TSTP Solution File: ALG055+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG055+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 15:33:55 EDT 2022
% Result : Theorem 6.66s 2.07s
% Output : Proof 21.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG055+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 19:55:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.53/0.58 ____ _
% 0.53/0.58 ___ / __ \_____(_)___ ________ __________
% 0.53/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.53/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.53/0.58
% 0.53/0.58 A Theorem Prover for First-Order Logic
% 0.53/0.58 (ePrincess v.1.0)
% 0.53/0.58
% 0.53/0.58 (c) Philipp Rümmer, 2009-2015
% 0.53/0.58 (c) Peter Backeman, 2014-2015
% 0.53/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.58 Bug reports to peter@backeman.se
% 0.53/0.58
% 0.53/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.58
% 0.53/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.66/1.16 Prover 0: Preprocessing ...
% 4.55/1.59 Prover 0: Constructing countermodel ...
% 6.66/2.07 Prover 0: proved (1442ms)
% 6.66/2.07
% 6.66/2.07 No countermodel exists, formula is valid
% 6.66/2.07 % SZS status Theorem for theBenchmark
% 6.66/2.07
% 6.66/2.07 Generating proof ... found it (size 6967)
% 18.66/4.94
% 18.66/4.94 % SZS output start Proof for theBenchmark
% 18.66/4.94 Assumed formulas after preprocessing and simplification:
% 18.66/4.94 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : ? [v31] : ? [v32] : ? [v33] : ? [v34] : ? [v35] : ? [v36] : ? [v37] : ? [v38] : ? [v39] : ? [v40] : ? [v41] : ? [v42] : ? [v43] : ? [v44] : ? [v45] : ? [v46] : ? [v47] : ? [v48] : ? [v49] : ? [v50] : ? [v51] : ? [v52] : ? [v53] : ? [v54] : ? [v55] : ? [v56] : ? [v57] : ? [v58] : ? [v59] : ( ~ (v20 = v19) & ~ (v20 = v18) & ~ (v20 = v17) & ~ (v20 = v16) & ~ (v20 = v12) & ~ (v20 = v8) & ~ (v20 = v3) & ~ (v20 = e0) & ~ (v19 = v18) & ~ (v19 = v17) & ~ (v19 = v15) & ~ (v19 = v7) & ~ (v19 = v2) & ~ (v19 = e4) & ~ (v19 = e0) & ~ (v18 = v17) & ~ (v18 = v14) & ~ (v18 = v11) & ~ (v18 = v6) & ~ (v18 = v1) & ~ (v18 = e0) & ~ (v17 = v13) & ~ (v17 = v10) & ~ (v17 = v5) & ~ (v17 = v0) & ~ (v17 = e0) & ~ (v16 = v15) & ~ (v16 = v14) & ~ (v16 = v13) & ~ (v16 = v12) & ~ (v16 = v8) & ~ (v16 = v3) & ~ (v16 = e1) & ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = v7) & ~ (v15 = v2) & ~ (v15 = e4) & ~ (v15 = e1) & ~ (v14 = v13) & ~ (v14 = v11) & ~ (v14 = v6) & ~ (v14 = v1) & ~ (v14 = e1) & ~ (v13 = v10) & ~ (v13 = v5) & ~ (v13 = v0) & ~ (v13 = e1) & ~ (v12 = v11) & ~ (v12 = v10) & ~ (v12 = v8) & ~ (v12 = v3) & ~ (v12 = e4) & ~ (v12 = e3) & ~ (v11 = v10) & ~ (v11 = v6) & ~ (v11 = v1) & ~ (v11 = e4) & ~ (v11 = e3) & ~ (v10 = v5) & ~ (v10 = v0) & ~ (v10 = e4) & ~ (v10 = e3) & ~ (v9 = v8) & ~ (v9 = v7) & ~ (v9 = v6) & ~ (v9 = v5) & ~ (v9 = v4) & ~ (v9 = e3) & ~ (v9 = e1) & ~ (v9 = e0) & ~ (v8 = v7) & ~ (v8 = v6) & ~ (v8 = v5) & ~ (v8 = v3) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v2) & ~ (v7 = e4) & ~ (v6 = v5) & ~ (v6 = v1) & ~ (v5 = v0) & ~ (v4 = v3) & ~ (v4 = v2) & ~ (v4 = v1) & ~ (v4 = v0) & ~ (v4 = e3) & ~ (v4 = e1) & ~ (v4 = e0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = v0) & ~ (v2 = e4) & ~ (v1 = v0) & ~ (e4 = e3) & ~ (e4 = e2) & ~ (e4 = e1) & ~ (e4 = e0) & ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ (e1 = e0) & op(unit, e4) = e4 & op(unit, e3) = e3 & op(unit, e2) = e2 & op(unit, e1) = e1 & op(unit, e0) = e0 & op(e4, v20) = v54 & op(e4, v19) = v45 & op(e4, v18) = v37 & op(e4, v17) = v28 & op(e4, v9) = v59 & op(e4, v4) = v57 & op(e4, unit) = e4 & op(e4, e4) = e0 & op(e4, e3) = v20 & op(e4, e2) = v19 & op(e4, e1) = v18 & op(e4, e0) = v17 & op(e3, v20) = v55 & op(e3, v16) = v53 & op(e3, v15) = v43 & op(e3, v14) = v35 & op(e3, v13) = v26 & op(e3, v12) = v52 & op(e3, v8) = v50 & op(e3, v3) = v48 & op(e3, unit) = e3 & op(e3, e4) = e1 & op(e3, e3) = v16 & op(e3, e2) = v15 & op(e3, e1) = v14 & op(e3, e0) = v13 & op(e2, v19) = v46 & op(e2, v15) = v44 & op(e2, v12) = v51 & op(e2, v11) = v33 & op(e2, v10) = v24 & op(e2, v7) = v42 & op(e2, v2) = v40 & op(e2, unit) = e2 & op(e2, e4) = e3 & op(e2, e3) = v12 & op(e2, e2) = e4 & op(e2, e1) = v11 & op(e2, e0) = v10 & op(e1, v18) = v38 & op(e1, v14) = v36 & op(e1, v11) = v34 & op(e1, v9) = v58 & op(e1, v8) = v49 & op(e1, v7) = v41 & op(e1, v6) = v32 & op(e1, v5) = v22 & op(e1, v1) = v31 & op(e1, unit) = e1 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = v7 & op(e1, e1) = v6 & op(e1, e0) = v5 & op(e0, v17) = v29 & op(e0, v13) = v27 & op(e0, v10) = v25 & op(e0, v5) = v23 & op(e0, v4) = v56 & op(e0, v3) = v47 & op(e0, v2) = v39 & op(e0, v1) = v30 & op(e0, v0) = v21 & op(e0, unit) = e0 & op(e0, e4) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & ! [v60] : ! [v61] : ! [v62] : ! [v63] : (v61 = v60 | ~ (op(v63, v62) = v61) | ~ (op(v63, v62) = v60)) & (v20 = e4 | v20 = e3 | v20 = e2 | v20 = e1) & (v20 = e4 | v18 = e4 | v17 = e4) & (v20 = e4 | v16 = e4 | v8 = e4 | v3 = e4) & (v20 = e3 | v19 = e3 | v18 = e3 | v17 = e3) & (v20 = e3 | v16 = e3 | v8 = e3 | v3 = e3) & (v20 = e2 | v19 = e2 | v18 = e2 | v17 = e2) & (v20 = e2 | v16 = e2 | v12 = e2 | v8 = e2 | v3 = e2) & (v20 = e2 | (v59 = e1 & ~ (v58 = e4)) | (v57 = e0 & ~ (v56 = e4)) | (v18 = e3 & ~ (v14 = e4))) & (v20 = e1 | v19 = e1 | v18 = e1 | v17 = e1) & (v20 = e1 | v12 = e1 | v8 = e1 | v3 = e1) & (v19 = e3 | v19 = e2 | v19 = e1) & (v19 = e3 | v15 = e3 | v7 = e3 | v2 = e3) & (v19 = e2 | v15 = e2 | v7 = e2 | v2 = e2) & (v19 = e1 | v7 = e1 | v2 = e1) & (v18 = e4 | v18 = e3 | v18 = e2 | v18 = e1) & (v18 = e4 | v14 = e4 | v6 = e4 | v1 = e4) & (v18 = e3 | v14 = e3 | v6 = e3 | v1 = e3) & (v18 = e2 | v14 = e2 | v11 = e2 | v6 = e2 | v1 = e2) & (v18 = e1 | v11 = e1 | v6 = e1 | v1 = e1) & (v17 = e4 | v17 = e3 | v17 = e2 | v17 = e1) & (v17 = e4 | v13 = e4 | v5 = e4 | v0 = e4) & (v17 = e3 | v13 = e3 | v5 = e3 | v0 = e3) & (v17 = e2 | v13 = e2 | v10 = e2 | v5 = e2 | v0 = e2) & (v17 = e1 | v10 = e1 | v5 = e1 | v0 = e1) & (v16 = e4 | v16 = e3 | v16 = e2 | v16 = e0) & (v16 = e4 | v14 = e4 | v13 = e4) & (v16 = e3 | v15 = e3 | v14 = e3 | v13 = e3) & (v16 = e2 | v15 = e2 | v14 = e2 | v13 = e2) & (v16 = e0 | v15 = e0 | v14 = e0 | v13 = e0) & (v16 = e0 | v12 = e0 | v8 = e0 | v3 = e0) & (v15 = e3 | v15 = e2 | v15 = e0) & (v15 = e0 | v7 = e0 | v2 = e0) & (v14 = e4 | v14 = e3 | v14 = e2 | v14 = e0) & (v14 = e0 | v11 = e0 | v6 = e0 | v1 = e0) & (v13 = e4 | v13 = e3 | v13 = e2 | v13 = e0) & (v13 = e0 | v10 = e0 | v5 = e0 | v0 = e0) & (v12 = e2 | v12 = e1 | v12 = e0) & (v12 = e2 | v11 = e2 | v10 = e2) & (v12 = e1 | v11 = e1 | v10 = e1) & (v12 = e0 | v11 = e0 | v10 = e0) & (v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e4 | v9 = e2) & (v9 = e4 | v8 = e4 | v6 = e4 | v5 = e4) & (v9 = e4 | v4 = e4) & (v9 = e2 | v8 = e2 | v7 = e2 | v6 = e2 | v5 = e2) & (v9 = e2 | v4 = e2) & (v8 = e4 | v8 = e3 | v8 = e2 | v8 = e1 | v8 = e0) & (v8 = e3 | v7 = e3 | v6 = e3 | v5 = e3) & (v8 = e1 | v7 = e1 | v6 = e1 | v5 = e1) & (v8 = e0 | v7 = e0 | v6 = e0 | v5 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e4 | v6 = e3 | v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e4 | v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & (v4 = e4 | v4 = e2) & (v4 = e4 | v3 = e4 | v1 = e4 | v0 = e4) & (v4 = e2 | v3 = e2 | v2 = e2 | v1 = e2 | v0 = e2) & (v3 = e4 | v3 = e3 | v3 = e2 | v3 = e1 | v3 = e0) & (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & (v3 = e1 | v2 = e1 | v1 = e1 | v0 = e1) & (v3 = e0 | v2 = e0 | v1 = e0 | v0 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e4 | v1 = e3 | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e4 | v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0) & (unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0) & ((v55 = e4 & ~ (v54 = e3)) | (v52 = e2 & ~ (v51 = e3)) | (v50 = e1 & ~ (v49 = e3)) | (v48 = e0 & ~ (v47 = e3))) & ((v46 = e4 & ~ (v45 = e2)) | (v44 = e3 & ~ (v43 = e2)) | (v42 = e1 & ~ (v41 = e2)) | (v40 = e0 & ~ (v39 = e2))) & ((v38 = e4 & ~ (v37 = e1)) | (v36 = e3 & ~ (v35 = e1)) | (v34 = e2 & ~ (v33 = e1)) | (v31 = e0 & ~ (v30 = e1))) & ((v29 = e4 & ~ (v28 = e0)) | (v27 = e3 & ~ (v26 = e0)) | (v25 = e2 & ~ (v24 = e0)) | (v23 = e1 & ~ (v22 = e0))) & ((v17 = e4 & ~ (v14 = e0) & ~ (v12 = e0) & ~ (unit = e0) & ( ~ (v16 = e0) | v13 = e3) & ( ~ (v15 = e0) | v13 = e2) & ( ~ (v11 = e0) | v10 = e1) & ( ~ (v8 = e0) | v5 = e3) & ( ~ (v7 = e0) | v5 = e2) & ( ~ (v6 = e0) | v5 = e1) & ( ~ (v3 = e0) | v0 = e3) & ( ~ (v2 = e0) | v0 = e2) & ( ~ (v1 = e0) | v0 = e1)) | (v14 = e4 & ~ (v17 = e1) & ~ (v12 = e1) & ~ (unit = e1) & ( ~ (v20 = e1) | v18 = e3) & ( ~ (v19 = e1) | v18 = e2) & ( ~ (v10 = e1) | v11 = e0) & ( ~ (v8 = e1) | v6 = e3) & ( ~ (v7 = e1) | v6 = e2) & ( ~ (v5 = e1) | v6 = e0) & ( ~ (v3 = e1) | v1 = e3) & ( ~ (v2 = e1) | v1 = e2) & ( ~ (v0 = e1) | v1 = e0)) | ( ~ (v17 = e2) & ~ (v14 = e2) & ~ (v12 = e2) & ~ (v11 = e2) & ~ (v10 = e2) & ~ (v9 = e2) & ~ (v4 = e2) & ( ~ (v20 = e2) | (v19 = e3 & ~ (unit = e2))) & ( ~ (v19 = e2) | ~ (unit = e2)) & ( ~ (v18 = e2) | (v19 = e1 & ~ (unit = e2))) & ( ~ (v16 = e2) | (v15 = e3 & ~ (unit = e2))) & ( ~ (v15 = e2) | ~ (unit = e2)) & ( ~ (v13 = e2) | (v15 = e0 & ~ (unit = e2))) & ( ~ (v8 = e2) | (v7 = e3 & ~ (unit = e2))) & ( ~ (v7 = e2) | ~ (unit = e2)) & ( ~ (v6 = e2) | (v7 = e1 & ~ (unit = e2))) & ( ~ (v5 = e2) | (v7 = e0 & ~ (unit = e2))) & ( ~ (v3 = e2) | (v2 = e3 & ~ (unit = e2))) & ( ~ (v2 = e2) | ~ (unit = e2)) & ( ~ (v1 = e2) | (v2 = e1 & ~ (unit = e2))) & ( ~ (v0 = e2) | (v2 = e0 & ~ (unit = e2))))))
% 18.88/5.00 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16, all_0_17_17, all_0_18_18, all_0_19_19, all_0_20_20, all_0_21_21, all_0_22_22, all_0_23_23, all_0_24_24, all_0_25_25, all_0_26_26, all_0_27_27, all_0_28_28, all_0_29_29, all_0_30_30, all_0_31_31, all_0_32_32, all_0_33_33, all_0_34_34, all_0_35_35, all_0_36_36, all_0_37_37, all_0_38_38, all_0_39_39, all_0_40_40, all_0_41_41, all_0_42_42, all_0_43_43, all_0_44_44, all_0_45_45, all_0_46_46, all_0_47_47, all_0_48_48, all_0_49_49, all_0_50_50, all_0_51_51, all_0_52_52, all_0_53_53, all_0_54_54, all_0_55_55, all_0_56_56, all_0_57_57, all_0_58_58, all_0_59_59 yields:
% 18.88/5.00 | (1) ~ (all_0_39_39 = all_0_40_40) & ~ (all_0_39_39 = all_0_41_41) & ~ (all_0_39_39 = all_0_42_42) & ~ (all_0_39_39 = all_0_43_43) & ~ (all_0_39_39 = all_0_47_47) & ~ (all_0_39_39 = all_0_51_51) & ~ (all_0_39_39 = all_0_56_56) & ~ (all_0_39_39 = e0) & ~ (all_0_40_40 = all_0_41_41) & ~ (all_0_40_40 = all_0_42_42) & ~ (all_0_40_40 = all_0_44_44) & ~ (all_0_40_40 = all_0_52_52) & ~ (all_0_40_40 = all_0_57_57) & ~ (all_0_40_40 = e4) & ~ (all_0_40_40 = e0) & ~ (all_0_41_41 = all_0_42_42) & ~ (all_0_41_41 = all_0_45_45) & ~ (all_0_41_41 = all_0_48_48) & ~ (all_0_41_41 = all_0_53_53) & ~ (all_0_41_41 = all_0_58_58) & ~ (all_0_41_41 = e0) & ~ (all_0_42_42 = all_0_46_46) & ~ (all_0_42_42 = all_0_49_49) & ~ (all_0_42_42 = all_0_54_54) & ~ (all_0_42_42 = all_0_59_59) & ~ (all_0_42_42 = e0) & ~ (all_0_43_43 = all_0_44_44) & ~ (all_0_43_43 = all_0_45_45) & ~ (all_0_43_43 = all_0_46_46) & ~ (all_0_43_43 = all_0_47_47) & ~ (all_0_43_43 = all_0_51_51) & ~ (all_0_43_43 = all_0_56_56) & ~ (all_0_43_43 = e1) & ~ (all_0_44_44 = all_0_45_45) & ~ (all_0_44_44 = all_0_46_46) & ~ (all_0_44_44 = all_0_52_52) & ~ (all_0_44_44 = all_0_57_57) & ~ (all_0_44_44 = e4) & ~ (all_0_44_44 = e1) & ~ (all_0_45_45 = all_0_46_46) & ~ (all_0_45_45 = all_0_48_48) & ~ (all_0_45_45 = all_0_53_53) & ~ (all_0_45_45 = all_0_58_58) & ~ (all_0_45_45 = e1) & ~ (all_0_46_46 = all_0_49_49) & ~ (all_0_46_46 = all_0_54_54) & ~ (all_0_46_46 = all_0_59_59) & ~ (all_0_46_46 = e1) & ~ (all_0_47_47 = all_0_48_48) & ~ (all_0_47_47 = all_0_49_49) & ~ (all_0_47_47 = all_0_51_51) & ~ (all_0_47_47 = all_0_56_56) & ~ (all_0_47_47 = e4) & ~ (all_0_47_47 = e3) & ~ (all_0_48_48 = all_0_49_49) & ~ (all_0_48_48 = all_0_53_53) & ~ (all_0_48_48 = all_0_58_58) & ~ (all_0_48_48 = e4) & ~ (all_0_48_48 = e3) & ~ (all_0_49_49 = all_0_54_54) & ~ (all_0_49_49 = all_0_59_59) & ~ (all_0_49_49 = e4) & ~ (all_0_49_49 = e3) & ~ (all_0_50_50 = all_0_51_51) & ~ (all_0_50_50 = all_0_52_52) & ~ (all_0_50_50 = all_0_53_53) & ~ (all_0_50_50 = all_0_54_54) & ~ (all_0_50_50 = all_0_55_55) & ~ (all_0_50_50 = e3) & ~ (all_0_50_50 = e1) & ~ (all_0_50_50 = e0) & ~ (all_0_51_51 = all_0_52_52) & ~ (all_0_51_51 = all_0_53_53) & ~ (all_0_51_51 = all_0_54_54) & ~ (all_0_51_51 = all_0_56_56) & ~ (all_0_52_52 = all_0_53_53) & ~ (all_0_52_52 = all_0_54_54) & ~ (all_0_52_52 = all_0_57_57) & ~ (all_0_52_52 = e4) & ~ (all_0_53_53 = all_0_54_54) & ~ (all_0_53_53 = all_0_58_58) & ~ (all_0_54_54 = all_0_59_59) & ~ (all_0_55_55 = all_0_56_56) & ~ (all_0_55_55 = all_0_57_57) & ~ (all_0_55_55 = all_0_58_58) & ~ (all_0_55_55 = all_0_59_59) & ~ (all_0_55_55 = e3) & ~ (all_0_55_55 = e1) & ~ (all_0_55_55 = e0) & ~ (all_0_56_56 = all_0_57_57) & ~ (all_0_56_56 = all_0_58_58) & ~ (all_0_56_56 = all_0_59_59) & ~ (all_0_57_57 = all_0_58_58) & ~ (all_0_57_57 = all_0_59_59) & ~ (all_0_57_57 = e4) & ~ (all_0_58_58 = all_0_59_59) & ~ (e4 = e3) & ~ (e4 = e2) & ~ (e4 = e1) & ~ (e4 = e0) & ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ (e1 = e0) & op(unit, e4) = e4 & op(unit, e3) = e3 & op(unit, e2) = e2 & op(unit, e1) = e1 & op(unit, e0) = e0 & op(e4, all_0_39_39) = all_0_5_5 & op(e4, all_0_40_40) = all_0_14_14 & op(e4, all_0_41_41) = all_0_22_22 & op(e4, all_0_42_42) = all_0_31_31 & op(e4, all_0_50_50) = all_0_0_0 & op(e4, all_0_55_55) = all_0_2_2 & op(e4, unit) = e4 & op(e4, e4) = e0 & op(e4, e3) = all_0_39_39 & op(e4, e2) = all_0_40_40 & op(e4, e1) = all_0_41_41 & op(e4, e0) = all_0_42_42 & op(e3, all_0_39_39) = all_0_4_4 & op(e3, all_0_43_43) = all_0_6_6 & op(e3, all_0_44_44) = all_0_16_16 & op(e3, all_0_45_45) = all_0_24_24 & op(e3, all_0_46_46) = all_0_33_33 & op(e3, all_0_47_47) = all_0_7_7 & op(e3, all_0_51_51) = all_0_9_9 & op(e3, all_0_56_56) = all_0_11_11 & op(e3, unit) = e3 & op(e3, e4) = e1 & op(e3, e3) = all_0_43_43 & op(e3, e2) = all_0_44_44 & op(e3, e1) = all_0_45_45 & op(e3, e0) = all_0_46_46 & op(e2, all_0_40_40) = all_0_13_13 & op(e2, all_0_44_44) = all_0_15_15 & op(e2, all_0_47_47) = all_0_8_8 & op(e2, all_0_48_48) = all_0_26_26 & op(e2, all_0_49_49) = all_0_35_35 & op(e2, all_0_52_52) = all_0_17_17 & op(e2, all_0_57_57) = all_0_19_19 & op(e2, unit) = e2 & op(e2, e4) = e3 & op(e2, e3) = all_0_47_47 & op(e2, e2) = e4 & op(e2, e1) = all_0_48_48 & op(e2, e0) = all_0_49_49 & op(e1, all_0_41_41) = all_0_21_21 & op(e1, all_0_45_45) = all_0_23_23 & op(e1, all_0_48_48) = all_0_25_25 & op(e1, all_0_50_50) = all_0_1_1 & op(e1, all_0_51_51) = all_0_10_10 & op(e1, all_0_52_52) = all_0_18_18 & op(e1, all_0_53_53) = all_0_27_27 & op(e1, all_0_54_54) = all_0_37_37 & op(e1, all_0_58_58) = all_0_28_28 & op(e1, unit) = e1 & op(e1, e4) = all_0_50_50 & op(e1, e3) = all_0_51_51 & op(e1, e2) = all_0_52_52 & op(e1, e1) = all_0_53_53 & op(e1, e0) = all_0_54_54 & op(e0, all_0_42_42) = all_0_30_30 & op(e0, all_0_46_46) = all_0_32_32 & op(e0, all_0_49_49) = all_0_34_34 & op(e0, all_0_54_54) = all_0_36_36 & op(e0, all_0_55_55) = all_0_3_3 & op(e0, all_0_56_56) = all_0_12_12 & op(e0, all_0_57_57) = all_0_20_20 & op(e0, all_0_58_58) = all_0_29_29 & op(e0, all_0_59_59) = all_0_38_38 & op(e0, unit) = e0 & op(e0, e4) = all_0_55_55 & op(e0, e3) = all_0_56_56 & op(e0, e2) = all_0_57_57 & op(e0, e1) = all_0_58_58 & op(e0, e0) = all_0_59_59 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) & (all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e2 | all_0_39_39 = e1) & (all_0_39_39 = e4 | all_0_41_41 = e4 | all_0_42_42 = e4) & (all_0_39_39 = e4 | all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4) & (all_0_39_39 = e3 | all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3) & (all_0_39_39 = e3 | all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3) & (all_0_39_39 = e2 | all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2) & (all_0_39_39 = e2 | all_0_43_43 = e2 | all_0_47_47 = e2 | all_0_51_51 = e2 | all_0_56_56 = e2) & (all_0_39_39 = e2 | (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))) & (all_0_39_39 = e1 | all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1) & (all_0_39_39 = e1 | all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1) & (all_0_40_40 = e3 | all_0_40_40 = e2 | all_0_40_40 = e1) & (all_0_40_40 = e3 | all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3) & (all_0_40_40 = e2 | all_0_44_44 = e2 | all_0_52_52 = e2 | all_0_57_57 = e2) & (all_0_40_40 = e1 | all_0_52_52 = e1 | all_0_57_57 = e1) & (all_0_41_41 = e4 | all_0_41_41 = e3 | all_0_41_41 = e2 | all_0_41_41 = e1) & (all_0_41_41 = e4 | all_0_45_45 = e4 | all_0_53_53 = e4 | all_0_58_58 = e4) & (all_0_41_41 = e3 | all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3) & (all_0_41_41 = e2 | all_0_45_45 = e2 | all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2) & (all_0_41_41 = e1 | all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1) & (all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e2 | all_0_42_42 = e1) & (all_0_42_42 = e4 | all_0_46_46 = e4 | all_0_54_54 = e4 | all_0_59_59 = e4) & (all_0_42_42 = e3 | all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3) & (all_0_42_42 = e2 | all_0_46_46 = e2 | all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2) & (all_0_42_42 = e1 | all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1) & (all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e2 | all_0_43_43 = e0) & (all_0_43_43 = e4 | all_0_45_45 = e4 | all_0_46_46 = e4) & (all_0_43_43 = e3 | all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3) & (all_0_43_43 = e2 | all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2) & (all_0_43_43 = e0 | all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0) & (all_0_43_43 = e0 | all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0) & (all_0_44_44 = e3 | all_0_44_44 = e2 | all_0_44_44 = e0) & (all_0_44_44 = e0 | all_0_52_52 = e0 | all_0_57_57 = e0) & (all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e2 | all_0_45_45 = e0) & (all_0_45_45 = e0 | all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0) & (all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e2 | all_0_46_46 = e0) & (all_0_46_46 = e0 | all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0) & (all_0_47_47 = e2 | all_0_47_47 = e1 | all_0_47_47 = e0) & (all_0_47_47 = e2 | all_0_48_48 = e2 | all_0_49_49 = e2) & (all_0_47_47 = e1 | all_0_48_48 = e1 | all_0_49_49 = e1) & (all_0_47_47 = e0 | all_0_48_48 = e0 | all_0_49_49 = e0) & (all_0_48_48 = e2 | all_0_48_48 = e1 | all_0_48_48 = e0) & (all_0_49_49 = e2 | all_0_49_49 = e1 | all_0_49_49 = e0) & (all_0_50_50 = e4 | all_0_50_50 = e2) & (all_0_50_50 = e4 | all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4) & (all_0_50_50 = e4 | all_0_55_55 = e4) & (all_0_50_50 = e2 | all_0_51_51 = e2 | all_0_52_52 = e2 | all_0_53_53 = e2 | all_0_54_54 = e2) & (all_0_50_50 = e2 | all_0_55_55 = e2) & (all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e2 | all_0_51_51 = e1 | all_0_51_51 = e0) & (all_0_51_51 = e3 | all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3) & (all_0_51_51 = e1 | all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1) & (all_0_51_51 = e0 | all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0) & (all_0_52_52 = e3 | all_0_52_52 = e2 | all_0_52_52 = e1 | all_0_52_52 = e0) & (all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e2 | all_0_53_53 = e1 | all_0_53_53 = e0) & (all_0_54_54 = e4 | all_0_54_54 = e3 | all_0_54_54 = e2 | all_0_54_54 = e1 | all_0_54_54 = e0) & (all_0_55_55 = e4 | all_0_55_55 = e2) & (all_0_55_55 = e4 | all_0_56_56 = e4 | all_0_58_58 = e4 | all_0_59_59 = e4) & (all_0_55_55 = e2 | all_0_56_56 = e2 | all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2) & (all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e2 | all_0_56_56 = e1 | all_0_56_56 = e0) & (all_0_56_56 = e3 | all_0_57_57 = e3 | all_0_58_58 = e3 | all_0_59_59 = e3) & (all_0_56_56 = e1 | all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1) & (all_0_56_56 = e0 | all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0) & (all_0_57_57 = e3 | all_0_57_57 = e2 | all_0_57_57 = e1 | all_0_57_57 = e0) & (all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e2 | all_0_58_58 = e1 | all_0_58_58 = e0) & (all_0_59_59 = e4 | all_0_59_59 = e3 | all_0_59_59 = e2 | all_0_59_59 = e1 | all_0_59_59 = e0) & (unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0) & ((all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3)) | (all_0_9_9 = e1 & ~ (all_0_10_10 = e3)) | (all_0_11_11 = e0 & ~ (all_0_12_12 = e3))) & ((all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e0 & ~ (all_0_20_20 = e2))) & ((all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1)) | (all_0_28_28 = e0 & ~ (all_0_29_29 = e1))) & ((all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0)) | (all_0_34_34 = e2 & ~ (all_0_35_35 = e0)) | (all_0_36_36 = e1 & ~ (all_0_37_37 = e0))) & ((all_0_42_42 = e4 & ~ (all_0_45_45 = e0) & ~ (all_0_47_47 = e0) & ~ (unit = e0) & ( ~ (all_0_43_43 = e0) | all_0_46_46 = e3) & ( ~ (all_0_44_44 = e0) | all_0_46_46 = e2) & ( ~ (all_0_48_48 = e0) | all_0_49_49 = e1) & ( ~ (all_0_51_51 = e0) | all_0_54_54 = e3) & ( ~ (all_0_52_52 = e0) | all_0_54_54 = e2) & ( ~ (all_0_53_53 = e0) | all_0_54_54 = e1) & ( ~ (all_0_56_56 = e0) | all_0_59_59 = e3) & ( ~ (all_0_57_57 = e0) | all_0_59_59 = e2) & ( ~ (all_0_58_58 = e0) | all_0_59_59 = e1)) | (all_0_45_45 = e4 & ~ (all_0_42_42 = e1) & ~ (all_0_47_47 = e1) & ~ (unit = e1) & ( ~ (all_0_39_39 = e1) | all_0_41_41 = e3) & ( ~ (all_0_40_40 = e1) | all_0_41_41 = e2) & ( ~ (all_0_49_49 = e1) | all_0_48_48 = e0) & ( ~ (all_0_51_51 = e1) | all_0_53_53 = e3) & ( ~ (all_0_52_52 = e1) | all_0_53_53 = e2) & ( ~ (all_0_54_54 = e1) | all_0_53_53 = e0) & ( ~ (all_0_56_56 = e1) | all_0_58_58 = e3) & ( ~ (all_0_57_57 = e1) | all_0_58_58 = e2) & ( ~ (all_0_59_59 = e1) | all_0_58_58 = e0)) | ( ~ (all_0_42_42 = e2) & ~ (all_0_45_45 = e2) & ~ (all_0_47_47 = e2) & ~ (all_0_48_48 = e2) & ~ (all_0_49_49 = e2) & ~ (all_0_50_50 = e2) & ~ (all_0_55_55 = e2) & ( ~ (all_0_39_39 = e2) | (all_0_40_40 = e3 & ~ (unit = e2))) & ( ~ (all_0_40_40 = e2) | ~ (unit = e2)) & ( ~ (all_0_41_41 = e2) | (all_0_40_40 = e1 & ~ (unit = e2))) & ( ~ (all_0_43_43 = e2) | (all_0_44_44 = e3 & ~ (unit = e2))) & ( ~ (all_0_44_44 = e2) | ~ (unit = e2)) & ( ~ (all_0_46_46 = e2) | (all_0_44_44 = e0 & ~ (unit = e2))) & ( ~ (all_0_51_51 = e2) | (all_0_52_52 = e3 & ~ (unit = e2))) & ( ~ (all_0_52_52 = e2) | ~ (unit = e2)) & ( ~ (all_0_53_53 = e2) | (all_0_52_52 = e1 & ~ (unit = e2))) & ( ~ (all_0_54_54 = e2) | (all_0_52_52 = e0 & ~ (unit = e2))) & ( ~ (all_0_56_56 = e2) | (all_0_57_57 = e3 & ~ (unit = e2))) & ( ~ (all_0_57_57 = e2) | ~ (unit = e2)) & ( ~ (all_0_58_58 = e2) | (all_0_57_57 = e1 & ~ (unit = e2))) & ( ~ (all_0_59_59 = e2) | (all_0_57_57 = e0 & ~ (unit = e2)))))
% 18.88/5.01 |
% 18.88/5.01 | Applying alpha-rule on (1) yields:
% 18.88/5.01 | (2) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e2 | all_0_58_58 = e1 | all_0_58_58 = e0
% 18.88/5.01 | (3) ~ (all_0_43_43 = all_0_46_46)
% 18.88/5.01 | (4) ~ (all_0_48_48 = e3)
% 18.88/5.02 | (5) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3)) | (all_0_9_9 = e1 & ~ (all_0_10_10 = e3)) | (all_0_11_11 = e0 & ~ (all_0_12_12 = e3))
% 18.88/5.02 | (6) op(e4, e3) = all_0_39_39
% 18.88/5.02 | (7) op(e3, all_0_56_56) = all_0_11_11
% 18.88/5.02 | (8) all_0_39_39 = e2 | (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 18.88/5.02 | (9) op(e4, all_0_50_50) = all_0_0_0
% 18.88/5.02 | (10) all_0_47_47 = e0 | all_0_48_48 = e0 | all_0_49_49 = e0
% 18.88/5.02 | (11) ~ (e4 = e0)
% 18.88/5.02 | (12) op(e1, all_0_50_50) = all_0_1_1
% 18.88/5.02 | (13) op(e1, e0) = all_0_54_54
% 18.88/5.02 | (14) all_0_43_43 = e4 | all_0_45_45 = e4 | all_0_46_46 = e4
% 18.88/5.02 | (15) all_0_41_41 = e1 | all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 18.88/5.02 | (16) ~ (all_0_51_51 = all_0_56_56)
% 18.88/5.02 | (17) all_0_40_40 = e3 | all_0_40_40 = e2 | all_0_40_40 = e1
% 18.88/5.02 | (18) ~ (all_0_39_39 = all_0_40_40)
% 18.88/5.02 | (19) all_0_51_51 = e1 | all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 18.88/5.02 | (20) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e2 | all_0_56_56 = e1 | all_0_56_56 = e0
% 18.88/5.02 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 18.88/5.02 | (22) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e2 | all_0_43_43 = e0
% 18.88/5.02 | (23) op(e3, e1) = all_0_45_45
% 18.88/5.02 | (24) op(e3, e4) = e1
% 18.88/5.02 | (25) ~ (all_0_55_55 = e0)
% 18.88/5.02 | (26) op(unit, e3) = e3
% 18.88/5.02 | (27) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e2 | all_0_53_53 = e1 | all_0_53_53 = e0
% 18.88/5.02 | (28) all_0_55_55 = e2 | all_0_56_56 = e2 | all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 18.88/5.02 | (29) all_0_39_39 = e4 | all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 18.88/5.02 | (30) ~ (all_0_51_51 = all_0_53_53)
% 18.88/5.02 | (31) ~ (all_0_50_50 = all_0_52_52)
% 18.88/5.02 | (32) all_0_39_39 = e4 | all_0_41_41 = e4 | all_0_42_42 = e4
% 18.88/5.02 | (33) ~ (all_0_48_48 = e4)
% 18.88/5.02 | (34) ~ (all_0_47_47 = all_0_51_51)
% 18.88/5.02 | (35) ~ (all_0_40_40 = all_0_44_44)
% 18.88/5.02 | (36) op(e0, all_0_42_42) = all_0_30_30
% 18.88/5.02 | (37) op(e2, unit) = e2
% 18.88/5.02 | (38) op(e2, all_0_49_49) = all_0_35_35
% 18.88/5.02 | (39) all_0_39_39 = e1 | all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1
% 18.88/5.02 | (40) all_0_41_41 = e2 | all_0_45_45 = e2 | all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 18.88/5.02 | (41) ~ (e4 = e3)
% 18.88/5.02 | (42) op(unit, e1) = e1
% 18.88/5.02 | (43) all_0_56_56 = e1 | all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 18.88/5.02 | (44) op(e0, all_0_56_56) = all_0_12_12
% 18.88/5.02 | (45) op(e4, all_0_40_40) = all_0_14_14
% 18.88/5.02 | (46) op(e1, all_0_53_53) = all_0_27_27
% 18.88/5.02 | (47) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e2 | all_0_39_39 = e1
% 18.88/5.02 | (48) ~ (all_0_47_47 = all_0_48_48)
% 18.88/5.02 | (49) op(e1, all_0_54_54) = all_0_37_37
% 18.88/5.02 | (50) all_0_49_49 = e2 | all_0_49_49 = e1 | all_0_49_49 = e0
% 18.88/5.02 | (51) op(e3, all_0_43_43) = all_0_6_6
% 18.88/5.02 | (52) op(e0, e4) = all_0_55_55
% 18.88/5.02 | (53) ~ (all_0_39_39 = all_0_56_56)
% 18.88/5.02 | (54) all_0_41_41 = e4 | all_0_45_45 = e4 | all_0_53_53 = e4 | all_0_58_58 = e4
% 18.88/5.02 | (55) op(e4, e0) = all_0_42_42
% 18.88/5.02 | (56) op(e0, all_0_57_57) = all_0_20_20
% 18.88/5.02 | (57) ~ (all_0_55_55 = e3)
% 18.88/5.02 | (58) ~ (e2 = e0)
% 18.88/5.02 | (59) ~ (all_0_46_46 = all_0_54_54)
% 18.88/5.02 | (60) all_0_54_54 = e4 | all_0_54_54 = e3 | all_0_54_54 = e2 | all_0_54_54 = e1 | all_0_54_54 = e0
% 18.88/5.02 | (61) op(e4, all_0_42_42) = all_0_31_31
% 18.88/5.02 | (62) ~ (all_0_52_52 = all_0_54_54)
% 18.88/5.02 | (63) all_0_51_51 = e0 | all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 18.88/5.02 | (64) ~ (all_0_40_40 = e4)
% 18.88/5.02 | (65) unit = e4 | unit = e3 | unit = e2 | unit = e1 | unit = e0
% 18.88/5.02 | (66) op(e0, e0) = all_0_59_59
% 18.88/5.02 | (67) op(e1, all_0_58_58) = all_0_28_28
% 18.88/5.02 | (68) ~ (all_0_45_45 = all_0_58_58)
% 18.88/5.02 | (69) op(e2, all_0_52_52) = all_0_17_17
% 18.88/5.02 | (70) op(e3, unit) = e3
% 18.88/5.02 | (71) ~ (all_0_52_52 = all_0_53_53)
% 18.88/5.02 | (72) ~ (e3 = e0)
% 18.88/5.02 | (73) all_0_55_55 = e4 | all_0_56_56 = e4 | all_0_58_58 = e4 | all_0_59_59 = e4
% 18.88/5.02 | (74) op(e3, e2) = all_0_44_44
% 18.88/5.02 | (75) op(e0, e1) = all_0_58_58
% 18.88/5.02 | (76) op(e2, all_0_48_48) = all_0_26_26
% 18.88/5.02 | (77) ~ (all_0_50_50 = e3)
% 18.88/5.02 | (78) op(e4, e4) = e0
% 18.88/5.02 | (79) op(e1, all_0_41_41) = all_0_21_21
% 18.88/5.02 | (80) ~ (all_0_50_50 = all_0_51_51)
% 18.88/5.02 | (81) ~ (all_0_54_54 = all_0_59_59)
% 18.88/5.02 | (82) ~ (all_0_49_49 = all_0_59_59)
% 18.88/5.02 | (83) ~ (all_0_49_49 = e4)
% 18.88/5.02 | (84) all_0_42_42 = e1 | all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 18.88/5.02 | (85) op(e1, all_0_48_48) = all_0_25_25
% 18.88/5.02 | (86) all_0_52_52 = e3 | all_0_52_52 = e2 | all_0_52_52 = e1 | all_0_52_52 = e0
% 18.88/5.02 | (87) ~ (all_0_44_44 = e1)
% 18.88/5.02 | (88) ~ (all_0_40_40 = all_0_41_41)
% 18.88/5.02 | (89) op(e1, all_0_52_52) = all_0_18_18
% 18.88/5.02 | (90) op(e1, e1) = all_0_53_53
% 18.88/5.02 | (91) op(e1, e4) = all_0_50_50
% 18.88/5.02 | (92) op(e4, all_0_39_39) = all_0_5_5
% 18.88/5.03 | (93) all_0_51_51 = e3 | all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 18.88/5.03 | (94) all_0_41_41 = e4 | all_0_41_41 = e3 | all_0_41_41 = e2 | all_0_41_41 = e1
% 18.88/5.03 | (95) ~ (all_0_57_57 = all_0_59_59)
% 18.88/5.03 | (96) ~ (all_0_55_55 = e1)
% 18.88/5.03 | (97) op(e0, all_0_58_58) = all_0_29_29
% 18.88/5.03 | (98) ~ (all_0_42_42 = all_0_54_54)
% 18.88/5.03 | (99) op(e3, all_0_47_47) = all_0_7_7
% 18.88/5.03 | (100) op(unit, e4) = e4
% 18.88/5.03 | (101) op(e3, e3) = all_0_43_43
% 18.88/5.03 | (102) ~ (all_0_40_40 = e0)
% 18.88/5.03 | (103) ~ (all_0_42_42 = all_0_59_59)
% 18.88/5.03 | (104) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0)) | (all_0_34_34 = e2 & ~ (all_0_35_35 = e0)) | (all_0_36_36 = e1 & ~ (all_0_37_37 = e0))
% 18.88/5.03 | (105) op(e3, all_0_46_46) = all_0_33_33
% 18.88/5.03 | (106) ~ (all_0_41_41 = all_0_53_53)
% 18.88/5.03 | (107) ~ (all_0_42_42 = all_0_46_46)
% 18.88/5.03 | (108) op(e4, e1) = all_0_41_41
% 18.88/5.03 | (109) op(e1, all_0_51_51) = all_0_10_10
% 18.88/5.03 | (110) all_0_44_44 = e0 | all_0_52_52 = e0 | all_0_57_57 = e0
% 18.88/5.03 | (111) op(e1, unit) = e1
% 18.88/5.03 | (112) ~ (all_0_50_50 = e0)
% 18.88/5.03 | (113) all_0_40_40 = e2 | all_0_44_44 = e2 | all_0_52_52 = e2 | all_0_57_57 = e2
% 18.88/5.03 | (114) ~ (all_0_43_43 = e1)
% 18.88/5.03 | (115) ~ (all_0_47_47 = e3)
% 18.88/5.03 | (116) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e2 | all_0_42_42 = e1
% 18.88/5.03 | (117) ~ (all_0_44_44 = all_0_45_45)
% 18.88/5.03 | (118) op(e1, e2) = all_0_52_52
% 18.88/5.03 | (119) ~ (all_0_53_53 = all_0_54_54)
% 18.88/5.03 | (120) op(e2, e4) = e3
% 18.88/5.03 | (121) ~ (all_0_44_44 = all_0_52_52)
% 18.88/5.03 | (122) ~ (all_0_41_41 = all_0_45_45)
% 18.88/5.03 | (123) all_0_55_55 = e4 | all_0_55_55 = e2
% 18.88/5.03 | (124) ~ (all_0_52_52 = all_0_57_57)
% 18.88/5.03 | (125) op(e1, all_0_45_45) = all_0_23_23
% 18.88/5.03 | (126) ~ (all_0_39_39 = all_0_51_51)
% 18.88/5.03 | (127) ~ (all_0_53_53 = all_0_58_58)
% 18.88/5.03 | (128) op(e2, e0) = all_0_49_49
% 18.88/5.03 | (129) all_0_39_39 = e2 | all_0_43_43 = e2 | all_0_47_47 = e2 | all_0_51_51 = e2 | all_0_56_56 = e2
% 18.88/5.03 | (130) ~ (all_0_56_56 = all_0_59_59)
% 18.88/5.03 | (131) all_0_47_47 = e2 | all_0_48_48 = e2 | all_0_49_49 = e2
% 18.88/5.03 | (132) all_0_50_50 = e4 | all_0_55_55 = e4
% 18.88/5.03 | (133) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2)) | (all_0_19_19 = e0 & ~ (all_0_20_20 = e2))
% 18.88/5.03 | (134) all_0_57_57 = e3 | all_0_57_57 = e2 | all_0_57_57 = e1 | all_0_57_57 = e0
% 18.88/5.03 | (135) op(e4, e2) = all_0_40_40
% 18.88/5.03 | (136) op(e0, all_0_59_59) = all_0_38_38
% 18.88/5.03 | (137) ~ (all_0_43_43 = all_0_51_51)
% 18.88/5.03 | (138) ~ (all_0_43_43 = all_0_47_47)
% 18.88/5.03 | (139) all_0_45_45 = e0 | all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 18.88/5.03 | (140) ~ (all_0_55_55 = all_0_58_58)
% 18.88/5.03 | (141) ~ (all_0_50_50 = all_0_55_55)
% 18.88/5.03 | (142) ~ (all_0_45_45 = all_0_53_53)
% 18.88/5.03 | (143) all_0_43_43 = e0 | all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 18.88/5.03 | (144) ~ (e1 = e0)
% 18.88/5.03 | (145) ~ (all_0_47_47 = all_0_49_49)
% 18.88/5.03 | (146) ~ (e3 = e1)
% 18.88/5.03 | (147) ~ (all_0_47_47 = all_0_56_56)
% 18.88/5.03 | (148) ~ (e2 = e1)
% 18.88/5.03 | (149) all_0_44_44 = e3 | all_0_44_44 = e2 | all_0_44_44 = e0
% 18.88/5.03 | (150) ~ (all_0_46_46 = all_0_59_59)
% 18.88/5.03 | (151) op(e3, all_0_51_51) = all_0_9_9
% 18.88/5.03 | (152) ~ (all_0_52_52 = e4)
% 18.88/5.03 | (153) all_0_50_50 = e4 | all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 18.88/5.03 | (154) all_0_39_39 = e2 | all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 18.88/5.03 | (155) ~ (all_0_42_42 = e0)
% 18.88/5.03 | (156) op(e2, all_0_40_40) = all_0_13_13
% 18.88/5.03 | (157) ~ (all_0_39_39 = all_0_42_42)
% 18.88/5.03 | (158) ~ (all_0_49_49 = e3)
% 18.88/5.03 | (159) ~ (all_0_51_51 = all_0_54_54)
% 18.88/5.03 | (160) op(e0, unit) = e0
% 18.88/5.03 | (161) op(e3, all_0_39_39) = all_0_4_4
% 18.88/5.03 | (162) all_0_43_43 = e3 | all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 18.88/5.03 | (163) ~ (all_0_46_46 = e1)
% 18.88/5.03 | (164) ~ (all_0_39_39 = all_0_47_47)
% 18.88/5.04 | (165) ~ (all_0_39_39 = e0)
% 18.88/5.04 | (166) ~ (all_0_46_46 = all_0_49_49)
% 18.88/5.04 | (167) ~ (all_0_41_41 = all_0_48_48)
% 18.88/5.04 | (168) ~ (all_0_40_40 = all_0_57_57)
% 18.88/5.04 | (169) all_0_42_42 = e3 | all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 18.88/5.04 | (170) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e2 | all_0_51_51 = e1 | all_0_51_51 = e0
% 18.88/5.04 | (171) all_0_43_43 = e0 | all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 18.88/5.04 | (172) ~ (all_0_50_50 = e1)
% 18.88/5.04 | (173) ~ (all_0_57_57 = e4)
% 18.88/5.04 | (174) ~ (all_0_48_48 = all_0_58_58)
% 18.88/5.04 | (175) op(e1, e3) = all_0_51_51
% 18.88/5.04 | (176) ~ (all_0_50_50 = all_0_54_54)
% 18.88/5.04 | (177) op(unit, e2) = e2
% 18.88/5.04 | (178) ~ (all_0_48_48 = all_0_49_49)
% 18.88/5.04 | (179) op(e2, e1) = all_0_48_48
% 18.88/5.04 | (180) ~ (all_0_42_42 = all_0_49_49)
% 18.88/5.04 | (181) op(e0, all_0_46_46) = all_0_32_32
% 18.88/5.04 | (182) all_0_50_50 = e4 | all_0_50_50 = e2
% 18.88/5.04 | (183) op(e0, all_0_49_49) = all_0_34_34
% 18.88/5.04 | (184) all_0_39_39 = e3 | all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 18.88/5.04 | (185) ~ (all_0_50_50 = all_0_53_53)
% 18.88/5.04 | (186) ~ (all_0_43_43 = all_0_45_45)
% 18.88/5.04 | (187) ~ (all_0_40_40 = all_0_52_52)
% 18.88/5.04 | (188) ~ (all_0_41_41 = e0)
% 18.88/5.04 | (189) all_0_47_47 = e2 | all_0_47_47 = e1 | all_0_47_47 = e0
% 18.88/5.04 | (190) ~ (all_0_44_44 = e4)
% 18.88/5.04 | (191) op(e3, all_0_45_45) = all_0_24_24
% 18.88/5.04 | (192) all_0_47_47 = e1 | all_0_48_48 = e1 | all_0_49_49 = e1
% 18.88/5.04 | (193) all_0_40_40 = e3 | all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 18.88/5.04 | (194) ~ (all_0_51_51 = all_0_52_52)
% 18.88/5.04 | (195) all_0_42_42 = e4 | all_0_46_46 = e4 | all_0_54_54 = e4 | all_0_59_59 = e4
% 18.88/5.04 | (196) ~ (all_0_45_45 = all_0_48_48)
% 18.88/5.04 | (197) all_0_48_48 = e2 | all_0_48_48 = e1 | all_0_48_48 = e0
% 18.88/5.04 | (198) ~ (all_0_58_58 = all_0_59_59)
% 18.88/5.04 | (199) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e2 | all_0_46_46 = e0
% 18.88/5.04 | (200) all_0_39_39 = e1 | all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 18.88/5.04 | (201) ~ (all_0_45_45 = all_0_46_46)
% 18.88/5.04 | (202) op(e0, e3) = all_0_56_56
% 18.88/5.04 | (203) op(e4, all_0_41_41) = all_0_22_22
% 18.88/5.04 | (204) all_0_39_39 = e3 | all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 18.88/5.04 | (205) op(e2, all_0_44_44) = all_0_15_15
% 18.88/5.04 | (206) all_0_46_46 = e0 | all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 18.88/5.04 | (207) ~ (all_0_40_40 = all_0_42_42)
% 18.88/5.04 | (208) ~ (all_0_41_41 = all_0_58_58)
% 18.88/5.04 | (209) op(e4, unit) = e4
% 18.88/5.04 | (210) ~ (all_0_44_44 = all_0_46_46)
% 18.88/5.04 | (211) all_0_56_56 = e0 | all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 18.88/5.04 | (212) all_0_59_59 = e4 | all_0_59_59 = e3 | all_0_59_59 = e2 | all_0_59_59 = e1 | all_0_59_59 = e0
% 18.88/5.04 | (213) all_0_41_41 = e3 | all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 18.88/5.04 | (214) ~ (all_0_41_41 = all_0_42_42)
% 18.88/5.04 | (215) ~ (all_0_45_45 = e1)
% 18.88/5.04 | (216) all_0_42_42 = e2 | all_0_46_46 = e2 | all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 18.88/5.04 | (217) ~ (all_0_49_49 = all_0_54_54)
% 18.88/5.04 | (218) op(e2, all_0_47_47) = all_0_8_8
% 18.88/5.04 | (219) all_0_50_50 = e2 | all_0_51_51 = e2 | all_0_52_52 = e2 | all_0_53_53 = e2 | all_0_54_54 = e2
% 18.88/5.04 | (220) (all_0_42_42 = e4 & ~ (all_0_45_45 = e0) & ~ (all_0_47_47 = e0) & ~ (unit = e0) & ( ~ (all_0_43_43 = e0) | all_0_46_46 = e3) & ( ~ (all_0_44_44 = e0) | all_0_46_46 = e2) & ( ~ (all_0_48_48 = e0) | all_0_49_49 = e1) & ( ~ (all_0_51_51 = e0) | all_0_54_54 = e3) & ( ~ (all_0_52_52 = e0) | all_0_54_54 = e2) & ( ~ (all_0_53_53 = e0) | all_0_54_54 = e1) & ( ~ (all_0_56_56 = e0) | all_0_59_59 = e3) & ( ~ (all_0_57_57 = e0) | all_0_59_59 = e2) & ( ~ (all_0_58_58 = e0) | all_0_59_59 = e1)) | (all_0_45_45 = e4 & ~ (all_0_42_42 = e1) & ~ (all_0_47_47 = e1) & ~ (unit = e1) & ( ~ (all_0_39_39 = e1) | all_0_41_41 = e3) & ( ~ (all_0_40_40 = e1) | all_0_41_41 = e2) & ( ~ (all_0_49_49 = e1) | all_0_48_48 = e0) & ( ~ (all_0_51_51 = e1) | all_0_53_53 = e3) & ( ~ (all_0_52_52 = e1) | all_0_53_53 = e2) & ( ~ (all_0_54_54 = e1) | all_0_53_53 = e0) & ( ~ (all_0_56_56 = e1) | all_0_58_58 = e3) & ( ~ (all_0_57_57 = e1) | all_0_58_58 = e2) & ( ~ (all_0_59_59 = e1) | all_0_58_58 = e0)) | ( ~ (all_0_42_42 = e2) & ~ (all_0_45_45 = e2) & ~ (all_0_47_47 = e2) & ~ (all_0_48_48 = e2) & ~ (all_0_49_49 = e2) & ~ (all_0_50_50 = e2) & ~ (all_0_55_55 = e2) & ( ~ (all_0_39_39 = e2) | (all_0_40_40 = e3 & ~ (unit = e2))) & ( ~ (all_0_40_40 = e2) | ~ (unit = e2)) & ( ~ (all_0_41_41 = e2) | (all_0_40_40 = e1 & ~ (unit = e2))) & ( ~ (all_0_43_43 = e2) | (all_0_44_44 = e3 & ~ (unit = e2))) & ( ~ (all_0_44_44 = e2) | ~ (unit = e2)) & ( ~ (all_0_46_46 = e2) | (all_0_44_44 = e0 & ~ (unit = e2))) & ( ~ (all_0_51_51 = e2) | (all_0_52_52 = e3 & ~ (unit = e2))) & ( ~ (all_0_52_52 = e2) | ~ (unit = e2)) & ( ~ (all_0_53_53 = e2) | (all_0_52_52 = e1 & ~ (unit = e2))) & ( ~ (all_0_54_54 = e2) | (all_0_52_52 = e0 & ~ (unit = e2))) & ( ~ (all_0_56_56 = e2) | (all_0_57_57 = e3 & ~ (unit = e2))) & ( ~ (all_0_57_57 = e2) | ~ (unit = e2)) & ( ~ (all_0_58_58 = e2) | (all_0_57_57 = e1 & ~ (unit = e2))) & ( ~ (all_0_59_59 = e2) | (all_0_57_57 = e0 & ~ (unit = e2))))
% 18.88/5.05 | (221) ~ (all_0_55_55 = all_0_56_56)
% 18.88/5.05 | (222) op(e2, e2) = e4
% 18.88/5.05 | (223) ~ (all_0_56_56 = all_0_58_58)
% 18.88/5.05 | (224) ~ (e3 = e2)
% 18.88/5.05 | (225) all_0_43_43 = e2 | all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2
% 18.88/5.05 | (226) ~ (all_0_39_39 = all_0_41_41)
% 18.88/5.05 | (227) ~ (all_0_56_56 = all_0_57_57)
% 18.88/5.05 | (228) ~ (all_0_43_43 = all_0_44_44)
% 18.88/5.05 | (229) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1)) | (all_0_28_28 = e0 & ~ (all_0_29_29 = e1))
% 18.88/5.05 | (230) ~ (e4 = e2)
% 18.88/5.05 | (231) op(e2, e3) = all_0_47_47
% 18.88/5.05 | (232) ~ (all_0_43_43 = all_0_56_56)
% 18.88/5.05 | (233) op(e3, e0) = all_0_46_46
% 18.88/5.05 | (234) ~ (all_0_39_39 = all_0_43_43)
% 18.88/5.05 | (235) op(e0, all_0_54_54) = all_0_36_36
% 18.88/5.05 | (236) op(e4, all_0_55_55) = all_0_2_2
% 18.88/5.05 | (237) all_0_50_50 = e2 | all_0_55_55 = e2
% 18.88/5.05 | (238) ~ (all_0_55_55 = all_0_59_59)
% 18.88/5.05 | (239) op(unit, e0) = e0
% 18.88/5.05 | (240) ~ (all_0_44_44 = all_0_57_57)
% 18.88/5.05 | (241) op(e0, e2) = all_0_57_57
% 18.88/5.05 | (242) ~ (all_0_55_55 = all_0_57_57)
% 18.88/5.05 | (243) all_0_56_56 = e3 | all_0_57_57 = e3 | all_0_58_58 = e3 | all_0_59_59 = e3
% 18.88/5.05 | (244) op(e2, all_0_57_57) = all_0_19_19
% 18.88/5.05 | (245) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e2 | all_0_45_45 = e0
% 18.88/5.05 | (246) all_0_40_40 = e1 | all_0_52_52 = e1 | all_0_57_57 = e1
% 18.88/5.05 | (247) op(e3, all_0_44_44) = all_0_16_16
% 18.88/5.05 | (248) ~ (all_0_47_47 = e4)
% 18.88/5.05 | (249) op(e0, all_0_55_55) = all_0_3_3
% 18.88/5.05 | (250) ~ (all_0_48_48 = all_0_53_53)
% 18.88/5.05 | (251) ~ (e4 = e1)
% 18.88/5.05 | (252) ~ (all_0_57_57 = all_0_58_58)
% 18.88/5.05 |
% 18.88/5.05 +-Applying beta-rule and splitting (182), into two cases.
% 18.88/5.05 |-Branch one:
% 18.88/5.05 | (253) all_0_50_50 = e2
% 18.88/5.05 |
% 18.88/5.05 | Equations (253) can reduce 80 to:
% 18.88/5.05 | (254) ~ (all_0_51_51 = e2)
% 18.88/5.05 |
% 18.88/5.05 | Simplifying 254 yields:
% 18.88/5.05 | (255) ~ (all_0_51_51 = e2)
% 18.88/5.05 |
% 18.88/5.05 | Equations (253) can reduce 31 to:
% 18.88/5.05 | (256) ~ (all_0_52_52 = e2)
% 18.88/5.05 |
% 18.88/5.05 | Simplifying 256 yields:
% 18.88/5.05 | (257) ~ (all_0_52_52 = e2)
% 18.88/5.05 |
% 18.88/5.05 | Equations (253) can reduce 185 to:
% 18.88/5.05 | (258) ~ (all_0_53_53 = e2)
% 18.88/5.05 |
% 18.88/5.05 | Simplifying 258 yields:
% 18.88/5.05 | (259) ~ (all_0_53_53 = e2)
% 18.88/5.06 |
% 18.88/5.06 | Equations (253) can reduce 176 to:
% 18.88/5.06 | (260) ~ (all_0_54_54 = e2)
% 18.88/5.06 |
% 18.88/5.06 | Simplifying 260 yields:
% 18.88/5.06 | (261) ~ (all_0_54_54 = e2)
% 18.88/5.06 |
% 18.88/5.06 | Equations (253) can reduce 141 to:
% 18.88/5.06 | (262) ~ (all_0_55_55 = e2)
% 18.88/5.06 |
% 18.88/5.06 | Simplifying 262 yields:
% 18.88/5.06 | (263) ~ (all_0_55_55 = e2)
% 18.88/5.06 |
% 18.88/5.06 | Equations (253) can reduce 172 to:
% 18.88/5.06 | (148) ~ (e2 = e1)
% 18.88/5.06 |
% 18.88/5.06 | From (253) and (9) follows:
% 18.88/5.06 | (265) op(e4, e2) = all_0_0_0
% 18.88/5.06 |
% 18.88/5.06 | From (253) and (12) follows:
% 18.88/5.06 | (266) op(e1, e2) = all_0_1_1
% 18.88/5.06 |
% 18.88/5.06 | From (253) and (91) follows:
% 18.88/5.06 | (267) op(e1, e4) = e2
% 18.88/5.06 |
% 18.88/5.06 +-Applying beta-rule and splitting (123), into two cases.
% 18.88/5.06 |-Branch one:
% 18.88/5.06 | (268) all_0_55_55 = e2
% 18.88/5.06 |
% 18.88/5.06 | Equations (268) can reduce 263 to:
% 18.88/5.06 | (269) $false
% 18.88/5.06 |
% 19.28/5.06 |-The branch is then unsatisfiable
% 19.28/5.06 |-Branch two:
% 19.28/5.06 | (263) ~ (all_0_55_55 = e2)
% 19.28/5.06 | (271) all_0_55_55 = e4
% 19.28/5.06 |
% 19.28/5.06 | Equations (271) can reduce 221 to:
% 19.28/5.06 | (272) ~ (all_0_56_56 = e4)
% 19.28/5.06 |
% 19.28/5.06 | Simplifying 272 yields:
% 19.28/5.06 | (273) ~ (all_0_56_56 = e4)
% 19.28/5.06 |
% 19.28/5.06 | Equations (271) can reduce 242 to:
% 19.28/5.06 | (274) ~ (all_0_57_57 = e4)
% 19.28/5.06 |
% 19.28/5.06 | Simplifying 274 yields:
% 19.28/5.06 | (173) ~ (all_0_57_57 = e4)
% 19.28/5.06 |
% 19.28/5.06 | Equations (271) can reduce 140 to:
% 19.28/5.06 | (276) ~ (all_0_58_58 = e4)
% 19.28/5.06 |
% 19.28/5.06 | Simplifying 276 yields:
% 19.28/5.06 | (277) ~ (all_0_58_58 = e4)
% 19.28/5.06 |
% 19.28/5.06 | Equations (271) can reduce 238 to:
% 19.28/5.06 | (278) ~ (all_0_59_59 = e4)
% 19.28/5.06 |
% 19.28/5.06 | Simplifying 278 yields:
% 19.28/5.06 | (279) ~ (all_0_59_59 = e4)
% 19.28/5.06 |
% 19.28/5.06 | Equations (271) can reduce 57 to:
% 19.28/5.06 | (41) ~ (e4 = e3)
% 19.28/5.06 |
% 19.28/5.06 | Equations (271) can reduce 25 to:
% 19.28/5.06 | (11) ~ (e4 = e0)
% 19.28/5.06 |
% 19.28/5.06 | From (271) and (236) follows:
% 19.28/5.06 | (282) op(e4, e4) = all_0_2_2
% 19.28/5.06 |
% 19.28/5.06 | From (271) and (249) follows:
% 19.28/5.06 | (283) op(e0, e4) = all_0_3_3
% 19.28/5.06 |
% 19.28/5.06 | From (271) and (52) follows:
% 19.28/5.06 | (284) op(e0, e4) = e4
% 19.28/5.06 |
% 19.28/5.07 | Instantiating formula (21) with e4, e4, all_0_2_2, e0 and discharging atoms op(e4, e4) = all_0_2_2, op(e4, e4) = e0, yields:
% 19.28/5.07 | (285) all_0_2_2 = e0
% 19.28/5.07 |
% 19.28/5.07 | Instantiating formula (21) with e4, e2, all_0_0_0, all_0_40_40 and discharging atoms op(e4, e2) = all_0_0_0, op(e4, e2) = all_0_40_40, yields:
% 19.28/5.07 | (286) all_0_0_0 = all_0_40_40
% 19.28/5.07 |
% 19.28/5.07 | Instantiating formula (21) with e1, e2, all_0_1_1, all_0_52_52 and discharging atoms op(e1, e2) = all_0_1_1, op(e1, e2) = all_0_52_52, yields:
% 19.28/5.07 | (287) all_0_1_1 = all_0_52_52
% 19.28/5.07 |
% 19.28/5.07 | Instantiating formula (21) with e0, e4, e4, all_0_3_3 and discharging atoms op(e0, e4) = all_0_3_3, op(e0, e4) = e4, yields:
% 19.28/5.07 | (288) all_0_3_3 = e4
% 19.28/5.07 |
% 19.28/5.07 | From (285) and (282) follows:
% 19.28/5.07 | (78) op(e4, e4) = e0
% 19.28/5.07 |
% 19.28/5.07 | From (287) and (266) follows:
% 19.28/5.07 | (118) op(e1, e2) = all_0_52_52
% 19.28/5.07 |
% 19.28/5.07 | From (288) and (283) follows:
% 19.28/5.07 | (284) op(e0, e4) = e4
% 19.28/5.07 |
% 19.28/5.07 +-Applying beta-rule and splitting (220), into two cases.
% 19.28/5.07 |-Branch one:
% 19.28/5.07 | (292) (all_0_42_42 = e4 & ~ (all_0_45_45 = e0) & ~ (all_0_47_47 = e0) & ~ (unit = e0) & ( ~ (all_0_43_43 = e0) | all_0_46_46 = e3) & ( ~ (all_0_44_44 = e0) | all_0_46_46 = e2) & ( ~ (all_0_48_48 = e0) | all_0_49_49 = e1) & ( ~ (all_0_51_51 = e0) | all_0_54_54 = e3) & ( ~ (all_0_52_52 = e0) | all_0_54_54 = e2) & ( ~ (all_0_53_53 = e0) | all_0_54_54 = e1) & ( ~ (all_0_56_56 = e0) | all_0_59_59 = e3) & ( ~ (all_0_57_57 = e0) | all_0_59_59 = e2) & ( ~ (all_0_58_58 = e0) | all_0_59_59 = e1)) | (all_0_45_45 = e4 & ~ (all_0_42_42 = e1) & ~ (all_0_47_47 = e1) & ~ (unit = e1) & ( ~ (all_0_39_39 = e1) | all_0_41_41 = e3) & ( ~ (all_0_40_40 = e1) | all_0_41_41 = e2) & ( ~ (all_0_49_49 = e1) | all_0_48_48 = e0) & ( ~ (all_0_51_51 = e1) | all_0_53_53 = e3) & ( ~ (all_0_52_52 = e1) | all_0_53_53 = e2) & ( ~ (all_0_54_54 = e1) | all_0_53_53 = e0) & ( ~ (all_0_56_56 = e1) | all_0_58_58 = e3) & ( ~ (all_0_57_57 = e1) | all_0_58_58 = e2) & ( ~ (all_0_59_59 = e1) | all_0_58_58 = e0))
% 19.28/5.07 |
% 19.28/5.07 +-Applying beta-rule and splitting (292), into two cases.
% 19.28/5.07 |-Branch one:
% 19.28/5.07 | (293) all_0_42_42 = e4 & ~ (all_0_45_45 = e0) & ~ (all_0_47_47 = e0) & ~ (unit = e0) & ( ~ (all_0_43_43 = e0) | all_0_46_46 = e3) & ( ~ (all_0_44_44 = e0) | all_0_46_46 = e2) & ( ~ (all_0_48_48 = e0) | all_0_49_49 = e1) & ( ~ (all_0_51_51 = e0) | all_0_54_54 = e3) & ( ~ (all_0_52_52 = e0) | all_0_54_54 = e2) & ( ~ (all_0_53_53 = e0) | all_0_54_54 = e1) & ( ~ (all_0_56_56 = e0) | all_0_59_59 = e3) & ( ~ (all_0_57_57 = e0) | all_0_59_59 = e2) & ( ~ (all_0_58_58 = e0) | all_0_59_59 = e1)
% 19.28/5.07 |
% 19.28/5.07 | Applying alpha-rule on (293) yields:
% 19.28/5.07 | (294) ~ (all_0_48_48 = e0) | all_0_49_49 = e1
% 19.28/5.07 | (295) ~ (all_0_44_44 = e0) | all_0_46_46 = e2
% 19.28/5.07 | (296) ~ (all_0_56_56 = e0) | all_0_59_59 = e3
% 19.28/5.07 | (297) ~ (all_0_47_47 = e0)
% 19.28/5.07 | (298) ~ (all_0_57_57 = e0) | all_0_59_59 = e2
% 19.28/5.07 | (299) ~ (all_0_45_45 = e0)
% 19.28/5.07 | (300) ~ (all_0_52_52 = e0) | all_0_54_54 = e2
% 19.28/5.07 | (301) ~ (all_0_43_43 = e0) | all_0_46_46 = e3
% 19.28/5.07 | (302) ~ (all_0_51_51 = e0) | all_0_54_54 = e3
% 19.28/5.07 | (303) ~ (all_0_53_53 = e0) | all_0_54_54 = e1
% 19.28/5.07 | (304) ~ (unit = e0)
% 19.28/5.07 | (305) all_0_42_42 = e4
% 19.28/5.07 | (306) ~ (all_0_58_58 = e0) | all_0_59_59 = e1
% 19.28/5.07 |
% 19.28/5.07 | Equations (305) can reduce 157 to:
% 19.28/5.07 | (307) ~ (all_0_39_39 = e4)
% 19.28/5.07 |
% 19.28/5.07 | Equations (305) can reduce 214 to:
% 19.28/5.07 | (308) ~ (all_0_41_41 = e4)
% 19.28/5.07 |
% 19.28/5.07 | Equations (305) can reduce 107 to:
% 19.28/5.07 | (309) ~ (all_0_46_46 = e4)
% 19.28/5.07 |
% 19.28/5.07 | Simplifying 309 yields:
% 19.28/5.07 | (310) ~ (all_0_46_46 = e4)
% 19.28/5.07 |
% 19.28/5.07 | Equations (305) can reduce 98 to:
% 19.28/5.07 | (311) ~ (all_0_54_54 = e4)
% 19.28/5.07 |
% 19.28/5.07 | Simplifying 311 yields:
% 19.28/5.07 | (312) ~ (all_0_54_54 = e4)
% 19.28/5.07 |
% 19.28/5.07 | Equations (305) can reduce 103 to:
% 19.28/5.07 | (278) ~ (all_0_59_59 = e4)
% 19.28/5.07 |
% 19.28/5.07 | Simplifying 278 yields:
% 19.28/5.07 | (279) ~ (all_0_59_59 = e4)
% 19.28/5.07 |
% 19.28/5.07 | Equations (305) can reduce 155 to:
% 19.28/5.07 | (11) ~ (e4 = e0)
% 19.28/5.07 |
% 19.28/5.07 | From (305) and (61) follows:
% 19.28/5.07 | (316) op(e4, e4) = all_0_31_31
% 19.28/5.07 |
% 19.28/5.07 +-Applying beta-rule and splitting (300), into two cases.
% 19.28/5.07 |-Branch one:
% 19.28/5.07 | (317) ~ (all_0_52_52 = e0)
% 19.28/5.07 |
% 19.28/5.07 | Instantiating formula (21) with e4, e4, all_0_31_31, e0 and discharging atoms op(e4, e4) = all_0_31_31, op(e4, e4) = e0, yields:
% 19.28/5.07 | (318) all_0_31_31 = e0
% 19.28/5.07 |
% 19.28/5.07 +-Applying beta-rule and splitting (189), into two cases.
% 19.28/5.07 |-Branch one:
% 19.28/5.07 | (319) all_0_47_47 = e2
% 19.28/5.07 |
% 19.28/5.07 | Equations (319) can reduce 164 to:
% 19.28/5.07 | (320) ~ (all_0_39_39 = e2)
% 19.28/5.07 |
% 19.28/5.07 | Equations (319) can reduce 138 to:
% 19.28/5.07 | (321) ~ (all_0_43_43 = e2)
% 19.28/5.07 |
% 19.28/5.07 | Equations (319) can reduce 145 to:
% 19.28/5.07 | (322) ~ (all_0_49_49 = e2)
% 19.28/5.07 |
% 19.28/5.07 | Simplifying 322 yields:
% 19.28/5.07 | (323) ~ (all_0_49_49 = e2)
% 19.28/5.07 |
% 19.28/5.07 | Equations (319) can reduce 34 to:
% 19.28/5.07 | (254) ~ (all_0_51_51 = e2)
% 19.28/5.07 |
% 19.28/5.07 | Simplifying 254 yields:
% 19.28/5.07 | (255) ~ (all_0_51_51 = e2)
% 19.28/5.07 |
% 19.28/5.07 | Equations (319) can reduce 248 to:
% 19.28/5.07 | (326) ~ (e4 = e2)
% 19.28/5.07 |
% 19.28/5.07 | Simplifying 326 yields:
% 19.28/5.07 | (230) ~ (e4 = e2)
% 19.28/5.07 |
% 19.28/5.07 | Equations (319) can reduce 115 to:
% 19.28/5.07 | (328) ~ (e3 = e2)
% 19.28/5.07 |
% 19.28/5.07 | Simplifying 328 yields:
% 19.28/5.07 | (224) ~ (e3 = e2)
% 19.28/5.07 |
% 19.28/5.07 | Equations (319) can reduce 297 to:
% 19.28/5.07 | (58) ~ (e2 = e0)
% 19.28/5.07 |
% 19.28/5.07 | From (319) and (99) follows:
% 19.28/5.07 | (331) op(e3, e2) = all_0_7_7
% 19.28/5.07 |
% 19.28/5.07 | From (319) and (218) follows:
% 19.28/5.07 | (332) op(e2, e2) = all_0_8_8
% 19.28/5.07 |
% 19.28/5.07 | From (319) and (231) follows:
% 19.28/5.07 | (333) op(e2, e3) = e2
% 19.28/5.07 |
% 19.28/5.07 | Instantiating formula (21) with e3, e2, all_0_7_7, all_0_44_44 and discharging atoms op(e3, e2) = all_0_7_7, op(e3, e2) = all_0_44_44, yields:
% 19.28/5.08 | (334) all_0_7_7 = all_0_44_44
% 19.28/5.08 |
% 19.28/5.08 | Instantiating formula (21) with e2, e2, all_0_8_8, e4 and discharging atoms op(e2, e2) = all_0_8_8, op(e2, e2) = e4, yields:
% 19.28/5.08 | (335) all_0_8_8 = e4
% 19.28/5.08 |
% 19.28/5.08 | From (335) and (332) follows:
% 19.28/5.08 | (222) op(e2, e2) = e4
% 19.28/5.08 |
% 19.28/5.08 +-Applying beta-rule and splitting (50), into two cases.
% 19.28/5.08 |-Branch one:
% 19.28/5.08 | (337) all_0_49_49 = e2
% 19.28/5.08 |
% 19.28/5.08 | Equations (337) can reduce 323 to:
% 19.28/5.08 | (269) $false
% 19.28/5.08 |
% 19.28/5.08 |-The branch is then unsatisfiable
% 19.28/5.08 |-Branch two:
% 19.28/5.08 | (323) ~ (all_0_49_49 = e2)
% 19.28/5.08 | (340) all_0_49_49 = e1 | all_0_49_49 = e0
% 19.28/5.08 |
% 19.37/5.08 +-Applying beta-rule and splitting (149), into two cases.
% 19.37/5.08 |-Branch one:
% 19.37/5.08 | (341) all_0_44_44 = e2
% 19.37/5.08 |
% 19.37/5.08 | Equations (341) can reduce 35 to:
% 19.37/5.08 | (342) ~ (all_0_40_40 = e2)
% 19.37/5.08 |
% 19.37/5.08 | Equations (341) can reduce 210 to:
% 19.37/5.08 | (343) ~ (all_0_46_46 = e2)
% 19.37/5.08 |
% 19.37/5.08 | Simplifying 343 yields:
% 19.37/5.08 | (344) ~ (all_0_46_46 = e2)
% 19.37/5.08 |
% 19.37/5.08 | Equations (341) can reduce 190 to:
% 19.37/5.08 | (326) ~ (e4 = e2)
% 19.37/5.08 |
% 19.37/5.08 | Simplifying 326 yields:
% 19.37/5.08 | (230) ~ (e4 = e2)
% 19.37/5.08 |
% 19.37/5.08 | From (341) and (205) follows:
% 19.37/5.08 | (347) op(e2, e2) = all_0_15_15
% 19.37/5.08 |
% 19.37/5.08 +-Applying beta-rule and splitting (154), into two cases.
% 19.37/5.08 |-Branch one:
% 19.37/5.08 | (348) all_0_39_39 = e2
% 19.37/5.08 |
% 19.37/5.08 | Equations (348) can reduce 320 to:
% 19.37/5.08 | (269) $false
% 19.37/5.08 |
% 19.37/5.08 |-The branch is then unsatisfiable
% 19.37/5.08 |-Branch two:
% 19.37/5.08 | (320) ~ (all_0_39_39 = e2)
% 19.37/5.08 | (351) all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 19.37/5.08 |
% 19.37/5.08 +-Applying beta-rule and splitting (110), into two cases.
% 19.37/5.08 |-Branch one:
% 19.37/5.08 | (352) all_0_44_44 = e0
% 19.37/5.08 |
% 19.37/5.08 | Combining equations (341,352) yields a new equation:
% 19.37/5.08 | (353) e2 = e0
% 19.37/5.08 |
% 19.37/5.08 | Simplifying 353 yields:
% 19.37/5.08 | (354) e2 = e0
% 19.37/5.08 |
% 19.37/5.08 | Equations (354) can reduce 58 to:
% 19.37/5.08 | (269) $false
% 19.37/5.08 |
% 19.37/5.08 |-The branch is then unsatisfiable
% 19.37/5.08 |-Branch two:
% 19.37/5.08 | (356) ~ (all_0_44_44 = e0)
% 19.37/5.08 | (357) all_0_52_52 = e0 | all_0_57_57 = e0
% 19.37/5.08 |
% 19.37/5.08 +-Applying beta-rule and splitting (216), into two cases.
% 19.37/5.08 |-Branch one:
% 19.37/5.08 | (358) all_0_42_42 = e2
% 19.37/5.08 |
% 19.37/5.08 | Combining equations (305,358) yields a new equation:
% 19.37/5.08 | (359) e4 = e2
% 19.37/5.08 |
% 19.37/5.08 | Simplifying 359 yields:
% 19.37/5.08 | (360) e4 = e2
% 19.37/5.08 |
% 19.37/5.08 | Equations (360) can reduce 230 to:
% 19.37/5.08 | (269) $false
% 19.37/5.08 |
% 19.37/5.08 |-The branch is then unsatisfiable
% 19.37/5.08 |-Branch two:
% 19.37/5.08 | (362) ~ (all_0_42_42 = e2)
% 19.37/5.08 | (363) all_0_46_46 = e2 | all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 19.37/5.08 |
% 19.37/5.08 +-Applying beta-rule and splitting (363), into two cases.
% 19.37/5.08 |-Branch one:
% 19.37/5.08 | (364) all_0_46_46 = e2
% 19.37/5.08 |
% 19.37/5.08 | Equations (364) can reduce 344 to:
% 19.37/5.08 | (269) $false
% 19.37/5.08 |
% 19.37/5.08 |-The branch is then unsatisfiable
% 19.37/5.08 |-Branch two:
% 19.37/5.08 | (344) ~ (all_0_46_46 = e2)
% 19.37/5.08 | (367) all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 19.37/5.08 |
% 19.37/5.08 +-Applying beta-rule and splitting (367), into two cases.
% 19.37/5.08 |-Branch one:
% 19.37/5.08 | (337) all_0_49_49 = e2
% 19.37/5.08 |
% 19.37/5.08 | Equations (337) can reduce 323 to:
% 19.37/5.08 | (269) $false
% 19.37/5.08 |
% 19.37/5.08 |-The branch is then unsatisfiable
% 19.37/5.08 |-Branch two:
% 19.37/5.08 | (323) ~ (all_0_49_49 = e2)
% 19.37/5.08 | (371) all_0_54_54 = e2 | all_0_59_59 = e2
% 19.37/5.08 |
% 19.37/5.08 +-Applying beta-rule and splitting (371), into two cases.
% 19.37/5.08 |-Branch one:
% 19.37/5.08 | (372) all_0_54_54 = e2
% 19.37/5.08 |
% 19.37/5.08 | Equations (372) can reduce 261 to:
% 19.37/5.08 | (269) $false
% 19.37/5.08 |
% 19.37/5.08 |-The branch is then unsatisfiable
% 19.37/5.08 |-Branch two:
% 19.37/5.08 | (261) ~ (all_0_54_54 = e2)
% 19.37/5.08 | (375) all_0_59_59 = e2
% 19.37/5.08 |
% 19.37/5.08 | Equations (375) can reduce 150 to:
% 19.37/5.08 | (344) ~ (all_0_46_46 = e2)
% 19.37/5.08 |
% 19.37/5.08 | Equations (375) can reduce 130 to:
% 19.37/5.08 | (377) ~ (all_0_56_56 = e2)
% 19.37/5.08 |
% 19.37/5.08 | Equations (375) can reduce 95 to:
% 19.37/5.08 | (378) ~ (all_0_57_57 = e2)
% 19.37/5.08 |
% 19.37/5.08 | Equations (375) can reduce 279 to:
% 19.37/5.08 | (326) ~ (e4 = e2)
% 19.37/5.08 |
% 19.37/5.08 | Simplifying 326 yields:
% 19.37/5.08 | (230) ~ (e4 = e2)
% 19.37/5.08 |
% 19.37/5.08 | From (375) and (66) follows:
% 19.37/5.08 | (381) op(e0, e0) = e2
% 19.37/5.08 |
% 19.37/5.08 +-Applying beta-rule and splitting (351), into two cases.
% 19.37/5.08 |-Branch one:
% 19.37/5.08 | (382) all_0_40_40 = e2
% 19.37/5.08 |
% 19.37/5.08 | Equations (382) can reduce 342 to:
% 19.37/5.08 | (269) $false
% 19.37/5.08 |
% 19.37/5.08 |-The branch is then unsatisfiable
% 19.37/5.08 |-Branch two:
% 19.37/5.08 | (342) ~ (all_0_40_40 = e2)
% 19.37/5.08 | (385) all_0_41_41 = e2 | all_0_42_42 = e2
% 19.37/5.08 |
% 19.37/5.08 +-Applying beta-rule and splitting (40), into two cases.
% 19.37/5.08 |-Branch one:
% 19.37/5.08 | (386) all_0_41_41 = e2
% 19.37/5.08 |
% 19.37/5.08 | Equations (386) can reduce 226 to:
% 19.37/5.08 | (320) ~ (all_0_39_39 = e2)
% 19.37/5.08 |
% 19.37/5.08 | Equations (386) can reduce 88 to:
% 19.37/5.08 | (342) ~ (all_0_40_40 = e2)
% 19.37/5.08 |
% 19.37/5.08 | Equations (386) can reduce 122 to:
% 19.37/5.08 | (389) ~ (all_0_45_45 = e2)
% 19.37/5.08 |
% 19.37/5.08 | Simplifying 389 yields:
% 19.37/5.08 | (390) ~ (all_0_45_45 = e2)
% 19.37/5.08 |
% 19.37/5.08 | Equations (386) can reduce 208 to:
% 19.37/5.08 | (391) ~ (all_0_58_58 = e2)
% 19.37/5.08 |
% 19.37/5.08 | Simplifying 391 yields:
% 19.37/5.08 | (392) ~ (all_0_58_58 = e2)
% 19.37/5.08 |
% 19.37/5.08 +-Applying beta-rule and splitting (8), into two cases.
% 19.37/5.08 |-Branch one:
% 19.37/5.08 | (348) all_0_39_39 = e2
% 19.37/5.08 |
% 19.37/5.08 | Equations (348) can reduce 320 to:
% 19.37/5.08 | (269) $false
% 19.37/5.08 |
% 19.37/5.08 |-The branch is then unsatisfiable
% 19.37/5.08 |-Branch two:
% 19.37/5.08 | (320) ~ (all_0_39_39 = e2)
% 19.37/5.08 | (396) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 19.37/5.08 |
% 19.37/5.08 +-Applying beta-rule and splitting (357), into two cases.
% 19.37/5.08 |-Branch one:
% 19.37/5.08 | (397) all_0_52_52 = e0
% 19.37/5.08 |
% 19.37/5.08 | Equations (397) can reduce 317 to:
% 19.37/5.08 | (269) $false
% 19.37/5.08 |
% 19.37/5.08 |-The branch is then unsatisfiable
% 19.37/5.08 |-Branch two:
% 19.37/5.08 | (317) ~ (all_0_52_52 = e0)
% 19.37/5.08 | (400) all_0_57_57 = e0
% 19.37/5.08 |
% 19.37/5.08 | Equations (400) can reduce 227 to:
% 19.37/5.08 | (401) ~ (all_0_56_56 = e0)
% 19.37/5.08 |
% 19.37/5.08 | Equations (400) can reduce 252 to:
% 19.37/5.08 | (402) ~ (all_0_58_58 = e0)
% 19.37/5.08 |
% 19.37/5.08 | Simplifying 402 yields:
% 19.37/5.08 | (403) ~ (all_0_58_58 = e0)
% 19.37/5.08 |
% 19.37/5.08 | Equations (400) can reduce 173 to:
% 19.37/5.08 | (404) ~ (e4 = e0)
% 19.37/5.08 |
% 19.37/5.08 | Simplifying 404 yields:
% 19.37/5.08 | (11) ~ (e4 = e0)
% 19.37/5.08 |
% 19.37/5.08 | Equations (400) can reduce 378 to:
% 19.37/5.08 | (406) ~ (e2 = e0)
% 19.37/5.08 |
% 19.37/5.08 | Simplifying 406 yields:
% 19.37/5.08 | (58) ~ (e2 = e0)
% 19.37/5.08 |
% 19.37/5.08 | From (400) and (56) follows:
% 19.37/5.08 | (408) op(e0, e0) = all_0_20_20
% 19.37/5.08 |
% 19.37/5.08 +-Applying beta-rule and splitting (396), into two cases.
% 19.37/5.08 |-Branch one:
% 19.37/5.08 | (409) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 19.37/5.08 |
% 19.37/5.08 +-Applying beta-rule and splitting (409), into two cases.
% 19.37/5.08 |-Branch one:
% 19.37/5.08 | (410) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 19.37/5.08 |
% 19.37/5.08 | Applying alpha-rule on (410) yields:
% 19.37/5.08 | (411) all_0_0_0 = e1
% 19.37/5.08 | (412) ~ (all_0_1_1 = e4)
% 19.37/5.08 |
% 19.37/5.08 | Combining equations (411,286) yields a new equation:
% 19.37/5.08 | (413) all_0_40_40 = e1
% 19.37/5.08 |
% 19.37/5.08 | Equations (413) can reduce 342 to:
% 19.37/5.08 | (414) ~ (e2 = e1)
% 19.37/5.08 |
% 19.37/5.08 | Simplifying 414 yields:
% 19.37/5.08 | (148) ~ (e2 = e1)
% 19.37/5.08 |
% 19.37/5.08 | From (413) and (156) follows:
% 19.37/5.08 | (416) op(e2, e1) = all_0_13_13
% 19.37/5.08 |
% 19.37/5.08 +-Applying beta-rule and splitting (193), into two cases.
% 19.37/5.08 |-Branch one:
% 19.37/5.08 | (417) all_0_40_40 = e3
% 19.37/5.08 |
% 19.37/5.08 | Combining equations (413,417) yields a new equation:
% 19.37/5.08 | (418) e3 = e1
% 19.37/5.08 |
% 19.37/5.08 | Equations (418) can reduce 146 to:
% 19.37/5.08 | (269) $false
% 19.37/5.08 |
% 19.37/5.08 |-The branch is then unsatisfiable
% 19.37/5.08 |-Branch two:
% 19.37/5.08 | (420) ~ (all_0_40_40 = e3)
% 19.37/5.08 | (421) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 19.37/5.08 |
% 19.37/5.08 +-Applying beta-rule and splitting (421), into two cases.
% 19.37/5.08 |-Branch one:
% 19.37/5.08 | (422) all_0_44_44 = e3
% 19.37/5.08 |
% 19.37/5.08 | Combining equations (341,422) yields a new equation:
% 19.37/5.08 | (423) e3 = e2
% 19.37/5.08 |
% 19.37/5.08 | Equations (423) can reduce 224 to:
% 19.37/5.08 | (269) $false
% 19.37/5.08 |
% 19.37/5.08 |-The branch is then unsatisfiable
% 19.37/5.08 |-Branch two:
% 19.37/5.08 | (425) ~ (all_0_44_44 = e3)
% 19.37/5.08 | (426) all_0_52_52 = e3 | all_0_57_57 = e3
% 19.37/5.08 |
% 19.37/5.08 +-Applying beta-rule and splitting (426), into two cases.
% 19.37/5.08 |-Branch one:
% 19.37/5.08 | (427) all_0_52_52 = e3
% 19.37/5.08 |
% 19.37/5.09 | Equations (427) can reduce 194 to:
% 19.37/5.09 | (428) ~ (all_0_51_51 = e3)
% 19.37/5.09 |
% 19.37/5.09 | Equations (427) can reduce 62 to:
% 19.37/5.09 | (429) ~ (all_0_54_54 = e3)
% 19.37/5.09 |
% 19.37/5.09 | Simplifying 429 yields:
% 19.37/5.09 | (430) ~ (all_0_54_54 = e3)
% 19.37/5.09 |
% 19.37/5.09 | From (427) and (69) follows:
% 19.37/5.09 | (431) op(e2, e3) = all_0_17_17
% 19.37/5.09 |
% 19.37/5.09 +-Applying beta-rule and splitting (302), into two cases.
% 19.37/5.09 |-Branch one:
% 19.37/5.09 | (432) ~ (all_0_51_51 = e0)
% 19.37/5.09 |
% 19.37/5.09 +-Applying beta-rule and splitting (171), into two cases.
% 19.37/5.09 |-Branch one:
% 19.37/5.09 | (433) all_0_43_43 = e0
% 19.37/5.09 |
% 19.37/5.09 | Equations (433) can reduce 3 to:
% 19.37/5.09 | (434) ~ (all_0_46_46 = e0)
% 19.37/5.09 |
% 19.37/5.09 | Simplifying 434 yields:
% 19.37/5.09 | (435) ~ (all_0_46_46 = e0)
% 19.37/5.09 |
% 19.37/5.09 | Equations (433) can reduce 114 to:
% 19.37/5.09 | (436) ~ (e1 = e0)
% 19.37/5.09 |
% 19.37/5.09 | Simplifying 436 yields:
% 19.37/5.09 | (144) ~ (e1 = e0)
% 19.37/5.09 |
% 19.37/5.09 +-Applying beta-rule and splitting (14), into two cases.
% 19.37/5.09 |-Branch one:
% 19.37/5.09 | (438) all_0_43_43 = e4
% 19.37/5.09 |
% 19.37/5.09 | Combining equations (433,438) yields a new equation:
% 19.37/5.09 | (439) e4 = e0
% 19.37/5.09 |
% 19.37/5.09 | Equations (439) can reduce 11 to:
% 19.37/5.09 | (269) $false
% 19.37/5.09 |
% 19.37/5.09 |-The branch is then unsatisfiable
% 19.37/5.09 |-Branch two:
% 19.37/5.09 | (441) ~ (all_0_43_43 = e4)
% 19.37/5.09 | (442) all_0_45_45 = e4 | all_0_46_46 = e4
% 19.37/5.09 |
% 19.37/5.09 +-Applying beta-rule and splitting (184), into two cases.
% 19.37/5.09 |-Branch one:
% 19.37/5.09 | (443) all_0_39_39 = e3
% 19.37/5.09 |
% 19.37/5.09 +-Applying beta-rule and splitting (442), into two cases.
% 19.37/5.09 |-Branch one:
% 19.37/5.09 | (444) all_0_45_45 = e4
% 19.37/5.09 |
% 19.37/5.09 | Equations (444) can reduce 196 to:
% 19.37/5.09 | (445) ~ (all_0_48_48 = e4)
% 19.37/5.09 |
% 19.37/5.09 | Simplifying 445 yields:
% 19.37/5.09 | (33) ~ (all_0_48_48 = e4)
% 19.37/5.09 |
% 19.37/5.09 | Equations (444) can reduce 142 to:
% 19.37/5.09 | (447) ~ (all_0_53_53 = e4)
% 19.37/5.09 |
% 19.37/5.09 | Simplifying 447 yields:
% 19.37/5.09 | (448) ~ (all_0_53_53 = e4)
% 19.37/5.09 |
% 19.37/5.09 | Equations (444) can reduce 68 to:
% 19.37/5.09 | (276) ~ (all_0_58_58 = e4)
% 19.37/5.09 |
% 19.37/5.09 | Simplifying 276 yields:
% 19.37/5.09 | (277) ~ (all_0_58_58 = e4)
% 19.37/5.09 |
% 19.37/5.09 | Equations (444) can reduce 390 to:
% 19.37/5.09 | (230) ~ (e4 = e2)
% 19.37/5.09 |
% 19.37/5.09 | Equations (444) can reduce 215 to:
% 19.37/5.09 | (251) ~ (e4 = e1)
% 19.37/5.09 |
% 19.37/5.09 +-Applying beta-rule and splitting (153), into two cases.
% 19.37/5.09 |-Branch one:
% 19.37/5.09 | (453) all_0_50_50 = e4
% 19.37/5.09 |
% 19.37/5.09 | Combining equations (253,453) yields a new equation:
% 19.37/5.09 | (360) e4 = e2
% 19.37/5.09 |
% 19.37/5.09 | Equations (360) can reduce 230 to:
% 19.37/5.09 | (269) $false
% 19.37/5.09 |
% 19.37/5.09 |-The branch is then unsatisfiable
% 19.37/5.09 |-Branch two:
% 19.37/5.09 | (456) ~ (all_0_50_50 = e4)
% 19.37/5.09 | (457) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 19.37/5.09 |
% 19.37/5.09 +-Applying beta-rule and splitting (457), into two cases.
% 19.37/5.09 |-Branch one:
% 19.37/5.09 | (458) all_0_51_51 = e4
% 19.37/5.09 |
% 19.37/5.09 +-Applying beta-rule and splitting (301), into two cases.
% 19.37/5.09 |-Branch one:
% 19.37/5.09 | (459) ~ (all_0_43_43 = e0)
% 19.37/5.09 |
% 19.37/5.09 | Equations (433) can reduce 459 to:
% 19.37/5.09 | (269) $false
% 19.37/5.09 |
% 19.37/5.09 |-The branch is then unsatisfiable
% 19.37/5.09 |-Branch two:
% 19.37/5.09 | (433) all_0_43_43 = e0
% 19.37/5.09 | (462) all_0_46_46 = e3
% 19.37/5.09 |
% 19.37/5.09 | Equations (462) can reduce 163 to:
% 19.37/5.09 | (146) ~ (e3 = e1)
% 19.37/5.09 |
% 19.37/5.09 +-Applying beta-rule and splitting (200), into two cases.
% 19.37/5.09 |-Branch one:
% 19.37/5.09 | (464) all_0_39_39 = e1
% 19.37/5.09 |
% 19.37/5.09 | Combining equations (464,443) yields a new equation:
% 19.37/5.09 | (418) e3 = e1
% 19.37/5.09 |
% 19.37/5.09 | Equations (418) can reduce 146 to:
% 19.37/5.09 | (269) $false
% 19.37/5.09 |
% 19.37/5.09 |-The branch is then unsatisfiable
% 19.37/5.09 |-Branch two:
% 19.37/5.09 | (467) ~ (all_0_39_39 = e1)
% 19.37/5.09 | (468) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 19.37/5.09 |
% 19.37/5.09 +-Applying beta-rule and splitting (468), into two cases.
% 19.37/5.09 |-Branch one:
% 19.37/5.09 | (469) all_0_47_47 = e1
% 19.37/5.09 |
% 19.37/5.09 | Combining equations (319,469) yields a new equation:
% 19.37/5.09 | (470) e2 = e1
% 19.37/5.09 |
% 19.37/5.09 | Simplifying 470 yields:
% 19.37/5.09 | (471) e2 = e1
% 19.37/5.09 |
% 19.37/5.09 | Equations (471) can reduce 148 to:
% 19.37/5.09 | (269) $false
% 19.37/5.09 |
% 19.37/5.09 |-The branch is then unsatisfiable
% 19.37/5.09 |-Branch two:
% 19.37/5.09 | (473) ~ (all_0_47_47 = e1)
% 19.37/5.09 | (474) all_0_51_51 = e1 | all_0_56_56 = e1
% 19.37/5.09 |
% 19.37/5.09 +-Applying beta-rule and splitting (474), into two cases.
% 19.37/5.09 |-Branch one:
% 19.37/5.09 | (475) all_0_51_51 = e1
% 19.37/5.09 |
% 19.37/5.09 | Combining equations (458,475) yields a new equation:
% 19.37/5.09 | (476) e4 = e1
% 19.37/5.09 |
% 19.37/5.09 | Simplifying 476 yields:
% 19.37/5.09 | (477) e4 = e1
% 19.37/5.09 |
% 19.37/5.09 | Equations (477) can reduce 251 to:
% 19.37/5.09 | (269) $false
% 19.37/5.09 |
% 19.37/5.09 |-The branch is then unsatisfiable
% 19.37/5.09 |-Branch two:
% 19.37/5.09 | (479) ~ (all_0_51_51 = e1)
% 19.37/5.09 | (480) all_0_56_56 = e1
% 19.37/5.09 |
% 19.37/5.09 | Equations (480) can reduce 223 to:
% 19.37/5.09 | (481) ~ (all_0_58_58 = e1)
% 19.37/5.09 |
% 19.37/5.09 | Simplifying 481 yields:
% 19.37/5.09 | (482) ~ (all_0_58_58 = e1)
% 19.37/5.09 |
% 19.37/5.09 | Equations (480) can reduce 377 to:
% 19.37/5.09 | (414) ~ (e2 = e1)
% 19.37/5.09 |
% 19.37/5.09 | Simplifying 414 yields:
% 19.37/5.09 | (148) ~ (e2 = e1)
% 19.37/5.09 |
% 19.37/5.09 +-Applying beta-rule and splitting (2), into two cases.
% 19.37/5.09 |-Branch one:
% 19.37/5.09 | (485) all_0_58_58 = e2
% 19.37/5.09 |
% 19.37/5.09 | Equations (485) can reduce 392 to:
% 19.37/5.09 | (269) $false
% 19.37/5.09 |
% 19.37/5.09 |-The branch is then unsatisfiable
% 19.37/5.09 |-Branch two:
% 19.37/5.09 | (392) ~ (all_0_58_58 = e2)
% 19.37/5.09 | (488) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1 | all_0_58_58 = e0
% 19.37/5.09 |
% 19.37/5.09 +-Applying beta-rule and splitting (488), into two cases.
% 19.37/5.09 |-Branch one:
% 19.37/5.09 | (489) all_0_58_58 = e1
% 19.37/5.09 |
% 19.37/5.09 | Equations (489) can reduce 482 to:
% 19.37/5.09 | (269) $false
% 19.37/5.09 |
% 19.37/5.09 |-The branch is then unsatisfiable
% 19.37/5.09 |-Branch two:
% 19.37/5.09 | (482) ~ (all_0_58_58 = e1)
% 19.37/5.09 | (492) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e0
% 19.37/5.09 |
% 19.37/5.09 +-Applying beta-rule and splitting (492), into two cases.
% 19.37/5.09 |-Branch one:
% 19.37/5.09 | (493) all_0_58_58 = e0
% 19.37/5.09 |
% 19.37/5.09 | Equations (493) can reduce 403 to:
% 19.37/5.09 | (269) $false
% 19.37/5.09 |
% 19.37/5.09 |-The branch is then unsatisfiable
% 19.37/5.09 |-Branch two:
% 19.37/5.09 | (403) ~ (all_0_58_58 = e0)
% 19.37/5.09 | (496) all_0_58_58 = e4 | all_0_58_58 = e3
% 19.37/5.09 |
% 19.37/5.09 +-Applying beta-rule and splitting (496), into two cases.
% 19.37/5.09 |-Branch one:
% 19.37/5.09 | (497) all_0_58_58 = e3
% 19.37/5.09 |
% 19.37/5.09 | Equations (497) can reduce 277 to:
% 19.37/5.09 | (498) ~ (e4 = e3)
% 19.37/5.09 |
% 19.37/5.09 | Simplifying 498 yields:
% 19.37/5.09 | (41) ~ (e4 = e3)
% 19.37/5.09 |
% 19.37/5.09 | Instantiating formula (21) with e2, e3, all_0_17_17, e2 and discharging atoms op(e2, e3) = all_0_17_17, op(e2, e3) = e2, yields:
% 19.37/5.09 | (500) all_0_17_17 = e2
% 19.37/5.09 |
% 19.37/5.09 | Instantiating formula (21) with e2, e2, all_0_15_15, e4 and discharging atoms op(e2, e2) = all_0_15_15, op(e2, e2) = e4, yields:
% 19.37/5.09 | (501) all_0_15_15 = e4
% 19.37/5.09 |
% 19.37/5.09 | Instantiating formula (21) with e2, e1, all_0_13_13, all_0_48_48 and discharging atoms op(e2, e1) = all_0_13_13, op(e2, e1) = all_0_48_48, yields:
% 19.37/5.09 | (502) all_0_13_13 = all_0_48_48
% 19.37/5.09 |
% 19.37/5.09 | Instantiating formula (21) with e0, e0, e2, all_0_20_20 and discharging atoms op(e0, e0) = all_0_20_20, op(e0, e0) = e2, yields:
% 19.37/5.09 | (503) all_0_20_20 = e2
% 19.37/5.09 |
% 19.37/5.09 +-Applying beta-rule and splitting (133), into two cases.
% 19.37/5.09 |-Branch one:
% 19.37/5.09 | (504) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 19.37/5.09 |
% 19.37/5.09 +-Applying beta-rule and splitting (504), into two cases.
% 19.37/5.09 |-Branch one:
% 19.37/5.09 | (505) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 19.37/5.09 |
% 19.37/5.09 +-Applying beta-rule and splitting (505), into two cases.
% 19.37/5.09 |-Branch one:
% 19.37/5.09 | (506) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 19.37/5.09 |
% 19.37/5.09 | Applying alpha-rule on (506) yields:
% 19.37/5.09 | (507) all_0_13_13 = e4
% 19.37/5.09 | (508) ~ (all_0_14_14 = e2)
% 19.37/5.09 |
% 19.37/5.09 | Combining equations (502,507) yields a new equation:
% 19.37/5.09 | (509) all_0_48_48 = e4
% 19.37/5.09 |
% 19.37/5.09 | Simplifying 509 yields:
% 19.37/5.09 | (510) all_0_48_48 = e4
% 19.37/5.09 |
% 19.37/5.09 | Equations (510) can reduce 33 to:
% 19.37/5.09 | (269) $false
% 19.37/5.09 |
% 19.37/5.09 |-The branch is then unsatisfiable
% 19.37/5.09 |-Branch two:
% 19.37/5.09 | (512) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 19.37/5.09 |
% 19.37/5.09 | Applying alpha-rule on (512) yields:
% 19.37/5.09 | (513) all_0_15_15 = e3
% 19.37/5.09 | (514) ~ (all_0_16_16 = e2)
% 19.37/5.09 |
% 19.37/5.09 | Combining equations (501,513) yields a new equation:
% 19.37/5.09 | (515) e4 = e3
% 19.37/5.09 |
% 19.37/5.09 | Simplifying 515 yields:
% 19.37/5.09 | (516) e4 = e3
% 19.37/5.09 |
% 19.37/5.09 | Equations (516) can reduce 41 to:
% 19.37/5.09 | (269) $false
% 19.37/5.09 |
% 19.37/5.09 |-The branch is then unsatisfiable
% 19.37/5.09 |-Branch two:
% 19.37/5.09 | (518) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 19.37/5.09 |
% 19.37/5.09 | Applying alpha-rule on (518) yields:
% 19.37/5.09 | (519) all_0_17_17 = e1
% 19.37/5.09 | (520) ~ (all_0_18_18 = e2)
% 19.37/5.09 |
% 19.37/5.09 | Combining equations (519,500) yields a new equation:
% 19.37/5.09 | (471) e2 = e1
% 19.37/5.09 |
% 19.37/5.09 | Equations (471) can reduce 148 to:
% 19.37/5.09 | (269) $false
% 19.37/5.09 |
% 19.37/5.09 |-The branch is then unsatisfiable
% 19.37/5.09 |-Branch two:
% 19.37/5.09 | (523) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 19.37/5.09 |
% 19.37/5.09 | Applying alpha-rule on (523) yields:
% 19.37/5.09 | (524) all_0_19_19 = e0
% 19.37/5.09 | (525) ~ (all_0_20_20 = e2)
% 19.37/5.09 |
% 19.37/5.09 | Equations (503) can reduce 525 to:
% 19.37/5.09 | (269) $false
% 19.37/5.09 |
% 19.37/5.09 |-The branch is then unsatisfiable
% 19.37/5.09 |-Branch two:
% 19.37/5.09 | (527) ~ (all_0_58_58 = e3)
% 19.37/5.09 | (528) all_0_58_58 = e4
% 19.37/5.09 |
% 19.37/5.10 | Equations (528) can reduce 277 to:
% 19.37/5.10 | (269) $false
% 19.37/5.10 |
% 19.37/5.10 |-The branch is then unsatisfiable
% 19.37/5.10 |-Branch two:
% 19.37/5.10 | (530) ~ (all_0_51_51 = e4)
% 19.37/5.10 | (531) all_0_53_53 = e4 | all_0_54_54 = e4
% 19.37/5.10 |
% 19.37/5.10 +-Applying beta-rule and splitting (531), into two cases.
% 19.37/5.10 |-Branch one:
% 19.37/5.10 | (532) all_0_53_53 = e4
% 19.37/5.10 |
% 19.37/5.10 | Equations (532) can reduce 448 to:
% 19.37/5.10 | (269) $false
% 19.37/5.10 |
% 19.37/5.10 |-The branch is then unsatisfiable
% 19.37/5.10 |-Branch two:
% 19.37/5.10 | (448) ~ (all_0_53_53 = e4)
% 19.37/5.10 | (535) all_0_54_54 = e4
% 19.37/5.10 |
% 19.37/5.10 | Equations (535) can reduce 312 to:
% 19.37/5.10 | (269) $false
% 19.37/5.10 |
% 19.37/5.10 |-The branch is then unsatisfiable
% 19.37/5.10 |-Branch two:
% 19.37/5.10 | (537) ~ (all_0_45_45 = e4)
% 19.37/5.10 | (538) all_0_46_46 = e4
% 19.37/5.10 |
% 19.37/5.10 | Equations (538) can reduce 310 to:
% 19.37/5.10 | (269) $false
% 19.37/5.10 |
% 19.37/5.10 |-The branch is then unsatisfiable
% 19.37/5.10 |-Branch two:
% 19.37/5.10 | (540) ~ (all_0_39_39 = e3)
% 19.37/5.10 | (541) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 19.37/5.10 |
% 19.37/5.10 +-Applying beta-rule and splitting (199), into two cases.
% 19.37/5.10 |-Branch one:
% 19.37/5.10 | (364) all_0_46_46 = e2
% 19.37/5.10 |
% 19.37/5.10 | Equations (364) can reduce 344 to:
% 19.37/5.10 | (269) $false
% 19.37/5.10 |
% 19.37/5.10 |-The branch is then unsatisfiable
% 19.37/5.10 |-Branch two:
% 19.37/5.10 | (344) ~ (all_0_46_46 = e2)
% 19.37/5.10 | (545) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e0
% 19.37/5.10 |
% 19.37/5.10 +-Applying beta-rule and splitting (545), into two cases.
% 19.37/5.10 |-Branch one:
% 19.37/5.10 | (546) all_0_46_46 = e0
% 19.37/5.10 |
% 19.37/5.10 | Equations (546) can reduce 435 to:
% 19.37/5.10 | (269) $false
% 19.37/5.10 |
% 19.37/5.10 |-The branch is then unsatisfiable
% 19.37/5.10 |-Branch two:
% 19.37/5.10 | (435) ~ (all_0_46_46 = e0)
% 19.37/5.10 | (549) all_0_46_46 = e4 | all_0_46_46 = e3
% 19.37/5.10 |
% 19.37/5.10 +-Applying beta-rule and splitting (549), into two cases.
% 19.37/5.10 |-Branch one:
% 19.37/5.10 | (462) all_0_46_46 = e3
% 19.37/5.10 |
% 19.37/5.10 | Equations (462) can reduce 166 to:
% 19.37/5.10 | (551) ~ (all_0_49_49 = e3)
% 19.37/5.10 |
% 19.37/5.10 | Simplifying 551 yields:
% 19.37/5.10 | (158) ~ (all_0_49_49 = e3)
% 19.37/5.10 |
% 19.37/5.10 | Equations (462) can reduce 163 to:
% 19.37/5.10 | (146) ~ (e3 = e1)
% 19.37/5.10 |
% 19.37/5.10 | Equations (462) can reduce 435 to:
% 19.37/5.10 | (72) ~ (e3 = e0)
% 19.37/5.10 |
% 19.37/5.10 +-Applying beta-rule and splitting (204), into two cases.
% 19.37/5.10 |-Branch one:
% 19.37/5.10 | (443) all_0_39_39 = e3
% 19.37/5.10 |
% 19.37/5.10 | Equations (443) can reduce 540 to:
% 19.37/5.10 | (269) $false
% 19.37/5.10 |
% 19.37/5.10 |-The branch is then unsatisfiable
% 19.37/5.10 |-Branch two:
% 19.37/5.10 | (540) ~ (all_0_39_39 = e3)
% 19.37/5.10 | (558) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 19.37/5.10 |
% 19.37/5.10 +-Applying beta-rule and splitting (558), into two cases.
% 19.37/5.10 |-Branch one:
% 19.37/5.10 | (559) all_0_43_43 = e3
% 19.37/5.10 |
% 19.37/5.10 | Combining equations (433,559) yields a new equation:
% 19.37/5.10 | (560) e3 = e0
% 19.37/5.10 |
% 19.37/5.10 | Equations (560) can reduce 72 to:
% 19.37/5.10 | (269) $false
% 19.37/5.10 |
% 19.37/5.10 |-The branch is then unsatisfiable
% 19.37/5.10 |-Branch two:
% 19.37/5.10 | (562) ~ (all_0_43_43 = e3)
% 19.37/5.10 | (563) all_0_51_51 = e3 | all_0_56_56 = e3
% 19.37/5.10 |
% 19.37/5.10 +-Applying beta-rule and splitting (563), into two cases.
% 19.37/5.10 |-Branch one:
% 19.37/5.10 | (564) all_0_51_51 = e3
% 19.37/5.10 |
% 19.37/5.10 | Equations (564) can reduce 428 to:
% 19.37/5.10 | (269) $false
% 19.37/5.10 |
% 19.37/5.10 |-The branch is then unsatisfiable
% 19.37/5.10 |-Branch two:
% 19.37/5.10 | (428) ~ (all_0_51_51 = e3)
% 19.37/5.10 | (567) all_0_56_56 = e3
% 19.37/5.10 |
% 19.37/5.10 | Equations (567) can reduce 273 to:
% 19.37/5.10 | (498) ~ (e4 = e3)
% 19.37/5.10 |
% 19.37/5.10 | Simplifying 498 yields:
% 19.37/5.10 | (41) ~ (e4 = e3)
% 19.37/5.10 |
% 19.37/5.10 | Equations (567) can reduce 377 to:
% 19.37/5.10 | (224) ~ (e3 = e2)
% 19.37/5.10 |
% 19.37/5.10 +-Applying beta-rule and splitting (43), into two cases.
% 19.37/5.10 |-Branch one:
% 19.37/5.10 | (480) all_0_56_56 = e1
% 19.37/5.10 |
% 19.37/5.10 | Combining equations (567,480) yields a new equation:
% 19.37/5.10 | (572) e3 = e1
% 19.37/5.10 |
% 19.37/5.10 | Simplifying 572 yields:
% 19.37/5.10 | (418) e3 = e1
% 19.37/5.10 |
% 19.37/5.10 | Equations (418) can reduce 146 to:
% 19.37/5.10 | (269) $false
% 19.37/5.10 |
% 19.37/5.10 |-The branch is then unsatisfiable
% 19.37/5.10 |-Branch two:
% 19.37/5.10 | (575) ~ (all_0_56_56 = e1)
% 19.37/5.10 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 19.37/5.10 |
% 19.37/5.10 +-Applying beta-rule and splitting (576), into two cases.
% 19.37/5.10 |-Branch one:
% 19.37/5.10 | (577) all_0_57_57 = e1
% 19.37/5.10 |
% 19.37/5.10 | Combining equations (577,400) yields a new equation:
% 19.37/5.10 | (578) e1 = e0
% 19.37/5.10 |
% 19.37/5.10 | Simplifying 578 yields:
% 19.37/5.10 | (579) e1 = e0
% 19.37/5.10 |
% 19.37/5.10 | Equations (579) can reduce 144 to:
% 19.37/5.10 | (269) $false
% 19.37/5.10 |
% 19.37/5.10 |-The branch is then unsatisfiable
% 19.37/5.10 |-Branch two:
% 19.37/5.10 | (581) ~ (all_0_57_57 = e1)
% 19.37/5.10 | (582) all_0_58_58 = e1 | all_0_59_59 = e1
% 19.37/5.10 |
% 19.37/5.10 +-Applying beta-rule and splitting (582), into two cases.
% 19.37/5.10 |-Branch one:
% 19.37/5.10 | (489) all_0_58_58 = e1
% 19.37/5.10 |
% 19.37/5.10 | Equations (489) can reduce 174 to:
% 19.37/5.10 | (584) ~ (all_0_48_48 = e1)
% 19.37/5.10 |
% 19.37/5.10 | Equations (489) can reduce 392 to:
% 19.37/5.10 | (414) ~ (e2 = e1)
% 19.37/5.10 |
% 19.37/5.10 | Simplifying 414 yields:
% 19.37/5.10 | (148) ~ (e2 = e1)
% 19.37/5.10 |
% 19.37/5.10 +-Applying beta-rule and splitting (192), into two cases.
% 19.37/5.10 |-Branch one:
% 19.37/5.10 | (469) all_0_47_47 = e1
% 19.37/5.10 |
% 19.37/5.10 | Combining equations (319,469) yields a new equation:
% 19.37/5.10 | (470) e2 = e1
% 19.37/5.10 |
% 19.37/5.10 | Simplifying 470 yields:
% 19.37/5.10 | (471) e2 = e1
% 19.37/5.10 |
% 19.37/5.10 | Equations (471) can reduce 148 to:
% 19.37/5.10 | (269) $false
% 19.37/5.10 |
% 19.37/5.10 |-The branch is then unsatisfiable
% 19.37/5.10 |-Branch two:
% 19.37/5.10 | (473) ~ (all_0_47_47 = e1)
% 19.37/5.10 | (592) all_0_48_48 = e1 | all_0_49_49 = e1
% 19.37/5.10 |
% 19.37/5.10 +-Applying beta-rule and splitting (592), into two cases.
% 19.37/5.10 |-Branch one:
% 19.37/5.10 | (593) all_0_48_48 = e1
% 19.37/5.10 |
% 19.37/5.10 | Equations (593) can reduce 584 to:
% 19.37/5.10 | (269) $false
% 19.37/5.10 |
% 19.37/5.10 |-The branch is then unsatisfiable
% 19.37/5.10 |-Branch two:
% 19.37/5.10 | (584) ~ (all_0_48_48 = e1)
% 19.37/5.10 | (596) all_0_49_49 = e1
% 19.37/5.10 |
% 19.37/5.10 | Equations (596) can reduce 158 to:
% 19.37/5.10 | (597) ~ (e3 = e1)
% 19.37/5.10 |
% 19.37/5.10 | Simplifying 597 yields:
% 19.37/5.10 | (146) ~ (e3 = e1)
% 19.37/5.10 |
% 19.37/5.10 +-Applying beta-rule and splitting (541), into two cases.
% 19.37/5.10 |-Branch one:
% 19.37/5.10 | (417) all_0_40_40 = e3
% 19.37/5.10 |
% 19.37/5.10 | Combining equations (417,413) yields a new equation:
% 19.37/5.10 | (572) e3 = e1
% 19.37/5.10 |
% 19.37/5.10 | Simplifying 572 yields:
% 19.37/5.10 | (418) e3 = e1
% 19.37/5.10 |
% 19.37/5.10 | Equations (418) can reduce 146 to:
% 19.37/5.10 | (269) $false
% 19.37/5.10 |
% 19.37/5.10 |-The branch is then unsatisfiable
% 19.37/5.10 |-Branch two:
% 19.37/5.10 | (420) ~ (all_0_40_40 = e3)
% 19.37/5.10 | (604) all_0_41_41 = e3 | all_0_42_42 = e3
% 19.37/5.10 |
% 19.37/5.10 +-Applying beta-rule and splitting (604), into two cases.
% 19.37/5.10 |-Branch one:
% 19.37/5.10 | (605) all_0_41_41 = e3
% 19.37/5.10 |
% 19.37/5.10 | Combining equations (605,386) yields a new equation:
% 19.37/5.10 | (606) e3 = e2
% 19.37/5.10 |
% 19.37/5.10 | Simplifying 606 yields:
% 19.37/5.10 | (423) e3 = e2
% 19.37/5.10 |
% 19.37/5.10 | Equations (423) can reduce 224 to:
% 19.37/5.10 | (269) $false
% 19.37/5.10 |
% 19.37/5.10 |-The branch is then unsatisfiable
% 19.37/5.10 |-Branch two:
% 19.37/5.10 | (609) ~ (all_0_41_41 = e3)
% 19.37/5.10 | (610) all_0_42_42 = e3
% 19.37/5.10 |
% 19.37/5.10 | Combining equations (610,305) yields a new equation:
% 19.37/5.10 | (516) e4 = e3
% 19.37/5.10 |
% 19.37/5.10 | Equations (516) can reduce 41 to:
% 19.37/5.10 | (269) $false
% 19.37/5.10 |
% 19.37/5.10 |-The branch is then unsatisfiable
% 19.37/5.10 |-Branch two:
% 19.37/5.10 | (482) ~ (all_0_58_58 = e1)
% 19.37/5.10 | (614) all_0_59_59 = e1
% 19.37/5.10 |
% 19.37/5.10 | Combining equations (375,614) yields a new equation:
% 19.37/5.10 | (470) e2 = e1
% 19.37/5.10 |
% 19.37/5.10 | Simplifying 470 yields:
% 19.37/5.10 | (471) e2 = e1
% 19.37/5.10 |
% 19.37/5.10 | Equations (471) can reduce 148 to:
% 19.37/5.10 | (269) $false
% 19.37/5.10 |
% 19.37/5.10 |-The branch is then unsatisfiable
% 19.37/5.10 |-Branch two:
% 19.37/5.10 | (618) ~ (all_0_46_46 = e3)
% 19.37/5.10 | (538) all_0_46_46 = e4
% 19.37/5.10 |
% 19.37/5.10 | Equations (538) can reduce 310 to:
% 19.37/5.10 | (269) $false
% 19.37/5.10 |
% 19.37/5.10 |-The branch is then unsatisfiable
% 19.37/5.11 |-Branch two:
% 19.37/5.11 | (459) ~ (all_0_43_43 = e0)
% 19.37/5.11 | (622) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 19.37/5.11 |
% 19.37/5.11 +-Applying beta-rule and splitting (622), into two cases.
% 19.37/5.11 |-Branch one:
% 19.37/5.11 | (623) all_0_47_47 = e0
% 19.37/5.11 |
% 19.37/5.11 | Combining equations (319,623) yields a new equation:
% 19.37/5.11 | (353) e2 = e0
% 19.37/5.11 |
% 19.37/5.11 | Simplifying 353 yields:
% 19.37/5.11 | (354) e2 = e0
% 19.37/5.11 |
% 19.37/5.11 | Equations (354) can reduce 58 to:
% 19.37/5.11 | (269) $false
% 19.37/5.11 |
% 19.37/5.11 |-The branch is then unsatisfiable
% 19.37/5.11 |-Branch two:
% 19.37/5.11 | (297) ~ (all_0_47_47 = e0)
% 19.37/5.11 | (628) all_0_51_51 = e0 | all_0_56_56 = e0
% 19.37/5.11 |
% 19.37/5.11 +-Applying beta-rule and splitting (628), into two cases.
% 19.37/5.11 |-Branch one:
% 19.37/5.11 | (629) all_0_51_51 = e0
% 19.37/5.11 |
% 19.37/5.11 | Equations (629) can reduce 432 to:
% 19.37/5.11 | (269) $false
% 19.37/5.11 |
% 19.37/5.11 |-The branch is then unsatisfiable
% 19.37/5.11 |-Branch two:
% 19.37/5.11 | (432) ~ (all_0_51_51 = e0)
% 19.37/5.11 | (632) all_0_56_56 = e0
% 19.37/5.11 |
% 19.37/5.11 | Equations (632) can reduce 401 to:
% 19.37/5.11 | (269) $false
% 19.37/5.11 |
% 19.37/5.11 |-The branch is then unsatisfiable
% 19.37/5.11 |-Branch two:
% 19.37/5.11 | (629) all_0_51_51 = e0
% 19.37/5.11 | (635) all_0_54_54 = e3
% 19.37/5.11 |
% 19.37/5.11 | Equations (635) can reduce 430 to:
% 19.37/5.11 | (269) $false
% 19.37/5.11 |
% 19.37/5.11 |-The branch is then unsatisfiable
% 19.37/5.11 |-Branch two:
% 19.37/5.11 | (637) ~ (all_0_52_52 = e3)
% 19.37/5.11 | (638) all_0_57_57 = e3
% 19.37/5.11 |
% 19.37/5.11 | Combining equations (400,638) yields a new equation:
% 19.37/5.11 | (560) e3 = e0
% 19.37/5.11 |
% 19.37/5.11 | Equations (560) can reduce 72 to:
% 19.37/5.11 | (269) $false
% 19.37/5.11 |
% 19.37/5.11 |-The branch is then unsatisfiable
% 19.37/5.11 |-Branch two:
% 19.37/5.11 | (641) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 19.37/5.11 |
% 19.37/5.11 | Applying alpha-rule on (641) yields:
% 19.37/5.11 | (285) all_0_2_2 = e0
% 19.37/5.11 | (643) ~ (all_0_3_3 = e4)
% 19.37/5.11 |
% 19.37/5.11 | Equations (288) can reduce 643 to:
% 19.37/5.11 | (269) $false
% 19.37/5.11 |
% 19.37/5.11 |-The branch is then unsatisfiable
% 19.37/5.11 |-Branch two:
% 19.37/5.11 | (645) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 19.37/5.11 |
% 19.37/5.11 | Applying alpha-rule on (645) yields:
% 19.37/5.11 | (605) all_0_41_41 = e3
% 19.37/5.11 | (537) ~ (all_0_45_45 = e4)
% 19.37/5.11 |
% 19.37/5.11 | Combining equations (386,605) yields a new equation:
% 19.37/5.11 | (423) e3 = e2
% 19.37/5.11 |
% 19.37/5.11 | Equations (423) can reduce 224 to:
% 19.37/5.11 | (269) $false
% 19.37/5.11 |
% 19.37/5.11 |-The branch is then unsatisfiable
% 19.37/5.11 |-Branch two:
% 19.37/5.11 | (650) ~ (all_0_41_41 = e2)
% 19.37/5.11 | (651) all_0_45_45 = e2 | all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 19.37/5.11 |
% 19.37/5.11 +-Applying beta-rule and splitting (385), into two cases.
% 19.37/5.11 |-Branch one:
% 19.37/5.11 | (386) all_0_41_41 = e2
% 19.37/5.11 |
% 19.37/5.11 | Equations (386) can reduce 650 to:
% 19.37/5.11 | (269) $false
% 19.37/5.11 |
% 19.37/5.11 |-The branch is then unsatisfiable
% 19.37/5.11 |-Branch two:
% 19.37/5.11 | (650) ~ (all_0_41_41 = e2)
% 19.37/5.11 | (358) all_0_42_42 = e2
% 19.37/5.11 |
% 19.37/5.11 | Combining equations (305,358) yields a new equation:
% 19.37/5.11 | (359) e4 = e2
% 19.37/5.11 |
% 19.37/5.11 | Simplifying 359 yields:
% 19.37/5.11 | (360) e4 = e2
% 19.37/5.11 |
% 19.37/5.11 | Equations (360) can reduce 230 to:
% 19.37/5.11 | (269) $false
% 19.37/5.11 |
% 19.37/5.11 |-The branch is then unsatisfiable
% 19.37/5.11 |-Branch two:
% 19.37/5.11 | (659) ~ (all_0_44_44 = e2)
% 19.37/5.11 | (660) all_0_44_44 = e3 | all_0_44_44 = e0
% 19.37/5.11 |
% 19.37/5.11 +-Applying beta-rule and splitting (225), into two cases.
% 19.37/5.11 |-Branch one:
% 19.37/5.11 | (661) all_0_43_43 = e2
% 19.37/5.11 |
% 19.37/5.11 | Equations (661) can reduce 321 to:
% 19.37/5.11 | (269) $false
% 19.37/5.11 |
% 19.37/5.11 |-The branch is then unsatisfiable
% 19.37/5.11 |-Branch two:
% 19.37/5.11 | (321) ~ (all_0_43_43 = e2)
% 19.37/5.11 | (664) all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2
% 19.37/5.11 |
% 19.37/5.11 +-Applying beta-rule and splitting (17), into two cases.
% 19.37/5.11 |-Branch one:
% 19.37/5.11 | (382) all_0_40_40 = e2
% 19.37/5.11 |
% 19.37/5.11 | Combining equations (382,286) yields a new equation:
% 19.37/5.11 | (666) all_0_0_0 = e2
% 19.37/5.11 |
% 19.37/5.11 | Equations (382) can reduce 18 to:
% 19.37/5.11 | (320) ~ (all_0_39_39 = e2)
% 19.37/5.11 |
% 19.37/5.11 | Equations (382) can reduce 187 to:
% 19.37/5.11 | (256) ~ (all_0_52_52 = e2)
% 19.37/5.11 |
% 19.37/5.11 | Simplifying 256 yields:
% 19.37/5.11 | (257) ~ (all_0_52_52 = e2)
% 19.37/5.11 |
% 19.37/5.11 +-Applying beta-rule and splitting (8), into two cases.
% 19.37/5.11 |-Branch one:
% 19.37/5.11 | (348) all_0_39_39 = e2
% 19.37/5.11 |
% 19.37/5.11 | Equations (348) can reduce 320 to:
% 19.37/5.11 | (269) $false
% 19.37/5.11 |
% 19.37/5.11 |-The branch is then unsatisfiable
% 19.37/5.11 |-Branch two:
% 19.37/5.11 | (320) ~ (all_0_39_39 = e2)
% 19.37/5.11 | (396) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 19.37/5.11 |
% 19.37/5.11 +-Applying beta-rule and splitting (396), into two cases.
% 19.37/5.11 |-Branch one:
% 19.37/5.11 | (409) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 19.37/5.11 |
% 19.37/5.11 +-Applying beta-rule and splitting (409), into two cases.
% 19.37/5.11 |-Branch one:
% 19.37/5.11 | (410) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 19.37/5.11 |
% 19.37/5.11 | Applying alpha-rule on (410) yields:
% 19.37/5.11 | (411) all_0_0_0 = e1
% 19.37/5.11 | (412) ~ (all_0_1_1 = e4)
% 19.37/5.11 |
% 19.37/5.11 | Combining equations (411,666) yields a new equation:
% 19.37/5.11 | (471) e2 = e1
% 19.37/5.11 |
% 19.37/5.11 | Equations (471) can reduce 148 to:
% 19.37/5.11 | (269) $false
% 19.37/5.11 |
% 19.37/5.11 |-The branch is then unsatisfiable
% 19.37/5.11 |-Branch two:
% 19.37/5.11 | (641) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 19.37/5.11 |
% 19.37/5.11 | Applying alpha-rule on (641) yields:
% 19.37/5.11 | (285) all_0_2_2 = e0
% 19.37/5.11 | (643) ~ (all_0_3_3 = e4)
% 19.37/5.11 |
% 19.37/5.11 | Equations (288) can reduce 643 to:
% 19.37/5.11 | (269) $false
% 19.37/5.11 |
% 19.37/5.11 |-The branch is then unsatisfiable
% 19.37/5.11 |-Branch two:
% 19.37/5.11 | (645) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 19.37/5.11 |
% 19.37/5.11 | Applying alpha-rule on (645) yields:
% 19.37/5.11 | (605) all_0_41_41 = e3
% 19.37/5.11 | (537) ~ (all_0_45_45 = e4)
% 19.37/5.11 |
% 19.37/5.11 | Equations (605) can reduce 226 to:
% 19.37/5.11 | (540) ~ (all_0_39_39 = e3)
% 19.37/5.11 |
% 19.37/5.11 | Equations (605) can reduce 122 to:
% 19.37/5.11 | (688) ~ (all_0_45_45 = e3)
% 19.37/5.11 |
% 19.37/5.11 | Simplifying 688 yields:
% 19.37/5.11 | (689) ~ (all_0_45_45 = e3)
% 19.37/5.11 |
% 19.37/5.11 | Equations (605) can reduce 308 to:
% 19.37/5.11 | (498) ~ (e4 = e3)
% 19.37/5.11 |
% 19.37/5.11 | Simplifying 498 yields:
% 19.37/5.11 | (41) ~ (e4 = e3)
% 19.37/5.11 |
% 19.37/5.11 | Equations (605) can reduce 188 to:
% 19.37/5.11 | (72) ~ (e3 = e0)
% 19.37/5.11 |
% 19.37/5.11 | From (605) and (79) follows:
% 19.37/5.11 | (693) op(e1, e3) = all_0_21_21
% 19.37/5.11 |
% 19.37/5.11 +-Applying beta-rule and splitting (245), into two cases.
% 19.37/5.11 |-Branch one:
% 19.37/5.11 | (694) all_0_45_45 = e2
% 19.37/5.11 |
% 19.37/5.11 | Equations (694) can reduce 117 to:
% 19.37/5.11 | (659) ~ (all_0_44_44 = e2)
% 19.37/5.11 |
% 19.37/5.11 | Equations (694) can reduce 201 to:
% 19.37/5.11 | (343) ~ (all_0_46_46 = e2)
% 19.37/5.11 |
% 19.37/5.11 | Simplifying 343 yields:
% 19.37/5.11 | (344) ~ (all_0_46_46 = e2)
% 19.37/5.11 |
% 19.37/5.11 | Equations (694) can reduce 142 to:
% 19.37/5.11 | (258) ~ (all_0_53_53 = e2)
% 19.37/5.11 |
% 19.37/5.11 | Simplifying 258 yields:
% 19.37/5.11 | (259) ~ (all_0_53_53 = e2)
% 19.37/5.11 |
% 19.37/5.11 | Equations (694) can reduce 537 to:
% 19.37/5.11 | (326) ~ (e4 = e2)
% 19.37/5.11 |
% 19.37/5.11 | Simplifying 326 yields:
% 19.37/5.11 | (230) ~ (e4 = e2)
% 19.37/5.11 |
% 19.37/5.11 | Equations (694) can reduce 689 to:
% 19.37/5.11 | (328) ~ (e3 = e2)
% 19.37/5.11 |
% 19.37/5.11 | Simplifying 328 yields:
% 19.37/5.11 | (224) ~ (e3 = e2)
% 19.37/5.11 |
% 19.37/5.11 | Equations (694) can reduce 299 to:
% 19.37/5.11 | (58) ~ (e2 = e0)
% 19.37/5.11 |
% 19.37/5.11 | From (694) and (125) follows:
% 19.37/5.11 | (705) op(e1, e2) = all_0_23_23
% 19.37/5.11 |
% 19.37/5.11 +-Applying beta-rule and splitting (47), into two cases.
% 19.37/5.11 |-Branch one:
% 19.37/5.11 | (348) all_0_39_39 = e2
% 19.37/5.11 |
% 19.37/5.11 | Equations (348) can reduce 320 to:
% 19.37/5.11 | (269) $false
% 19.37/5.11 |
% 19.37/5.11 |-The branch is then unsatisfiable
% 19.37/5.11 |-Branch two:
% 19.37/5.11 | (320) ~ (all_0_39_39 = e2)
% 19.37/5.11 | (709) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 19.37/5.11 |
% 19.37/5.11 +-Applying beta-rule and splitting (709), into two cases.
% 19.37/5.11 |-Branch one:
% 19.37/5.11 | (464) all_0_39_39 = e1
% 19.37/5.11 |
% 19.54/5.11 | Equations (464) can reduce 540 to:
% 19.54/5.11 | (597) ~ (e3 = e1)
% 19.54/5.11 |
% 19.54/5.11 | Simplifying 597 yields:
% 19.54/5.11 | (146) ~ (e3 = e1)
% 19.54/5.11 |
% 19.54/5.11 | Equations (464) can reduce 320 to:
% 19.54/5.11 | (414) ~ (e2 = e1)
% 19.54/5.11 |
% 19.54/5.11 | Simplifying 414 yields:
% 19.54/5.11 | (148) ~ (e2 = e1)
% 19.54/5.11 |
% 19.54/5.11 +-Applying beta-rule and splitting (216), into two cases.
% 19.54/5.11 |-Branch one:
% 19.54/5.11 | (358) all_0_42_42 = e2
% 19.54/5.11 |
% 19.54/5.11 | Combining equations (305,358) yields a new equation:
% 19.54/5.11 | (359) e4 = e2
% 19.54/5.11 |
% 19.54/5.11 | Simplifying 359 yields:
% 19.54/5.11 | (360) e4 = e2
% 19.54/5.11 |
% 19.54/5.11 | Equations (360) can reduce 230 to:
% 19.54/5.11 | (269) $false
% 19.54/5.11 |
% 19.54/5.11 |-The branch is then unsatisfiable
% 19.54/5.11 |-Branch two:
% 19.54/5.11 | (362) ~ (all_0_42_42 = e2)
% 19.54/5.11 | (363) all_0_46_46 = e2 | all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 19.54/5.11 |
% 19.54/5.11 +-Applying beta-rule and splitting (363), into two cases.
% 19.54/5.11 |-Branch one:
% 19.54/5.11 | (364) all_0_46_46 = e2
% 19.54/5.11 |
% 19.54/5.11 | Equations (364) can reduce 344 to:
% 19.54/5.11 | (269) $false
% 19.54/5.11 |
% 19.54/5.11 |-The branch is then unsatisfiable
% 19.54/5.11 |-Branch two:
% 19.54/5.11 | (344) ~ (all_0_46_46 = e2)
% 19.54/5.11 | (367) all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 19.54/5.11 |
% 19.54/5.11 +-Applying beta-rule and splitting (367), into two cases.
% 19.54/5.11 |-Branch one:
% 19.54/5.11 | (337) all_0_49_49 = e2
% 19.54/5.11 |
% 19.54/5.11 | Equations (337) can reduce 323 to:
% 19.54/5.11 | (269) $false
% 19.54/5.11 |
% 19.54/5.11 |-The branch is then unsatisfiable
% 19.54/5.11 |-Branch two:
% 19.54/5.11 | (323) ~ (all_0_49_49 = e2)
% 19.54/5.11 | (371) all_0_54_54 = e2 | all_0_59_59 = e2
% 19.54/5.11 |
% 19.54/5.11 +-Applying beta-rule and splitting (371), into two cases.
% 19.54/5.11 |-Branch one:
% 19.54/5.11 | (372) all_0_54_54 = e2
% 19.54/5.11 |
% 19.54/5.11 | Equations (372) can reduce 261 to:
% 19.54/5.11 | (269) $false
% 19.54/5.11 |
% 19.54/5.11 |-The branch is then unsatisfiable
% 19.54/5.11 |-Branch two:
% 19.54/5.11 | (261) ~ (all_0_54_54 = e2)
% 19.54/5.11 | (375) all_0_59_59 = e2
% 19.54/5.11 |
% 19.54/5.11 | Equations (375) can reduce 150 to:
% 19.54/5.11 | (344) ~ (all_0_46_46 = e2)
% 19.54/5.11 |
% 19.54/5.11 | Equations (375) can reduce 82 to:
% 19.54/5.11 | (323) ~ (all_0_49_49 = e2)
% 19.54/5.11 |
% 19.54/5.11 | Equations (375) can reduce 81 to:
% 19.54/5.11 | (261) ~ (all_0_54_54 = e2)
% 19.54/5.11 |
% 19.54/5.11 | Equations (375) can reduce 95 to:
% 19.54/5.11 | (378) ~ (all_0_57_57 = e2)
% 19.54/5.11 |
% 19.54/5.11 | Equations (375) can reduce 279 to:
% 19.54/5.11 | (326) ~ (e4 = e2)
% 19.54/5.11 |
% 19.54/5.11 | Simplifying 326 yields:
% 19.54/5.11 | (230) ~ (e4 = e2)
% 19.54/5.11 |
% 19.54/5.11 +-Applying beta-rule and splitting (296), into two cases.
