TSTP Solution File: ALG061+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG061+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n027.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 15:34:08 EDT 2022
% Result : Theorem 6.09s 1.93s
% Output : Proof 14.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG061+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 8 10:51:56 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.53/0.57 ____ _
% 0.53/0.57 ___ / __ \_____(_)___ ________ __________
% 0.53/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.53/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.53/0.57
% 0.53/0.57 A Theorem Prover for First-Order Logic
% 0.53/0.57 (ePrincess v.1.0)
% 0.53/0.57
% 0.53/0.57 (c) Philipp Rümmer, 2009-2015
% 0.53/0.57 (c) Peter Backeman, 2014-2015
% 0.53/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.57 Bug reports to peter@backeman.se
% 0.53/0.57
% 0.53/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.57
% 0.53/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.53/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.46/1.12 Prover 0: Preprocessing ...
% 4.15/1.47 Prover 0: Constructing countermodel ...
% 6.09/1.93 Prover 0: proved (1307ms)
% 6.09/1.93
% 6.09/1.93 No countermodel exists, formula is valid
% 6.09/1.93 % SZS status Theorem for theBenchmark
% 6.09/1.93
% 6.09/1.93 Generating proof ... found it (size 2754)
% 12.37/3.43
% 12.37/3.43 % SZS output start Proof for theBenchmark
% 12.37/3.43 Assumed formulas after preprocessing and simplification:
% 12.37/3.43 | (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] : ? [v60] : ( ~ (v20 = v19) & ~ (v20 = v18) & ~ (v20 = v17) & ~ (v20 = v15) & ~ (v20 = v10) & ~ (v20 = v6) & ~ (v20 = v3) & ~ (v20 = e2) & ~ (v19 = v18) & ~ (v19 = v17) & ~ (v19 = v14) & ~ (v19 = v2) & ~ (v19 = e3) & ~ (v19 = e2) & ~ (v19 = e0) & ~ (v18 = v17) & ~ (v18 = v13) & ~ (v18 = v9) & ~ (v18 = v1) & ~ (v18 = e4) & ~ (v18 = e2) & ~ (v17 = v12) & ~ (v17 = v8) & ~ (v17 = v5) & ~ (v17 = v0) & ~ (v17 = e2) & ~ (v16 = v15) & ~ (v16 = v14) & ~ (v16 = v13) & ~ (v16 = v12) & ~ (v16 = v11) & ~ (v16 = v7) & ~ (v16 = v4) & ~ (v16 = e2) & ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = v12) & ~ (v15 = v10) & ~ (v15 = v6) & ~ (v15 = v3) & ~ (v14 = v13) & ~ (v14 = v12) & ~ (v14 = v2) & ~ (v14 = e3) & ~ (v14 = e0) & ~ (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v1) & ~ (v13 = e4) & ~ (v12 = v8) & ~ (v12 = v5) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = v9) & ~ (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v4) & ~ (v11 = e3) & ~ (v11 = e2) & ~ (v10 = v9) & ~ (v10 = v8) & ~ (v10 = v6) & ~ (v10 = v3) & ~ (v10 = e3) & ~ (v9 = v8) & ~ (v9 = v1) & ~ (v9 = e4) & ~ (v9 = e3) & ~ (v8 = v5) & ~ (v8 = v0) & ~ (v8 = e3) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v4) & ~ (v7 = e4) & ~ (v7 = e2) & ~ (v7 = e0) & ~ (v6 = v5) & ~ (v6 = v3) & ~ (v6 = e4) & ~ (v6 = e0) & ~ (v5 = v0) & ~ (v5 = e4) & ~ (v5 = e0) & ~ (v4 = v3) & ~ (v4 = v2) & ~ (v4 = v1) & ~ (v4 = v0) & ~ (v4 = e2) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = v0) & ~ (v2 = e3) & ~ (v2 = e0) & ~ (v1 = v0) & ~ (v1 = e4) & ~ (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) = v51 & op(e4, v19) = v42 & op(e4, v18) = v36 & op(e4, v17) = v28 & op(e4, v16) = v60 & op(e4, v11) = v58 & op(e4, v7) = v56 & op(e4, v4) = v54 & op(e4, unit) = e4 & op(e4, e4) = e2 & op(e4, e3) = v20 & op(e4, e2) = v19 & op(e4, e1) = v18 & op(e4, e0) = v17 & op(e3, v20) = v52 & op(e3, v16) = v59 & op(e3, v15) = v50 & op(e3, v14) = v40 & op(e3, v13) = v34 & op(e3, v12) = v26 & op(e3, v10) = v49 & op(e3, v6) = v47 & op(e3, v3) = v45 & op(e3, unit) = e3 & op(e3, e4) = v16 & op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, v19) = v43 & op(e2, v14) = v41 & op(e2, v11) = v57 & op(e2, v10) = v48 & op(e2, v9) = v32 & op(e2, v8) = v24 & op(e2, v2) = v39 & op(e2, unit) = e2 & op(e2, e4) = v11 & op(e2, e3) = v10 & op(e2, e2) = e3 & op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, v18) = v37 & op(e1, v13) = v35 & op(e1, v9) = v33 & op(e1, v7) = v55 & op(e1, v6) = v46 & op(e1, v5) = v22 & op(e1, v1) = v31 & op(e1, unit) = e1 & op(e1, e4) = v7 & op(e1, e3) = v6 & op(e1, e2) = e0 & op(e1, e1) = e4 & op(e1, e0) = v5 & op(e0, v17) = v29 & op(e0, v12) = v27 & op(e0, v8) = v25 & op(e0, v5) = v23 & op(e0, v4) = v53 & op(e0, v3) = v44 & op(e0, v2) = v38 & 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 & ! [v61] : ! [v62] : ! [v63] : ! [v64] : (v62 = v61 | ~ (op(v64, v63) = v62) | ~ (op(v64, v63) = v61)) & (v20 = e4 | v20 = e3 | v20 = e1 | v20 = e0) & (v20 = e4 | v19 = e4 | v17 = e4) & (v20 = e4 | v15 = e4 | v10 = e4 | v3 = e4) & (v20 = e3 | v18 = e3 | v17 = e3) & (v20 = e3 | v15 = e3 | v6 = e3 | v3 = e3) & (v20 = e1 | v19 = e1 | v18 = e1 | v17 = e1) & (v20 = e1 | v15 = e1 | v10 = e1 | v6 = e1 | v3 = e1) & (v20 = e0 | v18 = e0 | v17 = e0) & (v20 = e0 | v15 = e0 | v10 = e0 | v3 = e0) & (v19 = e4 | v19 = e1) & (v19 = e4 | v14 = e4 | v2 = e4) & (v19 = e1 | v14 = e1 | v2 = e1) & (v18 = e3 | v18 = e1 | v18 = e0) & (v18 = e3 | v13 = e3 | v1 = e3) & (v18 = e1 | v13 = e1 | v9 = e1 | v1 = e1) & (v18 = e0 | v13 = e0 | v9 = e0 | v1 = e0) & (v17 = e4 | v17 = e3 | v17 = e1 | v17 = e0) & (v17 = e4 | v12 = e4 | v8 = e4 | v0 = e4) & (v17 = e3 | v12 = e3 | v5 = e3 | v0 = e3) & (v17 = e1 | v12 = e1 | v8 = e1 | v5 = e1 | v0 = e1) & (v17 = e0 | v12 = e0 | v8 = e0 | v0 = e0) & (v16 = e4 | v16 = e3 | v16 = e1 | v16 = e0) & (v16 = e4 | v15 = e4 | v14 = e4 | v12 = e4) & (v16 = e4 | v11 = e4 | v4 = e4) & (v16 = e3 | v15 = e3 | v13 = e3 | v12 = e3) & (v16 = e3 | v7 = e3 | v4 = e3) & (v16 = e1 | v15 = e1 | v14 = e1 | v13 = e1 | v12 = e1) & (v16 = e1 | v11 = e1 | v7 = e1 | v4 = e1) & (v16 = e0 | v15 = e0 | v13 = e0 | v12 = e0) & (v16 = e0 | v11 = e0 | v4 = e0) & (v15 = e4 | v15 = e3 | v15 = e2 | v15 = e1 | v15 = e0) & (v15 = e2 | v14 = e2 | v13 = e2 | v12 = e2) & (v15 = e2 | v10 = e2 | v6 = e2 | v3 = e2) & (v15 = e1 | v0 = e1) & (v15 = e0 | v0 = e0) & (v14 = e4 | v14 = e2 | v14 = e1) & (v14 = e2 | v2 = e2) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v13 = e2 | v9 = e2 | v1 = e2) & (v12 = e4 | v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v12 = e2 | v8 = e2 | v5 = e2 | v0 = e2) & (v11 = e4 | v11 = e1 | v11 = e0) & (v11 = e4 | v10 = e4 | v8 = e4) & (v11 = e1 | v10 = e1 | v9 = e1 | v8 = e1) & (v11 = e0 | v10 = e0 | v9 = e0 | v8 = e0) & (v10 = e4 | v10 = e2 | v10 = e1 | v10 = e0) & (v10 = e2 | v9 = e2 | v8 = e2) & (v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e4 | v8 = e2 | v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e1) & (v7 = e3 | v6 = e3 | v5 = e3) & (v7 = e1 | v6 = e1 | v5 = e1) & (v6 = e3 | v6 = e2 | v6 = e1) & (v6 = e2 | v5 = e2) & (v5 = e3 | v5 = e2 | v5 = e1) & (v4 = e4 | v4 = e3 | v4 = e1 | v4 = e0) & (v4 = e4 | v3 = e4 | v2 = e4 | v0 = e4) & (v4 = e3 | v3 = e3 | v1 = e3 | v0 = e3) & (v4 = e1 | v3 = e1 | v2 = e1 | v1 = e1 | v0 = e1) & (v4 = e0 | v3 = e0 | v1 = e0 | v0 = e0) & (v3 = e4 | v3 = e3 | v3 = e2 | v3 = e1 | v3 = e0) & (v3 = e2 | v2 = e2 | v1 = e2 | v0 = e2) & (v2 = e4 | v2 = e2 | v2 = e1) & (v1 = e3 | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e4 | v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0) & (unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0) & ((v60 = e3 & ~ (v59 = e4)) | (v58 = e2 & ~ (v57 = e4)) | (v56 = e1 & ~ (v55 = e4)) | (v54 = e0 & ~ (v53 = e4))) & ((v52 = e4 & ~ (v51 = e3)) | (v49 = e2 & ~ (v48 = e3)) | (v47 = e1 & ~ (v46 = e3)) | (v45 = e0 & ~ (v44 = e3))) & ((v43 = e4 & ~ (v42 = e2)) | (v41 = e3 & ~ (v40 = e2)) | (v39 = e0 & ~ (v38 = e2)) | (v8 = e1 & ~ (v5 = e2))) & ((v37 = e4 & ~ (v36 = e1)) | (v35 = e3 & ~ (v34 = e1)) | (v33 = e2 & ~ (v32 = e1)) | (v31 = e0 & ~ (v30 = e1))) & ((v29 = e4 & ~ (v28 = e0)) | (v27 = e3 & ~ (v26 = e0)) | (v25 = e2 & ~ (v24 = e0)) | (v23 = e1 & ~ (v22 = e0))))
% 12.86/3.48 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16, all_0_17_17, all_0_18_18, 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, all_0_60_60 yields:
% 12.86/3.48 | (1) ~ (all_0_40_40 = all_0_41_41) & ~ (all_0_40_40 = all_0_42_42) & ~ (all_0_40_40 = all_0_43_43) & ~ (all_0_40_40 = all_0_45_45) & ~ (all_0_40_40 = all_0_50_50) & ~ (all_0_40_40 = all_0_54_54) & ~ (all_0_40_40 = all_0_57_57) & ~ (all_0_40_40 = e2) & ~ (all_0_41_41 = all_0_42_42) & ~ (all_0_41_41 = all_0_43_43) & ~ (all_0_41_41 = all_0_46_46) & ~ (all_0_41_41 = all_0_58_58) & ~ (all_0_41_41 = e3) & ~ (all_0_41_41 = e2) & ~ (all_0_41_41 = e0) & ~ (all_0_42_42 = all_0_43_43) & ~ (all_0_42_42 = all_0_47_47) & ~ (all_0_42_42 = all_0_51_51) & ~ (all_0_42_42 = all_0_59_59) & ~ (all_0_42_42 = e4) & ~ (all_0_42_42 = e2) & ~ (all_0_43_43 = all_0_48_48) & ~ (all_0_43_43 = all_0_52_52) & ~ (all_0_43_43 = all_0_55_55) & ~ (all_0_43_43 = all_0_60_60) & ~ (all_0_43_43 = e2) & ~ (all_0_44_44 = all_0_45_45) & ~ (all_0_44_44 = all_0_46_46) & ~ (all_0_44_44 = all_0_47_47) & ~ (all_0_44_44 = all_0_48_48) & ~ (all_0_44_44 = all_0_49_49) & ~ (all_0_44_44 = all_0_53_53) & ~ (all_0_44_44 = all_0_56_56) & ~ (all_0_44_44 = e2) & ~ (all_0_45_45 = all_0_46_46) & ~ (all_0_45_45 = all_0_47_47) & ~ (all_0_45_45 = all_0_48_48) & ~ (all_0_45_45 = all_0_50_50) & ~ (all_0_45_45 = all_0_54_54) & ~ (all_0_45_45 = all_0_57_57) & ~ (all_0_46_46 = all_0_47_47) & ~ (all_0_46_46 = all_0_48_48) & ~ (all_0_46_46 = all_0_58_58) & ~ (all_0_46_46 = e3) & ~ (all_0_46_46 = e0) & ~ (all_0_47_47 = all_0_48_48) & ~ (all_0_47_47 = all_0_51_51) & ~ (all_0_47_47 = all_0_59_59) & ~ (all_0_47_47 = e4) & ~ (all_0_48_48 = all_0_52_52) & ~ (all_0_48_48 = all_0_55_55) & ~ (all_0_48_48 = all_0_60_60) & ~ (all_0_49_49 = all_0_50_50) & ~ (all_0_49_49 = all_0_51_51) & ~ (all_0_49_49 = all_0_52_52) & ~ (all_0_49_49 = all_0_53_53) & ~ (all_0_49_49 = all_0_56_56) & ~ (all_0_49_49 = e3) & ~ (all_0_49_49 = e2) & ~ (all_0_50_50 = all_0_51_51) & ~ (all_0_50_50 = all_0_52_52) & ~ (all_0_50_50 = all_0_54_54) & ~ (all_0_50_50 = all_0_57_57) & ~ (all_0_50_50 = e3) & ~ (all_0_51_51 = all_0_52_52) & ~ (all_0_51_51 = all_0_59_59) & ~ (all_0_51_51 = e4) & ~ (all_0_51_51 = e3) & ~ (all_0_52_52 = all_0_55_55) & ~ (all_0_52_52 = all_0_60_60) & ~ (all_0_52_52 = e3) & ~ (all_0_53_53 = all_0_54_54) & ~ (all_0_53_53 = all_0_55_55) & ~ (all_0_53_53 = all_0_56_56) & ~ (all_0_53_53 = e4) & ~ (all_0_53_53 = e2) & ~ (all_0_53_53 = e0) & ~ (all_0_54_54 = all_0_55_55) & ~ (all_0_54_54 = all_0_57_57) & ~ (all_0_54_54 = e4) & ~ (all_0_54_54 = e0) & ~ (all_0_55_55 = all_0_60_60) & ~ (all_0_55_55 = e4) & ~ (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_56_56 = all_0_60_60) & ~ (all_0_56_56 = e2) & ~ (all_0_57_57 = all_0_58_58) & ~ (all_0_57_57 = all_0_59_59) & ~ (all_0_57_57 = all_0_60_60) & ~ (all_0_58_58 = all_0_59_59) & ~ (all_0_58_58 = all_0_60_60) & ~ (all_0_58_58 = e3) & ~ (all_0_58_58 = e0) & ~ (all_0_59_59 = all_0_60_60) & ~ (all_0_59_59 = e4) & ~ (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_40_40) = all_0_9_9 & op(e4, all_0_41_41) = all_0_18_18 & op(e4, all_0_42_42) = all_0_24_24 & op(e4, all_0_43_43) = all_0_32_32 & op(e4, all_0_44_44) = all_0_0_0 & op(e4, all_0_49_49) = all_0_2_2 & op(e4, all_0_53_53) = all_0_4_4 & op(e4, all_0_56_56) = all_0_6_6 & op(e4, unit) = e4 & op(e4, e4) = e2 & op(e4, e3) = all_0_40_40 & op(e4, e2) = all_0_41_41 & op(e4, e1) = all_0_42_42 & op(e4, e0) = all_0_43_43 & op(e3, all_0_40_40) = all_0_8_8 & op(e3, all_0_44_44) = all_0_1_1 & op(e3, all_0_45_45) = all_0_10_10 & op(e3, all_0_46_46) = all_0_20_20 & op(e3, all_0_47_47) = all_0_26_26 & op(e3, all_0_48_48) = all_0_34_34 & op(e3, all_0_50_50) = all_0_11_11 & op(e3, all_0_54_54) = all_0_13_13 & op(e3, all_0_57_57) = all_0_15_15 & op(e3, unit) = e3 & op(e3, e4) = all_0_44_44 & op(e3, e3) = all_0_45_45 & op(e3, e2) = all_0_46_46 & op(e3, e1) = all_0_47_47 & op(e3, e0) = all_0_48_48 & op(e2, all_0_41_41) = all_0_17_17 & op(e2, all_0_46_46) = all_0_19_19 & op(e2, all_0_49_49) = all_0_3_3 & op(e2, all_0_50_50) = all_0_12_12 & op(e2, all_0_51_51) = all_0_28_28 & op(e2, all_0_52_52) = all_0_36_36 & op(e2, all_0_58_58) = all_0_21_21 & op(e2, unit) = e2 & op(e2, e4) = all_0_49_49 & op(e2, e3) = all_0_50_50 & op(e2, e2) = e3 & op(e2, e1) = all_0_51_51 & op(e2, e0) = all_0_52_52 & op(e1, all_0_42_42) = all_0_23_23 & op(e1, all_0_47_47) = all_0_25_25 & op(e1, all_0_51_51) = all_0_27_27 & op(e1, all_0_53_53) = all_0_5_5 & op(e1, all_0_54_54) = all_0_14_14 & op(e1, all_0_55_55) = all_0_38_38 & op(e1, all_0_59_59) = all_0_29_29 & op(e1, unit) = e1 & op(e1, e4) = all_0_53_53 & op(e1, e3) = all_0_54_54 & op(e1, e2) = e0 & op(e1, e1) = e4 & op(e1, e0) = all_0_55_55 & op(e0, all_0_43_43) = all_0_31_31 & op(e0, all_0_48_48) = all_0_33_33 & op(e0, all_0_52_52) = all_0_35_35 & op(e0, all_0_55_55) = all_0_37_37 & op(e0, all_0_56_56) = all_0_7_7 & op(e0, all_0_57_57) = all_0_16_16 & op(e0, all_0_58_58) = all_0_22_22 & op(e0, all_0_59_59) = all_0_30_30 & op(e0, all_0_60_60) = all_0_39_39 & op(e0, unit) = e0 & op(e0, e4) = all_0_56_56 & op(e0, e3) = all_0_57_57 & op(e0, e2) = all_0_58_58 & op(e0, e1) = all_0_59_59 & op(e0, e0) = all_0_60_60 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) & (all_0_40_40 = e4 | all_0_40_40 = e3 | all_0_40_40 = e1 | all_0_40_40 = e0) & (all_0_40_40 = e4 | all_0_41_41 = e4 | all_0_43_43 = e4) & (all_0_40_40 = e4 | all_0_45_45 = e4 | all_0_50_50 = e4 | all_0_57_57 = e4) & (all_0_40_40 = e3 | all_0_42_42 = e3 | all_0_43_43 = e3) & (all_0_40_40 = e3 | all_0_45_45 = e3 | all_0_54_54 = e3 | all_0_57_57 = e3) & (all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1 | all_0_43_43 = e1) & (all_0_40_40 = e1 | all_0_45_45 = e1 | all_0_50_50 = e1 | all_0_54_54 = e1 | all_0_57_57 = e1) & (all_0_40_40 = e0 | all_0_42_42 = e0 | all_0_43_43 = e0) & (all_0_40_40 = e0 | all_0_45_45 = e0 | all_0_50_50 = e0 | all_0_57_57 = e0) & (all_0_41_41 = e4 | all_0_41_41 = e1) & (all_0_41_41 = e4 | all_0_46_46 = e4 | all_0_58_58 = e4) & (all_0_41_41 = e1 | all_0_46_46 = e1 | all_0_58_58 = e1) & (all_0_42_42 = e3 | all_0_42_42 = e1 | all_0_42_42 = e0) & (all_0_42_42 = e3 | all_0_47_47 = e3 | all_0_59_59 = e3) & (all_0_42_42 = e1 | all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_59_59 = e1) & (all_0_42_42 = e0 | all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_59_59 = e0) & (all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e1 | all_0_43_43 = e0) & (all_0_43_43 = e4 | all_0_48_48 = e4 | all_0_52_52 = e4 | all_0_60_60 = e4) & (all_0_43_43 = e3 | all_0_48_48 = e3 | all_0_55_55 = e3 | all_0_60_60 = e3) & (all_0_43_43 = e1 | all_0_48_48 = e1 | all_0_52_52 = e1 | all_0_55_55 = e1 | all_0_60_60 = e1) & (all_0_43_43 = e0 | all_0_48_48 = e0 | all_0_52_52 = e0 | all_0_60_60 = e0) & (all_0_44_44 = e4 | all_0_44_44 = e3 | all_0_44_44 = e1 | all_0_44_44 = e0) & (all_0_44_44 = e4 | all_0_45_45 = e4 | all_0_46_46 = e4 | all_0_48_48 = e4) & (all_0_44_44 = e4 | all_0_49_49 = e4 | all_0_56_56 = e4) & (all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_47_47 = e3 | all_0_48_48 = e3) & (all_0_44_44 = e3 | all_0_53_53 = e3 | all_0_56_56 = e3) & (all_0_44_44 = e1 | all_0_45_45 = e1 | all_0_46_46 = e1 | all_0_47_47 = e1 | all_0_48_48 = e1) & (all_0_44_44 = e1 | all_0_49_49 = e1 | all_0_53_53 = e1 | all_0_56_56 = e1) & (all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_47_47 = e0 | all_0_48_48 = e0) & (all_0_44_44 = e0 | all_0_49_49 = e0 | all_0_56_56 = e0) & (all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e2 | all_0_45_45 = e1 | all_0_45_45 = e0) & (all_0_45_45 = e2 | all_0_46_46 = e2 | all_0_47_47 = e2 | all_0_48_48 = e2) & (all_0_45_45 = e2 | all_0_50_50 = e2 | all_0_54_54 = e2 | all_0_57_57 = e2) & (all_0_45_45 = e1 | all_0_60_60 = e1) & (all_0_45_45 = e0 | all_0_60_60 = e0) & (all_0_46_46 = e4 | all_0_46_46 = e2 | all_0_46_46 = e1) & (all_0_46_46 = e2 | all_0_58_58 = e2) & (all_0_47_47 = e3 | all_0_47_47 = e2 | all_0_47_47 = e1 | all_0_47_47 = e0) & (all_0_47_47 = e2 | all_0_51_51 = e2 | all_0_59_59 = e2) & (all_0_48_48 = e4 | all_0_48_48 = e3 | all_0_48_48 = e2 | all_0_48_48 = e1 | all_0_48_48 = e0) & (all_0_48_48 = e2 | all_0_52_52 = e2 | all_0_55_55 = e2 | all_0_60_60 = e2) & (all_0_49_49 = e4 | all_0_49_49 = e1 | all_0_49_49 = e0) & (all_0_49_49 = e4 | all_0_50_50 = e4 | all_0_52_52 = e4) & (all_0_49_49 = e1 | all_0_50_50 = e1 | all_0_51_51 = e1 | all_0_52_52 = e1) & (all_0_49_49 = e0 | all_0_50_50 = e0 | all_0_51_51 = e0 | all_0_52_52 = e0) & (all_0_50_50 = e4 | all_0_50_50 = e2 | all_0_50_50 = e1 | all_0_50_50 = e0) & (all_0_50_50 = e2 | all_0_51_51 = e2 | all_0_52_52 = e2) & (all_0_51_51 = e2 | all_0_51_51 = e1 | all_0_51_51 = e0) & (all_0_52_52 = e4 | all_0_52_52 = e2 | all_0_52_52 = e1 | all_0_52_52 = e0) & (all_0_53_53 = e3 | all_0_53_53 = e1) & (all_0_53_53 = e3 | all_0_54_54 = e3 | all_0_55_55 = e3) & (all_0_53_53 = e1 | all_0_54_54 = e1 | all_0_55_55 = e1) & (all_0_54_54 = e3 | all_0_54_54 = e2 | all_0_54_54 = e1) & (all_0_54_54 = e2 | all_0_55_55 = e2) & (all_0_55_55 = e3 | all_0_55_55 = e2 | all_0_55_55 = e1) & (all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1 | all_0_56_56 = e0) & (all_0_56_56 = e4 | all_0_57_57 = e4 | all_0_58_58 = e4 | all_0_60_60 = e4) & (all_0_56_56 = e3 | all_0_57_57 = e3 | all_0_59_59 = e3 | all_0_60_60 = e3) & (all_0_56_56 = e1 | all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1 | all_0_60_60 = e1) & (all_0_56_56 = e0 | all_0_57_57 = e0 | all_0_59_59 = e0 | all_0_60_60 = e0) & (all_0_57_57 = e4 | all_0_57_57 = e3 | all_0_57_57 = e2 | all_0_57_57 = e1 | all_0_57_57 = e0) & (all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2 | all_0_60_60 = e2) & (all_0_58_58 = e4 | all_0_58_58 = e2 | all_0_58_58 = e1) & (all_0_59_59 = e3 | all_0_59_59 = e2 | all_0_59_59 = e1 | all_0_59_59 = e0) & (all_0_60_60 = e4 | all_0_60_60 = e3 | all_0_60_60 = e2 | all_0_60_60 = e1 | all_0_60_60 = e0) & (unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0) & ((all_0_0_0 = e3 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e2 & ~ (all_0_3_3 = e4)) | (all_0_4_4 = e1 & ~ (all_0_5_5 = e4)) | (all_0_6_6 = e0 & ~ (all_0_7_7 = e4))) & ((all_0_8_8 = e4 & ~ (all_0_9_9 = e3)) | (all_0_11_11 = e2 & ~ (all_0_12_12 = e3)) | (all_0_13_13 = e1 & ~ (all_0_14_14 = e3)) | (all_0_15_15 = e0 & ~ (all_0_16_16 = e3))) & ((all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2)) | (all_0_21_21 = e0 & ~ (all_0_22_22 = e2)) | (all_0_52_52 = e1 & ~ (all_0_55_55 = e2))) & ((all_0_23_23 = e4 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e3 & ~ (all_0_26_26 = e1)) | (all_0_27_27 = e2 & ~ (all_0_28_28 = e1)) | (all_0_29_29 = e0 & ~ (all_0_30_30 = e1))) & ((all_0_31_31 = e4 & ~ (all_0_32_32 = e0)) | (all_0_33_33 = e3 & ~ (all_0_34_34 = e0)) | (all_0_35_35 = e2 & ~ (all_0_36_36 = e0)) | (all_0_37_37 = e1 & ~ (all_0_38_38 = e0)))
% 12.86/3.50 |
% 12.86/3.50 | Applying alpha-rule on (1) yields:
% 12.86/3.50 | (2) ~ (all_0_46_46 = all_0_48_48)
% 12.86/3.50 | (3) op(e2, e3) = all_0_50_50
% 12.86/3.50 | (4) ~ (all_0_41_41 = e3)
% 12.86/3.50 | (5) ~ (e4 = e0)
% 12.86/3.50 | (6) all_0_45_45 = e2 | all_0_50_50 = e2 | all_0_54_54 = e2 | all_0_57_57 = e2
% 12.86/3.50 | (7) all_0_58_58 = e4 | all_0_58_58 = e2 | all_0_58_58 = e1
% 12.86/3.50 | (8) ~ (all_0_59_59 = e4)
% 12.86/3.50 | (9) ~ (all_0_47_47 = all_0_48_48)
% 12.86/3.50 | (10) op(e1, e4) = all_0_53_53
% 12.86/3.50 | (11) op(e0, e2) = all_0_58_58
% 12.86/3.50 | (12) all_0_45_45 = e1 | all_0_60_60 = e1
% 12.86/3.50 | (13) ~ (all_0_52_52 = e3)
% 12.86/3.50 | (14) all_0_56_56 = e1 | all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1 | all_0_60_60 = e1
% 12.86/3.50 | (15) op(e3, e3) = all_0_45_45
% 12.86/3.50 | (16) all_0_44_44 = e3 | all_0_53_53 = e3 | all_0_56_56 = e3
% 12.86/3.50 | (17) ~ (all_0_44_44 = all_0_53_53)
% 12.86/3.50 | (18) ~ (all_0_57_57 = all_0_60_60)
% 12.86/3.50 | (19) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2)) | (all_0_21_21 = e0 & ~ (all_0_22_22 = e2)) | (all_0_52_52 = e1 & ~ (all_0_55_55 = e2))
% 12.86/3.50 | (20) ~ (all_0_42_42 = e2)
% 12.86/3.50 | (21) all_0_40_40 = e4 | all_0_41_41 = e4 | all_0_43_43 = e4
% 12.86/3.50 | (22) op(e1, unit) = e1
% 12.86/3.50 | (23) all_0_41_41 = e4 | all_0_46_46 = e4 | all_0_58_58 = e4
% 12.86/3.50 | (24) all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1 | all_0_43_43 = e1
% 12.86/3.50 | (25) all_0_45_45 = e0 | all_0_60_60 = e0
% 12.86/3.50 | (26) all_0_42_42 = e1 | all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_59_59 = e1
% 12.86/3.50 | (27) op(e2, all_0_58_58) = all_0_21_21
% 12.86/3.50 | (28) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_47_47 = e3 | all_0_48_48 = e3
% 12.86/3.50 | (29) ~ (all_0_42_42 = all_0_47_47)
% 12.86/3.50 | (30) ~ (e4 = e3)
% 12.86/3.50 | (31) op(e3, e1) = all_0_47_47
% 12.86/3.50 | (32) ~ (all_0_40_40 = all_0_41_41)
% 12.86/3.50 | (33) op(e0, all_0_58_58) = all_0_22_22
% 12.86/3.50 | (34) op(e1, all_0_53_53) = all_0_5_5
% 12.86/3.50 | (35) op(e4, e1) = all_0_42_42
% 12.86/3.50 | (36) (all_0_31_31 = e4 & ~ (all_0_32_32 = e0)) | (all_0_33_33 = e3 & ~ (all_0_34_34 = e0)) | (all_0_35_35 = e2 & ~ (all_0_36_36 = e0)) | (all_0_37_37 = e1 & ~ (all_0_38_38 = e0))
% 12.86/3.50 | (37) ~ (all_0_45_45 = all_0_54_54)
% 12.86/3.50 | (38) ~ (all_0_52_52 = all_0_60_60)
% 12.86/3.50 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 12.86/3.50 | (40) ~ (all_0_44_44 = all_0_48_48)
% 12.86/3.50 | (41) op(e3, all_0_44_44) = all_0_1_1
% 12.86/3.50 | (42) all_0_42_42 = e3 | all_0_42_42 = e1 | all_0_42_42 = e0
% 12.86/3.50 | (43) op(e0, all_0_59_59) = all_0_30_30
% 12.86/3.50 | (44) op(unit, e1) = e1
% 12.86/3.50 | (45) op(e1, e1) = e4
% 12.86/3.50 | (46) ~ (all_0_49_49 = e3)
% 12.86/3.50 | (47) all_0_44_44 = e1 | all_0_49_49 = e1 | all_0_53_53 = e1 | all_0_56_56 = e1
% 12.86/3.50 | (48) ~ (all_0_40_40 = all_0_50_50)
% 12.86/3.50 | (49) op(e2, e0) = all_0_52_52
% 12.86/3.50 | (50) op(e4, e4) = e2
% 12.86/3.50 | (51) ~ (all_0_40_40 = all_0_43_43)
% 12.86/3.50 | (52) ~ (all_0_50_50 = e3)
% 12.86/3.50 | (53) ~ (all_0_44_44 = all_0_49_49)
% 12.86/3.50 | (54) ~ (all_0_43_43 = all_0_52_52)
% 12.86/3.50 | (55) all_0_40_40 = e0 | all_0_45_45 = e0 | all_0_50_50 = e0 | all_0_57_57 = e0
% 12.86/3.50 | (56) ~ (all_0_51_51 = e4)
% 12.86/3.50 | (57) op(e4, all_0_40_40) = all_0_9_9
% 12.86/3.50 | (58) ~ (all_0_53_53 = e2)
% 12.86/3.50 | (59) all_0_60_60 = e4 | all_0_60_60 = e3 | all_0_60_60 = e2 | all_0_60_60 = e1 | all_0_60_60 = e0
% 12.86/3.50 | (60) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1 | all_0_56_56 = e0
% 12.86/3.50 | (61) ~ (e2 = e0)
% 12.86/3.50 | (62) ~ (all_0_44_44 = all_0_47_47)
% 12.86/3.50 | (63) all_0_44_44 = e4 | all_0_45_45 = e4 | all_0_46_46 = e4 | all_0_48_48 = e4
% 12.86/3.50 | (64) all_0_40_40 = e0 | all_0_42_42 = e0 | all_0_43_43 = e0
% 12.86/3.50 | (65) op(e2, all_0_46_46) = all_0_19_19
% 12.86/3.50 | (66) op(e1, all_0_47_47) = all_0_25_25
% 12.86/3.50 | (67) ~ (all_0_48_48 = all_0_60_60)
% 12.86/3.50 | (68) op(e3, e4) = all_0_44_44
% 12.86/3.50 | (69) unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0
% 12.86/3.50 | (70) ~ (all_0_51_51 = all_0_52_52)
% 12.86/3.50 | (71) ~ (all_0_46_46 = all_0_58_58)
% 12.86/3.50 | (72) ~ (all_0_40_40 = all_0_45_45)
% 12.86/3.50 | (73) ~ (all_0_40_40 = all_0_57_57)
% 12.86/3.50 | (74) ~ (e3 = e0)
% 12.86/3.50 | (75) ~ (all_0_47_47 = e4)
% 12.86/3.50 | (76) op(e1, e2) = e0
% 12.86/3.50 | (77) all_0_44_44 = e4 | all_0_49_49 = e4 | all_0_56_56 = e4
% 12.86/3.50 | (78) all_0_49_49 = e1 | all_0_50_50 = e1 | all_0_51_51 = e1 | all_0_52_52 = e1
% 12.86/3.51 | (79) ~ (all_0_44_44 = all_0_46_46)
% 12.86/3.51 | (80) ~ (all_0_47_47 = all_0_59_59)
% 12.86/3.51 | (81) all_0_42_42 = e3 | all_0_47_47 = e3 | all_0_59_59 = e3
% 12.86/3.51 | (82) ~ (all_0_57_57 = all_0_58_58)
% 12.86/3.51 | (83) ~ (all_0_49_49 = all_0_51_51)
% 12.86/3.51 | (84) all_0_43_43 = e4 | all_0_48_48 = e4 | all_0_52_52 = e4 | all_0_60_60 = e4
% 12.86/3.51 | (85) all_0_46_46 = e2 | all_0_58_58 = e2
% 12.86/3.51 | (86) ~ (all_0_58_58 = all_0_60_60)
% 12.86/3.51 | (87) all_0_56_56 = e3 | all_0_57_57 = e3 | all_0_59_59 = e3 | all_0_60_60 = e3
% 12.86/3.51 | (88) all_0_49_49 = e4 | all_0_50_50 = e4 | all_0_52_52 = e4
% 12.86/3.51 | (89) op(e1, e3) = all_0_54_54
% 12.86/3.51 | (90) ~ (all_0_56_56 = all_0_57_57)
% 12.86/3.51 | (91) ~ (all_0_41_41 = e2)
% 12.86/3.51 | (92) ~ (all_0_51_51 = all_0_59_59)
% 12.86/3.51 | (93) ~ (all_0_43_43 = all_0_60_60)
% 12.86/3.51 | (94) ~ (all_0_49_49 = all_0_53_53)
% 12.86/3.51 | (95) ~ (all_0_43_43 = e2)
% 12.86/3.51 | (96) ~ (all_0_41_41 = all_0_42_42)
% 12.86/3.51 | (97) ~ (all_0_40_40 = all_0_54_54)
% 12.86/3.51 | (98) op(e2, e4) = all_0_49_49
% 12.86/3.51 | (99) ~ (all_0_53_53 = all_0_55_55)
% 12.86/3.51 | (100) all_0_40_40 = e4 | all_0_45_45 = e4 | all_0_50_50 = e4 | all_0_57_57 = e4
% 12.86/3.51 | (101) ~ (all_0_54_54 = all_0_55_55)
% 12.86/3.51 | (102) all_0_55_55 = e3 | all_0_55_55 = e2 | all_0_55_55 = e1
% 12.86/3.51 | (103) ~ (all_0_46_46 = e0)
% 12.86/3.51 | (104) op(e0, all_0_60_60) = all_0_39_39
% 12.86/3.51 | (105) op(e1, all_0_54_54) = all_0_14_14
% 12.86/3.51 | (106) ~ (all_0_53_53 = all_0_56_56)
% 12.86/3.51 | (107) op(e3, all_0_48_48) = all_0_34_34
% 12.86/3.51 | (108) ~ (all_0_58_58 = all_0_59_59)
% 12.86/3.51 | (109) all_0_53_53 = e3 | all_0_53_53 = e1
% 12.86/3.51 | (110) ~ (all_0_44_44 = e2)
% 12.86/3.51 | (111) op(e4, all_0_41_41) = all_0_18_18
% 12.86/3.51 | (112) op(unit, e3) = e3
% 12.86/3.51 | (113) all_0_53_53 = e3 | all_0_54_54 = e3 | all_0_55_55 = e3
% 12.86/3.51 | (114) all_0_44_44 = e1 | all_0_45_45 = e1 | all_0_46_46 = e1 | all_0_47_47 = e1 | all_0_48_48 = e1
% 12.86/3.51 | (115) ~ (all_0_43_43 = all_0_48_48)
% 12.86/3.51 | (116) ~ (all_0_50_50 = all_0_51_51)
% 12.86/3.51 | (117) ~ (all_0_55_55 = all_0_60_60)
% 12.86/3.51 | (118) op(e1, all_0_59_59) = all_0_29_29
% 12.86/3.51 | (119) ~ (all_0_46_46 = all_0_47_47)
% 12.86/3.51 | (120) all_0_57_57 = e4 | all_0_57_57 = e3 | all_0_57_57 = e2 | all_0_57_57 = e1 | all_0_57_57 = e0
% 12.86/3.51 | (121) all_0_44_44 = e0 | all_0_49_49 = e0 | all_0_56_56 = e0
% 12.86/3.51 | (122) ~ (all_0_45_45 = all_0_57_57)
% 12.86/3.51 | (123) ~ (all_0_49_49 = all_0_50_50)
% 12.86/3.51 | (124) all_0_42_42 = e0 | all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_59_59 = e0
% 12.86/3.51 | (125) ~ (all_0_43_43 = all_0_55_55)
% 12.86/3.51 | (126) op(e4, all_0_44_44) = all_0_0_0
% 12.86/3.51 | (127) all_0_47_47 = e2 | all_0_51_51 = e2 | all_0_59_59 = e2
% 12.86/3.51 | (128) ~ (all_0_45_45 = all_0_46_46)
% 12.86/3.51 | (129) all_0_46_46 = e4 | all_0_46_46 = e2 | all_0_46_46 = e1
% 12.86/3.51 | (130) ~ (all_0_44_44 = all_0_56_56)
% 12.86/3.51 | (131) all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2 | all_0_60_60 = e2
% 12.86/3.51 | (132) op(e1, e0) = all_0_55_55
% 12.86/3.51 | (133) all_0_50_50 = e2 | all_0_51_51 = e2 | all_0_52_52 = e2
% 12.86/3.51 | (134) ~ (all_0_40_40 = e2)
% 12.86/3.51 | (135) op(e2, unit) = e2
% 12.86/3.51 | (136) ~ (all_0_41_41 = all_0_43_43)
% 12.86/3.51 | (137) all_0_49_49 = e0 | all_0_50_50 = e0 | all_0_51_51 = e0 | all_0_52_52 = e0
% 12.86/3.51 | (138) all_0_52_52 = e4 | all_0_52_52 = e2 | all_0_52_52 = e1 | all_0_52_52 = e0
% 12.86/3.51 | (139) op(e4, unit) = e4
% 12.86/3.51 | (140) ~ (all_0_56_56 = all_0_60_60)
% 12.86/3.51 | (141) op(e2, all_0_51_51) = all_0_28_28
% 12.86/3.51 | (142) op(e3, all_0_57_57) = all_0_15_15
% 12.86/3.51 | (143) ~ (e1 = e0)
% 12.86/3.51 | (144) ~ (all_0_42_42 = e4)
% 12.86/3.51 | (145) ~ (e3 = e1)
% 12.86/3.51 | (146) ~ (all_0_42_42 = all_0_59_59)
% 12.86/3.51 | (147) op(e4, all_0_53_53) = all_0_4_4
% 12.86/3.51 | (148) ~ (all_0_54_54 = e4)
% 12.86/3.51 | (149) ~ (all_0_46_46 = e3)
% 12.86/3.51 | (150) ~ (e2 = e1)
% 12.86/3.51 | (151) ~ (all_0_49_49 = e2)
% 12.86/3.51 | (152) op(e2, all_0_50_50) = all_0_12_12
% 12.86/3.51 | (153) op(e2, all_0_41_41) = all_0_17_17
% 12.86/3.52 | (154) op(e4, all_0_49_49) = all_0_2_2
% 12.86/3.52 | (155) (all_0_0_0 = e3 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e2 & ~ (all_0_3_3 = e4)) | (all_0_4_4 = e1 & ~ (all_0_5_5 = e4)) | (all_0_6_6 = e0 & ~ (all_0_7_7 = e4))
% 12.86/3.52 | (156) ~ (all_0_45_45 = all_0_47_47)
% 12.86/3.52 | (157) all_0_54_54 = e2 | all_0_55_55 = e2
% 12.86/3.52 | (158) ~ (all_0_41_41 = all_0_46_46)
% 12.86/3.52 | (159) ~ (all_0_56_56 = all_0_59_59)
% 12.86/3.52 | (160) ~ (all_0_52_52 = all_0_55_55)
% 12.86/3.52 | (161) op(e3, all_0_46_46) = all_0_20_20
% 12.86/3.52 | (162) op(e3, unit) = e3
% 12.86/3.52 | (163) op(e0, e1) = all_0_59_59
% 12.86/3.52 | (164) op(e1, all_0_55_55) = all_0_38_38
% 12.86/3.52 | (165) ~ (all_0_48_48 = all_0_55_55)
% 12.86/3.52 | (166) ~ (all_0_57_57 = all_0_59_59)
% 12.86/3.52 | (167) op(e4, all_0_42_42) = all_0_24_24
% 12.86/3.52 | (168) op(e0, all_0_55_55) = all_0_37_37
% 12.86/3.52 | (169) op(e1, all_0_51_51) = all_0_27_27
% 12.86/3.52 | (170) ~ (all_0_50_50 = all_0_57_57)
% 12.86/3.52 | (171) all_0_56_56 = e0 | all_0_57_57 = e0 | all_0_59_59 = e0 | all_0_60_60 = e0
% 12.86/3.52 | (172) all_0_40_40 = e4 | all_0_40_40 = e3 | all_0_40_40 = e1 | all_0_40_40 = e0
% 12.86/3.52 | (173) all_0_50_50 = e4 | all_0_50_50 = e2 | all_0_50_50 = e1 | all_0_50_50 = e0
% 12.86/3.52 | (174) all_0_43_43 = e3 | all_0_48_48 = e3 | all_0_55_55 = e3 | all_0_60_60 = e3
% 12.86/3.52 | (175) all_0_48_48 = e2 | all_0_52_52 = e2 | all_0_55_55 = e2 | all_0_60_60 = e2
% 12.86/3.52 | (176) ~ (all_0_47_47 = all_0_51_51)
% 12.86/3.52 | (177) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e2 | all_0_45_45 = e1 | all_0_45_45 = e0
% 12.86/3.52 | (178) op(e2, all_0_49_49) = all_0_3_3
% 12.86/3.52 | (179) ~ (all_0_42_42 = all_0_51_51)
% 12.86/3.52 | (180) all_0_40_40 = e3 | all_0_45_45 = e3 | all_0_54_54 = e3 | all_0_57_57 = e3
% 12.86/3.52 | (181) ~ (all_0_59_59 = all_0_60_60)
% 12.86/3.52 | (182) op(e3, all_0_50_50) = all_0_11_11
% 12.86/3.52 | (183) ~ (all_0_54_54 = e0)
% 12.86/3.52 | (184) ~ (all_0_55_55 = e0)
% 12.86/3.52 | (185) op(e3, all_0_40_40) = all_0_8_8
% 12.86/3.52 | (186) ~ (all_0_45_45 = all_0_50_50)
% 12.86/3.52 | (187) ~ (all_0_53_53 = e4)
% 12.86/3.52 | (188) ~ (all_0_50_50 = all_0_52_52)
% 12.86/3.52 | (189) ~ (all_0_40_40 = all_0_42_42)
% 12.86/3.52 | (190) all_0_40_40 = e1 | all_0_45_45 = e1 | all_0_50_50 = e1 | all_0_54_54 = e1 | all_0_57_57 = e1
% 12.86/3.52 | (191) ~ (all_0_44_44 = all_0_45_45)
% 12.86/3.52 | (192) all_0_43_43 = e1 | all_0_48_48 = e1 | all_0_52_52 = e1 | all_0_55_55 = e1 | all_0_60_60 = e1
% 12.86/3.52 | (193) all_0_45_45 = e2 | all_0_46_46 = e2 | all_0_47_47 = e2 | all_0_48_48 = e2
% 12.86/3.52 | (194) all_0_59_59 = e3 | all_0_59_59 = e2 | all_0_59_59 = e1 | all_0_59_59 = e0
% 12.86/3.52 | (195) all_0_56_56 = e4 | all_0_57_57 = e4 | all_0_58_58 = e4 | all_0_60_60 = e4
% 12.86/3.52 | (196) ~ (all_0_54_54 = all_0_57_57)
% 12.86/3.52 | (197) op(e4, e2) = all_0_41_41
% 12.86/3.52 | (198) op(e3, all_0_47_47) = all_0_26_26
% 12.86/3.52 | (199) op(unit, e2) = e2
% 12.86/3.52 | (200) op(unit, e0) = e0
% 12.86/3.52 | (201) all_0_48_48 = e4 | all_0_48_48 = e3 | all_0_48_48 = e2 | all_0_48_48 = e1 | all_0_48_48 = e0
% 12.86/3.52 | (202) all_0_51_51 = e2 | all_0_51_51 = e1 | all_0_51_51 = e0
% 12.86/3.52 | (203) ~ (all_0_58_58 = e0)
% 12.86/3.52 | (204) op(e0, e0) = all_0_60_60
% 12.86/3.52 | (205) op(e0, all_0_57_57) = all_0_16_16
% 12.86/3.52 | (206) ~ (all_0_56_56 = all_0_58_58)
% 12.86/3.52 | (207) op(unit, e4) = e4
% 12.86/3.52 | (208) ~ (all_0_56_56 = e2)
% 12.86/3.52 | (209) ~ (e3 = e2)
% 12.86/3.52 | (210) op(e2, e2) = e3
% 12.86/3.52 | (211) op(e0, all_0_48_48) = all_0_33_33
% 12.86/3.52 | (212) op(e3, all_0_45_45) = all_0_10_10
% 12.86/3.53 | (213) all_0_44_44 = e4 | all_0_44_44 = e3 | all_0_44_44 = e1 | all_0_44_44 = e0
% 12.86/3.53 | (214) all_0_41_41 = e1 | all_0_46_46 = e1 | all_0_58_58 = e1
% 12.86/3.53 | (215) op(e2, e1) = all_0_51_51
% 12.86/3.53 | (216) op(e4, all_0_43_43) = all_0_32_32
% 12.86/3.53 | (217) op(e0, e3) = all_0_57_57
% 12.86/3.53 | (218) op(e0, e4) = all_0_56_56
% 12.86/3.53 | (219) all_0_47_47 = e3 | all_0_47_47 = e2 | all_0_47_47 = e1 | all_0_47_47 = e0
% 12.86/3.53 | (220) op(e0, all_0_56_56) = all_0_7_7
% 12.86/3.53 | (221) op(e0, all_0_52_52) = all_0_35_35
% 12.86/3.53 | (222) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e1 | all_0_43_43 = e0
% 12.86/3.53 | (223) all_0_53_53 = e1 | all_0_54_54 = e1 | all_0_55_55 = e1
% 12.86/3.53 | (224) ~ (all_0_49_49 = all_0_56_56)
% 12.86/3.53 | (225) (all_0_23_23 = e4 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e3 & ~ (all_0_26_26 = e1)) | (all_0_27_27 = e2 & ~ (all_0_28_28 = e1)) | (all_0_29_29 = e0 & ~ (all_0_30_30 = e1))
% 12.86/3.53 | (226) ~ (all_0_50_50 = all_0_54_54)
% 12.86/3.53 | (227) ~ (e4 = e2)
% 12.86/3.53 | (228) (all_0_8_8 = e4 & ~ (all_0_9_9 = e3)) | (all_0_11_11 = e2 & ~ (all_0_12_12 = e3)) | (all_0_13_13 = e1 & ~ (all_0_14_14 = e3)) | (all_0_15_15 = e0 & ~ (all_0_16_16 = e3))
% 12.86/3.53 | (229) ~ (all_0_42_42 = all_0_43_43)
% 12.86/3.53 | (230) all_0_43_43 = e0 | all_0_48_48 = e0 | all_0_52_52 = e0 | all_0_60_60 = e0
% 12.86/3.53 | (231) ~ (all_0_53_53 = all_0_54_54)
% 12.86/3.53 | (232) op(e2, all_0_52_52) = all_0_36_36
% 13.13/3.53 | (233) ~ (all_0_48_48 = all_0_52_52)
% 13.13/3.53 | (234) op(e1, all_0_42_42) = all_0_23_23
% 13.13/3.53 | (235) op(e4, e3) = all_0_40_40
% 13.13/3.53 | (236) op(e0, unit) = e0
% 13.13/3.53 | (237) ~ (all_0_45_45 = all_0_48_48)
% 13.13/3.53 | (238) op(e3, all_0_54_54) = all_0_13_13
% 13.13/3.53 | (239) op(e3, e2) = all_0_46_46
% 13.13/3.53 | (240) ~ (all_0_58_58 = e3)
% 13.13/3.53 | (241) all_0_41_41 = e4 | all_0_41_41 = e1
% 13.13/3.53 | (242) op(e0, all_0_43_43) = all_0_31_31
% 13.13/3.53 | (243) all_0_40_40 = e3 | all_0_42_42 = e3 | all_0_43_43 = e3
% 13.13/3.53 | (244) ~ (all_0_49_49 = all_0_52_52)
% 13.13/3.53 | (245) op(e4, all_0_56_56) = all_0_6_6
% 13.13/3.53 | (246) ~ (all_0_41_41 = e0)
% 13.13/3.53 | (247) ~ (all_0_51_51 = e3)
% 13.13/3.53 | (248) all_0_49_49 = e4 | all_0_49_49 = e1 | all_0_49_49 = e0
% 13.13/3.53 | (249) ~ (all_0_41_41 = all_0_58_58)
% 13.13/3.53 | (250) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_47_47 = e0 | all_0_48_48 = e0
% 13.13/3.53 | (251) all_0_54_54 = e3 | all_0_54_54 = e2 | all_0_54_54 = e1
% 13.13/3.53 | (252) op(e3, e0) = all_0_48_48
% 13.13/3.53 | (253) ~ (e4 = e1)
% 13.13/3.53 | (254) op(e4, e0) = all_0_43_43
% 13.13/3.53 | (255) ~ (all_0_53_53 = e0)
% 13.13/3.53 | (256) ~ (all_0_55_55 = e4)
% 13.13/3.53 |
% 13.13/3.53 +-Applying beta-rule and splitting (241), into two cases.
% 13.13/3.53 |-Branch one:
% 13.13/3.53 | (257) all_0_41_41 = e1
% 13.13/3.53 |
% 13.13/3.53 | Equations (257) can reduce 32 to:
% 13.13/3.54 | (258) ~ (all_0_40_40 = e1)
% 13.13/3.54 |
% 13.13/3.54 | Equations (257) can reduce 96 to:
% 13.13/3.54 | (259) ~ (all_0_42_42 = e1)
% 13.13/3.54 |
% 13.13/3.54 | Simplifying 259 yields:
% 13.13/3.54 | (260) ~ (all_0_42_42 = e1)
% 13.13/3.54 |
% 13.13/3.54 | Equations (257) can reduce 136 to:
% 13.13/3.54 | (261) ~ (all_0_43_43 = e1)
% 13.13/3.54 |
% 13.13/3.54 | Simplifying 261 yields:
% 13.13/3.54 | (262) ~ (all_0_43_43 = e1)
% 13.13/3.54 |
% 13.13/3.54 | Equations (257) can reduce 158 to:
% 13.13/3.54 | (263) ~ (all_0_46_46 = e1)
% 13.13/3.54 |
% 13.13/3.54 | Simplifying 263 yields:
% 13.13/3.54 | (264) ~ (all_0_46_46 = e1)
% 13.13/3.54 |
% 13.13/3.54 | Equations (257) can reduce 249 to:
% 13.13/3.54 | (265) ~ (all_0_58_58 = e1)
% 13.13/3.54 |
% 13.13/3.54 | Simplifying 265 yields:
% 13.13/3.54 | (266) ~ (all_0_58_58 = e1)
% 13.13/3.54 |
% 13.13/3.54 | Equations (257) can reduce 91 to:
% 13.13/3.54 | (267) ~ (e2 = e1)
% 13.13/3.54 |
% 13.13/3.54 | Simplifying 267 yields:
% 13.13/3.54 | (150) ~ (e2 = e1)
% 13.13/3.54 |
% 13.13/3.54 | Equations (257) can reduce 246 to:
% 13.13/3.54 | (143) ~ (e1 = e0)
% 13.13/3.54 |
% 13.13/3.54 | From (257) and (111) follows:
% 13.13/3.54 | (270) op(e4, e1) = all_0_18_18
% 13.13/3.54 |
% 13.13/3.54 | From (257) and (153) follows:
% 13.13/3.54 | (271) op(e2, e1) = all_0_17_17
% 13.13/3.54 |
% 13.13/3.54 | Instantiating formula (39) with e4, e1, all_0_18_18, all_0_42_42 and discharging atoms op(e4, e1) = all_0_18_18, op(e4, e1) = all_0_42_42, yields:
% 13.13/3.54 | (272) all_0_18_18 = all_0_42_42
% 13.13/3.54 |
% 13.13/3.54 | Instantiating formula (39) with e2, e1, all_0_17_17, all_0_51_51 and discharging atoms op(e2, e1) = all_0_17_17, op(e2, e1) = all_0_51_51, yields:
% 13.13/3.54 | (273) all_0_17_17 = all_0_51_51
% 13.13/3.54 |
% 13.13/3.54 | From (272) and (270) follows:
% 13.13/3.54 | (35) op(e4, e1) = all_0_42_42
% 13.13/3.54 |
% 13.13/3.54 +-Applying beta-rule and splitting (109), into two cases.
% 13.13/3.54 |-Branch one:
% 13.13/3.54 | (275) all_0_53_53 = e1
% 13.13/3.54 |
% 13.13/3.54 | Equations (275) can reduce 17 to:
% 13.13/3.54 | (276) ~ (all_0_44_44 = e1)
% 13.13/3.54 |
% 13.13/3.54 | Equations (275) can reduce 231 to:
% 13.13/3.54 | (277) ~ (all_0_54_54 = e1)
% 13.13/3.54 |
% 13.13/3.54 | Simplifying 277 yields:
% 13.13/3.54 | (278) ~ (all_0_54_54 = e1)
% 13.13/3.54 |
% 13.13/3.54 | Equations (275) can reduce 99 to:
% 13.13/3.54 | (279) ~ (all_0_55_55 = e1)
% 13.13/3.54 |
% 13.13/3.54 | Simplifying 279 yields:
% 13.13/3.54 | (280) ~ (all_0_55_55 = e1)
% 13.13/3.54 |
% 13.13/3.54 | Equations (275) can reduce 106 to:
% 13.13/3.54 | (281) ~ (all_0_56_56 = e1)
% 13.13/3.54 |
% 13.13/3.54 | Simplifying 281 yields:
% 13.13/3.54 | (282) ~ (all_0_56_56 = e1)
% 13.13/3.54 |
% 13.13/3.54 | Equations (275) can reduce 255 to:
% 13.13/3.54 | (143) ~ (e1 = e0)
% 13.13/3.54 |
% 13.13/3.54 | From (275) and (147) follows:
% 13.13/3.54 | (284) op(e4, e1) = all_0_4_4
% 13.13/3.55 |
% 13.13/3.55 | From (275) and (34) follows:
% 13.13/3.55 | (285) op(e1, e1) = all_0_5_5
% 13.13/3.55 |
% 13.13/3.55 | Instantiating formula (39) with e4, e1, all_0_4_4, all_0_42_42 and discharging atoms op(e4, e1) = all_0_4_4, op(e4, e1) = all_0_42_42, yields:
% 13.13/3.55 | (286) all_0_4_4 = all_0_42_42
% 13.13/3.55 |
% 13.13/3.55 | Instantiating formula (39) with e1, e1, all_0_5_5, e4 and discharging atoms op(e1, e1) = all_0_5_5, op(e1, e1) = e4, yields:
% 13.13/3.55 | (287) all_0_5_5 = e4
% 13.13/3.55 |
% 13.13/3.55 | From (287) and (285) follows:
% 13.13/3.55 | (45) op(e1, e1) = e4
% 13.13/3.55 |
% 13.13/3.55 +-Applying beta-rule and splitting (12), into two cases.
% 13.13/3.55 |-Branch one:
% 13.13/3.55 | (289) all_0_45_45 = e1
% 13.13/3.55 |
% 13.13/3.55 | Equations (289) can reduce 72 to:
% 13.13/3.55 | (258) ~ (all_0_40_40 = e1)
% 13.13/3.55 |
% 13.13/3.55 | Equations (289) can reduce 191 to:
% 13.13/3.55 | (276) ~ (all_0_44_44 = e1)
% 13.13/3.55 |
% 13.13/3.55 | Equations (289) can reduce 128 to:
% 13.13/3.55 | (263) ~ (all_0_46_46 = e1)
% 13.13/3.55 |
% 13.13/3.55 | Simplifying 263 yields:
% 13.13/3.55 | (264) ~ (all_0_46_46 = e1)
% 13.13/3.55 |
% 13.13/3.55 | Equations (289) can reduce 237 to:
% 13.13/3.55 | (294) ~ (all_0_48_48 = e1)
% 13.13/3.55 |
% 13.13/3.55 | Simplifying 294 yields:
% 13.13/3.55 | (295) ~ (all_0_48_48 = e1)
% 13.13/3.55 |
% 13.13/3.55 | Equations (289) can reduce 37 to:
% 13.13/3.55 | (277) ~ (all_0_54_54 = e1)
% 13.13/3.55 |
% 13.13/3.55 | Simplifying 277 yields:
% 13.13/3.55 | (278) ~ (all_0_54_54 = e1)
% 13.13/3.55 |
% 13.13/3.55 | Equations (289) can reduce 122 to:
% 13.13/3.55 | (298) ~ (all_0_57_57 = e1)
% 13.13/3.55 |
% 13.13/3.55 | Simplifying 298 yields:
% 13.13/3.55 | (299) ~ (all_0_57_57 = e1)
% 13.13/3.55 |
% 13.13/3.55 +-Applying beta-rule and splitting (25), into two cases.
% 13.13/3.55 |-Branch one:
% 13.13/3.55 | (300) all_0_45_45 = e0
% 13.13/3.55 |
% 13.23/3.55 | Combining equations (289,300) yields a new equation:
% 13.23/3.55 | (301) e1 = e0
% 13.23/3.55 |
% 13.23/3.55 | Simplifying 301 yields:
% 13.23/3.55 | (302) e1 = e0
% 13.23/3.55 |
% 13.23/3.55 | Equations (302) can reduce 143 to:
% 13.23/3.55 | (303) $false
% 13.23/3.55 |
% 13.23/3.55 |-The branch is then unsatisfiable
% 13.23/3.55 |-Branch two:
% 13.23/3.55 | (304) ~ (all_0_45_45 = e0)
% 13.23/3.55 | (305) all_0_60_60 = e0
% 13.23/3.55 |
% 13.23/3.55 | Equations (305) can reduce 93 to:
% 13.23/3.55 | (306) ~ (all_0_43_43 = e0)
% 13.23/3.55 |
% 13.23/3.55 | Equations (289) can reduce 304 to:
% 13.23/3.55 | (143) ~ (e1 = e0)
% 13.23/3.55 |
% 13.23/3.55 | Equations (305) can reduce 38 to:
% 13.23/3.55 | (308) ~ (all_0_52_52 = e0)
% 13.23/3.55 |
% 13.23/3.55 | Equations (305) can reduce 18 to:
% 13.23/3.55 | (309) ~ (all_0_57_57 = e0)
% 13.23/3.55 |
% 13.23/3.55 +-Applying beta-rule and splitting (192), into two cases.
% 13.23/3.55 |-Branch one:
% 13.23/3.55 | (310) all_0_43_43 = e1
% 13.23/3.55 |
% 13.23/3.55 | Equations (310) can reduce 262 to:
% 13.23/3.55 | (303) $false
% 13.23/3.55 |
% 13.23/3.55 |-The branch is then unsatisfiable
% 13.23/3.55 |-Branch two:
% 13.23/3.56 | (262) ~ (all_0_43_43 = e1)
% 13.23/3.56 | (313) all_0_48_48 = e1 | all_0_52_52 = e1 | all_0_55_55 = e1 | all_0_60_60 = e1
% 13.23/3.56 |
% 13.23/3.56 +-Applying beta-rule and splitting (14), into two cases.
% 13.23/3.56 |-Branch one:
% 13.23/3.56 | (314) all_0_56_56 = e1
% 13.23/3.56 |
% 13.23/3.56 | Equations (314) can reduce 282 to:
% 13.23/3.56 | (303) $false
% 13.23/3.56 |
% 13.23/3.56 |-The branch is then unsatisfiable
% 13.23/3.56 |-Branch two:
% 13.23/3.56 | (282) ~ (all_0_56_56 = e1)
% 13.23/3.56 | (317) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1 | all_0_60_60 = e1
% 13.23/3.56 |
% 13.23/3.56 +-Applying beta-rule and splitting (313), into two cases.
% 13.23/3.56 |-Branch one:
% 13.23/3.56 | (318) all_0_48_48 = e1
% 13.23/3.56 |
% 13.23/3.56 | Equations (318) can reduce 295 to:
% 13.23/3.56 | (303) $false
% 13.23/3.56 |
% 13.23/3.56 |-The branch is then unsatisfiable
% 13.23/3.56 |-Branch two:
% 13.23/3.56 | (295) ~ (all_0_48_48 = e1)
% 13.23/3.56 | (321) all_0_52_52 = e1 | all_0_55_55 = e1 | all_0_60_60 = e1
% 13.23/3.56 |
% 13.23/3.56 +-Applying beta-rule and splitting (321), into two cases.
% 13.23/3.56 |-Branch one:
% 13.23/3.56 | (322) all_0_52_52 = e1
% 13.23/3.56 |
% 13.23/3.56 | Equations (322) can reduce 54 to:
% 13.23/3.56 | (262) ~ (all_0_43_43 = e1)
% 13.23/3.56 |
% 13.23/3.56 | Equations (322) can reduce 233 to:
% 13.23/3.56 | (295) ~ (all_0_48_48 = e1)
% 13.23/3.56 |
% 13.23/3.56 | Equations (322) can reduce 244 to:
% 13.23/3.56 | (325) ~ (all_0_49_49 = e1)
% 13.23/3.56 |
% 13.23/3.56 | Equations (322) can reduce 188 to:
% 13.23/3.56 | (326) ~ (all_0_50_50 = e1)
% 13.23/3.56 |
% 13.23/3.56 | Equations (322) can reduce 160 to:
% 13.23/3.56 | (279) ~ (all_0_55_55 = e1)
% 13.23/3.56 |
% 13.23/3.56 | Simplifying 279 yields:
% 13.23/3.56 | (280) ~ (all_0_55_55 = e1)
% 13.23/3.56 |
% 13.23/3.56 | Equations (322) can reduce 13 to:
% 13.23/3.56 | (329) ~ (e3 = e1)
% 13.23/3.56 |
% 13.23/3.56 | Simplifying 329 yields:
% 13.23/3.56 | (145) ~ (e3 = e1)
% 13.23/3.56 |
% 13.23/3.56 | Equations (322) can reduce 308 to:
% 13.23/3.56 | (143) ~ (e1 = e0)
% 13.23/3.56 |
% 13.23/3.56 | From (322) and (221) follows:
% 13.23/3.56 | (332) op(e0, e1) = all_0_35_35
% 13.23/3.56 |
% 13.23/3.56 +-Applying beta-rule and splitting (317), into two cases.
% 13.23/3.56 |-Branch one:
% 13.23/3.56 | (333) all_0_57_57 = e1
% 13.23/3.56 |
% 13.23/3.56 | Equations (333) can reduce 299 to:
% 13.23/3.56 | (303) $false
% 13.23/3.56 |
% 13.23/3.56 |-The branch is then unsatisfiable
% 13.23/3.56 |-Branch two:
% 13.23/3.56 | (299) ~ (all_0_57_57 = e1)
% 13.23/3.56 | (336) all_0_58_58 = e1 | all_0_59_59 = e1 | all_0_60_60 = e1
% 13.23/3.56 |
% 13.23/3.56 +-Applying beta-rule and splitting (336), into two cases.
% 13.23/3.56 |-Branch one:
% 13.23/3.56 | (337) all_0_58_58 = e1
% 13.23/3.56 |
% 13.23/3.56 | Equations (337) can reduce 266 to:
% 13.23/3.56 | (303) $false
% 13.23/3.56 |
% 13.23/3.56 |-The branch is then unsatisfiable
% 13.23/3.56 |-Branch two:
% 13.23/3.56 | (266) ~ (all_0_58_58 = e1)
% 13.23/3.56 | (340) all_0_59_59 = e1 | all_0_60_60 = e1
% 13.23/3.56 |
% 13.23/3.56 +-Applying beta-rule and splitting (340), into two cases.
% 13.23/3.56 |-Branch one:
% 13.23/3.56 | (341) all_0_59_59 = e1
% 13.23/3.56 |
% 13.23/3.56 | Equations (341) can reduce 146 to:
% 13.23/3.56 | (260) ~ (all_0_42_42 = e1)
% 13.23/3.56 |
% 13.23/3.56 | Equations (341) can reduce 92 to:
% 13.23/3.56 | (343) ~ (all_0_51_51 = e1)
% 13.23/3.56 |
% 13.23/3.56 | Equations (341) can reduce 159 to:
% 13.23/3.56 | (282) ~ (all_0_56_56 = e1)
% 13.23/3.56 |
% 13.23/3.56 | Equations (341) can reduce 166 to:
% 13.23/3.56 | (299) ~ (all_0_57_57 = e1)
% 13.23/3.56 |
% 13.23/3.56 | Equations (341) can reduce 8 to:
% 13.23/3.56 | (346) ~ (e4 = e1)
% 13.23/3.56 |
% 13.23/3.56 | Simplifying 346 yields:
% 13.23/3.56 | (253) ~ (e4 = e1)
% 13.23/3.56 |
% 13.23/3.56 | From (341) and (118) follows:
% 13.23/3.56 | (348) op(e1, e1) = all_0_29_29
% 13.23/3.56 |
% 13.23/3.56 | From (341) and (43) follows:
% 13.23/3.56 | (349) op(e0, e1) = all_0_30_30
% 13.23/3.56 |
% 13.23/3.56 | From (341) and (163) follows:
% 13.23/3.56 | (350) op(e0, e1) = e1
% 13.23/3.56 |
% 13.23/3.56 | Instantiating formula (39) with e1, e1, all_0_29_29, e4 and discharging atoms op(e1, e1) = all_0_29_29, op(e1, e1) = e4, yields:
% 13.23/3.56 | (351) all_0_29_29 = e4
% 13.23/3.56 |
% 13.23/3.56 | Instantiating formula (39) with e0, e1, all_0_35_35, all_0_30_30 and discharging atoms op(e0, e1) = all_0_30_30, op(e0, e1) = all_0_35_35, yields:
% 13.23/3.56 | (352) all_0_30_30 = all_0_35_35
% 13.23/3.56 |
% 13.23/3.56 | Instantiating formula (39) with e0, e1, e1, all_0_30_30 and discharging atoms op(e0, e1) = all_0_30_30, op(e0, e1) = e1, yields:
% 13.23/3.56 | (353) all_0_30_30 = e1
% 13.23/3.56 |
% 13.23/3.56 | Combining equations (353,352) yields a new equation:
% 13.23/3.56 | (354) all_0_35_35 = e1
% 13.23/3.56 |
% 13.23/3.56 +-Applying beta-rule and splitting (85), into two cases.
% 13.23/3.56 |-Branch one:
% 13.23/3.56 | (355) all_0_46_46 = e2
% 13.23/3.56 |
% 13.23/3.56 | Equations (355) can reduce 119 to:
% 13.23/3.56 | (356) ~ (all_0_47_47 = e2)
% 13.23/3.56 |
% 13.23/3.56 | Simplifying 356 yields:
% 13.23/3.56 | (357) ~ (all_0_47_47 = e2)
% 13.23/3.56 |
% 13.23/3.56 | Equations (355) can reduce 2 to:
% 13.23/3.56 | (358) ~ (all_0_48_48 = e2)
% 13.23/3.56 |
% 13.23/3.56 | Simplifying 358 yields:
% 13.23/3.56 | (359) ~ (all_0_48_48 = e2)
% 13.23/3.56 |
% 13.23/3.56 | Equations (355) can reduce 264 to:
% 13.23/3.56 | (150) ~ (e2 = e1)
% 13.23/3.56 |
% 13.23/3.56 | Equations (355) can reduce 103 to:
% 13.23/3.56 | (61) ~ (e2 = e0)
% 13.23/3.56 |
% 13.23/3.56 | From (355) and (161) follows:
% 13.23/3.56 | (362) op(e3, e2) = all_0_20_20
% 13.23/3.56 |
% 13.23/3.56 | From (355) and (239) follows:
% 13.23/3.56 | (363) op(e3, e2) = e2
% 13.23/3.56 |
% 13.23/3.56 +-Applying beta-rule and splitting (175), into two cases.
% 13.23/3.56 |-Branch one:
% 13.23/3.56 | (364) all_0_48_48 = e2
% 13.23/3.56 |
% 13.23/3.56 | Equations (364) can reduce 359 to:
% 13.23/3.56 | (303) $false
% 13.23/3.56 |
% 13.23/3.56 |-The branch is then unsatisfiable
% 13.23/3.56 |-Branch two:
% 13.23/3.56 | (359) ~ (all_0_48_48 = e2)
% 13.23/3.56 | (367) all_0_52_52 = e2 | all_0_55_55 = e2 | all_0_60_60 = e2
% 13.23/3.56 |
% 13.23/3.56 +-Applying beta-rule and splitting (367), into two cases.
% 13.23/3.56 |-Branch one:
% 13.23/3.56 | (368) all_0_52_52 = e2
% 13.23/3.56 |
% 13.23/3.56 | Combining equations (322,368) yields a new equation:
% 13.23/3.57 | (369) e2 = e1
% 13.23/3.57 |
% 13.23/3.57 | Equations (369) can reduce 150 to:
% 13.23/3.57 | (303) $false
% 13.23/3.57 |
% 13.23/3.57 |-The branch is then unsatisfiable
% 13.23/3.57 |-Branch two:
% 13.23/3.57 | (371) ~ (all_0_52_52 = e2)
% 13.23/3.57 | (372) all_0_55_55 = e2 | all_0_60_60 = e2
% 13.23/3.57 |
% 13.23/3.57 +-Applying beta-rule and splitting (372), into two cases.
