8.53 |-The branch is then unsatisfiable
% 30.66/8.53 |-Branch two:
% 30.66/8.53 | (644) ~ (all_0_57_57 = e1)
% 30.66/8.53 | (1000) all_0_58_58 = e1 | all_0_59_59 = e1
% 30.66/8.53 |
% 30.66/8.53 +-Applying beta-rule and splitting (1000), into two cases.
% 30.66/8.53 |-Branch one:
% 30.66/8.53 | (1001) all_0_58_58 = e1
% 30.66/8.53 |
% 30.66/8.53 | Combining equations (4713,1001) yields a new equation:
% 30.66/8.53 | (537) e3 = e1
% 30.66/8.53 |
% 30.66/8.53 | Simplifying 537 yields:
% 30.66/8.53 | (538) e3 = e1
% 30.66/8.53 |
% 30.66/8.53 | Equations (538) can reduce 136 to:
% 30.66/8.53 | (270) $false
% 30.66/8.53 |
% 30.66/8.53 |-The branch is then unsatisfiable
% 30.66/8.53 |-Branch two:
% 30.66/8.53 | (1004) ~ (all_0_58_58 = e1)
% 30.66/8.53 | (424) all_0_59_59 = e1
% 30.66/8.53 |
% 30.66/8.53 | Combining equations (424,402) yields a new equation:
% 30.66/8.53 | (526) e4 = e1
% 30.66/8.53 |
% 30.66/8.53 | Equations (526) can reduce 251 to:
% 30.66/8.53 | (270) $false
% 30.66/8.53 |
% 30.66/8.53 |-The branch is then unsatisfiable
% 30.66/8.53 |-Branch two:
% 30.66/8.53 | (413) ~ (all_0_46_46 = e3)
% 30.66/8.53 | (3700) all_0_54_54 = e3 | all_0_59_59 = e3
% 30.66/8.53 |
% 30.66/8.53 +-Applying beta-rule and splitting (3700), into two cases.
% 30.66/8.53 |-Branch one:
% 30.66/8.53 | (1119) all_0_54_54 = e3
% 30.66/8.53 |
% 30.66/8.53 | Combining equations (1119,3657) yields a new equation:
% 30.66/8.53 | (437) e3 = e2
% 30.66/8.53 |
% 30.66/8.53 | Simplifying 437 yields:
% 30.66/8.53 | (414) e3 = e2
% 30.66/8.53 |
% 30.66/8.53 | Equations (414) can reduce 223 to:
% 30.66/8.53 | (270) $false
% 30.66/8.53 |
% 30.66/8.53 |-The branch is then unsatisfiable
% 30.66/8.53 |-Branch two:
% 30.66/8.53 | (1093) ~ (all_0_54_54 = e3)
% 30.66/8.53 | (412) all_0_59_59 = e3
% 30.66/8.53 |
% 30.66/8.53 | Combining equations (402,412) yields a new equation:
% 30.66/8.53 | (660) e4 = e3
% 30.66/8.53 |
% 30.66/8.53 | Simplifying 660 yields:
% 30.66/8.53 | (359) e4 = e3
% 30.66/8.53 |
% 30.66/8.53 | Equations (359) can reduce 34 to:
% 30.66/8.53 | (270) $false
% 30.66/8.53 |
% 30.66/8.53 |-The branch is then unsatisfiable
% 30.66/8.53 |-Branch two:
% 30.66/8.53 | (925) ~ (all_0_52_52 = e0)
% 30.66/8.53 | (2258) all_0_57_57 = e0
% 30.66/8.53 |
% 30.66/8.53 | Equations (2258) can reduce 2301 to:
% 30.66/8.53 | (270) $false
% 30.66/8.53 |
% 30.66/8.53 |-The branch is then unsatisfiable
% 30.66/8.53 |-Branch two:
% 30.66/8.53 | (361) ~ (all_0_41_41 = e4)
% 30.66/8.53 | (512) all_0_42_42 = e4
% 30.66/8.53 |
% 30.66/8.53 | Equations (512) can reduce 520 to:
% 30.66/8.53 | (270) $false
% 30.66/8.53 |
% 30.66/8.53 |-The branch is then unsatisfiable
% 30.66/8.53 |-Branch two:
% 30.66/8.53 | (510) ~ (all_0_43_43 = e4)
% 30.66/8.53 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 30.66/8.53 |
% 30.66/8.53 +-Applying beta-rule and splitting (511), into two cases.
% 30.66/8.53 |-Branch one:
% 30.66/8.53 | (363) all_0_45_45 = e4
% 30.66/8.53 |
% 30.66/8.53 | Combining equations (454,363) yields a new equation:
% 30.66/8.53 | (479) e4 = e0
% 30.66/8.53 |
% 30.66/8.53 | Equations (479) can reduce 6 to:
% 30.66/8.53 | (270) $false
% 30.66/8.53 |
% 30.66/8.53 |-The branch is then unsatisfiable
% 30.66/8.53 |-Branch two:
% 30.66/8.53 | (352) ~ (all_0_45_45 = e4)
% 30.66/8.53 | (517) all_0_46_46 = e4
% 30.66/8.53 |
% 30.66/8.53 | Equations (517) can reduce 805 to:
% 30.66/8.53 | (270) $false
% 30.66/8.53 |
% 30.66/8.53 |-The branch is then unsatisfiable
% 30.66/8.53 |-Branch two:
% 30.66/8.53 | (280) ~ (all_0_59_59 = e4)
% 30.66/8.53 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 30.66/8.53 |
% 30.66/8.53 +-Applying beta-rule and splitting (1508), into two cases.
% 30.66/8.53 |-Branch one:
% 30.66/8.53 | (505) all_0_45_45 = e3
% 30.66/8.53 |
% 30.66/8.53 | Combining equations (454,505) yields a new equation:
% 30.66/8.53 | (784) e3 = e0
% 30.66/8.53 |
% 30.66/8.53 | Equations (784) can reduce 66 to:
% 30.66/8.53 | (270) $false
% 30.66/8.53 |
% 30.66/8.53 |-The branch is then unsatisfiable
% 30.66/8.53 |-Branch two:
% 30.66/8.53 | (354) ~ (all_0_45_45 = e3)
% 30.66/8.53 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 30.66/8.53 |
% 30.66/8.53 | Equations (454) can reduce 354 to:
% 30.66/8.53 | (788) ~ (e3 = e0)
% 30.66/8.53 |
% 30.66/8.53 | Simplifying 788 yields:
% 30.66/8.53 | (66) ~ (e3 = e0)
% 30.66/8.53 |
% 30.66/8.53 +-Applying beta-rule and splitting (787), into two cases.
% 30.66/8.53 |-Branch one:
% 30.66/8.53 | (858) all_0_44_44 = e3
% 30.66/8.53 |
% 30.66/8.53 | Combining equations (370,858) yields a new equation:
% 30.66/8.53 | (414) e3 = e2
% 30.66/8.53 |
% 30.66/8.53 | Equations (414) can reduce 223 to:
% 30.66/8.53 | (270) $false
% 30.66/8.53 |
% 30.66/8.53 |-The branch is then unsatisfiable
% 30.66/8.53 |-Branch two:
% 30.66/8.53 | (862) ~ (all_0_44_44 = e3)
% 30.66/8.53 | (1070) all_0_45_45 = e3 | all_0_46_46 = e3
% 30.66/8.53 |
% 30.66/8.53 +-Applying beta-rule and splitting (1070), into two cases.
% 30.66/8.53 |-Branch one:
% 30.66/8.53 | (505) all_0_45_45 = e3
% 30.66/8.53 |
% 30.66/8.53 | Combining equations (454,505) yields a new equation:
% 30.66/8.53 | (784) e3 = e0
% 30.66/8.53 |
% 30.66/8.53 | Equations (784) can reduce 66 to:
% 30.66/8.53 | (270) $false
% 30.66/8.53 |
% 30.66/8.53 |-The branch is then unsatisfiable
% 30.66/8.53 |-Branch two:
% 30.66/8.53 | (354) ~ (all_0_45_45 = e3)
% 30.66/8.53 | (1091) all_0_46_46 = e3
% 30.66/8.53 |
% 30.66/8.53 | Equations (1091) can reduce 106 to:
% 30.66/8.53 | (136) ~ (e3 = e1)
% 30.66/8.53 |
% 30.66/8.53 +-Applying beta-rule and splitting (44), into two cases.
% 30.66/8.53 |-Branch one:
% 30.66/8.53 | (502) all_0_43_43 = e4
% 30.66/8.53 |
% 30.66/8.53 +-Applying beta-rule and splitting (3067), into two cases.
% 30.66/8.53 |-Branch one:
% 30.66/8.53 | (827) all_0_52_52 = e0
% 30.66/8.53 |
% 30.66/8.53 | Equations (827) can reduce 213 to:
% 30.66/8.53 | (3103) ~ (all_0_53_53 = e0)
% 30.66/8.53 |
% 30.66/8.53 | Simplifying 3103 yields:
% 30.66/8.53 | (584) ~ (all_0_53_53 = e0)
% 30.66/8.53 |
% 30.66/8.53 | Equations (827) can reduce 230 to:
% 30.66/8.53 | (456) ~ (e4 = e0)
% 30.66/8.53 |
% 30.66/8.53 | Simplifying 456 yields:
% 30.66/8.53 | (6) ~ (e4 = e0)
% 30.66/8.53 |
% 30.66/8.53 +-Applying beta-rule and splitting (135), into two cases.
% 30.66/8.53 |-Branch one:
% 30.66/8.53 | (820) all_0_51_51 = e1
% 30.66/8.53 |
% 30.66/8.53 | Combining equations (820,824) yields a new equation:
% 30.66/8.53 | (538) e3 = e1
% 30.66/8.53 |
% 30.66/8.53 | Equations (538) can reduce 136 to:
% 30.66/8.53 | (270) $false
% 30.66/8.53 |
% 30.66/8.53 |-The branch is then unsatisfiable
% 30.66/8.53 |-Branch two:
% 30.66/8.53 | (748) ~ (all_0_51_51 = e1)
% 30.66/8.53 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 30.66/8.54 |
% 30.66/8.54 +-Applying beta-rule and splitting (823), into two cases.
% 30.66/8.54 |-Branch one:
% 30.66/8.54 | (848) all_0_52_52 = e1
% 30.66/8.54 |
% 30.66/8.54 | Combining equations (848,827) yields a new equation:
% 30.66/8.54 | (571) e1 = e0
% 30.66/8.54 |
% 30.66/8.54 | Simplifying 571 yields:
% 30.66/8.54 | (560) e1 = e0
% 30.66/8.54 |
% 30.66/8.54 | Equations (560) can reduce 132 to:
% 30.66/8.54 | (270) $false
% 30.66/8.54 |
% 30.66/8.54 |-The branch is then unsatisfiable
% 30.66/8.54 |-Branch two:
% 30.66/8.54 | (642) ~ (all_0_52_52 = e1)
% 30.66/8.54 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 30.66/8.54 |
% 30.66/8.54 +-Applying beta-rule and splitting (852), into two cases.
% 30.66/8.54 |-Branch one:
% 30.66/8.54 | (853) all_0_53_53 = e1
% 30.66/8.54 |
% 30.66/8.54 | Equations (853) can reduce 584 to:
% 30.66/8.54 | (132) ~ (e1 = e0)
% 30.66/8.54 |
% 30.66/8.54 +-Applying beta-rule and splitting (407), into two cases.
% 30.66/8.54 |-Branch one:
% 30.66/8.54 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 30.66/8.54 |
% 30.66/8.54 +-Applying beta-rule and splitting (408), into two cases.
% 30.66/8.54 |-Branch one:
% 30.66/8.54 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 30.66/8.54 |
% 30.66/8.54 +-Applying beta-rule and splitting (409), into two cases.
% 30.66/8.54 |-Branch one:
% 30.66/8.54 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 30.66/8.54 |
% 30.66/8.54 | Applying alpha-rule on (410) yields:
% 30.66/8.54 | (411) all_0_43_43 = e0
% 30.66/8.54 | (412) all_0_59_59 = e3
% 30.66/8.54 | (413) ~ (all_0_46_46 = e3)
% 30.66/8.54 |
% 30.66/8.54 | Combining equations (411,502) yields a new equation:
% 30.66/8.54 | (479) e4 = e0
% 30.66/8.54 |
% 30.66/8.54 | Equations (479) can reduce 6 to:
% 30.66/8.54 | (270) $false
% 30.66/8.54 |
% 30.66/8.54 |-The branch is then unsatisfiable
% 30.66/8.54 |-Branch two:
% 30.66/8.54 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 30.66/8.54 |
% 30.66/8.54 | Applying alpha-rule on (416) yields:
% 30.66/8.54 | (411) all_0_43_43 = e0
% 30.66/8.54 | (412) all_0_59_59 = e3
% 30.66/8.54 | (419) ~ (all_0_56_56 = e0)
% 30.66/8.54 |
% 30.66/8.54 | Combining equations (411,502) yields a new equation:
% 30.66/8.54 | (479) e4 = e0
% 30.66/8.54 |
% 30.66/8.54 | Equations (479) can reduce 6 to:
% 30.66/8.54 | (270) $false
% 30.66/8.54 |
% 30.66/8.54 |-The branch is then unsatisfiable
% 30.66/8.54 |-Branch two:
% 30.66/8.54 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 30.66/8.54 |
% 30.66/8.54 | Applying alpha-rule on (422) yields:
% 30.66/8.54 | (423) all_0_53_53 = e0
% 30.66/8.54 | (424) all_0_59_59 = e1
% 30.66/8.54 | (425) ~ (all_0_54_54 = e1)
% 30.66/8.54 |
% 30.66/8.54 | Combining equations (423,853) yields a new equation:
% 30.66/8.54 | (560) e1 = e0
% 30.66/8.54 |
% 30.66/8.54 | Equations (560) can reduce 132 to:
% 30.66/8.54 | (270) $false
% 30.66/8.54 |
% 30.66/8.54 |-The branch is then unsatisfiable
% 30.66/8.54 |-Branch two:
% 30.66/8.54 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 30.66/8.54 |
% 30.66/8.54 | Applying alpha-rule on (428) yields:
% 30.66/8.54 | (423) all_0_53_53 = e0
% 30.66/8.54 | (424) all_0_59_59 = e1
% 30.66/8.54 | (431) ~ (all_0_58_58 = e0)
% 30.66/8.54 |
% 30.66/8.54 | Combining equations (423,853) yields a new equation:
% 30.66/8.54 | (560) e1 = e0
% 30.66/8.54 |
% 30.66/8.54 | Equations (560) can reduce 132 to:
% 30.66/8.54 | (270) $false
% 30.66/8.54 |
% 30.66/8.54 |-The branch is then unsatisfiable
% 30.66/8.54 |-Branch two:
% 30.66/8.54 | (874) ~ (all_0_53_53 = e1)
% 30.66/8.54 | (875) all_0_54_54 = e1
% 30.66/8.54 |
% 30.66/8.54 | Combining equations (3657,875) yields a new equation:
% 30.66/8.54 | (531) e2 = e1
% 30.66/8.54 |
% 30.66/8.54 | Simplifying 531 yields:
% 30.66/8.54 | (322) e2 = e1
% 30.66/8.54 |
% 30.66/8.54 | Equations (322) can reduce 141 to:
% 30.66/8.54 | (270) $false
% 30.66/8.54 |
% 30.66/8.54 |-The branch is then unsatisfiable
% 30.66/8.54 |-Branch two:
% 30.66/8.54 | (925) ~ (all_0_52_52 = e0)
% 30.66/8.54 | (3073) all_0_53_53 = e0 | all_0_54_54 = e0
% 30.66/8.54 |
% 30.66/8.54 +-Applying beta-rule and splitting (3073), into two cases.
% 30.66/8.54 |-Branch one:
% 30.66/8.54 | (423) all_0_53_53 = e0
% 30.66/8.54 |
% 30.66/8.54 | Equations (423) can reduce 584 to:
% 30.66/8.54 | (270) $false
% 30.66/8.54 |
% 30.66/8.54 |-The branch is then unsatisfiable
% 30.66/8.54 |-Branch two:
% 30.66/8.54 | (584) ~ (all_0_53_53 = e0)
% 30.66/8.54 | (3084) all_0_54_54 = e0
% 30.66/8.54 |
% 30.66/8.54 | Combining equations (3084,3657) yields a new equation:
% 30.66/8.54 | (316) e2 = e0
% 30.66/8.54 |
% 30.66/8.54 | Equations (316) can reduce 57 to:
% 30.66/8.54 | (270) $false
% 30.66/8.54 |
% 30.66/8.54 |-The branch is then unsatisfiable
% 30.66/8.54 |-Branch two:
% 30.66/8.54 | (510) ~ (all_0_43_43 = e4)
% 30.66/8.54 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 30.66/8.54 |
% 30.66/8.54 +-Applying beta-rule and splitting (511), into two cases.
% 30.66/8.54 |-Branch one:
% 30.66/8.54 | (363) all_0_45_45 = e4
% 30.66/8.54 |
% 30.66/8.54 | Combining equations (454,363) yields a new equation:
% 30.66/8.54 | (479) e4 = e0
% 30.66/8.54 |
% 30.66/8.54 | Equations (479) can reduce 6 to:
% 30.66/8.54 | (270) $false
% 30.66/8.54 |
% 30.66/8.54 |-The branch is then unsatisfiable
% 30.66/8.54 |-Branch two:
% 30.66/8.54 | (352) ~ (all_0_45_45 = e4)
% 30.66/8.54 | (517) all_0_46_46 = e4
% 30.66/8.54 |
% 30.66/8.54 | Combining equations (1091,517) yields a new equation:
% 30.66/8.54 | (359) e4 = e3
% 30.66/8.54 |
% 30.66/8.54 | Equations (359) can reduce 34 to:
% 30.66/8.54 | (270) $false
% 30.66/8.54 |
% 30.66/8.54 |-The branch is then unsatisfiable
% 30.66/8.54 |-Branch two:
% 30.66/8.54 | (488) ~ (all_0_45_45 = e0)
% 30.66/8.54 | (1132) all_0_46_46 = e0
% 30.66/8.54 |
% 30.66/8.54 | Equations (1132) can reduce 1010 to:
% 30.66/8.54 | (270) $false
% 30.66/8.54 |
% 30.66/8.54 |-The branch is then unsatisfiable
% 30.66/8.54 |-Branch two:
% 30.66/8.54 | (932) ~ (all_0_51_51 = e3)
% 30.66/8.54 | (1101) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 30.66/8.54 |
% 30.66/8.54 +-Applying beta-rule and splitting (1101), into two cases.
% 30.66/8.54 |-Branch one:
% 30.66/8.54 | (864) all_0_52_52 = e3
% 30.66/8.54 |
% 30.66/8.54 | Equations (864) can reduce 826 to:
% 30.66/8.54 | (270) $false
% 30.66/8.54 |
% 30.66/8.54 |-The branch is then unsatisfiable
% 30.66/8.54 |-Branch two:
% 30.66/8.54 | (826) ~ (all_0_52_52 = e3)
% 30.66/8.54 | (1107) all_0_53_53 = e3 | all_0_54_54 = e3
% 30.66/8.54 |
% 30.66/8.54 +-Applying beta-rule and splitting (1107), into two cases.
% 30.66/8.54 |-Branch one:
% 30.66/8.54 | (1114) all_0_53_53 = e3
% 30.66/8.54 |
% 30.66/8.54 | Equations (1114) can reduce 12 to:
% 30.66/8.54 | (932) ~ (all_0_51_51 = e3)
% 30.66/8.54 |
% 30.66/8.54 | Equations (1114) can reduce 213 to:
% 30.66/8.54 | (826) ~ (all_0_52_52 = e3)
% 30.66/8.54 |
% 30.66/8.54 | Equations (1114) can reduce 599 to:
% 30.66/8.54 | (719) ~ (e4 = e3)
% 30.66/8.54 |
% 30.66/8.54 | Simplifying 719 yields:
% 30.66/8.54 | (34) ~ (e4 = e3)
% 30.66/8.54 |
% 30.66/8.54 +-Applying beta-rule and splitting (135), into two cases.
% 30.66/8.54 |-Branch one:
% 30.66/8.54 | (820) all_0_51_51 = e1
% 30.66/8.54 |
% 30.66/8.54 | Equations (820) can reduce 748 to:
% 30.66/8.54 | (270) $false
% 30.66/8.54 |
% 30.66/8.54 |-The branch is then unsatisfiable
% 30.66/8.54 |-Branch two:
% 30.66/8.54 | (748) ~ (all_0_51_51 = e1)
% 30.66/8.54 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 30.66/8.54 |
% 30.66/8.54 +-Applying beta-rule and splitting (823), into two cases.
% 30.66/8.54 |-Branch one:
% 30.66/8.54 | (848) all_0_52_52 = e1
% 30.66/8.54 |
% 30.66/8.54 | Equations (848) can reduce 230 to:
% 30.66/8.54 | (1021) ~ (e4 = e1)
% 30.66/8.54 |
% 30.66/8.54 | Simplifying 1021 yields:
% 30.66/8.54 | (251) ~ (e4 = e1)
% 30.66/8.54 |
% 30.66/8.54 | Equations (848) can reduce 826 to:
% 30.66/8.54 | (769) ~ (e3 = e1)
% 30.66/8.54 |
% 30.66/8.54 | Simplifying 769 yields:
% 30.66/8.54 | (136) ~ (e3 = e1)
% 30.66/8.54 |
% 30.66/8.54 | Equations (848) can reduce 257 to:
% 30.66/8.54 | (645) ~ (e2 = e1)
% 30.66/8.54 |
% 30.66/8.54 | Simplifying 645 yields:
% 30.66/8.54 | (141) ~ (e2 = e1)
% 30.66/8.54 |
% 30.66/8.54 +-Applying beta-rule and splitting (626), into two cases.
% 30.66/8.54 |-Branch one:
% 30.66/8.54 | (827) all_0_52_52 = e0
% 30.66/8.54 |
% 30.66/8.54 | Combining equations (848,827) yields a new equation:
% 30.66/8.54 | (571) e1 = e0
% 30.66/8.54 |
% 30.66/8.54 | Simplifying 571 yields:
% 30.66/8.54 | (560) e1 = e0
% 30.66/8.54 |
% 30.66/8.54 | Equations (560) can reduce 132 to:
% 30.66/8.54 | (270) $false
% 30.66/8.54 |
% 30.66/8.54 |-The branch is then unsatisfiable
% 30.66/8.54 |-Branch two:
% 30.66/8.54 | (925) ~ (all_0_52_52 = e0)
% 30.66/8.54 | (2258) all_0_57_57 = e0
% 30.66/8.54 |
% 30.66/8.54 | Equations (2258) can reduce 104 to:
% 30.66/8.54 | (419) ~ (all_0_56_56 = e0)
% 30.66/8.54 |
% 30.66/8.54 | Equations (2258) can reduce 37 to:
% 30.66/8.54 | (3530) ~ (all_0_58_58 = e0)
% 30.66/8.54 |
% 30.66/8.54 | Simplifying 3530 yields:
% 30.66/8.54 | (431) ~ (all_0_58_58 = e0)
% 30.66/8.54 |
% 30.91/8.54 | Equations (2258) can reduce 140 to:
% 30.91/8.54 | (4000) ~ (all_0_59_59 = e0)
% 30.91/8.54 |
% 30.91/8.54 | Simplifying 4000 yields:
% 30.91/8.54 | (4001) ~ (all_0_59_59 = e0)
% 30.91/8.54 |
% 30.91/8.54 | Equations (2258) can reduce 846 to:
% 30.91/8.54 | (788) ~ (e3 = e0)
% 30.91/8.54 |
% 30.91/8.54 | Simplifying 788 yields:
% 30.91/8.54 | (66) ~ (e3 = e0)
% 30.91/8.54 |
% 30.91/8.54 | Equations (2258) can reduce 335 to:
% 30.91/8.54 | (566) ~ (e2 = e0)
% 30.91/8.54 |
% 30.91/8.54 | Simplifying 566 yields:
% 30.91/8.54 | (57) ~ (e2 = e0)
% 30.91/8.54 |
% 30.91/8.54 | From (2258) and (120) follows:
% 30.91/8.54 | (6285) op(e0, e0) = all_0_20_20
% 30.91/8.54 |
% 30.91/8.54 +-Applying beta-rule and splitting (64), into two cases.
% 30.91/8.54 |-Branch one:
% 30.91/8.54 | (954) all_0_51_51 = e0
% 30.91/8.54 |
% 30.91/8.54 | Equations (954) can reduce 240 to:
% 30.91/8.54 | (455) ~ (all_0_43_43 = e0)
% 30.91/8.54 |
% 30.91/8.54 | Equations (954) can reduce 932 to:
% 30.91/8.54 | (788) ~ (e3 = e0)
% 30.91/8.54 |
% 30.91/8.54 | Simplifying 788 yields:
% 30.91/8.54 | (66) ~ (e3 = e0)
% 30.91/8.54 |
% 30.91/8.54 | Equations (954) can reduce 255 to:
% 30.91/8.54 | (566) ~ (e2 = e0)
% 30.91/8.54 |
% 30.91/8.54 | Simplifying 566 yields:
% 30.91/8.54 | (57) ~ (e2 = e0)
% 30.91/8.54 |
% 30.91/8.54 | From (954) and (7) follows:
% 30.91/8.54 | (14159) op(e3, e0) = all_0_9_9
% 30.91/8.54 |
% 30.91/8.54 +-Applying beta-rule and splitting (93), into two cases.
% 30.91/8.54 |-Branch one:
% 30.91/8.54 | (402) all_0_59_59 = e4
% 30.91/8.54 |
% 30.91/8.54 | Equations (402) can reduce 17 to:
% 30.91/8.54 | (520) ~ (all_0_42_42 = e4)
% 30.91/8.54 |
% 30.91/8.54 | Equations (402) can reduce 206 to:
% 30.91/8.54 | (805) ~ (all_0_46_46 = e4)
% 30.91/8.54 |
% 30.91/8.54 | Equations (402) can reduce 156 to:
% 30.91/8.54 | (278) ~ (all_0_58_58 = e4)
% 30.91/8.54 |
% 30.91/8.54 | Equations (402) can reduce 4001 to:
% 30.91/8.54 | (6) ~ (e4 = e0)
% 30.91/8.54 |
% 30.91/8.54 | From (402) and (161) follows:
% 30.91/8.54 | (11389) op(e0, e0) = e4
% 30.91/8.54 |
% 30.91/8.54 +-Applying beta-rule and splitting (220), into two cases.
% 30.91/8.54 |-Branch one:
% 30.91/8.54 | (497) all_0_46_46 = e2
% 30.91/8.54 |
% 30.91/8.54 | Equations (497) can reduce 1436 to:
% 30.91/8.54 | (270) $false
% 30.91/8.54 |
% 30.91/8.54 |-The branch is then unsatisfiable
% 30.91/8.54 |-Branch two:
% 30.91/8.54 | (1436) ~ (all_0_46_46 = e2)
% 30.91/8.54 | (1523) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e0
% 30.91/8.54 |
% 30.91/8.54 +-Applying beta-rule and splitting (127), into two cases.
% 30.91/8.54 |-Branch one:
% 30.91/8.54 | (541) all_0_42_42 = e1
% 30.91/8.54 |
% 30.91/8.54 | Equations (541) can reduce 94 to:
% 30.91/8.54 | (540) ~ (all_0_41_41 = e1)
% 30.91/8.54 |
% 30.91/8.54 | Equations (541) can reduce 18 to:
% 30.91/8.54 | (6201) ~ (all_0_46_46 = e1)
% 30.91/8.54 |
% 30.91/8.54 | Simplifying 6201 yields:
% 30.91/8.54 | (106) ~ (all_0_46_46 = e1)
% 30.91/8.54 |
% 30.91/8.54 | Equations (541) can reduce 498 to:
% 30.91/8.54 | (645) ~ (e2 = e1)
% 30.91/8.54 |
% 30.91/8.54 | Simplifying 645 yields:
% 30.91/8.54 | (141) ~ (e2 = e1)
% 30.91/8.54 |
% 30.91/8.54 +-Applying beta-rule and splitting (52), into two cases.
% 30.91/8.54 |-Branch one:
% 30.91/8.54 | (536) all_0_41_41 = e1
% 30.91/8.54 |
% 30.91/8.54 | Equations (536) can reduce 540 to:
% 30.91/8.54 | (270) $false
% 30.91/8.54 |
% 30.91/8.54 |-The branch is then unsatisfiable
% 30.91/8.54 |-Branch two:
% 30.91/8.54 | (540) ~ (all_0_41_41 = e1)
% 30.91/8.54 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 30.91/8.54 |
% 30.91/8.54 +-Applying beta-rule and splitting (116), into two cases.
% 30.91/8.54 |-Branch one:
% 30.91/8.54 | (411) all_0_43_43 = e0
% 30.91/8.54 |
% 30.91/8.54 | Equations (411) can reduce 455 to:
% 30.91/8.54 | (270) $false
% 30.91/8.54 |
% 30.91/8.54 |-The branch is then unsatisfiable
% 30.91/8.54 |-Branch two:
% 30.91/8.54 | (455) ~ (all_0_43_43 = e0)
% 30.91/8.54 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 30.91/8.54 |
% 30.91/8.54 +-Applying beta-rule and splitting (1122), into two cases.
% 30.91/8.54 |-Branch one:
% 30.91/8.54 | (621) all_0_44_44 = e0
% 30.91/8.54 |
% 30.91/8.54 | Combining equations (370,621) yields a new equation:
% 30.91/8.54 | (622) e2 = e0
% 30.91/8.54 |
% 30.91/8.54 | Simplifying 622 yields:
% 30.91/8.54 | (316) e2 = e0
% 30.91/8.54 |
% 30.91/8.54 | Equations (316) can reduce 57 to:
% 30.91/8.54 | (270) $false
% 30.91/8.54 |
% 30.91/8.54 |-The branch is then unsatisfiable
% 30.91/8.54 |-Branch two:
% 30.91/8.55 | (625) ~ (all_0_44_44 = e0)
% 30.91/8.55 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 30.91/8.55 |
% 30.91/8.55 +-Applying beta-rule and splitting (1128), into two cases.
% 30.91/8.55 |-Branch one:
% 30.91/8.55 | (454) all_0_45_45 = e0
% 30.91/8.55 |
% 30.91/8.55 | Combining equations (454,4011) yields a new equation:
% 30.91/8.55 | (14191) all_0_7_7 = e0
% 30.91/8.55 |
% 30.91/8.55 | Equations (454) can reduce 51 to:
% 30.91/8.55 | (232) ~ (all_0_41_41 = e0)
% 30.91/8.55 |
% 30.91/8.55 | Equations (454) can reduce 84 to:
% 30.91/8.55 | (455) ~ (all_0_43_43 = e0)
% 30.91/8.55 |
% 30.91/8.55 | Equations (454) can reduce 38 to:
% 30.91/8.55 | (1057) ~ (all_0_46_46 = e0)
% 30.91/8.55 |
% 30.91/8.55 | Simplifying 1057 yields:
% 30.91/8.55 | (1010) ~ (all_0_46_46 = e0)
% 30.91/8.55 |
% 30.91/8.55 | Equations (454) can reduce 434 to:
% 30.91/8.55 | (566) ~ (e2 = e0)
% 30.91/8.55 |
% 30.91/8.55 | Simplifying 566 yields:
% 30.91/8.55 | (57) ~ (e2 = e0)
% 30.91/8.55 |
% 30.91/8.55 +-Applying beta-rule and splitting (158), into two cases.
% 30.91/8.55 |-Branch one:
% 30.91/8.55 | (358) all_0_41_41 = e4
% 30.91/8.55 |
% 30.91/8.55 | Equations (358) can reduce 232 to:
% 30.91/8.55 | (6) ~ (e4 = e0)
% 30.91/8.55 |
% 30.91/8.55 +-Applying beta-rule and splitting (44), into two cases.
% 30.91/8.55 |-Branch one:
% 30.91/8.55 | (502) all_0_43_43 = e4
% 30.91/8.55 |
% 30.91/8.55 | Equations (502) can reduce 103 to:
% 30.91/8.55 | (804) ~ (all_0_46_46 = e4)
% 30.91/8.55 |
% 30.91/8.55 | Simplifying 804 yields:
% 30.91/8.55 | (805) ~ (all_0_46_46 = e4)
% 30.91/8.55 |
% 30.91/8.55 | Equations (502) can reduce 455 to:
% 30.91/8.55 | (6) ~ (e4 = e0)
% 30.91/8.55 |
% 30.91/8.55 | From (502) and (248) follows:
% 30.91/8.55 | (14204) op(e3, e3) = e4
% 30.91/8.55 |
% 30.91/8.55 +-Applying beta-rule and splitting (1523), into two cases.
% 30.91/8.55 |-Branch one:
% 30.91/8.55 | (1132) all_0_46_46 = e0
% 30.91/8.55 |
% 30.91/8.55 | Equations (1132) can reduce 1010 to:
% 30.91/8.55 | (270) $false
% 30.91/8.55 |
% 30.91/8.55 |-The branch is then unsatisfiable
% 30.91/8.55 |-Branch two:
% 30.91/8.55 | (1010) ~ (all_0_46_46 = e0)
% 30.91/8.55 | (1529) all_0_46_46 = e4 | all_0_46_46 = e3
% 30.91/8.55 |
% 30.91/8.55 +-Applying beta-rule and splitting (1529), into two cases.
% 30.91/8.55 |-Branch one:
% 30.91/8.55 | (1091) all_0_46_46 = e3
% 30.91/8.55 |
% 30.91/8.55 | Equations (1091) can reduce 805 to:
% 30.91/8.55 | (719) ~ (e4 = e3)
% 30.91/8.55 |
% 30.91/8.55 | Simplifying 719 yields:
% 30.91/8.55 | (34) ~ (e4 = e3)
% 30.91/8.55 |
% 30.91/8.55 | Equations (1091) can reduce 1436 to:
% 30.91/8.55 | (223) ~ (e3 = e2)
% 30.91/8.55 |
% 30.91/8.55 | Equations (1091) can reduce 106 to:
% 30.91/8.55 | (136) ~ (e3 = e1)
% 30.91/8.55 |
% 30.91/8.55 | Equations (1091) can reduce 1010 to:
% 30.91/8.55 | (66) ~ (e3 = e0)
% 30.91/8.55 |
% 30.91/8.55 | From (1091) and (74) follows:
% 30.91/8.55 | (14215) op(e3, e3) = all_0_33_33
% 30.91/8.55 |
% 30.91/8.55 | From (1091) and (242) follows:
% 30.91/8.55 | (14216) op(e3, e0) = e3
% 30.91/8.55 |
% 30.91/8.55 +-Applying beta-rule and splitting (762), into two cases.
% 30.91/8.55 |-Branch one:
% 30.91/8.55 | (552) all_0_48_48 = e1
% 30.91/8.55 |
% 30.91/8.55 | Combining equations (311,552) yields a new equation:
% 30.91/8.55 | (531) e2 = e1
% 30.91/8.55 |
% 30.91/8.55 | Simplifying 531 yields:
% 30.91/8.55 | (322) e2 = e1
% 30.91/8.55 |
% 30.91/8.55 | Equations (322) can reduce 141 to:
% 30.91/8.55 | (270) $false
% 30.91/8.55 |
% 30.91/8.55 |-The branch is then unsatisfiable
% 30.91/8.55 |-Branch two:
% 30.91/8.55 | (588) ~ (all_0_48_48 = e1)
% 30.91/8.55 | (4925) all_0_53_53 = e1 | all_0_58_58 = e1
% 30.91/8.55 |
% 30.91/8.55 +-Applying beta-rule and splitting (4925), into two cases.
% 30.91/8.55 |-Branch one:
% 30.91/8.55 | (853) all_0_53_53 = e1
% 30.91/8.55 |
% 30.91/8.55 | Combining equations (853,1114) yields a new equation:
% 30.91/8.55 | (538) e3 = e1
% 30.91/8.55 |
% 30.91/8.55 | Equations (538) can reduce 136 to:
% 30.91/8.55 | (270) $false
% 30.91/8.55 |
% 30.91/8.55 |-The branch is then unsatisfiable
% 30.91/8.55 |-Branch two:
% 30.91/8.55 | (874) ~ (all_0_53_53 = e1)
% 30.91/8.55 | (1001) all_0_58_58 = e1
% 30.91/8.55 |
% 30.91/8.55 | Equations (1001) can reduce 81 to:
% 30.91/8.55 | (995) ~ (all_0_56_56 = e1)
% 30.91/8.55 |
% 30.91/8.55 +-Applying beta-rule and splitting (236), into two cases.
% 30.91/8.55 |-Branch one:
% 30.91/8.55 | (764) all_0_56_56 = e3
% 30.91/8.55 |
% 30.91/8.55 | Equations (764) can reduce 995 to:
% 30.91/8.55 | (136) ~ (e3 = e1)
% 30.91/8.55 |
% 30.91/8.55 | From (764) and (239) follows:
% 30.91/8.55 | (14231) op(e3, e3) = all_0_11_11
% 30.91/8.55 |
% 30.91/8.55 | Instantiating formula (201) with e3, e3, all_0_33_33, all_0_11_11 and discharging atoms op(e3, e3) = all_0_11_11, op(e3, e3) = all_0_33_33, yields:
% 30.91/8.55 | (14232) all_0_11_11 = all_0_33_33
% 30.91/8.55 |
% 30.91/8.55 | Instantiating formula (201) with e3, e3, e4, all_0_11_11 and discharging atoms op(e3, e3) = all_0_11_11, op(e3, e3) = e4, yields:
% 30.91/8.55 | (14233) all_0_11_11 = e4
% 30.91/8.55 |
% 30.91/8.55 | Instantiating formula (201) with e3, e0, e3, all_0_9_9 and discharging atoms op(e3, e0) = all_0_9_9, op(e3, e0) = e3, yields:
% 30.91/8.55 | (14234) all_0_9_9 = e3
% 30.91/8.55 |
% 30.91/8.55 | Instantiating formula (201) with e0, e0, e4, all_0_20_20 and discharging atoms op(e0, e0) = all_0_20_20, op(e0, e0) = e4, yields:
% 30.91/8.55 | (14235) all_0_20_20 = e4
% 30.91/8.55 |
% 30.91/8.55 | Combining equations (14233,14232) yields a new equation:
% 30.91/8.55 | (11898) all_0_33_33 = e4
% 30.91/8.55 |
% 30.91/8.55 | Combining equations (11898,14232) yields a new equation:
% 30.91/8.55 | (14233) all_0_11_11 = e4
% 30.91/8.55 |
% 30.91/8.55 | Equations (14235) can reduce 1764 to:
% 30.91/8.55 | (231) ~ (e4 = e2)
% 30.91/8.55 |
% 30.91/8.55 +-Applying beta-rule and splitting (234), into two cases.
% 30.91/8.55 |-Branch one:
% 30.91/8.55 | (4239) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3)) | (all_0_9_9 = e1 & ~ (all_0_10_10 = e3))
% 30.91/8.55 |
% 30.91/8.55 +-Applying beta-rule and splitting (4239), into two cases.
% 30.91/8.55 |-Branch one:
% 30.91/8.55 | (4240) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3))
% 30.91/8.55 |
% 30.91/8.55 +-Applying beta-rule and splitting (4240), into two cases.
% 30.91/8.55 |-Branch one:
% 30.91/8.55 | (4241) all_0_4_4 = e4 & ~ (all_0_5_5 = e3)
% 30.91/8.55 |
% 30.91/8.55 | Applying alpha-rule on (4241) yields:
% 30.91/8.56 | (4242) all_0_4_4 = e4
% 30.91/8.56 | (4243) ~ (all_0_5_5 = e3)
% 30.91/8.56 |
% 30.91/8.56 | Combining equations (4242,12701) yields a new equation:
% 30.91/8.56 | (268) e4 = e2
% 30.91/8.56 |
% 30.91/8.56 | Simplifying 268 yields:
% 30.91/8.56 | (269) e4 = e2
% 30.91/8.56 |
% 30.91/8.56 | Equations (269) can reduce 231 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (4247) all_0_7_7 = e2 & ~ (all_0_8_8 = e3)
% 30.91/8.56 |
% 30.91/8.56 | Applying alpha-rule on (4247) yields:
% 30.91/8.56 | (4248) all_0_7_7 = e2
% 30.91/8.56 | (4249) ~ (all_0_8_8 = e3)
% 30.91/8.56 |
% 30.91/8.56 | Combining equations (14191,4248) yields a new equation:
% 30.91/8.56 | (316) e2 = e0
% 30.91/8.56 |
% 30.91/8.56 | Equations (316) can reduce 57 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (4253) all_0_9_9 = e1 & ~ (all_0_10_10 = e3)
% 30.91/8.56 |
% 30.91/8.56 | Applying alpha-rule on (4253) yields:
% 30.91/8.56 | (4254) all_0_9_9 = e1
% 30.91/8.56 | (4255) ~ (all_0_10_10 = e3)
% 30.91/8.56 |
% 30.91/8.56 | Combining equations (4254,14234) yields a new equation:
% 30.91/8.56 | (538) e3 = e1
% 30.91/8.56 |
% 30.91/8.56 | Equations (538) can reduce 136 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (4378) all_0_11_11 = e0 & ~ (all_0_12_12 = e3)
% 30.91/8.56 |
% 30.91/8.56 | Applying alpha-rule on (4378) yields:
% 30.91/8.56 | (4379) all_0_11_11 = e0
% 30.91/8.56 | (4380) ~ (all_0_12_12 = e3)
% 30.91/8.56 |
% 30.91/8.56 | Combining equations (14233,4379) yields a new equation:
% 30.91/8.56 | (478) e4 = e0
% 30.91/8.56 |
% 30.91/8.56 | Simplifying 478 yields:
% 30.91/8.56 | (479) e4 = e0
% 30.91/8.56 |
% 30.91/8.56 | Equations (479) can reduce 6 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (767) ~ (all_0_56_56 = e3)
% 30.91/8.56 | (768) all_0_57_57 = e3 | all_0_58_58 = e3 | all_0_59_59 = e3
% 30.91/8.56 |
% 30.91/8.56 +-Applying beta-rule and splitting (178), into two cases.
% 30.91/8.56 |-Branch one:
% 30.91/8.56 | (751) all_0_39_39 = e3
% 30.91/8.56 |
% 30.91/8.56 | Combining equations (751,336) yields a new equation:
% 30.91/8.56 | (437) e3 = e2
% 30.91/8.56 |
% 30.91/8.56 | Simplifying 437 yields:
% 30.91/8.56 | (414) e3 = e2
% 30.91/8.56 |
% 30.91/8.56 | Equations (414) can reduce 223 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (755) ~ (all_0_39_39 = e3)
% 30.91/8.56 | (756) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 30.91/8.56 |
% 30.91/8.56 +-Applying beta-rule and splitting (756), into two cases.
% 30.91/8.56 |-Branch one:
% 30.91/8.56 | (782) all_0_43_43 = e3
% 30.91/8.56 |
% 30.91/8.56 | Combining equations (502,782) yields a new equation:
% 30.91/8.56 | (660) e4 = e3
% 30.91/8.56 |
% 30.91/8.56 | Simplifying 660 yields:
% 30.91/8.56 | (359) e4 = e3
% 30.91/8.56 |
% 30.91/8.56 | Equations (359) can reduce 34 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (786) ~ (all_0_43_43 = e3)
% 30.91/8.56 | (799) all_0_51_51 = e3 | all_0_56_56 = e3
% 30.91/8.56 |
% 30.91/8.56 +-Applying beta-rule and splitting (799), into two cases.
% 30.91/8.56 |-Branch one:
% 30.91/8.56 | (824) all_0_51_51 = e3
% 30.91/8.56 |
% 30.91/8.56 | Combining equations (954,824) yields a new equation:
% 30.91/8.56 | (784) e3 = e0
% 30.91/8.56 |
% 30.91/8.56 | Equations (784) can reduce 66 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (932) ~ (all_0_51_51 = e3)
% 30.91/8.56 | (764) all_0_56_56 = e3
% 30.91/8.56 |
% 30.91/8.56 | Equations (764) can reduce 767 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (413) ~ (all_0_46_46 = e3)
% 30.91/8.56 | (517) all_0_46_46 = e4
% 30.91/8.56 |
% 30.91/8.56 | Equations (517) can reduce 805 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (510) ~ (all_0_43_43 = e4)
% 30.91/8.56 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 30.91/8.56 |
% 30.91/8.56 +-Applying beta-rule and splitting (1523), into two cases.
% 30.91/8.56 |-Branch one:
% 30.91/8.56 | (1132) all_0_46_46 = e0
% 30.91/8.56 |
% 30.91/8.56 | Equations (1132) can reduce 1010 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (1010) ~ (all_0_46_46 = e0)
% 30.91/8.56 | (1529) all_0_46_46 = e4 | all_0_46_46 = e3
% 30.91/8.56 |
% 30.91/8.56 +-Applying beta-rule and splitting (1529), into two cases.
% 30.91/8.56 |-Branch one:
% 30.91/8.56 | (1091) all_0_46_46 = e3
% 30.91/8.56 |
% 30.91/8.56 | Equations (1091) can reduce 805 to:
% 30.91/8.56 | (719) ~ (e4 = e3)
% 30.91/8.56 |
% 30.91/8.56 | Simplifying 719 yields:
% 30.91/8.56 | (34) ~ (e4 = e3)
% 30.91/8.56 |
% 30.91/8.56 +-Applying beta-rule and splitting (511), into two cases.
% 30.91/8.56 |-Branch one:
% 30.91/8.56 | (363) all_0_45_45 = e4
% 30.91/8.56 |
% 30.91/8.56 | Combining equations (454,363) yields a new equation:
% 30.91/8.56 | (479) e4 = e0
% 30.91/8.56 |
% 30.91/8.56 | Equations (479) can reduce 6 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (352) ~ (all_0_45_45 = e4)
% 30.91/8.56 | (517) all_0_46_46 = e4
% 30.91/8.56 |
% 30.91/8.56 | Combining equations (1091,517) yields a new equation:
% 30.91/8.56 | (359) e4 = e3
% 30.91/8.56 |
% 30.91/8.56 | Equations (359) can reduce 34 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (413) ~ (all_0_46_46 = e3)
% 30.91/8.56 | (517) all_0_46_46 = e4
% 30.91/8.56 |
% 30.91/8.56 | Equations (517) can reduce 805 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (361) ~ (all_0_41_41 = e4)
% 30.91/8.56 | (362) all_0_45_45 = e4 | all_0_53_53 = e4 | all_0_58_58 = e4
% 30.91/8.56 |
% 30.91/8.56 +-Applying beta-rule and splitting (362), into two cases.
% 30.91/8.56 |-Branch one:
% 30.91/8.56 | (363) all_0_45_45 = e4
% 30.91/8.56 |
% 30.91/8.56 | Combining equations (454,363) yields a new equation:
% 30.91/8.56 | (479) e4 = e0
% 30.91/8.56 |
% 30.91/8.56 | Equations (479) can reduce 6 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (352) ~ (all_0_45_45 = e4)
% 30.91/8.56 | (366) all_0_53_53 = e4 | all_0_58_58 = e4
% 30.91/8.56 |
% 30.91/8.56 +-Applying beta-rule and splitting (366), into two cases.
% 30.91/8.56 |-Branch one:
% 30.91/8.56 | (367) all_0_53_53 = e4
% 30.91/8.56 |
% 30.91/8.56 | Combining equations (1114,367) yields a new equation:
% 30.91/8.56 | (359) e4 = e3
% 30.91/8.56 |
% 30.91/8.56 | Equations (359) can reduce 34 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (599) ~ (all_0_53_53 = e4)
% 30.91/8.56 | (600) all_0_58_58 = e4
% 30.91/8.56 |
% 30.91/8.56 | Equations (600) can reduce 278 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (488) ~ (all_0_45_45 = e0)
% 30.91/8.56 | (1132) all_0_46_46 = e0
% 30.91/8.56 |
% 30.91/8.56 | Equations (1132) can reduce 1010 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (640) ~ (all_0_42_42 = e1)
% 30.91/8.56 | (4628) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 30.91/8.56 |
% 30.91/8.56 +-Applying beta-rule and splitting (592), into two cases.
% 30.91/8.56 |-Branch one:
% 30.91/8.56 | (358) all_0_41_41 = e4
% 30.91/8.56 |
% 30.91/8.56 | Equations (358) can reduce 157 to:
% 30.91/8.56 | (277) ~ (all_0_58_58 = e4)
% 30.91/8.56 |
% 30.91/8.56 | Simplifying 277 yields:
% 30.91/8.56 | (278) ~ (all_0_58_58 = e4)
% 30.91/8.56 |
% 30.91/8.56 +-Applying beta-rule and splitting (52), into two cases.
% 30.91/8.56 |-Branch one:
% 30.91/8.56 | (536) all_0_41_41 = e1
% 30.91/8.56 |
% 30.91/8.56 | Combining equations (358,536) yields a new equation:
% 30.91/8.56 | (525) e4 = e1
% 30.91/8.56 |
% 30.91/8.56 | Simplifying 525 yields:
% 30.91/8.56 | (526) e4 = e1
% 30.91/8.56 |
% 30.91/8.56 | Equations (526) can reduce 251 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (540) ~ (all_0_41_41 = e1)
% 30.91/8.56 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 30.91/8.56 |
% 30.91/8.56 +-Applying beta-rule and splitting (762), into two cases.
% 30.91/8.56 |-Branch one:
% 30.91/8.56 | (552) all_0_48_48 = e1
% 30.91/8.56 |
% 30.91/8.56 | Combining equations (311,552) yields a new equation:
% 30.91/8.56 | (531) e2 = e1
% 30.91/8.56 |
% 30.91/8.56 | Simplifying 531 yields:
% 30.91/8.56 | (322) e2 = e1
% 30.91/8.56 |
% 30.91/8.56 | Equations (322) can reduce 141 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (588) ~ (all_0_48_48 = e1)
% 30.91/8.56 | (4925) all_0_53_53 = e1 | all_0_58_58 = e1
% 30.91/8.56 |
% 30.91/8.56 +-Applying beta-rule and splitting (4925), into two cases.
% 30.91/8.56 |-Branch one:
% 30.91/8.56 | (853) all_0_53_53 = e1
% 30.91/8.56 |
% 30.91/8.56 | Combining equations (1114,853) yields a new equation:
% 30.91/8.56 | (537) e3 = e1
% 30.91/8.56 |
% 30.91/8.56 | Simplifying 537 yields:
% 30.91/8.56 | (538) e3 = e1
% 30.91/8.56 |
% 30.91/8.56 | Equations (538) can reduce 136 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (874) ~ (all_0_53_53 = e1)
% 30.91/8.56 | (1001) all_0_58_58 = e1
% 30.91/8.56 |
% 30.91/8.56 | Equations (1001) can reduce 278 to:
% 30.91/8.56 | (1021) ~ (e4 = e1)
% 30.91/8.56 |
% 30.91/8.56 | Simplifying 1021 yields:
% 30.91/8.56 | (251) ~ (e4 = e1)
% 30.91/8.56 |
% 30.91/8.56 | Equations (1001) can reduce 376 to:
% 30.91/8.56 | (645) ~ (e2 = e1)
% 30.91/8.56 |
% 30.91/8.56 | Simplifying 645 yields:
% 30.91/8.56 | (141) ~ (e2 = e1)
% 30.91/8.56 |
% 30.91/8.56 | Equations (1001) can reduce 431 to:
% 30.91/8.56 | (132) ~ (e1 = e0)
% 30.91/8.56 |
% 30.91/8.56 +-Applying beta-rule and splitting (4628), into two cases.
% 30.91/8.56 |-Branch one:
% 30.91/8.56 | (589) all_0_49_49 = e1
% 30.91/8.56 |
% 30.91/8.56 | Combining equations (589,563) yields a new equation:
% 30.91/8.56 | (571) e1 = e0
% 30.91/8.56 |
% 30.91/8.56 | Simplifying 571 yields:
% 30.91/8.56 | (560) e1 = e0
% 30.91/8.56 |
% 30.91/8.56 | Equations (560) can reduce 132 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (543) ~ (all_0_49_49 = e1)
% 30.91/8.56 | (4726) all_0_54_54 = e1 | all_0_59_59 = e1
% 30.91/8.56 |
% 30.91/8.56 +-Applying beta-rule and splitting (4726), into two cases.
% 30.91/8.56 |-Branch one:
% 30.91/8.56 | (875) all_0_54_54 = e1
% 30.91/8.56 |
% 30.91/8.56 | Combining equations (3657,875) yields a new equation:
% 30.91/8.56 | (531) e2 = e1
% 30.91/8.56 |
% 30.91/8.56 | Simplifying 531 yields:
% 30.91/8.56 | (322) e2 = e1
% 30.91/8.56 |
% 30.91/8.56 | Equations (322) can reduce 141 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (425) ~ (all_0_54_54 = e1)
% 30.91/8.56 | (424) all_0_59_59 = e1
% 30.91/8.56 |
% 30.91/8.56 | Combining equations (424,402) yields a new equation:
% 30.91/8.56 | (526) e4 = e1
% 30.91/8.56 |
% 30.91/8.56 | Equations (526) can reduce 251 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (361) ~ (all_0_41_41 = e4)
% 30.91/8.56 | (512) all_0_42_42 = e4
% 30.91/8.56 |
% 30.91/8.56 | Equations (512) can reduce 520 to:
% 30.91/8.56 | (270) $false
% 30.91/8.56 |
% 30.91/8.56 |-The branch is then unsatisfiable
% 30.91/8.56 |-Branch two:
% 30.91/8.56 | (280) ~ (all_0_59_59 = e4)
% 30.91/8.56 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 30.91/8.56 |
% 30.91/8.56 +-Applying beta-rule and splitting (407), into two cases.
% 30.91/8.56 |-Branch one:
% 30.91/8.56 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 30.91/8.56 |
% 30.91/8.56 +-Applying beta-rule and splitting (408), into two cases.
% 30.91/8.56 |-Branch one:
% 30.91/8.56 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 30.91/8.56 |
% 30.91/8.56 +-Applying beta-rule and splitting (409), into two cases.
% 30.91/8.56 |-Branch one:
% 30.91/8.57 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 30.91/8.57 |
% 30.91/8.57 | Applying alpha-rule on (410) yields:
% 30.91/8.57 | (411) all_0_43_43 = e0
% 30.91/8.57 | (412) all_0_59_59 = e3
% 30.91/8.57 | (413) ~ (all_0_46_46 = e3)
% 30.91/8.57 |
% 30.91/8.57 | Equations (411) can reduce 455 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 30.91/8.57 |
% 30.91/8.57 | Applying alpha-rule on (416) yields:
% 30.91/8.57 | (411) all_0_43_43 = e0
% 30.91/8.57 | (412) all_0_59_59 = e3
% 30.91/8.57 | (419) ~ (all_0_56_56 = e0)
% 30.91/8.57 |
% 30.91/8.57 | Equations (411) can reduce 455 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 30.91/8.57 |
% 30.91/8.57 | Applying alpha-rule on (422) yields:
% 30.91/8.57 | (423) all_0_53_53 = e0
% 30.91/8.57 | (424) all_0_59_59 = e1
% 30.91/8.57 | (425) ~ (all_0_54_54 = e1)
% 30.91/8.57 |
% 30.91/8.57 | Combining equations (423,1114) yields a new equation:
% 30.91/8.57 | (784) e3 = e0
% 30.91/8.57 |
% 30.91/8.57 | Equations (784) can reduce 66 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 30.91/8.57 |
% 30.91/8.57 | Applying alpha-rule on (428) yields:
% 30.91/8.57 | (423) all_0_53_53 = e0
% 30.91/8.57 | (424) all_0_59_59 = e1
% 30.91/8.57 | (431) ~ (all_0_58_58 = e0)
% 30.91/8.57 |
% 30.91/8.57 | Combining equations (423,1114) yields a new equation:
% 30.91/8.57 | (784) e3 = e0
% 30.91/8.57 |
% 30.91/8.57 | Equations (784) can reduce 66 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (987) ~ (all_0_51_51 = e0)
% 30.91/8.57 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 30.91/8.57 |
% 30.91/8.57 +-Applying beta-rule and splitting (182), into two cases.
% 30.91/8.57 |-Branch one:
% 30.91/8.57 | (454) all_0_45_45 = e0
% 30.91/8.57 |
% 30.91/8.57 | Equations (454) can reduce 84 to:
% 30.91/8.57 | (455) ~ (all_0_43_43 = e0)
% 30.91/8.57 |
% 30.91/8.57 | Equations (454) can reduce 26 to:
% 30.91/8.57 | (568) ~ (e1 = e0)
% 30.91/8.57 |
% 30.91/8.57 | Simplifying 568 yields:
% 30.91/8.57 | (132) ~ (e1 = e0)
% 30.91/8.57 |
% 30.91/8.57 +-Applying beta-rule and splitting (75), into two cases.
% 30.91/8.57 |-Branch one:
% 30.91/8.57 | (411) all_0_43_43 = e0
% 30.91/8.57 |
% 30.91/8.57 | Equations (411) can reduce 455 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (455) ~ (all_0_43_43 = e0)
% 30.91/8.57 | (940) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 30.91/8.57 |
% 30.91/8.57 +-Applying beta-rule and splitting (3067), into two cases.
% 30.91/8.57 |-Branch one:
% 30.91/8.57 | (827) all_0_52_52 = e0
% 30.91/8.57 |
% 30.91/8.57 | Combining equations (827,848) yields a new equation:
% 30.91/8.57 | (560) e1 = e0
% 30.91/8.57 |
% 30.91/8.57 | Equations (560) can reduce 132 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (925) ~ (all_0_52_52 = e0)
% 30.91/8.57 | (3073) all_0_53_53 = e0 | all_0_54_54 = e0
% 30.91/8.57 |
% 30.91/8.57 | Equations (848) can reduce 925 to:
% 30.91/8.57 | (132) ~ (e1 = e0)
% 30.91/8.57 |
% 30.91/8.57 +-Applying beta-rule and splitting (940), into two cases.
% 30.91/8.57 |-Branch one:
% 30.91/8.57 | (315) all_0_47_47 = e0
% 30.91/8.57 |
% 30.91/8.57 | Combining equations (321,315) yields a new equation:
% 30.91/8.57 | (571) e1 = e0
% 30.91/8.57 |
% 30.91/8.57 | Simplifying 571 yields:
% 30.91/8.57 | (560) e1 = e0
% 30.91/8.57 |
% 30.91/8.57 | Equations (560) can reduce 132 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (318) ~ (all_0_47_47 = e0)
% 30.91/8.57 | (950) all_0_51_51 = e0 | all_0_56_56 = e0
% 30.91/8.57 |
% 30.91/8.57 +-Applying beta-rule and splitting (173), into two cases.
% 30.91/8.57 |-Branch one:
% 30.91/8.57 | (4215) all_0_51_51 = e2
% 30.91/8.57 |
% 30.91/8.57 | Equations (4215) can reduce 255 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (255) ~ (all_0_51_51 = e2)
% 30.91/8.57 | (4888) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1 | all_0_51_51 = e0
% 30.91/8.57 |
% 30.91/8.57 +-Applying beta-rule and splitting (4888), into two cases.
% 30.91/8.57 |-Branch one:
% 30.91/8.57 | (954) all_0_51_51 = e0
% 30.91/8.57 |
% 30.91/8.57 | Equations (954) can reduce 987 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (987) ~ (all_0_51_51 = e0)
% 30.91/8.57 | (5003) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1
% 30.91/8.57 |
% 30.91/8.57 +-Applying beta-rule and splitting (950), into two cases.
% 30.91/8.57 |-Branch one:
% 30.91/8.57 | (954) all_0_51_51 = e0
% 30.91/8.57 |
% 30.91/8.57 | Equations (954) can reduce 987 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (987) ~ (all_0_51_51 = e0)
% 30.91/8.57 | (830) all_0_56_56 = e0
% 30.91/8.57 |
% 30.91/8.57 | Equations (830) can reduce 419 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (488) ~ (all_0_45_45 = e0)
% 30.91/8.57 | (558) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 30.91/8.57 |
% 30.91/8.57 +-Applying beta-rule and splitting (558), into two cases.
% 30.91/8.57 |-Branch one:
% 30.91/8.57 | (559) all_0_48_48 = e0
% 30.91/8.57 |
% 30.91/8.57 | Combining equations (311,559) yields a new equation:
% 30.91/8.57 | (622) e2 = e0
% 30.91/8.57 |
% 30.91/8.57 | Simplifying 622 yields:
% 30.91/8.57 | (316) e2 = e0
% 30.91/8.57 |
% 30.91/8.57 | Equations (316) can reduce 57 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (562) ~ (all_0_48_48 = e0)
% 30.91/8.57 | (575) all_0_53_53 = e0 | all_0_58_58 = e0
% 30.91/8.57 |
% 30.91/8.57 +-Applying beta-rule and splitting (575), into two cases.
% 30.91/8.57 |-Branch one:
% 30.91/8.57 | (423) all_0_53_53 = e0
% 30.91/8.57 |
% 30.91/8.57 | Combining equations (423,1114) yields a new equation:
% 30.91/8.57 | (784) e3 = e0
% 30.91/8.57 |
% 30.91/8.57 | Equations (784) can reduce 66 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (584) ~ (all_0_53_53 = e0)
% 30.91/8.57 | (585) all_0_58_58 = e0
% 30.91/8.57 |
% 30.91/8.57 | Equations (585) can reduce 431 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (642) ~ (all_0_52_52 = e1)
% 30.91/8.57 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 30.91/8.57 |
% 30.91/8.57 +-Applying beta-rule and splitting (3352), into two cases.
% 30.91/8.57 |-Branch one:
% 30.91/8.57 | (848) all_0_52_52 = e1
% 30.91/8.57 |
% 30.91/8.57 | Equations (848) can reduce 642 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (642) ~ (all_0_52_52 = e1)
% 30.91/8.57 | (997) all_0_57_57 = e1
% 30.91/8.57 |
% 30.91/8.57 | Equations (997) can reduce 37 to:
% 30.91/8.57 | (7725) ~ (all_0_58_58 = e1)
% 30.91/8.57 |
% 30.91/8.57 | Simplifying 7725 yields:
% 30.91/8.57 | (1004) ~ (all_0_58_58 = e1)
% 30.91/8.57 |
% 30.91/8.57 | Equations (997) can reduce 140 to:
% 30.91/8.57 | (749) ~ (all_0_59_59 = e1)
% 30.91/8.57 |
% 30.91/8.57 | Simplifying 749 yields:
% 30.91/8.57 | (750) ~ (all_0_59_59 = e1)
% 30.91/8.57 |
% 30.91/8.57 | Equations (997) can reduce 143 to:
% 30.91/8.57 | (1021) ~ (e4 = e1)
% 30.91/8.57 |
% 30.91/8.57 | Simplifying 1021 yields:
% 30.91/8.57 | (251) ~ (e4 = e1)
% 30.91/8.57 |
% 30.91/8.57 | Equations (997) can reduce 846 to:
% 30.91/8.57 | (769) ~ (e3 = e1)
% 30.91/8.57 |
% 30.91/8.57 | Simplifying 769 yields:
% 30.91/8.57 | (136) ~ (e3 = e1)
% 30.91/8.57 |
% 30.91/8.57 | Equations (997) can reduce 335 to:
% 30.91/8.57 | (645) ~ (e2 = e1)
% 30.91/8.57 |
% 30.91/8.57 | Simplifying 645 yields:
% 30.91/8.57 | (141) ~ (e2 = e1)
% 30.91/8.57 |
% 30.91/8.57 +-Applying beta-rule and splitting (52), into two cases.
% 30.91/8.57 |-Branch one:
% 30.91/8.57 | (536) all_0_41_41 = e1
% 30.91/8.57 |
% 30.91/8.57 | Equations (536) can reduce 94 to:
% 30.91/8.57 | (639) ~ (all_0_42_42 = e1)
% 30.91/8.57 |
% 30.91/8.57 | Simplifying 639 yields:
% 30.91/8.57 | (640) ~ (all_0_42_42 = e1)
% 30.91/8.57 |
% 30.91/8.57 | Equations (536) can reduce 331 to:
% 30.91/8.57 | (645) ~ (e2 = e1)
% 30.91/8.57 |
% 30.91/8.57 | Simplifying 645 yields:
% 30.91/8.57 | (141) ~ (e2 = e1)
% 30.91/8.57 |
% 30.91/8.57 | Equations (536) can reduce 232 to:
% 30.91/8.57 | (132) ~ (e1 = e0)
% 30.91/8.57 |
% 30.91/8.57 +-Applying beta-rule and splitting (592), into two cases.
% 30.91/8.57 |-Branch one:
% 30.91/8.57 | (358) all_0_41_41 = e4
% 30.91/8.57 |
% 30.91/8.57 | Combining equations (536,358) yields a new equation:
% 30.91/8.57 | (526) e4 = e1
% 30.91/8.57 |
% 30.91/8.57 | Equations (526) can reduce 251 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (361) ~ (all_0_41_41 = e4)
% 30.91/8.57 | (512) all_0_42_42 = e4
% 30.91/8.57 |
% 30.91/8.57 | Equations (512) can reduce 640 to:
% 30.91/8.57 | (251) ~ (e4 = e1)
% 30.91/8.57 |
% 30.91/8.57 +-Applying beta-rule and splitting (127), into two cases.
% 30.91/8.57 |-Branch one:
% 30.91/8.57 | (541) all_0_42_42 = e1
% 30.91/8.57 |
% 30.91/8.57 | Combining equations (512,541) yields a new equation:
% 30.91/8.57 | (525) e4 = e1
% 30.91/8.57 |
% 30.91/8.57 | Simplifying 525 yields:
% 30.91/8.57 | (526) e4 = e1
% 30.91/8.57 |
% 30.91/8.57 | Equations (526) can reduce 251 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (640) ~ (all_0_42_42 = e1)
% 30.91/8.57 | (4628) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 30.91/8.57 |
% 30.91/8.57 +-Applying beta-rule and splitting (4628), into two cases.
% 30.91/8.57 |-Branch one:
% 30.91/8.57 | (589) all_0_49_49 = e1
% 30.91/8.57 |
% 30.91/8.57 | Combining equations (589,563) yields a new equation:
% 30.91/8.57 | (571) e1 = e0
% 30.91/8.57 |
% 30.91/8.57 | Simplifying 571 yields:
% 30.91/8.57 | (560) e1 = e0
% 30.91/8.57 |
% 30.91/8.57 | Equations (560) can reduce 132 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (543) ~ (all_0_49_49 = e1)
% 30.91/8.57 | (4726) all_0_54_54 = e1 | all_0_59_59 = e1
% 30.91/8.57 |
% 30.91/8.57 +-Applying beta-rule and splitting (4726), into two cases.
% 30.91/8.57 |-Branch one:
% 30.91/8.57 | (875) all_0_54_54 = e1
% 30.91/8.57 |
% 30.91/8.57 | Combining equations (875,3657) yields a new equation:
% 30.91/8.57 | (322) e2 = e1
% 30.91/8.57 |
% 30.91/8.57 | Equations (322) can reduce 141 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (425) ~ (all_0_54_54 = e1)
% 30.91/8.57 | (424) all_0_59_59 = e1
% 30.91/8.57 |
% 30.91/8.57 | Equations (424) can reduce 750 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (540) ~ (all_0_41_41 = e1)
% 30.91/8.57 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 30.91/8.57 |
% 30.91/8.57 +-Applying beta-rule and splitting (762), into two cases.
% 30.91/8.57 |-Branch one:
% 30.91/8.57 | (552) all_0_48_48 = e1
% 30.91/8.57 |
% 30.91/8.57 | Combining equations (552,311) yields a new equation:
% 30.91/8.57 | (322) e2 = e1
% 30.91/8.57 |
% 30.91/8.57 | Equations (322) can reduce 141 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (588) ~ (all_0_48_48 = e1)
% 30.91/8.57 | (4925) all_0_53_53 = e1 | all_0_58_58 = e1
% 30.91/8.57 |
% 30.91/8.57 +-Applying beta-rule and splitting (4925), into two cases.
% 30.91/8.57 |-Branch one:
% 30.91/8.57 | (853) all_0_53_53 = e1
% 30.91/8.57 |
% 30.91/8.57 | Combining equations (1114,853) yields a new equation:
% 30.91/8.57 | (537) e3 = e1
% 30.91/8.57 |
% 30.91/8.57 | Simplifying 537 yields:
% 30.91/8.57 | (538) e3 = e1
% 30.91/8.57 |
% 30.91/8.57 | Equations (538) can reduce 136 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (874) ~ (all_0_53_53 = e1)
% 30.91/8.57 | (1001) all_0_58_58 = e1
% 30.91/8.57 |
% 30.91/8.57 | Equations (1001) can reduce 1004 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (356) ~ (all_0_53_53 = e3)
% 30.91/8.57 | (1119) all_0_54_54 = e3
% 30.91/8.57 |
% 30.91/8.57 | Combining equations (1119,3657) yields a new equation:
% 30.91/8.57 | (437) e3 = e2
% 30.91/8.57 |
% 30.91/8.57 | Simplifying 437 yields:
% 30.91/8.57 | (414) e3 = e2
% 30.91/8.57 |
% 30.91/8.57 | Equations (414) can reduce 223 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (675) ~ (all_0_40_40 = e3)
% 30.91/8.57 | (530) all_0_40_40 = e1
% 30.91/8.57 |
% 30.91/8.57 | Equations (530) can reduce 534 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (261) ~ (all_0_54_54 = e2)
% 30.91/8.57 | (399) all_0_59_59 = e2
% 30.91/8.57 |
% 30.91/8.57 | Equations (399) can reduce 701 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (291) ~ (all_0_39_39 = e2)
% 30.91/8.57 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 30.91/8.57 |
% 30.91/8.57 +-Applying beta-rule and splitting (164), into two cases.
% 30.91/8.57 |-Branch one:
% 30.91/8.57 | (336) all_0_39_39 = e2
% 30.91/8.57 |
% 30.91/8.57 | Equations (336) can reduce 291 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (291) ~ (all_0_39_39 = e2)
% 30.91/8.57 | (630) all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 30.91/8.57 |
% 30.91/8.57 +-Applying beta-rule and splitting (96), into two cases.
% 30.91/8.57 |-Branch one:
% 30.91/8.57 | (336) all_0_39_39 = e2
% 30.91/8.57 |
% 30.91/8.57 | Equations (336) can reduce 291 to:
% 30.91/8.57 | (270) $false
% 30.91/8.57 |
% 30.91/8.57 |-The branch is then unsatisfiable
% 30.91/8.57 |-Branch two:
% 30.91/8.57 | (291) ~ (all_0_39_39 = e2)
% 30.91/8.57 | (4205) all_0_43_43 = e2 | all_0_47_47 = e2 | all_0_51_51 = e2 | all_0_56_56 = e2
% 30.91/8.57 |
% 30.91/8.57 +-Applying beta-rule and splitting (4205), into two cases.
% 30.91/8.57 |-Branch one:
% 30.91/8.57 | (450) all_0_43_43 = e2
% 30.91/8.57 |
% 30.91/8.58 | Equations (450) can reduce 292 to:
% 30.91/8.58 | (270) $false
% 30.91/8.58 |
% 30.91/8.58 |-The branch is then unsatisfiable
% 30.91/8.58 |-Branch two:
% 30.91/8.58 | (292) ~ (all_0_43_43 = e2)
% 30.91/8.58 | (4209) all_0_47_47 = e2 | all_0_51_51 = e2 | all_0_56_56 = e2
% 30.91/8.58 |
% 30.91/8.58 +-Applying beta-rule and splitting (4209), into two cases.
% 30.91/8.58 |-Branch one:
% 30.91/8.58 | (290) all_0_47_47 = e2
% 30.91/8.58 |
% 30.91/8.58 | Combining equations (321,290) yields a new equation:
% 30.91/8.58 | (322) e2 = e1
% 30.91/8.58 |
% 30.91/8.58 | Equations (322) can reduce 141 to:
% 30.91/8.58 | (270) $false
% 30.91/8.58 |
% 30.91/8.58 |-The branch is then unsatisfiable
% 30.91/8.58 |-Branch two:
% 30.91/8.58 | (3951) ~ (all_0_47_47 = e2)
% 30.91/8.58 | (4214) all_0_51_51 = e2 | all_0_56_56 = e2
% 30.91/8.58 |
% 30.91/8.58 +-Applying beta-rule and splitting (339), into two cases.
% 30.91/8.58 |-Branch one:
% 30.91/8.58 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 30.91/8.58 |
% 30.91/8.58 +-Applying beta-rule and splitting (340), into two cases.
% 30.91/8.58 |-Branch one:
% 30.91/8.58 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 30.91/8.58 |
% 30.91/8.58 | Applying alpha-rule on (341) yields:
% 30.91/8.58 | (342) all_0_0_0 = e1
% 30.91/8.58 | (343) ~ (all_0_1_1 = e4)
% 30.91/8.58 |
% 30.91/8.58 | Combining equations (342,9064) yields a new equation:
% 30.91/8.58 | (571) e1 = e0
% 30.91/8.58 |
% 30.91/8.58 | Simplifying 571 yields:
% 30.91/8.58 | (560) e1 = e0
% 30.91/8.58 |
% 30.91/8.58 | Equations (560) can reduce 132 to:
% 30.91/8.58 | (270) $false
% 30.91/8.58 |
% 30.91/8.58 |-The branch is then unsatisfiable
% 30.91/8.58 |-Branch two:
% 30.91/8.58 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 30.91/8.58 |
% 30.91/8.58 | Applying alpha-rule on (346) yields:
% 30.91/8.58 | (347) all_0_2_2 = e0
% 30.91/8.58 | (348) ~ (all_0_3_3 = e4)
% 30.91/8.58 |
% 30.91/8.58 | Combining equations (9065,347) yields a new equation:
% 30.91/8.58 | (11698) all_0_40_40 = e0
% 30.91/8.58 |
% 30.91/8.58 | Simplifying 11698 yields:
% 30.98/8.58 | (11467) all_0_40_40 = e0
% 30.98/8.58 |
% 30.98/8.58 | Equations (11467) can reduce 238 to:
% 30.98/8.58 | (270) $false
% 30.98/8.58 |
% 30.98/8.58 |-The branch is then unsatisfiable
% 30.98/8.58 |-Branch two:
% 30.98/8.58 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 30.98/8.58 |
% 30.98/8.58 | Applying alpha-rule on (350) yields:
% 30.98/8.58 | (351) all_0_41_41 = e3
% 30.98/8.58 | (352) ~ (all_0_45_45 = e4)
% 30.98/8.58 |
% 30.98/8.58 | Equations (351) can reduce 226 to:
% 30.98/8.58 | (755) ~ (all_0_39_39 = e3)
% 30.98/8.58 |
% 30.98/8.58 | Equations (351) can reduce 147 to:
% 30.98/8.58 | (675) ~ (all_0_40_40 = e3)
% 30.98/8.58 |
% 30.98/8.58 | Equations (351) can reduce 214 to:
% 30.98/8.58 | (355) ~ (all_0_53_53 = e3)
% 30.98/8.58 |
% 30.98/8.58 | Simplifying 355 yields:
% 30.98/8.58 | (356) ~ (all_0_53_53 = e3)
% 30.98/8.58 |
% 30.98/8.58 +-Applying beta-rule and splitting (177), into two cases.
% 30.98/8.58 |-Branch one:
% 30.98/8.58 | (336) all_0_39_39 = e2
% 30.98/8.58 |
% 30.98/8.58 | Equations (336) can reduce 291 to:
% 30.98/8.58 | (270) $false
% 30.98/8.58 |
% 30.98/8.58 |-The branch is then unsatisfiable
% 30.98/8.58 |-Branch two:
% 30.98/8.58 | (291) ~ (all_0_39_39 = e2)
% 30.98/8.58 | (684) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 30.98/8.58 |
% 30.98/8.58 +-Applying beta-rule and splitting (4214), into two cases.
% 30.98/8.58 |-Branch one:
% 30.98/8.58 | (4215) all_0_51_51 = e2
% 30.98/8.58 |
% 30.98/8.58 | Equations (4215) can reduce 12 to:
% 30.98/8.58 | (258) ~ (all_0_53_53 = e2)
% 30.98/8.58 |
% 30.98/8.58 | Simplifying 258 yields:
% 30.98/8.58 | (259) ~ (all_0_53_53 = e2)
% 30.98/8.58 |
% 30.98/8.58 | Equations (4215) can reduce 50 to:
% 30.98/8.58 | (260) ~ (all_0_54_54 = e2)
% 30.98/8.58 |
% 30.98/8.58 | Simplifying 260 yields:
% 30.98/8.58 | (261) ~ (all_0_54_54 = e2)
% 30.98/8.58 |
% 30.98/8.58 +-Applying beta-rule and splitting (209), into two cases.
% 30.98/8.58 |-Branch one:
% 30.98/8.58 | (698) all_0_42_42 = e2
% 30.98/8.58 |
% 30.98/8.58 | Equations (698) can reduce 145 to:
% 30.98/8.58 | (602) ~ (all_0_40_40 = e2)
% 30.98/8.58 |
% 30.98/8.58 | Equations (698) can reduce 18 to:
% 30.98/8.58 | (1435) ~ (all_0_46_46 = e2)
% 30.98/8.58 |
% 30.98/8.58 | Simplifying 1435 yields:
% 30.98/8.58 | (1436) ~ (all_0_46_46 = e2)
% 30.98/8.58 |
% 30.98/8.58 | Equations (698) can reduce 199 to:
% 30.98/8.58 | (57) ~ (e2 = e0)
% 30.98/8.58 |
% 30.98/8.58 +-Applying beta-rule and splitting (603), into two cases.
% 30.98/8.58 |-Branch one:
% 30.98/8.58 | (671) all_0_40_40 = e3
% 30.98/8.58 |
% 30.98/8.58 | Equations (671) can reduce 675 to:
% 30.98/8.58 | (270) $false
% 30.98/8.58 |
% 30.98/8.58 |-The branch is then unsatisfiable
% 30.98/8.58 |-Branch two:
% 30.98/8.58 | (675) ~ (all_0_40_40 = e3)
% 30.98/8.58 | (530) all_0_40_40 = e1
% 30.98/8.58 |
% 30.98/8.58 | Equations (530) can reduce 114 to:
% 30.98/8.58 | (528) ~ (all_0_39_39 = e1)
% 30.98/8.58 |
% 30.98/8.58 | Equations (530) can reduce 675 to:
% 30.98/8.58 | (769) ~ (e3 = e1)
% 30.98/8.58 |
% 30.98/8.58 | Simplifying 769 yields:
% 30.98/8.58 | (136) ~ (e3 = e1)
% 30.98/8.58 |
% 30.98/8.58 | Equations (530) can reduce 602 to:
% 30.98/8.58 | (645) ~ (e2 = e1)
% 30.98/8.58 |
% 30.98/8.58 | Simplifying 645 yields:
% 30.98/8.58 | (141) ~ (e2 = e1)
% 30.98/8.58 |
% 30.98/8.58 | Equations (530) can reduce 238 to:
% 30.98/8.58 | (132) ~ (e1 = e0)
% 30.98/8.58 |
% 30.98/8.58 +-Applying beta-rule and splitting (684), into two cases.
% 30.98/8.58 |-Branch one:
% 30.98/8.58 | (751) all_0_39_39 = e3
% 30.98/8.58 |
% 30.98/8.58 | Equations (751) can reduce 755 to:
% 30.98/8.58 | (270) $false
% 30.98/8.58 |
% 30.98/8.58 |-The branch is then unsatisfiable
% 30.98/8.58 |-Branch two:
% 30.98/8.58 | (755) ~ (all_0_39_39 = e3)
% 30.98/8.58 | (1756) all_0_39_39 = e4 | all_0_39_39 = e1
% 30.98/8.58 |
% 30.98/8.58 +-Applying beta-rule and splitting (1756), into two cases.
% 30.98/8.58 |-Branch one:
% 30.98/8.58 | (524) all_0_39_39 = e1
% 30.98/8.58 |
% 30.98/8.58 | Equations (524) can reduce 528 to:
% 30.98/8.58 | (270) $false
% 30.98/8.58 |
% 30.98/8.58 |-The branch is then unsatisfiable
% 30.98/8.58 |-Branch two:
% 30.98/8.58 | (528) ~ (all_0_39_39 = e1)
% 30.98/8.58 | (522) all_0_39_39 = e4
% 30.98/8.58 |
% 30.98/8.58 | Equations (522) can reduce 167 to:
% 30.98/8.58 | (694) ~ (all_0_43_43 = e4)
% 30.98/8.58 |
% 30.98/8.58 | Simplifying 694 yields:
% 30.98/8.58 | (510) ~ (all_0_43_43 = e4)
% 30.98/8.58 |
% 30.98/8.58 | Equations (522) can reduce 212 to:
% 30.98/8.58 | (273) ~ (all_0_56_56 = e4)
% 30.98/8.58 |
% 30.98/8.58 | Simplifying 273 yields:
% 30.98/8.58 | (274) ~ (all_0_56_56 = e4)
% 30.98/8.58 |
% 30.98/8.58 +-Applying beta-rule and splitting (44), into two cases.
% 30.98/8.58 |-Branch one:
% 30.98/8.58 | (502) all_0_43_43 = e4
% 30.98/8.58 |
% 30.98/8.58 | Equations (502) can reduce 510 to:
% 30.98/8.58 | (270) $false
% 30.98/8.58 |
% 30.98/8.58 |-The branch is then unsatisfiable
% 30.98/8.58 |-Branch two:
% 30.98/8.58 | (510) ~ (all_0_43_43 = e4)
% 30.98/8.58 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 30.98/8.58 |
% 30.98/8.58 +-Applying beta-rule and splitting (511), into two cases.
% 30.98/8.58 |-Branch one:
% 30.98/8.58 | (363) all_0_45_45 = e4
% 30.98/8.58 |
% 30.98/8.58 | Equations (363) can reduce 352 to:
% 30.98/8.58 | (270) $false
% 30.98/8.58 |
% 30.98/8.58 |-The branch is then unsatisfiable
% 30.98/8.58 |-Branch two:
% 30.98/8.58 | (352) ~ (all_0_45_45 = e4)
% 30.98/8.58 | (517) all_0_46_46 = e4
% 30.98/8.58 |
% 30.98/8.58 | Equations (517) can reduce 206 to:
% 30.98/8.58 | (279) ~ (all_0_59_59 = e4)
% 30.98/8.58 |
% 30.98/8.58 | Simplifying 279 yields:
% 30.98/8.58 | (280) ~ (all_0_59_59 = e4)
% 30.98/8.58 |
% 30.98/8.58 | Equations (517) can reduce 1436 to:
% 30.98/8.58 | (231) ~ (e4 = e2)
% 30.98/8.58 |
% 30.98/8.58 | Equations (517) can reduce 106 to:
% 30.98/8.58 | (251) ~ (e4 = e1)
% 30.98/8.58 |
% 30.98/8.58 | Equations (517) can reduce 1010 to:
% 30.98/8.58 | (6) ~ (e4 = e0)
% 30.98/8.58 |
% 30.98/8.58 +-Applying beta-rule and splitting (163), into two cases.
% 30.98/8.58 |-Branch one:
% 30.98/8.58 | (272) all_0_55_55 = e4
% 30.98/8.58 |
% 30.98/8.58 | Combining equations (382,272) yields a new equation:
% 30.98/8.58 | (269) e4 = e2
% 30.98/8.58 |
% 30.98/8.58 | Equations (269) can reduce 231 to:
% 30.98/8.58 | (270) $false
% 30.98/8.58 |
% 30.98/8.58 |-The branch is then unsatisfiable
% 30.98/8.58 |-Branch two:
% 30.98/8.58 | (14603) ~ (all_0_55_55 = e4)
% 30.98/8.58 | (14604) all_0_56_56 = e4 | all_0_58_58 = e4 | all_0_59_59 = e4
% 30.98/8.58 |
% 30.98/8.58 +-Applying beta-rule and splitting (14604), into two cases.
% 30.98/8.58 |-Branch one:
% 30.98/8.58 | (4744) all_0_56_56 = e4
% 30.98/8.58 |
% 30.98/8.58 | Equations (4744) can reduce 274 to:
% 30.98/8.58 | (270) $false
% 30.98/8.58 |
% 30.98/8.58 |-The branch is then unsatisfiable
% 30.98/8.58 |-Branch two:
% 30.98/8.58 | (274) ~ (all_0_56_56 = e4)
% 30.98/8.58 | (14608) all_0_58_58 = e4 | all_0_59_59 = e4
% 30.98/8.58 |
% 30.98/8.58 +-Applying beta-rule and splitting (14608), into two cases.
% 30.98/8.58 |-Branch one:
% 30.98/8.58 | (600) all_0_58_58 = e4
% 30.98/8.58 |
% 30.98/8.58 | Equations (600) can reduce 156 to:
% 30.98/8.58 | (279) ~ (all_0_59_59 = e4)
% 30.98/8.58 |
% 30.98/8.58 | Simplifying 279 yields:
% 30.98/8.58 | (280) ~ (all_0_59_59 = e4)
% 30.98/8.58 |
% 30.98/8.58 +-Applying beta-rule and splitting (105), into two cases.
% 30.98/8.58 |-Branch one:
% 30.98/8.58 | (374) all_0_45_45 = e2
% 30.98/8.58 |
% 30.98/8.58 | Equations (374) can reduce 434 to:
% 30.98/8.58 | (270) $false
% 30.98/8.58 |
% 30.98/8.58 |-The branch is then unsatisfiable
% 30.98/8.58 |-Branch two:
% 30.98/8.58 | (434) ~ (all_0_45_45 = e2)
% 30.98/8.58 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 30.98/8.58 |
% 30.98/8.58 +-Applying beta-rule and splitting (52), into two cases.
% 30.98/8.58 |-Branch one:
% 30.98/8.58 | (536) all_0_41_41 = e1
% 30.98/8.58 |
% 30.98/8.58 | Combining equations (351,536) yields a new equation:
% 30.98/8.58 | (537) e3 = e1
% 30.98/8.58 |
% 30.98/8.58 | Simplifying 537 yields:
% 30.98/8.58 | (538) e3 = e1
% 30.98/8.58 |
% 30.98/8.58 | Equations (538) can reduce 136 to:
% 30.98/8.58 | (270) $false
% 30.98/8.58 |
% 30.98/8.58 |-The branch is then unsatisfiable
% 30.98/8.58 |-Branch two:
% 30.98/8.58 | (540) ~ (all_0_41_41 = e1)
% 30.98/8.58 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 30.98/8.58 |
% 30.98/8.58 +-Applying beta-rule and splitting (762), into two cases.
% 30.98/8.58 |-Branch one:
% 30.98/8.58 | (552) all_0_48_48 = e1
% 30.98/8.58 |
% 30.98/8.58 | Combining equations (311,552) yields a new equation:
% 30.98/8.58 | (531) e2 = e1
% 30.98/8.58 |
% 30.98/8.58 | Simplifying 531 yields:
% 30.98/8.58 | (322) e2 = e1
% 30.98/8.58 |
% 30.98/8.58 | Equations (322) can reduce 141 to:
% 30.98/8.58 | (270) $false
% 30.98/8.58 |
% 30.98/8.58 |-The branch is then unsatisfiable
% 30.98/8.58 |-Branch two:
% 30.98/8.58 | (588) ~ (all_0_48_48 = e1)
% 30.98/8.58 | (4925) all_0_53_53 = e1 | all_0_58_58 = e1
% 30.98/8.58 |
% 30.98/8.58 +-Applying beta-rule and splitting (4925), into two cases.
% 30.98/8.58 |-Branch one:
% 30.98/8.58 | (853) all_0_53_53 = e1
% 30.98/8.58 |
% 30.98/8.58 | Equations (853) can reduce 128 to:
% 30.98/8.58 | (26) ~ (all_0_45_45 = e1)
% 30.98/8.58 |
% 30.98/8.58 | Equations (853) can reduce 252 to:
% 30.98/8.58 | (2131) ~ (all_0_54_54 = e1)
% 30.98/8.58 |
% 30.98/8.58 | Simplifying 2131 yields:
% 30.98/8.58 | (425) ~ (all_0_54_54 = e1)
% 30.98/8.58 |
% 30.98/8.58 | Equations (853) can reduce 356 to:
% 30.98/8.58 | (769) ~ (e3 = e1)
% 30.98/8.58 |
% 30.98/8.58 | Simplifying 769 yields:
% 30.98/8.58 | (136) ~ (e3 = e1)
% 30.98/8.58 |
% 30.98/8.58 | Equations (853) can reduce 259 to:
% 30.98/8.58 | (645) ~ (e2 = e1)
% 30.98/8.58 |
% 30.98/8.58 | Simplifying 645 yields:
% 30.98/8.58 | (141) ~ (e2 = e1)
% 30.98/8.58 |
% 30.98/8.58 +-Applying beta-rule and splitting (127), into two cases.
% 30.98/8.58 |-Branch one:
% 30.98/8.58 | (541) all_0_42_42 = e1
% 30.98/8.58 |
% 30.98/8.58 | Combining equations (698,541) yields a new equation:
% 30.98/8.58 | (531) e2 = e1
% 30.98/8.58 |
% 30.98/8.58 | Simplifying 531 yields:
% 30.98/8.58 | (322) e2 = e1
% 30.98/8.58 |
% 30.98/8.58 | Equations (322) can reduce 141 to:
% 30.98/8.58 | (270) $false
% 30.98/8.58 |
% 30.98/8.58 |-The branch is then unsatisfiable
% 30.98/8.58 |-Branch two:
% 30.98/8.58 | (640) ~ (all_0_42_42 = e1)
% 30.98/8.58 | (4628) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 30.98/8.58 |
% 30.98/8.58 +-Applying beta-rule and splitting (4628), into two cases.
% 30.98/8.58 |-Branch one:
% 30.98/8.58 | (589) all_0_49_49 = e1
% 30.98/8.58 |
% 30.98/8.58 | Combining equations (563,589) yields a new equation:
% 30.98/8.58 | (560) e1 = e0
% 30.98/8.58 |
% 30.98/8.58 | Equations (560) can reduce 132 to:
% 30.98/8.58 | (270) $false
% 30.98/8.58 |
% 30.98/8.58 |-The branch is then unsatisfiable
% 30.98/8.58 |-Branch two:
% 30.98/8.58 | (543) ~ (all_0_49_49 = e1)
% 30.98/8.58 | (4726) all_0_54_54 = e1 | all_0_59_59 = e1
% 30.98/8.58 |
% 30.98/8.58 +-Applying beta-rule and splitting (4726), into two cases.
% 30.98/8.58 |-Branch one:
% 30.98/8.58 | (875) all_0_54_54 = e1
% 30.98/8.58 |
% 30.98/8.58 | Equations (875) can reduce 425 to:
% 30.98/8.58 | (270) $false
% 30.98/8.58 |
% 30.98/8.58 |-The branch is then unsatisfiable
% 30.98/8.58 |-Branch two:
% 30.98/8.58 | (425) ~ (all_0_54_54 = e1)
% 30.98/8.58 | (424) all_0_59_59 = e1
% 30.98/8.58 |
% 30.98/8.58 | Equations (424) can reduce 185 to:
% 30.98/8.58 | (995) ~ (all_0_56_56 = e1)
% 30.98/8.58 |
% 30.98/8.58 | Equations (424) can reduce 280 to:
% 30.98/8.58 | (1021) ~ (e4 = e1)
% 30.98/8.58 |
% 30.98/8.58 | Simplifying 1021 yields:
% 30.98/8.58 | (251) ~ (e4 = e1)
% 30.98/8.58 |
% 30.98/8.58 | Equations (424) can reduce 4001 to:
% 30.98/8.58 | (132) ~ (e1 = e0)
% 30.98/8.58 |
% 30.98/8.58 +-Applying beta-rule and splitting (182), into two cases.
% 30.98/8.58 |-Branch one:
% 30.98/8.58 | (454) all_0_45_45 = e0
% 30.98/8.58 |
% 30.98/8.58 | Equations (454) can reduce 84 to:
% 30.98/8.58 | (455) ~ (all_0_43_43 = e0)
% 30.98/8.58 |
% 30.98/8.58 | Equations (454) can reduce 434 to:
% 30.98/8.59 | (566) ~ (e2 = e0)
% 30.98/8.59 |
% 30.98/8.59 | Simplifying 566 yields:
% 30.98/8.59 | (57) ~ (e2 = e0)
% 30.98/8.59 |
% 30.98/8.59 | Equations (454) can reduce 26 to:
% 30.98/8.59 | (568) ~ (e1 = e0)
% 30.98/8.59 |
% 30.98/8.59 | Simplifying 568 yields:
% 30.98/8.59 | (132) ~ (e1 = e0)
% 30.98/8.59 |
% 30.98/8.59 +-Applying beta-rule and splitting (64), into two cases.
% 30.98/8.59 |-Branch one:
% 30.98/8.59 | (954) all_0_51_51 = e0
% 30.98/8.59 |
% 30.98/8.59 | Combining equations (954,4215) yields a new equation:
% 30.98/8.59 | (316) e2 = e0
% 30.98/8.59 |
% 30.98/8.59 | Equations (316) can reduce 57 to:
% 30.98/8.59 | (270) $false
% 30.98/8.59 |
% 30.98/8.59 |-The branch is then unsatisfiable
% 30.98/8.59 |-Branch two:
% 30.98/8.59 | (987) ~ (all_0_51_51 = e0)
% 30.98/8.59 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 30.98/8.59 |
% 30.98/8.59 | Equations (4215) can reduce 987 to:
% 30.98/8.59 | (57) ~ (e2 = e0)
% 30.98/8.59 |
% 30.98/8.59 +-Applying beta-rule and splitting (75), into two cases.
% 30.98/8.59 |-Branch one:
% 30.98/8.59 | (411) all_0_43_43 = e0
% 30.98/8.59 |
% 30.98/8.59 | Equations (411) can reduce 455 to:
% 30.98/8.59 | (270) $false
% 30.98/8.59 |
% 30.98/8.59 |-The branch is then unsatisfiable
% 30.98/8.59 |-Branch two:
% 30.98/8.59 | (455) ~ (all_0_43_43 = e0)
% 30.98/8.59 | (940) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 30.98/8.59 |
% 30.98/8.59 +-Applying beta-rule and splitting (940), into two cases.
% 30.98/8.59 |-Branch one:
% 30.98/8.59 | (315) all_0_47_47 = e0
% 30.98/8.59 |
% 30.98/8.59 | Combining equations (321,315) yields a new equation:
% 30.98/8.59 | (571) e1 = e0
% 30.98/8.59 |
% 30.98/8.59 | Simplifying 571 yields:
% 30.98/8.59 | (560) e1 = e0
% 30.98/8.59 |
% 30.98/8.59 | Equations (560) can reduce 132 to:
% 30.98/8.59 | (270) $false
% 30.98/8.59 |
% 30.98/8.59 |-The branch is then unsatisfiable
% 30.98/8.59 |-Branch two:
% 30.98/8.59 | (318) ~ (all_0_47_47 = e0)
% 30.98/8.59 | (950) all_0_51_51 = e0 | all_0_56_56 = e0
% 30.98/8.59 |
% 30.98/8.59 +-Applying beta-rule and splitting (950), into two cases.
% 30.98/8.59 |-Branch one:
% 30.98/8.59 | (954) all_0_51_51 = e0
% 30.98/8.59 |
% 30.98/8.59 | Combining equations (954,4215) yields a new equation:
% 30.98/8.59 | (316) e2 = e0
% 30.98/8.59 |
% 30.98/8.59 | Equations (316) can reduce 57 to:
% 30.98/8.59 | (270) $false
% 30.98/8.59 |
% 30.98/8.59 |-The branch is then unsatisfiable
% 30.98/8.59 |-Branch two:
% 30.98/8.59 | (987) ~ (all_0_51_51 = e0)
% 30.98/8.59 | (830) all_0_56_56 = e0
% 30.98/8.59 |
% 30.98/8.59 | Equations (830) can reduce 995 to:
% 30.98/8.59 | (568) ~ (e1 = e0)
% 30.98/8.59 |
% 30.98/8.59 | Simplifying 568 yields:
% 30.98/8.59 | (132) ~ (e1 = e0)
% 30.98/8.59 |
% 30.98/8.59 +-Applying beta-rule and splitting (93), into two cases.
% 30.98/8.59 |-Branch one:
% 30.98/8.59 | (402) all_0_59_59 = e4
% 30.98/8.59 |
% 30.98/8.59 | Combining equations (402,424) yields a new equation:
% 30.98/8.59 | (525) e4 = e1
% 30.98/8.59 |
% 30.98/8.59 | Simplifying 525 yields:
% 30.98/8.59 | (526) e4 = e1
% 30.98/8.59 |
% 30.98/8.59 | Equations (526) can reduce 251 to:
% 30.98/8.59 | (270) $false
% 30.98/8.59 |
% 30.98/8.59 |-The branch is then unsatisfiable
% 30.98/8.59 |-Branch two:
% 30.98/8.59 | (280) ~ (all_0_59_59 = e4)
% 30.98/8.59 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 30.98/8.59 |
% 30.98/8.59 +-Applying beta-rule and splitting (407), into two cases.
% 30.98/8.59 |-Branch one:
% 30.98/8.59 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 30.98/8.59 |
% 30.98/8.59 +-Applying beta-rule and splitting (408), into two cases.
% 30.98/8.59 |-Branch one:
% 30.98/8.59 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 30.98/8.59 |
% 30.98/8.59 +-Applying beta-rule and splitting (409), into two cases.
% 30.98/8.59 |-Branch one:
% 30.98/8.59 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 30.98/8.59 |
% 30.98/8.59 | Applying alpha-rule on (410) yields:
% 30.98/8.59 | (411) all_0_43_43 = e0
% 30.98/8.59 | (412) all_0_59_59 = e3
% 30.98/8.59 | (413) ~ (all_0_46_46 = e3)
% 30.98/8.59 |
% 30.98/8.59 | Combining equations (424,412) yields a new equation:
% 30.98/8.59 | (538) e3 = e1
% 30.98/8.59 |
% 30.98/8.59 | Equations (538) can reduce 136 to:
% 30.98/8.59 | (270) $false
% 30.98/8.59 |
% 30.98/8.59 |-The branch is then unsatisfiable
% 30.98/8.59 |-Branch two:
% 30.98/8.59 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 30.98/8.59 |
% 30.98/8.59 | Applying alpha-rule on (416) yields:
% 30.98/8.59 | (411) all_0_43_43 = e0
% 30.98/8.59 | (412) all_0_59_59 = e3
% 30.98/8.59 | (419) ~ (all_0_56_56 = e0)
% 30.98/8.59 |
% 30.98/8.59 | Combining equations (424,412) yields a new equation:
% 30.98/8.59 | (538) e3 = e1
% 30.98/8.59 |
% 30.98/8.59 | Equations (538) can reduce 136 to:
% 30.98/8.59 | (270) $false
% 30.98/8.59 |
% 30.98/8.59 |-The branch is then unsatisfiable
% 30.98/8.59 |-Branch two:
% 30.98/8.59 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 30.98/8.59 |
% 30.98/8.59 | Applying alpha-rule on (422) yields:
% 30.98/8.59 | (423) all_0_53_53 = e0
% 30.98/8.59 | (424) all_0_59_59 = e1
% 30.98/8.59 | (425) ~ (all_0_54_54 = e1)
% 30.98/8.59 |
% 30.98/8.59 | Combining equations (853,423) yields a new equation:
% 30.98/8.59 | (571) e1 = e0
% 30.98/8.59 |
% 30.98/8.59 | Simplifying 571 yields:
% 30.98/8.59 | (560) e1 = e0
% 30.98/8.59 |
% 30.98/8.59 | Equations (560) can reduce 132 to:
% 30.98/8.59 | (270) $false
% 30.98/8.59 |
% 30.98/8.59 |-The branch is then unsatisfiable
% 30.98/8.59 |-Branch two:
% 30.98/8.59 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 30.98/8.59 |
% 30.98/8.59 | Applying alpha-rule on (428) yields:
% 30.98/8.59 | (423) all_0_53_53 = e0
% 30.98/8.59 | (424) all_0_59_59 = e1
% 30.98/8.59 | (431) ~ (all_0_58_58 = e0)
% 30.98/8.59 |
% 30.98/8.59 | Combining equations (853,423) yields a new equation:
% 30.98/8.59 | (571) e1 = e0
% 30.98/8.59 |
% 30.98/8.59 | Simplifying 571 yields:
% 30.98/8.59 | (560) e1 = e0
% 30.98/8.59 |
% 30.98/8.59 | Equations (560) can reduce 132 to:
% 30.98/8.59 | (270) $false
% 30.98/8.59 |
% 30.98/8.59 |-The branch is then unsatisfiable
% 30.98/8.59 |-Branch two:
% 30.98/8.59 | (488) ~ (all_0_45_45 = e0)
% 30.98/8.59 | (558) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 30.98/8.59 |
% 30.98/8.59 +-Applying beta-rule and splitting (558), into two cases.