% 19.54/5.11 |-Branch one:
% 19.54/5.11 | (401) ~ (all_0_56_56 = e0)
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (54), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (740) all_0_41_41 = e4
% 19.54/5.12 |
% 19.54/5.12 | Combining equations (605,740) yields a new equation:
% 19.54/5.12 | (516) e4 = e3
% 19.54/5.12 |
% 19.54/5.12 | Equations (516) can reduce 41 to:
% 19.54/5.12 | (269) $false
% 19.54/5.12 |
% 19.54/5.12 |-The branch is then unsatisfiable
% 19.54/5.12 |-Branch two:
% 19.54/5.12 | (308) ~ (all_0_41_41 = e4)
% 19.54/5.12 | (744) all_0_45_45 = e4 | all_0_53_53 = e4 | all_0_58_58 = e4
% 19.54/5.12 |
% 19.54/5.12 | Equations (605) can reduce 308 to:
% 19.54/5.12 | (498) ~ (e4 = e3)
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 498 yields:
% 19.54/5.12 | (41) ~ (e4 = e3)
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (14), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (438) all_0_43_43 = e4
% 19.54/5.12 |
% 19.54/5.12 | Equations (438) can reduce 3 to:
% 19.54/5.12 | (309) ~ (all_0_46_46 = e4)
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 309 yields:
% 19.54/5.12 | (310) ~ (all_0_46_46 = e4)
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (171), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (433) all_0_43_43 = e0
% 19.54/5.12 |
% 19.54/5.12 | Combining equations (438,433) yields a new equation:
% 19.54/5.12 | (751) e4 = e0
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 751 yields:
% 19.54/5.12 | (439) e4 = e0
% 19.54/5.12 |
% 19.54/5.12 | Equations (439) can reduce 11 to:
% 19.54/5.12 | (269) $false
% 19.54/5.12 |
% 19.54/5.12 |-The branch is then unsatisfiable
% 19.54/5.12 |-Branch two:
% 19.54/5.12 | (459) ~ (all_0_43_43 = e0)
% 19.54/5.12 | (622) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (622), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (623) all_0_47_47 = e0
% 19.54/5.12 |
% 19.54/5.12 | Combining equations (623,319) yields a new equation:
% 19.54/5.12 | (354) e2 = e0
% 19.54/5.12 |
% 19.54/5.12 | Equations (354) can reduce 58 to:
% 19.54/5.12 | (269) $false
% 19.54/5.12 |
% 19.54/5.12 |-The branch is then unsatisfiable
% 19.54/5.12 |-Branch two:
% 19.54/5.12 | (297) ~ (all_0_47_47 = e0)
% 19.54/5.12 | (628) all_0_51_51 = e0 | all_0_56_56 = e0
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (628), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (629) all_0_51_51 = e0
% 19.54/5.12 |
% 19.54/5.12 | Equations (629) can reduce 194 to:
% 19.54/5.12 | (762) ~ (all_0_52_52 = e0)
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 762 yields:
% 19.54/5.12 | (317) ~ (all_0_52_52 = e0)
% 19.54/5.12 |
% 19.54/5.12 | Equations (629) can reduce 30 to:
% 19.54/5.12 | (764) ~ (all_0_53_53 = e0)
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 764 yields:
% 19.54/5.12 | (765) ~ (all_0_53_53 = e0)
% 19.54/5.12 |
% 19.54/5.12 | From (629) and (109) follows:
% 19.54/5.12 | (766) op(e1, e0) = all_0_10_10
% 19.54/5.12 |
% 19.54/5.12 | From (629) and (175) follows:
% 19.54/5.12 | (767) op(e1, e3) = e0
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (204), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (443) all_0_39_39 = e3
% 19.54/5.12 |
% 19.54/5.12 | Combining equations (443,464) yields a new equation:
% 19.54/5.12 | (572) e3 = e1
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 572 yields:
% 19.54/5.12 | (418) e3 = e1
% 19.54/5.12 |
% 19.54/5.12 | Equations (418) can reduce 146 to:
% 19.54/5.12 | (269) $false
% 19.54/5.12 |
% 19.54/5.12 |-The branch is then unsatisfiable
% 19.54/5.12 |-Branch two:
% 19.54/5.12 | (540) ~ (all_0_39_39 = e3)
% 19.54/5.12 | (558) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (558), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (559) all_0_43_43 = e3
% 19.54/5.12 |
% 19.54/5.12 | Combining equations (438,559) yields a new equation:
% 19.54/5.12 | (515) e4 = e3
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 515 yields:
% 19.54/5.12 | (516) e4 = e3
% 19.54/5.12 |
% 19.54/5.12 | Equations (516) can reduce 41 to:
% 19.54/5.12 | (269) $false
% 19.54/5.12 |
% 19.54/5.12 |-The branch is then unsatisfiable
% 19.54/5.12 |-Branch two:
% 19.54/5.12 | (562) ~ (all_0_43_43 = e3)
% 19.54/5.12 | (563) all_0_51_51 = e3 | all_0_56_56 = e3
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (563), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (564) all_0_51_51 = e3
% 19.54/5.12 |
% 19.54/5.12 | Combining equations (564,629) yields a new equation:
% 19.54/5.12 | (781) e3 = e0
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 781 yields:
% 19.54/5.12 | (560) e3 = e0
% 19.54/5.12 |
% 19.54/5.12 | Equations (560) can reduce 72 to:
% 19.54/5.12 | (269) $false
% 19.54/5.12 |
% 19.54/5.12 |-The branch is then unsatisfiable
% 19.54/5.12 |-Branch two:
% 19.54/5.12 | (428) ~ (all_0_51_51 = e3)
% 19.54/5.12 | (567) all_0_56_56 = e3
% 19.54/5.12 |
% 19.54/5.12 | Equations (567) can reduce 227 to:
% 19.54/5.12 | (786) ~ (all_0_57_57 = e3)
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 786 yields:
% 19.54/5.12 | (787) ~ (all_0_57_57 = e3)
% 19.54/5.12 |
% 19.54/5.12 | Equations (567) can reduce 223 to:
% 19.54/5.12 | (788) ~ (all_0_58_58 = e3)
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 788 yields:
% 19.54/5.12 | (527) ~ (all_0_58_58 = e3)
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (302), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (432) ~ (all_0_51_51 = e0)
% 19.54/5.12 |
% 19.54/5.12 | Equations (629) can reduce 432 to:
% 19.54/5.12 | (269) $false
% 19.54/5.12 |
% 19.54/5.12 |-The branch is then unsatisfiable
% 19.54/5.12 |-Branch two:
% 19.54/5.12 | (629) all_0_51_51 = e0
% 19.54/5.12 | (635) all_0_54_54 = e3
% 19.54/5.12 |
% 19.54/5.12 | Equations (635) can reduce 217 to:
% 19.54/5.12 | (158) ~ (all_0_49_49 = e3)
% 19.54/5.12 |
% 19.54/5.12 | Equations (635) can reduce 62 to:
% 19.54/5.12 | (637) ~ (all_0_52_52 = e3)
% 19.54/5.12 |
% 19.54/5.12 | Equations (635) can reduce 119 to:
% 19.54/5.12 | (796) ~ (all_0_53_53 = e3)
% 19.54/5.12 |
% 19.54/5.12 | Equations (635) can reduce 261 to:
% 19.54/5.12 | (224) ~ (e3 = e2)
% 19.54/5.12 |
% 19.54/5.12 | From (635) and (49) follows:
% 19.54/5.12 | (798) op(e1, e3) = all_0_37_37
% 19.54/5.12 |
% 19.54/5.12 | From (635) and (13) follows:
% 19.54/5.12 | (799) op(e1, e0) = e3
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (199), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (364) all_0_46_46 = e2
% 19.54/5.12 |
% 19.54/5.12 | Equations (364) can reduce 344 to:
% 19.54/5.12 | (269) $false
% 19.54/5.12 |
% 19.54/5.12 |-The branch is then unsatisfiable
% 19.54/5.12 |-Branch two:
% 19.54/5.12 | (344) ~ (all_0_46_46 = e2)
% 19.54/5.12 | (545) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e0
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (545), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (546) all_0_46_46 = e0
% 19.54/5.12 |
% 19.54/5.12 | Equations (546) can reduce 210 to:
% 19.54/5.12 | (356) ~ (all_0_44_44 = e0)
% 19.54/5.12 |
% 19.54/5.12 | Equations (546) can reduce 166 to:
% 19.54/5.12 | (806) ~ (all_0_49_49 = e0)
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 806 yields:
% 19.54/5.12 | (807) ~ (all_0_49_49 = e0)
% 19.54/5.12 |
% 19.54/5.12 | Equations (546) can reduce 344 to:
% 19.54/5.12 | (406) ~ (e2 = e0)
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 406 yields:
% 19.54/5.12 | (58) ~ (e2 = e0)
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (10), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (623) all_0_47_47 = e0
% 19.54/5.12 |
% 19.54/5.12 | Combining equations (319,623) yields a new equation:
% 19.54/5.12 | (353) e2 = e0
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 353 yields:
% 19.54/5.12 | (354) e2 = e0
% 19.54/5.12 |
% 19.54/5.12 | Equations (354) can reduce 58 to:
% 19.54/5.12 | (269) $false
% 19.54/5.12 |
% 19.54/5.12 |-The branch is then unsatisfiable
% 19.54/5.12 |-Branch two:
% 19.54/5.12 | (297) ~ (all_0_47_47 = e0)
% 19.54/5.12 | (815) all_0_48_48 = e0 | all_0_49_49 = e0
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (86), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (816) all_0_52_52 = e2
% 19.54/5.12 |
% 19.54/5.12 | Equations (816) can reduce 257 to:
% 19.54/5.12 | (269) $false
% 19.54/5.12 |
% 19.54/5.12 |-The branch is then unsatisfiable
% 19.54/5.12 |-Branch two:
% 19.54/5.12 | (257) ~ (all_0_52_52 = e2)
% 19.54/5.12 | (819) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (819), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (820) all_0_52_52 = e1
% 19.54/5.12 |
% 19.54/5.12 | Equations (820) can reduce 121 to:
% 19.54/5.12 | (87) ~ (all_0_44_44 = e1)
% 19.54/5.12 |
% 19.54/5.12 | Equations (820) can reduce 71 to:
% 19.54/5.12 | (822) ~ (all_0_53_53 = e1)
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 822 yields:
% 19.54/5.12 | (823) ~ (all_0_53_53 = e1)
% 19.54/5.12 |
% 19.54/5.12 | Equations (820) can reduce 124 to:
% 19.54/5.12 | (824) ~ (all_0_57_57 = e1)
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 824 yields:
% 19.54/5.12 | (581) ~ (all_0_57_57 = e1)
% 19.54/5.12 |
% 19.54/5.12 | Equations (820) can reduce 152 to:
% 19.54/5.12 | (826) ~ (e4 = e1)
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 826 yields:
% 19.54/5.12 | (251) ~ (e4 = e1)
% 19.54/5.12 |
% 19.54/5.12 | Equations (820) can reduce 637 to:
% 19.54/5.12 | (597) ~ (e3 = e1)
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 597 yields:
% 19.54/5.12 | (146) ~ (e3 = e1)
% 19.54/5.12 |
% 19.54/5.12 | From (820) and (89) follows:
% 19.54/5.12 | (830) op(e1, e1) = all_0_18_18
% 19.54/5.12 |
% 19.54/5.12 | From (820) and (118) follows:
% 19.54/5.12 | (831) op(e1, e2) = e1
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (84), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (832) all_0_42_42 = e1
% 19.54/5.12 |
% 19.54/5.12 | Combining equations (305,832) yields a new equation:
% 19.54/5.12 | (476) e4 = e1
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 476 yields:
% 19.54/5.12 | (477) e4 = e1
% 19.54/5.12 |
% 19.54/5.12 | Equations (477) can reduce 251 to:
% 19.54/5.12 | (269) $false
% 19.54/5.12 |
% 19.54/5.12 |-The branch is then unsatisfiable
% 19.54/5.12 |-Branch two:
% 19.54/5.12 | (836) ~ (all_0_42_42 = e1)
% 19.54/5.12 | (837) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (193), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (417) all_0_40_40 = e3
% 19.54/5.12 |
% 19.54/5.12 | Combining equations (417,382) yields a new equation:
% 19.54/5.12 | (606) e3 = e2
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 606 yields:
% 19.54/5.12 | (423) e3 = e2
% 19.54/5.12 |
% 19.54/5.12 | Equations (423) can reduce 224 to:
% 19.54/5.12 | (269) $false
% 19.54/5.12 |
% 19.54/5.12 |-The branch is then unsatisfiable
% 19.54/5.12 |-Branch two:
% 19.54/5.12 | (420) ~ (all_0_40_40 = e3)
% 19.54/5.12 | (421) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (421), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (422) all_0_44_44 = e3
% 19.54/5.12 |
% 19.54/5.12 | Equations (422) can reduce 240 to:
% 19.54/5.12 | (786) ~ (all_0_57_57 = e3)
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 786 yields:
% 19.54/5.12 | (787) ~ (all_0_57_57 = e3)
% 19.54/5.12 |
% 19.54/5.12 | Equations (422) can reduce 659 to:
% 19.54/5.12 | (224) ~ (e3 = e2)
% 19.54/5.12 |
% 19.54/5.12 | Equations (422) can reduce 87 to:
% 19.54/5.12 | (146) ~ (e3 = e1)
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (27), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (849) all_0_53_53 = e2
% 19.54/5.12 |
% 19.54/5.12 | Equations (849) can reduce 259 to:
% 19.54/5.12 | (269) $false
% 19.54/5.12 |
% 19.54/5.12 |-The branch is then unsatisfiable
% 19.54/5.12 |-Branch two:
% 19.54/5.12 | (259) ~ (all_0_53_53 = e2)
% 19.54/5.12 | (852) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (852), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (853) all_0_53_53 = e1
% 19.54/5.12 |
% 19.54/5.12 | Equations (853) can reduce 823 to:
% 19.54/5.12 | (269) $false
% 19.54/5.12 |
% 19.54/5.12 |-The branch is then unsatisfiable
% 19.54/5.12 |-Branch two:
% 19.54/5.12 | (823) ~ (all_0_53_53 = e1)
% 19.54/5.12 | (856) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e0
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (856), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (857) all_0_53_53 = e0
% 19.54/5.12 |
% 19.54/5.12 | Equations (857) can reduce 765 to:
% 19.54/5.12 | (269) $false
% 19.54/5.12 |
% 19.54/5.12 |-The branch is then unsatisfiable
% 19.54/5.12 |-Branch two:
% 19.54/5.12 | (765) ~ (all_0_53_53 = e0)
% 19.54/5.12 | (860) all_0_53_53 = e4 | all_0_53_53 = e3
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (860), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (861) all_0_53_53 = e3
% 19.54/5.12 |
% 19.54/5.12 | Equations (861) can reduce 796 to:
% 19.54/5.12 | (269) $false
% 19.54/5.12 |
% 19.54/5.12 |-The branch is then unsatisfiable
% 19.54/5.12 |-Branch two:
% 19.54/5.12 | (796) ~ (all_0_53_53 = e3)
% 19.54/5.12 | (532) all_0_53_53 = e4
% 19.54/5.12 |
% 19.54/5.12 | Equations (532) can reduce 250 to:
% 19.54/5.12 | (33) ~ (all_0_48_48 = e4)
% 19.54/5.12 |
% 19.54/5.12 | From (532) and (90) follows:
% 19.54/5.12 | (866) op(e1, e1) = e4
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (134), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (867) all_0_57_57 = e2
% 19.54/5.12 |
% 19.54/5.12 | Equations (867) can reduce 378 to:
% 19.54/5.12 | (269) $false
% 19.54/5.12 |
% 19.54/5.12 |-The branch is then unsatisfiable
% 19.54/5.12 |-Branch two:
% 19.54/5.12 | (378) ~ (all_0_57_57 = e2)
% 19.54/5.12 | (870) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (870), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (577) all_0_57_57 = e1
% 19.54/5.12 |
% 19.54/5.12 | Equations (577) can reduce 581 to:
% 19.54/5.12 | (269) $false
% 19.54/5.12 |
% 19.54/5.12 |-The branch is then unsatisfiable
% 19.54/5.12 |-Branch two:
% 19.54/5.12 | (581) ~ (all_0_57_57 = e1)
% 19.54/5.12 | (874) all_0_57_57 = e3 | all_0_57_57 = e0
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (874), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (400) all_0_57_57 = e0
% 19.54/5.12 |
% 19.54/5.12 | Equations (400) can reduce 252 to:
% 19.54/5.12 | (402) ~ (all_0_58_58 = e0)
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 402 yields:
% 19.54/5.12 | (403) ~ (all_0_58_58 = e0)
% 19.54/5.12 |
% 19.54/5.12 | Equations (400) can reduce 173 to:
% 19.54/5.12 | (404) ~ (e4 = e0)
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 404 yields:
% 19.54/5.12 | (11) ~ (e4 = e0)
% 19.54/5.12 |
% 19.54/5.12 | Equations (400) can reduce 378 to:
% 19.54/5.12 | (406) ~ (e2 = e0)
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 406 yields:
% 19.54/5.12 | (58) ~ (e2 = e0)
% 19.54/5.12 |
% 19.54/5.12 | Equations (400) can reduce 581 to:
% 19.54/5.12 | (436) ~ (e1 = e0)
% 19.54/5.12 |
% 19.54/5.12 | Simplifying 436 yields:
% 19.54/5.12 | (144) ~ (e1 = e0)
% 19.54/5.12 |
% 19.54/5.12 +-Applying beta-rule and splitting (43), into two cases.
% 19.54/5.12 |-Branch one:
% 19.54/5.12 | (480) all_0_56_56 = e1
% 19.54/5.12 |
% 19.54/5.12 | Combining equations (480,567) yields a new equation:
% 19.54/5.12 | (418) e3 = e1
% 19.54/5.12 |
% 19.54/5.13 | Equations (418) can reduce 146 to:
% 19.54/5.13 | (269) $false
% 19.54/5.13 |
% 19.54/5.13 |-The branch is then unsatisfiable
% 19.54/5.13 |-Branch two:
% 19.54/5.13 | (575) ~ (all_0_56_56 = e1)
% 19.54/5.13 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 19.54/5.13 |
% 19.54/5.13 +-Applying beta-rule and splitting (139), into two cases.
% 19.54/5.13 |-Branch one:
% 19.54/5.13 | (889) all_0_45_45 = e0
% 19.54/5.13 |
% 19.54/5.13 | Combining equations (694,889) yields a new equation:
% 19.54/5.13 | (353) e2 = e0
% 19.54/5.13 |
% 19.54/5.13 | Simplifying 353 yields:
% 19.54/5.13 | (354) e2 = e0
% 19.54/5.13 |
% 19.54/5.13 | Equations (354) can reduce 58 to:
% 19.54/5.13 | (269) $false
% 19.54/5.13 |
% 19.54/5.13 |-The branch is then unsatisfiable
% 19.54/5.13 |-Branch two:
% 19.54/5.13 | (299) ~ (all_0_45_45 = e0)
% 19.54/5.13 | (894) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 19.54/5.13 |
% 19.54/5.13 +-Applying beta-rule and splitting (576), into two cases.
% 19.54/5.13 |-Branch one:
% 19.54/5.13 | (577) all_0_57_57 = e1
% 19.54/5.13 |
% 19.54/5.13 | Combining equations (400,577) yields a new equation:
% 19.54/5.13 | (579) e1 = e0
% 19.54/5.13 |
% 19.54/5.13 | Equations (579) can reduce 144 to:
% 19.54/5.13 | (269) $false
% 19.54/5.13 |
% 19.54/5.13 |-The branch is then unsatisfiable
% 19.54/5.13 |-Branch two:
% 19.54/5.13 | (581) ~ (all_0_57_57 = e1)
% 19.54/5.13 | (582) all_0_58_58 = e1 | all_0_59_59 = e1
% 19.54/5.13 |
% 19.54/5.13 +-Applying beta-rule and splitting (837), into two cases.
% 19.54/5.13 |-Branch one:
% 19.54/5.13 | (596) all_0_49_49 = e1
% 19.54/5.13 |
% 19.54/5.13 | Equations (596) can reduce 323 to:
% 19.54/5.13 | (414) ~ (e2 = e1)
% 19.54/5.13 |
% 19.54/5.13 | Simplifying 414 yields:
% 19.54/5.13 | (148) ~ (e2 = e1)
% 19.54/5.13 |
% 19.54/5.13 +-Applying beta-rule and splitting (894), into two cases.
% 19.54/5.13 |-Branch one:
% 19.54/5.13 | (903) all_0_48_48 = e0
% 19.54/5.13 |
% 19.54/5.13 | Equations (903) can reduce 33 to:
% 19.54/5.13 | (404) ~ (e4 = e0)
% 19.54/5.13 |
% 19.54/5.13 | Simplifying 404 yields:
% 19.54/5.13 | (11) ~ (e4 = e0)
% 19.54/5.13 |
% 19.54/5.13 | From (903) and (85) follows:
% 19.54/5.13 | (906) op(e1, e0) = all_0_25_25
% 19.54/5.13 |
% 19.54/5.13 +-Applying beta-rule and splitting (582), into two cases.
% 19.54/5.13 |-Branch one:
% 19.54/5.13 | (489) all_0_58_58 = e1
% 19.54/5.13 |
% 19.54/5.13 | Equations (489) can reduce 527 to:
% 19.54/5.13 | (597) ~ (e3 = e1)
% 19.54/5.13 |
% 19.54/5.13 | Simplifying 597 yields:
% 19.54/5.13 | (146) ~ (e3 = e1)
% 19.54/5.13 |
% 19.54/5.13 | From (489) and (67) follows:
% 19.54/5.13 | (910) op(e1, e1) = all_0_28_28
% 19.54/5.13 |
% 19.54/5.13 | Instantiating formula (21) with e1, e3, all_0_37_37, all_0_21_21 and discharging atoms op(e1, e3) = all_0_21_21, op(e1, e3) = all_0_37_37, yields:
% 19.54/5.13 | (911) all_0_21_21 = all_0_37_37
% 19.54/5.13 |
% 19.54/5.13 | Instantiating formula (21) with e1, e3, e0, all_0_21_21 and discharging atoms op(e1, e3) = all_0_21_21, op(e1, e3) = e0, yields:
% 19.54/5.13 | (912) all_0_21_21 = e0
% 19.54/5.13 |
% 19.54/5.13 | Instantiating formula (21) with e1, e2, e1, all_0_23_23 and discharging atoms op(e1, e2) = all_0_23_23, op(e1, e2) = e1, yields:
% 19.54/5.13 | (913) all_0_23_23 = e1
% 19.54/5.13 |
% 19.54/5.13 | Instantiating formula (21) with e1, e1, all_0_28_28, all_0_18_18 and discharging atoms op(e1, e1) = all_0_18_18, op(e1, e1) = all_0_28_28, yields:
% 19.54/5.13 | (914) all_0_18_18 = all_0_28_28
% 19.54/5.13 |
% 19.54/5.13 | Instantiating formula (21) with e1, e1, e4, all_0_18_18 and discharging atoms op(e1, e1) = all_0_18_18, op(e1, e1) = e4, yields:
% 19.54/5.13 | (915) all_0_18_18 = e4
% 19.54/5.13 |
% 19.54/5.13 | Instantiating formula (21) with e1, e0, all_0_25_25, all_0_10_10 and discharging atoms op(e1, e0) = all_0_10_10, op(e1, e0) = all_0_25_25, yields:
% 19.54/5.13 | (916) all_0_10_10 = all_0_25_25
% 19.54/5.13 |
% 19.54/5.13 | Instantiating formula (21) with e1, e0, e3, all_0_10_10 and discharging atoms op(e1, e0) = all_0_10_10, op(e1, e0) = e3, yields:
% 19.54/5.13 | (917) all_0_10_10 = e3
% 19.54/5.13 |
% 19.54/5.13 | Combining equations (916,917) yields a new equation:
% 19.54/5.13 | (918) all_0_25_25 = e3
% 19.54/5.13 |
% 19.54/5.13 | Simplifying 918 yields:
% 19.54/5.13 | (919) all_0_25_25 = e3
% 19.54/5.13 |
% 19.54/5.13 | Combining equations (915,914) yields a new equation:
% 19.54/5.13 | (920) all_0_28_28 = e4
% 19.54/5.13 |
% 19.54/5.13 | Combining equations (912,911) yields a new equation:
% 19.54/5.13 | (921) all_0_37_37 = e0
% 19.54/5.13 |
% 19.54/5.13 | Combining equations (921,911) yields a new equation:
% 19.54/5.13 | (912) all_0_21_21 = e0
% 19.54/5.13 |
% 19.54/5.13 +-Applying beta-rule and splitting (229), into two cases.
% 19.54/5.13 |-Branch one:
% 19.54/5.13 | (923) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1))
% 19.54/5.13 |
% 19.54/5.13 +-Applying beta-rule and splitting (923), into two cases.
% 19.54/5.13 |-Branch one:
% 19.54/5.13 | (924) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1))
% 19.54/5.13 |
% 19.54/5.13 +-Applying beta-rule and splitting (924), into two cases.
% 19.54/5.13 |-Branch one:
% 19.54/5.13 | (925) all_0_21_21 = e4 & ~ (all_0_22_22 = e1)
% 19.54/5.13 |
% 19.54/5.13 | Applying alpha-rule on (925) yields:
% 19.54/5.13 | (926) all_0_21_21 = e4
% 19.54/5.13 | (927) ~ (all_0_22_22 = e1)
% 19.54/5.13 |
% 19.54/5.13 | Combining equations (926,912) yields a new equation:
% 19.54/5.13 | (751) e4 = e0
% 19.54/5.13 |
% 19.54/5.13 | Simplifying 751 yields:
% 19.54/5.13 | (439) e4 = e0
% 19.54/5.13 |
% 19.54/5.13 | Equations (439) can reduce 11 to:
% 19.54/5.13 | (269) $false
% 19.54/5.13 |
% 19.54/5.13 |-The branch is then unsatisfiable
% 19.54/5.13 |-Branch two:
% 19.54/5.13 | (931) all_0_23_23 = e3 & ~ (all_0_24_24 = e1)
% 19.54/5.13 |
% 19.54/5.13 | Applying alpha-rule on (931) yields:
% 19.54/5.13 | (932) all_0_23_23 = e3
% 19.54/5.13 | (933) ~ (all_0_24_24 = e1)
% 19.54/5.13 |
% 19.54/5.13 | Combining equations (932,913) yields a new equation:
% 19.54/5.13 | (572) e3 = e1
% 19.54/5.13 |
% 19.54/5.13 | Simplifying 572 yields:
% 19.54/5.13 | (418) e3 = e1
% 19.54/5.13 |
% 19.54/5.13 | Equations (418) can reduce 146 to:
% 19.54/5.13 | (269) $false
% 19.54/5.13 |
% 19.54/5.13 |-The branch is then unsatisfiable
% 19.54/5.13 |-Branch two:
% 19.54/5.13 | (937) all_0_25_25 = e2 & ~ (all_0_26_26 = e1)
% 19.54/5.13 |
% 19.54/5.13 | Applying alpha-rule on (937) yields:
% 19.54/5.13 | (938) all_0_25_25 = e2
% 19.54/5.13 | (939) ~ (all_0_26_26 = e1)
% 19.54/5.13 |
% 19.54/5.13 | Combining equations (938,919) yields a new equation:
% 19.54/5.13 | (423) e3 = e2
% 19.54/5.13 |
% 19.54/5.13 | Equations (423) can reduce 224 to:
% 19.54/5.13 | (269) $false
% 19.54/5.13 |
% 19.54/5.13 |-The branch is then unsatisfiable
% 19.54/5.13 |-Branch two:
% 19.54/5.13 | (942) all_0_28_28 = e0 & ~ (all_0_29_29 = e1)
% 19.54/5.13 |
% 19.54/5.13 | Applying alpha-rule on (942) yields:
% 19.54/5.13 | (943) all_0_28_28 = e0
% 19.54/5.13 | (944) ~ (all_0_29_29 = e1)
% 19.54/5.13 |
% 19.54/5.13 | Combining equations (943,920) yields a new equation:
% 19.54/5.13 | (439) e4 = e0
% 19.54/5.13 |
% 19.54/5.13 | Equations (439) can reduce 11 to:
% 19.54/5.13 | (269) $false
% 19.54/5.13 |
% 19.54/5.13 |-The branch is then unsatisfiable
% 19.54/5.13 |-Branch two:
% 19.54/5.13 | (482) ~ (all_0_58_58 = e1)
% 19.54/5.13 | (614) all_0_59_59 = e1
% 19.54/5.13 |
% 19.54/5.13 | Combining equations (375,614) yields a new equation:
% 19.54/5.13 | (470) e2 = e1
% 19.54/5.13 |
% 19.54/5.13 | Simplifying 470 yields:
% 19.54/5.13 | (471) e2 = e1
% 19.54/5.13 |
% 19.54/5.13 | Equations (471) can reduce 148 to:
% 19.54/5.13 | (269) $false
% 19.54/5.13 |
% 19.54/5.13 |-The branch is then unsatisfiable
% 19.54/5.13 |-Branch two:
% 19.54/5.13 | (952) ~ (all_0_48_48 = e0)
% 19.54/5.13 | (953) all_0_53_53 = e0 | all_0_58_58 = e0
% 19.54/5.13 |
% 19.54/5.13 +-Applying beta-rule and splitting (953), into two cases.
% 19.54/5.13 |-Branch one:
% 19.54/5.13 | (857) all_0_53_53 = e0
% 19.54/5.13 |
% 19.54/5.13 | Combining equations (857,532) yields a new equation:
% 19.54/5.13 | (439) e4 = e0
% 19.54/5.13 |
% 19.54/5.13 | Equations (439) can reduce 11 to:
% 19.54/5.13 | (269) $false
% 19.54/5.13 |
% 19.54/5.13 |-The branch is then unsatisfiable
% 19.54/5.13 |-Branch two:
% 19.54/5.13 | (765) ~ (all_0_53_53 = e0)
% 19.54/5.13 | (493) all_0_58_58 = e0
% 19.54/5.13 |
% 19.54/5.13 | Equations (493) can reduce 403 to:
% 19.54/5.13 | (269) $false
% 19.54/5.13 |
% 19.54/5.13 |-The branch is then unsatisfiable
% 19.54/5.13 |-Branch two:
% 19.54/5.13 | (960) ~ (all_0_49_49 = e1)
% 19.54/5.13 | (961) all_0_54_54 = e1 | all_0_59_59 = e1
% 19.54/5.13 |
% 19.54/5.13 +-Applying beta-rule and splitting (340), into two cases.
% 19.54/5.13 |-Branch one:
% 19.54/5.13 | (596) all_0_49_49 = e1
% 19.54/5.13 |
% 19.54/5.13 | Equations (596) can reduce 960 to:
% 19.54/5.13 | (269) $false
% 19.54/5.13 |
% 19.54/5.13 |-The branch is then unsatisfiable
% 19.54/5.13 |-Branch two:
% 19.54/5.13 | (960) ~ (all_0_49_49 = e1)
% 19.54/5.13 | (965) all_0_49_49 = e0
% 19.54/5.13 |
% 19.54/5.13 | Equations (965) can reduce 807 to:
% 19.54/5.13 | (269) $false
% 19.54/5.13 |
% 19.54/5.13 |-The branch is then unsatisfiable
% 19.54/5.13 |-Branch two:
% 19.54/5.13 | (967) ~ (all_0_57_57 = e0)
% 19.54/5.13 | (638) all_0_57_57 = e3
% 19.54/5.13 |
% 19.54/5.13 | Equations (638) can reduce 787 to:
% 19.54/5.13 | (269) $false
% 19.54/5.13 |
% 19.54/5.13 |-The branch is then unsatisfiable
% 19.54/5.13 |-Branch two:
% 19.54/5.13 | (425) ~ (all_0_44_44 = e3)
% 19.54/5.13 | (426) all_0_52_52 = e3 | all_0_57_57 = e3
% 19.54/5.13 |
% 19.54/5.13 +-Applying beta-rule and splitting (426), into two cases.
% 19.54/5.13 |-Branch one:
% 19.54/5.13 | (427) all_0_52_52 = e3
% 19.54/5.13 |
% 19.54/5.13 | Combining equations (820,427) yields a new equation:
% 19.54/5.13 | (418) e3 = e1
% 19.54/5.13 |
% 19.54/5.13 | Equations (418) can reduce 146 to:
% 19.54/5.13 | (269) $false
% 19.54/5.13 |
% 19.54/5.13 |-The branch is then unsatisfiable
% 19.54/5.13 |-Branch two:
% 19.54/5.13 | (637) ~ (all_0_52_52 = e3)
% 19.54/5.13 | (638) all_0_57_57 = e3
% 19.54/5.13 |
% 19.54/5.13 | Equations (638) can reduce 787 to:
% 19.54/5.13 | (269) $false
% 19.54/5.13 |
% 19.54/5.13 |-The branch is then unsatisfiable
% 19.54/5.13 |-Branch two:
% 19.54/5.13 | (978) ~ (all_0_52_52 = e1)
% 19.54/5.13 | (979) all_0_52_52 = e3 | all_0_52_52 = e0
% 19.54/5.13 |
% 19.54/5.13 +-Applying beta-rule and splitting (246), into two cases.
% 19.54/5.13 |-Branch one:
% 19.54/5.13 | (413) all_0_40_40 = e1
% 19.54/5.13 |
% 19.54/5.13 | Combining equations (413,382) yields a new equation:
% 19.54/5.13 | (471) e2 = e1
% 19.54/5.13 |
% 19.54/5.13 | Equations (471) can reduce 148 to:
% 19.54/5.13 | (269) $false
% 19.54/5.13 |
% 19.54/5.13 |-The branch is then unsatisfiable
% 19.54/5.13 |-Branch two:
% 19.54/5.13 | (983) ~ (all_0_40_40 = e1)
% 19.54/5.13 | (984) all_0_52_52 = e1 | all_0_57_57 = e1
% 19.54/5.13 |
% 19.54/5.13 +-Applying beta-rule and splitting (110), into two cases.
% 19.54/5.13 |-Branch one:
% 19.54/5.13 | (352) all_0_44_44 = e0
% 19.54/5.13 |
% 19.54/5.13 | Equations (352) can reduce 356 to:
% 19.54/5.13 | (269) $false
% 19.54/5.13 |
% 19.54/5.13 |-The branch is then unsatisfiable
% 19.54/5.13 |-Branch two:
% 19.54/5.13 | (356) ~ (all_0_44_44 = e0)
% 19.54/5.13 | (357) all_0_52_52 = e0 | all_0_57_57 = e0
% 19.54/5.13 |
% 19.54/5.13 +-Applying beta-rule and splitting (815), into two cases.
% 19.54/5.13 |-Branch one:
% 19.54/5.13 | (903) all_0_48_48 = e0
% 19.54/5.13 |
% 19.54/5.13 | Equations (903) can reduce 178 to:
% 19.54/5.13 | (806) ~ (all_0_49_49 = e0)
% 19.54/5.13 |
% 19.54/5.13 | Simplifying 806 yields:
% 19.54/5.13 | (807) ~ (all_0_49_49 = e0)
% 19.54/5.13 |
% 19.54/5.13 +-Applying beta-rule and splitting (294), into two cases.
% 19.54/5.13 |-Branch one:
% 19.54/5.13 | (952) ~ (all_0_48_48 = e0)
% 19.54/5.13 |
% 19.54/5.13 | Equations (903) can reduce 952 to:
% 19.54/5.13 | (269) $false
% 19.54/5.13 |
% 19.54/5.13 |-The branch is then unsatisfiable
% 19.54/5.13 |-Branch two:
% 19.54/5.13 | (903) all_0_48_48 = e0
% 19.54/5.13 | (596) all_0_49_49 = e1
% 19.54/5.13 |
% 19.54/5.13 | Equations (596) can reduce 158 to:
% 19.54/5.13 | (597) ~ (e3 = e1)
% 19.54/5.13 |
% 19.54/5.13 | Simplifying 597 yields:
% 19.54/5.13 | (146) ~ (e3 = e1)
% 19.54/5.13 |
% 19.54/5.13 | Equations (596) can reduce 323 to:
% 19.54/5.13 | (414) ~ (e2 = e1)
% 19.54/5.13 |
% 19.54/5.13 | Simplifying 414 yields:
% 19.54/5.13 | (148) ~ (e2 = e1)
% 19.54/5.13 |
% 19.54/5.13 | Equations (596) can reduce 807 to:
% 19.54/5.13 | (144) ~ (e1 = e0)
% 19.54/5.13 |
% 19.54/5.13 +-Applying beta-rule and splitting (357), into two cases.
% 19.54/5.13 |-Branch one:
% 19.54/5.13 | (397) all_0_52_52 = e0
% 19.54/5.13 |
% 19.54/5.13 | Equations (397) can reduce 317 to:
% 19.54/5.13 | (269) $false
% 19.54/5.13 |
% 19.54/5.13 |-The branch is then unsatisfiable
% 19.54/5.13 |-Branch two:
% 19.54/5.13 | (317) ~ (all_0_52_52 = e0)
% 19.54/5.13 | (400) all_0_57_57 = e0
% 19.54/5.13 |
% 19.54/5.13 | Equations (400) can reduce 252 to:
% 19.54/5.13 | (402) ~ (all_0_58_58 = e0)
% 19.54/5.13 |
% 19.54/5.13 | Simplifying 402 yields:
% 19.54/5.13 | (403) ~ (all_0_58_58 = e0)
% 19.54/5.13 |
% 19.54/5.13 +-Applying beta-rule and splitting (43), into two cases.
% 19.54/5.13 |-Branch one:
% 19.54/5.13 | (480) all_0_56_56 = e1
% 19.54/5.13 |
% 19.54/5.13 | Combining equations (480,567) yields a new equation:
% 19.54/5.13 | (418) e3 = e1
% 19.54/5.13 |
% 19.62/5.13 | Equations (418) can reduce 146 to:
% 19.62/5.13 | (269) $false
% 19.62/5.13 |
% 19.62/5.13 |-The branch is then unsatisfiable
% 19.62/5.13 |-Branch two:
% 19.62/5.13 | (575) ~ (all_0_56_56 = e1)
% 19.62/5.13 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 19.62/5.13 |
% 19.62/5.13 +-Applying beta-rule and splitting (576), into two cases.
% 19.62/5.13 |-Branch one:
% 19.62/5.13 | (577) all_0_57_57 = e1
% 19.62/5.13 |
% 19.62/5.13 | Combining equations (577,400) yields a new equation:
% 19.62/5.13 | (578) e1 = e0
% 19.62/5.13 |
% 19.62/5.13 | Simplifying 578 yields:
% 19.62/5.13 | (579) e1 = e0
% 19.62/5.13 |
% 19.62/5.13 | Equations (579) can reduce 144 to:
% 19.62/5.13 | (269) $false
% 19.62/5.13 |
% 19.62/5.13 |-The branch is then unsatisfiable
% 19.62/5.13 |-Branch two:
% 19.62/5.13 | (581) ~ (all_0_57_57 = e1)
% 19.62/5.13 | (582) all_0_58_58 = e1 | all_0_59_59 = e1
% 19.62/5.13 |
% 19.62/5.13 +-Applying beta-rule and splitting (582), into two cases.
% 19.62/5.13 |-Branch one:
% 19.62/5.13 | (489) all_0_58_58 = e1
% 19.62/5.13 |
% 19.62/5.14 | Equations (489) can reduce 403 to:
% 19.62/5.14 | (144) ~ (e1 = e0)
% 19.62/5.14 |
% 19.62/5.14 +-Applying beta-rule and splitting (984), into two cases.
% 19.62/5.14 |-Branch one:
% 19.62/5.14 | (820) all_0_52_52 = e1
% 19.62/5.14 |
% 19.62/5.14 | Equations (820) can reduce 978 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (978) ~ (all_0_52_52 = e1)
% 19.62/5.14 | (577) all_0_57_57 = e1
% 19.62/5.14 |
% 19.62/5.14 | Combining equations (577,400) yields a new equation:
% 19.62/5.14 | (578) e1 = e0
% 19.62/5.14 |
% 19.62/5.14 | Simplifying 578 yields:
% 19.62/5.14 | (579) e1 = e0
% 19.62/5.14 |
% 19.62/5.14 | Equations (579) can reduce 144 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (482) ~ (all_0_58_58 = e1)
% 19.62/5.14 | (614) all_0_59_59 = e1
% 19.62/5.14 |
% 19.62/5.14 | Combining equations (375,614) yields a new equation:
% 19.62/5.14 | (470) e2 = e1
% 19.62/5.14 |
% 19.62/5.14 | Simplifying 470 yields:
% 19.62/5.14 | (471) e2 = e1
% 19.62/5.14 |
% 19.62/5.14 | Equations (471) can reduce 148 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (952) ~ (all_0_48_48 = e0)
% 19.62/5.14 | (965) all_0_49_49 = e0
% 19.62/5.14 |
% 19.62/5.14 | Equations (965) can reduce 807 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (435) ~ (all_0_46_46 = e0)
% 19.62/5.14 | (549) all_0_46_46 = e4 | all_0_46_46 = e3
% 19.62/5.14 |
% 19.62/5.14 +-Applying beta-rule and splitting (193), into two cases.
% 19.62/5.14 |-Branch one:
% 19.62/5.14 | (417) all_0_40_40 = e3
% 19.62/5.14 |
% 19.62/5.14 | Combining equations (417,382) yields a new equation:
% 19.62/5.14 | (606) e3 = e2
% 19.62/5.14 |
% 19.62/5.14 | Simplifying 606 yields:
% 19.62/5.14 | (423) e3 = e2
% 19.62/5.14 |
% 19.62/5.14 | Equations (423) can reduce 224 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (420) ~ (all_0_40_40 = e3)
% 19.62/5.14 | (421) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 19.62/5.14 |
% 19.62/5.14 +-Applying beta-rule and splitting (421), into two cases.
% 19.62/5.14 |-Branch one:
% 19.62/5.14 | (422) all_0_44_44 = e3
% 19.62/5.14 |
% 19.62/5.14 | Equations (422) can reduce 210 to:
% 19.62/5.14 | (1044) ~ (all_0_46_46 = e3)
% 19.62/5.14 |
% 19.62/5.14 | Simplifying 1044 yields:
% 19.62/5.14 | (618) ~ (all_0_46_46 = e3)
% 19.62/5.14 |
% 19.62/5.14 +-Applying beta-rule and splitting (549), into two cases.
% 19.62/5.14 |-Branch one:
% 19.62/5.14 | (462) all_0_46_46 = e3
% 19.62/5.14 |
% 19.62/5.14 | Equations (462) can reduce 618 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (618) ~ (all_0_46_46 = e3)
% 19.62/5.14 | (538) all_0_46_46 = e4
% 19.62/5.14 |
% 19.62/5.14 | Equations (538) can reduce 310 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (425) ~ (all_0_44_44 = e3)
% 19.62/5.14 | (426) all_0_52_52 = e3 | all_0_57_57 = e3
% 19.62/5.14 |
% 19.62/5.14 +-Applying beta-rule and splitting (426), into two cases.
% 19.62/5.14 |-Branch one:
% 19.62/5.14 | (427) all_0_52_52 = e3
% 19.62/5.14 |
% 19.62/5.14 | Equations (427) can reduce 637 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (637) ~ (all_0_52_52 = e3)
% 19.62/5.14 | (638) all_0_57_57 = e3
% 19.62/5.14 |
% 19.62/5.14 | Equations (638) can reduce 787 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (432) ~ (all_0_51_51 = e0)
% 19.62/5.14 | (632) all_0_56_56 = e0
% 19.62/5.14 |
% 19.62/5.14 | Equations (632) can reduce 401 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (441) ~ (all_0_43_43 = e4)
% 19.62/5.14 | (442) all_0_45_45 = e4 | all_0_46_46 = e4
% 19.62/5.14 |
% 19.62/5.14 +-Applying beta-rule and splitting (442), into two cases.
% 19.62/5.14 |-Branch one:
% 19.62/5.14 | (444) all_0_45_45 = e4
% 19.62/5.14 |
% 19.62/5.14 | Combining equations (694,444) yields a new equation:
% 19.62/5.14 | (360) e4 = e2
% 19.62/5.14 |
% 19.62/5.14 | Equations (360) can reduce 230 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (537) ~ (all_0_45_45 = e4)
% 19.62/5.14 | (538) all_0_46_46 = e4
% 19.62/5.14 |
% 19.62/5.14 | Equations (538) can reduce 310 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (632) all_0_56_56 = e0
% 19.62/5.14 | (1070) all_0_59_59 = e3
% 19.62/5.14 |
% 19.62/5.14 | Combining equations (1070,375) yields a new equation:
% 19.62/5.14 | (606) e3 = e2
% 19.62/5.14 |
% 19.62/5.14 | Simplifying 606 yields:
% 19.62/5.14 | (423) e3 = e2
% 19.62/5.14 |
% 19.62/5.14 | Equations (423) can reduce 224 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (467) ~ (all_0_39_39 = e1)
% 19.62/5.14 | (1075) all_0_39_39 = e4 | all_0_39_39 = e3
% 19.62/5.14 |
% 19.62/5.14 +-Applying beta-rule and splitting (1075), into two cases.
% 19.62/5.14 |-Branch one:
% 19.62/5.14 | (443) all_0_39_39 = e3
% 19.62/5.14 |
% 19.62/5.14 | Equations (443) can reduce 540 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (540) ~ (all_0_39_39 = e3)
% 19.62/5.14 | (1079) all_0_39_39 = e4
% 19.62/5.14 |
% 19.62/5.14 | Equations (1079) can reduce 307 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (390) ~ (all_0_45_45 = e2)
% 19.62/5.14 | (1082) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 19.62/5.14 |
% 19.62/5.14 +-Applying beta-rule and splitting (1082), into two cases.
% 19.62/5.14 |-Branch one:
% 19.62/5.14 | (889) all_0_45_45 = e0
% 19.62/5.14 |
% 19.62/5.14 | Equations (889) can reduce 299 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (299) ~ (all_0_45_45 = e0)
% 19.62/5.14 | (1086) all_0_45_45 = e4 | all_0_45_45 = e3
% 19.62/5.14 |
% 19.62/5.14 +-Applying beta-rule and splitting (1086), into two cases.
% 19.62/5.14 |-Branch one:
% 19.62/5.14 | (1087) all_0_45_45 = e3
% 19.62/5.14 |
% 19.62/5.14 | Equations (1087) can reduce 689 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (689) ~ (all_0_45_45 = e3)
% 19.62/5.14 | (444) all_0_45_45 = e4
% 19.62/5.14 |
% 19.62/5.14 | Equations (444) can reduce 537 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (342) ~ (all_0_40_40 = e2)
% 19.62/5.14 | (1093) all_0_40_40 = e3 | all_0_40_40 = e1
% 19.62/5.14 |
% 19.62/5.14 +-Applying beta-rule and splitting (154), into two cases.
% 19.62/5.14 |-Branch one:
% 19.62/5.14 | (348) all_0_39_39 = e2
% 19.62/5.14 |
% 19.62/5.14 | Equations (348) can reduce 320 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (320) ~ (all_0_39_39 = e2)
% 19.62/5.14 | (351) all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 19.62/5.14 |
% 19.62/5.14 +-Applying beta-rule and splitting (113), into two cases.
% 19.62/5.14 |-Branch one:
% 19.62/5.14 | (382) all_0_40_40 = e2
% 19.62/5.14 |
% 19.62/5.14 | Equations (382) can reduce 342 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (342) ~ (all_0_40_40 = e2)
% 19.62/5.14 | (1101) all_0_44_44 = e2 | all_0_52_52 = e2 | all_0_57_57 = e2
% 19.62/5.14 |
% 19.62/5.14 +-Applying beta-rule and splitting (351), into two cases.
% 19.62/5.14 |-Branch one:
% 19.62/5.14 | (382) all_0_40_40 = e2
% 19.62/5.14 |
% 19.62/5.14 | Equations (382) can reduce 342 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (342) ~ (all_0_40_40 = e2)
% 19.62/5.14 | (385) all_0_41_41 = e2 | all_0_42_42 = e2
% 19.62/5.14 |
% 19.62/5.14 +-Applying beta-rule and splitting (1101), into two cases.
% 19.62/5.14 |-Branch one:
% 19.62/5.14 | (341) all_0_44_44 = e2
% 19.62/5.14 |
% 19.62/5.14 | Equations (341) can reduce 659 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (659) ~ (all_0_44_44 = e2)
% 19.62/5.14 | (1109) all_0_52_52 = e2 | all_0_57_57 = e2
% 19.62/5.14 |
% 19.62/5.14 +-Applying beta-rule and splitting (385), into two cases.
% 19.62/5.14 |-Branch one:
% 19.62/5.14 | (386) all_0_41_41 = e2
% 19.62/5.14 |
% 19.62/5.14 | Equations (386) can reduce 226 to:
% 19.62/5.14 | (320) ~ (all_0_39_39 = e2)
% 19.62/5.14 |
% 19.62/5.14 | Equations (386) can reduce 122 to:
% 19.62/5.14 | (389) ~ (all_0_45_45 = e2)
% 19.62/5.14 |
% 19.62/5.14 | Simplifying 389 yields:
% 19.62/5.14 | (390) ~ (all_0_45_45 = e2)
% 19.62/5.14 |
% 19.62/5.14 | Equations (386) can reduce 167 to:
% 19.62/5.14 | (1114) ~ (all_0_48_48 = e2)
% 19.62/5.14 |
% 19.62/5.14 | Simplifying 1114 yields:
% 19.62/5.14 | (1115) ~ (all_0_48_48 = e2)
% 19.62/5.14 |
% 19.62/5.14 | Equations (386) can reduce 188 to:
% 19.62/5.14 | (58) ~ (e2 = e0)
% 19.62/5.14 |
% 19.62/5.14 +-Applying beta-rule and splitting (664), into two cases.
% 19.62/5.14 |-Branch one:
% 19.62/5.14 | (341) all_0_44_44 = e2
% 19.62/5.14 |
% 19.62/5.14 | Equations (341) can reduce 659 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (659) ~ (all_0_44_44 = e2)
% 19.62/5.14 | (1120) all_0_45_45 = e2 | all_0_46_46 = e2
% 19.62/5.14 |
% 19.62/5.14 +-Applying beta-rule and splitting (1120), into two cases.
% 19.62/5.14 |-Branch one:
% 19.62/5.14 | (694) all_0_45_45 = e2
% 19.62/5.14 |
% 19.62/5.14 | Equations (694) can reduce 390 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (390) ~ (all_0_45_45 = e2)
% 19.62/5.14 | (364) all_0_46_46 = e2
% 19.62/5.14 |
% 19.62/5.14 | Equations (364) can reduce 3 to:
% 19.62/5.14 | (321) ~ (all_0_43_43 = e2)
% 19.62/5.14 |
% 19.62/5.14 | Equations (364) can reduce 166 to:
% 19.62/5.14 | (322) ~ (all_0_49_49 = e2)
% 19.62/5.14 |
% 19.62/5.14 | Simplifying 322 yields:
% 19.62/5.14 | (323) ~ (all_0_49_49 = e2)
% 19.62/5.14 |
% 19.62/5.14 | From (364) and (233) follows:
% 19.62/5.14 | (1128) op(e3, e0) = e2
% 19.62/5.14 |
% 19.62/5.14 +-Applying beta-rule and splitting (1109), into two cases.
% 19.62/5.14 |-Branch one:
% 19.62/5.14 | (816) all_0_52_52 = e2
% 19.62/5.14 |
% 19.62/5.14 | Equations (816) can reduce 257 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (257) ~ (all_0_52_52 = e2)
% 19.62/5.14 | (867) all_0_57_57 = e2
% 19.62/5.14 |
% 19.62/5.14 | Equations (867) can reduce 240 to:
% 19.62/5.14 | (659) ~ (all_0_44_44 = e2)
% 19.62/5.14 |
% 19.62/5.14 | Equations (867) can reduce 124 to:
% 19.62/5.14 | (257) ~ (all_0_52_52 = e2)
% 19.62/5.14 |
% 19.62/5.14 | Equations (867) can reduce 173 to:
% 19.62/5.14 | (326) ~ (e4 = e2)
% 19.62/5.14 |
% 19.62/5.14 | Simplifying 326 yields:
% 19.62/5.14 | (230) ~ (e4 = e2)
% 19.62/5.14 |
% 19.62/5.14 +-Applying beta-rule and splitting (110), into two cases.
% 19.62/5.14 |-Branch one:
% 19.62/5.14 | (352) all_0_44_44 = e0
% 19.62/5.14 |
% 19.62/5.14 | Combining equations (352,334) yields a new equation:
% 19.62/5.14 | (1138) all_0_7_7 = e0
% 19.62/5.14 |
% 19.62/5.14 | Equations (352) can reduce 228 to:
% 19.62/5.14 | (459) ~ (all_0_43_43 = e0)
% 19.62/5.14 |
% 19.62/5.14 | Equations (352) can reduce 117 to:
% 19.62/5.14 | (1140) ~ (all_0_45_45 = e0)
% 19.62/5.14 |
% 19.62/5.14 | Simplifying 1140 yields:
% 19.62/5.14 | (299) ~ (all_0_45_45 = e0)
% 19.62/5.14 |
% 19.62/5.14 | Equations (352) can reduce 121 to:
% 19.62/5.14 | (762) ~ (all_0_52_52 = e0)
% 19.62/5.14 |
% 19.62/5.14 | Simplifying 762 yields:
% 19.62/5.14 | (317) ~ (all_0_52_52 = e0)
% 19.62/5.14 |
% 19.62/5.14 | Equations (352) can reduce 659 to:
% 19.62/5.14 | (406) ~ (e2 = e0)
% 19.62/5.14 |
% 19.62/5.14 | Simplifying 406 yields:
% 19.62/5.14 | (58) ~ (e2 = e0)
% 19.62/5.14 |
% 19.62/5.14 | From (352) and (247) follows:
% 19.62/5.14 | (1146) op(e3, e0) = all_0_16_16
% 19.62/5.14 |
% 19.62/5.14 +-Applying beta-rule and splitting (8), into two cases.
% 19.62/5.14 |-Branch one:
% 19.62/5.14 | (348) all_0_39_39 = e2
% 19.62/5.14 |
% 19.62/5.14 | Equations (348) can reduce 320 to:
% 19.62/5.14 | (269) $false
% 19.62/5.14 |
% 19.62/5.14 |-The branch is then unsatisfiable
% 19.62/5.14 |-Branch two:
% 19.62/5.14 | (320) ~ (all_0_39_39 = e2)
% 19.62/5.14 | (396) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 19.62/5.14 |
% 19.62/5.14 +-Applying beta-rule and splitting (396), into two cases.
% 19.62/5.14 |-Branch one:
% 19.62/5.14 | (409) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 19.62/5.14 |
% 19.62/5.14 +-Applying beta-rule and splitting (409), into two cases.
% 19.62/5.14 |-Branch one:
% 19.62/5.14 | (410) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 19.62/5.14 |
% 19.62/5.14 | Applying alpha-rule on (410) yields:
% 19.62/5.14 | (411) all_0_0_0 = e1
% 19.62/5.14 | (412) ~ (all_0_1_1 = e4)
% 19.62/5.14 |
% 19.62/5.14 | Combining equations (411,286) yields a new equation:
% 19.62/5.14 | (413) all_0_40_40 = e1
% 19.62/5.14 |
% 19.62/5.14 | Equations (413) can reduce 18 to:
% 19.62/5.14 | (467) ~ (all_0_39_39 = e1)
% 19.62/5.14 |
% 19.62/5.14 | Equations (413) can reduce 187 to:
% 19.62/5.14 | (1157) ~ (all_0_52_52 = e1)
% 19.62/5.14 |
% 19.62/5.14 | Simplifying 1157 yields:
% 19.62/5.14 | (978) ~ (all_0_52_52 = e1)
% 19.62/5.14 |
% 19.62/5.14 +-Applying beta-rule and splitting (47), into two cases.
% 19.62/5.14 |-Branch one:
% 19.62/5.14 | (348) all_0_39_39 = e2
% 19.62/5.14 |
% 19.62/5.15 | Equations (348) can reduce 320 to:
% 19.62/5.15 | (269) $false
% 19.62/5.15 |
% 19.62/5.15 |-The branch is then unsatisfiable
% 19.62/5.15 |-Branch two:
% 19.62/5.15 | (320) ~ (all_0_39_39 = e2)
% 19.62/5.15 | (709) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (86), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (816) all_0_52_52 = e2
% 19.62/5.15 |
% 19.62/5.15 | Equations (816) can reduce 257 to:
% 19.62/5.15 | (269) $false
% 19.62/5.15 |
% 19.62/5.15 |-The branch is then unsatisfiable
% 19.62/5.15 |-Branch two:
% 19.62/5.15 | (257) ~ (all_0_52_52 = e2)
% 19.62/5.15 | (819) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (819), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (820) all_0_52_52 = e1
% 19.62/5.15 |
% 19.62/5.15 | Equations (820) can reduce 978 to:
% 19.62/5.15 | (269) $false
% 19.62/5.15 |
% 19.62/5.15 |-The branch is then unsatisfiable
% 19.62/5.15 |-Branch two:
% 19.62/5.15 | (978) ~ (all_0_52_52 = e1)
% 19.62/5.15 | (979) all_0_52_52 = e3 | all_0_52_52 = e0
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (979), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (397) all_0_52_52 = e0
% 19.62/5.15 |
% 19.62/5.15 | Equations (397) can reduce 317 to:
% 19.62/5.15 | (269) $false
% 19.62/5.15 |
% 19.62/5.15 |-The branch is then unsatisfiable
% 19.62/5.15 |-Branch two:
% 19.62/5.15 | (317) ~ (all_0_52_52 = e0)
% 19.62/5.15 | (427) all_0_52_52 = e3
% 19.62/5.15 |
% 19.62/5.15 | Equations (427) can reduce 62 to:
% 19.62/5.15 | (429) ~ (all_0_54_54 = e3)
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 429 yields:
% 19.62/5.15 | (430) ~ (all_0_54_54 = e3)
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (184), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (443) all_0_39_39 = e3
% 19.62/5.15 |
% 19.62/5.15 | Equations (443) can reduce 234 to:
% 19.62/5.15 | (1178) ~ (all_0_43_43 = e3)
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 1178 yields:
% 19.62/5.15 | (562) ~ (all_0_43_43 = e3)
% 19.62/5.15 |
% 19.62/5.15 | Equations (443) can reduce 126 to:
% 19.62/5.15 | (1180) ~ (all_0_51_51 = e3)
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 1180 yields:
% 19.62/5.15 | (428) ~ (all_0_51_51 = e3)
% 19.62/5.15 |
% 19.62/5.15 | Equations (443) can reduce 53 to:
% 19.62/5.15 | (1182) ~ (all_0_56_56 = e3)
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 1182 yields:
% 19.62/5.15 | (1183) ~ (all_0_56_56 = e3)
% 19.62/5.15 |
% 19.62/5.15 | Equations (443) can reduce 307 to:
% 19.62/5.15 | (498) ~ (e4 = e3)
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 498 yields:
% 19.62/5.15 | (41) ~ (e4 = e3)
% 19.62/5.15 |
% 19.62/5.15 | Equations (443) can reduce 320 to:
% 19.62/5.15 | (224) ~ (e3 = e2)
% 19.62/5.15 |
% 19.62/5.15 | Equations (443) can reduce 165 to:
% 19.62/5.15 | (72) ~ (e3 = e0)
% 19.62/5.15 |
% 19.62/5.15 | From (443) and (92) follows:
% 19.62/5.15 | (1188) op(e4, e3) = all_0_5_5
% 19.62/5.15 |
% 19.62/5.15 | From (443) and (6) follows:
% 19.62/5.15 | (1189) op(e4, e3) = e3
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (162), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (559) all_0_43_43 = e3
% 19.62/5.15 |
% 19.62/5.15 | Equations (559) can reduce 562 to:
% 19.62/5.15 | (269) $false
% 19.62/5.15 |
% 19.62/5.15 |-The branch is then unsatisfiable
% 19.62/5.15 |-Branch two:
% 19.62/5.15 | (562) ~ (all_0_43_43 = e3)
% 19.62/5.15 | (1193) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (302), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (432) ~ (all_0_51_51 = e0)
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (22), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (661) all_0_43_43 = e2
% 19.62/5.15 |
% 19.62/5.15 | Equations (661) can reduce 321 to:
% 19.62/5.15 | (269) $false
% 19.62/5.15 |
% 19.62/5.15 |-The branch is then unsatisfiable
% 19.62/5.15 |-Branch two:
% 19.62/5.15 | (321) ~ (all_0_43_43 = e2)
% 19.62/5.15 | (1198) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (1193), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (422) all_0_44_44 = e3
% 19.62/5.15 |
% 19.62/5.15 | Combining equations (352,422) yields a new equation:
% 19.62/5.15 | (560) e3 = e0
% 19.62/5.15 |
% 19.62/5.15 | Equations (560) can reduce 72 to:
% 19.62/5.15 | (269) $false
% 19.62/5.15 |
% 19.62/5.15 |-The branch is then unsatisfiable
% 19.62/5.15 |-Branch two:
% 19.62/5.15 | (425) ~ (all_0_44_44 = e3)
% 19.62/5.15 | (1203) all_0_45_45 = e3 | all_0_46_46 = e3
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (1203), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (1087) all_0_45_45 = e3
% 19.62/5.15 |
% 19.62/5.15 | Equations (1087) can reduce 299 to:
% 19.62/5.15 | (72) ~ (e3 = e0)
% 19.62/5.15 |
% 19.62/5.15 | From (1087) and (23) follows:
% 19.62/5.15 | (1206) op(e3, e1) = e3
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (14), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (438) all_0_43_43 = e4
% 19.62/5.15 |
% 19.62/5.15 | Equations (438) can reduce 137 to:
% 19.62/5.15 | (1208) ~ (all_0_51_51 = e4)
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 1208 yields:
% 19.62/5.15 | (530) ~ (all_0_51_51 = e4)
% 19.62/5.15 |
% 19.62/5.15 | Equations (438) can reduce 232 to:
% 19.62/5.15 | (272) ~ (all_0_56_56 = e4)
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 272 yields:
% 19.62/5.15 | (273) ~ (all_0_56_56 = e4)
% 19.62/5.15 |
% 19.62/5.15 | Equations (438) can reduce 321 to:
% 19.62/5.15 | (230) ~ (e4 = e2)
% 19.62/5.15 |
% 19.62/5.15 | Equations (438) can reduce 459 to:
% 19.62/5.15 | (11) ~ (e4 = e0)
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (153), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (453) all_0_50_50 = e4
% 19.62/5.15 |
% 19.62/5.15 | Combining equations (453,253) yields a new equation:
% 19.62/5.15 | (359) e4 = e2
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 359 yields:
% 19.62/5.15 | (360) e4 = e2
% 19.62/5.15 |
% 19.62/5.15 | Equations (360) can reduce 230 to:
% 19.62/5.15 | (269) $false
% 19.62/5.15 |
% 19.62/5.15 |-The branch is then unsatisfiable
% 19.62/5.15 |-Branch two:
% 19.62/5.15 | (456) ~ (all_0_50_50 = e4)
% 19.62/5.15 | (457) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (457), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (458) all_0_51_51 = e4
% 19.62/5.15 |
% 19.62/5.15 | Equations (458) can reduce 530 to:
% 19.62/5.15 | (269) $false
% 19.62/5.15 |
% 19.62/5.15 |-The branch is then unsatisfiable
% 19.62/5.15 |-Branch two:
% 19.62/5.15 | (530) ~ (all_0_51_51 = e4)
% 19.62/5.15 | (531) all_0_53_53 = e4 | all_0_54_54 = e4
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (531), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (532) all_0_53_53 = e4
% 19.62/5.15 |
% 19.62/5.15 | Equations (532) can reduce 30 to:
% 19.62/5.15 | (530) ~ (all_0_51_51 = e4)
% 19.62/5.15 |
% 19.62/5.15 | Equations (532) can reduce 119 to:
% 19.62/5.15 | (311) ~ (all_0_54_54 = e4)
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 311 yields:
% 19.62/5.15 | (312) ~ (all_0_54_54 = e4)
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (63), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (629) all_0_51_51 = e0
% 19.62/5.15 |
% 19.62/5.15 | Equations (629) can reduce 432 to:
% 19.62/5.15 | (269) $false
% 19.62/5.15 |
% 19.62/5.15 |-The branch is then unsatisfiable
% 19.62/5.15 |-Branch two:
% 19.62/5.15 | (432) ~ (all_0_51_51 = e0)
% 19.62/5.15 | (1231) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (170), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (1232) all_0_51_51 = e2
% 19.62/5.15 |
% 19.62/5.15 | Equations (1232) can reduce 255 to:
% 19.62/5.15 | (269) $false
% 19.62/5.15 |
% 19.62/5.15 |-The branch is then unsatisfiable
% 19.62/5.15 |-Branch two:
% 19.62/5.15 | (255) ~ (all_0_51_51 = e2)
% 19.62/5.15 | (1235) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1 | all_0_51_51 = e0
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (1235), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (475) all_0_51_51 = e1
% 19.62/5.15 |
% 19.62/5.15 | Equations (475) can reduce 159 to:
% 19.62/5.15 | (1237) ~ (all_0_54_54 = e1)
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 1237 yields:
% 19.62/5.15 | (1238) ~ (all_0_54_54 = e1)
% 19.62/5.15 |
% 19.62/5.15 | Equations (475) can reduce 432 to:
% 19.62/5.15 | (144) ~ (e1 = e0)
% 19.62/5.15 |
% 19.62/5.15 | From (475) and (151) follows:
% 19.62/5.15 | (1240) op(e3, e1) = all_0_9_9
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (1231), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (397) all_0_52_52 = e0
% 19.62/5.15 |
% 19.62/5.15 | Combining equations (397,427) yields a new equation:
% 19.62/5.15 | (560) e3 = e0
% 19.62/5.15 |
% 19.62/5.15 | Equations (560) can reduce 72 to:
% 19.62/5.15 | (269) $false
% 19.62/5.15 |
% 19.62/5.15 |-The branch is then unsatisfiable
% 19.62/5.15 |-Branch two:
% 19.62/5.15 | (317) ~ (all_0_52_52 = e0)
% 19.62/5.15 | (1245) all_0_53_53 = e0 | all_0_54_54 = e0
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (243), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (567) all_0_56_56 = e3
% 19.62/5.15 |
% 19.62/5.15 | Equations (567) can reduce 1183 to:
% 19.62/5.15 | (269) $false
% 19.62/5.15 |
% 19.62/5.15 |-The branch is then unsatisfiable
% 19.62/5.15 |-Branch two:
% 19.62/5.15 | (1183) ~ (all_0_56_56 = e3)
% 19.62/5.15 | (1249) all_0_57_57 = e3 | all_0_58_58 = e3 | all_0_59_59 = e3
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (171), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (433) all_0_43_43 = e0
% 19.62/5.15 |
% 19.62/5.15 | Combining equations (438,433) yields a new equation:
% 19.62/5.15 | (751) e4 = e0
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 751 yields:
% 19.62/5.15 | (439) e4 = e0
% 19.62/5.15 |
% 19.62/5.15 | Equations (439) can reduce 11 to:
% 19.62/5.15 | (269) $false
% 19.62/5.15 |
% 19.62/5.15 |-The branch is then unsatisfiable
% 19.62/5.15 |-Branch two:
% 19.62/5.15 | (459) ~ (all_0_43_43 = e0)
% 19.62/5.15 | (622) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (622), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (623) all_0_47_47 = e0
% 19.62/5.15 |
% 19.62/5.15 | Combining equations (319,623) yields a new equation:
% 19.62/5.15 | (353) e2 = e0
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 353 yields:
% 19.62/5.15 | (354) e2 = e0
% 19.62/5.15 |
% 19.62/5.15 | Equations (354) can reduce 58 to:
% 19.62/5.15 | (269) $false
% 19.62/5.15 |
% 19.62/5.15 |-The branch is then unsatisfiable
% 19.62/5.15 |-Branch two:
% 19.62/5.15 | (297) ~ (all_0_47_47 = e0)
% 19.62/5.15 | (628) all_0_51_51 = e0 | all_0_56_56 = e0
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (628), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (629) all_0_51_51 = e0
% 19.62/5.15 |
% 19.62/5.15 | Combining equations (475,629) yields a new equation:
% 19.62/5.15 | (578) e1 = e0
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 578 yields:
% 19.62/5.15 | (579) e1 = e0
% 19.62/5.15 |
% 19.62/5.15 | Equations (579) can reduce 144 to:
% 19.62/5.15 | (269) $false
% 19.62/5.15 |
% 19.62/5.15 |-The branch is then unsatisfiable
% 19.62/5.15 |-Branch two:
% 19.62/5.15 | (432) ~ (all_0_51_51 = e0)
% 19.62/5.15 | (632) all_0_56_56 = e0
% 19.62/5.15 |
% 19.62/5.15 | Equations (632) can reduce 223 to:
% 19.62/5.15 | (402) ~ (all_0_58_58 = e0)
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 402 yields:
% 19.62/5.15 | (403) ~ (all_0_58_58 = e0)
% 19.62/5.15 |
% 19.62/5.15 | Equations (632) can reduce 273 to:
% 19.62/5.15 | (404) ~ (e4 = e0)
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 404 yields:
% 19.62/5.15 | (11) ~ (e4 = e0)
% 19.62/5.15 |
% 19.62/5.15 | Equations (632) can reduce 1183 to:
% 19.62/5.15 | (1272) ~ (e3 = e0)
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 1272 yields:
% 19.62/5.15 | (72) ~ (e3 = e0)
% 19.62/5.15 |
% 19.62/5.15 | From (632) and (7) follows:
% 19.62/5.15 | (1274) op(e3, e0) = all_0_11_11
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (139), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (889) all_0_45_45 = e0
% 19.62/5.15 |
% 19.62/5.15 | Combining equations (1087,889) yields a new equation:
% 19.62/5.15 | (781) e3 = e0
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 781 yields:
% 19.62/5.15 | (560) e3 = e0
% 19.62/5.15 |
% 19.62/5.15 | Equations (560) can reduce 72 to:
% 19.62/5.15 | (269) $false
% 19.62/5.15 |
% 19.62/5.15 |-The branch is then unsatisfiable
% 19.62/5.15 |-Branch two:
% 19.62/5.15 | (299) ~ (all_0_45_45 = e0)
% 19.62/5.15 | (894) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (1245), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (857) all_0_53_53 = e0
% 19.62/5.15 |
% 19.62/5.15 | Combining equations (532,857) yields a new equation:
% 19.62/5.15 | (751) e4 = e0
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 751 yields:
% 19.62/5.15 | (439) e4 = e0
% 19.62/5.15 |
% 19.62/5.15 | Equations (439) can reduce 11 to:
% 19.62/5.15 | (269) $false
% 19.62/5.15 |
% 19.62/5.15 |-The branch is then unsatisfiable
% 19.62/5.15 |-Branch two:
% 19.62/5.15 | (765) ~ (all_0_53_53 = e0)
% 19.62/5.15 | (1286) all_0_54_54 = e0
% 19.62/5.15 |
% 19.62/5.15 | Equations (1286) can reduce 217 to:
% 19.62/5.15 | (807) ~ (all_0_49_49 = e0)
% 19.62/5.15 |
% 19.62/5.15 | Equations (1286) can reduce 312 to:
% 19.62/5.15 | (404) ~ (e4 = e0)
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 404 yields:
% 19.62/5.15 | (11) ~ (e4 = e0)
% 19.62/5.15 |
% 19.62/5.15 | Equations (1286) can reduce 1238 to:
% 19.62/5.15 | (436) ~ (e1 = e0)
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 436 yields:
% 19.62/5.15 | (144) ~ (e1 = e0)
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (296), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (401) ~ (all_0_56_56 = e0)
% 19.62/5.15 |
% 19.62/5.15 | Equations (632) can reduce 401 to:
% 19.62/5.15 | (269) $false
% 19.62/5.15 |
% 19.62/5.15 |-The branch is then unsatisfiable
% 19.62/5.15 |-Branch two:
% 19.62/5.15 | (632) all_0_56_56 = e0
% 19.62/5.15 | (1070) all_0_59_59 = e3
% 19.62/5.15 |
% 19.62/5.15 | Equations (1070) can reduce 82 to:
% 19.62/5.15 | (158) ~ (all_0_49_49 = e3)
% 19.62/5.15 |
% 19.62/5.15 | Equations (1070) can reduce 198 to:
% 19.62/5.15 | (527) ~ (all_0_58_58 = e3)
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (43), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (480) all_0_56_56 = e1
% 19.62/5.15 |
% 19.62/5.15 | Combining equations (480,632) yields a new equation:
% 19.62/5.15 | (578) e1 = e0
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 578 yields:
% 19.62/5.15 | (579) e1 = e0
% 19.62/5.15 |
% 19.62/5.15 | Equations (579) can reduce 144 to:
% 19.62/5.15 | (269) $false
% 19.62/5.15 |
% 19.62/5.15 |-The branch is then unsatisfiable
% 19.62/5.15 |-Branch two:
% 19.62/5.15 | (575) ~ (all_0_56_56 = e1)
% 19.62/5.15 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (340), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (596) all_0_49_49 = e1
% 19.62/5.15 |
% 19.62/5.15 | Equations (596) can reduce 158 to:
% 19.62/5.15 | (597) ~ (e3 = e1)
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 597 yields:
% 19.62/5.15 | (146) ~ (e3 = e1)
% 19.62/5.15 |
% 19.62/5.15 | Equations (596) can reduce 323 to:
% 19.62/5.15 | (414) ~ (e2 = e1)
% 19.62/5.15 |
% 19.62/5.15 | Simplifying 414 yields:
% 19.62/5.15 | (148) ~ (e2 = e1)
% 19.62/5.15 |
% 19.62/5.15 +-Applying beta-rule and splitting (894), into two cases.
% 19.62/5.15 |-Branch one:
% 19.62/5.15 | (903) all_0_48_48 = e0
% 19.62/5.15 |
% 19.62/5.16 | Equations (903) can reduce 1115 to:
% 19.62/5.16 | (406) ~ (e2 = e0)
% 19.62/5.16 |
% 19.62/5.16 | Simplifying 406 yields:
% 19.62/5.16 | (58) ~ (e2 = e0)
% 19.62/5.16 |
% 19.62/5.16 +-Applying beta-rule and splitting (15), into two cases.
% 19.62/5.16 |-Branch one:
% 19.62/5.16 | (1312) all_0_41_41 = e1
% 19.62/5.16 |
% 19.62/5.16 | Combining equations (1312,386) yields a new equation:
% 19.62/5.16 | (471) e2 = e1
% 19.62/5.16 |
% 19.62/5.16 | Equations (471) can reduce 148 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (1315) ~ (all_0_41_41 = e1)
% 19.62/5.16 | (1316) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 19.62/5.16 |
% 19.62/5.16 | Equations (386) can reduce 1315 to:
% 19.62/5.16 | (148) ~ (e2 = e1)
% 19.62/5.16 |
% 19.62/5.16 +-Applying beta-rule and splitting (576), into two cases.
% 19.62/5.16 |-Branch one:
% 19.62/5.16 | (577) all_0_57_57 = e1
% 19.62/5.16 |
% 19.62/5.16 | Combining equations (577,867) yields a new equation:
% 19.62/5.16 | (471) e2 = e1
% 19.62/5.16 |
% 19.62/5.16 | Equations (471) can reduce 148 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (581) ~ (all_0_57_57 = e1)
% 19.62/5.16 | (582) all_0_58_58 = e1 | all_0_59_59 = e1
% 19.62/5.16 |
% 19.62/5.16 +-Applying beta-rule and splitting (582), into two cases.
% 19.62/5.16 |-Branch one:
% 19.62/5.16 | (489) all_0_58_58 = e1
% 19.62/5.16 |
% 19.62/5.16 | Equations (489) can reduce 527 to:
% 19.62/5.16 | (597) ~ (e3 = e1)
% 19.62/5.16 |
% 19.62/5.16 | Simplifying 597 yields:
% 19.62/5.16 | (146) ~ (e3 = e1)
% 19.62/5.16 |
% 19.62/5.16 | Instantiating formula (21) with e4, e3, e3, all_0_5_5 and discharging atoms op(e4, e3) = all_0_5_5, op(e4, e3) = e3, yields:
% 19.62/5.16 | (1326) all_0_5_5 = e3
% 19.62/5.16 |
% 19.62/5.16 | Instantiating formula (21) with e3, e1, e3, all_0_9_9 and discharging atoms op(e3, e1) = all_0_9_9, op(e3, e1) = e3, yields:
% 19.62/5.16 | (1327) all_0_9_9 = e3
% 19.62/5.16 |
% 19.62/5.16 | Instantiating formula (21) with e3, e0, all_0_16_16, all_0_11_11 and discharging atoms op(e3, e0) = all_0_11_11, op(e3, e0) = all_0_16_16, yields:
% 19.62/5.16 | (1328) all_0_11_11 = all_0_16_16
% 19.62/5.16 |
% 19.62/5.16 | Instantiating formula (21) with e3, e0, e2, all_0_11_11 and discharging atoms op(e3, e0) = all_0_11_11, op(e3, e0) = e2, yields:
% 19.62/5.16 | (1329) all_0_11_11 = e2
% 19.62/5.16 |
% 19.62/5.16 | Combining equations (1329,1328) yields a new equation:
% 19.62/5.16 | (1330) all_0_16_16 = e2
% 19.62/5.16 |
% 19.62/5.16 | Combining equations (1330,1328) yields a new equation:
% 19.62/5.16 | (1329) all_0_11_11 = e2
% 19.62/5.16 |
% 19.62/5.16 +-Applying beta-rule and splitting (5), into two cases.
% 19.62/5.16 |-Branch one:
% 19.62/5.16 | (1332) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3)) | (all_0_9_9 = e1 & ~ (all_0_10_10 = e3))
% 19.62/5.16 |
% 19.62/5.16 +-Applying beta-rule and splitting (1332), into two cases.
% 19.62/5.16 |-Branch one:
% 19.62/5.16 | (1333) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3))
% 19.62/5.16 |
% 19.62/5.16 +-Applying beta-rule and splitting (1333), into two cases.
% 19.62/5.16 |-Branch one:
% 19.62/5.16 | (1334) all_0_4_4 = e4 & ~ (all_0_5_5 = e3)
% 19.62/5.16 |
% 19.62/5.16 | Applying alpha-rule on (1334) yields:
% 19.62/5.16 | (1335) all_0_4_4 = e4
% 19.62/5.16 | (1336) ~ (all_0_5_5 = e3)
% 19.62/5.16 |
% 19.62/5.16 | Equations (1326) can reduce 1336 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (1338) all_0_7_7 = e2 & ~ (all_0_8_8 = e3)
% 19.62/5.16 |
% 19.62/5.16 | Applying alpha-rule on (1338) yields:
% 19.62/5.16 | (1339) all_0_7_7 = e2
% 19.62/5.16 | (1340) ~ (all_0_8_8 = e3)
% 19.62/5.16 |
% 19.62/5.16 | Combining equations (1339,1138) yields a new equation:
% 19.62/5.16 | (353) e2 = e0
% 19.62/5.16 |
% 19.62/5.16 | Simplifying 353 yields:
% 19.62/5.16 | (354) e2 = e0
% 19.62/5.16 |
% 19.62/5.16 | Equations (354) can reduce 58 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (1344) all_0_9_9 = e1 & ~ (all_0_10_10 = e3)
% 19.62/5.16 |
% 19.62/5.16 | Applying alpha-rule on (1344) yields:
% 19.62/5.16 | (1345) all_0_9_9 = e1
% 19.62/5.16 | (1346) ~ (all_0_10_10 = e3)
% 19.62/5.16 |
% 19.62/5.16 | Combining equations (1345,1327) yields a new equation:
% 19.62/5.16 | (418) e3 = e1
% 19.62/5.16 |
% 19.62/5.16 | Equations (418) can reduce 146 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (1349) all_0_11_11 = e0 & ~ (all_0_12_12 = e3)
% 19.62/5.16 |
% 19.62/5.16 | Applying alpha-rule on (1349) yields:
% 19.62/5.16 | (1350) all_0_11_11 = e0
% 19.62/5.16 | (1351) ~ (all_0_12_12 = e3)
% 19.62/5.16 |
% 19.62/5.16 | Combining equations (1350,1329) yields a new equation:
% 19.62/5.16 | (354) e2 = e0
% 19.62/5.16 |
% 19.62/5.16 | Equations (354) can reduce 58 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (482) ~ (all_0_58_58 = e1)
% 19.62/5.16 | (614) all_0_59_59 = e1
% 19.62/5.16 |
% 19.62/5.16 | Combining equations (1070,614) yields a new equation:
% 19.62/5.16 | (572) e3 = e1
% 19.62/5.16 |
% 19.62/5.16 | Simplifying 572 yields:
% 19.62/5.16 | (418) e3 = e1
% 19.62/5.16 |
% 19.62/5.16 | Equations (418) can reduce 146 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (952) ~ (all_0_48_48 = e0)
% 19.62/5.16 | (953) all_0_53_53 = e0 | all_0_58_58 = e0
% 19.62/5.16 |
% 19.62/5.16 +-Applying beta-rule and splitting (953), into two cases.
% 19.62/5.16 |-Branch one:
% 19.62/5.16 | (857) all_0_53_53 = e0
% 19.62/5.16 |
% 19.62/5.16 | Combining equations (857,532) yields a new equation:
% 19.62/5.16 | (439) e4 = e0
% 19.62/5.16 |
% 19.62/5.16 | Equations (439) can reduce 11 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (765) ~ (all_0_53_53 = e0)
% 19.62/5.16 | (493) all_0_58_58 = e0
% 19.62/5.16 |
% 19.62/5.16 | Equations (493) can reduce 403 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (960) ~ (all_0_49_49 = e1)
% 19.62/5.16 | (965) all_0_49_49 = e0
% 19.62/5.16 |
% 19.62/5.16 | Equations (965) can reduce 807 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (479) ~ (all_0_51_51 = e1)
% 19.62/5.16 | (1371) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e0
% 19.62/5.16 |
% 19.62/5.16 +-Applying beta-rule and splitting (1371), into two cases.
% 19.62/5.16 |-Branch one:
% 19.62/5.16 | (629) all_0_51_51 = e0
% 19.62/5.16 |
% 19.62/5.16 | Equations (629) can reduce 432 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (432) ~ (all_0_51_51 = e0)
% 19.62/5.16 | (1375) all_0_51_51 = e4 | all_0_51_51 = e3
% 19.62/5.16 |
% 19.62/5.16 +-Applying beta-rule and splitting (1375), into two cases.
% 19.62/5.16 |-Branch one:
% 19.62/5.16 | (564) all_0_51_51 = e3
% 19.62/5.16 |
% 19.62/5.16 | Equations (564) can reduce 428 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (428) ~ (all_0_51_51 = e3)
% 19.62/5.16 | (458) all_0_51_51 = e4
% 19.62/5.16 |
% 19.62/5.16 | Equations (458) can reduce 530 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (448) ~ (all_0_53_53 = e4)
% 19.62/5.16 | (535) all_0_54_54 = e4
% 19.62/5.16 |
% 19.62/5.16 | Equations (535) can reduce 312 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (441) ~ (all_0_43_43 = e4)
% 19.62/5.16 | (442) all_0_45_45 = e4 | all_0_46_46 = e4
% 19.62/5.16 |
% 19.62/5.16 +-Applying beta-rule and splitting (29), into two cases.
% 19.62/5.16 |-Branch one:
% 19.62/5.16 | (1079) all_0_39_39 = e4
% 19.62/5.16 |
% 19.62/5.16 | Combining equations (1079,443) yields a new equation:
% 19.62/5.16 | (515) e4 = e3
% 19.62/5.16 |
% 19.62/5.16 | Simplifying 515 yields:
% 19.62/5.16 | (516) e4 = e3
% 19.62/5.16 |
% 19.62/5.16 | Equations (516) can reduce 41 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (307) ~ (all_0_39_39 = e4)
% 19.62/5.16 | (1391) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 19.62/5.16 |
% 19.62/5.16 | Equations (443) can reduce 307 to:
% 19.62/5.16 | (498) ~ (e4 = e3)
% 19.62/5.16 |
% 19.62/5.16 | Simplifying 498 yields:
% 19.62/5.16 | (41) ~ (e4 = e3)
% 19.62/5.16 |
% 19.62/5.16 +-Applying beta-rule and splitting (442), into two cases.
% 19.62/5.16 |-Branch one:
% 19.62/5.16 | (444) all_0_45_45 = e4
% 19.62/5.16 |
% 19.62/5.16 | Combining equations (1087,444) yields a new equation:
% 19.62/5.16 | (516) e4 = e3
% 19.62/5.16 |
% 19.62/5.16 | Equations (516) can reduce 41 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (537) ~ (all_0_45_45 = e4)
% 19.62/5.16 | (538) all_0_46_46 = e4
% 19.62/5.16 |
% 19.62/5.16 | Combining equations (538,364) yields a new equation:
% 19.62/5.16 | (359) e4 = e2
% 19.62/5.16 |
% 19.62/5.16 | Simplifying 359 yields:
% 19.62/5.16 | (360) e4 = e2
% 19.62/5.16 |
% 19.62/5.16 | Equations (360) can reduce 230 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (689) ~ (all_0_45_45 = e3)
% 19.62/5.16 | (462) all_0_46_46 = e3
% 19.62/5.16 |
% 19.62/5.16 | Combining equations (364,462) yields a new equation:
% 19.62/5.16 | (423) e3 = e2
% 19.62/5.16 |
% 19.62/5.16 | Equations (423) can reduce 224 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (629) all_0_51_51 = e0
% 19.62/5.16 | (635) all_0_54_54 = e3
% 19.62/5.16 |
% 19.62/5.16 | Equations (635) can reduce 430 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (540) ~ (all_0_39_39 = e3)
% 19.62/5.16 | (541) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 19.62/5.16 |
% 19.62/5.16 +-Applying beta-rule and splitting (709), into two cases.
% 19.62/5.16 |-Branch one:
% 19.62/5.16 | (464) all_0_39_39 = e1
% 19.62/5.16 |
% 19.62/5.16 | Equations (464) can reduce 467 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (467) ~ (all_0_39_39 = e1)
% 19.62/5.16 | (1075) all_0_39_39 = e4 | all_0_39_39 = e3
% 19.62/5.16 |
% 19.62/5.16 +-Applying beta-rule and splitting (1075), into two cases.
% 19.62/5.16 |-Branch one:
% 19.62/5.16 | (443) all_0_39_39 = e3
% 19.62/5.16 |
% 19.62/5.16 | Equations (443) can reduce 540 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (540) ~ (all_0_39_39 = e3)
% 19.62/5.16 | (1079) all_0_39_39 = e4
% 19.62/5.16 |
% 19.62/5.16 | Equations (1079) can reduce 307 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (641) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 19.62/5.16 |
% 19.62/5.16 | Applying alpha-rule on (641) yields:
% 19.62/5.16 | (285) all_0_2_2 = e0
% 19.62/5.16 | (643) ~ (all_0_3_3 = e4)
% 19.62/5.16 |
% 19.62/5.16 | Equations (288) can reduce 643 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (645) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 19.62/5.16 |
% 19.62/5.16 | Applying alpha-rule on (645) yields:
% 19.62/5.16 | (605) all_0_41_41 = e3
% 19.62/5.16 | (537) ~ (all_0_45_45 = e4)
% 19.62/5.16 |
% 19.62/5.16 | Combining equations (386,605) yields a new equation:
% 19.62/5.16 | (423) e3 = e2
% 19.62/5.16 |
% 19.62/5.16 | Equations (423) can reduce 224 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (356) ~ (all_0_44_44 = e0)
% 19.62/5.16 | (357) all_0_52_52 = e0 | all_0_57_57 = e0
% 19.62/5.16 |
% 19.62/5.16 +-Applying beta-rule and splitting (357), into two cases.
% 19.62/5.16 |-Branch one:
% 19.62/5.16 | (397) all_0_52_52 = e0
% 19.62/5.16 |
% 19.62/5.16 | Equations (397) can reduce 317 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (317) ~ (all_0_52_52 = e0)
% 19.62/5.16 | (400) all_0_57_57 = e0
% 19.62/5.16 |
% 19.62/5.16 | Combining equations (400,867) yields a new equation:
% 19.62/5.16 | (354) e2 = e0
% 19.62/5.16 |
% 19.62/5.16 | Equations (354) can reduce 58 to:
% 19.62/5.16 | (269) $false
% 19.62/5.16 |
% 19.62/5.16 |-The branch is then unsatisfiable
% 19.62/5.16 |-Branch two:
% 19.62/5.16 | (650) ~ (all_0_41_41 = e2)
% 19.62/5.16 | (358) all_0_42_42 = e2
% 19.62/5.16 |
% 19.62/5.16 | Combining equations (305,358) yields a new equation:
% 19.62/5.16 | (359) e4 = e2
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 359 yields:
% 19.62/5.17 | (360) e4 = e2
% 19.62/5.17 |
% 19.62/5.17 | Equations (360) can reduce 230 to:
% 19.62/5.17 | (269) $false
% 19.62/5.17 |
% 19.62/5.17 |-The branch is then unsatisfiable
% 19.62/5.17 |-Branch two:
% 19.62/5.17 | (1442) ~ (all_0_47_47 = e2)
% 19.62/5.17 | (1443) all_0_47_47 = e1 | all_0_47_47 = e0
% 19.62/5.17 |
% 19.62/5.17 +-Applying beta-rule and splitting (1443), into two cases.
% 19.62/5.17 |-Branch one:
% 19.62/5.17 | (469) all_0_47_47 = e1
% 19.62/5.17 |
% 19.62/5.17 | Equations (469) can reduce 164 to:
% 19.62/5.17 | (467) ~ (all_0_39_39 = e1)
% 19.62/5.17 |
% 19.62/5.17 | Equations (469) can reduce 48 to:
% 19.62/5.17 | (1446) ~ (all_0_48_48 = e1)
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 1446 yields:
% 19.62/5.17 | (584) ~ (all_0_48_48 = e1)
% 19.62/5.17 |
% 19.62/5.17 | Equations (469) can reduce 145 to:
% 19.62/5.17 | (1448) ~ (all_0_49_49 = e1)
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 1448 yields:
% 19.62/5.17 | (960) ~ (all_0_49_49 = e1)
% 19.62/5.17 |
% 19.62/5.17 | Equations (469) can reduce 34 to:
% 19.62/5.17 | (1450) ~ (all_0_51_51 = e1)
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 1450 yields:
% 19.62/5.17 | (479) ~ (all_0_51_51 = e1)
% 19.62/5.17 |
% 19.62/5.17 | Equations (469) can reduce 147 to:
% 19.62/5.17 | (1452) ~ (all_0_56_56 = e1)
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 1452 yields:
% 19.62/5.17 | (575) ~ (all_0_56_56 = e1)
% 19.62/5.17 |
% 19.62/5.17 | Equations (469) can reduce 115 to:
% 19.62/5.17 | (597) ~ (e3 = e1)
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 597 yields:
% 19.62/5.17 | (146) ~ (e3 = e1)
% 19.62/5.17 |
% 19.62/5.17 | From (469) and (218) follows:
% 19.62/5.17 | (1456) op(e2, e1) = all_0_8_8
% 19.62/5.17 |
% 19.62/5.17 +-Applying beta-rule and splitting (294), into two cases.
% 19.62/5.17 |-Branch one:
% 19.62/5.17 | (952) ~ (all_0_48_48 = e0)
% 19.62/5.17 |
% 19.62/5.17 +-Applying beta-rule and splitting (197), into two cases.
% 19.62/5.17 |-Branch one:
% 19.62/5.17 | (1458) all_0_48_48 = e2
% 19.62/5.17 |
% 19.62/5.17 | Equations (1458) can reduce 167 to:
% 19.62/5.17 | (650) ~ (all_0_41_41 = e2)
% 19.62/5.17 |
% 19.62/5.17 | Equations (1458) can reduce 196 to:
% 19.62/5.17 | (390) ~ (all_0_45_45 = e2)
% 19.62/5.17 |
% 19.62/5.17 | Equations (1458) can reduce 178 to:
% 19.62/5.17 | (322) ~ (all_0_49_49 = e2)
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 322 yields:
% 19.62/5.17 | (323) ~ (all_0_49_49 = e2)
% 19.62/5.17 |
% 19.62/5.17 | Equations (1458) can reduce 4 to:
% 19.62/5.17 | (328) ~ (e3 = e2)
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 328 yields:
% 19.62/5.17 | (224) ~ (e3 = e2)
% 19.62/5.17 |
% 19.62/5.17 | Equations (1458) can reduce 584 to:
% 19.62/5.17 | (148) ~ (e2 = e1)
% 19.62/5.17 |
% 19.62/5.17 | From (1458) and (76) follows:
% 19.62/5.17 | (1466) op(e2, e2) = all_0_26_26
% 19.62/5.17 |
% 19.62/5.17 | From (1458) and (179) follows:
% 19.62/5.17 | (1467) op(e2, e1) = e2
% 19.62/5.17 |
% 19.62/5.17 +-Applying beta-rule and splitting (50), into two cases.
% 19.62/5.17 |-Branch one:
% 19.62/5.17 | (337) all_0_49_49 = e2
% 19.62/5.17 |
% 19.62/5.17 | Equations (337) can reduce 323 to:
% 19.62/5.17 | (269) $false
% 19.62/5.17 |
% 19.62/5.17 |-The branch is then unsatisfiable
% 19.62/5.17 |-Branch two:
% 19.62/5.17 | (323) ~ (all_0_49_49 = e2)
% 19.62/5.17 | (340) all_0_49_49 = e1 | all_0_49_49 = e0
% 19.62/5.17 |
% 19.62/5.17 +-Applying beta-rule and splitting (340), into two cases.
% 19.62/5.17 |-Branch one:
% 19.62/5.17 | (596) all_0_49_49 = e1
% 19.62/5.17 |
% 19.62/5.17 | Equations (596) can reduce 960 to:
% 19.62/5.17 | (269) $false
% 19.62/5.17 |
% 19.62/5.17 |-The branch is then unsatisfiable
% 19.62/5.17 |-Branch two:
% 19.62/5.17 | (960) ~ (all_0_49_49 = e1)
% 19.62/5.17 | (965) all_0_49_49 = e0
% 19.62/5.17 |
% 19.62/5.17 | Equations (965) can reduce 166 to:
% 19.62/5.17 | (435) ~ (all_0_46_46 = e0)
% 19.62/5.17 |
% 19.62/5.17 | Equations (965) can reduce 217 to:
% 19.62/5.17 | (1477) ~ (all_0_54_54 = e0)
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 1477 yields:
% 19.62/5.17 | (1478) ~ (all_0_54_54 = e0)
% 19.62/5.17 |
% 19.62/5.17 | Equations (965) can reduce 82 to:
% 19.62/5.17 | (1479) ~ (all_0_59_59 = e0)
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 1479 yields:
% 19.62/5.17 | (1480) ~ (all_0_59_59 = e0)
% 19.62/5.17 |
% 19.62/5.17 | Equations (965) can reduce 158 to:
% 19.62/5.17 | (1272) ~ (e3 = e0)
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 1272 yields:
% 19.62/5.17 | (72) ~ (e3 = e0)
% 19.62/5.17 |
% 19.62/5.17 | Equations (965) can reduce 323 to:
% 19.62/5.17 | (406) ~ (e2 = e0)
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 406 yields:
% 19.62/5.17 | (58) ~ (e2 = e0)
% 19.62/5.17 |
% 19.62/5.17 | From (965) and (38) follows:
% 19.62/5.17 | (1485) op(e2, e0) = all_0_35_35
% 19.62/5.17 |
% 19.62/5.17 | From (965) and (128) follows:
% 19.62/5.17 | (1486) op(e2, e0) = e0
% 19.62/5.17 |
% 19.62/5.17 | From (965) and (183) follows:
% 19.62/5.17 | (1487) op(e0, e0) = all_0_34_34
% 19.62/5.17 |
% 19.62/5.17 | Instantiating formula (21) with e2, e2, all_0_26_26, e4 and discharging atoms op(e2, e2) = all_0_26_26, op(e2, e2) = e4, yields:
% 19.62/5.17 | (1488) all_0_26_26 = e4
% 19.62/5.17 |
% 19.62/5.17 | Instantiating formula (21) with e2, e1, e2, all_0_8_8 and discharging atoms op(e2, e1) = all_0_8_8, op(e2, e1) = e2, yields:
% 19.62/5.17 | (1489) all_0_8_8 = e2
% 19.62/5.17 |
% 19.62/5.17 | Instantiating formula (21) with e2, e0, e0, all_0_35_35 and discharging atoms op(e2, e0) = all_0_35_35, op(e2, e0) = e0, yields:
% 19.62/5.17 | (1490) all_0_35_35 = e0
% 19.62/5.17 |
% 19.62/5.17 | Instantiating formula (21) with e0, e0, all_0_34_34, all_0_59_59 and discharging atoms op(e0, e0) = all_0_34_34, op(e0, e0) = all_0_59_59, yields:
% 19.62/5.17 | (1491) all_0_34_34 = all_0_59_59
% 19.62/5.17 |
% 19.62/5.17 | From (1488) and (1466) follows:
% 19.62/5.17 | (222) op(e2, e2) = e4
% 19.62/5.17 |
% 19.62/5.17 | From (1489) and (1456) follows:
% 19.62/5.17 | (1467) op(e2, e1) = e2
% 19.62/5.17 |
% 19.62/5.17 | From (1490) and (1485) follows:
% 19.62/5.17 | (1486) op(e2, e0) = e0
% 19.62/5.17 |
% 19.62/5.17 +-Applying beta-rule and splitting (149), into two cases.
% 19.62/5.17 |-Branch one:
% 19.62/5.17 | (341) all_0_44_44 = e2
% 19.62/5.17 |
% 19.62/5.17 | Equations (341) can reduce 228 to:
% 19.62/5.17 | (321) ~ (all_0_43_43 = e2)
% 19.62/5.17 |
% 19.62/5.17 | Equations (341) can reduce 117 to:
% 19.62/5.17 | (389) ~ (all_0_45_45 = e2)
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 389 yields:
% 19.62/5.17 | (390) ~ (all_0_45_45 = e2)
% 19.62/5.17 |
% 19.62/5.17 | Equations (341) can reduce 210 to:
% 19.62/5.17 | (343) ~ (all_0_46_46 = e2)
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 343 yields:
% 19.62/5.17 | (344) ~ (all_0_46_46 = e2)
% 19.62/5.17 |
% 19.62/5.17 | Equations (341) can reduce 190 to:
% 19.62/5.17 | (326) ~ (e4 = e2)
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 326 yields:
% 19.62/5.17 | (230) ~ (e4 = e2)
% 19.62/5.17 |
% 19.62/5.17 | Equations (341) can reduce 87 to:
% 19.62/5.17 | (148) ~ (e2 = e1)
% 19.62/5.17 |
% 19.62/5.17 +-Applying beta-rule and splitting (216), into two cases.
% 19.62/5.17 |-Branch one:
% 19.62/5.17 | (358) all_0_42_42 = e2
% 19.62/5.17 |
% 19.62/5.17 | Combining equations (305,358) yields a new equation:
% 19.62/5.17 | (359) e4 = e2
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 359 yields:
% 19.62/5.17 | (360) e4 = e2
% 19.62/5.17 |
% 19.62/5.17 | Equations (360) can reduce 230 to:
% 19.62/5.17 | (269) $false
% 19.62/5.17 |
% 19.62/5.17 |-The branch is then unsatisfiable
% 19.62/5.17 |-Branch two:
% 19.62/5.17 | (362) ~ (all_0_42_42 = e2)
% 19.62/5.17 | (363) all_0_46_46 = e2 | all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 19.62/5.17 |
% 19.62/5.17 +-Applying beta-rule and splitting (363), into two cases.
% 19.62/5.17 |-Branch one:
% 19.62/5.17 | (364) all_0_46_46 = e2
% 19.62/5.17 |
% 19.62/5.17 | Equations (364) can reduce 344 to:
% 19.62/5.17 | (269) $false
% 19.62/5.17 |
% 19.62/5.17 |-The branch is then unsatisfiable
% 19.62/5.17 |-Branch two:
% 19.62/5.17 | (344) ~ (all_0_46_46 = e2)
% 19.62/5.17 | (367) all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 19.62/5.17 |
% 19.62/5.17 +-Applying beta-rule and splitting (367), into two cases.
% 19.62/5.17 |-Branch one:
% 19.62/5.17 | (337) all_0_49_49 = e2
% 19.62/5.17 |
% 19.62/5.17 | Combining equations (337,965) yields a new equation:
% 19.62/5.17 | (353) e2 = e0
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 353 yields:
% 19.62/5.17 | (354) e2 = e0
% 19.62/5.17 |
% 19.62/5.17 | Equations (354) can reduce 58 to:
% 19.62/5.17 | (269) $false
% 19.62/5.17 |
% 19.62/5.17 |-The branch is then unsatisfiable
% 19.62/5.17 |-Branch two:
% 19.62/5.17 | (323) ~ (all_0_49_49 = e2)
% 19.62/5.17 | (371) all_0_54_54 = e2 | all_0_59_59 = e2
% 19.62/5.17 |
% 19.62/5.17 +-Applying beta-rule and splitting (154), into two cases.
% 19.62/5.17 |-Branch one:
% 19.62/5.17 | (348) all_0_39_39 = e2
% 19.62/5.17 |
% 19.62/5.17 | Equations (348) can reduce 18 to:
% 19.62/5.17 | (1521) ~ (all_0_40_40 = e2)
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 1521 yields:
% 19.62/5.17 | (342) ~ (all_0_40_40 = e2)
% 19.62/5.17 |
% 19.62/5.17 | Equations (348) can reduce 234 to:
% 19.62/5.17 | (1523) ~ (all_0_43_43 = e2)
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 1523 yields:
% 19.62/5.17 | (321) ~ (all_0_43_43 = e2)
% 19.62/5.17 |
% 19.62/5.17 +-Applying beta-rule and splitting (371), into two cases.
% 19.62/5.17 |-Branch one:
% 19.62/5.17 | (372) all_0_54_54 = e2
% 19.62/5.17 |
% 19.62/5.17 | Equations (372) can reduce 261 to:
% 19.62/5.17 | (269) $false
% 19.62/5.17 |
% 19.62/5.17 |-The branch is then unsatisfiable
% 19.62/5.17 |-Branch two:
% 19.62/5.17 | (261) ~ (all_0_54_54 = e2)
% 19.62/5.17 | (375) all_0_59_59 = e2
% 19.62/5.17 |
% 19.62/5.17 | Equations (375) can reduce 150 to:
% 19.62/5.17 | (344) ~ (all_0_46_46 = e2)
% 19.62/5.17 |
% 19.62/5.17 | Equations (375) can reduce 130 to:
% 19.62/5.17 | (377) ~ (all_0_56_56 = e2)
% 19.62/5.17 |
% 19.62/5.17 | Equations (375) can reduce 1480 to:
% 19.62/5.17 | (58) ~ (e2 = e0)
% 19.62/5.17 |
% 19.62/5.17 +-Applying beta-rule and splitting (110), into two cases.
% 19.62/5.17 |-Branch one:
% 19.62/5.17 | (352) all_0_44_44 = e0
% 19.62/5.17 |
% 19.62/5.17 | Combining equations (341,352) yields a new equation:
% 19.62/5.17 | (353) e2 = e0
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 353 yields:
% 19.62/5.17 | (354) e2 = e0
% 19.62/5.17 |
% 19.62/5.17 | Equations (354) can reduce 58 to:
% 19.62/5.17 | (269) $false
% 19.62/5.17 |
% 19.62/5.17 |-The branch is then unsatisfiable
% 19.62/5.17 |-Branch two:
% 19.62/5.17 | (356) ~ (all_0_44_44 = e0)
% 19.62/5.17 | (357) all_0_52_52 = e0 | all_0_57_57 = e0
% 19.62/5.17 |
% 19.62/5.17 +-Applying beta-rule and splitting (199), into two cases.
% 19.62/5.17 |-Branch one:
% 19.62/5.17 | (364) all_0_46_46 = e2
% 19.62/5.17 |
% 19.62/5.17 | Equations (364) can reduce 344 to:
% 19.62/5.17 | (269) $false
% 19.62/5.17 |
% 19.62/5.17 |-The branch is then unsatisfiable
% 19.62/5.17 |-Branch two:
% 19.62/5.17 | (344) ~ (all_0_46_46 = e2)
% 19.62/5.17 | (545) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e0
% 19.62/5.17 |
% 19.62/5.17 +-Applying beta-rule and splitting (357), into two cases.
% 19.62/5.17 |-Branch one:
% 19.62/5.17 | (397) all_0_52_52 = e0
% 19.62/5.17 |
% 19.62/5.17 | Equations (397) can reduce 317 to:
% 19.62/5.17 | (269) $false
% 19.62/5.17 |
% 19.62/5.17 |-The branch is then unsatisfiable
% 19.62/5.17 |-Branch two:
% 19.62/5.17 | (317) ~ (all_0_52_52 = e0)
% 19.62/5.17 | (400) all_0_57_57 = e0
% 19.62/5.17 |
% 19.62/5.17 | Equations (400) can reduce 168 to:
% 19.62/5.17 | (102) ~ (all_0_40_40 = e0)
% 19.62/5.17 |
% 19.62/5.17 | Equations (400) can reduce 252 to:
% 19.62/5.17 | (402) ~ (all_0_58_58 = e0)
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 402 yields:
% 19.62/5.17 | (403) ~ (all_0_58_58 = e0)
% 19.62/5.17 |
% 19.62/5.17 +-Applying beta-rule and splitting (545), into two cases.
% 19.62/5.17 |-Branch one:
% 19.62/5.17 | (546) all_0_46_46 = e0
% 19.62/5.17 |
% 19.62/5.17 | Equations (546) can reduce 435 to:
% 19.62/5.17 | (269) $false
% 19.62/5.17 |
% 19.62/5.17 |-The branch is then unsatisfiable
% 19.62/5.17 |-Branch two:
% 19.62/5.17 | (435) ~ (all_0_46_46 = e0)
% 19.62/5.17 | (549) all_0_46_46 = e4 | all_0_46_46 = e3
% 19.62/5.17 |
% 19.62/5.17 +-Applying beta-rule and splitting (143), into two cases.
% 19.62/5.17 |-Branch one:
% 19.62/5.17 | (433) all_0_43_43 = e0
% 19.62/5.17 |
% 19.62/5.17 | Equations (433) can reduce 186 to:
% 19.62/5.17 | (1140) ~ (all_0_45_45 = e0)
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 1140 yields:
% 19.62/5.17 | (299) ~ (all_0_45_45 = e0)
% 19.62/5.17 |
% 19.62/5.17 | Equations (433) can reduce 232 to:
% 19.62/5.17 | (1556) ~ (all_0_56_56 = e0)
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 1556 yields:
% 19.62/5.17 | (401) ~ (all_0_56_56 = e0)
% 19.62/5.17 |
% 19.62/5.17 | Equations (433) can reduce 321 to:
% 19.62/5.17 | (406) ~ (e2 = e0)
% 19.62/5.17 |
% 19.62/5.17 | Simplifying 406 yields:
% 19.62/5.17 | (58) ~ (e2 = e0)
% 19.62/5.17 |
% 19.62/5.17 | From (433) and (101) follows:
% 19.62/5.17 | (1560) op(e3, e3) = e0
% 19.62/5.17 |
% 19.62/5.17 +-Applying beta-rule and splitting (549), into two cases.
% 19.62/5.17 |-Branch one:
% 19.62/5.17 | (462) all_0_46_46 = e3
% 19.62/5.17 |
% 19.62/5.17 | From (462) and (105) follows:
% 19.62/5.17 | (1562) op(e3, e3) = all_0_33_33
% 19.62/5.17 |
% 19.62/5.17 +-Applying beta-rule and splitting (245), into two cases.
% 19.62/5.17 |-Branch one:
% 19.62/5.17 | (694) all_0_45_45 = e2
% 19.62/5.17 |
% 19.62/5.17 | Equations (694) can reduce 390 to:
% 19.62/5.17 | (269) $false
% 19.62/5.17 |
% 19.62/5.17 |-The branch is then unsatisfiable
% 19.62/5.17 |-Branch two:
% 19.62/5.17 | (390) ~ (all_0_45_45 = e2)
% 19.62/5.17 | (1082) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 19.62/5.17 |
% 19.62/5.17 +-Applying beta-rule and splitting (1082), into two cases.
% 19.62/5.17 |-Branch one:
% 19.62/5.17 | (889) all_0_45_45 = e0
% 19.62/5.17 |
% 19.62/5.17 | Equations (889) can reduce 299 to:
% 19.62/5.17 | (269) $false
% 19.62/5.17 |
% 19.62/5.17 |-The branch is then unsatisfiable
% 19.62/5.17 |-Branch two:
% 19.62/5.17 | (299) ~ (all_0_45_45 = e0)
% 19.62/5.17 | (1086) all_0_45_45 = e4 | all_0_45_45 = e3
% 19.62/5.17 |
% 19.62/5.17 +-Applying beta-rule and splitting (139), into two cases.
% 19.62/5.17 |-Branch one:
% 19.62/5.18 | (889) all_0_45_45 = e0
% 19.62/5.18 |
% 19.62/5.18 | Equations (889) can reduce 299 to:
% 19.62/5.18 | (269) $false
% 19.62/5.18 |
% 19.62/5.18 |-The branch is then unsatisfiable
% 19.62/5.18 |-Branch two:
% 19.62/5.18 | (299) ~ (all_0_45_45 = e0)
% 19.62/5.18 | (894) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 19.62/5.18 |
% 19.62/5.18 +-Applying beta-rule and splitting (20), into two cases.
% 19.62/5.18 |-Branch one:
% 19.62/5.18 | (1575) all_0_56_56 = e2
% 19.62/5.18 |
% 19.62/5.18 | Equations (1575) can reduce 377 to:
% 19.62/5.18 | (269) $false
% 19.62/5.18 |
% 19.62/5.18 |-The branch is then unsatisfiable
% 19.62/5.18 |-Branch two:
% 19.62/5.18 | (377) ~ (all_0_56_56 = e2)
% 19.62/5.18 | (1578) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1 | all_0_56_56 = e0
% 19.62/5.18 |
% 19.62/5.18 +-Applying beta-rule and splitting (894), into two cases.
% 19.62/5.18 |-Branch one:
% 19.62/5.18 | (903) all_0_48_48 = e0
% 19.62/5.18 |
% 19.62/5.18 | Combining equations (1458,903) yields a new equation:
% 19.62/5.18 | (353) e2 = e0
% 19.62/5.18 |
% 19.62/5.18 | Simplifying 353 yields:
% 19.62/5.18 | (354) e2 = e0
% 19.62/5.18 |
% 19.62/5.18 | Equations (354) can reduce 58 to:
% 19.62/5.18 | (269) $false
% 19.62/5.18 |
% 19.62/5.18 |-The branch is then unsatisfiable
% 19.62/5.18 |-Branch two:
% 19.62/5.18 | (952) ~ (all_0_48_48 = e0)
% 19.62/5.18 | (953) all_0_53_53 = e0 | all_0_58_58 = e0
% 19.62/5.18 |
% 19.62/5.18 +-Applying beta-rule and splitting (953), into two cases.
% 19.62/5.18 |-Branch one:
% 19.62/5.18 | (857) all_0_53_53 = e0
% 19.62/5.18 |
% 19.62/5.18 | Equations (857) can reduce 119 to:
% 19.62/5.18 | (1477) ~ (all_0_54_54 = e0)
% 19.62/5.18 |
% 19.62/5.18 | Simplifying 1477 yields:
% 19.62/5.18 | (1478) ~ (all_0_54_54 = e0)
% 19.62/5.18 |
% 19.62/5.18 | From (857) and (90) follows:
% 19.62/5.18 | (1588) op(e1, e1) = e0
% 19.62/5.18 |
% 19.62/5.18 +-Applying beta-rule and splitting (303), into two cases.
% 19.62/5.18 |-Branch one:
% 19.62/5.18 | (765) ~ (all_0_53_53 = e0)
% 19.62/5.18 |
% 19.62/5.18 | Equations (857) can reduce 765 to:
% 19.62/5.18 | (269) $false
% 19.62/5.18 |
% 19.62/5.18 |-The branch is then unsatisfiable
% 19.62/5.18 |-Branch two:
% 19.62/5.18 | (857) all_0_53_53 = e0
% 19.62/5.18 | (1592) all_0_54_54 = e1
% 19.62/5.18 |
% 19.62/5.18 | Equations (1592) can reduce 62 to:
% 19.62/5.18 | (978) ~ (all_0_52_52 = e1)
% 19.62/5.18 |
% 19.62/5.18 | Equations (1592) can reduce 1478 to:
% 19.62/5.18 | (144) ~ (e1 = e0)
% 19.62/5.18 |
% 19.62/5.18 | From (1592) and (49) follows:
% 19.62/5.18 | (1595) op(e1, e1) = all_0_37_37
% 19.62/5.18 |
% 19.62/5.18 +-Applying beta-rule and splitting (246), into two cases.
% 19.62/5.18 |-Branch one:
% 19.62/5.18 | (413) all_0_40_40 = e1
% 19.62/5.18 |
% 19.62/5.18 | Equations (413) can reduce 88 to:
% 19.62/5.18 | (1597) ~ (all_0_41_41 = e1)
% 19.62/5.18 |
% 19.62/5.18 | Simplifying 1597 yields:
% 19.62/5.18 | (1315) ~ (all_0_41_41 = e1)
% 19.62/5.18 |
% 19.62/5.18 | Equations (413) can reduce 342 to:
% 19.62/5.18 | (414) ~ (e2 = e1)
% 19.62/5.18 |
% 19.62/5.18 | Simplifying 414 yields:
% 19.62/5.18 | (148) ~ (e2 = e1)
% 19.62/5.18 |
% 19.62/5.18 | Equations (413) can reduce 102 to:
% 19.62/5.18 | (144) ~ (e1 = e0)
% 19.62/5.18 |
% 19.62/5.18 +-Applying beta-rule and splitting (15), into two cases.
% 19.62/5.18 |-Branch one:
% 19.62/5.18 | (1312) all_0_41_41 = e1
% 19.62/5.18 |
% 19.62/5.18 | Equations (1312) can reduce 1315 to:
% 19.62/5.18 | (269) $false
% 19.62/5.18 |
% 19.62/5.18 |-The branch is then unsatisfiable
% 19.62/5.18 |-Branch two:
% 19.62/5.18 | (1315) ~ (all_0_41_41 = e1)
% 19.62/5.18 | (1316) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 19.62/5.18 |
% 19.62/5.18 +-Applying beta-rule and splitting (43), into two cases.
% 19.62/5.18 |-Branch one:
% 19.62/5.18 | (480) all_0_56_56 = e1
% 19.62/5.18 |
% 19.62/5.18 | Equations (480) can reduce 575 to:
% 19.62/5.18 | (269) $false
% 19.62/5.18 |
% 19.62/5.18 |-The branch is then unsatisfiable
% 19.62/5.18 |-Branch two:
% 19.62/5.18 | (575) ~ (all_0_56_56 = e1)
% 19.62/5.18 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 19.62/5.18 |
% 19.62/5.18 +-Applying beta-rule and splitting (1316), into two cases.
% 19.62/5.18 |-Branch one:
% 19.62/5.18 | (593) all_0_48_48 = e1
% 19.62/5.18 |
% 19.62/5.18 | Combining equations (1458,593) yields a new equation:
% 19.62/5.18 | (470) e2 = e1
% 19.62/5.18 |
% 19.62/5.18 | Simplifying 470 yields:
% 19.62/5.18 | (471) e2 = e1
% 19.62/5.18 |
% 19.62/5.18 | Equations (471) can reduce 148 to:
% 19.62/5.18 | (269) $false
% 19.62/5.18 |
% 19.62/5.18 |-The branch is then unsatisfiable
% 19.62/5.18 |-Branch two:
% 19.62/5.18 | (584) ~ (all_0_48_48 = e1)
% 19.62/5.18 | (1615) all_0_53_53 = e1 | all_0_58_58 = e1
% 19.62/5.18 |
% 19.62/5.18 +-Applying beta-rule and splitting (1578), into two cases.
% 19.62/5.18 |-Branch one:
% 19.62/5.18 | (480) all_0_56_56 = e1
% 19.62/5.18 |
% 19.62/5.18 | Equations (480) can reduce 575 to:
% 19.62/5.18 | (269) $false
% 19.62/5.18 |
% 19.62/5.18 |-The branch is then unsatisfiable
% 19.62/5.18 |-Branch two:
% 19.62/5.18 | (575) ~ (all_0_56_56 = e1)
% 19.62/5.18 | (1619) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e0
% 19.62/5.18 |
% 19.62/5.18 +-Applying beta-rule and splitting (1615), into two cases.
% 19.62/5.18 |-Branch one:
% 19.62/5.18 | (853) all_0_53_53 = e1
% 19.62/5.18 |
% 19.62/5.18 | Combining equations (853,857) yields a new equation:
% 19.62/5.18 | (578) e1 = e0
% 19.62/5.18 |
% 19.62/5.18 | Simplifying 578 yields:
% 19.62/5.18 | (579) e1 = e0
% 19.62/5.18 |
% 19.62/5.18 | Equations (579) can reduce 144 to:
% 19.62/5.18 | (269) $false
% 19.62/5.18 |
% 19.62/5.18 |-The branch is then unsatisfiable
% 19.62/5.18 |-Branch two:
% 19.62/5.18 | (823) ~ (all_0_53_53 = e1)
% 19.62/5.18 | (489) all_0_58_58 = e1
% 19.62/5.18 |
% 19.62/5.18 | From (489) and (67) follows:
% 19.62/5.18 | (910) op(e1, e1) = all_0_28_28
% 19.62/5.18 |
% 19.62/5.18 +-Applying beta-rule and splitting (1619), into two cases.
% 19.62/5.18 |-Branch one:
% 19.62/5.18 | (632) all_0_56_56 = e0
% 19.62/5.18 |
% 19.62/5.18 | Equations (632) can reduce 401 to:
% 19.62/5.18 | (269) $false
% 19.62/5.18 |
% 19.62/5.18 |-The branch is then unsatisfiable
% 19.62/5.18 |-Branch two:
% 19.62/5.18 | (401) ~ (all_0_56_56 = e0)
% 19.62/5.18 | (1630) all_0_56_56 = e4 | all_0_56_56 = e3
% 19.62/5.18 |
% 19.62/5.18 +-Applying beta-rule and splitting (1630), into two cases.
% 19.62/5.18 |-Branch one:
% 19.62/5.18 | (567) all_0_56_56 = e3
% 19.62/5.18 |
% 19.62/5.18 | From (567) and (7) follows:
% 19.62/5.18 | (1632) op(e3, e3) = all_0_11_11
% 19.62/5.18 |
% 19.62/5.18 | Instantiating formula (21) with e3, e3, all_0_33_33, all_0_11_11 and discharging atoms op(e3, e3) = all_0_11_11, op(e3, e3) = all_0_33_33, yields:
% 19.62/5.18 | (1633) all_0_11_11 = all_0_33_33
% 19.62/5.18 |
% 19.62/5.18 | Instantiating formula (21) with e3, e3, e0, all_0_11_11 and discharging atoms op(e3, e3) = all_0_11_11, op(e3, e3) = e0, yields:
% 19.62/5.18 | (1350) all_0_11_11 = e0
% 19.62/5.18 |
% 19.62/5.18 | Instantiating formula (21) with e1, e1, all_0_37_37, all_0_28_28 and discharging atoms op(e1, e1) = all_0_28_28, op(e1, e1) = all_0_37_37, yields:
% 19.62/5.18 | (1635) all_0_28_28 = all_0_37_37
% 19.62/5.18 |
% 19.62/5.18 | Instantiating formula (21) with e1, e1, e0, all_0_28_28 and discharging atoms op(e1, e1) = all_0_28_28, op(e1, e1) = e0, yields:
% 19.62/5.18 | (943) all_0_28_28 = e0
% 19.62/5.18 |
% 19.62/5.18 | Combining equations (1350,1633) yields a new equation:
% 19.62/5.18 | (1637) all_0_33_33 = e0
% 19.62/5.18 |
% 19.62/5.18 | Combining equations (943,1635) yields a new equation:
% 19.62/5.18 | (921) all_0_37_37 = e0
% 19.62/5.18 |
% 19.62/5.18 +-Applying beta-rule and splitting (104), into two cases.
% 19.62/5.18 |-Branch one:
% 19.62/5.18 | (1639) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0)) | (all_0_34_34 = e2 & ~ (all_0_35_35 = e0))
% 19.62/5.18 |
% 19.62/5.18 +-Applying beta-rule and splitting (1639), into two cases.
% 19.62/5.18 |-Branch one:
% 19.62/5.18 | (1640) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0))
% 19.62/5.18 |
% 19.62/5.18 +-Applying beta-rule and splitting (1640), into two cases.
% 19.62/5.18 |-Branch one:
% 19.62/5.18 | (1641) all_0_30_30 = e4 & ~ (all_0_31_31 = e0)
% 19.62/5.18 |
% 19.62/5.18 | Applying alpha-rule on (1641) yields:
% 19.62/5.18 | (1642) all_0_30_30 = e4
% 19.62/5.18 | (1643) ~ (all_0_31_31 = e0)
% 19.62/5.18 |
% 19.62/5.18 | Equations (318) can reduce 1643 to:
% 19.62/5.18 | (269) $false
% 19.62/5.18 |
% 19.62/5.18 |-The branch is then unsatisfiable
% 19.62/5.18 |-Branch two:
% 19.62/5.18 | (1645) all_0_32_32 = e3 & ~ (all_0_33_33 = e0)
% 19.62/5.18 |
% 19.62/5.18 | Applying alpha-rule on (1645) yields:
% 19.62/5.18 | (1646) all_0_32_32 = e3
% 19.62/5.18 | (1647) ~ (all_0_33_33 = e0)
% 19.62/5.18 |
% 19.62/5.18 | Equations (1637) can reduce 1647 to:
% 19.62/5.18 | (269) $false
% 19.62/5.18 |
% 19.62/5.18 |-The branch is then unsatisfiable
% 19.62/5.18 |-Branch two:
% 19.62/5.18 | (1649) all_0_34_34 = e2 & ~ (all_0_35_35 = e0)
% 19.62/5.18 |
% 19.62/5.18 | Applying alpha-rule on (1649) yields:
% 19.62/5.18 | (1650) all_0_34_34 = e2
% 19.62/5.18 | (1651) ~ (all_0_35_35 = e0)
% 19.62/5.18 |
% 19.62/5.18 | Equations (1490) can reduce 1651 to:
% 19.62/5.18 | (269) $false
% 19.62/5.18 |
% 19.62/5.18 |-The branch is then unsatisfiable
% 19.62/5.18 |-Branch two:
% 19.62/5.18 | (1653) all_0_36_36 = e1 & ~ (all_0_37_37 = e0)
% 19.62/5.18 |
% 19.62/5.18 | Applying alpha-rule on (1653) yields:
% 19.62/5.18 | (1654) all_0_36_36 = e1
% 19.62/5.18 | (1655) ~ (all_0_37_37 = e0)
% 19.62/5.18 |
% 19.62/5.18 | Equations (921) can reduce 1655 to:
% 19.62/5.18 | (269) $false
% 19.62/5.18 |
% 19.62/5.18 |-The branch is then unsatisfiable
% 19.62/5.18 |-Branch two:
% 19.62/5.18 | (1183) ~ (all_0_56_56 = e3)
% 19.62/5.18 | (1658) all_0_56_56 = e4
% 19.62/5.18 |
% 19.62/5.18 | Equations (1658) can reduce 273 to:
% 19.62/5.18 | (269) $false
% 19.62/5.18 |
% 19.62/5.18 |-The branch is then unsatisfiable
% 19.62/5.18 |-Branch two:
% 19.62/5.18 | (983) ~ (all_0_40_40 = e1)
% 19.62/5.18 | (984) all_0_52_52 = e1 | all_0_57_57 = e1
% 19.62/5.18 |
% 19.62/5.18 +-Applying beta-rule and splitting (984), into two cases.
% 19.62/5.18 |-Branch one:
% 19.62/5.18 | (820) all_0_52_52 = e1
% 19.62/5.18 |
% 19.62/5.18 | Equations (820) can reduce 978 to:
% 19.62/5.18 | (269) $false
% 19.62/5.18 |
% 19.62/5.18 |-The branch is then unsatisfiable
% 19.62/5.18 |-Branch two:
% 19.62/5.18 | (978) ~ (all_0_52_52 = e1)
% 19.62/5.18 | (577) all_0_57_57 = e1
% 19.62/5.18 |
% 19.62/5.18 | Combining equations (577,400) yields a new equation:
% 19.62/5.18 | (578) e1 = e0
% 19.62/5.18 |
% 19.62/5.18 | Simplifying 578 yields:
% 19.62/5.18 | (579) e1 = e0
% 19.62/5.18 |
% 19.62/5.18 | Equations (579) can reduce 144 to:
% 19.62/5.18 | (269) $false
% 19.62/5.18 |
% 19.62/5.18 |-The branch is then unsatisfiable
% 19.62/5.18 |-Branch two:
% 19.62/5.18 | (765) ~ (all_0_53_53 = e0)
% 19.62/5.18 | (493) all_0_58_58 = e0
% 19.62/5.18 |
% 19.62/5.18 | Equations (493) can reduce 403 to:
% 19.62/5.18 | (269) $false
% 19.62/5.18 |
% 19.62/5.18 |-The branch is then unsatisfiable
% 19.62/5.18 |-Branch two:
% 19.62/5.18 | (618) ~ (all_0_46_46 = e3)
% 19.62/5.18 | (538) all_0_46_46 = e4
% 19.62/5.18 |
% 19.62/5.18 | Equations (538) can reduce 310 to:
% 19.62/5.18 | (269) $false
% 19.62/5.18 |
% 19.62/5.18 |-The branch is then unsatisfiable
% 19.62/5.18 |-Branch two:
% 19.62/5.18 | (459) ~ (all_0_43_43 = e0)
% 19.62/5.18 | (1676) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 19.62/5.18 |
% 19.62/5.18 +-Applying beta-rule and splitting (549), into two cases.
% 19.62/5.18 |-Branch one:
% 19.62/5.18 | (462) all_0_46_46 = e3
% 19.62/5.18 |
% 19.62/5.18 | Equations (462) can reduce 3 to:
% 19.62/5.18 | (562) ~ (all_0_43_43 = e3)
% 19.62/5.18 |
% 19.62/5.18 | Equations (462) can reduce 201 to:
% 19.62/5.18 | (689) ~ (all_0_45_45 = e3)
% 19.62/5.18 |
% 19.62/5.18 +-Applying beta-rule and splitting (22), into two cases.
% 19.62/5.18 |-Branch one:
% 19.62/5.18 | (661) all_0_43_43 = e2
% 19.62/5.18 |
% 19.62/5.18 | Equations (661) can reduce 321 to:
% 19.62/5.18 | (269) $false
% 19.62/5.18 |
% 19.62/5.18 |-The branch is then unsatisfiable
% 19.62/5.18 |-Branch two:
% 19.62/5.18 | (321) ~ (all_0_43_43 = e2)
% 19.62/5.18 | (1198) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 19.62/5.18 |
% 19.62/5.18 +-Applying beta-rule and splitting (245), into two cases.
% 19.62/5.18 |-Branch one:
% 19.62/5.19 | (694) all_0_45_45 = e2
% 19.62/5.19 |
% 19.62/5.19 | Equations (694) can reduce 390 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (390) ~ (all_0_45_45 = e2)
% 19.62/5.19 | (1082) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (1082), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (889) all_0_45_45 = e0
% 19.62/5.19 |
% 19.62/5.19 | Equations (889) can reduce 299 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (299) ~ (all_0_45_45 = e0)
% 19.62/5.19 | (1086) all_0_45_45 = e4 | all_0_45_45 = e3
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (1198), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (433) all_0_43_43 = e0
% 19.62/5.19 |
% 19.62/5.19 | Equations (433) can reduce 459 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (459) ~ (all_0_43_43 = e0)
% 19.62/5.19 | (1695) all_0_43_43 = e4 | all_0_43_43 = e3
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (1695), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (559) all_0_43_43 = e3
% 19.62/5.19 |
% 19.62/5.19 | Equations (559) can reduce 562 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (562) ~ (all_0_43_43 = e3)
% 19.62/5.19 | (438) all_0_43_43 = e4
% 19.62/5.19 |
% 19.62/5.19 | Equations (438) can reduce 186 to:
% 19.62/5.19 | (1700) ~ (all_0_45_45 = e4)
% 19.62/5.19 |
% 19.62/5.19 | Simplifying 1700 yields:
% 19.62/5.19 | (537) ~ (all_0_45_45 = e4)
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (1086), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (1087) all_0_45_45 = e3
% 19.62/5.19 |
% 19.62/5.19 | Equations (1087) can reduce 689 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (689) ~ (all_0_45_45 = e3)
% 19.62/5.19 | (444) all_0_45_45 = e4
% 19.62/5.19 |
% 19.62/5.19 | Equations (444) can reduce 537 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (618) ~ (all_0_46_46 = e3)
% 19.62/5.19 | (538) all_0_46_46 = e4
% 19.62/5.19 |
% 19.62/5.19 | Equations (538) can reduce 310 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (320) ~ (all_0_39_39 = e2)
% 19.62/5.19 | (351) all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (47), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (348) all_0_39_39 = e2
% 19.62/5.19 |
% 19.62/5.19 | Equations (348) can reduce 320 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (320) ~ (all_0_39_39 = e2)
% 19.62/5.19 | (709) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (709), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (464) all_0_39_39 = e1
% 19.62/5.19 |
% 19.62/5.19 | Equations (464) can reduce 467 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (467) ~ (all_0_39_39 = e1)
% 19.62/5.19 | (1075) all_0_39_39 = e4 | all_0_39_39 = e3
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (1075), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (443) all_0_39_39 = e3
% 19.62/5.19 |
% 19.62/5.19 | Equations (443) can reduce 320 to:
% 19.62/5.19 | (224) ~ (e3 = e2)
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (129), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (348) all_0_39_39 = e2
% 19.62/5.19 |
% 19.62/5.19 | Combining equations (443,348) yields a new equation:
% 19.62/5.19 | (606) e3 = e2
% 19.62/5.19 |
% 19.62/5.19 | Simplifying 606 yields:
% 19.62/5.19 | (423) e3 = e2
% 19.62/5.19 |
% 19.62/5.19 | Equations (423) can reduce 224 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (320) ~ (all_0_39_39 = e2)
% 19.62/5.19 | (1727) all_0_43_43 = e2 | all_0_47_47 = e2 | all_0_51_51 = e2 | all_0_56_56 = e2
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (1727), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (661) all_0_43_43 = e2
% 19.62/5.19 |
% 19.62/5.19 | Equations (661) can reduce 321 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (321) ~ (all_0_43_43 = e2)
% 19.62/5.19 | (1731) all_0_47_47 = e2 | all_0_51_51 = e2 | all_0_56_56 = e2
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (1731), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (319) all_0_47_47 = e2
% 19.62/5.19 |
% 19.62/5.19 | Combining equations (469,319) yields a new equation:
% 19.62/5.19 | (471) e2 = e1
% 19.62/5.19 |
% 19.62/5.19 | Equations (471) can reduce 148 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (1442) ~ (all_0_47_47 = e2)
% 19.62/5.19 | (1736) all_0_51_51 = e2 | all_0_56_56 = e2
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (371), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (372) all_0_54_54 = e2
% 19.62/5.19 |
% 19.62/5.19 | Equations (372) can reduce 261 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (261) ~ (all_0_54_54 = e2)
% 19.62/5.19 | (375) all_0_59_59 = e2
% 19.62/5.19 |
% 19.62/5.19 | Equations (375) can reduce 130 to:
% 19.62/5.19 | (377) ~ (all_0_56_56 = e2)
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (1736), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (1232) all_0_51_51 = e2
% 19.62/5.19 |
% 19.62/5.19 | Equations (1232) can reduce 255 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (255) ~ (all_0_51_51 = e2)
% 19.62/5.19 | (1575) all_0_56_56 = e2
% 19.62/5.19 |
% 19.62/5.19 | Equations (1575) can reduce 377 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (540) ~ (all_0_39_39 = e3)
% 19.62/5.19 | (1079) all_0_39_39 = e4
% 19.62/5.19 |
% 19.62/5.19 | Equations (1079) can reduce 307 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (659) ~ (all_0_44_44 = e2)
% 19.62/5.19 | (660) all_0_44_44 = e3 | all_0_44_44 = e0
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (113), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (382) all_0_40_40 = e2
% 19.62/5.19 |
% 19.62/5.19 | Combining equations (382,286) yields a new equation:
% 19.62/5.19 | (666) all_0_0_0 = e2
% 19.62/5.19 |
% 19.62/5.19 | Equations (382) can reduce 18 to:
% 19.62/5.19 | (320) ~ (all_0_39_39 = e2)
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (47), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (348) all_0_39_39 = e2
% 19.62/5.19 |
% 19.62/5.19 | Equations (348) can reduce 320 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (320) ~ (all_0_39_39 = e2)
% 19.62/5.19 | (709) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (709), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (464) all_0_39_39 = e1
% 19.62/5.19 |
% 19.62/5.19 | Equations (464) can reduce 467 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (467) ~ (all_0_39_39 = e1)
% 19.62/5.19 | (1075) all_0_39_39 = e4 | all_0_39_39 = e3
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (1075), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (443) all_0_39_39 = e3
% 19.62/5.19 |
% 19.62/5.19 | Equations (443) can reduce 226 to:
% 19.62/5.19 | (1764) ~ (all_0_41_41 = e3)
% 19.62/5.19 |
% 19.62/5.19 | Simplifying 1764 yields:
% 19.62/5.19 | (609) ~ (all_0_41_41 = e3)
% 19.62/5.19 |
% 19.62/5.19 | Equations (443) can reduce 320 to:
% 19.62/5.19 | (224) ~ (e3 = e2)
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (8), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (348) all_0_39_39 = e2
% 19.62/5.19 |
% 19.62/5.19 | Combining equations (443,348) yields a new equation:
% 19.62/5.19 | (606) e3 = e2
% 19.62/5.19 |
% 19.62/5.19 | Simplifying 606 yields:
% 19.62/5.19 | (423) e3 = e2
% 19.62/5.19 |
% 19.62/5.19 | Equations (423) can reduce 224 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (320) ~ (all_0_39_39 = e2)
% 19.62/5.19 | (396) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (396), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (409) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (409), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (410) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 19.62/5.19 |
% 19.62/5.19 | Applying alpha-rule on (410) yields:
% 19.62/5.19 | (411) all_0_0_0 = e1
% 19.62/5.19 | (412) ~ (all_0_1_1 = e4)
% 19.62/5.19 |
% 19.62/5.19 | Combining equations (411,666) yields a new equation:
% 19.62/5.19 | (471) e2 = e1
% 19.62/5.19 |
% 19.62/5.19 | Equations (471) can reduce 148 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (641) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 19.62/5.19 |
% 19.62/5.19 | Applying alpha-rule on (641) yields:
% 19.62/5.19 | (285) all_0_2_2 = e0
% 19.62/5.19 | (643) ~ (all_0_3_3 = e4)
% 19.62/5.19 |
% 19.62/5.19 | Equations (288) can reduce 643 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (645) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 19.62/5.19 |
% 19.62/5.19 | Applying alpha-rule on (645) yields:
% 19.62/5.19 | (605) all_0_41_41 = e3
% 19.62/5.19 | (537) ~ (all_0_45_45 = e4)
% 19.62/5.19 |
% 19.62/5.19 | Equations (605) can reduce 609 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (540) ~ (all_0_39_39 = e3)
% 19.62/5.19 | (1079) all_0_39_39 = e4
% 19.62/5.19 |
% 19.62/5.19 | Equations (1079) can reduce 307 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (342) ~ (all_0_40_40 = e2)
% 19.62/5.19 | (1101) all_0_44_44 = e2 | all_0_52_52 = e2 | all_0_57_57 = e2
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (1101), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (341) all_0_44_44 = e2
% 19.62/5.19 |
% 19.62/5.19 | Equations (341) can reduce 659 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (659) ~ (all_0_44_44 = e2)
% 19.62/5.19 | (1109) all_0_52_52 = e2 | all_0_57_57 = e2
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (154), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (348) all_0_39_39 = e2
% 19.62/5.19 |
% 19.62/5.19 | Equations (348) can reduce 226 to:
% 19.62/5.19 | (1797) ~ (all_0_41_41 = e2)
% 19.62/5.19 |
% 19.62/5.19 | Simplifying 1797 yields:
% 19.62/5.19 | (650) ~ (all_0_41_41 = e2)
% 19.62/5.19 |
% 19.62/5.19 | Equations (348) can reduce 234 to:
% 19.62/5.19 | (1523) ~ (all_0_43_43 = e2)
% 19.62/5.19 |
% 19.62/5.19 | Simplifying 1523 yields:
% 19.62/5.19 | (321) ~ (all_0_43_43 = e2)
% 19.62/5.19 |
% 19.62/5.19 | Equations (348) can reduce 126 to:
% 19.62/5.19 | (254) ~ (all_0_51_51 = e2)
% 19.62/5.19 |
% 19.62/5.19 | Simplifying 254 yields:
% 19.62/5.19 | (255) ~ (all_0_51_51 = e2)
% 19.62/5.19 |
% 19.62/5.19 | Equations (348) can reduce 165 to:
% 19.62/5.19 | (58) ~ (e2 = e0)
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (1109), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (816) all_0_52_52 = e2
% 19.62/5.19 |
% 19.62/5.19 | Equations (816) can reduce 257 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (257) ~ (all_0_52_52 = e2)
% 19.62/5.19 | (867) all_0_57_57 = e2
% 19.62/5.19 |
% 19.62/5.19 | Equations (867) can reduce 168 to:
% 19.62/5.19 | (342) ~ (all_0_40_40 = e2)
% 19.62/5.19 |
% 19.62/5.19 | Equations (867) can reduce 240 to:
% 19.62/5.19 | (659) ~ (all_0_44_44 = e2)
% 19.62/5.19 |
% 19.62/5.19 | Equations (867) can reduce 124 to:
% 19.62/5.19 | (257) ~ (all_0_52_52 = e2)
% 19.62/5.19 |
% 19.62/5.19 | Equations (867) can reduce 227 to:
% 19.62/5.19 | (377) ~ (all_0_56_56 = e2)
% 19.62/5.19 |
% 19.62/5.19 | From (867) and (244) follows:
% 19.62/5.19 | (1812) op(e2, e2) = all_0_19_19
% 19.62/5.19 |
% 19.62/5.19 | From (867) and (56) follows:
% 19.62/5.19 | (1813) op(e0, e2) = all_0_20_20
% 19.62/5.19 |
% 19.62/5.19 | From (867) and (241) follows:
% 19.62/5.19 | (1814) op(e0, e2) = e2
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (110), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (352) all_0_44_44 = e0
% 19.62/5.19 |
% 19.62/5.19 | Equations (352) can reduce 228 to:
% 19.62/5.19 | (459) ~ (all_0_43_43 = e0)
% 19.62/5.19 |
% 19.62/5.19 | Equations (352) can reduce 117 to:
% 19.62/5.19 | (1140) ~ (all_0_45_45 = e0)
% 19.62/5.19 |
% 19.62/5.19 | Simplifying 1140 yields:
% 19.62/5.19 | (299) ~ (all_0_45_45 = e0)
% 19.62/5.19 |
% 19.62/5.19 | Equations (352) can reduce 210 to:
% 19.62/5.19 | (434) ~ (all_0_46_46 = e0)
% 19.62/5.19 |
% 19.62/5.19 | Simplifying 434 yields:
% 19.62/5.19 | (435) ~ (all_0_46_46 = e0)
% 19.62/5.19 |
% 19.62/5.19 | Equations (352) can reduce 121 to:
% 19.62/5.19 | (762) ~ (all_0_52_52 = e0)
% 19.62/5.19 |
% 19.62/5.19 | Simplifying 762 yields:
% 19.62/5.19 | (317) ~ (all_0_52_52 = e0)
% 19.62/5.19 |
% 19.62/5.19 | Equations (352) can reduce 190 to:
% 19.62/5.19 | (404) ~ (e4 = e0)
% 19.62/5.19 |
% 19.62/5.19 | Simplifying 404 yields:
% 19.62/5.19 | (11) ~ (e4 = e0)
% 19.62/5.19 |
% 19.62/5.19 | Equations (352) can reduce 659 to:
% 19.62/5.19 | (406) ~ (e2 = e0)
% 19.62/5.19 |
% 19.62/5.19 | Simplifying 406 yields:
% 19.62/5.19 | (58) ~ (e2 = e0)
% 19.62/5.19 |
% 19.62/5.19 | From (352) and (205) follows:
% 19.62/5.19 | (1827) op(e2, e0) = all_0_15_15
% 19.62/5.19 |
% 19.62/5.19 +-Applying beta-rule and splitting (225), into two cases.
% 19.62/5.19 |-Branch one:
% 19.62/5.19 | (661) all_0_43_43 = e2
% 19.62/5.19 |
% 19.62/5.19 | Equations (661) can reduce 321 to:
% 19.62/5.19 | (269) $false
% 19.62/5.19 |
% 19.62/5.19 |-The branch is then unsatisfiable
% 19.62/5.19 |-Branch two:
% 19.62/5.19 | (321) ~ (all_0_43_43 = e2)
% 19.62/5.19 | (664) all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (664), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (341) all_0_44_44 = e2
% 19.62/5.20 |
% 19.62/5.20 | Combining equations (352,341) yields a new equation:
% 19.62/5.20 | (354) e2 = e0
% 19.62/5.20 |
% 19.62/5.20 | Equations (354) can reduce 58 to:
% 19.62/5.20 | (269) $false
% 19.62/5.20 |
% 19.62/5.20 |-The branch is then unsatisfiable
% 19.62/5.20 |-Branch two:
% 19.62/5.20 | (659) ~ (all_0_44_44 = e2)
% 19.62/5.20 | (1120) all_0_45_45 = e2 | all_0_46_46 = e2
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (1120), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (694) all_0_45_45 = e2
% 19.62/5.20 |
% 19.62/5.20 | Equations (694) can reduce 390 to:
% 19.62/5.20 | (269) $false
% 19.62/5.20 |
% 19.62/5.20 |-The branch is then unsatisfiable
% 19.62/5.20 |-Branch two:
% 19.62/5.20 | (390) ~ (all_0_45_45 = e2)
% 19.62/5.20 | (364) all_0_46_46 = e2
% 19.62/5.20 |
% 19.62/5.20 | Equations (364) can reduce 201 to:
% 19.62/5.20 | (390) ~ (all_0_45_45 = e2)
% 19.62/5.20 |
% 19.62/5.20 | Equations (364) can reduce 150 to:
% 19.62/5.20 | (1842) ~ (all_0_59_59 = e2)
% 19.62/5.20 |
% 19.62/5.20 | Simplifying 1842 yields:
% 19.62/5.20 | (1843) ~ (all_0_59_59 = e2)
% 19.62/5.20 |
% 19.62/5.20 | Equations (364) can reduce 310 to:
% 19.62/5.20 | (326) ~ (e4 = e2)
% 19.62/5.20 |
% 19.62/5.20 | Simplifying 326 yields:
% 19.62/5.20 | (230) ~ (e4 = e2)
% 19.62/5.20 |
% 19.62/5.20 | Equations (364) can reduce 163 to:
% 19.62/5.20 | (148) ~ (e2 = e1)
% 19.62/5.20 |
% 19.62/5.20 | Equations (364) can reduce 435 to:
% 19.62/5.20 | (58) ~ (e2 = e0)
% 19.62/5.20 |
% 19.62/5.20 | From (364) and (181) follows:
% 19.62/5.20 | (1848) op(e0, e2) = all_0_32_32
% 19.62/5.20 |
% 19.62/5.20 | Instantiating formula (21) with e2, e2, all_0_19_19, e4 and discharging atoms op(e2, e2) = all_0_19_19, op(e2, e2) = e4, yields:
% 19.62/5.20 | (1849) all_0_19_19 = e4
% 19.62/5.20 |
% 19.62/5.20 | Instantiating formula (21) with e2, e0, all_0_15_15, e0 and discharging atoms op(e2, e0) = all_0_15_15, op(e2, e0) = e0, yields:
% 19.62/5.20 | (1850) all_0_15_15 = e0
% 19.62/5.20 |
% 19.62/5.20 | Instantiating formula (21) with e0, e2, all_0_32_32, all_0_20_20 and discharging atoms op(e0, e2) = all_0_20_20, op(e0, e2) = all_0_32_32, yields:
% 19.62/5.20 | (1851) all_0_20_20 = all_0_32_32
% 19.62/5.20 |
% 19.62/5.20 | Instantiating formula (21) with e0, e2, e2, all_0_20_20 and discharging atoms op(e0, e2) = all_0_20_20, op(e0, e2) = e2, yields:
% 19.62/5.20 | (503) all_0_20_20 = e2
% 19.62/5.20 |
% 19.62/5.20 | Combining equations (503,1851) yields a new equation:
% 19.62/5.20 | (1853) all_0_32_32 = e2
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (104), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (1639) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0)) | (all_0_34_34 = e2 & ~ (all_0_35_35 = e0))
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (1639), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (1640) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0))
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (1640), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (1641) all_0_30_30 = e4 & ~ (all_0_31_31 = e0)
% 19.62/5.20 |
% 19.62/5.20 | Applying alpha-rule on (1641) yields:
% 19.62/5.20 | (1642) all_0_30_30 = e4
% 19.62/5.20 | (1643) ~ (all_0_31_31 = e0)
% 19.62/5.20 |
% 19.62/5.20 | Equations (318) can reduce 1643 to:
% 19.62/5.20 | (269) $false
% 19.62/5.20 |
% 19.62/5.20 |-The branch is then unsatisfiable
% 19.62/5.20 |-Branch two:
% 19.62/5.20 | (1645) all_0_32_32 = e3 & ~ (all_0_33_33 = e0)
% 19.62/5.20 |
% 19.62/5.20 | Applying alpha-rule on (1645) yields:
% 19.62/5.20 | (1646) all_0_32_32 = e3
% 19.62/5.20 | (1647) ~ (all_0_33_33 = e0)
% 19.62/5.20 |
% 19.62/5.20 | Combining equations (1853,1646) yields a new equation:
% 19.62/5.20 | (423) e3 = e2
% 19.62/5.20 |
% 19.62/5.20 | Equations (423) can reduce 224 to:
% 19.62/5.20 | (269) $false
% 19.62/5.20 |
% 19.62/5.20 |-The branch is then unsatisfiable
% 19.62/5.20 |-Branch two:
% 19.62/5.20 | (1649) all_0_34_34 = e2 & ~ (all_0_35_35 = e0)
% 19.62/5.20 |
% 19.62/5.20 | Applying alpha-rule on (1649) yields:
% 19.62/5.20 | (1650) all_0_34_34 = e2
% 19.62/5.20 | (1651) ~ (all_0_35_35 = e0)
% 19.62/5.20 |
% 19.62/5.20 | Combining equations (1491,1650) yields a new equation:
% 19.62/5.20 | (1868) all_0_59_59 = e2
% 19.62/5.20 |
% 19.62/5.20 | Simplifying 1868 yields:
% 19.62/5.20 | (375) all_0_59_59 = e2
% 19.62/5.20 |
% 19.62/5.20 | Equations (375) can reduce 1843 to:
% 19.62/5.20 | (269) $false
% 19.62/5.20 |
% 19.62/5.20 |-The branch is then unsatisfiable
% 19.62/5.20 |-Branch two:
% 19.62/5.20 | (1653) all_0_36_36 = e1 & ~ (all_0_37_37 = e0)
% 19.62/5.20 |
% 19.62/5.20 | Applying alpha-rule on (1653) yields:
% 19.62/5.20 | (1654) all_0_36_36 = e1
% 19.62/5.20 | (1655) ~ (all_0_37_37 = e0)
% 19.62/5.20 |
% 19.62/5.20 | From (1654) and (235) follows:
% 19.62/5.20 | (1874) op(e0, all_0_54_54) = e1
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (17), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (382) all_0_40_40 = e2
% 19.62/5.20 |
% 19.62/5.20 | Equations (382) can reduce 342 to:
% 19.62/5.20 | (269) $false
% 19.62/5.20 |
% 19.62/5.20 |-The branch is then unsatisfiable
% 19.62/5.20 |-Branch two:
% 19.62/5.20 | (342) ~ (all_0_40_40 = e2)
% 19.62/5.20 | (1093) all_0_40_40 = e3 | all_0_40_40 = e1
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (133), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (504) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (504), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (505) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (505), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (506) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 19.62/5.20 |
% 19.62/5.20 | Applying alpha-rule on (506) yields:
% 19.62/5.20 | (507) all_0_13_13 = e4
% 19.62/5.20 | (508) ~ (all_0_14_14 = e2)
% 19.62/5.20 |
% 19.62/5.20 | From (507) and (156) follows:
% 19.62/5.20 | (1884) op(e2, all_0_40_40) = e4
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (246), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (413) all_0_40_40 = e1
% 19.62/5.20 |
% 19.62/5.20 | Equations (413) can reduce 187 to:
% 19.62/5.20 | (1157) ~ (all_0_52_52 = e1)
% 19.62/5.20 |
% 19.62/5.20 | Simplifying 1157 yields:
% 19.62/5.20 | (978) ~ (all_0_52_52 = e1)
% 19.62/5.20 |
% 19.62/5.20 | Equations (413) can reduce 342 to:
% 19.62/5.20 | (414) ~ (e2 = e1)
% 19.62/5.20 |
% 19.62/5.20 | Simplifying 414 yields:
% 19.62/5.20 | (148) ~ (e2 = e1)
% 19.62/5.20 |
% 19.62/5.20 | From (413) and (1884) follows:
% 19.62/5.20 | (1890) op(e2, e1) = e4
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (86), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (816) all_0_52_52 = e2
% 19.62/5.20 |
% 19.62/5.20 | Equations (816) can reduce 257 to:
% 19.62/5.20 | (269) $false
% 19.62/5.20 |
% 19.62/5.20 |-The branch is then unsatisfiable
% 19.62/5.20 |-Branch two:
% 19.62/5.20 | (257) ~ (all_0_52_52 = e2)
% 19.62/5.20 | (819) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (193), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (417) all_0_40_40 = e3
% 19.62/5.20 |
% 19.62/5.20 | Combining equations (413,417) yields a new equation:
% 19.62/5.20 | (418) e3 = e1
% 19.62/5.20 |
% 19.62/5.20 | Equations (418) can reduce 146 to:
% 19.62/5.20 | (269) $false
% 19.62/5.20 |
% 19.62/5.20 |-The branch is then unsatisfiable
% 19.62/5.20 |-Branch two:
% 19.62/5.20 | (420) ~ (all_0_40_40 = e3)
% 19.62/5.20 | (421) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (94), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (386) all_0_41_41 = e2
% 19.62/5.20 |
% 19.62/5.20 | Equations (386) can reduce 650 to:
% 19.62/5.20 | (269) $false
% 19.62/5.20 |
% 19.62/5.20 |-The branch is then unsatisfiable
% 19.62/5.20 |-Branch two:
% 19.62/5.20 | (650) ~ (all_0_41_41 = e2)
% 19.62/5.20 | (1903) all_0_41_41 = e4 | all_0_41_41 = e3 | all_0_41_41 = e1
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (421), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (422) all_0_44_44 = e3
% 19.62/5.20 |
% 19.62/5.20 | Combining equations (352,422) yields a new equation:
% 19.62/5.20 | (560) e3 = e0
% 19.62/5.20 |
% 19.62/5.20 | Equations (560) can reduce 72 to:
% 19.62/5.20 | (269) $false
% 19.62/5.20 |
% 19.62/5.20 |-The branch is then unsatisfiable
% 19.62/5.20 |-Branch two:
% 19.62/5.20 | (425) ~ (all_0_44_44 = e3)
% 19.62/5.20 | (426) all_0_52_52 = e3 | all_0_57_57 = e3
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (819), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (820) all_0_52_52 = e1
% 19.62/5.20 |
% 19.62/5.20 | Equations (820) can reduce 978 to:
% 19.62/5.20 | (269) $false
% 19.62/5.20 |
% 19.62/5.20 |-The branch is then unsatisfiable
% 19.62/5.20 |-Branch two:
% 19.62/5.20 | (978) ~ (all_0_52_52 = e1)
% 19.62/5.20 | (979) all_0_52_52 = e3 | all_0_52_52 = e0
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (426), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (427) all_0_52_52 = e3
% 19.62/5.20 |
% 19.62/5.20 | Equations (427) can reduce 62 to:
% 19.62/5.20 | (429) ~ (all_0_54_54 = e3)
% 19.62/5.20 |
% 19.62/5.20 | Simplifying 429 yields:
% 19.62/5.20 | (430) ~ (all_0_54_54 = e3)
% 19.62/5.20 |
% 19.62/5.20 | Equations (427) can reduce 152 to:
% 19.62/5.20 | (498) ~ (e4 = e3)
% 19.62/5.20 |
% 19.62/5.20 | Simplifying 498 yields:
% 19.62/5.20 | (41) ~ (e4 = e3)
% 19.62/5.20 |
% 19.62/5.20 | Equations (427) can reduce 257 to:
% 19.62/5.20 | (224) ~ (e3 = e2)
% 19.62/5.20 |
% 19.62/5.20 | Equations (427) can reduce 978 to:
% 19.62/5.20 | (146) ~ (e3 = e1)
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (169), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (610) all_0_42_42 = e3
% 19.62/5.20 |
% 19.62/5.20 | Combining equations (305,610) yields a new equation:
% 19.62/5.20 | (515) e4 = e3
% 19.62/5.20 |
% 19.62/5.20 | Simplifying 515 yields:
% 19.62/5.20 | (516) e4 = e3
% 19.62/5.20 |
% 19.62/5.20 | Equations (516) can reduce 41 to:
% 19.62/5.20 | (269) $false
% 19.62/5.20 |
% 19.62/5.20 |-The branch is then unsatisfiable
% 19.62/5.20 |-Branch two:
% 19.62/5.20 | (1924) ~ (all_0_42_42 = e3)
% 19.62/5.20 | (1925) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (1925), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (462) all_0_46_46 = e3
% 19.62/5.20 |
% 19.62/5.20 | Combining equations (364,462) yields a new equation:
% 19.62/5.20 | (423) e3 = e2
% 19.62/5.20 |
% 19.62/5.20 | Equations (423) can reduce 224 to:
% 19.62/5.20 | (269) $false
% 19.62/5.20 |
% 19.62/5.20 |-The branch is then unsatisfiable
% 19.62/5.20 |-Branch two:
% 19.62/5.20 | (618) ~ (all_0_46_46 = e3)
% 19.62/5.20 | (1930) all_0_54_54 = e3 | all_0_59_59 = e3
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (1930), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (635) all_0_54_54 = e3
% 19.62/5.20 |
% 19.62/5.20 | Equations (635) can reduce 430 to:
% 19.62/5.20 | (269) $false
% 19.62/5.20 |
% 19.62/5.20 |-The branch is then unsatisfiable
% 19.62/5.20 |-Branch two:
% 19.62/5.20 | (430) ~ (all_0_54_54 = e3)
% 19.62/5.20 | (1070) all_0_59_59 = e3
% 19.62/5.20 |
% 19.62/5.20 | Equations (1070) can reduce 130 to:
% 19.62/5.20 | (1183) ~ (all_0_56_56 = e3)
% 19.62/5.20 |
% 19.62/5.20 | Equations (1070) can reduce 198 to:
% 19.62/5.20 | (527) ~ (all_0_58_58 = e3)
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (43), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (480) all_0_56_56 = e1
% 19.62/5.20 |
% 19.62/5.20 | Equations (480) can reduce 575 to:
% 19.62/5.20 | (269) $false
% 19.62/5.20 |
% 19.62/5.20 |-The branch is then unsatisfiable
% 19.62/5.20 |-Branch two:
% 19.62/5.20 | (575) ~ (all_0_56_56 = e1)
% 19.62/5.20 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (576), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (577) all_0_57_57 = e1
% 19.62/5.20 |
% 19.62/5.20 | Combining equations (577,867) yields a new equation:
% 19.62/5.20 | (471) e2 = e1
% 19.62/5.20 |
% 19.62/5.20 | Equations (471) can reduce 148 to:
% 19.62/5.20 | (269) $false
% 19.62/5.20 |
% 19.62/5.20 |-The branch is then unsatisfiable
% 19.62/5.20 |-Branch two:
% 19.62/5.20 | (581) ~ (all_0_57_57 = e1)
% 19.62/5.20 | (582) all_0_58_58 = e1 | all_0_59_59 = e1
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (582), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (489) all_0_58_58 = e1
% 19.62/5.20 |
% 19.62/5.20 | Equations (489) can reduce 208 to:
% 19.62/5.20 | (1315) ~ (all_0_41_41 = e1)
% 19.62/5.20 |
% 19.62/5.20 | Equations (489) can reduce 127 to:
% 19.62/5.20 | (823) ~ (all_0_53_53 = e1)
% 19.62/5.20 |
% 19.62/5.20 | Equations (489) can reduce 527 to:
% 19.62/5.20 | (597) ~ (e3 = e1)
% 19.62/5.20 |
% 19.62/5.20 | Simplifying 597 yields:
% 19.62/5.20 | (146) ~ (e3 = e1)
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (19), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (475) all_0_51_51 = e1
% 19.62/5.20 |
% 19.62/5.20 | Equations (475) can reduce 479 to:
% 19.62/5.20 | (269) $false
% 19.62/5.20 |
% 19.62/5.20 |-The branch is then unsatisfiable
% 19.62/5.20 |-Branch two:
% 19.62/5.20 | (479) ~ (all_0_51_51 = e1)
% 19.62/5.20 | (1954) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 19.62/5.20 |
% 19.62/5.20 +-Applying beta-rule and splitting (1954), into two cases.