% 13.23/3.57 |-Branch one:
% 13.23/3.57 | (373) all_0_55_55 = e2
% 13.23/3.57 |
% 13.23/3.57 | Equations (373) can reduce 165 to:
% 13.23/3.57 | (359) ~ (all_0_48_48 = e2)
% 13.23/3.57 |
% 13.23/3.57 | Equations (373) can reduce 101 to:
% 13.23/3.57 | (375) ~ (all_0_54_54 = e2)
% 13.23/3.57 |
% 13.23/3.57 | Equations (373) can reduce 280 to:
% 13.23/3.57 | (150) ~ (e2 = e1)
% 13.23/3.57 |
% 13.23/3.57 | From (373) and (164) follows:
% 13.23/3.57 | (377) op(e1, e2) = all_0_38_38
% 13.23/3.57 |
% 13.23/3.57 | From (373) and (132) follows:
% 13.23/3.57 | (378) op(e1, e0) = e2
% 13.23/3.57 |
% 13.23/3.57 +-Applying beta-rule and splitting (127), into two cases.
% 13.23/3.57 |-Branch one:
% 13.23/3.57 | (379) all_0_47_47 = e2
% 13.23/3.57 |
% 13.23/3.57 | Equations (379) can reduce 357 to:
% 13.23/3.57 | (303) $false
% 13.23/3.57 |
% 13.23/3.57 |-The branch is then unsatisfiable
% 13.23/3.57 |-Branch two:
% 13.23/3.57 | (357) ~ (all_0_47_47 = e2)
% 13.23/3.57 | (382) all_0_51_51 = e2 | all_0_59_59 = e2
% 13.23/3.57 |
% 13.23/3.57 +-Applying beta-rule and splitting (382), into two cases.
% 13.23/3.57 |-Branch one:
% 13.23/3.57 | (383) all_0_51_51 = e2
% 13.23/3.57 |
% 13.23/3.57 | Combining equations (383,273) yields a new equation:
% 13.23/3.57 | (384) all_0_17_17 = e2
% 13.23/3.57 |
% 13.23/3.57 | Equations (383) can reduce 179 to:
% 13.23/3.57 | (20) ~ (all_0_42_42 = e2)
% 13.23/3.57 |
% 13.23/3.57 | Equations (383) can reduce 176 to:
% 13.23/3.57 | (357) ~ (all_0_47_47 = e2)
% 13.23/3.57 |
% 13.23/3.57 | Equations (383) can reduce 83 to:
% 13.23/3.57 | (151) ~ (all_0_49_49 = e2)
% 13.23/3.57 |
% 13.23/3.57 | Equations (383) can reduce 116 to:
% 13.23/3.57 | (388) ~ (all_0_50_50 = e2)
% 13.23/3.57 |
% 13.23/3.57 | Equations (383) can reduce 56 to:
% 13.23/3.57 | (389) ~ (e4 = e2)
% 13.23/3.57 |
% 13.23/3.57 | Simplifying 389 yields:
% 13.23/3.57 | (227) ~ (e4 = e2)
% 13.23/3.57 |
% 13.23/3.57 | Equations (383) can reduce 247 to:
% 13.23/3.57 | (391) ~ (e3 = e2)
% 13.23/3.57 |
% 13.23/3.57 | Simplifying 391 yields:
% 13.23/3.57 | (209) ~ (e3 = e2)
% 13.23/3.57 |
% 13.23/3.57 | Equations (383) can reduce 343 to:
% 13.23/3.57 | (150) ~ (e2 = e1)
% 13.23/3.57 |
% 13.23/3.57 | From (383) and (169) follows:
% 13.23/3.57 | (394) op(e1, e2) = all_0_27_27
% 13.23/3.57 |
% 13.23/3.57 +-Applying beta-rule and splitting (6), into two cases.
% 13.23/3.57 |-Branch one:
% 13.23/3.57 | (395) all_0_45_45 = e2
% 13.23/3.57 |
% 13.23/3.57 | Combining equations (289,395) yields a new equation:
% 13.23/3.57 | (369) e2 = e1
% 13.23/3.57 |
% 13.23/3.57 | Equations (369) can reduce 150 to:
% 13.23/3.57 | (303) $false
% 13.23/3.57 |
% 13.23/3.57 |-The branch is then unsatisfiable
% 13.23/3.57 |-Branch two:
% 13.23/3.57 | (398) ~ (all_0_45_45 = e2)
% 13.23/3.57 | (399) all_0_50_50 = e2 | all_0_54_54 = e2 | all_0_57_57 = e2
% 13.23/3.57 |
% 13.23/3.57 +-Applying beta-rule and splitting (399), into two cases.
% 13.23/3.57 |-Branch one:
% 13.23/3.57 | (400) all_0_50_50 = e2
% 13.23/3.57 |
% 13.23/3.57 | Equations (400) can reduce 388 to:
% 13.23/3.57 | (303) $false
% 13.23/3.57 |
% 13.23/3.57 |-The branch is then unsatisfiable
% 13.23/3.57 |-Branch two:
% 13.23/3.57 | (388) ~ (all_0_50_50 = e2)
% 13.23/3.57 | (403) all_0_54_54 = e2 | all_0_57_57 = e2
% 13.23/3.57 |
% 13.23/3.57 +-Applying beta-rule and splitting (403), into two cases.
% 13.23/3.57 |-Branch one:
% 13.23/3.57 | (404) all_0_54_54 = e2
% 13.23/3.57 |
% 13.23/3.57 | Equations (404) can reduce 375 to:
% 13.23/3.57 | (303) $false
% 13.23/3.57 |
% 13.23/3.57 |-The branch is then unsatisfiable
% 13.23/3.57 |-Branch two:
% 13.23/3.57 | (375) ~ (all_0_54_54 = e2)
% 13.23/3.57 | (407) all_0_57_57 = e2
% 13.23/3.57 |
% 13.23/3.57 | Equations (407) can reduce 73 to:
% 13.23/3.57 | (134) ~ (all_0_40_40 = e2)
% 13.23/3.57 |
% 13.23/3.57 | Equations (407) can reduce 196 to:
% 13.23/3.57 | (375) ~ (all_0_54_54 = e2)
% 13.23/3.57 |
% 13.23/3.57 | Equations (407) can reduce 82 to:
% 13.23/3.57 | (410) ~ (all_0_58_58 = e2)
% 13.23/3.57 |
% 13.23/3.57 | Simplifying 410 yields:
% 13.23/3.57 | (411) ~ (all_0_58_58 = e2)
% 13.23/3.57 |
% 13.23/3.57 | From (407) and (142) follows:
% 13.23/3.57 | (412) op(e3, e2) = all_0_15_15
% 13.23/3.57 |
% 13.23/3.57 +-Applying beta-rule and splitting (113), into two cases.
% 13.23/3.57 |-Branch one:
% 13.23/3.57 | (413) all_0_53_53 = e3
% 13.23/3.57 |
% 13.23/3.57 | Combining equations (275,413) yields a new equation:
% 13.23/3.57 | (414) e3 = e1
% 13.23/3.57 |
% 13.23/3.57 | Equations (414) can reduce 145 to:
% 13.23/3.57 | (303) $false
% 13.23/3.57 |
% 13.23/3.57 |-The branch is then unsatisfiable
% 13.23/3.57 |-Branch two:
% 13.23/3.57 | (416) ~ (all_0_53_53 = e3)
% 13.23/3.57 | (417) all_0_54_54 = e3 | all_0_55_55 = e3
% 13.23/3.57 |
% 13.23/3.57 +-Applying beta-rule and splitting (417), into two cases.
% 13.23/3.57 |-Branch one:
% 13.23/3.57 | (418) all_0_54_54 = e3
% 13.23/3.57 |
% 13.23/3.57 | Equations (418) can reduce 97 to:
% 13.23/3.57 | (419) ~ (all_0_40_40 = e3)
% 13.23/3.57 |
% 13.23/3.57 | Equations (418) can reduce 375 to:
% 13.23/3.57 | (209) ~ (e3 = e2)
% 13.23/3.57 |
% 13.23/3.57 | Equations (418) can reduce 278 to:
% 13.23/3.57 | (145) ~ (e3 = e1)
% 13.23/3.57 |
% 13.23/3.57 | Equations (418) can reduce 183 to:
% 13.23/3.57 | (74) ~ (e3 = e0)
% 13.23/3.57 |
% 13.23/3.57 | From (418) and (105) follows:
% 13.23/3.57 | (423) op(e1, e3) = all_0_14_14
% 13.23/3.57 |
% 13.23/3.57 | From (418) and (89) follows:
% 13.23/3.57 | (424) op(e1, e3) = e3
% 13.23/3.57 |
% 13.23/3.57 +-Applying beta-rule and splitting (23), into two cases.
% 13.23/3.57 |-Branch one:
% 13.23/3.57 | (425) all_0_41_41 = e4
% 13.23/3.57 |
% 13.23/3.57 | Combining equations (425,257) yields a new equation:
% 13.23/3.57 | (426) e4 = e1
% 13.23/3.57 |
% 13.23/3.57 | Simplifying 426 yields:
% 13.23/3.57 | (427) e4 = e1
% 13.23/3.57 |
% 13.23/3.57 | Equations (427) can reduce 253 to:
% 13.23/3.57 | (303) $false
% 13.23/3.57 |
% 13.23/3.57 |-The branch is then unsatisfiable
% 13.23/3.57 |-Branch two:
% 13.23/3.57 | (429) ~ (all_0_41_41 = e4)
% 13.23/3.57 | (430) all_0_46_46 = e4 | all_0_58_58 = e4
% 13.23/3.57 |
% 13.23/3.57 +-Applying beta-rule and splitting (87), into two cases.
% 13.23/3.57 |-Branch one:
% 13.23/3.57 | (431) all_0_56_56 = e3
% 13.23/3.57 |
% 13.23/3.57 | Equations (431) can reduce 282 to:
% 13.23/3.57 | (145) ~ (e3 = e1)
% 13.23/3.57 |
% 13.23/3.57 +-Applying beta-rule and splitting (430), into two cases.
% 13.23/3.57 |-Branch one:
% 13.23/3.57 | (433) all_0_46_46 = e4
% 13.23/3.57 |
% 13.23/3.57 | Combining equations (355,433) yields a new equation:
% 13.23/3.57 | (434) e4 = e2
% 13.23/3.57 |
% 13.23/3.57 | Equations (434) can reduce 227 to:
% 13.23/3.57 | (303) $false
% 13.23/3.57 |
% 13.23/3.57 |-The branch is then unsatisfiable
% 13.23/3.57 |-Branch two:
% 13.23/3.57 | (436) ~ (all_0_46_46 = e4)
% 13.23/3.57 | (437) all_0_58_58 = e4
% 13.23/3.57 |
% 13.23/3.57 | Equations (437) can reduce 411 to:
% 13.23/3.57 | (227) ~ (e4 = e2)
% 13.23/3.57 |
% 13.23/3.57 | From (437) and (27) follows:
% 13.23/3.57 | (439) op(e2, e4) = all_0_21_21
% 13.23/3.57 |
% 13.23/3.57 | Instantiating formula (39) with e3, e2, all_0_20_20, all_0_15_15 and discharging atoms op(e3, e2) = all_0_15_15, op(e3, e2) = all_0_20_20, yields:
% 13.23/3.57 | (440) all_0_15_15 = all_0_20_20
% 13.23/3.57 |
% 13.23/3.57 | Instantiating formula (39) with e3, e2, e2, all_0_15_15 and discharging atoms op(e3, e2) = all_0_15_15, op(e3, e2) = e2, yields:
% 13.23/3.57 | (441) all_0_15_15 = e2
% 13.23/3.57 |
% 13.23/3.57 | Instantiating formula (39) with e2, e4, all_0_21_21, all_0_49_49 and discharging atoms op(e2, e4) = all_0_21_21, op(e2, e4) = all_0_49_49, yields:
% 13.23/3.57 | (442) all_0_21_21 = all_0_49_49
% 13.23/3.57 |
% 13.23/3.57 | Instantiating formula (39) with e1, e3, e3, all_0_14_14 and discharging atoms op(e1, e3) = all_0_14_14, op(e1, e3) = e3, yields:
% 13.23/3.57 | (443) all_0_14_14 = e3
% 13.23/3.57 |
% 13.23/3.57 | Instantiating formula (39) with e1, e2, all_0_27_27, e0 and discharging atoms op(e1, e2) = all_0_27_27, op(e1, e2) = e0, yields:
% 13.23/3.57 | (444) all_0_27_27 = e0
% 13.23/3.57 |
% 13.23/3.57 | Instantiating formula (39) with e1, e2, all_0_38_38, all_0_27_27 and discharging atoms op(e1, e2) = all_0_27_27, op(e1, e2) = all_0_38_38, yields:
% 13.23/3.57 | (445) all_0_27_27 = all_0_38_38
% 13.23/3.57 |
% 13.23/3.57 | Combining equations (441,440) yields a new equation:
% 13.23/3.57 | (446) all_0_20_20 = e2
% 13.23/3.57 |
% 13.23/3.57 | Combining equations (444,445) yields a new equation:
% 13.23/3.57 | (447) all_0_38_38 = e0
% 13.23/3.57 |
% 13.23/3.57 | Combining equations (447,445) yields a new equation:
% 13.23/3.57 | (444) all_0_27_27 = e0
% 13.23/3.57 |
% 13.23/3.57 | From (443) and (423) follows:
% 13.23/3.57 | (424) op(e1, e3) = e3
% 13.23/3.57 |
% 13.23/3.57 +-Applying beta-rule and splitting (19), into two cases.
% 13.23/3.57 |-Branch one:
% 13.23/3.57 | (450) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2)) | (all_0_21_21 = e0 & ~ (all_0_22_22 = e2))
% 13.23/3.57 |
% 13.23/3.57 +-Applying beta-rule and splitting (450), into two cases.
% 13.23/3.57 |-Branch one:
% 13.23/3.57 | (451) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2))
% 13.23/3.57 |
% 13.23/3.57 +-Applying beta-rule and splitting (451), into two cases.
% 13.23/3.57 |-Branch one:
% 13.23/3.57 | (452) all_0_17_17 = e4 & ~ (all_0_18_18 = e2)
% 13.23/3.57 |
% 13.23/3.57 | Applying alpha-rule on (452) yields:
% 13.23/3.58 | (453) all_0_17_17 = e4
% 13.23/3.58 | (454) ~ (all_0_18_18 = e2)
% 13.23/3.58 |
% 13.23/3.58 | Combining equations (453,384) yields a new equation:
% 13.23/3.58 | (455) e4 = e2
% 13.23/3.58 |
% 13.23/3.58 | Simplifying 455 yields:
% 13.23/3.58 | (434) e4 = e2
% 13.23/3.58 |
% 13.23/3.58 | Equations (434) can reduce 227 to:
% 13.23/3.58 | (303) $false
% 13.23/3.58 |
% 13.23/3.58 |-The branch is then unsatisfiable
% 13.23/3.58 |-Branch two:
% 13.23/3.58 | (458) all_0_19_19 = e3 & ~ (all_0_20_20 = e2)
% 13.23/3.58 |
% 13.23/3.58 | Applying alpha-rule on (458) yields:
% 13.23/3.58 | (459) all_0_19_19 = e3
% 13.23/3.58 | (460) ~ (all_0_20_20 = e2)
% 13.23/3.58 |
% 13.23/3.58 | Equations (446) can reduce 460 to:
% 13.23/3.58 | (303) $false
% 13.23/3.58 |
% 13.23/3.58 |-The branch is then unsatisfiable
% 13.23/3.58 |-Branch two:
% 13.23/3.58 | (462) all_0_21_21 = e0 & ~ (all_0_22_22 = e2)
% 13.23/3.58 |
% 13.23/3.58 | Applying alpha-rule on (462) yields:
% 13.23/3.58 | (463) all_0_21_21 = e0
% 13.23/3.58 | (464) ~ (all_0_22_22 = e2)
% 13.23/3.58 |
% 13.23/3.58 | Combining equations (442,463) yields a new equation:
% 13.23/3.58 | (465) all_0_49_49 = e0
% 13.23/3.58 |
% 13.23/3.58 | Simplifying 465 yields:
% 13.23/3.58 | (466) all_0_49_49 = e0
% 13.23/3.58 |
% 13.23/3.58 | Equations (466) can reduce 123 to:
% 13.23/3.58 | (467) ~ (all_0_50_50 = e0)
% 13.23/3.58 |
% 13.23/3.58 | Simplifying 467 yields:
% 13.23/3.58 | (468) ~ (all_0_50_50 = e0)
% 13.23/3.58 |
% 13.23/3.58 | Equations (466) can reduce 151 to:
% 13.23/3.58 | (469) ~ (e2 = e0)
% 13.23/3.58 |
% 13.23/3.58 | Simplifying 469 yields:
% 13.23/3.58 | (61) ~ (e2 = e0)
% 13.23/3.58 |
% 13.23/3.58 | Equations (466) can reduce 325 to:
% 13.23/3.58 | (471) ~ (e1 = e0)
% 13.23/3.58 |
% 13.23/3.58 | Simplifying 471 yields:
% 13.23/3.58 | (143) ~ (e1 = e0)
% 13.23/3.58 |
% 13.23/3.58 +-Applying beta-rule and splitting (55), into two cases.
% 13.23/3.58 |-Branch one:
% 13.23/3.58 | (473) all_0_40_40 = e0
% 13.23/3.58 |
% 13.23/3.58 | Equations (473) can reduce 189 to:
% 13.23/3.58 | (474) ~ (all_0_42_42 = e0)
% 13.23/3.58 |
% 13.23/3.58 | Simplifying 474 yields:
% 13.23/3.58 | (475) ~ (all_0_42_42 = e0)
% 13.23/3.58 |
% 13.23/3.58 | Equations (473) can reduce 51 to:
% 13.23/3.58 | (476) ~ (all_0_43_43 = e0)
% 13.23/3.58 |
% 13.23/3.58 | Simplifying 476 yields:
% 13.23/3.58 | (306) ~ (all_0_43_43 = e0)
% 13.23/3.58 |
% 13.23/3.58 | Equations (473) can reduce 48 to:
% 13.23/3.58 | (467) ~ (all_0_50_50 = e0)
% 13.23/3.58 |
% 13.23/3.58 | Simplifying 467 yields:
% 13.23/3.58 | (468) ~ (all_0_50_50 = e0)
% 13.23/3.58 |
% 13.23/3.58 | Equations (473) can reduce 419 to:
% 13.23/3.58 | (480) ~ (e3 = e0)
% 13.23/3.58 |
% 13.23/3.58 | Simplifying 480 yields:
% 13.23/3.58 | (74) ~ (e3 = e0)
% 13.23/3.58 |
% 13.23/3.58 | Equations (473) can reduce 134 to:
% 13.23/3.58 | (469) ~ (e2 = e0)
% 13.23/3.58 |
% 13.23/3.58 | Simplifying 469 yields:
% 13.23/3.58 | (61) ~ (e2 = e0)
% 13.23/3.58 |
% 13.23/3.58 | Equations (473) can reduce 258 to:
% 13.23/3.58 | (471) ~ (e1 = e0)
% 13.23/3.58 |
% 13.23/3.58 | Simplifying 471 yields:
% 13.23/3.58 | (143) ~ (e1 = e0)
% 13.23/3.58 |
% 13.23/3.58 +-Applying beta-rule and splitting (124), into two cases.
% 13.23/3.58 |-Branch one:
% 13.23/3.58 | (486) all_0_42_42 = e0
% 13.23/3.58 |
% 13.23/3.58 | Equations (486) can reduce 475 to:
% 13.23/3.58 | (303) $false
% 13.23/3.58 |
% 13.23/3.58 |-The branch is then unsatisfiable
% 13.23/3.58 |-Branch two:
% 13.23/3.58 | (475) ~ (all_0_42_42 = e0)
% 13.23/3.58 | (489) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_59_59 = e0
% 13.23/3.58 |
% 13.23/3.58 +-Applying beta-rule and splitting (489), into two cases.
% 13.23/3.58 |-Branch one:
% 13.23/3.58 | (490) all_0_47_47 = e0
% 13.23/3.58 |
% 13.23/3.58 | Equations (490) can reduce 29 to:
% 13.23/3.58 | (475) ~ (all_0_42_42 = e0)
% 13.23/3.58 |
% 13.23/3.58 | Equations (490) can reduce 357 to:
% 13.23/3.58 | (469) ~ (e2 = e0)
% 13.23/3.58 |
% 13.23/3.58 | Simplifying 469 yields:
% 13.23/3.58 | (61) ~ (e2 = e0)
% 13.23/3.58 |
% 13.23/3.58 | From (490) and (66) follows:
% 13.23/3.58 | (494) op(e1, e0) = all_0_25_25
% 13.23/3.58 |
% 13.23/3.58 +-Applying beta-rule and splitting (81), into two cases.
% 13.23/3.58 |-Branch one:
% 13.23/3.58 | (495) all_0_42_42 = e3
% 13.23/3.58 |
% 13.23/3.58 | Equations (495) can reduce 229 to:
% 13.23/3.58 | (496) ~ (all_0_43_43 = e3)
% 13.23/3.58 |
% 13.23/3.58 | Simplifying 496 yields:
% 13.23/3.58 | (497) ~ (all_0_43_43 = e3)
% 13.23/3.58 |
% 13.23/3.58 | Equations (495) can reduce 20 to:
% 13.23/3.58 | (209) ~ (e3 = e2)
% 13.23/3.58 |
% 13.23/3.58 | Equations (495) can reduce 475 to:
% 13.23/3.58 | (74) ~ (e3 = e0)
% 13.23/3.58 |
% 13.23/3.58 | From (495) and (234) follows:
% 13.23/3.58 | (500) op(e1, e3) = all_0_23_23
% 13.23/3.58 |
% 13.23/3.58 +-Applying beta-rule and splitting (173), into two cases.
% 13.23/3.58 |-Branch one:
% 13.23/3.58 | (501) all_0_50_50 = e1
% 13.23/3.58 |
% 13.23/3.58 | Equations (501) can reduce 326 to:
% 13.23/3.58 | (303) $false
% 13.23/3.58 |
% 13.23/3.58 |-The branch is then unsatisfiable
% 13.23/3.58 |-Branch two:
% 13.23/3.58 | (326) ~ (all_0_50_50 = e1)
% 13.23/3.58 | (504) all_0_50_50 = e4 | all_0_50_50 = e2 | all_0_50_50 = e0
% 13.23/3.58 |
% 13.23/3.58 +-Applying beta-rule and splitting (84), into two cases.
% 13.23/3.58 |-Branch one:
% 13.23/3.58 | (505) all_0_43_43 = e4
% 13.23/3.58 |
% 13.23/3.58 | Equations (505) can reduce 115 to:
% 13.23/3.58 | (506) ~ (all_0_48_48 = e4)
% 13.23/3.58 |
% 13.23/3.58 | Simplifying 506 yields:
% 13.23/3.58 | (507) ~ (all_0_48_48 = e4)
% 13.23/3.58 |
% 13.23/3.58 | Equations (505) can reduce 497 to:
% 13.23/3.58 | (30) ~ (e4 = e3)
% 13.23/3.58 |
% 13.23/3.58 | Equations (505) can reduce 262 to:
% 13.23/3.58 | (253) ~ (e4 = e1)
% 13.23/3.58 |
% 13.23/3.58 | Equations (505) can reduce 306 to:
% 13.23/3.58 | (5) ~ (e4 = e0)
% 13.23/3.58 |
% 13.23/3.58 +-Applying beta-rule and splitting (100), into two cases.
% 13.23/3.58 |-Branch one:
% 13.23/3.58 | (511) all_0_40_40 = e4
% 13.23/3.58 |
% 13.23/3.58 | Combining equations (473,511) yields a new equation:
% 13.23/3.58 | (512) e4 = e0
% 13.23/3.58 |
% 13.23/3.58 | Equations (512) can reduce 5 to:
% 13.23/3.58 | (303) $false
% 13.23/3.58 |
% 13.23/3.58 |-The branch is then unsatisfiable
% 13.23/3.58 |-Branch two:
% 13.23/3.58 | (514) ~ (all_0_40_40 = e4)
% 13.23/3.58 | (515) all_0_45_45 = e4 | all_0_50_50 = e4 | all_0_57_57 = e4
% 13.23/3.58 |
% 13.23/3.58 | Equations (473) can reduce 514 to:
% 13.23/3.58 | (516) ~ (e4 = e0)
% 13.23/3.58 |
% 13.23/3.58 | Simplifying 516 yields:
% 13.23/3.58 | (5) ~ (e4 = e0)
% 13.23/3.58 |
% 13.23/3.58 +-Applying beta-rule and splitting (504), into two cases.
% 13.23/3.58 |-Branch one:
% 13.23/3.58 | (518) all_0_50_50 = e0
% 13.23/3.58 |
% 13.23/3.58 | Equations (518) can reduce 468 to:
% 13.23/3.58 | (303) $false
% 13.23/3.58 |
% 13.23/3.58 |-The branch is then unsatisfiable
% 13.23/3.58 |-Branch two:
% 13.23/3.58 | (468) ~ (all_0_50_50 = e0)
% 13.23/3.58 | (521) all_0_50_50 = e4 | all_0_50_50 = e2
% 13.23/3.58 |
% 13.23/3.58 +-Applying beta-rule and splitting (174), into two cases.
% 13.23/3.58 |-Branch one:
% 13.23/3.58 | (522) all_0_43_43 = e3
% 13.23/3.58 |
% 13.23/3.58 | Combining equations (505,522) yields a new equation:
% 13.23/3.58 | (523) e4 = e3
% 13.23/3.58 |
% 13.23/3.58 | Simplifying 523 yields:
% 13.23/3.58 | (524) e4 = e3
% 13.23/3.58 |
% 13.23/3.58 | Equations (524) can reduce 30 to:
% 13.23/3.58 | (303) $false
% 13.23/3.58 |
% 13.23/3.58 |-The branch is then unsatisfiable
% 13.23/3.58 |-Branch two:
% 13.23/3.58 | (497) ~ (all_0_43_43 = e3)
% 13.23/3.58 | (527) all_0_48_48 = e3 | all_0_55_55 = e3 | all_0_60_60 = e3
% 13.23/3.58 |
% 13.23/3.58 +-Applying beta-rule and splitting (88), into two cases.
% 13.23/3.58 |-Branch one:
% 13.23/3.58 | (528) all_0_49_49 = e4
% 13.23/3.58 |
% 13.23/3.58 | Combining equations (466,528) yields a new equation:
% 13.23/3.58 | (512) e4 = e0
% 13.23/3.58 |
% 13.23/3.58 | Equations (512) can reduce 5 to:
% 13.23/3.58 | (303) $false
% 13.23/3.58 |
% 13.23/3.58 |-The branch is then unsatisfiable
% 13.23/3.58 |-Branch two:
% 13.23/3.58 | (531) ~ (all_0_49_49 = e4)
% 13.23/3.58 | (532) all_0_50_50 = e4 | all_0_52_52 = e4
% 13.23/3.58 |
% 13.23/3.58 +-Applying beta-rule and splitting (532), into two cases.
% 13.23/3.58 |-Branch one:
% 13.23/3.58 | (533) all_0_50_50 = e4
% 13.23/3.58 |
% 13.23/3.58 | Equations (533) can reduce 468 to:
% 13.23/3.58 | (5) ~ (e4 = e0)
% 13.23/3.58 |
% 13.23/3.58 +-Applying beta-rule and splitting (527), into two cases.
% 13.23/3.58 |-Branch one:
% 13.23/3.58 | (535) all_0_48_48 = e3
% 13.23/3.58 |
% 13.23/3.58 | Equations (535) can reduce 507 to:
% 13.23/3.58 | (536) ~ (e4 = e3)
% 13.23/3.58 |
% 13.23/3.58 | Simplifying 536 yields:
% 13.23/3.58 | (30) ~ (e4 = e3)
% 13.23/3.58 |
% 13.23/3.58 | Equations (535) can reduce 359 to:
% 13.23/3.58 | (209) ~ (e3 = e2)
% 13.23/3.58 |
% 13.23/3.58 | Instantiating formula (39) with e1, e3, all_0_23_23, e3 and discharging atoms op(e1, e3) = all_0_23_23, op(e1, e3) = e3, yields:
% 13.23/3.58 | (539) all_0_23_23 = e3
% 13.23/3.58 |
% 13.23/3.58 | Instantiating formula (39) with e1, e0, all_0_25_25, e2 and discharging atoms op(e1, e0) = all_0_25_25, op(e1, e0) = e2, yields:
% 13.23/3.58 | (540) all_0_25_25 = e2
% 13.23/3.58 |
% 13.23/3.58 +-Applying beta-rule and splitting (225), into two cases.
% 13.23/3.58 |-Branch one:
% 13.23/3.58 | (541) (all_0_23_23 = e4 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e3 & ~ (all_0_26_26 = e1)) | (all_0_27_27 = e2 & ~ (all_0_28_28 = e1))
% 13.23/3.58 |
% 13.23/3.58 +-Applying beta-rule and splitting (541), into two cases.
% 13.23/3.58 |-Branch one:
% 13.23/3.58 | (542) (all_0_23_23 = e4 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e3 & ~ (all_0_26_26 = e1))
% 13.23/3.58 |
% 13.23/3.58 +-Applying beta-rule and splitting (542), into two cases.
% 13.23/3.58 |-Branch one:
% 13.23/3.58 | (543) all_0_23_23 = e4 & ~ (all_0_24_24 = e1)
% 13.23/3.58 |
% 13.23/3.58 | Applying alpha-rule on (543) yields:
% 13.23/3.58 | (544) all_0_23_23 = e4
% 13.23/3.58 | (545) ~ (all_0_24_24 = e1)
% 13.23/3.58 |
% 13.23/3.58 | Combining equations (544,539) yields a new equation:
% 13.23/3.58 | (523) e4 = e3
% 13.23/3.58 |
% 13.23/3.58 | Simplifying 523 yields:
% 13.23/3.58 | (524) e4 = e3
% 13.23/3.58 |
% 13.23/3.58 | Equations (524) can reduce 30 to:
% 13.23/3.58 | (303) $false
% 13.23/3.58 |
% 13.23/3.58 |-The branch is then unsatisfiable
% 13.23/3.58 |-Branch two:
% 13.23/3.58 | (549) all_0_25_25 = e3 & ~ (all_0_26_26 = e1)
% 13.23/3.58 |
% 13.23/3.58 | Applying alpha-rule on (549) yields:
% 13.23/3.59 | (550) all_0_25_25 = e3
% 13.23/3.59 | (551) ~ (all_0_26_26 = e1)
% 13.23/3.59 |
% 13.23/3.59 | Combining equations (550,540) yields a new equation:
% 13.23/3.59 | (552) e3 = e2
% 13.23/3.59 |
% 13.23/3.59 | Simplifying 552 yields:
% 13.23/3.59 | (553) e3 = e2
% 13.23/3.59 |
% 13.23/3.59 | Equations (553) can reduce 209 to:
% 13.23/3.59 | (303) $false
% 13.23/3.59 |
% 13.23/3.59 |-The branch is then unsatisfiable
% 13.23/3.59 |-Branch two:
% 13.23/3.59 | (555) all_0_27_27 = e2 & ~ (all_0_28_28 = e1)
% 13.23/3.59 |
% 13.23/3.59 | Applying alpha-rule on (555) yields:
% 13.23/3.59 | (556) all_0_27_27 = e2
% 13.23/3.59 | (557) ~ (all_0_28_28 = e1)
% 13.23/3.59 |
% 13.23/3.59 | Combining equations (556,444) yields a new equation:
% 13.23/3.59 | (558) e2 = e0
% 13.23/3.59 |
% 13.23/3.59 | Simplifying 558 yields:
% 13.23/3.59 | (559) e2 = e0
% 13.23/3.59 |
% 13.23/3.59 | Equations (559) can reduce 61 to:
% 13.23/3.59 | (303) $false
% 13.23/3.59 |
% 13.23/3.59 |-The branch is then unsatisfiable
% 13.23/3.59 |-Branch two:
% 13.23/3.59 | (561) all_0_29_29 = e0 & ~ (all_0_30_30 = e1)
% 13.23/3.59 |
% 13.23/3.59 | Applying alpha-rule on (561) yields:
% 13.23/3.59 | (562) all_0_29_29 = e0
% 13.23/3.59 | (563) ~ (all_0_30_30 = e1)
% 13.23/3.59 |
% 13.23/3.59 | Combining equations (562,351) yields a new equation:
% 13.23/3.59 | (512) e4 = e0
% 13.23/3.59 |
% 13.23/3.59 | Equations (512) can reduce 5 to:
% 13.23/3.59 | (303) $false
% 13.23/3.59 |
% 13.23/3.59 |-The branch is then unsatisfiable
% 13.23/3.59 |-Branch two:
% 13.23/3.59 | (566) ~ (all_0_48_48 = e3)
% 13.23/3.59 | (567) all_0_55_55 = e3 | all_0_60_60 = e3
% 13.23/3.59 |
% 13.23/3.59 +-Applying beta-rule and splitting (567), into two cases.
% 13.23/3.59 |-Branch one:
% 13.23/3.59 | (568) all_0_55_55 = e3
% 13.23/3.59 |
% 13.23/3.59 | Combining equations (568,373) yields a new equation:
% 13.23/3.59 | (552) e3 = e2
% 13.23/3.59 |
% 13.23/3.59 | Simplifying 552 yields:
% 13.23/3.59 | (553) e3 = e2
% 13.23/3.59 |
% 13.23/3.59 | Equations (553) can reduce 209 to:
% 13.23/3.59 | (303) $false
% 13.23/3.59 |
% 13.23/3.59 |-The branch is then unsatisfiable
% 13.23/3.59 |-Branch two:
% 13.23/3.59 | (572) ~ (all_0_55_55 = e3)
% 13.23/3.59 | (573) all_0_60_60 = e3
% 13.23/3.59 |
% 13.23/3.59 | Combining equations (573,305) yields a new equation:
% 13.23/3.59 | (574) e3 = e0
% 13.23/3.59 |
% 13.23/3.59 | Simplifying 574 yields:
% 13.23/3.59 | (575) e3 = e0
% 13.23/3.59 |
% 13.23/3.59 | Equations (575) can reduce 74 to:
% 13.23/3.59 | (303) $false
% 13.23/3.59 |
% 13.23/3.59 |-The branch is then unsatisfiable
% 13.23/3.59 |-Branch two:
% 13.23/3.59 | (577) ~ (all_0_50_50 = e4)
% 13.23/3.59 | (578) all_0_52_52 = e4
% 13.23/3.59 |
% 13.23/3.59 | Combining equations (578,322) yields a new equation:
% 13.23/3.59 | (426) e4 = e1
% 13.23/3.59 |
% 13.23/3.59 | Simplifying 426 yields:
% 13.23/3.59 | (427) e4 = e1
% 13.23/3.59 |
% 13.23/3.59 | Equations (427) can reduce 253 to:
% 13.23/3.59 | (303) $false
% 13.23/3.59 |
% 13.23/3.59 |-The branch is then unsatisfiable
% 13.23/3.59 |-Branch two:
% 13.23/3.59 | (582) ~ (all_0_43_43 = e4)
% 13.23/3.59 | (583) all_0_48_48 = e4 | all_0_52_52 = e4 | all_0_60_60 = e4
% 13.23/3.59 |
% 13.23/3.59 +-Applying beta-rule and splitting (222), into two cases.
% 13.23/3.59 |-Branch one:
% 13.23/3.59 | (310) all_0_43_43 = e1
% 13.23/3.59 |
% 13.23/3.59 | Equations (310) can reduce 262 to:
% 13.23/3.59 | (303) $false
% 13.23/3.59 |
% 13.23/3.59 |-The branch is then unsatisfiable
% 13.23/3.59 |-Branch two:
% 13.23/3.59 | (262) ~ (all_0_43_43 = e1)
% 13.23/3.59 | (587) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 13.23/3.59 |
% 13.23/3.59 +-Applying beta-rule and splitting (587), into two cases.
% 13.23/3.59 |-Branch one:
% 13.23/3.59 | (588) all_0_43_43 = e0
% 13.23/3.59 |
% 13.23/3.59 | Equations (588) can reduce 306 to:
% 13.23/3.59 | (303) $false
% 13.23/3.59 |
% 13.23/3.59 |-The branch is then unsatisfiable
% 13.23/3.59 |-Branch two:
% 13.23/3.59 | (306) ~ (all_0_43_43 = e0)
% 13.23/3.59 | (591) all_0_43_43 = e4 | all_0_43_43 = e3
% 13.23/3.59 |
% 13.23/3.59 +-Applying beta-rule and splitting (591), into two cases.
% 13.23/3.59 |-Branch one:
% 13.23/3.59 | (522) all_0_43_43 = e3
% 13.23/3.59 |
% 13.23/3.59 | Equations (522) can reduce 497 to:
% 13.23/3.59 | (303) $false
% 13.23/3.59 |
% 13.23/3.59 |-The branch is then unsatisfiable
% 13.23/3.59 |-Branch two:
% 13.23/3.59 | (497) ~ (all_0_43_43 = e3)
% 13.23/3.59 | (505) all_0_43_43 = e4
% 13.23/3.59 |
% 13.23/3.59 | Equations (505) can reduce 582 to:
% 13.23/3.59 | (303) $false
% 13.23/3.59 |
% 13.23/3.59 |-The branch is then unsatisfiable
% 13.23/3.59 |-Branch two:
% 13.23/3.59 | (597) ~ (all_0_42_42 = e3)
% 13.23/3.59 | (598) all_0_47_47 = e3 | all_0_59_59 = e3
% 13.23/3.59 |
% 13.23/3.59 +-Applying beta-rule and splitting (598), into two cases.
% 13.23/3.59 |-Branch one:
% 13.23/3.59 | (599) all_0_47_47 = e3
% 13.23/3.59 |
% 13.23/3.59 | Combining equations (490,599) yields a new equation:
% 13.23/3.59 | (575) e3 = e0
% 13.23/3.59 |
% 13.23/3.59 | Equations (575) can reduce 74 to:
% 13.23/3.59 | (303) $false
% 13.23/3.59 |
% 13.23/3.59 |-The branch is then unsatisfiable
% 13.23/3.59 |-Branch two:
% 13.23/3.59 | (602) ~ (all_0_47_47 = e3)
% 13.23/3.59 | (603) all_0_59_59 = e3
% 13.23/3.59 |
% 13.23/3.59 | Combining equations (603,341) yields a new equation:
% 13.23/3.59 | (604) e3 = e1
% 13.23/3.59 |
% 13.23/3.59 | Simplifying 604 yields:
% 13.23/3.59 | (414) e3 = e1
% 13.23/3.59 |
% 13.23/3.59 | Equations (414) can reduce 145 to:
% 13.23/3.59 | (303) $false
% 13.23/3.59 |
% 13.23/3.59 |-The branch is then unsatisfiable
% 13.23/3.59 |-Branch two:
% 13.23/3.59 | (607) ~ (all_0_47_47 = e0)
% 13.23/3.59 | (608) all_0_51_51 = e0 | all_0_59_59 = e0
% 13.23/3.59 |
% 13.23/3.59 +-Applying beta-rule and splitting (608), into two cases.
% 13.23/3.59 |-Branch one:
% 13.23/3.59 | (609) all_0_51_51 = e0
% 13.23/3.59 |
% 13.23/3.59 | Combining equations (383,609) yields a new equation:
% 13.23/3.59 | (558) e2 = e0
% 13.23/3.59 |
% 13.23/3.59 | Simplifying 558 yields:
% 13.23/3.59 | (559) e2 = e0
% 13.23/3.59 |
% 13.23/3.59 | Equations (559) can reduce 61 to:
% 13.23/3.59 | (303) $false
% 13.23/3.59 |
% 13.23/3.59 |-The branch is then unsatisfiable
% 13.23/3.59 |-Branch two:
% 13.23/3.59 | (613) ~ (all_0_51_51 = e0)
% 13.23/3.59 | (614) all_0_59_59 = e0
% 13.23/3.59 |
% 13.23/3.59 | Combining equations (614,341) yields a new equation:
% 13.23/3.59 | (302) e1 = e0
% 13.23/3.59 |
% 13.23/3.59 | Equations (302) can reduce 143 to:
% 13.23/3.59 | (303) $false
% 13.23/3.59 |
% 13.23/3.59 |-The branch is then unsatisfiable
% 13.23/3.59 |-Branch two:
% 13.23/3.59 | (617) ~ (all_0_40_40 = e0)
% 13.23/3.59 | (618) all_0_45_45 = e0 | all_0_50_50 = e0 | all_0_57_57 = e0
% 13.23/3.59 |
% 13.23/3.59 +-Applying beta-rule and splitting (618), into two cases.
% 13.23/3.59 |-Branch one:
% 13.23/3.59 | (300) all_0_45_45 = e0
% 13.23/3.59 |
% 13.23/3.59 | Combining equations (289,300) yields a new equation:
% 13.23/3.59 | (301) e1 = e0
% 13.23/3.59 |
% 13.23/3.59 | Simplifying 301 yields:
% 13.23/3.59 | (302) e1 = e0
% 13.23/3.59 |
% 13.23/3.59 | Equations (302) can reduce 143 to:
% 13.23/3.59 | (303) $false
% 13.23/3.59 |
% 13.23/3.59 |-The branch is then unsatisfiable
% 13.23/3.59 |-Branch two:
% 13.23/3.59 | (304) ~ (all_0_45_45 = e0)
% 13.23/3.59 | (624) all_0_50_50 = e0 | all_0_57_57 = e0
% 13.23/3.59 |
% 13.23/3.59 +-Applying beta-rule and splitting (624), into two cases.
% 13.23/3.59 |-Branch one:
% 13.23/3.59 | (518) all_0_50_50 = e0
% 13.23/3.59 |
% 13.23/3.59 | Equations (518) can reduce 468 to:
% 13.23/3.59 | (303) $false
% 13.23/3.59 |
% 13.23/3.59 |-The branch is then unsatisfiable
% 13.23/3.59 |-Branch two:
% 13.23/3.59 | (468) ~ (all_0_50_50 = e0)
% 13.23/3.59 | (628) all_0_57_57 = e0
% 13.23/3.59 |
% 13.23/3.59 | Combining equations (628,407) yields a new equation:
% 13.23/3.59 | (559) e2 = e0
% 13.23/3.59 |
% 13.23/3.59 | Equations (559) can reduce 61 to:
% 13.23/3.59 | (303) $false
% 13.23/3.59 |
% 13.23/3.59 |-The branch is then unsatisfiable
% 13.23/3.59 |-Branch two:
% 13.23/3.59 | (631) all_0_52_52 = e1 & ~ (all_0_55_55 = e2)
% 13.23/3.59 |
% 13.23/3.59 | Applying alpha-rule on (631) yields:
% 13.23/3.59 | (322) all_0_52_52 = e1
% 13.23/3.59 | (633) ~ (all_0_55_55 = e2)
% 13.23/3.59 |
% 13.23/3.59 | Equations (373) can reduce 633 to:
% 13.23/3.59 | (303) $false
% 13.23/3.59 |
% 13.23/3.59 |-The branch is then unsatisfiable
% 13.23/3.59 |-Branch two:
% 13.23/3.59 | (635) ~ (all_0_56_56 = e3)
% 13.23/3.59 | (636) all_0_57_57 = e3 | all_0_59_59 = e3 | all_0_60_60 = e3
% 13.23/3.59 |
% 13.23/3.59 +-Applying beta-rule and splitting (636), into two cases.
% 13.23/3.59 |-Branch one:
% 13.23/3.59 | (637) all_0_57_57 = e3
% 13.23/3.59 |
% 13.23/3.59 | Combining equations (407,637) yields a new equation:
% 13.23/3.59 | (553) e3 = e2
% 13.23/3.59 |
% 13.23/3.59 | Equations (553) can reduce 209 to:
% 13.23/3.59 | (303) $false
% 13.23/3.59 |
% 13.23/3.59 |-The branch is then unsatisfiable
% 13.23/3.59 |-Branch two:
% 13.23/3.59 | (640) ~ (all_0_57_57 = e3)
% 13.23/3.59 | (641) all_0_59_59 = e3 | all_0_60_60 = e3
% 13.23/3.59 |
% 13.23/3.59 +-Applying beta-rule and splitting (641), into two cases.
% 13.23/3.59 |-Branch one:
% 13.23/3.59 | (603) all_0_59_59 = e3
% 13.23/3.59 |
% 13.23/3.59 | Combining equations (341,603) yields a new equation:
% 13.23/3.60 | (414) e3 = e1
% 13.23/3.60 |
% 13.23/3.60 | Equations (414) can reduce 145 to:
% 13.23/3.60 | (303) $false
% 13.23/3.60 |
% 13.23/3.60 |-The branch is then unsatisfiable
% 13.23/3.60 |-Branch two:
% 13.23/3.60 | (645) ~ (all_0_59_59 = e3)
% 13.23/3.60 | (573) all_0_60_60 = e3
% 13.23/3.60 |
% 13.23/3.60 | Combining equations (305,573) yields a new equation:
% 13.23/3.60 | (575) e3 = e0
% 13.23/3.60 |
% 13.23/3.60 | Equations (575) can reduce 74 to:
% 13.23/3.60 | (303) $false
% 13.23/3.60 |
% 13.23/3.60 |-The branch is then unsatisfiable
% 13.23/3.60 |-Branch two:
% 13.23/3.60 | (649) ~ (all_0_54_54 = e3)
% 13.23/3.60 | (568) all_0_55_55 = e3
% 13.23/3.60 |
% 13.23/3.60 | Combining equations (568,373) yields a new equation:
% 13.23/3.60 | (552) e3 = e2
% 13.23/3.60 |
% 13.23/3.60 | Simplifying 552 yields:
% 13.23/3.60 | (553) e3 = e2
% 13.23/3.60 |
% 13.23/3.60 | Equations (553) can reduce 209 to:
% 13.23/3.60 | (303) $false
% 13.23/3.60 |
% 13.23/3.60 |-The branch is then unsatisfiable
% 13.23/3.60 |-Branch two:
% 13.23/3.60 | (654) ~ (all_0_51_51 = e2)
% 13.23/3.60 | (655) all_0_59_59 = e2
% 13.23/3.60 |
% 13.23/3.60 | Combining equations (341,655) yields a new equation:
% 13.23/3.60 | (369) e2 = e1
% 13.23/3.60 |
% 13.23/3.60 | Equations (369) can reduce 150 to:
% 13.23/3.60 | (303) $false
% 13.23/3.60 |
% 13.23/3.60 |-The branch is then unsatisfiable
% 13.23/3.60 |-Branch two:
% 13.23/3.60 | (633) ~ (all_0_55_55 = e2)
% 13.23/3.60 | (659) all_0_60_60 = e2
% 13.23/3.60 |
% 13.23/3.60 | Combining equations (659,305) yields a new equation:
% 13.23/3.60 | (558) e2 = e0
% 13.23/3.60 |
% 13.23/3.60 | Simplifying 558 yields:
% 13.23/3.60 | (559) e2 = e0
% 13.23/3.60 |
% 13.23/3.60 | Equations (559) can reduce 61 to:
% 13.23/3.60 | (303) $false
% 13.23/3.60 |
% 13.23/3.60 |-The branch is then unsatisfiable
% 13.23/3.60 |-Branch two:
% 13.23/3.60 | (663) ~ (all_0_46_46 = e2)
% 13.23/3.60 | (664) all_0_58_58 = e2
% 13.23/3.60 |
% 13.23/3.60 | Equations (664) can reduce 71 to:
% 13.23/3.60 | (663) ~ (all_0_46_46 = e2)
% 13.23/3.60 |
% 13.23/3.60 | From (664) and (27) follows:
% 13.23/3.60 | (666) op(e2, e2) = all_0_21_21
% 13.23/3.60 |
% 13.23/3.60 | From (664) and (33) follows:
% 13.23/3.60 | (667) op(e0, e2) = all_0_22_22
% 13.23/3.60 |
% 13.23/3.60 | From (664) and (11) follows:
% 13.23/3.60 | (668) op(e0, e2) = e2
% 13.23/3.60 |
% 13.23/3.60 +-Applying beta-rule and splitting (129), into two cases.
% 13.23/3.60 |-Branch one:
% 13.23/3.60 | (669) all_0_46_46 = e1
% 13.23/3.60 |
% 13.23/3.60 | Equations (669) can reduce 264 to:
% 13.23/3.60 | (303) $false
% 13.23/3.60 |
% 13.23/3.60 |-The branch is then unsatisfiable
% 13.23/3.60 |-Branch two:
% 13.23/3.60 | (264) ~ (all_0_46_46 = e1)
% 13.23/3.60 | (672) all_0_46_46 = e4 | all_0_46_46 = e2
% 13.23/3.60 |
% 13.23/3.60 +-Applying beta-rule and splitting (672), into two cases.
% 13.23/3.60 |-Branch one:
% 13.23/3.60 | (433) all_0_46_46 = e4
% 13.23/3.60 |
% 13.23/3.60 | Equations (433) can reduce 149 to:
% 13.23/3.60 | (30) ~ (e4 = e3)
% 13.23/3.60 |
% 13.23/3.60 | Equations (433) can reduce 264 to:
% 13.23/3.60 | (253) ~ (e4 = e1)
% 13.23/3.60 |
% 13.23/3.60 | Equations (433) can reduce 103 to:
% 13.23/3.60 | (5) ~ (e4 = e0)
% 13.23/3.60 |
% 13.23/3.60 | From (433) and (65) follows:
% 13.23/3.60 | (677) op(e2, e4) = all_0_19_19
% 13.23/3.60 |
% 13.23/3.60 +-Applying beta-rule and splitting (84), into two cases.
% 13.23/3.60 |-Branch one:
% 13.23/3.60 | (505) all_0_43_43 = e4
% 13.23/3.60 |
% 13.23/3.60 | Equations (505) can reduce 51 to:
% 13.23/3.60 | (514) ~ (all_0_40_40 = e4)
% 13.23/3.60 |
% 13.23/3.60 | Equations (505) can reduce 125 to:
% 13.23/3.60 | (680) ~ (all_0_55_55 = e4)
% 13.23/3.60 |
% 13.23/3.60 | Simplifying 680 yields:
% 13.23/3.60 | (256) ~ (all_0_55_55 = e4)
% 13.23/3.60 |
% 13.23/3.60 | From (505) and (216) follows:
% 13.23/3.60 | (682) op(e4, e4) = all_0_32_32
% 13.23/3.60 |
% 13.23/3.60 | From (505) and (254) follows:
% 13.23/3.60 | (683) op(e4, e0) = e4
% 13.23/3.60 |
% 13.23/3.60 | From (505) and (242) follows:
% 13.23/3.60 | (684) op(e0, e4) = all_0_31_31
% 13.23/3.60 |
% 13.23/3.60 | Instantiating formula (39) with e4, e4, all_0_32_32, e2 and discharging atoms op(e4, e4) = all_0_32_32, op(e4, e4) = e2, yields:
% 13.23/3.60 | (685) all_0_32_32 = e2
% 13.23/3.60 |
% 13.23/3.60 | Instantiating formula (39) with e2, e4, all_0_19_19, all_0_49_49 and discharging atoms op(e2, e4) = all_0_19_19, op(e2, e4) = all_0_49_49, yields:
% 13.23/3.60 | (686) all_0_19_19 = all_0_49_49
% 13.23/3.60 |
% 13.23/3.60 | Instantiating formula (39) with e2, e2, all_0_21_21, e3 and discharging atoms op(e2, e2) = all_0_21_21, op(e2, e2) = e3, yields:
% 13.23/3.60 | (687) all_0_21_21 = e3
% 13.23/3.60 |
% 13.23/3.60 | Instantiating formula (39) with e0, e4, all_0_31_31, all_0_56_56 and discharging atoms op(e0, e4) = all_0_31_31, op(e0, e4) = all_0_56_56, yields:
% 13.23/3.60 | (688) all_0_31_31 = all_0_56_56
% 13.23/3.60 |
% 13.23/3.60 | Instantiating formula (39) with e0, e2, e2, all_0_22_22 and discharging atoms op(e0, e2) = all_0_22_22, op(e0, e2) = e2, yields:
% 13.23/3.60 | (689) all_0_22_22 = e2
% 13.23/3.60 |
% 13.23/3.60 | From (685) and (682) follows:
% 13.23/3.60 | (50) op(e4, e4) = e2
% 13.23/3.60 |
% 13.23/3.60 | From (689) and (667) follows:
% 13.23/3.60 | (668) op(e0, e2) = e2
% 13.23/3.60 |
% 13.23/3.60 +-Applying beta-rule and splitting (19), into two cases.
% 13.23/3.60 |-Branch one:
% 13.23/3.60 | (450) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2)) | (all_0_21_21 = e0 & ~ (all_0_22_22 = e2))
% 13.23/3.60 |
% 13.23/3.60 +-Applying beta-rule and splitting (450), into two cases.
% 13.23/3.60 |-Branch one:
% 13.23/3.60 | (451) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2))
% 13.23/3.60 |
% 13.23/3.60 +-Applying beta-rule and splitting (451), into two cases.
% 13.23/3.60 |-Branch one:
% 13.23/3.60 | (452) all_0_17_17 = e4 & ~ (all_0_18_18 = e2)
% 13.23/3.60 |
% 13.23/3.60 | Applying alpha-rule on (452) yields:
% 13.23/3.60 | (453) all_0_17_17 = e4
% 13.23/3.60 | (454) ~ (all_0_18_18 = e2)
% 13.23/3.60 |
% 13.23/3.60 | Combining equations (453,273) yields a new equation:
% 13.23/3.60 | (697) all_0_51_51 = e4
% 13.23/3.60 |
% 13.23/3.60 | Equations (697) can reduce 56 to:
% 13.23/3.60 | (303) $false
% 13.23/3.60 |
% 13.23/3.60 |-The branch is then unsatisfiable
% 13.23/3.60 |-Branch two:
% 13.23/3.60 | (458) all_0_19_19 = e3 & ~ (all_0_20_20 = e2)
% 13.23/3.60 |
% 13.23/3.60 | Applying alpha-rule on (458) yields:
% 13.23/3.60 | (459) all_0_19_19 = e3
% 13.23/3.60 | (460) ~ (all_0_20_20 = e2)
% 13.23/3.60 |
% 13.23/3.60 | Combining equations (459,686) yields a new equation:
% 13.23/3.60 | (702) all_0_49_49 = e3
% 13.23/3.60 |
% 13.23/3.60 | Equations (702) can reduce 46 to:
% 13.23/3.60 | (303) $false
% 13.23/3.60 |
% 13.23/3.60 |-The branch is then unsatisfiable
% 13.23/3.60 |-Branch two:
% 13.23/3.60 | (462) all_0_21_21 = e0 & ~ (all_0_22_22 = e2)
% 13.23/3.60 |
% 13.23/3.60 | Applying alpha-rule on (462) yields:
% 13.23/3.60 | (463) all_0_21_21 = e0
% 13.23/3.60 | (464) ~ (all_0_22_22 = e2)
% 13.23/3.60 |
% 13.23/3.60 | Combining equations (687,463) yields a new equation:
% 13.23/3.60 | (574) e3 = e0
% 13.23/3.60 |
% 13.23/3.60 | Simplifying 574 yields:
% 13.23/3.60 | (575) e3 = e0
% 13.23/3.60 |
% 13.23/3.60 | Equations (575) can reduce 74 to:
% 13.23/3.60 | (303) $false
% 13.23/3.60 |
% 13.23/3.60 |-The branch is then unsatisfiable
% 13.23/3.60 |-Branch two:
% 13.23/3.60 | (631) all_0_52_52 = e1 & ~ (all_0_55_55 = e2)
% 13.23/3.60 |
% 13.23/3.60 | Applying alpha-rule on (631) yields:
% 13.23/3.60 | (322) all_0_52_52 = e1
% 13.23/3.60 | (633) ~ (all_0_55_55 = e2)
% 13.23/3.60 |
% 13.23/3.60 +-Applying beta-rule and splitting (157), into two cases.
% 13.23/3.60 |-Branch one:
% 13.23/3.60 | (404) all_0_54_54 = e2
% 13.23/3.60 |
% 13.23/3.60 | Equations (404) can reduce 101 to:
% 13.23/3.60 | (714) ~ (all_0_55_55 = e2)
% 13.23/3.60 |
% 13.23/3.60 | Simplifying 714 yields:
% 13.23/3.60 | (633) ~ (all_0_55_55 = e2)
% 13.23/3.60 |
% 13.23/3.60 | Equations (404) can reduce 196 to:
% 13.23/3.60 | (716) ~ (all_0_57_57 = e2)
% 13.23/3.60 |
% 13.23/3.60 | Simplifying 716 yields:
% 13.23/3.60 | (717) ~ (all_0_57_57 = e2)
% 13.23/3.60 |
% 13.23/3.60 | Equations (404) can reduce 278 to:
% 13.23/3.60 | (150) ~ (e2 = e1)
% 13.23/3.60 |
% 13.23/3.60 | Equations (404) can reduce 183 to:
% 13.23/3.60 | (61) ~ (e2 = e0)
% 13.23/3.60 |
% 13.23/3.60 +-Applying beta-rule and splitting (175), into two cases.
% 13.23/3.60 |-Branch one:
% 13.23/3.60 | (364) all_0_48_48 = e2
% 13.23/3.60 |
% 13.23/3.60 | Equations (364) can reduce 9 to:
% 13.23/3.60 | (357) ~ (all_0_47_47 = e2)
% 13.23/3.60 |
% 13.23/3.60 | Equations (364) can reduce 165 to:
% 13.23/3.60 | (714) ~ (all_0_55_55 = e2)
% 13.23/3.60 |
% 13.23/3.60 | Simplifying 714 yields:
% 13.23/3.60 | (633) ~ (all_0_55_55 = e2)
% 13.23/3.60 |
% 13.23/3.60 | Equations (364) can reduce 295 to:
% 13.23/3.60 | (150) ~ (e2 = e1)
% 13.23/3.60 |
% 13.23/3.60 | From (364) and (211) follows:
% 13.23/3.61 | (725) op(e0, e2) = all_0_33_33
% 13.23/3.61 |
% 13.23/3.61 +-Applying beta-rule and splitting (127), into two cases.
% 13.23/3.61 |-Branch one:
% 13.23/3.61 | (379) all_0_47_47 = e2
% 13.23/3.61 |
% 13.23/3.61 | Equations (379) can reduce 357 to:
% 13.23/3.61 | (303) $false
% 13.23/3.61 |
% 13.23/3.61 |-The branch is then unsatisfiable
% 13.23/3.61 |-Branch two:
% 13.23/3.61 | (357) ~ (all_0_47_47 = e2)
% 13.23/3.61 | (382) all_0_51_51 = e2 | all_0_59_59 = e2
% 13.23/3.61 |
% 13.23/3.61 +-Applying beta-rule and splitting (382), into two cases.
% 13.23/3.61 |-Branch one:
% 13.23/3.61 | (383) all_0_51_51 = e2
% 13.23/3.61 |
% 13.23/3.61 | Equations (383) can reduce 176 to:
% 13.23/3.61 | (357) ~ (all_0_47_47 = e2)
% 13.23/3.61 |
% 13.23/3.61 | Equations (383) can reduce 83 to:
% 13.23/3.61 | (151) ~ (all_0_49_49 = e2)
% 13.23/3.61 |
% 13.23/3.61 | Equations (383) can reduce 116 to:
% 13.23/3.61 | (388) ~ (all_0_50_50 = e2)
% 13.23/3.61 |
% 13.23/3.61 | Equations (383) can reduce 247 to:
% 13.23/3.61 | (391) ~ (e3 = e2)
% 13.23/3.61 |
% 13.23/3.61 | Simplifying 391 yields:
% 13.23/3.61 | (209) ~ (e3 = e2)
% 13.23/3.61 |
% 13.23/3.61 | Equations (383) can reduce 343 to:
% 13.23/3.61 | (150) ~ (e2 = e1)
% 13.23/3.61 |
% 13.23/3.61 +-Applying beta-rule and splitting (174), into two cases.
% 13.23/3.61 |-Branch one:
% 13.23/3.61 | (522) all_0_43_43 = e3
% 13.23/3.61 |
% 13.23/3.61 | Combining equations (505,522) yields a new equation:
% 13.23/3.61 | (523) e4 = e3
% 13.23/3.61 |
% 13.23/3.61 | Simplifying 523 yields:
% 13.23/3.61 | (524) e4 = e3
% 13.23/3.61 |
% 13.23/3.61 | Equations (524) can reduce 30 to:
% 13.23/3.61 | (303) $false
% 13.23/3.61 |
% 13.23/3.61 |-The branch is then unsatisfiable
% 13.23/3.61 |-Branch two:
% 13.23/3.61 | (497) ~ (all_0_43_43 = e3)
% 13.23/3.61 | (527) all_0_48_48 = e3 | all_0_55_55 = e3 | all_0_60_60 = e3
% 13.23/3.61 |
% 13.23/3.61 +-Applying beta-rule and splitting (527), into two cases.
% 13.23/3.61 |-Branch one:
% 13.23/3.61 | (535) all_0_48_48 = e3
% 13.23/3.61 |
% 13.23/3.61 | Combining equations (364,535) yields a new equation:
% 13.23/3.61 | (553) e3 = e2
% 13.23/3.61 |
% 13.23/3.61 | Equations (553) can reduce 209 to:
% 13.23/3.61 | (303) $false
% 13.23/3.61 |
% 13.23/3.61 |-The branch is then unsatisfiable
% 13.23/3.61 |-Branch two:
% 13.23/3.61 | (566) ~ (all_0_48_48 = e3)
% 13.23/3.61 | (567) all_0_55_55 = e3 | all_0_60_60 = e3
% 13.23/3.61 |
% 13.23/3.61 +-Applying beta-rule and splitting (567), into two cases.
% 13.23/3.61 |-Branch one:
% 13.23/3.61 | (568) all_0_55_55 = e3
% 13.23/3.61 |
% 13.23/3.61 | Equations (568) can reduce 256 to:
% 13.23/3.61 | (536) ~ (e4 = e3)
% 13.23/3.61 |
% 13.23/3.61 | Simplifying 536 yields:
% 13.23/3.61 | (30) ~ (e4 = e3)
% 13.23/3.61 |
% 13.23/3.61 | Equations (568) can reduce 633 to:
% 13.23/3.61 | (209) ~ (e3 = e2)
% 13.23/3.61 |
% 13.23/3.61 | Equations (568) can reduce 280 to:
% 13.23/3.61 | (145) ~ (e3 = e1)
% 13.23/3.61 |
% 13.23/3.61 | From (568) and (168) follows:
% 13.23/3.61 | (753) op(e0, e3) = all_0_37_37
% 13.23/3.61 |
% 13.23/3.61 | Instantiating formula (39) with e0, e3, all_0_37_37, all_0_57_57 and discharging atoms op(e0, e3) = all_0_37_37, op(e0, e3) = all_0_57_57, yields:
% 13.23/3.61 | (754) all_0_37_37 = all_0_57_57
% 13.23/3.61 |
% 13.23/3.61 | Instantiating formula (39) with e0, e2, all_0_33_33, e2 and discharging atoms op(e0, e2) = all_0_33_33, op(e0, e2) = e2, yields:
% 13.23/3.61 | (755) all_0_33_33 = e2
% 13.23/3.61 |
% 13.23/3.61 +-Applying beta-rule and splitting (36), into two cases.
% 13.23/3.61 |-Branch one:
% 13.23/3.61 | (756) (all_0_31_31 = e4 & ~ (all_0_32_32 = e0)) | (all_0_33_33 = e3 & ~ (all_0_34_34 = e0)) | (all_0_35_35 = e2 & ~ (all_0_36_36 = e0))
% 13.23/3.61 |
% 13.23/3.61 +-Applying beta-rule and splitting (756), into two cases.
% 13.23/3.61 |-Branch one:
% 13.23/3.61 | (757) (all_0_31_31 = e4 & ~ (all_0_32_32 = e0)) | (all_0_33_33 = e3 & ~ (all_0_34_34 = e0))
% 13.23/3.61 |
% 13.23/3.61 +-Applying beta-rule and splitting (757), into two cases.
% 13.23/3.61 |-Branch one:
% 13.23/3.61 | (758) all_0_31_31 = e4 & ~ (all_0_32_32 = e0)
% 13.23/3.61 |
% 13.23/3.61 | Applying alpha-rule on (758) yields:
% 13.23/3.61 | (759) all_0_31_31 = e4
% 13.23/3.61 | (760) ~ (all_0_32_32 = e0)
% 13.23/3.61 |
% 13.23/3.61 | Combining equations (688,759) yields a new equation:
% 13.23/3.61 | (761) all_0_56_56 = e4
% 13.23/3.61 |
% 13.23/3.61 | Simplifying 761 yields:
% 13.23/3.61 | (762) all_0_56_56 = e4
% 13.23/3.61 |
% 13.23/3.61 | Equations (762) can reduce 90 to:
% 13.23/3.61 | (763) ~ (all_0_57_57 = e4)
% 13.23/3.61 |
% 13.23/3.61 | Simplifying 763 yields:
% 13.23/3.61 | (764) ~ (all_0_57_57 = e4)
% 13.23/3.61 |
% 13.23/3.61 | Equations (762) can reduce 282 to:
% 13.23/3.61 | (253) ~ (e4 = e1)
% 13.23/3.61 |
% 13.23/3.61 | From (762) and (245) follows:
% 13.23/3.61 | (766) op(e4, e4) = all_0_6_6
% 13.23/3.61 |
% 13.23/3.61 +-Applying beta-rule and splitting (120), into two cases.
% 13.23/3.61 |-Branch one:
% 13.23/3.61 | (333) all_0_57_57 = e1
% 13.23/3.61 |
% 13.23/3.61 | Equations (333) can reduce 299 to:
% 13.23/3.61 | (303) $false
% 13.23/3.61 |
% 13.23/3.61 |-The branch is then unsatisfiable
% 13.23/3.61 |-Branch two:
% 13.23/3.61 | (299) ~ (all_0_57_57 = e1)
% 13.23/3.61 | (770) all_0_57_57 = e4 | all_0_57_57 = e3 | all_0_57_57 = e2 | all_0_57_57 = e0
% 13.23/3.61 |
% 13.23/3.61 +-Applying beta-rule and splitting (770), into two cases.
% 13.23/3.61 |-Branch one:
% 13.23/3.61 | (628) all_0_57_57 = e0
% 13.23/3.61 |
% 13.23/3.61 | Equations (628) can reduce 309 to:
% 13.23/3.61 | (303) $false
% 13.23/3.61 |
% 13.23/3.61 |-The branch is then unsatisfiable
% 13.23/3.61 |-Branch two:
% 13.23/3.61 | (309) ~ (all_0_57_57 = e0)
% 13.23/3.61 | (774) all_0_57_57 = e4 | all_0_57_57 = e3 | all_0_57_57 = e2
% 13.23/3.61 |
% 13.23/3.61 +-Applying beta-rule and splitting (16), into two cases.
% 13.23/3.61 |-Branch one:
% 13.23/3.61 | (775) all_0_44_44 = e3
% 13.23/3.61 |
% 13.23/3.61 | Equations (775) can reduce 62 to:
% 13.23/3.61 | (776) ~ (all_0_47_47 = e3)
% 13.23/3.61 |
% 13.23/3.61 | Simplifying 776 yields:
% 13.23/3.61 | (602) ~ (all_0_47_47 = e3)
% 13.23/3.61 |
% 13.23/3.61 | Equations (775) can reduce 276 to:
% 13.23/3.61 | (145) ~ (e3 = e1)
% 13.23/3.61 |
% 13.23/3.61 | From (775) and (126) follows:
% 13.23/3.61 | (779) op(e4, e3) = all_0_0_0
% 13.23/3.61 |
% 13.23/3.61 +-Applying beta-rule and splitting (100), into two cases.
% 13.23/3.61 |-Branch one:
% 13.23/3.61 | (511) all_0_40_40 = e4
% 13.23/3.61 |
% 13.23/3.61 | Equations (511) can reduce 514 to:
% 13.23/3.61 | (303) $false
% 13.23/3.61 |
% 13.23/3.61 |-The branch is then unsatisfiable
% 13.23/3.61 |-Branch two:
% 13.23/3.61 | (514) ~ (all_0_40_40 = e4)
% 13.23/3.61 | (515) all_0_45_45 = e4 | all_0_50_50 = e4 | all_0_57_57 = e4
% 13.23/3.61 |
% 13.23/3.61 +-Applying beta-rule and splitting (515), into two cases.
% 13.23/3.61 |-Branch one:
% 13.23/3.61 | (784) all_0_45_45 = e4
% 13.23/3.61 |
% 13.23/3.61 | Combining equations (289,784) yields a new equation:
% 13.23/3.61 | (427) e4 = e1
% 13.23/3.61 |
% 13.23/3.61 | Equations (427) can reduce 253 to:
% 13.23/3.61 | (303) $false
% 13.23/3.61 |
% 13.23/3.61 |-The branch is then unsatisfiable
% 13.23/3.61 |-Branch two:
% 13.23/3.61 | (787) ~ (all_0_45_45 = e4)
% 13.23/3.61 | (788) all_0_50_50 = e4 | all_0_57_57 = e4
% 13.23/3.61 |
% 13.23/3.61 +-Applying beta-rule and splitting (788), into two cases.
% 13.23/3.61 |-Branch one:
% 13.23/3.61 | (533) all_0_50_50 = e4
% 13.23/3.61 |
% 13.23/3.61 | Equations (533) can reduce 48 to:
% 13.23/3.61 | (514) ~ (all_0_40_40 = e4)
% 13.23/3.61 |
% 13.23/3.61 | Equations (533) can reduce 123 to:
% 13.23/3.61 | (531) ~ (all_0_49_49 = e4)
% 13.23/3.61 |
% 13.23/3.61 | Equations (533) can reduce 170 to:
% 13.23/3.61 | (763) ~ (all_0_57_57 = e4)
% 13.23/3.61 |
% 13.23/3.61 | Simplifying 763 yields:
% 13.23/3.61 | (764) ~ (all_0_57_57 = e4)
% 13.23/3.61 |
% 13.23/3.61 | Equations (533) can reduce 388 to:
% 13.23/3.61 | (227) ~ (e4 = e2)
% 13.23/3.61 |
% 13.23/3.61 +-Applying beta-rule and splitting (81), into two cases.
% 13.23/3.61 |-Branch one:
% 13.23/3.61 | (495) all_0_42_42 = e3
% 13.23/3.61 |
% 13.23/3.61 | Combining equations (495,286) yields a new equation:
% 13.23/3.61 | (796) all_0_4_4 = e3
% 13.23/3.61 |
% 13.23/3.61 | Equations (495) can reduce 29 to:
% 13.23/3.61 | (776) ~ (all_0_47_47 = e3)
% 13.23/3.61 |
% 13.23/3.61 | Simplifying 776 yields:
% 13.23/3.61 | (602) ~ (all_0_47_47 = e3)
% 13.23/3.61 |
% 13.23/3.61 +-Applying beta-rule and splitting (172), into two cases.
% 13.23/3.61 |-Branch one:
% 13.23/3.61 | (799) all_0_40_40 = e1
% 13.23/3.61 |
% 13.23/3.61 | Equations (799) can reduce 258 to:
% 13.23/3.61 | (303) $false
% 13.23/3.61 |
% 13.23/3.61 |-The branch is then unsatisfiable
% 13.23/3.61 |-Branch two:
% 13.23/3.61 | (258) ~ (all_0_40_40 = e1)
% 13.23/3.61 | (802) all_0_40_40 = e4 | all_0_40_40 = e3 | all_0_40_40 = e0
% 13.23/3.61 |
% 13.23/3.61 +-Applying beta-rule and splitting (774), into two cases.
% 13.23/3.61 |-Branch one:
% 13.23/3.61 | (637) all_0_57_57 = e3
% 13.23/3.61 |
% 13.23/3.61 | Equations (637) can reduce 73 to:
% 13.23/3.61 | (419) ~ (all_0_40_40 = e3)
% 13.23/3.61 |
% 13.23/3.61 | Equations (637) can reduce 299 to:
% 13.23/3.61 | (145) ~ (e3 = e1)
% 13.23/3.61 |
% 13.23/3.61 +-Applying beta-rule and splitting (802), into two cases.
