TSTP Solution File: ALG136+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG136+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 15:36:14 EDT 2022
% Result : Unsatisfiable 5.34s 1.83s
% Output : Proof 13.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ALG136+1 : TPTP v8.1.0. Released v2.7.0.
% 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 8 17:52:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.57/0.59 ____ _
% 0.57/0.59 ___ / __ \_____(_)___ ________ __________
% 0.57/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.59
% 0.57/0.59 A Theorem Prover for First-Order Logic
% 0.57/0.59 (ePrincess v.1.0)
% 0.57/0.59
% 0.57/0.59 (c) Philipp Rümmer, 2009-2015
% 0.57/0.59 (c) Peter Backeman, 2014-2015
% 0.57/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.59 Bug reports to peter@backeman.se
% 0.57/0.59
% 0.57/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.59
% 0.57/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.34/1.11 Prover 0: Preprocessing ...
% 3.46/1.39 Prover 0: Constructing countermodel ...
% 5.34/1.83 Prover 0: proved (1184ms)
% 5.34/1.83
% 5.34/1.83 No countermodel exists, formula is valid
% 5.34/1.83 % SZS status Unsatisfiable for theBenchmark
% 5.34/1.83
% 5.34/1.83 Generating proof ... found it (size 2839)
% 11.74/3.30
% 11.74/3.30 % SZS output start Proof for theBenchmark
% 11.74/3.30 Assumed formulas after preprocessing and simplification:
% 11.74/3.30 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = v12) & ~ (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v15 = e3) & ~ (v14 = v13) & ~ (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & ~ (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 = v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = v9) & ~ (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) & ~ (v10 = v8) & ~ (v10 = v6) & ~ (v10 = v2) & ~ (v10 = e2) & ~ (v9 = v8) & ~ (v9 = v5) & ~ (v9 = v1) & ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v4) & ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ (v5 = v1) & ~ (v5 = e1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & ~ (v0 = e0) & ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ (e1 = e0) & op(v22, v0) = v23 & op(v20, v5) = v21 & op(v18, v10) = v19 & op(v16, v15) = v17 & op(e3, v15) = v16 & op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, v10) = v18 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, v5) = v20 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, v0) = v22 & op(e0, e3) = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & ! [v24] : ! [v25] : ! [v26] : ! [v27] : (v25 = v24 | ~ (op(v27, v26) = v25) | ~ (op(v27, v26) = v24)) & ( ~ (v23 = e3) | ~ (v22 = e2) | ~ (v0 = e1)) & ( ~ (v23 = e3) | ~ (v22 = e1) | ~ (v0 = e2)) & ( ~ (v23 = e2) | ~ (v22 = e3) | ~ (v0 = e1)) & ( ~ (v23 = e2) | ~ (v22 = e1) | ~ (v0 = e3)) & ( ~ (v23 = e1) | ~ (v22 = e3) | ~ (v0 = e2)) & ( ~ (v23 = e1) | ~ (v22 = e2) | ~ (v0 = e3)) & ( ~ (v21 = e3) | ~ (v20 = e2) | ~ (v5 = e0)) & ( ~ (v21 = e3) | ~ (v20 = e0) | ~ (v5 = e2)) & ( ~ (v21 = e2) | ~ (v20 = e3) | ~ (v5 = e0)) & ( ~ (v21 = e2) | ~ (v20 = e0) | ~ (v5 = e3)) & ( ~ (v21 = e0) | ~ (v20 = e3) | ~ (v5 = e2)) & ( ~ (v21 = e0) | ~ (v20 = e2) | ~ (v5 = e3)) & ( ~ (v19 = e3) | ~ (v18 = e1) | ~ (v10 = e0)) & ( ~ (v19 = e3) | ~ (v18 = e0) | ~ (v10 = e1)) & ( ~ (v19 = e1) | ~ (v18 = e3) | ~ (v10 = e0)) & ( ~ (v19 = e1) | ~ (v18 = e0) | ~ (v10 = e3)) & ( ~ (v19 = e0) | ~ (v18 = e3) | ~ (v10 = e1)) & ( ~ (v19 = e0) | ~ (v18 = e1) | ~ (v10 = e3)) & ( ~ (v17 = e2) | ~ (v16 = e1) | ~ (v15 = e0)) & ( ~ (v17 = e2) | ~ (v16 = e0) | ~ (v15 = e1)) & ( ~ (v17 = e1) | ~ (v16 = e2) | ~ (v15 = e0)) & ( ~ (v17 = e1) | ~ (v16 = e0) | ~ (v15 = e2)) & ( ~ (v17 = e0) | ~ (v16 = e2) | ~ (v15 = e1)) & ( ~ (v17 = e0) | ~ (v16 = e1) | ~ (v15 = e2)) & ( ~ (v15 = e2) | ~ (v14 = e3)) & ( ~ (v15 = e2) | ~ (v6 = e1)) & ( ~ (v15 = e2) | ~ (v2 = e0)) & ( ~ (v15 = e1) | ~ (v13 = e3)) & ( ~ (v15 = e1) | ~ (v9 = e2)) & ( ~ (v15 = e1) | ~ (v1 = e0)) & ( ~ (v15 = e0) | ~ (v12 = e3)) & ( ~ (v15 = e0) | ~ (v8 = e2)) & ( ~ (v15 = e0) | ~ (v4 = e1)) & ( ~ (v14 = e3) | ~ (v5 = e2)) & ( ~ (v14 = e3) | ~ (v0 = e2)) & ( ~ (v13 = e3) | ~ (v10 = e1)) & ( ~ (v13 = e3) | ~ (v0 = e1)) & ( ~ (v12 = e3) | ~ (v10 = e0)) & ( ~ (v12 = e3) | ~ (v5 = e0)) & ( ~ (v11 = e2) | ~ (v10 = e3)) & ( ~ (v11 = e2) | ~ (v5 = e3)) & ( ~ (v11 = e2) | ~ (v0 = e3)) & ( ~ (v10 = e3) | ~ (v7 = e1)) & ( ~ (v10 = e3) | ~ (v3 = e0)) & ( ~ (v10 = e1) | ~ (v9 = e2)) & ( ~ (v10 = e1) | ~ (v1 = e0)) & ( ~ (v10 = e0) | ~ (v8 = e2)) & ( ~ (v10 = e0) | ~ (v4 = e1)) & ( ~ (v9 = e2) | ~ (v0 = e1)) & ( ~ (v8 = e2) | ~ (v5 = e0)) & ( ~ (v7 = e1) | ~ (v5 = e3)) & ( ~ (v7 = e1) | ~ (v0 = e3)) & ( ~ (v6 = e1) | ~ (v5 = e2)) & ( ~ (v6 = e1) | ~ (v0 = e2)) & ( ~ (v5 = e3) | ~ (v3 = e0)) & ( ~ (v5 = e2) | ~ (v2 = e0)) & ( ~ (v5 = e0) | ~ (v4 = e1)) & ( ~ (v3 = e0) | ~ (v0 = e3)) & ( ~ (v2 = e0) | ~ (v0 = e2)) & ( ~ (v1 = e0) | ~ (v0 = e1)) & (v15 = e2 | v15 = e1 | v15 = e0) & (v15 = e2 | v14 = e2 | v13 = e2 | v12 = e2) & (v15 = e2 | v11 = e2 | v7 = e2 | v3 = e2) & (v15 = e1 | v14 = e1 | v13 = e1 | v12 = e1) & (v15 = e1 | v11 = e1 | v7 = e1 | v3 = e1) & (v15 = e0 | v14 = e0 | v13 = e0 | v12 = e0) & (v15 = e0 | v11 = e0 | v7 = e0 | v3 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v14 = e3 | v13 = e3 | v12 = e3) & (v14 = e3 | v10 = e3 | v6 = e3 | v2 = e3) & (v14 = e2 | v6 = e2 | v2 = e2) & (v14 = e1 | v10 = e1 | v6 = e1 | v2 = e1) & (v14 = e0 | v10 = e0 | v6 = e0 | v2 = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v13 = e3 | v9 = e3 | v5 = e3 | v1 = e3) & (v13 = e2 | v9 = e2 | v5 = e2 | v1 = e2) & (v13 = e1 | v9 = e1 | v1 = e1) & (v13 = e0 | v9 = e0 | v5 = e0 | v1 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v12 = e3 | v8 = e3 | v4 = e3 | v0 = e3) & (v12 = e2 | v8 = e2 | v4 = e2 | v0 = e2) & (v12 = e1 | v8 = e1 | v4 = e1 | v0 = e1) & (v12 = e0 | v8 = e0 | v4 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v11 = e3 | v10 = e3 | v9 = e3 | v8 = e3) & (v11 = e3 | v7 = e3 | v3 = e3) & (v11 = e2 | v9 = e2 | v8 = e2) & (v11 = e1 | v10 = e1 | v9 = e1 | v8 = e1) & (v11 = e0 | v10 = e0 | v9 = e0 | v8 = e0) & (v10 = e3 | v10 = e1 | v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v7 = e3 | v6 = e3 | v5 = e3 | v4 = e3) & (v7 = e2 | v6 = e2 | v5 = e2 | v4 = e2) & (v7 = e1 | v6 = e1 | v4 = e1) & (v7 = e0 | v6 = e0 | v5 = e0 | v4 = e0) & (v6 = e3 | v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e0) & (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3 = e0) & (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & (v3 = e2 | v2 = e2 | v1 = e2 | v0 = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0 = e1) & (v3 = e0 | v2 = e0 | v1 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1))
% 11.74/3.35 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16, all_0_17_17, all_0_18_18, all_0_19_19, all_0_20_20, all_0_21_21, all_0_22_22, all_0_23_23 yields:
% 11.74/3.35 | (1) ~ (all_0_8_8 = all_0_9_9) & ~ (all_0_8_8 = all_0_10_10) & ~ (all_0_8_8 = all_0_11_11) & ~ (all_0_8_8 = all_0_12_12) & ~ (all_0_8_8 = all_0_16_16) & ~ (all_0_8_8 = all_0_20_20) & ~ (all_0_8_8 = e3) & ~ (all_0_9_9 = all_0_10_10) & ~ (all_0_9_9 = all_0_11_11) & ~ (all_0_9_9 = all_0_13_13) & ~ (all_0_9_9 = all_0_17_17) & ~ (all_0_9_9 = all_0_21_21) & ~ (all_0_10_10 = all_0_11_11) & ~ (all_0_10_10 = all_0_14_14) & ~ (all_0_10_10 = all_0_18_18) & ~ (all_0_10_10 = all_0_22_22) & ~ (all_0_11_11 = all_0_15_15) & ~ (all_0_11_11 = all_0_19_19) & ~ (all_0_11_11 = all_0_23_23) & ~ (all_0_12_12 = all_0_13_13) & ~ (all_0_12_12 = all_0_14_14) & ~ (all_0_12_12 = all_0_15_15) & ~ (all_0_12_12 = all_0_16_16) & ~ (all_0_12_12 = all_0_20_20) & ~ (all_0_13_13 = all_0_14_14) & ~ (all_0_13_13 = all_0_15_15) & ~ (all_0_13_13 = all_0_17_17) & ~ (all_0_13_13 = all_0_21_21) & ~ (all_0_13_13 = e2) & ~ (all_0_14_14 = all_0_15_15) & ~ (all_0_14_14 = all_0_18_18) & ~ (all_0_14_14 = all_0_22_22) & ~ (all_0_15_15 = all_0_19_19) & ~ (all_0_15_15 = all_0_23_23) & ~ (all_0_16_16 = all_0_17_17) & ~ (all_0_16_16 = all_0_18_18) & ~ (all_0_16_16 = all_0_19_19) & ~ (all_0_16_16 = all_0_20_20) & ~ (all_0_17_17 = all_0_18_18) & ~ (all_0_17_17 = all_0_19_19) & ~ (all_0_17_17 = all_0_21_21) & ~ (all_0_18_18 = all_0_19_19) & ~ (all_0_18_18 = all_0_22_22) & ~ (all_0_18_18 = e1) & ~ (all_0_19_19 = all_0_23_23) & ~ (all_0_20_20 = all_0_21_21) & ~ (all_0_20_20 = all_0_22_22) & ~ (all_0_20_20 = all_0_23_23) & ~ (all_0_21_21 = all_0_22_22) & ~ (all_0_21_21 = all_0_23_23) & ~ (all_0_22_22 = all_0_23_23) & ~ (all_0_23_23 = e0) & ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ (e1 = e0) & op(all_0_1_1, all_0_23_23) = all_0_0_0 & op(all_0_3_3, all_0_18_18) = all_0_2_2 & op(all_0_5_5, all_0_13_13) = all_0_4_4 & op(all_0_7_7, all_0_8_8) = all_0_6_6 & op(e3, all_0_8_8) = all_0_7_7 & op(e3, e3) = all_0_8_8 & op(e3, e2) = all_0_9_9 & op(e3, e1) = all_0_10_10 & op(e3, e0) = all_0_11_11 & op(e2, all_0_13_13) = all_0_5_5 & op(e2, e3) = all_0_12_12 & op(e2, e2) = all_0_13_13 & op(e2, e1) = all_0_14_14 & op(e2, e0) = all_0_15_15 & op(e1, all_0_18_18) = all_0_3_3 & op(e1, e3) = all_0_16_16 & op(e1, e2) = all_0_17_17 & op(e1, e1) = all_0_18_18 & op(e1, e0) = all_0_19_19 & op(e0, all_0_23_23) = all_0_1_1 & op(e0, e3) = all_0_20_20 & op(e0, e2) = all_0_21_21 & op(e0, e1) = all_0_22_22 & op(e0, e0) = all_0_23_23 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) & ( ~ (all_0_0_0 = e3) | ~ (all_0_1_1 = e2) | ~ (all_0_23_23 = e1)) & ( ~ (all_0_0_0 = e3) | ~ (all_0_1_1 = e1) | ~ (all_0_23_23 = e2)) & ( ~ (all_0_0_0 = e2) | ~ (all_0_1_1 = e3) | ~ (all_0_23_23 = e1)) & ( ~ (all_0_0_0 = e2) | ~ (all_0_1_1 = e1) | ~ (all_0_23_23 = e3)) & ( ~ (all_0_0_0 = e1) | ~ (all_0_1_1 = e3) | ~ (all_0_23_23 = e2)) & ( ~ (all_0_0_0 = e1) | ~ (all_0_1_1 = e2) | ~ (all_0_23_23 = e3)) & ( ~ (all_0_2_2 = e3) | ~ (all_0_3_3 = e2) | ~ (all_0_18_18 = e0)) & ( ~ (all_0_2_2 = e3) | ~ (all_0_3_3 = e0) | ~ (all_0_18_18 = e2)) & ( ~ (all_0_2_2 = e2) | ~ (all_0_3_3 = e3) | ~ (all_0_18_18 = e0)) & ( ~ (all_0_2_2 = e2) | ~ (all_0_3_3 = e0) | ~ (all_0_18_18 = e3)) & ( ~ (all_0_2_2 = e0) | ~ (all_0_3_3 = e3) | ~ (all_0_18_18 = e2)) & ( ~ (all_0_2_2 = e0) | ~ (all_0_3_3 = e2) | ~ (all_0_18_18 = e3)) & ( ~ (all_0_4_4 = e3) | ~ (all_0_5_5 = e1) | ~ (all_0_13_13 = e0)) & ( ~ (all_0_4_4 = e3) | ~ (all_0_5_5 = e0) | ~ (all_0_13_13 = e1)) & ( ~ (all_0_4_4 = e1) | ~ (all_0_5_5 = e3) | ~ (all_0_13_13 = e0)) & ( ~ (all_0_4_4 = e1) | ~ (all_0_5_5 = e0) | ~ (all_0_13_13 = e3)) & ( ~ (all_0_4_4 = e0) | ~ (all_0_5_5 = e3) | ~ (all_0_13_13 = e1)) & ( ~ (all_0_4_4 = e0) | ~ (all_0_5_5 = e1) | ~ (all_0_13_13 = e3)) & ( ~ (all_0_6_6 = e2) | ~ (all_0_7_7 = e1) | ~ (all_0_8_8 = e0)) & ( ~ (all_0_6_6 = e2) | ~ (all_0_7_7 = e0) | ~ (all_0_8_8 = e1)) & ( ~ (all_0_6_6 = e1) | ~ (all_0_7_7 = e2) | ~ (all_0_8_8 = e0)) & ( ~ (all_0_6_6 = e1) | ~ (all_0_7_7 = e0) | ~ (all_0_8_8 = e2)) & ( ~ (all_0_6_6 = e0) | ~ (all_0_7_7 = e2) | ~ (all_0_8_8 = e1)) & ( ~ (all_0_6_6 = e0) | ~ (all_0_7_7 = e1) | ~ (all_0_8_8 = e2)) & ( ~ (all_0_8_8 = e2) | ~ (all_0_9_9 = e3)) & ( ~ (all_0_8_8 = e2) | ~ (all_0_17_17 = e1)) & ( ~ (all_0_8_8 = e2) | ~ (all_0_21_21 = e0)) & ( ~ (all_0_8_8 = e1) | ~ (all_0_10_10 = e3)) & ( ~ (all_0_8_8 = e1) | ~ (all_0_14_14 = e2)) & ( ~ (all_0_8_8 = e1) | ~ (all_0_22_22 = e0)) & ( ~ (all_0_8_8 = e0) | ~ (all_0_11_11 = e3)) & ( ~ (all_0_8_8 = e0) | ~ (all_0_15_15 = e2)) & ( ~ (all_0_8_8 = e0) | ~ (all_0_19_19 = e1)) & ( ~ (all_0_9_9 = e3) | ~ (all_0_18_18 = e2)) & ( ~ (all_0_9_9 = e3) | ~ (all_0_23_23 = e2)) & ( ~ (all_0_10_10 = e3) | ~ (all_0_13_13 = e1)) & ( ~ (all_0_10_10 = e3) | ~ (all_0_23_23 = e1)) & ( ~ (all_0_11_11 = e3) | ~ (all_0_13_13 = e0)) & ( ~ (all_0_11_11 = e3) | ~ (all_0_18_18 = e0)) & ( ~ (all_0_12_12 = e2) | ~ (all_0_13_13 = e3)) & ( ~ (all_0_12_12 = e2) | ~ (all_0_18_18 = e3)) & ( ~ (all_0_12_12 = e2) | ~ (all_0_23_23 = e3)) & ( ~ (all_0_13_13 = e3) | ~ (all_0_16_16 = e1)) & ( ~ (all_0_13_13 = e3) | ~ (all_0_20_20 = e0)) & ( ~ (all_0_13_13 = e1) | ~ (all_0_14_14 = e2)) & ( ~ (all_0_13_13 = e1) | ~ (all_0_22_22 = e0)) & ( ~ (all_0_13_13 = e0) | ~ (all_0_15_15 = e2)) & ( ~ (all_0_13_13 = e0) | ~ (all_0_19_19 = e1)) & ( ~ (all_0_14_14 = e2) | ~ (all_0_23_23 = e1)) & ( ~ (all_0_15_15 = e2) | ~ (all_0_18_18 = e0)) & ( ~ (all_0_16_16 = e1) | ~ (all_0_18_18 = e3)) & ( ~ (all_0_16_16 = e1) | ~ (all_0_23_23 = e3)) & ( ~ (all_0_17_17 = e1) | ~ (all_0_18_18 = e2)) & ( ~ (all_0_17_17 = e1) | ~ (all_0_23_23 = e2)) & ( ~ (all_0_18_18 = e3) | ~ (all_0_20_20 = e0)) & ( ~ (all_0_18_18 = e2) | ~ (all_0_21_21 = e0)) & ( ~ (all_0_18_18 = e0) | ~ (all_0_19_19 = e1)) & ( ~ (all_0_20_20 = e0) | ~ (all_0_23_23 = e3)) & ( ~ (all_0_21_21 = e0) | ~ (all_0_23_23 = e2)) & ( ~ (all_0_22_22 = e0) | ~ (all_0_23_23 = e1)) & (all_0_8_8 = e2 | all_0_8_8 = e1 | all_0_8_8 = e0) & (all_0_8_8 = e2 | all_0_9_9 = e2 | all_0_10_10 = e2 | all_0_11_11 = e2) & (all_0_8_8 = e2 | all_0_12_12 = e2 | all_0_16_16 = e2 | all_0_20_20 = e2) & (all_0_8_8 = e1 | all_0_9_9 = e1 | all_0_10_10 = e1 | all_0_11_11 = e1) & (all_0_8_8 = e1 | all_0_12_12 = e1 | all_0_16_16 = e1 | all_0_20_20 = e1) & (all_0_8_8 = e0 | all_0_9_9 = e0 | all_0_10_10 = e0 | all_0_11_11 = e0) & (all_0_8_8 = e0 | all_0_12_12 = e0 | all_0_16_16 = e0 | all_0_20_20 = e0) & (all_0_9_9 = e3 | all_0_9_9 = e2 | all_0_9_9 = e1 | all_0_9_9 = e0) & (all_0_9_9 = e3 | all_0_10_10 = e3 | all_0_11_11 = e3) & (all_0_9_9 = e3 | all_0_13_13 = e3 | all_0_17_17 = e3 | all_0_21_21 = e3) & (all_0_9_9 = e2 | all_0_17_17 = e2 | all_0_21_21 = e2) & (all_0_9_9 = e1 | all_0_13_13 = e1 | all_0_17_17 = e1 | all_0_21_21 = e1) & (all_0_9_9 = e0 | all_0_13_13 = e0 | all_0_17_17 = e0 | all_0_21_21 = e0) & (all_0_10_10 = e3 | all_0_10_10 = e2 | all_0_10_10 = e1 | all_0_10_10 = e0) & (all_0_10_10 = e3 | all_0_14_14 = e3 | all_0_18_18 = e3 | all_0_22_22 = e3) & (all_0_10_10 = e2 | all_0_14_14 = e2 | all_0_18_18 = e2 | all_0_22_22 = e2) & (all_0_10_10 = e1 | all_0_14_14 = e1 | all_0_22_22 = e1) & (all_0_10_10 = e0 | all_0_14_14 = e0 | all_0_18_18 = e0 | all_0_22_22 = e0) & (all_0_11_11 = e3 | all_0_11_11 = e2 | all_0_11_11 = e1 | all_0_11_11 = e0) & (all_0_11_11 = e3 | all_0_15_15 = e3 | all_0_19_19 = e3 | all_0_23_23 = e3) & (all_0_11_11 = e2 | all_0_15_15 = e2 | all_0_19_19 = e2 | all_0_23_23 = e2) & (all_0_11_11 = e1 | all_0_15_15 = e1 | all_0_19_19 = e1 | all_0_23_23 = e1) & (all_0_11_11 = e0 | all_0_15_15 = e0 | all_0_19_19 = e0) & (all_0_12_12 = e3 | all_0_12_12 = e2 | all_0_12_12 = e1 | all_0_12_12 = e0) & (all_0_12_12 = e3 | all_0_13_13 = e3 | all_0_14_14 = e3 | all_0_15_15 = e3) & (all_0_12_12 = e3 | all_0_16_16 = e3 | all_0_20_20 = e3) & (all_0_12_12 = e2 | all_0_14_14 = e2 | all_0_15_15 = e2) & (all_0_12_12 = e1 | all_0_13_13 = e1 | all_0_14_14 = e1 | all_0_15_15 = e1) & (all_0_12_12 = e0 | all_0_13_13 = e0 | all_0_14_14 = e0 | all_0_15_15 = e0) & (all_0_13_13 = e3 | all_0_13_13 = e1 | all_0_13_13 = e0) & (all_0_14_14 = e3 | all_0_14_14 = e2 | all_0_14_14 = e1 | all_0_14_14 = e0) & (all_0_15_15 = e3 | all_0_15_15 = e2 | all_0_15_15 = e1 | all_0_15_15 = e0) & (all_0_16_16 = e3 | all_0_16_16 = e2 | all_0_16_16 = e1 | all_0_16_16 = e0) & (all_0_16_16 = e3 | all_0_17_17 = e3 | all_0_18_18 = e3 | all_0_19_19 = e3) & (all_0_16_16 = e2 | all_0_17_17 = e2 | all_0_18_18 = e2 | all_0_19_19 = e2) & (all_0_16_16 = e1 | all_0_17_17 = e1 | all_0_19_19 = e1) & (all_0_16_16 = e0 | all_0_17_17 = e0 | all_0_18_18 = e0 | all_0_19_19 = e0) & (all_0_17_17 = e3 | all_0_17_17 = e2 | all_0_17_17 = e1 | all_0_17_17 = e0) & (all_0_18_18 = e3 | all_0_18_18 = e2 | all_0_18_18 = e0) & (all_0_19_19 = e3 | all_0_19_19 = e2 | all_0_19_19 = e1 | all_0_19_19 = e0) & (all_0_20_20 = e3 | all_0_20_20 = e2 | all_0_20_20 = e1 | all_0_20_20 = e0) & (all_0_20_20 = e3 | all_0_21_21 = e3 | all_0_22_22 = e3 | all_0_23_23 = e3) & (all_0_20_20 = e2 | all_0_21_21 = e2 | all_0_22_22 = e2 | all_0_23_23 = e2) & (all_0_20_20 = e1 | all_0_21_21 = e1 | all_0_22_22 = e1 | all_0_23_23 = e1) & (all_0_20_20 = e0 | all_0_21_21 = e0 | all_0_22_22 = e0) & (all_0_21_21 = e3 | all_0_21_21 = e2 | all_0_21_21 = e1 | all_0_21_21 = e0) & (all_0_22_22 = e3 | all_0_22_22 = e2 | all_0_22_22 = e1 | all_0_22_22 = e0) & (all_0_23_23 = e3 | all_0_23_23 = e2 | all_0_23_23 = e1)
% 11.74/3.37 |
% 11.74/3.37 | Applying alpha-rule on (1) yields:
% 11.74/3.37 | (2) ~ (all_0_8_8 = all_0_12_12)
% 11.74/3.37 | (3) ~ (all_0_0_0 = e2) | ~ (all_0_1_1 = e3) | ~ (all_0_23_23 = e1)
% 11.74/3.37 | (4) ~ (all_0_18_18 = all_0_19_19)
% 11.74/3.37 | (5) ~ (all_0_18_18 = all_0_22_22)
% 11.74/3.37 | (6) ~ (all_0_13_13 = all_0_17_17)
% 11.74/3.37 | (7) all_0_16_16 = e3 | all_0_16_16 = e2 | all_0_16_16 = e1 | all_0_16_16 = e0
% 11.74/3.37 | (8) op(all_0_5_5, all_0_13_13) = all_0_4_4
% 11.74/3.37 | (9) ~ (all_0_23_23 = e0)
% 11.74/3.37 | (10) all_0_16_16 = e0 | all_0_17_17 = e0 | all_0_18_18 = e0 | all_0_19_19 = e0
% 11.74/3.37 | (11) all_0_11_11 = e1 | all_0_15_15 = e1 | all_0_19_19 = e1 | all_0_23_23 = e1
% 11.74/3.37 | (12) op(all_0_7_7, all_0_8_8) = all_0_6_6
% 11.74/3.37 | (13) ~ (e2 = e0)
% 11.74/3.37 | (14) ~ (all_0_0_0 = e3) | ~ (all_0_1_1 = e1) | ~ (all_0_23_23 = e2)
% 11.74/3.37 | (15) all_0_9_9 = e3 | all_0_13_13 = e3 | all_0_17_17 = e3 | all_0_21_21 = e3
% 11.74/3.37 | (16) ~ (all_0_9_9 = all_0_10_10)
% 11.74/3.37 | (17) ~ (all_0_17_17 = all_0_18_18)
% 11.74/3.37 | (18) all_0_20_20 = e1 | all_0_21_21 = e1 | all_0_22_22 = e1 | all_0_23_23 = e1
% 11.74/3.37 | (19) all_0_10_10 = e3 | all_0_10_10 = e2 | all_0_10_10 = e1 | all_0_10_10 = e0
% 11.74/3.37 | (20) all_0_8_8 = e0 | all_0_12_12 = e0 | all_0_16_16 = e0 | all_0_20_20 = e0
% 11.74/3.37 | (21) all_0_16_16 = e2 | all_0_17_17 = e2 | all_0_18_18 = e2 | all_0_19_19 = e2
% 11.74/3.37 | (22) ~ (all_0_18_18 = e0) | ~ (all_0_19_19 = e1)
% 11.74/3.38 | (23) ~ (all_0_13_13 = e1) | ~ (all_0_22_22 = e0)
% 11.74/3.38 | (24) ~ (all_0_8_8 = all_0_11_11)
% 11.74/3.38 | (25) ~ (all_0_18_18 = e1)
% 11.74/3.38 | (26) ~ (all_0_13_13 = e0) | ~ (all_0_15_15 = e2)
% 11.74/3.38 | (27) ~ (all_0_21_21 = all_0_22_22)
% 11.74/3.38 | (28) op(e0, e3) = all_0_20_20
% 11.74/3.38 | (29) ~ (all_0_6_6 = e1) | ~ (all_0_7_7 = e0) | ~ (all_0_8_8 = e2)
% 11.74/3.38 | (30) all_0_12_12 = e3 | all_0_12_12 = e2 | all_0_12_12 = e1 | all_0_12_12 = e0
% 11.74/3.38 | (31) ~ (all_0_9_9 = all_0_13_13)
% 11.74/3.38 | (32) ~ (all_0_12_12 = all_0_13_13)
% 11.74/3.38 | (33) ~ (all_0_8_8 = e0) | ~ (all_0_19_19 = e1)
% 11.74/3.38 | (34) ~ (all_0_14_14 = all_0_18_18)
% 11.74/3.38 | (35) all_0_8_8 = e2 | all_0_12_12 = e2 | all_0_16_16 = e2 | all_0_20_20 = e2
% 11.74/3.38 | (36) ~ (all_0_16_16 = e1) | ~ (all_0_23_23 = e3)
% 11.74/3.38 | (37) op(e0, e1) = all_0_22_22
% 11.74/3.38 | (38) ~ (all_0_11_11 = e3) | ~ (all_0_13_13 = e0)
% 12.14/3.38 | (39) ~ (all_0_16_16 = all_0_18_18)
% 12.14/3.38 | (40) ~ (all_0_9_9 = e3) | ~ (all_0_18_18 = e2)
% 12.14/3.38 | (41) op(e1, e0) = all_0_19_19
% 12.14/3.38 | (42) op(e3, e3) = all_0_8_8
% 12.14/3.38 | (43) op(e0, all_0_23_23) = all_0_1_1
% 12.14/3.38 | (44) ~ (all_0_14_14 = all_0_15_15)
% 12.14/3.38 | (45) ~ (all_0_0_0 = e1) | ~ (all_0_1_1 = e3) | ~ (all_0_23_23 = e2)
% 12.14/3.38 | (46) ~ (all_0_12_12 = e2) | ~ (all_0_18_18 = e3)
% 12.14/3.38 | (47) ~ (all_0_6_6 = e0) | ~ (all_0_7_7 = e2) | ~ (all_0_8_8 = e1)
% 12.14/3.38 | (48) all_0_8_8 = e0 | all_0_9_9 = e0 | all_0_10_10 = e0 | all_0_11_11 = e0
% 12.14/3.38 | (49) op(all_0_1_1, all_0_23_23) = all_0_0_0
% 12.14/3.38 | (50) ~ (all_0_11_11 = all_0_15_15)
% 12.14/3.38 | (51) ~ (all_0_8_8 = e3)
% 12.14/3.38 | (52) all_0_16_16 = e3 | all_0_17_17 = e3 | all_0_18_18 = e3 | all_0_19_19 = e3
% 12.14/3.38 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 12.14/3.38 | (54) op(e3, e1) = all_0_10_10
% 12.14/3.38 | (55) ~ (all_0_13_13 = e3) | ~ (all_0_16_16 = e1)
% 12.14/3.38 | (56) ~ (all_0_6_6 = e0) | ~ (all_0_7_7 = e1) | ~ (all_0_8_8 = e2)
% 12.14/3.38 | (57) ~ (all_0_2_2 = e2) | ~ (all_0_3_3 = e3) | ~ (all_0_18_18 = e0)
% 12.14/3.38 | (58) ~ (all_0_16_16 = all_0_17_17)
% 12.14/3.38 | (59) op(e0, e2) = all_0_21_21
% 12.14/3.38 | (60) ~ (all_0_2_2 = e3) | ~ (all_0_3_3 = e0) | ~ (all_0_18_18 = e2)
% 12.14/3.38 | (61) ~ (all_0_20_20 = all_0_21_21)
% 12.14/3.38 | (62) ~ (all_0_6_6 = e2) | ~ (all_0_7_7 = e0) | ~ (all_0_8_8 = e1)
% 12.14/3.38 | (63) ~ (all_0_4_4 = e1) | ~ (all_0_5_5 = e3) | ~ (all_0_13_13 = e0)
% 12.14/3.38 | (64) ~ (all_0_17_17 = all_0_21_21)
% 12.14/3.38 | (65) op(e3, e2) = all_0_9_9
% 12.14/3.38 | (66) ~ (all_0_4_4 = e3) | ~ (all_0_5_5 = e0) | ~ (all_0_13_13 = e1)
% 12.14/3.38 | (67) all_0_10_10 = e3 | all_0_14_14 = e3 | all_0_18_18 = e3 | all_0_22_22 = e3
% 12.14/3.38 | (68) all_0_20_20 = e3 | all_0_20_20 = e2 | all_0_20_20 = e1 | all_0_20_20 = e0
% 12.14/3.38 | (69) ~ (all_0_20_20 = all_0_22_22)
% 12.14/3.38 | (70) all_0_10_10 = e0 | all_0_14_14 = e0 | all_0_18_18 = e0 | all_0_22_22 = e0
% 12.14/3.38 | (71) ~ (e2 = e1)
% 12.14/3.38 | (72) ~ (all_0_13_13 = e1) | ~ (all_0_14_14 = e2)
% 12.14/3.38 | (73) ~ (all_0_11_11 = e3) | ~ (all_0_18_18 = e0)
% 12.14/3.38 | (74) all_0_12_12 = e2 | all_0_14_14 = e2 | all_0_15_15 = e2
% 12.14/3.38 | (75) ~ (all_0_12_12 = all_0_15_15)
% 12.14/3.38 | (76) ~ (all_0_12_12 = all_0_16_16)
% 12.14/3.38 | (77) all_0_12_12 = e1 | all_0_13_13 = e1 | all_0_14_14 = e1 | all_0_15_15 = e1
% 12.14/3.38 | (78) ~ (all_0_18_18 = e2) | ~ (all_0_21_21 = e0)
% 12.14/3.38 | (79) ~ (all_0_8_8 = e1) | ~ (all_0_14_14 = e2)
% 12.14/3.38 | (80) ~ (all_0_10_10 = e3) | ~ (all_0_23_23 = e1)
% 12.14/3.38 | (81) ~ (all_0_9_9 = e3) | ~ (all_0_23_23 = e2)
% 12.14/3.38 | (82) ~ (all_0_4_4 = e0) | ~ (all_0_5_5 = e1) | ~ (all_0_13_13 = e3)
% 12.14/3.38 | (83) all_0_17_17 = e3 | all_0_17_17 = e2 | all_0_17_17 = e1 | all_0_17_17 = e0
% 12.14/3.38 | (84) all_0_11_11 = e3 | all_0_11_11 = e2 | all_0_11_11 = e1 | all_0_11_11 = e0
% 12.14/3.38 | (85) ~ (all_0_0_0 = e3) | ~ (all_0_1_1 = e2) | ~ (all_0_23_23 = e1)
% 12.14/3.38 | (86) all_0_8_8 = e1 | all_0_12_12 = e1 | all_0_16_16 = e1 | all_0_20_20 = e1
% 12.14/3.38 | (87) all_0_22_22 = e3 | all_0_22_22 = e2 | all_0_22_22 = e1 | all_0_22_22 = e0
% 12.14/3.38 | (88) all_0_23_23 = e3 | all_0_23_23 = e2 | all_0_23_23 = e1
% 12.14/3.38 | (89) op(e2, e1) = all_0_14_14
% 12.14/3.38 | (90) op(e2, e2) = all_0_13_13
% 12.14/3.38 | (91) ~ (all_0_17_17 = e1) | ~ (all_0_23_23 = e2)
% 12.14/3.38 | (92) op(e1, e2) = all_0_17_17
% 12.14/3.38 | (93) all_0_12_12 = e3 | all_0_13_13 = e3 | all_0_14_14 = e3 | all_0_15_15 = e3
% 12.14/3.38 | (94) ~ (all_0_12_12 = e2) | ~ (all_0_23_23 = e3)
% 12.14/3.38 | (95) all_0_14_14 = e3 | all_0_14_14 = e2 | all_0_14_14 = e1 | all_0_14_14 = e0
% 12.14/3.38 | (96) ~ (all_0_13_13 = all_0_21_21)
% 12.14/3.38 | (97) all_0_8_8 = e2 | all_0_8_8 = e1 | all_0_8_8 = e0
% 12.14/3.38 | (98) ~ (all_0_13_13 = all_0_15_15)
% 12.14/3.38 | (99) ~ (all_0_0_0 = e1) | ~ (all_0_1_1 = e2) | ~ (all_0_23_23 = e3)
% 12.14/3.38 | (100) op(e2, e3) = all_0_12_12
% 12.14/3.38 | (101) ~ (e3 = e2)
% 12.14/3.38 | (102) op(e2, all_0_13_13) = all_0_5_5
% 12.14/3.39 | (103) op(e2, e0) = all_0_15_15
% 12.14/3.39 | (104) all_0_9_9 = e1 | all_0_13_13 = e1 | all_0_17_17 = e1 | all_0_21_21 = e1
% 12.14/3.39 | (105) ~ (all_0_10_10 = e3) | ~ (all_0_13_13 = e1)
% 12.14/3.39 | (106) op(e3, e0) = all_0_11_11
% 12.14/3.39 | (107) ~ (all_0_8_8 = e2) | ~ (all_0_21_21 = e0)
% 12.14/3.39 | (108) ~ (all_0_8_8 = e0) | ~ (all_0_15_15 = e2)
% 12.14/3.39 | (109) ~ (all_0_9_9 = all_0_17_17)
% 12.14/3.39 | (110) ~ (all_0_8_8 = all_0_9_9)
% 12.14/3.39 | (111) all_0_21_21 = e3 | all_0_21_21 = e2 | all_0_21_21 = e1 | all_0_21_21 = e0
% 12.14/3.39 | (112) all_0_20_20 = e0 | all_0_21_21 = e0 | all_0_22_22 = e0
% 12.14/3.39 | (113) all_0_13_13 = e3 | all_0_13_13 = e1 | all_0_13_13 = e0
% 12.14/3.39 | (114) all_0_10_10 = e2 | all_0_14_14 = e2 | all_0_18_18 = e2 | all_0_22_22 = e2
% 12.14/3.39 | (115) ~ (all_0_16_16 = e1) | ~ (all_0_18_18 = e3)
% 12.14/3.39 | (116) ~ (all_0_12_12 = e2) | ~ (all_0_13_13 = e3)
% 12.14/3.39 | (117) ~ (all_0_10_10 = all_0_22_22)
% 12.14/3.39 | (118) ~ (all_0_9_9 = all_0_21_21)
% 12.14/3.39 | (119) ~ (all_0_11_11 = all_0_23_23)
% 12.14/3.39 | (120) ~ (all_0_17_17 = all_0_19_19)
% 12.14/3.39 | (121) all_0_18_18 = e3 | all_0_18_18 = e2 | all_0_18_18 = e0
% 12.14/3.39 | (122) ~ (all_0_8_8 = all_0_20_20)
% 12.14/3.39 | (123) all_0_8_8 = e1 | all_0_9_9 = e1 | all_0_10_10 = e1 | all_0_11_11 = e1
% 12.14/3.39 | (124) ~ (all_0_4_4 = e1) | ~ (all_0_5_5 = e0) | ~ (all_0_13_13 = e3)
% 12.14/3.39 | (125) all_0_20_20 = e3 | all_0_21_21 = e3 | all_0_22_22 = e3 | all_0_23_23 = e3
% 12.14/3.39 | (126) all_0_15_15 = e3 | all_0_15_15 = e2 | all_0_15_15 = e1 | all_0_15_15 = e0
% 12.14/3.39 | (127) ~ (all_0_17_17 = e1) | ~ (all_0_18_18 = e2)
% 12.14/3.39 | (128) all_0_12_12 = e3 | all_0_16_16 = e3 | all_0_20_20 = e3
% 12.14/3.39 | (129) ~ (all_0_10_10 = all_0_18_18)
% 12.14/3.39 | (130) ~ (all_0_20_20 = all_0_23_23)
% 12.14/3.39 | (131) ~ (all_0_18_18 = e3) | ~ (all_0_20_20 = e0)
% 12.14/3.39 | (132) op(e1, e1) = all_0_18_18
% 12.14/3.39 | (133) all_0_11_11 = e2 | all_0_15_15 = e2 | all_0_19_19 = e2 | all_0_23_23 = e2
% 12.14/3.39 | (134) ~ (all_0_16_16 = all_0_20_20)
% 12.14/3.39 | (135) ~ (all_0_19_19 = all_0_23_23)
% 12.14/3.39 | (136) ~ (e3 = e0)
% 12.14/3.39 | (137) ~ (e3 = e1)
% 12.14/3.39 | (138) all_0_16_16 = e1 | all_0_17_17 = e1 | all_0_19_19 = e1
% 12.14/3.39 | (139) ~ (all_0_13_13 = e0) | ~ (all_0_19_19 = e1)
% 12.14/3.39 | (140) ~ (all_0_8_8 = e1) | ~ (all_0_22_22 = e0)
% 12.14/3.39 | (141) ~ (all_0_0_0 = e2) | ~ (all_0_1_1 = e1) | ~ (all_0_23_23 = e3)
% 12.14/3.39 | (142) all_0_9_9 = e3 | all_0_9_9 = e2 | all_0_9_9 = e1 | all_0_9_9 = e0
% 12.14/3.39 | (143) ~ (all_0_13_13 = e2)
% 12.14/3.39 | (144) all_0_9_9 = e2 | all_0_17_17 = e2 | all_0_21_21 = e2
% 12.14/3.39 | (145) ~ (all_0_9_9 = all_0_11_11)
% 12.14/3.39 | (146) all_0_12_12 = e0 | all_0_13_13 = e0 | all_0_14_14 = e0 | all_0_15_15 = e0
% 12.14/3.39 | (147) all_0_11_11 = e0 | all_0_15_15 = e0 | all_0_19_19 = e0
% 12.14/3.39 | (148) all_0_20_20 = e2 | all_0_21_21 = e2 | all_0_22_22 = e2 | all_0_23_23 = e2
% 12.14/3.39 | (149) ~ (all_0_13_13 = all_0_14_14)
% 12.14/3.39 | (150) ~ (all_0_2_2 = e0) | ~ (all_0_3_3 = e2) | ~ (all_0_18_18 = e3)
% 12.14/3.39 | (151) all_0_10_10 = e1 | all_0_14_14 = e1 | all_0_22_22 = e1
% 12.14/3.39 | (152) op(e1, e3) = all_0_16_16
% 12.14/3.39 | (153) all_0_9_9 = e0 | all_0_13_13 = e0 | all_0_17_17 = e0 | all_0_21_21 = e0
% 12.14/3.39 | (154) ~ (all_0_4_4 = e0) | ~ (all_0_5_5 = e3) | ~ (all_0_13_13 = e1)
% 12.14/3.39 | (155) all_0_9_9 = e3 | all_0_10_10 = e3 | all_0_11_11 = e3
% 12.14/3.39 | (156) ~ (all_0_6_6 = e2) | ~ (all_0_7_7 = e1) | ~ (all_0_8_8 = e0)
% 12.14/3.39 | (157) op(e3, all_0_8_8) = all_0_7_7
% 12.14/3.39 | (158) op(all_0_3_3, all_0_18_18) = all_0_2_2
% 12.14/3.39 | (159) ~ (all_0_22_22 = e0) | ~ (all_0_23_23 = e1)
% 12.14/3.39 | (160) ~ (all_0_12_12 = all_0_14_14)
% 12.14/3.39 | (161) ~ (all_0_2_2 = e3) | ~ (all_0_3_3 = e2) | ~ (all_0_18_18 = e0)
% 12.14/3.39 | (162) ~ (all_0_14_14 = all_0_22_22)
% 12.14/3.39 | (163) ~ (all_0_8_8 = e0) | ~ (all_0_11_11 = e3)
% 12.14/3.39 | (164) op(e1, all_0_18_18) = all_0_3_3
% 12.14/3.39 | (165) all_0_11_11 = e3 | all_0_15_15 = e3 | all_0_19_19 = e3 | all_0_23_23 = e3
% 12.14/3.39 | (166) all_0_8_8 = e2 | all_0_9_9 = e2 | all_0_10_10 = e2 | all_0_11_11 = e2
% 12.14/3.39 | (167) ~ (all_0_12_12 = all_0_20_20)
% 12.14/3.39 | (168) ~ (all_0_14_14 = e2) | ~ (all_0_23_23 = e1)
% 12.14/3.39 | (169) ~ (all_0_8_8 = e2) | ~ (all_0_9_9 = e3)
% 12.14/3.39 | (170) all_0_19_19 = e3 | all_0_19_19 = e2 | all_0_19_19 = e1 | all_0_19_19 = e0
% 12.14/3.39 | (171) ~ (all_0_11_11 = all_0_19_19)
% 12.14/3.39 | (172) ~ (all_0_2_2 = e2) | ~ (all_0_3_3 = e0) | ~ (all_0_18_18 = e3)
% 12.14/3.39 | (173) ~ (all_0_15_15 = all_0_23_23)
% 12.14/3.39 | (174) ~ (all_0_15_15 = e2) | ~ (all_0_18_18 = e0)
% 12.14/3.39 | (175) ~ (all_0_16_16 = all_0_19_19)
% 12.14/3.39 | (176) ~ (all_0_8_8 = e2) | ~ (all_0_17_17 = e1)
% 12.14/3.39 | (177) ~ (all_0_2_2 = e0) | ~ (all_0_3_3 = e3) | ~ (all_0_18_18 = e2)
% 12.14/3.39 | (178) ~ (all_0_13_13 = e3) | ~ (all_0_20_20 = e0)
% 12.14/3.39 | (179) ~ (all_0_8_8 = all_0_16_16)
% 12.14/3.39 | (180) ~ (all_0_10_10 = all_0_14_14)
% 12.14/3.39 | (181) ~ (e1 = e0)
% 12.14/3.39 | (182) ~ (all_0_8_8 = all_0_10_10)
% 12.14/3.39 | (183) ~ (all_0_8_8 = e1) | ~ (all_0_10_10 = e3)
% 12.14/3.39 | (184) op(e0, e0) = all_0_23_23
% 12.14/3.39 | (185) ~ (all_0_20_20 = e0) | ~ (all_0_23_23 = e3)
% 12.14/3.39 | (186) ~ (all_0_6_6 = e1) | ~ (all_0_7_7 = e2) | ~ (all_0_8_8 = e0)
% 12.14/3.39 | (187) ~ (all_0_10_10 = all_0_11_11)
% 12.14/3.39 | (188) ~ (all_0_15_15 = all_0_19_19)
% 12.14/3.39 | (189) ~ (all_0_4_4 = e3) | ~ (all_0_5_5 = e1) | ~ (all_0_13_13 = e0)
% 12.14/3.39 | (190) ~ (all_0_21_21 = e0) | ~ (all_0_23_23 = e2)
% 12.14/3.39 | (191) ~ (all_0_22_22 = all_0_23_23)
% 12.14/3.39 | (192) ~ (all_0_21_21 = all_0_23_23)
% 12.14/3.39 |
% 12.14/3.39 +-Applying beta-rule and splitting (79), into two cases.
% 12.14/3.39 |-Branch one:
% 12.14/3.39 | (193) ~ (all_0_8_8 = e1)
% 12.14/3.39 |
% 12.14/3.39 +-Applying beta-rule and splitting (159), into two cases.
% 12.14/3.39 |-Branch one:
% 12.14/3.39 | (194) ~ (all_0_22_22 = e0)
% 12.14/3.39 |
% 12.14/3.39 +-Applying beta-rule and splitting (33), into two cases.
% 12.14/3.39 |-Branch one:
% 12.14/3.39 | (195) ~ (all_0_8_8 = e0)
% 12.14/3.39 |
% 12.14/3.39 +-Applying beta-rule and splitting (97), into two cases.
% 12.14/3.39 |-Branch one:
% 12.14/3.39 | (196) all_0_8_8 = e2
% 12.14/3.39 |
% 12.14/3.39 | Equations (196) can reduce 110 to:
% 12.14/3.39 | (197) ~ (all_0_9_9 = e2)
% 12.14/3.39 |
% 12.14/3.39 | Simplifying 197 yields:
% 12.14/3.39 | (198) ~ (all_0_9_9 = e2)
% 12.14/3.39 |
% 12.14/3.39 | Equations (196) can reduce 2 to:
% 12.14/3.39 | (199) ~ (all_0_12_12 = e2)
% 12.14/3.39 |
% 12.14/3.39 | Simplifying 199 yields:
% 12.14/3.39 | (200) ~ (all_0_12_12 = e2)
% 12.14/3.39 |
% 12.14/3.39 +-Applying beta-rule and splitting (107), into two cases.
% 12.14/3.39 |-Branch one:
% 12.14/3.39 | (201) ~ (all_0_8_8 = e2)
% 12.14/3.39 |
% 12.14/3.39 | Equations (196) can reduce 201 to:
% 12.14/3.39 | (202) $false
% 12.14/3.39 |
% 12.20/3.39 |-The branch is then unsatisfiable
% 12.20/3.39 |-Branch two:
% 12.20/3.39 | (196) all_0_8_8 = e2
% 12.20/3.39 | (204) ~ (all_0_21_21 = e0)
% 12.20/3.39 |
% 12.20/3.39 +-Applying beta-rule and splitting (176), into two cases.
% 12.20/3.39 |-Branch one:
% 12.20/3.39 | (201) ~ (all_0_8_8 = e2)
% 12.20/3.39 |
% 12.20/3.39 | Equations (196) can reduce 201 to:
% 12.20/3.39 | (202) $false
% 12.20/3.39 |
% 12.20/3.39 |-The branch is then unsatisfiable
% 12.20/3.39 |-Branch two:
% 12.20/3.39 | (196) all_0_8_8 = e2
% 12.20/3.40 | (208) ~ (all_0_17_17 = e1)
% 12.20/3.40 |
% 12.20/3.40 +-Applying beta-rule and splitting (169), into two cases.
% 12.20/3.40 |-Branch one:
% 12.20/3.40 | (201) ~ (all_0_8_8 = e2)
% 12.20/3.40 |
% 12.20/3.40 | Equations (196) can reduce 201 to:
% 12.20/3.40 | (202) $false
% 12.20/3.40 |
% 12.20/3.40 |-The branch is then unsatisfiable
% 12.20/3.40 |-Branch two:
% 12.20/3.40 | (196) all_0_8_8 = e2
% 12.20/3.40 | (212) ~ (all_0_9_9 = e3)
% 12.20/3.40 |
% 12.20/3.40 +-Applying beta-rule and splitting (112), into two cases.
% 12.20/3.40 |-Branch one:
% 12.20/3.40 | (213) all_0_20_20 = e0
% 12.20/3.40 |
% 12.20/3.40 | Equations (213) can reduce 167 to:
% 12.20/3.40 | (214) ~ (all_0_12_12 = e0)
% 12.20/3.40 |
% 12.20/3.40 | Equations (213) can reduce 69 to:
% 12.20/3.40 | (215) ~ (all_0_22_22 = e0)
% 12.20/3.40 |
% 12.20/3.40 | Simplifying 215 yields:
% 12.20/3.40 | (194) ~ (all_0_22_22 = e0)
% 12.20/3.40 |
% 12.20/3.40 | Equations (213) can reduce 130 to:
% 12.20/3.40 | (217) ~ (all_0_23_23 = e0)
% 12.20/3.40 |
% 12.20/3.40 | Simplifying 217 yields:
% 12.20/3.40 | (9) ~ (all_0_23_23 = e0)
% 12.20/3.40 |
% 12.20/3.40 +-Applying beta-rule and splitting (178), into two cases.
% 12.20/3.40 |-Branch one:
% 12.20/3.40 | (219) ~ (all_0_13_13 = e3)
% 12.20/3.40 |
% 12.20/3.40 +-Applying beta-rule and splitting (185), into two cases.
% 12.20/3.40 |-Branch one:
% 12.20/3.40 | (220) ~ (all_0_20_20 = e0)
% 12.20/3.40 |
% 12.20/3.40 | Equations (213) can reduce 220 to:
% 12.20/3.40 | (202) $false
% 12.20/3.40 |
% 12.20/3.40 |-The branch is then unsatisfiable
% 12.20/3.40 |-Branch two:
% 12.20/3.40 | (213) all_0_20_20 = e0
% 12.20/3.40 | (223) ~ (all_0_23_23 = e3)
% 12.20/3.40 |
% 12.20/3.40 +-Applying beta-rule and splitting (131), into two cases.
% 12.20/3.40 |-Branch one:
% 12.20/3.40 | (224) ~ (all_0_18_18 = e3)
% 12.20/3.40 |
% 12.20/3.40 +-Applying beta-rule and splitting (105), into two cases.
% 12.20/3.40 |-Branch one:
% 12.20/3.40 | (225) ~ (all_0_10_10 = e3)
% 12.20/3.40 |
% 12.20/3.40 +-Applying beta-rule and splitting (155), into two cases.
% 12.20/3.40 |-Branch one:
% 12.20/3.40 | (226) all_0_9_9 = e3
% 12.20/3.40 |
% 12.20/3.40 | Equations (226) can reduce 212 to:
% 12.20/3.40 | (202) $false
% 12.20/3.40 |
% 12.20/3.40 |-The branch is then unsatisfiable
% 12.20/3.40 |-Branch two:
% 12.20/3.40 | (212) ~ (all_0_9_9 = e3)
% 12.20/3.40 | (229) all_0_10_10 = e3 | all_0_11_11 = e3
% 12.20/3.40 |
% 12.20/3.40 +-Applying beta-rule and splitting (229), into two cases.
% 12.20/3.40 |-Branch one:
% 12.20/3.40 | (230) all_0_10_10 = e3
% 12.20/3.40 |
% 12.20/3.40 | Equations (230) can reduce 225 to:
% 12.20/3.40 | (202) $false
% 12.20/3.40 |
% 12.20/3.40 |-The branch is then unsatisfiable
% 12.20/3.40 |-Branch two:
% 12.20/3.40 | (225) ~ (all_0_10_10 = e3)
% 12.20/3.40 | (233) all_0_11_11 = e3
% 12.20/3.40 |
% 12.20/3.40 | Equations (233) can reduce 145 to:
% 12.20/3.40 | (212) ~ (all_0_9_9 = e3)
% 12.20/3.40 |
% 12.20/3.40 | Equations (233) can reduce 187 to:
% 12.20/3.40 | (225) ~ (all_0_10_10 = e3)
% 12.20/3.40 |
% 12.20/3.40 | Equations (233) can reduce 50 to:
% 12.20/3.40 | (236) ~ (all_0_15_15 = e3)
% 12.20/3.40 |
% 12.20/3.40 | Simplifying 236 yields:
% 12.20/3.40 | (237) ~ (all_0_15_15 = e3)
% 12.20/3.40 |
% 12.20/3.40 | Equations (233) can reduce 171 to:
% 12.20/3.40 | (238) ~ (all_0_19_19 = e3)
% 12.20/3.40 |
% 12.20/3.40 | Simplifying 238 yields:
% 12.20/3.40 | (239) ~ (all_0_19_19 = e3)
% 12.20/3.40 |
% 12.20/3.40 | Equations (233) can reduce 119 to:
% 12.20/3.40 | (240) ~ (all_0_23_23 = e3)
% 12.20/3.40 |
% 12.20/3.40 | Simplifying 240 yields:
% 12.20/3.40 | (223) ~ (all_0_23_23 = e3)
% 12.20/3.40 |
% 12.20/3.40 +-Applying beta-rule and splitting (73), into two cases.
% 12.20/3.40 |-Branch one:
% 12.20/3.40 | (242) ~ (all_0_11_11 = e3)
% 12.20/3.40 |
% 12.20/3.40 | Equations (233) can reduce 242 to:
% 12.20/3.40 | (202) $false
% 12.20/3.40 |
% 12.20/3.40 |-The branch is then unsatisfiable
% 12.20/3.40 |-Branch two:
% 12.20/3.40 | (233) all_0_11_11 = e3
% 12.20/3.40 | (245) ~ (all_0_18_18 = e0)
% 12.20/3.40 |
% 12.20/3.40 +-Applying beta-rule and splitting (38), into two cases.