% 30.98/8.59 |-Branch one:
% 30.98/8.59 | (559) all_0_48_48 = e0
% 30.98/8.59 |
% 30.98/8.59 | Combining equations (559,311) yields a new equation:
% 30.98/8.59 | (316) e2 = e0
% 30.98/8.59 |
% 30.98/8.59 | Equations (316) can reduce 57 to:
% 30.98/8.59 | (270) $false
% 30.98/8.59 |
% 30.98/8.59 |-The branch is then unsatisfiable
% 30.98/8.59 |-Branch two:
% 30.98/8.59 | (562) ~ (all_0_48_48 = e0)
% 30.98/8.59 | (575) all_0_53_53 = e0 | all_0_58_58 = e0
% 30.98/8.59 |
% 30.98/8.59 +-Applying beta-rule and splitting (575), into two cases.
% 30.98/8.59 |-Branch one:
% 30.98/8.59 | (423) all_0_53_53 = e0
% 30.98/8.59 |
% 30.98/8.59 | Combining equations (423,853) yields a new equation:
% 30.98/8.59 | (560) e1 = e0
% 30.98/8.59 |
% 30.98/8.59 | Equations (560) can reduce 132 to:
% 30.98/8.59 | (270) $false
% 30.98/8.59 |
% 30.98/8.59 |-The branch is then unsatisfiable
% 30.98/8.59 |-Branch two:
% 30.98/8.59 | (584) ~ (all_0_53_53 = e0)
% 30.98/8.59 | (585) all_0_58_58 = e0
% 30.98/8.59 |
% 30.98/8.59 | Combining equations (585,600) yields a new equation:
% 30.98/8.59 | (479) e4 = e0
% 30.98/8.59 |
% 30.98/8.59 | Equations (479) can reduce 6 to:
% 30.98/8.59 | (270) $false
% 30.98/8.59 |
% 30.98/8.59 |-The branch is then unsatisfiable
% 30.98/8.59 |-Branch two:
% 30.98/8.59 | (874) ~ (all_0_53_53 = e1)
% 30.98/8.59 | (1001) all_0_58_58 = e1
% 30.98/8.59 |
% 30.98/8.59 | Combining equations (1001,600) yields a new equation:
% 30.98/8.59 | (526) e4 = e1
% 30.98/8.59 |
% 30.98/8.59 | Equations (526) can reduce 251 to:
% 30.98/8.59 | (270) $false
% 30.98/8.59 |
% 30.98/8.59 |-The branch is then unsatisfiable
% 30.98/8.59 |-Branch two:
% 30.98/8.59 | (278) ~ (all_0_58_58 = e4)
% 30.98/8.59 | (402) all_0_59_59 = e4
% 30.98/8.59 |
% 30.98/8.59 | Equations (402) can reduce 280 to:
% 30.98/8.59 | (270) $false
% 30.98/8.59 |
% 30.98/8.59 |-The branch is then unsatisfiable
% 30.98/8.59 |-Branch two:
% 30.98/8.59 | (498) ~ (all_0_42_42 = e2)
% 30.98/8.59 | (1732) all_0_46_46 = e2 | all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 30.98/8.59 |
% 30.98/8.59 +-Applying beta-rule and splitting (1732), into two cases.
% 30.98/8.59 |-Branch one:
% 30.98/8.59 | (497) all_0_46_46 = e2
% 30.98/8.59 |
% 30.98/8.59 | Equations (497) can reduce 1436 to:
% 30.98/8.59 | (270) $false
% 30.98/8.59 |
% 30.98/8.59 |-The branch is then unsatisfiable
% 30.98/8.59 |-Branch two:
% 30.98/8.59 | (1436) ~ (all_0_46_46 = e2)
% 30.98/8.59 | (3824) all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 30.98/8.59 |
% 30.98/8.59 +-Applying beta-rule and splitting (3824), into two cases.
% 30.98/8.59 |-Branch one:
% 30.98/8.59 | (307) all_0_49_49 = e2
% 30.98/8.59 |
% 30.98/8.59 | Combining equations (563,307) yields a new equation:
% 30.98/8.59 | (316) e2 = e0
% 30.98/8.59 |
% 30.98/8.59 | Equations (316) can reduce 57 to:
% 30.98/8.59 | (270) $false
% 30.98/8.59 |
% 30.98/8.59 |-The branch is then unsatisfiable
% 30.98/8.59 |-Branch two:
% 30.98/8.59 | (296) ~ (all_0_49_49 = e2)
% 30.98/8.59 | (3829) all_0_54_54 = e2 | all_0_59_59 = e2
% 30.98/8.59 |
% 30.98/8.59 +-Applying beta-rule and splitting (3829), into two cases.
% 30.98/8.59 |-Branch one:
% 30.98/8.59 | (3657) all_0_54_54 = e2
% 30.98/8.59 |
% 30.98/8.59 | Equations (3657) can reduce 261 to:
% 30.98/8.59 | (270) $false
% 30.98/8.59 |
% 30.98/8.59 |-The branch is then unsatisfiable
% 30.98/8.59 |-Branch two:
% 30.98/8.59 | (261) ~ (all_0_54_54 = e2)
% 30.98/8.59 | (399) all_0_59_59 = e2
% 30.98/8.59 |
% 30.98/8.59 | Equations (399) can reduce 701 to:
% 30.98/8.59 | (270) $false
% 30.98/8.59 |
% 30.98/8.59 |-The branch is then unsatisfiable
% 30.98/8.59 |-Branch two:
% 30.98/8.59 | (255) ~ (all_0_51_51 = e2)
% 30.98/8.59 | (388) all_0_56_56 = e2
% 30.98/8.59 |
% 30.98/8.59 | Equations (388) can reduce 300 to:
% 30.98/8.59 | (270) $false
% 30.98/8.59 |
% 30.98/8.59 |-The branch is then unsatisfiable
% 30.98/8.59 |-Branch two:
% 30.98/8.59 | (333) ~ (all_0_44_44 = e2)
% 30.98/8.59 | (373) all_0_44_44 = e3 | all_0_44_44 = e0
% 30.98/8.59 |
% 30.98/8.59 +-Applying beta-rule and splitting (607), into two cases.
% 30.98/8.59 |-Branch one:
% 30.98/8.59 | (370) all_0_44_44 = e2
% 30.98/8.59 |
% 30.98/8.59 | Equations (370) can reduce 333 to:
% 30.98/8.59 | (270) $false
% 30.98/8.59 |
% 30.98/8.59 |-The branch is then unsatisfiable
% 30.98/8.59 |-Branch two:
% 30.98/8.59 | (333) ~ (all_0_44_44 = e2)
% 30.98/8.59 | (3377) all_0_52_52 = e2 | all_0_57_57 = e2
% 30.98/8.59 |
% 30.98/8.59 +-Applying beta-rule and splitting (3377), into two cases.
% 30.98/8.59 |-Branch one:
% 30.98/8.59 | (685) all_0_52_52 = e2
% 30.98/8.59 |
% 30.98/8.59 | Equations (685) can reduce 137 to:
% 30.98/8.59 | (602) ~ (all_0_40_40 = e2)
% 30.98/8.59 |
% 30.98/8.59 | Equations (685) can reduce 213 to:
% 30.98/8.59 | (258) ~ (all_0_53_53 = e2)
% 30.98/8.59 |
% 30.98/8.59 | Simplifying 258 yields:
% 30.98/8.59 | (259) ~ (all_0_53_53 = e2)
% 30.98/8.59 |
% 30.98/8.59 | Equations (685) can reduce 118 to:
% 30.98/8.59 | (260) ~ (all_0_54_54 = e2)
% 30.98/8.59 |
% 30.98/8.59 | Simplifying 260 yields:
% 30.98/8.59 | (261) ~ (all_0_54_54 = e2)
% 30.98/8.59 |
% 30.98/8.59 | Equations (685) can reduce 235 to:
% 30.98/8.59 | (334) ~ (all_0_57_57 = e2)
% 30.98/8.59 |
% 30.98/8.59 | Simplifying 334 yields:
% 30.98/8.59 | (335) ~ (all_0_57_57 = e2)
% 30.98/8.59 |
% 30.98/8.59 | Equations (685) can reduce 230 to:
% 30.98/8.59 | (377) ~ (e4 = e2)
% 30.98/8.59 |
% 30.98/8.59 | Simplifying 377 yields:
% 30.98/8.59 | (231) ~ (e4 = e2)
% 30.98/8.59 |
% 30.98/8.59 | From (685) and (27) follows:
% 30.98/8.59 | (11734) op(e2, e2) = all_0_17_17
% 30.98/8.59 |
% 30.98/8.59 | Instantiating formula (201) with e2, e2, all_0_17_17, e4 and discharging atoms op(e2, e2) = all_0_17_17, op(e2, e2) = e4, yields:
% 30.98/8.59 | (11735) all_0_17_17 = e4
% 30.98/8.59 |
% 30.98/8.59 +-Applying beta-rule and splitting (9), into two cases.
% 30.98/8.59 |-Branch one:
% 30.98/8.59 | (621) all_0_44_44 = e0
% 30.98/8.59 |
% 30.98/8.59 | Equations (621) can reduce 15 to:
% 30.98/8.59 | (238) ~ (all_0_40_40 = e0)
% 30.98/8.59 |
% 30.98/8.59 | Equations (621) can reduce 241 to:
% 30.98/8.59 | (455) ~ (all_0_43_43 = e0)
% 30.98/8.59 |
% 30.98/8.59 | Equations (621) can reduce 229 to:
% 30.98/8.59 | (776) ~ (all_0_45_45 = e0)
% 30.98/8.59 |
% 30.98/8.59 | Simplifying 776 yields:
% 30.98/8.59 | (488) ~ (all_0_45_45 = e0)
% 30.98/8.59 |
% 30.98/8.59 | Equations (621) can reduce 10 to:
% 30.98/8.59 | (9326) ~ (all_0_57_57 = e0)
% 30.98/8.59 |
% 30.98/8.59 | Simplifying 9326 yields:
% 30.98/8.59 | (2301) ~ (all_0_57_57 = e0)
% 30.98/8.59 |
% 30.98/8.59 | From (621) and (165) follows:
% 30.98/8.59 | (3395) op(e2, e0) = all_0_15_15
% 30.98/8.59 |
% 30.98/8.59 | Instantiating formula (201) with e2, e0, all_0_15_15, e0 and discharging atoms op(e2, e0) = all_0_15_15, op(e2, e0) = e0, yields:
% 30.98/8.59 | (5959) all_0_15_15 = e0
% 30.98/8.59 |
% 30.98/8.59 +-Applying beta-rule and splitting (8), into two cases.
% 30.98/8.59 |-Branch one:
% 30.98/8.59 | (530) all_0_40_40 = e1
% 30.98/8.59 |
% 30.98/8.59 | Equations (530) can reduce 233 to:
% 30.98/8.59 | (1021) ~ (e4 = e1)
% 30.98/8.59 |
% 30.98/8.59 | Simplifying 1021 yields:
% 30.98/8.59 | (251) ~ (e4 = e1)
% 30.98/8.59 |
% 30.98/8.59 | Equations (530) can reduce 238 to:
% 30.98/8.59 | (132) ~ (e1 = e0)
% 30.98/8.59 |
% 30.98/8.59 | From (530) and (68) follows:
% 30.98/8.60 | (648) op(e2, e1) = all_0_13_13
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (133), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (671) all_0_40_40 = e3
% 30.98/8.60 |
% 30.98/8.60 | Combining equations (530,671) yields a new equation:
% 30.98/8.60 | (538) e3 = e1
% 30.98/8.60 |
% 30.98/8.60 | Equations (538) can reduce 136 to:
% 30.98/8.60 | (270) $false
% 30.98/8.60 |
% 30.98/8.60 |-The branch is then unsatisfiable
% 30.98/8.60 |-Branch two:
% 30.98/8.60 | (675) ~ (all_0_40_40 = e3)
% 30.98/8.60 | (676) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (676), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (858) all_0_44_44 = e3
% 30.98/8.60 |
% 30.98/8.60 | Combining equations (621,858) yields a new equation:
% 30.98/8.60 | (784) e3 = e0
% 30.98/8.60 |
% 30.98/8.60 | Equations (784) can reduce 66 to:
% 30.98/8.60 | (270) $false
% 30.98/8.60 |
% 30.98/8.60 |-The branch is then unsatisfiable
% 30.98/8.60 |-Branch two:
% 30.98/8.60 | (862) ~ (all_0_44_44 = e3)
% 30.98/8.60 | (863) all_0_52_52 = e3 | all_0_57_57 = e3
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (863), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (864) all_0_52_52 = e3
% 30.98/8.60 |
% 30.98/8.60 | Combining equations (685,864) yields a new equation:
% 30.98/8.60 | (414) e3 = e2
% 30.98/8.60 |
% 30.98/8.60 | Equations (414) can reduce 223 to:
% 30.98/8.60 | (270) $false
% 30.98/8.60 |
% 30.98/8.60 |-The branch is then unsatisfiable
% 30.98/8.60 |-Branch two:
% 30.98/8.60 | (826) ~ (all_0_52_52 = e3)
% 30.98/8.60 | (869) all_0_57_57 = e3
% 30.98/8.60 |
% 30.98/8.60 | Equations (869) can reduce 2301 to:
% 30.98/8.60 | (66) ~ (e3 = e0)
% 30.98/8.60 |
% 30.98/8.60 | From (869) and (30) follows:
% 30.98/8.60 | (14806) op(e2, e3) = all_0_19_19
% 30.98/8.60 |
% 30.98/8.60 | Instantiating formula (201) with e2, e3, all_0_19_19, e1 and discharging atoms op(e2, e3) = all_0_19_19, op(e2, e3) = e1, yields:
% 30.98/8.60 | (12301) all_0_19_19 = e1
% 30.98/8.60 |
% 30.98/8.60 | Instantiating formula (201) with e2, e1, all_0_13_13, e2 and discharging atoms op(e2, e1) = all_0_13_13, op(e2, e1) = e2, yields:
% 30.98/8.60 | (4829) all_0_13_13 = e2
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (87), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (650) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (650), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (651) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (651), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (652) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 30.98/8.60 |
% 30.98/8.60 | Applying alpha-rule on (652) yields:
% 30.98/8.60 | (653) all_0_13_13 = e4
% 30.98/8.60 | (654) ~ (all_0_14_14 = e2)
% 30.98/8.60 |
% 30.98/8.60 | Combining equations (4829,653) yields a new equation:
% 30.98/8.60 | (269) e4 = e2
% 30.98/8.60 |
% 30.98/8.60 | Equations (269) can reduce 231 to:
% 30.98/8.60 | (270) $false
% 30.98/8.60 |
% 30.98/8.60 |-The branch is then unsatisfiable
% 30.98/8.60 |-Branch two:
% 30.98/8.60 | (657) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 30.98/8.60 |
% 30.98/8.60 | Applying alpha-rule on (657) yields:
% 30.98/8.60 | (658) all_0_15_15 = e3
% 30.98/8.60 | (659) ~ (all_0_16_16 = e2)
% 30.98/8.60 |
% 30.98/8.60 | Combining equations (658,5959) yields a new equation:
% 30.98/8.60 | (783) e3 = e0
% 30.98/8.60 |
% 30.98/8.60 | Simplifying 783 yields:
% 30.98/8.60 | (784) e3 = e0
% 30.98/8.60 |
% 30.98/8.60 | Equations (784) can reduce 66 to:
% 30.98/8.60 | (270) $false
% 30.98/8.60 |
% 30.98/8.60 |-The branch is then unsatisfiable
% 30.98/8.60 |-Branch two:
% 30.98/8.60 | (663) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 30.98/8.60 |
% 30.98/8.60 | Applying alpha-rule on (663) yields:
% 30.98/8.60 | (664) all_0_17_17 = e1
% 30.98/8.60 | (665) ~ (all_0_18_18 = e2)
% 30.98/8.60 |
% 30.98/8.60 | Combining equations (664,11735) yields a new equation:
% 30.98/8.60 | (526) e4 = e1
% 30.98/8.60 |
% 30.98/8.60 | Equations (526) can reduce 251 to:
% 30.98/8.60 | (270) $false
% 30.98/8.60 |
% 30.98/8.60 |-The branch is then unsatisfiable
% 30.98/8.60 |-Branch two:
% 30.98/8.60 | (1762) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 30.98/8.60 |
% 30.98/8.60 | Applying alpha-rule on (1762) yields:
% 30.98/8.60 | (1763) all_0_19_19 = e0
% 30.98/8.60 | (1764) ~ (all_0_20_20 = e2)
% 30.98/8.60 |
% 30.98/8.60 | Combining equations (12301,1763) yields a new equation:
% 30.98/8.60 | (571) e1 = e0
% 30.98/8.60 |
% 30.98/8.60 | Simplifying 571 yields:
% 30.98/8.60 | (560) e1 = e0
% 30.98/8.60 |
% 30.98/8.60 | Equations (560) can reduce 132 to:
% 30.98/8.60 | (270) $false
% 30.98/8.60 |
% 30.98/8.60 |-The branch is then unsatisfiable
% 30.98/8.60 |-Branch two:
% 30.98/8.60 | (534) ~ (all_0_40_40 = e1)
% 30.98/8.60 | (3352) all_0_52_52 = e1 | all_0_57_57 = e1
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (3352), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (848) all_0_52_52 = e1
% 30.98/8.60 |
% 30.98/8.60 | Combining equations (848,685) yields a new equation:
% 30.98/8.60 | (322) e2 = e1
% 30.98/8.60 |
% 30.98/8.60 | Equations (322) can reduce 141 to:
% 30.98/8.60 | (270) $false
% 30.98/8.60 |
% 30.98/8.60 |-The branch is then unsatisfiable
% 30.98/8.60 |-Branch two:
% 30.98/8.60 | (642) ~ (all_0_52_52 = e1)
% 30.98/8.60 | (997) all_0_57_57 = e1
% 30.98/8.60 |
% 30.98/8.60 | Equations (997) can reduce 149 to:
% 30.98/8.60 | (534) ~ (all_0_40_40 = e1)
% 30.98/8.60 |
% 30.98/8.60 | Equations (997) can reduce 104 to:
% 30.98/8.60 | (995) ~ (all_0_56_56 = e1)
% 30.98/8.60 |
% 30.98/8.60 | Equations (997) can reduce 37 to:
% 30.98/8.60 | (7725) ~ (all_0_58_58 = e1)
% 30.98/8.60 |
% 30.98/8.60 | Simplifying 7725 yields:
% 30.98/8.60 | (1004) ~ (all_0_58_58 = e1)
% 30.98/8.60 |
% 30.98/8.60 | Equations (997) can reduce 140 to:
% 30.98/8.60 | (749) ~ (all_0_59_59 = e1)
% 30.98/8.60 |
% 30.98/8.60 | Simplifying 749 yields:
% 30.98/8.60 | (750) ~ (all_0_59_59 = e1)
% 30.98/8.60 |
% 30.98/8.60 | Equations (997) can reduce 2301 to:
% 30.98/8.60 | (132) ~ (e1 = e0)
% 30.98/8.60 |
% 30.98/8.60 | From (997) and (30) follows:
% 30.98/8.60 | (14847) op(e2, e1) = all_0_19_19
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (133), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (671) all_0_40_40 = e3
% 30.98/8.60 |
% 30.98/8.60 | Combining equations (671,9065) yields a new equation:
% 30.98/8.60 | (12353) all_0_2_2 = e3
% 30.98/8.60 |
% 30.98/8.60 | Equations (671) can reduce 147 to:
% 30.98/8.60 | (1329) ~ (all_0_41_41 = e3)
% 30.98/8.60 |
% 30.98/8.60 | Simplifying 1329 yields:
% 30.98/8.60 | (1237) ~ (all_0_41_41 = e3)
% 30.98/8.60 |
% 30.98/8.60 | Equations (671) can reduce 238 to:
% 30.98/8.60 | (66) ~ (e3 = e0)
% 30.98/8.60 |
% 30.98/8.60 | From (671) and (68) follows:
% 30.98/8.60 | (5921) op(e2, e3) = all_0_13_13
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (186), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (336) all_0_39_39 = e2
% 30.98/8.60 |
% 30.98/8.60 | Equations (336) can reduce 226 to:
% 30.98/8.60 | (330) ~ (all_0_41_41 = e2)
% 30.98/8.60 |
% 30.98/8.60 | Simplifying 330 yields:
% 30.98/8.60 | (331) ~ (all_0_41_41 = e2)
% 30.98/8.60 |
% 30.98/8.60 | Equations (336) can reduce 184 to:
% 30.98/8.60 | (1336) ~ (all_0_42_42 = e2)
% 30.98/8.60 |
% 30.98/8.60 | Simplifying 1336 yields:
% 30.98/8.60 | (498) ~ (all_0_42_42 = e2)
% 30.98/8.60 |
% 30.98/8.60 | Equations (336) can reduce 167 to:
% 30.98/8.60 | (5937) ~ (all_0_43_43 = e2)
% 30.98/8.60 |
% 30.98/8.60 | Simplifying 5937 yields:
% 30.98/8.60 | (292) ~ (all_0_43_43 = e2)
% 30.98/8.60 |
% 30.98/8.60 | Equations (336) can reduce 32 to:
% 30.98/8.60 | (254) ~ (all_0_51_51 = e2)
% 30.98/8.60 |
% 30.98/8.60 | Simplifying 254 yields:
% 30.98/8.60 | (255) ~ (all_0_51_51 = e2)
% 30.98/8.60 |
% 30.98/8.60 | Equations (336) can reduce 212 to:
% 30.98/8.60 | (299) ~ (all_0_56_56 = e2)
% 30.98/8.60 |
% 30.98/8.60 | Simplifying 299 yields:
% 30.98/8.60 | (300) ~ (all_0_56_56 = e2)
% 30.98/8.60 |
% 30.98/8.60 | Equations (336) can reduce 101 to:
% 30.98/8.60 | (57) ~ (e2 = e0)
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (47), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (450) all_0_43_43 = e2
% 30.98/8.60 |
% 30.98/8.60 | Equations (450) can reduce 292 to:
% 30.98/8.60 | (270) $false
% 30.98/8.60 |
% 30.98/8.60 |-The branch is then unsatisfiable
% 30.98/8.60 |-Branch two:
% 30.98/8.60 | (292) ~ (all_0_43_43 = e2)
% 30.98/8.60 | (453) all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (453), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (370) all_0_44_44 = e2
% 30.98/8.60 |
% 30.98/8.60 | Combining equations (621,370) yields a new equation:
% 30.98/8.60 | (316) e2 = e0
% 30.98/8.60 |
% 30.98/8.60 | Equations (316) can reduce 57 to:
% 30.98/8.60 | (270) $false
% 30.98/8.60 |
% 30.98/8.60 |-The branch is then unsatisfiable
% 30.98/8.60 |-Branch two:
% 30.98/8.60 | (333) ~ (all_0_44_44 = e2)
% 30.98/8.60 | (493) all_0_45_45 = e2 | all_0_46_46 = e2
% 30.98/8.60 |
% 30.98/8.60 | Equations (621) can reduce 333 to:
% 30.98/8.60 | (566) ~ (e2 = e0)
% 30.98/8.60 |
% 30.98/8.60 | Simplifying 566 yields:
% 30.98/8.60 | (57) ~ (e2 = e0)
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (93), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (402) all_0_59_59 = e4
% 30.98/8.60 |
% 30.98/8.60 | Equations (402) can reduce 17 to:
% 30.98/8.60 | (520) ~ (all_0_42_42 = e4)
% 30.98/8.60 |
% 30.98/8.60 | Equations (402) can reduce 72 to:
% 30.98/8.60 | (936) ~ (all_0_54_54 = e4)
% 30.98/8.60 |
% 30.98/8.60 | Equations (402) can reduce 701 to:
% 30.98/8.60 | (231) ~ (e4 = e2)
% 30.98/8.60 |
% 30.98/8.60 | Equations (402) can reduce 750 to:
% 30.98/8.60 | (251) ~ (e4 = e1)
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (222), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (522) all_0_39_39 = e4
% 30.98/8.60 |
% 30.98/8.60 | Combining equations (336,522) yields a new equation:
% 30.98/8.60 | (269) e4 = e2
% 30.98/8.60 |
% 30.98/8.60 | Equations (269) can reduce 231 to:
% 30.98/8.60 | (270) $false
% 30.98/8.60 |
% 30.98/8.60 |-The branch is then unsatisfiable
% 30.98/8.60 |-Branch two:
% 30.98/8.60 | (591) ~ (all_0_39_39 = e4)
% 30.98/8.60 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 30.98/8.60 |
% 30.98/8.60 | Equations (336) can reduce 591 to:
% 30.98/8.60 | (377) ~ (e4 = e2)
% 30.98/8.60 |
% 30.98/8.60 | Simplifying 377 yields:
% 30.98/8.60 | (231) ~ (e4 = e2)
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (209), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (698) all_0_42_42 = e2
% 30.98/8.60 |
% 30.98/8.60 | Equations (698) can reduce 498 to:
% 30.98/8.60 | (270) $false
% 30.98/8.60 |
% 30.98/8.60 |-The branch is then unsatisfiable
% 30.98/8.60 |-Branch two:
% 30.98/8.60 | (498) ~ (all_0_42_42 = e2)
% 30.98/8.60 | (1732) all_0_46_46 = e2 | all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (1732), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (497) all_0_46_46 = e2
% 30.98/8.60 |
% 30.98/8.60 | Equations (497) can reduce 18 to:
% 30.98/8.60 | (498) ~ (all_0_42_42 = e2)
% 30.98/8.60 |
% 30.98/8.60 | Equations (497) can reduce 38 to:
% 30.98/8.60 | (434) ~ (all_0_45_45 = e2)
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (592), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (358) all_0_41_41 = e4
% 30.98/8.60 |
% 30.98/8.60 | Equations (358) can reduce 51 to:
% 30.98/8.60 | (503) ~ (all_0_45_45 = e4)
% 30.98/8.60 |
% 30.98/8.60 | Simplifying 503 yields:
% 30.98/8.60 | (352) ~ (all_0_45_45 = e4)
% 30.98/8.60 |
% 30.98/8.60 | Equations (358) can reduce 214 to:
% 30.98/8.60 | (1444) ~ (all_0_53_53 = e4)
% 30.98/8.60 |
% 30.98/8.60 | Simplifying 1444 yields:
% 30.98/8.60 | (599) ~ (all_0_53_53 = e4)
% 30.98/8.60 |
% 30.98/8.60 | Equations (358) can reduce 157 to:
% 30.98/8.60 | (277) ~ (all_0_58_58 = e4)
% 30.98/8.60 |
% 30.98/8.60 | Simplifying 277 yields:
% 30.98/8.60 | (278) ~ (all_0_58_58 = e4)
% 30.98/8.60 |
% 30.98/8.60 | Equations (358) can reduce 331 to:
% 30.98/8.60 | (231) ~ (e4 = e2)
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (105), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (374) all_0_45_45 = e2
% 30.98/8.60 |
% 30.98/8.60 | Equations (374) can reduce 434 to:
% 30.98/8.60 | (270) $false
% 30.98/8.60 |
% 30.98/8.60 |-The branch is then unsatisfiable
% 30.98/8.60 |-Branch two:
% 30.98/8.60 | (434) ~ (all_0_45_45 = e2)
% 30.98/8.60 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (435), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (454) all_0_45_45 = e0
% 30.98/8.60 |
% 30.98/8.60 | Equations (454) can reduce 488 to:
% 30.98/8.60 | (270) $false
% 30.98/8.60 |
% 30.98/8.60 |-The branch is then unsatisfiable
% 30.98/8.60 |-Branch two:
% 30.98/8.60 | (488) ~ (all_0_45_45 = e0)
% 30.98/8.60 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (489), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (505) all_0_45_45 = e3
% 30.98/8.60 |
% 30.98/8.60 | Equations (505) can reduce 128 to:
% 30.98/8.60 | (355) ~ (all_0_53_53 = e3)
% 30.98/8.60 |
% 30.98/8.60 | Simplifying 355 yields:
% 30.98/8.60 | (356) ~ (all_0_53_53 = e3)
% 30.98/8.60 |
% 30.98/8.60 | Equations (505) can reduce 108 to:
% 30.98/8.60 | (717) ~ (all_0_58_58 = e3)
% 30.98/8.60 |
% 30.98/8.60 | Simplifying 717 yields:
% 30.98/8.60 | (718) ~ (all_0_58_58 = e3)
% 30.98/8.60 |
% 30.98/8.60 | Equations (505) can reduce 352 to:
% 30.98/8.60 | (719) ~ (e4 = e3)
% 30.98/8.60 |
% 30.98/8.60 | Simplifying 719 yields:
% 30.98/8.60 | (34) ~ (e4 = e3)
% 30.98/8.60 |
% 30.98/8.60 | Equations (505) can reduce 26 to:
% 30.98/8.60 | (136) ~ (e3 = e1)
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (236), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (764) all_0_56_56 = e3
% 30.98/8.60 |
% 30.98/8.60 | Equations (764) can reduce 60 to:
% 30.98/8.60 | (932) ~ (all_0_51_51 = e3)
% 30.98/8.60 |
% 30.98/8.60 | Equations (764) can reduce 81 to:
% 30.98/8.60 | (717) ~ (all_0_58_58 = e3)
% 30.98/8.60 |
% 30.98/8.60 | Simplifying 717 yields:
% 30.98/8.60 | (718) ~ (all_0_58_58 = e3)
% 30.98/8.60 |
% 30.98/8.60 | Equations (764) can reduce 300 to:
% 30.98/8.60 | (223) ~ (e3 = e2)
% 30.98/8.60 |
% 30.98/8.60 | Equations (764) can reduce 995 to:
% 30.98/8.60 | (136) ~ (e3 = e1)
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (204), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (396) all_0_58_58 = e2
% 30.98/8.60 |
% 30.98/8.60 | Equations (396) can reduce 376 to:
% 30.98/8.60 | (270) $false
% 30.98/8.60 |
% 30.98/8.60 |-The branch is then unsatisfiable
% 30.98/8.60 |-Branch two:
% 30.98/8.60 | (376) ~ (all_0_58_58 = e2)
% 30.98/8.60 | (3890) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1 | all_0_58_58 = e0
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (3890), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (585) all_0_58_58 = e0
% 30.98/8.60 |
% 30.98/8.60 | Equations (585) can reduce 70 to:
% 30.98/8.60 | (584) ~ (all_0_53_53 = e0)
% 30.98/8.60 |
% 30.98/8.60 | Equations (585) can reduce 376 to:
% 30.98/8.60 | (566) ~ (e2 = e0)
% 30.98/8.60 |
% 30.98/8.60 | Simplifying 566 yields:
% 30.98/8.60 | (57) ~ (e2 = e0)
% 30.98/8.60 |
% 30.98/8.60 | Equations (585) can reduce 1004 to:
% 30.98/8.60 | (568) ~ (e1 = e0)
% 30.98/8.60 |
% 30.98/8.60 | Simplifying 568 yields:
% 30.98/8.60 | (132) ~ (e1 = e0)
% 30.98/8.60 |
% 30.98/8.60 +-Applying beta-rule and splitting (16), into two cases.
% 30.98/8.60 |-Branch one:
% 30.98/8.60 | (698) all_0_42_42 = e2
% 30.98/8.60 |
% 30.98/8.60 | Equations (698) can reduce 498 to:
% 30.98/8.60 | (270) $false
% 30.98/8.60 |
% 30.98/8.60 |-The branch is then unsatisfiable
% 30.98/8.60 |-Branch two:
% 30.98/8.60 | (498) ~ (all_0_42_42 = e2)
% 30.98/8.61 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (52), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (536) all_0_41_41 = e1
% 30.98/8.61 |
% 30.98/8.61 | Combining equations (358,536) yields a new equation:
% 30.98/8.61 | (525) e4 = e1
% 30.98/8.61 |
% 30.98/8.61 | Simplifying 525 yields:
% 30.98/8.61 | (526) e4 = e1
% 30.98/8.61 |
% 30.98/8.61 | Equations (526) can reduce 251 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (540) ~ (all_0_41_41 = e1)
% 30.98/8.61 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (44), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (502) all_0_43_43 = e4
% 30.98/8.61 |
% 30.98/8.61 | Equations (502) can reduce 249 to:
% 30.98/8.61 | (251) ~ (e4 = e1)
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (21), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (824) all_0_51_51 = e3
% 30.98/8.61 |
% 30.98/8.61 | Equations (824) can reduce 932 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (932) ~ (all_0_51_51 = e3)
% 30.98/8.61 | (1101) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (1101), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (864) all_0_52_52 = e3
% 30.98/8.61 |
% 30.98/8.61 | Combining equations (685,864) yields a new equation:
% 30.98/8.61 | (414) e3 = e2
% 30.98/8.61 |
% 30.98/8.61 | Equations (414) can reduce 223 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (826) ~ (all_0_52_52 = e3)
% 30.98/8.61 | (1107) all_0_53_53 = e3 | all_0_54_54 = e3
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (1107), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (1114) all_0_53_53 = e3
% 30.98/8.61 |
% 30.98/8.61 | Equations (1114) can reduce 356 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (356) ~ (all_0_53_53 = e3)
% 30.98/8.61 | (1119) all_0_54_54 = e3
% 30.98/8.61 |
% 30.98/8.61 | Equations (1119) can reduce 50 to:
% 30.98/8.61 | (932) ~ (all_0_51_51 = e3)
% 30.98/8.61 |
% 30.98/8.61 | Equations (1119) can reduce 252 to:
% 30.98/8.61 | (356) ~ (all_0_53_53 = e3)
% 30.98/8.61 |
% 30.98/8.61 | Equations (1119) can reduce 3011 to:
% 30.98/8.61 | (66) ~ (e3 = e0)
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (127), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (541) all_0_42_42 = e1
% 30.98/8.61 |
% 30.98/8.61 | Equations (541) can reduce 498 to:
% 30.98/8.61 | (645) ~ (e2 = e1)
% 30.98/8.61 |
% 30.98/8.61 | Simplifying 645 yields:
% 30.98/8.61 | (141) ~ (e2 = e1)
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (64), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (954) all_0_51_51 = e0
% 30.98/8.61 |
% 30.98/8.61 | Equations (954) can reduce 932 to:
% 30.98/8.61 | (788) ~ (e3 = e0)
% 30.98/8.61 |
% 30.98/8.61 | Simplifying 788 yields:
% 30.98/8.61 | (66) ~ (e3 = e0)
% 30.98/8.61 |
% 30.98/8.61 | Equations (954) can reduce 255 to:
% 30.98/8.61 | (566) ~ (e2 = e0)
% 30.98/8.61 |
% 30.98/8.61 | Simplifying 566 yields:
% 30.98/8.61 | (57) ~ (e2 = e0)
% 30.98/8.61 |
% 30.98/8.61 | Equations (954) can reduce 748 to:
% 30.98/8.61 | (568) ~ (e1 = e0)
% 30.98/8.61 |
% 30.98/8.61 | Simplifying 568 yields:
% 30.98/8.61 | (132) ~ (e1 = e0)
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (135), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (820) all_0_51_51 = e1
% 30.98/8.61 |
% 30.98/8.61 | Combining equations (954,820) yields a new equation:
% 30.98/8.61 | (560) e1 = e0
% 30.98/8.61 |
% 30.98/8.61 | Equations (560) can reduce 132 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (748) ~ (all_0_51_51 = e1)
% 30.98/8.61 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 30.98/8.61 |
% 30.98/8.61 | Equations (954) can reduce 748 to:
% 30.98/8.61 | (568) ~ (e1 = e0)
% 30.98/8.61 |
% 30.98/8.61 | Simplifying 568 yields:
% 30.98/8.61 | (132) ~ (e1 = e0)
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (762), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (552) all_0_48_48 = e1
% 30.98/8.61 |
% 30.98/8.61 | Combining equations (311,552) yields a new equation:
% 30.98/8.61 | (531) e2 = e1
% 30.98/8.61 |
% 30.98/8.61 | Simplifying 531 yields:
% 30.98/8.61 | (322) e2 = e1
% 30.98/8.61 |
% 30.98/8.61 | Equations (322) can reduce 141 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (588) ~ (all_0_48_48 = e1)
% 30.98/8.61 | (4925) all_0_53_53 = e1 | all_0_58_58 = e1
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (4925), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (853) all_0_53_53 = e1
% 30.98/8.61 |
% 30.98/8.61 | Equations (853) can reduce 599 to:
% 30.98/8.61 | (1021) ~ (e4 = e1)
% 30.98/8.61 |
% 30.98/8.61 | Simplifying 1021 yields:
% 30.98/8.61 | (251) ~ (e4 = e1)
% 30.98/8.61 |
% 30.98/8.61 | Instantiating formula (201) with e2, e3, all_0_13_13, e1 and discharging atoms op(e2, e3) = all_0_13_13, op(e2, e3) = e1, yields:
% 30.98/8.61 | (5957) all_0_13_13 = e1
% 30.98/8.61 |
% 30.98/8.61 | Instantiating formula (201) with e2, e1, all_0_19_19, e2 and discharging atoms op(e2, e1) = all_0_19_19, op(e2, e1) = e2, yields:
% 30.98/8.61 | (14991) all_0_19_19 = e2
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (87), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (650) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (650), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (651) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (651), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (652) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 30.98/8.61 |
% 30.98/8.61 | Applying alpha-rule on (652) yields:
% 30.98/8.61 | (653) all_0_13_13 = e4
% 30.98/8.61 | (654) ~ (all_0_14_14 = e2)
% 30.98/8.61 |
% 30.98/8.61 | Combining equations (5957,653) yields a new equation:
% 30.98/8.61 | (526) e4 = e1
% 30.98/8.61 |
% 30.98/8.61 | Equations (526) can reduce 251 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (657) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 30.98/8.61 |
% 30.98/8.61 | Applying alpha-rule on (657) yields:
% 30.98/8.61 | (658) all_0_15_15 = e3
% 30.98/8.61 | (659) ~ (all_0_16_16 = e2)
% 30.98/8.61 |
% 30.98/8.61 | Combining equations (5959,658) yields a new equation:
% 30.98/8.61 | (784) e3 = e0
% 30.98/8.61 |
% 30.98/8.61 | Equations (784) can reduce 66 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (663) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 30.98/8.61 |
% 30.98/8.61 | Applying alpha-rule on (663) yields:
% 30.98/8.61 | (664) all_0_17_17 = e1
% 30.98/8.61 | (665) ~ (all_0_18_18 = e2)
% 30.98/8.61 |
% 30.98/8.61 | Combining equations (664,11735) yields a new equation:
% 30.98/8.61 | (526) e4 = e1
% 30.98/8.61 |
% 30.98/8.61 | Equations (526) can reduce 251 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (1762) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 30.98/8.61 |
% 30.98/8.61 | Applying alpha-rule on (1762) yields:
% 30.98/8.61 | (1763) all_0_19_19 = e0
% 30.98/8.61 | (1764) ~ (all_0_20_20 = e2)
% 30.98/8.61 |
% 30.98/8.61 | Combining equations (1763,14991) yields a new equation:
% 30.98/8.61 | (316) e2 = e0
% 30.98/8.61 |
% 30.98/8.61 | Equations (316) can reduce 57 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (874) ~ (all_0_53_53 = e1)
% 30.98/8.61 | (1001) all_0_58_58 = e1
% 30.98/8.61 |
% 30.98/8.61 | Combining equations (1001,585) yields a new equation:
% 30.98/8.61 | (571) e1 = e0
% 30.98/8.61 |
% 30.98/8.61 | Simplifying 571 yields:
% 30.98/8.61 | (560) e1 = e0
% 30.98/8.61 |
% 30.98/8.61 | Equations (560) can reduce 132 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (987) ~ (all_0_51_51 = e0)
% 30.98/8.61 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (13), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (576) all_0_53_53 = e2
% 30.98/8.61 |
% 30.98/8.61 | Equations (576) can reduce 259 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (259) ~ (all_0_53_53 = e2)
% 30.98/8.61 | (5715) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (5715), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (423) all_0_53_53 = e0
% 30.98/8.61 |
% 30.98/8.61 | Equations (423) can reduce 584 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (584) ~ (all_0_53_53 = e0)
% 30.98/8.61 | (5719) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (5719), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (1114) all_0_53_53 = e3
% 30.98/8.61 |
% 30.98/8.61 | Equations (1114) can reduce 356 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (356) ~ (all_0_53_53 = e3)
% 30.98/8.61 | (5723) all_0_53_53 = e4 | all_0_53_53 = e1
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (5723), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (853) all_0_53_53 = e1
% 30.98/8.61 |
% 30.98/8.61 | Equations (853) can reduce 584 to:
% 30.98/8.61 | (132) ~ (e1 = e0)
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (3067), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (827) all_0_52_52 = e0
% 30.98/8.61 |
% 30.98/8.61 | Combining equations (685,827) yields a new equation:
% 30.98/8.61 | (622) e2 = e0
% 30.98/8.61 |
% 30.98/8.61 | Simplifying 622 yields:
% 30.98/8.61 | (316) e2 = e0
% 30.98/8.61 |
% 30.98/8.61 | Equations (316) can reduce 57 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (925) ~ (all_0_52_52 = e0)
% 30.98/8.61 | (3073) all_0_53_53 = e0 | all_0_54_54 = e0
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (3073), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (423) all_0_53_53 = e0
% 30.98/8.61 |
% 30.98/8.61 | Combining equations (853,423) yields a new equation:
% 30.98/8.61 | (571) e1 = e0
% 30.98/8.61 |
% 30.98/8.61 | Simplifying 571 yields:
% 30.98/8.61 | (560) e1 = e0
% 30.98/8.61 |
% 30.98/8.61 | Equations (560) can reduce 132 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (584) ~ (all_0_53_53 = e0)
% 30.98/8.61 | (3084) all_0_54_54 = e0
% 30.98/8.61 |
% 30.98/8.61 | Combining equations (1119,3084) yields a new equation:
% 30.98/8.61 | (783) e3 = e0
% 30.98/8.61 |
% 30.98/8.61 | Simplifying 783 yields:
% 30.98/8.61 | (784) e3 = e0
% 30.98/8.61 |
% 30.98/8.61 | Equations (784) can reduce 66 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (874) ~ (all_0_53_53 = e1)
% 30.98/8.61 | (367) all_0_53_53 = e4
% 30.98/8.61 |
% 30.98/8.61 | Equations (367) can reduce 599 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (640) ~ (all_0_42_42 = e1)
% 30.98/8.61 | (4628) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (4628), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (589) all_0_49_49 = e1
% 30.98/8.61 |
% 30.98/8.61 | Combining equations (563,589) yields a new equation:
% 30.98/8.61 | (560) e1 = e0
% 30.98/8.61 |
% 30.98/8.61 | Equations (560) can reduce 132 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (543) ~ (all_0_49_49 = e1)
% 30.98/8.61 | (4726) all_0_54_54 = e1 | all_0_59_59 = e1
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (4726), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (875) all_0_54_54 = e1
% 30.98/8.61 |
% 30.98/8.61 | Combining equations (1119,875) yields a new equation:
% 30.98/8.61 | (537) e3 = e1
% 30.98/8.61 |
% 30.98/8.61 | Simplifying 537 yields:
% 30.98/8.61 | (538) e3 = e1
% 30.98/8.61 |
% 30.98/8.61 | Equations (538) can reduce 136 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (425) ~ (all_0_54_54 = e1)
% 30.98/8.61 | (424) all_0_59_59 = e1
% 30.98/8.61 |
% 30.98/8.61 | Combining equations (424,402) yields a new equation:
% 30.98/8.61 | (526) e4 = e1
% 30.98/8.61 |
% 30.98/8.61 | Equations (526) can reduce 251 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (510) ~ (all_0_43_43 = e4)
% 30.98/8.61 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (21), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (824) all_0_51_51 = e3
% 30.98/8.61 |
% 30.98/8.61 | Equations (824) can reduce 932 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (932) ~ (all_0_51_51 = e3)
% 30.98/8.61 | (1101) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 30.98/8.61 |
% 30.98/8.61 +-Applying beta-rule and splitting (166), into two cases.
% 30.98/8.61 |-Branch one:
% 30.98/8.61 | (522) all_0_39_39 = e4
% 30.98/8.61 |
% 30.98/8.61 | Combining equations (522,336) yields a new equation:
% 30.98/8.61 | (268) e4 = e2
% 30.98/8.61 |
% 30.98/8.61 | Simplifying 268 yields:
% 30.98/8.61 | (269) e4 = e2
% 30.98/8.61 |
% 30.98/8.61 | Equations (269) can reduce 231 to:
% 30.98/8.61 | (270) $false
% 30.98/8.61 |
% 30.98/8.61 |-The branch is then unsatisfiable
% 30.98/8.61 |-Branch two:
% 30.98/8.61 | (591) ~ (all_0_39_39 = e4)
% 30.98/8.62 | (4522) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 30.98/8.62 |
% 30.98/8.62 +-Applying beta-rule and splitting (1101), into two cases.
% 30.98/8.62 |-Branch one:
% 30.98/8.62 | (864) all_0_52_52 = e3
% 30.98/8.62 |
% 30.98/8.62 | Combining equations (864,685) yields a new equation:
% 30.98/8.62 | (437) e3 = e2
% 30.98/8.62 |
% 30.98/8.62 | Simplifying 437 yields:
% 30.98/8.62 | (414) e3 = e2
% 30.98/8.62 |
% 30.98/8.62 | Equations (414) can reduce 223 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (826) ~ (all_0_52_52 = e3)
% 30.98/8.62 | (1107) all_0_53_53 = e3 | all_0_54_54 = e3
% 30.98/8.62 |
% 30.98/8.62 +-Applying beta-rule and splitting (1107), into two cases.
% 30.98/8.62 |-Branch one:
% 30.98/8.62 | (1114) all_0_53_53 = e3
% 30.98/8.62 |
% 30.98/8.62 | Equations (1114) can reduce 356 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (356) ~ (all_0_53_53 = e3)
% 30.98/8.62 | (1119) all_0_54_54 = e3
% 30.98/8.62 |
% 30.98/8.62 | Equations (1119) can reduce 936 to:
% 30.98/8.62 | (719) ~ (e4 = e3)
% 30.98/8.62 |
% 30.98/8.62 | Simplifying 719 yields:
% 30.98/8.62 | (34) ~ (e4 = e3)
% 30.98/8.62 |
% 30.98/8.62 +-Applying beta-rule and splitting (4522), into two cases.
% 30.98/8.62 |-Branch one:
% 30.98/8.62 | (502) all_0_43_43 = e4
% 30.98/8.62 |
% 30.98/8.62 | Equations (502) can reduce 510 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (510) ~ (all_0_43_43 = e4)
% 30.98/8.62 | (4527) all_0_51_51 = e4 | all_0_56_56 = e4
% 30.98/8.62 |
% 30.98/8.62 +-Applying beta-rule and splitting (4527), into two cases.
% 30.98/8.62 |-Branch one:
% 30.98/8.62 | (1467) all_0_51_51 = e4
% 30.98/8.62 |
% 30.98/8.62 | Equations (1467) can reduce 697 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (697) ~ (all_0_51_51 = e4)
% 30.98/8.62 | (4744) all_0_56_56 = e4
% 30.98/8.62 |
% 30.98/8.62 | Combining equations (764,4744) yields a new equation:
% 30.98/8.62 | (359) e4 = e3
% 30.98/8.62 |
% 30.98/8.62 | Equations (359) can reduce 34 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (431) ~ (all_0_58_58 = e0)
% 30.98/8.62 | (4709) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1
% 30.98/8.62 |
% 30.98/8.62 +-Applying beta-rule and splitting (4709), into two cases.
% 30.98/8.62 |-Branch one:
% 30.98/8.62 | (4713) all_0_58_58 = e3
% 30.98/8.62 |
% 30.98/8.62 | Equations (4713) can reduce 718 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (718) ~ (all_0_58_58 = e3)
% 30.98/8.62 | (4716) all_0_58_58 = e4 | all_0_58_58 = e1
% 30.98/8.62 |
% 30.98/8.62 +-Applying beta-rule and splitting (4716), into two cases.
% 30.98/8.62 |-Branch one:
% 30.98/8.62 | (1001) all_0_58_58 = e1
% 30.98/8.62 |
% 30.98/8.62 | Equations (1001) can reduce 1004 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (1004) ~ (all_0_58_58 = e1)
% 30.98/8.62 | (600) all_0_58_58 = e4
% 30.98/8.62 |
% 30.98/8.62 | Equations (600) can reduce 278 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (767) ~ (all_0_56_56 = e3)
% 30.98/8.62 | (768) all_0_57_57 = e3 | all_0_58_58 = e3 | all_0_59_59 = e3
% 30.98/8.62 |
% 30.98/8.62 +-Applying beta-rule and splitting (768), into two cases.
% 30.98/8.62 |-Branch one:
% 30.98/8.62 | (869) all_0_57_57 = e3
% 30.98/8.62 |
% 30.98/8.62 | Combining equations (869,997) yields a new equation:
% 30.98/8.62 | (537) e3 = e1
% 30.98/8.62 |
% 30.98/8.62 | Simplifying 537 yields:
% 30.98/8.62 | (538) e3 = e1
% 30.98/8.62 |
% 30.98/8.62 | Equations (538) can reduce 136 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (846) ~ (all_0_57_57 = e3)
% 30.98/8.62 | (5225) all_0_58_58 = e3 | all_0_59_59 = e3
% 30.98/8.62 |
% 30.98/8.62 +-Applying beta-rule and splitting (5225), into two cases.
% 30.98/8.62 |-Branch one:
% 30.98/8.62 | (4713) all_0_58_58 = e3
% 30.98/8.62 |
% 30.98/8.62 | Equations (4713) can reduce 718 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (718) ~ (all_0_58_58 = e3)
% 30.98/8.62 | (412) all_0_59_59 = e3
% 30.98/8.62 |
% 30.98/8.62 | Combining equations (402,412) yields a new equation:
% 30.98/8.62 | (660) e4 = e3
% 30.98/8.62 |
% 30.98/8.62 | Simplifying 660 yields:
% 30.98/8.62 | (359) e4 = e3
% 30.98/8.62 |
% 30.98/8.62 | Equations (359) can reduce 34 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (354) ~ (all_0_45_45 = e3)
% 30.98/8.62 | (363) all_0_45_45 = e4
% 30.98/8.62 |
% 30.98/8.62 | Equations (363) can reduce 352 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (361) ~ (all_0_41_41 = e4)
% 30.98/8.62 | (512) all_0_42_42 = e4
% 30.98/8.62 |
% 30.98/8.62 | Equations (512) can reduce 520 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (1436) ~ (all_0_46_46 = e2)
% 30.98/8.62 | (3824) all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 30.98/8.62 |
% 30.98/8.62 +-Applying beta-rule and splitting (3824), into two cases.
% 30.98/8.62 |-Branch one:
% 30.98/8.62 | (307) all_0_49_49 = e2
% 30.98/8.62 |
% 30.98/8.62 | Combining equations (307,563) yields a new equation:
% 30.98/8.62 | (622) e2 = e0
% 30.98/8.62 |
% 30.98/8.62 | Simplifying 622 yields:
% 30.98/8.62 | (316) e2 = e0
% 30.98/8.62 |
% 30.98/8.62 | Equations (316) can reduce 57 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (296) ~ (all_0_49_49 = e2)
% 30.98/8.62 | (3829) all_0_54_54 = e2 | all_0_59_59 = e2
% 30.98/8.62 |
% 30.98/8.62 +-Applying beta-rule and splitting (3829), into two cases.
% 30.98/8.62 |-Branch one:
% 30.98/8.62 | (3657) all_0_54_54 = e2
% 30.98/8.62 |
% 30.98/8.62 | Equations (3657) can reduce 261 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (261) ~ (all_0_54_54 = e2)
% 30.98/8.62 | (399) all_0_59_59 = e2
% 30.98/8.62 |
% 30.98/8.62 | Combining equations (402,399) yields a new equation:
% 30.98/8.62 | (268) e4 = e2
% 30.98/8.62 |
% 30.98/8.62 | Simplifying 268 yields:
% 30.98/8.62 | (269) e4 = e2
% 30.98/8.62 |
% 30.98/8.62 | Equations (269) can reduce 231 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (280) ~ (all_0_59_59 = e4)
% 30.98/8.62 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 30.98/8.62 |
% 30.98/8.62 +-Applying beta-rule and splitting (407), into two cases.
% 30.98/8.62 |-Branch one:
% 30.98/8.62 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 30.98/8.62 |
% 30.98/8.62 +-Applying beta-rule and splitting (408), into two cases.
% 30.98/8.62 |-Branch one:
% 30.98/8.62 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 30.98/8.62 |
% 30.98/8.62 +-Applying beta-rule and splitting (409), into two cases.
% 30.98/8.62 |-Branch one:
% 30.98/8.62 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 30.98/8.62 |
% 30.98/8.62 | Applying alpha-rule on (410) yields:
% 30.98/8.62 | (411) all_0_43_43 = e0
% 30.98/8.62 | (412) all_0_59_59 = e3
% 30.98/8.62 | (413) ~ (all_0_46_46 = e3)
% 30.98/8.62 |
% 30.98/8.62 | Equations (411) can reduce 455 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 30.98/8.62 |
% 30.98/8.62 | Applying alpha-rule on (416) yields:
% 30.98/8.62 | (411) all_0_43_43 = e0
% 30.98/8.62 | (412) all_0_59_59 = e3
% 30.98/8.62 | (419) ~ (all_0_56_56 = e0)
% 30.98/8.62 |
% 30.98/8.62 | Equations (411) can reduce 455 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 30.98/8.62 |
% 30.98/8.62 | Applying alpha-rule on (422) yields:
% 30.98/8.62 | (423) all_0_53_53 = e0
% 30.98/8.62 | (424) all_0_59_59 = e1
% 30.98/8.62 | (425) ~ (all_0_54_54 = e1)
% 30.98/8.62 |
% 30.98/8.62 | Equations (424) can reduce 750 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 30.98/8.62 |
% 30.98/8.62 | Applying alpha-rule on (428) yields:
% 30.98/8.62 | (423) all_0_53_53 = e0
% 30.98/8.62 | (424) all_0_59_59 = e1
% 30.98/8.62 | (431) ~ (all_0_58_58 = e0)
% 30.98/8.62 |
% 30.98/8.62 | Equations (424) can reduce 750 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (291) ~ (all_0_39_39 = e2)
% 30.98/8.62 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 30.98/8.62 |
% 30.98/8.62 +-Applying beta-rule and splitting (339), into two cases.
% 30.98/8.62 |-Branch one:
% 30.98/8.62 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 30.98/8.62 |
% 30.98/8.62 +-Applying beta-rule and splitting (340), into two cases.
% 30.98/8.62 |-Branch one:
% 30.98/8.62 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 30.98/8.62 |
% 30.98/8.62 | Applying alpha-rule on (341) yields:
% 30.98/8.62 | (342) all_0_0_0 = e1
% 30.98/8.62 | (343) ~ (all_0_1_1 = e4)
% 30.98/8.62 |
% 30.98/8.62 | Combining equations (342,9064) yields a new equation:
% 30.98/8.62 | (571) e1 = e0
% 30.98/8.62 |
% 30.98/8.62 | Simplifying 571 yields:
% 30.98/8.62 | (560) e1 = e0
% 30.98/8.62 |
% 30.98/8.62 | Equations (560) can reduce 132 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 30.98/8.62 |
% 30.98/8.62 | Applying alpha-rule on (346) yields:
% 30.98/8.62 | (347) all_0_2_2 = e0
% 30.98/8.62 | (348) ~ (all_0_3_3 = e4)
% 30.98/8.62 |
% 30.98/8.62 | Combining equations (12353,347) yields a new equation:
% 30.98/8.62 | (783) e3 = e0
% 30.98/8.62 |
% 30.98/8.62 | Simplifying 783 yields:
% 30.98/8.62 | (784) e3 = e0
% 30.98/8.62 |
% 30.98/8.62 | Equations (784) can reduce 66 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 30.98/8.62 |
% 30.98/8.62 | Applying alpha-rule on (350) yields:
% 30.98/8.62 | (351) all_0_41_41 = e3
% 30.98/8.62 | (352) ~ (all_0_45_45 = e4)
% 30.98/8.62 |
% 30.98/8.62 | Equations (351) can reduce 1237 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (675) ~ (all_0_40_40 = e3)
% 30.98/8.62 | (676) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 30.98/8.62 |
% 30.98/8.62 +-Applying beta-rule and splitting (603), into two cases.
% 30.98/8.62 |-Branch one:
% 30.98/8.62 | (671) all_0_40_40 = e3
% 30.98/8.62 |
% 30.98/8.62 | Equations (671) can reduce 675 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (675) ~ (all_0_40_40 = e3)
% 30.98/8.62 | (530) all_0_40_40 = e1
% 30.98/8.62 |
% 30.98/8.62 | Equations (530) can reduce 534 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (625) ~ (all_0_44_44 = e0)
% 30.98/8.62 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 30.98/8.62 |
% 30.98/8.62 +-Applying beta-rule and splitting (373), into two cases.
% 30.98/8.62 |-Branch one:
% 30.98/8.62 | (621) all_0_44_44 = e0
% 30.98/8.62 |
% 30.98/8.62 | Equations (621) can reduce 625 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (625) ~ (all_0_44_44 = e0)
% 30.98/8.62 | (858) all_0_44_44 = e3
% 30.98/8.62 |
% 30.98/8.62 | Equations (858) can reduce 15 to:
% 30.98/8.62 | (675) ~ (all_0_40_40 = e3)
% 30.98/8.62 |
% 30.98/8.62 | Equations (858) can reduce 241 to:
% 30.98/8.62 | (786) ~ (all_0_43_43 = e3)
% 30.98/8.62 |
% 30.98/8.62 | Equations (858) can reduce 229 to:
% 30.98/8.62 | (353) ~ (all_0_45_45 = e3)
% 30.98/8.62 |
% 30.98/8.62 | Simplifying 353 yields:
% 30.98/8.62 | (354) ~ (all_0_45_45 = e3)
% 30.98/8.62 |
% 30.98/8.62 | Equations (858) can reduce 174 to:
% 30.98/8.62 | (1518) ~ (all_0_46_46 = e3)
% 30.98/8.62 |
% 30.98/8.62 | Simplifying 1518 yields:
% 30.98/8.62 | (413) ~ (all_0_46_46 = e3)
% 30.98/8.62 |
% 30.98/8.62 | Equations (858) can reduce 10 to:
% 30.98/8.62 | (2238) ~ (all_0_57_57 = e3)
% 30.98/8.62 |
% 30.98/8.62 | Simplifying 2238 yields:
% 30.98/8.62 | (846) ~ (all_0_57_57 = e3)
% 30.98/8.62 |
% 30.98/8.62 | From (858) and (5) follows:
% 30.98/8.62 | (15213) op(e3, e3) = all_0_16_16
% 30.98/8.62 |
% 30.98/8.62 | From (858) and (148) follows:
% 30.98/8.62 | (15214) op(e3, e2) = e3
% 30.98/8.62 |
% 30.98/8.62 +-Applying beta-rule and splitting (603), into two cases.
% 30.98/8.62 |-Branch one:
% 30.98/8.62 | (671) all_0_40_40 = e3
% 30.98/8.62 |
% 30.98/8.62 | Equations (671) can reduce 675 to:
% 30.98/8.62 | (270) $false
% 30.98/8.62 |
% 30.98/8.62 |-The branch is then unsatisfiable
% 30.98/8.62 |-Branch two:
% 30.98/8.62 | (675) ~ (all_0_40_40 = e3)
% 30.98/8.62 | (530) all_0_40_40 = e1
% 30.98/8.62 |
% 30.98/8.62 | Combining equations (530,9065) yields a new equation:
% 30.98/8.63 | (11737) all_0_2_2 = e1
% 30.98/8.63 |
% 30.98/8.63 | Equations (530) can reduce 114 to:
% 30.98/8.63 | (528) ~ (all_0_39_39 = e1)
% 30.98/8.63 |
% 30.98/8.63 | Equations (530) can reduce 147 to:
% 30.98/8.63 | (637) ~ (all_0_41_41 = e1)
% 30.98/8.63 |
% 30.98/8.63 | Simplifying 637 yields:
% 30.98/8.63 | (540) ~ (all_0_41_41 = e1)
% 30.98/8.63 |
% 30.98/8.63 | Equations (530) can reduce 145 to:
% 30.98/8.63 | (639) ~ (all_0_42_42 = e1)
% 30.98/8.63 |
% 30.98/8.63 | Simplifying 639 yields:
% 30.98/8.63 | (640) ~ (all_0_42_42 = e1)
% 30.98/8.63 |
% 30.98/8.63 | Equations (530) can reduce 149 to:
% 30.98/8.63 | (643) ~ (all_0_57_57 = e1)
% 30.98/8.63 |
% 30.98/8.63 | Simplifying 643 yields:
% 30.98/8.63 | (644) ~ (all_0_57_57 = e1)
% 30.98/8.63 |
% 30.98/8.63 | Equations (530) can reduce 675 to:
% 30.98/8.63 | (769) ~ (e3 = e1)
% 30.98/8.63 |
% 30.98/8.63 | Simplifying 769 yields:
% 30.98/8.63 | (136) ~ (e3 = e1)
% 30.98/8.63 |
% 30.98/8.63 | Equations (530) can reduce 602 to:
% 30.98/8.63 | (645) ~ (e2 = e1)
% 30.98/8.63 |
% 30.98/8.63 | Simplifying 645 yields:
% 30.98/8.63 | (141) ~ (e2 = e1)
% 30.98/8.63 |
% 30.98/8.63 +-Applying beta-rule and splitting (33), into two cases.
% 30.98/8.63 |-Branch one:
% 30.98/8.63 | (392) all_0_57_57 = e2
% 30.98/8.63 |
% 30.98/8.63 | Equations (392) can reduce 335 to:
% 30.98/8.63 | (270) $false
% 30.98/8.63 |
% 30.98/8.63 |-The branch is then unsatisfiable
% 30.98/8.63 |-Branch two:
% 30.98/8.63 | (335) ~ (all_0_57_57 = e2)
% 30.98/8.63 | (670) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 30.98/8.63 |
% 30.98/8.63 +-Applying beta-rule and splitting (670), into two cases.
% 30.98/8.63 |-Branch one:
% 30.98/8.63 | (2258) all_0_57_57 = e0
% 30.98/8.63 |
% 30.98/8.63 | Equations (2258) can reduce 104 to:
% 30.98/8.63 | (419) ~ (all_0_56_56 = e0)
% 30.98/8.63 |
% 30.98/8.63 | Equations (2258) can reduce 37 to:
% 30.98/8.63 | (3530) ~ (all_0_58_58 = e0)
% 30.98/8.63 |
% 30.98/8.63 | Simplifying 3530 yields:
% 30.98/8.63 | (431) ~ (all_0_58_58 = e0)
% 30.98/8.63 |
% 30.98/8.63 | Equations (2258) can reduce 140 to:
% 30.98/8.63 | (4000) ~ (all_0_59_59 = e0)
% 30.98/8.63 |
% 30.98/8.63 | Simplifying 4000 yields:
% 30.98/8.63 | (4001) ~ (all_0_59_59 = e0)
% 30.98/8.63 |
% 30.98/8.63 | Equations (2258) can reduce 143 to:
% 30.98/8.63 | (456) ~ (e4 = e0)
% 30.98/8.63 |
% 30.98/8.63 | Simplifying 456 yields:
% 30.98/8.63 | (6) ~ (e4 = e0)
% 30.98/8.63 |
% 30.98/8.63 | Equations (2258) can reduce 644 to:
% 30.98/8.63 | (568) ~ (e1 = e0)
% 30.98/8.63 |
% 30.98/8.63 | Simplifying 568 yields:
% 30.98/8.63 | (132) ~ (e1 = e0)
% 30.98/8.63 |
% 30.98/8.63 | From (2258) and (207) follows:
% 30.98/8.63 | (15245) op(e0, e2) = e0
% 30.98/8.63 |
% 30.98/8.63 | Instantiating formula (201) with e3, e3, all_0_16_16, all_0_43_43 and discharging atoms op(e3, e3) = all_0_16_16, op(e3, e3) = all_0_43_43, yields:
% 30.98/8.63 | (15246) all_0_16_16 = all_0_43_43
% 30.98/8.63 |
% 30.98/8.63 | From (15246) and (15213) follows:
% 30.98/8.63 | (248) op(e3, e3) = all_0_43_43
% 30.98/8.63 |
% 30.98/8.63 +-Applying beta-rule and splitting (220), into two cases.
% 30.98/8.63 |-Branch one:
% 30.98/8.63 | (497) all_0_46_46 = e2
% 30.98/8.63 |
% 30.98/8.63 | Equations (497) can reduce 18 to:
% 30.98/8.63 | (498) ~ (all_0_42_42 = e2)
% 30.98/8.63 |
% 30.98/8.63 | Equations (497) can reduce 38 to:
% 30.98/8.63 | (434) ~ (all_0_45_45 = e2)
% 30.98/8.63 |
% 30.98/8.63 | Equations (497) can reduce 215 to:
% 30.98/8.63 | (260) ~ (all_0_54_54 = e2)
% 30.98/8.63 |
% 30.98/8.63 | Simplifying 260 yields:
% 30.98/8.63 | (261) ~ (all_0_54_54 = e2)
% 30.98/8.63 |
% 30.98/8.63 | Equations (497) can reduce 206 to:
% 30.98/8.63 | (700) ~ (all_0_59_59 = e2)
% 30.98/8.63 |
% 30.98/8.63 | Simplifying 700 yields:
% 30.98/8.63 | (701) ~ (all_0_59_59 = e2)
% 30.98/8.63 |
% 30.98/8.63 | Equations (497) can reduce 413 to:
% 30.98/8.63 | (301) ~ (e3 = e2)
% 30.98/8.63 |
% 30.98/8.63 | Simplifying 301 yields:
% 30.98/8.63 | (223) ~ (e3 = e2)
% 30.98/8.63 |
% 30.98/8.63 | From (497) and (74) follows:
% 30.98/8.63 | (11896) op(e3, e2) = all_0_33_33
% 30.98/8.63 |
% 30.98/8.63 | From (497) and (242) follows:
% 30.98/8.63 | (15258) op(e3, e0) = e2
% 30.98/8.63 |
% 30.98/8.63 | From (497) and (89) follows:
% 30.98/8.63 | (15259) op(e0, e2) = all_0_32_32
% 30.98/8.63 |
% 30.98/8.63 +-Applying beta-rule and splitting (164), into two cases.
% 30.98/8.63 |-Branch one:
% 30.98/8.63 | (336) all_0_39_39 = e2
% 30.98/8.63 |
% 30.98/8.63 | Equations (336) can reduce 184 to:
% 30.98/8.63 | (1336) ~ (all_0_42_42 = e2)
% 30.98/8.63 |
% 30.98/8.63 | Simplifying 1336 yields:
% 30.98/8.63 | (498) ~ (all_0_42_42 = e2)
% 30.98/8.63 |
% 30.98/8.63 | Equations (336) can reduce 167 to:
% 30.98/8.63 | (5937) ~ (all_0_43_43 = e2)
% 30.98/8.63 |
% 30.98/8.63 | Simplifying 5937 yields:
% 30.98/8.63 | (292) ~ (all_0_43_43 = e2)
% 30.98/8.63 |
% 30.98/8.63 | Equations (336) can reduce 32 to:
% 30.98/8.63 | (254) ~ (all_0_51_51 = e2)
% 30.98/8.63 |
% 30.98/8.63 | Simplifying 254 yields:
% 30.98/8.63 | (255) ~ (all_0_51_51 = e2)
% 30.98/8.63 |
% 30.98/8.63 | Equations (336) can reduce 212 to:
% 30.98/8.63 | (299) ~ (all_0_56_56 = e2)
% 30.98/8.63 |
% 30.98/8.63 | Simplifying 299 yields:
% 30.98/8.63 | (300) ~ (all_0_56_56 = e2)
% 30.98/8.63 |
% 30.98/8.63 | Equations (336) can reduce 528 to:
% 30.98/8.63 | (141) ~ (e2 = e1)
% 30.98/8.63 |
% 30.98/8.63 | From (336) and (200) follows:
% 30.98/8.63 | (12057) op(e3, e2) = all_0_4_4
% 30.98/8.63 |
% 30.98/8.63 | Instantiating formula (201) with e3, e2, all_0_4_4, e3 and discharging atoms op(e3, e2) = all_0_4_4, op(e3, e2) = e3, yields:
% 30.98/8.63 | (15271) all_0_4_4 = e3
% 30.98/8.63 |
% 30.98/8.63 | Instantiating formula (201) with e3, e2, all_0_33_33, all_0_4_4 and discharging atoms op(e3, e2) = all_0_4_4, op(e3, e2) = all_0_33_33, yields:
% 30.98/8.63 | (12098) all_0_4_4 = all_0_33_33
% 30.98/8.63 |
% 30.98/8.63 | Instantiating formula (201) with e0, e2, all_0_32_32, e0 and discharging atoms op(e0, e2) = all_0_32_32, op(e0, e2) = e0, yields:
% 30.98/8.63 | (15273) all_0_32_32 = e0
% 30.98/8.63 |
% 31.06/8.63 | Combining equations (15271,12098) yields a new equation:
% 31.06/8.63 | (15274) all_0_33_33 = e3
% 31.06/8.63 |
% 31.06/8.63 | Combining equations (15274,12098) yields a new equation:
% 31.06/8.63 | (15271) all_0_4_4 = e3
% 31.06/8.63 |
% 31.06/8.63 +-Applying beta-rule and splitting (44), into two cases.
% 31.06/8.63 |-Branch one:
% 31.06/8.63 | (502) all_0_43_43 = e4
% 31.06/8.63 |
% 31.06/8.63 | Equations (502) can reduce 84 to:
% 31.06/8.63 | (503) ~ (all_0_45_45 = e4)
% 31.06/8.63 |
% 31.06/8.63 | Simplifying 503 yields:
% 31.06/8.63 | (352) ~ (all_0_45_45 = e4)
% 31.06/8.63 |
% 31.06/8.63 | Equations (502) can reduce 786 to:
% 31.06/8.63 | (34) ~ (e4 = e3)
% 31.06/8.63 |
% 31.06/8.63 | From (502) and (248) follows:
% 31.06/8.64 | (14204) op(e3, e3) = e4
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (75), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (411) all_0_43_43 = e0
% 31.06/8.64 |
% 31.06/8.64 | Combining equations (502,411) yields a new equation:
% 31.06/8.64 | (478) e4 = e0
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 478 yields:
% 31.06/8.64 | (479) e4 = e0
% 31.06/8.64 |
% 31.06/8.64 | Equations (479) can reduce 6 to:
% 31.06/8.64 | (270) $false
% 31.06/8.64 |
% 31.06/8.64 |-The branch is then unsatisfiable
% 31.06/8.64 |-Branch two:
% 31.06/8.64 | (455) ~ (all_0_43_43 = e0)
% 31.06/8.64 | (940) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (940), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (315) all_0_47_47 = e0
% 31.06/8.64 |
% 31.06/8.64 | Combining equations (321,315) yields a new equation:
% 31.06/8.64 | (571) e1 = e0
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 571 yields:
% 31.06/8.64 | (560) e1 = e0
% 31.06/8.64 |
% 31.06/8.64 | Equations (560) can reduce 132 to:
% 31.06/8.64 | (270) $false
% 31.06/8.64 |
% 31.06/8.64 |-The branch is then unsatisfiable
% 31.06/8.64 |-Branch two:
% 31.06/8.64 | (318) ~ (all_0_47_47 = e0)
% 31.06/8.64 | (950) all_0_51_51 = e0 | all_0_56_56 = e0
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (950), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (954) all_0_51_51 = e0
% 31.06/8.64 |
% 31.06/8.64 | Equations (954) can reduce 12 to:
% 31.06/8.64 | (3103) ~ (all_0_53_53 = e0)
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 3103 yields:
% 31.06/8.64 | (584) ~ (all_0_53_53 = e0)
% 31.06/8.64 |
% 31.06/8.64 | Equations (954) can reduce 255 to:
% 31.06/8.64 | (566) ~ (e2 = e0)
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 566 yields:
% 31.06/8.64 | (57) ~ (e2 = e0)
% 31.06/8.64 |
% 31.06/8.64 | From (954) and (7) follows:
% 31.06/8.64 | (14159) op(e3, e0) = all_0_9_9
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (182), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (454) all_0_45_45 = e0
% 31.06/8.64 |
% 31.06/8.64 | Combining equations (454,4011) yields a new equation:
% 31.06/8.64 | (14191) all_0_7_7 = e0
% 31.06/8.64 |
% 31.06/8.64 | Equations (454) can reduce 51 to:
% 31.06/8.64 | (232) ~ (all_0_41_41 = e0)
% 31.06/8.64 |
% 31.06/8.64 | Equations (454) can reduce 128 to:
% 31.06/8.64 | (3103) ~ (all_0_53_53 = e0)
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 3103 yields:
% 31.06/8.64 | (584) ~ (all_0_53_53 = e0)
% 31.06/8.64 |
% 31.06/8.64 | Equations (454) can reduce 108 to:
% 31.06/8.64 | (3530) ~ (all_0_58_58 = e0)
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 3530 yields:
% 31.06/8.64 | (431) ~ (all_0_58_58 = e0)
% 31.06/8.64 |
% 31.06/8.64 | Equations (454) can reduce 352 to:
% 31.06/8.64 | (456) ~ (e4 = e0)
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 456 yields:
% 31.06/8.64 | (6) ~ (e4 = e0)
% 31.06/8.64 |
% 31.06/8.64 | Equations (454) can reduce 354 to:
% 31.06/8.64 | (788) ~ (e3 = e0)
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 788 yields:
% 31.06/8.64 | (66) ~ (e3 = e0)
% 31.06/8.64 |
% 31.06/8.64 | Equations (454) can reduce 434 to:
% 31.06/8.64 | (566) ~ (e2 = e0)
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 566 yields:
% 31.06/8.64 | (57) ~ (e2 = e0)
% 31.06/8.64 |
% 31.06/8.64 | Equations (454) can reduce 26 to:
% 31.06/8.64 | (568) ~ (e1 = e0)
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 568 yields:
% 31.06/8.64 | (132) ~ (e1 = e0)
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (178), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (751) all_0_39_39 = e3
% 31.06/8.64 |
% 31.06/8.64 | Combining equations (751,336) yields a new equation:
% 31.06/8.64 | (437) e3 = e2
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 437 yields:
% 31.06/8.64 | (414) e3 = e2
% 31.06/8.64 |
% 31.06/8.64 | Equations (414) can reduce 223 to:
% 31.06/8.64 | (270) $false
% 31.06/8.64 |
% 31.06/8.64 |-The branch is then unsatisfiable
% 31.06/8.64 |-Branch two:
% 31.06/8.64 | (755) ~ (all_0_39_39 = e3)
% 31.06/8.64 | (756) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (756), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (782) all_0_43_43 = e3
% 31.06/8.64 |
% 31.06/8.64 | Combining equations (502,782) yields a new equation:
% 31.06/8.64 | (660) e4 = e3
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 660 yields:
% 31.06/8.64 | (359) e4 = e3
% 31.06/8.64 |
% 31.06/8.64 | Equations (359) can reduce 34 to:
% 31.06/8.64 | (270) $false
% 31.06/8.64 |
% 31.06/8.64 |-The branch is then unsatisfiable
% 31.06/8.64 |-Branch two:
% 31.06/8.64 | (786) ~ (all_0_43_43 = e3)
% 31.06/8.64 | (799) all_0_51_51 = e3 | all_0_56_56 = e3
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (799), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (824) all_0_51_51 = e3
% 31.06/8.64 |
% 31.06/8.64 | Combining equations (824,954) yields a new equation:
% 31.06/8.64 | (783) e3 = e0
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 783 yields:
% 31.06/8.64 | (784) e3 = e0
% 31.06/8.64 |
% 31.06/8.64 | Equations (784) can reduce 66 to:
% 31.06/8.64 | (270) $false
% 31.06/8.64 |
% 31.06/8.64 |-The branch is then unsatisfiable
% 31.06/8.64 |-Branch two:
% 31.06/8.64 | (932) ~ (all_0_51_51 = e3)
% 31.06/8.64 | (764) all_0_56_56 = e3
% 31.06/8.64 |
% 31.06/8.64 | Equations (764) can reduce 81 to:
% 31.06/8.64 | (717) ~ (all_0_58_58 = e3)
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 717 yields:
% 31.06/8.64 | (718) ~ (all_0_58_58 = e3)
% 31.06/8.64 |
% 31.06/8.64 | Equations (764) can reduce 185 to:
% 31.06/8.64 | (1259) ~ (all_0_59_59 = e3)
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 1259 yields:
% 31.06/8.64 | (1260) ~ (all_0_59_59 = e3)
% 31.06/8.64 |
% 31.06/8.64 | Equations (764) can reduce 300 to:
% 31.06/8.64 | (223) ~ (e3 = e2)
% 31.06/8.64 |
% 31.06/8.64 | Equations (764) can reduce 995 to:
% 31.06/8.64 | (136) ~ (e3 = e1)
% 31.06/8.64 |
% 31.06/8.64 | From (764) and (239) follows:
% 31.06/8.64 | (14231) op(e3, e3) = all_0_11_11
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (93), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (402) all_0_59_59 = e4
% 31.06/8.64 |
% 31.06/8.64 | Equations (402) can reduce 17 to:
% 31.06/8.64 | (520) ~ (all_0_42_42 = e4)
% 31.06/8.64 |
% 31.06/8.64 | Equations (402) can reduce 1260 to:
% 31.06/8.64 | (34) ~ (e4 = e3)
% 31.06/8.64 |
% 31.06/8.64 | Equations (402) can reduce 701 to:
% 31.06/8.64 | (231) ~ (e4 = e2)
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (222), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (522) all_0_39_39 = e4
% 31.06/8.64 |
% 31.06/8.64 | Combining equations (522,336) yields a new equation:
% 31.06/8.64 | (268) e4 = e2
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 268 yields:
% 31.06/8.64 | (269) e4 = e2
% 31.06/8.64 |
% 31.06/8.64 | Equations (269) can reduce 231 to:
% 31.06/8.64 | (270) $false
% 31.06/8.64 |
% 31.06/8.64 |-The branch is then unsatisfiable
% 31.06/8.64 |-Branch two:
% 31.06/8.64 | (591) ~ (all_0_39_39 = e4)
% 31.06/8.64 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (194), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (747) all_0_56_56 = e1
% 31.06/8.64 |
% 31.06/8.64 | Combining equations (747,764) yields a new equation:
% 31.06/8.64 | (538) e3 = e1
% 31.06/8.64 |
% 31.06/8.64 | Equations (538) can reduce 136 to:
% 31.06/8.64 | (270) $false
% 31.06/8.64 |
% 31.06/8.64 |-The branch is then unsatisfiable
% 31.06/8.64 |-Branch two:
% 31.06/8.64 | (995) ~ (all_0_56_56 = e1)
% 31.06/8.64 | (996) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (592), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (358) all_0_41_41 = e4
% 31.06/8.64 |
% 31.06/8.64 | Equations (358) can reduce 214 to:
% 31.06/8.64 | (1444) ~ (all_0_53_53 = e4)
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 1444 yields:
% 31.06/8.64 | (599) ~ (all_0_53_53 = e4)
% 31.06/8.64 |
% 31.06/8.64 | Equations (358) can reduce 540 to:
% 31.06/8.64 | (251) ~ (e4 = e1)
% 31.06/8.64 |
% 31.06/8.64 | Equations (358) can reduce 232 to:
% 31.06/8.64 | (6) ~ (e4 = e0)
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (996), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (997) all_0_57_57 = e1
% 31.06/8.64 |
% 31.06/8.64 | Combining equations (2258,997) yields a new equation:
% 31.06/8.64 | (560) e1 = e0
% 31.06/8.64 |
% 31.06/8.64 | Equations (560) can reduce 132 to:
% 31.06/8.64 | (270) $false
% 31.06/8.64 |
% 31.06/8.64 |-The branch is then unsatisfiable
% 31.06/8.64 |-Branch two:
% 31.06/8.64 | (644) ~ (all_0_57_57 = e1)
% 31.06/8.64 | (1000) all_0_58_58 = e1 | all_0_59_59 = e1
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (219), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (351) all_0_41_41 = e3
% 31.06/8.64 |
% 31.06/8.64 | Combining equations (351,358) yields a new equation:
% 31.06/8.64 | (359) e4 = e3
% 31.06/8.64 |
% 31.06/8.64 | Equations (359) can reduce 34 to:
% 31.06/8.64 | (270) $false
% 31.06/8.64 |
% 31.06/8.64 |-The branch is then unsatisfiable
% 31.06/8.64 |-Branch two:
% 31.06/8.64 | (1237) ~ (all_0_41_41 = e3)
% 31.06/8.64 | (1508) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 31.06/8.64 |
% 31.06/8.64 | Equations (358) can reduce 1237 to:
% 31.06/8.64 | (34) ~ (e4 = e3)
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (1000), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (1001) all_0_58_58 = e1
% 31.06/8.64 |
% 31.06/8.64 | Equations (1001) can reduce 70 to:
% 31.06/8.64 | (874) ~ (all_0_53_53 = e1)
% 31.06/8.64 |
% 31.06/8.64 | Equations (1001) can reduce 718 to:
% 31.06/8.64 | (769) ~ (e3 = e1)
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 769 yields:
% 31.06/8.64 | (136) ~ (e3 = e1)
% 31.06/8.64 |
% 31.06/8.64 | Equations (1001) can reduce 376 to:
% 31.06/8.64 | (645) ~ (e2 = e1)
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 645 yields:
% 31.06/8.64 | (141) ~ (e2 = e1)
% 31.06/8.64 |
% 31.06/8.64 | Equations (1001) can reduce 431 to:
% 31.06/8.64 | (132) ~ (e1 = e0)
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (135), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (820) all_0_51_51 = e1
% 31.06/8.64 |
% 31.06/8.64 | Combining equations (954,820) yields a new equation:
% 31.06/8.64 | (560) e1 = e0
% 31.06/8.64 |
% 31.06/8.64 | Equations (560) can reduce 132 to:
% 31.06/8.64 | (270) $false
% 31.06/8.64 |
% 31.06/8.64 |-The branch is then unsatisfiable
% 31.06/8.64 |-Branch two:
% 31.06/8.64 | (748) ~ (all_0_51_51 = e1)
% 31.06/8.64 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (823), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (848) all_0_52_52 = e1
% 31.06/8.64 |
% 31.06/8.64 | Combining equations (685,848) yields a new equation:
% 31.06/8.64 | (531) e2 = e1
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 531 yields:
% 31.06/8.64 | (322) e2 = e1
% 31.06/8.64 |
% 31.06/8.64 | Equations (322) can reduce 141 to:
% 31.06/8.64 | (270) $false
% 31.06/8.64 |
% 31.06/8.64 |-The branch is then unsatisfiable
% 31.06/8.64 |-Branch two:
% 31.06/8.64 | (642) ~ (all_0_52_52 = e1)
% 31.06/8.64 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (78), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (751) all_0_39_39 = e3
% 31.06/8.64 |
% 31.06/8.64 | Combining equations (751,336) yields a new equation:
% 31.06/8.64 | (437) e3 = e2
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 437 yields:
% 31.06/8.64 | (414) e3 = e2
% 31.06/8.64 |
% 31.06/8.64 | Equations (414) can reduce 223 to:
% 31.06/8.64 | (270) $false
% 31.06/8.64 |
% 31.06/8.64 |-The branch is then unsatisfiable
% 31.06/8.64 |-Branch two:
% 31.06/8.64 | (755) ~ (all_0_39_39 = e3)
% 31.06/8.64 | (4262) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (852), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (853) all_0_53_53 = e1
% 31.06/8.64 |
% 31.06/8.64 | Equations (853) can reduce 874 to:
% 31.06/8.64 | (270) $false
% 31.06/8.64 |
% 31.06/8.64 |-The branch is then unsatisfiable
% 31.06/8.64 |-Branch two:
% 31.06/8.64 | (874) ~ (all_0_53_53 = e1)
% 31.06/8.64 | (875) all_0_54_54 = e1
% 31.06/8.64 |
% 31.06/8.64 | Equations (875) can reduce 191 to:
% 31.06/8.64 | (640) ~ (all_0_42_42 = e1)
% 31.06/8.64 |
% 31.06/8.64 | Equations (875) can reduce 261 to:
% 31.06/8.64 | (645) ~ (e2 = e1)
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 645 yields:
% 31.06/8.64 | (141) ~ (e2 = e1)
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (95), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (1258) all_0_42_42 = e3
% 31.06/8.64 |
% 31.06/8.64 | Equations (1258) can reduce 640 to:
% 31.06/8.64 | (136) ~ (e3 = e1)
% 31.06/8.64 |
% 31.06/8.64 | Equations (1258) can reduce 199 to:
% 31.06/8.64 | (66) ~ (e3 = e0)
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (1508), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (505) all_0_45_45 = e3
% 31.06/8.64 |
% 31.06/8.64 | Combining equations (454,505) yields a new equation:
% 31.06/8.64 | (784) e3 = e0
% 31.06/8.64 |
% 31.06/8.64 | Equations (784) can reduce 66 to:
% 31.06/8.64 | (270) $false
% 31.06/8.64 |
% 31.06/8.64 |-The branch is then unsatisfiable
% 31.06/8.64 |-Branch two:
% 31.06/8.64 | (354) ~ (all_0_45_45 = e3)
% 31.06/8.64 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (1539), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (1114) all_0_53_53 = e3
% 31.06/8.64 |
% 31.06/8.64 | Equations (1114) can reduce 599 to:
% 31.06/8.64 | (719) ~ (e4 = e3)
% 31.06/8.64 |
% 31.06/8.64 | Simplifying 719 yields:
% 31.06/8.64 | (34) ~ (e4 = e3)
% 31.06/8.64 |
% 31.06/8.64 | Instantiating formula (201) with e3, e3, e4, all_0_11_11 and discharging atoms op(e3, e3) = all_0_11_11, op(e3, e3) = e4, yields:
% 31.06/8.64 | (14233) all_0_11_11 = e4
% 31.06/8.64 |
% 31.06/8.64 | Instantiating formula (201) with e3, e0, all_0_9_9, e2 and discharging atoms op(e3, e0) = all_0_9_9, op(e3, e0) = e2, yields:
% 31.06/8.64 | (15413) all_0_9_9 = e2
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (234), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (4239) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3)) | (all_0_9_9 = e1 & ~ (all_0_10_10 = e3))
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (4239), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (4240) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3))
% 31.06/8.64 |
% 31.06/8.64 +-Applying beta-rule and splitting (4240), into two cases.
% 31.06/8.64 |-Branch one:
% 31.06/8.64 | (4241) all_0_4_4 = e4 & ~ (all_0_5_5 = e3)
% 31.06/8.64 |
% 31.06/8.64 | Applying alpha-rule on (4241) yields:
% 31.06/8.64 | (4242) all_0_4_4 = e4
% 31.06/8.64 | (4243) ~ (all_0_5_5 = e3)
% 31.06/8.64 |
% 31.06/8.65 | Combining equations (4242,15271) yields a new equation:
% 31.06/8.65 | (660) e4 = e3
% 31.06/8.65 |
% 31.06/8.65 | Simplifying 660 yields:
% 31.06/8.65 | (359) e4 = e3
% 31.06/8.65 |
% 31.06/8.65 | Equations (359) can reduce 34 to:
% 31.06/8.65 | (270) $false
% 31.06/8.65 |
% 31.06/8.65 |-The branch is then unsatisfiable
% 31.06/8.65 |-Branch two:
% 31.06/8.65 | (4247) all_0_7_7 = e2 & ~ (all_0_8_8 = e3)
% 31.06/8.65 |
% 31.06/8.65 | Applying alpha-rule on (4247) yields:
% 31.06/8.65 | (4248) all_0_7_7 = e2
% 31.06/8.65 | (4249) ~ (all_0_8_8 = e3)
% 31.06/8.65 |
% 31.06/8.65 | Combining equations (14191,4248) yields a new equation:
% 31.06/8.65 | (316) e2 = e0
% 31.06/8.65 |
% 31.06/8.65 | Equations (316) can reduce 57 to:
% 31.06/8.65 | (270) $false
% 31.06/8.65 |
% 31.06/8.65 |-The branch is then unsatisfiable
% 31.06/8.65 |-Branch two:
% 31.06/8.65 | (4253) all_0_9_9 = e1 & ~ (all_0_10_10 = e3)
% 31.06/8.65 |
% 31.06/8.65 | Applying alpha-rule on (4253) yields:
% 31.06/8.65 | (4254) all_0_9_9 = e1
% 31.06/8.65 | (4255) ~ (all_0_10_10 = e3)
% 31.06/8.65 |
% 31.06/8.65 | Combining equations (15413,4254) yields a new equation:
% 31.06/8.65 | (531) e2 = e1
% 31.06/8.65 |
% 31.06/8.65 | Simplifying 531 yields:
% 31.06/8.65 | (322) e2 = e1
% 31.06/8.65 |
% 31.06/8.65 | Equations (322) can reduce 141 to:
% 31.06/8.65 | (270) $false
% 31.06/8.65 |
% 31.06/8.65 |-The branch is then unsatisfiable
% 31.06/8.65 |-Branch two:
% 31.06/8.65 | (4378) all_0_11_11 = e0 & ~ (all_0_12_12 = e3)
% 31.06/8.65 |
% 31.06/8.65 | Applying alpha-rule on (4378) yields:
% 31.06/8.65 | (4379) all_0_11_11 = e0
% 31.06/8.65 | (4380) ~ (all_0_12_12 = e3)
% 31.06/8.65 |
% 31.06/8.65 | Combining equations (14233,4379) yields a new equation:
% 31.06/8.65 | (478) e4 = e0
% 31.06/8.65 |
% 31.06/8.65 | Simplifying 478 yields:
% 31.06/8.65 | (479) e4 = e0
% 31.06/8.65 |
% 31.06/8.65 | Equations (479) can reduce 6 to:
% 31.06/8.65 | (270) $false
% 31.06/8.65 |
% 31.06/8.65 |-The branch is then unsatisfiable
% 31.06/8.65 |-Branch two:
% 31.06/8.65 | (356) ~ (all_0_53_53 = e3)
% 31.06/8.65 | (4713) all_0_58_58 = e3
% 31.06/8.65 |
% 31.06/8.65 | Combining equations (4713,1001) yields a new equation:
% 31.06/8.65 | (537) e3 = e1
% 31.06/8.65 |
% 31.06/8.65 | Simplifying 537 yields:
% 31.06/8.65 | (538) e3 = e1
% 31.06/8.65 |
% 31.06/8.65 | Equations (538) can reduce 136 to:
% 31.06/8.65 | (270) $false
% 31.06/8.65 |
% 31.06/8.65 |-The branch is then unsatisfiable
% 31.06/8.65 |-Branch two:
% 31.06/8.65 | (1316) ~ (all_0_42_42 = e3)
% 31.06/8.65 | (3656) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 31.06/8.65 |
% 31.06/8.65 +-Applying beta-rule and splitting (4262), into two cases.
% 31.06/8.65 |-Branch one:
% 31.06/8.65 | (671) all_0_40_40 = e3
% 31.06/8.65 |
% 31.06/8.65 | Combining equations (671,530) yields a new equation:
% 31.06/8.65 | (537) e3 = e1
% 31.06/8.65 |
% 31.06/8.65 | Simplifying 537 yields:
% 31.06/8.65 | (538) e3 = e1
% 31.06/8.65 |
% 31.06/8.65 | Equations (538) can reduce 136 to:
% 31.06/8.65 | (270) $false
% 31.06/8.65 |
% 31.06/8.65 |-The branch is then unsatisfiable
% 31.06/8.65 |-Branch two:
% 31.06/8.65 | (675) ~ (all_0_40_40 = e3)
% 31.06/8.65 | (5254) all_0_41_41 = e3 | all_0_42_42 = e3
% 31.06/8.65 |
% 31.06/8.65 +-Applying beta-rule and splitting (5254), into two cases.
% 31.06/8.65 |-Branch one:
% 31.06/8.65 | (351) all_0_41_41 = e3
% 31.06/8.65 |
% 31.06/8.65 | Combining equations (351,358) yields a new equation:
% 31.06/8.65 | (359) e4 = e3
% 31.06/8.65 |
% 31.06/8.65 | Equations (359) can reduce 34 to:
% 31.06/8.65 | (270) $false
% 31.06/8.65 |
% 31.06/8.65 |-The branch is then unsatisfiable
% 31.06/8.65 |-Branch two:
% 31.06/8.65 | (1237) ~ (all_0_41_41 = e3)
% 31.06/8.65 | (1258) all_0_42_42 = e3
% 31.06/8.65 |
% 31.06/8.65 | Equations (1258) can reduce 1316 to:
% 31.06/8.65 | (270) $false
% 31.06/8.65 |
% 31.06/8.65 |-The branch is then unsatisfiable
% 31.06/8.65 |-Branch two:
% 31.06/8.65 | (1004) ~ (all_0_58_58 = e1)
% 31.06/8.65 | (424) all_0_59_59 = e1
% 31.06/8.65 |
% 31.06/8.65 | Combining equations (402,424) yields a new equation:
% 31.06/8.65 | (525) e4 = e1
% 31.06/8.65 |
% 31.06/8.65 | Simplifying 525 yields:
% 31.06/8.65 | (526) e4 = e1
% 31.06/8.65 |
% 31.06/8.65 | Equations (526) can reduce 251 to:
% 31.06/8.65 | (270) $false
% 31.06/8.65 |
% 31.06/8.65 |-The branch is then unsatisfiable
% 31.06/8.65 |-Branch two:
% 31.06/8.65 | (361) ~ (all_0_41_41 = e4)
% 31.06/8.65 | (512) all_0_42_42 = e4
% 31.06/8.65 |
% 31.06/8.65 | Equations (512) can reduce 520 to:
% 31.06/8.65 | (270) $false
% 31.06/8.65 |
% 31.06/8.65 |-The branch is then unsatisfiable
% 31.06/8.65 |-Branch two:
% 31.06/8.65 | (280) ~ (all_0_59_59 = e4)
% 31.06/8.65 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 31.06/8.65 |
% 31.06/8.65 +-Applying beta-rule and splitting (407), into two cases.
% 31.06/8.65 |-Branch one:
% 31.06/8.65 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 31.06/8.65 |
% 31.06/8.65 +-Applying beta-rule and splitting (408), into two cases.
% 31.06/8.65 |-Branch one:
% 31.06/8.65 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 31.06/8.65 |
% 31.06/8.65 +-Applying beta-rule and splitting (409), into two cases.
% 31.06/8.65 |-Branch one:
% 31.06/8.65 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 31.06/8.65 |
% 31.06/8.65 | Applying alpha-rule on (410) yields:
% 31.06/8.65 | (411) all_0_43_43 = e0
% 31.06/8.65 | (412) all_0_59_59 = e3
% 31.06/8.65 | (413) ~ (all_0_46_46 = e3)
% 31.06/8.65 |
% 31.06/8.65 | Combining equations (411,502) yields a new equation:
% 31.06/8.65 | (479) e4 = e0
% 31.06/8.65 |
% 31.06/8.65 | Equations (479) can reduce 6 to:
% 31.06/8.65 | (270) $false
% 31.06/8.65 |
% 31.06/8.65 |-The branch is then unsatisfiable
% 31.06/8.65 |-Branch two:
% 31.06/8.65 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 31.06/8.65 |
% 31.06/8.65 | Applying alpha-rule on (416) yields:
% 31.06/8.65 | (411) all_0_43_43 = e0
% 31.06/8.65 | (412) all_0_59_59 = e3
% 31.06/8.65 | (419) ~ (all_0_56_56 = e0)
% 31.06/8.65 |
% 31.06/8.65 | Combining equations (411,502) yields a new equation:
% 31.06/8.65 | (479) e4 = e0
% 31.06/8.65 |
% 31.06/8.65 | Equations (479) can reduce 6 to:
% 31.06/8.65 | (270) $false
% 31.06/8.65 |
% 31.06/8.65 |-The branch is then unsatisfiable
% 31.06/8.65 |-Branch two:
% 31.06/8.65 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 31.06/8.65 |
% 31.06/8.65 | Applying alpha-rule on (422) yields:
% 31.06/8.65 | (423) all_0_53_53 = e0
% 31.06/8.65 | (424) all_0_59_59 = e1
% 31.06/8.65 | (425) ~ (all_0_54_54 = e1)
% 31.06/8.65 |
% 31.06/8.65 | Equations (423) can reduce 584 to:
% 31.06/8.65 | (270) $false
% 31.06/8.65 |
% 31.06/8.65 |-The branch is then unsatisfiable
% 31.06/8.65 |-Branch two:
% 31.06/8.65 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 31.06/8.65 |
% 31.06/8.65 | Applying alpha-rule on (428) yields:
% 31.06/8.65 | (423) all_0_53_53 = e0
% 31.06/8.65 | (424) all_0_59_59 = e1
% 31.06/8.65 | (431) ~ (all_0_58_58 = e0)
% 31.06/8.65 |
% 31.06/8.65 | Equations (423) can reduce 584 to:
% 31.06/8.65 | (270) $false
% 31.06/8.65 |
% 31.06/8.65 |-The branch is then unsatisfiable
% 31.06/8.65 |-Branch two:
% 31.06/8.65 | (488) ~ (all_0_45_45 = e0)
% 31.06/8.65 | (558) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 31.06/8.65 |
% 31.06/8.65 +-Applying beta-rule and splitting (558), into two cases.
% 31.06/8.65 |-Branch one:
% 31.06/8.65 | (559) all_0_48_48 = e0
% 31.06/8.65 |
% 31.06/8.65 | Combining equations (559,311) yields a new equation:
% 31.06/8.65 | (316) e2 = e0
% 31.06/8.65 |
% 31.06/8.65 | Equations (316) can reduce 57 to:
% 31.06/8.65 | (270) $false
% 31.06/8.65 |
% 31.06/8.65 |-The branch is then unsatisfiable
% 31.06/8.65 |-Branch two:
% 31.06/8.65 | (562) ~ (all_0_48_48 = e0)
% 31.06/8.65 | (575) all_0_53_53 = e0 | all_0_58_58 = e0
% 31.06/8.65 |
% 31.06/8.65 +-Applying beta-rule and splitting (575), into two cases.