% 13.23/3.61 |-Branch one:
% 13.23/3.61 | (473) all_0_40_40 = e0
% 13.23/3.61 |
% 13.23/3.61 | Equations (473) can reduce 419 to:
% 13.23/3.61 | (480) ~ (e3 = e0)
% 13.23/3.61 |
% 13.23/3.61 | Simplifying 480 yields:
% 13.23/3.61 | (74) ~ (e3 = e0)
% 13.23/3.61 |
% 13.23/3.61 | From (473) and (57) follows:
% 13.23/3.61 | (809) op(e4, e0) = all_0_9_9
% 13.23/3.61 |
% 13.23/3.61 | From (473) and (235) follows:
% 13.23/3.61 | (810) op(e4, e3) = e0
% 13.23/3.61 |
% 13.23/3.61 +-Applying beta-rule and splitting (248), into two cases.
% 13.23/3.61 |-Branch one:
% 13.23/3.61 | (811) all_0_49_49 = e1
% 13.23/3.61 |
% 13.23/3.61 | Equations (811) can reduce 325 to:
% 13.23/3.61 | (303) $false
% 13.23/3.61 |
% 13.23/3.61 |-The branch is then unsatisfiable
% 13.23/3.61 |-Branch two:
% 13.23/3.61 | (325) ~ (all_0_49_49 = e1)
% 13.23/3.61 | (814) all_0_49_49 = e4 | all_0_49_49 = e0
% 13.23/3.61 |
% 13.23/3.61 +-Applying beta-rule and splitting (121), into two cases.
% 13.23/3.61 |-Branch one:
% 13.23/3.62 | (815) all_0_44_44 = e0
% 13.23/3.62 |
% 13.23/3.62 | Combining equations (775,815) yields a new equation:
% 13.23/3.62 | (574) e3 = e0
% 13.23/3.62 |
% 13.23/3.62 | Simplifying 574 yields:
% 13.23/3.62 | (575) e3 = e0
% 13.23/3.62 |
% 13.23/3.62 | Equations (575) can reduce 74 to:
% 13.23/3.62 | (303) $false
% 13.23/3.62 |
% 13.23/3.62 |-The branch is then unsatisfiable
% 13.23/3.62 |-Branch two:
% 13.23/3.62 | (819) ~ (all_0_44_44 = e0)
% 13.23/3.62 | (820) all_0_49_49 = e0 | all_0_56_56 = e0
% 13.23/3.62 |
% 13.23/3.62 | Equations (775) can reduce 819 to:
% 13.23/3.62 | (74) ~ (e3 = e0)
% 13.23/3.62 |
% 13.23/3.62 +-Applying beta-rule and splitting (124), into two cases.
% 13.23/3.62 |-Branch one:
% 13.23/3.62 | (486) all_0_42_42 = e0
% 13.23/3.62 |
% 13.23/3.62 | Combining equations (495,486) yields a new equation:
% 13.23/3.62 | (574) e3 = e0
% 13.23/3.62 |
% 13.23/3.62 | Simplifying 574 yields:
% 13.23/3.62 | (575) e3 = e0
% 13.23/3.62 |
% 13.23/3.62 | Equations (575) can reduce 74 to:
% 13.23/3.62 | (303) $false
% 13.23/3.62 |
% 13.23/3.62 |-The branch is then unsatisfiable
% 13.23/3.62 |-Branch two:
% 13.23/3.62 | (475) ~ (all_0_42_42 = e0)
% 13.23/3.62 | (489) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_59_59 = e0
% 13.23/3.62 |
% 13.23/3.62 +-Applying beta-rule and splitting (814), into two cases.
% 13.23/3.62 |-Branch one:
% 13.23/3.62 | (466) all_0_49_49 = e0
% 13.23/3.62 |
% 13.23/3.62 | Equations (466) can reduce 151 to:
% 13.23/3.62 | (469) ~ (e2 = e0)
% 13.23/3.62 |
% 13.23/3.62 | Simplifying 469 yields:
% 13.23/3.62 | (61) ~ (e2 = e0)
% 13.23/3.62 |
% 13.23/3.62 | Equations (466) can reduce 325 to:
% 13.23/3.62 | (471) ~ (e1 = e0)
% 13.23/3.62 |
% 13.23/3.62 | Simplifying 471 yields:
% 13.23/3.62 | (143) ~ (e1 = e0)
% 13.23/3.62 |
% 13.23/3.62 | From (466) and (154) follows:
% 13.23/3.62 | (833) op(e4, e0) = all_0_2_2
% 13.23/3.62 |
% 13.23/3.62 +-Applying beta-rule and splitting (489), into two cases.
% 13.23/3.62 |-Branch one:
% 13.23/3.62 | (490) all_0_47_47 = e0
% 13.23/3.62 |
% 13.23/3.62 | Equations (490) can reduce 602 to:
% 13.23/3.62 | (480) ~ (e3 = e0)
% 13.23/3.62 |
% 13.23/3.62 | Simplifying 480 yields:
% 13.23/3.62 | (74) ~ (e3 = e0)
% 13.23/3.62 |
% 13.23/3.62 | Equations (490) can reduce 357 to:
% 13.23/3.62 | (469) ~ (e2 = e0)
% 13.23/3.62 |
% 13.23/3.62 | Simplifying 469 yields:
% 13.23/3.62 | (61) ~ (e2 = e0)
% 13.23/3.62 |
% 13.23/3.62 | Instantiating formula (39) with e4, e4, all_0_6_6, e2 and discharging atoms op(e4, e4) = all_0_6_6, op(e4, e4) = e2, yields:
% 13.23/3.62 | (839) all_0_6_6 = e2
% 13.23/3.62 |
% 13.23/3.62 | Instantiating formula (39) with e4, e3, e0, all_0_0_0 and discharging atoms op(e4, e3) = all_0_0_0, op(e4, e3) = e0, yields:
% 13.23/3.62 | (840) all_0_0_0 = e0
% 13.23/3.62 |
% 13.23/3.62 | Instantiating formula (39) with e4, e0, all_0_2_2, e4 and discharging atoms op(e4, e0) = all_0_2_2, op(e4, e0) = e4, yields:
% 13.23/3.62 | (841) all_0_2_2 = e4
% 13.23/3.62 |
% 13.23/3.62 | Instantiating formula (39) with e4, e0, all_0_9_9, all_0_2_2 and discharging atoms op(e4, e0) = all_0_2_2, op(e4, e0) = all_0_9_9, yields:
% 13.54/3.62 | (842) all_0_2_2 = all_0_9_9
% 13.54/3.62 |
% 13.54/3.62 | Combining equations (841,842) yields a new equation:
% 13.54/3.62 | (843) all_0_9_9 = e4
% 13.54/3.62 |
% 13.54/3.62 | Combining equations (843,842) yields a new equation:
% 13.54/3.62 | (841) all_0_2_2 = e4
% 13.54/3.62 |
% 13.54/3.62 +-Applying beta-rule and splitting (155), into two cases.
% 13.54/3.62 |-Branch one:
% 13.54/3.62 | (845) (all_0_0_0 = e3 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e2 & ~ (all_0_3_3 = e4)) | (all_0_4_4 = e1 & ~ (all_0_5_5 = e4))
% 13.54/3.62 |
% 13.54/3.62 +-Applying beta-rule and splitting (845), into two cases.
% 13.54/3.62 |-Branch one:
% 13.54/3.62 | (846) (all_0_0_0 = e3 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e2 & ~ (all_0_3_3 = e4))
% 13.54/3.62 |
% 13.54/3.62 +-Applying beta-rule and splitting (846), into two cases.
% 13.54/3.62 |-Branch one:
% 13.54/3.62 | (847) all_0_0_0 = e3 & ~ (all_0_1_1 = e4)
% 13.54/3.62 |
% 13.54/3.62 | Applying alpha-rule on (847) yields:
% 13.54/3.62 | (848) all_0_0_0 = e3
% 13.54/3.62 | (849) ~ (all_0_1_1 = e4)
% 13.54/3.62 |
% 13.54/3.62 | Combining equations (848,840) yields a new equation:
% 13.54/3.62 | (574) e3 = e0
% 13.54/3.62 |
% 13.54/3.62 | Simplifying 574 yields:
% 13.54/3.62 | (575) e3 = e0
% 13.54/3.62 |
% 13.54/3.62 | Equations (575) can reduce 74 to:
% 13.54/3.62 | (303) $false
% 13.54/3.62 |
% 13.54/3.62 |-The branch is then unsatisfiable
% 13.54/3.62 |-Branch two:
% 13.54/3.62 | (853) all_0_2_2 = e2 & ~ (all_0_3_3 = e4)
% 13.54/3.62 |
% 13.54/3.62 | Applying alpha-rule on (853) yields:
% 13.54/3.62 | (854) all_0_2_2 = e2
% 13.54/3.62 | (855) ~ (all_0_3_3 = e4)
% 13.54/3.62 |
% 13.54/3.62 | Combining equations (854,841) yields a new equation:
% 13.54/3.62 | (434) e4 = e2
% 13.54/3.62 |
% 13.54/3.62 | Equations (434) can reduce 227 to:
% 13.54/3.62 | (303) $false
% 13.54/3.62 |
% 13.54/3.62 |-The branch is then unsatisfiable
% 13.54/3.62 |-Branch two:
% 13.54/3.62 | (858) all_0_4_4 = e1 & ~ (all_0_5_5 = e4)
% 13.54/3.62 |
% 13.54/3.62 | Applying alpha-rule on (858) yields:
% 13.54/3.62 | (859) all_0_4_4 = e1
% 13.54/3.62 | (860) ~ (all_0_5_5 = e4)
% 13.54/3.62 |
% 13.54/3.62 | Combining equations (859,796) yields a new equation:
% 13.54/3.62 | (414) e3 = e1
% 13.54/3.62 |
% 13.54/3.62 | Equations (414) can reduce 145 to:
% 13.54/3.62 | (303) $false
% 13.54/3.62 |
% 13.54/3.62 |-The branch is then unsatisfiable
% 13.54/3.62 |-Branch two:
% 13.54/3.62 | (863) all_0_6_6 = e0 & ~ (all_0_7_7 = e4)
% 13.54/3.62 |
% 13.54/3.62 | Applying alpha-rule on (863) yields:
% 13.54/3.62 | (864) all_0_6_6 = e0
% 13.54/3.62 | (865) ~ (all_0_7_7 = e4)
% 13.54/3.62 |
% 13.54/3.62 | Combining equations (864,839) yields a new equation:
% 13.54/3.62 | (559) e2 = e0
% 13.54/3.62 |
% 13.54/3.62 | Equations (559) can reduce 61 to:
% 13.54/3.62 | (303) $false
% 13.54/3.62 |
% 13.54/3.62 |-The branch is then unsatisfiable
% 13.54/3.62 |-Branch two:
% 13.54/3.62 | (607) ~ (all_0_47_47 = e0)
% 13.54/3.62 | (608) all_0_51_51 = e0 | all_0_59_59 = e0
% 13.54/3.62 |
% 13.54/3.62 +-Applying beta-rule and splitting (608), into two cases.
% 13.54/3.62 |-Branch one:
% 13.54/3.62 | (609) all_0_51_51 = e0
% 13.54/3.62 |
% 13.54/3.62 | Combining equations (383,609) yields a new equation:
% 13.54/3.62 | (558) e2 = e0
% 13.54/3.62 |
% 13.54/3.62 | Simplifying 558 yields:
% 13.54/3.62 | (559) e2 = e0
% 13.54/3.62 |
% 13.54/3.62 | Equations (559) can reduce 61 to:
% 13.54/3.62 | (303) $false
% 13.54/3.62 |
% 13.54/3.62 |-The branch is then unsatisfiable
% 13.54/3.62 |-Branch two:
% 13.54/3.62 | (613) ~ (all_0_51_51 = e0)
% 13.54/3.62 | (614) all_0_59_59 = e0
% 13.54/3.62 |
% 13.54/3.62 | Combining equations (341,614) yields a new equation:
% 13.54/3.62 | (301) e1 = e0
% 13.54/3.62 |
% 13.54/3.62 | Simplifying 301 yields:
% 13.54/3.62 | (302) e1 = e0
% 13.54/3.62 |
% 13.54/3.62 | Equations (302) can reduce 143 to:
% 13.54/3.62 | (303) $false
% 13.54/3.62 |
% 13.54/3.62 |-The branch is then unsatisfiable
% 13.54/3.62 |-Branch two:
% 13.54/3.62 | (879) ~ (all_0_49_49 = e0)
% 13.54/3.62 | (528) all_0_49_49 = e4
% 13.54/3.62 |
% 13.54/3.62 | Equations (528) can reduce 531 to:
% 13.54/3.62 | (303) $false
% 13.54/3.62 |
% 13.54/3.62 |-The branch is then unsatisfiable
% 13.54/3.62 |-Branch two:
% 13.54/3.62 | (617) ~ (all_0_40_40 = e0)
% 13.54/3.62 | (883) all_0_40_40 = e4 | all_0_40_40 = e3
% 13.54/3.62 |
% 13.54/3.62 +-Applying beta-rule and splitting (883), into two cases.
% 13.54/3.62 |-Branch one:
% 13.54/3.62 | (884) all_0_40_40 = e3
% 13.54/3.62 |
% 13.54/3.62 | Equations (884) can reduce 419 to:
% 13.54/3.62 | (303) $false
% 13.54/3.62 |
% 13.54/3.62 |-The branch is then unsatisfiable
% 13.54/3.62 |-Branch two:
% 13.54/3.62 | (419) ~ (all_0_40_40 = e3)
% 13.54/3.62 | (511) all_0_40_40 = e4
% 13.54/3.62 |
% 13.54/3.62 | Equations (511) can reduce 514 to:
% 13.54/3.62 | (303) $false
% 13.54/3.62 |
% 13.54/3.62 |-The branch is then unsatisfiable
% 13.54/3.62 |-Branch two:
% 13.54/3.62 | (640) ~ (all_0_57_57 = e3)
% 13.54/3.62 | (890) all_0_57_57 = e4 | all_0_57_57 = e2
% 13.54/3.62 |
% 13.54/3.62 +-Applying beta-rule and splitting (890), into two cases.
% 13.54/3.62 |-Branch one:
% 13.54/3.62 | (891) all_0_57_57 = e4
% 13.54/3.62 |
% 13.54/3.62 | Equations (891) can reduce 764 to:
% 13.54/3.62 | (303) $false
% 13.54/3.62 |
% 13.54/3.62 |-The branch is then unsatisfiable
% 13.54/3.62 |-Branch two:
% 13.54/3.62 | (764) ~ (all_0_57_57 = e4)
% 13.54/3.62 | (407) all_0_57_57 = e2
% 13.54/3.62 |
% 13.54/3.62 | Equations (407) can reduce 717 to:
% 13.54/3.62 | (303) $false
% 13.54/3.62 |
% 13.54/3.62 |-The branch is then unsatisfiable
% 13.54/3.63 |-Branch two:
% 13.54/3.63 | (597) ~ (all_0_42_42 = e3)
% 13.54/3.63 | (598) all_0_47_47 = e3 | all_0_59_59 = e3
% 13.54/3.63 |
% 13.54/3.63 +-Applying beta-rule and splitting (598), into two cases.
% 13.54/3.63 |-Branch one:
% 13.54/3.63 | (599) all_0_47_47 = e3
% 13.54/3.63 |
% 13.54/3.63 | Equations (599) can reduce 602 to:
% 13.54/3.63 | (303) $false
% 13.54/3.63 |
% 13.54/3.63 |-The branch is then unsatisfiable
% 13.54/3.63 |-Branch two:
% 13.54/3.63 | (602) ~ (all_0_47_47 = e3)
% 13.54/3.63 | (603) all_0_59_59 = e3
% 13.54/3.63 |
% 13.54/3.63 | Combining equations (603,341) yields a new equation:
% 13.54/3.63 | (604) e3 = e1
% 13.54/3.63 |
% 13.54/3.63 | Simplifying 604 yields:
% 13.54/3.63 | (414) e3 = e1
% 13.54/3.63 |
% 13.54/3.63 | Equations (414) can reduce 145 to:
% 13.54/3.63 | (303) $false
% 13.54/3.63 |
% 13.54/3.63 |-The branch is then unsatisfiable
% 13.54/3.63 |-Branch two:
% 13.54/3.63 | (577) ~ (all_0_50_50 = e4)
% 13.54/3.63 | (891) all_0_57_57 = e4
% 13.54/3.63 |
% 13.54/3.63 | Equations (891) can reduce 764 to:
% 13.54/3.63 | (303) $false
% 13.54/3.63 |
% 13.54/3.63 |-The branch is then unsatisfiable
% 13.54/3.63 |-Branch two:
% 13.54/3.63 | (908) ~ (all_0_44_44 = e3)
% 13.54/3.63 | (909) all_0_53_53 = e3 | all_0_56_56 = e3
% 13.54/3.63 |
% 13.54/3.63 +-Applying beta-rule and splitting (909), into two cases.
% 13.54/3.63 |-Branch one:
% 13.54/3.63 | (413) all_0_53_53 = e3
% 13.54/3.63 |
% 13.54/3.63 | Combining equations (275,413) yields a new equation:
% 13.54/3.63 | (414) e3 = e1
% 13.54/3.63 |
% 13.54/3.63 | Equations (414) can reduce 145 to:
% 13.54/3.63 | (303) $false
% 13.54/3.63 |
% 13.54/3.63 |-The branch is then unsatisfiable
% 13.54/3.63 |-Branch two:
% 13.54/3.63 | (416) ~ (all_0_53_53 = e3)
% 13.54/3.63 | (431) all_0_56_56 = e3
% 13.54/3.63 |
% 13.54/3.63 | Combining equations (431,762) yields a new equation:
% 13.54/3.63 | (524) e4 = e3
% 13.54/3.63 |
% 13.54/3.63 | Equations (524) can reduce 30 to:
% 13.54/3.63 | (303) $false
% 13.54/3.63 |
% 13.54/3.63 |-The branch is then unsatisfiable
% 13.54/3.63 |-Branch two:
% 13.54/3.63 | (917) all_0_33_33 = e3 & ~ (all_0_34_34 = e0)
% 13.54/3.63 |
% 13.54/3.63 | Applying alpha-rule on (917) yields:
% 13.54/3.63 | (918) all_0_33_33 = e3
% 13.54/3.63 | (919) ~ (all_0_34_34 = e0)
% 13.54/3.63 |
% 13.54/3.63 | Combining equations (918,755) yields a new equation:
% 13.54/3.63 | (552) e3 = e2
% 13.54/3.63 |
% 13.54/3.63 | Simplifying 552 yields:
% 13.54/3.63 | (553) e3 = e2
% 13.54/3.63 |
% 13.54/3.63 | Equations (553) can reduce 209 to:
% 13.54/3.63 | (303) $false
% 13.54/3.63 |
% 13.54/3.63 |-The branch is then unsatisfiable
% 13.54/3.63 |-Branch two:
% 13.54/3.63 | (923) all_0_35_35 = e2 & ~ (all_0_36_36 = e0)
% 13.54/3.63 |
% 13.54/3.63 | Applying alpha-rule on (923) yields:
% 13.54/3.63 | (924) all_0_35_35 = e2
% 13.54/3.63 | (925) ~ (all_0_36_36 = e0)
% 13.54/3.63 |
% 13.54/3.63 | Combining equations (354,924) yields a new equation:
% 13.54/3.63 | (369) e2 = e1
% 13.54/3.63 |
% 13.54/3.63 | Equations (369) can reduce 150 to:
% 13.54/3.63 | (303) $false
% 13.54/3.63 |
% 13.54/3.63 |-The branch is then unsatisfiable
% 13.54/3.63 |-Branch two:
% 13.54/3.63 | (928) all_0_37_37 = e1 & ~ (all_0_38_38 = e0)
% 13.54/3.63 |
% 13.54/3.63 | Applying alpha-rule on (928) yields:
% 13.54/3.63 | (929) all_0_37_37 = e1
% 13.54/3.63 | (930) ~ (all_0_38_38 = e0)
% 13.54/3.63 |
% 13.54/3.63 | Combining equations (754,929) yields a new equation:
% 13.54/3.63 | (931) all_0_57_57 = e1
% 13.54/3.63 |
% 13.54/3.63 | Simplifying 931 yields:
% 13.54/3.63 | (333) all_0_57_57 = e1
% 13.54/3.63 |
% 13.54/3.63 | Equations (333) can reduce 299 to:
% 13.54/3.63 | (303) $false
% 13.54/3.63 |
% 13.54/3.63 |-The branch is then unsatisfiable
% 13.54/3.63 |-Branch two:
% 13.54/3.63 | (572) ~ (all_0_55_55 = e3)
% 13.54/3.63 | (573) all_0_60_60 = e3
% 13.54/3.63 |
% 13.54/3.63 | Combining equations (305,573) yields a new equation:
% 13.54/3.63 | (575) e3 = e0
% 13.54/3.63 |
% 13.54/3.63 | Equations (575) can reduce 74 to:
% 13.54/3.63 | (303) $false
% 13.54/3.63 |
% 13.54/3.63 |-The branch is then unsatisfiable
% 13.54/3.63 |-Branch two:
% 13.54/3.63 | (654) ~ (all_0_51_51 = e2)
% 13.54/3.63 | (655) all_0_59_59 = e2
% 13.54/3.63 |
% 13.54/3.63 | Combining equations (341,655) yields a new equation:
% 13.54/3.63 | (369) e2 = e1
% 13.54/3.63 |
% 13.54/3.63 | Equations (369) can reduce 150 to:
% 13.54/3.63 | (303) $false
% 13.54/3.63 |
% 13.54/3.63 |-The branch is then unsatisfiable
% 13.54/3.63 |-Branch two:
% 13.54/3.63 | (359) ~ (all_0_48_48 = e2)
% 13.54/3.63 | (367) all_0_52_52 = e2 | all_0_55_55 = e2 | all_0_60_60 = e2
% 13.54/3.63 |
% 13.54/3.63 +-Applying beta-rule and splitting (193), into two cases.
% 13.54/3.63 |-Branch one:
% 13.54/3.63 | (395) all_0_45_45 = e2
% 13.54/3.63 |
% 13.54/3.63 | Combining equations (289,395) yields a new equation:
% 13.54/3.63 | (369) e2 = e1
% 13.54/3.63 |
% 13.54/3.63 | Equations (369) can reduce 150 to:
% 13.54/3.63 | (303) $false
% 13.54/3.63 |
% 13.54/3.63 |-The branch is then unsatisfiable
% 13.54/3.63 |-Branch two:
% 13.54/3.63 | (398) ~ (all_0_45_45 = e2)
% 13.54/3.63 | (948) all_0_46_46 = e2 | all_0_47_47 = e2 | all_0_48_48 = e2
% 13.54/3.63 |
% 13.54/3.63 | Equations (289) can reduce 398 to:
% 13.54/3.63 | (267) ~ (e2 = e1)
% 13.54/3.63 |
% 13.54/3.63 | Simplifying 267 yields:
% 13.54/3.63 | (150) ~ (e2 = e1)
% 13.54/3.63 |
% 13.54/3.63 +-Applying beta-rule and splitting (367), into two cases.
% 13.54/3.63 |-Branch one:
% 13.54/3.63 | (368) all_0_52_52 = e2
% 13.54/3.63 |
% 13.54/3.63 | Combining equations (322,368) yields a new equation:
% 13.54/3.63 | (369) e2 = e1
% 13.54/3.63 |
% 13.54/3.63 | Equations (369) can reduce 150 to:
% 13.54/3.63 | (303) $false
% 13.54/3.63 |
% 13.54/3.63 |-The branch is then unsatisfiable
% 13.54/3.63 |-Branch two:
% 13.54/3.63 | (371) ~ (all_0_52_52 = e2)
% 13.54/3.63 | (372) all_0_55_55 = e2 | all_0_60_60 = e2
% 13.54/3.63 |
% 13.54/3.63 +-Applying beta-rule and splitting (372), into two cases.
% 13.54/3.63 |-Branch one:
% 13.54/3.63 | (373) all_0_55_55 = e2
% 13.54/3.63 |
% 13.54/3.63 | Equations (373) can reduce 633 to:
% 13.54/3.63 | (303) $false
% 13.54/3.63 |
% 13.54/3.63 |-The branch is then unsatisfiable
% 13.54/3.63 |-Branch two:
% 13.54/3.63 | (633) ~ (all_0_55_55 = e2)
% 13.54/3.63 | (659) all_0_60_60 = e2
% 13.54/3.63 |
% 13.54/3.63 | Combining equations (305,659) yields a new equation:
% 13.54/3.63 | (559) e2 = e0
% 13.54/3.63 |
% 13.54/3.63 | Equations (559) can reduce 61 to:
% 13.54/3.63 | (303) $false
% 13.54/3.63 |
% 13.54/3.63 |-The branch is then unsatisfiable
% 13.54/3.63 |-Branch two:
% 13.54/3.63 | (375) ~ (all_0_54_54 = e2)
% 13.54/3.63 | (373) all_0_55_55 = e2
% 13.54/3.63 |
% 13.54/3.63 | Equations (373) can reduce 633 to:
% 13.54/3.63 | (303) $false
% 13.54/3.63 |
% 13.54/3.63 |-The branch is then unsatisfiable
% 13.54/3.63 |-Branch two:
% 13.54/3.63 | (582) ~ (all_0_43_43 = e4)
% 13.54/3.63 | (583) all_0_48_48 = e4 | all_0_52_52 = e4 | all_0_60_60 = e4
% 13.54/3.63 |
% 13.54/3.63 +-Applying beta-rule and splitting (21), into two cases.
% 13.54/3.63 |-Branch one:
% 13.54/3.63 | (511) all_0_40_40 = e4
% 13.54/3.63 |
% 13.54/3.63 | Equations (511) can reduce 189 to:
% 13.54/3.63 | (968) ~ (all_0_42_42 = e4)
% 13.54/3.63 |
% 13.54/3.63 | Simplifying 968 yields:
% 13.54/3.63 | (144) ~ (all_0_42_42 = e4)
% 13.54/3.63 |
% 13.54/3.63 | Equations (511) can reduce 48 to:
% 13.54/3.63 | (970) ~ (all_0_50_50 = e4)
% 13.54/3.63 |
% 13.54/3.63 | Simplifying 970 yields:
% 13.54/3.63 | (577) ~ (all_0_50_50 = e4)
% 13.54/3.63 |
% 13.54/3.64 | Equations (511) can reduce 73 to:
% 13.54/3.64 | (763) ~ (all_0_57_57 = e4)
% 13.54/3.64 |
% 13.54/3.64 | Simplifying 763 yields:
% 13.54/3.64 | (764) ~ (all_0_57_57 = e4)
% 13.54/3.64 |
% 13.54/3.64 | Equations (511) can reduce 258 to:
% 13.54/3.64 | (253) ~ (e4 = e1)
% 13.54/3.64 |
% 13.54/3.64 +-Applying beta-rule and splitting (195), into two cases.
% 13.54/3.64 |-Branch one:
% 13.54/3.64 | (762) all_0_56_56 = e4
% 13.54/3.64 |
% 13.54/3.64 | Equations (762) can reduce 224 to:
% 13.54/3.64 | (531) ~ (all_0_49_49 = e4)
% 13.54/3.64 |
% 13.54/3.64 | Equations (762) can reduce 282 to:
% 13.54/3.64 | (253) ~ (e4 = e1)
% 13.54/3.64 |
% 13.54/3.64 +-Applying beta-rule and splitting (88), into two cases.
% 13.54/3.64 |-Branch one:
% 13.54/3.64 | (528) all_0_49_49 = e4
% 13.54/3.64 |
% 13.54/3.64 | Equations (528) can reduce 531 to:
% 13.54/3.64 | (303) $false
% 13.54/3.64 |
% 13.54/3.64 |-The branch is then unsatisfiable
% 13.54/3.64 |-Branch two:
% 13.54/3.64 | (531) ~ (all_0_49_49 = e4)
% 13.54/3.64 | (532) all_0_50_50 = e4 | all_0_52_52 = e4
% 13.54/3.64 |
% 13.54/3.64 +-Applying beta-rule and splitting (532), into two cases.
% 13.54/3.64 |-Branch one:
% 13.54/3.64 | (533) all_0_50_50 = e4
% 13.54/3.64 |
% 13.54/3.64 | Equations (533) can reduce 577 to:
% 13.54/3.64 | (303) $false
% 13.54/3.64 |
% 13.54/3.64 |-The branch is then unsatisfiable
% 13.54/3.64 |-Branch two:
% 13.54/3.64 | (577) ~ (all_0_50_50 = e4)
% 13.54/3.64 | (578) all_0_52_52 = e4
% 13.54/3.64 |
% 13.54/3.64 | Combining equations (322,578) yields a new equation:
% 13.54/3.64 | (427) e4 = e1
% 13.54/3.64 |
% 13.54/3.64 | Equations (427) can reduce 253 to:
% 13.54/3.64 | (303) $false
% 13.54/3.64 |
% 13.54/3.64 |-The branch is then unsatisfiable
% 13.54/3.64 |-Branch two:
% 13.54/3.64 | (988) ~ (all_0_56_56 = e4)
% 13.54/3.64 | (989) all_0_57_57 = e4 | all_0_58_58 = e4 | all_0_60_60 = e4
% 13.54/3.64 |
% 13.54/3.64 +-Applying beta-rule and splitting (88), into two cases.
% 13.54/3.64 |-Branch one:
% 13.54/3.64 | (528) all_0_49_49 = e4
% 13.54/3.64 |
% 13.54/3.64 | Equations (528) can reduce 123 to:
% 13.54/3.64 | (970) ~ (all_0_50_50 = e4)
% 13.54/3.64 |
% 13.54/3.64 | Simplifying 970 yields:
% 13.54/3.64 | (577) ~ (all_0_50_50 = e4)
% 13.54/3.64 |
% 13.54/3.64 | Equations (528) can reduce 151 to:
% 13.54/3.64 | (227) ~ (e4 = e2)
% 13.54/3.64 |
% 13.54/3.64 +-Applying beta-rule and splitting (64), into two cases.
% 13.54/3.64 |-Branch one:
% 13.54/3.64 | (473) all_0_40_40 = e0
% 13.54/3.64 |
% 13.54/3.64 | Combining equations (511,473) yields a new equation:
% 13.54/3.64 | (995) e4 = e0
% 13.54/3.64 |
% 13.54/3.64 | Simplifying 995 yields:
% 13.54/3.64 | (512) e4 = e0
% 13.54/3.64 |
% 13.54/3.64 | Equations (512) can reduce 5 to:
% 13.54/3.64 | (303) $false
% 13.54/3.64 |
% 13.54/3.64 |-The branch is then unsatisfiable
% 13.54/3.64 |-Branch two:
% 13.54/3.64 | (617) ~ (all_0_40_40 = e0)
% 13.54/3.64 | (999) all_0_42_42 = e0 | all_0_43_43 = e0
% 13.54/3.64 |
% 13.54/3.64 +-Applying beta-rule and splitting (999), into two cases.
% 13.54/3.64 |-Branch one:
% 13.54/3.64 | (486) all_0_42_42 = e0
% 13.54/3.64 |
% 13.54/3.64 | Equations (486) can reduce 179 to:
% 13.54/3.64 | (1001) ~ (all_0_51_51 = e0)
% 13.54/3.64 |
% 13.54/3.64 | Simplifying 1001 yields:
% 13.54/3.64 | (613) ~ (all_0_51_51 = e0)
% 13.54/3.64 |
% 13.54/3.64 | Equations (486) can reduce 144 to:
% 13.54/3.64 | (516) ~ (e4 = e0)
% 13.54/3.64 |
% 13.54/3.64 | Simplifying 516 yields:
% 13.54/3.64 | (5) ~ (e4 = e0)
% 13.54/3.64 |
% 13.54/3.64 | Equations (486) can reduce 260 to:
% 13.54/3.64 | (471) ~ (e1 = e0)
% 13.54/3.64 |
% 13.54/3.64 | Simplifying 471 yields:
% 13.54/3.64 | (143) ~ (e1 = e0)
% 13.54/3.64 |
% 13.54/3.64 +-Applying beta-rule and splitting (137), into two cases.
% 13.54/3.64 |-Branch one:
% 13.54/3.64 | (466) all_0_49_49 = e0
% 13.54/3.64 |
% 13.54/3.64 | Combining equations (528,466) yields a new equation:
% 13.54/3.64 | (995) e4 = e0
% 13.54/3.64 |
% 13.54/3.64 | Simplifying 995 yields:
% 13.54/3.64 | (512) e4 = e0
% 13.54/3.64 |
% 13.54/3.64 | Equations (512) can reduce 5 to:
% 13.54/3.64 | (303) $false
% 13.54/3.64 |
% 13.54/3.64 |-The branch is then unsatisfiable
% 13.54/3.64 |-Branch two:
% 13.54/3.64 | (879) ~ (all_0_49_49 = e0)
% 13.54/3.64 | (1012) all_0_50_50 = e0 | all_0_51_51 = e0 | all_0_52_52 = e0
% 13.54/3.64 |
% 13.54/3.64 +-Applying beta-rule and splitting (1012), into two cases.
% 13.54/3.64 |-Branch one:
% 13.54/3.64 | (518) all_0_50_50 = e0
% 13.54/3.64 |
% 13.54/3.64 | Equations (518) can reduce 577 to:
% 13.54/3.64 | (516) ~ (e4 = e0)
% 13.54/3.64 |
% 13.54/3.64 | Simplifying 516 yields:
% 13.54/3.64 | (5) ~ (e4 = e0)
% 13.54/3.64 |
% 13.54/3.64 +-Applying beta-rule and splitting (989), into two cases.
% 13.54/3.64 |-Branch one:
% 13.54/3.64 | (891) all_0_57_57 = e4
% 13.54/3.64 |
% 13.54/3.64 | Equations (891) can reduce 764 to:
% 13.54/3.64 | (303) $false
% 13.54/3.64 |
% 13.54/3.64 |-The branch is then unsatisfiable
% 13.54/3.64 |-Branch two:
% 13.54/3.64 | (764) ~ (all_0_57_57 = e4)
% 13.54/3.64 | (1019) all_0_58_58 = e4 | all_0_60_60 = e4
% 13.54/3.64 |
% 13.54/3.64 +-Applying beta-rule and splitting (1019), into two cases.
% 13.54/3.64 |-Branch one:
% 13.54/3.64 | (437) all_0_58_58 = e4
% 13.54/3.64 |
% 13.54/3.64 | Combining equations (664,437) yields a new equation:
% 13.54/3.64 | (434) e4 = e2
% 13.54/3.64 |
% 13.54/3.64 | Equations (434) can reduce 227 to:
% 13.54/3.64 | (303) $false
% 13.54/3.64 |
% 13.54/3.64 |-The branch is then unsatisfiable
% 13.54/3.64 |-Branch two:
% 13.54/3.64 | (1023) ~ (all_0_58_58 = e4)
% 13.54/3.64 | (1024) all_0_60_60 = e4
% 13.54/3.64 |
% 13.54/3.64 | Combining equations (305,1024) yields a new equation:
% 13.54/3.64 | (512) e4 = e0
% 13.54/3.64 |
% 13.54/3.64 | Equations (512) can reduce 5 to:
% 13.54/3.64 | (303) $false
% 13.54/3.64 |
% 13.54/3.64 |-The branch is then unsatisfiable
% 13.54/3.64 |-Branch two:
% 13.54/3.64 | (468) ~ (all_0_50_50 = e0)
% 13.54/3.64 | (1028) all_0_51_51 = e0 | all_0_52_52 = e0
% 13.54/3.64 |
% 13.54/3.64 +-Applying beta-rule and splitting (1028), into two cases.
% 13.54/3.64 |-Branch one:
% 13.54/3.64 | (609) all_0_51_51 = e0
% 13.54/3.64 |
% 13.54/3.64 | Equations (609) can reduce 613 to:
% 13.54/3.64 | (303) $false
% 13.54/3.64 |
% 13.54/3.64 |-The branch is then unsatisfiable
% 13.54/3.64 |-Branch two:
% 13.54/3.64 | (613) ~ (all_0_51_51 = e0)
% 13.54/3.64 | (1032) all_0_52_52 = e0
% 13.54/3.64 |
% 13.54/3.64 | Combining equations (322,1032) yields a new equation:
% 13.54/3.64 | (301) e1 = e0
% 13.54/3.64 |
% 13.54/3.64 | Simplifying 301 yields:
% 13.54/3.64 | (302) e1 = e0
% 13.54/3.64 |
% 13.54/3.64 | Equations (302) can reduce 143 to:
% 13.54/3.64 | (303) $false
% 13.54/3.64 |
% 13.54/3.64 |-The branch is then unsatisfiable
% 13.54/3.64 |-Branch two:
% 13.54/3.64 | (475) ~ (all_0_42_42 = e0)
% 13.54/3.64 | (588) all_0_43_43 = e0
% 13.54/3.64 |
% 13.54/3.64 | Equations (588) can reduce 306 to:
% 13.54/3.64 | (303) $false
% 13.54/3.64 |
% 13.54/3.64 |-The branch is then unsatisfiable
% 13.54/3.64 |-Branch two:
% 13.54/3.64 | (531) ~ (all_0_49_49 = e4)
% 13.54/3.64 | (532) all_0_50_50 = e4 | all_0_52_52 = e4
% 13.54/3.64 |
% 13.54/3.64 +-Applying beta-rule and splitting (532), into two cases.
% 13.54/3.64 |-Branch one:
% 13.54/3.64 | (533) all_0_50_50 = e4
% 13.54/3.64 |
% 13.54/3.64 | Equations (533) can reduce 577 to:
% 13.54/3.64 | (303) $false
% 13.54/3.64 |
% 13.54/3.64 |-The branch is then unsatisfiable
% 13.54/3.64 |-Branch two:
% 13.54/3.64 | (577) ~ (all_0_50_50 = e4)
% 13.54/3.64 | (578) all_0_52_52 = e4
% 13.54/3.64 |
% 13.54/3.64 | Combining equations (322,578) yields a new equation:
% 13.54/3.64 | (427) e4 = e1
% 13.54/3.64 |
% 13.54/3.64 | Equations (427) can reduce 253 to:
% 13.54/3.64 | (303) $false
% 13.54/3.64 |
% 13.54/3.64 |-The branch is then unsatisfiable
% 13.54/3.64 |-Branch two:
% 13.54/3.64 | (514) ~ (all_0_40_40 = e4)
% 13.54/3.64 | (1048) all_0_41_41 = e4 | all_0_43_43 = e4
% 13.54/3.64 |
% 13.54/3.64 +-Applying beta-rule and splitting (1048), into two cases.
% 13.54/3.64 |-Branch one:
% 13.54/3.64 | (425) all_0_41_41 = e4
% 13.54/3.64 |
% 13.54/3.64 | Combining equations (257,425) yields a new equation:
% 13.54/3.64 | (427) e4 = e1
% 13.54/3.64 |
% 13.54/3.64 | Equations (427) can reduce 253 to:
% 13.54/3.64 | (303) $false
% 13.54/3.64 |
% 13.54/3.64 |-The branch is then unsatisfiable
% 13.54/3.64 |-Branch two:
% 13.54/3.64 | (429) ~ (all_0_41_41 = e4)
% 13.54/3.64 | (505) all_0_43_43 = e4
% 13.54/3.64 |
% 13.54/3.64 | Equations (505) can reduce 582 to:
% 13.54/3.64 | (303) $false
% 13.54/3.64 |
% 13.54/3.64 |-The branch is then unsatisfiable
% 13.54/3.64 |-Branch two:
% 13.54/3.64 | (436) ~ (all_0_46_46 = e4)
% 13.54/3.64 | (355) all_0_46_46 = e2
% 13.54/3.64 |
% 13.54/3.65 | Equations (355) can reduce 663 to:
% 13.54/3.65 | (303) $false
% 13.54/3.65 |
% 13.54/3.65 |-The branch is then unsatisfiable
% 13.54/3.65 |-Branch two:
% 13.54/3.65 | (1058) ~ (all_0_59_59 = e1)
% 13.54/3.65 | (1059) all_0_60_60 = e1
% 13.54/3.65 |
% 13.54/3.65 | Combining equations (1059,305) yields a new equation:
% 13.54/3.65 | (301) e1 = e0
% 13.54/3.65 |
% 13.54/3.65 | Simplifying 301 yields:
% 13.54/3.65 | (302) e1 = e0
% 13.54/3.65 |
% 13.54/3.65 | Equations (302) can reduce 143 to:
% 13.54/3.65 | (303) $false
% 13.54/3.65 |
% 13.54/3.65 |-The branch is then unsatisfiable
% 13.54/3.65 |-Branch two:
% 13.54/3.65 | (1063) ~ (all_0_52_52 = e1)
% 13.54/3.65 | (1064) all_0_55_55 = e1 | all_0_60_60 = e1
% 13.54/3.65 |
% 13.54/3.65 +-Applying beta-rule and splitting (1064), into two cases.
% 13.54/3.65 |-Branch one:
% 13.54/3.65 | (1065) all_0_55_55 = e1
% 13.54/3.65 |
% 13.54/3.65 | Equations (1065) can reduce 280 to:
% 13.54/3.65 | (303) $false
% 13.54/3.65 |
% 13.54/3.65 |-The branch is then unsatisfiable
% 13.54/3.65 |-Branch two:
% 13.54/3.65 | (280) ~ (all_0_55_55 = e1)
% 13.54/3.65 | (1059) all_0_60_60 = e1
% 13.54/3.65 |
% 13.54/3.65 | Combining equations (1059,305) yields a new equation:
% 13.54/3.65 | (301) e1 = e0
% 13.54/3.65 |
% 13.54/3.65 | Simplifying 301 yields:
% 13.54/3.65 | (302) e1 = e0
% 13.54/3.65 |
% 13.54/3.65 | Equations (302) can reduce 143 to:
% 13.54/3.65 | (303) $false
% 13.54/3.65 |
% 13.54/3.65 |-The branch is then unsatisfiable
% 13.54/3.65 |-Branch two:
% 13.54/3.65 | (1072) ~ (all_0_45_45 = e1)
% 13.54/3.65 | (1059) all_0_60_60 = e1
% 13.54/3.65 |
% 13.54/3.65 | Equations (1059) can reduce 93 to:
% 13.54/3.65 | (262) ~ (all_0_43_43 = e1)
% 13.54/3.65 |
% 13.54/3.65 | Equations (1059) can reduce 67 to:
% 13.54/3.65 | (295) ~ (all_0_48_48 = e1)
% 13.54/3.65 |
% 13.54/3.65 | Equations (1059) can reduce 117 to:
% 13.54/3.65 | (280) ~ (all_0_55_55 = e1)
% 13.54/3.65 |
% 13.54/3.65 | Equations (1059) can reduce 140 to:
% 13.54/3.65 | (282) ~ (all_0_56_56 = e1)
% 13.54/3.65 |
% 13.54/3.65 | Equations (1059) can reduce 18 to:
% 13.54/3.65 | (299) ~ (all_0_57_57 = e1)
% 13.54/3.65 |
% 13.54/3.65 | Equations (1059) can reduce 86 to:
% 13.54/3.65 | (266) ~ (all_0_58_58 = e1)
% 13.54/3.65 |
% 13.54/3.65 +-Applying beta-rule and splitting (25), into two cases.
% 13.54/3.65 |-Branch one:
% 13.54/3.65 | (300) all_0_45_45 = e0
% 13.54/3.65 |
% 13.54/3.65 | Equations (300) can reduce 156 to:
% 13.54/3.65 | (1081) ~ (all_0_47_47 = e0)
% 13.54/3.65 |
% 13.54/3.65 | Simplifying 1081 yields:
% 13.54/3.65 | (607) ~ (all_0_47_47 = e0)
% 13.54/3.65 |
% 13.54/3.65 | Equations (300) can reduce 122 to:
% 13.54/3.65 | (1083) ~ (all_0_57_57 = e0)
% 13.54/3.65 |
% 13.54/3.65 | Simplifying 1083 yields:
% 13.54/3.65 | (309) ~ (all_0_57_57 = e0)
% 13.54/3.65 |
% 13.54/3.65 | Equations (300) can reduce 1072 to:
% 13.54/3.65 | (471) ~ (e1 = e0)
% 13.54/3.65 |
% 13.54/3.65 | Simplifying 471 yields:
% 13.54/3.65 | (143) ~ (e1 = e0)
% 13.54/3.65 |
% 13.54/3.65 +-Applying beta-rule and splitting (114), into two cases.
% 13.54/3.65 |-Branch one:
% 13.54/3.65 | (1087) all_0_44_44 = e1
% 13.54/3.65 |
% 13.54/3.65 | Equations (1087) can reduce 276 to:
% 13.54/3.65 | (303) $false
% 13.54/3.65 |
% 13.54/3.65 |-The branch is then unsatisfiable
% 13.54/3.65 |-Branch two:
% 13.54/3.65 | (276) ~ (all_0_44_44 = e1)
% 13.54/3.65 | (1090) all_0_45_45 = e1 | all_0_46_46 = e1 | all_0_47_47 = e1 | all_0_48_48 = e1
% 13.54/3.65 |
% 13.54/3.65 +-Applying beta-rule and splitting (1090), into two cases.
% 13.54/3.65 |-Branch one:
% 13.54/3.65 | (289) all_0_45_45 = e1
% 13.54/3.65 |
% 13.54/3.65 | Combining equations (300,289) yields a new equation:
% 13.54/3.65 | (302) e1 = e0
% 13.54/3.65 |
% 13.54/3.65 | Equations (302) can reduce 143 to:
% 13.54/3.65 | (303) $false
% 13.54/3.65 |
% 13.54/3.65 |-The branch is then unsatisfiable
% 13.54/3.65 |-Branch two:
% 13.54/3.65 | (1072) ~ (all_0_45_45 = e1)
% 13.54/3.65 | (1095) all_0_46_46 = e1 | all_0_47_47 = e1 | all_0_48_48 = e1
% 13.54/3.65 |
% 13.54/3.65 +-Applying beta-rule and splitting (1095), into two cases.
% 13.54/3.65 |-Branch one:
% 13.54/3.65 | (669) all_0_46_46 = e1
% 13.54/3.65 |
% 13.54/3.65 | Equations (669) can reduce 264 to:
% 13.54/3.65 | (303) $false
% 13.54/3.65 |
% 13.54/3.65 |-The branch is then unsatisfiable
% 13.54/3.65 |-Branch two:
% 13.54/3.65 | (264) ~ (all_0_46_46 = e1)
% 13.54/3.65 | (1099) all_0_47_47 = e1 | all_0_48_48 = e1
% 13.54/3.65 |
% 13.54/3.65 +-Applying beta-rule and splitting (1099), into two cases.
% 13.54/3.65 |-Branch one:
% 13.54/3.65 | (1100) all_0_47_47 = e1
% 13.54/3.65 |
% 13.54/3.65 | Equations (1100) can reduce 29 to:
% 13.54/3.65 | (260) ~ (all_0_42_42 = e1)
% 13.54/3.65 |
% 13.54/3.65 | Equations (1100) can reduce 62 to:
% 13.54/3.65 | (276) ~ (all_0_44_44 = e1)
% 13.54/3.65 |
% 13.54/3.65 | Equations (1100) can reduce 119 to:
% 13.54/3.65 | (264) ~ (all_0_46_46 = e1)
% 13.54/3.65 |
% 13.54/3.65 | Equations (1100) can reduce 75 to:
% 13.54/3.65 | (346) ~ (e4 = e1)
% 13.54/3.65 |
% 13.54/3.65 | Simplifying 346 yields:
% 13.54/3.65 | (253) ~ (e4 = e1)
% 13.54/3.65 |
% 13.54/3.65 | Equations (1100) can reduce 607 to:
% 13.54/3.65 | (143) ~ (e1 = e0)
% 13.54/3.65 |
% 13.54/3.65 | From (1100) and (66) follows:
% 13.54/3.65 | (1107) op(e1, e1) = all_0_25_25
% 13.54/3.65 |
% 13.54/3.65 +-Applying beta-rule and splitting (190), into two cases.
% 13.54/3.65 |-Branch one:
% 13.54/3.65 | (799) all_0_40_40 = e1
% 13.54/3.65 |
% 13.54/3.65 | Equations (799) can reduce 258 to:
% 13.54/3.65 | (303) $false
% 13.54/3.65 |
% 13.54/3.65 |-The branch is then unsatisfiable
% 13.54/3.65 |-Branch two:
% 13.54/3.65 | (258) ~ (all_0_40_40 = e1)
% 13.54/3.65 | (1111) all_0_45_45 = e1 | all_0_50_50 = e1 | all_0_54_54 = e1 | all_0_57_57 = e1
% 13.54/3.65 |
% 13.54/3.65 +-Applying beta-rule and splitting (1111), into two cases.
% 13.54/3.65 |-Branch one:
% 13.54/3.65 | (289) all_0_45_45 = e1
% 13.54/3.65 |
% 13.54/3.65 | Combining equations (300,289) yields a new equation:
% 13.54/3.65 | (302) e1 = e0
% 13.54/3.65 |
% 13.54/3.65 | Equations (302) can reduce 143 to:
% 13.54/3.65 | (303) $false
% 13.54/3.65 |
% 13.54/3.65 |-The branch is then unsatisfiable
% 13.54/3.65 |-Branch two:
% 13.54/3.65 | (1072) ~ (all_0_45_45 = e1)
% 13.54/3.65 | (1116) all_0_50_50 = e1 | all_0_54_54 = e1 | all_0_57_57 = e1
% 13.54/3.65 |
% 13.54/3.65 +-Applying beta-rule and splitting (1116), into two cases.
% 13.54/3.65 |-Branch one:
% 13.54/3.65 | (501) all_0_50_50 = e1
% 13.54/3.65 |
% 13.54/3.65 | Equations (501) can reduce 123 to:
% 13.54/3.65 | (325) ~ (all_0_49_49 = e1)
% 13.54/3.65 |
% 13.54/3.65 | Equations (501) can reduce 116 to:
% 13.54/3.65 | (1119) ~ (all_0_51_51 = e1)
% 13.54/3.65 |
% 13.54/3.65 | Simplifying 1119 yields:
% 13.54/3.65 | (343) ~ (all_0_51_51 = e1)
% 13.54/3.65 |
% 13.54/3.65 | Equations (501) can reduce 188 to:
% 13.54/3.65 | (1121) ~ (all_0_52_52 = e1)
% 13.54/3.65 |
% 13.54/3.65 | Simplifying 1121 yields:
% 13.54/3.65 | (1063) ~ (all_0_52_52 = e1)
% 13.54/3.65 |
% 13.54/3.65 | Equations (501) can reduce 226 to:
% 13.54/3.65 | (277) ~ (all_0_54_54 = e1)
% 13.54/3.65 |
% 13.54/3.65 | Simplifying 277 yields:
% 13.54/3.65 | (278) ~ (all_0_54_54 = e1)
% 13.54/3.65 |
% 13.54/3.65 | Equations (501) can reduce 170 to:
% 13.54/3.65 | (298) ~ (all_0_57_57 = e1)
% 13.54/3.65 |
% 13.54/3.65 | Simplifying 298 yields:
% 13.54/3.65 | (299) ~ (all_0_57_57 = e1)
% 13.54/3.65 |
% 13.54/3.65 | Equations (501) can reduce 52 to:
% 13.54/3.65 | (329) ~ (e3 = e1)
% 13.54/3.65 |
% 13.54/3.65 | Simplifying 329 yields:
% 13.54/3.65 | (145) ~ (e3 = e1)
% 13.54/3.65 |
% 13.54/3.65 | Instantiating formula (39) with e1, e1, all_0_25_25, e4 and discharging atoms op(e1, e1) = all_0_25_25, op(e1, e1) = e4, yields:
% 13.54/3.65 | (1129) all_0_25_25 = e4
% 13.54/3.65 |
% 13.54/3.65 +-Applying beta-rule and splitting (85), into two cases.
% 13.54/3.65 |-Branch one:
% 13.54/3.65 | (355) all_0_46_46 = e2
% 13.54/3.65 |
% 13.54/3.65 | From (355) and (161) follows:
% 13.54/3.65 | (362) op(e3, e2) = all_0_20_20
% 13.54/3.65 |
% 13.54/3.65 | From (355) and (239) follows:
% 13.54/3.65 | (363) op(e3, e2) = e2
% 13.54/3.65 |
% 13.54/3.65 +-Applying beta-rule and splitting (7), into two cases.
% 13.54/3.65 |-Branch one:
% 13.54/3.65 | (337) all_0_58_58 = e1
% 13.54/3.66 |
% 13.54/3.66 | Equations (337) can reduce 266 to:
% 13.54/3.66 | (303) $false
% 13.54/3.66 |
% 13.54/3.66 |-The branch is then unsatisfiable
% 13.54/3.66 |-Branch two:
% 13.54/3.66 | (266) ~ (all_0_58_58 = e1)
% 13.54/3.66 | (1136) all_0_58_58 = e4 | all_0_58_58 = e2
% 13.54/3.66 |
% 13.54/3.66 +-Applying beta-rule and splitting (23), into two cases.
% 13.54/3.66 |-Branch one:
% 13.54/3.66 | (425) all_0_41_41 = e4
% 13.54/3.66 |
% 13.54/3.66 | Combining equations (257,425) yields a new equation:
% 13.54/3.66 | (427) e4 = e1
% 13.54/3.66 |
% 13.54/3.66 | Equations (427) can reduce 253 to:
% 13.54/3.66 | (303) $false
% 13.54/3.66 |
% 13.54/3.66 |-The branch is then unsatisfiable
% 13.54/3.66 |-Branch two:
% 13.54/3.66 | (429) ~ (all_0_41_41 = e4)
% 13.54/3.66 | (430) all_0_46_46 = e4 | all_0_58_58 = e4
% 13.54/3.66 |
% 13.54/3.66 +-Applying beta-rule and splitting (430), into two cases.
% 13.54/3.66 |-Branch one:
% 13.54/3.66 | (433) all_0_46_46 = e4
% 13.54/3.66 |
% 13.54/3.66 | Combining equations (355,433) yields a new equation:
% 13.54/3.66 | (434) e4 = e2
% 13.54/3.66 |
% 13.54/3.66 | Equations (434) can reduce 227 to:
% 13.54/3.66 | (303) $false
% 13.54/3.66 |
% 13.54/3.66 |-The branch is then unsatisfiable
% 13.54/3.66 |-Branch two:
% 13.54/3.66 | (436) ~ (all_0_46_46 = e4)
% 13.54/3.66 | (437) all_0_58_58 = e4
% 13.54/3.66 |
% 13.54/3.66 | Equations (437) can reduce 206 to:
% 13.54/3.66 | (988) ~ (all_0_56_56 = e4)
% 13.54/3.66 |
% 13.54/3.66 | Equations (437) can reduce 82 to:
% 13.54/3.66 | (764) ~ (all_0_57_57 = e4)
% 13.54/3.66 |
% 13.54/3.66 | Equations (437) can reduce 108 to:
% 13.54/3.66 | (1149) ~ (all_0_59_59 = e4)
% 13.54/3.66 |
% 13.54/3.66 | Simplifying 1149 yields:
% 13.54/3.66 | (8) ~ (all_0_59_59 = e4)
% 13.54/3.66 |
% 13.54/3.66 | Equations (437) can reduce 240 to:
% 13.54/3.66 | (30) ~ (e4 = e3)
% 13.54/3.66 |
% 13.54/3.66 | Equations (437) can reduce 266 to:
% 13.54/3.66 | (253) ~ (e4 = e1)
% 13.54/3.66 |
% 13.54/3.66 | Equations (437) can reduce 203 to:
% 13.54/3.66 | (5) ~ (e4 = e0)
% 13.54/3.66 |
% 13.54/3.66 | From (437) and (27) follows:
% 13.54/3.66 | (439) op(e2, e4) = all_0_21_21
% 13.54/3.66 |
% 13.54/3.66 +-Applying beta-rule and splitting (100), into two cases.
% 13.54/3.66 |-Branch one:
% 13.54/3.66 | (511) all_0_40_40 = e4
% 13.54/3.66 |
% 13.54/3.66 | Equations (511) can reduce 51 to:
% 13.54/3.66 | (1156) ~ (all_0_43_43 = e4)
% 13.54/3.66 |
% 13.54/3.66 | Simplifying 1156 yields:
% 13.54/3.66 | (582) ~ (all_0_43_43 = e4)
% 13.54/3.66 |
% 13.54/3.66 | Equations (511) can reduce 73 to:
% 13.54/3.66 | (763) ~ (all_0_57_57 = e4)
% 13.54/3.66 |
% 13.54/3.66 | Simplifying 763 yields:
% 13.54/3.66 | (764) ~ (all_0_57_57 = e4)
% 13.54/3.66 |
% 13.54/3.66 | Instantiating formula (39) with e3, e2, e2, all_0_20_20 and discharging atoms op(e3, e2) = all_0_20_20, op(e3, e2) = e2, yields:
% 13.54/3.66 | (446) all_0_20_20 = e2
% 13.54/3.66 |
% 13.54/3.66 | Instantiating formula (39) with e2, e4, all_0_21_21, all_0_49_49 and discharging atoms op(e2, e4) = all_0_21_21, op(e2, e4) = all_0_49_49, yields:
% 13.54/3.66 | (442) all_0_21_21 = all_0_49_49
% 13.54/3.66 |
% 13.54/3.66 +-Applying beta-rule and splitting (19), into two cases.
% 13.54/3.66 |-Branch one:
% 13.54/3.66 | (450) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2)) | (all_0_21_21 = e0 & ~ (all_0_22_22 = e2))
% 13.54/3.66 |
% 13.54/3.66 +-Applying beta-rule and splitting (450), into two cases.
% 13.54/3.66 |-Branch one:
% 13.54/3.66 | (451) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2))
% 13.54/3.66 |
% 13.54/3.66 +-Applying beta-rule and splitting (451), into two cases.
% 13.54/3.66 |-Branch one:
% 13.54/3.66 | (452) all_0_17_17 = e4 & ~ (all_0_18_18 = e2)
% 13.54/3.66 |
% 13.54/3.66 | Applying alpha-rule on (452) yields:
% 13.54/3.66 | (453) all_0_17_17 = e4
% 13.54/3.66 | (454) ~ (all_0_18_18 = e2)
% 13.54/3.66 |
% 13.54/3.66 | Combining equations (273,453) yields a new equation:
% 13.54/3.66 | (1167) all_0_51_51 = e4
% 13.54/3.66 |
% 13.54/3.66 | Simplifying 1167 yields:
% 13.54/3.66 | (697) all_0_51_51 = e4
% 13.54/3.66 |
% 13.54/3.66 | Equations (697) can reduce 56 to:
% 13.54/3.66 | (303) $false
% 13.54/3.66 |
% 13.54/3.66 |-The branch is then unsatisfiable
% 13.54/3.66 |-Branch two:
% 13.54/3.66 | (458) all_0_19_19 = e3 & ~ (all_0_20_20 = e2)
% 13.54/3.66 |
% 13.54/3.66 | Applying alpha-rule on (458) yields:
% 13.54/3.66 | (459) all_0_19_19 = e3
% 13.54/3.66 | (460) ~ (all_0_20_20 = e2)
% 13.54/3.66 |
% 13.54/3.66 | Equations (446) can reduce 460 to:
% 13.54/3.66 | (303) $false
% 13.54/3.66 |
% 13.54/3.66 |-The branch is then unsatisfiable
% 13.54/3.66 |-Branch two:
% 13.54/3.66 | (462) all_0_21_21 = e0 & ~ (all_0_22_22 = e2)
% 13.54/3.66 |
% 13.54/3.66 | Applying alpha-rule on (462) yields:
% 13.54/3.66 | (463) all_0_21_21 = e0
% 13.54/3.66 | (464) ~ (all_0_22_22 = e2)
% 13.54/3.66 |
% 13.54/3.66 | Combining equations (463,442) yields a new equation:
% 13.54/3.66 | (466) all_0_49_49 = e0
% 13.54/3.66 |
% 13.54/3.66 | Equations (466) can reduce 53 to:
% 13.54/3.66 | (819) ~ (all_0_44_44 = e0)
% 13.54/3.66 |
% 13.54/3.66 | Equations (466) can reduce 83 to:
% 13.54/3.66 | (1001) ~ (all_0_51_51 = e0)
% 13.54/3.66 |
% 13.54/3.66 | Simplifying 1001 yields:
% 13.54/3.66 | (613) ~ (all_0_51_51 = e0)
% 13.54/3.66 |
% 13.54/3.66 | Equations (466) can reduce 224 to:
% 13.54/3.66 | (1181) ~ (all_0_56_56 = e0)
% 13.54/3.66 |
% 13.54/3.66 | Simplifying 1181 yields:
% 13.54/3.66 | (1182) ~ (all_0_56_56 = e0)
% 13.54/3.66 |
% 13.54/3.66 | Equations (466) can reduce 325 to:
% 13.54/3.66 | (471) ~ (e1 = e0)
% 13.54/3.66 |
% 13.54/3.66 | Simplifying 471 yields:
% 13.54/3.66 | (143) ~ (e1 = e0)
% 13.54/3.66 |
% 13.54/3.66 +-Applying beta-rule and splitting (202), into two cases.
% 13.54/3.66 |-Branch one:
% 13.54/3.66 | (1185) all_0_51_51 = e1
% 13.54/3.66 |
% 13.54/3.66 | Equations (1185) can reduce 343 to:
% 13.54/3.66 | (303) $false
% 13.54/3.66 |
% 13.54/3.66 |-The branch is then unsatisfiable
% 13.54/3.66 |-Branch two:
% 13.54/3.66 | (343) ~ (all_0_51_51 = e1)
% 13.54/3.66 | (1188) all_0_51_51 = e2 | all_0_51_51 = e0
% 13.54/3.66 |
% 13.54/3.66 +-Applying beta-rule and splitting (77), into two cases.
% 13.54/3.66 |-Branch one:
% 13.54/3.66 | (1189) all_0_44_44 = e4
% 13.54/3.66 |
% 13.54/3.66 | Equations (1189) can reduce 40 to:
% 13.54/3.66 | (506) ~ (all_0_48_48 = e4)
% 13.54/3.66 |
% 13.54/3.66 | Simplifying 506 yields:
% 13.54/3.66 | (507) ~ (all_0_48_48 = e4)
% 13.54/3.66 |
% 13.54/3.66 | Equations (1189) can reduce 276 to:
% 13.54/3.66 | (253) ~ (e4 = e1)
% 13.54/3.66 |
% 13.54/3.66 | Equations (1189) can reduce 819 to:
% 13.54/3.66 | (5) ~ (e4 = e0)
% 13.54/3.66 |
% 13.54/3.66 +-Applying beta-rule and splitting (171), into two cases.
% 13.54/3.66 |-Branch one:
% 13.54/3.66 | (1194) all_0_56_56 = e0
% 13.54/3.66 |
% 13.54/3.66 | Equations (1194) can reduce 1182 to:
% 13.54/3.66 | (303) $false
% 13.54/3.66 |
% 13.54/3.66 |-The branch is then unsatisfiable
% 13.54/3.66 |-Branch two:
% 13.54/3.66 | (1182) ~ (all_0_56_56 = e0)
% 13.54/3.66 | (1197) all_0_57_57 = e0 | all_0_59_59 = e0 | all_0_60_60 = e0
% 13.54/3.66 |
% 13.54/3.66 +-Applying beta-rule and splitting (28), into two cases.
% 13.54/3.66 |-Branch one:
% 13.54/3.66 | (775) all_0_44_44 = e3
% 13.54/3.66 |
% 13.54/3.66 | Combining equations (775,1189) yields a new equation:
% 13.54/3.66 | (524) e4 = e3
% 13.54/3.66 |
% 13.54/3.66 | Equations (524) can reduce 30 to:
% 13.54/3.66 | (303) $false
% 13.54/3.66 |
% 13.54/3.66 |-The branch is then unsatisfiable
% 13.54/3.66 |-Branch two:
% 13.54/3.66 | (908) ~ (all_0_44_44 = e3)
% 13.54/3.66 | (1202) all_0_45_45 = e3 | all_0_47_47 = e3 | all_0_48_48 = e3
% 13.54/3.66 |
% 13.54/3.66 | Equations (1189) can reduce 908 to:
% 13.54/3.66 | (30) ~ (e4 = e3)
% 13.54/3.66 |
% 13.54/3.66 +-Applying beta-rule and splitting (1188), into two cases.
% 13.54/3.66 |-Branch one:
% 13.54/3.66 | (609) all_0_51_51 = e0
% 13.54/3.66 |
% 13.54/3.66 | Equations (609) can reduce 613 to:
% 13.54/3.66 | (303) $false
% 13.54/3.66 |
% 13.54/3.66 |-The branch is then unsatisfiable
% 13.54/3.66 |-Branch two:
% 13.54/3.66 | (613) ~ (all_0_51_51 = e0)
% 13.54/3.66 | (383) all_0_51_51 = e2
% 13.54/3.66 |
% 13.54/3.66 | From (383) and (169) follows:
% 13.54/3.66 | (394) op(e1, e2) = all_0_27_27
% 13.54/3.66 |
% 13.54/3.66 +-Applying beta-rule and splitting (16), into two cases.
% 13.54/3.66 |-Branch one:
% 13.54/3.66 | (775) all_0_44_44 = e3
% 13.54/3.66 |
% 13.54/3.66 | Combining equations (1189,775) yields a new equation:
% 13.54/3.66 | (523) e4 = e3
% 13.54/3.66 |
% 13.54/3.66 | Simplifying 523 yields:
% 13.54/3.66 | (524) e4 = e3
% 13.54/3.66 |
% 13.54/3.66 | Equations (524) can reduce 30 to:
% 13.54/3.66 | (303) $false
% 13.54/3.66 |
% 13.54/3.66 |-The branch is then unsatisfiable
% 13.54/3.66 |-Branch two:
% 13.54/3.66 | (908) ~ (all_0_44_44 = e3)
% 13.73/3.66 | (909) all_0_53_53 = e3 | all_0_56_56 = e3
% 13.73/3.66 |
% 13.73/3.66 +-Applying beta-rule and splitting (84), into two cases.
% 13.73/3.66 |-Branch one:
% 13.73/3.66 | (505) all_0_43_43 = e4
% 13.73/3.66 |
% 13.73/3.66 | Equations (505) can reduce 582 to:
% 13.73/3.66 | (303) $false
% 13.73/3.66 |
% 13.73/3.66 |-The branch is then unsatisfiable
% 13.73/3.66 |-Branch two:
% 13.73/3.67 | (582) ~ (all_0_43_43 = e4)
% 13.73/3.67 | (583) all_0_48_48 = e4 | all_0_52_52 = e4 | all_0_60_60 = e4
% 13.73/3.67 |
% 13.73/3.67 +-Applying beta-rule and splitting (1197), into two cases.
% 13.73/3.67 |-Branch one:
% 13.73/3.67 | (628) all_0_57_57 = e0
% 13.73/3.67 |
% 13.73/3.67 | Equations (628) can reduce 309 to:
% 13.73/3.67 | (303) $false
% 13.73/3.67 |
% 13.73/3.67 |-The branch is then unsatisfiable
% 13.73/3.67 |-Branch two:
% 13.73/3.67 | (309) ~ (all_0_57_57 = e0)
% 13.73/3.67 | (1222) all_0_59_59 = e0 | all_0_60_60 = e0
% 13.73/3.67 |
% 13.73/3.67 +-Applying beta-rule and splitting (909), into two cases.
% 13.73/3.67 |-Branch one:
% 13.73/3.67 | (413) all_0_53_53 = e3
% 13.73/3.67 |
% 13.73/3.67 | Combining equations (413,275) yields a new equation:
% 13.73/3.67 | (604) e3 = e1
% 13.73/3.67 |
% 13.73/3.67 | Simplifying 604 yields:
% 13.73/3.67 | (414) e3 = e1
% 13.73/3.67 |
% 13.73/3.67 | Equations (414) can reduce 145 to:
% 13.73/3.67 | (303) $false
% 13.73/3.67 |
% 13.73/3.67 |-The branch is then unsatisfiable
% 13.73/3.67 |-Branch two:
% 13.73/3.67 | (416) ~ (all_0_53_53 = e3)
% 13.73/3.67 | (431) all_0_56_56 = e3
% 13.73/3.67 |
% 13.73/3.67 | Equations (431) can reduce 90 to:
% 13.73/3.67 | (1229) ~ (all_0_57_57 = e3)
% 13.73/3.67 |
% 13.73/3.67 | Simplifying 1229 yields:
% 13.73/3.67 | (640) ~ (all_0_57_57 = e3)
% 13.73/3.67 |
% 13.73/3.67 | Equations (431) can reduce 159 to:
% 13.73/3.67 | (1231) ~ (all_0_59_59 = e3)
% 13.73/3.67 |
% 13.73/3.67 | Simplifying 1231 yields:
% 13.73/3.67 | (645) ~ (all_0_59_59 = e3)
% 13.73/3.67 |
% 13.73/3.67 | Equations (431) can reduce 282 to:
% 13.73/3.67 | (145) ~ (e3 = e1)
% 13.73/3.67 |
% 13.73/3.67 | Equations (431) can reduce 1182 to:
% 13.73/3.67 | (74) ~ (e3 = e0)
% 13.73/3.67 |
% 13.73/3.67 +-Applying beta-rule and splitting (81), into two cases.
% 13.73/3.67 |-Branch one:
% 13.73/3.67 | (495) all_0_42_42 = e3
% 13.73/3.67 |
% 13.73/3.67 | Equations (495) can reduce 146 to:
% 13.73/3.67 | (1231) ~ (all_0_59_59 = e3)
% 13.73/3.67 |
% 13.73/3.67 | Simplifying 1231 yields:
% 13.73/3.67 | (645) ~ (all_0_59_59 = e3)
% 13.73/3.67 |
% 13.73/3.67 | From (495) and (234) follows:
% 13.73/3.67 | (500) op(e1, e3) = all_0_23_23
% 13.73/3.67 |
% 13.73/3.67 +-Applying beta-rule and splitting (64), into two cases.
% 13.73/3.67 |-Branch one:
% 13.73/3.67 | (473) all_0_40_40 = e0
% 13.73/3.67 |
% 13.73/3.67 | Combining equations (511,473) yields a new equation:
% 13.73/3.67 | (995) e4 = e0
% 13.73/3.67 |
% 13.73/3.67 | Simplifying 995 yields:
% 13.73/3.67 | (512) e4 = e0
% 13.73/3.67 |
% 13.73/3.67 | Equations (512) can reduce 5 to:
% 13.73/3.67 | (303) $false
% 13.73/3.67 |
% 13.73/3.67 |-The branch is then unsatisfiable
% 13.73/3.67 |-Branch two:
% 13.73/3.67 | (617) ~ (all_0_40_40 = e0)
% 13.73/3.67 | (999) all_0_42_42 = e0 | all_0_43_43 = e0
% 13.73/3.67 |
% 13.73/3.67 +-Applying beta-rule and splitting (999), into two cases.
% 13.73/3.67 |-Branch one:
% 13.73/3.67 | (486) all_0_42_42 = e0
% 13.73/3.67 |
% 13.73/3.67 | Combining equations (495,486) yields a new equation:
% 13.73/3.67 | (574) e3 = e0
% 13.73/3.67 |
% 13.73/3.67 | Simplifying 574 yields:
% 13.73/3.67 | (575) e3 = e0
% 13.73/3.67 |
% 13.73/3.67 | Equations (575) can reduce 74 to:
% 13.73/3.67 | (303) $false
% 13.73/3.67 |
% 13.73/3.67 |-The branch is then unsatisfiable
% 13.73/3.67 |-Branch two:
% 13.73/3.67 | (475) ~ (all_0_42_42 = e0)
% 13.73/3.67 | (588) all_0_43_43 = e0
% 13.73/3.67 |
% 13.73/3.67 | Equations (588) can reduce 125 to:
% 13.73/3.67 | (1251) ~ (all_0_55_55 = e0)
% 13.73/3.67 |
% 13.73/3.67 | Simplifying 1251 yields:
% 13.73/3.67 | (184) ~ (all_0_55_55 = e0)
% 13.73/3.67 |
% 13.73/3.67 | Equations (588) can reduce 262 to:
% 13.73/3.67 | (471) ~ (e1 = e0)
% 13.73/3.67 |
% 13.73/3.67 | Simplifying 471 yields:
% 13.73/3.67 | (143) ~ (e1 = e0)
% 13.73/3.67 |
% 13.73/3.67 +-Applying beta-rule and splitting (1222), into two cases.