% 12.20/3.40 |-Branch one:
% 12.20/3.40 | (242) ~ (all_0_11_11 = e3)
% 12.20/3.40 |
% 12.20/3.40 | Equations (233) can reduce 242 to:
% 12.20/3.40 | (202) $false
% 12.20/3.40 |
% 12.20/3.40 |-The branch is then unsatisfiable
% 12.20/3.40 |-Branch two:
% 12.20/3.40 | (233) all_0_11_11 = e3
% 12.20/3.40 | (249) ~ (all_0_13_13 = e0)
% 12.20/3.40 |
% 12.20/3.40 +-Applying beta-rule and splitting (121), into two cases.
% 12.20/3.40 |-Branch one:
% 12.20/3.40 | (250) all_0_18_18 = e3
% 12.20/3.40 |
% 12.20/3.40 | Equations (250) can reduce 224 to:
% 12.20/3.40 | (202) $false
% 12.20/3.40 |
% 12.20/3.40 |-The branch is then unsatisfiable
% 12.20/3.40 |-Branch two:
% 12.20/3.40 | (224) ~ (all_0_18_18 = e3)
% 12.20/3.40 | (253) all_0_18_18 = e2 | all_0_18_18 = e0
% 12.20/3.40 |
% 12.20/3.40 +-Applying beta-rule and splitting (253), into two cases.
% 12.20/3.40 |-Branch one:
% 12.20/3.40 | (254) all_0_18_18 = e2
% 12.20/3.40 |
% 12.20/3.40 | Equations (254) can reduce 34 to:
% 12.20/3.40 | (255) ~ (all_0_14_14 = e2)
% 12.20/3.40 |
% 12.20/3.40 | Equations (254) can reduce 39 to:
% 12.20/3.40 | (256) ~ (all_0_16_16 = e2)
% 12.20/3.40 |
% 12.20/3.40 | Equations (254) can reduce 5 to:
% 12.20/3.40 | (257) ~ (all_0_22_22 = e2)
% 12.20/3.40 |
% 12.20/3.40 | Simplifying 257 yields:
% 12.20/3.40 | (258) ~ (all_0_22_22 = e2)
% 12.20/3.40 |
% 12.20/3.40 | Equations (254) can reduce 245 to:
% 12.20/3.40 | (13) ~ (e2 = e0)
% 12.20/3.40 |
% 12.20/3.40 +-Applying beta-rule and splitting (74), into two cases.
% 12.20/3.40 |-Branch one:
% 12.20/3.40 | (260) all_0_12_12 = e2
% 12.20/3.40 |
% 12.20/3.40 | Equations (260) can reduce 200 to:
% 12.20/3.40 | (202) $false
% 12.20/3.40 |
% 12.20/3.40 |-The branch is then unsatisfiable
% 12.20/3.40 |-Branch two:
% 12.20/3.40 | (200) ~ (all_0_12_12 = e2)
% 12.20/3.40 | (263) all_0_14_14 = e2 | all_0_15_15 = e2
% 12.20/3.40 |
% 12.20/3.40 +-Applying beta-rule and splitting (263), into two cases.
% 12.20/3.40 |-Branch one:
% 12.20/3.40 | (264) all_0_14_14 = e2
% 12.20/3.40 |
% 12.20/3.40 | Equations (264) can reduce 255 to:
% 12.20/3.40 | (202) $false
% 12.20/3.40 |
% 12.20/3.40 |-The branch is then unsatisfiable
% 12.20/3.40 |-Branch two:
% 12.20/3.40 | (255) ~ (all_0_14_14 = e2)
% 12.20/3.40 | (267) all_0_15_15 = e2
% 12.20/3.40 |
% 12.20/3.40 | Equations (267) can reduce 75 to:
% 12.20/3.40 | (200) ~ (all_0_12_12 = e2)
% 12.20/3.40 |
% 12.20/3.40 | Equations (267) can reduce 44 to:
% 12.20/3.40 | (255) ~ (all_0_14_14 = e2)
% 12.20/3.40 |
% 12.20/3.40 | Equations (267) can reduce 188 to:
% 12.20/3.40 | (270) ~ (all_0_19_19 = e2)
% 12.20/3.40 |
% 12.20/3.40 | Simplifying 270 yields:
% 12.20/3.40 | (271) ~ (all_0_19_19 = e2)
% 12.20/3.40 |
% 12.20/3.40 | Equations (267) can reduce 173 to:
% 12.20/3.40 | (272) ~ (all_0_23_23 = e2)
% 12.20/3.40 |
% 12.20/3.40 | Simplifying 272 yields:
% 12.20/3.40 | (273) ~ (all_0_23_23 = e2)
% 12.20/3.40 |
% 12.20/3.40 | Equations (267) can reduce 237 to:
% 12.20/3.40 | (274) ~ (e3 = e2)
% 12.20/3.40 |
% 12.20/3.40 | Simplifying 274 yields:
% 12.20/3.40 | (101) ~ (e3 = e2)
% 12.20/3.40 |
% 12.20/3.40 +-Applying beta-rule and splitting (147), into two cases.
% 12.20/3.40 |-Branch one:
% 12.20/3.40 | (276) all_0_11_11 = e0
% 12.20/3.40 |
% 12.20/3.40 | Combining equations (233,276) yields a new equation:
% 12.20/3.40 | (277) e3 = e0
% 12.20/3.40 |
% 12.20/3.40 | Simplifying 277 yields:
% 12.20/3.40 | (278) e3 = e0
% 12.20/3.40 |
% 12.20/3.40 | Equations (278) can reduce 136 to:
% 12.20/3.40 | (202) $false
% 12.20/3.40 |
% 12.20/3.40 |-The branch is then unsatisfiable
% 12.20/3.40 |-Branch two:
% 12.20/3.40 | (280) ~ (all_0_11_11 = e0)
% 12.20/3.40 | (281) all_0_15_15 = e0 | all_0_19_19 = e0
% 12.20/3.40 |
% 12.20/3.40 +-Applying beta-rule and splitting (281), into two cases.
% 12.20/3.40 |-Branch one:
% 12.20/3.40 | (282) all_0_15_15 = e0
% 12.20/3.40 |
% 12.20/3.40 | Combining equations (267,282) yields a new equation:
% 12.20/3.40 | (283) e2 = e0
% 12.20/3.40 |
% 12.20/3.40 | Simplifying 283 yields:
% 12.20/3.40 | (284) e2 = e0
% 12.20/3.40 |
% 12.20/3.40 | Equations (284) can reduce 13 to:
% 12.20/3.40 | (202) $false
% 12.20/3.40 |
% 12.20/3.40 |-The branch is then unsatisfiable
% 12.20/3.40 |-Branch two:
% 12.20/3.40 | (286) ~ (all_0_15_15 = e0)
% 12.20/3.40 | (287) all_0_19_19 = e0
% 12.20/3.40 |
% 12.20/3.40 | Equations (287) can reduce 120 to:
% 12.20/3.40 | (288) ~ (all_0_17_17 = e0)
% 12.20/3.40 |
% 12.20/3.40 | Equations (287) can reduce 135 to:
% 12.20/3.40 | (217) ~ (all_0_23_23 = e0)
% 12.20/3.40 |
% 12.20/3.40 | Simplifying 217 yields:
% 12.20/3.40 | (9) ~ (all_0_23_23 = e0)
% 12.20/3.40 |
% 12.20/3.40 | Equations (287) can reduce 239 to:
% 12.20/3.40 | (291) ~ (e3 = e0)
% 12.20/3.40 |
% 12.20/3.40 | Simplifying 291 yields:
% 12.20/3.40 | (136) ~ (e3 = e0)
% 12.20/3.40 |
% 12.20/3.41 | Equations (287) can reduce 271 to:
% 12.20/3.41 | (293) ~ (e2 = e0)
% 12.20/3.41 |
% 12.20/3.41 | Simplifying 293 yields:
% 12.20/3.41 | (13) ~ (e2 = e0)
% 12.20/3.41 |
% 12.20/3.41 +-Applying beta-rule and splitting (83), into two cases.
% 12.20/3.41 |-Branch one:
% 12.20/3.41 | (295) all_0_17_17 = e3
% 12.20/3.41 |
% 12.20/3.41 | Equations (295) can reduce 109 to:
% 12.20/3.41 | (212) ~ (all_0_9_9 = e3)
% 12.20/3.41 |
% 12.20/3.41 | Equations (295) can reduce 6 to:
% 12.20/3.41 | (219) ~ (all_0_13_13 = e3)
% 12.20/3.41 |
% 12.20/3.41 | Equations (295) can reduce 58 to:
% 12.20/3.41 | (298) ~ (all_0_16_16 = e3)
% 12.20/3.41 |
% 12.20/3.41 | Equations (295) can reduce 64 to:
% 12.20/3.41 | (299) ~ (all_0_21_21 = e3)
% 12.20/3.41 |
% 12.20/3.41 | Simplifying 299 yields:
% 12.20/3.41 | (300) ~ (all_0_21_21 = e3)
% 12.20/3.41 |
% 12.20/3.41 +-Applying beta-rule and splitting (88), into two cases.
% 12.20/3.41 |-Branch one:
% 12.20/3.41 | (301) all_0_23_23 = e3
% 12.20/3.41 |
% 12.20/3.41 | Equations (301) can reduce 223 to:
% 12.20/3.41 | (202) $false
% 12.20/3.41 |
% 12.20/3.41 |-The branch is then unsatisfiable
% 12.20/3.41 |-Branch two:
% 12.20/3.41 | (223) ~ (all_0_23_23 = e3)
% 12.20/3.41 | (304) all_0_23_23 = e2 | all_0_23_23 = e1
% 12.20/3.41 |
% 12.20/3.41 +-Applying beta-rule and splitting (304), into two cases.
% 12.20/3.41 |-Branch one:
% 12.20/3.41 | (305) all_0_23_23 = e2
% 12.20/3.41 |
% 12.20/3.41 | Equations (305) can reduce 273 to:
% 12.20/3.41 | (202) $false
% 12.20/3.41 |
% 12.20/3.41 |-The branch is then unsatisfiable
% 12.20/3.41 |-Branch two:
% 12.20/3.41 | (273) ~ (all_0_23_23 = e2)
% 12.20/3.41 | (308) all_0_23_23 = e1
% 12.20/3.41 |
% 12.20/3.41 | Equations (308) can reduce 191 to:
% 12.20/3.41 | (309) ~ (all_0_22_22 = e1)
% 12.20/3.41 |
% 12.20/3.41 | From (308) and (43) follows:
% 12.20/3.41 | (310) op(e0, e1) = all_0_1_1
% 12.20/3.41 |
% 12.20/3.41 +-Applying beta-rule and splitting (113), into two cases.
% 12.20/3.41 |-Branch one:
% 12.20/3.41 | (311) all_0_13_13 = e3
% 12.20/3.41 |
% 12.20/3.41 | Equations (311) can reduce 219 to:
% 12.20/3.41 | (202) $false
% 12.20/3.41 |
% 12.20/3.41 |-The branch is then unsatisfiable
% 12.20/3.41 |-Branch two:
% 12.20/3.41 | (219) ~ (all_0_13_13 = e3)
% 12.20/3.41 | (314) all_0_13_13 = e1 | all_0_13_13 = e0
% 12.20/3.41 |
% 12.20/3.41 +-Applying beta-rule and splitting (314), into two cases.
% 12.20/3.41 |-Branch one:
% 12.20/3.41 | (315) all_0_13_13 = e1
% 12.20/3.41 |
% 12.20/3.41 | Equations (315) can reduce 31 to:
% 12.20/3.41 | (316) ~ (all_0_9_9 = e1)
% 12.20/3.41 |
% 12.20/3.41 | Equations (315) can reduce 32 to:
% 12.20/3.41 | (317) ~ (all_0_12_12 = e1)
% 12.20/3.41 |
% 12.20/3.41 | Equations (315) can reduce 149 to:
% 12.20/3.41 | (318) ~ (all_0_14_14 = e1)
% 12.20/3.41 |
% 12.20/3.41 | Simplifying 318 yields:
% 12.20/3.41 | (319) ~ (all_0_14_14 = e1)
% 12.20/3.41 |
% 12.20/3.41 | Equations (315) can reduce 249 to:
% 12.20/3.41 | (181) ~ (e1 = e0)
% 12.20/3.41 |
% 12.20/3.41 | From (315) and (8) follows:
% 12.20/3.41 | (321) op(all_0_5_5, e1) = all_0_4_4
% 12.20/3.41 |
% 12.20/3.41 | From (315) and (102) follows:
% 12.20/3.41 | (322) op(e2, e1) = all_0_5_5
% 12.20/3.41 |
% 12.20/3.41 +-Applying beta-rule and splitting (128), into two cases.
% 12.20/3.41 |-Branch one:
% 12.20/3.41 | (323) all_0_12_12 = e3
% 12.20/3.41 |
% 12.20/3.41 | Equations (323) can reduce 160 to:
% 12.20/3.41 | (324) ~ (all_0_14_14 = e3)
% 12.20/3.41 |
% 12.20/3.41 | Simplifying 324 yields:
% 12.20/3.41 | (325) ~ (all_0_14_14 = e3)
% 12.20/3.41 |
% 12.20/3.41 | Equations (323) can reduce 200 to:
% 12.20/3.41 | (101) ~ (e3 = e2)
% 12.20/3.41 |
% 12.20/3.41 | Equations (323) can reduce 317 to:
% 12.20/3.41 | (137) ~ (e3 = e1)
% 12.20/3.41 |
% 12.20/3.41 +-Applying beta-rule and splitting (138), into two cases.
% 12.20/3.41 |-Branch one:
% 12.20/3.41 | (328) all_0_16_16 = e1
% 12.20/3.41 |
% 12.20/3.41 | Equations (328) can reduce 256 to:
% 12.20/3.41 | (329) ~ (e2 = e1)
% 12.20/3.41 |
% 12.20/3.41 | Simplifying 329 yields:
% 12.20/3.41 | (71) ~ (e2 = e1)
% 12.20/3.41 |
% 12.20/3.41 +-Applying beta-rule and splitting (95), into two cases.
% 12.20/3.41 |-Branch one:
% 12.20/3.41 | (331) all_0_14_14 = e3
% 12.20/3.41 |
% 12.20/3.41 | Equations (331) can reduce 325 to:
% 12.20/3.41 | (202) $false
% 12.20/3.41 |
% 12.20/3.41 |-The branch is then unsatisfiable
% 12.20/3.41 |-Branch two:
% 12.20/3.41 | (325) ~ (all_0_14_14 = e3)
% 12.20/3.41 | (334) all_0_14_14 = e2 | all_0_14_14 = e1 | all_0_14_14 = e0
% 12.20/3.41 |
% 12.20/3.41 +-Applying beta-rule and splitting (334), into two cases.
% 12.20/3.41 |-Branch one:
% 12.20/3.41 | (264) all_0_14_14 = e2
% 12.20/3.41 |
% 12.20/3.41 | Equations (264) can reduce 255 to:
% 12.20/3.41 | (202) $false
% 12.20/3.41 |
% 12.20/3.41 |-The branch is then unsatisfiable
% 12.20/3.41 |-Branch two:
% 12.20/3.41 | (255) ~ (all_0_14_14 = e2)
% 12.20/3.41 | (338) all_0_14_14 = e1 | all_0_14_14 = e0
% 12.20/3.41 |
% 12.20/3.41 +-Applying beta-rule and splitting (338), into two cases.
% 12.20/3.41 |-Branch one:
% 12.20/3.41 | (339) all_0_14_14 = e1
% 12.20/3.41 |
% 12.20/3.41 | Equations (339) can reduce 319 to:
% 12.20/3.41 | (202) $false
% 12.20/3.41 |
% 12.20/3.41 |-The branch is then unsatisfiable
% 12.20/3.41 |-Branch two:
% 12.20/3.41 | (319) ~ (all_0_14_14 = e1)
% 12.20/3.41 | (342) all_0_14_14 = e0
% 12.20/3.41 |
% 12.20/3.41 | From (342) and (89) follows:
% 12.20/3.41 | (343) op(e2, e1) = e0
% 12.20/3.41 |
% 12.20/3.41 +-Applying beta-rule and splitting (87), into two cases.
% 12.20/3.41 |-Branch one:
% 12.20/3.41 | (344) all_0_22_22 = e3
% 12.20/3.41 |
% 12.20/3.41 | From (344) and (37) follows:
% 12.20/3.41 | (345) op(e0, e1) = e3
% 12.20/3.41 |
% 12.20/3.41 | Instantiating formula (53) with e2, e1, e0, all_0_5_5 and discharging atoms op(e2, e1) = all_0_5_5, op(e2, e1) = e0, yields:
% 12.20/3.41 | (346) all_0_5_5 = e0
% 12.20/3.41 |
% 12.20/3.41 | Instantiating formula (53) with e0, e1, e3, all_0_1_1 and discharging atoms op(e0, e1) = all_0_1_1, op(e0, e1) = e3, yields:
% 12.20/3.41 | (347) all_0_1_1 = e3
% 12.20/3.41 |
% 12.20/3.41 | From (346) and (321) follows:
% 12.20/3.41 | (348) op(e0, e1) = all_0_4_4
% 12.20/3.41 |
% 12.20/3.41 | From (347) and (310) follows:
% 12.20/3.41 | (345) op(e0, e1) = e3
% 12.20/3.41 |
% 12.20/3.41 +-Applying beta-rule and splitting (66), into two cases.
% 12.20/3.41 |-Branch one:
% 12.20/3.41 | (350) ~ (all_0_4_4 = e3)
% 12.20/3.41 |
% 12.20/3.41 | Instantiating formula (53) with e0, e1, all_0_4_4, e3 and discharging atoms op(e0, e1) = all_0_4_4, op(e0, e1) = e3, yields:
% 12.20/3.41 | (351) all_0_4_4 = e3
% 12.20/3.41 |
% 12.20/3.41 | Equations (351) can reduce 350 to:
% 12.31/3.41 | (202) $false
% 12.31/3.41 |
% 12.31/3.41 |-The branch is then unsatisfiable
% 12.31/3.41 |-Branch two:
% 12.31/3.41 | (351) all_0_4_4 = e3
% 12.31/3.41 | (354) ~ (all_0_5_5 = e0) | ~ (all_0_13_13 = e1)
% 12.31/3.41 |
% 12.31/3.41 +-Applying beta-rule and splitting (354), into two cases.
% 12.31/3.41 |-Branch one:
% 12.31/3.41 | (355) ~ (all_0_5_5 = e0)
% 12.31/3.41 |
% 12.31/3.41 | Equations (346) can reduce 355 to:
% 12.31/3.41 | (202) $false
% 12.31/3.41 |
% 12.31/3.41 |-The branch is then unsatisfiable
% 12.31/3.41 |-Branch two:
% 12.31/3.41 | (346) all_0_5_5 = e0
% 12.31/3.42 | (358) ~ (all_0_13_13 = e1)
% 12.31/3.42 |
% 12.31/3.42 | Equations (315) can reduce 358 to:
% 12.31/3.42 | (202) $false
% 12.31/3.42 |
% 12.31/3.42 |-The branch is then unsatisfiable
% 12.31/3.42 |-Branch two:
% 12.31/3.42 | (360) ~ (all_0_22_22 = e3)
% 12.31/3.42 | (361) all_0_22_22 = e2 | all_0_22_22 = e1 | all_0_22_22 = e0
% 12.31/3.42 |
% 12.31/3.42 +-Applying beta-rule and splitting (144), into two cases.
% 12.31/3.42 |-Branch one:
% 12.31/3.42 | (362) all_0_9_9 = e2
% 12.31/3.42 |
% 12.31/3.42 | Equations (362) can reduce 198 to:
% 12.31/3.42 | (202) $false
% 12.31/3.42 |
% 12.31/3.42 |-The branch is then unsatisfiable
% 12.31/3.42 |-Branch two:
% 12.31/3.42 | (198) ~ (all_0_9_9 = e2)
% 12.31/3.42 | (365) all_0_17_17 = e2 | all_0_21_21 = e2
% 12.31/3.42 |
% 12.31/3.42 +-Applying beta-rule and splitting (123), into two cases.
% 12.31/3.42 |-Branch one:
% 12.31/3.42 | (366) all_0_8_8 = e1
% 12.31/3.42 |
% 12.31/3.42 | Combining equations (366,196) yields a new equation:
% 12.31/3.42 | (367) e2 = e1
% 12.31/3.42 |
% 12.31/3.42 | Equations (367) can reduce 71 to:
% 12.31/3.42 | (202) $false
% 12.31/3.42 |
% 12.31/3.42 |-The branch is then unsatisfiable
% 12.31/3.42 |-Branch two:
% 12.31/3.42 | (193) ~ (all_0_8_8 = e1)
% 12.31/3.42 | (370) all_0_9_9 = e1 | all_0_10_10 = e1 | all_0_11_11 = e1
% 12.31/3.42 |
% 12.31/3.42 +-Applying beta-rule and splitting (365), into two cases.
% 12.31/3.42 |-Branch one:
% 12.31/3.42 | (371) all_0_17_17 = e2
% 12.31/3.42 |
% 12.31/3.42 | Combining equations (295,371) yields a new equation:
% 12.31/3.42 | (372) e3 = e2
% 12.31/3.42 |
% 12.31/3.42 | Simplifying 372 yields:
% 12.31/3.42 | (373) e3 = e2
% 12.31/3.42 |
% 12.31/3.42 | Equations (373) can reduce 101 to:
% 12.31/3.42 | (202) $false
% 12.31/3.42 |
% 12.31/3.42 |-The branch is then unsatisfiable
% 12.31/3.42 |-Branch two:
% 12.31/3.42 | (375) ~ (all_0_17_17 = e2)
% 12.31/3.42 | (376) all_0_21_21 = e2
% 12.31/3.42 |
% 12.31/3.42 | Equations (376) can reduce 118 to:
% 12.31/3.42 | (198) ~ (all_0_9_9 = e2)
% 12.31/3.42 |
% 12.31/3.42 | Equations (376) can reduce 300 to:
% 12.31/3.42 | (274) ~ (e3 = e2)
% 12.31/3.42 |
% 12.31/3.42 | Simplifying 274 yields:
% 12.31/3.42 | (101) ~ (e3 = e2)
% 12.31/3.42 |
% 12.31/3.42 +-Applying beta-rule and splitting (370), into two cases.
% 12.31/3.42 |-Branch one:
% 12.31/3.42 | (380) all_0_9_9 = e1
% 12.31/3.42 |
% 12.31/3.42 | Equations (380) can reduce 316 to:
% 12.31/3.42 | (202) $false
% 12.31/3.42 |
% 12.31/3.42 |-The branch is then unsatisfiable
% 12.31/3.42 |-Branch two:
% 12.31/3.42 | (316) ~ (all_0_9_9 = e1)
% 12.31/3.42 | (383) all_0_10_10 = e1 | all_0_11_11 = e1
% 12.31/3.42 |
% 12.31/3.42 +-Applying beta-rule and splitting (142), into two cases.
% 12.31/3.42 |-Branch one:
% 12.31/3.42 | (226) all_0_9_9 = e3
% 12.31/3.42 |
% 12.31/3.42 | Equations (226) can reduce 212 to:
% 12.31/3.42 | (202) $false
% 12.31/3.42 |
% 12.31/3.42 |-The branch is then unsatisfiable
% 12.31/3.42 |-Branch two:
% 12.31/3.42 | (212) ~ (all_0_9_9 = e3)
% 12.31/3.42 | (387) all_0_9_9 = e2 | all_0_9_9 = e1 | all_0_9_9 = e0
% 12.31/3.42 |
% 12.31/3.42 +-Applying beta-rule and splitting (387), into two cases.
% 12.31/3.42 |-Branch one:
% 12.31/3.42 | (362) all_0_9_9 = e2
% 12.31/3.42 |
% 12.31/3.42 | Equations (362) can reduce 198 to:
% 12.31/3.42 | (202) $false
% 12.31/3.42 |
% 12.31/3.42 |-The branch is then unsatisfiable
% 12.31/3.42 |-Branch two:
% 12.31/3.42 | (198) ~ (all_0_9_9 = e2)
% 12.31/3.42 | (391) all_0_9_9 = e1 | all_0_9_9 = e0
% 12.31/3.42 |
% 12.31/3.42 +-Applying beta-rule and splitting (391), into two cases.
% 12.31/3.42 |-Branch one:
% 12.31/3.42 | (380) all_0_9_9 = e1
% 12.31/3.42 |
% 12.31/3.42 | Equations (380) can reduce 316 to:
% 12.31/3.42 | (202) $false
% 12.31/3.42 |
% 12.31/3.42 |-The branch is then unsatisfiable
% 12.31/3.42 |-Branch two:
% 12.31/3.42 | (316) ~ (all_0_9_9 = e1)
% 12.31/3.42 | (395) all_0_9_9 = e0
% 12.31/3.42 |
% 12.31/3.42 | Equations (395) can reduce 212 to:
% 12.31/3.42 | (291) ~ (e3 = e0)
% 12.31/3.42 |
% 12.31/3.42 | Simplifying 291 yields:
% 12.31/3.42 | (136) ~ (e3 = e0)
% 12.31/3.42 |
% 12.31/3.42 +-Applying beta-rule and splitting (67), into two cases.
% 12.31/3.42 |-Branch one:
% 12.31/3.42 | (230) all_0_10_10 = e3
% 12.31/3.42 |
% 12.31/3.42 | Equations (230) can reduce 225 to:
% 12.31/3.42 | (202) $false
% 12.31/3.42 |
% 12.31/3.42 |-The branch is then unsatisfiable
% 12.31/3.42 |-Branch two:
% 12.31/3.42 | (225) ~ (all_0_10_10 = e3)
% 12.31/3.42 | (401) all_0_14_14 = e3 | all_0_18_18 = e3 | all_0_22_22 = e3
% 12.31/3.42 |
% 12.31/3.42 +-Applying beta-rule and splitting (401), into two cases.
% 12.31/3.42 |-Branch one:
% 12.31/3.42 | (331) all_0_14_14 = e3
% 12.31/3.42 |
% 12.31/3.42 | Combining equations (342,331) yields a new equation:
% 12.31/3.42 | (278) e3 = e0
% 12.31/3.42 |
% 12.31/3.42 | Equations (278) can reduce 136 to:
% 12.31/3.42 | (202) $false
% 12.31/3.42 |
% 12.31/3.42 |-The branch is then unsatisfiable
% 12.31/3.42 |-Branch two:
% 12.31/3.42 | (325) ~ (all_0_14_14 = e3)
% 12.31/3.42 | (406) all_0_18_18 = e3 | all_0_22_22 = e3
% 12.31/3.42 |
% 12.31/3.42 +-Applying beta-rule and splitting (406), into two cases.
% 12.31/3.42 |-Branch one:
% 12.31/3.42 | (250) all_0_18_18 = e3
% 12.31/3.42 |
% 12.31/3.42 | Combining equations (254,250) yields a new equation:
% 12.31/3.42 | (373) e3 = e2
% 12.31/3.42 |
% 12.31/3.42 | Equations (373) can reduce 101 to:
% 12.31/3.42 | (202) $false
% 12.31/3.42 |
% 12.31/3.42 |-The branch is then unsatisfiable
% 12.31/3.42 |-Branch two:
% 12.31/3.42 | (224) ~ (all_0_18_18 = e3)
% 12.31/3.42 | (344) all_0_22_22 = e3
% 12.31/3.42 |
% 12.31/3.42 | Equations (344) can reduce 360 to:
% 12.31/3.42 | (202) $false
% 12.31/3.42 |
% 12.31/3.42 |-The branch is then unsatisfiable
% 12.31/3.42 |-Branch two:
% 12.31/3.42 | (413) ~ (all_0_16_16 = e1)
% 12.31/3.42 | (414) all_0_17_17 = e1 | all_0_19_19 = e1
% 12.31/3.42 |
% 12.31/3.42 +-Applying beta-rule and splitting (414), into two cases.
% 12.31/3.42 |-Branch one:
% 12.31/3.42 | (415) all_0_17_17 = e1
% 12.31/3.42 |
% 12.31/3.42 | Combining equations (295,415) yields a new equation:
% 12.31/3.42 | (416) e3 = e1
% 12.31/3.42 |
% 12.31/3.42 | Simplifying 416 yields:
% 12.31/3.42 | (417) e3 = e1
% 12.31/3.42 |
% 12.31/3.42 | Equations (417) can reduce 137 to:
% 12.31/3.42 | (202) $false
% 12.31/3.42 |
% 12.31/3.42 |-The branch is then unsatisfiable
% 12.31/3.42 |-Branch two:
% 12.31/3.42 | (208) ~ (all_0_17_17 = e1)
% 12.31/3.42 | (420) all_0_19_19 = e1
% 12.31/3.42 |
% 12.31/3.42 | Combining equations (287,420) yields a new equation:
% 12.31/3.42 | (421) e1 = e0
% 12.31/3.42 |
% 12.31/3.42 | Equations (421) can reduce 181 to:
% 12.31/3.42 | (202) $false
% 12.31/3.42 |
% 12.31/3.42 |-The branch is then unsatisfiable
% 12.31/3.42 |-Branch two:
% 12.31/3.42 | (423) ~ (all_0_12_12 = e3)
% 12.31/3.42 | (424) all_0_16_16 = e3 | all_0_20_20 = e3
% 12.31/3.42 |
% 12.31/3.42 +-Applying beta-rule and splitting (87), into two cases.
% 12.31/3.42 |-Branch one:
% 12.31/3.42 | (344) all_0_22_22 = e3
% 12.31/3.42 |
% 12.31/3.42 | Equations (344) can reduce 194 to:
% 12.31/3.42 | (136) ~ (e3 = e0)
% 12.31/3.42 |
% 12.31/3.42 +-Applying beta-rule and splitting (7), into two cases.
% 12.31/3.42 |-Branch one:
% 12.31/3.42 | (427) all_0_16_16 = e3
% 12.31/3.42 |
% 12.31/3.42 | Equations (427) can reduce 298 to:
% 12.31/3.42 | (202) $false
% 12.31/3.42 |
% 12.31/3.42 |-The branch is then unsatisfiable
% 12.31/3.42 |-Branch two:
% 12.31/3.42 | (298) ~ (all_0_16_16 = e3)
% 12.31/3.42 | (430) all_0_16_16 = e2 | all_0_16_16 = e1 | all_0_16_16 = e0
% 12.31/3.42 |
% 12.31/3.42 +-Applying beta-rule and splitting (424), into two cases.
% 12.31/3.42 |-Branch one:
% 12.31/3.42 | (427) all_0_16_16 = e3
% 12.31/3.42 |
% 12.31/3.42 | Equations (427) can reduce 298 to:
% 12.31/3.42 | (202) $false
% 12.31/3.42 |
% 12.31/3.42 |-The branch is then unsatisfiable
% 12.31/3.42 |-Branch two:
% 12.31/3.42 | (298) ~ (all_0_16_16 = e3)
% 12.31/3.42 | (434) all_0_20_20 = e3
% 12.31/3.42 |
% 12.31/3.42 | Combining equations (213,434) yields a new equation:
% 12.31/3.42 | (278) e3 = e0
% 12.31/3.42 |
% 12.31/3.42 | Equations (278) can reduce 136 to:
% 12.31/3.42 | (202) $false
% 12.31/3.42 |
% 12.31/3.42 |-The branch is then unsatisfiable
% 12.31/3.42 |-Branch two:
% 12.31/3.42 | (360) ~ (all_0_22_22 = e3)
% 12.31/3.42 | (361) all_0_22_22 = e2 | all_0_22_22 = e1 | all_0_22_22 = e0
% 12.31/3.42 |
% 12.31/3.42 +-Applying beta-rule and splitting (361), into two cases.
% 12.31/3.42 |-Branch one:
% 12.31/3.42 | (439) all_0_22_22 = e2
% 12.31/3.42 |
% 12.31/3.42 | Equations (439) can reduce 258 to:
% 12.31/3.42 | (202) $false
% 12.31/3.42 |
% 12.31/3.42 |-The branch is then unsatisfiable
% 12.31/3.42 |-Branch two:
% 12.31/3.42 | (258) ~ (all_0_22_22 = e2)
% 12.31/3.42 | (442) all_0_22_22 = e1 | all_0_22_22 = e0
% 12.31/3.42 |
% 12.31/3.42 +-Applying beta-rule and splitting (442), into two cases.
% 12.31/3.42 |-Branch one:
% 12.31/3.42 | (443) all_0_22_22 = e1
% 12.31/3.42 |
% 12.31/3.43 | Equations (443) can reduce 309 to:
% 12.31/3.43 | (202) $false
% 12.31/3.43 |
% 12.31/3.43 |-The branch is then unsatisfiable
% 12.31/3.43 |-Branch two:
% 12.31/3.43 | (309) ~ (all_0_22_22 = e1)
% 12.31/3.43 | (446) all_0_22_22 = e0
% 12.31/3.43 |
% 12.31/3.43 | Equations (446) can reduce 194 to:
% 12.31/3.43 | (202) $false
% 12.31/3.43 |
% 12.31/3.43 |-The branch is then unsatisfiable
% 12.31/3.43 |-Branch two:
% 12.31/3.43 | (358) ~ (all_0_13_13 = e1)
% 12.31/3.43 | (449) all_0_13_13 = e0
% 12.31/3.43 |
% 12.31/3.43 | Equations (449) can reduce 249 to:
% 12.31/3.43 | (202) $false
% 12.31/3.43 |
% 12.31/3.43 |-The branch is then unsatisfiable
% 12.31/3.43 |-Branch two:
% 12.31/3.43 | (451) ~ (all_0_17_17 = e3)
% 12.31/3.43 | (452) all_0_17_17 = e2 | all_0_17_17 = e1 | all_0_17_17 = e0
% 12.31/3.43 |
% 12.31/3.43 +-Applying beta-rule and splitting (88), into two cases.
% 12.31/3.43 |-Branch one:
% 12.31/3.43 | (301) all_0_23_23 = e3
% 12.31/3.43 |
% 12.31/3.43 | Equations (301) can reduce 223 to:
% 12.31/3.43 | (202) $false
% 12.31/3.43 |
% 12.31/3.43 |-The branch is then unsatisfiable
% 12.31/3.43 |-Branch two:
% 12.31/3.43 | (223) ~ (all_0_23_23 = e3)
% 12.31/3.43 | (304) all_0_23_23 = e2 | all_0_23_23 = e1
% 12.31/3.43 |
% 12.31/3.43 +-Applying beta-rule and splitting (153), into two cases.
% 12.31/3.43 |-Branch one:
% 12.31/3.43 | (395) all_0_9_9 = e0
% 12.31/3.43 |
% 12.31/3.43 | Equations (395) can reduce 212 to:
% 12.31/3.43 | (291) ~ (e3 = e0)
% 12.31/3.43 |
% 12.31/3.43 | Simplifying 291 yields:
% 12.31/3.43 | (136) ~ (e3 = e0)
% 12.31/3.43 |
% 12.31/3.43 +-Applying beta-rule and splitting (304), into two cases.
% 12.31/3.43 |-Branch one:
% 12.31/3.43 | (305) all_0_23_23 = e2
% 12.31/3.43 |
% 12.31/3.43 | Equations (305) can reduce 273 to:
% 12.31/3.43 | (202) $false
% 12.31/3.43 |
% 12.31/3.43 |-The branch is then unsatisfiable
% 12.31/3.43 |-Branch two:
% 12.31/3.43 | (273) ~ (all_0_23_23 = e2)
% 12.31/3.43 | (308) all_0_23_23 = e1
% 12.31/3.43 |
% 12.31/3.43 | Equations (308) can reduce 223 to:
% 12.31/3.43 | (464) ~ (e3 = e1)
% 12.31/3.43 |
% 12.31/3.43 | Simplifying 464 yields:
% 12.31/3.43 | (137) ~ (e3 = e1)
% 12.31/3.43 |
% 12.31/3.43 | Equations (308) can reduce 9 to:
% 12.31/3.43 | (181) ~ (e1 = e0)
% 12.31/3.43 |
% 12.31/3.43 +-Applying beta-rule and splitting (138), into two cases.
% 12.31/3.43 |-Branch one:
% 12.31/3.43 | (328) all_0_16_16 = e1
% 12.31/3.43 |
% 12.31/3.43 +-Applying beta-rule and splitting (52), into two cases.
% 12.31/3.43 |-Branch one:
% 12.31/3.43 | (427) all_0_16_16 = e3
% 12.31/3.43 |
% 12.31/3.43 | Combining equations (328,427) yields a new equation:
% 12.31/3.43 | (417) e3 = e1
% 12.31/3.43 |
% 12.31/3.43 | Equations (417) can reduce 137 to:
% 12.31/3.43 | (202) $false
% 12.31/3.43 |
% 12.31/3.43 |-The branch is then unsatisfiable
% 12.31/3.43 |-Branch two:
% 12.31/3.43 | (298) ~ (all_0_16_16 = e3)
% 12.31/3.43 | (472) all_0_17_17 = e3 | all_0_18_18 = e3 | all_0_19_19 = e3
% 12.31/3.43 |
% 12.31/3.43 +-Applying beta-rule and splitting (472), into two cases.
% 12.31/3.43 |-Branch one:
% 12.31/3.43 | (295) all_0_17_17 = e3
% 12.31/3.43 |
% 12.31/3.43 | Equations (295) can reduce 451 to:
% 12.31/3.43 | (202) $false
% 12.31/3.43 |
% 12.31/3.43 |-The branch is then unsatisfiable
% 12.31/3.43 |-Branch two:
% 12.31/3.43 | (451) ~ (all_0_17_17 = e3)
% 12.31/3.43 | (476) all_0_18_18 = e3 | all_0_19_19 = e3
% 12.31/3.43 |
% 12.31/3.43 +-Applying beta-rule and splitting (476), into two cases.
% 12.31/3.43 |-Branch one:
% 12.31/3.43 | (250) all_0_18_18 = e3
% 12.31/3.43 |
% 12.31/3.43 | Combining equations (254,250) yields a new equation:
% 12.31/3.43 | (373) e3 = e2
% 12.31/3.43 |
% 12.31/3.43 | Equations (373) can reduce 101 to:
% 12.31/3.43 | (202) $false
% 12.31/3.43 |
% 12.31/3.43 |-The branch is then unsatisfiable
% 12.31/3.43 |-Branch two:
% 12.31/3.43 | (224) ~ (all_0_18_18 = e3)
% 12.31/3.43 | (481) all_0_19_19 = e3
% 12.31/3.43 |
% 12.31/3.43 | Combining equations (481,287) yields a new equation:
% 12.31/3.43 | (277) e3 = e0
% 12.31/3.43 |
% 12.31/3.43 | Simplifying 277 yields:
% 12.31/3.43 | (278) e3 = e0
% 12.31/3.43 |
% 12.31/3.43 | Equations (278) can reduce 136 to:
% 12.31/3.43 | (202) $false
% 12.31/3.43 |
% 12.31/3.43 |-The branch is then unsatisfiable
% 12.31/3.43 |-Branch two:
% 12.31/3.43 | (413) ~ (all_0_16_16 = e1)
% 12.31/3.43 | (414) all_0_17_17 = e1 | all_0_19_19 = e1
% 12.31/3.43 |
% 12.31/3.43 +-Applying beta-rule and splitting (414), into two cases.
% 12.31/3.43 |-Branch one:
% 12.31/3.43 | (415) all_0_17_17 = e1
% 12.31/3.43 |
% 12.31/3.43 | Equations (415) can reduce 208 to:
% 12.31/3.43 | (202) $false
% 12.31/3.43 |
% 12.31/3.43 |-The branch is then unsatisfiable
% 12.31/3.43 |-Branch two:
% 12.31/3.43 | (208) ~ (all_0_17_17 = e1)
% 12.31/3.43 | (420) all_0_19_19 = e1
% 12.31/3.43 |
% 12.31/3.43 | Combining equations (420,287) yields a new equation:
% 12.31/3.43 | (491) e1 = e0
% 12.31/3.43 |
% 12.31/3.43 | Simplifying 491 yields:
% 12.31/3.43 | (421) e1 = e0
% 12.31/3.43 |
% 12.31/3.43 | Equations (421) can reduce 181 to:
% 12.31/3.43 | (202) $false
% 12.31/3.43 |
% 12.31/3.43 |-The branch is then unsatisfiable
% 12.31/3.43 |-Branch two:
% 12.31/3.43 | (494) ~ (all_0_9_9 = e0)
% 12.31/3.43 | (495) all_0_13_13 = e0 | all_0_17_17 = e0 | all_0_21_21 = e0
% 12.31/3.43 |
% 12.31/3.43 +-Applying beta-rule and splitting (495), into two cases.
% 12.31/3.43 |-Branch one:
% 12.31/3.43 | (449) all_0_13_13 = e0
% 12.31/3.43 |
% 12.31/3.43 | Equations (449) can reduce 249 to:
% 12.31/3.43 | (202) $false
% 12.31/3.43 |
% 12.31/3.43 |-The branch is then unsatisfiable
% 12.31/3.43 |-Branch two:
% 12.31/3.43 | (249) ~ (all_0_13_13 = e0)
% 12.31/3.43 | (499) all_0_17_17 = e0 | all_0_21_21 = e0
% 12.31/3.43 |
% 12.31/3.43 +-Applying beta-rule and splitting (146), into two cases.
% 12.31/3.43 |-Branch one:
% 12.31/3.43 | (500) all_0_12_12 = e0
% 12.31/3.43 |
% 12.31/3.43 | Equations (500) can reduce 214 to:
% 12.31/3.43 | (202) $false
% 12.31/3.43 |
% 12.31/3.43 |-The branch is then unsatisfiable
% 12.31/3.43 |-Branch two:
% 12.31/3.43 | (214) ~ (all_0_12_12 = e0)
% 12.31/3.43 | (503) all_0_13_13 = e0 | all_0_14_14 = e0 | all_0_15_15 = e0
% 12.31/3.43 |
% 12.31/3.43 +-Applying beta-rule and splitting (503), into two cases.
% 12.31/3.43 |-Branch one:
% 12.31/3.43 | (449) all_0_13_13 = e0
% 12.31/3.43 |
% 12.31/3.43 | Equations (449) can reduce 249 to:
% 12.31/3.43 | (202) $false
% 12.31/3.43 |
% 12.31/3.43 |-The branch is then unsatisfiable
% 12.31/3.43 |-Branch two:
% 12.31/3.43 | (249) ~ (all_0_13_13 = e0)
% 12.31/3.43 | (507) all_0_14_14 = e0 | all_0_15_15 = e0
% 12.31/3.43 |
% 12.31/3.43 +-Applying beta-rule and splitting (507), into two cases.
% 12.31/3.43 |-Branch one:
% 12.31/3.43 | (342) all_0_14_14 = e0
% 12.31/3.43 |
% 12.31/3.43 | Equations (342) can reduce 255 to:
% 12.31/3.43 | (293) ~ (e2 = e0)
% 12.31/3.43 |
% 12.31/3.43 | Simplifying 293 yields:
% 12.31/3.43 | (13) ~ (e2 = e0)
% 12.31/3.43 |
% 12.31/3.43 +-Applying beta-rule and splitting (67), into two cases.
% 12.31/3.43 |-Branch one:
% 12.31/3.43 | (230) all_0_10_10 = e3
% 12.31/3.43 |
% 12.31/3.43 | Equations (230) can reduce 225 to:
% 12.31/3.43 | (202) $false
% 12.31/3.43 |
% 12.31/3.43 |-The branch is then unsatisfiable
% 12.31/3.43 |-Branch two:
% 12.31/3.43 | (225) ~ (all_0_10_10 = e3)
% 12.31/3.43 | (401) all_0_14_14 = e3 | all_0_18_18 = e3 | all_0_22_22 = e3
% 12.38/3.43 |
% 12.38/3.43 +-Applying beta-rule and splitting (401), into two cases.
% 12.38/3.43 |-Branch one:
% 12.38/3.43 | (331) all_0_14_14 = e3
% 12.38/3.43 |
% 12.38/3.43 | Combining equations (342,331) yields a new equation:
% 12.38/3.43 | (278) e3 = e0
% 12.38/3.43 |
% 12.38/3.43 | Equations (278) can reduce 136 to:
% 12.38/3.43 | (202) $false
% 12.38/3.43 |
% 12.38/3.43 |-The branch is then unsatisfiable
% 12.38/3.43 |-Branch two:
% 12.38/3.43 | (325) ~ (all_0_14_14 = e3)
% 12.38/3.43 | (406) all_0_18_18 = e3 | all_0_22_22 = e3
% 12.38/3.43 |
% 12.38/3.43 +-Applying beta-rule and splitting (406), into two cases.
% 12.38/3.43 |-Branch one:
% 12.38/3.43 | (250) all_0_18_18 = e3
% 12.38/3.43 |
% 12.38/3.43 | Combining equations (254,250) yields a new equation:
% 12.38/3.43 | (373) e3 = e2
% 12.38/3.43 |
% 12.38/3.43 | Equations (373) can reduce 101 to:
% 12.38/3.43 | (202) $false
% 12.38/3.43 |
% 12.38/3.43 |-The branch is then unsatisfiable
% 12.38/3.43 |-Branch two:
% 12.38/3.43 | (224) ~ (all_0_18_18 = e3)
% 12.38/3.43 | (344) all_0_22_22 = e3
% 12.38/3.43 |
% 12.38/3.43 | Equations (344) can reduce 258 to:
% 12.38/3.43 | (101) ~ (e3 = e2)
% 12.38/3.43 |
% 12.38/3.43 +-Applying beta-rule and splitting (148), into two cases.
% 12.38/3.43 |-Branch one:
% 12.38/3.43 | (526) all_0_20_20 = e2
% 12.38/3.43 |
% 12.38/3.43 | Combining equations (213,526) yields a new equation:
% 12.38/3.43 | (284) e2 = e0
% 12.38/3.43 |
% 12.38/3.43 | Equations (284) can reduce 13 to:
% 12.38/3.43 | (202) $false
% 12.38/3.43 |
% 12.38/3.43 |-The branch is then unsatisfiable
% 12.38/3.43 |-Branch two:
% 12.38/3.43 | (529) ~ (all_0_20_20 = e2)
% 12.38/3.43 | (530) all_0_21_21 = e2 | all_0_22_22 = e2 | all_0_23_23 = e2
% 12.38/3.43 |
% 12.38/3.43 +-Applying beta-rule and splitting (530), into two cases.
% 12.38/3.43 |-Branch one:
% 12.38/3.43 | (376) all_0_21_21 = e2
% 12.38/3.43 |
% 12.38/3.43 | Equations (376) can reduce 64 to:
% 12.38/3.43 | (375) ~ (all_0_17_17 = e2)
% 12.38/3.43 |
% 12.38/3.43 +-Applying beta-rule and splitting (452), into two cases.
% 12.38/3.43 |-Branch one:
% 12.38/3.43 | (371) all_0_17_17 = e2
% 12.38/3.43 |
% 12.38/3.44 | Equations (371) can reduce 375 to:
% 12.38/3.44 | (202) $false
% 12.38/3.44 |
% 12.38/3.44 |-The branch is then unsatisfiable
% 12.38/3.44 |-Branch two:
% 12.38/3.44 | (375) ~ (all_0_17_17 = e2)
% 12.38/3.44 | (536) all_0_17_17 = e1 | all_0_17_17 = e0
% 12.38/3.44 |
% 12.38/3.44 +-Applying beta-rule and splitting (536), into two cases.
% 12.38/3.44 |-Branch one:
% 12.38/3.44 | (415) all_0_17_17 = e1
% 12.38/3.44 |
% 12.38/3.44 | Equations (415) can reduce 208 to:
% 12.38/3.44 | (202) $false
% 12.38/3.44 |
% 12.38/3.44 |-The branch is then unsatisfiable
% 12.38/3.44 |-Branch two:
% 12.38/3.44 | (208) ~ (all_0_17_17 = e1)
% 12.38/3.44 | (540) all_0_17_17 = e0
% 12.38/3.44 |
% 12.38/3.44 | Equations (540) can reduce 288 to:
% 12.38/3.44 | (202) $false
% 12.38/3.44 |
% 12.38/3.44 |-The branch is then unsatisfiable
% 12.38/3.44 |-Branch two:
% 12.38/3.44 | (542) ~ (all_0_21_21 = e2)
% 12.38/3.44 | (543) all_0_22_22 = e2 | all_0_23_23 = e2
% 12.38/3.44 |
% 12.38/3.44 +-Applying beta-rule and splitting (543), into two cases.
% 12.38/3.44 |-Branch one:
% 12.38/3.44 | (439) all_0_22_22 = e2
% 12.38/3.44 |
% 12.38/3.44 | Combining equations (439,344) yields a new equation:
% 12.38/3.44 | (373) e3 = e2
% 12.38/3.44 |
% 12.38/3.44 | Equations (373) can reduce 101 to:
% 12.38/3.44 | (202) $false
% 12.38/3.44 |
% 12.38/3.44 |-The branch is then unsatisfiable
% 12.38/3.44 |-Branch two:
% 12.38/3.44 | (258) ~ (all_0_22_22 = e2)
% 12.38/3.44 | (305) all_0_23_23 = e2
% 12.38/3.44 |
% 12.38/3.44 | Equations (305) can reduce 273 to:
% 12.38/3.44 | (202) $false
% 12.38/3.44 |
% 12.38/3.44 |-The branch is then unsatisfiable
% 12.38/3.44 |-Branch two:
% 12.38/3.44 | (550) ~ (all_0_14_14 = e0)
% 12.38/3.44 | (282) all_0_15_15 = e0
% 12.38/3.44 |
% 12.38/3.44 | Combining equations (267,282) yields a new equation:
% 12.38/3.44 | (283) e2 = e0
% 12.38/3.44 |
% 12.38/3.44 | Simplifying 283 yields:
% 12.38/3.44 | (284) e2 = e0
% 12.38/3.44 |
% 12.38/3.44 | Equations (284) can reduce 13 to:
% 12.38/3.44 | (202) $false
% 12.38/3.44 |
% 12.38/3.44 |-The branch is then unsatisfiable
% 12.38/3.44 |-Branch two:
% 12.38/3.44 | (555) ~ (all_0_18_18 = e2)
% 12.38/3.44 | (556) all_0_18_18 = e0
% 12.38/3.44 |
% 12.38/3.44 | Equations (556) can reduce 245 to:
% 12.38/3.44 | (202) $false
% 12.38/3.44 |
% 12.38/3.44 |-The branch is then unsatisfiable
% 12.38/3.44 |-Branch two:
% 12.38/3.44 | (230) all_0_10_10 = e3
% 12.38/3.44 | (358) ~ (all_0_13_13 = e1)
% 12.38/3.44 |
% 12.38/3.44 | Equations (230) can reduce 16 to:
% 12.38/3.44 | (212) ~ (all_0_9_9 = e3)
% 12.38/3.44 |
% 12.38/3.44 | Equations (230) can reduce 117 to:
% 12.38/3.44 | (561) ~ (all_0_22_22 = e3)
% 12.38/3.44 |
% 12.38/3.44 | Simplifying 561 yields:
% 12.38/3.44 | (360) ~ (all_0_22_22 = e3)
% 12.38/3.44 |
% 12.38/3.44 +-Applying beta-rule and splitting (113), into two cases.
% 12.38/3.44 |-Branch one:
% 12.38/3.44 | (311) all_0_13_13 = e3
% 12.38/3.44 |
% 12.38/3.44 | Equations (311) can reduce 219 to:
% 12.38/3.44 | (202) $false
% 12.38/3.44 |
% 12.38/3.44 |-The branch is then unsatisfiable
% 12.38/3.44 |-Branch two:
% 12.38/3.44 | (219) ~ (all_0_13_13 = e3)
% 12.38/3.44 | (314) all_0_13_13 = e1 | all_0_13_13 = e0
% 12.38/3.44 |
% 12.38/3.44 +-Applying beta-rule and splitting (80), into two cases.
% 12.38/3.44 |-Branch one:
% 12.38/3.44 | (225) ~ (all_0_10_10 = e3)
% 12.38/3.44 |
% 12.38/3.44 | Equations (230) can reduce 225 to:
% 12.38/3.44 | (202) $false
% 12.38/3.44 |
% 12.38/3.44 |-The branch is then unsatisfiable
% 12.38/3.44 |-Branch two:
% 12.38/3.44 | (230) all_0_10_10 = e3
% 12.38/3.44 | (570) ~ (all_0_23_23 = e1)
% 12.38/3.44 |
% 12.38/3.44 +-Applying beta-rule and splitting (88), into two cases.
% 12.38/3.44 |-Branch one:
% 12.38/3.44 | (301) all_0_23_23 = e3
% 12.38/3.44 |
% 12.38/3.44 | Equations (301) can reduce 223 to:
% 12.38/3.44 | (202) $false
% 12.38/3.44 |
% 12.38/3.44 |-The branch is then unsatisfiable
% 12.38/3.44 |-Branch two:
% 12.38/3.44 | (223) ~ (all_0_23_23 = e3)
% 12.38/3.44 | (304) all_0_23_23 = e2 | all_0_23_23 = e1
% 12.38/3.44 |
% 12.38/3.44 +-Applying beta-rule and splitting (304), into two cases.
% 12.38/3.44 |-Branch one:
% 12.38/3.44 | (305) all_0_23_23 = e2
% 12.38/3.44 |
% 12.38/3.44 | Equations (305) can reduce 173 to:
% 12.38/3.44 | (576) ~ (all_0_15_15 = e2)
% 12.38/3.44 |
% 12.38/3.44 | Equations (305) can reduce 192 to:
% 12.38/3.44 | (542) ~ (all_0_21_21 = e2)
% 12.38/3.44 |
% 12.38/3.44 | Equations (305) can reduce 191 to:
% 12.38/3.44 | (258) ~ (all_0_22_22 = e2)
% 12.38/3.44 |
% 12.38/3.44 | Equations (305) can reduce 9 to:
% 12.38/3.44 | (13) ~ (e2 = e0)
% 12.38/3.44 |
% 12.38/3.44 +-Applying beta-rule and splitting (87), into two cases.
% 12.38/3.44 |-Branch one:
% 12.38/3.44 | (344) all_0_22_22 = e3
% 12.38/3.44 |
% 12.38/3.44 | Equations (344) can reduce 360 to:
% 12.38/3.44 | (202) $false
% 12.38/3.44 |
% 12.38/3.44 |-The branch is then unsatisfiable
% 12.38/3.44 |-Branch two:
% 12.38/3.44 | (360) ~ (all_0_22_22 = e3)
% 12.38/3.44 | (361) all_0_22_22 = e2 | all_0_22_22 = e1 | all_0_22_22 = e0
% 12.38/3.44 |
% 12.38/3.44 +-Applying beta-rule and splitting (361), into two cases.
% 12.38/3.44 |-Branch one:
% 12.38/3.44 | (439) all_0_22_22 = e2
% 12.38/3.44 |
% 12.38/3.44 | Equations (439) can reduce 258 to:
% 12.38/3.44 | (202) $false
% 12.38/3.44 |
% 12.38/3.44 |-The branch is then unsatisfiable
% 12.38/3.44 |-Branch two:
% 12.38/3.44 | (258) ~ (all_0_22_22 = e2)
% 12.38/3.44 | (442) all_0_22_22 = e1 | all_0_22_22 = e0
% 12.38/3.44 |
% 12.38/3.44 +-Applying beta-rule and splitting (442), into two cases.
% 12.38/3.44 |-Branch one:
% 12.38/3.44 | (443) all_0_22_22 = e1
% 12.38/3.44 |
% 12.38/3.44 | Equations (443) can reduce 194 to:
% 12.38/3.44 | (181) ~ (e1 = e0)
% 12.38/3.44 |
% 12.38/3.44 +-Applying beta-rule and splitting (74), into two cases.
% 12.38/3.44 |-Branch one:
% 12.38/3.44 | (260) all_0_12_12 = e2
% 12.38/3.44 |
% 12.38/3.44 | Equations (260) can reduce 200 to:
% 12.38/3.44 | (202) $false
% 12.38/3.44 |
% 12.38/3.44 |-The branch is then unsatisfiable
% 12.38/3.44 |-Branch two:
% 12.38/3.44 | (200) ~ (all_0_12_12 = e2)
% 12.38/3.44 | (263) all_0_14_14 = e2 | all_0_15_15 = e2
% 12.38/3.44 |
% 12.38/3.44 +-Applying beta-rule and splitting (263), into two cases.
% 12.38/3.44 |-Branch one:
% 12.38/3.44 | (264) all_0_14_14 = e2
% 12.38/3.44 |
% 12.38/3.44 | Equations (264) can reduce 160 to:
% 12.38/3.44 | (200) ~ (all_0_12_12 = e2)
% 12.38/3.44 |
% 12.38/3.44 | Equations (264) can reduce 44 to:
% 12.38/3.44 | (596) ~ (all_0_15_15 = e2)
% 12.38/3.44 |
% 12.38/3.44 | Simplifying 596 yields:
% 12.38/3.44 | (576) ~ (all_0_15_15 = e2)
% 12.38/3.44 |
% 12.38/3.44 +-Applying beta-rule and splitting (70), into two cases.