% 19.62/5.20 |-Branch one:
% 19.62/5.20 | (820) all_0_52_52 = e1
% 19.62/5.20 |
% 19.62/5.20 | Combining equations (820,427) yields a new equation:
% 19.62/5.20 | (418) e3 = e1
% 19.62/5.20 |
% 19.62/5.20 | Equations (418) can reduce 146 to:
% 19.62/5.20 | (269) $false
% 19.62/5.20 |
% 19.62/5.20 |-The branch is then unsatisfiable
% 19.62/5.20 |-Branch two:
% 19.62/5.20 | (978) ~ (all_0_52_52 = e1)
% 19.62/5.20 | (1959) all_0_53_53 = e1 | all_0_54_54 = e1
% 19.62/5.20 |
% 19.62/5.21 +-Applying beta-rule and splitting (139), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (889) all_0_45_45 = e0
% 19.62/5.21 |
% 19.62/5.21 | Equations (889) can reduce 299 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (299) ~ (all_0_45_45 = e0)
% 19.62/5.21 | (894) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 19.62/5.21 |
% 19.62/5.21 +-Applying beta-rule and splitting (1959), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (853) all_0_53_53 = e1
% 19.62/5.21 |
% 19.62/5.21 | Equations (853) can reduce 823 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (823) ~ (all_0_53_53 = e1)
% 19.62/5.21 | (1592) all_0_54_54 = e1
% 19.62/5.21 |
% 19.62/5.21 | Equations (1592) can reduce 1478 to:
% 19.62/5.21 | (144) ~ (e1 = e0)
% 19.62/5.21 |
% 19.62/5.21 +-Applying beta-rule and splitting (1903), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (1312) all_0_41_41 = e1
% 19.62/5.21 |
% 19.62/5.21 | Equations (1312) can reduce 1315 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (1315) ~ (all_0_41_41 = e1)
% 19.62/5.21 | (1972) all_0_41_41 = e4 | all_0_41_41 = e3
% 19.62/5.21 |
% 19.62/5.21 +-Applying beta-rule and splitting (1972), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (605) all_0_41_41 = e3
% 19.62/5.21 |
% 19.62/5.21 | Equations (605) can reduce 122 to:
% 19.62/5.21 | (688) ~ (all_0_45_45 = e3)
% 19.62/5.21 |
% 19.62/5.21 | Simplifying 688 yields:
% 19.62/5.21 | (689) ~ (all_0_45_45 = e3)
% 19.62/5.21 |
% 19.62/5.21 | Equations (605) can reduce 308 to:
% 19.62/5.21 | (498) ~ (e4 = e3)
% 19.62/5.21 |
% 19.62/5.21 | Simplifying 498 yields:
% 19.62/5.21 | (41) ~ (e4 = e3)
% 19.62/5.21 |
% 19.62/5.21 | Equations (605) can reduce 650 to:
% 19.62/5.21 | (224) ~ (e3 = e2)
% 19.62/5.21 |
% 19.62/5.21 | Equations (605) can reduce 188 to:
% 19.62/5.21 | (72) ~ (e3 = e0)
% 19.62/5.21 |
% 19.62/5.21 +-Applying beta-rule and splitting (245), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (694) all_0_45_45 = e2
% 19.62/5.21 |
% 19.62/5.21 | Equations (694) can reduce 390 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (390) ~ (all_0_45_45 = e2)
% 19.62/5.21 | (1082) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 19.62/5.21 |
% 19.62/5.21 +-Applying beta-rule and splitting (211), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (632) all_0_56_56 = e0
% 19.62/5.21 |
% 19.62/5.21 | Equations (632) can reduce 1183 to:
% 19.62/5.21 | (1272) ~ (e3 = e0)
% 19.62/5.21 |
% 19.62/5.21 | Simplifying 1272 yields:
% 19.62/5.21 | (72) ~ (e3 = e0)
% 19.62/5.21 |
% 19.62/5.21 +-Applying beta-rule and splitting (162), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (559) all_0_43_43 = e3
% 19.62/5.21 |
% 19.62/5.21 | Equations (559) can reduce 186 to:
% 19.62/5.21 | (688) ~ (all_0_45_45 = e3)
% 19.62/5.21 |
% 19.62/5.21 | Simplifying 688 yields:
% 19.62/5.21 | (689) ~ (all_0_45_45 = e3)
% 19.62/5.21 |
% 19.62/5.21 +-Applying beta-rule and splitting (14), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (438) all_0_43_43 = e4
% 19.62/5.21 |
% 19.62/5.21 | Combining equations (438,559) yields a new equation:
% 19.62/5.21 | (515) e4 = e3
% 19.62/5.21 |
% 19.62/5.21 | Simplifying 515 yields:
% 19.62/5.21 | (516) e4 = e3
% 19.62/5.21 |
% 19.62/5.21 | Equations (516) can reduce 41 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (441) ~ (all_0_43_43 = e4)
% 19.62/5.21 | (442) all_0_45_45 = e4 | all_0_46_46 = e4
% 19.62/5.21 |
% 19.62/5.21 +-Applying beta-rule and splitting (1082), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (889) all_0_45_45 = e0
% 19.62/5.21 |
% 19.62/5.21 | Equations (889) can reduce 299 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (299) ~ (all_0_45_45 = e0)
% 19.62/5.21 | (1086) all_0_45_45 = e4 | all_0_45_45 = e3
% 19.62/5.21 |
% 19.62/5.21 +-Applying beta-rule and splitting (442), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (444) all_0_45_45 = e4
% 19.62/5.21 |
% 19.62/5.21 | Equations (444) can reduce 689 to:
% 19.62/5.21 | (41) ~ (e4 = e3)
% 19.62/5.21 |
% 19.62/5.21 | Equations (444) can reduce 390 to:
% 19.62/5.21 | (230) ~ (e4 = e2)
% 19.62/5.21 |
% 19.62/5.21 | Equations (444) can reduce 299 to:
% 19.62/5.21 | (11) ~ (e4 = e0)
% 19.62/5.21 |
% 19.62/5.21 +-Applying beta-rule and splitting (170), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (1232) all_0_51_51 = e2
% 19.62/5.21 |
% 19.62/5.21 | Equations (1232) can reduce 255 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (255) ~ (all_0_51_51 = e2)
% 19.62/5.21 | (1235) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1 | all_0_51_51 = e0
% 19.62/5.21 |
% 19.62/5.21 +-Applying beta-rule and splitting (153), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (453) all_0_50_50 = e4
% 19.62/5.21 |
% 19.62/5.21 | Combining equations (253,453) yields a new equation:
% 19.62/5.21 | (360) e4 = e2
% 19.62/5.21 |
% 19.62/5.21 | Equations (360) can reduce 230 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (456) ~ (all_0_50_50 = e4)
% 19.62/5.21 | (457) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 19.62/5.21 |
% 19.62/5.21 | Equations (253) can reduce 456 to:
% 19.62/5.21 | (326) ~ (e4 = e2)
% 19.62/5.21 |
% 19.62/5.21 | Simplifying 326 yields:
% 19.62/5.21 | (230) ~ (e4 = e2)
% 19.62/5.21 |
% 19.62/5.21 +-Applying beta-rule and splitting (29), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (1079) all_0_39_39 = e4
% 19.62/5.21 |
% 19.62/5.21 | Combining equations (348,1079) yields a new equation:
% 19.62/5.21 | (360) e4 = e2
% 19.62/5.21 |
% 19.62/5.21 | Equations (360) can reduce 230 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (307) ~ (all_0_39_39 = e4)
% 19.62/5.21 | (1391) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 19.62/5.21 |
% 19.62/5.21 +-Applying beta-rule and splitting (1391), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (438) all_0_43_43 = e4
% 19.62/5.21 |
% 19.62/5.21 | Combining equations (438,559) yields a new equation:
% 19.62/5.21 | (515) e4 = e3
% 19.62/5.21 |
% 19.62/5.21 | Simplifying 515 yields:
% 19.62/5.21 | (516) e4 = e3
% 19.62/5.21 |
% 19.62/5.21 | Equations (516) can reduce 41 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (441) ~ (all_0_43_43 = e4)
% 19.62/5.21 | (2025) all_0_51_51 = e4 | all_0_56_56 = e4
% 19.62/5.21 |
% 19.62/5.21 +-Applying beta-rule and splitting (2025), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (458) all_0_51_51 = e4
% 19.62/5.21 |
% 19.62/5.21 | Equations (458) can reduce 255 to:
% 19.62/5.21 | (230) ~ (e4 = e2)
% 19.62/5.21 |
% 19.62/5.21 | Instantiating formula (21) with e2, e1, e4, e2 and discharging atoms op(e2, e1) = e4, op(e2, e1) = e2, yields:
% 19.62/5.21 | (360) e4 = e2
% 19.62/5.21 |
% 19.62/5.21 | Equations (360) can reduce 230 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (530) ~ (all_0_51_51 = e4)
% 19.62/5.21 | (1658) all_0_56_56 = e4
% 19.62/5.21 |
% 19.62/5.21 | Combining equations (632,1658) yields a new equation:
% 19.62/5.21 | (439) e4 = e0
% 19.62/5.21 |
% 19.62/5.21 | Equations (439) can reduce 11 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (537) ~ (all_0_45_45 = e4)
% 19.62/5.21 | (538) all_0_46_46 = e4
% 19.62/5.21 |
% 19.62/5.21 | Combining equations (364,538) yields a new equation:
% 19.62/5.21 | (360) e4 = e2
% 19.62/5.21 |
% 19.62/5.21 | Equations (360) can reduce 230 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (562) ~ (all_0_43_43 = e3)
% 19.62/5.21 | (1193) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 19.62/5.21 |
% 19.62/5.21 +-Applying beta-rule and splitting (1193), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (422) all_0_44_44 = e3
% 19.62/5.21 |
% 19.62/5.21 | Combining equations (352,422) yields a new equation:
% 19.62/5.21 | (560) e3 = e0
% 19.62/5.21 |
% 19.62/5.21 | Equations (560) can reduce 72 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (425) ~ (all_0_44_44 = e3)
% 19.62/5.21 | (1203) all_0_45_45 = e3 | all_0_46_46 = e3
% 19.62/5.21 |
% 19.62/5.21 +-Applying beta-rule and splitting (1203), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (1087) all_0_45_45 = e3
% 19.62/5.21 |
% 19.62/5.21 | Equations (1087) can reduce 689 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (689) ~ (all_0_45_45 = e3)
% 19.62/5.21 | (462) all_0_46_46 = e3
% 19.62/5.21 |
% 19.62/5.21 | Combining equations (364,462) yields a new equation:
% 19.62/5.21 | (423) e3 = e2
% 19.62/5.21 |
% 19.62/5.21 | Equations (423) can reduce 224 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (401) ~ (all_0_56_56 = e0)
% 19.62/5.21 | (2052) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 19.62/5.21 |
% 19.62/5.21 +-Applying beta-rule and splitting (162), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (559) all_0_43_43 = e3
% 19.62/5.21 |
% 19.62/5.21 | Equations (559) can reduce 459 to:
% 19.62/5.21 | (72) ~ (e3 = e0)
% 19.62/5.21 |
% 19.62/5.21 +-Applying beta-rule and splitting (2052), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (400) all_0_57_57 = e0
% 19.62/5.21 |
% 19.62/5.21 | Combining equations (400,867) yields a new equation:
% 19.62/5.21 | (354) e2 = e0
% 19.62/5.21 |
% 19.62/5.21 | Equations (354) can reduce 58 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (967) ~ (all_0_57_57 = e0)
% 19.62/5.21 | (2059) all_0_58_58 = e0 | all_0_59_59 = e0
% 19.62/5.21 |
% 19.62/5.21 +-Applying beta-rule and splitting (2059), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (493) all_0_58_58 = e0
% 19.62/5.21 |
% 19.62/5.21 | Combining equations (493,489) yields a new equation:
% 19.62/5.21 | (579) e1 = e0
% 19.62/5.21 |
% 19.62/5.21 | Equations (579) can reduce 144 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (403) ~ (all_0_58_58 = e0)
% 19.62/5.21 | (2064) all_0_59_59 = e0
% 19.62/5.21 |
% 19.62/5.21 | Combining equations (1070,2064) yields a new equation:
% 19.62/5.21 | (781) e3 = e0
% 19.62/5.21 |
% 19.62/5.21 | Simplifying 781 yields:
% 19.62/5.21 | (560) e3 = e0
% 19.62/5.21 |
% 19.62/5.21 | Equations (560) can reduce 72 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (562) ~ (all_0_43_43 = e3)
% 19.62/5.21 | (1193) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 19.62/5.21 |
% 19.62/5.21 +-Applying beta-rule and splitting (1193), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (422) all_0_44_44 = e3
% 19.62/5.21 |
% 19.62/5.21 | Combining equations (352,422) yields a new equation:
% 19.62/5.21 | (560) e3 = e0
% 19.62/5.21 |
% 19.62/5.21 | Equations (560) can reduce 72 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (425) ~ (all_0_44_44 = e3)
% 19.62/5.21 | (1203) all_0_45_45 = e3 | all_0_46_46 = e3
% 19.62/5.21 |
% 19.62/5.21 +-Applying beta-rule and splitting (1203), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (1087) all_0_45_45 = e3
% 19.62/5.21 |
% 19.62/5.21 | Equations (1087) can reduce 689 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (689) ~ (all_0_45_45 = e3)
% 19.62/5.21 | (462) all_0_46_46 = e3
% 19.62/5.21 |
% 19.62/5.21 | Combining equations (364,462) yields a new equation:
% 19.62/5.21 | (423) e3 = e2
% 19.62/5.21 |
% 19.62/5.21 | Equations (423) can reduce 224 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (609) ~ (all_0_41_41 = e3)
% 19.62/5.21 | (740) all_0_41_41 = e4
% 19.62/5.21 |
% 19.62/5.21 | Equations (740) can reduce 308 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (482) ~ (all_0_58_58 = e1)
% 19.62/5.21 | (614) all_0_59_59 = e1
% 19.62/5.21 |
% 19.62/5.21 | Combining equations (614,1070) yields a new equation:
% 19.62/5.21 | (418) e3 = e1
% 19.62/5.21 |
% 19.62/5.21 | Equations (418) can reduce 146 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (637) ~ (all_0_52_52 = e3)
% 19.62/5.21 | (638) all_0_57_57 = e3
% 19.62/5.21 |
% 19.62/5.21 | Combining equations (638,867) yields a new equation:
% 19.62/5.21 | (606) e3 = e2
% 19.62/5.21 |
% 19.62/5.21 | Simplifying 606 yields:
% 19.62/5.21 | (423) e3 = e2
% 19.62/5.21 |
% 19.62/5.21 | Equations (423) can reduce 224 to:
% 19.62/5.21 | (269) $false
% 19.62/5.21 |
% 19.62/5.21 |-The branch is then unsatisfiable
% 19.62/5.21 |-Branch two:
% 19.62/5.21 | (983) ~ (all_0_40_40 = e1)
% 19.62/5.21 | (984) all_0_52_52 = e1 | all_0_57_57 = e1
% 19.62/5.21 |
% 19.62/5.21 +-Applying beta-rule and splitting (39), into two cases.
% 19.62/5.21 |-Branch one:
% 19.62/5.21 | (464) all_0_39_39 = e1
% 19.62/5.21 |
% 19.62/5.21 | Combining equations (348,464) yields a new equation:
% 19.62/5.21 | (470) e2 = e1
% 19.62/5.21 |
% 19.62/5.21 | Simplifying 470 yields:
% 19.62/5.21 | (471) e2 = e1
% 19.62/5.22 |
% 19.62/5.22 | Equations (471) can reduce 148 to:
% 19.62/5.22 | (269) $false
% 19.62/5.22 |
% 19.62/5.22 |-The branch is then unsatisfiable
% 19.62/5.22 |-Branch two:
% 19.62/5.22 | (467) ~ (all_0_39_39 = e1)
% 19.62/5.22 | (2100) all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1
% 19.62/5.22 |
% 19.62/5.22 | Equations (348) can reduce 467 to:
% 19.62/5.22 | (148) ~ (e2 = e1)
% 19.62/5.22 |
% 19.62/5.22 +-Applying beta-rule and splitting (984), into two cases.
% 19.62/5.22 |-Branch one:
% 19.62/5.22 | (820) all_0_52_52 = e1
% 19.62/5.22 |
% 19.62/5.22 | Equations (820) can reduce 71 to:
% 19.62/5.22 | (822) ~ (all_0_53_53 = e1)
% 19.62/5.22 |
% 19.62/5.22 | Simplifying 822 yields:
% 19.62/5.22 | (823) ~ (all_0_53_53 = e1)
% 19.62/5.22 |
% 19.62/5.22 | Equations (820) can reduce 62 to:
% 19.62/5.22 | (1237) ~ (all_0_54_54 = e1)
% 19.62/5.22 |
% 19.62/5.22 | Simplifying 1237 yields:
% 19.62/5.22 | (1238) ~ (all_0_54_54 = e1)
% 19.62/5.22 |
% 19.62/5.22 | Equations (820) can reduce 317 to:
% 19.62/5.22 | (144) ~ (e1 = e0)
% 19.62/5.22 |
% 19.62/5.22 +-Applying beta-rule and splitting (303), into two cases.
% 19.62/5.22 |-Branch one:
% 19.62/5.22 | (765) ~ (all_0_53_53 = e0)
% 19.62/5.22 |
% 19.62/5.22 +-Applying beta-rule and splitting (63), into two cases.
% 19.62/5.22 |-Branch one:
% 19.62/5.22 | (629) all_0_51_51 = e0
% 19.62/5.22 |
% 19.62/5.22 | Equations (629) can reduce 16 to:
% 19.62/5.22 | (1556) ~ (all_0_56_56 = e0)
% 19.62/5.22 |
% 19.62/5.22 | Simplifying 1556 yields:
% 19.62/5.22 | (401) ~ (all_0_56_56 = e0)
% 19.62/5.22 |
% 19.62/5.22 | Equations (629) can reduce 255 to:
% 19.62/5.22 | (406) ~ (e2 = e0)
% 19.62/5.22 |
% 19.62/5.22 | Simplifying 406 yields:
% 19.62/5.22 | (58) ~ (e2 = e0)
% 19.62/5.22 |
% 19.62/5.22 +-Applying beta-rule and splitting (20), into two cases.
% 19.62/5.22 |-Branch one:
% 19.62/5.22 | (1575) all_0_56_56 = e2
% 19.62/5.22 |
% 19.62/5.22 | Equations (1575) can reduce 377 to:
% 19.62/5.22 | (269) $false
% 19.62/5.22 |
% 19.62/5.22 |-The branch is then unsatisfiable
% 19.62/5.22 |-Branch two:
% 19.62/5.22 | (377) ~ (all_0_56_56 = e2)
% 19.62/5.22 | (1578) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1 | all_0_56_56 = e0
% 19.62/5.22 |
% 19.62/5.22 +-Applying beta-rule and splitting (1578), into two cases.
% 19.62/5.22 |-Branch one:
% 19.62/5.22 | (480) all_0_56_56 = e1
% 19.62/5.22 |
% 19.62/5.22 | Equations (480) can reduce 575 to:
% 19.62/5.22 | (269) $false
% 19.62/5.22 |
% 19.62/5.22 |-The branch is then unsatisfiable
% 19.62/5.22 |-Branch two:
% 19.62/5.22 | (575) ~ (all_0_56_56 = e1)
% 19.62/5.22 | (1619) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e0
% 19.62/5.22 |
% 19.62/5.22 +-Applying beta-rule and splitting (211), into two cases.
% 19.62/5.22 |-Branch one:
% 19.62/5.22 | (632) all_0_56_56 = e0
% 19.62/5.22 |
% 19.62/5.22 | Equations (632) can reduce 401 to:
% 19.62/5.22 | (269) $false
% 19.62/5.22 |
% 19.62/5.22 |-The branch is then unsatisfiable
% 19.62/5.22 |-Branch two:
% 19.62/5.22 | (401) ~ (all_0_56_56 = e0)
% 19.62/5.22 | (2052) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 19.62/5.22 |
% 19.62/5.22 +-Applying beta-rule and splitting (1619), into two cases.
% 19.62/5.22 |-Branch one:
% 19.62/5.22 | (632) all_0_56_56 = e0
% 19.62/5.22 |
% 19.62/5.22 | Equations (632) can reduce 401 to:
% 19.62/5.22 | (269) $false
% 19.62/5.22 |
% 19.62/5.22 |-The branch is then unsatisfiable
% 19.62/5.22 |-Branch two:
% 19.62/5.22 | (401) ~ (all_0_56_56 = e0)
% 19.62/5.22 | (1630) all_0_56_56 = e4 | all_0_56_56 = e3
% 19.62/5.22 |
% 19.62/5.22 +-Applying beta-rule and splitting (1630), into two cases.
% 19.62/5.22 |-Branch one:
% 19.62/5.22 | (567) all_0_56_56 = e3
% 19.62/5.22 |
% 19.62/5.22 | Equations (567) can reduce 130 to:
% 19.62/5.22 | (2131) ~ (all_0_59_59 = e3)
% 19.62/5.22 |
% 19.62/5.22 | Simplifying 2131 yields:
% 19.62/5.22 | (2132) ~ (all_0_59_59 = e3)
% 19.62/5.22 |
% 19.62/5.22 | Equations (567) can reduce 273 to:
% 19.62/5.22 | (498) ~ (e4 = e3)
% 19.62/5.22 |
% 19.62/5.22 | Simplifying 498 yields:
% 19.62/5.22 | (41) ~ (e4 = e3)
% 19.97/5.22 |
% 19.97/5.22 | From (567) and (44) follows:
% 19.97/5.22 | (2135) op(e0, e3) = all_0_12_12
% 19.97/5.22 |
% 19.97/5.22 | From (567) and (202) follows:
% 19.97/5.22 | (2136) op(e0, e3) = e3
% 19.97/5.22 |
% 19.97/5.22 +-Applying beta-rule and splitting (2052), into two cases.
% 19.97/5.22 |-Branch one:
% 19.97/5.22 | (400) all_0_57_57 = e0
% 19.97/5.22 |
% 19.97/5.22 | Combining equations (400,867) yields a new equation:
% 19.97/5.22 | (354) e2 = e0
% 19.97/5.22 |
% 19.97/5.22 | Equations (354) can reduce 58 to:
% 19.97/5.22 | (269) $false
% 19.97/5.22 |
% 19.97/5.22 |-The branch is then unsatisfiable
% 19.97/5.22 |-Branch two:
% 19.97/5.22 | (967) ~ (all_0_57_57 = e0)
% 19.97/5.22 | (2059) all_0_58_58 = e0 | all_0_59_59 = e0
% 19.97/5.22 |
% 19.97/5.22 +-Applying beta-rule and splitting (2059), into two cases.
% 19.97/5.22 |-Branch one:
% 19.97/5.22 | (493) all_0_58_58 = e0
% 19.97/5.22 |
% 19.97/5.22 | Equations (493) can reduce 68 to:
% 19.97/5.22 | (299) ~ (all_0_45_45 = e0)
% 19.97/5.22 |
% 19.97/5.22 | Equations (493) can reduce 198 to:
% 19.97/5.22 | (1479) ~ (all_0_59_59 = e0)
% 19.97/5.22 |
% 19.97/5.22 | Simplifying 1479 yields:
% 19.97/5.22 | (1480) ~ (all_0_59_59 = e0)
% 19.97/5.22 |
% 19.97/5.22 | Equations (493) can reduce 277 to:
% 19.97/5.22 | (404) ~ (e4 = e0)
% 19.97/5.22 |
% 19.97/5.22 | Simplifying 404 yields:
% 19.97/5.22 | (11) ~ (e4 = e0)
% 19.97/5.22 |
% 19.97/5.22 +-Applying beta-rule and splitting (212), into two cases.
% 19.97/5.22 |-Branch one:
% 19.97/5.22 | (375) all_0_59_59 = e2
% 19.97/5.22 |
% 19.97/5.22 | Equations (375) can reduce 1843 to:
% 19.97/5.22 | (269) $false
% 19.97/5.22 |
% 19.97/5.22 |-The branch is then unsatisfiable
% 19.97/5.22 |-Branch two:
% 19.97/5.22 | (1843) ~ (all_0_59_59 = e2)
% 19.97/5.22 | (2151) all_0_59_59 = e4 | all_0_59_59 = e3 | all_0_59_59 = e1 | all_0_59_59 = e0
% 19.97/5.22 |
% 19.97/5.22 +-Applying beta-rule and splitting (2151), into two cases.
% 19.97/5.22 |-Branch one:
% 19.97/5.22 | (614) all_0_59_59 = e1
% 19.97/5.22 |
% 19.97/5.22 | Equations (614) can reduce 1843 to:
% 19.97/5.22 | (414) ~ (e2 = e1)
% 19.97/5.22 |
% 19.97/5.22 | Simplifying 414 yields:
% 19.97/5.22 | (148) ~ (e2 = e1)
% 19.97/5.22 |
% 19.97/5.22 | Equations (614) can reduce 1480 to:
% 19.97/5.22 | (144) ~ (e1 = e0)
% 19.97/5.22 |
% 19.97/5.22 +-Applying beta-rule and splitting (15), into two cases.
% 19.97/5.22 |-Branch one:
% 19.97/5.22 | (1312) all_0_41_41 = e1
% 19.97/5.22 |
% 19.97/5.22 | Equations (1312) can reduce 122 to:
% 19.97/5.22 | (2157) ~ (all_0_45_45 = e1)
% 19.97/5.22 |
% 19.97/5.22 | Simplifying 2157 yields:
% 19.97/5.22 | (215) ~ (all_0_45_45 = e1)
% 19.97/5.22 |
% 19.97/5.22 +-Applying beta-rule and splitting (169), into two cases.
% 19.97/5.22 |-Branch one:
% 19.97/5.22 | (610) all_0_42_42 = e3
% 19.97/5.22 |
% 19.97/5.22 | Combining equations (610,305) yields a new equation:
% 19.97/5.22 | (516) e4 = e3
% 19.97/5.22 |
% 19.97/5.22 | Equations (516) can reduce 41 to:
% 19.97/5.22 | (269) $false
% 19.97/5.22 |
% 19.97/5.22 |-The branch is then unsatisfiable
% 19.97/5.22 |-Branch two:
% 19.97/5.22 | (1924) ~ (all_0_42_42 = e3)
% 19.97/5.22 | (1925) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 19.97/5.22 |
% 19.97/5.22 | Equations (305) can reduce 1924 to:
% 19.97/5.22 | (41) ~ (e4 = e3)
% 19.97/5.22 |
% 19.97/5.22 +-Applying beta-rule and splitting (29), into two cases.
% 19.97/5.22 |-Branch one:
% 19.97/5.22 | (1079) all_0_39_39 = e4
% 19.97/5.22 |
% 19.97/5.22 | Combining equations (348,1079) yields a new equation:
% 19.97/5.22 | (360) e4 = e2
% 19.97/5.22 |
% 19.97/5.22 | Equations (360) can reduce 230 to:
% 19.97/5.22 | (269) $false
% 19.97/5.22 |
% 19.97/5.22 |-The branch is then unsatisfiable
% 19.97/5.22 |-Branch two:
% 19.97/5.22 | (307) ~ (all_0_39_39 = e4)
% 19.97/5.22 | (1391) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 19.97/5.22 |
% 19.97/5.22 +-Applying beta-rule and splitting (1391), into two cases.
% 19.97/5.22 |-Branch one:
% 19.97/5.22 | (438) all_0_43_43 = e4
% 19.97/5.22 |
% 19.97/5.22 | Equations (438) can reduce 186 to:
% 19.97/5.22 | (1700) ~ (all_0_45_45 = e4)
% 19.97/5.22 |
% 19.97/5.22 | Simplifying 1700 yields:
% 19.97/5.22 | (537) ~ (all_0_45_45 = e4)
% 19.97/5.22 |
% 19.97/5.22 +-Applying beta-rule and splitting (245), into two cases.
% 19.97/5.22 |-Branch one:
% 19.97/5.22 | (694) all_0_45_45 = e2
% 19.97/5.22 |
% 19.97/5.22 | Equations (694) can reduce 390 to:
% 19.97/5.22 | (269) $false
% 19.97/5.22 |
% 19.97/5.22 |-The branch is then unsatisfiable
% 19.97/5.22 |-Branch two:
% 19.97/5.22 | (390) ~ (all_0_45_45 = e2)
% 19.97/5.22 | (1082) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 19.97/5.22 |
% 19.97/5.22 +-Applying beta-rule and splitting (302), into two cases.
% 19.97/5.22 |-Branch one:
% 19.97/5.22 | (432) ~ (all_0_51_51 = e0)
% 19.97/5.22 |
% 19.97/5.22 | Equations (629) can reduce 432 to:
% 19.97/5.22 | (269) $false
% 19.97/5.22 |
% 19.97/5.22 |-The branch is then unsatisfiable
% 19.97/5.22 |-Branch two:
% 19.97/5.22 | (629) all_0_51_51 = e0
% 19.97/5.22 | (635) all_0_54_54 = e3
% 19.97/5.22 |
% 19.97/5.22 | From (635) and (1874) follows:
% 19.97/5.22 | (2181) op(e0, e3) = e1
% 19.97/5.22 |
% 19.97/5.22 +-Applying beta-rule and splitting (1082), into two cases.
% 19.97/5.22 |-Branch one:
% 19.97/5.22 | (889) all_0_45_45 = e0
% 19.97/5.22 |
% 19.97/5.22 | Equations (889) can reduce 299 to:
% 19.97/5.22 | (269) $false
% 19.97/5.22 |
% 19.97/5.22 |-The branch is then unsatisfiable
% 19.97/5.22 |-Branch two:
% 19.97/5.22 | (299) ~ (all_0_45_45 = e0)
% 19.97/5.22 | (1086) all_0_45_45 = e4 | all_0_45_45 = e3
% 19.97/5.22 |
% 19.97/5.22 +-Applying beta-rule and splitting (1086), into two cases.
% 19.97/5.22 |-Branch one:
% 19.97/5.22 | (1087) all_0_45_45 = e3
% 19.97/5.22 |
% 19.97/5.22 | Equations (1087) can reduce 215 to:
% 19.97/5.22 | (146) ~ (e3 = e1)
% 19.97/5.22 |
% 19.97/5.22 | Instantiating formula (21) with e0, e3, e3, all_0_12_12 and discharging atoms op(e0, e3) = all_0_12_12, op(e0, e3) = e3, yields:
% 19.97/5.22 | (2188) all_0_12_12 = e3
% 19.97/5.22 |
% 19.97/5.22 | Instantiating formula (21) with e0, e3, e1, all_0_12_12 and discharging atoms op(e0, e3) = all_0_12_12, op(e0, e3) = e1, yields:
% 19.97/5.22 | (2189) all_0_12_12 = e1
% 19.97/5.22 |
% 19.97/5.22 | Combining equations (2188,2189) yields a new equation:
% 19.97/5.22 | (572) e3 = e1
% 19.97/5.22 |
% 19.97/5.22 | Simplifying 572 yields:
% 19.97/5.22 | (418) e3 = e1
% 19.97/5.22 |
% 19.97/5.22 | Equations (418) can reduce 146 to:
% 19.97/5.22 | (269) $false
% 19.97/5.22 |
% 19.97/5.22 |-The branch is then unsatisfiable
% 19.97/5.22 |-Branch two:
% 19.97/5.22 | (689) ~ (all_0_45_45 = e3)
% 19.97/5.22 | (444) all_0_45_45 = e4
% 19.97/5.22 |
% 19.97/5.22 | Equations (444) can reduce 537 to:
% 19.97/5.22 | (269) $false
% 19.97/5.22 |
% 19.97/5.22 |-The branch is then unsatisfiable
% 19.97/5.22 |-Branch two:
% 19.97/5.22 | (441) ~ (all_0_43_43 = e4)
% 19.97/5.22 | (2025) all_0_51_51 = e4 | all_0_56_56 = e4
% 19.97/5.22 |
% 19.97/5.22 +-Applying beta-rule and splitting (2025), into two cases.
% 19.97/5.22 |-Branch one:
% 19.97/5.22 | (458) all_0_51_51 = e4
% 19.97/5.22 |
% 19.97/5.22 | Combining equations (458,629) yields a new equation:
% 19.97/5.22 | (751) e4 = e0
% 19.97/5.22 |
% 19.97/5.22 | Simplifying 751 yields:
% 19.97/5.22 | (439) e4 = e0
% 19.97/5.22 |
% 19.97/5.22 | Equations (439) can reduce 11 to:
% 19.97/5.22 | (269) $false
% 19.97/5.22 |
% 19.97/5.22 |-The branch is then unsatisfiable
% 19.97/5.22 |-Branch two:
% 19.97/5.22 | (530) ~ (all_0_51_51 = e4)
% 19.97/5.22 | (1658) all_0_56_56 = e4
% 19.97/5.22 |
% 19.97/5.22 | Combining equations (1658,567) yields a new equation:
% 19.97/5.22 | (515) e4 = e3
% 19.97/5.22 |
% 19.97/5.22 | Simplifying 515 yields:
% 19.97/5.22 | (516) e4 = e3
% 19.97/5.22 |
% 19.97/5.22 | Equations (516) can reduce 41 to:
% 19.97/5.22 | (269) $false
% 19.97/5.22 |
% 19.97/5.22 |-The branch is then unsatisfiable
% 19.97/5.22 |-Branch two:
% 19.97/5.22 | (1315) ~ (all_0_41_41 = e1)
% 19.97/5.22 | (1316) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 19.97/5.22 |
% 19.97/5.22 +-Applying beta-rule and splitting (1316), into two cases.
% 19.97/5.22 |-Branch one:
% 19.97/5.22 | (593) all_0_48_48 = e1
% 19.97/5.22 |
% 19.97/5.22 | Combining equations (1458,593) yields a new equation:
% 19.97/5.22 | (470) e2 = e1
% 19.97/5.22 |
% 19.97/5.22 | Simplifying 470 yields:
% 19.97/5.22 | (471) e2 = e1
% 19.97/5.22 |
% 19.97/5.22 | Equations (471) can reduce 148 to:
% 19.97/5.22 | (269) $false
% 19.97/5.22 |
% 19.97/5.22 |-The branch is then unsatisfiable
% 19.97/5.22 |-Branch two:
% 19.97/5.22 | (584) ~ (all_0_48_48 = e1)
% 19.97/5.22 | (1615) all_0_53_53 = e1 | all_0_58_58 = e1
% 19.97/5.22 |
% 19.97/5.22 +-Applying beta-rule and splitting (1615), into two cases.
% 19.97/5.22 |-Branch one:
% 19.97/5.22 | (853) all_0_53_53 = e1
% 19.97/5.22 |
% 19.97/5.22 | Equations (853) can reduce 823 to:
% 19.97/5.22 | (269) $false
% 19.97/5.22 |
% 19.97/5.22 |-The branch is then unsatisfiable
% 19.97/5.22 |-Branch two:
% 19.97/5.22 | (823) ~ (all_0_53_53 = e1)
% 19.97/5.22 | (489) all_0_58_58 = e1
% 19.97/5.22 |
% 19.97/5.22 | Combining equations (489,493) yields a new equation:
% 19.97/5.22 | (578) e1 = e0
% 19.97/5.22 |
% 19.97/5.22 | Simplifying 578 yields:
% 19.97/5.22 | (579) e1 = e0
% 19.97/5.22 |
% 19.97/5.22 | Equations (579) can reduce 144 to:
% 19.97/5.22 | (269) $false
% 19.97/5.22 |
% 19.97/5.22 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (2222) ~ (all_0_59_59 = e1)
% 19.97/5.23 | (2223) all_0_59_59 = e4 | all_0_59_59 = e3 | all_0_59_59 = e0
% 19.97/5.23 |
% 19.97/5.23 +-Applying beta-rule and splitting (2223), into two cases.
% 19.97/5.23 |-Branch one:
% 19.97/5.23 | (2064) all_0_59_59 = e0
% 19.97/5.23 |
% 19.97/5.23 | Equations (2064) can reduce 1480 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (1480) ~ (all_0_59_59 = e0)
% 19.97/5.23 | (2227) all_0_59_59 = e4 | all_0_59_59 = e3
% 19.97/5.23 |
% 19.97/5.23 +-Applying beta-rule and splitting (2227), into two cases.
% 19.97/5.23 |-Branch one:
% 19.97/5.23 | (1070) all_0_59_59 = e3
% 19.97/5.23 |
% 19.97/5.23 | Equations (1070) can reduce 2132 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (2132) ~ (all_0_59_59 = e3)
% 19.97/5.23 | (2231) all_0_59_59 = e4
% 19.97/5.23 |
% 19.97/5.23 | Equations (2231) can reduce 279 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (403) ~ (all_0_58_58 = e0)
% 19.97/5.23 | (2064) all_0_59_59 = e0
% 19.97/5.23 |
% 19.97/5.23 | Equations (2064) can reduce 1480 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (1183) ~ (all_0_56_56 = e3)
% 19.97/5.23 | (1658) all_0_56_56 = e4
% 19.97/5.23 |
% 19.97/5.23 | Equations (1658) can reduce 273 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (432) ~ (all_0_51_51 = e0)
% 19.97/5.23 | (1231) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 19.97/5.23 |
% 19.97/5.23 +-Applying beta-rule and splitting (1231), into two cases.
% 19.97/5.23 |-Branch one:
% 19.97/5.23 | (397) all_0_52_52 = e0
% 19.97/5.23 |
% 19.97/5.23 | Combining equations (820,397) yields a new equation:
% 19.97/5.23 | (578) e1 = e0
% 19.97/5.23 |
% 19.97/5.23 | Simplifying 578 yields:
% 19.97/5.23 | (579) e1 = e0
% 19.97/5.23 |
% 19.97/5.23 | Equations (579) can reduce 144 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (317) ~ (all_0_52_52 = e0)
% 19.97/5.23 | (1245) all_0_53_53 = e0 | all_0_54_54 = e0
% 19.97/5.23 |
% 19.97/5.23 +-Applying beta-rule and splitting (1245), into two cases.
% 19.97/5.23 |-Branch one:
% 19.97/5.23 | (857) all_0_53_53 = e0
% 19.97/5.23 |
% 19.97/5.23 | Equations (857) can reduce 765 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (765) ~ (all_0_53_53 = e0)
% 19.97/5.23 | (1286) all_0_54_54 = e0
% 19.97/5.23 |
% 19.97/5.23 | Equations (1286) can reduce 1478 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (857) all_0_53_53 = e0
% 19.97/5.23 | (1592) all_0_54_54 = e1
% 19.97/5.23 |
% 19.97/5.23 | Equations (1592) can reduce 1238 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (978) ~ (all_0_52_52 = e1)
% 19.97/5.23 | (577) all_0_57_57 = e1
% 19.97/5.23 |
% 19.97/5.23 | Combining equations (577,867) yields a new equation:
% 19.97/5.23 | (471) e2 = e1
% 19.97/5.23 |
% 19.97/5.23 | Equations (471) can reduce 148 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (512) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 19.97/5.23 |
% 19.97/5.23 | Applying alpha-rule on (512) yields:
% 19.97/5.23 | (513) all_0_15_15 = e3
% 19.97/5.23 | (514) ~ (all_0_16_16 = e2)
% 19.97/5.23 |
% 19.97/5.23 | Combining equations (513,1850) yields a new equation:
% 19.97/5.23 | (781) e3 = e0
% 19.97/5.23 |
% 19.97/5.23 | Simplifying 781 yields:
% 19.97/5.23 | (560) e3 = e0
% 19.97/5.23 |
% 19.97/5.23 | Equations (560) can reduce 72 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (518) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 19.97/5.23 |
% 19.97/5.23 | Applying alpha-rule on (518) yields:
% 19.97/5.23 | (519) all_0_17_17 = e1
% 19.97/5.23 | (520) ~ (all_0_18_18 = e2)
% 19.97/5.23 |
% 19.97/5.23 | From (519) and (69) follows:
% 19.97/5.23 | (2268) op(e2, all_0_52_52) = e1
% 19.97/5.23 |
% 19.97/5.23 +-Applying beta-rule and splitting (246), into two cases.
% 19.97/5.23 |-Branch one:
% 19.97/5.23 | (413) all_0_40_40 = e1
% 19.97/5.23 |
% 19.97/5.23 | Equations (413) can reduce 187 to:
% 19.97/5.23 | (1157) ~ (all_0_52_52 = e1)
% 19.97/5.23 |
% 19.97/5.23 | Simplifying 1157 yields:
% 19.97/5.23 | (978) ~ (all_0_52_52 = e1)
% 19.97/5.23 |
% 19.97/5.23 | Equations (413) can reduce 342 to:
% 19.97/5.23 | (414) ~ (e2 = e1)
% 19.97/5.23 |
% 19.97/5.23 | Simplifying 414 yields:
% 19.97/5.23 | (148) ~ (e2 = e1)
% 19.97/5.23 |
% 19.97/5.23 +-Applying beta-rule and splitting (86), into two cases.
% 19.97/5.23 |-Branch one:
% 19.97/5.23 | (816) all_0_52_52 = e2
% 19.97/5.23 |
% 19.97/5.23 | Equations (816) can reduce 257 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (257) ~ (all_0_52_52 = e2)
% 19.97/5.23 | (819) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 19.97/5.23 |
% 19.97/5.23 +-Applying beta-rule and splitting (193), into two cases.
% 19.97/5.23 |-Branch one:
% 19.97/5.23 | (417) all_0_40_40 = e3
% 19.97/5.23 |
% 19.97/5.23 | Combining equations (413,417) yields a new equation:
% 19.97/5.23 | (418) e3 = e1
% 19.97/5.23 |
% 19.97/5.23 | Equations (418) can reduce 146 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (420) ~ (all_0_40_40 = e3)
% 19.97/5.23 | (421) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 19.97/5.23 |
% 19.97/5.23 +-Applying beta-rule and splitting (94), into two cases.
% 19.97/5.23 |-Branch one:
% 19.97/5.23 | (386) all_0_41_41 = e2
% 19.97/5.23 |
% 19.97/5.23 | Equations (386) can reduce 650 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (650) ~ (all_0_41_41 = e2)
% 19.97/5.23 | (1903) all_0_41_41 = e4 | all_0_41_41 = e3 | all_0_41_41 = e1
% 19.97/5.23 |
% 19.97/5.23 +-Applying beta-rule and splitting (421), into two cases.
% 19.97/5.23 |-Branch one:
% 19.97/5.23 | (422) all_0_44_44 = e3
% 19.97/5.23 |
% 19.97/5.23 | Combining equations (352,422) yields a new equation:
% 19.97/5.23 | (560) e3 = e0
% 19.97/5.23 |
% 19.97/5.23 | Equations (560) can reduce 72 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (425) ~ (all_0_44_44 = e3)
% 19.97/5.23 | (426) all_0_52_52 = e3 | all_0_57_57 = e3
% 19.97/5.23 |
% 19.97/5.23 +-Applying beta-rule and splitting (819), into two cases.
% 19.97/5.23 |-Branch one:
% 19.97/5.23 | (820) all_0_52_52 = e1
% 19.97/5.23 |
% 19.97/5.23 | Equations (820) can reduce 978 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (978) ~ (all_0_52_52 = e1)
% 19.97/5.23 | (979) all_0_52_52 = e3 | all_0_52_52 = e0
% 19.97/5.23 |
% 19.97/5.23 +-Applying beta-rule and splitting (426), into two cases.
% 19.97/5.23 |-Branch one:
% 19.97/5.23 | (427) all_0_52_52 = e3
% 19.97/5.23 |
% 19.97/5.23 | Equations (427) can reduce 62 to:
% 19.97/5.23 | (429) ~ (all_0_54_54 = e3)
% 19.97/5.23 |
% 19.97/5.23 | Simplifying 429 yields:
% 19.97/5.23 | (430) ~ (all_0_54_54 = e3)
% 19.97/5.23 |
% 19.97/5.23 | Equations (427) can reduce 152 to:
% 19.97/5.23 | (498) ~ (e4 = e3)
% 19.97/5.23 |
% 19.97/5.23 | Simplifying 498 yields:
% 19.97/5.23 | (41) ~ (e4 = e3)
% 19.97/5.23 |
% 19.97/5.23 | Equations (427) can reduce 257 to:
% 19.97/5.23 | (224) ~ (e3 = e2)
% 19.97/5.23 |
% 19.97/5.23 | Equations (427) can reduce 978 to:
% 19.97/5.23 | (146) ~ (e3 = e1)
% 19.97/5.23 |
% 19.97/5.23 +-Applying beta-rule and splitting (169), into two cases.
% 19.97/5.23 |-Branch one:
% 19.97/5.23 | (610) all_0_42_42 = e3
% 19.97/5.23 |
% 19.97/5.23 | Combining equations (305,610) yields a new equation:
% 19.97/5.23 | (515) e4 = e3
% 19.97/5.23 |
% 19.97/5.23 | Simplifying 515 yields:
% 19.97/5.23 | (516) e4 = e3
% 19.97/5.23 |
% 19.97/5.23 | Equations (516) can reduce 41 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (1924) ~ (all_0_42_42 = e3)
% 19.97/5.23 | (1925) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 19.97/5.23 |
% 19.97/5.23 +-Applying beta-rule and splitting (1925), into two cases.
% 19.97/5.23 |-Branch one:
% 19.97/5.23 | (462) all_0_46_46 = e3
% 19.97/5.23 |
% 19.97/5.23 | Combining equations (364,462) yields a new equation:
% 19.97/5.23 | (423) e3 = e2
% 19.97/5.23 |
% 19.97/5.23 | Equations (423) can reduce 224 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (618) ~ (all_0_46_46 = e3)
% 19.97/5.23 | (1930) all_0_54_54 = e3 | all_0_59_59 = e3
% 19.97/5.23 |
% 19.97/5.23 +-Applying beta-rule and splitting (1930), into two cases.
% 19.97/5.23 |-Branch one:
% 19.97/5.23 | (635) all_0_54_54 = e3
% 19.97/5.23 |
% 19.97/5.23 | Equations (635) can reduce 430 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (430) ~ (all_0_54_54 = e3)
% 19.97/5.23 | (1070) all_0_59_59 = e3
% 19.97/5.23 |
% 19.97/5.23 | Equations (1070) can reduce 198 to:
% 19.97/5.23 | (527) ~ (all_0_58_58 = e3)
% 19.97/5.23 |
% 19.97/5.23 +-Applying beta-rule and splitting (43), into two cases.
% 19.97/5.23 |-Branch one:
% 19.97/5.23 | (480) all_0_56_56 = e1
% 19.97/5.23 |
% 19.97/5.23 | Equations (480) can reduce 575 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (575) ~ (all_0_56_56 = e1)
% 19.97/5.23 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 19.97/5.23 |
% 19.97/5.23 +-Applying beta-rule and splitting (576), into two cases.
% 19.97/5.23 |-Branch one:
% 19.97/5.23 | (577) all_0_57_57 = e1
% 19.97/5.23 |
% 19.97/5.23 | Combining equations (577,867) yields a new equation:
% 19.97/5.23 | (471) e2 = e1
% 19.97/5.23 |
% 19.97/5.23 | Equations (471) can reduce 148 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (581) ~ (all_0_57_57 = e1)
% 19.97/5.23 | (582) all_0_58_58 = e1 | all_0_59_59 = e1
% 19.97/5.23 |
% 19.97/5.23 +-Applying beta-rule and splitting (582), into two cases.
% 19.97/5.23 |-Branch one:
% 19.97/5.23 | (489) all_0_58_58 = e1
% 19.97/5.23 |
% 19.97/5.23 | Equations (489) can reduce 208 to:
% 19.97/5.23 | (1315) ~ (all_0_41_41 = e1)
% 19.97/5.23 |
% 19.97/5.23 | Equations (489) can reduce 127 to:
% 19.97/5.23 | (823) ~ (all_0_53_53 = e1)
% 19.97/5.23 |
% 19.97/5.23 | Equations (489) can reduce 223 to:
% 19.97/5.23 | (575) ~ (all_0_56_56 = e1)
% 19.97/5.23 |
% 19.97/5.23 | Equations (489) can reduce 527 to:
% 19.97/5.23 | (597) ~ (e3 = e1)
% 19.97/5.23 |
% 19.97/5.23 | Simplifying 597 yields:
% 19.97/5.23 | (146) ~ (e3 = e1)
% 19.97/5.23 |
% 19.97/5.23 | From (489) and (67) follows:
% 19.97/5.23 | (910) op(e1, e1) = all_0_28_28
% 19.97/5.23 |
% 19.97/5.23 +-Applying beta-rule and splitting (19), into two cases.
% 19.97/5.23 |-Branch one:
% 19.97/5.23 | (475) all_0_51_51 = e1
% 19.97/5.23 |
% 19.97/5.23 | Equations (475) can reduce 479 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (479) ~ (all_0_51_51 = e1)
% 19.97/5.23 | (1954) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 19.97/5.23 |
% 19.97/5.23 +-Applying beta-rule and splitting (1954), into two cases.
% 19.97/5.23 |-Branch one:
% 19.97/5.23 | (820) all_0_52_52 = e1
% 19.97/5.23 |
% 19.97/5.23 | Combining equations (820,427) yields a new equation:
% 19.97/5.23 | (418) e3 = e1
% 19.97/5.23 |
% 19.97/5.23 | Equations (418) can reduce 146 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (978) ~ (all_0_52_52 = e1)
% 19.97/5.23 | (1959) all_0_53_53 = e1 | all_0_54_54 = e1
% 19.97/5.23 |
% 19.97/5.23 +-Applying beta-rule and splitting (139), into two cases.
% 19.97/5.23 |-Branch one:
% 19.97/5.23 | (889) all_0_45_45 = e0
% 19.97/5.23 |
% 19.97/5.23 | Equations (889) can reduce 299 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (299) ~ (all_0_45_45 = e0)
% 19.97/5.23 | (894) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 19.97/5.23 |
% 19.97/5.23 +-Applying beta-rule and splitting (1959), into two cases.
% 19.97/5.23 |-Branch one:
% 19.97/5.23 | (853) all_0_53_53 = e1
% 19.97/5.23 |
% 19.97/5.23 | Equations (853) can reduce 823 to:
% 19.97/5.23 | (269) $false
% 19.97/5.23 |
% 19.97/5.23 |-The branch is then unsatisfiable
% 19.97/5.23 |-Branch two:
% 19.97/5.23 | (823) ~ (all_0_53_53 = e1)
% 19.97/5.23 | (1592) all_0_54_54 = e1
% 19.97/5.23 |
% 19.97/5.24 | Equations (1592) can reduce 1478 to:
% 19.97/5.24 | (144) ~ (e1 = e0)
% 19.97/5.24 |
% 19.97/5.24 | From (1592) and (49) follows:
% 19.97/5.24 | (1595) op(e1, e1) = all_0_37_37
% 19.97/5.24 |
% 19.97/5.24 +-Applying beta-rule and splitting (1903), into two cases.
% 19.97/5.24 |-Branch one:
% 19.97/5.24 | (1312) all_0_41_41 = e1
% 19.97/5.24 |
% 19.97/5.24 | Equations (1312) can reduce 1315 to:
% 19.97/5.24 | (269) $false
% 19.97/5.24 |
% 19.97/5.24 |-The branch is then unsatisfiable
% 19.97/5.24 |-Branch two:
% 19.97/5.24 | (1315) ~ (all_0_41_41 = e1)
% 19.97/5.24 | (1972) all_0_41_41 = e4 | all_0_41_41 = e3
% 19.97/5.24 |
% 19.97/5.24 +-Applying beta-rule and splitting (1972), into two cases.
% 19.97/5.24 |-Branch one:
% 19.97/5.24 | (605) all_0_41_41 = e3
% 19.97/5.24 |
% 19.97/5.24 | Equations (605) can reduce 122 to:
% 19.97/5.24 | (688) ~ (all_0_45_45 = e3)
% 19.97/5.24 |
% 19.97/5.24 | Simplifying 688 yields:
% 19.97/5.24 | (689) ~ (all_0_45_45 = e3)
% 19.97/5.24 |
% 19.97/5.24 | Equations (605) can reduce 650 to:
% 19.97/5.24 | (224) ~ (e3 = e2)
% 19.97/5.24 |
% 19.97/5.24 | Equations (605) can reduce 188 to:
% 19.97/5.24 | (72) ~ (e3 = e0)
% 19.97/5.24 |
% 19.97/5.24 +-Applying beta-rule and splitting (211), into two cases.
% 19.97/5.24 |-Branch one:
% 19.97/5.24 | (632) all_0_56_56 = e0
% 19.97/5.24 |
% 19.97/5.24 | Equations (632) can reduce 377 to:
% 19.97/5.24 | (406) ~ (e2 = e0)
% 19.97/5.24 |
% 19.97/5.24 | Simplifying 406 yields:
% 19.97/5.24 | (58) ~ (e2 = e0)
% 19.97/5.24 |
% 19.97/5.24 | Equations (632) can reduce 575 to:
% 19.97/5.24 | (436) ~ (e1 = e0)
% 19.97/5.24 |
% 19.97/5.24 | Simplifying 436 yields:
% 19.97/5.24 | (144) ~ (e1 = e0)
% 19.97/5.24 |
% 19.97/5.24 +-Applying beta-rule and splitting (894), into two cases.
% 19.97/5.24 |-Branch one:
% 19.97/5.24 | (903) all_0_48_48 = e0
% 19.97/5.24 |
% 19.97/5.24 | Combining equations (1458,903) yields a new equation:
% 19.97/5.24 | (353) e2 = e0
% 19.97/5.24 |
% 19.97/5.24 | Simplifying 353 yields:
% 19.97/5.24 | (354) e2 = e0
% 19.97/5.24 |
% 19.97/5.24 | Equations (354) can reduce 58 to:
% 19.97/5.24 | (269) $false
% 19.97/5.24 |
% 19.97/5.24 |-The branch is then unsatisfiable
% 19.97/5.24 |-Branch two:
% 19.97/5.24 | (952) ~ (all_0_48_48 = e0)
% 19.97/5.24 | (953) all_0_53_53 = e0 | all_0_58_58 = e0
% 19.97/5.24 |
% 19.97/5.24 +-Applying beta-rule and splitting (953), into two cases.
% 19.97/5.24 |-Branch one:
% 19.97/5.24 | (857) all_0_53_53 = e0
% 19.97/5.24 |
% 19.97/5.24 | From (857) and (90) follows:
% 19.97/5.24 | (1588) op(e1, e1) = e0
% 19.97/5.24 |
% 19.97/5.24 | Instantiating formula (21) with e1, e1, all_0_37_37, all_0_28_28 and discharging atoms op(e1, e1) = all_0_28_28, op(e1, e1) = all_0_37_37, yields:
% 19.97/5.24 | (1635) all_0_28_28 = all_0_37_37
% 19.97/5.24 |
% 19.97/5.24 | Instantiating formula (21) with e1, e1, e0, all_0_28_28 and discharging atoms op(e1, e1) = all_0_28_28, op(e1, e1) = e0, yields:
% 19.97/5.24 | (943) all_0_28_28 = e0
% 19.97/5.24 |
% 19.97/5.24 | Combining equations (1635,943) yields a new equation:
% 19.97/5.24 | (2378) all_0_37_37 = e0
% 19.97/5.24 |
% 19.97/5.24 | Simplifying 2378 yields:
% 19.97/5.24 | (921) all_0_37_37 = e0
% 19.97/5.24 |
% 19.97/5.24 | Equations (921) can reduce 1655 to:
% 19.97/5.24 | (269) $false
% 19.97/5.24 |
% 19.97/5.24 |-The branch is then unsatisfiable
% 19.97/5.24 |-Branch two:
% 19.97/5.24 | (765) ~ (all_0_53_53 = e0)
% 19.97/5.24 | (493) all_0_58_58 = e0
% 19.97/5.24 |
% 19.97/5.24 | Combining equations (489,493) yields a new equation:
% 19.97/5.24 | (578) e1 = e0
% 19.97/5.24 |
% 19.97/5.24 | Simplifying 578 yields:
% 19.97/5.24 | (579) e1 = e0
% 19.97/5.24 |
% 19.97/5.24 | Equations (579) can reduce 144 to:
% 19.97/5.24 | (269) $false
% 19.97/5.24 |
% 19.97/5.24 |-The branch is then unsatisfiable
% 19.97/5.24 |-Branch two:
% 19.97/5.24 | (401) ~ (all_0_56_56 = e0)
% 19.97/5.24 | (2052) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 19.97/5.24 |
% 19.97/5.24 +-Applying beta-rule and splitting (162), into two cases.
% 19.97/5.24 |-Branch one:
% 19.97/5.24 | (559) all_0_43_43 = e3
% 19.97/5.24 |
% 19.97/5.24 | Equations (559) can reduce 459 to:
% 19.97/5.24 | (72) ~ (e3 = e0)
% 19.97/5.24 |
% 19.97/5.24 +-Applying beta-rule and splitting (2052), into two cases.
% 19.97/5.24 |-Branch one:
% 19.97/5.24 | (400) all_0_57_57 = e0
% 19.97/5.24 |
% 19.97/5.24 | Combining equations (400,867) yields a new equation:
% 19.97/5.24 | (354) e2 = e0
% 19.97/5.24 |
% 19.97/5.24 | Equations (354) can reduce 58 to:
% 19.97/5.24 | (269) $false
% 19.97/5.24 |
% 19.97/5.24 |-The branch is then unsatisfiable
% 19.97/5.24 |-Branch two:
% 19.97/5.24 | (967) ~ (all_0_57_57 = e0)
% 19.97/5.24 | (2059) all_0_58_58 = e0 | all_0_59_59 = e0
% 19.97/5.24 |
% 19.97/5.24 +-Applying beta-rule and splitting (2059), into two cases.
% 19.97/5.24 |-Branch one:
% 19.97/5.24 | (493) all_0_58_58 = e0
% 19.97/5.24 |
% 19.97/5.24 | Combining equations (493,489) yields a new equation:
% 19.97/5.24 | (579) e1 = e0
% 19.97/5.24 |
% 19.97/5.24 | Equations (579) can reduce 144 to:
% 19.97/5.24 | (269) $false
% 19.97/5.24 |
% 19.97/5.24 |-The branch is then unsatisfiable
% 19.97/5.24 |-Branch two:
% 19.97/5.24 | (403) ~ (all_0_58_58 = e0)
% 19.97/5.24 | (2064) all_0_59_59 = e0
% 19.97/5.24 |
% 19.97/5.24 | Combining equations (1070,2064) yields a new equation:
% 19.97/5.24 | (781) e3 = e0
% 19.97/5.24 |
% 19.97/5.24 | Simplifying 781 yields:
% 19.97/5.24 | (560) e3 = e0
% 19.97/5.24 |
% 19.97/5.24 | Equations (560) can reduce 72 to:
% 19.97/5.24 | (269) $false
% 19.97/5.24 |
% 19.97/5.24 |-The branch is then unsatisfiable
% 19.97/5.24 |-Branch two:
% 19.97/5.24 | (562) ~ (all_0_43_43 = e3)
% 19.97/5.24 | (1193) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 19.97/5.24 |
% 19.97/5.24 +-Applying beta-rule and splitting (1193), into two cases.
% 19.97/5.24 |-Branch one:
% 19.97/5.24 | (422) all_0_44_44 = e3
% 19.97/5.24 |
% 19.97/5.24 | Combining equations (352,422) yields a new equation:
% 19.97/5.24 | (560) e3 = e0
% 19.97/5.24 |
% 19.97/5.24 | Equations (560) can reduce 72 to:
% 19.97/5.24 | (269) $false
% 19.97/5.24 |
% 19.97/5.24 |-The branch is then unsatisfiable
% 19.97/5.24 |-Branch two:
% 19.97/5.24 | (425) ~ (all_0_44_44 = e3)
% 19.97/5.24 | (1203) all_0_45_45 = e3 | all_0_46_46 = e3
% 19.97/5.24 |
% 19.97/5.24 +-Applying beta-rule and splitting (1203), into two cases.
% 19.97/5.24 |-Branch one:
% 19.97/5.24 | (1087) all_0_45_45 = e3
% 19.97/5.24 |
% 19.97/5.24 | Equations (1087) can reduce 689 to:
% 19.97/5.24 | (269) $false
% 19.97/5.24 |
% 19.97/5.24 |-The branch is then unsatisfiable
% 19.97/5.24 |-Branch two:
% 19.97/5.24 | (689) ~ (all_0_45_45 = e3)
% 19.97/5.24 | (462) all_0_46_46 = e3
% 19.97/5.24 |
% 19.97/5.24 | Combining equations (364,462) yields a new equation:
% 19.97/5.24 | (423) e3 = e2
% 19.97/5.24 |
% 19.97/5.24 | Equations (423) can reduce 224 to:
% 19.97/5.24 | (269) $false
% 19.97/5.24 |
% 19.97/5.24 |-The branch is then unsatisfiable
% 19.97/5.24 |-Branch two:
% 19.97/5.24 | (609) ~ (all_0_41_41 = e3)
% 19.97/5.24 | (740) all_0_41_41 = e4
% 19.97/5.24 |
% 19.97/5.24 | Equations (740) can reduce 308 to:
% 19.97/5.24 | (269) $false
% 19.97/5.24 |
% 19.97/5.24 |-The branch is then unsatisfiable
% 19.97/5.24 |-Branch two:
% 19.97/5.24 | (482) ~ (all_0_58_58 = e1)
% 19.97/5.24 | (614) all_0_59_59 = e1
% 19.97/5.24 |
% 19.97/5.24 | Combining equations (614,1070) yields a new equation:
% 19.97/5.24 | (418) e3 = e1
% 19.97/5.24 |
% 19.97/5.24 | Equations (418) can reduce 146 to:
% 19.97/5.24 | (269) $false
% 19.97/5.24 |
% 19.97/5.24 |-The branch is then unsatisfiable
% 19.97/5.24 |-Branch two:
% 19.97/5.24 | (637) ~ (all_0_52_52 = e3)
% 19.97/5.24 | (638) all_0_57_57 = e3
% 19.97/5.24 |
% 19.97/5.24 | Combining equations (638,867) yields a new equation:
% 19.97/5.24 | (606) e3 = e2
% 19.97/5.24 |
% 19.97/5.24 | Simplifying 606 yields:
% 19.97/5.24 | (423) e3 = e2
% 19.97/5.24 |
% 19.97/5.24 | Equations (423) can reduce 224 to:
% 19.97/5.24 | (269) $false
% 19.97/5.24 |
% 19.97/5.24 |-The branch is then unsatisfiable
% 19.97/5.24 |-Branch two:
% 19.97/5.24 | (983) ~ (all_0_40_40 = e1)
% 19.97/5.24 | (984) all_0_52_52 = e1 | all_0_57_57 = e1
% 19.97/5.24 |
% 19.97/5.24 +-Applying beta-rule and splitting (39), into two cases.
% 19.97/5.24 |-Branch one:
% 19.97/5.24 | (464) all_0_39_39 = e1
% 19.97/5.24 |
% 19.97/5.24 | Combining equations (348,464) yields a new equation:
% 19.97/5.24 | (470) e2 = e1
% 19.97/5.24 |
% 19.97/5.24 | Simplifying 470 yields:
% 19.97/5.24 | (471) e2 = e1
% 19.97/5.24 |
% 19.97/5.24 | Equations (471) can reduce 148 to:
% 19.97/5.24 | (269) $false
% 19.97/5.24 |
% 19.97/5.24 |-The branch is then unsatisfiable
% 19.97/5.24 |-Branch two:
% 19.97/5.24 | (467) ~ (all_0_39_39 = e1)
% 19.97/5.24 | (2100) all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1
% 19.97/5.24 |
% 19.97/5.24 | Equations (348) can reduce 467 to:
% 19.97/5.24 | (148) ~ (e2 = e1)
% 19.97/5.24 |
% 19.97/5.24 +-Applying beta-rule and splitting (984), into two cases.
% 19.97/5.24 |-Branch one:
% 19.97/5.24 | (820) all_0_52_52 = e1
% 19.97/5.24 |
% 19.97/5.24 | Equations (820) can reduce 71 to:
% 19.97/5.24 | (822) ~ (all_0_53_53 = e1)
% 19.97/5.24 |
% 19.97/5.24 | Simplifying 822 yields:
% 19.97/5.24 | (823) ~ (all_0_53_53 = e1)
% 19.97/5.24 |
% 19.97/5.24 | Equations (820) can reduce 62 to:
% 19.97/5.24 | (1237) ~ (all_0_54_54 = e1)
% 19.97/5.24 |
% 19.97/5.24 | Simplifying 1237 yields:
% 19.97/5.24 | (1238) ~ (all_0_54_54 = e1)
% 19.97/5.24 |
% 19.97/5.24 | Equations (820) can reduce 317 to:
% 19.97/5.24 | (144) ~ (e1 = e0)
% 19.97/5.24 |
% 19.97/5.24 | From (820) and (2268) follows:
% 19.97/5.24 | (2443) op(e2, e1) = e1
% 19.97/5.24 |
% 19.97/5.24 +-Applying beta-rule and splitting (303), into two cases.
% 19.97/5.24 |-Branch one:
% 19.97/5.24 | (765) ~ (all_0_53_53 = e0)
% 19.97/5.24 |
% 19.97/5.24 +-Applying beta-rule and splitting (63), into two cases.
% 19.97/5.24 |-Branch one:
% 19.97/5.24 | (629) all_0_51_51 = e0
% 19.97/5.24 |
% 19.97/5.24 | Equations (629) can reduce 16 to:
% 19.97/5.24 | (1556) ~ (all_0_56_56 = e0)
% 19.97/5.24 |
% 19.97/5.24 | Simplifying 1556 yields:
% 19.97/5.24 | (401) ~ (all_0_56_56 = e0)
% 19.97/5.24 |
% 19.97/5.24 | Equations (629) can reduce 255 to:
% 19.97/5.24 | (406) ~ (e2 = e0)
% 19.97/5.24 |
% 19.97/5.24 | Simplifying 406 yields:
% 19.97/5.24 | (58) ~ (e2 = e0)
% 19.97/5.24 |
% 19.97/5.24 +-Applying beta-rule and splitting (20), into two cases.
% 19.97/5.24 |-Branch one:
% 19.97/5.24 | (1575) all_0_56_56 = e2
% 19.97/5.24 |
% 19.97/5.24 | Equations (1575) can reduce 377 to:
% 19.97/5.24 | (269) $false
% 19.97/5.24 |
% 19.97/5.24 |-The branch is then unsatisfiable
% 19.97/5.24 |-Branch two:
% 19.97/5.24 | (377) ~ (all_0_56_56 = e2)
% 19.97/5.24 | (1578) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1 | all_0_56_56 = e0
% 19.97/5.24 |
% 19.97/5.24 +-Applying beta-rule and splitting (1578), into two cases.
% 19.97/5.24 |-Branch one:
% 19.97/5.24 | (480) all_0_56_56 = e1
% 19.97/5.24 |
% 19.97/5.24 | Equations (480) can reduce 575 to:
% 19.97/5.24 | (269) $false
% 19.97/5.24 |
% 19.97/5.24 |-The branch is then unsatisfiable
% 19.97/5.24 |-Branch two:
% 19.97/5.24 | (575) ~ (all_0_56_56 = e1)
% 19.97/5.24 | (1619) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e0
% 19.97/5.24 |
% 19.97/5.24 +-Applying beta-rule and splitting (211), into two cases.
% 19.97/5.24 |-Branch one:
% 19.97/5.24 | (632) all_0_56_56 = e0
% 19.97/5.24 |
% 19.97/5.24 | Equations (632) can reduce 401 to:
% 19.97/5.24 | (269) $false
% 19.97/5.24 |
% 19.97/5.24 |-The branch is then unsatisfiable
% 19.97/5.24 |-Branch two:
% 19.97/5.24 | (401) ~ (all_0_56_56 = e0)
% 19.97/5.24 | (2052) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 19.97/5.24 |
% 19.97/5.24 +-Applying beta-rule and splitting (94), into two cases.
% 19.97/5.24 |-Branch one:
% 19.97/5.24 | (386) all_0_41_41 = e2
% 19.97/5.24 |
% 19.97/5.24 | Equations (386) can reduce 650 to:
% 19.97/5.24 | (269) $false
% 19.97/5.24 |
% 19.97/5.24 |-The branch is then unsatisfiable
% 19.97/5.24 |-Branch two:
% 19.97/5.24 | (650) ~ (all_0_41_41 = e2)
% 19.97/5.24 | (1903) all_0_41_41 = e4 | all_0_41_41 = e3 | all_0_41_41 = e1
% 19.97/5.24 |
% 19.97/5.24 +-Applying beta-rule and splitting (1619), into two cases.
% 19.97/5.24 |-Branch one:
% 19.97/5.24 | (632) all_0_56_56 = e0
% 19.97/5.24 |
% 19.97/5.24 | Equations (632) can reduce 401 to:
% 19.97/5.24 | (269) $false
% 19.97/5.24 |
% 19.97/5.24 |-The branch is then unsatisfiable
% 19.97/5.24 |-Branch two:
% 19.97/5.24 | (401) ~ (all_0_56_56 = e0)
% 19.97/5.24 | (1630) all_0_56_56 = e4 | all_0_56_56 = e3
% 19.97/5.24 |
% 19.97/5.24 +-Applying beta-rule and splitting (1630), into two cases.
% 19.97/5.24 |-Branch one:
% 19.97/5.24 | (567) all_0_56_56 = e3
% 19.97/5.24 |
% 19.97/5.24 | Equations (567) can reduce 130 to:
% 19.97/5.24 | (2131) ~ (all_0_59_59 = e3)
% 19.97/5.24 |
% 19.97/5.25 | Simplifying 2131 yields:
% 19.97/5.25 | (2132) ~ (all_0_59_59 = e3)
% 19.97/5.25 |
% 19.97/5.25 +-Applying beta-rule and splitting (2052), into two cases.
% 19.97/5.25 |-Branch one:
% 19.97/5.25 | (400) all_0_57_57 = e0
% 19.97/5.25 |
% 19.97/5.25 | Combining equations (400,867) yields a new equation:
% 19.97/5.25 | (354) e2 = e0
% 19.97/5.25 |
% 19.97/5.25 | Equations (354) can reduce 58 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (967) ~ (all_0_57_57 = e0)
% 19.97/5.25 | (2059) all_0_58_58 = e0 | all_0_59_59 = e0
% 19.97/5.25 |
% 19.97/5.25 +-Applying beta-rule and splitting (2059), into two cases.
% 19.97/5.25 |-Branch one:
% 19.97/5.25 | (493) all_0_58_58 = e0
% 19.97/5.25 |
% 19.97/5.25 | Equations (493) can reduce 198 to:
% 19.97/5.25 | (1479) ~ (all_0_59_59 = e0)
% 19.97/5.25 |
% 19.97/5.25 | Simplifying 1479 yields:
% 19.97/5.25 | (1480) ~ (all_0_59_59 = e0)
% 19.97/5.25 |
% 19.97/5.25 +-Applying beta-rule and splitting (212), into two cases.
% 19.97/5.25 |-Branch one:
% 19.97/5.25 | (375) all_0_59_59 = e2
% 19.97/5.25 |
% 19.97/5.25 | Equations (375) can reduce 1843 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (1843) ~ (all_0_59_59 = e2)
% 19.97/5.25 | (2151) all_0_59_59 = e4 | all_0_59_59 = e3 | all_0_59_59 = e1 | all_0_59_59 = e0
% 19.97/5.25 |
% 19.97/5.25 +-Applying beta-rule and splitting (2151), into two cases.
% 19.97/5.25 |-Branch one:
% 19.97/5.25 | (614) all_0_59_59 = e1
% 19.97/5.25 |
% 19.97/5.25 | Equations (614) can reduce 1843 to:
% 19.97/5.25 | (414) ~ (e2 = e1)
% 19.97/5.25 |
% 19.97/5.25 | Simplifying 414 yields:
% 19.97/5.25 | (148) ~ (e2 = e1)
% 19.97/5.25 |
% 19.97/5.25 | Equations (614) can reduce 1480 to:
% 19.97/5.25 | (144) ~ (e1 = e0)
% 19.97/5.25 |
% 19.97/5.25 +-Applying beta-rule and splitting (15), into two cases.
% 19.97/5.25 |-Branch one:
% 19.97/5.25 | (1312) all_0_41_41 = e1
% 19.97/5.25 |
% 19.97/5.25 | Equations (1312) can reduce 650 to:
% 19.97/5.25 | (414) ~ (e2 = e1)
% 19.97/5.25 |
% 19.97/5.25 | Simplifying 414 yields:
% 19.97/5.25 | (148) ~ (e2 = e1)
% 19.97/5.25 |
% 19.97/5.25 | Instantiating formula (21) with e2, e1, e1, e2 and discharging atoms op(e2, e1) = e2, op(e2, e1) = e1, yields:
% 19.97/5.25 | (471) e2 = e1
% 19.97/5.25 |
% 19.97/5.25 | Equations (471) can reduce 148 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (1315) ~ (all_0_41_41 = e1)
% 19.97/5.25 | (1316) all_0_48_48 = e1 | all_0_53_53 = e1 | all_0_58_58 = e1
% 19.97/5.25 |
% 19.97/5.25 +-Applying beta-rule and splitting (1316), into two cases.
% 19.97/5.25 |-Branch one:
% 19.97/5.25 | (593) all_0_48_48 = e1
% 19.97/5.25 |
% 19.97/5.25 | Combining equations (1458,593) yields a new equation:
% 19.97/5.25 | (470) e2 = e1
% 19.97/5.25 |
% 19.97/5.25 | Simplifying 470 yields:
% 19.97/5.25 | (471) e2 = e1
% 19.97/5.25 |
% 19.97/5.25 | Equations (471) can reduce 148 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (584) ~ (all_0_48_48 = e1)
% 19.97/5.25 | (1615) all_0_53_53 = e1 | all_0_58_58 = e1
% 19.97/5.25 |
% 19.97/5.25 +-Applying beta-rule and splitting (1615), into two cases.
% 19.97/5.25 |-Branch one:
% 19.97/5.25 | (853) all_0_53_53 = e1
% 19.97/5.25 |
% 19.97/5.25 | Equations (853) can reduce 823 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (823) ~ (all_0_53_53 = e1)
% 19.97/5.25 | (489) all_0_58_58 = e1
% 19.97/5.25 |
% 19.97/5.25 | Combining equations (489,493) yields a new equation:
% 19.97/5.25 | (578) e1 = e0
% 19.97/5.25 |
% 19.97/5.25 | Simplifying 578 yields:
% 19.97/5.25 | (579) e1 = e0
% 19.97/5.25 |
% 19.97/5.25 | Equations (579) can reduce 144 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (2222) ~ (all_0_59_59 = e1)
% 19.97/5.25 | (2223) all_0_59_59 = e4 | all_0_59_59 = e3 | all_0_59_59 = e0
% 19.97/5.25 |
% 19.97/5.25 +-Applying beta-rule and splitting (2223), into two cases.
% 19.97/5.25 |-Branch one:
% 19.97/5.25 | (2064) all_0_59_59 = e0
% 19.97/5.25 |
% 19.97/5.25 | Equations (2064) can reduce 1480 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (1480) ~ (all_0_59_59 = e0)
% 19.97/5.25 | (2227) all_0_59_59 = e4 | all_0_59_59 = e3
% 19.97/5.25 |
% 19.97/5.25 +-Applying beta-rule and splitting (2227), into two cases.
% 19.97/5.25 |-Branch one:
% 19.97/5.25 | (1070) all_0_59_59 = e3
% 19.97/5.25 |
% 19.97/5.25 | Equations (1070) can reduce 2132 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (2132) ~ (all_0_59_59 = e3)
% 19.97/5.25 | (2231) all_0_59_59 = e4
% 19.97/5.25 |
% 19.97/5.25 | Equations (2231) can reduce 279 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (403) ~ (all_0_58_58 = e0)
% 19.97/5.25 | (2064) all_0_59_59 = e0
% 19.97/5.25 |
% 19.97/5.25 | Equations (2064) can reduce 1480 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (1183) ~ (all_0_56_56 = e3)
% 19.97/5.25 | (1658) all_0_56_56 = e4
% 19.97/5.25 |
% 19.97/5.25 | Equations (1658) can reduce 273 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (432) ~ (all_0_51_51 = e0)
% 19.97/5.25 | (1231) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 19.97/5.25 |
% 19.97/5.25 +-Applying beta-rule and splitting (1231), into two cases.
% 19.97/5.25 |-Branch one:
% 19.97/5.25 | (397) all_0_52_52 = e0
% 19.97/5.25 |
% 19.97/5.25 | Combining equations (820,397) yields a new equation:
% 19.97/5.25 | (578) e1 = e0
% 19.97/5.25 |
% 19.97/5.25 | Simplifying 578 yields:
% 19.97/5.25 | (579) e1 = e0
% 19.97/5.25 |
% 19.97/5.25 | Equations (579) can reduce 144 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (317) ~ (all_0_52_52 = e0)
% 19.97/5.25 | (1245) all_0_53_53 = e0 | all_0_54_54 = e0
% 19.97/5.25 |
% 19.97/5.25 +-Applying beta-rule and splitting (1245), into two cases.
% 19.97/5.25 |-Branch one:
% 19.97/5.25 | (857) all_0_53_53 = e0
% 19.97/5.25 |
% 19.97/5.25 | Equations (857) can reduce 765 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (765) ~ (all_0_53_53 = e0)
% 19.97/5.25 | (1286) all_0_54_54 = e0
% 19.97/5.25 |
% 19.97/5.25 | Equations (1286) can reduce 1478 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (857) all_0_53_53 = e0
% 19.97/5.25 | (1592) all_0_54_54 = e1
% 19.97/5.25 |
% 19.97/5.25 | Equations (1592) can reduce 1238 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (978) ~ (all_0_52_52 = e1)
% 19.97/5.25 | (577) all_0_57_57 = e1
% 19.97/5.25 |
% 19.97/5.25 | Combining equations (577,867) yields a new equation:
% 19.97/5.25 | (471) e2 = e1
% 19.97/5.25 |
% 19.97/5.25 | Equations (471) can reduce 148 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (523) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 19.97/5.25 |
% 19.97/5.25 | Applying alpha-rule on (523) yields:
% 19.97/5.25 | (524) all_0_19_19 = e0
% 19.97/5.25 | (525) ~ (all_0_20_20 = e2)
% 19.97/5.25 |
% 19.97/5.25 | Combining equations (1849,524) yields a new equation:
% 19.97/5.25 | (751) e4 = e0
% 19.97/5.25 |
% 19.97/5.25 | Simplifying 751 yields:
% 19.97/5.25 | (439) e4 = e0
% 19.97/5.25 |
% 19.97/5.25 | Equations (439) can reduce 11 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (356) ~ (all_0_44_44 = e0)
% 19.97/5.25 | (357) all_0_52_52 = e0 | all_0_57_57 = e0
% 19.97/5.25 |
% 19.97/5.25 +-Applying beta-rule and splitting (357), into two cases.
% 19.97/5.25 |-Branch one:
% 19.97/5.25 | (397) all_0_52_52 = e0
% 19.97/5.25 |
% 19.97/5.25 | Equations (397) can reduce 317 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (317) ~ (all_0_52_52 = e0)
% 19.97/5.25 | (400) all_0_57_57 = e0
% 19.97/5.25 |
% 19.97/5.25 | Combining equations (867,400) yields a new equation:
% 19.97/5.25 | (353) e2 = e0
% 19.97/5.25 |
% 19.97/5.25 | Simplifying 353 yields:
% 19.97/5.25 | (354) e2 = e0
% 19.97/5.25 |
% 19.97/5.25 | Equations (354) can reduce 58 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (320) ~ (all_0_39_39 = e2)
% 19.97/5.25 | (351) all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 19.97/5.25 |
% 19.97/5.25 +-Applying beta-rule and splitting (47), into two cases.
% 19.97/5.25 |-Branch one:
% 19.97/5.25 | (348) all_0_39_39 = e2
% 19.97/5.25 |
% 19.97/5.25 | Equations (348) can reduce 320 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (320) ~ (all_0_39_39 = e2)
% 19.97/5.25 | (709) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 19.97/5.25 |
% 19.97/5.25 +-Applying beta-rule and splitting (709), into two cases.
% 19.97/5.25 |-Branch one:
% 19.97/5.25 | (464) all_0_39_39 = e1
% 19.97/5.25 |
% 19.97/5.25 | Equations (464) can reduce 467 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (467) ~ (all_0_39_39 = e1)
% 19.97/5.25 | (1075) all_0_39_39 = e4 | all_0_39_39 = e3
% 19.97/5.25 |
% 19.97/5.25 +-Applying beta-rule and splitting (1109), into two cases.
% 19.97/5.25 |-Branch one:
% 19.97/5.25 | (816) all_0_52_52 = e2
% 19.97/5.25 |
% 19.97/5.25 | Equations (816) can reduce 257 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (257) ~ (all_0_52_52 = e2)
% 19.97/5.25 | (867) all_0_57_57 = e2
% 19.97/5.25 |
% 19.97/5.25 | Equations (867) can reduce 168 to:
% 19.97/5.25 | (342) ~ (all_0_40_40 = e2)
% 19.97/5.25 |
% 19.97/5.25 | Equations (867) can reduce 173 to:
% 19.97/5.25 | (326) ~ (e4 = e2)
% 19.97/5.25 |
% 19.97/5.25 | Simplifying 326 yields:
% 19.97/5.25 | (230) ~ (e4 = e2)
% 19.97/5.25 |
% 19.97/5.25 +-Applying beta-rule and splitting (1075), into two cases.
% 19.97/5.25 |-Branch one:
% 19.97/5.25 | (443) all_0_39_39 = e3
% 19.97/5.25 |
% 19.97/5.25 | Equations (443) can reduce 18 to:
% 19.97/5.25 | (2579) ~ (all_0_40_40 = e3)
% 19.97/5.25 |
% 19.97/5.25 | Simplifying 2579 yields:
% 19.97/5.25 | (420) ~ (all_0_40_40 = e3)
% 19.97/5.25 |
% 19.97/5.25 +-Applying beta-rule and splitting (17), into two cases.
% 19.97/5.25 |-Branch one:
% 19.97/5.25 | (382) all_0_40_40 = e2
% 19.97/5.25 |
% 19.97/5.25 | Equations (382) can reduce 342 to:
% 19.97/5.25 | (269) $false
% 19.97/5.25 |
% 19.97/5.25 |-The branch is then unsatisfiable
% 19.97/5.25 |-Branch two:
% 19.97/5.25 | (342) ~ (all_0_40_40 = e2)
% 19.97/5.25 | (1093) all_0_40_40 = e3 | all_0_40_40 = e1
% 19.97/5.25 |
% 19.97/5.25 +-Applying beta-rule and splitting (1093), into two cases.
% 19.97/5.25 |-Branch one:
% 19.97/5.25 | (413) all_0_40_40 = e1
% 19.97/5.25 |
% 19.97/5.25 | Equations (413) can reduce 342 to:
% 19.97/5.25 | (414) ~ (e2 = e1)
% 19.97/5.25 |
% 19.97/5.25 | Simplifying 414 yields:
% 19.97/5.25 | (148) ~ (e2 = e1)
% 19.97/5.25 |
% 19.97/5.25 +-Applying beta-rule and splitting (351), into two cases.
% 19.97/5.25 |-Branch one:
% 19.97/5.25 | (382) all_0_40_40 = e2
% 19.97/5.25 |
% 19.97/5.25 | Combining equations (413,382) yields a new equation:
% 19.97/5.26 | (471) e2 = e1
% 19.97/5.26 |
% 19.97/5.26 | Equations (471) can reduce 148 to:
% 19.97/5.26 | (269) $false
% 19.97/5.26 |
% 19.97/5.26 |-The branch is then unsatisfiable
% 19.97/5.26 |-Branch two:
% 19.97/5.26 | (342) ~ (all_0_40_40 = e2)
% 19.97/5.26 | (385) all_0_41_41 = e2 | all_0_42_42 = e2
% 19.97/5.26 |
% 19.97/5.26 +-Applying beta-rule and splitting (385), into two cases.
% 19.97/5.26 |-Branch one:
% 19.97/5.26 | (386) all_0_41_41 = e2
% 19.97/5.26 |
% 19.97/5.26 | Equations (386) can reduce 650 to:
% 19.97/5.26 | (269) $false
% 19.97/5.26 |
% 19.97/5.26 |-The branch is then unsatisfiable
% 19.97/5.26 |-Branch two:
% 19.97/5.26 | (650) ~ (all_0_41_41 = e2)
% 19.97/5.26 | (358) all_0_42_42 = e2
% 19.97/5.26 |
% 19.97/5.26 | Combining equations (305,358) yields a new equation:
% 19.97/5.26 | (359) e4 = e2
% 19.97/5.26 |
% 19.97/5.26 | Simplifying 359 yields:
% 19.97/5.26 | (360) e4 = e2
% 19.97/5.26 |
% 19.97/5.26 | Equations (360) can reduce 230 to:
% 19.97/5.26 | (269) $false
% 19.97/5.26 |
% 19.97/5.26 |-The branch is then unsatisfiable
% 19.97/5.26 |-Branch two:
% 19.97/5.26 | (983) ~ (all_0_40_40 = e1)
% 19.97/5.26 | (417) all_0_40_40 = e3
% 19.97/5.26 |
% 19.97/5.26 | Equations (417) can reduce 420 to:
% 19.97/5.26 | (269) $false
% 19.97/5.26 |
% 19.97/5.26 |-The branch is then unsatisfiable
% 19.97/5.26 |-Branch two:
% 19.97/5.26 | (540) ~ (all_0_39_39 = e3)
% 19.97/5.26 | (1079) all_0_39_39 = e4
% 19.97/5.26 |
% 19.97/5.26 | Equations (1079) can reduce 307 to:
% 19.97/5.26 | (269) $false
% 19.97/5.26 |
% 19.97/5.26 |-The branch is then unsatisfiable
% 19.97/5.26 |-Branch two:
% 19.97/5.26 | (1115) ~ (all_0_48_48 = e2)
% 19.97/5.26 | (2607) all_0_48_48 = e1 | all_0_48_48 = e0
% 19.97/5.26 |
% 19.97/5.26 +-Applying beta-rule and splitting (2607), into two cases.
% 19.97/5.26 |-Branch one:
% 19.97/5.26 | (593) all_0_48_48 = e1
% 19.97/5.26 |
% 19.97/5.26 | Equations (593) can reduce 584 to:
% 19.97/5.26 | (269) $false
% 19.97/5.26 |
% 19.97/5.26 |-The branch is then unsatisfiable
% 19.97/5.26 |-Branch two:
% 19.97/5.26 | (584) ~ (all_0_48_48 = e1)
% 19.97/5.26 | (903) all_0_48_48 = e0
% 19.97/5.26 |
% 19.97/5.26 | Equations (903) can reduce 952 to:
% 19.97/5.26 | (269) $false
% 19.97/5.26 |
% 19.97/5.26 |-The branch is then unsatisfiable
% 19.97/5.26 |-Branch two:
% 19.97/5.26 | (903) all_0_48_48 = e0
% 19.97/5.26 | (596) all_0_49_49 = e1
% 19.97/5.26 |
% 19.97/5.26 | Equations (596) can reduce 960 to:
% 19.97/5.26 | (269) $false
% 19.97/5.26 |
% 19.97/5.26 |-The branch is then unsatisfiable
% 19.97/5.26 |-Branch two:
% 19.97/5.26 | (473) ~ (all_0_47_47 = e1)
% 19.97/5.26 | (623) all_0_47_47 = e0
% 19.97/5.26 |
% 19.97/5.26 | Equations (623) can reduce 297 to:
% 19.97/5.26 | (269) $false
% 19.97/5.26 |
% 19.97/5.26 |-The branch is then unsatisfiable
% 19.97/5.26 |-Branch two:
% 19.97/5.26 | (397) all_0_52_52 = e0
% 19.97/5.26 | (372) all_0_54_54 = e2
% 19.97/5.26 |
% 19.97/5.26 | Equations (372) can reduce 261 to:
% 19.97/5.26 | (269) $false
% 19.97/5.26 |
% 19.97/5.26 |-The branch is then unsatisfiable
% 19.97/5.26 |-Branch two:
% 19.97/5.26 | (2622) all_0_45_45 = e4 & ~ (all_0_42_42 = e1) & ~ (all_0_47_47 = e1) & ~ (unit = e1) & ( ~ (all_0_39_39 = e1) | all_0_41_41 = e3) & ( ~ (all_0_40_40 = e1) | all_0_41_41 = e2) & ( ~ (all_0_49_49 = e1) | all_0_48_48 = e0) & ( ~ (all_0_51_51 = e1) | all_0_53_53 = e3) & ( ~ (all_0_52_52 = e1) | all_0_53_53 = e2) & ( ~ (all_0_54_54 = e1) | all_0_53_53 = e0) & ( ~ (all_0_56_56 = e1) | all_0_58_58 = e3) & ( ~ (all_0_57_57 = e1) | all_0_58_58 = e2) & ( ~ (all_0_59_59 = e1) | all_0_58_58 = e0)
% 19.97/5.26 |
% 19.97/5.26 | Applying alpha-rule on (2622) yields:
% 19.97/5.26 | (2623) ~ (all_0_52_52 = e1) | all_0_53_53 = e2
% 19.97/5.26 | (473) ~ (all_0_47_47 = e1)
% 19.97/5.26 | (2625) ~ (all_0_51_51 = e1) | all_0_53_53 = e3
% 19.97/5.26 | (2626) ~ (all_0_40_40 = e1) | all_0_41_41 = e2
% 19.97/5.26 | (2627) ~ (all_0_56_56 = e1) | all_0_58_58 = e3
% 19.97/5.26 | (2628) ~ (all_0_49_49 = e1) | all_0_48_48 = e0
% 19.97/5.26 | (2629) ~ (all_0_59_59 = e1) | all_0_58_58 = e0
% 19.97/5.26 | (2630) ~ (all_0_54_54 = e1) | all_0_53_53 = e0
% 19.97/5.26 | (2631) ~ (unit = e1)
% 19.97/5.26 | (836) ~ (all_0_42_42 = e1)
% 19.97/5.26 | (2633) ~ (all_0_39_39 = e1) | all_0_41_41 = e3
% 19.97/5.26 | (2634) ~ (all_0_57_57 = e1) | all_0_58_58 = e2
% 19.97/5.26 | (444) all_0_45_45 = e4
% 19.97/5.26 |
% 19.97/5.26 | Equations (444) can reduce 122 to:
% 19.97/5.26 | (308) ~ (all_0_41_41 = e4)
% 19.97/5.26 |
% 19.97/5.26 | Equations (444) can reduce 186 to:
% 19.97/5.26 | (441) ~ (all_0_43_43 = e4)
% 19.97/5.26 |
% 19.97/5.26 | Equations (444) can reduce 117 to:
% 19.97/5.26 | (190) ~ (all_0_44_44 = e4)
% 19.97/5.26 |
% 19.97/5.26 | Equations (444) can reduce 201 to:
% 19.97/5.26 | (309) ~ (all_0_46_46 = e4)
% 19.97/5.26 |
% 19.97/5.26 | Simplifying 309 yields:
% 19.97/5.26 | (310) ~ (all_0_46_46 = e4)
% 19.97/5.26 |
% 19.97/5.26 | Equations (444) can reduce 196 to:
% 19.97/5.26 | (445) ~ (all_0_48_48 = e4)
% 19.97/5.26 |
% 19.97/5.26 | Simplifying 445 yields:
% 19.97/5.26 | (33) ~ (all_0_48_48 = e4)
% 19.97/5.26 |
% 19.97/5.26 | Equations (444) can reduce 142 to:
% 19.97/5.26 | (447) ~ (all_0_53_53 = e4)
% 19.97/5.26 |
% 19.97/5.26 | Simplifying 447 yields:
% 19.97/5.26 | (448) ~ (all_0_53_53 = e4)
% 19.97/5.26 |
% 19.97/5.26 | Equations (444) can reduce 68 to:
% 19.97/5.26 | (276) ~ (all_0_58_58 = e4)
% 19.97/5.26 |
% 19.97/5.26 | Simplifying 276 yields:
% 19.97/5.26 | (277) ~ (all_0_58_58 = e4)
% 19.97/5.26 |
% 19.97/5.26 | From (444) and (125) follows:
% 19.97/5.26 | (2647) op(e1, e4) = all_0_23_23
% 19.97/5.26 |
% 19.97/5.26 +-Applying beta-rule and splitting (2623), into two cases.
% 19.97/5.26 |-Branch one:
% 19.97/5.26 | (978) ~ (all_0_52_52 = e1)
% 19.97/5.26 |
% 19.97/5.26 | Instantiating formula (21) with e1, e4, all_0_23_23, e2 and discharging atoms op(e1, e4) = all_0_23_23, op(e1, e4) = e2, yields:
% 19.97/5.26 | (2649) all_0_23_23 = e2
% 19.97/5.26 |
% 19.97/5.26 +-Applying beta-rule and splitting (189), into two cases.
% 19.97/5.26 |-Branch one:
% 19.97/5.26 | (319) all_0_47_47 = e2
% 19.97/5.26 |
% 19.97/5.26 | Equations (319) can reduce 164 to:
% 19.97/5.26 | (320) ~ (all_0_39_39 = e2)
% 19.97/5.26 |
% 19.97/5.26 | Equations (319) can reduce 138 to:
% 19.97/5.26 | (321) ~ (all_0_43_43 = e2)
% 19.97/5.26 |
% 19.97/5.26 | Equations (319) can reduce 145 to:
% 19.97/5.26 | (322) ~ (all_0_49_49 = e2)
% 19.97/5.26 |
% 19.97/5.26 | Simplifying 322 yields:
% 19.97/5.26 | (323) ~ (all_0_49_49 = e2)
% 19.97/5.26 |
% 19.97/5.26 | Equations (319) can reduce 147 to:
% 19.97/5.26 | (2655) ~ (all_0_56_56 = e2)
% 19.97/5.26 |
% 19.97/5.26 | Simplifying 2655 yields:
% 19.97/5.26 | (377) ~ (all_0_56_56 = e2)
% 19.97/5.26 |
% 19.97/5.26 | Equations (319) can reduce 115 to:
% 19.97/5.26 | (328) ~ (e3 = e2)
% 19.97/5.26 |
% 19.97/5.26 | Simplifying 328 yields:
% 19.97/5.26 | (224) ~ (e3 = e2)
% 19.97/5.26 |
% 19.97/5.26 | From (319) and (218) follows:
% 19.97/5.26 | (332) op(e2, e2) = all_0_8_8
% 19.97/5.26 |
% 19.97/5.26 | From (319) and (231) follows:
% 19.97/5.26 | (333) op(e2, e3) = e2
% 19.97/5.26 |
% 19.97/5.26 +-Applying beta-rule and splitting (8), into two cases.
% 19.97/5.26 |-Branch one:
% 19.97/5.26 | (348) all_0_39_39 = e2
% 19.97/5.26 |
% 19.97/5.26 | Equations (348) can reduce 320 to:
% 19.97/5.26 | (269) $false
% 19.97/5.26 |
% 19.97/5.26 |-The branch is then unsatisfiable
% 19.97/5.26 |-Branch two:
% 19.97/5.26 | (320) ~ (all_0_39_39 = e2)
% 19.97/5.26 | (396) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 19.97/5.26 |
% 19.97/5.26 +-Applying beta-rule and splitting (396), into two cases.
% 19.97/5.26 |-Branch one:
% 19.97/5.26 | (409) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 19.97/5.26 |
% 19.97/5.26 +-Applying beta-rule and splitting (409), into two cases.
% 19.97/5.26 |-Branch one:
% 19.97/5.26 | (410) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 19.97/5.26 |
% 19.97/5.26 | Applying alpha-rule on (410) yields:
% 19.97/5.26 | (411) all_0_0_0 = e1
% 19.97/5.26 | (412) ~ (all_0_1_1 = e4)
% 19.97/5.26 |
% 19.97/5.26 | Combining equations (411,286) yields a new equation:
% 19.97/5.26 | (413) all_0_40_40 = e1
% 19.97/5.26 |
% 19.97/5.26 | Equations (287) can reduce 412 to:
% 19.97/5.26 | (152) ~ (all_0_52_52 = e4)
% 19.97/5.26 |
% 19.97/5.26 | Equations (413) can reduce 18 to:
% 19.97/5.26 | (467) ~ (all_0_39_39 = e1)
% 19.97/5.26 |
% 19.97/5.26 | Equations (413) can reduce 207 to:
% 19.97/5.26 | (2672) ~ (all_0_42_42 = e1)
% 19.97/5.26 |
% 19.97/5.26 | Simplifying 2672 yields:
% 19.97/5.26 | (836) ~ (all_0_42_42 = e1)
% 19.97/5.26 |
% 19.97/5.26 | Equations (413) can reduce 35 to:
% 19.97/5.26 | (2674) ~ (all_0_44_44 = e1)
% 19.97/5.26 |
% 19.97/5.26 | Simplifying 2674 yields:
% 19.97/5.26 | (87) ~ (all_0_44_44 = e1)
% 19.97/5.26 |
% 19.97/5.26 | Equations (413) can reduce 187 to:
% 19.97/5.26 | (1157) ~ (all_0_52_52 = e1)
% 19.97/5.26 |
% 19.97/5.26 | Simplifying 1157 yields:
% 19.97/5.26 | (978) ~ (all_0_52_52 = e1)
% 19.97/5.26 |
% 19.97/5.26 | Equations (413) can reduce 168 to:
% 19.97/5.26 | (824) ~ (all_0_57_57 = e1)
% 19.97/5.26 |
% 19.97/5.26 | Simplifying 824 yields:
% 19.97/5.26 | (581) ~ (all_0_57_57 = e1)
% 19.97/5.26 |
% 19.97/5.26 | From (413) and (156) follows:
% 19.97/5.26 | (416) op(e2, e1) = all_0_13_13
% 19.97/5.26 |
% 19.97/5.26 +-Applying beta-rule and splitting (2626), into two cases.
% 19.97/5.26 |-Branch one:
% 19.97/5.26 | (983) ~ (all_0_40_40 = e1)
% 19.97/5.26 |
% 19.97/5.26 | Equations (413) can reduce 983 to:
% 19.97/5.26 | (269) $false
% 19.97/5.26 |
% 19.97/5.26 |-The branch is then unsatisfiable
% 19.97/5.26 |-Branch two:
% 19.97/5.26 | (413) all_0_40_40 = e1
% 19.97/5.26 | (386) all_0_41_41 = e2
% 19.97/5.26 |
% 19.97/5.26 | Equations (386) can reduce 226 to:
% 19.97/5.26 | (320) ~ (all_0_39_39 = e2)
% 19.97/5.26 |
% 19.97/5.26 | Equations (386) can reduce 167 to:
% 19.97/5.26 | (1114) ~ (all_0_48_48 = e2)
% 19.97/5.26 |
% 19.97/5.26 | Simplifying 1114 yields:
% 19.97/5.26 | (1115) ~ (all_0_48_48 = e2)
% 19.97/5.26 |
% 19.97/5.26 | Equations (386) can reduce 106 to:
% 19.97/5.26 | (258) ~ (all_0_53_53 = e2)
% 19.97/5.26 |
% 19.97/5.26 | Simplifying 258 yields:
% 19.97/5.26 | (259) ~ (all_0_53_53 = e2)
% 19.97/5.26 |
% 19.97/5.26 | Equations (386) can reduce 208 to:
% 19.97/5.26 | (391) ~ (all_0_58_58 = e2)
% 19.97/5.26 |
% 19.97/5.26 | Simplifying 391 yields:
% 19.97/5.26 | (392) ~ (all_0_58_58 = e2)
% 19.97/5.26 |
% 19.97/5.26 | Equations (386) can reduce 308 to:
% 19.97/5.26 | (326) ~ (e4 = e2)
% 19.97/5.26 |
% 19.97/5.26 | Simplifying 326 yields:
% 19.97/5.26 | (230) ~ (e4 = e2)
% 19.97/5.26 |
% 19.97/5.26 | Equations (386) can reduce 188 to:
% 19.97/5.26 | (58) ~ (e2 = e0)
% 19.97/5.26 |
% 19.97/5.26 | From (386) and (79) follows:
% 19.97/5.26 | (2695) op(e1, e2) = all_0_21_21
% 19.97/5.26 |
% 19.97/5.26 | Instantiating formula (21) with e2, e2, all_0_8_8, e4 and discharging atoms op(e2, e2) = all_0_8_8, op(e2, e2) = e4, yields:
% 19.97/5.26 | (335) all_0_8_8 = e4
% 19.97/5.26 |
% 19.97/5.26 | Instantiating formula (21) with e2, e1, all_0_13_13, all_0_48_48 and discharging atoms op(e2, e1) = all_0_13_13, op(e2, e1) = all_0_48_48, yields:
% 19.97/5.26 | (502) all_0_13_13 = all_0_48_48
% 19.97/5.26 |
% 19.97/5.26 | Instantiating formula (21) with e1, e2, all_0_21_21, all_0_52_52 and discharging atoms op(e1, e2) = all_0_21_21, op(e1, e2) = all_0_52_52, yields:
% 19.97/5.26 | (2698) all_0_21_21 = all_0_52_52
% 19.97/5.26 |
% 19.97/5.26 | From (335) and (332) follows:
% 19.97/5.26 | (222) op(e2, e2) = e4
% 19.97/5.26 |
% 19.97/5.26 +-Applying beta-rule and splitting (50), into two cases.
% 19.97/5.26 |-Branch one:
% 19.97/5.26 | (337) all_0_49_49 = e2
% 19.97/5.26 |
% 19.97/5.26 | Equations (337) can reduce 323 to:
% 19.97/5.26 | (269) $false
% 19.97/5.26 |
% 19.97/5.26 |-The branch is then unsatisfiable
% 19.97/5.26 |-Branch two:
% 19.97/5.26 | (323) ~ (all_0_49_49 = e2)
% 19.97/5.26 | (340) all_0_49_49 = e1 | all_0_49_49 = e0
% 19.97/5.26 |
% 19.97/5.26 +-Applying beta-rule and splitting (197), into two cases.
% 19.97/5.26 |-Branch one:
% 19.97/5.26 | (1458) all_0_48_48 = e2
% 19.97/5.26 |
% 19.97/5.26 | Equations (1458) can reduce 1115 to:
% 19.97/5.26 | (269) $false
% 19.97/5.26 |
% 19.97/5.26 |-The branch is then unsatisfiable
% 19.97/5.26 |-Branch two:
% 19.97/5.26 | (1115) ~ (all_0_48_48 = e2)
% 19.97/5.26 | (2607) all_0_48_48 = e1 | all_0_48_48 = e0
% 19.97/5.26 |
% 19.97/5.26 +-Applying beta-rule and splitting (225), into two cases.
% 19.97/5.26 |-Branch one:
% 19.97/5.26 | (661) all_0_43_43 = e2
% 19.97/5.26 |
% 19.97/5.26 | Equations (661) can reduce 321 to:
% 19.97/5.26 | (269) $false
% 19.97/5.26 |
% 19.97/5.26 |-The branch is then unsatisfiable
% 19.97/5.26 |-Branch two:
% 19.97/5.26 | (321) ~ (all_0_43_43 = e2)
% 19.97/5.26 | (664) all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2
% 19.97/5.26 |
% 19.97/5.26 +-Applying beta-rule and splitting (149), into two cases.
% 19.97/5.26 |-Branch one:
% 19.97/5.26 | (341) all_0_44_44 = e2
% 19.97/5.26 |
% 19.97/5.26 | Equations (341) can reduce 228 to:
% 19.97/5.26 | (321) ~ (all_0_43_43 = e2)
% 19.97/5.26 |
% 19.97/5.26 | Equations (341) can reduce 121 to:
% 19.97/5.26 | (256) ~ (all_0_52_52 = e2)
% 19.97/5.26 |
% 19.97/5.26 | Simplifying 256 yields:
% 19.97/5.26 | (257) ~ (all_0_52_52 = e2)
% 19.97/5.27 |
% 19.97/5.27 | Equations (341) can reduce 240 to:
% 19.97/5.27 | (2716) ~ (all_0_57_57 = e2)
% 19.97/5.27 |
% 19.97/5.27 | Simplifying 2716 yields:
% 19.97/5.27 | (378) ~ (all_0_57_57 = e2)
% 19.97/5.27 |
% 19.97/5.27 | Equations (341) can reduce 190 to:
% 19.97/5.27 | (326) ~ (e4 = e2)
% 19.97/5.27 |
% 19.97/5.27 | Simplifying 326 yields:
% 19.97/5.27 | (230) ~ (e4 = e2)
% 19.97/5.27 |
% 19.97/5.27 | Equations (341) can reduce 87 to:
% 19.97/5.27 | (148) ~ (e2 = e1)
% 19.97/5.27 |
% 19.97/5.27 | From (341) and (205) follows:
% 19.97/5.27 | (347) op(e2, e2) = all_0_15_15
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (28), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (268) all_0_55_55 = e2
% 19.97/5.27 |
% 19.97/5.27 | Combining equations (268,271) yields a new equation:
% 19.97/5.27 | (360) e4 = e2
% 19.97/5.27 |
% 19.97/5.27 | Equations (360) can reduce 230 to:
% 19.97/5.27 | (269) $false
% 19.97/5.27 |
% 19.97/5.27 |-The branch is then unsatisfiable
% 19.97/5.27 |-Branch two:
% 19.97/5.27 | (263) ~ (all_0_55_55 = e2)
% 19.97/5.27 | (2726) all_0_56_56 = e2 | all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (2726), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (1575) all_0_56_56 = e2
% 19.97/5.27 |
% 19.97/5.27 | Equations (1575) can reduce 377 to:
% 19.97/5.27 | (269) $false
% 19.97/5.27 |
% 19.97/5.27 |-The branch is then unsatisfiable
% 19.97/5.27 |-Branch two:
% 19.97/5.27 | (377) ~ (all_0_56_56 = e2)
% 19.97/5.27 | (2730) all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (2730), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (867) all_0_57_57 = e2
% 19.97/5.27 |
% 19.97/5.27 | Equations (867) can reduce 378 to:
% 19.97/5.27 | (269) $false
% 19.97/5.27 |
% 19.97/5.27 |-The branch is then unsatisfiable
% 19.97/5.27 |-Branch two:
% 19.97/5.27 | (378) ~ (all_0_57_57 = e2)
% 19.97/5.27 | (2734) all_0_58_58 = e2 | all_0_59_59 = e2
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (2734), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (485) all_0_58_58 = e2
% 19.97/5.27 |
% 19.97/5.27 | Equations (485) can reduce 392 to:
% 19.97/5.27 | (269) $false
% 19.97/5.27 |
% 19.97/5.27 |-The branch is then unsatisfiable
% 19.97/5.27 |-Branch two:
% 19.97/5.27 | (392) ~ (all_0_58_58 = e2)
% 19.97/5.27 | (375) all_0_59_59 = e2
% 19.97/5.27 |
% 19.97/5.27 | Equations (375) can reduce 103 to:
% 19.97/5.27 | (362) ~ (all_0_42_42 = e2)
% 19.97/5.27 |
% 19.97/5.27 | Equations (375) can reduce 150 to:
% 19.97/5.27 | (344) ~ (all_0_46_46 = e2)
% 19.97/5.27 |
% 19.97/5.27 | Equations (375) can reduce 81 to:
% 19.97/5.27 | (261) ~ (all_0_54_54 = e2)
% 19.97/5.27 |
% 19.97/5.27 | Equations (375) can reduce 130 to:
% 19.97/5.27 | (377) ~ (all_0_56_56 = e2)
% 19.97/5.27 |
% 19.97/5.27 | Equations (375) can reduce 95 to:
% 19.97/5.27 | (378) ~ (all_0_57_57 = e2)
% 19.97/5.27 |
% 19.97/5.27 | Equations (375) can reduce 198 to:
% 19.97/5.27 | (392) ~ (all_0_58_58 = e2)
% 19.97/5.27 |
% 19.97/5.27 | Equations (375) can reduce 279 to:
% 19.97/5.27 | (326) ~ (e4 = e2)
% 19.97/5.27 |
% 19.97/5.27 | Simplifying 326 yields:
% 19.97/5.27 | (230) ~ (e4 = e2)
% 19.97/5.27 |
% 19.97/5.27 | From (375) and (66) follows:
% 19.97/5.27 | (381) op(e0, e0) = e2
% 19.97/5.27 |
% 19.97/5.27 | Instantiating formula (21) with e2, e2, all_0_15_15, e4 and discharging atoms op(e2, e2) = all_0_15_15, op(e2, e2) = e4, yields:
% 19.97/5.27 | (501) all_0_15_15 = e4
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (133), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (504) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (504), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (505) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (505), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (506) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 19.97/5.27 |
% 19.97/5.27 | Applying alpha-rule on (506) yields:
% 19.97/5.27 | (507) all_0_13_13 = e4
% 19.97/5.27 | (508) ~ (all_0_14_14 = e2)
% 19.97/5.27 |
% 19.97/5.27 | Combining equations (507,502) yields a new equation:
% 19.97/5.27 | (510) all_0_48_48 = e4
% 19.97/5.27 |
% 19.97/5.27 | Equations (510) can reduce 33 to:
% 19.97/5.27 | (269) $false
% 19.97/5.27 |
% 19.97/5.27 |-The branch is then unsatisfiable
% 19.97/5.27 |-Branch two:
% 19.97/5.27 | (512) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 19.97/5.27 |
% 19.97/5.27 | Applying alpha-rule on (512) yields:
% 19.97/5.27 | (513) all_0_15_15 = e3
% 19.97/5.27 | (514) ~ (all_0_16_16 = e2)
% 19.97/5.27 |
% 19.97/5.27 | Combining equations (501,513) yields a new equation:
% 19.97/5.27 | (515) e4 = e3
% 19.97/5.27 |
% 19.97/5.27 | Simplifying 515 yields:
% 19.97/5.27 | (516) e4 = e3
% 19.97/5.27 |
% 19.97/5.27 | Equations (516) can reduce 41 to:
% 19.97/5.27 | (269) $false
% 19.97/5.27 |
% 19.97/5.27 |-The branch is then unsatisfiable
% 19.97/5.27 |-Branch two:
% 19.97/5.27 | (518) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 19.97/5.27 |
% 19.97/5.27 | Applying alpha-rule on (518) yields:
% 19.97/5.27 | (519) all_0_17_17 = e1
% 19.97/5.27 | (520) ~ (all_0_18_18 = e2)
% 19.97/5.27 |
% 19.97/5.27 | From (519) and (69) follows:
% 19.97/5.27 | (2268) op(e2, all_0_52_52) = e1
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (10), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (623) all_0_47_47 = e0
% 19.97/5.27 |
% 19.97/5.27 | Combining equations (623,319) yields a new equation:
% 19.97/5.27 | (354) e2 = e0
% 19.97/5.27 |
% 19.97/5.27 | Equations (354) can reduce 58 to:
% 19.97/5.27 | (269) $false
% 19.97/5.27 |
% 19.97/5.27 |-The branch is then unsatisfiable
% 19.97/5.27 |-Branch two:
% 19.97/5.27 | (297) ~ (all_0_47_47 = e0)
% 19.97/5.27 | (815) all_0_48_48 = e0 | all_0_49_49 = e0
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (192), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (469) all_0_47_47 = e1
% 19.97/5.27 |
% 19.97/5.27 | Combining equations (469,319) yields a new equation:
% 19.97/5.27 | (471) e2 = e1
% 19.97/5.27 |
% 19.97/5.27 | Equations (471) can reduce 148 to:
% 19.97/5.27 | (269) $false
% 19.97/5.27 |
% 19.97/5.27 |-The branch is then unsatisfiable
% 19.97/5.27 |-Branch two:
% 19.97/5.27 | (473) ~ (all_0_47_47 = e1)
% 19.97/5.27 | (592) all_0_48_48 = e1 | all_0_49_49 = e1
% 19.97/5.27 |
% 19.97/5.27 | Equations (319) can reduce 473 to:
% 19.97/5.27 | (148) ~ (e2 = e1)
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (47), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (348) all_0_39_39 = e2
% 19.97/5.27 |
% 19.97/5.27 | Equations (348) can reduce 320 to:
% 19.97/5.27 | (269) $false
% 19.97/5.27 |
% 19.97/5.27 |-The branch is then unsatisfiable
% 19.97/5.27 |-Branch two:
% 19.97/5.27 | (320) ~ (all_0_39_39 = e2)
% 19.97/5.27 | (709) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (116), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (358) all_0_42_42 = e2
% 19.97/5.27 |
% 19.97/5.27 | Equations (358) can reduce 362 to:
% 19.97/5.27 | (269) $false
% 19.97/5.27 |
% 19.97/5.27 |-The branch is then unsatisfiable
% 19.97/5.27 |-Branch two:
% 19.97/5.27 | (362) ~ (all_0_42_42 = e2)
% 19.97/5.27 | (2784) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (32), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (1079) all_0_39_39 = e4
% 19.97/5.27 |
% 19.97/5.27 | Equations (1079) can reduce 157 to:
% 19.97/5.27 | (2786) ~ (all_0_42_42 = e4)
% 19.97/5.27 |
% 19.97/5.27 | Simplifying 2786 yields:
% 19.97/5.27 | (2787) ~ (all_0_42_42 = e4)
% 19.97/5.27 |
% 19.97/5.27 | Equations (1079) can reduce 234 to:
% 19.97/5.27 | (2788) ~ (all_0_43_43 = e4)
% 19.97/5.27 |
% 19.97/5.27 | Simplifying 2788 yields:
% 19.97/5.27 | (441) ~ (all_0_43_43 = e4)
% 19.97/5.27 |
% 19.97/5.27 | Equations (1079) can reduce 126 to:
% 19.97/5.27 | (1208) ~ (all_0_51_51 = e4)
% 19.97/5.27 |
% 19.97/5.27 | Simplifying 1208 yields:
% 19.97/5.27 | (530) ~ (all_0_51_51 = e4)
% 19.97/5.27 |
% 19.97/5.27 | Equations (1079) can reduce 53 to:
% 19.97/5.27 | (272) ~ (all_0_56_56 = e4)
% 19.97/5.27 |
% 19.97/5.27 | Simplifying 272 yields:
% 19.97/5.27 | (273) ~ (all_0_56_56 = e4)
% 19.97/5.27 |
% 19.97/5.27 | Equations (1079) can reduce 320 to:
% 19.97/5.27 | (230) ~ (e4 = e2)
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (2784), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (832) all_0_42_42 = e1
% 19.97/5.27 |
% 19.97/5.27 | Equations (832) can reduce 836 to:
% 19.97/5.27 | (269) $false
% 19.97/5.27 |
% 19.97/5.27 |-The branch is then unsatisfiable
% 19.97/5.27 |-Branch two:
% 19.97/5.27 | (836) ~ (all_0_42_42 = e1)
% 19.97/5.27 | (2798) all_0_42_42 = e4 | all_0_42_42 = e3
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (2798), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (610) all_0_42_42 = e3
% 19.97/5.27 |
% 19.97/5.27 | Equations (610) can reduce 2787 to:
% 19.97/5.27 | (498) ~ (e4 = e3)
% 19.97/5.27 |
% 19.97/5.27 | Simplifying 498 yields:
% 19.97/5.27 | (41) ~ (e4 = e3)
% 19.97/5.27 |
% 19.97/5.27 | Equations (610) can reduce 836 to:
% 19.97/5.27 | (146) ~ (e3 = e1)
% 19.97/5.27 |
% 19.97/5.27 | From (610) and (36) follows:
% 19.97/5.27 | (2803) op(e0, e3) = all_0_30_30
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (199), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (364) all_0_46_46 = e2
% 19.97/5.27 |
% 19.97/5.27 | Equations (364) can reduce 344 to:
% 19.97/5.27 | (269) $false
% 19.97/5.27 |
% 19.97/5.27 |-The branch is then unsatisfiable
% 19.97/5.27 |-Branch two:
% 19.97/5.27 | (344) ~ (all_0_46_46 = e2)
% 19.97/5.27 | (545) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e0
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (162), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (559) all_0_43_43 = e3
% 19.97/5.27 |
% 19.97/5.27 | Equations (559) can reduce 3 to:
% 19.97/5.27 | (1044) ~ (all_0_46_46 = e3)
% 19.97/5.27 |
% 19.97/5.27 | Simplifying 1044 yields:
% 19.97/5.27 | (618) ~ (all_0_46_46 = e3)
% 19.97/5.27 |
% 19.97/5.27 | Equations (559) can reduce 321 to:
% 19.97/5.27 | (224) ~ (e3 = e2)
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (545), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (546) all_0_46_46 = e0
% 19.97/5.27 |
% 19.97/5.27 | Equations (546) can reduce 166 to:
% 19.97/5.27 | (806) ~ (all_0_49_49 = e0)
% 19.97/5.27 |
% 19.97/5.27 | Simplifying 806 yields:
% 19.97/5.27 | (807) ~ (all_0_49_49 = e0)
% 19.97/5.27 |
% 19.97/5.27 | From (546) and (181) follows:
% 19.97/5.27 | (2815) op(e0, e0) = all_0_32_32
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (153), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (453) all_0_50_50 = e4
% 19.97/5.27 |
% 19.97/5.27 | Combining equations (453,253) yields a new equation:
% 19.97/5.27 | (359) e4 = e2
% 19.97/5.27 |
% 19.97/5.27 | Simplifying 359 yields:
% 19.97/5.27 | (360) e4 = e2
% 19.97/5.27 |
% 19.97/5.27 | Equations (360) can reduce 230 to:
% 19.97/5.27 | (269) $false
% 19.97/5.27 |
% 19.97/5.27 |-The branch is then unsatisfiable
% 19.97/5.27 |-Branch two:
% 19.97/5.27 | (456) ~ (all_0_50_50 = e4)
% 19.97/5.27 | (457) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (457), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (458) all_0_51_51 = e4
% 19.97/5.27 |
% 19.97/5.27 | Equations (458) can reduce 530 to:
% 19.97/5.27 | (269) $false
% 19.97/5.27 |
% 19.97/5.27 |-The branch is then unsatisfiable
% 19.97/5.27 |-Branch two:
% 19.97/5.27 | (530) ~ (all_0_51_51 = e4)
% 19.97/5.27 | (531) all_0_53_53 = e4 | all_0_54_54 = e4
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (340), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (596) all_0_49_49 = e1
% 19.97/5.27 |
% 19.97/5.27 | Equations (596) can reduce 217 to:
% 19.97/5.27 | (1237) ~ (all_0_54_54 = e1)
% 19.97/5.27 |
% 19.97/5.27 | Simplifying 1237 yields:
% 19.97/5.27 | (1238) ~ (all_0_54_54 = e1)
% 19.97/5.27 |
% 19.97/5.27 | From (596) and (183) follows:
% 19.97/5.27 | (2829) op(e0, e1) = all_0_34_34
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (531), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (532) all_0_53_53 = e4
% 19.97/5.27 |
% 19.97/5.27 | Equations (532) can reduce 448 to:
% 19.97/5.27 | (269) $false
% 19.97/5.27 |
% 19.97/5.27 |-The branch is then unsatisfiable
% 19.97/5.27 |-Branch two:
% 19.97/5.27 | (448) ~ (all_0_53_53 = e4)
% 19.97/5.27 | (535) all_0_54_54 = e4
% 19.97/5.27 |
% 19.97/5.27 | Equations (535) can reduce 1238 to:
% 19.97/5.27 | (251) ~ (e4 = e1)
% 19.97/5.27 |
% 19.97/5.27 | From (535) and (235) follows:
% 19.97/5.27 | (2835) op(e0, e4) = all_0_36_36
% 19.97/5.27 |
% 19.97/5.27 | Instantiating formula (21) with e0, e4, all_0_36_36, e4 and discharging atoms op(e0, e4) = all_0_36_36, op(e0, e4) = e4, yields:
% 19.97/5.27 | (2836) all_0_36_36 = e4
% 19.97/5.27 |
% 19.97/5.27 | Instantiating formula (21) with e0, e3, all_0_30_30, all_0_56_56 and discharging atoms op(e0, e3) = all_0_30_30, op(e0, e3) = all_0_56_56, yields:
% 19.97/5.27 | (2837) all_0_30_30 = all_0_56_56
% 19.97/5.27 |
% 19.97/5.27 | Instantiating formula (21) with e0, e1, all_0_34_34, all_0_58_58 and discharging atoms op(e0, e1) = all_0_34_34, op(e0, e1) = all_0_58_58, yields:
% 19.97/5.27 | (2838) all_0_34_34 = all_0_58_58
% 19.97/5.27 |
% 19.97/5.27 | Instantiating formula (21) with e0, e0, all_0_32_32, e2 and discharging atoms op(e0, e0) = all_0_32_32, op(e0, e0) = e2, yields:
% 19.97/5.27 | (1853) all_0_32_32 = e2
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (104), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (1639) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0)) | (all_0_34_34 = e2 & ~ (all_0_35_35 = e0))
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (1639), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (1640) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0))
% 19.97/5.27 |
% 19.97/5.27 +-Applying beta-rule and splitting (1640), into two cases.
% 19.97/5.27 |-Branch one:
% 19.97/5.27 | (1641) all_0_30_30 = e4 & ~ (all_0_31_31 = e0)
% 19.97/5.27 |
% 19.97/5.28 | Applying alpha-rule on (1641) yields:
% 19.97/5.28 | (1642) all_0_30_30 = e4
% 19.97/5.28 | (1643) ~ (all_0_31_31 = e0)
% 19.97/5.28 |
% 19.97/5.28 | Combining equations (1642,2837) yields a new equation:
% 19.97/5.28 | (1658) all_0_56_56 = e4
% 19.97/5.28 |
% 19.97/5.28 | Equations (1658) can reduce 273 to:
% 19.97/5.28 | (269) $false
% 19.97/5.28 |
% 19.97/5.28 |-The branch is then unsatisfiable
% 19.97/5.28 |-Branch two:
% 19.97/5.28 | (1645) all_0_32_32 = e3 & ~ (all_0_33_33 = e0)
% 19.97/5.28 |
% 19.97/5.28 | Applying alpha-rule on (1645) yields:
% 19.97/5.28 | (1646) all_0_32_32 = e3
% 19.97/5.28 | (1647) ~ (all_0_33_33 = e0)
% 19.97/5.28 |
% 19.97/5.28 | Combining equations (1853,1646) yields a new equation:
% 19.97/5.28 | (423) e3 = e2
% 19.97/5.28 |
% 19.97/5.28 | Equations (423) can reduce 224 to:
% 19.97/5.28 | (269) $false
% 19.97/5.28 |
% 19.97/5.28 |-The branch is then unsatisfiable
% 19.97/5.28 |-Branch two:
% 19.97/5.28 | (1649) all_0_34_34 = e2 & ~ (all_0_35_35 = e0)
% 19.97/5.28 |
% 19.97/5.28 | Applying alpha-rule on (1649) yields:
% 19.97/5.28 | (1650) all_0_34_34 = e2
% 19.97/5.28 | (1651) ~ (all_0_35_35 = e0)
% 19.97/5.28 |
% 19.97/5.28 | Combining equations (1650,2838) yields a new equation:
% 19.97/5.28 | (485) all_0_58_58 = e2
% 19.97/5.28 |
% 19.97/5.28 | Equations (485) can reduce 392 to:
% 19.97/5.28 | (269) $false
% 19.97/5.28 |
% 19.97/5.28 |-The branch is then unsatisfiable
% 19.97/5.28 |-Branch two:
% 19.97/5.28 | (1653) all_0_36_36 = e1 & ~ (all_0_37_37 = e0)
% 19.97/5.28 |
% 19.97/5.28 | Applying alpha-rule on (1653) yields:
% 19.97/5.28 | (1654) all_0_36_36 = e1
% 19.97/5.28 | (1655) ~ (all_0_37_37 = e0)
% 19.97/5.28 |
% 19.97/5.28 | Combining equations (2836,1654) yields a new equation:
% 19.97/5.28 | (476) e4 = e1
% 19.97/5.28 |
% 19.97/5.28 | Simplifying 476 yields:
% 19.97/5.28 | (477) e4 = e1
% 19.97/5.28 |
% 19.97/5.28 | Equations (477) can reduce 251 to:
% 19.97/5.28 | (269) $false
% 19.97/5.28 |
% 19.97/5.28 |-The branch is then unsatisfiable
% 19.97/5.28 |-Branch two:
% 19.97/5.28 | (960) ~ (all_0_49_49 = e1)
% 19.97/5.28 | (965) all_0_49_49 = e0
% 19.97/5.28 |
% 19.97/5.28 | Equations (965) can reduce 807 to:
% 19.97/5.28 | (269) $false
% 19.97/5.28 |
% 19.97/5.28 |-The branch is then unsatisfiable
% 19.97/5.28 |-Branch two:
% 19.97/5.28 | (435) ~ (all_0_46_46 = e0)
% 19.97/5.28 | (549) all_0_46_46 = e4 | all_0_46_46 = e3
% 19.97/5.28 |
% 19.97/5.28 +-Applying beta-rule and splitting (549), into two cases.
% 19.97/5.28 |-Branch one:
% 19.97/5.28 | (462) all_0_46_46 = e3
% 19.97/5.28 |
% 19.97/5.28 | Equations (462) can reduce 618 to:
% 19.97/5.28 | (269) $false
% 19.97/5.28 |
% 19.97/5.28 |-The branch is then unsatisfiable
% 19.97/5.28 |-Branch two:
% 19.97/5.28 | (618) ~ (all_0_46_46 = e3)
% 19.97/5.28 | (538) all_0_46_46 = e4
% 19.97/5.28 |
% 19.97/5.28 | Equations (538) can reduce 310 to:
% 19.97/5.28 | (269) $false
% 19.97/5.28 |
% 19.97/5.28 |-The branch is then unsatisfiable
% 19.97/5.28 |-Branch two:
% 19.97/5.28 | (562) ~ (all_0_43_43 = e3)
% 19.97/5.28 | (1193) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 19.97/5.28 |
% 19.97/5.28 +-Applying beta-rule and splitting (153), into two cases.
% 19.97/5.28 |-Branch one:
% 19.97/5.28 | (453) all_0_50_50 = e4
% 19.97/5.28 |
% 19.97/5.28 | Combining equations (253,453) yields a new equation:
% 19.97/5.28 | (360) e4 = e2
% 19.97/5.28 |
% 19.97/5.28 | Equations (360) can reduce 230 to:
% 19.97/5.28 | (269) $false
% 19.97/5.28 |
% 19.97/5.28 |-The branch is then unsatisfiable
% 19.97/5.28 |-Branch two:
% 19.97/5.28 | (456) ~ (all_0_50_50 = e4)
% 19.97/5.28 | (457) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 19.97/5.28 |
% 19.97/5.28 | Equations (253) can reduce 456 to:
% 19.97/5.28 | (326) ~ (e4 = e2)
% 19.97/5.28 |
% 19.97/5.28 | Simplifying 326 yields:
% 19.97/5.28 | (230) ~ (e4 = e2)
% 19.97/5.28 |
% 19.97/5.28 +-Applying beta-rule and splitting (22), into two cases.
% 19.97/5.28 |-Branch one:
% 19.97/5.28 | (661) all_0_43_43 = e2
% 19.97/5.28 |
% 19.97/5.28 | Equations (661) can reduce 321 to:
% 19.97/5.28 | (269) $false
% 19.97/5.28 |
% 19.97/5.28 |-The branch is then unsatisfiable
% 19.97/5.28 |-Branch two:
% 19.97/5.28 | (321) ~ (all_0_43_43 = e2)
% 19.97/5.28 | (1198) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 19.97/5.28 |
% 19.97/5.28 +-Applying beta-rule and splitting (1198), into two cases.
% 19.97/5.28 |-Branch one:
% 19.97/5.28 | (433) all_0_43_43 = e0
% 19.97/5.28 |
% 19.97/5.28 | Equations (433) can reduce 3 to:
% 19.97/5.28 | (434) ~ (all_0_46_46 = e0)
% 19.97/5.28 |
% 19.97/5.28 | Simplifying 434 yields:
% 19.97/5.28 | (435) ~ (all_0_46_46 = e0)
% 19.97/5.28 |
% 19.97/5.28 | Equations (433) can reduce 137 to:
% 19.97/5.28 | (2889) ~ (all_0_51_51 = e0)
% 19.97/5.28 |
% 19.97/5.28 | Simplifying 2889 yields:
% 19.97/5.28 | (432) ~ (all_0_51_51 = e0)
% 19.97/5.28 |
% 19.97/5.28 | Equations (433) can reduce 114 to:
% 19.97/5.28 | (436) ~ (e1 = e0)
% 19.97/5.28 |
% 19.97/5.28 | Simplifying 436 yields:
% 19.97/5.28 | (144) ~ (e1 = e0)
% 19.97/5.28 |
% 19.97/5.28 +-Applying beta-rule and splitting (195), into two cases.
% 19.97/5.28 |-Branch one:
% 19.97/5.28 | (305) all_0_42_42 = e4
% 19.97/5.28 |
% 19.97/5.28 | Combining equations (305,610) yields a new equation:
% 19.97/5.28 | (515) e4 = e3
% 19.97/5.28 |
% 19.97/5.28 | Simplifying 515 yields:
% 19.97/5.28 | (516) e4 = e3
% 19.97/5.28 |
% 19.97/5.28 | Equations (516) can reduce 41 to:
% 19.97/5.28 | (269) $false
% 19.97/5.28 |
% 19.97/5.28 |-The branch is then unsatisfiable
% 19.97/5.28 |-Branch two:
% 19.97/5.28 | (2787) ~ (all_0_42_42 = e4)
% 19.97/5.28 | (2898) all_0_46_46 = e4 | all_0_54_54 = e4 | all_0_59_59 = e4
% 19.97/5.28 |
% 19.97/5.28 +-Applying beta-rule and splitting (2898), into two cases.
% 19.97/5.28 |-Branch one:
% 19.97/5.28 | (538) all_0_46_46 = e4
% 19.97/5.28 |
% 19.97/5.28 | Equations (538) can reduce 310 to:
% 19.97/5.28 | (269) $false
% 19.97/5.28 |
% 19.97/5.28 |-The branch is then unsatisfiable
% 19.97/5.28 |-Branch two:
% 19.97/5.28 | (310) ~ (all_0_46_46 = e4)
% 19.97/5.28 | (2902) all_0_54_54 = e4 | all_0_59_59 = e4
% 19.97/5.28 |
% 19.97/5.28 +-Applying beta-rule and splitting (2902), into two cases.
% 19.97/5.28 |-Branch one:
% 19.97/5.28 | (535) all_0_54_54 = e4
% 19.97/5.28 |
% 19.97/5.28 | Equations (535) can reduce 62 to:
% 19.97/5.28 | (152) ~ (all_0_52_52 = e4)
% 19.97/5.28 |
% 19.97/5.28 +-Applying beta-rule and splitting (84), into two cases.
% 19.97/5.28 |-Branch one:
% 19.97/5.28 | (832) all_0_42_42 = e1
% 19.97/5.28 |
% 19.97/5.28 | Combining equations (832,610) yields a new equation:
% 19.97/5.28 | (418) e3 = e1
% 19.97/5.28 |
% 19.97/5.28 | Equations (418) can reduce 146 to:
% 19.97/5.28 | (269) $false
% 19.97/5.28 |
% 19.97/5.28 |-The branch is then unsatisfiable
% 19.97/5.28 |-Branch two:
% 20.24/5.28 | (836) ~ (all_0_42_42 = e1)
% 20.24/5.28 | (837) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 20.24/5.28 |
% 20.24/5.28 +-Applying beta-rule and splitting (837), into two cases.
% 20.24/5.28 |-Branch one:
% 20.24/5.28 | (596) all_0_49_49 = e1
% 20.24/5.28 |
% 20.24/5.28 +-Applying beta-rule and splitting (815), into two cases.
% 20.24/5.28 |-Branch one:
% 20.24/5.28 | (903) all_0_48_48 = e0
% 20.24/5.28 |
% 20.24/5.28 | Equations (903) can reduce 250 to:
% 20.24/5.28 | (764) ~ (all_0_53_53 = e0)
% 20.24/5.28 |
% 20.24/5.28 | Simplifying 764 yields:
% 20.24/5.28 | (765) ~ (all_0_53_53 = e0)
% 20.24/5.28 |
% 20.24/5.28 | Equations (903) can reduce 33 to:
% 20.24/5.28 | (404) ~ (e4 = e0)
% 20.24/5.28 |
% 20.24/5.28 | Simplifying 404 yields:
% 20.24/5.28 | (11) ~ (e4 = e0)
% 20.24/5.28 |
% 20.24/5.28 +-Applying beta-rule and splitting (63), into two cases.
% 20.24/5.28 |-Branch one:
% 20.24/5.28 | (629) all_0_51_51 = e0
% 20.24/5.28 |
% 20.24/5.28 | Equations (629) can reduce 432 to:
% 20.24/5.28 | (269) $false
% 20.24/5.28 |
% 20.24/5.28 |-The branch is then unsatisfiable
% 20.24/5.28 |-Branch two:
% 20.24/5.28 | (432) ~ (all_0_51_51 = e0)
% 20.24/5.28 | (1231) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 20.24/5.28 |
% 20.24/5.28 +-Applying beta-rule and splitting (1231), into two cases.
% 20.24/5.28 |-Branch one:
% 20.24/5.28 | (397) all_0_52_52 = e0
% 20.24/5.28 |
% 20.24/5.28 | Equations (397) can reduce 152 to:
% 20.24/5.28 | (404) ~ (e4 = e0)
% 20.24/5.28 |
% 20.24/5.28 | Simplifying 404 yields:
% 20.24/5.28 | (11) ~ (e4 = e0)
% 20.24/5.28 |
% 20.24/5.28 | Equations (397) can reduce 257 to:
% 20.24/5.28 | (406) ~ (e2 = e0)
% 20.24/5.28 |
% 20.24/5.28 | Simplifying 406 yields:
% 20.24/5.28 | (58) ~ (e2 = e0)
% 20.24/5.28 |
% 20.24/5.28 | Equations (397) can reduce 978 to:
% 20.24/5.28 | (436) ~ (e1 = e0)
% 20.24/5.28 |
% 20.24/5.28 | Simplifying 436 yields:
% 20.24/5.28 | (144) ~ (e1 = e0)
% 20.24/5.28 |
% 20.24/5.28 +-Applying beta-rule and splitting (206), into two cases.
% 20.24/5.28 |-Branch one:
% 20.24/5.28 | (546) all_0_46_46 = e0
% 20.24/5.28 |
% 20.24/5.28 | Equations (546) can reduce 435 to:
% 20.24/5.28 | (269) $false
% 20.24/5.28 |
% 20.24/5.28 |-The branch is then unsatisfiable
% 20.24/5.28 |-Branch two:
% 20.24/5.28 | (435) ~ (all_0_46_46 = e0)
% 20.24/5.28 | (2930) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 20.24/5.28 |
% 20.24/5.28 +-Applying beta-rule and splitting (2930), into two cases.
% 20.24/5.28 |-Branch one:
% 20.24/5.28 | (965) all_0_49_49 = e0
% 20.24/5.28 |
% 20.24/5.28 | Combining equations (596,965) yields a new equation:
% 20.24/5.28 | (578) e1 = e0
% 20.24/5.28 |
% 20.24/5.28 | Simplifying 578 yields:
% 20.24/5.28 | (579) e1 = e0
% 20.24/5.28 |
% 20.24/5.28 | Equations (579) can reduce 144 to:
% 20.24/5.28 | (269) $false
% 20.24/5.28 |
% 20.24/5.28 |-The branch is then unsatisfiable
% 20.24/5.28 |-Branch two:
% 20.24/5.28 | (807) ~ (all_0_49_49 = e0)
% 20.24/5.28 | (2936) all_0_54_54 = e0 | all_0_59_59 = e0
% 20.24/5.28 |
% 20.24/5.28 +-Applying beta-rule and splitting (2936), into two cases.
% 20.24/5.28 |-Branch one:
% 20.24/5.28 | (1286) all_0_54_54 = e0
% 20.24/5.28 |
% 20.24/5.28 | Combining equations (535,1286) yields a new equation:
% 20.24/5.28 | (751) e4 = e0
% 20.24/5.28 |
% 20.24/5.28 | Simplifying 751 yields:
% 20.24/5.28 | (439) e4 = e0
% 20.24/5.28 |
% 20.24/5.28 | Equations (439) can reduce 11 to:
% 20.24/5.28 | (269) $false
% 20.24/5.28 |
% 20.24/5.28 |-The branch is then unsatisfiable
% 20.24/5.28 |-Branch two:
% 20.24/5.28 | (1478) ~ (all_0_54_54 = e0)
% 20.24/5.28 | (2064) all_0_59_59 = e0
% 20.24/5.28 |
% 20.24/5.28 | Combining equations (375,2064) yields a new equation:
% 20.24/5.28 | (353) e2 = e0
% 20.24/5.28 |
% 20.24/5.28 | Simplifying 353 yields:
% 20.24/5.28 | (354) e2 = e0
% 20.24/5.28 |
% 20.24/5.28 | Equations (354) can reduce 58 to:
% 20.24/5.28 | (269) $false
% 20.24/5.28 |
% 20.24/5.28 |-The branch is then unsatisfiable
% 20.24/5.28 |-Branch two:
% 20.24/5.28 | (317) ~ (all_0_52_52 = e0)
% 20.24/5.28 | (1245) all_0_53_53 = e0 | all_0_54_54 = e0
% 20.24/5.28 |
% 20.24/5.28 +-Applying beta-rule and splitting (1245), into two cases.