% 13.73/3.67 |-Branch one:
% 13.73/3.67 | (614) all_0_59_59 = e0
% 13.73/3.67 |
% 13.73/3.67 | Equations (614) can reduce 166 to:
% 13.73/3.67 | (309) ~ (all_0_57_57 = e0)
% 13.73/3.67 |
% 13.73/3.67 | Equations (614) can reduce 645 to:
% 13.73/3.67 | (480) ~ (e3 = e0)
% 13.73/3.67 |
% 13.73/3.67 | Simplifying 480 yields:
% 13.73/3.67 | (74) ~ (e3 = e0)
% 13.73/3.67 |
% 13.73/3.67 | From (614) and (118) follows:
% 13.73/3.67 | (1259) op(e1, e0) = all_0_29_29
% 13.73/3.67 |
% 13.73/3.67 +-Applying beta-rule and splitting (1202), into two cases.
% 13.73/3.67 |-Branch one:
% 13.73/3.67 | (1260) all_0_45_45 = e3
% 13.73/3.67 |
% 13.73/3.67 | Combining equations (300,1260) yields a new equation:
% 13.73/3.67 | (575) e3 = e0
% 13.73/3.67 |
% 13.73/3.67 | Equations (575) can reduce 74 to:
% 13.73/3.67 | (303) $false
% 13.73/3.67 |
% 13.73/3.67 |-The branch is then unsatisfiable
% 13.73/3.67 |-Branch two:
% 13.73/3.67 | (1263) ~ (all_0_45_45 = e3)
% 13.73/3.67 | (1264) all_0_47_47 = e3 | all_0_48_48 = e3
% 13.73/3.67 |
% 13.73/3.67 +-Applying beta-rule and splitting (120), into two cases.
% 13.73/3.67 |-Branch one:
% 13.73/3.67 | (333) all_0_57_57 = e1
% 13.73/3.67 |
% 13.73/3.67 | Equations (333) can reduce 299 to:
% 13.73/3.67 | (303) $false
% 13.73/3.67 |
% 13.73/3.67 |-The branch is then unsatisfiable
% 13.73/3.67 |-Branch two:
% 13.73/3.67 | (299) ~ (all_0_57_57 = e1)
% 13.73/3.67 | (770) all_0_57_57 = e4 | all_0_57_57 = e3 | all_0_57_57 = e2 | all_0_57_57 = e0
% 13.73/3.67 |
% 13.73/3.67 +-Applying beta-rule and splitting (770), into two cases.
% 13.73/3.67 |-Branch one:
% 13.73/3.67 | (628) all_0_57_57 = e0
% 13.73/3.67 |
% 13.73/3.67 | Equations (628) can reduce 309 to:
% 13.73/3.67 | (303) $false
% 13.73/3.67 |
% 13.73/3.67 |-The branch is then unsatisfiable
% 13.73/3.67 |-Branch two:
% 13.73/3.67 | (309) ~ (all_0_57_57 = e0)
% 13.73/3.67 | (774) all_0_57_57 = e4 | all_0_57_57 = e3 | all_0_57_57 = e2
% 13.73/3.67 |
% 13.73/3.67 +-Applying beta-rule and splitting (774), into two cases.
% 13.73/3.67 |-Branch one:
% 13.73/3.67 | (637) all_0_57_57 = e3
% 13.73/3.67 |
% 13.73/3.67 | Equations (637) can reduce 640 to:
% 13.73/3.67 | (303) $false
% 13.73/3.67 |
% 13.73/3.67 |-The branch is then unsatisfiable
% 13.73/3.67 |-Branch two:
% 13.73/3.67 | (640) ~ (all_0_57_57 = e3)
% 13.73/3.67 | (890) all_0_57_57 = e4 | all_0_57_57 = e2
% 13.73/3.67 |
% 13.73/3.67 +-Applying beta-rule and splitting (890), into two cases.
% 13.73/3.67 |-Branch one:
% 13.73/3.67 | (891) all_0_57_57 = e4
% 13.73/3.67 |
% 13.73/3.67 | Equations (891) can reduce 764 to:
% 13.73/3.67 | (303) $false
% 13.73/3.67 |
% 13.73/3.67 |-The branch is then unsatisfiable
% 13.73/3.67 |-Branch two:
% 13.73/3.67 | (764) ~ (all_0_57_57 = e4)
% 13.73/3.67 | (407) all_0_57_57 = e2
% 13.73/3.67 |
% 13.73/3.67 | Equations (407) can reduce 196 to:
% 13.73/3.67 | (375) ~ (all_0_54_54 = e2)
% 13.73/3.67 |
% 13.73/3.67 +-Applying beta-rule and splitting (157), into two cases.
% 13.73/3.67 |-Branch one:
% 13.73/3.67 | (404) all_0_54_54 = e2
% 13.73/3.67 |
% 13.73/3.67 | Equations (404) can reduce 375 to:
% 13.73/3.67 | (303) $false
% 13.73/3.67 |
% 13.73/3.67 |-The branch is then unsatisfiable
% 13.73/3.67 |-Branch two:
% 13.73/3.67 | (375) ~ (all_0_54_54 = e2)
% 13.73/3.67 | (373) all_0_55_55 = e2
% 13.73/3.67 |
% 13.73/3.67 | Equations (373) can reduce 101 to:
% 13.73/3.67 | (375) ~ (all_0_54_54 = e2)
% 13.73/3.67 |
% 13.73/3.67 | Equations (373) can reduce 184 to:
% 13.73/3.67 | (61) ~ (e2 = e0)
% 13.73/3.67 |
% 13.73/3.67 | From (373) and (132) follows:
% 13.73/3.67 | (378) op(e1, e0) = e2
% 13.73/3.67 |
% 13.73/3.67 +-Applying beta-rule and splitting (251), into two cases.
% 13.73/3.67 |-Branch one:
% 13.73/3.67 | (1289) all_0_54_54 = e1
% 13.73/3.67 |
% 13.73/3.67 | Equations (1289) can reduce 278 to:
% 13.73/3.67 | (303) $false
% 13.73/3.67 |
% 13.73/3.67 |-The branch is then unsatisfiable
% 13.73/3.67 |-Branch two:
% 13.73/3.67 | (278) ~ (all_0_54_54 = e1)
% 13.73/3.67 | (1292) all_0_54_54 = e3 | all_0_54_54 = e2
% 13.73/3.67 |
% 13.73/3.67 +-Applying beta-rule and splitting (1292), into two cases.
% 13.73/3.67 |-Branch one:
% 13.73/3.67 | (418) all_0_54_54 = e3
% 13.73/3.67 |
% 13.73/3.67 | Equations (418) can reduce 278 to:
% 13.73/3.67 | (145) ~ (e3 = e1)
% 13.73/3.67 |
% 13.73/3.67 | From (418) and (105) follows:
% 13.73/3.67 | (423) op(e1, e3) = all_0_14_14
% 13.73/3.67 |
% 13.73/3.67 | From (418) and (89) follows:
% 13.73/3.67 | (424) op(e1, e3) = e3
% 13.73/3.67 |
% 13.73/3.67 +-Applying beta-rule and splitting (583), into two cases.
% 13.73/3.67 |-Branch one:
% 13.73/3.67 | (1297) all_0_48_48 = e4
% 13.73/3.67 |
% 13.73/3.68 | Equations (1297) can reduce 507 to:
% 13.73/3.68 | (303) $false
% 13.73/3.68 |
% 13.73/3.68 |-The branch is then unsatisfiable
% 13.73/3.68 |-Branch two:
% 13.73/3.68 | (507) ~ (all_0_48_48 = e4)
% 13.73/3.68 | (1300) all_0_52_52 = e4 | all_0_60_60 = e4
% 13.73/3.68 |
% 13.73/3.68 +-Applying beta-rule and splitting (1300), into two cases.
% 13.73/3.68 |-Branch one:
% 13.73/3.68 | (578) all_0_52_52 = e4
% 13.73/3.68 |
% 13.73/3.68 | Equations (578) can reduce 233 to:
% 13.73/3.68 | (507) ~ (all_0_48_48 = e4)
% 13.73/3.68 |
% 13.73/3.68 +-Applying beta-rule and splitting (1264), into two cases.
% 13.73/3.68 |-Branch one:
% 13.73/3.68 | (599) all_0_47_47 = e3
% 13.73/3.68 |
% 13.73/3.68 | Combining equations (1100,599) yields a new equation:
% 13.73/3.68 | (414) e3 = e1
% 13.73/3.68 |
% 13.73/3.68 | Equations (414) can reduce 145 to:
% 13.73/3.68 | (303) $false
% 13.73/3.68 |
% 13.73/3.68 |-The branch is then unsatisfiable
% 13.73/3.68 |-Branch two:
% 13.73/3.68 | (602) ~ (all_0_47_47 = e3)
% 13.73/3.68 | (535) all_0_48_48 = e3
% 13.73/3.68 |
% 13.73/3.68 | Equations (535) can reduce 507 to:
% 13.73/3.68 | (536) ~ (e4 = e3)
% 13.73/3.68 |
% 13.73/3.68 | Simplifying 536 yields:
% 13.73/3.68 | (30) ~ (e4 = e3)
% 13.73/3.68 |
% 13.73/3.68 | Instantiating formula (39) with e1, e3, all_0_23_23, all_0_14_14 and discharging atoms op(e1, e3) = all_0_14_14, op(e1, e3) = all_0_23_23, yields:
% 13.73/3.68 | (1310) all_0_14_14 = all_0_23_23
% 13.73/3.68 |
% 13.73/3.68 | Instantiating formula (39) with e1, e3, e3, all_0_14_14 and discharging atoms op(e1, e3) = all_0_14_14, op(e1, e3) = e3, yields:
% 13.73/3.68 | (443) all_0_14_14 = e3
% 13.73/3.68 |
% 13.73/3.68 | Instantiating formula (39) with e1, e2, all_0_27_27, e0 and discharging atoms op(e1, e2) = all_0_27_27, op(e1, e2) = e0, yields:
% 13.73/3.68 | (444) all_0_27_27 = e0
% 13.73/3.68 |
% 13.73/3.68 | Instantiating formula (39) with e1, e0, e2, all_0_29_29 and discharging atoms op(e1, e0) = all_0_29_29, op(e1, e0) = e2, yields:
% 13.73/3.68 | (1313) all_0_29_29 = e2
% 13.73/3.68 |
% 13.73/3.68 | Combining equations (1310,443) yields a new equation:
% 13.73/3.68 | (1314) all_0_23_23 = e3
% 13.73/3.68 |
% 13.73/3.68 | Simplifying 1314 yields:
% 13.73/3.68 | (539) all_0_23_23 = e3
% 13.73/3.68 |
% 13.73/3.68 +-Applying beta-rule and splitting (225), into two cases.
% 13.73/3.68 |-Branch one:
% 13.73/3.68 | (541) (all_0_23_23 = e4 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e3 & ~ (all_0_26_26 = e1)) | (all_0_27_27 = e2 & ~ (all_0_28_28 = e1))
% 13.73/3.68 |
% 13.73/3.68 +-Applying beta-rule and splitting (541), into two cases.
% 13.73/3.68 |-Branch one:
% 13.73/3.68 | (542) (all_0_23_23 = e4 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e3 & ~ (all_0_26_26 = e1))
% 13.73/3.68 |
% 13.73/3.68 +-Applying beta-rule and splitting (542), into two cases.
% 13.73/3.68 |-Branch one:
% 13.73/3.68 | (543) all_0_23_23 = e4 & ~ (all_0_24_24 = e1)
% 13.73/3.68 |
% 13.73/3.68 | Applying alpha-rule on (543) yields:
% 13.73/3.68 | (544) all_0_23_23 = e4
% 13.73/3.68 | (545) ~ (all_0_24_24 = e1)
% 13.73/3.68 |
% 13.73/3.68 | Combining equations (544,539) yields a new equation:
% 13.73/3.68 | (523) e4 = e3
% 13.73/3.68 |
% 13.73/3.68 | Simplifying 523 yields:
% 13.73/3.68 | (524) e4 = e3
% 13.73/3.68 |
% 13.73/3.68 | Equations (524) can reduce 30 to:
% 13.73/3.68 | (303) $false
% 13.73/3.68 |
% 13.73/3.68 |-The branch is then unsatisfiable
% 13.73/3.68 |-Branch two:
% 13.73/3.68 | (549) all_0_25_25 = e3 & ~ (all_0_26_26 = e1)
% 13.73/3.68 |
% 13.73/3.68 | Applying alpha-rule on (549) yields:
% 13.73/3.68 | (550) all_0_25_25 = e3
% 13.73/3.68 | (551) ~ (all_0_26_26 = e1)
% 13.73/3.68 |
% 13.73/3.68 | Combining equations (550,1129) yields a new equation:
% 13.73/3.68 | (524) e4 = e3
% 13.73/3.68 |
% 13.73/3.68 | Equations (524) can reduce 30 to:
% 13.73/3.68 | (303) $false
% 13.73/3.68 |
% 13.73/3.68 |-The branch is then unsatisfiable
% 13.73/3.68 |-Branch two:
% 13.73/3.68 | (555) all_0_27_27 = e2 & ~ (all_0_28_28 = e1)
% 13.73/3.68 |
% 13.73/3.68 | Applying alpha-rule on (555) yields:
% 13.73/3.68 | (556) all_0_27_27 = e2
% 13.73/3.68 | (557) ~ (all_0_28_28 = e1)
% 13.73/3.68 |
% 13.73/3.68 | Combining equations (556,444) yields a new equation:
% 13.73/3.68 | (558) e2 = e0
% 13.73/3.68 |
% 13.73/3.68 | Simplifying 558 yields:
% 13.73/3.68 | (559) e2 = e0
% 13.73/3.68 |
% 13.73/3.68 | Equations (559) can reduce 61 to:
% 13.73/3.68 | (303) $false
% 13.73/3.68 |
% 13.73/3.68 |-The branch is then unsatisfiable
% 13.73/3.68 |-Branch two:
% 13.73/3.68 | (561) all_0_29_29 = e0 & ~ (all_0_30_30 = e1)
% 13.73/3.68 |
% 13.73/3.68 | Applying alpha-rule on (561) yields:
% 13.73/3.68 | (562) all_0_29_29 = e0
% 13.73/3.68 | (563) ~ (all_0_30_30 = e1)
% 13.73/3.68 |
% 13.73/3.68 | Combining equations (562,1313) yields a new equation:
% 13.73/3.68 | (559) e2 = e0
% 13.73/3.68 |
% 13.73/3.68 | Equations (559) can reduce 61 to:
% 13.73/3.68 | (303) $false
% 13.73/3.68 |
% 13.73/3.68 |-The branch is then unsatisfiable
% 13.73/3.68 |-Branch two:
% 13.73/3.68 | (1340) ~ (all_0_52_52 = e4)
% 13.73/3.68 | (1024) all_0_60_60 = e4
% 13.73/3.68 |
% 13.73/3.68 | Combining equations (1024,1059) yields a new equation:
% 13.73/3.68 | (426) e4 = e1
% 13.73/3.68 |
% 13.73/3.68 | Simplifying 426 yields:
% 13.73/3.68 | (427) e4 = e1
% 13.73/3.68 |
% 13.73/3.68 | Equations (427) can reduce 253 to:
% 13.73/3.68 | (303) $false
% 13.73/3.68 |
% 13.73/3.68 |-The branch is then unsatisfiable
% 13.73/3.68 |-Branch two:
% 13.73/3.68 | (649) ~ (all_0_54_54 = e3)
% 13.73/3.68 | (404) all_0_54_54 = e2
% 13.73/3.68 |
% 13.73/3.68 | Equations (404) can reduce 375 to:
% 13.73/3.68 | (303) $false
% 13.73/3.68 |
% 13.73/3.68 |-The branch is then unsatisfiable
% 13.73/3.68 |-Branch two:
% 13.73/3.68 | (1348) ~ (all_0_59_59 = e0)
% 13.73/3.68 | (305) all_0_60_60 = e0
% 13.73/3.68 |
% 13.73/3.68 | Combining equations (305,1059) yields a new equation:
% 13.73/3.68 | (302) e1 = e0
% 13.73/3.68 |
% 13.73/3.68 | Equations (302) can reduce 143 to:
% 13.73/3.68 | (303) $false
% 13.73/3.68 |
% 13.73/3.68 |-The branch is then unsatisfiable
% 13.73/3.68 |-Branch two:
% 13.73/3.68 | (597) ~ (all_0_42_42 = e3)
% 13.73/3.68 | (598) all_0_47_47 = e3 | all_0_59_59 = e3
% 13.73/3.68 |
% 13.73/3.68 +-Applying beta-rule and splitting (598), into two cases.
% 13.73/3.68 |-Branch one:
% 13.73/3.68 | (599) all_0_47_47 = e3
% 13.73/3.68 |
% 13.73/3.68 | Combining equations (599,1100) yields a new equation:
% 13.73/3.68 | (604) e3 = e1
% 13.73/3.68 |
% 13.73/3.68 | Simplifying 604 yields:
% 13.73/3.68 | (414) e3 = e1
% 13.73/3.68 |
% 13.73/3.68 | Equations (414) can reduce 145 to:
% 13.73/3.68 | (303) $false
% 13.73/3.68 |
% 13.73/3.68 |-The branch is then unsatisfiable
% 13.73/3.68 |-Branch two:
% 13.73/3.68 | (602) ~ (all_0_47_47 = e3)
% 13.73/3.68 | (603) all_0_59_59 = e3
% 13.73/3.68 |
% 13.73/3.68 | Equations (603) can reduce 645 to:
% 13.73/3.68 | (303) $false
% 13.73/3.68 |
% 13.73/3.68 |-The branch is then unsatisfiable
% 13.73/3.68 |-Branch two:
% 13.73/3.68 | (1361) ~ (all_0_44_44 = e4)
% 13.73/3.69 | (1362) all_0_49_49 = e4 | all_0_56_56 = e4
% 13.73/3.69 |
% 13.73/3.69 +-Applying beta-rule and splitting (171), into two cases.
% 13.73/3.69 |-Branch one:
% 13.73/3.69 | (1194) all_0_56_56 = e0
% 13.73/3.69 |
% 13.73/3.69 | Equations (1194) can reduce 1182 to:
% 13.73/3.69 | (303) $false
% 13.73/3.69 |
% 13.73/3.69 |-The branch is then unsatisfiable
% 13.73/3.69 |-Branch two:
% 13.73/3.69 | (1182) ~ (all_0_56_56 = e0)
% 13.73/3.69 | (1197) all_0_57_57 = e0 | all_0_59_59 = e0 | all_0_60_60 = e0
% 13.73/3.69 |
% 13.73/3.69 +-Applying beta-rule and splitting (1197), into two cases.
% 13.73/3.69 |-Branch one:
% 13.73/3.69 | (628) all_0_57_57 = e0
% 13.73/3.69 |
% 13.73/3.69 | Equations (628) can reduce 309 to:
% 13.73/3.69 | (303) $false
% 13.73/3.69 |
% 13.73/3.69 |-The branch is then unsatisfiable
% 13.73/3.69 |-Branch two:
% 13.73/3.69 | (309) ~ (all_0_57_57 = e0)
% 13.73/3.69 | (1222) all_0_59_59 = e0 | all_0_60_60 = e0
% 13.73/3.69 |
% 13.73/3.69 +-Applying beta-rule and splitting (1222), into two cases.
% 13.73/3.69 |-Branch one:
% 13.73/3.69 | (614) all_0_59_59 = e0
% 13.73/3.69 |
% 13.73/3.69 | Equations (614) can reduce 146 to:
% 13.73/3.69 | (475) ~ (all_0_42_42 = e0)
% 13.73/3.69 |
% 13.73/3.69 | Equations (614) can reduce 8 to:
% 13.73/3.69 | (516) ~ (e4 = e0)
% 13.73/3.69 |
% 13.73/3.69 | Simplifying 516 yields:
% 13.73/3.69 | (5) ~ (e4 = e0)
% 13.73/3.69 |
% 13.73/3.69 +-Applying beta-rule and splitting (42), into two cases.
% 13.73/3.69 |-Branch one:
% 13.73/3.69 | (1375) all_0_42_42 = e1
% 13.73/3.69 |
% 13.73/3.69 | Equations (1375) can reduce 260 to:
% 13.73/3.69 | (303) $false
% 13.73/3.69 |
% 13.73/3.69 |-The branch is then unsatisfiable
% 13.73/3.69 |-Branch two:
% 13.73/3.69 | (260) ~ (all_0_42_42 = e1)
% 13.73/3.69 | (1378) all_0_42_42 = e3 | all_0_42_42 = e0
% 13.73/3.69 |
% 13.73/3.69 +-Applying beta-rule and splitting (1378), into two cases.
% 13.73/3.69 |-Branch one:
% 13.73/3.69 | (486) all_0_42_42 = e0
% 13.73/3.69 |
% 13.73/3.69 | Equations (486) can reduce 475 to:
% 13.73/3.69 | (303) $false
% 13.73/3.69 |
% 13.73/3.69 |-The branch is then unsatisfiable
% 13.73/3.69 |-Branch two:
% 13.73/3.69 | (475) ~ (all_0_42_42 = e0)
% 13.73/3.69 | (495) all_0_42_42 = e3
% 13.73/3.69 |
% 13.73/3.69 | Equations (495) can reduce 475 to:
% 13.73/3.69 | (74) ~ (e3 = e0)
% 13.73/3.69 |
% 13.73/3.69 +-Applying beta-rule and splitting (64), into two cases.
% 13.73/3.69 |-Branch one:
% 13.73/3.69 | (473) all_0_40_40 = e0
% 13.73/3.69 |
% 13.73/3.69 | Combining equations (511,473) yields a new equation:
% 13.73/3.69 | (995) e4 = e0
% 13.73/3.69 |
% 13.73/3.69 | Simplifying 995 yields:
% 13.73/3.69 | (512) e4 = e0
% 13.73/3.69 |
% 13.73/3.69 | Equations (512) can reduce 5 to:
% 13.73/3.69 | (303) $false
% 13.73/3.69 |
% 13.73/3.69 |-The branch is then unsatisfiable
% 13.73/3.69 |-Branch two:
% 13.73/3.69 | (617) ~ (all_0_40_40 = e0)
% 13.73/3.69 | (999) all_0_42_42 = e0 | all_0_43_43 = e0
% 13.73/3.69 |
% 13.73/3.69 +-Applying beta-rule and splitting (999), into two cases.
% 13.73/3.69 |-Branch one:
% 13.73/3.69 | (486) all_0_42_42 = e0
% 13.73/3.69 |
% 13.73/3.69 | Combining equations (495,486) yields a new equation:
% 13.73/3.69 | (574) e3 = e0
% 13.73/3.69 |
% 13.73/3.69 | Simplifying 574 yields:
% 13.73/3.69 | (575) e3 = e0
% 13.73/3.69 |
% 13.73/3.69 | Equations (575) can reduce 74 to:
% 13.73/3.69 | (303) $false
% 13.73/3.69 |
% 13.73/3.69 |-The branch is then unsatisfiable
% 13.73/3.69 |-Branch two:
% 13.73/3.69 | (475) ~ (all_0_42_42 = e0)
% 13.73/3.69 | (588) all_0_43_43 = e0
% 13.73/3.69 |
% 13.73/3.69 | Equations (588) can reduce 582 to:
% 13.73/3.69 | (516) ~ (e4 = e0)
% 13.73/3.69 |
% 13.73/3.69 | Simplifying 516 yields:
% 13.73/3.69 | (5) ~ (e4 = e0)
% 13.73/3.69 |
% 13.73/3.69 +-Applying beta-rule and splitting (88), into two cases.
% 13.73/3.69 |-Branch one:
% 13.73/3.69 | (528) all_0_49_49 = e4
% 13.73/3.69 |
% 13.73/3.69 | Combining equations (466,528) yields a new equation:
% 13.73/3.69 | (512) e4 = e0
% 13.73/3.69 |
% 13.73/3.69 | Equations (512) can reduce 5 to:
% 13.73/3.69 | (303) $false
% 13.73/3.69 |
% 13.73/3.69 |-The branch is then unsatisfiable
% 13.73/3.69 |-Branch two:
% 13.73/3.69 | (531) ~ (all_0_49_49 = e4)
% 13.73/3.69 | (532) all_0_50_50 = e4 | all_0_52_52 = e4
% 13.73/3.69 |
% 13.73/3.69 | Equations (466) can reduce 531 to:
% 13.73/3.69 | (516) ~ (e4 = e0)
% 13.73/3.69 |
% 13.73/3.69 | Simplifying 516 yields:
% 13.73/3.69 | (5) ~ (e4 = e0)
% 13.73/3.69 |
% 13.73/3.69 +-Applying beta-rule and splitting (1362), into two cases.
% 13.73/3.69 |-Branch one:
% 13.73/3.69 | (528) all_0_49_49 = e4
% 13.73/3.69 |
% 13.73/3.69 | Combining equations (466,528) yields a new equation:
% 13.73/3.69 | (512) e4 = e0
% 13.73/3.69 |
% 13.73/3.69 | Equations (512) can reduce 5 to:
% 13.73/3.69 | (303) $false
% 13.73/3.69 |
% 13.73/3.69 |-The branch is then unsatisfiable
% 13.73/3.69 |-Branch two:
% 13.73/3.69 | (531) ~ (all_0_49_49 = e4)
% 13.73/3.69 | (762) all_0_56_56 = e4
% 13.73/3.69 |
% 13.73/3.69 | Equations (762) can reduce 988 to:
% 13.73/3.69 | (303) $false
% 13.73/3.69 |
% 13.73/3.69 |-The branch is then unsatisfiable
% 13.73/3.69 |-Branch two:
% 13.73/3.69 | (1348) ~ (all_0_59_59 = e0)
% 13.73/3.69 | (305) all_0_60_60 = e0
% 13.73/3.69 |
% 13.73/3.69 | Combining equations (305,1059) yields a new equation:
% 13.73/3.69 | (302) e1 = e0
% 13.73/3.69 |
% 13.73/3.69 | Equations (302) can reduce 143 to:
% 13.73/3.69 | (303) $false
% 13.73/3.69 |
% 13.73/3.69 |-The branch is then unsatisfiable
% 13.73/3.69 |-Branch two:
% 13.73/3.69 | (631) all_0_52_52 = e1 & ~ (all_0_55_55 = e2)
% 13.73/3.69 |
% 13.73/3.69 | Applying alpha-rule on (631) yields:
% 13.73/3.69 | (322) all_0_52_52 = e1
% 13.73/3.69 | (633) ~ (all_0_55_55 = e2)
% 13.73/3.69 |
% 13.73/3.69 | Equations (322) can reduce 1063 to:
% 13.73/3.69 | (303) $false
% 13.73/3.69 |
% 13.73/3.69 |-The branch is then unsatisfiable
% 13.73/3.69 |-Branch two:
% 13.73/3.69 | (514) ~ (all_0_40_40 = e4)
% 13.73/3.69 | (515) all_0_45_45 = e4 | all_0_50_50 = e4 | all_0_57_57 = e4
% 13.73/3.69 |
% 13.73/3.69 +-Applying beta-rule and splitting (515), into two cases.
% 13.73/3.69 |-Branch one:
% 13.73/3.69 | (784) all_0_45_45 = e4
% 13.73/3.69 |
% 13.73/3.69 | Combining equations (300,784) yields a new equation:
% 13.73/3.69 | (512) e4 = e0
% 13.73/3.69 |
% 13.73/3.69 | Equations (512) can reduce 5 to:
% 13.73/3.69 | (303) $false
% 13.73/3.69 |
% 13.73/3.69 |-The branch is then unsatisfiable
% 13.73/3.69 |-Branch two:
% 13.73/3.69 | (787) ~ (all_0_45_45 = e4)
% 13.73/3.69 | (788) all_0_50_50 = e4 | all_0_57_57 = e4
% 13.73/3.69 |
% 13.73/3.69 +-Applying beta-rule and splitting (788), into two cases.
% 13.73/3.69 |-Branch one:
% 13.73/3.69 | (533) all_0_50_50 = e4
% 13.73/3.69 |
% 13.73/3.69 | Combining equations (501,533) yields a new equation:
% 13.73/3.69 | (427) e4 = e1
% 13.73/3.69 |
% 13.73/3.69 | Equations (427) can reduce 253 to:
% 13.73/3.69 | (303) $false
% 13.73/3.69 |
% 13.73/3.69 |-The branch is then unsatisfiable
% 13.73/3.69 |-Branch two:
% 13.73/3.69 | (577) ~ (all_0_50_50 = e4)
% 13.73/3.69 | (891) all_0_57_57 = e4
% 13.73/3.69 |
% 13.73/3.69 | Equations (891) can reduce 764 to:
% 13.73/3.69 | (303) $false
% 13.73/3.69 |
% 13.73/3.69 |-The branch is then unsatisfiable
% 13.73/3.69 |-Branch two:
% 13.73/3.69 | (663) ~ (all_0_46_46 = e2)
% 13.73/3.70 | (664) all_0_58_58 = e2
% 13.73/3.70 |
% 13.73/3.70 | Equations (664) can reduce 71 to:
% 13.73/3.70 | (663) ~ (all_0_46_46 = e2)
% 13.73/3.70 |
% 13.73/3.70 | Equations (664) can reduce 82 to:
% 13.73/3.70 | (717) ~ (all_0_57_57 = e2)
% 13.73/3.70 |
% 13.73/3.70 | Equations (664) can reduce 108 to:
% 13.73/3.70 | (1436) ~ (all_0_59_59 = e2)
% 13.73/3.70 |
% 13.73/3.70 | Simplifying 1436 yields:
% 13.73/3.70 | (1437) ~ (all_0_59_59 = e2)
% 13.73/3.70 |
% 13.73/3.70 | Equations (664) can reduce 240 to:
% 13.73/3.70 | (391) ~ (e3 = e2)
% 13.73/3.70 |
% 13.73/3.70 | Simplifying 391 yields:
% 13.73/3.70 | (209) ~ (e3 = e2)
% 13.73/3.70 |
% 13.73/3.70 | Equations (664) can reduce 266 to:
% 13.73/3.70 | (150) ~ (e2 = e1)
% 13.73/3.70 |
% 13.73/3.70 | Equations (664) can reduce 203 to:
% 13.73/3.70 | (61) ~ (e2 = e0)
% 13.73/3.70 |
% 13.73/3.70 | From (664) and (27) follows:
% 13.73/3.70 | (666) op(e2, e2) = all_0_21_21
% 13.73/3.70 |
% 13.73/3.70 +-Applying beta-rule and splitting (127), into two cases.
% 13.73/3.70 |-Branch one:
% 13.73/3.70 | (379) all_0_47_47 = e2
% 13.73/3.70 |
% 13.73/3.70 | Combining equations (1100,379) yields a new equation:
% 13.73/3.70 | (369) e2 = e1
% 13.73/3.70 |
% 13.73/3.70 | Equations (369) can reduce 150 to:
% 13.73/3.70 | (303) $false
% 13.73/3.70 |
% 13.73/3.70 |-The branch is then unsatisfiable
% 13.73/3.70 |-Branch two:
% 13.73/3.70 | (357) ~ (all_0_47_47 = e2)
% 13.73/3.70 | (382) all_0_51_51 = e2 | all_0_59_59 = e2
% 13.73/3.70 |
% 13.73/3.70 | Equations (1100) can reduce 357 to:
% 13.73/3.70 | (267) ~ (e2 = e1)
% 13.73/3.70 |
% 13.73/3.70 | Simplifying 267 yields:
% 13.73/3.70 | (150) ~ (e2 = e1)
% 13.73/3.70 |
% 13.73/3.70 +-Applying beta-rule and splitting (129), into two cases.
% 13.73/3.70 |-Branch one:
% 13.73/3.70 | (669) all_0_46_46 = e1
% 13.73/3.70 |
% 13.73/3.70 | Equations (669) can reduce 264 to:
% 13.73/3.70 | (303) $false
% 13.73/3.70 |
% 13.73/3.70 |-The branch is then unsatisfiable
% 13.73/3.70 |-Branch two:
% 13.73/3.70 | (264) ~ (all_0_46_46 = e1)
% 13.73/3.70 | (672) all_0_46_46 = e4 | all_0_46_46 = e2
% 13.73/3.70 |
% 13.73/3.70 +-Applying beta-rule and splitting (6), into two cases.
% 13.73/3.70 |-Branch one:
% 13.73/3.70 | (395) all_0_45_45 = e2
% 13.73/3.70 |
% 13.73/3.70 | Combining equations (300,395) yields a new equation:
% 13.73/3.70 | (559) e2 = e0
% 13.73/3.70 |
% 13.73/3.70 | Equations (559) can reduce 61 to:
% 13.73/3.70 | (303) $false
% 13.73/3.70 |
% 13.73/3.70 |-The branch is then unsatisfiable
% 13.73/3.70 |-Branch two:
% 13.73/3.70 | (398) ~ (all_0_45_45 = e2)
% 13.73/3.70 | (399) all_0_50_50 = e2 | all_0_54_54 = e2 | all_0_57_57 = e2
% 13.73/3.70 |
% 13.73/3.70 | Equations (300) can reduce 398 to:
% 13.73/3.70 | (469) ~ (e2 = e0)
% 13.73/3.70 |
% 13.73/3.70 | Simplifying 469 yields:
% 13.73/3.70 | (61) ~ (e2 = e0)
% 13.73/3.70 |
% 13.73/3.70 +-Applying beta-rule and splitting (193), into two cases.
% 13.73/3.70 |-Branch one:
% 13.73/3.70 | (395) all_0_45_45 = e2
% 13.73/3.70 |
% 13.73/3.70 | Combining equations (300,395) yields a new equation:
% 13.73/3.70 | (559) e2 = e0
% 13.73/3.70 |
% 13.73/3.70 | Equations (559) can reduce 61 to:
% 13.73/3.70 | (303) $false
% 13.73/3.70 |
% 13.73/3.70 |-The branch is then unsatisfiable
% 13.73/3.70 |-Branch two:
% 13.73/3.70 | (398) ~ (all_0_45_45 = e2)
% 13.73/3.70 | (948) all_0_46_46 = e2 | all_0_47_47 = e2 | all_0_48_48 = e2
% 13.73/3.70 |
% 13.73/3.70 +-Applying beta-rule and splitting (399), into two cases.
% 13.73/3.70 |-Branch one:
% 13.73/3.70 | (400) all_0_50_50 = e2
% 13.73/3.70 |
% 13.73/3.70 | Combining equations (501,400) yields a new equation:
% 13.73/3.70 | (369) e2 = e1
% 13.73/3.70 |
% 13.73/3.70 | Equations (369) can reduce 150 to:
% 13.73/3.70 | (303) $false
% 13.73/3.70 |
% 13.73/3.70 |-The branch is then unsatisfiable
% 13.73/3.70 |-Branch two:
% 13.73/3.70 | (388) ~ (all_0_50_50 = e2)
% 13.73/3.70 | (403) all_0_54_54 = e2 | all_0_57_57 = e2
% 13.73/3.70 |
% 13.73/3.70 +-Applying beta-rule and splitting (948), into two cases.
% 13.73/3.70 |-Branch one:
% 13.73/3.70 | (355) all_0_46_46 = e2
% 13.73/3.70 |
% 13.73/3.70 | Equations (355) can reduce 663 to:
% 13.73/3.70 | (303) $false
% 13.73/3.70 |
% 13.73/3.70 |-The branch is then unsatisfiable
% 13.73/3.70 |-Branch two:
% 13.73/3.70 | (663) ~ (all_0_46_46 = e2)
% 13.73/3.70 | (1474) all_0_47_47 = e2 | all_0_48_48 = e2
% 13.73/3.70 |
% 13.73/3.70 +-Applying beta-rule and splitting (403), into two cases.
% 13.73/3.70 |-Branch one:
% 13.73/3.70 | (404) all_0_54_54 = e2
% 13.73/3.70 |
% 13.73/3.70 | Equations (404) can reduce 278 to:
% 13.73/3.70 | (150) ~ (e2 = e1)
% 13.73/3.70 |
% 13.73/3.70 +-Applying beta-rule and splitting (1474), into two cases.
% 13.73/3.70 |-Branch one:
% 13.73/3.70 | (379) all_0_47_47 = e2
% 13.73/3.70 |
% 13.73/3.70 | Combining equations (379,1100) yields a new equation:
% 13.73/3.70 | (1478) e2 = e1
% 13.73/3.70 |
% 13.73/3.70 | Simplifying 1478 yields:
% 13.73/3.70 | (369) e2 = e1
% 13.73/3.70 |
% 13.73/3.70 | Equations (369) can reduce 150 to:
% 13.73/3.70 | (303) $false
% 13.73/3.70 |
% 13.73/3.70 |-The branch is then unsatisfiable
% 13.73/3.70 |-Branch two:
% 13.73/3.70 | (357) ~ (all_0_47_47 = e2)
% 13.73/3.70 | (364) all_0_48_48 = e2
% 13.73/3.70 |
% 13.73/3.70 | Equations (364) can reduce 2 to:
% 13.73/3.70 | (663) ~ (all_0_46_46 = e2)
% 13.73/3.70 |
% 13.73/3.70 | Equations (364) can reduce 165 to:
% 13.73/3.70 | (714) ~ (all_0_55_55 = e2)
% 13.73/3.70 |
% 13.73/3.70 | Simplifying 714 yields:
% 13.73/3.70 | (633) ~ (all_0_55_55 = e2)
% 13.73/3.70 |
% 13.73/3.70 +-Applying beta-rule and splitting (28), into two cases.
% 13.73/3.70 |-Branch one:
% 13.73/3.70 | (775) all_0_44_44 = e3
% 13.73/3.70 |
% 13.73/3.70 | Equations (775) can reduce 53 to:
% 13.73/3.70 | (1487) ~ (all_0_49_49 = e3)
% 13.73/3.70 |
% 13.73/3.70 | Simplifying 1487 yields:
% 13.73/3.70 | (46) ~ (all_0_49_49 = e3)
% 13.73/3.70 |
% 13.73/3.70 +-Applying beta-rule and splitting (672), into two cases.
% 13.73/3.70 |-Branch one:
% 13.73/3.70 | (433) all_0_46_46 = e4
% 13.73/3.70 |
% 13.73/3.70 | From (433) and (65) follows:
% 13.73/3.70 | (677) op(e2, e4) = all_0_19_19
% 13.73/3.70 |
% 13.73/3.70 +-Applying beta-rule and splitting (102), into two cases.
% 13.73/3.70 |-Branch one:
% 13.73/3.70 | (1065) all_0_55_55 = e1
% 13.73/3.70 |
% 13.73/3.70 | Equations (1065) can reduce 280 to:
% 13.73/3.70 | (303) $false
% 13.73/3.70 |
% 13.73/3.70 |-The branch is then unsatisfiable
% 13.73/3.70 |-Branch two:
% 13.73/3.70 | (280) ~ (all_0_55_55 = e1)
% 13.73/3.70 | (1494) all_0_55_55 = e3 | all_0_55_55 = e2
% 13.73/3.70 |
% 13.73/3.70 +-Applying beta-rule and splitting (382), into two cases.
% 13.73/3.70 |-Branch one:
% 13.73/3.70 | (383) all_0_51_51 = e2
% 13.73/3.70 |
% 13.73/3.70 | Combining equations (383,273) yields a new equation:
% 13.73/3.70 | (384) all_0_17_17 = e2
% 13.73/3.70 |
% 13.73/3.70 | Equations (383) can reduce 56 to:
% 13.73/3.70 | (389) ~ (e4 = e2)
% 13.73/3.70 |
% 13.73/3.70 | Simplifying 389 yields:
% 13.73/3.70 | (227) ~ (e4 = e2)
% 13.73/3.70 |
% 13.73/3.70 +-Applying beta-rule and splitting (1494), into two cases.
% 13.73/3.70 |-Branch one:
% 13.73/3.70 | (568) all_0_55_55 = e3
% 13.73/3.70 |
% 13.73/3.70 | Equations (568) can reduce 184 to:
% 13.73/3.70 | (74) ~ (e3 = e0)
% 13.73/3.70 |
% 13.73/3.70 | Instantiating formula (39) with e2, e4, all_0_19_19, all_0_49_49 and discharging atoms op(e2, e4) = all_0_19_19, op(e2, e4) = all_0_49_49, yields:
% 13.73/3.70 | (686) all_0_19_19 = all_0_49_49
% 13.73/3.70 |
% 13.73/3.70 | Instantiating formula (39) with e2, e2, all_0_21_21, e3 and discharging atoms op(e2, e2) = all_0_21_21, op(e2, e2) = e3, yields:
% 13.73/3.70 | (687) all_0_21_21 = e3
% 13.73/3.70 |
% 13.73/3.70 +-Applying beta-rule and splitting (19), into two cases.
% 13.73/3.70 |-Branch one:
% 13.73/3.70 | (450) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2)) | (all_0_21_21 = e0 & ~ (all_0_22_22 = e2))
% 13.73/3.70 |
% 13.73/3.70 +-Applying beta-rule and splitting (450), into two cases.
% 13.73/3.70 |-Branch one:
% 13.73/3.70 | (451) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2))
% 13.73/3.70 |
% 13.73/3.70 +-Applying beta-rule and splitting (451), into two cases.
% 13.73/3.70 |-Branch one:
% 13.73/3.70 | (452) all_0_17_17 = e4 & ~ (all_0_18_18 = e2)
% 13.73/3.70 |
% 13.73/3.70 | Applying alpha-rule on (452) yields:
% 13.73/3.70 | (453) all_0_17_17 = e4
% 13.73/3.70 | (454) ~ (all_0_18_18 = e2)
% 13.73/3.70 |
% 13.73/3.70 | Combining equations (453,384) yields a new equation:
% 13.73/3.70 | (455) e4 = e2
% 13.73/3.70 |
% 13.73/3.70 | Simplifying 455 yields:
% 13.73/3.70 | (434) e4 = e2
% 13.73/3.70 |
% 13.73/3.70 | Equations (434) can reduce 227 to:
% 13.73/3.70 | (303) $false
% 13.73/3.70 |
% 13.73/3.70 |-The branch is then unsatisfiable
% 13.73/3.70 |-Branch two:
% 13.73/3.70 | (458) all_0_19_19 = e3 & ~ (all_0_20_20 = e2)
% 13.73/3.70 |
% 13.73/3.70 | Applying alpha-rule on (458) yields:
% 13.73/3.70 | (459) all_0_19_19 = e3
% 13.73/3.70 | (460) ~ (all_0_20_20 = e2)
% 13.73/3.70 |
% 13.73/3.70 | Combining equations (686,459) yields a new equation:
% 13.73/3.70 | (1514) all_0_49_49 = e3
% 13.73/3.70 |
% 13.73/3.70 | Simplifying 1514 yields:
% 13.73/3.70 | (702) all_0_49_49 = e3
% 13.73/3.70 |
% 13.73/3.70 | Equations (702) can reduce 46 to:
% 13.73/3.70 | (303) $false
% 13.73/3.70 |
% 13.73/3.70 |-The branch is then unsatisfiable
% 13.73/3.70 |-Branch two:
% 13.73/3.70 | (462) all_0_21_21 = e0 & ~ (all_0_22_22 = e2)
% 13.73/3.70 |
% 13.73/3.70 | Applying alpha-rule on (462) yields:
% 13.73/3.70 | (463) all_0_21_21 = e0
% 13.73/3.70 | (464) ~ (all_0_22_22 = e2)
% 13.73/3.70 |
% 13.73/3.70 | Combining equations (687,463) yields a new equation:
% 13.73/3.70 | (574) e3 = e0
% 13.73/3.70 |
% 13.73/3.70 | Simplifying 574 yields:
% 13.73/3.70 | (575) e3 = e0
% 13.73/3.70 |
% 13.73/3.70 | Equations (575) can reduce 74 to:
% 13.73/3.70 | (303) $false
% 13.73/3.70 |
% 13.73/3.70 |-The branch is then unsatisfiable
% 13.73/3.70 |-Branch two:
% 13.73/3.70 | (631) all_0_52_52 = e1 & ~ (all_0_55_55 = e2)
% 13.73/3.70 |
% 13.73/3.70 | Applying alpha-rule on (631) yields:
% 13.73/3.70 | (322) all_0_52_52 = e1
% 13.73/3.70 | (633) ~ (all_0_55_55 = e2)
% 13.73/3.70 |
% 13.73/3.70 | Equations (322) can reduce 1063 to:
% 13.73/3.70 | (303) $false
% 13.73/3.70 |
% 13.73/3.70 |-The branch is then unsatisfiable
% 13.73/3.70 |-Branch two:
% 13.73/3.70 | (572) ~ (all_0_55_55 = e3)
% 13.73/3.70 | (373) all_0_55_55 = e2
% 13.73/3.70 |
% 13.73/3.70 | Equations (373) can reduce 633 to:
% 13.73/3.70 | (303) $false
% 13.73/3.70 |
% 13.73/3.70 |-The branch is then unsatisfiable
% 13.73/3.70 |-Branch two:
% 13.73/3.70 | (654) ~ (all_0_51_51 = e2)
% 13.73/3.70 | (655) all_0_59_59 = e2
% 13.73/3.70 |
% 13.73/3.70 | Equations (655) can reduce 1437 to:
% 13.73/3.70 | (303) $false
% 13.73/3.70 |
% 13.73/3.70 |-The branch is then unsatisfiable
% 13.73/3.70 |-Branch two:
% 13.73/3.70 | (436) ~ (all_0_46_46 = e4)
% 13.73/3.71 | (355) all_0_46_46 = e2
% 13.73/3.71 |
% 13.73/3.71 | Equations (355) can reduce 663 to:
% 13.73/3.71 | (303) $false
% 13.73/3.71 |
% 13.73/3.71 |-The branch is then unsatisfiable
% 13.73/3.71 |-Branch two:
% 13.73/3.71 | (908) ~ (all_0_44_44 = e3)
% 13.73/3.71 | (1202) all_0_45_45 = e3 | all_0_47_47 = e3 | all_0_48_48 = e3
% 13.73/3.71 |
% 13.73/3.71 +-Applying beta-rule and splitting (1202), into two cases.
% 13.73/3.71 |-Branch one:
% 13.73/3.71 | (1260) all_0_45_45 = e3
% 13.73/3.71 |
% 13.73/3.71 | Combining equations (300,1260) yields a new equation:
% 13.73/3.71 | (575) e3 = e0
% 13.73/3.71 |
% 13.73/3.71 | Equations (575) can reduce 74 to:
% 13.73/3.71 | (303) $false
% 13.73/3.71 |
% 13.73/3.71 |-The branch is then unsatisfiable
% 13.73/3.71 |-Branch two:
% 13.73/3.71 | (1263) ~ (all_0_45_45 = e3)
% 13.73/3.71 | (1264) all_0_47_47 = e3 | all_0_48_48 = e3
% 13.73/3.71 |
% 13.73/3.71 +-Applying beta-rule and splitting (1264), into two cases.
% 13.73/3.71 |-Branch one:
% 13.73/3.71 | (599) all_0_47_47 = e3
% 13.73/3.71 |
% 13.73/3.71 | Combining equations (1100,599) yields a new equation:
% 13.73/3.71 | (414) e3 = e1
% 13.73/3.71 |
% 13.73/3.71 | Equations (414) can reduce 145 to:
% 13.73/3.71 | (303) $false
% 13.73/3.71 |
% 13.73/3.71 |-The branch is then unsatisfiable
% 13.73/3.71 |-Branch two:
% 13.73/3.71 | (602) ~ (all_0_47_47 = e3)
% 13.73/3.71 | (535) all_0_48_48 = e3
% 13.73/3.71 |
% 13.73/3.71 | Combining equations (364,535) yields a new equation:
% 13.73/3.71 | (553) e3 = e2
% 13.73/3.71 |
% 13.73/3.71 | Equations (553) can reduce 209 to:
% 13.73/3.71 | (303) $false
% 13.73/3.71 |
% 13.73/3.71 |-The branch is then unsatisfiable
% 13.73/3.71 |-Branch two:
% 13.73/3.71 | (375) ~ (all_0_54_54 = e2)
% 13.73/3.71 | (407) all_0_57_57 = e2
% 13.73/3.71 |
% 13.73/3.71 | Equations (407) can reduce 717 to:
% 13.73/3.71 | (303) $false
% 13.73/3.71 |
% 13.73/3.71 |-The branch is then unsatisfiable
% 13.73/3.71 |-Branch two:
% 13.73/3.71 | (326) ~ (all_0_50_50 = e1)
% 13.73/3.71 | (1554) all_0_54_54 = e1 | all_0_57_57 = e1
% 13.73/3.71 |
% 13.73/3.71 +-Applying beta-rule and splitting (1554), into two cases.
% 13.73/3.71 |-Branch one:
% 13.73/3.71 | (1289) all_0_54_54 = e1
% 13.73/3.71 |
% 13.73/3.71 | Equations (1289) can reduce 278 to:
% 13.73/3.71 | (303) $false
% 13.73/3.71 |
% 13.73/3.71 |-The branch is then unsatisfiable
% 13.73/3.71 |-Branch two:
% 13.73/3.71 | (278) ~ (all_0_54_54 = e1)
% 13.73/3.71 | (333) all_0_57_57 = e1
% 13.73/3.71 |
% 13.73/3.71 | Equations (333) can reduce 299 to:
% 13.73/3.71 | (303) $false
% 13.73/3.71 |
% 13.73/3.71 |-The branch is then unsatisfiable
% 13.73/3.71 |-Branch two:
% 13.73/3.71 | (1560) ~ (all_0_47_47 = e1)
% 13.73/3.71 | (318) all_0_48_48 = e1
% 13.73/3.71 |
% 13.73/3.71 | Equations (318) can reduce 295 to:
% 13.73/3.71 | (303) $false
% 13.73/3.71 |
% 13.73/3.71 |-The branch is then unsatisfiable
% 13.73/3.71 |-Branch two:
% 13.73/3.71 | (304) ~ (all_0_45_45 = e0)
% 13.73/3.71 | (305) all_0_60_60 = e0
% 13.73/3.71 |
% 13.73/3.71 | Combining equations (1059,305) yields a new equation:
% 13.73/3.71 | (301) e1 = e0
% 13.73/3.71 |
% 13.73/3.71 | Simplifying 301 yields:
% 13.73/3.71 | (302) e1 = e0
% 13.73/3.71 |
% 13.73/3.71 | Equations (302) can reduce 143 to:
% 13.73/3.71 | (303) $false
% 13.73/3.71 |
% 13.73/3.71 |-The branch is then unsatisfiable
% 13.73/3.71 |-Branch two:
% 13.73/3.71 | (1568) ~ (all_0_53_53 = e1)
% 13.73/3.71 | (413) all_0_53_53 = e3
% 13.73/3.71 |
% 13.73/3.71 | Equations (413) can reduce 17 to:
% 13.73/3.71 | (908) ~ (all_0_44_44 = e3)
% 13.73/3.71 |
% 13.73/3.71 | Equations (413) can reduce 94 to:
% 13.73/3.71 | (46) ~ (all_0_49_49 = e3)
% 13.73/3.71 |
% 13.73/3.71 | Equations (413) can reduce 231 to:
% 13.73/3.71 | (1572) ~ (all_0_54_54 = e3)
% 13.73/3.71 |
% 13.73/3.71 | Simplifying 1572 yields:
% 13.73/3.71 | (649) ~ (all_0_54_54 = e3)
% 13.73/3.71 |
% 13.73/3.71 | Equations (413) can reduce 99 to:
% 13.73/3.71 | (1574) ~ (all_0_55_55 = e3)
% 13.73/3.71 |
% 13.73/3.71 | Simplifying 1574 yields:
% 13.73/3.71 | (572) ~ (all_0_55_55 = e3)
% 13.73/3.71 |
% 13.73/3.71 | Equations (413) can reduce 106 to:
% 13.73/3.71 | (1576) ~ (all_0_56_56 = e3)
% 13.73/3.71 |
% 13.73/3.71 | Simplifying 1576 yields:
% 13.73/3.71 | (635) ~ (all_0_56_56 = e3)
% 13.73/3.71 |
% 13.73/3.71 | Equations (413) can reduce 187 to:
% 13.73/3.71 | (536) ~ (e4 = e3)
% 13.73/3.71 |
% 13.73/3.71 | Simplifying 536 yields:
% 13.73/3.71 | (30) ~ (e4 = e3)
% 13.73/3.71 |
% 13.73/3.71 | Equations (413) can reduce 1568 to:
% 13.73/3.71 | (145) ~ (e3 = e1)
% 13.73/3.71 |
% 13.73/3.71 | Equations (413) can reduce 255 to:
% 13.73/3.71 | (74) ~ (e3 = e0)
% 13.73/3.71 |
% 13.73/3.71 | From (413) and (147) follows:
% 13.73/3.71 | (1582) op(e4, e3) = all_0_4_4
% 13.73/3.71 |
% 13.73/3.71 | Instantiating formula (39) with e4, e3, all_0_4_4, all_0_40_40 and discharging atoms op(e4, e3) = all_0_4_4, op(e4, e3) = all_0_40_40, yields:
% 13.73/3.71 | (1583) all_0_4_4 = all_0_40_40
% 13.73/3.71 |
% 13.73/3.71 +-Applying beta-rule and splitting (12), into two cases.
% 13.73/3.71 |-Branch one:
% 13.73/3.71 | (289) all_0_45_45 = e1
% 13.73/3.71 |
% 13.73/3.71 | Equations (289) can reduce 72 to:
% 13.73/3.71 | (258) ~ (all_0_40_40 = e1)
% 13.73/3.71 |
% 13.73/3.71 | Equations (289) can reduce 191 to:
% 13.73/3.71 | (276) ~ (all_0_44_44 = e1)
% 13.73/3.71 |
% 13.73/3.71 | Equations (289) can reduce 128 to:
% 13.73/3.71 | (263) ~ (all_0_46_46 = e1)
% 13.73/3.71 |
% 13.73/3.71 | Simplifying 263 yields:
% 13.73/3.71 | (264) ~ (all_0_46_46 = e1)
% 13.73/3.71 |
% 13.73/3.71 | Equations (289) can reduce 186 to:
% 13.73/3.71 | (1589) ~ (all_0_50_50 = e1)
% 13.73/3.71 |
% 13.73/3.71 | Simplifying 1589 yields:
% 13.73/3.71 | (326) ~ (all_0_50_50 = e1)
% 13.73/3.71 |
% 13.73/3.71 | Equations (289) can reduce 37 to:
% 13.73/3.71 | (277) ~ (all_0_54_54 = e1)
% 13.73/3.71 |
% 13.73/3.71 | Simplifying 277 yields:
% 13.73/3.71 | (278) ~ (all_0_54_54 = e1)
% 13.73/3.71 |
% 13.73/3.71 +-Applying beta-rule and splitting (25), into two cases.
% 13.73/3.71 |-Branch one:
% 13.73/3.71 | (300) all_0_45_45 = e0
% 13.73/3.71 |
% 13.73/3.71 | Combining equations (289,300) yields a new equation:
% 13.73/3.71 | (301) e1 = e0
% 13.73/3.71 |
% 13.73/3.71 | Simplifying 301 yields:
% 13.73/3.71 | (302) e1 = e0
% 13.73/3.71 |
% 13.73/3.71 | Equations (302) can reduce 143 to:
% 13.73/3.71 | (303) $false
% 13.73/3.71 |
% 13.73/3.71 |-The branch is then unsatisfiable
% 13.73/3.71 |-Branch two:
% 13.73/3.71 | (304) ~ (all_0_45_45 = e0)
% 13.73/3.71 | (305) all_0_60_60 = e0
% 13.73/3.71 |
% 13.73/3.71 | Equations (305) can reduce 67 to:
% 13.73/3.71 | (1599) ~ (all_0_48_48 = e0)
% 13.73/3.71 |
% 13.73/3.71 | Equations (305) can reduce 38 to:
% 13.73/3.71 | (308) ~ (all_0_52_52 = e0)
% 13.73/3.71 |
% 13.73/3.71 | Equations (305) can reduce 140 to:
% 13.73/3.71 | (1182) ~ (all_0_56_56 = e0)
% 13.73/3.71 |
% 13.73/3.71 | Equations (305) can reduce 18 to:
% 13.73/3.71 | (309) ~ (all_0_57_57 = e0)
% 13.73/3.71 |
% 13.73/3.71 | Equations (305) can reduce 86 to:
% 13.73/3.71 | (203) ~ (all_0_58_58 = e0)
% 13.73/3.71 |
% 13.73/3.71 +-Applying beta-rule and splitting (223), into two cases.
% 13.73/3.71 |-Branch one:
% 13.73/3.71 | (275) all_0_53_53 = e1
% 13.73/3.71 |
% 13.73/3.71 | Combining equations (413,275) yields a new equation:
% 13.73/3.71 | (604) e3 = e1
% 13.73/3.71 |
% 13.73/3.71 | Simplifying 604 yields:
% 13.73/3.71 | (414) e3 = e1
% 13.73/3.71 |
% 13.73/3.71 | Equations (414) can reduce 145 to:
% 13.73/3.71 | (303) $false
% 13.73/3.71 |
% 13.73/3.71 |-The branch is then unsatisfiable
% 13.73/3.71 |-Branch two:
% 13.73/3.71 | (1568) ~ (all_0_53_53 = e1)
% 13.73/3.71 | (1609) all_0_54_54 = e1 | all_0_55_55 = e1
% 13.73/3.71 |
% 13.73/3.71 +-Applying beta-rule and splitting (1609), into two cases.
% 13.73/3.71 |-Branch one:
% 13.73/3.71 | (1289) all_0_54_54 = e1
% 13.73/3.71 |
% 13.73/3.71 | Equations (1289) can reduce 278 to:
% 13.73/3.71 | (303) $false
% 13.73/3.71 |
% 13.73/3.71 |-The branch is then unsatisfiable
% 13.73/3.71 |-Branch two:
% 13.73/3.71 | (278) ~ (all_0_54_54 = e1)
% 13.73/3.71 | (1065) all_0_55_55 = e1
% 13.73/3.71 |
% 13.73/3.71 | Equations (1065) can reduce 160 to:
% 13.73/3.71 | (1063) ~ (all_0_52_52 = e1)
% 13.73/3.71 |
% 13.73/3.71 | Equations (1065) can reduce 256 to:
% 13.73/3.71 | (346) ~ (e4 = e1)
% 13.73/3.71 |
% 13.73/3.71 | Simplifying 346 yields:
% 13.73/3.71 | (253) ~ (e4 = e1)
% 13.73/3.71 |
% 13.73/3.71 +-Applying beta-rule and splitting (157), into two cases.
% 13.73/3.71 |-Branch one:
% 13.73/3.71 | (404) all_0_54_54 = e2
% 13.73/3.71 |
% 13.73/3.71 | Equations (404) can reduce 196 to:
% 13.73/3.71 | (716) ~ (all_0_57_57 = e2)
% 13.73/3.71 |
% 13.73/3.71 | Simplifying 716 yields:
% 13.73/3.71 | (717) ~ (all_0_57_57 = e2)
% 13.73/3.71 |
% 13.73/3.71 | Equations (404) can reduce 148 to:
% 13.73/3.71 | (389) ~ (e4 = e2)
% 13.73/3.71 |
% 13.73/3.71 | Simplifying 389 yields:
% 13.73/3.71 | (227) ~ (e4 = e2)
% 13.73/3.71 |
% 13.73/3.71 | From (404) and (238) follows:
% 13.73/3.71 | (1622) op(e3, e2) = all_0_13_13
% 13.73/3.71 |
% 13.73/3.71 | Instantiating formula (39) with e3, e2, all_0_13_13, all_0_46_46 and discharging atoms op(e3, e2) = all_0_13_13, op(e3, e2) = all_0_46_46, yields:
% 13.73/3.71 | (1623) all_0_13_13 = all_0_46_46
% 13.73/3.71 |
% 13.73/3.71 | From (1623) and (1622) follows:
% 13.73/3.71 | (239) op(e3, e2) = all_0_46_46
% 13.73/3.71 |
% 13.73/3.71 +-Applying beta-rule and splitting (85), into two cases.
% 13.73/3.71 |-Branch one:
% 13.73/3.71 | (355) all_0_46_46 = e2
% 13.73/3.71 |
% 13.73/3.71 | Equations (355) can reduce 79 to:
% 13.73/3.71 | (110) ~ (all_0_44_44 = e2)
% 13.73/3.71 |
% 13.73/3.71 | Equations (355) can reduce 119 to:
% 13.73/3.71 | (356) ~ (all_0_47_47 = e2)
% 13.73/3.71 |
% 13.73/3.71 | Simplifying 356 yields:
% 13.73/3.71 | (357) ~ (all_0_47_47 = e2)
% 13.73/3.71 |
% 13.73/3.71 | Equations (355) can reduce 2 to:
% 13.73/3.71 | (358) ~ (all_0_48_48 = e2)
% 13.73/3.71 |
% 13.73/3.71 | Simplifying 358 yields:
% 13.73/3.71 | (359) ~ (all_0_48_48 = e2)
% 13.73/3.71 |
% 13.73/3.71 | Equations (355) can reduce 71 to:
% 13.73/3.71 | (410) ~ (all_0_58_58 = e2)
% 13.73/3.71 |
% 13.73/3.71 | Simplifying 410 yields:
% 13.73/3.71 | (411) ~ (all_0_58_58 = e2)
% 13.73/3.71 |
% 13.73/3.71 | Equations (355) can reduce 264 to:
% 13.73/3.71 | (150) ~ (e2 = e1)
% 13.73/3.71 |
% 13.73/3.71 | Equations (355) can reduce 103 to:
% 13.73/3.71 | (61) ~ (e2 = e0)
% 13.73/3.71 |
% 13.73/3.71 | From (355) and (161) follows:
% 13.73/3.71 | (362) op(e3, e2) = all_0_20_20
% 13.73/3.71 |
% 13.73/3.71 | From (355) and (239) follows:
% 13.73/3.71 | (363) op(e3, e2) = e2
% 13.73/3.71 |
% 13.73/3.71 +-Applying beta-rule and splitting (23), into two cases.
% 13.73/3.71 |-Branch one:
% 13.73/3.71 | (425) all_0_41_41 = e4
% 13.73/3.71 |
% 13.73/3.71 | Combining equations (257,425) yields a new equation:
% 13.73/3.71 | (427) e4 = e1
% 13.73/3.71 |
% 13.73/3.71 | Equations (427) can reduce 253 to:
% 13.73/3.71 | (303) $false
% 13.73/3.71 |
% 13.73/3.71 |-The branch is then unsatisfiable
% 13.73/3.71 |-Branch two:
% 13.73/3.71 | (429) ~ (all_0_41_41 = e4)
% 13.73/3.71 | (430) all_0_46_46 = e4 | all_0_58_58 = e4
% 13.73/3.71 |
% 13.73/3.71 +-Applying beta-rule and splitting (175), into two cases.
% 13.73/3.71 |-Branch one:
% 13.73/3.71 | (364) all_0_48_48 = e2
% 13.73/3.71 |
% 13.73/3.71 | Equations (364) can reduce 359 to:
% 13.73/3.71 | (303) $false
% 13.73/3.71 |
% 13.73/3.71 |-The branch is then unsatisfiable
% 13.73/3.71 |-Branch two:
% 13.73/3.71 | (359) ~ (all_0_48_48 = e2)
% 13.73/3.71 | (367) all_0_52_52 = e2 | all_0_55_55 = e2 | all_0_60_60 = e2
% 13.73/3.71 |
% 13.73/3.71 +-Applying beta-rule and splitting (367), into two cases.
% 13.73/3.71 |-Branch one:
% 13.73/3.71 | (368) all_0_52_52 = e2
% 13.73/3.71 |
% 13.73/3.71 | Equations (368) can reduce 54 to:
% 13.73/3.71 | (95) ~ (all_0_43_43 = e2)
% 13.73/3.71 |
% 13.73/3.71 | Equations (368) can reduce 233 to:
% 13.73/3.71 | (359) ~ (all_0_48_48 = e2)
% 13.73/3.71 |
% 13.73/3.71 | Equations (368) can reduce 70 to:
% 13.73/3.71 | (654) ~ (all_0_51_51 = e2)
% 13.73/3.71 |
% 13.73/3.71 | Equations (368) can reduce 308 to:
% 13.73/3.71 | (61) ~ (e2 = e0)
% 13.73/3.71 |
% 13.73/3.71 +-Applying beta-rule and splitting (430), into two cases.
% 13.73/3.71 |-Branch one:
% 13.73/3.71 | (433) all_0_46_46 = e4
% 13.73/3.72 |
% 13.73/3.72 | Combining equations (433,355) yields a new equation:
% 13.73/3.72 | (455) e4 = e2
% 13.73/3.72 |
% 13.73/3.72 | Simplifying 455 yields:
% 13.73/3.72 | (434) e4 = e2
% 13.73/3.72 |
% 13.73/3.72 | Equations (434) can reduce 227 to:
% 13.73/3.72 | (303) $false
% 13.73/3.72 |
% 13.73/3.72 |-The branch is then unsatisfiable
% 13.73/3.72 |-Branch two:
% 13.73/3.72 | (436) ~ (all_0_46_46 = e4)
% 13.73/3.72 | (437) all_0_58_58 = e4
% 13.73/3.72 |
% 13.73/3.72 | Equations (437) can reduce 206 to:
% 13.73/3.72 | (988) ~ (all_0_56_56 = e4)
% 13.73/3.72 |
% 13.73/3.72 | Equations (437) can reduce 82 to:
% 13.73/3.72 | (764) ~ (all_0_57_57 = e4)
% 13.73/3.72 |
% 13.73/3.72 | Equations (437) can reduce 108 to:
% 13.73/3.72 | (1149) ~ (all_0_59_59 = e4)
% 13.73/3.72 |
% 13.73/3.72 | Simplifying 1149 yields:
% 13.73/3.72 | (8) ~ (all_0_59_59 = e4)
% 13.73/3.72 |
% 13.73/3.72 | Equations (437) can reduce 411 to:
% 13.73/3.72 | (227) ~ (e4 = e2)
% 13.73/3.72 |
% 13.73/3.72 | Equations (437) can reduce 203 to:
% 13.73/3.72 | (5) ~ (e4 = e0)
% 13.73/3.72 |
% 13.73/3.72 | From (437) and (27) follows:
% 13.73/3.72 | (439) op(e2, e4) = all_0_21_21
% 13.73/3.72 |
% 13.73/3.72 +-Applying beta-rule and splitting (60), into two cases.
% 13.73/3.72 |-Branch one:
% 13.73/3.72 | (314) all_0_56_56 = e1
% 13.73/3.72 |
% 13.73/3.72 | Equations (314) can reduce 130 to:
% 13.73/3.72 | (276) ~ (all_0_44_44 = e1)
% 13.73/3.72 |
% 13.73/3.72 | Equations (314) can reduce 224 to:
% 13.73/3.72 | (325) ~ (all_0_49_49 = e1)
% 13.73/3.72 |
% 13.73/3.72 | Equations (314) can reduce 90 to:
% 13.73/3.72 | (298) ~ (all_0_57_57 = e1)
% 13.73/3.72 |
% 13.73/3.72 | Simplifying 298 yields:
% 13.73/3.72 | (299) ~ (all_0_57_57 = e1)
% 13.73/3.72 |
% 13.73/3.72 | Equations (314) can reduce 208 to:
% 13.73/3.72 | (267) ~ (e2 = e1)
% 13.73/3.72 |
% 13.73/3.72 | Simplifying 267 yields:
% 13.73/3.72 | (150) ~ (e2 = e1)
% 13.73/3.72 |
% 13.73/3.72 | From (314) and (245) follows:
% 13.73/3.72 | (1671) op(e4, e1) = all_0_6_6
% 13.73/3.72 |
% 13.73/3.72 +-Applying beta-rule and splitting (120), into two cases.
% 13.73/3.72 |-Branch one:
% 13.73/3.72 | (333) all_0_57_57 = e1
% 13.73/3.72 |
% 13.73/3.72 | Equations (333) can reduce 299 to:
% 13.73/3.72 | (303) $false
% 13.73/3.72 |
% 13.73/3.72 |-The branch is then unsatisfiable
% 13.73/3.72 |-Branch two:
% 13.73/3.72 | (299) ~ (all_0_57_57 = e1)
% 13.73/3.72 | (770) all_0_57_57 = e4 | all_0_57_57 = e3 | all_0_57_57 = e2 | all_0_57_57 = e0
% 13.73/3.72 |
% 13.73/3.72 +-Applying beta-rule and splitting (78), into two cases.
% 13.73/3.72 |-Branch one:
% 13.73/3.72 | (811) all_0_49_49 = e1
% 13.73/3.72 |
% 13.73/3.72 | Equations (811) can reduce 325 to:
% 13.73/3.72 | (303) $false
% 13.73/3.72 |
% 13.73/3.72 |-The branch is then unsatisfiable
% 13.73/3.72 |-Branch two:
% 13.73/3.72 | (325) ~ (all_0_49_49 = e1)
% 13.73/3.72 | (1679) all_0_50_50 = e1 | all_0_51_51 = e1 | all_0_52_52 = e1
% 13.73/3.72 |
% 13.73/3.72 +-Applying beta-rule and splitting (770), into two cases.
% 13.73/3.72 |-Branch one:
% 13.73/3.72 | (628) all_0_57_57 = e0
% 13.73/3.72 |
% 13.73/3.72 | Equations (628) can reduce 309 to:
% 13.73/3.72 | (303) $false
% 13.73/3.72 |
% 13.73/3.72 |-The branch is then unsatisfiable
% 13.73/3.72 |-Branch two:
% 13.73/3.72 | (309) ~ (all_0_57_57 = e0)
% 13.73/3.72 | (774) all_0_57_57 = e4 | all_0_57_57 = e3 | all_0_57_57 = e2
% 13.73/3.72 |
% 13.73/3.72 +-Applying beta-rule and splitting (774), into two cases.
% 13.73/3.72 |-Branch one:
% 13.73/3.72 | (637) all_0_57_57 = e3
% 13.73/3.72 |
% 13.73/3.72 +-Applying beta-rule and splitting (1679), into two cases.
% 13.73/3.72 |-Branch one:
% 13.73/3.72 | (501) all_0_50_50 = e1
% 13.73/3.72 |
% 13.73/3.72 | Equations (501) can reduce 326 to:
% 13.73/3.72 | (303) $false
% 13.73/3.72 |
% 13.73/3.72 |-The branch is then unsatisfiable
% 13.73/3.72 |-Branch two:
% 13.73/3.72 | (326) ~ (all_0_50_50 = e1)
% 13.73/3.72 | (1688) all_0_51_51 = e1 | all_0_52_52 = e1
% 13.73/3.72 |
% 13.73/3.72 +-Applying beta-rule and splitting (1688), into two cases.
% 13.73/3.72 |-Branch one:
% 13.73/3.72 | (1185) all_0_51_51 = e1
% 13.73/3.72 |
% 13.73/3.72 | Combining equations (1185,273) yields a new equation:
% 13.73/3.72 | (1690) all_0_17_17 = e1
% 13.73/3.72 |
% 13.73/3.72 | Equations (1185) can reduce 179 to:
% 13.73/3.72 | (260) ~ (all_0_42_42 = e1)
% 13.73/3.72 |
% 13.73/3.72 | Equations (1185) can reduce 176 to:
% 13.73/3.72 | (1560) ~ (all_0_47_47 = e1)
% 13.73/3.72 |
% 13.73/3.72 | Equations (1185) can reduce 83 to:
% 13.73/3.72 | (325) ~ (all_0_49_49 = e1)
% 13.73/3.72 |
% 13.73/3.72 | Equations (1185) can reduce 92 to:
% 13.73/3.72 | (1694) ~ (all_0_59_59 = e1)
% 13.73/3.72 |
% 13.73/3.72 | Simplifying 1694 yields:
% 13.73/3.72 | (1058) ~ (all_0_59_59 = e1)
% 13.73/3.72 |
% 13.73/3.72 | Equations (1185) can reduce 56 to:
% 13.73/3.72 | (346) ~ (e4 = e1)
% 13.73/3.72 |
% 13.73/3.72 | Simplifying 346 yields:
% 13.73/3.72 | (253) ~ (e4 = e1)
% 13.73/3.72 |
% 13.73/3.72 | Equations (1185) can reduce 654 to:
% 13.73/3.72 | (267) ~ (e2 = e1)
% 13.73/3.72 |
% 13.73/3.72 | Simplifying 267 yields:
% 13.73/3.72 | (150) ~ (e2 = e1)
% 13.73/3.72 |
% 13.73/3.72 +-Applying beta-rule and splitting (127), into two cases.