% 31.06/8.65 |-Branch one:
% 31.06/8.65 | (423) all_0_53_53 = e0
% 31.06/8.65 |
% 31.06/8.65 | Equations (423) can reduce 584 to:
% 31.06/8.65 | (270) $false
% 31.06/8.65 |
% 31.06/8.65 |-The branch is then unsatisfiable
% 31.06/8.65 |-Branch two:
% 31.06/8.65 | (584) ~ (all_0_53_53 = e0)
% 31.06/8.65 | (585) all_0_58_58 = e0
% 31.06/8.65 |
% 31.06/8.65 | Equations (585) can reduce 431 to:
% 31.06/8.65 | (270) $false
% 31.06/8.65 |
% 31.06/8.65 |-The branch is then unsatisfiable
% 31.06/8.65 |-Branch two:
% 31.06/8.65 | (987) ~ (all_0_51_51 = e0)
% 31.06/8.65 | (830) all_0_56_56 = e0
% 31.06/8.65 |
% 31.06/8.65 | Equations (830) can reduce 419 to:
% 31.06/8.65 | (270) $false
% 31.06/8.65 |
% 31.06/8.65 |-The branch is then unsatisfiable
% 31.06/8.65 |-Branch two:
% 31.06/8.65 | (510) ~ (all_0_43_43 = e4)
% 31.06/8.65 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 31.06/8.65 |
% 31.06/8.65 +-Applying beta-rule and splitting (511), into two cases.
% 31.06/8.65 |-Branch one:
% 31.06/8.65 | (363) all_0_45_45 = e4
% 31.06/8.65 |
% 31.06/8.65 | Equations (363) can reduce 51 to:
% 31.06/8.65 | (361) ~ (all_0_41_41 = e4)
% 31.06/8.65 |
% 31.06/8.65 | Equations (363) can reduce 84 to:
% 31.06/8.65 | (510) ~ (all_0_43_43 = e4)
% 31.06/8.65 |
% 31.06/8.65 | Equations (363) can reduce 108 to:
% 31.06/8.65 | (277) ~ (all_0_58_58 = e4)
% 31.06/8.65 |
% 31.06/8.65 | Simplifying 277 yields:
% 31.06/8.65 | (278) ~ (all_0_58_58 = e4)
% 31.06/8.65 |
% 31.08/8.65 | Equations (363) can reduce 354 to:
% 31.08/8.65 | (34) ~ (e4 = e3)
% 31.08/8.65 |
% 31.08/8.65 | Equations (363) can reduce 434 to:
% 31.08/8.65 | (231) ~ (e4 = e2)
% 31.08/8.65 |
% 31.08/8.65 +-Applying beta-rule and splitting (222), into two cases.
% 31.08/8.65 |-Branch one:
% 31.08/8.65 | (522) all_0_39_39 = e4
% 31.08/8.65 |
% 31.08/8.65 | Combining equations (522,336) yields a new equation:
% 31.08/8.65 | (268) e4 = e2
% 31.08/8.65 |
% 31.08/8.65 | Simplifying 268 yields:
% 31.08/8.65 | (269) e4 = e2
% 31.08/8.65 |
% 31.08/8.65 | Equations (269) can reduce 231 to:
% 31.08/8.65 | (270) $false
% 31.08/8.65 |
% 31.08/8.65 |-The branch is then unsatisfiable
% 31.08/8.65 |-Branch two:
% 31.08/8.65 | (591) ~ (all_0_39_39 = e4)
% 31.08/8.65 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 31.08/8.65 |
% 31.08/8.65 | Equations (336) can reduce 591 to:
% 31.08/8.65 | (377) ~ (e4 = e2)
% 31.08/8.65 |
% 31.08/8.65 | Simplifying 377 yields:
% 31.08/8.65 | (231) ~ (e4 = e2)
% 31.08/8.65 |
% 31.08/8.65 +-Applying beta-rule and splitting (166), into two cases.
% 31.08/8.65 |-Branch one:
% 31.08/8.65 | (522) all_0_39_39 = e4
% 31.08/8.65 |
% 31.08/8.65 | Combining equations (522,336) yields a new equation:
% 31.08/8.65 | (268) e4 = e2
% 31.08/8.65 |
% 31.08/8.65 | Simplifying 268 yields:
% 31.08/8.65 | (269) e4 = e2
% 31.08/8.65 |
% 31.08/8.65 | Equations (269) can reduce 231 to:
% 31.08/8.65 | (270) $false
% 31.08/8.65 |
% 31.08/8.65 |-The branch is then unsatisfiable
% 31.08/8.65 |-Branch two:
% 31.08/8.65 | (591) ~ (all_0_39_39 = e4)
% 31.08/8.65 | (4522) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 31.08/8.65 |
% 31.08/8.65 +-Applying beta-rule and splitting (159), into two cases.
% 31.08/8.65 |-Branch one:
% 31.08/8.65 | (450) all_0_43_43 = e2
% 31.08/8.65 |
% 31.08/8.65 | Equations (450) can reduce 292 to:
% 31.08/8.65 | (270) $false
% 31.08/8.65 |
% 31.08/8.65 |-The branch is then unsatisfiable
% 31.08/8.65 |-Branch two:
% 31.08/8.65 | (292) ~ (all_0_43_43 = e2)
% 31.08/8.65 | (774) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 31.08/8.65 |
% 31.08/8.65 +-Applying beta-rule and splitting (774), into two cases.
% 31.08/8.65 |-Branch one:
% 31.08/8.65 | (411) all_0_43_43 = e0
% 31.08/8.65 |
% 31.08/8.65 | Equations (411) can reduce 240 to:
% 31.08/8.65 | (6253) ~ (all_0_51_51 = e0)
% 31.08/8.65 |
% 31.08/8.65 | Simplifying 6253 yields:
% 31.08/8.65 | (987) ~ (all_0_51_51 = e0)
% 31.08/8.65 |
% 31.08/8.65 | Equations (411) can reduce 510 to:
% 31.08/8.65 | (456) ~ (e4 = e0)
% 31.08/8.65 |
% 31.08/8.65 | Simplifying 456 yields:
% 31.08/8.65 | (6) ~ (e4 = e0)
% 31.08/8.65 |
% 31.08/8.65 | Equations (411) can reduce 292 to:
% 31.08/8.65 | (566) ~ (e2 = e0)
% 31.08/8.65 |
% 31.08/8.65 | Simplifying 566 yields:
% 31.08/8.65 | (57) ~ (e2 = e0)
% 31.08/8.65 |
% 31.08/8.65 | Equations (411) can reduce 249 to:
% 31.08/8.65 | (568) ~ (e1 = e0)
% 31.08/8.65 |
% 31.08/8.65 | Simplifying 568 yields:
% 31.08/8.65 | (132) ~ (e1 = e0)
% 31.08/8.65 |
% 31.08/8.65 +-Applying beta-rule and splitting (64), into two cases.
% 31.08/8.65 |-Branch one:
% 31.08/8.65 | (954) all_0_51_51 = e0
% 31.08/8.65 |
% 31.08/8.65 | Equations (954) can reduce 987 to:
% 31.08/8.65 | (270) $false
% 31.08/8.65 |
% 31.08/8.65 |-The branch is then unsatisfiable
% 31.08/8.65 |-Branch two:
% 31.08/8.65 | (987) ~ (all_0_51_51 = e0)
% 31.08/8.65 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 31.08/8.65 |
% 31.08/8.65 +-Applying beta-rule and splitting (4522), into two cases.
% 31.08/8.65 |-Branch one:
% 31.08/8.65 | (502) all_0_43_43 = e4
% 31.08/8.65 |
% 31.08/8.65 | Combining equations (411,502) yields a new equation:
% 31.08/8.65 | (479) e4 = e0
% 31.08/8.65 |
% 31.08/8.65 | Equations (479) can reduce 6 to:
% 31.08/8.65 | (270) $false
% 31.08/8.65 |
% 31.08/8.65 |-The branch is then unsatisfiable
% 31.08/8.65 |-Branch two:
% 31.08/8.65 | (510) ~ (all_0_43_43 = e4)
% 31.08/8.65 | (4527) all_0_51_51 = e4 | all_0_56_56 = e4
% 31.08/8.65 |
% 31.08/8.65 +-Applying beta-rule and splitting (4527), into two cases.
% 31.08/8.65 |-Branch one:
% 31.08/8.65 | (1467) all_0_51_51 = e4
% 31.08/8.65 |
% 31.08/8.65 | Equations (1467) can reduce 697 to:
% 31.08/8.65 | (270) $false
% 31.08/8.65 |
% 31.08/8.65 |-The branch is then unsatisfiable
% 31.08/8.65 |-Branch two:
% 31.08/8.65 | (697) ~ (all_0_51_51 = e4)
% 31.08/8.65 | (4744) all_0_56_56 = e4
% 31.08/8.65 |
% 31.08/8.66 | Equations (4744) can reduce 81 to:
% 31.08/8.66 | (277) ~ (all_0_58_58 = e4)
% 31.08/8.66 |
% 31.08/8.66 | Simplifying 277 yields:
% 31.08/8.66 | (278) ~ (all_0_58_58 = e4)
% 31.08/8.66 |
% 31.08/8.66 | Equations (4744) can reduce 185 to:
% 31.08/8.66 | (279) ~ (all_0_59_59 = e4)
% 31.08/8.66 |
% 31.08/8.66 | Simplifying 279 yields:
% 31.08/8.66 | (280) ~ (all_0_59_59 = e4)
% 31.08/8.66 |
% 31.08/8.66 | Equations (4744) can reduce 300 to:
% 31.08/8.66 | (231) ~ (e4 = e2)
% 31.08/8.66 |
% 31.08/8.66 | From (4744) and (205) follows:
% 31.08/8.66 | (15561) op(e0, e4) = all_0_12_12
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (179), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.66 | (512) all_0_42_42 = e4
% 31.08/8.66 |
% 31.08/8.66 | Equations (512) can reduce 17 to:
% 31.08/8.66 | (279) ~ (all_0_59_59 = e4)
% 31.08/8.66 |
% 31.08/8.66 | Simplifying 279 yields:
% 31.08/8.66 | (280) ~ (all_0_59_59 = e4)
% 31.08/8.66 |
% 31.08/8.66 | Equations (512) can reduce 498 to:
% 31.08/8.66 | (231) ~ (e4 = e2)
% 31.08/8.66 |
% 31.08/8.66 | From (512) and (243) follows:
% 31.08/8.66 | (15566) op(e0, e4) = all_0_30_30
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (178), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.66 | (751) all_0_39_39 = e3
% 31.08/8.66 |
% 31.08/8.66 | Combining equations (751,336) yields a new equation:
% 31.08/8.66 | (437) e3 = e2
% 31.08/8.66 |
% 31.08/8.66 | Simplifying 437 yields:
% 31.08/8.66 | (414) e3 = e2
% 31.08/8.66 |
% 31.08/8.66 | Equations (414) can reduce 223 to:
% 31.08/8.66 | (270) $false
% 31.08/8.66 |
% 31.08/8.66 |-The branch is then unsatisfiable
% 31.08/8.66 |-Branch two:
% 31.08/8.66 | (755) ~ (all_0_39_39 = e3)
% 31.08/8.66 | (756) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 31.08/8.66 |
% 31.08/8.66 | Equations (336) can reduce 755 to:
% 31.08/8.66 | (301) ~ (e3 = e2)
% 31.08/8.66 |
% 31.08/8.66 | Simplifying 301 yields:
% 31.08/8.66 | (223) ~ (e3 = e2)
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (78), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.66 | (751) all_0_39_39 = e3
% 31.08/8.66 |
% 31.08/8.66 | Combining equations (751,336) yields a new equation:
% 31.08/8.66 | (437) e3 = e2
% 31.08/8.66 |
% 31.08/8.66 | Simplifying 437 yields:
% 31.08/8.66 | (414) e3 = e2
% 31.08/8.66 |
% 31.08/8.66 | Equations (414) can reduce 223 to:
% 31.08/8.66 | (270) $false
% 31.08/8.66 |
% 31.08/8.66 |-The branch is then unsatisfiable
% 31.08/8.66 |-Branch two:
% 31.08/8.66 | (755) ~ (all_0_39_39 = e3)
% 31.08/8.66 | (4262) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (4262), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.66 | (671) all_0_40_40 = e3
% 31.08/8.66 |
% 31.08/8.66 | Combining equations (671,530) yields a new equation:
% 31.08/8.66 | (537) e3 = e1
% 31.08/8.66 |
% 31.08/8.66 | Simplifying 537 yields:
% 31.08/8.66 | (538) e3 = e1
% 31.08/8.66 |
% 31.08/8.66 | Equations (538) can reduce 136 to:
% 31.08/8.66 | (270) $false
% 31.08/8.66 |
% 31.08/8.66 |-The branch is then unsatisfiable
% 31.08/8.66 |-Branch two:
% 31.08/8.66 | (675) ~ (all_0_40_40 = e3)
% 31.08/8.66 | (5254) all_0_41_41 = e3 | all_0_42_42 = e3
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (3067), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.66 | (827) all_0_52_52 = e0
% 31.08/8.66 |
% 31.08/8.66 | Combining equations (827,685) yields a new equation:
% 31.08/8.66 | (316) e2 = e0
% 31.08/8.66 |
% 31.08/8.66 | Equations (316) can reduce 57 to:
% 31.08/8.66 | (270) $false
% 31.08/8.66 |
% 31.08/8.66 |-The branch is then unsatisfiable
% 31.08/8.66 |-Branch two:
% 31.08/8.66 | (925) ~ (all_0_52_52 = e0)
% 31.08/8.66 | (3073) all_0_53_53 = e0 | all_0_54_54 = e0
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (5254), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.66 | (351) all_0_41_41 = e3
% 31.08/8.66 |
% 31.08/8.66 | Equations (351) can reduce 157 to:
% 31.08/8.66 | (717) ~ (all_0_58_58 = e3)
% 31.08/8.66 |
% 31.08/8.66 | Simplifying 717 yields:
% 31.08/8.66 | (718) ~ (all_0_58_58 = e3)
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (3073), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.66 | (423) all_0_53_53 = e0
% 31.08/8.66 |
% 31.08/8.66 | Equations (423) can reduce 70 to:
% 31.08/8.66 | (3530) ~ (all_0_58_58 = e0)
% 31.08/8.66 |
% 31.08/8.66 | Simplifying 3530 yields:
% 31.08/8.66 | (431) ~ (all_0_58_58 = e0)
% 31.08/8.66 |
% 31.08/8.66 | From (423) and (227) follows:
% 31.08/8.66 | (2167) op(e1, e1) = e0
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (204), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.66 | (396) all_0_58_58 = e2
% 31.08/8.66 |
% 31.08/8.66 | Equations (396) can reduce 376 to:
% 31.08/8.66 | (270) $false
% 31.08/8.66 |
% 31.08/8.66 |-The branch is then unsatisfiable
% 31.08/8.66 |-Branch two:
% 31.08/8.66 | (376) ~ (all_0_58_58 = e2)
% 31.08/8.66 | (3890) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1 | all_0_58_58 = e0
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (135), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.66 | (820) all_0_51_51 = e1
% 31.08/8.66 |
% 31.08/8.66 | Equations (820) can reduce 748 to:
% 31.08/8.66 | (270) $false
% 31.08/8.66 |
% 31.08/8.66 |-The branch is then unsatisfiable
% 31.08/8.66 |-Branch two:
% 31.08/8.66 | (748) ~ (all_0_51_51 = e1)
% 31.08/8.66 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (3890), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.66 | (585) all_0_58_58 = e0
% 31.08/8.66 |
% 31.08/8.66 | Equations (585) can reduce 431 to:
% 31.08/8.66 | (270) $false
% 31.08/8.66 |
% 31.08/8.66 |-The branch is then unsatisfiable
% 31.08/8.66 |-Branch two:
% 31.08/8.66 | (431) ~ (all_0_58_58 = e0)
% 31.08/8.66 | (4709) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (823), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.66 | (848) all_0_52_52 = e1
% 31.08/8.66 |
% 31.08/8.66 | Combining equations (685,848) yields a new equation:
% 31.08/8.66 | (531) e2 = e1
% 31.08/8.66 |
% 31.08/8.66 | Simplifying 531 yields:
% 31.08/8.66 | (322) e2 = e1
% 31.08/8.66 |
% 31.08/8.66 | Equations (322) can reduce 141 to:
% 31.08/8.66 | (270) $false
% 31.08/8.66 |
% 31.08/8.66 |-The branch is then unsatisfiable
% 31.08/8.66 |-Branch two:
% 31.08/8.66 | (642) ~ (all_0_52_52 = e1)
% 31.08/8.66 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (4709), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.66 | (4713) all_0_58_58 = e3
% 31.08/8.66 |
% 31.08/8.66 | Equations (4713) can reduce 718 to:
% 31.08/8.66 | (270) $false
% 31.08/8.66 |
% 31.08/8.66 |-The branch is then unsatisfiable
% 31.08/8.66 |-Branch two:
% 31.08/8.66 | (718) ~ (all_0_58_58 = e3)
% 31.08/8.66 | (4716) all_0_58_58 = e4 | all_0_58_58 = e1
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (852), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.66 | (853) all_0_53_53 = e1
% 31.08/8.66 |
% 31.08/8.66 | Combining equations (423,853) yields a new equation:
% 31.08/8.66 | (560) e1 = e0
% 31.08/8.66 |
% 31.08/8.66 | Equations (560) can reduce 132 to:
% 31.08/8.66 | (270) $false
% 31.08/8.66 |
% 31.08/8.66 |-The branch is then unsatisfiable
% 31.08/8.66 |-Branch two:
% 31.08/8.66 | (874) ~ (all_0_53_53 = e1)
% 31.08/8.66 | (875) all_0_54_54 = e1
% 31.08/8.66 |
% 31.08/8.66 | From (875) and (29) follows:
% 31.08/8.66 | (3061) op(e1, e1) = all_0_37_37
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (109), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.66 | (399) all_0_59_59 = e2
% 31.08/8.66 |
% 31.08/8.66 | Equations (399) can reduce 701 to:
% 31.08/8.66 | (270) $false
% 31.08/8.66 |
% 31.08/8.66 |-The branch is then unsatisfiable
% 31.08/8.66 |-Branch two:
% 31.08/8.66 | (701) ~ (all_0_59_59 = e2)
% 31.08/8.66 | (4636) all_0_59_59 = e4 | all_0_59_59 = e3 | all_0_59_59 = e1 | all_0_59_59 = e0
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (4716), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.66 | (1001) all_0_58_58 = e1
% 31.08/8.66 |
% 31.08/8.66 | Equations (1001) can reduce 156 to:
% 31.08/8.66 | (749) ~ (all_0_59_59 = e1)
% 31.08/8.66 |
% 31.08/8.66 | Simplifying 749 yields:
% 31.08/8.66 | (750) ~ (all_0_59_59 = e1)
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (93), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.66 | (402) all_0_59_59 = e4
% 31.08/8.66 |
% 31.08/8.66 | Equations (402) can reduce 280 to:
% 31.08/8.66 | (270) $false
% 31.08/8.66 |
% 31.08/8.66 |-The branch is then unsatisfiable
% 31.08/8.66 |-Branch two:
% 31.08/8.66 | (280) ~ (all_0_59_59 = e4)
% 31.08/8.66 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (4636), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.66 | (2308) all_0_59_59 = e0
% 31.08/8.66 |
% 31.08/8.66 | Equations (2308) can reduce 4001 to:
% 31.08/8.66 | (270) $false
% 31.08/8.66 |
% 31.08/8.66 |-The branch is then unsatisfiable
% 31.08/8.66 |-Branch two:
% 31.08/8.66 | (4001) ~ (all_0_59_59 = e0)
% 31.08/8.66 | (15641) all_0_59_59 = e4 | all_0_59_59 = e3 | all_0_59_59 = e1
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (407), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.66 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (408), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.66 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (409), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.66 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 31.08/8.66 |
% 31.08/8.66 | Applying alpha-rule on (410) yields:
% 31.08/8.66 | (411) all_0_43_43 = e0
% 31.08/8.66 | (412) all_0_59_59 = e3
% 31.08/8.66 | (413) ~ (all_0_46_46 = e3)
% 31.08/8.66 |
% 31.08/8.66 | Combining equations (412,4014) yields a new equation:
% 31.08/8.66 | (15648) all_0_34_34 = e3
% 31.08/8.66 |
% 31.08/8.66 | Equations (412) can reduce 701 to:
% 31.08/8.66 | (223) ~ (e3 = e2)
% 31.08/8.66 |
% 31.08/8.66 | Equations (412) can reduce 4001 to:
% 31.08/8.66 | (66) ~ (e3 = e0)
% 31.08/8.66 |
% 31.08/8.66 | Instantiating formula (201) with e1, e1, e0, all_0_37_37 and discharging atoms op(e1, e1) = all_0_37_37, op(e1, e1) = e0, yields:
% 31.08/8.66 | (3079) all_0_37_37 = e0
% 31.08/8.66 |
% 31.08/8.66 | Instantiating formula (201) with e0, e4, all_0_12_12, e2 and discharging atoms op(e0, e4) = all_0_12_12, op(e0, e4) = e2, yields:
% 31.08/8.66 | (15652) all_0_12_12 = e2
% 31.08/8.66 |
% 31.08/8.66 | Instantiating formula (201) with e0, e4, all_0_30_30, all_0_12_12 and discharging atoms op(e0, e4) = all_0_12_12, op(e0, e4) = all_0_30_30, yields:
% 31.08/8.66 | (4233) all_0_12_12 = all_0_30_30
% 31.08/8.66 |
% 31.08/8.66 | Combining equations (15652,4233) yields a new equation:
% 31.08/8.66 | (15654) all_0_30_30 = e2
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (111), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.66 | (4557) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0)) | (all_0_34_34 = e2 & ~ (all_0_35_35 = e0))
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (4557), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.66 | (4558) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0))
% 31.08/8.66 |
% 31.08/8.66 +-Applying beta-rule and splitting (4558), into two cases.
% 31.08/8.66 |-Branch one:
% 31.08/8.67 | (4559) all_0_30_30 = e4 & ~ (all_0_31_31 = e0)
% 31.08/8.67 |
% 31.08/8.67 | Applying alpha-rule on (4559) yields:
% 31.08/8.67 | (4560) all_0_30_30 = e4
% 31.08/8.67 | (4561) ~ (all_0_31_31 = e0)
% 31.08/8.67 |
% 31.08/8.67 | Combining equations (4560,15654) yields a new equation:
% 31.08/8.67 | (268) e4 = e2
% 31.08/8.67 |
% 31.08/8.67 | Simplifying 268 yields:
% 31.08/8.67 | (269) e4 = e2
% 31.08/8.67 |
% 31.08/8.67 | Equations (269) can reduce 231 to:
% 31.08/8.67 | (270) $false
% 31.08/8.67 |
% 31.08/8.67 |-The branch is then unsatisfiable
% 31.08/8.67 |-Branch two:
% 31.08/8.67 | (4565) all_0_32_32 = e3 & ~ (all_0_33_33 = e0)
% 31.08/8.67 |
% 31.08/8.67 | Applying alpha-rule on (4565) yields:
% 31.08/8.67 | (4566) all_0_32_32 = e3
% 31.08/8.67 | (4567) ~ (all_0_33_33 = e0)
% 31.08/8.67 |
% 31.08/8.67 | Combining equations (15273,4566) yields a new equation:
% 31.08/8.67 | (784) e3 = e0
% 31.08/8.67 |
% 31.08/8.67 | Equations (784) can reduce 66 to:
% 31.08/8.67 | (270) $false
% 31.08/8.67 |
% 31.08/8.67 |-The branch is then unsatisfiable
% 31.08/8.67 |-Branch two:
% 31.08/8.67 | (4571) all_0_34_34 = e2 & ~ (all_0_35_35 = e0)
% 31.08/8.67 |
% 31.08/8.67 | Applying alpha-rule on (4571) yields:
% 31.08/8.67 | (4572) all_0_34_34 = e2
% 31.08/8.67 | (4573) ~ (all_0_35_35 = e0)
% 31.08/8.67 |
% 31.08/8.67 | Combining equations (15648,4572) yields a new equation:
% 31.08/8.67 | (437) e3 = e2
% 31.08/8.67 |
% 31.08/8.67 | Simplifying 437 yields:
% 31.08/8.67 | (414) e3 = e2
% 31.08/8.67 |
% 31.08/8.67 | Equations (414) can reduce 223 to:
% 31.08/8.67 | (270) $false
% 31.08/8.67 |
% 31.08/8.67 |-The branch is then unsatisfiable
% 31.08/8.67 |-Branch two:
% 31.08/8.67 | (4577) all_0_36_36 = e1 & ~ (all_0_37_37 = e0)
% 31.08/8.67 |
% 31.08/8.67 | Applying alpha-rule on (4577) yields:
% 31.08/8.67 | (4578) all_0_36_36 = e1
% 31.08/8.67 | (4579) ~ (all_0_37_37 = e0)
% 31.08/8.67 |
% 31.08/8.67 | Equations (3079) can reduce 4579 to:
% 31.08/8.67 | (270) $false
% 31.08/8.67 |
% 31.08/8.67 |-The branch is then unsatisfiable
% 31.08/8.67 |-Branch two:
% 31.08/8.67 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 31.08/8.67 |
% 31.08/8.67 | Applying alpha-rule on (416) yields:
% 31.08/8.67 | (411) all_0_43_43 = e0
% 31.08/8.67 | (412) all_0_59_59 = e3
% 31.08/8.67 | (419) ~ (all_0_56_56 = e0)
% 31.08/8.67 |
% 31.08/8.67 | Combining equations (412,4014) yields a new equation:
% 31.08/8.67 | (15648) all_0_34_34 = e3
% 31.08/8.67 |
% 31.08/8.67 | Equations (412) can reduce 701 to:
% 31.08/8.67 | (223) ~ (e3 = e2)
% 31.08/8.67 |
% 31.08/8.67 | Equations (412) can reduce 4001 to:
% 31.08/8.67 | (66) ~ (e3 = e0)
% 31.08/8.67 |
% 31.08/8.67 | Instantiating formula (201) with e1, e1, e0, all_0_37_37 and discharging atoms op(e1, e1) = all_0_37_37, op(e1, e1) = e0, yields:
% 31.08/8.67 | (3079) all_0_37_37 = e0
% 31.08/8.67 |
% 31.08/8.67 | Instantiating formula (201) with e0, e4, all_0_12_12, e2 and discharging atoms op(e0, e4) = all_0_12_12, op(e0, e4) = e2, yields:
% 31.08/8.67 | (15652) all_0_12_12 = e2
% 31.08/8.67 |
% 31.08/8.67 | Instantiating formula (201) with e0, e4, all_0_30_30, all_0_12_12 and discharging atoms op(e0, e4) = all_0_12_12, op(e0, e4) = all_0_30_30, yields:
% 31.08/8.67 | (4233) all_0_12_12 = all_0_30_30
% 31.08/8.67 |
% 31.08/8.67 | Combining equations (15652,4233) yields a new equation:
% 31.08/8.67 | (15654) all_0_30_30 = e2
% 31.08/8.67 |
% 31.08/8.67 +-Applying beta-rule and splitting (111), into two cases.
% 31.08/8.67 |-Branch one:
% 31.08/8.67 | (4557) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0)) | (all_0_34_34 = e2 & ~ (all_0_35_35 = e0))
% 31.08/8.67 |
% 31.08/8.67 +-Applying beta-rule and splitting (4557), into two cases.
% 31.08/8.67 |-Branch one:
% 31.08/8.67 | (4558) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0))
% 31.08/8.67 |
% 31.08/8.67 +-Applying beta-rule and splitting (4558), into two cases.
% 31.08/8.67 |-Branch one:
% 31.08/8.67 | (4559) all_0_30_30 = e4 & ~ (all_0_31_31 = e0)
% 31.08/8.67 |
% 31.08/8.67 | Applying alpha-rule on (4559) yields:
% 31.08/8.67 | (4560) all_0_30_30 = e4
% 31.08/8.67 | (4561) ~ (all_0_31_31 = e0)
% 31.08/8.67 |
% 31.08/8.67 | Combining equations (4560,15654) yields a new equation:
% 31.08/8.67 | (268) e4 = e2
% 31.08/8.67 |
% 31.08/8.67 | Simplifying 268 yields:
% 31.08/8.67 | (269) e4 = e2
% 31.08/8.67 |
% 31.08/8.67 | Equations (269) can reduce 231 to:
% 31.08/8.67 | (270) $false
% 31.08/8.67 |
% 31.08/8.67 |-The branch is then unsatisfiable
% 31.08/8.67 |-Branch two:
% 31.08/8.67 | (4565) all_0_32_32 = e3 & ~ (all_0_33_33 = e0)
% 31.08/8.67 |
% 31.08/8.67 | Applying alpha-rule on (4565) yields:
% 31.08/8.67 | (4566) all_0_32_32 = e3
% 31.08/8.67 | (4567) ~ (all_0_33_33 = e0)
% 31.08/8.67 |
% 31.08/8.67 | Combining equations (15273,4566) yields a new equation:
% 31.08/8.67 | (784) e3 = e0
% 31.08/8.67 |
% 31.08/8.67 | Equations (784) can reduce 66 to:
% 31.08/8.67 | (270) $false
% 31.08/8.67 |
% 31.08/8.67 |-The branch is then unsatisfiable
% 31.08/8.67 |-Branch two:
% 31.08/8.67 | (4571) all_0_34_34 = e2 & ~ (all_0_35_35 = e0)
% 31.08/8.67 |
% 31.08/8.67 | Applying alpha-rule on (4571) yields:
% 31.08/8.67 | (4572) all_0_34_34 = e2
% 31.08/8.67 | (4573) ~ (all_0_35_35 = e0)
% 31.08/8.67 |
% 31.08/8.68 | Combining equations (15648,4572) yields a new equation:
% 31.08/8.68 | (437) e3 = e2
% 31.08/8.68 |
% 31.08/8.68 | Simplifying 437 yields:
% 31.08/8.68 | (414) e3 = e2
% 31.08/8.68 |
% 31.08/8.68 | Equations (414) can reduce 223 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.68 |-Branch two:
% 31.08/8.68 | (4577) all_0_36_36 = e1 & ~ (all_0_37_37 = e0)
% 31.08/8.68 |
% 31.08/8.68 | Applying alpha-rule on (4577) yields:
% 31.08/8.68 | (4578) all_0_36_36 = e1
% 31.08/8.68 | (4579) ~ (all_0_37_37 = e0)
% 31.08/8.68 |
% 31.08/8.68 | Equations (3079) can reduce 4579 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.68 |-Branch two:
% 31.08/8.68 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 31.08/8.68 |
% 31.08/8.68 | Applying alpha-rule on (422) yields:
% 31.08/8.68 | (423) all_0_53_53 = e0
% 31.08/8.68 | (424) all_0_59_59 = e1
% 31.08/8.68 | (425) ~ (all_0_54_54 = e1)
% 31.08/8.68 |
% 31.08/8.68 | Equations (424) can reduce 750 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.68 |-Branch two:
% 31.08/8.68 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 31.08/8.68 |
% 31.08/8.68 | Applying alpha-rule on (428) yields:
% 31.08/8.68 | (423) all_0_53_53 = e0
% 31.08/8.68 | (424) all_0_59_59 = e1
% 31.08/8.68 | (431) ~ (all_0_58_58 = e0)
% 31.08/8.68 |
% 31.08/8.68 | Equations (424) can reduce 750 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.68 |-Branch two:
% 31.08/8.68 | (1004) ~ (all_0_58_58 = e1)
% 31.08/8.68 | (600) all_0_58_58 = e4
% 31.08/8.68 |
% 31.08/8.68 | Equations (600) can reduce 278 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.68 |-Branch two:
% 31.08/8.68 | (584) ~ (all_0_53_53 = e0)
% 31.08/8.68 | (3084) all_0_54_54 = e0
% 31.08/8.68 |
% 31.08/8.68 | Equations (3084) can reduce 3011 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.68 |-Branch two:
% 31.08/8.68 | (1237) ~ (all_0_41_41 = e3)
% 31.08/8.68 | (1258) all_0_42_42 = e3
% 31.08/8.68 |
% 31.08/8.68 | Combining equations (512,1258) yields a new equation:
% 31.08/8.68 | (660) e4 = e3
% 31.08/8.68 |
% 31.08/8.68 | Simplifying 660 yields:
% 31.08/8.68 | (359) e4 = e3
% 31.08/8.68 |
% 31.08/8.68 | Equations (359) can reduce 34 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.68 |-Branch two:
% 31.08/8.68 | (520) ~ (all_0_42_42 = e4)
% 31.08/8.68 | (521) all_0_46_46 = e4 | all_0_54_54 = e4 | all_0_59_59 = e4
% 31.08/8.68 |
% 31.08/8.68 +-Applying beta-rule and splitting (521), into two cases.
% 31.08/8.68 |-Branch one:
% 31.08/8.68 | (517) all_0_46_46 = e4
% 31.08/8.68 |
% 31.08/8.68 | Combining equations (497,517) yields a new equation:
% 31.08/8.68 | (269) e4 = e2
% 31.08/8.68 |
% 31.08/8.68 | Equations (269) can reduce 231 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.68 |-Branch two:
% 31.08/8.68 | (805) ~ (all_0_46_46 = e4)
% 31.08/8.68 | (816) all_0_54_54 = e4 | all_0_59_59 = e4
% 31.08/8.68 |
% 31.08/8.68 +-Applying beta-rule and splitting (816), into two cases.
% 31.08/8.68 |-Branch one:
% 31.08/8.68 | (817) all_0_54_54 = e4
% 31.08/8.68 |
% 31.08/8.68 | Equations (817) can reduce 936 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.68 |-Branch two:
% 31.08/8.68 | (936) ~ (all_0_54_54 = e4)
% 31.08/8.68 | (402) all_0_59_59 = e4
% 31.08/8.68 |
% 31.08/8.68 | Equations (402) can reduce 280 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.68 |-Branch two:
% 31.08/8.68 | (455) ~ (all_0_43_43 = e0)
% 31.08/8.68 | (944) all_0_43_43 = e4 | all_0_43_43 = e3
% 31.08/8.68 |
% 31.08/8.68 +-Applying beta-rule and splitting (116), into two cases.
% 31.08/8.68 |-Branch one:
% 31.08/8.68 | (411) all_0_43_43 = e0
% 31.08/8.68 |
% 31.08/8.68 | Equations (411) can reduce 455 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.68 |-Branch two:
% 31.08/8.68 | (455) ~ (all_0_43_43 = e0)
% 31.08/8.68 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 31.08/8.68 |
% 31.08/8.68 +-Applying beta-rule and splitting (592), into two cases.
% 31.08/8.68 |-Branch one:
% 31.08/8.68 | (358) all_0_41_41 = e4
% 31.08/8.68 |
% 31.08/8.68 | Equations (358) can reduce 361 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.68 |-Branch two:
% 31.08/8.68 | (361) ~ (all_0_41_41 = e4)
% 31.08/8.68 | (512) all_0_42_42 = e4
% 31.08/8.68 |
% 31.08/8.68 | Equations (512) can reduce 17 to:
% 31.08/8.68 | (279) ~ (all_0_59_59 = e4)
% 31.08/8.68 |
% 31.08/8.68 | Simplifying 279 yields:
% 31.08/8.68 | (280) ~ (all_0_59_59 = e4)
% 31.08/8.68 |
% 31.08/8.68 | Equations (512) can reduce 498 to:
% 31.08/8.68 | (231) ~ (e4 = e2)
% 31.08/8.68 |
% 31.08/8.68 +-Applying beta-rule and splitting (163), into two cases.
% 31.08/8.68 |-Branch one:
% 31.08/8.68 | (272) all_0_55_55 = e4
% 31.08/8.68 |
% 31.08/8.68 | Combining equations (272,382) yields a new equation:
% 31.08/8.68 | (268) e4 = e2
% 31.08/8.68 |
% 31.08/8.68 | Simplifying 268 yields:
% 31.08/8.68 | (269) e4 = e2
% 31.08/8.68 |
% 31.08/8.68 | Equations (269) can reduce 231 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.68 |-Branch two:
% 31.08/8.68 | (14603) ~ (all_0_55_55 = e4)
% 31.08/8.68 | (14604) all_0_56_56 = e4 | all_0_58_58 = e4 | all_0_59_59 = e4
% 31.08/8.68 |
% 31.08/8.68 +-Applying beta-rule and splitting (14604), into two cases.
% 31.08/8.68 |-Branch one:
% 31.08/8.68 | (4744) all_0_56_56 = e4
% 31.08/8.68 |
% 31.08/8.68 | Equations (4744) can reduce 188 to:
% 31.08/8.68 | (510) ~ (all_0_43_43 = e4)
% 31.08/8.68 |
% 31.08/8.68 +-Applying beta-rule and splitting (944), into two cases.
% 31.08/8.68 |-Branch one:
% 31.08/8.68 | (782) all_0_43_43 = e3
% 31.08/8.68 |
% 31.08/8.68 | Equations (782) can reduce 786 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.68 |-Branch two:
% 31.08/8.68 | (786) ~ (all_0_43_43 = e3)
% 31.08/8.68 | (502) all_0_43_43 = e4
% 31.08/8.68 |
% 31.08/8.68 | Equations (502) can reduce 510 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.68 |-Branch two:
% 31.08/8.68 | (274) ~ (all_0_56_56 = e4)
% 31.08/8.68 | (14608) all_0_58_58 = e4 | all_0_59_59 = e4
% 31.08/8.68 |
% 31.08/8.68 +-Applying beta-rule and splitting (75), into two cases.
% 31.08/8.68 |-Branch one:
% 31.08/8.68 | (411) all_0_43_43 = e0
% 31.08/8.68 |
% 31.08/8.68 | Equations (411) can reduce 455 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.68 |-Branch two:
% 31.08/8.68 | (455) ~ (all_0_43_43 = e0)
% 31.08/8.68 | (940) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 31.08/8.68 |
% 31.08/8.68 +-Applying beta-rule and splitting (93), into two cases.
% 31.08/8.68 |-Branch one:
% 31.08/8.68 | (402) all_0_59_59 = e4
% 31.08/8.68 |
% 31.08/8.68 | Equations (402) can reduce 280 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.68 |-Branch two:
% 31.08/8.68 | (280) ~ (all_0_59_59 = e4)
% 31.08/8.68 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 31.08/8.68 |
% 31.08/8.68 +-Applying beta-rule and splitting (407), into two cases.
% 31.08/8.68 |-Branch one:
% 31.08/8.68 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 31.08/8.68 |
% 31.08/8.68 +-Applying beta-rule and splitting (408), into two cases.
% 31.08/8.68 |-Branch one:
% 31.08/8.68 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 31.08/8.68 |
% 31.08/8.68 +-Applying beta-rule and splitting (409), into two cases.
% 31.08/8.68 |-Branch one:
% 31.08/8.68 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 31.08/8.68 |
% 31.08/8.68 | Applying alpha-rule on (410) yields:
% 31.08/8.68 | (411) all_0_43_43 = e0
% 31.08/8.68 | (412) all_0_59_59 = e3
% 31.08/8.68 | (413) ~ (all_0_46_46 = e3)
% 31.08/8.68 |
% 31.08/8.68 | Equations (411) can reduce 455 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.68 |-Branch two:
% 31.08/8.68 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 31.08/8.68 |
% 31.08/8.68 | Applying alpha-rule on (416) yields:
% 31.08/8.68 | (411) all_0_43_43 = e0
% 31.08/8.68 | (412) all_0_59_59 = e3
% 31.08/8.68 | (419) ~ (all_0_56_56 = e0)
% 31.08/8.68 |
% 31.08/8.68 | Equations (411) can reduce 455 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.68 |-Branch two:
% 31.08/8.68 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 31.08/8.68 |
% 31.08/8.68 | Applying alpha-rule on (422) yields:
% 31.08/8.68 | (423) all_0_53_53 = e0
% 31.08/8.68 | (424) all_0_59_59 = e1
% 31.08/8.68 | (425) ~ (all_0_54_54 = e1)
% 31.08/8.68 |
% 31.08/8.68 | Equations (424) can reduce 280 to:
% 31.08/8.68 | (1021) ~ (e4 = e1)
% 31.08/8.68 |
% 31.08/8.68 | Simplifying 1021 yields:
% 31.08/8.68 | (251) ~ (e4 = e1)
% 31.08/8.68 |
% 31.08/8.68 +-Applying beta-rule and splitting (14608), into two cases.
% 31.08/8.68 |-Branch one:
% 31.08/8.68 | (600) all_0_58_58 = e4
% 31.08/8.68 |
% 31.08/8.68 | Equations (600) can reduce 278 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.68 |-Branch two:
% 31.08/8.68 | (278) ~ (all_0_58_58 = e4)
% 31.08/8.68 | (402) all_0_59_59 = e4
% 31.08/8.68 |
% 31.08/8.68 | Combining equations (424,402) yields a new equation:
% 31.08/8.68 | (526) e4 = e1
% 31.08/8.68 |
% 31.08/8.68 | Equations (526) can reduce 251 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.68 |-Branch two:
% 31.08/8.68 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 31.08/8.68 |
% 31.08/8.68 | Applying alpha-rule on (428) yields:
% 31.08/8.68 | (423) all_0_53_53 = e0
% 31.08/8.68 | (424) all_0_59_59 = e1
% 31.08/8.68 | (431) ~ (all_0_58_58 = e0)
% 31.08/8.68 |
% 31.08/8.68 | Equations (424) can reduce 280 to:
% 31.08/8.68 | (1021) ~ (e4 = e1)
% 31.08/8.68 |
% 31.08/8.68 | Simplifying 1021 yields:
% 31.08/8.68 | (251) ~ (e4 = e1)
% 31.08/8.68 |
% 31.08/8.68 +-Applying beta-rule and splitting (14608), into two cases.
% 31.08/8.68 |-Branch one:
% 31.08/8.68 | (600) all_0_58_58 = e4
% 31.08/8.68 |
% 31.08/8.68 | Equations (600) can reduce 278 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.68 |-Branch two:
% 31.08/8.68 | (278) ~ (all_0_58_58 = e4)
% 31.08/8.68 | (402) all_0_59_59 = e4
% 31.08/8.68 |
% 31.08/8.68 | Combining equations (424,402) yields a new equation:
% 31.08/8.68 | (526) e4 = e1
% 31.08/8.68 |
% 31.08/8.68 | Equations (526) can reduce 251 to:
% 31.08/8.68 | (270) $false
% 31.08/8.68 |
% 31.08/8.68 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (352) ~ (all_0_45_45 = e4)
% 31.08/8.69 | (517) all_0_46_46 = e4
% 31.08/8.69 |
% 31.08/8.69 | Combining equations (497,517) yields a new equation:
% 31.08/8.69 | (269) e4 = e2
% 31.08/8.69 |
% 31.08/8.69 | Equations (269) can reduce 231 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (291) ~ (all_0_39_39 = e2)
% 31.08/8.69 | (630) all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (186), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (336) all_0_39_39 = e2
% 31.08/8.69 |
% 31.08/8.69 | Equations (336) can reduce 291 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (291) ~ (all_0_39_39 = e2)
% 31.08/8.69 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (339), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (340), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 31.08/8.69 |
% 31.08/8.69 | Applying alpha-rule on (341) yields:
% 31.08/8.69 | (342) all_0_0_0 = e1
% 31.08/8.69 | (343) ~ (all_0_1_1 = e4)
% 31.08/8.69 |
% 31.08/8.69 | Combining equations (342,9064) yields a new equation:
% 31.08/8.69 | (571) e1 = e0
% 31.08/8.69 |
% 31.08/8.69 | Simplifying 571 yields:
% 31.08/8.69 | (560) e1 = e0
% 31.08/8.69 |
% 31.08/8.69 | Equations (560) can reduce 132 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 31.08/8.69 |
% 31.08/8.69 | Applying alpha-rule on (346) yields:
% 31.08/8.69 | (347) all_0_2_2 = e0
% 31.08/8.69 | (348) ~ (all_0_3_3 = e4)
% 31.08/8.69 |
% 31.08/8.69 | Combining equations (11737,347) yields a new equation:
% 31.08/8.69 | (571) e1 = e0
% 31.08/8.69 |
% 31.08/8.69 | Simplifying 571 yields:
% 31.08/8.69 | (560) e1 = e0
% 31.08/8.69 |
% 31.08/8.69 | Equations (560) can reduce 132 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 31.08/8.69 |
% 31.08/8.69 | Applying alpha-rule on (350) yields:
% 31.08/8.69 | (351) all_0_41_41 = e3
% 31.08/8.69 | (352) ~ (all_0_45_45 = e4)
% 31.08/8.69 |
% 31.08/8.69 | Equations (351) can reduce 226 to:
% 31.08/8.69 | (755) ~ (all_0_39_39 = e3)
% 31.08/8.69 |
% 31.08/8.69 | Equations (351) can reduce 94 to:
% 31.08/8.69 | (1331) ~ (all_0_42_42 = e3)
% 31.08/8.69 |
% 31.08/8.69 | Simplifying 1331 yields:
% 31.08/8.69 | (1316) ~ (all_0_42_42 = e3)
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (16), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (698) all_0_42_42 = e2
% 31.08/8.69 |
% 31.08/8.69 | Equations (698) can reduce 498 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (498) ~ (all_0_42_42 = e2)
% 31.08/8.69 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (1245), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (1258) all_0_42_42 = e3
% 31.08/8.69 |
% 31.08/8.69 | Equations (1258) can reduce 1316 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (1316) ~ (all_0_42_42 = e3)
% 31.08/8.69 | (1317) all_0_42_42 = e4 | all_0_42_42 = e1
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (1317), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (541) all_0_42_42 = e1
% 31.08/8.69 |
% 31.08/8.69 | Equations (541) can reduce 640 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (640) ~ (all_0_42_42 = e1)
% 31.08/8.69 | (512) all_0_42_42 = e4
% 31.08/8.69 |
% 31.08/8.69 | Equations (512) can reduce 184 to:
% 31.08/8.69 | (591) ~ (all_0_39_39 = e4)
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (96), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (336) all_0_39_39 = e2
% 31.08/8.69 |
% 31.08/8.69 | Equations (336) can reduce 291 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (291) ~ (all_0_39_39 = e2)
% 31.08/8.69 | (4205) all_0_43_43 = e2 | all_0_47_47 = e2 | all_0_51_51 = e2 | all_0_56_56 = e2
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (177), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (336) all_0_39_39 = e2
% 31.08/8.69 |
% 31.08/8.69 | Equations (336) can reduce 291 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (291) ~ (all_0_39_39 = e2)
% 31.08/8.69 | (684) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (684), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (751) all_0_39_39 = e3
% 31.08/8.69 |
% 31.08/8.69 | Equations (751) can reduce 755 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (755) ~ (all_0_39_39 = e3)
% 31.08/8.69 | (1756) all_0_39_39 = e4 | all_0_39_39 = e1
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (1756), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (524) all_0_39_39 = e1
% 31.08/8.69 |
% 31.08/8.69 | Equations (524) can reduce 528 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (528) ~ (all_0_39_39 = e1)
% 31.08/8.69 | (522) all_0_39_39 = e4
% 31.08/8.69 |
% 31.08/8.69 | Equations (522) can reduce 591 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (1436) ~ (all_0_46_46 = e2)
% 31.08/8.69 | (1523) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e0
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (209), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (698) all_0_42_42 = e2
% 31.08/8.69 |
% 31.08/8.69 | Equations (698) can reduce 184 to:
% 31.08/8.69 | (291) ~ (all_0_39_39 = e2)
% 31.08/8.69 |
% 31.08/8.69 | Equations (698) can reduce 94 to:
% 31.08/8.69 | (331) ~ (all_0_41_41 = e2)
% 31.08/8.69 |
% 31.08/8.69 | Equations (698) can reduce 18 to:
% 31.08/8.69 | (1435) ~ (all_0_46_46 = e2)
% 31.08/8.69 |
% 31.08/8.69 | Simplifying 1435 yields:
% 31.08/8.69 | (1436) ~ (all_0_46_46 = e2)
% 31.08/8.69 |
% 31.08/8.69 | Equations (698) can reduce 199 to:
% 31.08/8.69 | (57) ~ (e2 = e0)
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (186), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (336) all_0_39_39 = e2
% 31.08/8.69 |
% 31.08/8.69 | Equations (336) can reduce 291 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (291) ~ (all_0_39_39 = e2)
% 31.08/8.69 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (47), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (450) all_0_43_43 = e2
% 31.08/8.69 |
% 31.08/8.69 | Equations (450) can reduce 167 to:
% 31.08/8.69 | (291) ~ (all_0_39_39 = e2)
% 31.08/8.69 |
% 31.08/8.69 | Equations (450) can reduce 84 to:
% 31.08/8.69 | (611) ~ (all_0_45_45 = e2)
% 31.08/8.69 |
% 31.08/8.69 | Simplifying 611 yields:
% 31.08/8.69 | (434) ~ (all_0_45_45 = e2)
% 31.08/8.69 |
% 31.08/8.69 | Equations (450) can reduce 240 to:
% 31.08/8.69 | (254) ~ (all_0_51_51 = e2)
% 31.08/8.69 |
% 31.08/8.69 | Simplifying 254 yields:
% 31.08/8.69 | (255) ~ (all_0_51_51 = e2)
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (339), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (340), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 31.08/8.69 |
% 31.08/8.69 | Applying alpha-rule on (341) yields:
% 31.08/8.69 | (342) all_0_0_0 = e1
% 31.08/8.69 | (343) ~ (all_0_1_1 = e4)
% 31.08/8.69 |
% 31.08/8.69 | Combining equations (342,9064) yields a new equation:
% 31.08/8.69 | (571) e1 = e0
% 31.08/8.69 |
% 31.08/8.69 | Simplifying 571 yields:
% 31.08/8.69 | (560) e1 = e0
% 31.08/8.69 |
% 31.08/8.69 | Equations (560) can reduce 132 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 31.08/8.69 |
% 31.08/8.69 | Applying alpha-rule on (346) yields:
% 31.08/8.69 | (347) all_0_2_2 = e0
% 31.08/8.69 | (348) ~ (all_0_3_3 = e4)
% 31.08/8.69 |
% 31.08/8.69 | Combining equations (11737,347) yields a new equation:
% 31.08/8.69 | (571) e1 = e0
% 31.08/8.69 |
% 31.08/8.69 | Simplifying 571 yields:
% 31.08/8.69 | (560) e1 = e0
% 31.08/8.69 |
% 31.08/8.69 | Equations (560) can reduce 132 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 31.08/8.69 |
% 31.08/8.69 | Applying alpha-rule on (350) yields:
% 31.08/8.69 | (351) all_0_41_41 = e3
% 31.08/8.69 | (352) ~ (all_0_45_45 = e4)
% 31.08/8.69 |
% 31.08/8.69 | Equations (351) can reduce 226 to:
% 31.08/8.69 | (755) ~ (all_0_39_39 = e3)
% 31.08/8.69 |
% 31.08/8.69 | Equations (351) can reduce 232 to:
% 31.08/8.69 | (66) ~ (e3 = e0)
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (116), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (411) all_0_43_43 = e0
% 31.08/8.69 |
% 31.08/8.69 | Combining equations (450,411) yields a new equation:
% 31.08/8.69 | (622) e2 = e0
% 31.08/8.69 |
% 31.08/8.69 | Simplifying 622 yields:
% 31.08/8.69 | (316) e2 = e0
% 31.08/8.69 |
% 31.08/8.69 | Equations (316) can reduce 57 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (455) ~ (all_0_43_43 = e0)
% 31.08/8.69 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 31.08/8.69 |
% 31.08/8.69 | Equations (450) can reduce 455 to:
% 31.08/8.69 | (57) ~ (e2 = e0)
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (105), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (374) all_0_45_45 = e2
% 31.08/8.69 |
% 31.08/8.69 | Equations (374) can reduce 434 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (434) ~ (all_0_45_45 = e2)
% 31.08/8.69 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (75), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (411) all_0_43_43 = e0
% 31.08/8.69 |
% 31.08/8.69 | Combining equations (450,411) yields a new equation:
% 31.08/8.69 | (622) e2 = e0
% 31.08/8.69 |
% 31.08/8.69 | Simplifying 622 yields:
% 31.08/8.69 | (316) e2 = e0
% 31.08/8.69 |
% 31.08/8.69 | Equations (316) can reduce 57 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (455) ~ (all_0_43_43 = e0)
% 31.08/8.69 | (940) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (1122), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (621) all_0_44_44 = e0
% 31.08/8.69 |
% 31.08/8.69 | Combining equations (858,621) yields a new equation:
% 31.08/8.69 | (783) e3 = e0
% 31.08/8.69 |
% 31.08/8.69 | Simplifying 783 yields:
% 31.08/8.69 | (784) e3 = e0
% 31.08/8.69 |
% 31.08/8.69 | Equations (784) can reduce 66 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (625) ~ (all_0_44_44 = e0)
% 31.08/8.69 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (435), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (454) all_0_45_45 = e0
% 31.08/8.69 |
% 31.08/8.69 | Equations (454) can reduce 26 to:
% 31.08/8.69 | (568) ~ (e1 = e0)
% 31.08/8.69 |
% 31.08/8.69 | Simplifying 568 yields:
% 31.08/8.69 | (132) ~ (e1 = e0)
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (177), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (336) all_0_39_39 = e2
% 31.08/8.69 |
% 31.08/8.69 | Equations (336) can reduce 291 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (291) ~ (all_0_39_39 = e2)
% 31.08/8.69 | (684) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (684), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (751) all_0_39_39 = e3
% 31.08/8.69 |
% 31.08/8.69 | Equations (751) can reduce 755 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (755) ~ (all_0_39_39 = e3)
% 31.08/8.69 | (1756) all_0_39_39 = e4 | all_0_39_39 = e1
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (64), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (954) all_0_51_51 = e0
% 31.08/8.69 |
% 31.08/8.69 | Equations (954) can reduce 32 to:
% 31.08/8.69 | (101) ~ (all_0_39_39 = e0)
% 31.08/8.69 |
% 31.08/8.69 | Equations (954) can reduce 12 to:
% 31.08/8.69 | (3103) ~ (all_0_53_53 = e0)
% 31.08/8.69 |
% 31.08/8.69 | Simplifying 3103 yields:
% 31.08/8.69 | (584) ~ (all_0_53_53 = e0)
% 31.08/8.69 |
% 31.08/8.69 | Equations (954) can reduce 255 to:
% 31.08/8.69 | (566) ~ (e2 = e0)
% 31.08/8.69 |
% 31.08/8.69 | Simplifying 566 yields:
% 31.08/8.69 | (57) ~ (e2 = e0)
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (1756), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (524) all_0_39_39 = e1
% 31.08/8.69 |
% 31.08/8.69 | Equations (524) can reduce 528 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (528) ~ (all_0_39_39 = e1)
% 31.08/8.69 | (522) all_0_39_39 = e4
% 31.08/8.69 |
% 31.08/8.69 | Equations (522) can reduce 291 to:
% 31.08/8.69 | (231) ~ (e4 = e2)
% 31.08/8.69 |
% 31.08/8.69 | Equations (522) can reduce 101 to:
% 31.08/8.69 | (6) ~ (e4 = e0)
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (44), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (502) all_0_43_43 = e4
% 31.08/8.69 |
% 31.08/8.69 | Combining equations (450,502) yields a new equation:
% 31.08/8.69 | (269) e4 = e2
% 31.08/8.69 |
% 31.08/8.69 | Equations (269) can reduce 231 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (510) ~ (all_0_43_43 = e4)
% 31.08/8.69 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (511), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (363) all_0_45_45 = e4
% 31.08/8.69 |
% 31.08/8.69 | Combining equations (454,363) yields a new equation:
% 31.08/8.69 | (479) e4 = e0
% 31.08/8.69 |
% 31.08/8.69 | Equations (479) can reduce 6 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (352) ~ (all_0_45_45 = e4)
% 31.08/8.69 | (517) all_0_46_46 = e4
% 31.08/8.69 |
% 31.08/8.69 | Equations (517) can reduce 206 to:
% 31.08/8.69 | (279) ~ (all_0_59_59 = e4)
% 31.08/8.69 |
% 31.08/8.69 | Simplifying 279 yields:
% 31.08/8.69 | (280) ~ (all_0_59_59 = e4)
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (93), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (402) all_0_59_59 = e4
% 31.08/8.69 |
% 31.08/8.69 | Equations (402) can reduce 280 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (280) ~ (all_0_59_59 = e4)
% 31.08/8.69 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (407), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (408), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (409), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 31.08/8.69 |
% 31.08/8.69 | Applying alpha-rule on (410) yields:
% 31.08/8.69 | (411) all_0_43_43 = e0
% 31.08/8.69 | (412) all_0_59_59 = e3
% 31.08/8.69 | (413) ~ (all_0_46_46 = e3)
% 31.08/8.69 |
% 31.08/8.69 | Combining equations (450,411) yields a new equation:
% 31.08/8.69 | (622) e2 = e0
% 31.08/8.69 |
% 31.08/8.69 | Simplifying 622 yields:
% 31.08/8.69 | (316) e2 = e0
% 31.08/8.69 |
% 31.08/8.69 | Equations (316) can reduce 57 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 31.08/8.69 |
% 31.08/8.69 | Applying alpha-rule on (416) yields:
% 31.08/8.69 | (411) all_0_43_43 = e0
% 31.08/8.69 | (412) all_0_59_59 = e3
% 31.08/8.69 | (419) ~ (all_0_56_56 = e0)
% 31.08/8.69 |
% 31.08/8.69 | Combining equations (450,411) yields a new equation:
% 31.08/8.69 | (622) e2 = e0
% 31.08/8.69 |
% 31.08/8.69 | Simplifying 622 yields:
% 31.08/8.69 | (316) e2 = e0
% 31.08/8.69 |
% 31.08/8.69 | Equations (316) can reduce 57 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 31.08/8.69 |
% 31.08/8.69 | Applying alpha-rule on (422) yields:
% 31.08/8.69 | (423) all_0_53_53 = e0
% 31.08/8.69 | (424) all_0_59_59 = e1
% 31.08/8.69 | (425) ~ (all_0_54_54 = e1)
% 31.08/8.69 |
% 31.08/8.69 | Equations (423) can reduce 584 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 31.08/8.69 |
% 31.08/8.69 | Applying alpha-rule on (428) yields:
% 31.08/8.69 | (423) all_0_53_53 = e0
% 31.08/8.69 | (424) all_0_59_59 = e1
% 31.08/8.69 | (431) ~ (all_0_58_58 = e0)
% 31.08/8.69 |
% 31.08/8.69 | Equations (423) can reduce 584 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (987) ~ (all_0_51_51 = e0)
% 31.08/8.69 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (940), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (315) all_0_47_47 = e0
% 31.08/8.69 |
% 31.08/8.69 | Combining equations (315,321) yields a new equation:
% 31.08/8.69 | (560) e1 = e0
% 31.08/8.69 |
% 31.08/8.69 | Equations (560) can reduce 132 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (318) ~ (all_0_47_47 = e0)
% 31.08/8.69 | (950) all_0_51_51 = e0 | all_0_56_56 = e0
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (950), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (954) all_0_51_51 = e0
% 31.08/8.69 |
% 31.08/8.69 | Equations (954) can reduce 987 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (987) ~ (all_0_51_51 = e0)
% 31.08/8.69 | (830) all_0_56_56 = e0
% 31.08/8.69 |
% 31.08/8.69 | Equations (830) can reduce 419 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (488) ~ (all_0_45_45 = e0)
% 31.08/8.69 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (182), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (454) all_0_45_45 = e0
% 31.08/8.69 |
% 31.08/8.69 | Equations (454) can reduce 488 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (488) ~ (all_0_45_45 = e0)
% 31.08/8.69 | (558) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (1128), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (454) all_0_45_45 = e0
% 31.08/8.69 |
% 31.08/8.69 | Equations (454) can reduce 488 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (488) ~ (all_0_45_45 = e0)
% 31.08/8.69 | (1132) all_0_46_46 = e0
% 31.08/8.69 |
% 31.08/8.69 | Equations (1132) can reduce 1010 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (292) ~ (all_0_43_43 = e2)
% 31.08/8.69 | (453) all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (339), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (340), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 31.08/8.69 |
% 31.08/8.69 | Applying alpha-rule on (341) yields:
% 31.08/8.69 | (342) all_0_0_0 = e1
% 31.08/8.69 | (343) ~ (all_0_1_1 = e4)
% 31.08/8.69 |
% 31.08/8.69 | Combining equations (342,9064) yields a new equation:
% 31.08/8.69 | (571) e1 = e0
% 31.08/8.69 |
% 31.08/8.69 | Simplifying 571 yields:
% 31.08/8.69 | (560) e1 = e0
% 31.08/8.69 |
% 31.08/8.69 | Equations (560) can reduce 132 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 31.08/8.69 |
% 31.08/8.69 | Applying alpha-rule on (346) yields:
% 31.08/8.69 | (347) all_0_2_2 = e0
% 31.08/8.69 | (348) ~ (all_0_3_3 = e4)
% 31.08/8.69 |
% 31.08/8.69 | Combining equations (11737,347) yields a new equation:
% 31.08/8.69 | (571) e1 = e0
% 31.08/8.69 |
% 31.08/8.69 | Simplifying 571 yields:
% 31.08/8.69 | (560) e1 = e0
% 31.08/8.69 |
% 31.08/8.69 | Equations (560) can reduce 132 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.69 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 31.08/8.69 |
% 31.08/8.69 | Applying alpha-rule on (350) yields:
% 31.08/8.69 | (351) all_0_41_41 = e3
% 31.08/8.69 | (352) ~ (all_0_45_45 = e4)
% 31.08/8.69 |
% 31.08/8.69 | Equations (351) can reduce 331 to:
% 31.08/8.69 | (223) ~ (e3 = e2)
% 31.08/8.69 |
% 31.08/8.69 +-Applying beta-rule and splitting (453), into two cases.
% 31.08/8.69 |-Branch one:
% 31.08/8.69 | (370) all_0_44_44 = e2
% 31.08/8.69 |
% 31.08/8.69 | Combining equations (858,370) yields a new equation:
% 31.08/8.69 | (437) e3 = e2
% 31.08/8.69 |
% 31.08/8.69 | Simplifying 437 yields:
% 31.08/8.69 | (414) e3 = e2
% 31.08/8.69 |
% 31.08/8.69 | Equations (414) can reduce 223 to:
% 31.08/8.69 | (270) $false
% 31.08/8.69 |
% 31.08/8.69 |-The branch is then unsatisfiable
% 31.08/8.69 |-Branch two:
% 31.08/8.70 | (333) ~ (all_0_44_44 = e2)
% 31.08/8.70 | (493) all_0_45_45 = e2 | all_0_46_46 = e2
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (493), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (374) all_0_45_45 = e2
% 31.08/8.70 |
% 31.08/8.70 | Equations (374) can reduce 434 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (434) ~ (all_0_45_45 = e2)
% 31.08/8.70 | (497) all_0_46_46 = e2
% 31.08/8.70 |
% 31.08/8.70 | Equations (497) can reduce 1436 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (498) ~ (all_0_42_42 = e2)
% 31.08/8.70 | (1732) all_0_46_46 = e2 | all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (1523), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (1132) all_0_46_46 = e0
% 31.08/8.70 |
% 31.08/8.70 | Equations (1132) can reduce 1010 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (1010) ~ (all_0_46_46 = e0)
% 31.08/8.70 | (1529) all_0_46_46 = e4 | all_0_46_46 = e3
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (164), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (336) all_0_39_39 = e2
% 31.08/8.70 |
% 31.08/8.70 | Equations (336) can reduce 167 to:
% 31.08/8.70 | (5937) ~ (all_0_43_43 = e2)
% 31.08/8.70 |
% 31.08/8.70 | Simplifying 5937 yields:
% 31.08/8.70 | (292) ~ (all_0_43_43 = e2)
% 31.08/8.70 |
% 31.08/8.70 | Equations (336) can reduce 528 to:
% 31.08/8.70 | (141) ~ (e2 = e1)
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (1529), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (1091) all_0_46_46 = e3
% 31.08/8.70 |
% 31.08/8.70 | Equations (1091) can reduce 413 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (413) ~ (all_0_46_46 = e3)
% 31.08/8.70 | (517) all_0_46_46 = e4
% 31.08/8.70 |
% 31.08/8.70 | Equations (517) can reduce 103 to:
% 31.08/8.70 | (510) ~ (all_0_43_43 = e4)
% 31.08/8.70 |
% 31.08/8.70 | Equations (517) can reduce 1436 to:
% 31.08/8.70 | (231) ~ (e4 = e2)
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (159), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (450) all_0_43_43 = e2
% 31.08/8.70 |
% 31.08/8.70 | Equations (450) can reduce 292 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (292) ~ (all_0_43_43 = e2)
% 31.08/8.70 | (774) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (1732), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (497) all_0_46_46 = e2
% 31.08/8.70 |
% 31.08/8.70 | Combining equations (517,497) yields a new equation:
% 31.08/8.70 | (268) e4 = e2
% 31.08/8.70 |
% 31.08/8.70 | Simplifying 268 yields:
% 31.08/8.70 | (269) e4 = e2
% 31.08/8.70 |
% 31.08/8.70 | Equations (269) can reduce 231 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (1436) ~ (all_0_46_46 = e2)
% 31.08/8.70 | (3824) all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (774), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (411) all_0_43_43 = e0
% 31.08/8.70 |
% 31.08/8.70 | Equations (411) can reduce 240 to:
% 31.08/8.70 | (6253) ~ (all_0_51_51 = e0)
% 31.08/8.70 |
% 31.08/8.70 | Simplifying 6253 yields:
% 31.08/8.70 | (987) ~ (all_0_51_51 = e0)
% 31.08/8.70 |
% 31.08/8.70 | Equations (411) can reduce 292 to:
% 31.08/8.70 | (566) ~ (e2 = e0)
% 31.08/8.70 |
% 31.08/8.70 | Simplifying 566 yields:
% 31.08/8.70 | (57) ~ (e2 = e0)
% 31.08/8.70 |
% 31.08/8.70 | Equations (411) can reduce 249 to:
% 31.08/8.70 | (568) ~ (e1 = e0)
% 31.08/8.70 |
% 31.08/8.70 | Simplifying 568 yields:
% 31.08/8.70 | (132) ~ (e1 = e0)
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (64), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (954) all_0_51_51 = e0
% 31.08/8.70 |
% 31.08/8.70 | Equations (954) can reduce 987 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (987) ~ (all_0_51_51 = e0)
% 31.08/8.70 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (3067), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (827) all_0_52_52 = e0
% 31.08/8.70 |
% 31.08/8.70 | Combining equations (827,685) yields a new equation:
% 31.08/8.70 | (316) e2 = e0
% 31.08/8.70 |
% 31.08/8.70 | Equations (316) can reduce 57 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (925) ~ (all_0_52_52 = e0)
% 31.08/8.70 | (3073) all_0_53_53 = e0 | all_0_54_54 = e0
% 31.08/8.70 |
% 31.08/8.70 | Equations (685) can reduce 925 to:
% 31.08/8.70 | (57) ~ (e2 = e0)
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (3824), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (307) all_0_49_49 = e2
% 31.08/8.70 |
% 31.08/8.70 | Combining equations (563,307) yields a new equation:
% 31.08/8.70 | (316) e2 = e0
% 31.08/8.70 |
% 31.08/8.70 | Equations (316) can reduce 57 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (296) ~ (all_0_49_49 = e2)
% 31.08/8.70 | (3829) all_0_54_54 = e2 | all_0_59_59 = e2
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (3073), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (423) all_0_53_53 = e0
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (135), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (820) all_0_51_51 = e1
% 31.08/8.70 |
% 31.08/8.70 | Equations (820) can reduce 748 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (748) ~ (all_0_51_51 = e1)
% 31.08/8.70 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (823), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (848) all_0_52_52 = e1
% 31.08/8.70 |
% 31.08/8.70 | Combining equations (848,685) yields a new equation:
% 31.08/8.70 | (322) e2 = e1
% 31.08/8.70 |
% 31.08/8.70 | Equations (322) can reduce 141 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (642) ~ (all_0_52_52 = e1)
% 31.08/8.70 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (852), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (853) all_0_53_53 = e1
% 31.08/8.70 |
% 31.08/8.70 | Combining equations (853,423) yields a new equation:
% 31.08/8.70 | (571) e1 = e0
% 31.08/8.70 |
% 31.08/8.70 | Simplifying 571 yields:
% 31.08/8.70 | (560) e1 = e0
% 31.08/8.70 |
% 31.08/8.70 | Equations (560) can reduce 132 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (874) ~ (all_0_53_53 = e1)
% 31.08/8.70 | (875) all_0_54_54 = e1
% 31.08/8.70 |
% 31.08/8.70 | Equations (875) can reduce 261 to:
% 31.08/8.70 | (645) ~ (e2 = e1)
% 31.08/8.70 |
% 31.08/8.70 | Simplifying 645 yields:
% 31.08/8.70 | (141) ~ (e2 = e1)
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (3829), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (3657) all_0_54_54 = e2
% 31.08/8.70 |
% 31.08/8.70 | Combining equations (3657,875) yields a new equation:
% 31.08/8.70 | (531) e2 = e1
% 31.08/8.70 |
% 31.08/8.70 | Simplifying 531 yields:
% 31.08/8.70 | (322) e2 = e1
% 31.08/8.70 |
% 31.08/8.70 | Equations (322) can reduce 141 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (261) ~ (all_0_54_54 = e2)
% 31.08/8.70 | (399) all_0_59_59 = e2
% 31.08/8.70 |
% 31.08/8.70 | Equations (399) can reduce 701 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (584) ~ (all_0_53_53 = e0)
% 31.08/8.70 | (3084) all_0_54_54 = e0
% 31.08/8.70 |
% 31.08/8.70 | Equations (3084) can reduce 3011 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (455) ~ (all_0_43_43 = e0)
% 31.08/8.70 | (944) all_0_43_43 = e4 | all_0_43_43 = e3
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (944), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (782) all_0_43_43 = e3
% 31.08/8.70 |
% 31.08/8.70 | Equations (782) can reduce 786 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (786) ~ (all_0_43_43 = e3)
% 31.08/8.70 | (502) all_0_43_43 = e4
% 31.08/8.70 |
% 31.08/8.70 | Equations (502) can reduce 510 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (291) ~ (all_0_39_39 = e2)
% 31.08/8.70 | (630) all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (630), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (327) all_0_40_40 = e2
% 31.08/8.70 |
% 31.08/8.70 | Combining equations (530,327) yields a new equation:
% 31.08/8.70 | (322) e2 = e1
% 31.08/8.70 |
% 31.08/8.70 | Equations (322) can reduce 141 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (602) ~ (all_0_40_40 = e2)
% 31.08/8.70 | (1251) all_0_41_41 = e2 | all_0_42_42 = e2
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (1251), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (436) all_0_41_41 = e2
% 31.08/8.70 |
% 31.08/8.70 | Equations (436) can reduce 331 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (331) ~ (all_0_41_41 = e2)
% 31.08/8.70 | (698) all_0_42_42 = e2
% 31.08/8.70 |
% 31.08/8.70 | Equations (698) can reduce 498 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (2301) ~ (all_0_57_57 = e0)
% 31.08/8.70 | (9345) all_0_57_57 = e3 | all_0_57_57 = e1
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (9345), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (869) all_0_57_57 = e3
% 31.08/8.70 |
% 31.08/8.70 | Equations (869) can reduce 846 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (846) ~ (all_0_57_57 = e3)
% 31.08/8.70 | (997) all_0_57_57 = e1
% 31.08/8.70 |
% 31.08/8.70 | Equations (997) can reduce 644 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (257) ~ (all_0_52_52 = e2)
% 31.08/8.70 | (392) all_0_57_57 = e2
% 31.08/8.70 |
% 31.08/8.70 | Equations (392) can reduce 335 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (324) ~ (all_0_47_47 = e1)
% 31.08/8.70 | (325) all_0_48_48 = e1 | all_0_49_49 = e1
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (325), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (552) all_0_48_48 = e1
% 31.08/8.70 |
% 31.08/8.70 | Combining equations (311,552) yields a new equation:
% 31.08/8.70 | (531) e2 = e1
% 31.08/8.70 |
% 31.08/8.70 | Simplifying 531 yields:
% 31.08/8.70 | (322) e2 = e1
% 31.08/8.70 |
% 31.08/8.70 | Equations (322) can reduce 141 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (588) ~ (all_0_48_48 = e1)
% 31.08/8.70 | (589) all_0_49_49 = e1
% 31.08/8.70 |
% 31.08/8.70 | Combining equations (589,563) yields a new equation:
% 31.08/8.70 | (571) e1 = e0
% 31.08/8.70 |
% 31.08/8.70 | Simplifying 571 yields:
% 31.08/8.70 | (560) e1 = e0
% 31.08/8.70 |
% 31.08/8.70 | Equations (560) can reduce 132 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (294) ~ (all_0_48_48 = e2)
% 31.08/8.70 | (314) all_0_48_48 = e1 | all_0_48_48 = e0
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (124), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (290) all_0_47_47 = e2
% 31.08/8.70 |
% 31.08/8.70 | Equations (290) can reduce 100 to:
% 31.08/8.70 | (291) ~ (all_0_39_39 = e2)
% 31.08/8.70 |
% 31.08/8.70 | Equations (290) can reduce 170 to:
% 31.08/8.70 | (292) ~ (all_0_43_43 = e2)
% 31.08/8.70 |
% 31.08/8.70 | Equations (290) can reduce 225 to:
% 31.08/8.70 | (293) ~ (all_0_48_48 = e2)
% 31.08/8.70 |
% 31.08/8.70 | Simplifying 293 yields:
% 31.08/8.70 | (294) ~ (all_0_48_48 = e2)
% 31.08/8.70 |
% 31.08/8.70 | Equations (290) can reduce 3 to:
% 31.08/8.70 | (254) ~ (all_0_51_51 = e2)
% 31.08/8.70 |
% 31.08/8.70 | Simplifying 254 yields:
% 31.08/8.70 | (255) ~ (all_0_51_51 = e2)
% 31.08/8.70 |
% 31.08/8.70 | Equations (290) can reduce 218 to:
% 31.08/8.70 | (299) ~ (all_0_56_56 = e2)
% 31.08/8.70 |
% 31.08/8.70 | Simplifying 299 yields:
% 31.08/8.70 | (300) ~ (all_0_56_56 = e2)
% 31.08/8.70 |
% 31.08/8.70 | Equations (290) can reduce 247 to:
% 31.08/8.70 | (301) ~ (e3 = e2)
% 31.08/8.70 |
% 31.08/8.70 | Simplifying 301 yields:
% 31.08/8.70 | (223) ~ (e3 = e2)
% 31.08/8.70 |
% 31.08/8.70 | From (290) and (42) follows:
% 31.08/8.70 | (303) op(e2, e2) = all_0_8_8
% 31.08/8.70 |
% 31.08/8.70 | From (290) and (40) follows:
% 31.08/8.70 | (304) op(e2, e3) = e2
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (186), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (336) all_0_39_39 = e2
% 31.08/8.70 |
% 31.08/8.70 | Equations (336) can reduce 291 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (291) ~ (all_0_39_39 = e2)
% 31.08/8.70 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (339), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 31.08/8.70 |
% 31.08/8.70 +-Applying beta-rule and splitting (340), into two cases.
% 31.08/8.70 |-Branch one:
% 31.08/8.70 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 31.08/8.70 |
% 31.08/8.70 | Applying alpha-rule on (341) yields:
% 31.08/8.70 | (342) all_0_0_0 = e1
% 31.08/8.70 | (343) ~ (all_0_1_1 = e4)
% 31.08/8.70 |
% 31.08/8.70 | Combining equations (342,9064) yields a new equation:
% 31.08/8.70 | (571) e1 = e0
% 31.08/8.70 |
% 31.08/8.70 | Simplifying 571 yields:
% 31.08/8.70 | (560) e1 = e0
% 31.08/8.70 |
% 31.08/8.70 | Equations (560) can reduce 132 to:
% 31.08/8.70 | (270) $false
% 31.08/8.70 |
% 31.08/8.70 |-The branch is then unsatisfiable
% 31.08/8.70 |-Branch two:
% 31.08/8.70 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 31.08/8.70 |
% 31.08/8.70 | Applying alpha-rule on (346) yields:
% 31.08/8.70 | (347) all_0_2_2 = e0
% 31.08/8.70 | (348) ~ (all_0_3_3 = e4)
% 31.08/8.70 |
% 31.08/8.70 | Combining equations (9065,347) yields a new equation:
% 31.08/8.70 | (11698) all_0_40_40 = e0
% 31.08/8.70 |
% 31.08/8.70 | Simplifying 11698 yields:
% 31.08/8.70 | (11467) all_0_40_40 = e0
% 31.08/8.70 |
% 31.08/8.71 | Equations (11467) can reduce 238 to:
% 31.08/8.71 | (270) $false
% 31.08/8.71 |
% 31.08/8.71 |-The branch is then unsatisfiable
% 31.08/8.71 |-Branch two:
% 31.08/8.71 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 31.08/8.71 |
% 31.08/8.71 | Applying alpha-rule on (350) yields:
% 31.08/8.71 | (351) all_0_41_41 = e3
% 31.08/8.71 | (352) ~ (all_0_45_45 = e4)
% 31.08/8.71 |
% 31.08/8.71 | Equations (351) can reduce 226 to:
% 31.08/8.71 | (755) ~ (all_0_39_39 = e3)
% 31.08/8.71 |
% 31.08/8.71 | Equations (351) can reduce 147 to:
% 31.08/8.71 | (675) ~ (all_0_40_40 = e3)
% 31.08/8.71 |
% 31.08/8.71 | Equations (351) can reduce 94 to:
% 31.08/8.71 | (1331) ~ (all_0_42_42 = e3)
% 31.08/8.71 |
% 31.08/8.71 | Simplifying 1331 yields:
% 31.08/8.71 | (1316) ~ (all_0_42_42 = e3)
% 31.08/8.71 |
% 31.08/8.71 | Equations (351) can reduce 51 to:
% 31.08/8.71 | (353) ~ (all_0_45_45 = e3)
% 31.08/8.71 |
% 31.08/8.71 | Simplifying 353 yields:
% 31.08/8.71 | (354) ~ (all_0_45_45 = e3)
% 31.08/8.71 |
% 31.08/8.71 | Equations (351) can reduce 214 to:
% 31.08/8.71 | (355) ~ (all_0_53_53 = e3)
% 31.08/8.71 |
% 31.08/8.71 | Simplifying 355 yields:
% 31.08/8.71 | (356) ~ (all_0_53_53 = e3)
% 31.08/8.71 |
% 31.08/8.71 | Equations (351) can reduce 232 to:
% 31.08/8.71 | (66) ~ (e3 = e0)
% 31.08/8.71 |
% 31.08/8.71 | From (351) and (112) follows:
% 31.08/8.71 | (1824) op(e1, e3) = all_0_21_21
% 31.08/8.71 |
% 31.08/8.71 +-Applying beta-rule and splitting (164), into two cases.
% 31.08/8.71 |-Branch one:
% 31.08/8.71 | (336) all_0_39_39 = e2
% 31.08/8.71 |
% 31.08/8.71 | Equations (336) can reduce 291 to:
% 31.08/8.71 | (270) $false
% 31.08/8.71 |
% 31.08/8.71 |-The branch is then unsatisfiable
% 31.08/8.71 |-Branch two:
% 31.08/8.71 | (291) ~ (all_0_39_39 = e2)
% 31.08/8.71 | (630) all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 31.08/8.71 |
% 31.08/8.71 +-Applying beta-rule and splitting (630), into two cases.
% 31.08/8.71 |-Branch one:
% 31.08/8.71 | (327) all_0_40_40 = e2
% 31.08/8.71 |
% 31.08/8.71 | Equations (327) can reduce 602 to:
% 31.08/8.71 | (270) $false
% 31.08/8.71 |
% 31.08/8.71 |-The branch is then unsatisfiable
% 31.08/8.71 |-Branch two:
% 31.08/8.71 | (602) ~ (all_0_40_40 = e2)
% 31.08/8.71 | (1251) all_0_41_41 = e2 | all_0_42_42 = e2
% 31.08/8.71 |
% 31.08/8.71 +-Applying beta-rule and splitting (1251), into two cases.
% 31.08/8.71 |-Branch one:
% 31.08/8.71 | (436) all_0_41_41 = e2
% 31.08/8.71 |
% 31.08/8.71 | Combining equations (351,436) yields a new equation:
% 31.08/8.71 | (437) e3 = e2
% 31.08/8.71 |
% 31.08/8.71 | Simplifying 437 yields:
% 31.08/8.71 | (414) e3 = e2
% 31.08/8.71 |
% 31.08/8.71 | Equations (414) can reduce 223 to:
% 31.08/8.71 | (270) $false
% 31.08/8.71 |
% 31.08/8.71 |-The branch is then unsatisfiable
% 31.08/8.71 |-Branch two:
% 31.08/8.71 | (331) ~ (all_0_41_41 = e2)
% 31.08/8.71 | (698) all_0_42_42 = e2
% 31.08/8.71 |
% 31.08/8.71 | Equations (698) can reduce 184 to:
% 31.08/8.71 | (291) ~ (all_0_39_39 = e2)
% 31.08/8.71 |
% 31.08/8.71 | Equations (698) can reduce 145 to:
% 31.08/8.71 | (602) ~ (all_0_40_40 = e2)
% 31.08/8.71 |
% 31.08/8.71 | Equations (698) can reduce 169 to:
% 31.08/8.71 | (295) ~ (all_0_49_49 = e2)
% 31.08/8.71 |
% 31.08/8.71 | Simplifying 295 yields:
% 31.08/8.71 | (296) ~ (all_0_49_49 = e2)
% 31.08/8.71 |
% 31.08/8.71 | Equations (698) can reduce 191 to:
% 31.08/8.71 | (260) ~ (all_0_54_54 = e2)
% 31.08/8.71 |
% 31.08/8.71 | Simplifying 260 yields:
% 31.08/8.71 | (261) ~ (all_0_54_54 = e2)
% 31.08/8.71 |
% 31.08/8.71 | Equations (698) can reduce 17 to:
% 31.08/8.71 | (700) ~ (all_0_59_59 = e2)
% 31.08/8.71 |
% 31.08/8.71 | Simplifying 700 yields:
% 31.08/8.71 | (701) ~ (all_0_59_59 = e2)
% 31.08/8.71 |
% 31.08/8.71 | Equations (698) can reduce 1316 to:
% 31.08/8.71 | (301) ~ (e3 = e2)
% 31.08/8.71 |
% 31.08/8.71 | Simplifying 301 yields:
% 31.08/8.71 | (223) ~ (e3 = e2)
% 31.08/8.71 |
% 31.08/8.71 | Equations (698) can reduce 199 to:
% 31.08/8.71 | (57) ~ (e2 = e0)
% 31.08/8.71 |
% 31.08/8.71 +-Applying beta-rule and splitting (603), into two cases.
% 31.08/8.71 |-Branch one:
% 31.08/8.71 | (671) all_0_40_40 = e3
% 31.08/8.71 |
% 31.08/8.71 | Equations (671) can reduce 675 to:
% 31.08/8.71 | (270) $false
% 31.08/8.71 |
% 31.08/8.71 |-The branch is then unsatisfiable
% 31.08/8.71 |-Branch two:
% 31.08/8.71 | (675) ~ (all_0_40_40 = e3)
% 31.08/8.71 | (530) all_0_40_40 = e1
% 31.08/8.71 |
% 31.08/8.71 | Equations (530) can reduce 114 to:
% 31.08/8.71 | (528) ~ (all_0_39_39 = e1)
% 31.08/8.71 |
% 31.08/8.71 | Equations (530) can reduce 15 to:
% 31.08/8.71 | (4822) ~ (all_0_44_44 = e1)
% 31.08/8.71 |
% 31.08/8.71 | Simplifying 4822 yields:
% 31.08/8.71 | (131) ~ (all_0_44_44 = e1)
% 31.08/8.71 |
% 31.08/8.71 | Equations (530) can reduce 137 to:
% 31.08/8.71 | (641) ~ (all_0_52_52 = e1)
% 31.08/8.71 |
% 31.08/8.71 | Simplifying 641 yields:
% 31.08/8.71 | (642) ~ (all_0_52_52 = e1)
% 31.08/8.71 |
% 31.08/8.71 | Equations (530) can reduce 149 to:
% 31.08/8.71 | (643) ~ (all_0_57_57 = e1)
% 31.08/8.71 |
% 31.08/8.71 | Simplifying 643 yields:
% 31.08/8.71 | (644) ~ (all_0_57_57 = e1)
% 31.08/8.71 |
% 31.08/8.71 | Equations (530) can reduce 675 to:
% 31.08/8.71 | (769) ~ (e3 = e1)
% 31.08/8.71 |
% 31.08/8.71 | Simplifying 769 yields:
% 31.08/8.71 | (136) ~ (e3 = e1)
% 31.08/8.71 |
% 31.08/8.71 | Equations (530) can reduce 602 to:
% 31.08/8.71 | (645) ~ (e2 = e1)
% 31.08/8.71 |
% 31.08/8.71 | Simplifying 645 yields:
% 31.08/8.71 | (141) ~ (e2 = e1)
% 31.08/8.71 |
% 31.08/8.71 | From (530) and (68) follows:
% 31.08/8.71 | (648) op(e2, e1) = all_0_13_13
% 31.08/8.71 |
% 31.08/8.71 +-Applying beta-rule and splitting (177), into two cases.
% 31.08/8.71 |-Branch one:
% 31.08/8.71 | (336) all_0_39_39 = e2
% 31.08/8.71 |
% 31.08/8.71 | Equations (336) can reduce 291 to:
% 31.08/8.71 | (270) $false
% 31.08/8.71 |
% 31.08/8.71 |-The branch is then unsatisfiable
% 31.08/8.71 |-Branch two:
% 31.08/8.71 | (291) ~ (all_0_39_39 = e2)
% 31.08/8.71 | (684) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 31.08/8.71 |
% 31.08/8.71 +-Applying beta-rule and splitting (684), into two cases.
% 31.08/8.71 |-Branch one:
% 31.08/8.71 | (751) all_0_39_39 = e3
% 31.08/8.71 |
% 31.08/8.71 | Equations (751) can reduce 755 to:
% 31.08/8.71 | (270) $false
% 31.08/8.71 |
% 31.08/8.71 |-The branch is then unsatisfiable
% 31.08/8.71 |-Branch two:
% 31.08/8.71 | (755) ~ (all_0_39_39 = e3)
% 31.08/8.71 | (1756) all_0_39_39 = e4 | all_0_39_39 = e1
% 31.08/8.71 |
% 31.08/8.71 +-Applying beta-rule and splitting (222), into two cases.
% 31.08/8.71 |-Branch one:
% 31.08/8.71 | (522) all_0_39_39 = e4
% 31.08/8.71 |
% 31.08/8.71 | Equations (522) can reduce 167 to:
% 31.08/8.71 | (694) ~ (all_0_43_43 = e4)
% 31.08/8.71 |
% 31.08/8.71 | Simplifying 694 yields:
% 31.08/8.71 | (510) ~ (all_0_43_43 = e4)
% 31.08/8.71 |
% 31.08/8.71 | Equations (522) can reduce 32 to:
% 31.08/8.71 | (696) ~ (all_0_51_51 = e4)
% 31.08/8.71 |
% 31.08/8.71 | Simplifying 696 yields:
% 31.08/8.71 | (697) ~ (all_0_51_51 = e4)
% 31.08/8.71 |
% 31.08/8.71 | Equations (522) can reduce 755 to:
% 31.08/8.71 | (34) ~ (e4 = e3)
% 31.08/8.71 |
% 31.08/8.71 | Equations (522) can reduce 101 to:
% 31.08/8.71 | (6) ~ (e4 = e0)
% 31.08/8.71 |
% 31.08/8.71 +-Applying beta-rule and splitting (158), into two cases.
% 31.08/8.71 |-Branch one:
% 31.08/8.71 | (358) all_0_41_41 = e4
% 31.08/8.71 |
% 31.08/8.71 | Combining equations (351,358) yields a new equation:
% 31.08/8.71 | (359) e4 = e3
% 31.08/8.71 |
% 31.08/8.71 | Equations (359) can reduce 34 to:
% 31.08/8.71 | (270) $false
% 31.08/8.71 |
% 31.08/8.71 |-The branch is then unsatisfiable
% 31.08/8.71 |-Branch two:
% 31.08/8.71 | (361) ~ (all_0_41_41 = e4)
% 31.08/8.71 | (362) all_0_45_45 = e4 | all_0_53_53 = e4 | all_0_58_58 = e4
% 31.08/8.71 |
% 31.08/8.71 +-Applying beta-rule and splitting (44), into two cases.
% 31.08/8.71 |-Branch one:
% 31.08/8.71 | (502) all_0_43_43 = e4
% 31.08/8.71 |
% 31.08/8.71 | Equations (502) can reduce 510 to:
% 31.08/8.71 | (270) $false
% 31.08/8.71 |
% 31.08/8.71 |-The branch is then unsatisfiable
% 31.08/8.71 |-Branch two:
% 31.08/8.71 | (510) ~ (all_0_43_43 = e4)
% 31.08/8.71 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 31.08/8.71 |
% 31.08/8.71 +-Applying beta-rule and splitting (362), into two cases.
% 31.08/8.71 |-Branch one:
% 31.08/8.71 | (363) all_0_45_45 = e4
% 31.08/8.71 |
% 31.08/8.71 | Equations (363) can reduce 352 to:
% 31.08/8.71 | (270) $false
% 31.08/8.71 |
% 31.08/8.71 |-The branch is then unsatisfiable
% 31.08/8.71 |-Branch two:
% 31.08/8.71 | (352) ~ (all_0_45_45 = e4)
% 31.08/8.71 | (366) all_0_53_53 = e4 | all_0_58_58 = e4
% 31.08/8.71 |
% 31.08/8.71 +-Applying beta-rule and splitting (511), into two cases.
% 31.08/8.71 |-Branch one:
% 31.08/8.71 | (363) all_0_45_45 = e4
% 31.08/8.71 |
% 31.08/8.71 | Equations (363) can reduce 352 to:
% 31.08/8.71 | (270) $false
% 31.08/8.71 |
% 31.08/8.71 |-The branch is then unsatisfiable
% 31.08/8.71 |-Branch two:
% 31.08/8.71 | (352) ~ (all_0_45_45 = e4)
% 31.08/8.71 | (517) all_0_46_46 = e4
% 31.08/8.71 |
% 31.08/8.71 | Equations (517) can reduce 103 to:
% 31.08/8.71 | (510) ~ (all_0_43_43 = e4)
% 31.08/8.71 |
% 31.08/8.71 | Equations (517) can reduce 174 to:
% 31.08/8.71 | (45) ~ (all_0_44_44 = e4)
% 31.08/8.71 |
% 31.08/8.71 | Equations (517) can reduce 198 to:
% 31.08/8.71 | (2914) ~ (all_0_49_49 = e4)
% 31.08/8.71 |
% 31.08/8.71 | Simplifying 2914 yields:
% 31.08/8.71 | (202) ~ (all_0_49_49 = e4)
% 31.08/8.71 |
% 31.08/8.71 | Equations (517) can reduce 215 to:
% 31.08/8.71 | (1599) ~ (all_0_54_54 = e4)
% 31.08/8.71 |
% 31.08/8.71 | Simplifying 1599 yields:
% 31.08/8.71 | (936) ~ (all_0_54_54 = e4)
% 31.08/8.71 |
% 31.08/8.71 | Equations (517) can reduce 106 to:
% 31.08/8.71 | (251) ~ (e4 = e1)
% 31.08/8.71 |
% 31.08/8.71 +-Applying beta-rule and splitting (366), into two cases.
% 31.08/8.71 |-Branch one:
% 31.08/8.71 | (367) all_0_53_53 = e4
% 31.08/8.71 |
% 31.08/8.71 | Equations (367) can reduce 599 to:
% 31.08/8.71 | (270) $false
% 31.08/8.71 |
% 31.08/8.71 |-The branch is then unsatisfiable
% 31.08/8.71 |-Branch two:
% 31.08/8.71 | (599) ~ (all_0_53_53 = e4)
% 31.08/8.71 | (600) all_0_58_58 = e4
% 31.08/8.71 |
% 31.08/8.71 | Equations (600) can reduce 108 to:
% 31.08/8.71 | (352) ~ (all_0_45_45 = e4)
% 31.08/8.71 |
% 31.08/8.71 | Equations (600) can reduce 59 to:
% 31.08/8.71 | (192) ~ (all_0_48_48 = e4)
% 31.08/8.71 |
% 31.08/8.71 | Equations (600) can reduce 156 to:
% 31.08/8.71 | (279) ~ (all_0_59_59 = e4)
% 31.08/8.71 |
% 31.08/8.71 | Simplifying 279 yields:
% 31.08/8.71 | (280) ~ (all_0_59_59 = e4)
% 31.08/8.71 |
% 31.08/8.71 | Equations (600) can reduce 376 to:
% 31.08/8.71 | (231) ~ (e4 = e2)
% 31.08/8.71 |
% 31.08/8.71 | From (600) and (63) follows:
% 31.08/8.71 | (9134) op(e1, e4) = all_0_28_28
% 31.08/8.71 |
% 31.08/8.71 | Instantiating formula (201) with e2, e2, all_0_8_8, e4 and discharging atoms op(e2, e2) = all_0_8_8, op(e2, e2) = e4, yields:
% 31.08/8.71 | (305) all_0_8_8 = e4
% 31.08/8.71 |
% 31.08/8.71 | Instantiating formula (201) with e2, e1, all_0_13_13, all_0_48_48 and discharging atoms op(e2, e1) = all_0_13_13, op(e2, e1) = all_0_48_48, yields:
% 31.08/8.71 | (649) all_0_13_13 = all_0_48_48
% 31.08/8.71 |
% 31.08/8.71 | Instantiating formula (201) with e1, e4, all_0_28_28, e4 and discharging atoms op(e1, e4) = all_0_28_28, op(e1, e4) = e4, yields:
% 31.08/8.71 | (9135) all_0_28_28 = e4
% 31.08/8.71 |
% 31.08/8.71 | Instantiating formula (201) with e1, e3, all_0_21_21, all_0_51_51 and discharging atoms op(e1, e3) = all_0_21_21, op(e1, e3) = all_0_51_51, yields:
% 31.08/8.71 | (1847) all_0_21_21 = all_0_51_51
% 31.08/8.71 |
% 31.08/8.71 | From (305) and (303) follows:
% 31.08/8.71 | (115) op(e2, e2) = e4
% 31.08/8.71 |
% 31.08/8.71 +-Applying beta-rule and splitting (117), into two cases.
% 31.08/8.71 |-Branch one:
% 31.08/8.71 | (307) all_0_49_49 = e2
% 31.08/8.71 |
% 31.08/8.71 | Equations (307) can reduce 296 to:
% 31.08/8.71 | (270) $false
% 31.08/8.71 |
% 31.08/8.71 |-The branch is then unsatisfiable
% 31.08/8.71 |-Branch two:
% 31.08/8.71 | (296) ~ (all_0_49_49 = e2)
% 31.08/8.71 | (310) all_0_49_49 = e1 | all_0_49_49 = e0
% 31.08/8.71 |
% 31.08/8.71 +-Applying beta-rule and splitting (77), into two cases.
% 31.08/8.71 |-Branch one:
% 31.08/8.71 | (315) all_0_47_47 = e0
% 31.08/8.71 |
% 31.08/8.71 | Combining equations (315,290) yields a new equation:
% 31.08/8.71 | (316) e2 = e0
% 31.08/8.71 |
% 31.08/8.71 | Equations (316) can reduce 57 to:
% 31.08/8.71 | (270) $false
% 31.08/8.71 |
% 31.08/8.71 |-The branch is then unsatisfiable
% 31.08/8.71 |-Branch two:
% 31.08/8.71 | (318) ~ (all_0_47_47 = e0)
% 31.08/8.71 | (319) all_0_48_48 = e0 | all_0_49_49 = e0
% 31.08/8.71 |
% 31.08/8.71 | Equations (290) can reduce 318 to:
% 31.08/8.71 | (57) ~ (e2 = e0)
% 31.08/8.71 |
% 31.08/8.71 +-Applying beta-rule and splitting (83), into two cases.
% 31.08/8.71 |-Branch one:
% 31.08/8.71 | (321) all_0_47_47 = e1
% 31.08/8.71 |
% 31.08/8.71 | Combining equations (321,290) yields a new equation:
% 31.08/8.71 | (322) e2 = e1
% 31.08/8.71 |
% 31.08/8.71 | Equations (322) can reduce 141 to:
% 31.08/8.71 | (270) $false
% 31.08/8.71 |
% 31.08/8.71 |-The branch is then unsatisfiable
% 31.08/8.71 |-Branch two:
% 31.08/8.71 | (324) ~ (all_0_47_47 = e1)
% 31.08/8.71 | (325) all_0_48_48 = e1 | all_0_49_49 = e1
% 31.08/8.71 |
% 31.08/8.71 +-Applying beta-rule and splitting (47), into two cases.
% 31.08/8.71 |-Branch one:
% 31.08/8.71 | (450) all_0_43_43 = e2
% 31.08/8.71 |
% 31.08/8.71 | Equations (450) can reduce 292 to:
% 31.08/8.71 | (270) $false
% 31.08/8.71 |
% 31.08/8.71 |-The branch is then unsatisfiable
% 31.08/8.71 |-Branch two:
% 31.08/8.71 | (292) ~ (all_0_43_43 = e2)
% 31.08/8.71 | (453) all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2
% 31.08/8.71 |
% 31.08/8.71 +-Applying beta-rule and splitting (14), into two cases.
% 31.08/8.71 |-Branch one:
% 31.08/8.71 | (2277) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1))
% 31.08/8.71 |
% 31.08/8.71 +-Applying beta-rule and splitting (2277), into two cases.
% 31.08/8.71 |-Branch one:
% 31.08/8.71 | (2278) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1))
% 31.08/8.71 |
% 31.08/8.71 +-Applying beta-rule and splitting (2278), into two cases.
% 31.08/8.71 |-Branch one:
% 31.08/8.71 | (2279) all_0_21_21 = e4 & ~ (all_0_22_22 = e1)
% 31.08/8.71 |
% 31.08/8.71 | Applying alpha-rule on (2279) yields:
% 31.08/8.71 | (2280) all_0_21_21 = e4
% 31.08/8.71 | (2281) ~ (all_0_22_22 = e1)
% 31.08/8.71 |
% 31.08/8.71 | Combining equations (1847,2280) yields a new equation:
% 31.08/8.71 | (16333) all_0_51_51 = e4
% 31.08/8.71 |
% 31.08/8.71 | Simplifying 16333 yields:
% 31.08/8.71 | (1467) all_0_51_51 = e4
% 31.08/8.71 |
% 31.08/8.71 | Equations (1467) can reduce 697 to:
% 31.08/8.71 | (270) $false
% 31.08/8.71 |
% 31.08/8.71 |-The branch is then unsatisfiable
% 31.08/8.71 |-Branch two:
% 31.08/8.71 | (2285) all_0_23_23 = e3 & ~ (all_0_24_24 = e1)
% 31.08/8.71 |
% 31.08/8.71 | Applying alpha-rule on (2285) yields:
% 31.08/8.71 | (2286) all_0_23_23 = e3
% 31.08/8.71 | (2287) ~ (all_0_24_24 = e1)
% 31.08/8.71 |
% 31.08/8.71 | From (2286) and (142) follows:
% 31.08/8.71 | (16339) op(e1, all_0_45_45) = e3
% 31.08/8.71 |
% 31.08/8.71 +-Applying beta-rule and splitting (105), into two cases.
% 31.08/8.71 |-Branch one:
% 31.08/8.71 | (374) all_0_45_45 = e2
% 31.08/8.71 |
% 31.08/8.71 | Equations (374) can reduce 229 to:
% 31.08/8.71 | (333) ~ (all_0_44_44 = e2)
% 31.08/8.71 |
% 31.08/8.71 | Equations (374) can reduce 354 to:
% 31.08/8.71 | (301) ~ (e3 = e2)
% 31.08/8.71 |
% 31.08/8.71 | Simplifying 301 yields:
% 31.08/8.71 | (223) ~ (e3 = e2)
% 31.08/8.71 |
% 31.08/8.71 | From (374) and (16339) follows:
% 31.08/8.71 | (16344) op(e1, e2) = e3
% 31.08/8.71 |
% 31.08/8.71 +-Applying beta-rule and splitting (607), into two cases.