% 20.24/5.28 |-Branch one:
% 20.24/5.28 | (857) all_0_53_53 = e0
% 20.24/5.28 |
% 20.24/5.28 | Equations (857) can reduce 765 to:
% 20.24/5.28 | (269) $false
% 20.24/5.28 |
% 20.24/5.28 |-The branch is then unsatisfiable
% 20.24/5.28 |-Branch two:
% 20.24/5.28 | (765) ~ (all_0_53_53 = e0)
% 20.24/5.28 | (1286) all_0_54_54 = e0
% 20.24/5.28 |
% 20.24/5.28 | Combining equations (535,1286) yields a new equation:
% 20.24/5.28 | (751) e4 = e0
% 20.24/5.28 |
% 20.24/5.28 | Simplifying 751 yields:
% 20.24/5.28 | (439) e4 = e0
% 20.24/5.28 |
% 20.24/5.28 | Equations (439) can reduce 11 to:
% 20.24/5.28 | (269) $false
% 20.24/5.28 |
% 20.24/5.28 |-The branch is then unsatisfiable
% 20.24/5.28 |-Branch two:
% 20.24/5.28 | (952) ~ (all_0_48_48 = e0)
% 20.24/5.28 | (965) all_0_49_49 = e0
% 20.24/5.28 |
% 20.24/5.28 | Combining equations (596,965) yields a new equation:
% 20.24/5.28 | (578) e1 = e0
% 20.24/5.28 |
% 20.24/5.28 | Simplifying 578 yields:
% 20.24/5.28 | (579) e1 = e0
% 20.24/5.28 |
% 20.24/5.28 | Equations (579) can reduce 144 to:
% 20.24/5.28 | (269) $false
% 20.24/5.28 |
% 20.24/5.28 |-The branch is then unsatisfiable
% 20.24/5.28 |-Branch two:
% 20.24/5.28 | (960) ~ (all_0_49_49 = e1)
% 20.24/5.28 | (961) all_0_54_54 = e1 | all_0_59_59 = e1
% 20.24/5.28 |
% 20.24/5.28 +-Applying beta-rule and splitting (340), into two cases.
% 20.24/5.28 |-Branch one:
% 20.24/5.28 | (596) all_0_49_49 = e1
% 20.24/5.28 |
% 20.24/5.28 | Equations (596) can reduce 960 to:
% 20.24/5.28 | (269) $false
% 20.24/5.28 |
% 20.24/5.28 |-The branch is then unsatisfiable
% 20.24/5.28 |-Branch two:
% 20.24/5.28 | (960) ~ (all_0_49_49 = e1)
% 20.24/5.28 | (965) all_0_49_49 = e0
% 20.24/5.28 |
% 20.24/5.28 | Equations (965) can reduce 960 to:
% 20.24/5.28 | (436) ~ (e1 = e0)
% 20.24/5.28 |
% 20.24/5.28 | Simplifying 436 yields:
% 20.24/5.28 | (144) ~ (e1 = e0)
% 20.24/5.28 |
% 20.24/5.28 +-Applying beta-rule and splitting (592), into two cases.
% 20.24/5.28 |-Branch one:
% 20.24/5.28 | (593) all_0_48_48 = e1
% 20.24/5.28 |
% 20.24/5.28 | Equations (593) can reduce 174 to:
% 20.24/5.28 | (481) ~ (all_0_58_58 = e1)
% 20.24/5.28 |
% 20.24/5.28 | Simplifying 481 yields:
% 20.24/5.28 | (482) ~ (all_0_58_58 = e1)
% 20.24/5.28 |
% 20.24/5.28 | Equations (593) can reduce 1115 to:
% 20.24/5.28 | (414) ~ (e2 = e1)
% 20.24/5.28 |
% 20.24/5.28 | Simplifying 414 yields:
% 20.24/5.28 | (148) ~ (e2 = e1)
% 20.24/5.28 |
% 20.24/5.28 +-Applying beta-rule and splitting (43), into two cases.
% 20.24/5.28 |-Branch one:
% 20.24/5.28 | (480) all_0_56_56 = e1
% 20.24/5.28 |
% 20.24/5.28 | Equations (480) can reduce 273 to:
% 20.24/5.28 | (826) ~ (e4 = e1)
% 20.24/5.28 |
% 20.24/5.28 | Simplifying 826 yields:
% 20.24/5.28 | (251) ~ (e4 = e1)
% 20.24/5.29 |
% 20.24/5.29 | Equations (480) can reduce 377 to:
% 20.24/5.29 | (414) ~ (e2 = e1)
% 20.24/5.29 |
% 20.24/5.29 | Simplifying 414 yields:
% 20.24/5.29 | (148) ~ (e2 = e1)
% 20.24/5.29 |
% 20.24/5.29 +-Applying beta-rule and splitting (961), into two cases.
% 20.24/5.29 |-Branch one:
% 20.24/5.29 | (1592) all_0_54_54 = e1
% 20.24/5.29 |
% 20.24/5.29 | Combining equations (535,1592) yields a new equation:
% 20.24/5.29 | (476) e4 = e1
% 20.24/5.29 |
% 20.24/5.29 | Simplifying 476 yields:
% 20.24/5.29 | (477) e4 = e1
% 20.24/5.29 |
% 20.24/5.29 | Equations (477) can reduce 251 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (1238) ~ (all_0_54_54 = e1)
% 20.24/5.29 | (614) all_0_59_59 = e1
% 20.24/5.29 |
% 20.24/5.29 | Combining equations (614,375) yields a new equation:
% 20.24/5.29 | (471) e2 = e1
% 20.24/5.29 |
% 20.24/5.29 | Equations (471) can reduce 148 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (575) ~ (all_0_56_56 = e1)
% 20.24/5.29 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 20.24/5.29 |
% 20.24/5.29 +-Applying beta-rule and splitting (576), into two cases.
% 20.24/5.29 |-Branch one:
% 20.24/5.29 | (577) all_0_57_57 = e1
% 20.24/5.29 |
% 20.24/5.29 | Equations (577) can reduce 581 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (581) ~ (all_0_57_57 = e1)
% 20.24/5.29 | (582) all_0_58_58 = e1 | all_0_59_59 = e1
% 20.24/5.29 |
% 20.24/5.29 +-Applying beta-rule and splitting (582), into two cases.
% 20.24/5.29 |-Branch one:
% 20.24/5.29 | (489) all_0_58_58 = e1
% 20.24/5.29 |
% 20.24/5.29 | Equations (489) can reduce 482 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (482) ~ (all_0_58_58 = e1)
% 20.24/5.29 | (614) all_0_59_59 = e1
% 20.24/5.29 |
% 20.24/5.29 | Combining equations (614,375) yields a new equation:
% 20.24/5.29 | (471) e2 = e1
% 20.24/5.29 |
% 20.24/5.29 | Equations (471) can reduce 148 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (584) ~ (all_0_48_48 = e1)
% 20.24/5.29 | (596) all_0_49_49 = e1
% 20.24/5.29 |
% 20.24/5.29 | Combining equations (965,596) yields a new equation:
% 20.24/5.29 | (579) e1 = e0
% 20.24/5.29 |
% 20.24/5.29 | Equations (579) can reduce 144 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (312) ~ (all_0_54_54 = e4)
% 20.24/5.29 | (2231) all_0_59_59 = e4
% 20.24/5.29 |
% 20.24/5.29 | Combining equations (2231,375) yields a new equation:
% 20.24/5.29 | (359) e4 = e2
% 20.24/5.29 |
% 20.24/5.29 | Simplifying 359 yields:
% 20.24/5.29 | (360) e4 = e2
% 20.24/5.29 |
% 20.24/5.29 | Equations (360) can reduce 230 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (459) ~ (all_0_43_43 = e0)
% 20.24/5.29 | (1695) all_0_43_43 = e4 | all_0_43_43 = e3
% 20.24/5.29 |
% 20.24/5.29 +-Applying beta-rule and splitting (1695), into two cases.
% 20.24/5.29 |-Branch one:
% 20.24/5.29 | (559) all_0_43_43 = e3
% 20.24/5.29 |
% 20.24/5.29 | Equations (559) can reduce 562 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (562) ~ (all_0_43_43 = e3)
% 20.24/5.29 | (438) all_0_43_43 = e4
% 20.24/5.29 |
% 20.24/5.29 | Equations (438) can reduce 441 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (1924) ~ (all_0_42_42 = e3)
% 20.24/5.29 | (305) all_0_42_42 = e4
% 20.24/5.29 |
% 20.24/5.29 | Equations (305) can reduce 2787 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (307) ~ (all_0_39_39 = e4)
% 20.24/5.29 | (3018) all_0_41_41 = e4 | all_0_42_42 = e4
% 20.24/5.29 |
% 20.24/5.29 +-Applying beta-rule and splitting (709), into two cases.
% 20.24/5.29 |-Branch one:
% 20.24/5.29 | (464) all_0_39_39 = e1
% 20.24/5.29 |
% 20.24/5.29 | Equations (464) can reduce 467 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (467) ~ (all_0_39_39 = e1)
% 20.24/5.29 | (1075) all_0_39_39 = e4 | all_0_39_39 = e3
% 20.24/5.29 |
% 20.24/5.29 +-Applying beta-rule and splitting (29), into two cases.
% 20.24/5.29 |-Branch one:
% 20.24/5.29 | (1079) all_0_39_39 = e4
% 20.24/5.29 |
% 20.24/5.29 | Equations (1079) can reduce 307 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (307) ~ (all_0_39_39 = e4)
% 20.24/5.29 | (1391) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 20.24/5.29 |
% 20.24/5.29 +-Applying beta-rule and splitting (1075), into two cases.
% 20.24/5.29 |-Branch one:
% 20.24/5.29 | (443) all_0_39_39 = e3
% 20.24/5.29 |
% 20.24/5.29 | Equations (443) can reduce 157 to:
% 20.24/5.29 | (3028) ~ (all_0_42_42 = e3)
% 20.24/5.29 |
% 20.24/5.29 | Simplifying 3028 yields:
% 20.24/5.29 | (1924) ~ (all_0_42_42 = e3)
% 20.24/5.29 |
% 20.24/5.29 | Equations (443) can reduce 234 to:
% 20.24/5.29 | (1178) ~ (all_0_43_43 = e3)
% 20.24/5.29 |
% 20.24/5.29 | Simplifying 1178 yields:
% 20.24/5.29 | (562) ~ (all_0_43_43 = e3)
% 20.24/5.29 |
% 20.24/5.29 | Equations (443) can reduce 320 to:
% 20.24/5.29 | (224) ~ (e3 = e2)
% 20.24/5.29 |
% 20.24/5.29 +-Applying beta-rule and splitting (3018), into two cases.
% 20.24/5.29 |-Branch one:
% 20.24/5.29 | (740) all_0_41_41 = e4
% 20.24/5.29 |
% 20.24/5.29 | Combining equations (386,740) yields a new equation:
% 20.24/5.29 | (360) e4 = e2
% 20.24/5.29 |
% 20.24/5.29 | Equations (360) can reduce 230 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (308) ~ (all_0_41_41 = e4)
% 20.24/5.29 | (305) all_0_42_42 = e4
% 20.24/5.29 |
% 20.24/5.29 | Equations (305) can reduce 1924 to:
% 20.24/5.29 | (41) ~ (e4 = e3)
% 20.24/5.29 |
% 20.24/5.29 | Equations (305) can reduce 836 to:
% 20.24/5.29 | (251) ~ (e4 = e1)
% 20.24/5.29 |
% 20.24/5.29 +-Applying beta-rule and splitting (162), into two cases.
% 20.24/5.29 |-Branch one:
% 20.24/5.29 | (559) all_0_43_43 = e3
% 20.24/5.29 |
% 20.24/5.29 | Equations (559) can reduce 562 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (562) ~ (all_0_43_43 = e3)
% 20.24/5.29 | (1193) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 20.24/5.29 |
% 20.24/5.29 +-Applying beta-rule and splitting (1391), into two cases.
% 20.24/5.29 |-Branch one:
% 20.24/5.29 | (438) all_0_43_43 = e4
% 20.24/5.29 |
% 20.24/5.29 | Equations (438) can reduce 441 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (441) ~ (all_0_43_43 = e4)
% 20.24/5.29 | (2025) all_0_51_51 = e4 | all_0_56_56 = e4
% 20.24/5.29 |
% 20.24/5.29 +-Applying beta-rule and splitting (1193), into two cases.
% 20.24/5.29 |-Branch one:
% 20.24/5.29 | (422) all_0_44_44 = e3
% 20.24/5.29 |
% 20.24/5.29 | Combining equations (341,422) yields a new equation:
% 20.24/5.29 | (423) e3 = e2
% 20.24/5.29 |
% 20.24/5.29 | Equations (423) can reduce 224 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (425) ~ (all_0_44_44 = e3)
% 20.24/5.29 | (1203) all_0_45_45 = e3 | all_0_46_46 = e3
% 20.24/5.29 |
% 20.24/5.29 +-Applying beta-rule and splitting (1203), into two cases.
% 20.24/5.29 |-Branch one:
% 20.24/5.29 | (1087) all_0_45_45 = e3
% 20.24/5.29 |
% 20.24/5.29 | Combining equations (444,1087) yields a new equation:
% 20.24/5.29 | (515) e4 = e3
% 20.24/5.29 |
% 20.24/5.29 | Simplifying 515 yields:
% 20.24/5.29 | (516) e4 = e3
% 20.24/5.29 |
% 20.24/5.29 | Equations (516) can reduce 41 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (689) ~ (all_0_45_45 = e3)
% 20.24/5.29 | (462) all_0_46_46 = e3
% 20.24/5.29 |
% 20.24/5.29 | Equations (462) can reduce 59 to:
% 20.24/5.29 | (429) ~ (all_0_54_54 = e3)
% 20.24/5.29 |
% 20.24/5.29 | Simplifying 429 yields:
% 20.24/5.29 | (430) ~ (all_0_54_54 = e3)
% 20.24/5.29 |
% 20.24/5.29 | Equations (462) can reduce 163 to:
% 20.24/5.29 | (146) ~ (e3 = e1)
% 20.24/5.29 |
% 20.24/5.29 +-Applying beta-rule and splitting (2025), into two cases.
% 20.24/5.29 |-Branch one:
% 20.24/5.29 | (458) all_0_51_51 = e4
% 20.24/5.29 |
% 20.24/5.29 +-Applying beta-rule and splitting (200), into two cases.
% 20.24/5.29 |-Branch one:
% 20.24/5.29 | (464) all_0_39_39 = e1
% 20.24/5.29 |
% 20.24/5.29 | Combining equations (464,443) yields a new equation:
% 20.24/5.29 | (418) e3 = e1
% 20.24/5.29 |
% 20.24/5.29 | Equations (418) can reduce 146 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (467) ~ (all_0_39_39 = e1)
% 20.24/5.29 | (468) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 20.24/5.29 |
% 20.24/5.29 +-Applying beta-rule and splitting (468), into two cases.
% 20.24/5.29 |-Branch one:
% 20.24/5.29 | (469) all_0_47_47 = e1
% 20.24/5.29 |
% 20.24/5.29 | Combining equations (319,469) yields a new equation:
% 20.24/5.29 | (470) e2 = e1
% 20.24/5.29 |
% 20.24/5.29 | Simplifying 470 yields:
% 20.24/5.29 | (471) e2 = e1
% 20.24/5.29 |
% 20.24/5.29 | Equations (471) can reduce 148 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (473) ~ (all_0_47_47 = e1)
% 20.24/5.29 | (474) all_0_51_51 = e1 | all_0_56_56 = e1
% 20.24/5.29 |
% 20.24/5.29 +-Applying beta-rule and splitting (474), into two cases.
% 20.24/5.29 |-Branch one:
% 20.24/5.29 | (475) all_0_51_51 = e1
% 20.24/5.29 |
% 20.24/5.29 | Combining equations (475,458) yields a new equation:
% 20.24/5.29 | (477) e4 = e1
% 20.24/5.29 |
% 20.24/5.29 | Equations (477) can reduce 251 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (479) ~ (all_0_51_51 = e1)
% 20.24/5.29 | (480) all_0_56_56 = e1
% 20.24/5.29 |
% 20.24/5.29 | Equations (480) can reduce 377 to:
% 20.24/5.29 | (414) ~ (e2 = e1)
% 20.24/5.29 |
% 20.24/5.29 | Simplifying 414 yields:
% 20.24/5.29 | (148) ~ (e2 = e1)
% 20.24/5.29 |
% 20.24/5.29 +-Applying beta-rule and splitting (2627), into two cases.
% 20.24/5.29 |-Branch one:
% 20.24/5.29 | (575) ~ (all_0_56_56 = e1)
% 20.24/5.29 |
% 20.24/5.29 | Equations (480) can reduce 575 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (480) all_0_56_56 = e1
% 20.24/5.29 | (497) all_0_58_58 = e3
% 20.24/5.29 |
% 20.24/5.29 | Equations (497) can reduce 127 to:
% 20.24/5.29 | (796) ~ (all_0_53_53 = e3)
% 20.24/5.29 |
% 20.24/5.29 | Equations (497) can reduce 277 to:
% 20.24/5.29 | (498) ~ (e4 = e3)
% 20.24/5.29 |
% 20.24/5.29 | Simplifying 498 yields:
% 20.24/5.29 | (41) ~ (e4 = e3)
% 20.24/5.29 |
% 20.24/5.29 +-Applying beta-rule and splitting (93), into two cases.
% 20.24/5.29 |-Branch one:
% 20.24/5.29 | (564) all_0_51_51 = e3
% 20.24/5.29 |
% 20.24/5.29 | Combining equations (458,564) yields a new equation:
% 20.24/5.29 | (515) e4 = e3
% 20.24/5.29 |
% 20.24/5.29 | Simplifying 515 yields:
% 20.24/5.29 | (516) e4 = e3
% 20.24/5.29 |
% 20.24/5.29 | Equations (516) can reduce 41 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (428) ~ (all_0_51_51 = e3)
% 20.24/5.29 | (3093) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 20.24/5.29 |
% 20.24/5.29 +-Applying beta-rule and splitting (3093), into two cases.
% 20.24/5.29 |-Branch one:
% 20.24/5.29 | (427) all_0_52_52 = e3
% 20.24/5.29 |
% 20.24/5.29 | From (427) and (2268) follows:
% 20.24/5.29 | (3095) op(e2, e3) = e1
% 20.24/5.29 |
% 20.24/5.29 | Instantiating formula (21) with e2, e3, e1, e2 and discharging atoms op(e2, e3) = e2, op(e2, e3) = e1, yields:
% 20.24/5.29 | (471) e2 = e1
% 20.24/5.29 |
% 20.24/5.29 | Equations (471) can reduce 148 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (637) ~ (all_0_52_52 = e3)
% 20.24/5.29 | (3099) all_0_53_53 = e3 | all_0_54_54 = e3
% 20.24/5.29 |
% 20.24/5.29 +-Applying beta-rule and splitting (3099), into two cases.
% 20.24/5.29 |-Branch one:
% 20.24/5.29 | (861) all_0_53_53 = e3
% 20.24/5.29 |
% 20.24/5.29 | Equations (861) can reduce 796 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (796) ~ (all_0_53_53 = e3)
% 20.24/5.29 | (635) all_0_54_54 = e3
% 20.24/5.29 |
% 20.24/5.29 | Equations (635) can reduce 430 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.29 |-Branch two:
% 20.24/5.29 | (530) ~ (all_0_51_51 = e4)
% 20.24/5.29 | (1658) all_0_56_56 = e4
% 20.24/5.29 |
% 20.24/5.29 | Equations (1658) can reduce 273 to:
% 20.24/5.29 | (269) $false
% 20.24/5.29 |
% 20.24/5.29 |-The branch is then unsatisfiable
% 20.24/5.30 |-Branch two:
% 20.24/5.30 | (540) ~ (all_0_39_39 = e3)
% 20.24/5.30 | (1079) all_0_39_39 = e4
% 20.24/5.30 |
% 20.24/5.30 | Equations (1079) can reduce 307 to:
% 20.24/5.30 | (269) $false
% 20.24/5.30 |
% 20.24/5.30 |-The branch is then unsatisfiable
% 20.24/5.30 |-Branch two:
% 20.24/5.30 | (523) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 20.24/5.30 |
% 20.24/5.30 | Applying alpha-rule on (523) yields:
% 20.24/5.30 | (524) all_0_19_19 = e0
% 20.24/5.30 | (525) ~ (all_0_20_20 = e2)
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (229), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (923) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1))
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (923), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (924) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1))
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (924), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (925) all_0_21_21 = e4 & ~ (all_0_22_22 = e1)
% 20.24/5.30 |
% 20.24/5.30 | Applying alpha-rule on (925) yields:
% 20.24/5.30 | (926) all_0_21_21 = e4
% 20.24/5.30 | (927) ~ (all_0_22_22 = e1)
% 20.24/5.30 |
% 20.24/5.30 | Combining equations (926,2698) yields a new equation:
% 20.24/5.30 | (3119) all_0_52_52 = e4
% 20.24/5.30 |
% 20.24/5.30 | Equations (3119) can reduce 152 to:
% 20.24/5.30 | (269) $false
% 20.24/5.30 |
% 20.24/5.30 |-The branch is then unsatisfiable
% 20.24/5.30 |-Branch two:
% 20.24/5.30 | (931) all_0_23_23 = e3 & ~ (all_0_24_24 = e1)
% 20.24/5.30 |
% 20.24/5.30 | Applying alpha-rule on (931) yields:
% 20.24/5.30 | (932) all_0_23_23 = e3
% 20.24/5.30 | (933) ~ (all_0_24_24 = e1)
% 20.24/5.30 |
% 20.24/5.30 | Combining equations (932,2649) yields a new equation:
% 20.24/5.30 | (606) e3 = e2
% 20.24/5.30 |
% 20.24/5.30 | Simplifying 606 yields:
% 20.24/5.30 | (423) e3 = e2
% 20.24/5.30 |
% 20.24/5.30 | Equations (423) can reduce 224 to:
% 20.24/5.30 | (269) $false
% 20.24/5.30 |
% 20.24/5.30 |-The branch is then unsatisfiable
% 20.24/5.30 |-Branch two:
% 20.24/5.30 | (937) all_0_25_25 = e2 & ~ (all_0_26_26 = e1)
% 20.24/5.30 |
% 20.24/5.30 | Applying alpha-rule on (937) yields:
% 20.24/5.30 | (938) all_0_25_25 = e2
% 20.24/5.30 | (939) ~ (all_0_26_26 = e1)
% 20.24/5.30 |
% 20.24/5.30 | From (938) and (85) follows:
% 20.24/5.30 | (3130) op(e1, all_0_48_48) = e2
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (10), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (623) all_0_47_47 = e0
% 20.24/5.30 |
% 20.24/5.30 | Combining equations (623,319) yields a new equation:
% 20.24/5.30 | (354) e2 = e0
% 20.24/5.30 |
% 20.24/5.30 | Equations (354) can reduce 58 to:
% 20.24/5.30 | (269) $false
% 20.24/5.30 |
% 20.24/5.30 |-The branch is then unsatisfiable
% 20.24/5.30 |-Branch two:
% 20.24/5.30 | (297) ~ (all_0_47_47 = e0)
% 20.24/5.30 | (815) all_0_48_48 = e0 | all_0_49_49 = e0
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (192), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (469) all_0_47_47 = e1
% 20.24/5.30 |
% 20.24/5.30 | Combining equations (469,319) yields a new equation:
% 20.24/5.30 | (471) e2 = e1
% 20.24/5.30 |
% 20.24/5.30 | Equations (471) can reduce 148 to:
% 20.24/5.30 | (269) $false
% 20.24/5.30 |
% 20.24/5.30 |-The branch is then unsatisfiable
% 20.24/5.30 |-Branch two:
% 20.24/5.30 | (473) ~ (all_0_47_47 = e1)
% 20.24/5.30 | (592) all_0_48_48 = e1 | all_0_49_49 = e1
% 20.24/5.30 |
% 20.24/5.30 | Equations (319) can reduce 473 to:
% 20.24/5.30 | (148) ~ (e2 = e1)
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (47), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (348) all_0_39_39 = e2
% 20.24/5.30 |
% 20.24/5.30 | Equations (348) can reduce 320 to:
% 20.24/5.30 | (269) $false
% 20.24/5.30 |
% 20.24/5.30 |-The branch is then unsatisfiable
% 20.24/5.30 |-Branch two:
% 20.24/5.30 | (320) ~ (all_0_39_39 = e2)
% 20.24/5.30 | (709) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (116), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (358) all_0_42_42 = e2
% 20.24/5.30 |
% 20.24/5.30 | Equations (358) can reduce 362 to:
% 20.24/5.30 | (269) $false
% 20.24/5.30 |
% 20.24/5.30 |-The branch is then unsatisfiable
% 20.24/5.30 |-Branch two:
% 20.24/5.30 | (362) ~ (all_0_42_42 = e2)
% 20.24/5.30 | (2784) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (32), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (1079) all_0_39_39 = e4
% 20.24/5.30 |
% 20.24/5.30 | Equations (1079) can reduce 157 to:
% 20.24/5.30 | (2786) ~ (all_0_42_42 = e4)
% 20.24/5.30 |
% 20.24/5.30 | Simplifying 2786 yields:
% 20.24/5.30 | (2787) ~ (all_0_42_42 = e4)
% 20.24/5.30 |
% 20.24/5.30 | Equations (1079) can reduce 234 to:
% 20.24/5.30 | (2788) ~ (all_0_43_43 = e4)
% 20.24/5.30 |
% 20.24/5.30 | Simplifying 2788 yields:
% 20.24/5.30 | (441) ~ (all_0_43_43 = e4)
% 20.24/5.30 |
% 20.24/5.30 | Equations (1079) can reduce 126 to:
% 20.24/5.30 | (1208) ~ (all_0_51_51 = e4)
% 20.24/5.30 |
% 20.24/5.30 | Simplifying 1208 yields:
% 20.24/5.30 | (530) ~ (all_0_51_51 = e4)
% 20.24/5.30 |
% 20.24/5.30 | Equations (1079) can reduce 53 to:
% 20.24/5.30 | (272) ~ (all_0_56_56 = e4)
% 20.24/5.30 |
% 20.24/5.30 | Simplifying 272 yields:
% 20.24/5.30 | (273) ~ (all_0_56_56 = e4)
% 20.24/5.30 |
% 20.24/5.30 | Equations (1079) can reduce 320 to:
% 20.24/5.30 | (230) ~ (e4 = e2)
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (2784), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (832) all_0_42_42 = e1
% 20.24/5.30 |
% 20.24/5.30 | Equations (832) can reduce 836 to:
% 20.24/5.30 | (269) $false
% 20.24/5.30 |
% 20.24/5.30 |-The branch is then unsatisfiable
% 20.24/5.30 |-Branch two:
% 20.24/5.30 | (836) ~ (all_0_42_42 = e1)
% 20.24/5.30 | (2798) all_0_42_42 = e4 | all_0_42_42 = e3
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (2798), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (610) all_0_42_42 = e3
% 20.24/5.30 |
% 20.24/5.30 | Equations (610) can reduce 2787 to:
% 20.24/5.30 | (498) ~ (e4 = e3)
% 20.24/5.30 |
% 20.24/5.30 | Simplifying 498 yields:
% 20.24/5.30 | (41) ~ (e4 = e3)
% 20.24/5.30 |
% 20.24/5.30 | Equations (610) can reduce 836 to:
% 20.24/5.30 | (146) ~ (e3 = e1)
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (199), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (364) all_0_46_46 = e2
% 20.24/5.30 |
% 20.24/5.30 | Equations (364) can reduce 344 to:
% 20.24/5.30 | (269) $false
% 20.24/5.30 |
% 20.24/5.30 |-The branch is then unsatisfiable
% 20.24/5.30 |-Branch two:
% 20.24/5.30 | (344) ~ (all_0_46_46 = e2)
% 20.24/5.30 | (545) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e0
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (162), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (559) all_0_43_43 = e3
% 20.24/5.30 |
% 20.24/5.30 | Equations (559) can reduce 3 to:
% 20.24/5.30 | (1044) ~ (all_0_46_46 = e3)
% 20.24/5.30 |
% 20.24/5.30 | Simplifying 1044 yields:
% 20.24/5.30 | (618) ~ (all_0_46_46 = e3)
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (545), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (546) all_0_46_46 = e0
% 20.24/5.30 |
% 20.24/5.30 | Equations (546) can reduce 166 to:
% 20.24/5.30 | (806) ~ (all_0_49_49 = e0)
% 20.24/5.30 |
% 20.24/5.30 | Simplifying 806 yields:
% 20.24/5.30 | (807) ~ (all_0_49_49 = e0)
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (153), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (453) all_0_50_50 = e4
% 20.24/5.30 |
% 20.24/5.30 | Combining equations (453,253) yields a new equation:
% 20.24/5.30 | (359) e4 = e2
% 20.24/5.30 |
% 20.24/5.30 | Simplifying 359 yields:
% 20.24/5.30 | (360) e4 = e2
% 20.24/5.30 |
% 20.24/5.30 | Equations (360) can reduce 230 to:
% 20.24/5.30 | (269) $false
% 20.24/5.30 |
% 20.24/5.30 |-The branch is then unsatisfiable
% 20.24/5.30 |-Branch two:
% 20.24/5.30 | (456) ~ (all_0_50_50 = e4)
% 20.24/5.30 | (457) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (457), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (458) all_0_51_51 = e4
% 20.24/5.30 |
% 20.24/5.30 | Equations (458) can reduce 530 to:
% 20.24/5.30 | (269) $false
% 20.24/5.30 |
% 20.24/5.30 |-The branch is then unsatisfiable
% 20.24/5.30 |-Branch two:
% 20.24/5.30 | (530) ~ (all_0_51_51 = e4)
% 20.24/5.30 | (531) all_0_53_53 = e4 | all_0_54_54 = e4
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (340), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (596) all_0_49_49 = e1
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (531), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (532) all_0_53_53 = e4
% 20.24/5.30 |
% 20.24/5.30 | Equations (532) can reduce 448 to:
% 20.24/5.30 | (269) $false
% 20.24/5.30 |
% 20.24/5.30 |-The branch is then unsatisfiable
% 20.24/5.30 |-Branch two:
% 20.24/5.30 | (448) ~ (all_0_53_53 = e4)
% 20.24/5.30 | (535) all_0_54_54 = e4
% 20.24/5.30 |
% 20.24/5.30 | Equations (535) can reduce 261 to:
% 20.24/5.30 | (230) ~ (e4 = e2)
% 20.24/5.30 |
% 20.24/5.30 | From (535) and (13) follows:
% 20.24/5.30 | (3194) op(e1, e0) = e4
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (2628), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (960) ~ (all_0_49_49 = e1)
% 20.24/5.30 |
% 20.24/5.30 | Equations (596) can reduce 960 to:
% 20.24/5.30 | (269) $false
% 20.24/5.30 |
% 20.24/5.30 |-The branch is then unsatisfiable
% 20.24/5.30 |-Branch two:
% 20.24/5.30 | (596) all_0_49_49 = e1
% 20.24/5.30 | (903) all_0_48_48 = e0
% 20.24/5.30 |
% 20.24/5.30 | From (903) and (3130) follows:
% 20.24/5.30 | (3199) op(e1, e0) = e2
% 20.24/5.30 |
% 20.24/5.30 | Instantiating formula (21) with e1, e0, e2, e4 and discharging atoms op(e1, e0) = e4, op(e1, e0) = e2, yields:
% 20.24/5.30 | (360) e4 = e2
% 20.24/5.30 |
% 20.24/5.30 | Equations (360) can reduce 230 to:
% 20.24/5.30 | (269) $false
% 20.24/5.30 |
% 20.24/5.30 |-The branch is then unsatisfiable
% 20.24/5.30 |-Branch two:
% 20.24/5.30 | (960) ~ (all_0_49_49 = e1)
% 20.24/5.30 | (965) all_0_49_49 = e0
% 20.24/5.30 |
% 20.24/5.30 | Equations (965) can reduce 807 to:
% 20.24/5.30 | (269) $false
% 20.24/5.30 |
% 20.24/5.30 |-The branch is then unsatisfiable
% 20.24/5.30 |-Branch two:
% 20.24/5.30 | (435) ~ (all_0_46_46 = e0)
% 20.24/5.30 | (549) all_0_46_46 = e4 | all_0_46_46 = e3
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (549), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (462) all_0_46_46 = e3
% 20.24/5.30 |
% 20.24/5.30 | Equations (462) can reduce 618 to:
% 20.24/5.30 | (269) $false
% 20.24/5.30 |
% 20.24/5.30 |-The branch is then unsatisfiable
% 20.24/5.30 |-Branch two:
% 20.24/5.30 | (618) ~ (all_0_46_46 = e3)
% 20.24/5.30 | (538) all_0_46_46 = e4
% 20.24/5.30 |
% 20.24/5.30 | Equations (538) can reduce 310 to:
% 20.24/5.30 | (269) $false
% 20.24/5.30 |
% 20.24/5.30 |-The branch is then unsatisfiable
% 20.24/5.30 |-Branch two:
% 20.24/5.30 | (562) ~ (all_0_43_43 = e3)
% 20.24/5.30 | (1193) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (153), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (453) all_0_50_50 = e4
% 20.24/5.30 |
% 20.24/5.30 | Combining equations (253,453) yields a new equation:
% 20.24/5.30 | (360) e4 = e2
% 20.24/5.30 |
% 20.24/5.30 | Equations (360) can reduce 230 to:
% 20.24/5.30 | (269) $false
% 20.24/5.30 |
% 20.24/5.30 |-The branch is then unsatisfiable
% 20.24/5.30 |-Branch two:
% 20.24/5.30 | (456) ~ (all_0_50_50 = e4)
% 20.24/5.30 | (457) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 20.24/5.30 |
% 20.24/5.30 | Equations (253) can reduce 456 to:
% 20.24/5.30 | (326) ~ (e4 = e2)
% 20.24/5.30 |
% 20.24/5.30 | Simplifying 326 yields:
% 20.24/5.30 | (230) ~ (e4 = e2)
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (22), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (661) all_0_43_43 = e2
% 20.24/5.30 |
% 20.24/5.30 | Equations (661) can reduce 321 to:
% 20.24/5.30 | (269) $false
% 20.24/5.30 |
% 20.24/5.30 |-The branch is then unsatisfiable
% 20.24/5.30 |-Branch two:
% 20.24/5.30 | (321) ~ (all_0_43_43 = e2)
% 20.24/5.30 | (1198) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (1198), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (433) all_0_43_43 = e0
% 20.24/5.30 |
% 20.24/5.30 | Equations (433) can reduce 3 to:
% 20.24/5.30 | (434) ~ (all_0_46_46 = e0)
% 20.24/5.30 |
% 20.24/5.30 | Simplifying 434 yields:
% 20.24/5.30 | (435) ~ (all_0_46_46 = e0)
% 20.24/5.30 |
% 20.24/5.30 | Equations (433) can reduce 137 to:
% 20.24/5.30 | (2889) ~ (all_0_51_51 = e0)
% 20.24/5.30 |
% 20.24/5.30 | Simplifying 2889 yields:
% 20.24/5.30 | (432) ~ (all_0_51_51 = e0)
% 20.24/5.30 |
% 20.24/5.30 | Equations (433) can reduce 114 to:
% 20.24/5.30 | (436) ~ (e1 = e0)
% 20.24/5.30 |
% 20.24/5.30 | Simplifying 436 yields:
% 20.24/5.30 | (144) ~ (e1 = e0)
% 20.24/5.30 |
% 20.24/5.30 +-Applying beta-rule and splitting (195), into two cases.
% 20.24/5.30 |-Branch one:
% 20.24/5.30 | (305) all_0_42_42 = e4
% 20.24/5.30 |
% 20.24/5.30 | Combining equations (305,610) yields a new equation:
% 20.24/5.30 | (515) e4 = e3
% 20.24/5.30 |
% 20.24/5.30 | Simplifying 515 yields:
% 20.24/5.30 | (516) e4 = e3
% 20.24/5.30 |
% 20.24/5.30 | Equations (516) can reduce 41 to:
% 20.24/5.30 | (269) $false
% 20.24/5.30 |
% 20.24/5.30 |-The branch is then unsatisfiable
% 20.24/5.30 |-Branch two:
% 20.24/5.30 | (2787) ~ (all_0_42_42 = e4)
% 20.24/5.30 | (2898) all_0_46_46 = e4 | all_0_54_54 = e4 | all_0_59_59 = e4
% 20.24/5.30 |
% 20.24/5.31 +-Applying beta-rule and splitting (2898), into two cases.
% 20.24/5.31 |-Branch one:
% 20.24/5.31 | (538) all_0_46_46 = e4
% 20.24/5.31 |
% 20.24/5.31 | Equations (538) can reduce 310 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (310) ~ (all_0_46_46 = e4)
% 20.24/5.31 | (2902) all_0_54_54 = e4 | all_0_59_59 = e4
% 20.24/5.31 |
% 20.24/5.31 +-Applying beta-rule and splitting (2902), into two cases.
% 20.24/5.31 |-Branch one:
% 20.24/5.31 | (535) all_0_54_54 = e4
% 20.24/5.31 |
% 20.24/5.31 | Equations (535) can reduce 62 to:
% 20.24/5.31 | (152) ~ (all_0_52_52 = e4)
% 20.24/5.31 |
% 20.24/5.31 +-Applying beta-rule and splitting (84), into two cases.
% 20.24/5.31 |-Branch one:
% 20.24/5.31 | (832) all_0_42_42 = e1
% 20.24/5.31 |
% 20.24/5.31 | Combining equations (832,610) yields a new equation:
% 20.24/5.31 | (418) e3 = e1
% 20.24/5.31 |
% 20.24/5.31 | Equations (418) can reduce 146 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (836) ~ (all_0_42_42 = e1)
% 20.24/5.31 | (837) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 20.24/5.31 |
% 20.24/5.31 +-Applying beta-rule and splitting (837), into two cases.
% 20.24/5.31 |-Branch one:
% 20.24/5.31 | (596) all_0_49_49 = e1
% 20.24/5.31 |
% 20.24/5.31 +-Applying beta-rule and splitting (815), into two cases.
% 20.24/5.31 |-Branch one:
% 20.24/5.31 | (903) all_0_48_48 = e0
% 20.24/5.31 |
% 20.24/5.31 | Equations (903) can reduce 250 to:
% 20.24/5.31 | (764) ~ (all_0_53_53 = e0)
% 20.24/5.31 |
% 20.24/5.31 | Simplifying 764 yields:
% 20.24/5.31 | (765) ~ (all_0_53_53 = e0)
% 20.24/5.31 |
% 20.24/5.31 | Equations (903) can reduce 33 to:
% 20.24/5.31 | (404) ~ (e4 = e0)
% 20.24/5.31 |
% 20.24/5.31 | Simplifying 404 yields:
% 20.24/5.31 | (11) ~ (e4 = e0)
% 20.24/5.31 |
% 20.24/5.31 +-Applying beta-rule and splitting (63), into two cases.
% 20.24/5.31 |-Branch one:
% 20.24/5.31 | (629) all_0_51_51 = e0
% 20.24/5.31 |
% 20.24/5.31 | Equations (629) can reduce 432 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (432) ~ (all_0_51_51 = e0)
% 20.24/5.31 | (1231) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 20.24/5.31 |
% 20.24/5.31 +-Applying beta-rule and splitting (1231), into two cases.
% 20.24/5.31 |-Branch one:
% 20.24/5.31 | (397) all_0_52_52 = e0
% 20.24/5.31 |
% 20.24/5.31 | Equations (397) can reduce 152 to:
% 20.24/5.31 | (404) ~ (e4 = e0)
% 20.24/5.31 |
% 20.24/5.31 | Simplifying 404 yields:
% 20.24/5.31 | (11) ~ (e4 = e0)
% 20.24/5.31 |
% 20.24/5.31 | Equations (397) can reduce 257 to:
% 20.24/5.31 | (406) ~ (e2 = e0)
% 20.24/5.31 |
% 20.24/5.31 | Simplifying 406 yields:
% 20.24/5.31 | (58) ~ (e2 = e0)
% 20.24/5.31 |
% 20.24/5.31 | Equations (397) can reduce 978 to:
% 20.24/5.31 | (436) ~ (e1 = e0)
% 20.24/5.31 |
% 20.24/5.31 | Simplifying 436 yields:
% 20.24/5.31 | (144) ~ (e1 = e0)
% 20.24/5.31 |
% 20.24/5.31 +-Applying beta-rule and splitting (206), into two cases.
% 20.24/5.31 |-Branch one:
% 20.24/5.31 | (546) all_0_46_46 = e0
% 20.24/5.31 |
% 20.24/5.31 | Equations (546) can reduce 435 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (435) ~ (all_0_46_46 = e0)
% 20.24/5.31 | (2930) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 20.24/5.31 |
% 20.24/5.31 +-Applying beta-rule and splitting (2930), into two cases.
% 20.24/5.31 |-Branch one:
% 20.24/5.31 | (965) all_0_49_49 = e0
% 20.24/5.31 |
% 20.24/5.31 | Combining equations (596,965) yields a new equation:
% 20.24/5.31 | (578) e1 = e0
% 20.24/5.31 |
% 20.24/5.31 | Simplifying 578 yields:
% 20.24/5.31 | (579) e1 = e0
% 20.24/5.31 |
% 20.24/5.31 | Equations (579) can reduce 144 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (807) ~ (all_0_49_49 = e0)
% 20.24/5.31 | (2936) all_0_54_54 = e0 | all_0_59_59 = e0
% 20.24/5.31 |
% 20.24/5.31 +-Applying beta-rule and splitting (2936), into two cases.
% 20.24/5.31 |-Branch one:
% 20.24/5.31 | (1286) all_0_54_54 = e0
% 20.24/5.31 |
% 20.24/5.31 | Combining equations (535,1286) yields a new equation:
% 20.24/5.31 | (751) e4 = e0
% 20.24/5.31 |
% 20.24/5.31 | Simplifying 751 yields:
% 20.24/5.31 | (439) e4 = e0
% 20.24/5.31 |
% 20.24/5.31 | Equations (439) can reduce 11 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (1478) ~ (all_0_54_54 = e0)
% 20.24/5.31 | (2064) all_0_59_59 = e0
% 20.24/5.31 |
% 20.24/5.31 | Combining equations (375,2064) yields a new equation:
% 20.24/5.31 | (353) e2 = e0
% 20.24/5.31 |
% 20.24/5.31 | Simplifying 353 yields:
% 20.24/5.31 | (354) e2 = e0
% 20.24/5.31 |
% 20.24/5.31 | Equations (354) can reduce 58 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (317) ~ (all_0_52_52 = e0)
% 20.24/5.31 | (1245) all_0_53_53 = e0 | all_0_54_54 = e0
% 20.24/5.31 |
% 20.24/5.31 +-Applying beta-rule and splitting (1245), into two cases.
% 20.24/5.31 |-Branch one:
% 20.24/5.31 | (857) all_0_53_53 = e0
% 20.24/5.31 |
% 20.24/5.31 | Equations (857) can reduce 765 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (765) ~ (all_0_53_53 = e0)
% 20.24/5.31 | (1286) all_0_54_54 = e0
% 20.24/5.31 |
% 20.24/5.31 | Combining equations (535,1286) yields a new equation:
% 20.24/5.31 | (751) e4 = e0
% 20.24/5.31 |
% 20.24/5.31 | Simplifying 751 yields:
% 20.24/5.31 | (439) e4 = e0
% 20.24/5.31 |
% 20.24/5.31 | Equations (439) can reduce 11 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (952) ~ (all_0_48_48 = e0)
% 20.24/5.31 | (965) all_0_49_49 = e0
% 20.24/5.31 |
% 20.24/5.31 | Combining equations (596,965) yields a new equation:
% 20.24/5.31 | (578) e1 = e0
% 20.24/5.31 |
% 20.24/5.31 | Simplifying 578 yields:
% 20.24/5.31 | (579) e1 = e0
% 20.24/5.31 |
% 20.24/5.31 | Equations (579) can reduce 144 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (960) ~ (all_0_49_49 = e1)
% 20.24/5.31 | (961) all_0_54_54 = e1 | all_0_59_59 = e1
% 20.24/5.31 |
% 20.24/5.31 +-Applying beta-rule and splitting (340), into two cases.
% 20.24/5.31 |-Branch one:
% 20.24/5.31 | (596) all_0_49_49 = e1
% 20.24/5.31 |
% 20.24/5.31 | Equations (596) can reduce 960 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (960) ~ (all_0_49_49 = e1)
% 20.24/5.31 | (965) all_0_49_49 = e0
% 20.24/5.31 |
% 20.24/5.31 | Equations (965) can reduce 960 to:
% 20.24/5.31 | (436) ~ (e1 = e0)
% 20.24/5.31 |
% 20.24/5.31 | Simplifying 436 yields:
% 20.24/5.31 | (144) ~ (e1 = e0)
% 20.24/5.31 |
% 20.24/5.31 +-Applying beta-rule and splitting (592), into two cases.
% 20.24/5.31 |-Branch one:
% 20.24/5.31 | (593) all_0_48_48 = e1
% 20.24/5.31 |
% 20.24/5.31 | Equations (593) can reduce 174 to:
% 20.24/5.31 | (481) ~ (all_0_58_58 = e1)
% 20.24/5.31 |
% 20.24/5.31 | Simplifying 481 yields:
% 20.24/5.31 | (482) ~ (all_0_58_58 = e1)
% 20.24/5.31 |
% 20.24/5.31 | Equations (593) can reduce 1115 to:
% 20.24/5.31 | (414) ~ (e2 = e1)
% 20.24/5.31 |
% 20.24/5.31 | Simplifying 414 yields:
% 20.24/5.31 | (148) ~ (e2 = e1)
% 20.24/5.31 |
% 20.24/5.31 +-Applying beta-rule and splitting (43), into two cases.
% 20.24/5.31 |-Branch one:
% 20.24/5.31 | (480) all_0_56_56 = e1
% 20.24/5.31 |
% 20.24/5.31 | Equations (480) can reduce 273 to:
% 20.24/5.31 | (826) ~ (e4 = e1)
% 20.24/5.31 |
% 20.24/5.31 | Simplifying 826 yields:
% 20.24/5.31 | (251) ~ (e4 = e1)
% 20.24/5.31 |
% 20.24/5.31 | Equations (480) can reduce 377 to:
% 20.24/5.31 | (414) ~ (e2 = e1)
% 20.24/5.31 |
% 20.24/5.31 | Simplifying 414 yields:
% 20.24/5.31 | (148) ~ (e2 = e1)
% 20.24/5.31 |
% 20.24/5.31 +-Applying beta-rule and splitting (961), into two cases.
% 20.24/5.31 |-Branch one:
% 20.24/5.31 | (1592) all_0_54_54 = e1
% 20.24/5.31 |
% 20.24/5.31 | Combining equations (535,1592) yields a new equation:
% 20.24/5.31 | (476) e4 = e1
% 20.24/5.31 |
% 20.24/5.31 | Simplifying 476 yields:
% 20.24/5.31 | (477) e4 = e1
% 20.24/5.31 |
% 20.24/5.31 | Equations (477) can reduce 251 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (1238) ~ (all_0_54_54 = e1)
% 20.24/5.31 | (614) all_0_59_59 = e1
% 20.24/5.31 |
% 20.24/5.31 | Combining equations (614,375) yields a new equation:
% 20.24/5.31 | (471) e2 = e1
% 20.24/5.31 |
% 20.24/5.31 | Equations (471) can reduce 148 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (575) ~ (all_0_56_56 = e1)
% 20.24/5.31 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 20.24/5.31 |
% 20.24/5.31 +-Applying beta-rule and splitting (576), into two cases.
% 20.24/5.31 |-Branch one:
% 20.24/5.31 | (577) all_0_57_57 = e1
% 20.24/5.31 |
% 20.24/5.31 | Equations (577) can reduce 581 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (581) ~ (all_0_57_57 = e1)
% 20.24/5.31 | (582) all_0_58_58 = e1 | all_0_59_59 = e1
% 20.24/5.31 |
% 20.24/5.31 +-Applying beta-rule and splitting (582), into two cases.
% 20.24/5.31 |-Branch one:
% 20.24/5.31 | (489) all_0_58_58 = e1
% 20.24/5.31 |
% 20.24/5.31 | Equations (489) can reduce 482 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (482) ~ (all_0_58_58 = e1)
% 20.24/5.31 | (614) all_0_59_59 = e1
% 20.24/5.31 |
% 20.24/5.31 | Combining equations (614,375) yields a new equation:
% 20.24/5.31 | (471) e2 = e1
% 20.24/5.31 |
% 20.24/5.31 | Equations (471) can reduce 148 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (584) ~ (all_0_48_48 = e1)
% 20.24/5.31 | (596) all_0_49_49 = e1
% 20.24/5.31 |
% 20.24/5.31 | Combining equations (965,596) yields a new equation:
% 20.24/5.31 | (579) e1 = e0
% 20.24/5.31 |
% 20.24/5.31 | Equations (579) can reduce 144 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (312) ~ (all_0_54_54 = e4)
% 20.24/5.31 | (2231) all_0_59_59 = e4
% 20.24/5.31 |
% 20.24/5.31 | Combining equations (2231,375) yields a new equation:
% 20.24/5.31 | (359) e4 = e2
% 20.24/5.31 |
% 20.24/5.31 | Simplifying 359 yields:
% 20.24/5.31 | (360) e4 = e2
% 20.24/5.31 |
% 20.24/5.31 | Equations (360) can reduce 230 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (459) ~ (all_0_43_43 = e0)
% 20.24/5.31 | (1695) all_0_43_43 = e4 | all_0_43_43 = e3
% 20.24/5.31 |
% 20.24/5.31 +-Applying beta-rule and splitting (1695), into two cases.
% 20.24/5.31 |-Branch one:
% 20.24/5.31 | (559) all_0_43_43 = e3
% 20.24/5.31 |
% 20.24/5.31 | Equations (559) can reduce 562 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (562) ~ (all_0_43_43 = e3)
% 20.24/5.31 | (438) all_0_43_43 = e4
% 20.24/5.31 |
% 20.24/5.31 | Equations (438) can reduce 441 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (1924) ~ (all_0_42_42 = e3)
% 20.24/5.31 | (305) all_0_42_42 = e4
% 20.24/5.31 |
% 20.24/5.31 | Equations (305) can reduce 2787 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (307) ~ (all_0_39_39 = e4)
% 20.24/5.31 | (3018) all_0_41_41 = e4 | all_0_42_42 = e4
% 20.24/5.31 |
% 20.24/5.31 +-Applying beta-rule and splitting (709), into two cases.
% 20.24/5.31 |-Branch one:
% 20.24/5.31 | (464) all_0_39_39 = e1
% 20.24/5.31 |
% 20.24/5.31 | Equations (464) can reduce 467 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (467) ~ (all_0_39_39 = e1)
% 20.24/5.31 | (1075) all_0_39_39 = e4 | all_0_39_39 = e3
% 20.24/5.31 |
% 20.24/5.31 +-Applying beta-rule and splitting (29), into two cases.
% 20.24/5.31 |-Branch one:
% 20.24/5.31 | (1079) all_0_39_39 = e4
% 20.24/5.31 |
% 20.24/5.31 | Equations (1079) can reduce 307 to:
% 20.24/5.31 | (269) $false
% 20.24/5.31 |
% 20.24/5.31 |-The branch is then unsatisfiable
% 20.24/5.31 |-Branch two:
% 20.24/5.31 | (307) ~ (all_0_39_39 = e4)
% 20.24/5.31 | (1391) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 20.24/5.31 |
% 20.24/5.31 +-Applying beta-rule and splitting (1075), into two cases.
% 20.24/5.31 |-Branch one:
% 20.24/5.31 | (443) all_0_39_39 = e3
% 20.24/5.31 |
% 20.24/5.31 | Equations (443) can reduce 157 to:
% 20.24/5.31 | (3028) ~ (all_0_42_42 = e3)
% 20.24/5.31 |
% 20.24/5.32 | Simplifying 3028 yields:
% 20.24/5.32 | (1924) ~ (all_0_42_42 = e3)
% 20.24/5.32 |
% 20.24/5.32 | Equations (443) can reduce 234 to:
% 20.24/5.32 | (1178) ~ (all_0_43_43 = e3)
% 20.24/5.32 |
% 20.24/5.32 | Simplifying 1178 yields:
% 20.24/5.32 | (562) ~ (all_0_43_43 = e3)
% 20.24/5.32 |
% 20.24/5.32 | Equations (443) can reduce 320 to:
% 20.24/5.32 | (224) ~ (e3 = e2)
% 20.24/5.32 |
% 20.24/5.32 +-Applying beta-rule and splitting (3018), into two cases.
% 20.24/5.32 |-Branch one:
% 20.24/5.32 | (740) all_0_41_41 = e4
% 20.24/5.32 |
% 20.24/5.32 | Combining equations (386,740) yields a new equation:
% 20.24/5.32 | (360) e4 = e2
% 20.24/5.32 |
% 20.24/5.32 | Equations (360) can reduce 230 to:
% 20.24/5.32 | (269) $false
% 20.24/5.32 |
% 20.24/5.32 |-The branch is then unsatisfiable
% 20.24/5.32 |-Branch two:
% 20.24/5.32 | (308) ~ (all_0_41_41 = e4)
% 20.24/5.32 | (305) all_0_42_42 = e4
% 20.24/5.32 |
% 20.24/5.32 | Equations (305) can reduce 1924 to:
% 20.24/5.32 | (41) ~ (e4 = e3)
% 20.24/5.32 |
% 20.24/5.32 | Equations (305) can reduce 836 to:
% 20.24/5.32 | (251) ~ (e4 = e1)
% 20.24/5.32 |
% 20.24/5.32 +-Applying beta-rule and splitting (162), into two cases.
% 20.24/5.32 |-Branch one:
% 20.24/5.32 | (559) all_0_43_43 = e3
% 20.24/5.32 |
% 20.24/5.32 | Equations (559) can reduce 562 to:
% 20.24/5.32 | (269) $false
% 20.24/5.32 |
% 20.24/5.32 |-The branch is then unsatisfiable
% 20.24/5.32 |-Branch two:
% 20.24/5.32 | (562) ~ (all_0_43_43 = e3)
% 20.24/5.32 | (1193) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 20.24/5.32 |
% 20.24/5.32 +-Applying beta-rule and splitting (1391), into two cases.
% 20.24/5.32 |-Branch one:
% 20.24/5.32 | (438) all_0_43_43 = e4
% 20.24/5.32 |
% 20.24/5.32 | Equations (438) can reduce 441 to:
% 20.24/5.32 | (269) $false
% 20.24/5.32 |
% 20.24/5.32 |-The branch is then unsatisfiable
% 20.24/5.32 |-Branch two:
% 20.24/5.32 | (441) ~ (all_0_43_43 = e4)
% 20.24/5.32 | (2025) all_0_51_51 = e4 | all_0_56_56 = e4
% 20.24/5.32 |
% 20.24/5.32 +-Applying beta-rule and splitting (1193), into two cases.
% 20.24/5.32 |-Branch one:
% 20.24/5.32 | (422) all_0_44_44 = e3
% 20.24/5.32 |
% 20.24/5.32 | Combining equations (341,422) yields a new equation:
% 20.24/5.32 | (423) e3 = e2
% 20.24/5.32 |
% 20.24/5.32 | Equations (423) can reduce 224 to:
% 20.24/5.32 | (269) $false
% 20.24/5.32 |
% 20.24/5.32 |-The branch is then unsatisfiable
% 20.24/5.32 |-Branch two:
% 20.24/5.32 | (425) ~ (all_0_44_44 = e3)
% 20.24/5.32 | (1203) all_0_45_45 = e3 | all_0_46_46 = e3
% 20.24/5.32 |
% 20.24/5.32 +-Applying beta-rule and splitting (1203), into two cases.
% 20.24/5.32 |-Branch one:
% 20.24/5.32 | (1087) all_0_45_45 = e3
% 20.24/5.32 |
% 20.24/5.32 | Combining equations (444,1087) yields a new equation:
% 20.24/5.32 | (515) e4 = e3
% 20.24/5.32 |
% 20.24/5.32 | Simplifying 515 yields:
% 20.24/5.32 | (516) e4 = e3
% 20.24/5.32 |
% 20.24/5.32 | Equations (516) can reduce 41 to:
% 20.24/5.32 | (269) $false
% 20.24/5.32 |
% 20.24/5.32 |-The branch is then unsatisfiable
% 20.24/5.32 |-Branch two:
% 20.24/5.32 | (689) ~ (all_0_45_45 = e3)
% 20.24/5.32 | (462) all_0_46_46 = e3
% 20.24/5.32 |
% 20.24/5.32 | Equations (462) can reduce 163 to:
% 20.24/5.32 | (146) ~ (e3 = e1)
% 20.24/5.32 |
% 20.24/5.32 +-Applying beta-rule and splitting (2025), into two cases.
% 20.24/5.32 |-Branch one:
% 20.24/5.32 | (458) all_0_51_51 = e4
% 20.24/5.32 |
% 20.24/5.32 +-Applying beta-rule and splitting (200), into two cases.
% 20.24/5.32 |-Branch one:
% 20.24/5.32 | (464) all_0_39_39 = e1
% 20.24/5.32 |
% 20.24/5.32 | Combining equations (464,443) yields a new equation:
% 20.24/5.32 | (418) e3 = e1
% 20.24/5.32 |
% 20.24/5.32 | Equations (418) can reduce 146 to:
% 20.24/5.32 | (269) $false
% 20.24/5.32 |
% 20.24/5.32 |-The branch is then unsatisfiable
% 20.24/5.32 |-Branch two:
% 20.24/5.32 | (467) ~ (all_0_39_39 = e1)
% 20.24/5.32 | (468) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 20.24/5.32 |
% 20.24/5.32 +-Applying beta-rule and splitting (468), into two cases.
% 20.24/5.32 |-Branch one:
% 20.24/5.32 | (469) all_0_47_47 = e1
% 20.24/5.32 |
% 20.24/5.32 | Combining equations (319,469) yields a new equation:
% 20.24/5.32 | (470) e2 = e1
% 20.24/5.32 |
% 20.24/5.32 | Simplifying 470 yields:
% 20.24/5.32 | (471) e2 = e1
% 20.24/5.32 |
% 20.24/5.32 | Equations (471) can reduce 148 to:
% 20.24/5.32 | (269) $false
% 20.24/5.32 |
% 20.24/5.32 |-The branch is then unsatisfiable
% 20.24/5.32 |-Branch two:
% 20.24/5.32 | (473) ~ (all_0_47_47 = e1)
% 20.24/5.32 | (474) all_0_51_51 = e1 | all_0_56_56 = e1
% 20.24/5.32 |
% 20.24/5.32 +-Applying beta-rule and splitting (474), into two cases.
% 20.24/5.32 |-Branch one:
% 20.24/5.32 | (475) all_0_51_51 = e1
% 20.24/5.32 |
% 20.24/5.32 | Combining equations (475,458) yields a new equation:
% 20.24/5.32 | (477) e4 = e1
% 20.24/5.32 |
% 20.24/5.32 | Equations (477) can reduce 251 to:
% 20.24/5.32 | (269) $false
% 20.24/5.32 |
% 20.24/5.32 |-The branch is then unsatisfiable
% 20.24/5.32 |-Branch two:
% 20.24/5.32 | (479) ~ (all_0_51_51 = e1)
% 20.24/5.32 | (480) all_0_56_56 = e1
% 20.24/5.32 |
% 20.24/5.32 | Equations (480) can reduce 227 to:
% 20.24/5.32 | (824) ~ (all_0_57_57 = e1)
% 20.24/5.32 |
% 20.24/5.32 | Simplifying 824 yields:
% 20.24/5.32 | (581) ~ (all_0_57_57 = e1)
% 20.24/5.32 |
% 20.24/5.32 +-Applying beta-rule and splitting (2627), into two cases.
% 20.24/5.32 |-Branch one:
% 20.24/5.32 | (575) ~ (all_0_56_56 = e1)
% 20.24/5.32 |
% 20.24/5.32 | Equations (480) can reduce 575 to:
% 20.24/5.32 | (269) $false
% 20.24/5.32 |
% 20.24/5.32 |-The branch is then unsatisfiable
% 20.24/5.32 |-Branch two:
% 20.24/5.32 | (480) all_0_56_56 = e1
% 20.24/5.32 | (497) all_0_58_58 = e3
% 20.24/5.32 |
% 20.24/5.32 | Equations (497) can reduce 252 to:
% 20.24/5.32 | (787) ~ (all_0_57_57 = e3)
% 20.24/5.32 |
% 20.24/5.32 +-Applying beta-rule and splitting (134), into two cases.
% 20.24/5.32 |-Branch one:
% 20.24/5.32 | (867) all_0_57_57 = e2
% 20.24/5.32 |
% 20.24/5.32 | Equations (867) can reduce 378 to:
% 20.24/5.32 | (269) $false
% 20.24/5.32 |
% 20.24/5.32 |-The branch is then unsatisfiable
% 20.24/5.32 |-Branch two:
% 20.24/5.32 | (378) ~ (all_0_57_57 = e2)
% 20.24/5.32 | (870) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 20.24/5.32 |
% 20.24/5.32 +-Applying beta-rule and splitting (870), into two cases.
% 20.24/5.32 |-Branch one:
% 20.24/5.32 | (577) all_0_57_57 = e1
% 20.24/5.32 |
% 20.24/5.32 | Equations (577) can reduce 581 to:
% 20.24/5.32 | (269) $false
% 20.24/5.32 |
% 20.24/5.32 |-The branch is then unsatisfiable
% 20.24/5.32 |-Branch two:
% 20.24/5.32 | (581) ~ (all_0_57_57 = e1)
% 20.24/5.32 | (874) all_0_57_57 = e3 | all_0_57_57 = e0
% 20.24/5.32 |
% 20.24/5.32 +-Applying beta-rule and splitting (874), into two cases.
% 20.24/5.32 |-Branch one:
% 20.24/5.32 | (400) all_0_57_57 = e0
% 20.24/5.32 |
% 20.24/5.32 | From (400) and (56) follows:
% 20.24/5.32 | (408) op(e0, e0) = all_0_20_20
% 20.24/5.32 |
% 20.24/5.32 | Instantiating formula (21) with e0, e0, all_0_20_20, e2 and discharging atoms op(e0, e0) = all_0_20_20, op(e0, e0) = e2, yields:
% 20.24/5.32 | (503) all_0_20_20 = e2
% 20.24/5.32 |
% 20.24/5.32 | Equations (503) can reduce 525 to:
% 20.24/5.32 | (269) $false
% 20.24/5.32 |
% 20.24/5.32 |-The branch is then unsatisfiable
% 20.24/5.32 |-Branch two:
% 20.24/5.32 | (967) ~ (all_0_57_57 = e0)
% 20.24/5.32 | (638) all_0_57_57 = e3
% 20.24/5.32 |
% 20.24/5.32 | Equations (638) can reduce 787 to:
% 20.24/5.32 | (269) $false
% 20.24/5.32 |
% 20.24/5.32 |-The branch is then unsatisfiable
% 20.24/5.32 |-Branch two:
% 20.24/5.32 | (530) ~ (all_0_51_51 = e4)
% 20.24/5.32 | (1658) all_0_56_56 = e4
% 20.24/5.32 |
% 20.24/5.32 | Equations (1658) can reduce 273 to:
% 20.24/5.32 | (269) $false
% 20.24/5.32 |
% 20.24/5.32 |-The branch is then unsatisfiable
% 20.24/5.32 |-Branch two:
% 20.24/5.32 | (540) ~ (all_0_39_39 = e3)
% 20.24/5.32 | (1079) all_0_39_39 = e4
% 20.24/5.32 |
% 20.24/5.32 | Equations (1079) can reduce 307 to:
% 20.24/5.32 | (269) $false
% 20.24/5.32 |
% 20.24/5.32 |-The branch is then unsatisfiable
% 20.24/5.32 |-Branch two:
% 20.24/5.32 | (942) all_0_28_28 = e0 & ~ (all_0_29_29 = e1)
% 20.24/5.32 |
% 20.24/5.32 | Applying alpha-rule on (942) yields:
% 20.24/5.32 | (943) all_0_28_28 = e0
% 20.24/5.32 | (944) ~ (all_0_29_29 = e1)
% 20.24/5.32 |
% 20.24/5.32 | From (943) and (67) follows:
% 20.24/5.32 | (3447) op(e1, all_0_58_58) = e0
% 20.24/5.32 |
% 20.24/5.32 +-Applying beta-rule and splitting (10), into two cases.
% 20.24/5.32 |-Branch one:
% 20.24/5.32 | (623) all_0_47_47 = e0
% 20.24/5.32 |
% 20.24/5.32 | Combining equations (623,319) yields a new equation:
% 20.24/5.32 | (354) e2 = e0
% 20.24/5.32 |
% 20.24/5.32 | Equations (354) can reduce 58 to:
% 20.24/5.32 | (269) $false
% 20.24/5.32 |
% 20.24/5.32 |-The branch is then unsatisfiable
% 20.24/5.32 |-Branch two:
% 20.24/5.32 | (297) ~ (all_0_47_47 = e0)
% 20.24/5.32 | (815) all_0_48_48 = e0 | all_0_49_49 = e0
% 20.24/5.32 |
% 20.24/5.32 +-Applying beta-rule and splitting (192), into two cases.
% 20.24/5.32 |-Branch one:
% 20.24/5.32 | (469) all_0_47_47 = e1
% 20.24/5.32 |
% 20.24/5.32 | Combining equations (469,319) yields a new equation:
% 20.24/5.32 | (471) e2 = e1
% 20.24/5.32 |
% 20.24/5.32 | Equations (471) can reduce 148 to:
% 20.24/5.32 | (269) $false
% 20.24/5.32 |
% 20.24/5.32 |-The branch is then unsatisfiable
% 20.24/5.32 |-Branch two:
% 20.24/5.32 | (473) ~ (all_0_47_47 = e1)
% 20.24/5.32 | (592) all_0_48_48 = e1 | all_0_49_49 = e1
% 20.24/5.32 |
% 20.24/5.32 | Equations (319) can reduce 473 to:
% 20.24/5.32 | (148) ~ (e2 = e1)
% 20.24/5.32 |
% 20.24/5.32 +-Applying beta-rule and splitting (47), into two cases.
% 20.24/5.32 |-Branch one:
% 20.24/5.32 | (348) all_0_39_39 = e2
% 20.24/5.32 |
% 20.24/5.32 | Equations (348) can reduce 320 to:
% 20.24/5.32 | (269) $false
% 20.24/5.32 |
% 20.24/5.32 |-The branch is then unsatisfiable
% 20.24/5.32 |-Branch two:
% 20.24/5.32 | (320) ~ (all_0_39_39 = e2)
% 20.24/5.32 | (709) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 20.24/5.32 |
% 20.24/5.32 +-Applying beta-rule and splitting (116), into two cases.
% 20.24/5.32 |-Branch one:
% 20.24/5.32 | (358) all_0_42_42 = e2
% 20.24/5.32 |
% 20.24/5.32 | Equations (358) can reduce 362 to:
% 20.24/5.32 | (269) $false
% 20.24/5.32 |
% 20.24/5.32 |-The branch is then unsatisfiable
% 20.24/5.32 |-Branch two:
% 20.24/5.32 | (362) ~ (all_0_42_42 = e2)
% 20.24/5.32 | (2784) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 20.24/5.32 |
% 20.24/5.32 +-Applying beta-rule and splitting (32), into two cases.
% 20.24/5.32 |-Branch one:
% 20.24/5.32 | (1079) all_0_39_39 = e4
% 20.24/5.32 |
% 20.24/5.32 | Equations (1079) can reduce 157 to:
% 20.24/5.32 | (2786) ~ (all_0_42_42 = e4)
% 20.24/5.32 |
% 20.24/5.32 | Simplifying 2786 yields:
% 20.24/5.32 | (2787) ~ (all_0_42_42 = e4)
% 20.24/5.32 |
% 20.24/5.32 | Equations (1079) can reduce 234 to:
% 20.24/5.32 | (2788) ~ (all_0_43_43 = e4)
% 20.24/5.32 |
% 20.24/5.32 | Simplifying 2788 yields:
% 20.24/5.32 | (441) ~ (all_0_43_43 = e4)
% 20.24/5.32 |
% 20.24/5.32 | Equations (1079) can reduce 126 to:
% 20.24/5.32 | (1208) ~ (all_0_51_51 = e4)
% 20.24/5.32 |
% 20.24/5.32 | Simplifying 1208 yields:
% 20.24/5.32 | (530) ~ (all_0_51_51 = e4)
% 20.24/5.32 |
% 20.24/5.32 | Equations (1079) can reduce 53 to:
% 20.24/5.32 | (272) ~ (all_0_56_56 = e4)
% 20.24/5.32 |
% 20.24/5.32 | Simplifying 272 yields:
% 20.24/5.32 | (273) ~ (all_0_56_56 = e4)
% 20.24/5.32 |
% 20.24/5.32 | Equations (1079) can reduce 320 to:
% 20.24/5.32 | (230) ~ (e4 = e2)
% 20.24/5.32 |
% 20.24/5.32 +-Applying beta-rule and splitting (2784), into two cases.
% 20.24/5.32 |-Branch one:
% 20.24/5.32 | (832) all_0_42_42 = e1
% 20.24/5.32 |
% 20.24/5.32 | Equations (832) can reduce 836 to:
% 20.24/5.32 | (269) $false
% 20.24/5.32 |
% 20.24/5.32 |-The branch is then unsatisfiable
% 20.24/5.32 |-Branch two:
% 20.24/5.32 | (836) ~ (all_0_42_42 = e1)
% 20.24/5.32 | (2798) all_0_42_42 = e4 | all_0_42_42 = e3
% 20.24/5.32 |
% 20.24/5.32 +-Applying beta-rule and splitting (2798), into two cases.
% 20.24/5.32 |-Branch one:
% 20.24/5.32 | (610) all_0_42_42 = e3
% 20.24/5.32 |
% 20.24/5.32 | Equations (610) can reduce 2787 to:
% 20.24/5.32 | (498) ~ (e4 = e3)
% 20.24/5.32 |
% 20.24/5.32 | Simplifying 498 yields:
% 20.24/5.32 | (41) ~ (e4 = e3)
% 20.24/5.32 |
% 20.24/5.32 | Equations (610) can reduce 836 to:
% 20.24/5.32 | (146) ~ (e3 = e1)
% 20.24/5.32 |
% 20.24/5.32 | From (610) and (36) follows:
% 20.24/5.32 | (2803) op(e0, e3) = all_0_30_30
% 20.24/5.32 |
% 20.24/5.32 +-Applying beta-rule and splitting (199), into two cases.
% 20.24/5.32 |-Branch one:
% 20.24/5.32 | (364) all_0_46_46 = e2
% 20.24/5.32 |
% 20.24/5.32 | Equations (364) can reduce 344 to:
% 20.24/5.32 | (269) $false
% 20.24/5.32 |
% 20.24/5.32 |-The branch is then unsatisfiable
% 20.24/5.32 |-Branch two:
% 20.24/5.32 | (344) ~ (all_0_46_46 = e2)
% 20.24/5.32 | (545) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e0
% 20.24/5.32 |
% 20.24/5.32 +-Applying beta-rule and splitting (162), into two cases.
% 20.24/5.32 |-Branch one:
% 20.24/5.32 | (559) all_0_43_43 = e3
% 20.24/5.32 |
% 20.24/5.32 | Equations (559) can reduce 3 to:
% 20.24/5.33 | (1044) ~ (all_0_46_46 = e3)
% 20.24/5.33 |
% 20.24/5.33 | Simplifying 1044 yields:
% 20.24/5.33 | (618) ~ (all_0_46_46 = e3)
% 20.24/5.33 |
% 20.24/5.33 | Equations (559) can reduce 321 to:
% 20.24/5.33 | (224) ~ (e3 = e2)
% 20.24/5.33 |
% 20.24/5.33 +-Applying beta-rule and splitting (545), into two cases.
% 20.24/5.33 |-Branch one:
% 20.24/5.33 | (546) all_0_46_46 = e0
% 20.24/5.33 |
% 20.24/5.33 | Equations (546) can reduce 166 to:
% 20.24/5.33 | (806) ~ (all_0_49_49 = e0)
% 20.24/5.33 |
% 20.24/5.33 | Simplifying 806 yields:
% 20.24/5.33 | (807) ~ (all_0_49_49 = e0)
% 20.24/5.33 |
% 20.24/5.33 | From (546) and (181) follows:
% 20.24/5.33 | (2815) op(e0, e0) = all_0_32_32
% 20.24/5.33 |
% 20.24/5.33 +-Applying beta-rule and splitting (153), into two cases.
% 20.24/5.33 |-Branch one:
% 20.24/5.33 | (453) all_0_50_50 = e4
% 20.24/5.33 |
% 20.24/5.33 | Combining equations (453,253) yields a new equation:
% 20.24/5.33 | (359) e4 = e2
% 20.24/5.33 |
% 20.24/5.33 | Simplifying 359 yields:
% 20.24/5.33 | (360) e4 = e2
% 20.24/5.33 |
% 20.24/5.33 | Equations (360) can reduce 230 to:
% 20.24/5.33 | (269) $false
% 20.24/5.33 |
% 20.24/5.33 |-The branch is then unsatisfiable
% 20.24/5.33 |-Branch two:
% 20.24/5.33 | (456) ~ (all_0_50_50 = e4)
% 20.24/5.33 | (457) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 20.24/5.33 |
% 20.24/5.33 +-Applying beta-rule and splitting (457), into two cases.
% 20.24/5.33 |-Branch one:
% 20.24/5.33 | (458) all_0_51_51 = e4
% 20.24/5.33 |
% 20.24/5.33 | Equations (458) can reduce 530 to:
% 20.24/5.33 | (269) $false
% 20.24/5.33 |
% 20.24/5.33 |-The branch is then unsatisfiable
% 20.24/5.33 |-Branch two:
% 20.24/5.33 | (530) ~ (all_0_51_51 = e4)
% 20.24/5.33 | (531) all_0_53_53 = e4 | all_0_54_54 = e4
% 20.24/5.33 |
% 20.24/5.33 +-Applying beta-rule and splitting (340), into two cases.
% 20.24/5.33 |-Branch one:
% 20.24/5.33 | (596) all_0_49_49 = e1
% 20.24/5.33 |
% 20.24/5.33 | Equations (596) can reduce 217 to:
% 20.24/5.33 | (1237) ~ (all_0_54_54 = e1)
% 20.24/5.33 |
% 20.24/5.33 | Simplifying 1237 yields:
% 20.24/5.33 | (1238) ~ (all_0_54_54 = e1)
% 20.24/5.33 |
% 20.24/5.33 | From (596) and (183) follows:
% 20.24/5.33 | (2829) op(e0, e1) = all_0_34_34
% 20.24/5.33 |
% 20.24/5.33 +-Applying beta-rule and splitting (531), into two cases.
% 20.24/5.33 |-Branch one:
% 20.24/5.33 | (532) all_0_53_53 = e4
% 20.24/5.33 |
% 20.24/5.33 | Equations (532) can reduce 448 to:
% 20.24/5.33 | (269) $false
% 20.24/5.33 |
% 20.24/5.33 |-The branch is then unsatisfiable
% 20.24/5.33 |-Branch two:
% 20.24/5.33 | (448) ~ (all_0_53_53 = e4)
% 20.24/5.33 | (535) all_0_54_54 = e4
% 20.24/5.33 |
% 20.24/5.33 | Equations (535) can reduce 1238 to:
% 20.24/5.33 | (251) ~ (e4 = e1)
% 20.24/5.33 |
% 20.24/5.33 | From (535) and (235) follows:
% 20.24/5.33 | (2835) op(e0, e4) = all_0_36_36
% 20.24/5.33 |
% 20.24/5.33 | Instantiating formula (21) with e0, e4, all_0_36_36, e4 and discharging atoms op(e0, e4) = all_0_36_36, op(e0, e4) = e4, yields:
% 20.24/5.33 | (2836) all_0_36_36 = e4
% 20.24/5.33 |
% 20.24/5.33 | Instantiating formula (21) with e0, e3, all_0_30_30, all_0_56_56 and discharging atoms op(e0, e3) = all_0_30_30, op(e0, e3) = all_0_56_56, yields:
% 20.24/5.33 | (2837) all_0_30_30 = all_0_56_56
% 20.24/5.33 |
% 20.24/5.33 | Instantiating formula (21) with e0, e1, all_0_34_34, all_0_58_58 and discharging atoms op(e0, e1) = all_0_34_34, op(e0, e1) = all_0_58_58, yields:
% 20.24/5.33 | (2838) all_0_34_34 = all_0_58_58
% 20.24/5.33 |
% 20.24/5.33 | Instantiating formula (21) with e0, e0, all_0_32_32, e2 and discharging atoms op(e0, e0) = all_0_32_32, op(e0, e0) = e2, yields:
% 20.24/5.33 | (1853) all_0_32_32 = e2
% 20.24/5.33 |
% 20.24/5.33 +-Applying beta-rule and splitting (104), into two cases.
% 20.24/5.33 |-Branch one:
% 20.24/5.33 | (1639) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0)) | (all_0_34_34 = e2 & ~ (all_0_35_35 = e0))
% 20.24/5.33 |
% 20.24/5.33 +-Applying beta-rule and splitting (1639), into two cases.
% 20.24/5.33 |-Branch one:
% 20.24/5.33 | (1640) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0))
% 20.24/5.33 |
% 20.24/5.33 +-Applying beta-rule and splitting (1640), into two cases.
% 20.24/5.33 |-Branch one:
% 20.24/5.33 | (1641) all_0_30_30 = e4 & ~ (all_0_31_31 = e0)
% 20.24/5.33 |
% 20.24/5.33 | Applying alpha-rule on (1641) yields:
% 20.24/5.33 | (1642) all_0_30_30 = e4
% 20.24/5.33 | (1643) ~ (all_0_31_31 = e0)
% 20.24/5.33 |
% 20.24/5.33 | Combining equations (1642,2837) yields a new equation:
% 20.24/5.33 | (1658) all_0_56_56 = e4
% 20.24/5.33 |
% 20.24/5.33 | Equations (1658) can reduce 273 to:
% 20.24/5.33 | (269) $false
% 20.24/5.33 |
% 20.24/5.33 |-The branch is then unsatisfiable
% 20.24/5.33 |-Branch two:
% 20.24/5.33 | (1645) all_0_32_32 = e3 & ~ (all_0_33_33 = e0)
% 20.24/5.33 |
% 20.24/5.33 | Applying alpha-rule on (1645) yields:
% 20.24/5.33 | (1646) all_0_32_32 = e3
% 20.24/5.33 | (1647) ~ (all_0_33_33 = e0)
% 20.24/5.33 |
% 20.24/5.33 | Combining equations (1853,1646) yields a new equation:
% 20.24/5.33 | (423) e3 = e2
% 20.24/5.33 |
% 20.24/5.33 | Equations (423) can reduce 224 to:
% 20.24/5.33 | (269) $false
% 20.24/5.33 |
% 20.24/5.33 |-The branch is then unsatisfiable
% 20.24/5.33 |-Branch two:
% 20.24/5.33 | (1649) all_0_34_34 = e2 & ~ (all_0_35_35 = e0)
% 20.24/5.33 |
% 20.24/5.33 | Applying alpha-rule on (1649) yields:
% 20.24/5.33 | (1650) all_0_34_34 = e2
% 20.24/5.33 | (1651) ~ (all_0_35_35 = e0)
% 20.24/5.33 |
% 20.24/5.33 | Combining equations (1650,2838) yields a new equation:
% 20.24/5.33 | (485) all_0_58_58 = e2
% 20.24/5.33 |
% 20.24/5.33 | Equations (485) can reduce 392 to:
% 20.24/5.33 | (269) $false
% 20.24/5.33 |
% 20.24/5.33 |-The branch is then unsatisfiable
% 20.24/5.33 |-Branch two:
% 20.24/5.33 | (1653) all_0_36_36 = e1 & ~ (all_0_37_37 = e0)
% 20.24/5.33 |
% 20.24/5.33 | Applying alpha-rule on (1653) yields:
% 20.24/5.33 | (1654) all_0_36_36 = e1
% 20.24/5.33 | (1655) ~ (all_0_37_37 = e0)
% 20.24/5.33 |
% 20.24/5.33 | Combining equations (2836,1654) yields a new equation:
% 20.24/5.33 | (476) e4 = e1
% 20.24/5.33 |
% 20.24/5.33 | Simplifying 476 yields:
% 20.24/5.33 | (477) e4 = e1
% 20.24/5.33 |
% 20.24/5.33 | Equations (477) can reduce 251 to:
% 20.24/5.33 | (269) $false
% 20.24/5.33 |
% 20.24/5.33 |-The branch is then unsatisfiable
% 20.24/5.33 |-Branch two:
% 20.24/5.33 | (960) ~ (all_0_49_49 = e1)
% 20.24/5.33 | (965) all_0_49_49 = e0
% 20.24/5.33 |
% 20.24/5.33 | Equations (965) can reduce 807 to:
% 20.24/5.33 | (269) $false
% 20.24/5.33 |
% 20.24/5.33 |-The branch is then unsatisfiable
% 20.24/5.33 |-Branch two:
% 20.24/5.33 | (435) ~ (all_0_46_46 = e0)
% 20.24/5.33 | (549) all_0_46_46 = e4 | all_0_46_46 = e3
% 20.24/5.33 |
% 20.24/5.33 +-Applying beta-rule and splitting (549), into two cases.
% 20.24/5.33 |-Branch one:
% 20.24/5.33 | (462) all_0_46_46 = e3
% 20.24/5.33 |
% 20.24/5.33 | Equations (462) can reduce 618 to:
% 20.24/5.33 | (269) $false
% 20.24/5.33 |
% 20.24/5.33 |-The branch is then unsatisfiable
% 20.24/5.33 |-Branch two:
% 20.24/5.33 | (618) ~ (all_0_46_46 = e3)
% 20.24/5.33 | (538) all_0_46_46 = e4
% 20.24/5.33 |
% 20.24/5.33 | Equations (538) can reduce 310 to:
% 20.24/5.33 | (269) $false
% 20.24/5.33 |
% 20.24/5.33 |-The branch is then unsatisfiable
% 20.24/5.33 |-Branch two:
% 20.24/5.33 | (562) ~ (all_0_43_43 = e3)
% 20.24/5.33 | (1193) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 20.24/5.33 |
% 20.24/5.33 +-Applying beta-rule and splitting (153), into two cases.
% 20.24/5.33 |-Branch one:
% 20.24/5.33 | (453) all_0_50_50 = e4
% 20.24/5.33 |
% 20.24/5.33 | Combining equations (253,453) yields a new equation:
% 20.24/5.33 | (360) e4 = e2
% 20.24/5.33 |
% 20.24/5.33 | Equations (360) can reduce 230 to:
% 20.24/5.33 | (269) $false
% 20.24/5.33 |
% 20.24/5.33 |-The branch is then unsatisfiable
% 20.24/5.33 |-Branch two:
% 20.24/5.33 | (456) ~ (all_0_50_50 = e4)
% 20.24/5.33 | (457) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 20.24/5.33 |
% 20.24/5.33 | Equations (253) can reduce 456 to:
% 20.24/5.33 | (326) ~ (e4 = e2)
% 20.24/5.33 |
% 20.24/5.33 | Simplifying 326 yields:
% 20.24/5.33 | (230) ~ (e4 = e2)
% 20.24/5.33 |
% 20.24/5.33 +-Applying beta-rule and splitting (22), into two cases.
% 20.24/5.33 |-Branch one:
% 20.24/5.33 | (661) all_0_43_43 = e2
% 20.24/5.33 |
% 20.24/5.33 | Equations (661) can reduce 321 to:
% 20.24/5.33 | (269) $false
% 20.24/5.33 |
% 20.24/5.33 |-The branch is then unsatisfiable
% 20.24/5.33 |-Branch two:
% 20.24/5.33 | (321) ~ (all_0_43_43 = e2)
% 20.24/5.33 | (1198) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 20.24/5.33 |
% 20.24/5.33 +-Applying beta-rule and splitting (1198), into two cases.
% 20.24/5.33 |-Branch one:
% 20.24/5.33 | (433) all_0_43_43 = e0
% 20.24/5.33 |
% 20.24/5.33 | Equations (433) can reduce 3 to:
% 20.24/5.33 | (434) ~ (all_0_46_46 = e0)
% 20.24/5.33 |
% 20.24/5.33 | Simplifying 434 yields:
% 20.24/5.33 | (435) ~ (all_0_46_46 = e0)
% 20.24/5.33 |
% 20.24/5.33 | Equations (433) can reduce 137 to:
% 20.24/5.33 | (2889) ~ (all_0_51_51 = e0)
% 20.24/5.33 |
% 20.24/5.33 | Simplifying 2889 yields:
% 20.24/5.33 | (432) ~ (all_0_51_51 = e0)
% 20.24/5.33 |
% 20.24/5.33 | Equations (433) can reduce 114 to:
% 20.24/5.33 | (436) ~ (e1 = e0)
% 20.24/5.33 |
% 20.24/5.33 | Simplifying 436 yields:
% 20.24/5.33 | (144) ~ (e1 = e0)
% 20.24/5.33 |
% 20.24/5.33 +-Applying beta-rule and splitting (195), into two cases.
% 20.24/5.33 |-Branch one:
% 20.24/5.33 | (305) all_0_42_42 = e4
% 20.24/5.33 |
% 20.24/5.33 | Combining equations (305,610) yields a new equation:
% 20.24/5.33 | (515) e4 = e3
% 20.24/5.33 |
% 20.24/5.33 | Simplifying 515 yields:
% 20.24/5.33 | (516) e4 = e3
% 20.24/5.33 |
% 20.24/5.33 | Equations (516) can reduce 41 to:
% 20.24/5.33 | (269) $false
% 20.24/5.33 |
% 20.24/5.33 |-The branch is then unsatisfiable
% 20.24/5.33 |-Branch two:
% 20.24/5.33 | (2787) ~ (all_0_42_42 = e4)
% 20.24/5.33 | (2898) all_0_46_46 = e4 | all_0_54_54 = e4 | all_0_59_59 = e4
% 20.24/5.33 |
% 20.24/5.33 +-Applying beta-rule and splitting (2898), into two cases.
% 20.24/5.33 |-Branch one:
% 20.24/5.33 | (538) all_0_46_46 = e4
% 20.24/5.33 |
% 20.24/5.33 | Equations (538) can reduce 310 to:
% 20.24/5.33 | (269) $false
% 20.24/5.33 |
% 20.24/5.33 |-The branch is then unsatisfiable
% 20.24/5.33 |-Branch two:
% 20.24/5.33 | (310) ~ (all_0_46_46 = e4)
% 20.24/5.33 | (2902) all_0_54_54 = e4 | all_0_59_59 = e4
% 20.24/5.33 |
% 20.24/5.33 +-Applying beta-rule and splitting (2902), into two cases.
% 20.24/5.33 |-Branch one:
% 20.24/5.33 | (535) all_0_54_54 = e4
% 20.24/5.33 |
% 20.24/5.33 | Equations (535) can reduce 62 to:
% 20.24/5.33 | (152) ~ (all_0_52_52 = e4)
% 20.24/5.33 |
% 20.24/5.33 +-Applying beta-rule and splitting (84), into two cases.
% 20.24/5.33 |-Branch one:
% 20.24/5.33 | (832) all_0_42_42 = e1
% 20.24/5.33 |
% 20.24/5.33 | Combining equations (832,610) yields a new equation:
% 20.24/5.33 | (418) e3 = e1
% 20.24/5.33 |
% 20.24/5.33 | Equations (418) can reduce 146 to:
% 20.24/5.33 | (269) $false
% 20.24/5.33 |
% 20.24/5.33 |-The branch is then unsatisfiable
% 20.24/5.33 |-Branch two:
% 20.24/5.33 | (836) ~ (all_0_42_42 = e1)
% 20.24/5.33 | (837) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 20.24/5.33 |
% 20.24/5.33 +-Applying beta-rule and splitting (837), into two cases.
% 20.24/5.33 |-Branch one:
% 20.24/5.33 | (596) all_0_49_49 = e1
% 20.24/5.33 |
% 20.24/5.33 +-Applying beta-rule and splitting (815), into two cases.
% 20.24/5.33 |-Branch one:
% 20.24/5.33 | (903) all_0_48_48 = e0
% 20.24/5.33 |
% 20.24/5.33 | Equations (903) can reduce 250 to:
% 20.24/5.33 | (764) ~ (all_0_53_53 = e0)
% 20.24/5.33 |
% 20.24/5.33 | Simplifying 764 yields:
% 20.24/5.33 | (765) ~ (all_0_53_53 = e0)
% 20.24/5.33 |
% 20.24/5.33 | Equations (903) can reduce 33 to:
% 20.24/5.33 | (404) ~ (e4 = e0)
% 20.24/5.33 |
% 20.24/5.33 | Simplifying 404 yields:
% 20.24/5.33 | (11) ~ (e4 = e0)
% 20.24/5.33 |
% 20.24/5.33 +-Applying beta-rule and splitting (63), into two cases.
% 20.24/5.33 |-Branch one:
% 20.24/5.33 | (629) all_0_51_51 = e0
% 20.24/5.33 |
% 20.24/5.33 | Equations (629) can reduce 432 to:
% 20.24/5.33 | (269) $false
% 20.24/5.33 |
% 20.24/5.33 |-The branch is then unsatisfiable
% 20.24/5.33 |-Branch two:
% 20.24/5.33 | (432) ~ (all_0_51_51 = e0)
% 20.24/5.33 | (1231) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 20.24/5.33 |
% 20.24/5.33 +-Applying beta-rule and splitting (1231), into two cases.
% 20.24/5.33 |-Branch one:
% 20.24/5.33 | (397) all_0_52_52 = e0
% 20.24/5.33 |
% 20.24/5.33 | Equations (397) can reduce 152 to:
% 20.24/5.33 | (404) ~ (e4 = e0)
% 20.24/5.33 |
% 20.24/5.33 | Simplifying 404 yields:
% 20.24/5.33 | (11) ~ (e4 = e0)
% 20.24/5.33 |
% 20.24/5.33 | Equations (397) can reduce 257 to:
% 20.24/5.33 | (406) ~ (e2 = e0)
% 20.24/5.33 |
% 20.24/5.33 | Simplifying 406 yields:
% 20.24/5.33 | (58) ~ (e2 = e0)
% 20.24/5.33 |
% 20.24/5.33 | Equations (397) can reduce 978 to:
% 20.24/5.33 | (436) ~ (e1 = e0)
% 20.24/5.33 |
% 20.24/5.33 | Simplifying 436 yields:
% 20.24/5.33 | (144) ~ (e1 = e0)
% 20.24/5.33 |
% 20.24/5.33 +-Applying beta-rule and splitting (206), into two cases.
% 20.24/5.33 |-Branch one:
% 20.24/5.33 | (546) all_0_46_46 = e0
% 20.24/5.33 |
% 20.24/5.33 | Equations (546) can reduce 435 to:
% 20.24/5.33 | (269) $false
% 20.24/5.33 |
% 20.24/5.33 |-The branch is then unsatisfiable
% 20.24/5.33 |-Branch two:
% 20.24/5.33 | (435) ~ (all_0_46_46 = e0)
% 20.24/5.34 | (2930) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 20.24/5.34 |
% 20.24/5.34 +-Applying beta-rule and splitting (2930), into two cases.
% 20.24/5.34 |-Branch one:
% 20.24/5.34 | (965) all_0_49_49 = e0
% 20.24/5.34 |
% 20.24/5.34 | Combining equations (596,965) yields a new equation:
% 20.24/5.34 | (578) e1 = e0
% 20.24/5.34 |
% 20.24/5.34 | Simplifying 578 yields:
% 20.24/5.34 | (579) e1 = e0
% 20.24/5.34 |
% 20.24/5.34 | Equations (579) can reduce 144 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (807) ~ (all_0_49_49 = e0)
% 20.24/5.34 | (2936) all_0_54_54 = e0 | all_0_59_59 = e0
% 20.24/5.34 |
% 20.24/5.34 +-Applying beta-rule and splitting (2936), into two cases.
% 20.24/5.34 |-Branch one:
% 20.24/5.34 | (1286) all_0_54_54 = e0
% 20.24/5.34 |
% 20.24/5.34 | Combining equations (535,1286) yields a new equation:
% 20.24/5.34 | (751) e4 = e0
% 20.24/5.34 |
% 20.24/5.34 | Simplifying 751 yields:
% 20.24/5.34 | (439) e4 = e0
% 20.24/5.34 |
% 20.24/5.34 | Equations (439) can reduce 11 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (1478) ~ (all_0_54_54 = e0)
% 20.24/5.34 | (2064) all_0_59_59 = e0
% 20.24/5.34 |
% 20.24/5.34 | Combining equations (375,2064) yields a new equation:
% 20.24/5.34 | (353) e2 = e0
% 20.24/5.34 |
% 20.24/5.34 | Simplifying 353 yields:
% 20.24/5.34 | (354) e2 = e0
% 20.24/5.34 |
% 20.24/5.34 | Equations (354) can reduce 58 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (317) ~ (all_0_52_52 = e0)
% 20.24/5.34 | (1245) all_0_53_53 = e0 | all_0_54_54 = e0
% 20.24/5.34 |
% 20.24/5.34 +-Applying beta-rule and splitting (1245), into two cases.
% 20.24/5.34 |-Branch one:
% 20.24/5.34 | (857) all_0_53_53 = e0
% 20.24/5.34 |
% 20.24/5.34 | Equations (857) can reduce 765 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (765) ~ (all_0_53_53 = e0)
% 20.24/5.34 | (1286) all_0_54_54 = e0
% 20.24/5.34 |
% 20.24/5.34 | Combining equations (535,1286) yields a new equation:
% 20.24/5.34 | (751) e4 = e0
% 20.24/5.34 |
% 20.24/5.34 | Simplifying 751 yields:
% 20.24/5.34 | (439) e4 = e0
% 20.24/5.34 |
% 20.24/5.34 | Equations (439) can reduce 11 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (952) ~ (all_0_48_48 = e0)
% 20.24/5.34 | (965) all_0_49_49 = e0
% 20.24/5.34 |
% 20.24/5.34 | Combining equations (596,965) yields a new equation:
% 20.24/5.34 | (578) e1 = e0
% 20.24/5.34 |
% 20.24/5.34 | Simplifying 578 yields:
% 20.24/5.34 | (579) e1 = e0
% 20.24/5.34 |
% 20.24/5.34 | Equations (579) can reduce 144 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (960) ~ (all_0_49_49 = e1)
% 20.24/5.34 | (961) all_0_54_54 = e1 | all_0_59_59 = e1
% 20.24/5.34 |
% 20.24/5.34 +-Applying beta-rule and splitting (340), into two cases.
% 20.24/5.34 |-Branch one:
% 20.24/5.34 | (596) all_0_49_49 = e1
% 20.24/5.34 |
% 20.24/5.34 | Equations (596) can reduce 960 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (960) ~ (all_0_49_49 = e1)
% 20.24/5.34 | (965) all_0_49_49 = e0
% 20.24/5.34 |
% 20.24/5.34 | Equations (965) can reduce 960 to:
% 20.24/5.34 | (436) ~ (e1 = e0)
% 20.24/5.34 |
% 20.24/5.34 | Simplifying 436 yields:
% 20.24/5.34 | (144) ~ (e1 = e0)
% 20.24/5.34 |
% 20.24/5.34 +-Applying beta-rule and splitting (592), into two cases.
% 20.24/5.34 |-Branch one:
% 20.24/5.34 | (593) all_0_48_48 = e1
% 20.24/5.34 |
% 20.24/5.34 | Equations (593) can reduce 174 to:
% 20.24/5.34 | (481) ~ (all_0_58_58 = e1)
% 20.24/5.34 |
% 20.24/5.34 | Simplifying 481 yields:
% 20.24/5.34 | (482) ~ (all_0_58_58 = e1)
% 20.24/5.34 |
% 20.24/5.34 | Equations (593) can reduce 1115 to:
% 20.24/5.34 | (414) ~ (e2 = e1)
% 20.24/5.34 |
% 20.24/5.34 | Simplifying 414 yields:
% 20.24/5.34 | (148) ~ (e2 = e1)
% 20.24/5.34 |
% 20.24/5.34 +-Applying beta-rule and splitting (43), into two cases.
% 20.24/5.34 |-Branch one:
% 20.24/5.34 | (480) all_0_56_56 = e1
% 20.24/5.34 |
% 20.24/5.34 | Equations (480) can reduce 273 to:
% 20.24/5.34 | (826) ~ (e4 = e1)
% 20.24/5.34 |
% 20.24/5.34 | Simplifying 826 yields:
% 20.24/5.34 | (251) ~ (e4 = e1)
% 20.24/5.34 |
% 20.24/5.34 | Equations (480) can reduce 377 to:
% 20.24/5.34 | (414) ~ (e2 = e1)
% 20.24/5.34 |
% 20.24/5.34 | Simplifying 414 yields:
% 20.24/5.34 | (148) ~ (e2 = e1)
% 20.24/5.34 |
% 20.24/5.34 +-Applying beta-rule and splitting (961), into two cases.
% 20.24/5.34 |-Branch one:
% 20.24/5.34 | (1592) all_0_54_54 = e1
% 20.24/5.34 |
% 20.24/5.34 | Combining equations (535,1592) yields a new equation:
% 20.24/5.34 | (476) e4 = e1
% 20.24/5.34 |
% 20.24/5.34 | Simplifying 476 yields:
% 20.24/5.34 | (477) e4 = e1
% 20.24/5.34 |
% 20.24/5.34 | Equations (477) can reduce 251 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (1238) ~ (all_0_54_54 = e1)
% 20.24/5.34 | (614) all_0_59_59 = e1
% 20.24/5.34 |
% 20.24/5.34 | Combining equations (614,375) yields a new equation:
% 20.24/5.34 | (471) e2 = e1
% 20.24/5.34 |
% 20.24/5.34 | Equations (471) can reduce 148 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (575) ~ (all_0_56_56 = e1)
% 20.24/5.34 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 20.24/5.34 |
% 20.24/5.34 +-Applying beta-rule and splitting (576), into two cases.
% 20.24/5.34 |-Branch one:
% 20.24/5.34 | (577) all_0_57_57 = e1
% 20.24/5.34 |
% 20.24/5.34 | Equations (577) can reduce 581 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (581) ~ (all_0_57_57 = e1)
% 20.24/5.34 | (582) all_0_58_58 = e1 | all_0_59_59 = e1
% 20.24/5.34 |
% 20.24/5.34 +-Applying beta-rule and splitting (582), into two cases.
% 20.24/5.34 |-Branch one:
% 20.24/5.34 | (489) all_0_58_58 = e1
% 20.24/5.34 |
% 20.24/5.34 | Equations (489) can reduce 482 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (482) ~ (all_0_58_58 = e1)
% 20.24/5.34 | (614) all_0_59_59 = e1
% 20.24/5.34 |
% 20.24/5.34 | Combining equations (614,375) yields a new equation:
% 20.24/5.34 | (471) e2 = e1
% 20.24/5.34 |
% 20.24/5.34 | Equations (471) can reduce 148 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (584) ~ (all_0_48_48 = e1)
% 20.24/5.34 | (596) all_0_49_49 = e1
% 20.24/5.34 |
% 20.24/5.34 | Combining equations (965,596) yields a new equation:
% 20.24/5.34 | (579) e1 = e0
% 20.24/5.34 |
% 20.24/5.34 | Equations (579) can reduce 144 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (312) ~ (all_0_54_54 = e4)
% 20.24/5.34 | (2231) all_0_59_59 = e4
% 20.24/5.34 |
% 20.24/5.34 | Combining equations (2231,375) yields a new equation:
% 20.24/5.34 | (359) e4 = e2
% 20.24/5.34 |
% 20.24/5.34 | Simplifying 359 yields:
% 20.24/5.34 | (360) e4 = e2
% 20.24/5.34 |
% 20.24/5.34 | Equations (360) can reduce 230 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (459) ~ (all_0_43_43 = e0)
% 20.24/5.34 | (1695) all_0_43_43 = e4 | all_0_43_43 = e3
% 20.24/5.34 |
% 20.24/5.34 +-Applying beta-rule and splitting (1695), into two cases.
% 20.24/5.34 |-Branch one:
% 20.24/5.34 | (559) all_0_43_43 = e3
% 20.24/5.34 |
% 20.24/5.34 | Equations (559) can reduce 562 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (562) ~ (all_0_43_43 = e3)
% 20.24/5.34 | (438) all_0_43_43 = e4
% 20.24/5.34 |
% 20.24/5.34 | Equations (438) can reduce 441 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (1924) ~ (all_0_42_42 = e3)
% 20.24/5.34 | (305) all_0_42_42 = e4
% 20.24/5.34 |
% 20.24/5.34 | Equations (305) can reduce 2787 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (307) ~ (all_0_39_39 = e4)
% 20.24/5.34 | (3018) all_0_41_41 = e4 | all_0_42_42 = e4
% 20.24/5.34 |
% 20.24/5.34 +-Applying beta-rule and splitting (709), into two cases.
% 20.24/5.34 |-Branch one:
% 20.24/5.34 | (464) all_0_39_39 = e1
% 20.24/5.34 |
% 20.24/5.34 | Equations (464) can reduce 467 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (467) ~ (all_0_39_39 = e1)
% 20.24/5.34 | (1075) all_0_39_39 = e4 | all_0_39_39 = e3
% 20.24/5.34 |
% 20.24/5.34 +-Applying beta-rule and splitting (29), into two cases.
% 20.24/5.34 |-Branch one:
% 20.24/5.34 | (1079) all_0_39_39 = e4
% 20.24/5.34 |
% 20.24/5.34 | Equations (1079) can reduce 307 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (307) ~ (all_0_39_39 = e4)
% 20.24/5.34 | (1391) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 20.24/5.34 |
% 20.24/5.34 +-Applying beta-rule and splitting (1075), into two cases.
% 20.24/5.34 |-Branch one:
% 20.24/5.34 | (443) all_0_39_39 = e3
% 20.24/5.34 |
% 20.24/5.34 | Equations (443) can reduce 157 to:
% 20.24/5.34 | (3028) ~ (all_0_42_42 = e3)
% 20.24/5.34 |
% 20.24/5.34 | Simplifying 3028 yields:
% 20.24/5.34 | (1924) ~ (all_0_42_42 = e3)
% 20.24/5.34 |
% 20.24/5.34 | Equations (443) can reduce 234 to:
% 20.24/5.34 | (1178) ~ (all_0_43_43 = e3)
% 20.24/5.34 |
% 20.24/5.34 | Simplifying 1178 yields:
% 20.24/5.34 | (562) ~ (all_0_43_43 = e3)
% 20.24/5.34 |
% 20.24/5.34 | Equations (443) can reduce 320 to:
% 20.24/5.34 | (224) ~ (e3 = e2)
% 20.24/5.34 |
% 20.24/5.34 +-Applying beta-rule and splitting (3018), into two cases.
% 20.24/5.34 |-Branch one:
% 20.24/5.34 | (740) all_0_41_41 = e4
% 20.24/5.34 |
% 20.24/5.34 | Combining equations (386,740) yields a new equation:
% 20.24/5.34 | (360) e4 = e2
% 20.24/5.34 |
% 20.24/5.34 | Equations (360) can reduce 230 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (308) ~ (all_0_41_41 = e4)
% 20.24/5.34 | (305) all_0_42_42 = e4
% 20.24/5.34 |
% 20.24/5.34 | Equations (305) can reduce 1924 to:
% 20.24/5.34 | (41) ~ (e4 = e3)
% 20.24/5.34 |
% 20.24/5.34 | Equations (305) can reduce 836 to:
% 20.24/5.34 | (251) ~ (e4 = e1)
% 20.24/5.34 |
% 20.24/5.34 +-Applying beta-rule and splitting (162), into two cases.
% 20.24/5.34 |-Branch one:
% 20.24/5.34 | (559) all_0_43_43 = e3
% 20.24/5.34 |
% 20.24/5.34 | Equations (559) can reduce 562 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (562) ~ (all_0_43_43 = e3)
% 20.24/5.34 | (1193) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 20.24/5.34 |
% 20.24/5.34 +-Applying beta-rule and splitting (1391), into two cases.
% 20.24/5.34 |-Branch one:
% 20.24/5.34 | (438) all_0_43_43 = e4
% 20.24/5.34 |
% 20.24/5.34 | Equations (438) can reduce 441 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (441) ~ (all_0_43_43 = e4)
% 20.24/5.34 | (2025) all_0_51_51 = e4 | all_0_56_56 = e4
% 20.24/5.34 |
% 20.24/5.34 +-Applying beta-rule and splitting (1193), into two cases.
% 20.24/5.34 |-Branch one:
% 20.24/5.34 | (422) all_0_44_44 = e3
% 20.24/5.34 |
% 20.24/5.34 | Combining equations (341,422) yields a new equation:
% 20.24/5.34 | (423) e3 = e2
% 20.24/5.34 |
% 20.24/5.34 | Equations (423) can reduce 224 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (425) ~ (all_0_44_44 = e3)
% 20.24/5.34 | (1203) all_0_45_45 = e3 | all_0_46_46 = e3
% 20.24/5.34 |
% 20.24/5.34 +-Applying beta-rule and splitting (1203), into two cases.
% 20.24/5.34 |-Branch one:
% 20.24/5.34 | (1087) all_0_45_45 = e3
% 20.24/5.34 |
% 20.24/5.34 | Combining equations (444,1087) yields a new equation:
% 20.24/5.34 | (515) e4 = e3
% 20.24/5.34 |
% 20.24/5.34 | Simplifying 515 yields:
% 20.24/5.34 | (516) e4 = e3
% 20.24/5.34 |
% 20.24/5.34 | Equations (516) can reduce 41 to:
% 20.24/5.34 | (269) $false
% 20.24/5.34 |
% 20.24/5.34 |-The branch is then unsatisfiable
% 20.24/5.34 |-Branch two:
% 20.24/5.34 | (689) ~ (all_0_45_45 = e3)
% 20.24/5.34 | (462) all_0_46_46 = e3
% 20.24/5.34 |
% 20.24/5.34 | Equations (462) can reduce 163 to:
% 20.24/5.34 | (146) ~ (e3 = e1)
% 20.24/5.34 |
% 20.24/5.34 +-Applying beta-rule and splitting (2025), into two cases.
% 20.24/5.34 |-Branch one:
% 20.24/5.34 | (458) all_0_51_51 = e4
% 20.24/5.34 |
% 20.24/5.34 | From (458) and (175) follows:
% 20.24/5.34 | (3743) op(e1, e3) = e4
% 20.24/5.34 |
% 20.24/5.34 +-Applying beta-rule and splitting (200), into two cases.
% 20.24/5.34 |-Branch one:
% 20.24/5.34 | (464) all_0_39_39 = e1
% 20.24/5.34 |
% 20.24/5.35 | Combining equations (464,443) yields a new equation:
% 20.24/5.35 | (418) e3 = e1
% 20.24/5.35 |
% 20.24/5.35 | Equations (418) can reduce 146 to:
% 20.24/5.35 | (269) $false
% 20.24/5.35 |
% 20.24/5.35 |-The branch is then unsatisfiable
% 20.24/5.35 |-Branch two:
% 20.24/5.35 | (467) ~ (all_0_39_39 = e1)
% 20.24/5.35 | (468) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 20.24/5.35 |
% 20.24/5.35 +-Applying beta-rule and splitting (468), into two cases.
% 20.24/5.35 |-Branch one:
% 20.24/5.35 | (469) all_0_47_47 = e1
% 20.24/5.35 |
% 20.24/5.35 | Combining equations (319,469) yields a new equation:
% 20.24/5.35 | (470) e2 = e1
% 20.24/5.35 |
% 20.24/5.35 | Simplifying 470 yields:
% 20.24/5.35 | (471) e2 = e1
% 20.24/5.35 |
% 20.24/5.35 | Equations (471) can reduce 148 to:
% 20.24/5.35 | (269) $false
% 20.24/5.35 |
% 20.24/5.35 |-The branch is then unsatisfiable
% 20.24/5.35 |-Branch two:
% 20.24/5.35 | (473) ~ (all_0_47_47 = e1)
% 20.24/5.35 | (474) all_0_51_51 = e1 | all_0_56_56 = e1
% 20.24/5.35 |
% 20.24/5.35 +-Applying beta-rule and splitting (474), into two cases.
% 20.24/5.35 |-Branch one:
% 20.24/5.35 | (475) all_0_51_51 = e1
% 20.24/5.35 |
% 20.24/5.35 | Combining equations (475,458) yields a new equation:
% 20.24/5.35 | (477) e4 = e1
% 20.24/5.35 |
% 20.24/5.35 | Equations (477) can reduce 251 to:
% 20.24/5.35 | (269) $false
% 20.24/5.35 |
% 20.24/5.35 |-The branch is then unsatisfiable
% 20.24/5.35 |-Branch two:
% 20.24/5.35 | (479) ~ (all_0_51_51 = e1)
% 20.24/5.35 | (480) all_0_56_56 = e1
% 20.24/5.35 |
% 20.24/5.35 | Equations (480) can reduce 227 to:
% 20.24/5.35 | (824) ~ (all_0_57_57 = e1)
% 20.24/5.35 |
% 20.24/5.35 | Simplifying 824 yields:
% 20.24/5.35 | (581) ~ (all_0_57_57 = e1)
% 20.24/5.35 |
% 20.24/5.35 +-Applying beta-rule and splitting (2627), into two cases.
% 20.24/5.35 |-Branch one:
% 20.24/5.35 | (575) ~ (all_0_56_56 = e1)
% 20.24/5.35 |
% 20.24/5.35 | Equations (480) can reduce 575 to:
% 20.24/5.35 | (269) $false
% 20.24/5.35 |
% 20.24/5.35 |-The branch is then unsatisfiable
% 20.24/5.35 |-Branch two:
% 20.24/5.35 | (480) all_0_56_56 = e1
% 20.24/5.35 | (497) all_0_58_58 = e3
% 20.24/5.35 |
% 20.24/5.35 | Equations (497) can reduce 252 to:
% 20.24/5.35 | (787) ~ (all_0_57_57 = e3)
% 20.24/5.35 |
% 20.24/5.35 | From (497) and (3447) follows:
% 20.24/5.35 | (767) op(e1, e3) = e0
% 20.24/5.35 |
% 20.24/5.35 +-Applying beta-rule and splitting (134), into two cases.
% 20.24/5.35 |-Branch one:
% 20.24/5.35 | (867) all_0_57_57 = e2
% 20.24/5.35 |
% 20.24/5.35 | Equations (867) can reduce 378 to:
% 20.24/5.35 | (269) $false
% 20.24/5.35 |
% 20.24/5.35 |-The branch is then unsatisfiable
% 20.24/5.35 |-Branch two:
% 20.24/5.35 | (378) ~ (all_0_57_57 = e2)
% 20.24/5.35 | (870) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 20.24/5.35 |
% 20.24/5.35 +-Applying beta-rule and splitting (870), into two cases.
% 20.24/5.35 |-Branch one:
% 20.24/5.35 | (577) all_0_57_57 = e1
% 20.24/5.35 |
% 20.24/5.35 | Equations (577) can reduce 581 to:
% 20.24/5.35 | (269) $false
% 20.24/5.35 |
% 20.24/5.35 |-The branch is then unsatisfiable
% 20.24/5.35 |-Branch two:
% 20.24/5.35 | (581) ~ (all_0_57_57 = e1)
% 20.24/5.35 | (874) all_0_57_57 = e3 | all_0_57_57 = e0
% 20.24/5.35 |
% 20.24/5.35 +-Applying beta-rule and splitting (874), into two cases.
% 20.24/5.35 |-Branch one:
% 20.24/5.35 | (400) all_0_57_57 = e0
% 20.24/5.35 |
% 20.24/5.35 | Equations (400) can reduce 173 to:
% 20.24/5.35 | (404) ~ (e4 = e0)
% 20.24/5.35 |
% 20.24/5.35 | Simplifying 404 yields:
% 20.24/5.35 | (11) ~ (e4 = e0)
% 20.24/5.35 |
% 20.24/5.35 | Instantiating formula (21) with e1, e3, e0, e4 and discharging atoms op(e1, e3) = e4, op(e1, e3) = e0, yields:
% 20.24/5.35 | (439) e4 = e0
% 20.24/5.35 |
% 20.24/5.35 | Equations (439) can reduce 11 to:
% 20.24/5.35 | (269) $false
% 20.24/5.35 |
% 20.24/5.35 |-The branch is then unsatisfiable
% 20.24/5.35 |-Branch two:
% 20.24/5.35 | (967) ~ (all_0_57_57 = e0)
% 20.24/5.35 | (638) all_0_57_57 = e3
% 20.24/5.35 |
% 20.24/5.35 | Equations (638) can reduce 787 to:
% 20.24/5.35 | (269) $false
% 20.24/5.35 |
% 20.24/5.35 |-The branch is then unsatisfiable
% 20.24/5.35 |-Branch two:
% 20.24/5.35 | (530) ~ (all_0_51_51 = e4)
% 20.24/5.35 | (1658) all_0_56_56 = e4
% 20.24/5.35 |
% 20.24/5.35 | Equations (1658) can reduce 273 to:
% 20.24/5.35 | (269) $false
% 20.24/5.35 |
% 20.24/5.35 |-The branch is then unsatisfiable
% 20.24/5.35 |-Branch two:
% 20.24/5.35 | (540) ~ (all_0_39_39 = e3)
% 20.24/5.35 | (1079) all_0_39_39 = e4
% 20.24/5.35 |
% 20.24/5.35 | Equations (1079) can reduce 307 to:
% 20.24/5.35 | (269) $false
% 20.24/5.35 |
% 20.24/5.35 |-The branch is then unsatisfiable
% 20.24/5.35 |-Branch two:
% 20.24/5.35 | (659) ~ (all_0_44_44 = e2)
% 20.24/5.35 | (660) all_0_44_44 = e3 | all_0_44_44 = e0
% 20.24/5.35 |
% 20.24/5.35 +-Applying beta-rule and splitting (664), into two cases.
% 20.24/5.35 |-Branch one:
% 20.24/5.35 | (341) all_0_44_44 = e2
% 20.24/5.35 |
% 20.24/5.35 | Equations (341) can reduce 659 to:
% 20.24/5.35 | (269) $false
% 20.24/5.35 |
% 20.24/5.35 |-The branch is then unsatisfiable
% 20.24/5.35 |-Branch two:
% 20.24/5.35 | (659) ~ (all_0_44_44 = e2)
% 20.24/5.35 | (1120) all_0_45_45 = e2 | all_0_46_46 = e2
% 20.24/5.35 |
% 20.24/5.35 +-Applying beta-rule and splitting (1120), into two cases.
% 20.24/5.35 |-Branch one:
% 20.24/5.35 | (694) all_0_45_45 = e2
% 20.24/5.35 |
% 20.24/5.35 | Combining equations (444,694) yields a new equation:
% 20.24/5.35 | (359) e4 = e2
% 20.24/5.35 |
% 20.24/5.35 | Simplifying 359 yields:
% 20.24/5.35 | (360) e4 = e2
% 20.24/5.35 |
% 20.24/5.35 | Equations (360) can reduce 230 to:
% 20.24/5.35 | (269) $false
% 20.24/5.35 |
% 20.24/5.35 |-The branch is then unsatisfiable
% 20.24/5.35 |-Branch two:
% 20.24/5.35 | (390) ~ (all_0_45_45 = e2)
% 20.24/5.35 | (364) all_0_46_46 = e2
% 20.24/5.35 |
% 20.24/5.35 | Equations (364) can reduce 107 to:
% 20.24/5.35 | (362) ~ (all_0_42_42 = e2)
% 20.24/5.35 |
% 20.24/5.35 | Equations (364) can reduce 3 to:
% 20.24/5.35 | (321) ~ (all_0_43_43 = e2)
% 20.24/5.35 |
% 20.24/5.35 | Equations (364) can reduce 150 to:
% 20.24/5.35 | (1842) ~ (all_0_59_59 = e2)
% 20.24/5.35 |
% 20.24/5.35 | Simplifying 1842 yields:
% 20.24/5.35 | (1843) ~ (all_0_59_59 = e2)
% 20.24/5.35 |
% 20.24/5.35 | Equations (364) can reduce 310 to:
% 20.24/5.35 | (326) ~ (e4 = e2)
% 20.24/5.35 |
% 20.24/5.35 | Simplifying 326 yields:
% 20.24/5.35 | (230) ~ (e4 = e2)
% 20.24/5.35 |
% 20.24/5.35 | From (364) and (181) follows:
% 20.24/5.35 | (1848) op(e0, e2) = all_0_32_32
% 20.24/5.35 |
% 20.24/5.35 +-Applying beta-rule and splitting (28), into two cases.
% 20.24/5.35 |-Branch one:
% 20.24/5.35 | (268) all_0_55_55 = e2
% 20.24/5.35 |
% 20.24/5.35 | Combining equations (268,271) yields a new equation:
% 20.24/5.35 | (360) e4 = e2
% 20.24/5.35 |
% 20.24/5.35 | Equations (360) can reduce 230 to:
% 20.24/5.35 | (269) $false
% 20.24/5.35 |
% 20.24/5.35 |-The branch is then unsatisfiable
% 20.24/5.35 |-Branch two:
% 20.24/5.35 | (263) ~ (all_0_55_55 = e2)
% 20.24/5.35 | (2726) all_0_56_56 = e2 | all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 20.24/5.35 |
% 20.24/5.35 +-Applying beta-rule and splitting (2726), into two cases.
% 20.24/5.35 |-Branch one:
% 20.24/5.35 | (1575) all_0_56_56 = e2
% 20.24/5.35 |
% 20.24/5.35 | Equations (1575) can reduce 377 to:
% 20.24/5.35 | (269) $false
% 20.24/5.35 |
% 20.24/5.35 |-The branch is then unsatisfiable
% 20.24/5.35 |-Branch two:
% 20.24/5.35 | (377) ~ (all_0_56_56 = e2)
% 20.24/5.35 | (2730) all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 20.24/5.35 |
% 20.24/5.35 +-Applying beta-rule and splitting (2730), into two cases.
% 20.24/5.35 |-Branch one:
% 20.24/5.35 | (867) all_0_57_57 = e2
% 20.24/5.35 |
% 20.24/5.35 | Equations (867) can reduce 240 to:
% 20.24/5.35 | (659) ~ (all_0_44_44 = e2)
% 20.24/5.35 |
% 20.24/5.35 | Equations (867) can reduce 124 to:
% 20.24/5.35 | (257) ~ (all_0_52_52 = e2)
% 20.24/5.35 |
% 20.24/5.35 | Equations (867) can reduce 227 to:
% 20.24/5.35 | (377) ~ (all_0_56_56 = e2)
% 20.24/5.35 |
% 20.24/5.35 | Equations (867) can reduce 252 to:
% 20.24/5.35 | (391) ~ (all_0_58_58 = e2)
% 20.24/5.35 |
% 20.24/5.35 | Simplifying 391 yields:
% 20.24/5.35 | (392) ~ (all_0_58_58 = e2)
% 20.24/5.35 |
% 20.24/5.35 | Equations (867) can reduce 173 to:
% 20.24/5.35 | (326) ~ (e4 = e2)
% 20.24/5.35 |
% 20.24/5.35 | Simplifying 326 yields:
% 20.24/5.35 | (230) ~ (e4 = e2)
% 20.24/5.35 |
% 20.24/5.35 | Equations (867) can reduce 581 to:
% 20.24/5.35 | (148) ~ (e2 = e1)
% 20.24/5.35 |
% 20.24/5.35 | From (867) and (244) follows:
% 20.24/5.35 | (1812) op(e2, e2) = all_0_19_19
% 20.24/5.35 |
% 20.24/5.35 | From (867) and (56) follows:
% 20.24/5.35 | (1813) op(e0, e2) = all_0_20_20
% 20.24/5.35 |
% 20.24/5.35 | From (867) and (241) follows:
% 20.24/5.35 | (1814) op(e0, e2) = e2
% 20.24/5.35 |
% 20.24/5.35 | Instantiating formula (21) with e2, e2, all_0_19_19, e4 and discharging atoms op(e2, e2) = all_0_19_19, op(e2, e2) = e4, yields:
% 20.24/5.35 | (1849) all_0_19_19 = e4
% 20.24/5.35 |
% 20.24/5.35 | Instantiating formula (21) with e0, e2, all_0_32_32, all_0_20_20 and discharging atoms op(e0, e2) = all_0_20_20, op(e0, e2) = all_0_32_32, yields:
% 20.24/5.35 | (1851) all_0_20_20 = all_0_32_32
% 20.24/5.35 |
% 20.24/5.35 | Instantiating formula (21) with e0, e2, e2, all_0_20_20 and discharging atoms op(e0, e2) = all_0_20_20, op(e0, e2) = e2, yields:
% 20.24/5.35 | (503) all_0_20_20 = e2
% 20.24/5.35 |
% 20.24/5.35 | Combining equations (1851,503) yields a new equation:
% 20.24/5.35 | (3833) all_0_32_32 = e2
% 20.24/5.35 |
% 20.24/5.35 | Simplifying 3833 yields:
% 20.24/5.35 | (1853) all_0_32_32 = e2
% 20.24/5.35 |
% 20.24/5.35 +-Applying beta-rule and splitting (133), into two cases.
% 20.24/5.35 |-Branch one:
% 20.24/5.35 | (504) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 20.24/5.35 |
% 20.24/5.35 +-Applying beta-rule and splitting (504), into two cases.
% 20.24/5.35 |-Branch one:
% 20.24/5.35 | (505) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 20.24/5.35 |
% 20.24/5.35 +-Applying beta-rule and splitting (505), into two cases.
% 20.24/5.35 |-Branch one:
% 20.24/5.35 | (506) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 20.24/5.35 |
% 20.24/5.35 | Applying alpha-rule on (506) yields:
% 20.24/5.35 | (507) all_0_13_13 = e4
% 20.24/5.35 | (508) ~ (all_0_14_14 = e2)
% 20.24/5.35 |
% 20.24/5.35 | Combining equations (502,507) yields a new equation:
% 20.24/5.35 | (509) all_0_48_48 = e4
% 20.24/5.35 |
% 20.24/5.35 | Simplifying 509 yields:
% 20.24/5.35 | (510) all_0_48_48 = e4
% 20.24/5.35 |
% 20.24/5.35 | Equations (510) can reduce 33 to:
% 20.24/5.35 | (269) $false
% 20.24/5.35 |
% 20.24/5.35 |-The branch is then unsatisfiable
% 20.24/5.35 |-Branch two:
% 20.24/5.35 | (512) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 20.24/5.35 |
% 20.24/5.35 | Applying alpha-rule on (512) yields:
% 20.24/5.35 | (513) all_0_15_15 = e3
% 20.24/5.35 | (514) ~ (all_0_16_16 = e2)
% 20.24/5.35 |
% 20.24/5.35 | From (513) and (205) follows:
% 20.24/5.35 | (3846) op(e2, all_0_44_44) = e3
% 20.24/5.35 |
% 20.24/5.35 +-Applying beta-rule and splitting (110), into two cases.
% 20.24/5.35 |-Branch one:
% 20.24/5.35 | (352) all_0_44_44 = e0
% 20.24/5.35 |
% 20.24/5.35 | Equations (352) can reduce 228 to:
% 20.24/5.35 | (459) ~ (all_0_43_43 = e0)
% 20.24/5.35 |
% 20.24/5.35 | Equations (352) can reduce 659 to:
% 20.24/5.35 | (406) ~ (e2 = e0)
% 20.24/5.35 |
% 20.24/5.36 | Simplifying 406 yields:
% 20.24/5.36 | (58) ~ (e2 = e0)
% 20.24/5.36 |
% 20.24/5.36 | Equations (352) can reduce 87 to:
% 20.24/5.36 | (436) ~ (e1 = e0)
% 20.24/5.36 |
% 20.24/5.36 | Simplifying 436 yields:
% 20.24/5.36 | (144) ~ (e1 = e0)
% 20.24/5.36 |
% 20.24/5.36 | From (352) and (3846) follows:
% 20.24/5.36 | (3853) op(e2, e0) = e3
% 20.24/5.36 |
% 20.24/5.36 +-Applying beta-rule and splitting (193), into two cases.
% 20.24/5.36 |-Branch one:
% 20.24/5.36 | (417) all_0_40_40 = e3
% 20.24/5.36 |
% 20.24/5.36 | Combining equations (417,413) yields a new equation:
% 20.24/5.36 | (572) e3 = e1
% 20.24/5.36 |
% 20.24/5.36 | Simplifying 572 yields:
% 20.24/5.36 | (418) e3 = e1
% 20.24/5.36 |
% 20.24/5.36 | Equations (418) can reduce 146 to:
% 20.24/5.36 | (269) $false
% 20.24/5.36 |
% 20.24/5.36 |-The branch is then unsatisfiable
% 20.24/5.36 |-Branch two:
% 20.24/5.36 | (420) ~ (all_0_40_40 = e3)
% 20.24/5.36 | (421) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 20.24/5.36 |
% 20.24/5.36 +-Applying beta-rule and splitting (421), into two cases.
% 20.24/5.36 |-Branch one:
% 20.24/5.36 | (422) all_0_44_44 = e3
% 20.24/5.36 |
% 20.24/5.36 | Combining equations (352,422) yields a new equation:
% 20.24/5.36 | (560) e3 = e0
% 20.24/5.36 |
% 20.24/5.36 | Equations (560) can reduce 72 to:
% 20.24/5.36 | (269) $false
% 20.24/5.36 |
% 20.24/5.36 |-The branch is then unsatisfiable
% 20.24/5.36 |-Branch two:
% 20.24/5.36 | (425) ~ (all_0_44_44 = e3)
% 20.24/5.36 | (426) all_0_52_52 = e3 | all_0_57_57 = e3
% 20.24/5.36 |
% 20.24/5.36 +-Applying beta-rule and splitting (426), into two cases.
% 20.24/5.36 |-Branch one:
% 20.24/5.36 | (427) all_0_52_52 = e3
% 20.24/5.36 |
% 20.24/5.36 | Equations (427) can reduce 71 to:
% 20.24/5.36 | (3866) ~ (all_0_53_53 = e3)
% 20.24/5.36 |
% 20.24/5.36 | Simplifying 3866 yields:
% 20.24/5.36 | (796) ~ (all_0_53_53 = e3)
% 20.24/5.36 |
% 20.24/5.36 | Equations (427) can reduce 62 to:
% 20.24/5.36 | (429) ~ (all_0_54_54 = e3)
% 20.24/5.36 |
% 20.24/5.36 | Simplifying 429 yields:
% 20.24/5.36 | (430) ~ (all_0_54_54 = e3)
% 20.24/5.36 |
% 20.24/5.36 +-Applying beta-rule and splitting (200), into two cases.
% 20.24/5.36 |-Branch one:
% 20.24/5.36 | (464) all_0_39_39 = e1
% 20.24/5.36 |
% 20.24/5.36 | Equations (464) can reduce 467 to:
% 20.24/5.36 | (269) $false
% 20.24/5.36 |
% 20.24/5.36 |-The branch is then unsatisfiable
% 20.24/5.36 |-Branch two:
% 20.24/5.36 | (467) ~ (all_0_39_39 = e1)
% 20.24/5.36 | (468) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 20.24/5.36 |
% 20.24/5.36 +-Applying beta-rule and splitting (22), into two cases.
% 20.24/5.36 |-Branch one:
% 20.24/5.36 | (661) all_0_43_43 = e2
% 20.24/5.36 |
% 20.24/5.36 | Equations (661) can reduce 321 to:
% 20.24/5.36 | (269) $false
% 20.24/5.36 |
% 20.24/5.36 |-The branch is then unsatisfiable
% 20.24/5.36 |-Branch two:
% 20.24/5.36 | (321) ~ (all_0_43_43 = e2)
% 20.24/5.36 | (1198) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 20.24/5.36 |
% 20.24/5.36 +-Applying beta-rule and splitting (1198), into two cases.
% 20.24/5.36 |-Branch one:
% 20.24/5.36 | (433) all_0_43_43 = e0
% 20.24/5.36 |
% 20.24/5.36 | Equations (433) can reduce 459 to:
% 20.24/5.36 | (269) $false
% 20.24/5.36 |
% 20.24/5.36 |-The branch is then unsatisfiable
% 20.24/5.36 |-Branch two:
% 20.24/5.36 | (459) ~ (all_0_43_43 = e0)
% 20.24/5.36 | (1695) all_0_43_43 = e4 | all_0_43_43 = e3
% 20.24/5.36 |
% 20.24/5.36 +-Applying beta-rule and splitting (162), into two cases.
% 20.24/5.36 |-Branch one:
% 20.24/5.36 | (559) all_0_43_43 = e3
% 20.24/5.36 |
% 20.24/5.36 | Equations (559) can reduce 441 to:
% 20.24/5.36 | (498) ~ (e4 = e3)
% 20.24/5.36 |
% 20.24/5.36 | Simplifying 498 yields:
% 20.24/5.36 | (41) ~ (e4 = e3)
% 20.24/5.36 |
% 20.24/5.36 | Equations (559) can reduce 321 to:
% 20.24/5.36 | (224) ~ (e3 = e2)
% 20.24/5.36 |
% 20.24/5.36 +-Applying beta-rule and splitting (213), into two cases.
% 20.24/5.36 |-Branch one:
% 20.24/5.36 | (605) all_0_41_41 = e3
% 20.24/5.36 |
% 20.24/5.36 | Combining equations (605,386) yields a new equation:
% 20.24/5.36 | (606) e3 = e2
% 20.24/5.36 |
% 20.24/5.36 | Simplifying 606 yields:
% 20.24/5.36 | (423) e3 = e2
% 20.24/5.36 |
% 20.24/5.36 | Equations (423) can reduce 224 to:
% 20.24/5.36 | (269) $false
% 20.24/5.36 |
% 20.24/5.36 |-The branch is then unsatisfiable
% 20.24/5.36 |-Branch two:
% 20.24/5.36 | (609) ~ (all_0_41_41 = e3)
% 20.24/5.36 | (3891) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 20.24/5.36 |
% 20.24/5.36 +-Applying beta-rule and splitting (468), into two cases.
% 20.24/5.36 |-Branch one:
% 20.24/5.36 | (469) all_0_47_47 = e1
% 20.24/5.36 |
% 20.24/5.36 | Combining equations (319,469) yields a new equation:
% 20.24/5.36 | (470) e2 = e1
% 20.24/5.36 |
% 20.24/5.36 | Simplifying 470 yields:
% 20.24/5.36 | (471) e2 = e1
% 20.24/5.36 |
% 20.24/5.36 | Equations (471) can reduce 148 to:
% 20.24/5.36 | (269) $false
% 20.24/5.36 |
% 20.24/5.36 |-The branch is then unsatisfiable
% 20.24/5.36 |-Branch two:
% 20.24/5.36 | (473) ~ (all_0_47_47 = e1)
% 20.24/5.36 | (474) all_0_51_51 = e1 | all_0_56_56 = e1
% 20.24/5.36 |
% 20.24/5.36 | Equations (319) can reduce 473 to:
% 20.24/5.36 | (148) ~ (e2 = e1)
% 20.24/5.36 |
% 20.24/5.36 +-Applying beta-rule and splitting (3891), into two cases.
% 20.24/5.36 |-Branch one:
% 20.24/5.36 | (1087) all_0_45_45 = e3
% 20.24/5.36 |
% 20.24/5.36 | Combining equations (1087,444) yields a new equation:
% 20.24/5.36 | (516) e4 = e3
% 20.24/5.36 |
% 20.24/5.36 | Equations (516) can reduce 41 to:
% 20.24/5.36 | (269) $false
% 20.24/5.36 |
% 20.24/5.36 |-The branch is then unsatisfiable
% 20.24/5.36 |-Branch two:
% 20.24/5.36 | (689) ~ (all_0_45_45 = e3)
% 20.24/5.36 | (3903) all_0_53_53 = e3 | all_0_58_58 = e3
% 20.24/5.36 |
% 20.24/5.36 +-Applying beta-rule and splitting (47), into two cases.
% 20.24/5.36 |-Branch one:
% 20.24/5.36 | (348) all_0_39_39 = e2
% 20.24/5.36 |
% 20.24/5.36 | Equations (348) can reduce 320 to:
% 20.24/5.36 | (269) $false
% 20.24/5.36 |
% 20.24/5.36 |-The branch is then unsatisfiable
% 20.24/5.36 |-Branch two:
% 20.24/5.36 | (320) ~ (all_0_39_39 = e2)
% 20.24/5.36 | (709) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 20.24/5.36 |
% 20.24/5.36 +-Applying beta-rule and splitting (3903), into two cases.
% 20.24/5.36 |-Branch one:
% 20.24/5.36 | (861) all_0_53_53 = e3
% 20.24/5.36 |
% 20.24/5.36 | Equations (861) can reduce 796 to:
% 20.24/5.36 | (269) $false
% 20.24/5.36 |
% 20.24/5.36 |-The branch is then unsatisfiable
% 20.24/5.36 |-Branch two:
% 20.24/5.36 | (796) ~ (all_0_53_53 = e3)
% 20.24/5.36 | (497) all_0_58_58 = e3
% 20.24/5.36 |
% 20.24/5.36 | Equations (497) can reduce 127 to:
% 20.24/5.36 | (796) ~ (all_0_53_53 = e3)
% 20.24/5.36 |
% 20.24/5.36 | Equations (497) can reduce 223 to:
% 20.24/5.36 | (1183) ~ (all_0_56_56 = e3)
% 20.24/5.36 |
% 20.24/5.36 | Equations (497) can reduce 198 to:
% 20.61/5.36 | (2131) ~ (all_0_59_59 = e3)
% 20.61/5.36 |
% 20.61/5.36 | Simplifying 2131 yields:
% 20.61/5.36 | (2132) ~ (all_0_59_59 = e3)
% 20.61/5.36 |
% 20.61/5.36 | Equations (497) can reduce 277 to:
% 20.61/5.36 | (498) ~ (e4 = e3)
% 20.61/5.36 |
% 20.61/5.36 | Simplifying 498 yields:
% 20.61/5.36 | (41) ~ (e4 = e3)
% 20.61/5.36 |
% 20.61/5.36 | Equations (497) can reduce 392 to:
% 20.61/5.36 | (224) ~ (e3 = e2)
% 20.61/5.36 |
% 20.61/5.36 +-Applying beta-rule and splitting (169), into two cases.
% 20.61/5.36 |-Branch one:
% 20.61/5.36 | (610) all_0_42_42 = e3
% 20.61/5.36 |
% 20.61/5.36 | Equations (610) can reduce 836 to:
% 20.61/5.36 | (146) ~ (e3 = e1)
% 20.61/5.36 |
% 20.61/5.36 | Equations (610) can reduce 155 to:
% 20.61/5.36 | (72) ~ (e3 = e0)
% 20.61/5.36 |
% 20.61/5.36 +-Applying beta-rule and splitting (32), into two cases.
% 20.61/5.36 |-Branch one:
% 20.61/5.36 | (1079) all_0_39_39 = e4
% 20.61/5.36 |
% 20.61/5.36 | Equations (1079) can reduce 126 to:
% 20.61/5.36 | (1208) ~ (all_0_51_51 = e4)
% 20.61/5.36 |
% 20.61/5.36 | Simplifying 1208 yields:
% 20.61/5.36 | (530) ~ (all_0_51_51 = e4)
% 20.61/5.36 |
% 20.61/5.36 | Equations (1079) can reduce 320 to:
% 20.61/5.36 | (230) ~ (e4 = e2)
% 20.61/5.36 |
% 20.61/5.36 +-Applying beta-rule and splitting (153), into two cases.
% 20.61/5.36 |-Branch one:
% 20.61/5.36 | (453) all_0_50_50 = e4
% 20.61/5.36 |
% 20.61/5.36 | Combining equations (253,453) yields a new equation:
% 20.61/5.36 | (360) e4 = e2
% 20.61/5.36 |
% 20.61/5.36 | Equations (360) can reduce 230 to:
% 20.61/5.36 | (269) $false
% 20.61/5.36 |
% 20.61/5.36 |-The branch is then unsatisfiable
% 20.61/5.36 |-Branch two:
% 20.61/5.36 | (456) ~ (all_0_50_50 = e4)
% 20.61/5.36 | (457) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 20.61/5.36 |
% 20.61/5.36 +-Applying beta-rule and splitting (2629), into two cases.
% 20.61/5.36 |-Branch one:
% 20.61/5.36 | (2222) ~ (all_0_59_59 = e1)
% 20.61/5.36 |
% 20.61/5.36 +-Applying beta-rule and splitting (43), into two cases.
% 20.61/5.36 |-Branch one:
% 20.61/5.36 | (480) all_0_56_56 = e1
% 20.61/5.36 |
% 20.61/5.36 | Equations (480) can reduce 16 to:
% 20.61/5.36 | (479) ~ (all_0_51_51 = e1)
% 20.61/5.36 |
% 20.61/5.36 | Equations (480) can reduce 1183 to:
% 20.61/5.36 | (597) ~ (e3 = e1)
% 20.61/5.36 |
% 20.61/5.36 | Simplifying 597 yields:
% 20.61/5.36 | (146) ~ (e3 = e1)
% 20.61/5.36 |
% 20.61/5.36 | Equations (480) can reduce 377 to:
% 20.61/5.36 | (414) ~ (e2 = e1)
% 20.61/5.36 |
% 20.61/5.36 | Simplifying 414 yields:
% 20.61/5.36 | (148) ~ (e2 = e1)
% 20.61/5.36 |
% 20.61/5.36 +-Applying beta-rule and splitting (211), into two cases.
% 20.61/5.36 |-Branch one:
% 20.61/5.36 | (632) all_0_56_56 = e0
% 20.61/5.36 |
% 20.61/5.36 | Combining equations (480,632) yields a new equation:
% 20.61/5.36 | (578) e1 = e0
% 20.61/5.36 |
% 20.61/5.36 | Simplifying 578 yields:
% 20.61/5.36 | (579) e1 = e0
% 20.61/5.36 |
% 20.61/5.36 | Equations (579) can reduce 144 to:
% 20.61/5.36 | (269) $false
% 20.61/5.36 |
% 20.61/5.36 |-The branch is then unsatisfiable
% 20.61/5.36 |-Branch two:
% 20.61/5.36 | (401) ~ (all_0_56_56 = e0)
% 20.61/5.36 | (2052) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 20.61/5.36 |
% 20.61/5.36 | Equations (480) can reduce 401 to:
% 20.61/5.36 | (144) ~ (e1 = e0)
% 20.61/5.36 |
% 20.61/5.36 +-Applying beta-rule and splitting (171), into two cases.
% 20.61/5.36 |-Branch one:
% 20.61/5.36 | (433) all_0_43_43 = e0
% 20.61/5.36 |
% 20.61/5.36 | Combining equations (559,433) yields a new equation:
% 20.61/5.36 | (781) e3 = e0
% 20.61/5.36 |
% 20.61/5.36 | Simplifying 781 yields:
% 20.61/5.36 | (560) e3 = e0
% 20.61/5.36 |
% 20.61/5.36 | Equations (560) can reduce 72 to:
% 20.61/5.36 | (269) $false
% 20.61/5.36 |
% 20.61/5.36 |-The branch is then unsatisfiable
% 20.61/5.36 |-Branch two:
% 20.61/5.36 | (459) ~ (all_0_43_43 = e0)
% 20.61/5.36 | (622) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 20.61/5.36 |
% 20.61/5.36 +-Applying beta-rule and splitting (457), into two cases.
% 20.61/5.36 |-Branch one:
% 20.61/5.36 | (458) all_0_51_51 = e4
% 20.61/5.36 |
% 20.61/5.36 | Equations (458) can reduce 530 to:
% 20.61/5.36 | (269) $false
% 20.61/5.36 |
% 20.61/5.36 |-The branch is then unsatisfiable
% 20.61/5.36 |-Branch two:
% 20.61/5.36 | (530) ~ (all_0_51_51 = e4)
% 20.61/5.36 | (531) all_0_53_53 = e4 | all_0_54_54 = e4
% 20.61/5.36 |
% 20.61/5.36 +-Applying beta-rule and splitting (531), into two cases.
% 20.61/5.36 |-Branch one:
% 20.61/5.36 | (532) all_0_53_53 = e4
% 20.61/5.36 |
% 20.61/5.36 | Equations (532) can reduce 448 to:
% 20.61/5.36 | (269) $false
% 20.61/5.36 |
% 20.61/5.36 |-The branch is then unsatisfiable
% 20.61/5.36 |-Branch two:
% 20.61/5.36 | (448) ~ (all_0_53_53 = e4)
% 20.61/5.36 | (535) all_0_54_54 = e4
% 20.61/5.36 |
% 20.61/5.36 | Equations (535) can reduce 217 to:
% 20.61/5.36 | (83) ~ (all_0_49_49 = e4)
% 20.61/5.36 |
% 20.61/5.36 | Equations (535) can reduce 119 to:
% 20.61/5.36 | (448) ~ (all_0_53_53 = e4)
% 20.61/5.36 |
% 20.61/5.36 +-Applying beta-rule and splitting (622), into two cases.
% 20.61/5.36 |-Branch one:
% 20.61/5.36 | (623) all_0_47_47 = e0
% 20.61/5.36 |
% 20.61/5.36 | Combining equations (319,623) yields a new equation:
% 20.61/5.36 | (353) e2 = e0
% 20.61/5.36 |
% 20.61/5.36 | Simplifying 353 yields:
% 20.61/5.36 | (354) e2 = e0
% 20.61/5.36 |
% 20.61/5.36 | Equations (354) can reduce 58 to:
% 20.61/5.36 | (269) $false
% 20.61/5.36 |
% 20.61/5.36 |-The branch is then unsatisfiable
% 20.61/5.36 |-Branch two:
% 20.61/5.36 | (297) ~ (all_0_47_47 = e0)
% 20.61/5.36 | (628) all_0_51_51 = e0 | all_0_56_56 = e0
% 20.61/5.36 |
% 20.61/5.36 +-Applying beta-rule and splitting (19), into two cases.
% 20.61/5.36 |-Branch one:
% 20.61/5.36 | (475) all_0_51_51 = e1
% 20.61/5.36 |
% 20.61/5.36 | Equations (475) can reduce 479 to:
% 20.61/5.36 | (269) $false
% 20.61/5.36 |
% 20.61/5.36 |-The branch is then unsatisfiable
% 20.61/5.36 |-Branch two:
% 20.61/5.36 | (479) ~ (all_0_51_51 = e1)
% 20.61/5.36 | (1954) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 20.61/5.36 |
% 20.61/5.36 +-Applying beta-rule and splitting (84), into two cases.
% 20.61/5.36 |-Branch one:
% 20.61/5.36 | (832) all_0_42_42 = e1
% 20.61/5.36 |
% 20.61/5.36 | Combining equations (832,610) yields a new equation:
% 20.61/5.36 | (418) e3 = e1
% 20.61/5.36 |
% 20.61/5.36 | Equations (418) can reduce 146 to:
% 20.61/5.36 | (269) $false
% 20.61/5.36 |
% 20.61/5.36 |-The branch is then unsatisfiable
% 20.61/5.36 |-Branch two:
% 20.61/5.36 | (836) ~ (all_0_42_42 = e1)
% 20.61/5.36 | (837) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 20.61/5.36 |
% 20.61/5.36 | Equations (610) can reduce 836 to:
% 20.61/5.36 | (146) ~ (e3 = e1)
% 20.61/5.36 |
% 20.61/5.36 +-Applying beta-rule and splitting (1954), into two cases.