% 13.73/3.72 |-Branch one:
% 13.73/3.72 | (379) all_0_47_47 = e2
% 13.73/3.72 |
% 13.73/3.72 | Equations (379) can reduce 357 to:
% 13.73/3.72 | (303) $false
% 13.73/3.72 |
% 13.73/3.72 |-The branch is then unsatisfiable
% 13.73/3.72 |-Branch two:
% 13.73/3.72 | (357) ~ (all_0_47_47 = e2)
% 13.73/3.72 | (382) all_0_51_51 = e2 | all_0_59_59 = e2
% 13.73/3.72 |
% 13.73/3.72 +-Applying beta-rule and splitting (382), into two cases.
% 13.73/3.72 |-Branch one:
% 13.73/3.72 | (383) all_0_51_51 = e2
% 13.73/3.72 |
% 13.73/3.72 | Combining equations (1185,383) yields a new equation:
% 13.73/3.72 | (369) e2 = e1
% 13.73/3.72 |
% 13.73/3.72 | Equations (369) can reduce 150 to:
% 13.73/3.72 | (303) $false
% 13.73/3.72 |
% 13.73/3.72 |-The branch is then unsatisfiable
% 13.73/3.72 |-Branch two:
% 13.73/3.72 | (654) ~ (all_0_51_51 = e2)
% 13.73/3.72 | (655) all_0_59_59 = e2
% 13.73/3.72 |
% 13.73/3.72 | Equations (655) can reduce 8 to:
% 13.73/3.72 | (389) ~ (e4 = e2)
% 13.73/3.72 |
% 13.73/3.72 | Simplifying 389 yields:
% 13.73/3.72 | (227) ~ (e4 = e2)
% 13.73/3.72 |
% 13.73/3.72 | Equations (655) can reduce 1058 to:
% 13.73/3.72 | (150) ~ (e2 = e1)
% 13.73/3.72 |
% 13.73/3.72 | Instantiating formula (39) with e4, e1, all_0_6_6, all_0_42_42 and discharging atoms op(e4, e1) = all_0_6_6, op(e4, e1) = all_0_42_42, yields:
% 13.73/3.72 | (1712) all_0_6_6 = all_0_42_42
% 13.73/3.72 |
% 13.73/3.72 | Instantiating formula (39) with e3, e2, e2, all_0_20_20 and discharging atoms op(e3, e2) = all_0_20_20, op(e3, e2) = e2, yields:
% 13.73/3.72 | (446) all_0_20_20 = e2
% 13.73/3.72 |
% 13.73/3.72 | Instantiating formula (39) with e2, e4, all_0_21_21, all_0_49_49 and discharging atoms op(e2, e4) = all_0_21_21, op(e2, e4) = all_0_49_49, yields:
% 13.73/3.72 | (442) all_0_21_21 = all_0_49_49
% 13.73/3.72 |
% 13.73/3.72 +-Applying beta-rule and splitting (19), into two cases.
% 13.73/3.72 |-Branch one:
% 13.73/3.72 | (450) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2)) | (all_0_21_21 = e0 & ~ (all_0_22_22 = e2))
% 13.73/3.72 |
% 13.73/3.72 +-Applying beta-rule and splitting (450), into two cases.
% 13.73/3.72 |-Branch one:
% 13.73/3.72 | (451) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2))
% 13.73/3.72 |
% 13.73/3.72 +-Applying beta-rule and splitting (451), into two cases.
% 13.73/3.72 |-Branch one:
% 13.73/3.72 | (452) all_0_17_17 = e4 & ~ (all_0_18_18 = e2)
% 13.73/3.72 |
% 13.73/3.72 | Applying alpha-rule on (452) yields:
% 13.73/3.72 | (453) all_0_17_17 = e4
% 13.73/3.72 | (454) ~ (all_0_18_18 = e2)
% 13.73/3.72 |
% 13.73/3.72 | Combining equations (453,1690) yields a new equation:
% 13.73/3.72 | (426) e4 = e1
% 13.73/3.72 |
% 13.73/3.72 | Simplifying 426 yields:
% 13.73/3.72 | (427) e4 = e1
% 13.73/3.72 |
% 13.73/3.72 | Equations (427) can reduce 253 to:
% 13.73/3.72 | (303) $false
% 13.73/3.72 |
% 13.73/3.72 |-The branch is then unsatisfiable
% 13.73/3.72 |-Branch two:
% 13.73/3.72 | (458) all_0_19_19 = e3 & ~ (all_0_20_20 = e2)
% 13.73/3.72 |
% 13.73/3.72 | Applying alpha-rule on (458) yields:
% 13.73/3.72 | (459) all_0_19_19 = e3
% 13.73/3.72 | (460) ~ (all_0_20_20 = e2)
% 13.73/3.72 |
% 13.73/3.72 | Equations (446) can reduce 460 to:
% 13.73/3.72 | (303) $false
% 13.73/3.72 |
% 13.73/3.72 |-The branch is then unsatisfiable
% 13.73/3.72 |-Branch two:
% 13.73/3.72 | (462) all_0_21_21 = e0 & ~ (all_0_22_22 = e2)
% 13.73/3.72 |
% 13.73/3.72 | Applying alpha-rule on (462) yields:
% 13.73/3.72 | (463) all_0_21_21 = e0
% 13.73/3.72 | (464) ~ (all_0_22_22 = e2)
% 13.73/3.72 |
% 13.73/3.72 | Combining equations (442,463) yields a new equation:
% 13.73/3.72 | (465) all_0_49_49 = e0
% 13.73/3.72 |
% 13.73/3.72 | Simplifying 465 yields:
% 13.73/3.72 | (466) all_0_49_49 = e0
% 13.73/3.72 |
% 13.73/3.72 | Equations (466) can reduce 53 to:
% 13.73/3.72 | (819) ~ (all_0_44_44 = e0)
% 13.73/3.72 |
% 13.73/3.72 | Equations (466) can reduce 123 to:
% 13.73/3.72 | (467) ~ (all_0_50_50 = e0)
% 13.73/3.72 |
% 13.73/3.72 | Simplifying 467 yields:
% 13.73/3.72 | (468) ~ (all_0_50_50 = e0)
% 13.73/3.72 |
% 13.73/3.72 | Equations (466) can reduce 46 to:
% 13.73/3.72 | (480) ~ (e3 = e0)
% 13.73/3.72 |
% 13.73/3.72 | Simplifying 480 yields:
% 13.73/3.72 | (74) ~ (e3 = e0)
% 13.73/3.72 |
% 13.73/3.72 | Equations (466) can reduce 325 to:
% 13.73/3.72 | (471) ~ (e1 = e0)
% 13.73/3.72 |
% 13.73/3.72 | Simplifying 471 yields:
% 13.73/3.72 | (143) ~ (e1 = e0)
% 13.73/3.72 |
% 13.73/3.72 | From (466) and (154) follows:
% 13.73/3.72 | (833) op(e4, e0) = all_0_2_2
% 13.73/3.72 |
% 13.73/3.72 +-Applying beta-rule and splitting (88), into two cases.
% 13.73/3.72 |-Branch one:
% 13.73/3.72 | (528) all_0_49_49 = e4
% 13.73/3.72 |
% 13.73/3.72 | Combining equations (466,528) yields a new equation:
% 13.73/3.72 | (512) e4 = e0
% 13.73/3.72 |
% 13.73/3.72 | Equations (512) can reduce 5 to:
% 13.73/3.72 | (303) $false
% 13.73/3.72 |
% 13.73/3.72 |-The branch is then unsatisfiable
% 13.73/3.72 |-Branch two:
% 13.73/3.72 | (531) ~ (all_0_49_49 = e4)
% 13.73/3.72 | (532) all_0_50_50 = e4 | all_0_52_52 = e4
% 13.73/3.72 |
% 13.73/3.72 +-Applying beta-rule and splitting (532), into two cases.
% 13.73/3.72 |-Branch one:
% 13.73/3.72 | (533) all_0_50_50 = e4
% 13.73/3.72 |
% 13.73/3.72 | Equations (533) can reduce 468 to:
% 13.73/3.72 | (5) ~ (e4 = e0)
% 13.73/3.72 |
% 13.73/3.72 +-Applying beta-rule and splitting (213), into two cases.
% 13.73/3.72 |-Branch one:
% 13.73/3.72 | (1087) all_0_44_44 = e1
% 13.73/3.72 |
% 13.73/3.72 | Equations (1087) can reduce 276 to:
% 13.73/3.72 | (303) $false
% 13.73/3.72 |
% 13.73/3.72 |-The branch is then unsatisfiable
% 13.73/3.72 |-Branch two:
% 13.73/3.72 | (276) ~ (all_0_44_44 = e1)
% 13.73/3.72 | (1750) all_0_44_44 = e4 | all_0_44_44 = e3 | all_0_44_44 = e0
% 13.73/3.72 |
% 13.73/3.72 +-Applying beta-rule and splitting (55), into two cases.
% 13.73/3.72 |-Branch one:
% 13.73/3.72 | (473) all_0_40_40 = e0
% 13.73/3.72 |
% 13.73/3.72 | Combining equations (473,1583) yields a new equation:
% 13.73/3.72 | (1752) all_0_4_4 = e0
% 13.73/3.72 |
% 13.73/3.72 | Equations (473) can reduce 189 to:
% 13.73/3.72 | (474) ~ (all_0_42_42 = e0)
% 13.73/3.72 |
% 13.73/3.72 | Simplifying 474 yields:
% 13.73/3.72 | (475) ~ (all_0_42_42 = e0)
% 13.73/3.72 |
% 13.73/3.72 | Equations (473) can reduce 51 to:
% 13.73/3.72 | (476) ~ (all_0_43_43 = e0)
% 13.73/3.72 |
% 13.73/3.72 | Simplifying 476 yields:
% 13.73/3.72 | (306) ~ (all_0_43_43 = e0)
% 13.73/3.72 |
% 13.73/3.72 | Equations (473) can reduce 258 to:
% 13.73/3.72 | (471) ~ (e1 = e0)
% 13.73/3.72 |
% 13.73/3.72 | Simplifying 471 yields:
% 13.73/3.72 | (143) ~ (e1 = e0)
% 13.73/3.72 |
% 13.73/3.72 +-Applying beta-rule and splitting (42), into two cases.
% 13.73/3.72 |-Branch one:
% 13.73/3.72 | (1375) all_0_42_42 = e1
% 13.73/3.72 |
% 13.73/3.72 | Equations (1375) can reduce 260 to:
% 13.73/3.72 | (303) $false
% 13.73/3.72 |
% 13.73/3.72 |-The branch is then unsatisfiable
% 13.73/3.72 |-Branch two:
% 13.73/3.72 | (260) ~ (all_0_42_42 = e1)
% 13.73/3.72 | (1378) all_0_42_42 = e3 | all_0_42_42 = e0
% 13.73/3.72 |
% 13.73/3.72 +-Applying beta-rule and splitting (1750), into two cases.
% 13.73/3.72 |-Branch one:
% 13.73/3.72 | (815) all_0_44_44 = e0
% 13.73/3.72 |
% 13.73/3.72 | Equations (815) can reduce 819 to:
% 13.73/3.72 | (303) $false
% 13.73/3.72 |
% 13.73/3.72 |-The branch is then unsatisfiable
% 13.73/3.72 |-Branch two:
% 13.73/3.72 | (819) ~ (all_0_44_44 = e0)
% 13.73/3.72 | (1766) all_0_44_44 = e4 | all_0_44_44 = e3
% 13.73/3.72 |
% 13.73/3.72 +-Applying beta-rule and splitting (1766), into two cases.
% 13.73/3.72 |-Branch one:
% 13.73/3.72 | (775) all_0_44_44 = e3
% 13.73/3.72 |
% 13.73/3.72 | Equations (775) can reduce 908 to:
% 13.73/3.72 | (303) $false
% 13.73/3.72 |
% 13.73/3.72 |-The branch is then unsatisfiable
% 13.73/3.72 |-Branch two:
% 13.73/3.72 | (908) ~ (all_0_44_44 = e3)
% 13.73/3.72 | (1189) all_0_44_44 = e4
% 13.73/3.72 |
% 13.73/3.72 | Equations (1189) can reduce 40 to:
% 13.73/3.72 | (506) ~ (all_0_48_48 = e4)
% 13.73/3.72 |
% 13.73/3.72 | Simplifying 506 yields:
% 13.73/3.72 | (507) ~ (all_0_48_48 = e4)
% 13.73/3.72 |
% 13.73/3.72 | Equations (1189) can reduce 908 to:
% 13.73/3.72 | (30) ~ (e4 = e3)
% 13.73/3.72 |
% 13.73/3.72 | Equations (1189) can reduce 110 to:
% 13.73/3.72 | (227) ~ (e4 = e2)
% 13.73/3.72 |
% 13.73/3.72 | Equations (1189) can reduce 819 to:
% 13.73/3.72 | (5) ~ (e4 = e0)
% 13.73/3.72 |
% 13.73/3.72 | From (1189) and (126) follows:
% 13.73/3.72 | (1776) op(e4, e4) = all_0_0_0
% 13.73/3.72 |
% 13.73/3.72 +-Applying beta-rule and splitting (84), into two cases.
% 13.73/3.72 |-Branch one:
% 13.73/3.72 | (505) all_0_43_43 = e4
% 13.73/3.72 |
% 13.73/3.72 | Equations (505) can reduce 95 to:
% 13.73/3.72 | (227) ~ (e4 = e2)
% 13.73/3.73 |
% 13.73/3.73 | Equations (505) can reduce 306 to:
% 13.73/3.73 | (5) ~ (e4 = e0)
% 13.73/3.73 |
% 13.73/3.73 | From (505) and (216) follows:
% 13.73/3.73 | (682) op(e4, e4) = all_0_32_32
% 13.73/3.73 |
% 13.73/3.73 | From (505) and (254) follows:
% 13.73/3.73 | (683) op(e4, e0) = e4
% 13.73/3.73 |
% 13.73/3.73 +-Applying beta-rule and splitting (174), into two cases.
% 13.73/3.73 |-Branch one:
% 13.73/3.73 | (522) all_0_43_43 = e3
% 13.73/3.73 |
% 13.73/3.73 | Combining equations (505,522) yields a new equation:
% 13.73/3.73 | (523) e4 = e3
% 13.73/3.73 |
% 13.73/3.73 | Simplifying 523 yields:
% 13.73/3.73 | (524) e4 = e3
% 13.73/3.73 |
% 13.73/3.73 | Equations (524) can reduce 30 to:
% 13.73/3.73 | (303) $false
% 13.73/3.73 |
% 13.73/3.73 |-The branch is then unsatisfiable
% 13.73/3.73 |-Branch two:
% 13.73/3.73 | (497) ~ (all_0_43_43 = e3)
% 13.73/3.73 | (527) all_0_48_48 = e3 | all_0_55_55 = e3 | all_0_60_60 = e3
% 13.73/3.73 |
% 13.73/3.73 +-Applying beta-rule and splitting (1378), into two cases.
% 13.73/3.73 |-Branch one:
% 13.73/3.73 | (486) all_0_42_42 = e0
% 13.73/3.73 |
% 13.73/3.73 | Equations (486) can reduce 475 to:
% 13.73/3.73 | (303) $false
% 13.73/3.73 |
% 13.73/3.73 |-The branch is then unsatisfiable
% 13.73/3.73 |-Branch two:
% 13.73/3.73 | (475) ~ (all_0_42_42 = e0)
% 13.73/3.73 | (495) all_0_42_42 = e3
% 13.73/3.73 |
% 13.73/3.73 | Combining equations (495,1712) yields a new equation:
% 13.73/3.73 | (1792) all_0_6_6 = e3
% 13.73/3.73 |
% 13.73/3.73 | Equations (495) can reduce 260 to:
% 13.73/3.73 | (145) ~ (e3 = e1)
% 13.73/3.73 |
% 13.73/3.73 | Equations (495) can reduce 475 to:
% 13.73/3.73 | (74) ~ (e3 = e0)
% 13.73/3.73 |
% 13.73/3.73 +-Applying beta-rule and splitting (250), into two cases.
% 13.73/3.73 |-Branch one:
% 13.73/3.73 | (815) all_0_44_44 = e0
% 13.73/3.73 |
% 13.73/3.73 | Combining equations (1189,815) yields a new equation:
% 13.73/3.73 | (995) e4 = e0
% 13.73/3.73 |
% 13.73/3.73 | Simplifying 995 yields:
% 13.73/3.73 | (512) e4 = e0
% 13.73/3.73 |
% 13.73/3.73 | Equations (512) can reduce 5 to:
% 13.73/3.73 | (303) $false
% 13.73/3.73 |
% 13.73/3.73 |-The branch is then unsatisfiable
% 13.73/3.73 |-Branch two:
% 13.73/3.73 | (819) ~ (all_0_44_44 = e0)
% 13.73/3.73 | (1800) all_0_45_45 = e0 | all_0_47_47 = e0 | all_0_48_48 = e0
% 13.73/3.73 |
% 13.73/3.73 +-Applying beta-rule and splitting (527), into two cases.
% 13.73/3.73 |-Branch one:
% 13.73/3.73 | (535) all_0_48_48 = e3
% 13.73/3.73 |
% 13.73/3.73 | Equations (535) can reduce 9 to:
% 13.73/3.73 | (602) ~ (all_0_47_47 = e3)
% 13.73/3.73 |
% 13.73/3.73 | Equations (535) can reduce 359 to:
% 13.73/3.73 | (209) ~ (e3 = e2)
% 13.73/3.73 |
% 13.73/3.73 | Equations (535) can reduce 1599 to:
% 13.73/3.73 | (74) ~ (e3 = e0)
% 13.73/3.73 |
% 13.73/3.73 +-Applying beta-rule and splitting (1800), into two cases.
% 13.73/3.73 |-Branch one:
% 13.73/3.73 | (300) all_0_45_45 = e0
% 13.73/3.73 |
% 13.73/3.73 | Combining equations (289,300) yields a new equation:
% 13.73/3.73 | (301) e1 = e0
% 13.73/3.73 |
% 13.73/3.73 | Simplifying 301 yields:
% 13.73/3.73 | (302) e1 = e0
% 13.73/3.73 |
% 13.73/3.73 | Equations (302) can reduce 143 to:
% 13.73/3.73 | (303) $false
% 13.73/3.73 |
% 13.73/3.73 |-The branch is then unsatisfiable
% 13.73/3.73 |-Branch two:
% 13.73/3.73 | (304) ~ (all_0_45_45 = e0)
% 13.73/3.73 | (1810) all_0_47_47 = e0 | all_0_48_48 = e0
% 13.73/3.73 |
% 13.73/3.73 +-Applying beta-rule and splitting (1810), into two cases.
% 13.73/3.73 |-Branch one:
% 13.73/3.73 | (490) all_0_47_47 = e0
% 13.73/3.73 |
% 13.73/3.73 | Equations (490) can reduce 602 to:
% 13.73/3.73 | (480) ~ (e3 = e0)
% 13.73/3.73 |
% 13.73/3.73 | Simplifying 480 yields:
% 13.73/3.73 | (74) ~ (e3 = e0)
% 13.73/3.73 |
% 13.73/3.73 | Equations (490) can reduce 1560 to:
% 13.73/3.73 | (471) ~ (e1 = e0)
% 13.73/3.73 |
% 13.73/3.73 | Simplifying 471 yields:
% 13.73/3.73 | (143) ~ (e1 = e0)
% 13.73/3.73 |
% 13.73/3.73 | Instantiating formula (39) with e4, e4, all_0_0_0, e2 and discharging atoms op(e4, e4) = all_0_0_0, op(e4, e4) = e2, yields:
% 13.73/3.73 | (1816) all_0_0_0 = e2
% 13.73/3.73 |
% 13.73/3.73 | Instantiating formula (39) with e4, e4, all_0_32_32, all_0_0_0 and discharging atoms op(e4, e4) = all_0_0_0, op(e4, e4) = all_0_32_32, yields:
% 13.73/3.73 | (1817) all_0_0_0 = all_0_32_32
% 13.73/3.73 |
% 13.73/3.73 | Instantiating formula (39) with e4, e0, e4, all_0_2_2 and discharging atoms op(e4, e0) = all_0_2_2, op(e4, e0) = e4, yields:
% 13.73/3.73 | (841) all_0_2_2 = e4
% 13.73/3.73 |
% 13.73/3.73 | Combining equations (1816,1817) yields a new equation:
% 13.73/3.73 | (685) all_0_32_32 = e2
% 13.73/3.73 |
% 13.73/3.73 | Combining equations (685,1817) yields a new equation:
% 13.73/3.73 | (1816) all_0_0_0 = e2
% 13.73/3.73 |
% 13.73/3.73 +-Applying beta-rule and splitting (155), into two cases.
% 13.73/3.73 |-Branch one:
% 13.73/3.73 | (845) (all_0_0_0 = e3 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e2 & ~ (all_0_3_3 = e4)) | (all_0_4_4 = e1 & ~ (all_0_5_5 = e4))
% 13.73/3.73 |
% 13.73/3.73 +-Applying beta-rule and splitting (845), into two cases.
% 13.73/3.73 |-Branch one:
% 13.73/3.73 | (846) (all_0_0_0 = e3 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e2 & ~ (all_0_3_3 = e4))
% 13.73/3.73 |
% 13.73/3.73 +-Applying beta-rule and splitting (846), into two cases.
% 13.73/3.73 |-Branch one:
% 13.73/3.73 | (847) all_0_0_0 = e3 & ~ (all_0_1_1 = e4)
% 13.73/3.73 |
% 13.73/3.73 | Applying alpha-rule on (847) yields:
% 13.73/3.73 | (848) all_0_0_0 = e3
% 13.73/3.73 | (849) ~ (all_0_1_1 = e4)
% 13.73/3.73 |
% 13.73/3.73 | Combining equations (848,1816) yields a new equation:
% 13.73/3.73 | (552) e3 = e2
% 13.73/3.73 |
% 13.73/3.73 | Simplifying 552 yields:
% 13.73/3.73 | (553) e3 = e2
% 13.73/3.73 |
% 13.73/3.73 | Equations (553) can reduce 209 to:
% 13.73/3.73 | (303) $false
% 13.73/3.73 |
% 13.73/3.73 |-The branch is then unsatisfiable
% 13.73/3.73 |-Branch two:
% 13.73/3.73 | (853) all_0_2_2 = e2 & ~ (all_0_3_3 = e4)
% 13.73/3.73 |
% 13.73/3.73 | Applying alpha-rule on (853) yields:
% 13.73/3.73 | (854) all_0_2_2 = e2
% 13.73/3.73 | (855) ~ (all_0_3_3 = e4)
% 13.73/3.73 |
% 13.73/3.73 | Combining equations (854,841) yields a new equation:
% 13.73/3.73 | (434) e4 = e2
% 13.73/3.73 |
% 13.73/3.73 | Equations (434) can reduce 227 to:
% 13.73/3.73 | (303) $false
% 13.73/3.73 |
% 13.73/3.73 |-The branch is then unsatisfiable
% 13.73/3.73 |-Branch two:
% 13.73/3.73 | (858) all_0_4_4 = e1 & ~ (all_0_5_5 = e4)
% 13.73/3.73 |
% 13.73/3.73 | Applying alpha-rule on (858) yields:
% 13.73/3.73 | (859) all_0_4_4 = e1
% 13.73/3.73 | (860) ~ (all_0_5_5 = e4)
% 13.73/3.73 |
% 13.73/3.73 | Combining equations (859,1752) yields a new equation:
% 13.73/3.73 | (301) e1 = e0
% 13.73/3.73 |
% 13.73/3.73 | Simplifying 301 yields:
% 13.73/3.73 | (302) e1 = e0
% 13.73/3.73 |
% 13.73/3.73 | Equations (302) can reduce 143 to:
% 13.73/3.73 | (303) $false
% 13.73/3.73 |
% 13.73/3.73 |-The branch is then unsatisfiable
% 13.73/3.73 |-Branch two:
% 13.73/3.73 | (863) all_0_6_6 = e0 & ~ (all_0_7_7 = e4)
% 13.73/3.73 |
% 13.73/3.73 | Applying alpha-rule on (863) yields:
% 13.73/3.73 | (864) all_0_6_6 = e0
% 13.73/3.73 | (865) ~ (all_0_7_7 = e4)
% 13.73/3.73 |
% 13.73/3.73 | Combining equations (864,1792) yields a new equation:
% 13.73/3.73 | (575) e3 = e0
% 13.73/3.73 |
% 13.73/3.73 | Equations (575) can reduce 74 to:
% 13.73/3.73 | (303) $false
% 13.73/3.73 |
% 13.73/3.73 |-The branch is then unsatisfiable
% 13.73/3.73 |-Branch two:
% 13.73/3.73 | (607) ~ (all_0_47_47 = e0)
% 13.73/3.73 | (1846) all_0_48_48 = e0
% 13.73/3.73 |
% 13.73/3.73 | Combining equations (535,1846) yields a new equation:
% 13.73/3.73 | (574) e3 = e0
% 13.73/3.73 |
% 13.73/3.73 | Simplifying 574 yields:
% 13.73/3.73 | (575) e3 = e0
% 13.73/3.73 |
% 13.73/3.73 | Equations (575) can reduce 74 to:
% 13.73/3.73 | (303) $false
% 13.73/3.73 |
% 13.73/3.73 |-The branch is then unsatisfiable
% 13.73/3.73 |-Branch two:
% 13.73/3.73 | (566) ~ (all_0_48_48 = e3)
% 13.73/3.73 | (567) all_0_55_55 = e3 | all_0_60_60 = e3
% 13.73/3.73 |
% 13.73/3.73 +-Applying beta-rule and splitting (567), into two cases.
% 13.73/3.73 |-Branch one:
% 13.73/3.73 | (568) all_0_55_55 = e3
% 13.73/3.73 |
% 13.73/3.73 | Combining equations (568,1065) yields a new equation:
% 13.73/3.73 | (604) e3 = e1
% 13.73/3.73 |
% 13.73/3.73 | Simplifying 604 yields:
% 13.73/3.73 | (414) e3 = e1
% 13.73/3.73 |
% 13.73/3.73 | Equations (414) can reduce 145 to:
% 13.73/3.73 | (303) $false
% 13.73/3.73 |
% 13.73/3.73 |-The branch is then unsatisfiable
% 13.73/3.73 |-Branch two:
% 13.73/3.73 | (572) ~ (all_0_55_55 = e3)
% 13.73/3.73 | (573) all_0_60_60 = e3
% 13.73/3.73 |
% 13.73/3.73 | Combining equations (573,305) yields a new equation:
% 13.73/3.73 | (574) e3 = e0
% 13.73/3.73 |
% 13.73/3.73 | Simplifying 574 yields:
% 13.73/3.73 | (575) e3 = e0
% 13.73/3.73 |
% 13.73/3.73 | Equations (575) can reduce 74 to:
% 13.73/3.73 | (303) $false
% 13.73/3.73 |
% 13.73/3.73 |-The branch is then unsatisfiable
% 13.73/3.73 |-Branch two:
% 13.73/3.73 | (582) ~ (all_0_43_43 = e4)
% 13.73/3.73 | (583) all_0_48_48 = e4 | all_0_52_52 = e4 | all_0_60_60 = e4
% 13.73/3.73 |
% 13.73/3.73 +-Applying beta-rule and splitting (583), into two cases.
% 13.73/3.73 |-Branch one:
% 13.73/3.73 | (1297) all_0_48_48 = e4
% 13.73/3.73 |
% 13.73/3.73 | Equations (1297) can reduce 507 to:
% 13.73/3.73 | (303) $false
% 13.73/3.73 |
% 13.73/3.73 |-The branch is then unsatisfiable
% 13.73/3.73 |-Branch two:
% 13.73/3.73 | (507) ~ (all_0_48_48 = e4)
% 13.73/3.73 | (1300) all_0_52_52 = e4 | all_0_60_60 = e4
% 13.73/3.73 |
% 13.73/3.73 +-Applying beta-rule and splitting (1300), into two cases.
% 13.73/3.73 |-Branch one:
% 13.73/3.73 | (578) all_0_52_52 = e4
% 13.73/3.73 |
% 13.73/3.73 | Combining equations (578,368) yields a new equation:
% 13.73/3.73 | (455) e4 = e2
% 13.73/3.73 |
% 13.73/3.73 | Simplifying 455 yields:
% 13.73/3.73 | (434) e4 = e2
% 13.73/3.73 |
% 13.73/3.73 | Equations (434) can reduce 227 to:
% 13.73/3.73 | (303) $false
% 13.73/3.73 |
% 13.73/3.73 |-The branch is then unsatisfiable
% 13.73/3.73 |-Branch two:
% 13.73/3.73 | (1340) ~ (all_0_52_52 = e4)
% 13.73/3.73 | (1024) all_0_60_60 = e4
% 13.73/3.73 |
% 13.73/3.73 | Combining equations (1024,305) yields a new equation:
% 13.73/3.73 | (995) e4 = e0
% 13.73/3.73 |
% 13.73/3.73 | Simplifying 995 yields:
% 13.73/3.73 | (512) e4 = e0
% 13.73/3.73 |
% 13.73/3.73 | Equations (512) can reduce 5 to:
% 13.73/3.73 | (303) $false
% 13.73/3.73 |
% 13.73/3.73 |-The branch is then unsatisfiable
% 13.73/3.73 |-Branch two:
% 13.73/3.73 | (617) ~ (all_0_40_40 = e0)
% 13.73/3.73 | (618) all_0_45_45 = e0 | all_0_50_50 = e0 | all_0_57_57 = e0
% 13.73/3.73 |
% 13.73/3.73 +-Applying beta-rule and splitting (618), into two cases.
% 13.73/3.73 |-Branch one:
% 13.73/3.73 | (300) all_0_45_45 = e0
% 13.73/3.73 |
% 13.73/3.73 | Combining equations (289,300) yields a new equation:
% 13.73/3.73 | (301) e1 = e0
% 13.73/3.73 |
% 13.73/3.73 | Simplifying 301 yields:
% 13.73/3.73 | (302) e1 = e0
% 13.73/3.73 |
% 13.73/3.73 | Equations (302) can reduce 143 to:
% 13.73/3.73 | (303) $false
% 13.73/3.73 |
% 13.73/3.73 |-The branch is then unsatisfiable
% 13.73/3.73 |-Branch two:
% 13.73/3.73 | (304) ~ (all_0_45_45 = e0)
% 13.73/3.73 | (624) all_0_50_50 = e0 | all_0_57_57 = e0
% 13.73/3.73 |
% 13.73/3.73 +-Applying beta-rule and splitting (624), into two cases.
% 13.73/3.73 |-Branch one:
% 13.73/3.73 | (518) all_0_50_50 = e0
% 13.73/3.73 |
% 13.73/3.73 | Combining equations (533,518) yields a new equation:
% 13.73/3.73 | (995) e4 = e0
% 13.73/3.73 |
% 13.73/3.73 | Simplifying 995 yields:
% 13.73/3.73 | (512) e4 = e0
% 13.73/3.73 |
% 13.73/3.73 | Equations (512) can reduce 5 to:
% 13.73/3.73 | (303) $false
% 13.73/3.73 |
% 13.73/3.73 |-The branch is then unsatisfiable
% 13.73/3.73 |-Branch two:
% 13.73/3.73 | (468) ~ (all_0_50_50 = e0)
% 13.73/3.73 | (628) all_0_57_57 = e0
% 13.73/3.73 |
% 13.73/3.73 | Combining equations (637,628) yields a new equation:
% 13.73/3.73 | (574) e3 = e0
% 13.73/3.73 |
% 13.73/3.73 | Simplifying 574 yields:
% 13.73/3.73 | (575) e3 = e0
% 13.73/3.73 |
% 13.73/3.73 | Equations (575) can reduce 74 to:
% 13.73/3.73 | (303) $false
% 13.73/3.73 |
% 13.73/3.73 |-The branch is then unsatisfiable
% 13.73/3.73 |-Branch two:
% 13.73/3.73 | (577) ~ (all_0_50_50 = e4)
% 13.73/3.73 | (578) all_0_52_52 = e4
% 13.73/3.73 |
% 13.73/3.73 | Combining equations (368,578) yields a new equation:
% 13.73/3.73 | (434) e4 = e2
% 13.73/3.73 |
% 13.73/3.73 | Equations (434) can reduce 227 to:
% 13.73/3.73 | (303) $false
% 13.73/3.73 |
% 13.73/3.73 |-The branch is then unsatisfiable
% 13.73/3.73 |-Branch two:
% 13.73/3.73 | (631) all_0_52_52 = e1 & ~ (all_0_55_55 = e2)
% 13.73/3.74 |
% 13.73/3.74 | Applying alpha-rule on (631) yields:
% 13.73/3.74 | (322) all_0_52_52 = e1
% 13.73/3.74 | (633) ~ (all_0_55_55 = e2)
% 13.73/3.74 |
% 13.73/3.74 | Combining equations (322,368) yields a new equation:
% 13.73/3.74 | (369) e2 = e1
% 13.73/3.74 |
% 13.73/3.74 | Equations (369) can reduce 150 to:
% 13.73/3.74 | (303) $false
% 13.73/3.74 |
% 13.73/3.74 |-The branch is then unsatisfiable
% 13.73/3.74 |-Branch two:
% 13.73/3.74 | (343) ~ (all_0_51_51 = e1)
% 13.73/3.74 | (322) all_0_52_52 = e1
% 13.73/3.74 |
% 13.73/3.74 | Combining equations (368,322) yields a new equation:
% 13.73/3.74 | (1478) e2 = e1
% 13.73/3.74 |
% 13.73/3.74 | Simplifying 1478 yields:
% 13.73/3.74 | (369) e2 = e1
% 13.73/3.74 |
% 13.73/3.74 | Equations (369) can reduce 150 to:
% 13.73/3.74 | (303) $false
% 13.73/3.74 |
% 13.73/3.74 |-The branch is then unsatisfiable
% 13.73/3.74 |-Branch two:
% 13.73/3.74 | (640) ~ (all_0_57_57 = e3)
% 13.73/3.74 | (890) all_0_57_57 = e4 | all_0_57_57 = e2
% 13.73/3.74 |
% 13.73/3.74 +-Applying beta-rule and splitting (131), into two cases.
% 13.73/3.74 |-Branch one:
% 13.73/3.74 | (407) all_0_57_57 = e2
% 13.73/3.74 |
% 13.73/3.74 | Equations (407) can reduce 717 to:
% 13.73/3.74 | (303) $false
% 13.73/3.74 |
% 13.73/3.74 |-The branch is then unsatisfiable
% 13.73/3.74 |-Branch two:
% 13.73/3.74 | (717) ~ (all_0_57_57 = e2)
% 13.73/3.74 | (1912) all_0_58_58 = e2 | all_0_59_59 = e2 | all_0_60_60 = e2
% 13.73/3.74 |
% 13.73/3.74 +-Applying beta-rule and splitting (1912), into two cases.
% 13.73/3.74 |-Branch one:
% 13.73/3.74 | (664) all_0_58_58 = e2
% 13.73/3.74 |
% 13.73/3.74 | Combining equations (437,664) yields a new equation:
% 13.73/3.74 | (455) e4 = e2
% 13.73/3.74 |
% 13.73/3.74 | Simplifying 455 yields:
% 13.73/3.74 | (434) e4 = e2
% 13.73/3.74 |
% 13.73/3.74 | Equations (434) can reduce 227 to:
% 13.73/3.74 | (303) $false
% 13.73/3.74 |
% 13.73/3.74 |-The branch is then unsatisfiable
% 13.73/3.74 |-Branch two:
% 13.73/3.74 | (411) ~ (all_0_58_58 = e2)
% 13.73/3.74 | (1918) all_0_59_59 = e2 | all_0_60_60 = e2
% 13.73/3.74 |
% 13.73/3.74 +-Applying beta-rule and splitting (1918), into two cases.
% 13.73/3.74 |-Branch one:
% 13.73/3.74 | (655) all_0_59_59 = e2
% 13.73/3.74 |
% 13.73/3.74 | Equations (655) can reduce 166 to:
% 13.73/3.74 | (717) ~ (all_0_57_57 = e2)
% 13.73/3.74 |
% 13.73/3.74 +-Applying beta-rule and splitting (890), into two cases.
% 13.73/3.74 |-Branch one:
% 13.73/3.74 | (891) all_0_57_57 = e4
% 13.73/3.74 |
% 13.73/3.74 | Equations (891) can reduce 764 to:
% 13.73/3.74 | (303) $false
% 13.73/3.74 |
% 13.73/3.74 |-The branch is then unsatisfiable
% 13.73/3.74 |-Branch two:
% 13.73/3.74 | (764) ~ (all_0_57_57 = e4)
% 13.73/3.74 | (407) all_0_57_57 = e2
% 13.73/3.74 |
% 13.73/3.74 | Equations (407) can reduce 717 to:
% 13.73/3.74 | (303) $false
% 13.73/3.74 |
% 13.73/3.74 |-The branch is then unsatisfiable
% 13.73/3.74 |-Branch two:
% 13.73/3.74 | (1437) ~ (all_0_59_59 = e2)
% 13.73/3.74 | (659) all_0_60_60 = e2
% 13.73/3.74 |
% 13.73/3.74 | Combining equations (305,659) yields a new equation:
% 13.73/3.74 | (559) e2 = e0
% 13.73/3.74 |
% 13.73/3.74 | Equations (559) can reduce 61 to:
% 13.73/3.74 | (303) $false
% 13.73/3.74 |
% 13.73/3.74 |-The branch is then unsatisfiable
% 13.73/3.74 |-Branch two:
% 13.73/3.74 | (282) ~ (all_0_56_56 = e1)
% 13.73/3.74 | (1931) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e0
% 13.73/3.74 |
% 13.73/3.74 +-Applying beta-rule and splitting (1931), into two cases.
% 13.73/3.74 |-Branch one:
% 13.73/3.74 | (1194) all_0_56_56 = e0
% 13.73/3.74 |
% 13.73/3.74 | Equations (1194) can reduce 1182 to:
% 13.73/3.74 | (303) $false
% 13.73/3.74 |
% 13.73/3.74 |-The branch is then unsatisfiable
% 13.73/3.74 |-Branch two:
% 13.73/3.74 | (1182) ~ (all_0_56_56 = e0)
% 13.73/3.74 | (1935) all_0_56_56 = e4 | all_0_56_56 = e3
% 13.73/3.74 |
% 13.73/3.74 +-Applying beta-rule and splitting (1935), into two cases.
% 13.73/3.74 |-Branch one:
% 13.73/3.74 | (431) all_0_56_56 = e3
% 13.73/3.74 |
% 13.73/3.74 | Equations (431) can reduce 635 to:
% 13.73/3.74 | (303) $false
% 13.73/3.74 |
% 13.73/3.74 |-The branch is then unsatisfiable
% 13.73/3.74 |-Branch two:
% 13.73/3.74 | (635) ~ (all_0_56_56 = e3)
% 13.73/3.74 | (762) all_0_56_56 = e4
% 13.73/3.74 |
% 13.73/3.74 | Equations (762) can reduce 988 to:
% 13.73/3.74 | (303) $false
% 13.73/3.74 |
% 13.73/3.74 |-The branch is then unsatisfiable
% 13.73/3.74 |-Branch two:
% 13.73/3.74 | (371) ~ (all_0_52_52 = e2)
% 13.73/3.74 | (372) all_0_55_55 = e2 | all_0_60_60 = e2
% 13.73/3.74 |
% 13.73/3.74 +-Applying beta-rule and splitting (372), into two cases.
% 13.73/3.74 |-Branch one:
% 13.73/3.74 | (373) all_0_55_55 = e2
% 13.73/3.74 |
% 13.73/3.74 | Combining equations (1065,373) yields a new equation:
% 13.73/3.74 | (369) e2 = e1
% 13.73/3.74 |
% 13.73/3.74 | Equations (369) can reduce 150 to:
% 13.73/3.74 | (303) $false
% 13.73/3.74 |
% 13.73/3.74 |-The branch is then unsatisfiable
% 13.73/3.74 |-Branch two:
% 13.73/3.74 | (633) ~ (all_0_55_55 = e2)
% 13.73/3.74 | (659) all_0_60_60 = e2
% 13.73/3.74 |
% 13.73/3.74 | Combining equations (659,305) yields a new equation:
% 13.73/3.74 | (558) e2 = e0
% 13.73/3.74 |
% 13.73/3.74 | Simplifying 558 yields:
% 13.73/3.74 | (559) e2 = e0
% 13.73/3.74 |
% 13.73/3.74 | Equations (559) can reduce 61 to:
% 13.73/3.74 | (303) $false
% 13.73/3.74 |
% 13.73/3.74 |-The branch is then unsatisfiable
% 13.73/3.74 |-Branch two:
% 13.73/3.74 | (663) ~ (all_0_46_46 = e2)
% 13.73/3.74 | (664) all_0_58_58 = e2
% 13.73/3.74 |
% 13.73/3.74 | From (664) and (27) follows:
% 13.73/3.74 | (666) op(e2, e2) = all_0_21_21
% 13.73/3.74 |
% 13.73/3.74 +-Applying beta-rule and splitting (23), into two cases.
% 13.73/3.74 |-Branch one:
% 13.73/3.74 | (425) all_0_41_41 = e4
% 13.73/3.74 |
% 13.73/3.74 | Combining equations (257,425) yields a new equation:
% 13.73/3.74 | (427) e4 = e1
% 13.73/3.74 |
% 13.73/3.74 | Equations (427) can reduce 253 to:
% 13.73/3.74 | (303) $false
% 13.73/3.74 |
% 13.73/3.74 |-The branch is then unsatisfiable
% 13.73/3.74 |-Branch two:
% 13.73/3.74 | (429) ~ (all_0_41_41 = e4)
% 13.73/3.74 | (430) all_0_46_46 = e4 | all_0_58_58 = e4
% 13.73/3.74 |
% 13.73/3.74 +-Applying beta-rule and splitting (430), into two cases.
% 13.73/3.74 |-Branch one:
% 13.73/3.74 | (433) all_0_46_46 = e4
% 13.73/3.74 |
% 13.73/3.74 | Equations (433) can reduce 79 to:
% 13.73/3.74 | (1361) ~ (all_0_44_44 = e4)
% 13.73/3.74 |
% 13.73/3.74 | From (433) and (65) follows:
% 13.73/3.74 | (677) op(e2, e4) = all_0_19_19
% 13.73/3.74 |
% 13.73/3.74 +-Applying beta-rule and splitting (213), into two cases.
% 13.73/3.74 |-Branch one:
% 13.73/3.74 | (1087) all_0_44_44 = e1
% 13.73/3.74 |
% 13.73/3.74 | Equations (1087) can reduce 276 to:
% 13.73/3.74 | (303) $false
% 13.73/3.74 |
% 13.73/3.74 |-The branch is then unsatisfiable
% 13.73/3.74 |-Branch two:
% 13.73/3.74 | (276) ~ (all_0_44_44 = e1)
% 13.73/3.74 | (1750) all_0_44_44 = e4 | all_0_44_44 = e3 | all_0_44_44 = e0
% 13.73/3.74 |
% 13.73/3.74 +-Applying beta-rule and splitting (1750), into two cases.
% 13.73/3.74 |-Branch one:
% 13.73/3.74 | (815) all_0_44_44 = e0
% 13.73/3.74 |
% 13.73/3.74 | Equations (815) can reduce 908 to:
% 13.73/3.74 | (480) ~ (e3 = e0)
% 13.73/3.74 |
% 13.73/3.74 | Simplifying 480 yields:
% 13.73/3.74 | (74) ~ (e3 = e0)
% 13.73/3.74 |
% 13.73/3.74 | Instantiating formula (39) with e2, e4, all_0_19_19, all_0_49_49 and discharging atoms op(e2, e4) = all_0_19_19, op(e2, e4) = all_0_49_49, yields:
% 13.73/3.74 | (686) all_0_19_19 = all_0_49_49
% 13.73/3.74 |
% 13.73/3.74 | Instantiating formula (39) with e2, e2, all_0_21_21, e3 and discharging atoms op(e2, e2) = all_0_21_21, op(e2, e2) = e3, yields:
% 13.73/3.74 | (687) all_0_21_21 = e3
% 13.73/3.74 |
% 13.73/3.74 +-Applying beta-rule and splitting (19), into two cases.
% 13.73/3.74 |-Branch one:
% 13.73/3.74 | (450) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2)) | (all_0_21_21 = e0 & ~ (all_0_22_22 = e2))
% 13.73/3.74 |
% 13.73/3.74 +-Applying beta-rule and splitting (450), into two cases.
% 13.73/3.74 |-Branch one:
% 13.73/3.74 | (451) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2))
% 13.73/3.74 |
% 13.73/3.74 +-Applying beta-rule and splitting (451), into two cases.
% 13.73/3.74 |-Branch one:
% 13.73/3.74 | (452) all_0_17_17 = e4 & ~ (all_0_18_18 = e2)
% 13.73/3.74 |
% 13.73/3.74 | Applying alpha-rule on (452) yields:
% 13.73/3.74 | (453) all_0_17_17 = e4
% 13.73/3.74 | (454) ~ (all_0_18_18 = e2)
% 13.73/3.74 |
% 13.73/3.74 | Combining equations (273,453) yields a new equation:
% 13.73/3.74 | (1167) all_0_51_51 = e4
% 13.73/3.74 |
% 13.73/3.74 | Simplifying 1167 yields:
% 13.73/3.74 | (697) all_0_51_51 = e4
% 13.73/3.74 |
% 13.73/3.74 | Equations (697) can reduce 56 to:
% 13.73/3.74 | (303) $false
% 13.73/3.74 |
% 13.73/3.74 |-The branch is then unsatisfiable
% 13.73/3.74 |-Branch two:
% 13.73/3.74 | (458) all_0_19_19 = e3 & ~ (all_0_20_20 = e2)
% 13.73/3.74 |
% 13.73/3.74 | Applying alpha-rule on (458) yields:
% 13.73/3.74 | (459) all_0_19_19 = e3
% 13.73/3.74 | (460) ~ (all_0_20_20 = e2)
% 13.73/3.74 |
% 13.73/3.74 | Combining equations (459,686) yields a new equation:
% 13.73/3.74 | (702) all_0_49_49 = e3
% 13.73/3.74 |
% 13.73/3.74 | Equations (702) can reduce 46 to:
% 13.73/3.74 | (303) $false
% 13.73/3.74 |
% 13.73/3.74 |-The branch is then unsatisfiable
% 13.73/3.74 |-Branch two:
% 13.73/3.74 | (462) all_0_21_21 = e0 & ~ (all_0_22_22 = e2)
% 13.73/3.74 |
% 13.73/3.74 | Applying alpha-rule on (462) yields:
% 13.73/3.74 | (463) all_0_21_21 = e0
% 13.73/3.74 | (464) ~ (all_0_22_22 = e2)
% 13.73/3.74 |
% 13.73/3.74 | Combining equations (463,687) yields a new equation:
% 13.73/3.74 | (575) e3 = e0
% 13.73/3.74 |
% 13.73/3.74 | Equations (575) can reduce 74 to:
% 13.73/3.74 | (303) $false
% 13.73/3.74 |
% 13.73/3.74 |-The branch is then unsatisfiable
% 13.73/3.74 |-Branch two:
% 13.73/3.74 | (631) all_0_52_52 = e1 & ~ (all_0_55_55 = e2)
% 13.73/3.74 |
% 13.73/3.74 | Applying alpha-rule on (631) yields:
% 13.73/3.74 | (322) all_0_52_52 = e1
% 13.73/3.74 | (633) ~ (all_0_55_55 = e2)
% 13.73/3.74 |
% 13.73/3.74 | Equations (322) can reduce 1063 to:
% 13.73/3.74 | (303) $false
% 13.73/3.74 |
% 13.73/3.74 |-The branch is then unsatisfiable
% 13.73/3.74 |-Branch two:
% 13.73/3.74 | (819) ~ (all_0_44_44 = e0)
% 13.73/3.74 | (1766) all_0_44_44 = e4 | all_0_44_44 = e3
% 13.73/3.74 |
% 13.73/3.74 +-Applying beta-rule and splitting (1766), into two cases.
% 13.73/3.74 |-Branch one:
% 13.73/3.74 | (775) all_0_44_44 = e3
% 13.73/3.74 |
% 13.73/3.74 | Equations (775) can reduce 908 to:
% 13.73/3.74 | (303) $false
% 13.73/3.74 |
% 13.73/3.74 |-The branch is then unsatisfiable
% 13.73/3.74 |-Branch two:
% 13.73/3.74 | (908) ~ (all_0_44_44 = e3)
% 13.73/3.74 | (1189) all_0_44_44 = e4
% 13.73/3.74 |
% 13.73/3.74 | Equations (1189) can reduce 1361 to:
% 13.73/3.74 | (303) $false
% 13.73/3.74 |
% 13.73/3.74 |-The branch is then unsatisfiable
% 14.10/3.74 |-Branch two:
% 14.10/3.74 | (436) ~ (all_0_46_46 = e4)
% 14.10/3.74 | (437) all_0_58_58 = e4
% 14.10/3.74 |
% 14.10/3.74 | Combining equations (664,437) yields a new equation:
% 14.10/3.74 | (434) e4 = e2
% 14.10/3.74 |
% 14.10/3.74 | Equations (434) can reduce 227 to:
% 14.10/3.74 | (303) $false
% 14.10/3.74 |
% 14.10/3.74 |-The branch is then unsatisfiable
% 14.10/3.74 |-Branch two:
% 14.10/3.74 | (375) ~ (all_0_54_54 = e2)
% 14.10/3.74 | (373) all_0_55_55 = e2
% 14.10/3.74 |
% 14.10/3.74 | Combining equations (1065,373) yields a new equation:
% 14.10/3.74 | (369) e2 = e1
% 14.10/3.74 |
% 14.10/3.74 | Equations (369) can reduce 150 to:
% 14.10/3.74 | (303) $false
% 14.10/3.74 |
% 14.10/3.74 |-The branch is then unsatisfiable
% 14.10/3.74 |-Branch two:
% 14.10/3.74 | (1072) ~ (all_0_45_45 = e1)
% 14.10/3.74 | (1059) all_0_60_60 = e1
% 14.10/3.74 |
% 14.10/3.74 | Equations (1059) can reduce 93 to:
% 14.10/3.74 | (262) ~ (all_0_43_43 = e1)
% 14.10/3.74 |
% 14.10/3.74 | Equations (1059) can reduce 67 to:
% 14.10/3.74 | (295) ~ (all_0_48_48 = e1)
% 14.10/3.74 |
% 14.10/3.74 | Equations (1059) can reduce 38 to:
% 14.10/3.74 | (1063) ~ (all_0_52_52 = e1)
% 14.10/3.74 |
% 14.10/3.74 | Equations (1059) can reduce 117 to:
% 14.10/3.74 | (280) ~ (all_0_55_55 = e1)
% 14.10/3.74 |
% 14.10/3.74 | Equations (1059) can reduce 140 to:
% 14.10/3.74 | (282) ~ (all_0_56_56 = e1)
% 14.10/3.74 |
% 14.10/3.74 | Equations (1059) can reduce 86 to:
% 14.10/3.74 | (266) ~ (all_0_58_58 = e1)
% 14.10/3.74 |
% 14.10/3.74 | Equations (1059) can reduce 181 to:
% 14.10/3.74 | (1058) ~ (all_0_59_59 = e1)
% 14.10/3.74 |
% 14.10/3.74 +-Applying beta-rule and splitting (25), into two cases.
% 14.10/3.75 |-Branch one:
% 14.10/3.75 | (300) all_0_45_45 = e0
% 14.10/3.75 |
% 14.10/3.75 | Equations (300) can reduce 191 to:
% 14.10/3.75 | (819) ~ (all_0_44_44 = e0)
% 14.10/3.75 |
% 14.10/3.75 | Equations (300) can reduce 156 to:
% 14.10/3.75 | (1081) ~ (all_0_47_47 = e0)
% 14.10/3.75 |
% 14.10/3.75 | Simplifying 1081 yields:
% 14.10/3.75 | (607) ~ (all_0_47_47 = e0)
% 14.10/3.75 |
% 14.10/3.75 | Equations (300) can reduce 237 to:
% 14.10/3.75 | (2021) ~ (all_0_48_48 = e0)
% 14.10/3.75 |
% 14.10/3.75 | Simplifying 2021 yields:
% 14.10/3.75 | (1599) ~ (all_0_48_48 = e0)
% 14.10/3.75 |
% 14.10/3.75 | Equations (300) can reduce 37 to:
% 14.10/3.75 | (2023) ~ (all_0_54_54 = e0)
% 14.10/3.75 |
% 14.10/3.75 | Simplifying 2023 yields:
% 14.10/3.75 | (183) ~ (all_0_54_54 = e0)
% 14.10/3.75 |
% 14.10/3.75 +-Applying beta-rule and splitting (102), into two cases.
% 14.10/3.75 |-Branch one:
% 14.10/3.75 | (1065) all_0_55_55 = e1
% 14.10/3.75 |
% 14.10/3.75 | Equations (1065) can reduce 280 to:
% 14.10/3.75 | (303) $false
% 14.10/3.75 |
% 14.10/3.75 |-The branch is then unsatisfiable
% 14.10/3.75 |-Branch two:
% 14.10/3.75 | (280) ~ (all_0_55_55 = e1)
% 14.10/3.75 | (1494) all_0_55_55 = e3 | all_0_55_55 = e2
% 14.10/3.75 |
% 14.10/3.75 +-Applying beta-rule and splitting (1494), into two cases.
% 14.10/3.75 |-Branch one:
% 14.10/3.75 | (568) all_0_55_55 = e3
% 14.10/3.75 |
% 14.10/3.75 | Equations (568) can reduce 572 to:
% 14.10/3.75 | (303) $false
% 14.10/3.75 |
% 14.10/3.75 |-The branch is then unsatisfiable
% 14.10/3.75 |-Branch two:
% 14.10/3.75 | (572) ~ (all_0_55_55 = e3)
% 14.10/3.75 | (373) all_0_55_55 = e2
% 14.10/3.75 |
% 14.10/3.75 | Equations (373) can reduce 165 to:
% 14.10/3.75 | (359) ~ (all_0_48_48 = e2)
% 14.10/3.75 |
% 14.10/3.75 | Equations (373) can reduce 160 to:
% 14.10/3.75 | (371) ~ (all_0_52_52 = e2)
% 14.10/3.75 |
% 14.10/3.75 | Equations (373) can reduce 256 to:
% 14.10/3.75 | (389) ~ (e4 = e2)
% 14.10/3.75 |
% 14.10/3.75 | Simplifying 389 yields:
% 14.10/3.75 | (227) ~ (e4 = e2)
% 14.10/3.75 |
% 14.10/3.75 | Equations (373) can reduce 280 to:
% 14.10/3.75 | (150) ~ (e2 = e1)
% 14.10/3.75 |
% 14.10/3.75 +-Applying beta-rule and splitting (223), into two cases.
% 14.10/3.75 |-Branch one:
% 14.10/3.75 | (275) all_0_53_53 = e1
% 14.10/3.75 |
% 14.10/3.75 | Combining equations (275,413) yields a new equation:
% 14.10/3.75 | (414) e3 = e1
% 14.10/3.75 |
% 14.10/3.75 | Equations (414) can reduce 145 to:
% 14.10/3.75 | (303) $false
% 14.10/3.75 |
% 14.10/3.75 |-The branch is then unsatisfiable
% 14.10/3.75 |-Branch two:
% 14.10/3.75 | (1568) ~ (all_0_53_53 = e1)
% 14.10/3.75 | (1609) all_0_54_54 = e1 | all_0_55_55 = e1
% 14.10/3.75 |
% 14.10/3.75 +-Applying beta-rule and splitting (1609), into two cases.
% 14.10/3.75 |-Branch one:
% 14.10/3.75 | (1289) all_0_54_54 = e1
% 14.10/3.75 |
% 14.10/3.75 | Equations (1289) can reduce 226 to:
% 14.10/3.75 | (326) ~ (all_0_50_50 = e1)
% 14.10/3.75 |
% 14.10/3.75 | Equations (1289) can reduce 196 to:
% 14.10/3.75 | (298) ~ (all_0_57_57 = e1)
% 14.10/3.75 |
% 14.10/3.75 | Simplifying 298 yields:
% 14.10/3.75 | (299) ~ (all_0_57_57 = e1)
% 14.10/3.75 |
% 14.10/3.75 | Equations (1289) can reduce 148 to:
% 14.10/3.75 | (346) ~ (e4 = e1)
% 14.10/3.75 |
% 14.10/3.75 | Simplifying 346 yields:
% 14.10/3.75 | (253) ~ (e4 = e1)
% 14.10/3.75 |
% 14.10/3.75 | Equations (1289) can reduce 649 to:
% 14.10/3.75 | (329) ~ (e3 = e1)
% 14.10/3.75 |
% 14.10/3.75 | Simplifying 329 yields:
% 14.10/3.75 | (145) ~ (e3 = e1)
% 14.10/3.75 |
% 14.10/3.75 | Equations (1289) can reduce 183 to:
% 14.10/3.75 | (143) ~ (e1 = e0)
% 14.10/3.75 |
% 14.10/3.75 +-Applying beta-rule and splitting (85), into two cases.
% 14.10/3.75 |-Branch one:
% 14.10/3.75 | (355) all_0_46_46 = e2
% 14.10/3.75 |
% 14.10/3.75 | From (355) and (161) follows:
% 14.10/3.75 | (362) op(e3, e2) = all_0_20_20
% 14.10/3.75 |
% 14.10/3.75 | From (355) and (239) follows:
% 14.10/3.75 | (363) op(e3, e2) = e2
% 14.10/3.75 |
% 14.10/3.75 +-Applying beta-rule and splitting (7), into two cases.
% 14.10/3.75 |-Branch one:
% 14.10/3.75 | (337) all_0_58_58 = e1
% 14.10/3.75 |
% 14.10/3.75 | Equations (337) can reduce 266 to:
% 14.10/3.75 | (303) $false
% 14.10/3.75 |
% 14.10/3.75 |-The branch is then unsatisfiable
% 14.10/3.75 |-Branch two:
% 14.10/3.75 | (266) ~ (all_0_58_58 = e1)
% 14.10/3.75 | (1136) all_0_58_58 = e4 | all_0_58_58 = e2
% 14.10/3.75 |
% 14.10/3.75 +-Applying beta-rule and splitting (23), into two cases.
% 14.10/3.75 |-Branch one:
% 14.10/3.75 | (425) all_0_41_41 = e4
% 14.10/3.75 |
% 14.10/3.75 | Combining equations (257,425) yields a new equation:
% 14.10/3.75 | (427) e4 = e1
% 14.10/3.75 |
% 14.10/3.75 | Equations (427) can reduce 253 to:
% 14.10/3.75 | (303) $false
% 14.10/3.75 |
% 14.10/3.75 |-The branch is then unsatisfiable
% 14.10/3.75 |-Branch two:
% 14.10/3.75 | (429) ~ (all_0_41_41 = e4)
% 14.10/3.75 | (430) all_0_46_46 = e4 | all_0_58_58 = e4
% 14.10/3.75 |
% 14.10/3.75 +-Applying beta-rule and splitting (430), into two cases.
% 14.10/3.75 |-Branch one:
% 14.10/3.75 | (433) all_0_46_46 = e4
% 14.10/3.75 |
% 14.10/3.75 | Combining equations (355,433) yields a new equation:
% 14.10/3.75 | (434) e4 = e2
% 14.10/3.75 |
% 14.10/3.75 | Equations (434) can reduce 227 to:
% 14.10/3.75 | (303) $false
% 14.10/3.75 |
% 14.10/3.75 |-The branch is then unsatisfiable
% 14.10/3.75 |-Branch two:
% 14.10/3.75 | (436) ~ (all_0_46_46 = e4)
% 14.10/3.75 | (437) all_0_58_58 = e4
% 14.10/3.75 |
% 14.10/3.75 | Equations (437) can reduce 206 to:
% 14.10/3.75 | (988) ~ (all_0_56_56 = e4)
% 14.10/3.75 |
% 14.10/3.75 | Equations (437) can reduce 266 to:
% 14.10/3.75 | (253) ~ (e4 = e1)
% 14.10/3.75 |
% 14.10/3.75 | Equations (437) can reduce 203 to:
% 14.10/3.75 | (5) ~ (e4 = e0)
% 14.10/3.75 |
% 14.10/3.75 | From (437) and (27) follows:
% 14.10/3.75 | (439) op(e2, e4) = all_0_21_21
% 14.10/3.75 |
% 14.10/3.75 +-Applying beta-rule and splitting (60), into two cases.
% 14.10/3.75 |-Branch one:
% 14.10/3.75 | (314) all_0_56_56 = e1
% 14.10/3.75 |
% 14.10/3.75 | Equations (314) can reduce 282 to:
% 14.10/3.75 | (303) $false
% 14.10/3.75 |
% 14.10/3.75 |-The branch is then unsatisfiable
% 14.10/3.75 |-Branch two:
% 14.10/3.75 | (282) ~ (all_0_56_56 = e1)
% 14.10/3.75 | (1931) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e0
% 14.10/3.75 |
% 14.10/3.75 +-Applying beta-rule and splitting (1931), into two cases.
% 14.10/3.75 |-Branch one:
% 14.10/3.75 | (1194) all_0_56_56 = e0
% 14.10/3.75 |
% 14.10/3.75 | Equations (1194) can reduce 224 to:
% 14.10/3.75 | (879) ~ (all_0_49_49 = e0)
% 14.10/3.75 |
% 14.10/3.75 | Instantiating formula (39) with e3, e2, e2, all_0_20_20 and discharging atoms op(e3, e2) = all_0_20_20, op(e3, e2) = e2, yields:
% 14.10/3.75 | (446) all_0_20_20 = e2
% 14.10/3.75 |
% 14.10/3.75 | Instantiating formula (39) with e2, e4, all_0_21_21, all_0_49_49 and discharging atoms op(e2, e4) = all_0_21_21, op(e2, e4) = all_0_49_49, yields:
% 14.10/3.75 | (442) all_0_21_21 = all_0_49_49
% 14.10/3.75 |
% 14.10/3.75 +-Applying beta-rule and splitting (19), into two cases.
% 14.10/3.75 |-Branch one:
% 14.10/3.75 | (450) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2)) | (all_0_21_21 = e0 & ~ (all_0_22_22 = e2))
% 14.10/3.75 |
% 14.10/3.75 +-Applying beta-rule and splitting (450), into two cases.
% 14.10/3.75 |-Branch one:
% 14.10/3.75 | (451) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2))
% 14.10/3.75 |
% 14.10/3.75 +-Applying beta-rule and splitting (451), into two cases.
% 14.10/3.75 |-Branch one:
% 14.10/3.75 | (452) all_0_17_17 = e4 & ~ (all_0_18_18 = e2)
% 14.10/3.75 |
% 14.10/3.75 | Applying alpha-rule on (452) yields:
% 14.10/3.75 | (453) all_0_17_17 = e4
% 14.10/3.75 | (454) ~ (all_0_18_18 = e2)
% 14.10/3.75 |
% 14.10/3.75 | Combining equations (273,453) yields a new equation:
% 14.10/3.75 | (1167) all_0_51_51 = e4
% 14.10/3.75 |
% 14.10/3.75 | Simplifying 1167 yields:
% 14.10/3.75 | (697) all_0_51_51 = e4
% 14.10/3.75 |
% 14.10/3.75 | Equations (697) can reduce 56 to:
% 14.10/3.75 | (303) $false
% 14.10/3.75 |
% 14.10/3.75 |-The branch is then unsatisfiable
% 14.10/3.75 |-Branch two:
% 14.10/3.75 | (458) all_0_19_19 = e3 & ~ (all_0_20_20 = e2)
% 14.10/3.75 |
% 14.10/3.75 | Applying alpha-rule on (458) yields:
% 14.10/3.75 | (459) all_0_19_19 = e3
% 14.10/3.75 | (460) ~ (all_0_20_20 = e2)
% 14.10/3.75 |
% 14.10/3.75 | Equations (446) can reduce 460 to:
% 14.10/3.75 | (303) $false
% 14.10/3.75 |
% 14.10/3.75 |-The branch is then unsatisfiable
% 14.10/3.75 |-Branch two:
% 14.10/3.75 | (462) all_0_21_21 = e0 & ~ (all_0_22_22 = e2)
% 14.10/3.75 |
% 14.10/3.75 | Applying alpha-rule on (462) yields:
% 14.10/3.75 | (463) all_0_21_21 = e0
% 14.10/3.75 | (464) ~ (all_0_22_22 = e2)
% 14.10/3.75 |
% 14.10/3.75 | Combining equations (463,442) yields a new equation:
% 14.10/3.75 | (466) all_0_49_49 = e0
% 14.10/3.75 |
% 14.10/3.75 | Equations (466) can reduce 879 to:
% 14.10/3.75 | (303) $false
% 14.10/3.75 |
% 14.10/3.75 |-The branch is then unsatisfiable
% 14.10/3.75 |-Branch two:
% 14.10/3.75 | (631) all_0_52_52 = e1 & ~ (all_0_55_55 = e2)
% 14.10/3.75 |
% 14.10/3.75 | Applying alpha-rule on (631) yields:
% 14.10/3.75 | (322) all_0_52_52 = e1
% 14.10/3.75 | (633) ~ (all_0_55_55 = e2)
% 14.10/3.75 |
% 14.10/3.75 | Equations (373) can reduce 633 to:
% 14.10/3.75 | (303) $false
% 14.10/3.75 |
% 14.10/3.75 |-The branch is then unsatisfiable
% 14.10/3.75 |-Branch two:
% 14.10/3.75 | (1182) ~ (all_0_56_56 = e0)
% 14.10/3.75 | (1935) all_0_56_56 = e4 | all_0_56_56 = e3
% 14.10/3.75 |
% 14.10/3.75 +-Applying beta-rule and splitting (121), into two cases.
% 14.10/3.75 |-Branch one:
% 14.10/3.75 | (815) all_0_44_44 = e0
% 14.10/3.75 |
% 14.10/3.75 | Equations (815) can reduce 819 to:
% 14.10/3.75 | (303) $false
% 14.10/3.75 |
% 14.10/3.75 |-The branch is then unsatisfiable
% 14.10/3.75 |-Branch two:
% 14.10/3.75 | (819) ~ (all_0_44_44 = e0)
% 14.10/3.75 | (820) all_0_49_49 = e0 | all_0_56_56 = e0
% 14.10/3.75 |
% 14.10/3.75 +-Applying beta-rule and splitting (820), into two cases.
% 14.10/3.75 |-Branch one:
% 14.10/3.75 | (466) all_0_49_49 = e0
% 14.10/3.75 |
% 14.10/3.75 | Equations (466) can reduce 53 to:
% 14.10/3.75 | (819) ~ (all_0_44_44 = e0)
% 14.10/3.75 |
% 14.10/3.75 | Equations (466) can reduce 244 to:
% 14.10/3.75 | (2110) ~ (all_0_52_52 = e0)
% 14.10/3.75 |
% 14.10/3.75 | Simplifying 2110 yields:
% 14.10/3.75 | (308) ~ (all_0_52_52 = e0)
% 14.10/3.75 |
% 14.10/3.75 | Equations (466) can reduce 46 to:
% 14.10/3.75 | (480) ~ (e3 = e0)
% 14.10/3.75 |
% 14.10/3.75 | Simplifying 480 yields:
% 14.10/3.75 | (74) ~ (e3 = e0)
% 14.10/3.75 |
% 14.10/3.75 +-Applying beta-rule and splitting (77), into two cases.
% 14.10/3.75 |-Branch one:
% 14.10/3.75 | (1189) all_0_44_44 = e4
% 14.10/3.75 |
% 14.10/3.75 | Equations (1189) can reduce 908 to:
% 14.10/3.75 | (30) ~ (e4 = e3)
% 14.10/3.75 |
% 14.10/3.75 | Equations (1189) can reduce 819 to:
% 14.10/3.75 | (5) ~ (e4 = e0)
% 14.10/3.75 |
% 14.10/3.75 +-Applying beta-rule and splitting (230), into two cases.
% 14.10/3.75 |-Branch one:
% 14.10/3.75 | (588) all_0_43_43 = e0
% 14.10/3.75 |
% 14.10/3.75 | Equations (588) can reduce 54 to:
% 14.10/3.75 | (2110) ~ (all_0_52_52 = e0)
% 14.10/3.75 |
% 14.10/3.75 | Simplifying 2110 yields:
% 14.10/3.75 | (308) ~ (all_0_52_52 = e0)
% 14.10/3.75 |
% 14.10/3.75 | Equations (588) can reduce 262 to:
% 14.10/3.75 | (471) ~ (e1 = e0)
% 14.10/3.75 |
% 14.10/3.75 | Simplifying 471 yields:
% 14.10/3.75 | (143) ~ (e1 = e0)
% 14.10/3.75 |
% 14.10/3.75 +-Applying beta-rule and splitting (21), into two cases.
% 14.10/3.75 |-Branch one:
% 14.10/3.75 | (511) all_0_40_40 = e4
% 14.10/3.75 |
% 14.10/3.75 +-Applying beta-rule and splitting (180), into two cases.
% 14.10/3.75 |-Branch one:
% 14.10/3.75 | (884) all_0_40_40 = e3
% 14.10/3.75 |
% 14.10/3.75 | Combining equations (884,511) yields a new equation:
% 14.10/3.75 | (524) e4 = e3
% 14.10/3.75 |
% 14.10/3.75 | Equations (524) can reduce 30 to:
% 14.10/3.75 | (303) $false
% 14.10/3.75 |
% 14.10/3.75 |-The branch is then unsatisfiable
% 14.10/3.75 |-Branch two:
% 14.10/3.75 | (419) ~ (all_0_40_40 = e3)
% 14.10/3.75 | (2127) all_0_45_45 = e3 | all_0_54_54 = e3 | all_0_57_57 = e3
% 14.10/3.75 |
% 14.10/3.75 +-Applying beta-rule and splitting (138), into two cases.
% 14.10/3.75 |-Branch one:
% 14.10/3.75 | (322) all_0_52_52 = e1
% 14.10/3.75 |
% 14.10/3.75 | Equations (322) can reduce 1063 to:
% 14.10/3.75 | (303) $false
% 14.10/3.75 |
% 14.10/3.75 |-The branch is then unsatisfiable
% 14.10/3.75 |-Branch two:
% 14.10/3.75 | (1063) ~ (all_0_52_52 = e1)
% 14.10/3.75 | (2131) all_0_52_52 = e4 | all_0_52_52 = e2 | all_0_52_52 = e0
% 14.10/3.75 |
% 14.10/3.75 +-Applying beta-rule and splitting (2127), into two cases.
% 14.10/3.75 |-Branch one:
% 14.10/3.75 | (1260) all_0_45_45 = e3
% 14.10/3.75 |
% 14.10/3.75 | Combining equations (300,1260) yields a new equation:
% 14.10/3.75 | (575) e3 = e0
% 14.10/3.76 |
% 14.10/3.76 | Equations (575) can reduce 74 to:
% 14.10/3.76 | (303) $false
% 14.10/3.76 |
% 14.10/3.76 |-The branch is then unsatisfiable
% 14.10/3.76 |-Branch two:
% 14.10/3.76 | (1263) ~ (all_0_45_45 = e3)
% 14.10/3.76 | (2136) all_0_54_54 = e3 | all_0_57_57 = e3
% 14.10/3.76 |
% 14.10/3.76 +-Applying beta-rule and splitting (2131), into two cases.
% 14.10/3.76 |-Branch one:
% 14.10/3.76 | (1032) all_0_52_52 = e0
% 14.10/3.76 |
% 14.10/3.76 | Equations (1032) can reduce 308 to:
% 14.10/3.76 | (303) $false
% 14.10/3.76 |
% 14.10/3.76 |-The branch is then unsatisfiable
% 14.10/3.76 |-Branch two:
% 14.10/3.76 | (308) ~ (all_0_52_52 = e0)
% 14.10/3.76 | (2140) all_0_52_52 = e4 | all_0_52_52 = e2
% 14.10/3.76 |
% 14.10/3.76 +-Applying beta-rule and splitting (2136), into two cases.
% 14.10/3.76 |-Branch one:
% 14.10/3.76 | (418) all_0_54_54 = e3
% 14.10/3.76 |
% 14.10/3.76 | Combining equations (1289,418) yields a new equation:
% 14.10/3.76 | (414) e3 = e1
% 14.10/3.76 |
% 14.10/3.76 | Equations (414) can reduce 145 to:
% 14.10/3.76 | (303) $false
% 14.10/3.76 |
% 14.10/3.76 |-The branch is then unsatisfiable
% 14.10/3.76 |-Branch two:
% 14.10/3.76 | (649) ~ (all_0_54_54 = e3)
% 14.10/3.76 | (637) all_0_57_57 = e3
% 14.10/3.76 |
% 14.10/3.76 | Equations (637) can reduce 299 to:
% 14.10/3.76 | (145) ~ (e3 = e1)
% 14.10/3.76 |
% 14.10/3.76 +-Applying beta-rule and splitting (2140), into two cases.