% 12.38/3.44 |-Branch one:
% 12.38/3.44 | (598) all_0_10_10 = e0
% 12.38/3.44 |
% 12.38/3.44 | Combining equations (230,598) yields a new equation:
% 12.38/3.44 | (277) e3 = e0
% 12.38/3.44 |
% 12.38/3.44 | Simplifying 277 yields:
% 12.38/3.44 | (278) e3 = e0
% 12.38/3.44 |
% 12.38/3.44 | Equations (278) can reduce 136 to:
% 12.38/3.44 | (202) $false
% 12.38/3.44 |
% 12.38/3.44 |-The branch is then unsatisfiable
% 12.38/3.44 |-Branch two:
% 12.38/3.44 | (602) ~ (all_0_10_10 = e0)
% 12.38/3.44 | (603) all_0_14_14 = e0 | all_0_18_18 = e0 | all_0_22_22 = e0
% 12.38/3.44 |
% 12.38/3.44 +-Applying beta-rule and splitting (603), into two cases.
% 12.38/3.44 |-Branch one:
% 12.38/3.44 | (342) all_0_14_14 = e0
% 12.38/3.44 |
% 12.38/3.44 | Combining equations (264,342) yields a new equation:
% 12.38/3.44 | (283) e2 = e0
% 12.38/3.44 |
% 12.38/3.44 | Simplifying 283 yields:
% 12.38/3.44 | (284) e2 = e0
% 12.38/3.44 |
% 12.38/3.44 | Equations (284) can reduce 13 to:
% 12.38/3.44 | (202) $false
% 12.38/3.44 |
% 12.38/3.44 |-The branch is then unsatisfiable
% 12.38/3.44 |-Branch two:
% 12.38/3.44 | (550) ~ (all_0_14_14 = e0)
% 12.38/3.44 | (609) all_0_18_18 = e0 | all_0_22_22 = e0
% 12.38/3.44 |
% 12.38/3.44 +-Applying beta-rule and splitting (609), into two cases.
% 12.38/3.44 |-Branch one:
% 12.38/3.44 | (556) all_0_18_18 = e0
% 12.38/3.44 |
% 12.38/3.44 | Equations (556) can reduce 39 to:
% 12.38/3.45 | (611) ~ (all_0_16_16 = e0)
% 12.38/3.45 |
% 12.38/3.45 | Equations (556) can reduce 4 to:
% 12.38/3.45 | (612) ~ (all_0_19_19 = e0)
% 12.38/3.45 |
% 12.38/3.45 | Simplifying 612 yields:
% 12.38/3.45 | (613) ~ (all_0_19_19 = e0)
% 12.38/3.45 |
% 12.38/3.45 | From (556) and (164) follows:
% 12.38/3.45 | (614) op(e1, e0) = all_0_3_3
% 12.38/3.45 |
% 12.38/3.45 +-Applying beta-rule and splitting (144), into two cases.
% 12.38/3.45 |-Branch one:
% 12.38/3.45 | (362) all_0_9_9 = e2
% 12.38/3.45 |
% 12.38/3.45 | Equations (362) can reduce 198 to:
% 12.38/3.45 | (202) $false
% 12.38/3.45 |
% 12.38/3.45 |-The branch is then unsatisfiable
% 12.38/3.45 |-Branch two:
% 12.38/3.45 | (198) ~ (all_0_9_9 = e2)
% 12.38/3.45 | (365) all_0_17_17 = e2 | all_0_21_21 = e2
% 12.38/3.45 |
% 12.38/3.45 +-Applying beta-rule and splitting (22), into two cases.
% 12.38/3.45 |-Branch one:
% 12.38/3.45 | (245) ~ (all_0_18_18 = e0)
% 12.38/3.45 |
% 12.38/3.45 | Equations (556) can reduce 245 to:
% 12.38/3.45 | (202) $false
% 12.38/3.45 |
% 12.38/3.45 |-The branch is then unsatisfiable
% 12.38/3.45 |-Branch two:
% 12.38/3.45 | (556) all_0_18_18 = e0
% 12.38/3.45 | (622) ~ (all_0_19_19 = e1)
% 12.38/3.45 |
% 12.38/3.45 +-Applying beta-rule and splitting (314), into two cases.
% 12.38/3.45 |-Branch one:
% 12.38/3.45 | (315) all_0_13_13 = e1
% 12.38/3.45 |
% 12.38/3.45 | Equations (315) can reduce 358 to:
% 12.38/3.45 | (202) $false
% 12.38/3.45 |
% 12.38/3.45 |-The branch is then unsatisfiable
% 12.38/3.45 |-Branch two:
% 12.38/3.45 | (358) ~ (all_0_13_13 = e1)
% 12.38/3.45 | (449) all_0_13_13 = e0
% 12.38/3.45 |
% 12.38/3.45 | Equations (449) can reduce 32 to:
% 12.38/3.45 | (214) ~ (all_0_12_12 = e0)
% 12.38/3.45 |
% 12.38/3.45 | Equations (449) can reduce 98 to:
% 12.38/3.45 | (628) ~ (all_0_15_15 = e0)
% 12.38/3.45 |
% 12.38/3.45 | Simplifying 628 yields:
% 12.38/3.45 | (286) ~ (all_0_15_15 = e0)
% 12.38/3.45 |
% 12.38/3.45 | From (449) and (8) follows:
% 12.38/3.45 | (630) op(all_0_5_5, e0) = all_0_4_4
% 12.38/3.45 |
% 12.38/3.45 | From (449) and (102) follows:
% 12.38/3.45 | (631) op(e2, e0) = all_0_5_5
% 12.38/3.45 |
% 12.38/3.45 +-Applying beta-rule and splitting (147), into two cases.
% 12.38/3.45 |-Branch one:
% 12.38/3.45 | (276) all_0_11_11 = e0
% 12.38/3.45 |
% 12.38/3.45 | Equations (276) can reduce 145 to:
% 12.38/3.45 | (494) ~ (all_0_9_9 = e0)
% 12.38/3.45 |
% 12.38/3.45 | Equations (276) can reduce 50 to:
% 12.38/3.45 | (628) ~ (all_0_15_15 = e0)
% 12.38/3.45 |
% 12.38/3.45 | Simplifying 628 yields:
% 12.38/3.45 | (286) ~ (all_0_15_15 = e0)
% 12.38/3.45 |
% 12.38/3.45 | Equations (276) can reduce 171 to:
% 12.38/3.45 | (612) ~ (all_0_19_19 = e0)
% 12.38/3.45 |
% 12.38/3.45 | Simplifying 612 yields:
% 12.38/3.45 | (613) ~ (all_0_19_19 = e0)
% 12.38/3.45 |
% 12.38/3.45 +-Applying beta-rule and splitting (365), into two cases.
% 12.38/3.45 |-Branch one:
% 12.38/3.45 | (371) all_0_17_17 = e2
% 12.38/3.45 |
% 12.38/3.45 | Equations (371) can reduce 109 to:
% 12.38/3.45 | (198) ~ (all_0_9_9 = e2)
% 12.38/3.45 |
% 12.38/3.45 | Equations (371) can reduce 58 to:
% 12.38/3.45 | (256) ~ (all_0_16_16 = e2)
% 12.38/3.45 |
% 12.38/3.45 | Equations (371) can reduce 120 to:
% 12.38/3.45 | (270) ~ (all_0_19_19 = e2)
% 12.38/3.45 |
% 12.38/3.45 | Simplifying 270 yields:
% 12.38/3.45 | (271) ~ (all_0_19_19 = e2)
% 12.38/3.45 |
% 12.38/3.45 +-Applying beta-rule and splitting (142), into two cases.
% 12.38/3.45 |-Branch one:
% 12.38/3.45 | (226) all_0_9_9 = e3
% 12.38/3.45 |
% 12.38/3.45 | Equations (226) can reduce 212 to:
% 12.38/3.45 | (202) $false
% 12.38/3.45 |
% 12.38/3.45 |-The branch is then unsatisfiable
% 12.38/3.45 |-Branch two:
% 12.38/3.45 | (212) ~ (all_0_9_9 = e3)
% 12.38/3.45 | (387) all_0_9_9 = e2 | all_0_9_9 = e1 | all_0_9_9 = e0
% 12.38/3.45 |
% 12.38/3.45 +-Applying beta-rule and splitting (387), into two cases.
% 12.38/3.45 |-Branch one:
% 12.38/3.45 | (362) all_0_9_9 = e2
% 12.38/3.45 |
% 12.38/3.45 | Equations (362) can reduce 198 to:
% 12.38/3.45 | (202) $false
% 12.38/3.45 |
% 12.38/3.45 |-The branch is then unsatisfiable
% 12.38/3.45 |-Branch two:
% 12.38/3.45 | (198) ~ (all_0_9_9 = e2)
% 12.38/3.45 | (391) all_0_9_9 = e1 | all_0_9_9 = e0
% 12.38/3.45 |
% 12.38/3.45 +-Applying beta-rule and splitting (391), into two cases.
% 12.38/3.45 |-Branch one:
% 12.38/3.45 | (380) all_0_9_9 = e1
% 12.38/3.45 |
% 12.38/3.45 | Equations (380) can reduce 198 to:
% 12.38/3.45 | (329) ~ (e2 = e1)
% 12.38/3.45 |
% 12.38/3.45 | Simplifying 329 yields:
% 12.38/3.45 | (71) ~ (e2 = e1)
% 12.38/3.45 |
% 12.38/3.45 | Equations (380) can reduce 494 to:
% 12.38/3.45 | (181) ~ (e1 = e0)
% 12.38/3.45 |
% 12.38/3.45 +-Applying beta-rule and splitting (138), into two cases.
% 12.38/3.45 |-Branch one:
% 12.38/3.45 | (328) all_0_16_16 = e1
% 12.38/3.45 |
% 12.38/3.45 | Equations (328) can reduce 76 to:
% 12.38/3.45 | (317) ~ (all_0_12_12 = e1)
% 12.38/3.45 |
% 12.38/3.45 | Equations (328) can reduce 175 to:
% 12.38/3.45 | (657) ~ (all_0_19_19 = e1)
% 12.38/3.45 |
% 12.38/3.45 | Simplifying 657 yields:
% 12.38/3.45 | (622) ~ (all_0_19_19 = e1)
% 12.38/3.45 |
% 12.38/3.45 | Equations (328) can reduce 256 to:
% 12.38/3.45 | (329) ~ (e2 = e1)
% 12.38/3.45 |
% 12.38/3.45 | Simplifying 329 yields:
% 12.38/3.45 | (71) ~ (e2 = e1)
% 12.38/3.45 |
% 12.38/3.45 | Equations (328) can reduce 611 to:
% 12.38/3.45 | (181) ~ (e1 = e0)
% 12.38/3.45 |
% 12.38/3.45 +-Applying beta-rule and splitting (30), into two cases.
% 12.38/3.45 |-Branch one:
% 12.38/3.45 | (323) all_0_12_12 = e3
% 12.38/3.45 |
% 12.38/3.45 | Equations (323) can reduce 75 to:
% 12.38/3.45 | (236) ~ (all_0_15_15 = e3)
% 12.38/3.45 |
% 12.38/3.45 | Simplifying 236 yields:
% 12.38/3.45 | (237) ~ (all_0_15_15 = e3)
% 12.38/3.45 |
% 12.38/3.45 +-Applying beta-rule and splitting (126), into two cases.
% 12.38/3.45 |-Branch one:
% 12.38/3.45 | (665) all_0_15_15 = e3
% 12.38/3.45 |
% 12.38/3.45 | Equations (665) can reduce 237 to:
% 12.38/3.45 | (202) $false
% 12.38/3.45 |
% 12.38/3.45 |-The branch is then unsatisfiable
% 12.38/3.45 |-Branch two:
% 12.38/3.45 | (237) ~ (all_0_15_15 = e3)
% 12.38/3.45 | (668) all_0_15_15 = e2 | all_0_15_15 = e1 | all_0_15_15 = e0
% 12.38/3.45 |
% 12.38/3.45 +-Applying beta-rule and splitting (170), into two cases.
% 12.38/3.45 |-Branch one:
% 12.38/3.45 | (481) all_0_19_19 = e3
% 12.38/3.45 |
% 12.38/3.45 | Equations (481) can reduce 622 to:
% 12.38/3.45 | (137) ~ (e3 = e1)
% 12.38/3.45 |
% 12.38/3.45 | From (481) and (41) follows:
% 12.38/3.45 | (671) op(e1, e0) = e3
% 12.38/3.45 |
% 12.38/3.45 +-Applying beta-rule and splitting (11), into two cases.
% 12.38/3.45 |-Branch one:
% 12.38/3.45 | (672) all_0_11_11 = e1
% 12.38/3.45 |
% 12.38/3.45 | Combining equations (276,672) yields a new equation:
% 12.38/3.45 | (421) e1 = e0
% 12.38/3.45 |
% 12.38/3.45 | Equations (421) can reduce 181 to:
% 12.38/3.45 | (202) $false
% 12.38/3.45 |
% 12.38/3.45 |-The branch is then unsatisfiable
% 12.38/3.45 |-Branch two:
% 12.38/3.45 | (675) ~ (all_0_11_11 = e1)
% 12.38/3.45 | (676) all_0_15_15 = e1 | all_0_19_19 = e1 | all_0_23_23 = e1
% 12.38/3.45 |
% 12.38/3.45 +-Applying beta-rule and splitting (676), into two cases.
% 12.38/3.45 |-Branch one:
% 12.38/3.45 | (677) all_0_15_15 = e1
% 12.38/3.45 |
% 12.38/3.45 | From (677) and (103) follows:
% 12.38/3.45 | (678) op(e2, e0) = e1
% 12.38/3.45 |
% 12.38/3.45 | Instantiating formula (53) with e2, e0, e1, all_0_5_5 and discharging atoms op(e2, e0) = all_0_5_5, op(e2, e0) = e1, yields:
% 12.38/3.45 | (679) all_0_5_5 = e1
% 12.38/3.45 |
% 12.38/3.46 | Instantiating formula (53) with e1, e0, e3, all_0_3_3 and discharging atoms op(e1, e0) = all_0_3_3, op(e1, e0) = e3, yields:
% 12.38/3.46 | (680) all_0_3_3 = e3
% 12.38/3.46 |
% 12.38/3.46 | From (679) and (630) follows:
% 12.38/3.46 | (681) op(e1, e0) = all_0_4_4
% 12.38/3.46 |
% 12.38/3.46 | From (680) and (614) follows:
% 12.38/3.46 | (671) op(e1, e0) = e3
% 12.38/3.46 |
% 12.38/3.46 +-Applying beta-rule and splitting (189), into two cases.
% 12.38/3.46 |-Branch one:
% 12.38/3.46 | (350) ~ (all_0_4_4 = e3)
% 12.38/3.46 |
% 12.38/3.46 | Instantiating formula (53) with e1, e0, all_0_4_4, e3 and discharging atoms op(e1, e0) = all_0_4_4, op(e1, e0) = e3, yields:
% 12.38/3.46 | (351) all_0_4_4 = e3
% 12.38/3.46 |
% 12.38/3.46 | Equations (351) can reduce 350 to:
% 12.38/3.46 | (202) $false
% 12.38/3.46 |
% 12.38/3.46 |-The branch is then unsatisfiable
% 12.38/3.46 |-Branch two:
% 12.38/3.46 | (351) all_0_4_4 = e3
% 12.38/3.46 | (687) ~ (all_0_5_5 = e1) | ~ (all_0_13_13 = e0)
% 12.38/3.46 |
% 12.38/3.46 +-Applying beta-rule and splitting (687), into two cases.
% 12.38/3.46 |-Branch one:
% 12.38/3.46 | (688) ~ (all_0_5_5 = e1)
% 12.38/3.46 |
% 12.38/3.46 | Equations (679) can reduce 688 to:
% 12.38/3.46 | (202) $false
% 12.38/3.46 |
% 12.38/3.46 |-The branch is then unsatisfiable
% 12.38/3.46 |-Branch two:
% 12.38/3.46 | (679) all_0_5_5 = e1
% 12.38/3.46 | (249) ~ (all_0_13_13 = e0)
% 12.38/3.46 |
% 12.38/3.46 | Equations (449) can reduce 249 to:
% 12.38/3.46 | (202) $false
% 12.38/3.46 |
% 12.38/3.46 |-The branch is then unsatisfiable
% 12.38/3.46 |-Branch two:
% 12.38/3.46 | (693) ~ (all_0_15_15 = e1)
% 12.38/3.46 | (694) all_0_19_19 = e1 | all_0_23_23 = e1
% 12.38/3.46 |
% 12.38/3.46 +-Applying beta-rule and splitting (694), into two cases.
% 12.38/3.46 |-Branch one:
% 12.38/3.46 | (420) all_0_19_19 = e1
% 12.38/3.46 |
% 12.38/3.46 | Combining equations (481,420) yields a new equation:
% 12.38/3.46 | (416) e3 = e1
% 12.38/3.46 |
% 12.38/3.46 | Simplifying 416 yields:
% 12.38/3.46 | (417) e3 = e1
% 12.38/3.46 |
% 12.38/3.46 | Equations (417) can reduce 137 to:
% 12.38/3.46 | (202) $false
% 12.38/3.46 |
% 12.38/3.46 |-The branch is then unsatisfiable
% 12.38/3.46 |-Branch two:
% 12.38/3.46 | (622) ~ (all_0_19_19 = e1)
% 12.38/3.46 | (308) all_0_23_23 = e1
% 12.38/3.46 |
% 12.38/3.46 | Combining equations (308,305) yields a new equation:
% 12.38/3.46 | (367) e2 = e1
% 12.38/3.46 |
% 12.38/3.46 | Equations (367) can reduce 71 to:
% 12.38/3.46 | (202) $false
% 12.38/3.46 |
% 12.38/3.46 |-The branch is then unsatisfiable
% 12.38/3.46 |-Branch two:
% 12.38/3.46 | (239) ~ (all_0_19_19 = e3)
% 12.38/3.46 | (704) all_0_19_19 = e2 | all_0_19_19 = e1 | all_0_19_19 = e0
% 12.38/3.46 |
% 12.38/3.46 +-Applying beta-rule and splitting (668), into two cases.
% 12.38/3.46 |-Branch one:
% 12.38/3.46 | (267) all_0_15_15 = e2
% 12.38/3.46 |
% 12.38/3.46 | Equations (267) can reduce 576 to:
% 12.38/3.46 | (202) $false
% 12.38/3.46 |
% 12.38/3.46 |-The branch is then unsatisfiable
% 12.38/3.46 |-Branch two:
% 12.38/3.46 | (576) ~ (all_0_15_15 = e2)
% 12.38/3.46 | (708) all_0_15_15 = e1 | all_0_15_15 = e0
% 12.38/3.46 |
% 12.38/3.46 +-Applying beta-rule and splitting (704), into two cases.
% 12.38/3.46 |-Branch one:
% 12.38/3.46 | (709) all_0_19_19 = e2
% 12.38/3.46 |
% 12.38/3.46 | Equations (709) can reduce 271 to:
% 12.38/3.46 | (202) $false
% 12.38/3.46 |
% 12.38/3.46 |-The branch is then unsatisfiable
% 12.38/3.46 |-Branch two:
% 12.38/3.46 | (271) ~ (all_0_19_19 = e2)
% 12.38/3.46 | (712) all_0_19_19 = e1 | all_0_19_19 = e0
% 12.38/3.46 |
% 12.38/3.46 +-Applying beta-rule and splitting (708), into two cases.
% 12.38/3.46 |-Branch one:
% 12.38/3.46 | (677) all_0_15_15 = e1
% 12.38/3.46 |
% 12.38/3.46 | Equations (677) can reduce 188 to:
% 12.38/3.46 | (657) ~ (all_0_19_19 = e1)
% 12.38/3.46 |
% 12.38/3.46 | Simplifying 657 yields:
% 12.38/3.46 | (622) ~ (all_0_19_19 = e1)
% 12.38/3.46 |
% 12.38/3.46 +-Applying beta-rule and splitting (712), into two cases.
% 12.38/3.46 |-Branch one:
% 12.38/3.46 | (420) all_0_19_19 = e1
% 12.38/3.46 |
% 12.38/3.46 | Equations (420) can reduce 622 to:
% 12.38/3.46 | (202) $false
% 12.38/3.46 |
% 12.38/3.46 |-The branch is then unsatisfiable
% 12.38/3.46 |-Branch two:
% 12.38/3.46 | (622) ~ (all_0_19_19 = e1)
% 12.38/3.46 | (287) all_0_19_19 = e0
% 12.38/3.46 |
% 12.38/3.46 | Equations (287) can reduce 613 to:
% 12.38/3.46 | (202) $false
% 12.38/3.46 |
% 12.38/3.46 |-The branch is then unsatisfiable
% 12.38/3.46 |-Branch two:
% 12.38/3.46 | (693) ~ (all_0_15_15 = e1)
% 12.38/3.46 | (282) all_0_15_15 = e0
% 12.38/3.46 |
% 12.38/3.46 | Equations (282) can reduce 286 to:
% 12.38/3.46 | (202) $false
% 12.38/3.46 |
% 12.38/3.46 |-The branch is then unsatisfiable
% 12.38/3.46 |-Branch two:
% 12.38/3.46 | (423) ~ (all_0_12_12 = e3)
% 12.38/3.46 | (725) all_0_12_12 = e2 | all_0_12_12 = e1 | all_0_12_12 = e0
% 12.38/3.46 |
% 12.38/3.46 +-Applying beta-rule and splitting (725), into two cases.
% 12.38/3.46 |-Branch one:
% 12.38/3.46 | (260) all_0_12_12 = e2
% 12.38/3.46 |
% 12.38/3.46 | Equations (260) can reduce 200 to:
% 12.38/3.46 | (202) $false
% 12.38/3.46 |
% 12.38/3.46 |-The branch is then unsatisfiable
% 12.38/3.46 |-Branch two:
% 12.38/3.46 | (200) ~ (all_0_12_12 = e2)
% 12.38/3.46 | (729) all_0_12_12 = e1 | all_0_12_12 = e0
% 12.38/3.46 |
% 12.38/3.46 +-Applying beta-rule and splitting (729), into two cases.
% 12.38/3.46 |-Branch one:
% 12.38/3.46 | (730) all_0_12_12 = e1
% 12.38/3.46 |
% 12.38/3.46 | Equations (730) can reduce 317 to:
% 12.38/3.46 | (202) $false
% 12.38/3.46 |
% 12.38/3.46 |-The branch is then unsatisfiable
% 12.38/3.46 |-Branch two:
% 12.38/3.46 | (317) ~ (all_0_12_12 = e1)
% 12.38/3.46 | (500) all_0_12_12 = e0
% 12.38/3.46 |
% 12.38/3.46 | Equations (500) can reduce 214 to:
% 12.38/3.46 | (202) $false
% 12.38/3.46 |
% 12.38/3.46 |-The branch is then unsatisfiable
% 12.38/3.46 |-Branch two:
% 12.38/3.46 | (413) ~ (all_0_16_16 = e1)
% 12.38/3.46 | (414) all_0_17_17 = e1 | all_0_19_19 = e1
% 12.38/3.46 |
% 12.38/3.46 +-Applying beta-rule and splitting (7), into two cases.
% 12.38/3.46 |-Branch one:
% 12.38/3.46 | (427) all_0_16_16 = e3
% 12.38/3.46 |
% 12.38/3.46 | Equations (427) can reduce 175 to:
% 12.38/3.46 | (238) ~ (all_0_19_19 = e3)
% 12.38/3.46 |
% 12.38/3.46 | Simplifying 238 yields:
% 12.38/3.46 | (239) ~ (all_0_19_19 = e3)
% 12.38/3.46 |
% 12.38/3.46 | Equations (427) can reduce 256 to:
% 12.38/3.46 | (101) ~ (e3 = e2)
% 12.38/3.46 |
% 12.38/3.46 | Equations (427) can reduce 413 to:
% 12.38/3.46 | (137) ~ (e3 = e1)
% 12.38/3.46 |
% 12.38/3.46 | Equations (427) can reduce 611 to:
% 12.38/3.46 | (136) ~ (e3 = e0)
% 12.38/3.46 |
% 12.38/3.46 +-Applying beta-rule and splitting (165), into two cases.
% 12.38/3.46 |-Branch one:
% 12.38/3.46 | (233) all_0_11_11 = e3
% 12.38/3.46 |
% 12.38/3.46 | Combining equations (233,276) yields a new equation:
% 12.38/3.46 | (277) e3 = e0
% 12.38/3.46 |
% 12.38/3.46 | Simplifying 277 yields:
% 12.38/3.46 | (278) e3 = e0
% 12.38/3.46 |
% 12.38/3.46 | Equations (278) can reduce 136 to:
% 12.38/3.46 | (202) $false
% 12.38/3.46 |
% 12.38/3.46 |-The branch is then unsatisfiable
% 12.38/3.46 |-Branch two:
% 12.38/3.46 | (242) ~ (all_0_11_11 = e3)
% 12.38/3.46 | (748) all_0_15_15 = e3 | all_0_19_19 = e3 | all_0_23_23 = e3
% 12.38/3.46 |
% 12.38/3.46 +-Applying beta-rule and splitting (748), into two cases.
% 12.38/3.46 |-Branch one:
% 12.38/3.46 | (665) all_0_15_15 = e3
% 12.38/3.46 |
% 12.38/3.46 +-Applying beta-rule and splitting (77), into two cases.
% 12.38/3.46 |-Branch one:
% 12.38/3.46 | (730) all_0_12_12 = e1
% 12.38/3.46 |
% 12.38/3.46 | Equations (730) can reduce 200 to:
% 12.38/3.46 | (329) ~ (e2 = e1)
% 12.38/3.46 |
% 12.38/3.46 | Simplifying 329 yields:
% 12.38/3.46 | (71) ~ (e2 = e1)
% 12.38/3.46 |
% 12.38/3.46 +-Applying beta-rule and splitting (414), into two cases.
% 12.38/3.46 |-Branch one:
% 12.38/3.46 | (415) all_0_17_17 = e1
% 12.38/3.46 |
% 12.38/3.46 | Combining equations (415,371) yields a new equation:
% 12.38/3.46 | (367) e2 = e1
% 12.38/3.46 |
% 12.38/3.46 | Equations (367) can reduce 71 to:
% 12.38/3.46 | (202) $false
% 12.38/3.46 |
% 12.38/3.46 |-The branch is then unsatisfiable
% 12.38/3.46 |-Branch two:
% 12.38/3.46 | (208) ~ (all_0_17_17 = e1)
% 12.38/3.46 | (420) all_0_19_19 = e1
% 12.38/3.46 |
% 12.38/3.46 | Equations (420) can reduce 622 to:
% 12.38/3.46 | (202) $false
% 12.38/3.46 |
% 12.38/3.46 |-The branch is then unsatisfiable
% 12.38/3.46 |-Branch two:
% 12.38/3.46 | (317) ~ (all_0_12_12 = e1)
% 12.38/3.46 | (760) all_0_13_13 = e1 | all_0_14_14 = e1 | all_0_15_15 = e1
% 12.38/3.46 |
% 12.38/3.46 +-Applying beta-rule and splitting (760), into two cases.
% 12.38/3.46 |-Branch one:
% 12.38/3.46 | (315) all_0_13_13 = e1
% 12.38/3.46 |
% 12.38/3.46 | Combining equations (449,315) yields a new equation:
% 12.38/3.46 | (421) e1 = e0
% 12.38/3.46 |
% 12.38/3.46 | Equations (421) can reduce 181 to:
% 12.38/3.46 | (202) $false
% 12.38/3.46 |
% 12.38/3.46 |-The branch is then unsatisfiable
% 12.38/3.46 |-Branch two:
% 12.38/3.46 | (358) ~ (all_0_13_13 = e1)
% 12.38/3.46 | (765) all_0_14_14 = e1 | all_0_15_15 = e1
% 12.38/3.46 |
% 12.38/3.46 +-Applying beta-rule and splitting (765), into two cases.
% 12.38/3.46 |-Branch one:
% 12.38/3.46 | (339) all_0_14_14 = e1
% 12.38/3.46 |
% 12.38/3.47 | Combining equations (264,339) yields a new equation:
% 12.38/3.47 | (767) e2 = e1
% 12.38/3.47 |
% 12.38/3.47 | Simplifying 767 yields:
% 12.38/3.47 | (367) e2 = e1
% 12.38/3.47 |
% 12.38/3.47 | Equations (367) can reduce 71 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (319) ~ (all_0_14_14 = e1)
% 12.38/3.47 | (677) all_0_15_15 = e1
% 12.38/3.47 |
% 12.38/3.47 | Combining equations (665,677) yields a new equation:
% 12.38/3.47 | (416) e3 = e1
% 12.38/3.47 |
% 12.38/3.47 | Simplifying 416 yields:
% 12.38/3.47 | (417) e3 = e1
% 12.38/3.47 |
% 12.38/3.47 | Equations (417) can reduce 137 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (237) ~ (all_0_15_15 = e3)
% 12.38/3.47 | (776) all_0_19_19 = e3 | all_0_23_23 = e3
% 12.38/3.47 |
% 12.38/3.47 +-Applying beta-rule and splitting (776), into two cases.
% 12.38/3.47 |-Branch one:
% 12.38/3.47 | (481) all_0_19_19 = e3
% 12.38/3.47 |
% 12.38/3.47 | Equations (481) can reduce 239 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (239) ~ (all_0_19_19 = e3)
% 12.38/3.47 | (301) all_0_23_23 = e3
% 12.38/3.47 |
% 12.38/3.47 | Combining equations (305,301) yields a new equation:
% 12.38/3.47 | (373) e3 = e2
% 12.38/3.47 |
% 12.38/3.47 | Equations (373) can reduce 101 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (298) ~ (all_0_16_16 = e3)
% 12.38/3.47 | (430) all_0_16_16 = e2 | all_0_16_16 = e1 | all_0_16_16 = e0
% 12.38/3.47 |
% 12.38/3.47 +-Applying beta-rule and splitting (430), into two cases.
% 12.38/3.47 |-Branch one:
% 12.38/3.47 | (785) all_0_16_16 = e2
% 12.38/3.47 |
% 12.38/3.47 | Equations (785) can reduce 256 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (256) ~ (all_0_16_16 = e2)
% 12.38/3.47 | (788) all_0_16_16 = e1 | all_0_16_16 = e0
% 12.38/3.47 |
% 12.38/3.47 +-Applying beta-rule and splitting (788), into two cases.
% 12.38/3.47 |-Branch one:
% 12.38/3.47 | (328) all_0_16_16 = e1
% 12.38/3.47 |
% 12.38/3.47 | Equations (328) can reduce 413 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (413) ~ (all_0_16_16 = e1)
% 12.38/3.47 | (792) all_0_16_16 = e0
% 12.38/3.47 |
% 12.38/3.47 | Equations (792) can reduce 611 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (316) ~ (all_0_9_9 = e1)
% 12.38/3.47 | (395) all_0_9_9 = e0
% 12.38/3.47 |
% 12.38/3.47 | Equations (395) can reduce 494 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (375) ~ (all_0_17_17 = e2)
% 12.38/3.47 | (376) all_0_21_21 = e2
% 12.38/3.47 |
% 12.38/3.47 | Equations (376) can reduce 542 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (280) ~ (all_0_11_11 = e0)
% 12.38/3.47 | (281) all_0_15_15 = e0 | all_0_19_19 = e0
% 12.38/3.47 |
% 12.38/3.47 +-Applying beta-rule and splitting (281), into two cases.
% 12.38/3.47 |-Branch one:
% 12.38/3.47 | (282) all_0_15_15 = e0
% 12.38/3.47 |
% 12.38/3.47 | Equations (282) can reduce 286 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (286) ~ (all_0_15_15 = e0)
% 12.38/3.47 | (287) all_0_19_19 = e0
% 12.38/3.47 |
% 12.38/3.47 | Equations (287) can reduce 613 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (245) ~ (all_0_18_18 = e0)
% 12.38/3.47 | (446) all_0_22_22 = e0
% 12.38/3.47 |
% 12.38/3.47 | Combining equations (443,446) yields a new equation:
% 12.38/3.47 | (491) e1 = e0
% 12.38/3.47 |
% 12.38/3.47 | Simplifying 491 yields:
% 12.38/3.47 | (421) e1 = e0
% 12.38/3.47 |
% 12.38/3.47 | Equations (421) can reduce 181 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (255) ~ (all_0_14_14 = e2)
% 12.38/3.47 | (267) all_0_15_15 = e2
% 12.38/3.47 |
% 12.38/3.47 | Equations (267) can reduce 576 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (309) ~ (all_0_22_22 = e1)
% 12.38/3.47 | (446) all_0_22_22 = e0
% 12.38/3.47 |
% 12.38/3.47 | Equations (446) can reduce 194 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (273) ~ (all_0_23_23 = e2)
% 12.38/3.47 | (308) all_0_23_23 = e1
% 12.38/3.47 |
% 12.38/3.47 | Equations (308) can reduce 570 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (250) all_0_18_18 = e3
% 12.38/3.47 | (220) ~ (all_0_20_20 = e0)
% 12.38/3.47 |
% 12.38/3.47 | Equations (213) can reduce 220 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (311) all_0_13_13 = e3
% 12.38/3.47 | (220) ~ (all_0_20_20 = e0)
% 12.38/3.47 |
% 12.38/3.47 | Equations (213) can reduce 220 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (220) ~ (all_0_20_20 = e0)
% 12.38/3.47 | (828) all_0_21_21 = e0 | all_0_22_22 = e0
% 12.38/3.47 |
% 12.38/3.47 +-Applying beta-rule and splitting (828), into two cases.
% 12.38/3.47 |-Branch one:
% 12.38/3.47 | (829) all_0_21_21 = e0
% 12.38/3.47 |
% 12.38/3.47 | Equations (829) can reduce 204 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (204) ~ (all_0_21_21 = e0)
% 12.38/3.47 | (446) all_0_22_22 = e0
% 12.38/3.47 |
% 12.38/3.47 | Equations (446) can reduce 194 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (201) ~ (all_0_8_8 = e2)
% 12.38/3.47 | (835) all_0_8_8 = e1 | all_0_8_8 = e0
% 12.38/3.47 |
% 12.38/3.47 +-Applying beta-rule and splitting (835), into two cases.
% 12.38/3.47 |-Branch one:
% 12.38/3.47 | (366) all_0_8_8 = e1
% 12.38/3.47 |
% 12.38/3.47 | Equations (366) can reduce 193 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (193) ~ (all_0_8_8 = e1)
% 12.38/3.47 | (839) all_0_8_8 = e0
% 12.38/3.47 |
% 12.38/3.47 | Equations (839) can reduce 195 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (839) all_0_8_8 = e0
% 12.38/3.47 | (622) ~ (all_0_19_19 = e1)
% 12.38/3.47 |
% 12.38/3.47 | Equations (839) can reduce 24 to:
% 12.38/3.47 | (843) ~ (all_0_11_11 = e0)
% 12.38/3.47 |
% 12.38/3.47 | Simplifying 843 yields:
% 12.38/3.47 | (280) ~ (all_0_11_11 = e0)
% 12.38/3.47 |
% 12.38/3.47 | Equations (839) can reduce 2 to:
% 12.38/3.47 | (845) ~ (all_0_12_12 = e0)
% 12.38/3.47 |
% 12.38/3.47 | Simplifying 845 yields:
% 12.38/3.47 | (214) ~ (all_0_12_12 = e0)
% 12.38/3.47 |
% 12.38/3.47 | Equations (839) can reduce 122 to:
% 12.38/3.47 | (847) ~ (all_0_20_20 = e0)
% 12.38/3.47 |
% 12.38/3.47 | Simplifying 847 yields:
% 12.38/3.47 | (220) ~ (all_0_20_20 = e0)
% 12.38/3.47 |
% 12.38/3.47 | From (839) and (12) follows:
% 12.38/3.47 | (849) op(all_0_7_7, e0) = all_0_6_6
% 12.38/3.47 |
% 12.38/3.47 | From (839) and (157) follows:
% 12.38/3.47 | (850) op(e3, e0) = all_0_7_7
% 12.38/3.47 |
% 12.38/3.47 +-Applying beta-rule and splitting (163), into two cases.
% 12.38/3.47 |-Branch one:
% 12.38/3.47 | (195) ~ (all_0_8_8 = e0)
% 12.38/3.47 |
% 12.38/3.47 | Equations (839) can reduce 195 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (839) all_0_8_8 = e0
% 12.38/3.47 | (242) ~ (all_0_11_11 = e3)
% 12.38/3.47 |
% 12.38/3.47 +-Applying beta-rule and splitting (108), into two cases.
% 12.38/3.47 |-Branch one:
% 12.38/3.47 | (195) ~ (all_0_8_8 = e0)
% 12.38/3.47 |
% 12.38/3.47 | Equations (839) can reduce 195 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (839) all_0_8_8 = e0
% 12.38/3.47 | (576) ~ (all_0_15_15 = e2)
% 12.38/3.47 |
% 12.38/3.47 +-Applying beta-rule and splitting (112), into two cases.
% 12.38/3.47 |-Branch one:
% 12.38/3.47 | (213) all_0_20_20 = e0
% 12.38/3.47 |
% 12.38/3.47 | Equations (213) can reduce 220 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (220) ~ (all_0_20_20 = e0)
% 12.38/3.47 | (828) all_0_21_21 = e0 | all_0_22_22 = e0
% 12.38/3.47 |
% 12.38/3.47 +-Applying beta-rule and splitting (828), into two cases.
% 12.38/3.47 |-Branch one:
% 12.38/3.47 | (829) all_0_21_21 = e0
% 12.38/3.47 |
% 12.38/3.47 | Equations (829) can reduce 118 to:
% 12.38/3.47 | (494) ~ (all_0_9_9 = e0)
% 12.38/3.47 |
% 12.38/3.47 | Equations (829) can reduce 96 to:
% 12.38/3.47 | (249) ~ (all_0_13_13 = e0)
% 12.38/3.47 |
% 12.38/3.47 | Equations (829) can reduce 64 to:
% 12.38/3.47 | (288) ~ (all_0_17_17 = e0)
% 12.38/3.47 |
% 12.38/3.47 | Equations (829) can reduce 61 to:
% 12.38/3.47 | (220) ~ (all_0_20_20 = e0)
% 12.38/3.47 |
% 12.38/3.47 | Equations (829) can reduce 192 to:
% 12.38/3.47 | (217) ~ (all_0_23_23 = e0)
% 12.38/3.47 |
% 12.38/3.47 | Simplifying 217 yields:
% 12.38/3.47 | (9) ~ (all_0_23_23 = e0)
% 12.38/3.47 |
% 12.38/3.47 +-Applying beta-rule and splitting (190), into two cases.
% 12.38/3.47 |-Branch one:
% 12.38/3.47 | (204) ~ (all_0_21_21 = e0)
% 12.38/3.47 |
% 12.38/3.47 | Equations (829) can reduce 204 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (829) all_0_21_21 = e0
% 12.38/3.47 | (273) ~ (all_0_23_23 = e2)
% 12.38/3.47 |
% 12.38/3.47 | Instantiating formula (53) with e3, e0, all_0_7_7, all_0_11_11 and discharging atoms op(e3, e0) = all_0_7_7, op(e3, e0) = all_0_11_11, yields:
% 12.38/3.47 | (874) all_0_7_7 = all_0_11_11
% 12.38/3.47 |
% 12.38/3.47 | From (874) and (849) follows:
% 12.38/3.47 | (875) op(all_0_11_11, e0) = all_0_6_6
% 12.38/3.47 |
% 12.38/3.47 | From (874) and (850) follows:
% 12.38/3.47 | (106) op(e3, e0) = all_0_11_11
% 12.38/3.47 |
% 12.38/3.47 +-Applying beta-rule and splitting (55), into two cases.
% 12.38/3.47 |-Branch one:
% 12.38/3.47 | (219) ~ (all_0_13_13 = e3)
% 12.38/3.47 |
% 12.38/3.47 +-Applying beta-rule and splitting (113), into two cases.
% 12.38/3.47 |-Branch one:
% 12.38/3.47 | (311) all_0_13_13 = e3
% 12.38/3.47 |
% 12.38/3.47 | Equations (311) can reduce 219 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (219) ~ (all_0_13_13 = e3)
% 12.38/3.47 | (314) all_0_13_13 = e1 | all_0_13_13 = e0
% 12.38/3.47 |
% 12.38/3.47 +-Applying beta-rule and splitting (314), into two cases.
% 12.38/3.47 |-Branch one:
% 12.38/3.47 | (315) all_0_13_13 = e1
% 12.38/3.47 |
% 12.38/3.47 | Equations (315) can reduce 31 to:
% 12.38/3.47 | (316) ~ (all_0_9_9 = e1)
% 12.38/3.47 |
% 12.38/3.47 | Equations (315) can reduce 6 to:
% 12.38/3.47 | (884) ~ (all_0_17_17 = e1)
% 12.38/3.47 |
% 12.38/3.47 | Simplifying 884 yields:
% 12.38/3.47 | (208) ~ (all_0_17_17 = e1)
% 12.38/3.47 |
% 12.38/3.47 +-Applying beta-rule and splitting (72), into two cases.
% 12.38/3.47 |-Branch one:
% 12.38/3.47 | (358) ~ (all_0_13_13 = e1)
% 12.38/3.47 |
% 12.38/3.47 | Equations (315) can reduce 358 to:
% 12.38/3.47 | (202) $false
% 12.38/3.47 |
% 12.38/3.47 |-The branch is then unsatisfiable
% 12.38/3.47 |-Branch two:
% 12.38/3.47 | (315) all_0_13_13 = e1
% 12.38/3.47 | (255) ~ (all_0_14_14 = e2)
% 12.38/3.47 |
% 12.38/3.47 +-Applying beta-rule and splitting (74), into two cases.
% 12.38/3.47 |-Branch one:
% 12.38/3.47 | (260) all_0_12_12 = e2
% 12.38/3.47 |
% 12.38/3.47 | Equations (260) can reduce 160 to:
% 12.38/3.47 | (891) ~ (all_0_14_14 = e2)
% 12.38/3.47 |
% 12.38/3.47 | Simplifying 891 yields:
% 12.38/3.47 | (255) ~ (all_0_14_14 = e2)
% 12.38/3.47 |
% 12.38/3.47 | Equations (260) can reduce 75 to:
% 12.38/3.47 | (596) ~ (all_0_15_15 = e2)
% 12.38/3.47 |
% 12.38/3.47 | Simplifying 596 yields:
% 12.38/3.47 | (576) ~ (all_0_15_15 = e2)
% 12.38/3.47 |
% 12.38/3.47 | Equations (260) can reduce 167 to:
% 12.38/3.47 | (895) ~ (all_0_20_20 = e2)
% 12.38/3.47 |
% 12.38/3.47 | Simplifying 895 yields:
% 12.38/3.47 | (529) ~ (all_0_20_20 = e2)
% 12.38/3.47 |
% 12.38/3.48 | Equations (260) can reduce 214 to:
% 12.38/3.48 | (13) ~ (e2 = e0)
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (138), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (328) all_0_16_16 = e1
% 12.38/3.48 |
% 12.38/3.48 | Equations (328) can reduce 58 to:
% 12.38/3.48 | (884) ~ (all_0_17_17 = e1)
% 12.38/3.48 |
% 12.38/3.48 | Simplifying 884 yields:
% 12.38/3.48 | (208) ~ (all_0_17_17 = e1)
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (115), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (413) ~ (all_0_16_16 = e1)
% 12.38/3.48 |
% 12.38/3.48 | Equations (328) can reduce 413 to:
% 12.38/3.48 | (202) $false
% 12.38/3.48 |
% 12.38/3.48 |-The branch is then unsatisfiable
% 12.38/3.48 |-Branch two:
% 12.38/3.48 | (328) all_0_16_16 = e1
% 12.38/3.48 | (224) ~ (all_0_18_18 = e3)
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (105), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (225) ~ (all_0_10_10 = e3)
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (36), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (413) ~ (all_0_16_16 = e1)
% 12.38/3.48 |
% 12.38/3.48 | Equations (328) can reduce 413 to:
% 12.38/3.48 | (202) $false
% 12.38/3.48 |
% 12.38/3.48 |-The branch is then unsatisfiable
% 12.38/3.48 |-Branch two:
% 12.38/3.48 | (328) all_0_16_16 = e1
% 12.38/3.48 | (223) ~ (all_0_23_23 = e3)
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (88), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (301) all_0_23_23 = e3
% 12.38/3.48 |
% 12.38/3.48 | Equations (301) can reduce 223 to:
% 12.38/3.48 | (202) $false
% 12.38/3.48 |
% 12.38/3.48 |-The branch is then unsatisfiable
% 12.38/3.48 |-Branch two:
% 12.38/3.48 | (223) ~ (all_0_23_23 = e3)
% 12.38/3.48 | (304) all_0_23_23 = e2 | all_0_23_23 = e1
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (304), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (305) all_0_23_23 = e2
% 12.38/3.48 |
% 12.38/3.48 | Equations (305) can reduce 273 to:
% 12.38/3.48 | (202) $false
% 12.38/3.48 |
% 12.38/3.48 |-The branch is then unsatisfiable
% 12.38/3.48 |-Branch two:
% 12.38/3.48 | (273) ~ (all_0_23_23 = e2)
% 12.38/3.48 | (308) all_0_23_23 = e1
% 12.38/3.48 |
% 12.38/3.48 | Equations (308) can reduce 119 to:
% 12.38/3.48 | (675) ~ (all_0_11_11 = e1)
% 12.38/3.48 |
% 12.38/3.48 | Equations (308) can reduce 135 to:
% 12.38/3.48 | (622) ~ (all_0_19_19 = e1)
% 12.38/3.48 |
% 12.38/3.48 | Equations (308) can reduce 130 to:
% 12.38/3.48 | (920) ~ (all_0_20_20 = e1)
% 12.38/3.48 |
% 12.38/3.48 | Equations (308) can reduce 9 to:
% 12.38/3.48 | (181) ~ (e1 = e0)
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (123), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (366) all_0_8_8 = e1
% 12.38/3.48 |
% 12.38/3.48 | Combining equations (366,839) yields a new equation:
% 12.38/3.48 | (491) e1 = e0
% 12.38/3.48 |
% 12.38/3.48 | Simplifying 491 yields:
% 12.38/3.48 | (421) e1 = e0
% 12.38/3.48 |
% 12.38/3.48 | Equations (421) can reduce 181 to:
% 12.38/3.48 | (202) $false
% 12.38/3.48 |
% 12.38/3.48 |-The branch is then unsatisfiable
% 12.38/3.48 |-Branch two:
% 12.38/3.48 | (193) ~ (all_0_8_8 = e1)
% 12.38/3.48 | (370) all_0_9_9 = e1 | all_0_10_10 = e1 | all_0_11_11 = e1
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (370), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (380) all_0_9_9 = e1
% 12.38/3.48 |
% 12.38/3.48 | Equations (380) can reduce 316 to:
% 12.38/3.48 | (202) $false
% 12.38/3.48 |
% 12.38/3.48 |-The branch is then unsatisfiable
% 12.38/3.48 |-Branch two:
% 12.38/3.48 | (316) ~ (all_0_9_9 = e1)
% 12.38/3.48 | (383) all_0_10_10 = e1 | all_0_11_11 = e1
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (383), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (932) all_0_10_10 = e1
% 12.38/3.48 |
% 12.38/3.48 | Equations (932) can reduce 16 to:
% 12.38/3.48 | (316) ~ (all_0_9_9 = e1)
% 12.38/3.48 |
% 12.38/3.48 | Equations (932) can reduce 187 to:
% 12.38/3.48 | (934) ~ (all_0_11_11 = e1)
% 12.38/3.48 |
% 12.38/3.48 | Simplifying 934 yields:
% 12.38/3.48 | (675) ~ (all_0_11_11 = e1)
% 12.38/3.48 |
% 12.38/3.48 | Equations (932) can reduce 180 to:
% 12.38/3.48 | (318) ~ (all_0_14_14 = e1)
% 12.38/3.48 |
% 12.38/3.48 | Simplifying 318 yields:
% 12.38/3.48 | (319) ~ (all_0_14_14 = e1)
% 12.38/3.48 |
% 12.38/3.48 | Equations (932) can reduce 117 to:
% 12.38/3.48 | (938) ~ (all_0_22_22 = e1)
% 12.38/3.48 |
% 12.38/3.48 | Simplifying 938 yields:
% 12.38/3.48 | (309) ~ (all_0_22_22 = e1)
% 12.38/3.48 |
% 12.38/3.48 | Equations (932) can reduce 225 to:
% 12.38/3.48 | (464) ~ (e3 = e1)
% 12.38/3.48 |
% 12.38/3.48 | Simplifying 464 yields:
% 12.38/3.48 | (137) ~ (e3 = e1)
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (148), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (526) all_0_20_20 = e2
% 12.38/3.48 |
% 12.38/3.48 | Equations (526) can reduce 529 to:
% 12.38/3.48 | (202) $false
% 12.38/3.48 |
% 12.38/3.48 |-The branch is then unsatisfiable
% 12.38/3.48 |-Branch two:
% 12.38/3.48 | (529) ~ (all_0_20_20 = e2)
% 12.38/3.48 | (530) all_0_21_21 = e2 | all_0_22_22 = e2 | all_0_23_23 = e2
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (530), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (376) all_0_21_21 = e2
% 12.38/3.48 |
% 12.38/3.48 | Combining equations (829,376) yields a new equation:
% 12.38/3.48 | (284) e2 = e0
% 12.38/3.48 |
% 12.38/3.48 | Equations (284) can reduce 13 to:
% 12.38/3.48 | (202) $false
% 12.38/3.48 |
% 12.38/3.48 |-The branch is then unsatisfiable
% 12.38/3.48 |-Branch two:
% 12.38/3.48 | (542) ~ (all_0_21_21 = e2)
% 12.38/3.48 | (543) all_0_22_22 = e2 | all_0_23_23 = e2
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (155), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (226) all_0_9_9 = e3
% 12.38/3.48 |
% 12.38/3.48 | Equations (226) can reduce 145 to:
% 12.38/3.48 | (952) ~ (all_0_11_11 = e3)
% 12.38/3.48 |
% 12.38/3.48 | Simplifying 952 yields:
% 12.38/3.48 | (242) ~ (all_0_11_11 = e3)
% 12.38/3.48 |
% 12.38/3.48 | Equations (226) can reduce 109 to:
% 12.38/3.48 | (954) ~ (all_0_17_17 = e3)
% 12.38/3.48 |
% 12.38/3.48 | Simplifying 954 yields:
% 12.38/3.48 | (451) ~ (all_0_17_17 = e3)
% 12.38/3.48 |
% 12.38/3.48 | Equations (226) can reduce 316 to:
% 12.38/3.48 | (137) ~ (e3 = e1)
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (83), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (295) all_0_17_17 = e3
% 12.38/3.48 |
% 12.38/3.48 | Equations (295) can reduce 451 to:
% 12.38/3.48 | (202) $false
% 12.38/3.48 |
% 12.38/3.48 |-The branch is then unsatisfiable
% 12.38/3.48 |-Branch two:
% 12.38/3.48 | (451) ~ (all_0_17_17 = e3)
% 12.38/3.48 | (452) all_0_17_17 = e2 | all_0_17_17 = e1 | all_0_17_17 = e0
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (452), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (371) all_0_17_17 = e2
% 12.38/3.48 |
% 12.38/3.48 | Equations (371) can reduce 17 to:
% 12.38/3.48 | (962) ~ (all_0_18_18 = e2)
% 12.38/3.48 |
% 12.38/3.48 | Simplifying 962 yields:
% 12.38/3.48 | (555) ~ (all_0_18_18 = e2)
% 12.38/3.48 |
% 12.38/3.48 | Equations (371) can reduce 120 to:
% 12.38/3.48 | (270) ~ (all_0_19_19 = e2)
% 12.38/3.48 |
% 12.38/3.48 | Simplifying 270 yields:
% 12.38/3.48 | (271) ~ (all_0_19_19 = e2)
% 12.38/3.48 |
% 12.38/3.48 | Equations (371) can reduce 208 to:
% 12.38/3.48 | (71) ~ (e2 = e1)
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (121), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (250) all_0_18_18 = e3
% 12.38/3.48 |
% 12.38/3.48 | Equations (250) can reduce 224 to:
% 12.38/3.48 | (202) $false
% 12.38/3.48 |
% 12.38/3.48 |-The branch is then unsatisfiable
% 12.38/3.48 |-Branch two:
% 12.38/3.48 | (224) ~ (all_0_18_18 = e3)
% 12.38/3.48 | (253) all_0_18_18 = e2 | all_0_18_18 = e0
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (253), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (254) all_0_18_18 = e2
% 12.38/3.48 |
% 12.38/3.48 | Equations (254) can reduce 555 to:
% 12.38/3.48 | (202) $false
% 12.38/3.48 |
% 12.38/3.48 |-The branch is then unsatisfiable
% 12.38/3.48 |-Branch two:
% 12.38/3.48 | (555) ~ (all_0_18_18 = e2)
% 12.38/3.48 | (556) all_0_18_18 = e0
% 12.38/3.48 |
% 12.38/3.48 | Equations (556) can reduce 4 to:
% 12.38/3.48 | (612) ~ (all_0_19_19 = e0)
% 12.38/3.48 |
% 12.38/3.48 | Simplifying 612 yields:
% 12.38/3.48 | (613) ~ (all_0_19_19 = e0)
% 12.38/3.48 |
% 12.38/3.48 | Equations (556) can reduce 5 to:
% 12.38/3.48 | (215) ~ (all_0_22_22 = e0)
% 12.38/3.48 |
% 12.38/3.48 | Simplifying 215 yields:
% 12.38/3.48 | (194) ~ (all_0_22_22 = e0)
% 12.38/3.48 |
% 12.38/3.48 | From (556) and (158) follows:
% 12.38/3.48 | (979) op(all_0_3_3, e0) = all_0_2_2
% 12.38/3.48 |
% 12.38/3.48 | From (556) and (164) follows:
% 12.38/3.48 | (614) op(e1, e0) = all_0_3_3
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (133), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (981) all_0_11_11 = e2
% 12.38/3.48 |
% 12.38/3.48 | Equations (981) can reduce 242 to:
% 12.38/3.48 | (274) ~ (e3 = e2)
% 12.38/3.48 |
% 12.38/3.48 | Simplifying 274 yields:
% 12.38/3.48 | (101) ~ (e3 = e2)
% 12.38/3.48 |
% 12.38/3.48 | Equations (981) can reduce 675 to:
% 12.38/3.48 | (71) ~ (e2 = e1)
% 12.38/3.48 |
% 12.38/3.48 | Equations (981) can reduce 280 to:
% 12.38/3.48 | (13) ~ (e2 = e0)
% 12.38/3.48 |
% 12.38/3.48 | From (981) and (106) follows:
% 12.38/3.48 | (986) op(e3, e0) = e2
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (95), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (331) all_0_14_14 = e3
% 12.38/3.48 |
% 12.38/3.48 | Equations (331) can reduce 44 to:
% 12.38/3.48 | (236) ~ (all_0_15_15 = e3)
% 12.38/3.48 |
% 12.38/3.48 | Simplifying 236 yields:
% 12.38/3.48 | (237) ~ (all_0_15_15 = e3)
% 12.38/3.48 |
% 12.38/3.48 | Equations (331) can reduce 162 to:
% 12.38/3.48 | (561) ~ (all_0_22_22 = e3)
% 12.38/3.48 |
% 12.38/3.48 | Simplifying 561 yields:
% 12.38/3.48 | (360) ~ (all_0_22_22 = e3)
% 12.38/3.48 |
% 12.38/3.48 | Equations (331) can reduce 255 to:
% 12.38/3.48 | (101) ~ (e3 = e2)
% 12.38/3.48 |
% 12.38/3.48 | Equations (331) can reduce 319 to:
% 12.38/3.48 | (137) ~ (e3 = e1)
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (147), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (276) all_0_11_11 = e0
% 12.38/3.48 |
% 12.38/3.48 | Combining equations (276,981) yields a new equation:
% 12.38/3.48 | (284) e2 = e0
% 12.38/3.48 |
% 12.38/3.48 | Equations (284) can reduce 13 to:
% 12.38/3.48 | (202) $false
% 12.38/3.48 |
% 12.38/3.48 |-The branch is then unsatisfiable
% 12.38/3.48 |-Branch two:
% 12.38/3.48 | (280) ~ (all_0_11_11 = e0)
% 12.38/3.48 | (281) all_0_15_15 = e0 | all_0_19_19 = e0
% 12.38/3.48 |
% 12.38/3.48 | Equations (981) can reduce 280 to:
% 12.38/3.48 | (13) ~ (e2 = e0)
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (114), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (1000) all_0_10_10 = e2
% 12.38/3.48 |
% 12.38/3.48 | Combining equations (1000,932) yields a new equation:
% 12.38/3.48 | (767) e2 = e1
% 12.38/3.48 |
% 12.38/3.48 | Simplifying 767 yields:
% 12.38/3.48 | (367) e2 = e1
% 12.38/3.48 |
% 12.38/3.48 | Equations (367) can reduce 71 to:
% 12.38/3.48 | (202) $false
% 12.38/3.48 |
% 12.38/3.48 |-The branch is then unsatisfiable
% 12.38/3.48 |-Branch two:
% 12.38/3.48 | (1004) ~ (all_0_10_10 = e2)
% 12.38/3.48 | (1005) all_0_14_14 = e2 | all_0_18_18 = e2 | all_0_22_22 = e2
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (1005), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (264) all_0_14_14 = e2
% 12.38/3.48 |
% 12.38/3.48 | Combining equations (331,264) yields a new equation:
% 12.38/3.48 | (372) e3 = e2
% 12.38/3.48 |
% 12.38/3.48 | Simplifying 372 yields:
% 12.38/3.48 | (373) e3 = e2
% 12.38/3.48 |
% 12.38/3.48 | Equations (373) can reduce 101 to:
% 12.38/3.48 | (202) $false
% 12.38/3.48 |
% 12.38/3.48 |-The branch is then unsatisfiable
% 12.38/3.48 |-Branch two:
% 12.38/3.48 | (255) ~ (all_0_14_14 = e2)
% 12.38/3.48 | (1011) all_0_18_18 = e2 | all_0_22_22 = e2
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (146), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (500) all_0_12_12 = e0
% 12.38/3.48 |
% 12.38/3.48 | Combining equations (500,260) yields a new equation:
% 12.38/3.48 | (284) e2 = e0
% 12.38/3.48 |
% 12.38/3.48 | Equations (284) can reduce 13 to:
% 12.38/3.48 | (202) $false
% 12.38/3.48 |
% 12.38/3.48 |-The branch is then unsatisfiable
% 12.38/3.48 |-Branch two:
% 12.38/3.48 | (214) ~ (all_0_12_12 = e0)
% 12.38/3.48 | (503) all_0_13_13 = e0 | all_0_14_14 = e0 | all_0_15_15 = e0
% 12.38/3.48 |
% 12.38/3.48 | Equations (260) can reduce 214 to:
% 12.38/3.48 | (13) ~ (e2 = e0)
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (1011), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (254) all_0_18_18 = e2
% 12.38/3.48 |
% 12.38/3.48 | Combining equations (556,254) yields a new equation:
% 12.38/3.48 | (284) e2 = e0
% 12.38/3.48 |
% 12.38/3.48 | Equations (284) can reduce 13 to:
% 12.38/3.48 | (202) $false
% 12.38/3.48 |
% 12.38/3.48 |-The branch is then unsatisfiable
% 12.38/3.48 |-Branch two:
% 12.38/3.48 | (555) ~ (all_0_18_18 = e2)
% 12.38/3.48 | (439) all_0_22_22 = e2
% 12.38/3.48 |
% 12.38/3.48 | Equations (439) can reduce 360 to:
% 12.38/3.48 | (274) ~ (e3 = e2)
% 12.38/3.48 |
% 12.38/3.48 | Simplifying 274 yields:
% 12.38/3.48 | (101) ~ (e3 = e2)
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (165), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (233) all_0_11_11 = e3
% 12.38/3.48 |
% 12.38/3.48 | Combining equations (233,981) yields a new equation:
% 12.38/3.48 | (372) e3 = e2
% 12.38/3.48 |
% 12.38/3.48 | Simplifying 372 yields:
% 12.38/3.48 | (373) e3 = e2
% 12.38/3.48 |
% 12.38/3.48 | Equations (373) can reduce 101 to:
% 12.38/3.48 | (202) $false
% 12.38/3.48 |
% 12.38/3.48 |-The branch is then unsatisfiable
% 12.38/3.48 |-Branch two:
% 12.38/3.48 | (242) ~ (all_0_11_11 = e3)
% 12.38/3.48 | (748) all_0_15_15 = e3 | all_0_19_19 = e3 | all_0_23_23 = e3
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (748), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (665) all_0_15_15 = e3
% 12.38/3.48 |
% 12.38/3.48 | Equations (665) can reduce 237 to:
% 12.38/3.48 | (202) $false
% 12.38/3.48 |
% 12.38/3.48 |-The branch is then unsatisfiable
% 12.38/3.48 |-Branch two:
% 12.38/3.48 | (237) ~ (all_0_15_15 = e3)
% 12.38/3.48 | (776) all_0_19_19 = e3 | all_0_23_23 = e3
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (776), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (481) all_0_19_19 = e3
% 12.38/3.48 |
% 12.38/3.48 | From (481) and (41) follows:
% 12.38/3.48 | (671) op(e1, e0) = e3
% 12.38/3.48 |
% 12.38/3.48 | Instantiating formula (53) with e1, e0, e3, all_0_3_3 and discharging atoms op(e1, e0) = all_0_3_3, op(e1, e0) = e3, yields:
% 12.38/3.48 | (680) all_0_3_3 = e3
% 12.38/3.48 |
% 12.38/3.48 | From (680) and (979) follows:
% 12.38/3.48 | (1038) op(e3, e0) = all_0_2_2
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (57), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.48 | (1039) ~ (all_0_2_2 = e2)
% 12.38/3.48 |
% 12.38/3.48 | Instantiating formula (53) with e3, e0, all_0_2_2, e2 and discharging atoms op(e3, e0) = all_0_2_2, op(e3, e0) = e2, yields:
% 12.38/3.48 | (1040) all_0_2_2 = e2
% 12.38/3.48 |
% 12.38/3.48 | Equations (1040) can reduce 1039 to:
% 12.38/3.48 | (202) $false
% 12.38/3.48 |
% 12.38/3.48 |-The branch is then unsatisfiable
% 12.38/3.48 |-Branch two:
% 12.38/3.48 | (1040) all_0_2_2 = e2
% 12.38/3.48 | (1043) ~ (all_0_3_3 = e3) | ~ (all_0_18_18 = e0)
% 12.38/3.48 |
% 12.38/3.48 +-Applying beta-rule and splitting (1043), into two cases.