% 31.08/8.71 |-Branch one:
% 31.08/8.71 | (370) all_0_44_44 = e2
% 31.08/8.71 |
% 31.08/8.71 | Equations (370) can reduce 333 to:
% 31.08/8.71 | (270) $false
% 31.08/8.71 |
% 31.08/8.71 |-The branch is then unsatisfiable
% 31.08/8.71 |-Branch two:
% 31.08/8.71 | (333) ~ (all_0_44_44 = e2)
% 31.08/8.71 | (3377) all_0_52_52 = e2 | all_0_57_57 = e2
% 31.08/8.71 |
% 31.08/8.71 +-Applying beta-rule and splitting (3377), into two cases.
% 31.08/8.71 |-Branch one:
% 31.08/8.71 | (685) all_0_52_52 = e2
% 31.08/8.71 |
% 31.08/8.71 | From (685) and (195) follows:
% 31.08/8.71 | (16350) op(e1, e2) = all_0_18_18
% 31.08/8.71 |
% 31.08/8.71 | From (685) and (203) follows:
% 31.08/8.72 | (16351) op(e1, e2) = e2
% 31.08/8.72 |
% 31.08/8.72 | Instantiating formula (201) with e1, e2, e3, all_0_18_18 and discharging atoms op(e1, e2) = all_0_18_18, op(e1, e2) = e3, yields:
% 31.08/8.72 | (16352) all_0_18_18 = e3
% 31.08/8.72 |
% 31.08/8.72 | Instantiating formula (201) with e1, e2, e2, all_0_18_18 and discharging atoms op(e1, e2) = all_0_18_18, op(e1, e2) = e2, yields:
% 31.08/8.72 | (10555) all_0_18_18 = e2
% 31.08/8.72 |
% 31.14/8.72 | Combining equations (10555,16352) yields a new equation:
% 31.14/8.72 | (414) e3 = e2
% 31.14/8.72 |
% 31.14/8.72 | Equations (414) can reduce 223 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (257) ~ (all_0_52_52 = e2)
% 31.14/8.72 | (392) all_0_57_57 = e2
% 31.14/8.72 |
% 31.14/8.72 | Equations (392) can reduce 335 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (434) ~ (all_0_45_45 = e2)
% 31.14/8.72 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (187), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (436) all_0_41_41 = e2
% 31.14/8.72 |
% 31.14/8.72 | Combining equations (351,436) yields a new equation:
% 31.14/8.72 | (437) e3 = e2
% 31.14/8.72 |
% 31.14/8.72 | Simplifying 437 yields:
% 31.14/8.72 | (414) e3 = e2
% 31.14/8.72 |
% 31.14/8.72 | Equations (414) can reduce 223 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (331) ~ (all_0_41_41 = e2)
% 31.14/8.72 | (441) all_0_45_45 = e2 | all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 31.14/8.72 |
% 31.14/8.72 | Equations (351) can reduce 331 to:
% 31.14/8.72 | (223) ~ (e3 = e2)
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (453), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (370) all_0_44_44 = e2
% 31.14/8.72 |
% 31.14/8.72 | Equations (370) can reduce 241 to:
% 31.14/8.72 | (292) ~ (all_0_43_43 = e2)
% 31.14/8.72 |
% 31.14/8.72 | Equations (370) can reduce 229 to:
% 31.14/8.72 | (611) ~ (all_0_45_45 = e2)
% 31.14/8.72 |
% 31.14/8.72 | Simplifying 611 yields:
% 31.14/8.72 | (434) ~ (all_0_45_45 = e2)
% 31.14/8.72 |
% 31.14/8.72 | Equations (370) can reduce 122 to:
% 31.14/8.72 | (256) ~ (all_0_52_52 = e2)
% 31.14/8.72 |
% 31.14/8.72 | Simplifying 256 yields:
% 31.14/8.72 | (257) ~ (all_0_52_52 = e2)
% 31.14/8.72 |
% 31.14/8.72 | Equations (370) can reduce 45 to:
% 31.14/8.72 | (377) ~ (e4 = e2)
% 31.14/8.72 |
% 31.14/8.72 | Simplifying 377 yields:
% 31.14/8.72 | (231) ~ (e4 = e2)
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (22), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (782) all_0_43_43 = e3
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (435), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (454) all_0_45_45 = e0
% 31.14/8.72 |
% 31.14/8.72 | Equations (454) can reduce 65 to:
% 31.14/8.72 | (7709) ~ (all_0_48_48 = e0)
% 31.14/8.72 |
% 31.14/8.72 | Simplifying 7709 yields:
% 31.14/8.72 | (562) ~ (all_0_48_48 = e0)
% 31.14/8.72 |
% 31.14/8.72 | Equations (454) can reduce 128 to:
% 31.14/8.72 | (3103) ~ (all_0_53_53 = e0)
% 31.14/8.72 |
% 31.14/8.72 | Simplifying 3103 yields:
% 31.14/8.72 | (584) ~ (all_0_53_53 = e0)
% 31.14/8.72 |
% 31.14/8.72 | Equations (454) can reduce 434 to:
% 31.14/8.72 | (566) ~ (e2 = e0)
% 31.14/8.72 |
% 31.14/8.72 | Simplifying 566 yields:
% 31.14/8.72 | (57) ~ (e2 = e0)
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (314), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (559) all_0_48_48 = e0
% 31.14/8.72 |
% 31.14/8.72 | Equations (559) can reduce 562 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (562) ~ (all_0_48_48 = e0)
% 31.14/8.72 | (552) all_0_48_48 = e1
% 31.14/8.72 |
% 31.14/8.72 | Equations (552) can reduce 4 to:
% 31.14/8.72 | (542) ~ (all_0_49_49 = e1)
% 31.14/8.72 |
% 31.14/8.72 | Simplifying 542 yields:
% 31.14/8.72 | (543) ~ (all_0_49_49 = e1)
% 31.14/8.72 |
% 31.14/8.72 | Equations (552) can reduce 294 to:
% 31.14/8.72 | (645) ~ (e2 = e1)
% 31.14/8.72 |
% 31.14/8.72 | Simplifying 645 yields:
% 31.14/8.72 | (141) ~ (e2 = e1)
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (441), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (374) all_0_45_45 = e2
% 31.14/8.72 |
% 31.14/8.72 | Combining equations (374,454) yields a new equation:
% 31.14/8.72 | (622) e2 = e0
% 31.14/8.72 |
% 31.14/8.72 | Simplifying 622 yields:
% 31.14/8.72 | (316) e2 = e0
% 31.14/8.72 |
% 31.14/8.72 | Equations (316) can reduce 57 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (434) ~ (all_0_45_45 = e2)
% 31.14/8.72 | (445) all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (58), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (253) all_0_50_50 = e2
% 31.14/8.72 |
% 31.14/8.72 | Combining equations (253,267) yields a new equation:
% 31.14/8.72 | (269) e4 = e2
% 31.14/8.72 |
% 31.14/8.72 | Equations (269) can reduce 231 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (9032) ~ (all_0_50_50 = e2)
% 31.14/8.72 | (9860) all_0_51_51 = e2 | all_0_52_52 = e2 | all_0_53_53 = e2 | all_0_54_54 = e2
% 31.14/8.72 |
% 31.14/8.72 | Equations (267) can reduce 9032 to:
% 31.14/8.72 | (231) ~ (e4 = e2)
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (93), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (402) all_0_59_59 = e4
% 31.14/8.72 |
% 31.14/8.72 | Equations (402) can reduce 280 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (280) ~ (all_0_59_59 = e4)
% 31.14/8.72 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (310), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (563) all_0_49_49 = e0
% 31.14/8.72 |
% 31.14/8.72 | Equations (563) can reduce 150 to:
% 31.14/8.72 | (788) ~ (e3 = e0)
% 31.14/8.72 |
% 31.14/8.72 | Simplifying 788 yields:
% 31.14/8.72 | (66) ~ (e3 = e0)
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (13), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (576) all_0_53_53 = e2
% 31.14/8.72 |
% 31.14/8.72 | Equations (576) can reduce 584 to:
% 31.14/8.72 | (57) ~ (e2 = e0)
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (407), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (408), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (409), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 31.14/8.72 |
% 31.14/8.72 | Applying alpha-rule on (410) yields:
% 31.14/8.72 | (411) all_0_43_43 = e0
% 31.14/8.72 | (412) all_0_59_59 = e3
% 31.14/8.72 | (413) ~ (all_0_46_46 = e3)
% 31.14/8.72 |
% 31.14/8.72 | Combining equations (782,411) yields a new equation:
% 31.14/8.72 | (783) e3 = e0
% 31.14/8.72 |
% 31.14/8.72 | Simplifying 783 yields:
% 31.14/8.72 | (784) e3 = e0
% 31.14/8.72 |
% 31.14/8.72 | Equations (784) can reduce 66 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 31.14/8.72 |
% 31.14/8.72 | Applying alpha-rule on (416) yields:
% 31.14/8.72 | (411) all_0_43_43 = e0
% 31.14/8.72 | (412) all_0_59_59 = e3
% 31.14/8.72 | (419) ~ (all_0_56_56 = e0)
% 31.14/8.72 |
% 31.14/8.72 | Combining equations (782,411) yields a new equation:
% 31.14/8.72 | (783) e3 = e0
% 31.14/8.72 |
% 31.14/8.72 | Simplifying 783 yields:
% 31.14/8.72 | (784) e3 = e0
% 31.14/8.72 |
% 31.14/8.72 | Equations (784) can reduce 66 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 31.14/8.72 |
% 31.14/8.72 | Applying alpha-rule on (422) yields:
% 31.14/8.72 | (423) all_0_53_53 = e0
% 31.14/8.72 | (424) all_0_59_59 = e1
% 31.14/8.72 | (425) ~ (all_0_54_54 = e1)
% 31.14/8.72 |
% 31.14/8.72 | Combining equations (423,576) yields a new equation:
% 31.14/8.72 | (316) e2 = e0
% 31.14/8.72 |
% 31.14/8.72 | Equations (316) can reduce 57 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 31.14/8.72 |
% 31.14/8.72 | Applying alpha-rule on (428) yields:
% 31.14/8.72 | (423) all_0_53_53 = e0
% 31.14/8.72 | (424) all_0_59_59 = e1
% 31.14/8.72 | (431) ~ (all_0_58_58 = e0)
% 31.14/8.72 |
% 31.14/8.72 | Combining equations (423,576) yields a new equation:
% 31.14/8.72 | (316) e2 = e0
% 31.14/8.72 |
% 31.14/8.72 | Equations (316) can reduce 57 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (259) ~ (all_0_53_53 = e2)
% 31.14/8.72 | (5715) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (445), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (311) all_0_48_48 = e2
% 31.14/8.72 |
% 31.14/8.72 | Combining equations (311,552) yields a new equation:
% 31.14/8.72 | (531) e2 = e1
% 31.14/8.72 |
% 31.14/8.72 | Simplifying 531 yields:
% 31.14/8.72 | (322) e2 = e1
% 31.14/8.72 |
% 31.14/8.72 | Equations (322) can reduce 141 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (294) ~ (all_0_48_48 = e2)
% 31.14/8.72 | (449) all_0_53_53 = e2 | all_0_58_58 = e2
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (449), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (576) all_0_53_53 = e2
% 31.14/8.72 |
% 31.14/8.72 | Equations (576) can reduce 259 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (259) ~ (all_0_53_53 = e2)
% 31.14/8.72 | (396) all_0_58_58 = e2
% 31.14/8.72 |
% 31.14/8.72 | Combining equations (396,600) yields a new equation:
% 31.14/8.72 | (269) e4 = e2
% 31.14/8.72 |
% 31.14/8.72 | Equations (269) can reduce 231 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (1231) ~ (all_0_49_49 = e0)
% 31.14/8.72 | (589) all_0_49_49 = e1
% 31.14/8.72 |
% 31.14/8.72 | Equations (589) can reduce 543 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (488) ~ (all_0_45_45 = e0)
% 31.14/8.72 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (116), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (411) all_0_43_43 = e0
% 31.14/8.72 |
% 31.14/8.72 | Combining equations (411,782) yields a new equation:
% 31.14/8.72 | (784) e3 = e0
% 31.14/8.72 |
% 31.14/8.72 | Equations (784) can reduce 66 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (455) ~ (all_0_43_43 = e0)
% 31.14/8.72 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (1122), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (621) all_0_44_44 = e0
% 31.14/8.72 |
% 31.14/8.72 | Combining equations (621,370) yields a new equation:
% 31.14/8.72 | (316) e2 = e0
% 31.14/8.72 |
% 31.14/8.72 | Equations (316) can reduce 57 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (625) ~ (all_0_44_44 = e0)
% 31.14/8.72 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (1128), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (454) all_0_45_45 = e0
% 31.14/8.72 |
% 31.14/8.72 | Equations (454) can reduce 488 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (488) ~ (all_0_45_45 = e0)
% 31.14/8.72 | (1132) all_0_46_46 = e0
% 31.14/8.72 |
% 31.14/8.72 | Combining equations (517,1132) yields a new equation:
% 31.14/8.72 | (478) e4 = e0
% 31.14/8.72 |
% 31.14/8.72 | Simplifying 478 yields:
% 31.14/8.72 | (479) e4 = e0
% 31.14/8.72 |
% 31.14/8.72 | Equations (479) can reduce 6 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (786) ~ (all_0_43_43 = e3)
% 31.14/8.72 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (787), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (858) all_0_44_44 = e3
% 31.14/8.72 |
% 31.14/8.72 | Combining equations (370,858) yields a new equation:
% 31.14/8.72 | (414) e3 = e2
% 31.14/8.72 |
% 31.14/8.72 | Equations (414) can reduce 223 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (862) ~ (all_0_44_44 = e3)
% 31.14/8.72 | (1070) all_0_45_45 = e3 | all_0_46_46 = e3
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (159), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (450) all_0_43_43 = e2
% 31.14/8.72 |
% 31.14/8.72 | Equations (450) can reduce 292 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (292) ~ (all_0_43_43 = e2)
% 31.14/8.72 | (774) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (774), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (411) all_0_43_43 = e0
% 31.14/8.72 |
% 31.14/8.72 | Equations (411) can reduce 292 to:
% 31.14/8.72 | (566) ~ (e2 = e0)
% 31.14/8.72 |
% 31.14/8.72 | Simplifying 566 yields:
% 31.14/8.72 | (57) ~ (e2 = e0)
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (58), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (253) all_0_50_50 = e2
% 31.14/8.72 |
% 31.14/8.72 | Combining equations (267,253) yields a new equation:
% 31.14/8.72 | (268) e4 = e2
% 31.14/8.72 |
% 31.14/8.72 | Simplifying 268 yields:
% 31.14/8.72 | (269) e4 = e2
% 31.14/8.72 |
% 31.14/8.72 | Equations (269) can reduce 231 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (9032) ~ (all_0_50_50 = e2)
% 31.14/8.72 | (9860) all_0_51_51 = e2 | all_0_52_52 = e2 | all_0_53_53 = e2 | all_0_54_54 = e2
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (9860), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (4215) all_0_51_51 = e2
% 31.14/8.72 |
% 31.14/8.72 | Equations (4215) can reduce 255 to:
% 31.14/8.72 | (270) $false
% 31.14/8.72 |
% 31.14/8.72 |-The branch is then unsatisfiable
% 31.14/8.72 |-Branch two:
% 31.14/8.72 | (255) ~ (all_0_51_51 = e2)
% 31.14/8.72 | (9864) all_0_52_52 = e2 | all_0_53_53 = e2 | all_0_54_54 = e2
% 31.14/8.72 |
% 31.14/8.72 +-Applying beta-rule and splitting (9864), into two cases.
% 31.14/8.72 |-Branch one:
% 31.14/8.72 | (685) all_0_52_52 = e2
% 31.14/8.72 |
% 31.14/8.73 | Equations (685) can reduce 257 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (257) ~ (all_0_52_52 = e2)
% 31.14/8.73 | (9868) all_0_53_53 = e2 | all_0_54_54 = e2
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (9868), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (576) all_0_53_53 = e2
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (93), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (402) all_0_59_59 = e4
% 31.14/8.73 |
% 31.14/8.73 | Equations (402) can reduce 280 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (280) ~ (all_0_59_59 = e4)
% 31.14/8.73 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (407), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (408), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (409), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 31.14/8.73 |
% 31.14/8.73 | Applying alpha-rule on (410) yields:
% 31.14/8.73 | (411) all_0_43_43 = e0
% 31.14/8.73 | (412) all_0_59_59 = e3
% 31.14/8.73 | (413) ~ (all_0_46_46 = e3)
% 31.14/8.73 |
% 31.14/8.73 | Equations (412) can reduce 140 to:
% 31.14/8.73 | (846) ~ (all_0_57_57 = e3)
% 31.14/8.73 |
% 31.14/8.73 | Equations (412) can reduce 701 to:
% 31.14/8.73 | (223) ~ (e3 = e2)
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (133), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (671) all_0_40_40 = e3
% 31.14/8.73 |
% 31.14/8.73 | Combining equations (530,671) yields a new equation:
% 31.14/8.73 | (538) e3 = e1
% 31.14/8.73 |
% 31.14/8.73 | Equations (538) can reduce 136 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (675) ~ (all_0_40_40 = e3)
% 31.14/8.73 | (676) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (676), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (858) all_0_44_44 = e3
% 31.14/8.73 |
% 31.14/8.73 | Combining equations (370,858) yields a new equation:
% 31.14/8.73 | (414) e3 = e2
% 31.14/8.73 |
% 31.14/8.73 | Equations (414) can reduce 223 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (862) ~ (all_0_44_44 = e3)
% 31.14/8.73 | (863) all_0_52_52 = e3 | all_0_57_57 = e3
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (863), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (864) all_0_52_52 = e3
% 31.14/8.73 |
% 31.14/8.73 | Equations (864) can reduce 230 to:
% 31.14/8.73 | (719) ~ (e4 = e3)
% 31.14/8.73 |
% 31.14/8.73 | Simplifying 719 yields:
% 31.14/8.73 | (34) ~ (e4 = e3)
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (1070), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (505) all_0_45_45 = e3
% 31.14/8.73 |
% 31.14/8.73 | Equations (505) can reduce 354 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (354) ~ (all_0_45_45 = e3)
% 31.14/8.73 | (1091) all_0_46_46 = e3
% 31.14/8.73 |
% 31.14/8.73 | Combining equations (517,1091) yields a new equation:
% 31.14/8.73 | (660) e4 = e3
% 31.14/8.73 |
% 31.14/8.73 | Simplifying 660 yields:
% 31.14/8.73 | (359) e4 = e3
% 31.14/8.73 |
% 31.14/8.73 | Equations (359) can reduce 34 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (826) ~ (all_0_52_52 = e3)
% 31.14/8.73 | (869) all_0_57_57 = e3
% 31.14/8.73 |
% 31.14/8.73 | Equations (869) can reduce 846 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 31.14/8.73 |
% 31.14/8.73 | Applying alpha-rule on (416) yields:
% 31.14/8.73 | (411) all_0_43_43 = e0
% 31.14/8.73 | (412) all_0_59_59 = e3
% 31.14/8.73 | (419) ~ (all_0_56_56 = e0)
% 31.14/8.73 |
% 31.14/8.73 | Equations (412) can reduce 140 to:
% 31.14/8.73 | (846) ~ (all_0_57_57 = e3)
% 31.14/8.73 |
% 31.14/8.73 | Equations (412) can reduce 701 to:
% 31.14/8.73 | (223) ~ (e3 = e2)
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (133), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (671) all_0_40_40 = e3
% 31.14/8.73 |
% 31.14/8.73 | Combining equations (530,671) yields a new equation:
% 31.14/8.73 | (538) e3 = e1
% 31.14/8.73 |
% 31.14/8.73 | Equations (538) can reduce 136 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (675) ~ (all_0_40_40 = e3)
% 31.14/8.73 | (676) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (676), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (858) all_0_44_44 = e3
% 31.14/8.73 |
% 31.14/8.73 | Combining equations (370,858) yields a new equation:
% 31.14/8.73 | (414) e3 = e2
% 31.14/8.73 |
% 31.14/8.73 | Equations (414) can reduce 223 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (862) ~ (all_0_44_44 = e3)
% 31.14/8.73 | (863) all_0_52_52 = e3 | all_0_57_57 = e3
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (863), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (864) all_0_52_52 = e3
% 31.14/8.73 |
% 31.14/8.73 | Equations (864) can reduce 230 to:
% 31.14/8.73 | (719) ~ (e4 = e3)
% 31.14/8.73 |
% 31.14/8.73 | Simplifying 719 yields:
% 31.14/8.73 | (34) ~ (e4 = e3)
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (1070), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (505) all_0_45_45 = e3
% 31.14/8.73 |
% 31.14/8.73 | Equations (505) can reduce 354 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (354) ~ (all_0_45_45 = e3)
% 31.14/8.73 | (1091) all_0_46_46 = e3
% 31.14/8.73 |
% 31.14/8.73 | Combining equations (517,1091) yields a new equation:
% 31.14/8.73 | (660) e4 = e3
% 31.14/8.73 |
% 31.14/8.73 | Simplifying 660 yields:
% 31.14/8.73 | (359) e4 = e3
% 31.14/8.73 |
% 31.14/8.73 | Equations (359) can reduce 34 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (826) ~ (all_0_52_52 = e3)
% 31.14/8.73 | (869) all_0_57_57 = e3
% 31.14/8.73 |
% 31.14/8.73 | Equations (869) can reduce 846 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 31.14/8.73 |
% 31.14/8.73 | Applying alpha-rule on (422) yields:
% 31.14/8.73 | (423) all_0_53_53 = e0
% 31.14/8.73 | (424) all_0_59_59 = e1
% 31.14/8.73 | (425) ~ (all_0_54_54 = e1)
% 31.14/8.73 |
% 31.14/8.73 | Combining equations (423,576) yields a new equation:
% 31.14/8.73 | (316) e2 = e0
% 31.14/8.73 |
% 31.14/8.73 | Equations (316) can reduce 57 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 31.14/8.73 |
% 31.14/8.73 | Applying alpha-rule on (428) yields:
% 31.14/8.73 | (423) all_0_53_53 = e0
% 31.14/8.73 | (424) all_0_59_59 = e1
% 31.14/8.73 | (431) ~ (all_0_58_58 = e0)
% 31.14/8.73 |
% 31.14/8.73 | Combining equations (423,576) yields a new equation:
% 31.14/8.73 | (316) e2 = e0
% 31.14/8.73 |
% 31.14/8.73 | Equations (316) can reduce 57 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (259) ~ (all_0_53_53 = e2)
% 31.14/8.73 | (3657) all_0_54_54 = e2
% 31.14/8.73 |
% 31.14/8.73 | Equations (3657) can reduce 261 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (455) ~ (all_0_43_43 = e0)
% 31.14/8.73 | (944) all_0_43_43 = e4 | all_0_43_43 = e3
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (944), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (782) all_0_43_43 = e3
% 31.14/8.73 |
% 31.14/8.73 | Equations (782) can reduce 786 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (786) ~ (all_0_43_43 = e3)
% 31.14/8.73 | (502) all_0_43_43 = e4
% 31.14/8.73 |
% 31.14/8.73 | Equations (502) can reduce 510 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (333) ~ (all_0_44_44 = e2)
% 31.14/8.73 | (493) all_0_45_45 = e2 | all_0_46_46 = e2
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (435), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (454) all_0_45_45 = e0
% 31.14/8.73 |
% 31.14/8.73 | Equations (454) can reduce 434 to:
% 31.14/8.73 | (566) ~ (e2 = e0)
% 31.14/8.73 |
% 31.14/8.73 | Simplifying 566 yields:
% 31.14/8.73 | (57) ~ (e2 = e0)
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (493), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (374) all_0_45_45 = e2
% 31.14/8.73 |
% 31.14/8.73 | Combining equations (454,374) yields a new equation:
% 31.14/8.73 | (316) e2 = e0
% 31.14/8.73 |
% 31.14/8.73 | Equations (316) can reduce 57 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (434) ~ (all_0_45_45 = e2)
% 31.14/8.73 | (497) all_0_46_46 = e2
% 31.14/8.73 |
% 31.14/8.73 | Combining equations (497,517) yields a new equation:
% 31.14/8.73 | (269) e4 = e2
% 31.14/8.73 |
% 31.14/8.73 | Equations (269) can reduce 231 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (488) ~ (all_0_45_45 = e0)
% 31.14/8.73 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (489), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (505) all_0_45_45 = e3
% 31.14/8.73 |
% 31.14/8.73 | Equations (505) can reduce 354 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (354) ~ (all_0_45_45 = e3)
% 31.14/8.73 | (363) all_0_45_45 = e4
% 31.14/8.73 |
% 31.14/8.73 | Equations (363) can reduce 352 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (2291) all_0_25_25 = e2 & ~ (all_0_26_26 = e1)
% 31.14/8.73 |
% 31.14/8.73 | Applying alpha-rule on (2291) yields:
% 31.14/8.73 | (2292) all_0_25_25 = e2
% 31.14/8.73 | (2293) ~ (all_0_26_26 = e1)
% 31.14/8.73 |
% 31.14/8.73 | From (2292) and (76) follows:
% 31.14/8.73 | (3032) op(e1, all_0_48_48) = e2
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (105), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (374) all_0_45_45 = e2
% 31.14/8.73 |
% 31.14/8.73 | Equations (374) can reduce 84 to:
% 31.14/8.73 | (292) ~ (all_0_43_43 = e2)
% 31.14/8.73 |
% 31.14/8.73 | Equations (374) can reduce 229 to:
% 31.14/8.73 | (333) ~ (all_0_44_44 = e2)
% 31.14/8.73 |
% 31.14/8.73 | Equations (374) can reduce 65 to:
% 31.14/8.73 | (293) ~ (all_0_48_48 = e2)
% 31.14/8.73 |
% 31.14/8.73 | Simplifying 293 yields:
% 31.14/8.73 | (294) ~ (all_0_48_48 = e2)
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (607), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (370) all_0_44_44 = e2
% 31.14/8.73 |
% 31.14/8.73 | Equations (370) can reduce 333 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (333) ~ (all_0_44_44 = e2)
% 31.14/8.73 | (3377) all_0_52_52 = e2 | all_0_57_57 = e2
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (3377), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (685) all_0_52_52 = e2
% 31.14/8.73 |
% 31.14/8.73 | Equations (685) can reduce 122 to:
% 31.14/8.73 | (333) ~ (all_0_44_44 = e2)
% 31.14/8.73 |
% 31.14/8.73 | Equations (685) can reduce 213 to:
% 31.14/8.73 | (258) ~ (all_0_53_53 = e2)
% 31.14/8.73 |
% 31.14/8.73 | Simplifying 258 yields:
% 31.14/8.73 | (259) ~ (all_0_53_53 = e2)
% 31.14/8.73 |
% 31.14/8.73 | Equations (685) can reduce 235 to:
% 31.14/8.73 | (334) ~ (all_0_57_57 = e2)
% 31.14/8.73 |
% 31.14/8.73 | Simplifying 334 yields:
% 31.14/8.73 | (335) ~ (all_0_57_57 = e2)
% 31.14/8.73 |
% 31.14/8.73 | Equations (685) can reduce 642 to:
% 31.14/8.73 | (141) ~ (e2 = e1)
% 31.14/8.73 |
% 31.14/8.73 | From (685) and (27) follows:
% 31.14/8.73 | (11734) op(e2, e2) = all_0_17_17
% 31.14/8.73 |
% 31.14/8.73 | Instantiating formula (201) with e2, e2, all_0_17_17, e4 and discharging atoms op(e2, e2) = all_0_17_17, op(e2, e2) = e4, yields:
% 31.14/8.73 | (11735) all_0_17_17 = e4
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (193), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (370) all_0_44_44 = e2
% 31.14/8.73 |
% 31.14/8.73 | Equations (370) can reduce 333 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (333) ~ (all_0_44_44 = e2)
% 31.14/8.73 | (373) all_0_44_44 = e3 | all_0_44_44 = e0
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (9), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (621) all_0_44_44 = e0
% 31.14/8.73 |
% 31.14/8.73 | Equations (621) can reduce 241 to:
% 31.14/8.73 | (455) ~ (all_0_43_43 = e0)
% 31.14/8.73 |
% 31.14/8.73 | Equations (621) can reduce 10 to:
% 31.14/8.73 | (9326) ~ (all_0_57_57 = e0)
% 31.14/8.73 |
% 31.14/8.73 | Simplifying 9326 yields:
% 31.14/8.73 | (2301) ~ (all_0_57_57 = e0)
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (159), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (450) all_0_43_43 = e2
% 31.14/8.73 |
% 31.14/8.73 | Equations (450) can reduce 292 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (292) ~ (all_0_43_43 = e2)
% 31.14/8.73 | (774) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (133), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (671) all_0_40_40 = e3
% 31.14/8.73 |
% 31.14/8.73 | Combining equations (530,671) yields a new equation:
% 31.14/8.73 | (538) e3 = e1
% 31.14/8.73 |
% 31.14/8.73 | Equations (538) can reduce 136 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (675) ~ (all_0_40_40 = e3)
% 31.14/8.73 | (676) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (676), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (858) all_0_44_44 = e3
% 31.14/8.73 |
% 31.14/8.73 | Combining equations (858,621) yields a new equation:
% 31.14/8.73 | (783) e3 = e0
% 31.14/8.73 |
% 31.14/8.73 | Simplifying 783 yields:
% 31.14/8.73 | (784) e3 = e0
% 31.14/8.73 |
% 31.14/8.73 | Equations (784) can reduce 66 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (862) ~ (all_0_44_44 = e3)
% 31.14/8.73 | (863) all_0_52_52 = e3 | all_0_57_57 = e3
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (33), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (392) all_0_57_57 = e2
% 31.14/8.73 |
% 31.14/8.73 | Equations (392) can reduce 335 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (335) ~ (all_0_57_57 = e2)
% 31.14/8.73 | (670) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (774), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (411) all_0_43_43 = e0
% 31.14/8.73 |
% 31.14/8.73 | Equations (411) can reduce 455 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (455) ~ (all_0_43_43 = e0)
% 31.14/8.73 | (944) all_0_43_43 = e4 | all_0_43_43 = e3
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (944), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (782) all_0_43_43 = e3
% 31.14/8.73 |
% 31.14/8.73 | Equations (782) can reduce 240 to:
% 31.14/8.73 | (952) ~ (all_0_51_51 = e3)
% 31.14/8.73 |
% 31.14/8.73 | Simplifying 952 yields:
% 31.14/8.73 | (932) ~ (all_0_51_51 = e3)
% 31.14/8.73 |
% 31.14/8.73 | Equations (782) can reduce 292 to:
% 31.14/8.73 | (223) ~ (e3 = e2)
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (863), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (864) all_0_52_52 = e3
% 31.14/8.73 |
% 31.14/8.73 | Combining equations (685,864) yields a new equation:
% 31.14/8.73 | (414) e3 = e2
% 31.14/8.73 |
% 31.14/8.73 | Equations (414) can reduce 223 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (826) ~ (all_0_52_52 = e3)
% 31.14/8.73 | (869) all_0_57_57 = e3
% 31.14/8.73 |
% 31.14/8.73 | Equations (869) can reduce 335 to:
% 31.14/8.73 | (223) ~ (e3 = e2)
% 31.14/8.73 |
% 31.14/8.73 | Equations (869) can reduce 2301 to:
% 31.14/8.73 | (66) ~ (e3 = e0)
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (21), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (824) all_0_51_51 = e3
% 31.14/8.73 |
% 31.14/8.73 | Equations (824) can reduce 932 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.73 | (932) ~ (all_0_51_51 = e3)
% 31.14/8.73 | (1101) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 31.14/8.73 |
% 31.14/8.73 +-Applying beta-rule and splitting (1101), into two cases.
% 31.14/8.73 |-Branch one:
% 31.14/8.73 | (864) all_0_52_52 = e3
% 31.14/8.73 |
% 31.14/8.73 | Combining equations (864,685) yields a new equation:
% 31.14/8.73 | (437) e3 = e2
% 31.14/8.73 |
% 31.14/8.73 | Simplifying 437 yields:
% 31.14/8.73 | (414) e3 = e2
% 31.14/8.73 |
% 31.14/8.73 | Equations (414) can reduce 223 to:
% 31.14/8.73 | (270) $false
% 31.14/8.73 |
% 31.14/8.73 |-The branch is then unsatisfiable
% 31.14/8.73 |-Branch two:
% 31.14/8.74 | (826) ~ (all_0_52_52 = e3)
% 31.14/8.74 | (1107) all_0_53_53 = e3 | all_0_54_54 = e3
% 31.14/8.74 |
% 31.14/8.74 +-Applying beta-rule and splitting (1107), into two cases.
% 31.14/8.74 |-Branch one:
% 31.14/8.74 | (1114) all_0_53_53 = e3
% 31.14/8.74 |
% 31.14/8.74 | Equations (1114) can reduce 356 to:
% 31.14/8.74 | (270) $false
% 31.14/8.74 |
% 31.14/8.74 |-The branch is then unsatisfiable
% 31.14/8.74 |-Branch two:
% 31.14/8.74 | (356) ~ (all_0_53_53 = e3)
% 31.14/8.74 | (1119) all_0_54_54 = e3
% 31.14/8.74 |
% 31.14/8.74 | Equations (1119) can reduce 162 to:
% 31.14/8.74 | (150) ~ (all_0_49_49 = e3)
% 31.14/8.74 |
% 31.14/8.74 +-Applying beta-rule and splitting (93), into two cases.
% 31.14/8.74 |-Branch one:
% 31.14/8.74 | (402) all_0_59_59 = e4
% 31.14/8.74 |
% 31.14/8.74 | Equations (402) can reduce 280 to:
% 31.14/8.74 | (270) $false
% 31.14/8.74 |
% 31.14/8.74 |-The branch is then unsatisfiable
% 31.14/8.74 |-Branch two:
% 31.14/8.74 | (280) ~ (all_0_59_59 = e4)
% 31.14/8.74 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 31.14/8.74 |
% 31.14/8.74 +-Applying beta-rule and splitting (407), into two cases.
% 31.14/8.74 |-Branch one:
% 31.14/8.74 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 31.14/8.74 |
% 31.14/8.74 +-Applying beta-rule and splitting (408), into two cases.
% 31.14/8.74 |-Branch one:
% 31.14/8.74 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 31.14/8.74 |
% 31.14/8.74 +-Applying beta-rule and splitting (409), into two cases.
% 31.14/8.74 |-Branch one:
% 31.14/8.74 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 31.14/8.74 |
% 31.14/8.74 | Applying alpha-rule on (410) yields:
% 31.14/8.74 | (411) all_0_43_43 = e0
% 31.14/8.74 | (412) all_0_59_59 = e3
% 31.14/8.74 | (413) ~ (all_0_46_46 = e3)
% 31.14/8.74 |
% 31.14/8.74 | Combining equations (411,782) yields a new equation:
% 31.14/8.74 | (784) e3 = e0
% 31.14/8.74 |
% 31.14/8.74 | Equations (784) can reduce 66 to:
% 31.14/8.74 | (270) $false
% 31.14/8.74 |
% 31.14/8.74 |-The branch is then unsatisfiable
% 31.14/8.74 |-Branch two:
% 31.14/8.74 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 31.14/8.74 |
% 31.14/8.74 | Applying alpha-rule on (416) yields:
% 31.14/8.74 | (411) all_0_43_43 = e0
% 31.14/8.74 | (412) all_0_59_59 = e3
% 31.14/8.74 | (419) ~ (all_0_56_56 = e0)
% 31.14/8.74 |
% 31.14/8.74 | Combining equations (411,782) yields a new equation:
% 31.14/8.74 | (784) e3 = e0
% 31.14/8.74 |
% 31.14/8.74 | Equations (784) can reduce 66 to:
% 31.14/8.74 | (270) $false
% 31.14/8.74 |
% 31.14/8.74 |-The branch is then unsatisfiable
% 31.14/8.74 |-Branch two:
% 31.14/8.74 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 31.14/8.74 |
% 31.14/8.74 | Applying alpha-rule on (422) yields:
% 31.14/8.74 | (423) all_0_53_53 = e0
% 31.14/8.74 | (424) all_0_59_59 = e1
% 31.14/8.74 | (425) ~ (all_0_54_54 = e1)
% 31.14/8.74 |
% 31.14/8.74 | Equations (423) can reduce 48 to:
% 31.14/8.74 | (562) ~ (all_0_48_48 = e0)
% 31.14/8.74 |
% 31.14/8.74 | Equations (424) can reduce 113 to:
% 31.14/8.74 | (543) ~ (all_0_49_49 = e1)
% 31.14/8.74 |
% 31.14/8.74 | Equations (424) can reduce 185 to:
% 31.14/8.74 | (995) ~ (all_0_56_56 = e1)
% 31.14/8.74 |
% 31.14/8.74 | From (423) and (227) follows:
% 31.14/8.74 | (2167) op(e1, e1) = e0
% 31.14/8.74 |
% 31.14/8.74 +-Applying beta-rule and splitting (325), into two cases.
% 31.14/8.74 |-Branch one:
% 31.14/8.74 | (552) all_0_48_48 = e1
% 31.14/8.74 |
% 31.14/8.74 | Equations (552) can reduce 4 to:
% 31.14/8.74 | (542) ~ (all_0_49_49 = e1)
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 542 yields:
% 31.14/8.74 | (543) ~ (all_0_49_49 = e1)
% 31.14/8.74 |
% 31.14/8.74 | Equations (552) can reduce 192 to:
% 31.14/8.74 | (1021) ~ (e4 = e1)
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 1021 yields:
% 31.14/8.74 | (251) ~ (e4 = e1)
% 31.14/8.74 |
% 31.14/8.74 | Equations (552) can reduce 294 to:
% 31.14/8.74 | (645) ~ (e2 = e1)
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 645 yields:
% 31.14/8.74 | (141) ~ (e2 = e1)
% 31.14/8.74 |
% 31.14/8.74 | Equations (552) can reduce 562 to:
% 31.14/8.74 | (132) ~ (e1 = e0)
% 31.14/8.74 |
% 31.14/8.74 | From (552) and (3032) follows:
% 31.14/8.74 | (3043) op(e1, e1) = e2
% 31.14/8.74 |
% 31.14/8.74 +-Applying beta-rule and splitting (319), into two cases.
% 31.14/8.74 |-Branch one:
% 31.14/8.74 | (559) all_0_48_48 = e0
% 31.14/8.74 |
% 31.14/8.74 | Combining equations (552,559) yields a new equation:
% 31.14/8.74 | (571) e1 = e0
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 571 yields:
% 31.14/8.74 | (560) e1 = e0
% 31.14/8.74 |
% 31.14/8.74 | Equations (560) can reduce 132 to:
% 31.14/8.74 | (270) $false
% 31.14/8.74 |
% 31.14/8.74 |-The branch is then unsatisfiable
% 31.14/8.74 |-Branch two:
% 31.14/8.74 | (562) ~ (all_0_48_48 = e0)
% 31.14/8.74 | (563) all_0_49_49 = e0
% 31.14/8.74 |
% 31.14/8.74 | Equations (563) can reduce 202 to:
% 31.14/8.74 | (456) ~ (e4 = e0)
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 456 yields:
% 31.14/8.74 | (6) ~ (e4 = e0)
% 31.14/8.74 |
% 31.14/8.74 | Equations (563) can reduce 150 to:
% 31.14/8.74 | (788) ~ (e3 = e0)
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 788 yields:
% 31.14/8.74 | (66) ~ (e3 = e0)
% 31.14/8.74 |
% 31.14/8.74 | Equations (563) can reduce 543 to:
% 31.14/8.74 | (568) ~ (e1 = e0)
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 568 yields:
% 31.14/8.74 | (132) ~ (e1 = e0)
% 31.14/8.74 |
% 31.14/8.74 +-Applying beta-rule and splitting (176), into two cases.
% 31.14/8.74 |-Branch one:
% 31.14/8.74 | (830) all_0_56_56 = e0
% 31.14/8.74 |
% 31.14/8.74 | Equations (830) can reduce 300 to:
% 31.14/8.74 | (566) ~ (e2 = e0)
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 566 yields:
% 31.14/8.74 | (57) ~ (e2 = e0)
% 31.14/8.74 |
% 31.14/8.74 | Equations (830) can reduce 995 to:
% 31.14/8.74 | (568) ~ (e1 = e0)
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 568 yields:
% 31.14/8.74 | (132) ~ (e1 = e0)
% 31.14/8.74 |
% 31.14/8.74 +-Applying beta-rule and splitting (99), into two cases.
% 31.14/8.74 |-Branch one:
% 31.14/8.74 | (524) all_0_39_39 = e1
% 31.14/8.74 |
% 31.14/8.74 | Combining equations (524,522) yields a new equation:
% 31.14/8.74 | (526) e4 = e1
% 31.14/8.74 |
% 31.14/8.74 | Equations (526) can reduce 251 to:
% 31.14/8.74 | (270) $false
% 31.14/8.74 |
% 31.14/8.74 |-The branch is then unsatisfiable
% 31.14/8.74 |-Branch two:
% 31.14/8.74 | (528) ~ (all_0_39_39 = e1)
% 31.14/8.74 | (680) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 31.14/8.74 |
% 31.14/8.74 +-Applying beta-rule and splitting (135), into two cases.
% 31.14/8.74 |-Branch one:
% 31.14/8.74 | (820) all_0_51_51 = e1
% 31.14/8.74 |
% 31.14/8.74 | From (820) and (216) follows:
% 31.14/8.74 | (16748) op(e1, e1) = all_0_10_10
% 31.14/8.74 |
% 31.14/8.74 | Instantiating formula (201) with e1, e1, e2, all_0_10_10 and discharging atoms op(e1, e1) = all_0_10_10, op(e1, e1) = e2, yields:
% 31.14/8.74 | (6801) all_0_10_10 = e2
% 31.14/8.74 |
% 31.14/8.74 | Instantiating formula (201) with e1, e1, e0, all_0_10_10 and discharging atoms op(e1, e1) = all_0_10_10, op(e1, e1) = e0, yields:
% 31.14/8.74 | (16750) all_0_10_10 = e0
% 31.14/8.74 |
% 31.14/8.74 | Combining equations (6801,16750) yields a new equation:
% 31.14/8.74 | (622) e2 = e0
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 622 yields:
% 31.14/8.74 | (316) e2 = e0
% 31.14/8.74 |
% 31.14/8.74 | Equations (316) can reduce 57 to:
% 31.14/8.74 | (270) $false
% 31.14/8.74 |
% 31.14/8.74 |-The branch is then unsatisfiable
% 31.14/8.74 |-Branch two:
% 31.14/8.74 | (748) ~ (all_0_51_51 = e1)
% 31.14/8.74 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 31.14/8.74 |
% 31.14/8.74 +-Applying beta-rule and splitting (680), into two cases.
% 31.14/8.74 |-Branch one:
% 31.14/8.74 | (321) all_0_47_47 = e1
% 31.14/8.74 |
% 31.14/8.74 | Combining equations (290,321) yields a new equation:
% 31.14/8.74 | (531) e2 = e1
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 531 yields:
% 31.14/8.74 | (322) e2 = e1
% 31.14/8.74 |
% 31.14/8.74 | Equations (322) can reduce 141 to:
% 31.14/8.74 | (270) $false
% 31.14/8.74 |
% 31.14/8.74 |-The branch is then unsatisfiable
% 31.14/8.74 |-Branch two:
% 31.14/8.74 | (324) ~ (all_0_47_47 = e1)
% 31.14/8.74 | (1625) all_0_51_51 = e1 | all_0_56_56 = e1
% 31.14/8.74 |
% 31.14/8.74 +-Applying beta-rule and splitting (1625), into two cases.
% 31.14/8.74 |-Branch one:
% 31.14/8.74 | (820) all_0_51_51 = e1
% 31.14/8.74 |
% 31.14/8.74 | Equations (820) can reduce 748 to:
% 31.14/8.74 | (270) $false
% 31.14/8.74 |
% 31.14/8.74 |-The branch is then unsatisfiable
% 31.14/8.74 |-Branch two:
% 31.14/8.74 | (748) ~ (all_0_51_51 = e1)
% 31.14/8.74 | (747) all_0_56_56 = e1
% 31.14/8.74 |
% 31.14/8.74 | Combining equations (830,747) yields a new equation:
% 31.14/8.74 | (560) e1 = e0
% 31.14/8.74 |
% 31.14/8.74 | Equations (560) can reduce 132 to:
% 31.14/8.74 | (270) $false
% 31.14/8.74 |
% 31.14/8.74 |-The branch is then unsatisfiable
% 31.14/8.74 |-Branch two:
% 31.14/8.74 | (419) ~ (all_0_56_56 = e0)
% 31.14/8.74 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 31.14/8.74 |
% 31.14/8.74 +-Applying beta-rule and splitting (834), into two cases.
% 31.14/8.74 |-Branch one:
% 31.14/8.74 | (2258) all_0_57_57 = e0
% 31.14/8.74 |
% 31.14/8.74 | Combining equations (869,2258) yields a new equation:
% 31.14/8.74 | (783) e3 = e0
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 783 yields:
% 31.14/8.74 | (784) e3 = e0
% 31.14/8.74 |
% 31.14/8.74 | Equations (784) can reduce 66 to:
% 31.14/8.74 | (270) $false
% 31.14/8.74 |
% 31.14/8.74 |-The branch is then unsatisfiable
% 31.14/8.74 |-Branch two:
% 31.14/8.74 | (2301) ~ (all_0_57_57 = e0)
% 31.14/8.74 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 31.14/8.74 |
% 31.14/8.74 +-Applying beta-rule and splitting (2302), into two cases.
% 31.14/8.74 |-Branch one:
% 31.14/8.74 | (585) all_0_58_58 = e0
% 31.14/8.74 |
% 31.14/8.74 | Combining equations (600,585) yields a new equation:
% 31.14/8.74 | (478) e4 = e0
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 478 yields:
% 31.14/8.74 | (479) e4 = e0
% 31.14/8.74 |
% 31.14/8.74 | Equations (479) can reduce 6 to:
% 31.14/8.74 | (270) $false
% 31.14/8.74 |
% 31.14/8.74 |-The branch is then unsatisfiable
% 31.14/8.74 |-Branch two:
% 31.14/8.74 | (431) ~ (all_0_58_58 = e0)
% 31.14/8.74 | (2308) all_0_59_59 = e0
% 31.14/8.74 |
% 31.14/8.74 | Combining equations (2308,424) yields a new equation:
% 31.14/8.74 | (560) e1 = e0
% 31.14/8.74 |
% 31.14/8.74 | Equations (560) can reduce 132 to:
% 31.14/8.74 | (270) $false
% 31.14/8.74 |
% 31.14/8.74 |-The branch is then unsatisfiable
% 31.14/8.74 |-Branch two:
% 31.14/8.74 | (588) ~ (all_0_48_48 = e1)
% 31.14/8.74 | (589) all_0_49_49 = e1
% 31.14/8.74 |
% 31.14/8.74 | Equations (589) can reduce 543 to:
% 31.14/8.74 | (270) $false
% 31.14/8.74 |
% 31.14/8.74 |-The branch is then unsatisfiable
% 31.14/8.74 |-Branch two:
% 31.14/8.74 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 31.14/8.74 |
% 31.14/8.74 | Applying alpha-rule on (428) yields:
% 31.14/8.74 | (423) all_0_53_53 = e0
% 31.14/8.74 | (424) all_0_59_59 = e1
% 31.14/8.74 | (431) ~ (all_0_58_58 = e0)
% 31.14/8.74 |
% 31.14/8.74 | Equations (423) can reduce 48 to:
% 31.14/8.74 | (562) ~ (all_0_48_48 = e0)
% 31.14/8.74 |
% 31.14/8.74 | Equations (424) can reduce 113 to:
% 31.14/8.74 | (543) ~ (all_0_49_49 = e1)
% 31.14/8.74 |
% 31.14/8.74 | Equations (424) can reduce 185 to:
% 31.14/8.74 | (995) ~ (all_0_56_56 = e1)
% 31.14/8.74 |
% 31.14/8.74 | From (423) and (227) follows:
% 31.14/8.74 | (2167) op(e1, e1) = e0
% 31.14/8.74 |
% 31.14/8.74 +-Applying beta-rule and splitting (325), into two cases.
% 31.14/8.74 |-Branch one:
% 31.14/8.74 | (552) all_0_48_48 = e1
% 31.14/8.74 |
% 31.14/8.74 | Equations (552) can reduce 4 to:
% 31.14/8.74 | (542) ~ (all_0_49_49 = e1)
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 542 yields:
% 31.14/8.74 | (543) ~ (all_0_49_49 = e1)
% 31.14/8.74 |
% 31.14/8.74 | Equations (552) can reduce 192 to:
% 31.14/8.74 | (1021) ~ (e4 = e1)
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 1021 yields:
% 31.14/8.74 | (251) ~ (e4 = e1)
% 31.14/8.74 |
% 31.14/8.74 | Equations (552) can reduce 294 to:
% 31.14/8.74 | (645) ~ (e2 = e1)
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 645 yields:
% 31.14/8.74 | (141) ~ (e2 = e1)
% 31.14/8.74 |
% 31.14/8.74 | Equations (552) can reduce 562 to:
% 31.14/8.74 | (132) ~ (e1 = e0)
% 31.14/8.74 |
% 31.14/8.74 | From (552) and (3032) follows:
% 31.14/8.74 | (3043) op(e1, e1) = e2
% 31.14/8.74 |
% 31.14/8.74 +-Applying beta-rule and splitting (319), into two cases.
% 31.14/8.74 |-Branch one:
% 31.14/8.74 | (559) all_0_48_48 = e0
% 31.14/8.74 |
% 31.14/8.74 | Combining equations (552,559) yields a new equation:
% 31.14/8.74 | (571) e1 = e0
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 571 yields:
% 31.14/8.74 | (560) e1 = e0
% 31.14/8.74 |
% 31.14/8.74 | Equations (560) can reduce 132 to:
% 31.14/8.74 | (270) $false
% 31.14/8.74 |
% 31.14/8.74 |-The branch is then unsatisfiable
% 31.14/8.74 |-Branch two:
% 31.14/8.74 | (562) ~ (all_0_48_48 = e0)
% 31.14/8.74 | (563) all_0_49_49 = e0
% 31.14/8.74 |
% 31.14/8.74 | Equations (563) can reduce 202 to:
% 31.14/8.74 | (456) ~ (e4 = e0)
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 456 yields:
% 31.14/8.74 | (6) ~ (e4 = e0)
% 31.14/8.74 |
% 31.14/8.74 | Equations (563) can reduce 150 to:
% 31.14/8.74 | (788) ~ (e3 = e0)
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 788 yields:
% 31.14/8.74 | (66) ~ (e3 = e0)
% 31.14/8.74 |
% 31.14/8.74 | Equations (563) can reduce 543 to:
% 31.14/8.74 | (568) ~ (e1 = e0)
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 568 yields:
% 31.14/8.74 | (132) ~ (e1 = e0)
% 31.14/8.74 |
% 31.14/8.74 +-Applying beta-rule and splitting (176), into two cases.
% 31.14/8.74 |-Branch one:
% 31.14/8.74 | (830) all_0_56_56 = e0
% 31.14/8.74 |
% 31.14/8.74 | Equations (830) can reduce 300 to:
% 31.14/8.74 | (566) ~ (e2 = e0)
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 566 yields:
% 31.14/8.74 | (57) ~ (e2 = e0)
% 31.14/8.74 |
% 31.14/8.74 | Equations (830) can reduce 995 to:
% 31.14/8.74 | (568) ~ (e1 = e0)
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 568 yields:
% 31.14/8.74 | (132) ~ (e1 = e0)
% 31.14/8.74 |
% 31.14/8.74 +-Applying beta-rule and splitting (99), into two cases.
% 31.14/8.74 |-Branch one:
% 31.14/8.74 | (524) all_0_39_39 = e1
% 31.14/8.74 |
% 31.14/8.74 | Combining equations (524,522) yields a new equation:
% 31.14/8.74 | (526) e4 = e1
% 31.14/8.74 |
% 31.14/8.74 | Equations (526) can reduce 251 to:
% 31.14/8.74 | (270) $false
% 31.14/8.74 |
% 31.14/8.74 |-The branch is then unsatisfiable
% 31.14/8.74 |-Branch two:
% 31.14/8.74 | (528) ~ (all_0_39_39 = e1)
% 31.14/8.74 | (680) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 31.14/8.74 |
% 31.14/8.74 +-Applying beta-rule and splitting (135), into two cases.
% 31.14/8.74 |-Branch one:
% 31.14/8.74 | (820) all_0_51_51 = e1
% 31.14/8.74 |
% 31.14/8.74 | From (820) and (216) follows:
% 31.14/8.74 | (16748) op(e1, e1) = all_0_10_10
% 31.14/8.74 |
% 31.14/8.74 | Instantiating formula (201) with e1, e1, e2, all_0_10_10 and discharging atoms op(e1, e1) = all_0_10_10, op(e1, e1) = e2, yields:
% 31.14/8.74 | (6801) all_0_10_10 = e2
% 31.14/8.74 |
% 31.14/8.74 | Instantiating formula (201) with e1, e1, e0, all_0_10_10 and discharging atoms op(e1, e1) = all_0_10_10, op(e1, e1) = e0, yields:
% 31.14/8.74 | (16750) all_0_10_10 = e0
% 31.14/8.74 |
% 31.14/8.74 | Combining equations (6801,16750) yields a new equation:
% 31.14/8.74 | (622) e2 = e0
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 622 yields:
% 31.14/8.74 | (316) e2 = e0
% 31.14/8.74 |
% 31.14/8.74 | Equations (316) can reduce 57 to:
% 31.14/8.74 | (270) $false
% 31.14/8.74 |
% 31.14/8.74 |-The branch is then unsatisfiable
% 31.14/8.74 |-Branch two:
% 31.14/8.74 | (748) ~ (all_0_51_51 = e1)
% 31.14/8.74 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 31.14/8.74 |
% 31.14/8.74 +-Applying beta-rule and splitting (680), into two cases.
% 31.14/8.74 |-Branch one:
% 31.14/8.74 | (321) all_0_47_47 = e1
% 31.14/8.74 |
% 31.14/8.74 | Combining equations (290,321) yields a new equation:
% 31.14/8.74 | (531) e2 = e1
% 31.14/8.74 |
% 31.14/8.74 | Simplifying 531 yields:
% 31.14/8.74 | (322) e2 = e1
% 31.14/8.74 |
% 31.14/8.74 | Equations (322) can reduce 141 to:
% 31.14/8.74 | (270) $false
% 31.14/8.74 |
% 31.14/8.74 |-The branch is then unsatisfiable
% 31.14/8.74 |-Branch two:
% 31.14/8.74 | (324) ~ (all_0_47_47 = e1)
% 31.14/8.74 | (1625) all_0_51_51 = e1 | all_0_56_56 = e1
% 31.14/8.74 |
% 31.14/8.74 +-Applying beta-rule and splitting (1625), into two cases.
% 31.14/8.74 |-Branch one:
% 31.14/8.75 | (820) all_0_51_51 = e1
% 31.14/8.75 |
% 31.14/8.75 | Equations (820) can reduce 748 to:
% 31.14/8.75 | (270) $false
% 31.14/8.75 |
% 31.14/8.75 |-The branch is then unsatisfiable
% 31.14/8.75 |-Branch two:
% 31.14/8.75 | (748) ~ (all_0_51_51 = e1)
% 31.14/8.75 | (747) all_0_56_56 = e1
% 31.14/8.75 |
% 31.14/8.75 | Combining equations (830,747) yields a new equation:
% 31.14/8.75 | (560) e1 = e0
% 31.14/8.75 |
% 31.14/8.75 | Equations (560) can reduce 132 to:
% 31.14/8.75 | (270) $false
% 31.14/8.75 |
% 31.14/8.75 |-The branch is then unsatisfiable
% 31.14/8.75 |-Branch two:
% 31.14/8.75 | (419) ~ (all_0_56_56 = e0)
% 31.14/8.75 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 31.14/8.75 |
% 31.14/8.75 +-Applying beta-rule and splitting (834), into two cases.
% 31.14/8.75 |-Branch one:
% 31.14/8.75 | (2258) all_0_57_57 = e0
% 31.14/8.75 |
% 31.14/8.75 | Combining equations (869,2258) yields a new equation:
% 31.14/8.75 | (783) e3 = e0
% 31.14/8.75 |
% 31.14/8.75 | Simplifying 783 yields:
% 31.14/8.75 | (784) e3 = e0
% 31.14/8.75 |
% 31.14/8.75 | Equations (784) can reduce 66 to:
% 31.14/8.75 | (270) $false
% 31.14/8.75 |
% 31.14/8.75 |-The branch is then unsatisfiable
% 31.14/8.75 |-Branch two:
% 31.14/8.75 | (2301) ~ (all_0_57_57 = e0)
% 31.14/8.75 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 31.14/8.75 |
% 31.14/8.75 +-Applying beta-rule and splitting (2302), into two cases.
% 31.14/8.75 |-Branch one:
% 31.14/8.75 | (585) all_0_58_58 = e0
% 31.14/8.75 |
% 31.14/8.75 | Combining equations (600,585) yields a new equation:
% 31.14/8.75 | (478) e4 = e0
% 31.14/8.75 |
% 31.14/8.75 | Simplifying 478 yields:
% 31.14/8.75 | (479) e4 = e0
% 31.14/8.75 |
% 31.14/8.75 | Equations (479) can reduce 6 to:
% 31.14/8.75 | (270) $false
% 31.14/8.75 |
% 31.14/8.75 |-The branch is then unsatisfiable
% 31.14/8.75 |-Branch two:
% 31.14/8.75 | (431) ~ (all_0_58_58 = e0)
% 31.14/8.75 | (2308) all_0_59_59 = e0
% 31.14/8.75 |
% 31.14/8.75 | Combining equations (2308,424) yields a new equation:
% 31.14/8.75 | (560) e1 = e0
% 31.14/8.75 |
% 31.14/8.75 | Equations (560) can reduce 132 to:
% 31.14/8.75 | (270) $false
% 31.14/8.75 |
% 31.14/8.75 |-The branch is then unsatisfiable
% 31.14/8.75 |-Branch two:
% 31.14/8.75 | (588) ~ (all_0_48_48 = e1)
% 31.14/8.75 | (589) all_0_49_49 = e1
% 31.14/8.75 |
% 31.14/8.75 | Equations (589) can reduce 543 to:
% 31.14/8.75 | (270) $false
% 31.14/8.75 |
% 31.14/8.75 |-The branch is then unsatisfiable
% 31.14/8.75 |-Branch two:
% 31.14/8.75 | (786) ~ (all_0_43_43 = e3)
% 31.14/8.75 | (502) all_0_43_43 = e4
% 31.14/8.75 |
% 31.14/8.75 | Equations (502) can reduce 510 to:
% 31.14/8.75 | (270) $false
% 31.14/8.75 |
% 31.14/8.75 |-The branch is then unsatisfiable
% 31.14/8.75 |-Branch two:
% 31.14/8.75 | (625) ~ (all_0_44_44 = e0)
% 31.14/8.75 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 31.14/8.75 |
% 31.14/8.75 +-Applying beta-rule and splitting (373), into two cases.
% 31.14/8.75 |-Branch one:
% 31.14/8.75 | (621) all_0_44_44 = e0
% 31.14/8.75 |
% 31.14/8.75 | Equations (621) can reduce 625 to:
% 31.14/8.75 | (270) $false
% 31.14/8.75 |
% 31.14/8.75 |-The branch is then unsatisfiable
% 31.14/8.75 |-Branch two:
% 31.14/8.75 | (625) ~ (all_0_44_44 = e0)
% 31.14/8.75 | (858) all_0_44_44 = e3
% 31.14/8.75 |
% 31.14/8.75 | Equations (858) can reduce 241 to:
% 31.14/8.75 | (786) ~ (all_0_43_43 = e3)
% 31.14/8.75 |
% 31.14/8.75 | Equations (858) can reduce 10 to:
% 31.14/8.75 | (2238) ~ (all_0_57_57 = e3)
% 31.14/8.75 |
% 31.14/8.75 | Simplifying 2238 yields:
% 31.14/8.75 | (846) ~ (all_0_57_57 = e3)
% 31.14/8.75 |
% 31.14/8.75 | Equations (858) can reduce 333 to:
% 31.14/8.75 | (223) ~ (e3 = e2)
% 31.14/8.75 |
% 31.14/8.75 | Equations (858) can reduce 131 to:
% 31.14/8.75 | (136) ~ (e3 = e1)
% 31.14/8.75 |
% 31.14/8.75 | From (858) and (165) follows:
% 31.14/8.75 | (3499) op(e2, e3) = all_0_15_15
% 31.14/8.75 |
% 31.14/8.75 +-Applying beta-rule and splitting (33), into two cases.
% 31.14/8.75 |-Branch one:
% 31.14/8.75 | (392) all_0_57_57 = e2
% 31.14/8.75 |
% 31.14/8.75 | Equations (392) can reduce 335 to:
% 31.14/8.75 | (270) $false
% 31.14/8.75 |
% 31.14/8.75 |-The branch is then unsatisfiable
% 31.14/8.75 |-Branch two:
% 31.14/8.75 | (335) ~ (all_0_57_57 = e2)
% 31.14/8.75 | (670) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 31.14/8.75 |
% 31.14/8.75 +-Applying beta-rule and splitting (116), into two cases.
% 31.14/8.75 |-Branch one:
% 31.14/8.75 | (411) all_0_43_43 = e0
% 31.14/8.75 |
% 31.14/8.75 | Equations (411) can reduce 292 to:
% 31.14/8.75 | (566) ~ (e2 = e0)
% 31.14/8.75 |
% 31.14/8.75 | Simplifying 566 yields:
% 31.14/8.75 | (57) ~ (e2 = e0)
% 31.14/8.75 |
% 31.14/8.75 +-Applying beta-rule and splitting (626), into two cases.
% 31.14/8.75 |-Branch one:
% 31.14/8.75 | (827) all_0_52_52 = e0
% 31.14/8.75 |
% 31.14/8.75 | Combining equations (685,827) yields a new equation:
% 31.14/8.75 | (622) e2 = e0
% 31.14/8.75 |
% 31.14/8.75 | Simplifying 622 yields:
% 31.14/8.75 | (316) e2 = e0
% 31.14/8.75 |
% 31.14/8.75 | Equations (316) can reduce 57 to:
% 31.14/8.75 | (270) $false
% 31.14/8.75 |
% 31.14/8.75 |-The branch is then unsatisfiable
% 31.14/8.75 |-Branch two:
% 31.14/8.75 | (925) ~ (all_0_52_52 = e0)
% 31.14/8.75 | (2258) all_0_57_57 = e0
% 31.14/8.75 |
% 31.14/8.75 | From (2258) and (30) follows:
% 31.14/8.75 | (12293) op(e2, e0) = all_0_19_19
% 31.14/8.75 |
% 31.14/8.75 | Instantiating formula (201) with e2, e3, all_0_15_15, e2 and discharging atoms op(e2, e3) = all_0_15_15, op(e2, e3) = e2, yields:
% 31.14/8.75 | (3500) all_0_15_15 = e2
% 31.14/8.75 |
% 31.14/8.75 | Instantiating formula (201) with e2, e0, all_0_19_19, all_0_49_49 and discharging atoms op(e2, e0) = all_0_19_19, op(e2, e0) = all_0_49_49, yields:
% 31.14/8.75 | (16896) all_0_19_19 = all_0_49_49
% 31.14/8.75 |
% 31.14/8.75 +-Applying beta-rule and splitting (87), into two cases.
% 31.14/8.75 |-Branch one:
% 31.14/8.75 | (650) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 31.14/8.75 |
% 31.14/8.75 +-Applying beta-rule and splitting (650), into two cases.
% 31.14/8.75 |-Branch one:
% 31.14/8.75 | (651) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 31.14/8.75 |
% 31.14/8.75 +-Applying beta-rule and splitting (651), into two cases.
% 31.14/8.75 |-Branch one:
% 31.14/8.75 | (652) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 31.14/8.75 |
% 31.14/8.75 | Applying alpha-rule on (652) yields:
% 31.14/8.75 | (653) all_0_13_13 = e4
% 31.14/8.75 | (654) ~ (all_0_14_14 = e2)
% 31.14/8.75 |
% 31.14/8.75 | Combining equations (653,649) yields a new equation:
% 31.14/8.75 | (655) all_0_48_48 = e4
% 31.14/8.75 |
% 31.14/8.75 | Equations (655) can reduce 192 to:
% 31.14/8.75 | (270) $false
% 31.14/8.75 |
% 31.14/8.75 |-The branch is then unsatisfiable
% 31.14/8.75 |-Branch two:
% 31.14/8.75 | (657) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 31.14/8.75 |
% 31.14/8.75 | Applying alpha-rule on (657) yields:
% 31.14/8.75 | (658) all_0_15_15 = e3
% 31.14/8.75 | (659) ~ (all_0_16_16 = e2)
% 31.14/8.75 |
% 31.14/8.75 | Combining equations (658,3500) yields a new equation:
% 31.14/8.75 | (437) e3 = e2
% 31.14/8.75 |
% 31.14/8.75 | Simplifying 437 yields:
% 31.14/8.75 | (414) e3 = e2
% 31.14/8.75 |
% 31.14/8.75 | Equations (414) can reduce 223 to:
% 31.14/8.75 | (270) $false
% 31.14/8.75 |
% 31.14/8.75 |-The branch is then unsatisfiable
% 31.14/8.75 |-Branch two:
% 31.14/8.75 | (663) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 31.14/8.75 |
% 31.14/8.75 | Applying alpha-rule on (663) yields:
% 31.14/8.75 | (664) all_0_17_17 = e1
% 31.14/8.75 | (665) ~ (all_0_18_18 = e2)
% 31.14/8.75 |
% 31.14/8.75 | Combining equations (664,11735) yields a new equation:
% 31.14/8.75 | (526) e4 = e1
% 31.14/8.75 |
% 31.14/8.75 | Equations (526) can reduce 251 to:
% 31.14/8.75 | (270) $false
% 31.14/8.75 |
% 31.14/8.75 |-The branch is then unsatisfiable
% 31.14/8.75 |-Branch two:
% 31.14/8.75 | (1762) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 31.14/8.75 |
% 31.14/8.75 | Applying alpha-rule on (1762) yields:
% 31.14/8.75 | (1763) all_0_19_19 = e0
% 31.14/8.75 | (1764) ~ (all_0_20_20 = e2)
% 31.14/8.75 |
% 31.14/8.75 | Combining equations (1763,16896) yields a new equation:
% 31.14/8.75 | (563) all_0_49_49 = e0
% 31.14/8.75 |
% 31.14/8.75 | Equations (563) can reduce 4 to:
% 31.14/8.75 | (562) ~ (all_0_48_48 = e0)
% 31.14/8.75 |
% 31.14/8.75 | Equations (563) can reduce 202 to:
% 31.14/8.75 | (456) ~ (e4 = e0)
% 31.14/8.75 |
% 31.14/8.75 | Simplifying 456 yields:
% 31.14/8.75 | (6) ~ (e4 = e0)
% 31.14/8.75 |
% 31.14/8.75 | Equations (563) can reduce 296 to:
% 31.14/8.75 | (566) ~ (e2 = e0)
% 31.14/8.75 |
% 31.14/8.75 | Simplifying 566 yields:
% 31.14/8.75 | (57) ~ (e2 = e0)
% 31.14/8.75 |
% 31.14/8.75 +-Applying beta-rule and splitting (314), into two cases.
% 31.14/8.75 |-Branch one:
% 31.14/8.75 | (559) all_0_48_48 = e0
% 31.14/8.75 |
% 31.14/8.75 | Equations (559) can reduce 562 to:
% 31.14/8.75 | (270) $false
% 31.14/8.75 |
% 31.14/8.75 |-The branch is then unsatisfiable
% 31.14/8.75 |-Branch two:
% 31.14/8.75 | (562) ~ (all_0_48_48 = e0)
% 31.14/8.75 | (552) all_0_48_48 = e1
% 31.14/8.75 |
% 31.14/8.75 | Equations (552) can reduce 562 to:
% 31.14/8.75 | (132) ~ (e1 = e0)
% 31.14/8.75 |
% 31.14/8.75 | From (552) and (3032) follows:
% 31.14/8.75 | (3043) op(e1, e1) = e2
% 31.14/8.75 |
% 31.14/8.75 +-Applying beta-rule and splitting (182), into two cases.
% 31.14/8.75 |-Branch one:
% 31.14/8.75 | (454) all_0_45_45 = e0
% 31.14/8.75 |
% 31.14/8.75 | Combining equations (374,454) yields a new equation:
% 31.14/8.75 | (622) e2 = e0
% 31.14/8.75 |
% 31.14/8.75 | Simplifying 622 yields:
% 31.14/8.75 | (316) e2 = e0
% 31.14/8.75 |
% 31.14/8.75 | Equations (316) can reduce 57 to:
% 31.14/8.75 | (270) $false
% 31.14/8.75 |
% 31.14/8.75 |-The branch is then unsatisfiable
% 31.14/8.75 |-Branch two:
% 31.14/8.75 | (488) ~ (all_0_45_45 = e0)
% 31.14/8.75 | (558) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 31.14/8.75 |
% 31.14/8.75 +-Applying beta-rule and splitting (558), into two cases.
% 31.14/8.75 |-Branch one:
% 31.14/8.75 | (559) all_0_48_48 = e0
% 31.14/8.75 |
% 31.14/8.75 | Combining equations (552,559) yields a new equation:
% 31.14/8.75 | (571) e1 = e0
% 31.14/8.75 |
% 31.14/8.75 | Simplifying 571 yields:
% 31.14/8.75 | (560) e1 = e0
% 31.14/8.75 |
% 31.14/8.75 | Equations (560) can reduce 132 to:
% 31.14/8.75 | (270) $false
% 31.14/8.75 |
% 31.14/8.75 |-The branch is then unsatisfiable
% 31.14/8.75 |-Branch two:
% 31.14/8.75 | (562) ~ (all_0_48_48 = e0)
% 31.14/8.75 | (575) all_0_53_53 = e0 | all_0_58_58 = e0
% 31.14/8.75 |
% 31.14/8.75 +-Applying beta-rule and splitting (575), into two cases.
% 31.14/8.75 |-Branch one:
% 31.14/8.75 | (423) all_0_53_53 = e0
% 31.14/8.75 |
% 31.14/8.75 | Equations (423) can reduce 259 to:
% 31.14/8.75 | (566) ~ (e2 = e0)
% 31.14/8.75 |
% 31.14/8.75 | Simplifying 566 yields:
% 31.14/8.75 | (57) ~ (e2 = e0)
% 31.14/8.75 |
% 31.14/8.75 | From (423) and (227) follows:
% 31.14/8.75 | (2167) op(e1, e1) = e0
% 31.14/8.75 |
% 31.14/8.75 | Instantiating formula (201) with e1, e1, e0, e2 and discharging atoms op(e1, e1) = e2, op(e1, e1) = e0, yields:
% 31.14/8.75 | (316) e2 = e0
% 31.14/8.75 |
% 31.14/8.75 | Equations (316) can reduce 57 to:
% 31.14/8.75 | (270) $false
% 31.14/8.75 |
% 31.14/8.75 |-The branch is then unsatisfiable
% 31.14/8.75 |-Branch two:
% 31.14/8.75 | (584) ~ (all_0_53_53 = e0)
% 31.14/8.75 | (585) all_0_58_58 = e0
% 31.14/8.75 |
% 31.14/8.75 | Combining equations (585,600) yields a new equation:
% 31.14/8.75 | (479) e4 = e0
% 31.14/8.75 |
% 31.14/8.75 | Equations (479) can reduce 6 to:
% 31.14/8.75 | (270) $false
% 31.14/8.75 |
% 31.14/8.75 |-The branch is then unsatisfiable
% 31.14/8.75 |-Branch two:
% 31.14/8.75 | (455) ~ (all_0_43_43 = e0)
% 31.14/8.75 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 31.14/8.75 |
% 31.14/8.75 +-Applying beta-rule and splitting (670), into two cases.
% 31.14/8.75 |-Branch one:
% 31.14/8.75 | (2258) all_0_57_57 = e0
% 31.14/8.75 |
% 31.14/8.75 | Equations (2258) can reduce 104 to:
% 31.14/8.75 | (419) ~ (all_0_56_56 = e0)
% 31.14/8.75 |
% 31.14/8.75 | Equations (2258) can reduce 140 to:
% 31.14/8.75 | (4000) ~ (all_0_59_59 = e0)
% 31.14/8.75 |
% 31.14/8.75 | Simplifying 4000 yields:
% 31.14/8.75 | (4001) ~ (all_0_59_59 = e0)
% 31.14/8.75 |
% 31.14/8.75 | Equations (2258) can reduce 335 to:
% 31.14/8.75 | (566) ~ (e2 = e0)
% 31.14/8.75 |
% 31.14/8.75 | Simplifying 566 yields:
% 31.14/8.75 | (57) ~ (e2 = e0)
% 31.14/8.75 |
% 31.14/8.75 | Equations (2258) can reduce 644 to:
% 31.14/8.75 | (568) ~ (e1 = e0)
% 31.14/8.75 |
% 31.14/8.75 | Simplifying 568 yields:
% 31.14/8.75 | (132) ~ (e1 = e0)
% 31.14/8.75 |
% 31.14/8.75 +-Applying beta-rule and splitting (75), into two cases.
% 31.14/8.75 |-Branch one:
% 31.14/8.75 | (411) all_0_43_43 = e0
% 31.14/8.75 |
% 31.14/8.75 | Equations (411) can reduce 455 to:
% 31.14/8.75 | (270) $false
% 31.14/8.75 |
% 31.14/8.75 |-The branch is then unsatisfiable
% 31.14/8.75 |-Branch two:
% 31.14/8.75 | (455) ~ (all_0_43_43 = e0)
% 31.14/8.75 | (940) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 31.14/8.75 |
% 31.14/8.75 +-Applying beta-rule and splitting (940), into two cases.
% 31.14/8.75 |-Branch one:
% 31.14/8.75 | (315) all_0_47_47 = e0
% 31.14/8.75 |
% 31.14/8.75 | Combining equations (315,290) yields a new equation:
% 31.14/8.75 | (316) e2 = e0
% 31.14/8.75 |
% 31.14/8.75 | Equations (316) can reduce 57 to:
% 31.14/8.75 | (270) $false
% 31.14/8.75 |
% 31.14/8.75 |-The branch is then unsatisfiable
% 31.14/8.75 |-Branch two:
% 31.14/8.75 | (318) ~ (all_0_47_47 = e0)
% 31.14/8.75 | (950) all_0_51_51 = e0 | all_0_56_56 = e0
% 31.14/8.75 |
% 31.14/8.75 +-Applying beta-rule and splitting (950), into two cases.
% 31.14/8.75 |-Branch one:
% 31.14/8.75 | (954) all_0_51_51 = e0
% 31.14/8.75 |
% 31.14/8.75 | Equations (954) can reduce 50 to:
% 31.14/8.75 | (3010) ~ (all_0_54_54 = e0)
% 31.14/8.75 |
% 31.14/8.75 | Simplifying 3010 yields:
% 31.14/8.75 | (3011) ~ (all_0_54_54 = e0)
% 31.14/8.75 |
% 31.14/8.75 | Equations (954) can reduce 697 to:
% 31.14/8.75 | (456) ~ (e4 = e0)
% 31.14/8.75 |
% 31.14/8.75 | Simplifying 456 yields:
% 31.14/8.75 | (6) ~ (e4 = e0)
% 31.14/8.75 |
% 31.14/8.75 +-Applying beta-rule and splitting (221), into two cases.
% 31.14/8.75 |-Branch one:
% 31.14/8.75 | (1132) all_0_46_46 = e0
% 31.14/8.75 |
% 31.14/8.75 | Combining equations (517,1132) yields a new equation:
% 31.14/8.75 | (478) e4 = e0
% 31.14/8.75 |
% 31.14/8.75 | Simplifying 478 yields:
% 31.14/8.75 | (479) e4 = e0
% 31.14/8.75 |
% 31.14/8.75 | Equations (479) can reduce 6 to:
% 31.14/8.75 | (270) $false
% 31.14/8.75 |
% 31.14/8.75 |-The branch is then unsatisfiable
% 31.14/8.75 |-Branch two:
% 31.14/8.75 | (1010) ~ (all_0_46_46 = e0)
% 31.14/8.75 | (3629) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 31.14/8.75 |
% 31.14/8.75 +-Applying beta-rule and splitting (3629), into two cases.
% 31.14/8.75 |-Branch one:
% 31.14/8.75 | (563) all_0_49_49 = e0
% 31.14/8.75 |
% 31.14/8.75 | Equations (563) can reduce 162 to:
% 31.14/8.75 | (3010) ~ (all_0_54_54 = e0)
% 31.14/8.75 |
% 31.14/8.75 | Simplifying 3010 yields:
% 31.14/8.75 | (3011) ~ (all_0_54_54 = e0)
% 31.14/8.75 |
% 31.14/8.75 | Equations (563) can reduce 150 to:
% 31.14/8.75 | (788) ~ (e3 = e0)
% 31.14/8.75 |
% 31.14/8.75 | Simplifying 788 yields:
% 31.14/8.76 | (66) ~ (e3 = e0)
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (99), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (524) all_0_39_39 = e1
% 31.14/8.76 |
% 31.14/8.76 | Combining equations (522,524) yields a new equation:
% 31.14/8.76 | (525) e4 = e1
% 31.14/8.76 |
% 31.14/8.76 | Simplifying 525 yields:
% 31.14/8.76 | (526) e4 = e1
% 31.14/8.76 |
% 31.14/8.76 | Equations (526) can reduce 251 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (528) ~ (all_0_39_39 = e1)
% 31.14/8.76 | (680) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (21), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (824) all_0_51_51 = e3
% 31.14/8.76 |
% 31.14/8.76 | Combining equations (954,824) yields a new equation:
% 31.14/8.76 | (784) e3 = e0
% 31.14/8.76 |
% 31.14/8.76 | Equations (784) can reduce 66 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (932) ~ (all_0_51_51 = e3)
% 31.14/8.76 | (1101) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (680), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (321) all_0_47_47 = e1
% 31.14/8.76 |
% 31.14/8.76 | Combining equations (290,321) yields a new equation:
% 31.14/8.76 | (531) e2 = e1
% 31.14/8.76 |
% 31.14/8.76 | Simplifying 531 yields:
% 31.14/8.76 | (322) e2 = e1
% 31.14/8.76 |
% 31.14/8.76 | Equations (322) can reduce 141 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (324) ~ (all_0_47_47 = e1)
% 31.14/8.76 | (1625) all_0_51_51 = e1 | all_0_56_56 = e1
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (1101), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (864) all_0_52_52 = e3
% 31.14/8.76 |
% 31.14/8.76 | Combining equations (685,864) yields a new equation:
% 31.14/8.76 | (414) e3 = e2
% 31.14/8.76 |
% 31.14/8.76 | Equations (414) can reduce 223 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (826) ~ (all_0_52_52 = e3)
% 31.14/8.76 | (1107) all_0_53_53 = e3 | all_0_54_54 = e3
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (1107), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (1114) all_0_53_53 = e3
% 31.14/8.76 |
% 31.14/8.76 | Equations (1114) can reduce 356 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (356) ~ (all_0_53_53 = e3)
% 31.14/8.76 | (1119) all_0_54_54 = e3
% 31.14/8.76 |
% 31.14/8.76 | Equations (1119) can reduce 936 to:
% 31.14/8.76 | (719) ~ (e4 = e3)
% 31.14/8.76 |
% 31.14/8.76 | Simplifying 719 yields:
% 31.14/8.76 | (34) ~ (e4 = e3)
% 31.14/8.76 |
% 31.14/8.76 | Equations (1119) can reduce 3011 to:
% 31.14/8.76 | (66) ~ (e3 = e0)
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (178), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (751) all_0_39_39 = e3
% 31.14/8.76 |
% 31.14/8.76 | Combining equations (522,751) yields a new equation:
% 31.14/8.76 | (660) e4 = e3
% 31.14/8.76 |
% 31.14/8.76 | Simplifying 660 yields:
% 31.14/8.76 | (359) e4 = e3
% 31.14/8.76 |
% 31.14/8.76 | Equations (359) can reduce 34 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (755) ~ (all_0_39_39 = e3)
% 31.14/8.76 | (756) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (756), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (782) all_0_43_43 = e3
% 31.14/8.76 |
% 31.14/8.76 | Equations (782) can reduce 786 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (786) ~ (all_0_43_43 = e3)
% 31.14/8.76 | (799) all_0_51_51 = e3 | all_0_56_56 = e3
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (1625), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (820) all_0_51_51 = e1
% 31.14/8.76 |
% 31.14/8.76 | Combining equations (954,820) yields a new equation:
% 31.14/8.76 | (560) e1 = e0
% 31.14/8.76 |
% 31.14/8.76 | Equations (560) can reduce 132 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (748) ~ (all_0_51_51 = e1)
% 31.14/8.76 | (747) all_0_56_56 = e1
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (799), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (824) all_0_51_51 = e3
% 31.14/8.76 |
% 31.14/8.76 | Combining equations (824,954) yields a new equation:
% 31.14/8.76 | (783) e3 = e0
% 31.14/8.76 |
% 31.14/8.76 | Simplifying 783 yields:
% 31.14/8.76 | (784) e3 = e0
% 31.14/8.76 |
% 31.14/8.76 | Equations (784) can reduce 66 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (932) ~ (all_0_51_51 = e3)
% 31.14/8.76 | (764) all_0_56_56 = e3
% 31.14/8.76 |
% 31.14/8.76 | Combining equations (764,747) yields a new equation:
% 31.14/8.76 | (537) e3 = e1
% 31.14/8.76 |
% 31.14/8.76 | Simplifying 537 yields:
% 31.14/8.76 | (538) e3 = e1
% 31.14/8.76 |
% 31.14/8.76 | Equations (538) can reduce 136 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (1231) ~ (all_0_49_49 = e0)
% 31.14/8.76 | (3638) all_0_54_54 = e0 | all_0_59_59 = e0
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (3638), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (3084) all_0_54_54 = e0
% 31.14/8.76 |
% 31.14/8.76 | Equations (3084) can reduce 3011 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (3011) ~ (all_0_54_54 = e0)
% 31.14/8.76 | (2308) all_0_59_59 = e0
% 31.14/8.76 |
% 31.14/8.76 | Equations (2308) can reduce 4001 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (987) ~ (all_0_51_51 = e0)
% 31.14/8.76 | (830) all_0_56_56 = e0
% 31.14/8.76 |
% 31.14/8.76 | Equations (830) can reduce 419 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (2301) ~ (all_0_57_57 = e0)
% 31.14/8.76 | (9345) all_0_57_57 = e3 | all_0_57_57 = e1
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (9345), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (869) all_0_57_57 = e3
% 31.14/8.76 |
% 31.14/8.76 | Equations (869) can reduce 846 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (846) ~ (all_0_57_57 = e3)
% 31.14/8.76 | (997) all_0_57_57 = e1
% 31.14/8.76 |
% 31.14/8.76 | Equations (997) can reduce 644 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (257) ~ (all_0_52_52 = e2)
% 31.14/8.76 | (392) all_0_57_57 = e2
% 31.14/8.76 |
% 31.14/8.76 | Equations (392) can reduce 335 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (434) ~ (all_0_45_45 = e2)
% 31.14/8.76 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (187), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (436) all_0_41_41 = e2
% 31.14/8.76 |
% 31.14/8.76 | Combining equations (351,436) yields a new equation:
% 31.14/8.76 | (437) e3 = e2
% 31.14/8.76 |
% 31.14/8.76 | Simplifying 437 yields:
% 31.14/8.76 | (414) e3 = e2
% 31.14/8.76 |
% 31.14/8.76 | Equations (414) can reduce 223 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (331) ~ (all_0_41_41 = e2)
% 31.14/8.76 | (441) all_0_45_45 = e2 | all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 31.14/8.76 |
% 31.14/8.76 | Equations (351) can reduce 331 to:
% 31.14/8.76 | (223) ~ (e3 = e2)
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (453), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (370) all_0_44_44 = e2
% 31.14/8.76 |
% 31.14/8.76 | Equations (370) can reduce 241 to:
% 31.14/8.76 | (292) ~ (all_0_43_43 = e2)
% 31.14/8.76 |
% 31.14/8.76 | Equations (370) can reduce 229 to:
% 31.14/8.76 | (611) ~ (all_0_45_45 = e2)
% 31.14/8.76 |
% 31.14/8.76 | Simplifying 611 yields:
% 31.14/8.76 | (434) ~ (all_0_45_45 = e2)
% 31.14/8.76 |
% 31.14/8.76 | Equations (370) can reduce 122 to:
% 31.14/8.76 | (256) ~ (all_0_52_52 = e2)
% 31.14/8.76 |
% 31.14/8.76 | Simplifying 256 yields:
% 31.14/8.76 | (257) ~ (all_0_52_52 = e2)
% 31.14/8.76 |
% 31.14/8.76 | Equations (370) can reduce 45 to:
% 31.14/8.76 | (377) ~ (e4 = e2)
% 31.14/8.76 |
% 31.14/8.76 | Simplifying 377 yields:
% 31.14/8.76 | (231) ~ (e4 = e2)
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (22), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (782) all_0_43_43 = e3
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (435), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (454) all_0_45_45 = e0
% 31.14/8.76 |
% 31.14/8.76 | Equations (454) can reduce 65 to:
% 31.14/8.76 | (7709) ~ (all_0_48_48 = e0)
% 31.14/8.76 |
% 31.14/8.76 | Simplifying 7709 yields:
% 31.14/8.76 | (562) ~ (all_0_48_48 = e0)
% 31.14/8.76 |
% 31.14/8.76 | Equations (454) can reduce 128 to:
% 31.14/8.76 | (3103) ~ (all_0_53_53 = e0)
% 31.14/8.76 |
% 31.14/8.76 | Simplifying 3103 yields:
% 31.14/8.76 | (584) ~ (all_0_53_53 = e0)
% 31.14/8.76 |
% 31.14/8.76 | Equations (454) can reduce 434 to:
% 31.14/8.76 | (566) ~ (e2 = e0)
% 31.14/8.76 |
% 31.14/8.76 | Simplifying 566 yields:
% 31.14/8.76 | (57) ~ (e2 = e0)
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (314), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (559) all_0_48_48 = e0
% 31.14/8.76 |
% 31.14/8.76 | Equations (559) can reduce 562 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (562) ~ (all_0_48_48 = e0)
% 31.14/8.76 | (552) all_0_48_48 = e1
% 31.14/8.76 |
% 31.14/8.76 | Equations (552) can reduce 4 to:
% 31.14/8.76 | (542) ~ (all_0_49_49 = e1)
% 31.14/8.76 |
% 31.14/8.76 | Simplifying 542 yields:
% 31.14/8.76 | (543) ~ (all_0_49_49 = e1)
% 31.14/8.76 |
% 31.14/8.76 | Equations (552) can reduce 294 to:
% 31.14/8.76 | (645) ~ (e2 = e1)
% 31.14/8.76 |
% 31.14/8.76 | Simplifying 645 yields:
% 31.14/8.76 | (141) ~ (e2 = e1)
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (441), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (374) all_0_45_45 = e2
% 31.14/8.76 |
% 31.14/8.76 | Combining equations (374,454) yields a new equation:
% 31.14/8.76 | (622) e2 = e0
% 31.14/8.76 |
% 31.14/8.76 | Simplifying 622 yields:
% 31.14/8.76 | (316) e2 = e0
% 31.14/8.76 |
% 31.14/8.76 | Equations (316) can reduce 57 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (434) ~ (all_0_45_45 = e2)
% 31.14/8.76 | (445) all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (58), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (253) all_0_50_50 = e2
% 31.14/8.76 |
% 31.14/8.76 | Combining equations (253,267) yields a new equation:
% 31.14/8.76 | (269) e4 = e2
% 31.14/8.76 |
% 31.14/8.76 | Equations (269) can reduce 231 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (9032) ~ (all_0_50_50 = e2)
% 31.14/8.76 | (9860) all_0_51_51 = e2 | all_0_52_52 = e2 | all_0_53_53 = e2 | all_0_54_54 = e2
% 31.14/8.76 |
% 31.14/8.76 | Equations (267) can reduce 9032 to:
% 31.14/8.76 | (231) ~ (e4 = e2)
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (93), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (402) all_0_59_59 = e4
% 31.14/8.76 |
% 31.14/8.76 | Equations (402) can reduce 280 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (280) ~ (all_0_59_59 = e4)
% 31.14/8.76 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (310), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (563) all_0_49_49 = e0
% 31.14/8.76 |
% 31.14/8.76 | Equations (563) can reduce 150 to:
% 31.14/8.76 | (788) ~ (e3 = e0)
% 31.14/8.76 |
% 31.14/8.76 | Simplifying 788 yields:
% 31.14/8.76 | (66) ~ (e3 = e0)
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (13), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (576) all_0_53_53 = e2
% 31.14/8.76 |
% 31.14/8.76 | Equations (576) can reduce 584 to:
% 31.14/8.76 | (57) ~ (e2 = e0)
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (407), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (408), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (409), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 31.14/8.76 |
% 31.14/8.76 | Applying alpha-rule on (410) yields:
% 31.14/8.76 | (411) all_0_43_43 = e0
% 31.14/8.76 | (412) all_0_59_59 = e3
% 31.14/8.76 | (413) ~ (all_0_46_46 = e3)
% 31.14/8.76 |
% 31.14/8.76 | Combining equations (782,411) yields a new equation:
% 31.14/8.76 | (783) e3 = e0
% 31.14/8.76 |
% 31.14/8.76 | Simplifying 783 yields:
% 31.14/8.76 | (784) e3 = e0
% 31.14/8.76 |
% 31.14/8.76 | Equations (784) can reduce 66 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 31.14/8.76 |
% 31.14/8.76 | Applying alpha-rule on (416) yields:
% 31.14/8.76 | (411) all_0_43_43 = e0
% 31.14/8.76 | (412) all_0_59_59 = e3
% 31.14/8.76 | (419) ~ (all_0_56_56 = e0)
% 31.14/8.76 |
% 31.14/8.76 | Combining equations (782,411) yields a new equation:
% 31.14/8.76 | (783) e3 = e0
% 31.14/8.76 |
% 31.14/8.76 | Simplifying 783 yields:
% 31.14/8.76 | (784) e3 = e0
% 31.14/8.76 |
% 31.14/8.76 | Equations (784) can reduce 66 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 31.14/8.76 |
% 31.14/8.76 | Applying alpha-rule on (422) yields:
% 31.14/8.76 | (423) all_0_53_53 = e0
% 31.14/8.76 | (424) all_0_59_59 = e1
% 31.14/8.76 | (425) ~ (all_0_54_54 = e1)
% 31.14/8.76 |
% 31.14/8.76 | Combining equations (423,576) yields a new equation:
% 31.14/8.76 | (316) e2 = e0
% 31.14/8.76 |
% 31.14/8.76 | Equations (316) can reduce 57 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 31.14/8.76 |
% 31.14/8.76 | Applying alpha-rule on (428) yields:
% 31.14/8.76 | (423) all_0_53_53 = e0
% 31.14/8.76 | (424) all_0_59_59 = e1
% 31.14/8.76 | (431) ~ (all_0_58_58 = e0)
% 31.14/8.76 |
% 31.14/8.76 | Combining equations (423,576) yields a new equation:
% 31.14/8.76 | (316) e2 = e0
% 31.14/8.76 |
% 31.14/8.76 | Equations (316) can reduce 57 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (259) ~ (all_0_53_53 = e2)
% 31.14/8.76 | (5715) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (445), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (311) all_0_48_48 = e2
% 31.14/8.76 |
% 31.14/8.76 | Combining equations (311,552) yields a new equation:
% 31.14/8.76 | (531) e2 = e1
% 31.14/8.76 |
% 31.14/8.76 | Simplifying 531 yields:
% 31.14/8.76 | (322) e2 = e1
% 31.14/8.76 |
% 31.14/8.76 | Equations (322) can reduce 141 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (294) ~ (all_0_48_48 = e2)
% 31.14/8.76 | (449) all_0_53_53 = e2 | all_0_58_58 = e2
% 31.14/8.76 |
% 31.14/8.76 +-Applying beta-rule and splitting (449), into two cases.
% 31.14/8.76 |-Branch one:
% 31.14/8.76 | (576) all_0_53_53 = e2
% 31.14/8.76 |
% 31.14/8.76 | Equations (576) can reduce 259 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (259) ~ (all_0_53_53 = e2)
% 31.14/8.76 | (396) all_0_58_58 = e2
% 31.14/8.76 |
% 31.14/8.76 | Combining equations (396,600) yields a new equation:
% 31.14/8.76 | (269) e4 = e2
% 31.14/8.76 |
% 31.14/8.76 | Equations (269) can reduce 231 to:
% 31.14/8.76 | (270) $false
% 31.14/8.76 |
% 31.14/8.76 |-The branch is then unsatisfiable
% 31.14/8.76 |-Branch two:
% 31.14/8.76 | (1231) ~ (all_0_49_49 = e0)
% 31.14/8.76 | (589) all_0_49_49 = e1
% 31.14/8.76 |
% 31.14/8.77 | Equations (589) can reduce 543 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (488) ~ (all_0_45_45 = e0)
% 31.14/8.77 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (116), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (411) all_0_43_43 = e0
% 31.14/8.77 |
% 31.14/8.77 | Combining equations (411,782) yields a new equation:
% 31.14/8.77 | (784) e3 = e0
% 31.14/8.77 |
% 31.14/8.77 | Equations (784) can reduce 66 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (455) ~ (all_0_43_43 = e0)
% 31.14/8.77 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (1122), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (621) all_0_44_44 = e0
% 31.14/8.77 |
% 31.14/8.77 | Combining equations (621,370) yields a new equation:
% 31.14/8.77 | (316) e2 = e0
% 31.14/8.77 |
% 31.14/8.77 | Equations (316) can reduce 57 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (625) ~ (all_0_44_44 = e0)
% 31.14/8.77 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (1128), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (454) all_0_45_45 = e0
% 31.14/8.77 |
% 31.14/8.77 | Equations (454) can reduce 488 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (488) ~ (all_0_45_45 = e0)
% 31.14/8.77 | (1132) all_0_46_46 = e0
% 31.14/8.77 |
% 31.14/8.77 | Combining equations (517,1132) yields a new equation:
% 31.14/8.77 | (478) e4 = e0
% 31.14/8.77 |
% 31.14/8.77 | Simplifying 478 yields:
% 31.14/8.77 | (479) e4 = e0
% 31.14/8.77 |
% 31.14/8.77 | Equations (479) can reduce 6 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (786) ~ (all_0_43_43 = e3)
% 31.14/8.77 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (787), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (858) all_0_44_44 = e3
% 31.14/8.77 |
% 31.14/8.77 | Combining equations (370,858) yields a new equation:
% 31.14/8.77 | (414) e3 = e2
% 31.14/8.77 |
% 31.14/8.77 | Equations (414) can reduce 223 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (862) ~ (all_0_44_44 = e3)
% 31.14/8.77 | (1070) all_0_45_45 = e3 | all_0_46_46 = e3
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (159), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (450) all_0_43_43 = e2
% 31.14/8.77 |
% 31.14/8.77 | Equations (450) can reduce 292 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (292) ~ (all_0_43_43 = e2)
% 31.14/8.77 | (774) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (774), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (411) all_0_43_43 = e0
% 31.14/8.77 |
% 31.14/8.77 | Equations (411) can reduce 292 to:
% 31.14/8.77 | (566) ~ (e2 = e0)
% 31.14/8.77 |
% 31.14/8.77 | Simplifying 566 yields:
% 31.14/8.77 | (57) ~ (e2 = e0)
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (58), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (253) all_0_50_50 = e2
% 31.14/8.77 |
% 31.14/8.77 | Combining equations (267,253) yields a new equation:
% 31.14/8.77 | (268) e4 = e2
% 31.14/8.77 |
% 31.14/8.77 | Simplifying 268 yields:
% 31.14/8.77 | (269) e4 = e2
% 31.14/8.77 |
% 31.14/8.77 | Equations (269) can reduce 231 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (9032) ~ (all_0_50_50 = e2)
% 31.14/8.77 | (9860) all_0_51_51 = e2 | all_0_52_52 = e2 | all_0_53_53 = e2 | all_0_54_54 = e2
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (9860), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (4215) all_0_51_51 = e2
% 31.14/8.77 |
% 31.14/8.77 | Equations (4215) can reduce 255 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (255) ~ (all_0_51_51 = e2)
% 31.14/8.77 | (9864) all_0_52_52 = e2 | all_0_53_53 = e2 | all_0_54_54 = e2
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (9864), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (685) all_0_52_52 = e2
% 31.14/8.77 |
% 31.14/8.77 | Equations (685) can reduce 257 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (257) ~ (all_0_52_52 = e2)
% 31.14/8.77 | (9868) all_0_53_53 = e2 | all_0_54_54 = e2
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (9868), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (576) all_0_53_53 = e2
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (93), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (402) all_0_59_59 = e4
% 31.14/8.77 |
% 31.14/8.77 | Equations (402) can reduce 280 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (280) ~ (all_0_59_59 = e4)
% 31.14/8.77 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (407), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (408), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (409), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 31.14/8.77 |
% 31.14/8.77 | Applying alpha-rule on (410) yields:
% 31.14/8.77 | (411) all_0_43_43 = e0
% 31.14/8.77 | (412) all_0_59_59 = e3
% 31.14/8.77 | (413) ~ (all_0_46_46 = e3)
% 31.14/8.77 |
% 31.14/8.77 | Equations (412) can reduce 140 to:
% 31.14/8.77 | (846) ~ (all_0_57_57 = e3)
% 31.14/8.77 |
% 31.14/8.77 | Equations (412) can reduce 701 to:
% 31.14/8.77 | (223) ~ (e3 = e2)
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (133), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (671) all_0_40_40 = e3
% 31.14/8.77 |
% 31.14/8.77 | Combining equations (530,671) yields a new equation:
% 31.14/8.77 | (538) e3 = e1
% 31.14/8.77 |
% 31.14/8.77 | Equations (538) can reduce 136 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (675) ~ (all_0_40_40 = e3)
% 31.14/8.77 | (676) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (676), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (858) all_0_44_44 = e3
% 31.14/8.77 |
% 31.14/8.77 | Combining equations (370,858) yields a new equation:
% 31.14/8.77 | (414) e3 = e2
% 31.14/8.77 |
% 31.14/8.77 | Equations (414) can reduce 223 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (862) ~ (all_0_44_44 = e3)
% 31.14/8.77 | (863) all_0_52_52 = e3 | all_0_57_57 = e3
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (863), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (864) all_0_52_52 = e3
% 31.14/8.77 |
% 31.14/8.77 | Equations (864) can reduce 230 to:
% 31.14/8.77 | (719) ~ (e4 = e3)
% 31.14/8.77 |
% 31.14/8.77 | Simplifying 719 yields:
% 31.14/8.77 | (34) ~ (e4 = e3)
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (1070), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (505) all_0_45_45 = e3
% 31.14/8.77 |
% 31.14/8.77 | Equations (505) can reduce 354 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (354) ~ (all_0_45_45 = e3)
% 31.14/8.77 | (1091) all_0_46_46 = e3
% 31.14/8.77 |
% 31.14/8.77 | Combining equations (517,1091) yields a new equation:
% 31.14/8.77 | (660) e4 = e3
% 31.14/8.77 |
% 31.14/8.77 | Simplifying 660 yields:
% 31.14/8.77 | (359) e4 = e3
% 31.14/8.77 |
% 31.14/8.77 | Equations (359) can reduce 34 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (826) ~ (all_0_52_52 = e3)
% 31.14/8.77 | (869) all_0_57_57 = e3
% 31.14/8.77 |
% 31.14/8.77 | Equations (869) can reduce 846 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 31.14/8.77 |
% 31.14/8.77 | Applying alpha-rule on (416) yields:
% 31.14/8.77 | (411) all_0_43_43 = e0
% 31.14/8.77 | (412) all_0_59_59 = e3
% 31.14/8.77 | (419) ~ (all_0_56_56 = e0)
% 31.14/8.77 |
% 31.14/8.77 | Equations (412) can reduce 140 to:
% 31.14/8.77 | (846) ~ (all_0_57_57 = e3)
% 31.14/8.77 |
% 31.14/8.77 | Equations (412) can reduce 701 to:
% 31.14/8.77 | (223) ~ (e3 = e2)
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (133), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (671) all_0_40_40 = e3
% 31.14/8.77 |
% 31.14/8.77 | Combining equations (530,671) yields a new equation:
% 31.14/8.77 | (538) e3 = e1
% 31.14/8.77 |
% 31.14/8.77 | Equations (538) can reduce 136 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (675) ~ (all_0_40_40 = e3)
% 31.14/8.77 | (676) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (676), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (858) all_0_44_44 = e3
% 31.14/8.77 |
% 31.14/8.77 | Combining equations (370,858) yields a new equation:
% 31.14/8.77 | (414) e3 = e2
% 31.14/8.77 |
% 31.14/8.77 | Equations (414) can reduce 223 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (862) ~ (all_0_44_44 = e3)
% 31.14/8.77 | (863) all_0_52_52 = e3 | all_0_57_57 = e3
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (863), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (864) all_0_52_52 = e3
% 31.14/8.77 |
% 31.14/8.77 | Equations (864) can reduce 230 to:
% 31.14/8.77 | (719) ~ (e4 = e3)
% 31.14/8.77 |
% 31.14/8.77 | Simplifying 719 yields:
% 31.14/8.77 | (34) ~ (e4 = e3)
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (1070), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (505) all_0_45_45 = e3
% 31.14/8.77 |
% 31.14/8.77 | Equations (505) can reduce 354 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (354) ~ (all_0_45_45 = e3)
% 31.14/8.77 | (1091) all_0_46_46 = e3
% 31.14/8.77 |
% 31.14/8.77 | Combining equations (517,1091) yields a new equation:
% 31.14/8.77 | (660) e4 = e3
% 31.14/8.77 |
% 31.14/8.77 | Simplifying 660 yields:
% 31.14/8.77 | (359) e4 = e3
% 31.14/8.77 |
% 31.14/8.77 | Equations (359) can reduce 34 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (826) ~ (all_0_52_52 = e3)
% 31.14/8.77 | (869) all_0_57_57 = e3
% 31.14/8.77 |
% 31.14/8.77 | Equations (869) can reduce 846 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 31.14/8.77 |
% 31.14/8.77 | Applying alpha-rule on (422) yields:
% 31.14/8.77 | (423) all_0_53_53 = e0
% 31.14/8.77 | (424) all_0_59_59 = e1
% 31.14/8.77 | (425) ~ (all_0_54_54 = e1)
% 31.14/8.77 |
% 31.14/8.77 | Combining equations (423,576) yields a new equation:
% 31.14/8.77 | (316) e2 = e0
% 31.14/8.77 |
% 31.14/8.77 | Equations (316) can reduce 57 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 31.14/8.77 |
% 31.14/8.77 | Applying alpha-rule on (428) yields:
% 31.14/8.77 | (423) all_0_53_53 = e0
% 31.14/8.77 | (424) all_0_59_59 = e1
% 31.14/8.77 | (431) ~ (all_0_58_58 = e0)
% 31.14/8.77 |
% 31.14/8.77 | Combining equations (423,576) yields a new equation:
% 31.14/8.77 | (316) e2 = e0
% 31.14/8.77 |
% 31.14/8.77 | Equations (316) can reduce 57 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (259) ~ (all_0_53_53 = e2)
% 31.14/8.77 | (3657) all_0_54_54 = e2
% 31.14/8.77 |
% 31.14/8.77 | Equations (3657) can reduce 261 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (455) ~ (all_0_43_43 = e0)
% 31.14/8.77 | (944) all_0_43_43 = e4 | all_0_43_43 = e3
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (944), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (782) all_0_43_43 = e3
% 31.14/8.77 |
% 31.14/8.77 | Equations (782) can reduce 786 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (786) ~ (all_0_43_43 = e3)
% 31.14/8.77 | (502) all_0_43_43 = e4
% 31.14/8.77 |
% 31.14/8.77 | Equations (502) can reduce 510 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (333) ~ (all_0_44_44 = e2)
% 31.14/8.77 | (493) all_0_45_45 = e2 | all_0_46_46 = e2
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (435), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (454) all_0_45_45 = e0
% 31.14/8.77 |
% 31.14/8.77 | Equations (454) can reduce 434 to:
% 31.14/8.77 | (566) ~ (e2 = e0)
% 31.14/8.77 |
% 31.14/8.77 | Simplifying 566 yields:
% 31.14/8.77 | (57) ~ (e2 = e0)
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (493), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (374) all_0_45_45 = e2
% 31.14/8.77 |
% 31.14/8.77 | Combining equations (454,374) yields a new equation:
% 31.14/8.77 | (316) e2 = e0
% 31.14/8.77 |
% 31.14/8.77 | Equations (316) can reduce 57 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (434) ~ (all_0_45_45 = e2)
% 31.14/8.77 | (497) all_0_46_46 = e2
% 31.14/8.77 |
% 31.14/8.77 | Combining equations (497,517) yields a new equation:
% 31.14/8.77 | (269) e4 = e2
% 31.14/8.77 |
% 31.14/8.77 | Equations (269) can reduce 231 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (488) ~ (all_0_45_45 = e0)
% 31.14/8.77 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (489), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (505) all_0_45_45 = e3
% 31.14/8.77 |
% 31.14/8.77 | Equations (505) can reduce 354 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (354) ~ (all_0_45_45 = e3)
% 31.14/8.77 | (363) all_0_45_45 = e4
% 31.14/8.77 |
% 31.14/8.77 | Equations (363) can reduce 352 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (2296) all_0_28_28 = e0 & ~ (all_0_29_29 = e1)
% 31.14/8.77 |
% 31.14/8.77 | Applying alpha-rule on (2296) yields:
% 31.14/8.77 | (2297) all_0_28_28 = e0
% 31.14/8.77 | (2298) ~ (all_0_29_29 = e1)
% 31.14/8.77 |
% 31.14/8.77 | Combining equations (2297,9135) yields a new equation:
% 31.14/8.77 | (479) e4 = e0
% 31.14/8.77 |
% 31.14/8.77 | Equations (479) can reduce 6 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (591) ~ (all_0_39_39 = e4)
% 31.14/8.77 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 31.14/8.77 |
% 31.14/8.77 +-Applying beta-rule and splitting (1756), into two cases.