% 14.10/3.76 |-Branch one:
% 14.10/3.76 | (578) all_0_52_52 = e4
% 14.10/3.76 |
% 14.10/3.76 | Equations (578) can reduce 1063 to:
% 14.10/3.76 | (253) ~ (e4 = e1)
% 14.10/3.76 |
% 14.10/3.76 +-Applying beta-rule and splitting (47), into two cases.
% 14.10/3.76 |-Branch one:
% 14.10/3.76 | (1087) all_0_44_44 = e1
% 14.10/3.76 |
% 14.10/3.76 | Combining equations (1189,1087) yields a new equation:
% 14.10/3.76 | (426) e4 = e1
% 14.10/3.76 |
% 14.10/3.76 | Simplifying 426 yields:
% 14.10/3.76 | (427) e4 = e1
% 14.10/3.76 |
% 14.10/3.76 | Equations (427) can reduce 253 to:
% 14.10/3.76 | (303) $false
% 14.10/3.76 |
% 14.10/3.76 |-The branch is then unsatisfiable
% 14.10/3.76 |-Branch two:
% 14.10/3.76 | (276) ~ (all_0_44_44 = e1)
% 14.10/3.76 | (2154) all_0_49_49 = e1 | all_0_53_53 = e1 | all_0_56_56 = e1
% 14.10/3.76 |
% 14.10/3.76 +-Applying beta-rule and splitting (2154), into two cases.
% 14.10/3.76 |-Branch one:
% 14.10/3.76 | (811) all_0_49_49 = e1
% 14.10/3.76 |
% 14.10/3.76 | Combining equations (466,811) yields a new equation:
% 14.10/3.76 | (302) e1 = e0
% 14.10/3.76 |
% 14.10/3.76 | Equations (302) can reduce 143 to:
% 14.10/3.76 | (303) $false
% 14.10/3.76 |
% 14.10/3.76 |-The branch is then unsatisfiable
% 14.10/3.76 |-Branch two:
% 14.10/3.76 | (325) ~ (all_0_49_49 = e1)
% 14.10/3.76 | (2159) all_0_53_53 = e1 | all_0_56_56 = e1
% 14.10/3.76 |
% 14.10/3.76 +-Applying beta-rule and splitting (2159), into two cases.
% 14.10/3.76 |-Branch one:
% 14.10/3.76 | (275) all_0_53_53 = e1
% 14.10/3.76 |
% 14.10/3.76 | Combining equations (275,413) yields a new equation:
% 14.10/3.76 | (414) e3 = e1
% 14.10/3.76 |
% 14.10/3.76 | Equations (414) can reduce 145 to:
% 14.10/3.76 | (303) $false
% 14.10/3.76 |
% 14.10/3.76 |-The branch is then unsatisfiable
% 14.10/3.76 |-Branch two:
% 14.10/3.76 | (1568) ~ (all_0_53_53 = e1)
% 14.10/3.76 | (314) all_0_56_56 = e1
% 14.10/3.76 |
% 14.10/3.76 | Equations (314) can reduce 282 to:
% 14.10/3.76 | (303) $false
% 14.10/3.76 |
% 14.10/3.76 |-The branch is then unsatisfiable
% 14.10/3.76 |-Branch two:
% 14.10/3.76 | (1340) ~ (all_0_52_52 = e4)
% 14.10/3.76 | (368) all_0_52_52 = e2
% 14.10/3.76 |
% 14.10/3.76 | Equations (368) can reduce 371 to:
% 14.10/3.76 | (303) $false
% 14.10/3.76 |
% 14.10/3.76 |-The branch is then unsatisfiable
% 14.10/3.76 |-Branch two:
% 14.10/3.76 | (514) ~ (all_0_40_40 = e4)
% 14.10/3.76 | (1048) all_0_41_41 = e4 | all_0_43_43 = e4
% 14.10/3.76 |
% 14.10/3.76 +-Applying beta-rule and splitting (1048), into two cases.
% 14.10/3.76 |-Branch one:
% 14.10/3.76 | (425) all_0_41_41 = e4
% 14.10/3.76 |
% 14.10/3.76 | Combining equations (425,257) yields a new equation:
% 14.10/3.76 | (426) e4 = e1
% 14.10/3.76 |
% 14.10/3.76 | Simplifying 426 yields:
% 14.10/3.76 | (427) e4 = e1
% 14.10/3.76 |
% 14.10/3.76 | Equations (427) can reduce 253 to:
% 14.10/3.76 | (303) $false
% 14.10/3.76 |
% 14.10/3.76 |-The branch is then unsatisfiable
% 14.10/3.76 |-Branch two:
% 14.10/3.76 | (429) ~ (all_0_41_41 = e4)
% 14.10/3.76 | (505) all_0_43_43 = e4
% 14.10/3.76 |
% 14.10/3.76 | Combining equations (588,505) yields a new equation:
% 14.10/3.76 | (512) e4 = e0
% 14.10/3.76 |
% 14.10/3.76 | Equations (512) can reduce 5 to:
% 14.10/3.76 | (303) $false
% 14.10/3.76 |
% 14.10/3.76 |-The branch is then unsatisfiable
% 14.10/3.76 |-Branch two:
% 14.10/3.76 | (306) ~ (all_0_43_43 = e0)
% 14.10/3.76 | (2180) all_0_48_48 = e0 | all_0_52_52 = e0 | all_0_60_60 = e0
% 14.10/3.76 |
% 14.10/3.76 +-Applying beta-rule and splitting (2180), into two cases.
% 14.10/3.76 |-Branch one:
% 14.10/3.76 | (1846) all_0_48_48 = e0
% 14.10/3.76 |
% 14.10/3.76 | Equations (1846) can reduce 1599 to:
% 14.10/3.76 | (303) $false
% 14.10/3.76 |
% 14.10/3.76 |-The branch is then unsatisfiable
% 14.10/3.76 |-Branch two:
% 14.10/3.76 | (1599) ~ (all_0_48_48 = e0)
% 14.10/3.76 | (2184) all_0_52_52 = e0 | all_0_60_60 = e0
% 14.10/3.76 |
% 14.10/3.76 +-Applying beta-rule and splitting (2184), into two cases.
% 14.10/3.76 |-Branch one:
% 14.10/3.76 | (1032) all_0_52_52 = e0
% 14.10/3.76 |
% 14.10/3.76 | Equations (1032) can reduce 308 to:
% 14.10/3.76 | (303) $false
% 14.10/3.76 |
% 14.10/3.76 |-The branch is then unsatisfiable
% 14.10/3.76 |-Branch two:
% 14.10/3.76 | (308) ~ (all_0_52_52 = e0)
% 14.10/3.76 | (305) all_0_60_60 = e0
% 14.10/3.76 |
% 14.10/3.76 | Combining equations (305,1059) yields a new equation:
% 14.10/3.76 | (302) e1 = e0
% 14.10/3.76 |
% 14.10/3.76 | Equations (302) can reduce 143 to:
% 14.10/3.76 | (303) $false
% 14.10/3.76 |
% 14.10/3.76 |-The branch is then unsatisfiable
% 14.10/3.76 |-Branch two:
% 14.10/3.76 | (1361) ~ (all_0_44_44 = e4)
% 14.10/3.76 | (1362) all_0_49_49 = e4 | all_0_56_56 = e4
% 14.10/3.76 |
% 14.10/3.76 +-Applying beta-rule and splitting (1362), into two cases.
% 14.10/3.76 |-Branch one:
% 14.10/3.76 | (528) all_0_49_49 = e4
% 14.10/3.76 |
% 14.10/3.76 | Combining equations (466,528) yields a new equation:
% 14.10/3.76 | (512) e4 = e0
% 14.10/3.76 |
% 14.10/3.76 | Equations (512) can reduce 5 to:
% 14.10/3.76 | (303) $false
% 14.10/3.76 |
% 14.10/3.76 |-The branch is then unsatisfiable
% 14.10/3.76 |-Branch two:
% 14.10/3.76 | (531) ~ (all_0_49_49 = e4)
% 14.10/3.76 | (762) all_0_56_56 = e4
% 14.10/3.76 |
% 14.10/3.76 | Equations (762) can reduce 988 to:
% 14.10/3.76 | (303) $false
% 14.10/3.76 |
% 14.10/3.76 |-The branch is then unsatisfiable
% 14.10/3.76 |-Branch two:
% 14.10/3.76 | (879) ~ (all_0_49_49 = e0)
% 14.10/3.76 | (1194) all_0_56_56 = e0
% 14.10/3.76 |
% 14.10/3.76 | Equations (1194) can reduce 1182 to:
% 14.10/3.76 | (303) $false
% 14.10/3.76 |
% 14.10/3.76 |-The branch is then unsatisfiable
% 14.10/3.76 |-Branch two:
% 14.10/3.76 | (663) ~ (all_0_46_46 = e2)
% 14.10/3.76 | (664) all_0_58_58 = e2
% 14.10/3.76 |
% 14.10/3.76 | Equations (664) can reduce 71 to:
% 14.10/3.76 | (663) ~ (all_0_46_46 = e2)
% 14.10/3.76 |
% 14.10/3.76 | Equations (664) can reduce 82 to:
% 14.10/3.76 | (717) ~ (all_0_57_57 = e2)
% 14.10/3.76 |
% 14.10/3.76 | Equations (664) can reduce 240 to:
% 14.10/3.76 | (391) ~ (e3 = e2)
% 14.10/3.76 |
% 14.10/3.76 | Simplifying 391 yields:
% 14.10/3.76 | (209) ~ (e3 = e2)
% 14.10/3.76 |
% 14.10/3.76 | Equations (664) can reduce 266 to:
% 14.10/3.76 | (150) ~ (e2 = e1)
% 14.10/3.76 |
% 14.10/3.76 | Equations (664) can reduce 203 to:
% 14.10/3.76 | (61) ~ (e2 = e0)
% 14.10/3.76 |
% 14.10/3.76 | From (664) and (27) follows:
% 14.10/3.76 | (666) op(e2, e2) = all_0_21_21
% 14.10/3.76 |
% 14.10/3.76 +-Applying beta-rule and splitting (193), into two cases.
% 14.10/3.76 |-Branch one:
% 14.10/3.76 | (395) all_0_45_45 = e2
% 14.10/3.76 |
% 14.10/3.76 | Combining equations (300,395) yields a new equation:
% 14.10/3.76 | (559) e2 = e0
% 14.10/3.76 |
% 14.10/3.76 | Equations (559) can reduce 61 to:
% 14.10/3.76 | (303) $false
% 14.10/3.76 |
% 14.10/3.76 |-The branch is then unsatisfiable
% 14.10/3.76 |-Branch two:
% 14.10/3.76 | (398) ~ (all_0_45_45 = e2)
% 14.10/3.76 | (948) all_0_46_46 = e2 | all_0_47_47 = e2 | all_0_48_48 = e2
% 14.10/3.76 |
% 14.10/3.76 +-Applying beta-rule and splitting (948), into two cases.
% 14.10/3.76 |-Branch one:
% 14.10/3.76 | (355) all_0_46_46 = e2
% 14.10/3.76 |
% 14.10/3.76 | Equations (355) can reduce 663 to:
% 14.10/3.76 | (303) $false
% 14.10/3.76 |
% 14.10/3.76 |-The branch is then unsatisfiable
% 14.10/3.76 |-Branch two:
% 14.10/3.76 | (663) ~ (all_0_46_46 = e2)
% 14.10/3.76 | (1474) all_0_47_47 = e2 | all_0_48_48 = e2
% 14.10/3.76 |
% 14.10/3.76 +-Applying beta-rule and splitting (1474), into two cases.
% 14.10/3.76 |-Branch one:
% 14.10/3.76 | (379) all_0_47_47 = e2
% 14.10/3.76 |
% 14.10/3.76 | Equations (379) can reduce 62 to:
% 14.10/3.76 | (110) ~ (all_0_44_44 = e2)
% 14.10/3.76 |
% 14.10/3.76 | Equations (379) can reduce 119 to:
% 14.10/3.76 | (663) ~ (all_0_46_46 = e2)
% 14.10/3.76 |
% 14.10/3.76 | Equations (379) can reduce 607 to:
% 14.10/3.76 | (61) ~ (e2 = e0)
% 14.10/3.76 |
% 14.10/3.76 +-Applying beta-rule and splitting (26), into two cases.
% 14.10/3.76 |-Branch one:
% 14.10/3.76 | (1375) all_0_42_42 = e1
% 14.10/3.76 |
% 14.10/3.76 | Equations (1375) can reduce 260 to:
% 14.10/3.76 | (303) $false
% 14.10/3.76 |
% 14.10/3.76 |-The branch is then unsatisfiable
% 14.10/3.76 |-Branch two:
% 14.10/3.76 | (260) ~ (all_0_42_42 = e1)
% 14.10/3.76 | (2227) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_59_59 = e1
% 14.10/3.76 |
% 14.10/3.76 +-Applying beta-rule and splitting (133), into two cases.
% 14.10/3.76 |-Branch one:
% 14.10/3.76 | (400) all_0_50_50 = e2
% 14.10/3.76 |
% 14.10/3.76 | Equations (400) can reduce 52 to:
% 14.10/3.76 | (391) ~ (e3 = e2)
% 14.10/3.76 |
% 14.10/3.76 | Simplifying 391 yields:
% 14.10/3.76 | (209) ~ (e3 = e2)
% 14.10/3.76 |
% 14.10/3.76 | Equations (400) can reduce 326 to:
% 14.10/3.76 | (150) ~ (e2 = e1)
% 14.10/3.76 |
% 14.10/3.76 | From (400) and (152) follows:
% 14.10/3.76 | (2232) op(e2, e2) = all_0_12_12
% 14.10/3.76 |
% 14.10/3.76 +-Applying beta-rule and splitting (2227), into two cases.
% 14.10/3.76 |-Branch one:
% 14.10/3.76 | (1100) all_0_47_47 = e1
% 14.10/3.76 |
% 14.10/3.76 | Combining equations (379,1100) yields a new equation:
% 14.10/3.76 | (1478) e2 = e1
% 14.10/3.76 |
% 14.10/3.76 | Simplifying 1478 yields:
% 14.10/3.76 | (369) e2 = e1
% 14.10/3.76 |
% 14.10/3.76 | Equations (369) can reduce 150 to:
% 14.10/3.76 | (303) $false
% 14.10/3.76 |
% 14.10/3.76 |-The branch is then unsatisfiable
% 14.10/3.76 |-Branch two:
% 14.10/3.76 | (1560) ~ (all_0_47_47 = e1)
% 14.10/3.76 | (2238) all_0_51_51 = e1 | all_0_59_59 = e1
% 14.10/3.76 |
% 14.10/3.76 +-Applying beta-rule and splitting (2238), into two cases.
% 14.10/3.76 |-Branch one:
% 14.10/3.76 | (1185) all_0_51_51 = e1
% 14.10/3.76 |
% 14.10/3.76 | Combining equations (1185,273) yields a new equation:
% 14.10/3.76 | (1690) all_0_17_17 = e1
% 14.10/3.76 |
% 14.10/3.76 | Equations (1185) can reduce 83 to:
% 14.10/3.76 | (325) ~ (all_0_49_49 = e1)
% 14.10/3.76 |
% 14.10/3.76 | Equations (1185) can reduce 56 to:
% 14.10/3.76 | (346) ~ (e4 = e1)
% 14.10/3.76 |
% 14.10/3.76 | Simplifying 346 yields:
% 14.10/3.76 | (253) ~ (e4 = e1)
% 14.10/3.76 |
% 14.10/3.76 | Equations (1185) can reduce 247 to:
% 14.10/3.76 | (329) ~ (e3 = e1)
% 14.10/3.76 |
% 14.10/3.76 | Simplifying 329 yields:
% 14.10/3.76 | (145) ~ (e3 = e1)
% 14.10/3.76 |
% 14.10/3.76 +-Applying beta-rule and splitting (47), into two cases.
% 14.10/3.76 |-Branch one:
% 14.10/3.76 | (1087) all_0_44_44 = e1
% 14.10/3.76 |
% 14.10/3.77 | Equations (1087) can reduce 79 to:
% 14.10/3.77 | (263) ~ (all_0_46_46 = e1)
% 14.10/3.77 |
% 14.10/3.77 | Simplifying 263 yields:
% 14.10/3.77 | (264) ~ (all_0_46_46 = e1)
% 14.10/3.77 |
% 14.10/3.77 | Equations (1087) can reduce 908 to:
% 14.10/3.77 | (329) ~ (e3 = e1)
% 14.10/3.77 |
% 14.10/3.77 | Simplifying 329 yields:
% 14.10/3.77 | (145) ~ (e3 = e1)
% 14.10/3.77 |
% 14.10/3.77 +-Applying beta-rule and splitting (28), into two cases.
% 14.10/3.77 |-Branch one:
% 14.10/3.77 | (775) all_0_44_44 = e3
% 14.10/3.77 |
% 14.10/3.77 | Combining equations (1087,775) yields a new equation:
% 14.10/3.77 | (414) e3 = e1
% 14.10/3.77 |
% 14.10/3.77 | Equations (414) can reduce 145 to:
% 14.10/3.77 | (303) $false
% 14.10/3.77 |
% 14.10/3.77 |-The branch is then unsatisfiable
% 14.10/3.77 |-Branch two:
% 14.10/3.77 | (908) ~ (all_0_44_44 = e3)
% 14.10/3.77 | (1202) all_0_45_45 = e3 | all_0_47_47 = e3 | all_0_48_48 = e3
% 14.10/3.77 |
% 14.10/3.77 +-Applying beta-rule and splitting (1202), into two cases.
% 14.10/3.77 |-Branch one:
% 14.10/3.77 | (1260) all_0_45_45 = e3
% 14.10/3.77 |
% 14.10/3.77 | Combining equations (300,1260) yields a new equation:
% 14.10/3.77 | (575) e3 = e0
% 14.10/3.77 |
% 14.10/3.77 | Equations (575) can reduce 74 to:
% 14.10/3.77 | (303) $false
% 14.10/3.77 |
% 14.10/3.77 |-The branch is then unsatisfiable
% 14.10/3.77 |-Branch two:
% 14.10/3.77 | (1263) ~ (all_0_45_45 = e3)
% 14.10/3.77 | (1264) all_0_47_47 = e3 | all_0_48_48 = e3
% 14.10/3.77 |
% 14.10/3.77 +-Applying beta-rule and splitting (1264), into two cases.
% 14.10/3.77 |-Branch one:
% 14.10/3.77 | (599) all_0_47_47 = e3
% 14.10/3.77 |
% 14.10/3.77 | Combining equations (379,599) yields a new equation:
% 14.10/3.77 | (553) e3 = e2
% 14.10/3.77 |
% 14.10/3.77 | Equations (553) can reduce 209 to:
% 14.10/3.77 | (303) $false
% 14.10/3.77 |
% 14.10/3.77 |-The branch is then unsatisfiable
% 14.10/3.77 |-Branch two:
% 14.10/3.77 | (602) ~ (all_0_47_47 = e3)
% 14.10/3.77 | (535) all_0_48_48 = e3
% 14.10/3.77 |
% 14.10/3.77 | Equations (535) can reduce 1599 to:
% 14.10/3.77 | (74) ~ (e3 = e0)
% 14.10/3.77 |
% 14.10/3.77 +-Applying beta-rule and splitting (63), into two cases.
% 14.10/3.77 |-Branch one:
% 14.10/3.77 | (1189) all_0_44_44 = e4
% 14.10/3.77 |
% 14.10/3.77 | Combining equations (1087,1189) yields a new equation:
% 14.10/3.77 | (427) e4 = e1
% 14.10/3.77 |
% 14.10/3.77 | Equations (427) can reduce 253 to:
% 14.10/3.77 | (303) $false
% 14.10/3.77 |
% 14.10/3.77 |-The branch is then unsatisfiable
% 14.10/3.77 |-Branch two:
% 14.10/3.77 | (1361) ~ (all_0_44_44 = e4)
% 14.10/3.77 | (2271) all_0_45_45 = e4 | all_0_46_46 = e4 | all_0_48_48 = e4
% 14.10/3.77 |
% 14.10/3.77 +-Applying beta-rule and splitting (2271), into two cases.
% 14.10/3.77 |-Branch one:
% 14.10/3.77 | (784) all_0_45_45 = e4
% 14.10/3.77 |
% 14.10/3.77 | Combining equations (300,784) yields a new equation:
% 14.10/3.77 | (512) e4 = e0
% 14.10/3.77 |
% 14.10/3.77 | Equations (512) can reduce 5 to:
% 14.10/3.77 | (303) $false
% 14.10/3.77 |
% 14.10/3.77 |-The branch is then unsatisfiable
% 14.10/3.77 |-Branch two:
% 14.10/3.77 | (787) ~ (all_0_45_45 = e4)
% 14.10/3.77 | (2276) all_0_46_46 = e4 | all_0_48_48 = e4
% 14.10/3.77 |
% 14.10/3.77 +-Applying beta-rule and splitting (2276), into two cases.
% 14.10/3.77 |-Branch one:
% 14.10/3.77 | (433) all_0_46_46 = e4
% 14.10/3.77 |
% 14.10/3.77 | Equations (433) can reduce 264 to:
% 14.10/3.77 | (253) ~ (e4 = e1)
% 14.10/3.77 |
% 14.10/3.77 | From (433) and (65) follows:
% 14.10/3.77 | (677) op(e2, e4) = all_0_19_19
% 14.10/3.77 |
% 14.10/3.77 | Instantiating formula (39) with e2, e4, all_0_19_19, all_0_49_49 and discharging atoms op(e2, e4) = all_0_19_19, op(e2, e4) = all_0_49_49, yields:
% 14.10/3.77 | (686) all_0_19_19 = all_0_49_49
% 14.10/3.77 |
% 14.10/3.77 | Instantiating formula (39) with e2, e2, all_0_12_12, e3 and discharging atoms op(e2, e2) = all_0_12_12, op(e2, e2) = e3, yields:
% 14.10/3.77 | (2281) all_0_12_12 = e3
% 14.10/3.77 |
% 14.10/3.77 | Instantiating formula (39) with e2, e2, all_0_21_21, all_0_12_12 and discharging atoms op(e2, e2) = all_0_12_12, op(e2, e2) = all_0_21_21, yields:
% 14.10/3.77 | (2282) all_0_12_12 = all_0_21_21
% 14.10/3.77 |
% 14.10/3.77 | Combining equations (2281,2282) yields a new equation:
% 14.10/3.77 | (687) all_0_21_21 = e3
% 14.10/3.77 |
% 14.10/3.77 +-Applying beta-rule and splitting (19), into two cases.
% 14.10/3.77 |-Branch one:
% 14.10/3.77 | (450) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2)) | (all_0_21_21 = e0 & ~ (all_0_22_22 = e2))
% 14.10/3.77 |
% 14.10/3.77 +-Applying beta-rule and splitting (450), into two cases.
% 14.10/3.77 |-Branch one:
% 14.10/3.77 | (451) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2))
% 14.10/3.77 |
% 14.10/3.77 +-Applying beta-rule and splitting (451), into two cases.
% 14.10/3.77 |-Branch one:
% 14.10/3.77 | (452) all_0_17_17 = e4 & ~ (all_0_18_18 = e2)
% 14.10/3.77 |
% 14.10/3.77 | Applying alpha-rule on (452) yields:
% 14.10/3.77 | (453) all_0_17_17 = e4
% 14.10/3.77 | (454) ~ (all_0_18_18 = e2)
% 14.10/3.77 |
% 14.10/3.77 | Combining equations (453,1690) yields a new equation:
% 14.10/3.77 | (426) e4 = e1
% 14.10/3.77 |
% 14.10/3.77 | Simplifying 426 yields:
% 14.10/3.77 | (427) e4 = e1
% 14.10/3.77 |
% 14.10/3.77 | Equations (427) can reduce 253 to:
% 14.10/3.77 | (303) $false
% 14.10/3.77 |
% 14.10/3.77 |-The branch is then unsatisfiable
% 14.10/3.77 |-Branch two:
% 14.10/3.77 | (458) all_0_19_19 = e3 & ~ (all_0_20_20 = e2)
% 14.10/3.77 |
% 14.10/3.77 | Applying alpha-rule on (458) yields:
% 14.10/3.77 | (459) all_0_19_19 = e3
% 14.10/3.77 | (460) ~ (all_0_20_20 = e2)
% 14.10/3.77 |
% 14.10/3.77 | Combining equations (686,459) yields a new equation:
% 14.10/3.77 | (1514) all_0_49_49 = e3
% 14.10/3.77 |
% 14.10/3.77 | Simplifying 1514 yields:
% 14.10/3.77 | (702) all_0_49_49 = e3
% 14.10/3.77 |
% 14.10/3.77 | Equations (702) can reduce 46 to:
% 14.10/3.77 | (303) $false
% 14.10/3.77 |
% 14.10/3.77 |-The branch is then unsatisfiable
% 14.10/3.77 |-Branch two:
% 14.10/3.77 | (462) all_0_21_21 = e0 & ~ (all_0_22_22 = e2)
% 14.10/3.77 |
% 14.10/3.77 | Applying alpha-rule on (462) yields:
% 14.10/3.77 | (463) all_0_21_21 = e0
% 14.10/3.77 | (464) ~ (all_0_22_22 = e2)
% 14.10/3.77 |
% 14.10/3.77 | Combining equations (687,463) yields a new equation:
% 14.10/3.77 | (574) e3 = e0
% 14.10/3.77 |
% 14.10/3.77 | Simplifying 574 yields:
% 14.10/3.77 | (575) e3 = e0
% 14.10/3.77 |
% 14.10/3.77 | Equations (575) can reduce 74 to:
% 14.10/3.77 | (303) $false
% 14.10/3.77 |
% 14.10/3.77 |-The branch is then unsatisfiable
% 14.10/3.77 |-Branch two:
% 14.10/3.77 | (631) all_0_52_52 = e1 & ~ (all_0_55_55 = e2)
% 14.10/3.77 |
% 14.10/3.77 | Applying alpha-rule on (631) yields:
% 14.10/3.77 | (322) all_0_52_52 = e1
% 14.10/3.77 | (633) ~ (all_0_55_55 = e2)
% 14.10/3.77 |
% 14.10/3.77 | Equations (373) can reduce 633 to:
% 14.10/3.77 | (303) $false
% 14.10/3.77 |
% 14.10/3.77 |-The branch is then unsatisfiable
% 14.10/3.77 |-Branch two:
% 14.10/3.77 | (436) ~ (all_0_46_46 = e4)
% 14.10/3.77 | (1297) all_0_48_48 = e4
% 14.10/3.77 |
% 14.10/3.77 | Combining equations (535,1297) yields a new equation:
% 14.10/3.77 | (524) e4 = e3
% 14.10/3.77 |
% 14.10/3.77 | Equations (524) can reduce 30 to:
% 14.10/3.77 | (303) $false
% 14.10/3.77 |
% 14.10/3.77 |-The branch is then unsatisfiable
% 14.10/3.77 |-Branch two:
% 14.10/3.77 | (276) ~ (all_0_44_44 = e1)
% 14.10/3.77 | (2154) all_0_49_49 = e1 | all_0_53_53 = e1 | all_0_56_56 = e1
% 14.10/3.77 |
% 14.10/3.77 +-Applying beta-rule and splitting (2154), into two cases.
% 14.10/3.77 |-Branch one:
% 14.10/3.77 | (811) all_0_49_49 = e1
% 14.10/3.77 |
% 14.10/3.77 | Equations (811) can reduce 325 to:
% 14.10/3.77 | (303) $false
% 14.10/3.77 |
% 14.10/3.77 |-The branch is then unsatisfiable
% 14.10/3.77 |-Branch two:
% 14.10/3.77 | (325) ~ (all_0_49_49 = e1)
% 14.10/3.77 | (2159) all_0_53_53 = e1 | all_0_56_56 = e1
% 14.10/3.77 |
% 14.10/3.77 +-Applying beta-rule and splitting (2159), into two cases.
% 14.10/3.77 |-Branch one:
% 14.10/3.77 | (275) all_0_53_53 = e1
% 14.10/3.77 |
% 14.10/3.77 | Combining equations (413,275) yields a new equation:
% 14.10/3.77 | (604) e3 = e1
% 14.10/3.77 |
% 14.10/3.77 | Simplifying 604 yields:
% 14.10/3.77 | (414) e3 = e1
% 14.10/3.77 |
% 14.10/3.77 | Equations (414) can reduce 145 to:
% 14.10/3.77 | (303) $false
% 14.10/3.77 |
% 14.10/3.77 |-The branch is then unsatisfiable
% 14.10/3.77 |-Branch two:
% 14.10/3.77 | (1568) ~ (all_0_53_53 = e1)
% 14.10/3.77 | (314) all_0_56_56 = e1
% 14.10/3.77 |
% 14.10/3.77 | Equations (314) can reduce 282 to:
% 14.10/3.77 | (303) $false
% 14.10/3.77 |
% 14.10/3.77 |-The branch is then unsatisfiable
% 14.10/3.77 |-Branch two:
% 14.10/3.77 | (343) ~ (all_0_51_51 = e1)
% 14.10/3.77 | (341) all_0_59_59 = e1
% 14.10/3.77 |
% 14.10/3.77 | Equations (341) can reduce 1058 to:
% 14.10/3.77 | (303) $false
% 14.10/3.77 |
% 14.10/3.77 |-The branch is then unsatisfiable
% 14.10/3.77 |-Branch two:
% 14.10/3.77 | (388) ~ (all_0_50_50 = e2)
% 14.10/3.77 | (2329) all_0_51_51 = e2 | all_0_52_52 = e2
% 14.10/3.77 |
% 14.10/3.77 +-Applying beta-rule and splitting (28), into two cases.
% 14.10/3.77 |-Branch one:
% 14.10/3.77 | (775) all_0_44_44 = e3
% 14.10/3.77 |
% 14.10/3.77 | Equations (775) can reduce 908 to:
% 14.10/3.77 | (303) $false
% 14.10/3.77 |
% 14.10/3.77 |-The branch is then unsatisfiable
% 14.10/3.77 |-Branch two:
% 14.10/3.77 | (908) ~ (all_0_44_44 = e3)
% 14.10/3.77 | (1202) all_0_45_45 = e3 | all_0_47_47 = e3 | all_0_48_48 = e3
% 14.10/3.77 |
% 14.10/3.77 +-Applying beta-rule and splitting (1202), into two cases.
% 14.10/3.77 |-Branch one:
% 14.10/3.77 | (1260) all_0_45_45 = e3
% 14.10/3.77 |
% 14.10/3.77 | Combining equations (300,1260) yields a new equation:
% 14.10/3.77 | (575) e3 = e0
% 14.10/3.77 |
% 14.10/3.77 | Equations (575) can reduce 74 to:
% 14.10/3.77 | (303) $false
% 14.10/3.77 |
% 14.10/3.77 |-The branch is then unsatisfiable
% 14.10/3.77 |-Branch two:
% 14.10/3.77 | (1263) ~ (all_0_45_45 = e3)
% 14.10/3.77 | (1264) all_0_47_47 = e3 | all_0_48_48 = e3
% 14.10/3.77 |
% 14.10/3.77 +-Applying beta-rule and splitting (1264), into two cases.
% 14.10/3.77 |-Branch one:
% 14.10/3.77 | (599) all_0_47_47 = e3
% 14.10/3.77 |
% 14.10/3.77 | Combining equations (599,379) yields a new equation:
% 14.10/3.77 | (552) e3 = e2
% 14.10/3.77 |
% 14.10/3.77 | Simplifying 552 yields:
% 14.10/3.77 | (553) e3 = e2
% 14.10/3.77 |
% 14.10/3.77 | Equations (553) can reduce 209 to:
% 14.10/3.77 | (303) $false
% 14.10/3.77 |
% 14.10/3.77 |-The branch is then unsatisfiable
% 14.10/3.77 |-Branch two:
% 14.10/3.77 | (602) ~ (all_0_47_47 = e3)
% 14.10/3.77 | (535) all_0_48_48 = e3
% 14.10/3.77 |
% 14.10/3.77 | Equations (535) can reduce 295 to:
% 14.10/3.77 | (145) ~ (e3 = e1)
% 14.10/3.77 |
% 14.10/3.77 +-Applying beta-rule and splitting (129), into two cases.
% 14.10/3.77 |-Branch one:
% 14.10/3.77 | (669) all_0_46_46 = e1
% 14.10/3.77 |
% 14.10/3.77 | Equations (669) can reduce 264 to:
% 14.10/3.77 | (303) $false
% 14.10/3.77 |
% 14.10/3.77 |-The branch is then unsatisfiable
% 14.10/3.77 |-Branch two:
% 14.10/3.77 | (264) ~ (all_0_46_46 = e1)
% 14.10/3.77 | (672) all_0_46_46 = e4 | all_0_46_46 = e2
% 14.10/3.77 |
% 14.10/3.77 +-Applying beta-rule and splitting (114), into two cases.
% 14.10/3.77 |-Branch one:
% 14.10/3.77 | (1087) all_0_44_44 = e1
% 14.10/3.77 |
% 14.10/3.77 | Equations (1087) can reduce 110 to:
% 14.10/3.77 | (267) ~ (e2 = e1)
% 14.10/3.77 |
% 14.10/3.77 | Simplifying 267 yields:
% 14.10/3.77 | (150) ~ (e2 = e1)
% 14.10/3.77 |
% 14.10/3.77 +-Applying beta-rule and splitting (6), into two cases.
% 14.10/3.77 |-Branch one:
% 14.10/3.77 | (395) all_0_45_45 = e2
% 14.10/3.77 |
% 14.10/3.77 | Combining equations (300,395) yields a new equation:
% 14.10/3.77 | (559) e2 = e0
% 14.10/3.77 |
% 14.10/3.77 | Equations (559) can reduce 61 to:
% 14.10/3.77 | (303) $false
% 14.10/3.77 |
% 14.10/3.77 |-The branch is then unsatisfiable
% 14.10/3.77 |-Branch two:
% 14.10/3.77 | (398) ~ (all_0_45_45 = e2)
% 14.10/3.77 | (399) all_0_50_50 = e2 | all_0_54_54 = e2 | all_0_57_57 = e2
% 14.10/3.77 |
% 14.10/3.77 +-Applying beta-rule and splitting (399), into two cases.
% 14.10/3.77 |-Branch one:
% 14.10/3.77 | (400) all_0_50_50 = e2
% 14.10/3.77 |
% 14.10/3.77 | Equations (400) can reduce 388 to:
% 14.10/3.77 | (303) $false
% 14.10/3.77 |
% 14.10/3.77 |-The branch is then unsatisfiable
% 14.10/3.77 |-Branch two:
% 14.10/3.77 | (388) ~ (all_0_50_50 = e2)
% 14.10/3.77 | (403) all_0_54_54 = e2 | all_0_57_57 = e2
% 14.10/3.77 |
% 14.10/3.77 +-Applying beta-rule and splitting (403), into two cases.
% 14.10/3.77 |-Branch one:
% 14.10/3.77 | (404) all_0_54_54 = e2
% 14.10/3.77 |
% 14.10/3.77 | Combining equations (404,1289) yields a new equation:
% 14.10/3.77 | (1478) e2 = e1
% 14.10/3.77 |
% 14.10/3.77 | Simplifying 1478 yields:
% 14.10/3.77 | (369) e2 = e1
% 14.10/3.77 |
% 14.10/3.77 | Equations (369) can reduce 150 to:
% 14.10/3.77 | (303) $false
% 14.10/3.77 |
% 14.10/3.77 |-The branch is then unsatisfiable
% 14.10/3.77 |-Branch two:
% 14.10/3.77 | (375) ~ (all_0_54_54 = e2)
% 14.10/3.77 | (407) all_0_57_57 = e2
% 14.10/3.77 |
% 14.10/3.77 | Equations (407) can reduce 717 to:
% 14.10/3.77 | (303) $false
% 14.10/3.77 |
% 14.10/3.77 |-The branch is then unsatisfiable
% 14.10/3.77 |-Branch two:
% 14.10/3.77 | (276) ~ (all_0_44_44 = e1)
% 14.10/3.77 | (1090) all_0_45_45 = e1 | all_0_46_46 = e1 | all_0_47_47 = e1 | all_0_48_48 = e1
% 14.10/3.78 |
% 14.10/3.78 +-Applying beta-rule and splitting (672), into two cases.
% 14.10/3.78 |-Branch one:
% 14.10/3.78 | (433) all_0_46_46 = e4
% 14.10/3.78 |
% 14.10/3.78 | Equations (433) can reduce 264 to:
% 14.10/3.78 | (253) ~ (e4 = e1)
% 14.10/3.78 |
% 14.10/3.78 +-Applying beta-rule and splitting (1090), into two cases.
% 14.10/3.78 |-Branch one:
% 14.10/3.78 | (289) all_0_45_45 = e1
% 14.10/3.78 |
% 14.10/3.78 | Combining equations (300,289) yields a new equation:
% 14.10/3.78 | (302) e1 = e0
% 14.10/3.78 |
% 14.10/3.78 | Equations (302) can reduce 143 to:
% 14.10/3.78 | (303) $false
% 14.10/3.78 |
% 14.10/3.78 |-The branch is then unsatisfiable
% 14.10/3.78 |-Branch two:
% 14.10/3.78 | (1072) ~ (all_0_45_45 = e1)
% 14.10/3.78 | (1095) all_0_46_46 = e1 | all_0_47_47 = e1 | all_0_48_48 = e1
% 14.10/3.78 |
% 14.10/3.78 +-Applying beta-rule and splitting (1095), into two cases.
% 14.10/3.78 |-Branch one:
% 14.10/3.78 | (669) all_0_46_46 = e1
% 14.10/3.78 |
% 14.26/3.78 | Combining equations (433,669) yields a new equation:
% 14.26/3.78 | (426) e4 = e1
% 14.26/3.78 |
% 14.26/3.78 | Simplifying 426 yields:
% 14.26/3.78 | (427) e4 = e1
% 14.26/3.78 |
% 14.26/3.78 | Equations (427) can reduce 253 to:
% 14.26/3.78 | (303) $false
% 14.26/3.78 |
% 14.26/3.78 |-The branch is then unsatisfiable
% 14.26/3.78 |-Branch two:
% 14.26/3.78 | (264) ~ (all_0_46_46 = e1)
% 14.26/3.78 | (1099) all_0_47_47 = e1 | all_0_48_48 = e1
% 14.26/3.78 |
% 14.26/3.78 +-Applying beta-rule and splitting (1099), into two cases.
% 14.26/3.78 |-Branch one:
% 14.26/3.78 | (1100) all_0_47_47 = e1
% 14.26/3.78 |
% 14.26/3.78 | Combining equations (379,1100) yields a new equation:
% 14.26/3.78 | (1478) e2 = e1
% 14.26/3.78 |
% 14.26/3.78 | Simplifying 1478 yields:
% 14.26/3.78 | (369) e2 = e1
% 14.26/3.78 |
% 14.26/3.78 | Equations (369) can reduce 150 to:
% 14.26/3.78 | (303) $false
% 14.26/3.78 |
% 14.26/3.78 |-The branch is then unsatisfiable
% 14.26/3.78 |-Branch two:
% 14.26/3.78 | (1560) ~ (all_0_47_47 = e1)
% 14.26/3.78 | (318) all_0_48_48 = e1
% 14.26/3.78 |
% 14.26/3.78 | Combining equations (535,318) yields a new equation:
% 14.26/3.78 | (604) e3 = e1
% 14.26/3.78 |
% 14.26/3.78 | Simplifying 604 yields:
% 14.26/3.78 | (414) e3 = e1
% 14.26/3.78 |
% 14.26/3.78 | Equations (414) can reduce 145 to:
% 14.26/3.78 | (303) $false
% 14.26/3.78 |
% 14.26/3.78 |-The branch is then unsatisfiable
% 14.26/3.78 |-Branch two:
% 14.26/3.78 | (436) ~ (all_0_46_46 = e4)
% 14.26/3.78 | (355) all_0_46_46 = e2
% 14.26/3.78 |
% 14.26/3.78 | Equations (355) can reduce 663 to:
% 14.26/3.78 | (303) $false
% 14.26/3.78 |
% 14.26/3.78 |-The branch is then unsatisfiable
% 14.26/3.78 |-Branch two:
% 14.26/3.78 | (357) ~ (all_0_47_47 = e2)
% 14.26/3.78 | (364) all_0_48_48 = e2
% 14.26/3.78 |
% 14.26/3.78 | Equations (364) can reduce 359 to:
% 14.26/3.78 | (303) $false
% 14.26/3.78 |
% 14.26/3.78 |-The branch is then unsatisfiable
% 14.26/3.78 |-Branch two:
% 14.26/3.78 | (278) ~ (all_0_54_54 = e1)
% 14.26/3.78 | (1065) all_0_55_55 = e1
% 14.26/3.78 |
% 14.26/3.78 | Combining equations (373,1065) yields a new equation:
% 14.26/3.78 | (1478) e2 = e1
% 14.26/3.78 |
% 14.26/3.78 | Simplifying 1478 yields:
% 14.26/3.78 | (369) e2 = e1
% 14.26/3.78 |
% 14.26/3.78 | Equations (369) can reduce 150 to:
% 14.26/3.78 | (303) $false
% 14.26/3.78 |
% 14.26/3.78 |-The branch is then unsatisfiable
% 14.26/3.78 |-Branch two:
% 14.26/3.78 | (304) ~ (all_0_45_45 = e0)
% 14.26/3.78 | (305) all_0_60_60 = e0
% 14.26/3.78 |
% 14.26/3.78 | Combining equations (1059,305) yields a new equation:
% 14.26/3.78 | (301) e1 = e0
% 14.26/3.78 |
% 14.26/3.78 | Simplifying 301 yields:
% 14.26/3.78 | (302) e1 = e0
% 14.26/3.78 |
% 14.26/3.78 | Equations (302) can reduce 143 to:
% 14.26/3.78 | (303) $false
% 14.26/3.78 |
% 14.26/3.78 |-The branch is then unsatisfiable
% 14.26/3.78 |-Branch two:
% 14.26/3.78 | (2409) ~ (all_0_41_41 = e1)
% 14.26/3.78 | (425) all_0_41_41 = e4
% 14.26/3.78 |
% 14.26/3.78 | Equations (425) can reduce 32 to:
% 14.26/3.78 | (514) ~ (all_0_40_40 = e4)
% 14.26/3.78 |
% 14.26/3.78 | Equations (425) can reduce 96 to:
% 14.26/3.78 | (968) ~ (all_0_42_42 = e4)
% 14.26/3.78 |
% 14.26/3.78 | Simplifying 968 yields:
% 14.26/3.78 | (144) ~ (all_0_42_42 = e4)
% 14.26/3.78 |
% 14.26/3.78 | Equations (425) can reduce 136 to:
% 14.26/3.78 | (1156) ~ (all_0_43_43 = e4)
% 14.26/3.78 |
% 14.26/3.78 | Simplifying 1156 yields:
% 14.26/3.78 | (582) ~ (all_0_43_43 = e4)
% 14.26/3.78 |
% 14.26/3.78 | Equations (425) can reduce 158 to:
% 14.26/3.78 | (2416) ~ (all_0_46_46 = e4)
% 14.26/3.78 |
% 14.26/3.78 | Simplifying 2416 yields:
% 14.26/3.78 | (436) ~ (all_0_46_46 = e4)
% 14.26/3.78 |
% 14.26/3.78 | Equations (425) can reduce 249 to:
% 14.26/3.78 | (2418) ~ (all_0_58_58 = e4)
% 14.26/3.78 |
% 14.26/3.78 | Simplifying 2418 yields:
% 14.26/3.78 | (1023) ~ (all_0_58_58 = e4)
% 14.26/3.78 |
% 14.26/3.78 | From (425) and (111) follows:
% 14.26/3.78 | (2420) op(e4, e4) = all_0_18_18
% 14.26/3.78 |
% 14.26/3.78 | From (425) and (153) follows:
% 14.26/3.78 | (2421) op(e2, e4) = all_0_17_17
% 14.26/3.78 |
% 14.26/3.78 | Instantiating formula (39) with e4, e4, all_0_18_18, e2 and discharging atoms op(e4, e4) = all_0_18_18, op(e4, e4) = e2, yields:
% 14.26/3.78 | (2422) all_0_18_18 = e2
% 14.26/3.78 |
% 14.26/3.78 | Instantiating formula (39) with e2, e4, all_0_17_17, all_0_49_49 and discharging atoms op(e2, e4) = all_0_17_17, op(e2, e4) = all_0_49_49, yields:
% 14.26/3.78 | (2423) all_0_17_17 = all_0_49_49
% 14.26/3.78 |
% 14.26/3.78 +-Applying beta-rule and splitting (109), into two cases.
% 14.26/3.78 |-Branch one:
% 14.26/3.78 | (275) all_0_53_53 = e1
% 14.26/3.78 |
% 14.26/3.78 | Equations (275) can reduce 187 to:
% 14.26/3.78 | (346) ~ (e4 = e1)
% 14.26/3.78 |
% 14.26/3.78 | Simplifying 346 yields:
% 14.26/3.78 | (253) ~ (e4 = e1)
% 14.26/3.78 |
% 14.26/3.78 | Equations (275) can reduce 58 to:
% 14.26/3.78 | (267) ~ (e2 = e1)
% 14.26/3.78 |
% 14.26/3.78 | Simplifying 267 yields:
% 14.26/3.78 | (150) ~ (e2 = e1)
% 14.26/3.78 |
% 14.26/3.78 | Equations (275) can reduce 255 to:
% 14.26/3.78 | (143) ~ (e1 = e0)
% 14.26/3.78 |
% 14.26/3.78 +-Applying beta-rule and splitting (12), into two cases.
% 14.26/3.78 |-Branch one:
% 14.26/3.78 | (289) all_0_45_45 = e1
% 14.26/3.78 |
% 14.26/3.78 | Equations (289) can reduce 72 to:
% 14.26/3.78 | (258) ~ (all_0_40_40 = e1)
% 14.26/3.78 |
% 14.26/3.78 | Equations (289) can reduce 128 to:
% 14.26/3.78 | (263) ~ (all_0_46_46 = e1)
% 14.26/3.78 |
% 14.26/3.78 | Simplifying 263 yields:
% 14.26/3.78 | (264) ~ (all_0_46_46 = e1)
% 14.26/3.78 |
% 14.26/3.78 | Equations (289) can reduce 37 to:
% 14.26/3.78 | (277) ~ (all_0_54_54 = e1)
% 14.26/3.78 |
% 14.26/3.78 | Simplifying 277 yields:
% 14.26/3.78 | (278) ~ (all_0_54_54 = e1)
% 14.26/3.78 |
% 14.26/3.78 +-Applying beta-rule and splitting (25), into two cases.
% 14.26/3.78 |-Branch one:
% 14.26/3.78 | (300) all_0_45_45 = e0
% 14.26/3.78 |
% 14.26/3.78 | Combining equations (289,300) yields a new equation:
% 14.26/3.78 | (301) e1 = e0
% 14.26/3.78 |
% 14.26/3.78 | Simplifying 301 yields:
% 14.26/3.78 | (302) e1 = e0
% 14.26/3.78 |
% 14.26/3.78 | Equations (302) can reduce 143 to:
% 14.26/3.78 | (303) $false
% 14.26/3.78 |
% 14.26/3.78 |-The branch is then unsatisfiable
% 14.26/3.78 |-Branch two:
% 14.26/3.78 | (304) ~ (all_0_45_45 = e0)
% 14.26/3.78 | (305) all_0_60_60 = e0
% 14.26/3.78 |
% 14.26/3.78 | Equations (305) can reduce 67 to:
% 14.26/3.78 | (1599) ~ (all_0_48_48 = e0)
% 14.26/3.78 |
% 14.26/3.78 | Equations (305) can reduce 140 to:
% 14.26/3.78 | (1182) ~ (all_0_56_56 = e0)
% 14.26/3.78 |
% 14.26/3.78 +-Applying beta-rule and splitting (129), into two cases.
% 14.26/3.78 |-Branch one:
% 14.26/3.78 | (669) all_0_46_46 = e1
% 14.26/3.78 |
% 14.26/3.78 | Equations (669) can reduce 264 to:
% 14.26/3.78 | (303) $false
% 14.26/3.78 |
% 14.26/3.78 |-The branch is then unsatisfiable
% 14.26/3.78 |-Branch two:
% 14.26/3.78 | (264) ~ (all_0_46_46 = e1)
% 14.26/3.78 | (672) all_0_46_46 = e4 | all_0_46_46 = e2
% 14.26/3.78 |
% 14.26/3.78 +-Applying beta-rule and splitting (214), into two cases.
% 14.26/3.78 |-Branch one:
% 14.26/3.78 | (257) all_0_41_41 = e1
% 14.26/3.78 |
% 14.26/3.78 | Combining equations (425,257) yields a new equation:
% 14.26/3.78 | (426) e4 = e1
% 14.26/3.78 |
% 14.26/3.78 | Simplifying 426 yields:
% 14.26/3.78 | (427) e4 = e1
% 14.26/3.78 |
% 14.26/3.78 | Equations (427) can reduce 253 to:
% 14.26/3.78 | (303) $false
% 14.26/3.78 |
% 14.26/3.78 |-The branch is then unsatisfiable
% 14.26/3.78 |-Branch two:
% 14.26/3.78 | (2409) ~ (all_0_41_41 = e1)
% 14.26/3.78 | (2453) all_0_46_46 = e1 | all_0_58_58 = e1
% 14.26/3.78 |
% 14.26/3.78 +-Applying beta-rule and splitting (2453), into two cases.
% 14.26/3.78 |-Branch one:
% 14.26/3.78 | (669) all_0_46_46 = e1
% 14.26/3.78 |
% 14.26/3.78 | Equations (669) can reduce 264 to:
% 14.26/3.78 | (303) $false
% 14.26/3.78 |
% 14.26/3.78 |-The branch is then unsatisfiable
% 14.26/3.78 |-Branch two:
% 14.26/3.78 | (264) ~ (all_0_46_46 = e1)
% 14.26/3.78 | (337) all_0_58_58 = e1
% 14.26/3.78 |
% 14.26/3.78 | Equations (337) can reduce 240 to:
% 14.26/3.78 | (329) ~ (e3 = e1)
% 14.26/3.78 |
% 14.26/3.78 | Simplifying 329 yields:
% 14.26/3.78 | (145) ~ (e3 = e1)
% 14.26/3.78 |
% 14.26/3.78 | From (337) and (27) follows:
% 14.26/3.78 | (2460) op(e2, e1) = all_0_21_21
% 14.26/3.78 |
% 14.26/3.78 | From (337) and (33) follows:
% 14.26/3.78 | (2461) op(e0, e1) = all_0_22_22
% 14.26/3.78 |
% 14.26/3.78 +-Applying beta-rule and splitting (85), into two cases.
% 14.26/3.78 |-Branch one:
% 14.26/3.78 | (355) all_0_46_46 = e2
% 14.26/3.78 |
% 14.26/3.78 | Equations (355) can reduce 79 to:
% 14.26/3.78 | (110) ~ (all_0_44_44 = e2)
% 14.26/3.78 |
% 14.26/3.78 | Equations (355) can reduce 119 to:
% 14.26/3.78 | (356) ~ (all_0_47_47 = e2)
% 14.26/3.78 |
% 14.26/3.78 | Simplifying 356 yields:
% 14.26/3.78 | (357) ~ (all_0_47_47 = e2)
% 14.26/3.78 |
% 14.26/3.78 | Equations (355) can reduce 2 to:
% 14.26/3.78 | (358) ~ (all_0_48_48 = e2)
% 14.26/3.78 |
% 14.26/3.78 | Simplifying 358 yields:
% 14.26/3.78 | (359) ~ (all_0_48_48 = e2)
% 14.26/3.78 |
% 14.26/3.78 | Equations (355) can reduce 149 to:
% 14.26/3.78 | (391) ~ (e3 = e2)
% 14.26/3.78 |
% 14.26/3.78 | Simplifying 391 yields:
% 14.26/3.78 | (209) ~ (e3 = e2)
% 14.26/3.78 |
% 14.26/3.78 | From (355) and (161) follows:
% 14.26/3.78 | (362) op(e3, e2) = all_0_20_20
% 14.26/3.78 |
% 14.26/3.78 | From (355) and (239) follows:
% 14.26/3.78 | (363) op(e3, e2) = e2
% 14.26/3.78 |
% 14.26/3.78 | Instantiating formula (39) with e3, e2, e2, all_0_20_20 and discharging atoms op(e3, e2) = all_0_20_20, op(e3, e2) = e2, yields:
% 14.26/3.78 | (446) all_0_20_20 = e2
% 14.26/3.78 |
% 14.26/3.78 | Instantiating formula (39) with e2, e1, all_0_21_21, all_0_51_51 and discharging atoms op(e2, e1) = all_0_21_21, op(e2, e1) = all_0_51_51, yields:
% 14.26/3.78 | (2473) all_0_21_21 = all_0_51_51
% 14.26/3.78 |
% 14.26/3.78 | Instantiating formula (39) with e0, e1, all_0_22_22, all_0_59_59 and discharging atoms op(e0, e1) = all_0_22_22, op(e0, e1) = all_0_59_59, yields:
% 14.26/3.78 | (2474) all_0_22_22 = all_0_59_59
% 14.26/3.78 |
% 14.26/3.78 +-Applying beta-rule and splitting (157), into two cases.
% 14.26/3.78 |-Branch one:
% 14.26/3.78 | (404) all_0_54_54 = e2
% 14.26/3.78 |
% 14.26/3.78 | Equations (404) can reduce 101 to:
% 14.26/3.79 | (714) ~ (all_0_55_55 = e2)
% 14.26/3.79 |
% 14.26/3.79 | Simplifying 714 yields:
% 14.26/3.79 | (633) ~ (all_0_55_55 = e2)
% 14.26/3.79 |
% 14.26/3.79 | Equations (404) can reduce 278 to:
% 14.26/3.79 | (150) ~ (e2 = e1)
% 14.26/3.79 |
% 14.26/3.79 | Equations (404) can reduce 183 to:
% 14.26/3.79 | (61) ~ (e2 = e0)
% 14.26/3.79 |
% 14.26/3.79 +-Applying beta-rule and splitting (175), into two cases.
% 14.26/3.79 |-Branch one:
% 14.26/3.79 | (364) all_0_48_48 = e2
% 14.26/3.79 |
% 14.26/3.79 | Equations (364) can reduce 359 to:
% 14.26/3.79 | (303) $false
% 14.26/3.79 |
% 14.26/3.79 |-The branch is then unsatisfiable
% 14.26/3.79 |-Branch two:
% 14.26/3.79 | (359) ~ (all_0_48_48 = e2)
% 14.26/3.79 | (367) all_0_52_52 = e2 | all_0_55_55 = e2 | all_0_60_60 = e2
% 14.26/3.79 |
% 14.26/3.79 +-Applying beta-rule and splitting (367), into two cases.
% 14.26/3.79 |-Branch one:
% 14.26/3.79 | (368) all_0_52_52 = e2
% 14.26/3.79 |
% 14.26/3.79 +-Applying beta-rule and splitting (127), into two cases.
% 14.26/3.79 |-Branch one:
% 14.26/3.79 | (379) all_0_47_47 = e2
% 14.26/3.79 |
% 14.26/3.79 | Equations (379) can reduce 357 to:
% 14.26/3.79 | (303) $false
% 14.26/3.79 |
% 14.26/3.79 |-The branch is then unsatisfiable
% 14.26/3.79 |-Branch two:
% 14.26/3.79 | (357) ~ (all_0_47_47 = e2)
% 14.26/3.79 | (382) all_0_51_51 = e2 | all_0_59_59 = e2
% 14.26/3.79 |
% 14.26/3.79 +-Applying beta-rule and splitting (19), into two cases.
% 14.26/3.79 |-Branch one:
% 14.26/3.79 | (450) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2)) | (all_0_21_21 = e0 & ~ (all_0_22_22 = e2))
% 14.26/3.79 |
% 14.26/3.79 +-Applying beta-rule and splitting (450), into two cases.
% 14.26/3.79 |-Branch one:
% 14.26/3.79 | (451) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2))
% 14.26/3.79 |
% 14.26/3.79 +-Applying beta-rule and splitting (451), into two cases.
% 14.26/3.79 |-Branch one:
% 14.26/3.79 | (452) all_0_17_17 = e4 & ~ (all_0_18_18 = e2)
% 14.26/3.79 |
% 14.26/3.79 | Applying alpha-rule on (452) yields:
% 14.26/3.79 | (453) all_0_17_17 = e4
% 14.26/3.79 | (454) ~ (all_0_18_18 = e2)
% 14.26/3.79 |
% 14.26/3.79 | Equations (2422) can reduce 454 to:
% 14.26/3.79 | (303) $false
% 14.26/3.79 |
% 14.26/3.79 |-The branch is then unsatisfiable
% 14.26/3.79 |-Branch two:
% 14.26/3.79 | (458) all_0_19_19 = e3 & ~ (all_0_20_20 = e2)
% 14.26/3.79 |
% 14.26/3.79 | Applying alpha-rule on (458) yields:
% 14.26/3.79 | (459) all_0_19_19 = e3
% 14.26/3.79 | (460) ~ (all_0_20_20 = e2)
% 14.26/3.79 |
% 14.26/3.79 | Equations (446) can reduce 460 to:
% 14.26/3.79 | (303) $false
% 14.26/3.79 |
% 14.26/3.79 |-The branch is then unsatisfiable
% 14.26/3.79 |-Branch two:
% 14.26/3.79 | (462) all_0_21_21 = e0 & ~ (all_0_22_22 = e2)
% 14.26/3.79 |
% 14.26/3.79 | Applying alpha-rule on (462) yields:
% 14.26/3.79 | (463) all_0_21_21 = e0
% 14.26/3.79 | (464) ~ (all_0_22_22 = e2)
% 14.26/3.79 |
% 14.26/3.79 | Combining equations (2473,463) yields a new equation:
% 14.26/3.79 | (2502) all_0_51_51 = e0
% 14.26/3.79 |
% 14.26/3.79 | Simplifying 2502 yields:
% 14.26/3.79 | (609) all_0_51_51 = e0
% 14.26/3.79 |
% 14.26/3.79 | Equations (2474) can reduce 464 to:
% 14.26/3.79 | (1437) ~ (all_0_59_59 = e2)
% 14.26/3.79 |
% 14.26/3.79 | Equations (609) can reduce 83 to:
% 14.26/3.79 | (879) ~ (all_0_49_49 = e0)
% 14.26/3.79 |
% 14.26/3.79 +-Applying beta-rule and splitting (121), into two cases.
% 14.26/3.79 |-Branch one:
% 14.26/3.79 | (815) all_0_44_44 = e0
% 14.26/3.79 |
% 14.26/3.79 | Equations (815) can reduce 110 to:
% 14.26/3.79 | (469) ~ (e2 = e0)
% 14.26/3.79 |
% 14.26/3.79 | Simplifying 469 yields:
% 14.26/3.79 | (61) ~ (e2 = e0)
% 14.26/3.79 |
% 14.26/3.79 +-Applying beta-rule and splitting (382), into two cases.
% 14.26/3.79 |-Branch one:
% 14.26/3.79 | (383) all_0_51_51 = e2
% 14.26/3.79 |
% 14.26/3.79 | Combining equations (609,383) yields a new equation:
% 14.26/3.79 | (559) e2 = e0
% 14.26/3.79 |
% 14.26/3.79 | Equations (559) can reduce 61 to:
% 14.26/3.79 | (303) $false
% 14.26/3.79 |
% 14.26/3.79 |-The branch is then unsatisfiable
% 14.26/3.79 |-Branch two:
% 14.26/3.79 | (654) ~ (all_0_51_51 = e2)
% 14.26/3.79 | (655) all_0_59_59 = e2
% 14.26/3.79 |
% 14.26/3.79 | Equations (655) can reduce 1437 to:
% 14.26/3.79 | (303) $false
% 14.26/3.79 |
% 14.26/3.79 |-The branch is then unsatisfiable
% 14.26/3.79 |-Branch two:
% 14.26/3.79 | (819) ~ (all_0_44_44 = e0)
% 14.26/3.79 | (820) all_0_49_49 = e0 | all_0_56_56 = e0
% 14.26/3.79 |
% 14.26/3.79 +-Applying beta-rule and splitting (820), into two cases.
% 14.26/3.79 |-Branch one:
% 14.26/3.79 | (466) all_0_49_49 = e0
% 14.26/3.79 |
% 14.26/3.79 | Equations (466) can reduce 879 to:
% 14.26/3.79 | (303) $false
% 14.26/3.79 |
% 14.26/3.79 |-The branch is then unsatisfiable
% 14.26/3.79 |-Branch two:
% 14.26/3.79 | (879) ~ (all_0_49_49 = e0)
% 14.26/3.79 | (1194) all_0_56_56 = e0
% 14.26/3.79 |
% 14.26/3.79 | Equations (1194) can reduce 1182 to:
% 14.26/3.79 | (303) $false
% 14.26/3.79 |
% 14.26/3.79 |-The branch is then unsatisfiable
% 14.26/3.79 |-Branch two:
% 14.26/3.79 | (631) all_0_52_52 = e1 & ~ (all_0_55_55 = e2)
% 14.26/3.79 |
% 14.26/3.79 | Applying alpha-rule on (631) yields:
% 14.26/3.79 | (322) all_0_52_52 = e1
% 14.26/3.79 | (633) ~ (all_0_55_55 = e2)
% 14.26/3.79 |
% 14.26/3.79 | Combining equations (368,322) yields a new equation:
% 14.26/3.79 | (1478) e2 = e1
% 14.26/3.79 |
% 14.26/3.79 | Simplifying 1478 yields:
% 14.26/3.79 | (369) e2 = e1
% 14.26/3.79 |
% 14.26/3.79 | Equations (369) can reduce 150 to:
% 14.26/3.79 | (303) $false
% 14.26/3.79 |
% 14.26/3.79 |-The branch is then unsatisfiable
% 14.26/3.79 |-Branch two:
% 14.26/3.79 | (371) ~ (all_0_52_52 = e2)
% 14.26/3.79 | (372) all_0_55_55 = e2 | all_0_60_60 = e2
% 14.26/3.79 |
% 14.26/3.79 +-Applying beta-rule and splitting (372), into two cases.
% 14.26/3.79 |-Branch one:
% 14.26/3.79 | (373) all_0_55_55 = e2
% 14.26/3.79 |
% 14.26/3.79 | Equations (373) can reduce 633 to:
% 14.26/3.79 | (303) $false
% 14.26/3.79 |
% 14.26/3.79 |-The branch is then unsatisfiable
% 14.26/3.79 |-Branch two:
% 14.26/3.79 | (633) ~ (all_0_55_55 = e2)
% 14.26/3.79 | (659) all_0_60_60 = e2
% 14.26/3.79 |
% 14.26/3.79 | Combining equations (659,305) yields a new equation:
% 14.26/3.79 | (558) e2 = e0
% 14.26/3.79 |
% 14.26/3.79 | Simplifying 558 yields:
% 14.26/3.79 | (559) e2 = e0
% 14.26/3.79 |
% 14.26/3.79 | Equations (559) can reduce 61 to:
% 14.26/3.79 | (303) $false
% 14.26/3.79 |
% 14.26/3.79 |-The branch is then unsatisfiable
% 14.26/3.79 |-Branch two:
% 14.26/3.79 | (375) ~ (all_0_54_54 = e2)
% 14.26/3.79 | (373) all_0_55_55 = e2
% 14.26/3.79 |
% 14.26/3.79 +-Applying beta-rule and splitting (113), into two cases.
% 14.26/3.79 |-Branch one:
% 14.26/3.79 | (413) all_0_53_53 = e3
% 14.26/3.79 |
% 14.26/3.79 | Combining equations (275,413) yields a new equation:
% 14.26/3.79 | (414) e3 = e1
% 14.26/3.79 |
% 14.26/3.79 | Equations (414) can reduce 145 to:
% 14.26/3.79 | (303) $false
% 14.26/3.79 |
% 14.26/3.79 |-The branch is then unsatisfiable
% 14.26/3.79 |-Branch two:
% 14.26/3.79 | (416) ~ (all_0_53_53 = e3)
% 14.26/3.79 | (417) all_0_54_54 = e3 | all_0_55_55 = e3
% 14.26/3.79 |
% 14.26/3.79 +-Applying beta-rule and splitting (417), into two cases.
% 14.26/3.79 |-Branch one:
% 14.26/3.79 | (418) all_0_54_54 = e3
% 14.26/3.79 |
% 14.26/3.79 | Equations (418) can reduce 97 to:
% 14.26/3.79 | (419) ~ (all_0_40_40 = e3)
% 14.26/3.79 |
% 14.26/3.79 +-Applying beta-rule and splitting (172), into two cases.
% 14.26/3.79 |-Branch one:
% 14.26/3.79 | (799) all_0_40_40 = e1
% 14.26/3.79 |
% 14.26/3.79 | Equations (799) can reduce 258 to:
% 14.26/3.79 | (303) $false
% 14.26/3.79 |
% 14.26/3.79 |-The branch is then unsatisfiable
% 14.26/3.79 |-Branch two:
% 14.26/3.79 | (258) ~ (all_0_40_40 = e1)
% 14.26/3.79 | (802) all_0_40_40 = e4 | all_0_40_40 = e3 | all_0_40_40 = e0
% 14.26/3.79 |
% 14.26/3.79 +-Applying beta-rule and splitting (19), into two cases.
% 14.26/3.79 |-Branch one:
% 14.26/3.79 | (450) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2)) | (all_0_21_21 = e0 & ~ (all_0_22_22 = e2))
% 14.26/3.79 |
% 14.26/3.79 +-Applying beta-rule and splitting (450), into two cases.
% 14.26/3.79 |-Branch one:
% 14.26/3.79 | (451) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2))
% 14.26/3.79 |
% 14.26/3.79 +-Applying beta-rule and splitting (451), into two cases.
% 14.26/3.79 |-Branch one:
% 14.26/3.79 | (452) all_0_17_17 = e4 & ~ (all_0_18_18 = e2)
% 14.26/3.79 |
% 14.26/3.79 | Applying alpha-rule on (452) yields:
% 14.26/3.79 | (453) all_0_17_17 = e4
% 14.26/3.79 | (454) ~ (all_0_18_18 = e2)
% 14.26/3.79 |
% 14.26/3.79 | Equations (2422) can reduce 454 to:
% 14.26/3.79 | (303) $false
% 14.26/3.79 |
% 14.26/3.79 |-The branch is then unsatisfiable
% 14.26/3.79 |-Branch two:
% 14.26/3.79 | (458) all_0_19_19 = e3 & ~ (all_0_20_20 = e2)
% 14.26/3.79 |
% 14.26/3.79 | Applying alpha-rule on (458) yields:
% 14.26/3.79 | (459) all_0_19_19 = e3
% 14.26/3.79 | (460) ~ (all_0_20_20 = e2)
% 14.26/3.79 |
% 14.26/3.79 | Equations (446) can reduce 460 to:
% 14.26/3.79 | (303) $false
% 14.26/3.79 |
% 14.26/3.79 |-The branch is then unsatisfiable
% 14.26/3.79 |-Branch two:
% 14.26/3.79 | (462) all_0_21_21 = e0 & ~ (all_0_22_22 = e2)
% 14.26/3.79 |
% 14.26/3.79 | Applying alpha-rule on (462) yields:
% 14.26/3.79 | (463) all_0_21_21 = e0
% 14.26/3.79 | (464) ~ (all_0_22_22 = e2)
% 14.26/3.79 |
% 14.26/3.79 | Combining equations (2473,463) yields a new equation:
% 14.26/3.79 | (2502) all_0_51_51 = e0
% 14.26/3.79 |
% 14.26/3.79 | Simplifying 2502 yields:
% 14.26/3.79 | (609) all_0_51_51 = e0
% 14.26/3.79 |
% 14.26/3.79 | Equations (2474) can reduce 464 to:
% 14.26/3.79 | (1437) ~ (all_0_59_59 = e2)
% 14.26/3.79 |
% 14.26/3.79 | Equations (609) can reduce 176 to:
% 14.26/3.79 | (607) ~ (all_0_47_47 = e0)
% 14.26/3.79 |
% 14.26/3.79 +-Applying beta-rule and splitting (802), into two cases.
% 14.26/3.79 |-Branch one:
% 14.26/3.79 | (473) all_0_40_40 = e0
% 14.26/3.79 |
% 14.26/3.79 | Equations (473) can reduce 258 to:
% 14.26/3.79 | (471) ~ (e1 = e0)
% 14.26/3.79 |
% 14.26/3.79 | Simplifying 471 yields:
% 14.26/3.79 | (143) ~ (e1 = e0)
% 14.26/3.79 |
% 14.26/3.79 +-Applying beta-rule and splitting (127), into two cases.
% 14.26/3.79 |-Branch one:
% 14.26/3.79 | (379) all_0_47_47 = e2
% 14.26/3.79 |
% 14.26/3.79 | Equations (379) can reduce 357 to:
% 14.26/3.79 | (303) $false
% 14.26/3.79 |
% 14.26/3.79 |-The branch is then unsatisfiable
% 14.26/3.79 |-Branch two:
% 14.26/3.79 | (357) ~ (all_0_47_47 = e2)
% 14.26/3.79 | (382) all_0_51_51 = e2 | all_0_59_59 = e2
% 14.26/3.79 |
% 14.26/3.79 +-Applying beta-rule and splitting (250), into two cases.
% 14.26/3.79 |-Branch one:
% 14.26/3.79 | (815) all_0_44_44 = e0
% 14.26/3.79 |
% 14.26/3.79 | Equations (815) can reduce 110 to:
% 14.26/3.79 | (469) ~ (e2 = e0)
% 14.26/3.79 |
% 14.26/3.79 | Simplifying 469 yields:
% 14.26/3.79 | (61) ~ (e2 = e0)
% 14.26/3.79 |
% 14.26/3.79 +-Applying beta-rule and splitting (382), into two cases.
% 14.26/3.79 |-Branch one:
% 14.26/3.79 | (383) all_0_51_51 = e2
% 14.26/3.79 |
% 14.26/3.79 | Combining equations (383,609) yields a new equation:
% 14.26/3.79 | (558) e2 = e0
% 14.26/3.79 |
% 14.26/3.79 | Simplifying 558 yields:
% 14.26/3.79 | (559) e2 = e0
% 14.26/3.79 |
% 14.26/3.79 | Equations (559) can reduce 61 to:
% 14.26/3.79 | (303) $false
% 14.26/3.79 |
% 14.26/3.79 |-The branch is then unsatisfiable
% 14.26/3.79 |-Branch two:
% 14.26/3.79 | (654) ~ (all_0_51_51 = e2)
% 14.26/3.79 | (655) all_0_59_59 = e2
% 14.26/3.79 |
% 14.26/3.79 | Equations (655) can reduce 1437 to:
% 14.26/3.79 | (303) $false
% 14.26/3.79 |
% 14.26/3.79 |-The branch is then unsatisfiable
% 14.26/3.79 |-Branch two:
% 14.26/3.79 | (819) ~ (all_0_44_44 = e0)
% 14.26/3.79 | (1800) all_0_45_45 = e0 | all_0_47_47 = e0 | all_0_48_48 = e0
% 14.26/3.79 |
% 14.26/3.79 +-Applying beta-rule and splitting (1800), into two cases.
% 14.26/3.79 |-Branch one:
% 14.26/3.79 | (300) all_0_45_45 = e0
% 14.26/3.79 |
% 14.26/3.79 | Combining equations (289,300) yields a new equation:
% 14.26/3.79 | (301) e1 = e0
% 14.26/3.79 |
% 14.26/3.79 | Simplifying 301 yields:
% 14.26/3.79 | (302) e1 = e0
% 14.26/3.79 |
% 14.26/3.79 | Equations (302) can reduce 143 to:
% 14.26/3.79 | (303) $false
% 14.26/3.79 |
% 14.26/3.79 |-The branch is then unsatisfiable
% 14.26/3.79 |-Branch two:
% 14.26/3.79 | (304) ~ (all_0_45_45 = e0)
% 14.26/3.79 | (1810) all_0_47_47 = e0 | all_0_48_48 = e0
% 14.26/3.79 |
% 14.26/3.79 +-Applying beta-rule and splitting (1810), into two cases.