% 20.61/5.36 |-Branch one:
% 20.61/5.36 | (820) all_0_52_52 = e1
% 20.61/5.36 |
% 20.61/5.36 | Combining equations (427,820) yields a new equation:
% 20.61/5.36 | (572) e3 = e1
% 20.61/5.36 |
% 20.61/5.36 | Simplifying 572 yields:
% 20.61/5.36 | (418) e3 = e1
% 20.61/5.36 |
% 20.61/5.36 | Equations (418) can reduce 146 to:
% 20.61/5.36 | (269) $false
% 20.61/5.36 |
% 20.61/5.36 |-The branch is then unsatisfiable
% 20.61/5.36 |-Branch two:
% 20.61/5.36 | (978) ~ (all_0_52_52 = e1)
% 20.61/5.36 | (1959) all_0_53_53 = e1 | all_0_54_54 = e1
% 20.61/5.36 |
% 20.61/5.36 +-Applying beta-rule and splitting (628), into two cases.
% 20.61/5.36 |-Branch one:
% 20.61/5.36 | (629) all_0_51_51 = e0
% 20.61/5.36 |
% 20.61/5.36 | Equations (629) can reduce 30 to:
% 20.61/5.36 | (764) ~ (all_0_53_53 = e0)
% 20.61/5.36 |
% 20.61/5.36 | Simplifying 764 yields:
% 20.61/5.36 | (765) ~ (all_0_53_53 = e0)
% 20.61/5.36 |
% 20.61/5.36 +-Applying beta-rule and splitting (27), into two cases.
% 20.61/5.36 |-Branch one:
% 20.61/5.36 | (849) all_0_53_53 = e2
% 20.61/5.36 |
% 20.61/5.36 | Equations (849) can reduce 259 to:
% 20.61/5.36 | (269) $false
% 20.61/5.36 |
% 20.61/5.36 |-The branch is then unsatisfiable
% 20.61/5.36 |-Branch two:
% 20.61/5.36 | (259) ~ (all_0_53_53 = e2)
% 20.61/5.36 | (852) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 20.61/5.36 |
% 20.61/5.36 +-Applying beta-rule and splitting (837), into two cases.
% 20.61/5.36 |-Branch one:
% 20.61/5.36 | (596) all_0_49_49 = e1
% 20.61/5.36 |
% 20.61/5.36 | Equations (596) can reduce 83 to:
% 20.61/5.36 | (826) ~ (e4 = e1)
% 20.61/5.36 |
% 20.61/5.36 | Simplifying 826 yields:
% 20.61/5.36 | (251) ~ (e4 = e1)
% 20.61/5.36 |
% 20.61/5.36 | From (596) and (128) follows:
% 20.61/5.36 | (3993) op(e2, e0) = e1
% 20.61/5.36 |
% 20.61/5.36 +-Applying beta-rule and splitting (1959), into two cases.
% 20.61/5.36 |-Branch one:
% 20.61/5.36 | (853) all_0_53_53 = e1
% 20.61/5.36 |
% 20.61/5.36 | Equations (853) can reduce 796 to:
% 20.61/5.36 | (597) ~ (e3 = e1)
% 20.61/5.36 |
% 20.61/5.36 | Simplifying 597 yields:
% 20.61/5.36 | (146) ~ (e3 = e1)
% 20.61/5.36 |
% 20.61/5.36 +-Applying beta-rule and splitting (2628), into two cases.
% 20.61/5.36 |-Branch one:
% 20.61/5.36 | (960) ~ (all_0_49_49 = e1)
% 20.61/5.36 |
% 20.61/5.36 | Equations (596) can reduce 960 to:
% 20.61/5.36 | (269) $false
% 20.61/5.36 |
% 20.61/5.36 |-The branch is then unsatisfiable
% 20.61/5.36 |-Branch two:
% 20.61/5.36 | (596) all_0_49_49 = e1
% 20.61/5.36 | (903) all_0_48_48 = e0
% 20.61/5.36 |
% 20.61/5.36 | From (903) and (76) follows:
% 20.61/5.36 | (4001) op(e2, e0) = all_0_26_26
% 20.61/5.36 |
% 20.61/5.36 | Instantiating formula (21) with e2, e0, e3, all_0_26_26 and discharging atoms op(e2, e0) = all_0_26_26, op(e2, e0) = e3, yields:
% 20.61/5.37 | (4002) all_0_26_26 = e3
% 20.61/5.37 |
% 20.61/5.37 | Instantiating formula (21) with e2, e0, e1, all_0_26_26 and discharging atoms op(e2, e0) = all_0_26_26, op(e2, e0) = e1, yields:
% 20.61/5.37 | (4003) all_0_26_26 = e1
% 20.61/5.37 |
% 20.61/5.37 | Combining equations (4002,4003) yields a new equation:
% 20.61/5.37 | (572) e3 = e1
% 20.61/5.37 |
% 20.61/5.37 | Simplifying 572 yields:
% 20.61/5.37 | (418) e3 = e1
% 20.61/5.37 |
% 20.61/5.37 | Equations (418) can reduce 146 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (823) ~ (all_0_53_53 = e1)
% 20.61/5.37 | (1592) all_0_54_54 = e1
% 20.61/5.37 |
% 20.61/5.37 | Combining equations (1592,535) yields a new equation:
% 20.61/5.37 | (477) e4 = e1
% 20.61/5.37 |
% 20.61/5.37 | Equations (477) can reduce 251 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (960) ~ (all_0_49_49 = e1)
% 20.61/5.37 | (961) all_0_54_54 = e1 | all_0_59_59 = e1
% 20.61/5.37 |
% 20.61/5.37 +-Applying beta-rule and splitting (192), into two cases.
% 20.61/5.37 |-Branch one:
% 20.61/5.37 | (469) all_0_47_47 = e1
% 20.61/5.37 |
% 20.61/5.37 | Combining equations (319,469) yields a new equation:
% 20.61/5.37 | (470) e2 = e1
% 20.61/5.37 |
% 20.61/5.37 | Simplifying 470 yields:
% 20.61/5.37 | (471) e2 = e1
% 20.61/5.37 |
% 20.61/5.37 | Equations (471) can reduce 148 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (473) ~ (all_0_47_47 = e1)
% 20.61/5.37 | (592) all_0_48_48 = e1 | all_0_49_49 = e1
% 20.61/5.37 |
% 20.61/5.37 +-Applying beta-rule and splitting (852), into two cases.
% 20.61/5.37 |-Branch one:
% 20.61/5.37 | (853) all_0_53_53 = e1
% 20.61/5.37 |
% 20.61/5.37 | Equations (853) can reduce 250 to:
% 20.61/5.37 | (584) ~ (all_0_48_48 = e1)
% 20.61/5.37 |
% 20.61/5.37 +-Applying beta-rule and splitting (592), into two cases.
% 20.61/5.37 |-Branch one:
% 20.61/5.37 | (593) all_0_48_48 = e1
% 20.61/5.37 |
% 20.61/5.37 | Equations (593) can reduce 584 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (584) ~ (all_0_48_48 = e1)
% 20.61/5.37 | (596) all_0_49_49 = e1
% 20.61/5.37 |
% 20.61/5.37 | Equations (596) can reduce 960 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (823) ~ (all_0_53_53 = e1)
% 20.61/5.37 | (856) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e0
% 20.61/5.37 |
% 20.61/5.37 +-Applying beta-rule and splitting (856), into two cases.
% 20.61/5.37 |-Branch one:
% 20.61/5.37 | (857) all_0_53_53 = e0
% 20.61/5.37 |
% 20.61/5.37 | Equations (857) can reduce 765 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (765) ~ (all_0_53_53 = e0)
% 20.61/5.37 | (860) all_0_53_53 = e4 | all_0_53_53 = e3
% 20.61/5.37 |
% 20.61/5.37 +-Applying beta-rule and splitting (860), into two cases.
% 20.61/5.37 |-Branch one:
% 20.61/5.37 | (861) all_0_53_53 = e3
% 20.61/5.37 |
% 20.61/5.37 | Equations (861) can reduce 796 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (796) ~ (all_0_53_53 = e3)
% 20.61/5.37 | (532) all_0_53_53 = e4
% 20.61/5.37 |
% 20.61/5.37 | Equations (532) can reduce 448 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (432) ~ (all_0_51_51 = e0)
% 20.61/5.37 | (632) all_0_56_56 = e0
% 20.61/5.37 |
% 20.61/5.37 | Combining equations (632,480) yields a new equation:
% 20.61/5.37 | (579) e1 = e0
% 20.61/5.37 |
% 20.61/5.37 | Equations (579) can reduce 144 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (575) ~ (all_0_56_56 = e1)
% 20.61/5.37 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 20.61/5.37 |
% 20.61/5.37 +-Applying beta-rule and splitting (576), into two cases.
% 20.61/5.37 |-Branch one:
% 20.61/5.37 | (577) all_0_57_57 = e1
% 20.61/5.37 |
% 20.61/5.37 | Combining equations (867,577) yields a new equation:
% 20.61/5.37 | (470) e2 = e1
% 20.61/5.37 |
% 20.61/5.37 | Simplifying 470 yields:
% 20.61/5.37 | (471) e2 = e1
% 20.61/5.37 |
% 20.61/5.37 | Equations (471) can reduce 148 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (581) ~ (all_0_57_57 = e1)
% 20.61/5.37 | (582) all_0_58_58 = e1 | all_0_59_59 = e1
% 20.61/5.37 |
% 20.61/5.37 +-Applying beta-rule and splitting (582), into two cases.
% 20.61/5.37 |-Branch one:
% 20.61/5.37 | (489) all_0_58_58 = e1
% 20.61/5.37 |
% 20.61/5.37 | Combining equations (489,497) yields a new equation:
% 20.61/5.37 | (418) e3 = e1
% 20.61/5.37 |
% 20.61/5.37 | Equations (418) can reduce 146 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (482) ~ (all_0_58_58 = e1)
% 20.61/5.37 | (614) all_0_59_59 = e1
% 20.61/5.37 |
% 20.61/5.37 | Equations (614) can reduce 2222 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (614) all_0_59_59 = e1
% 20.61/5.37 | (493) all_0_58_58 = e0
% 20.61/5.37 |
% 20.61/5.37 | Combining equations (493,497) yields a new equation:
% 20.61/5.37 | (560) e3 = e0
% 20.61/5.37 |
% 20.61/5.37 | Equations (560) can reduce 72 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (307) ~ (all_0_39_39 = e4)
% 20.61/5.37 | (3018) all_0_41_41 = e4 | all_0_42_42 = e4
% 20.61/5.37 |
% 20.61/5.37 +-Applying beta-rule and splitting (3018), into two cases.
% 20.61/5.37 |-Branch one:
% 20.61/5.37 | (740) all_0_41_41 = e4
% 20.61/5.37 |
% 20.61/5.37 | Combining equations (386,740) yields a new equation:
% 20.61/5.37 | (360) e4 = e2
% 20.61/5.37 |
% 20.61/5.37 | Equations (360) can reduce 230 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (308) ~ (all_0_41_41 = e4)
% 20.61/5.37 | (305) all_0_42_42 = e4
% 20.61/5.37 |
% 20.61/5.37 | Combining equations (610,305) yields a new equation:
% 20.61/5.37 | (516) e4 = e3
% 20.61/5.37 |
% 20.61/5.37 | Equations (516) can reduce 41 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (1924) ~ (all_0_42_42 = e3)
% 20.61/5.37 | (1925) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 20.61/5.37 |
% 20.61/5.37 +-Applying beta-rule and splitting (1925), into two cases.
% 20.61/5.37 |-Branch one:
% 20.61/5.37 | (462) all_0_46_46 = e3
% 20.61/5.37 |
% 20.61/5.37 | Combining equations (364,462) yields a new equation:
% 20.61/5.37 | (423) e3 = e2
% 20.61/5.37 |
% 20.61/5.37 | Equations (423) can reduce 224 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (618) ~ (all_0_46_46 = e3)
% 20.61/5.37 | (1930) all_0_54_54 = e3 | all_0_59_59 = e3
% 20.61/5.37 |
% 20.61/5.37 +-Applying beta-rule and splitting (1930), into two cases.
% 20.61/5.37 |-Branch one:
% 20.61/5.37 | (635) all_0_54_54 = e3
% 20.61/5.37 |
% 20.61/5.37 | Equations (635) can reduce 430 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (430) ~ (all_0_54_54 = e3)
% 20.61/5.37 | (1070) all_0_59_59 = e3
% 20.61/5.37 |
% 20.61/5.37 | Equations (1070) can reduce 2132 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (562) ~ (all_0_43_43 = e3)
% 20.61/5.37 | (1193) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 20.61/5.37 |
% 20.61/5.37 +-Applying beta-rule and splitting (1695), into two cases.
% 20.61/5.37 |-Branch one:
% 20.61/5.37 | (559) all_0_43_43 = e3
% 20.61/5.37 |
% 20.61/5.37 | Equations (559) can reduce 562 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (562) ~ (all_0_43_43 = e3)
% 20.61/5.37 | (438) all_0_43_43 = e4
% 20.61/5.37 |
% 20.61/5.37 | Equations (438) can reduce 441 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (637) ~ (all_0_52_52 = e3)
% 20.61/5.37 | (638) all_0_57_57 = e3
% 20.61/5.37 |
% 20.61/5.37 | Combining equations (867,638) yields a new equation:
% 20.61/5.37 | (423) e3 = e2
% 20.61/5.37 |
% 20.61/5.37 | Equations (423) can reduce 224 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (356) ~ (all_0_44_44 = e0)
% 20.61/5.37 | (357) all_0_52_52 = e0 | all_0_57_57 = e0
% 20.61/5.37 |
% 20.61/5.37 +-Applying beta-rule and splitting (143), into two cases.
% 20.61/5.37 |-Branch one:
% 20.61/5.37 | (433) all_0_43_43 = e0
% 20.61/5.37 |
% 20.61/5.37 | Equations (433) can reduce 228 to:
% 20.61/5.37 | (4094) ~ (all_0_44_44 = e0)
% 20.61/5.37 |
% 20.61/5.37 | Simplifying 4094 yields:
% 20.61/5.37 | (356) ~ (all_0_44_44 = e0)
% 20.61/5.37 |
% 20.61/5.37 +-Applying beta-rule and splitting (660), into two cases.
% 20.61/5.37 |-Branch one:
% 20.61/5.37 | (352) all_0_44_44 = e0
% 20.61/5.37 |
% 20.61/5.37 | Equations (352) can reduce 356 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (356) ~ (all_0_44_44 = e0)
% 20.61/5.37 | (422) all_0_44_44 = e3
% 20.61/5.37 |
% 20.61/5.37 | Equations (422) can reduce 659 to:
% 20.61/5.37 | (224) ~ (e3 = e2)
% 20.61/5.37 |
% 20.61/5.37 | From (422) and (3846) follows:
% 20.61/5.37 | (4101) op(e2, e3) = e3
% 20.61/5.37 |
% 20.61/5.37 | Instantiating formula (21) with e2, e3, e3, e2 and discharging atoms op(e2, e3) = e3, op(e2, e3) = e2, yields:
% 20.61/5.37 | (423) e3 = e2
% 20.61/5.37 |
% 20.61/5.37 | Equations (423) can reduce 224 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (459) ~ (all_0_43_43 = e0)
% 20.61/5.37 | (1676) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 20.61/5.37 |
% 20.61/5.37 +-Applying beta-rule and splitting (357), into two cases.
% 20.61/5.37 |-Branch one:
% 20.61/5.37 | (397) all_0_52_52 = e0
% 20.61/5.37 |
% 20.61/5.37 | Equations (397) can reduce 121 to:
% 20.61/5.37 | (356) ~ (all_0_44_44 = e0)
% 20.61/5.37 |
% 20.61/5.37 | Equations (397) can reduce 152 to:
% 20.61/5.37 | (404) ~ (e4 = e0)
% 20.61/5.37 |
% 20.61/5.37 | Simplifying 404 yields:
% 20.61/5.37 | (11) ~ (e4 = e0)
% 20.61/5.37 |
% 20.61/5.37 | Equations (397) can reduce 257 to:
% 20.61/5.37 | (406) ~ (e2 = e0)
% 20.61/5.37 |
% 20.61/5.37 | Simplifying 406 yields:
% 20.61/5.37 | (58) ~ (e2 = e0)
% 20.61/5.37 |
% 20.61/5.37 +-Applying beta-rule and splitting (1676), into two cases.
% 20.61/5.37 |-Branch one:
% 20.61/5.37 | (352) all_0_44_44 = e0
% 20.61/5.37 |
% 20.61/5.37 | Equations (352) can reduce 356 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (356) ~ (all_0_44_44 = e0)
% 20.61/5.37 | (4115) all_0_45_45 = e0 | all_0_46_46 = e0
% 20.61/5.37 |
% 20.61/5.37 +-Applying beta-rule and splitting (4115), into two cases.
% 20.61/5.37 |-Branch one:
% 20.61/5.37 | (889) all_0_45_45 = e0
% 20.61/5.37 |
% 20.61/5.37 | Combining equations (444,889) yields a new equation:
% 20.61/5.37 | (751) e4 = e0
% 20.61/5.37 |
% 20.61/5.37 | Simplifying 751 yields:
% 20.61/5.37 | (439) e4 = e0
% 20.61/5.37 |
% 20.61/5.37 | Equations (439) can reduce 11 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (299) ~ (all_0_45_45 = e0)
% 20.61/5.37 | (546) all_0_46_46 = e0
% 20.61/5.37 |
% 20.61/5.37 | Combining equations (364,546) yields a new equation:
% 20.61/5.37 | (353) e2 = e0
% 20.61/5.37 |
% 20.61/5.37 | Simplifying 353 yields:
% 20.61/5.37 | (354) e2 = e0
% 20.61/5.37 |
% 20.61/5.37 | Equations (354) can reduce 58 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.37 |-Branch two:
% 20.61/5.37 | (317) ~ (all_0_52_52 = e0)
% 20.61/5.37 | (400) all_0_57_57 = e0
% 20.61/5.37 |
% 20.61/5.37 | Combining equations (867,400) yields a new equation:
% 20.61/5.37 | (353) e2 = e0
% 20.61/5.37 |
% 20.61/5.37 | Simplifying 353 yields:
% 20.61/5.37 | (354) e2 = e0
% 20.61/5.37 |
% 20.61/5.37 | Equations (354) can reduce 58 to:
% 20.61/5.37 | (269) $false
% 20.61/5.37 |
% 20.61/5.37 |-The branch is then unsatisfiable
% 20.61/5.38 |-Branch two:
% 20.61/5.38 | (518) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 20.61/5.38 |
% 20.61/5.38 | Applying alpha-rule on (518) yields:
% 20.61/5.38 | (519) all_0_17_17 = e1
% 20.61/5.38 | (520) ~ (all_0_18_18 = e2)
% 20.61/5.38 |
% 20.61/5.38 | From (519) and (69) follows:
% 20.61/5.38 | (2268) op(e2, all_0_52_52) = e1
% 20.61/5.38 |
% 20.61/5.38 +-Applying beta-rule and splitting (229), into two cases.
% 20.61/5.38 |-Branch one:
% 20.61/5.38 | (923) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1))
% 20.61/5.38 |
% 20.61/5.38 +-Applying beta-rule and splitting (923), into two cases.
% 20.61/5.38 |-Branch one:
% 20.61/5.38 | (924) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1))
% 20.61/5.38 |
% 20.61/5.38 +-Applying beta-rule and splitting (924), into two cases.
% 20.61/5.38 |-Branch one:
% 20.61/5.38 | (925) all_0_21_21 = e4 & ~ (all_0_22_22 = e1)
% 20.61/5.38 |
% 20.61/5.38 | Applying alpha-rule on (925) yields:
% 20.61/5.38 | (926) all_0_21_21 = e4
% 20.61/5.38 | (927) ~ (all_0_22_22 = e1)
% 20.61/5.38 |
% 20.67/5.38 | Combining equations (2698,926) yields a new equation:
% 20.67/5.38 | (4139) all_0_52_52 = e4
% 20.67/5.38 |
% 20.67/5.38 | Simplifying 4139 yields:
% 20.67/5.38 | (3119) all_0_52_52 = e4
% 20.67/5.38 |
% 20.67/5.38 | Equations (3119) can reduce 152 to:
% 20.67/5.38 | (269) $false
% 20.67/5.38 |
% 20.67/5.38 |-The branch is then unsatisfiable
% 20.67/5.38 |-Branch two:
% 20.67/5.38 | (931) all_0_23_23 = e3 & ~ (all_0_24_24 = e1)
% 20.67/5.38 |
% 20.67/5.38 | Applying alpha-rule on (931) yields:
% 20.67/5.38 | (932) all_0_23_23 = e3
% 20.67/5.38 | (933) ~ (all_0_24_24 = e1)
% 20.67/5.38 |
% 20.67/5.38 | Combining equations (2649,932) yields a new equation:
% 20.67/5.38 | (423) e3 = e2
% 20.67/5.38 |
% 20.67/5.38 | Equations (423) can reduce 224 to:
% 20.67/5.38 | (269) $false
% 20.67/5.38 |
% 20.67/5.38 |-The branch is then unsatisfiable
% 20.67/5.38 |-Branch two:
% 20.67/5.38 | (937) all_0_25_25 = e2 & ~ (all_0_26_26 = e1)
% 20.67/5.38 |
% 20.67/5.38 | Applying alpha-rule on (937) yields:
% 20.67/5.38 | (938) all_0_25_25 = e2
% 20.67/5.38 | (939) ~ (all_0_26_26 = e1)
% 20.67/5.38 |
% 20.67/5.38 | From (938) and (85) follows:
% 20.67/5.38 | (3130) op(e1, all_0_48_48) = e2
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (110), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (352) all_0_44_44 = e0
% 20.67/5.38 |
% 20.67/5.38 | Equations (352) can reduce 228 to:
% 20.67/5.38 | (459) ~ (all_0_43_43 = e0)
% 20.67/5.38 |
% 20.67/5.38 | Equations (352) can reduce 659 to:
% 20.67/5.38 | (406) ~ (e2 = e0)
% 20.67/5.38 |
% 20.67/5.38 | Simplifying 406 yields:
% 20.67/5.38 | (58) ~ (e2 = e0)
% 20.67/5.38 |
% 20.67/5.38 | Equations (352) can reduce 87 to:
% 20.67/5.38 | (436) ~ (e1 = e0)
% 20.67/5.38 |
% 20.67/5.38 | Simplifying 436 yields:
% 20.67/5.38 | (144) ~ (e1 = e0)
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (193), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (417) all_0_40_40 = e3
% 20.67/5.38 |
% 20.67/5.38 | Combining equations (417,413) yields a new equation:
% 20.67/5.38 | (572) e3 = e1
% 20.67/5.38 |
% 20.67/5.38 | Simplifying 572 yields:
% 20.67/5.38 | (418) e3 = e1
% 20.67/5.38 |
% 20.67/5.38 | Equations (418) can reduce 146 to:
% 20.67/5.38 | (269) $false
% 20.67/5.38 |
% 20.67/5.38 |-The branch is then unsatisfiable
% 20.67/5.38 |-Branch two:
% 20.67/5.38 | (420) ~ (all_0_40_40 = e3)
% 20.67/5.38 | (421) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (421), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (422) all_0_44_44 = e3
% 20.67/5.38 |
% 20.67/5.38 | Combining equations (352,422) yields a new equation:
% 20.67/5.38 | (560) e3 = e0
% 20.67/5.38 |
% 20.67/5.38 | Equations (560) can reduce 72 to:
% 20.67/5.38 | (269) $false
% 20.67/5.38 |
% 20.67/5.38 |-The branch is then unsatisfiable
% 20.67/5.38 |-Branch two:
% 20.67/5.38 | (425) ~ (all_0_44_44 = e3)
% 20.67/5.38 | (426) all_0_52_52 = e3 | all_0_57_57 = e3
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (426), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (427) all_0_52_52 = e3
% 20.67/5.38 |
% 20.67/5.38 | Equations (427) can reduce 71 to:
% 20.67/5.38 | (3866) ~ (all_0_53_53 = e3)
% 20.67/5.38 |
% 20.67/5.38 | Simplifying 3866 yields:
% 20.67/5.38 | (796) ~ (all_0_53_53 = e3)
% 20.67/5.38 |
% 20.67/5.38 | Equations (427) can reduce 62 to:
% 20.67/5.38 | (429) ~ (all_0_54_54 = e3)
% 20.67/5.38 |
% 20.67/5.38 | Simplifying 429 yields:
% 20.67/5.38 | (430) ~ (all_0_54_54 = e3)
% 20.67/5.38 |
% 20.67/5.38 | From (427) and (2268) follows:
% 20.67/5.38 | (3095) op(e2, e3) = e1
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (200), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (464) all_0_39_39 = e1
% 20.67/5.38 |
% 20.67/5.38 | Equations (464) can reduce 467 to:
% 20.67/5.38 | (269) $false
% 20.67/5.38 |
% 20.67/5.38 |-The branch is then unsatisfiable
% 20.67/5.38 |-Branch two:
% 20.67/5.38 | (467) ~ (all_0_39_39 = e1)
% 20.67/5.38 | (468) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (22), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (661) all_0_43_43 = e2
% 20.67/5.38 |
% 20.67/5.38 | Equations (661) can reduce 321 to:
% 20.67/5.38 | (269) $false
% 20.67/5.38 |
% 20.67/5.38 |-The branch is then unsatisfiable
% 20.67/5.38 |-Branch two:
% 20.67/5.38 | (321) ~ (all_0_43_43 = e2)
% 20.67/5.38 | (1198) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (1198), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (433) all_0_43_43 = e0
% 20.67/5.38 |
% 20.67/5.38 | Equations (433) can reduce 459 to:
% 20.67/5.38 | (269) $false
% 20.67/5.38 |
% 20.67/5.38 |-The branch is then unsatisfiable
% 20.67/5.38 |-Branch two:
% 20.67/5.38 | (459) ~ (all_0_43_43 = e0)
% 20.67/5.38 | (1695) all_0_43_43 = e4 | all_0_43_43 = e3
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (162), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (559) all_0_43_43 = e3
% 20.67/5.38 |
% 20.67/5.38 | Equations (559) can reduce 441 to:
% 20.67/5.38 | (498) ~ (e4 = e3)
% 20.67/5.38 |
% 20.67/5.38 | Simplifying 498 yields:
% 20.67/5.38 | (41) ~ (e4 = e3)
% 20.67/5.38 |
% 20.67/5.38 | Equations (559) can reduce 321 to:
% 20.67/5.38 | (224) ~ (e3 = e2)
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (213), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (605) all_0_41_41 = e3
% 20.67/5.38 |
% 20.67/5.38 | Combining equations (605,386) yields a new equation:
% 20.67/5.38 | (606) e3 = e2
% 20.67/5.38 |
% 20.67/5.38 | Simplifying 606 yields:
% 20.67/5.38 | (423) e3 = e2
% 20.67/5.38 |
% 20.67/5.38 | Equations (423) can reduce 224 to:
% 20.67/5.38 | (269) $false
% 20.67/5.38 |
% 20.67/5.38 |-The branch is then unsatisfiable
% 20.67/5.38 |-Branch two:
% 20.67/5.38 | (609) ~ (all_0_41_41 = e3)
% 20.67/5.38 | (3891) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (468), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (469) all_0_47_47 = e1
% 20.67/5.38 |
% 20.67/5.38 | Combining equations (319,469) yields a new equation:
% 20.67/5.38 | (470) e2 = e1
% 20.67/5.38 |
% 20.67/5.38 | Simplifying 470 yields:
% 20.67/5.38 | (471) e2 = e1
% 20.67/5.38 |
% 20.67/5.38 | Equations (471) can reduce 148 to:
% 20.67/5.38 | (269) $false
% 20.67/5.38 |
% 20.67/5.38 |-The branch is then unsatisfiable
% 20.67/5.38 |-Branch two:
% 20.67/5.38 | (473) ~ (all_0_47_47 = e1)
% 20.67/5.38 | (474) all_0_51_51 = e1 | all_0_56_56 = e1
% 20.67/5.38 |
% 20.67/5.38 | Equations (319) can reduce 473 to:
% 20.67/5.38 | (148) ~ (e2 = e1)
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (3891), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (1087) all_0_45_45 = e3
% 20.67/5.38 |
% 20.67/5.38 | Combining equations (1087,444) yields a new equation:
% 20.67/5.38 | (516) e4 = e3
% 20.67/5.38 |
% 20.67/5.38 | Equations (516) can reduce 41 to:
% 20.67/5.38 | (269) $false
% 20.67/5.38 |
% 20.67/5.38 |-The branch is then unsatisfiable
% 20.67/5.38 |-Branch two:
% 20.67/5.38 | (689) ~ (all_0_45_45 = e3)
% 20.67/5.38 | (3903) all_0_53_53 = e3 | all_0_58_58 = e3
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (47), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (348) all_0_39_39 = e2
% 20.67/5.38 |
% 20.67/5.38 | Equations (348) can reduce 320 to:
% 20.67/5.38 | (269) $false
% 20.67/5.38 |
% 20.67/5.38 |-The branch is then unsatisfiable
% 20.67/5.38 |-Branch two:
% 20.67/5.38 | (320) ~ (all_0_39_39 = e2)
% 20.67/5.38 | (709) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (3903), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (861) all_0_53_53 = e3
% 20.67/5.38 |
% 20.67/5.38 | Equations (861) can reduce 796 to:
% 20.67/5.38 | (269) $false
% 20.67/5.38 |
% 20.67/5.38 |-The branch is then unsatisfiable
% 20.67/5.38 |-Branch two:
% 20.67/5.38 | (796) ~ (all_0_53_53 = e3)
% 20.67/5.38 | (497) all_0_58_58 = e3
% 20.67/5.38 |
% 20.67/5.38 | Equations (497) can reduce 127 to:
% 20.67/5.38 | (796) ~ (all_0_53_53 = e3)
% 20.67/5.38 |
% 20.67/5.38 | Equations (497) can reduce 223 to:
% 20.67/5.38 | (1183) ~ (all_0_56_56 = e3)
% 20.67/5.38 |
% 20.67/5.38 | Equations (497) can reduce 198 to:
% 20.67/5.38 | (2131) ~ (all_0_59_59 = e3)
% 20.67/5.38 |
% 20.67/5.38 | Simplifying 2131 yields:
% 20.67/5.38 | (2132) ~ (all_0_59_59 = e3)
% 20.67/5.38 |
% 20.67/5.38 | Equations (497) can reduce 277 to:
% 20.67/5.38 | (498) ~ (e4 = e3)
% 20.67/5.38 |
% 20.67/5.38 | Simplifying 498 yields:
% 20.67/5.38 | (41) ~ (e4 = e3)
% 20.67/5.38 |
% 20.67/5.38 | Equations (497) can reduce 392 to:
% 20.67/5.38 | (224) ~ (e3 = e2)
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (169), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (610) all_0_42_42 = e3
% 20.67/5.38 |
% 20.67/5.38 | Equations (610) can reduce 836 to:
% 20.67/5.38 | (146) ~ (e3 = e1)
% 20.67/5.38 |
% 20.67/5.38 | Equations (610) can reduce 155 to:
% 20.67/5.38 | (72) ~ (e3 = e0)
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (32), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (1079) all_0_39_39 = e4
% 20.67/5.38 |
% 20.67/5.38 | Equations (1079) can reduce 126 to:
% 20.67/5.38 | (1208) ~ (all_0_51_51 = e4)
% 20.67/5.38 |
% 20.67/5.38 | Simplifying 1208 yields:
% 20.67/5.38 | (530) ~ (all_0_51_51 = e4)
% 20.67/5.38 |
% 20.67/5.38 | Equations (1079) can reduce 320 to:
% 20.67/5.38 | (230) ~ (e4 = e2)
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (153), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (453) all_0_50_50 = e4
% 20.67/5.38 |
% 20.67/5.38 | Combining equations (253,453) yields a new equation:
% 20.67/5.38 | (360) e4 = e2
% 20.67/5.38 |
% 20.67/5.38 | Equations (360) can reduce 230 to:
% 20.67/5.38 | (269) $false
% 20.67/5.38 |
% 20.67/5.38 |-The branch is then unsatisfiable
% 20.67/5.38 |-Branch two:
% 20.67/5.38 | (456) ~ (all_0_50_50 = e4)
% 20.67/5.38 | (457) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (2629), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (2222) ~ (all_0_59_59 = e1)
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (43), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (480) all_0_56_56 = e1
% 20.67/5.38 |
% 20.67/5.38 | Equations (480) can reduce 16 to:
% 20.67/5.38 | (479) ~ (all_0_51_51 = e1)
% 20.67/5.38 |
% 20.67/5.38 | Equations (480) can reduce 1183 to:
% 20.67/5.38 | (597) ~ (e3 = e1)
% 20.67/5.38 |
% 20.67/5.38 | Simplifying 597 yields:
% 20.67/5.38 | (146) ~ (e3 = e1)
% 20.67/5.38 |
% 20.67/5.38 | Equations (480) can reduce 377 to:
% 20.67/5.38 | (414) ~ (e2 = e1)
% 20.67/5.38 |
% 20.67/5.38 | Simplifying 414 yields:
% 20.67/5.38 | (148) ~ (e2 = e1)
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (211), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (632) all_0_56_56 = e0
% 20.67/5.38 |
% 20.67/5.38 | Combining equations (480,632) yields a new equation:
% 20.67/5.38 | (578) e1 = e0
% 20.67/5.38 |
% 20.67/5.38 | Simplifying 578 yields:
% 20.67/5.38 | (579) e1 = e0
% 20.67/5.38 |
% 20.67/5.38 | Equations (579) can reduce 144 to:
% 20.67/5.38 | (269) $false
% 20.67/5.38 |
% 20.67/5.38 |-The branch is then unsatisfiable
% 20.67/5.38 |-Branch two:
% 20.67/5.38 | (401) ~ (all_0_56_56 = e0)
% 20.67/5.38 | (2052) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 20.67/5.38 |
% 20.67/5.38 | Equations (480) can reduce 401 to:
% 20.67/5.38 | (144) ~ (e1 = e0)
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (171), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (433) all_0_43_43 = e0
% 20.67/5.38 |
% 20.67/5.38 | Combining equations (559,433) yields a new equation:
% 20.67/5.38 | (781) e3 = e0
% 20.67/5.38 |
% 20.67/5.38 | Simplifying 781 yields:
% 20.67/5.38 | (560) e3 = e0
% 20.67/5.38 |
% 20.67/5.38 | Equations (560) can reduce 72 to:
% 20.67/5.38 | (269) $false
% 20.67/5.38 |
% 20.67/5.38 |-The branch is then unsatisfiable
% 20.67/5.38 |-Branch two:
% 20.67/5.38 | (459) ~ (all_0_43_43 = e0)
% 20.67/5.38 | (622) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (457), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (458) all_0_51_51 = e4
% 20.67/5.38 |
% 20.67/5.38 | Equations (458) can reduce 530 to:
% 20.67/5.38 | (269) $false
% 20.67/5.38 |
% 20.67/5.38 |-The branch is then unsatisfiable
% 20.67/5.38 |-Branch two:
% 20.67/5.38 | (530) ~ (all_0_51_51 = e4)
% 20.67/5.38 | (531) all_0_53_53 = e4 | all_0_54_54 = e4
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (531), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (532) all_0_53_53 = e4
% 20.67/5.38 |
% 20.67/5.38 | Equations (532) can reduce 448 to:
% 20.67/5.38 | (269) $false
% 20.67/5.38 |
% 20.67/5.38 |-The branch is then unsatisfiable
% 20.67/5.38 |-Branch two:
% 20.67/5.38 | (448) ~ (all_0_53_53 = e4)
% 20.67/5.38 | (535) all_0_54_54 = e4
% 20.67/5.38 |
% 20.67/5.38 | Equations (535) can reduce 217 to:
% 20.67/5.38 | (83) ~ (all_0_49_49 = e4)
% 20.67/5.38 |
% 20.67/5.38 | Equations (535) can reduce 119 to:
% 20.67/5.38 | (448) ~ (all_0_53_53 = e4)
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (622), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (623) all_0_47_47 = e0
% 20.67/5.38 |
% 20.67/5.38 | Combining equations (319,623) yields a new equation:
% 20.67/5.38 | (353) e2 = e0
% 20.67/5.38 |
% 20.67/5.38 | Simplifying 353 yields:
% 20.67/5.38 | (354) e2 = e0
% 20.67/5.38 |
% 20.67/5.38 | Equations (354) can reduce 58 to:
% 20.67/5.38 | (269) $false
% 20.67/5.38 |
% 20.67/5.38 |-The branch is then unsatisfiable
% 20.67/5.38 |-Branch two:
% 20.67/5.38 | (297) ~ (all_0_47_47 = e0)
% 20.67/5.38 | (628) all_0_51_51 = e0 | all_0_56_56 = e0
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (19), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (475) all_0_51_51 = e1
% 20.67/5.38 |
% 20.67/5.38 | Equations (475) can reduce 479 to:
% 20.67/5.38 | (269) $false
% 20.67/5.38 |
% 20.67/5.38 |-The branch is then unsatisfiable
% 20.67/5.38 |-Branch two:
% 20.67/5.38 | (479) ~ (all_0_51_51 = e1)
% 20.67/5.38 | (1954) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 20.67/5.38 |
% 20.67/5.38 +-Applying beta-rule and splitting (84), into two cases.
% 20.67/5.38 |-Branch one:
% 20.67/5.38 | (832) all_0_42_42 = e1
% 20.67/5.38 |
% 20.67/5.38 | Combining equations (832,610) yields a new equation:
% 20.67/5.38 | (418) e3 = e1
% 20.67/5.38 |
% 20.67/5.38 | Equations (418) can reduce 146 to:
% 20.67/5.38 | (269) $false
% 20.67/5.38 |
% 20.67/5.38 |-The branch is then unsatisfiable
% 20.67/5.38 |-Branch two:
% 20.67/5.38 | (836) ~ (all_0_42_42 = e1)
% 20.67/5.39 | (837) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 20.67/5.39 |
% 20.67/5.39 | Equations (610) can reduce 836 to:
% 20.67/5.39 | (146) ~ (e3 = e1)
% 20.67/5.39 |
% 20.67/5.39 +-Applying beta-rule and splitting (1954), into two cases.
% 20.67/5.39 |-Branch one:
% 20.67/5.39 | (820) all_0_52_52 = e1
% 20.67/5.39 |
% 20.67/5.39 | Combining equations (427,820) yields a new equation:
% 20.67/5.39 | (572) e3 = e1
% 20.67/5.39 |
% 20.67/5.39 | Simplifying 572 yields:
% 20.67/5.39 | (418) e3 = e1
% 20.67/5.39 |
% 20.67/5.39 | Equations (418) can reduce 146 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (978) ~ (all_0_52_52 = e1)
% 20.67/5.39 | (1959) all_0_53_53 = e1 | all_0_54_54 = e1
% 20.67/5.39 |
% 20.67/5.39 +-Applying beta-rule and splitting (628), into two cases.
% 20.67/5.39 |-Branch one:
% 20.67/5.39 | (629) all_0_51_51 = e0
% 20.67/5.39 |
% 20.67/5.39 | Equations (629) can reduce 30 to:
% 20.67/5.39 | (764) ~ (all_0_53_53 = e0)
% 20.67/5.39 |
% 20.67/5.39 | Simplifying 764 yields:
% 20.67/5.39 | (765) ~ (all_0_53_53 = e0)
% 20.67/5.39 |
% 20.67/5.39 +-Applying beta-rule and splitting (27), into two cases.
% 20.67/5.39 |-Branch one:
% 20.67/5.39 | (849) all_0_53_53 = e2
% 20.67/5.39 |
% 20.67/5.39 | Equations (849) can reduce 259 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (259) ~ (all_0_53_53 = e2)
% 20.67/5.39 | (852) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 20.67/5.39 |
% 20.67/5.39 +-Applying beta-rule and splitting (837), into two cases.
% 20.67/5.39 |-Branch one:
% 20.67/5.39 | (596) all_0_49_49 = e1
% 20.67/5.39 |
% 20.67/5.39 | Equations (596) can reduce 83 to:
% 20.67/5.39 | (826) ~ (e4 = e1)
% 20.67/5.39 |
% 20.67/5.39 | Simplifying 826 yields:
% 20.67/5.39 | (251) ~ (e4 = e1)
% 20.67/5.39 |
% 20.67/5.39 +-Applying beta-rule and splitting (1959), into two cases.
% 20.67/5.39 |-Branch one:
% 20.67/5.39 | (853) all_0_53_53 = e1
% 20.67/5.39 |
% 20.67/5.39 | Equations (853) can reduce 259 to:
% 20.67/5.39 | (414) ~ (e2 = e1)
% 20.67/5.39 |
% 20.67/5.39 | Simplifying 414 yields:
% 20.67/5.39 | (148) ~ (e2 = e1)
% 20.67/5.39 |
% 20.67/5.39 | Instantiating formula (21) with e2, e3, e1, e2 and discharging atoms op(e2, e3) = e2, op(e2, e3) = e1, yields:
% 20.67/5.39 | (471) e2 = e1
% 20.67/5.39 |
% 20.67/5.39 | Equations (471) can reduce 148 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (823) ~ (all_0_53_53 = e1)
% 20.67/5.39 | (1592) all_0_54_54 = e1
% 20.67/5.39 |
% 20.67/5.39 | Combining equations (1592,535) yields a new equation:
% 20.67/5.39 | (477) e4 = e1
% 20.67/5.39 |
% 20.67/5.39 | Equations (477) can reduce 251 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (960) ~ (all_0_49_49 = e1)
% 20.67/5.39 | (961) all_0_54_54 = e1 | all_0_59_59 = e1
% 20.67/5.39 |
% 20.67/5.39 +-Applying beta-rule and splitting (192), into two cases.
% 20.67/5.39 |-Branch one:
% 20.67/5.39 | (469) all_0_47_47 = e1
% 20.67/5.39 |
% 20.67/5.39 | Combining equations (319,469) yields a new equation:
% 20.67/5.39 | (470) e2 = e1
% 20.67/5.39 |
% 20.67/5.39 | Simplifying 470 yields:
% 20.67/5.39 | (471) e2 = e1
% 20.67/5.39 |
% 20.67/5.39 | Equations (471) can reduce 148 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (473) ~ (all_0_47_47 = e1)
% 20.67/5.39 | (592) all_0_48_48 = e1 | all_0_49_49 = e1
% 20.67/5.39 |
% 20.67/5.39 +-Applying beta-rule and splitting (852), into two cases.
% 20.67/5.39 |-Branch one:
% 20.67/5.39 | (853) all_0_53_53 = e1
% 20.67/5.39 |
% 20.67/5.39 | Equations (853) can reduce 250 to:
% 20.67/5.39 | (584) ~ (all_0_48_48 = e1)
% 20.67/5.39 |
% 20.67/5.39 +-Applying beta-rule and splitting (592), into two cases.
% 20.67/5.39 |-Branch one:
% 20.67/5.39 | (593) all_0_48_48 = e1
% 20.67/5.39 |
% 20.67/5.39 | Equations (593) can reduce 584 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (584) ~ (all_0_48_48 = e1)
% 20.67/5.39 | (596) all_0_49_49 = e1
% 20.67/5.39 |
% 20.67/5.39 | Equations (596) can reduce 960 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (823) ~ (all_0_53_53 = e1)
% 20.67/5.39 | (856) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e0
% 20.67/5.39 |
% 20.67/5.39 +-Applying beta-rule and splitting (856), into two cases.
% 20.67/5.39 |-Branch one:
% 20.67/5.39 | (857) all_0_53_53 = e0
% 20.67/5.39 |
% 20.67/5.39 | Equations (857) can reduce 765 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (765) ~ (all_0_53_53 = e0)
% 20.67/5.39 | (860) all_0_53_53 = e4 | all_0_53_53 = e3
% 20.67/5.39 |
% 20.67/5.39 +-Applying beta-rule and splitting (860), into two cases.
% 20.67/5.39 |-Branch one:
% 20.67/5.39 | (861) all_0_53_53 = e3
% 20.67/5.39 |
% 20.67/5.39 | Equations (861) can reduce 796 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (796) ~ (all_0_53_53 = e3)
% 20.67/5.39 | (532) all_0_53_53 = e4
% 20.67/5.39 |
% 20.67/5.39 | Equations (532) can reduce 448 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (432) ~ (all_0_51_51 = e0)
% 20.67/5.39 | (632) all_0_56_56 = e0
% 20.67/5.39 |
% 20.67/5.39 | Combining equations (632,480) yields a new equation:
% 20.67/5.39 | (579) e1 = e0
% 20.67/5.39 |
% 20.67/5.39 | Equations (579) can reduce 144 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (575) ~ (all_0_56_56 = e1)
% 20.67/5.39 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 20.67/5.39 |
% 20.67/5.39 +-Applying beta-rule and splitting (576), into two cases.
% 20.67/5.39 |-Branch one:
% 20.67/5.39 | (577) all_0_57_57 = e1
% 20.67/5.39 |
% 20.67/5.39 | Combining equations (867,577) yields a new equation:
% 20.67/5.39 | (470) e2 = e1
% 20.67/5.39 |
% 20.67/5.39 | Simplifying 470 yields:
% 20.67/5.39 | (471) e2 = e1
% 20.67/5.39 |
% 20.67/5.39 | Equations (471) can reduce 148 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (581) ~ (all_0_57_57 = e1)
% 20.67/5.39 | (582) all_0_58_58 = e1 | all_0_59_59 = e1
% 20.67/5.39 |
% 20.67/5.39 +-Applying beta-rule and splitting (582), into two cases.
% 20.67/5.39 |-Branch one:
% 20.67/5.39 | (489) all_0_58_58 = e1
% 20.67/5.39 |
% 20.67/5.39 | Combining equations (489,497) yields a new equation:
% 20.67/5.39 | (418) e3 = e1
% 20.67/5.39 |
% 20.67/5.39 | Equations (418) can reduce 146 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (482) ~ (all_0_58_58 = e1)
% 20.67/5.39 | (614) all_0_59_59 = e1
% 20.67/5.39 |
% 20.67/5.39 | Equations (614) can reduce 2222 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (614) all_0_59_59 = e1
% 20.67/5.39 | (493) all_0_58_58 = e0
% 20.67/5.39 |
% 20.67/5.39 | Combining equations (493,497) yields a new equation:
% 20.67/5.39 | (560) e3 = e0
% 20.67/5.39 |
% 20.67/5.39 | Equations (560) can reduce 72 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (307) ~ (all_0_39_39 = e4)
% 20.67/5.39 | (3018) all_0_41_41 = e4 | all_0_42_42 = e4
% 20.67/5.39 |
% 20.67/5.39 +-Applying beta-rule and splitting (3018), into two cases.
% 20.67/5.39 |-Branch one:
% 20.67/5.39 | (740) all_0_41_41 = e4
% 20.67/5.39 |
% 20.67/5.39 | Combining equations (386,740) yields a new equation:
% 20.67/5.39 | (360) e4 = e2
% 20.67/5.39 |
% 20.67/5.39 | Equations (360) can reduce 230 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (308) ~ (all_0_41_41 = e4)
% 20.67/5.39 | (305) all_0_42_42 = e4
% 20.67/5.39 |
% 20.67/5.39 | Combining equations (610,305) yields a new equation:
% 20.67/5.39 | (516) e4 = e3
% 20.67/5.39 |
% 20.67/5.39 | Equations (516) can reduce 41 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (1924) ~ (all_0_42_42 = e3)
% 20.67/5.39 | (1925) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 20.67/5.39 |
% 20.67/5.39 +-Applying beta-rule and splitting (1925), into two cases.
% 20.67/5.39 |-Branch one:
% 20.67/5.39 | (462) all_0_46_46 = e3
% 20.67/5.39 |
% 20.67/5.39 | Combining equations (364,462) yields a new equation:
% 20.67/5.39 | (423) e3 = e2
% 20.67/5.39 |
% 20.67/5.39 | Equations (423) can reduce 224 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (618) ~ (all_0_46_46 = e3)
% 20.67/5.39 | (1930) all_0_54_54 = e3 | all_0_59_59 = e3
% 20.67/5.39 |
% 20.67/5.39 +-Applying beta-rule and splitting (1930), into two cases.
% 20.67/5.39 |-Branch one:
% 20.67/5.39 | (635) all_0_54_54 = e3
% 20.67/5.39 |
% 20.67/5.39 | Equations (635) can reduce 430 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (430) ~ (all_0_54_54 = e3)
% 20.67/5.39 | (1070) all_0_59_59 = e3
% 20.67/5.39 |
% 20.67/5.39 | Equations (1070) can reduce 2132 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (562) ~ (all_0_43_43 = e3)
% 20.67/5.39 | (1193) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 20.67/5.39 |
% 20.67/5.39 +-Applying beta-rule and splitting (1695), into two cases.
% 20.67/5.39 |-Branch one:
% 20.67/5.39 | (559) all_0_43_43 = e3
% 20.67/5.39 |
% 20.67/5.39 | Equations (559) can reduce 562 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (562) ~ (all_0_43_43 = e3)
% 20.67/5.39 | (438) all_0_43_43 = e4
% 20.67/5.39 |
% 20.67/5.39 | Equations (438) can reduce 441 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (637) ~ (all_0_52_52 = e3)
% 20.67/5.39 | (638) all_0_57_57 = e3
% 20.67/5.39 |
% 20.67/5.39 | Combining equations (867,638) yields a new equation:
% 20.67/5.39 | (423) e3 = e2
% 20.67/5.39 |
% 20.67/5.39 | Equations (423) can reduce 224 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (356) ~ (all_0_44_44 = e0)
% 20.67/5.39 | (357) all_0_52_52 = e0 | all_0_57_57 = e0
% 20.67/5.39 |
% 20.67/5.39 +-Applying beta-rule and splitting (143), into two cases.
% 20.67/5.39 |-Branch one:
% 20.67/5.39 | (433) all_0_43_43 = e0
% 20.67/5.39 |
% 20.67/5.39 | Equations (433) can reduce 321 to:
% 20.67/5.39 | (406) ~ (e2 = e0)
% 20.67/5.39 |
% 20.67/5.39 | Simplifying 406 yields:
% 20.67/5.39 | (58) ~ (e2 = e0)
% 20.67/5.39 |
% 20.67/5.39 +-Applying beta-rule and splitting (86), into two cases.
% 20.67/5.39 |-Branch one:
% 20.67/5.39 | (816) all_0_52_52 = e2
% 20.67/5.39 |
% 20.67/5.39 | Equations (816) can reduce 257 to:
% 20.67/5.39 | (269) $false
% 20.67/5.39 |
% 20.67/5.39 |-The branch is then unsatisfiable
% 20.67/5.39 |-Branch two:
% 20.67/5.39 | (257) ~ (all_0_52_52 = e2)
% 20.67/5.39 | (819) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 20.67/5.39 |
% 20.67/5.39 +-Applying beta-rule and splitting (357), into two cases.
% 20.67/5.39 |-Branch one:
% 20.67/5.39 | (397) all_0_52_52 = e0
% 20.67/5.39 |
% 20.67/5.39 | Equations (397) can reduce 257 to:
% 20.67/5.39 | (406) ~ (e2 = e0)
% 20.67/5.39 |
% 20.67/5.39 | Simplifying 406 yields:
% 20.67/5.39 | (58) ~ (e2 = e0)
% 20.67/5.39 |
% 20.67/5.39 | Equations (397) can reduce 978 to:
% 20.67/5.39 | (436) ~ (e1 = e0)
% 20.67/5.39 |
% 20.67/5.39 | Simplifying 436 yields:
% 20.67/5.39 | (144) ~ (e1 = e0)
% 20.67/5.39 |
% 20.67/5.39 | From (397) and (2268) follows:
% 20.67/5.39 | (3993) op(e2, e0) = e1
% 20.67/5.39 |
% 20.67/5.39 | From (397) and (89) follows:
% 20.67/5.39 | (4401) op(e1, e0) = all_0_18_18
% 20.67/5.39 |
% 20.67/5.39 | Instantiating formula (21) with e2, e0, e1, all_0_49_49 and discharging atoms op(e2, e0) = all_0_49_49, op(e2, e0) = e1, yields:
% 20.67/5.39 | (596) all_0_49_49 = e1
% 20.67/5.39 |
% 20.67/5.39 | Instantiating formula (21) with e1, e0, all_0_18_18, all_0_54_54 and discharging atoms op(e1, e0) = all_0_18_18, op(e1, e0) = all_0_54_54, yields:
% 20.67/5.39 | (4403) all_0_18_18 = all_0_54_54
% 20.67/5.39 |
% 20.67/5.39 | Equations (4403) can reduce 520 to:
% 20.67/5.39 | (261) ~ (all_0_54_54 = e2)
% 20.67/5.39 |
% 20.67/5.39 | From (4403) and (4401) follows:
% 20.67/5.39 | (13) op(e1, e0) = all_0_54_54
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (10), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (623) all_0_47_47 = e0
% 20.67/5.40 |
% 20.67/5.40 | Combining equations (319,623) yields a new equation:
% 20.67/5.40 | (353) e2 = e0
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 353 yields:
% 20.67/5.40 | (354) e2 = e0
% 20.67/5.40 |
% 20.67/5.40 | Equations (354) can reduce 58 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (297) ~ (all_0_47_47 = e0)
% 20.67/5.40 | (815) all_0_48_48 = e0 | all_0_49_49 = e0
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (815), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (903) all_0_48_48 = e0
% 20.67/5.40 |
% 20.67/5.40 | From (903) and (3130) follows:
% 20.67/5.40 | (3199) op(e1, e0) = e2
% 20.67/5.40 |
% 20.67/5.40 | Instantiating formula (21) with e1, e0, e2, all_0_54_54 and discharging atoms op(e1, e0) = all_0_54_54, op(e1, e0) = e2, yields:
% 20.67/5.40 | (372) all_0_54_54 = e2
% 20.67/5.40 |
% 20.67/5.40 | Equations (372) can reduce 261 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (952) ~ (all_0_48_48 = e0)
% 20.67/5.40 | (965) all_0_49_49 = e0
% 20.67/5.40 |
% 20.67/5.40 | Combining equations (596,965) yields a new equation:
% 20.67/5.40 | (578) e1 = e0
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 578 yields:
% 20.67/5.40 | (579) e1 = e0
% 20.67/5.40 |
% 20.67/5.40 | Equations (579) can reduce 144 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (317) ~ (all_0_52_52 = e0)
% 20.67/5.40 | (400) all_0_57_57 = e0
% 20.67/5.40 |
% 20.67/5.40 | Combining equations (400,867) yields a new equation:
% 20.67/5.40 | (354) e2 = e0
% 20.67/5.40 |
% 20.67/5.40 | Equations (354) can reduce 58 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (459) ~ (all_0_43_43 = e0)
% 20.67/5.40 | (1676) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (357), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (397) all_0_52_52 = e0
% 20.67/5.40 |
% 20.67/5.40 | Equations (397) can reduce 121 to:
% 20.67/5.40 | (356) ~ (all_0_44_44 = e0)
% 20.67/5.40 |
% 20.67/5.40 | Equations (397) can reduce 152 to:
% 20.67/5.40 | (404) ~ (e4 = e0)
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 404 yields:
% 20.67/5.40 | (11) ~ (e4 = e0)
% 20.67/5.40 |
% 20.67/5.40 | Equations (397) can reduce 257 to:
% 20.67/5.40 | (406) ~ (e2 = e0)
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 406 yields:
% 20.67/5.40 | (58) ~ (e2 = e0)
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (1676), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (352) all_0_44_44 = e0
% 20.67/5.40 |
% 20.67/5.40 | Equations (352) can reduce 356 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (356) ~ (all_0_44_44 = e0)
% 20.67/5.40 | (4115) all_0_45_45 = e0 | all_0_46_46 = e0
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (4115), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (889) all_0_45_45 = e0
% 20.67/5.40 |
% 20.67/5.40 | Combining equations (444,889) yields a new equation:
% 20.67/5.40 | (751) e4 = e0
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 751 yields:
% 20.67/5.40 | (439) e4 = e0
% 20.67/5.40 |
% 20.67/5.40 | Equations (439) can reduce 11 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (299) ~ (all_0_45_45 = e0)
% 20.67/5.40 | (546) all_0_46_46 = e0
% 20.67/5.40 |
% 20.67/5.40 | Combining equations (364,546) yields a new equation:
% 20.67/5.40 | (353) e2 = e0
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 353 yields:
% 20.67/5.40 | (354) e2 = e0
% 20.67/5.40 |
% 20.67/5.40 | Equations (354) can reduce 58 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (317) ~ (all_0_52_52 = e0)
% 20.67/5.40 | (400) all_0_57_57 = e0
% 20.67/5.40 |
% 20.67/5.40 | Combining equations (867,400) yields a new equation:
% 20.67/5.40 | (353) e2 = e0
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 353 yields:
% 20.67/5.40 | (354) e2 = e0
% 20.67/5.40 |
% 20.67/5.40 | Equations (354) can reduce 58 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (942) all_0_28_28 = e0 & ~ (all_0_29_29 = e1)
% 20.67/5.40 |
% 20.67/5.40 | Applying alpha-rule on (942) yields:
% 20.67/5.40 | (943) all_0_28_28 = e0
% 20.67/5.40 | (944) ~ (all_0_29_29 = e1)
% 20.67/5.40 |
% 20.67/5.40 | From (943) and (67) follows:
% 20.67/5.40 | (3447) op(e1, all_0_58_58) = e0
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (110), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (352) all_0_44_44 = e0
% 20.67/5.40 |
% 20.67/5.40 | Equations (352) can reduce 228 to:
% 20.67/5.40 | (459) ~ (all_0_43_43 = e0)
% 20.67/5.40 |
% 20.67/5.40 | Equations (352) can reduce 659 to:
% 20.67/5.40 | (406) ~ (e2 = e0)
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 406 yields:
% 20.67/5.40 | (58) ~ (e2 = e0)
% 20.67/5.40 |
% 20.67/5.40 | Equations (352) can reduce 87 to:
% 20.67/5.40 | (436) ~ (e1 = e0)
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 436 yields:
% 20.67/5.40 | (144) ~ (e1 = e0)
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (193), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (417) all_0_40_40 = e3
% 20.67/5.40 |
% 20.67/5.40 | Combining equations (417,413) yields a new equation:
% 20.67/5.40 | (572) e3 = e1
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 572 yields:
% 20.67/5.40 | (418) e3 = e1
% 20.67/5.40 |
% 20.67/5.40 | Equations (418) can reduce 146 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (420) ~ (all_0_40_40 = e3)
% 20.67/5.40 | (421) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (421), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (422) all_0_44_44 = e3
% 20.67/5.40 |
% 20.67/5.40 | Combining equations (352,422) yields a new equation:
% 20.67/5.40 | (560) e3 = e0
% 20.67/5.40 |
% 20.67/5.40 | Equations (560) can reduce 72 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (425) ~ (all_0_44_44 = e3)
% 20.67/5.40 | (426) all_0_52_52 = e3 | all_0_57_57 = e3
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (426), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (427) all_0_52_52 = e3
% 20.67/5.40 |
% 20.67/5.40 | Equations (427) can reduce 71 to:
% 20.67/5.40 | (3866) ~ (all_0_53_53 = e3)
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 3866 yields:
% 20.67/5.40 | (796) ~ (all_0_53_53 = e3)
% 20.67/5.40 |
% 20.67/5.40 | Equations (427) can reduce 62 to:
% 20.67/5.40 | (429) ~ (all_0_54_54 = e3)
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 429 yields:
% 20.67/5.40 | (430) ~ (all_0_54_54 = e3)
% 20.67/5.40 |
% 20.67/5.40 | From (427) and (2268) follows:
% 20.67/5.40 | (3095) op(e2, e3) = e1
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (200), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (464) all_0_39_39 = e1
% 20.67/5.40 |
% 20.67/5.40 | Equations (464) can reduce 467 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (467) ~ (all_0_39_39 = e1)
% 20.67/5.40 | (468) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (22), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (661) all_0_43_43 = e2
% 20.67/5.40 |
% 20.67/5.40 | Equations (661) can reduce 321 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (321) ~ (all_0_43_43 = e2)
% 20.67/5.40 | (1198) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (1198), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (433) all_0_43_43 = e0
% 20.67/5.40 |
% 20.67/5.40 | Equations (433) can reduce 459 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (459) ~ (all_0_43_43 = e0)
% 20.67/5.40 | (1695) all_0_43_43 = e4 | all_0_43_43 = e3
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (162), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (559) all_0_43_43 = e3
% 20.67/5.40 |
% 20.67/5.40 | Equations (559) can reduce 441 to:
% 20.67/5.40 | (498) ~ (e4 = e3)
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 498 yields:
% 20.67/5.40 | (41) ~ (e4 = e3)
% 20.67/5.40 |
% 20.67/5.40 | Equations (559) can reduce 321 to:
% 20.67/5.40 | (224) ~ (e3 = e2)
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (213), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (605) all_0_41_41 = e3
% 20.67/5.40 |
% 20.67/5.40 | Combining equations (605,386) yields a new equation:
% 20.67/5.40 | (606) e3 = e2
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 606 yields:
% 20.67/5.40 | (423) e3 = e2
% 20.67/5.40 |
% 20.67/5.40 | Equations (423) can reduce 224 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (609) ~ (all_0_41_41 = e3)
% 20.67/5.40 | (3891) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (468), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (469) all_0_47_47 = e1
% 20.67/5.40 |
% 20.67/5.40 | Combining equations (319,469) yields a new equation:
% 20.67/5.40 | (470) e2 = e1
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 470 yields:
% 20.67/5.40 | (471) e2 = e1
% 20.67/5.40 |
% 20.67/5.40 | Equations (471) can reduce 148 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (473) ~ (all_0_47_47 = e1)
% 20.67/5.40 | (474) all_0_51_51 = e1 | all_0_56_56 = e1
% 20.67/5.40 |
% 20.67/5.40 | Equations (319) can reduce 473 to:
% 20.67/5.40 | (148) ~ (e2 = e1)
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (3891), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (1087) all_0_45_45 = e3
% 20.67/5.40 |
% 20.67/5.40 | Combining equations (1087,444) yields a new equation:
% 20.67/5.40 | (516) e4 = e3
% 20.67/5.40 |
% 20.67/5.40 | Equations (516) can reduce 41 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (689) ~ (all_0_45_45 = e3)
% 20.67/5.40 | (3903) all_0_53_53 = e3 | all_0_58_58 = e3
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (47), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (348) all_0_39_39 = e2
% 20.67/5.40 |
% 20.67/5.40 | Equations (348) can reduce 320 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (320) ~ (all_0_39_39 = e2)
% 20.67/5.40 | (709) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (3903), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (861) all_0_53_53 = e3
% 20.67/5.40 |
% 20.67/5.40 | Equations (861) can reduce 796 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (796) ~ (all_0_53_53 = e3)
% 20.67/5.40 | (497) all_0_58_58 = e3
% 20.67/5.40 |
% 20.67/5.40 | Equations (497) can reduce 127 to:
% 20.67/5.40 | (796) ~ (all_0_53_53 = e3)
% 20.67/5.40 |
% 20.67/5.40 | Equations (497) can reduce 223 to:
% 20.67/5.40 | (1183) ~ (all_0_56_56 = e3)
% 20.67/5.40 |
% 20.67/5.40 | Equations (497) can reduce 198 to:
% 20.67/5.40 | (2131) ~ (all_0_59_59 = e3)
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 2131 yields:
% 20.67/5.40 | (2132) ~ (all_0_59_59 = e3)
% 20.67/5.40 |
% 20.67/5.40 | Equations (497) can reduce 277 to:
% 20.67/5.40 | (498) ~ (e4 = e3)
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 498 yields:
% 20.67/5.40 | (41) ~ (e4 = e3)
% 20.67/5.40 |
% 20.67/5.40 | Equations (497) can reduce 392 to:
% 20.67/5.40 | (224) ~ (e3 = e2)
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (169), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (610) all_0_42_42 = e3
% 20.67/5.40 |
% 20.67/5.40 | Equations (610) can reduce 836 to:
% 20.67/5.40 | (146) ~ (e3 = e1)
% 20.67/5.40 |
% 20.67/5.40 | Equations (610) can reduce 155 to:
% 20.67/5.40 | (72) ~ (e3 = e0)
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (32), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (1079) all_0_39_39 = e4
% 20.67/5.40 |
% 20.67/5.40 | Equations (1079) can reduce 126 to:
% 20.67/5.40 | (1208) ~ (all_0_51_51 = e4)
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 1208 yields:
% 20.67/5.40 | (530) ~ (all_0_51_51 = e4)
% 20.67/5.40 |
% 20.67/5.40 | Equations (1079) can reduce 320 to:
% 20.67/5.40 | (230) ~ (e4 = e2)
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (153), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (453) all_0_50_50 = e4
% 20.67/5.40 |
% 20.67/5.40 | Combining equations (253,453) yields a new equation:
% 20.67/5.40 | (360) e4 = e2
% 20.67/5.40 |
% 20.67/5.40 | Equations (360) can reduce 230 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (456) ~ (all_0_50_50 = e4)
% 20.67/5.40 | (457) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (2629), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (2222) ~ (all_0_59_59 = e1)
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (43), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (480) all_0_56_56 = e1
% 20.67/5.40 |
% 20.67/5.40 | Equations (480) can reduce 16 to:
% 20.67/5.40 | (479) ~ (all_0_51_51 = e1)
% 20.67/5.40 |
% 20.67/5.40 | Equations (480) can reduce 1183 to:
% 20.67/5.40 | (597) ~ (e3 = e1)
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 597 yields:
% 20.67/5.40 | (146) ~ (e3 = e1)
% 20.67/5.40 |
% 20.67/5.40 | Equations (480) can reduce 377 to:
% 20.67/5.40 | (414) ~ (e2 = e1)
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 414 yields:
% 20.67/5.40 | (148) ~ (e2 = e1)
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (211), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (632) all_0_56_56 = e0
% 20.67/5.40 |
% 20.67/5.40 | Combining equations (480,632) yields a new equation:
% 20.67/5.40 | (578) e1 = e0
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 578 yields:
% 20.67/5.40 | (579) e1 = e0
% 20.67/5.40 |
% 20.67/5.40 | Equations (579) can reduce 144 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (401) ~ (all_0_56_56 = e0)
% 20.67/5.40 | (2052) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 20.67/5.40 |
% 20.67/5.40 | Equations (480) can reduce 401 to:
% 20.67/5.40 | (144) ~ (e1 = e0)
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (171), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (433) all_0_43_43 = e0
% 20.67/5.40 |
% 20.67/5.40 | Combining equations (559,433) yields a new equation:
% 20.67/5.40 | (781) e3 = e0
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 781 yields:
% 20.67/5.40 | (560) e3 = e0
% 20.67/5.40 |
% 20.67/5.40 | Equations (560) can reduce 72 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (459) ~ (all_0_43_43 = e0)
% 20.67/5.40 | (622) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (457), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (458) all_0_51_51 = e4
% 20.67/5.40 |
% 20.67/5.40 | Equations (458) can reduce 530 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (530) ~ (all_0_51_51 = e4)
% 20.67/5.40 | (531) all_0_53_53 = e4 | all_0_54_54 = e4
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (531), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (532) all_0_53_53 = e4
% 20.67/5.40 |
% 20.67/5.40 | Equations (532) can reduce 448 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (448) ~ (all_0_53_53 = e4)
% 20.67/5.40 | (535) all_0_54_54 = e4
% 20.67/5.40 |
% 20.67/5.40 | Equations (535) can reduce 217 to:
% 20.67/5.40 | (83) ~ (all_0_49_49 = e4)
% 20.67/5.40 |
% 20.67/5.40 | Equations (535) can reduce 119 to:
% 20.67/5.40 | (448) ~ (all_0_53_53 = e4)
% 20.67/5.40 |
% 20.67/5.40 +-Applying beta-rule and splitting (622), into two cases.
% 20.67/5.40 |-Branch one:
% 20.67/5.40 | (623) all_0_47_47 = e0
% 20.67/5.40 |
% 20.67/5.40 | Combining equations (319,623) yields a new equation:
% 20.67/5.40 | (353) e2 = e0
% 20.67/5.40 |
% 20.67/5.40 | Simplifying 353 yields:
% 20.67/5.40 | (354) e2 = e0
% 20.67/5.40 |
% 20.67/5.40 | Equations (354) can reduce 58 to:
% 20.67/5.40 | (269) $false
% 20.67/5.40 |
% 20.67/5.40 |-The branch is then unsatisfiable
% 20.67/5.40 |-Branch two:
% 20.67/5.40 | (297) ~ (all_0_47_47 = e0)
% 20.67/5.40 | (628) all_0_51_51 = e0 | all_0_56_56 = e0
% 20.67/5.41 |
% 20.67/5.41 +-Applying beta-rule and splitting (19), into two cases.
% 20.67/5.41 |-Branch one:
% 20.67/5.41 | (475) all_0_51_51 = e1
% 20.67/5.41 |
% 20.67/5.41 | Equations (475) can reduce 479 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (479) ~ (all_0_51_51 = e1)
% 20.67/5.41 | (1954) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 20.67/5.41 |
% 20.67/5.41 +-Applying beta-rule and splitting (84), into two cases.
% 20.67/5.41 |-Branch one:
% 20.67/5.41 | (832) all_0_42_42 = e1
% 20.67/5.41 |
% 20.67/5.41 | Combining equations (832,610) yields a new equation:
% 20.67/5.41 | (418) e3 = e1
% 20.67/5.41 |
% 20.67/5.41 | Equations (418) can reduce 146 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (836) ~ (all_0_42_42 = e1)
% 20.67/5.41 | (837) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 20.67/5.41 |
% 20.67/5.41 | Equations (610) can reduce 836 to:
% 20.67/5.41 | (146) ~ (e3 = e1)
% 20.67/5.41 |
% 20.67/5.41 +-Applying beta-rule and splitting (1954), into two cases.
% 20.67/5.41 |-Branch one:
% 20.67/5.41 | (820) all_0_52_52 = e1
% 20.67/5.41 |
% 20.67/5.41 | Combining equations (427,820) yields a new equation:
% 20.67/5.41 | (572) e3 = e1
% 20.67/5.41 |
% 20.67/5.41 | Simplifying 572 yields:
% 20.67/5.41 | (418) e3 = e1
% 20.67/5.41 |
% 20.67/5.41 | Equations (418) can reduce 146 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (978) ~ (all_0_52_52 = e1)
% 20.67/5.41 | (1959) all_0_53_53 = e1 | all_0_54_54 = e1
% 20.67/5.41 |
% 20.67/5.41 +-Applying beta-rule and splitting (628), into two cases.
% 20.67/5.41 |-Branch one:
% 20.67/5.41 | (629) all_0_51_51 = e0
% 20.67/5.41 |
% 20.67/5.41 | Equations (629) can reduce 30 to:
% 20.67/5.41 | (764) ~ (all_0_53_53 = e0)
% 20.67/5.41 |
% 20.67/5.41 | Simplifying 764 yields:
% 20.67/5.41 | (765) ~ (all_0_53_53 = e0)
% 20.67/5.41 |
% 20.67/5.41 +-Applying beta-rule and splitting (27), into two cases.
% 20.67/5.41 |-Branch one:
% 20.67/5.41 | (849) all_0_53_53 = e2
% 20.67/5.41 |
% 20.67/5.41 | Equations (849) can reduce 259 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (259) ~ (all_0_53_53 = e2)
% 20.67/5.41 | (852) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 20.67/5.41 |
% 20.67/5.41 +-Applying beta-rule and splitting (837), into two cases.
% 20.67/5.41 |-Branch one:
% 20.67/5.41 | (596) all_0_49_49 = e1
% 20.67/5.41 |
% 20.67/5.41 | Equations (596) can reduce 83 to:
% 20.67/5.41 | (826) ~ (e4 = e1)
% 20.67/5.41 |
% 20.67/5.41 | Simplifying 826 yields:
% 20.67/5.41 | (251) ~ (e4 = e1)
% 20.67/5.41 |
% 20.67/5.41 +-Applying beta-rule and splitting (1959), into two cases.
% 20.67/5.41 |-Branch one:
% 20.67/5.41 | (853) all_0_53_53 = e1
% 20.67/5.41 |
% 20.67/5.41 | Equations (853) can reduce 259 to:
% 20.67/5.41 | (414) ~ (e2 = e1)
% 20.67/5.41 |
% 20.67/5.41 | Simplifying 414 yields:
% 20.67/5.41 | (148) ~ (e2 = e1)
% 20.67/5.41 |
% 20.67/5.41 | Instantiating formula (21) with e2, e3, e1, e2 and discharging atoms op(e2, e3) = e2, op(e2, e3) = e1, yields:
% 20.67/5.41 | (471) e2 = e1
% 20.67/5.41 |
% 20.67/5.41 | Equations (471) can reduce 148 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (823) ~ (all_0_53_53 = e1)
% 20.67/5.41 | (1592) all_0_54_54 = e1
% 20.67/5.41 |
% 20.67/5.41 | Combining equations (1592,535) yields a new equation:
% 20.67/5.41 | (477) e4 = e1
% 20.67/5.41 |
% 20.67/5.41 | Equations (477) can reduce 251 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (960) ~ (all_0_49_49 = e1)
% 20.67/5.41 | (961) all_0_54_54 = e1 | all_0_59_59 = e1
% 20.67/5.41 |
% 20.67/5.41 +-Applying beta-rule and splitting (192), into two cases.
% 20.67/5.41 |-Branch one:
% 20.67/5.41 | (469) all_0_47_47 = e1
% 20.67/5.41 |
% 20.67/5.41 | Combining equations (319,469) yields a new equation:
% 20.67/5.41 | (470) e2 = e1
% 20.67/5.41 |
% 20.67/5.41 | Simplifying 470 yields:
% 20.67/5.41 | (471) e2 = e1
% 20.67/5.41 |
% 20.67/5.41 | Equations (471) can reduce 148 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (473) ~ (all_0_47_47 = e1)
% 20.67/5.41 | (592) all_0_48_48 = e1 | all_0_49_49 = e1
% 20.67/5.41 |
% 20.67/5.41 +-Applying beta-rule and splitting (852), into two cases.
% 20.67/5.41 |-Branch one:
% 20.67/5.41 | (853) all_0_53_53 = e1
% 20.67/5.41 |
% 20.67/5.41 | Equations (853) can reduce 250 to:
% 20.67/5.41 | (584) ~ (all_0_48_48 = e1)
% 20.67/5.41 |
% 20.67/5.41 +-Applying beta-rule and splitting (592), into two cases.
% 20.67/5.41 |-Branch one:
% 20.67/5.41 | (593) all_0_48_48 = e1
% 20.67/5.41 |
% 20.67/5.41 | Equations (593) can reduce 584 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (584) ~ (all_0_48_48 = e1)
% 20.67/5.41 | (596) all_0_49_49 = e1
% 20.67/5.41 |
% 20.67/5.41 | Equations (596) can reduce 960 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (823) ~ (all_0_53_53 = e1)
% 20.67/5.41 | (856) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e0
% 20.67/5.41 |
% 20.67/5.41 +-Applying beta-rule and splitting (856), into two cases.
% 20.67/5.41 |-Branch one:
% 20.67/5.41 | (857) all_0_53_53 = e0
% 20.67/5.41 |
% 20.67/5.41 | Equations (857) can reduce 765 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (765) ~ (all_0_53_53 = e0)
% 20.67/5.41 | (860) all_0_53_53 = e4 | all_0_53_53 = e3
% 20.67/5.41 |
% 20.67/5.41 +-Applying beta-rule and splitting (860), into two cases.
% 20.67/5.41 |-Branch one:
% 20.67/5.41 | (861) all_0_53_53 = e3
% 20.67/5.41 |
% 20.67/5.41 | Equations (861) can reduce 796 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (796) ~ (all_0_53_53 = e3)
% 20.67/5.41 | (532) all_0_53_53 = e4
% 20.67/5.41 |
% 20.67/5.41 | Equations (532) can reduce 448 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (432) ~ (all_0_51_51 = e0)
% 20.67/5.41 | (632) all_0_56_56 = e0
% 20.67/5.41 |
% 20.67/5.41 | Combining equations (632,480) yields a new equation:
% 20.67/5.41 | (579) e1 = e0
% 20.67/5.41 |
% 20.67/5.41 | Equations (579) can reduce 144 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (575) ~ (all_0_56_56 = e1)
% 20.67/5.41 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 20.67/5.41 |
% 20.67/5.41 +-Applying beta-rule and splitting (576), into two cases.
% 20.67/5.41 |-Branch one:
% 20.67/5.41 | (577) all_0_57_57 = e1
% 20.67/5.41 |
% 20.67/5.41 | Combining equations (867,577) yields a new equation:
% 20.67/5.41 | (470) e2 = e1
% 20.67/5.41 |
% 20.67/5.41 | Simplifying 470 yields:
% 20.67/5.41 | (471) e2 = e1
% 20.67/5.41 |
% 20.67/5.41 | Equations (471) can reduce 148 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (581) ~ (all_0_57_57 = e1)
% 20.67/5.41 | (582) all_0_58_58 = e1 | all_0_59_59 = e1
% 20.67/5.41 |
% 20.67/5.41 +-Applying beta-rule and splitting (582), into two cases.
% 20.67/5.41 |-Branch one:
% 20.67/5.41 | (489) all_0_58_58 = e1
% 20.67/5.41 |
% 20.67/5.41 | Combining equations (489,497) yields a new equation:
% 20.67/5.41 | (418) e3 = e1
% 20.67/5.41 |
% 20.67/5.41 | Equations (418) can reduce 146 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (482) ~ (all_0_58_58 = e1)
% 20.67/5.41 | (614) all_0_59_59 = e1
% 20.67/5.41 |
% 20.67/5.41 | Equations (614) can reduce 2222 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (614) all_0_59_59 = e1
% 20.67/5.41 | (493) all_0_58_58 = e0
% 20.67/5.41 |
% 20.67/5.41 | Combining equations (493,497) yields a new equation:
% 20.67/5.41 | (560) e3 = e0
% 20.67/5.41 |
% 20.67/5.41 | Equations (560) can reduce 72 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (307) ~ (all_0_39_39 = e4)
% 20.67/5.41 | (3018) all_0_41_41 = e4 | all_0_42_42 = e4
% 20.67/5.41 |
% 20.67/5.41 +-Applying beta-rule and splitting (3018), into two cases.
% 20.67/5.41 |-Branch one:
% 20.67/5.41 | (740) all_0_41_41 = e4
% 20.67/5.41 |
% 20.67/5.41 | Combining equations (386,740) yields a new equation:
% 20.67/5.41 | (360) e4 = e2
% 20.67/5.41 |
% 20.67/5.41 | Equations (360) can reduce 230 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (308) ~ (all_0_41_41 = e4)
% 20.67/5.41 | (305) all_0_42_42 = e4
% 20.67/5.41 |
% 20.67/5.41 | Combining equations (610,305) yields a new equation:
% 20.67/5.41 | (516) e4 = e3
% 20.67/5.41 |
% 20.67/5.41 | Equations (516) can reduce 41 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (1924) ~ (all_0_42_42 = e3)
% 20.67/5.41 | (1925) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 20.67/5.41 |
% 20.67/5.41 +-Applying beta-rule and splitting (1925), into two cases.
% 20.67/5.41 |-Branch one:
% 20.67/5.41 | (462) all_0_46_46 = e3
% 20.67/5.41 |
% 20.67/5.41 | Combining equations (364,462) yields a new equation:
% 20.67/5.41 | (423) e3 = e2
% 20.67/5.41 |
% 20.67/5.41 | Equations (423) can reduce 224 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (618) ~ (all_0_46_46 = e3)
% 20.67/5.41 | (1930) all_0_54_54 = e3 | all_0_59_59 = e3
% 20.67/5.41 |
% 20.67/5.41 +-Applying beta-rule and splitting (1930), into two cases.
% 20.67/5.41 |-Branch one:
% 20.67/5.41 | (635) all_0_54_54 = e3
% 20.67/5.41 |
% 20.67/5.41 | Equations (635) can reduce 430 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (430) ~ (all_0_54_54 = e3)
% 20.67/5.41 | (1070) all_0_59_59 = e3
% 20.67/5.41 |
% 20.67/5.41 | Equations (1070) can reduce 2132 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (562) ~ (all_0_43_43 = e3)
% 20.67/5.41 | (1193) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 20.67/5.41 |
% 20.67/5.41 +-Applying beta-rule and splitting (1695), into two cases.
% 20.67/5.41 |-Branch one:
% 20.67/5.41 | (559) all_0_43_43 = e3
% 20.67/5.41 |
% 20.67/5.41 | Equations (559) can reduce 562 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (562) ~ (all_0_43_43 = e3)
% 20.67/5.41 | (438) all_0_43_43 = e4
% 20.67/5.41 |
% 20.67/5.41 | Equations (438) can reduce 441 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (637) ~ (all_0_52_52 = e3)
% 20.67/5.41 | (638) all_0_57_57 = e3
% 20.67/5.41 |
% 20.67/5.41 | Combining equations (867,638) yields a new equation:
% 20.67/5.41 | (423) e3 = e2
% 20.67/5.41 |
% 20.67/5.41 | Equations (423) can reduce 224 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (356) ~ (all_0_44_44 = e0)
% 20.67/5.41 | (357) all_0_52_52 = e0 | all_0_57_57 = e0
% 20.67/5.41 |
% 20.67/5.41 +-Applying beta-rule and splitting (143), into two cases.
% 20.67/5.41 |-Branch one:
% 20.67/5.41 | (433) all_0_43_43 = e0
% 20.67/5.41 |
% 20.67/5.41 | Equations (433) can reduce 234 to:
% 20.67/5.41 | (165) ~ (all_0_39_39 = e0)
% 20.67/5.41 |
% 20.67/5.41 | Equations (433) can reduce 228 to:
% 20.67/5.41 | (4094) ~ (all_0_44_44 = e0)
% 20.67/5.41 |
% 20.67/5.41 | Simplifying 4094 yields:
% 20.67/5.41 | (356) ~ (all_0_44_44 = e0)
% 20.67/5.41 |
% 20.67/5.41 | Equations (433) can reduce 232 to:
% 20.67/5.41 | (1556) ~ (all_0_56_56 = e0)
% 20.67/5.41 |
% 20.67/5.41 | Simplifying 1556 yields:
% 20.67/5.41 | (401) ~ (all_0_56_56 = e0)
% 20.67/5.41 |
% 20.67/5.41 | Equations (433) can reduce 321 to:
% 20.67/5.41 | (406) ~ (e2 = e0)
% 20.67/5.41 |
% 20.67/5.41 | Simplifying 406 yields:
% 20.67/5.41 | (58) ~ (e2 = e0)
% 20.67/5.41 |
% 20.67/5.41 +-Applying beta-rule and splitting (660), into two cases.
% 20.67/5.41 |-Branch one:
% 20.67/5.41 | (352) all_0_44_44 = e0
% 20.67/5.41 |
% 20.67/5.41 | Equations (352) can reduce 356 to:
% 20.67/5.41 | (269) $false
% 20.67/5.41 |
% 20.67/5.41 |-The branch is then unsatisfiable
% 20.67/5.41 |-Branch two:
% 20.67/5.41 | (356) ~ (all_0_44_44 = e0)
% 20.67/5.41 | (422) all_0_44_44 = e3
% 20.67/5.41 |
% 20.82/5.41 | Equations (422) can reduce 190 to:
% 20.82/5.41 | (498) ~ (e4 = e3)
% 20.82/5.41 |
% 20.82/5.41 | Simplifying 498 yields:
% 20.82/5.41 | (41) ~ (e4 = e3)
% 20.82/5.41 |
% 20.82/5.41 | Equations (422) can reduce 659 to:
% 20.82/5.41 | (224) ~ (e3 = e2)
% 20.82/5.41 |
% 20.82/5.41 +-Applying beta-rule and splitting (86), into two cases.
% 20.82/5.41 |-Branch one:
% 20.82/5.41 | (816) all_0_52_52 = e2
% 20.82/5.41 |
% 20.82/5.41 | Equations (816) can reduce 257 to:
% 20.82/5.41 | (269) $false
% 20.82/5.41 |
% 20.82/5.41 |-The branch is then unsatisfiable
% 20.82/5.41 |-Branch two:
% 20.82/5.41 | (257) ~ (all_0_52_52 = e2)
% 20.82/5.41 | (819) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 20.82/5.41 |
% 20.82/5.41 +-Applying beta-rule and splitting (357), into two cases.
% 20.82/5.41 |-Branch one:
% 20.82/5.41 | (397) all_0_52_52 = e0
% 20.82/5.41 |
% 20.82/5.41 | Equations (397) can reduce 194 to:
% 20.82/5.41 | (432) ~ (all_0_51_51 = e0)
% 20.82/5.41 |
% 20.82/5.41 | Equations (397) can reduce 257 to:
% 20.82/5.41 | (406) ~ (e2 = e0)
% 20.82/5.41 |
% 20.82/5.41 | Simplifying 406 yields:
% 20.82/5.41 | (58) ~ (e2 = e0)
% 20.82/5.41 |
% 20.82/5.41 | Equations (397) can reduce 978 to:
% 20.82/5.41 | (436) ~ (e1 = e0)
% 20.82/5.41 |
% 20.82/5.41 | Simplifying 436 yields:
% 20.82/5.41 | (144) ~ (e1 = e0)
% 20.82/5.41 |
% 20.82/5.41 | From (397) and (2268) follows:
% 20.82/5.41 | (3993) op(e2, e0) = e1
% 20.82/5.41 |
% 20.82/5.41 | From (397) and (89) follows:
% 20.82/5.41 | (4401) op(e1, e0) = all_0_18_18
% 20.82/5.41 |
% 20.82/5.41 | Instantiating formula (21) with e2, e0, e1, all_0_49_49 and discharging atoms op(e2, e0) = all_0_49_49, op(e2, e0) = e1, yields:
% 20.82/5.42 | (596) all_0_49_49 = e1
% 20.82/5.42 |
% 20.82/5.42 | Instantiating formula (21) with e1, e0, all_0_18_18, all_0_54_54 and discharging atoms op(e1, e0) = all_0_18_18, op(e1, e0) = all_0_54_54, yields:
% 20.82/5.42 | (4403) all_0_18_18 = all_0_54_54
% 20.82/5.42 |
% 20.82/5.42 | Equations (4403) can reduce 520 to:
% 20.82/5.42 | (261) ~ (all_0_54_54 = e2)
% 20.82/5.42 |
% 20.82/5.42 | Equations (596) can reduce 217 to:
% 20.82/5.42 | (1237) ~ (all_0_54_54 = e1)
% 20.82/5.42 |
% 20.82/5.42 | Simplifying 1237 yields:
% 20.82/5.42 | (1238) ~ (all_0_54_54 = e1)
% 20.82/5.42 |
% 20.82/5.42 | From (596) and (183) follows:
% 20.82/5.42 | (2829) op(e0, e1) = all_0_34_34
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (10), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (623) all_0_47_47 = e0
% 20.82/5.42 |
% 20.82/5.42 | Combining equations (319,623) yields a new equation:
% 20.82/5.42 | (353) e2 = e0
% 20.82/5.42 |
% 20.82/5.42 | Simplifying 353 yields:
% 20.82/5.42 | (354) e2 = e0
% 20.82/5.42 |
% 20.82/5.42 | Equations (354) can reduce 58 to:
% 20.82/5.42 | (269) $false
% 20.82/5.42 |
% 20.82/5.42 |-The branch is then unsatisfiable
% 20.82/5.42 |-Branch two:
% 20.82/5.42 | (297) ~ (all_0_47_47 = e0)
% 20.82/5.42 | (815) all_0_48_48 = e0 | all_0_49_49 = e0
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (815), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (903) all_0_48_48 = e0
% 20.82/5.42 |
% 20.82/5.42 | Equations (903) can reduce 250 to:
% 20.82/5.42 | (764) ~ (all_0_53_53 = e0)
% 20.82/5.42 |
% 20.82/5.42 | Simplifying 764 yields:
% 20.82/5.42 | (765) ~ (all_0_53_53 = e0)
% 20.82/5.42 |
% 20.82/5.42 | Equations (903) can reduce 174 to:
% 20.82/5.42 | (402) ~ (all_0_58_58 = e0)
% 20.82/5.42 |
% 20.82/5.42 | Simplifying 402 yields:
% 20.82/5.42 | (403) ~ (all_0_58_58 = e0)
% 20.82/5.42 |
% 20.82/5.42 | Equations (903) can reduce 4 to:
% 20.82/5.42 | (1272) ~ (e3 = e0)
% 20.82/5.42 |
% 20.82/5.42 | Simplifying 1272 yields:
% 20.82/5.42 | (72) ~ (e3 = e0)
% 20.82/5.42 |
% 20.82/5.42 | Equations (903) can reduce 1115 to:
% 20.82/5.42 | (406) ~ (e2 = e0)
% 20.82/5.42 |
% 20.82/5.42 | Simplifying 406 yields:
% 20.82/5.42 | (58) ~ (e2 = e0)
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (211), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (632) all_0_56_56 = e0
% 20.82/5.42 |
% 20.82/5.42 | Equations (632) can reduce 401 to:
% 20.82/5.42 | (269) $false
% 20.82/5.42 |
% 20.82/5.42 |-The branch is then unsatisfiable
% 20.82/5.42 |-Branch two:
% 20.82/5.42 | (401) ~ (all_0_56_56 = e0)
% 20.82/5.42 | (2052) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (2052), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (400) all_0_57_57 = e0
% 20.82/5.42 |
% 20.82/5.42 | Combining equations (400,867) yields a new equation:
% 20.82/5.42 | (354) e2 = e0
% 20.82/5.42 |
% 20.82/5.42 | Equations (354) can reduce 58 to:
% 20.82/5.42 | (269) $false
% 20.82/5.42 |
% 20.82/5.42 |-The branch is then unsatisfiable
% 20.82/5.42 |-Branch two:
% 20.82/5.42 | (967) ~ (all_0_57_57 = e0)
% 20.82/5.42 | (2059) all_0_58_58 = e0 | all_0_59_59 = e0
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (2059), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (493) all_0_58_58 = e0
% 20.82/5.42 |
% 20.82/5.42 | Equations (493) can reduce 403 to:
% 20.82/5.42 | (269) $false
% 20.82/5.42 |
% 20.82/5.42 |-The branch is then unsatisfiable
% 20.82/5.42 |-Branch two:
% 20.82/5.42 | (403) ~ (all_0_58_58 = e0)
% 20.82/5.42 | (2064) all_0_59_59 = e0
% 20.82/5.42 |
% 20.82/5.42 | Instantiating formula (21) with e0, e1, all_0_34_34, all_0_58_58 and discharging atoms op(e0, e1) = all_0_34_34, op(e0, e1) = all_0_58_58, yields:
% 20.82/5.42 | (2838) all_0_34_34 = all_0_58_58
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (104), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (1639) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0)) | (all_0_34_34 = e2 & ~ (all_0_35_35 = e0))
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (1639), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (1640) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0))
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (1640), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (1641) all_0_30_30 = e4 & ~ (all_0_31_31 = e0)
% 20.82/5.42 |
% 20.82/5.42 | Applying alpha-rule on (1641) yields:
% 20.82/5.42 | (1642) all_0_30_30 = e4
% 20.82/5.42 | (1643) ~ (all_0_31_31 = e0)
% 20.82/5.42 |
% 20.82/5.42 | From (1642) and (36) follows:
% 20.82/5.42 | (4759) op(e0, all_0_42_42) = e4
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (47), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (348) all_0_39_39 = e2
% 20.82/5.42 |
% 20.82/5.42 | Equations (348) can reduce 320 to:
% 20.82/5.42 | (269) $false
% 20.82/5.42 |
% 20.82/5.42 |-The branch is then unsatisfiable
% 20.82/5.42 |-Branch two:
% 20.82/5.42 | (320) ~ (all_0_39_39 = e2)
% 20.82/5.42 | (709) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (116), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (358) all_0_42_42 = e2
% 20.82/5.42 |
% 20.82/5.42 | Equations (358) can reduce 362 to:
% 20.82/5.42 | (269) $false
% 20.82/5.42 |
% 20.82/5.42 |-The branch is then unsatisfiable
% 20.82/5.42 |-Branch two:
% 20.82/5.42 | (362) ~ (all_0_42_42 = e2)
% 20.82/5.42 | (2784) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (32), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (1079) all_0_39_39 = e4
% 20.82/5.42 |
% 20.82/5.42 | Equations (1079) can reduce 157 to:
% 20.82/5.42 | (2786) ~ (all_0_42_42 = e4)
% 20.82/5.42 |
% 20.82/5.42 | Simplifying 2786 yields:
% 20.82/5.42 | (2787) ~ (all_0_42_42 = e4)
% 20.82/5.42 |
% 20.82/5.42 | Equations (1079) can reduce 53 to:
% 20.82/5.42 | (272) ~ (all_0_56_56 = e4)
% 20.82/5.42 |
% 20.82/5.42 | Simplifying 272 yields:
% 20.82/5.42 | (273) ~ (all_0_56_56 = e4)
% 20.82/5.42 |
% 20.82/5.42 | Equations (1079) can reduce 320 to:
% 20.82/5.42 | (230) ~ (e4 = e2)
% 20.82/5.42 |
% 20.82/5.42 | Equations (1079) can reduce 165 to:
% 20.82/5.42 | (11) ~ (e4 = e0)
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (184), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (443) all_0_39_39 = e3
% 20.82/5.42 |
% 20.82/5.42 | Combining equations (443,1079) yields a new equation:
% 20.82/5.42 | (516) e4 = e3
% 20.82/5.42 |
% 20.82/5.42 | Equations (516) can reduce 41 to:
% 20.82/5.42 | (269) $false
% 20.82/5.42 |
% 20.82/5.42 |-The branch is then unsatisfiable
% 20.82/5.42 |-Branch two:
% 20.82/5.42 | (540) ~ (all_0_39_39 = e3)
% 20.82/5.42 | (541) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 20.82/5.42 |
% 20.82/5.42 | Equations (1079) can reduce 540 to:
% 20.82/5.42 | (41) ~ (e4 = e3)
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (195), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (305) all_0_42_42 = e4
% 20.82/5.42 |
% 20.82/5.42 | Equations (305) can reduce 2787 to:
% 20.82/5.42 | (269) $false
% 20.82/5.42 |
% 20.82/5.42 |-The branch is then unsatisfiable
% 20.82/5.42 |-Branch two:
% 20.82/5.42 | (2787) ~ (all_0_42_42 = e4)
% 20.82/5.42 | (2898) all_0_46_46 = e4 | all_0_54_54 = e4 | all_0_59_59 = e4
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (2898), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (538) all_0_46_46 = e4
% 20.82/5.42 |
% 20.82/5.42 | Combining equations (364,538) yields a new equation:
% 20.82/5.42 | (360) e4 = e2
% 20.82/5.42 |
% 20.82/5.42 | Equations (360) can reduce 230 to:
% 20.82/5.42 | (269) $false
% 20.82/5.42 |
% 20.82/5.42 |-The branch is then unsatisfiable
% 20.82/5.42 |-Branch two:
% 20.82/5.42 | (310) ~ (all_0_46_46 = e4)
% 20.82/5.42 | (2902) all_0_54_54 = e4 | all_0_59_59 = e4
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (2902), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (535) all_0_54_54 = e4
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (169), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (610) all_0_42_42 = e3
% 20.82/5.42 |
% 20.82/5.42 | From (610) and (4759) follows:
% 20.82/5.42 | (4792) op(e0, e3) = e4
% 20.82/5.42 |
% 20.82/5.42 | Instantiating formula (21) with e0, e3, e4, all_0_56_56 and discharging atoms op(e0, e3) = all_0_56_56, op(e0, e3) = e4, yields:
% 20.82/5.42 | (1658) all_0_56_56 = e4
% 20.82/5.42 |
% 20.82/5.42 | Equations (1658) can reduce 273 to:
% 20.82/5.42 | (269) $false
% 20.82/5.42 |
% 20.82/5.42 |-The branch is then unsatisfiable
% 20.82/5.42 |-Branch two:
% 20.82/5.42 | (1924) ~ (all_0_42_42 = e3)
% 20.82/5.42 | (1925) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (1925), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (462) all_0_46_46 = e3
% 20.82/5.42 |
% 20.82/5.42 | Combining equations (364,462) yields a new equation:
% 20.82/5.42 | (423) e3 = e2
% 20.82/5.42 |
% 20.82/5.42 | Equations (423) can reduce 224 to:
% 20.82/5.42 | (269) $false
% 20.82/5.42 |
% 20.82/5.42 |-The branch is then unsatisfiable
% 20.82/5.42 |-Branch two:
% 20.82/5.42 | (618) ~ (all_0_46_46 = e3)
% 20.82/5.42 | (1930) all_0_54_54 = e3 | all_0_59_59 = e3
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (1930), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (635) all_0_54_54 = e3
% 20.82/5.42 |
% 20.82/5.42 | Combining equations (635,535) yields a new equation:
% 20.82/5.42 | (516) e4 = e3
% 20.82/5.42 |
% 20.82/5.42 | Equations (516) can reduce 41 to:
% 20.82/5.42 | (269) $false
% 20.82/5.42 |
% 20.82/5.42 |-The branch is then unsatisfiable
% 20.82/5.42 |-Branch two:
% 20.82/5.42 | (430) ~ (all_0_54_54 = e3)
% 20.82/5.42 | (1070) all_0_59_59 = e3
% 20.82/5.42 |
% 20.82/5.42 | Combining equations (1070,2064) yields a new equation:
% 20.82/5.42 | (781) e3 = e0
% 20.82/5.42 |
% 20.82/5.42 | Simplifying 781 yields:
% 20.82/5.42 | (560) e3 = e0
% 20.82/5.42 |
% 20.82/5.42 | Equations (560) can reduce 72 to:
% 20.82/5.42 | (269) $false
% 20.82/5.42 |
% 20.82/5.42 |-The branch is then unsatisfiable
% 20.82/5.42 |-Branch two:
% 20.82/5.42 | (312) ~ (all_0_54_54 = e4)
% 20.82/5.42 | (2231) all_0_59_59 = e4
% 20.82/5.42 |
% 20.82/5.42 | Combining equations (2064,2231) yields a new equation:
% 20.82/5.42 | (439) e4 = e0
% 20.82/5.42 |
% 20.82/5.42 | Equations (439) can reduce 11 to:
% 20.82/5.42 | (269) $false
% 20.82/5.42 |
% 20.82/5.42 |-The branch is then unsatisfiable
% 20.82/5.42 |-Branch two:
% 20.82/5.42 | (307) ~ (all_0_39_39 = e4)
% 20.82/5.42 | (3018) all_0_41_41 = e4 | all_0_42_42 = e4
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (709), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (464) all_0_39_39 = e1
% 20.82/5.42 |
% 20.82/5.42 | Equations (464) can reduce 467 to:
% 20.82/5.42 | (269) $false
% 20.82/5.42 |
% 20.82/5.42 |-The branch is then unsatisfiable
% 20.82/5.42 |-Branch two:
% 20.82/5.42 | (467) ~ (all_0_39_39 = e1)
% 20.82/5.42 | (1075) all_0_39_39 = e4 | all_0_39_39 = e3
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (29), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (1079) all_0_39_39 = e4
% 20.82/5.42 |
% 20.82/5.42 | Equations (1079) can reduce 307 to:
% 20.82/5.42 | (269) $false
% 20.82/5.42 |
% 20.82/5.42 |-The branch is then unsatisfiable
% 20.82/5.42 |-Branch two:
% 20.82/5.42 | (307) ~ (all_0_39_39 = e4)
% 20.82/5.42 | (1391) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (1075), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (443) all_0_39_39 = e3
% 20.82/5.42 |
% 20.82/5.42 | Equations (443) can reduce 157 to:
% 20.82/5.42 | (3028) ~ (all_0_42_42 = e3)
% 20.82/5.42 |
% 20.82/5.42 | Simplifying 3028 yields:
% 20.82/5.42 | (1924) ~ (all_0_42_42 = e3)
% 20.82/5.42 |
% 20.82/5.42 | Equations (443) can reduce 53 to:
% 20.82/5.42 | (1182) ~ (all_0_56_56 = e3)
% 20.82/5.42 |
% 20.82/5.42 | Simplifying 1182 yields:
% 20.82/5.42 | (1183) ~ (all_0_56_56 = e3)
% 20.82/5.42 |
% 20.82/5.42 | Equations (443) can reduce 320 to:
% 20.82/5.42 | (224) ~ (e3 = e2)
% 20.82/5.42 |
% 20.82/5.42 | Equations (443) can reduce 165 to:
% 20.82/5.42 | (72) ~ (e3 = e0)
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (3018), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (740) all_0_41_41 = e4
% 20.82/5.42 |
% 20.82/5.42 | Combining equations (740,386) yields a new equation:
% 20.82/5.42 | (359) e4 = e2
% 20.82/5.42 |
% 20.82/5.42 | Simplifying 359 yields:
% 20.82/5.42 | (360) e4 = e2
% 20.82/5.42 |
% 20.82/5.42 | Equations (360) can reduce 230 to:
% 20.82/5.42 | (269) $false
% 20.82/5.42 |
% 20.82/5.42 |-The branch is then unsatisfiable
% 20.82/5.42 |-Branch two:
% 20.82/5.42 | (308) ~ (all_0_41_41 = e4)
% 20.82/5.42 | (305) all_0_42_42 = e4
% 20.82/5.42 |
% 20.82/5.42 | Equations (305) can reduce 98 to:
% 20.82/5.42 | (311) ~ (all_0_54_54 = e4)
% 20.82/5.42 |
% 20.82/5.42 | Simplifying 311 yields:
% 20.82/5.42 | (312) ~ (all_0_54_54 = e4)
% 20.82/5.42 |
% 20.82/5.42 | Equations (305) can reduce 1924 to:
% 20.82/5.42 | (41) ~ (e4 = e3)
% 20.82/5.42 |
% 20.82/5.42 | Equations (305) can reduce 362 to:
% 20.82/5.42 | (230) ~ (e4 = e2)
% 20.82/5.42 |
% 20.82/5.42 +-Applying beta-rule and splitting (169), into two cases.
% 20.82/5.42 |-Branch one:
% 20.82/5.42 | (610) all_0_42_42 = e3
% 20.82/5.42 |
% 20.82/5.42 | Combining equations (305,610) yields a new equation:
% 20.82/5.42 | (515) e4 = e3
% 20.82/5.42 |
% 20.82/5.42 | Simplifying 515 yields:
% 20.82/5.42 | (516) e4 = e3
% 20.82/5.42 |
% 20.82/5.42 | Equations (516) can reduce 41 to:
% 20.82/5.42 | (269) $false
% 20.82/5.42 |
% 20.82/5.42 |-The branch is then unsatisfiable
% 20.82/5.42 |-Branch two:
% 20.82/5.42 | (1924) ~ (all_0_42_42 = e3)
% 20.82/5.43 | (1925) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 20.82/5.43 |
% 20.82/5.43 +-Applying beta-rule and splitting (1925), into two cases.
% 20.82/5.43 |-Branch one:
% 20.82/5.43 | (462) all_0_46_46 = e3
% 20.82/5.43 |
% 20.82/5.43 | Combining equations (364,462) yields a new equation:
% 20.82/5.43 | (423) e3 = e2
% 20.82/5.43 |
% 20.82/5.43 | Equations (423) can reduce 224 to:
% 20.82/5.43 | (269) $false
% 20.82/5.43 |
% 20.82/5.43 |-The branch is then unsatisfiable
% 20.82/5.43 |-Branch two:
% 20.82/5.43 | (618) ~ (all_0_46_46 = e3)
% 20.82/5.43 | (1930) all_0_54_54 = e3 | all_0_59_59 = e3
% 20.82/5.43 |
% 20.82/5.43 +-Applying beta-rule and splitting (1930), into two cases.
% 20.82/5.43 |-Branch one:
% 20.82/5.43 | (635) all_0_54_54 = e3
% 20.82/5.43 |
% 20.82/5.43 | Equations (635) can reduce 119 to:
% 20.82/5.43 | (796) ~ (all_0_53_53 = e3)
% 20.82/5.43 |
% 20.82/5.43 | Equations (635) can reduce 312 to:
% 20.82/5.43 | (498) ~ (e4 = e3)
% 20.82/5.43 |
% 20.82/5.43 | Simplifying 498 yields:
% 20.82/5.43 | (41) ~ (e4 = e3)
% 20.82/5.43 |
% 20.82/5.43 | Equations (635) can reduce 261 to:
% 20.82/5.43 | (224) ~ (e3 = e2)
% 20.82/5.43 |
% 20.82/5.43 +-Applying beta-rule and splitting (213), into two cases.
% 20.82/5.43 |-Branch one:
% 20.82/5.43 | (605) all_0_41_41 = e3
% 20.82/5.43 |
% 20.82/5.43 | Combining equations (386,605) yields a new equation:
% 20.82/5.43 | (423) e3 = e2
% 20.82/5.43 |
% 20.82/5.43 | Equations (423) can reduce 224 to:
% 20.82/5.43 | (269) $false
% 20.82/5.43 |
% 20.82/5.43 |-The branch is then unsatisfiable
% 20.82/5.43 |-Branch two:
% 20.82/5.43 | (609) ~ (all_0_41_41 = e3)
% 20.82/5.43 | (3891) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 20.82/5.43 |
% 20.82/5.43 +-Applying beta-rule and splitting (27), into two cases.
% 20.82/5.43 |-Branch one:
% 20.82/5.43 | (849) all_0_53_53 = e2
% 20.82/5.43 |
% 20.82/5.43 | Equations (849) can reduce 259 to:
% 20.82/5.43 | (269) $false
% 20.82/5.43 |
% 20.82/5.43 |-The branch is then unsatisfiable
% 20.82/5.43 |-Branch two:
% 20.82/5.43 | (259) ~ (all_0_53_53 = e2)
% 20.82/5.43 | (852) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 20.82/5.43 |
% 20.82/5.43 +-Applying beta-rule and splitting (243), into two cases.
% 20.82/5.43 |-Branch one:
% 20.82/5.43 | (567) all_0_56_56 = e3
% 20.82/5.43 |
% 20.82/5.43 | Equations (567) can reduce 1183 to:
% 20.82/5.43 | (269) $false
% 20.82/5.43 |
% 20.82/5.43 |-The branch is then unsatisfiable
% 20.82/5.43 |-Branch two:
% 20.82/5.43 | (1183) ~ (all_0_56_56 = e3)
% 20.82/5.43 | (1249) all_0_57_57 = e3 | all_0_58_58 = e3 | all_0_59_59 = e3
% 20.82/5.43 |
% 20.82/5.43 +-Applying beta-rule and splitting (3891), into two cases.
% 20.82/5.43 |-Branch one:
% 20.82/5.43 | (1087) all_0_45_45 = e3
% 20.82/5.43 |
% 20.82/5.43 | Combining equations (444,1087) yields a new equation:
% 20.82/5.43 | (515) e4 = e3
% 20.82/5.43 |
% 20.82/5.43 | Simplifying 515 yields:
% 20.82/5.43 | (516) e4 = e3
% 20.82/5.43 |
% 20.82/5.43 | Equations (516) can reduce 41 to:
% 20.82/5.43 | (269) $false
% 20.82/5.43 |
% 20.82/5.43 |-The branch is then unsatisfiable
% 20.82/5.43 |-Branch two:
% 20.82/5.43 | (689) ~ (all_0_45_45 = e3)
% 20.82/5.43 | (3903) all_0_53_53 = e3 | all_0_58_58 = e3
% 20.82/5.43 |
% 20.82/5.43 | Equations (444) can reduce 689 to:
% 20.82/5.43 | (41) ~ (e4 = e3)
% 20.82/5.43 |
% 20.82/5.43 +-Applying beta-rule and splitting (852), into two cases.
% 20.82/5.43 |-Branch one:
% 20.82/5.43 | (853) all_0_53_53 = e1
% 20.82/5.43 |
% 20.82/5.43 | Equations (853) can reduce 127 to:
% 20.82/5.43 | (481) ~ (all_0_58_58 = e1)
% 20.82/5.43 |
% 20.82/5.43 | Simplifying 481 yields:
% 20.82/5.43 | (482) ~ (all_0_58_58 = e1)
% 20.82/5.43 |
% 20.82/5.43 | Equations (853) can reduce 796 to:
% 20.82/5.43 | (597) ~ (e3 = e1)
% 20.82/5.43 |
% 20.82/5.43 | Simplifying 597 yields:
% 20.82/5.43 | (146) ~ (e3 = e1)
% 20.82/5.43 |
% 20.82/5.43 | Equations (853) can reduce 259 to:
% 20.82/5.43 | (414) ~ (e2 = e1)
% 20.82/5.43 |
% 20.82/5.43 | Simplifying 414 yields:
% 20.82/5.43 | (148) ~ (e2 = e1)
% 20.82/5.43 |
% 20.82/5.43 | Equations (853) can reduce 765 to:
% 20.82/5.43 | (144) ~ (e1 = e0)
% 20.82/5.43 |
% 20.82/5.43 +-Applying beta-rule and splitting (43), into two cases.
% 20.82/5.43 |-Branch one:
% 20.82/5.43 | (480) all_0_56_56 = e1
% 20.82/5.43 |
% 20.82/5.43 | Equations (480) can reduce 273 to:
% 20.82/5.43 | (826) ~ (e4 = e1)
% 20.82/5.43 |
% 20.82/5.43 | Simplifying 826 yields:
% 20.82/5.43 | (251) ~ (e4 = e1)
% 20.82/5.43 |
% 20.82/5.43 | Equations (480) can reduce 1183 to:
% 20.82/5.43 | (597) ~ (e3 = e1)
% 20.82/5.43 |
% 20.82/5.43 | Simplifying 597 yields:
% 20.82/5.43 | (146) ~ (e3 = e1)
% 20.82/5.43 |
% 20.82/5.43 +-Applying beta-rule and splitting (153), into two cases.
% 20.82/5.43 |-Branch one:
% 20.82/5.43 | (453) all_0_50_50 = e4
% 20.82/5.43 |
% 20.82/5.43 | Combining equations (253,453) yields a new equation:
% 20.82/5.43 | (360) e4 = e2
% 20.82/5.43 |
% 20.82/5.43 | Equations (360) can reduce 230 to:
% 20.82/5.43 | (269) $false
% 20.82/5.43 |
% 20.82/5.43 |-The branch is then unsatisfiable
% 20.82/5.43 |-Branch two:
% 20.82/5.43 | (456) ~ (all_0_50_50 = e4)
% 20.82/5.43 | (457) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 20.82/5.43 |
% 20.82/5.43 +-Applying beta-rule and splitting (457), into two cases.
% 20.82/5.43 |-Branch one:
% 20.82/5.43 | (458) all_0_51_51 = e4
% 20.82/5.43 |
% 20.82/5.43 | Equations (458) can reduce 432 to:
% 20.82/5.43 | (11) ~ (e4 = e0)
% 20.82/5.43 |
% 20.82/5.43 | From (458) and (175) follows:
% 20.82/5.43 | (3743) op(e1, e3) = e4
% 20.82/5.43 |
% 20.82/5.43 +-Applying beta-rule and splitting (3903), into two cases.
% 20.82/5.43 |-Branch one:
% 20.82/5.43 | (861) all_0_53_53 = e3
% 20.82/5.43 |
% 20.82/5.43 | Combining equations (853,861) yields a new equation:
% 20.82/5.43 | (418) e3 = e1
% 20.82/5.43 |
% 20.82/5.43 | Equations (418) can reduce 146 to:
% 20.82/5.43 | (269) $false
% 20.82/5.43 |
% 20.82/5.43 |-The branch is then unsatisfiable
% 20.82/5.43 |-Branch two:
% 20.82/5.43 | (796) ~ (all_0_53_53 = e3)
% 20.82/5.43 | (497) all_0_58_58 = e3
% 20.82/5.43 |
% 20.82/5.43 | From (497) and (3447) follows:
% 20.82/5.43 | (767) op(e1, e3) = e0
% 20.82/5.43 |
% 20.82/5.43 | Instantiating formula (21) with e1, e3, e0, e4 and discharging atoms op(e1, e3) = e4, op(e1, e3) = e0, yields:
% 20.82/5.43 | (439) e4 = e0
% 20.82/5.43 |
% 20.82/5.43 | Equations (439) can reduce 11 to:
% 20.82/5.43 | (269) $false
% 20.82/5.43 |
% 20.82/5.43 |-The branch is then unsatisfiable
% 20.82/5.43 |-Branch two:
% 20.82/5.43 | (530) ~ (all_0_51_51 = e4)
% 20.82/5.43 | (531) all_0_53_53 = e4 | all_0_54_54 = e4
% 20.82/5.43 |
% 20.82/5.43 +-Applying beta-rule and splitting (531), into two cases.
% 20.82/5.43 |-Branch one:
% 20.82/5.43 | (532) all_0_53_53 = e4
% 20.82/5.43 |
% 20.82/5.43 | Combining equations (853,532) yields a new equation:
% 20.82/5.43 | (477) e4 = e1
% 20.82/5.43 |
% 20.82/5.43 | Equations (477) can reduce 251 to:
% 20.82/5.43 | (269) $false
% 20.82/5.43 |
% 20.82/5.43 |-The branch is then unsatisfiable
% 20.82/5.43 |-Branch two:
% 20.82/5.43 | (448) ~ (all_0_53_53 = e4)
% 20.82/5.43 | (535) all_0_54_54 = e4
% 20.82/5.43 |
% 20.82/5.43 | Combining equations (535,635) yields a new equation:
% 20.82/5.43 | (515) e4 = e3
% 20.82/5.43 |
% 20.82/5.43 | Simplifying 515 yields:
% 20.82/5.43 | (516) e4 = e3
% 20.82/5.43 |
% 20.82/5.43 | Equations (516) can reduce 41 to:
% 20.82/5.43 | (269) $false
% 20.82/5.43 |
% 20.82/5.43 |-The branch is then unsatisfiable
% 20.82/5.43 |-Branch two:
% 20.82/5.43 | (575) ~ (all_0_56_56 = e1)
% 20.82/5.43 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 20.82/5.43 |
% 20.82/5.43 +-Applying beta-rule and splitting (3903), into two cases.
% 20.82/5.43 |-Branch one:
% 20.82/5.43 | (861) all_0_53_53 = e3
% 20.82/5.43 |
% 20.82/5.43 | Combining equations (853,861) yields a new equation:
% 20.82/5.43 | (418) e3 = e1
% 20.82/5.43 |
% 20.82/5.43 | Equations (418) can reduce 146 to:
% 20.82/5.43 | (269) $false
% 20.82/5.43 |
% 20.82/5.43 |-The branch is then unsatisfiable
% 20.82/5.43 |-Branch two:
% 20.82/5.43 | (796) ~ (all_0_53_53 = e3)
% 20.82/5.43 | (497) all_0_58_58 = e3
% 20.82/5.43 |
% 20.82/5.43 | Equations (497) can reduce 482 to:
% 20.82/5.43 | (146) ~ (e3 = e1)
% 20.82/5.43 |
% 20.82/5.43 +-Applying beta-rule and splitting (576), into two cases.
% 20.82/5.43 |-Branch one:
% 20.82/5.43 | (577) all_0_57_57 = e1
% 20.82/5.43 |
% 20.82/5.43 | Combining equations (867,577) yields a new equation:
% 20.82/5.43 | (470) e2 = e1
% 20.82/5.43 |
% 20.82/5.43 | Simplifying 470 yields:
% 20.82/5.43 | (471) e2 = e1
% 20.82/5.43 |
% 20.82/5.43 | Equations (471) can reduce 148 to:
% 20.82/5.43 | (269) $false
% 20.82/5.43 |
% 20.82/5.43 |-The branch is then unsatisfiable
% 20.82/5.43 |-Branch two:
% 20.82/5.43 | (581) ~ (all_0_57_57 = e1)
% 20.82/5.43 | (582) all_0_58_58 = e1 | all_0_59_59 = e1
% 20.82/5.43 |
% 20.82/5.43 +-Applying beta-rule and splitting (582), into two cases.
% 20.82/5.43 |-Branch one:
% 20.82/5.43 | (489) all_0_58_58 = e1
% 20.82/5.43 |
% 20.82/5.43 | Combining equations (489,497) yields a new equation:
% 20.82/5.43 | (418) e3 = e1
% 20.82/5.43 |
% 20.82/5.43 | Equations (418) can reduce 146 to:
% 20.82/5.43 | (269) $false
% 20.82/5.43 |
% 20.82/5.43 |-The branch is then unsatisfiable
% 20.82/5.43 |-Branch two:
% 20.82/5.43 | (482) ~ (all_0_58_58 = e1)
% 20.82/5.43 | (614) all_0_59_59 = e1
% 20.82/5.43 |
% 20.82/5.43 | Combining equations (614,2064) yields a new equation:
% 20.82/5.43 | (578) e1 = e0
% 20.82/5.43 |
% 20.82/5.43 | Simplifying 578 yields:
% 20.82/5.43 | (579) e1 = e0
% 20.82/5.43 |
% 20.82/5.43 | Equations (579) can reduce 144 to:
% 20.82/5.43 | (269) $false
% 20.82/5.43 |
% 20.82/5.43 |-The branch is then unsatisfiable
% 20.82/5.43 |-Branch two:
% 20.82/5.43 | (823) ~ (all_0_53_53 = e1)
% 20.82/5.43 | (856) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e0
% 20.82/5.43 |
% 20.82/5.43 +-Applying beta-rule and splitting (3903), into two cases.
% 20.82/5.43 |-Branch one:
% 20.82/5.43 | (861) all_0_53_53 = e3
% 20.82/5.43 |
% 20.82/5.43 | Equations (861) can reduce 796 to:
% 20.82/5.43 | (269) $false
% 20.82/5.43 |
% 20.82/5.43 |-The branch is then unsatisfiable
% 20.82/5.43 |-Branch two:
% 20.82/5.43 | (796) ~ (all_0_53_53 = e3)
% 20.82/5.43 | (497) all_0_58_58 = e3
% 20.82/5.43 |
% 20.82/5.43 | Equations (497) can reduce 127 to:
% 20.82/5.43 | (796) ~ (all_0_53_53 = e3)
% 20.82/5.43 |
% 20.82/5.43 +-Applying beta-rule and splitting (856), into two cases.
% 20.82/5.43 |-Branch one:
% 20.82/5.43 | (857) all_0_53_53 = e0
% 20.82/5.43 |
% 20.82/5.43 | Equations (857) can reduce 765 to:
% 20.82/5.43 | (269) $false
% 20.82/5.43 |
% 20.82/5.43 |-The branch is then unsatisfiable
% 20.82/5.43 |-Branch two:
% 20.82/5.43 | (765) ~ (all_0_53_53 = e0)
% 20.82/5.43 | (860) all_0_53_53 = e4 | all_0_53_53 = e3
% 20.82/5.43 |
% 20.82/5.43 +-Applying beta-rule and splitting (860), into two cases.
% 20.82/5.43 |-Branch one:
% 20.82/5.43 | (861) all_0_53_53 = e3
% 20.82/5.43 |
% 20.82/5.43 | Equations (861) can reduce 796 to:
% 20.82/5.43 | (269) $false
% 20.82/5.43 |
% 20.82/5.43 |-The branch is then unsatisfiable
% 20.82/5.43 |-Branch two:
% 20.82/5.43 | (796) ~ (all_0_53_53 = e3)
% 20.82/5.43 | (532) all_0_53_53 = e4
% 20.82/5.43 |
% 20.82/5.43 | Equations (532) can reduce 448 to:
% 20.82/5.43 | (269) $false
% 20.82/5.43 |
% 20.82/5.43 |-The branch is then unsatisfiable
% 20.82/5.43 |-Branch two:
% 20.82/5.43 | (430) ~ (all_0_54_54 = e3)
% 20.82/5.43 | (1070) all_0_59_59 = e3
% 20.82/5.43 |
% 20.82/5.43 | Combining equations (1070,2064) yields a new equation:
% 20.82/5.43 | (781) e3 = e0
% 20.82/5.43 |
% 20.82/5.43 | Simplifying 781 yields:
% 20.82/5.43 | (560) e3 = e0
% 20.82/5.43 |
% 20.82/5.43 | Equations (560) can reduce 72 to:
% 20.82/5.43 | (269) $false
% 20.82/5.43 |
% 20.82/5.43 |-The branch is then unsatisfiable
% 20.82/5.43 |-Branch two:
% 20.82/5.43 | (540) ~ (all_0_39_39 = e3)
% 20.82/5.43 | (1079) all_0_39_39 = e4
% 20.82/5.43 |
% 20.82/5.43 | Equations (1079) can reduce 307 to:
% 20.82/5.43 | (269) $false
% 20.82/5.43 |
% 20.82/5.43 |-The branch is then unsatisfiable
% 20.82/5.43 |-Branch two:
% 20.82/5.43 | (1645) all_0_32_32 = e3 & ~ (all_0_33_33 = e0)
% 20.82/5.43 |
% 20.82/5.43 | Applying alpha-rule on (1645) yields:
% 20.82/5.43 | (1646) all_0_32_32 = e3
% 20.82/5.43 | (1647) ~ (all_0_33_33 = e0)
% 20.82/5.43 |
% 20.82/5.43 | Combining equations (1853,1646) yields a new equation:
% 20.82/5.43 | (423) e3 = e2
% 20.82/5.43 |
% 20.82/5.43 | Equations (423) can reduce 224 to:
% 20.82/5.43 | (269) $false
% 20.82/5.43 |
% 20.82/5.43 |-The branch is then unsatisfiable
% 20.82/5.43 |-Branch two:
% 20.82/5.43 | (1649) all_0_34_34 = e2 & ~ (all_0_35_35 = e0)
% 20.82/5.43 |
% 20.82/5.43 | Applying alpha-rule on (1649) yields:
% 20.82/5.43 | (1650) all_0_34_34 = e2
% 20.82/5.43 | (1651) ~ (all_0_35_35 = e0)
% 20.82/5.43 |
% 20.82/5.43 | Combining equations (2838,1650) yields a new equation:
% 20.82/5.43 | (4970) all_0_58_58 = e2
% 20.82/5.43 |
% 20.82/5.43 | Simplifying 4970 yields:
% 20.82/5.43 | (485) all_0_58_58 = e2
% 20.82/5.43 |
% 20.82/5.43 | Equations (485) can reduce 392 to:
% 20.82/5.43 | (269) $false
% 20.82/5.43 |
% 20.82/5.43 |-The branch is then unsatisfiable
% 20.82/5.43 |-Branch two:
% 20.82/5.43 | (1653) all_0_36_36 = e1 & ~ (all_0_37_37 = e0)
% 20.82/5.43 |
% 20.82/5.43 | Applying alpha-rule on (1653) yields:
% 20.82/5.43 | (1654) all_0_36_36 = e1
% 20.82/5.43 | (1655) ~ (all_0_37_37 = e0)
% 20.82/5.43 |
% 20.82/5.43 | From (1654) and (235) follows:
% 20.82/5.43 | (1874) op(e0, all_0_54_54) = e1
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (47), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (348) all_0_39_39 = e2
% 20.82/5.44 |
% 20.82/5.44 | Equations (348) can reduce 320 to:
% 20.82/5.44 | (269) $false
% 20.82/5.44 |
% 20.82/5.44 |-The branch is then unsatisfiable
% 20.82/5.44 |-Branch two:
% 20.82/5.44 | (320) ~ (all_0_39_39 = e2)
% 20.82/5.44 | (709) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (116), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (358) all_0_42_42 = e2
% 20.82/5.44 |
% 20.82/5.44 | Equations (358) can reduce 362 to:
% 20.82/5.44 | (269) $false
% 20.82/5.44 |
% 20.82/5.44 |-The branch is then unsatisfiable
% 20.82/5.44 |-Branch two:
% 20.82/5.44 | (362) ~ (all_0_42_42 = e2)
% 20.82/5.44 | (2784) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (32), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (1079) all_0_39_39 = e4
% 20.82/5.44 |
% 20.82/5.44 | Equations (1079) can reduce 157 to:
% 20.82/5.44 | (2786) ~ (all_0_42_42 = e4)
% 20.82/5.44 |
% 20.82/5.44 | Simplifying 2786 yields:
% 20.82/5.44 | (2787) ~ (all_0_42_42 = e4)
% 20.82/5.44 |
% 20.82/5.44 | Equations (1079) can reduce 320 to:
% 20.82/5.44 | (230) ~ (e4 = e2)
% 20.82/5.44 |
% 20.82/5.44 | Equations (1079) can reduce 165 to:
% 20.82/5.44 | (11) ~ (e4 = e0)
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (195), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (305) all_0_42_42 = e4
% 20.82/5.44 |
% 20.82/5.44 | Equations (305) can reduce 2787 to:
% 20.82/5.44 | (269) $false
% 20.82/5.44 |
% 20.82/5.44 |-The branch is then unsatisfiable
% 20.82/5.44 |-Branch two:
% 20.82/5.44 | (2787) ~ (all_0_42_42 = e4)
% 20.82/5.44 | (2898) all_0_46_46 = e4 | all_0_54_54 = e4 | all_0_59_59 = e4
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (2898), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (538) all_0_46_46 = e4
% 20.82/5.44 |
% 20.82/5.44 | Combining equations (364,538) yields a new equation:
% 20.82/5.44 | (360) e4 = e2
% 20.82/5.44 |
% 20.82/5.44 | Equations (360) can reduce 230 to:
% 20.82/5.44 | (269) $false
% 20.82/5.44 |
% 20.82/5.44 |-The branch is then unsatisfiable
% 20.82/5.44 |-Branch two:
% 20.82/5.44 | (310) ~ (all_0_46_46 = e4)
% 20.82/5.44 | (2902) all_0_54_54 = e4 | all_0_59_59 = e4
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (2902), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (535) all_0_54_54 = e4
% 20.82/5.44 |
% 20.82/5.44 | Equations (535) can reduce 1238 to:
% 20.82/5.44 | (251) ~ (e4 = e1)
% 20.82/5.44 |
% 20.82/5.44 | From (535) and (1874) follows:
% 20.82/5.44 | (5001) op(e0, e4) = e1
% 20.82/5.44 |
% 20.82/5.44 | Instantiating formula (21) with e0, e4, e1, e4 and discharging atoms op(e0, e4) = e4, op(e0, e4) = e1, yields:
% 20.82/5.44 | (477) e4 = e1
% 20.82/5.44 |
% 20.82/5.44 | Equations (477) can reduce 251 to:
% 20.82/5.44 | (269) $false
% 20.82/5.44 |
% 20.82/5.44 |-The branch is then unsatisfiable
% 20.82/5.44 |-Branch two:
% 20.82/5.44 | (312) ~ (all_0_54_54 = e4)
% 20.82/5.44 | (2231) all_0_59_59 = e4
% 20.82/5.44 |
% 20.82/5.44 | Combining equations (2064,2231) yields a new equation:
% 20.82/5.44 | (439) e4 = e0
% 20.82/5.44 |
% 20.82/5.44 | Equations (439) can reduce 11 to:
% 20.82/5.44 | (269) $false
% 20.82/5.44 |
% 20.82/5.44 |-The branch is then unsatisfiable
% 20.82/5.44 |-Branch two:
% 20.82/5.44 | (307) ~ (all_0_39_39 = e4)
% 20.82/5.44 | (3018) all_0_41_41 = e4 | all_0_42_42 = e4
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (709), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (464) all_0_39_39 = e1
% 20.82/5.44 |
% 20.82/5.44 | Equations (464) can reduce 467 to:
% 20.82/5.44 | (269) $false
% 20.82/5.44 |
% 20.82/5.44 |-The branch is then unsatisfiable
% 20.82/5.44 |-Branch two:
% 20.82/5.44 | (467) ~ (all_0_39_39 = e1)
% 20.82/5.44 | (1075) all_0_39_39 = e4 | all_0_39_39 = e3
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (29), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (1079) all_0_39_39 = e4
% 20.82/5.44 |
% 20.82/5.44 | Equations (1079) can reduce 307 to:
% 20.82/5.44 | (269) $false
% 20.82/5.44 |
% 20.82/5.44 |-The branch is then unsatisfiable
% 20.82/5.44 |-Branch two:
% 20.82/5.44 | (307) ~ (all_0_39_39 = e4)
% 20.82/5.44 | (1391) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (1075), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (443) all_0_39_39 = e3
% 20.82/5.44 |
% 20.82/5.44 | Equations (443) can reduce 157 to:
% 20.82/5.44 | (3028) ~ (all_0_42_42 = e3)
% 20.82/5.44 |
% 20.82/5.44 | Simplifying 3028 yields:
% 20.82/5.44 | (1924) ~ (all_0_42_42 = e3)
% 20.82/5.44 |
% 20.82/5.44 | Equations (443) can reduce 53 to:
% 20.82/5.44 | (1182) ~ (all_0_56_56 = e3)
% 20.82/5.44 |
% 20.82/5.44 | Simplifying 1182 yields:
% 20.82/5.44 | (1183) ~ (all_0_56_56 = e3)
% 20.82/5.44 |
% 20.82/5.44 | Equations (443) can reduce 320 to:
% 20.82/5.44 | (224) ~ (e3 = e2)
% 20.82/5.44 |
% 20.82/5.44 | Equations (443) can reduce 165 to:
% 20.82/5.44 | (72) ~ (e3 = e0)
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (3018), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (740) all_0_41_41 = e4
% 20.82/5.44 |
% 20.82/5.44 | Combining equations (740,386) yields a new equation:
% 20.82/5.44 | (359) e4 = e2
% 20.82/5.44 |
% 20.82/5.44 | Simplifying 359 yields:
% 20.82/5.44 | (360) e4 = e2
% 20.82/5.44 |
% 20.82/5.44 | Equations (360) can reduce 230 to:
% 20.82/5.44 | (269) $false
% 20.82/5.44 |
% 20.82/5.44 |-The branch is then unsatisfiable
% 20.82/5.44 |-Branch two:
% 20.82/5.44 | (308) ~ (all_0_41_41 = e4)
% 20.82/5.44 | (305) all_0_42_42 = e4
% 20.82/5.44 |
% 20.82/5.44 | Equations (305) can reduce 98 to:
% 20.82/5.44 | (311) ~ (all_0_54_54 = e4)
% 20.82/5.44 |
% 20.82/5.44 | Simplifying 311 yields:
% 20.82/5.44 | (312) ~ (all_0_54_54 = e4)
% 20.82/5.44 |
% 20.82/5.44 | Equations (305) can reduce 1924 to:
% 20.82/5.44 | (41) ~ (e4 = e3)
% 20.82/5.44 |
% 20.82/5.44 | Equations (305) can reduce 362 to:
% 20.82/5.44 | (230) ~ (e4 = e2)
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (169), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (610) all_0_42_42 = e3
% 20.82/5.44 |
% 20.82/5.44 | Combining equations (305,610) yields a new equation:
% 20.82/5.44 | (515) e4 = e3
% 20.82/5.44 |
% 20.82/5.44 | Simplifying 515 yields:
% 20.82/5.44 | (516) e4 = e3
% 20.82/5.44 |
% 20.82/5.44 | Equations (516) can reduce 41 to:
% 20.82/5.44 | (269) $false
% 20.82/5.44 |
% 20.82/5.44 |-The branch is then unsatisfiable
% 20.82/5.44 |-Branch two:
% 20.82/5.44 | (1924) ~ (all_0_42_42 = e3)
% 20.82/5.44 | (1925) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (1925), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (462) all_0_46_46 = e3
% 20.82/5.44 |
% 20.82/5.44 | Combining equations (364,462) yields a new equation:
% 20.82/5.44 | (423) e3 = e2
% 20.82/5.44 |
% 20.82/5.44 | Equations (423) can reduce 224 to:
% 20.82/5.44 | (269) $false
% 20.82/5.44 |
% 20.82/5.44 |-The branch is then unsatisfiable
% 20.82/5.44 |-Branch two:
% 20.82/5.44 | (618) ~ (all_0_46_46 = e3)
% 20.82/5.44 | (1930) all_0_54_54 = e3 | all_0_59_59 = e3
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (1930), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (635) all_0_54_54 = e3
% 20.82/5.44 |
% 20.82/5.44 | Equations (635) can reduce 119 to:
% 20.82/5.44 | (796) ~ (all_0_53_53 = e3)
% 20.82/5.44 |
% 20.82/5.44 | Equations (635) can reduce 312 to:
% 20.82/5.44 | (498) ~ (e4 = e3)
% 20.82/5.44 |
% 20.82/5.44 | Simplifying 498 yields:
% 20.82/5.44 | (41) ~ (e4 = e3)
% 20.82/5.44 |
% 20.82/5.44 | Equations (635) can reduce 261 to:
% 20.82/5.44 | (224) ~ (e3 = e2)
% 20.82/5.44 |
% 20.82/5.44 | From (635) and (49) follows:
% 20.82/5.44 | (798) op(e1, e3) = all_0_37_37
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (213), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (605) all_0_41_41 = e3
% 20.82/5.44 |
% 20.82/5.44 | Combining equations (386,605) yields a new equation:
% 20.82/5.44 | (423) e3 = e2
% 20.82/5.44 |
% 20.82/5.44 | Equations (423) can reduce 224 to:
% 20.82/5.44 | (269) $false
% 20.82/5.44 |
% 20.82/5.44 |-The branch is then unsatisfiable
% 20.82/5.44 |-Branch two:
% 20.82/5.44 | (609) ~ (all_0_41_41 = e3)
% 20.82/5.44 | (3891) all_0_45_45 = e3 | all_0_53_53 = e3 | all_0_58_58 = e3
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (27), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (849) all_0_53_53 = e2
% 20.82/5.44 |
% 20.82/5.44 | Equations (849) can reduce 259 to:
% 20.82/5.44 | (269) $false
% 20.82/5.44 |
% 20.82/5.44 |-The branch is then unsatisfiable
% 20.82/5.44 |-Branch two:
% 20.82/5.44 | (259) ~ (all_0_53_53 = e2)
% 20.82/5.44 | (852) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (243), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (567) all_0_56_56 = e3
% 20.82/5.44 |
% 20.82/5.44 | Equations (567) can reduce 1183 to:
% 20.82/5.44 | (269) $false
% 20.82/5.44 |
% 20.82/5.44 |-The branch is then unsatisfiable
% 20.82/5.44 |-Branch two:
% 20.82/5.44 | (1183) ~ (all_0_56_56 = e3)
% 20.82/5.44 | (1249) all_0_57_57 = e3 | all_0_58_58 = e3 | all_0_59_59 = e3
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (3891), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (1087) all_0_45_45 = e3
% 20.82/5.44 |
% 20.82/5.44 | Combining equations (444,1087) yields a new equation:
% 20.82/5.44 | (515) e4 = e3
% 20.82/5.44 |
% 20.82/5.44 | Simplifying 515 yields:
% 20.82/5.44 | (516) e4 = e3
% 20.82/5.44 |
% 20.82/5.44 | Equations (516) can reduce 41 to:
% 20.82/5.44 | (269) $false
% 20.82/5.44 |
% 20.82/5.44 |-The branch is then unsatisfiable
% 20.82/5.44 |-Branch two:
% 20.82/5.44 | (689) ~ (all_0_45_45 = e3)
% 20.82/5.44 | (3903) all_0_53_53 = e3 | all_0_58_58 = e3
% 20.82/5.44 |
% 20.82/5.44 | Equations (444) can reduce 689 to:
% 20.82/5.44 | (41) ~ (e4 = e3)
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (852), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (853) all_0_53_53 = e1
% 20.82/5.44 |
% 20.82/5.44 | Equations (853) can reduce 127 to:
% 20.82/5.44 | (481) ~ (all_0_58_58 = e1)
% 20.82/5.44 |
% 20.82/5.44 | Simplifying 481 yields:
% 20.82/5.44 | (482) ~ (all_0_58_58 = e1)
% 20.82/5.44 |
% 20.82/5.44 | Equations (853) can reduce 796 to:
% 20.82/5.44 | (597) ~ (e3 = e1)
% 20.82/5.44 |
% 20.82/5.44 | Simplifying 597 yields:
% 20.82/5.44 | (146) ~ (e3 = e1)
% 20.82/5.44 |
% 20.82/5.44 | Equations (853) can reduce 259 to:
% 20.82/5.44 | (414) ~ (e2 = e1)
% 20.82/5.44 |
% 20.82/5.44 | Simplifying 414 yields:
% 20.82/5.44 | (148) ~ (e2 = e1)
% 20.82/5.44 |
% 20.82/5.44 | Equations (853) can reduce 765 to:
% 20.82/5.44 | (144) ~ (e1 = e0)
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (43), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (480) all_0_56_56 = e1
% 20.82/5.44 |
% 20.82/5.44 | Equations (480) can reduce 273 to:
% 20.82/5.44 | (826) ~ (e4 = e1)
% 20.82/5.44 |
% 20.82/5.44 | Simplifying 826 yields:
% 20.82/5.44 | (251) ~ (e4 = e1)
% 20.82/5.44 |
% 20.82/5.44 | Equations (480) can reduce 1183 to:
% 20.82/5.44 | (597) ~ (e3 = e1)
% 20.82/5.44 |
% 20.82/5.44 | Simplifying 597 yields:
% 20.82/5.44 | (146) ~ (e3 = e1)
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (153), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (453) all_0_50_50 = e4
% 20.82/5.44 |
% 20.82/5.44 | Combining equations (253,453) yields a new equation:
% 20.82/5.44 | (360) e4 = e2
% 20.82/5.44 |
% 20.82/5.44 | Equations (360) can reduce 230 to:
% 20.82/5.44 | (269) $false
% 20.82/5.44 |
% 20.82/5.44 |-The branch is then unsatisfiable
% 20.82/5.44 |-Branch two:
% 20.82/5.44 | (456) ~ (all_0_50_50 = e4)
% 20.82/5.44 | (457) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (457), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (458) all_0_51_51 = e4
% 20.82/5.44 |
% 20.82/5.44 | Equations (458) can reduce 432 to:
% 20.82/5.44 | (11) ~ (e4 = e0)
% 20.82/5.44 |
% 20.82/5.44 | From (458) and (175) follows:
% 20.82/5.44 | (3743) op(e1, e3) = e4
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (3903), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (861) all_0_53_53 = e3
% 20.82/5.44 |
% 20.82/5.44 | Combining equations (853,861) yields a new equation:
% 20.82/5.44 | (418) e3 = e1
% 20.82/5.44 |
% 20.82/5.44 | Equations (418) can reduce 146 to:
% 20.82/5.44 | (269) $false
% 20.82/5.44 |
% 20.82/5.44 |-The branch is then unsatisfiable
% 20.82/5.44 |-Branch two:
% 20.82/5.44 | (796) ~ (all_0_53_53 = e3)
% 20.82/5.44 | (497) all_0_58_58 = e3
% 20.82/5.44 |
% 20.82/5.44 | From (497) and (3447) follows:
% 20.82/5.44 | (767) op(e1, e3) = e0
% 20.82/5.44 |
% 20.82/5.44 | Instantiating formula (21) with e1, e3, e4, all_0_37_37 and discharging atoms op(e1, e3) = all_0_37_37, op(e1, e3) = e4, yields:
% 20.82/5.44 | (5099) all_0_37_37 = e4
% 20.82/5.44 |
% 20.82/5.44 | Instantiating formula (21) with e1, e3, e0, all_0_37_37 and discharging atoms op(e1, e3) = all_0_37_37, op(e1, e3) = e0, yields:
% 20.82/5.44 | (921) all_0_37_37 = e0
% 20.82/5.44 |
% 20.82/5.44 | Combining equations (5099,921) yields a new equation:
% 20.82/5.44 | (751) e4 = e0
% 20.82/5.44 |
% 20.82/5.44 | Simplifying 751 yields:
% 20.82/5.44 | (439) e4 = e0
% 20.82/5.44 |
% 20.82/5.44 | Equations (439) can reduce 11 to:
% 20.82/5.44 | (269) $false
% 20.82/5.44 |
% 20.82/5.44 |-The branch is then unsatisfiable
% 20.82/5.44 |-Branch two:
% 20.82/5.44 | (530) ~ (all_0_51_51 = e4)
% 20.82/5.44 | (531) all_0_53_53 = e4 | all_0_54_54 = e4
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (531), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (532) all_0_53_53 = e4
% 20.82/5.44 |
% 20.82/5.44 | Combining equations (853,532) yields a new equation:
% 20.82/5.44 | (477) e4 = e1
% 20.82/5.44 |
% 20.82/5.44 | Equations (477) can reduce 251 to:
% 20.82/5.44 | (269) $false
% 20.82/5.44 |
% 20.82/5.44 |-The branch is then unsatisfiable
% 20.82/5.44 |-Branch two:
% 20.82/5.44 | (448) ~ (all_0_53_53 = e4)
% 20.82/5.44 | (535) all_0_54_54 = e4
% 20.82/5.44 |
% 20.82/5.44 | Combining equations (535,635) yields a new equation:
% 20.82/5.44 | (515) e4 = e3
% 20.82/5.44 |
% 20.82/5.44 | Simplifying 515 yields:
% 20.82/5.44 | (516) e4 = e3
% 20.82/5.44 |
% 20.82/5.44 | Equations (516) can reduce 41 to:
% 20.82/5.44 | (269) $false
% 20.82/5.44 |
% 20.82/5.44 |-The branch is then unsatisfiable
% 20.82/5.44 |-Branch two:
% 20.82/5.44 | (575) ~ (all_0_56_56 = e1)
% 20.82/5.44 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (3903), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (861) all_0_53_53 = e3
% 20.82/5.44 |
% 20.82/5.44 | Combining equations (853,861) yields a new equation:
% 20.82/5.44 | (418) e3 = e1
% 20.82/5.44 |
% 20.82/5.44 | Equations (418) can reduce 146 to:
% 20.82/5.44 | (269) $false
% 20.82/5.44 |
% 20.82/5.44 |-The branch is then unsatisfiable
% 20.82/5.44 |-Branch two:
% 20.82/5.44 | (796) ~ (all_0_53_53 = e3)
% 20.82/5.44 | (497) all_0_58_58 = e3
% 20.82/5.44 |
% 20.82/5.44 | Equations (497) can reduce 482 to:
% 20.82/5.44 | (146) ~ (e3 = e1)
% 20.82/5.44 |
% 20.82/5.44 +-Applying beta-rule and splitting (576), into two cases.
% 20.82/5.44 |-Branch one:
% 20.82/5.44 | (577) all_0_57_57 = e1
% 20.82/5.44 |
% 20.82/5.44 | Combining equations (867,577) yields a new equation:
% 20.82/5.44 | (470) e2 = e1
% 20.82/5.44 |
% 20.82/5.44 | Simplifying 470 yields:
% 20.82/5.44 | (471) e2 = e1
% 20.82/5.44 |
% 20.82/5.44 | Equations (471) can reduce 148 to:
% 20.82/5.44 | (269) $false
% 20.82/5.44 |
% 20.82/5.44 |-The branch is then unsatisfiable
% 20.82/5.45 |-Branch two:
% 20.82/5.45 | (581) ~ (all_0_57_57 = e1)
% 20.82/5.45 | (582) all_0_58_58 = e1 | all_0_59_59 = e1
% 20.82/5.45 |
% 20.82/5.45 +-Applying beta-rule and splitting (582), into two cases.