% 31.14/8.77 |-Branch one:
% 31.14/8.77 | (524) all_0_39_39 = e1
% 31.14/8.77 |
% 31.14/8.77 | Equations (524) can reduce 528 to:
% 31.14/8.77 | (270) $false
% 31.14/8.77 |
% 31.14/8.77 |-The branch is then unsatisfiable
% 31.14/8.77 |-Branch two:
% 31.14/8.77 | (528) ~ (all_0_39_39 = e1)
% 31.14/8.78 | (522) all_0_39_39 = e4
% 31.14/8.78 |
% 31.14/8.78 | Equations (522) can reduce 591 to:
% 31.14/8.78 | (270) $false
% 31.14/8.78 |
% 31.14/8.78 |-The branch is then unsatisfiable
% 31.14/8.78 |-Branch two:
% 31.14/8.78 | (3951) ~ (all_0_47_47 = e2)
% 31.14/8.78 | (3952) all_0_48_48 = e2 | all_0_49_49 = e2
% 31.14/8.78 |
% 31.14/8.78 +-Applying beta-rule and splitting (3952), into two cases.
% 31.14/8.78 |-Branch one:
% 31.14/8.78 | (311) all_0_48_48 = e2
% 31.14/8.78 |
% 31.14/8.78 | Equations (311) can reduce 294 to:
% 31.14/8.78 | (270) $false
% 31.14/8.78 |
% 31.14/8.78 |-The branch is then unsatisfiable
% 31.14/8.78 |-Branch two:
% 31.14/8.78 | (294) ~ (all_0_48_48 = e2)
% 31.14/8.78 | (307) all_0_49_49 = e2
% 31.14/8.78 |
% 31.14/8.78 | Equations (307) can reduce 169 to:
% 31.14/8.78 | (498) ~ (all_0_42_42 = e2)
% 31.14/8.78 |
% 31.14/8.78 | Equations (307) can reduce 198 to:
% 31.14/8.78 | (1436) ~ (all_0_46_46 = e2)
% 31.14/8.78 |
% 31.14/8.78 | Equations (307) can reduce 4 to:
% 31.14/8.78 | (294) ~ (all_0_48_48 = e2)
% 31.14/8.78 |
% 31.14/8.78 | Equations (307) can reduce 113 to:
% 31.14/8.78 | (700) ~ (all_0_59_59 = e2)
% 31.14/8.78 |
% 31.14/8.78 | Simplifying 700 yields:
% 31.14/8.78 | (701) ~ (all_0_59_59 = e2)
% 31.14/8.78 |
% 31.14/8.78 | Equations (307) can reduce 202 to:
% 31.14/8.78 | (377) ~ (e4 = e2)
% 31.14/8.78 |
% 31.14/8.78 | Simplifying 377 yields:
% 31.14/8.78 | (231) ~ (e4 = e2)
% 31.14/8.78 |
% 31.14/8.78 | Equations (307) can reduce 150 to:
% 31.14/8.78 | (301) ~ (e3 = e2)
% 31.14/8.78 |
% 31.14/8.78 | Simplifying 301 yields:
% 31.14/8.78 | (223) ~ (e3 = e2)
% 31.14/8.78 |
% 31.14/8.78 | From (307) and (153) follows:
% 31.14/8.78 | (6091) op(e2, e2) = all_0_35_35
% 31.14/8.78 |
% 31.14/8.78 | From (307) and (134) follows:
% 31.14/8.78 | (6092) op(e2, e0) = e2
% 31.14/8.78 |
% 31.14/8.78 | From (307) and (88) follows:
% 31.14/8.78 | (6093) op(e0, e2) = all_0_34_34
% 31.22/8.78 |
% 31.22/8.78 | Instantiating formula (201) with e2, e2, all_0_35_35, e4 and discharging atoms op(e2, e2) = all_0_35_35, op(e2, e2) = e4, yields:
% 31.22/8.78 | (6094) all_0_35_35 = e4
% 31.22/8.78 |
% 31.22/8.78 | Instantiating formula (201) with e0, e2, all_0_34_34, all_0_57_57 and discharging atoms op(e0, e2) = all_0_34_34, op(e0, e2) = all_0_57_57, yields:
% 31.22/8.78 | (6095) all_0_34_34 = all_0_57_57
% 31.22/8.78 |
% 31.22/8.78 | From (6094) and (6091) follows:
% 31.22/8.78 | (115) op(e2, e2) = e4
% 31.22/8.78 |
% 31.22/8.78 +-Applying beta-rule and splitting (83), into two cases.
% 31.22/8.78 |-Branch one:
% 31.22/8.78 | (321) all_0_47_47 = e1
% 31.22/8.78 |
% 31.22/8.78 | Equations (321) can reduce 170 to:
% 31.22/8.78 | (249) ~ (all_0_43_43 = e1)
% 31.22/8.78 |
% 31.22/8.78 | Equations (321) can reduce 225 to:
% 31.22/8.78 | (6100) ~ (all_0_48_48 = e1)
% 31.22/8.78 |
% 31.22/8.78 | Simplifying 6100 yields:
% 31.22/8.78 | (588) ~ (all_0_48_48 = e1)
% 31.22/8.78 |
% 31.22/8.78 | Equations (321) can reduce 3 to:
% 31.22/8.78 | (3984) ~ (all_0_51_51 = e1)
% 31.22/8.78 |
% 31.22/8.78 | Simplifying 3984 yields:
% 31.22/8.78 | (748) ~ (all_0_51_51 = e1)
% 31.22/8.78 |
% 31.22/8.78 | Equations (321) can reduce 218 to:
% 31.22/8.78 | (3986) ~ (all_0_56_56 = e1)
% 31.22/8.78 |
% 31.22/8.78 | Simplifying 3986 yields:
% 31.22/8.78 | (995) ~ (all_0_56_56 = e1)
% 31.22/8.78 |
% 31.22/8.78 | Equations (321) can reduce 172 to:
% 31.22/8.78 | (1021) ~ (e4 = e1)
% 31.22/8.78 |
% 31.22/8.78 | Simplifying 1021 yields:
% 31.22/8.78 | (251) ~ (e4 = e1)
% 31.22/8.78 |
% 31.22/8.78 | Equations (321) can reduce 247 to:
% 31.22/8.78 | (769) ~ (e3 = e1)
% 31.22/8.78 |
% 31.22/8.78 | Simplifying 769 yields:
% 31.22/8.78 | (136) ~ (e3 = e1)
% 31.22/8.78 |
% 31.22/8.78 | From (321) and (237) follows:
% 31.22/8.78 | (3992) op(e3, e1) = all_0_7_7
% 31.22/8.78 |
% 31.22/8.78 | From (321) and (42) follows:
% 31.22/8.78 | (3993) op(e2, e1) = all_0_8_8
% 31.22/8.78 |
% 31.22/8.78 | From (321) and (40) follows:
% 31.22/8.78 | (1103) op(e2, e3) = e1
% 31.22/8.78 |
% 31.22/8.78 +-Applying beta-rule and splitting (77), into two cases.
% 31.22/8.78 |-Branch one:
% 31.22/8.78 | (315) all_0_47_47 = e0
% 31.22/8.78 |
% 31.22/8.78 | Combining equations (321,315) yields a new equation:
% 31.22/8.78 | (571) e1 = e0
% 31.22/8.78 |
% 31.22/8.78 | Simplifying 571 yields:
% 31.22/8.78 | (560) e1 = e0
% 31.22/8.78 |
% 31.22/8.78 | Equations (560) can reduce 132 to:
% 31.22/8.78 | (270) $false
% 31.22/8.78 |
% 31.22/8.78 |-The branch is then unsatisfiable
% 31.22/8.78 |-Branch two:
% 31.22/8.78 | (318) ~ (all_0_47_47 = e0)
% 31.22/8.78 | (319) all_0_48_48 = e0 | all_0_49_49 = e0
% 31.22/8.78 |
% 31.22/8.78 +-Applying beta-rule and splitting (319), into two cases.
% 31.22/8.78 |-Branch one:
% 31.22/8.78 | (559) all_0_48_48 = e0
% 31.22/8.78 |
% 31.22/8.78 | Equations (559) can reduce 190 to:
% 31.22/8.78 | (232) ~ (all_0_41_41 = e0)
% 31.22/8.78 |
% 31.22/8.78 | Equations (559) can reduce 65 to:
% 31.22/8.78 | (488) ~ (all_0_45_45 = e0)
% 31.22/8.78 |
% 31.22/8.78 | Equations (559) can reduce 48 to:
% 31.22/8.78 | (3103) ~ (all_0_53_53 = e0)
% 31.22/8.78 |
% 31.22/8.78 | Simplifying 3103 yields:
% 31.22/8.78 | (584) ~ (all_0_53_53 = e0)
% 31.22/8.78 |
% 31.22/8.78 | Equations (559) can reduce 59 to:
% 31.22/8.78 | (3530) ~ (all_0_58_58 = e0)
% 31.22/8.78 |
% 31.22/8.78 | Simplifying 3530 yields:
% 31.22/8.78 | (431) ~ (all_0_58_58 = e0)
% 31.22/8.78 |
% 31.22/8.78 | Equations (559) can reduce 192 to:
% 31.22/8.78 | (456) ~ (e4 = e0)
% 31.22/8.78 |
% 31.22/8.78 | Simplifying 456 yields:
% 31.22/8.78 | (6) ~ (e4 = e0)
% 31.22/8.78 |
% 31.22/8.78 | Equations (559) can reduce 121 to:
% 31.22/8.78 | (788) ~ (e3 = e0)
% 31.22/8.78 |
% 31.22/8.78 | Simplifying 788 yields:
% 31.22/8.78 | (66) ~ (e3 = e0)
% 31.22/8.78 |
% 31.22/8.78 | Equations (559) can reduce 588 to:
% 31.22/8.78 | (568) ~ (e1 = e0)
% 31.22/8.78 |
% 31.22/8.78 | Simplifying 568 yields:
% 31.22/8.78 | (132) ~ (e1 = e0)
% 31.22/8.78 |
% 31.22/8.78 | From (559) and (183) follows:
% 31.22/8.78 | (6125) op(e2, e0) = all_0_26_26
% 31.22/8.78 |
% 31.22/8.78 | From (559) and (56) follows:
% 31.22/8.78 | (6126) op(e2, e1) = e0
% 31.22/8.78 |
% 31.22/8.78 | Instantiating formula (201) with e3, e1, all_0_7_7, all_0_45_45 and discharging atoms op(e3, e1) = all_0_7_7, op(e3, e1) = all_0_45_45, yields:
% 31.22/8.78 | (4011) all_0_7_7 = all_0_45_45
% 31.22/8.78 |
% 31.22/8.78 | Instantiating formula (201) with e2, e1, e0, all_0_8_8 and discharging atoms op(e2, e1) = all_0_8_8, op(e2, e1) = e0, yields:
% 31.22/8.78 | (6128) all_0_8_8 = e0
% 31.22/8.78 |
% 31.22/8.78 | Instantiating formula (201) with e2, e0, all_0_26_26, e2 and discharging atoms op(e2, e0) = all_0_26_26, op(e2, e0) = e2, yields:
% 31.22/8.78 | (6129) all_0_26_26 = e2
% 31.22/8.78 |
% 31.22/8.78 | From (6128) and (3993) follows:
% 31.22/8.78 | (6126) op(e2, e1) = e0
% 31.22/8.78 |
% 31.22/8.78 | From (6129) and (6125) follows:
% 31.22/8.78 | (6092) op(e2, e0) = e2
% 31.22/8.78 |
% 31.22/8.78 +-Applying beta-rule and splitting (186), into two cases.
% 31.22/8.78 |-Branch one:
% 31.22/8.78 | (336) all_0_39_39 = e2
% 31.22/8.78 |
% 31.22/8.78 | Equations (336) can reduce 226 to:
% 31.22/8.78 | (330) ~ (all_0_41_41 = e2)
% 31.22/8.78 |
% 31.22/8.78 | Simplifying 330 yields:
% 31.22/8.78 | (331) ~ (all_0_41_41 = e2)
% 31.22/8.78 |
% 31.22/8.78 | Equations (336) can reduce 184 to:
% 31.22/8.78 | (1336) ~ (all_0_42_42 = e2)
% 31.22/8.78 |
% 31.22/8.78 | Simplifying 1336 yields:
% 31.22/8.78 | (498) ~ (all_0_42_42 = e2)
% 31.22/8.78 |
% 31.22/8.78 | Equations (336) can reduce 167 to:
% 31.22/8.78 | (5937) ~ (all_0_43_43 = e2)
% 31.22/8.78 |
% 31.22/8.78 | Simplifying 5937 yields:
% 31.22/8.78 | (292) ~ (all_0_43_43 = e2)
% 31.22/8.78 |
% 31.22/8.78 | Equations (336) can reduce 212 to:
% 31.22/8.78 | (299) ~ (all_0_56_56 = e2)
% 31.22/8.78 |
% 31.22/8.78 | Simplifying 299 yields:
% 31.22/8.78 | (300) ~ (all_0_56_56 = e2)
% 31.22/8.78 |
% 31.22/8.78 | Equations (336) can reduce 101 to:
% 31.22/8.78 | (57) ~ (e2 = e0)
% 31.22/8.78 |
% 31.22/8.78 | From (336) and (200) follows:
% 31.22/8.78 | (12057) op(e3, e2) = all_0_4_4
% 31.22/8.78 |
% 31.22/8.78 | Instantiating formula (201) with e3, e2, all_0_4_4, all_0_44_44 and discharging atoms op(e3, e2) = all_0_4_4, op(e3, e2) = all_0_44_44, yields:
% 31.22/8.78 | (17397) all_0_4_4 = all_0_44_44
% 31.22/8.78 |
% 31.22/8.78 +-Applying beta-rule and splitting (222), into two cases.
% 31.22/8.78 |-Branch one:
% 31.22/8.78 | (522) all_0_39_39 = e4
% 31.22/8.78 |
% 31.22/8.78 | Combining equations (522,336) yields a new equation:
% 31.22/8.78 | (268) e4 = e2
% 31.22/8.78 |
% 31.22/8.78 | Simplifying 268 yields:
% 31.22/8.78 | (269) e4 = e2
% 31.22/8.78 |
% 31.22/8.78 | Equations (269) can reduce 231 to:
% 31.22/8.78 | (270) $false
% 31.22/8.78 |
% 31.22/8.78 |-The branch is then unsatisfiable
% 31.22/8.78 |-Branch two:
% 31.22/8.78 | (591) ~ (all_0_39_39 = e4)
% 31.22/8.78 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 31.22/8.78 |
% 31.22/8.78 +-Applying beta-rule and splitting (193), into two cases.
% 31.22/8.78 |-Branch one:
% 31.22/8.78 | (370) all_0_44_44 = e2
% 31.22/8.78 |
% 31.22/8.78 | Combining equations (370,17397) yields a new equation:
% 31.22/8.78 | (12701) all_0_4_4 = e2
% 31.22/8.78 |
% 31.22/8.78 | Equations (370) can reduce 15 to:
% 31.22/8.78 | (602) ~ (all_0_40_40 = e2)
% 31.22/8.78 |
% 31.22/8.78 | Equations (370) can reduce 241 to:
% 31.22/8.78 | (292) ~ (all_0_43_43 = e2)
% 31.22/8.78 |
% 31.22/8.78 | Equations (370) can reduce 229 to:
% 31.22/8.78 | (611) ~ (all_0_45_45 = e2)
% 31.22/8.78 |
% 31.22/8.78 | Simplifying 611 yields:
% 31.22/8.78 | (434) ~ (all_0_45_45 = e2)
% 31.22/8.78 |
% 31.22/8.78 | Equations (370) can reduce 174 to:
% 31.22/8.78 | (1435) ~ (all_0_46_46 = e2)
% 31.22/8.78 |
% 31.22/8.78 | Simplifying 1435 yields:
% 31.22/8.78 | (1436) ~ (all_0_46_46 = e2)
% 31.22/8.78 |
% 31.22/8.78 | Equations (370) can reduce 10 to:
% 31.22/8.78 | (334) ~ (all_0_57_57 = e2)
% 31.22/8.78 |
% 31.22/8.78 | Simplifying 334 yields:
% 31.22/8.78 | (335) ~ (all_0_57_57 = e2)
% 31.22/8.78 |
% 31.22/8.78 | Equations (370) can reduce 131 to:
% 31.22/8.78 | (141) ~ (e2 = e1)
% 31.22/8.78 |
% 31.22/8.78 | From (370) and (165) follows:
% 31.22/8.78 | (619) op(e2, e2) = all_0_15_15
% 31.22/8.78 |
% 31.22/8.78 +-Applying beta-rule and splitting (187), into two cases.
% 31.22/8.78 |-Branch one:
% 31.22/8.78 | (436) all_0_41_41 = e2
% 31.22/8.78 |
% 31.22/8.78 | Equations (436) can reduce 331 to:
% 31.22/8.78 | (270) $false
% 31.22/8.78 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (331) ~ (all_0_41_41 = e2)
% 31.22/8.79 | (441) all_0_45_45 = e2 | all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (441), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (374) all_0_45_45 = e2
% 31.22/8.79 |
% 31.22/8.79 | Equations (374) can reduce 434 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (434) ~ (all_0_45_45 = e2)
% 31.22/8.79 | (445) all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (445), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (311) all_0_48_48 = e2
% 31.22/8.79 |
% 31.22/8.79 | Combining equations (559,311) yields a new equation:
% 31.22/8.79 | (316) e2 = e0
% 31.22/8.79 |
% 31.22/8.79 | Equations (316) can reduce 57 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (294) ~ (all_0_48_48 = e2)
% 31.22/8.79 | (449) all_0_53_53 = e2 | all_0_58_58 = e2
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (449), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (576) all_0_53_53 = e2
% 31.22/8.79 |
% 31.22/8.79 | Equations (576) can reduce 128 to:
% 31.22/8.79 | (434) ~ (all_0_45_45 = e2)
% 31.22/8.79 |
% 31.22/8.79 | Equations (576) can reduce 12 to:
% 31.22/8.79 | (255) ~ (all_0_51_51 = e2)
% 31.22/8.79 |
% 31.22/8.79 | Equations (576) can reduce 213 to:
% 31.22/8.79 | (257) ~ (all_0_52_52 = e2)
% 31.22/8.79 |
% 31.22/8.79 | Equations (576) can reduce 252 to:
% 31.22/8.79 | (260) ~ (all_0_54_54 = e2)
% 31.22/8.79 |
% 31.22/8.79 | Simplifying 260 yields:
% 31.22/8.79 | (261) ~ (all_0_54_54 = e2)
% 31.22/8.79 |
% 31.22/8.79 | Equations (576) can reduce 70 to:
% 31.22/8.79 | (375) ~ (all_0_58_58 = e2)
% 31.22/8.79 |
% 31.22/8.79 | Simplifying 375 yields:
% 31.22/8.79 | (376) ~ (all_0_58_58 = e2)
% 31.22/8.79 |
% 31.22/8.79 | Equations (576) can reduce 584 to:
% 31.22/8.79 | (57) ~ (e2 = e0)
% 31.22/8.79 |
% 31.22/8.79 | Instantiating formula (201) with e2, e2, all_0_15_15, e4 and discharging atoms op(e2, e2) = all_0_15_15, op(e2, e2) = e4, yields:
% 31.22/8.79 | (620) all_0_15_15 = e4
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (9), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (621) all_0_44_44 = e0
% 31.22/8.79 |
% 31.22/8.79 | Combining equations (370,621) yields a new equation:
% 31.22/8.79 | (622) e2 = e0
% 31.22/8.79 |
% 31.22/8.79 | Simplifying 622 yields:
% 31.22/8.79 | (316) e2 = e0
% 31.22/8.79 |
% 31.22/8.79 | Equations (316) can reduce 57 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (625) ~ (all_0_44_44 = e0)
% 31.22/8.79 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 31.22/8.79 |
% 31.22/8.79 | Equations (370) can reduce 625 to:
% 31.22/8.79 | (57) ~ (e2 = e0)
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (52), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (536) all_0_41_41 = e1
% 31.22/8.79 |
% 31.22/8.79 | Equations (536) can reduce 147 to:
% 31.22/8.79 | (534) ~ (all_0_40_40 = e1)
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (592), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (358) all_0_41_41 = e4
% 31.22/8.79 |
% 31.22/8.79 | Combining equations (536,358) yields a new equation:
% 31.22/8.79 | (526) e4 = e1
% 31.22/8.79 |
% 31.22/8.79 | Equations (526) can reduce 251 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (361) ~ (all_0_41_41 = e4)
% 31.22/8.79 | (512) all_0_42_42 = e4
% 31.22/8.79 |
% 31.22/8.79 | Equations (512) can reduce 145 to:
% 31.22/8.79 | (233) ~ (all_0_40_40 = e4)
% 31.22/8.79 |
% 31.22/8.79 | Equations (512) can reduce 18 to:
% 31.22/8.79 | (804) ~ (all_0_46_46 = e4)
% 31.22/8.79 |
% 31.22/8.79 | Simplifying 804 yields:
% 31.22/8.79 | (805) ~ (all_0_46_46 = e4)
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (603), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (671) all_0_40_40 = e3
% 31.22/8.79 |
% 31.22/8.79 | Equations (671) can reduce 233 to:
% 31.22/8.79 | (719) ~ (e4 = e3)
% 31.22/8.79 |
% 31.22/8.79 | Simplifying 719 yields:
% 31.22/8.79 | (34) ~ (e4 = e3)
% 31.22/8.79 |
% 31.22/8.79 | Equations (671) can reduce 602 to:
% 31.22/8.79 | (223) ~ (e3 = e2)
% 31.22/8.79 |
% 31.22/8.79 | Equations (671) can reduce 534 to:
% 31.22/8.79 | (136) ~ (e3 = e1)
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (8), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (530) all_0_40_40 = e1
% 31.22/8.79 |
% 31.22/8.79 | Combining equations (671,530) yields a new equation:
% 31.22/8.79 | (537) e3 = e1
% 31.22/8.79 |
% 31.22/8.79 | Simplifying 537 yields:
% 31.22/8.79 | (538) e3 = e1
% 31.22/8.79 |
% 31.22/8.79 | Equations (538) can reduce 136 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (534) ~ (all_0_40_40 = e1)
% 31.22/8.79 | (3352) all_0_52_52 = e1 | all_0_57_57 = e1
% 31.22/8.79 |
% 31.22/8.79 | Equations (671) can reduce 534 to:
% 31.22/8.79 | (136) ~ (e3 = e1)
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (44), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (502) all_0_43_43 = e4
% 31.22/8.79 |
% 31.22/8.79 | Equations (502) can reduce 84 to:
% 31.22/8.79 | (503) ~ (all_0_45_45 = e4)
% 31.22/8.79 |
% 31.22/8.79 | Simplifying 503 yields:
% 31.22/8.79 | (352) ~ (all_0_45_45 = e4)
% 31.22/8.79 |
% 31.22/8.79 | Equations (502) can reduce 292 to:
% 31.22/8.79 | (231) ~ (e4 = e2)
% 31.22/8.79 |
% 31.22/8.79 | Equations (502) can reduce 249 to:
% 31.22/8.79 | (251) ~ (e4 = e1)
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (163), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (272) all_0_55_55 = e4
% 31.22/8.79 |
% 31.22/8.79 | Combining equations (272,382) yields a new equation:
% 31.22/8.79 | (268) e4 = e2
% 31.22/8.79 |
% 31.22/8.79 | Simplifying 268 yields:
% 31.22/8.79 | (269) e4 = e2
% 31.22/8.79 |
% 31.22/8.79 | Equations (269) can reduce 231 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (14603) ~ (all_0_55_55 = e4)
% 31.22/8.79 | (14604) all_0_56_56 = e4 | all_0_58_58 = e4 | all_0_59_59 = e4
% 31.22/8.79 |
% 31.22/8.79 | Equations (382) can reduce 14603 to:
% 31.22/8.79 | (377) ~ (e4 = e2)
% 31.22/8.79 |
% 31.22/8.79 | Simplifying 377 yields:
% 31.22/8.79 | (231) ~ (e4 = e2)
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (158), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (358) all_0_41_41 = e4
% 31.22/8.79 |
% 31.22/8.79 | Combining equations (536,358) yields a new equation:
% 31.22/8.79 | (526) e4 = e1
% 31.22/8.79 |
% 31.22/8.79 | Equations (526) can reduce 251 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (361) ~ (all_0_41_41 = e4)
% 31.22/8.79 | (362) all_0_45_45 = e4 | all_0_53_53 = e4 | all_0_58_58 = e4
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (362), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (363) all_0_45_45 = e4
% 31.22/8.79 |
% 31.22/8.79 | Equations (363) can reduce 352 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (352) ~ (all_0_45_45 = e4)
% 31.22/8.79 | (366) all_0_53_53 = e4 | all_0_58_58 = e4
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (366), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (367) all_0_53_53 = e4
% 31.22/8.79 |
% 31.22/8.79 | Combining equations (576,367) yields a new equation:
% 31.22/8.79 | (269) e4 = e2
% 31.22/8.79 |
% 31.22/8.79 | Equations (269) can reduce 231 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (599) ~ (all_0_53_53 = e4)
% 31.22/8.79 | (600) all_0_58_58 = e4
% 31.22/8.79 |
% 31.22/8.79 | Equations (600) can reduce 156 to:
% 31.22/8.79 | (279) ~ (all_0_59_59 = e4)
% 31.22/8.79 |
% 31.22/8.79 | Simplifying 279 yields:
% 31.22/8.79 | (280) ~ (all_0_59_59 = e4)
% 31.22/8.79 |
% 31.22/8.79 | Equations (600) can reduce 431 to:
% 31.22/8.79 | (6) ~ (e4 = e0)
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (116), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (411) all_0_43_43 = e0
% 31.22/8.79 |
% 31.22/8.79 | Combining equations (502,411) yields a new equation:
% 31.22/8.79 | (478) e4 = e0
% 31.22/8.79 |
% 31.22/8.79 | Simplifying 478 yields:
% 31.22/8.79 | (479) e4 = e0
% 31.22/8.79 |
% 31.22/8.79 | Equations (479) can reduce 6 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (455) ~ (all_0_43_43 = e0)
% 31.22/8.79 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 31.22/8.79 |
% 31.22/8.79 | Equations (502) can reduce 455 to:
% 31.22/8.79 | (6) ~ (e4 = e0)
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (93), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (402) all_0_59_59 = e4
% 31.22/8.79 |
% 31.22/8.79 | Equations (402) can reduce 280 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (280) ~ (all_0_59_59 = e4)
% 31.22/8.79 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (407), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (408), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (409), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 31.22/8.79 |
% 31.22/8.79 | Applying alpha-rule on (410) yields:
% 31.22/8.79 | (411) all_0_43_43 = e0
% 31.22/8.79 | (412) all_0_59_59 = e3
% 31.22/8.79 | (413) ~ (all_0_46_46 = e3)
% 31.22/8.79 |
% 31.22/8.79 | Combining equations (411,502) yields a new equation:
% 31.22/8.79 | (479) e4 = e0
% 31.22/8.79 |
% 31.22/8.79 | Equations (479) can reduce 6 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 31.22/8.79 |
% 31.22/8.79 | Applying alpha-rule on (416) yields:
% 31.22/8.79 | (411) all_0_43_43 = e0
% 31.22/8.79 | (412) all_0_59_59 = e3
% 31.22/8.79 | (419) ~ (all_0_56_56 = e0)
% 31.22/8.79 |
% 31.22/8.79 | Combining equations (411,502) yields a new equation:
% 31.22/8.79 | (479) e4 = e0
% 31.22/8.79 |
% 31.22/8.79 | Equations (479) can reduce 6 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 31.22/8.79 |
% 31.22/8.79 | Applying alpha-rule on (422) yields:
% 31.22/8.79 | (423) all_0_53_53 = e0
% 31.22/8.79 | (424) all_0_59_59 = e1
% 31.22/8.79 | (425) ~ (all_0_54_54 = e1)
% 31.22/8.79 |
% 31.22/8.79 | Combining equations (576,423) yields a new equation:
% 31.22/8.79 | (622) e2 = e0
% 31.22/8.79 |
% 31.22/8.79 | Simplifying 622 yields:
% 31.22/8.79 | (316) e2 = e0
% 31.22/8.79 |
% 31.22/8.79 | Equations (316) can reduce 57 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 31.22/8.79 |
% 31.22/8.79 | Applying alpha-rule on (428) yields:
% 31.22/8.79 | (423) all_0_53_53 = e0
% 31.22/8.79 | (424) all_0_59_59 = e1
% 31.22/8.79 | (431) ~ (all_0_58_58 = e0)
% 31.22/8.79 |
% 31.22/8.79 | Combining equations (576,423) yields a new equation:
% 31.22/8.79 | (622) e2 = e0
% 31.22/8.79 |
% 31.22/8.79 | Simplifying 622 yields:
% 31.22/8.79 | (316) e2 = e0
% 31.22/8.79 |
% 31.22/8.79 | Equations (316) can reduce 57 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (510) ~ (all_0_43_43 = e4)
% 31.22/8.79 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (511), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (363) all_0_45_45 = e4
% 31.22/8.79 |
% 31.22/8.79 | Equations (363) can reduce 84 to:
% 31.22/8.79 | (510) ~ (all_0_43_43 = e4)
% 31.22/8.79 |
% 31.22/8.79 | Equations (363) can reduce 434 to:
% 31.22/8.79 | (231) ~ (e4 = e2)
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (219), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (351) all_0_41_41 = e3
% 31.22/8.79 |
% 31.22/8.79 | Combining equations (536,351) yields a new equation:
% 31.22/8.79 | (538) e3 = e1
% 31.22/8.79 |
% 31.22/8.79 | Equations (538) can reduce 136 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (1237) ~ (all_0_41_41 = e3)
% 31.22/8.79 | (1508) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (166), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (522) all_0_39_39 = e4
% 31.22/8.79 |
% 31.22/8.79 | Combining equations (522,336) yields a new equation:
% 31.22/8.79 | (268) e4 = e2
% 31.22/8.79 |
% 31.22/8.79 | Simplifying 268 yields:
% 31.22/8.79 | (269) e4 = e2
% 31.22/8.79 |
% 31.22/8.79 | Equations (269) can reduce 231 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (591) ~ (all_0_39_39 = e4)
% 31.22/8.79 | (4522) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (4522), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (502) all_0_43_43 = e4
% 31.22/8.79 |
% 31.22/8.79 | Equations (502) can reduce 510 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (510) ~ (all_0_43_43 = e4)
% 31.22/8.79 | (4527) all_0_51_51 = e4 | all_0_56_56 = e4
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (4527), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (1467) all_0_51_51 = e4
% 31.22/8.79 |
% 31.22/8.79 | Equations (1467) can reduce 697 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (697) ~ (all_0_51_51 = e4)
% 31.22/8.79 | (4744) all_0_56_56 = e4
% 31.22/8.79 |
% 31.22/8.79 | Equations (4744) can reduce 185 to:
% 31.22/8.79 | (279) ~ (all_0_59_59 = e4)
% 31.22/8.79 |
% 31.22/8.79 | Simplifying 279 yields:
% 31.22/8.79 | (280) ~ (all_0_59_59 = e4)
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (1508), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (505) all_0_45_45 = e3
% 31.22/8.79 |
% 31.22/8.79 | Combining equations (363,505) yields a new equation:
% 31.22/8.79 | (660) e4 = e3
% 31.22/8.79 |
% 31.22/8.79 | Simplifying 660 yields:
% 31.22/8.79 | (359) e4 = e3
% 31.22/8.79 |
% 31.22/8.79 | Equations (359) can reduce 34 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (354) ~ (all_0_45_45 = e3)
% 31.22/8.79 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (1539), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (1114) all_0_53_53 = e3
% 31.22/8.79 |
% 31.22/8.79 | Combining equations (1114,576) yields a new equation:
% 31.22/8.79 | (437) e3 = e2
% 31.22/8.79 |
% 31.22/8.79 | Simplifying 437 yields:
% 31.22/8.79 | (414) e3 = e2
% 31.22/8.79 |
% 31.22/8.79 | Equations (414) can reduce 223 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (356) ~ (all_0_53_53 = e3)
% 31.22/8.79 | (4713) all_0_58_58 = e3
% 31.22/8.79 |
% 31.22/8.79 | Equations (4713) can reduce 156 to:
% 31.22/8.79 | (1259) ~ (all_0_59_59 = e3)
% 31.22/8.79 |
% 31.22/8.79 | Simplifying 1259 yields:
% 31.22/8.79 | (1260) ~ (all_0_59_59 = e3)
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (93), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (402) all_0_59_59 = e4
% 31.22/8.79 |
% 31.22/8.79 | Equations (402) can reduce 280 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (280) ~ (all_0_59_59 = e4)
% 31.22/8.79 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (407), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (408), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (409), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 31.22/8.79 |
% 31.22/8.79 | Applying alpha-rule on (410) yields:
% 31.22/8.79 | (411) all_0_43_43 = e0
% 31.22/8.79 | (412) all_0_59_59 = e3
% 31.22/8.79 | (413) ~ (all_0_46_46 = e3)
% 31.22/8.79 |
% 31.22/8.79 | Equations (412) can reduce 1260 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 31.22/8.79 |
% 31.22/8.79 | Applying alpha-rule on (416) yields:
% 31.22/8.79 | (411) all_0_43_43 = e0
% 31.22/8.79 | (412) all_0_59_59 = e3
% 31.22/8.79 | (419) ~ (all_0_56_56 = e0)
% 31.22/8.79 |
% 31.22/8.79 | Equations (412) can reduce 1260 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 31.22/8.79 |
% 31.22/8.79 | Applying alpha-rule on (422) yields:
% 31.22/8.79 | (423) all_0_53_53 = e0
% 31.22/8.79 | (424) all_0_59_59 = e1
% 31.22/8.79 | (425) ~ (all_0_54_54 = e1)
% 31.22/8.79 |
% 31.22/8.79 | Combining equations (423,576) yields a new equation:
% 31.22/8.79 | (316) e2 = e0
% 31.22/8.79 |
% 31.22/8.79 | Equations (316) can reduce 57 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 31.22/8.79 |
% 31.22/8.79 | Applying alpha-rule on (428) yields:
% 31.22/8.79 | (423) all_0_53_53 = e0
% 31.22/8.79 | (424) all_0_59_59 = e1
% 31.22/8.79 | (431) ~ (all_0_58_58 = e0)
% 31.22/8.79 |
% 31.22/8.79 | Combining equations (423,576) yields a new equation:
% 31.22/8.79 | (316) e2 = e0
% 31.22/8.79 |
% 31.22/8.79 | Equations (316) can reduce 57 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (352) ~ (all_0_45_45 = e4)
% 31.22/8.79 | (517) all_0_46_46 = e4
% 31.22/8.79 |
% 31.22/8.79 | Equations (517) can reduce 805 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (675) ~ (all_0_40_40 = e3)
% 31.22/8.79 | (530) all_0_40_40 = e1
% 31.22/8.79 |
% 31.22/8.79 | Equations (530) can reduce 534 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (540) ~ (all_0_41_41 = e1)
% 31.22/8.79 | (762) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (762), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (552) all_0_48_48 = e1
% 31.22/8.79 |
% 31.22/8.79 | Combining equations (559,552) yields a new equation:
% 31.22/8.79 | (560) e1 = e0
% 31.22/8.79 |
% 31.22/8.79 | Equations (560) can reduce 132 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (588) ~ (all_0_48_48 = e1)
% 31.22/8.79 | (4925) all_0_53_53 = e1 | all_0_58_58 = e1
% 31.22/8.79 |
% 31.22/8.79 +-Applying beta-rule and splitting (4925), into two cases.
% 31.22/8.79 |-Branch one:
% 31.22/8.79 | (853) all_0_53_53 = e1
% 31.22/8.79 |
% 31.22/8.79 | Combining equations (576,853) yields a new equation:
% 31.22/8.79 | (531) e2 = e1
% 31.22/8.79 |
% 31.22/8.79 | Simplifying 531 yields:
% 31.22/8.79 | (322) e2 = e1
% 31.22/8.79 |
% 31.22/8.79 | Equations (322) can reduce 141 to:
% 31.22/8.79 | (270) $false
% 31.22/8.79 |
% 31.22/8.79 |-The branch is then unsatisfiable
% 31.22/8.79 |-Branch two:
% 31.22/8.79 | (874) ~ (all_0_53_53 = e1)
% 31.22/8.79 | (1001) all_0_58_58 = e1
% 31.22/8.79 |
% 31.22/8.79 | Equations (1001) can reduce 157 to:
% 31.22/8.79 | (540) ~ (all_0_41_41 = e1)
% 31.22/8.79 |
% 31.22/8.79 | Equations (1001) can reduce 108 to:
% 31.22/8.79 | (26) ~ (all_0_45_45 = e1)
% 31.22/8.79 |
% 31.22/8.79 | Equations (1001) can reduce 81 to:
% 31.22/8.79 | (995) ~ (all_0_56_56 = e1)
% 31.22/8.80 |
% 31.22/8.80 | Equations (1001) can reduce 37 to:
% 31.22/8.80 | (644) ~ (all_0_57_57 = e1)
% 31.22/8.80 |
% 31.22/8.80 | Equations (1001) can reduce 156 to:
% 31.22/8.80 | (749) ~ (all_0_59_59 = e1)
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 749 yields:
% 31.22/8.80 | (750) ~ (all_0_59_59 = e1)
% 31.22/8.80 |
% 31.22/8.80 | Equations (1001) can reduce 376 to:
% 31.22/8.80 | (645) ~ (e2 = e1)
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 645 yields:
% 31.22/8.80 | (141) ~ (e2 = e1)
% 31.22/8.80 |
% 31.22/8.80 | Equations (1001) can reduce 431 to:
% 31.22/8.80 | (132) ~ (e1 = e0)
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (8), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (530) all_0_40_40 = e1
% 31.22/8.80 |
% 31.22/8.80 | Equations (530) can reduce 145 to:
% 31.22/8.80 | (639) ~ (all_0_42_42 = e1)
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 639 yields:
% 31.22/8.80 | (640) ~ (all_0_42_42 = e1)
% 31.22/8.80 |
% 31.22/8.80 | Equations (530) can reduce 149 to:
% 31.22/8.80 | (643) ~ (all_0_57_57 = e1)
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 643 yields:
% 31.22/8.80 | (644) ~ (all_0_57_57 = e1)
% 31.22/8.80 |
% 31.22/8.80 | Equations (530) can reduce 602 to:
% 31.22/8.80 | (645) ~ (e2 = e1)
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 645 yields:
% 31.22/8.80 | (141) ~ (e2 = e1)
% 31.22/8.80 |
% 31.22/8.80 | Equations (530) can reduce 238 to:
% 31.22/8.80 | (132) ~ (e1 = e0)
% 31.22/8.80 |
% 31.22/8.80 | From (530) and (68) follows:
% 31.22/8.80 | (648) op(e2, e1) = all_0_13_13
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (127), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (541) all_0_42_42 = e1
% 31.22/8.80 |
% 31.22/8.80 | Equations (541) can reduce 640 to:
% 31.22/8.80 | (270) $false
% 31.22/8.80 |
% 31.22/8.80 |-The branch is then unsatisfiable
% 31.22/8.80 |-Branch two:
% 31.22/8.80 | (640) ~ (all_0_42_42 = e1)
% 31.22/8.80 | (4628) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (4628), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (589) all_0_49_49 = e1
% 31.22/8.80 |
% 31.22/8.80 | Combining equations (307,589) yields a new equation:
% 31.22/8.80 | (531) e2 = e1
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 531 yields:
% 31.22/8.80 | (322) e2 = e1
% 31.22/8.80 |
% 31.22/8.80 | Equations (322) can reduce 141 to:
% 31.22/8.80 | (270) $false
% 31.22/8.80 |
% 31.22/8.80 |-The branch is then unsatisfiable
% 31.22/8.80 |-Branch two:
% 31.22/8.80 | (543) ~ (all_0_49_49 = e1)
% 31.22/8.80 | (4726) all_0_54_54 = e1 | all_0_59_59 = e1
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (4726), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (875) all_0_54_54 = e1
% 31.22/8.80 |
% 31.22/8.80 | Equations (875) can reduce 191 to:
% 31.22/8.80 | (640) ~ (all_0_42_42 = e1)
% 31.22/8.80 |
% 31.22/8.80 | Equations (875) can reduce 215 to:
% 31.22/8.80 | (106) ~ (all_0_46_46 = e1)
% 31.22/8.80 |
% 31.22/8.80 | Equations (875) can reduce 50 to:
% 31.22/8.80 | (748) ~ (all_0_51_51 = e1)
% 31.22/8.80 |
% 31.22/8.80 | Equations (875) can reduce 118 to:
% 31.22/8.80 | (642) ~ (all_0_52_52 = e1)
% 31.22/8.80 |
% 31.22/8.80 | Equations (875) can reduce 261 to:
% 31.22/8.80 | (645) ~ (e2 = e1)
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 645 yields:
% 31.22/8.80 | (141) ~ (e2 = e1)
% 31.22/8.80 |
% 31.22/8.80 | Instantiating formula (201) with e2, e1, all_0_13_13, e0 and discharging atoms op(e2, e1) = all_0_13_13, op(e2, e1) = e0, yields:
% 31.22/8.80 | (7585) all_0_13_13 = e0
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (87), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (650) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (650), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (651) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (651), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (652) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 31.22/8.80 |
% 31.22/8.80 | Applying alpha-rule on (652) yields:
% 31.22/8.80 | (653) all_0_13_13 = e4
% 31.22/8.80 | (654) ~ (all_0_14_14 = e2)
% 31.22/8.80 |
% 31.22/8.80 | Combining equations (653,7585) yields a new equation:
% 31.22/8.80 | (478) e4 = e0
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 478 yields:
% 31.22/8.80 | (479) e4 = e0
% 31.22/8.80 |
% 31.22/8.80 | Equations (479) can reduce 6 to:
% 31.22/8.80 | (270) $false
% 31.22/8.80 |
% 31.22/8.80 |-The branch is then unsatisfiable
% 31.22/8.80 |-Branch two:
% 31.22/8.80 | (657) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 31.22/8.80 |
% 31.22/8.80 | Applying alpha-rule on (657) yields:
% 31.22/8.80 | (658) all_0_15_15 = e3
% 31.22/8.80 | (659) ~ (all_0_16_16 = e2)
% 31.22/8.80 |
% 31.22/8.80 | Combining equations (620,658) yields a new equation:
% 31.22/8.80 | (660) e4 = e3
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 660 yields:
% 31.22/8.80 | (359) e4 = e3
% 31.22/8.80 |
% 31.22/8.80 | Equations (359) can reduce 34 to:
% 31.22/8.80 | (270) $false
% 31.22/8.80 |
% 31.22/8.80 |-The branch is then unsatisfiable
% 31.22/8.80 |-Branch two:
% 31.22/8.80 | (663) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 31.22/8.80 |
% 31.22/8.80 | Applying alpha-rule on (663) yields:
% 31.22/8.80 | (664) all_0_17_17 = e1
% 31.22/8.80 | (665) ~ (all_0_18_18 = e2)
% 31.22/8.80 |
% 31.22/8.80 | From (664) and (27) follows:
% 31.22/8.80 | (666) op(e2, all_0_52_52) = e1
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (21), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (824) all_0_51_51 = e3
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (64), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (954) all_0_51_51 = e0
% 31.22/8.80 |
% 31.22/8.80 | Combining equations (824,954) yields a new equation:
% 31.22/8.80 | (783) e3 = e0
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 783 yields:
% 31.22/8.80 | (784) e3 = e0
% 31.22/8.80 |
% 31.22/8.80 | Equations (784) can reduce 66 to:
% 31.22/8.80 | (270) $false
% 31.22/8.80 |
% 31.22/8.80 |-The branch is then unsatisfiable
% 31.22/8.80 |-Branch two:
% 31.22/8.80 | (987) ~ (all_0_51_51 = e0)
% 31.22/8.80 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (3067), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (827) all_0_52_52 = e0
% 31.22/8.80 |
% 31.22/8.80 | From (827) and (666) follows:
% 31.22/8.80 | (11382) op(e2, e0) = e1
% 31.22/8.80 |
% 31.22/8.80 | Instantiating formula (201) with e2, e0, e1, e2 and discharging atoms op(e2, e0) = e2, op(e2, e0) = e1, yields:
% 31.22/8.80 | (322) e2 = e1
% 31.22/8.80 |
% 31.22/8.80 | Equations (322) can reduce 141 to:
% 31.22/8.80 | (270) $false
% 31.22/8.80 |
% 31.22/8.80 |-The branch is then unsatisfiable
% 31.22/8.80 |-Branch two:
% 31.22/8.80 | (925) ~ (all_0_52_52 = e0)
% 31.22/8.80 | (3073) all_0_53_53 = e0 | all_0_54_54 = e0
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (3073), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (423) all_0_53_53 = e0
% 31.22/8.80 |
% 31.22/8.80 | Combining equations (423,576) yields a new equation:
% 31.22/8.80 | (316) e2 = e0
% 31.22/8.80 |
% 31.22/8.80 | Equations (316) can reduce 57 to:
% 31.22/8.80 | (270) $false
% 31.22/8.80 |
% 31.22/8.80 |-The branch is then unsatisfiable
% 31.22/8.80 |-Branch two:
% 31.22/8.80 | (584) ~ (all_0_53_53 = e0)
% 31.22/8.80 | (3084) all_0_54_54 = e0
% 31.22/8.80 |
% 31.22/8.80 | Combining equations (875,3084) yields a new equation:
% 31.22/8.80 | (571) e1 = e0
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 571 yields:
% 31.22/8.80 | (560) e1 = e0
% 31.22/8.80 |
% 31.22/8.80 | Equations (560) can reduce 132 to:
% 31.22/8.80 | (270) $false
% 31.22/8.80 |
% 31.22/8.80 |-The branch is then unsatisfiable
% 31.22/8.80 |-Branch two:
% 31.22/8.80 | (932) ~ (all_0_51_51 = e3)
% 31.22/8.80 | (1101) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (173), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (4215) all_0_51_51 = e2
% 31.22/8.80 |
% 31.22/8.80 | Equations (4215) can reduce 255 to:
% 31.22/8.80 | (270) $false
% 31.22/8.80 |
% 31.22/8.80 |-The branch is then unsatisfiable
% 31.22/8.80 |-Branch two:
% 31.22/8.80 | (255) ~ (all_0_51_51 = e2)
% 31.22/8.80 | (4888) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1 | all_0_51_51 = e0
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (1101), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (864) all_0_52_52 = e3
% 31.22/8.80 |
% 31.22/8.80 | Equations (864) can reduce 154 to:
% 31.22/8.80 | (932) ~ (all_0_51_51 = e3)
% 31.22/8.80 |
% 31.22/8.80 | Equations (864) can reduce 230 to:
% 31.22/8.80 | (719) ~ (e4 = e3)
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 719 yields:
% 31.22/8.80 | (34) ~ (e4 = e3)
% 31.22/8.80 |
% 31.22/8.80 | Equations (864) can reduce 642 to:
% 31.22/8.80 | (136) ~ (e3 = e1)
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (626), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (827) all_0_52_52 = e0
% 31.22/8.80 |
% 31.22/8.80 | Combining equations (864,827) yields a new equation:
% 31.22/8.80 | (783) e3 = e0
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 783 yields:
% 31.22/8.80 | (784) e3 = e0
% 31.22/8.80 |
% 31.22/8.80 | Equations (784) can reduce 66 to:
% 31.22/8.80 | (270) $false
% 31.22/8.80 |
% 31.22/8.80 |-The branch is then unsatisfiable
% 31.22/8.80 |-Branch two:
% 31.22/8.80 | (925) ~ (all_0_52_52 = e0)
% 31.22/8.80 | (2258) all_0_57_57 = e0
% 31.22/8.80 |
% 31.22/8.80 | Equations (2258) can reduce 140 to:
% 31.22/8.80 | (4000) ~ (all_0_59_59 = e0)
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 4000 yields:
% 31.22/8.80 | (4001) ~ (all_0_59_59 = e0)
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (64), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (954) all_0_51_51 = e0
% 31.22/8.80 |
% 31.22/8.80 | Equations (954) can reduce 240 to:
% 31.22/8.80 | (455) ~ (all_0_43_43 = e0)
% 31.22/8.80 |
% 31.22/8.80 | Equations (954) can reduce 60 to:
% 31.22/8.80 | (3852) ~ (all_0_56_56 = e0)
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 3852 yields:
% 31.22/8.80 | (419) ~ (all_0_56_56 = e0)
% 31.22/8.80 |
% 31.22/8.80 | Equations (954) can reduce 932 to:
% 31.22/8.80 | (788) ~ (e3 = e0)
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 788 yields:
% 31.22/8.80 | (66) ~ (e3 = e0)
% 31.22/8.80 |
% 31.22/8.80 | Equations (954) can reduce 255 to:
% 31.22/8.80 | (566) ~ (e2 = e0)
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 566 yields:
% 31.22/8.80 | (57) ~ (e2 = e0)
% 31.22/8.80 |
% 31.22/8.80 | Equations (954) can reduce 748 to:
% 31.22/8.80 | (568) ~ (e1 = e0)
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 568 yields:
% 31.22/8.80 | (132) ~ (e1 = e0)
% 31.22/8.80 |
% 31.22/8.80 | From (954) and (7) follows:
% 31.22/8.80 | (14159) op(e3, e0) = all_0_9_9
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (221), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (1132) all_0_46_46 = e0
% 31.22/8.80 |
% 31.22/8.80 | Equations (1132) can reduce 103 to:
% 31.22/8.80 | (455) ~ (all_0_43_43 = e0)
% 31.22/8.80 |
% 31.22/8.80 | Equations (1132) can reduce 1436 to:
% 31.22/8.80 | (566) ~ (e2 = e0)
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 566 yields:
% 31.22/8.80 | (57) ~ (e2 = e0)
% 31.22/8.80 |
% 31.22/8.80 | Equations (1132) can reduce 106 to:
% 31.22/8.80 | (568) ~ (e1 = e0)
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 568 yields:
% 31.22/8.80 | (132) ~ (e1 = e0)
% 31.22/8.80 |
% 31.22/8.80 | From (1132) and (242) follows:
% 31.22/8.80 | (17735) op(e3, e0) = e0
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (93), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (402) all_0_59_59 = e4
% 31.22/8.80 |
% 31.22/8.80 | Equations (402) can reduce 17 to:
% 31.22/8.80 | (520) ~ (all_0_42_42 = e4)
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (236), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (764) all_0_56_56 = e3
% 31.22/8.80 |
% 31.22/8.80 | Equations (764) can reduce 188 to:
% 31.22/8.80 | (786) ~ (all_0_43_43 = e3)
% 31.22/8.80 |
% 31.22/8.80 | Equations (764) can reduce 300 to:
% 31.22/8.80 | (223) ~ (e3 = e2)
% 31.22/8.80 |
% 31.22/8.80 | Equations (764) can reduce 419 to:
% 31.22/8.80 | (66) ~ (e3 = e0)
% 31.22/8.80 |
% 31.22/8.80 | From (764) and (239) follows:
% 31.22/8.80 | (14231) op(e3, e3) = all_0_11_11
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (16), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (698) all_0_42_42 = e2
% 31.22/8.80 |
% 31.22/8.80 | Equations (698) can reduce 498 to:
% 31.22/8.80 | (270) $false
% 31.22/8.80 |
% 31.22/8.80 |-The branch is then unsatisfiable
% 31.22/8.80 |-Branch two:
% 31.22/8.80 | (498) ~ (all_0_42_42 = e2)
% 31.22/8.80 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (592), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (358) all_0_41_41 = e4
% 31.22/8.80 |
% 31.22/8.80 | Equations (358) can reduce 94 to:
% 31.22/8.80 | (692) ~ (all_0_42_42 = e4)
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 692 yields:
% 31.22/8.80 | (520) ~ (all_0_42_42 = e4)
% 31.22/8.80 |
% 31.22/8.80 | Equations (358) can reduce 51 to:
% 31.22/8.80 | (503) ~ (all_0_45_45 = e4)
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 503 yields:
% 31.22/8.80 | (352) ~ (all_0_45_45 = e4)
% 31.22/8.80 |
% 31.22/8.80 | Equations (358) can reduce 232 to:
% 31.22/8.80 | (6) ~ (e4 = e0)
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (44), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (502) all_0_43_43 = e4
% 31.22/8.80 |
% 31.22/8.80 | Equations (502) can reduce 84 to:
% 31.22/8.80 | (503) ~ (all_0_45_45 = e4)
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 503 yields:
% 31.22/8.80 | (352) ~ (all_0_45_45 = e4)
% 31.22/8.80 |
% 31.22/8.80 | Equations (502) can reduce 786 to:
% 31.22/8.80 | (34) ~ (e4 = e3)
% 31.22/8.80 |
% 31.22/8.80 | Equations (502) can reduce 292 to:
% 31.22/8.80 | (231) ~ (e4 = e2)
% 31.22/8.80 |
% 31.22/8.80 | Equations (502) can reduce 455 to:
% 31.22/8.80 | (6) ~ (e4 = e0)
% 31.22/8.80 |
% 31.22/8.80 | From (502) and (248) follows:
% 31.22/8.80 | (14204) op(e3, e3) = e4
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (219), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (351) all_0_41_41 = e3
% 31.22/8.80 |
% 31.22/8.80 | Combining equations (351,358) yields a new equation:
% 31.22/8.80 | (359) e4 = e3
% 31.22/8.80 |
% 31.22/8.80 | Equations (359) can reduce 34 to:
% 31.22/8.80 | (270) $false
% 31.22/8.80 |
% 31.22/8.80 |-The branch is then unsatisfiable
% 31.22/8.80 |-Branch two:
% 31.22/8.80 | (1237) ~ (all_0_41_41 = e3)
% 31.22/8.80 | (1508) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 31.22/8.80 |
% 31.22/8.80 | Equations (358) can reduce 1237 to:
% 31.22/8.80 | (34) ~ (e4 = e3)
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (95), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (1258) all_0_42_42 = e3
% 31.22/8.80 |
% 31.22/8.80 | Equations (1258) can reduce 520 to:
% 31.22/8.80 | (719) ~ (e4 = e3)
% 31.22/8.80 |
% 31.22/8.80 | Simplifying 719 yields:
% 31.22/8.80 | (34) ~ (e4 = e3)
% 31.22/8.80 |
% 31.22/8.80 | Equations (1258) can reduce 498 to:
% 31.22/8.80 | (223) ~ (e3 = e2)
% 31.22/8.80 |
% 31.22/8.80 | Equations (1258) can reduce 640 to:
% 31.22/8.80 | (136) ~ (e3 = e1)
% 31.22/8.80 |
% 31.22/8.80 +-Applying beta-rule and splitting (1508), into two cases.
% 31.22/8.80 |-Branch one:
% 31.22/8.80 | (505) all_0_45_45 = e3
% 31.22/8.80 |
% 31.22/8.80 | Combining equations (505,4011) yields a new equation:
% 31.22/8.81 | (17772) all_0_7_7 = e3
% 31.22/8.81 |
% 31.22/8.81 | Equations (505) can reduce 434 to:
% 31.22/8.81 | (223) ~ (e3 = e2)
% 31.22/8.81 |
% 31.22/8.81 | Instantiating formula (201) with e3, e3, e4, all_0_11_11 and discharging atoms op(e3, e3) = all_0_11_11, op(e3, e3) = e4, yields:
% 31.22/8.81 | (14233) all_0_11_11 = e4
% 31.22/8.81 |
% 31.22/8.81 | Instantiating formula (201) with e3, e0, e0, all_0_9_9 and discharging atoms op(e3, e0) = all_0_9_9, op(e3, e0) = e0, yields:
% 31.22/8.81 | (17775) all_0_9_9 = e0
% 31.22/8.81 |
% 31.22/8.81 +-Applying beta-rule and splitting (234), into two cases.
% 31.22/8.81 |-Branch one:
% 31.22/8.81 | (4239) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3)) | (all_0_9_9 = e1 & ~ (all_0_10_10 = e3))
% 31.22/8.81 |
% 31.22/8.81 +-Applying beta-rule and splitting (4239), into two cases.
% 31.22/8.81 |-Branch one:
% 31.22/8.81 | (4240) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3))
% 31.22/8.81 |
% 31.22/8.81 +-Applying beta-rule and splitting (4240), into two cases.
% 31.22/8.81 |-Branch one:
% 31.22/8.81 | (4241) all_0_4_4 = e4 & ~ (all_0_5_5 = e3)
% 31.22/8.81 |
% 31.22/8.81 | Applying alpha-rule on (4241) yields:
% 31.22/8.81 | (4242) all_0_4_4 = e4
% 31.22/8.81 | (4243) ~ (all_0_5_5 = e3)
% 31.22/8.81 |
% 31.22/8.81 | Combining equations (4242,12701) yields a new equation:
% 31.22/8.81 | (268) e4 = e2
% 31.22/8.81 |
% 31.22/8.81 | Simplifying 268 yields:
% 31.22/8.81 | (269) e4 = e2
% 31.22/8.81 |
% 31.22/8.81 | Equations (269) can reduce 231 to:
% 31.22/8.81 | (270) $false
% 31.22/8.81 |
% 31.22/8.81 |-The branch is then unsatisfiable
% 31.22/8.81 |-Branch two:
% 31.22/8.81 | (4247) all_0_7_7 = e2 & ~ (all_0_8_8 = e3)
% 31.22/8.81 |
% 31.22/8.81 | Applying alpha-rule on (4247) yields:
% 31.22/8.81 | (4248) all_0_7_7 = e2
% 31.22/8.81 | (4249) ~ (all_0_8_8 = e3)
% 31.22/8.81 |
% 31.22/8.81 | Combining equations (17772,4248) yields a new equation:
% 31.22/8.81 | (437) e3 = e2
% 31.22/8.81 |
% 31.22/8.81 | Simplifying 437 yields:
% 31.22/8.81 | (414) e3 = e2
% 31.22/8.81 |
% 31.22/8.81 | Equations (414) can reduce 223 to:
% 31.22/8.81 | (270) $false
% 31.22/8.81 |
% 31.22/8.81 |-The branch is then unsatisfiable
% 31.22/8.81 |-Branch two:
% 31.22/8.81 | (4253) all_0_9_9 = e1 & ~ (all_0_10_10 = e3)
% 31.22/8.81 |
% 31.22/8.81 | Applying alpha-rule on (4253) yields:
% 31.22/8.81 | (4254) all_0_9_9 = e1
% 31.22/8.81 | (4255) ~ (all_0_10_10 = e3)
% 31.22/8.81 |
% 31.22/8.81 | Combining equations (17775,4254) yields a new equation:
% 31.22/8.81 | (560) e1 = e0
% 31.22/8.81 |
% 31.22/8.81 | Equations (560) can reduce 132 to:
% 31.22/8.81 | (270) $false
% 31.22/8.81 |
% 31.22/8.81 |-The branch is then unsatisfiable
% 31.22/8.81 |-Branch two:
% 31.22/8.81 | (4378) all_0_11_11 = e0 & ~ (all_0_12_12 = e3)
% 31.22/8.81 |
% 31.22/8.81 | Applying alpha-rule on (4378) yields:
% 31.22/8.81 | (4379) all_0_11_11 = e0
% 31.22/8.81 | (4380) ~ (all_0_12_12 = e3)
% 31.22/8.81 |
% 31.22/8.81 | Combining equations (14233,4379) yields a new equation:
% 31.22/8.81 | (478) e4 = e0
% 31.22/8.81 |
% 31.22/8.81 | Simplifying 478 yields:
% 31.22/8.81 | (479) e4 = e0
% 31.22/8.81 |
% 31.22/8.81 | Equations (479) can reduce 6 to:
% 31.22/8.81 | (270) $false
% 31.22/8.81 |
% 31.22/8.81 |-The branch is then unsatisfiable
% 31.22/8.81 |-Branch two:
% 31.22/8.81 | (354) ~ (all_0_45_45 = e3)
% 31.22/8.81 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 31.22/8.81 |
% 31.22/8.81 +-Applying beta-rule and splitting (22), into two cases.
% 31.22/8.81 |-Branch one:
% 31.22/8.81 | (782) all_0_43_43 = e3
% 31.22/8.81 |
% 31.22/8.81 | Combining equations (502,782) yields a new equation:
% 31.22/8.81 | (660) e4 = e3
% 31.22/8.81 |
% 31.22/8.81 | Simplifying 660 yields:
% 31.22/8.81 | (359) e4 = e3
% 31.22/8.81 |
% 31.22/8.81 | Equations (359) can reduce 34 to:
% 31.22/8.81 | (270) $false
% 31.22/8.81 |
% 31.22/8.81 |-The branch is then unsatisfiable
% 31.22/8.81 |-Branch two:
% 31.22/8.81 | (786) ~ (all_0_43_43 = e3)
% 31.22/8.81 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 31.22/8.81 |
% 31.22/8.81 +-Applying beta-rule and splitting (787), into two cases.
% 31.22/8.81 |-Branch one:
% 31.22/8.81 | (858) all_0_44_44 = e3
% 31.22/8.81 |
% 31.22/8.81 | Combining equations (370,858) yields a new equation:
% 31.22/8.81 | (414) e3 = e2
% 31.22/8.81 |
% 31.22/8.81 | Equations (414) can reduce 223 to:
% 31.22/8.81 | (270) $false
% 31.22/8.81 |
% 31.22/8.81 |-The branch is then unsatisfiable
% 31.22/8.81 |-Branch two:
% 31.22/8.81 | (862) ~ (all_0_44_44 = e3)
% 31.22/8.81 | (1070) all_0_45_45 = e3 | all_0_46_46 = e3
% 31.22/8.81 |
% 31.22/8.81 | Equations (370) can reduce 862 to:
% 31.22/8.81 | (301) ~ (e3 = e2)
% 31.22/8.81 |
% 31.22/8.81 | Simplifying 301 yields:
% 31.22/8.81 | (223) ~ (e3 = e2)
% 31.22/8.81 |
% 31.22/8.81 +-Applying beta-rule and splitting (1539), into two cases.
% 31.22/8.81 |-Branch one:
% 31.22/8.81 | (1114) all_0_53_53 = e3
% 31.22/8.81 |
% 31.22/8.81 | Combining equations (576,1114) yields a new equation:
% 31.22/8.81 | (414) e3 = e2
% 31.22/8.81 |
% 31.22/8.81 | Equations (414) can reduce 223 to:
% 31.22/8.81 | (270) $false
% 31.22/8.81 |
% 31.22/8.81 |-The branch is then unsatisfiable
% 31.22/8.81 |-Branch two:
% 31.22/8.81 | (356) ~ (all_0_53_53 = e3)
% 31.22/8.81 | (4713) all_0_58_58 = e3
% 31.22/8.81 |
% 31.22/8.81 | Combining equations (1001,4713) yields a new equation:
% 31.22/8.81 | (538) e3 = e1
% 31.22/8.81 |
% 31.22/8.81 | Equations (538) can reduce 136 to:
% 31.22/8.81 | (270) $false
% 31.22/8.81 |
% 31.22/8.81 |-The branch is then unsatisfiable
% 31.22/8.81 |-Branch two:
% 31.22/8.81 | (1316) ~ (all_0_42_42 = e3)
% 31.22/8.81 | (3656) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 31.22/8.81 |
% 31.22/8.81 +-Applying beta-rule and splitting (22), into two cases.
% 31.22/8.81 |-Branch one:
% 31.22/8.81 | (782) all_0_43_43 = e3
% 31.22/8.81 |
% 31.22/8.81 | Combining equations (782,502) yields a new equation:
% 31.22/8.81 | (359) e4 = e3
% 31.22/8.81 |
% 31.22/8.81 | Equations (359) can reduce 34 to:
% 31.22/8.81 | (270) $false
% 31.22/8.81 |
% 31.22/8.81 |-The branch is then unsatisfiable
% 31.22/8.81 |-Branch two:
% 31.22/8.81 | (786) ~ (all_0_43_43 = e3)
% 31.22/8.81 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 31.22/8.81 |
% 31.22/8.81 +-Applying beta-rule and splitting (3656), into two cases.
% 31.22/8.81 |-Branch one:
% 31.22/8.81 | (1091) all_0_46_46 = e3
% 31.22/8.81 |
% 31.22/8.81 | Combining equations (1132,1091) yields a new equation:
% 31.22/8.81 | (784) e3 = e0
% 31.22/8.81 |
% 31.22/8.81 | Equations (784) can reduce 66 to:
% 31.22/8.81 | (270) $false
% 31.22/8.81 |
% 31.22/8.81 |-The branch is then unsatisfiable
% 31.22/8.81 |-Branch two:
% 31.22/8.81 | (413) ~ (all_0_46_46 = e3)
% 31.22/8.81 | (3700) all_0_54_54 = e3 | all_0_59_59 = e3
% 31.22/8.81 |
% 31.22/8.81 | Equations (1132) can reduce 413 to:
% 31.22/8.81 | (788) ~ (e3 = e0)
% 31.22/8.81 |
% 31.22/8.81 | Simplifying 788 yields:
% 31.22/8.81 | (66) ~ (e3 = e0)
% 31.22/8.81 |
% 31.22/8.81 +-Applying beta-rule and splitting (1508), into two cases.
% 31.22/8.81 |-Branch one:
% 31.22/8.81 | (505) all_0_45_45 = e3
% 31.22/8.81 |
% 31.22/8.81 | Equations (505) can reduce 352 to:
% 31.22/8.81 | (719) ~ (e4 = e3)
% 31.22/8.81 |
% 31.22/8.81 | Simplifying 719 yields:
% 31.22/8.81 | (34) ~ (e4 = e3)
% 31.22/8.81 |
% 31.22/8.81 | Equations (505) can reduce 26 to:
% 31.22/8.81 | (136) ~ (e3 = e1)
% 31.22/8.81 |
% 31.22/8.81 +-Applying beta-rule and splitting (3700), into two cases.
% 31.22/8.81 |-Branch one:
% 31.22/8.81 | (1119) all_0_54_54 = e3
% 31.22/8.81 |
% 31.22/8.81 | Combining equations (875,1119) yields a new equation:
% 31.22/8.81 | (538) e3 = e1
% 31.22/8.81 |
% 31.22/8.81 | Equations (538) can reduce 136 to:
% 31.22/8.81 | (270) $false
% 31.22/8.81 |
% 31.22/8.81 |-The branch is then unsatisfiable
% 31.22/8.81 |-Branch two:
% 31.22/8.81 | (1093) ~ (all_0_54_54 = e3)
% 31.22/8.81 | (412) all_0_59_59 = e3
% 31.22/8.81 |
% 31.22/8.81 | Combining equations (402,412) yields a new equation:
% 31.22/8.81 | (660) e4 = e3
% 31.22/8.81 |
% 31.22/8.81 | Simplifying 660 yields:
% 31.22/8.81 | (359) e4 = e3
% 31.22/8.81 |
% 31.22/8.81 | Equations (359) can reduce 34 to:
% 31.22/8.81 | (270) $false
% 31.22/8.81 |
% 31.22/8.81 |-The branch is then unsatisfiable
% 31.22/8.81 |-Branch two:
% 31.22/8.81 | (354) ~ (all_0_45_45 = e3)
% 31.22/8.81 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 31.22/8.81 |
% 31.22/8.81 +-Applying beta-rule and splitting (78), into two cases.
% 31.22/8.81 |-Branch one:
% 31.22/8.81 | (751) all_0_39_39 = e3
% 31.22/8.81 |
% 31.22/8.81 | Combining equations (751,336) yields a new equation:
% 31.22/8.81 | (437) e3 = e2
% 31.22/8.81 |
% 31.22/8.81 | Simplifying 437 yields:
% 31.22/8.81 | (414) e3 = e2
% 31.22/8.81 |
% 31.22/8.81 | Equations (414) can reduce 223 to:
% 31.22/8.81 | (270) $false
% 31.22/8.81 |
% 31.22/8.81 |-The branch is then unsatisfiable
% 31.22/8.81 |-Branch two:
% 31.22/8.81 | (755) ~ (all_0_39_39 = e3)
% 31.22/8.81 | (4262) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 31.22/8.81 |
% 31.22/8.81 | Equations (336) can reduce 755 to:
% 31.22/8.81 | (301) ~ (e3 = e2)
% 31.22/8.81 |
% 31.22/8.81 | Simplifying 301 yields:
% 31.22/8.81 | (223) ~ (e3 = e2)
% 31.22/8.81 |
% 31.22/8.81 +-Applying beta-rule and splitting (787), into two cases.
% 31.22/8.81 |-Branch one:
% 31.22/8.81 | (858) all_0_44_44 = e3
% 31.22/8.81 |
% 31.22/8.81 | Combining equations (370,858) yields a new equation:
% 31.22/8.81 | (414) e3 = e2
% 31.22/8.81 |
% 31.22/8.81 | Equations (414) can reduce 223 to:
% 31.22/8.81 | (270) $false
% 31.22/8.81 |
% 31.22/8.81 |-The branch is then unsatisfiable
% 31.22/8.81 |-Branch two:
% 31.22/8.81 | (862) ~ (all_0_44_44 = e3)
% 31.22/8.81 | (1070) all_0_45_45 = e3 | all_0_46_46 = e3
% 31.22/8.81 |
% 31.22/8.81 +-Applying beta-rule and splitting (1070), into two cases.
% 31.22/8.81 |-Branch one:
% 31.22/8.81 | (505) all_0_45_45 = e3
% 31.22/8.81 |
% 31.22/8.81 | Equations (505) can reduce 354 to:
% 31.22/8.81 | (270) $false
% 31.22/8.81 |
% 31.22/8.81 |-The branch is then unsatisfiable
% 31.22/8.81 |-Branch two:
% 31.22/8.81 | (354) ~ (all_0_45_45 = e3)
% 31.22/8.81 | (1091) all_0_46_46 = e3
% 31.22/8.81 |
% 31.22/8.81 | Combining equations (1132,1091) yields a new equation:
% 31.22/8.81 | (784) e3 = e0
% 31.22/8.81 |
% 31.22/8.81 | Equations (784) can reduce 66 to:
% 31.22/8.81 | (270) $false
% 31.22/8.81 |
% 31.22/8.81 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (510) ~ (all_0_43_43 = e4)
% 31.22/8.82 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (511), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (363) all_0_45_45 = e4
% 31.22/8.82 |
% 31.22/8.82 | Equations (363) can reduce 352 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (352) ~ (all_0_45_45 = e4)
% 31.22/8.82 | (517) all_0_46_46 = e4
% 31.22/8.82 |
% 31.22/8.82 | Combining equations (1132,517) yields a new equation:
% 31.22/8.82 | (479) e4 = e0
% 31.22/8.82 |
% 31.22/8.82 | Equations (479) can reduce 6 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (361) ~ (all_0_41_41 = e4)
% 31.22/8.82 | (512) all_0_42_42 = e4
% 31.22/8.82 |
% 31.22/8.82 | Equations (512) can reduce 520 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (767) ~ (all_0_56_56 = e3)
% 31.22/8.82 | (768) all_0_57_57 = e3 | all_0_58_58 = e3 | all_0_59_59 = e3
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (768), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (869) all_0_57_57 = e3
% 31.22/8.82 |
% 31.22/8.82 | Combining equations (869,2258) yields a new equation:
% 31.22/8.82 | (783) e3 = e0
% 31.22/8.82 |
% 31.22/8.82 | Simplifying 783 yields:
% 31.22/8.82 | (784) e3 = e0
% 31.22/8.82 |
% 31.22/8.82 | Equations (784) can reduce 66 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (846) ~ (all_0_57_57 = e3)
% 31.22/8.82 | (5225) all_0_58_58 = e3 | all_0_59_59 = e3
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (5225), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (4713) all_0_58_58 = e3
% 31.22/8.82 |
% 31.22/8.82 | Combining equations (4713,1001) yields a new equation:
% 31.22/8.82 | (537) e3 = e1
% 31.22/8.82 |
% 31.22/8.82 | Simplifying 537 yields:
% 31.22/8.82 | (538) e3 = e1
% 31.22/8.82 |
% 31.22/8.82 | Equations (538) can reduce 136 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (718) ~ (all_0_58_58 = e3)
% 31.22/8.82 | (412) all_0_59_59 = e3
% 31.22/8.82 |
% 31.22/8.82 | Combining equations (402,412) yields a new equation:
% 31.22/8.82 | (660) e4 = e3
% 31.22/8.82 |
% 31.22/8.82 | Simplifying 660 yields:
% 31.22/8.82 | (359) e4 = e3
% 31.22/8.82 |
% 31.22/8.82 | Equations (359) can reduce 34 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (280) ~ (all_0_59_59 = e4)
% 31.22/8.82 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (407), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (408), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (409), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 31.22/8.82 |
% 31.22/8.82 | Applying alpha-rule on (410) yields:
% 31.22/8.82 | (411) all_0_43_43 = e0
% 31.22/8.82 | (412) all_0_59_59 = e3
% 31.22/8.82 | (413) ~ (all_0_46_46 = e3)
% 31.22/8.82 |
% 31.22/8.82 | Equations (411) can reduce 455 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 31.22/8.82 |
% 31.22/8.82 | Applying alpha-rule on (416) yields:
% 31.22/8.82 | (411) all_0_43_43 = e0
% 31.22/8.82 | (412) all_0_59_59 = e3
% 31.22/8.82 | (419) ~ (all_0_56_56 = e0)
% 31.22/8.82 |
% 31.22/8.82 | Equations (411) can reduce 455 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 31.22/8.82 |
% 31.22/8.82 | Applying alpha-rule on (422) yields:
% 31.22/8.82 | (423) all_0_53_53 = e0
% 31.22/8.82 | (424) all_0_59_59 = e1
% 31.22/8.82 | (425) ~ (all_0_54_54 = e1)
% 31.22/8.82 |
% 31.22/8.82 | Combining equations (423,576) yields a new equation:
% 31.22/8.82 | (316) e2 = e0
% 31.22/8.82 |
% 31.22/8.82 | Equations (316) can reduce 57 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 31.22/8.82 |
% 31.22/8.82 | Applying alpha-rule on (428) yields:
% 31.22/8.82 | (423) all_0_53_53 = e0
% 31.22/8.82 | (424) all_0_59_59 = e1
% 31.22/8.82 | (431) ~ (all_0_58_58 = e0)
% 31.22/8.82 |
% 31.22/8.82 | Combining equations (423,576) yields a new equation:
% 31.22/8.82 | (316) e2 = e0
% 31.22/8.82 |
% 31.22/8.82 | Equations (316) can reduce 57 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (1010) ~ (all_0_46_46 = e0)
% 31.22/8.82 | (3629) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (3629), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (563) all_0_49_49 = e0
% 31.22/8.82 |
% 31.22/8.82 | Combining equations (307,563) yields a new equation:
% 31.22/8.82 | (622) e2 = e0
% 31.22/8.82 |
% 31.22/8.82 | Simplifying 622 yields:
% 31.22/8.82 | (316) e2 = e0
% 31.22/8.82 |
% 31.22/8.82 | Equations (316) can reduce 57 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (1231) ~ (all_0_49_49 = e0)
% 31.22/8.82 | (3638) all_0_54_54 = e0 | all_0_59_59 = e0
% 31.22/8.82 |
% 31.22/8.82 | Equations (307) can reduce 1231 to:
% 31.22/8.82 | (57) ~ (e2 = e0)
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (116), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (411) all_0_43_43 = e0
% 31.22/8.82 |
% 31.22/8.82 | Equations (411) can reduce 455 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (455) ~ (all_0_43_43 = e0)
% 31.22/8.82 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (93), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (402) all_0_59_59 = e4
% 31.22/8.82 |
% 31.22/8.82 | Equations (402) can reduce 185 to:
% 31.22/8.82 | (274) ~ (all_0_56_56 = e4)
% 31.22/8.82 |
% 31.22/8.82 | Equations (402) can reduce 701 to:
% 31.22/8.82 | (231) ~ (e4 = e2)
% 31.22/8.82 |
% 31.22/8.82 | Equations (402) can reduce 4001 to:
% 31.22/8.82 | (6) ~ (e4 = e0)
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (166), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (522) all_0_39_39 = e4
% 31.22/8.82 |
% 31.22/8.82 | Combining equations (522,336) yields a new equation:
% 31.22/8.82 | (268) e4 = e2
% 31.22/8.82 |
% 31.22/8.82 | Simplifying 268 yields:
% 31.22/8.82 | (269) e4 = e2
% 31.22/8.82 |
% 31.22/8.82 | Equations (269) can reduce 231 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (591) ~ (all_0_39_39 = e4)
% 31.22/8.82 | (4522) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (4522), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (502) all_0_43_43 = e4
% 31.22/8.82 |
% 31.22/8.82 | Equations (502) can reduce 455 to:
% 31.22/8.82 | (6) ~ (e4 = e0)
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (3638), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (3084) all_0_54_54 = e0
% 31.22/8.82 |
% 31.22/8.82 | Combining equations (3084,875) yields a new equation:
% 31.22/8.82 | (560) e1 = e0
% 31.22/8.82 |
% 31.22/8.82 | Equations (560) can reduce 132 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (3011) ~ (all_0_54_54 = e0)
% 31.22/8.82 | (2308) all_0_59_59 = e0
% 31.22/8.82 |
% 31.22/8.82 | Combining equations (2308,402) yields a new equation:
% 31.22/8.82 | (479) e4 = e0
% 31.22/8.82 |
% 31.22/8.82 | Equations (479) can reduce 6 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (510) ~ (all_0_43_43 = e4)
% 31.22/8.82 | (4527) all_0_51_51 = e4 | all_0_56_56 = e4
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (4527), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (1467) all_0_51_51 = e4
% 31.22/8.82 |
% 31.22/8.82 | Combining equations (954,1467) yields a new equation:
% 31.22/8.82 | (479) e4 = e0
% 31.22/8.82 |
% 31.22/8.82 | Equations (479) can reduce 6 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (697) ~ (all_0_51_51 = e4)
% 31.22/8.82 | (4744) all_0_56_56 = e4
% 31.22/8.82 |
% 31.22/8.82 | Equations (4744) can reduce 274 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (280) ~ (all_0_59_59 = e4)
% 31.22/8.82 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (407), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (408), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (409), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 31.22/8.82 |
% 31.22/8.82 | Applying alpha-rule on (410) yields:
% 31.22/8.82 | (411) all_0_43_43 = e0
% 31.22/8.82 | (412) all_0_59_59 = e3
% 31.22/8.82 | (413) ~ (all_0_46_46 = e3)
% 31.22/8.82 |
% 31.22/8.82 | Equations (411) can reduce 455 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 31.22/8.82 |
% 31.22/8.82 | Applying alpha-rule on (416) yields:
% 31.22/8.82 | (411) all_0_43_43 = e0
% 31.22/8.82 | (412) all_0_59_59 = e3
% 31.22/8.82 | (419) ~ (all_0_56_56 = e0)
% 31.22/8.82 |
% 31.22/8.82 | Equations (411) can reduce 455 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 31.22/8.82 |
% 31.22/8.82 | Applying alpha-rule on (422) yields:
% 31.22/8.82 | (423) all_0_53_53 = e0
% 31.22/8.82 | (424) all_0_59_59 = e1
% 31.22/8.82 | (425) ~ (all_0_54_54 = e1)
% 31.22/8.82 |
% 31.22/8.82 | Combining equations (423,576) yields a new equation:
% 31.22/8.82 | (316) e2 = e0
% 31.22/8.82 |
% 31.22/8.82 | Equations (316) can reduce 57 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 31.22/8.82 |
% 31.22/8.82 | Applying alpha-rule on (428) yields:
% 31.22/8.82 | (423) all_0_53_53 = e0
% 31.22/8.82 | (424) all_0_59_59 = e1
% 31.22/8.82 | (431) ~ (all_0_58_58 = e0)
% 31.22/8.82 |
% 31.22/8.82 | Combining equations (423,576) yields a new equation:
% 31.22/8.82 | (316) e2 = e0
% 31.22/8.82 |
% 31.22/8.82 | Equations (316) can reduce 57 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (987) ~ (all_0_51_51 = e0)
% 31.22/8.82 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (4888), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (954) all_0_51_51 = e0
% 31.22/8.82 |
% 31.22/8.82 | Equations (954) can reduce 987 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (987) ~ (all_0_51_51 = e0)
% 31.22/8.82 | (5003) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (5003), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (824) all_0_51_51 = e3
% 31.22/8.82 |
% 31.22/8.82 | Equations (824) can reduce 932 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (932) ~ (all_0_51_51 = e3)
% 31.22/8.82 | (5007) all_0_51_51 = e4 | all_0_51_51 = e1
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (5007), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (820) all_0_51_51 = e1
% 31.22/8.82 |
% 31.22/8.82 | Equations (820) can reduce 748 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (748) ~ (all_0_51_51 = e1)
% 31.22/8.82 | (1467) all_0_51_51 = e4
% 31.22/8.82 |
% 31.22/8.82 | Equations (1467) can reduce 697 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (826) ~ (all_0_52_52 = e3)
% 31.22/8.82 | (1107) all_0_53_53 = e3 | all_0_54_54 = e3
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (1107), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (1114) all_0_53_53 = e3
% 31.22/8.82 |
% 31.22/8.82 | Combining equations (1114,576) yields a new equation:
% 31.22/8.82 | (437) e3 = e2
% 31.22/8.82 |
% 31.22/8.82 | Simplifying 437 yields:
% 31.22/8.82 | (414) e3 = e2
% 31.22/8.82 |
% 31.22/8.82 | Equations (414) can reduce 223 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (356) ~ (all_0_53_53 = e3)
% 31.22/8.82 | (1119) all_0_54_54 = e3
% 31.22/8.82 |
% 31.22/8.82 | Combining equations (875,1119) yields a new equation:
% 31.22/8.82 | (538) e3 = e1
% 31.22/8.82 |
% 31.22/8.82 | Equations (538) can reduce 136 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (1762) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 31.22/8.82 |
% 31.22/8.82 | Applying alpha-rule on (1762) yields:
% 31.22/8.82 | (1763) all_0_19_19 = e0
% 31.22/8.82 | (1764) ~ (all_0_20_20 = e2)
% 31.22/8.82 |
% 31.22/8.82 | From (1763) and (30) follows:
% 31.22/8.82 | (1765) op(e2, all_0_57_57) = e0
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (21), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (824) all_0_51_51 = e3
% 31.22/8.82 |
% 31.22/8.82 | Equations (824) can reduce 240 to:
% 31.22/8.82 | (786) ~ (all_0_43_43 = e3)
% 31.22/8.82 |
% 31.22/8.82 | Equations (824) can reduce 154 to:
% 31.22/8.82 | (825) ~ (all_0_52_52 = e3)
% 31.22/8.82 |
% 31.22/8.82 | Simplifying 825 yields:
% 31.22/8.82 | (826) ~ (all_0_52_52 = e3)
% 31.22/8.82 |
% 31.22/8.82 | Equations (824) can reduce 255 to:
% 31.22/8.82 | (223) ~ (e3 = e2)
% 31.22/8.82 |
% 31.22/8.82 | Equations (824) can reduce 748 to:
% 31.22/8.82 | (136) ~ (e3 = e1)
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (133), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (671) all_0_40_40 = e3
% 31.22/8.82 |
% 31.22/8.82 | Combining equations (530,671) yields a new equation:
% 31.22/8.82 | (538) e3 = e1
% 31.22/8.82 |
% 31.22/8.82 | Equations (538) can reduce 136 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (675) ~ (all_0_40_40 = e3)
% 31.22/8.82 | (676) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 31.22/8.82 |
% 31.22/8.82 +-Applying beta-rule and splitting (64), into two cases.
% 31.22/8.82 |-Branch one:
% 31.22/8.82 | (954) all_0_51_51 = e0
% 31.22/8.82 |
% 31.22/8.82 | Combining equations (824,954) yields a new equation:
% 31.22/8.82 | (783) e3 = e0
% 31.22/8.82 |
% 31.22/8.82 | Simplifying 783 yields:
% 31.22/8.82 | (784) e3 = e0
% 31.22/8.82 |
% 31.22/8.82 | Equations (784) can reduce 66 to:
% 31.22/8.82 | (270) $false
% 31.22/8.82 |
% 31.22/8.82 |-The branch is then unsatisfiable
% 31.22/8.82 |-Branch two:
% 31.22/8.82 | (987) ~ (all_0_51_51 = e0)
% 31.22/8.83 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (676), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (858) all_0_44_44 = e3
% 31.22/8.83 |
% 31.22/8.83 | Combining equations (370,858) yields a new equation:
% 31.22/8.83 | (414) e3 = e2
% 31.22/8.83 |
% 31.22/8.83 | Equations (414) can reduce 223 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (862) ~ (all_0_44_44 = e3)
% 31.22/8.83 | (863) all_0_52_52 = e3 | all_0_57_57 = e3
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (3067), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (827) all_0_52_52 = e0
% 31.22/8.83 |
% 31.22/8.83 | Equations (827) can reduce 235 to:
% 31.22/8.83 | (9326) ~ (all_0_57_57 = e0)
% 31.22/8.83 |
% 31.22/8.83 | Simplifying 9326 yields:
% 31.22/8.83 | (2301) ~ (all_0_57_57 = e0)
% 31.22/8.83 |
% 31.22/8.83 | Equations (827) can reduce 826 to:
% 31.22/8.83 | (788) ~ (e3 = e0)
% 31.22/8.83 |
% 31.22/8.83 | Simplifying 788 yields:
% 31.22/8.83 | (66) ~ (e3 = e0)
% 31.22/8.83 |
% 31.22/8.83 | Equations (827) can reduce 257 to:
% 31.22/8.83 | (566) ~ (e2 = e0)
% 31.22/8.83 |
% 31.22/8.83 | Simplifying 566 yields:
% 31.22/8.83 | (57) ~ (e2 = e0)
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (33), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (392) all_0_57_57 = e2
% 31.22/8.83 |
% 31.22/8.83 | Equations (392) can reduce 335 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (335) ~ (all_0_57_57 = e2)
% 31.22/8.83 | (670) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (863), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (864) all_0_52_52 = e3
% 31.22/8.83 |
% 31.22/8.83 | Combining equations (827,864) yields a new equation:
% 31.22/8.83 | (784) e3 = e0
% 31.22/8.83 |
% 31.22/8.83 | Equations (784) can reduce 66 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (826) ~ (all_0_52_52 = e3)
% 31.22/8.83 | (869) all_0_57_57 = e3
% 31.22/8.83 |
% 31.22/8.83 | Equations (869) can reduce 140 to:
% 31.22/8.83 | (1259) ~ (all_0_59_59 = e3)
% 31.22/8.83 |
% 31.22/8.83 | Simplifying 1259 yields:
% 31.22/8.83 | (1260) ~ (all_0_59_59 = e3)
% 31.22/8.83 |
% 31.22/8.83 | Equations (869) can reduce 335 to:
% 31.22/8.83 | (223) ~ (e3 = e2)
% 31.22/8.83 |
% 31.22/8.83 | Equations (869) can reduce 644 to:
% 31.22/8.83 | (136) ~ (e3 = e1)
% 31.22/8.83 |
% 31.22/8.83 | Equations (869) can reduce 2301 to:
% 31.22/8.83 | (66) ~ (e3 = e0)
% 31.22/8.83 |
% 31.22/8.83 | From (869) and (1765) follows:
% 31.22/8.83 | (7718) op(e2, e3) = e0
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (93), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (402) all_0_59_59 = e4
% 31.22/8.83 |
% 31.22/8.83 | Equations (402) can reduce 17 to:
% 31.22/8.83 | (520) ~ (all_0_42_42 = e4)
% 31.22/8.83 |
% 31.22/8.83 | Equations (402) can reduce 206 to:
% 31.22/8.83 | (805) ~ (all_0_46_46 = e4)
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (592), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (358) all_0_41_41 = e4
% 31.22/8.83 |
% 31.22/8.83 | Equations (358) can reduce 51 to:
% 31.22/8.83 | (503) ~ (all_0_45_45 = e4)
% 31.22/8.83 |
% 31.22/8.83 | Simplifying 503 yields:
% 31.22/8.83 | (352) ~ (all_0_45_45 = e4)
% 31.22/8.83 |
% 31.22/8.83 | Equations (358) can reduce 232 to:
% 31.22/8.83 | (6) ~ (e4 = e0)
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (78), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (751) all_0_39_39 = e3
% 31.22/8.83 |
% 31.22/8.83 | Combining equations (751,336) yields a new equation:
% 31.22/8.83 | (437) e3 = e2
% 31.22/8.83 |
% 31.22/8.83 | Simplifying 437 yields:
% 31.22/8.83 | (414) e3 = e2
% 31.22/8.83 |
% 31.22/8.83 | Equations (414) can reduce 223 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (755) ~ (all_0_39_39 = e3)
% 31.22/8.83 | (4262) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 31.22/8.83 |
% 31.22/8.83 | Equations (336) can reduce 755 to:
% 31.22/8.83 | (301) ~ (e3 = e2)
% 31.22/8.83 |
% 31.22/8.83 | Simplifying 301 yields:
% 31.22/8.83 | (223) ~ (e3 = e2)
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (221), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (1132) all_0_46_46 = e0
% 31.22/8.83 |
% 31.22/8.83 | Equations (1132) can reduce 805 to:
% 31.22/8.83 | (456) ~ (e4 = e0)
% 31.22/8.83 |
% 31.22/8.83 | Simplifying 456 yields:
% 31.22/8.83 | (6) ~ (e4 = e0)
% 31.22/8.83 |
% 31.22/8.83 | Equations (1132) can reduce 106 to:
% 31.22/8.83 | (568) ~ (e1 = e0)
% 31.22/8.83 |
% 31.22/8.83 | Simplifying 568 yields:
% 31.22/8.83 | (132) ~ (e1 = e0)
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (176), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (830) all_0_56_56 = e0
% 31.22/8.83 |
% 31.22/8.83 | Equations (830) can reduce 995 to:
% 31.22/8.83 | (568) ~ (e1 = e0)
% 31.22/8.83 |
% 31.22/8.83 | Simplifying 568 yields:
% 31.22/8.83 | (132) ~ (e1 = e0)
% 31.22/8.83 |
% 31.22/8.83 | Instantiating formula (201) with e2, e3, e0, e1 and discharging atoms op(e2, e3) = e1, op(e2, e3) = e0, yields:
% 31.22/8.83 | (560) e1 = e0
% 31.22/8.83 |
% 31.22/8.83 | Equations (560) can reduce 132 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (419) ~ (all_0_56_56 = e0)
% 31.22/8.83 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (834), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (2258) all_0_57_57 = e0
% 31.22/8.83 |
% 31.22/8.83 | Combining equations (2258,869) yields a new equation:
% 31.22/8.83 | (784) e3 = e0
% 31.22/8.83 |
% 31.22/8.83 | Equations (784) can reduce 66 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (2301) ~ (all_0_57_57 = e0)
% 31.22/8.83 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (2302), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (585) all_0_58_58 = e0
% 31.22/8.83 |
% 31.22/8.83 | Combining equations (1001,585) yields a new equation:
% 31.22/8.83 | (571) e1 = e0
% 31.22/8.83 |
% 31.22/8.83 | Simplifying 571 yields:
% 31.22/8.83 | (560) e1 = e0
% 31.22/8.83 |
% 31.22/8.83 | Equations (560) can reduce 132 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (431) ~ (all_0_58_58 = e0)
% 31.22/8.83 | (2308) all_0_59_59 = e0
% 31.22/8.83 |
% 31.22/8.83 | Combining equations (402,2308) yields a new equation:
% 31.22/8.83 | (478) e4 = e0
% 31.22/8.83 |
% 31.22/8.83 | Simplifying 478 yields:
% 31.22/8.83 | (479) e4 = e0
% 31.22/8.83 |
% 31.22/8.83 | Equations (479) can reduce 6 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (1010) ~ (all_0_46_46 = e0)
% 31.22/8.83 | (3629) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (75), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (411) all_0_43_43 = e0
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (44), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (502) all_0_43_43 = e4
% 31.22/8.83 |
% 31.22/8.83 | Combining equations (411,502) yields a new equation:
% 31.22/8.83 | (479) e4 = e0
% 31.22/8.83 |
% 31.22/8.83 | Equations (479) can reduce 6 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (510) ~ (all_0_43_43 = e4)
% 31.22/8.83 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (511), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (363) all_0_45_45 = e4
% 31.22/8.83 |
% 31.22/8.83 | Equations (363) can reduce 352 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (352) ~ (all_0_45_45 = e4)
% 31.22/8.83 | (517) all_0_46_46 = e4
% 31.22/8.83 |
% 31.22/8.83 | Equations (517) can reduce 805 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (455) ~ (all_0_43_43 = e0)
% 31.22/8.83 | (940) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (116), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (411) all_0_43_43 = e0
% 31.22/8.83 |
% 31.22/8.83 | Equations (411) can reduce 455 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (455) ~ (all_0_43_43 = e0)
% 31.22/8.83 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (44), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (502) all_0_43_43 = e4
% 31.22/8.83 |
% 31.22/8.83 | Equations (502) can reduce 786 to:
% 31.22/8.83 | (34) ~ (e4 = e3)
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (105), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (374) all_0_45_45 = e2
% 31.22/8.83 |
% 31.22/8.83 | Equations (374) can reduce 434 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (434) ~ (all_0_45_45 = e2)
% 31.22/8.83 | (435) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (219), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (351) all_0_41_41 = e3
% 31.22/8.83 |
% 31.22/8.83 | Combining equations (351,358) yields a new equation:
% 31.22/8.83 | (359) e4 = e3
% 31.22/8.83 |
% 31.22/8.83 | Equations (359) can reduce 34 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (1237) ~ (all_0_41_41 = e3)
% 31.22/8.83 | (1508) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (435), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (454) all_0_45_45 = e0
% 31.22/8.83 |
% 31.22/8.83 | Equations (454) can reduce 488 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (488) ~ (all_0_45_45 = e0)
% 31.22/8.83 | (489) all_0_45_45 = e4 | all_0_45_45 = e3
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (1508), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (505) all_0_45_45 = e3
% 31.22/8.83 |
% 31.22/8.83 | Equations (505) can reduce 488 to:
% 31.22/8.83 | (66) ~ (e3 = e0)
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (1122), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (621) all_0_44_44 = e0
% 31.22/8.83 |
% 31.22/8.83 | Combining equations (370,621) yields a new equation:
% 31.22/8.83 | (622) e2 = e0
% 31.22/8.83 |
% 31.22/8.83 | Simplifying 622 yields:
% 31.22/8.83 | (316) e2 = e0
% 31.22/8.83 |
% 31.22/8.83 | Equations (316) can reduce 57 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (625) ~ (all_0_44_44 = e0)
% 31.22/8.83 | (1128) all_0_45_45 = e0 | all_0_46_46 = e0
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (1128), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (454) all_0_45_45 = e0
% 31.22/8.83 |
% 31.22/8.83 | Combining equations (505,454) yields a new equation:
% 31.22/8.83 | (783) e3 = e0
% 31.22/8.83 |
% 31.22/8.83 | Simplifying 783 yields:
% 31.22/8.83 | (784) e3 = e0
% 31.22/8.83 |
% 31.22/8.83 | Equations (784) can reduce 66 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (488) ~ (all_0_45_45 = e0)
% 31.22/8.83 | (1132) all_0_46_46 = e0
% 31.22/8.83 |
% 31.22/8.83 | Equations (1132) can reduce 1010 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (354) ~ (all_0_45_45 = e3)
% 31.22/8.83 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (1539), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (1114) all_0_53_53 = e3
% 31.22/8.83 |
% 31.22/8.83 | Combining equations (1114,576) yields a new equation:
% 31.22/8.83 | (437) e3 = e2
% 31.22/8.83 |
% 31.22/8.83 | Simplifying 437 yields:
% 31.22/8.83 | (414) e3 = e2
% 31.22/8.83 |
% 31.22/8.83 | Equations (414) can reduce 223 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (356) ~ (all_0_53_53 = e3)
% 31.22/8.83 | (4713) all_0_58_58 = e3
% 31.22/8.83 |
% 31.22/8.83 | Combining equations (1001,4713) yields a new equation:
% 31.22/8.83 | (538) e3 = e1
% 31.22/8.83 |
% 31.22/8.83 | Equations (538) can reduce 136 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (510) ~ (all_0_43_43 = e4)
% 31.22/8.83 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (511), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (363) all_0_45_45 = e4
% 31.22/8.83 |
% 31.22/8.83 | Equations (363) can reduce 352 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (352) ~ (all_0_45_45 = e4)
% 31.22/8.83 | (517) all_0_46_46 = e4
% 31.22/8.83 |
% 31.22/8.83 | Equations (517) can reduce 805 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (361) ~ (all_0_41_41 = e4)
% 31.22/8.83 | (512) all_0_42_42 = e4
% 31.22/8.83 |
% 31.22/8.83 | Equations (512) can reduce 520 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (280) ~ (all_0_59_59 = e4)
% 31.22/8.83 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (407), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (408), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (409), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 31.22/8.83 |
% 31.22/8.83 | Applying alpha-rule on (410) yields:
% 31.22/8.83 | (411) all_0_43_43 = e0
% 31.22/8.83 | (412) all_0_59_59 = e3
% 31.22/8.83 | (413) ~ (all_0_46_46 = e3)
% 31.22/8.83 |
% 31.22/8.83 | Equations (412) can reduce 1260 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 31.22/8.83 |
% 31.22/8.83 | Applying alpha-rule on (416) yields:
% 31.22/8.83 | (411) all_0_43_43 = e0
% 31.22/8.83 | (412) all_0_59_59 = e3
% 31.22/8.83 | (419) ~ (all_0_56_56 = e0)
% 31.22/8.83 |
% 31.22/8.83 | Equations (412) can reduce 1260 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 31.22/8.83 |
% 31.22/8.83 | Applying alpha-rule on (422) yields:
% 31.22/8.83 | (423) all_0_53_53 = e0
% 31.22/8.83 | (424) all_0_59_59 = e1
% 31.22/8.83 | (425) ~ (all_0_54_54 = e1)
% 31.22/8.83 |
% 31.22/8.83 | Combining equations (423,576) yields a new equation:
% 31.22/8.83 | (316) e2 = e0
% 31.22/8.83 |
% 31.22/8.83 | Equations (316) can reduce 57 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 31.22/8.83 |
% 31.22/8.83 | Applying alpha-rule on (428) yields:
% 31.22/8.83 | (423) all_0_53_53 = e0
% 31.22/8.83 | (424) all_0_59_59 = e1
% 31.22/8.83 | (431) ~ (all_0_58_58 = e0)
% 31.22/8.83 |
% 31.22/8.83 | Combining equations (423,576) yields a new equation:
% 31.22/8.83 | (316) e2 = e0
% 31.22/8.83 |
% 31.22/8.83 | Equations (316) can reduce 57 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (925) ~ (all_0_52_52 = e0)
% 31.22/8.83 | (3073) all_0_53_53 = e0 | all_0_54_54 = e0
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (3073), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (423) all_0_53_53 = e0
% 31.22/8.83 |
% 31.22/8.83 | Combining equations (423,576) yields a new equation:
% 31.22/8.83 | (316) e2 = e0
% 31.22/8.83 |
% 31.22/8.83 | Equations (316) can reduce 57 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (584) ~ (all_0_53_53 = e0)
% 31.22/8.83 | (3084) all_0_54_54 = e0
% 31.22/8.83 |
% 31.22/8.83 | Combining equations (875,3084) yields a new equation:
% 31.22/8.83 | (571) e1 = e0
% 31.22/8.83 |
% 31.22/8.83 | Simplifying 571 yields:
% 31.22/8.83 | (560) e1 = e0
% 31.22/8.83 |
% 31.22/8.83 | Equations (560) can reduce 132 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (932) ~ (all_0_51_51 = e3)
% 31.22/8.83 | (1101) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (173), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (4215) all_0_51_51 = e2
% 31.22/8.83 |
% 31.22/8.83 | Equations (4215) can reduce 255 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (255) ~ (all_0_51_51 = e2)
% 31.22/8.83 | (4888) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1 | all_0_51_51 = e0
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (1101), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (864) all_0_52_52 = e3
% 31.22/8.83 |
% 31.22/8.83 | Equations (864) can reduce 154 to:
% 31.22/8.83 | (932) ~ (all_0_51_51 = e3)
% 31.22/8.83 |
% 31.22/8.83 +-Applying beta-rule and splitting (626), into two cases.