% 12.38/3.48 |-Branch one:
% 12.38/3.49 | (1044) ~ (all_0_3_3 = e3)
% 12.38/3.49 |
% 12.38/3.49 | Equations (680) can reduce 1044 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (680) all_0_3_3 = e3
% 12.38/3.49 | (245) ~ (all_0_18_18 = e0)
% 12.38/3.49 |
% 12.38/3.49 | Equations (556) can reduce 245 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (239) ~ (all_0_19_19 = e3)
% 12.38/3.49 | (301) all_0_23_23 = e3
% 12.38/3.49 |
% 12.38/3.49 | Combining equations (308,301) yields a new equation:
% 12.38/3.49 | (417) e3 = e1
% 12.38/3.49 |
% 12.38/3.49 | Equations (417) can reduce 137 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (325) ~ (all_0_14_14 = e3)
% 12.38/3.49 | (334) all_0_14_14 = e2 | all_0_14_14 = e1 | all_0_14_14 = e0
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (68), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (434) all_0_20_20 = e3
% 12.38/3.49 |
% 12.38/3.49 | Equations (434) can reduce 69 to:
% 12.38/3.49 | (561) ~ (all_0_22_22 = e3)
% 12.38/3.49 |
% 12.38/3.49 | Simplifying 561 yields:
% 12.38/3.49 | (360) ~ (all_0_22_22 = e3)
% 12.38/3.49 |
% 12.38/3.49 | Equations (434) can reduce 920 to:
% 12.38/3.49 | (137) ~ (e3 = e1)
% 12.38/3.49 |
% 12.38/3.49 | Equations (434) can reduce 220 to:
% 12.38/3.49 | (136) ~ (e3 = e0)
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (87), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (344) all_0_22_22 = e3
% 12.38/3.49 |
% 12.38/3.49 | Equations (344) can reduce 360 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (360) ~ (all_0_22_22 = e3)
% 12.38/3.49 | (361) all_0_22_22 = e2 | all_0_22_22 = e1 | all_0_22_22 = e0
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (361), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (439) all_0_22_22 = e2
% 12.38/3.49 |
% 12.38/3.49 | Equations (439) can reduce 360 to:
% 12.38/3.49 | (274) ~ (e3 = e2)
% 12.38/3.49 |
% 12.38/3.49 | Simplifying 274 yields:
% 12.38/3.49 | (101) ~ (e3 = e2)
% 12.38/3.49 |
% 12.38/3.49 | Equations (439) can reduce 194 to:
% 12.38/3.49 | (13) ~ (e2 = e0)
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (147), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (276) all_0_11_11 = e0
% 12.38/3.49 |
% 12.38/3.49 | Combining equations (276,981) yields a new equation:
% 12.38/3.49 | (284) e2 = e0
% 12.38/3.49 |
% 12.38/3.49 | Equations (284) can reduce 13 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (280) ~ (all_0_11_11 = e0)
% 12.38/3.49 | (281) all_0_15_15 = e0 | all_0_19_19 = e0
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (281), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (282) all_0_15_15 = e0
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (93), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (323) all_0_12_12 = e3
% 12.38/3.49 |
% 12.38/3.49 | Combining equations (260,323) yields a new equation:
% 12.38/3.49 | (373) e3 = e2
% 12.38/3.49 |
% 12.38/3.49 | Equations (373) can reduce 101 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (423) ~ (all_0_12_12 = e3)
% 12.38/3.49 | (1078) all_0_13_13 = e3 | all_0_14_14 = e3 | all_0_15_15 = e3
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (1078), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (311) all_0_13_13 = e3
% 12.38/3.49 |
% 12.38/3.49 | Combining equations (315,311) yields a new equation:
% 12.38/3.49 | (417) e3 = e1
% 12.38/3.49 |
% 12.38/3.49 | Equations (417) can reduce 137 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (219) ~ (all_0_13_13 = e3)
% 12.38/3.49 | (1083) all_0_14_14 = e3 | all_0_15_15 = e3
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (1083), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (331) all_0_14_14 = e3
% 12.38/3.49 |
% 12.38/3.49 | Equations (331) can reduce 325 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (325) ~ (all_0_14_14 = e3)
% 12.38/3.49 | (665) all_0_15_15 = e3
% 12.38/3.49 |
% 12.38/3.49 | Combining equations (282,665) yields a new equation:
% 12.38/3.49 | (278) e3 = e0
% 12.38/3.49 |
% 12.38/3.49 | Equations (278) can reduce 136 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (286) ~ (all_0_15_15 = e0)
% 12.38/3.49 | (287) all_0_19_19 = e0
% 12.38/3.49 |
% 12.38/3.49 | Equations (287) can reduce 613 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (258) ~ (all_0_22_22 = e2)
% 12.38/3.49 | (442) all_0_22_22 = e1 | all_0_22_22 = e0
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (442), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (443) all_0_22_22 = e1
% 12.38/3.49 |
% 12.38/3.49 | Equations (443) can reduce 309 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (309) ~ (all_0_22_22 = e1)
% 12.38/3.49 | (446) all_0_22_22 = e0
% 12.38/3.49 |
% 12.38/3.49 | Equations (446) can reduce 194 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (1100) ~ (all_0_20_20 = e3)
% 12.38/3.49 | (1101) all_0_20_20 = e2 | all_0_20_20 = e1 | all_0_20_20 = e0
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (128), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (323) all_0_12_12 = e3
% 12.38/3.49 |
% 12.38/3.49 | Combining equations (260,323) yields a new equation:
% 12.38/3.49 | (373) e3 = e2
% 12.38/3.49 |
% 12.38/3.49 | Equations (373) can reduce 101 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (423) ~ (all_0_12_12 = e3)
% 12.38/3.49 | (424) all_0_16_16 = e3 | all_0_20_20 = e3
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (424), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (427) all_0_16_16 = e3
% 12.38/3.49 |
% 12.38/3.49 | Combining equations (328,427) yields a new equation:
% 12.38/3.49 | (417) e3 = e1
% 12.38/3.49 |
% 12.38/3.49 | Equations (417) can reduce 137 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (298) ~ (all_0_16_16 = e3)
% 12.38/3.49 | (434) all_0_20_20 = e3
% 12.38/3.49 |
% 12.38/3.49 | Equations (434) can reduce 1100 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (1113) ~ (all_0_11_11 = e2)
% 12.38/3.49 | (1114) all_0_15_15 = e2 | all_0_19_19 = e2 | all_0_23_23 = e2
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (170), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (481) all_0_19_19 = e3
% 12.38/3.49 |
% 12.38/3.49 | Equations (481) can reduce 271 to:
% 12.38/3.49 | (101) ~ (e3 = e2)
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (114), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (1000) all_0_10_10 = e2
% 12.38/3.49 |
% 12.38/3.49 | Combining equations (1000,932) yields a new equation:
% 12.38/3.49 | (767) e2 = e1
% 12.38/3.49 |
% 12.38/3.49 | Simplifying 767 yields:
% 12.38/3.49 | (367) e2 = e1
% 12.38/3.49 |
% 12.38/3.49 | Equations (367) can reduce 71 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (1004) ~ (all_0_10_10 = e2)
% 12.38/3.49 | (1005) all_0_14_14 = e2 | all_0_18_18 = e2 | all_0_22_22 = e2
% 12.38/3.49 |
% 12.38/3.49 | Equations (932) can reduce 1004 to:
% 12.38/3.49 | (329) ~ (e2 = e1)
% 12.38/3.49 |
% 12.38/3.49 | Simplifying 329 yields:
% 12.38/3.49 | (71) ~ (e2 = e1)
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (1114), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (267) all_0_15_15 = e2
% 12.38/3.49 |
% 12.38/3.49 | Equations (267) can reduce 576 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (576) ~ (all_0_15_15 = e2)
% 12.38/3.49 | (1128) all_0_19_19 = e2 | all_0_23_23 = e2
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (543), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (439) all_0_22_22 = e2
% 12.38/3.49 |
% 12.38/3.49 | Equations (439) can reduce 309 to:
% 12.38/3.49 | (71) ~ (e2 = e1)
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (1128), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (709) all_0_19_19 = e2
% 12.38/3.49 |
% 12.38/3.49 | Combining equations (481,709) yields a new equation:
% 12.38/3.49 | (372) e3 = e2
% 12.38/3.49 |
% 12.38/3.49 | Simplifying 372 yields:
% 12.38/3.49 | (373) e3 = e2
% 12.38/3.49 |
% 12.38/3.49 | Equations (373) can reduce 101 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (271) ~ (all_0_19_19 = e2)
% 12.38/3.49 | (305) all_0_23_23 = e2
% 12.38/3.49 |
% 12.38/3.49 | Combining equations (305,308) yields a new equation:
% 12.38/3.49 | (767) e2 = e1
% 12.38/3.49 |
% 12.38/3.49 | Simplifying 767 yields:
% 12.38/3.49 | (367) e2 = e1
% 12.38/3.49 |
% 12.38/3.49 | Equations (367) can reduce 71 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (258) ~ (all_0_22_22 = e2)
% 12.38/3.49 | (305) all_0_23_23 = e2
% 12.38/3.49 |
% 12.38/3.49 | Combining equations (308,305) yields a new equation:
% 12.38/3.49 | (367) e2 = e1
% 12.38/3.49 |
% 12.38/3.49 | Equations (367) can reduce 71 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (239) ~ (all_0_19_19 = e3)
% 12.38/3.49 | (704) all_0_19_19 = e2 | all_0_19_19 = e1 | all_0_19_19 = e0
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (704), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (709) all_0_19_19 = e2
% 12.38/3.49 |
% 12.38/3.49 | Equations (709) can reduce 271 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (271) ~ (all_0_19_19 = e2)
% 12.38/3.49 | (712) all_0_19_19 = e1 | all_0_19_19 = e0
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (712), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (420) all_0_19_19 = e1
% 12.38/3.49 |
% 12.38/3.49 | Equations (420) can reduce 622 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (622) ~ (all_0_19_19 = e1)
% 12.38/3.49 | (287) all_0_19_19 = e0
% 12.38/3.49 |
% 12.38/3.49 | Equations (287) can reduce 613 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (375) ~ (all_0_17_17 = e2)
% 12.38/3.49 | (536) all_0_17_17 = e1 | all_0_17_17 = e0
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (536), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (415) all_0_17_17 = e1
% 12.38/3.49 |
% 12.38/3.49 | Equations (415) can reduce 208 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (208) ~ (all_0_17_17 = e1)
% 12.38/3.49 | (540) all_0_17_17 = e0
% 12.38/3.49 |
% 12.38/3.49 | Equations (540) can reduce 288 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (212) ~ (all_0_9_9 = e3)
% 12.38/3.49 | (229) all_0_10_10 = e3 | all_0_11_11 = e3
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (229), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (230) all_0_10_10 = e3
% 12.38/3.49 |
% 12.38/3.49 | Combining equations (932,230) yields a new equation:
% 12.38/3.49 | (417) e3 = e1
% 12.38/3.49 |
% 12.38/3.49 | Equations (417) can reduce 137 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (225) ~ (all_0_10_10 = e3)
% 12.38/3.49 | (233) all_0_11_11 = e3
% 12.38/3.49 |
% 12.38/3.49 | Equations (233) can reduce 242 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (1170) ~ (all_0_10_10 = e1)
% 12.38/3.49 | (672) all_0_11_11 = e1
% 12.38/3.49 |
% 12.38/3.49 | Equations (672) can reduce 675 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (230) all_0_10_10 = e3
% 12.38/3.49 | (358) ~ (all_0_13_13 = e1)
% 12.38/3.49 |
% 12.38/3.49 | Equations (315) can reduce 358 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (413) ~ (all_0_16_16 = e1)
% 12.38/3.49 | (414) all_0_17_17 = e1 | all_0_19_19 = e1
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (414), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (415) all_0_17_17 = e1
% 12.38/3.49 |
% 12.38/3.49 | Equations (415) can reduce 208 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (208) ~ (all_0_17_17 = e1)
% 12.38/3.49 | (420) all_0_19_19 = e1
% 12.38/3.49 |
% 12.38/3.49 | Equations (420) can reduce 622 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (200) ~ (all_0_12_12 = e2)
% 12.38/3.49 | (263) all_0_14_14 = e2 | all_0_15_15 = e2
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (263), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (264) all_0_14_14 = e2
% 12.38/3.49 |
% 12.38/3.49 | Equations (264) can reduce 255 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (255) ~ (all_0_14_14 = e2)
% 12.38/3.49 | (267) all_0_15_15 = e2
% 12.38/3.49 |
% 12.38/3.49 | Equations (267) can reduce 576 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (358) ~ (all_0_13_13 = e1)
% 12.38/3.49 | (449) all_0_13_13 = e0
% 12.38/3.49 |
% 12.38/3.49 | Equations (449) can reduce 249 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (311) all_0_13_13 = e3
% 12.38/3.49 | (413) ~ (all_0_16_16 = e1)
% 12.38/3.49 |
% 12.38/3.49 | Equations (311) can reduce 31 to:
% 12.38/3.49 | (212) ~ (all_0_9_9 = e3)
% 12.38/3.49 |
% 12.38/3.49 | Equations (311) can reduce 32 to:
% 12.38/3.49 | (423) ~ (all_0_12_12 = e3)
% 12.38/3.49 |
% 12.38/3.49 | Equations (311) can reduce 149 to:
% 12.38/3.49 | (324) ~ (all_0_14_14 = e3)
% 12.38/3.49 |
% 12.38/3.49 | Simplifying 324 yields:
% 12.38/3.49 | (325) ~ (all_0_14_14 = e3)
% 12.38/3.49 |
% 12.38/3.49 | Equations (311) can reduce 98 to:
% 12.38/3.49 | (236) ~ (all_0_15_15 = e3)
% 12.38/3.49 |
% 12.38/3.49 | Simplifying 236 yields:
% 12.38/3.49 | (237) ~ (all_0_15_15 = e3)
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (138), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (328) all_0_16_16 = e1
% 12.38/3.49 |
% 12.38/3.49 | Equations (328) can reduce 413 to:
% 12.38/3.49 | (202) $false
% 12.38/3.49 |
% 12.38/3.49 |-The branch is then unsatisfiable
% 12.38/3.49 |-Branch two:
% 12.38/3.49 | (413) ~ (all_0_16_16 = e1)
% 12.38/3.49 | (414) all_0_17_17 = e1 | all_0_19_19 = e1
% 12.38/3.49 |
% 12.38/3.49 +-Applying beta-rule and splitting (414), into two cases.
% 12.38/3.49 |-Branch one:
% 12.38/3.49 | (415) all_0_17_17 = e1
% 12.38/3.49 |
% 12.38/3.49 | Equations (415) can reduce 109 to:
% 12.38/3.49 | (316) ~ (all_0_9_9 = e1)
% 12.38/3.49 |
% 12.38/3.49 | Equations (415) can reduce 120 to:
% 12.38/3.49 | (657) ~ (all_0_19_19 = e1)
% 12.38/3.49 |
% 12.38/3.49 | Simplifying 657 yields:
% 12.38/3.49 | (622) ~ (all_0_19_19 = e1)
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (142), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (226) all_0_9_9 = e3
% 12.38/3.50 |
% 12.38/3.50 | Equations (226) can reduce 212 to:
% 12.38/3.50 | (202) $false
% 12.38/3.50 |
% 12.38/3.50 |-The branch is then unsatisfiable
% 12.38/3.50 |-Branch two:
% 12.38/3.50 | (212) ~ (all_0_9_9 = e3)
% 12.38/3.50 | (387) all_0_9_9 = e2 | all_0_9_9 = e1 | all_0_9_9 = e0
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (387), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (362) all_0_9_9 = e2
% 12.38/3.50 |
% 12.38/3.50 | Equations (362) can reduce 145 to:
% 12.38/3.50 | (1214) ~ (all_0_11_11 = e2)
% 12.38/3.50 |
% 12.38/3.50 | Simplifying 1214 yields:
% 12.38/3.50 | (1113) ~ (all_0_11_11 = e2)
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (116), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (200) ~ (all_0_12_12 = e2)
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (30), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (323) all_0_12_12 = e3
% 12.38/3.50 |
% 12.38/3.50 | Equations (323) can reduce 423 to:
% 12.38/3.50 | (202) $false
% 12.38/3.50 |
% 12.38/3.50 |-The branch is then unsatisfiable
% 12.38/3.50 |-Branch two:
% 12.38/3.50 | (423) ~ (all_0_12_12 = e3)
% 12.38/3.50 | (725) all_0_12_12 = e2 | all_0_12_12 = e1 | all_0_12_12 = e0
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (725), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (260) all_0_12_12 = e2
% 12.38/3.50 |
% 12.38/3.50 | Equations (260) can reduce 200 to:
% 12.38/3.50 | (202) $false
% 12.38/3.50 |
% 12.38/3.50 |-The branch is then unsatisfiable
% 12.38/3.50 |-Branch two:
% 12.38/3.50 | (200) ~ (all_0_12_12 = e2)
% 12.38/3.50 | (729) all_0_12_12 = e1 | all_0_12_12 = e0
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (729), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (730) all_0_12_12 = e1
% 12.38/3.50 |
% 12.38/3.50 | Equations (730) can reduce 75 to:
% 12.38/3.50 | (1226) ~ (all_0_15_15 = e1)
% 12.38/3.50 |
% 12.38/3.50 | Simplifying 1226 yields:
% 12.38/3.50 | (693) ~ (all_0_15_15 = e1)
% 12.38/3.50 |
% 12.38/3.50 | Equations (730) can reduce 76 to:
% 12.38/3.50 | (1228) ~ (all_0_16_16 = e1)
% 12.38/3.50 |
% 12.38/3.50 | Simplifying 1228 yields:
% 12.38/3.50 | (413) ~ (all_0_16_16 = e1)
% 12.38/3.50 |
% 12.38/3.50 | Equations (730) can reduce 423 to:
% 12.38/3.50 | (464) ~ (e3 = e1)
% 12.38/3.50 |
% 12.38/3.50 | Simplifying 464 yields:
% 12.38/3.50 | (137) ~ (e3 = e1)
% 12.38/3.50 |
% 12.38/3.50 | Equations (730) can reduce 200 to:
% 12.38/3.50 | (329) ~ (e2 = e1)
% 12.38/3.50 |
% 12.38/3.50 | Simplifying 329 yields:
% 12.38/3.50 | (71) ~ (e2 = e1)
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (74), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (260) all_0_12_12 = e2
% 12.38/3.50 |
% 12.38/3.50 | Combining equations (730,260) yields a new equation:
% 12.38/3.50 | (367) e2 = e1
% 12.38/3.50 |
% 12.38/3.50 | Equations (367) can reduce 71 to:
% 12.38/3.50 | (202) $false
% 12.38/3.50 |
% 12.38/3.50 |-The branch is then unsatisfiable
% 12.38/3.50 |-Branch two:
% 12.38/3.50 | (200) ~ (all_0_12_12 = e2)
% 12.38/3.50 | (263) all_0_14_14 = e2 | all_0_15_15 = e2
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (126), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (665) all_0_15_15 = e3
% 12.38/3.50 |
% 12.38/3.50 | Equations (665) can reduce 237 to:
% 12.38/3.50 | (202) $false
% 12.38/3.50 |
% 12.38/3.50 |-The branch is then unsatisfiable
% 12.38/3.50 |-Branch two:
% 12.38/3.50 | (237) ~ (all_0_15_15 = e3)
% 12.38/3.50 | (668) all_0_15_15 = e2 | all_0_15_15 = e1 | all_0_15_15 = e0
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (668), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (267) all_0_15_15 = e2
% 12.38/3.50 |
% 12.38/3.50 | Equations (267) can reduce 576 to:
% 12.38/3.50 | (202) $false
% 12.38/3.50 |
% 12.38/3.50 |-The branch is then unsatisfiable
% 12.38/3.50 |-Branch two:
% 12.38/3.50 | (576) ~ (all_0_15_15 = e2)
% 12.38/3.50 | (708) all_0_15_15 = e1 | all_0_15_15 = e0
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (708), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (677) all_0_15_15 = e1
% 12.38/3.50 |
% 12.38/3.50 | Equations (677) can reduce 693 to:
% 12.38/3.50 | (202) $false
% 12.38/3.50 |
% 12.38/3.50 |-The branch is then unsatisfiable
% 12.38/3.50 |-Branch two:
% 12.38/3.50 | (693) ~ (all_0_15_15 = e1)
% 12.38/3.50 | (282) all_0_15_15 = e0
% 12.38/3.50 |
% 12.38/3.50 | Equations (282) can reduce 44 to:
% 12.38/3.50 | (550) ~ (all_0_14_14 = e0)
% 12.38/3.50 |
% 12.38/3.50 | Equations (282) can reduce 576 to:
% 12.38/3.50 | (293) ~ (e2 = e0)
% 12.38/3.50 |
% 12.38/3.50 | Simplifying 293 yields:
% 12.38/3.50 | (13) ~ (e2 = e0)
% 12.38/3.50 |
% 12.38/3.50 | Equations (282) can reduce 693 to:
% 12.38/3.50 | (1254) ~ (e1 = e0)
% 12.38/3.50 |
% 12.38/3.50 | Simplifying 1254 yields:
% 12.38/3.50 | (181) ~ (e1 = e0)
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (263), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (264) all_0_14_14 = e2
% 12.38/3.50 |
% 12.38/3.50 | Equations (264) can reduce 180 to:
% 12.38/3.50 | (1004) ~ (all_0_10_10 = e2)
% 12.38/3.50 |
% 12.38/3.50 | Equations (264) can reduce 162 to:
% 12.38/3.50 | (257) ~ (all_0_22_22 = e2)
% 12.38/3.50 |
% 12.38/3.50 | Simplifying 257 yields:
% 12.38/3.50 | (258) ~ (all_0_22_22 = e2)
% 12.38/3.50 |
% 12.38/3.50 | Equations (264) can reduce 325 to:
% 12.38/3.50 | (274) ~ (e3 = e2)
% 12.38/3.50 |
% 12.38/3.50 | Simplifying 274 yields:
% 12.38/3.50 | (101) ~ (e3 = e2)
% 12.38/3.50 |
% 12.38/3.50 | Equations (264) can reduce 550 to:
% 12.38/3.50 | (13) ~ (e2 = e0)
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (148), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (526) all_0_20_20 = e2
% 12.38/3.50 |
% 12.38/3.50 | Equations (526) can reduce 130 to:
% 12.38/3.50 | (272) ~ (all_0_23_23 = e2)
% 12.38/3.50 |
% 12.38/3.50 | Simplifying 272 yields:
% 12.38/3.50 | (273) ~ (all_0_23_23 = e2)
% 12.38/3.50 |
% 12.38/3.50 | Equations (526) can reduce 220 to:
% 12.38/3.50 | (13) ~ (e2 = e0)
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (155), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (226) all_0_9_9 = e3
% 12.38/3.50 |
% 12.38/3.50 | Combining equations (362,226) yields a new equation:
% 12.38/3.50 | (373) e3 = e2
% 12.38/3.50 |
% 12.38/3.50 | Equations (373) can reduce 101 to:
% 12.38/3.50 | (202) $false
% 12.38/3.50 |
% 12.38/3.50 |-The branch is then unsatisfiable
% 12.38/3.50 |-Branch two:
% 12.38/3.50 | (212) ~ (all_0_9_9 = e3)
% 12.38/3.50 | (229) all_0_10_10 = e3 | all_0_11_11 = e3
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (133), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (981) all_0_11_11 = e2
% 12.38/3.50 |
% 12.38/3.50 | Equations (981) can reduce 1113 to:
% 12.38/3.50 | (202) $false
% 12.38/3.50 |
% 12.38/3.50 |-The branch is then unsatisfiable
% 12.38/3.50 |-Branch two:
% 12.38/3.50 | (1113) ~ (all_0_11_11 = e2)
% 12.38/3.50 | (1114) all_0_15_15 = e2 | all_0_19_19 = e2 | all_0_23_23 = e2
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (1114), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (267) all_0_15_15 = e2
% 12.38/3.50 |
% 12.38/3.50 | Combining equations (282,267) yields a new equation:
% 12.38/3.50 | (284) e2 = e0
% 12.38/3.50 |
% 12.38/3.50 | Equations (284) can reduce 13 to:
% 12.38/3.50 | (202) $false
% 12.38/3.50 |
% 12.38/3.50 |-The branch is then unsatisfiable
% 12.38/3.50 |-Branch two:
% 12.38/3.50 | (576) ~ (all_0_15_15 = e2)
% 12.38/3.50 | (1128) all_0_19_19 = e2 | all_0_23_23 = e2
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (1128), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (709) all_0_19_19 = e2
% 12.38/3.50 |
% 12.38/3.50 | Equations (709) can reduce 4 to:
% 12.38/3.50 | (555) ~ (all_0_18_18 = e2)
% 12.38/3.50 |
% 12.38/3.50 | Equations (709) can reduce 622 to:
% 12.38/3.50 | (71) ~ (e2 = e1)
% 12.38/3.50 |
% 12.38/3.50 | From (709) and (41) follows:
% 12.38/3.50 | (1284) op(e1, e0) = e2
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (128), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (323) all_0_12_12 = e3
% 12.38/3.50 |
% 12.38/3.50 | Combining equations (323,730) yields a new equation:
% 12.38/3.50 | (416) e3 = e1
% 12.38/3.50 |
% 12.38/3.50 | Simplifying 416 yields:
% 12.38/3.50 | (417) e3 = e1
% 12.38/3.50 |
% 12.38/3.50 | Equations (417) can reduce 137 to:
% 12.38/3.50 | (202) $false
% 12.38/3.50 |
% 12.38/3.50 |-The branch is then unsatisfiable
% 12.38/3.50 |-Branch two:
% 12.38/3.50 | (423) ~ (all_0_12_12 = e3)
% 12.38/3.50 | (424) all_0_16_16 = e3 | all_0_20_20 = e3
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (229), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (230) all_0_10_10 = e3
% 12.38/3.50 |
% 12.38/3.50 | Equations (230) can reduce 1004 to:
% 12.38/3.50 | (101) ~ (e3 = e2)
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (123), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (366) all_0_8_8 = e1
% 12.38/3.50 |
% 12.38/3.50 | Combining equations (366,839) yields a new equation:
% 12.38/3.50 | (491) e1 = e0
% 12.38/3.50 |
% 12.38/3.50 | Simplifying 491 yields:
% 12.38/3.50 | (421) e1 = e0
% 12.38/3.50 |
% 12.38/3.50 | Equations (421) can reduce 181 to:
% 12.38/3.50 | (202) $false
% 12.38/3.50 |
% 12.38/3.50 |-The branch is then unsatisfiable
% 12.38/3.50 |-Branch two:
% 12.38/3.50 | (193) ~ (all_0_8_8 = e1)
% 12.38/3.50 | (370) all_0_9_9 = e1 | all_0_10_10 = e1 | all_0_11_11 = e1
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (424), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (427) all_0_16_16 = e3
% 12.38/3.50 |
% 12.38/3.50 | Equations (427) can reduce 39 to:
% 12.38/3.50 | (1300) ~ (all_0_18_18 = e3)
% 12.38/3.50 |
% 12.38/3.50 | Simplifying 1300 yields:
% 12.38/3.50 | (224) ~ (all_0_18_18 = e3)
% 12.38/3.50 |
% 12.38/3.50 | Equations (427) can reduce 413 to:
% 12.38/3.50 | (137) ~ (e3 = e1)
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (370), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (380) all_0_9_9 = e1
% 12.38/3.50 |
% 12.38/3.50 | Combining equations (380,362) yields a new equation:
% 12.38/3.50 | (367) e2 = e1
% 12.38/3.50 |
% 12.38/3.50 | Equations (367) can reduce 71 to:
% 12.38/3.50 | (202) $false
% 12.38/3.50 |
% 12.38/3.50 |-The branch is then unsatisfiable
% 12.38/3.50 |-Branch two:
% 12.38/3.50 | (316) ~ (all_0_9_9 = e1)
% 12.38/3.50 | (383) all_0_10_10 = e1 | all_0_11_11 = e1
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (383), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (932) all_0_10_10 = e1
% 12.38/3.50 |
% 12.38/3.50 | Combining equations (932,230) yields a new equation:
% 12.38/3.50 | (417) e3 = e1
% 12.38/3.50 |
% 12.38/3.50 | Equations (417) can reduce 137 to:
% 12.38/3.50 | (202) $false
% 12.38/3.50 |
% 12.38/3.50 |-The branch is then unsatisfiable
% 12.38/3.50 |-Branch two:
% 12.38/3.50 | (1170) ~ (all_0_10_10 = e1)
% 12.38/3.50 | (672) all_0_11_11 = e1
% 12.38/3.50 |
% 12.38/3.50 | Combining equations (672,874) yields a new equation:
% 12.38/3.50 | (1313) all_0_7_7 = e1
% 12.38/3.50 |
% 12.38/3.50 | From (672) and (875) follows:
% 12.38/3.50 | (1314) op(e1, e0) = all_0_6_6
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (156), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (1315) ~ (all_0_6_6 = e2)
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (121), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (250) all_0_18_18 = e3
% 12.38/3.50 |
% 12.38/3.50 | Equations (250) can reduce 224 to:
% 12.38/3.50 | (202) $false
% 12.38/3.50 |
% 12.38/3.50 |-The branch is then unsatisfiable
% 12.38/3.50 |-Branch two:
% 12.38/3.50 | (224) ~ (all_0_18_18 = e3)
% 12.38/3.50 | (253) all_0_18_18 = e2 | all_0_18_18 = e0
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (253), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (254) all_0_18_18 = e2
% 12.38/3.50 |
% 12.38/3.50 | Equations (254) can reduce 555 to:
% 12.38/3.50 | (202) $false
% 12.38/3.50 |
% 12.38/3.50 |-The branch is then unsatisfiable
% 12.38/3.50 |-Branch two:
% 12.38/3.50 | (555) ~ (all_0_18_18 = e2)
% 12.38/3.50 | (556) all_0_18_18 = e0
% 12.38/3.50 |
% 12.38/3.50 | From (556) and (164) follows:
% 12.38/3.50 | (614) op(e1, e0) = all_0_3_3
% 12.38/3.50 |
% 12.38/3.50 | Instantiating formula (53) with e1, e0, all_0_6_6, all_0_3_3 and discharging atoms op(e1, e0) = all_0_3_3, op(e1, e0) = all_0_6_6, yields:
% 12.38/3.50 | (1325) all_0_3_3 = all_0_6_6
% 12.38/3.50 |
% 12.38/3.50 | Instantiating formula (53) with e1, e0, e2, all_0_3_3 and discharging atoms op(e1, e0) = all_0_3_3, op(e1, e0) = e2, yields:
% 12.38/3.50 | (1326) all_0_3_3 = e2
% 12.38/3.50 |
% 12.38/3.50 | Combining equations (1325,1326) yields a new equation:
% 12.38/3.50 | (1327) all_0_6_6 = e2
% 12.38/3.50 |
% 12.38/3.50 | Simplifying 1327 yields:
% 12.38/3.50 | (1328) all_0_6_6 = e2
% 12.38/3.50 |
% 12.38/3.50 | Equations (1328) can reduce 1315 to:
% 12.38/3.50 | (202) $false
% 12.38/3.50 |
% 12.38/3.50 |-The branch is then unsatisfiable
% 12.38/3.50 |-Branch two:
% 12.38/3.50 | (1328) all_0_6_6 = e2
% 12.38/3.50 | (1331) ~ (all_0_7_7 = e1) | ~ (all_0_8_8 = e0)
% 12.38/3.50 |
% 12.38/3.50 +-Applying beta-rule and splitting (1331), into two cases.
% 12.38/3.50 |-Branch one:
% 12.38/3.50 | (1332) ~ (all_0_7_7 = e1)
% 12.38/3.50 |
% 12.38/3.50 | Equations (1313) can reduce 1332 to:
% 12.38/3.50 | (202) $false
% 12.38/3.50 |
% 12.38/3.50 |-The branch is then unsatisfiable
% 12.38/3.50 |-Branch two:
% 12.38/3.50 | (1313) all_0_7_7 = e1
% 12.38/3.50 | (195) ~ (all_0_8_8 = e0)
% 12.38/3.50 |
% 12.38/3.50 | Equations (839) can reduce 195 to:
% 12.38/3.50 | (202) $false
% 12.38/3.50 |
% 12.38/3.50 |-The branch is then unsatisfiable
% 12.38/3.50 |-Branch two:
% 12.38/3.50 | (298) ~ (all_0_16_16 = e3)
% 12.38/3.50 | (434) all_0_20_20 = e3
% 12.38/3.50 |
% 12.38/3.50 | Combining equations (434,526) yields a new equation:
% 12.38/3.50 | (372) e3 = e2
% 12.38/3.50 |
% 12.38/3.50 | Simplifying 372 yields:
% 12.38/3.50 | (373) e3 = e2
% 12.38/3.50 |
% 12.38/3.50 | Equations (373) can reduce 101 to:
% 12.38/3.50 | (202) $false
% 12.38/3.50 |
% 12.38/3.50 |-The branch is then unsatisfiable
% 12.38/3.50 |-Branch two:
% 12.38/3.50 | (225) ~ (all_0_10_10 = e3)
% 12.38/3.50 | (233) all_0_11_11 = e3
% 12.38/3.50 |
% 12.38/3.50 | Equations (233) can reduce 242 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (271) ~ (all_0_19_19 = e2)
% 12.38/3.51 | (305) all_0_23_23 = e2
% 12.38/3.51 |
% 12.38/3.51 | Equations (305) can reduce 273 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (529) ~ (all_0_20_20 = e2)
% 12.38/3.51 | (530) all_0_21_21 = e2 | all_0_22_22 = e2 | all_0_23_23 = e2
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (530), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (376) all_0_21_21 = e2
% 12.38/3.51 |
% 12.38/3.51 | Combining equations (376,829) yields a new equation:
% 12.38/3.51 | (283) e2 = e0
% 12.38/3.51 |
% 12.38/3.51 | Simplifying 283 yields:
% 12.38/3.51 | (284) e2 = e0
% 12.38/3.51 |
% 12.38/3.51 | Equations (284) can reduce 13 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (542) ~ (all_0_21_21 = e2)
% 12.38/3.51 | (543) all_0_22_22 = e2 | all_0_23_23 = e2
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (543), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (439) all_0_22_22 = e2
% 12.38/3.51 |
% 12.38/3.51 | Equations (439) can reduce 258 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (258) ~ (all_0_22_22 = e2)
% 12.38/3.51 | (305) all_0_23_23 = e2
% 12.38/3.51 |
% 12.38/3.51 | Equations (305) can reduce 273 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (255) ~ (all_0_14_14 = e2)
% 12.38/3.51 | (267) all_0_15_15 = e2
% 12.38/3.51 |
% 12.38/3.51 | Combining equations (282,267) yields a new equation:
% 12.38/3.51 | (284) e2 = e0
% 12.38/3.51 |
% 12.38/3.51 | Equations (284) can reduce 13 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (317) ~ (all_0_12_12 = e1)
% 12.38/3.51 | (500) all_0_12_12 = e0
% 12.38/3.51 |
% 12.38/3.51 | Equations (500) can reduce 214 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (260) all_0_12_12 = e2
% 12.38/3.51 | (219) ~ (all_0_13_13 = e3)
% 12.38/3.51 |
% 12.38/3.51 | Equations (311) can reduce 219 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (198) ~ (all_0_9_9 = e2)
% 12.38/3.51 | (391) all_0_9_9 = e1 | all_0_9_9 = e0
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (391), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (380) all_0_9_9 = e1
% 12.38/3.51 |
% 12.38/3.51 | Equations (380) can reduce 316 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (316) ~ (all_0_9_9 = e1)
% 12.38/3.51 | (395) all_0_9_9 = e0
% 12.38/3.51 |
% 12.38/3.51 | Equations (395) can reduce 494 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (208) ~ (all_0_17_17 = e1)
% 12.38/3.51 | (420) all_0_19_19 = e1
% 12.38/3.51 |
% 12.38/3.51 | Equations (420) can reduce 622 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (204) ~ (all_0_21_21 = e0)
% 12.38/3.51 | (446) all_0_22_22 = e0
% 12.38/3.51 |
% 12.38/3.51 | Equations (446) can reduce 194 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (446) all_0_22_22 = e0
% 12.38/3.51 | (570) ~ (all_0_23_23 = e1)
% 12.38/3.51 |
% 12.38/3.51 | Equations (446) can reduce 117 to:
% 12.38/3.51 | (602) ~ (all_0_10_10 = e0)
% 12.38/3.51 |
% 12.38/3.51 | Equations (446) can reduce 162 to:
% 12.38/3.51 | (550) ~ (all_0_14_14 = e0)
% 12.38/3.51 |
% 12.38/3.51 | Equations (446) can reduce 5 to:
% 12.38/3.51 | (245) ~ (all_0_18_18 = e0)
% 12.38/3.51 |
% 12.38/3.51 | Equations (446) can reduce 27 to:
% 12.38/3.51 | (204) ~ (all_0_21_21 = e0)
% 12.38/3.51 |
% 12.38/3.51 | Equations (446) can reduce 191 to:
% 12.38/3.51 | (217) ~ (all_0_23_23 = e0)
% 12.38/3.51 |
% 12.38/3.51 | Simplifying 217 yields:
% 12.38/3.51 | (9) ~ (all_0_23_23 = e0)
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (23), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (358) ~ (all_0_13_13 = e1)
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (91), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (208) ~ (all_0_17_17 = e1)
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (115), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (413) ~ (all_0_16_16 = e1)
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (138), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (328) all_0_16_16 = e1
% 12.38/3.51 |
% 12.38/3.51 | Equations (328) can reduce 413 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (413) ~ (all_0_16_16 = e1)
% 12.38/3.51 | (414) all_0_17_17 = e1 | all_0_19_19 = e1
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (414), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (415) all_0_17_17 = e1
% 12.38/3.51 |
% 12.38/3.51 | Equations (415) can reduce 208 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (208) ~ (all_0_17_17 = e1)
% 12.38/3.51 | (420) all_0_19_19 = e1
% 12.38/3.51 |
% 12.38/3.51 | Equations (420) can reduce 188 to:
% 12.38/3.51 | (693) ~ (all_0_15_15 = e1)
% 12.38/3.51 |
% 12.38/3.51 | Equations (420) can reduce 175 to:
% 12.38/3.51 | (413) ~ (all_0_16_16 = e1)
% 12.38/3.51 |
% 12.38/3.51 | Equations (420) can reduce 120 to:
% 12.38/3.51 | (208) ~ (all_0_17_17 = e1)
% 12.38/3.51 |
% 12.38/3.51 | Equations (420) can reduce 135 to:
% 12.38/3.51 | (1406) ~ (all_0_23_23 = e1)
% 12.38/3.51 |
% 12.38/3.51 | Simplifying 1406 yields:
% 12.38/3.51 | (570) ~ (all_0_23_23 = e1)
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (139), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (249) ~ (all_0_13_13 = e0)
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (33), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (195) ~ (all_0_8_8 = e0)
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (97), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (196) all_0_8_8 = e2
% 12.38/3.51 |
% 12.38/3.51 | Equations (196) can reduce 110 to:
% 12.38/3.51 | (197) ~ (all_0_9_9 = e2)
% 12.38/3.51 |
% 12.38/3.51 | Simplifying 197 yields:
% 12.38/3.51 | (198) ~ (all_0_9_9 = e2)
% 12.38/3.51 |
% 12.38/3.51 | Equations (196) can reduce 24 to:
% 12.38/3.51 | (1214) ~ (all_0_11_11 = e2)
% 12.38/3.51 |
% 12.38/3.51 | Simplifying 1214 yields:
% 12.38/3.51 | (1113) ~ (all_0_11_11 = e2)
% 12.38/3.51 |
% 12.38/3.51 | Equations (196) can reduce 179 to:
% 12.38/3.51 | (1415) ~ (all_0_16_16 = e2)
% 12.38/3.51 |
% 12.38/3.51 | Simplifying 1415 yields:
% 12.38/3.51 | (256) ~ (all_0_16_16 = e2)
% 12.38/3.51 |
% 12.38/3.51 | Equations (196) can reduce 122 to:
% 12.38/3.51 | (895) ~ (all_0_20_20 = e2)
% 12.38/3.51 |
% 12.38/3.51 | Simplifying 895 yields:
% 12.38/3.51 | (529) ~ (all_0_20_20 = e2)
% 12.38/3.51 |
% 12.38/3.51 | Equations (196) can reduce 193 to:
% 12.38/3.51 | (71) ~ (e2 = e1)
% 12.38/3.51 |
% 12.38/3.51 | Equations (196) can reduce 195 to:
% 12.38/3.51 | (13) ~ (e2 = e0)
% 12.38/3.51 |
% 12.38/3.51 | From (196) and (12) follows:
% 12.38/3.51 | (1421) op(all_0_7_7, e2) = all_0_6_6
% 12.38/3.51 |
% 12.38/3.51 | From (196) and (157) follows:
% 12.38/3.51 | (1422) op(e3, e2) = all_0_7_7
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (169), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (201) ~ (all_0_8_8 = e2)
% 12.38/3.51 |
% 12.38/3.51 | Equations (196) can reduce 201 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (196) all_0_8_8 = e2
% 12.38/3.51 | (212) ~ (all_0_9_9 = e3)
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (113), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (311) all_0_13_13 = e3
% 12.38/3.51 |
% 12.38/3.51 | Equations (311) can reduce 31 to:
% 12.38/3.51 | (212) ~ (all_0_9_9 = e3)
% 12.38/3.51 |
% 12.38/3.51 | Equations (311) can reduce 32 to:
% 12.38/3.51 | (423) ~ (all_0_12_12 = e3)
% 12.38/3.51 |
% 12.38/3.51 | Equations (311) can reduce 149 to:
% 12.38/3.51 | (324) ~ (all_0_14_14 = e3)
% 12.38/3.51 |
% 12.38/3.51 | Simplifying 324 yields:
% 12.38/3.51 | (325) ~ (all_0_14_14 = e3)
% 12.38/3.51 |
% 12.38/3.51 | Equations (311) can reduce 98 to:
% 12.38/3.51 | (236) ~ (all_0_15_15 = e3)
% 12.38/3.51 |
% 12.38/3.51 | Simplifying 236 yields:
% 12.38/3.51 | (237) ~ (all_0_15_15 = e3)
% 12.38/3.51 |
% 12.38/3.51 | Equations (311) can reduce 96 to:
% 12.38/3.51 | (299) ~ (all_0_21_21 = e3)
% 12.38/3.51 |
% 12.38/3.51 | Simplifying 299 yields:
% 12.38/3.51 | (300) ~ (all_0_21_21 = e3)
% 12.38/3.51 |
% 12.38/3.51 | Equations (311) can reduce 143 to:
% 12.38/3.51 | (101) ~ (e3 = e2)
% 12.38/3.51 |
% 12.38/3.51 | Instantiating formula (53) with e3, e2, all_0_7_7, all_0_9_9 and discharging atoms op(e3, e2) = all_0_7_7, op(e3, e2) = all_0_9_9, yields:
% 12.38/3.51 | (1437) all_0_7_7 = all_0_9_9
% 12.38/3.51 |
% 12.38/3.51 | From (1437) and (1421) follows:
% 12.38/3.51 | (1438) op(all_0_9_9, e2) = all_0_6_6
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (88), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (301) all_0_23_23 = e3
% 12.38/3.51 |
% 12.38/3.51 | Equations (301) can reduce 119 to:
% 12.38/3.51 | (242) ~ (all_0_11_11 = e3)
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (133), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (981) all_0_11_11 = e2
% 12.38/3.51 |
% 12.38/3.51 | Equations (981) can reduce 1113 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (1113) ~ (all_0_11_11 = e2)
% 12.38/3.51 | (1114) all_0_15_15 = e2 | all_0_19_19 = e2 | all_0_23_23 = e2
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (1114), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (267) all_0_15_15 = e2
% 12.38/3.51 |
% 12.38/3.51 | Equations (267) can reduce 50 to:
% 12.38/3.51 | (1113) ~ (all_0_11_11 = e2)
% 12.38/3.51 |
% 12.38/3.51 | Equations (267) can reduce 75 to:
% 12.38/3.51 | (200) ~ (all_0_12_12 = e2)
% 12.38/3.51 |
% 12.38/3.51 | Equations (267) can reduce 44 to:
% 12.38/3.51 | (255) ~ (all_0_14_14 = e2)
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (147), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (276) all_0_11_11 = e0
% 12.38/3.51 |
% 12.38/3.51 | Equations (276) can reduce 242 to:
% 12.38/3.51 | (291) ~ (e3 = e0)
% 12.38/3.51 |
% 12.38/3.51 | Simplifying 291 yields:
% 12.38/3.51 | (136) ~ (e3 = e0)
% 12.38/3.51 |
% 12.38/3.51 | Equations (276) can reduce 1113 to:
% 12.38/3.51 | (293) ~ (e2 = e0)
% 12.38/3.51 |
% 12.38/3.51 | Simplifying 293 yields:
% 12.38/3.51 | (13) ~ (e2 = e0)
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (142), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (226) all_0_9_9 = e3
% 12.38/3.51 |
% 12.38/3.51 | Equations (226) can reduce 212 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (212) ~ (all_0_9_9 = e3)
% 12.38/3.51 | (387) all_0_9_9 = e2 | all_0_9_9 = e1 | all_0_9_9 = e0
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (387), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (362) all_0_9_9 = e2
% 12.38/3.51 |
% 12.38/3.51 | Equations (362) can reduce 198 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (198) ~ (all_0_9_9 = e2)
% 12.38/3.51 | (391) all_0_9_9 = e1 | all_0_9_9 = e0
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (146), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (500) all_0_12_12 = e0
% 12.38/3.51 |
% 12.38/3.51 | Equations (500) can reduce 160 to:
% 12.38/3.51 | (1463) ~ (all_0_14_14 = e0)
% 12.38/3.51 |
% 12.38/3.51 | Simplifying 1463 yields:
% 12.38/3.51 | (550) ~ (all_0_14_14 = e0)
% 12.38/3.51 |
% 12.38/3.51 | Equations (500) can reduce 76 to:
% 12.38/3.51 | (1465) ~ (all_0_16_16 = e0)
% 12.38/3.51 |
% 12.38/3.51 | Simplifying 1465 yields:
% 12.38/3.51 | (611) ~ (all_0_16_16 = e0)
% 12.38/3.51 |
% 12.38/3.51 | Equations (500) can reduce 423 to:
% 12.38/3.51 | (291) ~ (e3 = e0)
% 12.38/3.51 |
% 12.38/3.51 | Simplifying 291 yields:
% 12.38/3.51 | (136) ~ (e3 = e0)
% 12.38/3.51 |
% 12.38/3.51 | Equations (500) can reduce 200 to:
% 12.38/3.51 | (293) ~ (e2 = e0)
% 12.38/3.51 |
% 12.38/3.51 | Simplifying 293 yields:
% 12.38/3.51 | (13) ~ (e2 = e0)
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (95), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (331) all_0_14_14 = e3
% 12.38/3.51 |
% 12.38/3.51 | Equations (331) can reduce 325 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (325) ~ (all_0_14_14 = e3)
% 12.38/3.51 | (334) all_0_14_14 = e2 | all_0_14_14 = e1 | all_0_14_14 = e0
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (334), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (264) all_0_14_14 = e2
% 12.38/3.51 |
% 12.38/3.51 | Equations (264) can reduce 255 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (255) ~ (all_0_14_14 = e2)
% 12.38/3.51 | (338) all_0_14_14 = e1 | all_0_14_14 = e0
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (338), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (339) all_0_14_14 = e1
% 12.38/3.51 |
% 12.38/3.51 | Equations (339) can reduce 255 to:
% 12.38/3.51 | (329) ~ (e2 = e1)
% 12.38/3.51 |
% 12.38/3.51 | Simplifying 329 yields:
% 12.38/3.51 | (71) ~ (e2 = e1)
% 12.38/3.51 |
% 12.38/3.51 | Equations (339) can reduce 550 to:
% 12.38/3.51 | (181) ~ (e1 = e0)
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (155), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (226) all_0_9_9 = e3
% 12.38/3.51 |
% 12.38/3.51 | Equations (226) can reduce 212 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (212) ~ (all_0_9_9 = e3)
% 12.38/3.51 | (229) all_0_10_10 = e3 | all_0_11_11 = e3
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (229), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (230) all_0_10_10 = e3
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (86), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (366) all_0_8_8 = e1
% 12.38/3.51 |
% 12.38/3.51 | Combining equations (366,196) yields a new equation:
% 12.38/3.51 | (367) e2 = e1
% 12.38/3.51 |
% 12.38/3.51 | Equations (367) can reduce 71 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (193) ~ (all_0_8_8 = e1)
% 12.38/3.51 | (1492) all_0_12_12 = e1 | all_0_16_16 = e1 | all_0_20_20 = e1
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (1492), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (730) all_0_12_12 = e1
% 12.38/3.51 |
% 12.38/3.51 | Combining equations (500,730) yields a new equation:
% 12.38/3.51 | (421) e1 = e0
% 12.38/3.51 |
% 12.38/3.51 | Equations (421) can reduce 181 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (317) ~ (all_0_12_12 = e1)
% 12.38/3.51 | (1497) all_0_16_16 = e1 | all_0_20_20 = e1
% 12.38/3.51 |
% 12.38/3.51 +-Applying beta-rule and splitting (1497), into two cases.
% 12.38/3.51 |-Branch one:
% 12.38/3.51 | (328) all_0_16_16 = e1
% 12.38/3.51 |
% 12.38/3.51 | Equations (328) can reduce 413 to:
% 12.38/3.51 | (202) $false
% 12.38/3.51 |
% 12.38/3.51 |-The branch is then unsatisfiable
% 12.38/3.51 |-Branch two:
% 12.38/3.51 | (413) ~ (all_0_16_16 = e1)
% 12.38/3.51 | (1501) all_0_20_20 = e1
% 12.38/3.52 |
% 12.38/3.52 | Equations (1501) can reduce 134 to:
% 12.38/3.52 | (413) ~ (all_0_16_16 = e1)
% 12.38/3.52 |
% 12.38/3.52 | Equations (1501) can reduce 529 to:
% 12.38/3.52 | (329) ~ (e2 = e1)
% 12.38/3.52 |
% 12.38/3.52 | Simplifying 329 yields:
% 12.38/3.52 | (71) ~ (e2 = e1)
% 12.38/3.52 |
% 12.38/3.52 +-Applying beta-rule and splitting (7), into two cases.
% 12.38/3.52 |-Branch one:
% 12.38/3.52 | (427) all_0_16_16 = e3
% 12.38/3.52 |
% 12.38/3.52 | Equations (427) can reduce 58 to:
% 12.38/3.52 | (954) ~ (all_0_17_17 = e3)
% 12.38/3.52 |
% 12.38/3.52 | Simplifying 954 yields:
% 12.38/3.52 | (451) ~ (all_0_17_17 = e3)
% 12.38/3.52 |
% 12.38/3.52 | Equations (427) can reduce 256 to:
% 12.38/3.52 | (101) ~ (e3 = e2)
% 12.38/3.52 |
% 12.38/3.52 +-Applying beta-rule and splitting (114), into two cases.