% 20.82/5.45 |-Branch one:
% 20.82/5.45 | (489) all_0_58_58 = e1
% 20.82/5.45 |
% 20.82/5.45 | Combining equations (489,497) yields a new equation:
% 20.82/5.45 | (418) e3 = e1
% 20.82/5.45 |
% 20.82/5.45 | Equations (418) can reduce 146 to:
% 20.82/5.45 | (269) $false
% 20.82/5.45 |
% 20.82/5.45 |-The branch is then unsatisfiable
% 20.82/5.45 |-Branch two:
% 20.82/5.45 | (482) ~ (all_0_58_58 = e1)
% 20.82/5.45 | (614) all_0_59_59 = e1
% 20.82/5.45 |
% 20.82/5.45 | Combining equations (614,2064) yields a new equation:
% 20.82/5.45 | (578) e1 = e0
% 20.82/5.45 |
% 20.82/5.45 | Simplifying 578 yields:
% 20.82/5.45 | (579) e1 = e0
% 20.82/5.45 |
% 20.82/5.45 | Equations (579) can reduce 144 to:
% 20.82/5.45 | (269) $false
% 20.82/5.45 |
% 20.82/5.45 |-The branch is then unsatisfiable
% 20.82/5.45 |-Branch two:
% 20.82/5.45 | (823) ~ (all_0_53_53 = e1)
% 20.82/5.45 | (856) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e0
% 20.82/5.45 |
% 20.82/5.45 +-Applying beta-rule and splitting (3903), into two cases.
% 20.82/5.45 |-Branch one:
% 20.82/5.45 | (861) all_0_53_53 = e3
% 20.82/5.45 |
% 20.82/5.45 | Equations (861) can reduce 796 to:
% 20.82/5.45 | (269) $false
% 20.82/5.45 |
% 20.82/5.45 |-The branch is then unsatisfiable
% 20.82/5.45 |-Branch two:
% 20.82/5.45 | (796) ~ (all_0_53_53 = e3)
% 20.82/5.45 | (497) all_0_58_58 = e3
% 20.82/5.45 |
% 20.82/5.45 | Equations (497) can reduce 127 to:
% 20.82/5.45 | (796) ~ (all_0_53_53 = e3)
% 20.82/5.45 |
% 20.82/5.45 +-Applying beta-rule and splitting (856), into two cases.
% 20.82/5.45 |-Branch one:
% 20.82/5.45 | (857) all_0_53_53 = e0
% 20.82/5.45 |
% 20.82/5.45 | Equations (857) can reduce 765 to:
% 20.82/5.45 | (269) $false
% 20.82/5.45 |
% 20.82/5.45 |-The branch is then unsatisfiable
% 20.82/5.45 |-Branch two:
% 20.82/5.45 | (765) ~ (all_0_53_53 = e0)
% 20.82/5.45 | (860) all_0_53_53 = e4 | all_0_53_53 = e3
% 20.82/5.45 |
% 20.82/5.45 +-Applying beta-rule and splitting (860), into two cases.
% 20.82/5.45 |-Branch one:
% 20.82/5.45 | (861) all_0_53_53 = e3
% 20.82/5.45 |
% 20.82/5.45 | Equations (861) can reduce 796 to:
% 20.82/5.45 | (269) $false
% 20.82/5.45 |
% 20.82/5.45 |-The branch is then unsatisfiable
% 20.82/5.45 |-Branch two:
% 20.82/5.45 | (796) ~ (all_0_53_53 = e3)
% 20.82/5.45 | (532) all_0_53_53 = e4
% 20.82/5.45 |
% 20.82/5.45 | Equations (532) can reduce 448 to:
% 20.82/5.45 | (269) $false
% 20.82/5.45 |
% 20.82/5.45 |-The branch is then unsatisfiable
% 20.82/5.45 |-Branch two:
% 20.82/5.45 | (430) ~ (all_0_54_54 = e3)
% 20.82/5.45 | (1070) all_0_59_59 = e3
% 20.82/5.45 |
% 20.82/5.45 | Combining equations (1070,2064) yields a new equation:
% 20.82/5.45 | (781) e3 = e0
% 20.82/5.45 |
% 20.82/5.45 | Simplifying 781 yields:
% 20.82/5.45 | (560) e3 = e0
% 20.82/5.45 |
% 20.82/5.45 | Equations (560) can reduce 72 to:
% 20.82/5.45 | (269) $false
% 20.82/5.45 |
% 20.82/5.45 |-The branch is then unsatisfiable
% 20.82/5.45 |-Branch two:
% 20.82/5.45 | (540) ~ (all_0_39_39 = e3)
% 20.82/5.45 | (1079) all_0_39_39 = e4
% 20.82/5.45 |
% 20.82/5.45 | Equations (1079) can reduce 307 to:
% 20.82/5.45 | (269) $false
% 20.82/5.45 |
% 20.82/5.45 |-The branch is then unsatisfiable
% 20.82/5.45 |-Branch two:
% 20.82/5.45 | (952) ~ (all_0_48_48 = e0)
% 20.82/5.45 | (965) all_0_49_49 = e0
% 20.82/5.45 |
% 20.82/5.45 | Combining equations (596,965) yields a new equation:
% 20.82/5.45 | (578) e1 = e0
% 20.82/5.45 |
% 20.82/5.45 | Simplifying 578 yields:
% 20.82/5.45 | (579) e1 = e0
% 20.82/5.45 |
% 20.82/5.45 | Equations (579) can reduce 144 to:
% 20.82/5.45 | (269) $false
% 20.82/5.45 |
% 20.82/5.45 |-The branch is then unsatisfiable
% 20.82/5.45 |-Branch two:
% 20.82/5.45 | (317) ~ (all_0_52_52 = e0)
% 20.82/5.45 | (400) all_0_57_57 = e0
% 20.82/5.45 |
% 20.82/5.45 | Combining equations (400,867) yields a new equation:
% 20.82/5.45 | (354) e2 = e0
% 20.82/5.45 |
% 20.82/5.45 | Equations (354) can reduce 58 to:
% 20.82/5.45 | (269) $false
% 20.82/5.45 |
% 20.82/5.45 |-The branch is then unsatisfiable
% 20.82/5.45 |-Branch two:
% 20.82/5.45 | (459) ~ (all_0_43_43 = e0)
% 20.82/5.45 | (1676) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 20.82/5.45 |
% 20.82/5.45 +-Applying beta-rule and splitting (357), into two cases.
% 20.82/5.45 |-Branch one:
% 20.82/5.45 | (397) all_0_52_52 = e0
% 20.82/5.45 |
% 20.82/5.45 | Equations (397) can reduce 121 to:
% 20.82/5.45 | (356) ~ (all_0_44_44 = e0)
% 20.82/5.45 |
% 20.82/5.45 | Equations (397) can reduce 152 to:
% 20.82/5.45 | (404) ~ (e4 = e0)
% 20.82/5.45 |
% 20.82/5.45 | Simplifying 404 yields:
% 20.82/5.45 | (11) ~ (e4 = e0)
% 20.82/5.45 |
% 20.82/5.45 | Equations (397) can reduce 257 to:
% 20.82/5.45 | (406) ~ (e2 = e0)
% 20.82/5.45 |
% 20.82/5.45 | Simplifying 406 yields:
% 20.82/5.45 | (58) ~ (e2 = e0)
% 20.82/5.45 |
% 20.82/5.45 +-Applying beta-rule and splitting (1676), into two cases.
% 20.82/5.45 |-Branch one:
% 20.82/5.45 | (352) all_0_44_44 = e0
% 20.82/5.45 |
% 20.82/5.45 | Equations (352) can reduce 356 to:
% 20.82/5.45 | (269) $false
% 20.82/5.45 |
% 20.82/5.45 |-The branch is then unsatisfiable
% 20.82/5.45 |-Branch two:
% 20.82/5.45 | (356) ~ (all_0_44_44 = e0)
% 20.82/5.45 | (4115) all_0_45_45 = e0 | all_0_46_46 = e0
% 20.82/5.45 |
% 20.82/5.45 +-Applying beta-rule and splitting (4115), into two cases.
% 20.82/5.45 |-Branch one:
% 20.82/5.45 | (889) all_0_45_45 = e0
% 20.82/5.45 |
% 20.82/5.45 | Combining equations (444,889) yields a new equation:
% 20.82/5.45 | (751) e4 = e0
% 20.82/5.45 |
% 20.82/5.45 | Simplifying 751 yields:
% 20.82/5.45 | (439) e4 = e0
% 20.82/5.45 |
% 20.82/5.45 | Equations (439) can reduce 11 to:
% 20.82/5.45 | (269) $false
% 20.82/5.45 |
% 20.82/5.45 |-The branch is then unsatisfiable
% 20.82/5.45 |-Branch two:
% 20.82/5.45 | (299) ~ (all_0_45_45 = e0)
% 20.82/5.45 | (546) all_0_46_46 = e0
% 20.82/5.45 |
% 20.82/5.45 | Combining equations (364,546) yields a new equation:
% 20.82/5.45 | (353) e2 = e0
% 20.82/5.45 |
% 20.82/5.45 | Simplifying 353 yields:
% 20.82/5.45 | (354) e2 = e0
% 20.82/5.45 |
% 20.82/5.45 | Equations (354) can reduce 58 to:
% 20.82/5.45 | (269) $false
% 20.82/5.45 |
% 20.82/5.45 |-The branch is then unsatisfiable
% 20.82/5.45 |-Branch two:
% 20.82/5.45 | (317) ~ (all_0_52_52 = e0)
% 20.82/5.45 | (400) all_0_57_57 = e0
% 20.82/5.45 |
% 20.82/5.45 | Combining equations (867,400) yields a new equation:
% 20.82/5.45 | (353) e2 = e0
% 20.82/5.45 |
% 20.82/5.45 | Simplifying 353 yields:
% 20.82/5.45 | (354) e2 = e0
% 20.82/5.45 |
% 20.82/5.45 | Equations (354) can reduce 58 to:
% 20.82/5.45 | (269) $false
% 20.82/5.45 |
% 20.82/5.45 |-The branch is then unsatisfiable
% 20.82/5.45 |-Branch two:
% 20.82/5.45 | (523) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 20.82/5.45 |
% 20.82/5.45 | Applying alpha-rule on (523) yields:
% 20.82/5.45 | (524) all_0_19_19 = e0
% 20.82/5.45 | (525) ~ (all_0_20_20 = e2)
% 20.82/5.45 |
% 20.82/5.45 | Combining equations (524,1849) yields a new equation:
% 20.82/5.45 | (439) e4 = e0
% 20.82/5.45 |
% 20.82/5.45 | Equations (439) can reduce 11 to:
% 20.82/5.45 | (269) $false
% 20.82/5.45 |
% 20.82/5.45 |-The branch is then unsatisfiable
% 20.82/5.45 |-Branch two:
% 20.82/5.45 | (378) ~ (all_0_57_57 = e2)
% 20.82/5.45 | (2734) all_0_58_58 = e2 | all_0_59_59 = e2
% 20.82/5.45 |
% 20.82/5.45 +-Applying beta-rule and splitting (2734), into two cases.
% 20.82/5.45 |-Branch one:
% 20.82/5.45 | (485) all_0_58_58 = e2
% 20.82/5.45 |
% 20.82/5.45 | Equations (485) can reduce 392 to:
% 20.82/5.45 | (269) $false
% 20.82/5.45 |
% 20.82/5.45 |-The branch is then unsatisfiable
% 20.82/5.45 |-Branch two:
% 20.82/5.45 | (392) ~ (all_0_58_58 = e2)
% 20.82/5.45 | (375) all_0_59_59 = e2
% 20.82/5.45 |
% 20.82/5.45 | Equations (375) can reduce 1843 to:
% 20.82/5.45 | (269) $false
% 20.82/5.45 |
% 20.82/5.45 |-The branch is then unsatisfiable
% 20.82/5.45 |-Branch two:
% 20.82/5.45 | (641) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 20.82/5.45 |
% 20.82/5.45 | Applying alpha-rule on (641) yields:
% 20.82/5.45 | (285) all_0_2_2 = e0
% 20.82/5.45 | (643) ~ (all_0_3_3 = e4)
% 20.82/5.45 |
% 20.82/5.45 | Equations (288) can reduce 643 to:
% 20.82/5.45 | (269) $false
% 20.82/5.45 |
% 20.82/5.45 |-The branch is then unsatisfiable
% 20.82/5.45 |-Branch two:
% 20.82/5.45 | (645) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 20.82/5.45 |
% 20.82/5.45 | Applying alpha-rule on (645) yields:
% 20.82/5.45 | (605) all_0_41_41 = e3
% 20.82/5.45 | (537) ~ (all_0_45_45 = e4)
% 20.82/5.45 |
% 20.82/5.45 | Equations (444) can reduce 537 to:
% 20.82/5.45 | (269) $false
% 20.82/5.45 |
% 20.82/5.45 |-The branch is then unsatisfiable
% 20.82/5.45 |-Branch two:
% 20.82/5.45 | (1442) ~ (all_0_47_47 = e2)
% 20.82/5.45 | (1443) all_0_47_47 = e1 | all_0_47_47 = e0
% 20.82/5.45 |
% 20.97/5.45 +-Applying beta-rule and splitting (1443), into two cases.
% 20.97/5.45 |-Branch one:
% 20.97/5.45 | (469) all_0_47_47 = e1
% 20.97/5.45 |
% 20.97/5.45 | Equations (469) can reduce 473 to:
% 20.97/5.45 | (269) $false
% 20.97/5.45 |
% 20.97/5.45 |-The branch is then unsatisfiable
% 20.97/5.45 |-Branch two:
% 20.97/5.45 | (473) ~ (all_0_47_47 = e1)
% 20.97/5.45 | (623) all_0_47_47 = e0
% 20.97/5.45 |
% 20.97/5.45 | Equations (623) can reduce 164 to:
% 20.97/5.45 | (165) ~ (all_0_39_39 = e0)
% 20.97/5.45 |
% 20.97/5.45 | Equations (623) can reduce 138 to:
% 20.97/5.45 | (459) ~ (all_0_43_43 = e0)
% 20.97/5.45 |
% 20.97/5.45 | Equations (623) can reduce 48 to:
% 20.97/5.45 | (5223) ~ (all_0_48_48 = e0)
% 20.97/5.45 |
% 20.97/5.45 | Simplifying 5223 yields:
% 20.97/5.45 | (952) ~ (all_0_48_48 = e0)
% 20.97/5.45 |
% 20.97/5.45 | Equations (623) can reduce 34 to:
% 20.97/5.45 | (2889) ~ (all_0_51_51 = e0)
% 20.97/5.45 |
% 20.97/5.45 | Simplifying 2889 yields:
% 20.97/5.45 | (432) ~ (all_0_51_51 = e0)
% 20.97/5.45 |
% 20.97/5.45 | Equations (623) can reduce 147 to:
% 20.97/5.45 | (1556) ~ (all_0_56_56 = e0)
% 20.97/5.45 |
% 20.97/5.45 | Simplifying 1556 yields:
% 20.97/5.45 | (401) ~ (all_0_56_56 = e0)
% 20.97/5.45 |
% 20.97/5.45 | Equations (623) can reduce 248 to:
% 20.97/5.45 | (404) ~ (e4 = e0)
% 20.97/5.45 |
% 20.97/5.45 | Simplifying 404 yields:
% 20.97/5.45 | (11) ~ (e4 = e0)
% 20.97/5.45 |
% 20.97/5.45 | Equations (623) can reduce 1442 to:
% 20.97/5.45 | (406) ~ (e2 = e0)
% 20.97/5.45 |
% 20.97/5.45 | Simplifying 406 yields:
% 20.97/5.45 | (58) ~ (e2 = e0)
% 20.97/5.45 |
% 20.97/5.45 | Equations (623) can reduce 473 to:
% 20.97/5.45 | (436) ~ (e1 = e0)
% 20.97/5.45 |
% 20.97/5.45 | Simplifying 436 yields:
% 20.97/5.45 | (144) ~ (e1 = e0)
% 20.97/5.45 |
% 20.97/5.45 | From (623) and (218) follows:
% 20.97/5.45 | (5235) op(e2, e0) = all_0_8_8
% 20.97/5.45 |
% 20.97/5.45 | From (623) and (231) follows:
% 20.97/5.45 | (5236) op(e2, e3) = e0
% 20.97/5.45 |
% 20.97/5.45 +-Applying beta-rule and splitting (2628), into two cases.
% 20.97/5.45 |-Branch one:
% 20.97/5.45 | (960) ~ (all_0_49_49 = e1)
% 20.97/5.45 |
% 20.97/5.45 +-Applying beta-rule and splitting (50), into two cases.
% 20.97/5.45 |-Branch one:
% 20.97/5.45 | (337) all_0_49_49 = e2
% 20.97/5.45 |
% 20.97/5.45 | Equations (337) can reduce 166 to:
% 20.97/5.45 | (344) ~ (all_0_46_46 = e2)
% 20.97/5.45 |
% 20.97/5.45 | Equations (337) can reduce 178 to:
% 20.97/5.45 | (1115) ~ (all_0_48_48 = e2)
% 20.97/5.45 |
% 20.97/5.45 | Equations (337) can reduce 217 to:
% 20.97/5.45 | (260) ~ (all_0_54_54 = e2)
% 20.97/5.45 |
% 20.97/5.45 | Simplifying 260 yields:
% 20.97/5.45 | (261) ~ (all_0_54_54 = e2)
% 20.97/5.45 |
% 20.97/5.45 | Equations (337) can reduce 82 to:
% 20.97/5.45 | (1842) ~ (all_0_59_59 = e2)
% 20.97/5.45 |
% 20.97/5.45 | Simplifying 1842 yields:
% 20.97/5.45 | (1843) ~ (all_0_59_59 = e2)
% 20.97/5.45 |
% 20.97/5.45 | Equations (337) can reduce 83 to:
% 20.97/5.45 | (326) ~ (e4 = e2)
% 20.97/5.45 |
% 20.97/5.45 | Simplifying 326 yields:
% 20.97/5.45 | (230) ~ (e4 = e2)
% 20.97/5.45 |
% 20.97/5.45 | Equations (337) can reduce 158 to:
% 20.97/5.45 | (328) ~ (e3 = e2)
% 20.97/5.45 |
% 20.97/5.45 | Simplifying 328 yields:
% 20.97/5.45 | (224) ~ (e3 = e2)
% 20.97/5.45 |
% 20.97/5.45 | From (337) and (38) follows:
% 20.97/5.45 | (5249) op(e2, e2) = all_0_35_35
% 20.97/5.45 |
% 20.97/5.45 | From (337) and (128) follows:
% 20.97/5.45 | (5250) op(e2, e0) = e2
% 20.97/5.45 |
% 20.97/5.45 +-Applying beta-rule and splitting (197), into two cases.
% 20.97/5.45 |-Branch one:
% 20.97/5.45 | (1458) all_0_48_48 = e2
% 20.97/5.45 |
% 20.97/5.46 | Equations (1458) can reduce 1115 to:
% 20.97/5.46 | (269) $false
% 20.97/5.46 |
% 20.97/5.46 |-The branch is then unsatisfiable
% 20.97/5.46 |-Branch two:
% 20.97/5.46 | (1115) ~ (all_0_48_48 = e2)
% 20.97/5.46 | (2607) all_0_48_48 = e1 | all_0_48_48 = e0
% 20.97/5.46 |
% 20.97/5.46 +-Applying beta-rule and splitting (2607), into two cases.
% 20.97/5.46 |-Branch one:
% 20.97/5.46 | (593) all_0_48_48 = e1
% 20.97/5.46 |
% 20.97/5.46 | Equations (593) can reduce 167 to:
% 20.97/5.46 | (1315) ~ (all_0_41_41 = e1)
% 20.97/5.46 |
% 20.97/5.46 | Equations (593) can reduce 250 to:
% 20.97/5.46 | (822) ~ (all_0_53_53 = e1)
% 20.97/5.46 |
% 20.97/5.46 | Simplifying 822 yields:
% 20.97/5.46 | (823) ~ (all_0_53_53 = e1)
% 20.97/5.46 |
% 20.97/5.46 | Equations (593) can reduce 174 to:
% 20.97/5.46 | (481) ~ (all_0_58_58 = e1)
% 20.97/5.46 |
% 20.97/5.46 | Simplifying 481 yields:
% 20.97/5.46 | (482) ~ (all_0_58_58 = e1)
% 20.97/5.46 |
% 20.97/5.46 | From (593) and (76) follows:
% 20.97/5.46 | (5261) op(e2, e1) = all_0_26_26
% 20.97/5.46 |
% 20.97/5.46 | From (593) and (179) follows:
% 20.97/5.46 | (2443) op(e2, e1) = e1
% 20.97/5.46 |
% 20.97/5.46 | From (593) and (85) follows:
% 20.97/5.46 | (5263) op(e1, e1) = all_0_25_25
% 20.97/5.46 |
% 20.97/5.46 | Instantiating formula (21) with e2, e2, all_0_35_35, e4 and discharging atoms op(e2, e2) = all_0_35_35, op(e2, e2) = e4, yields:
% 20.97/5.46 | (5264) all_0_35_35 = e4
% 20.97/5.46 |
% 20.97/5.46 | Instantiating formula (21) with e2, e1, e1, all_0_26_26 and discharging atoms op(e2, e1) = all_0_26_26, op(e2, e1) = e1, yields:
% 20.97/5.46 | (4003) all_0_26_26 = e1
% 20.97/5.46 |
% 20.97/5.46 | Instantiating formula (21) with e2, e0, e2, all_0_8_8 and discharging atoms op(e2, e0) = all_0_8_8, op(e2, e0) = e2, yields:
% 20.97/5.46 | (1489) all_0_8_8 = e2
% 20.97/5.46 |
% 20.97/5.46 | Instantiating formula (21) with e1, e1, all_0_25_25, all_0_53_53 and discharging atoms op(e1, e1) = all_0_25_25, op(e1, e1) = all_0_53_53, yields:
% 20.97/5.46 | (5267) all_0_25_25 = all_0_53_53
% 20.97/5.46 |
% 20.97/5.46 | From (5264) and (5249) follows:
% 20.97/5.46 | (222) op(e2, e2) = e4
% 20.97/5.46 |
% 20.97/5.46 | From (4003) and (5261) follows:
% 20.97/5.46 | (2443) op(e2, e1) = e1
% 20.97/5.46 |
% 20.97/5.46 | From (1489) and (5235) follows:
% 20.97/5.46 | (5250) op(e2, e0) = e2
% 20.97/5.46 |
% 20.97/5.46 +-Applying beta-rule and splitting (8), into two cases.
% 20.97/5.46 |-Branch one:
% 20.97/5.46 | (348) all_0_39_39 = e2
% 20.97/5.46 |
% 20.97/5.46 | Equations (348) can reduce 226 to:
% 20.97/5.46 | (1797) ~ (all_0_41_41 = e2)
% 20.97/5.46 |
% 20.97/5.46 | Simplifying 1797 yields:
% 20.97/5.46 | (650) ~ (all_0_41_41 = e2)
% 20.97/5.46 |
% 20.97/5.46 | Equations (348) can reduce 157 to:
% 20.97/5.46 | (5274) ~ (all_0_42_42 = e2)
% 20.97/5.46 |
% 20.97/5.46 | Simplifying 5274 yields:
% 20.97/5.46 | (362) ~ (all_0_42_42 = e2)
% 20.97/5.46 |
% 20.97/5.46 | Equations (348) can reduce 234 to:
% 20.97/5.46 | (1523) ~ (all_0_43_43 = e2)
% 20.97/5.46 |
% 20.97/5.46 | Simplifying 1523 yields:
% 20.97/5.46 | (321) ~ (all_0_43_43 = e2)
% 20.97/5.46 |
% 20.97/5.46 | Equations (348) can reduce 126 to:
% 20.97/5.46 | (254) ~ (all_0_51_51 = e2)
% 20.97/5.46 |
% 20.97/5.46 | Simplifying 254 yields:
% 20.97/5.46 | (255) ~ (all_0_51_51 = e2)
% 20.97/5.46 |
% 20.97/5.46 +-Applying beta-rule and splitting (94), into two cases.
% 20.97/5.46 |-Branch one:
% 20.97/5.46 | (386) all_0_41_41 = e2
% 20.97/5.46 |
% 20.97/5.46 | Equations (386) can reduce 650 to:
% 20.97/5.46 | (269) $false
% 20.97/5.46 |
% 20.97/5.46 |-The branch is then unsatisfiable
% 20.97/5.46 |-Branch two:
% 20.97/5.46 | (650) ~ (all_0_41_41 = e2)
% 20.97/5.46 | (1903) all_0_41_41 = e4 | all_0_41_41 = e3 | all_0_41_41 = e1
% 20.97/5.46 |
% 20.97/5.46 +-Applying beta-rule and splitting (29), into two cases.
% 20.97/5.46 |-Branch one:
% 20.97/5.46 | (1079) all_0_39_39 = e4
% 20.97/5.46 |
% 20.97/5.46 | Combining equations (348,1079) yields a new equation:
% 20.97/5.46 | (360) e4 = e2
% 20.97/5.46 |
% 20.97/5.46 | Equations (360) can reduce 230 to:
% 20.97/5.46 | (269) $false
% 20.97/5.46 |
% 20.97/5.46 |-The branch is then unsatisfiable
% 20.97/5.46 |-Branch two:
% 20.97/5.46 | (307) ~ (all_0_39_39 = e4)
% 20.97/5.46 | (1391) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 20.97/5.46 |
% 20.97/5.46 | Equations (348) can reduce 307 to:
% 20.97/5.46 | (326) ~ (e4 = e2)
% 20.97/5.46 |
% 20.97/5.46 | Simplifying 326 yields:
% 20.97/5.46 | (230) ~ (e4 = e2)
% 20.97/5.46 |
% 20.97/5.46 +-Applying beta-rule and splitting (22), into two cases.
% 20.97/5.46 |-Branch one:
% 20.97/5.46 | (661) all_0_43_43 = e2
% 20.97/5.46 |
% 20.97/5.46 | Equations (661) can reduce 321 to:
% 20.97/5.46 | (269) $false
% 20.97/5.46 |
% 20.97/5.46 |-The branch is then unsatisfiable
% 20.97/5.46 |-Branch two:
% 20.97/5.46 | (321) ~ (all_0_43_43 = e2)
% 20.97/5.46 | (1198) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 20.97/5.46 |
% 20.97/5.46 +-Applying beta-rule and splitting (40), into two cases.
% 20.97/5.46 |-Branch one:
% 20.97/5.46 | (386) all_0_41_41 = e2
% 20.97/5.46 |
% 20.97/5.46 | Equations (386) can reduce 650 to:
% 20.97/5.46 | (269) $false
% 20.97/5.46 |
% 20.97/5.46 |-The branch is then unsatisfiable
% 20.97/5.46 |-Branch two:
% 20.97/5.46 | (650) ~ (all_0_41_41 = e2)
% 20.97/5.46 | (651) all_0_45_45 = e2 | all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 20.97/5.46 |
% 20.97/5.46 +-Applying beta-rule and splitting (225), into two cases.
% 20.97/5.46 |-Branch one:
% 20.97/5.46 | (661) all_0_43_43 = e2
% 20.97/5.46 |
% 20.97/5.46 | Equations (661) can reduce 321 to:
% 20.97/5.46 | (269) $false
% 20.97/5.46 |
% 20.97/5.46 |-The branch is then unsatisfiable
% 20.97/5.46 |-Branch two:
% 20.97/5.46 | (321) ~ (all_0_43_43 = e2)
% 20.97/5.46 | (664) all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2
% 20.97/5.46 |
% 20.97/5.46 +-Applying beta-rule and splitting (664), into two cases.
% 20.97/5.46 |-Branch one:
% 20.97/5.46 | (341) all_0_44_44 = e2
% 20.97/5.46 |
% 20.97/5.46 | Equations (341) can reduce 35 to:
% 20.97/5.46 | (342) ~ (all_0_40_40 = e2)
% 20.97/5.46 |
% 20.97/5.46 | Equations (341) can reduce 190 to:
% 20.97/5.46 | (326) ~ (e4 = e2)
% 20.97/5.46 |
% 20.97/5.46 | Simplifying 326 yields:
% 20.97/5.46 | (230) ~ (e4 = e2)
% 20.97/5.46 |
% 20.97/5.46 | Equations (341) can reduce 87 to:
% 20.97/5.46 | (148) ~ (e2 = e1)
% 20.97/5.46 |
% 20.97/5.46 +-Applying beta-rule and splitting (32), into two cases.
% 20.97/5.46 |-Branch one:
% 20.97/5.46 | (1079) all_0_39_39 = e4
% 20.97/5.46 |
% 20.97/5.46 | Combining equations (348,1079) yields a new equation:
% 20.97/5.46 | (360) e4 = e2
% 20.97/5.46 |
% 20.97/5.46 | Equations (360) can reduce 230 to:
% 20.97/5.46 | (269) $false
% 20.97/5.46 |
% 20.97/5.46 |-The branch is then unsatisfiable
% 20.97/5.46 |-Branch two:
% 20.97/5.46 | (307) ~ (all_0_39_39 = e4)
% 20.97/5.46 | (3018) all_0_41_41 = e4 | all_0_42_42 = e4
% 20.97/5.46 |
% 20.97/5.46 +-Applying beta-rule and splitting (1903), into two cases.
% 20.97/5.46 |-Branch one:
% 20.97/5.46 | (1312) all_0_41_41 = e1
% 20.97/5.46 |
% 20.97/5.46 | Equations (1312) can reduce 1315 to:
% 20.97/5.46 | (269) $false
% 20.97/5.46 |
% 20.97/5.46 |-The branch is then unsatisfiable
% 20.97/5.46 |-Branch two:
% 20.97/5.46 | (1315) ~ (all_0_41_41 = e1)
% 20.97/5.46 | (1972) all_0_41_41 = e4 | all_0_41_41 = e3
% 20.97/5.46 |
% 20.97/5.46 +-Applying beta-rule and splitting (1972), into two cases.
% 20.97/5.46 |-Branch one:
% 20.97/5.46 | (605) all_0_41_41 = e3
% 20.97/5.46 |
% 20.97/5.46 | Equations (605) can reduce 106 to:
% 20.97/5.46 | (3866) ~ (all_0_53_53 = e3)
% 20.97/5.46 |
% 20.97/5.46 | Simplifying 3866 yields:
% 20.97/5.46 | (796) ~ (all_0_53_53 = e3)
% 20.97/5.46 |
% 20.97/5.46 | Equations (605) can reduce 208 to:
% 20.97/5.46 | (788) ~ (all_0_58_58 = e3)
% 20.97/5.46 |
% 20.97/5.46 | Simplifying 788 yields:
% 20.97/5.46 | (527) ~ (all_0_58_58 = e3)
% 20.97/5.46 |
% 20.97/5.46 | Equations (605) can reduce 308 to:
% 20.97/5.46 | (498) ~ (e4 = e3)
% 20.97/5.46 |
% 20.97/5.46 | Simplifying 498 yields:
% 20.97/5.46 | (41) ~ (e4 = e3)
% 20.97/5.46 |
% 20.97/5.46 +-Applying beta-rule and splitting (2625), into two cases.
% 20.97/5.46 |-Branch one:
% 20.97/5.46 | (479) ~ (all_0_51_51 = e1)
% 20.97/5.46 |
% 20.97/5.46 +-Applying beta-rule and splitting (3018), into two cases.
% 20.97/5.46 |-Branch one:
% 20.97/5.46 | (740) all_0_41_41 = e4
% 20.97/5.46 |
% 20.97/5.46 | Combining equations (605,740) yields a new equation:
% 20.97/5.46 | (516) e4 = e3
% 20.97/5.46 |
% 20.97/5.46 | Equations (516) can reduce 41 to:
% 20.97/5.46 | (269) $false
% 20.97/5.46 |
% 20.97/5.46 |-The branch is then unsatisfiable
% 20.97/5.46 |-Branch two:
% 20.97/5.46 | (308) ~ (all_0_41_41 = e4)
% 20.97/5.46 | (305) all_0_42_42 = e4
% 20.97/5.46 |
% 20.97/5.46 | Equations (305) can reduce 207 to:
% 20.97/5.46 | (64) ~ (all_0_40_40 = e4)
% 20.97/5.46 |
% 20.97/5.46 | Equations (305) can reduce 362 to:
% 20.97/5.46 | (230) ~ (e4 = e2)
% 20.97/5.46 |
% 20.97/5.46 +-Applying beta-rule and splitting (17), into two cases.
% 20.97/5.46 |-Branch one:
% 20.97/5.46 | (382) all_0_40_40 = e2
% 20.97/5.46 |
% 20.97/5.46 | Equations (382) can reduce 342 to:
% 20.97/5.46 | (269) $false
% 20.97/5.46 |
% 20.97/5.46 |-The branch is then unsatisfiable
% 20.97/5.46 |-Branch two:
% 20.97/5.46 | (342) ~ (all_0_40_40 = e2)
% 20.97/5.46 | (1093) all_0_40_40 = e3 | all_0_40_40 = e1
% 20.97/5.46 |
% 20.97/5.46 +-Applying beta-rule and splitting (153), into two cases.
% 20.97/5.46 |-Branch one:
% 20.97/5.46 | (453) all_0_50_50 = e4
% 20.97/5.46 |
% 20.97/5.46 | Combining equations (453,253) yields a new equation:
% 20.97/5.46 | (359) e4 = e2
% 20.97/5.46 |
% 20.97/5.46 | Simplifying 359 yields:
% 20.97/5.46 | (360) e4 = e2
% 20.97/5.46 |
% 20.97/5.46 | Equations (360) can reduce 230 to:
% 20.97/5.46 | (269) $false
% 20.97/5.46 |
% 20.97/5.46 |-The branch is then unsatisfiable
% 20.97/5.46 |-Branch two:
% 20.97/5.46 | (456) ~ (all_0_50_50 = e4)
% 20.97/5.46 | (457) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 20.97/5.46 |
% 20.97/5.46 +-Applying beta-rule and splitting (457), into two cases.
% 20.97/5.46 |-Branch one:
% 20.97/5.46 | (458) all_0_51_51 = e4
% 20.97/5.46 |
% 20.97/5.46 | Equations (458) can reduce 137 to:
% 20.97/5.46 | (441) ~ (all_0_43_43 = e4)
% 20.97/5.46 |
% 20.97/5.46 | Equations (458) can reduce 30 to:
% 20.97/5.46 | (447) ~ (all_0_53_53 = e4)
% 20.97/5.46 |
% 20.97/5.46 | Simplifying 447 yields:
% 20.97/5.46 | (448) ~ (all_0_53_53 = e4)
% 20.97/5.46 |
% 20.97/5.46 | Equations (458) can reduce 159 to:
% 20.97/5.46 | (311) ~ (all_0_54_54 = e4)
% 20.97/5.46 |
% 20.97/5.46 | Simplifying 311 yields:
% 20.97/5.46 | (312) ~ (all_0_54_54 = e4)
% 20.97/5.46 |
% 20.97/5.46 | Equations (458) can reduce 255 to:
% 20.97/5.46 | (230) ~ (e4 = e2)
% 20.97/5.46 |
% 20.97/5.46 | Equations (458) can reduce 479 to:
% 20.97/5.46 | (251) ~ (e4 = e1)
% 20.97/5.46 |
% 20.97/5.46 +-Applying beta-rule and splitting (39), into two cases.
% 20.97/5.46 |-Branch one:
% 20.97/5.46 | (464) all_0_39_39 = e1
% 20.97/5.46 |
% 20.97/5.46 | Combining equations (348,464) yields a new equation:
% 20.97/5.46 | (470) e2 = e1
% 20.97/5.46 |
% 20.97/5.46 | Simplifying 470 yields:
% 20.97/5.46 | (471) e2 = e1
% 20.97/5.46 |
% 20.97/5.46 | Equations (471) can reduce 148 to:
% 20.97/5.46 | (269) $false
% 20.97/5.46 |
% 20.97/5.46 |-The branch is then unsatisfiable
% 20.97/5.46 |-Branch two:
% 20.97/5.46 | (467) ~ (all_0_39_39 = e1)
% 20.97/5.46 | (2100) all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1
% 20.97/5.46 |
% 20.97/5.46 +-Applying beta-rule and splitting (2100), into two cases.
% 20.97/5.46 |-Branch one:
% 20.97/5.46 | (413) all_0_40_40 = e1
% 20.97/5.46 |
% 20.97/5.46 | Equations (413) can reduce 168 to:
% 20.97/5.46 | (824) ~ (all_0_57_57 = e1)
% 20.97/5.46 |
% 20.97/5.46 | Simplifying 824 yields:
% 20.97/5.46 | (581) ~ (all_0_57_57 = e1)
% 20.97/5.46 |
% 20.97/5.46 | Equations (413) can reduce 64 to:
% 20.97/5.46 | (826) ~ (e4 = e1)
% 20.97/5.46 |
% 20.97/5.46 | Simplifying 826 yields:
% 20.97/5.46 | (251) ~ (e4 = e1)
% 20.97/5.46 |
% 20.97/5.46 | Equations (413) can reduce 342 to:
% 20.97/5.46 | (414) ~ (e2 = e1)
% 20.97/5.46 |
% 20.97/5.46 | Simplifying 414 yields:
% 20.97/5.46 | (148) ~ (e2 = e1)
% 20.97/5.46 |
% 20.97/5.46 +-Applying beta-rule and splitting (143), into two cases.
% 20.97/5.46 |-Branch one:
% 20.97/5.46 | (433) all_0_43_43 = e0
% 20.97/5.46 |
% 20.97/5.46 | Equations (433) can reduce 459 to:
% 20.97/5.46 | (269) $false
% 20.97/5.46 |
% 20.97/5.46 |-The branch is then unsatisfiable
% 20.97/5.46 |-Branch two:
% 20.97/5.46 | (459) ~ (all_0_43_43 = e0)
% 20.97/5.46 | (1676) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 20.97/5.46 |
% 20.97/5.46 +-Applying beta-rule and splitting (19), into two cases.
% 20.97/5.46 |-Branch one:
% 20.97/5.46 | (475) all_0_51_51 = e1
% 20.97/5.46 |
% 20.97/5.46 | Combining equations (458,475) yields a new equation:
% 20.97/5.46 | (476) e4 = e1
% 20.97/5.46 |
% 20.97/5.46 | Simplifying 476 yields:
% 20.97/5.46 | (477) e4 = e1
% 20.97/5.46 |
% 20.97/5.46 | Equations (477) can reduce 251 to:
% 20.97/5.46 | (269) $false
% 20.97/5.46 |
% 20.97/5.46 |-The branch is then unsatisfiable
% 20.97/5.46 |-Branch two:
% 20.97/5.46 | (479) ~ (all_0_51_51 = e1)
% 20.97/5.46 | (1954) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 20.97/5.46 |
% 20.97/5.46 | Equations (458) can reduce 479 to:
% 20.97/5.46 | (251) ~ (e4 = e1)
% 20.97/5.46 |
% 20.97/5.46 +-Applying beta-rule and splitting (27), into two cases.
% 20.97/5.46 |-Branch one:
% 20.97/5.46 | (849) all_0_53_53 = e2
% 20.97/5.46 |
% 20.97/5.46 | Equations (849) can reduce 259 to:
% 20.97/5.46 | (269) $false
% 20.97/5.46 |
% 20.97/5.46 |-The branch is then unsatisfiable
% 20.97/5.46 |-Branch two:
% 20.97/5.46 | (259) ~ (all_0_53_53 = e2)
% 20.97/5.46 | (852) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (651), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (694) all_0_45_45 = e2
% 20.97/5.47 |
% 20.97/5.47 | Combining equations (444,694) yields a new equation:
% 20.97/5.47 | (359) e4 = e2
% 20.97/5.47 |
% 20.97/5.47 | Simplifying 359 yields:
% 20.97/5.47 | (360) e4 = e2
% 20.97/5.47 |
% 20.97/5.47 | Equations (360) can reduce 230 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (390) ~ (all_0_45_45 = e2)
% 20.97/5.47 | (5383) all_0_48_48 = e2 | all_0_53_53 = e2 | all_0_58_58 = e2
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (5383), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (1458) all_0_48_48 = e2
% 20.97/5.47 |
% 20.97/5.47 | Combining equations (593,1458) yields a new equation:
% 20.97/5.47 | (471) e2 = e1
% 20.97/5.47 |
% 20.97/5.47 | Equations (471) can reduce 148 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (1115) ~ (all_0_48_48 = e2)
% 20.97/5.47 | (5388) all_0_53_53 = e2 | all_0_58_58 = e2
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (5388), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (849) all_0_53_53 = e2
% 20.97/5.47 |
% 20.97/5.47 | Equations (849) can reduce 259 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (259) ~ (all_0_53_53 = e2)
% 20.97/5.47 | (485) all_0_58_58 = e2
% 20.97/5.47 |
% 20.97/5.47 | Equations (485) can reduce 127 to:
% 20.97/5.47 | (259) ~ (all_0_53_53 = e2)
% 20.97/5.47 |
% 20.97/5.47 | Equations (485) can reduce 223 to:
% 20.97/5.47 | (377) ~ (all_0_56_56 = e2)
% 20.97/5.47 |
% 20.97/5.47 | Equations (485) can reduce 527 to:
% 20.97/5.47 | (328) ~ (e3 = e2)
% 20.97/5.47 |
% 20.97/5.47 | Simplifying 328 yields:
% 20.97/5.47 | (224) ~ (e3 = e2)
% 20.97/5.47 |
% 20.97/5.47 | Equations (485) can reduce 482 to:
% 20.97/5.47 | (148) ~ (e2 = e1)
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (852), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (853) all_0_53_53 = e1
% 20.97/5.47 |
% 20.97/5.47 | Equations (853) can reduce 823 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (823) ~ (all_0_53_53 = e1)
% 20.97/5.47 | (856) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e0
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (856), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (857) all_0_53_53 = e0
% 20.97/5.47 |
% 20.97/5.47 | Equations (857) can reduce 71 to:
% 20.97/5.47 | (317) ~ (all_0_52_52 = e0)
% 20.97/5.47 |
% 20.97/5.47 | Equations (857) can reduce 259 to:
% 20.97/5.47 | (406) ~ (e2 = e0)
% 20.97/5.47 |
% 20.97/5.47 | Simplifying 406 yields:
% 20.97/5.47 | (58) ~ (e2 = e0)
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (2627), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (575) ~ (all_0_56_56 = e1)
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (20), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (1575) all_0_56_56 = e2
% 20.97/5.47 |
% 20.97/5.47 | Equations (1575) can reduce 377 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (377) ~ (all_0_56_56 = e2)
% 20.97/5.47 | (1578) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1 | all_0_56_56 = e0
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (1578), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (480) all_0_56_56 = e1
% 20.97/5.47 |
% 20.97/5.47 | Equations (480) can reduce 575 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (575) ~ (all_0_56_56 = e1)
% 20.97/5.47 | (1619) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e0
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (1676), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (352) all_0_44_44 = e0
% 20.97/5.47 |
% 20.97/5.47 | Combining equations (341,352) yields a new equation:
% 20.97/5.47 | (353) e2 = e0
% 20.97/5.47 |
% 20.97/5.47 | Simplifying 353 yields:
% 20.97/5.47 | (354) e2 = e0
% 20.97/5.47 |
% 20.97/5.47 | Equations (354) can reduce 58 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (356) ~ (all_0_44_44 = e0)
% 20.97/5.47 | (4115) all_0_45_45 = e0 | all_0_46_46 = e0
% 20.97/5.47 |
% 20.97/5.47 | Equations (341) can reduce 356 to:
% 20.97/5.47 | (58) ~ (e2 = e0)
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (43), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (480) all_0_56_56 = e1
% 20.97/5.47 |
% 20.97/5.47 | Equations (480) can reduce 575 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (575) ~ (all_0_56_56 = e1)
% 20.97/5.47 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (110), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (352) all_0_44_44 = e0
% 20.97/5.47 |
% 20.97/5.47 | Combining equations (341,352) yields a new equation:
% 20.97/5.47 | (353) e2 = e0
% 20.97/5.47 |
% 20.97/5.47 | Simplifying 353 yields:
% 20.97/5.47 | (354) e2 = e0
% 20.97/5.47 |
% 20.97/5.47 | Equations (354) can reduce 58 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (356) ~ (all_0_44_44 = e0)
% 20.97/5.47 | (357) all_0_52_52 = e0 | all_0_57_57 = e0
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (357), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (397) all_0_52_52 = e0
% 20.97/5.47 |
% 20.97/5.47 | Equations (397) can reduce 317 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (317) ~ (all_0_52_52 = e0)
% 20.97/5.47 | (400) all_0_57_57 = e0
% 20.97/5.47 |
% 20.97/5.47 | Equations (400) can reduce 581 to:
% 20.97/5.47 | (436) ~ (e1 = e0)
% 20.97/5.47 |
% 20.97/5.47 | Simplifying 436 yields:
% 20.97/5.47 | (144) ~ (e1 = e0)
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (200), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (464) all_0_39_39 = e1
% 20.97/5.47 |
% 20.97/5.47 | Combining equations (464,348) yields a new equation:
% 20.97/5.47 | (471) e2 = e1
% 20.97/5.47 |
% 20.97/5.47 | Equations (471) can reduce 148 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (467) ~ (all_0_39_39 = e1)
% 20.97/5.47 | (468) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (468), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (469) all_0_47_47 = e1
% 20.97/5.47 |
% 20.97/5.47 | Combining equations (469,623) yields a new equation:
% 20.97/5.47 | (578) e1 = e0
% 20.97/5.47 |
% 20.97/5.47 | Simplifying 578 yields:
% 20.97/5.47 | (579) e1 = e0
% 20.97/5.47 |
% 20.97/5.47 | Equations (579) can reduce 144 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (473) ~ (all_0_47_47 = e1)
% 20.97/5.47 | (474) all_0_51_51 = e1 | all_0_56_56 = e1
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (474), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (475) all_0_51_51 = e1
% 20.97/5.47 |
% 20.97/5.47 | Combining equations (458,475) yields a new equation:
% 20.97/5.47 | (476) e4 = e1
% 20.97/5.47 |
% 20.97/5.47 | Simplifying 476 yields:
% 20.97/5.47 | (477) e4 = e1
% 20.97/5.47 |
% 20.97/5.47 | Equations (477) can reduce 251 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (479) ~ (all_0_51_51 = e1)
% 20.97/5.47 | (480) all_0_56_56 = e1
% 20.97/5.47 |
% 20.97/5.47 | Equations (480) can reduce 575 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (480) all_0_56_56 = e1
% 20.97/5.47 | (497) all_0_58_58 = e3
% 20.97/5.47 |
% 20.97/5.47 | Combining equations (485,497) yields a new equation:
% 20.97/5.47 | (423) e3 = e2
% 20.97/5.47 |
% 20.97/5.47 | Equations (423) can reduce 224 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (765) ~ (all_0_53_53 = e0)
% 20.97/5.47 | (860) all_0_53_53 = e4 | all_0_53_53 = e3
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (860), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (861) all_0_53_53 = e3
% 20.97/5.47 |
% 20.97/5.47 | Equations (861) can reduce 796 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (796) ~ (all_0_53_53 = e3)
% 20.97/5.47 | (532) all_0_53_53 = e4
% 20.97/5.47 |
% 20.97/5.47 | Equations (532) can reduce 448 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (983) ~ (all_0_40_40 = e1)
% 20.97/5.47 | (5468) all_0_41_41 = e1 | all_0_42_42 = e1
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (19), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (475) all_0_51_51 = e1
% 20.97/5.47 |
% 20.97/5.47 | Combining equations (458,475) yields a new equation:
% 20.97/5.47 | (476) e4 = e1
% 20.97/5.47 |
% 20.97/5.47 | Simplifying 476 yields:
% 20.97/5.47 | (477) e4 = e1
% 20.97/5.47 |
% 20.97/5.47 | Equations (477) can reduce 251 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (479) ~ (all_0_51_51 = e1)
% 20.97/5.47 | (1954) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (1954), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (820) all_0_52_52 = e1
% 20.97/5.47 |
% 20.97/5.47 | Equations (820) can reduce 978 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (978) ~ (all_0_52_52 = e1)
% 20.97/5.47 | (1959) all_0_53_53 = e1 | all_0_54_54 = e1
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (1959), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (853) all_0_53_53 = e1
% 20.97/5.47 |
% 20.97/5.47 | Equations (853) can reduce 823 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (823) ~ (all_0_53_53 = e1)
% 20.97/5.47 | (1592) all_0_54_54 = e1
% 20.97/5.47 |
% 20.97/5.47 | Equations (1592) can reduce 312 to:
% 20.97/5.47 | (826) ~ (e4 = e1)
% 20.97/5.47 |
% 20.97/5.47 | Simplifying 826 yields:
% 20.97/5.47 | (251) ~ (e4 = e1)
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (143), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (433) all_0_43_43 = e0
% 20.97/5.47 |
% 20.97/5.47 | Equations (433) can reduce 459 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (459) ~ (all_0_43_43 = e0)
% 20.97/5.47 | (1676) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (1198), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (433) all_0_43_43 = e0
% 20.97/5.47 |
% 20.97/5.47 | Equations (433) can reduce 459 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (459) ~ (all_0_43_43 = e0)
% 20.97/5.47 | (1695) all_0_43_43 = e4 | all_0_43_43 = e3
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (1695), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (559) all_0_43_43 = e3
% 20.97/5.47 |
% 20.97/5.47 | Equations (559) can reduce 114 to:
% 20.97/5.47 | (146) ~ (e3 = e1)
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (5468), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (1312) all_0_41_41 = e1
% 20.97/5.47 |
% 20.97/5.47 | Combining equations (605,1312) yields a new equation:
% 20.97/5.47 | (572) e3 = e1
% 20.97/5.47 |
% 20.97/5.47 | Simplifying 572 yields:
% 20.97/5.47 | (418) e3 = e1
% 20.97/5.47 |
% 20.97/5.47 | Equations (418) can reduce 146 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (1315) ~ (all_0_41_41 = e1)
% 20.97/5.47 | (832) all_0_42_42 = e1
% 20.97/5.47 |
% 20.97/5.47 | Combining equations (305,832) yields a new equation:
% 20.97/5.47 | (476) e4 = e1
% 20.97/5.47 |
% 20.97/5.47 | Simplifying 476 yields:
% 20.97/5.47 | (477) e4 = e1
% 20.97/5.47 |
% 20.97/5.47 | Equations (477) can reduce 251 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (562) ~ (all_0_43_43 = e3)
% 20.97/5.47 | (438) all_0_43_43 = e4
% 20.97/5.47 |
% 20.97/5.47 | Equations (438) can reduce 441 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (530) ~ (all_0_51_51 = e4)
% 20.97/5.47 | (531) all_0_53_53 = e4 | all_0_54_54 = e4
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (1391), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (438) all_0_43_43 = e4
% 20.97/5.47 |
% 20.97/5.47 | Equations (438) can reduce 441 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (441) ~ (all_0_43_43 = e4)
% 20.97/5.47 | (2025) all_0_51_51 = e4 | all_0_56_56 = e4
% 20.97/5.47 |
% 20.97/5.47 +-Applying beta-rule and splitting (2025), into two cases.
% 20.97/5.47 |-Branch one:
% 20.97/5.47 | (458) all_0_51_51 = e4
% 20.97/5.47 |
% 20.97/5.47 | Equations (458) can reduce 530 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (530) ~ (all_0_51_51 = e4)
% 20.97/5.47 | (1658) all_0_56_56 = e4
% 20.97/5.47 |
% 20.97/5.47 | Equations (1658) can reduce 273 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (475) all_0_51_51 = e1
% 20.97/5.47 | (861) all_0_53_53 = e3
% 20.97/5.47 |
% 20.97/5.47 | Equations (861) can reduce 796 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.47 |-Branch two:
% 20.97/5.47 | (609) ~ (all_0_41_41 = e3)
% 20.97/5.47 | (740) all_0_41_41 = e4
% 20.97/5.47 |
% 20.97/5.47 | Equations (740) can reduce 308 to:
% 20.97/5.47 | (269) $false
% 20.97/5.47 |
% 20.97/5.47 |-The branch is then unsatisfiable
% 20.97/5.48 |-Branch two:
% 20.97/5.48 | (659) ~ (all_0_44_44 = e2)
% 20.97/5.48 | (1120) all_0_45_45 = e2 | all_0_46_46 = e2
% 20.97/5.48 |
% 20.97/5.48 +-Applying beta-rule and splitting (1120), into two cases.
% 20.97/5.48 |-Branch one:
% 20.97/5.48 | (694) all_0_45_45 = e2
% 20.97/5.48 |
% 20.97/5.48 | Combining equations (444,694) yields a new equation:
% 20.97/5.48 | (359) e4 = e2
% 20.97/5.48 |
% 20.97/5.48 | Simplifying 359 yields:
% 20.97/5.48 | (360) e4 = e2
% 20.97/5.48 |
% 20.97/5.48 | Equations (360) can reduce 230 to:
% 20.97/5.48 | (269) $false
% 20.97/5.48 |
% 20.97/5.48 |-The branch is then unsatisfiable
% 20.97/5.48 |-Branch two:
% 20.97/5.48 | (390) ~ (all_0_45_45 = e2)
% 20.97/5.48 | (364) all_0_46_46 = e2
% 20.97/5.48 |
% 20.97/5.48 | Equations (364) can reduce 344 to:
% 20.97/5.48 | (269) $false
% 20.97/5.48 |
% 20.97/5.48 |-The branch is then unsatisfiable
% 20.97/5.48 |-Branch two:
% 20.97/5.48 | (320) ~ (all_0_39_39 = e2)
% 20.97/5.48 | (396) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 20.97/5.48 |
% 20.97/5.48 +-Applying beta-rule and splitting (396), into two cases.
% 20.97/5.48 |-Branch one:
% 20.97/5.48 | (409) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 20.97/5.48 |
% 20.97/5.48 +-Applying beta-rule and splitting (409), into two cases.
% 20.97/5.48 |-Branch one:
% 20.97/5.48 | (410) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 20.97/5.48 |
% 20.97/5.48 | Applying alpha-rule on (410) yields:
% 20.97/5.48 | (411) all_0_0_0 = e1
% 20.97/5.48 | (412) ~ (all_0_1_1 = e4)
% 20.97/5.48 |
% 20.97/5.48 | Combining equations (411,286) yields a new equation:
% 20.97/5.48 | (413) all_0_40_40 = e1
% 20.97/5.48 |
% 20.97/5.48 | Equations (287) can reduce 412 to:
% 20.97/5.48 | (152) ~ (all_0_52_52 = e4)
% 20.97/5.48 |
% 20.97/5.48 | Equations (413) can reduce 18 to:
% 20.97/5.48 | (467) ~ (all_0_39_39 = e1)
% 20.97/5.48 |
% 20.97/5.48 | Equations (413) can reduce 207 to:
% 20.97/5.48 | (2672) ~ (all_0_42_42 = e1)
% 20.97/5.48 |
% 20.97/5.48 | Simplifying 2672 yields:
% 20.97/5.48 | (836) ~ (all_0_42_42 = e1)
% 20.97/5.48 |
% 20.97/5.48 | Equations (413) can reduce 35 to:
% 20.97/5.48 | (2674) ~ (all_0_44_44 = e1)
% 20.97/5.48 |
% 20.97/5.48 | Simplifying 2674 yields:
% 20.97/5.48 | (87) ~ (all_0_44_44 = e1)
% 20.97/5.48 |
% 20.97/5.48 | Equations (413) can reduce 187 to:
% 20.97/5.48 | (1157) ~ (all_0_52_52 = e1)
% 20.97/5.48 |
% 20.97/5.48 | Simplifying 1157 yields:
% 20.97/5.48 | (978) ~ (all_0_52_52 = e1)
% 20.97/5.48 |
% 20.97/5.48 | Equations (413) can reduce 64 to:
% 20.97/5.48 | (826) ~ (e4 = e1)
% 20.97/5.48 |
% 20.97/5.48 | Simplifying 826 yields:
% 20.97/5.48 | (251) ~ (e4 = e1)
% 20.97/5.48 |
% 20.97/5.48 | From (413) and (156) follows:
% 20.97/5.48 | (416) op(e2, e1) = all_0_13_13
% 20.97/5.48 |
% 20.97/5.48 +-Applying beta-rule and splitting (2626), into two cases.
% 20.97/5.48 |-Branch one:
% 20.97/5.48 | (983) ~ (all_0_40_40 = e1)
% 20.97/5.48 |
% 20.97/5.48 | Equations (413) can reduce 983 to:
% 20.97/5.48 | (269) $false
% 20.97/5.48 |
% 20.97/5.48 |-The branch is then unsatisfiable
% 20.97/5.48 |-Branch two:
% 20.97/5.48 | (413) all_0_40_40 = e1
% 20.97/5.48 | (386) all_0_41_41 = e2
% 20.97/5.48 |
% 20.97/5.48 | Equations (386) can reduce 226 to:
% 20.97/5.48 | (320) ~ (all_0_39_39 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Equations (386) can reduce 214 to:
% 20.97/5.48 | (5274) ~ (all_0_42_42 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Simplifying 5274 yields:
% 20.97/5.48 | (362) ~ (all_0_42_42 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Equations (386) can reduce 106 to:
% 20.97/5.48 | (258) ~ (all_0_53_53 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Simplifying 258 yields:
% 20.97/5.48 | (259) ~ (all_0_53_53 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Equations (386) can reduce 208 to:
% 20.97/5.48 | (391) ~ (all_0_58_58 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Simplifying 391 yields:
% 20.97/5.48 | (392) ~ (all_0_58_58 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Equations (386) can reduce 308 to:
% 20.97/5.48 | (326) ~ (e4 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Simplifying 326 yields:
% 20.97/5.48 | (230) ~ (e4 = e2)
% 20.97/5.48 |
% 20.97/5.48 | From (386) and (79) follows:
% 20.97/5.48 | (2695) op(e1, e2) = all_0_21_21
% 20.97/5.48 |
% 20.97/5.48 | Instantiating formula (21) with e2, e1, all_0_13_13, e1 and discharging atoms op(e2, e1) = all_0_13_13, op(e2, e1) = e1, yields:
% 20.97/5.48 | (5565) all_0_13_13 = e1
% 20.97/5.48 |
% 20.97/5.48 | Instantiating formula (21) with e1, e2, all_0_21_21, all_0_52_52 and discharging atoms op(e1, e2) = all_0_21_21, op(e1, e2) = all_0_52_52, yields:
% 20.97/5.48 | (2698) all_0_21_21 = all_0_52_52
% 20.97/5.48 |
% 20.97/5.48 +-Applying beta-rule and splitting (229), into two cases.
% 20.97/5.48 |-Branch one:
% 20.97/5.48 | (923) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1))
% 20.97/5.48 |
% 20.97/5.48 +-Applying beta-rule and splitting (923), into two cases.
% 20.97/5.48 |-Branch one:
% 20.97/5.48 | (924) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1))
% 20.97/5.48 |
% 20.97/5.48 +-Applying beta-rule and splitting (924), into two cases.
% 20.97/5.48 |-Branch one:
% 20.97/5.48 | (925) all_0_21_21 = e4 & ~ (all_0_22_22 = e1)
% 20.97/5.48 |
% 20.97/5.48 | Applying alpha-rule on (925) yields:
% 20.97/5.48 | (926) all_0_21_21 = e4
% 20.97/5.48 | (927) ~ (all_0_22_22 = e1)
% 20.97/5.48 |
% 20.97/5.48 | Combining equations (926,2698) yields a new equation:
% 20.97/5.48 | (3119) all_0_52_52 = e4
% 20.97/5.48 |
% 20.97/5.48 | Equations (3119) can reduce 152 to:
% 20.97/5.48 | (269) $false
% 20.97/5.48 |
% 20.97/5.48 |-The branch is then unsatisfiable
% 20.97/5.48 |-Branch two:
% 20.97/5.48 | (931) all_0_23_23 = e3 & ~ (all_0_24_24 = e1)
% 20.97/5.48 |
% 20.97/5.48 | Applying alpha-rule on (931) yields:
% 20.97/5.48 | (932) all_0_23_23 = e3
% 20.97/5.48 | (933) ~ (all_0_24_24 = e1)
% 20.97/5.48 |
% 20.97/5.48 | Combining equations (932,2649) yields a new equation:
% 20.97/5.48 | (606) e3 = e2
% 20.97/5.48 |
% 20.97/5.48 | Simplifying 606 yields:
% 20.97/5.48 | (423) e3 = e2
% 20.97/5.48 |
% 20.97/5.48 | Equations (423) can reduce 224 to:
% 20.97/5.48 | (269) $false
% 20.97/5.48 |
% 20.97/5.48 |-The branch is then unsatisfiable
% 20.97/5.48 |-Branch two:
% 20.97/5.48 | (937) all_0_25_25 = e2 & ~ (all_0_26_26 = e1)
% 20.97/5.48 |
% 20.97/5.48 | Applying alpha-rule on (937) yields:
% 20.97/5.48 | (938) all_0_25_25 = e2
% 20.97/5.48 | (939) ~ (all_0_26_26 = e1)
% 20.97/5.48 |
% 20.97/5.48 | Combining equations (5267,938) yields a new equation:
% 20.97/5.48 | (5583) all_0_53_53 = e2
% 20.97/5.48 |
% 20.97/5.48 | Simplifying 5583 yields:
% 20.97/5.48 | (849) all_0_53_53 = e2
% 20.97/5.48 |
% 20.97/5.48 | Equations (849) can reduce 259 to:
% 20.97/5.48 | (269) $false
% 20.97/5.48 |
% 20.97/5.48 |-The branch is then unsatisfiable
% 20.97/5.48 |-Branch two:
% 20.97/5.48 | (942) all_0_28_28 = e0 & ~ (all_0_29_29 = e1)
% 20.97/5.48 |
% 20.97/5.48 | Applying alpha-rule on (942) yields:
% 20.97/5.48 | (943) all_0_28_28 = e0
% 20.97/5.48 | (944) ~ (all_0_29_29 = e1)
% 20.97/5.48 |
% 20.97/5.48 | From (943) and (67) follows:
% 20.97/5.48 | (3447) op(e1, all_0_58_58) = e0
% 20.97/5.48 |
% 20.97/5.48 +-Applying beta-rule and splitting (22), into two cases.
% 20.97/5.48 |-Branch one:
% 20.97/5.48 | (661) all_0_43_43 = e2
% 20.97/5.48 |
% 20.97/5.48 | Equations (661) can reduce 3 to:
% 20.97/5.48 | (343) ~ (all_0_46_46 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Simplifying 343 yields:
% 20.97/5.48 | (344) ~ (all_0_46_46 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Equations (661) can reduce 137 to:
% 20.97/5.48 | (254) ~ (all_0_51_51 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Simplifying 254 yields:
% 20.97/5.48 | (255) ~ (all_0_51_51 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Equations (661) can reduce 232 to:
% 20.97/5.48 | (2655) ~ (all_0_56_56 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Simplifying 2655 yields:
% 20.97/5.48 | (377) ~ (all_0_56_56 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Equations (661) can reduce 441 to:
% 20.97/5.48 | (326) ~ (e4 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Simplifying 326 yields:
% 20.97/5.48 | (230) ~ (e4 = e2)
% 20.97/5.48 |
% 20.97/5.48 +-Applying beta-rule and splitting (28), into two cases.
% 20.97/5.48 |-Branch one:
% 20.97/5.48 | (268) all_0_55_55 = e2
% 20.97/5.48 |
% 20.97/5.48 | Combining equations (268,271) yields a new equation:
% 20.97/5.48 | (360) e4 = e2
% 20.97/5.48 |
% 20.97/5.48 | Equations (360) can reduce 230 to:
% 20.97/5.48 | (269) $false
% 20.97/5.48 |
% 20.97/5.48 |-The branch is then unsatisfiable
% 20.97/5.48 |-Branch two:
% 20.97/5.48 | (263) ~ (all_0_55_55 = e2)
% 20.97/5.48 | (2726) all_0_56_56 = e2 | all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 20.97/5.48 |
% 20.97/5.48 +-Applying beta-rule and splitting (2726), into two cases.
% 20.97/5.48 |-Branch one:
% 20.97/5.48 | (1575) all_0_56_56 = e2
% 20.97/5.48 |
% 20.97/5.48 | Equations (1575) can reduce 377 to:
% 20.97/5.48 | (269) $false
% 20.97/5.48 |
% 20.97/5.48 |-The branch is then unsatisfiable
% 20.97/5.48 |-Branch two:
% 20.97/5.48 | (377) ~ (all_0_56_56 = e2)
% 20.97/5.48 | (2730) all_0_57_57 = e2 | all_0_58_58 = e2 | all_0_59_59 = e2
% 20.97/5.48 |
% 20.97/5.48 +-Applying beta-rule and splitting (2730), into two cases.
% 20.97/5.48 |-Branch one:
% 20.97/5.48 | (867) all_0_57_57 = e2
% 20.97/5.48 |
% 20.97/5.48 | Equations (867) can reduce 240 to:
% 20.97/5.48 | (659) ~ (all_0_44_44 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Equations (867) can reduce 124 to:
% 20.97/5.48 | (257) ~ (all_0_52_52 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Equations (867) can reduce 252 to:
% 20.97/5.48 | (391) ~ (all_0_58_58 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Simplifying 391 yields:
% 20.97/5.48 | (392) ~ (all_0_58_58 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Equations (867) can reduce 95 to:
% 20.97/5.48 | (1842) ~ (all_0_59_59 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Simplifying 1842 yields:
% 20.97/5.48 | (1843) ~ (all_0_59_59 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Equations (867) can reduce 173 to:
% 20.97/5.48 | (326) ~ (e4 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Simplifying 326 yields:
% 20.97/5.48 | (230) ~ (e4 = e2)
% 20.97/5.48 |
% 20.97/5.48 | From (867) and (244) follows:
% 20.97/5.48 | (1812) op(e2, e2) = all_0_19_19
% 20.97/5.48 |
% 20.97/5.48 | Instantiating formula (21) with e2, e2, all_0_19_19, e4 and discharging atoms op(e2, e2) = all_0_19_19, op(e2, e2) = e4, yields:
% 20.97/5.48 | (1849) all_0_19_19 = e4
% 20.97/5.48 |
% 20.97/5.48 +-Applying beta-rule and splitting (149), into two cases.
% 20.97/5.48 |-Branch one:
% 20.97/5.48 | (341) all_0_44_44 = e2
% 20.97/5.48 |
% 20.97/5.48 | Equations (341) can reduce 659 to:
% 20.97/5.48 | (269) $false
% 20.97/5.48 |
% 20.97/5.48 |-The branch is then unsatisfiable
% 20.97/5.48 |-Branch two:
% 20.97/5.48 | (659) ~ (all_0_44_44 = e2)
% 20.97/5.48 | (660) all_0_44_44 = e3 | all_0_44_44 = e0
% 20.97/5.48 |
% 20.97/5.48 +-Applying beta-rule and splitting (133), into two cases.
% 20.97/5.48 |-Branch one:
% 20.97/5.48 | (504) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 20.97/5.48 |
% 20.97/5.48 +-Applying beta-rule and splitting (504), into two cases.
% 20.97/5.48 |-Branch one:
% 20.97/5.48 | (505) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 20.97/5.48 |
% 20.97/5.48 +-Applying beta-rule and splitting (505), into two cases.
% 20.97/5.48 |-Branch one:
% 20.97/5.48 | (506) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Applying alpha-rule on (506) yields:
% 20.97/5.48 | (507) all_0_13_13 = e4
% 20.97/5.48 | (508) ~ (all_0_14_14 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Combining equations (5565,507) yields a new equation:
% 20.97/5.48 | (477) e4 = e1
% 20.97/5.48 |
% 20.97/5.48 | Equations (477) can reduce 251 to:
% 20.97/5.48 | (269) $false
% 20.97/5.48 |
% 20.97/5.48 |-The branch is then unsatisfiable
% 20.97/5.48 |-Branch two:
% 20.97/5.48 | (512) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 20.97/5.48 |
% 20.97/5.48 | Applying alpha-rule on (512) yields:
% 20.97/5.48 | (513) all_0_15_15 = e3
% 20.97/5.48 | (514) ~ (all_0_16_16 = e2)
% 20.97/5.48 |
% 20.97/5.48 | From (513) and (205) follows:
% 20.97/5.48 | (3846) op(e2, all_0_44_44) = e3
% 20.97/5.48 |
% 20.97/5.48 +-Applying beta-rule and splitting (110), into two cases.
% 20.97/5.48 |-Branch one:
% 20.97/5.48 | (352) all_0_44_44 = e0
% 20.97/5.48 |
% 20.97/5.48 | Equations (352) can reduce 210 to:
% 20.97/5.48 | (434) ~ (all_0_46_46 = e0)
% 20.97/5.48 |
% 20.97/5.48 | Simplifying 434 yields:
% 20.97/5.48 | (435) ~ (all_0_46_46 = e0)
% 20.97/5.48 |
% 20.97/5.48 | Equations (352) can reduce 121 to:
% 20.97/5.48 | (762) ~ (all_0_52_52 = e0)
% 20.97/5.48 |
% 20.97/5.48 | Simplifying 762 yields:
% 20.97/5.48 | (317) ~ (all_0_52_52 = e0)
% 20.97/5.48 |
% 20.97/5.48 | Equations (352) can reduce 659 to:
% 20.97/5.48 | (406) ~ (e2 = e0)
% 20.97/5.48 |
% 20.97/5.48 | Simplifying 406 yields:
% 20.97/5.48 | (58) ~ (e2 = e0)
% 20.97/5.48 |
% 20.97/5.48 | Equations (352) can reduce 87 to:
% 20.97/5.48 | (436) ~ (e1 = e0)
% 20.97/5.48 |
% 20.97/5.48 | Simplifying 436 yields:
% 20.97/5.48 | (144) ~ (e1 = e0)
% 20.97/5.48 |
% 20.97/5.48 | From (352) and (3846) follows:
% 20.97/5.48 | (3853) op(e2, e0) = e3
% 20.97/5.48 |
% 20.97/5.48 +-Applying beta-rule and splitting (86), into two cases.
% 20.97/5.48 |-Branch one:
% 20.97/5.48 | (816) all_0_52_52 = e2
% 20.97/5.48 |
% 20.97/5.48 | Equations (816) can reduce 257 to:
% 20.97/5.48 | (269) $false
% 20.97/5.48 |
% 20.97/5.48 |-The branch is then unsatisfiable
% 20.97/5.48 |-Branch two:
% 20.97/5.48 | (257) ~ (all_0_52_52 = e2)
% 20.97/5.48 | (819) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 20.97/5.48 |
% 20.97/5.48 +-Applying beta-rule and splitting (199), into two cases.
% 20.97/5.48 |-Branch one:
% 20.97/5.48 | (364) all_0_46_46 = e2
% 20.97/5.48 |
% 20.97/5.48 | Equations (364) can reduce 344 to:
% 20.97/5.48 | (269) $false
% 20.97/5.48 |
% 20.97/5.48 |-The branch is then unsatisfiable
% 20.97/5.48 |-Branch two:
% 20.97/5.48 | (344) ~ (all_0_46_46 = e2)
% 20.97/5.48 | (545) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e0
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (819), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (820) all_0_52_52 = e1
% 20.97/5.49 |
% 20.97/5.49 | Equations (820) can reduce 978 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (978) ~ (all_0_52_52 = e1)
% 20.97/5.49 | (979) all_0_52_52 = e3 | all_0_52_52 = e0
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (545), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (546) all_0_46_46 = e0
% 20.97/5.49 |
% 20.97/5.49 | Equations (546) can reduce 435 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (435) ~ (all_0_46_46 = e0)
% 20.97/5.49 | (549) all_0_46_46 = e4 | all_0_46_46 = e3
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (979), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (397) all_0_52_52 = e0
% 20.97/5.49 |
% 20.97/5.49 | Equations (397) can reduce 317 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (317) ~ (all_0_52_52 = e0)
% 20.97/5.49 | (427) all_0_52_52 = e3
% 20.97/5.49 |
% 20.97/5.49 | Equations (427) can reduce 194 to:
% 20.97/5.49 | (428) ~ (all_0_51_51 = e3)
% 20.97/5.49 |
% 20.97/5.49 | Equations (427) can reduce 71 to:
% 20.97/5.49 | (3866) ~ (all_0_53_53 = e3)
% 20.97/5.49 |
% 20.97/5.49 | Simplifying 3866 yields:
% 20.97/5.49 | (796) ~ (all_0_53_53 = e3)
% 20.97/5.49 |
% 20.97/5.49 | Equations (427) can reduce 978 to:
% 20.97/5.49 | (146) ~ (e3 = e1)
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (27), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (849) all_0_53_53 = e2
% 20.97/5.49 |
% 20.97/5.49 | Equations (849) can reduce 259 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (259) ~ (all_0_53_53 = e2)
% 20.97/5.49 | (852) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (2625), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (479) ~ (all_0_51_51 = e1)
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (19), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (475) all_0_51_51 = e1
% 20.97/5.49 |
% 20.97/5.49 | Equations (475) can reduce 479 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (479) ~ (all_0_51_51 = e1)
% 20.97/5.49 | (1954) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (1954), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (820) all_0_52_52 = e1
% 20.97/5.49 |
% 20.97/5.49 | Combining equations (427,820) yields a new equation:
% 20.97/5.49 | (572) e3 = e1
% 20.97/5.49 |
% 20.97/5.49 | Simplifying 572 yields:
% 20.97/5.49 | (418) e3 = e1
% 20.97/5.49 |
% 20.97/5.49 | Equations (418) can reduce 146 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (978) ~ (all_0_52_52 = e1)
% 20.97/5.49 | (1959) all_0_53_53 = e1 | all_0_54_54 = e1
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (852), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (853) all_0_53_53 = e1
% 20.97/5.49 |
% 20.97/5.49 | Equations (853) can reduce 823 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (823) ~ (all_0_53_53 = e1)
% 20.97/5.49 | (856) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e0
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (856), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (857) all_0_53_53 = e0
% 20.97/5.49 |
% 20.97/5.49 | Equations (857) can reduce 30 to:
% 20.97/5.49 | (432) ~ (all_0_51_51 = e0)
% 20.97/5.49 |
% 20.97/5.49 | Equations (857) can reduce 823 to:
% 20.97/5.49 | (436) ~ (e1 = e0)
% 20.97/5.49 |
% 20.97/5.49 | Simplifying 436 yields:
% 20.97/5.49 | (144) ~ (e1 = e0)
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (1959), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (853) all_0_53_53 = e1
% 20.97/5.49 |
% 20.97/5.49 | Combining equations (857,853) yields a new equation:
% 20.97/5.49 | (579) e1 = e0
% 20.97/5.49 |
% 20.97/5.49 | Equations (579) can reduce 144 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (823) ~ (all_0_53_53 = e1)
% 20.97/5.49 | (1592) all_0_54_54 = e1
% 20.97/5.49 |
% 20.97/5.49 | Equations (1592) can reduce 81 to:
% 20.97/5.49 | (5696) ~ (all_0_59_59 = e1)
% 20.97/5.49 |
% 20.97/5.49 | Simplifying 5696 yields:
% 20.97/5.49 | (2222) ~ (all_0_59_59 = e1)
% 20.97/5.49 |
% 20.97/5.49 | Equations (1592) can reduce 261 to:
% 20.97/5.49 | (414) ~ (e2 = e1)
% 20.97/5.49 |
% 20.97/5.49 | Simplifying 414 yields:
% 20.97/5.49 | (148) ~ (e2 = e1)
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (43), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (480) all_0_56_56 = e1
% 20.97/5.49 |
% 20.97/5.49 | Equations (480) can reduce 16 to:
% 20.97/5.49 | (479) ~ (all_0_51_51 = e1)
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (170), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (1232) all_0_51_51 = e2
% 20.97/5.49 |
% 20.97/5.49 | Equations (1232) can reduce 255 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (255) ~ (all_0_51_51 = e2)
% 20.97/5.49 | (1235) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1 | all_0_51_51 = e0
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (1235), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (475) all_0_51_51 = e1
% 20.97/5.49 |
% 20.97/5.49 | Equations (475) can reduce 479 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (479) ~ (all_0_51_51 = e1)
% 20.97/5.49 | (1371) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e0
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (1371), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (629) all_0_51_51 = e0
% 20.97/5.49 |
% 20.97/5.49 | Equations (629) can reduce 432 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (432) ~ (all_0_51_51 = e0)
% 20.97/5.49 | (1375) all_0_51_51 = e4 | all_0_51_51 = e3
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (1375), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (564) all_0_51_51 = e3
% 20.97/5.49 |
% 20.97/5.49 | Equations (564) can reduce 428 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (428) ~ (all_0_51_51 = e3)
% 20.97/5.49 | (458) all_0_51_51 = e4
% 20.97/5.49 |
% 20.97/5.49 | Equations (458) can reduce 126 to:
% 20.97/5.49 | (307) ~ (all_0_39_39 = e4)
% 20.97/5.49 |
% 20.97/5.49 | Equations (458) can reduce 255 to:
% 20.97/5.49 | (230) ~ (e4 = e2)
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (32), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (1079) all_0_39_39 = e4
% 20.97/5.49 |
% 20.97/5.49 | Equations (1079) can reduce 307 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (307) ~ (all_0_39_39 = e4)
% 20.97/5.49 | (3018) all_0_41_41 = e4 | all_0_42_42 = e4
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (3018), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (740) all_0_41_41 = e4
% 20.97/5.49 |
% 20.97/5.49 | Combining equations (740,386) yields a new equation:
% 20.97/5.49 | (359) e4 = e2
% 20.97/5.49 |
% 20.97/5.49 | Simplifying 359 yields:
% 20.97/5.49 | (360) e4 = e2
% 20.97/5.49 |
% 20.97/5.49 | Equations (360) can reduce 230 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (308) ~ (all_0_41_41 = e4)
% 20.97/5.49 | (305) all_0_42_42 = e4
% 20.97/5.49 |
% 20.97/5.49 | Equations (305) can reduce 107 to:
% 20.97/5.49 | (309) ~ (all_0_46_46 = e4)
% 20.97/5.49 |
% 20.97/5.49 | Simplifying 309 yields:
% 20.97/5.49 | (310) ~ (all_0_46_46 = e4)
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (549), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (462) all_0_46_46 = e3
% 20.97/5.49 |
% 20.97/5.49 | Equations (462) can reduce 344 to:
% 20.97/5.49 | (224) ~ (e3 = e2)
% 20.97/5.49 |
% 20.97/5.49 | Instantiating formula (21) with e2, e0, e3, e2 and discharging atoms op(e2, e0) = e3, op(e2, e0) = e2, yields:
% 20.97/5.49 | (423) e3 = e2
% 20.97/5.49 |
% 20.97/5.49 | Equations (423) can reduce 224 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (618) ~ (all_0_46_46 = e3)
% 20.97/5.49 | (538) all_0_46_46 = e4
% 20.97/5.49 |
% 20.97/5.49 | Equations (538) can reduce 310 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (575) ~ (all_0_56_56 = e1)
% 20.97/5.49 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (2), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (485) all_0_58_58 = e2
% 20.97/5.49 |
% 20.97/5.49 | Equations (485) can reduce 392 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (392) ~ (all_0_58_58 = e2)
% 20.97/5.49 | (488) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1 | all_0_58_58 = e0
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (576), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (577) all_0_57_57 = e1
% 20.97/5.49 |
% 20.97/5.49 | Combining equations (577,867) yields a new equation:
% 20.97/5.49 | (471) e2 = e1
% 20.97/5.49 |
% 20.97/5.49 | Equations (471) can reduce 148 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (581) ~ (all_0_57_57 = e1)
% 20.97/5.49 | (582) all_0_58_58 = e1 | all_0_59_59 = e1
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (488), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (489) all_0_58_58 = e1
% 20.97/5.49 |
% 20.97/5.49 | Equations (489) can reduce 482 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (482) ~ (all_0_58_58 = e1)
% 20.97/5.49 | (492) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e0
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (582), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (489) all_0_58_58 = e1
% 20.97/5.49 |
% 20.97/5.49 | Equations (489) can reduce 482 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (482) ~ (all_0_58_58 = e1)
% 20.97/5.49 | (614) all_0_59_59 = e1
% 20.97/5.49 |
% 20.97/5.49 | Equations (614) can reduce 2222 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (765) ~ (all_0_53_53 = e0)
% 20.97/5.49 | (860) all_0_53_53 = e4 | all_0_53_53 = e3
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (63), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (629) all_0_51_51 = e0
% 20.97/5.49 |
% 20.97/5.49 | Equations (629) can reduce 432 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (432) ~ (all_0_51_51 = e0)
% 20.97/5.49 | (1231) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (170), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (1232) all_0_51_51 = e2
% 20.97/5.49 |
% 20.97/5.49 | Equations (1232) can reduce 255 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (255) ~ (all_0_51_51 = e2)
% 20.97/5.49 | (1235) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1 | all_0_51_51 = e0
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (549), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (462) all_0_46_46 = e3
% 20.97/5.49 |
% 20.97/5.49 | Equations (462) can reduce 107 to:
% 20.97/5.49 | (1924) ~ (all_0_42_42 = e3)
% 20.97/5.49 |
% 20.97/5.49 | Equations (462) can reduce 344 to:
% 20.97/5.49 | (224) ~ (e3 = e2)
% 20.97/5.49 |
% 20.97/5.49 | Equations (462) can reduce 163 to:
% 20.97/5.49 | (146) ~ (e3 = e1)
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (116), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (358) all_0_42_42 = e2
% 20.97/5.49 |
% 20.97/5.49 | Equations (358) can reduce 362 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (362) ~ (all_0_42_42 = e2)
% 20.97/5.49 | (2784) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (2784), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (832) all_0_42_42 = e1
% 20.97/5.49 |
% 20.97/5.49 | Equations (832) can reduce 836 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (836) ~ (all_0_42_42 = e1)
% 20.97/5.49 | (2798) all_0_42_42 = e4 | all_0_42_42 = e3
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (2798), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (610) all_0_42_42 = e3
% 20.97/5.49 |
% 20.97/5.49 | Equations (610) can reduce 1924 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (1924) ~ (all_0_42_42 = e3)
% 20.97/5.49 | (305) all_0_42_42 = e4
% 20.97/5.49 |
% 20.97/5.49 | Equations (305) can reduce 1924 to:
% 20.97/5.49 | (41) ~ (e4 = e3)
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (184), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (443) all_0_39_39 = e3
% 20.97/5.49 |
% 20.97/5.49 | Equations (443) can reduce 126 to:
% 20.97/5.49 | (1180) ~ (all_0_51_51 = e3)
% 20.97/5.49 |
% 20.97/5.49 | Simplifying 1180 yields:
% 20.97/5.49 | (428) ~ (all_0_51_51 = e3)
% 20.97/5.49 |
% 20.97/5.49 | Equations (443) can reduce 467 to:
% 20.97/5.49 | (146) ~ (e3 = e1)
% 20.97/5.49 |
% 20.97/5.49 | Equations (443) can reduce 165 to:
% 20.97/5.49 | (72) ~ (e3 = e0)
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (200), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (464) all_0_39_39 = e1
% 20.97/5.49 |
% 20.97/5.49 | Combining equations (443,464) yields a new equation:
% 20.97/5.49 | (572) e3 = e1
% 20.97/5.49 |
% 20.97/5.49 | Simplifying 572 yields:
% 20.97/5.49 | (418) e3 = e1
% 20.97/5.49 |
% 20.97/5.49 | Equations (418) can reduce 146 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (467) ~ (all_0_39_39 = e1)
% 20.97/5.49 | (468) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (468), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (469) all_0_47_47 = e1
% 20.97/5.49 |
% 20.97/5.49 | Combining equations (469,623) yields a new equation:
% 20.97/5.49 | (578) e1 = e0
% 20.97/5.49 |
% 20.97/5.49 | Simplifying 578 yields:
% 20.97/5.49 | (579) e1 = e0
% 20.97/5.49 |
% 20.97/5.49 | Equations (579) can reduce 144 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (473) ~ (all_0_47_47 = e1)
% 20.97/5.49 | (474) all_0_51_51 = e1 | all_0_56_56 = e1
% 20.97/5.49 |
% 20.97/5.49 | Equations (623) can reduce 473 to:
% 20.97/5.49 | (436) ~ (e1 = e0)
% 20.97/5.49 |
% 20.97/5.49 | Simplifying 436 yields:
% 20.97/5.49 | (144) ~ (e1 = e0)
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (1235), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (475) all_0_51_51 = e1
% 20.97/5.49 |
% 20.97/5.49 | Equations (475) can reduce 479 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (479) ~ (all_0_51_51 = e1)
% 20.97/5.49 | (1371) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e0
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (1371), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (629) all_0_51_51 = e0
% 20.97/5.49 |
% 20.97/5.49 | Equations (629) can reduce 432 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (432) ~ (all_0_51_51 = e0)
% 20.97/5.49 | (1375) all_0_51_51 = e4 | all_0_51_51 = e3
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (1375), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (564) all_0_51_51 = e3
% 20.97/5.49 |
% 20.97/5.49 | Equations (564) can reduce 428 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (428) ~ (all_0_51_51 = e3)
% 20.97/5.49 | (458) all_0_51_51 = e4
% 20.97/5.49 |
% 20.97/5.49 | Equations (458) can reduce 30 to:
% 20.97/5.49 | (447) ~ (all_0_53_53 = e4)
% 20.97/5.49 |
% 20.97/5.49 | Simplifying 447 yields:
% 20.97/5.49 | (448) ~ (all_0_53_53 = e4)
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (1959), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (853) all_0_53_53 = e1
% 20.97/5.49 |
% 20.97/5.49 | Equations (853) can reduce 823 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (823) ~ (all_0_53_53 = e1)
% 20.97/5.49 | (1592) all_0_54_54 = e1
% 20.97/5.49 |
% 20.97/5.49 +-Applying beta-rule and splitting (206), into two cases.
% 20.97/5.49 |-Branch one:
% 20.97/5.49 | (546) all_0_46_46 = e0
% 20.97/5.49 |
% 20.97/5.49 | Combining equations (462,546) yields a new equation:
% 20.97/5.49 | (781) e3 = e0
% 20.97/5.49 |
% 20.97/5.49 | Simplifying 781 yields:
% 20.97/5.49 | (560) e3 = e0
% 20.97/5.49 |
% 20.97/5.49 | Equations (560) can reduce 72 to:
% 20.97/5.49 | (269) $false
% 20.97/5.49 |
% 20.97/5.49 |-The branch is then unsatisfiable
% 20.97/5.49 |-Branch two:
% 20.97/5.49 | (435) ~ (all_0_46_46 = e0)
% 20.97/5.49 | (2930) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (2930), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (965) all_0_49_49 = e0
% 20.97/5.50 |
% 20.97/5.50 | Combining equations (337,965) yields a new equation:
% 20.97/5.50 | (353) e2 = e0
% 20.97/5.50 |
% 20.97/5.50 | Simplifying 353 yields:
% 20.97/5.50 | (354) e2 = e0
% 20.97/5.50 |
% 20.97/5.50 | Equations (354) can reduce 58 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (807) ~ (all_0_49_49 = e0)
% 20.97/5.50 | (2936) all_0_54_54 = e0 | all_0_59_59 = e0
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (2936), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (1286) all_0_54_54 = e0
% 20.97/5.50 |
% 20.97/5.50 | Combining equations (1286,1592) yields a new equation:
% 20.97/5.50 | (579) e1 = e0
% 20.97/5.50 |
% 20.97/5.50 | Equations (579) can reduce 144 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (1478) ~ (all_0_54_54 = e0)
% 20.97/5.50 | (2064) all_0_59_59 = e0
% 20.97/5.50 |
% 20.97/5.50 | Equations (2064) can reduce 198 to:
% 20.97/5.50 | (403) ~ (all_0_58_58 = e0)
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (2), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (485) all_0_58_58 = e2
% 20.97/5.50 |
% 20.97/5.50 | Equations (485) can reduce 392 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (392) ~ (all_0_58_58 = e2)
% 20.97/5.50 | (488) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1 | all_0_58_58 = e0
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (488), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (489) all_0_58_58 = e1
% 20.97/5.50 |
% 20.97/5.50 | Equations (489) can reduce 482 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (482) ~ (all_0_58_58 = e1)
% 20.97/5.50 | (492) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e0
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (492), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (493) all_0_58_58 = e0
% 20.97/5.50 |
% 20.97/5.50 | Equations (493) can reduce 403 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (403) ~ (all_0_58_58 = e0)
% 20.97/5.50 | (496) all_0_58_58 = e4 | all_0_58_58 = e3
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (496), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (497) all_0_58_58 = e3
% 20.97/5.50 |
% 20.97/5.50 | Equations (497) can reduce 127 to:
% 20.97/5.50 | (796) ~ (all_0_53_53 = e3)
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (860), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (861) all_0_53_53 = e3
% 20.97/5.50 |
% 20.97/5.50 | Equations (861) can reduce 796 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (796) ~ (all_0_53_53 = e3)
% 20.97/5.50 | (532) all_0_53_53 = e4
% 20.97/5.50 |
% 20.97/5.50 | Equations (532) can reduce 448 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (527) ~ (all_0_58_58 = e3)
% 20.97/5.50 | (528) all_0_58_58 = e4
% 20.97/5.50 |
% 20.97/5.50 | Equations (528) can reduce 277 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (540) ~ (all_0_39_39 = e3)
% 20.97/5.50 | (541) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (541), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (417) all_0_40_40 = e3
% 20.97/5.50 |
% 20.97/5.50 | Combining equations (413,417) yields a new equation:
% 20.97/5.50 | (418) e3 = e1
% 20.97/5.50 |
% 20.97/5.50 | Equations (418) can reduce 146 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (420) ~ (all_0_40_40 = e3)
% 20.97/5.50 | (604) all_0_41_41 = e3 | all_0_42_42 = e3
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (604), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (605) all_0_41_41 = e3
% 20.97/5.50 |
% 20.97/5.50 | Combining equations (605,386) yields a new equation:
% 20.97/5.50 | (606) e3 = e2
% 20.97/5.50 |
% 20.97/5.50 | Simplifying 606 yields:
% 20.97/5.50 | (423) e3 = e2
% 20.97/5.50 |
% 20.97/5.50 | Equations (423) can reduce 224 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (609) ~ (all_0_41_41 = e3)
% 20.97/5.50 | (610) all_0_42_42 = e3
% 20.97/5.50 |
% 20.97/5.50 | Combining equations (305,610) yields a new equation:
% 20.97/5.50 | (515) e4 = e3
% 20.97/5.50 |
% 20.97/5.50 | Simplifying 515 yields:
% 20.97/5.50 | (516) e4 = e3
% 20.97/5.50 |
% 20.97/5.50 | Equations (516) can reduce 41 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (618) ~ (all_0_46_46 = e3)
% 20.97/5.50 | (538) all_0_46_46 = e4
% 20.97/5.50 |
% 20.97/5.50 | Equations (538) can reduce 310 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (475) all_0_51_51 = e1
% 20.97/5.50 | (861) all_0_53_53 = e3
% 20.97/5.50 |
% 20.97/5.50 | Equations (861) can reduce 796 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (356) ~ (all_0_44_44 = e0)
% 20.97/5.50 | (357) all_0_52_52 = e0 | all_0_57_57 = e0
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (660), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (352) all_0_44_44 = e0
% 20.97/5.50 |
% 20.97/5.50 | Equations (352) can reduce 356 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (356) ~ (all_0_44_44 = e0)
% 20.97/5.50 | (422) all_0_44_44 = e3
% 20.97/5.50 |
% 20.97/5.50 | Equations (422) can reduce 121 to:
% 20.97/5.50 | (5891) ~ (all_0_52_52 = e3)
% 20.97/5.50 |
% 20.97/5.50 | Simplifying 5891 yields:
% 20.97/5.50 | (637) ~ (all_0_52_52 = e3)
% 20.97/5.50 |
% 20.97/5.50 | From (422) and (3846) follows:
% 20.97/5.50 | (4101) op(e2, e3) = e3
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (86), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (816) all_0_52_52 = e2
% 20.97/5.50 |
% 20.97/5.50 | Equations (816) can reduce 257 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (257) ~ (all_0_52_52 = e2)
% 20.97/5.50 | (819) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (819), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (820) all_0_52_52 = e1
% 20.97/5.50 |
% 20.97/5.50 | Equations (820) can reduce 978 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (978) ~ (all_0_52_52 = e1)
% 20.97/5.50 | (979) all_0_52_52 = e3 | all_0_52_52 = e0
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (979), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (397) all_0_52_52 = e0
% 20.97/5.50 |
% 20.97/5.50 | Equations (397) can reduce 71 to:
% 20.97/5.50 | (764) ~ (all_0_53_53 = e0)
% 20.97/5.50 |
% 20.97/5.50 | Simplifying 764 yields:
% 20.97/5.50 | (765) ~ (all_0_53_53 = e0)
% 20.97/5.50 |
% 20.97/5.50 | Equations (397) can reduce 978 to:
% 20.97/5.50 | (436) ~ (e1 = e0)
% 20.97/5.50 |
% 20.97/5.50 | Simplifying 436 yields:
% 20.97/5.50 | (144) ~ (e1 = e0)
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (2630), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (1238) ~ (all_0_54_54 = e1)
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (19), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (475) all_0_51_51 = e1
% 20.97/5.50 |
% 20.97/5.50 | Equations (475) can reduce 16 to:
% 20.97/5.50 | (1452) ~ (all_0_56_56 = e1)
% 20.97/5.50 |
% 20.97/5.50 | Simplifying 1452 yields:
% 20.97/5.50 | (575) ~ (all_0_56_56 = e1)
% 20.97/5.50 |
% 20.97/5.50 | Equations (475) can reduce 255 to:
% 20.97/5.50 | (414) ~ (e2 = e1)
% 20.97/5.50 |
% 20.97/5.50 | Simplifying 414 yields:
% 20.97/5.50 | (148) ~ (e2 = e1)
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (153), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (453) all_0_50_50 = e4
% 20.97/5.50 |
% 20.97/5.50 | Combining equations (253,453) yields a new equation:
% 20.97/5.50 | (360) e4 = e2
% 20.97/5.50 |
% 20.97/5.50 | Equations (360) can reduce 230 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (456) ~ (all_0_50_50 = e4)
% 20.97/5.50 | (457) all_0_51_51 = e4 | all_0_53_53 = e4 | all_0_54_54 = e4
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (2625), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (479) ~ (all_0_51_51 = e1)
% 20.97/5.50 |
% 20.97/5.50 | Equations (475) can reduce 479 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (475) all_0_51_51 = e1
% 20.97/5.50 | (861) all_0_53_53 = e3
% 20.97/5.50 |
% 20.97/5.50 | Equations (861) can reduce 119 to:
% 20.97/5.50 | (429) ~ (all_0_54_54 = e3)
% 20.97/5.50 |
% 20.97/5.50 | Simplifying 429 yields:
% 20.97/5.50 | (430) ~ (all_0_54_54 = e3)
% 20.97/5.50 |
% 20.97/5.50 | Equations (861) can reduce 448 to:
% 20.97/5.50 | (498) ~ (e4 = e3)
% 20.97/5.50 |
% 20.97/5.50 | Simplifying 498 yields:
% 20.97/5.50 | (41) ~ (e4 = e3)
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (457), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (458) all_0_51_51 = e4
% 20.97/5.50 |
% 20.97/5.50 | Combining equations (475,458) yields a new equation:
% 20.97/5.50 | (477) e4 = e1
% 20.97/5.50 |
% 20.97/5.50 | Equations (477) can reduce 251 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (530) ~ (all_0_51_51 = e4)
% 20.97/5.50 | (531) all_0_53_53 = e4 | all_0_54_54 = e4
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (2), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (485) all_0_58_58 = e2
% 20.97/5.50 |
% 20.97/5.50 | Equations (485) can reduce 392 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (392) ~ (all_0_58_58 = e2)
% 20.97/5.50 | (488) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1 | all_0_58_58 = e0
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (531), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (532) all_0_53_53 = e4
% 20.97/5.50 |
% 20.97/5.50 | Combining equations (861,532) yields a new equation:
% 20.97/5.50 | (516) e4 = e3
% 20.97/5.50 |
% 20.97/5.50 | Equations (516) can reduce 41 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (448) ~ (all_0_53_53 = e4)
% 20.97/5.50 | (535) all_0_54_54 = e4
% 20.97/5.50 |
% 20.97/5.50 | Equations (535) can reduce 98 to:
% 20.97/5.50 | (2787) ~ (all_0_42_42 = e4)
% 20.97/5.50 |
% 20.97/5.50 | Equations (535) can reduce 430 to:
% 20.97/5.50 | (41) ~ (e4 = e3)
% 20.97/5.50 |
% 20.97/5.50 | Equations (535) can reduce 261 to:
% 20.97/5.50 | (230) ~ (e4 = e2)
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (116), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (358) all_0_42_42 = e2
% 20.97/5.50 |
% 20.97/5.50 | Equations (358) can reduce 362 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (362) ~ (all_0_42_42 = e2)
% 20.97/5.50 | (2784) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (84), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (832) all_0_42_42 = e1
% 20.97/5.50 |
% 20.97/5.50 | Equations (832) can reduce 836 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (836) ~ (all_0_42_42 = e1)
% 20.97/5.50 | (837) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (32), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (1079) all_0_39_39 = e4
% 20.97/5.50 |
% 20.97/5.50 | Equations (1079) can reduce 157 to:
% 20.97/5.50 | (2786) ~ (all_0_42_42 = e4)
% 20.97/5.50 |
% 20.97/5.50 | Simplifying 2786 yields:
% 20.97/5.50 | (2787) ~ (all_0_42_42 = e4)
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (488), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (489) all_0_58_58 = e1
% 20.97/5.50 |
% 20.97/5.50 | Equations (489) can reduce 482 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (482) ~ (all_0_58_58 = e1)
% 20.97/5.50 | (492) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e0
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (184), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (443) all_0_39_39 = e3
% 20.97/5.50 |
% 20.97/5.50 | Combining equations (1079,443) yields a new equation:
% 20.97/5.50 | (515) e4 = e3
% 20.97/5.50 |
% 20.97/5.50 | Simplifying 515 yields:
% 20.97/5.50 | (516) e4 = e3
% 20.97/5.50 |
% 20.97/5.50 | Equations (516) can reduce 41 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (540) ~ (all_0_39_39 = e3)
% 20.97/5.50 | (541) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 20.97/5.50 |
% 20.97/5.50 | Equations (1079) can reduce 540 to:
% 20.97/5.50 | (41) ~ (e4 = e3)
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (43), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (480) all_0_56_56 = e1
% 20.97/5.50 |
% 20.97/5.50 | Equations (480) can reduce 575 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (575) ~ (all_0_56_56 = e1)
% 20.97/5.50 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (204), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (443) all_0_39_39 = e3
% 20.97/5.50 |
% 20.97/5.50 | Combining equations (1079,443) yields a new equation:
% 20.97/5.50 | (515) e4 = e3
% 20.97/5.50 |
% 20.97/5.50 | Simplifying 515 yields:
% 20.97/5.50 | (516) e4 = e3
% 20.97/5.50 |
% 20.97/5.50 | Equations (516) can reduce 41 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (540) ~ (all_0_39_39 = e3)
% 20.97/5.50 | (558) all_0_43_43 = e3 | all_0_51_51 = e3 | all_0_56_56 = e3
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (2784), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (832) all_0_42_42 = e1
% 20.97/5.50 |
% 20.97/5.50 | Equations (832) can reduce 836 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (836) ~ (all_0_42_42 = e1)
% 20.97/5.50 | (2798) all_0_42_42 = e4 | all_0_42_42 = e3
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (576), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (577) all_0_57_57 = e1
% 20.97/5.50 |
% 20.97/5.50 | Combining equations (577,867) yields a new equation:
% 20.97/5.50 | (471) e2 = e1
% 20.97/5.50 |
% 20.97/5.50 | Equations (471) can reduce 148 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (581) ~ (all_0_57_57 = e1)
% 20.97/5.50 | (582) all_0_58_58 = e1 | all_0_59_59 = e1
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (2798), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (610) all_0_42_42 = e3
% 20.97/5.50 |
% 20.97/5.50 | Equations (610) can reduce 103 to:
% 20.97/5.50 | (2131) ~ (all_0_59_59 = e3)
% 20.97/5.50 |
% 20.97/5.50 | Simplifying 2131 yields:
% 20.97/5.50 | (2132) ~ (all_0_59_59 = e3)
% 20.97/5.50 |
% 20.97/5.50 | Equations (610) can reduce 362 to:
% 20.97/5.50 | (224) ~ (e3 = e2)
% 20.97/5.50 |
% 20.97/5.50 +-Applying beta-rule and splitting (582), into two cases.
% 20.97/5.50 |-Branch one:
% 20.97/5.50 | (489) all_0_58_58 = e1
% 20.97/5.50 |
% 20.97/5.50 | Equations (489) can reduce 482 to:
% 20.97/5.50 | (269) $false
% 20.97/5.50 |
% 20.97/5.50 |-The branch is then unsatisfiable
% 20.97/5.50 |-Branch two:
% 20.97/5.50 | (482) ~ (all_0_58_58 = e1)
% 20.97/5.51 | (614) all_0_59_59 = e1
% 20.97/5.51 |
% 20.97/5.51 | Equations (614) can reduce 2132 to:
% 20.97/5.51 | (597) ~ (e3 = e1)
% 20.97/5.51 |
% 20.97/5.51 | Simplifying 597 yields:
% 20.97/5.51 | (146) ~ (e3 = e1)
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (558), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (559) all_0_43_43 = e3
% 20.97/5.51 |
% 20.97/5.51 | Combining equations (661,559) yields a new equation:
% 20.97/5.51 | (423) e3 = e2
% 20.97/5.51 |
% 20.97/5.51 | Equations (423) can reduce 224 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (562) ~ (all_0_43_43 = e3)
% 20.97/5.51 | (563) all_0_51_51 = e3 | all_0_56_56 = e3
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (563), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (564) all_0_51_51 = e3
% 20.97/5.51 |
% 20.97/5.51 | Combining equations (564,475) yields a new equation:
% 20.97/5.51 | (572) e3 = e1
% 20.97/5.51 |
% 20.97/5.51 | Simplifying 572 yields:
% 20.97/5.51 | (418) e3 = e1
% 20.97/5.51 |
% 20.97/5.51 | Equations (418) can reduce 146 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (428) ~ (all_0_51_51 = e3)
% 20.97/5.51 | (567) all_0_56_56 = e3
% 20.97/5.51 |
% 20.97/5.51 | Equations (567) can reduce 223 to:
% 20.97/5.51 | (788) ~ (all_0_58_58 = e3)
% 20.97/5.51 |
% 20.97/5.51 | Simplifying 788 yields:
% 20.97/5.51 | (527) ~ (all_0_58_58 = e3)
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (2629), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (2222) ~ (all_0_59_59 = e1)
% 20.97/5.51 |
% 20.97/5.51 | Equations (614) can reduce 2222 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (614) all_0_59_59 = e1
% 20.97/5.51 | (493) all_0_58_58 = e0
% 20.97/5.51 |
% 20.97/5.51 | Equations (493) can reduce 527 to:
% 20.97/5.51 | (1272) ~ (e3 = e0)
% 20.97/5.51 |
% 20.97/5.51 | Simplifying 1272 yields:
% 20.97/5.51 | (72) ~ (e3 = e0)
% 20.97/5.51 |
% 20.97/5.51 | Instantiating formula (21) with e2, e3, e3, e0 and discharging atoms op(e2, e3) = e3, op(e2, e3) = e0, yields:
% 20.97/5.51 | (560) e3 = e0
% 20.97/5.51 |
% 20.97/5.51 | Equations (560) can reduce 72 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (1924) ~ (all_0_42_42 = e3)
% 20.97/5.51 | (305) all_0_42_42 = e4
% 20.97/5.51 |
% 20.97/5.51 | Equations (305) can reduce 2787 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (307) ~ (all_0_39_39 = e4)
% 20.97/5.51 | (3018) all_0_41_41 = e4 | all_0_42_42 = e4
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (2784), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (832) all_0_42_42 = e1
% 20.97/5.51 |
% 20.97/5.51 | Equations (832) can reduce 836 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (836) ~ (all_0_42_42 = e1)
% 20.97/5.51 | (2798) all_0_42_42 = e4 | all_0_42_42 = e3
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (2798), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (610) all_0_42_42 = e3
% 20.97/5.51 |
% 20.97/5.51 | Equations (610) can reduce 2787 to:
% 20.97/5.51 | (498) ~ (e4 = e3)
% 20.97/5.51 |
% 20.97/5.51 | Simplifying 498 yields:
% 20.97/5.51 | (41) ~ (e4 = e3)
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (3018), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (740) all_0_41_41 = e4
% 20.97/5.51 |
% 20.97/5.51 | Combining equations (740,386) yields a new equation:
% 20.97/5.51 | (359) e4 = e2
% 20.97/5.51 |
% 20.97/5.51 | Simplifying 359 yields:
% 20.97/5.51 | (360) e4 = e2
% 20.97/5.51 |
% 20.97/5.51 | Equations (360) can reduce 230 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (308) ~ (all_0_41_41 = e4)
% 20.97/5.51 | (305) all_0_42_42 = e4
% 20.97/5.51 |
% 20.97/5.51 | Combining equations (305,610) yields a new equation:
% 20.97/5.51 | (515) e4 = e3
% 20.97/5.51 |
% 20.97/5.51 | Simplifying 515 yields:
% 20.97/5.51 | (516) e4 = e3
% 20.97/5.51 |
% 20.97/5.51 | Equations (516) can reduce 41 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (1924) ~ (all_0_42_42 = e3)
% 20.97/5.51 | (305) all_0_42_42 = e4
% 20.97/5.51 |
% 20.97/5.51 | Equations (305) can reduce 2787 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (479) ~ (all_0_51_51 = e1)
% 20.97/5.51 | (1954) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (1954), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (820) all_0_52_52 = e1
% 20.97/5.51 |
% 20.97/5.51 | Combining equations (397,820) yields a new equation:
% 20.97/5.51 | (579) e1 = e0
% 20.97/5.51 |
% 20.97/5.51 | Equations (579) can reduce 144 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (978) ~ (all_0_52_52 = e1)
% 20.97/5.51 | (1959) all_0_53_53 = e1 | all_0_54_54 = e1
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (27), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (849) all_0_53_53 = e2
% 20.97/5.51 |
% 20.97/5.51 | Equations (849) can reduce 259 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (259) ~ (all_0_53_53 = e2)
% 20.97/5.51 | (852) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (852), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (853) all_0_53_53 = e1
% 20.97/5.51 |
% 20.97/5.51 | Equations (853) can reduce 823 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (823) ~ (all_0_53_53 = e1)
% 20.97/5.51 | (856) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e0
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (856), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (857) all_0_53_53 = e0
% 20.97/5.51 |
% 20.97/5.51 | Equations (857) can reduce 765 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (765) ~ (all_0_53_53 = e0)
% 20.97/5.51 | (860) all_0_53_53 = e4 | all_0_53_53 = e3
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (860), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (861) all_0_53_53 = e3
% 20.97/5.51 |
% 20.97/5.51 | Equations (861) can reduce 823 to:
% 20.97/5.51 | (146) ~ (e3 = e1)
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (1959), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (853) all_0_53_53 = e1
% 20.97/5.51 |
% 20.97/5.51 | Combining equations (861,853) yields a new equation:
% 20.97/5.51 | (572) e3 = e1
% 20.97/5.51 |
% 20.97/5.51 | Simplifying 572 yields:
% 20.97/5.51 | (418) e3 = e1
% 20.97/5.51 |
% 20.97/5.51 | Equations (418) can reduce 146 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (823) ~ (all_0_53_53 = e1)
% 20.97/5.51 | (1592) all_0_54_54 = e1
% 20.97/5.51 |
% 20.97/5.51 | Equations (1592) can reduce 1238 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (796) ~ (all_0_53_53 = e3)
% 20.97/5.51 | (532) all_0_53_53 = e4
% 20.97/5.51 |
% 20.97/5.51 | Equations (532) can reduce 448 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (1592) all_0_54_54 = e1
% 20.97/5.51 | (857) all_0_53_53 = e0
% 20.97/5.51 |
% 20.97/5.51 | Equations (857) can reduce 765 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (317) ~ (all_0_52_52 = e0)
% 20.97/5.51 | (427) all_0_52_52 = e3
% 20.97/5.51 |
% 20.97/5.51 | Equations (427) can reduce 637 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (518) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 20.97/5.51 |
% 20.97/5.51 | Applying alpha-rule on (518) yields:
% 20.97/5.51 | (519) all_0_17_17 = e1
% 20.97/5.51 | (520) ~ (all_0_18_18 = e2)
% 20.97/5.51 |
% 20.97/5.51 | From (519) and (69) follows:
% 20.97/5.51 | (2268) op(e2, all_0_52_52) = e1
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (110), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (352) all_0_44_44 = e0
% 20.97/5.51 |
% 20.97/5.51 | Equations (352) can reduce 210 to:
% 20.97/5.51 | (434) ~ (all_0_46_46 = e0)
% 20.97/5.51 |
% 20.97/5.51 | Simplifying 434 yields:
% 20.97/5.51 | (435) ~ (all_0_46_46 = e0)
% 20.97/5.51 |
% 20.97/5.51 | Equations (352) can reduce 121 to:
% 20.97/5.51 | (762) ~ (all_0_52_52 = e0)
% 20.97/5.51 |
% 20.97/5.51 | Simplifying 762 yields:
% 20.97/5.51 | (317) ~ (all_0_52_52 = e0)
% 20.97/5.51 |
% 20.97/5.51 | Equations (352) can reduce 659 to:
% 20.97/5.51 | (406) ~ (e2 = e0)
% 20.97/5.51 |
% 20.97/5.51 | Simplifying 406 yields:
% 20.97/5.51 | (58) ~ (e2 = e0)
% 20.97/5.51 |
% 20.97/5.51 | Equations (352) can reduce 87 to:
% 20.97/5.51 | (436) ~ (e1 = e0)
% 20.97/5.51 |
% 20.97/5.51 | Simplifying 436 yields:
% 20.97/5.51 | (144) ~ (e1 = e0)
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (86), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (816) all_0_52_52 = e2
% 20.97/5.51 |
% 20.97/5.51 | Equations (816) can reduce 257 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (257) ~ (all_0_52_52 = e2)
% 20.97/5.51 | (819) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (199), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (364) all_0_46_46 = e2
% 20.97/5.51 |
% 20.97/5.51 | Equations (364) can reduce 344 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (344) ~ (all_0_46_46 = e2)
% 20.97/5.51 | (545) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e0
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (819), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (820) all_0_52_52 = e1
% 20.97/5.51 |
% 20.97/5.51 | Equations (820) can reduce 978 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (978) ~ (all_0_52_52 = e1)
% 20.97/5.51 | (979) all_0_52_52 = e3 | all_0_52_52 = e0
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (545), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (546) all_0_46_46 = e0
% 20.97/5.51 |
% 20.97/5.51 | Equations (546) can reduce 435 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (435) ~ (all_0_46_46 = e0)
% 20.97/5.51 | (549) all_0_46_46 = e4 | all_0_46_46 = e3
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (979), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (397) all_0_52_52 = e0
% 20.97/5.51 |
% 20.97/5.51 | Equations (397) can reduce 317 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (317) ~ (all_0_52_52 = e0)
% 20.97/5.51 | (427) all_0_52_52 = e3
% 20.97/5.51 |
% 20.97/5.51 | Equations (427) can reduce 71 to:
% 20.97/5.51 | (3866) ~ (all_0_53_53 = e3)
% 20.97/5.51 |
% 20.97/5.51 | Simplifying 3866 yields:
% 20.97/5.51 | (796) ~ (all_0_53_53 = e3)
% 20.97/5.51 |
% 20.97/5.51 | Equations (427) can reduce 978 to:
% 20.97/5.51 | (146) ~ (e3 = e1)
% 20.97/5.51 |
% 20.97/5.51 | From (427) and (2268) follows:
% 20.97/5.51 | (3095) op(e2, e3) = e1
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (27), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (849) all_0_53_53 = e2
% 20.97/5.51 |
% 20.97/5.51 | Equations (849) can reduce 259 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (259) ~ (all_0_53_53 = e2)
% 20.97/5.51 | (852) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (2625), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (479) ~ (all_0_51_51 = e1)
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (19), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (475) all_0_51_51 = e1
% 20.97/5.51 |
% 20.97/5.51 | Equations (475) can reduce 479 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (479) ~ (all_0_51_51 = e1)
% 20.97/5.51 | (1954) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (1954), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (820) all_0_52_52 = e1
% 20.97/5.51 |
% 20.97/5.51 | Combining equations (427,820) yields a new equation:
% 20.97/5.51 | (572) e3 = e1
% 20.97/5.51 |
% 20.97/5.51 | Simplifying 572 yields:
% 20.97/5.51 | (418) e3 = e1
% 20.97/5.51 |
% 20.97/5.51 | Equations (418) can reduce 146 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (978) ~ (all_0_52_52 = e1)
% 20.97/5.51 | (1959) all_0_53_53 = e1 | all_0_54_54 = e1
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (852), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (853) all_0_53_53 = e1
% 20.97/5.51 |
% 20.97/5.51 | Equations (853) can reduce 823 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (823) ~ (all_0_53_53 = e1)
% 20.97/5.51 | (856) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e0
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (856), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (857) all_0_53_53 = e0
% 20.97/5.51 |
% 20.97/5.51 | Equations (857) can reduce 259 to:
% 20.97/5.51 | (406) ~ (e2 = e0)
% 20.97/5.51 |
% 20.97/5.51 | Simplifying 406 yields:
% 20.97/5.51 | (58) ~ (e2 = e0)
% 20.97/5.51 |
% 20.97/5.51 | Equations (857) can reduce 823 to:
% 20.97/5.51 | (436) ~ (e1 = e0)
% 20.97/5.51 |
% 20.97/5.51 | Simplifying 436 yields:
% 20.97/5.51 | (144) ~ (e1 = e0)
% 20.97/5.51 |
% 20.97/5.51 +-Applying beta-rule and splitting (1959), into two cases.
% 20.97/5.51 |-Branch one:
% 20.97/5.51 | (853) all_0_53_53 = e1
% 20.97/5.51 |
% 20.97/5.51 | Combining equations (857,853) yields a new equation:
% 20.97/5.51 | (579) e1 = e0
% 20.97/5.51 |
% 20.97/5.51 | Equations (579) can reduce 144 to:
% 20.97/5.51 | (269) $false
% 20.97/5.51 |
% 20.97/5.51 |-The branch is then unsatisfiable
% 20.97/5.51 |-Branch two:
% 20.97/5.51 | (823) ~ (all_0_53_53 = e1)
% 20.97/5.51 | (1592) all_0_54_54 = e1
% 20.97/5.51 |
% 20.97/5.51 | Equations (1592) can reduce 81 to:
% 20.97/5.52 | (5696) ~ (all_0_59_59 = e1)
% 20.97/5.52 |
% 20.97/5.52 | Simplifying 5696 yields:
% 20.97/5.52 | (2222) ~ (all_0_59_59 = e1)
% 20.97/5.52 |
% 20.97/5.52 | Equations (1592) can reduce 261 to:
% 20.97/5.52 | (414) ~ (e2 = e1)
% 20.97/5.52 |
% 20.97/5.52 | Simplifying 414 yields:
% 20.97/5.52 | (148) ~ (e2 = e1)
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (43), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (480) all_0_56_56 = e1
% 20.97/5.52 |
% 20.97/5.52 | Equations (480) can reduce 130 to:
% 20.97/5.52 | (5696) ~ (all_0_59_59 = e1)
% 20.97/5.52 |
% 20.97/5.52 | Simplifying 5696 yields:
% 20.97/5.52 | (2222) ~ (all_0_59_59 = e1)
% 20.97/5.52 |
% 20.97/5.52 | Equations (480) can reduce 401 to:
% 20.97/5.52 | (144) ~ (e1 = e0)
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (211), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (632) all_0_56_56 = e0
% 20.97/5.52 |
% 20.97/5.52 | Combining equations (480,632) yields a new equation:
% 20.97/5.52 | (578) e1 = e0
% 20.97/5.52 |
% 20.97/5.52 | Simplifying 578 yields:
% 20.97/5.52 | (579) e1 = e0
% 20.97/5.52 |
% 20.97/5.52 | Equations (579) can reduce 144 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (401) ~ (all_0_56_56 = e0)
% 20.97/5.52 | (2052) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 20.97/5.52 |
% 20.97/5.52 | Equations (480) can reduce 401 to:
% 20.97/5.52 | (144) ~ (e1 = e0)
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (206), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (546) all_0_46_46 = e0
% 20.97/5.52 |
% 20.97/5.52 | Equations (546) can reduce 435 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (435) ~ (all_0_46_46 = e0)
% 20.97/5.52 | (2930) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (212), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (375) all_0_59_59 = e2
% 20.97/5.52 |
% 20.97/5.52 | Equations (375) can reduce 1843 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (1843) ~ (all_0_59_59 = e2)
% 20.97/5.52 | (2151) all_0_59_59 = e4 | all_0_59_59 = e3 | all_0_59_59 = e1 | all_0_59_59 = e0
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (2930), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (965) all_0_49_49 = e0
% 20.97/5.52 |
% 20.97/5.52 | Combining equations (337,965) yields a new equation:
% 20.97/5.52 | (353) e2 = e0
% 20.97/5.52 |
% 20.97/5.52 | Simplifying 353 yields:
% 20.97/5.52 | (354) e2 = e0
% 20.97/5.52 |
% 20.97/5.52 | Equations (354) can reduce 58 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (807) ~ (all_0_49_49 = e0)
% 20.97/5.52 | (2936) all_0_54_54 = e0 | all_0_59_59 = e0
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (2151), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (614) all_0_59_59 = e1
% 20.97/5.52 |
% 20.97/5.52 | Equations (614) can reduce 2222 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (2222) ~ (all_0_59_59 = e1)
% 20.97/5.52 | (2223) all_0_59_59 = e4 | all_0_59_59 = e3 | all_0_59_59 = e0
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (2936), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (1286) all_0_54_54 = e0
% 20.97/5.52 |
% 20.97/5.52 | Combining equations (1592,1286) yields a new equation:
% 20.97/5.52 | (578) e1 = e0
% 20.97/5.52 |
% 20.97/5.52 | Simplifying 578 yields:
% 20.97/5.52 | (579) e1 = e0
% 20.97/5.52 |
% 20.97/5.52 | Equations (579) can reduce 144 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (1478) ~ (all_0_54_54 = e0)
% 20.97/5.52 | (2064) all_0_59_59 = e0
% 20.97/5.52 |
% 20.97/5.52 | Equations (2064) can reduce 2222 to:
% 20.97/5.52 | (436) ~ (e1 = e0)
% 20.97/5.52 |
% 20.97/5.52 | Simplifying 436 yields:
% 20.97/5.52 | (144) ~ (e1 = e0)
% 20.97/5.52 |
% 20.97/5.52 | Instantiating formula (21) with e2, e3, e1, e0 and discharging atoms op(e2, e3) = e1, op(e2, e3) = e0, yields:
% 20.97/5.52 | (579) e1 = e0
% 20.97/5.52 |
% 20.97/5.52 | Equations (579) can reduce 144 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (575) ~ (all_0_56_56 = e1)
% 20.97/5.52 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (2), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (485) all_0_58_58 = e2
% 20.97/5.52 |
% 20.97/5.52 | Equations (485) can reduce 392 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (392) ~ (all_0_58_58 = e2)
% 20.97/5.52 | (488) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1 | all_0_58_58 = e0
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (576), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (577) all_0_57_57 = e1
% 20.97/5.52 |
% 20.97/5.52 | Combining equations (577,867) yields a new equation:
% 20.97/5.52 | (471) e2 = e1
% 20.97/5.52 |
% 20.97/5.52 | Equations (471) can reduce 148 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (581) ~ (all_0_57_57 = e1)
% 20.97/5.52 | (582) all_0_58_58 = e1 | all_0_59_59 = e1
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (488), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (489) all_0_58_58 = e1
% 20.97/5.52 |
% 20.97/5.52 | Equations (489) can reduce 482 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (482) ~ (all_0_58_58 = e1)
% 20.97/5.52 | (492) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e0
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (582), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (489) all_0_58_58 = e1
% 20.97/5.52 |
% 20.97/5.52 | Equations (489) can reduce 482 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (482) ~ (all_0_58_58 = e1)
% 20.97/5.52 | (614) all_0_59_59 = e1
% 20.97/5.52 |
% 20.97/5.52 | Equations (614) can reduce 2222 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (765) ~ (all_0_53_53 = e0)
% 20.97/5.52 | (860) all_0_53_53 = e4 | all_0_53_53 = e3
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (63), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (629) all_0_51_51 = e0
% 20.97/5.52 |
% 20.97/5.52 | Equations (629) can reduce 432 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (432) ~ (all_0_51_51 = e0)
% 20.97/5.52 | (1231) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (170), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (1232) all_0_51_51 = e2
% 20.97/5.52 |
% 20.97/5.52 | Equations (1232) can reduce 255 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (255) ~ (all_0_51_51 = e2)
% 20.97/5.52 | (1235) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1 | all_0_51_51 = e0
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (549), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (462) all_0_46_46 = e3
% 20.97/5.52 |
% 20.97/5.52 | Equations (462) can reduce 107 to:
% 20.97/5.52 | (1924) ~ (all_0_42_42 = e3)
% 20.97/5.52 |
% 20.97/5.52 | Equations (462) can reduce 344 to:
% 20.97/5.52 | (224) ~ (e3 = e2)
% 20.97/5.52 |
% 20.97/5.52 | Equations (462) can reduce 163 to:
% 20.97/5.52 | (146) ~ (e3 = e1)
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (116), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (358) all_0_42_42 = e2
% 20.97/5.52 |
% 20.97/5.52 | Equations (358) can reduce 362 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (362) ~ (all_0_42_42 = e2)
% 20.97/5.52 | (2784) all_0_42_42 = e4 | all_0_42_42 = e3 | all_0_42_42 = e1
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (2784), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (832) all_0_42_42 = e1
% 20.97/5.52 |
% 20.97/5.52 | Equations (832) can reduce 836 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (836) ~ (all_0_42_42 = e1)
% 20.97/5.52 | (2798) all_0_42_42 = e4 | all_0_42_42 = e3
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (2798), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (610) all_0_42_42 = e3
% 20.97/5.52 |
% 20.97/5.52 | Equations (610) can reduce 1924 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (1924) ~ (all_0_42_42 = e3)
% 20.97/5.52 | (305) all_0_42_42 = e4
% 20.97/5.52 |
% 20.97/5.52 | Equations (305) can reduce 1924 to:
% 20.97/5.52 | (41) ~ (e4 = e3)
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (184), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (443) all_0_39_39 = e3
% 20.97/5.52 |
% 20.97/5.52 | Equations (443) can reduce 126 to:
% 20.97/5.52 | (1180) ~ (all_0_51_51 = e3)
% 20.97/5.52 |
% 20.97/5.52 | Simplifying 1180 yields:
% 20.97/5.52 | (428) ~ (all_0_51_51 = e3)
% 20.97/5.52 |
% 20.97/5.52 | Equations (443) can reduce 467 to:
% 20.97/5.52 | (146) ~ (e3 = e1)
% 20.97/5.52 |
% 20.97/5.52 | Equations (443) can reduce 165 to:
% 20.97/5.52 | (72) ~ (e3 = e0)
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (200), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (464) all_0_39_39 = e1
% 20.97/5.52 |
% 20.97/5.52 | Combining equations (443,464) yields a new equation:
% 20.97/5.52 | (572) e3 = e1
% 20.97/5.52 |
% 20.97/5.52 | Simplifying 572 yields:
% 20.97/5.52 | (418) e3 = e1
% 20.97/5.52 |
% 20.97/5.52 | Equations (418) can reduce 146 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (467) ~ (all_0_39_39 = e1)
% 20.97/5.52 | (468) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (468), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (469) all_0_47_47 = e1
% 20.97/5.52 |
% 20.97/5.52 | Combining equations (469,623) yields a new equation:
% 20.97/5.52 | (578) e1 = e0
% 20.97/5.52 |
% 20.97/5.52 | Simplifying 578 yields:
% 20.97/5.52 | (579) e1 = e0
% 20.97/5.52 |
% 20.97/5.52 | Equations (579) can reduce 144 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (473) ~ (all_0_47_47 = e1)
% 20.97/5.52 | (474) all_0_51_51 = e1 | all_0_56_56 = e1
% 20.97/5.52 |
% 20.97/5.52 | Equations (623) can reduce 473 to:
% 20.97/5.52 | (436) ~ (e1 = e0)
% 20.97/5.52 |
% 20.97/5.52 | Simplifying 436 yields:
% 20.97/5.52 | (144) ~ (e1 = e0)
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (1235), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (475) all_0_51_51 = e1
% 20.97/5.52 |
% 20.97/5.52 | Equations (475) can reduce 479 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (479) ~ (all_0_51_51 = e1)
% 20.97/5.52 | (1371) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e0
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (1371), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (629) all_0_51_51 = e0
% 20.97/5.52 |
% 20.97/5.52 | Equations (629) can reduce 432 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (432) ~ (all_0_51_51 = e0)
% 20.97/5.52 | (1375) all_0_51_51 = e4 | all_0_51_51 = e3
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (1375), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (564) all_0_51_51 = e3
% 20.97/5.52 |
% 20.97/5.52 | Equations (564) can reduce 428 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (428) ~ (all_0_51_51 = e3)
% 20.97/5.52 | (458) all_0_51_51 = e4
% 20.97/5.52 |
% 20.97/5.52 | Equations (458) can reduce 30 to:
% 20.97/5.52 | (447) ~ (all_0_53_53 = e4)
% 20.97/5.52 |
% 20.97/5.52 | Simplifying 447 yields:
% 20.97/5.52 | (448) ~ (all_0_53_53 = e4)
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (1959), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (853) all_0_53_53 = e1
% 20.97/5.52 |
% 20.97/5.52 | Equations (853) can reduce 823 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (823) ~ (all_0_53_53 = e1)
% 20.97/5.52 | (1592) all_0_54_54 = e1
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (206), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (546) all_0_46_46 = e0
% 20.97/5.52 |
% 20.97/5.52 | Combining equations (462,546) yields a new equation:
% 20.97/5.52 | (781) e3 = e0
% 20.97/5.52 |
% 20.97/5.52 | Simplifying 781 yields:
% 20.97/5.52 | (560) e3 = e0
% 20.97/5.52 |
% 20.97/5.52 | Equations (560) can reduce 72 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (435) ~ (all_0_46_46 = e0)
% 20.97/5.52 | (2930) all_0_49_49 = e0 | all_0_54_54 = e0 | all_0_59_59 = e0
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (2930), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (965) all_0_49_49 = e0
% 20.97/5.52 |
% 20.97/5.52 | Combining equations (337,965) yields a new equation:
% 20.97/5.52 | (353) e2 = e0
% 20.97/5.52 |
% 20.97/5.52 | Simplifying 353 yields:
% 20.97/5.52 | (354) e2 = e0
% 20.97/5.52 |
% 20.97/5.52 | Equations (354) can reduce 58 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (807) ~ (all_0_49_49 = e0)
% 20.97/5.52 | (2936) all_0_54_54 = e0 | all_0_59_59 = e0
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (2936), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (1286) all_0_54_54 = e0
% 20.97/5.52 |
% 20.97/5.52 | Combining equations (1286,1592) yields a new equation:
% 20.97/5.52 | (579) e1 = e0
% 20.97/5.52 |
% 20.97/5.52 | Equations (579) can reduce 144 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (1478) ~ (all_0_54_54 = e0)
% 20.97/5.52 | (2064) all_0_59_59 = e0
% 20.97/5.52 |
% 20.97/5.52 | Equations (2064) can reduce 198 to:
% 20.97/5.52 | (403) ~ (all_0_58_58 = e0)
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (2), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (485) all_0_58_58 = e2
% 20.97/5.52 |
% 20.97/5.52 | Equations (485) can reduce 392 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (392) ~ (all_0_58_58 = e2)
% 20.97/5.52 | (488) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1 | all_0_58_58 = e0
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (488), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (489) all_0_58_58 = e1
% 20.97/5.52 |
% 20.97/5.52 | Equations (489) can reduce 482 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (482) ~ (all_0_58_58 = e1)
% 20.97/5.52 | (492) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e0
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (492), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (493) all_0_58_58 = e0
% 20.97/5.52 |
% 20.97/5.52 | Equations (493) can reduce 403 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (403) ~ (all_0_58_58 = e0)
% 20.97/5.52 | (496) all_0_58_58 = e4 | all_0_58_58 = e3
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (496), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (497) all_0_58_58 = e3
% 20.97/5.52 |
% 20.97/5.52 | Equations (497) can reduce 127 to:
% 20.97/5.52 | (796) ~ (all_0_53_53 = e3)
% 20.97/5.52 |
% 20.97/5.52 +-Applying beta-rule and splitting (860), into two cases.
% 20.97/5.52 |-Branch one:
% 20.97/5.52 | (861) all_0_53_53 = e3
% 20.97/5.52 |
% 20.97/5.52 | Equations (861) can reduce 796 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (796) ~ (all_0_53_53 = e3)
% 20.97/5.52 | (532) all_0_53_53 = e4
% 20.97/5.52 |
% 20.97/5.52 | Equations (532) can reduce 448 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.52 |-Branch two:
% 20.97/5.52 | (527) ~ (all_0_58_58 = e3)
% 20.97/5.52 | (528) all_0_58_58 = e4
% 20.97/5.52 |
% 20.97/5.52 | Equations (528) can reduce 277 to:
% 20.97/5.52 | (269) $false
% 20.97/5.52 |
% 20.97/5.52 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (540) ~ (all_0_39_39 = e3)
% 20.97/5.53 | (541) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (541), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (417) all_0_40_40 = e3
% 20.97/5.53 |
% 20.97/5.53 | Combining equations (413,417) yields a new equation:
% 20.97/5.53 | (418) e3 = e1
% 20.97/5.53 |
% 20.97/5.53 | Equations (418) can reduce 146 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (420) ~ (all_0_40_40 = e3)
% 20.97/5.53 | (604) all_0_41_41 = e3 | all_0_42_42 = e3
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (604), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (605) all_0_41_41 = e3
% 20.97/5.53 |
% 20.97/5.53 | Combining equations (605,386) yields a new equation:
% 20.97/5.53 | (606) e3 = e2
% 20.97/5.53 |
% 20.97/5.53 | Simplifying 606 yields:
% 20.97/5.53 | (423) e3 = e2
% 20.97/5.53 |
% 20.97/5.53 | Equations (423) can reduce 224 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (609) ~ (all_0_41_41 = e3)
% 20.97/5.53 | (610) all_0_42_42 = e3
% 20.97/5.53 |
% 20.97/5.53 | Combining equations (305,610) yields a new equation:
% 20.97/5.53 | (515) e4 = e3
% 20.97/5.53 |
% 20.97/5.53 | Simplifying 515 yields:
% 20.97/5.53 | (516) e4 = e3
% 20.97/5.53 |
% 20.97/5.53 | Equations (516) can reduce 41 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (618) ~ (all_0_46_46 = e3)
% 20.97/5.53 | (538) all_0_46_46 = e4
% 20.97/5.53 |
% 20.97/5.53 | Equations (538) can reduce 310 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (475) all_0_51_51 = e1
% 20.97/5.53 | (861) all_0_53_53 = e3
% 20.97/5.53 |
% 20.97/5.53 | Equations (861) can reduce 796 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (356) ~ (all_0_44_44 = e0)
% 20.97/5.53 | (357) all_0_52_52 = e0 | all_0_57_57 = e0
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (660), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (352) all_0_44_44 = e0
% 20.97/5.53 |
% 20.97/5.53 | Equations (352) can reduce 356 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (356) ~ (all_0_44_44 = e0)
% 20.97/5.53 | (422) all_0_44_44 = e3
% 20.97/5.53 |
% 20.97/5.53 | Equations (422) can reduce 121 to:
% 20.97/5.53 | (5891) ~ (all_0_52_52 = e3)
% 20.97/5.53 |
% 20.97/5.53 | Simplifying 5891 yields:
% 20.97/5.53 | (637) ~ (all_0_52_52 = e3)
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (86), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (816) all_0_52_52 = e2
% 20.97/5.53 |
% 20.97/5.53 | Equations (816) can reduce 257 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (257) ~ (all_0_52_52 = e2)
% 20.97/5.53 | (819) all_0_52_52 = e3 | all_0_52_52 = e1 | all_0_52_52 = e0
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (819), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (820) all_0_52_52 = e1
% 20.97/5.53 |
% 20.97/5.53 | Equations (820) can reduce 978 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (978) ~ (all_0_52_52 = e1)
% 20.97/5.53 | (979) all_0_52_52 = e3 | all_0_52_52 = e0
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (979), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (397) all_0_52_52 = e0
% 20.97/5.53 |
% 20.97/5.53 | Equations (397) can reduce 71 to:
% 20.97/5.53 | (764) ~ (all_0_53_53 = e0)
% 20.97/5.53 |
% 20.97/5.53 | Simplifying 764 yields:
% 20.97/5.53 | (765) ~ (all_0_53_53 = e0)
% 20.97/5.53 |
% 20.97/5.53 | Equations (397) can reduce 978 to:
% 20.97/5.53 | (436) ~ (e1 = e0)
% 20.97/5.53 |
% 20.97/5.53 | Simplifying 436 yields:
% 20.97/5.53 | (144) ~ (e1 = e0)
% 20.97/5.53 |
% 20.97/5.53 | From (397) and (2268) follows:
% 20.97/5.53 | (3993) op(e2, e0) = e1
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (2630), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (1238) ~ (all_0_54_54 = e1)
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (19), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (475) all_0_51_51 = e1
% 20.97/5.53 |
% 20.97/5.53 | Equations (475) can reduce 16 to:
% 20.97/5.53 | (1452) ~ (all_0_56_56 = e1)
% 20.97/5.53 |
% 20.97/5.53 | Simplifying 1452 yields:
% 20.97/5.53 | (575) ~ (all_0_56_56 = e1)
% 20.97/5.53 |
% 20.97/5.53 | Equations (475) can reduce 255 to:
% 20.97/5.53 | (414) ~ (e2 = e1)
% 20.97/5.53 |
% 20.97/5.53 | Simplifying 414 yields:
% 20.97/5.53 | (148) ~ (e2 = e1)
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (2), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (485) all_0_58_58 = e2
% 20.97/5.53 |
% 20.97/5.53 | Equations (485) can reduce 392 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (392) ~ (all_0_58_58 = e2)
% 20.97/5.53 | (488) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1 | all_0_58_58 = e0
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (488), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (489) all_0_58_58 = e1
% 20.97/5.53 |
% 20.97/5.53 | Equations (489) can reduce 482 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (482) ~ (all_0_58_58 = e1)
% 20.97/5.53 | (492) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e0
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (43), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (480) all_0_56_56 = e1
% 20.97/5.53 |
% 20.97/5.53 | Equations (480) can reduce 575 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (575) ~ (all_0_56_56 = e1)
% 20.97/5.53 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (576), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (577) all_0_57_57 = e1
% 20.97/5.53 |
% 20.97/5.53 | Combining equations (577,867) yields a new equation:
% 20.97/5.53 | (471) e2 = e1
% 20.97/5.53 |
% 20.97/5.53 | Equations (471) can reduce 148 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (581) ~ (all_0_57_57 = e1)
% 20.97/5.53 | (582) all_0_58_58 = e1 | all_0_59_59 = e1
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (212), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (375) all_0_59_59 = e2
% 20.97/5.53 |
% 20.97/5.53 | Equations (375) can reduce 1843 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (1843) ~ (all_0_59_59 = e2)
% 20.97/5.53 | (2151) all_0_59_59 = e4 | all_0_59_59 = e3 | all_0_59_59 = e1 | all_0_59_59 = e0
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (582), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (489) all_0_58_58 = e1
% 20.97/5.53 |
% 20.97/5.53 | Equations (489) can reduce 482 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (482) ~ (all_0_58_58 = e1)
% 20.97/5.53 | (614) all_0_59_59 = e1
% 20.97/5.53 |
% 20.97/5.53 | Equations (614) can reduce 1843 to:
% 20.97/5.53 | (414) ~ (e2 = e1)
% 20.97/5.53 |
% 20.97/5.53 | Simplifying 414 yields:
% 20.97/5.53 | (148) ~ (e2 = e1)
% 20.97/5.53 |
% 20.97/5.53 | Instantiating formula (21) with e2, e0, e1, e2 and discharging atoms op(e2, e0) = e2, op(e2, e0) = e1, yields:
% 20.97/5.53 | (471) e2 = e1
% 20.97/5.53 |
% 20.97/5.53 | Equations (471) can reduce 148 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (479) ~ (all_0_51_51 = e1)
% 20.97/5.53 | (1954) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (1954), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (820) all_0_52_52 = e1
% 20.97/5.53 |
% 20.97/5.53 | Combining equations (397,820) yields a new equation:
% 20.97/5.53 | (579) e1 = e0
% 20.97/5.53 |
% 20.97/5.53 | Equations (579) can reduce 144 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (978) ~ (all_0_52_52 = e1)
% 20.97/5.53 | (1959) all_0_53_53 = e1 | all_0_54_54 = e1
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (27), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (849) all_0_53_53 = e2
% 20.97/5.53 |
% 20.97/5.53 | Equations (849) can reduce 259 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (259) ~ (all_0_53_53 = e2)
% 20.97/5.53 | (852) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (852), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (853) all_0_53_53 = e1
% 20.97/5.53 |
% 20.97/5.53 | Equations (853) can reduce 823 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (823) ~ (all_0_53_53 = e1)
% 20.97/5.53 | (856) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e0
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (856), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (857) all_0_53_53 = e0
% 20.97/5.53 |
% 20.97/5.53 | Equations (857) can reduce 765 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (765) ~ (all_0_53_53 = e0)
% 20.97/5.53 | (860) all_0_53_53 = e4 | all_0_53_53 = e3
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (860), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (861) all_0_53_53 = e3
% 20.97/5.53 |
% 20.97/5.53 | Equations (861) can reduce 823 to:
% 20.97/5.53 | (146) ~ (e3 = e1)
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (1959), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (853) all_0_53_53 = e1
% 20.97/5.53 |
% 20.97/5.53 | Combining equations (861,853) yields a new equation:
% 20.97/5.53 | (572) e3 = e1
% 20.97/5.53 |
% 20.97/5.53 | Simplifying 572 yields:
% 20.97/5.53 | (418) e3 = e1
% 20.97/5.53 |
% 20.97/5.53 | Equations (418) can reduce 146 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (823) ~ (all_0_53_53 = e1)
% 20.97/5.53 | (1592) all_0_54_54 = e1
% 20.97/5.53 |
% 20.97/5.53 | Equations (1592) can reduce 1238 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (796) ~ (all_0_53_53 = e3)
% 20.97/5.53 | (532) all_0_53_53 = e4
% 20.97/5.53 |
% 20.97/5.53 | Equations (532) can reduce 448 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (1592) all_0_54_54 = e1
% 20.97/5.53 | (857) all_0_53_53 = e0
% 20.97/5.53 |
% 20.97/5.53 | Equations (857) can reduce 765 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (317) ~ (all_0_52_52 = e0)
% 20.97/5.53 | (427) all_0_52_52 = e3
% 20.97/5.53 |
% 20.97/5.53 | Equations (427) can reduce 637 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (523) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 20.97/5.53 |
% 20.97/5.53 | Applying alpha-rule on (523) yields:
% 20.97/5.53 | (524) all_0_19_19 = e0
% 20.97/5.53 | (525) ~ (all_0_20_20 = e2)
% 20.97/5.53 |
% 20.97/5.53 | Combining equations (1849,524) yields a new equation:
% 20.97/5.53 | (751) e4 = e0
% 20.97/5.53 |
% 20.97/5.53 | Simplifying 751 yields:
% 20.97/5.53 | (439) e4 = e0
% 20.97/5.53 |
% 20.97/5.53 | Equations (439) can reduce 11 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (378) ~ (all_0_57_57 = e2)
% 20.97/5.53 | (2734) all_0_58_58 = e2 | all_0_59_59 = e2
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (2734), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (485) all_0_58_58 = e2
% 20.97/5.53 |
% 20.97/5.53 | Equations (485) can reduce 392 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (392) ~ (all_0_58_58 = e2)
% 20.97/5.53 | (375) all_0_59_59 = e2
% 20.97/5.53 |
% 20.97/5.53 | Equations (375) can reduce 1843 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (321) ~ (all_0_43_43 = e2)
% 20.97/5.53 | (1198) all_0_43_43 = e4 | all_0_43_43 = e3 | all_0_43_43 = e0
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (225), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (661) all_0_43_43 = e2
% 20.97/5.53 |
% 20.97/5.53 | Equations (661) can reduce 321 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (321) ~ (all_0_43_43 = e2)
% 20.97/5.53 | (664) all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (1198), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (433) all_0_43_43 = e0
% 20.97/5.53 |
% 20.97/5.53 | Equations (433) can reduce 459 to:
% 20.97/5.53 | (269) $false
% 20.97/5.53 |
% 20.97/5.53 |-The branch is then unsatisfiable
% 20.97/5.53 |-Branch two:
% 20.97/5.53 | (459) ~ (all_0_43_43 = e0)
% 20.97/5.53 | (1695) all_0_43_43 = e4 | all_0_43_43 = e3
% 20.97/5.53 |
% 20.97/5.53 +-Applying beta-rule and splitting (664), into two cases.
% 20.97/5.53 |-Branch one:
% 20.97/5.53 | (341) all_0_44_44 = e2
% 20.97/5.53 |
% 20.97/5.53 | Equations (341) can reduce 228 to:
% 20.97/5.53 | (321) ~ (all_0_43_43 = e2)
% 20.97/5.53 |
% 20.97/5.53 | Equations (341) can reduce 210 to:
% 20.97/5.53 | (343) ~ (all_0_46_46 = e2)
% 20.97/5.53 |
% 20.97/5.53 | Simplifying 343 yields:
% 20.97/5.53 | (344) ~ (all_0_46_46 = e2)
% 20.97/5.53 |
% 21.25/5.53 | Equations (341) can reduce 190 to:
% 21.25/5.53 | (326) ~ (e4 = e2)
% 21.25/5.53 |
% 21.25/5.53 | Simplifying 326 yields:
% 21.25/5.53 | (230) ~ (e4 = e2)
% 21.25/5.53 |
% 21.25/5.53 | Equations (341) can reduce 87 to:
% 21.25/5.53 | (148) ~ (e2 = e1)
% 21.25/5.53 |
% 21.25/5.53 +-Applying beta-rule and splitting (1695), into two cases.