% 31.22/8.83 |-Branch one:
% 31.22/8.83 | (827) all_0_52_52 = e0
% 31.22/8.83 |
% 31.22/8.83 | Combining equations (864,827) yields a new equation:
% 31.22/8.83 | (783) e3 = e0
% 31.22/8.83 |
% 31.22/8.83 | Simplifying 783 yields:
% 31.22/8.83 | (784) e3 = e0
% 31.22/8.83 |
% 31.22/8.83 | Equations (784) can reduce 66 to:
% 31.22/8.83 | (270) $false
% 31.22/8.83 |
% 31.22/8.83 |-The branch is then unsatisfiable
% 31.22/8.83 |-Branch two:
% 31.22/8.83 | (925) ~ (all_0_52_52 = e0)
% 31.22/8.84 | (2258) all_0_57_57 = e0
% 31.22/8.84 |
% 31.22/8.84 | Equations (2258) can reduce 140 to:
% 31.22/8.84 | (4000) ~ (all_0_59_59 = e0)
% 31.22/8.84 |
% 31.22/8.84 | Simplifying 4000 yields:
% 31.22/8.84 | (4001) ~ (all_0_59_59 = e0)
% 31.22/8.84 |
% 31.22/8.84 | From (2258) and (1765) follows:
% 31.22/8.84 | (2996) op(e2, e0) = e0
% 31.22/8.84 |
% 31.22/8.84 +-Applying beta-rule and splitting (64), into two cases.
% 31.22/8.84 |-Branch one:
% 31.22/8.84 | (954) all_0_51_51 = e0
% 31.22/8.84 |
% 31.22/8.84 | Equations (954) can reduce 240 to:
% 31.22/8.84 | (455) ~ (all_0_43_43 = e0)
% 31.22/8.84 |
% 31.22/8.84 | Equations (954) can reduce 255 to:
% 31.22/8.84 | (566) ~ (e2 = e0)
% 31.22/8.84 |
% 31.22/8.84 | Simplifying 566 yields:
% 31.22/8.84 | (57) ~ (e2 = e0)
% 31.22/8.84 |
% 31.22/8.84 | Equations (954) can reduce 748 to:
% 31.22/8.84 | (568) ~ (e1 = e0)
% 31.22/8.84 |
% 31.22/8.84 | Simplifying 568 yields:
% 31.22/8.84 | (132) ~ (e1 = e0)
% 31.22/8.84 |
% 31.22/8.84 +-Applying beta-rule and splitting (221), into two cases.
% 31.22/8.84 |-Branch one:
% 31.22/8.84 | (1132) all_0_46_46 = e0
% 31.22/8.84 |
% 31.22/8.84 | Equations (1132) can reduce 1436 to:
% 31.22/8.84 | (566) ~ (e2 = e0)
% 31.22/8.84 |
% 31.22/8.84 | Simplifying 566 yields:
% 31.22/8.84 | (57) ~ (e2 = e0)
% 31.22/8.84 |
% 31.22/8.84 | Instantiating formula (201) with e2, e0, e0, e2 and discharging atoms op(e2, e0) = e2, op(e2, e0) = e0, yields:
% 31.22/8.84 | (316) e2 = e0
% 31.22/8.84 |
% 31.22/8.84 | Equations (316) can reduce 57 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.84 |-Branch two:
% 31.22/8.84 | (1010) ~ (all_0_46_46 = e0)
% 31.22/8.84 | (3629) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 31.22/8.84 |
% 31.22/8.84 +-Applying beta-rule and splitting (3629), into two cases.
% 31.22/8.84 |-Branch one:
% 31.22/8.84 | (563) all_0_49_49 = e0
% 31.22/8.84 |
% 31.22/8.84 | Combining equations (307,563) yields a new equation:
% 31.22/8.84 | (622) e2 = e0
% 31.22/8.84 |
% 31.22/8.84 | Simplifying 622 yields:
% 31.22/8.84 | (316) e2 = e0
% 31.22/8.84 |
% 31.22/8.84 | Equations (316) can reduce 57 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.84 |-Branch two:
% 31.22/8.84 | (1231) ~ (all_0_49_49 = e0)
% 31.22/8.84 | (3638) all_0_54_54 = e0 | all_0_59_59 = e0
% 31.22/8.84 |
% 31.22/8.84 | Equations (307) can reduce 1231 to:
% 31.22/8.84 | (57) ~ (e2 = e0)
% 31.22/8.84 |
% 31.22/8.84 +-Applying beta-rule and splitting (116), into two cases.
% 31.22/8.84 |-Branch one:
% 31.22/8.84 | (411) all_0_43_43 = e0
% 31.22/8.84 |
% 31.22/8.84 | Equations (411) can reduce 455 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.84 |-Branch two:
% 31.22/8.84 | (455) ~ (all_0_43_43 = e0)
% 31.22/8.84 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 31.22/8.84 |
% 31.22/8.84 +-Applying beta-rule and splitting (93), into two cases.
% 31.22/8.84 |-Branch one:
% 31.22/8.84 | (402) all_0_59_59 = e4
% 31.22/8.84 |
% 31.22/8.84 | Equations (402) can reduce 185 to:
% 31.22/8.84 | (274) ~ (all_0_56_56 = e4)
% 31.22/8.84 |
% 31.22/8.84 | Equations (402) can reduce 701 to:
% 31.22/8.84 | (231) ~ (e4 = e2)
% 31.22/8.84 |
% 31.22/8.84 | Equations (402) can reduce 4001 to:
% 31.22/8.84 | (6) ~ (e4 = e0)
% 31.22/8.84 |
% 31.22/8.84 +-Applying beta-rule and splitting (166), into two cases.
% 31.22/8.84 |-Branch one:
% 31.22/8.84 | (522) all_0_39_39 = e4
% 31.22/8.84 |
% 31.22/8.84 | Combining equations (522,336) yields a new equation:
% 31.22/8.84 | (268) e4 = e2
% 31.22/8.84 |
% 31.22/8.84 | Simplifying 268 yields:
% 31.22/8.84 | (269) e4 = e2
% 31.22/8.84 |
% 31.22/8.84 | Equations (269) can reduce 231 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.84 |-Branch two:
% 31.22/8.84 | (591) ~ (all_0_39_39 = e4)
% 31.22/8.84 | (4522) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 31.22/8.84 |
% 31.22/8.84 +-Applying beta-rule and splitting (4522), into two cases.
% 31.22/8.84 |-Branch one:
% 31.22/8.84 | (502) all_0_43_43 = e4
% 31.22/8.84 |
% 31.22/8.84 | Equations (502) can reduce 455 to:
% 31.22/8.84 | (6) ~ (e4 = e0)
% 31.22/8.84 |
% 31.22/8.84 +-Applying beta-rule and splitting (3638), into two cases.
% 31.22/8.84 |-Branch one:
% 31.22/8.84 | (3084) all_0_54_54 = e0
% 31.22/8.84 |
% 31.22/8.84 | Combining equations (3084,875) yields a new equation:
% 31.22/8.84 | (560) e1 = e0
% 31.22/8.84 |
% 31.22/8.84 | Equations (560) can reduce 132 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.84 |-Branch two:
% 31.22/8.84 | (3011) ~ (all_0_54_54 = e0)
% 31.22/8.84 | (2308) all_0_59_59 = e0
% 31.22/8.84 |
% 31.22/8.84 | Combining equations (2308,402) yields a new equation:
% 31.22/8.84 | (479) e4 = e0
% 31.22/8.84 |
% 31.22/8.84 | Equations (479) can reduce 6 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.84 |-Branch two:
% 31.22/8.84 | (510) ~ (all_0_43_43 = e4)
% 31.22/8.84 | (4527) all_0_51_51 = e4 | all_0_56_56 = e4
% 31.22/8.84 |
% 31.22/8.84 +-Applying beta-rule and splitting (4527), into two cases.
% 31.22/8.84 |-Branch one:
% 31.22/8.84 | (1467) all_0_51_51 = e4
% 31.22/8.84 |
% 31.22/8.84 | Combining equations (954,1467) yields a new equation:
% 31.22/8.84 | (479) e4 = e0
% 31.22/8.84 |
% 31.22/8.84 | Equations (479) can reduce 6 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.84 |-Branch two:
% 31.22/8.84 | (697) ~ (all_0_51_51 = e4)
% 31.22/8.84 | (4744) all_0_56_56 = e4
% 31.22/8.84 |
% 31.22/8.84 | Equations (4744) can reduce 274 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.84 |-Branch two:
% 31.22/8.84 | (280) ~ (all_0_59_59 = e4)
% 31.22/8.84 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 31.22/8.84 |
% 31.22/8.84 +-Applying beta-rule and splitting (407), into two cases.
% 31.22/8.84 |-Branch one:
% 31.22/8.84 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 31.22/8.84 |
% 31.22/8.84 +-Applying beta-rule and splitting (408), into two cases.
% 31.22/8.84 |-Branch one:
% 31.22/8.84 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 31.22/8.84 |
% 31.22/8.84 +-Applying beta-rule and splitting (409), into two cases.
% 31.22/8.84 |-Branch one:
% 31.22/8.84 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 31.22/8.84 |
% 31.22/8.84 | Applying alpha-rule on (410) yields:
% 31.22/8.84 | (411) all_0_43_43 = e0
% 31.22/8.84 | (412) all_0_59_59 = e3
% 31.22/8.84 | (413) ~ (all_0_46_46 = e3)
% 31.22/8.84 |
% 31.22/8.84 | Equations (411) can reduce 455 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.84 |-Branch two:
% 31.22/8.84 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 31.22/8.84 |
% 31.22/8.84 | Applying alpha-rule on (416) yields:
% 31.22/8.84 | (411) all_0_43_43 = e0
% 31.22/8.84 | (412) all_0_59_59 = e3
% 31.22/8.84 | (419) ~ (all_0_56_56 = e0)
% 31.22/8.84 |
% 31.22/8.84 | Equations (411) can reduce 455 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.84 |-Branch two:
% 31.22/8.84 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 31.22/8.84 |
% 31.22/8.84 | Applying alpha-rule on (422) yields:
% 31.22/8.84 | (423) all_0_53_53 = e0
% 31.22/8.84 | (424) all_0_59_59 = e1
% 31.22/8.84 | (425) ~ (all_0_54_54 = e1)
% 31.22/8.84 |
% 31.22/8.84 | Combining equations (423,576) yields a new equation:
% 31.22/8.84 | (316) e2 = e0
% 31.22/8.84 |
% 31.22/8.84 | Equations (316) can reduce 57 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.84 |-Branch two:
% 31.22/8.84 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 31.22/8.84 |
% 31.22/8.84 | Applying alpha-rule on (428) yields:
% 31.22/8.84 | (423) all_0_53_53 = e0
% 31.22/8.84 | (424) all_0_59_59 = e1
% 31.22/8.84 | (431) ~ (all_0_58_58 = e0)
% 31.22/8.84 |
% 31.22/8.84 | Combining equations (423,576) yields a new equation:
% 31.22/8.84 | (316) e2 = e0
% 31.22/8.84 |
% 31.22/8.84 | Equations (316) can reduce 57 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.84 |-Branch two:
% 31.22/8.84 | (987) ~ (all_0_51_51 = e0)
% 31.22/8.84 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 31.22/8.84 |
% 31.22/8.84 +-Applying beta-rule and splitting (4888), into two cases.
% 31.22/8.84 |-Branch one:
% 31.22/8.84 | (954) all_0_51_51 = e0
% 31.22/8.84 |
% 31.22/8.84 | Equations (954) can reduce 987 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.84 |-Branch two:
% 31.22/8.84 | (987) ~ (all_0_51_51 = e0)
% 31.22/8.84 | (5003) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1
% 31.22/8.84 |
% 31.22/8.84 +-Applying beta-rule and splitting (5003), into two cases.
% 31.22/8.84 |-Branch one:
% 31.22/8.84 | (824) all_0_51_51 = e3
% 31.22/8.84 |
% 31.22/8.84 | Equations (824) can reduce 932 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.84 |-Branch two:
% 31.22/8.84 | (932) ~ (all_0_51_51 = e3)
% 31.22/8.84 | (5007) all_0_51_51 = e4 | all_0_51_51 = e1
% 31.22/8.84 |
% 31.22/8.84 +-Applying beta-rule and splitting (5007), into two cases.
% 31.22/8.84 |-Branch one:
% 31.22/8.84 | (820) all_0_51_51 = e1
% 31.22/8.84 |
% 31.22/8.84 | Equations (820) can reduce 748 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.84 |-Branch two:
% 31.22/8.84 | (748) ~ (all_0_51_51 = e1)
% 31.22/8.84 | (1467) all_0_51_51 = e4
% 31.22/8.84 |
% 31.22/8.84 | Equations (1467) can reduce 697 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.84 |-Branch two:
% 31.22/8.84 | (826) ~ (all_0_52_52 = e3)
% 31.22/8.84 | (1107) all_0_53_53 = e3 | all_0_54_54 = e3
% 31.22/8.84 |
% 31.22/8.84 +-Applying beta-rule and splitting (1107), into two cases.
% 31.22/8.84 |-Branch one:
% 31.22/8.84 | (1114) all_0_53_53 = e3
% 31.22/8.84 |
% 31.22/8.84 | Combining equations (1114,576) yields a new equation:
% 31.22/8.84 | (437) e3 = e2
% 31.22/8.84 |
% 31.22/8.84 | Simplifying 437 yields:
% 31.22/8.84 | (414) e3 = e2
% 31.22/8.84 |
% 31.22/8.84 | Equations (414) can reduce 223 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.84 |-Branch two:
% 31.22/8.84 | (356) ~ (all_0_53_53 = e3)
% 31.22/8.84 | (1119) all_0_54_54 = e3
% 31.22/8.84 |
% 31.22/8.84 | Combining equations (875,1119) yields a new equation:
% 31.22/8.84 | (538) e3 = e1
% 31.22/8.84 |
% 31.22/8.84 | Equations (538) can reduce 136 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.84 |-Branch two:
% 31.22/8.84 | (425) ~ (all_0_54_54 = e1)
% 31.22/8.84 | (424) all_0_59_59 = e1
% 31.22/8.84 |
% 31.22/8.84 | Equations (424) can reduce 750 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.84 |-Branch two:
% 31.22/8.84 | (534) ~ (all_0_40_40 = e1)
% 31.22/8.84 | (3352) all_0_52_52 = e1 | all_0_57_57 = e1
% 31.22/8.84 |
% 31.22/8.84 +-Applying beta-rule and splitting (210), into two cases.
% 31.22/8.84 |-Branch one:
% 31.22/8.84 | (524) all_0_39_39 = e1
% 31.22/8.84 |
% 31.22/8.84 | Combining equations (336,524) yields a new equation:
% 31.22/8.84 | (531) e2 = e1
% 31.22/8.84 |
% 31.22/8.84 | Simplifying 531 yields:
% 31.22/8.84 | (322) e2 = e1
% 31.22/8.84 |
% 31.22/8.84 | Equations (322) can reduce 141 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.84 |-Branch two:
% 31.22/8.84 | (528) ~ (all_0_39_39 = e1)
% 31.22/8.84 | (529) all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1
% 31.22/8.84 |
% 31.22/8.84 +-Applying beta-rule and splitting (603), into two cases.
% 31.22/8.84 |-Branch one:
% 31.22/8.84 | (671) all_0_40_40 = e3
% 31.22/8.84 |
% 31.22/8.84 | Equations (671) can reduce 147 to:
% 31.22/8.84 | (1329) ~ (all_0_41_41 = e3)
% 31.22/8.84 |
% 31.22/8.84 | Simplifying 1329 yields:
% 31.22/8.84 | (1237) ~ (all_0_41_41 = e3)
% 31.22/8.84 |
% 31.22/8.84 | Equations (671) can reduce 145 to:
% 31.22/8.84 | (1331) ~ (all_0_42_42 = e3)
% 31.22/8.84 |
% 31.22/8.84 | Simplifying 1331 yields:
% 31.22/8.84 | (1316) ~ (all_0_42_42 = e3)
% 31.22/8.84 |
% 31.22/8.84 | Equations (671) can reduce 137 to:
% 31.22/8.84 | (825) ~ (all_0_52_52 = e3)
% 31.22/8.84 |
% 31.22/8.84 | Simplifying 825 yields:
% 31.22/8.84 | (826) ~ (all_0_52_52 = e3)
% 31.22/8.84 |
% 31.22/8.84 | Equations (671) can reduce 602 to:
% 31.22/8.84 | (223) ~ (e3 = e2)
% 31.22/8.84 |
% 31.22/8.84 | From (671) and (68) follows:
% 31.22/8.84 | (5921) op(e2, e3) = all_0_13_13
% 31.22/8.84 |
% 31.22/8.84 +-Applying beta-rule and splitting (33), into two cases.
% 31.22/8.84 |-Branch one:
% 31.22/8.84 | (392) all_0_57_57 = e2
% 31.22/8.84 |
% 31.22/8.84 | Equations (392) can reduce 335 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.84 |-Branch two:
% 31.22/8.84 | (335) ~ (all_0_57_57 = e2)
% 31.22/8.84 | (670) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 31.22/8.84 |
% 31.22/8.84 +-Applying beta-rule and splitting (3352), into two cases.
% 31.22/8.84 |-Branch one:
% 31.22/8.84 | (848) all_0_52_52 = e1
% 31.22/8.84 |
% 31.22/8.84 | Equations (848) can reduce 230 to:
% 31.22/8.84 | (1021) ~ (e4 = e1)
% 31.22/8.84 |
% 31.22/8.84 | Simplifying 1021 yields:
% 31.22/8.84 | (251) ~ (e4 = e1)
% 31.22/8.84 |
% 31.22/8.84 | Equations (848) can reduce 826 to:
% 31.22/8.84 | (769) ~ (e3 = e1)
% 31.22/8.84 |
% 31.22/8.84 | Simplifying 769 yields:
% 31.22/8.84 | (136) ~ (e3 = e1)
% 31.22/8.84 |
% 31.22/8.84 | From (848) and (27) follows:
% 31.22/8.84 | (5933) op(e2, e1) = all_0_17_17
% 31.22/8.84 |
% 31.22/8.84 +-Applying beta-rule and splitting (219), into two cases.
% 31.22/8.84 |-Branch one:
% 31.22/8.84 | (351) all_0_41_41 = e3
% 31.22/8.84 |
% 31.22/8.84 | Equations (351) can reduce 1237 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.84 |-Branch two:
% 31.22/8.84 | (1237) ~ (all_0_41_41 = e3)
% 31.22/8.84 | (1508) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 31.22/8.84 |
% 31.22/8.84 +-Applying beta-rule and splitting (626), into two cases.
% 31.22/8.84 |-Branch one:
% 31.22/8.84 | (827) all_0_52_52 = e0
% 31.22/8.84 |
% 31.22/8.84 | Combining equations (827,848) yields a new equation:
% 31.22/8.84 | (560) e1 = e0
% 31.22/8.84 |
% 31.22/8.84 | Equations (560) can reduce 132 to:
% 31.22/8.84 | (270) $false
% 31.22/8.84 |
% 31.22/8.84 |-The branch is then unsatisfiable
% 31.22/8.85 |-Branch two:
% 31.22/8.85 | (925) ~ (all_0_52_52 = e0)
% 31.22/8.85 | (2258) all_0_57_57 = e0
% 31.22/8.85 |
% 31.22/8.85 | Equations (2258) can reduce 335 to:
% 31.22/8.85 | (566) ~ (e2 = e0)
% 31.22/8.85 |
% 31.22/8.85 | Simplifying 566 yields:
% 31.22/8.85 | (57) ~ (e2 = e0)
% 31.22/8.85 |
% 31.22/8.85 | From (2258) and (30) follows:
% 31.22/8.85 | (12293) op(e2, e0) = all_0_19_19
% 31.22/8.85 |
% 31.22/8.85 +-Applying beta-rule and splitting (127), into two cases.
% 31.22/8.85 |-Branch one:
% 31.22/8.85 | (541) all_0_42_42 = e1
% 31.22/8.85 |
% 31.22/8.85 | Equations (541) can reduce 94 to:
% 31.22/8.85 | (540) ~ (all_0_41_41 = e1)
% 31.22/8.85 |
% 31.22/8.85 | Equations (541) can reduce 1316 to:
% 31.22/8.85 | (769) ~ (e3 = e1)
% 31.22/8.85 |
% 31.22/8.85 | Simplifying 769 yields:
% 31.22/8.85 | (136) ~ (e3 = e1)
% 31.22/8.85 |
% 31.22/8.85 | Equations (541) can reduce 199 to:
% 31.22/8.85 | (132) ~ (e1 = e0)
% 31.22/8.85 |
% 31.22/8.85 +-Applying beta-rule and splitting (592), into two cases.
% 31.22/8.85 |-Branch one:
% 31.22/8.85 | (358) all_0_41_41 = e4
% 31.22/8.85 |
% 31.22/8.85 | Equations (358) can reduce 51 to:
% 31.22/8.85 | (503) ~ (all_0_45_45 = e4)
% 31.22/8.85 |
% 31.22/8.85 | Simplifying 503 yields:
% 31.22/8.85 | (352) ~ (all_0_45_45 = e4)
% 31.22/8.85 |
% 31.22/8.85 | Equations (358) can reduce 540 to:
% 31.22/8.85 | (251) ~ (e4 = e1)
% 31.22/8.85 |
% 31.22/8.85 +-Applying beta-rule and splitting (1508), into two cases.
% 31.22/8.85 |-Branch one:
% 31.22/8.85 | (505) all_0_45_45 = e3
% 31.22/8.85 |
% 31.22/8.85 | Equations (505) can reduce 352 to:
% 31.22/8.85 | (719) ~ (e4 = e3)
% 31.22/8.85 |
% 31.22/8.85 | Simplifying 719 yields:
% 31.22/8.85 | (34) ~ (e4 = e3)
% 31.22/8.85 |
% 31.22/8.85 | Instantiating formula (201) with e2, e3, all_0_13_13, e1 and discharging atoms op(e2, e3) = all_0_13_13, op(e2, e3) = e1, yields:
% 31.22/8.85 | (5957) all_0_13_13 = e1
% 31.22/8.85 |
% 31.22/8.85 | Instantiating formula (201) with e2, e1, all_0_17_17, e0 and discharging atoms op(e2, e1) = all_0_17_17, op(e2, e1) = e0, yields:
% 31.22/8.85 | (5880) all_0_17_17 = e0
% 31.22/8.85 |
% 31.22/8.85 | Instantiating formula (201) with e2, e0, all_0_19_19, e2 and discharging atoms op(e2, e0) = all_0_19_19, op(e2, e0) = e2, yields:
% 31.22/8.85 | (14991) all_0_19_19 = e2
% 31.22/8.85 |
% 31.22/8.85 +-Applying beta-rule and splitting (87), into two cases.
% 31.22/8.85 |-Branch one:
% 31.22/8.85 | (650) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 31.22/8.85 |
% 31.22/8.85 +-Applying beta-rule and splitting (650), into two cases.
% 31.22/8.85 |-Branch one:
% 31.22/8.85 | (651) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 31.22/8.85 |
% 31.22/8.85 +-Applying beta-rule and splitting (651), into two cases.
% 31.22/8.85 |-Branch one:
% 31.22/8.85 | (652) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 31.22/8.85 |
% 31.22/8.85 | Applying alpha-rule on (652) yields:
% 31.22/8.85 | (653) all_0_13_13 = e4
% 31.22/8.85 | (654) ~ (all_0_14_14 = e2)
% 31.22/8.85 |
% 31.22/8.85 | Combining equations (5957,653) yields a new equation:
% 31.22/8.85 | (526) e4 = e1
% 31.22/8.85 |
% 31.22/8.85 | Equations (526) can reduce 251 to:
% 31.22/8.85 | (270) $false
% 31.22/8.85 |
% 31.22/8.85 |-The branch is then unsatisfiable
% 31.22/8.85 |-Branch two:
% 31.22/8.85 | (657) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 31.22/8.85 |
% 31.22/8.85 | Applying alpha-rule on (657) yields:
% 31.22/8.85 | (658) all_0_15_15 = e3
% 31.22/8.85 | (659) ~ (all_0_16_16 = e2)
% 31.22/8.85 |
% 31.22/8.85 | Combining equations (620,658) yields a new equation:
% 31.22/8.85 | (660) e4 = e3
% 31.22/8.85 |
% 31.22/8.85 | Simplifying 660 yields:
% 31.22/8.85 | (359) e4 = e3
% 31.22/8.85 |
% 31.22/8.85 | Equations (359) can reduce 34 to:
% 31.22/8.85 | (270) $false
% 31.22/8.85 |
% 31.22/8.85 |-The branch is then unsatisfiable
% 31.22/8.85 |-Branch two:
% 31.22/8.85 | (663) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 31.22/8.85 |
% 31.22/8.85 | Applying alpha-rule on (663) yields:
% 31.22/8.85 | (664) all_0_17_17 = e1
% 31.22/8.85 | (665) ~ (all_0_18_18 = e2)
% 31.22/8.85 |
% 31.22/8.85 | Combining equations (664,5880) yields a new equation:
% 31.22/8.85 | (571) e1 = e0
% 31.22/8.85 |
% 31.22/8.85 | Simplifying 571 yields:
% 31.22/8.85 | (560) e1 = e0
% 31.22/8.85 |
% 31.22/8.85 | Equations (560) can reduce 132 to:
% 31.22/8.85 | (270) $false
% 31.22/8.85 |
% 31.22/8.85 |-The branch is then unsatisfiable
% 31.22/8.85 |-Branch two:
% 31.22/8.85 | (1762) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 31.22/8.85 |
% 31.22/8.85 | Applying alpha-rule on (1762) yields:
% 31.22/8.85 | (1763) all_0_19_19 = e0
% 31.22/8.85 | (1764) ~ (all_0_20_20 = e2)
% 31.22/8.85 |
% 31.22/8.85 | Combining equations (14991,1763) yields a new equation:
% 31.22/8.85 | (622) e2 = e0
% 31.22/8.85 |
% 31.22/8.85 | Simplifying 622 yields:
% 31.22/8.85 | (316) e2 = e0
% 31.22/8.85 |
% 31.22/8.85 | Equations (316) can reduce 57 to:
% 31.22/8.85 | (270) $false
% 31.22/8.85 |
% 31.22/8.85 |-The branch is then unsatisfiable
% 31.22/8.85 |-Branch two:
% 31.22/8.85 | (354) ~ (all_0_45_45 = e3)
% 31.22/8.85 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 31.22/8.85 |
% 31.22/8.85 +-Applying beta-rule and splitting (1539), into two cases.
% 31.22/8.85 |-Branch one:
% 31.22/8.85 | (1114) all_0_53_53 = e3
% 31.22/8.85 |
% 31.22/8.85 | Combining equations (576,1114) yields a new equation:
% 31.22/8.85 | (414) e3 = e2
% 31.22/8.85 |
% 31.22/8.85 | Equations (414) can reduce 223 to:
% 31.22/8.85 | (270) $false
% 31.22/8.85 |
% 31.22/8.85 |-The branch is then unsatisfiable
% 31.22/8.85 |-Branch two:
% 31.22/8.85 | (356) ~ (all_0_53_53 = e3)
% 31.22/8.85 | (4713) all_0_58_58 = e3
% 31.22/8.85 |
% 31.22/8.85 | Combining equations (1001,4713) yields a new equation:
% 31.22/8.85 | (538) e3 = e1
% 31.22/8.85 |
% 31.22/8.85 | Equations (538) can reduce 136 to:
% 31.22/8.85 | (270) $false
% 31.22/8.85 |
% 31.22/8.85 |-The branch is then unsatisfiable
% 31.22/8.85 |-Branch two:
% 31.22/8.85 | (361) ~ (all_0_41_41 = e4)
% 31.22/8.85 | (512) all_0_42_42 = e4
% 31.22/8.85 |
% 31.22/8.85 | Combining equations (512,541) yields a new equation:
% 31.22/8.85 | (525) e4 = e1
% 31.22/8.85 |
% 31.22/8.85 | Simplifying 525 yields:
% 31.22/8.85 | (526) e4 = e1
% 31.22/8.85 |
% 31.22/8.85 | Equations (526) can reduce 251 to:
% 31.22/8.85 | (270) $false
% 31.22/8.85 |
% 31.22/8.85 |-The branch is then unsatisfiable
% 31.22/8.85 |-Branch two:
% 31.22/8.85 | (640) ~ (all_0_42_42 = e1)
% 31.22/8.85 | (4628) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 31.22/8.85 |
% 31.22/8.85 +-Applying beta-rule and splitting (529), into two cases.
% 31.22/8.85 |-Branch one:
% 31.22/8.85 | (530) all_0_40_40 = e1
% 31.22/8.85 |
% 31.22/8.85 | Combining equations (671,530) yields a new equation:
% 31.22/8.85 | (537) e3 = e1
% 31.22/8.85 |
% 31.22/8.85 | Simplifying 537 yields:
% 31.22/8.85 | (538) e3 = e1
% 31.22/8.85 |
% 31.22/8.85 | Equations (538) can reduce 136 to:
% 31.22/8.85 | (270) $false
% 31.22/8.85 |
% 31.22/8.85 |-The branch is then unsatisfiable
% 31.22/8.85 |-Branch two:
% 31.22/8.85 | (534) ~ (all_0_40_40 = e1)
% 31.22/8.85 | (535) all_0_41_41 = e1 | all_0_42_42 = e1
% 31.22/8.85 |
% 31.22/8.85 +-Applying beta-rule and splitting (535), into two cases.
% 31.22/8.85 |-Branch one:
% 31.22/8.85 | (536) all_0_41_41 = e1
% 31.22/8.85 |
% 31.22/8.85 | Equations (536) can reduce 540 to:
% 31.22/8.85 | (270) $false
% 31.22/8.85 |
% 31.22/8.85 |-The branch is then unsatisfiable
% 31.22/8.85 |-Branch two:
% 31.22/8.85 | (540) ~ (all_0_41_41 = e1)
% 31.22/8.85 | (541) all_0_42_42 = e1
% 31.22/8.85 |
% 31.22/8.85 | Equations (541) can reduce 640 to:
% 31.22/8.85 | (270) $false
% 31.22/8.85 |
% 31.22/8.85 |-The branch is then unsatisfiable
% 31.22/8.85 |-Branch two:
% 31.22/8.85 | (642) ~ (all_0_52_52 = e1)
% 31.22/8.85 | (997) all_0_57_57 = e1
% 31.22/8.85 |
% 31.22/8.85 | Equations (997) can reduce 644 to:
% 31.22/8.85 | (270) $false
% 31.22/8.85 |
% 31.22/8.85 |-The branch is then unsatisfiable
% 31.22/8.85 |-Branch two:
% 31.22/8.85 | (675) ~ (all_0_40_40 = e3)
% 31.22/8.85 | (530) all_0_40_40 = e1
% 31.22/8.85 |
% 31.22/8.85 | Equations (530) can reduce 534 to:
% 31.22/8.85 | (270) $false
% 31.22/8.85 |
% 31.22/8.85 |-The branch is then unsatisfiable
% 31.22/8.85 |-Branch two:
% 31.22/8.85 | (259) ~ (all_0_53_53 = e2)
% 31.22/8.85 | (396) all_0_58_58 = e2
% 31.22/8.85 |
% 31.22/8.85 | Equations (396) can reduce 376 to:
% 31.22/8.85 | (270) $false
% 31.22/8.85 |
% 31.22/8.85 |-The branch is then unsatisfiable
% 31.22/8.85 |-Branch two:
% 31.22/8.85 | (333) ~ (all_0_44_44 = e2)
% 31.22/8.85 | (373) all_0_44_44 = e3 | all_0_44_44 = e0
% 31.22/8.85 |
% 31.22/8.85 +-Applying beta-rule and splitting (47), into two cases.
% 31.22/8.85 |-Branch one:
% 31.22/8.85 | (450) all_0_43_43 = e2
% 31.22/8.85 |
% 31.22/8.85 | Equations (450) can reduce 292 to:
% 31.22/8.85 | (270) $false
% 31.22/8.85 |
% 31.22/8.85 |-The branch is then unsatisfiable
% 31.22/8.85 |-Branch two:
% 31.22/8.85 | (292) ~ (all_0_43_43 = e2)
% 31.22/8.85 | (453) all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2
% 31.22/8.85 |
% 31.22/8.85 +-Applying beta-rule and splitting (607), into two cases.
% 31.22/8.85 |-Branch one:
% 31.22/8.85 | (370) all_0_44_44 = e2
% 31.22/8.85 |
% 31.22/8.85 | Equations (370) can reduce 333 to:
% 31.22/8.85 | (270) $false
% 31.22/8.85 |
% 31.22/8.85 |-The branch is then unsatisfiable
% 31.22/8.85 |-Branch two:
% 31.22/8.85 | (333) ~ (all_0_44_44 = e2)
% 31.22/8.85 | (3377) all_0_52_52 = e2 | all_0_57_57 = e2
% 31.22/8.85 |
% 31.22/8.85 +-Applying beta-rule and splitting (3377), into two cases.
% 31.22/8.85 |-Branch one:
% 31.22/8.85 | (685) all_0_52_52 = e2
% 31.22/8.85 |
% 31.22/8.85 | Equations (685) can reduce 137 to:
% 31.22/8.85 | (602) ~ (all_0_40_40 = e2)
% 31.22/8.85 |
% 31.22/8.85 | Equations (685) can reduce 122 to:
% 31.22/8.85 | (333) ~ (all_0_44_44 = e2)
% 31.22/8.85 |
% 31.22/8.85 | Equations (685) can reduce 154 to:
% 31.22/8.85 | (255) ~ (all_0_51_51 = e2)
% 31.22/8.85 |
% 31.22/8.85 | Equations (685) can reduce 235 to:
% 31.22/8.85 | (334) ~ (all_0_57_57 = e2)
% 31.22/8.85 |
% 31.22/8.85 | Simplifying 334 yields:
% 31.22/8.85 | (335) ~ (all_0_57_57 = e2)
% 31.22/8.85 |
% 31.22/8.85 | From (685) and (27) follows:
% 31.22/8.85 | (11734) op(e2, e2) = all_0_17_17
% 31.22/8.85 |
% 31.22/8.85 +-Applying beta-rule and splitting (187), into two cases.
% 31.22/8.85 |-Branch one:
% 31.22/8.85 | (436) all_0_41_41 = e2
% 31.22/8.85 |
% 31.22/8.85 | Equations (436) can reduce 331 to:
% 31.22/8.85 | (270) $false
% 31.22/8.85 |
% 31.22/8.85 |-The branch is then unsatisfiable
% 31.22/8.85 |-Branch two:
% 31.22/8.85 | (331) ~ (all_0_41_41 = e2)
% 31.22/8.85 | (441) all_0_45_45 = e2 | all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 31.22/8.85 |
% 31.22/8.85 +-Applying beta-rule and splitting (453), into two cases.
% 31.22/8.85 |-Branch one:
% 31.22/8.85 | (370) all_0_44_44 = e2
% 31.22/8.85 |
% 31.22/8.85 | Equations (370) can reduce 333 to:
% 31.22/8.85 | (270) $false
% 31.22/8.85 |
% 31.22/8.85 |-The branch is then unsatisfiable
% 31.22/8.85 |-Branch two:
% 31.22/8.85 | (333) ~ (all_0_44_44 = e2)
% 31.22/8.85 | (493) all_0_45_45 = e2 | all_0_46_46 = e2
% 31.22/8.85 |
% 31.22/8.85 +-Applying beta-rule and splitting (441), into two cases.
% 31.22/8.85 |-Branch one:
% 31.22/8.85 | (374) all_0_45_45 = e2
% 31.22/8.85 |
% 31.22/8.85 | Equations (374) can reduce 229 to:
% 31.22/8.85 | (333) ~ (all_0_44_44 = e2)
% 31.22/8.85 |
% 31.22/8.85 | Equations (374) can reduce 38 to:
% 31.22/8.85 | (1435) ~ (all_0_46_46 = e2)
% 31.22/8.85 |
% 31.22/8.85 | Simplifying 1435 yields:
% 31.22/8.85 | (1436) ~ (all_0_46_46 = e2)
% 31.22/8.85 |
% 31.22/8.85 | Equations (374) can reduce 128 to:
% 31.22/8.85 | (258) ~ (all_0_53_53 = e2)
% 31.22/8.85 |
% 31.22/8.85 | Simplifying 258 yields:
% 31.22/8.85 | (259) ~ (all_0_53_53 = e2)
% 31.22/8.85 |
% 31.22/8.85 | Equations (374) can reduce 26 to:
% 31.22/8.85 | (141) ~ (e2 = e1)
% 31.22/8.85 |
% 31.22/8.85 | Instantiating formula (201) with e2, e2, all_0_17_17, e4 and discharging atoms op(e2, e2) = all_0_17_17, op(e2, e2) = e4, yields:
% 31.22/8.85 | (11735) all_0_17_17 = e4
% 31.22/8.85 |
% 31.22/8.85 +-Applying beta-rule and splitting (9), into two cases.
% 31.22/8.85 |-Branch one:
% 31.22/8.85 | (621) all_0_44_44 = e0
% 31.22/8.85 |
% 31.22/8.85 | Equations (621) can reduce 15 to:
% 31.22/8.85 | (238) ~ (all_0_40_40 = e0)
% 31.22/8.85 |
% 31.22/8.85 | Equations (621) can reduce 241 to:
% 31.22/8.85 | (455) ~ (all_0_43_43 = e0)
% 31.22/8.85 |
% 31.22/8.85 | Equations (621) can reduce 174 to:
% 31.22/8.85 | (1057) ~ (all_0_46_46 = e0)
% 31.22/8.85 |
% 31.22/8.85 | Simplifying 1057 yields:
% 31.22/8.85 | (1010) ~ (all_0_46_46 = e0)
% 31.22/8.85 |
% 31.22/8.85 | Equations (621) can reduce 333 to:
% 31.22/8.85 | (566) ~ (e2 = e0)
% 31.22/8.85 |
% 31.22/8.85 | Simplifying 566 yields:
% 31.22/8.85 | (57) ~ (e2 = e0)
% 31.22/8.85 |
% 31.22/8.85 +-Applying beta-rule and splitting (93), into two cases.
% 31.22/8.85 |-Branch one:
% 31.22/8.85 | (402) all_0_59_59 = e4
% 31.22/8.85 |
% 31.22/8.85 | Equations (402) can reduce 17 to:
% 31.22/8.85 | (520) ~ (all_0_42_42 = e4)
% 31.22/8.85 |
% 31.22/8.85 | Equations (402) can reduce 206 to:
% 31.22/8.85 | (805) ~ (all_0_46_46 = e4)
% 31.22/8.85 |
% 31.22/8.85 | Equations (402) can reduce 140 to:
% 31.22/8.85 | (143) ~ (all_0_57_57 = e4)
% 31.22/8.85 |
% 31.22/8.85 | Equations (402) can reduce 701 to:
% 31.22/8.85 | (231) ~ (e4 = e2)
% 31.22/8.85 |
% 31.22/8.85 | From (402) and (161) follows:
% 31.22/8.85 | (11389) op(e0, e0) = e4
% 31.22/8.85 |
% 31.22/8.85 +-Applying beta-rule and splitting (44), into two cases.
% 31.22/8.85 |-Branch one:
% 31.22/8.85 | (502) all_0_43_43 = e4
% 31.22/8.85 |
% 31.22/8.85 | Equations (502) can reduce 103 to:
% 31.22/8.85 | (804) ~ (all_0_46_46 = e4)
% 31.22/8.85 |
% 31.22/8.85 | Simplifying 804 yields:
% 31.22/8.85 | (805) ~ (all_0_46_46 = e4)
% 31.22/8.85 |
% 31.22/8.85 | Equations (502) can reduce 240 to:
% 31.22/8.85 | (696) ~ (all_0_51_51 = e4)
% 31.22/8.85 |
% 31.22/8.85 | Simplifying 696 yields:
% 31.22/8.85 | (697) ~ (all_0_51_51 = e4)
% 31.22/8.85 |
% 31.22/8.85 | Equations (502) can reduce 188 to:
% 31.22/8.85 | (273) ~ (all_0_56_56 = e4)
% 31.22/8.85 |
% 31.22/8.85 | Simplifying 273 yields:
% 31.22/8.85 | (274) ~ (all_0_56_56 = e4)
% 31.22/8.85 |
% 31.22/8.85 +-Applying beta-rule and splitting (592), into two cases.
% 31.22/8.85 |-Branch one:
% 31.22/8.85 | (358) all_0_41_41 = e4
% 31.22/8.85 |
% 31.22/8.85 | Equations (358) can reduce 147 to:
% 31.22/8.85 | (233) ~ (all_0_40_40 = e4)
% 31.22/8.85 |
% 31.22/8.85 | Equations (358) can reduce 214 to:
% 31.22/8.85 | (1444) ~ (all_0_53_53 = e4)
% 31.22/8.85 |
% 31.22/8.85 | Simplifying 1444 yields:
% 31.22/8.85 | (599) ~ (all_0_53_53 = e4)
% 31.22/8.85 |
% 31.22/8.85 | Equations (358) can reduce 157 to:
% 31.22/8.85 | (277) ~ (all_0_58_58 = e4)
% 31.22/8.85 |
% 31.22/8.85 | Simplifying 277 yields:
% 31.22/8.85 | (278) ~ (all_0_58_58 = e4)
% 31.22/8.85 |
% 31.22/8.85 | Equations (358) can reduce 232 to:
% 31.22/8.85 | (6) ~ (e4 = e0)
% 31.22/8.85 |
% 31.22/8.85 +-Applying beta-rule and splitting (22), into two cases.
% 31.22/8.85 |-Branch one:
% 31.22/8.85 | (782) all_0_43_43 = e3
% 31.22/8.85 |
% 31.22/8.85 | Combining equations (502,782) yields a new equation:
% 31.22/8.85 | (660) e4 = e3
% 31.22/8.85 |
% 31.22/8.85 | Simplifying 660 yields:
% 31.22/8.85 | (359) e4 = e3
% 31.22/8.85 |
% 31.22/8.85 | Equations (359) can reduce 34 to:
% 31.22/8.85 | (270) $false
% 31.22/8.85 |
% 31.22/8.85 |-The branch is then unsatisfiable
% 31.22/8.85 |-Branch two:
% 31.22/8.85 | (786) ~ (all_0_43_43 = e3)
% 31.22/8.85 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 31.22/8.85 |
% 31.22/8.85 +-Applying beta-rule and splitting (176), into two cases.
% 31.22/8.85 |-Branch one:
% 31.22/8.85 | (830) all_0_56_56 = e0
% 31.22/8.85 |
% 31.22/8.85 | Equations (830) can reduce 104 to:
% 31.22/8.85 | (9326) ~ (all_0_57_57 = e0)
% 31.22/8.85 |
% 31.22/8.86 | Simplifying 9326 yields:
% 31.22/8.86 | (2301) ~ (all_0_57_57 = e0)
% 31.22/8.86 |
% 31.22/8.86 | Equations (830) can reduce 81 to:
% 31.22/8.86 | (3530) ~ (all_0_58_58 = e0)
% 31.22/8.86 |
% 31.22/8.86 | Simplifying 3530 yields:
% 31.22/8.86 | (431) ~ (all_0_58_58 = e0)
% 31.22/8.86 |
% 31.22/8.86 | Equations (830) can reduce 274 to:
% 31.22/8.86 | (456) ~ (e4 = e0)
% 31.22/8.86 |
% 31.22/8.86 | Simplifying 456 yields:
% 31.22/8.86 | (6) ~ (e4 = e0)
% 31.22/8.86 |
% 31.22/8.86 | Equations (830) can reduce 300 to:
% 31.22/8.86 | (566) ~ (e2 = e0)
% 31.22/8.86 |
% 31.22/8.86 | Simplifying 566 yields:
% 31.22/8.86 | (57) ~ (e2 = e0)
% 31.22/8.86 |
% 31.22/8.86 | Equations (830) can reduce 995 to:
% 31.22/8.86 | (568) ~ (e1 = e0)
% 31.22/8.86 |
% 31.22/8.86 | Simplifying 568 yields:
% 31.22/8.86 | (132) ~ (e1 = e0)
% 31.22/8.86 |
% 31.22/8.86 | From (830) and (245) follows:
% 31.22/8.86 | (18523) op(e0, e3) = e0
% 31.22/8.86 |
% 31.22/8.86 +-Applying beta-rule and splitting (220), into two cases.
% 31.22/8.86 |-Branch one:
% 31.22/8.86 | (497) all_0_46_46 = e2
% 31.22/8.86 |
% 31.22/8.86 | Equations (497) can reduce 1436 to:
% 31.22/8.86 | (270) $false
% 31.22/8.86 |
% 31.22/8.86 |-The branch is then unsatisfiable
% 31.22/8.86 |-Branch two:
% 31.22/8.86 | (1436) ~ (all_0_46_46 = e2)
% 31.22/8.86 | (1523) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e0
% 31.22/8.86 |
% 31.22/8.86 +-Applying beta-rule and splitting (221), into two cases.
% 31.22/8.86 |-Branch one:
% 31.22/8.86 | (1132) all_0_46_46 = e0
% 31.22/8.86 |
% 31.22/8.86 | Equations (1132) can reduce 1010 to:
% 31.22/8.86 | (270) $false
% 31.22/8.86 |
% 31.22/8.86 |-The branch is then unsatisfiable
% 31.22/8.86 |-Branch two:
% 31.22/8.86 | (1010) ~ (all_0_46_46 = e0)
% 31.22/8.86 | (3629) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 31.22/8.86 |
% 31.30/8.86 +-Applying beta-rule and splitting (3629), into two cases.
% 31.30/8.86 |-Branch one:
% 31.30/8.86 | (563) all_0_49_49 = e0
% 31.30/8.86 |
% 31.30/8.86 | Combining equations (307,563) yields a new equation:
% 31.30/8.86 | (622) e2 = e0
% 31.30/8.86 |
% 31.30/8.86 | Simplifying 622 yields:
% 31.30/8.86 | (316) e2 = e0
% 31.30/8.86 |
% 31.30/8.86 | Equations (316) can reduce 57 to:
% 31.30/8.86 | (270) $false
% 31.30/8.86 |
% 31.30/8.86 |-The branch is then unsatisfiable
% 31.30/8.86 |-Branch two:
% 31.30/8.86 | (1231) ~ (all_0_49_49 = e0)
% 31.30/8.86 | (3638) all_0_54_54 = e0 | all_0_59_59 = e0
% 31.30/8.86 |
% 31.30/8.86 +-Applying beta-rule and splitting (3638), into two cases.
% 31.30/8.86 |-Branch one:
% 31.30/8.86 | (3084) all_0_54_54 = e0
% 31.30/8.86 |
% 31.30/8.86 | Equations (3084) can reduce 215 to:
% 31.30/8.86 | (1010) ~ (all_0_46_46 = e0)
% 31.30/8.86 |
% 31.30/8.86 | Equations (3084) can reduce 50 to:
% 31.30/8.86 | (987) ~ (all_0_51_51 = e0)
% 31.30/8.86 |
% 31.30/8.86 | From (3084) and (138) follows:
% 31.30/8.86 | (6320) op(e0, e0) = all_0_36_36
% 31.30/8.86 |
% 31.30/8.86 +-Applying beta-rule and splitting (135), into two cases.
% 31.30/8.86 |-Branch one:
% 31.30/8.86 | (820) all_0_51_51 = e1
% 31.30/8.86 |
% 31.30/8.86 | Equations (820) can reduce 748 to:
% 31.30/8.86 | (270) $false
% 31.30/8.86 |
% 31.30/8.86 |-The branch is then unsatisfiable
% 31.30/8.86 |-Branch two:
% 31.30/8.86 | (748) ~ (all_0_51_51 = e1)
% 31.30/8.86 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 31.30/8.86 |
% 31.30/8.86 +-Applying beta-rule and splitting (173), into two cases.
% 31.30/8.86 |-Branch one:
% 31.30/8.86 | (4215) all_0_51_51 = e2
% 31.30/8.86 |
% 31.30/8.86 | Equations (4215) can reduce 255 to:
% 31.30/8.86 | (270) $false
% 31.30/8.86 |
% 31.30/8.86 |-The branch is then unsatisfiable
% 31.30/8.86 |-Branch two:
% 31.30/8.86 | (255) ~ (all_0_51_51 = e2)
% 31.30/8.86 | (4888) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1 | all_0_51_51 = e0
% 31.30/8.86 |
% 31.30/8.86 +-Applying beta-rule and splitting (823), into two cases.
% 31.30/8.86 |-Branch one:
% 31.30/8.86 | (848) all_0_52_52 = e1
% 31.30/8.86 |
% 31.30/8.86 | Combining equations (685,848) yields a new equation:
% 31.30/8.86 | (531) e2 = e1
% 31.30/8.86 |
% 31.30/8.86 | Simplifying 531 yields:
% 31.30/8.86 | (322) e2 = e1
% 31.30/8.86 |
% 31.30/8.86 | Equations (322) can reduce 141 to:
% 31.30/8.86 | (270) $false
% 31.30/8.86 |
% 31.30/8.86 |-The branch is then unsatisfiable
% 31.30/8.86 |-Branch two:
% 31.30/8.86 | (642) ~ (all_0_52_52 = e1)
% 31.30/8.86 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 31.30/8.86 |
% 31.30/8.86 +-Applying beta-rule and splitting (4888), into two cases.
% 31.30/8.86 |-Branch one:
% 31.30/8.86 | (954) all_0_51_51 = e0
% 31.30/8.86 |
% 31.30/8.86 | Equations (954) can reduce 987 to:
% 31.30/8.86 | (270) $false
% 31.30/8.86 |
% 31.30/8.86 |-The branch is then unsatisfiable
% 31.30/8.86 |-Branch two:
% 31.30/8.86 | (987) ~ (all_0_51_51 = e0)
% 31.30/8.86 | (5003) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1
% 31.30/8.86 |
% 31.30/8.86 +-Applying beta-rule and splitting (5003), into two cases.
% 31.30/8.86 |-Branch one:
% 31.30/8.86 | (824) all_0_51_51 = e3
% 31.30/8.86 |
% 31.30/8.86 | Equations (824) can reduce 12 to:
% 31.30/8.86 | (355) ~ (all_0_53_53 = e3)
% 31.30/8.86 |
% 31.30/8.86 | Simplifying 355 yields:
% 31.30/8.86 | (356) ~ (all_0_53_53 = e3)
% 31.30/8.86 |
% 31.30/8.86 | Equations (824) can reduce 697 to:
% 31.30/8.86 | (719) ~ (e4 = e3)
% 31.30/8.86 |
% 31.30/8.86 | Simplifying 719 yields:
% 31.30/8.86 | (34) ~ (e4 = e3)
% 31.30/8.86 |
% 31.30/8.86 | Equations (824) can reduce 255 to:
% 31.30/8.86 | (223) ~ (e3 = e2)
% 31.30/8.86 |
% 31.30/8.86 | Equations (824) can reduce 748 to:
% 31.30/8.86 | (136) ~ (e3 = e1)
% 31.30/8.86 |
% 31.30/8.86 +-Applying beta-rule and splitting (13), into two cases.
% 31.30/8.86 |-Branch one:
% 31.30/8.86 | (576) all_0_53_53 = e2
% 31.30/8.86 |
% 31.30/8.86 | Equations (576) can reduce 259 to:
% 31.30/8.86 | (270) $false
% 31.30/8.86 |
% 31.30/8.86 |-The branch is then unsatisfiable
% 31.30/8.86 |-Branch two:
% 31.30/8.86 | (259) ~ (all_0_53_53 = e2)
% 31.30/8.86 | (5715) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 31.30/8.86 |
% 31.30/8.86 +-Applying beta-rule and splitting (219), into two cases.
% 31.30/8.86 |-Branch one:
% 31.30/8.86 | (351) all_0_41_41 = e3
% 31.30/8.86 |
% 31.30/8.86 | Combining equations (351,358) yields a new equation:
% 31.30/8.86 | (359) e4 = e3
% 31.30/8.86 |
% 31.30/8.86 | Equations (359) can reduce 34 to:
% 31.30/8.86 | (270) $false
% 31.30/8.86 |
% 31.30/8.86 |-The branch is then unsatisfiable
% 31.30/8.86 |-Branch two:
% 31.30/8.86 | (1237) ~ (all_0_41_41 = e3)
% 31.30/8.86 | (1508) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 31.30/8.86 |
% 31.30/8.86 +-Applying beta-rule and splitting (1508), into two cases.
% 31.30/8.86 |-Branch one:
% 31.30/8.86 | (505) all_0_45_45 = e3
% 31.30/8.86 |
% 31.30/8.86 | Combining equations (374,505) yields a new equation:
% 31.30/8.86 | (414) e3 = e2
% 31.30/8.86 |
% 31.30/8.86 | Equations (414) can reduce 223 to:
% 31.30/8.86 | (270) $false
% 31.30/8.86 |
% 31.30/8.86 |-The branch is then unsatisfiable
% 31.30/8.86 |-Branch two:
% 31.30/8.86 | (354) ~ (all_0_45_45 = e3)
% 31.30/8.86 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 31.30/8.86 |
% 31.30/8.86 +-Applying beta-rule and splitting (1539), into two cases.
% 31.30/8.86 |-Branch one:
% 31.30/8.86 | (1114) all_0_53_53 = e3
% 31.30/8.86 |
% 31.30/8.86 | Equations (1114) can reduce 356 to:
% 31.30/8.86 | (270) $false
% 31.30/8.86 |
% 31.30/8.86 |-The branch is then unsatisfiable
% 31.30/8.86 |-Branch two:
% 31.30/8.86 | (356) ~ (all_0_53_53 = e3)
% 31.30/8.86 | (4713) all_0_58_58 = e3
% 31.30/8.86 |
% 31.30/8.86 | Equations (4713) can reduce 37 to:
% 31.30/8.86 | (846) ~ (all_0_57_57 = e3)
% 31.30/8.86 |
% 31.30/8.86 | Equations (4713) can reduce 278 to:
% 31.30/8.86 | (719) ~ (e4 = e3)
% 31.30/8.86 |
% 31.30/8.86 | Simplifying 719 yields:
% 31.30/8.86 | (34) ~ (e4 = e3)
% 31.30/8.86 |
% 31.30/8.86 | Equations (4713) can reduce 431 to:
% 31.30/8.86 | (66) ~ (e3 = e0)
% 31.30/8.86 |
% 31.30/8.86 | From (4713) and (61) follows:
% 31.30/8.86 | (18589) op(e0, e3) = all_0_29_29
% 31.30/8.86 |
% 31.30/8.86 | From (4713) and (228) follows:
% 31.30/8.86 | (18590) op(e0, e1) = e3
% 31.30/8.86 |
% 31.30/8.86 +-Applying beta-rule and splitting (127), into two cases.
% 31.30/8.86 |-Branch one:
% 31.30/8.86 | (541) all_0_42_42 = e1
% 31.30/8.86 |
% 31.30/8.86 | Equations (541) can reduce 145 to:
% 31.30/8.86 | (534) ~ (all_0_40_40 = e1)
% 31.30/8.86 |
% 31.30/8.86 | Equations (541) can reduce 498 to:
% 31.30/8.86 | (645) ~ (e2 = e1)
% 31.30/8.86 |
% 31.30/8.86 | Simplifying 645 yields:
% 31.30/8.86 | (141) ~ (e2 = e1)
% 31.30/8.86 |
% 31.30/8.86 | From (541) and (243) follows:
% 31.30/8.86 | (6205) op(e0, e1) = all_0_30_30
% 31.30/8.86 |
% 31.30/8.86 +-Applying beta-rule and splitting (8), into two cases.
% 31.30/8.86 |-Branch one:
% 31.30/8.86 | (530) all_0_40_40 = e1
% 31.30/8.86 |
% 31.30/8.86 | Equations (530) can reduce 534 to:
% 31.30/8.86 | (270) $false
% 31.30/8.86 |
% 31.30/8.86 |-The branch is then unsatisfiable
% 31.30/8.86 |-Branch two:
% 31.30/8.86 | (534) ~ (all_0_40_40 = e1)
% 31.30/8.86 | (3352) all_0_52_52 = e1 | all_0_57_57 = e1
% 31.30/8.86 |
% 31.30/8.86 +-Applying beta-rule and splitting (133), into two cases.
% 31.30/8.86 |-Branch one:
% 31.30/8.86 | (671) all_0_40_40 = e3
% 31.30/8.86 |
% 31.30/8.86 | Equations (671) can reduce 233 to:
% 31.30/8.86 | (719) ~ (e4 = e3)
% 31.30/8.86 |
% 31.30/8.86 | Simplifying 719 yields:
% 31.30/8.86 | (34) ~ (e4 = e3)
% 31.30/8.86 |
% 31.30/8.86 | Equations (671) can reduce 534 to:
% 31.30/8.86 | (136) ~ (e3 = e1)
% 31.30/8.86 |
% 31.30/8.86 | Equations (671) can reduce 238 to:
% 31.30/8.86 | (66) ~ (e3 = e0)
% 31.30/8.86 |
% 31.30/8.86 +-Applying beta-rule and splitting (95), into two cases.
% 31.30/8.86 |-Branch one:
% 31.30/8.86 | (1258) all_0_42_42 = e3
% 31.30/8.86 |
% 31.30/8.86 | Combining equations (1258,541) yields a new equation:
% 31.30/8.86 | (537) e3 = e1
% 31.30/8.86 |
% 31.30/8.86 | Simplifying 537 yields:
% 31.30/8.86 | (538) e3 = e1
% 31.30/8.86 |
% 31.30/8.86 | Equations (538) can reduce 136 to:
% 31.30/8.86 | (270) $false
% 31.30/8.86 |
% 31.30/8.86 |-The branch is then unsatisfiable
% 31.30/8.86 |-Branch two:
% 31.30/8.86 | (1316) ~ (all_0_42_42 = e3)
% 31.30/8.86 | (3656) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 31.30/8.86 |
% 31.30/8.86 +-Applying beta-rule and splitting (3352), into two cases.
% 31.30/8.86 |-Branch one:
% 31.30/8.86 | (848) all_0_52_52 = e1
% 31.30/8.86 |
% 31.30/8.86 | Combining equations (685,848) yields a new equation:
% 31.30/8.86 | (531) e2 = e1
% 31.30/8.86 |
% 31.30/8.86 | Simplifying 531 yields:
% 31.30/8.86 | (322) e2 = e1
% 31.30/8.86 |
% 31.30/8.86 | Equations (322) can reduce 141 to:
% 31.30/8.86 | (270) $false
% 31.30/8.86 |
% 31.30/8.86 |-The branch is then unsatisfiable
% 31.30/8.86 |-Branch two:
% 31.30/8.86 | (642) ~ (all_0_52_52 = e1)
% 31.30/8.86 | (997) all_0_57_57 = e1
% 31.30/8.86 |
% 31.30/8.86 | Combining equations (997,6095) yields a new equation:
% 31.30/8.86 | (18617) all_0_34_34 = e1
% 31.30/8.86 |
% 31.30/8.86 | Equations (997) can reduce 2301 to:
% 31.30/8.86 | (132) ~ (e1 = e0)
% 31.30/8.86 |
% 31.30/8.86 | From (997) and (120) follows:
% 31.30/8.87 | (6976) op(e0, e1) = all_0_20_20
% 31.30/8.87 |
% 31.30/8.87 +-Applying beta-rule and splitting (3656), into two cases.
% 31.30/8.87 |-Branch one:
% 31.30/8.87 | (1091) all_0_46_46 = e3
% 31.30/8.87 |
% 31.30/8.87 | Equations (1091) can reduce 805 to:
% 31.30/8.87 | (719) ~ (e4 = e3)
% 31.30/8.87 |
% 31.30/8.87 | Simplifying 719 yields:
% 31.30/8.87 | (34) ~ (e4 = e3)
% 31.30/8.87 |
% 31.30/8.87 | Equations (1091) can reduce 1010 to:
% 31.30/8.87 | (66) ~ (e3 = e0)
% 31.30/8.87 |
% 31.30/8.87 | From (1091) and (89) follows:
% 31.30/8.87 | (18624) op(e0, e3) = all_0_32_32
% 31.30/8.87 |
% 31.30/8.87 +-Applying beta-rule and splitting (852), into two cases.
% 31.30/8.87 |-Branch one:
% 31.30/8.87 | (853) all_0_53_53 = e1
% 31.30/8.87 |
% 31.30/8.87 | Equations (853) can reduce 599 to:
% 31.30/8.87 | (1021) ~ (e4 = e1)
% 31.30/8.87 |
% 31.30/8.87 | Simplifying 1021 yields:
% 31.30/8.87 | (251) ~ (e4 = e1)
% 31.30/8.87 |
% 31.30/8.87 | Equations (853) can reduce 259 to:
% 31.30/8.87 | (645) ~ (e2 = e1)
% 31.30/8.87 |
% 31.30/8.87 | Simplifying 645 yields:
% 31.30/8.87 | (141) ~ (e2 = e1)
% 31.30/8.87 |
% 31.30/8.87 | Instantiating formula (201) with e0, e3, all_0_32_32, all_0_29_29 and discharging atoms op(e0, e3) = all_0_29_29, op(e0, e3) = all_0_32_32, yields:
% 31.30/8.87 | (18630) all_0_29_29 = all_0_32_32
% 31.30/8.87 |
% 31.30/8.87 | Instantiating formula (201) with e0, e3, e0, all_0_29_29 and discharging atoms op(e0, e3) = all_0_29_29, op(e0, e3) = e0, yields:
% 31.30/8.87 | (18631) all_0_29_29 = e0
% 31.30/8.87 |
% 31.30/8.87 | Instantiating formula (201) with e0, e1, all_0_30_30, all_0_20_20 and discharging atoms op(e0, e1) = all_0_20_20, op(e0, e1) = all_0_30_30, yields:
% 31.30/8.87 | (18632) all_0_20_20 = all_0_30_30
% 31.30/8.87 |
% 31.30/8.87 | Instantiating formula (201) with e0, e1, e3, all_0_20_20 and discharging atoms op(e0, e1) = all_0_20_20, op(e0, e1) = e3, yields:
% 31.30/8.87 | (6344) all_0_20_20 = e3
% 31.30/8.87 |
% 31.30/8.87 | Instantiating formula (201) with e0, e0, e4, all_0_36_36 and discharging atoms op(e0, e0) = all_0_36_36, op(e0, e0) = e4, yields:
% 31.30/8.87 | (11850) all_0_36_36 = e4
% 31.30/8.87 |
% 31.30/8.87 | Combining equations (6344,18632) yields a new equation:
% 31.30/8.87 | (18635) all_0_30_30 = e3
% 31.30/8.87 |
% 31.30/8.87 | Combining equations (18630,18631) yields a new equation:
% 31.30/8.87 | (18636) all_0_32_32 = e0
% 31.30/8.87 |
% 31.30/8.87 | Simplifying 18636 yields:
% 31.30/8.87 | (15273) all_0_32_32 = e0
% 31.30/8.87 |
% 31.30/8.87 +-Applying beta-rule and splitting (111), into two cases.
% 31.30/8.87 |-Branch one:
% 31.30/8.87 | (4557) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0)) | (all_0_34_34 = e2 & ~ (all_0_35_35 = e0))
% 31.30/8.87 |
% 31.30/8.87 +-Applying beta-rule and splitting (4557), into two cases.
% 31.30/8.87 |-Branch one:
% 31.30/8.87 | (4558) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0))
% 31.30/8.87 |
% 31.30/8.87 +-Applying beta-rule and splitting (4558), into two cases.
% 31.30/8.87 |-Branch one:
% 31.30/8.87 | (4559) all_0_30_30 = e4 & ~ (all_0_31_31 = e0)
% 31.30/8.87 |
% 31.30/8.87 | Applying alpha-rule on (4559) yields:
% 31.30/8.87 | (4560) all_0_30_30 = e4
% 31.30/8.87 | (4561) ~ (all_0_31_31 = e0)
% 31.30/8.87 |
% 31.30/8.87 | Combining equations (4560,18635) yields a new equation:
% 31.30/8.87 | (660) e4 = e3
% 31.30/8.87 |
% 31.30/8.87 | Simplifying 660 yields:
% 31.30/8.87 | (359) e4 = e3
% 31.30/8.87 |
% 31.30/8.87 | Equations (359) can reduce 34 to:
% 31.30/8.87 | (270) $false
% 31.30/8.87 |
% 31.30/8.87 |-The branch is then unsatisfiable
% 31.30/8.87 |-Branch two:
% 31.30/8.87 | (4565) all_0_32_32 = e3 & ~ (all_0_33_33 = e0)
% 31.30/8.87 |
% 31.30/8.87 | Applying alpha-rule on (4565) yields:
% 31.30/8.87 | (4566) all_0_32_32 = e3
% 31.30/8.87 | (4567) ~ (all_0_33_33 = e0)
% 31.30/8.87 |
% 31.30/8.87 | Combining equations (4566,15273) yields a new equation:
% 31.30/8.87 | (783) e3 = e0
% 31.30/8.87 |
% 31.30/8.87 | Simplifying 783 yields:
% 31.30/8.87 | (784) e3 = e0
% 31.30/8.87 |
% 31.30/8.87 | Equations (784) can reduce 66 to:
% 31.30/8.87 | (270) $false
% 31.30/8.87 |
% 31.30/8.87 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (4571) all_0_34_34 = e2 & ~ (all_0_35_35 = e0)
% 31.30/8.88 |
% 31.30/8.88 | Applying alpha-rule on (4571) yields:
% 31.30/8.88 | (4572) all_0_34_34 = e2
% 31.30/8.88 | (4573) ~ (all_0_35_35 = e0)
% 31.30/8.88 |
% 31.30/8.88 | Combining equations (4572,18617) yields a new equation:
% 31.30/8.88 | (531) e2 = e1
% 31.30/8.88 |
% 31.30/8.88 | Simplifying 531 yields:
% 31.30/8.88 | (322) e2 = e1
% 31.30/8.88 |
% 31.30/8.88 | Equations (322) can reduce 141 to:
% 31.30/8.88 | (270) $false
% 31.30/8.88 |
% 31.30/8.88 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (4577) all_0_36_36 = e1 & ~ (all_0_37_37 = e0)
% 31.30/8.88 |
% 31.30/8.88 | Applying alpha-rule on (4577) yields:
% 31.30/8.88 | (4578) all_0_36_36 = e1
% 31.30/8.88 | (4579) ~ (all_0_37_37 = e0)
% 31.30/8.88 |
% 31.30/8.88 | Combining equations (11850,4578) yields a new equation:
% 31.30/8.88 | (525) e4 = e1
% 31.30/8.88 |
% 31.30/8.88 | Simplifying 525 yields:
% 31.30/8.88 | (526) e4 = e1
% 31.30/8.88 |
% 31.30/8.88 | Equations (526) can reduce 251 to:
% 31.30/8.88 | (270) $false
% 31.30/8.88 |
% 31.30/8.88 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (874) ~ (all_0_53_53 = e1)
% 31.30/8.88 | (875) all_0_54_54 = e1
% 31.30/8.88 |
% 31.30/8.88 | Combining equations (875,3084) yields a new equation:
% 31.30/8.88 | (571) e1 = e0
% 31.30/8.88 |
% 31.30/8.88 | Simplifying 571 yields:
% 31.30/8.88 | (560) e1 = e0
% 31.30/8.88 |
% 31.30/8.88 | Equations (560) can reduce 132 to:
% 31.30/8.88 | (270) $false
% 31.30/8.88 |
% 31.30/8.88 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (413) ~ (all_0_46_46 = e3)
% 31.30/8.88 | (3700) all_0_54_54 = e3 | all_0_59_59 = e3
% 31.30/8.88 |
% 31.30/8.88 +-Applying beta-rule and splitting (3700), into two cases.
% 31.30/8.88 |-Branch one:
% 31.30/8.88 | (1119) all_0_54_54 = e3
% 31.30/8.88 |
% 31.30/8.88 | Combining equations (3084,1119) yields a new equation:
% 31.30/8.88 | (784) e3 = e0
% 31.30/8.88 |
% 31.30/8.88 | Equations (784) can reduce 66 to:
% 31.30/8.88 | (270) $false
% 31.30/8.88 |
% 31.30/8.88 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (1093) ~ (all_0_54_54 = e3)
% 31.30/8.88 | (412) all_0_59_59 = e3
% 31.30/8.88 |
% 31.30/8.88 | Combining equations (402,412) yields a new equation:
% 31.30/8.88 | (660) e4 = e3
% 31.30/8.88 |
% 31.30/8.88 | Simplifying 660 yields:
% 31.30/8.88 | (359) e4 = e3
% 31.30/8.88 |
% 31.30/8.88 | Equations (359) can reduce 34 to:
% 31.30/8.88 | (270) $false
% 31.30/8.88 |
% 31.30/8.88 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (675) ~ (all_0_40_40 = e3)
% 31.30/8.88 | (676) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 31.30/8.88 |
% 31.30/8.88 +-Applying beta-rule and splitting (95), into two cases.
% 31.30/8.88 |-Branch one:
% 31.30/8.88 | (1258) all_0_42_42 = e3
% 31.30/8.88 |
% 31.30/8.88 | Combining equations (1258,541) yields a new equation:
% 31.30/8.88 | (537) e3 = e1
% 31.30/8.88 |
% 31.30/8.88 | Simplifying 537 yields:
% 31.30/8.88 | (538) e3 = e1
% 31.30/8.88 |
% 31.30/8.88 | Equations (538) can reduce 136 to:
% 31.30/8.88 | (270) $false
% 31.30/8.88 |
% 31.30/8.88 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (1316) ~ (all_0_42_42 = e3)
% 31.30/8.88 | (3656) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 31.30/8.88 |
% 31.30/8.88 +-Applying beta-rule and splitting (3656), into two cases.
% 31.30/8.88 |-Branch one:
% 31.30/8.88 | (1091) all_0_46_46 = e3
% 31.30/8.88 |
% 31.30/8.88 | Equations (1091) can reduce 1436 to:
% 31.30/8.88 | (223) ~ (e3 = e2)
% 31.30/8.88 |
% 31.30/8.88 | Equations (1091) can reduce 1010 to:
% 31.30/8.88 | (66) ~ (e3 = e0)
% 31.30/8.88 |
% 31.30/8.88 +-Applying beta-rule and splitting (3352), into two cases.
% 31.30/8.88 |-Branch one:
% 31.30/8.88 | (848) all_0_52_52 = e1
% 31.30/8.88 |
% 31.30/8.88 | Combining equations (685,848) yields a new equation:
% 31.30/8.88 | (531) e2 = e1
% 31.30/8.88 |
% 31.30/8.88 | Simplifying 531 yields:
% 31.30/8.88 | (322) e2 = e1
% 31.30/8.88 |
% 31.30/8.88 | Equations (322) can reduce 141 to:
% 31.30/8.88 | (270) $false
% 31.30/8.88 |
% 31.30/8.88 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (642) ~ (all_0_52_52 = e1)
% 31.30/8.88 | (997) all_0_57_57 = e1
% 31.30/8.88 |
% 31.30/8.88 | Equations (997) can reduce 846 to:
% 31.30/8.88 | (769) ~ (e3 = e1)
% 31.30/8.88 |
% 31.30/8.88 | Simplifying 769 yields:
% 31.30/8.88 | (136) ~ (e3 = e1)
% 31.30/8.88 |
% 31.30/8.88 +-Applying beta-rule and splitting (676), into two cases.
% 31.30/8.88 |-Branch one:
% 31.30/8.88 | (858) all_0_44_44 = e3
% 31.30/8.88 |
% 31.30/8.88 | Combining equations (621,858) yields a new equation:
% 31.30/8.88 | (784) e3 = e0
% 31.30/8.88 |
% 31.30/8.88 | Equations (784) can reduce 66 to:
% 31.30/8.88 | (270) $false
% 31.30/8.88 |
% 31.30/8.88 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (862) ~ (all_0_44_44 = e3)
% 31.30/8.88 | (863) all_0_52_52 = e3 | all_0_57_57 = e3
% 31.30/8.88 |
% 31.30/8.88 +-Applying beta-rule and splitting (863), into two cases.
% 31.30/8.88 |-Branch one:
% 31.30/8.88 | (864) all_0_52_52 = e3
% 31.30/8.88 |
% 31.30/8.88 | Combining equations (685,864) yields a new equation:
% 31.30/8.88 | (414) e3 = e2
% 31.30/8.88 |
% 31.30/8.88 | Equations (414) can reduce 223 to:
% 31.30/8.88 | (270) $false
% 31.30/8.88 |
% 31.30/8.88 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (826) ~ (all_0_52_52 = e3)
% 31.30/8.88 | (869) all_0_57_57 = e3
% 31.30/8.88 |
% 31.30/8.88 | Combining equations (869,997) yields a new equation:
% 31.30/8.88 | (537) e3 = e1
% 31.30/8.88 |
% 31.30/8.88 | Simplifying 537 yields:
% 31.30/8.88 | (538) e3 = e1
% 31.30/8.88 |
% 31.30/8.88 | Equations (538) can reduce 136 to:
% 31.30/8.88 | (270) $false
% 31.30/8.88 |
% 31.30/8.88 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (413) ~ (all_0_46_46 = e3)
% 31.30/8.88 | (3700) all_0_54_54 = e3 | all_0_59_59 = e3
% 31.30/8.88 |
% 31.30/8.88 +-Applying beta-rule and splitting (787), into two cases.
% 31.30/8.88 |-Branch one:
% 31.30/8.88 | (858) all_0_44_44 = e3
% 31.30/8.88 |
% 31.30/8.88 | Combining equations (621,858) yields a new equation:
% 31.30/8.88 | (784) e3 = e0
% 31.30/8.88 |
% 31.30/8.88 | Equations (784) can reduce 66 to:
% 31.30/8.88 | (270) $false
% 31.30/8.88 |
% 31.30/8.88 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (862) ~ (all_0_44_44 = e3)
% 31.30/8.88 | (1070) all_0_45_45 = e3 | all_0_46_46 = e3
% 31.30/8.88 |
% 31.30/8.88 | Equations (621) can reduce 862 to:
% 31.30/8.88 | (788) ~ (e3 = e0)
% 31.30/8.88 |
% 31.30/8.88 | Simplifying 788 yields:
% 31.30/8.88 | (66) ~ (e3 = e0)
% 31.30/8.88 |
% 31.30/8.88 +-Applying beta-rule and splitting (3700), into two cases.
% 31.30/8.88 |-Branch one:
% 31.30/8.88 | (1119) all_0_54_54 = e3
% 31.30/8.88 |
% 31.30/8.88 | Combining equations (3084,1119) yields a new equation:
% 31.30/8.88 | (784) e3 = e0
% 31.30/8.88 |
% 31.30/8.88 | Equations (784) can reduce 66 to:
% 31.30/8.88 | (270) $false
% 31.30/8.88 |
% 31.30/8.88 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (1093) ~ (all_0_54_54 = e3)
% 31.30/8.88 | (412) all_0_59_59 = e3
% 31.30/8.88 |
% 31.30/8.88 | Combining equations (402,412) yields a new equation:
% 31.30/8.88 | (660) e4 = e3
% 31.30/8.88 |
% 31.30/8.88 | Simplifying 660 yields:
% 31.30/8.88 | (359) e4 = e3
% 31.30/8.88 |
% 31.30/8.88 | Equations (359) can reduce 34 to:
% 31.30/8.88 | (270) $false
% 31.30/8.88 |
% 31.30/8.88 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (640) ~ (all_0_42_42 = e1)
% 31.30/8.88 | (4628) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 31.30/8.88 |
% 31.30/8.88 +-Applying beta-rule and splitting (194), into two cases.
% 31.30/8.88 |-Branch one:
% 31.30/8.88 | (747) all_0_56_56 = e1
% 31.30/8.88 |
% 31.30/8.88 | Combining equations (747,830) yields a new equation:
% 31.30/8.88 | (571) e1 = e0
% 31.30/8.88 |
% 31.30/8.88 | Simplifying 571 yields:
% 31.30/8.88 | (560) e1 = e0
% 31.30/8.88 |
% 31.30/8.88 | Equations (560) can reduce 132 to:
% 31.30/8.88 | (270) $false
% 31.30/8.88 |
% 31.30/8.88 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (995) ~ (all_0_56_56 = e1)
% 31.30/8.88 | (996) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 31.30/8.88 |
% 31.30/8.88 | Equations (830) can reduce 995 to:
% 31.30/8.88 | (568) ~ (e1 = e0)
% 31.30/8.88 |
% 31.30/8.88 | Simplifying 568 yields:
% 31.30/8.88 | (132) ~ (e1 = e0)
% 31.30/8.88 |
% 31.30/8.88 +-Applying beta-rule and splitting (852), into two cases.
% 31.30/8.88 |-Branch one:
% 31.30/8.88 | (853) all_0_53_53 = e1
% 31.30/8.88 |
% 31.30/8.88 | Equations (853) can reduce 599 to:
% 31.30/8.88 | (1021) ~ (e4 = e1)
% 31.30/8.88 |
% 31.30/8.88 | Simplifying 1021 yields:
% 31.30/8.88 | (251) ~ (e4 = e1)
% 31.30/8.88 |
% 31.30/8.88 +-Applying beta-rule and splitting (996), into two cases.
% 31.30/8.88 |-Branch one:
% 31.30/8.88 | (997) all_0_57_57 = e1
% 31.30/8.88 |
% 31.30/8.88 | Equations (997) can reduce 149 to:
% 31.30/8.88 | (534) ~ (all_0_40_40 = e1)
% 31.30/8.88 |
% 31.30/8.88 | Equations (997) can reduce 143 to:
% 31.30/8.88 | (1021) ~ (e4 = e1)
% 31.30/8.88 |
% 31.30/8.88 | Simplifying 1021 yields:
% 31.30/8.88 | (251) ~ (e4 = e1)
% 31.30/8.88 |
% 31.30/8.88 | Equations (997) can reduce 335 to:
% 31.30/8.88 | (645) ~ (e2 = e1)
% 31.30/8.88 |
% 31.30/8.88 | Simplifying 645 yields:
% 31.30/8.88 | (141) ~ (e2 = e1)
% 31.30/8.88 |
% 31.30/8.88 +-Applying beta-rule and splitting (210), into two cases.
% 31.30/8.88 |-Branch one:
% 31.30/8.88 | (524) all_0_39_39 = e1
% 31.30/8.88 |
% 31.30/8.88 | Combining equations (524,336) yields a new equation:
% 31.30/8.88 | (322) e2 = e1
% 31.30/8.88 |
% 31.30/8.88 | Equations (322) can reduce 141 to:
% 31.30/8.88 | (270) $false
% 31.30/8.88 |
% 31.30/8.88 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (528) ~ (all_0_39_39 = e1)
% 31.30/8.88 | (529) all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1
% 31.30/8.88 |
% 31.30/8.88 +-Applying beta-rule and splitting (603), into two cases.
% 31.30/8.88 |-Branch one:
% 31.30/8.88 | (671) all_0_40_40 = e3
% 31.30/8.88 |
% 31.30/8.88 | Equations (671) can reduce 534 to:
% 31.30/8.88 | (136) ~ (e3 = e1)
% 31.30/8.88 |
% 31.30/8.88 +-Applying beta-rule and splitting (529), into two cases.
% 31.30/8.88 |-Branch one:
% 31.30/8.88 | (530) all_0_40_40 = e1
% 31.30/8.88 |
% 31.30/8.88 | Combining equations (530,671) yields a new equation:
% 31.30/8.88 | (538) e3 = e1
% 31.30/8.88 |
% 31.30/8.88 | Equations (538) can reduce 136 to:
% 31.30/8.88 | (270) $false
% 31.30/8.88 |
% 31.30/8.88 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (534) ~ (all_0_40_40 = e1)
% 31.30/8.88 | (535) all_0_41_41 = e1 | all_0_42_42 = e1
% 31.30/8.88 |
% 31.30/8.88 +-Applying beta-rule and splitting (535), into two cases.
% 31.30/8.88 |-Branch one:
% 31.30/8.88 | (536) all_0_41_41 = e1
% 31.30/8.88 |
% 31.30/8.88 | Combining equations (536,358) yields a new equation:
% 31.30/8.88 | (526) e4 = e1
% 31.30/8.88 |
% 31.30/8.88 | Equations (526) can reduce 251 to:
% 31.30/8.88 | (270) $false
% 31.30/8.88 |
% 31.30/8.88 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (540) ~ (all_0_41_41 = e1)
% 31.30/8.88 | (541) all_0_42_42 = e1
% 31.30/8.88 |
% 31.30/8.88 | Equations (541) can reduce 640 to:
% 31.30/8.88 | (270) $false
% 31.30/8.88 |
% 31.30/8.88 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (675) ~ (all_0_40_40 = e3)
% 31.30/8.88 | (530) all_0_40_40 = e1
% 31.30/8.88 |
% 31.30/8.88 | Equations (530) can reduce 534 to:
% 31.30/8.88 | (270) $false
% 31.30/8.88 |
% 31.30/8.88 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (644) ~ (all_0_57_57 = e1)
% 31.30/8.88 | (1000) all_0_58_58 = e1 | all_0_59_59 = e1
% 31.30/8.88 |
% 31.30/8.88 +-Applying beta-rule and splitting (8), into two cases.
% 31.30/8.88 |-Branch one:
% 31.30/8.88 | (530) all_0_40_40 = e1
% 31.30/8.88 |
% 31.30/8.88 | Equations (530) can reduce 233 to:
% 31.30/8.88 | (1021) ~ (e4 = e1)
% 31.30/8.88 |
% 31.30/8.88 | Simplifying 1021 yields:
% 31.30/8.88 | (251) ~ (e4 = e1)
% 31.30/8.88 |
% 31.30/8.88 | Equations (530) can reduce 602 to:
% 31.30/8.88 | (645) ~ (e2 = e1)
% 31.30/8.88 |
% 31.30/8.88 | Simplifying 645 yields:
% 31.30/8.88 | (141) ~ (e2 = e1)
% 31.30/8.88 |
% 31.30/8.88 | Equations (530) can reduce 238 to:
% 31.30/8.88 | (132) ~ (e1 = e0)
% 31.30/8.88 |
% 31.30/8.88 +-Applying beta-rule and splitting (4628), into two cases.
% 31.30/8.88 |-Branch one:
% 31.30/8.88 | (589) all_0_49_49 = e1
% 31.30/8.88 |
% 31.30/8.88 | Combining equations (589,307) yields a new equation:
% 31.30/8.88 | (322) e2 = e1
% 31.30/8.88 |
% 31.30/8.88 | Equations (322) can reduce 141 to:
% 31.30/8.88 | (270) $false
% 31.30/8.88 |
% 31.30/8.88 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (543) ~ (all_0_49_49 = e1)
% 31.30/8.88 | (4726) all_0_54_54 = e1 | all_0_59_59 = e1
% 31.30/8.88 |
% 31.30/8.88 +-Applying beta-rule and splitting (4726), into two cases.
% 31.30/8.88 |-Branch one:
% 31.30/8.88 | (875) all_0_54_54 = e1
% 31.30/8.88 |
% 31.30/8.88 | Combining equations (3084,875) yields a new equation:
% 31.30/8.88 | (560) e1 = e0
% 31.30/8.88 |
% 31.30/8.88 | Equations (560) can reduce 132 to:
% 31.30/8.88 | (270) $false
% 31.30/8.88 |
% 31.30/8.88 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (425) ~ (all_0_54_54 = e1)
% 31.30/8.88 | (424) all_0_59_59 = e1
% 31.30/8.88 |
% 31.30/8.88 | Combining equations (424,402) yields a new equation:
% 31.30/8.88 | (526) e4 = e1
% 31.30/8.88 |
% 31.30/8.88 | Equations (526) can reduce 251 to:
% 31.30/8.88 | (270) $false
% 31.30/8.88 |
% 31.30/8.88 |-The branch is then unsatisfiable
% 31.30/8.88 |-Branch two:
% 31.30/8.88 | (534) ~ (all_0_40_40 = e1)
% 31.30/8.88 | (3352) all_0_52_52 = e1 | all_0_57_57 = e1
% 31.30/8.88 |
% 31.30/8.88 +-Applying beta-rule and splitting (133), into two cases.
% 31.30/8.88 |-Branch one:
% 31.30/8.88 | (671) all_0_40_40 = e3
% 31.30/8.88 |
% 31.30/8.89 | Equations (671) can reduce 534 to:
% 31.30/8.89 | (136) ~ (e3 = e1)
% 31.30/8.89 |
% 31.30/8.89 +-Applying beta-rule and splitting (1000), into two cases.
% 31.30/8.89 |-Branch one:
% 31.30/8.89 | (1001) all_0_58_58 = e1
% 31.30/8.89 |
% 31.30/8.89 | Combining equations (4713,1001) yields a new equation:
% 31.30/8.89 | (537) e3 = e1
% 31.30/8.89 |
% 31.30/8.89 | Simplifying 537 yields:
% 31.30/8.89 | (538) e3 = e1
% 31.30/8.89 |
% 31.30/8.89 | Equations (538) can reduce 136 to:
% 31.30/8.89 | (270) $false
% 31.30/8.89 |
% 31.30/8.89 |-The branch is then unsatisfiable
% 31.30/8.89 |-Branch two:
% 31.30/8.89 | (1004) ~ (all_0_58_58 = e1)
% 31.30/8.89 | (424) all_0_59_59 = e1
% 31.30/8.89 |
% 31.30/8.89 | Combining equations (424,402) yields a new equation:
% 31.30/8.89 | (526) e4 = e1
% 31.30/8.89 |
% 31.30/8.89 | Equations (526) can reduce 251 to:
% 31.30/8.89 | (270) $false
% 31.30/8.89 |
% 31.30/8.89 |-The branch is then unsatisfiable
% 31.30/8.89 |-Branch two:
% 31.30/8.89 | (675) ~ (all_0_40_40 = e3)
% 31.30/8.89 | (676) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 31.30/8.89 |
% 31.30/8.89 +-Applying beta-rule and splitting (603), into two cases.
% 31.30/8.89 |-Branch one:
% 31.30/8.89 | (671) all_0_40_40 = e3
% 31.30/8.89 |
% 31.30/8.89 | Equations (671) can reduce 675 to:
% 31.30/8.89 | (270) $false
% 31.30/8.89 |
% 31.30/8.89 |-The branch is then unsatisfiable
% 31.30/8.89 |-Branch two:
% 31.30/8.89 | (675) ~ (all_0_40_40 = e3)
% 31.30/8.89 | (530) all_0_40_40 = e1
% 31.30/8.89 |
% 31.30/8.89 | Equations (530) can reduce 534 to:
% 31.30/8.89 | (270) $false
% 31.30/8.89 |
% 31.30/8.89 |-The branch is then unsatisfiable
% 31.30/8.89 |-Branch two:
% 31.30/8.89 | (874) ~ (all_0_53_53 = e1)
% 31.30/8.89 | (875) all_0_54_54 = e1
% 31.30/8.89 |
% 31.30/8.89 | Combining equations (3084,875) yields a new equation:
% 31.30/8.89 | (560) e1 = e0
% 31.30/8.89 |
% 31.30/8.89 | Equations (560) can reduce 132 to:
% 31.30/8.89 | (270) $false
% 31.30/8.89 |
% 31.30/8.89 |-The branch is then unsatisfiable
% 31.30/8.89 |-Branch two:
% 31.30/8.89 | (932) ~ (all_0_51_51 = e3)
% 31.30/8.89 | (5007) all_0_51_51 = e4 | all_0_51_51 = e1
% 31.30/8.89 |
% 31.30/8.89 +-Applying beta-rule and splitting (5007), into two cases.
% 31.30/8.89 |-Branch one:
% 31.30/8.89 | (820) all_0_51_51 = e1
% 31.30/8.89 |
% 31.30/8.89 | Equations (820) can reduce 748 to:
% 31.30/8.89 | (270) $false
% 31.30/8.89 |
% 31.30/8.89 |-The branch is then unsatisfiable
% 31.30/8.89 |-Branch two:
% 31.30/8.89 | (748) ~ (all_0_51_51 = e1)
% 31.30/8.89 | (1467) all_0_51_51 = e4
% 31.30/8.89 |
% 31.30/8.89 | Equations (1467) can reduce 697 to:
% 31.30/8.89 | (270) $false
% 31.30/8.89 |
% 31.30/8.89 |-The branch is then unsatisfiable
% 31.30/8.89 |-Branch two:
% 31.30/8.89 | (3011) ~ (all_0_54_54 = e0)
% 31.30/8.89 | (2308) all_0_59_59 = e0
% 31.30/8.89 |
% 31.30/8.89 | Combining equations (402,2308) yields a new equation:
% 31.30/8.89 | (478) e4 = e0
% 31.30/8.89 |
% 31.30/8.89 | Simplifying 478 yields:
% 31.30/8.89 | (479) e4 = e0
% 31.30/8.89 |
% 31.30/8.89 | Equations (479) can reduce 6 to:
% 31.30/8.89 | (270) $false
% 31.30/8.89 |
% 31.30/8.89 |-The branch is then unsatisfiable
% 31.30/8.89 |-Branch two:
% 31.30/8.89 | (419) ~ (all_0_56_56 = e0)
% 31.30/8.89 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 31.30/8.89 |
% 31.30/8.89 +-Applying beta-rule and splitting (787), into two cases.
% 31.30/8.89 |-Branch one:
% 31.30/8.89 | (858) all_0_44_44 = e3
% 31.30/8.89 |
% 31.30/8.89 | Combining equations (621,858) yields a new equation:
% 31.30/8.89 | (784) e3 = e0
% 31.30/8.89 |
% 31.30/8.89 | Equations (784) can reduce 66 to:
% 31.30/8.89 | (270) $false
% 31.30/8.89 |
% 31.30/8.89 |-The branch is then unsatisfiable
% 31.30/8.89 |-Branch two:
% 31.30/8.89 | (862) ~ (all_0_44_44 = e3)
% 31.30/8.89 | (1070) all_0_45_45 = e3 | all_0_46_46 = e3
% 31.30/8.89 |
% 31.30/8.89 +-Applying beta-rule and splitting (1070), into two cases.
% 31.30/8.89 |-Branch one:
% 31.30/8.89 | (505) all_0_45_45 = e3
% 31.30/8.89 |
% 31.30/8.89 | Combining equations (374,505) yields a new equation:
% 31.30/8.89 | (414) e3 = e2
% 31.30/8.89 |
% 31.30/8.89 | Equations (414) can reduce 223 to:
% 31.30/8.89 | (270) $false
% 31.30/8.89 |
% 31.30/8.89 |-The branch is then unsatisfiable
% 31.30/8.89 |-Branch two:
% 31.30/8.89 | (354) ~ (all_0_45_45 = e3)
% 31.30/8.89 | (1091) all_0_46_46 = e3
% 31.30/8.89 |
% 31.30/8.89 | Equations (1091) can reduce 1010 to:
% 31.30/8.89 | (66) ~ (e3 = e0)
% 31.30/8.89 |
% 31.30/8.89 +-Applying beta-rule and splitting (75), into two cases.
% 31.30/8.89 |-Branch one:
% 31.30/8.89 | (411) all_0_43_43 = e0
% 31.30/8.89 |
% 31.30/8.89 | Combining equations (502,411) yields a new equation:
% 31.30/8.89 | (478) e4 = e0
% 31.30/8.89 |
% 31.30/8.89 | Simplifying 478 yields:
% 31.30/8.89 | (479) e4 = e0
% 31.30/8.89 |
% 31.30/8.89 | Equations (479) can reduce 6 to:
% 31.30/8.89 | (270) $false
% 31.30/8.89 |
% 31.30/8.89 |-The branch is then unsatisfiable
% 31.30/8.89 |-Branch two:
% 31.30/8.89 | (455) ~ (all_0_43_43 = e0)
% 31.30/8.89 | (940) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 31.30/8.89 |
% 31.30/8.89 | Equations (502) can reduce 455 to:
% 31.30/8.89 | (6) ~ (e4 = e0)
% 31.30/8.89 |
% 31.30/8.89 +-Applying beta-rule and splitting (208), into two cases.
% 31.30/8.89 |-Branch one:
% 31.30/8.89 | (388) all_0_56_56 = e2
% 31.30/8.89 |
% 31.30/8.89 | Equations (388) can reduce 300 to:
% 31.30/8.89 | (270) $false
% 31.30/8.89 |
% 31.30/8.89 |-The branch is then unsatisfiable
% 31.30/8.89 |-Branch two:
% 31.30/8.89 | (300) ~ (all_0_56_56 = e2)
% 31.30/8.89 | (5076) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1 | all_0_56_56 = e0
% 31.30/8.89 |
% 31.30/8.89 +-Applying beta-rule and splitting (221), into two cases.
% 31.30/8.89 |-Branch one:
% 31.30/8.89 | (1132) all_0_46_46 = e0
% 31.30/8.89 |
% 31.30/8.89 | Combining equations (1091,1132) yields a new equation:
% 31.30/8.89 | (783) e3 = e0
% 31.30/8.89 |
% 31.30/8.89 | Simplifying 783 yields:
% 31.30/8.89 | (784) e3 = e0
% 31.30/8.89 |
% 31.30/8.89 | Equations (784) can reduce 66 to:
% 31.30/8.89 | (270) $false
% 31.30/8.89 |
% 31.30/8.89 |-The branch is then unsatisfiable
% 31.30/8.89 |-Branch two:
% 31.30/8.89 | (1010) ~ (all_0_46_46 = e0)
% 31.30/8.89 | (3629) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 31.30/8.89 |
% 31.30/8.89 +-Applying beta-rule and splitting (3629), into two cases.