% 12.38/3.52 |-Branch one:
% 12.74/3.52 | (1000) all_0_10_10 = e2
% 12.74/3.52 |
% 12.74/3.52 | Combining equations (1000,230) yields a new equation:
% 12.74/3.52 | (373) e3 = e2
% 12.74/3.52 |
% 12.74/3.52 | Equations (373) can reduce 101 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (1004) ~ (all_0_10_10 = e2)
% 12.74/3.52 | (1005) all_0_14_14 = e2 | all_0_18_18 = e2 | all_0_22_22 = e2
% 12.74/3.52 |
% 12.74/3.52 +-Applying beta-rule and splitting (1005), into two cases.
% 12.74/3.52 |-Branch one:
% 12.74/3.52 | (264) all_0_14_14 = e2
% 12.74/3.52 |
% 12.74/3.52 | Combining equations (339,264) yields a new equation:
% 12.74/3.52 | (367) e2 = e1
% 12.74/3.52 |
% 12.74/3.52 | Equations (367) can reduce 71 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (255) ~ (all_0_14_14 = e2)
% 12.74/3.52 | (1011) all_0_18_18 = e2 | all_0_22_22 = e2
% 12.74/3.52 |
% 12.74/3.52 +-Applying beta-rule and splitting (1011), into two cases.
% 12.74/3.52 |-Branch one:
% 12.74/3.52 | (254) all_0_18_18 = e2
% 12.74/3.52 |
% 12.74/3.52 | Equations (254) can reduce 17 to:
% 12.74/3.52 | (375) ~ (all_0_17_17 = e2)
% 12.74/3.52 |
% 12.74/3.52 | From (254) and (164) follows:
% 12.74/3.52 | (1521) op(e1, e2) = all_0_3_3
% 12.74/3.52 |
% 12.74/3.52 +-Applying beta-rule and splitting (83), into two cases.
% 12.74/3.52 |-Branch one:
% 12.74/3.52 | (295) all_0_17_17 = e3
% 12.74/3.52 |
% 12.74/3.52 | Equations (295) can reduce 451 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (451) ~ (all_0_17_17 = e3)
% 12.74/3.52 | (452) all_0_17_17 = e2 | all_0_17_17 = e1 | all_0_17_17 = e0
% 12.74/3.52 |
% 12.74/3.52 +-Applying beta-rule and splitting (452), into two cases.
% 12.74/3.52 |-Branch one:
% 12.74/3.52 | (371) all_0_17_17 = e2
% 12.74/3.52 |
% 12.74/3.52 | Equations (371) can reduce 375 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (375) ~ (all_0_17_17 = e2)
% 12.74/3.52 | (536) all_0_17_17 = e1 | all_0_17_17 = e0
% 12.74/3.52 |
% 12.74/3.52 +-Applying beta-rule and splitting (536), into two cases.
% 12.74/3.52 |-Branch one:
% 12.74/3.52 | (415) all_0_17_17 = e1
% 12.74/3.52 |
% 12.74/3.52 | Equations (415) can reduce 208 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (208) ~ (all_0_17_17 = e1)
% 12.74/3.52 | (540) all_0_17_17 = e0
% 12.74/3.52 |
% 12.74/3.52 | Equations (540) can reduce 109 to:
% 12.74/3.52 | (494) ~ (all_0_9_9 = e0)
% 12.74/3.52 |
% 12.74/3.52 | From (540) and (92) follows:
% 12.74/3.52 | (1535) op(e1, e2) = e0
% 12.74/3.52 |
% 12.74/3.52 +-Applying beta-rule and splitting (391), into two cases.
% 12.74/3.52 |-Branch one:
% 12.74/3.52 | (380) all_0_9_9 = e1
% 12.74/3.52 |
% 12.74/3.52 | Combining equations (380,1437) yields a new equation:
% 12.74/3.52 | (1313) all_0_7_7 = e1
% 12.74/3.52 |
% 12.74/3.52 | From (380) and (1438) follows:
% 12.74/3.52 | (1538) op(e1, e2) = all_0_6_6
% 12.74/3.52 |
% 12.74/3.52 +-Applying beta-rule and splitting (56), into two cases.
% 12.74/3.52 |-Branch one:
% 12.74/3.52 | (1539) ~ (all_0_6_6 = e0)
% 12.74/3.52 |
% 12.74/3.52 | Instantiating formula (53) with e1, e2, all_0_6_6, all_0_3_3 and discharging atoms op(e1, e2) = all_0_3_3, op(e1, e2) = all_0_6_6, yields:
% 12.74/3.52 | (1325) all_0_3_3 = all_0_6_6
% 12.74/3.52 |
% 12.74/3.52 | Instantiating formula (53) with e1, e2, e0, all_0_3_3 and discharging atoms op(e1, e2) = all_0_3_3, op(e1, e2) = e0, yields:
% 12.74/3.52 | (1541) all_0_3_3 = e0
% 12.74/3.52 |
% 12.74/3.52 | Combining equations (1325,1541) yields a new equation:
% 12.74/3.52 | (1542) all_0_6_6 = e0
% 12.74/3.52 |
% 12.74/3.52 | Simplifying 1542 yields:
% 12.74/3.52 | (1543) all_0_6_6 = e0
% 12.74/3.52 |
% 12.74/3.52 | Equations (1543) can reduce 1539 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (1543) all_0_6_6 = e0
% 12.74/3.52 | (1546) ~ (all_0_7_7 = e1) | ~ (all_0_8_8 = e2)
% 12.74/3.52 |
% 12.74/3.52 +-Applying beta-rule and splitting (1546), into two cases.
% 12.74/3.52 |-Branch one:
% 12.74/3.52 | (1332) ~ (all_0_7_7 = e1)
% 12.74/3.52 |
% 12.74/3.52 | Equations (1313) can reduce 1332 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (1313) all_0_7_7 = e1
% 12.74/3.52 | (201) ~ (all_0_8_8 = e2)
% 12.74/3.52 |
% 12.74/3.52 | Equations (196) can reduce 201 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (316) ~ (all_0_9_9 = e1)
% 12.74/3.52 | (395) all_0_9_9 = e0
% 12.74/3.52 |
% 12.74/3.52 | Equations (395) can reduce 494 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (555) ~ (all_0_18_18 = e2)
% 12.74/3.52 | (439) all_0_22_22 = e2
% 12.74/3.52 |
% 12.74/3.52 | Combining equations (446,439) yields a new equation:
% 12.74/3.52 | (284) e2 = e0
% 12.74/3.52 |
% 12.74/3.52 | Equations (284) can reduce 13 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (298) ~ (all_0_16_16 = e3)
% 12.74/3.52 | (430) all_0_16_16 = e2 | all_0_16_16 = e1 | all_0_16_16 = e0
% 12.74/3.52 |
% 12.74/3.52 +-Applying beta-rule and splitting (430), into two cases.
% 12.74/3.52 |-Branch one:
% 12.74/3.52 | (785) all_0_16_16 = e2
% 12.74/3.52 |
% 12.74/3.52 | Equations (785) can reduce 256 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (256) ~ (all_0_16_16 = e2)
% 12.74/3.52 | (788) all_0_16_16 = e1 | all_0_16_16 = e0
% 12.74/3.52 |
% 12.74/3.52 +-Applying beta-rule and splitting (788), into two cases.
% 12.74/3.52 |-Branch one:
% 12.74/3.52 | (328) all_0_16_16 = e1
% 12.74/3.52 |
% 12.74/3.52 | Equations (328) can reduce 413 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (413) ~ (all_0_16_16 = e1)
% 12.74/3.52 | (792) all_0_16_16 = e0
% 12.74/3.52 |
% 12.74/3.52 | Equations (792) can reduce 611 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (225) ~ (all_0_10_10 = e3)
% 12.74/3.52 | (233) all_0_11_11 = e3
% 12.74/3.52 |
% 12.74/3.52 | Combining equations (233,276) yields a new equation:
% 12.74/3.52 | (277) e3 = e0
% 12.74/3.52 |
% 12.74/3.52 | Simplifying 277 yields:
% 12.74/3.52 | (278) e3 = e0
% 12.74/3.52 |
% 12.74/3.52 | Equations (278) can reduce 136 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (319) ~ (all_0_14_14 = e1)
% 12.74/3.52 | (342) all_0_14_14 = e0
% 12.74/3.52 |
% 12.74/3.52 | Equations (342) can reduce 550 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (214) ~ (all_0_12_12 = e0)
% 12.74/3.52 | (503) all_0_13_13 = e0 | all_0_14_14 = e0 | all_0_15_15 = e0
% 12.74/3.52 |
% 12.74/3.52 +-Applying beta-rule and splitting (20), into two cases.
% 12.74/3.52 |-Branch one:
% 12.74/3.52 | (839) all_0_8_8 = e0
% 12.74/3.52 |
% 12.74/3.52 | Combining equations (196,839) yields a new equation:
% 12.74/3.52 | (283) e2 = e0
% 12.74/3.52 |
% 12.74/3.52 | Simplifying 283 yields:
% 12.74/3.52 | (284) e2 = e0
% 12.74/3.52 |
% 12.74/3.52 | Equations (284) can reduce 13 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (195) ~ (all_0_8_8 = e0)
% 12.74/3.52 | (1585) all_0_12_12 = e0 | all_0_16_16 = e0 | all_0_20_20 = e0
% 12.74/3.52 |
% 12.74/3.52 | Equations (196) can reduce 195 to:
% 12.74/3.52 | (13) ~ (e2 = e0)
% 12.74/3.52 |
% 12.74/3.52 +-Applying beta-rule and splitting (503), into two cases.
% 12.74/3.52 |-Branch one:
% 12.74/3.52 | (449) all_0_13_13 = e0
% 12.74/3.52 |
% 12.74/3.52 | Combining equations (311,449) yields a new equation:
% 12.74/3.52 | (277) e3 = e0
% 12.74/3.52 |
% 12.74/3.52 | Simplifying 277 yields:
% 12.74/3.52 | (278) e3 = e0
% 12.74/3.52 |
% 12.74/3.52 | Equations (278) can reduce 136 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (249) ~ (all_0_13_13 = e0)
% 12.74/3.52 | (507) all_0_14_14 = e0 | all_0_15_15 = e0
% 12.74/3.52 |
% 12.74/3.52 +-Applying beta-rule and splitting (507), into two cases.
% 12.74/3.52 |-Branch one:
% 12.74/3.52 | (342) all_0_14_14 = e0
% 12.74/3.52 |
% 12.74/3.52 | Equations (342) can reduce 550 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (550) ~ (all_0_14_14 = e0)
% 12.74/3.52 | (282) all_0_15_15 = e0
% 12.74/3.52 |
% 12.74/3.52 | Combining equations (267,282) yields a new equation:
% 12.74/3.52 | (283) e2 = e0
% 12.74/3.52 |
% 12.74/3.52 | Simplifying 283 yields:
% 12.74/3.52 | (284) e2 = e0
% 12.74/3.52 |
% 12.74/3.52 | Equations (284) can reduce 13 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (280) ~ (all_0_11_11 = e0)
% 12.74/3.52 | (281) all_0_15_15 = e0 | all_0_19_19 = e0
% 12.74/3.52 |
% 12.74/3.52 +-Applying beta-rule and splitting (95), into two cases.
% 12.74/3.52 |-Branch one:
% 12.74/3.52 | (331) all_0_14_14 = e3
% 12.74/3.52 |
% 12.74/3.52 | Equations (331) can reduce 325 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (325) ~ (all_0_14_14 = e3)
% 12.74/3.52 | (334) all_0_14_14 = e2 | all_0_14_14 = e1 | all_0_14_14 = e0
% 12.74/3.52 |
% 12.74/3.52 +-Applying beta-rule and splitting (334), into two cases.
% 12.74/3.52 |-Branch one:
% 12.74/3.52 | (264) all_0_14_14 = e2
% 12.74/3.52 |
% 12.74/3.52 | Equations (264) can reduce 255 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (255) ~ (all_0_14_14 = e2)
% 12.74/3.52 | (338) all_0_14_14 = e1 | all_0_14_14 = e0
% 12.74/3.52 |
% 12.74/3.52 +-Applying beta-rule and splitting (338), into two cases.
% 12.74/3.52 |-Branch one:
% 12.74/3.52 | (339) all_0_14_14 = e1
% 12.74/3.52 |
% 12.74/3.52 | Equations (339) can reduce 550 to:
% 12.74/3.52 | (181) ~ (e1 = e0)
% 12.74/3.52 |
% 12.74/3.52 +-Applying beta-rule and splitting (281), into two cases.
% 12.74/3.52 |-Branch one:
% 12.74/3.52 | (282) all_0_15_15 = e0
% 12.74/3.52 |
% 12.74/3.52 | Combining equations (267,282) yields a new equation:
% 12.74/3.52 | (283) e2 = e0
% 12.74/3.52 |
% 12.74/3.52 | Simplifying 283 yields:
% 12.74/3.52 | (284) e2 = e0
% 12.74/3.52 |
% 12.74/3.52 | Equations (284) can reduce 13 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (286) ~ (all_0_15_15 = e0)
% 12.74/3.52 | (287) all_0_19_19 = e0
% 12.74/3.52 |
% 12.74/3.52 | Combining equations (287,420) yields a new equation:
% 12.74/3.52 | (421) e1 = e0
% 12.74/3.52 |
% 12.74/3.52 | Equations (421) can reduce 181 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (319) ~ (all_0_14_14 = e1)
% 12.74/3.52 | (342) all_0_14_14 = e0
% 12.74/3.52 |
% 12.74/3.52 | Equations (342) can reduce 550 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (576) ~ (all_0_15_15 = e2)
% 12.74/3.52 | (1128) all_0_19_19 = e2 | all_0_23_23 = e2
% 12.74/3.52 |
% 12.74/3.52 +-Applying beta-rule and splitting (1128), into two cases.
% 12.74/3.52 |-Branch one:
% 12.74/3.52 | (709) all_0_19_19 = e2
% 12.74/3.52 |
% 12.74/3.52 | Combining equations (709,420) yields a new equation:
% 12.74/3.52 | (767) e2 = e1
% 12.74/3.52 |
% 12.74/3.52 | Simplifying 767 yields:
% 12.74/3.52 | (367) e2 = e1
% 12.74/3.52 |
% 12.74/3.52 | Equations (367) can reduce 71 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (271) ~ (all_0_19_19 = e2)
% 12.74/3.52 | (305) all_0_23_23 = e2
% 12.74/3.52 |
% 12.74/3.52 | Combining equations (301,305) yields a new equation:
% 12.74/3.52 | (372) e3 = e2
% 12.74/3.52 |
% 12.74/3.52 | Simplifying 372 yields:
% 12.74/3.52 | (373) e3 = e2
% 12.74/3.52 |
% 12.74/3.52 | Equations (373) can reduce 101 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (223) ~ (all_0_23_23 = e3)
% 12.74/3.52 | (304) all_0_23_23 = e2 | all_0_23_23 = e1
% 12.74/3.52 |
% 12.74/3.52 +-Applying beta-rule and splitting (304), into two cases.
% 12.74/3.52 |-Branch one:
% 12.74/3.52 | (305) all_0_23_23 = e2
% 12.74/3.52 |
% 12.74/3.52 | Equations (305) can reduce 173 to:
% 12.74/3.52 | (576) ~ (all_0_15_15 = e2)
% 12.74/3.52 |
% 12.74/3.52 | Equations (305) can reduce 192 to:
% 12.74/3.52 | (542) ~ (all_0_21_21 = e2)
% 12.74/3.52 |
% 12.74/3.52 | From (305) and (43) follows:
% 12.74/3.52 | (1639) op(e0, e2) = all_0_1_1
% 12.74/3.52 |
% 12.74/3.52 +-Applying beta-rule and splitting (126), into two cases.
% 12.74/3.52 |-Branch one:
% 12.74/3.52 | (665) all_0_15_15 = e3
% 12.74/3.52 |
% 12.74/3.52 | Equations (665) can reduce 237 to:
% 12.74/3.52 | (202) $false
% 12.74/3.52 |
% 12.74/3.52 |-The branch is then unsatisfiable
% 12.74/3.52 |-Branch two:
% 12.74/3.52 | (237) ~ (all_0_15_15 = e3)
% 12.74/3.53 | (668) all_0_15_15 = e2 | all_0_15_15 = e1 | all_0_15_15 = e0
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (668), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (267) all_0_15_15 = e2
% 12.74/3.53 |
% 12.74/3.53 | Equations (267) can reduce 576 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (576) ~ (all_0_15_15 = e2)
% 12.74/3.53 | (708) all_0_15_15 = e1 | all_0_15_15 = e0
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (708), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (677) all_0_15_15 = e1
% 12.74/3.53 |
% 12.74/3.53 | Equations (677) can reduce 693 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (693) ~ (all_0_15_15 = e1)
% 12.74/3.53 | (282) all_0_15_15 = e0
% 12.74/3.53 |
% 12.74/3.53 | Equations (282) can reduce 50 to:
% 12.74/3.53 | (280) ~ (all_0_11_11 = e0)
% 12.74/3.53 |
% 12.74/3.53 | Equations (282) can reduce 576 to:
% 12.74/3.53 | (293) ~ (e2 = e0)
% 12.74/3.53 |
% 12.74/3.53 | Simplifying 293 yields:
% 12.74/3.53 | (13) ~ (e2 = e0)
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (48), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (839) all_0_8_8 = e0
% 12.74/3.53 |
% 12.74/3.53 | Combining equations (196,839) yields a new equation:
% 12.74/3.53 | (283) e2 = e0
% 12.74/3.53 |
% 12.74/3.53 | Simplifying 283 yields:
% 12.74/3.53 | (284) e2 = e0
% 12.74/3.53 |
% 12.74/3.53 | Equations (284) can reduce 13 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (195) ~ (all_0_8_8 = e0)
% 12.74/3.53 | (1660) all_0_9_9 = e0 | all_0_10_10 = e0 | all_0_11_11 = e0
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (1660), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (395) all_0_9_9 = e0
% 12.74/3.53 |
% 12.74/3.53 | Combining equations (395,1437) yields a new equation:
% 12.74/3.53 | (1662) all_0_7_7 = e0
% 12.74/3.53 |
% 12.74/3.53 | Equations (395) can reduce 118 to:
% 12.74/3.53 | (1663) ~ (all_0_21_21 = e0)
% 12.74/3.53 |
% 12.74/3.53 | Simplifying 1663 yields:
% 12.74/3.53 | (204) ~ (all_0_21_21 = e0)
% 12.74/3.53 |
% 12.74/3.53 | From (395) and (1438) follows:
% 12.74/3.53 | (1665) op(e0, e2) = all_0_6_6
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (111), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (1666) all_0_21_21 = e3
% 12.74/3.53 |
% 12.74/3.53 | Equations (1666) can reduce 300 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (300) ~ (all_0_21_21 = e3)
% 12.74/3.53 | (1669) all_0_21_21 = e2 | all_0_21_21 = e1 | all_0_21_21 = e0
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (1669), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (376) all_0_21_21 = e2
% 12.74/3.53 |
% 12.74/3.53 | Equations (376) can reduce 542 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (542) ~ (all_0_21_21 = e2)
% 12.74/3.53 | (1673) all_0_21_21 = e1 | all_0_21_21 = e0
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (1673), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (1674) all_0_21_21 = e1
% 12.74/3.53 |
% 12.74/3.53 | From (1674) and (59) follows:
% 12.74/3.53 | (1675) op(e0, e2) = e1
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (29), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (1676) ~ (all_0_6_6 = e1)
% 12.74/3.53 |
% 12.74/3.53 | Instantiating formula (53) with e0, e2, all_0_6_6, all_0_1_1 and discharging atoms op(e0, e2) = all_0_1_1, op(e0, e2) = all_0_6_6, yields:
% 12.74/3.53 | (1677) all_0_1_1 = all_0_6_6
% 12.74/3.53 |
% 12.74/3.53 | Instantiating formula (53) with e0, e2, e1, all_0_1_1 and discharging atoms op(e0, e2) = all_0_1_1, op(e0, e2) = e1, yields:
% 12.74/3.53 | (1678) all_0_1_1 = e1
% 12.74/3.53 |
% 12.74/3.53 | Combining equations (1678,1677) yields a new equation:
% 12.74/3.53 | (1679) all_0_6_6 = e1
% 12.74/3.53 |
% 12.74/3.53 | Equations (1679) can reduce 1676 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (1679) all_0_6_6 = e1
% 12.74/3.53 | (1682) ~ (all_0_7_7 = e0) | ~ (all_0_8_8 = e2)
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (1682), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (1683) ~ (all_0_7_7 = e0)
% 12.74/3.53 |
% 12.74/3.53 | Equations (1662) can reduce 1683 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (1662) all_0_7_7 = e0
% 12.74/3.53 | (201) ~ (all_0_8_8 = e2)
% 12.74/3.53 |
% 12.74/3.53 | Equations (196) can reduce 201 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (1688) ~ (all_0_21_21 = e1)
% 12.74/3.53 | (829) all_0_21_21 = e0
% 12.74/3.53 |
% 12.74/3.53 | Equations (829) can reduce 204 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (494) ~ (all_0_9_9 = e0)
% 12.74/3.53 | (1692) all_0_10_10 = e0 | all_0_11_11 = e0
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (1692), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (598) all_0_10_10 = e0
% 12.74/3.53 |
% 12.74/3.53 | Equations (598) can reduce 602 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (602) ~ (all_0_10_10 = e0)
% 12.74/3.53 | (276) all_0_11_11 = e0
% 12.74/3.53 |
% 12.74/3.53 | Equations (276) can reduce 280 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (273) ~ (all_0_23_23 = e2)
% 12.74/3.53 | (308) all_0_23_23 = e1
% 12.74/3.53 |
% 12.74/3.53 | Equations (308) can reduce 570 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (219) ~ (all_0_13_13 = e3)
% 12.74/3.53 | (314) all_0_13_13 = e1 | all_0_13_13 = e0
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (314), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (315) all_0_13_13 = e1
% 12.74/3.53 |
% 12.74/3.53 | Equations (315) can reduce 358 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (358) ~ (all_0_13_13 = e1)
% 12.74/3.53 | (449) all_0_13_13 = e0
% 12.74/3.53 |
% 12.74/3.53 | Equations (449) can reduce 249 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (201) ~ (all_0_8_8 = e2)
% 12.74/3.53 | (835) all_0_8_8 = e1 | all_0_8_8 = e0
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (835), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (366) all_0_8_8 = e1
% 12.74/3.53 |
% 12.74/3.53 | Equations (366) can reduce 193 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (193) ~ (all_0_8_8 = e1)
% 12.74/3.53 | (839) all_0_8_8 = e0
% 12.74/3.53 |
% 12.74/3.53 | Equations (839) can reduce 195 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (839) all_0_8_8 = e0
% 12.74/3.53 | (622) ~ (all_0_19_19 = e1)
% 12.74/3.53 |
% 12.74/3.53 | Equations (420) can reduce 622 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (449) all_0_13_13 = e0
% 12.74/3.53 | (622) ~ (all_0_19_19 = e1)
% 12.74/3.53 |
% 12.74/3.53 | Equations (420) can reduce 622 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (328) all_0_16_16 = e1
% 12.74/3.53 | (224) ~ (all_0_18_18 = e3)
% 12.74/3.53 |
% 12.74/3.53 | Equations (328) can reduce 179 to:
% 12.74/3.53 | (193) ~ (all_0_8_8 = e1)
% 12.74/3.53 |
% 12.74/3.53 | Equations (328) can reduce 76 to:
% 12.74/3.53 | (317) ~ (all_0_12_12 = e1)
% 12.74/3.53 |
% 12.74/3.53 | Equations (328) can reduce 39 to:
% 12.74/3.53 | (1725) ~ (all_0_18_18 = e1)
% 12.74/3.53 |
% 12.74/3.53 | Simplifying 1725 yields:
% 12.74/3.53 | (25) ~ (all_0_18_18 = e1)
% 12.74/3.53 |
% 12.74/3.53 | Equations (328) can reduce 134 to:
% 12.74/3.53 | (1727) ~ (all_0_20_20 = e1)
% 12.74/3.53 |
% 12.74/3.53 | Simplifying 1727 yields:
% 12.74/3.53 | (920) ~ (all_0_20_20 = e1)
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (18), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (1501) all_0_20_20 = e1
% 12.74/3.53 |
% 12.74/3.53 | Equations (1501) can reduce 920 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (920) ~ (all_0_20_20 = e1)
% 12.74/3.53 | (1732) all_0_21_21 = e1 | all_0_22_22 = e1 | all_0_23_23 = e1
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (55), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (219) ~ (all_0_13_13 = e3)
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (1732), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (1674) all_0_21_21 = e1
% 12.74/3.53 |
% 12.74/3.53 | Equations (1674) can reduce 96 to:
% 12.74/3.53 | (358) ~ (all_0_13_13 = e1)
% 12.74/3.53 |
% 12.74/3.53 | Equations (1674) can reduce 64 to:
% 12.74/3.53 | (208) ~ (all_0_17_17 = e1)
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (36), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (413) ~ (all_0_16_16 = e1)
% 12.74/3.53 |
% 12.74/3.53 | Equations (328) can reduce 413 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (328) all_0_16_16 = e1
% 12.74/3.53 | (223) ~ (all_0_23_23 = e3)
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (125), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (434) all_0_20_20 = e3
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (121), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (250) all_0_18_18 = e3
% 12.74/3.53 |
% 12.74/3.53 | Equations (250) can reduce 224 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (224) ~ (all_0_18_18 = e3)
% 12.74/3.53 | (253) all_0_18_18 = e2 | all_0_18_18 = e0
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (253), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (254) all_0_18_18 = e2
% 12.74/3.53 |
% 12.74/3.53 | Equations (254) can reduce 34 to:
% 12.74/3.53 | (255) ~ (all_0_14_14 = e2)
% 12.74/3.53 |
% 12.74/3.53 | Equations (254) can reduce 17 to:
% 12.74/3.53 | (375) ~ (all_0_17_17 = e2)
% 12.74/3.53 |
% 12.74/3.53 | Equations (254) can reduce 224 to:
% 12.74/3.53 | (274) ~ (e3 = e2)
% 12.74/3.53 |
% 12.74/3.53 | Simplifying 274 yields:
% 12.74/3.53 | (101) ~ (e3 = e2)
% 12.74/3.53 |
% 12.74/3.53 | Equations (254) can reduce 25 to:
% 12.74/3.53 | (71) ~ (e2 = e1)
% 12.74/3.53 |
% 12.74/3.53 | Equations (254) can reduce 245 to:
% 12.74/3.53 | (13) ~ (e2 = e0)
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (148), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (526) all_0_20_20 = e2
% 12.74/3.53 |
% 12.74/3.53 | Combining equations (434,526) yields a new equation:
% 12.74/3.53 | (372) e3 = e2
% 12.74/3.53 |
% 12.74/3.53 | Simplifying 372 yields:
% 12.74/3.53 | (373) e3 = e2
% 12.74/3.53 |
% 12.74/3.53 | Equations (373) can reduce 101 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (529) ~ (all_0_20_20 = e2)
% 12.74/3.53 | (530) all_0_21_21 = e2 | all_0_22_22 = e2 | all_0_23_23 = e2
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (530), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (376) all_0_21_21 = e2
% 12.74/3.53 |
% 12.74/3.53 | Combining equations (376,1674) yields a new equation:
% 12.74/3.53 | (767) e2 = e1
% 12.74/3.53 |
% 12.74/3.53 | Simplifying 767 yields:
% 12.74/3.53 | (367) e2 = e1
% 12.74/3.53 |
% 12.74/3.53 | Equations (367) can reduce 71 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (542) ~ (all_0_21_21 = e2)
% 12.74/3.53 | (543) all_0_22_22 = e2 | all_0_23_23 = e2
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (543), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (439) all_0_22_22 = e2
% 12.74/3.53 |
% 12.74/3.53 | Combining equations (439,446) yields a new equation:
% 12.74/3.53 | (283) e2 = e0
% 12.74/3.53 |
% 12.74/3.53 | Simplifying 283 yields:
% 12.74/3.53 | (284) e2 = e0
% 12.74/3.53 |
% 12.74/3.53 | Equations (284) can reduce 13 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (258) ~ (all_0_22_22 = e2)
% 12.74/3.53 | (305) all_0_23_23 = e2
% 12.74/3.53 |
% 12.74/3.53 | Equations (305) can reduce 173 to:
% 12.74/3.53 | (576) ~ (all_0_15_15 = e2)
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (74), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (260) all_0_12_12 = e2
% 12.74/3.53 |
% 12.74/3.53 | Equations (260) can reduce 2 to:
% 12.74/3.53 | (201) ~ (all_0_8_8 = e2)
% 12.74/3.53 |
% 12.74/3.53 | Equations (260) can reduce 317 to:
% 12.74/3.53 | (71) ~ (e2 = e1)
% 12.74/3.53 |
% 12.74/3.53 +-Applying beta-rule and splitting (97), into two cases.
% 12.74/3.53 |-Branch one:
% 12.74/3.53 | (196) all_0_8_8 = e2
% 12.74/3.53 |
% 12.74/3.53 | Equations (196) can reduce 201 to:
% 12.74/3.53 | (202) $false
% 12.74/3.53 |
% 12.74/3.53 |-The branch is then unsatisfiable
% 12.74/3.53 |-Branch two:
% 12.74/3.53 | (201) ~ (all_0_8_8 = e2)
% 12.74/3.53 | (835) all_0_8_8 = e1 | all_0_8_8 = e0
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (835), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (366) all_0_8_8 = e1
% 12.74/3.54 |
% 12.74/3.54 | Equations (366) can reduce 193 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (193) ~ (all_0_8_8 = e1)
% 12.74/3.54 | (839) all_0_8_8 = e0
% 12.74/3.54 |
% 12.74/3.54 | Equations (839) can reduce 24 to:
% 12.74/3.54 | (843) ~ (all_0_11_11 = e0)
% 12.74/3.54 |
% 12.74/3.54 | Simplifying 843 yields:
% 12.74/3.54 | (280) ~ (all_0_11_11 = e0)
% 12.74/3.54 |
% 12.74/3.54 | From (839) and (157) follows:
% 12.74/3.54 | (850) op(e3, e0) = all_0_7_7
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (113), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (311) all_0_13_13 = e3
% 12.74/3.54 |
% 12.74/3.54 | Equations (311) can reduce 219 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (219) ~ (all_0_13_13 = e3)
% 12.74/3.54 | (314) all_0_13_13 = e1 | all_0_13_13 = e0
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (144), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (362) all_0_9_9 = e2
% 12.74/3.54 |
% 12.74/3.54 | Equations (362) can reduce 145 to:
% 12.74/3.54 | (1214) ~ (all_0_11_11 = e2)
% 12.74/3.54 |
% 12.74/3.54 | Simplifying 1214 yields:
% 12.74/3.54 | (1113) ~ (all_0_11_11 = e2)
% 12.74/3.54 |
% 12.74/3.54 | Equations (362) can reduce 109 to:
% 12.74/3.54 | (1793) ~ (all_0_17_17 = e2)
% 12.74/3.54 |
% 12.74/3.54 | Simplifying 1793 yields:
% 12.74/3.54 | (375) ~ (all_0_17_17 = e2)
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (314), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (315) all_0_13_13 = e1
% 12.74/3.54 |
% 12.74/3.54 | Equations (315) can reduce 358 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (358) ~ (all_0_13_13 = e1)
% 12.74/3.54 | (449) all_0_13_13 = e0
% 12.74/3.54 |
% 12.74/3.54 | Equations (449) can reduce 98 to:
% 12.74/3.54 | (628) ~ (all_0_15_15 = e0)
% 12.74/3.54 |
% 12.74/3.54 | Simplifying 628 yields:
% 12.74/3.54 | (286) ~ (all_0_15_15 = e0)
% 12.74/3.54 |
% 12.74/3.54 | From (449) and (8) follows:
% 12.74/3.54 | (630) op(all_0_5_5, e0) = all_0_4_4
% 12.74/3.54 |
% 12.74/3.54 | From (449) and (102) follows:
% 12.74/3.54 | (631) op(e2, e0) = all_0_5_5
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (147), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (276) all_0_11_11 = e0
% 12.74/3.54 |
% 12.74/3.54 | Equations (276) can reduce 280 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (280) ~ (all_0_11_11 = e0)
% 12.74/3.54 | (281) all_0_15_15 = e0 | all_0_19_19 = e0
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (83), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (295) all_0_17_17 = e3
% 12.74/3.54 |
% 12.74/3.54 | Equations (295) can reduce 120 to:
% 12.74/3.54 | (238) ~ (all_0_19_19 = e3)
% 12.74/3.54 |
% 12.74/3.54 | Simplifying 238 yields:
% 12.74/3.54 | (239) ~ (all_0_19_19 = e3)
% 12.74/3.54 |
% 12.74/3.54 | Equations (295) can reduce 375 to:
% 12.74/3.54 | (101) ~ (e3 = e2)
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (281), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (282) all_0_15_15 = e0
% 12.74/3.54 |
% 12.74/3.54 | Equations (282) can reduce 286 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (286) ~ (all_0_15_15 = e0)
% 12.74/3.54 | (287) all_0_19_19 = e0
% 12.74/3.54 |
% 12.74/3.54 | Equations (287) can reduce 171 to:
% 12.74/3.54 | (280) ~ (all_0_11_11 = e0)
% 12.74/3.54 |
% 12.74/3.54 | Equations (287) can reduce 239 to:
% 12.74/3.54 | (291) ~ (e3 = e0)
% 12.74/3.54 |
% 12.74/3.54 | Simplifying 291 yields:
% 12.74/3.54 | (136) ~ (e3 = e0)
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (38), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (242) ~ (all_0_11_11 = e3)
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (84), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (233) all_0_11_11 = e3
% 12.74/3.54 |
% 12.74/3.54 | Equations (233) can reduce 242 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (242) ~ (all_0_11_11 = e3)
% 12.74/3.54 | (1822) all_0_11_11 = e2 | all_0_11_11 = e1 | all_0_11_11 = e0
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (165), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (233) all_0_11_11 = e3
% 12.74/3.54 |
% 12.74/3.54 | Equations (233) can reduce 242 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (242) ~ (all_0_11_11 = e3)
% 12.74/3.54 | (748) all_0_15_15 = e3 | all_0_19_19 = e3 | all_0_23_23 = e3
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (748), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (665) all_0_15_15 = e3
% 12.74/3.54 |
% 12.74/3.54 | From (665) and (103) follows:
% 12.74/3.54 | (1828) op(e2, e0) = e3
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (1822), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (981) all_0_11_11 = e2
% 12.74/3.54 |
% 12.74/3.54 | Equations (981) can reduce 1113 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (1113) ~ (all_0_11_11 = e2)
% 12.74/3.54 | (1832) all_0_11_11 = e1 | all_0_11_11 = e0
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (1832), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (672) all_0_11_11 = e1
% 12.74/3.54 |
% 12.74/3.54 | From (672) and (106) follows:
% 12.74/3.54 | (1834) op(e3, e0) = e1
% 12.74/3.54 |
% 12.74/3.54 | Instantiating formula (53) with e3, e0, e1, all_0_7_7 and discharging atoms op(e3, e0) = all_0_7_7, op(e3, e0) = e1, yields:
% 12.74/3.54 | (1313) all_0_7_7 = e1
% 12.74/3.54 |
% 12.74/3.54 | Instantiating formula (53) with e2, e0, e3, all_0_5_5 and discharging atoms op(e2, e0) = all_0_5_5, op(e2, e0) = e3, yields:
% 12.74/3.54 | (1836) all_0_5_5 = e3
% 12.74/3.54 |
% 12.74/3.54 | From (1836) and (630) follows:
% 12.74/3.54 | (1837) op(e3, e0) = all_0_4_4
% 12.74/3.54 |
% 12.74/3.54 | From (1313) and (850) follows:
% 12.74/3.54 | (1834) op(e3, e0) = e1
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (63), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (1839) ~ (all_0_4_4 = e1)
% 12.74/3.54 |
% 12.74/3.54 | Instantiating formula (53) with e3, e0, all_0_4_4, e1 and discharging atoms op(e3, e0) = all_0_4_4, op(e3, e0) = e1, yields:
% 12.74/3.54 | (1840) all_0_4_4 = e1
% 12.74/3.54 |
% 12.74/3.54 | Equations (1840) can reduce 1839 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (1840) all_0_4_4 = e1
% 12.74/3.54 | (1843) ~ (all_0_5_5 = e3) | ~ (all_0_13_13 = e0)
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (1843), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (1844) ~ (all_0_5_5 = e3)
% 12.74/3.54 |
% 12.74/3.54 | Equations (1836) can reduce 1844 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (1836) all_0_5_5 = e3
% 12.74/3.54 | (249) ~ (all_0_13_13 = e0)
% 12.74/3.54 |
% 12.74/3.54 | Equations (449) can reduce 249 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (675) ~ (all_0_11_11 = e1)
% 12.74/3.54 | (276) all_0_11_11 = e0
% 12.74/3.54 |
% 12.74/3.54 | Equations (276) can reduce 280 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (237) ~ (all_0_15_15 = e3)
% 12.74/3.54 | (776) all_0_19_19 = e3 | all_0_23_23 = e3
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (776), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (481) all_0_19_19 = e3
% 12.74/3.54 |
% 12.74/3.54 | Combining equations (287,481) yields a new equation:
% 12.74/3.54 | (278) e3 = e0
% 12.74/3.54 |
% 12.74/3.54 | Equations (278) can reduce 136 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (239) ~ (all_0_19_19 = e3)
% 12.74/3.54 | (301) all_0_23_23 = e3
% 12.74/3.54 |
% 12.74/3.54 | Combining equations (305,301) yields a new equation:
% 12.74/3.54 | (373) e3 = e2
% 12.74/3.54 |
% 12.74/3.54 | Equations (373) can reduce 101 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (233) all_0_11_11 = e3
% 12.74/3.54 | (249) ~ (all_0_13_13 = e0)
% 12.74/3.54 |
% 12.74/3.54 | Equations (449) can reduce 249 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (451) ~ (all_0_17_17 = e3)
% 12.74/3.54 | (452) all_0_17_17 = e2 | all_0_17_17 = e1 | all_0_17_17 = e0
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (281), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (282) all_0_15_15 = e0
% 12.74/3.54 |
% 12.74/3.54 | Equations (282) can reduce 286 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (286) ~ (all_0_15_15 = e0)
% 12.74/3.54 | (287) all_0_19_19 = e0
% 12.74/3.54 |
% 12.74/3.54 | Equations (287) can reduce 120 to:
% 12.74/3.54 | (288) ~ (all_0_17_17 = e0)
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (452), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (371) all_0_17_17 = e2
% 12.74/3.54 |
% 12.74/3.54 | Equations (371) can reduce 375 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (375) ~ (all_0_17_17 = e2)
% 12.74/3.54 | (536) all_0_17_17 = e1 | all_0_17_17 = e0
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (536), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (415) all_0_17_17 = e1
% 12.74/3.54 |
% 12.74/3.54 | Equations (415) can reduce 208 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (208) ~ (all_0_17_17 = e1)
% 12.74/3.54 | (540) all_0_17_17 = e0
% 12.74/3.54 |
% 12.74/3.54 | Equations (540) can reduce 288 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (198) ~ (all_0_9_9 = e2)
% 12.74/3.54 | (365) all_0_17_17 = e2 | all_0_21_21 = e2
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (365), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (371) all_0_17_17 = e2
% 12.74/3.54 |
% 12.74/3.54 | Equations (371) can reduce 375 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (375) ~ (all_0_17_17 = e2)
% 12.74/3.54 | (376) all_0_21_21 = e2
% 12.74/3.54 |
% 12.74/3.54 | Combining equations (1674,376) yields a new equation:
% 12.74/3.54 | (367) e2 = e1
% 12.74/3.54 |
% 12.74/3.54 | Equations (367) can reduce 71 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (200) ~ (all_0_12_12 = e2)
% 12.74/3.54 | (263) all_0_14_14 = e2 | all_0_15_15 = e2
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (263), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (264) all_0_14_14 = e2
% 12.74/3.54 |
% 12.74/3.54 | Equations (264) can reduce 255 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (255) ~ (all_0_14_14 = e2)
% 12.74/3.54 | (267) all_0_15_15 = e2
% 12.74/3.54 |
% 12.74/3.54 | Equations (267) can reduce 576 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (555) ~ (all_0_18_18 = e2)
% 12.74/3.54 | (556) all_0_18_18 = e0
% 12.74/3.54 |
% 12.74/3.54 | Equations (556) can reduce 245 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (1100) ~ (all_0_20_20 = e3)
% 12.74/3.54 | (1899) all_0_21_21 = e3 | all_0_22_22 = e3 | all_0_23_23 = e3
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (1899), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (1666) all_0_21_21 = e3
% 12.74/3.54 |
% 12.74/3.54 | Combining equations (1674,1666) yields a new equation:
% 12.74/3.54 | (417) e3 = e1
% 12.74/3.54 |
% 12.74/3.54 | Equations (417) can reduce 137 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (300) ~ (all_0_21_21 = e3)
% 12.74/3.54 | (1904) all_0_22_22 = e3 | all_0_23_23 = e3
% 12.74/3.54 |
% 12.74/3.54 +-Applying beta-rule and splitting (1904), into two cases.
% 12.74/3.54 |-Branch one:
% 12.74/3.54 | (344) all_0_22_22 = e3
% 12.74/3.54 |
% 12.74/3.54 | Combining equations (344,446) yields a new equation:
% 12.74/3.54 | (277) e3 = e0
% 12.74/3.54 |
% 12.74/3.54 | Simplifying 277 yields:
% 12.74/3.54 | (278) e3 = e0
% 12.74/3.54 |
% 12.74/3.54 | Equations (278) can reduce 136 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (360) ~ (all_0_22_22 = e3)
% 12.74/3.54 | (301) all_0_23_23 = e3
% 12.74/3.54 |
% 12.74/3.54 | Equations (301) can reduce 223 to:
% 12.74/3.54 | (202) $false
% 12.74/3.54 |
% 12.74/3.54 |-The branch is then unsatisfiable
% 12.74/3.54 |-Branch two:
% 12.74/3.54 | (1688) ~ (all_0_21_21 = e1)
% 12.74/3.54 | (1913) all_0_22_22 = e1 | all_0_23_23 = e1
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (1913), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (443) all_0_22_22 = e1
% 12.74/3.55 |
% 12.74/3.55 | Combining equations (446,443) yields a new equation:
% 12.74/3.55 | (421) e1 = e0
% 12.74/3.55 |
% 12.74/3.55 | Equations (421) can reduce 181 to:
% 12.74/3.55 | (202) $false
% 12.74/3.55 |
% 12.74/3.55 |-The branch is then unsatisfiable
% 12.74/3.55 |-Branch two:
% 12.74/3.55 | (309) ~ (all_0_22_22 = e1)
% 12.74/3.55 | (308) all_0_23_23 = e1
% 12.74/3.55 |
% 12.74/3.55 | Equations (308) can reduce 570 to:
% 12.74/3.55 | (202) $false
% 12.74/3.55 |
% 12.74/3.55 |-The branch is then unsatisfiable
% 12.74/3.55 |-Branch two:
% 12.74/3.55 | (311) all_0_13_13 = e3
% 12.74/3.55 | (413) ~ (all_0_16_16 = e1)
% 12.74/3.55 |
% 12.74/3.55 | Equations (328) can reduce 413 to:
% 12.74/3.55 | (202) $false
% 12.74/3.55 |
% 12.74/3.55 |-The branch is then unsatisfiable
% 12.74/3.55 |-Branch two:
% 12.74/3.55 | (415) all_0_17_17 = e1
% 12.74/3.55 | (273) ~ (all_0_23_23 = e2)
% 12.74/3.55 |
% 12.74/3.55 | Equations (415) can reduce 109 to:
% 12.74/3.55 | (316) ~ (all_0_9_9 = e1)
% 12.74/3.55 |
% 12.74/3.55 | Equations (415) can reduce 6 to:
% 12.74/3.55 | (358) ~ (all_0_13_13 = e1)
% 12.74/3.55 |
% 12.74/3.55 | Equations (415) can reduce 58 to:
% 12.74/3.55 | (413) ~ (all_0_16_16 = e1)
% 12.74/3.55 |
% 12.74/3.55 | Equations (415) can reduce 17 to:
% 12.74/3.55 | (1725) ~ (all_0_18_18 = e1)
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 1725 yields:
% 12.74/3.55 | (25) ~ (all_0_18_18 = e1)
% 12.74/3.55 |
% 12.74/3.55 | Equations (415) can reduce 120 to:
% 12.74/3.55 | (657) ~ (all_0_19_19 = e1)
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 657 yields:
% 12.74/3.55 | (622) ~ (all_0_19_19 = e1)
% 12.74/3.55 |
% 12.74/3.55 | Equations (415) can reduce 64 to:
% 12.74/3.55 | (1932) ~ (all_0_21_21 = e1)
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 1932 yields:
% 12.74/3.55 | (1688) ~ (all_0_21_21 = e1)
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (176), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (201) ~ (all_0_8_8 = e2)
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (97), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (196) all_0_8_8 = e2
% 12.74/3.55 |
% 12.74/3.55 | Equations (196) can reduce 201 to:
% 12.74/3.55 | (202) $false
% 12.74/3.55 |
% 12.74/3.55 |-The branch is then unsatisfiable
% 12.74/3.55 |-Branch two:
% 12.74/3.55 | (201) ~ (all_0_8_8 = e2)
% 12.74/3.55 | (835) all_0_8_8 = e1 | all_0_8_8 = e0
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (835), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (366) all_0_8_8 = e1
% 12.74/3.55 |
% 12.74/3.55 | Equations (366) can reduce 193 to:
% 12.74/3.55 | (202) $false
% 12.74/3.55 |
% 12.74/3.55 |-The branch is then unsatisfiable
% 12.74/3.55 |-Branch two:
% 12.74/3.55 | (193) ~ (all_0_8_8 = e1)
% 12.74/3.55 | (839) all_0_8_8 = e0
% 12.74/3.55 |
% 12.74/3.55 | Equations (839) can reduce 110 to:
% 12.74/3.55 | (1943) ~ (all_0_9_9 = e0)
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 1943 yields:
% 12.74/3.55 | (494) ~ (all_0_9_9 = e0)
% 12.74/3.55 |
% 12.74/3.55 | Equations (839) can reduce 182 to:
% 12.74/3.55 | (1945) ~ (all_0_10_10 = e0)
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 1945 yields:
% 12.74/3.55 | (602) ~ (all_0_10_10 = e0)
% 12.74/3.55 |
% 12.74/3.55 | Equations (839) can reduce 24 to:
% 12.74/3.55 | (843) ~ (all_0_11_11 = e0)
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 843 yields:
% 12.74/3.55 | (280) ~ (all_0_11_11 = e0)
% 12.74/3.55 |
% 12.74/3.55 | Equations (839) can reduce 179 to:
% 12.74/3.55 | (1465) ~ (all_0_16_16 = e0)
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 1465 yields:
% 12.74/3.55 | (611) ~ (all_0_16_16 = e0)
% 12.74/3.55 |
% 12.74/3.55 | Equations (839) can reduce 122 to:
% 12.74/3.55 | (847) ~ (all_0_20_20 = e0)
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 847 yields:
% 12.74/3.55 | (220) ~ (all_0_20_20 = e0)
% 12.74/3.55 |
% 12.74/3.55 | Equations (839) can reduce 201 to:
% 12.74/3.55 | (293) ~ (e2 = e0)
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 293 yields:
% 12.74/3.55 | (13) ~ (e2 = e0)
% 12.74/3.55 |
% 12.74/3.55 | Equations (839) can reduce 193 to:
% 12.74/3.55 | (1254) ~ (e1 = e0)
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 1254 yields:
% 12.74/3.55 | (181) ~ (e1 = e0)
% 12.74/3.55 |
% 12.74/3.55 | From (839) and (12) follows:
% 12.74/3.55 | (849) op(all_0_7_7, e0) = all_0_6_6
% 12.74/3.55 |
% 12.74/3.55 | From (839) and (157) follows:
% 12.74/3.55 | (850) op(e3, e0) = all_0_7_7
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (88), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (301) all_0_23_23 = e3
% 12.74/3.55 |
% 12.74/3.55 | Equations (301) can reduce 173 to:
% 12.74/3.55 | (237) ~ (all_0_15_15 = e3)
% 12.74/3.55 |
% 12.74/3.55 | Equations (301) can reduce 192 to:
% 12.74/3.55 | (300) ~ (all_0_21_21 = e3)
% 12.74/3.55 |
% 12.74/3.55 | Equations (301) can reduce 273 to:
% 12.74/3.55 | (101) ~ (e3 = e2)
% 12.74/3.55 |
% 12.74/3.55 | Equations (301) can reduce 9 to:
% 12.74/3.55 | (136) ~ (e3 = e0)
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (108), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (195) ~ (all_0_8_8 = e0)
% 12.74/3.55 |
% 12.74/3.55 | Equations (839) can reduce 195 to:
% 12.74/3.55 | (202) $false
% 12.74/3.55 |
% 12.74/3.55 |-The branch is then unsatisfiable
% 12.74/3.55 |-Branch two:
% 12.74/3.55 | (839) all_0_8_8 = e0
% 12.74/3.55 | (576) ~ (all_0_15_15 = e2)
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (153), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (395) all_0_9_9 = e0
% 12.74/3.55 |
% 12.74/3.55 | Equations (395) can reduce 494 to:
% 12.74/3.55 | (202) $false
% 12.74/3.55 |
% 12.74/3.55 |-The branch is then unsatisfiable
% 12.74/3.55 |-Branch two:
% 12.74/3.55 | (494) ~ (all_0_9_9 = e0)
% 12.74/3.55 | (495) all_0_13_13 = e0 | all_0_17_17 = e0 | all_0_21_21 = e0
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (495), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (449) all_0_13_13 = e0
% 12.74/3.55 |
% 12.74/3.55 | Equations (449) can reduce 31 to:
% 12.74/3.55 | (494) ~ (all_0_9_9 = e0)
% 12.74/3.55 |
% 12.74/3.55 | Equations (449) can reduce 98 to:
% 12.74/3.55 | (628) ~ (all_0_15_15 = e0)
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 628 yields:
% 12.74/3.55 | (286) ~ (all_0_15_15 = e0)
% 12.74/3.55 |
% 12.74/3.55 | Equations (449) can reduce 96 to:
% 12.74/3.55 | (1663) ~ (all_0_21_21 = e0)
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 1663 yields:
% 12.74/3.55 | (204) ~ (all_0_21_21 = e0)
% 12.74/3.55 |
% 12.74/3.55 | Equations (449) can reduce 358 to:
% 12.74/3.55 | (1254) ~ (e1 = e0)
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 1254 yields:
% 12.74/3.55 | (181) ~ (e1 = e0)
% 12.74/3.55 |
% 12.74/3.55 | From (449) and (102) follows:
% 12.74/3.55 | (631) op(e2, e0) = all_0_5_5
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (127), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (208) ~ (all_0_17_17 = e1)
% 12.74/3.55 |
% 12.74/3.55 | Equations (415) can reduce 208 to:
% 12.74/3.55 | (202) $false
% 12.74/3.55 |
% 12.74/3.55 |-The branch is then unsatisfiable
% 12.74/3.55 |-Branch two:
% 12.74/3.55 | (415) all_0_17_17 = e1
% 12.74/3.55 | (555) ~ (all_0_18_18 = e2)
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (94), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (200) ~ (all_0_12_12 = e2)
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (111), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (1666) all_0_21_21 = e3
% 12.74/3.55 |
% 12.74/3.55 | Equations (1666) can reduce 300 to:
% 12.74/3.55 | (202) $false
% 12.74/3.55 |
% 12.74/3.55 |-The branch is then unsatisfiable
% 12.74/3.55 |-Branch two:
% 12.74/3.55 | (300) ~ (all_0_21_21 = e3)
% 12.74/3.55 | (1669) all_0_21_21 = e2 | all_0_21_21 = e1 | all_0_21_21 = e0
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (74), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (260) all_0_12_12 = e2
% 12.74/3.55 |
% 12.74/3.55 | Equations (260) can reduce 200 to:
% 12.74/3.55 | (202) $false
% 12.74/3.55 |
% 12.74/3.55 |-The branch is then unsatisfiable
% 12.74/3.55 |-Branch two:
% 12.74/3.55 | (200) ~ (all_0_12_12 = e2)
% 12.74/3.55 | (263) all_0_14_14 = e2 | all_0_15_15 = e2
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (263), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (264) all_0_14_14 = e2
% 12.74/3.55 |
% 12.74/3.55 | Equations (264) can reduce 44 to:
% 12.74/3.55 | (596) ~ (all_0_15_15 = e2)
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 596 yields:
% 12.74/3.55 | (576) ~ (all_0_15_15 = e2)
% 12.74/3.55 |
% 12.74/3.55 | Equations (264) can reduce 34 to:
% 12.74/3.55 | (962) ~ (all_0_18_18 = e2)
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 962 yields:
% 12.74/3.55 | (555) ~ (all_0_18_18 = e2)
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (93), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (323) all_0_12_12 = e3
% 12.74/3.55 |
% 12.74/3.55 | Equations (323) can reduce 75 to:
% 12.74/3.55 | (236) ~ (all_0_15_15 = e3)
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 236 yields:
% 12.74/3.55 | (237) ~ (all_0_15_15 = e3)
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (151), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (932) all_0_10_10 = e1
% 12.74/3.55 |
% 12.74/3.55 | Equations (932) can reduce 16 to:
% 12.74/3.55 | (316) ~ (all_0_9_9 = e1)
% 12.74/3.55 |
% 12.74/3.55 | Equations (932) can reduce 187 to:
% 12.74/3.55 | (934) ~ (all_0_11_11 = e1)
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 934 yields:
% 12.74/3.55 | (675) ~ (all_0_11_11 = e1)
% 12.74/3.55 |
% 12.74/3.55 | Equations (932) can reduce 129 to:
% 12.74/3.55 | (1725) ~ (all_0_18_18 = e1)
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 1725 yields:
% 12.74/3.55 | (25) ~ (all_0_18_18 = e1)
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (11), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (672) all_0_11_11 = e1
% 12.74/3.55 |
% 12.74/3.55 | Equations (672) can reduce 675 to:
% 12.74/3.55 | (202) $false
% 12.74/3.55 |
% 12.74/3.55 |-The branch is then unsatisfiable
% 12.74/3.55 |-Branch two:
% 12.74/3.55 | (675) ~ (all_0_11_11 = e1)
% 12.74/3.55 | (676) all_0_15_15 = e1 | all_0_19_19 = e1 | all_0_23_23 = e1
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (1669), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (376) all_0_21_21 = e2
% 12.74/3.55 |
% 12.74/3.55 | Equations (376) can reduce 118 to:
% 12.74/3.55 | (198) ~ (all_0_9_9 = e2)
% 12.74/3.55 |
% 12.74/3.55 | Equations (376) can reduce 204 to:
% 12.74/3.55 | (13) ~ (e2 = e0)
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (142), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (226) all_0_9_9 = e3
% 12.74/3.55 |
% 12.74/3.55 | Equations (226) can reduce 145 to:
% 12.74/3.55 | (952) ~ (all_0_11_11 = e3)
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 952 yields:
% 12.74/3.55 | (242) ~ (all_0_11_11 = e3)
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (126), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (665) all_0_15_15 = e3
% 12.74/3.55 |
% 12.74/3.55 | Equations (665) can reduce 237 to:
% 12.74/3.55 | (202) $false
% 12.74/3.55 |
% 12.74/3.55 |-The branch is then unsatisfiable
% 12.74/3.55 |-Branch two:
% 12.74/3.55 | (237) ~ (all_0_15_15 = e3)
% 12.74/3.55 | (668) all_0_15_15 = e2 | all_0_15_15 = e1 | all_0_15_15 = e0
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (668), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (267) all_0_15_15 = e2
% 12.74/3.55 |
% 12.74/3.55 | Equations (267) can reduce 576 to:
% 12.74/3.55 | (202) $false
% 12.74/3.55 |
% 12.74/3.55 |-The branch is then unsatisfiable
% 12.74/3.55 |-Branch two:
% 12.74/3.55 | (576) ~ (all_0_15_15 = e2)
% 12.74/3.55 | (708) all_0_15_15 = e1 | all_0_15_15 = e0
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (676), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (677) all_0_15_15 = e1
% 12.74/3.55 |
% 12.74/3.55 | Equations (677) can reduce 50 to:
% 12.74/3.55 | (675) ~ (all_0_11_11 = e1)
% 12.74/3.55 |
% 12.74/3.55 | Equations (677) can reduce 188 to:
% 12.74/3.55 | (657) ~ (all_0_19_19 = e1)
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 657 yields:
% 12.74/3.55 | (622) ~ (all_0_19_19 = e1)
% 12.74/3.55 |
% 12.74/3.55 | Equations (677) can reduce 576 to:
% 12.74/3.55 | (329) ~ (e2 = e1)
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 329 yields:
% 12.74/3.55 | (71) ~ (e2 = e1)
% 12.74/3.55 |
% 12.74/3.55 | Equations (677) can reduce 286 to:
% 12.74/3.55 | (181) ~ (e1 = e0)
% 12.74/3.55 |
% 12.74/3.55 | From (677) and (103) follows:
% 12.74/3.55 | (678) op(e2, e0) = e1
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (121), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (250) all_0_18_18 = e3
% 12.74/3.55 |
% 12.74/3.55 | Equations (250) can reduce 39 to:
% 12.74/3.55 | (298) ~ (all_0_16_16 = e3)
% 12.74/3.55 |
% 12.74/3.55 | Equations (250) can reduce 555 to:
% 12.74/3.55 | (101) ~ (e3 = e2)
% 12.74/3.55 |
% 12.74/3.55 | Equations (250) can reduce 25 to:
% 12.74/3.55 | (137) ~ (e3 = e1)
% 12.74/3.55 |
% 12.74/3.55 | Equations (250) can reduce 245 to:
% 12.74/3.55 | (136) ~ (e3 = e0)
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (35), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (196) all_0_8_8 = e2
% 12.74/3.55 |
% 12.74/3.55 | Combining equations (196,839) yields a new equation:
% 12.74/3.55 | (283) e2 = e0
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 283 yields:
% 12.74/3.55 | (284) e2 = e0
% 12.74/3.55 |
% 12.74/3.55 | Equations (284) can reduce 13 to:
% 12.74/3.55 | (202) $false
% 12.74/3.55 |
% 12.74/3.55 |-The branch is then unsatisfiable
% 12.74/3.55 |-Branch two:
% 12.74/3.55 | (201) ~ (all_0_8_8 = e2)
% 12.74/3.55 | (2044) all_0_12_12 = e2 | all_0_16_16 = e2 | all_0_20_20 = e2
% 12.74/3.55 |
% 12.74/3.55 | Equations (839) can reduce 201 to:
% 12.74/3.55 | (293) ~ (e2 = e0)
% 12.74/3.55 |
% 12.74/3.55 | Simplifying 293 yields:
% 12.74/3.55 | (13) ~ (e2 = e0)
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (18), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (1501) all_0_20_20 = e1
% 12.74/3.55 |
% 12.74/3.55 | Equations (1501) can reduce 134 to:
% 12.74/3.55 | (413) ~ (all_0_16_16 = e1)
% 12.74/3.55 |
% 12.74/3.55 | Equations (1501) can reduce 220 to:
% 12.74/3.55 | (181) ~ (e1 = e0)
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (7), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (427) all_0_16_16 = e3
% 12.74/3.55 |
% 12.74/3.55 | Equations (427) can reduce 298 to:
% 12.74/3.55 | (202) $false
% 12.74/3.55 |
% 12.74/3.55 |-The branch is then unsatisfiable
% 12.74/3.55 |-Branch two:
% 12.74/3.55 | (298) ~ (all_0_16_16 = e3)
% 12.74/3.55 | (430) all_0_16_16 = e2 | all_0_16_16 = e1 | all_0_16_16 = e0
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (430), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (785) all_0_16_16 = e2
% 12.74/3.55 |
% 12.74/3.55 | Equations (785) can reduce 611 to:
% 12.74/3.55 | (13) ~ (e2 = e0)
% 12.74/3.55 |
% 12.74/3.55 +-Applying beta-rule and splitting (10), into two cases.