% 21.25/5.53 |-Branch one:
% 21.25/5.53 | (559) all_0_43_43 = e3
% 21.25/5.53 |
% 21.25/5.53 | Equations (559) can reduce 234 to:
% 21.25/5.53 | (540) ~ (all_0_39_39 = e3)
% 21.25/5.53 |
% 21.25/5.53 | Equations (559) can reduce 3 to:
% 21.25/5.53 | (1044) ~ (all_0_46_46 = e3)
% 21.25/5.53 |
% 21.25/5.53 | Simplifying 1044 yields:
% 21.25/5.53 | (618) ~ (all_0_46_46 = e3)
% 21.25/5.53 |
% 21.25/5.53 | Equations (559) can reduce 441 to:
% 21.25/5.53 | (498) ~ (e4 = e3)
% 21.25/5.53 |
% 21.25/5.54 | Simplifying 498 yields:
% 21.25/5.54 | (41) ~ (e4 = e3)
% 21.25/5.54 |
% 21.25/5.54 | Equations (559) can reduce 321 to:
% 21.25/5.54 | (224) ~ (e3 = e2)
% 21.25/5.54 |
% 21.25/5.54 | Equations (559) can reduce 114 to:
% 21.25/5.54 | (146) ~ (e3 = e1)
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (199), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (364) all_0_46_46 = e2
% 21.25/5.54 |
% 21.25/5.54 | Equations (364) can reduce 344 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (344) ~ (all_0_46_46 = e2)
% 21.25/5.54 | (545) all_0_46_46 = e4 | all_0_46_46 = e3 | all_0_46_46 = e0
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (545), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (546) all_0_46_46 = e0
% 21.25/5.54 |
% 21.25/5.54 | Equations (546) can reduce 107 to:
% 21.25/5.54 | (155) ~ (all_0_42_42 = e0)
% 21.25/5.54 |
% 21.25/5.54 | Equations (546) can reduce 344 to:
% 21.25/5.54 | (406) ~ (e2 = e0)
% 21.25/5.54 |
% 21.25/5.54 | Simplifying 406 yields:
% 21.25/5.54 | (58) ~ (e2 = e0)
% 21.25/5.54 |
% 21.25/5.54 | Equations (546) can reduce 163 to:
% 21.25/5.54 | (436) ~ (e1 = e0)
% 21.25/5.54 |
% 21.25/5.54 | Simplifying 436 yields:
% 21.25/5.54 | (144) ~ (e1 = e0)
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (184), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (443) all_0_39_39 = e3
% 21.25/5.54 |
% 21.25/5.54 | Equations (443) can reduce 540 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (540) ~ (all_0_39_39 = e3)
% 21.25/5.54 | (541) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (541), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (417) all_0_40_40 = e3
% 21.25/5.54 |
% 21.25/5.54 | Combining equations (413,417) yields a new equation:
% 21.25/5.54 | (418) e3 = e1
% 21.25/5.54 |
% 21.25/5.54 | Equations (418) can reduce 146 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (420) ~ (all_0_40_40 = e3)
% 21.25/5.54 | (604) all_0_41_41 = e3 | all_0_42_42 = e3
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (604), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (605) all_0_41_41 = e3
% 21.25/5.54 |
% 21.25/5.54 | Combining equations (605,386) yields a new equation:
% 21.25/5.54 | (606) e3 = e2
% 21.25/5.54 |
% 21.25/5.54 | Simplifying 606 yields:
% 21.25/5.54 | (423) e3 = e2
% 21.25/5.54 |
% 21.25/5.54 | Equations (423) can reduce 224 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (609) ~ (all_0_41_41 = e3)
% 21.25/5.54 | (610) all_0_42_42 = e3
% 21.25/5.54 |
% 21.25/5.54 | Equations (610) can reduce 362 to:
% 21.25/5.54 | (224) ~ (e3 = e2)
% 21.25/5.54 |
% 21.25/5.54 | Equations (610) can reduce 155 to:
% 21.25/5.54 | (72) ~ (e3 = e0)
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (32), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (1079) all_0_39_39 = e4
% 21.25/5.54 |
% 21.25/5.54 | Equations (1079) can reduce 320 to:
% 21.25/5.54 | (230) ~ (e4 = e2)
% 21.25/5.54 |
% 21.25/5.54 | Equations (1079) can reduce 467 to:
% 21.25/5.54 | (251) ~ (e4 = e1)
% 21.25/5.54 |
% 21.25/5.54 | Equations (1079) can reduce 165 to:
% 21.25/5.54 | (11) ~ (e4 = e0)
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (129), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (348) all_0_39_39 = e2
% 21.25/5.54 |
% 21.25/5.54 | Combining equations (1079,348) yields a new equation:
% 21.25/5.54 | (359) e4 = e2
% 21.25/5.54 |
% 21.25/5.54 | Simplifying 359 yields:
% 21.25/5.54 | (360) e4 = e2
% 21.25/5.54 |
% 21.25/5.54 | Equations (360) can reduce 230 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (320) ~ (all_0_39_39 = e2)
% 21.25/5.54 | (1727) all_0_43_43 = e2 | all_0_47_47 = e2 | all_0_51_51 = e2 | all_0_56_56 = e2
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (1727), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (661) all_0_43_43 = e2
% 21.25/5.54 |
% 21.25/5.54 | Combining equations (559,661) yields a new equation:
% 21.25/5.54 | (606) e3 = e2
% 21.25/5.54 |
% 21.25/5.54 | Simplifying 606 yields:
% 21.25/5.54 | (423) e3 = e2
% 21.25/5.54 |
% 21.25/5.54 | Equations (423) can reduce 224 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (321) ~ (all_0_43_43 = e2)
% 21.25/5.54 | (1731) all_0_47_47 = e2 | all_0_51_51 = e2 | all_0_56_56 = e2
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (1731), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (319) all_0_47_47 = e2
% 21.25/5.54 |
% 21.25/5.54 | Combining equations (623,319) yields a new equation:
% 21.25/5.54 | (354) e2 = e0
% 21.25/5.54 |
% 21.25/5.54 | Equations (354) can reduce 58 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (1442) ~ (all_0_47_47 = e2)
% 21.25/5.54 | (1736) all_0_51_51 = e2 | all_0_56_56 = e2
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (1736), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (1232) all_0_51_51 = e2
% 21.25/5.54 |
% 21.25/5.54 | Equations (1232) can reduce 255 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (255) ~ (all_0_51_51 = e2)
% 21.25/5.54 | (1575) all_0_56_56 = e2
% 21.25/5.54 |
% 21.25/5.54 | Equations (1575) can reduce 401 to:
% 21.25/5.54 | (58) ~ (e2 = e0)
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (43), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (480) all_0_56_56 = e1
% 21.25/5.54 |
% 21.25/5.54 | Combining equations (1575,480) yields a new equation:
% 21.25/5.54 | (470) e2 = e1
% 21.25/5.54 |
% 21.25/5.54 | Simplifying 470 yields:
% 21.25/5.54 | (471) e2 = e1
% 21.25/5.54 |
% 21.25/5.54 | Equations (471) can reduce 148 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (575) ~ (all_0_56_56 = e1)
% 21.25/5.54 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 21.25/5.54 |
% 21.25/5.54 | Equations (1575) can reduce 575 to:
% 21.25/5.54 | (148) ~ (e2 = e1)
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (200), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (464) all_0_39_39 = e1
% 21.25/5.54 |
% 21.25/5.54 | Combining equations (1079,464) yields a new equation:
% 21.25/5.54 | (476) e4 = e1
% 21.25/5.54 |
% 21.25/5.54 | Simplifying 476 yields:
% 21.25/5.54 | (477) e4 = e1
% 21.25/5.54 |
% 21.25/5.54 | Equations (477) can reduce 251 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (467) ~ (all_0_39_39 = e1)
% 21.25/5.54 | (468) all_0_47_47 = e1 | all_0_51_51 = e1 | all_0_56_56 = e1
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (468), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (469) all_0_47_47 = e1
% 21.25/5.54 |
% 21.25/5.54 | Combining equations (469,623) yields a new equation:
% 21.25/5.54 | (578) e1 = e0
% 21.25/5.54 |
% 21.25/5.54 | Simplifying 578 yields:
% 21.25/5.54 | (579) e1 = e0
% 21.25/5.54 |
% 21.25/5.54 | Equations (579) can reduce 144 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (473) ~ (all_0_47_47 = e1)
% 21.25/5.54 | (474) all_0_51_51 = e1 | all_0_56_56 = e1
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (474), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (475) all_0_51_51 = e1
% 21.25/5.54 |
% 21.25/5.54 | Equations (475) can reduce 194 to:
% 21.25/5.54 | (1157) ~ (all_0_52_52 = e1)
% 21.25/5.54 |
% 21.25/5.54 | Simplifying 1157 yields:
% 21.25/5.54 | (978) ~ (all_0_52_52 = e1)
% 21.25/5.54 |
% 21.25/5.54 | Equations (475) can reduce 30 to:
% 21.25/5.54 | (822) ~ (all_0_53_53 = e1)
% 21.25/5.54 |
% 21.25/5.54 | Simplifying 822 yields:
% 21.25/5.54 | (823) ~ (all_0_53_53 = e1)
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (2625), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (479) ~ (all_0_51_51 = e1)
% 21.25/5.54 |
% 21.25/5.54 | Equations (475) can reduce 479 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (475) all_0_51_51 = e1
% 21.25/5.54 | (861) all_0_53_53 = e3
% 21.25/5.54 |
% 21.25/5.54 | Equations (861) can reduce 71 to:
% 21.25/5.54 | (637) ~ (all_0_52_52 = e3)
% 21.25/5.54 |
% 21.25/5.54 | Equations (861) can reduce 259 to:
% 21.25/5.54 | (224) ~ (e3 = e2)
% 21.25/5.54 |
% 21.25/5.54 | Equations (861) can reduce 823 to:
% 21.25/5.54 | (146) ~ (e3 = e1)
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (193), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (417) all_0_40_40 = e3
% 21.25/5.54 |
% 21.25/5.54 | Combining equations (417,413) yields a new equation:
% 21.25/5.54 | (572) e3 = e1
% 21.25/5.54 |
% 21.25/5.54 | Simplifying 572 yields:
% 21.25/5.54 | (418) e3 = e1
% 21.25/5.54 |
% 21.25/5.54 | Equations (418) can reduce 146 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (420) ~ (all_0_40_40 = e3)
% 21.25/5.54 | (421) all_0_44_44 = e3 | all_0_52_52 = e3 | all_0_57_57 = e3
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (421), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (422) all_0_44_44 = e3
% 21.25/5.54 |
% 21.25/5.54 | Combining equations (341,422) yields a new equation:
% 21.25/5.54 | (423) e3 = e2
% 21.25/5.54 |
% 21.25/5.54 | Equations (423) can reduce 224 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (425) ~ (all_0_44_44 = e3)
% 21.25/5.54 | (426) all_0_52_52 = e3 | all_0_57_57 = e3
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (426), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (427) all_0_52_52 = e3
% 21.25/5.54 |
% 21.25/5.54 | Equations (427) can reduce 637 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (637) ~ (all_0_52_52 = e3)
% 21.25/5.54 | (638) all_0_57_57 = e3
% 21.25/5.54 |
% 21.25/5.54 | Equations (638) can reduce 124 to:
% 21.25/5.54 | (637) ~ (all_0_52_52 = e3)
% 21.25/5.54 |
% 21.25/5.54 | Equations (638) can reduce 173 to:
% 21.25/5.54 | (498) ~ (e4 = e3)
% 21.25/5.54 |
% 21.25/5.54 | Simplifying 498 yields:
% 21.25/5.54 | (41) ~ (e4 = e3)
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (110), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (352) all_0_44_44 = e0
% 21.25/5.54 |
% 21.25/5.54 | Combining equations (341,352) yields a new equation:
% 21.25/5.54 | (353) e2 = e0
% 21.25/5.54 |
% 21.25/5.54 | Simplifying 353 yields:
% 21.25/5.54 | (354) e2 = e0
% 21.25/5.54 |
% 21.25/5.54 | Equations (354) can reduce 58 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (356) ~ (all_0_44_44 = e0)
% 21.25/5.54 | (357) all_0_52_52 = e0 | all_0_57_57 = e0
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (139), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (889) all_0_45_45 = e0
% 21.25/5.54 |
% 21.25/5.54 | Combining equations (444,889) yields a new equation:
% 21.25/5.54 | (751) e4 = e0
% 21.25/5.54 |
% 21.25/5.54 | Simplifying 751 yields:
% 21.25/5.54 | (439) e4 = e0
% 21.25/5.54 |
% 21.25/5.54 | Equations (439) can reduce 11 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (299) ~ (all_0_45_45 = e0)
% 21.25/5.54 | (894) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 21.25/5.54 |
% 21.25/5.54 | Equations (444) can reduce 299 to:
% 21.25/5.54 | (11) ~ (e4 = e0)
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (195), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (305) all_0_42_42 = e4
% 21.25/5.54 |
% 21.25/5.54 | Combining equations (305,610) yields a new equation:
% 21.25/5.54 | (515) e4 = e3
% 21.25/5.54 |
% 21.25/5.54 | Simplifying 515 yields:
% 21.25/5.54 | (516) e4 = e3
% 21.25/5.54 |
% 21.25/5.54 | Equations (516) can reduce 41 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (2787) ~ (all_0_42_42 = e4)
% 21.25/5.54 | (2898) all_0_46_46 = e4 | all_0_54_54 = e4 | all_0_59_59 = e4
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (2898), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (538) all_0_46_46 = e4
% 21.25/5.54 |
% 21.25/5.54 | Combining equations (546,538) yields a new equation:
% 21.25/5.54 | (439) e4 = e0
% 21.25/5.54 |
% 21.25/5.54 | Equations (439) can reduce 11 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (310) ~ (all_0_46_46 = e4)
% 21.25/5.54 | (2902) all_0_54_54 = e4 | all_0_59_59 = e4
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (357), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (397) all_0_52_52 = e0
% 21.25/5.54 |
% 21.25/5.54 | Equations (397) can reduce 637 to:
% 21.25/5.54 | (1272) ~ (e3 = e0)
% 21.25/5.54 |
% 21.25/5.54 | Simplifying 1272 yields:
% 21.25/5.54 | (72) ~ (e3 = e0)
% 21.25/5.54 |
% 21.25/5.54 | Equations (397) can reduce 978 to:
% 21.25/5.54 | (436) ~ (e1 = e0)
% 21.25/5.54 |
% 21.25/5.54 | Simplifying 436 yields:
% 21.25/5.54 | (144) ~ (e1 = e0)
% 21.25/5.54 |
% 21.25/5.54 | From (397) and (89) follows:
% 21.25/5.54 | (4401) op(e1, e0) = all_0_18_18
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (2902), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (535) all_0_54_54 = e4
% 21.25/5.54 |
% 21.25/5.54 | From (535) and (13) follows:
% 21.25/5.54 | (3194) op(e1, e0) = e4
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (894), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (903) all_0_48_48 = e0
% 21.25/5.54 |
% 21.25/5.54 | Combining equations (593,903) yields a new equation:
% 21.25/5.54 | (578) e1 = e0
% 21.25/5.54 |
% 21.25/5.54 | Simplifying 578 yields:
% 21.25/5.54 | (579) e1 = e0
% 21.25/5.54 |
% 21.25/5.54 | Equations (579) can reduce 144 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (952) ~ (all_0_48_48 = e0)
% 21.25/5.54 | (953) all_0_53_53 = e0 | all_0_58_58 = e0
% 21.25/5.54 |
% 21.25/5.54 +-Applying beta-rule and splitting (953), into two cases.
% 21.25/5.54 |-Branch one:
% 21.25/5.54 | (857) all_0_53_53 = e0
% 21.25/5.54 |
% 21.25/5.54 | Combining equations (861,857) yields a new equation:
% 21.25/5.54 | (781) e3 = e0
% 21.25/5.54 |
% 21.25/5.54 | Simplifying 781 yields:
% 21.25/5.54 | (560) e3 = e0
% 21.25/5.54 |
% 21.25/5.54 | Equations (560) can reduce 72 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (765) ~ (all_0_53_53 = e0)
% 21.25/5.54 | (493) all_0_58_58 = e0
% 21.25/5.54 |
% 21.25/5.54 | Equations (493) can reduce 277 to:
% 21.25/5.54 | (404) ~ (e4 = e0)
% 21.25/5.54 |
% 21.25/5.54 | Simplifying 404 yields:
% 21.25/5.54 | (11) ~ (e4 = e0)
% 21.25/5.54 |
% 21.25/5.54 | From (493) and (3447) follows:
% 21.25/5.54 | (6611) op(e1, e0) = e0
% 21.25/5.54 |
% 21.25/5.54 | Instantiating formula (21) with e1, e0, e4, all_0_18_18 and discharging atoms op(e1, e0) = all_0_18_18, op(e1, e0) = e4, yields:
% 21.25/5.54 | (915) all_0_18_18 = e4
% 21.25/5.54 |
% 21.25/5.54 | Instantiating formula (21) with e1, e0, e0, all_0_18_18 and discharging atoms op(e1, e0) = all_0_18_18, op(e1, e0) = e0, yields:
% 21.25/5.54 | (6613) all_0_18_18 = e0
% 21.25/5.54 |
% 21.25/5.54 | Combining equations (915,6613) yields a new equation:
% 21.25/5.54 | (751) e4 = e0
% 21.25/5.54 |
% 21.25/5.54 | Simplifying 751 yields:
% 21.25/5.54 | (439) e4 = e0
% 21.25/5.54 |
% 21.25/5.54 | Equations (439) can reduce 11 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (312) ~ (all_0_54_54 = e4)
% 21.25/5.54 | (2231) all_0_59_59 = e4
% 21.25/5.54 |
% 21.25/5.54 | Equations (2231) can reduce 279 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (317) ~ (all_0_52_52 = e0)
% 21.25/5.54 | (400) all_0_57_57 = e0
% 21.25/5.54 |
% 21.25/5.54 | Combining equations (400,638) yields a new equation:
% 21.25/5.54 | (560) e3 = e0
% 21.25/5.54 |
% 21.25/5.54 | Equations (560) can reduce 72 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.54 |-Branch two:
% 21.25/5.54 | (479) ~ (all_0_51_51 = e1)
% 21.25/5.54 | (480) all_0_56_56 = e1
% 21.25/5.54 |
% 21.25/5.54 | Combining equations (1575,480) yields a new equation:
% 21.25/5.54 | (470) e2 = e1
% 21.25/5.54 |
% 21.25/5.54 | Simplifying 470 yields:
% 21.25/5.54 | (471) e2 = e1
% 21.25/5.54 |
% 21.25/5.54 | Equations (471) can reduce 148 to:
% 21.25/5.54 | (269) $false
% 21.25/5.54 |
% 21.25/5.54 |-The branch is then unsatisfiable
% 21.25/5.55 |-Branch two:
% 21.25/5.55 | (307) ~ (all_0_39_39 = e4)
% 21.25/5.55 | (3018) all_0_41_41 = e4 | all_0_42_42 = e4
% 21.25/5.55 |
% 21.25/5.55 +-Applying beta-rule and splitting (3018), into two cases.
% 21.25/5.55 |-Branch one:
% 21.25/5.55 | (740) all_0_41_41 = e4
% 21.25/5.55 |
% 21.25/5.55 | Combining equations (740,386) yields a new equation:
% 21.25/5.55 | (359) e4 = e2
% 21.25/5.55 |
% 21.25/5.55 | Simplifying 359 yields:
% 21.25/5.55 | (360) e4 = e2
% 21.25/5.55 |
% 21.25/5.55 | Equations (360) can reduce 230 to:
% 21.25/5.55 | (269) $false
% 21.25/5.55 |
% 21.25/5.55 |-The branch is then unsatisfiable
% 21.25/5.55 |-Branch two:
% 21.25/5.55 | (308) ~ (all_0_41_41 = e4)
% 21.25/5.55 | (305) all_0_42_42 = e4
% 21.25/5.55 |
% 21.25/5.55 | Combining equations (610,305) yields a new equation:
% 21.25/5.55 | (516) e4 = e3
% 21.25/5.55 |
% 21.25/5.55 | Equations (516) can reduce 41 to:
% 21.25/5.55 | (269) $false
% 21.25/5.55 |
% 21.25/5.55 |-The branch is then unsatisfiable
% 21.25/5.55 |-Branch two:
% 21.25/5.55 | (435) ~ (all_0_46_46 = e0)
% 21.25/5.55 | (549) all_0_46_46 = e4 | all_0_46_46 = e3
% 21.25/5.55 |
% 21.25/5.55 +-Applying beta-rule and splitting (549), into two cases.
% 21.25/5.55 |-Branch one:
% 21.25/5.55 | (462) all_0_46_46 = e3
% 21.25/5.55 |
% 21.25/5.55 | Equations (462) can reduce 618 to:
% 21.25/5.55 | (269) $false
% 21.25/5.55 |
% 21.25/5.55 |-The branch is then unsatisfiable
% 21.25/5.55 |-Branch two:
% 21.25/5.55 | (618) ~ (all_0_46_46 = e3)
% 21.25/5.55 | (538) all_0_46_46 = e4
% 21.25/5.55 |
% 21.25/5.55 | Equations (538) can reduce 310 to:
% 21.25/5.55 | (269) $false
% 21.25/5.55 |
% 21.25/5.55 |-The branch is then unsatisfiable
% 21.25/5.55 |-Branch two:
% 21.25/5.55 | (562) ~ (all_0_43_43 = e3)
% 21.25/5.55 | (438) all_0_43_43 = e4
% 21.25/5.55 |
% 21.25/5.55 | Equations (438) can reduce 441 to:
% 21.25/5.55 | (269) $false
% 21.25/5.55 |
% 21.25/5.55 |-The branch is then unsatisfiable
% 21.25/5.55 |-Branch two:
% 21.25/5.55 | (659) ~ (all_0_44_44 = e2)
% 21.25/5.55 | (1120) all_0_45_45 = e2 | all_0_46_46 = e2
% 21.25/5.55 |
% 21.25/5.55 +-Applying beta-rule and splitting (1120), into two cases.
% 21.25/5.55 |-Branch one:
% 21.25/5.55 | (694) all_0_45_45 = e2
% 21.25/5.55 |
% 21.25/5.55 | Combining equations (694,444) yields a new equation:
% 21.25/5.55 | (360) e4 = e2
% 21.25/5.55 |
% 21.25/5.55 | Equations (360) can reduce 230 to:
% 21.25/5.55 | (269) $false
% 21.25/5.55 |
% 21.25/5.55 |-The branch is then unsatisfiable
% 21.25/5.55 |-Branch two:
% 21.25/5.55 | (390) ~ (all_0_45_45 = e2)
% 21.25/5.55 | (364) all_0_46_46 = e2
% 21.25/5.55 |
% 21.25/5.55 | Equations (364) can reduce 344 to:
% 21.25/5.55 | (269) $false
% 21.25/5.55 |
% 21.25/5.55 |-The branch is then unsatisfiable
% 21.25/5.55 |-Branch two:
% 21.25/5.55 | (641) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 21.25/5.55 |
% 21.25/5.55 | Applying alpha-rule on (641) yields:
% 21.25/5.55 | (285) all_0_2_2 = e0
% 21.25/5.55 | (643) ~ (all_0_3_3 = e4)
% 21.25/5.55 |
% 21.25/5.55 | Equations (288) can reduce 643 to:
% 21.25/5.55 | (269) $false
% 21.25/5.55 |
% 21.25/5.55 |-The branch is then unsatisfiable
% 21.25/5.55 |-Branch two:
% 21.25/5.55 | (645) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 21.25/5.55 |
% 21.25/5.55 | Applying alpha-rule on (645) yields:
% 21.25/5.55 | (605) all_0_41_41 = e3
% 21.25/5.55 | (537) ~ (all_0_45_45 = e4)
% 21.25/5.55 |
% 21.25/5.55 | Equations (444) can reduce 537 to:
% 21.25/5.55 | (269) $false
% 21.25/5.55 |
% 21.25/5.55 |-The branch is then unsatisfiable
% 21.25/5.55 |-Branch two:
% 21.25/5.55 | (584) ~ (all_0_48_48 = e1)
% 21.25/5.55 | (903) all_0_48_48 = e0
% 21.25/5.55 |
% 21.25/5.55 | Equations (903) can reduce 952 to:
% 21.25/5.55 | (269) $false
% 21.25/5.55 |
% 21.25/5.55 |-The branch is then unsatisfiable
% 21.25/5.55 |-Branch two:
% 21.25/5.55 | (323) ~ (all_0_49_49 = e2)
% 21.25/5.55 | (340) all_0_49_49 = e1 | all_0_49_49 = e0
% 21.25/5.55 |
% 21.25/5.55 +-Applying beta-rule and splitting (192), into two cases.
% 21.25/5.55 |-Branch one:
% 21.25/5.55 | (469) all_0_47_47 = e1
% 21.25/5.55 |
% 21.25/5.55 | Combining equations (469,623) yields a new equation:
% 21.25/5.55 | (578) e1 = e0
% 21.25/5.55 |
% 21.25/5.55 | Simplifying 578 yields:
% 21.25/5.55 | (579) e1 = e0
% 21.25/5.55 |
% 21.25/5.55 | Equations (579) can reduce 144 to:
% 21.25/5.55 | (269) $false
% 21.25/5.55 |
% 21.25/5.55 |-The branch is then unsatisfiable
% 21.25/5.55 |-Branch two:
% 21.25/5.55 | (473) ~ (all_0_47_47 = e1)
% 21.25/5.55 | (592) all_0_48_48 = e1 | all_0_49_49 = e1
% 21.25/5.55 |
% 21.25/5.55 +-Applying beta-rule and splitting (592), into two cases.
% 21.25/5.55 |-Branch one:
% 21.25/5.55 | (593) all_0_48_48 = e1
% 21.25/5.55 |
% 21.25/5.55 +-Applying beta-rule and splitting (131), into two cases.
% 21.25/5.55 |-Branch one:
% 21.25/5.55 | (319) all_0_47_47 = e2
% 21.25/5.55 |
% 21.25/5.55 | Combining equations (623,319) yields a new equation:
% 21.25/5.55 | (354) e2 = e0
% 21.25/5.55 |
% 21.25/5.55 | Equations (354) can reduce 58 to:
% 21.25/5.55 | (269) $false
% 21.25/5.55 |
% 21.25/5.55 |-The branch is then unsatisfiable
% 21.25/5.55 |-Branch two:
% 21.25/5.55 | (1442) ~ (all_0_47_47 = e2)
% 21.25/5.55 | (6681) all_0_48_48 = e2 | all_0_49_49 = e2
% 21.25/5.55 |
% 21.25/5.55 +-Applying beta-rule and splitting (6681), into two cases.
% 21.25/5.55 |-Branch one:
% 21.25/5.55 | (1458) all_0_48_48 = e2
% 21.25/5.55 |
% 21.25/5.55 | Combining equations (1458,593) yields a new equation:
% 21.25/5.55 | (470) e2 = e1
% 21.25/5.55 |
% 21.25/5.55 | Simplifying 470 yields:
% 21.25/5.55 | (471) e2 = e1
% 21.25/5.55 |
% 21.25/5.55 | Equations (471) can reduce 148 to:
% 21.25/5.55 | (269) $false
% 21.25/5.55 |
% 21.25/5.55 |-The branch is then unsatisfiable
% 21.25/5.55 |-Branch two:
% 21.25/5.55 | (1115) ~ (all_0_48_48 = e2)
% 21.25/5.55 | (337) all_0_49_49 = e2
% 21.25/5.55 |
% 21.25/5.55 | Equations (337) can reduce 323 to:
% 21.25/5.55 | (269) $false
% 21.25/5.55 |
% 21.25/5.55 |-The branch is then unsatisfiable
% 21.25/5.55 |-Branch two:
% 21.25/5.55 | (584) ~ (all_0_48_48 = e1)
% 21.25/5.55 | (596) all_0_49_49 = e1
% 21.25/5.55 |
% 21.25/5.55 | Equations (596) can reduce 960 to:
% 21.25/5.55 | (269) $false
% 21.25/5.55 |
% 21.25/5.55 |-The branch is then unsatisfiable
% 21.25/5.55 |-Branch two:
% 21.25/5.55 | (596) all_0_49_49 = e1
% 21.25/5.55 | (903) all_0_48_48 = e0
% 21.25/5.55 |
% 21.25/5.55 | Equations (903) can reduce 952 to:
% 21.25/5.55 | (269) $false
% 21.25/5.55 |
% 21.25/5.55 |-The branch is then unsatisfiable
% 21.25/5.55 |-Branch two:
% 21.25/5.55 | (820) all_0_52_52 = e1
% 21.25/5.55 | (849) all_0_53_53 = e2
% 21.25/5.55 |
% 21.25/5.55 | Equations (849) can reduce 259 to:
% 21.25/5.55 | (269) $false
% 21.25/5.55 |
% 21.25/5.55 |-The branch is then unsatisfiable
% 21.25/5.55 |-Branch two:
% 21.25/5.55 | (6698) ~ (all_0_42_42 = e2) & ~ (all_0_45_45 = e2) & ~ (all_0_47_47 = e2) & ~ (all_0_48_48 = e2) & ~ (all_0_49_49 = e2) & ~ (all_0_50_50 = e2) & ~ (all_0_55_55 = e2) & ( ~ (all_0_39_39 = e2) | (all_0_40_40 = e3 & ~ (unit = e2))) & ( ~ (all_0_40_40 = e2) | ~ (unit = e2)) & ( ~ (all_0_41_41 = e2) | (all_0_40_40 = e1 & ~ (unit = e2))) & ( ~ (all_0_43_43 = e2) | (all_0_44_44 = e3 & ~ (unit = e2))) & ( ~ (all_0_44_44 = e2) | ~ (unit = e2)) & ( ~ (all_0_46_46 = e2) | (all_0_44_44 = e0 & ~ (unit = e2))) & ( ~ (all_0_51_51 = e2) | (all_0_52_52 = e3 & ~ (unit = e2))) & ( ~ (all_0_52_52 = e2) | ~ (unit = e2)) & ( ~ (all_0_53_53 = e2) | (all_0_52_52 = e1 & ~ (unit = e2))) & ( ~ (all_0_54_54 = e2) | (all_0_52_52 = e0 & ~ (unit = e2))) & ( ~ (all_0_56_56 = e2) | (all_0_57_57 = e3 & ~ (unit = e2))) & ( ~ (all_0_57_57 = e2) | ~ (unit = e2)) & ( ~ (all_0_58_58 = e2) | (all_0_57_57 = e1 & ~ (unit = e2))) & ( ~ (all_0_59_59 = e2) | (all_0_57_57 = e0 & ~ (unit = e2)))
% 21.25/5.55 |
% 21.25/5.55 | Applying alpha-rule on (6698) yields:
% 21.25/5.55 | (6699) ~ (all_0_57_57 = e2) | ~ (unit = e2)
% 21.25/5.55 | (6700) ~ (all_0_53_53 = e2) | (all_0_52_52 = e1 & ~ (unit = e2))
% 21.25/5.55 | (362) ~ (all_0_42_42 = e2)
% 21.25/5.55 | (6702) ~ (all_0_52_52 = e2) | ~ (unit = e2)
% 21.25/5.55 | (390) ~ (all_0_45_45 = e2)
% 21.25/5.55 | (1442) ~ (all_0_47_47 = e2)
% 21.25/5.55 | (6705) ~ (all_0_54_54 = e2) | (all_0_52_52 = e0 & ~ (unit = e2))
% 21.25/5.55 | (6706) ~ (all_0_39_39 = e2) | (all_0_40_40 = e3 & ~ (unit = e2))
% 21.25/5.55 | (6707) ~ (all_0_40_40 = e2) | ~ (unit = e2)
% 21.25/5.55 | (6708) ~ (all_0_59_59 = e2) | (all_0_57_57 = e0 & ~ (unit = e2))
% 21.25/5.55 | (6709) ~ (all_0_58_58 = e2) | (all_0_57_57 = e1 & ~ (unit = e2))
% 21.25/5.55 | (6710) ~ (all_0_46_46 = e2) | (all_0_44_44 = e0 & ~ (unit = e2))
% 21.25/5.55 | (263) ~ (all_0_55_55 = e2)
% 21.25/5.55 | (323) ~ (all_0_49_49 = e2)
% 21.25/5.55 | (6713) ~ (all_0_51_51 = e2) | (all_0_52_52 = e3 & ~ (unit = e2))
% 21.25/5.55 | (6714) ~ (all_0_43_43 = e2) | (all_0_44_44 = e3 & ~ (unit = e2))
% 21.25/5.55 | (6715) ~ (all_0_41_41 = e2) | (all_0_40_40 = e1 & ~ (unit = e2))
% 21.25/5.55 | (6716) ~ (all_0_50_50 = e2)
% 21.25/5.55 | (1115) ~ (all_0_48_48 = e2)
% 21.25/5.55 | (6718) ~ (all_0_56_56 = e2) | (all_0_57_57 = e3 & ~ (unit = e2))
% 21.25/5.55 | (6719) ~ (all_0_44_44 = e2) | ~ (unit = e2)
% 21.25/5.55 |
% 21.25/5.55 | Equations (253) can reduce 6716 to:
% 21.25/5.55 | (269) $false
% 21.25/5.55 |
% 21.25/5.55 |-The branch is then unsatisfiable
% 21.25/5.55 |-Branch two:
% 21.25/5.55 | (6716) ~ (all_0_50_50 = e2)
% 21.25/5.55 | (453) all_0_50_50 = e4
% 21.25/5.55 |
% 21.25/5.55 | Equations (453) can reduce 80 to:
% 21.25/5.55 | (1208) ~ (all_0_51_51 = e4)
% 21.25/5.55 |
% 21.25/5.55 | Simplifying 1208 yields:
% 21.25/5.55 | (530) ~ (all_0_51_51 = e4)
% 21.25/5.55 |
% 21.25/5.55 | Equations (453) can reduce 31 to:
% 21.25/5.55 | (6725) ~ (all_0_52_52 = e4)
% 21.25/5.55 |
% 21.25/5.55 | Simplifying 6725 yields:
% 21.25/5.55 | (152) ~ (all_0_52_52 = e4)
% 21.25/5.55 |
% 21.25/5.55 | Equations (453) can reduce 185 to:
% 21.25/5.55 | (447) ~ (all_0_53_53 = e4)
% 21.25/5.55 |
% 21.25/5.55 | Simplifying 447 yields:
% 21.25/5.55 | (448) ~ (all_0_53_53 = e4)
% 21.25/5.55 |
% 21.25/5.55 | Equations (453) can reduce 141 to:
% 21.25/5.55 | (6729) ~ (all_0_55_55 = e4)
% 21.25/5.55 |
% 21.25/5.55 | Simplifying 6729 yields:
% 21.25/5.55 | (6730) ~ (all_0_55_55 = e4)
% 21.25/5.55 |
% 21.25/5.55 | From (453) and (9) follows:
% 21.25/5.55 | (6731) op(e4, e4) = all_0_0_0
% 21.25/5.55 |
% 21.25/5.55 | From (453) and (12) follows:
% 21.25/5.56 | (6732) op(e1, e4) = all_0_1_1
% 21.25/5.56 |
% 21.25/5.56 | From (453) and (91) follows:
% 21.25/5.56 | (6733) op(e1, e4) = e4
% 21.25/5.56 |
% 21.25/5.56 +-Applying beta-rule and splitting (123), into two cases.
% 21.25/5.56 |-Branch one:
% 21.25/5.56 | (268) all_0_55_55 = e2
% 21.25/5.56 |
% 21.25/5.56 | Equations (268) can reduce 221 to:
% 21.25/5.56 | (2655) ~ (all_0_56_56 = e2)
% 21.25/5.56 |
% 21.25/5.56 | Simplifying 2655 yields:
% 21.25/5.56 | (377) ~ (all_0_56_56 = e2)
% 21.25/5.56 |
% 21.25/5.56 | Equations (268) can reduce 242 to:
% 21.25/5.56 | (2716) ~ (all_0_57_57 = e2)
% 21.25/5.56 |
% 21.25/5.56 | Simplifying 2716 yields:
% 21.25/5.56 | (378) ~ (all_0_57_57 = e2)
% 21.25/5.56 |
% 21.25/5.56 | Equations (268) can reduce 140 to:
% 21.25/5.56 | (391) ~ (all_0_58_58 = e2)
% 21.25/5.56 |
% 21.25/5.56 | Simplifying 391 yields:
% 21.25/5.56 | (392) ~ (all_0_58_58 = e2)
% 21.25/5.56 |
% 21.25/5.56 | Equations (268) can reduce 238 to:
% 21.25/5.56 | (1842) ~ (all_0_59_59 = e2)
% 21.25/5.56 |
% 21.25/5.56 | Simplifying 1842 yields:
% 21.25/5.56 | (1843) ~ (all_0_59_59 = e2)
% 21.25/5.56 |
% 21.25/5.56 | Equations (268) can reduce 6730 to:
% 21.25/5.56 | (326) ~ (e4 = e2)
% 21.25/5.56 |
% 21.25/5.56 | Simplifying 326 yields:
% 21.25/5.56 | (230) ~ (e4 = e2)
% 21.25/5.56 |
% 21.25/5.56 | From (268) and (236) follows:
% 21.25/5.56 | (6745) op(e4, e2) = all_0_2_2
% 21.25/5.56 |
% 21.25/5.56 | From (268) and (52) follows:
% 21.25/5.56 | (6746) op(e0, e4) = e2
% 21.25/5.56 |
% 21.25/5.56 | Instantiating formula (21) with e4, e4, all_0_0_0, e0 and discharging atoms op(e4, e4) = all_0_0_0, op(e4, e4) = e0, yields:
% 21.25/5.56 | (6747) all_0_0_0 = e0
% 21.25/5.56 |
% 21.25/5.56 | Instantiating formula (21) with e4, e2, all_0_2_2, all_0_40_40 and discharging atoms op(e4, e2) = all_0_2_2, op(e4, e2) = all_0_40_40, yields:
% 21.25/5.56 | (6748) all_0_2_2 = all_0_40_40
% 21.25/5.56 |
% 21.25/5.56 | Instantiating formula (21) with e1, e4, e4, all_0_1_1 and discharging atoms op(e1, e4) = all_0_1_1, op(e1, e4) = e4, yields:
% 21.25/5.56 | (6749) all_0_1_1 = e4
% 21.25/5.56 |
% 21.25/5.56 | From (6749) and (6732) follows:
% 21.25/5.56 | (6733) op(e1, e4) = e4
% 21.25/5.56 |
% 21.25/5.56 +-Applying beta-rule and splitting (220), into two cases.
% 21.25/5.56 |-Branch one:
% 21.25/5.56 | (292) (all_0_42_42 = e4 & ~ (all_0_45_45 = e0) & ~ (all_0_47_47 = e0) & ~ (unit = e0) & ( ~ (all_0_43_43 = e0) | all_0_46_46 = e3) & ( ~ (all_0_44_44 = e0) | all_0_46_46 = e2) & ( ~ (all_0_48_48 = e0) | all_0_49_49 = e1) & ( ~ (all_0_51_51 = e0) | all_0_54_54 = e3) & ( ~ (all_0_52_52 = e0) | all_0_54_54 = e2) & ( ~ (all_0_53_53 = e0) | all_0_54_54 = e1) & ( ~ (all_0_56_56 = e0) | all_0_59_59 = e3) & ( ~ (all_0_57_57 = e0) | all_0_59_59 = e2) & ( ~ (all_0_58_58 = e0) | all_0_59_59 = e1)) | (all_0_45_45 = e4 & ~ (all_0_42_42 = e1) & ~ (all_0_47_47 = e1) & ~ (unit = e1) & ( ~ (all_0_39_39 = e1) | all_0_41_41 = e3) & ( ~ (all_0_40_40 = e1) | all_0_41_41 = e2) & ( ~ (all_0_49_49 = e1) | all_0_48_48 = e0) & ( ~ (all_0_51_51 = e1) | all_0_53_53 = e3) & ( ~ (all_0_52_52 = e1) | all_0_53_53 = e2) & ( ~ (all_0_54_54 = e1) | all_0_53_53 = e0) & ( ~ (all_0_56_56 = e1) | all_0_58_58 = e3) & ( ~ (all_0_57_57 = e1) | all_0_58_58 = e2) & ( ~ (all_0_59_59 = e1) | all_0_58_58 = e0))
% 21.25/5.56 |
% 21.25/5.56 +-Applying beta-rule and splitting (292), into two cases.
% 21.25/5.56 |-Branch one:
% 21.25/5.56 | (293) all_0_42_42 = e4 & ~ (all_0_45_45 = e0) & ~ (all_0_47_47 = e0) & ~ (unit = e0) & ( ~ (all_0_43_43 = e0) | all_0_46_46 = e3) & ( ~ (all_0_44_44 = e0) | all_0_46_46 = e2) & ( ~ (all_0_48_48 = e0) | all_0_49_49 = e1) & ( ~ (all_0_51_51 = e0) | all_0_54_54 = e3) & ( ~ (all_0_52_52 = e0) | all_0_54_54 = e2) & ( ~ (all_0_53_53 = e0) | all_0_54_54 = e1) & ( ~ (all_0_56_56 = e0) | all_0_59_59 = e3) & ( ~ (all_0_57_57 = e0) | all_0_59_59 = e2) & ( ~ (all_0_58_58 = e0) | all_0_59_59 = e1)
% 21.25/5.56 |
% 21.25/5.56 | Applying alpha-rule on (293) yields:
% 21.25/5.56 | (294) ~ (all_0_48_48 = e0) | all_0_49_49 = e1
% 21.25/5.56 | (295) ~ (all_0_44_44 = e0) | all_0_46_46 = e2
% 21.25/5.56 | (296) ~ (all_0_56_56 = e0) | all_0_59_59 = e3
% 21.25/5.56 | (297) ~ (all_0_47_47 = e0)
% 21.25/5.56 | (298) ~ (all_0_57_57 = e0) | all_0_59_59 = e2
% 21.25/5.56 | (299) ~ (all_0_45_45 = e0)
% 21.25/5.56 | (300) ~ (all_0_52_52 = e0) | all_0_54_54 = e2
% 21.25/5.56 | (301) ~ (all_0_43_43 = e0) | all_0_46_46 = e3
% 21.25/5.56 | (302) ~ (all_0_51_51 = e0) | all_0_54_54 = e3
% 21.25/5.56 | (303) ~ (all_0_53_53 = e0) | all_0_54_54 = e1
% 21.25/5.56 | (304) ~ (unit = e0)
% 21.25/5.56 | (305) all_0_42_42 = e4
% 21.25/5.56 | (306) ~ (all_0_58_58 = e0) | all_0_59_59 = e1
% 21.25/5.56 |
% 21.25/5.56 | Equations (305) can reduce 157 to:
% 21.25/5.56 | (307) ~ (all_0_39_39 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Equations (305) can reduce 207 to:
% 21.25/5.56 | (64) ~ (all_0_40_40 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Equations (305) can reduce 214 to:
% 21.25/5.56 | (308) ~ (all_0_41_41 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Equations (305) can reduce 107 to:
% 21.25/5.56 | (309) ~ (all_0_46_46 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Simplifying 309 yields:
% 21.25/5.56 | (310) ~ (all_0_46_46 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Equations (305) can reduce 180 to:
% 21.25/5.56 | (6771) ~ (all_0_49_49 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Simplifying 6771 yields:
% 21.25/5.56 | (83) ~ (all_0_49_49 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Equations (305) can reduce 98 to:
% 21.25/5.56 | (311) ~ (all_0_54_54 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Simplifying 311 yields:
% 21.25/5.56 | (312) ~ (all_0_54_54 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Equations (305) can reduce 103 to:
% 21.25/5.56 | (278) ~ (all_0_59_59 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Simplifying 278 yields:
% 21.25/5.56 | (279) ~ (all_0_59_59 = e4)
% 21.25/5.56 |
% 21.25/5.56 | From (305) and (36) follows:
% 21.25/5.56 | (6777) op(e0, e4) = all_0_30_30
% 21.25/5.56 |
% 21.25/5.56 +-Applying beta-rule and splitting (298), into two cases.
% 21.25/5.56 |-Branch one:
% 21.25/5.56 | (967) ~ (all_0_57_57 = e0)
% 21.25/5.56 |
% 21.25/5.56 | Instantiating formula (21) with e0, e4, all_0_30_30, e2 and discharging atoms op(e0, e4) = all_0_30_30, op(e0, e4) = e2, yields:
% 21.25/5.56 | (6779) all_0_30_30 = e2
% 21.25/5.56 |
% 21.25/5.56 +-Applying beta-rule and splitting (189), into two cases.
% 21.25/5.56 |-Branch one:
% 21.25/5.56 | (319) all_0_47_47 = e2
% 21.25/5.56 |
% 21.25/5.56 | Equations (319) can reduce 164 to:
% 21.25/5.56 | (320) ~ (all_0_39_39 = e2)
% 21.25/5.56 |
% 21.25/5.56 | Equations (319) can reduce 138 to:
% 21.25/5.56 | (321) ~ (all_0_43_43 = e2)
% 21.25/5.56 |
% 21.25/5.56 | Equations (319) can reduce 145 to:
% 21.25/5.56 | (322) ~ (all_0_49_49 = e2)
% 21.25/5.56 |
% 21.25/5.56 | Simplifying 322 yields:
% 21.25/5.56 | (323) ~ (all_0_49_49 = e2)
% 21.25/5.56 |
% 21.25/5.56 | Equations (319) can reduce 147 to:
% 21.25/5.56 | (2655) ~ (all_0_56_56 = e2)
% 21.25/5.56 |
% 21.25/5.56 | Simplifying 2655 yields:
% 21.25/5.56 | (377) ~ (all_0_56_56 = e2)
% 21.25/5.56 |
% 21.25/5.56 | Equations (319) can reduce 115 to:
% 21.25/5.56 | (328) ~ (e3 = e2)
% 21.25/5.56 |
% 21.25/5.56 | Simplifying 328 yields:
% 21.25/5.56 | (224) ~ (e3 = e2)
% 21.25/5.56 |
% 21.25/5.56 | From (319) and (99) follows:
% 21.25/5.56 | (331) op(e3, e2) = all_0_7_7
% 21.25/5.56 |
% 21.25/5.56 +-Applying beta-rule and splitting (8), into two cases.
% 21.25/5.56 |-Branch one:
% 21.25/5.56 | (348) all_0_39_39 = e2
% 21.25/5.56 |
% 21.25/5.56 | Equations (348) can reduce 320 to:
% 21.25/5.56 | (269) $false
% 21.25/5.56 |
% 21.25/5.56 |-The branch is then unsatisfiable
% 21.25/5.56 |-Branch two:
% 21.25/5.56 | (320) ~ (all_0_39_39 = e2)
% 21.25/5.56 | (396) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 21.25/5.56 |
% 21.25/5.56 +-Applying beta-rule and splitting (396), into two cases.
% 21.25/5.56 |-Branch one:
% 21.25/5.56 | (409) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 21.25/5.56 |
% 21.25/5.56 +-Applying beta-rule and splitting (409), into two cases.
% 21.25/5.56 |-Branch one:
% 21.25/5.56 | (410) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Applying alpha-rule on (410) yields:
% 21.25/5.56 | (411) all_0_0_0 = e1
% 21.25/5.56 | (412) ~ (all_0_1_1 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Combining equations (411,6747) yields a new equation:
% 21.25/5.56 | (578) e1 = e0
% 21.25/5.56 |
% 21.25/5.56 | Simplifying 578 yields:
% 21.25/5.56 | (579) e1 = e0
% 21.25/5.56 |
% 21.25/5.56 | Equations (579) can reduce 144 to:
% 21.25/5.56 | (269) $false
% 21.25/5.56 |
% 21.25/5.56 |-The branch is then unsatisfiable
% 21.25/5.56 |-Branch two:
% 21.25/5.56 | (641) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Applying alpha-rule on (641) yields:
% 21.25/5.56 | (285) all_0_2_2 = e0
% 21.25/5.56 | (643) ~ (all_0_3_3 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Combining equations (6748,285) yields a new equation:
% 21.25/5.56 | (6804) all_0_40_40 = e0
% 21.25/5.56 |
% 21.25/5.56 | Simplifying 6804 yields:
% 21.25/5.56 | (6805) all_0_40_40 = e0
% 21.25/5.56 |
% 21.25/5.56 | Equations (6805) can reduce 102 to:
% 21.25/5.56 | (269) $false
% 21.25/5.56 |
% 21.25/5.56 |-The branch is then unsatisfiable
% 21.25/5.56 |-Branch two:
% 21.25/5.56 | (645) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Applying alpha-rule on (645) yields:
% 21.25/5.56 | (605) all_0_41_41 = e3
% 21.25/5.56 | (537) ~ (all_0_45_45 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Equations (605) can reduce 226 to:
% 21.25/5.56 | (540) ~ (all_0_39_39 = e3)
% 21.25/5.56 |
% 21.25/5.56 | Equations (605) can reduce 122 to:
% 21.25/5.56 | (688) ~ (all_0_45_45 = e3)
% 21.25/5.56 |
% 21.25/5.56 | Simplifying 688 yields:
% 21.25/5.56 | (689) ~ (all_0_45_45 = e3)
% 21.25/5.56 |
% 21.25/5.56 +-Applying beta-rule and splitting (14), into two cases.
% 21.25/5.56 |-Branch one:
% 21.25/5.56 | (438) all_0_43_43 = e4
% 21.25/5.56 |
% 21.25/5.56 | Equations (438) can reduce 234 to:
% 21.25/5.56 | (307) ~ (all_0_39_39 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Equations (438) can reduce 228 to:
% 21.25/5.56 | (6815) ~ (all_0_44_44 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Simplifying 6815 yields:
% 21.25/5.56 | (190) ~ (all_0_44_44 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Equations (438) can reduce 186 to:
% 21.25/5.56 | (1700) ~ (all_0_45_45 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Simplifying 1700 yields:
% 21.25/5.56 | (537) ~ (all_0_45_45 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Equations (438) can reduce 137 to:
% 21.25/5.56 | (1208) ~ (all_0_51_51 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Simplifying 1208 yields:
% 21.25/5.56 | (530) ~ (all_0_51_51 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Equations (438) can reduce 232 to:
% 21.25/5.56 | (272) ~ (all_0_56_56 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Simplifying 272 yields:
% 21.25/5.56 | (273) ~ (all_0_56_56 = e4)
% 21.25/5.56 |
% 21.25/5.56 | Equations (438) can reduce 321 to:
% 21.25/5.56 | (230) ~ (e4 = e2)
% 21.25/5.56 |
% 21.25/5.56 | From (438) and (101) follows:
% 21.25/5.56 | (6824) op(e3, e3) = e4
% 21.25/5.56 |
% 21.25/5.56 +-Applying beta-rule and splitting (154), into two cases.
% 21.25/5.56 |-Branch one:
% 21.25/5.56 | (348) all_0_39_39 = e2
% 21.25/5.56 |
% 21.25/5.56 | Equations (348) can reduce 320 to:
% 21.25/5.56 | (269) $false
% 21.25/5.56 |
% 21.25/5.56 |-The branch is then unsatisfiable
% 21.25/5.56 |-Branch two:
% 21.25/5.56 | (320) ~ (all_0_39_39 = e2)
% 21.25/5.56 | (351) all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 21.25/5.56 |
% 21.25/5.56 +-Applying beta-rule and splitting (351), into two cases.
% 21.25/5.56 |-Branch one:
% 21.25/5.56 | (382) all_0_40_40 = e2
% 21.25/5.56 |
% 21.25/5.56 | Equations (382) can reduce 18 to:
% 21.25/5.56 | (320) ~ (all_0_39_39 = e2)
% 21.25/5.56 |
% 21.25/5.56 | Equations (382) can reduce 64 to:
% 21.25/5.56 | (326) ~ (e4 = e2)
% 21.25/5.56 |
% 21.25/5.56 | Simplifying 326 yields:
% 21.25/5.56 | (230) ~ (e4 = e2)
% 21.25/5.56 |
% 21.25/5.56 +-Applying beta-rule and splitting (39), into two cases.
% 21.25/5.56 |-Branch one:
% 21.25/5.56 | (464) all_0_39_39 = e1
% 21.25/5.56 |
% 21.25/5.56 | Equations (464) can reduce 126 to:
% 21.25/5.56 | (1450) ~ (all_0_51_51 = e1)
% 21.25/5.56 |
% 21.25/5.56 | Simplifying 1450 yields:
% 21.25/5.56 | (479) ~ (all_0_51_51 = e1)
% 21.25/5.56 |
% 21.25/5.56 | Equations (464) can reduce 53 to:
% 21.25/5.57 | (1452) ~ (all_0_56_56 = e1)
% 21.25/5.57 |
% 21.25/5.57 | Simplifying 1452 yields:
% 21.25/5.57 | (575) ~ (all_0_56_56 = e1)
% 21.25/5.57 |
% 21.25/5.57 | From (464) and (161) follows:
% 21.25/5.57 | (6838) op(e3, e1) = all_0_4_4
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (73), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (271) all_0_55_55 = e4
% 21.25/5.57 |
% 21.25/5.57 | Combining equations (268,271) yields a new equation:
% 21.25/5.57 | (360) e4 = e2
% 21.25/5.57 |
% 21.25/5.57 | Equations (360) can reduce 230 to:
% 21.25/5.57 | (269) $false
% 21.25/5.57 |
% 21.25/5.57 |-The branch is then unsatisfiable
% 21.25/5.57 |-Branch two:
% 21.25/5.57 | (6730) ~ (all_0_55_55 = e4)
% 21.25/5.57 | (6843) all_0_56_56 = e4 | all_0_58_58 = e4 | all_0_59_59 = e4
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (245), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (694) all_0_45_45 = e2
% 21.25/5.57 |
% 21.25/5.57 | Equations (694) can reduce 117 to:
% 21.25/5.57 | (659) ~ (all_0_44_44 = e2)
% 21.25/5.57 |
% 21.25/5.57 | Equations (694) can reduce 201 to:
% 21.25/5.57 | (343) ~ (all_0_46_46 = e2)
% 21.25/5.57 |
% 21.25/5.57 | Simplifying 343 yields:
% 21.25/5.57 | (344) ~ (all_0_46_46 = e2)
% 21.25/5.57 |
% 21.25/5.57 | Equations (694) can reduce 68 to:
% 21.25/5.57 | (391) ~ (all_0_58_58 = e2)
% 21.25/5.57 |
% 21.25/5.57 | Simplifying 391 yields:
% 21.25/5.57 | (392) ~ (all_0_58_58 = e2)
% 21.25/5.57 |
% 21.25/5.57 | Equations (694) can reduce 537 to:
% 21.25/5.57 | (326) ~ (e4 = e2)
% 21.25/5.57 |
% 21.25/5.57 | Simplifying 326 yields:
% 21.25/5.57 | (230) ~ (e4 = e2)
% 21.25/5.57 |
% 21.25/5.57 | Equations (694) can reduce 689 to:
% 21.25/5.57 | (328) ~ (e3 = e2)
% 21.25/5.57 |
% 21.25/5.57 | Simplifying 328 yields:
% 21.25/5.57 | (224) ~ (e3 = e2)
% 21.25/5.57 |
% 21.25/5.57 | Equations (694) can reduce 215 to:
% 21.25/5.57 | (148) ~ (e2 = e1)
% 21.25/5.57 |
% 21.25/5.57 | From (694) and (23) follows:
% 21.25/5.57 | (6855) op(e3, e1) = e2
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (216), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (358) all_0_42_42 = e2
% 21.25/5.57 |
% 21.25/5.57 | Combining equations (305,358) yields a new equation:
% 21.25/5.57 | (359) e4 = e2
% 21.25/5.57 |
% 21.25/5.57 | Simplifying 359 yields:
% 21.25/5.57 | (360) e4 = e2
% 21.25/5.57 |
% 21.25/5.57 | Equations (360) can reduce 230 to:
% 21.25/5.57 | (269) $false
% 21.25/5.57 |
% 21.25/5.57 |-The branch is then unsatisfiable
% 21.25/5.57 |-Branch two:
% 21.25/5.57 | (362) ~ (all_0_42_42 = e2)
% 21.25/5.57 | (363) all_0_46_46 = e2 | all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (363), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (364) all_0_46_46 = e2
% 21.25/5.57 |
% 21.25/5.57 | Equations (364) can reduce 344 to:
% 21.25/5.57 | (269) $false
% 21.25/5.57 |
% 21.25/5.57 |-The branch is then unsatisfiable
% 21.25/5.57 |-Branch two:
% 21.25/5.57 | (344) ~ (all_0_46_46 = e2)
% 21.25/5.57 | (367) all_0_49_49 = e2 | all_0_54_54 = e2 | all_0_59_59 = e2
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (367), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (337) all_0_49_49 = e2
% 21.25/5.57 |
% 21.25/5.57 | Equations (337) can reduce 323 to:
% 21.25/5.57 | (269) $false
% 21.25/5.57 |
% 21.25/5.57 |-The branch is then unsatisfiable
% 21.25/5.57 |-Branch two:
% 21.25/5.57 | (323) ~ (all_0_49_49 = e2)
% 21.25/5.57 | (371) all_0_54_54 = e2 | all_0_59_59 = e2
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (371), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (372) all_0_54_54 = e2
% 21.25/5.57 |
% 21.25/5.57 | Equations (372) can reduce 59 to:
% 21.25/5.57 | (344) ~ (all_0_46_46 = e2)
% 21.25/5.57 |
% 21.25/5.57 | Equations (372) can reduce 159 to:
% 21.25/5.57 | (255) ~ (all_0_51_51 = e2)
% 21.25/5.57 |
% 21.25/5.57 | Equations (372) can reduce 62 to:
% 21.25/5.57 | (257) ~ (all_0_52_52 = e2)
% 21.25/5.57 |
% 21.25/5.57 | Equations (372) can reduce 119 to:
% 21.25/5.57 | (259) ~ (all_0_53_53 = e2)
% 21.25/5.57 |
% 21.25/5.57 | Equations (372) can reduce 81 to:
% 21.25/5.57 | (1842) ~ (all_0_59_59 = e2)
% 21.25/5.57 |
% 21.25/5.57 | Simplifying 1842 yields:
% 21.25/5.57 | (1843) ~ (all_0_59_59 = e2)
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (6843), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (1658) all_0_56_56 = e4
% 21.25/5.57 |
% 21.25/5.57 | Equations (1658) can reduce 273 to:
% 21.25/5.57 | (269) $false
% 21.25/5.57 |
% 21.25/5.57 |-The branch is then unsatisfiable
% 21.25/5.57 |-Branch two:
% 21.25/5.57 | (273) ~ (all_0_56_56 = e4)
% 21.25/5.57 | (6880) all_0_58_58 = e4 | all_0_59_59 = e4
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (302), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (432) ~ (all_0_51_51 = e0)
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (170), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (1232) all_0_51_51 = e2
% 21.25/5.57 |
% 21.25/5.57 | Equations (1232) can reduce 255 to:
% 21.25/5.57 | (269) $false
% 21.25/5.57 |
% 21.25/5.57 |-The branch is then unsatisfiable
% 21.25/5.57 |-Branch two:
% 21.25/5.57 | (255) ~ (all_0_51_51 = e2)
% 21.25/5.57 | (1235) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1 | all_0_51_51 = e0
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (1235), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (475) all_0_51_51 = e1
% 21.25/5.57 |
% 21.25/5.57 | Equations (475) can reduce 479 to:
% 21.25/5.57 | (269) $false
% 21.25/5.57 |
% 21.25/5.57 |-The branch is then unsatisfiable
% 21.25/5.57 |-Branch two:
% 21.25/5.57 | (479) ~ (all_0_51_51 = e1)
% 21.25/5.57 | (1371) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e0
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (1371), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (629) all_0_51_51 = e0
% 21.25/5.57 |
% 21.25/5.57 | Equations (629) can reduce 432 to:
% 21.25/5.57 | (269) $false
% 21.25/5.57 |
% 21.25/5.57 |-The branch is then unsatisfiable
% 21.25/5.57 |-Branch two:
% 21.25/5.57 | (432) ~ (all_0_51_51 = e0)
% 21.25/5.57 | (1375) all_0_51_51 = e4 | all_0_51_51 = e3
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (1375), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (564) all_0_51_51 = e3
% 21.25/5.57 |
% 21.25/5.57 | Equations (564) can reduce 30 to:
% 21.25/5.57 | (3866) ~ (all_0_53_53 = e3)
% 21.25/5.57 |
% 21.25/5.57 | Simplifying 3866 yields:
% 21.25/5.57 | (796) ~ (all_0_53_53 = e3)
% 21.25/5.57 |
% 21.25/5.57 | Equations (564) can reduce 16 to:
% 21.25/5.57 | (1182) ~ (all_0_56_56 = e3)
% 21.25/5.57 |
% 21.25/5.57 | Simplifying 1182 yields:
% 21.25/5.57 | (1183) ~ (all_0_56_56 = e3)
% 21.25/5.57 |
% 21.25/5.57 | From (564) and (151) follows:
% 21.25/5.57 | (6899) op(e3, e3) = all_0_9_9
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (6880), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (528) all_0_58_58 = e4
% 21.25/5.57 |
% 21.25/5.57 | Equations (528) can reduce 127 to:
% 21.25/5.57 | (448) ~ (all_0_53_53 = e4)
% 21.25/5.57 |
% 21.25/5.57 | Equations (528) can reduce 223 to:
% 21.25/5.57 | (273) ~ (all_0_56_56 = e4)
% 21.25/5.57 |
% 21.25/5.57 | Equations (528) can reduce 252 to:
% 21.25/5.57 | (173) ~ (all_0_57_57 = e4)
% 21.25/5.57 |
% 21.25/5.57 | Equations (528) can reduce 392 to:
% 21.25/5.57 | (230) ~ (e4 = e2)
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (20), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (1575) all_0_56_56 = e2
% 21.25/5.57 |
% 21.25/5.57 | Equations (1575) can reduce 377 to:
% 21.25/5.57 | (269) $false
% 21.25/5.57 |
% 21.25/5.57 |-The branch is then unsatisfiable
% 21.25/5.57 |-Branch two:
% 21.25/5.57 | (377) ~ (all_0_56_56 = e2)
% 21.25/5.57 | (1578) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1 | all_0_56_56 = e0
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (1578), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (480) all_0_56_56 = e1
% 21.25/5.57 |
% 21.25/5.57 | Equations (480) can reduce 575 to:
% 21.25/5.57 | (269) $false
% 21.25/5.57 |
% 21.25/5.57 |-The branch is then unsatisfiable
% 21.25/5.57 |-Branch two:
% 21.25/5.57 | (575) ~ (all_0_56_56 = e1)
% 21.25/5.57 | (1619) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e0
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (1619), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (632) all_0_56_56 = e0
% 21.25/5.57 |
% 21.25/5.57 | Equations (632) can reduce 227 to:
% 21.25/5.57 | (6914) ~ (all_0_57_57 = e0)
% 21.25/5.57 |
% 21.25/5.57 | Simplifying 6914 yields:
% 21.25/5.57 | (967) ~ (all_0_57_57 = e0)
% 21.25/5.57 |
% 21.25/5.57 | From (632) and (44) follows:
% 21.25/5.57 | (6916) op(e0, e0) = all_0_12_12
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (295), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (356) ~ (all_0_44_44 = e0)
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (149), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (341) all_0_44_44 = e2
% 21.25/5.57 |
% 21.25/5.57 | Equations (341) can reduce 659 to:
% 21.25/5.57 | (269) $false
% 21.25/5.57 |
% 21.25/5.57 |-The branch is then unsatisfiable
% 21.25/5.57 |-Branch two:
% 21.25/5.57 | (659) ~ (all_0_44_44 = e2)
% 21.25/5.57 | (660) all_0_44_44 = e3 | all_0_44_44 = e0
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (660), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (352) all_0_44_44 = e0
% 21.25/5.57 |
% 21.25/5.57 | Equations (352) can reduce 356 to:
% 21.25/5.57 | (269) $false
% 21.25/5.57 |
% 21.25/5.57 |-The branch is then unsatisfiable
% 21.25/5.57 |-Branch two:
% 21.25/5.57 | (356) ~ (all_0_44_44 = e0)
% 21.25/5.57 | (422) all_0_44_44 = e3
% 21.25/5.57 |
% 21.25/5.57 | Equations (422) can reduce 210 to:
% 21.25/5.57 | (1044) ~ (all_0_46_46 = e3)
% 21.25/5.57 |
% 21.25/5.57 | Simplifying 1044 yields:
% 21.25/5.57 | (618) ~ (all_0_46_46 = e3)
% 21.25/5.57 |
% 21.25/5.57 | Equations (422) can reduce 190 to:
% 21.25/5.57 | (498) ~ (e4 = e3)
% 21.25/5.57 |
% 21.25/5.57 | Simplifying 498 yields:
% 21.25/5.57 | (41) ~ (e4 = e3)
% 21.25/5.57 |
% 21.25/5.57 | Equations (422) can reduce 659 to:
% 21.25/5.57 | (224) ~ (e3 = e2)
% 21.25/5.57 |
% 21.25/5.57 | Equations (422) can reduce 356 to:
% 21.25/5.57 | (72) ~ (e3 = e0)
% 21.25/5.57 |
% 21.25/5.57 | From (422) and (247) follows:
% 21.25/5.57 | (6932) op(e3, e3) = all_0_16_16
% 21.25/5.57 |
% 21.25/5.57 | From (422) and (74) follows:
% 21.25/5.57 | (6933) op(e3, e2) = e3
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (110), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (352) all_0_44_44 = e0
% 21.25/5.57 |
% 21.25/5.57 | Combining equations (422,352) yields a new equation:
% 21.25/5.57 | (781) e3 = e0
% 21.25/5.57 |
% 21.25/5.57 | Simplifying 781 yields:
% 21.25/5.57 | (560) e3 = e0
% 21.25/5.57 |
% 21.25/5.57 | Equations (560) can reduce 72 to:
% 21.25/5.57 | (269) $false
% 21.25/5.57 |
% 21.25/5.57 |-The branch is then unsatisfiable
% 21.25/5.57 |-Branch two:
% 21.25/5.57 | (356) ~ (all_0_44_44 = e0)
% 21.25/5.57 | (357) all_0_52_52 = e0 | all_0_57_57 = e0
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (357), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (397) all_0_52_52 = e0
% 21.25/5.57 |
% 21.25/5.57 | Equations (397) can reduce 71 to:
% 21.25/5.57 | (764) ~ (all_0_53_53 = e0)
% 21.25/5.57 |
% 21.25/5.57 | Simplifying 764 yields:
% 21.25/5.57 | (765) ~ (all_0_53_53 = e0)
% 21.25/5.57 |
% 21.25/5.57 | Equations (397) can reduce 152 to:
% 21.25/5.57 | (404) ~ (e4 = e0)
% 21.25/5.57 |
% 21.25/5.57 | Simplifying 404 yields:
% 21.25/5.57 | (11) ~ (e4 = e0)
% 21.25/5.57 |
% 21.25/5.57 | Equations (397) can reduce 257 to:
% 21.25/5.57 | (406) ~ (e2 = e0)
% 21.25/5.57 |
% 21.25/5.57 | Simplifying 406 yields:
% 21.25/5.57 | (58) ~ (e2 = e0)
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (139), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (889) all_0_45_45 = e0
% 21.25/5.57 |
% 21.25/5.57 | Combining equations (694,889) yields a new equation:
% 21.25/5.57 | (353) e2 = e0
% 21.25/5.57 |
% 21.25/5.57 | Simplifying 353 yields:
% 21.25/5.57 | (354) e2 = e0
% 21.25/5.57 |
% 21.25/5.57 | Equations (354) can reduce 58 to:
% 21.25/5.57 | (269) $false
% 21.25/5.57 |
% 21.25/5.57 |-The branch is then unsatisfiable
% 21.25/5.57 |-Branch two:
% 21.25/5.57 | (299) ~ (all_0_45_45 = e0)
% 21.25/5.57 | (894) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (894), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (903) all_0_48_48 = e0
% 21.25/5.57 |
% 21.25/5.57 | Equations (903) can reduce 178 to:
% 21.25/5.57 | (806) ~ (all_0_49_49 = e0)
% 21.25/5.57 |
% 21.25/5.57 | Simplifying 806 yields:
% 21.25/5.57 | (807) ~ (all_0_49_49 = e0)
% 21.25/5.57 |
% 21.25/5.57 | Equations (903) can reduce 250 to:
% 21.25/5.57 | (764) ~ (all_0_53_53 = e0)
% 21.25/5.57 |
% 21.25/5.57 | Simplifying 764 yields:
% 21.25/5.57 | (765) ~ (all_0_53_53 = e0)
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (192), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (469) all_0_47_47 = e1
% 21.25/5.57 |
% 21.25/5.57 | Combining equations (319,469) yields a new equation:
% 21.25/5.57 | (470) e2 = e1
% 21.25/5.57 |
% 21.25/5.57 | Simplifying 470 yields:
% 21.25/5.57 | (471) e2 = e1
% 21.25/5.57 |
% 21.25/5.57 | Equations (471) can reduce 148 to:
% 21.25/5.57 | (269) $false
% 21.25/5.57 |
% 21.25/5.57 |-The branch is then unsatisfiable
% 21.25/5.57 |-Branch two:
% 21.25/5.57 | (473) ~ (all_0_47_47 = e1)
% 21.25/5.57 | (592) all_0_48_48 = e1 | all_0_49_49 = e1
% 21.25/5.57 |
% 21.25/5.57 | Equations (319) can reduce 473 to:
% 21.25/5.57 | (148) ~ (e2 = e1)
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (246), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (413) all_0_40_40 = e1
% 21.25/5.57 |
% 21.25/5.57 | Combining equations (413,382) yields a new equation:
% 21.25/5.57 | (471) e2 = e1
% 21.25/5.57 |
% 21.25/5.57 | Equations (471) can reduce 148 to:
% 21.25/5.57 | (269) $false
% 21.25/5.57 |
% 21.25/5.57 |-The branch is then unsatisfiable
% 21.25/5.57 |-Branch two:
% 21.25/5.57 | (983) ~ (all_0_40_40 = e1)
% 21.25/5.57 | (984) all_0_52_52 = e1 | all_0_57_57 = e1
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (27), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (849) all_0_53_53 = e2
% 21.25/5.57 |
% 21.25/5.57 | Equations (849) can reduce 259 to:
% 21.25/5.57 | (269) $false
% 21.25/5.57 |
% 21.25/5.57 |-The branch is then unsatisfiable
% 21.25/5.57 |-Branch two:
% 21.25/5.57 | (259) ~ (all_0_53_53 = e2)
% 21.25/5.57 | (852) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (852), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (853) all_0_53_53 = e1
% 21.25/5.57 |
% 21.25/5.57 | Equations (853) can reduce 765 to:
% 21.25/5.57 | (144) ~ (e1 = e0)
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (169), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (610) all_0_42_42 = e3
% 21.25/5.57 |
% 21.25/5.57 | Combining equations (610,305) yields a new equation:
% 21.25/5.57 | (516) e4 = e3
% 21.25/5.57 |
% 21.25/5.57 | Equations (516) can reduce 41 to:
% 21.25/5.57 | (269) $false
% 21.25/5.57 |
% 21.25/5.57 |-The branch is then unsatisfiable
% 21.25/5.57 |-Branch two:
% 21.25/5.57 | (1924) ~ (all_0_42_42 = e3)
% 21.25/5.57 | (1925) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (592), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (593) all_0_48_48 = e1
% 21.25/5.57 |
% 21.25/5.57 | Combining equations (593,903) yields a new equation:
% 21.25/5.57 | (578) e1 = e0
% 21.25/5.57 |
% 21.25/5.57 | Simplifying 578 yields:
% 21.25/5.57 | (579) e1 = e0
% 21.25/5.57 |
% 21.25/5.57 | Equations (579) can reduce 144 to:
% 21.25/5.57 | (269) $false
% 21.25/5.57 |
% 21.25/5.57 |-The branch is then unsatisfiable
% 21.25/5.57 |-Branch two:
% 21.25/5.57 | (584) ~ (all_0_48_48 = e1)
% 21.25/5.57 | (596) all_0_49_49 = e1
% 21.25/5.57 |
% 21.25/5.57 | Equations (596) can reduce 807 to:
% 21.25/5.57 | (144) ~ (e1 = e0)
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (984), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (820) all_0_52_52 = e1
% 21.25/5.57 |
% 21.25/5.57 | Combining equations (397,820) yields a new equation:
% 21.25/5.57 | (579) e1 = e0
% 21.25/5.57 |
% 21.25/5.57 | Equations (579) can reduce 144 to:
% 21.25/5.57 | (269) $false
% 21.25/5.57 |
% 21.25/5.57 |-The branch is then unsatisfiable
% 21.25/5.57 |-Branch two:
% 21.25/5.57 | (978) ~ (all_0_52_52 = e1)
% 21.25/5.57 | (577) all_0_57_57 = e1
% 21.25/5.57 |
% 21.25/5.57 | Equations (577) can reduce 173 to:
% 21.25/5.57 | (826) ~ (e4 = e1)
% 21.25/5.57 |
% 21.25/5.57 | Simplifying 826 yields:
% 21.25/5.57 | (251) ~ (e4 = e1)
% 21.25/5.57 |
% 21.25/5.57 +-Applying beta-rule and splitting (1925), into two cases.
% 21.25/5.57 |-Branch one:
% 21.25/5.57 | (462) all_0_46_46 = e3
% 21.25/5.57 |
% 21.25/5.58 | Equations (462) can reduce 618 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (618) ~ (all_0_46_46 = e3)
% 21.25/5.58 | (1930) all_0_54_54 = e3 | all_0_59_59 = e3
% 21.25/5.58 |
% 21.25/5.58 +-Applying beta-rule and splitting (1930), into two cases.
% 21.25/5.58 |-Branch one:
% 21.25/5.58 | (635) all_0_54_54 = e3
% 21.25/5.58 |
% 21.25/5.58 | Combining equations (372,635) yields a new equation:
% 21.25/5.58 | (423) e3 = e2
% 21.25/5.58 |
% 21.25/5.58 | Equations (423) can reduce 224 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (430) ~ (all_0_54_54 = e3)
% 21.25/5.58 | (1070) all_0_59_59 = e3
% 21.25/5.58 |
% 21.25/5.58 | Equations (1070) can reduce 1843 to:
% 21.25/5.58 | (224) ~ (e3 = e2)
% 21.25/5.58 |
% 21.25/5.58 | From (1070) and (66) follows:
% 21.25/5.58 | (7005) op(e0, e0) = e3
% 21.25/5.58 |
% 21.25/5.58 | Instantiating formula (21) with e3, e3, all_0_16_16, all_0_9_9 and discharging atoms op(e3, e3) = all_0_9_9, op(e3, e3) = all_0_16_16, yields:
% 21.25/5.58 | (7006) all_0_9_9 = all_0_16_16
% 21.25/5.58 |
% 21.25/5.58 | Instantiating formula (21) with e3, e3, e4, all_0_9_9 and discharging atoms op(e3, e3) = all_0_9_9, op(e3, e3) = e4, yields:
% 21.25/5.58 | (7007) all_0_9_9 = e4
% 21.25/5.58 |
% 21.25/5.58 | Instantiating formula (21) with e3, e2, e3, all_0_7_7 and discharging atoms op(e3, e2) = all_0_7_7, op(e3, e2) = e3, yields:
% 21.25/5.58 | (7008) all_0_7_7 = e3
% 21.25/5.58 |
% 21.25/5.58 | Instantiating formula (21) with e3, e1, e2, all_0_4_4 and discharging atoms op(e3, e1) = all_0_4_4, op(e3, e1) = e2, yields:
% 21.25/5.58 | (7009) all_0_4_4 = e2
% 21.25/5.58 |
% 21.25/5.58 | Instantiating formula (21) with e0, e0, e3, all_0_12_12 and discharging atoms op(e0, e0) = all_0_12_12, op(e0, e0) = e3, yields:
% 21.25/5.58 | (2188) all_0_12_12 = e3
% 21.25/5.58 |
% 21.25/5.58 | Combining equations (7007,7006) yields a new equation:
% 21.25/5.58 | (7011) all_0_16_16 = e4
% 21.25/5.58 |
% 21.25/5.58 | Combining equations (7011,7006) yields a new equation:
% 21.25/5.58 | (7007) all_0_9_9 = e4
% 21.25/5.58 |
% 21.25/5.58 +-Applying beta-rule and splitting (5), into two cases.
% 21.25/5.58 |-Branch one:
% 21.25/5.58 | (1332) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3)) | (all_0_9_9 = e1 & ~ (all_0_10_10 = e3))
% 21.25/5.58 |
% 21.25/5.58 +-Applying beta-rule and splitting (1332), into two cases.
% 21.25/5.58 |-Branch one:
% 21.25/5.58 | (1333) (all_0_4_4 = e4 & ~ (all_0_5_5 = e3)) | (all_0_7_7 = e2 & ~ (all_0_8_8 = e3))
% 21.25/5.58 |
% 21.25/5.58 +-Applying beta-rule and splitting (1333), into two cases.
% 21.25/5.58 |-Branch one:
% 21.25/5.58 | (1334) all_0_4_4 = e4 & ~ (all_0_5_5 = e3)
% 21.25/5.58 |
% 21.25/5.58 | Applying alpha-rule on (1334) yields:
% 21.25/5.58 | (1335) all_0_4_4 = e4
% 21.25/5.58 | (1336) ~ (all_0_5_5 = e3)
% 21.25/5.58 |
% 21.25/5.58 | Combining equations (1335,7009) yields a new equation:
% 21.25/5.58 | (359) e4 = e2
% 21.25/5.58 |
% 21.25/5.58 | Simplifying 359 yields:
% 21.25/5.58 | (360) e4 = e2
% 21.25/5.58 |
% 21.25/5.58 | Equations (360) can reduce 230 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (1338) all_0_7_7 = e2 & ~ (all_0_8_8 = e3)
% 21.25/5.58 |
% 21.25/5.58 | Applying alpha-rule on (1338) yields:
% 21.25/5.58 | (1339) all_0_7_7 = e2
% 21.25/5.58 | (1340) ~ (all_0_8_8 = e3)
% 21.25/5.58 |
% 21.25/5.58 | Combining equations (1339,7008) yields a new equation:
% 21.25/5.58 | (423) e3 = e2
% 21.25/5.58 |
% 21.25/5.58 | Equations (423) can reduce 224 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (1344) all_0_9_9 = e1 & ~ (all_0_10_10 = e3)
% 21.25/5.58 |
% 21.25/5.58 | Applying alpha-rule on (1344) yields:
% 21.25/5.58 | (1345) all_0_9_9 = e1
% 21.25/5.58 | (1346) ~ (all_0_10_10 = e3)
% 21.25/5.58 |
% 21.25/5.58 | Combining equations (1345,7007) yields a new equation:
% 21.25/5.58 | (477) e4 = e1
% 21.25/5.58 |
% 21.25/5.58 | Equations (477) can reduce 251 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (1349) all_0_11_11 = e0 & ~ (all_0_12_12 = e3)
% 21.25/5.58 |
% 21.25/5.58 | Applying alpha-rule on (1349) yields:
% 21.25/5.58 | (1350) all_0_11_11 = e0
% 21.25/5.58 | (1351) ~ (all_0_12_12 = e3)
% 21.25/5.58 |
% 21.25/5.58 | Equations (2188) can reduce 1351 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (823) ~ (all_0_53_53 = e1)
% 21.25/5.58 | (856) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e0
% 21.25/5.58 |
% 21.25/5.58 +-Applying beta-rule and splitting (856), into two cases.
% 21.25/5.58 |-Branch one:
% 21.25/5.58 | (857) all_0_53_53 = e0
% 21.25/5.58 |
% 21.25/5.58 | Equations (857) can reduce 765 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (765) ~ (all_0_53_53 = e0)
% 21.25/5.58 | (860) all_0_53_53 = e4 | all_0_53_53 = e3
% 21.25/5.58 |
% 21.25/5.58 +-Applying beta-rule and splitting (860), into two cases.
% 21.25/5.58 |-Branch one:
% 21.25/5.58 | (861) all_0_53_53 = e3
% 21.25/5.58 |
% 21.25/5.58 | Equations (861) can reduce 796 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (796) ~ (all_0_53_53 = e3)
% 21.25/5.58 | (532) all_0_53_53 = e4
% 21.25/5.58 |
% 21.25/5.58 | Equations (532) can reduce 448 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (952) ~ (all_0_48_48 = e0)
% 21.25/5.58 | (953) all_0_53_53 = e0 | all_0_58_58 = e0
% 21.25/5.58 |
% 21.25/5.58 +-Applying beta-rule and splitting (953), into two cases.
% 21.25/5.58 |-Branch one:
% 21.25/5.58 | (857) all_0_53_53 = e0
% 21.25/5.58 |
% 21.25/5.58 | Equations (857) can reduce 765 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (765) ~ (all_0_53_53 = e0)
% 21.25/5.58 | (493) all_0_58_58 = e0
% 21.25/5.58 |
% 21.25/5.58 | Combining equations (528,493) yields a new equation:
% 21.25/5.58 | (751) e4 = e0
% 21.25/5.58 |
% 21.25/5.58 | Simplifying 751 yields:
% 21.25/5.58 | (439) e4 = e0
% 21.25/5.58 |
% 21.25/5.58 | Equations (439) can reduce 11 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (317) ~ (all_0_52_52 = e0)
% 21.25/5.58 | (400) all_0_57_57 = e0
% 21.25/5.58 |
% 21.25/5.58 | Equations (400) can reduce 967 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (352) all_0_44_44 = e0
% 21.25/5.58 | (364) all_0_46_46 = e2
% 21.25/5.58 |
% 21.25/5.58 | Equations (364) can reduce 344 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (401) ~ (all_0_56_56 = e0)
% 21.25/5.58 | (1630) all_0_56_56 = e4 | all_0_56_56 = e3
% 21.25/5.58 |
% 21.25/5.58 +-Applying beta-rule and splitting (243), into two cases.
% 21.25/5.58 |-Branch one:
% 21.25/5.58 | (567) all_0_56_56 = e3
% 21.25/5.58 |
% 21.25/5.58 | Equations (567) can reduce 1183 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (1183) ~ (all_0_56_56 = e3)
% 21.25/5.58 | (1249) all_0_57_57 = e3 | all_0_58_58 = e3 | all_0_59_59 = e3
% 21.25/5.58 |
% 21.25/5.58 +-Applying beta-rule and splitting (1630), into two cases.
% 21.25/5.58 |-Branch one:
% 21.25/5.58 | (567) all_0_56_56 = e3
% 21.25/5.58 |
% 21.25/5.58 | Equations (567) can reduce 1183 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (1183) ~ (all_0_56_56 = e3)
% 21.25/5.58 | (1658) all_0_56_56 = e4
% 21.25/5.58 |
% 21.25/5.58 | Equations (1658) can reduce 273 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (277) ~ (all_0_58_58 = e4)
% 21.25/5.58 | (2231) all_0_59_59 = e4
% 21.25/5.58 |
% 21.25/5.58 | Equations (2231) can reduce 279 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (428) ~ (all_0_51_51 = e3)
% 21.25/5.58 | (458) all_0_51_51 = e4
% 21.25/5.58 |
% 21.25/5.58 | Equations (458) can reduce 530 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (629) all_0_51_51 = e0
% 21.25/5.58 | (635) all_0_54_54 = e3
% 21.25/5.58 |
% 21.25/5.58 | Combining equations (635,372) yields a new equation:
% 21.25/5.58 | (606) e3 = e2
% 21.25/5.58 |
% 21.25/5.58 | Simplifying 606 yields:
% 21.25/5.58 | (423) e3 = e2
% 21.25/5.58 |
% 21.25/5.58 | Equations (423) can reduce 224 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (261) ~ (all_0_54_54 = e2)
% 21.25/5.58 | (375) all_0_59_59 = e2
% 21.25/5.58 |
% 21.25/5.58 | Equations (375) can reduce 1843 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (390) ~ (all_0_45_45 = e2)
% 21.25/5.58 | (1082) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 21.25/5.58 |
% 21.25/5.58 +-Applying beta-rule and splitting (1082), into two cases.
% 21.25/5.58 |-Branch one:
% 21.25/5.58 | (889) all_0_45_45 = e0
% 21.25/5.58 |
% 21.25/5.58 | Equations (889) can reduce 299 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (299) ~ (all_0_45_45 = e0)
% 21.25/5.58 | (1086) all_0_45_45 = e4 | all_0_45_45 = e3
% 21.25/5.58 |
% 21.25/5.58 +-Applying beta-rule and splitting (1086), into two cases.
% 21.25/5.58 |-Branch one:
% 21.25/5.58 | (1087) all_0_45_45 = e3
% 21.25/5.58 |
% 21.25/5.58 | Equations (1087) can reduce 689 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (689) ~ (all_0_45_45 = e3)
% 21.25/5.58 | (444) all_0_45_45 = e4
% 21.25/5.58 |
% 21.25/5.58 | Equations (444) can reduce 537 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (467) ~ (all_0_39_39 = e1)
% 21.25/5.58 | (2100) all_0_40_40 = e1 | all_0_41_41 = e1 | all_0_42_42 = e1
% 21.25/5.58 |
% 21.25/5.58 +-Applying beta-rule and splitting (47), into two cases.
% 21.25/5.58 |-Branch one:
% 21.25/5.58 | (348) all_0_39_39 = e2
% 21.25/5.58 |
% 21.25/5.58 | Equations (348) can reduce 320 to:
% 21.25/5.58 | (269) $false
% 21.25/5.58 |
% 21.25/5.58 |-The branch is then unsatisfiable
% 21.25/5.58 |-Branch two:
% 21.25/5.58 | (320) ~ (all_0_39_39 = e2)
% 21.25/5.58 | (709) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 21.25/5.58 |
% 21.25/5.59 +-Applying beta-rule and splitting (709), into two cases.
% 21.25/5.59 |-Branch one:
% 21.25/5.59 | (464) all_0_39_39 = e1
% 21.25/5.59 |
% 21.25/5.59 | Equations (464) can reduce 467 to:
% 21.25/5.59 | (269) $false
% 21.25/5.59 |
% 21.25/5.59 |-The branch is then unsatisfiable
% 21.25/5.59 |-Branch two:
% 21.25/5.59 | (467) ~ (all_0_39_39 = e1)
% 21.25/5.59 | (1075) all_0_39_39 = e4 | all_0_39_39 = e3
% 21.25/5.59 |
% 21.25/5.59 +-Applying beta-rule and splitting (1075), into two cases.
% 21.25/5.59 |-Branch one:
% 21.25/5.59 | (443) all_0_39_39 = e3
% 21.25/5.59 |
% 21.25/5.59 | Equations (443) can reduce 540 to:
% 21.25/5.59 | (269) $false
% 21.25/5.59 |
% 21.25/5.59 |-The branch is then unsatisfiable
% 21.25/5.59 |-Branch two:
% 21.25/5.59 | (540) ~ (all_0_39_39 = e3)
% 21.25/5.59 | (1079) all_0_39_39 = e4
% 21.25/5.59 |
% 21.25/5.59 | Equations (1079) can reduce 307 to:
% 21.25/5.59 | (269) $false
% 21.25/5.59 |
% 21.25/5.59 |-The branch is then unsatisfiable
% 21.25/5.59 |-Branch two:
% 21.25/5.59 | (342) ~ (all_0_40_40 = e2)
% 21.25/5.59 | (385) all_0_41_41 = e2 | all_0_42_42 = e2
% 21.25/5.59 |
% 21.25/5.59 +-Applying beta-rule and splitting (385), into two cases.
% 21.25/5.59 |-Branch one:
% 21.25/5.59 | (386) all_0_41_41 = e2
% 21.25/5.59 |
% 21.25/5.59 | Combining equations (605,386) yields a new equation:
% 21.25/5.59 | (606) e3 = e2
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 606 yields:
% 21.25/5.59 | (423) e3 = e2
% 21.25/5.59 |
% 21.25/5.59 | Equations (423) can reduce 224 to:
% 21.25/5.59 | (269) $false
% 21.25/5.59 |
% 21.25/5.59 |-The branch is then unsatisfiable
% 21.25/5.59 |-Branch two:
% 21.25/5.59 | (650) ~ (all_0_41_41 = e2)
% 21.25/5.59 | (358) all_0_42_42 = e2
% 21.25/5.59 |
% 21.25/5.59 | Combining equations (305,358) yields a new equation:
% 21.25/5.59 | (359) e4 = e2
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 359 yields:
% 21.25/5.59 | (360) e4 = e2
% 21.25/5.59 |
% 21.25/5.59 | Equations (360) can reduce 230 to:
% 21.25/5.59 | (269) $false
% 21.25/5.59 |
% 21.25/5.59 |-The branch is then unsatisfiable
% 21.25/5.59 |-Branch two:
% 21.25/5.59 | (441) ~ (all_0_43_43 = e4)
% 21.25/5.59 | (442) all_0_45_45 = e4 | all_0_46_46 = e4
% 21.25/5.59 |
% 21.25/5.59 +-Applying beta-rule and splitting (442), into two cases.
% 21.25/5.59 |-Branch one:
% 21.25/5.59 | (444) all_0_45_45 = e4
% 21.25/5.59 |
% 21.25/5.59 | Equations (444) can reduce 537 to:
% 21.25/5.59 | (269) $false
% 21.25/5.59 |
% 21.25/5.59 |-The branch is then unsatisfiable
% 21.25/5.59 |-Branch two:
% 21.25/5.59 | (537) ~ (all_0_45_45 = e4)
% 21.25/5.59 | (538) all_0_46_46 = e4
% 21.25/5.59 |
% 21.25/5.59 | Equations (538) can reduce 310 to:
% 21.25/5.59 | (269) $false
% 21.25/5.59 |
% 21.25/5.59 |-The branch is then unsatisfiable
% 21.25/5.59 |-Branch two:
% 21.25/5.59 | (1442) ~ (all_0_47_47 = e2)
% 21.25/5.59 | (1443) all_0_47_47 = e1 | all_0_47_47 = e0
% 21.25/5.59 |
% 21.25/5.59 +-Applying beta-rule and splitting (1443), into two cases.
% 21.25/5.59 |-Branch one:
% 21.25/5.59 | (469) all_0_47_47 = e1
% 21.25/5.59 |
% 21.25/5.59 | Equations (469) can reduce 164 to:
% 21.25/5.59 | (467) ~ (all_0_39_39 = e1)
% 21.25/5.59 |
% 21.25/5.59 | Equations (469) can reduce 138 to:
% 21.25/5.59 | (114) ~ (all_0_43_43 = e1)
% 21.25/5.59 |
% 21.25/5.59 | Equations (469) can reduce 48 to:
% 21.25/5.59 | (1446) ~ (all_0_48_48 = e1)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 1446 yields:
% 21.25/5.59 | (584) ~ (all_0_48_48 = e1)
% 21.25/5.59 |
% 21.25/5.59 | Equations (469) can reduce 145 to:
% 21.25/5.59 | (1448) ~ (all_0_49_49 = e1)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 1448 yields:
% 21.25/5.59 | (960) ~ (all_0_49_49 = e1)
% 21.25/5.59 |
% 21.25/5.59 | Equations (469) can reduce 34 to:
% 21.25/5.59 | (1450) ~ (all_0_51_51 = e1)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 1450 yields:
% 21.25/5.59 | (479) ~ (all_0_51_51 = e1)
% 21.25/5.59 |
% 21.25/5.59 | Equations (469) can reduce 147 to:
% 21.25/5.59 | (1452) ~ (all_0_56_56 = e1)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 1452 yields:
% 21.25/5.59 | (575) ~ (all_0_56_56 = e1)
% 21.25/5.59 |
% 21.25/5.59 | Equations (469) can reduce 248 to:
% 21.25/5.59 | (826) ~ (e4 = e1)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 826 yields:
% 21.25/5.59 | (251) ~ (e4 = e1)
% 21.25/5.59 |
% 21.25/5.59 | Equations (469) can reduce 297 to:
% 21.25/5.59 | (144) ~ (e1 = e0)
% 21.25/5.59 |
% 21.25/5.59 | From (469) and (218) follows:
% 21.25/5.59 | (1456) op(e2, e1) = all_0_8_8
% 21.25/5.59 |
% 21.25/5.59 | From (469) and (231) follows:
% 21.25/5.59 | (3095) op(e2, e3) = e1
% 21.25/5.59 |
% 21.25/5.59 +-Applying beta-rule and splitting (294), into two cases.
% 21.25/5.59 |-Branch one:
% 21.25/5.59 | (952) ~ (all_0_48_48 = e0)
% 21.25/5.59 |
% 21.25/5.59 +-Applying beta-rule and splitting (197), into two cases.
% 21.25/5.59 |-Branch one:
% 21.25/5.59 | (1458) all_0_48_48 = e2
% 21.25/5.59 |
% 21.25/5.59 | Equations (1458) can reduce 167 to:
% 21.25/5.59 | (650) ~ (all_0_41_41 = e2)
% 21.25/5.59 |
% 21.25/5.59 | Equations (1458) can reduce 196 to:
% 21.25/5.59 | (390) ~ (all_0_45_45 = e2)
% 21.25/5.59 |
% 21.25/5.59 | Equations (1458) can reduce 178 to:
% 21.25/5.59 | (322) ~ (all_0_49_49 = e2)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 322 yields:
% 21.25/5.59 | (323) ~ (all_0_49_49 = e2)
% 21.25/5.59 |
% 21.25/5.59 | Equations (1458) can reduce 250 to:
% 21.25/5.59 | (258) ~ (all_0_53_53 = e2)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 258 yields:
% 21.25/5.59 | (259) ~ (all_0_53_53 = e2)
% 21.25/5.59 |
% 21.25/5.59 | Equations (1458) can reduce 174 to:
% 21.25/5.59 | (391) ~ (all_0_58_58 = e2)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 391 yields:
% 21.25/5.59 | (392) ~ (all_0_58_58 = e2)
% 21.25/5.59 |
% 21.25/5.59 | Equations (1458) can reduce 4 to:
% 21.25/5.59 | (328) ~ (e3 = e2)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 328 yields:
% 21.25/5.59 | (224) ~ (e3 = e2)
% 21.25/5.59 |
% 21.25/5.59 | Equations (1458) can reduce 952 to:
% 21.25/5.59 | (58) ~ (e2 = e0)
% 21.25/5.59 |
% 21.25/5.59 | From (1458) and (76) follows:
% 21.25/5.59 | (1466) op(e2, e2) = all_0_26_26
% 21.25/5.59 |
% 21.25/5.59 | From (1458) and (179) follows:
% 21.25/5.59 | (1467) op(e2, e1) = e2
% 21.25/5.59 |
% 21.25/5.59 | From (1458) and (85) follows:
% 21.25/5.59 | (7163) op(e1, e2) = all_0_25_25
% 21.25/5.59 |
% 21.25/5.59 +-Applying beta-rule and splitting (10), into two cases.
% 21.25/5.59 |-Branch one:
% 21.25/5.59 | (623) all_0_47_47 = e0
% 21.25/5.59 |
% 21.25/5.59 | Combining equations (469,623) yields a new equation:
% 21.25/5.59 | (578) e1 = e0
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 578 yields:
% 21.25/5.59 | (579) e1 = e0
% 21.25/5.59 |
% 21.25/5.59 | Equations (579) can reduce 144 to:
% 21.25/5.59 | (269) $false
% 21.25/5.59 |
% 21.25/5.59 |-The branch is then unsatisfiable
% 21.25/5.59 |-Branch two:
% 21.25/5.59 | (297) ~ (all_0_47_47 = e0)
% 21.25/5.59 | (815) all_0_48_48 = e0 | all_0_49_49 = e0
% 21.25/5.59 |
% 21.25/5.59 +-Applying beta-rule and splitting (815), into two cases.
% 21.25/5.59 |-Branch one:
% 21.25/5.59 | (903) all_0_48_48 = e0
% 21.25/5.59 |
% 21.25/5.59 | Combining equations (903,1458) yields a new equation:
% 21.25/5.59 | (354) e2 = e0
% 21.25/5.59 |
% 21.25/5.59 | Equations (354) can reduce 58 to:
% 21.25/5.59 | (269) $false
% 21.25/5.59 |
% 21.25/5.59 |-The branch is then unsatisfiable
% 21.25/5.59 |-Branch two:
% 21.25/5.59 | (952) ~ (all_0_48_48 = e0)
% 21.25/5.59 | (965) all_0_49_49 = e0
% 21.25/5.59 |
% 21.25/5.59 | Equations (965) can reduce 166 to:
% 21.25/5.59 | (435) ~ (all_0_46_46 = e0)
% 21.25/5.59 |
% 21.25/5.59 | Equations (965) can reduce 217 to:
% 21.25/5.59 | (1477) ~ (all_0_54_54 = e0)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 1477 yields:
% 21.25/5.59 | (1478) ~ (all_0_54_54 = e0)
% 21.25/5.59 |
% 21.25/5.59 | Equations (965) can reduce 82 to:
% 21.25/5.59 | (1479) ~ (all_0_59_59 = e0)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 1479 yields:
% 21.25/5.59 | (1480) ~ (all_0_59_59 = e0)
% 21.25/5.59 |
% 21.25/5.59 | Equations (965) can reduce 83 to:
% 21.25/5.59 | (404) ~ (e4 = e0)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 404 yields:
% 21.25/5.59 | (11) ~ (e4 = e0)
% 21.25/5.59 |
% 21.25/5.59 | Equations (965) can reduce 158 to:
% 21.25/5.59 | (1272) ~ (e3 = e0)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 1272 yields:
% 21.25/5.59 | (72) ~ (e3 = e0)
% 21.25/5.59 |
% 21.25/5.59 | Equations (965) can reduce 323 to:
% 21.25/5.59 | (406) ~ (e2 = e0)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 406 yields:
% 21.25/5.59 | (58) ~ (e2 = e0)
% 21.25/5.59 |
% 21.25/5.59 | Equations (965) can reduce 960 to:
% 21.25/5.59 | (436) ~ (e1 = e0)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 436 yields:
% 21.25/5.59 | (144) ~ (e1 = e0)
% 21.25/5.59 |
% 21.25/5.59 | From (965) and (38) follows:
% 21.25/5.59 | (1485) op(e2, e0) = all_0_35_35
% 21.25/5.59 |
% 21.25/5.59 | From (965) and (128) follows:
% 21.25/5.59 | (1486) op(e2, e0) = e0
% 21.25/5.59 |
% 21.25/5.59 | From (965) and (183) follows:
% 21.25/5.59 | (1487) op(e0, e0) = all_0_34_34
% 21.25/5.59 |
% 21.25/5.59 | Instantiating formula (21) with e2, e2, all_0_26_26, e4 and discharging atoms op(e2, e2) = all_0_26_26, op(e2, e2) = e4, yields:
% 21.25/5.59 | (1488) all_0_26_26 = e4
% 21.25/5.59 |
% 21.25/5.59 | Instantiating formula (21) with e2, e1, e2, all_0_8_8 and discharging atoms op(e2, e1) = all_0_8_8, op(e2, e1) = e2, yields:
% 21.25/5.59 | (1489) all_0_8_8 = e2
% 21.25/5.59 |
% 21.25/5.59 | Instantiating formula (21) with e2, e0, e0, all_0_35_35 and discharging atoms op(e2, e0) = all_0_35_35, op(e2, e0) = e0, yields:
% 21.25/5.59 | (1490) all_0_35_35 = e0
% 21.25/5.59 |
% 21.25/5.59 | Instantiating formula (21) with e1, e2, all_0_25_25, all_0_52_52 and discharging atoms op(e1, e2) = all_0_25_25, op(e1, e2) = all_0_52_52, yields:
% 21.25/5.59 | (7194) all_0_25_25 = all_0_52_52
% 21.25/5.59 |
% 21.25/5.59 | Instantiating formula (21) with e0, e0, all_0_34_34, all_0_59_59 and discharging atoms op(e0, e0) = all_0_34_34, op(e0, e0) = all_0_59_59, yields:
% 21.25/5.59 | (1491) all_0_34_34 = all_0_59_59
% 21.25/5.59 |
% 21.25/5.59 | From (1488) and (1466) follows:
% 21.25/5.59 | (222) op(e2, e2) = e4
% 21.25/5.59 |
% 21.25/5.59 | From (1489) and (1456) follows:
% 21.25/5.59 | (1467) op(e2, e1) = e2
% 21.25/5.59 |
% 21.25/5.59 | From (1490) and (1485) follows:
% 21.25/5.59 | (1486) op(e2, e0) = e0
% 21.25/5.59 |
% 21.25/5.59 +-Applying beta-rule and splitting (149), into two cases.
% 21.25/5.59 |-Branch one:
% 21.25/5.59 | (341) all_0_44_44 = e2
% 21.25/5.59 |
% 21.25/5.59 | Equations (341) can reduce 35 to:
% 21.25/5.59 | (342) ~ (all_0_40_40 = e2)
% 21.25/5.59 |
% 21.25/5.59 | Equations (341) can reduce 121 to:
% 21.25/5.59 | (256) ~ (all_0_52_52 = e2)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 256 yields:
% 21.25/5.59 | (257) ~ (all_0_52_52 = e2)
% 21.25/5.59 |
% 21.25/5.59 | Equations (341) can reduce 240 to:
% 21.25/5.59 | (2716) ~ (all_0_57_57 = e2)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 2716 yields:
% 21.25/5.59 | (378) ~ (all_0_57_57 = e2)
% 21.25/5.59 |
% 21.25/5.59 +-Applying beta-rule and splitting (143), into two cases.
% 21.25/5.59 |-Branch one:
% 21.25/5.59 | (433) all_0_43_43 = e0
% 21.25/5.59 |
% 21.25/5.59 | Equations (433) can reduce 114 to:
% 21.25/5.59 | (436) ~ (e1 = e0)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 436 yields:
% 21.25/5.59 | (144) ~ (e1 = e0)
% 21.25/5.59 |
% 21.25/5.59 +-Applying beta-rule and splitting (14), into two cases.
% 21.25/5.59 |-Branch one:
% 21.25/5.59 | (438) all_0_43_43 = e4
% 21.25/5.59 |
% 21.25/5.59 | Combining equations (433,438) yields a new equation:
% 21.25/5.59 | (439) e4 = e0
% 21.25/5.59 |
% 21.25/5.59 | Equations (439) can reduce 11 to:
% 21.25/5.59 | (269) $false
% 21.25/5.59 |
% 21.25/5.59 |-The branch is then unsatisfiable
% 21.25/5.59 |-Branch two:
% 21.25/5.59 | (441) ~ (all_0_43_43 = e4)
% 21.25/5.59 | (442) all_0_45_45 = e4 | all_0_46_46 = e4
% 21.25/5.59 |
% 21.25/5.59 | Equations (433) can reduce 441 to:
% 21.25/5.59 | (404) ~ (e4 = e0)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 404 yields:
% 21.25/5.59 | (11) ~ (e4 = e0)
% 21.25/5.59 |
% 21.25/5.59 +-Applying beta-rule and splitting (29), into two cases.
% 21.25/5.59 |-Branch one:
% 21.25/5.59 | (1079) all_0_39_39 = e4
% 21.25/5.59 |
% 21.25/5.59 | Equations (1079) can reduce 307 to:
% 21.25/5.59 | (269) $false
% 21.25/5.59 |
% 21.25/5.59 |-The branch is then unsatisfiable
% 21.25/5.59 |-Branch two:
% 21.25/5.59 | (307) ~ (all_0_39_39 = e4)
% 21.25/5.59 | (1391) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 21.25/5.59 |
% 21.25/5.59 +-Applying beta-rule and splitting (1391), into two cases.
% 21.25/5.59 |-Branch one:
% 21.25/5.59 | (438) all_0_43_43 = e4
% 21.25/5.59 |
% 21.25/5.59 | Combining equations (433,438) yields a new equation:
% 21.25/5.59 | (439) e4 = e0
% 21.25/5.59 |
% 21.25/5.59 | Equations (439) can reduce 11 to:
% 21.25/5.59 | (269) $false
% 21.25/5.59 |
% 21.25/5.59 |-The branch is then unsatisfiable
% 21.25/5.59 |-Branch two:
% 21.25/5.59 | (441) ~ (all_0_43_43 = e4)
% 21.25/5.59 | (2025) all_0_51_51 = e4 | all_0_56_56 = e4
% 21.25/5.59 |
% 21.25/5.59 +-Applying beta-rule and splitting (2025), into two cases.
% 21.25/5.59 |-Branch one:
% 21.25/5.59 | (458) all_0_51_51 = e4
% 21.25/5.59 |
% 21.25/5.59 | Equations (458) can reduce 530 to:
% 21.25/5.59 | (269) $false
% 21.25/5.59 |
% 21.25/5.59 |-The branch is then unsatisfiable
% 21.25/5.59 |-Branch two:
% 21.25/5.59 | (530) ~ (all_0_51_51 = e4)
% 21.25/5.59 | (1658) all_0_56_56 = e4
% 21.25/5.59 |
% 21.25/5.59 | Equations (1658) can reduce 53 to:
% 21.25/5.59 | (307) ~ (all_0_39_39 = e4)
% 21.25/5.59 |
% 21.25/5.59 | Equations (1658) can reduce 227 to:
% 21.25/5.59 | (274) ~ (all_0_57_57 = e4)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 274 yields:
% 21.25/5.59 | (173) ~ (all_0_57_57 = e4)
% 21.25/5.59 |
% 21.25/5.59 | Equations (1658) can reduce 223 to:
% 21.25/5.59 | (276) ~ (all_0_58_58 = e4)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 276 yields:
% 21.25/5.59 | (277) ~ (all_0_58_58 = e4)
% 21.25/5.59 |
% 21.25/5.59 | Equations (1658) can reduce 377 to:
% 21.25/5.59 | (230) ~ (e4 = e2)
% 21.25/5.59 |
% 21.25/5.59 +-Applying beta-rule and splitting (154), into two cases.
% 21.25/5.59 |-Branch one:
% 21.25/5.59 | (348) all_0_39_39 = e2
% 21.25/5.59 |
% 21.25/5.59 | Equations (348) can reduce 226 to:
% 21.25/5.59 | (1797) ~ (all_0_41_41 = e2)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 1797 yields:
% 21.25/5.59 | (650) ~ (all_0_41_41 = e2)
% 21.25/5.59 |
% 21.25/5.59 | Equations (348) can reduce 126 to:
% 21.25/5.59 | (254) ~ (all_0_51_51 = e2)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 254 yields:
% 21.25/5.59 | (255) ~ (all_0_51_51 = e2)
% 21.25/5.59 |
% 21.25/5.59 | Equations (348) can reduce 307 to:
% 21.25/5.59 | (326) ~ (e4 = e2)
% 21.25/5.59 |
% 21.25/5.59 | Simplifying 326 yields:
% 21.25/5.59 | (230) ~ (e4 = e2)
% 21.25/5.59 |
% 21.25/5.59 | Equations (348) can reduce 467 to:
% 21.25/5.59 | (148) ~ (e2 = e1)
% 21.25/5.59 |
% 21.25/5.59 +-Applying beta-rule and splitting (219), into two cases.
% 21.25/5.59 |-Branch one:
% 21.25/5.59 | (253) all_0_50_50 = e2
% 21.25/5.59 |
% 21.25/5.59 | Combining equations (253,453) yields a new equation:
% 21.25/5.59 | (360) e4 = e2
% 21.25/5.59 |
% 21.25/5.59 | Equations (360) can reduce 230 to:
% 21.25/5.59 | (269) $false
% 21.25/5.59 |
% 21.25/5.59 |-The branch is then unsatisfiable
% 21.25/5.59 |-Branch two:
% 21.25/5.59 | (6716) ~ (all_0_50_50 = e2)
% 21.25/5.59 | (7246) all_0_51_51 = e2 | all_0_52_52 = e2 | all_0_53_53 = e2 | all_0_54_54 = e2
% 21.25/5.59 |
% 21.25/5.59 +-Applying beta-rule and splitting (7246), into two cases.
% 21.25/5.59 |-Branch one:
% 21.25/5.59 | (1232) all_0_51_51 = e2
% 21.25/5.59 |
% 21.25/5.59 | Equations (1232) can reduce 255 to:
% 21.25/5.59 | (269) $false
% 21.25/5.59 |
% 21.25/5.59 |-The branch is then unsatisfiable
% 21.25/5.59 |-Branch two:
% 21.25/5.59 | (255) ~ (all_0_51_51 = e2)
% 21.25/5.59 | (7250) all_0_52_52 = e2 | all_0_53_53 = e2 | all_0_54_54 = e2
% 21.25/5.59 |
% 21.25/5.59 +-Applying beta-rule and splitting (7250), into two cases.
% 21.25/5.59 |-Branch one:
% 21.25/5.59 | (816) all_0_52_52 = e2
% 21.25/5.59 |
% 21.25/5.59 | Equations (816) can reduce 257 to:
% 21.25/5.59 | (269) $false
% 21.25/5.59 |
% 21.25/5.59 |-The branch is then unsatisfiable
% 21.25/5.59 |-Branch two:
% 21.25/5.59 | (257) ~ (all_0_52_52 = e2)
% 21.25/5.60 | (7254) all_0_53_53 = e2 | all_0_54_54 = e2
% 21.25/5.60 |
% 21.25/5.60 +-Applying beta-rule and splitting (7254), into two cases.
% 21.25/5.60 |-Branch one:
% 21.25/5.60 | (849) all_0_53_53 = e2
% 21.25/5.60 |
% 21.25/5.60 | Equations (849) can reduce 259 to:
% 21.25/5.60 | (269) $false
% 21.25/5.60 |
% 21.25/5.60 |-The branch is then unsatisfiable
% 21.25/5.60 |-Branch two:
% 21.25/5.60 | (259) ~ (all_0_53_53 = e2)
% 21.25/5.60 | (372) all_0_54_54 = e2
% 21.25/5.60 |
% 21.25/5.60 | Equations (372) can reduce 1478 to:
% 21.25/5.60 | (58) ~ (e2 = e0)
% 21.25/5.60 |
% 21.25/5.60 | From (372) and (13) follows:
% 21.25/5.60 | (3199) op(e1, e0) = e2
% 21.25/5.60 |
% 21.25/5.60 +-Applying beta-rule and splitting (54), into two cases.
% 21.25/5.60 |-Branch one:
% 21.25/5.60 | (740) all_0_41_41 = e4
% 21.25/5.60 |
% 21.25/5.60 | Equations (740) can reduce 308 to:
% 21.25/5.60 | (269) $false
% 21.25/5.60 |
% 21.25/5.60 |-The branch is then unsatisfiable
% 21.25/5.60 |-Branch two:
% 21.25/5.60 | (308) ~ (all_0_41_41 = e4)
% 21.25/5.60 | (744) all_0_45_45 = e4 | all_0_53_53 = e4 | all_0_58_58 = e4
% 21.25/5.60 |
% 21.25/5.60 +-Applying beta-rule and splitting (744), into two cases.
% 21.25/5.60 |-Branch one:
% 21.25/5.60 | (444) all_0_45_45 = e4
% 21.25/5.60 |
% 21.25/5.60 | Equations (444) can reduce 201 to:
% 21.25/5.60 | (309) ~ (all_0_46_46 = e4)
% 21.25/5.60 |
% 21.25/5.60 | Simplifying 309 yields:
% 21.25/5.60 | (310) ~ (all_0_46_46 = e4)
% 21.25/5.60 |
% 21.25/5.60 | Equations (444) can reduce 215 to:
% 21.25/5.60 | (251) ~ (e4 = e1)
% 21.25/5.60 |
% 21.25/5.60 | From (444) and (125) follows:
% 21.25/5.60 | (2647) op(e1, e4) = all_0_23_23
% 21.25/5.60 |
% 21.25/5.60 +-Applying beta-rule and splitting (110), into two cases.
% 21.25/5.60 |-Branch one:
% 21.25/5.60 | (352) all_0_44_44 = e0
% 21.25/5.60 |
% 21.25/5.60 | Combining equations (341,352) yields a new equation:
% 21.25/5.60 | (353) e2 = e0
% 21.25/5.60 |
% 21.25/5.60 | Simplifying 353 yields:
% 21.25/5.60 | (354) e2 = e0
% 21.25/5.60 |
% 21.25/5.60 | Equations (354) can reduce 58 to:
% 21.25/5.60 | (269) $false
% 21.25/5.60 |
% 21.25/5.60 |-The branch is then unsatisfiable
% 21.25/5.60 |-Branch two:
% 21.25/5.60 | (356) ~ (all_0_44_44 = e0)
% 21.25/5.60 | (357) all_0_52_52 = e0 | all_0_57_57 = e0
% 21.25/5.60 |
% 21.25/5.60 +-Applying beta-rule and splitting (84), into two cases.
% 21.25/5.60 |-Branch one:
% 21.25/5.60 | (832) all_0_42_42 = e1
% 21.25/5.60 |
% 21.25/5.60 | Combining equations (305,832) yields a new equation:
% 21.25/5.60 | (476) e4 = e1
% 21.25/5.60 |
% 21.25/5.60 | Simplifying 476 yields:
% 21.25/5.60 | (477) e4 = e1
% 21.25/5.60 |
% 21.25/5.60 | Equations (477) can reduce 251 to:
% 21.25/5.60 | (269) $false
% 21.25/5.60 |
% 21.25/5.60 |-The branch is then unsatisfiable
% 21.25/5.60 |-Branch two:
% 21.25/5.60 | (836) ~ (all_0_42_42 = e1)
% 21.25/5.60 | (837) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 21.25/5.60 |
% 21.25/5.60 +-Applying beta-rule and splitting (357), into two cases.
% 21.25/5.60 |-Branch one:
% 21.25/5.60 | (397) all_0_52_52 = e0
% 21.25/5.60 |
% 21.25/5.60 | Combining equations (397,7194) yields a new equation:
% 21.25/5.60 | (7283) all_0_25_25 = e0
% 21.25/5.60 |
% 21.25/5.60 | Equations (397) can reduce 194 to:
% 21.25/5.60 | (432) ~ (all_0_51_51 = e0)
% 21.25/5.60 |
% 21.25/5.60 | Equations (397) can reduce 124 to:
% 21.25/5.60 | (6914) ~ (all_0_57_57 = e0)
% 21.25/5.60 |
% 21.44/5.60 | Simplifying 6914 yields:
% 21.44/5.60 | (967) ~ (all_0_57_57 = e0)
% 21.44/5.60 |
% 21.44/5.60 | Equations (397) can reduce 152 to:
% 21.44/5.60 | (404) ~ (e4 = e0)
% 21.44/5.60 |
% 21.44/5.60 | Simplifying 404 yields:
% 21.44/5.60 | (11) ~ (e4 = e0)
% 21.44/5.60 |
% 21.44/5.60 | From (397) and (89) follows:
% 21.44/5.60 | (4401) op(e1, e0) = all_0_18_18
% 21.44/5.60 |
% 21.44/5.60 +-Applying beta-rule and splitting (837), into two cases.
% 21.44/5.60 |-Branch one:
% 21.44/5.60 | (596) all_0_49_49 = e1
% 21.44/5.60 |
% 21.44/5.60 | Combining equations (965,596) yields a new equation:
% 21.44/5.60 | (579) e1 = e0
% 21.44/5.60 |
% 21.44/5.60 | Equations (579) can reduce 144 to:
% 21.44/5.60 | (269) $false
% 21.44/5.60 |
% 21.44/5.60 |-The branch is then unsatisfiable
% 21.44/5.60 |-Branch two:
% 21.44/5.60 | (960) ~ (all_0_49_49 = e1)
% 21.44/5.60 | (961) all_0_54_54 = e1 | all_0_59_59 = e1
% 21.44/5.60 |
% 21.44/5.60 +-Applying beta-rule and splitting (211), into two cases.
% 21.44/5.60 |-Branch one:
% 21.44/5.60 | (632) all_0_56_56 = e0
% 21.44/5.60 |
% 21.44/5.60 | Combining equations (632,1658) yields a new equation:
% 21.44/5.60 | (439) e4 = e0
% 21.44/5.60 |
% 21.44/5.60 | Equations (439) can reduce 11 to:
% 21.44/5.60 | (269) $false
% 21.44/5.60 |
% 21.44/5.60 |-The branch is then unsatisfiable
% 21.44/5.60 |-Branch two:
% 21.44/5.60 | (401) ~ (all_0_56_56 = e0)
% 21.44/5.60 | (2052) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 21.44/5.60 |
% 21.44/5.60 +-Applying beta-rule and splitting (961), into two cases.
% 21.44/5.60 |-Branch one:
% 21.44/5.60 | (1592) all_0_54_54 = e1
% 21.44/5.60 |
% 21.44/5.60 | Combining equations (372,1592) yields a new equation:
% 21.44/5.60 | (470) e2 = e1
% 21.44/5.60 |
% 21.44/5.60 | Simplifying 470 yields:
% 21.44/5.60 | (471) e2 = e1
% 21.44/5.60 |
% 21.44/5.60 | Equations (471) can reduce 148 to:
% 21.44/5.60 | (269) $false
% 21.44/5.60 |
% 21.44/5.60 |-The branch is then unsatisfiable
% 21.44/5.60 |-Branch two:
% 21.44/5.60 | (1238) ~ (all_0_54_54 = e1)
% 21.44/5.60 | (614) all_0_59_59 = e1
% 21.44/5.60 |
% 21.44/5.60 | Equations (614) can reduce 95 to:
% 21.44/5.60 | (581) ~ (all_0_57_57 = e1)
% 21.44/5.60 |
% 21.44/5.60 | Equations (614) can reduce 1480 to:
% 21.44/5.60 | (144) ~ (e1 = e0)
% 21.44/5.60 |
% 21.44/5.60 +-Applying beta-rule and splitting (134), into two cases.
% 21.44/5.60 |-Branch one:
% 21.44/5.60 | (867) all_0_57_57 = e2
% 21.44/5.60 |
% 21.44/5.60 | Equations (867) can reduce 378 to:
% 21.44/5.60 | (269) $false
% 21.44/5.60 |
% 21.44/5.60 |-The branch is then unsatisfiable
% 21.44/5.60 |-Branch two:
% 21.44/5.60 | (378) ~ (all_0_57_57 = e2)
% 21.44/5.60 | (870) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 21.44/5.60 |
% 21.44/5.60 +-Applying beta-rule and splitting (870), into two cases.
% 21.44/5.60 |-Branch one:
% 21.44/5.60 | (577) all_0_57_57 = e1
% 21.44/5.60 |
% 21.44/5.60 | Equations (577) can reduce 581 to:
% 21.44/5.60 | (269) $false
% 21.44/5.60 |
% 21.44/5.60 |-The branch is then unsatisfiable
% 21.44/5.60 |-Branch two:
% 21.44/5.60 | (581) ~ (all_0_57_57 = e1)
% 21.44/5.60 | (874) all_0_57_57 = e3 | all_0_57_57 = e0
% 21.44/5.60 |
% 21.44/5.60 +-Applying beta-rule and splitting (874), into two cases.
% 21.44/5.60 |-Branch one:
% 21.44/5.60 | (400) all_0_57_57 = e0
% 21.44/5.60 |
% 21.44/5.60 | Equations (400) can reduce 967 to:
% 21.44/5.60 | (269) $false
% 21.44/5.60 |
% 21.44/5.60 |-The branch is then unsatisfiable
% 21.44/5.60 |-Branch two:
% 21.44/5.60 | (967) ~ (all_0_57_57 = e0)
% 21.44/5.60 | (638) all_0_57_57 = e3
% 21.44/5.60 |
% 21.44/5.60 | Equations (638) can reduce 168 to:
% 21.44/5.60 | (420) ~ (all_0_40_40 = e3)
% 21.44/5.60 |
% 21.44/5.60 | Equations (638) can reduce 173 to:
% 21.44/5.60 | (498) ~ (e4 = e3)
% 21.44/5.60 |
% 21.44/5.60 | Simplifying 498 yields:
% 21.44/5.60 | (41) ~ (e4 = e3)
% 21.44/5.60 |
% 21.44/5.60 | Equations (638) can reduce 378 to:
% 21.44/5.60 | (224) ~ (e3 = e2)
% 21.44/5.60 |
% 21.44/5.60 +-Applying beta-rule and splitting (184), into two cases.
% 21.44/5.60 |-Branch one:
% 21.44/5.60 | (443) all_0_39_39 = e3
% 21.44/5.60 |
% 21.44/5.60 | Combining equations (443,348) yields a new equation:
% 21.44/5.60 | (606) e3 = e2
% 21.44/5.60 |
% 21.44/5.60 | Simplifying 606 yields:
% 21.44/5.60 | (423) e3 = e2
% 21.44/5.60 |
% 21.44/5.60 | Equations (423) can reduce 224 to:
% 21.44/5.60 | (269) $false
% 21.44/5.60 |
% 21.44/5.60 |-The branch is then unsatisfiable
% 21.44/5.60 |-Branch two:
% 21.44/5.60 | (540) ~ (all_0_39_39 = e3)
% 21.44/5.60 | (541) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 21.44/5.60 |
% 21.44/5.60 +-Applying beta-rule and splitting (541), into two cases.
% 21.44/5.60 |-Branch one:
% 21.44/5.60 | (417) all_0_40_40 = e3
% 21.44/5.60 |
% 21.44/5.60 | Equations (417) can reduce 420 to:
% 21.44/5.60 | (269) $false
% 21.44/5.60 |
% 21.44/5.60 |-The branch is then unsatisfiable
% 21.44/5.60 |-Branch two:
% 21.44/5.60 | (420) ~ (all_0_40_40 = e3)
% 21.44/5.60 | (604) all_0_41_41 = e3 | all_0_42_42 = e3
% 21.44/5.60 |
% 21.44/5.60 +-Applying beta-rule and splitting (604), into two cases.
% 21.44/5.60 |-Branch one:
% 21.44/5.60 | (605) all_0_41_41 = e3
% 21.44/5.60 |
% 21.44/5.60 | Equations (605) can reduce 106 to:
% 21.44/5.60 | (3866) ~ (all_0_53_53 = e3)
% 21.44/5.60 |
% 21.44/5.60 | Simplifying 3866 yields:
% 21.44/5.60 | (796) ~ (all_0_53_53 = e3)
% 21.44/5.60 |
% 21.44/5.60 | Equations (605) can reduce 208 to:
% 21.44/5.60 | (788) ~ (all_0_58_58 = e3)
% 21.44/5.60 |
% 21.44/5.60 | Simplifying 788 yields:
% 21.44/5.60 | (527) ~ (all_0_58_58 = e3)
% 21.44/5.60 |
% 21.44/5.60 | Equations (605) can reduce 650 to:
% 21.44/5.60 | (224) ~ (e3 = e2)
% 21.44/5.60 |
% 21.44/5.60 | Equations (605) can reduce 188 to:
% 21.44/5.60 | (72) ~ (e3 = e0)
% 21.44/5.60 |
% 21.44/5.60 | From (605) and (79) follows:
% 21.44/5.60 | (693) op(e1, e3) = all_0_21_21
% 21.44/5.60 |
% 21.44/5.60 +-Applying beta-rule and splitting (93), into two cases.
% 21.44/5.60 |-Branch one:
% 21.44/5.60 | (564) all_0_51_51 = e3
% 21.44/5.60 |
% 21.44/5.60 | Equations (564) can reduce 432 to:
% 21.44/5.60 | (72) ~ (e3 = e0)
% 21.44/5.60 |
% 21.44/5.60 | From (564) and (109) follows:
% 21.44/5.60 | (7344) op(e1, e3) = all_0_10_10
% 21.44/5.60 |
% 21.44/5.60 | From (564) and (175) follows:
% 21.44/5.60 | (7345) op(e1, e3) = e3
% 21.44/5.60 |
% 21.44/5.60 +-Applying beta-rule and splitting (2052), into two cases.
% 21.44/5.60 |-Branch one:
% 21.44/5.60 | (400) all_0_57_57 = e0
% 21.44/5.60 |
% 21.44/5.60 | Combining equations (638,400) yields a new equation:
% 21.44/5.60 | (781) e3 = e0
% 21.44/5.60 |
% 21.44/5.60 | Simplifying 781 yields:
% 21.44/5.60 | (560) e3 = e0
% 21.44/5.60 |
% 21.44/5.60 | Equations (560) can reduce 72 to:
% 21.44/5.60 | (269) $false
% 21.44/5.60 |
% 21.44/5.60 |-The branch is then unsatisfiable
% 21.44/5.60 |-Branch two:
% 21.44/5.60 | (967) ~ (all_0_57_57 = e0)
% 21.44/5.60 | (2059) all_0_58_58 = e0 | all_0_59_59 = e0
% 21.44/5.60 |
% 21.44/5.60 +-Applying beta-rule and splitting (2059), into two cases.
% 21.44/5.60 |-Branch one:
% 21.44/5.60 | (493) all_0_58_58 = e0
% 21.44/5.60 |
% 21.44/5.60 | Equations (493) can reduce 392 to:
% 21.44/5.60 | (406) ~ (e2 = e0)
% 21.44/5.60 |
% 21.44/5.60 | Simplifying 406 yields:
% 21.44/5.60 | (58) ~ (e2 = e0)
% 21.44/5.60 |
% 21.44/5.60 | From (493) and (67) follows:
% 21.44/5.60 | (7355) op(e1, e0) = all_0_28_28
% 21.44/5.60 |
% 21.44/5.60 +-Applying beta-rule and splitting (301), into two cases.
% 21.44/5.60 |-Branch one:
% 21.44/5.60 | (459) ~ (all_0_43_43 = e0)
% 21.44/5.60 |
% 21.44/5.60 | Equations (433) can reduce 459 to:
% 21.44/5.60 | (269) $false
% 21.44/5.60 |
% 21.44/5.60 |-The branch is then unsatisfiable
% 21.44/5.60 |-Branch two:
% 21.44/5.60 | (433) all_0_43_43 = e0
% 21.44/5.60 | (462) all_0_46_46 = e3
% 21.44/5.60 |
% 21.44/5.60 | Equations (462) can reduce 310 to:
% 21.44/5.60 | (498) ~ (e4 = e3)
% 21.44/5.60 |
% 21.44/5.60 | Simplifying 498 yields:
% 21.44/5.60 | (41) ~ (e4 = e3)
% 21.44/5.60 |
% 21.44/5.60 | Instantiating formula (21) with e1, e4, all_0_23_23, e4 and discharging atoms op(e1, e4) = all_0_23_23, op(e1, e4) = e4, yields:
% 21.44/5.60 | (7362) all_0_23_23 = e4
% 21.44/5.60 |
% 21.44/5.60 | Instantiating formula (21) with e1, e3, all_0_21_21, all_0_10_10 and discharging atoms op(e1, e3) = all_0_10_10, op(e1, e3) = all_0_21_21, yields:
% 21.44/5.60 | (7363) all_0_10_10 = all_0_21_21
% 21.44/5.60 |
% 21.44/5.60 | Instantiating formula (21) with e1, e3, e3, all_0_10_10 and discharging atoms op(e1, e3) = all_0_10_10, op(e1, e3) = e3, yields:
% 21.44/5.60 | (917) all_0_10_10 = e3
% 21.44/5.60 |
% 21.44/5.60 | Instantiating formula (21) with e1, e0, all_0_28_28, all_0_18_18 and discharging atoms op(e1, e0) = all_0_18_18, op(e1, e0) = all_0_28_28, yields:
% 21.44/5.60 | (914) all_0_18_18 = all_0_28_28
% 21.44/5.60 |
% 21.44/5.60 | Instantiating formula (21) with e1, e0, e2, all_0_18_18 and discharging atoms op(e1, e0) = all_0_18_18, op(e1, e0) = e2, yields:
% 21.44/5.60 | (7366) all_0_18_18 = e2
% 21.44/5.60 |
% 21.44/5.60 | Combining equations (917,7363) yields a new equation:
% 21.44/5.60 | (7367) all_0_21_21 = e3
% 21.44/5.60 |
% 21.44/5.60 | Combining equations (914,7366) yields a new equation:
% 21.44/5.60 | (7368) all_0_28_28 = e2
% 21.44/5.60 |
% 21.44/5.60 | Simplifying 7368 yields:
% 21.44/5.60 | (7369) all_0_28_28 = e2
% 21.44/5.60 |
% 21.44/5.60 +-Applying beta-rule and splitting (229), into two cases.
% 21.44/5.60 |-Branch one:
% 21.44/5.60 | (923) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1)) | (all_0_25_25 = e2 & ~ (all_0_26_26 = e1))
% 21.44/5.60 |
% 21.44/5.60 +-Applying beta-rule and splitting (923), into two cases.
% 21.44/5.60 |-Branch one:
% 21.44/5.60 | (924) (all_0_21_21 = e4 & ~ (all_0_22_22 = e1)) | (all_0_23_23 = e3 & ~ (all_0_24_24 = e1))
% 21.44/5.60 |
% 21.44/5.60 +-Applying beta-rule and splitting (924), into two cases.
% 21.44/5.60 |-Branch one:
% 21.44/5.60 | (925) all_0_21_21 = e4 & ~ (all_0_22_22 = e1)
% 21.44/5.60 |
% 21.44/5.60 | Applying alpha-rule on (925) yields:
% 21.44/5.60 | (926) all_0_21_21 = e4
% 21.44/5.60 | (927) ~ (all_0_22_22 = e1)
% 21.44/5.60 |
% 21.44/5.60 | Combining equations (926,7367) yields a new equation:
% 21.44/5.60 | (515) e4 = e3
% 21.44/5.60 |
% 21.44/5.60 | Simplifying 515 yields:
% 21.44/5.60 | (516) e4 = e3
% 21.44/5.60 |
% 21.44/5.60 | Equations (516) can reduce 41 to:
% 21.44/5.60 | (269) $false
% 21.44/5.60 |
% 21.44/5.60 |-The branch is then unsatisfiable
% 21.44/5.60 |-Branch two:
% 21.44/5.60 | (931) all_0_23_23 = e3 & ~ (all_0_24_24 = e1)
% 21.44/5.60 |
% 21.44/5.60 | Applying alpha-rule on (931) yields:
% 21.44/5.60 | (932) all_0_23_23 = e3
% 21.44/5.60 | (933) ~ (all_0_24_24 = e1)
% 21.44/5.60 |
% 21.44/5.60 | Combining equations (932,7362) yields a new equation:
% 21.44/5.60 | (516) e4 = e3
% 21.44/5.60 |
% 21.44/5.60 | Equations (516) can reduce 41 to:
% 21.44/5.60 | (269) $false
% 21.44/5.60 |
% 21.44/5.60 |-The branch is then unsatisfiable
% 21.44/5.60 |-Branch two:
% 21.44/5.60 | (937) all_0_25_25 = e2 & ~ (all_0_26_26 = e1)
% 21.44/5.60 |
% 21.44/5.60 | Applying alpha-rule on (937) yields:
% 21.44/5.60 | (938) all_0_25_25 = e2
% 21.44/5.60 | (939) ~ (all_0_26_26 = e1)
% 21.44/5.60 |
% 21.44/5.61 | Combining equations (938,7283) yields a new equation:
% 21.44/5.61 | (353) e2 = e0
% 21.44/5.61 |
% 21.44/5.61 | Simplifying 353 yields:
% 21.44/5.61 | (354) e2 = e0
% 21.44/5.61 |
% 21.44/5.61 | Equations (354) can reduce 58 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (942) all_0_28_28 = e0 & ~ (all_0_29_29 = e1)
% 21.44/5.61 |
% 21.44/5.61 | Applying alpha-rule on (942) yields:
% 21.44/5.61 | (943) all_0_28_28 = e0
% 21.44/5.61 | (944) ~ (all_0_29_29 = e1)
% 21.44/5.61 |
% 21.44/5.61 | Combining equations (943,7369) yields a new equation:
% 21.44/5.61 | (354) e2 = e0
% 21.44/5.61 |
% 21.44/5.61 | Equations (354) can reduce 58 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (403) ~ (all_0_58_58 = e0)
% 21.44/5.61 | (2064) all_0_59_59 = e0
% 21.44/5.61 |
% 21.44/5.61 | Combining equations (2064,614) yields a new equation:
% 21.44/5.61 | (579) e1 = e0
% 21.44/5.61 |
% 21.44/5.61 | Equations (579) can reduce 144 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (428) ~ (all_0_51_51 = e3)
% 21.44/5.61 | (3093) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 21.44/5.61 |
% 21.44/5.61 +-Applying beta-rule and splitting (2052), into two cases.
% 21.44/5.61 |-Branch one:
% 21.44/5.61 | (400) all_0_57_57 = e0
% 21.44/5.61 |
% 21.44/5.61 | Combining equations (400,638) yields a new equation:
% 21.44/5.61 | (560) e3 = e0
% 21.44/5.61 |
% 21.44/5.61 | Equations (560) can reduce 72 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (967) ~ (all_0_57_57 = e0)
% 21.44/5.61 | (2059) all_0_58_58 = e0 | all_0_59_59 = e0
% 21.44/5.61 |
% 21.44/5.61 +-Applying beta-rule and splitting (2059), into two cases.
% 21.44/5.61 |-Branch one:
% 21.44/5.61 | (493) all_0_58_58 = e0
% 21.44/5.61 |
% 21.44/5.61 | Equations (493) can reduce 527 to:
% 21.44/5.61 | (1272) ~ (e3 = e0)
% 21.44/5.61 |
% 21.44/5.61 | Simplifying 1272 yields:
% 21.44/5.61 | (72) ~ (e3 = e0)
% 21.44/5.61 |
% 21.44/5.61 +-Applying beta-rule and splitting (3093), into two cases.
% 21.44/5.61 |-Branch one:
% 21.44/5.61 | (427) all_0_52_52 = e3
% 21.44/5.61 |
% 21.44/5.61 | Combining equations (427,397) yields a new equation:
% 21.44/5.61 | (781) e3 = e0
% 21.44/5.61 |
% 21.44/5.61 | Simplifying 781 yields:
% 21.44/5.61 | (560) e3 = e0
% 21.44/5.61 |
% 21.44/5.61 | Equations (560) can reduce 72 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (637) ~ (all_0_52_52 = e3)
% 21.44/5.61 | (3099) all_0_53_53 = e3 | all_0_54_54 = e3
% 21.44/5.61 |
% 21.44/5.61 +-Applying beta-rule and splitting (3099), into two cases.
% 21.44/5.61 |-Branch one:
% 21.44/5.61 | (861) all_0_53_53 = e3
% 21.44/5.61 |
% 21.44/5.61 | Equations (861) can reduce 796 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (796) ~ (all_0_53_53 = e3)
% 21.44/5.61 | (635) all_0_54_54 = e3
% 21.44/5.61 |
% 21.44/5.61 | Combining equations (372,635) yields a new equation:
% 21.44/5.61 | (423) e3 = e2
% 21.44/5.61 |
% 21.44/5.61 | Equations (423) can reduce 224 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (403) ~ (all_0_58_58 = e0)
% 21.44/5.61 | (2064) all_0_59_59 = e0
% 21.44/5.61 |
% 21.44/5.61 | Combining equations (614,2064) yields a new equation:
% 21.44/5.61 | (578) e1 = e0
% 21.44/5.61 |
% 21.44/5.61 | Simplifying 578 yields:
% 21.44/5.61 | (579) e1 = e0
% 21.44/5.61 |
% 21.44/5.61 | Equations (579) can reduce 144 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (609) ~ (all_0_41_41 = e3)
% 21.44/5.61 | (610) all_0_42_42 = e3
% 21.44/5.61 |
% 21.44/5.61 | Combining equations (305,610) yields a new equation:
% 21.44/5.61 | (515) e4 = e3
% 21.44/5.61 |
% 21.44/5.61 | Simplifying 515 yields:
% 21.44/5.61 | (516) e4 = e3
% 21.44/5.61 |
% 21.44/5.61 | Equations (516) can reduce 41 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (317) ~ (all_0_52_52 = e0)
% 21.44/5.61 | (400) all_0_57_57 = e0
% 21.44/5.61 |
% 21.44/5.61 | Equations (400) can reduce 967 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (537) ~ (all_0_45_45 = e4)
% 21.44/5.61 | (7434) all_0_53_53 = e4 | all_0_58_58 = e4
% 21.44/5.61 |
% 21.44/5.61 +-Applying beta-rule and splitting (7434), into two cases.
% 21.44/5.61 |-Branch one:
% 21.44/5.61 | (532) all_0_53_53 = e4
% 21.44/5.61 |
% 21.44/5.61 | Equations (532) can reduce 448 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (448) ~ (all_0_53_53 = e4)
% 21.44/5.61 | (528) all_0_58_58 = e4
% 21.44/5.61 |
% 21.44/5.61 | Equations (528) can reduce 277 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (320) ~ (all_0_39_39 = e2)
% 21.44/5.61 | (351) all_0_40_40 = e2 | all_0_41_41 = e2 | all_0_42_42 = e2
% 21.44/5.61 |
% 21.44/5.61 +-Applying beta-rule and splitting (351), into two cases.
% 21.44/5.61 |-Branch one:
% 21.44/5.61 | (382) all_0_40_40 = e2
% 21.44/5.61 |
% 21.44/5.61 | Equations (382) can reduce 342 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (342) ~ (all_0_40_40 = e2)
% 21.44/5.61 | (385) all_0_41_41 = e2 | all_0_42_42 = e2
% 21.44/5.61 |
% 21.44/5.61 +-Applying beta-rule and splitting (385), into two cases.
% 21.44/5.61 |-Branch one:
% 21.44/5.61 | (386) all_0_41_41 = e2
% 21.44/5.61 |
% 21.44/5.61 | Equations (386) can reduce 650 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (650) ~ (all_0_41_41 = e2)
% 21.44/5.61 | (358) all_0_42_42 = e2
% 21.44/5.61 |
% 21.44/5.61 | Combining equations (305,358) yields a new equation:
% 21.44/5.61 | (359) e4 = e2
% 21.44/5.61 |
% 21.44/5.61 | Simplifying 359 yields:
% 21.44/5.61 | (360) e4 = e2
% 21.44/5.61 |
% 21.44/5.61 | Equations (360) can reduce 230 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (459) ~ (all_0_43_43 = e0)
% 21.44/5.61 | (1676) all_0_44_44 = e0 | all_0_45_45 = e0 | all_0_46_46 = e0
% 21.44/5.61 |
% 21.44/5.61 +-Applying beta-rule and splitting (1676), into two cases.
% 21.44/5.61 |-Branch one:
% 21.44/5.61 | (352) all_0_44_44 = e0
% 21.44/5.61 |
% 21.44/5.61 | Combining equations (341,352) yields a new equation:
% 21.44/5.61 | (353) e2 = e0
% 21.44/5.61 |
% 21.44/5.61 | Simplifying 353 yields:
% 21.44/5.61 | (354) e2 = e0
% 21.44/5.61 |
% 21.44/5.61 | Equations (354) can reduce 58 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (356) ~ (all_0_44_44 = e0)
% 21.44/5.61 | (4115) all_0_45_45 = e0 | all_0_46_46 = e0
% 21.44/5.61 |
% 21.44/5.61 +-Applying beta-rule and splitting (4115), into two cases.
% 21.44/5.61 |-Branch one:
% 21.44/5.61 | (889) all_0_45_45 = e0
% 21.44/5.61 |
% 21.44/5.61 | Equations (889) can reduce 299 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (299) ~ (all_0_45_45 = e0)
% 21.44/5.61 | (546) all_0_46_46 = e0
% 21.44/5.61 |
% 21.44/5.61 | Equations (546) can reduce 435 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (659) ~ (all_0_44_44 = e2)
% 21.44/5.61 | (660) all_0_44_44 = e3 | all_0_44_44 = e0
% 21.44/5.61 |
% 21.44/5.61 +-Applying beta-rule and splitting (47), into two cases.
% 21.44/5.61 |-Branch one:
% 21.44/5.61 | (348) all_0_39_39 = e2
% 21.44/5.61 |
% 21.44/5.61 | Equations (348) can reduce 18 to:
% 21.44/5.61 | (1521) ~ (all_0_40_40 = e2)
% 21.44/5.61 |
% 21.44/5.61 | Simplifying 1521 yields:
% 21.44/5.61 | (342) ~ (all_0_40_40 = e2)
% 21.44/5.61 |
% 21.44/5.61 | Equations (348) can reduce 226 to:
% 21.44/5.61 | (1797) ~ (all_0_41_41 = e2)
% 21.44/5.61 |
% 21.44/5.61 | Simplifying 1797 yields:
% 21.44/5.61 | (650) ~ (all_0_41_41 = e2)
% 21.44/5.61 |
% 21.44/5.61 | Equations (348) can reduce 234 to:
% 21.44/5.61 | (1523) ~ (all_0_43_43 = e2)
% 21.44/5.61 |
% 21.44/5.61 | Simplifying 1523 yields:
% 21.44/5.61 | (321) ~ (all_0_43_43 = e2)
% 21.44/5.61 |
% 21.44/5.61 | Equations (348) can reduce 53 to:
% 21.44/5.61 | (2655) ~ (all_0_56_56 = e2)
% 21.44/5.61 |
% 21.44/5.61 | Simplifying 2655 yields:
% 21.44/5.61 | (377) ~ (all_0_56_56 = e2)
% 21.44/5.61 |
% 21.44/5.61 | From (348) and (161) follows:
% 21.44/5.61 | (7477) op(e3, e2) = all_0_4_4
% 21.44/5.61 |
% 21.44/5.61 +-Applying beta-rule and splitting (113), into two cases.
% 21.44/5.61 |-Branch one:
% 21.44/5.61 | (382) all_0_40_40 = e2
% 21.44/5.61 |
% 21.44/5.61 | Equations (382) can reduce 342 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (342) ~ (all_0_40_40 = e2)
% 21.44/5.61 | (1101) all_0_44_44 = e2 | all_0_52_52 = e2 | all_0_57_57 = e2
% 21.44/5.61 |
% 21.44/5.61 +-Applying beta-rule and splitting (1101), into two cases.
% 21.44/5.61 |-Branch one:
% 21.44/5.61 | (341) all_0_44_44 = e2
% 21.44/5.61 |
% 21.44/5.61 | Equations (341) can reduce 659 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (659) ~ (all_0_44_44 = e2)
% 21.44/5.61 | (1109) all_0_52_52 = e2 | all_0_57_57 = e2
% 21.44/5.61 |
% 21.44/5.61 +-Applying beta-rule and splitting (1109), into two cases.
% 21.44/5.61 |-Branch one:
% 21.44/5.61 | (816) all_0_52_52 = e2
% 21.44/5.61 |
% 21.44/5.61 | Equations (816) can reduce 187 to:
% 21.44/5.61 | (342) ~ (all_0_40_40 = e2)
% 21.44/5.61 |
% 21.44/5.61 | Equations (816) can reduce 121 to:
% 21.44/5.61 | (659) ~ (all_0_44_44 = e2)
% 21.44/5.61 |
% 21.44/5.61 | Equations (816) can reduce 194 to:
% 21.44/5.61 | (255) ~ (all_0_51_51 = e2)
% 21.44/5.61 |
% 21.44/5.61 | Equations (816) can reduce 71 to:
% 21.44/5.61 | (258) ~ (all_0_53_53 = e2)
% 21.44/5.61 |
% 21.44/5.61 | Simplifying 258 yields:
% 21.44/5.61 | (259) ~ (all_0_53_53 = e2)
% 21.44/5.61 |
% 21.44/5.61 | Equations (816) can reduce 124 to:
% 21.44/5.61 | (2716) ~ (all_0_57_57 = e2)
% 21.44/5.61 |
% 21.44/5.61 | Simplifying 2716 yields:
% 21.44/5.61 | (378) ~ (all_0_57_57 = e2)
% 21.44/5.61 |
% 21.44/5.61 | From (816) and (69) follows:
% 21.44/5.61 | (7494) op(e2, e2) = all_0_17_17
% 21.44/5.61 |
% 21.44/5.61 +-Applying beta-rule and splitting (225), into two cases.
% 21.44/5.61 |-Branch one:
% 21.44/5.61 | (661) all_0_43_43 = e2
% 21.44/5.61 |
% 21.44/5.61 | Equations (661) can reduce 321 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (321) ~ (all_0_43_43 = e2)
% 21.44/5.61 | (664) all_0_44_44 = e2 | all_0_45_45 = e2 | all_0_46_46 = e2
% 21.44/5.61 |
% 21.44/5.61 +-Applying beta-rule and splitting (664), into two cases.
% 21.44/5.61 |-Branch one:
% 21.44/5.61 | (341) all_0_44_44 = e2
% 21.44/5.61 |
% 21.44/5.61 | Equations (341) can reduce 659 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (659) ~ (all_0_44_44 = e2)
% 21.44/5.61 | (1120) all_0_45_45 = e2 | all_0_46_46 = e2
% 21.44/5.61 |
% 21.44/5.61 +-Applying beta-rule and splitting (1120), into two cases.