% 31.30/8.89 |-Branch one:
% 31.30/8.89 | (563) all_0_49_49 = e0
% 31.30/8.89 |
% 31.30/8.89 | Combining equations (307,563) yields a new equation:
% 31.30/8.89 | (622) e2 = e0
% 31.30/8.89 |
% 31.30/8.89 | Simplifying 622 yields:
% 31.30/8.89 | (316) e2 = e0
% 31.30/8.89 |
% 31.30/8.89 | Equations (316) can reduce 57 to:
% 31.30/8.89 | (270) $false
% 31.30/8.89 |
% 31.30/8.89 |-The branch is then unsatisfiable
% 31.30/8.89 |-Branch two:
% 31.30/8.89 | (1231) ~ (all_0_49_49 = e0)
% 31.30/8.89 | (3638) all_0_54_54 = e0 | all_0_59_59 = e0
% 31.30/8.89 |
% 31.30/8.89 +-Applying beta-rule and splitting (3638), into two cases.
% 31.30/8.89 |-Branch one:
% 31.30/8.89 | (3084) all_0_54_54 = e0
% 31.30/8.89 |
% 31.30/8.89 | Equations (3084) can reduce 50 to:
% 31.30/8.89 | (987) ~ (all_0_51_51 = e0)
% 31.30/8.89 |
% 31.30/8.89 +-Applying beta-rule and splitting (173), into two cases.
% 31.30/8.89 |-Branch one:
% 31.30/8.89 | (4215) all_0_51_51 = e2
% 31.30/8.89 |
% 31.30/8.89 | Equations (4215) can reduce 255 to:
% 31.30/8.89 | (270) $false
% 31.30/8.89 |
% 31.30/8.89 |-The branch is then unsatisfiable
% 31.30/8.89 |-Branch two:
% 31.30/8.89 | (255) ~ (all_0_51_51 = e2)
% 31.30/8.89 | (4888) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1 | all_0_51_51 = e0
% 31.30/8.89 |
% 31.30/8.89 +-Applying beta-rule and splitting (4888), into two cases.
% 31.30/8.89 |-Branch one:
% 31.30/8.89 | (954) all_0_51_51 = e0
% 31.30/8.89 |
% 31.30/8.89 | Equations (954) can reduce 987 to:
% 31.30/8.89 | (270) $false
% 31.30/8.89 |
% 31.30/8.89 |-The branch is then unsatisfiable
% 31.30/8.89 |-Branch two:
% 31.30/8.89 | (987) ~ (all_0_51_51 = e0)
% 31.30/8.89 | (5003) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1
% 31.30/8.89 |
% 31.30/8.89 +-Applying beta-rule and splitting (5003), into two cases.
% 31.30/8.89 |-Branch one:
% 31.30/8.89 | (824) all_0_51_51 = e3
% 31.30/8.89 |
% 31.30/8.89 | Equations (824) can reduce 60 to:
% 31.30/8.89 | (5066) ~ (all_0_56_56 = e3)
% 31.30/8.89 |
% 31.30/8.89 | Simplifying 5066 yields:
% 31.30/8.89 | (767) ~ (all_0_56_56 = e3)
% 31.30/8.89 |
% 31.30/8.89 +-Applying beta-rule and splitting (5076), into two cases.
% 31.30/8.89 |-Branch one:
% 31.30/8.89 | (830) all_0_56_56 = e0
% 31.30/8.89 |
% 31.30/8.89 | Equations (830) can reduce 419 to:
% 31.30/8.89 | (270) $false
% 31.30/8.89 |
% 31.30/8.89 |-The branch is then unsatisfiable
% 31.30/8.89 |-Branch two:
% 31.30/8.89 | (419) ~ (all_0_56_56 = e0)
% 31.30/8.89 | (5667) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1
% 31.30/8.89 |
% 31.30/8.89 +-Applying beta-rule and splitting (5667), into two cases.
% 31.30/8.89 |-Branch one:
% 31.30/8.89 | (764) all_0_56_56 = e3
% 31.30/8.89 |
% 31.30/8.89 | Equations (764) can reduce 767 to:
% 31.30/8.89 | (270) $false
% 31.30/8.89 |
% 31.30/8.89 |-The branch is then unsatisfiable
% 31.30/8.89 |-Branch two:
% 31.30/8.89 | (767) ~ (all_0_56_56 = e3)
% 31.30/8.89 | (10136) all_0_56_56 = e4 | all_0_56_56 = e1
% 31.30/8.89 |
% 31.30/8.89 +-Applying beta-rule and splitting (10136), into two cases.
% 31.30/8.89 |-Branch one:
% 31.30/8.89 | (747) all_0_56_56 = e1
% 31.30/8.89 |
% 31.30/8.89 | Equations (747) can reduce 995 to:
% 31.30/8.89 | (270) $false
% 31.30/8.89 |
% 31.30/8.89 |-The branch is then unsatisfiable
% 31.30/8.89 |-Branch two:
% 31.30/8.89 | (995) ~ (all_0_56_56 = e1)
% 31.30/8.89 | (4744) all_0_56_56 = e4
% 31.30/8.89 |
% 31.30/8.89 | Equations (4744) can reduce 274 to:
% 31.30/8.89 | (270) $false
% 31.30/8.89 |
% 31.30/8.89 |-The branch is then unsatisfiable
% 31.37/8.89 |-Branch two:
% 31.37/8.89 | (932) ~ (all_0_51_51 = e3)
% 31.37/8.89 | (5007) all_0_51_51 = e4 | all_0_51_51 = e1
% 31.37/8.89 |
% 31.37/8.89 +-Applying beta-rule and splitting (5007), into two cases.
% 31.37/8.89 |-Branch one:
% 31.37/8.89 | (820) all_0_51_51 = e1
% 31.37/8.89 |
% 31.37/8.89 | Equations (820) can reduce 748 to:
% 31.37/8.89 | (270) $false
% 31.37/8.89 |
% 31.37/8.89 |-The branch is then unsatisfiable
% 31.37/8.89 |-Branch two:
% 31.37/8.89 | (748) ~ (all_0_51_51 = e1)
% 31.37/8.89 | (1467) all_0_51_51 = e4
% 31.37/8.89 |
% 31.37/8.89 | Equations (1467) can reduce 697 to:
% 31.37/8.89 | (270) $false
% 31.37/8.89 |
% 31.37/8.89 |-The branch is then unsatisfiable
% 31.37/8.89 |-Branch two:
% 31.37/8.89 | (3011) ~ (all_0_54_54 = e0)
% 31.37/8.89 | (2308) all_0_59_59 = e0
% 31.37/8.89 |
% 31.37/8.89 | Combining equations (402,2308) yields a new equation:
% 31.37/8.89 | (478) e4 = e0
% 31.37/8.89 |
% 31.37/8.90 | Simplifying 478 yields:
% 31.37/8.90 | (479) e4 = e0
% 31.37/8.90 |
% 31.37/8.90 | Equations (479) can reduce 6 to:
% 31.37/8.90 | (270) $false
% 31.37/8.90 |
% 31.37/8.90 |-The branch is then unsatisfiable
% 31.37/8.90 |-Branch two:
% 31.37/8.90 | (361) ~ (all_0_41_41 = e4)
% 31.37/8.90 | (512) all_0_42_42 = e4
% 31.37/8.90 |
% 31.37/8.90 | Equations (512) can reduce 520 to:
% 31.37/8.90 | (270) $false
% 31.37/8.90 |
% 31.37/8.90 |-The branch is then unsatisfiable
% 31.37/8.90 |-Branch two:
% 31.37/8.90 | (510) ~ (all_0_43_43 = e4)
% 31.37/8.90 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 31.37/8.90 |
% 31.37/8.90 +-Applying beta-rule and splitting (511), into two cases.
% 31.37/8.90 |-Branch one:
% 31.37/8.90 | (363) all_0_45_45 = e4
% 31.37/8.90 |
% 31.37/8.90 | Combining equations (374,363) yields a new equation:
% 31.37/8.90 | (269) e4 = e2
% 31.37/8.90 |
% 31.37/8.90 | Equations (269) can reduce 231 to:
% 31.37/8.90 | (270) $false
% 31.37/8.90 |
% 31.37/8.90 |-The branch is then unsatisfiable
% 31.37/8.90 |-Branch two:
% 31.37/8.90 | (352) ~ (all_0_45_45 = e4)
% 31.37/8.90 | (517) all_0_46_46 = e4
% 31.37/8.90 |
% 31.37/8.90 | Equations (517) can reduce 805 to:
% 31.37/8.90 | (270) $false
% 31.37/8.90 |
% 31.37/8.90 |-The branch is then unsatisfiable
% 31.37/8.90 |-Branch two:
% 31.37/8.90 | (280) ~ (all_0_59_59 = e4)
% 31.37/8.90 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 31.37/8.90 |
% 31.37/8.90 +-Applying beta-rule and splitting (407), into two cases.
% 31.37/8.90 |-Branch one:
% 31.37/8.90 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 31.37/8.90 |
% 31.37/8.90 +-Applying beta-rule and splitting (408), into two cases.
% 31.37/8.90 |-Branch one:
% 31.37/8.90 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 31.37/8.90 |
% 31.37/8.90 +-Applying beta-rule and splitting (409), into two cases.
% 31.37/8.90 |-Branch one:
% 31.37/8.90 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 31.37/8.90 |
% 31.37/8.90 | Applying alpha-rule on (410) yields:
% 31.37/8.90 | (411) all_0_43_43 = e0
% 31.37/8.90 | (412) all_0_59_59 = e3
% 31.37/8.90 | (413) ~ (all_0_46_46 = e3)
% 31.37/8.90 |
% 31.37/8.90 | Equations (411) can reduce 455 to:
% 31.37/8.90 | (270) $false
% 31.37/8.90 |
% 31.37/8.90 |-The branch is then unsatisfiable
% 31.37/8.90 |-Branch two:
% 31.37/8.90 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 31.37/8.90 |
% 31.37/8.90 | Applying alpha-rule on (416) yields:
% 31.37/8.90 | (411) all_0_43_43 = e0
% 31.37/8.90 | (412) all_0_59_59 = e3
% 31.37/8.90 | (419) ~ (all_0_56_56 = e0)
% 31.37/8.90 |
% 31.37/8.90 | Equations (411) can reduce 455 to:
% 31.37/8.90 | (270) $false
% 31.37/8.90 |
% 31.37/8.90 |-The branch is then unsatisfiable
% 31.37/8.90 |-Branch two:
% 31.37/8.90 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 31.37/8.90 |
% 31.37/8.90 | Applying alpha-rule on (422) yields:
% 31.37/8.90 | (423) all_0_53_53 = e0
% 31.37/8.90 | (424) all_0_59_59 = e1
% 31.37/8.90 | (425) ~ (all_0_54_54 = e1)
% 31.37/8.90 |
% 31.37/8.90 | Equations (423) can reduce 584 to:
% 31.37/8.90 | (270) $false
% 31.37/8.90 |
% 31.37/8.90 |-The branch is then unsatisfiable
% 31.37/8.90 |-Branch two:
% 31.37/8.90 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 31.37/8.90 |
% 31.37/8.90 | Applying alpha-rule on (428) yields:
% 31.37/8.90 | (423) all_0_53_53 = e0
% 31.37/8.90 | (424) all_0_59_59 = e1
% 31.37/8.90 | (431) ~ (all_0_58_58 = e0)
% 31.37/8.90 |
% 31.37/8.90 | Equations (423) can reduce 584 to:
% 31.37/8.90 | (270) $false
% 31.37/8.90 |
% 31.37/8.90 |-The branch is then unsatisfiable
% 31.37/8.90 |-Branch two:
% 31.37/8.90 | (625) ~ (all_0_44_44 = e0)
% 31.37/8.90 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 31.37/8.90 |
% 31.37/8.90 +-Applying beta-rule and splitting (373), into two cases.
% 31.37/8.90 |-Branch one:
% 31.37/8.90 | (621) all_0_44_44 = e0
% 31.37/8.90 |
% 31.37/8.90 | Equations (621) can reduce 625 to:
% 31.37/8.90 | (270) $false
% 31.37/8.90 |
% 31.37/8.90 |-The branch is then unsatisfiable
% 31.37/8.90 |-Branch two:
% 31.37/8.90 | (625) ~ (all_0_44_44 = e0)
% 31.37/8.90 | (858) all_0_44_44 = e3
% 31.37/8.90 |
% 31.37/8.90 | Equations (858) can reduce 15 to:
% 31.37/8.90 | (675) ~ (all_0_40_40 = e3)
% 31.37/8.90 |
% 31.37/8.90 | Equations (858) can reduce 10 to:
% 31.37/8.90 | (2238) ~ (all_0_57_57 = e3)
% 31.37/8.90 |
% 31.37/8.90 | Simplifying 2238 yields:
% 31.37/8.90 | (846) ~ (all_0_57_57 = e3)
% 31.37/8.90 |
% 31.37/8.90 | From (858) and (165) follows:
% 31.37/8.90 | (3499) op(e2, e3) = all_0_15_15
% 31.37/8.90 |
% 31.37/8.90 +-Applying beta-rule and splitting (603), into two cases.
% 31.37/8.90 |-Branch one:
% 31.37/8.90 | (671) all_0_40_40 = e3
% 31.37/8.90 |
% 31.37/8.90 | Equations (671) can reduce 675 to:
% 31.37/8.90 | (270) $false
% 31.37/8.90 |
% 31.37/8.90 |-The branch is then unsatisfiable
% 31.37/8.90 |-Branch two:
% 31.37/8.90 | (675) ~ (all_0_40_40 = e3)
% 31.37/8.90 | (530) all_0_40_40 = e1
% 31.37/8.90 |
% 31.37/8.90 | Equations (530) can reduce 149 to:
% 31.37/8.90 | (643) ~ (all_0_57_57 = e1)
% 31.37/8.90 |
% 31.37/8.90 | Simplifying 643 yields:
% 31.37/8.90 | (644) ~ (all_0_57_57 = e1)
% 31.37/8.90 |
% 31.37/8.90 | Equations (530) can reduce 233 to:
% 31.37/8.90 | (1021) ~ (e4 = e1)
% 31.37/8.90 |
% 31.37/8.90 | Simplifying 1021 yields:
% 31.37/8.90 | (251) ~ (e4 = e1)
% 31.37/8.90 |
% 31.37/8.90 | Equations (530) can reduce 675 to:
% 31.37/8.90 | (769) ~ (e3 = e1)
% 31.37/8.90 |
% 31.37/8.90 | Simplifying 769 yields:
% 31.37/8.90 | (136) ~ (e3 = e1)
% 31.37/8.90 |
% 31.37/8.90 | From (530) and (68) follows:
% 31.37/8.90 | (648) op(e2, e1) = all_0_13_13
% 31.37/8.90 |
% 31.37/8.90 +-Applying beta-rule and splitting (33), into two cases.
% 31.37/8.90 |-Branch one:
% 31.37/8.90 | (392) all_0_57_57 = e2
% 31.37/8.90 |
% 31.37/8.90 | Equations (392) can reduce 335 to:
% 31.37/8.90 | (270) $false
% 31.37/8.90 |
% 31.37/8.90 |-The branch is then unsatisfiable
% 31.37/8.90 |-Branch two:
% 31.37/8.90 | (335) ~ (all_0_57_57 = e2)
% 31.37/8.90 | (670) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 31.37/8.90 |
% 31.37/8.90 +-Applying beta-rule and splitting (670), into two cases.
% 31.37/8.90 |-Branch one:
% 31.37/8.90 | (2258) all_0_57_57 = e0
% 31.37/8.90 |
% 31.37/8.90 | Equations (2258) can reduce 143 to:
% 31.37/8.90 | (456) ~ (e4 = e0)
% 31.37/8.90 |
% 31.37/8.90 | Simplifying 456 yields:
% 31.37/8.90 | (6) ~ (e4 = e0)
% 31.37/8.90 |
% 31.37/8.90 | Equations (2258) can reduce 335 to:
% 31.37/8.90 | (566) ~ (e2 = e0)
% 31.37/8.90 |
% 31.37/8.90 | Simplifying 566 yields:
% 31.37/8.90 | (57) ~ (e2 = e0)
% 31.37/8.90 |
% 31.37/8.90 | From (2258) and (30) follows:
% 31.37/8.90 | (12293) op(e2, e0) = all_0_19_19
% 31.37/8.90 |
% 31.37/8.90 | Instantiating formula (201) with e2, e3, all_0_15_15, e1 and discharging atoms op(e2, e3) = all_0_15_15, op(e2, e3) = e1, yields:
% 31.37/8.90 | (5879) all_0_15_15 = e1
% 31.37/8.90 |
% 31.37/8.90 | Instantiating formula (201) with e2, e1, all_0_13_13, e0 and discharging atoms op(e2, e1) = all_0_13_13, op(e2, e1) = e0, yields:
% 31.37/8.90 | (7585) all_0_13_13 = e0
% 31.37/8.90 |
% 31.37/8.90 | Instantiating formula (201) with e2, e0, all_0_19_19, e2 and discharging atoms op(e2, e0) = all_0_19_19, op(e2, e0) = e2, yields:
% 31.37/8.90 | (14991) all_0_19_19 = e2
% 31.37/8.90 |
% 31.37/8.90 +-Applying beta-rule and splitting (87), into two cases.
% 31.37/8.90 |-Branch one:
% 31.37/8.90 | (650) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 31.37/8.90 |
% 31.37/8.90 +-Applying beta-rule and splitting (650), into two cases.
% 31.37/8.90 |-Branch one:
% 31.37/8.90 | (651) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 31.37/8.90 |
% 31.37/8.90 +-Applying beta-rule and splitting (651), into two cases.
% 31.37/8.90 |-Branch one:
% 31.37/8.90 | (652) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 31.37/8.90 |
% 31.37/8.90 | Applying alpha-rule on (652) yields:
% 31.37/8.90 | (653) all_0_13_13 = e4
% 31.37/8.90 | (654) ~ (all_0_14_14 = e2)
% 31.37/8.90 |
% 31.37/8.90 | Combining equations (653,7585) yields a new equation:
% 31.37/8.90 | (478) e4 = e0
% 31.37/8.90 |
% 31.37/8.90 | Simplifying 478 yields:
% 31.37/8.90 | (479) e4 = e0
% 31.37/8.90 |
% 31.37/8.90 | Equations (479) can reduce 6 to:
% 31.37/8.90 | (270) $false
% 31.37/8.90 |
% 31.37/8.90 |-The branch is then unsatisfiable
% 31.37/8.90 |-Branch two:
% 31.37/8.90 | (657) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 31.37/8.90 |
% 31.37/8.90 | Applying alpha-rule on (657) yields:
% 31.37/8.90 | (658) all_0_15_15 = e3
% 31.37/8.90 | (659) ~ (all_0_16_16 = e2)
% 31.37/8.90 |
% 31.37/8.90 | Combining equations (658,5879) yields a new equation:
% 31.37/8.90 | (537) e3 = e1
% 31.37/8.90 |
% 31.37/8.90 | Simplifying 537 yields:
% 31.37/8.90 | (538) e3 = e1
% 31.37/8.90 |
% 31.37/8.90 | Equations (538) can reduce 136 to:
% 31.37/8.90 | (270) $false
% 31.37/8.90 |
% 31.37/8.90 |-The branch is then unsatisfiable
% 31.37/8.90 |-Branch two:
% 31.37/8.90 | (663) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 31.37/8.90 |
% 31.37/8.90 | Applying alpha-rule on (663) yields:
% 31.37/8.90 | (664) all_0_17_17 = e1
% 31.37/8.90 | (665) ~ (all_0_18_18 = e2)
% 31.37/8.90 |
% 31.37/8.90 | Combining equations (664,11735) yields a new equation:
% 31.37/8.90 | (526) e4 = e1
% 31.37/8.90 |
% 31.37/8.90 | Equations (526) can reduce 251 to:
% 31.37/8.90 | (270) $false
% 31.37/8.90 |
% 31.37/8.90 |-The branch is then unsatisfiable
% 31.37/8.90 |-Branch two:
% 31.37/8.90 | (1762) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 31.37/8.90 |
% 31.37/8.90 | Applying alpha-rule on (1762) yields:
% 31.37/8.90 | (1763) all_0_19_19 = e0
% 31.37/8.90 | (1764) ~ (all_0_20_20 = e2)
% 31.37/8.90 |
% 31.37/8.90 | Combining equations (14991,1763) yields a new equation:
% 31.37/8.90 | (622) e2 = e0
% 31.37/8.90 |
% 31.37/8.90 | Simplifying 622 yields:
% 31.37/8.90 | (316) e2 = e0
% 31.37/8.90 |
% 31.37/8.90 | Equations (316) can reduce 57 to:
% 31.37/8.90 | (270) $false
% 31.37/8.90 |
% 31.37/8.90 |-The branch is then unsatisfiable
% 31.37/8.90 |-Branch two:
% 31.37/8.90 | (2301) ~ (all_0_57_57 = e0)
% 31.37/8.90 | (9345) all_0_57_57 = e3 | all_0_57_57 = e1
% 31.37/8.90 |
% 31.37/8.90 +-Applying beta-rule and splitting (9345), into two cases.
% 31.37/8.90 |-Branch one:
% 31.37/8.90 | (869) all_0_57_57 = e3
% 31.37/8.90 |
% 31.37/8.90 | Equations (869) can reduce 846 to:
% 31.37/8.90 | (270) $false
% 31.37/8.90 |
% 31.37/8.90 |-The branch is then unsatisfiable
% 31.37/8.90 |-Branch two:
% 31.37/8.90 | (846) ~ (all_0_57_57 = e3)
% 31.37/8.90 | (997) all_0_57_57 = e1
% 31.37/8.90 |
% 31.37/8.90 | Equations (997) can reduce 644 to:
% 31.37/8.90 | (270) $false
% 31.37/8.90 |
% 31.37/8.90 |-The branch is then unsatisfiable
% 31.37/8.90 |-Branch two:
% 31.37/8.90 | (434) ~ (all_0_45_45 = e2)
% 31.37/8.90 | (445) all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 31.37/8.90 |
% 31.37/8.90 +-Applying beta-rule and splitting (493), into two cases.
% 31.37/8.90 |-Branch one:
% 31.37/8.90 | (374) all_0_45_45 = e2
% 31.37/8.90 |
% 31.37/8.90 | Equations (374) can reduce 434 to:
% 31.37/8.90 | (270) $false
% 31.37/8.90 |
% 31.37/8.90 |-The branch is then unsatisfiable
% 31.37/8.90 |-Branch two:
% 31.37/8.90 | (434) ~ (all_0_45_45 = e2)
% 31.37/8.90 | (497) all_0_46_46 = e2
% 31.37/8.90 |
% 31.37/8.90 | Equations (497) can reduce 1436 to:
% 31.37/8.90 | (270) $false
% 31.37/8.90 |
% 31.37/8.90 |-The branch is then unsatisfiable
% 31.37/8.90 |-Branch two:
% 31.37/8.90 | (257) ~ (all_0_52_52 = e2)
% 31.37/8.90 | (392) all_0_57_57 = e2
% 31.37/8.90 |
% 31.37/8.90 | Equations (392) can reduce 335 to:
% 31.37/8.90 | (270) $false
% 31.37/8.90 |
% 31.37/8.90 |-The branch is then unsatisfiable
% 31.37/8.90 |-Branch two:
% 31.37/8.90 | (291) ~ (all_0_39_39 = e2)
% 31.37/8.90 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 31.37/8.90 |
% 31.37/8.90 +-Applying beta-rule and splitting (164), into two cases.
% 31.37/8.90 |-Branch one:
% 31.37/8.90 | (336) all_0_39_39 = e2
% 31.37/8.90 |
% 31.37/8.90 | Equations (336) can reduce 291 to:
% 31.37/8.90 | (270) $false
% 31.37/8.90 |
% 31.37/8.90 |-The branch is then unsatisfiable
% 31.37/8.90 |-Branch two:
% 31.37/8.90 | (291) ~ (all_0_39_39 = e2)
% 31.37/8.90 | (630) all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 31.37/8.90 |
% 31.37/8.90 +-Applying beta-rule and splitting (339), into two cases.
% 31.37/8.90 |-Branch one:
% 31.37/8.90 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 31.37/8.90 |
% 31.37/8.90 +-Applying beta-rule and splitting (340), into two cases.
% 31.37/8.90 |-Branch one:
% 31.37/8.90 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 31.37/8.90 |
% 31.37/8.90 | Applying alpha-rule on (341) yields:
% 31.37/8.90 | (342) all_0_0_0 = e1
% 31.37/8.90 | (343) ~ (all_0_1_1 = e4)
% 31.37/8.90 |
% 31.37/8.90 | Combining equations (342,9064) yields a new equation:
% 31.37/8.90 | (571) e1 = e0
% 31.37/8.90 |
% 31.37/8.90 | Simplifying 571 yields:
% 31.37/8.90 | (560) e1 = e0
% 31.37/8.90 |
% 31.37/8.90 | Equations (560) can reduce 132 to:
% 31.37/8.90 | (270) $false
% 31.37/8.90 |
% 31.37/8.90 |-The branch is then unsatisfiable
% 31.37/8.90 |-Branch two:
% 31.37/8.90 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 31.37/8.90 |
% 31.37/8.90 | Applying alpha-rule on (346) yields:
% 31.37/8.90 | (347) all_0_2_2 = e0
% 31.37/8.90 | (348) ~ (all_0_3_3 = e4)
% 31.37/8.90 |
% 31.37/8.90 | Combining equations (9065,347) yields a new equation:
% 31.37/8.91 | (11698) all_0_40_40 = e0
% 31.37/8.91 |
% 31.37/8.91 | Simplifying 11698 yields:
% 31.37/8.91 | (11467) all_0_40_40 = e0
% 31.37/8.91 |
% 31.37/8.91 | Equations (11467) can reduce 238 to:
% 31.37/8.91 | (270) $false
% 31.37/8.91 |
% 31.37/8.91 |-The branch is then unsatisfiable
% 31.37/8.91 |-Branch two:
% 31.37/8.91 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 31.37/8.91 |
% 31.37/8.91 | Applying alpha-rule on (350) yields:
% 31.37/8.91 | (351) all_0_41_41 = e3
% 31.37/8.91 | (352) ~ (all_0_45_45 = e4)
% 31.37/8.91 |
% 31.37/8.91 | Equations (351) can reduce 147 to:
% 31.37/8.91 | (675) ~ (all_0_40_40 = e3)
% 31.37/8.91 |
% 31.37/8.91 +-Applying beta-rule and splitting (603), into two cases.
% 31.37/8.91 |-Branch one:
% 31.37/8.91 | (671) all_0_40_40 = e3
% 31.37/8.91 |
% 31.37/8.91 | Equations (671) can reduce 675 to:
% 31.37/8.91 | (270) $false
% 31.37/8.91 |
% 31.37/8.91 |-The branch is then unsatisfiable
% 31.37/8.91 |-Branch two:
% 31.37/8.91 | (675) ~ (all_0_40_40 = e3)
% 31.37/8.91 | (530) all_0_40_40 = e1
% 31.37/8.91 |
% 31.37/8.91 | Equations (530) can reduce 602 to:
% 31.37/8.91 | (645) ~ (e2 = e1)
% 31.37/8.91 |
% 31.37/8.91 | Simplifying 645 yields:
% 31.37/8.91 | (141) ~ (e2 = e1)
% 31.37/8.91 |
% 31.37/8.91 +-Applying beta-rule and splitting (630), into two cases.
% 31.37/8.91 |-Branch one:
% 31.37/8.91 | (327) all_0_40_40 = e2
% 31.37/8.91 |
% 31.37/8.91 | Combining equations (530,327) yields a new equation:
% 31.37/8.91 | (322) e2 = e1
% 31.37/8.91 |
% 31.37/8.91 | Equations (322) can reduce 141 to:
% 31.37/8.91 | (270) $false
% 31.37/8.91 |
% 31.37/8.91 |-The branch is then unsatisfiable
% 31.37/8.91 |-Branch two:
% 31.37/8.91 | (602) ~ (all_0_40_40 = e2)
% 31.37/8.91 | (1251) all_0_41_41 = e2 | all_0_42_42 = e2
% 31.37/8.91 |
% 31.37/8.91 +-Applying beta-rule and splitting (1251), into two cases.
% 31.37/8.91 |-Branch one:
% 31.37/8.91 | (436) all_0_41_41 = e2
% 31.37/8.91 |
% 31.37/8.91 | Combining equations (351,436) yields a new equation:
% 31.37/8.91 | (437) e3 = e2
% 31.37/8.91 |
% 31.37/8.91 | Simplifying 437 yields:
% 31.37/8.91 | (414) e3 = e2
% 31.37/8.91 |
% 31.37/8.91 | Equations (414) can reduce 223 to:
% 31.37/8.91 | (270) $false
% 31.37/8.91 |
% 31.37/8.91 |-The branch is then unsatisfiable
% 31.37/8.91 |-Branch two:
% 31.37/8.91 | (331) ~ (all_0_41_41 = e2)
% 31.37/8.91 | (698) all_0_42_42 = e2
% 31.37/8.91 |
% 31.37/8.91 | Equations (698) can reduce 498 to:
% 31.37/8.91 | (270) $false
% 31.37/8.91 |
% 31.37/8.91 |-The branch is then unsatisfiable
% 31.37/8.91 |-Branch two:
% 31.37/8.91 | (562) ~ (all_0_48_48 = e0)
% 31.37/8.91 | (563) all_0_49_49 = e0
% 31.37/8.91 |
% 31.37/8.91 | Combining equations (563,307) yields a new equation:
% 31.37/8.91 | (316) e2 = e0
% 31.37/8.91 |
% 31.37/8.91 | Equations (316) can reduce 57 to:
% 31.37/8.91 | (270) $false
% 31.37/8.91 |
% 31.37/8.91 |-The branch is then unsatisfiable
% 31.37/8.91 |-Branch two:
% 31.37/8.91 | (324) ~ (all_0_47_47 = e1)
% 31.37/8.91 | (325) all_0_48_48 = e1 | all_0_49_49 = e1
% 31.37/8.91 |
% 31.37/8.91 +-Applying beta-rule and splitting (325), into two cases.
% 31.37/8.91 |-Branch one:
% 31.37/8.91 | (552) all_0_48_48 = e1
% 31.37/8.91 |
% 31.37/8.91 | Equations (552) can reduce 190 to:
% 31.37/8.91 | (540) ~ (all_0_41_41 = e1)
% 31.37/8.91 |
% 31.37/8.91 | Equations (552) can reduce 65 to:
% 31.37/8.91 | (26) ~ (all_0_45_45 = e1)
% 31.37/8.91 |
% 31.37/8.91 | Equations (552) can reduce 225 to:
% 31.37/8.91 | (324) ~ (all_0_47_47 = e1)
% 31.37/8.91 |
% 31.37/8.91 | Equations (552) can reduce 48 to:
% 31.37/8.91 | (1016) ~ (all_0_53_53 = e1)
% 31.37/8.91 |
% 31.37/8.91 | Simplifying 1016 yields:
% 31.37/8.91 | (874) ~ (all_0_53_53 = e1)
% 31.37/8.91 |
% 31.37/8.91 | Equations (552) can reduce 59 to:
% 31.37/8.91 | (7725) ~ (all_0_58_58 = e1)
% 31.37/8.91 |
% 31.37/8.91 | Simplifying 7725 yields:
% 31.37/8.91 | (1004) ~ (all_0_58_58 = e1)
% 31.37/8.91 |
% 31.37/8.91 | Equations (552) can reduce 121 to:
% 31.37/8.91 | (769) ~ (e3 = e1)
% 31.37/8.91 |
% 31.37/8.91 | Simplifying 769 yields:
% 31.37/8.91 | (136) ~ (e3 = e1)
% 31.37/8.91 |
% 31.37/8.91 | Equations (552) can reduce 294 to:
% 31.37/8.91 | (645) ~ (e2 = e1)
% 31.37/8.91 |
% 31.37/8.91 | Simplifying 645 yields:
% 31.37/8.91 | (141) ~ (e2 = e1)
% 31.37/8.91 |
% 31.37/8.91 | From (552) and (183) follows:
% 31.37/8.91 | (7731) op(e2, e1) = all_0_26_26
% 31.37/8.91 |
% 31.37/8.91 | From (552) and (56) follows:
% 31.37/8.91 | (7732) op(e2, e1) = e1
% 31.37/8.91 |
% 31.37/8.91 +-Applying beta-rule and splitting (77), into two cases.
% 31.37/8.91 |-Branch one:
% 31.37/8.91 | (315) all_0_47_47 = e0
% 31.37/8.91 |
% 31.37/8.91 | Equations (315) can reduce 100 to:
% 31.37/8.91 | (101) ~ (all_0_39_39 = e0)
% 31.37/8.91 |
% 31.37/8.91 | Equations (315) can reduce 170 to:
% 31.37/8.91 | (455) ~ (all_0_43_43 = e0)
% 31.37/8.91 |
% 31.37/8.91 | Equations (315) can reduce 3 to:
% 31.37/8.91 | (6253) ~ (all_0_51_51 = e0)
% 31.37/8.91 |
% 31.37/8.91 | Simplifying 6253 yields:
% 31.37/8.91 | (987) ~ (all_0_51_51 = e0)
% 31.37/8.91 |
% 31.37/8.91 | Equations (315) can reduce 218 to:
% 31.37/8.91 | (3852) ~ (all_0_56_56 = e0)
% 31.37/8.91 |
% 31.37/8.91 | Simplifying 3852 yields:
% 31.37/8.91 | (419) ~ (all_0_56_56 = e0)
% 31.37/8.91 |
% 31.37/8.91 | Equations (315) can reduce 247 to:
% 31.37/8.91 | (788) ~ (e3 = e0)
% 31.37/8.91 |
% 31.37/8.91 | Simplifying 788 yields:
% 31.37/8.91 | (66) ~ (e3 = e0)
% 31.37/8.91 |
% 31.37/8.91 | Equations (315) can reduce 324 to:
% 31.37/8.91 | (568) ~ (e1 = e0)
% 31.37/8.91 |
% 31.37/8.91 | Simplifying 568 yields:
% 31.37/8.91 | (132) ~ (e1 = e0)
% 31.37/8.91 |
% 31.37/8.91 | From (315) and (237) follows:
% 31.37/8.91 | (11363) op(e3, e0) = all_0_7_7
% 31.37/8.91 |
% 31.37/8.91 | From (315) and (42) follows:
% 31.37/8.91 | (7717) op(e2, e0) = all_0_8_8
% 31.37/8.91 |
% 31.37/8.91 | From (315) and (40) follows:
% 31.37/8.91 | (7718) op(e2, e3) = e0
% 31.37/8.91 |
% 31.37/8.91 | Instantiating formula (201) with e3, e0, all_0_7_7, all_0_46_46 and discharging atoms op(e3, e0) = all_0_7_7, op(e3, e0) = all_0_46_46, yields:
% 31.37/8.91 | (11390) all_0_7_7 = all_0_46_46
% 31.37/8.91 |
% 31.37/8.91 | Instantiating formula (201) with e2, e1, e1, all_0_26_26 and discharging atoms op(e2, e1) = all_0_26_26, op(e2, e1) = e1, yields:
% 31.37/8.91 | (7734) all_0_26_26 = e1
% 31.37/8.91 |
% 31.37/8.91 | Instantiating formula (201) with e2, e0, all_0_8_8, e2 and discharging atoms op(e2, e0) = all_0_8_8, op(e2, e0) = e2, yields:
% 31.37/8.91 | (4012) all_0_8_8 = e2
% 31.37/8.91 |
% 31.37/8.91 | From (7734) and (7731) follows:
% 31.37/8.91 | (7732) op(e2, e1) = e1
% 31.37/8.91 |
% 31.37/8.91 | From (4012) and (7717) follows:
% 31.37/8.91 | (6092) op(e2, e0) = e2
% 31.37/8.91 |
% 31.37/8.91 +-Applying beta-rule and splitting (186), into two cases.
% 31.37/8.91 |-Branch one:
% 31.37/8.91 | (336) all_0_39_39 = e2
% 31.37/8.91 |
% 31.37/8.91 | Equations (336) can reduce 226 to:
% 31.37/8.91 | (330) ~ (all_0_41_41 = e2)
% 31.37/8.91 |
% 31.37/8.91 | Simplifying 330 yields:
% 31.37/8.91 | (331) ~ (all_0_41_41 = e2)
% 31.37/8.91 |
% 31.37/8.91 | Equations (336) can reduce 184 to:
% 31.37/8.91 | (1336) ~ (all_0_42_42 = e2)
% 31.37/8.91 |
% 31.37/8.91 | Simplifying 1336 yields:
% 31.37/8.91 | (498) ~ (all_0_42_42 = e2)
% 31.37/8.91 |
% 31.37/8.91 | Equations (336) can reduce 212 to:
% 31.37/8.91 | (299) ~ (all_0_56_56 = e2)
% 31.37/8.91 |
% 31.37/8.91 | Simplifying 299 yields:
% 31.37/8.91 | (300) ~ (all_0_56_56 = e2)
% 31.37/8.91 |
% 31.37/8.91 | Equations (336) can reduce 101 to:
% 31.37/8.91 | (57) ~ (e2 = e0)
% 31.37/8.91 |
% 31.37/8.91 | From (336) and (200) follows:
% 31.37/8.91 | (12057) op(e3, e2) = all_0_4_4
% 31.37/8.91 |
% 31.37/8.91 | Instantiating formula (201) with e3, e2, all_0_4_4, all_0_44_44 and discharging atoms op(e3, e2) = all_0_4_4, op(e3, e2) = all_0_44_44, yields:
% 31.37/8.91 | (17397) all_0_4_4 = all_0_44_44
% 31.37/8.91 |
% 31.37/8.91 +-Applying beta-rule and splitting (193), into two cases.
% 31.37/8.91 |-Branch one:
% 31.37/8.91 | (370) all_0_44_44 = e2
% 31.37/8.91 |
% 31.37/8.91 | Combining equations (370,17397) yields a new equation:
% 31.37/8.91 | (12701) all_0_4_4 = e2
% 31.37/8.91 |
% 31.37/8.91 | Equations (370) can reduce 15 to:
% 31.37/8.91 | (602) ~ (all_0_40_40 = e2)
% 31.37/8.91 |
% 31.37/8.91 | Equations (370) can reduce 229 to:
% 31.37/8.91 | (611) ~ (all_0_45_45 = e2)
% 31.37/8.91 |
% 31.37/8.91 | Simplifying 611 yields:
% 31.37/8.91 | (434) ~ (all_0_45_45 = e2)
% 31.37/8.91 |
% 31.37/8.91 | Equations (370) can reduce 174 to:
% 31.37/8.91 | (1435) ~ (all_0_46_46 = e2)
% 31.37/8.91 |
% 31.37/8.91 | Simplifying 1435 yields:
% 31.37/8.91 | (1436) ~ (all_0_46_46 = e2)
% 31.37/8.91 |
% 31.37/8.91 | Equations (370) can reduce 10 to:
% 31.37/8.91 | (334) ~ (all_0_57_57 = e2)
% 31.37/8.91 |
% 31.37/8.91 | Simplifying 334 yields:
% 31.37/8.91 | (335) ~ (all_0_57_57 = e2)
% 31.37/8.91 |
% 31.37/8.91 | Equations (370) can reduce 131 to:
% 31.37/8.91 | (141) ~ (e2 = e1)
% 31.37/8.91 |
% 31.37/8.91 +-Applying beta-rule and splitting (187), into two cases.
% 31.37/8.91 |-Branch one:
% 31.37/8.91 | (436) all_0_41_41 = e2
% 31.37/8.91 |
% 31.37/8.91 | Equations (436) can reduce 331 to:
% 31.37/8.91 | (270) $false
% 31.37/8.91 |
% 31.37/8.91 |-The branch is then unsatisfiable
% 31.37/8.91 |-Branch two:
% 31.37/8.91 | (331) ~ (all_0_41_41 = e2)
% 31.37/8.91 | (441) all_0_45_45 = e2 | all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 31.37/8.91 |
% 31.37/8.91 +-Applying beta-rule and splitting (441), into two cases.
% 31.37/8.91 |-Branch one:
% 31.37/8.91 | (374) all_0_45_45 = e2
% 31.37/8.91 |
% 31.37/8.91 | Equations (374) can reduce 434 to:
% 31.37/8.91 | (270) $false
% 31.37/8.91 |
% 31.37/8.91 |-The branch is then unsatisfiable
% 31.37/8.91 |-Branch two:
% 31.37/8.91 | (434) ~ (all_0_45_45 = e2)
% 31.37/8.91 | (445) all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 31.37/8.91 |
% 31.37/8.91 +-Applying beta-rule and splitting (445), into two cases.
% 31.37/8.91 |-Branch one:
% 31.37/8.91 | (311) all_0_48_48 = e2
% 31.37/8.91 |
% 31.37/8.91 | Combining equations (552,311) yields a new equation:
% 31.37/8.91 | (322) e2 = e1
% 31.37/8.91 |
% 31.37/8.91 | Equations (322) can reduce 141 to:
% 31.37/8.92 | (270) $false
% 31.37/8.92 |
% 31.37/8.92 |-The branch is then unsatisfiable
% 31.37/8.92 |-Branch two:
% 31.37/8.92 | (294) ~ (all_0_48_48 = e2)
% 31.37/8.92 | (449) all_0_53_53 = e2 | all_0_58_58 = e2
% 31.37/8.92 |
% 31.37/8.92 +-Applying beta-rule and splitting (449), into two cases.
% 31.37/8.92 |-Branch one:
% 31.37/8.92 | (576) all_0_53_53 = e2
% 31.37/8.92 |
% 31.37/8.92 | Equations (576) can reduce 214 to:
% 31.37/8.92 | (331) ~ (all_0_41_41 = e2)
% 31.37/8.92 |
% 31.37/8.92 | Equations (576) can reduce 252 to:
% 31.37/8.92 | (260) ~ (all_0_54_54 = e2)
% 31.37/8.92 |
% 31.37/8.92 | Simplifying 260 yields:
% 31.37/8.92 | (261) ~ (all_0_54_54 = e2)
% 31.37/8.92 |
% 31.37/8.92 | Equations (576) can reduce 70 to:
% 31.37/8.92 | (375) ~ (all_0_58_58 = e2)
% 31.37/8.92 |
% 31.37/8.92 | Simplifying 375 yields:
% 31.37/8.92 | (376) ~ (all_0_58_58 = e2)
% 31.37/8.92 |
% 31.37/8.92 +-Applying beta-rule and splitting (93), into two cases.
% 31.37/8.92 |-Branch one:
% 31.37/8.92 | (402) all_0_59_59 = e4
% 31.37/8.92 |
% 31.37/8.92 | Equations (402) can reduce 17 to:
% 31.37/8.92 | (520) ~ (all_0_42_42 = e4)
% 31.37/8.92 |
% 31.37/8.92 | Equations (402) can reduce 72 to:
% 31.37/8.92 | (936) ~ (all_0_54_54 = e4)
% 31.37/8.92 |
% 31.37/8.92 | Equations (402) can reduce 185 to:
% 31.37/8.92 | (274) ~ (all_0_56_56 = e4)
% 31.37/8.92 |
% 31.37/8.92 | Equations (402) can reduce 140 to:
% 31.37/8.92 | (143) ~ (all_0_57_57 = e4)
% 31.37/8.92 |
% 31.37/8.92 | Equations (402) can reduce 701 to:
% 31.37/8.92 | (231) ~ (e4 = e2)
% 31.37/8.92 |
% 31.37/8.92 +-Applying beta-rule and splitting (222), into two cases.
% 31.37/8.92 |-Branch one:
% 31.37/8.92 | (522) all_0_39_39 = e4
% 31.37/8.92 |
% 31.37/8.92 | Combining equations (336,522) yields a new equation:
% 31.37/8.92 | (269) e4 = e2
% 31.37/8.92 |
% 31.37/8.92 | Equations (269) can reduce 231 to:
% 31.37/8.92 | (270) $false
% 31.37/8.92 |
% 31.37/8.92 |-The branch is then unsatisfiable
% 31.37/8.92 |-Branch two:
% 31.37/8.92 | (591) ~ (all_0_39_39 = e4)
% 31.37/8.92 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 31.37/8.92 |
% 31.37/8.92 | Equations (336) can reduce 591 to:
% 31.37/8.92 | (377) ~ (e4 = e2)
% 31.37/8.92 |
% 31.37/8.92 | Simplifying 377 yields:
% 31.37/8.92 | (231) ~ (e4 = e2)
% 31.37/8.92 |
% 31.37/8.92 +-Applying beta-rule and splitting (166), into two cases.
% 31.37/8.92 |-Branch one:
% 31.37/8.92 | (522) all_0_39_39 = e4
% 31.37/8.92 |
% 31.37/8.92 | Combining equations (336,522) yields a new equation:
% 31.37/8.92 | (269) e4 = e2
% 31.37/8.92 |
% 31.37/8.92 | Equations (269) can reduce 231 to:
% 31.37/8.92 | (270) $false
% 31.37/8.92 |
% 31.37/8.92 |-The branch is then unsatisfiable
% 31.37/8.92 |-Branch two:
% 31.37/8.92 | (591) ~ (all_0_39_39 = e4)
% 31.37/8.92 | (4522) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 31.37/8.92 |
% 31.37/8.92 +-Applying beta-rule and splitting (4522), into two cases.
% 31.37/8.92 |-Branch one:
% 31.37/8.92 | (502) all_0_43_43 = e4
% 31.37/8.92 |
% 31.37/8.92 | Equations (502) can reduce 103 to:
% 31.37/8.92 | (804) ~ (all_0_46_46 = e4)
% 31.37/8.92 |
% 31.37/8.92 | Simplifying 804 yields:
% 31.37/8.92 | (805) ~ (all_0_46_46 = e4)
% 31.37/8.92 |
% 31.37/8.92 | Equations (502) can reduce 188 to:
% 31.37/8.92 | (273) ~ (all_0_56_56 = e4)
% 31.37/8.92 |
% 31.37/8.92 | Simplifying 273 yields:
% 31.37/8.92 | (274) ~ (all_0_56_56 = e4)
% 31.37/8.92 |
% 31.37/8.92 | From (502) and (248) follows:
% 31.37/8.92 | (14204) op(e3, e3) = e4
% 31.37/8.92 |
% 31.37/8.92 +-Applying beta-rule and splitting (158), into two cases.
% 31.37/8.92 |-Branch one:
% 31.37/8.92 | (358) all_0_41_41 = e4
% 31.37/8.92 |
% 31.37/8.92 | Equations (358) can reduce 147 to:
% 31.37/8.92 | (233) ~ (all_0_40_40 = e4)
% 31.37/8.92 |
% 31.37/8.92 | Equations (358) can reduce 157 to:
% 31.37/8.92 | (277) ~ (all_0_58_58 = e4)
% 31.37/8.92 |
% 31.37/8.92 | Simplifying 277 yields:
% 31.37/8.92 | (278) ~ (all_0_58_58 = e4)
% 31.37/8.92 |
% 31.37/8.92 | Equations (358) can reduce 331 to:
% 31.37/8.92 | (231) ~ (e4 = e2)
% 31.37/8.92 |
% 31.37/8.92 | Equations (358) can reduce 540 to:
% 31.37/8.92 | (251) ~ (e4 = e1)
% 31.37/8.92 |
% 31.37/8.92 +-Applying beta-rule and splitting (9), into two cases.
% 31.37/8.92 |-Branch one:
% 31.37/8.92 | (621) all_0_44_44 = e0
% 31.37/8.92 |
% 31.37/8.92 | Combining equations (370,621) yields a new equation:
% 31.37/8.92 | (622) e2 = e0
% 31.37/8.92 |
% 31.37/8.92 | Simplifying 622 yields:
% 31.37/8.92 | (316) e2 = e0
% 31.37/8.92 |
% 31.37/8.92 | Equations (316) can reduce 57 to:
% 31.37/8.92 | (270) $false
% 31.37/8.92 |
% 31.37/8.92 |-The branch is then unsatisfiable
% 31.37/8.92 |-Branch two:
% 31.37/8.92 | (625) ~ (all_0_44_44 = e0)
% 31.37/8.92 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 31.37/8.92 |
% 31.37/8.92 +-Applying beta-rule and splitting (194), into two cases.
% 31.37/8.92 |-Branch one:
% 31.37/8.92 | (747) all_0_56_56 = e1
% 31.37/8.92 |
% 31.37/8.92 | Equations (747) can reduce 81 to:
% 31.37/8.92 | (7725) ~ (all_0_58_58 = e1)
% 31.37/8.92 |
% 31.37/8.92 | Simplifying 7725 yields:
% 31.37/8.92 | (1004) ~ (all_0_58_58 = e1)
% 31.37/8.92 |
% 31.37/8.92 | Equations (747) can reduce 274 to:
% 31.37/8.92 | (1021) ~ (e4 = e1)
% 31.37/8.92 |
% 31.37/8.92 | Simplifying 1021 yields:
% 31.37/8.92 | (251) ~ (e4 = e1)
% 31.37/8.92 |
% 31.37/8.92 | From (747) and (239) follows:
% 31.37/8.92 | (11832) op(e3, e1) = all_0_11_11
% 31.37/8.92 |
% 31.37/8.92 | From (747) and (205) follows:
% 31.37/8.92 | (19169) op(e0, e1) = all_0_12_12
% 31.37/8.92 |
% 31.37/8.92 +-Applying beta-rule and splitting (178), into two cases.
% 31.37/8.92 |-Branch one:
% 31.37/8.92 | (751) all_0_39_39 = e3
% 31.37/8.92 |
% 31.37/8.92 | Combining equations (336,751) yields a new equation:
% 31.37/8.92 | (414) e3 = e2
% 31.37/8.92 |
% 31.37/8.92 | Equations (414) can reduce 223 to:
% 31.37/8.92 | (270) $false
% 31.37/8.92 |
% 31.37/8.92 |-The branch is then unsatisfiable
% 31.37/8.92 |-Branch two:
% 31.37/8.92 | (755) ~ (all_0_39_39 = e3)
% 31.37/8.92 | (756) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 31.37/8.92 |
% 31.37/8.92 +-Applying beta-rule and splitting (756), into two cases.
% 31.37/8.92 |-Branch one:
% 31.37/8.92 | (782) all_0_43_43 = e3
% 31.37/8.92 |
% 31.37/8.92 | Combining equations (502,782) yields a new equation:
% 31.37/8.92 | (660) e4 = e3
% 31.37/8.92 |
% 31.37/8.92 | Simplifying 660 yields:
% 31.37/8.92 | (359) e4 = e3
% 31.37/8.92 |
% 31.37/8.92 | Equations (359) can reduce 34 to:
% 31.37/8.92 | (270) $false
% 31.37/8.92 |
% 31.37/8.92 |-The branch is then unsatisfiable
% 31.37/8.92 |-Branch two:
% 31.37/8.92 | (786) ~ (all_0_43_43 = e3)
% 31.37/8.92 | (799) all_0_51_51 = e3 | all_0_56_56 = e3
% 31.37/8.92 |
% 31.37/8.92 +-Applying beta-rule and splitting (799), into two cases.
% 31.37/8.92 |-Branch one:
% 31.37/8.92 | (824) all_0_51_51 = e3
% 31.37/8.92 |
% 31.37/8.92 | From (824) and (7) follows:
% 31.37/8.92 | (11846) op(e3, e3) = all_0_9_9
% 31.37/8.92 |
% 31.37/8.92 | Instantiating formula (201) with e3, e3, all_0_9_9, e4 and discharging atoms op(e3, e3) = all_0_9_9, op(e3, e3) = e4, yields:
% 31.37/8.92 | (19183) all_0_9_9 = e4
% 31.37/8.92 |
% 31.37/8.92 | Instantiating formula (201) with e3, e1, all_0_11_11, all_0_45_45 and discharging atoms op(e3, e1) = all_0_11_11, op(e3, e1) = all_0_45_45, yields:
% 31.37/8.92 | (11848) all_0_11_11 = all_0_45_45
% 31.37/8.92 |
% 31.37/8.92 | Instantiating formula (201) with e0, e1, all_0_12_12, all_0_58_58 and discharging atoms op(e0, e1) = all_0_12_12, op(e0, e1) = all_0_58_58, yields:
% 31.37/8.92 | (19185) all_0_12_12 = all_0_58_58
% 31.37/8.92 |
% 31.37/8.92 +-Applying beta-rule and splitting (234), into two cases.
% 31.37/8.92 |-Branch one:
% 31.37/8.92 | (4239) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3)) | (all_0_9_9 = e1 & ~ (all_0_10_10 = e3))
% 31.37/8.92 |
% 31.37/8.92 +-Applying beta-rule and splitting (4239), into two cases.
% 31.37/8.92 |-Branch one:
% 31.37/8.92 | (4240) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3))
% 31.37/8.92 |
% 31.37/8.92 +-Applying beta-rule and splitting (4240), into two cases.
% 31.37/8.92 |-Branch one:
% 31.37/8.92 | (4241) all_0_4_4 = e4 & ~ (all_0_5_5 = e3)
% 31.37/8.92 |
% 31.37/8.92 | Applying alpha-rule on (4241) yields:
% 31.37/8.92 | (4242) all_0_4_4 = e4
% 31.37/8.92 | (4243) ~ (all_0_5_5 = e3)
% 31.37/8.92 |
% 31.37/8.92 | Combining equations (4242,12701) yields a new equation:
% 31.37/8.92 | (268) e4 = e2
% 31.37/8.92 |
% 31.37/8.92 | Simplifying 268 yields:
% 31.37/8.92 | (269) e4 = e2
% 31.37/8.92 |
% 31.37/8.92 | Equations (269) can reduce 231 to:
% 31.37/8.92 | (270) $false
% 31.37/8.92 |
% 31.37/8.92 |-The branch is then unsatisfiable
% 31.37/8.92 |-Branch two:
% 31.37/8.92 | (4247) all_0_7_7 = e2 & ~ (all_0_8_8 = e3)
% 31.37/8.92 |
% 31.37/8.92 | Applying alpha-rule on (4247) yields:
% 31.37/8.92 | (4248) all_0_7_7 = e2
% 31.37/8.92 | (4249) ~ (all_0_8_8 = e3)
% 31.37/8.92 |
% 31.37/8.92 | Combining equations (4248,11390) yields a new equation:
% 31.37/8.92 | (497) all_0_46_46 = e2
% 31.37/8.92 |
% 31.37/8.92 | Equations (497) can reduce 1436 to:
% 31.37/8.92 | (270) $false
% 31.37/8.92 |
% 31.37/8.92 |-The branch is then unsatisfiable
% 31.37/8.92 |-Branch two:
% 31.37/8.92 | (4253) all_0_9_9 = e1 & ~ (all_0_10_10 = e3)
% 31.37/8.92 |
% 31.37/8.92 | Applying alpha-rule on (4253) yields:
% 31.37/8.92 | (4254) all_0_9_9 = e1
% 31.37/8.92 | (4255) ~ (all_0_10_10 = e3)
% 31.37/8.92 |
% 31.37/8.93 | Combining equations (4254,19183) yields a new equation:
% 31.37/8.93 | (526) e4 = e1
% 31.37/8.93 |
% 31.37/8.93 | Equations (526) can reduce 251 to:
% 31.37/8.93 | (270) $false
% 31.37/8.93 |
% 31.37/8.93 |-The branch is then unsatisfiable
% 31.37/8.93 |-Branch two:
% 31.37/8.93 | (4378) all_0_11_11 = e0 & ~ (all_0_12_12 = e3)
% 31.37/8.93 |
% 31.37/8.93 | Applying alpha-rule on (4378) yields:
% 31.37/8.93 | (4379) all_0_11_11 = e0
% 31.37/8.93 | (4380) ~ (all_0_12_12 = e3)
% 31.37/8.93 |
% 31.37/8.93 | Combining equations (11848,4379) yields a new equation:
% 31.37/8.93 | (19207) all_0_45_45 = e0
% 31.37/8.93 |
% 31.37/8.93 | Simplifying 19207 yields:
% 31.37/8.93 | (454) all_0_45_45 = e0
% 31.37/8.93 |
% 31.37/8.93 | Equations (19185) can reduce 4380 to:
% 31.37/8.93 | (718) ~ (all_0_58_58 = e3)
% 31.37/8.93 |
% 31.37/8.93 | Equations (454) can reduce 108 to:
% 31.37/8.93 | (3530) ~ (all_0_58_58 = e0)
% 31.37/8.93 |
% 31.37/8.93 | Simplifying 3530 yields:
% 31.37/8.93 | (431) ~ (all_0_58_58 = e0)
% 31.37/8.93 |
% 31.37/8.93 +-Applying beta-rule and splitting (204), into two cases.
% 31.37/8.93 |-Branch one:
% 31.37/8.93 | (396) all_0_58_58 = e2
% 31.37/8.93 |
% 31.37/8.93 | Equations (396) can reduce 376 to:
% 31.37/8.93 | (270) $false
% 31.37/8.93 |
% 31.37/8.93 |-The branch is then unsatisfiable
% 31.37/8.93 |-Branch two:
% 31.37/8.93 | (376) ~ (all_0_58_58 = e2)
% 31.37/8.93 | (3890) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1 | all_0_58_58 = e0
% 31.37/8.93 |
% 31.37/8.93 +-Applying beta-rule and splitting (3890), into two cases.
% 31.37/8.93 |-Branch one:
% 31.37/8.93 | (585) all_0_58_58 = e0
% 31.37/8.93 |
% 31.37/8.93 | Equations (585) can reduce 431 to:
% 31.37/8.93 | (270) $false
% 31.37/8.93 |
% 31.37/8.93 |-The branch is then unsatisfiable
% 31.37/8.93 |-Branch two:
% 31.37/8.93 | (431) ~ (all_0_58_58 = e0)
% 31.37/8.93 | (4709) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1
% 31.37/8.93 |
% 31.37/8.93 +-Applying beta-rule and splitting (4709), into two cases.
% 31.37/8.93 |-Branch one:
% 31.37/8.93 | (4713) all_0_58_58 = e3
% 31.37/8.93 |
% 31.37/8.93 | Equations (4713) can reduce 718 to:
% 31.37/8.93 | (270) $false
% 31.37/8.93 |
% 31.37/8.93 |-The branch is then unsatisfiable
% 31.37/8.93 |-Branch two:
% 31.37/8.93 | (718) ~ (all_0_58_58 = e3)
% 31.37/8.93 | (4716) all_0_58_58 = e4 | all_0_58_58 = e1
% 31.37/8.93 |
% 31.37/8.93 +-Applying beta-rule and splitting (4716), into two cases.
% 31.37/8.93 |-Branch one:
% 31.37/8.93 | (1001) all_0_58_58 = e1
% 31.37/8.93 |
% 31.37/8.93 | Equations (1001) can reduce 1004 to:
% 31.37/8.93 | (270) $false
% 31.37/8.93 |
% 31.37/8.93 |-The branch is then unsatisfiable
% 31.37/8.93 |-Branch two:
% 31.37/8.93 | (1004) ~ (all_0_58_58 = e1)
% 31.37/8.93 | (600) all_0_58_58 = e4
% 31.37/8.93 |
% 31.37/8.93 | Equations (600) can reduce 278 to:
% 31.37/8.93 | (270) $false
% 31.37/8.93 |
% 31.37/8.93 |-The branch is then unsatisfiable
% 31.37/8.93 |-Branch two:
% 31.37/8.93 | (932) ~ (all_0_51_51 = e3)
% 31.37/8.93 | (764) all_0_56_56 = e3
% 31.37/8.93 |
% 31.37/8.93 | Combining equations (764,747) yields a new equation:
% 31.37/8.93 | (537) e3 = e1
% 31.37/8.93 |
% 31.37/8.93 | Simplifying 537 yields:
% 31.37/8.93 | (538) e3 = e1
% 31.37/8.93 |
% 31.37/8.93 | Equations (538) can reduce 136 to:
% 31.37/8.93 | (270) $false
% 31.37/8.93 |
% 31.37/8.93 |-The branch is then unsatisfiable
% 31.37/8.93 |-Branch two:
% 31.37/8.93 | (995) ~ (all_0_56_56 = e1)
% 31.37/8.93 | (996) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 31.37/8.93 |
% 31.37/8.93 +-Applying beta-rule and splitting (208), into two cases.
% 31.37/8.93 |-Branch one:
% 31.37/8.93 | (388) all_0_56_56 = e2
% 31.37/8.93 |
% 31.37/8.93 | Equations (388) can reduce 300 to:
% 31.37/8.93 | (270) $false
% 31.37/8.93 |
% 31.37/8.93 |-The branch is then unsatisfiable
% 31.37/8.93 |-Branch two:
% 31.37/8.93 | (300) ~ (all_0_56_56 = e2)
% 31.37/8.93 | (5076) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1 | all_0_56_56 = e0
% 31.37/8.93 |
% 31.37/8.93 +-Applying beta-rule and splitting (996), into two cases.
% 31.37/8.93 |-Branch one:
% 31.37/8.93 | (997) all_0_57_57 = e1
% 31.37/8.93 |
% 31.37/8.93 | Equations (997) can reduce 149 to:
% 31.37/8.93 | (534) ~ (all_0_40_40 = e1)
% 31.37/8.93 |
% 31.37/8.93 | Equations (997) can reduce 235 to:
% 31.37/8.93 | (642) ~ (all_0_52_52 = e1)
% 31.37/8.93 |
% 31.37/8.93 | Equations (997) can reduce 143 to:
% 31.37/8.93 | (1021) ~ (e4 = e1)
% 31.37/8.93 |
% 31.37/8.93 | Simplifying 1021 yields:
% 31.37/8.93 | (251) ~ (e4 = e1)
% 31.37/8.93 |
% 31.37/8.93 | Equations (997) can reduce 335 to:
% 31.37/8.93 | (645) ~ (e2 = e1)
% 31.37/8.93 |
% 31.37/8.93 | Simplifying 645 yields:
% 31.37/8.93 | (141) ~ (e2 = e1)
% 31.37/8.93 |
% 31.37/8.93 +-Applying beta-rule and splitting (210), into two cases.
% 31.37/8.93 |-Branch one:
% 31.37/8.93 | (524) all_0_39_39 = e1
% 31.37/8.93 |
% 31.37/8.93 | Combining equations (336,524) yields a new equation:
% 31.37/8.93 | (531) e2 = e1
% 31.37/8.93 |
% 31.37/8.93 | Simplifying 531 yields:
% 31.37/8.93 | (322) e2 = e1
% 31.37/8.93 |
% 31.37/8.93 | Equations (322) can reduce 141 to:
% 31.37/8.93 | (270) $false
% 31.37/8.93 |
% 31.37/8.93 |-The branch is then unsatisfiable
% 31.37/8.93 |-Branch two:
% 31.37/8.93 | (528) ~ (all_0_39_39 = e1)
% 31.37/8.93 | (529) all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1
% 31.37/8.93 |
% 31.37/8.93 +-Applying beta-rule and splitting (529), into two cases.
% 31.37/8.93 |-Branch one:
% 31.37/8.93 | (530) all_0_40_40 = e1
% 31.37/8.93 |
% 31.37/8.93 | Equations (530) can reduce 534 to:
% 31.37/8.93 | (270) $false
% 31.37/8.93 |
% 31.37/8.93 |-The branch is then unsatisfiable
% 31.37/8.93 |-Branch two:
% 31.37/8.93 | (534) ~ (all_0_40_40 = e1)
% 31.37/8.93 | (535) all_0_41_41 = e1 | all_0_42_42 = e1
% 31.37/8.93 |
% 31.37/8.93 +-Applying beta-rule and splitting (535), into two cases.
% 31.37/8.93 |-Branch one:
% 31.37/8.93 | (536) all_0_41_41 = e1
% 31.37/8.93 |
% 31.37/8.93 | Combining equations (358,536) yields a new equation:
% 31.37/8.93 | (525) e4 = e1
% 31.37/8.93 |
% 31.37/8.93 | Simplifying 525 yields:
% 31.37/8.93 | (526) e4 = e1
% 31.37/8.93 |
% 31.37/8.93 | Equations (526) can reduce 251 to:
% 31.37/8.93 | (270) $false
% 31.37/8.93 |
% 31.37/8.93 |-The branch is then unsatisfiable
% 31.37/8.93 |-Branch two:
% 31.37/8.93 | (540) ~ (all_0_41_41 = e1)
% 31.37/8.93 | (541) all_0_42_42 = e1
% 31.37/8.93 |
% 31.37/8.93 | Equations (541) can reduce 145 to:
% 31.37/8.93 | (534) ~ (all_0_40_40 = e1)
% 31.37/8.93 |
% 31.37/8.93 | Equations (541) can reduce 18 to:
% 31.37/8.93 | (6201) ~ (all_0_46_46 = e1)
% 31.37/8.93 |
% 31.37/8.93 | Simplifying 6201 yields:
% 31.37/8.93 | (106) ~ (all_0_46_46 = e1)
% 31.37/8.93 |
% 31.37/8.93 | Equations (541) can reduce 191 to:
% 31.37/8.93 | (2131) ~ (all_0_54_54 = e1)
% 31.37/8.93 |
% 31.37/8.93 | Simplifying 2131 yields:
% 31.37/8.93 | (425) ~ (all_0_54_54 = e1)
% 31.37/8.93 |
% 31.37/8.93 | Equations (541) can reduce 498 to:
% 31.37/8.93 | (645) ~ (e2 = e1)
% 31.37/8.93 |
% 31.37/8.93 | Simplifying 645 yields:
% 31.37/8.93 | (141) ~ (e2 = e1)
% 31.37/8.93 |
% 31.37/8.93 | Equations (541) can reduce 199 to:
% 31.37/8.93 | (132) ~ (e1 = e0)
% 31.37/8.93 |
% 31.37/8.93 +-Applying beta-rule and splitting (626), into two cases.
% 31.37/8.93 |-Branch one:
% 31.37/8.93 | (827) all_0_52_52 = e0
% 31.37/8.93 |
% 31.37/8.93 | Equations (827) can reduce 137 to:
% 31.37/8.93 | (238) ~ (all_0_40_40 = e0)
% 31.37/8.93 |
% 31.37/8.93 | Equations (827) can reduce 154 to:
% 31.37/8.93 | (987) ~ (all_0_51_51 = e0)
% 31.37/8.93 |
% 31.37/8.93 | Equations (827) can reduce 118 to:
% 31.37/8.93 | (3010) ~ (all_0_54_54 = e0)
% 31.37/8.93 |
% 31.37/8.93 | Simplifying 3010 yields:
% 31.37/8.93 | (3011) ~ (all_0_54_54 = e0)
% 31.37/8.93 |
% 31.46/8.93 | Equations (827) can reduce 230 to:
% 31.46/8.93 | (456) ~ (e4 = e0)
% 31.46/8.93 |
% 31.46/8.93 | Simplifying 456 yields:
% 31.46/8.93 | (6) ~ (e4 = e0)
% 31.46/8.93 |
% 31.46/8.93 | Equations (827) can reduce 642 to:
% 31.46/8.93 | (568) ~ (e1 = e0)
% 31.46/8.93 |
% 31.46/8.93 | Simplifying 568 yields:
% 31.46/8.93 | (132) ~ (e1 = e0)
% 31.46/8.93 |
% 31.46/8.93 +-Applying beta-rule and splitting (78), into two cases.
% 31.46/8.93 |-Branch one:
% 31.46/8.93 | (751) all_0_39_39 = e3
% 31.46/8.93 |
% 31.46/8.93 | Combining equations (751,336) yields a new equation:
% 31.46/8.93 | (437) e3 = e2
% 31.46/8.93 |
% 31.46/8.93 | Simplifying 437 yields:
% 31.46/8.93 | (414) e3 = e2
% 31.46/8.93 |
% 31.46/8.93 | Equations (414) can reduce 223 to:
% 31.46/8.93 | (270) $false
% 31.46/8.93 |
% 31.46/8.93 |-The branch is then unsatisfiable
% 31.46/8.93 |-Branch two:
% 31.46/8.93 | (755) ~ (all_0_39_39 = e3)
% 31.46/8.93 | (4262) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 31.46/8.93 |
% 31.46/8.93 +-Applying beta-rule and splitting (135), into two cases.
% 31.46/8.93 |-Branch one:
% 31.46/8.93 | (820) all_0_51_51 = e1
% 31.46/8.93 |
% 31.46/8.93 | Equations (820) can reduce 987 to:
% 31.46/8.93 | (132) ~ (e1 = e0)
% 31.46/8.93 |
% 31.46/8.93 | From (820) and (7) follows:
% 31.46/8.93 | (19288) op(e3, e1) = all_0_9_9
% 31.46/8.93 |
% 31.46/8.93 +-Applying beta-rule and splitting (4262), into two cases.
% 31.46/8.93 |-Branch one:
% 31.46/8.93 | (671) all_0_40_40 = e3
% 31.46/8.93 |
% 31.46/8.93 | Equations (671) can reduce 233 to:
% 31.46/8.93 | (719) ~ (e4 = e3)
% 31.46/8.93 |
% 31.46/8.93 | Simplifying 719 yields:
% 31.46/8.93 | (34) ~ (e4 = e3)
% 31.46/8.93 |
% 31.46/8.93 | Equations (671) can reduce 602 to:
% 31.46/8.93 | (223) ~ (e3 = e2)
% 31.46/8.93 |
% 31.46/8.93 | Equations (671) can reduce 534 to:
% 31.46/8.93 | (136) ~ (e3 = e1)
% 31.46/8.93 |
% 31.46/8.93 | Equations (671) can reduce 238 to:
% 31.46/8.93 | (66) ~ (e3 = e0)
% 31.46/8.93 |
% 31.46/8.93 +-Applying beta-rule and splitting (5076), into two cases.
% 31.46/8.93 |-Branch one:
% 31.46/8.93 | (830) all_0_56_56 = e0
% 31.46/8.93 |
% 31.46/8.93 | Equations (830) can reduce 419 to:
% 31.46/8.93 | (270) $false
% 31.46/8.93 |
% 31.46/8.93 |-The branch is then unsatisfiable
% 31.46/8.93 |-Branch two:
% 31.46/8.93 | (419) ~ (all_0_56_56 = e0)
% 31.46/8.93 | (5667) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1
% 31.46/8.93 |
% 31.46/8.93 +-Applying beta-rule and splitting (178), into two cases.
% 31.46/8.93 |-Branch one:
% 31.46/8.93 | (751) all_0_39_39 = e3
% 31.46/8.93 |
% 31.46/8.93 | Combining equations (751,336) yields a new equation:
% 31.46/8.93 | (437) e3 = e2
% 31.46/8.93 |
% 31.46/8.94 | Simplifying 437 yields:
% 31.46/8.94 | (414) e3 = e2
% 31.46/8.94 |
% 31.46/8.94 | Equations (414) can reduce 223 to:
% 31.46/8.94 | (270) $false
% 31.46/8.94 |
% 31.46/8.94 |-The branch is then unsatisfiable
% 31.46/8.94 |-Branch two:
% 31.46/8.94 | (755) ~ (all_0_39_39 = e3)
% 31.46/8.94 | (756) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 31.46/8.94 |
% 31.46/8.94 +-Applying beta-rule and splitting (221), into two cases.
% 31.46/8.94 |-Branch one:
% 31.46/8.94 | (1132) all_0_46_46 = e0
% 31.46/8.94 |
% 31.46/8.94 | Combining equations (1132,11390) yields a new equation:
% 31.46/8.94 | (14191) all_0_7_7 = e0
% 31.46/8.94 |
% 31.46/8.94 | Equations (1132) can reduce 215 to:
% 31.46/8.94 | (3010) ~ (all_0_54_54 = e0)
% 31.46/8.94 |
% 31.46/8.94 | Simplifying 3010 yields:
% 31.46/8.94 | (3011) ~ (all_0_54_54 = e0)
% 31.46/8.94 |
% 31.46/8.94 | Equations (1132) can reduce 805 to:
% 31.46/8.94 | (456) ~ (e4 = e0)
% 31.46/8.94 |
% 31.46/8.94 | Simplifying 456 yields:
% 31.46/8.94 | (6) ~ (e4 = e0)
% 31.46/8.94 |
% 31.46/8.94 | Equations (1132) can reduce 106 to:
% 31.46/8.94 | (568) ~ (e1 = e0)
% 31.46/8.94 |
% 31.47/8.94 | Simplifying 568 yields:
% 31.47/8.94 | (132) ~ (e1 = e0)
% 31.47/8.94 |
% 31.47/8.94 +-Applying beta-rule and splitting (21), into two cases.
% 31.47/8.94 |-Branch one:
% 31.47/8.94 | (824) all_0_51_51 = e3
% 31.47/8.94 |
% 31.47/8.94 | Combining equations (820,824) yields a new equation:
% 31.47/8.94 | (538) e3 = e1
% 31.47/8.94 |
% 31.47/8.94 | Equations (538) can reduce 136 to:
% 31.47/8.94 | (270) $false
% 31.47/8.94 |
% 31.47/8.94 |-The branch is then unsatisfiable
% 31.47/8.94 |-Branch two:
% 31.47/8.94 | (932) ~ (all_0_51_51 = e3)
% 31.47/8.94 | (1101) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 31.47/8.94 |
% 31.47/8.94 | Equations (820) can reduce 932 to:
% 31.47/8.94 | (769) ~ (e3 = e1)
% 31.47/8.94 |
% 31.47/8.94 | Simplifying 769 yields:
% 31.47/8.94 | (136) ~ (e3 = e1)
% 31.47/8.94 |
% 31.47/8.94 +-Applying beta-rule and splitting (1101), into two cases.
% 31.47/8.94 |-Branch one:
% 31.47/8.94 | (864) all_0_52_52 = e3
% 31.47/8.94 |
% 31.47/8.94 | Combining equations (864,827) yields a new equation:
% 31.47/8.94 | (783) e3 = e0
% 31.47/8.94 |
% 31.47/8.94 | Simplifying 783 yields:
% 31.47/8.94 | (784) e3 = e0
% 31.47/8.94 |
% 31.47/8.94 | Equations (784) can reduce 66 to:
% 31.47/8.94 | (270) $false
% 31.47/8.94 |
% 31.47/8.94 |-The branch is then unsatisfiable
% 31.47/8.94 |-Branch two:
% 31.47/8.94 | (826) ~ (all_0_52_52 = e3)
% 31.47/8.94 | (1107) all_0_53_53 = e3 | all_0_54_54 = e3
% 31.47/8.94 |
% 31.47/8.94 +-Applying beta-rule and splitting (5667), into two cases.
% 31.47/8.94 |-Branch one:
% 31.47/8.94 | (764) all_0_56_56 = e3
% 31.47/8.94 |
% 31.47/8.94 | Equations (764) can reduce 81 to:
% 31.47/8.94 | (717) ~ (all_0_58_58 = e3)
% 31.47/8.94 |
% 31.47/8.94 | Simplifying 717 yields:
% 31.47/8.94 | (718) ~ (all_0_58_58 = e3)
% 31.47/8.94 |
% 31.47/8.94 | Equations (764) can reduce 300 to:
% 31.47/8.94 | (223) ~ (e3 = e2)
% 31.47/8.94 |
% 31.47/8.94 | From (764) and (239) follows:
% 31.47/8.94 | (14231) op(e3, e3) = all_0_11_11
% 31.47/8.94 |
% 31.47/8.94 +-Applying beta-rule and splitting (1107), into two cases.
% 31.47/8.94 |-Branch one:
% 31.47/8.94 | (1114) all_0_53_53 = e3
% 31.47/8.94 |
% 31.47/8.94 | Combining equations (576,1114) yields a new equation:
% 31.47/8.94 | (414) e3 = e2
% 31.47/8.94 |
% 31.47/8.94 | Equations (414) can reduce 223 to:
% 31.47/8.94 | (270) $false
% 31.47/8.94 |
% 31.47/8.94 |-The branch is then unsatisfiable
% 31.47/8.94 |-Branch two:
% 31.47/8.94 | (356) ~ (all_0_53_53 = e3)
% 31.47/8.94 | (1119) all_0_54_54 = e3
% 31.47/8.94 |
% 31.47/8.94 | Equations (1119) can reduce 936 to:
% 31.47/8.94 | (719) ~ (e4 = e3)
% 31.47/8.94 |
% 31.47/8.94 | Simplifying 719 yields:
% 31.47/8.94 | (34) ~ (e4 = e3)
% 31.47/8.94 |
% 31.47/8.94 | Equations (1119) can reduce 261 to:
% 31.47/8.94 | (223) ~ (e3 = e2)
% 31.47/8.94 |
% 31.47/8.94 | Equations (1119) can reduce 3011 to:
% 31.47/8.94 | (66) ~ (e3 = e0)
% 31.47/8.94 |
% 31.47/8.94 +-Applying beta-rule and splitting (176), into two cases.
% 31.47/8.94 |-Branch one:
% 31.47/8.94 | (830) all_0_56_56 = e0
% 31.47/8.94 |
% 31.47/8.94 | Combining equations (764,830) yields a new equation:
% 31.47/8.94 | (783) e3 = e0
% 31.47/8.94 |
% 31.47/8.94 | Simplifying 783 yields:
% 31.47/8.94 | (784) e3 = e0
% 31.47/8.94 |
% 31.47/8.94 | Equations (784) can reduce 66 to:
% 31.47/8.94 | (270) $false
% 31.47/8.94 |
% 31.47/8.94 |-The branch is then unsatisfiable
% 31.47/8.94 |-Branch two:
% 31.47/8.94 | (419) ~ (all_0_56_56 = e0)
% 31.47/8.94 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 31.47/8.94 |
% 31.47/8.94 +-Applying beta-rule and splitting (219), into two cases.
% 31.47/8.94 |-Branch one:
% 31.47/8.94 | (351) all_0_41_41 = e3
% 31.47/8.94 |
% 31.47/8.94 | Combining equations (351,358) yields a new equation:
% 31.47/8.94 | (359) e4 = e3
% 31.47/8.94 |
% 31.47/8.94 | Equations (359) can reduce 34 to:
% 31.47/8.94 | (270) $false
% 31.47/8.94 |
% 31.47/8.94 |-The branch is then unsatisfiable
% 31.47/8.94 |-Branch two:
% 31.47/8.94 | (1237) ~ (all_0_41_41 = e3)
% 31.47/8.94 | (1508) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 31.47/8.94 |
% 31.47/8.94 | Equations (358) can reduce 1237 to:
% 31.47/8.94 | (34) ~ (e4 = e3)
% 31.47/8.94 |
% 31.47/8.94 +-Applying beta-rule and splitting (22), into two cases.
% 31.47/8.94 |-Branch one:
% 31.47/8.94 | (782) all_0_43_43 = e3
% 31.47/8.94 |
% 31.47/8.94 | Combining equations (502,782) yields a new equation:
% 31.47/8.94 | (660) e4 = e3
% 31.47/8.94 |
% 31.47/8.94 | Simplifying 660 yields:
% 31.47/8.94 | (359) e4 = e3
% 31.47/8.94 |
% 31.47/8.94 | Equations (359) can reduce 34 to:
% 31.47/8.94 | (270) $false
% 31.47/8.94 |
% 31.47/8.94 |-The branch is then unsatisfiable
% 31.47/8.94 |-Branch two:
% 31.47/8.94 | (786) ~ (all_0_43_43 = e3)
% 31.47/8.94 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 31.47/8.94 |
% 31.47/8.94 +-Applying beta-rule and splitting (204), into two cases.
% 31.47/8.94 |-Branch one:
% 31.47/8.94 | (396) all_0_58_58 = e2
% 31.47/8.94 |
% 31.47/8.94 | Equations (396) can reduce 376 to:
% 31.47/8.94 | (270) $false
% 31.47/8.94 |
% 31.47/8.94 |-The branch is then unsatisfiable
% 31.47/8.94 |-Branch two:
% 31.47/8.94 | (376) ~ (all_0_58_58 = e2)
% 31.47/8.94 | (3890) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1 | all_0_58_58 = e0
% 31.47/8.94 |
% 31.47/8.94 +-Applying beta-rule and splitting (1508), into two cases.
% 31.47/8.94 |-Branch one:
% 31.47/8.94 | (505) all_0_45_45 = e3
% 31.47/8.94 |
% 31.47/8.94 | Equations (505) can reduce 26 to:
% 31.47/8.94 | (136) ~ (e3 = e1)
% 31.47/8.94 |
% 31.47/8.94 | From (505) and (197) follows:
% 31.47/8.94 | (19364) op(e3, e1) = e3
% 31.47/8.94 |
% 31.47/8.94 +-Applying beta-rule and splitting (834), into two cases.
% 31.47/8.94 |-Branch one:
% 31.47/8.94 | (2258) all_0_57_57 = e0
% 31.47/8.94 |
% 31.47/8.94 | Combining equations (997,2258) yields a new equation:
% 31.47/8.94 | (571) e1 = e0
% 31.47/8.94 |
% 31.47/8.94 | Simplifying 571 yields:
% 31.47/8.94 | (560) e1 = e0
% 31.47/8.94 |
% 31.47/8.94 | Equations (560) can reduce 132 to:
% 31.47/8.94 | (270) $false
% 31.47/8.94 |
% 31.47/8.94 |-The branch is then unsatisfiable
% 31.47/8.94 |-Branch two:
% 31.47/8.94 | (2301) ~ (all_0_57_57 = e0)
% 31.47/8.94 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 31.47/8.94 |
% 31.47/8.94 +-Applying beta-rule and splitting (2302), into two cases.
% 31.47/8.94 |-Branch one:
% 31.47/8.94 | (585) all_0_58_58 = e0
% 31.47/8.94 |
% 31.47/8.94 | Equations (585) can reduce 278 to:
% 31.47/8.94 | (456) ~ (e4 = e0)
% 31.47/8.94 |
% 31.47/8.94 | Simplifying 456 yields:
% 31.47/8.94 | (6) ~ (e4 = e0)
% 31.47/8.94 |
% 31.47/8.94 | Equations (585) can reduce 376 to:
% 31.47/8.94 | (566) ~ (e2 = e0)
% 31.47/8.94 |
% 31.47/8.94 | Simplifying 566 yields:
% 31.47/8.94 | (57) ~ (e2 = e0)
% 31.47/8.94 |
% 31.47/8.94 | Instantiating formula (201) with e3, e3, all_0_11_11, e4 and discharging atoms op(e3, e3) = all_0_11_11, op(e3, e3) = e4, yields:
% 31.47/8.94 | (14233) all_0_11_11 = e4
% 31.47/8.94 |
% 31.47/8.94 | Instantiating formula (201) with e3, e1, e3, all_0_9_9 and discharging atoms op(e3, e1) = all_0_9_9, op(e3, e1) = e3, yields:
% 31.47/8.94 | (14234) all_0_9_9 = e3
% 31.47/8.94 |
% 31.47/8.94 +-Applying beta-rule and splitting (234), into two cases.
% 31.47/8.94 |-Branch one:
% 31.47/8.94 | (4239) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3)) | (all_0_9_9 = e1 & ~ (all_0_10_10 = e3))
% 31.47/8.94 |
% 31.47/8.94 +-Applying beta-rule and splitting (4239), into two cases.
% 31.47/8.94 |-Branch one:
% 31.47/8.94 | (4240) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3))
% 31.47/8.94 |
% 31.47/8.94 +-Applying beta-rule and splitting (4240), into two cases.
% 31.47/8.94 |-Branch one:
% 31.47/8.94 | (4241) all_0_4_4 = e4 & ~ (all_0_5_5 = e3)
% 31.47/8.94 |
% 31.47/8.94 | Applying alpha-rule on (4241) yields:
% 31.47/8.94 | (4242) all_0_4_4 = e4
% 31.47/8.94 | (4243) ~ (all_0_5_5 = e3)
% 31.47/8.94 |
% 31.47/8.94 | Combining equations (4242,12701) yields a new equation:
% 31.47/8.94 | (268) e4 = e2
% 31.47/8.94 |
% 31.47/8.94 | Simplifying 268 yields:
% 31.47/8.94 | (269) e4 = e2
% 31.47/8.94 |
% 31.47/8.94 | Equations (269) can reduce 231 to:
% 31.47/8.94 | (270) $false
% 31.47/8.94 |
% 31.47/8.94 |-The branch is then unsatisfiable
% 31.47/8.94 |-Branch two:
% 31.47/8.94 | (4247) all_0_7_7 = e2 & ~ (all_0_8_8 = e3)
% 31.47/8.94 |
% 31.47/8.94 | Applying alpha-rule on (4247) yields:
% 31.47/8.94 | (4248) all_0_7_7 = e2
% 31.47/8.94 | (4249) ~ (all_0_8_8 = e3)
% 31.47/8.94 |
% 31.47/8.94 | Combining equations (14191,4248) yields a new equation:
% 31.47/8.94 | (316) e2 = e0
% 31.47/8.94 |
% 31.47/8.94 | Equations (316) can reduce 57 to:
% 31.47/8.94 | (270) $false
% 31.47/8.94 |
% 31.47/8.94 |-The branch is then unsatisfiable
% 31.47/8.94 |-Branch two:
% 31.47/8.94 | (4253) all_0_9_9 = e1 & ~ (all_0_10_10 = e3)
% 31.47/8.94 |
% 31.47/8.94 | Applying alpha-rule on (4253) yields:
% 31.47/8.94 | (4254) all_0_9_9 = e1
% 31.47/8.94 | (4255) ~ (all_0_10_10 = e3)
% 31.47/8.94 |
% 31.47/8.95 | Combining equations (4254,14234) yields a new equation:
% 31.47/8.95 | (538) e3 = e1
% 31.47/8.95 |
% 31.47/8.95 | Equations (538) can reduce 136 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.95 | (4378) all_0_11_11 = e0 & ~ (all_0_12_12 = e3)
% 31.47/8.95 |
% 31.47/8.95 | Applying alpha-rule on (4378) yields:
% 31.47/8.95 | (4379) all_0_11_11 = e0
% 31.47/8.95 | (4380) ~ (all_0_12_12 = e3)
% 31.47/8.95 |
% 31.47/8.95 | Combining equations (14233,4379) yields a new equation:
% 31.47/8.95 | (478) e4 = e0
% 31.47/8.95 |
% 31.47/8.95 | Simplifying 478 yields:
% 31.47/8.95 | (479) e4 = e0
% 31.47/8.95 |
% 31.47/8.95 | Equations (479) can reduce 6 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.95 | (431) ~ (all_0_58_58 = e0)
% 31.47/8.95 | (2308) all_0_59_59 = e0
% 31.47/8.95 |
% 31.47/8.95 | Combining equations (402,2308) yields a new equation:
% 31.47/8.95 | (478) e4 = e0
% 31.47/8.95 |
% 31.47/8.95 | Simplifying 478 yields:
% 31.47/8.95 | (479) e4 = e0
% 31.47/8.95 |
% 31.47/8.95 | Equations (479) can reduce 6 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.95 | (354) ~ (all_0_45_45 = e3)
% 31.47/8.95 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 31.47/8.95 |
% 31.47/8.95 +-Applying beta-rule and splitting (787), into two cases.
% 31.47/8.95 |-Branch one:
% 31.47/8.95 | (858) all_0_44_44 = e3
% 31.47/8.95 |
% 31.47/8.95 | Combining equations (370,858) yields a new equation:
% 31.47/8.95 | (414) e3 = e2
% 31.47/8.95 |
% 31.47/8.95 | Equations (414) can reduce 223 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.95 | (862) ~ (all_0_44_44 = e3)
% 31.47/8.95 | (1070) all_0_45_45 = e3 | all_0_46_46 = e3
% 31.47/8.95 |
% 31.47/8.95 | Equations (370) can reduce 862 to:
% 31.47/8.95 | (301) ~ (e3 = e2)
% 31.47/8.95 |
% 31.47/8.95 | Simplifying 301 yields:
% 31.47/8.95 | (223) ~ (e3 = e2)
% 31.47/8.95 |
% 31.47/8.95 +-Applying beta-rule and splitting (1539), into two cases.
% 31.47/8.95 |-Branch one:
% 31.47/8.95 | (1114) all_0_53_53 = e3
% 31.47/8.95 |
% 31.47/8.95 | Combining equations (576,1114) yields a new equation:
% 31.47/8.95 | (414) e3 = e2
% 31.47/8.95 |
% 31.47/8.95 | Equations (414) can reduce 223 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.95 | (356) ~ (all_0_53_53 = e3)
% 31.47/8.95 | (4713) all_0_58_58 = e3
% 31.47/8.95 |
% 31.47/8.95 | Equations (4713) can reduce 718 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.95 | (767) ~ (all_0_56_56 = e3)
% 31.47/8.95 | (10136) all_0_56_56 = e4 | all_0_56_56 = e1
% 31.47/8.95 |
% 31.47/8.95 +-Applying beta-rule and splitting (756), into two cases.
% 31.47/8.95 |-Branch one:
% 31.47/8.95 | (782) all_0_43_43 = e3
% 31.47/8.95 |
% 31.47/8.95 | Combining equations (502,782) yields a new equation:
% 31.47/8.95 | (660) e4 = e3
% 31.47/8.95 |
% 31.47/8.95 | Simplifying 660 yields:
% 31.47/8.95 | (359) e4 = e3
% 31.47/8.95 |
% 31.47/8.95 | Equations (359) can reduce 34 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.95 | (786) ~ (all_0_43_43 = e3)
% 31.47/8.95 | (799) all_0_51_51 = e3 | all_0_56_56 = e3
% 31.47/8.95 |
% 31.47/8.95 +-Applying beta-rule and splitting (799), into two cases.
% 31.47/8.95 |-Branch one:
% 31.47/8.95 | (824) all_0_51_51 = e3
% 31.47/8.95 |
% 31.47/8.95 | Combining equations (820,824) yields a new equation:
% 31.47/8.95 | (538) e3 = e1
% 31.47/8.95 |
% 31.47/8.95 | Equations (538) can reduce 136 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.95 | (932) ~ (all_0_51_51 = e3)
% 31.47/8.95 | (764) all_0_56_56 = e3
% 31.47/8.95 |
% 31.47/8.95 | Equations (764) can reduce 767 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.95 | (1010) ~ (all_0_46_46 = e0)
% 31.47/8.95 | (3629) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 31.47/8.95 |
% 31.47/8.95 +-Applying beta-rule and splitting (116), into two cases.
% 31.47/8.95 |-Branch one:
% 31.47/8.95 | (411) all_0_43_43 = e0
% 31.47/8.95 |
% 31.47/8.95 | Combining equations (502,411) yields a new equation:
% 31.47/8.95 | (478) e4 = e0
% 31.47/8.95 |
% 31.47/8.95 | Simplifying 478 yields:
% 31.47/8.95 | (479) e4 = e0
% 31.47/8.95 |
% 31.47/8.95 | Equations (479) can reduce 6 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.95 | (455) ~ (all_0_43_43 = e0)
% 31.47/8.95 | (1122) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 31.47/8.95 |
% 31.47/8.95 | Equations (502) can reduce 455 to:
% 31.47/8.95 | (6) ~ (e4 = e0)
% 31.47/8.95 |
% 31.47/8.95 +-Applying beta-rule and splitting (176), into two cases.
% 31.47/8.95 |-Branch one:
% 31.47/8.95 | (830) all_0_56_56 = e0
% 31.47/8.95 |
% 31.47/8.95 | Equations (830) can reduce 419 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.95 | (419) ~ (all_0_56_56 = e0)
% 31.47/8.95 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 31.47/8.95 |
% 31.47/8.95 +-Applying beta-rule and splitting (204), into two cases.
% 31.47/8.95 |-Branch one:
% 31.47/8.95 | (396) all_0_58_58 = e2
% 31.47/8.95 |
% 31.47/8.95 | Equations (396) can reduce 376 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.95 | (376) ~ (all_0_58_58 = e2)
% 31.47/8.95 | (3890) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1 | all_0_58_58 = e0
% 31.47/8.95 |
% 31.47/8.95 +-Applying beta-rule and splitting (834), into two cases.
% 31.47/8.95 |-Branch one:
% 31.47/8.95 | (2258) all_0_57_57 = e0
% 31.47/8.95 |
% 31.47/8.95 | Combining equations (997,2258) yields a new equation:
% 31.47/8.95 | (571) e1 = e0
% 31.47/8.95 |
% 31.47/8.95 | Simplifying 571 yields:
% 31.47/8.95 | (560) e1 = e0
% 31.47/8.95 |
% 31.47/8.95 | Equations (560) can reduce 132 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.95 | (2301) ~ (all_0_57_57 = e0)
% 31.47/8.95 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 31.47/8.95 |
% 31.47/8.95 +-Applying beta-rule and splitting (2302), into two cases.
% 31.47/8.95 |-Branch one:
% 31.47/8.95 | (585) all_0_58_58 = e0
% 31.47/8.95 |
% 31.47/8.95 | Equations (585) can reduce 278 to:
% 31.47/8.95 | (456) ~ (e4 = e0)
% 31.47/8.95 |
% 31.47/8.95 | Simplifying 456 yields:
% 31.47/8.95 | (6) ~ (e4 = e0)
% 31.47/8.95 |
% 31.47/8.95 | Equations (585) can reduce 376 to:
% 31.47/8.95 | (566) ~ (e2 = e0)
% 31.47/8.95 |
% 31.47/8.95 | Simplifying 566 yields:
% 31.47/8.95 | (57) ~ (e2 = e0)
% 31.47/8.95 |
% 31.47/8.95 +-Applying beta-rule and splitting (3629), into two cases.
% 31.47/8.95 |-Branch one:
% 31.47/8.95 | (563) all_0_49_49 = e0
% 31.47/8.95 |
% 31.47/8.95 | Combining equations (307,563) yields a new equation:
% 31.47/8.95 | (622) e2 = e0
% 31.47/8.95 |
% 31.47/8.95 | Simplifying 622 yields:
% 31.47/8.95 | (316) e2 = e0
% 31.47/8.95 |
% 31.47/8.95 | Equations (316) can reduce 57 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.95 | (1231) ~ (all_0_49_49 = e0)
% 31.47/8.95 | (3638) all_0_54_54 = e0 | all_0_59_59 = e0
% 31.47/8.95 |
% 31.47/8.95 +-Applying beta-rule and splitting (3638), into two cases.
% 31.47/8.95 |-Branch one:
% 31.47/8.95 | (3084) all_0_54_54 = e0
% 31.47/8.95 |
% 31.47/8.95 | Equations (3084) can reduce 3011 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.95 | (3011) ~ (all_0_54_54 = e0)
% 31.47/8.95 | (2308) all_0_59_59 = e0
% 31.47/8.95 |
% 31.47/8.95 | Combining equations (2308,402) yields a new equation:
% 31.47/8.95 | (479) e4 = e0
% 31.47/8.95 |
% 31.47/8.95 | Equations (479) can reduce 6 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.95 | (431) ~ (all_0_58_58 = e0)
% 31.47/8.95 | (2308) all_0_59_59 = e0
% 31.47/8.95 |
% 31.47/8.95 | Combining equations (402,2308) yields a new equation:
% 31.47/8.95 | (478) e4 = e0
% 31.47/8.95 |
% 31.47/8.95 | Simplifying 478 yields:
% 31.47/8.95 | (479) e4 = e0
% 31.47/8.95 |
% 31.47/8.95 | Equations (479) can reduce 6 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.95 | (675) ~ (all_0_40_40 = e3)
% 31.47/8.95 | (5254) all_0_41_41 = e3 | all_0_42_42 = e3
% 31.47/8.95 |
% 31.47/8.95 +-Applying beta-rule and splitting (95), into two cases.
% 31.47/8.95 |-Branch one:
% 31.47/8.95 | (1258) all_0_42_42 = e3
% 31.47/8.95 |
% 31.47/8.95 | Combining equations (541,1258) yields a new equation:
% 31.47/8.95 | (538) e3 = e1
% 31.47/8.95 |
% 31.47/8.95 | Equations (538) can reduce 136 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.95 | (1316) ~ (all_0_42_42 = e3)
% 31.47/8.95 | (3656) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 31.47/8.95 |
% 31.47/8.95 | Equations (541) can reduce 1316 to:
% 31.47/8.95 | (769) ~ (e3 = e1)
% 31.47/8.95 |
% 31.47/8.95 | Simplifying 769 yields:
% 31.47/8.95 | (136) ~ (e3 = e1)
% 31.47/8.95 |
% 31.47/8.95 +-Applying beta-rule and splitting (22), into two cases.
% 31.47/8.95 |-Branch one:
% 31.47/8.95 | (782) all_0_43_43 = e3
% 31.47/8.95 |
% 31.47/8.95 | Combining equations (502,782) yields a new equation:
% 31.47/8.95 | (660) e4 = e3
% 31.47/8.95 |
% 31.47/8.95 | Simplifying 660 yields:
% 31.47/8.95 | (359) e4 = e3
% 31.47/8.95 |
% 31.47/8.95 | Equations (359) can reduce 34 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.95 | (786) ~ (all_0_43_43 = e3)
% 31.47/8.95 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 31.47/8.95 |
% 31.47/8.95 | Equations (502) can reduce 786 to:
% 31.47/8.95 | (34) ~ (e4 = e3)
% 31.47/8.95 |
% 31.47/8.95 +-Applying beta-rule and splitting (5254), into two cases.
% 31.47/8.95 |-Branch one:
% 31.47/8.95 | (351) all_0_41_41 = e3
% 31.47/8.95 |
% 31.47/8.95 | Combining equations (351,358) yields a new equation:
% 31.47/8.95 | (359) e4 = e3
% 31.47/8.95 |
% 31.47/8.95 | Equations (359) can reduce 34 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.95 | (1237) ~ (all_0_41_41 = e3)
% 31.47/8.95 | (1258) all_0_42_42 = e3
% 31.47/8.95 |
% 31.47/8.95 | Combining equations (541,1258) yields a new equation:
% 31.47/8.95 | (538) e3 = e1
% 31.47/8.95 |
% 31.47/8.95 | Equations (538) can reduce 136 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.95 | (748) ~ (all_0_51_51 = e1)
% 31.47/8.95 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 31.47/8.95 |
% 31.47/8.95 +-Applying beta-rule and splitting (823), into two cases.
% 31.47/8.95 |-Branch one:
% 31.47/8.95 | (848) all_0_52_52 = e1
% 31.47/8.95 |
% 31.47/8.95 | Combining equations (848,827) yields a new equation:
% 31.47/8.95 | (571) e1 = e0
% 31.47/8.95 |
% 31.47/8.95 | Simplifying 571 yields:
% 31.47/8.95 | (560) e1 = e0
% 31.47/8.95 |
% 31.47/8.95 | Equations (560) can reduce 132 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.95 | (642) ~ (all_0_52_52 = e1)
% 31.47/8.95 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 31.47/8.95 |
% 31.47/8.95 +-Applying beta-rule and splitting (852), into two cases.