% 12.74/3.55 |-Branch one:
% 12.74/3.55 | (792) all_0_16_16 = e0
% 12.74/3.55 |
% 12.74/3.56 | Combining equations (785,792) yields a new equation:
% 12.74/3.56 | (283) e2 = e0
% 12.74/3.56 |
% 12.74/3.56 | Simplifying 283 yields:
% 12.74/3.56 | (284) e2 = e0
% 12.74/3.56 |
% 12.74/3.56 | Equations (284) can reduce 13 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (611) ~ (all_0_16_16 = e0)
% 12.74/3.56 | (2061) all_0_17_17 = e0 | all_0_18_18 = e0 | all_0_19_19 = e0
% 12.74/3.56 |
% 12.74/3.56 +-Applying beta-rule and splitting (2061), into two cases.
% 12.74/3.56 |-Branch one:
% 12.74/3.56 | (540) all_0_17_17 = e0
% 12.74/3.56 |
% 12.74/3.56 | Combining equations (540,415) yields a new equation:
% 12.74/3.56 | (421) e1 = e0
% 12.74/3.56 |
% 12.74/3.56 | Equations (421) can reduce 181 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (288) ~ (all_0_17_17 = e0)
% 12.74/3.56 | (2066) all_0_18_18 = e0 | all_0_19_19 = e0
% 12.74/3.56 |
% 12.74/3.56 +-Applying beta-rule and splitting (2066), into two cases.
% 12.74/3.56 |-Branch one:
% 12.74/3.56 | (556) all_0_18_18 = e0
% 12.74/3.56 |
% 12.74/3.56 | Combining equations (250,556) yields a new equation:
% 12.74/3.56 | (277) e3 = e0
% 12.74/3.56 |
% 12.74/3.56 | Simplifying 277 yields:
% 12.74/3.56 | (278) e3 = e0
% 12.74/3.56 |
% 12.74/3.56 | Equations (278) can reduce 136 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (245) ~ (all_0_18_18 = e0)
% 12.74/3.56 | (287) all_0_19_19 = e0
% 12.74/3.56 |
% 12.74/3.56 | Equations (287) can reduce 171 to:
% 12.74/3.56 | (280) ~ (all_0_11_11 = e0)
% 12.74/3.56 |
% 12.74/3.56 +-Applying beta-rule and splitting (133), into two cases.
% 12.74/3.56 |-Branch one:
% 12.74/3.56 | (981) all_0_11_11 = e2
% 12.74/3.56 |
% 12.74/3.56 | From (981) and (106) follows:
% 12.74/3.56 | (986) op(e3, e0) = e2
% 12.74/3.56 |
% 12.74/3.56 | Instantiating formula (53) with e3, e0, e2, all_0_7_7 and discharging atoms op(e3, e0) = all_0_7_7, op(e3, e0) = e2, yields:
% 12.74/3.56 | (2076) all_0_7_7 = e2
% 12.74/3.56 |
% 12.74/3.56 | Instantiating formula (53) with e2, e0, e1, all_0_5_5 and discharging atoms op(e2, e0) = all_0_5_5, op(e2, e0) = e1, yields:
% 12.74/3.56 | (679) all_0_5_5 = e1
% 12.74/3.56 |
% 12.74/3.56 | From (2076) and (849) follows:
% 12.74/3.56 | (2078) op(e2, e0) = all_0_6_6
% 12.74/3.56 |
% 12.74/3.56 | From (679) and (631) follows:
% 12.74/3.56 | (678) op(e2, e0) = e1
% 12.74/3.56 |
% 12.74/3.56 +-Applying beta-rule and splitting (186), into two cases.
% 12.74/3.56 |-Branch one:
% 12.74/3.56 | (1676) ~ (all_0_6_6 = e1)
% 12.74/3.56 |
% 12.74/3.56 | Instantiating formula (53) with e2, e0, all_0_6_6, e1 and discharging atoms op(e2, e0) = all_0_6_6, op(e2, e0) = e1, yields:
% 12.74/3.56 | (1679) all_0_6_6 = e1
% 12.74/3.56 |
% 12.74/3.56 | Equations (1679) can reduce 1676 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (1679) all_0_6_6 = e1
% 12.74/3.56 | (2084) ~ (all_0_7_7 = e2) | ~ (all_0_8_8 = e0)
% 12.74/3.56 |
% 12.74/3.56 +-Applying beta-rule and splitting (2084), into two cases.
% 12.74/3.56 |-Branch one:
% 12.74/3.56 | (2085) ~ (all_0_7_7 = e2)
% 12.74/3.56 |
% 12.74/3.56 | Equations (2076) can reduce 2085 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (2076) all_0_7_7 = e2
% 12.74/3.56 | (195) ~ (all_0_8_8 = e0)
% 12.74/3.56 |
% 12.74/3.56 | Equations (839) can reduce 195 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (1113) ~ (all_0_11_11 = e2)
% 12.74/3.56 | (1114) all_0_15_15 = e2 | all_0_19_19 = e2 | all_0_23_23 = e2
% 12.74/3.56 |
% 12.74/3.56 +-Applying beta-rule and splitting (84), into two cases.
% 12.74/3.56 |-Branch one:
% 12.74/3.56 | (233) all_0_11_11 = e3
% 12.74/3.56 |
% 12.74/3.56 | Equations (233) can reduce 242 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (242) ~ (all_0_11_11 = e3)
% 12.74/3.56 | (1822) all_0_11_11 = e2 | all_0_11_11 = e1 | all_0_11_11 = e0
% 12.74/3.56 |
% 12.74/3.56 +-Applying beta-rule and splitting (1822), into two cases.
% 12.74/3.56 |-Branch one:
% 12.74/3.56 | (981) all_0_11_11 = e2
% 12.74/3.56 |
% 12.74/3.56 | Equations (981) can reduce 1113 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (1113) ~ (all_0_11_11 = e2)
% 12.74/3.56 | (1832) all_0_11_11 = e1 | all_0_11_11 = e0
% 12.74/3.56 |
% 12.74/3.56 +-Applying beta-rule and splitting (1832), into two cases.
% 12.74/3.56 |-Branch one:
% 12.74/3.56 | (672) all_0_11_11 = e1
% 12.74/3.56 |
% 12.74/3.56 | Equations (672) can reduce 675 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (675) ~ (all_0_11_11 = e1)
% 12.74/3.56 | (276) all_0_11_11 = e0
% 12.74/3.56 |
% 12.74/3.56 | Equations (276) can reduce 280 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (256) ~ (all_0_16_16 = e2)
% 12.74/3.56 | (788) all_0_16_16 = e1 | all_0_16_16 = e0
% 12.74/3.56 |
% 12.74/3.56 +-Applying beta-rule and splitting (788), into two cases.
% 12.74/3.56 |-Branch one:
% 12.74/3.56 | (328) all_0_16_16 = e1
% 12.74/3.56 |
% 12.74/3.56 | Equations (328) can reduce 413 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (413) ~ (all_0_16_16 = e1)
% 12.74/3.56 | (792) all_0_16_16 = e0
% 12.74/3.56 |
% 12.74/3.56 | Equations (792) can reduce 611 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (920) ~ (all_0_20_20 = e1)
% 12.74/3.56 | (1732) all_0_21_21 = e1 | all_0_22_22 = e1 | all_0_23_23 = e1
% 12.74/3.56 |
% 12.74/3.56 +-Applying beta-rule and splitting (147), into two cases.
% 12.74/3.56 |-Branch one:
% 12.74/3.56 | (276) all_0_11_11 = e0
% 12.74/3.56 |
% 12.74/3.56 | Equations (276) can reduce 280 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (280) ~ (all_0_11_11 = e0)
% 12.74/3.56 | (281) all_0_15_15 = e0 | all_0_19_19 = e0
% 12.74/3.56 |
% 12.74/3.56 +-Applying beta-rule and splitting (281), into two cases.
% 12.74/3.56 |-Branch one:
% 12.74/3.56 | (282) all_0_15_15 = e0
% 12.74/3.56 |
% 12.74/3.56 | Combining equations (677,282) yields a new equation:
% 12.74/3.56 | (491) e1 = e0
% 12.74/3.56 |
% 12.74/3.56 | Simplifying 491 yields:
% 12.74/3.56 | (421) e1 = e0
% 12.74/3.56 |
% 12.74/3.56 | Equations (421) can reduce 181 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (286) ~ (all_0_15_15 = e0)
% 12.74/3.56 | (287) all_0_19_19 = e0
% 12.74/3.56 |
% 12.74/3.56 | Equations (287) can reduce 622 to:
% 12.74/3.56 | (1254) ~ (e1 = e0)
% 12.74/3.56 |
% 12.74/3.56 | Simplifying 1254 yields:
% 12.74/3.56 | (181) ~ (e1 = e0)
% 12.74/3.56 |
% 12.74/3.56 +-Applying beta-rule and splitting (21), into two cases.
% 12.74/3.56 |-Branch one:
% 12.74/3.56 | (785) all_0_16_16 = e2
% 12.74/3.56 |
% 12.74/3.56 | Equations (785) can reduce 413 to:
% 12.74/3.56 | (71) ~ (e2 = e1)
% 12.74/3.56 |
% 12.74/3.56 +-Applying beta-rule and splitting (86), into two cases.
% 12.74/3.56 |-Branch one:
% 12.74/3.56 | (366) all_0_8_8 = e1
% 12.74/3.56 |
% 12.74/3.56 | Combining equations (366,839) yields a new equation:
% 12.74/3.56 | (491) e1 = e0
% 12.74/3.56 |
% 12.74/3.56 | Simplifying 491 yields:
% 12.74/3.56 | (421) e1 = e0
% 12.74/3.56 |
% 12.74/3.56 | Equations (421) can reduce 181 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (193) ~ (all_0_8_8 = e1)
% 12.74/3.56 | (1492) all_0_12_12 = e1 | all_0_16_16 = e1 | all_0_20_20 = e1
% 12.74/3.56 |
% 12.74/3.56 +-Applying beta-rule and splitting (1492), into two cases.
% 12.74/3.56 |-Branch one:
% 12.74/3.56 | (730) all_0_12_12 = e1
% 12.74/3.56 |
% 12.74/3.56 | Combining equations (730,323) yields a new equation:
% 12.74/3.56 | (417) e3 = e1
% 12.74/3.56 |
% 12.74/3.56 | Equations (417) can reduce 137 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (317) ~ (all_0_12_12 = e1)
% 12.74/3.56 | (1497) all_0_16_16 = e1 | all_0_20_20 = e1
% 12.74/3.56 |
% 12.74/3.56 +-Applying beta-rule and splitting (1497), into two cases.
% 12.74/3.56 |-Branch one:
% 12.74/3.56 | (328) all_0_16_16 = e1
% 12.74/3.56 |
% 12.74/3.56 | Combining equations (785,328) yields a new equation:
% 12.74/3.56 | (767) e2 = e1
% 12.74/3.56 |
% 12.74/3.56 | Simplifying 767 yields:
% 12.74/3.56 | (367) e2 = e1
% 12.74/3.56 |
% 12.74/3.56 | Equations (367) can reduce 71 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (413) ~ (all_0_16_16 = e1)
% 12.74/3.56 | (1501) all_0_20_20 = e1
% 12.74/3.56 |
% 12.74/3.56 | Equations (1501) can reduce 920 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (256) ~ (all_0_16_16 = e2)
% 12.74/3.56 | (2147) all_0_17_17 = e2 | all_0_18_18 = e2 | all_0_19_19 = e2
% 12.74/3.56 |
% 12.74/3.56 +-Applying beta-rule and splitting (2147), into two cases.
% 12.74/3.56 |-Branch one:
% 12.74/3.56 | (371) all_0_17_17 = e2
% 12.74/3.56 |
% 12.74/3.56 | Combining equations (415,371) yields a new equation:
% 12.74/3.56 | (367) e2 = e1
% 12.74/3.56 |
% 12.74/3.56 | Equations (367) can reduce 71 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (375) ~ (all_0_17_17 = e2)
% 12.74/3.56 | (2152) all_0_18_18 = e2 | all_0_19_19 = e2
% 12.74/3.56 |
% 12.74/3.56 +-Applying beta-rule and splitting (2152), into two cases.
% 12.74/3.56 |-Branch one:
% 12.74/3.56 | (254) all_0_18_18 = e2
% 12.74/3.56 |
% 12.74/3.56 | Combining equations (250,254) yields a new equation:
% 12.74/3.56 | (372) e3 = e2
% 12.74/3.56 |
% 12.74/3.56 | Simplifying 372 yields:
% 12.74/3.56 | (373) e3 = e2
% 12.74/3.56 |
% 12.74/3.56 | Equations (373) can reduce 101 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (555) ~ (all_0_18_18 = e2)
% 12.74/3.56 | (709) all_0_19_19 = e2
% 12.74/3.56 |
% 12.74/3.56 | Combining equations (287,709) yields a new equation:
% 12.74/3.56 | (284) e2 = e0
% 12.74/3.56 |
% 12.74/3.56 | Equations (284) can reduce 13 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (224) ~ (all_0_18_18 = e3)
% 12.74/3.56 | (253) all_0_18_18 = e2 | all_0_18_18 = e0
% 12.74/3.56 |
% 12.74/3.56 +-Applying beta-rule and splitting (86), into two cases.
% 12.74/3.56 |-Branch one:
% 12.74/3.56 | (366) all_0_8_8 = e1
% 12.74/3.56 |
% 12.74/3.56 | Combining equations (366,839) yields a new equation:
% 12.74/3.56 | (491) e1 = e0
% 12.74/3.56 |
% 12.74/3.56 | Simplifying 491 yields:
% 12.74/3.56 | (421) e1 = e0
% 12.74/3.56 |
% 12.74/3.56 | Equations (421) can reduce 181 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (193) ~ (all_0_8_8 = e1)
% 12.74/3.56 | (1492) all_0_12_12 = e1 | all_0_16_16 = e1 | all_0_20_20 = e1
% 12.74/3.56 |
% 12.74/3.56 | Equations (839) can reduce 193 to:
% 12.74/3.56 | (1254) ~ (e1 = e0)
% 12.74/3.56 |
% 12.74/3.56 | Simplifying 1254 yields:
% 12.74/3.56 | (181) ~ (e1 = e0)
% 12.74/3.56 |
% 12.74/3.56 +-Applying beta-rule and splitting (10), into two cases.
% 12.74/3.56 |-Branch one:
% 12.74/3.56 | (792) all_0_16_16 = e0
% 12.74/3.56 |
% 12.74/3.56 | Equations (792) can reduce 611 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (611) ~ (all_0_16_16 = e0)
% 12.74/3.56 | (2061) all_0_17_17 = e0 | all_0_18_18 = e0 | all_0_19_19 = e0
% 12.74/3.56 |
% 12.74/3.56 +-Applying beta-rule and splitting (2061), into two cases.
% 12.74/3.56 |-Branch one:
% 12.74/3.56 | (540) all_0_17_17 = e0
% 12.74/3.56 |
% 12.74/3.56 | Combining equations (415,540) yields a new equation:
% 12.74/3.56 | (491) e1 = e0
% 12.74/3.56 |
% 12.74/3.56 | Simplifying 491 yields:
% 12.74/3.56 | (421) e1 = e0
% 12.74/3.56 |
% 12.74/3.56 | Equations (421) can reduce 181 to:
% 12.74/3.56 | (202) $false
% 12.74/3.56 |
% 12.74/3.56 |-The branch is then unsatisfiable
% 12.74/3.56 |-Branch two:
% 12.74/3.56 | (288) ~ (all_0_17_17 = e0)
% 12.74/3.57 | (2066) all_0_18_18 = e0 | all_0_19_19 = e0
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (2066), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (556) all_0_18_18 = e0
% 12.74/3.57 |
% 12.74/3.57 | Equations (556) can reduce 245 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (245) ~ (all_0_18_18 = e0)
% 12.74/3.57 | (287) all_0_19_19 = e0
% 12.74/3.57 |
% 12.74/3.57 | Equations (287) can reduce 4 to:
% 12.74/3.57 | (245) ~ (all_0_18_18 = e0)
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (253), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (254) all_0_18_18 = e2
% 12.74/3.57 |
% 12.74/3.57 | Equations (254) can reduce 555 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (555) ~ (all_0_18_18 = e2)
% 12.74/3.57 | (556) all_0_18_18 = e0
% 12.74/3.57 |
% 12.74/3.57 | Equations (556) can reduce 245 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (693) ~ (all_0_15_15 = e1)
% 12.74/3.57 | (694) all_0_19_19 = e1 | all_0_23_23 = e1
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (708), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (677) all_0_15_15 = e1
% 12.74/3.57 |
% 12.74/3.57 | Equations (677) can reduce 693 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (693) ~ (all_0_15_15 = e1)
% 12.74/3.57 | (282) all_0_15_15 = e0
% 12.74/3.57 |
% 12.74/3.57 | Equations (282) can reduce 286 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (212) ~ (all_0_9_9 = e3)
% 12.74/3.57 | (387) all_0_9_9 = e2 | all_0_9_9 = e1 | all_0_9_9 = e0
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (387), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (362) all_0_9_9 = e2
% 12.74/3.57 |
% 12.74/3.57 | Equations (362) can reduce 198 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (198) ~ (all_0_9_9 = e2)
% 12.74/3.57 | (391) all_0_9_9 = e1 | all_0_9_9 = e0
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (391), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (380) all_0_9_9 = e1
% 12.74/3.57 |
% 12.74/3.57 | Equations (380) can reduce 316 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (316) ~ (all_0_9_9 = e1)
% 12.74/3.57 | (395) all_0_9_9 = e0
% 12.74/3.57 |
% 12.74/3.57 | Equations (395) can reduce 494 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (542) ~ (all_0_21_21 = e2)
% 12.74/3.57 | (1673) all_0_21_21 = e1 | all_0_21_21 = e0
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (1673), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (1674) all_0_21_21 = e1
% 12.74/3.57 |
% 12.74/3.57 | Equations (1674) can reduce 1688 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (1688) ~ (all_0_21_21 = e1)
% 12.74/3.57 | (829) all_0_21_21 = e0
% 12.74/3.57 |
% 12.74/3.57 | Equations (829) can reduce 204 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (1170) ~ (all_0_10_10 = e1)
% 12.74/3.57 | (2217) all_0_14_14 = e1 | all_0_22_22 = e1
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (2217), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (339) all_0_14_14 = e1
% 12.74/3.57 |
% 12.74/3.57 | Combining equations (264,339) yields a new equation:
% 12.74/3.57 | (767) e2 = e1
% 12.74/3.57 |
% 12.74/3.57 | Simplifying 767 yields:
% 12.74/3.57 | (367) e2 = e1
% 12.74/3.57 |
% 12.74/3.57 | Equations (367) can reduce 71 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (319) ~ (all_0_14_14 = e1)
% 12.74/3.57 | (443) all_0_22_22 = e1
% 12.74/3.57 |
% 12.74/3.57 | Combining equations (446,443) yields a new equation:
% 12.74/3.57 | (421) e1 = e0
% 12.74/3.57 |
% 12.74/3.57 | Equations (421) can reduce 181 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (423) ~ (all_0_12_12 = e3)
% 12.74/3.57 | (1078) all_0_13_13 = e3 | all_0_14_14 = e3 | all_0_15_15 = e3
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (1078), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (311) all_0_13_13 = e3
% 12.74/3.57 |
% 12.74/3.57 | Combining equations (311,449) yields a new equation:
% 12.74/3.57 | (277) e3 = e0
% 12.74/3.57 |
% 12.74/3.57 | Simplifying 277 yields:
% 12.74/3.57 | (278) e3 = e0
% 12.74/3.57 |
% 12.74/3.57 | Equations (278) can reduce 136 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (219) ~ (all_0_13_13 = e3)
% 12.74/3.57 | (1083) all_0_14_14 = e3 | all_0_15_15 = e3
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (1083), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (331) all_0_14_14 = e3
% 12.74/3.57 |
% 12.74/3.57 | Combining equations (264,331) yields a new equation:
% 12.74/3.57 | (373) e3 = e2
% 12.74/3.57 |
% 12.74/3.57 | Equations (373) can reduce 101 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (325) ~ (all_0_14_14 = e3)
% 12.74/3.57 | (665) all_0_15_15 = e3
% 12.74/3.57 |
% 12.74/3.57 | Equations (665) can reduce 237 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (255) ~ (all_0_14_14 = e2)
% 12.74/3.57 | (267) all_0_15_15 = e2
% 12.74/3.57 |
% 12.74/3.57 | Equations (267) can reduce 576 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (260) all_0_12_12 = e2
% 12.74/3.57 | (223) ~ (all_0_23_23 = e3)
% 12.74/3.57 |
% 12.74/3.57 | Equations (301) can reduce 223 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (249) ~ (all_0_13_13 = e0)
% 12.74/3.57 | (499) all_0_17_17 = e0 | all_0_21_21 = e0
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (113), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (311) all_0_13_13 = e3
% 12.74/3.57 |
% 12.74/3.57 | Equations (311) can reduce 31 to:
% 12.74/3.57 | (212) ~ (all_0_9_9 = e3)
% 12.74/3.57 |
% 12.74/3.57 | Equations (311) can reduce 96 to:
% 12.74/3.57 | (299) ~ (all_0_21_21 = e3)
% 12.74/3.57 |
% 12.74/3.57 | Simplifying 299 yields:
% 12.74/3.57 | (300) ~ (all_0_21_21 = e3)
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (155), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (226) all_0_9_9 = e3
% 12.74/3.57 |
% 12.74/3.57 | Equations (226) can reduce 212 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (212) ~ (all_0_9_9 = e3)
% 12.74/3.57 | (229) all_0_10_10 = e3 | all_0_11_11 = e3
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (10), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (792) all_0_16_16 = e0
% 12.74/3.57 |
% 12.74/3.57 | Equations (792) can reduce 611 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (611) ~ (all_0_16_16 = e0)
% 12.74/3.57 | (2061) all_0_17_17 = e0 | all_0_18_18 = e0 | all_0_19_19 = e0
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (2061), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (540) all_0_17_17 = e0
% 12.74/3.57 |
% 12.74/3.57 | Combining equations (415,540) yields a new equation:
% 12.74/3.57 | (491) e1 = e0
% 12.74/3.57 |
% 12.74/3.57 | Simplifying 491 yields:
% 12.74/3.57 | (421) e1 = e0
% 12.74/3.57 |
% 12.74/3.57 | Equations (421) can reduce 181 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (288) ~ (all_0_17_17 = e0)
% 12.74/3.57 | (2066) all_0_18_18 = e0 | all_0_19_19 = e0
% 12.74/3.57 |
% 12.74/3.57 | Equations (415) can reduce 288 to:
% 12.74/3.57 | (181) ~ (e1 = e0)
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (127), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (208) ~ (all_0_17_17 = e1)
% 12.74/3.57 |
% 12.74/3.57 | Equations (415) can reduce 208 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (415) all_0_17_17 = e1
% 12.74/3.57 | (555) ~ (all_0_18_18 = e2)
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (121), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (250) all_0_18_18 = e3
% 12.74/3.57 |
% 12.74/3.57 | Equations (250) can reduce 555 to:
% 12.74/3.57 | (101) ~ (e3 = e2)
% 12.74/3.57 |
% 12.74/3.57 | Equations (250) can reduce 25 to:
% 12.74/3.57 | (137) ~ (e3 = e1)
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (111), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (1666) all_0_21_21 = e3
% 12.74/3.57 |
% 12.74/3.57 | Equations (1666) can reduce 300 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (300) ~ (all_0_21_21 = e3)
% 12.74/3.57 | (1669) all_0_21_21 = e2 | all_0_21_21 = e1 | all_0_21_21 = e0
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (1669), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (376) all_0_21_21 = e2
% 12.74/3.57 |
% 12.74/3.57 | Equations (376) can reduce 118 to:
% 12.74/3.57 | (198) ~ (all_0_9_9 = e2)
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (142), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (226) all_0_9_9 = e3
% 12.74/3.57 |
% 12.74/3.57 | Equations (226) can reduce 212 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (212) ~ (all_0_9_9 = e3)
% 12.74/3.57 | (387) all_0_9_9 = e2 | all_0_9_9 = e1 | all_0_9_9 = e0
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (387), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (362) all_0_9_9 = e2
% 12.74/3.57 |
% 12.74/3.57 | Equations (362) can reduce 198 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (198) ~ (all_0_9_9 = e2)
% 12.74/3.57 | (391) all_0_9_9 = e1 | all_0_9_9 = e0
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (391), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (380) all_0_9_9 = e1
% 12.74/3.57 |
% 12.74/3.57 | Equations (380) can reduce 316 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (316) ~ (all_0_9_9 = e1)
% 12.74/3.57 | (395) all_0_9_9 = e0
% 12.74/3.57 |
% 12.74/3.57 | Equations (395) can reduce 494 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (542) ~ (all_0_21_21 = e2)
% 12.74/3.57 | (1673) all_0_21_21 = e1 | all_0_21_21 = e0
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (148), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (526) all_0_20_20 = e2
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (86), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (366) all_0_8_8 = e1
% 12.74/3.57 |
% 12.74/3.57 | Combining equations (366,839) yields a new equation:
% 12.74/3.57 | (491) e1 = e0
% 12.74/3.57 |
% 12.74/3.57 | Simplifying 491 yields:
% 12.74/3.57 | (421) e1 = e0
% 12.74/3.57 |
% 12.74/3.57 | Equations (421) can reduce 181 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (193) ~ (all_0_8_8 = e1)
% 12.74/3.57 | (1492) all_0_12_12 = e1 | all_0_16_16 = e1 | all_0_20_20 = e1
% 12.74/3.57 |
% 12.74/3.57 | Equations (839) can reduce 193 to:
% 12.74/3.57 | (1254) ~ (e1 = e0)
% 12.74/3.57 |
% 12.74/3.57 | Simplifying 1254 yields:
% 12.74/3.57 | (181) ~ (e1 = e0)
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (18), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (1501) all_0_20_20 = e1
% 12.74/3.57 |
% 12.74/3.57 | Combining equations (1501,526) yields a new equation:
% 12.74/3.57 | (367) e2 = e1
% 12.74/3.57 |
% 12.74/3.57 | Equations (367) can reduce 71 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (920) ~ (all_0_20_20 = e1)
% 12.74/3.57 | (1732) all_0_21_21 = e1 | all_0_22_22 = e1 | all_0_23_23 = e1
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (1732), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (1674) all_0_21_21 = e1
% 12.74/3.57 |
% 12.74/3.57 | Equations (1674) can reduce 1688 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (1688) ~ (all_0_21_21 = e1)
% 12.74/3.57 | (1913) all_0_22_22 = e1 | all_0_23_23 = e1
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (1913), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (443) all_0_22_22 = e1
% 12.74/3.57 |
% 12.74/3.57 | Combining equations (446,443) yields a new equation:
% 12.74/3.57 | (421) e1 = e0
% 12.74/3.57 |
% 12.74/3.57 | Equations (421) can reduce 181 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (309) ~ (all_0_22_22 = e1)
% 12.74/3.57 | (308) all_0_23_23 = e1
% 12.74/3.57 |
% 12.74/3.57 | Combining equations (301,308) yields a new equation:
% 12.74/3.57 | (416) e3 = e1
% 12.74/3.57 |
% 12.74/3.57 | Simplifying 416 yields:
% 12.74/3.57 | (417) e3 = e1
% 12.74/3.57 |
% 12.74/3.57 | Equations (417) can reduce 137 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (529) ~ (all_0_20_20 = e2)
% 12.74/3.57 | (530) all_0_21_21 = e2 | all_0_22_22 = e2 | all_0_23_23 = e2
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (530), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (376) all_0_21_21 = e2
% 12.74/3.57 |
% 12.74/3.57 | Equations (376) can reduce 542 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (542) ~ (all_0_21_21 = e2)
% 12.74/3.57 | (543) all_0_22_22 = e2 | all_0_23_23 = e2
% 12.74/3.57 |
% 12.74/3.57 +-Applying beta-rule and splitting (543), into two cases.
% 12.74/3.57 |-Branch one:
% 12.74/3.57 | (439) all_0_22_22 = e2
% 12.74/3.57 |
% 12.74/3.57 | Combining equations (446,439) yields a new equation:
% 12.74/3.57 | (284) e2 = e0
% 12.74/3.57 |
% 12.74/3.57 | Equations (284) can reduce 13 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.57 |-Branch two:
% 12.74/3.57 | (258) ~ (all_0_22_22 = e2)
% 12.74/3.57 | (305) all_0_23_23 = e2
% 12.74/3.57 |
% 12.74/3.57 | Combining equations (305,301) yields a new equation:
% 12.74/3.57 | (373) e3 = e2
% 12.74/3.57 |
% 12.74/3.57 | Equations (373) can reduce 101 to:
% 12.74/3.57 | (202) $false
% 12.74/3.57 |
% 12.74/3.57 |-The branch is then unsatisfiable
% 12.74/3.58 |-Branch two:
% 12.74/3.58 | (224) ~ (all_0_18_18 = e3)
% 12.74/3.58 | (253) all_0_18_18 = e2 | all_0_18_18 = e0
% 12.74/3.58 |
% 12.74/3.58 +-Applying beta-rule and splitting (253), into two cases.
% 12.74/3.58 |-Branch one:
% 12.74/3.58 | (254) all_0_18_18 = e2
% 12.74/3.58 |
% 12.74/3.58 | Equations (254) can reduce 555 to:
% 12.74/3.58 | (202) $false
% 12.74/3.58 |
% 12.74/3.58 |-The branch is then unsatisfiable
% 12.74/3.58 |-Branch two:
% 12.74/3.58 | (555) ~ (all_0_18_18 = e2)
% 12.74/3.58 | (556) all_0_18_18 = e0
% 12.74/3.58 |
% 12.74/3.58 | Equations (556) can reduce 245 to:
% 12.74/3.58 | (202) $false
% 12.74/3.58 |
% 12.74/3.58 |-The branch is then unsatisfiable
% 12.74/3.58 |-Branch two:
% 12.74/3.58 | (219) ~ (all_0_13_13 = e3)
% 12.74/3.58 | (314) all_0_13_13 = e1 | all_0_13_13 = e0
% 12.74/3.58 |
% 12.74/3.58 +-Applying beta-rule and splitting (314), into two cases.
% 12.74/3.58 |-Branch one:
% 12.74/3.58 | (315) all_0_13_13 = e1
% 12.74/3.58 |
% 12.74/3.58 | Equations (315) can reduce 358 to:
% 12.74/3.58 | (202) $false
% 12.74/3.58 |
% 12.74/3.58 |-The branch is then unsatisfiable
% 12.74/3.58 |-Branch two:
% 12.74/3.58 | (358) ~ (all_0_13_13 = e1)
% 12.74/3.58 | (449) all_0_13_13 = e0
% 12.74/3.58 |
% 12.74/3.58 | Equations (449) can reduce 249 to:
% 12.74/3.58 | (202) $false
% 12.74/3.58 |
% 12.74/3.58 |-The branch is then unsatisfiable
% 12.74/3.58 |-Branch two:
% 12.74/3.58 | (223) ~ (all_0_23_23 = e3)
% 12.74/3.58 | (304) all_0_23_23 = e2 | all_0_23_23 = e1
% 12.74/3.58 |
% 12.74/3.58 +-Applying beta-rule and splitting (108), into two cases.
% 12.74/3.58 |-Branch one:
% 12.74/3.58 | (195) ~ (all_0_8_8 = e0)
% 12.74/3.58 |
% 12.74/3.58 | Equations (839) can reduce 195 to:
% 12.74/3.58 | (202) $false
% 12.74/3.58 |
% 12.74/3.58 |-The branch is then unsatisfiable
% 12.74/3.58 |-Branch two:
% 12.74/3.58 | (839) all_0_8_8 = e0
% 12.74/3.58 | (576) ~ (all_0_15_15 = e2)
% 12.74/3.58 |
% 12.74/3.58 +-Applying beta-rule and splitting (153), into two cases.
% 12.74/3.58 |-Branch one:
% 12.74/3.58 | (395) all_0_9_9 = e0
% 12.74/3.58 |
% 12.74/3.58 | Equations (395) can reduce 494 to:
% 12.74/3.58 | (202) $false
% 12.74/3.58 |
% 12.74/3.58 |-The branch is then unsatisfiable
% 12.74/3.58 |-Branch two:
% 12.74/3.58 | (494) ~ (all_0_9_9 = e0)
% 12.74/3.58 | (495) all_0_13_13 = e0 | all_0_17_17 = e0 | all_0_21_21 = e0
% 12.74/3.58 |
% 12.74/3.58 +-Applying beta-rule and splitting (495), into two cases.
% 12.74/3.58 |-Branch one:
% 12.74/3.58 | (449) all_0_13_13 = e0
% 12.74/3.58 |
% 12.74/3.58 | Equations (449) can reduce 149 to:
% 12.74/3.58 | (1463) ~ (all_0_14_14 = e0)
% 12.74/3.58 |
% 12.74/3.58 | Simplifying 1463 yields:
% 12.74/3.58 | (550) ~ (all_0_14_14 = e0)
% 12.74/3.58 |
% 12.74/3.58 | Equations (449) can reduce 143 to:
% 12.74/3.58 | (293) ~ (e2 = e0)
% 12.74/3.58 |
% 12.74/3.58 | Simplifying 293 yields:
% 12.74/3.58 | (13) ~ (e2 = e0)
% 12.74/3.58 |
% 12.74/3.58 | Equations (449) can reduce 358 to:
% 12.74/3.58 | (1254) ~ (e1 = e0)
% 12.74/3.58 |
% 12.74/3.58 | Simplifying 1254 yields:
% 12.74/3.58 | (181) ~ (e1 = e0)
% 12.74/3.58 |
% 12.74/3.58 +-Applying beta-rule and splitting (127), into two cases.
% 12.74/3.58 |-Branch one:
% 12.74/3.58 | (208) ~ (all_0_17_17 = e1)
% 12.74/3.58 |
% 12.74/3.58 | Equations (415) can reduce 208 to:
% 12.74/3.58 | (202) $false
% 12.74/3.58 |
% 12.74/3.58 |-The branch is then unsatisfiable
% 12.74/3.58 |-Branch two:
% 12.74/3.58 | (415) all_0_17_17 = e1
% 12.74/3.58 | (555) ~ (all_0_18_18 = e2)
% 12.74/3.58 |
% 12.74/3.58 +-Applying beta-rule and splitting (18), into two cases.
% 12.74/3.58 |-Branch one:
% 12.74/3.58 | (1501) all_0_20_20 = e1
% 12.74/3.58 |
% 12.74/3.58 | Equations (1501) can reduce 167 to:
% 12.74/3.58 | (317) ~ (all_0_12_12 = e1)
% 12.74/3.58 |
% 12.74/3.58 | Equations (1501) can reduce 134 to:
% 12.74/3.58 | (413) ~ (all_0_16_16 = e1)
% 12.74/3.58 |
% 12.74/3.58 | Equations (1501) can reduce 61 to:
% 12.74/3.58 | (1932) ~ (all_0_21_21 = e1)
% 12.74/3.58 |
% 12.74/3.58 | Simplifying 1932 yields:
% 12.74/3.58 | (1688) ~ (all_0_21_21 = e1)
% 12.74/3.58 |
% 12.74/3.58 | Equations (1501) can reduce 220 to:
% 12.74/3.58 | (181) ~ (e1 = e0)
% 12.74/3.58 |
% 12.74/3.58 +-Applying beta-rule and splitting (121), into two cases.
% 12.74/3.58 |-Branch one:
% 12.74/3.58 | (250) all_0_18_18 = e3
% 12.74/3.58 |
% 12.74/3.58 | Equations (250) can reduce 129 to:
% 12.74/3.58 | (225) ~ (all_0_10_10 = e3)
% 12.74/3.58 |
% 12.74/3.58 | Equations (250) can reduce 39 to:
% 12.74/3.58 | (298) ~ (all_0_16_16 = e3)
% 12.74/3.58 |
% 12.74/3.58 | Equations (250) can reduce 4 to:
% 12.74/3.58 | (238) ~ (all_0_19_19 = e3)
% 12.74/3.58 |
% 12.74/3.58 | Simplifying 238 yields:
% 12.74/3.58 | (239) ~ (all_0_19_19 = e3)
% 12.74/3.58 |
% 12.74/3.58 | Equations (250) can reduce 555 to:
% 12.74/3.58 | (101) ~ (e3 = e2)
% 12.74/3.58 |
% 12.74/3.58 | Equations (250) can reduce 245 to:
% 12.74/3.58 | (136) ~ (e3 = e0)
% 12.74/3.58 |
% 12.74/3.58 +-Applying beta-rule and splitting (10), into two cases.
% 12.74/3.58 |-Branch one:
% 12.74/3.58 | (792) all_0_16_16 = e0
% 12.74/3.58 |
% 12.74/3.58 | Equations (792) can reduce 611 to:
% 12.74/3.58 | (202) $false
% 12.74/3.58 |
% 12.74/3.58 |-The branch is then unsatisfiable
% 12.74/3.58 |-Branch two:
% 12.74/3.58 | (611) ~ (all_0_16_16 = e0)
% 12.74/3.58 | (2061) all_0_17_17 = e0 | all_0_18_18 = e0 | all_0_19_19 = e0
% 12.74/3.58 |
% 12.74/3.58 +-Applying beta-rule and splitting (2061), into two cases.
% 12.74/3.58 |-Branch one:
% 12.74/3.58 | (540) all_0_17_17 = e0
% 12.74/3.58 |
% 12.74/3.58 | Combining equations (415,540) yields a new equation:
% 12.74/3.58 | (491) e1 = e0
% 12.74/3.58 |
% 12.74/3.58 | Simplifying 491 yields:
% 12.74/3.58 | (421) e1 = e0
% 12.74/3.58 |
% 12.74/3.58 | Equations (421) can reduce 181 to:
% 12.74/3.58 | (202) $false
% 12.74/3.58 |
% 12.74/3.58 |-The branch is then unsatisfiable
% 12.74/3.58 |-Branch two:
% 12.74/3.58 | (288) ~ (all_0_17_17 = e0)
% 12.74/3.58 | (2066) all_0_18_18 = e0 | all_0_19_19 = e0
% 12.74/3.58 |
% 12.74/3.58 +-Applying beta-rule and splitting (2066), into two cases.
% 12.74/3.58 |-Branch one:
% 12.74/3.58 | (556) all_0_18_18 = e0
% 12.74/3.58 |
% 12.74/3.58 | Combining equations (250,556) yields a new equation:
% 12.74/3.58 | (277) e3 = e0
% 12.74/3.58 |
% 12.74/3.58 | Simplifying 277 yields:
% 12.74/3.58 | (278) e3 = e0
% 12.74/3.58 |
% 12.74/3.58 | Equations (278) can reduce 136 to:
% 12.74/3.58 | (202) $false
% 12.74/3.58 |
% 12.74/3.58 |-The branch is then unsatisfiable
% 12.74/3.58 |-Branch two:
% 12.74/3.58 | (245) ~ (all_0_18_18 = e0)
% 12.74/3.58 | (287) all_0_19_19 = e0
% 12.74/3.58 |
% 12.74/3.58 | Equations (287) can reduce 175 to:
% 12.74/3.58 | (611) ~ (all_0_16_16 = e0)
% 12.74/3.58 |
% 12.74/3.58 | Equations (287) can reduce 239 to:
% 12.74/3.58 | (291) ~ (e3 = e0)
% 12.74/3.58 |
% 12.74/3.58 | Simplifying 291 yields:
% 12.74/3.58 | (136) ~ (e3 = e0)
% 12.74/3.58 |
% 12.74/3.58 | Equations (287) can reduce 622 to:
% 12.74/3.58 | (1254) ~ (e1 = e0)
% 12.74/3.58 |
% 12.74/3.58 | Simplifying 1254 yields:
% 12.74/3.58 | (181) ~ (e1 = e0)
% 12.74/3.58 |
% 12.74/3.58 +-Applying beta-rule and splitting (133), into two cases.
% 12.74/3.58 |-Branch one:
% 12.74/3.58 | (981) all_0_11_11 = e2
% 12.74/3.58 |
% 12.74/3.58 | Equations (981) can reduce 145 to:
% 12.74/3.58 | (198) ~ (all_0_9_9 = e2)
% 12.74/3.58 |
% 13.01/3.58 +-Applying beta-rule and splitting (144), into two cases.
% 13.01/3.58 |-Branch one:
% 13.01/3.58 | (362) all_0_9_9 = e2
% 13.01/3.58 |
% 13.01/3.58 | Equations (362) can reduce 198 to:
% 13.01/3.58 | (202) $false
% 13.01/3.58 |
% 13.01/3.58 |-The branch is then unsatisfiable
% 13.01/3.58 |-Branch two:
% 13.01/3.58 | (198) ~ (all_0_9_9 = e2)
% 13.01/3.58 | (365) all_0_17_17 = e2 | all_0_21_21 = e2
% 13.01/3.58 |
% 13.01/3.58 +-Applying beta-rule and splitting (365), into two cases.
% 13.01/3.58 |-Branch one:
% 13.01/3.58 | (371) all_0_17_17 = e2
% 13.01/3.58 |
% 13.01/3.58 | Combining equations (415,371) yields a new equation:
% 13.01/3.58 | (367) e2 = e1
% 13.01/3.58 |
% 13.01/3.58 | Equations (367) can reduce 71 to:
% 13.01/3.58 | (202) $false
% 13.01/3.58 |
% 13.01/3.58 |-The branch is then unsatisfiable
% 13.01/3.58 |-Branch two:
% 13.01/3.58 | (375) ~ (all_0_17_17 = e2)
% 13.01/3.58 | (376) all_0_21_21 = e2
% 13.01/3.58 |
% 13.01/3.58 | Equations (376) can reduce 1688 to:
% 13.01/3.58 | (71) ~ (e2 = e1)
% 13.01/3.58 |
% 13.01/3.58 +-Applying beta-rule and splitting (7), into two cases.
% 13.01/3.58 |-Branch one:
% 13.01/3.58 | (427) all_0_16_16 = e3
% 13.01/3.58 |
% 13.01/3.58 | Equations (427) can reduce 298 to:
% 13.01/3.58 | (202) $false
% 13.01/3.58 |
% 13.01/3.58 |-The branch is then unsatisfiable
% 13.01/3.58 |-Branch two:
% 13.01/3.58 | (298) ~ (all_0_16_16 = e3)
% 13.01/3.58 | (430) all_0_16_16 = e2 | all_0_16_16 = e1 | all_0_16_16 = e0
% 13.01/3.58 |
% 13.01/3.58 +-Applying beta-rule and splitting (165), into two cases.
% 13.01/3.58 |-Branch one:
% 13.01/3.58 | (233) all_0_11_11 = e3
% 13.01/3.58 |
% 13.01/3.58 | Combining equations (233,981) yields a new equation:
% 13.01/3.58 | (372) e3 = e2
% 13.01/3.58 |
% 13.01/3.58 | Simplifying 372 yields:
% 13.01/3.58 | (373) e3 = e2
% 13.01/3.58 |
% 13.01/3.58 | Equations (373) can reduce 101 to:
% 13.01/3.58 | (202) $false
% 13.01/3.58 |
% 13.01/3.58 |-The branch is then unsatisfiable
% 13.01/3.58 |-Branch two:
% 13.01/3.58 | (242) ~ (all_0_11_11 = e3)
% 13.01/3.58 | (748) all_0_15_15 = e3 | all_0_19_19 = e3 | all_0_23_23 = e3
% 13.01/3.58 |
% 13.01/3.58 +-Applying beta-rule and splitting (123), into two cases.
% 13.01/3.58 |-Branch one:
% 13.01/3.58 | (366) all_0_8_8 = e1
% 13.01/3.58 |
% 13.01/3.58 | Combining equations (366,839) yields a new equation:
% 13.01/3.58 | (491) e1 = e0
% 13.01/3.58 |
% 13.01/3.58 | Simplifying 491 yields:
% 13.01/3.58 | (421) e1 = e0
% 13.01/3.58 |
% 13.01/3.58 | Equations (421) can reduce 181 to:
% 13.01/3.58 | (202) $false
% 13.01/3.58 |
% 13.01/3.58 |-The branch is then unsatisfiable
% 13.01/3.58 |-Branch two:
% 13.01/3.58 | (193) ~ (all_0_8_8 = e1)
% 13.01/3.58 | (370) all_0_9_9 = e1 | all_0_10_10 = e1 | all_0_11_11 = e1
% 13.01/3.58 |
% 13.01/3.58 +-Applying beta-rule and splitting (748), into two cases.
% 13.01/3.58 |-Branch one:
% 13.01/3.58 | (665) all_0_15_15 = e3
% 13.01/3.58 |
% 13.01/3.58 | Equations (665) can reduce 44 to:
% 13.01/3.58 | (325) ~ (all_0_14_14 = e3)
% 13.01/3.58 |
% 13.01/3.58 +-Applying beta-rule and splitting (370), into two cases.
% 13.01/3.58 |-Branch one:
% 13.01/3.58 | (380) all_0_9_9 = e1
% 13.01/3.58 |
% 13.01/3.58 | Equations (380) can reduce 316 to:
% 13.01/3.58 | (202) $false
% 13.01/3.58 |
% 13.01/3.58 |-The branch is then unsatisfiable
% 13.01/3.58 |-Branch two:
% 13.01/3.58 | (316) ~ (all_0_9_9 = e1)
% 13.01/3.58 | (383) all_0_10_10 = e1 | all_0_11_11 = e1
% 13.01/3.58 |
% 13.01/3.58 +-Applying beta-rule and splitting (383), into two cases.
% 13.01/3.58 |-Branch one:
% 13.01/3.58 | (932) all_0_10_10 = e1
% 13.01/3.58 |
% 13.01/3.58 | Equations (932) can reduce 180 to:
% 13.01/3.58 | (318) ~ (all_0_14_14 = e1)
% 13.01/3.58 |
% 13.01/3.58 | Simplifying 318 yields:
% 13.01/3.58 | (319) ~ (all_0_14_14 = e1)
% 13.01/3.58 |
% 13.01/3.58 | Equations (932) can reduce 225 to:
% 13.01/3.58 | (464) ~ (e3 = e1)
% 13.01/3.58 |
% 13.01/3.58 | Simplifying 464 yields:
% 13.01/3.58 | (137) ~ (e3 = e1)
% 13.01/3.58 |
% 13.01/3.58 | Equations (932) can reduce 602 to:
% 13.01/3.58 | (181) ~ (e1 = e0)
% 13.01/3.58 |
% 13.01/3.58 +-Applying beta-rule and splitting (95), into two cases.
% 13.01/3.58 |-Branch one:
% 13.01/3.58 | (331) all_0_14_14 = e3
% 13.01/3.58 |
% 13.01/3.58 | Equations (331) can reduce 325 to:
% 13.01/3.58 | (202) $false
% 13.01/3.58 |
% 13.01/3.58 |-The branch is then unsatisfiable
% 13.01/3.58 |-Branch two:
% 13.01/3.58 | (325) ~ (all_0_14_14 = e3)
% 13.01/3.58 | (334) all_0_14_14 = e2 | all_0_14_14 = e1 | all_0_14_14 = e0
% 13.01/3.58 |
% 13.01/3.58 +-Applying beta-rule and splitting (334), into two cases.
% 13.01/3.58 |-Branch one:
% 13.01/3.58 | (264) all_0_14_14 = e2
% 13.01/3.58 |
% 13.01/3.58 +-Applying beta-rule and splitting (430), into two cases.
% 13.01/3.58 |-Branch one:
% 13.01/3.58 | (785) all_0_16_16 = e2
% 13.01/3.58 |
% 13.01/3.58 | Equations (785) can reduce 413 to:
% 13.01/3.58 | (71) ~ (e2 = e1)
% 13.01/3.58 |
% 13.01/3.58 +-Applying beta-rule and splitting (77), into two cases.
% 13.01/3.58 |-Branch one:
% 13.01/3.58 | (730) all_0_12_12 = e1
% 13.01/3.58 |
% 13.01/3.58 | Equations (730) can reduce 317 to:
% 13.01/3.58 | (202) $false
% 13.01/3.58 |
% 13.01/3.58 |-The branch is then unsatisfiable
% 13.01/3.58 |-Branch two:
% 13.01/3.58 | (317) ~ (all_0_12_12 = e1)
% 13.01/3.58 | (760) all_0_13_13 = e1 | all_0_14_14 = e1 | all_0_15_15 = e1
% 13.01/3.58 |
% 13.01/3.58 +-Applying beta-rule and splitting (760), into two cases.
% 13.01/3.58 |-Branch one:
% 13.01/3.58 | (315) all_0_13_13 = e1
% 13.01/3.58 |
% 13.01/3.58 | Combining equations (315,449) yields a new equation:
% 13.01/3.58 | (491) e1 = e0
% 13.01/3.58 |
% 13.01/3.58 | Simplifying 491 yields:
% 13.01/3.58 | (421) e1 = e0
% 13.01/3.58 |
% 13.01/3.58 | Equations (421) can reduce 181 to:
% 13.01/3.58 | (202) $false
% 13.01/3.58 |
% 13.01/3.58 |-The branch is then unsatisfiable
% 13.01/3.58 |-Branch two:
% 13.01/3.58 | (358) ~ (all_0_13_13 = e1)
% 13.01/3.58 | (765) all_0_14_14 = e1 | all_0_15_15 = e1
% 13.01/3.58 |
% 13.01/3.58 +-Applying beta-rule and splitting (765), into two cases.
% 13.01/3.58 |-Branch one:
% 13.01/3.58 | (339) all_0_14_14 = e1
% 13.01/3.58 |
% 13.01/3.58 | Combining equations (339,264) yields a new equation:
% 13.01/3.58 | (367) e2 = e1
% 13.01/3.58 |
% 13.01/3.58 | Equations (367) can reduce 71 to:
% 13.01/3.58 | (202) $false
% 13.01/3.58 |
% 13.01/3.58 |-The branch is then unsatisfiable
% 13.01/3.58 |-Branch two:
% 13.01/3.58 | (319) ~ (all_0_14_14 = e1)
% 13.01/3.58 | (677) all_0_15_15 = e1
% 13.01/3.58 |
% 13.01/3.58 | Combining equations (677,665) yields a new equation:
% 13.01/3.58 | (417) e3 = e1
% 13.01/3.58 |
% 13.01/3.58 | Equations (417) can reduce 137 to:
% 13.01/3.58 | (202) $false
% 13.01/3.58 |
% 13.01/3.58 |-The branch is then unsatisfiable
% 13.01/3.58 |-Branch two:
% 13.01/3.58 | (256) ~ (all_0_16_16 = e2)
% 13.01/3.58 | (788) all_0_16_16 = e1 | all_0_16_16 = e0
% 13.01/3.58 |
% 13.01/3.58 +-Applying beta-rule and splitting (788), into two cases.
% 13.01/3.58 |-Branch one:
% 13.01/3.58 | (328) all_0_16_16 = e1
% 13.01/3.58 |
% 13.01/3.58 | Equations (328) can reduce 413 to:
% 13.01/3.58 | (202) $false
% 13.01/3.58 |
% 13.01/3.58 |-The branch is then unsatisfiable
% 13.01/3.58 |-Branch two:
% 13.01/3.58 | (413) ~ (all_0_16_16 = e1)
% 13.01/3.58 | (792) all_0_16_16 = e0
% 13.01/3.58 |
% 13.01/3.58 | Equations (792) can reduce 611 to:
% 13.01/3.58 | (202) $false
% 13.01/3.58 |
% 13.01/3.58 |-The branch is then unsatisfiable
% 13.01/3.58 |-Branch two:
% 13.01/3.58 | (255) ~ (all_0_14_14 = e2)
% 13.01/3.58 | (338) all_0_14_14 = e1 | all_0_14_14 = e0
% 13.01/3.58 |
% 13.01/3.58 +-Applying beta-rule and splitting (338), into two cases.
% 13.01/3.58 |-Branch one:
% 13.01/3.58 | (339) all_0_14_14 = e1
% 13.01/3.58 |
% 13.01/3.58 | Equations (339) can reduce 319 to:
% 13.01/3.58 | (202) $false
% 13.01/3.58 |
% 13.01/3.58 |-The branch is then unsatisfiable
% 13.01/3.58 |-Branch two:
% 13.01/3.58 | (319) ~ (all_0_14_14 = e1)
% 13.01/3.58 | (342) all_0_14_14 = e0
% 13.01/3.58 |
% 13.01/3.58 | Equations (342) can reduce 550 to:
% 13.01/3.58 | (202) $false
% 13.01/3.58 |
% 13.01/3.58 |-The branch is then unsatisfiable
% 13.01/3.58 |-Branch two:
% 13.01/3.58 | (1170) ~ (all_0_10_10 = e1)
% 13.01/3.58 | (672) all_0_11_11 = e1
% 13.01/3.58 |
% 13.01/3.58 | Combining equations (672,981) yields a new equation:
% 13.01/3.58 | (367) e2 = e1
% 13.01/3.58 |
% 13.01/3.58 | Equations (367) can reduce 71 to:
% 13.01/3.58 | (202) $false
% 13.01/3.58 |
% 13.01/3.58 |-The branch is then unsatisfiable
% 13.01/3.58 |-Branch two:
% 13.01/3.58 | (237) ~ (all_0_15_15 = e3)
% 13.01/3.58 | (776) all_0_19_19 = e3 | all_0_23_23 = e3
% 13.01/3.58 |
% 13.01/3.58 +-Applying beta-rule and splitting (776), into two cases.