% 21.44/5.61 |-Branch one:
% 21.44/5.61 | (694) all_0_45_45 = e2
% 21.44/5.61 |
% 21.44/5.61 | Equations (694) can reduce 390 to:
% 21.44/5.61 | (269) $false
% 21.44/5.61 |
% 21.44/5.61 |-The branch is then unsatisfiable
% 21.44/5.61 |-Branch two:
% 21.44/5.61 | (390) ~ (all_0_45_45 = e2)
% 21.44/5.61 | (364) all_0_46_46 = e2
% 21.44/5.61 |
% 21.44/5.61 | Equations (364) can reduce 210 to:
% 21.44/5.61 | (659) ~ (all_0_44_44 = e2)
% 21.44/5.61 |
% 21.44/5.61 | Equations (364) can reduce 201 to:
% 21.44/5.61 | (390) ~ (all_0_45_45 = e2)
% 21.44/5.61 |
% 21.44/5.61 | Equations (364) can reduce 59 to:
% 21.44/5.61 | (260) ~ (all_0_54_54 = e2)
% 21.44/5.61 |
% 21.44/5.61 | Simplifying 260 yields:
% 21.44/5.61 | (261) ~ (all_0_54_54 = e2)
% 21.44/5.61 |
% 21.44/5.61 | Equations (364) can reduce 150 to:
% 21.44/5.61 | (1842) ~ (all_0_59_59 = e2)
% 21.44/5.61 |
% 21.44/5.61 | Simplifying 1842 yields:
% 21.44/5.61 | (1843) ~ (all_0_59_59 = e2)
% 21.44/5.61 |
% 21.44/5.61 | Equations (364) can reduce 310 to:
% 21.44/5.61 | (326) ~ (e4 = e2)
% 21.44/5.61 |
% 21.44/5.61 | Simplifying 326 yields:
% 21.44/5.61 | (230) ~ (e4 = e2)
% 21.44/5.61 |
% 21.44/5.61 | Equations (364) can reduce 435 to:
% 21.44/5.61 | (58) ~ (e2 = e0)
% 21.44/5.61 |
% 21.44/5.61 | From (364) and (105) follows:
% 21.44/5.61 | (7516) op(e3, e2) = all_0_33_33
% 21.44/5.61 |
% 21.44/5.61 +-Applying beta-rule and splitting (110), into two cases.
% 21.44/5.61 |-Branch one:
% 21.44/5.61 | (352) all_0_44_44 = e0
% 21.44/5.61 |
% 21.44/5.61 | Equations (352) can reduce 35 to:
% 21.44/5.61 | (102) ~ (all_0_40_40 = e0)
% 21.44/5.61 |
% 21.44/5.61 | Equations (352) can reduce 228 to:
% 21.44/5.61 | (459) ~ (all_0_43_43 = e0)
% 21.44/5.61 |
% 21.44/5.61 | Equations (352) can reduce 117 to:
% 21.44/5.61 | (1140) ~ (all_0_45_45 = e0)
% 21.44/5.61 |
% 21.44/5.61 | Simplifying 1140 yields:
% 21.44/5.61 | (299) ~ (all_0_45_45 = e0)
% 21.44/5.61 |
% 21.44/5.61 | Equations (352) can reduce 240 to:
% 21.44/5.61 | (6914) ~ (all_0_57_57 = e0)
% 21.44/5.61 |
% 21.44/5.61 | Simplifying 6914 yields:
% 21.44/5.62 | (967) ~ (all_0_57_57 = e0)
% 21.44/5.62 |
% 21.44/5.62 | Equations (352) can reduce 190 to:
% 21.44/5.62 | (404) ~ (e4 = e0)
% 21.44/5.62 |
% 21.44/5.62 | Simplifying 404 yields:
% 21.44/5.62 | (11) ~ (e4 = e0)
% 21.44/5.62 |
% 21.44/5.62 | Equations (352) can reduce 659 to:
% 21.44/5.62 | (406) ~ (e2 = e0)
% 21.44/5.62 |
% 21.44/5.62 | Simplifying 406 yields:
% 21.44/5.62 | (58) ~ (e2 = e0)
% 21.44/5.62 |
% 21.44/5.62 | From (352) and (74) follows:
% 21.44/5.62 | (7528) op(e3, e2) = e0
% 21.44/5.62 |
% 21.44/5.62 | From (352) and (205) follows:
% 21.44/5.62 | (1827) op(e2, e0) = all_0_15_15
% 21.44/5.62 |
% 21.44/5.62 | Instantiating formula (21) with e3, e2, all_0_33_33, all_0_4_4 and discharging atoms op(e3, e2) = all_0_4_4, op(e3, e2) = all_0_33_33, yields:
% 21.44/5.62 | (7530) all_0_4_4 = all_0_33_33
% 21.44/5.62 |
% 21.44/5.62 | Instantiating formula (21) with e3, e2, e0, all_0_4_4 and discharging atoms op(e3, e2) = all_0_4_4, op(e3, e2) = e0, yields:
% 21.44/5.62 | (7531) all_0_4_4 = e0
% 21.44/5.62 |
% 21.44/5.62 | Instantiating formula (21) with e2, e2, all_0_17_17, e4 and discharging atoms op(e2, e2) = all_0_17_17, op(e2, e2) = e4, yields:
% 21.44/5.62 | (7532) all_0_17_17 = e4
% 21.44/5.62 |
% 21.44/5.62 | Instantiating formula (21) with e2, e0, all_0_15_15, e0 and discharging atoms op(e2, e0) = all_0_15_15, op(e2, e0) = e0, yields:
% 21.44/5.62 | (1850) all_0_15_15 = e0
% 21.44/5.62 |
% 21.44/5.62 | Combining equations (7530,7531) yields a new equation:
% 21.44/5.62 | (7534) all_0_33_33 = e0
% 21.44/5.62 |
% 21.44/5.62 | Simplifying 7534 yields:
% 21.44/5.62 | (1637) all_0_33_33 = e0
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (104), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (1639) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0)) | (all_0_34_34 = e2 & ~ (all_0_35_35 = e0))
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (1639), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (1640) (all_0_30_30 = e4 & ~ (all_0_31_31 = e0)) | (all_0_32_32 = e3 & ~ (all_0_33_33 = e0))
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (1640), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (1641) all_0_30_30 = e4 & ~ (all_0_31_31 = e0)
% 21.44/5.62 |
% 21.44/5.62 | Applying alpha-rule on (1641) yields:
% 21.44/5.62 | (1642) all_0_30_30 = e4
% 21.44/5.62 | (1643) ~ (all_0_31_31 = e0)
% 21.44/5.62 |
% 21.44/5.62 | Combining equations (6779,1642) yields a new equation:
% 21.44/5.62 | (360) e4 = e2
% 21.44/5.62 |
% 21.44/5.62 | Equations (360) can reduce 230 to:
% 21.44/5.62 | (269) $false
% 21.44/5.62 |
% 21.44/5.62 |-The branch is then unsatisfiable
% 21.44/5.62 |-Branch two:
% 21.44/5.62 | (1645) all_0_32_32 = e3 & ~ (all_0_33_33 = e0)
% 21.44/5.62 |
% 21.44/5.62 | Applying alpha-rule on (1645) yields:
% 21.44/5.62 | (1646) all_0_32_32 = e3
% 21.44/5.62 | (1647) ~ (all_0_33_33 = e0)
% 21.44/5.62 |
% 21.44/5.62 | Equations (1637) can reduce 1647 to:
% 21.44/5.62 | (269) $false
% 21.44/5.62 |
% 21.44/5.62 |-The branch is then unsatisfiable
% 21.44/5.62 |-Branch two:
% 21.44/5.62 | (1649) all_0_34_34 = e2 & ~ (all_0_35_35 = e0)
% 21.44/5.62 |
% 21.44/5.62 | Applying alpha-rule on (1649) yields:
% 21.44/5.62 | (1650) all_0_34_34 = e2
% 21.44/5.62 | (1651) ~ (all_0_35_35 = e0)
% 21.44/5.62 |
% 21.44/5.62 | Combining equations (1491,1650) yields a new equation:
% 21.44/5.62 | (1868) all_0_59_59 = e2
% 21.44/5.62 |
% 21.44/5.62 | Simplifying 1868 yields:
% 21.44/5.62 | (375) all_0_59_59 = e2
% 21.44/5.62 |
% 21.44/5.62 | Equations (375) can reduce 1843 to:
% 21.44/5.62 | (269) $false
% 21.44/5.62 |
% 21.44/5.62 |-The branch is then unsatisfiable
% 21.44/5.62 |-Branch two:
% 21.44/5.62 | (1653) all_0_36_36 = e1 & ~ (all_0_37_37 = e0)
% 21.44/5.62 |
% 21.44/5.62 | Applying alpha-rule on (1653) yields:
% 21.44/5.62 | (1654) all_0_36_36 = e1
% 21.44/5.62 | (1655) ~ (all_0_37_37 = e0)
% 21.44/5.62 |
% 21.44/5.62 | From (1654) and (235) follows:
% 21.44/5.62 | (1874) op(e0, all_0_54_54) = e1
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (17), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (382) all_0_40_40 = e2
% 21.44/5.62 |
% 21.44/5.62 | Equations (382) can reduce 342 to:
% 21.44/5.62 | (269) $false
% 21.44/5.62 |
% 21.44/5.62 |-The branch is then unsatisfiable
% 21.44/5.62 |-Branch two:
% 21.44/5.62 | (342) ~ (all_0_40_40 = e2)
% 21.44/5.62 | (1093) all_0_40_40 = e3 | all_0_40_40 = e1
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (133), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (504) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2)) | (all_0_17_17 = e1 & ~ (all_0_18_18 = e2))
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (504), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (505) (all_0_13_13 = e4 & ~ (all_0_14_14 = e2)) | (all_0_15_15 = e3 & ~ (all_0_16_16 = e2))
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (505), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (506) all_0_13_13 = e4 & ~ (all_0_14_14 = e2)
% 21.44/5.62 |
% 21.44/5.62 | Applying alpha-rule on (506) yields:
% 21.44/5.62 | (507) all_0_13_13 = e4
% 21.44/5.62 | (508) ~ (all_0_14_14 = e2)
% 21.44/5.62 |
% 21.44/5.62 | From (507) and (156) follows:
% 21.44/5.62 | (1884) op(e2, all_0_40_40) = e4
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (246), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (413) all_0_40_40 = e1
% 21.44/5.62 |
% 21.44/5.62 | Equations (413) can reduce 88 to:
% 21.44/5.62 | (1597) ~ (all_0_41_41 = e1)
% 21.44/5.62 |
% 21.44/5.62 | Simplifying 1597 yields:
% 21.44/5.62 | (1315) ~ (all_0_41_41 = e1)
% 21.44/5.62 |
% 21.44/5.62 | Equations (413) can reduce 168 to:
% 21.44/5.62 | (824) ~ (all_0_57_57 = e1)
% 21.44/5.62 |
% 21.44/5.62 | Simplifying 824 yields:
% 21.44/5.62 | (581) ~ (all_0_57_57 = e1)
% 21.44/5.62 |
% 21.44/5.62 | Equations (413) can reduce 64 to:
% 21.44/5.62 | (826) ~ (e4 = e1)
% 21.44/5.62 |
% 21.44/5.62 | Simplifying 826 yields:
% 21.44/5.62 | (251) ~ (e4 = e1)
% 21.44/5.62 |
% 21.44/5.62 | Equations (413) can reduce 102 to:
% 21.44/5.62 | (144) ~ (e1 = e0)
% 21.44/5.62 |
% 21.44/5.62 | From (413) and (1884) follows:
% 21.44/5.62 | (1890) op(e2, e1) = e4
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (134), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (867) all_0_57_57 = e2
% 21.44/5.62 |
% 21.44/5.62 | Equations (867) can reduce 378 to:
% 21.44/5.62 | (269) $false
% 21.44/5.62 |
% 21.44/5.62 |-The branch is then unsatisfiable
% 21.44/5.62 |-Branch two:
% 21.44/5.62 | (378) ~ (all_0_57_57 = e2)
% 21.44/5.62 | (870) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (94), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (386) all_0_41_41 = e2
% 21.44/5.62 |
% 21.44/5.62 | Equations (386) can reduce 650 to:
% 21.44/5.62 | (269) $false
% 21.44/5.62 |
% 21.44/5.62 |-The branch is then unsatisfiable
% 21.44/5.62 |-Branch two:
% 21.44/5.62 | (650) ~ (all_0_41_41 = e2)
% 21.44/5.62 | (1903) all_0_41_41 = e4 | all_0_41_41 = e3 | all_0_41_41 = e1
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (870), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (577) all_0_57_57 = e1
% 21.44/5.62 |
% 21.44/5.62 | Equations (577) can reduce 581 to:
% 21.44/5.62 | (269) $false
% 21.44/5.62 |
% 21.44/5.62 |-The branch is then unsatisfiable
% 21.44/5.62 |-Branch two:
% 21.44/5.62 | (581) ~ (all_0_57_57 = e1)
% 21.44/5.62 | (874) all_0_57_57 = e3 | all_0_57_57 = e0
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (184), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (443) all_0_39_39 = e3
% 21.44/5.62 |
% 21.44/5.62 | Combining equations (443,348) yields a new equation:
% 21.44/5.62 | (606) e3 = e2
% 21.44/5.62 |
% 21.44/5.62 | Simplifying 606 yields:
% 21.44/5.62 | (423) e3 = e2
% 21.44/5.62 |
% 21.44/5.62 | Equations (423) can reduce 224 to:
% 21.44/5.62 | (269) $false
% 21.44/5.62 |
% 21.44/5.62 |-The branch is then unsatisfiable
% 21.44/5.62 |-Branch two:
% 21.44/5.62 | (540) ~ (all_0_39_39 = e3)
% 21.44/5.62 | (541) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (874), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (400) all_0_57_57 = e0
% 21.44/5.62 |
% 21.44/5.62 | Equations (400) can reduce 967 to:
% 21.44/5.62 | (269) $false
% 21.44/5.62 |
% 21.44/5.62 |-The branch is then unsatisfiable
% 21.44/5.62 |-Branch two:
% 21.44/5.62 | (967) ~ (all_0_57_57 = e0)
% 21.44/5.62 | (638) all_0_57_57 = e3
% 21.44/5.62 |
% 21.44/5.62 | Equations (638) can reduce 95 to:
% 21.44/5.62 | (2131) ~ (all_0_59_59 = e3)
% 21.44/5.62 |
% 21.44/5.62 | Simplifying 2131 yields:
% 21.44/5.62 | (2132) ~ (all_0_59_59 = e3)
% 21.44/5.62 |
% 21.44/5.62 | Equations (638) can reduce 173 to:
% 21.44/5.62 | (498) ~ (e4 = e3)
% 21.44/5.62 |
% 21.44/5.62 | Simplifying 498 yields:
% 21.44/5.62 | (41) ~ (e4 = e3)
% 21.44/5.62 |
% 21.44/5.62 | Equations (638) can reduce 581 to:
% 21.44/5.62 | (146) ~ (e3 = e1)
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (169), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (610) all_0_42_42 = e3
% 21.44/5.62 |
% 21.44/5.62 | Combining equations (305,610) yields a new equation:
% 21.44/5.62 | (515) e4 = e3
% 21.44/5.62 |
% 21.44/5.62 | Simplifying 515 yields:
% 21.44/5.62 | (516) e4 = e3
% 21.44/5.62 |
% 21.44/5.62 | Equations (516) can reduce 41 to:
% 21.44/5.62 | (269) $false
% 21.44/5.62 |
% 21.44/5.62 |-The branch is then unsatisfiable
% 21.44/5.62 |-Branch two:
% 21.44/5.62 | (1924) ~ (all_0_42_42 = e3)
% 21.44/5.62 | (1925) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 21.44/5.62 |
% 21.44/5.62 | Equations (305) can reduce 1924 to:
% 21.44/5.62 | (41) ~ (e4 = e3)
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (296), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (401) ~ (all_0_56_56 = e0)
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (211), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (632) all_0_56_56 = e0
% 21.44/5.62 |
% 21.44/5.62 | Equations (632) can reduce 401 to:
% 21.44/5.62 | (269) $false
% 21.44/5.62 |
% 21.44/5.62 |-The branch is then unsatisfiable
% 21.44/5.62 |-Branch two:
% 21.44/5.62 | (401) ~ (all_0_56_56 = e0)
% 21.44/5.62 | (2052) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (541), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (417) all_0_40_40 = e3
% 21.44/5.62 |
% 21.44/5.62 | Combining equations (413,417) yields a new equation:
% 21.44/5.62 | (418) e3 = e1
% 21.44/5.62 |
% 21.44/5.62 | Equations (418) can reduce 146 to:
% 21.44/5.62 | (269) $false
% 21.44/5.62 |
% 21.44/5.62 |-The branch is then unsatisfiable
% 21.44/5.62 |-Branch two:
% 21.44/5.62 | (420) ~ (all_0_40_40 = e3)
% 21.44/5.62 | (604) all_0_41_41 = e3 | all_0_42_42 = e3
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (604), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (605) all_0_41_41 = e3
% 21.44/5.62 |
% 21.44/5.62 | Equations (605) can reduce 122 to:
% 21.44/5.62 | (688) ~ (all_0_45_45 = e3)
% 21.44/5.62 |
% 21.44/5.62 | Simplifying 688 yields:
% 21.44/5.62 | (689) ~ (all_0_45_45 = e3)
% 21.44/5.62 |
% 21.44/5.62 | Equations (605) can reduce 106 to:
% 21.44/5.62 | (3866) ~ (all_0_53_53 = e3)
% 21.44/5.62 |
% 21.44/5.62 | Simplifying 3866 yields:
% 21.44/5.62 | (796) ~ (all_0_53_53 = e3)
% 21.44/5.62 |
% 21.44/5.62 | Equations (605) can reduce 208 to:
% 21.44/5.62 | (788) ~ (all_0_58_58 = e3)
% 21.44/5.62 |
% 21.44/5.62 | Simplifying 788 yields:
% 21.44/5.62 | (527) ~ (all_0_58_58 = e3)
% 21.44/5.62 |
% 21.44/5.62 | Equations (605) can reduce 650 to:
% 21.44/5.62 | (224) ~ (e3 = e2)
% 21.44/5.62 |
% 21.44/5.62 | Equations (605) can reduce 1315 to:
% 21.44/5.62 | (146) ~ (e3 = e1)
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (171), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (433) all_0_43_43 = e0
% 21.44/5.62 |
% 21.44/5.62 | Equations (433) can reduce 459 to:
% 21.44/5.62 | (269) $false
% 21.44/5.62 |
% 21.44/5.62 |-The branch is then unsatisfiable
% 21.44/5.62 |-Branch two:
% 21.44/5.62 | (459) ~ (all_0_43_43 = e0)
% 21.44/5.62 | (622) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (20), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (1575) all_0_56_56 = e2
% 21.44/5.62 |
% 21.44/5.62 | Equations (1575) can reduce 377 to:
% 21.44/5.62 | (269) $false
% 21.44/5.62 |
% 21.44/5.62 |-The branch is then unsatisfiable
% 21.44/5.62 |-Branch two:
% 21.44/5.62 | (377) ~ (all_0_56_56 = e2)
% 21.44/5.62 | (1578) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e1 | all_0_56_56 = e0
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (212), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (375) all_0_59_59 = e2
% 21.44/5.62 |
% 21.44/5.62 | Equations (375) can reduce 1843 to:
% 21.44/5.62 | (269) $false
% 21.44/5.62 |
% 21.44/5.62 |-The branch is then unsatisfiable
% 21.44/5.62 |-Branch two:
% 21.44/5.62 | (1843) ~ (all_0_59_59 = e2)
% 21.44/5.62 | (2151) all_0_59_59 = e4 | all_0_59_59 = e3 | all_0_59_59 = e1 | all_0_59_59 = e0
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (1925), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (462) all_0_46_46 = e3
% 21.44/5.62 |
% 21.44/5.62 | Combining equations (364,462) yields a new equation:
% 21.44/5.62 | (423) e3 = e2
% 21.44/5.62 |
% 21.44/5.62 | Equations (423) can reduce 224 to:
% 21.44/5.62 | (269) $false
% 21.44/5.62 |
% 21.44/5.62 |-The branch is then unsatisfiable
% 21.44/5.62 |-Branch two:
% 21.44/5.62 | (618) ~ (all_0_46_46 = e3)
% 21.44/5.62 | (1930) all_0_54_54 = e3 | all_0_59_59 = e3
% 21.44/5.62 |
% 21.44/5.62 | Equations (364) can reduce 618 to:
% 21.44/5.62 | (328) ~ (e3 = e2)
% 21.44/5.62 |
% 21.44/5.62 | Simplifying 328 yields:
% 21.44/5.62 | (224) ~ (e3 = e2)
% 21.44/5.62 |
% 21.44/5.62 +-Applying beta-rule and splitting (2151), into two cases.
% 21.44/5.62 |-Branch one:
% 21.44/5.62 | (614) all_0_59_59 = e1
% 21.44/5.62 |
% 21.44/5.63 | Equations (614) can reduce 130 to:
% 21.44/5.63 | (575) ~ (all_0_56_56 = e1)
% 21.44/5.63 |
% 21.44/5.63 | Equations (614) can reduce 2132 to:
% 21.44/5.63 | (597) ~ (e3 = e1)
% 21.44/5.63 |
% 21.44/5.63 | Simplifying 597 yields:
% 21.44/5.63 | (146) ~ (e3 = e1)
% 21.44/5.63 |
% 21.44/5.63 | Equations (614) can reduce 1480 to:
% 21.44/5.63 | (144) ~ (e1 = e0)
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (1930), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (635) all_0_54_54 = e3
% 21.44/5.63 |
% 21.44/5.63 | Equations (635) can reduce 119 to:
% 21.44/5.63 | (796) ~ (all_0_53_53 = e3)
% 21.44/5.63 |
% 21.44/5.63 | Equations (635) can reduce 312 to:
% 21.44/5.63 | (498) ~ (e4 = e3)
% 21.44/5.63 |
% 21.44/5.63 | Simplifying 498 yields:
% 21.44/5.63 | (41) ~ (e4 = e3)
% 21.44/5.63 |
% 21.44/5.63 | Equations (635) can reduce 261 to:
% 21.44/5.63 | (224) ~ (e3 = e2)
% 21.44/5.63 |
% 21.44/5.63 | Equations (635) can reduce 1478 to:
% 21.44/5.63 | (72) ~ (e3 = e0)
% 21.44/5.63 |
% 21.44/5.63 | From (635) and (1874) follows:
% 21.44/5.63 | (2181) op(e0, e3) = e1
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (622), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (623) all_0_47_47 = e0
% 21.44/5.63 |
% 21.44/5.63 | Combining equations (469,623) yields a new equation:
% 21.44/5.63 | (578) e1 = e0
% 21.44/5.63 |
% 21.44/5.63 | Simplifying 578 yields:
% 21.44/5.63 | (579) e1 = e0
% 21.44/5.63 |
% 21.44/5.63 | Equations (579) can reduce 144 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (297) ~ (all_0_47_47 = e0)
% 21.44/5.63 | (628) all_0_51_51 = e0 | all_0_56_56 = e0
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (162), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (559) all_0_43_43 = e3
% 21.44/5.63 |
% 21.44/5.63 | Equations (559) can reduce 232 to:
% 21.44/5.63 | (1182) ~ (all_0_56_56 = e3)
% 21.44/5.63 |
% 21.44/5.63 | Simplifying 1182 yields:
% 21.44/5.63 | (1183) ~ (all_0_56_56 = e3)
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (14), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (438) all_0_43_43 = e4
% 21.44/5.63 |
% 21.44/5.63 | Combining equations (438,559) yields a new equation:
% 21.44/5.63 | (515) e4 = e3
% 21.44/5.63 |
% 21.44/5.63 | Simplifying 515 yields:
% 21.44/5.63 | (516) e4 = e3
% 21.44/5.63 |
% 21.44/5.63 | Equations (516) can reduce 41 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (441) ~ (all_0_43_43 = e4)
% 21.44/5.63 | (442) all_0_45_45 = e4 | all_0_46_46 = e4
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (442), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (444) all_0_45_45 = e4
% 21.44/5.63 |
% 21.44/5.63 | Equations (444) can reduce 142 to:
% 21.44/5.63 | (447) ~ (all_0_53_53 = e4)
% 21.44/5.63 |
% 21.44/5.63 | Simplifying 447 yields:
% 21.44/5.63 | (448) ~ (all_0_53_53 = e4)
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (628), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (629) all_0_51_51 = e0
% 21.44/5.63 |
% 21.44/5.63 | Equations (629) can reduce 30 to:
% 21.44/5.63 | (764) ~ (all_0_53_53 = e0)
% 21.44/5.63 |
% 21.44/5.63 | Simplifying 764 yields:
% 21.44/5.63 | (765) ~ (all_0_53_53 = e0)
% 21.44/5.63 |
% 21.44/5.63 | Equations (629) can reduce 16 to:
% 21.44/5.63 | (1556) ~ (all_0_56_56 = e0)
% 21.44/5.63 |
% 21.44/5.63 | Simplifying 1556 yields:
% 21.44/5.63 | (401) ~ (all_0_56_56 = e0)
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (27), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (849) all_0_53_53 = e2
% 21.44/5.63 |
% 21.44/5.63 | Equations (849) can reduce 259 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (259) ~ (all_0_53_53 = e2)
% 21.44/5.63 | (852) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (1578), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (480) all_0_56_56 = e1
% 21.44/5.63 |
% 21.44/5.63 | Equations (480) can reduce 575 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (575) ~ (all_0_56_56 = e1)
% 21.44/5.63 | (1619) all_0_56_56 = e4 | all_0_56_56 = e3 | all_0_56_56 = e0
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (852), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (853) all_0_53_53 = e1
% 21.44/5.63 |
% 21.44/5.63 | Equations (853) can reduce 259 to:
% 21.44/5.63 | (414) ~ (e2 = e1)
% 21.44/5.63 |
% 21.44/5.63 | Simplifying 414 yields:
% 21.44/5.63 | (148) ~ (e2 = e1)
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (1619), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (632) all_0_56_56 = e0
% 21.44/5.63 |
% 21.44/5.63 | Equations (632) can reduce 401 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (401) ~ (all_0_56_56 = e0)
% 21.44/5.63 | (1630) all_0_56_56 = e4 | all_0_56_56 = e3
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (1630), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (567) all_0_56_56 = e3
% 21.44/5.63 |
% 21.44/5.63 | Equations (567) can reduce 1183 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (1183) ~ (all_0_56_56 = e3)
% 21.44/5.63 | (1658) all_0_56_56 = e4
% 21.44/5.63 |
% 21.44/5.63 | From (1658) and (202) follows:
% 21.44/5.63 | (4792) op(e0, e3) = e4
% 21.44/5.63 |
% 21.44/5.63 | Instantiating formula (21) with e2, e1, e4, e2 and discharging atoms op(e2, e1) = e4, op(e2, e1) = e2, yields:
% 21.44/5.63 | (360) e4 = e2
% 21.44/5.63 |
% 21.44/5.63 | Instantiating formula (21) with e0, e3, e1, e4 and discharging atoms op(e0, e3) = e4, op(e0, e3) = e1, yields:
% 21.44/5.63 | (477) e4 = e1
% 21.44/5.63 |
% 21.44/5.63 | Combining equations (360,477) yields a new equation:
% 21.44/5.63 | (470) e2 = e1
% 21.44/5.63 |
% 21.44/5.63 | Simplifying 470 yields:
% 21.44/5.63 | (471) e2 = e1
% 21.44/5.63 |
% 21.44/5.63 | Equations (471) can reduce 148 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (823) ~ (all_0_53_53 = e1)
% 21.44/5.63 | (856) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e0
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (856), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (857) all_0_53_53 = e0
% 21.44/5.63 |
% 21.44/5.63 | Equations (857) can reduce 765 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (765) ~ (all_0_53_53 = e0)
% 21.44/5.63 | (860) all_0_53_53 = e4 | all_0_53_53 = e3
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (860), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (861) all_0_53_53 = e3
% 21.44/5.63 |
% 21.44/5.63 | Equations (861) can reduce 796 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (796) ~ (all_0_53_53 = e3)
% 21.44/5.63 | (532) all_0_53_53 = e4
% 21.44/5.63 |
% 21.44/5.63 | Equations (532) can reduce 448 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (432) ~ (all_0_51_51 = e0)
% 21.44/5.63 | (632) all_0_56_56 = e0
% 21.44/5.63 |
% 21.44/5.63 | Equations (632) can reduce 401 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (537) ~ (all_0_45_45 = e4)
% 21.44/5.63 | (538) all_0_46_46 = e4
% 21.44/5.63 |
% 21.44/5.63 | Combining equations (364,538) yields a new equation:
% 21.44/5.63 | (360) e4 = e2
% 21.44/5.63 |
% 21.44/5.63 | Equations (360) can reduce 230 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (562) ~ (all_0_43_43 = e3)
% 21.44/5.63 | (1193) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (1193), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (422) all_0_44_44 = e3
% 21.44/5.63 |
% 21.44/5.63 | Combining equations (352,422) yields a new equation:
% 21.44/5.63 | (560) e3 = e0
% 21.44/5.63 |
% 21.44/5.63 | Equations (560) can reduce 72 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (425) ~ (all_0_44_44 = e3)
% 21.44/5.63 | (1203) all_0_45_45 = e3 | all_0_46_46 = e3
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (1203), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (1087) all_0_45_45 = e3
% 21.44/5.63 |
% 21.44/5.63 | Equations (1087) can reduce 689 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (689) ~ (all_0_45_45 = e3)
% 21.44/5.63 | (462) all_0_46_46 = e3
% 21.44/5.63 |
% 21.44/5.63 | Combining equations (364,462) yields a new equation:
% 21.44/5.63 | (423) e3 = e2
% 21.44/5.63 |
% 21.44/5.63 | Equations (423) can reduce 224 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (430) ~ (all_0_54_54 = e3)
% 21.44/5.63 | (1070) all_0_59_59 = e3
% 21.44/5.63 |
% 21.44/5.63 | Combining equations (1070,614) yields a new equation:
% 21.44/5.63 | (572) e3 = e1
% 21.44/5.63 |
% 21.44/5.63 | Simplifying 572 yields:
% 21.44/5.63 | (418) e3 = e1
% 21.44/5.63 |
% 21.44/5.63 | Equations (418) can reduce 146 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (2222) ~ (all_0_59_59 = e1)
% 21.44/5.63 | (2223) all_0_59_59 = e4 | all_0_59_59 = e3 | all_0_59_59 = e0
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (43), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (480) all_0_56_56 = e1
% 21.44/5.63 |
% 21.44/5.63 | Equations (480) can reduce 575 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (575) ~ (all_0_56_56 = e1)
% 21.44/5.63 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (84), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (832) all_0_42_42 = e1
% 21.44/5.63 |
% 21.44/5.63 | Combining equations (305,832) yields a new equation:
% 21.44/5.63 | (476) e4 = e1
% 21.44/5.63 |
% 21.44/5.63 | Simplifying 476 yields:
% 21.44/5.63 | (477) e4 = e1
% 21.44/5.63 |
% 21.44/5.63 | Equations (477) can reduce 251 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (836) ~ (all_0_42_42 = e1)
% 21.44/5.63 | (837) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (837), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (596) all_0_49_49 = e1
% 21.44/5.63 |
% 21.44/5.63 | Combining equations (965,596) yields a new equation:
% 21.44/5.63 | (579) e1 = e0
% 21.44/5.63 |
% 21.44/5.63 | Equations (579) can reduce 144 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (960) ~ (all_0_49_49 = e1)
% 21.44/5.63 | (961) all_0_54_54 = e1 | all_0_59_59 = e1
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (576), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (577) all_0_57_57 = e1
% 21.44/5.63 |
% 21.44/5.63 | Combining equations (577,638) yields a new equation:
% 21.44/5.63 | (418) e3 = e1
% 21.44/5.63 |
% 21.44/5.63 | Equations (418) can reduce 146 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (581) ~ (all_0_57_57 = e1)
% 21.44/5.63 | (582) all_0_58_58 = e1 | all_0_59_59 = e1
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (961), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (1592) all_0_54_54 = e1
% 21.44/5.63 |
% 21.44/5.63 | Equations (1592) can reduce 159 to:
% 21.44/5.63 | (479) ~ (all_0_51_51 = e1)
% 21.44/5.63 |
% 21.44/5.63 | Equations (1592) can reduce 81 to:
% 21.44/5.63 | (5696) ~ (all_0_59_59 = e1)
% 21.44/5.63 |
% 21.44/5.63 | Simplifying 5696 yields:
% 21.44/5.63 | (2222) ~ (all_0_59_59 = e1)
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (93), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (564) all_0_51_51 = e3
% 21.44/5.63 |
% 21.44/5.63 | Equations (564) can reduce 479 to:
% 21.44/5.63 | (146) ~ (e3 = e1)
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (1930), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (635) all_0_54_54 = e3
% 21.44/5.63 |
% 21.44/5.63 | Combining equations (1592,635) yields a new equation:
% 21.44/5.63 | (418) e3 = e1
% 21.44/5.63 |
% 21.44/5.63 | Equations (418) can reduce 146 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (430) ~ (all_0_54_54 = e3)
% 21.44/5.63 | (1070) all_0_59_59 = e3
% 21.44/5.63 |
% 21.44/5.63 | Equations (1070) can reduce 2132 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (428) ~ (all_0_51_51 = e3)
% 21.44/5.63 | (3093) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (582), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (489) all_0_58_58 = e1
% 21.44/5.63 |
% 21.44/5.63 | Equations (489) can reduce 527 to:
% 21.44/5.63 | (597) ~ (e3 = e1)
% 21.44/5.63 |
% 21.44/5.63 | Simplifying 597 yields:
% 21.44/5.63 | (146) ~ (e3 = e1)
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (3093), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (427) all_0_52_52 = e3
% 21.44/5.63 |
% 21.44/5.63 | Combining equations (816,427) yields a new equation:
% 21.44/5.63 | (423) e3 = e2
% 21.44/5.63 |
% 21.44/5.63 | Equations (423) can reduce 224 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (637) ~ (all_0_52_52 = e3)
% 21.44/5.63 | (3099) all_0_53_53 = e3 | all_0_54_54 = e3
% 21.44/5.63 |
% 21.44/5.63 +-Applying beta-rule and splitting (3099), into two cases.
% 21.44/5.63 |-Branch one:
% 21.44/5.63 | (861) all_0_53_53 = e3
% 21.44/5.63 |
% 21.44/5.63 | Equations (861) can reduce 796 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (796) ~ (all_0_53_53 = e3)
% 21.44/5.63 | (635) all_0_54_54 = e3
% 21.44/5.63 |
% 21.44/5.63 | Combining equations (635,1592) yields a new equation:
% 21.44/5.63 | (572) e3 = e1
% 21.44/5.63 |
% 21.44/5.63 | Simplifying 572 yields:
% 21.44/5.63 | (418) e3 = e1
% 21.44/5.63 |
% 21.44/5.63 | Equations (418) can reduce 146 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (482) ~ (all_0_58_58 = e1)
% 21.44/5.63 | (614) all_0_59_59 = e1
% 21.44/5.63 |
% 21.44/5.63 | Equations (614) can reduce 2222 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (1238) ~ (all_0_54_54 = e1)
% 21.44/5.63 | (614) all_0_59_59 = e1
% 21.44/5.63 |
% 21.44/5.63 | Equations (614) can reduce 2222 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (609) ~ (all_0_41_41 = e3)
% 21.44/5.63 | (610) all_0_42_42 = e3
% 21.44/5.63 |
% 21.44/5.63 | Combining equations (305,610) yields a new equation:
% 21.44/5.63 | (515) e4 = e3
% 21.44/5.63 |
% 21.44/5.63 | Simplifying 515 yields:
% 21.44/5.63 | (516) e4 = e3
% 21.44/5.63 |
% 21.44/5.63 | Equations (516) can reduce 41 to:
% 21.44/5.63 | (269) $false
% 21.44/5.63 |
% 21.44/5.63 |-The branch is then unsatisfiable
% 21.44/5.63 |-Branch two:
% 21.44/5.63 | (632) all_0_56_56 = e0
% 21.44/5.64 | (1070) all_0_59_59 = e3
% 21.44/5.64 |
% 21.44/5.64 | Equations (1070) can reduce 2132 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (983) ~ (all_0_40_40 = e1)
% 21.44/5.64 | (984) all_0_52_52 = e1 | all_0_57_57 = e1
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (1093), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (413) all_0_40_40 = e1
% 21.44/5.64 |
% 21.44/5.64 | Equations (413) can reduce 983 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (983) ~ (all_0_40_40 = e1)
% 21.44/5.64 | (417) all_0_40_40 = e3
% 21.44/5.64 |
% 21.44/5.64 | Equations (417) can reduce 88 to:
% 21.44/5.64 | (1764) ~ (all_0_41_41 = e3)
% 21.44/5.64 |
% 21.44/5.64 | Simplifying 1764 yields:
% 21.44/5.64 | (609) ~ (all_0_41_41 = e3)
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (94), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (386) all_0_41_41 = e2
% 21.44/5.64 |
% 21.44/5.64 | Equations (386) can reduce 650 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (650) ~ (all_0_41_41 = e2)
% 21.44/5.64 | (1903) all_0_41_41 = e4 | all_0_41_41 = e3 | all_0_41_41 = e1
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (134), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (867) all_0_57_57 = e2
% 21.44/5.64 |
% 21.44/5.64 | Equations (867) can reduce 378 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (378) ~ (all_0_57_57 = e2)
% 21.44/5.64 | (870) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (1903), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (1312) all_0_41_41 = e1
% 21.44/5.64 |
% 21.44/5.64 | Equations (1312) can reduce 106 to:
% 21.44/5.64 | (822) ~ (all_0_53_53 = e1)
% 21.44/5.64 |
% 21.44/5.64 | Simplifying 822 yields:
% 21.44/5.64 | (823) ~ (all_0_53_53 = e1)
% 21.44/5.64 |
% 21.44/5.64 | Equations (1312) can reduce 650 to:
% 21.44/5.64 | (414) ~ (e2 = e1)
% 21.44/5.64 |
% 21.44/5.64 | Simplifying 414 yields:
% 21.44/5.64 | (148) ~ (e2 = e1)
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (984), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (820) all_0_52_52 = e1
% 21.44/5.64 |
% 21.44/5.64 | Combining equations (816,820) yields a new equation:
% 21.44/5.64 | (470) e2 = e1
% 21.44/5.64 |
% 21.44/5.64 | Simplifying 470 yields:
% 21.44/5.64 | (471) e2 = e1
% 21.44/5.64 |
% 21.44/5.64 | Equations (471) can reduce 148 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (978) ~ (all_0_52_52 = e1)
% 21.44/5.64 | (577) all_0_57_57 = e1
% 21.44/5.64 |
% 21.44/5.64 | Equations (577) can reduce 252 to:
% 21.44/5.64 | (481) ~ (all_0_58_58 = e1)
% 21.44/5.64 |
% 21.44/5.64 | Simplifying 481 yields:
% 21.44/5.64 | (482) ~ (all_0_58_58 = e1)
% 21.44/5.64 |
% 21.44/5.64 | Equations (577) can reduce 95 to:
% 21.44/5.64 | (5696) ~ (all_0_59_59 = e1)
% 21.44/5.64 |
% 21.44/5.64 | Simplifying 5696 yields:
% 21.44/5.64 | (2222) ~ (all_0_59_59 = e1)
% 21.44/5.64 |
% 21.44/5.64 | Equations (577) can reduce 378 to:
% 21.44/5.64 | (414) ~ (e2 = e1)
% 21.44/5.64 |
% 21.44/5.64 | Simplifying 414 yields:
% 21.44/5.64 | (148) ~ (e2 = e1)
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (306), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (403) ~ (all_0_58_58 = e0)
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (139), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (889) all_0_45_45 = e0
% 21.44/5.64 |
% 21.44/5.64 | Equations (889) can reduce 299 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (299) ~ (all_0_45_45 = e0)
% 21.44/5.64 | (894) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (211), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (632) all_0_56_56 = e0
% 21.44/5.64 |
% 21.44/5.64 | Equations (632) can reduce 16 to:
% 21.44/5.64 | (432) ~ (all_0_51_51 = e0)
% 21.44/5.64 |
% 21.44/5.64 | Equations (632) can reduce 377 to:
% 21.44/5.64 | (406) ~ (e2 = e0)
% 21.44/5.64 |
% 21.44/5.64 | Simplifying 406 yields:
% 21.44/5.64 | (58) ~ (e2 = e0)
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (73), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (271) all_0_55_55 = e4
% 21.44/5.64 |
% 21.44/5.64 | Combining equations (271,268) yields a new equation:
% 21.44/5.64 | (359) e4 = e2
% 21.44/5.64 |
% 21.44/5.64 | Simplifying 359 yields:
% 21.44/5.64 | (360) e4 = e2
% 21.44/5.64 |
% 21.44/5.64 | Equations (360) can reduce 230 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (6730) ~ (all_0_55_55 = e4)
% 21.44/5.64 | (6843) all_0_56_56 = e4 | all_0_58_58 = e4 | all_0_59_59 = e4
% 21.44/5.64 |
% 21.44/5.64 | Equations (268) can reduce 6730 to:
% 21.44/5.64 | (326) ~ (e4 = e2)
% 21.44/5.64 |
% 21.44/5.64 | Simplifying 326 yields:
% 21.44/5.64 | (230) ~ (e4 = e2)
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (6843), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (1658) all_0_56_56 = e4
% 21.44/5.64 |
% 21.44/5.64 | Combining equations (632,1658) yields a new equation:
% 21.44/5.64 | (439) e4 = e0
% 21.44/5.64 |
% 21.44/5.64 | Equations (439) can reduce 11 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (273) ~ (all_0_56_56 = e4)
% 21.44/5.64 | (6880) all_0_58_58 = e4 | all_0_59_59 = e4
% 21.44/5.64 |
% 21.44/5.64 | Equations (632) can reduce 273 to:
% 21.44/5.64 | (404) ~ (e4 = e0)
% 21.44/5.64 |
% 21.44/5.64 | Simplifying 404 yields:
% 21.44/5.64 | (11) ~ (e4 = e0)
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (29), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (1079) all_0_39_39 = e4
% 21.44/5.64 |
% 21.44/5.64 | Combining equations (348,1079) yields a new equation:
% 21.44/5.64 | (360) e4 = e2
% 21.44/5.64 |
% 21.44/5.64 | Equations (360) can reduce 230 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (307) ~ (all_0_39_39 = e4)
% 21.44/5.64 | (1391) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (1391), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (438) all_0_43_43 = e4
% 21.44/5.64 |
% 21.44/5.64 | Equations (438) can reduce 186 to:
% 21.44/5.64 | (1700) ~ (all_0_45_45 = e4)
% 21.44/5.64 |
% 21.44/5.64 | Simplifying 1700 yields:
% 21.44/5.64 | (537) ~ (all_0_45_45 = e4)
% 21.44/5.64 |
% 21.44/5.64 | Equations (438) can reduce 114 to:
% 21.44/5.64 | (251) ~ (e4 = e1)
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (245), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (694) all_0_45_45 = e2
% 21.44/5.64 |
% 21.44/5.64 | Equations (694) can reduce 390 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (390) ~ (all_0_45_45 = e2)
% 21.44/5.64 | (1082) all_0_45_45 = e4 | all_0_45_45 = e3 | all_0_45_45 = e0
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (63), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (629) all_0_51_51 = e0
% 21.44/5.64 |
% 21.44/5.64 | Equations (629) can reduce 432 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (432) ~ (all_0_51_51 = e0)
% 21.44/5.64 | (1231) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (1082), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (889) all_0_45_45 = e0
% 21.44/5.64 |
% 21.44/5.64 | Equations (889) can reduce 299 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (299) ~ (all_0_45_45 = e0)
% 21.44/5.64 | (1086) all_0_45_45 = e4 | all_0_45_45 = e3
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (1231), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (397) all_0_52_52 = e0
% 21.44/5.64 |
% 21.44/5.64 | Combining equations (397,816) yields a new equation:
% 21.44/5.64 | (354) e2 = e0
% 21.44/5.64 |
% 21.44/5.64 | Equations (354) can reduce 58 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (317) ~ (all_0_52_52 = e0)
% 21.44/5.64 | (1245) all_0_53_53 = e0 | all_0_54_54 = e0
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (1245), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (857) all_0_53_53 = e0
% 21.44/5.64 |
% 21.44/5.64 | Equations (857) can reduce 448 to:
% 21.44/5.64 | (404) ~ (e4 = e0)
% 21.44/5.64 |
% 21.44/5.64 | Simplifying 404 yields:
% 21.44/5.64 | (11) ~ (e4 = e0)
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (54), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (740) all_0_41_41 = e4
% 21.44/5.64 |
% 21.44/5.64 | Combining equations (1312,740) yields a new equation:
% 21.44/5.64 | (477) e4 = e1
% 21.44/5.64 |
% 21.44/5.64 | Equations (477) can reduce 251 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (308) ~ (all_0_41_41 = e4)
% 21.44/5.64 | (744) all_0_45_45 = e4 | all_0_53_53 = e4 | all_0_58_58 = e4
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (1086), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (1087) all_0_45_45 = e3
% 21.44/5.64 |
% 21.44/5.64 | Equations (1087) can reduce 537 to:
% 21.44/5.64 | (498) ~ (e4 = e3)
% 21.44/5.64 |
% 21.44/5.64 | Simplifying 498 yields:
% 21.44/5.64 | (41) ~ (e4 = e3)
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (303), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (765) ~ (all_0_53_53 = e0)
% 21.44/5.64 |
% 21.44/5.64 | Equations (857) can reduce 765 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (857) all_0_53_53 = e0
% 21.44/5.64 | (1592) all_0_54_54 = e1
% 21.44/5.64 |
% 21.44/5.64 | From (1592) and (1874) follows:
% 21.44/5.64 | (7907) op(e0, e1) = e1
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (2), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (485) all_0_58_58 = e2
% 21.44/5.64 |
% 21.44/5.64 | Equations (485) can reduce 392 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (392) ~ (all_0_58_58 = e2)
% 21.44/5.64 | (488) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1 | all_0_58_58 = e0
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (744), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (444) all_0_45_45 = e4
% 21.44/5.64 |
% 21.44/5.64 | Combining equations (1087,444) yields a new equation:
% 21.44/5.64 | (516) e4 = e3
% 21.44/5.64 |
% 21.44/5.64 | Equations (516) can reduce 41 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (537) ~ (all_0_45_45 = e4)
% 21.44/5.64 | (7434) all_0_53_53 = e4 | all_0_58_58 = e4
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (488), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (489) all_0_58_58 = e1
% 21.44/5.64 |
% 21.44/5.64 | Equations (489) can reduce 482 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (482) ~ (all_0_58_58 = e1)
% 21.44/5.64 | (492) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e0
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (7434), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (532) all_0_53_53 = e4
% 21.44/5.64 |
% 21.44/5.64 | Combining equations (532,857) yields a new equation:
% 21.44/5.64 | (751) e4 = e0
% 21.44/5.64 |
% 21.44/5.64 | Simplifying 751 yields:
% 21.44/5.64 | (439) e4 = e0
% 21.44/5.64 |
% 21.44/5.64 | Equations (439) can reduce 11 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (448) ~ (all_0_53_53 = e4)
% 21.44/5.64 | (528) all_0_58_58 = e4
% 21.44/5.64 |
% 21.44/5.64 | Equations (528) can reduce 482 to:
% 21.44/5.64 | (251) ~ (e4 = e1)
% 21.44/5.64 |
% 21.44/5.64 | From (528) and (75) follows:
% 21.44/5.64 | (7928) op(e0, e1) = e4
% 21.44/5.64 |
% 21.44/5.64 | Instantiating formula (21) with e0, e1, e1, e4 and discharging atoms op(e0, e1) = e4, op(e0, e1) = e1, yields:
% 21.44/5.64 | (477) e4 = e1
% 21.44/5.64 |
% 21.44/5.64 | Equations (477) can reduce 251 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (689) ~ (all_0_45_45 = e3)
% 21.44/5.64 | (444) all_0_45_45 = e4
% 21.44/5.64 |
% 21.44/5.64 | Equations (444) can reduce 537 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (765) ~ (all_0_53_53 = e0)
% 21.44/5.64 | (1286) all_0_54_54 = e0
% 21.44/5.64 |
% 21.44/5.64 | Equations (1286) can reduce 1478 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (441) ~ (all_0_43_43 = e4)
% 21.44/5.64 | (2025) all_0_51_51 = e4 | all_0_56_56 = e4
% 21.44/5.64 |
% 21.44/5.64 +-Applying beta-rule and splitting (2025), into two cases.
% 21.44/5.64 |-Branch one:
% 21.44/5.64 | (458) all_0_51_51 = e4
% 21.44/5.64 |
% 21.44/5.64 | Equations (458) can reduce 530 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.64 |-Branch two:
% 21.44/5.64 | (530) ~ (all_0_51_51 = e4)
% 21.44/5.64 | (1658) all_0_56_56 = e4
% 21.44/5.64 |
% 21.44/5.64 | Combining equations (632,1658) yields a new equation:
% 21.44/5.64 | (439) e4 = e0
% 21.44/5.64 |
% 21.44/5.64 | Equations (439) can reduce 11 to:
% 21.44/5.64 | (269) $false
% 21.44/5.64 |
% 21.44/5.64 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (401) ~ (all_0_56_56 = e0)
% 21.44/5.65 | (2052) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (19), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (475) all_0_51_51 = e1
% 21.44/5.65 |
% 21.44/5.65 | Equations (475) can reduce 479 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (479) ~ (all_0_51_51 = e1)
% 21.44/5.65 | (1954) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (894), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (903) all_0_48_48 = e0
% 21.44/5.65 |
% 21.44/5.65 | Combining equations (1458,903) yields a new equation:
% 21.44/5.65 | (353) e2 = e0
% 21.44/5.65 |
% 21.44/5.65 | Simplifying 353 yields:
% 21.44/5.65 | (354) e2 = e0
% 21.44/5.65 |
% 21.44/5.65 | Equations (354) can reduce 58 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (952) ~ (all_0_48_48 = e0)
% 21.44/5.65 | (953) all_0_53_53 = e0 | all_0_58_58 = e0
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (1954), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (820) all_0_52_52 = e1
% 21.44/5.65 |
% 21.44/5.65 | Combining equations (816,820) yields a new equation:
% 21.44/5.65 | (470) e2 = e1
% 21.44/5.65 |
% 21.44/5.65 | Simplifying 470 yields:
% 21.44/5.65 | (471) e2 = e1
% 21.44/5.65 |
% 21.44/5.65 | Equations (471) can reduce 148 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (978) ~ (all_0_52_52 = e1)
% 21.44/5.65 | (1959) all_0_53_53 = e1 | all_0_54_54 = e1
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (953), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (857) all_0_53_53 = e0
% 21.44/5.65 |
% 21.44/5.65 | Equations (857) can reduce 30 to:
% 21.44/5.65 | (432) ~ (all_0_51_51 = e0)
% 21.44/5.65 |
% 21.44/5.65 | Equations (857) can reduce 119 to:
% 21.44/5.65 | (1477) ~ (all_0_54_54 = e0)
% 21.44/5.65 |
% 21.44/5.65 | Simplifying 1477 yields:
% 21.44/5.65 | (1478) ~ (all_0_54_54 = e0)
% 21.44/5.65 |
% 21.44/5.65 | Equations (857) can reduce 823 to:
% 21.44/5.65 | (436) ~ (e1 = e0)
% 21.44/5.65 |
% 21.44/5.65 | Simplifying 436 yields:
% 21.44/5.65 | (144) ~ (e1 = e0)
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (1959), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (853) all_0_53_53 = e1
% 21.44/5.65 |
% 21.44/5.65 | Combining equations (853,857) yields a new equation:
% 21.44/5.65 | (578) e1 = e0
% 21.44/5.65 |
% 21.44/5.65 | Simplifying 578 yields:
% 21.44/5.65 | (579) e1 = e0
% 21.44/5.65 |
% 21.44/5.65 | Equations (579) can reduce 144 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (823) ~ (all_0_53_53 = e1)
% 21.44/5.65 | (1592) all_0_54_54 = e1
% 21.44/5.65 |
% 21.44/5.65 | Equations (1592) can reduce 1478 to:
% 21.44/5.65 | (144) ~ (e1 = e0)
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (171), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (433) all_0_43_43 = e0
% 21.44/5.65 |
% 21.44/5.65 | Equations (433) can reduce 459 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (459) ~ (all_0_43_43 = e0)
% 21.44/5.65 | (622) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (622), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (623) all_0_47_47 = e0
% 21.44/5.65 |
% 21.44/5.65 | Combining equations (469,623) yields a new equation:
% 21.44/5.65 | (578) e1 = e0
% 21.44/5.65 |
% 21.44/5.65 | Simplifying 578 yields:
% 21.44/5.65 | (579) e1 = e0
% 21.44/5.65 |
% 21.44/5.65 | Equations (579) can reduce 144 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (297) ~ (all_0_47_47 = e0)
% 21.44/5.65 | (628) all_0_51_51 = e0 | all_0_56_56 = e0
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (628), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (629) all_0_51_51 = e0
% 21.44/5.65 |
% 21.44/5.65 | Equations (629) can reduce 432 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (432) ~ (all_0_51_51 = e0)
% 21.44/5.65 | (632) all_0_56_56 = e0
% 21.44/5.65 |
% 21.44/5.65 | Equations (632) can reduce 401 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (765) ~ (all_0_53_53 = e0)
% 21.44/5.65 | (493) all_0_58_58 = e0
% 21.44/5.65 |
% 21.44/5.65 | Equations (493) can reduce 403 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (493) all_0_58_58 = e0
% 21.44/5.65 | (614) all_0_59_59 = e1
% 21.44/5.65 |
% 21.44/5.65 | Equations (614) can reduce 2222 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (1315) ~ (all_0_41_41 = e1)
% 21.44/5.65 | (1972) all_0_41_41 = e4 | all_0_41_41 = e3
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (1972), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (605) all_0_41_41 = e3
% 21.44/5.65 |
% 21.44/5.65 | Equations (605) can reduce 609 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (609) ~ (all_0_41_41 = e3)
% 21.44/5.65 | (740) all_0_41_41 = e4
% 21.44/5.65 |
% 21.44/5.65 | Equations (740) can reduce 308 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (512) all_0_15_15 = e3 & ~ (all_0_16_16 = e2)
% 21.44/5.65 |
% 21.44/5.65 | Applying alpha-rule on (512) yields:
% 21.44/5.65 | (513) all_0_15_15 = e3
% 21.44/5.65 | (514) ~ (all_0_16_16 = e2)
% 21.44/5.65 |
% 21.44/5.65 | Combining equations (1850,513) yields a new equation:
% 21.44/5.65 | (560) e3 = e0
% 21.44/5.65 |
% 21.44/5.65 | Equations (560) can reduce 72 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (518) all_0_17_17 = e1 & ~ (all_0_18_18 = e2)
% 21.44/5.65 |
% 21.44/5.65 | Applying alpha-rule on (518) yields:
% 21.44/5.65 | (519) all_0_17_17 = e1
% 21.44/5.65 | (520) ~ (all_0_18_18 = e2)
% 21.44/5.65 |
% 21.44/5.65 | Combining equations (7532,519) yields a new equation:
% 21.44/5.65 | (476) e4 = e1
% 21.44/5.65 |
% 21.44/5.65 | Simplifying 476 yields:
% 21.44/5.65 | (477) e4 = e1
% 21.44/5.65 |
% 21.44/5.65 | Equations (477) can reduce 251 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (523) all_0_19_19 = e0 & ~ (all_0_20_20 = e2)
% 21.44/5.65 |
% 21.44/5.65 | Applying alpha-rule on (523) yields:
% 21.44/5.65 | (524) all_0_19_19 = e0
% 21.44/5.65 | (525) ~ (all_0_20_20 = e2)
% 21.44/5.65 |
% 21.44/5.65 | From (524) and (244) follows:
% 21.44/5.65 | (8018) op(e2, all_0_57_57) = e0
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (246), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (413) all_0_40_40 = e1
% 21.44/5.65 |
% 21.44/5.65 | Equations (413) can reduce 88 to:
% 21.44/5.65 | (1597) ~ (all_0_41_41 = e1)
% 21.44/5.65 |
% 21.44/5.65 | Simplifying 1597 yields:
% 21.44/5.65 | (1315) ~ (all_0_41_41 = e1)
% 21.44/5.65 |
% 21.44/5.65 | Equations (413) can reduce 168 to:
% 21.44/5.65 | (824) ~ (all_0_57_57 = e1)
% 21.44/5.65 |
% 21.44/5.65 | Simplifying 824 yields:
% 21.44/5.65 | (581) ~ (all_0_57_57 = e1)
% 21.44/5.65 |
% 21.44/5.65 | Equations (413) can reduce 64 to:
% 21.44/5.65 | (826) ~ (e4 = e1)
% 21.44/5.65 |
% 21.44/5.65 | Simplifying 826 yields:
% 21.44/5.65 | (251) ~ (e4 = e1)
% 21.44/5.65 |
% 21.44/5.65 | Equations (413) can reduce 102 to:
% 21.44/5.65 | (144) ~ (e1 = e0)
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (134), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (867) all_0_57_57 = e2
% 21.44/5.65 |
% 21.44/5.65 | Equations (867) can reduce 378 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (378) ~ (all_0_57_57 = e2)
% 21.44/5.65 | (870) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (94), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (386) all_0_41_41 = e2
% 21.44/5.65 |
% 21.44/5.65 | Equations (386) can reduce 650 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (650) ~ (all_0_41_41 = e2)
% 21.44/5.65 | (1903) all_0_41_41 = e4 | all_0_41_41 = e3 | all_0_41_41 = e1
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (870), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (577) all_0_57_57 = e1
% 21.44/5.65 |
% 21.44/5.65 | Equations (577) can reduce 581 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (581) ~ (all_0_57_57 = e1)
% 21.44/5.65 | (874) all_0_57_57 = e3 | all_0_57_57 = e0
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (184), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (443) all_0_39_39 = e3
% 21.44/5.65 |
% 21.44/5.65 | Combining equations (443,348) yields a new equation:
% 21.44/5.65 | (606) e3 = e2
% 21.44/5.65 |
% 21.44/5.65 | Simplifying 606 yields:
% 21.44/5.65 | (423) e3 = e2
% 21.44/5.65 |
% 21.44/5.65 | Equations (423) can reduce 224 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (540) ~ (all_0_39_39 = e3)
% 21.44/5.65 | (541) all_0_40_40 = e3 | all_0_41_41 = e3 | all_0_42_42 = e3
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (874), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (400) all_0_57_57 = e0
% 21.44/5.65 |
% 21.44/5.65 | Equations (400) can reduce 967 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (967) ~ (all_0_57_57 = e0)
% 21.44/5.65 | (638) all_0_57_57 = e3
% 21.44/5.65 |
% 21.44/5.65 | Equations (638) can reduce 95 to:
% 21.44/5.65 | (2131) ~ (all_0_59_59 = e3)
% 21.44/5.65 |
% 21.44/5.65 | Simplifying 2131 yields:
% 21.44/5.65 | (2132) ~ (all_0_59_59 = e3)
% 21.44/5.65 |
% 21.44/5.65 | Equations (638) can reduce 173 to:
% 21.44/5.65 | (498) ~ (e4 = e3)
% 21.44/5.65 |
% 21.44/5.65 | Simplifying 498 yields:
% 21.44/5.65 | (41) ~ (e4 = e3)
% 21.44/5.65 |
% 21.44/5.65 | Equations (638) can reduce 581 to:
% 21.44/5.65 | (146) ~ (e3 = e1)
% 21.44/5.65 |
% 21.44/5.65 | From (638) and (8018) follows:
% 21.44/5.65 | (5236) op(e2, e3) = e0
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (169), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (610) all_0_42_42 = e3
% 21.44/5.65 |
% 21.44/5.65 | Combining equations (305,610) yields a new equation:
% 21.44/5.65 | (515) e4 = e3
% 21.44/5.65 |
% 21.44/5.65 | Simplifying 515 yields:
% 21.44/5.65 | (516) e4 = e3
% 21.44/5.65 |
% 21.44/5.65 | Equations (516) can reduce 41 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (1924) ~ (all_0_42_42 = e3)
% 21.44/5.65 | (1925) all_0_46_46 = e3 | all_0_54_54 = e3 | all_0_59_59 = e3
% 21.44/5.65 |
% 21.44/5.65 | Equations (305) can reduce 1924 to:
% 21.44/5.65 | (41) ~ (e4 = e3)
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (296), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (401) ~ (all_0_56_56 = e0)
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (211), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (632) all_0_56_56 = e0
% 21.44/5.65 |
% 21.44/5.65 | Equations (632) can reduce 401 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (401) ~ (all_0_56_56 = e0)
% 21.44/5.65 | (2052) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (541), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (417) all_0_40_40 = e3
% 21.44/5.65 |
% 21.44/5.65 | Combining equations (413,417) yields a new equation:
% 21.44/5.65 | (418) e3 = e1
% 21.44/5.65 |
% 21.44/5.65 | Equations (418) can reduce 146 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (420) ~ (all_0_40_40 = e3)
% 21.44/5.65 | (604) all_0_41_41 = e3 | all_0_42_42 = e3
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (604), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (605) all_0_41_41 = e3
% 21.44/5.65 |
% 21.44/5.65 | Equations (605) can reduce 122 to:
% 21.44/5.65 | (688) ~ (all_0_45_45 = e3)
% 21.44/5.65 |
% 21.44/5.65 | Simplifying 688 yields:
% 21.44/5.65 | (689) ~ (all_0_45_45 = e3)
% 21.44/5.65 |
% 21.44/5.65 | Equations (605) can reduce 106 to:
% 21.44/5.65 | (3866) ~ (all_0_53_53 = e3)
% 21.44/5.65 |
% 21.44/5.65 | Simplifying 3866 yields:
% 21.44/5.65 | (796) ~ (all_0_53_53 = e3)
% 21.44/5.65 |
% 21.44/5.65 | Equations (605) can reduce 208 to:
% 21.44/5.65 | (788) ~ (all_0_58_58 = e3)
% 21.44/5.65 |
% 21.44/5.65 | Simplifying 788 yields:
% 21.44/5.65 | (527) ~ (all_0_58_58 = e3)
% 21.44/5.65 |
% 21.44/5.65 | Equations (605) can reduce 650 to:
% 21.44/5.65 | (224) ~ (e3 = e2)
% 21.44/5.65 |
% 21.44/5.65 | Equations (605) can reduce 1315 to:
% 21.44/5.65 | (146) ~ (e3 = e1)
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (171), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (433) all_0_43_43 = e0
% 21.44/5.65 |
% 21.44/5.65 | Equations (433) can reduce 459 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (459) ~ (all_0_43_43 = e0)
% 21.44/5.65 | (622) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (212), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (375) all_0_59_59 = e2
% 21.44/5.65 |
% 21.44/5.65 | Equations (375) can reduce 1843 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (1843) ~ (all_0_59_59 = e2)
% 21.44/5.65 | (2151) all_0_59_59 = e4 | all_0_59_59 = e3 | all_0_59_59 = e1 | all_0_59_59 = e0
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (1925), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (462) all_0_46_46 = e3
% 21.44/5.65 |
% 21.44/5.65 | Combining equations (364,462) yields a new equation:
% 21.44/5.65 | (423) e3 = e2
% 21.44/5.65 |
% 21.44/5.65 | Equations (423) can reduce 224 to:
% 21.44/5.65 | (269) $false
% 21.44/5.65 |
% 21.44/5.65 |-The branch is then unsatisfiable
% 21.44/5.65 |-Branch two:
% 21.44/5.65 | (618) ~ (all_0_46_46 = e3)
% 21.44/5.65 | (1930) all_0_54_54 = e3 | all_0_59_59 = e3
% 21.44/5.65 |
% 21.44/5.65 | Equations (364) can reduce 618 to:
% 21.44/5.65 | (328) ~ (e3 = e2)
% 21.44/5.65 |
% 21.44/5.65 | Simplifying 328 yields:
% 21.44/5.65 | (224) ~ (e3 = e2)
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (2151), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (614) all_0_59_59 = e1
% 21.44/5.65 |
% 21.44/5.65 | Equations (614) can reduce 2132 to:
% 21.44/5.65 | (597) ~ (e3 = e1)
% 21.44/5.65 |
% 21.44/5.65 | Simplifying 597 yields:
% 21.44/5.65 | (146) ~ (e3 = e1)
% 21.44/5.65 |
% 21.44/5.65 | Equations (614) can reduce 1480 to:
% 21.44/5.65 | (144) ~ (e1 = e0)
% 21.44/5.65 |
% 21.44/5.65 +-Applying beta-rule and splitting (1930), into two cases.
% 21.44/5.65 |-Branch one:
% 21.44/5.65 | (635) all_0_54_54 = e3
% 21.44/5.65 |
% 21.44/5.65 | Equations (635) can reduce 119 to:
% 21.44/5.65 | (796) ~ (all_0_53_53 = e3)
% 21.44/5.65 |
% 21.44/5.65 | Equations (635) can reduce 312 to:
% 21.44/5.65 | (498) ~ (e4 = e3)
% 21.44/5.65 |
% 21.44/5.65 | Simplifying 498 yields:
% 21.44/5.65 | (41) ~ (e4 = e3)
% 21.44/5.65 |
% 21.44/5.65 | Equations (635) can reduce 261 to:
% 21.44/5.65 | (224) ~ (e3 = e2)
% 21.44/5.65 |
% 21.44/5.66 | Equations (635) can reduce 1478 to:
% 21.44/5.66 | (72) ~ (e3 = e0)
% 21.44/5.66 |
% 21.44/5.66 +-Applying beta-rule and splitting (170), into two cases.
% 21.44/5.66 |-Branch one:
% 21.44/5.66 | (1232) all_0_51_51 = e2
% 21.44/5.66 |
% 21.44/5.66 | Equations (1232) can reduce 255 to:
% 21.44/5.66 | (269) $false
% 21.44/5.66 |
% 21.44/5.66 |-The branch is then unsatisfiable
% 21.44/5.66 |-Branch two:
% 21.44/5.66 | (255) ~ (all_0_51_51 = e2)
% 21.44/5.66 | (1235) all_0_51_51 = e4 | all_0_51_51 = e3 | all_0_51_51 = e1 | all_0_51_51 = e0
% 21.44/5.66 |
% 21.44/5.66 +-Applying beta-rule and splitting (622), into two cases.
% 21.44/5.66 |-Branch one:
% 21.44/5.66 | (623) all_0_47_47 = e0
% 21.44/5.66 |
% 21.44/5.66 | Combining equations (469,623) yields a new equation:
% 21.44/5.66 | (578) e1 = e0
% 21.44/5.66 |
% 21.44/5.66 | Simplifying 578 yields:
% 21.44/5.66 | (579) e1 = e0
% 21.44/5.66 |
% 21.44/5.66 | Equations (579) can reduce 144 to:
% 21.44/5.66 | (269) $false
% 21.44/5.66 |
% 21.44/5.66 |-The branch is then unsatisfiable
% 21.44/5.66 |-Branch two:
% 21.44/5.66 | (297) ~ (all_0_47_47 = e0)
% 21.44/5.66 | (628) all_0_51_51 = e0 | all_0_56_56 = e0
% 21.44/5.66 |
% 21.44/5.66 +-Applying beta-rule and splitting (162), into two cases.
% 21.44/5.66 |-Branch one:
% 21.44/5.66 | (559) all_0_43_43 = e3
% 21.44/5.66 |
% 21.44/5.66 +-Applying beta-rule and splitting (14), into two cases.
% 21.44/5.66 |-Branch one:
% 21.44/5.66 | (438) all_0_43_43 = e4
% 21.44/5.66 |
% 21.44/5.66 | Combining equations (438,559) yields a new equation:
% 21.44/5.66 | (515) e4 = e3
% 21.44/5.66 |
% 21.44/5.66 | Simplifying 515 yields:
% 21.44/5.66 | (516) e4 = e3
% 21.44/5.66 |
% 21.44/5.66 | Equations (516) can reduce 41 to:
% 21.44/5.66 | (269) $false
% 21.44/5.66 |
% 21.44/5.66 |-The branch is then unsatisfiable
% 21.44/5.66 |-Branch two:
% 21.44/5.66 | (441) ~ (all_0_43_43 = e4)
% 21.44/5.66 | (442) all_0_45_45 = e4 | all_0_46_46 = e4
% 21.44/5.66 |
% 21.44/5.66 +-Applying beta-rule and splitting (442), into two cases.
% 21.44/5.66 |-Branch one:
% 21.44/5.66 | (444) all_0_45_45 = e4
% 21.44/5.66 |
% 21.44/5.66 | Equations (444) can reduce 142 to:
% 21.44/5.66 | (447) ~ (all_0_53_53 = e4)
% 21.44/5.66 |
% 21.44/5.66 | Simplifying 447 yields:
% 21.44/5.66 | (448) ~ (all_0_53_53 = e4)
% 21.44/5.66 |
% 21.44/5.66 +-Applying beta-rule and splitting (628), into two cases.
% 21.44/5.66 |-Branch one:
% 21.44/5.66 | (629) all_0_51_51 = e0
% 21.44/5.66 |
% 21.44/5.66 | Equations (629) can reduce 30 to:
% 21.44/5.66 | (764) ~ (all_0_53_53 = e0)
% 21.44/5.66 |
% 21.44/5.66 | Simplifying 764 yields:
% 21.44/5.66 | (765) ~ (all_0_53_53 = e0)
% 21.44/5.66 |
% 21.44/5.66 | Equations (629) can reduce 530 to:
% 21.44/5.66 | (404) ~ (e4 = e0)
% 21.44/5.66 |
% 21.44/5.66 | Simplifying 404 yields:
% 21.44/5.66 | (11) ~ (e4 = e0)
% 21.44/5.66 |
% 21.44/5.66 | Equations (629) can reduce 255 to:
% 21.44/5.66 | (406) ~ (e2 = e0)
% 21.44/5.66 |
% 21.44/5.66 | Simplifying 406 yields:
% 21.44/5.66 | (58) ~ (e2 = e0)
% 21.44/5.66 |
% 21.44/5.66 +-Applying beta-rule and splitting (27), into two cases.
% 21.44/5.66 |-Branch one:
% 21.44/5.66 | (849) all_0_53_53 = e2
% 21.44/5.66 |
% 21.44/5.66 | Equations (849) can reduce 259 to:
% 21.44/5.66 | (269) $false
% 21.44/5.66 |
% 21.44/5.66 |-The branch is then unsatisfiable
% 21.44/5.66 |-Branch two:
% 21.44/5.66 | (259) ~ (all_0_53_53 = e2)
% 21.44/5.66 | (852) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e1 | all_0_53_53 = e0
% 21.44/5.66 |
% 21.44/5.66 +-Applying beta-rule and splitting (139), into two cases.
% 21.44/5.66 |-Branch one:
% 21.44/5.66 | (889) all_0_45_45 = e0
% 21.44/5.66 |
% 21.44/5.66 | Combining equations (444,889) yields a new equation:
% 21.44/5.66 | (751) e4 = e0
% 21.44/5.66 |
% 21.44/5.66 | Simplifying 751 yields:
% 21.44/5.66 | (439) e4 = e0
% 21.44/5.66 |
% 21.44/5.66 | Equations (439) can reduce 11 to:
% 21.44/5.66 | (269) $false
% 21.44/5.66 |
% 21.44/5.66 |-The branch is then unsatisfiable
% 21.44/5.66 |-Branch two:
% 21.44/5.66 | (299) ~ (all_0_45_45 = e0)
% 21.44/5.66 | (894) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 21.44/5.66 |
% 21.44/5.66 +-Applying beta-rule and splitting (852), into two cases.
% 21.44/5.66 |-Branch one:
% 21.44/5.66 | (853) all_0_53_53 = e1
% 21.44/5.66 |
% 21.44/5.66 | Equations (853) can reduce 127 to:
% 21.44/5.66 | (481) ~ (all_0_58_58 = e1)
% 21.44/5.66 |
% 21.44/5.66 | Simplifying 481 yields:
% 21.44/5.66 | (482) ~ (all_0_58_58 = e1)
% 21.44/5.66 |
% 21.44/5.66 | Equations (853) can reduce 765 to:
% 21.44/5.66 | (144) ~ (e1 = e0)
% 21.44/5.66 |
% 21.44/5.66 +-Applying beta-rule and splitting (894), into two cases.
% 21.44/5.66 |-Branch one:
% 21.44/5.66 | (903) all_0_48_48 = e0
% 21.44/5.66 |
% 21.44/5.66 | Combining equations (1458,903) yields a new equation:
% 21.44/5.66 | (353) e2 = e0
% 21.44/5.66 |
% 21.44/5.66 | Simplifying 353 yields:
% 21.44/5.66 | (354) e2 = e0
% 21.44/5.66 |
% 21.44/5.66 | Equations (354) can reduce 58 to:
% 21.44/5.66 | (269) $false
% 21.44/5.66 |
% 21.44/5.66 |-The branch is then unsatisfiable
% 21.44/5.66 |-Branch two:
% 21.44/5.66 | (952) ~ (all_0_48_48 = e0)
% 21.44/5.66 | (953) all_0_53_53 = e0 | all_0_58_58 = e0
% 21.44/5.66 |
% 21.44/5.66 +-Applying beta-rule and splitting (953), into two cases.
% 21.44/5.66 |-Branch one:
% 21.44/5.66 | (857) all_0_53_53 = e0
% 21.44/5.66 |
% 21.44/5.66 | Combining equations (857,853) yields a new equation:
% 21.44/5.66 | (579) e1 = e0
% 21.44/5.66 |
% 21.44/5.66 | Equations (579) can reduce 144 to:
% 21.44/5.66 | (269) $false
% 21.44/5.66 |
% 21.44/5.66 |-The branch is then unsatisfiable
% 21.44/5.66 |-Branch two:
% 21.44/5.66 | (765) ~ (all_0_53_53 = e0)
% 21.44/5.66 | (493) all_0_58_58 = e0
% 21.44/5.66 |
% 21.44/5.66 | Equations (493) can reduce 482 to:
% 21.44/5.66 | (436) ~ (e1 = e0)
% 21.44/5.66 |
% 21.44/5.66 | Simplifying 436 yields:
% 21.44/5.66 | (144) ~ (e1 = e0)
% 21.44/5.66 |
% 21.44/5.66 | Instantiating formula (21) with e2, e3, e0, e1 and discharging atoms op(e2, e3) = e1, op(e2, e3) = e0, yields:
% 21.44/5.66 | (579) e1 = e0
% 21.44/5.66 |
% 21.44/5.66 | Equations (579) can reduce 144 to:
% 21.44/5.66 | (269) $false
% 21.44/5.66 |
% 21.44/5.66 |-The branch is then unsatisfiable
% 21.44/5.66 |-Branch two:
% 21.44/5.66 | (823) ~ (all_0_53_53 = e1)
% 21.44/5.66 | (856) all_0_53_53 = e4 | all_0_53_53 = e3 | all_0_53_53 = e0
% 21.44/5.66 |
% 21.44/5.66 +-Applying beta-rule and splitting (856), into two cases.
% 21.44/5.66 |-Branch one:
% 21.44/5.66 | (857) all_0_53_53 = e0
% 21.44/5.66 |
% 21.44/5.66 | Equations (857) can reduce 765 to:
% 21.44/5.66 | (269) $false
% 21.44/5.66 |
% 21.44/5.66 |-The branch is then unsatisfiable
% 21.44/5.66 |-Branch two:
% 21.44/5.66 | (765) ~ (all_0_53_53 = e0)
% 21.44/5.66 | (860) all_0_53_53 = e4 | all_0_53_53 = e3
% 21.44/5.66 |
% 21.44/5.66 +-Applying beta-rule and splitting (860), into two cases.
% 21.44/5.66 |-Branch one:
% 21.44/5.66 | (861) all_0_53_53 = e3
% 21.44/5.66 |
% 21.44/5.66 | Equations (861) can reduce 796 to:
% 21.44/5.66 | (269) $false
% 21.44/5.66 |
% 21.44/5.66 |-The branch is then unsatisfiable
% 21.44/5.66 |-Branch two:
% 21.44/5.66 | (796) ~ (all_0_53_53 = e3)
% 21.44/5.66 | (532) all_0_53_53 = e4
% 21.44/5.66 |
% 21.44/5.66 | Equations (532) can reduce 448 to:
% 21.44/5.66 | (269) $false
% 21.44/5.66 |
% 21.44/5.66 |-The branch is then unsatisfiable
% 21.44/5.66 |-Branch two:
% 21.44/5.66 | (432) ~ (all_0_51_51 = e0)
% 21.44/5.66 | (632) all_0_56_56 = e0
% 21.44/5.66 |
% 21.44/5.66 | Equations (632) can reduce 401 to:
% 21.44/5.66 | (269) $false
% 21.44/5.66 |
% 21.44/5.66 |-The branch is then unsatisfiable
% 21.44/5.66 |-Branch two:
% 21.44/5.66 | (537) ~ (all_0_45_45 = e4)
% 21.44/5.66 | (538) all_0_46_46 = e4
% 21.44/5.66 |
% 21.44/5.66 | Combining equations (364,538) yields a new equation:
% 21.44/5.66 | (360) e4 = e2
% 21.44/5.66 |
% 21.44/5.66 | Equations (360) can reduce 230 to:
% 21.44/5.66 | (269) $false
% 21.44/5.66 |
% 21.44/5.66 |-The branch is then unsatisfiable
% 21.44/5.66 |-Branch two:
% 21.44/5.66 | (562) ~ (all_0_43_43 = e3)
% 21.44/5.66 | (1193) all_0_44_44 = e3 | all_0_45_45 = e3 | all_0_46_46 = e3
% 21.44/5.66 |
% 21.44/5.66 +-Applying beta-rule and splitting (1193), into two cases.
% 21.44/5.66 |-Branch one:
% 21.44/5.66 | (422) all_0_44_44 = e3
% 21.44/5.66 |
% 21.44/5.66 | Combining equations (352,422) yields a new equation:
% 21.44/5.66 | (560) e3 = e0
% 21.44/5.66 |
% 21.44/5.66 | Equations (560) can reduce 72 to:
% 21.44/5.66 | (269) $false
% 21.44/5.66 |
% 21.44/5.66 |-The branch is then unsatisfiable
% 21.44/5.66 |-Branch two:
% 21.44/5.66 | (425) ~ (all_0_44_44 = e3)
% 21.44/5.66 | (1203) all_0_45_45 = e3 | all_0_46_46 = e3
% 21.59/5.66 |
% 21.59/5.66 +-Applying beta-rule and splitting (1203), into two cases.
% 21.59/5.66 |-Branch one:
% 21.59/5.66 | (1087) all_0_45_45 = e3
% 21.59/5.66 |
% 21.59/5.66 | Equations (1087) can reduce 689 to:
% 21.59/5.66 | (269) $false
% 21.59/5.66 |
% 21.59/5.66 |-The branch is then unsatisfiable
% 21.59/5.66 |-Branch two:
% 21.59/5.66 | (689) ~ (all_0_45_45 = e3)
% 21.59/5.66 | (462) all_0_46_46 = e3
% 21.59/5.66 |
% 21.59/5.66 | Combining equations (364,462) yields a new equation:
% 21.59/5.66 | (423) e3 = e2
% 21.59/5.66 |
% 21.59/5.66 | Equations (423) can reduce 224 to:
% 21.59/5.66 | (269) $false
% 21.59/5.66 |
% 21.59/5.66 |-The branch is then unsatisfiable
% 21.59/5.66 |-Branch two:
% 21.59/5.66 | (430) ~ (all_0_54_54 = e3)
% 21.59/5.66 | (1070) all_0_59_59 = e3
% 21.59/5.66 |
% 21.59/5.66 | Combining equations (1070,614) yields a new equation:
% 21.59/5.66 | (572) e3 = e1
% 21.59/5.66 |
% 21.59/5.66 | Simplifying 572 yields:
% 21.59/5.66 | (418) e3 = e1
% 21.59/5.66 |
% 21.59/5.66 | Equations (418) can reduce 146 to:
% 21.59/5.66 | (269) $false
% 21.59/5.66 |
% 21.59/5.66 |-The branch is then unsatisfiable
% 21.59/5.66 |-Branch two:
% 21.59/5.66 | (2222) ~ (all_0_59_59 = e1)
% 21.59/5.66 | (2223) all_0_59_59 = e4 | all_0_59_59 = e3 | all_0_59_59 = e0
% 21.59/5.66 |
% 21.59/5.66 +-Applying beta-rule and splitting (43), into two cases.
% 21.59/5.66 |-Branch one:
% 21.59/5.66 | (480) all_0_56_56 = e1
% 21.59/5.66 |
% 21.59/5.66 | Equations (480) can reduce 575 to:
% 21.59/5.66 | (269) $false
% 21.59/5.66 |
% 21.59/5.66 |-The branch is then unsatisfiable
% 21.59/5.66 |-Branch two:
% 21.59/5.66 | (575) ~ (all_0_56_56 = e1)
% 21.59/5.66 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 21.59/5.66 |
% 21.59/5.66 +-Applying beta-rule and splitting (84), into two cases.
% 21.59/5.66 |-Branch one:
% 21.59/5.66 | (832) all_0_42_42 = e1
% 21.59/5.66 |
% 21.59/5.66 | Combining equations (305,832) yields a new equation:
% 21.59/5.66 | (476) e4 = e1
% 21.59/5.66 |
% 21.59/5.66 | Simplifying 476 yields:
% 21.59/5.66 | (477) e4 = e1
% 21.59/5.66 |
% 21.59/5.66 | Equations (477) can reduce 251 to:
% 21.59/5.66 | (269) $false
% 21.59/5.66 |
% 21.59/5.66 |-The branch is then unsatisfiable
% 21.59/5.66 |-Branch two:
% 21.59/5.66 | (836) ~ (all_0_42_42 = e1)
% 21.59/5.66 | (837) all_0_49_49 = e1 | all_0_54_54 = e1 | all_0_59_59 = e1
% 21.59/5.66 |
% 21.59/5.66 +-Applying beta-rule and splitting (837), into two cases.
% 21.59/5.66 |-Branch one:
% 21.59/5.66 | (596) all_0_49_49 = e1
% 21.59/5.66 |
% 21.59/5.66 | Combining equations (965,596) yields a new equation:
% 21.59/5.66 | (579) e1 = e0
% 21.59/5.66 |
% 21.59/5.66 | Equations (579) can reduce 144 to:
% 21.59/5.66 | (269) $false
% 21.59/5.66 |
% 21.59/5.66 |-The branch is then unsatisfiable
% 21.59/5.66 |-Branch two:
% 21.59/5.66 | (960) ~ (all_0_49_49 = e1)
% 21.59/5.66 | (961) all_0_54_54 = e1 | all_0_59_59 = e1
% 21.59/5.66 |
% 21.59/5.66 +-Applying beta-rule and splitting (576), into two cases.
% 21.59/5.66 |-Branch one:
% 21.59/5.66 | (577) all_0_57_57 = e1
% 21.59/5.66 |
% 21.59/5.66 | Combining equations (577,638) yields a new equation:
% 21.59/5.66 | (418) e3 = e1
% 21.59/5.66 |
% 21.59/5.66 | Equations (418) can reduce 146 to:
% 21.59/5.66 | (269) $false
% 21.59/5.66 |
% 21.59/5.66 |-The branch is then unsatisfiable
% 21.59/5.66 |-Branch two:
% 21.59/5.66 | (581) ~ (all_0_57_57 = e1)
% 21.59/5.66 | (582) all_0_58_58 = e1 | all_0_59_59 = e1
% 21.59/5.66 |
% 21.59/5.66 +-Applying beta-rule and splitting (961), into two cases.
% 21.59/5.66 |-Branch one:
% 21.59/5.66 | (1592) all_0_54_54 = e1
% 21.59/5.66 |
% 21.59/5.66 | Equations (1592) can reduce 159 to:
% 21.59/5.66 | (479) ~ (all_0_51_51 = e1)
% 21.59/5.66 |
% 21.59/5.66 | Equations (1592) can reduce 81 to:
% 21.59/5.66 | (5696) ~ (all_0_59_59 = e1)
% 21.59/5.66 |
% 21.59/5.66 | Simplifying 5696 yields:
% 21.59/5.66 | (2222) ~ (all_0_59_59 = e1)
% 21.59/5.66 |
% 21.59/5.66 +-Applying beta-rule and splitting (93), into two cases.
% 21.59/5.66 |-Branch one:
% 21.59/5.66 | (564) all_0_51_51 = e3
% 21.59/5.66 |
% 21.59/5.66 | Equations (564) can reduce 479 to:
% 21.59/5.66 | (146) ~ (e3 = e1)
% 21.59/5.66 |
% 21.59/5.66 +-Applying beta-rule and splitting (1930), into two cases.
% 21.59/5.66 |-Branch one:
% 21.59/5.66 | (635) all_0_54_54 = e3
% 21.59/5.66 |
% 21.59/5.66 | Combining equations (1592,635) yields a new equation:
% 21.59/5.66 | (418) e3 = e1
% 21.59/5.66 |
% 21.59/5.66 | Equations (418) can reduce 146 to:
% 21.59/5.66 | (269) $false
% 21.59/5.66 |
% 21.59/5.66 |-The branch is then unsatisfiable
% 21.59/5.66 |-Branch two:
% 21.59/5.66 | (430) ~ (all_0_54_54 = e3)
% 21.59/5.66 | (1070) all_0_59_59 = e3
% 21.59/5.66 |
% 21.59/5.66 | Equations (1070) can reduce 2132 to:
% 21.59/5.66 | (269) $false
% 21.59/5.66 |
% 21.59/5.66 |-The branch is then unsatisfiable
% 21.59/5.66 |-Branch two:
% 21.59/5.66 | (428) ~ (all_0_51_51 = e3)
% 21.59/5.66 | (3093) all_0_52_52 = e3 | all_0_53_53 = e3 | all_0_54_54 = e3
% 21.59/5.66 |
% 21.59/5.66 +-Applying beta-rule and splitting (582), into two cases.
% 21.59/5.66 |-Branch one:
% 21.59/5.66 | (489) all_0_58_58 = e1
% 21.59/5.66 |
% 21.59/5.66 | Equations (489) can reduce 527 to:
% 21.59/5.66 | (597) ~ (e3 = e1)
% 21.59/5.66 |
% 21.59/5.66 | Simplifying 597 yields:
% 21.59/5.66 | (146) ~ (e3 = e1)
% 21.59/5.66 |
% 21.59/5.66 +-Applying beta-rule and splitting (3093), into two cases.
% 21.59/5.66 |-Branch one:
% 21.59/5.66 | (427) all_0_52_52 = e3
% 21.59/5.66 |
% 21.59/5.66 | Combining equations (816,427) yields a new equation:
% 21.59/5.66 | (423) e3 = e2
% 21.59/5.66 |
% 21.59/5.66 | Equations (423) can reduce 224 to:
% 21.59/5.66 | (269) $false
% 21.59/5.66 |
% 21.59/5.66 |-The branch is then unsatisfiable
% 21.59/5.66 |-Branch two:
% 21.59/5.66 | (637) ~ (all_0_52_52 = e3)
% 21.59/5.66 | (3099) all_0_53_53 = e3 | all_0_54_54 = e3
% 21.59/5.66 |
% 21.59/5.66 +-Applying beta-rule and splitting (3099), into two cases.
% 21.59/5.66 |-Branch one:
% 21.59/5.66 | (861) all_0_53_53 = e3
% 21.59/5.66 |
% 21.59/5.66 | Equations (861) can reduce 796 to:
% 21.59/5.66 | (269) $false
% 21.59/5.66 |
% 21.59/5.66 |-The branch is then unsatisfiable
% 21.59/5.66 |-Branch two:
% 21.59/5.66 | (796) ~ (all_0_53_53 = e3)
% 21.59/5.66 | (635) all_0_54_54 = e3
% 21.59/5.66 |
% 21.59/5.66 | Combining equations (635,1592) yields a new equation:
% 21.59/5.66 | (572) e3 = e1
% 21.59/5.66 |
% 21.59/5.66 | Simplifying 572 yields:
% 21.59/5.66 | (418) e3 = e1
% 21.59/5.66 |
% 21.59/5.66 | Equations (418) can reduce 146 to:
% 21.59/5.66 | (269) $false
% 21.59/5.66 |
% 21.59/5.66 |-The branch is then unsatisfiable
% 21.59/5.66 |-Branch two:
% 21.59/5.66 | (482) ~ (all_0_58_58 = e1)
% 21.59/5.66 | (614) all_0_59_59 = e1
% 21.59/5.66 |
% 21.59/5.66 | Equations (614) can reduce 2222 to:
% 21.59/5.66 | (269) $false
% 21.59/5.66 |
% 21.59/5.66 |-The branch is then unsatisfiable
% 21.59/5.66 |-Branch two:
% 21.59/5.66 | (1238) ~ (all_0_54_54 = e1)
% 21.59/5.66 | (614) all_0_59_59 = e1
% 21.59/5.66 |
% 21.59/5.66 | Equations (614) can reduce 2222 to:
% 21.59/5.66 | (269) $false
% 21.59/5.66 |
% 21.59/5.66 |-The branch is then unsatisfiable
% 21.59/5.66 |-Branch two:
% 21.59/5.66 | (609) ~ (all_0_41_41 = e3)
% 21.59/5.66 | (610) all_0_42_42 = e3
% 21.59/5.66 |
% 21.59/5.66 | Combining equations (305,610) yields a new equation:
% 21.59/5.66 | (515) e4 = e3
% 21.59/5.66 |
% 21.59/5.66 | Simplifying 515 yields:
% 21.59/5.66 | (516) e4 = e3
% 21.59/5.66 |
% 21.59/5.66 | Equations (516) can reduce 41 to:
% 21.59/5.66 | (269) $false
% 21.59/5.66 |
% 21.59/5.66 |-The branch is then unsatisfiable
% 21.59/5.66 |-Branch two:
% 21.59/5.66 | (632) all_0_56_56 = e0
% 21.59/5.66 | (1070) all_0_59_59 = e3
% 21.59/5.66 |
% 21.59/5.66 | Equations (1070) can reduce 2132 to:
% 21.59/5.66 | (269) $false
% 21.59/5.66 |
% 21.59/5.66 |-The branch is then unsatisfiable
% 21.59/5.66 |-Branch two:
% 21.59/5.66 | (983) ~ (all_0_40_40 = e1)
% 21.59/5.66 | (984) all_0_52_52 = e1 | all_0_57_57 = e1
% 21.59/5.66 |
% 21.59/5.66 +-Applying beta-rule and splitting (1093), into two cases.
% 21.59/5.66 |-Branch one:
% 21.59/5.66 | (413) all_0_40_40 = e1
% 21.59/5.66 |
% 21.59/5.66 | Equations (413) can reduce 983 to:
% 21.59/5.66 | (269) $false
% 21.59/5.66 |
% 21.59/5.66 |-The branch is then unsatisfiable
% 21.59/5.66 |-Branch two:
% 21.59/5.66 | (983) ~ (all_0_40_40 = e1)
% 21.59/5.66 | (417) all_0_40_40 = e3
% 21.59/5.66 |
% 21.59/5.66 | Equations (417) can reduce 88 to:
% 21.59/5.66 | (1764) ~ (all_0_41_41 = e3)
% 21.59/5.66 |
% 21.59/5.66 | Simplifying 1764 yields:
% 21.59/5.66 | (609) ~ (all_0_41_41 = e3)
% 21.59/5.66 |
% 21.59/5.66 +-Applying beta-rule and splitting (94), into two cases.
% 21.59/5.66 |-Branch one:
% 21.59/5.66 | (386) all_0_41_41 = e2
% 21.59/5.66 |
% 21.59/5.66 | Equations (386) can reduce 650 to:
% 21.59/5.66 | (269) $false
% 21.59/5.66 |
% 21.59/5.66 |-The branch is then unsatisfiable
% 21.59/5.66 |-Branch two:
% 21.59/5.66 | (650) ~ (all_0_41_41 = e2)
% 21.59/5.66 | (1903) all_0_41_41 = e4 | all_0_41_41 = e3 | all_0_41_41 = e1
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (134), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (867) all_0_57_57 = e2
% 21.59/5.67 |
% 21.59/5.67 | Equations (867) can reduce 378 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (378) ~ (all_0_57_57 = e2)
% 21.59/5.67 | (870) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (1903), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (1312) all_0_41_41 = e1
% 21.59/5.67 |
% 21.59/5.67 | Equations (1312) can reduce 106 to:
% 21.59/5.67 | (822) ~ (all_0_53_53 = e1)
% 21.59/5.67 |
% 21.59/5.67 | Simplifying 822 yields:
% 21.59/5.67 | (823) ~ (all_0_53_53 = e1)
% 21.59/5.67 |
% 21.59/5.67 | Equations (1312) can reduce 650 to:
% 21.59/5.67 | (414) ~ (e2 = e1)
% 21.59/5.67 |
% 21.59/5.67 | Simplifying 414 yields:
% 21.59/5.67 | (148) ~ (e2 = e1)
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (984), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (820) all_0_52_52 = e1
% 21.59/5.67 |
% 21.59/5.67 | Combining equations (816,820) yields a new equation:
% 21.59/5.67 | (470) e2 = e1
% 21.59/5.67 |
% 21.59/5.67 | Simplifying 470 yields:
% 21.59/5.67 | (471) e2 = e1
% 21.59/5.67 |
% 21.59/5.67 | Equations (471) can reduce 148 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (978) ~ (all_0_52_52 = e1)
% 21.59/5.67 | (577) all_0_57_57 = e1
% 21.59/5.67 |
% 21.59/5.67 | Equations (577) can reduce 95 to:
% 21.59/5.67 | (5696) ~ (all_0_59_59 = e1)
% 21.59/5.67 |
% 21.59/5.67 | Simplifying 5696 yields:
% 21.59/5.67 | (2222) ~ (all_0_59_59 = e1)
% 21.59/5.67 |
% 21.59/5.67 | Equations (577) can reduce 378 to:
% 21.59/5.67 | (414) ~ (e2 = e1)
% 21.59/5.67 |
% 21.59/5.67 | Simplifying 414 yields:
% 21.59/5.67 | (148) ~ (e2 = e1)
% 21.59/5.67 |
% 21.59/5.67 | From (577) and (8018) follows:
% 21.59/5.67 | (8294) op(e2, e1) = e0
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (306), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (403) ~ (all_0_58_58 = e0)
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (139), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (889) all_0_45_45 = e0
% 21.59/5.67 |
% 21.59/5.67 | Equations (889) can reduce 299 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (299) ~ (all_0_45_45 = e0)
% 21.59/5.67 | (894) all_0_48_48 = e0 | all_0_53_53 = e0 | all_0_58_58 = e0
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (211), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (632) all_0_56_56 = e0
% 21.59/5.67 |
% 21.59/5.67 | Equations (632) can reduce 16 to:
% 21.59/5.67 | (432) ~ (all_0_51_51 = e0)
% 21.59/5.67 |
% 21.59/5.67 | Equations (632) can reduce 377 to:
% 21.59/5.67 | (406) ~ (e2 = e0)
% 21.59/5.67 |
% 21.59/5.67 | Simplifying 406 yields:
% 21.59/5.67 | (58) ~ (e2 = e0)
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (63), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (629) all_0_51_51 = e0
% 21.59/5.67 |
% 21.59/5.67 | Equations (629) can reduce 432 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (432) ~ (all_0_51_51 = e0)
% 21.59/5.67 | (1231) all_0_52_52 = e0 | all_0_53_53 = e0 | all_0_54_54 = e0
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (1231), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (397) all_0_52_52 = e0
% 21.59/5.67 |
% 21.59/5.67 | Combining equations (397,816) yields a new equation:
% 21.59/5.67 | (354) e2 = e0
% 21.59/5.67 |
% 21.59/5.67 | Equations (354) can reduce 58 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (317) ~ (all_0_52_52 = e0)
% 21.59/5.67 | (1245) all_0_53_53 = e0 | all_0_54_54 = e0
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (1245), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (857) all_0_53_53 = e0
% 21.59/5.67 |
% 21.59/5.67 | Equations (857) can reduce 259 to:
% 21.59/5.67 | (406) ~ (e2 = e0)
% 21.59/5.67 |
% 21.59/5.67 | Simplifying 406 yields:
% 21.59/5.67 | (58) ~ (e2 = e0)
% 21.59/5.67 |
% 21.59/5.67 | Instantiating formula (21) with e2, e1, e0, e2 and discharging atoms op(e2, e1) = e2, op(e2, e1) = e0, yields:
% 21.59/5.67 | (354) e2 = e0
% 21.59/5.67 |
% 21.59/5.67 | Equations (354) can reduce 58 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (765) ~ (all_0_53_53 = e0)
% 21.59/5.67 | (1286) all_0_54_54 = e0
% 21.59/5.67 |
% 21.59/5.67 | Equations (1286) can reduce 1478 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (401) ~ (all_0_56_56 = e0)
% 21.59/5.67 | (2052) all_0_57_57 = e0 | all_0_58_58 = e0 | all_0_59_59 = e0
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (19), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (475) all_0_51_51 = e1
% 21.59/5.67 |
% 21.59/5.67 | Equations (475) can reduce 479 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (479) ~ (all_0_51_51 = e1)
% 21.59/5.67 | (1954) all_0_52_52 = e1 | all_0_53_53 = e1 | all_0_54_54 = e1
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (894), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (903) all_0_48_48 = e0
% 21.59/5.67 |
% 21.59/5.67 | Combining equations (1458,903) yields a new equation:
% 21.59/5.67 | (353) e2 = e0
% 21.59/5.67 |
% 21.59/5.67 | Simplifying 353 yields:
% 21.59/5.67 | (354) e2 = e0
% 21.59/5.67 |
% 21.59/5.67 | Equations (354) can reduce 58 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (952) ~ (all_0_48_48 = e0)
% 21.59/5.67 | (953) all_0_53_53 = e0 | all_0_58_58 = e0
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (1954), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (820) all_0_52_52 = e1
% 21.59/5.67 |
% 21.59/5.67 | Combining equations (816,820) yields a new equation:
% 21.59/5.67 | (470) e2 = e1
% 21.59/5.67 |
% 21.59/5.67 | Simplifying 470 yields:
% 21.59/5.67 | (471) e2 = e1
% 21.59/5.67 |
% 21.59/5.67 | Equations (471) can reduce 148 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (978) ~ (all_0_52_52 = e1)
% 21.59/5.67 | (1959) all_0_53_53 = e1 | all_0_54_54 = e1
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (953), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (857) all_0_53_53 = e0
% 21.59/5.67 |
% 21.59/5.67 | Equations (857) can reduce 30 to:
% 21.59/5.67 | (432) ~ (all_0_51_51 = e0)
% 21.59/5.67 |
% 21.59/5.67 | Equations (857) can reduce 119 to:
% 21.59/5.67 | (1477) ~ (all_0_54_54 = e0)
% 21.59/5.67 |
% 21.59/5.67 | Simplifying 1477 yields:
% 21.59/5.67 | (1478) ~ (all_0_54_54 = e0)
% 21.59/5.67 |
% 21.59/5.67 | Equations (857) can reduce 823 to:
% 21.59/5.67 | (436) ~ (e1 = e0)
% 21.59/5.67 |
% 21.59/5.67 | Simplifying 436 yields:
% 21.59/5.67 | (144) ~ (e1 = e0)
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (1959), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (853) all_0_53_53 = e1
% 21.59/5.67 |
% 21.59/5.67 | Combining equations (853,857) yields a new equation:
% 21.59/5.67 | (578) e1 = e0
% 21.59/5.67 |
% 21.59/5.67 | Simplifying 578 yields:
% 21.59/5.67 | (579) e1 = e0
% 21.59/5.67 |
% 21.59/5.67 | Equations (579) can reduce 144 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (823) ~ (all_0_53_53 = e1)
% 21.59/5.67 | (1592) all_0_54_54 = e1
% 21.59/5.67 |
% 21.59/5.67 | Equations (1592) can reduce 1478 to:
% 21.59/5.67 | (144) ~ (e1 = e0)
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (171), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (433) all_0_43_43 = e0
% 21.59/5.67 |
% 21.59/5.67 | Equations (433) can reduce 459 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (459) ~ (all_0_43_43 = e0)
% 21.59/5.67 | (622) all_0_47_47 = e0 | all_0_51_51 = e0 | all_0_56_56 = e0
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (622), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (623) all_0_47_47 = e0
% 21.59/5.67 |
% 21.59/5.67 | Combining equations (469,623) yields a new equation:
% 21.59/5.67 | (578) e1 = e0
% 21.59/5.67 |
% 21.59/5.67 | Simplifying 578 yields:
% 21.59/5.67 | (579) e1 = e0
% 21.59/5.67 |
% 21.59/5.67 | Equations (579) can reduce 144 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (297) ~ (all_0_47_47 = e0)
% 21.59/5.67 | (628) all_0_51_51 = e0 | all_0_56_56 = e0
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (628), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (629) all_0_51_51 = e0
% 21.59/5.67 |
% 21.59/5.67 | Equations (629) can reduce 432 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (432) ~ (all_0_51_51 = e0)
% 21.59/5.67 | (632) all_0_56_56 = e0
% 21.59/5.67 |
% 21.59/5.67 | Equations (632) can reduce 401 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (765) ~ (all_0_53_53 = e0)
% 21.59/5.67 | (493) all_0_58_58 = e0
% 21.59/5.67 |
% 21.59/5.67 | Equations (493) can reduce 403 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (493) all_0_58_58 = e0
% 21.59/5.67 | (614) all_0_59_59 = e1
% 21.59/5.67 |
% 21.59/5.67 | Equations (614) can reduce 2222 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (1315) ~ (all_0_41_41 = e1)
% 21.59/5.67 | (1972) all_0_41_41 = e4 | all_0_41_41 = e3
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (1972), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (605) all_0_41_41 = e3
% 21.59/5.67 |
% 21.59/5.67 | Equations (605) can reduce 609 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (609) ~ (all_0_41_41 = e3)
% 21.59/5.67 | (740) all_0_41_41 = e4
% 21.59/5.67 |
% 21.59/5.67 | Equations (740) can reduce 308 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (356) ~ (all_0_44_44 = e0)
% 21.59/5.67 | (357) all_0_52_52 = e0 | all_0_57_57 = e0
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (357), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (397) all_0_52_52 = e0
% 21.59/5.67 |
% 21.59/5.67 | Combining equations (397,816) yields a new equation:
% 21.59/5.67 | (354) e2 = e0
% 21.59/5.67 |
% 21.59/5.67 | Equations (354) can reduce 58 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (317) ~ (all_0_52_52 = e0)
% 21.59/5.67 | (400) all_0_57_57 = e0
% 21.59/5.67 |
% 21.59/5.67 | Equations (400) can reduce 967 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (257) ~ (all_0_52_52 = e2)
% 21.59/5.67 | (867) all_0_57_57 = e2
% 21.59/5.67 |
% 21.59/5.67 | Equations (867) can reduce 378 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (320) ~ (all_0_39_39 = e2)
% 21.59/5.67 | (709) all_0_39_39 = e4 | all_0_39_39 = e3 | all_0_39_39 = e1
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (709), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (464) all_0_39_39 = e1
% 21.59/5.67 |
% 21.59/5.67 | Equations (464) can reduce 467 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (467) ~ (all_0_39_39 = e1)
% 21.59/5.67 | (1075) all_0_39_39 = e4 | all_0_39_39 = e3
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (1075), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (443) all_0_39_39 = e3
% 21.59/5.67 |
% 21.59/5.67 | Equations (443) can reduce 226 to:
% 21.59/5.67 | (1764) ~ (all_0_41_41 = e3)
% 21.59/5.67 |
% 21.59/5.67 | Simplifying 1764 yields:
% 21.59/5.67 | (609) ~ (all_0_41_41 = e3)
% 21.59/5.67 |
% 21.59/5.67 | Equations (443) can reduce 320 to:
% 21.59/5.67 | (224) ~ (e3 = e2)
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (8), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (348) all_0_39_39 = e2
% 21.59/5.67 |
% 21.59/5.67 | Combining equations (443,348) yields a new equation:
% 21.59/5.67 | (606) e3 = e2
% 21.59/5.67 |
% 21.59/5.67 | Simplifying 606 yields:
% 21.59/5.67 | (423) e3 = e2
% 21.59/5.67 |
% 21.59/5.67 | Equations (423) can reduce 224 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (320) ~ (all_0_39_39 = e2)
% 21.59/5.67 | (396) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (396), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (409) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 21.59/5.67 |
% 21.59/5.67 +-Applying beta-rule and splitting (409), into two cases.
% 21.59/5.67 |-Branch one:
% 21.59/5.67 | (410) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 21.59/5.67 |
% 21.59/5.67 | Applying alpha-rule on (410) yields:
% 21.59/5.67 | (411) all_0_0_0 = e1
% 21.59/5.67 | (412) ~ (all_0_1_1 = e4)
% 21.59/5.67 |
% 21.59/5.67 | Combining equations (411,6747) yields a new equation:
% 21.59/5.67 | (578) e1 = e0
% 21.59/5.67 |
% 21.59/5.67 | Simplifying 578 yields:
% 21.59/5.67 | (579) e1 = e0
% 21.59/5.67 |
% 21.59/5.67 | Equations (579) can reduce 144 to:
% 21.59/5.67 | (269) $false
% 21.59/5.67 |
% 21.59/5.67 |-The branch is then unsatisfiable
% 21.59/5.67 |-Branch two:
% 21.59/5.67 | (641) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 21.59/5.67 |
% 21.59/5.67 | Applying alpha-rule on (641) yields:
% 21.59/5.67 | (285) all_0_2_2 = e0
% 21.59/5.67 | (643) ~ (all_0_3_3 = e4)
% 21.59/5.67 |
% 21.59/5.67 | Combining equations (6748,285) yields a new equation:
% 21.59/5.67 | (6804) all_0_40_40 = e0
% 21.59/5.67 |
% 21.59/5.67 | Simplifying 6804 yields:
% 21.59/5.68 | (6805) all_0_40_40 = e0
% 21.59/5.68 |
% 21.59/5.68 | Equations (6805) can reduce 102 to:
% 21.59/5.68 | (269) $false
% 21.59/5.68 |
% 21.59/5.68 |-The branch is then unsatisfiable
% 21.59/5.68 |-Branch two:
% 21.59/5.68 | (645) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 21.59/5.68 |
% 21.59/5.68 | Applying alpha-rule on (645) yields:
% 21.59/5.68 | (605) all_0_41_41 = e3
% 21.59/5.68 | (537) ~ (all_0_45_45 = e4)
% 21.59/5.68 |
% 21.59/5.68 | Equations (605) can reduce 609 to:
% 21.59/5.68 | (269) $false
% 21.59/5.68 |
% 21.59/5.68 |-The branch is then unsatisfiable
% 21.59/5.68 |-Branch two:
% 21.59/5.68 | (540) ~ (all_0_39_39 = e3)
% 21.59/5.68 | (1079) all_0_39_39 = e4
% 21.59/5.68 |
% 21.59/5.68 | Equations (1079) can reduce 307 to:
% 21.59/5.68 | (269) $false
% 21.59/5.68 |
% 21.59/5.68 |-The branch is then unsatisfiable
% 21.59/5.68 |-Branch two:
% 21.59/5.68 | (1115) ~ (all_0_48_48 = e2)
% 21.59/5.68 | (2607) all_0_48_48 = e1 | all_0_48_48 = e0
% 21.59/5.68 |
% 21.59/5.68 +-Applying beta-rule and splitting (2607), into two cases.
% 21.59/5.68 |-Branch one:
% 21.59/5.68 | (593) all_0_48_48 = e1
% 21.59/5.68 |
% 21.59/5.68 | Equations (593) can reduce 584 to:
% 21.59/5.68 | (269) $false
% 21.59/5.68 |
% 21.59/5.68 |-The branch is then unsatisfiable
% 21.59/5.68 |-Branch two:
% 21.59/5.68 | (584) ~ (all_0_48_48 = e1)
% 21.59/5.68 | (903) all_0_48_48 = e0
% 21.59/5.68 |
% 21.59/5.68 | Equations (903) can reduce 952 to:
% 21.59/5.68 | (269) $false
% 21.59/5.68 |
% 21.59/5.68 |-The branch is then unsatisfiable
% 21.59/5.68 |-Branch two:
% 21.59/5.68 | (903) all_0_48_48 = e0
% 21.59/5.68 | (596) all_0_49_49 = e1
% 21.59/5.68 |
% 21.59/5.68 | Equations (596) can reduce 960 to:
% 21.59/5.68 | (269) $false
% 21.59/5.68 |
% 21.59/5.68 |-The branch is then unsatisfiable
% 21.59/5.68 |-Branch two:
% 21.59/5.68 | (473) ~ (all_0_47_47 = e1)
% 21.59/5.68 | (623) all_0_47_47 = e0
% 21.59/5.68 |
% 21.59/5.68 | Equations (623) can reduce 297 to:
% 21.59/5.68 | (269) $false
% 21.59/5.68 |
% 21.59/5.68 |-The branch is then unsatisfiable
% 21.59/5.68 |-Branch two:
% 21.59/5.68 | (400) all_0_57_57 = e0
% 21.59/5.68 | (375) all_0_59_59 = e2
% 21.59/5.68 |
% 21.59/5.68 | Equations (375) can reduce 1843 to:
% 21.59/5.68 | (269) $false
% 21.59/5.68 |
% 21.59/5.68 |-The branch is then unsatisfiable
% 21.59/5.68 |-Branch two:
% 21.59/5.68 | (2622) all_0_45_45 = e4 & ~ (all_0_42_42 = e1) & ~ (all_0_47_47 = e1) & ~ (unit = e1) & ( ~ (all_0_39_39 = e1) | all_0_41_41 = e3) & ( ~ (all_0_40_40 = e1) | all_0_41_41 = e2) & ( ~ (all_0_49_49 = e1) | all_0_48_48 = e0) & ( ~ (all_0_51_51 = e1) | all_0_53_53 = e3) & ( ~ (all_0_52_52 = e1) | all_0_53_53 = e2) & ( ~ (all_0_54_54 = e1) | all_0_53_53 = e0) & ( ~ (all_0_56_56 = e1) | all_0_58_58 = e3) & ( ~ (all_0_57_57 = e1) | all_0_58_58 = e2) & ( ~ (all_0_59_59 = e1) | all_0_58_58 = e0)
% 21.59/5.68 |
% 21.59/5.68 | Applying alpha-rule on (2622) yields:
% 21.59/5.68 | (2623) ~ (all_0_52_52 = e1) | all_0_53_53 = e2
% 21.59/5.68 | (473) ~ (all_0_47_47 = e1)
% 21.59/5.68 | (2625) ~ (all_0_51_51 = e1) | all_0_53_53 = e3
% 21.59/5.68 | (2626) ~ (all_0_40_40 = e1) | all_0_41_41 = e2
% 21.59/5.68 | (2627) ~ (all_0_56_56 = e1) | all_0_58_58 = e3
% 21.59/5.68 | (2628) ~ (all_0_49_49 = e1) | all_0_48_48 = e0
% 21.59/5.68 | (2629) ~ (all_0_59_59 = e1) | all_0_58_58 = e0
% 21.59/5.68 | (2630) ~ (all_0_54_54 = e1) | all_0_53_53 = e0
% 21.59/5.68 | (2631) ~ (unit = e1)
% 21.59/5.68 | (836) ~ (all_0_42_42 = e1)
% 21.59/5.68 | (2633) ~ (all_0_39_39 = e1) | all_0_41_41 = e3
% 21.59/5.68 | (2634) ~ (all_0_57_57 = e1) | all_0_58_58 = e2
% 21.59/5.68 | (444) all_0_45_45 = e4
% 21.59/5.68 |
% 21.59/5.68 | Equations (444) can reduce 122 to:
% 21.59/5.68 | (308) ~ (all_0_41_41 = e4)
% 21.59/5.68 |
% 21.59/5.68 | Equations (444) can reduce 68 to:
% 21.59/5.68 | (276) ~ (all_0_58_58 = e4)
% 21.59/5.68 |
% 21.59/5.68 | Simplifying 276 yields:
% 21.59/5.68 | (277) ~ (all_0_58_58 = e4)
% 21.59/5.68 |
% 21.59/5.68 +-Applying beta-rule and splitting (2634), into two cases.
% 21.59/5.68 |-Branch one:
% 21.59/5.68 | (581) ~ (all_0_57_57 = e1)
% 21.59/5.68 |
% 21.59/5.68 +-Applying beta-rule and splitting (8), into two cases.
% 21.59/5.68 |-Branch one:
% 21.59/5.68 | (348) all_0_39_39 = e2
% 21.59/5.68 |
% 21.59/5.68 | Equations (348) can reduce 18 to:
% 21.59/5.68 | (1521) ~ (all_0_40_40 = e2)
% 21.59/5.68 |
% 21.59/5.68 | Simplifying 1521 yields:
% 21.59/5.68 | (342) ~ (all_0_40_40 = e2)
% 21.59/5.68 |
% 21.59/5.68 | Equations (348) can reduce 226 to:
% 21.59/5.68 | (1797) ~ (all_0_41_41 = e2)
% 21.59/5.68 |
% 21.59/5.68 | Simplifying 1797 yields:
% 21.59/5.68 | (650) ~ (all_0_41_41 = e2)
% 21.59/5.68 |
% 21.59/5.68 | Equations (348) can reduce 157 to:
% 21.59/5.68 | (5274) ~ (all_0_42_42 = e2)
% 21.59/5.68 |
% 21.59/5.68 | Simplifying 5274 yields:
% 21.59/5.68 | (362) ~ (all_0_42_42 = e2)
% 21.59/5.68 |
% 21.59/5.68 | Equations (348) can reduce 164 to:
% 21.59/5.68 | (8468) ~ (all_0_47_47 = e2)
% 21.59/5.68 |
% 21.59/5.68 | Simplifying 8468 yields:
% 21.59/5.68 | (1442) ~ (all_0_47_47 = e2)
% 21.59/5.68 |
% 21.59/5.68 +-Applying beta-rule and splitting (29), into two cases.
% 21.59/5.68 |-Branch one:
% 21.59/5.68 | (1079) all_0_39_39 = e4
% 21.59/5.68 |
% 21.59/5.68 | Combining equations (348,1079) yields a new equation:
% 21.59/5.68 | (360) e4 = e2
% 21.59/5.68 |
% 21.59/5.68 | Equations (360) can reduce 230 to:
% 21.59/5.68 | (269) $false
% 21.59/5.68 |
% 21.59/5.68 |-The branch is then unsatisfiable
% 21.59/5.68 |-Branch two:
% 21.59/5.68 | (307) ~ (all_0_39_39 = e4)
% 21.59/5.68 | (1391) all_0_43_43 = e4 | all_0_51_51 = e4 | all_0_56_56 = e4
% 21.59/5.68 |
% 21.59/5.68 | Equations (348) can reduce 307 to:
% 21.59/5.68 | (326) ~ (e4 = e2)
% 21.59/5.68 |
% 21.59/5.68 | Simplifying 326 yields:
% 21.59/5.68 | (230) ~ (e4 = e2)
% 21.59/5.68 |
% 21.59/5.68 +-Applying beta-rule and splitting (32), into two cases.
% 21.59/5.68 |-Branch one:
% 21.59/5.68 | (1079) all_0_39_39 = e4
% 21.59/5.68 |
% 21.59/5.68 | Combining equations (348,1079) yields a new equation:
% 21.59/5.68 | (360) e4 = e2
% 21.59/5.68 |
% 21.59/5.68 | Equations (360) can reduce 230 to:
% 21.59/5.68 | (269) $false
% 21.59/5.68 |
% 21.59/5.68 |-The branch is then unsatisfiable
% 21.59/5.68 |-Branch two:
% 21.59/5.68 | (307) ~ (all_0_39_39 = e4)
% 21.59/5.68 | (3018) all_0_41_41 = e4 | all_0_42_42 = e4
% 21.59/5.68 |
% 21.59/5.68 +-Applying beta-rule and splitting (3018), into two cases.
% 21.59/5.68 |-Branch one:
% 21.59/5.68 | (740) all_0_41_41 = e4
% 21.59/5.68 |
% 21.59/5.68 | Equations (740) can reduce 308 to:
% 21.59/5.68 | (269) $false
% 21.59/5.68 |
% 21.59/5.68 |-The branch is then unsatisfiable
% 21.59/5.68 |-Branch two:
% 21.59/5.68 | (308) ~ (all_0_41_41 = e4)
% 21.59/5.68 | (305) all_0_42_42 = e4
% 21.59/5.68 |
% 21.59/5.68 | Equations (305) can reduce 214 to:
% 21.59/5.68 | (308) ~ (all_0_41_41 = e4)
% 21.59/5.68 |
% 21.59/5.68 | Equations (305) can reduce 103 to:
% 21.59/5.68 | (278) ~ (all_0_59_59 = e4)
% 21.59/5.68 |
% 21.59/5.68 | Simplifying 278 yields:
% 21.59/5.68 | (279) ~ (all_0_59_59 = e4)
% 21.59/5.68 |
% 21.59/5.68 | Equations (305) can reduce 362 to:
% 21.59/5.68 | (230) ~ (e4 = e2)
% 21.59/5.68 |
% 21.59/5.68 +-Applying beta-rule and splitting (73), into two cases.
% 21.59/5.68 |-Branch one:
% 21.59/5.68 | (271) all_0_55_55 = e4
% 21.59/5.68 |
% 21.59/5.68 | Combining equations (271,268) yields a new equation:
% 21.59/5.68 | (359) e4 = e2
% 21.59/5.68 |
% 21.59/5.68 | Simplifying 359 yields:
% 21.59/5.68 | (360) e4 = e2
% 21.59/5.68 |
% 21.59/5.68 | Equations (360) can reduce 230 to:
% 21.59/5.68 | (269) $false
% 21.59/5.68 |
% 21.59/5.68 |-The branch is then unsatisfiable
% 21.59/5.68 |-Branch two:
% 21.59/5.68 | (6730) ~ (all_0_55_55 = e4)
% 21.59/5.68 | (6843) all_0_56_56 = e4 | all_0_58_58 = e4 | all_0_59_59 = e4
% 21.59/5.68 |
% 21.59/5.68 +-Applying beta-rule and splitting (6843), into two cases.
% 21.59/5.68 |-Branch one:
% 21.59/5.68 | (1658) all_0_56_56 = e4
% 21.59/5.68 |
% 21.59/5.68 | Equations (1658) can reduce 223 to:
% 21.59/5.68 | (276) ~ (all_0_58_58 = e4)
% 21.59/5.68 |
% 21.59/5.68 | Simplifying 276 yields:
% 21.59/5.68 | (277) ~ (all_0_58_58 = e4)
% 21.59/5.68 |
% 21.59/5.68 +-Applying beta-rule and splitting (2626), into two cases.
% 21.59/5.68 |-Branch one:
% 21.59/5.68 | (983) ~ (all_0_40_40 = e1)
% 21.59/5.68 |
% 21.59/5.68 +-Applying beta-rule and splitting (17), into two cases.
% 21.59/5.68 |-Branch one:
% 21.59/5.68 | (382) all_0_40_40 = e2
% 21.59/5.68 |
% 21.59/5.68 | Equations (382) can reduce 342 to:
% 21.59/5.68 | (269) $false
% 21.59/5.68 |
% 21.59/5.68 |-The branch is then unsatisfiable
% 21.59/5.68 |-Branch two:
% 21.59/5.68 | (342) ~ (all_0_40_40 = e2)
% 21.59/5.68 | (1093) all_0_40_40 = e3 | all_0_40_40 = e1
% 21.59/5.68 |
% 21.59/5.68 +-Applying beta-rule and splitting (1093), into two cases.
% 21.59/5.68 |-Branch one:
% 21.59/5.68 | (413) all_0_40_40 = e1
% 21.59/5.68 |
% 21.59/5.68 | Equations (413) can reduce 983 to:
% 21.59/5.68 | (269) $false
% 21.59/5.68 |
% 21.59/5.68 |-The branch is then unsatisfiable
% 21.59/5.68 |-Branch two:
% 21.59/5.68 | (983) ~ (all_0_40_40 = e1)
% 21.59/5.68 | (417) all_0_40_40 = e3
% 21.59/5.68 |
% 21.59/5.68 | Equations (417) can reduce 88 to:
% 21.59/5.68 | (1764) ~ (all_0_41_41 = e3)
% 21.59/5.68 |
% 21.59/5.68 | Simplifying 1764 yields:
% 21.59/5.68 | (609) ~ (all_0_41_41 = e3)
% 21.59/5.68 |
% 21.59/5.68 | Equations (417) can reduce 168 to:
% 21.59/5.68 | (786) ~ (all_0_57_57 = e3)
% 21.59/5.68 |
% 21.59/5.68 | Simplifying 786 yields:
% 21.59/5.68 | (787) ~ (all_0_57_57 = e3)
% 21.59/5.68 |
% 21.59/5.68 +-Applying beta-rule and splitting (94), into two cases.
% 21.59/5.68 |-Branch one:
% 21.59/5.68 | (386) all_0_41_41 = e2
% 21.59/5.68 |
% 21.59/5.68 | Equations (386) can reduce 650 to:
% 21.59/5.68 | (269) $false
% 21.59/5.68 |
% 21.59/5.68 |-The branch is then unsatisfiable
% 21.59/5.68 |-Branch two:
% 21.59/5.68 | (650) ~ (all_0_41_41 = e2)
% 21.59/5.68 | (1903) all_0_41_41 = e4 | all_0_41_41 = e3 | all_0_41_41 = e1
% 21.59/5.68 |
% 21.59/5.68 +-Applying beta-rule and splitting (1903), into two cases.
% 21.59/5.68 |-Branch one:
% 21.59/5.68 | (1312) all_0_41_41 = e1
% 21.59/5.68 |
% 21.59/5.68 | Equations (1312) can reduce 167 to:
% 21.59/5.68 | (1446) ~ (all_0_48_48 = e1)
% 21.59/5.68 |
% 21.59/5.68 | Simplifying 1446 yields:
% 21.59/5.68 | (584) ~ (all_0_48_48 = e1)
% 21.59/5.68 |
% 21.59/5.68 | Equations (1312) can reduce 208 to:
% 21.59/5.68 | (481) ~ (all_0_58_58 = e1)
% 21.59/5.68 |
% 21.59/5.68 | Simplifying 481 yields:
% 21.59/5.68 | (482) ~ (all_0_58_58 = e1)
% 21.59/5.68 |
% 21.59/5.68 | Equations (1312) can reduce 308 to:
% 21.59/5.68 | (826) ~ (e4 = e1)
% 21.59/5.68 |
% 21.59/5.68 | Simplifying 826 yields:
% 21.59/5.68 | (251) ~ (e4 = e1)
% 21.59/5.68 |
% 21.59/5.68 +-Applying beta-rule and splitting (134), into two cases.
% 21.59/5.68 |-Branch one:
% 21.59/5.68 | (867) all_0_57_57 = e2
% 21.59/5.68 |
% 21.59/5.68 | Equations (867) can reduce 378 to:
% 21.59/5.68 | (269) $false
% 21.59/5.68 |
% 21.59/5.68 |-The branch is then unsatisfiable
% 21.59/5.68 |-Branch two:
% 21.59/5.68 | (378) ~ (all_0_57_57 = e2)
% 21.59/5.68 | (870) all_0_57_57 = e3 | all_0_57_57 = e1 | all_0_57_57 = e0
% 21.59/5.68 |
% 21.59/5.68 +-Applying beta-rule and splitting (870), into two cases.
% 21.59/5.68 |-Branch one:
% 21.59/5.68 | (577) all_0_57_57 = e1
% 21.59/5.68 |
% 21.59/5.68 | Equations (577) can reduce 581 to:
% 21.59/5.68 | (269) $false
% 21.59/5.68 |
% 21.59/5.68 |-The branch is then unsatisfiable
% 21.59/5.68 |-Branch two:
% 21.59/5.68 | (581) ~ (all_0_57_57 = e1)
% 21.59/5.68 | (874) all_0_57_57 = e3 | all_0_57_57 = e0
% 21.59/5.68 |
% 21.59/5.68 +-Applying beta-rule and splitting (874), into two cases.
% 21.59/5.68 |-Branch one:
% 21.59/5.68 | (400) all_0_57_57 = e0
% 21.59/5.68 |
% 21.59/5.68 | Equations (400) can reduce 252 to:
% 21.59/5.68 | (402) ~ (all_0_58_58 = e0)
% 21.59/5.68 |
% 21.59/5.68 | Simplifying 402 yields:
% 21.59/5.68 | (403) ~ (all_0_58_58 = e0)
% 21.59/5.68 |
% 21.59/5.68 +-Applying beta-rule and splitting (189), into two cases.
% 21.59/5.68 |-Branch one:
% 21.59/5.68 | (319) all_0_47_47 = e2
% 21.59/5.68 |
% 21.59/5.68 | Equations (319) can reduce 1442 to:
% 21.59/5.68 | (269) $false
% 21.59/5.68 |
% 21.59/5.68 |-The branch is then unsatisfiable
% 21.59/5.68 |-Branch two:
% 21.59/5.68 | (1442) ~ (all_0_47_47 = e2)
% 21.59/5.68 | (1443) all_0_47_47 = e1 | all_0_47_47 = e0
% 21.59/5.68 |
% 21.59/5.68 +-Applying beta-rule and splitting (192), into two cases.
% 21.59/5.68 |-Branch one:
% 21.59/5.68 | (469) all_0_47_47 = e1
% 21.59/5.68 |
% 21.59/5.68 | Equations (469) can reduce 473 to:
% 21.59/5.68 | (269) $false
% 21.59/5.68 |
% 21.59/5.68 |-The branch is then unsatisfiable
% 21.59/5.68 |-Branch two:
% 21.59/5.68 | (473) ~ (all_0_47_47 = e1)
% 21.59/5.68 | (592) all_0_48_48 = e1 | all_0_49_49 = e1
% 21.59/5.68 |
% 21.59/5.68 +-Applying beta-rule and splitting (1443), into two cases.
% 21.59/5.68 |-Branch one:
% 21.59/5.68 | (469) all_0_47_47 = e1
% 21.59/5.68 |
% 21.59/5.68 | Equations (469) can reduce 473 to:
% 21.59/5.68 | (269) $false
% 21.59/5.68 |
% 21.59/5.68 |-The branch is then unsatisfiable
% 21.59/5.68 |-Branch two:
% 21.59/5.68 | (473) ~ (all_0_47_47 = e1)
% 21.59/5.68 | (623) all_0_47_47 = e0
% 21.59/5.68 |
% 21.59/5.68 | Equations (623) can reduce 145 to:
% 21.59/5.68 | (806) ~ (all_0_49_49 = e0)
% 21.59/5.68 |
% 21.59/5.68 | Simplifying 806 yields:
% 21.59/5.68 | (807) ~ (all_0_49_49 = e0)
% 21.59/5.68 |
% 21.59/5.68 +-Applying beta-rule and splitting (43), into two cases.
% 21.59/5.68 |-Branch one:
% 21.59/5.68 | (480) all_0_56_56 = e1
% 21.59/5.68 |
% 21.59/5.68 | Combining equations (1658,480) yields a new equation:
% 21.59/5.68 | (476) e4 = e1
% 21.59/5.68 |
% 21.59/5.68 | Simplifying 476 yields:
% 21.59/5.68 | (477) e4 = e1
% 21.59/5.68 |
% 21.59/5.68 | Equations (477) can reduce 251 to:
% 21.59/5.68 | (269) $false
% 21.59/5.68 |
% 21.59/5.68 |-The branch is then unsatisfiable
% 21.59/5.68 |-Branch two:
% 21.59/5.68 | (575) ~ (all_0_56_56 = e1)
% 21.59/5.68 | (576) all_0_57_57 = e1 | all_0_58_58 = e1 | all_0_59_59 = e1
% 21.59/5.68 |
% 21.59/5.68 +-Applying beta-rule and splitting (592), into two cases.
% 21.59/5.68 |-Branch one:
% 21.59/5.68 | (593) all_0_48_48 = e1
% 21.59/5.68 |
% 21.59/5.68 | Equations (593) can reduce 584 to:
% 21.59/5.68 | (269) $false
% 21.59/5.68 |
% 21.59/5.68 |-The branch is then unsatisfiable
% 21.59/5.68 |-Branch two:
% 21.59/5.68 | (584) ~ (all_0_48_48 = e1)
% 21.59/5.68 | (596) all_0_49_49 = e1
% 21.59/5.68 |
% 21.59/5.68 | Equations (596) can reduce 82 to:
% 21.59/5.68 | (5696) ~ (all_0_59_59 = e1)
% 21.59/5.68 |
% 21.59/5.69 | Simplifying 5696 yields:
% 21.59/5.69 | (2222) ~ (all_0_59_59 = e1)
% 21.59/5.69 |
% 21.59/5.69 | Equations (596) can reduce 807 to:
% 21.59/5.69 | (144) ~ (e1 = e0)
% 21.59/5.69 |
% 21.59/5.69 +-Applying beta-rule and splitting (2), into two cases.
% 21.59/5.69 |-Branch one:
% 21.59/5.69 | (485) all_0_58_58 = e2
% 21.59/5.69 |
% 21.59/5.69 | Equations (485) can reduce 392 to:
% 21.59/5.69 | (269) $false
% 21.59/5.69 |
% 21.59/5.69 |-The branch is then unsatisfiable
% 21.59/5.69 |-Branch two:
% 21.59/5.69 | (392) ~ (all_0_58_58 = e2)
% 21.59/5.69 | (488) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e1 | all_0_58_58 = e0
% 21.59/5.69 |
% 21.59/5.69 +-Applying beta-rule and splitting (488), into two cases.
% 21.59/5.69 |-Branch one:
% 21.59/5.69 | (489) all_0_58_58 = e1
% 21.59/5.69 |
% 21.59/5.69 | Equations (489) can reduce 482 to:
% 21.59/5.69 | (269) $false
% 21.59/5.69 |
% 21.59/5.69 |-The branch is then unsatisfiable
% 21.59/5.69 |-Branch two:
% 21.59/5.69 | (482) ~ (all_0_58_58 = e1)
% 21.59/5.69 | (492) all_0_58_58 = e4 | all_0_58_58 = e3 | all_0_58_58 = e0
% 21.59/5.69 |
% 21.59/5.69 +-Applying beta-rule and splitting (492), into two cases.
% 21.59/5.69 |-Branch one:
% 21.59/5.69 | (493) all_0_58_58 = e0
% 21.59/5.69 |
% 21.59/5.69 | Equations (493) can reduce 403 to:
% 21.59/5.69 | (269) $false
% 21.59/5.69 |
% 21.59/5.69 |-The branch is then unsatisfiable
% 21.59/5.69 |-Branch two:
% 21.59/5.69 | (403) ~ (all_0_58_58 = e0)
% 21.59/5.69 | (496) all_0_58_58 = e4 | all_0_58_58 = e3
% 21.59/5.69 |
% 21.59/5.69 +-Applying beta-rule and splitting (496), into two cases.
% 21.59/5.69 |-Branch one:
% 21.59/5.69 | (497) all_0_58_58 = e3
% 21.59/5.69 |
% 21.59/5.69 | Equations (497) can reduce 482 to:
% 21.59/5.69 | (146) ~ (e3 = e1)
% 21.59/5.69 |
% 21.59/5.69 +-Applying beta-rule and splitting (576), into two cases.
% 21.59/5.69 |-Branch one:
% 21.59/5.69 | (577) all_0_57_57 = e1
% 21.59/5.69 |
% 21.59/5.69 | Combining equations (400,577) yields a new equation:
% 21.59/5.69 | (579) e1 = e0
% 21.59/5.69 |
% 21.59/5.69 | Equations (579) can reduce 144 to:
% 21.59/5.69 | (269) $false
% 21.59/5.69 |
% 21.59/5.69 |-The branch is then unsatisfiable
% 21.59/5.69 |-Branch two:
% 21.59/5.69 | (581) ~ (all_0_57_57 = e1)
% 21.59/5.69 | (582) all_0_58_58 = e1 | all_0_59_59 = e1
% 21.59/5.69 |
% 21.59/5.69 +-Applying beta-rule and splitting (582), into two cases.
% 21.59/5.69 |-Branch one:
% 21.59/5.69 | (489) all_0_58_58 = e1
% 21.59/5.69 |
% 21.59/5.69 | Combining equations (489,497) yields a new equation:
% 21.59/5.69 | (418) e3 = e1
% 21.59/5.69 |
% 21.59/5.69 | Equations (418) can reduce 146 to:
% 21.59/5.69 | (269) $false
% 21.59/5.69 |
% 21.59/5.69 |-The branch is then unsatisfiable
% 21.59/5.69 |-Branch two:
% 21.59/5.69 | (482) ~ (all_0_58_58 = e1)
% 21.59/5.69 | (614) all_0_59_59 = e1
% 21.59/5.69 |
% 21.59/5.69 | Equations (614) can reduce 2222 to:
% 21.59/5.69 | (269) $false
% 21.59/5.69 |
% 21.59/5.69 |-The branch is then unsatisfiable
% 21.59/5.69 |-Branch two:
% 21.59/5.69 | (527) ~ (all_0_58_58 = e3)
% 21.59/5.69 | (528) all_0_58_58 = e4
% 21.59/5.69 |
% 21.59/5.69 | Equations (528) can reduce 277 to:
% 21.59/5.69 | (269) $false
% 21.59/5.69 |
% 21.59/5.69 |-The branch is then unsatisfiable
% 21.59/5.69 |-Branch two:
% 21.59/5.69 | (967) ~ (all_0_57_57 = e0)
% 21.59/5.69 | (638) all_0_57_57 = e3
% 21.59/5.69 |
% 21.59/5.69 | Equations (638) can reduce 787 to:
% 21.59/5.69 | (269) $false
% 21.59/5.69 |
% 21.59/5.69 |-The branch is then unsatisfiable
% 21.59/5.69 |-Branch two:
% 21.59/5.69 | (1315) ~ (all_0_41_41 = e1)
% 21.59/5.69 | (1972) all_0_41_41 = e4 | all_0_41_41 = e3
% 21.59/5.69 |
% 21.59/5.69 +-Applying beta-rule and splitting (1972), into two cases.
% 21.59/5.69 |-Branch one:
% 21.59/5.69 | (605) all_0_41_41 = e3
% 21.59/5.69 |
% 21.59/5.69 | Equations (605) can reduce 609 to:
% 21.59/5.69 | (269) $false
% 21.59/5.69 |
% 21.59/5.69 |-The branch is then unsatisfiable
% 21.59/5.69 |-Branch two:
% 21.59/5.69 | (609) ~ (all_0_41_41 = e3)
% 21.59/5.69 | (740) all_0_41_41 = e4
% 21.59/5.69 |
% 21.59/5.69 | Equations (740) can reduce 308 to:
% 21.59/5.69 | (269) $false
% 21.59/5.69 |
% 21.59/5.69 |-The branch is then unsatisfiable
% 21.59/5.69 |-Branch two:
% 21.59/5.69 | (413) all_0_40_40 = e1
% 21.59/5.69 | (386) all_0_41_41 = e2
% 21.59/5.69 |
% 21.59/5.69 | Equations (386) can reduce 650 to:
% 21.59/5.69 | (269) $false
% 21.59/5.69 |
% 21.59/5.69 |-The branch is then unsatisfiable
% 21.59/5.69 |-Branch two:
% 21.59/5.69 | (273) ~ (all_0_56_56 = e4)
% 21.59/5.69 | (6880) all_0_58_58 = e4 | all_0_59_59 = e4
% 21.59/5.69 |
% 21.59/5.69 +-Applying beta-rule and splitting (6880), into two cases.
% 21.59/5.69 |-Branch one:
% 21.59/5.69 | (528) all_0_58_58 = e4
% 21.59/5.69 |
% 21.59/5.69 | Equations (528) can reduce 277 to:
% 21.59/5.69 | (269) $false
% 21.59/5.69 |
% 21.59/5.69 |-The branch is then unsatisfiable
% 21.59/5.69 |-Branch two:
% 21.59/5.69 | (277) ~ (all_0_58_58 = e4)
% 21.59/5.69 | (2231) all_0_59_59 = e4
% 21.59/5.69 |
% 21.59/5.69 | Equations (2231) can reduce 279 to:
% 21.59/5.69 | (269) $false
% 21.59/5.69 |
% 21.59/5.69 |-The branch is then unsatisfiable
% 21.59/5.69 |-Branch two:
% 21.59/5.69 | (320) ~ (all_0_39_39 = e2)
% 21.59/5.69 | (396) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4)) | (all_0_41_41 = e3 & ~ (all_0_45_45 = e4))
% 21.59/5.69 |
% 21.59/5.69 +-Applying beta-rule and splitting (396), into two cases.
% 21.59/5.69 |-Branch one:
% 21.59/5.69 | (409) (all_0_0_0 = e1 & ~ (all_0_1_1 = e4)) | (all_0_2_2 = e0 & ~ (all_0_3_3 = e4))
% 21.59/5.69 |
% 21.59/5.69 +-Applying beta-rule and splitting (409), into two cases.
% 21.59/5.69 |-Branch one:
% 21.59/5.69 | (410) all_0_0_0 = e1 & ~ (all_0_1_1 = e4)
% 21.59/5.69 |
% 21.59/5.69 | Applying alpha-rule on (410) yields:
% 21.59/5.69 | (411) all_0_0_0 = e1
% 21.59/5.69 | (412) ~ (all_0_1_1 = e4)
% 21.59/5.69 |
% 21.59/5.69 | Combining equations (411,6747) yields a new equation:
% 21.59/5.69 | (578) e1 = e0
% 21.59/5.69 |
% 21.59/5.69 | Simplifying 578 yields:
% 21.59/5.69 | (579) e1 = e0
% 21.59/5.69 |
% 21.59/5.69 | Equations (579) can reduce 144 to:
% 21.59/5.69 | (269) $false
% 21.59/5.69 |
% 21.59/5.69 |-The branch is then unsatisfiable
% 21.59/5.69 |-Branch two:
% 21.59/5.69 | (641) all_0_2_2 = e0 & ~ (all_0_3_3 = e4)
% 21.59/5.69 |
% 21.59/5.69 | Applying alpha-rule on (641) yields:
% 21.59/5.69 | (285) all_0_2_2 = e0
% 21.59/5.69 | (643) ~ (all_0_3_3 = e4)
% 21.59/5.69 |
% 21.59/5.69 | Combining equations (6748,285) yields a new equation:
% 21.59/5.69 | (6804) all_0_40_40 = e0
% 21.59/5.69 |
% 21.59/5.69 | Simplifying 6804 yields:
% 21.59/5.69 | (6805) all_0_40_40 = e0
% 21.59/5.69 |
% 21.59/5.69 | Equations (6805) can reduce 102 to:
% 21.59/5.69 | (269) $false
% 21.59/5.69 |
% 21.59/5.69 |-The branch is then unsatisfiable
% 21.59/5.69 |-Branch two:
% 21.59/5.69 | (645) all_0_41_41 = e3 & ~ (all_0_45_45 = e4)
% 21.59/5.69 |
% 21.59/5.69 | Applying alpha-rule on (645) yields:
% 21.59/5.69 | (605) all_0_41_41 = e3
% 21.59/5.69 | (537) ~ (all_0_45_45 = e4)
% 21.59/5.69 |
% 21.59/5.69 | Equations (444) can reduce 537 to:
% 21.59/5.69 | (269) $false
% 21.59/5.69 |
% 21.59/5.69 |-The branch is then unsatisfiable
% 21.59/5.69 |-Branch two:
% 21.59/5.69 | (577) all_0_57_57 = e1
% 21.59/5.69 | (485) all_0_58_58 = e2
% 21.59/5.69 |
% 21.59/5.69 | Equations (485) can reduce 392 to:
% 21.59/5.69 | (269) $false
% 21.59/5.69 |
% 21.59/5.69 |-The branch is then unsatisfiable
% 21.59/5.69 |-Branch two:
% 21.59/5.69 | (6698) ~ (all_0_42_42 = e2) & ~ (all_0_45_45 = e2) & ~ (all_0_47_47 = e2) & ~ (all_0_48_48 = e2) & ~ (all_0_49_49 = e2) & ~ (all_0_50_50 = e2) & ~ (all_0_55_55 = e2) & ( ~ (all_0_39_39 = e2) | (all_0_40_40 = e3 & ~ (unit = e2))) & ( ~ (all_0_40_40 = e2) | ~ (unit = e2)) & ( ~ (all_0_41_41 = e2) | (all_0_40_40 = e1 & ~ (unit = e2))) & ( ~ (all_0_43_43 = e2) | (all_0_44_44 = e3 & ~ (unit = e2))) & ( ~ (all_0_44_44 = e2) | ~ (unit = e2)) & ( ~ (all_0_46_46 = e2) | (all_0_44_44 = e0 & ~ (unit = e2))) & ( ~ (all_0_51_51 = e2) | (all_0_52_52 = e3 & ~ (unit = e2))) & ( ~ (all_0_52_52 = e2) | ~ (unit = e2)) & ( ~ (all_0_53_53 = e2) | (all_0_52_52 = e1 & ~ (unit = e2))) & ( ~ (all_0_54_54 = e2) | (all_0_52_52 = e0 & ~ (unit = e2))) & ( ~ (all_0_56_56 = e2) | (all_0_57_57 = e3 & ~ (unit = e2))) & ( ~ (all_0_57_57 = e2) | ~ (unit = e2)) & ( ~ (all_0_58_58 = e2) | (all_0_57_57 = e1 & ~ (unit = e2))) & ( ~ (all_0_59_59 = e2) | (all_0_57_57 = e0 & ~ (unit = e2)))
% 21.59/5.69 |
% 21.59/5.69 | Applying alpha-rule on (6698) yields:
% 21.59/5.69 | (6699) ~ (all_0_57_57 = e2) | ~ (unit = e2)
% 21.59/5.69 | (6700) ~ (all_0_53_53 = e2) | (all_0_52_52 = e1 & ~ (unit = e2))
% 21.59/5.69 | (362) ~ (all_0_42_42 = e2)
% 21.59/5.69 | (6702) ~ (all_0_52_52 = e2) | ~ (unit = e2)
% 21.59/5.69 | (390) ~ (all_0_45_45 = e2)
% 21.59/5.69 | (1442) ~ (all_0_47_47 = e2)
% 21.59/5.69 | (6705) ~ (all_0_54_54 = e2) | (all_0_52_52 = e0 & ~ (unit = e2))
% 21.59/5.69 | (6706) ~ (all_0_39_39 = e2) | (all_0_40_40 = e3 & ~ (unit = e2))
% 21.59/5.69 | (6707) ~ (all_0_40_40 = e2) | ~ (unit = e2)
% 21.59/5.69 | (6708) ~ (all_0_59_59 = e2) | (all_0_57_57 = e0 & ~ (unit = e2))
% 21.59/5.69 | (6709) ~ (all_0_58_58 = e2) | (all_0_57_57 = e1 & ~ (unit = e2))
% 21.59/5.69 | (6710) ~ (all_0_46_46 = e2) | (all_0_44_44 = e0 & ~ (unit = e2))
% 21.59/5.69 | (263) ~ (all_0_55_55 = e2)
% 21.59/5.69 | (323) ~ (all_0_49_49 = e2)
% 21.59/5.69 | (6713) ~ (all_0_51_51 = e2) | (all_0_52_52 = e3 & ~ (unit = e2))
% 21.59/5.69 | (6714) ~ (all_0_43_43 = e2) | (all_0_44_44 = e3 & ~ (unit = e2))
% 21.59/5.69 | (6715) ~ (all_0_41_41 = e2) | (all_0_40_40 = e1 & ~ (unit = e2))
% 21.59/5.69 | (6716) ~ (all_0_50_50 = e2)
% 21.59/5.69 | (1115) ~ (all_0_48_48 = e2)
% 21.59/5.69 | (6718) ~ (all_0_56_56 = e2) | (all_0_57_57 = e3 & ~ (unit = e2))
% 21.59/5.69 | (6719) ~ (all_0_44_44 = e2) | ~ (unit = e2)
% 21.59/5.69 |
% 21.59/5.69 | Equations (268) can reduce 263 to:
% 21.59/5.69 | (269) $false
% 21.59/5.69 |
% 21.59/5.69 |-The branch is then unsatisfiable
% 21.59/5.69 |-Branch two:
% 21.59/5.69 | (263) ~ (all_0_55_55 = e2)
% 21.59/5.69 | (271) all_0_55_55 = e4
% 21.59/5.69 |
% 21.59/5.69 | Equations (271) can reduce 6730 to:
% 21.59/5.69 | (269) $false
% 21.59/5.69 |
% 21.59/5.69 |-The branch is then unsatisfiable
% 21.59/5.69 % SZS output end Proof for theBenchmark
% 21.59/5.69
% 21.59/5.69 5105ms
%------------------------------------------------------------------------------