% 14.26/3.79 |-Branch one:
% 14.26/3.79 | (490) all_0_47_47 = e0
% 14.26/3.79 |
% 14.26/3.79 | Equations (490) can reduce 607 to:
% 14.26/3.79 | (303) $false
% 14.26/3.79 |
% 14.26/3.79 |-The branch is then unsatisfiable
% 14.26/3.79 |-Branch two:
% 14.26/3.79 | (607) ~ (all_0_47_47 = e0)
% 14.26/3.79 | (1846) all_0_48_48 = e0
% 14.26/3.79 |
% 14.26/3.79 | Equations (1846) can reduce 1599 to:
% 14.26/3.79 | (303) $false
% 14.26/3.79 |
% 14.26/3.79 |-The branch is then unsatisfiable
% 14.26/3.80 |-Branch two:
% 14.26/3.80 | (617) ~ (all_0_40_40 = e0)
% 14.26/3.80 | (883) all_0_40_40 = e4 | all_0_40_40 = e3
% 14.26/3.80 |
% 14.26/3.80 +-Applying beta-rule and splitting (883), into two cases.
% 14.26/3.80 |-Branch one:
% 14.26/3.80 | (884) all_0_40_40 = e3
% 14.26/3.80 |
% 14.26/3.80 | Equations (884) can reduce 419 to:
% 14.26/3.80 | (303) $false
% 14.26/3.80 |
% 14.26/3.80 |-The branch is then unsatisfiable
% 14.26/3.80 |-Branch two:
% 14.26/3.80 | (419) ~ (all_0_40_40 = e3)
% 14.26/3.80 | (511) all_0_40_40 = e4
% 14.26/3.80 |
% 14.26/3.80 | Equations (511) can reduce 514 to:
% 14.26/3.80 | (303) $false
% 14.26/3.80 |
% 14.26/3.80 |-The branch is then unsatisfiable
% 14.26/3.80 |-Branch two:
% 14.26/3.80 | (631) all_0_52_52 = e1 & ~ (all_0_55_55 = e2)
% 14.26/3.80 |
% 14.26/3.80 | Applying alpha-rule on (631) yields:
% 14.26/3.80 | (322) all_0_52_52 = e1
% 14.26/3.80 | (633) ~ (all_0_55_55 = e2)
% 14.26/3.80 |
% 14.26/3.80 | Equations (373) can reduce 633 to:
% 14.26/3.80 | (303) $false
% 14.26/3.80 |
% 14.26/3.80 |-The branch is then unsatisfiable
% 14.26/3.80 |-Branch two:
% 14.26/3.80 | (649) ~ (all_0_54_54 = e3)
% 14.26/3.80 | (568) all_0_55_55 = e3
% 14.26/3.80 |
% 14.26/3.80 | Combining equations (568,373) yields a new equation:
% 14.26/3.80 | (552) e3 = e2
% 14.26/3.80 |
% 14.26/3.80 | Simplifying 552 yields:
% 14.26/3.80 | (553) e3 = e2
% 14.26/3.80 |
% 14.26/3.80 | Equations (553) can reduce 209 to:
% 14.26/3.80 | (303) $false
% 14.26/3.80 |
% 14.26/3.80 |-The branch is then unsatisfiable
% 14.26/3.80 |-Branch two:
% 14.26/3.80 | (663) ~ (all_0_46_46 = e2)
% 14.26/3.80 | (664) all_0_58_58 = e2
% 14.26/3.80 |
% 14.26/3.80 | Combining equations (337,664) yields a new equation:
% 14.26/3.80 | (369) e2 = e1
% 14.26/3.80 |
% 14.26/3.80 | Equations (369) can reduce 150 to:
% 14.26/3.80 | (303) $false
% 14.26/3.80 |
% 14.26/3.80 |-The branch is then unsatisfiable
% 14.26/3.80 |-Branch two:
% 14.26/3.80 | (1072) ~ (all_0_45_45 = e1)
% 14.26/3.80 | (1059) all_0_60_60 = e1
% 14.26/3.80 |
% 14.26/3.80 | Equations (1059) can reduce 38 to:
% 14.26/3.80 | (1063) ~ (all_0_52_52 = e1)
% 14.26/3.80 |
% 14.26/3.80 | Equations (1059) can reduce 86 to:
% 14.26/3.80 | (266) ~ (all_0_58_58 = e1)
% 14.26/3.80 |
% 14.26/3.80 +-Applying beta-rule and splitting (214), into two cases.
% 14.26/3.80 |-Branch one:
% 14.26/3.80 | (257) all_0_41_41 = e1
% 14.26/3.80 |
% 14.26/3.80 | Combining equations (425,257) yields a new equation:
% 14.26/3.80 | (426) e4 = e1
% 14.26/3.80 |
% 14.26/3.80 | Simplifying 426 yields:
% 14.26/3.80 | (427) e4 = e1
% 14.26/3.80 |
% 14.26/3.80 | Equations (427) can reduce 253 to:
% 14.26/3.80 | (303) $false
% 14.26/3.80 |
% 14.26/3.80 |-The branch is then unsatisfiable
% 14.26/3.80 |-Branch two:
% 14.26/3.80 | (2409) ~ (all_0_41_41 = e1)
% 14.26/3.80 | (2453) all_0_46_46 = e1 | all_0_58_58 = e1
% 14.26/3.80 |
% 14.26/3.80 +-Applying beta-rule and splitting (7), into two cases.
% 14.26/3.80 |-Branch one:
% 14.26/3.80 | (337) all_0_58_58 = e1
% 14.26/3.80 |
% 14.26/3.80 | Equations (337) can reduce 266 to:
% 14.26/3.80 | (303) $false
% 14.26/3.80 |
% 14.26/3.80 |-The branch is then unsatisfiable
% 14.26/3.80 |-Branch two:
% 14.26/3.80 | (266) ~ (all_0_58_58 = e1)
% 14.26/3.80 | (1136) all_0_58_58 = e4 | all_0_58_58 = e2
% 14.26/3.80 |
% 14.26/3.80 +-Applying beta-rule and splitting (2453), into two cases.
% 14.26/3.80 |-Branch one:
% 14.26/3.80 | (669) all_0_46_46 = e1
% 14.26/3.80 |
% 14.26/3.80 | From (669) and (65) follows:
% 14.26/3.80 | (2632) op(e2, e1) = all_0_19_19
% 14.26/3.80 |
% 14.26/3.80 +-Applying beta-rule and splitting (85), into two cases.
% 14.26/3.80 |-Branch one:
% 14.26/3.80 | (355) all_0_46_46 = e2
% 14.26/3.80 |
% 14.26/3.80 | Combining equations (355,669) yields a new equation:
% 14.26/3.80 | (1478) e2 = e1
% 14.26/3.80 |
% 14.26/3.80 | Simplifying 1478 yields:
% 14.26/3.80 | (369) e2 = e1
% 14.26/3.80 |
% 14.26/3.80 | Equations (369) can reduce 150 to:
% 14.26/3.80 | (303) $false
% 14.26/3.80 |
% 14.26/3.80 |-The branch is then unsatisfiable
% 14.26/3.80 |-Branch two:
% 14.26/3.80 | (663) ~ (all_0_46_46 = e2)
% 14.26/3.80 | (664) all_0_58_58 = e2
% 14.26/3.80 |
% 14.26/3.80 | From (664) and (27) follows:
% 14.26/3.80 | (666) op(e2, e2) = all_0_21_21
% 14.26/3.80 |
% 14.26/3.80 | Instantiating formula (39) with e2, e2, all_0_21_21, e3 and discharging atoms op(e2, e2) = all_0_21_21, op(e2, e2) = e3, yields:
% 14.26/3.80 | (687) all_0_21_21 = e3
% 14.26/3.80 |
% 14.26/3.80 | Instantiating formula (39) with e2, e1, all_0_19_19, all_0_51_51 and discharging atoms op(e2, e1) = all_0_19_19, op(e2, e1) = all_0_51_51, yields:
% 14.26/3.80 | (2641) all_0_19_19 = all_0_51_51
% 14.26/3.80 |
% 14.26/3.80 +-Applying beta-rule and splitting (19), into two cases.
% 14.26/3.80 |-Branch one:
% 14.26/3.80 | (450) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2)) | (all_0_21_21 = e0 & ~ (all_0_22_22 = e2))
% 14.26/3.80 |
% 14.26/3.80 +-Applying beta-rule and splitting (450), into two cases.
% 14.26/3.80 |-Branch one:
% 14.26/3.80 | (451) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2))
% 14.26/3.80 |
% 14.26/3.80 +-Applying beta-rule and splitting (451), into two cases.
% 14.26/3.80 |-Branch one:
% 14.26/3.80 | (452) all_0_17_17 = e4 & ~ (all_0_18_18 = e2)
% 14.26/3.80 |
% 14.26/3.80 | Applying alpha-rule on (452) yields:
% 14.26/3.80 | (453) all_0_17_17 = e4
% 14.26/3.80 | (454) ~ (all_0_18_18 = e2)
% 14.26/3.80 |
% 14.26/3.80 | Equations (2422) can reduce 454 to:
% 14.26/3.80 | (303) $false
% 14.26/3.80 |
% 14.26/3.80 |-The branch is then unsatisfiable
% 14.26/3.80 |-Branch two:
% 14.26/3.80 | (458) all_0_19_19 = e3 & ~ (all_0_20_20 = e2)
% 14.26/3.80 |
% 14.26/3.80 | Applying alpha-rule on (458) yields:
% 14.26/3.80 | (459) all_0_19_19 = e3
% 14.26/3.80 | (460) ~ (all_0_20_20 = e2)
% 14.26/3.80 |
% 14.26/3.80 | Combining equations (459,2641) yields a new equation:
% 14.26/3.80 | (2651) all_0_51_51 = e3
% 14.26/3.80 |
% 14.26/3.80 | Equations (2651) can reduce 247 to:
% 14.26/3.80 | (303) $false
% 14.26/3.80 |
% 14.26/3.80 |-The branch is then unsatisfiable
% 14.26/3.80 |-Branch two:
% 14.26/3.80 | (462) all_0_21_21 = e0 & ~ (all_0_22_22 = e2)
% 14.26/3.80 |
% 14.26/3.80 | Applying alpha-rule on (462) yields:
% 14.26/3.80 | (463) all_0_21_21 = e0
% 14.26/3.80 | (464) ~ (all_0_22_22 = e2)
% 14.26/3.80 |
% 14.26/3.80 | Combining equations (687,463) yields a new equation:
% 14.26/3.80 | (574) e3 = e0
% 14.26/3.80 |
% 14.26/3.80 | Simplifying 574 yields:
% 14.26/3.80 | (575) e3 = e0
% 14.26/3.80 |
% 14.26/3.80 | Equations (575) can reduce 74 to:
% 14.26/3.80 | (303) $false
% 14.26/3.80 |
% 14.26/3.80 |-The branch is then unsatisfiable
% 14.26/3.80 |-Branch two:
% 14.26/3.80 | (631) all_0_52_52 = e1 & ~ (all_0_55_55 = e2)
% 14.26/3.80 |
% 14.26/3.80 | Applying alpha-rule on (631) yields:
% 14.26/3.80 | (322) all_0_52_52 = e1
% 14.26/3.80 | (633) ~ (all_0_55_55 = e2)
% 14.26/3.80 |
% 14.26/3.80 | Equations (322) can reduce 1063 to:
% 14.26/3.80 | (303) $false
% 14.26/3.80 |
% 14.26/3.80 |-The branch is then unsatisfiable
% 14.26/3.80 |-Branch two:
% 14.26/3.80 | (264) ~ (all_0_46_46 = e1)
% 14.26/3.80 | (337) all_0_58_58 = e1
% 14.26/3.80 |
% 14.26/3.80 | Equations (337) can reduce 266 to:
% 14.26/3.80 | (303) $false
% 14.26/3.80 |
% 14.26/3.80 |-The branch is then unsatisfiable
% 14.26/3.80 |-Branch two:
% 14.26/3.80 | (1568) ~ (all_0_53_53 = e1)
% 14.26/3.80 | (413) all_0_53_53 = e3
% 14.26/3.80 |
% 14.26/3.80 | Equations (413) can reduce 17 to:
% 14.26/3.80 | (908) ~ (all_0_44_44 = e3)
% 14.26/3.80 |
% 14.26/3.80 | Equations (413) can reduce 94 to:
% 14.26/3.80 | (46) ~ (all_0_49_49 = e3)
% 14.26/3.80 |
% 14.26/3.80 | Equations (413) can reduce 99 to:
% 14.26/3.80 | (1574) ~ (all_0_55_55 = e3)
% 14.26/3.80 |
% 14.26/3.80 | Simplifying 1574 yields:
% 14.26/3.80 | (572) ~ (all_0_55_55 = e3)
% 14.26/3.80 |
% 14.26/3.80 | Equations (413) can reduce 1568 to:
% 14.26/3.80 | (145) ~ (e3 = e1)
% 14.26/3.80 |
% 14.26/3.80 +-Applying beta-rule and splitting (12), into two cases.
% 14.26/3.80 |-Branch one:
% 14.26/3.80 | (289) all_0_45_45 = e1
% 14.26/3.80 |
% 14.26/3.80 | Equations (289) can reduce 72 to:
% 14.26/3.80 | (258) ~ (all_0_40_40 = e1)
% 14.26/3.80 |
% 14.26/3.80 | Equations (289) can reduce 191 to:
% 14.26/3.80 | (276) ~ (all_0_44_44 = e1)
% 14.26/3.80 |
% 14.26/3.80 | Equations (289) can reduce 128 to:
% 14.26/3.80 | (263) ~ (all_0_46_46 = e1)
% 14.26/3.80 |
% 14.26/3.80 | Simplifying 263 yields:
% 14.26/3.80 | (264) ~ (all_0_46_46 = e1)
% 14.26/3.80 |
% 14.26/3.80 | Equations (289) can reduce 37 to:
% 14.26/3.80 | (277) ~ (all_0_54_54 = e1)
% 14.26/3.80 |
% 14.26/3.80 | Simplifying 277 yields:
% 14.26/3.80 | (278) ~ (all_0_54_54 = e1)
% 14.26/3.80 |
% 14.26/3.80 +-Applying beta-rule and splitting (25), into two cases.
% 14.26/3.80 |-Branch one:
% 14.26/3.80 | (300) all_0_45_45 = e0
% 14.26/3.80 |
% 14.26/3.80 | Combining equations (289,300) yields a new equation:
% 14.26/3.80 | (301) e1 = e0
% 14.26/3.80 |
% 14.26/3.80 | Simplifying 301 yields:
% 14.26/3.80 | (302) e1 = e0
% 14.26/3.80 |
% 14.26/3.80 | Equations (302) can reduce 143 to:
% 14.26/3.80 | (303) $false
% 14.26/3.80 |
% 14.26/3.80 |-The branch is then unsatisfiable
% 14.26/3.80 |-Branch two:
% 14.26/3.80 | (304) ~ (all_0_45_45 = e0)
% 14.26/3.80 | (305) all_0_60_60 = e0
% 14.26/3.80 |
% 14.26/3.80 | Equations (305) can reduce 93 to:
% 14.26/3.80 | (306) ~ (all_0_43_43 = e0)
% 14.26/3.80 |
% 14.26/3.80 | Equations (305) can reduce 38 to:
% 14.26/3.80 | (308) ~ (all_0_52_52 = e0)
% 14.26/3.80 |
% 14.26/3.80 | Equations (305) can reduce 140 to:
% 14.26/3.80 | (1182) ~ (all_0_56_56 = e0)
% 14.26/3.80 |
% 14.26/3.80 | Equations (305) can reduce 18 to:
% 14.26/3.80 | (309) ~ (all_0_57_57 = e0)
% 14.26/3.80 |
% 14.26/3.80 | Equations (305) can reduce 86 to:
% 14.26/3.80 | (203) ~ (all_0_58_58 = e0)
% 14.26/3.80 |
% 14.26/3.80 +-Applying beta-rule and splitting (223), into two cases.
% 14.26/3.80 |-Branch one:
% 14.26/3.80 | (275) all_0_53_53 = e1
% 14.26/3.80 |
% 14.26/3.80 | Combining equations (413,275) yields a new equation:
% 14.26/3.80 | (604) e3 = e1
% 14.26/3.80 |
% 14.26/3.80 | Simplifying 604 yields:
% 14.26/3.80 | (414) e3 = e1
% 14.26/3.80 |
% 14.26/3.80 | Equations (414) can reduce 145 to:
% 14.26/3.80 | (303) $false
% 14.26/3.80 |
% 14.26/3.80 |-The branch is then unsatisfiable
% 14.26/3.80 |-Branch two:
% 14.26/3.80 | (1568) ~ (all_0_53_53 = e1)
% 14.26/3.80 | (1609) all_0_54_54 = e1 | all_0_55_55 = e1
% 14.26/3.80 |
% 14.26/3.80 +-Applying beta-rule and splitting (1609), into two cases.
% 14.26/3.80 |-Branch one:
% 14.26/3.80 | (1289) all_0_54_54 = e1
% 14.26/3.80 |
% 14.26/3.80 | Equations (1289) can reduce 278 to:
% 14.26/3.80 | (303) $false
% 14.26/3.80 |
% 14.26/3.80 |-The branch is then unsatisfiable
% 14.26/3.80 |-Branch two:
% 14.26/3.80 | (278) ~ (all_0_54_54 = e1)
% 14.26/3.80 | (1065) all_0_55_55 = e1
% 14.26/3.80 |
% 14.26/3.80 | Equations (1065) can reduce 125 to:
% 14.26/3.80 | (262) ~ (all_0_43_43 = e1)
% 14.26/3.80 |
% 14.26/3.80 | Equations (1065) can reduce 165 to:
% 14.26/3.80 | (295) ~ (all_0_48_48 = e1)
% 14.26/3.80 |
% 14.26/3.80 | Equations (1065) can reduce 256 to:
% 14.26/3.80 | (346) ~ (e4 = e1)
% 14.26/3.80 |
% 14.26/3.80 | Simplifying 346 yields:
% 14.26/3.80 | (253) ~ (e4 = e1)
% 14.26/3.80 |
% 14.26/3.80 | From (1065) and (168) follows:
% 14.26/3.80 | (2705) op(e0, e1) = all_0_37_37
% 14.26/3.80 |
% 14.26/3.80 +-Applying beta-rule and splitting (157), into two cases.
% 14.26/3.80 |-Branch one:
% 14.26/3.80 | (404) all_0_54_54 = e2
% 14.26/3.80 |
% 14.26/3.80 | Equations (404) can reduce 226 to:
% 14.26/3.80 | (388) ~ (all_0_50_50 = e2)
% 14.26/3.80 |
% 14.26/3.80 | Equations (404) can reduce 196 to:
% 14.26/3.80 | (716) ~ (all_0_57_57 = e2)
% 14.26/3.81 |
% 14.26/3.81 | Simplifying 716 yields:
% 14.26/3.81 | (717) ~ (all_0_57_57 = e2)
% 14.26/3.81 |
% 14.26/3.81 +-Applying beta-rule and splitting (214), into two cases.
% 14.26/3.81 |-Branch one:
% 14.26/3.81 | (257) all_0_41_41 = e1
% 14.26/3.81 |
% 14.26/3.81 | Combining equations (425,257) yields a new equation:
% 14.26/3.81 | (426) e4 = e1
% 14.26/3.81 |
% 14.26/3.81 | Simplifying 426 yields:
% 14.26/3.81 | (427) e4 = e1
% 14.26/3.81 |
% 14.26/3.81 | Equations (427) can reduce 253 to:
% 14.26/3.81 | (303) $false
% 14.26/3.81 |
% 14.26/3.81 |-The branch is then unsatisfiable
% 14.26/3.81 |-Branch two:
% 14.26/3.81 | (2409) ~ (all_0_41_41 = e1)
% 14.26/3.81 | (2453) all_0_46_46 = e1 | all_0_58_58 = e1
% 14.26/3.81 |
% 14.26/3.81 | Equations (425) can reduce 2409 to:
% 14.26/3.81 | (253) ~ (e4 = e1)
% 14.26/3.81 |
% 14.26/3.81 +-Applying beta-rule and splitting (24), into two cases.
% 14.26/3.81 |-Branch one:
% 14.26/3.81 | (799) all_0_40_40 = e1
% 14.26/3.81 |
% 14.26/3.81 | Equations (799) can reduce 258 to:
% 14.26/3.81 | (303) $false
% 14.26/3.81 |
% 14.26/3.81 |-The branch is then unsatisfiable
% 14.26/3.81 |-Branch two:
% 14.26/3.81 | (258) ~ (all_0_40_40 = e1)
% 14.26/3.81 | (2720) all_0_41_41 = e1 | all_0_42_42 = e1 | all_0_43_43 = e1
% 14.26/3.81 |
% 14.26/3.81 +-Applying beta-rule and splitting (2720), into two cases.
% 14.26/3.81 |-Branch one:
% 14.26/3.81 | (257) all_0_41_41 = e1
% 14.26/3.81 |
% 14.26/3.81 | Combining equations (425,257) yields a new equation:
% 14.26/3.81 | (426) e4 = e1
% 14.26/3.81 |
% 14.26/3.81 | Simplifying 426 yields:
% 14.26/3.81 | (427) e4 = e1
% 14.26/3.81 |
% 14.26/3.81 | Equations (427) can reduce 253 to:
% 14.26/3.81 | (303) $false
% 14.26/3.81 |
% 14.26/3.81 |-The branch is then unsatisfiable
% 14.26/3.81 |-Branch two:
% 14.26/3.81 | (2409) ~ (all_0_41_41 = e1)
% 14.26/3.81 | (2726) all_0_42_42 = e1 | all_0_43_43 = e1
% 14.26/3.81 |
% 14.26/3.81 +-Applying beta-rule and splitting (2726), into two cases.
% 14.26/3.81 |-Branch one:
% 14.26/3.81 | (1375) all_0_42_42 = e1
% 14.26/3.81 |
% 14.26/3.81 | Equations (1375) can reduce 189 to:
% 14.26/3.81 | (258) ~ (all_0_40_40 = e1)
% 14.26/3.81 |
% 14.26/3.81 | Equations (1375) can reduce 229 to:
% 14.26/3.81 | (261) ~ (all_0_43_43 = e1)
% 14.26/3.81 |
% 14.26/3.81 | Simplifying 261 yields:
% 14.26/3.81 | (262) ~ (all_0_43_43 = e1)
% 14.26/3.81 |
% 14.26/3.81 | Equations (1375) can reduce 29 to:
% 14.26/3.81 | (2731) ~ (all_0_47_47 = e1)
% 14.26/3.81 |
% 14.26/3.81 | Simplifying 2731 yields:
% 14.26/3.81 | (1560) ~ (all_0_47_47 = e1)
% 14.26/3.81 |
% 14.26/3.81 | Equations (1375) can reduce 20 to:
% 14.26/3.81 | (267) ~ (e2 = e1)
% 14.26/3.81 |
% 14.26/3.81 | Simplifying 267 yields:
% 14.26/3.81 | (150) ~ (e2 = e1)
% 14.26/3.81 |
% 14.26/3.81 +-Applying beta-rule and splitting (129), into two cases.
% 14.26/3.81 |-Branch one:
% 14.26/3.81 | (669) all_0_46_46 = e1
% 14.26/3.81 |
% 14.26/3.81 | Equations (669) can reduce 264 to:
% 14.26/3.81 | (303) $false
% 14.26/3.81 |
% 14.26/3.81 |-The branch is then unsatisfiable
% 14.26/3.81 |-Branch two:
% 14.26/3.81 | (264) ~ (all_0_46_46 = e1)
% 14.26/3.81 | (672) all_0_46_46 = e4 | all_0_46_46 = e2
% 14.26/3.81 |
% 14.26/3.81 +-Applying beta-rule and splitting (2453), into two cases.
% 14.26/3.81 |-Branch one:
% 14.26/3.81 | (669) all_0_46_46 = e1
% 14.26/3.81 |
% 14.26/3.81 | Equations (669) can reduce 264 to:
% 14.26/3.81 | (303) $false
% 14.26/3.81 |
% 14.26/3.81 |-The branch is then unsatisfiable
% 14.26/3.81 |-Branch two:
% 14.26/3.81 | (264) ~ (all_0_46_46 = e1)
% 14.26/3.81 | (337) all_0_58_58 = e1
% 14.26/3.81 |
% 14.26/3.81 | Equations (337) can reduce 206 to:
% 14.26/3.81 | (282) ~ (all_0_56_56 = e1)
% 14.26/3.81 |
% 14.26/3.81 | Equations (337) can reduce 1023 to:
% 14.26/3.81 | (346) ~ (e4 = e1)
% 14.26/3.81 |
% 14.26/3.81 | Simplifying 346 yields:
% 14.26/3.81 | (253) ~ (e4 = e1)
% 14.26/3.81 |
% 14.26/3.81 | Equations (337) can reduce 203 to:
% 14.26/3.81 | (143) ~ (e1 = e0)
% 14.26/3.81 |
% 14.26/3.81 | From (337) and (33) follows:
% 14.26/3.81 | (2461) op(e0, e1) = all_0_22_22
% 14.26/3.81 |
% 14.26/3.81 | From (337) and (11) follows:
% 14.26/3.81 | (2748) op(e0, e2) = e1
% 14.26/3.81 |
% 14.26/3.81 +-Applying beta-rule and splitting (222), into two cases.
% 14.26/3.81 |-Branch one:
% 14.26/3.81 | (310) all_0_43_43 = e1
% 14.26/3.81 |
% 14.26/3.81 | Equations (310) can reduce 262 to:
% 14.26/3.81 | (303) $false
% 14.26/3.81 |
% 14.26/3.81 |-The branch is then unsatisfiable
% 14.26/3.81 |-Branch two:
% 14.26/3.81 | (262) ~ (all_0_43_43 = e1)
% 14.26/3.81 | (587) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 14.26/3.81 |
% 14.26/3.81 +-Applying beta-rule and splitting (587), into two cases.
% 14.26/3.81 |-Branch one:
% 14.26/3.81 | (588) all_0_43_43 = e0
% 14.26/3.81 |
% 14.26/3.81 | Equations (588) can reduce 306 to:
% 14.26/3.81 | (303) $false
% 14.26/3.81 |
% 14.26/3.81 |-The branch is then unsatisfiable
% 14.26/3.81 |-Branch two:
% 14.26/3.81 | (306) ~ (all_0_43_43 = e0)
% 14.26/3.81 | (591) all_0_43_43 = e4 | all_0_43_43 = e3
% 14.26/3.81 |
% 14.26/3.81 +-Applying beta-rule and splitting (591), into two cases.
% 14.26/3.81 |-Branch one:
% 14.26/3.81 | (522) all_0_43_43 = e3
% 14.26/3.81 |
% 14.26/3.81 | Equations (522) can reduce 115 to:
% 14.26/3.81 | (2758) ~ (all_0_48_48 = e3)
% 14.26/3.81 |
% 14.26/3.81 | Simplifying 2758 yields:
% 14.26/3.81 | (566) ~ (all_0_48_48 = e3)
% 14.26/3.81 |
% 14.26/3.81 | Equations (522) can reduce 262 to:
% 14.26/3.81 | (145) ~ (e3 = e1)
% 14.26/3.81 |
% 14.26/3.81 | From (522) and (242) follows:
% 14.26/3.81 | (2761) op(e0, e3) = all_0_31_31
% 14.26/3.81 |
% 14.26/3.81 +-Applying beta-rule and splitting (85), into two cases.
% 14.26/3.81 |-Branch one:
% 14.26/3.81 | (355) all_0_46_46 = e2
% 14.26/3.81 |
% 14.26/3.81 | Equations (355) can reduce 79 to:
% 14.26/3.81 | (110) ~ (all_0_44_44 = e2)
% 14.26/3.81 |
% 14.26/3.81 | Equations (355) can reduce 2 to:
% 14.26/3.81 | (358) ~ (all_0_48_48 = e2)
% 14.26/3.81 |
% 14.26/3.81 | Simplifying 358 yields:
% 14.26/3.81 | (359) ~ (all_0_48_48 = e2)
% 14.26/3.81 |
% 14.26/3.81 | Equations (355) can reduce 436 to:
% 14.26/3.81 | (389) ~ (e4 = e2)
% 14.26/3.81 |
% 14.26/3.81 | Simplifying 389 yields:
% 14.26/3.81 | (227) ~ (e4 = e2)
% 14.26/3.81 |
% 14.26/3.81 +-Applying beta-rule and splitting (64), into two cases.
% 14.26/3.81 |-Branch one:
% 14.26/3.81 | (473) all_0_40_40 = e0
% 14.26/3.81 |
% 14.26/3.81 | Equations (473) can reduce 48 to:
% 14.26/3.81 | (467) ~ (all_0_50_50 = e0)
% 14.26/3.81 |
% 14.26/3.81 | Simplifying 467 yields:
% 14.26/3.81 | (468) ~ (all_0_50_50 = e0)
% 14.26/3.81 |
% 14.26/3.81 | Equations (473) can reduce 514 to:
% 14.26/3.81 | (516) ~ (e4 = e0)
% 14.26/3.81 |
% 14.26/3.81 | Simplifying 516 yields:
% 14.26/3.81 | (5) ~ (e4 = e0)
% 14.26/3.81 |
% 14.26/3.81 | Equations (473) can reduce 258 to:
% 14.26/3.81 | (471) ~ (e1 = e0)
% 14.26/3.81 |
% 14.26/3.81 | Simplifying 471 yields:
% 14.26/3.81 | (143) ~ (e1 = e0)
% 14.26/3.81 |
% 14.26/3.81 +-Applying beta-rule and splitting (47), into two cases.
% 14.26/3.81 |-Branch one:
% 14.26/3.81 | (1087) all_0_44_44 = e1
% 14.26/3.81 |
% 14.26/3.81 | Equations (1087) can reduce 276 to:
% 14.26/3.81 | (303) $false
% 14.26/3.81 |
% 14.26/3.81 |-The branch is then unsatisfiable
% 14.26/3.81 |-Branch two:
% 14.26/3.81 | (276) ~ (all_0_44_44 = e1)
% 14.26/3.81 | (2154) all_0_49_49 = e1 | all_0_53_53 = e1 | all_0_56_56 = e1
% 14.26/3.81 |
% 14.26/3.81 +-Applying beta-rule and splitting (2154), into two cases.
% 14.26/3.81 |-Branch one:
% 14.26/3.81 | (811) all_0_49_49 = e1
% 14.26/3.81 |
% 14.26/3.81 | Equations (811) can reduce 53 to:
% 14.26/3.81 | (276) ~ (all_0_44_44 = e1)
% 14.26/3.81 |
% 14.26/3.81 | Equations (811) can reduce 244 to:
% 14.26/3.81 | (1121) ~ (all_0_52_52 = e1)
% 14.26/3.81 |
% 14.26/3.81 | Simplifying 1121 yields:
% 14.26/3.81 | (1063) ~ (all_0_52_52 = e1)
% 14.26/3.81 |
% 14.26/3.81 | Equations (811) can reduce 224 to:
% 14.26/3.81 | (281) ~ (all_0_56_56 = e1)
% 14.26/3.81 |
% 14.26/3.81 | Simplifying 281 yields:
% 14.26/3.81 | (282) ~ (all_0_56_56 = e1)
% 14.26/3.81 |
% 14.26/3.81 | Equations (811) can reduce 46 to:
% 14.26/3.81 | (329) ~ (e3 = e1)
% 14.26/3.81 |
% 14.26/3.81 | Simplifying 329 yields:
% 14.26/3.81 | (145) ~ (e3 = e1)
% 14.26/3.81 |
% 14.26/3.81 | Equations (811) can reduce 151 to:
% 14.26/3.81 | (267) ~ (e2 = e1)
% 14.26/3.81 |
% 14.26/3.81 | Simplifying 267 yields:
% 14.26/3.81 | (150) ~ (e2 = e1)
% 14.26/3.81 |
% 14.26/3.81 +-Applying beta-rule and splitting (121), into two cases.
% 14.26/3.81 |-Branch one:
% 14.26/3.81 | (815) all_0_44_44 = e0
% 14.26/3.81 |
% 14.26/3.81 | Equations (815) can reduce 908 to:
% 14.26/3.81 | (480) ~ (e3 = e0)
% 14.26/3.81 |
% 14.26/3.81 | Simplifying 480 yields:
% 14.26/3.81 | (74) ~ (e3 = e0)
% 14.26/3.81 |
% 14.26/3.81 | Equations (815) can reduce 110 to:
% 14.26/3.81 | (469) ~ (e2 = e0)
% 14.26/3.81 |
% 14.26/3.81 | Simplifying 469 yields:
% 14.26/3.81 | (61) ~ (e2 = e0)
% 14.26/3.81 |
% 14.26/3.81 | Equations (815) can reduce 276 to:
% 14.26/3.81 | (471) ~ (e1 = e0)
% 14.26/3.81 |
% 14.26/3.81 | Simplifying 471 yields:
% 14.26/3.81 | (143) ~ (e1 = e0)
% 14.26/3.81 |
% 14.26/3.81 +-Applying beta-rule and splitting (60), into two cases.
% 14.26/3.81 |-Branch one:
% 14.26/3.81 | (314) all_0_56_56 = e1
% 14.26/3.81 |
% 14.26/3.81 | Equations (314) can reduce 282 to:
% 14.26/3.81 | (303) $false
% 14.26/3.81 |
% 14.26/3.81 |-The branch is then unsatisfiable
% 14.26/3.81 |-Branch two:
% 14.26/3.81 | (282) ~ (all_0_56_56 = e1)
% 14.26/3.81 | (1931) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e0
% 14.26/3.81 |
% 14.26/3.81 +-Applying beta-rule and splitting (28), into two cases.
% 14.26/3.81 |-Branch one:
% 14.26/3.81 | (775) all_0_44_44 = e3
% 14.26/3.81 |
% 14.26/3.81 | Combining equations (815,775) yields a new equation:
% 14.26/3.81 | (575) e3 = e0
% 14.26/3.81 |
% 14.26/3.81 | Equations (575) can reduce 74 to:
% 14.26/3.81 | (303) $false
% 14.26/3.81 |
% 14.26/3.81 |-The branch is then unsatisfiable
% 14.26/3.81 |-Branch two:
% 14.26/3.81 | (908) ~ (all_0_44_44 = e3)
% 14.26/3.81 | (1202) all_0_45_45 = e3 | all_0_47_47 = e3 | all_0_48_48 = e3
% 14.26/3.81 |
% 14.26/3.81 +-Applying beta-rule and splitting (63), into two cases.
% 14.26/3.81 |-Branch one:
% 14.26/3.81 | (1189) all_0_44_44 = e4
% 14.26/3.81 |
% 14.26/3.81 | Combining equations (815,1189) yields a new equation:
% 14.26/3.81 | (512) e4 = e0
% 14.26/3.81 |
% 14.26/3.81 | Equations (512) can reduce 5 to:
% 14.26/3.81 | (303) $false
% 14.26/3.81 |
% 14.26/3.81 |-The branch is then unsatisfiable
% 14.26/3.81 |-Branch two:
% 14.26/3.81 | (1361) ~ (all_0_44_44 = e4)
% 14.26/3.81 | (2271) all_0_45_45 = e4 | all_0_46_46 = e4 | all_0_48_48 = e4
% 14.26/3.81 |
% 14.26/3.81 +-Applying beta-rule and splitting (2271), into two cases.
% 14.26/3.81 |-Branch one:
% 14.26/3.81 | (784) all_0_45_45 = e4
% 14.26/3.81 |
% 14.26/3.81 | Combining equations (289,784) yields a new equation:
% 14.26/3.81 | (427) e4 = e1
% 14.26/3.81 |
% 14.26/3.81 | Equations (427) can reduce 253 to:
% 14.26/3.81 | (303) $false
% 14.26/3.81 |
% 14.26/3.81 |-The branch is then unsatisfiable
% 14.26/3.81 |-Branch two:
% 14.26/3.81 | (787) ~ (all_0_45_45 = e4)
% 14.26/3.81 | (2276) all_0_46_46 = e4 | all_0_48_48 = e4
% 14.26/3.81 |
% 14.26/3.81 +-Applying beta-rule and splitting (2276), into two cases.
% 14.26/3.81 |-Branch one:
% 14.26/3.81 | (433) all_0_46_46 = e4
% 14.26/3.81 |
% 14.26/3.81 | Combining equations (355,433) yields a new equation:
% 14.26/3.81 | (434) e4 = e2
% 14.26/3.81 |
% 14.26/3.81 | Equations (434) can reduce 227 to:
% 14.26/3.81 | (303) $false
% 14.26/3.81 |
% 14.26/3.81 |-The branch is then unsatisfiable
% 14.26/3.81 |-Branch two:
% 14.26/3.81 | (436) ~ (all_0_46_46 = e4)
% 14.26/3.82 | (1297) all_0_48_48 = e4
% 14.26/3.82 |
% 14.26/3.82 | Equations (1297) can reduce 566 to:
% 14.26/3.82 | (30) ~ (e4 = e3)
% 14.26/3.82 |
% 14.26/3.82 | Equations (1297) can reduce 359 to:
% 14.26/3.82 | (227) ~ (e4 = e2)
% 14.26/3.82 |
% 14.26/3.82 | Equations (1297) can reduce 295 to:
% 14.26/3.82 | (253) ~ (e4 = e1)
% 14.26/3.82 |
% 14.26/3.82 | From (1297) and (211) follows:
% 14.26/3.82 | (2823) op(e0, e4) = all_0_33_33
% 14.26/3.82 |
% 14.26/3.82 +-Applying beta-rule and splitting (137), into two cases.
% 14.26/3.82 |-Branch one:
% 14.26/3.82 | (466) all_0_49_49 = e0
% 14.26/3.82 |
% 14.26/3.82 | Combining equations (811,466) yields a new equation:
% 14.26/3.82 | (301) e1 = e0
% 14.26/3.82 |
% 14.26/3.82 | Simplifying 301 yields:
% 14.26/3.82 | (302) e1 = e0
% 14.26/3.82 |
% 14.26/3.82 | Equations (302) can reduce 143 to:
% 14.26/3.82 | (303) $false
% 14.26/3.82 |
% 14.26/3.82 |-The branch is then unsatisfiable
% 14.26/3.82 |-Branch two:
% 14.26/3.82 | (879) ~ (all_0_49_49 = e0)
% 14.26/3.82 | (1012) all_0_50_50 = e0 | all_0_51_51 = e0 | all_0_52_52 = e0
% 14.26/3.82 |
% 14.26/3.82 +-Applying beta-rule and splitting (1012), into two cases.
% 14.26/3.82 |-Branch one:
% 14.26/3.82 | (518) all_0_50_50 = e0
% 14.26/3.82 |
% 14.26/3.82 | Equations (518) can reduce 468 to:
% 14.26/3.82 | (303) $false
% 14.26/3.82 |
% 14.26/3.82 |-The branch is then unsatisfiable
% 14.26/3.82 |-Branch two:
% 14.26/3.82 | (468) ~ (all_0_50_50 = e0)
% 14.26/3.82 | (1028) all_0_51_51 = e0 | all_0_52_52 = e0
% 14.26/3.82 |
% 14.26/3.82 +-Applying beta-rule and splitting (1028), into two cases.
% 14.26/3.82 |-Branch one:
% 14.26/3.82 | (609) all_0_51_51 = e0
% 14.26/3.82 |
% 14.26/3.82 | Equations (609) can reduce 176 to:
% 14.26/3.82 | (607) ~ (all_0_47_47 = e0)
% 14.26/3.82 |
% 14.26/3.82 | Equations (609) can reduce 92 to:
% 14.26/3.82 | (2836) ~ (all_0_59_59 = e0)
% 14.26/3.82 |
% 14.26/3.82 | Simplifying 2836 yields:
% 14.26/3.82 | (1348) ~ (all_0_59_59 = e0)
% 14.26/3.82 |
% 14.26/3.82 | Equations (609) can reduce 56 to:
% 14.26/3.82 | (516) ~ (e4 = e0)
% 14.26/3.82 |
% 14.26/3.82 | Simplifying 516 yields:
% 14.26/3.82 | (5) ~ (e4 = e0)
% 14.26/3.82 |
% 14.26/3.82 +-Applying beta-rule and splitting (88), into two cases.
% 14.26/3.82 |-Branch one:
% 14.26/3.82 | (528) all_0_49_49 = e4
% 14.26/3.82 |
% 14.26/3.82 | Combining equations (811,528) yields a new equation:
% 14.26/3.82 | (427) e4 = e1
% 14.26/3.82 |
% 14.26/3.82 | Equations (427) can reduce 253 to:
% 14.26/3.82 | (303) $false
% 14.26/3.82 |
% 14.26/3.82 |-The branch is then unsatisfiable
% 14.26/3.82 |-Branch two:
% 14.26/3.82 | (531) ~ (all_0_49_49 = e4)
% 14.26/3.82 | (532) all_0_50_50 = e4 | all_0_52_52 = e4
% 14.26/3.82 |
% 14.26/3.82 | Equations (811) can reduce 531 to:
% 14.26/3.82 | (346) ~ (e4 = e1)
% 14.26/3.82 |
% 14.26/3.82 | Simplifying 346 yields:
% 14.26/3.82 | (253) ~ (e4 = e1)
% 14.26/3.82 |
% 14.26/3.82 +-Applying beta-rule and splitting (1202), into two cases.
% 14.26/3.82 |-Branch one:
% 14.26/3.82 | (1260) all_0_45_45 = e3
% 14.26/3.82 |
% 14.26/3.82 | Combining equations (289,1260) yields a new equation:
% 14.26/3.82 | (414) e3 = e1
% 14.26/3.82 |
% 14.26/3.82 | Equations (414) can reduce 145 to:
% 14.26/3.82 | (303) $false
% 14.26/3.82 |
% 14.26/3.82 |-The branch is then unsatisfiable
% 14.26/3.82 |-Branch two:
% 14.26/3.82 | (1263) ~ (all_0_45_45 = e3)
% 14.26/3.82 | (1264) all_0_47_47 = e3 | all_0_48_48 = e3
% 14.26/3.82 |
% 14.26/3.82 +-Applying beta-rule and splitting (1264), into two cases.
% 14.26/3.82 |-Branch one:
% 14.26/3.82 | (599) all_0_47_47 = e3
% 14.26/3.82 |
% 14.26/3.82 | Equations (599) can reduce 80 to:
% 14.26/3.82 | (1231) ~ (all_0_59_59 = e3)
% 14.26/3.82 |
% 14.26/3.82 | Simplifying 1231 yields:
% 14.26/3.82 | (645) ~ (all_0_59_59 = e3)
% 14.26/3.82 |
% 14.26/3.82 | Equations (599) can reduce 1560 to:
% 14.26/3.82 | (145) ~ (e3 = e1)
% 14.26/3.82 |
% 14.26/3.82 | Equations (599) can reduce 607 to:
% 14.26/3.82 | (74) ~ (e3 = e0)
% 14.26/3.82 |
% 14.26/3.82 +-Applying beta-rule and splitting (77), into two cases.
% 14.26/3.82 |-Branch one:
% 14.26/3.82 | (1189) all_0_44_44 = e4
% 14.26/3.82 |
% 14.26/3.82 | Combining equations (1189,815) yields a new equation:
% 14.26/3.82 | (995) e4 = e0
% 14.26/3.82 |
% 14.26/3.82 | Simplifying 995 yields:
% 14.26/3.82 | (512) e4 = e0
% 14.26/3.82 |
% 14.26/3.82 | Equations (512) can reduce 5 to:
% 14.26/3.82 | (303) $false
% 14.26/3.82 |
% 14.26/3.82 |-The branch is then unsatisfiable
% 14.26/3.82 |-Branch two:
% 14.26/3.82 | (1361) ~ (all_0_44_44 = e4)
% 14.26/3.82 | (1362) all_0_49_49 = e4 | all_0_56_56 = e4
% 14.26/3.82 |
% 14.26/3.82 | Equations (815) can reduce 1361 to:
% 14.26/3.82 | (516) ~ (e4 = e0)
% 14.26/3.82 |
% 14.26/3.82 | Simplifying 516 yields:
% 14.26/3.82 | (5) ~ (e4 = e0)
% 14.26/3.82 |
% 14.26/3.82 +-Applying beta-rule and splitting (133), into two cases.
% 14.26/3.82 |-Branch one:
% 14.26/3.82 | (400) all_0_50_50 = e2
% 14.26/3.82 |
% 14.26/3.82 | Equations (400) can reduce 388 to:
% 14.26/3.82 | (303) $false
% 14.26/3.82 |
% 14.26/3.82 |-The branch is then unsatisfiable
% 14.26/3.82 |-Branch two:
% 14.26/3.82 | (388) ~ (all_0_50_50 = e2)
% 14.26/3.82 | (2329) all_0_51_51 = e2 | all_0_52_52 = e2
% 14.26/3.82 |
% 14.26/3.82 +-Applying beta-rule and splitting (175), into two cases.
% 14.26/3.82 |-Branch one:
% 14.26/3.82 | (364) all_0_48_48 = e2
% 14.26/3.82 |
% 14.26/3.82 | Combining equations (1297,364) yields a new equation:
% 14.26/3.82 | (455) e4 = e2
% 14.26/3.82 |
% 14.26/3.82 | Simplifying 455 yields:
% 14.26/3.82 | (434) e4 = e2
% 14.26/3.82 |
% 14.26/3.82 | Equations (434) can reduce 227 to:
% 14.26/3.82 | (303) $false
% 14.26/3.82 |
% 14.26/3.82 |-The branch is then unsatisfiable
% 14.26/3.82 |-Branch two:
% 14.26/3.82 | (359) ~ (all_0_48_48 = e2)
% 14.26/3.82 | (367) all_0_52_52 = e2 | all_0_55_55 = e2 | all_0_60_60 = e2
% 14.26/3.82 |
% 14.26/3.82 +-Applying beta-rule and splitting (131), into two cases.
% 14.26/3.82 |-Branch one:
% 14.26/3.82 | (407) all_0_57_57 = e2
% 14.26/3.82 |
% 14.26/3.82 | Equations (407) can reduce 717 to:
% 14.26/3.82 | (303) $false
% 14.26/3.82 |
% 14.26/3.82 |-The branch is then unsatisfiable
% 14.26/3.82 |-Branch two:
% 14.26/3.82 | (717) ~ (all_0_57_57 = e2)
% 14.26/3.82 | (1912) all_0_58_58 = e2 | all_0_59_59 = e2 | all_0_60_60 = e2
% 14.26/3.82 |
% 14.26/3.82 +-Applying beta-rule and splitting (1912), into two cases.
% 14.26/3.82 |-Branch one:
% 14.26/3.82 | (664) all_0_58_58 = e2
% 14.26/3.82 |
% 14.26/3.82 | Combining equations (337,664) yields a new equation:
% 14.26/3.82 | (369) e2 = e1
% 14.26/3.82 |
% 14.26/3.82 | Equations (369) can reduce 150 to:
% 14.26/3.82 | (303) $false
% 14.26/3.82 |
% 14.26/3.82 |-The branch is then unsatisfiable
% 14.26/3.82 |-Branch two:
% 14.26/3.82 | (411) ~ (all_0_58_58 = e2)
% 14.26/3.82 | (1918) all_0_59_59 = e2 | all_0_60_60 = e2
% 14.26/3.82 |
% 14.26/3.82 +-Applying beta-rule and splitting (1918), into two cases.
% 14.26/3.82 |-Branch one:
% 14.26/3.82 | (655) all_0_59_59 = e2
% 14.26/3.82 |
% 14.26/3.82 | Equations (655) can reduce 645 to:
% 14.26/3.82 | (391) ~ (e3 = e2)
% 14.26/3.82 |
% 14.26/3.82 | Simplifying 391 yields:
% 14.26/3.82 | (209) ~ (e3 = e2)
% 14.26/3.82 |
% 14.26/3.82 | Equations (655) can reduce 1348 to:
% 14.26/3.82 | (61) ~ (e2 = e0)
% 14.26/3.82 |
% 14.26/3.82 | From (655) and (43) follows:
% 14.26/3.82 | (2888) op(e0, e2) = all_0_30_30
% 14.26/3.82 |
% 14.26/3.82 | From (655) and (163) follows:
% 14.26/3.82 | (2889) op(e0, e1) = e2
% 14.26/3.82 |
% 14.26/3.82 +-Applying beta-rule and splitting (180), into two cases.
% 14.26/3.82 |-Branch one:
% 14.26/3.82 | (884) all_0_40_40 = e3
% 14.26/3.82 |
% 14.26/3.82 | Combining equations (884,473) yields a new equation:
% 14.26/3.82 | (574) e3 = e0
% 14.26/3.82 |
% 14.26/3.82 | Simplifying 574 yields:
% 14.26/3.82 | (575) e3 = e0
% 14.26/3.82 |
% 14.26/3.82 | Equations (575) can reduce 74 to:
% 14.26/3.82 | (303) $false
% 14.26/3.82 |
% 14.26/3.82 |-The branch is then unsatisfiable
% 14.26/3.82 |-Branch two:
% 14.26/3.82 | (419) ~ (all_0_40_40 = e3)
% 14.26/3.82 | (2127) all_0_45_45 = e3 | all_0_54_54 = e3 | all_0_57_57 = e3
% 14.26/3.82 |
% 14.26/3.82 +-Applying beta-rule and splitting (2127), into two cases.
% 14.26/3.82 |-Branch one:
% 14.26/3.82 | (1260) all_0_45_45 = e3
% 14.26/3.82 |
% 14.26/3.82 | Combining equations (1260,289) yields a new equation:
% 14.26/3.82 | (604) e3 = e1
% 14.26/3.82 |
% 14.26/3.82 | Simplifying 604 yields:
% 14.26/3.82 | (414) e3 = e1
% 14.26/3.82 |
% 14.26/3.82 | Equations (414) can reduce 145 to:
% 14.26/3.82 | (303) $false
% 14.26/3.82 |
% 14.26/3.82 |-The branch is then unsatisfiable
% 14.26/3.82 |-Branch two:
% 14.26/3.82 | (1263) ~ (all_0_45_45 = e3)
% 14.26/3.82 | (2136) all_0_54_54 = e3 | all_0_57_57 = e3
% 14.26/3.82 |
% 14.26/3.82 +-Applying beta-rule and splitting (2136), into two cases.
% 14.26/3.82 |-Branch one:
% 14.26/3.82 | (418) all_0_54_54 = e3
% 14.26/3.82 |
% 14.26/3.82 | Combining equations (404,418) yields a new equation:
% 14.26/3.82 | (553) e3 = e2
% 14.26/3.82 |
% 14.26/3.82 | Equations (553) can reduce 209 to:
% 14.26/3.82 | (303) $false
% 14.26/3.82 |
% 14.26/3.82 |-The branch is then unsatisfiable
% 14.26/3.82 |-Branch two:
% 14.26/3.82 | (649) ~ (all_0_54_54 = e3)
% 14.26/3.82 | (637) all_0_57_57 = e3
% 14.26/3.82 |
% 14.26/3.82 | Equations (637) can reduce 170 to:
% 14.26/3.82 | (52) ~ (all_0_50_50 = e3)
% 14.26/3.82 |
% 14.26/3.82 | Equations (637) can reduce 90 to:
% 14.26/3.82 | (635) ~ (all_0_56_56 = e3)
% 14.26/3.82 |
% 14.26/3.82 | From (637) and (205) follows:
% 14.26/3.82 | (2909) op(e0, e3) = all_0_16_16
% 14.26/3.82 |
% 14.26/3.82 | From (637) and (217) follows:
% 14.26/3.82 | (2910) op(e0, e3) = e3
% 14.26/3.82 |
% 14.26/3.82 +-Applying beta-rule and splitting (100), into two cases.
% 14.26/3.82 |-Branch one:
% 14.26/3.82 | (511) all_0_40_40 = e4
% 14.26/3.82 |
% 14.26/3.82 | Combining equations (511,473) yields a new equation:
% 14.26/3.82 | (995) e4 = e0
% 14.26/3.82 |
% 14.26/3.82 | Simplifying 995 yields:
% 14.26/3.82 | (512) e4 = e0
% 14.26/3.82 |
% 14.26/3.82 | Equations (512) can reduce 5 to:
% 14.26/3.82 | (303) $false
% 14.26/3.82 |
% 14.26/3.82 |-The branch is then unsatisfiable
% 14.26/3.82 |-Branch two:
% 14.26/3.82 | (514) ~ (all_0_40_40 = e4)
% 14.26/3.82 | (515) all_0_45_45 = e4 | all_0_50_50 = e4 | all_0_57_57 = e4
% 14.26/3.82 |
% 14.26/3.82 +-Applying beta-rule and splitting (195), into two cases.
% 14.26/3.82 |-Branch one:
% 14.26/3.82 | (762) all_0_56_56 = e4
% 14.26/3.82 |
% 14.26/3.82 | Equations (762) can reduce 635 to:
% 14.26/3.82 | (30) ~ (e4 = e3)
% 14.26/3.82 |
% 14.26/3.82 | Equations (762) can reduce 282 to:
% 14.26/3.82 | (253) ~ (e4 = e1)
% 14.26/3.82 |
% 14.26/3.82 | From (762) and (220) follows:
% 14.26/3.82 | (2920) op(e0, e4) = all_0_7_7
% 14.26/3.82 |
% 14.26/3.82 | From (762) and (218) follows:
% 14.26/3.82 | (2921) op(e0, e4) = e4
% 14.26/3.82 |
% 14.26/3.82 +-Applying beta-rule and splitting (515), into two cases.
% 14.26/3.82 |-Branch one:
% 14.26/3.82 | (784) all_0_45_45 = e4
% 14.26/3.82 |
% 14.26/3.82 | Combining equations (784,289) yields a new equation:
% 14.26/3.82 | (426) e4 = e1
% 14.26/3.82 |
% 14.26/3.82 | Simplifying 426 yields:
% 14.26/3.82 | (427) e4 = e1
% 14.26/3.82 |
% 14.26/3.82 | Equations (427) can reduce 253 to:
% 14.26/3.82 | (303) $false
% 14.26/3.82 |
% 14.26/3.82 |-The branch is then unsatisfiable
% 14.26/3.82 |-Branch two:
% 14.26/3.82 | (787) ~ (all_0_45_45 = e4)
% 14.26/3.82 | (788) all_0_50_50 = e4 | all_0_57_57 = e4
% 14.26/3.83 |
% 14.26/3.83 +-Applying beta-rule and splitting (788), into two cases.
% 14.26/3.83 |-Branch one:
% 14.26/3.83 | (533) all_0_50_50 = e4
% 14.26/3.83 |
% 14.26/3.83 | Equations (533) can reduce 52 to:
% 14.26/3.83 | (30) ~ (e4 = e3)
% 14.26/3.83 |
% 14.26/3.83 +-Applying beta-rule and splitting (138), into two cases.
% 14.26/3.83 |-Branch one:
% 14.26/3.83 | (322) all_0_52_52 = e1
% 14.26/3.83 |
% 14.26/3.83 | Equations (322) can reduce 1063 to:
% 14.26/3.83 | (303) $false
% 14.26/3.83 |
% 14.26/3.83 |-The branch is then unsatisfiable
% 14.26/3.83 |-Branch two:
% 14.26/3.83 | (1063) ~ (all_0_52_52 = e1)
% 14.26/3.83 | (2131) all_0_52_52 = e4 | all_0_52_52 = e2 | all_0_52_52 = e0
% 14.26/3.83 |
% 14.26/3.83 +-Applying beta-rule and splitting (367), into two cases.
% 14.26/3.83 |-Branch one:
% 14.26/3.83 | (368) all_0_52_52 = e2
% 14.26/3.83 |
% 14.26/3.83 | Equations (368) can reduce 1063 to:
% 14.26/3.83 | (150) ~ (e2 = e1)
% 14.26/3.83 |
% 14.26/3.83 | From (368) and (221) follows:
% 14.26/3.83 | (2936) op(e0, e2) = all_0_35_35
% 14.26/3.83 |
% 14.26/3.83 | Instantiating formula (39) with e0, e4, all_0_33_33, all_0_7_7 and discharging atoms op(e0, e4) = all_0_7_7, op(e0, e4) = all_0_33_33, yields:
% 14.26/3.83 | (2937) all_0_7_7 = all_0_33_33
% 14.26/3.83 |
% 14.26/3.83 | Instantiating formula (39) with e0, e4, e4, all_0_7_7 and discharging atoms op(e0, e4) = all_0_7_7, op(e0, e4) = e4, yields:
% 14.26/3.83 | (2938) all_0_7_7 = e4
% 14.26/3.83 |
% 14.26/3.83 | Instantiating formula (39) with e0, e3, all_0_31_31, all_0_16_16 and discharging atoms op(e0, e3) = all_0_16_16, op(e0, e3) = all_0_31_31, yields:
% 14.26/3.83 | (2939) all_0_16_16 = all_0_31_31
% 14.26/3.83 |
% 14.26/3.83 | Instantiating formula (39) with e0, e3, e3, all_0_16_16 and discharging atoms op(e0, e3) = all_0_16_16, op(e0, e3) = e3, yields:
% 14.26/3.83 | (2940) all_0_16_16 = e3
% 14.26/3.83 |
% 14.26/3.83 | Instantiating formula (39) with e0, e2, all_0_35_35, all_0_30_30 and discharging atoms op(e0, e2) = all_0_30_30, op(e0, e2) = all_0_35_35, yields:
% 14.26/3.83 | (352) all_0_30_30 = all_0_35_35
% 14.26/3.83 |
% 14.26/3.83 | Instantiating formula (39) with e0, e2, e1, all_0_30_30 and discharging atoms op(e0, e2) = all_0_30_30, op(e0, e2) = e1, yields:
% 14.26/3.83 | (353) all_0_30_30 = e1
% 14.26/3.83 |
% 14.26/3.83 | Instantiating formula (39) with e0, e1, all_0_37_37, all_0_22_22 and discharging atoms op(e0, e1) = all_0_22_22, op(e0, e1) = all_0_37_37, yields:
% 14.26/3.83 | (2943) all_0_22_22 = all_0_37_37
% 14.26/3.83 |
% 14.26/3.83 | Instantiating formula (39) with e0, e1, e2, all_0_22_22 and discharging atoms op(e0, e1) = all_0_22_22, op(e0, e1) = e2, yields:
% 14.26/3.83 | (689) all_0_22_22 = e2
% 14.26/3.83 |
% 14.26/3.83 | Combining equations (2937,2938) yields a new equation:
% 14.26/3.83 | (2945) all_0_33_33 = e4
% 14.26/3.83 |
% 14.26/3.83 | Simplifying 2945 yields:
% 14.26/3.83 | (2946) all_0_33_33 = e4
% 14.26/3.83 |
% 14.26/3.83 | Combining equations (2939,2940) yields a new equation:
% 14.26/3.83 | (2947) all_0_31_31 = e3
% 14.26/3.83 |
% 14.26/3.83 | Simplifying 2947 yields:
% 14.26/3.83 | (2948) all_0_31_31 = e3
% 14.26/3.83 |
% 14.26/3.83 | Combining equations (689,2943) yields a new equation:
% 14.26/3.83 | (2949) all_0_37_37 = e2
% 14.26/3.83 |
% 14.26/3.83 | Combining equations (352,353) yields a new equation:
% 14.26/3.83 | (2950) all_0_35_35 = e1
% 14.26/3.83 |
% 14.26/3.83 | Simplifying 2950 yields:
% 14.26/3.83 | (354) all_0_35_35 = e1
% 14.26/3.83 |
% 14.26/3.83 +-Applying beta-rule and splitting (36), into two cases.
% 14.26/3.83 |-Branch one:
% 14.26/3.83 | (756) (all_0_31_31 = e4 & ~ (all_0_32_32 = e0)) | (all_0_33_33 = e3 & ~ (all_0_34_34 = e0)) | (all_0_35_35 = e2 & ~ (all_0_36_36 = e0))
% 14.26/3.83 |
% 14.26/3.83 +-Applying beta-rule and splitting (756), into two cases.
% 14.26/3.83 |-Branch one:
% 14.26/3.83 | (757) (all_0_31_31 = e4 & ~ (all_0_32_32 = e0)) | (all_0_33_33 = e3 & ~ (all_0_34_34 = e0))
% 14.26/3.83 |
% 14.26/3.83 +-Applying beta-rule and splitting (757), into two cases.
% 14.26/3.83 |-Branch one:
% 14.26/3.83 | (758) all_0_31_31 = e4 & ~ (all_0_32_32 = e0)
% 14.26/3.83 |
% 14.26/3.83 | Applying alpha-rule on (758) yields:
% 14.26/3.83 | (759) all_0_31_31 = e4
% 14.26/3.83 | (760) ~ (all_0_32_32 = e0)
% 14.26/3.83 |
% 14.26/3.83 | Combining equations (2948,759) yields a new equation:
% 14.26/3.83 | (524) e4 = e3
% 14.26/3.83 |
% 14.26/3.83 | Equations (524) can reduce 30 to:
% 14.26/3.83 | (303) $false
% 14.26/3.83 |
% 14.26/3.83 |-The branch is then unsatisfiable
% 14.26/3.83 |-Branch two:
% 14.26/3.83 | (917) all_0_33_33 = e3 & ~ (all_0_34_34 = e0)
% 14.26/3.83 |
% 14.26/3.83 | Applying alpha-rule on (917) yields:
% 14.26/3.83 | (918) all_0_33_33 = e3
% 14.26/3.83 | (919) ~ (all_0_34_34 = e0)
% 14.26/3.83 |
% 14.26/3.83 | Combining equations (2946,918) yields a new equation:
% 14.26/3.83 | (523) e4 = e3
% 14.26/3.83 |
% 14.26/3.83 | Simplifying 523 yields:
% 14.26/3.83 | (524) e4 = e3
% 14.26/3.83 |
% 14.26/3.83 | Equations (524) can reduce 30 to:
% 14.26/3.83 | (303) $false
% 14.26/3.83 |
% 14.26/3.83 |-The branch is then unsatisfiable
% 14.26/3.83 |-Branch two:
% 14.26/3.83 | (923) all_0_35_35 = e2 & ~ (all_0_36_36 = e0)
% 14.26/3.83 |
% 14.26/3.83 | Applying alpha-rule on (923) yields:
% 14.26/3.83 | (924) all_0_35_35 = e2
% 14.26/3.83 | (925) ~ (all_0_36_36 = e0)
% 14.26/3.83 |
% 14.26/3.83 | Combining equations (354,924) yields a new equation:
% 14.26/3.83 | (369) e2 = e1
% 14.26/3.83 |
% 14.26/3.83 | Equations (369) can reduce 150 to:
% 14.26/3.83 | (303) $false
% 14.26/3.83 |
% 14.26/3.83 |-The branch is then unsatisfiable
% 14.26/3.83 |-Branch two:
% 14.26/3.83 | (928) all_0_37_37 = e1 & ~ (all_0_38_38 = e0)
% 14.26/3.83 |
% 14.26/3.83 | Applying alpha-rule on (928) yields:
% 14.26/3.83 | (929) all_0_37_37 = e1
% 14.26/3.83 | (930) ~ (all_0_38_38 = e0)
% 14.26/3.83 |
% 14.26/3.83 | Combining equations (2949,929) yields a new equation:
% 14.26/3.83 | (1478) e2 = e1
% 14.26/3.83 |
% 14.26/3.83 | Simplifying 1478 yields:
% 14.26/3.83 | (369) e2 = e1
% 14.26/3.83 |
% 14.26/3.83 | Equations (369) can reduce 150 to:
% 14.26/3.83 | (303) $false
% 14.26/3.83 |
% 14.26/3.83 |-The branch is then unsatisfiable
% 14.26/3.83 |-Branch two:
% 14.26/3.83 | (371) ~ (all_0_52_52 = e2)
% 14.26/3.83 | (372) all_0_55_55 = e2 | all_0_60_60 = e2
% 14.26/3.83 |
% 14.26/3.83 +-Applying beta-rule and splitting (2329), into two cases.
% 14.26/3.83 |-Branch one:
% 14.26/3.83 | (383) all_0_51_51 = e2
% 14.26/3.83 |
% 14.26/3.83 | Combining equations (609,383) yields a new equation:
% 14.26/3.83 | (559) e2 = e0
% 14.26/3.83 |
% 14.26/3.83 | Equations (559) can reduce 61 to:
% 14.26/3.83 | (303) $false
% 14.26/3.83 |
% 14.26/3.83 |-The branch is then unsatisfiable
% 14.26/3.83 |-Branch two:
% 14.26/3.83 | (654) ~ (all_0_51_51 = e2)
% 14.26/3.83 | (368) all_0_52_52 = e2
% 14.26/3.83 |
% 14.26/3.83 | Equations (368) can reduce 371 to:
% 14.26/3.83 | (303) $false
% 14.26/3.83 |
% 14.26/3.83 |-The branch is then unsatisfiable
% 14.26/3.83 |-Branch two:
% 14.26/3.83 | (577) ~ (all_0_50_50 = e4)
% 14.26/3.83 | (891) all_0_57_57 = e4
% 14.26/3.83 |
% 14.26/3.83 | Combining equations (891,637) yields a new equation:
% 14.26/3.83 | (523) e4 = e3
% 14.26/3.83 |
% 14.26/3.83 | Simplifying 523 yields:
% 14.26/3.83 | (524) e4 = e3
% 14.26/3.83 |
% 14.26/3.83 | Equations (524) can reduce 30 to:
% 14.26/3.83 | (303) $false
% 14.26/3.83 |
% 14.26/3.83 |-The branch is then unsatisfiable
% 14.26/3.83 |-Branch two:
% 14.26/3.83 | (988) ~ (all_0_56_56 = e4)
% 14.26/3.83 | (989) all_0_57_57 = e4 | all_0_58_58 = e4 | all_0_60_60 = e4
% 14.26/3.83 |
% 14.26/3.83 +-Applying beta-rule and splitting (1362), into two cases.
% 14.26/3.83 |-Branch one:
% 14.26/3.83 | (528) all_0_49_49 = e4
% 14.26/3.83 |
% 14.26/3.83 | Combining equations (811,528) yields a new equation:
% 14.26/3.83 | (427) e4 = e1
% 14.26/3.83 |
% 14.26/3.83 | Equations (427) can reduce 253 to:
% 14.26/3.83 | (303) $false
% 14.26/3.83 |
% 14.26/3.83 |-The branch is then unsatisfiable
% 14.26/3.83 |-Branch two:
% 14.26/3.83 | (531) ~ (all_0_49_49 = e4)
% 14.26/3.83 | (762) all_0_56_56 = e4
% 14.26/3.83 |
% 14.26/3.83 | Equations (762) can reduce 988 to:
% 14.26/3.83 | (303) $false
% 14.26/3.83 |
% 14.26/3.83 |-The branch is then unsatisfiable
% 14.26/3.83 |-Branch two:
% 14.26/3.83 | (1437) ~ (all_0_59_59 = e2)
% 14.26/3.83 | (659) all_0_60_60 = e2
% 14.26/3.83 |
% 14.26/3.83 | Combining equations (305,659) yields a new equation:
% 14.26/3.83 | (559) e2 = e0
% 14.26/3.83 |
% 14.26/3.83 | Equations (559) can reduce 61 to:
% 14.26/3.83 | (303) $false
% 14.26/3.83 |
% 14.26/3.83 |-The branch is then unsatisfiable
% 14.26/3.83 |-Branch two:
% 14.26/3.83 | (602) ~ (all_0_47_47 = e3)
% 14.26/3.83 | (535) all_0_48_48 = e3
% 14.26/3.83 |
% 14.26/3.83 | Combining equations (1297,535) yields a new equation:
% 14.26/3.83 | (523) e4 = e3
% 14.26/3.83 |
% 14.26/3.83 | Simplifying 523 yields:
% 14.26/3.83 | (524) e4 = e3
% 14.26/3.83 |
% 14.26/3.83 | Equations (524) can reduce 30 to:
% 14.26/3.83 | (303) $false
% 14.26/3.83 |
% 14.26/3.83 |-The branch is then unsatisfiable
% 14.26/3.84 |-Branch two:
% 14.26/3.84 | (613) ~ (all_0_51_51 = e0)
% 14.26/3.84 | (1032) all_0_52_52 = e0
% 14.26/3.84 |
% 14.26/3.84 | Equations (1032) can reduce 308 to:
% 14.26/3.84 | (303) $false
% 14.26/3.84 |
% 14.26/3.84 |-The branch is then unsatisfiable
% 14.26/3.84 |-Branch two:
% 14.26/3.84 | (819) ~ (all_0_44_44 = e0)
% 14.26/3.84 | (820) all_0_49_49 = e0 | all_0_56_56 = e0
% 14.26/3.84 |
% 14.26/3.84 +-Applying beta-rule and splitting (820), into two cases.
% 14.26/3.84 |-Branch one:
% 14.26/3.84 | (466) all_0_49_49 = e0
% 14.26/3.84 |
% 14.26/3.84 | Combining equations (466,811) yields a new equation:
% 14.26/3.84 | (302) e1 = e0
% 14.26/3.84 |
% 14.26/3.84 | Equations (302) can reduce 143 to:
% 14.26/3.84 | (303) $false
% 14.26/3.84 |
% 14.26/3.84 |-The branch is then unsatisfiable
% 14.26/3.84 |-Branch two:
% 14.26/3.84 | (879) ~ (all_0_49_49 = e0)
% 14.26/3.84 | (1194) all_0_56_56 = e0
% 14.26/3.84 |
% 14.26/3.84 | Equations (1194) can reduce 1182 to:
% 14.26/3.84 | (303) $false
% 14.26/3.84 |
% 14.26/3.84 |-The branch is then unsatisfiable
% 14.26/3.84 |-Branch two:
% 14.26/3.84 | (325) ~ (all_0_49_49 = e1)
% 14.26/3.84 | (2159) all_0_53_53 = e1 | all_0_56_56 = e1
% 14.26/3.84 |
% 14.26/3.84 +-Applying beta-rule and splitting (2159), into two cases.
% 14.26/3.84 |-Branch one:
% 14.26/3.84 | (275) all_0_53_53 = e1
% 14.26/3.84 |
% 14.26/3.84 | Combining equations (413,275) yields a new equation:
% 14.26/3.84 | (604) e3 = e1
% 14.26/3.84 |
% 14.26/3.84 | Simplifying 604 yields:
% 14.26/3.84 | (414) e3 = e1
% 14.26/3.84 |
% 14.26/3.84 | Equations (414) can reduce 145 to:
% 14.26/3.84 | (303) $false
% 14.26/3.84 |
% 14.26/3.84 |-The branch is then unsatisfiable
% 14.26/3.84 |-Branch two:
% 14.26/3.84 | (1568) ~ (all_0_53_53 = e1)
% 14.26/3.84 | (314) all_0_56_56 = e1
% 14.26/3.84 |
% 14.26/3.84 | Equations (314) can reduce 282 to:
% 14.26/3.84 | (303) $false
% 14.26/3.84 |
% 14.26/3.84 |-The branch is then unsatisfiable
% 14.26/3.84 |-Branch two:
% 14.26/3.84 | (617) ~ (all_0_40_40 = e0)
% 14.26/3.84 | (999) all_0_42_42 = e0 | all_0_43_43 = e0
% 14.26/3.84 |
% 14.26/3.84 +-Applying beta-rule and splitting (78), into two cases.
% 14.26/3.84 |-Branch one:
% 14.26/3.84 | (811) all_0_49_49 = e1
% 14.26/3.84 |
% 14.26/3.84 | Equations (811) can reduce 123 to:
% 14.26/3.84 | (1589) ~ (all_0_50_50 = e1)
% 14.26/3.84 |
% 14.26/3.84 | Simplifying 1589 yields:
% 14.26/3.84 | (326) ~ (all_0_50_50 = e1)
% 14.26/3.84 |
% 14.26/3.84 +-Applying beta-rule and splitting (55), into two cases.
% 14.26/3.84 |-Branch one:
% 14.26/3.84 | (473) all_0_40_40 = e0
% 14.26/3.84 |
% 14.26/3.84 | Equations (473) can reduce 617 to:
% 14.26/3.84 | (303) $false
% 14.26/3.84 |
% 14.26/3.84 |-The branch is then unsatisfiable
% 14.26/3.84 |-Branch two:
% 14.26/3.84 | (617) ~ (all_0_40_40 = e0)
% 14.26/3.84 | (618) all_0_45_45 = e0 | all_0_50_50 = e0 | all_0_57_57 = e0
% 14.26/3.84 |
% 14.26/3.84 +-Applying beta-rule and splitting (618), into two cases.