% 13.01/3.58 |-Branch one:
% 13.01/3.58 | (481) all_0_19_19 = e3
% 13.01/3.58 |
% 13.01/3.58 | Combining equations (287,481) yields a new equation:
% 13.01/3.58 | (278) e3 = e0
% 13.01/3.58 |
% 13.01/3.58 | Equations (278) can reduce 136 to:
% 13.01/3.58 | (202) $false
% 13.01/3.58 |
% 13.01/3.58 |-The branch is then unsatisfiable
% 13.01/3.58 |-Branch two:
% 13.01/3.58 | (239) ~ (all_0_19_19 = e3)
% 13.01/3.58 | (301) all_0_23_23 = e3
% 13.01/3.58 |
% 13.01/3.58 | Equations (301) can reduce 223 to:
% 13.01/3.58 | (202) $false
% 13.01/3.58 |
% 13.01/3.58 |-The branch is then unsatisfiable
% 13.01/3.58 |-Branch two:
% 13.01/3.58 | (1113) ~ (all_0_11_11 = e2)
% 13.01/3.58 | (1114) all_0_15_15 = e2 | all_0_19_19 = e2 | all_0_23_23 = e2
% 13.01/3.58 |
% 13.01/3.58 +-Applying beta-rule and splitting (1114), into two cases.
% 13.01/3.58 |-Branch one:
% 13.01/3.58 | (267) all_0_15_15 = e2
% 13.01/3.59 |
% 13.01/3.59 | Equations (267) can reduce 576 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (576) ~ (all_0_15_15 = e2)
% 13.01/3.59 | (1128) all_0_19_19 = e2 | all_0_23_23 = e2
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (1128), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (709) all_0_19_19 = e2
% 13.01/3.59 |
% 13.01/3.59 | Combining equations (709,287) yields a new equation:
% 13.01/3.59 | (283) e2 = e0
% 13.01/3.59 |
% 13.01/3.59 | Simplifying 283 yields:
% 13.01/3.59 | (284) e2 = e0
% 13.01/3.59 |
% 13.01/3.59 | Equations (284) can reduce 13 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (271) ~ (all_0_19_19 = e2)
% 13.01/3.59 | (305) all_0_23_23 = e2
% 13.01/3.59 |
% 13.01/3.59 | Equations (305) can reduce 273 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (224) ~ (all_0_18_18 = e3)
% 13.01/3.59 | (253) all_0_18_18 = e2 | all_0_18_18 = e0
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (253), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (254) all_0_18_18 = e2
% 13.01/3.59 |
% 13.01/3.59 | Equations (254) can reduce 555 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (555) ~ (all_0_18_18 = e2)
% 13.01/3.59 | (556) all_0_18_18 = e0
% 13.01/3.59 |
% 13.01/3.59 | Equations (556) can reduce 245 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (920) ~ (all_0_20_20 = e1)
% 13.01/3.59 | (1732) all_0_21_21 = e1 | all_0_22_22 = e1 | all_0_23_23 = e1
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (1732), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (1674) all_0_21_21 = e1
% 13.01/3.59 |
% 13.01/3.59 | Equations (1674) can reduce 1688 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (1688) ~ (all_0_21_21 = e1)
% 13.01/3.59 | (1913) all_0_22_22 = e1 | all_0_23_23 = e1
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (121), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (250) all_0_18_18 = e3
% 13.01/3.59 |
% 13.01/3.59 | Equations (250) can reduce 39 to:
% 13.01/3.59 | (298) ~ (all_0_16_16 = e3)
% 13.01/3.59 |
% 13.01/3.59 | Equations (250) can reduce 245 to:
% 13.01/3.59 | (136) ~ (e3 = e0)
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (7), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (427) all_0_16_16 = e3
% 13.01/3.59 |
% 13.01/3.59 | Equations (427) can reduce 298 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (298) ~ (all_0_16_16 = e3)
% 13.01/3.59 | (430) all_0_16_16 = e2 | all_0_16_16 = e1 | all_0_16_16 = e0
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (430), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (785) all_0_16_16 = e2
% 13.01/3.59 |
% 13.01/3.59 | Equations (785) can reduce 175 to:
% 13.01/3.59 | (270) ~ (all_0_19_19 = e2)
% 13.01/3.59 |
% 13.01/3.59 | Simplifying 270 yields:
% 13.01/3.59 | (271) ~ (all_0_19_19 = e2)
% 13.01/3.59 |
% 13.01/3.59 | Equations (785) can reduce 413 to:
% 13.01/3.59 | (71) ~ (e2 = e1)
% 13.01/3.59 |
% 13.01/3.59 | Equations (785) can reduce 611 to:
% 13.01/3.59 | (13) ~ (e2 = e0)
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (10), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (792) all_0_16_16 = e0
% 13.01/3.59 |
% 13.01/3.59 | Combining equations (785,792) yields a new equation:
% 13.01/3.59 | (283) e2 = e0
% 13.01/3.59 |
% 13.01/3.59 | Simplifying 283 yields:
% 13.01/3.59 | (284) e2 = e0
% 13.01/3.59 |
% 13.01/3.59 | Equations (284) can reduce 13 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (611) ~ (all_0_16_16 = e0)
% 13.01/3.59 | (2061) all_0_17_17 = e0 | all_0_18_18 = e0 | all_0_19_19 = e0
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (2061), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (540) all_0_17_17 = e0
% 13.01/3.59 |
% 13.01/3.59 | Combining equations (415,540) yields a new equation:
% 13.01/3.59 | (491) e1 = e0
% 13.01/3.59 |
% 13.01/3.59 | Simplifying 491 yields:
% 13.01/3.59 | (421) e1 = e0
% 13.01/3.59 |
% 13.01/3.59 | Equations (421) can reduce 181 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (288) ~ (all_0_17_17 = e0)
% 13.01/3.59 | (2066) all_0_18_18 = e0 | all_0_19_19 = e0
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (2066), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (556) all_0_18_18 = e0
% 13.01/3.59 |
% 13.01/3.59 | Combining equations (250,556) yields a new equation:
% 13.01/3.59 | (277) e3 = e0
% 13.01/3.59 |
% 13.01/3.59 | Simplifying 277 yields:
% 13.01/3.59 | (278) e3 = e0
% 13.01/3.59 |
% 13.01/3.59 | Equations (278) can reduce 136 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (245) ~ (all_0_18_18 = e0)
% 13.01/3.59 | (287) all_0_19_19 = e0
% 13.01/3.59 |
% 13.01/3.59 | Equations (287) can reduce 271 to:
% 13.01/3.59 | (293) ~ (e2 = e0)
% 13.01/3.59 |
% 13.01/3.59 | Simplifying 293 yields:
% 13.01/3.59 | (13) ~ (e2 = e0)
% 13.01/3.59 |
% 13.01/3.59 | Equations (287) can reduce 622 to:
% 13.01/3.59 | (1254) ~ (e1 = e0)
% 13.01/3.59 |
% 13.01/3.59 | Simplifying 1254 yields:
% 13.01/3.59 | (181) ~ (e1 = e0)
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (163), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (195) ~ (all_0_8_8 = e0)
% 13.01/3.59 |
% 13.01/3.59 | Equations (839) can reduce 195 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (839) all_0_8_8 = e0
% 13.01/3.59 | (242) ~ (all_0_11_11 = e3)
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (133), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (981) all_0_11_11 = e2
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (123), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (366) all_0_8_8 = e1
% 13.01/3.59 |
% 13.01/3.59 | Combining equations (366,839) yields a new equation:
% 13.01/3.59 | (491) e1 = e0
% 13.01/3.59 |
% 13.01/3.59 | Simplifying 491 yields:
% 13.01/3.59 | (421) e1 = e0
% 13.01/3.59 |
% 13.01/3.59 | Equations (421) can reduce 181 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (193) ~ (all_0_8_8 = e1)
% 13.01/3.59 | (370) all_0_9_9 = e1 | all_0_10_10 = e1 | all_0_11_11 = e1
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (370), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (380) all_0_9_9 = e1
% 13.01/3.59 |
% 13.01/3.59 | Equations (380) can reduce 316 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (316) ~ (all_0_9_9 = e1)
% 13.01/3.59 | (383) all_0_10_10 = e1 | all_0_11_11 = e1
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (383), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (932) all_0_10_10 = e1
% 13.01/3.59 |
% 13.01/3.59 | Equations (932) can reduce 602 to:
% 13.01/3.59 | (181) ~ (e1 = e0)
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (1913), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (443) all_0_22_22 = e1
% 13.01/3.59 |
% 13.01/3.59 | Combining equations (446,443) yields a new equation:
% 13.01/3.59 | (421) e1 = e0
% 13.01/3.59 |
% 13.01/3.59 | Equations (421) can reduce 181 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (309) ~ (all_0_22_22 = e1)
% 13.01/3.59 | (308) all_0_23_23 = e1
% 13.01/3.59 |
% 13.01/3.59 | Equations (308) can reduce 570 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (1170) ~ (all_0_10_10 = e1)
% 13.01/3.59 | (672) all_0_11_11 = e1
% 13.01/3.59 |
% 13.01/3.59 | Combining equations (672,981) yields a new equation:
% 13.01/3.59 | (367) e2 = e1
% 13.01/3.59 |
% 13.01/3.59 | Equations (367) can reduce 71 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (1113) ~ (all_0_11_11 = e2)
% 13.01/3.59 | (1114) all_0_15_15 = e2 | all_0_19_19 = e2 | all_0_23_23 = e2
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (1114), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (267) all_0_15_15 = e2
% 13.01/3.59 |
% 13.01/3.59 | Equations (267) can reduce 576 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (576) ~ (all_0_15_15 = e2)
% 13.01/3.59 | (1128) all_0_19_19 = e2 | all_0_23_23 = e2
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (1128), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (709) all_0_19_19 = e2
% 13.01/3.59 |
% 13.01/3.59 | Combining equations (287,709) yields a new equation:
% 13.01/3.59 | (284) e2 = e0
% 13.01/3.59 |
% 13.01/3.59 | Equations (284) can reduce 13 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (271) ~ (all_0_19_19 = e2)
% 13.01/3.59 | (305) all_0_23_23 = e2
% 13.01/3.59 |
% 13.01/3.59 | Equations (305) can reduce 273 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (256) ~ (all_0_16_16 = e2)
% 13.01/3.59 | (788) all_0_16_16 = e1 | all_0_16_16 = e0
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (788), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (328) all_0_16_16 = e1
% 13.01/3.59 |
% 13.01/3.59 | Equations (328) can reduce 413 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (413) ~ (all_0_16_16 = e1)
% 13.01/3.59 | (792) all_0_16_16 = e0
% 13.01/3.59 |
% 13.01/3.59 | Equations (792) can reduce 611 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (224) ~ (all_0_18_18 = e3)
% 13.01/3.59 | (253) all_0_18_18 = e2 | all_0_18_18 = e0
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (253), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (254) all_0_18_18 = e2
% 13.01/3.59 |
% 13.01/3.59 | Equations (254) can reduce 555 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (555) ~ (all_0_18_18 = e2)
% 13.01/3.59 | (556) all_0_18_18 = e0
% 13.01/3.59 |
% 13.01/3.59 | Equations (556) can reduce 245 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (249) ~ (all_0_13_13 = e0)
% 13.01/3.59 | (499) all_0_17_17 = e0 | all_0_21_21 = e0
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (10), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (792) all_0_16_16 = e0
% 13.01/3.59 |
% 13.01/3.59 | Equations (792) can reduce 611 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (611) ~ (all_0_16_16 = e0)
% 13.01/3.59 | (2061) all_0_17_17 = e0 | all_0_18_18 = e0 | all_0_19_19 = e0
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (2061), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (540) all_0_17_17 = e0
% 13.01/3.59 |
% 13.01/3.59 | Combining equations (415,540) yields a new equation:
% 13.01/3.59 | (491) e1 = e0
% 13.01/3.59 |
% 13.01/3.59 | Simplifying 491 yields:
% 13.01/3.59 | (421) e1 = e0
% 13.01/3.59 |
% 13.01/3.59 | Equations (421) can reduce 181 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (288) ~ (all_0_17_17 = e0)
% 13.01/3.59 | (2066) all_0_18_18 = e0 | all_0_19_19 = e0
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (2066), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (556) all_0_18_18 = e0
% 13.01/3.59 |
% 13.01/3.59 | Equations (556) can reduce 245 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (245) ~ (all_0_18_18 = e0)
% 13.01/3.59 | (287) all_0_19_19 = e0
% 13.01/3.59 |
% 13.01/3.59 | Equations (287) can reduce 622 to:
% 13.01/3.59 | (1254) ~ (e1 = e0)
% 13.01/3.59 |
% 13.01/3.59 | Simplifying 1254 yields:
% 13.01/3.59 | (181) ~ (e1 = e0)
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (127), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (208) ~ (all_0_17_17 = e1)
% 13.01/3.59 |
% 13.01/3.59 | Equations (415) can reduce 208 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (415) all_0_17_17 = e1
% 13.01/3.59 | (555) ~ (all_0_18_18 = e2)
% 13.01/3.59 |
% 13.01/3.59 +-Applying beta-rule and splitting (499), into two cases.
% 13.01/3.59 |-Branch one:
% 13.01/3.59 | (540) all_0_17_17 = e0
% 13.01/3.59 |
% 13.01/3.59 | Combining equations (415,540) yields a new equation:
% 13.01/3.59 | (491) e1 = e0
% 13.01/3.59 |
% 13.01/3.59 | Simplifying 491 yields:
% 13.01/3.59 | (421) e1 = e0
% 13.01/3.59 |
% 13.01/3.59 | Equations (421) can reduce 181 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (288) ~ (all_0_17_17 = e0)
% 13.01/3.59 | (829) all_0_21_21 = e0
% 13.01/3.59 |
% 13.01/3.59 | Equations (829) can reduce 204 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (196) all_0_8_8 = e2
% 13.01/3.59 | (208) ~ (all_0_17_17 = e1)
% 13.01/3.59 |
% 13.01/3.59 | Equations (415) can reduce 208 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (315) all_0_13_13 = e1
% 13.01/3.59 | (194) ~ (all_0_22_22 = e0)
% 13.01/3.59 |
% 13.01/3.59 | Equations (446) can reduce 194 to:
% 13.01/3.59 | (202) $false
% 13.01/3.59 |
% 13.01/3.59 |-The branch is then unsatisfiable
% 13.01/3.59 |-Branch two:
% 13.01/3.59 | (366) all_0_8_8 = e1
% 13.01/3.59 | (255) ~ (all_0_14_14 = e2)
% 13.01/3.59 |
% 13.01/3.59 | Equations (366) can reduce 110 to:
% 13.01/3.59 | (2643) ~ (all_0_9_9 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Simplifying 2643 yields:
% 13.01/3.60 | (316) ~ (all_0_9_9 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Equations (366) can reduce 182 to:
% 13.01/3.60 | (2645) ~ (all_0_10_10 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Simplifying 2645 yields:
% 13.01/3.60 | (1170) ~ (all_0_10_10 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Equations (366) can reduce 24 to:
% 13.01/3.60 | (934) ~ (all_0_11_11 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Simplifying 934 yields:
% 13.01/3.60 | (675) ~ (all_0_11_11 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Equations (366) can reduce 2 to:
% 13.01/3.60 | (2649) ~ (all_0_12_12 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Simplifying 2649 yields:
% 13.01/3.60 | (317) ~ (all_0_12_12 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Equations (366) can reduce 179 to:
% 13.01/3.60 | (1228) ~ (all_0_16_16 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Simplifying 1228 yields:
% 13.01/3.60 | (413) ~ (all_0_16_16 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Equations (366) can reduce 122 to:
% 13.01/3.60 | (1727) ~ (all_0_20_20 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Simplifying 1727 yields:
% 13.01/3.60 | (920) ~ (all_0_20_20 = e1)
% 13.01/3.60 |
% 13.01/3.60 | From (366) and (12) follows:
% 13.01/3.60 | (2655) op(all_0_7_7, e1) = all_0_6_6
% 13.01/3.60 |
% 13.01/3.60 | From (366) and (157) follows:
% 13.01/3.60 | (2656) op(e3, e1) = all_0_7_7
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (140), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (193) ~ (all_0_8_8 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Equations (366) can reduce 193 to:
% 13.01/3.60 | (202) $false
% 13.01/3.60 |
% 13.01/3.60 |-The branch is then unsatisfiable
% 13.01/3.60 |-Branch two:
% 13.01/3.60 | (366) all_0_8_8 = e1
% 13.01/3.60 | (194) ~ (all_0_22_22 = e0)
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (183), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (193) ~ (all_0_8_8 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Equations (366) can reduce 193 to:
% 13.01/3.60 | (202) $false
% 13.01/3.60 |
% 13.01/3.60 |-The branch is then unsatisfiable
% 13.01/3.60 |-Branch two:
% 13.01/3.60 | (366) all_0_8_8 = e1
% 13.01/3.60 | (225) ~ (all_0_10_10 = e3)
% 13.01/3.60 |
% 13.01/3.60 | Instantiating formula (53) with e3, e1, all_0_7_7, all_0_10_10 and discharging atoms op(e3, e1) = all_0_7_7, op(e3, e1) = all_0_10_10, yields:
% 13.01/3.60 | (2665) all_0_7_7 = all_0_10_10
% 13.01/3.60 |
% 13.01/3.60 | From (2665) and (2655) follows:
% 13.01/3.60 | (2666) op(all_0_10_10, e1) = all_0_6_6
% 13.01/3.60 |
% 13.01/3.60 | From (2665) and (2656) follows:
% 13.01/3.60 | (54) op(e3, e1) = all_0_10_10
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (22), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (245) ~ (all_0_18_18 = e0)
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (91), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (208) ~ (all_0_17_17 = e1)
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (138), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (328) all_0_16_16 = e1
% 13.01/3.60 |
% 13.01/3.60 | Equations (328) can reduce 413 to:
% 13.01/3.60 | (202) $false
% 13.01/3.60 |
% 13.01/3.60 |-The branch is then unsatisfiable
% 13.01/3.60 |-Branch two:
% 13.01/3.60 | (413) ~ (all_0_16_16 = e1)
% 13.01/3.60 | (414) all_0_17_17 = e1 | all_0_19_19 = e1
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (414), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (415) all_0_17_17 = e1
% 13.01/3.60 |
% 13.01/3.60 | Equations (415) can reduce 208 to:
% 13.01/3.60 | (202) $false
% 13.01/3.60 |
% 13.01/3.60 |-The branch is then unsatisfiable
% 13.01/3.60 |-Branch two:
% 13.01/3.60 | (208) ~ (all_0_17_17 = e1)
% 13.01/3.60 | (420) all_0_19_19 = e1
% 13.01/3.60 |
% 13.01/3.60 | Equations (420) can reduce 188 to:
% 13.01/3.60 | (693) ~ (all_0_15_15 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Equations (420) can reduce 175 to:
% 13.01/3.60 | (413) ~ (all_0_16_16 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Equations (420) can reduce 120 to:
% 13.01/3.60 | (208) ~ (all_0_17_17 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Equations (420) can reduce 135 to:
% 13.01/3.60 | (1406) ~ (all_0_23_23 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Simplifying 1406 yields:
% 13.01/3.60 | (570) ~ (all_0_23_23 = e1)
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (78), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (555) ~ (all_0_18_18 = e2)
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (121), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (250) all_0_18_18 = e3
% 13.01/3.60 |
% 13.01/3.60 | Equations (250) can reduce 17 to:
% 13.01/3.60 | (451) ~ (all_0_17_17 = e3)
% 13.01/3.60 |
% 13.01/3.60 | Equations (250) can reduce 5 to:
% 13.01/3.60 | (561) ~ (all_0_22_22 = e3)
% 13.01/3.60 |
% 13.01/3.60 | Simplifying 561 yields:
% 13.01/3.60 | (360) ~ (all_0_22_22 = e3)
% 13.01/3.60 |
% 13.01/3.60 | Equations (250) can reduce 245 to:
% 13.01/3.60 | (136) ~ (e3 = e0)
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (131), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (224) ~ (all_0_18_18 = e3)
% 13.01/3.60 |
% 13.01/3.60 | Equations (250) can reduce 224 to:
% 13.01/3.60 | (202) $false
% 13.01/3.60 |
% 13.01/3.60 |-The branch is then unsatisfiable
% 13.01/3.60 |-Branch two:
% 13.01/3.60 | (250) all_0_18_18 = e3
% 13.01/3.60 | (220) ~ (all_0_20_20 = e0)
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (46), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (200) ~ (all_0_12_12 = e2)
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (112), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (213) all_0_20_20 = e0
% 13.01/3.60 |
% 13.01/3.60 | Equations (213) can reduce 220 to:
% 13.01/3.60 | (202) $false
% 13.01/3.60 |
% 13.01/3.60 |-The branch is then unsatisfiable
% 13.01/3.60 |-Branch two:
% 13.01/3.60 | (220) ~ (all_0_20_20 = e0)
% 13.01/3.60 | (828) all_0_21_21 = e0 | all_0_22_22 = e0
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (828), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (829) all_0_21_21 = e0
% 13.01/3.60 |
% 13.01/3.60 | Equations (829) can reduce 118 to:
% 13.01/3.60 | (494) ~ (all_0_9_9 = e0)
% 13.01/3.60 |
% 13.01/3.60 | Equations (829) can reduce 64 to:
% 13.01/3.60 | (288) ~ (all_0_17_17 = e0)
% 13.01/3.60 |
% 13.01/3.60 | Equations (829) can reduce 27 to:
% 13.01/3.60 | (215) ~ (all_0_22_22 = e0)
% 13.01/3.60 |
% 13.01/3.60 | Simplifying 215 yields:
% 13.01/3.60 | (194) ~ (all_0_22_22 = e0)
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (10), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (792) all_0_16_16 = e0
% 13.01/3.60 |
% 13.01/3.60 | Equations (792) can reduce 76 to:
% 13.01/3.60 | (214) ~ (all_0_12_12 = e0)
% 13.01/3.60 |
% 13.01/3.60 | Equations (792) can reduce 58 to:
% 13.01/3.60 | (2705) ~ (all_0_17_17 = e0)
% 13.01/3.60 |
% 13.01/3.60 | Simplifying 2705 yields:
% 13.01/3.60 | (288) ~ (all_0_17_17 = e0)
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (30), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (323) all_0_12_12 = e3
% 13.01/3.60 |
% 13.01/3.60 | Equations (323) can reduce 32 to:
% 13.01/3.60 | (2708) ~ (all_0_13_13 = e3)
% 13.01/3.60 |
% 13.01/3.60 | Simplifying 2708 yields:
% 13.01/3.60 | (219) ~ (all_0_13_13 = e3)
% 13.01/3.60 |
% 13.01/3.60 | Equations (323) can reduce 160 to:
% 13.01/3.60 | (324) ~ (all_0_14_14 = e3)
% 13.01/3.60 |
% 13.01/3.60 | Simplifying 324 yields:
% 13.01/3.60 | (325) ~ (all_0_14_14 = e3)
% 13.01/3.60 |
% 13.01/3.60 | Equations (323) can reduce 167 to:
% 13.01/3.60 | (2712) ~ (all_0_20_20 = e3)
% 13.01/3.60 |
% 13.01/3.60 | Simplifying 2712 yields:
% 13.01/3.60 | (1100) ~ (all_0_20_20 = e3)
% 13.01/3.60 |
% 13.01/3.60 | Equations (323) can reduce 200 to:
% 13.01/3.60 | (101) ~ (e3 = e2)
% 13.01/3.60 |
% 13.01/3.60 | Equations (323) can reduce 214 to:
% 13.01/3.60 | (136) ~ (e3 = e0)
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (190), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (204) ~ (all_0_21_21 = e0)
% 13.01/3.60 |
% 13.01/3.60 | Equations (829) can reduce 204 to:
% 13.01/3.60 | (202) $false
% 13.01/3.60 |
% 13.01/3.60 |-The branch is then unsatisfiable
% 13.01/3.60 |-Branch two:
% 13.01/3.60 | (829) all_0_21_21 = e0
% 13.01/3.60 | (273) ~ (all_0_23_23 = e2)
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (15), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (226) all_0_9_9 = e3
% 13.01/3.60 |
% 13.01/3.60 | Equations (226) can reduce 494 to:
% 13.01/3.60 | (136) ~ (e3 = e0)
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (144), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (362) all_0_9_9 = e2
% 13.01/3.60 |
% 13.01/3.60 | Combining equations (226,362) yields a new equation:
% 13.01/3.60 | (372) e3 = e2
% 13.01/3.60 |
% 13.01/3.60 | Simplifying 372 yields:
% 13.01/3.60 | (373) e3 = e2
% 13.01/3.60 |
% 13.01/3.60 | Equations (373) can reduce 101 to:
% 13.01/3.60 | (202) $false
% 13.01/3.60 |
% 13.01/3.60 |-The branch is then unsatisfiable
% 13.01/3.60 |-Branch two:
% 13.01/3.60 | (198) ~ (all_0_9_9 = e2)
% 13.01/3.60 | (365) all_0_17_17 = e2 | all_0_21_21 = e2
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (365), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (371) all_0_17_17 = e2
% 13.01/3.60 |
% 13.01/3.60 | Equations (371) can reduce 208 to:
% 13.01/3.60 | (71) ~ (e2 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Equations (371) can reduce 288 to:
% 13.01/3.60 | (13) ~ (e2 = e0)
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (125), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (434) all_0_20_20 = e3
% 13.01/3.60 |
% 13.01/3.60 | Equations (434) can reduce 1100 to:
% 13.01/3.60 | (202) $false
% 13.01/3.60 |
% 13.01/3.60 |-The branch is then unsatisfiable
% 13.01/3.60 |-Branch two:
% 13.01/3.60 | (1100) ~ (all_0_20_20 = e3)
% 13.01/3.60 | (1899) all_0_21_21 = e3 | all_0_22_22 = e3 | all_0_23_23 = e3
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (1899), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (1666) all_0_21_21 = e3
% 13.01/3.60 |
% 13.01/3.60 | Combining equations (1666,829) yields a new equation:
% 13.01/3.60 | (277) e3 = e0
% 13.01/3.60 |
% 13.01/3.60 | Simplifying 277 yields:
% 13.01/3.60 | (278) e3 = e0
% 13.01/3.60 |
% 13.01/3.60 | Equations (278) can reduce 136 to:
% 13.01/3.60 | (202) $false
% 13.01/3.60 |
% 13.01/3.60 |-The branch is then unsatisfiable
% 13.01/3.60 |-Branch two:
% 13.01/3.60 | (300) ~ (all_0_21_21 = e3)
% 13.01/3.60 | (1904) all_0_22_22 = e3 | all_0_23_23 = e3
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (1904), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (344) all_0_22_22 = e3
% 13.01/3.60 |
% 13.01/3.60 | Equations (344) can reduce 360 to:
% 13.01/3.60 | (202) $false
% 13.01/3.60 |
% 13.01/3.60 |-The branch is then unsatisfiable
% 13.01/3.60 |-Branch two:
% 13.01/3.60 | (360) ~ (all_0_22_22 = e3)
% 13.01/3.60 | (301) all_0_23_23 = e3
% 13.01/3.60 |
% 13.01/3.60 | Equations (301) can reduce 130 to:
% 13.01/3.60 | (1100) ~ (all_0_20_20 = e3)
% 13.01/3.60 |
% 13.01/3.60 | Equations (301) can reduce 191 to:
% 13.01/3.60 | (360) ~ (all_0_22_22 = e3)
% 13.01/3.60 |
% 13.01/3.60 | Equations (301) can reduce 273 to:
% 13.01/3.60 | (101) ~ (e3 = e2)
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (35), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (196) all_0_8_8 = e2
% 13.01/3.60 |
% 13.01/3.60 | Combining equations (196,366) yields a new equation:
% 13.01/3.60 | (767) e2 = e1
% 13.01/3.60 |
% 13.01/3.60 | Simplifying 767 yields:
% 13.01/3.60 | (367) e2 = e1
% 13.01/3.60 |
% 13.01/3.60 | Equations (367) can reduce 71 to:
% 13.01/3.60 | (202) $false
% 13.01/3.60 |
% 13.01/3.60 |-The branch is then unsatisfiable
% 13.01/3.60 |-Branch two:
% 13.01/3.60 | (201) ~ (all_0_8_8 = e2)
% 13.01/3.60 | (2044) all_0_12_12 = e2 | all_0_16_16 = e2 | all_0_20_20 = e2
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (2044), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (260) all_0_12_12 = e2
% 13.01/3.60 |
% 13.01/3.60 | Combining equations (260,323) yields a new equation:
% 13.01/3.60 | (373) e3 = e2
% 13.01/3.60 |
% 13.01/3.60 | Equations (373) can reduce 101 to:
% 13.01/3.60 | (202) $false
% 13.01/3.60 |
% 13.01/3.60 |-The branch is then unsatisfiable
% 13.01/3.60 |-Branch two:
% 13.01/3.60 | (200) ~ (all_0_12_12 = e2)
% 13.01/3.60 | (2758) all_0_16_16 = e2 | all_0_20_20 = e2
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (2758), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (785) all_0_16_16 = e2
% 13.01/3.60 |
% 13.01/3.60 | Combining equations (792,785) yields a new equation:
% 13.01/3.60 | (284) e2 = e0
% 13.01/3.60 |
% 13.01/3.60 | Equations (284) can reduce 13 to:
% 13.01/3.60 | (202) $false
% 13.01/3.60 |
% 13.01/3.60 |-The branch is then unsatisfiable
% 13.01/3.60 |-Branch two:
% 13.01/3.60 | (256) ~ (all_0_16_16 = e2)
% 13.01/3.60 | (526) all_0_20_20 = e2
% 13.01/3.60 |
% 13.01/3.60 | Equations (526) can reduce 69 to:
% 13.01/3.60 | (257) ~ (all_0_22_22 = e2)
% 13.01/3.60 |
% 13.01/3.60 | Simplifying 257 yields:
% 13.01/3.60 | (258) ~ (all_0_22_22 = e2)
% 13.01/3.60 |
% 13.01/3.60 | Equations (526) can reduce 1100 to:
% 13.01/3.60 | (274) ~ (e3 = e2)
% 13.01/3.60 |
% 13.01/3.60 | Simplifying 274 yields:
% 13.01/3.60 | (101) ~ (e3 = e2)
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (87), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (344) all_0_22_22 = e3
% 13.01/3.60 |
% 13.01/3.60 | Equations (344) can reduce 360 to:
% 13.01/3.60 | (202) $false
% 13.01/3.60 |
% 13.01/3.60 |-The branch is then unsatisfiable
% 13.01/3.60 |-Branch two:
% 13.01/3.60 | (360) ~ (all_0_22_22 = e3)
% 13.01/3.60 | (361) all_0_22_22 = e2 | all_0_22_22 = e1 | all_0_22_22 = e0
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (361), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (439) all_0_22_22 = e2
% 13.01/3.60 |
% 13.01/3.60 | Equations (439) can reduce 258 to:
% 13.01/3.60 | (202) $false
% 13.01/3.60 |
% 13.01/3.60 |-The branch is then unsatisfiable
% 13.01/3.60 |-Branch two:
% 13.01/3.60 | (258) ~ (all_0_22_22 = e2)
% 13.01/3.60 | (442) all_0_22_22 = e1 | all_0_22_22 = e0
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (442), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.60 | (443) all_0_22_22 = e1
% 13.01/3.60 |
% 13.01/3.60 | Equations (443) can reduce 117 to:
% 13.01/3.60 | (1170) ~ (all_0_10_10 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Equations (443) can reduce 360 to:
% 13.01/3.60 | (464) ~ (e3 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Simplifying 464 yields:
% 13.01/3.60 | (137) ~ (e3 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Equations (443) can reduce 258 to:
% 13.01/3.60 | (329) ~ (e2 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Simplifying 329 yields:
% 13.01/3.60 | (71) ~ (e2 = e1)
% 13.01/3.60 |
% 13.01/3.60 | Equations (443) can reduce 194 to:
% 13.01/3.60 | (181) ~ (e1 = e0)
% 13.01/3.60 |
% 13.01/3.60 +-Applying beta-rule and splitting (114), into two cases.
% 13.01/3.60 |-Branch one:
% 13.01/3.61 | (1000) all_0_10_10 = e2
% 13.01/3.61 |
% 13.01/3.61 | Combining equations (1000,2665) yields a new equation:
% 13.01/3.61 | (2076) all_0_7_7 = e2
% 13.01/3.61 |
% 13.01/3.61 | Equations (1000) can reduce 180 to:
% 13.01/3.61 | (891) ~ (all_0_14_14 = e2)
% 13.01/3.61 |
% 13.01/3.61 | Simplifying 891 yields:
% 13.01/3.61 | (255) ~ (all_0_14_14 = e2)
% 13.01/3.61 |
% 13.01/3.61 | Equations (1000) can reduce 1170 to:
% 13.01/3.61 | (71) ~ (e2 = e1)
% 13.01/3.61 |
% 13.01/3.61 | From (1000) and (2666) follows:
% 13.01/3.61 | (2788) op(e2, e1) = all_0_6_6
% 13.01/3.61 |
% 13.01/3.61 +-Applying beta-rule and splitting (104), into two cases.
% 13.01/3.61 |-Branch one:
% 13.01/3.61 | (380) all_0_9_9 = e1
% 13.01/3.61 |
% 13.01/3.61 | Combining equations (380,226) yields a new equation:
% 13.01/3.61 | (417) e3 = e1
% 13.01/3.61 |
% 13.01/3.61 | Equations (417) can reduce 137 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (316) ~ (all_0_9_9 = e1)
% 13.01/3.61 | (2793) all_0_13_13 = e1 | all_0_17_17 = e1 | all_0_21_21 = e1
% 13.01/3.61 |
% 13.01/3.61 +-Applying beta-rule and splitting (2793), into two cases.
% 13.01/3.61 |-Branch one:
% 13.01/3.61 | (315) all_0_13_13 = e1
% 13.01/3.61 |
% 13.01/3.61 | Equations (315) can reduce 149 to:
% 13.01/3.61 | (318) ~ (all_0_14_14 = e1)
% 13.01/3.61 |
% 13.01/3.61 | Simplifying 318 yields:
% 13.01/3.61 | (319) ~ (all_0_14_14 = e1)
% 13.01/3.61 |
% 13.01/3.61 | From (315) and (102) follows:
% 13.01/3.61 | (322) op(e2, e1) = all_0_5_5
% 13.01/3.61 |
% 13.01/3.61 +-Applying beta-rule and splitting (95), into two cases.
% 13.01/3.61 |-Branch one:
% 13.01/3.61 | (331) all_0_14_14 = e3
% 13.01/3.61 |
% 13.01/3.61 | Equations (331) can reduce 325 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (325) ~ (all_0_14_14 = e3)
% 13.01/3.61 | (334) all_0_14_14 = e2 | all_0_14_14 = e1 | all_0_14_14 = e0
% 13.01/3.61 |
% 13.01/3.61 +-Applying beta-rule and splitting (334), into two cases.
% 13.01/3.61 |-Branch one:
% 13.01/3.61 | (264) all_0_14_14 = e2
% 13.01/3.61 |
% 13.01/3.61 | Equations (264) can reduce 255 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (255) ~ (all_0_14_14 = e2)
% 13.01/3.61 | (338) all_0_14_14 = e1 | all_0_14_14 = e0
% 13.01/3.61 |
% 13.01/3.61 +-Applying beta-rule and splitting (338), into two cases.
% 13.01/3.61 |-Branch one:
% 13.01/3.61 | (339) all_0_14_14 = e1
% 13.01/3.61 |
% 13.01/3.61 | Equations (339) can reduce 319 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (319) ~ (all_0_14_14 = e1)
% 13.01/3.61 | (342) all_0_14_14 = e0
% 13.01/3.61 |
% 13.01/3.61 | From (342) and (89) follows:
% 13.01/3.61 | (343) op(e2, e1) = e0
% 13.01/3.61 |
% 13.01/3.61 +-Applying beta-rule and splitting (47), into two cases.
% 13.01/3.61 |-Branch one:
% 13.01/3.61 | (1539) ~ (all_0_6_6 = e0)
% 13.01/3.61 |
% 13.01/3.61 | Instantiating formula (53) with e2, e1, all_0_6_6, all_0_5_5 and discharging atoms op(e2, e1) = all_0_5_5, op(e2, e1) = all_0_6_6, yields:
% 13.01/3.61 | (2812) all_0_5_5 = all_0_6_6
% 13.01/3.61 |
% 13.01/3.61 | Instantiating formula (53) with e2, e1, e0, all_0_5_5 and discharging atoms op(e2, e1) = all_0_5_5, op(e2, e1) = e0, yields:
% 13.01/3.61 | (346) all_0_5_5 = e0
% 13.01/3.61 |
% 13.01/3.61 | Combining equations (2812,346) yields a new equation:
% 13.01/3.61 | (1542) all_0_6_6 = e0
% 13.01/3.61 |
% 13.01/3.61 | Simplifying 1542 yields:
% 13.01/3.61 | (1543) all_0_6_6 = e0
% 13.01/3.61 |
% 13.01/3.61 | Equations (1543) can reduce 1539 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (1543) all_0_6_6 = e0
% 13.01/3.61 | (2818) ~ (all_0_7_7 = e2) | ~ (all_0_8_8 = e1)
% 13.01/3.61 |
% 13.01/3.61 +-Applying beta-rule and splitting (2818), into two cases.
% 13.01/3.61 |-Branch one:
% 13.01/3.61 | (2085) ~ (all_0_7_7 = e2)
% 13.01/3.61 |
% 13.01/3.61 | Equations (2076) can reduce 2085 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (2076) all_0_7_7 = e2
% 13.01/3.61 | (193) ~ (all_0_8_8 = e1)
% 13.01/3.61 |
% 13.01/3.61 | Equations (366) can reduce 193 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (358) ~ (all_0_13_13 = e1)
% 13.01/3.61 | (2825) all_0_17_17 = e1 | all_0_21_21 = e1
% 13.01/3.61 |
% 13.01/3.61 +-Applying beta-rule and splitting (2825), into two cases.
% 13.01/3.61 |-Branch one:
% 13.01/3.61 | (415) all_0_17_17 = e1
% 13.01/3.61 |
% 13.01/3.61 | Combining equations (371,415) yields a new equation:
% 13.01/3.61 | (767) e2 = e1
% 13.01/3.61 |
% 13.01/3.61 | Simplifying 767 yields:
% 13.01/3.61 | (367) e2 = e1
% 13.01/3.61 |
% 13.01/3.61 | Equations (367) can reduce 71 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (208) ~ (all_0_17_17 = e1)
% 13.01/3.61 | (1674) all_0_21_21 = e1
% 13.01/3.61 |
% 13.01/3.61 | Combining equations (829,1674) yields a new equation:
% 13.01/3.61 | (421) e1 = e0
% 13.01/3.61 |
% 13.01/3.61 | Equations (421) can reduce 181 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (1004) ~ (all_0_10_10 = e2)
% 13.01/3.61 | (1005) all_0_14_14 = e2 | all_0_18_18 = e2 | all_0_22_22 = e2
% 13.01/3.61 |
% 13.01/3.61 +-Applying beta-rule and splitting (1005), into two cases.
% 13.01/3.61 |-Branch one:
% 13.01/3.61 | (264) all_0_14_14 = e2
% 13.01/3.61 |
% 13.01/3.61 | Equations (264) can reduce 255 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (255) ~ (all_0_14_14 = e2)
% 13.01/3.61 | (1011) all_0_18_18 = e2 | all_0_22_22 = e2
% 13.01/3.61 |
% 13.01/3.61 +-Applying beta-rule and splitting (1011), into two cases.
% 13.01/3.61 |-Branch one:
% 13.01/3.61 | (254) all_0_18_18 = e2
% 13.01/3.61 |
% 13.01/3.61 | Combining equations (250,254) yields a new equation:
% 13.01/3.61 | (372) e3 = e2
% 13.01/3.61 |
% 13.01/3.61 | Simplifying 372 yields:
% 13.01/3.61 | (373) e3 = e2
% 13.01/3.61 |
% 13.01/3.61 | Equations (373) can reduce 101 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (555) ~ (all_0_18_18 = e2)
% 13.01/3.61 | (439) all_0_22_22 = e2
% 13.01/3.61 |
% 13.01/3.61 | Combining equations (439,443) yields a new equation:
% 13.01/3.61 | (767) e2 = e1
% 13.01/3.61 |
% 13.01/3.61 | Simplifying 767 yields:
% 13.01/3.61 | (367) e2 = e1
% 13.01/3.61 |
% 13.01/3.61 | Equations (367) can reduce 71 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (309) ~ (all_0_22_22 = e1)
% 13.01/3.61 | (446) all_0_22_22 = e0
% 13.01/3.61 |
% 13.01/3.61 | Equations (446) can reduce 194 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (375) ~ (all_0_17_17 = e2)
% 13.01/3.61 | (376) all_0_21_21 = e2
% 13.01/3.61 |
% 13.01/3.61 | Combining equations (376,829) yields a new equation:
% 13.01/3.61 | (283) e2 = e0
% 13.01/3.61 |
% 13.01/3.61 | Simplifying 283 yields:
% 13.01/3.61 | (284) e2 = e0
% 13.01/3.61 |
% 13.01/3.61 | Equations (284) can reduce 13 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (212) ~ (all_0_9_9 = e3)
% 13.01/3.61 | (2858) all_0_13_13 = e3 | all_0_17_17 = e3 | all_0_21_21 = e3
% 13.01/3.61 |
% 13.01/3.61 +-Applying beta-rule and splitting (2858), into two cases.
% 13.01/3.61 |-Branch one:
% 13.01/3.61 | (311) all_0_13_13 = e3
% 13.01/3.61 |
% 13.01/3.61 | Equations (311) can reduce 219 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (219) ~ (all_0_13_13 = e3)
% 13.01/3.61 | (2862) all_0_17_17 = e3 | all_0_21_21 = e3
% 13.01/3.61 |
% 13.01/3.61 +-Applying beta-rule and splitting (2862), into two cases.
% 13.01/3.61 |-Branch one:
% 13.01/3.61 | (295) all_0_17_17 = e3
% 13.01/3.61 |
% 13.01/3.61 | Equations (295) can reduce 451 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (451) ~ (all_0_17_17 = e3)
% 13.01/3.61 | (1666) all_0_21_21 = e3
% 13.01/3.61 |
% 13.01/3.61 | Combining equations (1666,829) yields a new equation:
% 13.01/3.61 | (277) e3 = e0
% 13.01/3.61 |
% 13.01/3.61 | Simplifying 277 yields:
% 13.01/3.61 | (278) e3 = e0
% 13.01/3.61 |
% 13.01/3.61 | Equations (278) can reduce 136 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (423) ~ (all_0_12_12 = e3)
% 13.01/3.61 | (725) all_0_12_12 = e2 | all_0_12_12 = e1 | all_0_12_12 = e0
% 13.01/3.61 |
% 13.01/3.61 +-Applying beta-rule and splitting (725), into two cases.
% 13.01/3.61 |-Branch one:
% 13.01/3.61 | (260) all_0_12_12 = e2
% 13.01/3.61 |
% 13.01/3.61 | Equations (260) can reduce 200 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (200) ~ (all_0_12_12 = e2)
% 13.01/3.61 | (729) all_0_12_12 = e1 | all_0_12_12 = e0
% 13.01/3.61 |
% 13.01/3.61 +-Applying beta-rule and splitting (729), into two cases.
% 13.01/3.61 |-Branch one:
% 13.01/3.61 | (730) all_0_12_12 = e1
% 13.01/3.61 |
% 13.01/3.61 | Equations (730) can reduce 317 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (317) ~ (all_0_12_12 = e1)
% 13.01/3.61 | (500) all_0_12_12 = e0
% 13.01/3.61 |
% 13.01/3.61 | Equations (500) can reduce 214 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (611) ~ (all_0_16_16 = e0)
% 13.01/3.61 | (2061) all_0_17_17 = e0 | all_0_18_18 = e0 | all_0_19_19 = e0
% 13.01/3.61 |
% 13.01/3.61 +-Applying beta-rule and splitting (2061), into two cases.
% 13.01/3.61 |-Branch one:
% 13.01/3.61 | (540) all_0_17_17 = e0
% 13.01/3.61 |
% 13.01/3.61 | Equations (540) can reduce 288 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (288) ~ (all_0_17_17 = e0)
% 13.01/3.61 | (2066) all_0_18_18 = e0 | all_0_19_19 = e0
% 13.01/3.61 |
% 13.01/3.61 +-Applying beta-rule and splitting (2066), into two cases.
% 13.01/3.61 |-Branch one:
% 13.01/3.61 | (556) all_0_18_18 = e0
% 13.01/3.61 |
% 13.01/3.61 | Combining equations (250,556) yields a new equation:
% 13.01/3.61 | (277) e3 = e0
% 13.01/3.61 |
% 13.01/3.61 | Simplifying 277 yields:
% 13.01/3.61 | (278) e3 = e0
% 13.01/3.61 |
% 13.01/3.61 | Equations (278) can reduce 136 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (245) ~ (all_0_18_18 = e0)
% 13.01/3.61 | (287) all_0_19_19 = e0
% 13.01/3.61 |
% 13.01/3.61 | Combining equations (287,420) yields a new equation:
% 13.01/3.61 | (421) e1 = e0
% 13.01/3.61 |
% 13.01/3.61 | Equations (421) can reduce 181 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (204) ~ (all_0_21_21 = e0)
% 13.01/3.61 | (446) all_0_22_22 = e0
% 13.01/3.61 |
% 13.01/3.61 | Equations (446) can reduce 194 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (260) all_0_12_12 = e2
% 13.01/3.61 | (224) ~ (all_0_18_18 = e3)
% 13.01/3.61 |
% 13.01/3.61 | Equations (250) can reduce 224 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (224) ~ (all_0_18_18 = e3)
% 13.01/3.61 | (253) all_0_18_18 = e2 | all_0_18_18 = e0
% 13.01/3.61 |
% 13.01/3.61 +-Applying beta-rule and splitting (253), into two cases.
% 13.01/3.61 |-Branch one:
% 13.01/3.61 | (254) all_0_18_18 = e2
% 13.01/3.61 |
% 13.01/3.61 | Equations (254) can reduce 555 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (555) ~ (all_0_18_18 = e2)
% 13.01/3.61 | (556) all_0_18_18 = e0
% 13.01/3.61 |
% 13.01/3.61 | Equations (556) can reduce 245 to:
% 13.01/3.61 | (202) $false
% 13.01/3.61 |
% 13.01/3.61 |-The branch is then unsatisfiable
% 13.01/3.61 |-Branch two:
% 13.01/3.61 | (254) all_0_18_18 = e2
% 13.01/3.61 | (204) ~ (all_0_21_21 = e0)
% 13.01/3.61 |
% 13.01/3.61 | Equations (254) can reduce 39 to:
% 13.01/3.61 | (256) ~ (all_0_16_16 = e2)
% 13.01/3.61 |
% 13.01/3.61 +-Applying beta-rule and splitting (40), into two cases.
% 13.01/3.61 |-Branch one:
% 13.01/3.61 | (212) ~ (all_0_9_9 = e3)
% 13.01/3.61 |
% 13.01/3.61 +-Applying beta-rule and splitting (155), into two cases.
% 13.01/3.61 |-Branch one:
% 13.01/3.61 | (226) all_0_9_9 = e3
% 13.01/3.61 |
% 13.01/3.62 | Equations (226) can reduce 212 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (212) ~ (all_0_9_9 = e3)
% 13.01/3.62 | (229) all_0_10_10 = e3 | all_0_11_11 = e3
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (112), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (213) all_0_20_20 = e0
% 13.01/3.62 |
% 13.01/3.62 | Equations (213) can reduce 167 to:
% 13.01/3.62 | (214) ~ (all_0_12_12 = e0)
% 13.01/3.62 |
% 13.01/3.62 | Equations (213) can reduce 134 to:
% 13.01/3.62 | (611) ~ (all_0_16_16 = e0)
% 13.01/3.62 |
% 13.01/3.62 | Equations (213) can reduce 130 to:
% 13.01/3.62 | (217) ~ (all_0_23_23 = e0)
% 13.01/3.62 |
% 13.01/3.62 | Simplifying 217 yields:
% 13.01/3.62 | (9) ~ (all_0_23_23 = e0)
% 13.01/3.62 |
% 13.01/3.62 | Equations (213) can reduce 920 to:
% 13.01/3.62 | (1254) ~ (e1 = e0)
% 13.01/3.62 |
% 13.01/3.62 | Simplifying 1254 yields:
% 13.01/3.62 | (181) ~ (e1 = e0)
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (185), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (220) ~ (all_0_20_20 = e0)
% 13.01/3.62 |
% 13.01/3.62 | Equations (213) can reduce 220 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (213) all_0_20_20 = e0
% 13.01/3.62 | (223) ~ (all_0_23_23 = e3)
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (229), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (230) all_0_10_10 = e3
% 13.01/3.62 |
% 13.01/3.62 | Equations (230) can reduce 225 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (225) ~ (all_0_10_10 = e3)
% 13.01/3.62 | (233) all_0_11_11 = e3
% 13.01/3.62 |
% 13.01/3.62 | Equations (233) can reduce 145 to:
% 13.01/3.62 | (212) ~ (all_0_9_9 = e3)
% 13.01/3.62 |
% 13.01/3.62 | Equations (233) can reduce 187 to:
% 13.01/3.62 | (225) ~ (all_0_10_10 = e3)
% 13.01/3.62 |
% 13.01/3.62 | Equations (233) can reduce 50 to:
% 13.01/3.62 | (236) ~ (all_0_15_15 = e3)
% 13.01/3.62 |
% 13.01/3.62 | Simplifying 236 yields:
% 13.01/3.62 | (237) ~ (all_0_15_15 = e3)
% 13.01/3.62 |
% 13.01/3.62 | Equations (233) can reduce 119 to:
% 13.01/3.62 | (240) ~ (all_0_23_23 = e3)
% 13.01/3.62 |
% 13.01/3.62 | Simplifying 240 yields:
% 13.01/3.62 | (223) ~ (all_0_23_23 = e3)
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (178), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (219) ~ (all_0_13_13 = e3)
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (88), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (301) all_0_23_23 = e3
% 13.01/3.62 |
% 13.01/3.62 | Equations (301) can reduce 223 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (223) ~ (all_0_23_23 = e3)
% 13.01/3.62 | (304) all_0_23_23 = e2 | all_0_23_23 = e1
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (304), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (305) all_0_23_23 = e2
% 13.01/3.62 |
% 13.01/3.62 | Equations (305) can reduce 173 to:
% 13.01/3.62 | (576) ~ (all_0_15_15 = e2)
% 13.01/3.62 |
% 13.01/3.62 | Equations (305) can reduce 191 to:
% 13.01/3.62 | (258) ~ (all_0_22_22 = e2)
% 13.01/3.62 |
% 13.01/3.62 | Equations (305) can reduce 9 to:
% 13.01/3.62 | (13) ~ (e2 = e0)
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (126), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (665) all_0_15_15 = e3
% 13.01/3.62 |
% 13.01/3.62 | Equations (665) can reduce 237 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (237) ~ (all_0_15_15 = e3)
% 13.01/3.62 | (668) all_0_15_15 = e2 | all_0_15_15 = e1 | all_0_15_15 = e0
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (19), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (230) all_0_10_10 = e3
% 13.01/3.62 |
% 13.01/3.62 | Equations (230) can reduce 225 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (225) ~ (all_0_10_10 = e3)
% 13.01/3.62 | (2953) all_0_10_10 = e2 | all_0_10_10 = e1 | all_0_10_10 = e0
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (10), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (792) all_0_16_16 = e0
% 13.01/3.62 |
% 13.01/3.62 | Equations (792) can reduce 611 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (611) ~ (all_0_16_16 = e0)
% 13.01/3.62 | (2061) all_0_17_17 = e0 | all_0_18_18 = e0 | all_0_19_19 = e0
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (2061), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (540) all_0_17_17 = e0
% 13.01/3.62 |
% 13.01/3.62 | Equations (540) can reduce 109 to:
% 13.01/3.62 | (494) ~ (all_0_9_9 = e0)
% 13.01/3.62 |
% 13.01/3.62 | Equations (540) can reduce 6 to:
% 13.01/3.62 | (249) ~ (all_0_13_13 = e0)
% 13.01/3.62 |
% 13.01/3.62 | Equations (540) can reduce 58 to:
% 13.01/3.62 | (611) ~ (all_0_16_16 = e0)
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (142), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (226) all_0_9_9 = e3
% 13.01/3.62 |
% 13.01/3.62 | Equations (226) can reduce 212 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (212) ~ (all_0_9_9 = e3)
% 13.01/3.62 | (387) all_0_9_9 = e2 | all_0_9_9 = e1 | all_0_9_9 = e0
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (387), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (362) all_0_9_9 = e2
% 13.01/3.62 |
% 13.01/3.62 | Equations (362) can reduce 16 to:
% 13.01/3.62 | (2967) ~ (all_0_10_10 = e2)
% 13.01/3.62 |
% 13.01/3.62 | Simplifying 2967 yields:
% 13.01/3.62 | (1004) ~ (all_0_10_10 = e2)
% 13.01/3.62 |
% 13.01/3.62 | Equations (362) can reduce 316 to:
% 13.01/3.62 | (71) ~ (e2 = e1)
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (7), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (427) all_0_16_16 = e3
% 13.01/3.62 |
% 13.01/3.62 | Equations (427) can reduce 76 to:
% 13.01/3.62 | (423) ~ (all_0_12_12 = e3)
% 13.01/3.62 |
% 13.01/3.62 | Equations (427) can reduce 256 to:
% 13.01/3.62 | (101) ~ (e3 = e2)
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (668), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (267) all_0_15_15 = e2
% 13.01/3.62 |
% 13.01/3.62 | Equations (267) can reduce 576 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (576) ~ (all_0_15_15 = e2)
% 13.01/3.62 | (708) all_0_15_15 = e1 | all_0_15_15 = e0
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (2953), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (1000) all_0_10_10 = e2
% 13.01/3.62 |
% 13.01/3.62 | Equations (1000) can reduce 1004 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (1004) ~ (all_0_10_10 = e2)
% 13.01/3.62 | (2980) all_0_10_10 = e1 | all_0_10_10 = e0
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (2980), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (932) all_0_10_10 = e1
% 13.01/3.62 |
% 13.01/3.62 | Equations (932) can reduce 1170 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (1170) ~ (all_0_10_10 = e1)
% 13.01/3.62 | (598) all_0_10_10 = e0
% 13.01/3.62 |
% 13.01/3.62 | Equations (598) can reduce 180 to:
% 13.01/3.62 | (1463) ~ (all_0_14_14 = e0)
% 13.01/3.62 |
% 13.01/3.62 | Simplifying 1463 yields:
% 13.01/3.62 | (550) ~ (all_0_14_14 = e0)
% 13.01/3.62 |
% 13.01/3.62 | Equations (598) can reduce 117 to:
% 13.01/3.62 | (215) ~ (all_0_22_22 = e0)
% 13.01/3.62 |
% 13.01/3.62 | Simplifying 215 yields:
% 13.01/3.62 | (194) ~ (all_0_22_22 = e0)
% 13.01/3.62 |
% 13.01/3.62 | From (598) and (54) follows:
% 13.01/3.62 | (2989) op(e3, e1) = e0
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (74), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (260) all_0_12_12 = e2
% 13.01/3.62 |
% 13.01/3.62 | Equations (260) can reduce 160 to:
% 13.01/3.62 | (891) ~ (all_0_14_14 = e2)
% 13.01/3.62 |
% 13.01/3.62 | Simplifying 891 yields:
% 13.01/3.62 | (255) ~ (all_0_14_14 = e2)
% 13.01/3.62 |
% 13.01/3.62 | Equations (260) can reduce 423 to:
% 13.01/3.62 | (274) ~ (e3 = e2)
% 13.01/3.62 |
% 13.01/3.62 | Simplifying 274 yields:
% 13.01/3.62 | (101) ~ (e3 = e2)
% 13.01/3.62 |
% 13.01/3.62 | Equations (260) can reduce 214 to:
% 13.01/3.62 | (13) ~ (e2 = e0)
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (113), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (311) all_0_13_13 = e3
% 13.01/3.62 |
% 13.01/3.62 | Equations (311) can reduce 219 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (219) ~ (all_0_13_13 = e3)
% 13.01/3.62 | (314) all_0_13_13 = e1 | all_0_13_13 = e0
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (146), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (500) all_0_12_12 = e0
% 13.01/3.62 |
% 13.01/3.62 | Combining equations (260,500) yields a new equation:
% 13.01/3.62 | (283) e2 = e0
% 13.01/3.62 |
% 13.01/3.62 | Simplifying 283 yields:
% 13.01/3.62 | (284) e2 = e0
% 13.01/3.62 |
% 13.01/3.62 | Equations (284) can reduce 13 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (214) ~ (all_0_12_12 = e0)
% 13.01/3.62 | (503) all_0_13_13 = e0 | all_0_14_14 = e0 | all_0_15_15 = e0
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (503), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (449) all_0_13_13 = e0
% 13.01/3.62 |
% 13.01/3.62 | Equations (449) can reduce 249 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (249) ~ (all_0_13_13 = e0)
% 13.01/3.62 | (507) all_0_14_14 = e0 | all_0_15_15 = e0
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (507), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (342) all_0_14_14 = e0
% 13.01/3.62 |
% 13.01/3.62 | Equations (342) can reduce 550 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (550) ~ (all_0_14_14 = e0)
% 13.01/3.62 | (282) all_0_15_15 = e0
% 13.01/3.62 |
% 13.01/3.62 | Equations (282) can reduce 44 to:
% 13.01/3.62 | (550) ~ (all_0_14_14 = e0)
% 13.01/3.62 |
% 13.01/3.62 | Equations (282) can reduce 237 to:
% 13.01/3.62 | (291) ~ (e3 = e0)
% 13.01/3.62 |
% 13.01/3.62 | Simplifying 291 yields:
% 13.01/3.62 | (136) ~ (e3 = e0)
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (93), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (323) all_0_12_12 = e3
% 13.01/3.62 |
% 13.01/3.62 | Combining equations (323,260) yields a new equation:
% 13.01/3.62 | (372) e3 = e2
% 13.01/3.62 |
% 13.01/3.62 | Simplifying 372 yields:
% 13.01/3.62 | (373) e3 = e2
% 13.01/3.62 |
% 13.01/3.62 | Equations (373) can reduce 101 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (423) ~ (all_0_12_12 = e3)
% 13.01/3.62 | (1078) all_0_13_13 = e3 | all_0_14_14 = e3 | all_0_15_15 = e3
% 13.01/3.62 |
% 13.01/3.62 | Equations (260) can reduce 423 to:
% 13.01/3.62 | (274) ~ (e3 = e2)
% 13.01/3.62 |
% 13.01/3.62 | Simplifying 274 yields:
% 13.01/3.62 | (101) ~ (e3 = e2)
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (15), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (226) all_0_9_9 = e3
% 13.01/3.62 |
% 13.01/3.62 | Combining equations (226,362) yields a new equation:
% 13.01/3.62 | (372) e3 = e2
% 13.01/3.62 |
% 13.01/3.62 | Simplifying 372 yields:
% 13.01/3.62 | (373) e3 = e2
% 13.01/3.62 |
% 13.01/3.62 | Equations (373) can reduce 101 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (212) ~ (all_0_9_9 = e3)
% 13.01/3.62 | (2858) all_0_13_13 = e3 | all_0_17_17 = e3 | all_0_21_21 = e3
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (2858), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (311) all_0_13_13 = e3
% 13.01/3.62 |
% 13.01/3.62 | Equations (311) can reduce 219 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (219) ~ (all_0_13_13 = e3)
% 13.01/3.62 | (2862) all_0_17_17 = e3 | all_0_21_21 = e3
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (2862), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (295) all_0_17_17 = e3
% 13.01/3.62 |
% 13.01/3.62 | Combining equations (540,295) yields a new equation:
% 13.01/3.62 | (278) e3 = e0
% 13.01/3.62 |
% 13.01/3.62 | Equations (278) can reduce 136 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (451) ~ (all_0_17_17 = e3)
% 13.01/3.62 | (1666) all_0_21_21 = e3
% 13.01/3.62 |
% 13.01/3.62 | Equations (1666) can reduce 27 to:
% 13.01/3.62 | (561) ~ (all_0_22_22 = e3)
% 13.01/3.62 |
% 13.01/3.62 | Simplifying 561 yields:
% 13.01/3.62 | (360) ~ (all_0_22_22 = e3)
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (87), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (344) all_0_22_22 = e3
% 13.01/3.62 |
% 13.01/3.62 | Equations (344) can reduce 360 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (360) ~ (all_0_22_22 = e3)
% 13.01/3.62 | (361) all_0_22_22 = e2 | all_0_22_22 = e1 | all_0_22_22 = e0
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (361), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (439) all_0_22_22 = e2
% 13.01/3.62 |
% 13.01/3.62 | Equations (439) can reduce 258 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (258) ~ (all_0_22_22 = e2)
% 13.01/3.62 | (442) all_0_22_22 = e1 | all_0_22_22 = e0
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (442), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (443) all_0_22_22 = e1
% 13.01/3.62 |
% 13.01/3.62 | Equations (443) can reduce 162 to:
% 13.01/3.62 | (319) ~ (all_0_14_14 = e1)
% 13.01/3.62 |
% 13.01/3.62 | Equations (443) can reduce 258 to:
% 13.01/3.62 | (329) ~ (e2 = e1)
% 13.01/3.62 |
% 13.01/3.62 | Simplifying 329 yields:
% 13.01/3.62 | (71) ~ (e2 = e1)
% 13.01/3.62 |
% 13.01/3.62 | Equations (443) can reduce 194 to:
% 13.01/3.62 | (181) ~ (e1 = e0)
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (95), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (331) all_0_14_14 = e3
% 13.01/3.62 |
% 13.01/3.62 | Equations (331) can reduce 319 to:
% 13.01/3.62 | (137) ~ (e3 = e1)
% 13.01/3.62 |
% 13.01/3.62 | From (331) and (89) follows:
% 13.01/3.62 | (3057) op(e2, e1) = e3
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (77), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (730) all_0_12_12 = e1
% 13.01/3.62 |
% 13.01/3.62 | Combining equations (260,730) yields a new equation:
% 13.01/3.62 | (767) e2 = e1
% 13.01/3.62 |
% 13.01/3.62 | Simplifying 767 yields:
% 13.01/3.62 | (367) e2 = e1
% 13.01/3.62 |
% 13.01/3.62 | Equations (367) can reduce 71 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (317) ~ (all_0_12_12 = e1)
% 13.01/3.62 | (760) all_0_13_13 = e1 | all_0_14_14 = e1 | all_0_15_15 = e1
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (760), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (315) all_0_13_13 = e1
% 13.01/3.62 |
% 13.01/3.62 | From (315) and (8) follows:
% 13.01/3.62 | (321) op(all_0_5_5, e1) = all_0_4_4
% 13.01/3.62 |
% 13.01/3.62 | From (315) and (102) follows:
% 13.01/3.62 | (322) op(e2, e1) = all_0_5_5
% 13.01/3.62 |
% 13.01/3.62 | Instantiating formula (53) with e2, e1, e3, all_0_5_5 and discharging atoms op(e2, e1) = all_0_5_5, op(e2, e1) = e3, yields:
% 13.01/3.62 | (1836) all_0_5_5 = e3
% 13.01/3.62 |
% 13.01/3.62 | From (1836) and (321) follows:
% 13.01/3.62 | (3068) op(e3, e1) = all_0_4_4
% 13.01/3.62 |
% 13.01/3.62 +-Applying beta-rule and splitting (154), into two cases.