% 31.47/8.95 |-Branch one:
% 31.47/8.95 | (853) all_0_53_53 = e1
% 31.47/8.95 |
% 31.47/8.95 | Combining equations (853,576) yields a new equation:
% 31.47/8.95 | (322) e2 = e1
% 31.47/8.95 |
% 31.47/8.95 | Equations (322) can reduce 141 to:
% 31.47/8.95 | (270) $false
% 31.47/8.95 |
% 31.47/8.95 |-The branch is then unsatisfiable
% 31.47/8.95 |-Branch two:
% 31.47/8.96 | (874) ~ (all_0_53_53 = e1)
% 31.47/8.96 | (875) all_0_54_54 = e1
% 31.47/8.96 |
% 31.47/8.96 | Equations (875) can reduce 425 to:
% 31.47/8.96 | (270) $false
% 31.47/8.96 |
% 31.47/8.96 |-The branch is then unsatisfiable
% 31.47/8.96 |-Branch two:
% 31.47/8.96 | (925) ~ (all_0_52_52 = e0)
% 31.47/8.96 | (2258) all_0_57_57 = e0
% 31.47/8.96 |
% 31.47/8.96 | Combining equations (997,2258) yields a new equation:
% 31.47/8.96 | (571) e1 = e0
% 31.47/8.96 |
% 31.47/8.96 | Simplifying 571 yields:
% 31.47/8.96 | (560) e1 = e0
% 31.47/8.96 |
% 31.47/8.96 | Equations (560) can reduce 132 to:
% 31.47/8.96 | (270) $false
% 31.47/8.96 |
% 31.47/8.96 |-The branch is then unsatisfiable
% 31.47/8.96 |-Branch two:
% 31.47/8.96 | (644) ~ (all_0_57_57 = e1)
% 31.47/8.96 | (1000) all_0_58_58 = e1 | all_0_59_59 = e1
% 31.47/8.96 |
% 31.47/8.96 +-Applying beta-rule and splitting (1000), into two cases.
% 31.47/8.96 |-Branch one:
% 31.47/8.96 | (1001) all_0_58_58 = e1
% 31.47/8.96 |
% 31.47/8.96 | Equations (1001) can reduce 1004 to:
% 31.47/8.96 | (270) $false
% 31.47/8.96 |
% 31.47/8.96 |-The branch is then unsatisfiable
% 31.47/8.96 |-Branch two:
% 31.47/8.96 | (1004) ~ (all_0_58_58 = e1)
% 31.47/8.96 | (424) all_0_59_59 = e1
% 31.47/8.96 |
% 31.47/8.96 | Combining equations (424,402) yields a new equation:
% 31.47/8.96 | (526) e4 = e1
% 31.47/8.96 |
% 31.47/8.96 | Equations (526) can reduce 251 to:
% 31.47/8.96 | (270) $false
% 31.47/8.96 |
% 31.47/8.96 |-The branch is then unsatisfiable
% 31.47/8.96 |-Branch two:
% 31.47/8.96 | (361) ~ (all_0_41_41 = e4)
% 31.47/8.96 | (362) all_0_45_45 = e4 | all_0_53_53 = e4 | all_0_58_58 = e4
% 31.47/8.96 |
% 31.47/8.96 +-Applying beta-rule and splitting (592), into two cases.
% 31.47/8.96 |-Branch one:
% 31.47/8.96 | (358) all_0_41_41 = e4
% 31.47/8.96 |
% 31.47/8.96 | Equations (358) can reduce 361 to:
% 31.47/8.96 | (270) $false
% 31.47/8.96 |
% 31.47/8.96 |-The branch is then unsatisfiable
% 31.47/8.96 |-Branch two:
% 31.47/8.96 | (361) ~ (all_0_41_41 = e4)
% 31.47/8.96 | (512) all_0_42_42 = e4
% 31.47/8.96 |
% 31.47/8.96 | Equations (512) can reduce 520 to:
% 31.47/8.96 | (270) $false
% 31.47/8.96 |
% 31.47/8.96 |-The branch is then unsatisfiable
% 31.47/8.96 |-Branch two:
% 31.47/8.96 | (510) ~ (all_0_43_43 = e4)
% 31.47/8.96 | (4527) all_0_51_51 = e4 | all_0_56_56 = e4
% 31.47/8.96 |
% 31.47/8.96 +-Applying beta-rule and splitting (4527), into two cases.
% 31.47/8.96 |-Branch one:
% 31.47/8.96 | (1467) all_0_51_51 = e4
% 31.47/8.96 |
% 31.47/8.96 | Equations (1467) can reduce 697 to:
% 31.47/8.96 | (270) $false
% 31.47/8.96 |
% 31.47/8.96 |-The branch is then unsatisfiable
% 31.47/8.96 |-Branch two:
% 31.47/8.96 | (697) ~ (all_0_51_51 = e4)
% 31.47/8.96 | (4744) all_0_56_56 = e4
% 31.47/8.96 |
% 31.47/8.96 | Equations (4744) can reduce 274 to:
% 31.47/8.96 | (270) $false
% 31.47/8.96 |
% 31.47/8.96 |-The branch is then unsatisfiable
% 31.47/8.96 |-Branch two:
% 31.47/8.96 | (280) ~ (all_0_59_59 = e4)
% 31.47/8.96 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 31.47/8.96 |
% 31.47/8.96 +-Applying beta-rule and splitting (407), into two cases.
% 31.47/8.96 |-Branch one:
% 31.47/8.96 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 31.47/8.96 |
% 31.47/8.96 +-Applying beta-rule and splitting (408), into two cases.
% 31.47/8.96 |-Branch one:
% 31.47/8.96 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 31.47/8.96 |
% 31.47/8.96 +-Applying beta-rule and splitting (409), into two cases.
% 31.47/8.96 |-Branch one:
% 31.47/8.96 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 31.47/8.96 |
% 31.47/8.96 | Applying alpha-rule on (410) yields:
% 31.47/8.96 | (411) all_0_43_43 = e0
% 31.47/8.96 | (412) all_0_59_59 = e3
% 31.47/8.96 | (413) ~ (all_0_46_46 = e3)
% 31.47/8.96 |
% 31.47/8.96 | Equations (411) can reduce 455 to:
% 31.47/8.96 | (270) $false
% 31.47/8.96 |
% 31.47/8.96 |-The branch is then unsatisfiable
% 31.47/8.96 |-Branch two:
% 31.47/8.96 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 31.47/8.96 |
% 31.47/8.96 | Applying alpha-rule on (416) yields:
% 31.47/8.96 | (411) all_0_43_43 = e0
% 31.47/8.96 | (412) all_0_59_59 = e3
% 31.47/8.96 | (419) ~ (all_0_56_56 = e0)
% 31.47/8.96 |
% 31.47/8.96 | Equations (411) can reduce 455 to:
% 31.47/8.96 | (270) $false
% 31.47/8.96 |
% 31.47/8.96 |-The branch is then unsatisfiable
% 31.47/8.96 |-Branch two:
% 31.47/8.96 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 31.47/8.96 |
% 31.47/8.96 | Applying alpha-rule on (422) yields:
% 31.47/8.96 | (423) all_0_53_53 = e0
% 31.47/8.96 | (424) all_0_59_59 = e1
% 31.47/8.96 | (425) ~ (all_0_54_54 = e1)
% 31.47/8.96 |
% 31.47/8.96 | Combining equations (423,576) yields a new equation:
% 31.47/8.96 | (316) e2 = e0
% 31.47/8.96 |
% 31.47/8.96 | Equations (316) can reduce 57 to:
% 31.47/8.96 | (270) $false
% 31.47/8.96 |
% 31.47/8.96 |-The branch is then unsatisfiable
% 31.47/8.96 |-Branch two:
% 31.47/8.96 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 31.47/8.96 |
% 31.47/8.96 | Applying alpha-rule on (428) yields:
% 31.47/8.96 | (423) all_0_53_53 = e0
% 31.47/8.96 | (424) all_0_59_59 = e1
% 31.47/8.96 | (431) ~ (all_0_58_58 = e0)
% 31.47/8.96 |
% 31.47/8.96 | Combining equations (423,576) yields a new equation:
% 31.47/8.96 | (316) e2 = e0
% 31.47/8.96 |
% 31.47/8.96 | Equations (316) can reduce 57 to:
% 31.47/8.96 | (270) $false
% 31.47/8.96 |
% 31.47/8.96 |-The branch is then unsatisfiable
% 31.47/8.96 |-Branch two:
% 31.47/8.96 | (259) ~ (all_0_53_53 = e2)
% 31.47/8.96 | (396) all_0_58_58 = e2
% 31.47/8.96 |
% 31.47/8.96 | Equations (396) can reduce 376 to:
% 31.47/8.96 | (270) $false
% 31.47/8.96 |
% 31.47/8.96 |-The branch is then unsatisfiable
% 31.47/8.96 |-Branch two:
% 31.47/8.96 | (333) ~ (all_0_44_44 = e2)
% 31.47/8.96 | (373) all_0_44_44 = e3 | all_0_44_44 = e0
% 31.47/8.96 |
% 31.47/8.96 +-Applying beta-rule and splitting (607), into two cases.
% 31.47/8.96 |-Branch one:
% 31.47/8.96 | (370) all_0_44_44 = e2
% 31.47/8.96 |
% 31.47/8.96 | Equations (370) can reduce 333 to:
% 31.47/8.96 | (270) $false
% 31.47/8.96 |
% 31.47/8.96 |-The branch is then unsatisfiable
% 31.47/8.96 |-Branch two:
% 31.47/8.96 | (333) ~ (all_0_44_44 = e2)
% 31.47/8.96 | (3377) all_0_52_52 = e2 | all_0_57_57 = e2
% 31.47/8.96 |
% 31.47/8.96 +-Applying beta-rule and splitting (3377), into two cases.
% 31.47/8.96 |-Branch one:
% 31.47/8.96 | (685) all_0_52_52 = e2
% 31.47/8.96 |
% 31.47/8.96 | Equations (685) can reduce 154 to:
% 31.47/8.96 | (255) ~ (all_0_51_51 = e2)
% 31.47/8.96 |
% 31.47/8.96 | Equations (685) can reduce 213 to:
% 31.47/8.96 | (258) ~ (all_0_53_53 = e2)
% 31.47/8.96 |
% 31.47/8.96 | Simplifying 258 yields:
% 31.47/8.96 | (259) ~ (all_0_53_53 = e2)
% 31.47/8.96 |
% 31.47/8.96 | Equations (685) can reduce 235 to:
% 31.47/8.96 | (334) ~ (all_0_57_57 = e2)
% 31.47/8.96 |
% 31.47/8.96 | Simplifying 334 yields:
% 31.47/8.96 | (335) ~ (all_0_57_57 = e2)
% 31.47/8.96 |
% 31.47/8.96 | Equations (685) can reduce 230 to:
% 31.47/8.96 | (377) ~ (e4 = e2)
% 31.47/8.96 |
% 31.47/8.96 | Simplifying 377 yields:
% 31.47/8.96 | (231) ~ (e4 = e2)
% 31.47/8.96 |
% 31.47/8.96 | From (685) and (27) follows:
% 31.47/8.96 | (11734) op(e2, e2) = all_0_17_17
% 31.47/8.96 |
% 31.47/8.96 +-Applying beta-rule and splitting (187), into two cases.
% 31.47/8.96 |-Branch one:
% 31.47/8.96 | (436) all_0_41_41 = e2
% 31.47/8.96 |
% 31.47/8.96 | Equations (436) can reduce 331 to:
% 31.47/8.96 | (270) $false
% 31.47/8.96 |
% 31.47/8.96 |-The branch is then unsatisfiable
% 31.47/8.96 |-Branch two:
% 31.47/8.96 | (331) ~ (all_0_41_41 = e2)
% 31.47/8.96 | (441) all_0_45_45 = e2 | all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 31.47/8.96 |
% 31.47/8.96 +-Applying beta-rule and splitting (441), into two cases.
% 31.47/8.96 |-Branch one:
% 31.47/8.96 | (374) all_0_45_45 = e2
% 31.47/8.96 |
% 31.47/8.96 | Equations (374) can reduce 51 to:
% 31.47/8.96 | (331) ~ (all_0_41_41 = e2)
% 31.47/8.96 |
% 31.47/8.96 | Equations (374) can reduce 84 to:
% 31.47/8.96 | (292) ~ (all_0_43_43 = e2)
% 31.47/8.96 |
% 31.47/8.96 | Equations (374) can reduce 38 to:
% 31.47/8.96 | (1435) ~ (all_0_46_46 = e2)
% 31.47/8.96 |
% 31.47/8.96 | Simplifying 1435 yields:
% 31.47/8.96 | (1436) ~ (all_0_46_46 = e2)
% 31.47/8.96 |
% 31.47/8.96 | Equations (374) can reduce 128 to:
% 31.47/8.96 | (258) ~ (all_0_53_53 = e2)
% 31.47/8.96 |
% 31.47/8.96 | Simplifying 258 yields:
% 31.47/8.96 | (259) ~ (all_0_53_53 = e2)
% 31.47/8.96 |
% 31.47/8.96 | Equations (374) can reduce 108 to:
% 31.47/8.96 | (375) ~ (all_0_58_58 = e2)
% 31.47/8.96 |
% 31.47/8.96 | Simplifying 375 yields:
% 31.47/8.96 | (376) ~ (all_0_58_58 = e2)
% 31.47/8.96 |
% 31.47/8.96 | Equations (374) can reduce 26 to:
% 31.47/8.96 | (141) ~ (e2 = e1)
% 31.47/8.96 |
% 31.47/8.96 | From (374) and (197) follows:
% 31.47/8.96 | (19603) op(e3, e1) = e2
% 31.47/8.96 |
% 31.47/8.96 | Instantiating formula (201) with e2, e2, all_0_17_17, e4 and discharging atoms op(e2, e2) = all_0_17_17, op(e2, e2) = e4, yields:
% 31.47/8.96 | (11735) all_0_17_17 = e4
% 31.47/8.96 |
% 31.47/8.96 +-Applying beta-rule and splitting (8), into two cases.
% 31.47/8.96 |-Branch one:
% 31.47/8.96 | (530) all_0_40_40 = e1
% 31.47/8.96 |
% 31.47/8.96 | Equations (530) can reduce 145 to:
% 31.47/8.96 | (639) ~ (all_0_42_42 = e1)
% 31.47/8.96 |
% 31.47/8.96 | Simplifying 639 yields:
% 31.47/8.96 | (640) ~ (all_0_42_42 = e1)
% 31.47/8.96 |
% 31.47/8.96 | Equations (530) can reduce 149 to:
% 31.47/8.96 | (643) ~ (all_0_57_57 = e1)
% 31.47/8.96 |
% 31.47/8.96 | Simplifying 643 yields:
% 31.47/8.96 | (644) ~ (all_0_57_57 = e1)
% 31.47/8.96 |
% 31.47/8.96 | From (530) and (68) follows:
% 31.47/8.96 | (648) op(e2, e1) = all_0_13_13
% 31.47/8.96 |
% 31.47/8.96 | Instantiating formula (201) with e2, e1, all_0_13_13, e1 and discharging atoms op(e2, e1) = all_0_13_13, op(e2, e1) = e1, yields:
% 31.47/8.96 | (5957) all_0_13_13 = e1
% 31.47/8.96 |
% 31.47/8.96 +-Applying beta-rule and splitting (9), into two cases.
% 31.47/8.96 |-Branch one:
% 31.47/8.96 | (621) all_0_44_44 = e0
% 31.47/8.96 |
% 31.47/8.96 | Equations (621) can reduce 174 to:
% 31.47/8.96 | (1057) ~ (all_0_46_46 = e0)
% 31.47/8.96 |
% 31.47/8.96 | Simplifying 1057 yields:
% 31.47/8.96 | (1010) ~ (all_0_46_46 = e0)
% 31.47/8.96 |
% 31.47/8.96 | Equations (621) can reduce 10 to:
% 31.47/8.96 | (9326) ~ (all_0_57_57 = e0)
% 31.47/8.96 |
% 31.47/8.96 | Simplifying 9326 yields:
% 31.47/8.96 | (2301) ~ (all_0_57_57 = e0)
% 31.47/8.96 |
% 31.47/8.96 +-Applying beta-rule and splitting (33), into two cases.
% 31.47/8.96 |-Branch one:
% 31.47/8.96 | (392) all_0_57_57 = e2
% 31.47/8.96 |
% 31.47/8.96 | Equations (392) can reduce 335 to:
% 31.47/8.96 | (270) $false
% 31.47/8.96 |
% 31.47/8.96 |-The branch is then unsatisfiable
% 31.47/8.96 |-Branch two:
% 31.47/8.96 | (335) ~ (all_0_57_57 = e2)
% 31.47/8.96 | (670) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 31.47/8.96 |
% 31.47/8.96 +-Applying beta-rule and splitting (670), into two cases.
% 31.47/8.96 |-Branch one:
% 31.47/8.96 | (2258) all_0_57_57 = e0
% 31.47/8.96 |
% 31.47/8.96 | Equations (2258) can reduce 2301 to:
% 31.47/8.96 | (270) $false
% 31.47/8.96 |
% 31.47/8.96 |-The branch is then unsatisfiable
% 31.47/8.96 |-Branch two:
% 31.47/8.96 | (2301) ~ (all_0_57_57 = e0)
% 31.47/8.96 | (9345) all_0_57_57 = e3 | all_0_57_57 = e1
% 31.47/8.96 |
% 31.47/8.96 +-Applying beta-rule and splitting (9345), into two cases.
% 31.47/8.96 |-Branch one:
% 31.47/8.96 | (869) all_0_57_57 = e3
% 31.47/8.96 |
% 31.47/8.96 | Equations (869) can reduce 104 to:
% 31.47/8.96 | (767) ~ (all_0_56_56 = e3)
% 31.47/8.96 |
% 31.47/8.96 | Equations (869) can reduce 37 to:
% 31.47/8.96 | (717) ~ (all_0_58_58 = e3)
% 31.47/8.96 |
% 31.47/8.96 | Simplifying 717 yields:
% 31.47/8.96 | (718) ~ (all_0_58_58 = e3)
% 31.47/8.96 |
% 31.47/8.96 | Equations (869) can reduce 2301 to:
% 31.47/8.96 | (66) ~ (e3 = e0)
% 31.47/8.96 |
% 31.47/8.96 +-Applying beta-rule and splitting (222), into two cases.
% 31.47/8.96 |-Branch one:
% 31.47/8.96 | (522) all_0_39_39 = e4
% 31.47/8.96 |
% 31.47/8.96 | Combining equations (336,522) yields a new equation:
% 31.47/8.96 | (269) e4 = e2
% 31.47/8.96 |
% 31.47/8.96 | Equations (269) can reduce 231 to:
% 31.47/8.96 | (270) $false
% 31.47/8.96 |
% 31.47/8.96 |-The branch is then unsatisfiable
% 31.47/8.96 |-Branch two:
% 31.47/8.96 | (591) ~ (all_0_39_39 = e4)
% 31.47/8.96 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 31.47/8.96 |
% 31.47/8.96 | Equations (336) can reduce 591 to:
% 31.47/8.96 | (377) ~ (e4 = e2)
% 31.47/8.96 |
% 31.47/8.96 | Simplifying 377 yields:
% 31.47/8.96 | (231) ~ (e4 = e2)
% 31.47/8.96 |
% 31.47/8.96 +-Applying beta-rule and splitting (44), into two cases.
% 31.47/8.96 |-Branch one:
% 31.47/8.96 | (502) all_0_43_43 = e4
% 31.47/8.96 |
% 31.47/8.96 | Equations (502) can reduce 103 to:
% 31.47/8.96 | (804) ~ (all_0_46_46 = e4)
% 31.47/8.96 |
% 31.47/8.96 | Simplifying 804 yields:
% 31.47/8.96 | (805) ~ (all_0_46_46 = e4)
% 31.47/8.96 |
% 31.47/8.96 | Equations (502) can reduce 188 to:
% 31.47/8.96 | (273) ~ (all_0_56_56 = e4)
% 31.47/8.96 |
% 31.47/8.96 | Simplifying 273 yields:
% 31.47/8.96 | (274) ~ (all_0_56_56 = e4)
% 31.47/8.96 |
% 31.47/8.96 +-Applying beta-rule and splitting (208), into two cases.
% 31.47/8.96 |-Branch one:
% 31.47/8.96 | (388) all_0_56_56 = e2
% 31.47/8.96 |
% 31.47/8.96 | Equations (388) can reduce 300 to:
% 31.47/8.96 | (270) $false
% 31.47/8.96 |
% 31.47/8.96 |-The branch is then unsatisfiable
% 31.47/8.96 |-Branch two:
% 31.47/8.96 | (300) ~ (all_0_56_56 = e2)
% 31.47/8.96 | (5076) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1 | all_0_56_56 = e0
% 31.47/8.96 |
% 31.47/8.96 +-Applying beta-rule and splitting (5076), into two cases.
% 31.47/8.96 |-Branch one:
% 31.47/8.96 | (830) all_0_56_56 = e0
% 31.47/8.96 |
% 31.47/8.96 | Equations (830) can reduce 419 to:
% 31.47/8.96 | (270) $false
% 31.47/8.96 |
% 31.47/8.96 |-The branch is then unsatisfiable
% 31.47/8.96 |-Branch two:
% 31.47/8.96 | (419) ~ (all_0_56_56 = e0)
% 31.47/8.96 | (5667) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1
% 31.47/8.96 |
% 31.47/8.96 +-Applying beta-rule and splitting (220), into two cases.
% 31.47/8.96 |-Branch one:
% 31.47/8.96 | (497) all_0_46_46 = e2
% 31.47/8.96 |
% 31.47/8.96 | Equations (497) can reduce 1436 to:
% 31.47/8.96 | (270) $false
% 31.47/8.96 |
% 31.47/8.96 |-The branch is then unsatisfiable
% 31.47/8.96 |-Branch two:
% 31.47/8.96 | (1436) ~ (all_0_46_46 = e2)
% 31.47/8.96 | (1523) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e0
% 31.47/8.96 |
% 31.47/8.96 +-Applying beta-rule and splitting (1523), into two cases.
% 31.47/8.96 |-Branch one:
% 31.47/8.96 | (1132) all_0_46_46 = e0
% 31.47/8.96 |
% 31.47/8.96 | Equations (1132) can reduce 1010 to:
% 31.47/8.96 | (270) $false
% 31.47/8.96 |
% 31.47/8.96 |-The branch is then unsatisfiable
% 31.47/8.96 |-Branch two:
% 31.47/8.96 | (1010) ~ (all_0_46_46 = e0)
% 31.47/8.96 | (1529) all_0_46_46 = e4 | all_0_46_46 = e3
% 31.47/8.96 |
% 31.47/8.97 +-Applying beta-rule and splitting (5667), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (764) all_0_56_56 = e3
% 31.47/8.97 |
% 31.47/8.97 | Equations (764) can reduce 767 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (767) ~ (all_0_56_56 = e3)
% 31.47/8.97 | (10136) all_0_56_56 = e4 | all_0_56_56 = e1
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (1529), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (1091) all_0_46_46 = e3
% 31.47/8.97 |
% 31.47/8.97 | Equations (1091) can reduce 18 to:
% 31.47/8.97 | (1316) ~ (all_0_42_42 = e3)
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (16), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (698) all_0_42_42 = e2
% 31.47/8.97 |
% 31.47/8.97 | Equations (698) can reduce 498 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (498) ~ (all_0_42_42 = e2)
% 31.47/8.97 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (1245), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (1258) all_0_42_42 = e3
% 31.47/8.97 |
% 31.47/8.97 | Equations (1258) can reduce 1316 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (1316) ~ (all_0_42_42 = e3)
% 31.47/8.97 | (1317) all_0_42_42 = e4 | all_0_42_42 = e1
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (1317), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (541) all_0_42_42 = e1
% 31.47/8.97 |
% 31.47/8.97 | Equations (541) can reduce 640 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (640) ~ (all_0_42_42 = e1)
% 31.47/8.97 | (512) all_0_42_42 = e4
% 31.47/8.97 |
% 31.47/8.97 | Equations (512) can reduce 94 to:
% 31.47/8.97 | (361) ~ (all_0_41_41 = e4)
% 31.47/8.97 |
% 31.47/8.97 | Equations (512) can reduce 498 to:
% 31.47/8.97 | (231) ~ (e4 = e2)
% 31.47/8.97 |
% 31.47/8.97 | Equations (512) can reduce 199 to:
% 31.47/8.97 | (6) ~ (e4 = e0)
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (158), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (358) all_0_41_41 = e4
% 31.47/8.97 |
% 31.47/8.97 | Equations (358) can reduce 361 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (361) ~ (all_0_41_41 = e4)
% 31.47/8.97 | (362) all_0_45_45 = e4 | all_0_53_53 = e4 | all_0_58_58 = e4
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (163), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (272) all_0_55_55 = e4
% 31.47/8.97 |
% 31.47/8.97 | Combining equations (382,272) yields a new equation:
% 31.47/8.97 | (269) e4 = e2
% 31.47/8.97 |
% 31.47/8.97 | Equations (269) can reduce 231 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (14603) ~ (all_0_55_55 = e4)
% 31.47/8.97 | (14604) all_0_56_56 = e4 | all_0_58_58 = e4 | all_0_59_59 = e4
% 31.47/8.97 |
% 31.47/8.97 | Equations (382) can reduce 14603 to:
% 31.47/8.97 | (377) ~ (e4 = e2)
% 31.47/8.97 |
% 31.47/8.97 | Simplifying 377 yields:
% 31.47/8.97 | (231) ~ (e4 = e2)
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (10136), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (747) all_0_56_56 = e1
% 31.47/8.97 |
% 31.47/8.97 | Equations (747) can reduce 185 to:
% 31.47/8.97 | (749) ~ (all_0_59_59 = e1)
% 31.47/8.97 |
% 31.47/8.97 | Simplifying 749 yields:
% 31.47/8.97 | (750) ~ (all_0_59_59 = e1)
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (362), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (363) all_0_45_45 = e4
% 31.47/8.97 |
% 31.47/8.97 | Combining equations (374,363) yields a new equation:
% 31.47/8.97 | (269) e4 = e2
% 31.47/8.97 |
% 31.47/8.97 | Equations (269) can reduce 231 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (352) ~ (all_0_45_45 = e4)
% 31.47/8.97 | (366) all_0_53_53 = e4 | all_0_58_58 = e4
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (366), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (367) all_0_53_53 = e4
% 31.47/8.97 |
% 31.47/8.97 | Equations (367) can reduce 599 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (599) ~ (all_0_53_53 = e4)
% 31.47/8.97 | (600) all_0_58_58 = e4
% 31.47/8.97 |
% 31.47/8.97 | Equations (600) can reduce 156 to:
% 31.47/8.97 | (279) ~ (all_0_59_59 = e4)
% 31.47/8.97 |
% 31.47/8.97 | Simplifying 279 yields:
% 31.47/8.97 | (280) ~ (all_0_59_59 = e4)
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (93), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (402) all_0_59_59 = e4
% 31.47/8.97 |
% 31.47/8.97 | Equations (402) can reduce 280 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (280) ~ (all_0_59_59 = e4)
% 31.47/8.97 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (407), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (408), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (409), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 31.47/8.97 |
% 31.47/8.97 | Applying alpha-rule on (410) yields:
% 31.47/8.97 | (411) all_0_43_43 = e0
% 31.47/8.97 | (412) all_0_59_59 = e3
% 31.47/8.97 | (413) ~ (all_0_46_46 = e3)
% 31.47/8.97 |
% 31.47/8.97 | Combining equations (502,411) yields a new equation:
% 31.47/8.97 | (478) e4 = e0
% 31.47/8.97 |
% 31.47/8.97 | Simplifying 478 yields:
% 31.47/8.97 | (479) e4 = e0
% 31.47/8.97 |
% 31.47/8.97 | Equations (479) can reduce 6 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 31.47/8.97 |
% 31.47/8.97 | Applying alpha-rule on (416) yields:
% 31.47/8.97 | (411) all_0_43_43 = e0
% 31.47/8.97 | (412) all_0_59_59 = e3
% 31.47/8.97 | (419) ~ (all_0_56_56 = e0)
% 31.47/8.97 |
% 31.47/8.97 | Combining equations (502,411) yields a new equation:
% 31.47/8.97 | (478) e4 = e0
% 31.47/8.97 |
% 31.47/8.97 | Simplifying 478 yields:
% 31.47/8.97 | (479) e4 = e0
% 31.47/8.97 |
% 31.47/8.97 | Equations (479) can reduce 6 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 31.47/8.97 |
% 31.47/8.97 | Applying alpha-rule on (422) yields:
% 31.47/8.97 | (423) all_0_53_53 = e0
% 31.47/8.97 | (424) all_0_59_59 = e1
% 31.47/8.97 | (425) ~ (all_0_54_54 = e1)
% 31.47/8.97 |
% 31.47/8.97 | Equations (424) can reduce 750 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 31.47/8.97 |
% 31.47/8.97 | Applying alpha-rule on (428) yields:
% 31.47/8.97 | (423) all_0_53_53 = e0
% 31.47/8.97 | (424) all_0_59_59 = e1
% 31.47/8.97 | (431) ~ (all_0_58_58 = e0)
% 31.47/8.97 |
% 31.47/8.97 | Equations (424) can reduce 750 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (995) ~ (all_0_56_56 = e1)
% 31.47/8.97 | (4744) all_0_56_56 = e4
% 31.47/8.97 |
% 31.47/8.97 | Equations (4744) can reduce 274 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (413) ~ (all_0_46_46 = e3)
% 31.47/8.97 | (517) all_0_46_46 = e4
% 31.47/8.97 |
% 31.47/8.97 | Equations (517) can reduce 805 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (510) ~ (all_0_43_43 = e4)
% 31.47/8.97 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (511), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (363) all_0_45_45 = e4
% 31.47/8.97 |
% 31.47/8.97 | Combining equations (374,363) yields a new equation:
% 31.47/8.97 | (269) e4 = e2
% 31.47/8.97 |
% 31.47/8.97 | Equations (269) can reduce 231 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (352) ~ (all_0_45_45 = e4)
% 31.47/8.97 | (517) all_0_46_46 = e4
% 31.47/8.97 |
% 31.47/8.97 | Equations (517) can reduce 18 to:
% 31.47/8.97 | (520) ~ (all_0_42_42 = e4)
% 31.47/8.97 |
% 31.47/8.97 | Equations (517) can reduce 1436 to:
% 31.47/8.97 | (231) ~ (e4 = e2)
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (16), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (698) all_0_42_42 = e2
% 31.47/8.97 |
% 31.47/8.97 | Equations (698) can reduce 498 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (498) ~ (all_0_42_42 = e2)
% 31.47/8.97 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (166), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (522) all_0_39_39 = e4
% 31.47/8.97 |
% 31.47/8.97 | Combining equations (336,522) yields a new equation:
% 31.47/8.97 | (269) e4 = e2
% 31.47/8.97 |
% 31.47/8.97 | Equations (269) can reduce 231 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (591) ~ (all_0_39_39 = e4)
% 31.47/8.97 | (4522) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (22), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (782) all_0_43_43 = e3
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (1245), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (1258) all_0_42_42 = e3
% 31.47/8.97 |
% 31.47/8.97 | Equations (1258) can reduce 94 to:
% 31.47/8.97 | (1237) ~ (all_0_41_41 = e3)
% 31.47/8.97 |
% 31.47/8.97 | Equations (1258) can reduce 520 to:
% 31.47/8.97 | (719) ~ (e4 = e3)
% 31.47/8.97 |
% 31.47/8.97 | Simplifying 719 yields:
% 31.47/8.97 | (34) ~ (e4 = e3)
% 31.47/8.97 |
% 31.47/8.97 | Equations (1258) can reduce 498 to:
% 31.47/8.97 | (223) ~ (e3 = e2)
% 31.47/8.97 |
% 31.47/8.97 | Equations (1258) can reduce 199 to:
% 31.47/8.97 | (66) ~ (e3 = e0)
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (219), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (351) all_0_41_41 = e3
% 31.47/8.97 |
% 31.47/8.97 | Equations (351) can reduce 1237 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (1237) ~ (all_0_41_41 = e3)
% 31.47/8.97 | (1508) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (4522), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (502) all_0_43_43 = e4
% 31.47/8.97 |
% 31.47/8.97 | Combining equations (782,502) yields a new equation:
% 31.47/8.97 | (359) e4 = e3
% 31.47/8.97 |
% 31.47/8.97 | Equations (359) can reduce 34 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (510) ~ (all_0_43_43 = e4)
% 31.47/8.97 | (4527) all_0_51_51 = e4 | all_0_56_56 = e4
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (1508), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (505) all_0_45_45 = e3
% 31.47/8.97 |
% 31.47/8.97 | Combining equations (374,505) yields a new equation:
% 31.47/8.97 | (414) e3 = e2
% 31.47/8.97 |
% 31.47/8.97 | Equations (414) can reduce 223 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (354) ~ (all_0_45_45 = e3)
% 31.47/8.97 | (1539) all_0_53_53 = e3 | all_0_58_58 = e3
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (4527), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (1467) all_0_51_51 = e4
% 31.47/8.97 |
% 31.47/8.97 | Equations (1467) can reduce 697 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (697) ~ (all_0_51_51 = e4)
% 31.47/8.97 | (4744) all_0_56_56 = e4
% 31.47/8.97 |
% 31.47/8.97 | Equations (4744) can reduce 185 to:
% 31.47/8.97 | (279) ~ (all_0_59_59 = e4)
% 31.47/8.97 |
% 31.47/8.97 | Simplifying 279 yields:
% 31.47/8.97 | (280) ~ (all_0_59_59 = e4)
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (1539), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (1114) all_0_53_53 = e3
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (93), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (402) all_0_59_59 = e4
% 31.47/8.97 |
% 31.47/8.97 | Equations (402) can reduce 280 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (280) ~ (all_0_59_59 = e4)
% 31.47/8.97 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (407), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (408), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 31.47/8.97 |
% 31.47/8.97 +-Applying beta-rule and splitting (409), into two cases.
% 31.47/8.97 |-Branch one:
% 31.47/8.97 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 31.47/8.97 |
% 31.47/8.97 | Applying alpha-rule on (410) yields:
% 31.47/8.97 | (411) all_0_43_43 = e0
% 31.47/8.97 | (412) all_0_59_59 = e3
% 31.47/8.97 | (413) ~ (all_0_46_46 = e3)
% 31.47/8.97 |
% 31.47/8.97 | Combining equations (782,411) yields a new equation:
% 31.47/8.97 | (783) e3 = e0
% 31.47/8.97 |
% 31.47/8.97 | Simplifying 783 yields:
% 31.47/8.97 | (784) e3 = e0
% 31.47/8.97 |
% 31.47/8.97 | Equations (784) can reduce 66 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 31.47/8.97 |
% 31.47/8.97 | Applying alpha-rule on (416) yields:
% 31.47/8.97 | (411) all_0_43_43 = e0
% 31.47/8.97 | (412) all_0_59_59 = e3
% 31.47/8.97 | (419) ~ (all_0_56_56 = e0)
% 31.47/8.97 |
% 31.47/8.97 | Combining equations (782,411) yields a new equation:
% 31.47/8.97 | (783) e3 = e0
% 31.47/8.97 |
% 31.47/8.97 | Simplifying 783 yields:
% 31.47/8.97 | (784) e3 = e0
% 31.47/8.97 |
% 31.47/8.97 | Equations (784) can reduce 66 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 31.47/8.97 |
% 31.47/8.97 | Applying alpha-rule on (422) yields:
% 31.47/8.97 | (423) all_0_53_53 = e0
% 31.47/8.97 | (424) all_0_59_59 = e1
% 31.47/8.97 | (425) ~ (all_0_54_54 = e1)
% 31.47/8.97 |
% 31.47/8.97 | Combining equations (1114,423) yields a new equation:
% 31.47/8.97 | (783) e3 = e0
% 31.47/8.97 |
% 31.47/8.97 | Simplifying 783 yields:
% 31.47/8.97 | (784) e3 = e0
% 31.47/8.97 |
% 31.47/8.97 | Equations (784) can reduce 66 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 31.47/8.97 |
% 31.47/8.97 | Applying alpha-rule on (428) yields:
% 31.47/8.97 | (423) all_0_53_53 = e0
% 31.47/8.97 | (424) all_0_59_59 = e1
% 31.47/8.97 | (431) ~ (all_0_58_58 = e0)
% 31.47/8.97 |
% 31.47/8.97 | Combining equations (1114,423) yields a new equation:
% 31.47/8.97 | (783) e3 = e0
% 31.47/8.97 |
% 31.47/8.97 | Simplifying 783 yields:
% 31.47/8.97 | (784) e3 = e0
% 31.47/8.97 |
% 31.47/8.97 | Equations (784) can reduce 66 to:
% 31.47/8.97 | (270) $false
% 31.47/8.97 |
% 31.47/8.97 |-The branch is then unsatisfiable
% 31.47/8.97 |-Branch two:
% 31.47/8.97 | (356) ~ (all_0_53_53 = e3)
% 31.47/8.98 | (4713) all_0_58_58 = e3
% 31.47/8.98 |
% 31.47/8.98 | Equations (4713) can reduce 718 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (1316) ~ (all_0_42_42 = e3)
% 31.47/8.98 | (1317) all_0_42_42 = e4 | all_0_42_42 = e1
% 31.47/8.98 |
% 31.47/8.98 +-Applying beta-rule and splitting (592), into two cases.
% 31.47/8.98 |-Branch one:
% 31.47/8.98 | (358) all_0_41_41 = e4
% 31.47/8.98 |
% 31.47/8.98 | Equations (358) can reduce 94 to:
% 31.47/8.98 | (692) ~ (all_0_42_42 = e4)
% 31.47/8.98 |
% 31.47/8.98 | Simplifying 692 yields:
% 31.47/8.98 | (520) ~ (all_0_42_42 = e4)
% 31.47/8.98 |
% 31.47/8.98 +-Applying beta-rule and splitting (1317), into two cases.
% 31.47/8.98 |-Branch one:
% 31.47/8.98 | (541) all_0_42_42 = e1
% 31.47/8.98 |
% 31.47/8.98 | Equations (541) can reduce 640 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (640) ~ (all_0_42_42 = e1)
% 31.47/8.98 | (512) all_0_42_42 = e4
% 31.47/8.98 |
% 31.47/8.98 | Equations (512) can reduce 520 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (361) ~ (all_0_41_41 = e4)
% 31.47/8.98 | (512) all_0_42_42 = e4
% 31.47/8.98 |
% 31.47/8.98 | Equations (512) can reduce 520 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (786) ~ (all_0_43_43 = e3)
% 31.47/8.98 | (787) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 31.47/8.98 |
% 31.47/8.98 +-Applying beta-rule and splitting (787), into two cases.
% 31.47/8.98 |-Branch one:
% 31.47/8.98 | (858) all_0_44_44 = e3
% 31.47/8.98 |
% 31.47/8.98 | Combining equations (621,858) yields a new equation:
% 31.47/8.98 | (784) e3 = e0
% 31.47/8.98 |
% 31.47/8.98 | Equations (784) can reduce 66 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (862) ~ (all_0_44_44 = e3)
% 31.47/8.98 | (1070) all_0_45_45 = e3 | all_0_46_46 = e3
% 31.47/8.98 |
% 31.47/8.98 +-Applying beta-rule and splitting (1245), into two cases.
% 31.47/8.98 |-Branch one:
% 31.47/8.98 | (1258) all_0_42_42 = e3
% 31.47/8.98 |
% 31.47/8.98 | Equations (1258) can reduce 520 to:
% 31.47/8.98 | (719) ~ (e4 = e3)
% 31.47/8.98 |
% 31.47/8.98 | Simplifying 719 yields:
% 31.47/8.98 | (34) ~ (e4 = e3)
% 31.47/8.98 |
% 31.47/8.98 | Equations (1258) can reduce 498 to:
% 31.47/8.98 | (223) ~ (e3 = e2)
% 31.47/8.98 |
% 31.47/8.98 +-Applying beta-rule and splitting (1070), into two cases.
% 31.47/8.98 |-Branch one:
% 31.47/8.98 | (505) all_0_45_45 = e3
% 31.47/8.98 |
% 31.47/8.98 | Combining equations (374,505) yields a new equation:
% 31.47/8.98 | (414) e3 = e2
% 31.47/8.98 |
% 31.47/8.98 | Equations (414) can reduce 223 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (354) ~ (all_0_45_45 = e3)
% 31.47/8.98 | (1091) all_0_46_46 = e3
% 31.47/8.98 |
% 31.47/8.98 | Combining equations (517,1091) yields a new equation:
% 31.47/8.98 | (660) e4 = e3
% 31.47/8.98 |
% 31.47/8.98 | Simplifying 660 yields:
% 31.47/8.98 | (359) e4 = e3
% 31.47/8.98 |
% 31.47/8.98 | Equations (359) can reduce 34 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (1316) ~ (all_0_42_42 = e3)
% 31.47/8.98 | (1317) all_0_42_42 = e4 | all_0_42_42 = e1
% 31.47/8.98 |
% 31.47/8.98 +-Applying beta-rule and splitting (1317), into two cases.
% 31.47/8.98 |-Branch one:
% 31.47/8.98 | (541) all_0_42_42 = e1
% 31.47/8.98 |
% 31.47/8.98 | Equations (541) can reduce 640 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (640) ~ (all_0_42_42 = e1)
% 31.47/8.98 | (512) all_0_42_42 = e4
% 31.47/8.98 |
% 31.47/8.98 | Equations (512) can reduce 520 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (846) ~ (all_0_57_57 = e3)
% 31.47/8.98 | (997) all_0_57_57 = e1
% 31.47/8.98 |
% 31.47/8.98 | Equations (997) can reduce 644 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (625) ~ (all_0_44_44 = e0)
% 31.47/8.98 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 31.47/8.98 |
% 31.47/8.98 +-Applying beta-rule and splitting (373), into two cases.
% 31.47/8.98 |-Branch one:
% 31.47/8.98 | (621) all_0_44_44 = e0
% 31.47/8.98 |
% 31.47/8.98 | Equations (621) can reduce 625 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (625) ~ (all_0_44_44 = e0)
% 31.47/8.98 | (858) all_0_44_44 = e3
% 31.47/8.98 |
% 31.47/8.98 | Equations (858) can reduce 241 to:
% 31.47/8.98 | (786) ~ (all_0_43_43 = e3)
% 31.47/8.98 |
% 31.47/8.98 | Equations (858) can reduce 174 to:
% 31.47/8.98 | (1518) ~ (all_0_46_46 = e3)
% 31.47/8.98 |
% 31.47/8.98 | Simplifying 1518 yields:
% 31.47/8.98 | (413) ~ (all_0_46_46 = e3)
% 31.47/8.98 |
% 31.47/8.98 | From (858) and (165) follows:
% 31.47/8.98 | (3499) op(e2, e3) = all_0_15_15
% 31.47/8.98 |
% 31.47/8.98 +-Applying beta-rule and splitting (626), into two cases.
% 31.47/8.98 |-Branch one:
% 31.47/8.98 | (827) all_0_52_52 = e0
% 31.47/8.98 |
% 31.47/8.98 | Combining equations (685,827) yields a new equation:
% 31.47/8.98 | (622) e2 = e0
% 31.47/8.98 |
% 31.47/8.98 | Simplifying 622 yields:
% 31.47/8.98 | (316) e2 = e0
% 31.47/8.98 |
% 31.47/8.98 | Equations (316) can reduce 57 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (925) ~ (all_0_52_52 = e0)
% 31.47/8.98 | (2258) all_0_57_57 = e0
% 31.47/8.98 |
% 31.47/8.98 | Equations (2258) can reduce 37 to:
% 31.47/8.98 | (3530) ~ (all_0_58_58 = e0)
% 31.47/8.98 |
% 31.47/8.98 | Simplifying 3530 yields:
% 31.47/8.98 | (431) ~ (all_0_58_58 = e0)
% 31.47/8.98 |
% 31.47/8.98 | Equations (2258) can reduce 335 to:
% 31.47/8.98 | (566) ~ (e2 = e0)
% 31.47/8.98 |
% 31.47/8.98 | Simplifying 566 yields:
% 31.47/8.98 | (57) ~ (e2 = e0)
% 31.47/8.98 |
% 31.47/8.98 | Equations (2258) can reduce 644 to:
% 31.47/8.98 | (568) ~ (e1 = e0)
% 31.47/8.98 |
% 31.47/8.98 | Simplifying 568 yields:
% 31.47/8.98 | (132) ~ (e1 = e0)
% 31.47/8.98 |
% 31.47/8.98 | From (2258) and (30) follows:
% 31.47/8.98 | (12293) op(e2, e0) = all_0_19_19
% 31.47/8.98 |
% 31.47/8.98 +-Applying beta-rule and splitting (159), into two cases.
% 31.47/8.98 |-Branch one:
% 31.47/8.98 | (450) all_0_43_43 = e2
% 31.47/8.98 |
% 31.47/8.98 | Equations (450) can reduce 292 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (292) ~ (all_0_43_43 = e2)
% 31.47/8.98 | (774) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 31.47/8.98 |
% 31.47/8.98 +-Applying beta-rule and splitting (774), into two cases.
% 31.47/8.98 |-Branch one:
% 31.47/8.98 | (411) all_0_43_43 = e0
% 31.47/8.98 |
% 31.47/8.98 | Equations (411) can reduce 455 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (455) ~ (all_0_43_43 = e0)
% 31.47/8.98 | (944) all_0_43_43 = e4 | all_0_43_43 = e3
% 31.47/8.98 |
% 31.47/8.98 +-Applying beta-rule and splitting (182), into two cases.
% 31.47/8.98 |-Branch one:
% 31.47/8.98 | (454) all_0_45_45 = e0
% 31.47/8.98 |
% 31.47/8.98 | Combining equations (374,454) yields a new equation:
% 31.47/8.98 | (622) e2 = e0
% 31.47/8.98 |
% 31.47/8.98 | Simplifying 622 yields:
% 31.47/8.98 | (316) e2 = e0
% 31.47/8.98 |
% 31.47/8.98 | Equations (316) can reduce 57 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (488) ~ (all_0_45_45 = e0)
% 31.47/8.98 | (558) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 31.47/8.98 |
% 31.47/8.98 +-Applying beta-rule and splitting (944), into two cases.
% 31.47/8.98 |-Branch one:
% 31.47/8.98 | (782) all_0_43_43 = e3
% 31.47/8.98 |
% 31.47/8.98 | Equations (782) can reduce 786 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (786) ~ (all_0_43_43 = e3)
% 31.47/8.98 | (502) all_0_43_43 = e4
% 31.47/8.98 |
% 31.47/8.98 | Equations (502) can reduce 103 to:
% 31.47/8.98 | (804) ~ (all_0_46_46 = e4)
% 31.47/8.98 |
% 31.47/8.98 | Simplifying 804 yields:
% 31.47/8.98 | (805) ~ (all_0_46_46 = e4)
% 31.47/8.98 |
% 31.47/8.98 | Equations (502) can reduce 249 to:
% 31.47/8.98 | (251) ~ (e4 = e1)
% 31.47/8.98 |
% 31.47/8.98 +-Applying beta-rule and splitting (220), into two cases.
% 31.47/8.98 |-Branch one:
% 31.47/8.98 | (497) all_0_46_46 = e2
% 31.47/8.98 |
% 31.47/8.98 | Equations (497) can reduce 1436 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (1436) ~ (all_0_46_46 = e2)
% 31.47/8.98 | (1523) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e0
% 31.47/8.98 |
% 31.47/8.98 +-Applying beta-rule and splitting (558), into two cases.
% 31.47/8.98 |-Branch one:
% 31.47/8.98 | (559) all_0_48_48 = e0
% 31.47/8.98 |
% 31.47/8.98 | Combining equations (552,559) yields a new equation:
% 31.47/8.98 | (571) e1 = e0
% 31.47/8.98 |
% 31.47/8.98 | Simplifying 571 yields:
% 31.47/8.98 | (560) e1 = e0
% 31.47/8.98 |
% 31.47/8.98 | Equations (560) can reduce 132 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (562) ~ (all_0_48_48 = e0)
% 31.47/8.98 | (575) all_0_53_53 = e0 | all_0_58_58 = e0
% 31.47/8.98 |
% 31.47/8.98 +-Applying beta-rule and splitting (1523), into two cases.
% 31.47/8.98 |-Branch one:
% 31.47/8.98 | (1132) all_0_46_46 = e0
% 31.47/8.98 |
% 31.47/8.98 | Equations (1132) can reduce 413 to:
% 31.47/8.98 | (788) ~ (e3 = e0)
% 31.47/8.98 |
% 31.47/8.98 | Simplifying 788 yields:
% 31.47/8.98 | (66) ~ (e3 = e0)
% 31.47/8.98 |
% 31.47/8.98 +-Applying beta-rule and splitting (575), into two cases.
% 31.47/8.98 |-Branch one:
% 31.47/8.98 | (423) all_0_53_53 = e0
% 31.47/8.98 |
% 31.47/8.98 | Equations (423) can reduce 259 to:
% 31.47/8.98 | (566) ~ (e2 = e0)
% 31.47/8.98 |
% 31.47/8.98 | Simplifying 566 yields:
% 31.47/8.98 | (57) ~ (e2 = e0)
% 31.47/8.98 |
% 31.47/8.98 | Instantiating formula (201) with e2, e3, all_0_15_15, e0 and discharging atoms op(e2, e3) = all_0_15_15, op(e2, e3) = e0, yields:
% 31.47/8.98 | (5959) all_0_15_15 = e0
% 31.47/8.98 |
% 31.47/8.98 | Instantiating formula (201) with e2, e0, all_0_19_19, e2 and discharging atoms op(e2, e0) = all_0_19_19, op(e2, e0) = e2, yields:
% 31.47/8.98 | (14991) all_0_19_19 = e2
% 31.47/8.98 |
% 31.47/8.98 +-Applying beta-rule and splitting (87), into two cases.
% 31.47/8.98 |-Branch one:
% 31.47/8.98 | (650) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 31.47/8.98 |
% 31.47/8.98 +-Applying beta-rule and splitting (650), into two cases.
% 31.47/8.98 |-Branch one:
% 31.47/8.98 | (651) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 31.47/8.98 |
% 31.47/8.98 +-Applying beta-rule and splitting (651), into two cases.
% 31.47/8.98 |-Branch one:
% 31.47/8.98 | (652) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 31.47/8.98 |
% 31.47/8.98 | Applying alpha-rule on (652) yields:
% 31.47/8.98 | (653) all_0_13_13 = e4
% 31.47/8.98 | (654) ~ (all_0_14_14 = e2)
% 31.47/8.98 |
% 31.47/8.98 | Combining equations (5957,653) yields a new equation:
% 31.47/8.98 | (526) e4 = e1
% 31.47/8.98 |
% 31.47/8.98 | Equations (526) can reduce 251 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (657) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 31.47/8.98 |
% 31.47/8.98 | Applying alpha-rule on (657) yields:
% 31.47/8.98 | (658) all_0_15_15 = e3
% 31.47/8.98 | (659) ~ (all_0_16_16 = e2)
% 31.47/8.98 |
% 31.47/8.98 | Combining equations (5959,658) yields a new equation:
% 31.47/8.98 | (784) e3 = e0
% 31.47/8.98 |
% 31.47/8.98 | Equations (784) can reduce 66 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (663) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 31.47/8.98 |
% 31.47/8.98 | Applying alpha-rule on (663) yields:
% 31.47/8.98 | (664) all_0_17_17 = e1
% 31.47/8.98 | (665) ~ (all_0_18_18 = e2)
% 31.47/8.98 |
% 31.47/8.98 | Combining equations (11735,664) yields a new equation:
% 31.47/8.98 | (525) e4 = e1
% 31.47/8.98 |
% 31.47/8.98 | Simplifying 525 yields:
% 31.47/8.98 | (526) e4 = e1
% 31.47/8.98 |
% 31.47/8.98 | Equations (526) can reduce 251 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (1762) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 31.47/8.98 |
% 31.47/8.98 | Applying alpha-rule on (1762) yields:
% 31.47/8.98 | (1763) all_0_19_19 = e0
% 31.47/8.98 | (1764) ~ (all_0_20_20 = e2)
% 31.47/8.98 |
% 31.47/8.98 | Combining equations (14991,1763) yields a new equation:
% 31.47/8.98 | (622) e2 = e0
% 31.47/8.98 |
% 31.47/8.98 | Simplifying 622 yields:
% 31.47/8.98 | (316) e2 = e0
% 31.47/8.98 |
% 31.47/8.98 | Equations (316) can reduce 57 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (584) ~ (all_0_53_53 = e0)
% 31.47/8.98 | (585) all_0_58_58 = e0
% 31.47/8.98 |
% 31.47/8.98 | Equations (585) can reduce 431 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (1010) ~ (all_0_46_46 = e0)
% 31.47/8.98 | (1529) all_0_46_46 = e4 | all_0_46_46 = e3
% 31.47/8.98 |
% 31.47/8.98 +-Applying beta-rule and splitting (1529), into two cases.
% 31.47/8.98 |-Branch one:
% 31.47/8.98 | (1091) all_0_46_46 = e3
% 31.47/8.98 |
% 31.47/8.98 | Equations (1091) can reduce 413 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (413) ~ (all_0_46_46 = e3)
% 31.47/8.98 | (517) all_0_46_46 = e4
% 31.47/8.98 |
% 31.47/8.98 | Equations (517) can reduce 805 to:
% 31.47/8.98 | (270) $false
% 31.47/8.98 |
% 31.47/8.98 |-The branch is then unsatisfiable
% 31.47/8.98 |-Branch two:
% 31.47/8.98 | (534) ~ (all_0_40_40 = e1)
% 31.47/8.98 | (3352) all_0_52_52 = e1 | all_0_57_57 = e1
% 31.47/8.98 |
% 31.47/8.99 +-Applying beta-rule and splitting (3352), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (848) all_0_52_52 = e1
% 31.47/8.99 |
% 31.47/8.99 | Combining equations (685,848) yields a new equation:
% 31.47/8.99 | (531) e2 = e1
% 31.47/8.99 |
% 31.47/8.99 | Simplifying 531 yields:
% 31.47/8.99 | (322) e2 = e1
% 31.47/8.99 |
% 31.47/8.99 | Equations (322) can reduce 141 to:
% 31.47/8.99 | (270) $false
% 31.47/8.99 |
% 31.47/8.99 |-The branch is then unsatisfiable
% 31.47/8.99 |-Branch two:
% 31.47/8.99 | (642) ~ (all_0_52_52 = e1)
% 31.47/8.99 | (997) all_0_57_57 = e1
% 31.47/8.99 |
% 31.47/8.99 | Equations (997) can reduce 149 to:
% 31.47/8.99 | (534) ~ (all_0_40_40 = e1)
% 31.47/8.99 |
% 31.47/8.99 | Equations (997) can reduce 10 to:
% 31.47/8.99 | (131) ~ (all_0_44_44 = e1)
% 31.47/8.99 |
% 31.47/8.99 | Equations (997) can reduce 37 to:
% 31.47/8.99 | (7725) ~ (all_0_58_58 = e1)
% 31.47/8.99 |
% 31.47/8.99 | Simplifying 7725 yields:
% 31.47/8.99 | (1004) ~ (all_0_58_58 = e1)
% 31.47/8.99 |
% 31.47/8.99 | Equations (997) can reduce 140 to:
% 31.47/8.99 | (749) ~ (all_0_59_59 = e1)
% 31.47/8.99 |
% 31.47/8.99 | Simplifying 749 yields:
% 31.47/8.99 | (750) ~ (all_0_59_59 = e1)
% 31.47/8.99 |
% 31.47/8.99 | Equations (997) can reduce 335 to:
% 31.47/8.99 | (645) ~ (e2 = e1)
% 31.47/8.99 |
% 31.47/8.99 | Simplifying 645 yields:
% 31.47/8.99 | (141) ~ (e2 = e1)
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (9), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (621) all_0_44_44 = e0
% 31.47/8.99 |
% 31.47/8.99 | Combining equations (621,17397) yields a new equation:
% 31.47/8.99 | (12097) all_0_4_4 = e0
% 31.47/8.99 |
% 31.47/8.99 | Equations (621) can reduce 15 to:
% 31.47/8.99 | (238) ~ (all_0_40_40 = e0)
% 31.47/8.99 |
% 31.47/8.99 | Equations (621) can reduce 241 to:
% 31.47/8.99 | (455) ~ (all_0_43_43 = e0)
% 31.47/8.99 |
% 31.47/8.99 | Equations (621) can reduce 174 to:
% 31.47/8.99 | (1057) ~ (all_0_46_46 = e0)
% 31.47/8.99 |
% 31.47/8.99 | Simplifying 1057 yields:
% 31.47/8.99 | (1010) ~ (all_0_46_46 = e0)
% 31.47/8.99 |
% 31.47/8.99 | Equations (621) can reduce 131 to:
% 31.47/8.99 | (568) ~ (e1 = e0)
% 31.47/8.99 |
% 31.47/8.99 | Simplifying 568 yields:
% 31.47/8.99 | (132) ~ (e1 = e0)
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (210), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (524) all_0_39_39 = e1
% 31.47/8.99 |
% 31.47/8.99 | Combining equations (336,524) yields a new equation:
% 31.47/8.99 | (531) e2 = e1
% 31.47/8.99 |
% 31.47/8.99 | Simplifying 531 yields:
% 31.47/8.99 | (322) e2 = e1
% 31.47/8.99 |
% 31.47/8.99 | Equations (322) can reduce 141 to:
% 31.47/8.99 | (270) $false
% 31.47/8.99 |
% 31.47/8.99 |-The branch is then unsatisfiable
% 31.47/8.99 |-Branch two:
% 31.47/8.99 | (528) ~ (all_0_39_39 = e1)
% 31.47/8.99 | (529) all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1
% 31.47/8.99 |
% 31.47/8.99 | Equations (336) can reduce 528 to:
% 31.47/8.99 | (141) ~ (e2 = e1)
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (93), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (402) all_0_59_59 = e4
% 31.47/8.99 |
% 31.47/8.99 | Equations (402) can reduce 17 to:
% 31.47/8.99 | (520) ~ (all_0_42_42 = e4)
% 31.47/8.99 |
% 31.47/8.99 | Equations (402) can reduce 72 to:
% 31.47/8.99 | (936) ~ (all_0_54_54 = e4)
% 31.47/8.99 |
% 31.47/8.99 | Equations (402) can reduce 185 to:
% 31.47/8.99 | (274) ~ (all_0_56_56 = e4)
% 31.47/8.99 |
% 31.47/8.99 | Equations (402) can reduce 701 to:
% 31.47/8.99 | (231) ~ (e4 = e2)
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (44), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (502) all_0_43_43 = e4
% 31.47/8.99 |
% 31.47/8.99 | Equations (502) can reduce 103 to:
% 31.47/8.99 | (804) ~ (all_0_46_46 = e4)
% 31.47/8.99 |
% 31.47/8.99 | Simplifying 804 yields:
% 31.47/8.99 | (805) ~ (all_0_46_46 = e4)
% 31.47/8.99 |
% 31.47/8.99 | Equations (502) can reduce 240 to:
% 31.47/8.99 | (696) ~ (all_0_51_51 = e4)
% 31.47/8.99 |
% 31.47/8.99 | Simplifying 696 yields:
% 31.47/8.99 | (697) ~ (all_0_51_51 = e4)
% 31.47/8.99 |
% 31.47/8.99 | Equations (502) can reduce 292 to:
% 31.47/8.99 | (231) ~ (e4 = e2)
% 31.47/8.99 |
% 31.47/8.99 | From (502) and (248) follows:
% 31.47/8.99 | (14204) op(e3, e3) = e4
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (222), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (522) all_0_39_39 = e4
% 31.47/8.99 |
% 31.47/8.99 | Combining equations (336,522) yields a new equation:
% 31.47/8.99 | (269) e4 = e2
% 31.47/8.99 |
% 31.47/8.99 | Equations (269) can reduce 231 to:
% 31.47/8.99 | (270) $false
% 31.47/8.99 |
% 31.47/8.99 |-The branch is then unsatisfiable
% 31.47/8.99 |-Branch two:
% 31.47/8.99 | (591) ~ (all_0_39_39 = e4)
% 31.47/8.99 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (592), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (358) all_0_41_41 = e4
% 31.47/8.99 |
% 31.47/8.99 | Equations (358) can reduce 147 to:
% 31.47/8.99 | (233) ~ (all_0_40_40 = e4)
% 31.47/8.99 |
% 31.47/8.99 | Equations (358) can reduce 232 to:
% 31.47/8.99 | (6) ~ (e4 = e0)
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (99), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (524) all_0_39_39 = e1
% 31.47/8.99 |
% 31.47/8.99 | Combining equations (336,524) yields a new equation:
% 31.47/8.99 | (531) e2 = e1
% 31.47/8.99 |
% 31.47/8.99 | Simplifying 531 yields:
% 31.47/8.99 | (322) e2 = e1
% 31.47/8.99 |
% 31.47/8.99 | Equations (322) can reduce 141 to:
% 31.47/8.99 | (270) $false
% 31.47/8.99 |
% 31.47/8.99 |-The branch is then unsatisfiable
% 31.47/8.99 |-Branch two:
% 31.47/8.99 | (528) ~ (all_0_39_39 = e1)
% 31.47/8.99 | (680) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 31.47/8.99 |
% 31.47/8.99 | Equations (336) can reduce 528 to:
% 31.47/8.99 | (141) ~ (e2 = e1)
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (220), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (497) all_0_46_46 = e2
% 31.47/8.99 |
% 31.47/8.99 | Equations (497) can reduce 1436 to:
% 31.47/8.99 | (270) $false
% 31.47/8.99 |
% 31.47/8.99 |-The branch is then unsatisfiable
% 31.47/8.99 |-Branch two:
% 31.47/8.99 | (1436) ~ (all_0_46_46 = e2)
% 31.47/8.99 | (1523) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e0
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (176), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (830) all_0_56_56 = e0
% 31.47/8.99 |
% 31.47/8.99 | Equations (830) can reduce 419 to:
% 31.47/8.99 | (270) $false
% 31.47/8.99 |
% 31.47/8.99 |-The branch is then unsatisfiable
% 31.47/8.99 |-Branch two:
% 31.47/8.99 | (419) ~ (all_0_56_56 = e0)
% 31.47/8.99 | (834) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (133), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (671) all_0_40_40 = e3
% 31.47/8.99 |
% 31.47/8.99 | Equations (671) can reduce 233 to:
% 31.47/8.99 | (719) ~ (e4 = e3)
% 31.47/8.99 |
% 31.47/8.99 | Simplifying 719 yields:
% 31.47/8.99 | (34) ~ (e4 = e3)
% 31.47/8.99 |
% 31.47/8.99 | Equations (671) can reduce 534 to:
% 31.47/8.99 | (136) ~ (e3 = e1)
% 31.47/8.99 |
% 31.47/8.99 | Equations (671) can reduce 238 to:
% 31.47/8.99 | (66) ~ (e3 = e0)
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (16), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (698) all_0_42_42 = e2
% 31.47/8.99 |
% 31.47/8.99 | Equations (698) can reduce 498 to:
% 31.47/8.99 | (270) $false
% 31.47/8.99 |
% 31.47/8.99 |-The branch is then unsatisfiable
% 31.47/8.99 |-Branch two:
% 31.47/8.99 | (498) ~ (all_0_42_42 = e2)
% 31.47/8.99 | (1245) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (1523), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (1132) all_0_46_46 = e0
% 31.47/8.99 |
% 31.47/8.99 | Equations (1132) can reduce 1010 to:
% 31.47/8.99 | (270) $false
% 31.47/8.99 |
% 31.47/8.99 |-The branch is then unsatisfiable
% 31.47/8.99 |-Branch two:
% 31.47/8.99 | (1010) ~ (all_0_46_46 = e0)
% 31.47/8.99 | (1529) all_0_46_46 = e4 | all_0_46_46 = e3
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (834), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (2258) all_0_57_57 = e0
% 31.47/8.99 |
% 31.47/8.99 | Combining equations (997,2258) yields a new equation:
% 31.47/8.99 | (571) e1 = e0
% 31.47/8.99 |
% 31.47/8.99 | Simplifying 571 yields:
% 31.47/8.99 | (560) e1 = e0
% 31.47/8.99 |
% 31.47/8.99 | Equations (560) can reduce 132 to:
% 31.47/8.99 | (270) $false
% 31.47/8.99 |
% 31.47/8.99 |-The branch is then unsatisfiable
% 31.47/8.99 |-Branch two:
% 31.47/8.99 | (2301) ~ (all_0_57_57 = e0)
% 31.47/8.99 | (2302) all_0_58_58 = e0 | all_0_59_59 = e0
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (2302), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (585) all_0_58_58 = e0
% 31.47/8.99 |
% 31.47/8.99 | Equations (585) can reduce 70 to:
% 31.47/8.99 | (584) ~ (all_0_53_53 = e0)
% 31.47/8.99 |
% 31.47/8.99 | Equations (585) can reduce 81 to:
% 31.47/8.99 | (419) ~ (all_0_56_56 = e0)
% 31.47/8.99 |
% 31.47/8.99 | Equations (585) can reduce 376 to:
% 31.47/8.99 | (566) ~ (e2 = e0)
% 31.47/8.99 |
% 31.47/8.99 | Simplifying 566 yields:
% 31.47/8.99 | (57) ~ (e2 = e0)
% 31.47/8.99 |
% 31.47/8.99 | Equations (585) can reduce 1004 to:
% 31.47/8.99 | (568) ~ (e1 = e0)
% 31.47/8.99 |
% 31.47/8.99 | Simplifying 568 yields:
% 31.47/8.99 | (132) ~ (e1 = e0)
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (236), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (764) all_0_56_56 = e3
% 31.47/8.99 |
% 31.47/8.99 | Equations (764) can reduce 60 to:
% 31.47/8.99 | (932) ~ (all_0_51_51 = e3)
% 31.47/8.99 |
% 31.47/8.99 | Equations (764) can reduce 300 to:
% 31.47/8.99 | (223) ~ (e3 = e2)
% 31.47/8.99 |
% 31.47/8.99 | Equations (764) can reduce 419 to:
% 31.47/8.99 | (66) ~ (e3 = e0)
% 31.47/8.99 |
% 31.47/8.99 | From (764) and (239) follows:
% 31.47/8.99 | (14231) op(e3, e3) = all_0_11_11
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (64), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (954) all_0_51_51 = e0
% 31.47/8.99 |
% 31.47/8.99 | Equations (954) can reduce 987 to:
% 31.47/8.99 | (270) $false
% 31.47/8.99 |
% 31.47/8.99 |-The branch is then unsatisfiable
% 31.47/8.99 |-Branch two:
% 31.47/8.99 | (987) ~ (all_0_51_51 = e0)
% 31.47/8.99 | (3067) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (173), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (4215) all_0_51_51 = e2
% 31.47/8.99 |
% 31.47/8.99 | Equations (4215) can reduce 255 to:
% 31.47/8.99 | (270) $false
% 31.47/8.99 |
% 31.47/8.99 |-The branch is then unsatisfiable
% 31.47/8.99 |-Branch two:
% 31.47/8.99 | (255) ~ (all_0_51_51 = e2)
% 31.47/8.99 | (4888) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1 | all_0_51_51 = e0
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (3067), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (827) all_0_52_52 = e0
% 31.47/8.99 |
% 31.47/8.99 | Combining equations (827,685) yields a new equation:
% 31.47/8.99 | (316) e2 = e0
% 31.47/8.99 |
% 31.47/8.99 | Equations (316) can reduce 57 to:
% 31.47/8.99 | (270) $false
% 31.47/8.99 |
% 31.47/8.99 |-The branch is then unsatisfiable
% 31.47/8.99 |-Branch two:
% 31.47/8.99 | (925) ~ (all_0_52_52 = e0)
% 31.47/8.99 | (3073) all_0_53_53 = e0 | all_0_54_54 = e0
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (3073), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (423) all_0_53_53 = e0
% 31.47/8.99 |
% 31.47/8.99 | Equations (423) can reduce 584 to:
% 31.47/8.99 | (270) $false
% 31.47/8.99 |
% 31.47/8.99 |-The branch is then unsatisfiable
% 31.47/8.99 |-Branch two:
% 31.47/8.99 | (584) ~ (all_0_53_53 = e0)
% 31.47/8.99 | (3084) all_0_54_54 = e0
% 31.47/8.99 |
% 31.47/8.99 | Equations (3084) can reduce 50 to:
% 31.47/8.99 | (987) ~ (all_0_51_51 = e0)
% 31.47/8.99 |
% 31.47/8.99 | Equations (3084) can reduce 936 to:
% 31.47/8.99 | (456) ~ (e4 = e0)
% 31.47/8.99 |
% 31.47/8.99 | Simplifying 456 yields:
% 31.47/8.99 | (6) ~ (e4 = e0)
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (21), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (824) all_0_51_51 = e3
% 31.47/8.99 |
% 31.47/8.99 | Equations (824) can reduce 932 to:
% 31.47/8.99 | (270) $false
% 31.47/8.99 |
% 31.47/8.99 |-The branch is then unsatisfiable
% 31.47/8.99 |-Branch two:
% 31.47/8.99 | (932) ~ (all_0_51_51 = e3)
% 31.47/8.99 | (1101) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (135), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (820) all_0_51_51 = e1
% 31.47/8.99 |
% 31.47/8.99 | Equations (820) can reduce 697 to:
% 31.47/8.99 | (1021) ~ (e4 = e1)
% 31.47/8.99 |
% 31.47/8.99 | Simplifying 1021 yields:
% 31.47/8.99 | (251) ~ (e4 = e1)
% 31.47/8.99 |
% 31.47/8.99 | Equations (820) can reduce 255 to:
% 31.47/8.99 | (645) ~ (e2 = e1)
% 31.47/8.99 |
% 31.47/8.99 | Simplifying 645 yields:
% 31.47/8.99 | (141) ~ (e2 = e1)
% 31.47/8.99 |
% 31.47/8.99 | Equations (820) can reduce 987 to:
% 31.47/8.99 | (132) ~ (e1 = e0)
% 31.47/8.99 |
% 31.47/8.99 | From (820) and (7) follows:
% 31.47/8.99 | (19288) op(e3, e1) = all_0_9_9
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (127), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (541) all_0_42_42 = e1
% 31.47/8.99 |
% 31.47/8.99 | Equations (541) can reduce 498 to:
% 31.47/8.99 | (645) ~ (e2 = e1)
% 31.47/8.99 |
% 31.47/8.99 | Simplifying 645 yields:
% 31.47/8.99 | (141) ~ (e2 = e1)
% 31.47/8.99 |
% 31.47/8.99 +-Applying beta-rule and splitting (1529), into two cases.
% 31.47/8.99 |-Branch one:
% 31.47/8.99 | (1091) all_0_46_46 = e3
% 31.47/8.99 |
% 31.47/8.99 | Combining equations (1091,11390) yields a new equation:
% 31.47/8.99 | (17772) all_0_7_7 = e3
% 31.47/8.99 |
% 31.47/8.99 | Equations (1091) can reduce 1436 to:
% 31.47/8.99 | (223) ~ (e3 = e2)
% 31.47/8.99 |
% 31.47/8.99 | Instantiating formula (201) with e3, e3, e4, all_0_11_11 and discharging atoms op(e3, e3) = all_0_11_11, op(e3, e3) = e4, yields:
% 31.47/9.00 | (14233) all_0_11_11 = e4
% 31.47/9.00 |
% 31.47/9.00 | Instantiating formula (201) with e3, e1, all_0_9_9, e2 and discharging atoms op(e3, e1) = all_0_9_9, op(e3, e1) = e2, yields:
% 31.47/9.00 | (15413) all_0_9_9 = e2
% 31.47/9.00 |
% 31.47/9.00 +-Applying beta-rule and splitting (234), into two cases.
% 31.47/9.00 |-Branch one:
% 31.47/9.00 | (4239) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3)) | (all_0_9_9 = e1 & ~ (all_0_10_10 = e3))
% 31.47/9.00 |
% 31.47/9.00 +-Applying beta-rule and splitting (4239), into two cases.
% 31.47/9.00 |-Branch one:
% 31.47/9.00 | (4240) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3))
% 31.47/9.00 |
% 31.47/9.00 +-Applying beta-rule and splitting (4240), into two cases.
% 31.47/9.00 |-Branch one:
% 31.47/9.00 | (4241) all_0_4_4 = e4 & ~ (all_0_5_5 = e3)
% 31.47/9.00 |
% 31.47/9.00 | Applying alpha-rule on (4241) yields:
% 31.47/9.00 | (4242) all_0_4_4 = e4
% 31.47/9.00 | (4243) ~ (all_0_5_5 = e3)
% 31.47/9.00 |
% 31.47/9.00 | Combining equations (4242,12097) yields a new equation:
% 31.47/9.00 | (478) e4 = e0
% 31.47/9.00 |
% 31.47/9.00 | Simplifying 478 yields:
% 31.47/9.00 | (479) e4 = e0
% 31.47/9.00 |
% 31.47/9.00 | Equations (479) can reduce 6 to:
% 31.47/9.00 | (270) $false
% 31.47/9.00 |
% 31.47/9.00 |-The branch is then unsatisfiable
% 31.47/9.00 |-Branch two:
% 31.47/9.00 | (4247) all_0_7_7 = e2 & ~ (all_0_8_8 = e3)
% 31.47/9.00 |
% 31.47/9.00 | Applying alpha-rule on (4247) yields:
% 31.47/9.00 | (4248) all_0_7_7 = e2
% 31.47/9.00 | (4249) ~ (all_0_8_8 = e3)
% 31.47/9.00 |
% 31.47/9.00 | Combining equations (4248,17772) yields a new equation:
% 31.47/9.00 | (414) e3 = e2
% 31.47/9.00 |
% 31.47/9.00 | Equations (414) can reduce 223 to:
% 31.47/9.00 | (270) $false
% 31.47/9.00 |
% 31.47/9.00 |-The branch is then unsatisfiable
% 31.47/9.00 |-Branch two:
% 31.47/9.00 | (4253) all_0_9_9 = e1 & ~ (all_0_10_10 = e3)
% 31.47/9.00 |
% 31.47/9.00 | Applying alpha-rule on (4253) yields:
% 31.47/9.00 | (4254) all_0_9_9 = e1
% 31.47/9.00 | (4255) ~ (all_0_10_10 = e3)
% 31.47/9.00 |
% 31.47/9.00 | Combining equations (4254,15413) yields a new equation:
% 31.47/9.00 | (322) e2 = e1
% 31.47/9.00 |
% 31.47/9.00 | Equations (322) can reduce 141 to:
% 31.47/9.00 | (270) $false
% 31.47/9.00 |
% 31.47/9.00 |-The branch is then unsatisfiable
% 31.47/9.00 |-Branch two:
% 31.47/9.00 | (4378) all_0_11_11 = e0 & ~ (all_0_12_12 = e3)
% 31.47/9.00 |
% 31.47/9.00 | Applying alpha-rule on (4378) yields:
% 31.47/9.00 | (4379) all_0_11_11 = e0
% 31.47/9.00 | (4380) ~ (all_0_12_12 = e3)
% 31.47/9.00 |
% 31.60/9.00 | Combining equations (14233,4379) yields a new equation:
% 31.60/9.00 | (478) e4 = e0
% 31.60/9.00 |
% 31.60/9.00 | Simplifying 478 yields:
% 31.60/9.00 | (479) e4 = e0
% 31.60/9.00 |
% 31.60/9.00 | Equations (479) can reduce 6 to:
% 31.60/9.00 | (270) $false
% 31.60/9.00 |
% 31.60/9.00 |-The branch is then unsatisfiable
% 31.60/9.00 |-Branch two:
% 31.60/9.00 | (413) ~ (all_0_46_46 = e3)
% 31.60/9.00 | (517) all_0_46_46 = e4
% 31.60/9.00 |
% 31.60/9.00 | Equations (517) can reduce 805 to:
% 31.60/9.00 | (270) $false
% 31.60/9.00 |
% 31.60/9.00 |-The branch is then unsatisfiable
% 31.60/9.00 |-Branch two:
% 31.60/9.00 | (640) ~ (all_0_42_42 = e1)
% 31.60/9.00 | (4628) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 31.60/9.00 |
% 31.60/9.00 +-Applying beta-rule and splitting (4628), into two cases.
% 31.60/9.00 |-Branch one:
% 31.60/9.00 | (589) all_0_49_49 = e1
% 31.60/9.00 |
% 31.60/9.00 | Combining equations (307,589) yields a new equation:
% 31.60/9.00 | (531) e2 = e1
% 31.60/9.00 |
% 31.60/9.00 | Simplifying 531 yields:
% 31.60/9.00 | (322) e2 = e1
% 31.60/9.00 |
% 31.60/9.00 | Equations (322) can reduce 141 to:
% 31.60/9.00 | (270) $false
% 31.60/9.00 |
% 31.60/9.00 |-The branch is then unsatisfiable
% 31.60/9.00 |-Branch two:
% 31.60/9.00 | (543) ~ (all_0_49_49 = e1)
% 31.60/9.00 | (4726) all_0_54_54 = e1 | all_0_59_59 = e1
% 31.60/9.00 |
% 31.60/9.00 +-Applying beta-rule and splitting (4726), into two cases.
% 31.60/9.00 |-Branch one:
% 31.60/9.00 | (875) all_0_54_54 = e1
% 31.60/9.00 |
% 31.60/9.00 | Combining equations (3084,875) yields a new equation:
% 31.60/9.00 | (560) e1 = e0
% 31.60/9.00 |
% 31.60/9.00 | Equations (560) can reduce 132 to:
% 31.60/9.00 | (270) $false
% 31.60/9.00 |
% 31.60/9.00 |-The branch is then unsatisfiable
% 31.60/9.00 |-Branch two:
% 31.60/9.00 | (425) ~ (all_0_54_54 = e1)
% 31.60/9.00 | (424) all_0_59_59 = e1
% 31.60/9.00 |
% 31.60/9.00 | Combining equations (424,402) yields a new equation:
% 31.60/9.00 | (526) e4 = e1
% 31.60/9.00 |
% 31.60/9.00 | Equations (526) can reduce 251 to:
% 31.60/9.00 | (270) $false
% 31.60/9.00 |
% 31.60/9.00 |-The branch is then unsatisfiable
% 31.60/9.00 |-Branch two:
% 31.60/9.00 | (748) ~ (all_0_51_51 = e1)
% 31.60/9.00 | (823) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 31.60/9.00 |
% 31.60/9.00 +-Applying beta-rule and splitting (823), into two cases.
% 31.60/9.00 |-Branch one:
% 31.60/9.00 | (848) all_0_52_52 = e1
% 31.60/9.00 |
% 31.60/9.00 | Combining equations (685,848) yields a new equation:
% 31.60/9.00 | (531) e2 = e1
% 31.60/9.00 |
% 31.60/9.00 | Simplifying 531 yields:
% 31.60/9.00 | (322) e2 = e1
% 31.60/9.00 |
% 31.60/9.00 | Equations (322) can reduce 141 to:
% 31.60/9.00 | (270) $false
% 31.60/9.00 |
% 31.60/9.00 |-The branch is then unsatisfiable
% 31.60/9.00 |-Branch two:
% 31.60/9.00 | (642) ~ (all_0_52_52 = e1)
% 31.60/9.00 | (852) all_0_53_53 = e1 | all_0_54_54 = e1
% 31.60/9.00 |
% 31.60/9.00 +-Applying beta-rule and splitting (1101), into two cases.
% 31.60/9.00 |-Branch one:
% 31.60/9.00 | (864) all_0_52_52 = e3
% 31.60/9.00 |
% 31.60/9.00 | Combining equations (685,864) yields a new equation:
% 31.60/9.00 | (414) e3 = e2
% 31.60/9.00 |
% 31.60/9.00 | Equations (414) can reduce 223 to:
% 31.60/9.00 | (270) $false
% 31.60/9.00 |
% 31.60/9.00 |-The branch is then unsatisfiable
% 31.60/9.00 |-Branch two:
% 31.60/9.00 | (826) ~ (all_0_52_52 = e3)
% 31.60/9.00 | (1107) all_0_53_53 = e3 | all_0_54_54 = e3
% 31.60/9.00 |
% 31.60/9.00 +-Applying beta-rule and splitting (1107), into two cases.
% 31.60/9.00 |-Branch one:
% 31.60/9.00 | (1114) all_0_53_53 = e3
% 31.60/9.00 |
% 31.60/9.00 | Equations (1114) can reduce 874 to:
% 31.60/9.00 | (136) ~ (e3 = e1)
% 31.60/9.00 |
% 31.60/9.00 +-Applying beta-rule and splitting (852), into two cases.
% 31.60/9.00 |-Branch one:
% 31.60/9.00 | (853) all_0_53_53 = e1
% 31.60/9.00 |
% 31.60/9.00 | Combining equations (853,1114) yields a new equation:
% 31.60/9.00 | (538) e3 = e1
% 31.60/9.00 |
% 31.60/9.00 | Equations (538) can reduce 136 to:
% 31.60/9.00 | (270) $false
% 31.60/9.00 |
% 31.60/9.00 |-The branch is then unsatisfiable
% 31.60/9.00 |-Branch two:
% 31.60/9.00 | (874) ~ (all_0_53_53 = e1)
% 31.60/9.00 | (875) all_0_54_54 = e1
% 31.60/9.00 |
% 31.60/9.00 | Combining equations (3084,875) yields a new equation:
% 31.60/9.00 | (560) e1 = e0
% 31.60/9.00 |
% 31.60/9.00 | Equations (560) can reduce 132 to:
% 31.60/9.00 | (270) $false
% 31.60/9.00 |
% 31.60/9.00 |-The branch is then unsatisfiable
% 31.60/9.00 |-Branch two:
% 31.60/9.00 | (356) ~ (all_0_53_53 = e3)
% 31.60/9.00 | (1119) all_0_54_54 = e3
% 31.60/9.00 |
% 31.60/9.00 | Combining equations (3084,1119) yields a new equation:
% 31.60/9.00 | (784) e3 = e0
% 31.60/9.00 |
% 31.60/9.00 | Equations (784) can reduce 66 to:
% 31.60/9.00 | (270) $false
% 31.60/9.00 |
% 31.60/9.00 |-The branch is then unsatisfiable
% 31.60/9.00 |-Branch two:
% 31.60/9.00 | (767) ~ (all_0_56_56 = e3)
% 31.60/9.00 | (768) all_0_57_57 = e3 | all_0_58_58 = e3 | all_0_59_59 = e3
% 31.60/9.00 |
% 31.60/9.00 +-Applying beta-rule and splitting (768), into two cases.
% 31.60/9.00 |-Branch one:
% 31.60/9.00 | (869) all_0_57_57 = e3
% 31.60/9.00 |
% 31.60/9.00 | Combining equations (869,997) yields a new equation:
% 31.60/9.00 | (537) e3 = e1
% 31.60/9.00 |
% 31.60/9.00 | Simplifying 537 yields:
% 31.60/9.00 | (538) e3 = e1
% 31.60/9.00 |
% 31.60/9.00 | Equations (538) can reduce 136 to:
% 31.60/9.00 | (270) $false
% 31.60/9.00 |
% 31.60/9.00 |-The branch is then unsatisfiable
% 31.60/9.00 |-Branch two:
% 31.60/9.00 | (846) ~ (all_0_57_57 = e3)
% 31.60/9.00 | (5225) all_0_58_58 = e3 | all_0_59_59 = e3
% 31.60/9.00 |
% 31.60/9.00 +-Applying beta-rule and splitting (219), into two cases.
% 31.60/9.00 |-Branch one:
% 31.60/9.00 | (351) all_0_41_41 = e3
% 31.60/9.00 |
% 31.60/9.00 | Combining equations (358,351) yields a new equation:
% 31.60/9.00 | (660) e4 = e3
% 31.60/9.00 |
% 31.60/9.00 | Simplifying 660 yields:
% 31.60/9.00 | (359) e4 = e3
% 31.60/9.00 |
% 31.60/9.00 | Equations (359) can reduce 34 to:
% 31.60/9.00 | (270) $false
% 31.60/9.00 |
% 31.60/9.00 |-The branch is then unsatisfiable
% 31.60/9.00 |-Branch two:
% 31.60/9.00 | (1237) ~ (all_0_41_41 = e3)
% 31.60/9.00 | (1508) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 31.60/9.00 |
% 31.60/9.00 | Equations (358) can reduce 1237 to:
% 31.60/9.00 | (34) ~ (e4 = e3)
% 31.60/9.00 |
% 31.60/9.01 +-Applying beta-rule and splitting (5225), into two cases.
% 31.60/9.01 |-Branch one:
% 31.60/9.01 | (4713) all_0_58_58 = e3
% 31.60/9.01 |
% 31.60/9.01 | Combining equations (4713,585) yields a new equation:
% 31.60/9.01 | (783) e3 = e0
% 31.60/9.01 |
% 31.60/9.01 | Simplifying 783 yields:
% 31.60/9.01 | (784) e3 = e0
% 31.60/9.01 |
% 31.60/9.01 | Equations (784) can reduce 66 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (718) ~ (all_0_58_58 = e3)
% 31.60/9.01 | (412) all_0_59_59 = e3
% 31.60/9.01 |
% 31.60/9.01 | Combining equations (402,412) yields a new equation:
% 31.60/9.01 | (660) e4 = e3
% 31.60/9.01 |
% 31.60/9.01 | Simplifying 660 yields:
% 31.60/9.01 | (359) e4 = e3
% 31.60/9.01 |
% 31.60/9.01 | Equations (359) can reduce 34 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (431) ~ (all_0_58_58 = e0)
% 31.60/9.01 | (2308) all_0_59_59 = e0
% 31.60/9.01 |
% 31.60/9.01 | Combining equations (2308,402) yields a new equation:
% 31.60/9.01 | (479) e4 = e0
% 31.60/9.01 |
% 31.60/9.01 | Equations (479) can reduce 6 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (675) ~ (all_0_40_40 = e3)
% 31.60/9.01 | (676) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 31.60/9.01 |
% 31.60/9.01 +-Applying beta-rule and splitting (676), into two cases.
% 31.60/9.01 |-Branch one:
% 31.60/9.01 | (858) all_0_44_44 = e3
% 31.60/9.01 |
% 31.60/9.01 | Combining equations (621,858) yields a new equation:
% 31.60/9.01 | (784) e3 = e0
% 31.60/9.01 |
% 31.60/9.01 | Equations (784) can reduce 66 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (862) ~ (all_0_44_44 = e3)
% 31.60/9.01 | (863) all_0_52_52 = e3 | all_0_57_57 = e3
% 31.60/9.01 |
% 31.60/9.01 +-Applying beta-rule and splitting (863), into two cases.
% 31.60/9.01 |-Branch one:
% 31.60/9.01 | (864) all_0_52_52 = e3
% 31.60/9.01 |
% 31.60/9.01 | Combining equations (685,864) yields a new equation:
% 31.60/9.01 | (414) e3 = e2
% 31.60/9.01 |
% 31.60/9.01 | Equations (414) can reduce 223 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (826) ~ (all_0_52_52 = e3)
% 31.60/9.01 | (869) all_0_57_57 = e3
% 31.60/9.01 |
% 31.60/9.01 | Combining equations (997,869) yields a new equation:
% 31.60/9.01 | (538) e3 = e1
% 31.60/9.01 |
% 31.60/9.01 | Equations (538) can reduce 136 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (361) ~ (all_0_41_41 = e4)
% 31.60/9.01 | (512) all_0_42_42 = e4
% 31.60/9.01 |
% 31.60/9.01 | Equations (512) can reduce 520 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (510) ~ (all_0_43_43 = e4)
% 31.60/9.01 | (511) all_0_45_45 = e4 | all_0_46_46 = e4
% 31.60/9.01 |
% 31.60/9.01 +-Applying beta-rule and splitting (222), into two cases.
% 31.60/9.01 |-Branch one:
% 31.60/9.01 | (522) all_0_39_39 = e4
% 31.60/9.01 |
% 31.60/9.01 | Combining equations (336,522) yields a new equation:
% 31.60/9.01 | (269) e4 = e2
% 31.60/9.01 |
% 31.60/9.01 | Equations (269) can reduce 231 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (591) ~ (all_0_39_39 = e4)
% 31.60/9.01 | (592) all_0_41_41 = e4 | all_0_42_42 = e4
% 31.60/9.01 |
% 31.60/9.01 +-Applying beta-rule and splitting (592), into two cases.
% 31.60/9.01 |-Branch one:
% 31.60/9.01 | (358) all_0_41_41 = e4
% 31.60/9.01 |
% 31.60/9.01 | Equations (358) can reduce 331 to:
% 31.60/9.01 | (231) ~ (e4 = e2)
% 31.60/9.01 |
% 31.60/9.01 +-Applying beta-rule and splitting (166), into two cases.
% 31.60/9.01 |-Branch one:
% 31.60/9.01 | (522) all_0_39_39 = e4
% 31.60/9.01 |
% 31.60/9.01 | Combining equations (336,522) yields a new equation:
% 31.60/9.01 | (269) e4 = e2
% 31.60/9.01 |
% 31.60/9.01 | Equations (269) can reduce 231 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (591) ~ (all_0_39_39 = e4)
% 31.60/9.01 | (4522) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 31.60/9.01 |
% 31.60/9.01 +-Applying beta-rule and splitting (4522), into two cases.
% 31.60/9.01 |-Branch one:
% 31.60/9.01 | (502) all_0_43_43 = e4
% 31.60/9.01 |
% 31.60/9.01 | Equations (502) can reduce 510 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (510) ~ (all_0_43_43 = e4)
% 31.60/9.01 | (4527) all_0_51_51 = e4 | all_0_56_56 = e4
% 31.60/9.01 |
% 31.60/9.01 +-Applying beta-rule and splitting (4527), into two cases.
% 31.60/9.01 |-Branch one:
% 31.60/9.01 | (1467) all_0_51_51 = e4
% 31.60/9.01 |
% 31.60/9.01 | Equations (1467) can reduce 697 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (697) ~ (all_0_51_51 = e4)
% 31.60/9.01 | (4744) all_0_56_56 = e4
% 31.60/9.01 |
% 31.60/9.01 | Equations (4744) can reduce 274 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (361) ~ (all_0_41_41 = e4)
% 31.60/9.01 | (512) all_0_42_42 = e4
% 31.60/9.01 |
% 31.60/9.01 | Equations (512) can reduce 520 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (280) ~ (all_0_59_59 = e4)
% 31.60/9.01 | (407) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0))
% 31.60/9.01 |
% 31.60/9.01 +-Applying beta-rule and splitting (407), into two cases.
% 31.60/9.01 |-Branch one:
% 31.60/9.01 | (408) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)) | (all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1))
% 31.60/9.01 |
% 31.60/9.01 +-Applying beta-rule and splitting (408), into two cases.
% 31.60/9.01 |-Branch one:
% 31.60/9.01 | (409) (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)) | (all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0))
% 31.60/9.01 |
% 31.60/9.01 +-Applying beta-rule and splitting (409), into two cases.
% 31.60/9.01 |-Branch one:
% 31.60/9.01 | (410) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_46_46 = e3)
% 31.60/9.01 |
% 31.60/9.01 | Applying alpha-rule on (410) yields:
% 31.60/9.01 | (411) all_0_43_43 = e0
% 31.60/9.01 | (412) all_0_59_59 = e3
% 31.60/9.01 | (413) ~ (all_0_46_46 = e3)
% 31.60/9.01 |
% 31.60/9.01 | Equations (411) can reduce 455 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (416) all_0_43_43 = e0 & all_0_59_59 = e3 & ~ (all_0_56_56 = e0)
% 31.60/9.01 |
% 31.60/9.01 | Applying alpha-rule on (416) yields:
% 31.60/9.01 | (411) all_0_43_43 = e0
% 31.60/9.01 | (412) all_0_59_59 = e3
% 31.60/9.01 | (419) ~ (all_0_56_56 = e0)
% 31.60/9.01 |
% 31.60/9.01 | Equations (411) can reduce 455 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (422) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_54_54 = e1)
% 31.60/9.01 |
% 31.60/9.01 | Applying alpha-rule on (422) yields:
% 31.60/9.01 | (423) all_0_53_53 = e0
% 31.60/9.01 | (424) all_0_59_59 = e1
% 31.60/9.01 | (425) ~ (all_0_54_54 = e1)
% 31.60/9.01 |
% 31.60/9.01 | Equations (424) can reduce 750 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (428) all_0_53_53 = e0 & all_0_59_59 = e1 & ~ (all_0_58_58 = e0)
% 31.60/9.01 |
% 31.60/9.01 | Applying alpha-rule on (428) yields:
% 31.60/9.01 | (423) all_0_53_53 = e0
% 31.60/9.01 | (424) all_0_59_59 = e1
% 31.60/9.01 | (431) ~ (all_0_58_58 = e0)
% 31.60/9.01 |
% 31.60/9.01 | Equations (424) can reduce 750 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (625) ~ (all_0_44_44 = e0)
% 31.60/9.01 | (626) all_0_52_52 = e0 | all_0_57_57 = e0
% 31.60/9.01 |
% 31.60/9.01 +-Applying beta-rule and splitting (626), into two cases.
% 31.60/9.01 |-Branch one:
% 31.60/9.01 | (827) all_0_52_52 = e0
% 31.60/9.01 |
% 31.60/9.01 | Combining equations (685,827) yields a new equation:
% 31.60/9.01 | (622) e2 = e0
% 31.60/9.01 |
% 31.60/9.01 | Simplifying 622 yields:
% 31.60/9.01 | (316) e2 = e0
% 31.60/9.01 |
% 31.60/9.01 | Equations (316) can reduce 57 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (925) ~ (all_0_52_52 = e0)
% 31.60/9.01 | (2258) all_0_57_57 = e0
% 31.60/9.01 |
% 31.60/9.01 | Combining equations (997,2258) yields a new equation:
% 31.60/9.01 | (571) e1 = e0
% 31.60/9.01 |
% 31.60/9.01 | Simplifying 571 yields:
% 31.60/9.01 | (560) e1 = e0
% 31.60/9.01 |
% 31.60/9.01 | Equations (560) can reduce 132 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (434) ~ (all_0_45_45 = e2)
% 31.60/9.01 | (445) all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 31.60/9.01 |
% 31.60/9.01 +-Applying beta-rule and splitting (445), into two cases.
% 31.60/9.01 |-Branch one:
% 31.60/9.01 | (311) all_0_48_48 = e2
% 31.60/9.01 |
% 31.60/9.01 | Combining equations (552,311) yields a new equation:
% 31.60/9.01 | (322) e2 = e1
% 31.60/9.01 |
% 31.60/9.01 | Equations (322) can reduce 141 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (294) ~ (all_0_48_48 = e2)
% 31.60/9.01 | (449) all_0_53_53 = e2 | all_0_58_58 = e2
% 31.60/9.01 |
% 31.60/9.01 +-Applying beta-rule and splitting (449), into two cases.
% 31.60/9.01 |-Branch one:
% 31.60/9.01 | (576) all_0_53_53 = e2
% 31.60/9.01 |
% 31.60/9.01 | Equations (576) can reduce 259 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (259) ~ (all_0_53_53 = e2)
% 31.60/9.01 | (396) all_0_58_58 = e2
% 31.60/9.01 |
% 31.60/9.01 | Equations (396) can reduce 376 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (257) ~ (all_0_52_52 = e2)
% 31.60/9.01 | (392) all_0_57_57 = e2
% 31.60/9.01 |
% 31.60/9.01 | Equations (392) can reduce 335 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (291) ~ (all_0_39_39 = e2)
% 31.60/9.01 | (339) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 31.60/9.01 |
% 31.60/9.01 +-Applying beta-rule and splitting (339), into two cases.
% 31.60/9.01 |-Branch one:
% 31.60/9.01 | (340) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 31.60/9.01 |
% 31.60/9.01 +-Applying beta-rule and splitting (340), into two cases.
% 31.60/9.01 |-Branch one:
% 31.60/9.01 | (341) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 31.60/9.01 |
% 31.60/9.01 | Applying alpha-rule on (341) yields:
% 31.60/9.01 | (342) all_0_0_0 = e1
% 31.60/9.01 | (343) ~ (all_0_1_1 = e4)
% 31.60/9.01 |
% 31.60/9.01 | Combining equations (342,9064) yields a new equation:
% 31.60/9.01 | (571) e1 = e0
% 31.60/9.01 |
% 31.60/9.01 | Simplifying 571 yields:
% 31.60/9.01 | (560) e1 = e0
% 31.60/9.01 |
% 31.60/9.01 | Equations (560) can reduce 132 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (346) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 31.60/9.01 |
% 31.60/9.01 | Applying alpha-rule on (346) yields:
% 31.60/9.01 | (347) all_0_2_2 = e0
% 31.60/9.01 | (348) ~ (all_0_3_3 = e4)
% 31.60/9.01 |
% 31.60/9.01 | Combining equations (9065,347) yields a new equation:
% 31.60/9.01 | (11698) all_0_40_40 = e0
% 31.60/9.01 |
% 31.60/9.01 | Simplifying 11698 yields:
% 31.60/9.01 | (11467) all_0_40_40 = e0
% 31.60/9.01 |
% 31.60/9.01 | Equations (11467) can reduce 238 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (350) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 31.60/9.01 |
% 31.60/9.01 | Applying alpha-rule on (350) yields:
% 31.60/9.01 | (351) all_0_41_41 = e3
% 31.60/9.01 | (352) ~ (all_0_45_45 = e4)
% 31.60/9.01 |
% 31.60/9.01 +-Applying beta-rule and splitting (164), into two cases.
% 31.60/9.01 |-Branch one:
% 31.60/9.01 | (336) all_0_39_39 = e2
% 31.60/9.01 |
% 31.60/9.01 | Equations (336) can reduce 291 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (291) ~ (all_0_39_39 = e2)
% 31.60/9.01 | (630) all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 31.60/9.01 |
% 31.60/9.01 +-Applying beta-rule and splitting (630), into two cases.
% 31.60/9.01 |-Branch one:
% 31.60/9.01 | (327) all_0_40_40 = e2
% 31.60/9.01 |
% 31.60/9.01 | Equations (327) can reduce 602 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (602) ~ (all_0_40_40 = e2)
% 31.60/9.01 | (1251) all_0_41_41 = e2 | all_0_42_42 = e2
% 31.60/9.01 |
% 31.60/9.01 +-Applying beta-rule and splitting (1251), into two cases.
% 31.60/9.01 |-Branch one:
% 31.60/9.01 | (436) all_0_41_41 = e2
% 31.60/9.01 |
% 31.60/9.01 | Combining equations (351,436) yields a new equation:
% 31.60/9.01 | (437) e3 = e2
% 31.60/9.01 |
% 31.60/9.01 | Simplifying 437 yields:
% 31.60/9.01 | (414) e3 = e2
% 31.60/9.01 |
% 31.60/9.01 | Equations (414) can reduce 223 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (331) ~ (all_0_41_41 = e2)
% 31.60/9.01 | (698) all_0_42_42 = e2
% 31.60/9.01 |
% 31.60/9.01 | Equations (698) can reduce 498 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (318) ~ (all_0_47_47 = e0)
% 31.60/9.01 | (319) all_0_48_48 = e0 | all_0_49_49 = e0
% 31.60/9.01 |
% 31.60/9.01 +-Applying beta-rule and splitting (319), into two cases.
% 31.60/9.01 |-Branch one:
% 31.60/9.01 | (559) all_0_48_48 = e0
% 31.60/9.01 |
% 31.60/9.01 | Combining equations (552,559) yields a new equation:
% 31.60/9.01 | (571) e1 = e0
% 31.60/9.01 |
% 31.60/9.01 | Simplifying 571 yields:
% 31.60/9.01 | (560) e1 = e0
% 31.60/9.01 |
% 31.60/9.01 | Equations (560) can reduce 132 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (562) ~ (all_0_48_48 = e0)
% 31.60/9.01 | (563) all_0_49_49 = e0
% 31.60/9.01 |
% 31.60/9.01 | Combining equations (563,307) yields a new equation:
% 31.60/9.01 | (316) e2 = e0
% 31.60/9.01 |
% 31.60/9.01 | Equations (316) can reduce 57 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 |-Branch two:
% 31.60/9.01 | (588) ~ (all_0_48_48 = e1)
% 31.60/9.01 | (589) all_0_49_49 = e1
% 31.60/9.01 |
% 31.60/9.01 | Combining equations (589,307) yields a new equation:
% 31.60/9.01 | (322) e2 = e1
% 31.60/9.01 |
% 31.60/9.01 | Equations (322) can reduce 141 to:
% 31.60/9.01 | (270) $false
% 31.60/9.01 |
% 31.60/9.01 |-The branch is then unsatisfiable
% 31.60/9.01 % SZS output end Proof for theBenchmark
% 31.60/9.02
% 31.60/9.02 8429ms
%------------------------------------------------------------------------------