% 14.26/3.84 |-Branch one:
% 14.26/3.84 | (300) all_0_45_45 = e0
% 14.26/3.84 |
% 14.26/3.84 | Combining equations (289,300) yields a new equation:
% 14.26/3.84 | (301) e1 = e0
% 14.26/3.84 |
% 14.26/3.84 | Simplifying 301 yields:
% 14.26/3.84 | (302) e1 = e0
% 14.26/3.84 |
% 14.26/3.84 | Equations (302) can reduce 143 to:
% 14.26/3.84 | (303) $false
% 14.26/3.84 |
% 14.26/3.84 |-The branch is then unsatisfiable
% 14.26/3.84 |-Branch two:
% 14.26/3.84 | (304) ~ (all_0_45_45 = e0)
% 14.26/3.84 | (624) all_0_50_50 = e0 | all_0_57_57 = e0
% 14.26/3.84 |
% 14.26/3.84 +-Applying beta-rule and splitting (624), into two cases.
% 14.26/3.84 |-Branch one:
% 14.26/3.84 | (518) all_0_50_50 = e0
% 14.26/3.84 |
% 14.26/3.84 | Equations (518) can reduce 52 to:
% 14.26/3.84 | (480) ~ (e3 = e0)
% 14.26/3.84 |
% 14.26/3.84 | Simplifying 480 yields:
% 14.26/3.84 | (74) ~ (e3 = e0)
% 14.26/3.84 |
% 14.26/3.84 | Equations (518) can reduce 326 to:
% 14.26/3.84 | (471) ~ (e1 = e0)
% 14.26/3.84 |
% 14.26/3.84 | Simplifying 471 yields:
% 14.26/3.84 | (143) ~ (e1 = e0)
% 14.26/3.84 |
% 14.26/3.84 +-Applying beta-rule and splitting (999), into two cases.
% 14.26/3.84 |-Branch one:
% 14.26/3.84 | (486) all_0_42_42 = e0
% 14.26/3.84 |
% 14.26/3.84 | Combining equations (1375,486) yields a new equation:
% 14.26/3.84 | (301) e1 = e0
% 14.26/3.84 |
% 14.26/3.84 | Simplifying 301 yields:
% 14.26/3.84 | (302) e1 = e0
% 14.26/3.84 |
% 14.26/3.84 | Equations (302) can reduce 143 to:
% 14.26/3.84 | (303) $false
% 14.26/3.84 |
% 14.26/3.84 |-The branch is then unsatisfiable
% 14.26/3.84 |-Branch two:
% 14.26/3.84 | (475) ~ (all_0_42_42 = e0)
% 14.26/3.84 | (588) all_0_43_43 = e0
% 14.26/3.84 |
% 14.26/3.84 | Combining equations (522,588) yields a new equation:
% 14.26/3.84 | (574) e3 = e0
% 14.26/3.84 |
% 14.26/3.84 | Simplifying 574 yields:
% 14.26/3.84 | (575) e3 = e0
% 14.26/3.84 |
% 14.26/3.84 | Equations (575) can reduce 74 to:
% 14.26/3.84 | (303) $false
% 14.26/3.84 |
% 14.26/3.84 |-The branch is then unsatisfiable
% 14.26/3.84 |-Branch two:
% 14.26/3.84 | (468) ~ (all_0_50_50 = e0)
% 14.26/3.84 | (628) all_0_57_57 = e0
% 14.26/3.84 |
% 14.26/3.84 | Equations (628) can reduce 309 to:
% 14.26/3.84 | (303) $false
% 14.26/3.84 |
% 14.26/3.84 |-The branch is then unsatisfiable
% 14.26/3.84 |-Branch two:
% 14.26/3.84 | (325) ~ (all_0_49_49 = e1)
% 14.26/3.84 | (1679) all_0_50_50 = e1 | all_0_51_51 = e1 | all_0_52_52 = e1
% 14.26/3.84 |
% 14.26/3.84 +-Applying beta-rule and splitting (47), into two cases.
% 14.26/3.84 |-Branch one:
% 14.26/3.84 | (1087) all_0_44_44 = e1
% 14.26/3.84 |
% 14.26/3.84 | Equations (1087) can reduce 276 to:
% 14.26/3.84 | (303) $false
% 14.26/3.84 |
% 14.26/3.84 |-The branch is then unsatisfiable
% 14.26/3.84 |-Branch two:
% 14.26/3.84 | (276) ~ (all_0_44_44 = e1)
% 14.26/3.84 | (2154) all_0_49_49 = e1 | all_0_53_53 = e1 | all_0_56_56 = e1
% 14.26/3.84 |
% 14.26/3.84 +-Applying beta-rule and splitting (2154), into two cases.
% 14.26/3.84 |-Branch one:
% 14.26/3.84 | (811) all_0_49_49 = e1
% 14.26/3.84 |
% 14.26/3.84 | Equations (811) can reduce 325 to:
% 14.26/3.84 | (303) $false
% 14.26/3.84 |
% 14.26/3.84 |-The branch is then unsatisfiable
% 14.26/3.84 |-Branch two:
% 14.26/3.84 | (325) ~ (all_0_49_49 = e1)
% 14.26/3.84 | (2159) all_0_53_53 = e1 | all_0_56_56 = e1
% 14.26/3.84 |
% 14.26/3.84 +-Applying beta-rule and splitting (2159), into two cases.
% 14.26/3.84 |-Branch one:
% 14.26/3.84 | (275) all_0_53_53 = e1
% 14.26/3.84 |
% 14.26/3.84 | Combining equations (413,275) yields a new equation:
% 14.26/3.84 | (604) e3 = e1
% 14.26/3.84 |
% 14.26/3.84 | Simplifying 604 yields:
% 14.26/3.84 | (414) e3 = e1
% 14.26/3.84 |
% 14.26/3.84 | Equations (414) can reduce 145 to:
% 14.26/3.84 | (303) $false
% 14.26/3.84 |
% 14.26/3.84 |-The branch is then unsatisfiable
% 14.26/3.84 |-Branch two:
% 14.26/3.84 | (1568) ~ (all_0_53_53 = e1)
% 14.26/3.84 | (314) all_0_56_56 = e1
% 14.26/3.84 |
% 14.26/3.84 | Equations (314) can reduce 282 to:
% 14.26/3.84 | (303) $false
% 14.26/3.84 |
% 14.26/3.84 |-The branch is then unsatisfiable
% 14.26/3.84 |-Branch two:
% 14.26/3.84 | (663) ~ (all_0_46_46 = e2)
% 14.26/3.84 | (664) all_0_58_58 = e2
% 14.26/3.84 |
% 14.26/3.84 | Combining equations (337,664) yields a new equation:
% 14.26/3.84 | (369) e2 = e1
% 14.26/3.84 |
% 14.26/3.84 | Equations (369) can reduce 150 to:
% 14.26/3.84 | (303) $false
% 14.26/3.84 |
% 14.26/3.84 |-The branch is then unsatisfiable
% 14.26/3.84 |-Branch two:
% 14.26/3.84 | (497) ~ (all_0_43_43 = e3)
% 14.26/3.84 | (505) all_0_43_43 = e4
% 14.26/3.84 |
% 14.26/3.84 | Equations (505) can reduce 582 to:
% 14.26/3.84 | (303) $false
% 14.26/3.84 |
% 14.26/3.84 |-The branch is then unsatisfiable
% 14.26/3.84 |-Branch two:
% 14.26/3.84 | (260) ~ (all_0_42_42 = e1)
% 14.26/3.84 | (310) all_0_43_43 = e1
% 14.26/3.84 |
% 14.26/3.84 | Equations (310) can reduce 262 to:
% 14.26/3.84 | (303) $false
% 14.26/3.84 |
% 14.26/3.84 |-The branch is then unsatisfiable
% 14.26/3.84 |-Branch two:
% 14.26/3.84 | (375) ~ (all_0_54_54 = e2)
% 14.26/3.84 | (373) all_0_55_55 = e2
% 14.26/3.84 |
% 14.26/3.84 | Combining equations (1065,373) yields a new equation:
% 14.26/3.84 | (369) e2 = e1
% 14.26/3.84 |
% 14.26/3.84 | Equations (369) can reduce 150 to:
% 14.26/3.84 | (303) $false
% 14.26/3.84 |
% 14.26/3.84 |-The branch is then unsatisfiable
% 14.26/3.84 |-Branch two:
% 14.26/3.84 | (1072) ~ (all_0_45_45 = e1)
% 14.26/3.84 | (1059) all_0_60_60 = e1
% 14.26/3.84 |
% 14.26/3.84 | Equations (1059) can reduce 38 to:
% 14.26/3.84 | (1063) ~ (all_0_52_52 = e1)
% 14.26/3.84 |
% 14.26/3.84 | Equations (1059) can reduce 117 to:
% 14.26/3.84 | (280) ~ (all_0_55_55 = e1)
% 14.26/3.84 |
% 14.26/3.84 | Equations (1059) can reduce 140 to:
% 14.26/3.84 | (282) ~ (all_0_56_56 = e1)
% 14.26/3.84 |
% 14.26/3.84 | Equations (1059) can reduce 86 to:
% 14.26/3.84 | (266) ~ (all_0_58_58 = e1)
% 14.26/3.84 |
% 14.26/3.84 | Equations (1059) can reduce 181 to:
% 14.26/3.84 | (1058) ~ (all_0_59_59 = e1)
% 14.26/3.84 |
% 14.26/3.84 +-Applying beta-rule and splitting (25), into two cases.
% 14.26/3.84 |-Branch one:
% 14.26/3.84 | (300) all_0_45_45 = e0
% 14.26/3.84 |
% 14.26/3.84 | Equations (300) can reduce 191 to:
% 14.26/3.84 | (819) ~ (all_0_44_44 = e0)
% 14.26/3.84 |
% 14.26/3.84 | Equations (300) can reduce 128 to:
% 14.26/3.84 | (3098) ~ (all_0_46_46 = e0)
% 14.26/3.84 |
% 14.26/3.84 | Simplifying 3098 yields:
% 14.26/3.84 | (103) ~ (all_0_46_46 = e0)
% 14.26/3.84 |
% 14.26/3.84 | Equations (300) can reduce 237 to:
% 14.26/3.84 | (2021) ~ (all_0_48_48 = e0)
% 14.26/3.84 |
% 14.26/3.84 | Simplifying 2021 yields:
% 14.26/3.84 | (1599) ~ (all_0_48_48 = e0)
% 14.26/3.84 |
% 14.26/3.84 | Equations (300) can reduce 122 to:
% 14.26/3.84 | (1083) ~ (all_0_57_57 = e0)
% 14.26/3.84 |
% 14.26/3.84 | Simplifying 1083 yields:
% 14.26/3.84 | (309) ~ (all_0_57_57 = e0)
% 14.26/3.84 |
% 14.26/3.84 +-Applying beta-rule and splitting (102), into two cases.
% 14.26/3.84 |-Branch one:
% 14.26/3.84 | (1065) all_0_55_55 = e1
% 14.26/3.84 |
% 14.26/3.84 | Equations (1065) can reduce 280 to:
% 14.26/3.84 | (303) $false
% 14.26/3.84 |
% 14.26/3.84 |-The branch is then unsatisfiable
% 14.26/3.84 |-Branch two:
% 14.26/3.84 | (280) ~ (all_0_55_55 = e1)
% 14.26/3.84 | (1494) all_0_55_55 = e3 | all_0_55_55 = e2
% 14.26/3.84 |
% 14.26/3.85 +-Applying beta-rule and splitting (1494), into two cases.
% 14.26/3.85 |-Branch one:
% 14.26/3.85 | (568) all_0_55_55 = e3
% 14.26/3.85 |
% 14.26/3.85 | Equations (568) can reduce 572 to:
% 14.26/3.85 | (303) $false
% 14.26/3.85 |
% 14.26/3.85 |-The branch is then unsatisfiable
% 14.26/3.85 |-Branch two:
% 14.26/3.85 | (572) ~ (all_0_55_55 = e3)
% 14.26/3.85 | (373) all_0_55_55 = e2
% 14.26/3.85 |
% 14.26/3.85 | Equations (373) can reduce 101 to:
% 14.26/3.85 | (375) ~ (all_0_54_54 = e2)
% 14.26/3.85 |
% 14.26/3.85 +-Applying beta-rule and splitting (7), into two cases.
% 14.26/3.85 |-Branch one:
% 14.26/3.85 | (337) all_0_58_58 = e1
% 14.26/3.85 |
% 14.26/3.85 | Equations (337) can reduce 266 to:
% 14.26/3.85 | (303) $false
% 14.26/3.85 |
% 14.26/3.85 |-The branch is then unsatisfiable
% 14.26/3.85 |-Branch two:
% 14.26/3.85 | (266) ~ (all_0_58_58 = e1)
% 14.26/3.85 | (1136) all_0_58_58 = e4 | all_0_58_58 = e2
% 14.26/3.85 |
% 14.26/3.85 +-Applying beta-rule and splitting (1136), into two cases.
% 14.26/3.85 |-Branch one:
% 14.26/3.85 | (437) all_0_58_58 = e4
% 14.26/3.85 |
% 14.26/3.85 | Equations (437) can reduce 1023 to:
% 14.26/3.85 | (303) $false
% 14.26/3.85 |
% 14.26/3.85 |-The branch is then unsatisfiable
% 14.26/3.85 |-Branch two:
% 14.26/3.85 | (1023) ~ (all_0_58_58 = e4)
% 14.26/3.85 | (664) all_0_58_58 = e2
% 14.26/3.85 |
% 14.26/3.85 | Equations (664) can reduce 71 to:
% 14.26/3.85 | (663) ~ (all_0_46_46 = e2)
% 14.26/3.85 |
% 14.26/3.85 | Equations (664) can reduce 206 to:
% 14.26/3.85 | (208) ~ (all_0_56_56 = e2)
% 14.26/3.85 |
% 14.26/3.85 | Equations (664) can reduce 82 to:
% 14.26/3.85 | (717) ~ (all_0_57_57 = e2)
% 14.26/3.85 |
% 14.26/3.85 | Equations (664) can reduce 108 to:
% 14.58/3.85 | (1436) ~ (all_0_59_59 = e2)
% 14.58/3.85 |
% 14.58/3.85 | Simplifying 1436 yields:
% 14.58/3.85 | (1437) ~ (all_0_59_59 = e2)
% 14.58/3.85 |
% 14.58/3.85 | Equations (664) can reduce 266 to:
% 14.58/3.85 | (150) ~ (e2 = e1)
% 14.58/3.85 |
% 14.58/3.85 | Equations (664) can reduce 203 to:
% 14.58/3.85 | (61) ~ (e2 = e0)
% 14.58/3.85 |
% 14.58/3.85 | From (664) and (27) follows:
% 14.58/3.85 | (666) op(e2, e2) = all_0_21_21
% 14.58/3.85 |
% 14.58/3.85 +-Applying beta-rule and splitting (251), into two cases.
% 14.58/3.85 |-Branch one:
% 14.58/3.85 | (1289) all_0_54_54 = e1
% 14.58/3.85 |
% 14.58/3.85 | Equations (1289) can reduce 148 to:
% 14.58/3.85 | (346) ~ (e4 = e1)
% 14.58/3.85 |
% 14.58/3.85 | Simplifying 346 yields:
% 14.58/3.85 | (253) ~ (e4 = e1)
% 14.58/3.85 |
% 14.58/3.85 | Equations (1289) can reduce 375 to:
% 14.58/3.85 | (267) ~ (e2 = e1)
% 14.58/3.85 |
% 14.58/3.85 | Simplifying 267 yields:
% 14.58/3.85 | (150) ~ (e2 = e1)
% 14.58/3.85 |
% 14.58/3.85 +-Applying beta-rule and splitting (214), into two cases.
% 14.58/3.85 |-Branch one:
% 14.58/3.85 | (257) all_0_41_41 = e1
% 14.58/3.85 |
% 14.58/3.85 | Combining equations (257,425) yields a new equation:
% 14.58/3.85 | (427) e4 = e1
% 14.58/3.85 |
% 14.58/3.85 | Equations (427) can reduce 253 to:
% 14.58/3.85 | (303) $false
% 14.58/3.85 |
% 14.58/3.85 |-The branch is then unsatisfiable
% 14.58/3.85 |-Branch two:
% 14.58/3.85 | (2409) ~ (all_0_41_41 = e1)
% 14.58/3.85 | (2453) all_0_46_46 = e1 | all_0_58_58 = e1
% 14.58/3.85 |
% 14.58/3.85 +-Applying beta-rule and splitting (2453), into two cases.
% 14.58/3.85 |-Branch one:
% 14.58/3.85 | (669) all_0_46_46 = e1
% 14.58/3.85 |
% 14.58/3.85 | Equations (669) can reduce 79 to:
% 14.58/3.85 | (276) ~ (all_0_44_44 = e1)
% 14.58/3.85 |
% 14.58/3.85 | Equations (669) can reduce 2 to:
% 14.58/3.85 | (294) ~ (all_0_48_48 = e1)
% 14.58/3.85 |
% 14.58/3.85 | Simplifying 294 yields:
% 14.58/3.85 | (295) ~ (all_0_48_48 = e1)
% 14.58/3.85 |
% 14.58/3.85 | Equations (669) can reduce 663 to:
% 14.58/3.85 | (267) ~ (e2 = e1)
% 14.58/3.85 |
% 14.58/3.85 | Simplifying 267 yields:
% 14.58/3.85 | (150) ~ (e2 = e1)
% 14.58/3.85 |
% 14.58/3.85 | Equations (669) can reduce 103 to:
% 14.58/3.85 | (143) ~ (e1 = e0)
% 14.58/3.85 |
% 14.58/3.85 | From (669) and (65) follows:
% 14.58/3.85 | (2632) op(e2, e1) = all_0_19_19
% 14.58/3.85 |
% 14.58/3.85 +-Applying beta-rule and splitting (213), into two cases.
% 14.58/3.85 |-Branch one:
% 14.58/3.85 | (1087) all_0_44_44 = e1
% 14.58/3.85 |
% 14.58/3.85 | Equations (1087) can reduce 276 to:
% 14.58/3.85 | (303) $false
% 14.58/3.85 |
% 14.58/3.85 |-The branch is then unsatisfiable
% 14.58/3.85 |-Branch two:
% 14.58/3.85 | (276) ~ (all_0_44_44 = e1)
% 14.58/3.85 | (1750) all_0_44_44 = e4 | all_0_44_44 = e3 | all_0_44_44 = e0
% 14.58/3.85 |
% 14.58/3.85 +-Applying beta-rule and splitting (6), into two cases.
% 14.58/3.85 |-Branch one:
% 14.58/3.85 | (395) all_0_45_45 = e2
% 14.58/3.85 |
% 14.58/3.85 | Combining equations (300,395) yields a new equation:
% 14.58/3.85 | (559) e2 = e0
% 14.58/3.85 |
% 14.58/3.85 | Equations (559) can reduce 61 to:
% 14.58/3.85 | (303) $false
% 14.58/3.85 |
% 14.58/3.85 |-The branch is then unsatisfiable
% 14.58/3.85 |-Branch two:
% 14.58/3.85 | (398) ~ (all_0_45_45 = e2)
% 14.58/3.85 | (399) all_0_50_50 = e2 | all_0_54_54 = e2 | all_0_57_57 = e2
% 14.58/3.85 |
% 14.58/3.85 +-Applying beta-rule and splitting (399), into two cases.
% 14.58/3.85 |-Branch one:
% 14.58/3.85 | (400) all_0_50_50 = e2
% 14.58/3.85 |
% 14.58/3.85 | Equations (400) can reduce 48 to:
% 14.58/3.85 | (134) ~ (all_0_40_40 = e2)
% 14.58/3.85 |
% 14.58/3.85 | Equations (400) can reduce 123 to:
% 14.58/3.85 | (151) ~ (all_0_49_49 = e2)
% 14.58/3.85 |
% 14.58/3.85 | Equations (400) can reduce 116 to:
% 14.58/3.85 | (3159) ~ (all_0_51_51 = e2)
% 14.58/3.85 |
% 14.58/3.85 | Simplifying 3159 yields:
% 14.58/3.85 | (654) ~ (all_0_51_51 = e2)
% 14.58/3.85 |
% 14.58/3.85 | Equations (400) can reduce 188 to:
% 14.58/3.85 | (3161) ~ (all_0_52_52 = e2)
% 14.58/3.85 |
% 14.58/3.85 | Simplifying 3161 yields:
% 14.58/3.85 | (371) ~ (all_0_52_52 = e2)
% 14.58/3.85 |
% 14.58/3.85 | Equations (400) can reduce 170 to:
% 14.58/3.85 | (716) ~ (all_0_57_57 = e2)
% 14.58/3.85 |
% 14.58/3.85 | Simplifying 716 yields:
% 14.58/3.85 | (717) ~ (all_0_57_57 = e2)
% 14.58/3.85 |
% 14.58/3.85 | From (400) and (152) follows:
% 14.58/3.85 | (2232) op(e2, e2) = all_0_12_12
% 14.58/3.85 |
% 14.58/3.85 +-Applying beta-rule and splitting (127), into two cases.
% 14.58/3.85 |-Branch one:
% 14.58/3.85 | (379) all_0_47_47 = e2
% 14.58/3.85 |
% 14.58/3.85 | Equations (379) can reduce 62 to:
% 14.58/3.85 | (110) ~ (all_0_44_44 = e2)
% 14.58/3.85 |
% 14.58/3.85 | Equations (379) can reduce 9 to:
% 14.58/3.85 | (358) ~ (all_0_48_48 = e2)
% 14.58/3.85 |
% 14.58/3.85 | Simplifying 358 yields:
% 14.58/3.85 | (359) ~ (all_0_48_48 = e2)
% 14.58/3.85 |
% 14.58/3.85 +-Applying beta-rule and splitting (1750), into two cases.
% 14.58/3.85 |-Branch one:
% 14.58/3.85 | (815) all_0_44_44 = e0
% 14.58/3.85 |
% 14.58/3.85 | Equations (815) can reduce 819 to:
% 14.58/3.85 | (303) $false
% 14.58/3.85 |
% 14.58/3.85 |-The branch is then unsatisfiable
% 14.58/3.85 |-Branch two:
% 14.58/3.85 | (819) ~ (all_0_44_44 = e0)
% 14.58/3.85 | (1766) all_0_44_44 = e4 | all_0_44_44 = e3
% 14.58/3.85 |
% 14.58/3.85 +-Applying beta-rule and splitting (1766), into two cases.
% 14.58/3.85 |-Branch one:
% 14.58/3.85 | (775) all_0_44_44 = e3
% 14.58/3.85 |
% 14.58/3.85 | Equations (775) can reduce 908 to:
% 14.58/3.85 | (303) $false
% 14.58/3.85 |
% 14.58/3.85 |-The branch is then unsatisfiable
% 14.58/3.85 |-Branch two:
% 14.58/3.85 | (908) ~ (all_0_44_44 = e3)
% 14.58/3.85 | (1189) all_0_44_44 = e4
% 14.58/3.85 |
% 14.58/3.85 | Equations (1189) can reduce 40 to:
% 14.58/3.85 | (506) ~ (all_0_48_48 = e4)
% 14.58/3.85 |
% 14.58/3.85 | Simplifying 506 yields:
% 14.58/3.85 | (507) ~ (all_0_48_48 = e4)
% 14.58/3.85 |
% 14.58/3.85 | Equations (1189) can reduce 53 to:
% 14.58/3.85 | (3180) ~ (all_0_49_49 = e4)
% 14.58/3.85 |
% 14.58/3.85 | Simplifying 3180 yields:
% 14.58/3.85 | (531) ~ (all_0_49_49 = e4)
% 14.58/3.85 |
% 14.58/3.85 | Equations (1189) can reduce 130 to:
% 14.58/3.85 | (3182) ~ (all_0_56_56 = e4)
% 14.58/3.85 |
% 14.58/3.85 | Simplifying 3182 yields:
% 14.58/3.85 | (988) ~ (all_0_56_56 = e4)
% 14.58/3.85 |
% 14.58/3.85 | Equations (1189) can reduce 110 to:
% 14.58/3.85 | (227) ~ (e4 = e2)
% 14.58/3.85 |
% 14.58/3.85 | Equations (1189) can reduce 819 to:
% 14.58/3.85 | (5) ~ (e4 = e0)
% 14.58/3.85 |
% 14.58/3.85 +-Applying beta-rule and splitting (201), into two cases.
% 14.58/3.85 |-Branch one:
% 14.58/3.85 | (318) all_0_48_48 = e1
% 14.58/3.85 |
% 14.58/3.85 | Equations (318) can reduce 295 to:
% 14.58/3.85 | (303) $false
% 14.58/3.85 |
% 14.58/3.85 |-The branch is then unsatisfiable
% 14.58/3.85 |-Branch two:
% 14.58/3.85 | (295) ~ (all_0_48_48 = e1)
% 14.58/3.85 | (3189) all_0_48_48 = e4 | all_0_48_48 = e3 | all_0_48_48 = e2 | all_0_48_48 = e0
% 14.58/3.85 |
% 14.58/3.85 +-Applying beta-rule and splitting (3189), into two cases.
% 14.58/3.85 |-Branch one:
% 14.58/3.85 | (1846) all_0_48_48 = e0
% 14.58/3.85 |
% 14.58/3.85 | Equations (1846) can reduce 1599 to:
% 14.58/3.85 | (303) $false
% 14.58/3.85 |
% 14.58/3.85 |-The branch is then unsatisfiable
% 14.58/3.85 |-Branch two:
% 14.58/3.85 | (1599) ~ (all_0_48_48 = e0)
% 14.58/3.85 | (3193) all_0_48_48 = e4 | all_0_48_48 = e3 | all_0_48_48 = e2
% 14.58/3.85 |
% 14.58/3.85 +-Applying beta-rule and splitting (195), into two cases.
% 14.58/3.85 |-Branch one:
% 14.58/3.85 | (762) all_0_56_56 = e4
% 14.58/3.85 |
% 14.58/3.85 | Equations (762) can reduce 988 to:
% 14.58/3.85 | (303) $false
% 14.58/3.85 |
% 14.58/3.85 |-The branch is then unsatisfiable
% 14.58/3.85 |-Branch two:
% 14.58/3.85 | (988) ~ (all_0_56_56 = e4)
% 14.58/3.85 | (989) all_0_57_57 = e4 | all_0_58_58 = e4 | all_0_60_60 = e4
% 14.58/3.85 |
% 14.58/3.85 +-Applying beta-rule and splitting (3193), into two cases.
% 14.58/3.85 |-Branch one:
% 14.58/3.85 | (535) all_0_48_48 = e3
% 14.58/3.85 |
% 14.58/3.85 | Equations (535) can reduce 115 to:
% 14.58/3.85 | (497) ~ (all_0_43_43 = e3)
% 14.58/3.85 |
% 14.58/3.85 | Equations (535) can reduce 233 to:
% 14.58/3.85 | (3200) ~ (all_0_52_52 = e3)
% 14.58/3.85 |
% 14.58/3.85 | Simplifying 3200 yields:
% 14.58/3.85 | (13) ~ (all_0_52_52 = e3)
% 14.58/3.85 |
% 14.58/3.86 | Equations (535) can reduce 295 to:
% 14.58/3.86 | (145) ~ (e3 = e1)
% 14.58/3.86 |
% 14.58/3.86 | Equations (535) can reduce 1599 to:
% 14.58/3.86 | (74) ~ (e3 = e0)
% 14.58/3.86 |
% 14.58/3.86 +-Applying beta-rule and splitting (88), into two cases.
% 14.58/3.86 |-Branch one:
% 14.58/3.86 | (528) all_0_49_49 = e4
% 14.58/3.86 |
% 14.58/3.86 | Equations (528) can reduce 531 to:
% 14.58/3.86 | (303) $false
% 14.58/3.86 |
% 14.58/3.86 |-The branch is then unsatisfiable
% 14.58/3.86 |-Branch two:
% 14.58/3.86 | (531) ~ (all_0_49_49 = e4)
% 14.58/3.86 | (532) all_0_50_50 = e4 | all_0_52_52 = e4
% 14.58/3.86 |
% 14.58/3.86 +-Applying beta-rule and splitting (989), into two cases.
% 14.58/3.86 |-Branch one:
% 14.58/3.86 | (891) all_0_57_57 = e4
% 14.58/3.86 |
% 14.58/3.86 | Equations (891) can reduce 90 to:
% 14.58/3.86 | (988) ~ (all_0_56_56 = e4)
% 14.58/3.86 |
% 14.58/3.86 | Equations (891) can reduce 717 to:
% 14.58/3.86 | (227) ~ (e4 = e2)
% 14.58/3.86 |
% 14.58/3.86 | Equations (891) can reduce 309 to:
% 14.58/3.86 | (5) ~ (e4 = e0)
% 14.58/3.86 |
% 14.58/3.86 +-Applying beta-rule and splitting (532), into two cases.
% 14.58/3.86 |-Branch one:
% 14.58/3.86 | (533) all_0_50_50 = e4
% 14.58/3.86 |
% 14.58/3.86 | Combining equations (400,533) yields a new equation:
% 14.58/3.86 | (434) e4 = e2
% 14.58/3.86 |
% 14.58/3.86 | Equations (434) can reduce 227 to:
% 14.58/3.86 | (303) $false
% 14.58/3.86 |
% 14.58/3.86 |-The branch is then unsatisfiable
% 14.58/3.86 |-Branch two:
% 14.58/3.86 | (577) ~ (all_0_50_50 = e4)
% 14.58/3.86 | (578) all_0_52_52 = e4
% 14.58/3.86 |
% 14.58/3.86 | Equations (578) can reduce 54 to:
% 14.58/3.86 | (582) ~ (all_0_43_43 = e4)
% 14.58/3.86 |
% 14.58/3.86 | Equations (578) can reduce 13 to:
% 14.58/3.86 | (30) ~ (e4 = e3)
% 14.58/3.86 |
% 14.58/3.86 | Equations (578) can reduce 1063 to:
% 14.58/3.86 | (253) ~ (e4 = e1)
% 14.58/3.86 |
% 14.58/3.86 +-Applying beta-rule and splitting (230), into two cases.
% 14.58/3.86 |-Branch one:
% 14.58/3.86 | (588) all_0_43_43 = e0
% 14.58/3.86 |
% 14.58/3.86 | Equations (588) can reduce 229 to:
% 14.58/3.86 | (475) ~ (all_0_42_42 = e0)
% 14.58/3.86 |
% 14.58/3.86 | Equations (588) can reduce 582 to:
% 14.58/3.86 | (516) ~ (e4 = e0)
% 14.58/3.86 |
% 14.58/3.86 | Simplifying 516 yields:
% 14.58/3.86 | (5) ~ (e4 = e0)
% 14.58/3.86 |
% 14.58/3.86 | Equations (588) can reduce 497 to:
% 14.58/3.86 | (480) ~ (e3 = e0)
% 14.58/3.86 |
% 14.58/3.86 | Simplifying 480 yields:
% 14.58/3.86 | (74) ~ (e3 = e0)
% 14.58/3.86 |
% 14.58/3.86 +-Applying beta-rule and splitting (47), into two cases.
% 14.58/3.86 |-Branch one:
% 14.58/3.86 | (1087) all_0_44_44 = e1
% 14.58/3.86 |
% 14.58/3.86 | Combining equations (1189,1087) yields a new equation:
% 14.58/3.86 | (426) e4 = e1
% 14.58/3.86 |
% 14.58/3.86 | Simplifying 426 yields:
% 14.58/3.86 | (427) e4 = e1
% 14.58/3.86 |
% 14.58/3.86 | Equations (427) can reduce 253 to:
% 14.58/3.86 | (303) $false
% 14.58/3.86 |
% 14.58/3.86 |-The branch is then unsatisfiable
% 14.58/3.86 |-Branch two:
% 14.58/3.86 | (276) ~ (all_0_44_44 = e1)
% 14.58/3.86 | (2154) all_0_49_49 = e1 | all_0_53_53 = e1 | all_0_56_56 = e1
% 14.58/3.86 |
% 14.58/3.86 +-Applying beta-rule and splitting (2154), into two cases.
% 14.58/3.86 |-Branch one:
% 14.58/3.86 | (811) all_0_49_49 = e1
% 14.58/3.86 |
% 14.58/3.86 | Combining equations (811,2423) yields a new equation:
% 14.58/3.86 | (1690) all_0_17_17 = e1
% 14.58/3.86 |
% 14.58/3.86 | Equations (811) can reduce 83 to:
% 14.58/3.86 | (1119) ~ (all_0_51_51 = e1)
% 14.58/3.86 |
% 14.58/3.86 | Simplifying 1119 yields:
% 14.58/3.86 | (343) ~ (all_0_51_51 = e1)
% 14.58/3.86 |
% 14.58/3.86 | Equations (811) can reduce 224 to:
% 14.58/3.86 | (281) ~ (all_0_56_56 = e1)
% 14.58/3.86 |
% 14.58/3.86 | Simplifying 281 yields:
% 14.58/3.86 | (282) ~ (all_0_56_56 = e1)
% 14.58/3.86 |
% 14.58/3.86 | Equations (811) can reduce 46 to:
% 14.58/3.86 | (329) ~ (e3 = e1)
% 14.58/3.86 |
% 14.58/3.86 | Simplifying 329 yields:
% 14.58/3.86 | (145) ~ (e3 = e1)
% 14.58/3.86 |
% 14.58/3.86 | Equations (811) can reduce 151 to:
% 14.58/3.86 | (267) ~ (e2 = e1)
% 14.58/3.86 |
% 14.58/3.86 | Simplifying 267 yields:
% 14.58/3.86 | (150) ~ (e2 = e1)
% 14.58/3.86 |
% 14.58/3.86 | From (811) and (178) follows:
% 14.58/3.86 | (3242) op(e2, e1) = all_0_3_3
% 14.58/3.86 |
% 14.58/3.86 +-Applying beta-rule and splitting (180), into two cases.
% 14.58/3.86 |-Branch one:
% 14.58/3.86 | (884) all_0_40_40 = e3
% 14.58/3.86 |
% 14.58/3.86 | Equations (884) can reduce 189 to:
% 14.58/3.86 | (3244) ~ (all_0_42_42 = e3)
% 14.58/3.86 |
% 14.58/3.86 | Simplifying 3244 yields:
% 14.58/3.86 | (597) ~ (all_0_42_42 = e3)
% 14.58/3.86 |
% 14.58/3.86 | Equations (884) can reduce 134 to:
% 14.58/3.86 | (209) ~ (e3 = e2)
% 14.58/3.86 |
% 14.58/3.86 +-Applying beta-rule and splitting (202), into two cases.
% 14.58/3.86 |-Branch one:
% 14.58/3.86 | (1185) all_0_51_51 = e1
% 14.58/3.86 |
% 14.58/3.86 | Equations (1185) can reduce 343 to:
% 14.58/3.86 | (303) $false
% 14.58/3.86 |
% 14.58/3.86 |-The branch is then unsatisfiable
% 14.58/3.86 |-Branch two:
% 14.58/3.86 | (343) ~ (all_0_51_51 = e1)
% 14.58/3.86 | (1188) all_0_51_51 = e2 | all_0_51_51 = e0
% 14.58/3.86 |
% 14.58/3.86 +-Applying beta-rule and splitting (81), into two cases.
% 14.58/3.86 |-Branch one:
% 14.58/3.86 | (495) all_0_42_42 = e3
% 14.58/3.86 |
% 14.58/3.86 | Equations (495) can reduce 597 to:
% 14.58/3.86 | (303) $false
% 14.58/3.86 |
% 14.58/3.86 |-The branch is then unsatisfiable
% 14.58/3.86 |-Branch two:
% 14.58/3.86 | (597) ~ (all_0_42_42 = e3)
% 14.58/3.86 | (598) all_0_47_47 = e3 | all_0_59_59 = e3
% 14.58/3.86 |
% 14.58/3.86 +-Applying beta-rule and splitting (121), into two cases.
% 14.58/3.86 |-Branch one:
% 14.58/3.86 | (815) all_0_44_44 = e0
% 14.58/3.86 |
% 14.58/3.86 | Combining equations (815,1189) yields a new equation:
% 14.58/3.86 | (512) e4 = e0
% 14.58/3.86 |
% 14.58/3.86 | Equations (512) can reduce 5 to:
% 14.58/3.86 | (303) $false
% 14.58/3.86 |
% 14.58/3.86 |-The branch is then unsatisfiable
% 14.58/3.86 |-Branch two:
% 14.58/3.86 | (819) ~ (all_0_44_44 = e0)
% 14.58/3.86 | (820) all_0_49_49 = e0 | all_0_56_56 = e0
% 14.58/3.86 |
% 14.58/3.86 +-Applying beta-rule and splitting (26), into two cases.
% 14.58/3.86 |-Branch one:
% 14.58/3.86 | (1375) all_0_42_42 = e1
% 14.58/3.86 |
% 14.58/3.86 | Equations (1375) can reduce 144 to:
% 14.58/3.86 | (346) ~ (e4 = e1)
% 14.58/3.86 |
% 14.58/3.86 | Simplifying 346 yields:
% 14.58/3.86 | (253) ~ (e4 = e1)
% 14.58/3.86 |
% 14.58/3.86 | Equations (1375) can reduce 475 to:
% 14.58/3.86 | (143) ~ (e1 = e0)
% 14.58/3.86 |
% 14.58/3.86 +-Applying beta-rule and splitting (598), into two cases.
% 14.58/3.86 |-Branch one:
% 14.58/3.86 | (599) all_0_47_47 = e3
% 14.58/3.86 |
% 14.58/3.86 | Combining equations (379,599) yields a new equation:
% 14.58/3.86 | (553) e3 = e2
% 14.58/3.86 |
% 14.58/3.86 | Equations (553) can reduce 209 to:
% 14.58/3.86 | (303) $false
% 14.58/3.86 |
% 14.58/3.86 |-The branch is then unsatisfiable
% 14.58/3.86 |-Branch two:
% 14.58/3.86 | (602) ~ (all_0_47_47 = e3)
% 14.58/3.86 | (603) all_0_59_59 = e3
% 14.58/3.86 |
% 14.58/3.86 | Equations (603) can reduce 92 to:
% 14.58/3.86 | (247) ~ (all_0_51_51 = e3)
% 14.58/3.86 |
% 14.58/3.86 +-Applying beta-rule and splitting (820), into two cases.
% 14.58/3.86 |-Branch one:
% 14.58/3.86 | (466) all_0_49_49 = e0
% 14.58/3.86 |
% 14.58/3.86 | Combining equations (811,466) yields a new equation:
% 14.58/3.86 | (301) e1 = e0
% 14.58/3.86 |
% 14.58/3.86 | Simplifying 301 yields:
% 14.58/3.86 | (302) e1 = e0
% 14.58/3.86 |
% 14.58/3.86 | Equations (302) can reduce 143 to:
% 14.58/3.86 | (303) $false
% 14.58/3.86 |
% 14.58/3.86 |-The branch is then unsatisfiable
% 14.58/3.86 |-Branch two:
% 14.58/3.86 | (879) ~ (all_0_49_49 = e0)
% 14.58/3.86 | (1194) all_0_56_56 = e0
% 14.58/3.86 |
% 14.58/3.86 | Equations (1194) can reduce 988 to:
% 14.58/3.86 | (516) ~ (e4 = e0)
% 14.58/3.86 |
% 14.58/3.86 | Simplifying 516 yields:
% 14.58/3.86 | (5) ~ (e4 = e0)
% 14.58/3.86 |
% 14.58/3.86 | Equations (1194) can reduce 208 to:
% 14.58/3.86 | (469) ~ (e2 = e0)
% 14.58/3.86 |
% 14.58/3.86 | Simplifying 469 yields:
% 14.58/3.86 | (61) ~ (e2 = e0)
% 14.58/3.86 |
% 14.58/3.86 | Equations (1194) can reduce 282 to:
% 14.58/3.86 | (471) ~ (e1 = e0)
% 14.58/3.86 |
% 14.58/3.86 | Simplifying 471 yields:
% 14.58/3.86 | (143) ~ (e1 = e0)
% 14.58/3.86 |
% 14.58/3.86 +-Applying beta-rule and splitting (137), into two cases.
% 14.58/3.86 |-Branch one:
% 14.58/3.86 | (466) all_0_49_49 = e0
% 14.58/3.86 |
% 14.58/3.86 | Combining equations (811,466) yields a new equation:
% 14.58/3.86 | (301) e1 = e0
% 14.58/3.86 |
% 14.58/3.86 | Simplifying 301 yields:
% 14.58/3.86 | (302) e1 = e0
% 14.58/3.86 |
% 14.58/3.86 | Equations (302) can reduce 143 to:
% 14.58/3.86 | (303) $false
% 14.58/3.86 |
% 14.58/3.86 |-The branch is then unsatisfiable
% 14.58/3.86 |-Branch two:
% 14.58/3.86 | (879) ~ (all_0_49_49 = e0)
% 14.58/3.86 | (1012) all_0_50_50 = e0 | all_0_51_51 = e0 | all_0_52_52 = e0
% 14.58/3.86 |
% 14.58/3.86 +-Applying beta-rule and splitting (1012), into two cases.
% 14.58/3.86 |-Branch one:
% 14.58/3.86 | (518) all_0_50_50 = e0
% 14.58/3.86 |
% 14.58/3.86 | Combining equations (400,518) yields a new equation:
% 14.58/3.86 | (558) e2 = e0
% 14.58/3.86 |
% 14.58/3.86 | Simplifying 558 yields:
% 14.58/3.86 | (559) e2 = e0
% 14.58/3.86 |
% 14.58/3.86 | Equations (559) can reduce 61 to:
% 14.58/3.86 | (303) $false
% 14.58/3.86 |
% 14.58/3.86 |-The branch is then unsatisfiable
% 14.58/3.86 |-Branch two:
% 14.58/3.86 | (468) ~ (all_0_50_50 = e0)
% 14.58/3.86 | (1028) all_0_51_51 = e0 | all_0_52_52 = e0
% 14.58/3.86 |
% 14.58/3.86 +-Applying beta-rule and splitting (1028), into two cases.
% 14.58/3.86 |-Branch one:
% 14.58/3.86 | (609) all_0_51_51 = e0
% 14.58/3.86 |
% 14.58/3.86 | Equations (609) can reduce 247 to:
% 14.58/3.86 | (480) ~ (e3 = e0)
% 14.58/3.86 |
% 14.58/3.86 | Simplifying 480 yields:
% 14.58/3.86 | (74) ~ (e3 = e0)
% 14.58/3.86 |
% 14.58/3.86 | From (609) and (215) follows:
% 14.58/3.86 | (3297) op(e2, e1) = e0
% 14.58/3.86 |
% 14.58/3.86 | Instantiating formula (39) with e2, e2, all_0_12_12, e3 and discharging atoms op(e2, e2) = all_0_12_12, op(e2, e2) = e3, yields:
% 14.58/3.86 | (2281) all_0_12_12 = e3
% 14.58/3.86 |
% 14.58/3.86 | Instantiating formula (39) with e2, e2, all_0_21_21, all_0_12_12 and discharging atoms op(e2, e2) = all_0_12_12, op(e2, e2) = all_0_21_21, yields:
% 14.58/3.86 | (2282) all_0_12_12 = all_0_21_21
% 14.58/3.86 |
% 14.58/3.86 | Instantiating formula (39) with e2, e1, all_0_19_19, all_0_3_3 and discharging atoms op(e2, e1) = all_0_3_3, op(e2, e1) = all_0_19_19, yields:
% 14.58/3.86 | (3300) all_0_3_3 = all_0_19_19
% 14.58/3.86 |
% 14.58/3.86 | Instantiating formula (39) with e2, e1, e0, all_0_3_3 and discharging atoms op(e2, e1) = all_0_3_3, op(e2, e1) = e0, yields:
% 14.58/3.86 | (3301) all_0_3_3 = e0
% 14.58/3.87 |
% 14.58/3.87 | Combining equations (3300,3301) yields a new equation:
% 14.58/3.87 | (3302) all_0_19_19 = e0
% 14.58/3.87 |
% 14.58/3.87 | Simplifying 3302 yields:
% 14.58/3.87 | (3303) all_0_19_19 = e0
% 14.58/3.87 |
% 14.58/3.87 | Combining equations (2282,2281) yields a new equation:
% 14.58/3.87 | (3304) all_0_21_21 = e3
% 14.58/3.87 |
% 14.58/3.87 | Simplifying 3304 yields:
% 14.58/3.87 | (687) all_0_21_21 = e3
% 14.58/3.87 |
% 14.58/3.87 +-Applying beta-rule and splitting (19), into two cases.
% 14.58/3.87 |-Branch one:
% 14.58/3.87 | (450) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2)) | (all_0_21_21 = e0 & ~ (all_0_22_22 = e2))
% 14.58/3.87 |
% 14.58/3.87 +-Applying beta-rule and splitting (450), into two cases.
% 14.58/3.87 |-Branch one:
% 14.58/3.87 | (451) (all_0_17_17 = e4 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e3 & ~ (all_0_20_20 = e2))
% 14.58/3.87 |
% 14.58/3.87 +-Applying beta-rule and splitting (451), into two cases.
% 14.58/3.87 |-Branch one:
% 14.58/3.87 | (452) all_0_17_17 = e4 & ~ (all_0_18_18 = e2)
% 14.58/3.87 |
% 14.58/3.87 | Applying alpha-rule on (452) yields:
% 14.58/3.87 | (453) all_0_17_17 = e4
% 14.58/3.87 | (454) ~ (all_0_18_18 = e2)
% 14.58/3.87 |
% 14.58/3.87 | Combining equations (453,1690) yields a new equation:
% 14.58/3.87 | (426) e4 = e1
% 14.58/3.87 |
% 14.58/3.87 | Simplifying 426 yields:
% 14.58/3.87 | (427) e4 = e1
% 14.58/3.87 |
% 14.58/3.87 | Equations (427) can reduce 253 to:
% 14.58/3.87 | (303) $false
% 14.58/3.87 |
% 14.58/3.87 |-The branch is then unsatisfiable
% 14.58/3.87 |-Branch two:
% 14.58/3.87 | (458) all_0_19_19 = e3 & ~ (all_0_20_20 = e2)
% 14.58/3.87 |
% 14.58/3.87 | Applying alpha-rule on (458) yields:
% 14.58/3.87 | (459) all_0_19_19 = e3
% 14.58/3.87 | (460) ~ (all_0_20_20 = e2)
% 14.58/3.87 |
% 14.58/3.87 | Combining equations (459,3303) yields a new equation:
% 14.58/3.87 | (574) e3 = e0
% 14.58/3.87 |
% 14.58/3.87 | Simplifying 574 yields:
% 14.58/3.87 | (575) e3 = e0
% 14.58/3.87 |
% 14.58/3.87 | Equations (575) can reduce 74 to:
% 14.58/3.87 | (303) $false
% 14.58/3.87 |
% 14.58/3.87 |-The branch is then unsatisfiable
% 14.58/3.87 |-Branch two:
% 14.58/3.87 | (462) all_0_21_21 = e0 & ~ (all_0_22_22 = e2)
% 14.58/3.87 |
% 14.58/3.87 | Applying alpha-rule on (462) yields:
% 14.58/3.87 | (463) all_0_21_21 = e0
% 14.58/3.87 | (464) ~ (all_0_22_22 = e2)
% 14.58/3.87 |
% 14.58/3.87 | Combining equations (463,687) yields a new equation:
% 14.58/3.87 | (575) e3 = e0
% 14.58/3.87 |
% 14.58/3.87 | Equations (575) can reduce 74 to:
% 14.58/3.87 | (303) $false
% 14.58/3.87 |
% 14.58/3.87 |-The branch is then unsatisfiable
% 14.58/3.87 |-Branch two:
% 14.58/3.87 | (631) all_0_52_52 = e1 & ~ (all_0_55_55 = e2)
% 14.58/3.87 |
% 14.58/3.87 | Applying alpha-rule on (631) yields:
% 14.58/3.87 | (322) all_0_52_52 = e1
% 14.58/3.87 | (633) ~ (all_0_55_55 = e2)
% 14.66/3.87 |
% 14.66/3.87 | Combining equations (578,322) yields a new equation:
% 14.66/3.87 | (426) e4 = e1
% 14.66/3.87 |
% 14.66/3.87 | Simplifying 426 yields:
% 14.66/3.87 | (427) e4 = e1
% 14.66/3.87 |
% 14.66/3.87 | Equations (427) can reduce 253 to:
% 14.66/3.87 | (303) $false
% 14.66/3.87 |
% 14.66/3.87 |-The branch is then unsatisfiable
% 14.66/3.87 |-Branch two:
% 14.66/3.87 | (613) ~ (all_0_51_51 = e0)
% 14.66/3.87 | (1032) all_0_52_52 = e0
% 14.66/3.87 |
% 14.66/3.87 | Combining equations (578,1032) yields a new equation:
% 14.66/3.87 | (995) e4 = e0
% 14.66/3.87 |
% 14.66/3.87 | Simplifying 995 yields:
% 14.66/3.87 | (512) e4 = e0
% 14.66/3.87 |
% 14.66/3.87 | Equations (512) can reduce 5 to:
% 14.66/3.87 | (303) $false
% 14.66/3.87 |
% 14.66/3.87 |-The branch is then unsatisfiable
% 14.66/3.87 |-Branch two:
% 14.66/3.87 | (260) ~ (all_0_42_42 = e1)
% 14.66/3.87 | (2227) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_59_59 = e1
% 14.66/3.87 |
% 14.66/3.87 +-Applying beta-rule and splitting (598), into two cases.
% 14.66/3.87 |-Branch one:
% 14.66/3.87 | (599) all_0_47_47 = e3
% 14.66/3.87 |
% 14.66/3.87 | Combining equations (379,599) yields a new equation:
% 14.66/3.87 | (553) e3 = e2
% 14.66/3.87 |
% 14.66/3.87 | Equations (553) can reduce 209 to:
% 14.66/3.87 | (303) $false
% 14.66/3.87 |
% 14.66/3.87 |-The branch is then unsatisfiable
% 14.66/3.87 |-Branch two:
% 14.66/3.87 | (602) ~ (all_0_47_47 = e3)
% 14.66/3.87 | (603) all_0_59_59 = e3
% 14.66/3.87 |
% 14.66/3.87 | Equations (603) can reduce 1058 to:
% 14.66/3.87 | (145) ~ (e3 = e1)
% 14.66/3.87 |
% 14.66/3.87 +-Applying beta-rule and splitting (2227), into two cases.
% 14.66/3.87 |-Branch one:
% 14.66/3.87 | (1100) all_0_47_47 = e1
% 14.66/3.87 |
% 14.66/3.87 | Combining equations (379,1100) yields a new equation:
% 14.66/3.87 | (1478) e2 = e1
% 14.66/3.87 |
% 14.66/3.87 | Simplifying 1478 yields:
% 14.66/3.87 | (369) e2 = e1
% 14.66/3.87 |
% 14.66/3.87 | Equations (369) can reduce 150 to:
% 14.66/3.87 | (303) $false
% 14.66/3.87 |
% 14.66/3.87 |-The branch is then unsatisfiable
% 14.66/3.87 |-Branch two:
% 14.66/3.87 | (1560) ~ (all_0_47_47 = e1)
% 14.66/3.87 | (2238) all_0_51_51 = e1 | all_0_59_59 = e1
% 14.66/3.87 |
% 14.66/3.87 +-Applying beta-rule and splitting (2238), into two cases.
% 14.66/3.87 |-Branch one:
% 14.66/3.87 | (1185) all_0_51_51 = e1
% 14.66/3.87 |
% 14.66/3.87 | Equations (1185) can reduce 343 to:
% 14.66/3.87 | (303) $false
% 14.66/3.87 |
% 14.66/3.87 |-The branch is then unsatisfiable
% 14.66/3.87 |-Branch two:
% 14.66/3.87 | (343) ~ (all_0_51_51 = e1)
% 14.66/3.87 | (341) all_0_59_59 = e1
% 14.66/3.87 |
% 14.66/3.87 | Combining equations (341,603) yields a new equation:
% 14.66/3.87 | (414) e3 = e1
% 14.66/3.87 |
% 14.66/3.87 | Equations (414) can reduce 145 to:
% 14.66/3.87 | (303) $false
% 14.66/3.87 |
% 14.66/3.87 |-The branch is then unsatisfiable
% 14.66/3.87 |-Branch two:
% 14.66/3.87 | (419) ~ (all_0_40_40 = e3)
% 14.66/3.87 | (2127) all_0_45_45 = e3 | all_0_54_54 = e3 | all_0_57_57 = e3
% 14.66/3.87 |
% 14.66/3.87 +-Applying beta-rule and splitting (2127), into two cases.
% 14.66/3.87 |-Branch one:
% 14.66/3.87 | (1260) all_0_45_45 = e3
% 14.66/3.87 |
% 14.66/3.87 | Combining equations (1260,300) yields a new equation:
% 14.66/3.87 | (574) e3 = e0
% 14.66/3.87 |
% 14.66/3.87 | Simplifying 574 yields:
% 14.66/3.87 | (575) e3 = e0
% 14.66/3.87 |
% 14.66/3.87 | Equations (575) can reduce 74 to:
% 14.66/3.87 | (303) $false
% 14.66/3.87 |
% 14.66/3.87 |-The branch is then unsatisfiable
% 14.66/3.87 |-Branch two:
% 14.66/3.87 | (1263) ~ (all_0_45_45 = e3)
% 14.66/3.87 | (2136) all_0_54_54 = e3 | all_0_57_57 = e3
% 14.66/3.87 |
% 14.66/3.87 +-Applying beta-rule and splitting (2136), into two cases.
% 14.66/3.87 |-Branch one:
% 14.66/3.87 | (418) all_0_54_54 = e3
% 14.66/3.87 |
% 14.66/3.87 | Combining equations (1289,418) yields a new equation:
% 14.66/3.87 | (414) e3 = e1
% 14.66/3.87 |
% 14.66/3.87 | Equations (414) can reduce 145 to:
% 14.66/3.87 | (303) $false
% 14.66/3.87 |
% 14.66/3.87 |-The branch is then unsatisfiable
% 14.66/3.87 |-Branch two:
% 14.66/3.87 | (649) ~ (all_0_54_54 = e3)
% 14.66/3.87 | (637) all_0_57_57 = e3
% 14.66/3.87 |
% 14.66/3.87 | Combining equations (891,637) yields a new equation:
% 14.66/3.87 | (523) e4 = e3
% 14.66/3.87 |
% 14.66/3.87 | Simplifying 523 yields:
% 14.66/3.87 | (524) e4 = e3
% 14.66/3.87 |
% 14.66/3.87 | Equations (524) can reduce 30 to:
% 14.66/3.87 | (303) $false
% 14.66/3.87 |
% 14.66/3.87 |-The branch is then unsatisfiable
% 14.66/3.87 |-Branch two:
% 14.66/3.87 | (325) ~ (all_0_49_49 = e1)
% 14.66/3.87 | (2159) all_0_53_53 = e1 | all_0_56_56 = e1
% 14.66/3.87 |
% 14.66/3.87 +-Applying beta-rule and splitting (2159), into two cases.
% 14.66/3.87 |-Branch one:
% 14.66/3.87 | (275) all_0_53_53 = e1
% 14.66/3.87 |
% 14.66/3.87 | Combining equations (413,275) yields a new equation:
% 14.66/3.87 | (604) e3 = e1
% 14.66/3.87 |
% 14.66/3.87 | Simplifying 604 yields:
% 14.66/3.87 | (414) e3 = e1
% 14.66/3.87 |
% 14.66/3.87 | Equations (414) can reduce 145 to:
% 14.66/3.87 | (303) $false
% 14.66/3.87 |
% 14.66/3.87 |-The branch is then unsatisfiable
% 14.66/3.87 |-Branch two:
% 14.66/3.87 | (1568) ~ (all_0_53_53 = e1)
% 14.66/3.87 | (314) all_0_56_56 = e1
% 14.66/3.87 |
% 14.66/3.87 | Equations (314) can reduce 282 to:
% 14.66/3.87 | (303) $false
% 14.66/3.87 |
% 14.66/3.87 |-The branch is then unsatisfiable
% 14.66/3.87 |-Branch two:
% 14.66/3.87 | (306) ~ (all_0_43_43 = e0)
% 14.66/3.87 | (2180) all_0_48_48 = e0 | all_0_52_52 = e0 | all_0_60_60 = e0
% 14.66/3.87 |
% 14.66/3.87 +-Applying beta-rule and splitting (2180), into two cases.
% 14.66/3.87 |-Branch one:
% 14.66/3.87 | (1846) all_0_48_48 = e0
% 14.66/3.87 |
% 14.66/3.87 | Combining equations (535,1846) yields a new equation:
% 14.66/3.87 | (574) e3 = e0
% 14.66/3.87 |
% 14.66/3.87 | Simplifying 574 yields:
% 14.66/3.87 | (575) e3 = e0
% 14.66/3.87 |
% 14.66/3.87 | Equations (575) can reduce 74 to:
% 14.66/3.87 | (303) $false
% 14.66/3.87 |
% 14.66/3.87 |-The branch is then unsatisfiable
% 14.66/3.87 |-Branch two:
% 14.66/3.87 | (1599) ~ (all_0_48_48 = e0)
% 14.66/3.87 | (2184) all_0_52_52 = e0 | all_0_60_60 = e0
% 14.66/3.87 |
% 14.66/3.87 +-Applying beta-rule and splitting (2184), into two cases.
% 14.66/3.87 |-Branch one:
% 14.66/3.87 | (1032) all_0_52_52 = e0
% 14.66/3.87 |
% 14.66/3.87 | Combining equations (578,1032) yields a new equation:
% 14.66/3.87 | (995) e4 = e0
% 14.66/3.87 |
% 14.66/3.87 | Simplifying 995 yields:
% 14.66/3.87 | (512) e4 = e0
% 14.66/3.87 |
% 14.66/3.87 | Equations (512) can reduce 5 to:
% 14.66/3.87 | (303) $false
% 14.66/3.87 |
% 14.66/3.87 |-The branch is then unsatisfiable
% 14.66/3.87 |-Branch two:
% 14.66/3.87 | (308) ~ (all_0_52_52 = e0)
% 14.66/3.87 | (305) all_0_60_60 = e0
% 14.66/3.87 |
% 14.66/3.87 | Combining equations (305,1059) yields a new equation:
% 14.66/3.87 | (302) e1 = e0
% 14.66/3.87 |
% 14.66/3.87 | Equations (302) can reduce 143 to:
% 14.66/3.87 | (303) $false
% 14.66/3.87 |
% 14.66/3.87 |-The branch is then unsatisfiable
% 14.66/3.87 |-Branch two:
% 14.66/3.87 | (764) ~ (all_0_57_57 = e4)
% 14.66/3.87 | (1019) all_0_58_58 = e4 | all_0_60_60 = e4
% 14.66/3.87 |
% 14.66/3.87 +-Applying beta-rule and splitting (100), into two cases.
% 14.66/3.87 |-Branch one:
% 14.66/3.87 | (511) all_0_40_40 = e4
% 14.66/3.87 |
% 14.66/3.87 | Equations (511) can reduce 514 to:
% 14.66/3.87 | (303) $false
% 14.66/3.87 |
% 14.66/3.87 |-The branch is then unsatisfiable
% 14.66/3.87 |-Branch two:
% 14.66/3.87 | (514) ~ (all_0_40_40 = e4)
% 14.66/3.88 | (515) all_0_45_45 = e4 | all_0_50_50 = e4 | all_0_57_57 = e4
% 14.66/3.88 |
% 14.66/3.88 +-Applying beta-rule and splitting (532), into two cases.
% 14.66/3.88 |-Branch one:
% 14.66/3.88 | (533) all_0_50_50 = e4
% 14.66/3.88 |
% 14.66/3.88 | Combining equations (533,400) yields a new equation:
% 14.66/3.88 | (455) e4 = e2
% 14.66/3.88 |
% 14.66/3.88 | Simplifying 455 yields:
% 14.66/3.88 | (434) e4 = e2
% 14.66/3.88 |
% 14.66/3.88 | Equations (434) can reduce 227 to:
% 14.66/3.88 | (303) $false
% 14.66/3.88 |
% 14.66/3.88 |-The branch is then unsatisfiable
% 14.66/3.88 |-Branch two:
% 14.66/3.88 | (577) ~ (all_0_50_50 = e4)
% 14.66/3.88 | (578) all_0_52_52 = e4
% 14.66/3.88 |
% 14.66/3.88 | Equations (578) can reduce 54 to:
% 14.66/3.88 | (582) ~ (all_0_43_43 = e4)
% 14.66/3.88 |
% 14.66/3.88 | Equations (578) can reduce 371 to:
% 14.66/3.88 | (227) ~ (e4 = e2)
% 14.66/3.88 |
% 14.66/3.88 +-Applying beta-rule and splitting (230), into two cases.
% 14.66/3.88 |-Branch one:
% 14.66/3.88 | (588) all_0_43_43 = e0
% 14.66/3.88 |
% 14.66/3.88 | Equations (588) can reduce 582 to:
% 14.66/3.88 | (516) ~ (e4 = e0)
% 14.66/3.88 |
% 14.66/3.88 | Simplifying 516 yields:
% 14.66/3.88 | (5) ~ (e4 = e0)
% 14.66/3.88 |
% 14.66/3.88 +-Applying beta-rule and splitting (515), into two cases.
% 14.66/3.88 |-Branch one:
% 14.66/3.88 | (784) all_0_45_45 = e4
% 14.66/3.88 |
% 14.66/3.88 | Combining equations (784,300) yields a new equation:
% 14.66/3.88 | (995) e4 = e0
% 14.66/3.88 |
% 14.66/3.88 | Simplifying 995 yields:
% 14.66/3.88 | (512) e4 = e0
% 14.66/3.88 |
% 14.66/3.88 | Equations (512) can reduce 5 to:
% 14.66/3.88 | (303) $false
% 14.66/3.88 |
% 14.66/3.88 |-The branch is then unsatisfiable
% 14.66/3.88 |-Branch two:
% 14.66/3.88 | (787) ~ (all_0_45_45 = e4)
% 14.66/3.88 | (788) all_0_50_50 = e4 | all_0_57_57 = e4
% 14.66/3.88 |
% 14.66/3.88 +-Applying beta-rule and splitting (788), into two cases.
% 14.66/3.88 |-Branch one:
% 14.66/3.88 | (533) all_0_50_50 = e4
% 14.66/3.88 |
% 14.66/3.88 | Combining equations (400,533) yields a new equation:
% 14.66/3.88 | (434) e4 = e2
% 14.66/3.88 |
% 14.66/3.88 | Equations (434) can reduce 227 to:
% 14.66/3.88 | (303) $false
% 14.66/3.88 |
% 14.66/3.88 |-The branch is then unsatisfiable
% 14.66/3.88 |-Branch two:
% 14.66/3.88 | (577) ~ (all_0_50_50 = e4)
% 14.66/3.88 | (891) all_0_57_57 = e4
% 14.66/3.88 |
% 14.66/3.88 | Equations (891) can reduce 764 to:
% 14.66/3.88 | (303) $false
% 14.66/3.88 |
% 14.66/3.88 |-The branch is then unsatisfiable
% 14.66/3.88 |-Branch two:
% 14.66/3.88 | (306) ~ (all_0_43_43 = e0)
% 14.66/3.88 | (2180) all_0_48_48 = e0 | all_0_52_52 = e0 | all_0_60_60 = e0
% 14.66/3.88 |
% 14.66/3.88 +-Applying beta-rule and splitting (2180), into two cases.
% 14.66/3.88 |-Branch one:
% 14.66/3.88 | (1846) all_0_48_48 = e0
% 14.66/3.88 |
% 14.66/3.88 | Combining equations (535,1846) yields a new equation:
% 14.66/3.88 | (574) e3 = e0
% 14.66/3.88 |
% 14.66/3.88 | Simplifying 574 yields:
% 14.66/3.88 | (575) e3 = e0
% 14.66/3.88 |
% 14.66/3.88 | Equations (575) can reduce 74 to:
% 14.66/3.88 | (303) $false
% 14.66/3.88 |
% 14.66/3.88 |-The branch is then unsatisfiable
% 14.66/3.88 |-Branch two:
% 14.66/3.88 | (1599) ~ (all_0_48_48 = e0)
% 14.66/3.88 | (2184) all_0_52_52 = e0 | all_0_60_60 = e0
% 14.66/3.88 |
% 14.66/3.88 +-Applying beta-rule and splitting (2184), into two cases.
% 14.66/3.88 |-Branch one:
% 14.66/3.88 | (1032) all_0_52_52 = e0
% 14.66/3.88 |
% 14.66/3.88 | Combining equations (578,1032) yields a new equation:
% 14.66/3.88 | (995) e4 = e0
% 14.66/3.88 |
% 14.66/3.88 | Simplifying 995 yields:
% 14.66/3.88 | (512) e4 = e0
% 14.66/3.88 |
% 14.66/3.88 | Equations (512) can reduce 5 to:
% 14.66/3.88 | (303) $false
% 14.66/3.88 |
% 14.66/3.88 |-The branch is then unsatisfiable
% 14.66/3.88 |-Branch two:
% 14.66/3.88 | (308) ~ (all_0_52_52 = e0)
% 14.66/3.88 | (305) all_0_60_60 = e0
% 14.66/3.88 |
% 14.66/3.88 | Combining equations (305,1059) yields a new equation:
% 14.66/3.88 | (302) e1 = e0
% 14.66/3.88 |
% 14.66/3.88 | Equations (302) can reduce 143 to:
% 14.66/3.88 | (303) $false
% 14.66/3.88 |
% 14.66/3.88 |-The branch is then unsatisfiable
% 14.66/3.88 |-Branch two:
% 14.66/3.88 | (566) ~ (all_0_48_48 = e3)
% 14.66/3.88 | (3443) all_0_48_48 = e4 | all_0_48_48 = e2
% 14.66/3.88 |
% 14.66/3.88 +-Applying beta-rule and splitting (3443), into two cases.
% 14.66/3.88 |-Branch one:
% 14.66/3.88 | (1297) all_0_48_48 = e4
% 14.66/3.88 |
% 14.66/3.88 | Equations (1297) can reduce 507 to:
% 14.66/3.88 | (303) $false
% 14.66/3.88 |
% 14.66/3.88 |-The branch is then unsatisfiable
% 14.66/3.88 |-Branch two:
% 14.66/3.88 | (507) ~ (all_0_48_48 = e4)
% 14.66/3.88 | (364) all_0_48_48 = e2
% 14.66/3.88 |
% 14.66/3.88 | Equations (364) can reduce 359 to:
% 14.66/3.88 | (303) $false
% 14.66/3.88 |
% 14.66/3.88 |-The branch is then unsatisfiable
% 14.66/3.88 |-Branch two:
% 14.66/3.88 | (357) ~ (all_0_47_47 = e2)
% 14.66/3.88 | (382) all_0_51_51 = e2 | all_0_59_59 = e2
% 14.66/3.88 |
% 14.66/3.88 +-Applying beta-rule and splitting (382), into two cases.
% 14.66/3.88 |-Branch one:
% 14.66/3.88 | (383) all_0_51_51 = e2
% 14.66/3.88 |
% 14.66/3.88 | Equations (383) can reduce 654 to:
% 14.66/3.88 | (303) $false
% 14.66/3.88 |
% 14.66/3.88 |-The branch is then unsatisfiable
% 14.66/3.88 |-Branch two:
% 14.66/3.88 | (654) ~ (all_0_51_51 = e2)
% 14.66/3.88 | (655) all_0_59_59 = e2
% 14.66/3.88 |
% 14.66/3.88 | Equations (655) can reduce 1437 to:
% 14.66/3.88 | (303) $false
% 14.66/3.88 |
% 14.66/3.88 |-The branch is then unsatisfiable
% 14.66/3.88 |-Branch two:
% 14.66/3.88 | (388) ~ (all_0_50_50 = e2)
% 14.66/3.88 | (403) all_0_54_54 = e2 | all_0_57_57 = e2
% 14.66/3.88 |
% 14.66/3.88 +-Applying beta-rule and splitting (403), into two cases.
% 14.66/3.88 |-Branch one:
% 14.66/3.88 | (404) all_0_54_54 = e2
% 14.66/3.88 |
% 14.66/3.88 | Combining equations (1289,404) yields a new equation:
% 14.66/3.88 | (369) e2 = e1
% 14.66/3.88 |
% 14.66/3.88 | Equations (369) can reduce 150 to:
% 14.66/3.88 | (303) $false
% 14.66/3.88 |
% 14.66/3.88 |-The branch is then unsatisfiable
% 14.66/3.88 |-Branch two:
% 14.66/3.88 | (375) ~ (all_0_54_54 = e2)
% 14.66/3.88 | (407) all_0_57_57 = e2
% 14.66/3.88 |
% 14.66/3.88 | Equations (407) can reduce 717 to:
% 14.66/3.88 | (303) $false
% 14.66/3.88 |
% 14.66/3.88 |-The branch is then unsatisfiable
% 14.66/3.88 |-Branch two:
% 14.66/3.88 | (264) ~ (all_0_46_46 = e1)
% 14.66/3.88 | (337) all_0_58_58 = e1
% 14.66/3.88 |
% 14.66/3.88 | Combining equations (337,664) yields a new equation:
% 14.66/3.88 | (369) e2 = e1
% 14.66/3.88 |
% 14.66/3.88 | Equations (369) can reduce 150 to:
% 14.66/3.88 | (303) $false
% 14.66/3.88 |
% 14.66/3.88 |-The branch is then unsatisfiable
% 14.66/3.88 |-Branch two:
% 14.66/3.88 | (278) ~ (all_0_54_54 = e1)
% 14.66/3.88 | (1292) all_0_54_54 = e3 | all_0_54_54 = e2
% 14.66/3.88 |
% 14.66/3.88 +-Applying beta-rule and splitting (223), into two cases.
% 14.66/3.88 |-Branch one:
% 14.66/3.88 | (275) all_0_53_53 = e1
% 14.66/3.88 |
% 14.66/3.88 | Combining equations (413,275) yields a new equation:
% 14.66/3.88 | (604) e3 = e1
% 14.66/3.88 |
% 14.66/3.88 | Simplifying 604 yields:
% 14.66/3.88 | (414) e3 = e1
% 14.66/3.88 |
% 14.66/3.88 | Equations (414) can reduce 145 to:
% 14.66/3.88 | (303) $false
% 14.66/3.88 |
% 14.66/3.88 |-The branch is then unsatisfiable
% 14.66/3.88 |-Branch two:
% 14.66/3.88 | (1568) ~ (all_0_53_53 = e1)
% 14.66/3.88 | (1609) all_0_54_54 = e1 | all_0_55_55 = e1
% 14.66/3.88 |
% 14.66/3.88 +-Applying beta-rule and splitting (1609), into two cases.
% 14.66/3.88 |-Branch one:
% 14.66/3.88 | (1289) all_0_54_54 = e1
% 14.66/3.88 |
% 14.66/3.88 | Equations (1289) can reduce 278 to:
% 14.66/3.88 | (303) $false
% 14.66/3.88 |
% 14.66/3.88 |-The branch is then unsatisfiable
% 14.66/3.88 |-Branch two:
% 14.66/3.88 | (278) ~ (all_0_54_54 = e1)
% 14.66/3.88 | (1065) all_0_55_55 = e1
% 14.66/3.88 |
% 14.66/3.88 | Combining equations (1065,373) yields a new equation:
% 14.66/3.88 | (369) e2 = e1
% 14.66/3.88 |
% 14.66/3.88 | Equations (369) can reduce 150 to:
% 14.66/3.88 | (303) $false
% 14.66/3.88 |
% 14.66/3.88 |-The branch is then unsatisfiable
% 14.66/3.88 |-Branch two:
% 14.66/3.88 | (304) ~ (all_0_45_45 = e0)
% 14.66/3.88 | (305) all_0_60_60 = e0
% 14.66/3.88 |
% 14.66/3.88 | Combining equations (1059,305) yields a new equation:
% 14.66/3.88 | (301) e1 = e0
% 14.66/3.88 |
% 14.66/3.88 | Simplifying 301 yields:
% 14.66/3.88 | (302) e1 = e0
% 14.66/3.88 |
% 14.66/3.88 | Equations (302) can reduce 143 to:
% 14.66/3.88 | (303) $false
% 14.66/3.88 |
% 14.66/3.88 |-The branch is then unsatisfiable
% 14.66/3.88 % SZS output end Proof for theBenchmark
% 14.66/3.88
% 14.66/3.88 3300ms
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