% 13.01/3.62 |-Branch one:
% 13.01/3.62 | (3069) ~ (all_0_4_4 = e0)
% 13.01/3.62 |
% 13.01/3.62 | Instantiating formula (53) with e3, e1, all_0_4_4, e0 and discharging atoms op(e3, e1) = all_0_4_4, op(e3, e1) = e0, yields:
% 13.01/3.62 | (3070) all_0_4_4 = e0
% 13.01/3.62 |
% 13.01/3.62 | Equations (3070) can reduce 3069 to:
% 13.01/3.62 | (202) $false
% 13.01/3.62 |
% 13.01/3.62 |-The branch is then unsatisfiable
% 13.01/3.62 |-Branch two:
% 13.01/3.62 | (3070) all_0_4_4 = e0
% 13.01/3.62 | (3073) ~ (all_0_5_5 = e3) | ~ (all_0_13_13 = e1)
% 13.01/3.62 |
% 13.01/3.63 +-Applying beta-rule and splitting (3073), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (1844) ~ (all_0_5_5 = e3)
% 13.01/3.63 |
% 13.01/3.63 | Equations (1836) can reduce 1844 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (1836) all_0_5_5 = e3
% 13.01/3.63 | (358) ~ (all_0_13_13 = e1)
% 13.01/3.63 |
% 13.01/3.63 | Equations (315) can reduce 358 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (358) ~ (all_0_13_13 = e1)
% 13.01/3.63 | (765) all_0_14_14 = e1 | all_0_15_15 = e1
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (765), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (339) all_0_14_14 = e1
% 13.01/3.63 |
% 13.01/3.63 | Combining equations (331,339) yields a new equation:
% 13.01/3.63 | (416) e3 = e1
% 13.01/3.63 |
% 13.01/3.63 | Simplifying 416 yields:
% 13.01/3.63 | (417) e3 = e1
% 13.01/3.63 |
% 13.01/3.63 | Equations (417) can reduce 137 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (319) ~ (all_0_14_14 = e1)
% 13.01/3.63 | (677) all_0_15_15 = e1
% 13.01/3.63 |
% 13.01/3.63 | Combining equations (282,677) yields a new equation:
% 13.01/3.63 | (421) e1 = e0
% 13.01/3.63 |
% 13.01/3.63 | Equations (421) can reduce 181 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (325) ~ (all_0_14_14 = e3)
% 13.01/3.63 | (334) all_0_14_14 = e2 | all_0_14_14 = e1 | all_0_14_14 = e0
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (334), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (264) all_0_14_14 = e2
% 13.01/3.63 |
% 13.01/3.63 | Equations (264) can reduce 255 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (255) ~ (all_0_14_14 = e2)
% 13.01/3.63 | (338) all_0_14_14 = e1 | all_0_14_14 = e0
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (338), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (339) all_0_14_14 = e1
% 13.01/3.63 |
% 13.01/3.63 | Equations (339) can reduce 319 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (319) ~ (all_0_14_14 = e1)
% 13.01/3.63 | (342) all_0_14_14 = e0
% 13.01/3.63 |
% 13.01/3.63 | Equations (342) can reduce 550 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (309) ~ (all_0_22_22 = e1)
% 13.01/3.63 | (446) all_0_22_22 = e0
% 13.01/3.63 |
% 13.01/3.63 | Equations (446) can reduce 194 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (200) ~ (all_0_12_12 = e2)
% 13.01/3.63 | (263) all_0_14_14 = e2 | all_0_15_15 = e2
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (708), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (677) all_0_15_15 = e1
% 13.01/3.63 |
% 13.01/3.63 | Equations (677) can reduce 693 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (693) ~ (all_0_15_15 = e1)
% 13.01/3.63 | (282) all_0_15_15 = e0
% 13.01/3.63 |
% 13.01/3.63 | Equations (282) can reduce 576 to:
% 13.01/3.63 | (293) ~ (e2 = e0)
% 13.01/3.63 |
% 13.01/3.63 | Simplifying 293 yields:
% 13.01/3.63 | (13) ~ (e2 = e0)
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (35), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (196) all_0_8_8 = e2
% 13.01/3.63 |
% 13.01/3.63 | Combining equations (196,366) yields a new equation:
% 13.01/3.63 | (767) e2 = e1
% 13.01/3.63 |
% 13.01/3.63 | Simplifying 767 yields:
% 13.01/3.63 | (367) e2 = e1
% 13.01/3.63 |
% 13.01/3.63 | Equations (367) can reduce 71 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (201) ~ (all_0_8_8 = e2)
% 13.01/3.63 | (2044) all_0_12_12 = e2 | all_0_16_16 = e2 | all_0_20_20 = e2
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (2044), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (260) all_0_12_12 = e2
% 13.01/3.63 |
% 13.01/3.63 | Equations (260) can reduce 200 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (200) ~ (all_0_12_12 = e2)
% 13.01/3.63 | (2758) all_0_16_16 = e2 | all_0_20_20 = e2
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (2758), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (785) all_0_16_16 = e2
% 13.01/3.63 |
% 13.01/3.63 | Combining equations (427,785) yields a new equation:
% 13.01/3.63 | (372) e3 = e2
% 13.01/3.63 |
% 13.01/3.63 | Simplifying 372 yields:
% 13.01/3.63 | (373) e3 = e2
% 13.01/3.63 |
% 13.01/3.63 | Equations (373) can reduce 101 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (256) ~ (all_0_16_16 = e2)
% 13.01/3.63 | (526) all_0_20_20 = e2
% 13.01/3.63 |
% 13.01/3.63 | Combining equations (526,213) yields a new equation:
% 13.01/3.63 | (283) e2 = e0
% 13.01/3.63 |
% 13.01/3.63 | Simplifying 283 yields:
% 13.01/3.63 | (284) e2 = e0
% 13.01/3.63 |
% 13.01/3.63 | Equations (284) can reduce 13 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (298) ~ (all_0_16_16 = e3)
% 13.01/3.63 | (430) all_0_16_16 = e2 | all_0_16_16 = e1 | all_0_16_16 = e0
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (430), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (785) all_0_16_16 = e2
% 13.01/3.63 |
% 13.01/3.63 | Equations (785) can reduce 256 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (256) ~ (all_0_16_16 = e2)
% 13.01/3.63 | (788) all_0_16_16 = e1 | all_0_16_16 = e0
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (788), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (328) all_0_16_16 = e1
% 13.01/3.63 |
% 13.01/3.63 | Equations (328) can reduce 413 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (413) ~ (all_0_16_16 = e1)
% 13.01/3.63 | (792) all_0_16_16 = e0
% 13.01/3.63 |
% 13.01/3.63 | Equations (792) can reduce 611 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (198) ~ (all_0_9_9 = e2)
% 13.01/3.63 | (391) all_0_9_9 = e1 | all_0_9_9 = e0
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (391), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (380) all_0_9_9 = e1
% 13.01/3.63 |
% 13.01/3.63 | Equations (380) can reduce 316 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (316) ~ (all_0_9_9 = e1)
% 13.01/3.63 | (395) all_0_9_9 = e0
% 13.01/3.63 |
% 13.01/3.63 | Equations (395) can reduce 494 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (288) ~ (all_0_17_17 = e0)
% 13.01/3.63 | (2066) all_0_18_18 = e0 | all_0_19_19 = e0
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (2066), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (556) all_0_18_18 = e0
% 13.01/3.63 |
% 13.01/3.63 | Combining equations (254,556) yields a new equation:
% 13.01/3.63 | (283) e2 = e0
% 13.01/3.63 |
% 13.01/3.63 | Simplifying 283 yields:
% 13.01/3.63 | (284) e2 = e0
% 13.01/3.63 |
% 13.01/3.63 | Equations (284) can reduce 13 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (245) ~ (all_0_18_18 = e0)
% 13.01/3.63 | (287) all_0_19_19 = e0
% 13.01/3.63 |
% 13.01/3.63 | Combining equations (420,287) yields a new equation:
% 13.01/3.63 | (491) e1 = e0
% 13.01/3.63 |
% 13.01/3.63 | Simplifying 491 yields:
% 13.01/3.63 | (421) e1 = e0
% 13.01/3.63 |
% 13.01/3.63 | Equations (421) can reduce 181 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (273) ~ (all_0_23_23 = e2)
% 13.01/3.63 | (308) all_0_23_23 = e1
% 13.01/3.63 |
% 13.01/3.63 | Equations (308) can reduce 570 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (311) all_0_13_13 = e3
% 13.01/3.63 | (220) ~ (all_0_20_20 = e0)
% 13.01/3.63 |
% 13.01/3.63 | Equations (213) can reduce 220 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (220) ~ (all_0_20_20 = e0)
% 13.01/3.63 | (828) all_0_21_21 = e0 | all_0_22_22 = e0
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (828), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (829) all_0_21_21 = e0
% 13.01/3.63 |
% 13.01/3.63 | Equations (829) can reduce 204 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (204) ~ (all_0_21_21 = e0)
% 13.01/3.63 | (446) all_0_22_22 = e0
% 13.01/3.63 |
% 13.01/3.63 | Equations (446) can reduce 194 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (226) all_0_9_9 = e3
% 13.01/3.63 | (555) ~ (all_0_18_18 = e2)
% 13.01/3.63 |
% 13.01/3.63 | Equations (254) can reduce 555 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (415) all_0_17_17 = e1
% 13.01/3.63 | (273) ~ (all_0_23_23 = e2)
% 13.01/3.63 |
% 13.01/3.63 | Equations (415) can reduce 120 to:
% 13.01/3.63 | (657) ~ (all_0_19_19 = e1)
% 13.01/3.63 |
% 13.01/3.63 | Simplifying 657 yields:
% 13.01/3.63 | (622) ~ (all_0_19_19 = e1)
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (127), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (208) ~ (all_0_17_17 = e1)
% 13.01/3.63 |
% 13.01/3.63 | Equations (415) can reduce 208 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (415) all_0_17_17 = e1
% 13.01/3.63 | (555) ~ (all_0_18_18 = e2)
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (121), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (250) all_0_18_18 = e3
% 13.01/3.63 |
% 13.01/3.63 | Equations (250) can reduce 4 to:
% 13.01/3.63 | (238) ~ (all_0_19_19 = e3)
% 13.01/3.63 |
% 13.01/3.63 | Simplifying 238 yields:
% 13.01/3.63 | (239) ~ (all_0_19_19 = e3)
% 13.01/3.63 |
% 13.01/3.63 | Equations (250) can reduce 5 to:
% 13.01/3.63 | (561) ~ (all_0_22_22 = e3)
% 13.01/3.63 |
% 13.01/3.63 | Simplifying 561 yields:
% 13.01/3.63 | (360) ~ (all_0_22_22 = e3)
% 13.01/3.63 |
% 13.01/3.63 | Equations (250) can reduce 555 to:
% 13.01/3.63 | (101) ~ (e3 = e2)
% 13.01/3.63 |
% 13.01/3.63 | Equations (250) can reduce 245 to:
% 13.01/3.63 | (136) ~ (e3 = e0)
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (46), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (200) ~ (all_0_12_12 = e2)
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (131), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (224) ~ (all_0_18_18 = e3)
% 13.01/3.63 |
% 13.01/3.63 | Equations (250) can reduce 224 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (250) all_0_18_18 = e3
% 13.01/3.63 | (220) ~ (all_0_20_20 = e0)
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (112), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (213) all_0_20_20 = e0
% 13.01/3.63 |
% 13.01/3.63 | Equations (213) can reduce 220 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (220) ~ (all_0_20_20 = e0)
% 13.01/3.63 | (828) all_0_21_21 = e0 | all_0_22_22 = e0
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (74), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (260) all_0_12_12 = e2
% 13.01/3.63 |
% 13.01/3.63 | Equations (260) can reduce 200 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (200) ~ (all_0_12_12 = e2)
% 13.01/3.63 | (263) all_0_14_14 = e2 | all_0_15_15 = e2
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (828), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (829) all_0_21_21 = e0
% 13.01/3.63 |
% 13.01/3.63 | Equations (829) can reduce 61 to:
% 13.01/3.63 | (220) ~ (all_0_20_20 = e0)
% 13.01/3.63 |
% 13.01/3.63 | Equations (829) can reduce 27 to:
% 13.01/3.63 | (215) ~ (all_0_22_22 = e0)
% 13.01/3.63 |
% 13.01/3.63 | Simplifying 215 yields:
% 13.01/3.63 | (194) ~ (all_0_22_22 = e0)
% 13.01/3.63 |
% 13.01/3.63 | Equations (829) can reduce 192 to:
% 13.01/3.63 | (217) ~ (all_0_23_23 = e0)
% 13.01/3.63 |
% 13.01/3.63 | Simplifying 217 yields:
% 13.01/3.63 | (9) ~ (all_0_23_23 = e0)
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (263), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (264) all_0_14_14 = e2
% 13.01/3.63 |
% 13.01/3.63 | Equations (264) can reduce 255 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (255) ~ (all_0_14_14 = e2)
% 13.01/3.63 | (267) all_0_15_15 = e2
% 13.01/3.63 |
% 13.01/3.63 | Equations (267) can reduce 75 to:
% 13.01/3.63 | (200) ~ (all_0_12_12 = e2)
% 13.01/3.63 |
% 13.01/3.63 | Equations (267) can reduce 44 to:
% 13.01/3.63 | (255) ~ (all_0_14_14 = e2)
% 13.01/3.63 |
% 13.01/3.63 | Equations (267) can reduce 188 to:
% 13.01/3.63 | (270) ~ (all_0_19_19 = e2)
% 13.01/3.63 |
% 13.01/3.63 | Simplifying 270 yields:
% 13.01/3.63 | (271) ~ (all_0_19_19 = e2)
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (11), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (672) all_0_11_11 = e1
% 13.01/3.63 |
% 13.01/3.63 | Equations (672) can reduce 675 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (675) ~ (all_0_11_11 = e1)
% 13.01/3.63 | (676) all_0_15_15 = e1 | all_0_19_19 = e1 | all_0_23_23 = e1
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (676), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (677) all_0_15_15 = e1
% 13.01/3.63 |
% 13.01/3.63 | Combining equations (267,677) yields a new equation:
% 13.01/3.63 | (767) e2 = e1
% 13.01/3.63 |
% 13.01/3.63 | Simplifying 767 yields:
% 13.01/3.63 | (367) e2 = e1
% 13.01/3.63 |
% 13.01/3.63 | Equations (367) can reduce 71 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (693) ~ (all_0_15_15 = e1)
% 13.01/3.63 | (694) all_0_19_19 = e1 | all_0_23_23 = e1
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (694), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (420) all_0_19_19 = e1
% 13.01/3.63 |
% 13.01/3.63 | Equations (420) can reduce 622 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (622) ~ (all_0_19_19 = e1)
% 13.01/3.63 | (308) all_0_23_23 = e1
% 13.01/3.63 |
% 13.01/3.63 | Equations (308) can reduce 130 to:
% 13.01/3.63 | (920) ~ (all_0_20_20 = e1)
% 13.01/3.63 |
% 13.01/3.63 | Equations (308) can reduce 191 to:
% 13.01/3.63 | (309) ~ (all_0_22_22 = e1)
% 13.01/3.63 |
% 13.01/3.63 | Equations (308) can reduce 9 to:
% 13.01/3.63 | (181) ~ (e1 = e0)
% 13.01/3.63 |
% 13.01/3.63 | From (308) and (43) follows:
% 13.01/3.63 | (310) op(e0, e1) = all_0_1_1
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (21), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (785) all_0_16_16 = e2
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (20), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (839) all_0_8_8 = e0
% 13.01/3.63 |
% 13.01/3.63 | Combining equations (839,366) yields a new equation:
% 13.01/3.63 | (421) e1 = e0
% 13.01/3.63 |
% 13.01/3.63 | Equations (421) can reduce 181 to:
% 13.01/3.63 | (202) $false
% 13.01/3.63 |
% 13.01/3.63 |-The branch is then unsatisfiable
% 13.01/3.63 |-Branch two:
% 13.01/3.63 | (195) ~ (all_0_8_8 = e0)
% 13.01/3.63 | (1585) all_0_12_12 = e0 | all_0_16_16 = e0 | all_0_20_20 = e0
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (1585), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (500) all_0_12_12 = e0
% 13.01/3.63 |
% 13.01/3.63 | Equations (500) can reduce 160 to:
% 13.01/3.63 | (1463) ~ (all_0_14_14 = e0)
% 13.01/3.63 |
% 13.01/3.63 | Simplifying 1463 yields:
% 13.01/3.63 | (550) ~ (all_0_14_14 = e0)
% 13.01/3.63 |
% 13.01/3.63 +-Applying beta-rule and splitting (70), into two cases.
% 13.01/3.63 |-Branch one:
% 13.01/3.63 | (598) all_0_10_10 = e0
% 13.01/3.63 |
% 13.01/3.64 | Combining equations (598,2665) yields a new equation:
% 13.01/3.64 | (1662) all_0_7_7 = e0
% 13.01/3.64 |
% 13.01/3.64 | Equations (598) can reduce 117 to:
% 13.01/3.64 | (215) ~ (all_0_22_22 = e0)
% 13.01/3.64 |
% 13.01/3.64 | Simplifying 215 yields:
% 13.01/3.64 | (194) ~ (all_0_22_22 = e0)
% 13.01/3.64 |
% 13.01/3.64 | Equations (598) can reduce 1170 to:
% 13.01/3.64 | (1254) ~ (e1 = e0)
% 13.01/3.64 |
% 13.01/3.64 | Simplifying 1254 yields:
% 13.01/3.64 | (181) ~ (e1 = e0)
% 13.01/3.64 |
% 13.01/3.64 | From (598) and (2666) follows:
% 13.01/3.64 | (3250) op(e0, e1) = all_0_6_6
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (62), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (1315) ~ (all_0_6_6 = e2)
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (87), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (344) all_0_22_22 = e3
% 13.01/3.64 |
% 13.01/3.64 | Equations (344) can reduce 360 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (360) ~ (all_0_22_22 = e3)
% 13.01/3.64 | (361) all_0_22_22 = e2 | all_0_22_22 = e1 | all_0_22_22 = e0
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (151), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (932) all_0_10_10 = e1
% 13.01/3.64 |
% 13.01/3.64 | Combining equations (598,932) yields a new equation:
% 13.01/3.64 | (421) e1 = e0
% 13.01/3.64 |
% 13.01/3.64 | Equations (421) can reduce 181 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (1170) ~ (all_0_10_10 = e1)
% 13.01/3.64 | (2217) all_0_14_14 = e1 | all_0_22_22 = e1
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (2217), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (339) all_0_14_14 = e1
% 13.01/3.64 |
% 13.01/3.64 | Equations (339) can reduce 162 to:
% 13.01/3.64 | (938) ~ (all_0_22_22 = e1)
% 13.01/3.64 |
% 13.01/3.64 | Simplifying 938 yields:
% 13.01/3.64 | (309) ~ (all_0_22_22 = e1)
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (361), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (439) all_0_22_22 = e2
% 13.01/3.64 |
% 13.01/3.64 | From (439) and (37) follows:
% 13.01/3.64 | (3265) op(e0, e1) = e2
% 13.01/3.64 |
% 13.01/3.64 | Instantiating formula (53) with e0, e1, all_0_6_6, all_0_1_1 and discharging atoms op(e0, e1) = all_0_1_1, op(e0, e1) = all_0_6_6, yields:
% 13.01/3.64 | (1677) all_0_1_1 = all_0_6_6
% 13.01/3.64 |
% 13.01/3.64 | Instantiating formula (53) with e0, e1, e2, all_0_1_1 and discharging atoms op(e0, e1) = all_0_1_1, op(e0, e1) = e2, yields:
% 13.01/3.64 | (3267) all_0_1_1 = e2
% 13.01/3.64 |
% 13.01/3.64 | Combining equations (1677,3267) yields a new equation:
% 13.01/3.64 | (1327) all_0_6_6 = e2
% 13.01/3.64 |
% 13.01/3.64 | Simplifying 1327 yields:
% 13.01/3.64 | (1328) all_0_6_6 = e2
% 13.01/3.64 |
% 13.01/3.64 | Equations (1328) can reduce 1315 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (258) ~ (all_0_22_22 = e2)
% 13.01/3.64 | (442) all_0_22_22 = e1 | all_0_22_22 = e0
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (442), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (443) all_0_22_22 = e1
% 13.01/3.64 |
% 13.01/3.64 | Equations (443) can reduce 309 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (309) ~ (all_0_22_22 = e1)
% 13.01/3.64 | (446) all_0_22_22 = e0
% 13.01/3.64 |
% 13.01/3.64 | Equations (446) can reduce 194 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (319) ~ (all_0_14_14 = e1)
% 13.01/3.64 | (443) all_0_22_22 = e1
% 13.01/3.64 |
% 13.01/3.64 | Equations (443) can reduce 309 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (1328) all_0_6_6 = e2
% 13.01/3.64 | (3282) ~ (all_0_7_7 = e0) | ~ (all_0_8_8 = e1)
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (3282), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (1683) ~ (all_0_7_7 = e0)
% 13.01/3.64 |
% 13.01/3.64 | Equations (1662) can reduce 1683 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (1662) all_0_7_7 = e0
% 13.01/3.64 | (193) ~ (all_0_8_8 = e1)
% 13.01/3.64 |
% 13.01/3.64 | Equations (366) can reduce 193 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (602) ~ (all_0_10_10 = e0)
% 13.01/3.64 | (603) all_0_14_14 = e0 | all_0_18_18 = e0 | all_0_22_22 = e0
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (603), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (342) all_0_14_14 = e0
% 13.01/3.64 |
% 13.01/3.64 | Equations (342) can reduce 550 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (550) ~ (all_0_14_14 = e0)
% 13.01/3.64 | (609) all_0_18_18 = e0 | all_0_22_22 = e0
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (609), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (556) all_0_18_18 = e0
% 13.01/3.64 |
% 13.01/3.64 | Combining equations (556,250) yields a new equation:
% 13.01/3.64 | (278) e3 = e0
% 13.01/3.64 |
% 13.01/3.64 | Equations (278) can reduce 136 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (245) ~ (all_0_18_18 = e0)
% 13.01/3.64 | (446) all_0_22_22 = e0
% 13.01/3.64 |
% 13.01/3.64 | Equations (446) can reduce 194 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (214) ~ (all_0_12_12 = e0)
% 13.01/3.64 | (3301) all_0_16_16 = e0 | all_0_20_20 = e0
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (3301), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (792) all_0_16_16 = e0
% 13.01/3.64 |
% 13.01/3.64 | Combining equations (785,792) yields a new equation:
% 13.01/3.64 | (283) e2 = e0
% 13.01/3.64 |
% 13.01/3.64 | Simplifying 283 yields:
% 13.01/3.64 | (284) e2 = e0
% 13.01/3.64 |
% 13.01/3.64 | Equations (284) can reduce 13 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (611) ~ (all_0_16_16 = e0)
% 13.01/3.64 | (213) all_0_20_20 = e0
% 13.01/3.64 |
% 13.01/3.64 | Equations (213) can reduce 220 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (256) ~ (all_0_16_16 = e2)
% 13.01/3.64 | (2147) all_0_17_17 = e2 | all_0_18_18 = e2 | all_0_19_19 = e2
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (170), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (481) all_0_19_19 = e3
% 13.01/3.64 |
% 13.01/3.64 | Equations (481) can reduce 239 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (239) ~ (all_0_19_19 = e3)
% 13.01/3.64 | (704) all_0_19_19 = e2 | all_0_19_19 = e1 | all_0_19_19 = e0
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (704), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (709) all_0_19_19 = e2
% 13.01/3.64 |
% 13.01/3.64 | Equations (709) can reduce 271 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (271) ~ (all_0_19_19 = e2)
% 13.01/3.64 | (712) all_0_19_19 = e1 | all_0_19_19 = e0
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (151), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (932) all_0_10_10 = e1
% 13.01/3.64 |
% 13.01/3.64 | Equations (932) can reduce 1170 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (1170) ~ (all_0_10_10 = e1)
% 13.01/3.64 | (2217) all_0_14_14 = e1 | all_0_22_22 = e1
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (2217), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (339) all_0_14_14 = e1
% 13.01/3.64 |
% 13.01/3.64 | Equations (339) can reduce 255 to:
% 13.01/3.64 | (329) ~ (e2 = e1)
% 13.01/3.64 |
% 13.01/3.64 | Simplifying 329 yields:
% 13.01/3.64 | (71) ~ (e2 = e1)
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (35), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (196) all_0_8_8 = e2
% 13.01/3.64 |
% 13.01/3.64 | Combining equations (196,366) yields a new equation:
% 13.01/3.64 | (767) e2 = e1
% 13.01/3.64 |
% 13.01/3.64 | Simplifying 767 yields:
% 13.01/3.64 | (367) e2 = e1
% 13.01/3.64 |
% 13.01/3.64 | Equations (367) can reduce 71 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (201) ~ (all_0_8_8 = e2)
% 13.01/3.64 | (2044) all_0_12_12 = e2 | all_0_16_16 = e2 | all_0_20_20 = e2
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (2044), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (260) all_0_12_12 = e2
% 13.01/3.64 |
% 13.01/3.64 | Equations (260) can reduce 200 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (200) ~ (all_0_12_12 = e2)
% 13.01/3.64 | (2758) all_0_16_16 = e2 | all_0_20_20 = e2
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (2758), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (785) all_0_16_16 = e2
% 13.01/3.64 |
% 13.01/3.64 | Equations (785) can reduce 256 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (256) ~ (all_0_16_16 = e2)
% 13.01/3.64 | (526) all_0_20_20 = e2
% 13.01/3.64 |
% 13.01/3.64 | Equations (526) can reduce 920 to:
% 13.01/3.64 | (71) ~ (e2 = e1)
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (2147), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (371) all_0_17_17 = e2
% 13.01/3.64 |
% 13.01/3.64 | Combining equations (415,371) yields a new equation:
% 13.01/3.64 | (367) e2 = e1
% 13.01/3.64 |
% 13.01/3.64 | Equations (367) can reduce 71 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (375) ~ (all_0_17_17 = e2)
% 13.01/3.64 | (2152) all_0_18_18 = e2 | all_0_19_19 = e2
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (2152), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (254) all_0_18_18 = e2
% 13.01/3.64 |
% 13.01/3.64 | Combining equations (250,254) yields a new equation:
% 13.01/3.64 | (372) e3 = e2
% 13.01/3.64 |
% 13.01/3.64 | Simplifying 372 yields:
% 13.01/3.64 | (373) e3 = e2
% 13.01/3.64 |
% 13.01/3.64 | Equations (373) can reduce 101 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (555) ~ (all_0_18_18 = e2)
% 13.01/3.64 | (709) all_0_19_19 = e2
% 13.01/3.64 |
% 13.01/3.64 | Equations (709) can reduce 271 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (319) ~ (all_0_14_14 = e1)
% 13.01/3.64 | (443) all_0_22_22 = e1
% 13.01/3.64 |
% 13.01/3.64 | Equations (443) can reduce 309 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (204) ~ (all_0_21_21 = e0)
% 13.01/3.64 | (446) all_0_22_22 = e0
% 13.01/3.64 |
% 13.01/3.64 | Equations (446) can reduce 194 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (260) all_0_12_12 = e2
% 13.01/3.64 | (224) ~ (all_0_18_18 = e3)
% 13.01/3.64 |
% 13.01/3.64 | Equations (250) can reduce 224 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (224) ~ (all_0_18_18 = e3)
% 13.01/3.64 | (253) all_0_18_18 = e2 | all_0_18_18 = e0
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (253), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (254) all_0_18_18 = e2
% 13.01/3.64 |
% 13.01/3.64 | Equations (254) can reduce 555 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (555) ~ (all_0_18_18 = e2)
% 13.01/3.64 | (556) all_0_18_18 = e0
% 13.01/3.64 |
% 13.01/3.64 | Equations (556) can reduce 245 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (556) all_0_18_18 = e0
% 13.01/3.64 | (622) ~ (all_0_19_19 = e1)
% 13.01/3.64 |
% 13.01/3.64 | Equations (556) can reduce 129 to:
% 13.01/3.64 | (602) ~ (all_0_10_10 = e0)
% 13.01/3.64 |
% 13.01/3.64 | Equations (556) can reduce 4 to:
% 13.01/3.64 | (612) ~ (all_0_19_19 = e0)
% 13.01/3.64 |
% 13.01/3.64 | Simplifying 612 yields:
% 13.01/3.64 | (613) ~ (all_0_19_19 = e0)
% 13.01/3.64 |
% 13.01/3.64 | Equations (556) can reduce 5 to:
% 13.01/3.64 | (215) ~ (all_0_22_22 = e0)
% 13.01/3.64 |
% 13.01/3.64 | Simplifying 215 yields:
% 13.01/3.64 | (194) ~ (all_0_22_22 = e0)
% 13.01/3.64 |
% 13.01/3.64 | From (556) and (158) follows:
% 13.01/3.64 | (979) op(all_0_3_3, e0) = all_0_2_2
% 13.01/3.64 |
% 13.01/3.64 | From (556) and (164) follows:
% 13.01/3.64 | (614) op(e1, e0) = all_0_3_3
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (138), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (328) all_0_16_16 = e1
% 13.01/3.64 |
% 13.01/3.64 | Equations (328) can reduce 413 to:
% 13.01/3.64 | (202) $false
% 13.01/3.64 |
% 13.01/3.64 |-The branch is then unsatisfiable
% 13.01/3.64 |-Branch two:
% 13.01/3.64 | (413) ~ (all_0_16_16 = e1)
% 13.01/3.64 | (414) all_0_17_17 = e1 | all_0_19_19 = e1
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (414), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (415) all_0_17_17 = e1
% 13.01/3.64 |
% 13.01/3.64 | Equations (415) can reduce 6 to:
% 13.01/3.64 | (358) ~ (all_0_13_13 = e1)
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (174), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (576) ~ (all_0_15_15 = e2)
% 13.01/3.64 |
% 13.01/3.64 +-Applying beta-rule and splitting (74), into two cases.
% 13.01/3.64 |-Branch one:
% 13.01/3.64 | (260) all_0_12_12 = e2
% 13.01/3.64 |
% 13.01/3.64 | Equations (260) can reduce 76 to:
% 13.01/3.64 | (1415) ~ (all_0_16_16 = e2)
% 13.01/3.64 |
% 13.01/3.64 | Simplifying 1415 yields:
% 13.01/3.64 | (256) ~ (all_0_16_16 = e2)
% 13.01/3.65 |
% 13.01/3.65 | Equations (260) can reduce 167 to:
% 13.01/3.65 | (895) ~ (all_0_20_20 = e2)
% 13.01/3.65 |
% 13.01/3.65 | Simplifying 895 yields:
% 13.01/3.65 | (529) ~ (all_0_20_20 = e2)
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (94), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (200) ~ (all_0_12_12 = e2)
% 13.01/3.65 |
% 13.01/3.65 | Equations (260) can reduce 200 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (260) all_0_12_12 = e2
% 13.01/3.65 | (223) ~ (all_0_23_23 = e3)
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (91), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (208) ~ (all_0_17_17 = e1)
% 13.01/3.65 |
% 13.01/3.65 | Equations (415) can reduce 208 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (415) all_0_17_17 = e1
% 13.01/3.65 | (273) ~ (all_0_23_23 = e2)
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (88), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (301) all_0_23_23 = e3
% 13.01/3.65 |
% 13.01/3.65 | Equations (301) can reduce 223 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (223) ~ (all_0_23_23 = e3)
% 13.01/3.65 | (304) all_0_23_23 = e2 | all_0_23_23 = e1
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (304), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (305) all_0_23_23 = e2
% 13.01/3.65 |
% 13.01/3.65 | Equations (305) can reduce 273 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (273) ~ (all_0_23_23 = e2)
% 13.01/3.65 | (308) all_0_23_23 = e1
% 13.01/3.65 |
% 13.01/3.65 | Equations (308) can reduce 173 to:
% 13.01/3.65 | (693) ~ (all_0_15_15 = e1)
% 13.01/3.65 |
% 13.01/3.65 | Equations (308) can reduce 130 to:
% 13.01/3.65 | (920) ~ (all_0_20_20 = e1)
% 13.01/3.65 |
% 13.01/3.65 | Equations (308) can reduce 192 to:
% 13.01/3.65 | (1688) ~ (all_0_21_21 = e1)
% 13.01/3.65 |
% 13.01/3.65 | Equations (308) can reduce 191 to:
% 13.01/3.65 | (309) ~ (all_0_22_22 = e1)
% 13.01/3.65 |
% 13.01/3.65 | Equations (308) can reduce 223 to:
% 13.01/3.65 | (464) ~ (e3 = e1)
% 13.01/3.65 |
% 13.01/3.65 | Simplifying 464 yields:
% 13.01/3.65 | (137) ~ (e3 = e1)
% 13.01/3.65 |
% 13.01/3.65 | Equations (308) can reduce 273 to:
% 13.01/3.65 | (329) ~ (e2 = e1)
% 13.01/3.65 |
% 13.01/3.65 | Simplifying 329 yields:
% 13.01/3.65 | (71) ~ (e2 = e1)
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (116), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (200) ~ (all_0_12_12 = e2)
% 13.01/3.65 |
% 13.01/3.65 | Equations (260) can reduce 200 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (260) all_0_12_12 = e2
% 13.01/3.65 | (219) ~ (all_0_13_13 = e3)
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (7), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (427) all_0_16_16 = e3
% 13.01/3.65 |
% 13.01/3.65 | Equations (427) can reduce 134 to:
% 13.01/3.65 | (2712) ~ (all_0_20_20 = e3)
% 13.01/3.65 |
% 13.01/3.65 | Simplifying 2712 yields:
% 13.01/3.65 | (1100) ~ (all_0_20_20 = e3)
% 13.01/3.65 |
% 13.01/3.65 | Equations (427) can reduce 256 to:
% 13.01/3.65 | (101) ~ (e3 = e2)
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (68), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (434) all_0_20_20 = e3
% 13.01/3.65 |
% 13.01/3.65 | Equations (434) can reduce 1100 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (1100) ~ (all_0_20_20 = e3)
% 13.01/3.65 | (1101) all_0_20_20 = e2 | all_0_20_20 = e1 | all_0_20_20 = e0
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (113), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (311) all_0_13_13 = e3
% 13.01/3.65 |
% 13.01/3.65 | Equations (311) can reduce 219 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (219) ~ (all_0_13_13 = e3)
% 13.01/3.65 | (314) all_0_13_13 = e1 | all_0_13_13 = e0
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (314), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (315) all_0_13_13 = e1
% 13.01/3.65 |
% 13.01/3.65 | Equations (315) can reduce 358 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (358) ~ (all_0_13_13 = e1)
% 13.01/3.65 | (449) all_0_13_13 = e0
% 13.01/3.65 |
% 13.01/3.65 | Equations (449) can reduce 98 to:
% 13.01/3.65 | (628) ~ (all_0_15_15 = e0)
% 13.01/3.65 |
% 13.01/3.65 | Simplifying 628 yields:
% 13.01/3.65 | (286) ~ (all_0_15_15 = e0)
% 13.01/3.65 |
% 13.01/3.65 | From (449) and (102) follows:
% 13.01/3.65 | (631) op(e2, e0) = all_0_5_5
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (112), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (213) all_0_20_20 = e0
% 13.01/3.65 |
% 13.01/3.65 | Equations (213) can reduce 529 to:
% 13.01/3.65 | (293) ~ (e2 = e0)
% 13.01/3.65 |
% 13.01/3.65 | Simplifying 293 yields:
% 13.01/3.65 | (13) ~ (e2 = e0)
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (147), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (276) all_0_11_11 = e0
% 13.01/3.65 |
% 13.01/3.65 | Equations (276) can reduce 50 to:
% 13.01/3.65 | (628) ~ (all_0_15_15 = e0)
% 13.01/3.65 |
% 13.01/3.65 | Simplifying 628 yields:
% 13.01/3.65 | (286) ~ (all_0_15_15 = e0)
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (21), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (785) all_0_16_16 = e2
% 13.01/3.65 |
% 13.01/3.65 | Combining equations (427,785) yields a new equation:
% 13.01/3.65 | (372) e3 = e2
% 13.01/3.65 |
% 13.01/3.65 | Simplifying 372 yields:
% 13.01/3.65 | (373) e3 = e2
% 13.01/3.65 |
% 13.01/3.65 | Equations (373) can reduce 101 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (256) ~ (all_0_16_16 = e2)
% 13.01/3.65 | (2147) all_0_17_17 = e2 | all_0_18_18 = e2 | all_0_19_19 = e2
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (2147), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (371) all_0_17_17 = e2
% 13.01/3.65 |
% 13.01/3.65 | Combining equations (415,371) yields a new equation:
% 13.01/3.65 | (367) e2 = e1
% 13.01/3.65 |
% 13.01/3.65 | Equations (367) can reduce 71 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (375) ~ (all_0_17_17 = e2)
% 13.01/3.65 | (2152) all_0_18_18 = e2 | all_0_19_19 = e2
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (2152), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (254) all_0_18_18 = e2
% 13.01/3.65 |
% 13.01/3.65 | Combining equations (254,556) yields a new equation:
% 13.01/3.65 | (283) e2 = e0
% 13.01/3.65 |
% 13.01/3.65 | Simplifying 283 yields:
% 13.01/3.65 | (284) e2 = e0
% 13.01/3.65 |
% 13.01/3.65 | Equations (284) can reduce 13 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (555) ~ (all_0_18_18 = e2)
% 13.01/3.65 | (709) all_0_19_19 = e2
% 13.01/3.65 |
% 13.01/3.65 | Equations (709) can reduce 188 to:
% 13.01/3.65 | (576) ~ (all_0_15_15 = e2)
% 13.01/3.65 |
% 13.01/3.65 | From (709) and (41) follows:
% 13.01/3.65 | (1284) op(e1, e0) = e2
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (126), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (665) all_0_15_15 = e3
% 13.01/3.65 |
% 13.01/3.65 | From (665) and (103) follows:
% 13.01/3.65 | (1828) op(e2, e0) = e3
% 13.01/3.65 |
% 13.01/3.65 | Instantiating formula (53) with e2, e0, e3, all_0_5_5 and discharging atoms op(e2, e0) = all_0_5_5, op(e2, e0) = e3, yields:
% 13.01/3.65 | (1836) all_0_5_5 = e3
% 13.01/3.65 |
% 13.01/3.65 | Instantiating formula (53) with e1, e0, e2, all_0_3_3 and discharging atoms op(e1, e0) = all_0_3_3, op(e1, e0) = e2, yields:
% 13.01/3.65 | (1326) all_0_3_3 = e2
% 13.01/3.65 |
% 13.01/3.65 | From (1326) and (979) follows:
% 13.01/3.65 | (3466) op(e2, e0) = all_0_2_2
% 13.01/3.65 |
% 13.01/3.65 | From (1836) and (631) follows:
% 13.01/3.65 | (1828) op(e2, e0) = e3
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (161), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (3468) ~ (all_0_2_2 = e3)
% 13.01/3.65 |
% 13.01/3.65 | Instantiating formula (53) with e2, e0, all_0_2_2, e3 and discharging atoms op(e2, e0) = all_0_2_2, op(e2, e0) = e3, yields:
% 13.01/3.65 | (3469) all_0_2_2 = e3
% 13.01/3.65 |
% 13.01/3.65 | Equations (3469) can reduce 3468 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (3469) all_0_2_2 = e3
% 13.01/3.65 | (3472) ~ (all_0_3_3 = e2) | ~ (all_0_18_18 = e0)
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (3472), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (3473) ~ (all_0_3_3 = e2)
% 13.01/3.65 |
% 13.01/3.65 | Equations (1326) can reduce 3473 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (1326) all_0_3_3 = e2
% 13.01/3.65 | (245) ~ (all_0_18_18 = e0)
% 13.01/3.65 |
% 13.01/3.65 | Equations (556) can reduce 245 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (237) ~ (all_0_15_15 = e3)
% 13.01/3.65 | (668) all_0_15_15 = e2 | all_0_15_15 = e1 | all_0_15_15 = e0
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (668), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (267) all_0_15_15 = e2
% 13.01/3.65 |
% 13.01/3.65 | Equations (267) can reduce 576 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (576) ~ (all_0_15_15 = e2)
% 13.01/3.65 | (708) all_0_15_15 = e1 | all_0_15_15 = e0
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (708), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (677) all_0_15_15 = e1
% 13.01/3.65 |
% 13.01/3.65 | Equations (677) can reduce 693 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (693) ~ (all_0_15_15 = e1)
% 13.01/3.65 | (282) all_0_15_15 = e0
% 13.01/3.65 |
% 13.01/3.65 | Equations (282) can reduce 286 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (280) ~ (all_0_11_11 = e0)
% 13.01/3.65 | (281) all_0_15_15 = e0 | all_0_19_19 = e0
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (281), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (282) all_0_15_15 = e0
% 13.01/3.65 |
% 13.01/3.65 | Equations (282) can reduce 286 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (286) ~ (all_0_15_15 = e0)
% 13.01/3.65 | (287) all_0_19_19 = e0
% 13.01/3.65 |
% 13.01/3.65 | Equations (287) can reduce 613 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (220) ~ (all_0_20_20 = e0)
% 13.01/3.65 | (828) all_0_21_21 = e0 | all_0_22_22 = e0
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (1101), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (526) all_0_20_20 = e2
% 13.01/3.65 |
% 13.01/3.65 | Equations (526) can reduce 529 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (529) ~ (all_0_20_20 = e2)
% 13.01/3.65 | (3501) all_0_20_20 = e1 | all_0_20_20 = e0
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (3501), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (1501) all_0_20_20 = e1
% 13.01/3.65 |
% 13.01/3.65 | Equations (1501) can reduce 920 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (920) ~ (all_0_20_20 = e1)
% 13.01/3.65 | (213) all_0_20_20 = e0
% 13.01/3.65 |
% 13.01/3.65 | Equations (213) can reduce 220 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (298) ~ (all_0_16_16 = e3)
% 13.01/3.65 | (430) all_0_16_16 = e2 | all_0_16_16 = e1 | all_0_16_16 = e0
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (113), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (311) all_0_13_13 = e3
% 13.01/3.65 |
% 13.01/3.65 | Equations (311) can reduce 219 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (219) ~ (all_0_13_13 = e3)
% 13.01/3.65 | (314) all_0_13_13 = e1 | all_0_13_13 = e0
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (314), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (315) all_0_13_13 = e1
% 13.01/3.65 |
% 13.01/3.65 | Equations (315) can reduce 358 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (358) ~ (all_0_13_13 = e1)
% 13.01/3.65 | (449) all_0_13_13 = e0
% 13.01/3.65 |
% 13.01/3.65 | Equations (449) can reduce 31 to:
% 13.01/3.65 | (494) ~ (all_0_9_9 = e0)
% 13.01/3.65 |
% 13.01/3.65 | Equations (449) can reduce 149 to:
% 13.01/3.65 | (1463) ~ (all_0_14_14 = e0)
% 13.01/3.65 |
% 13.01/3.65 | Simplifying 1463 yields:
% 13.01/3.65 | (550) ~ (all_0_14_14 = e0)
% 13.01/3.65 |
% 13.01/3.65 | Equations (449) can reduce 96 to:
% 13.01/3.65 | (1663) ~ (all_0_21_21 = e0)
% 13.01/3.65 |
% 13.01/3.65 | Simplifying 1663 yields:
% 13.01/3.65 | (204) ~ (all_0_21_21 = e0)
% 13.01/3.65 |
% 13.01/3.65 | Equations (449) can reduce 219 to:
% 13.01/3.65 | (291) ~ (e3 = e0)
% 13.01/3.65 |
% 13.01/3.65 | Simplifying 291 yields:
% 13.01/3.65 | (136) ~ (e3 = e0)
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (112), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (213) all_0_20_20 = e0
% 13.01/3.65 |
% 13.01/3.65 | Equations (213) can reduce 61 to:
% 13.01/3.65 | (1663) ~ (all_0_21_21 = e0)
% 13.01/3.65 |
% 13.01/3.65 | Simplifying 1663 yields:
% 13.01/3.65 | (204) ~ (all_0_21_21 = e0)
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (151), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (932) all_0_10_10 = e1
% 13.01/3.65 |
% 13.01/3.65 | Equations (932) can reduce 1170 to:
% 13.01/3.65 | (202) $false
% 13.01/3.65 |
% 13.01/3.65 |-The branch is then unsatisfiable
% 13.01/3.65 |-Branch two:
% 13.01/3.65 | (1170) ~ (all_0_10_10 = e1)
% 13.01/3.65 | (2217) all_0_14_14 = e1 | all_0_22_22 = e1
% 13.01/3.65 |
% 13.01/3.65 +-Applying beta-rule and splitting (155), into two cases.
% 13.01/3.65 |-Branch one:
% 13.01/3.65 | (226) all_0_9_9 = e3
% 13.01/3.65 |
% 13.01/3.65 | Equations (226) can reduce 145 to:
% 13.01/3.65 | (952) ~ (all_0_11_11 = e3)
% 13.01/3.65 |
% 13.01/3.65 | Simplifying 952 yields:
% 13.01/3.65 | (242) ~ (all_0_11_11 = e3)
% 13.01/3.65 |
% 13.01/3.65 | Equations (226) can reduce 494 to:
% 13.01/3.65 | (136) ~ (e3 = e0)
% 13.01/3.65 |
% 13.01/3.66 +-Applying beta-rule and splitting (2217), into two cases.
% 13.01/3.66 |-Branch one:
% 13.01/3.66 | (339) all_0_14_14 = e1
% 13.01/3.66 |
% 13.01/3.66 | Equations (339) can reduce 550 to:
% 13.01/3.66 | (181) ~ (e1 = e0)
% 13.01/3.66 |
% 13.01/3.66 +-Applying beta-rule and splitting (48), into two cases.
% 13.01/3.66 |-Branch one:
% 13.01/3.66 | (839) all_0_8_8 = e0
% 13.01/3.66 |
% 13.01/3.66 | Combining equations (839,366) yields a new equation:
% 13.01/3.66 | (421) e1 = e0
% 13.01/3.66 |
% 13.01/3.66 | Equations (421) can reduce 181 to:
% 13.01/3.66 | (202) $false
% 13.01/3.66 |
% 13.01/3.66 |-The branch is then unsatisfiable
% 13.01/3.66 |-Branch two:
% 13.01/3.66 | (195) ~ (all_0_8_8 = e0)
% 13.01/3.66 | (1660) all_0_9_9 = e0 | all_0_10_10 = e0 | all_0_11_11 = e0
% 13.01/3.66 |
% 13.01/3.66 +-Applying beta-rule and splitting (1660), into two cases.
% 13.01/3.66 |-Branch one:
% 13.01/3.66 | (395) all_0_9_9 = e0
% 13.01/3.66 |
% 13.01/3.66 | Combining equations (226,395) yields a new equation:
% 13.01/3.66 | (277) e3 = e0
% 13.01/3.66 |
% 13.01/3.66 | Simplifying 277 yields:
% 13.01/3.66 | (278) e3 = e0
% 13.01/3.66 |
% 13.01/3.66 | Equations (278) can reduce 136 to:
% 13.01/3.66 | (202) $false
% 13.01/3.66 |
% 13.01/3.66 |-The branch is then unsatisfiable
% 13.01/3.66 |-Branch two:
% 13.01/3.66 | (494) ~ (all_0_9_9 = e0)
% 13.01/3.66 | (1692) all_0_10_10 = e0 | all_0_11_11 = e0
% 13.01/3.66 |
% 13.01/3.66 +-Applying beta-rule and splitting (1692), into two cases.
% 13.01/3.66 |-Branch one:
% 13.01/3.66 | (598) all_0_10_10 = e0
% 13.01/3.66 |
% 13.01/3.66 | Equations (598) can reduce 602 to:
% 13.01/3.66 | (202) $false
% 13.01/3.66 |
% 13.01/3.66 |-The branch is then unsatisfiable
% 13.01/3.66 |-Branch two:
% 13.01/3.66 | (602) ~ (all_0_10_10 = e0)
% 13.01/3.66 | (276) all_0_11_11 = e0
% 13.01/3.66 |
% 13.01/3.66 | Equations (276) can reduce 242 to:
% 13.01/3.66 | (291) ~ (e3 = e0)
% 13.01/3.66 |
% 13.01/3.66 | Simplifying 291 yields:
% 13.01/3.66 | (136) ~ (e3 = e0)
% 13.01/3.66 |
% 13.01/3.66 +-Applying beta-rule and splitting (144), into two cases.
% 13.01/3.66 |-Branch one:
% 13.01/3.66 | (362) all_0_9_9 = e2
% 13.01/3.66 |
% 13.01/3.66 | Combining equations (362,226) yields a new equation:
% 13.01/3.66 | (373) e3 = e2
% 13.01/3.66 |
% 13.01/3.66 | Equations (373) can reduce 101 to:
% 13.01/3.66 | (202) $false
% 13.01/3.66 |
% 13.01/3.66 |-The branch is then unsatisfiable
% 13.01/3.66 |-Branch two:
% 13.01/3.66 | (198) ~ (all_0_9_9 = e2)
% 13.01/3.66 | (365) all_0_17_17 = e2 | all_0_21_21 = e2
% 13.01/3.66 |
% 13.01/3.66 | Equations (226) can reduce 198 to:
% 13.01/3.66 | (101) ~ (e3 = e2)
% 13.01/3.66 |
% 13.01/3.66 +-Applying beta-rule and splitting (128), into two cases.
% 13.01/3.66 |-Branch one:
% 13.01/3.66 | (323) all_0_12_12 = e3
% 13.01/3.66 |
% 13.01/3.66 | Combining equations (323,260) yields a new equation:
% 13.01/3.66 | (372) e3 = e2
% 13.01/3.66 |
% 13.01/3.66 | Simplifying 372 yields:
% 13.01/3.66 | (373) e3 = e2
% 13.01/3.66 |
% 13.01/3.66 | Equations (373) can reduce 101 to:
% 13.01/3.66 | (202) $false
% 13.01/3.66 |
% 13.01/3.66 |-The branch is then unsatisfiable
% 13.01/3.66 |-Branch two:
% 13.01/3.66 | (423) ~ (all_0_12_12 = e3)
% 13.01/3.66 | (424) all_0_16_16 = e3 | all_0_20_20 = e3
% 13.01/3.66 |
% 13.01/3.66 +-Applying beta-rule and splitting (424), into two cases.
% 13.01/3.66 |-Branch one:
% 13.01/3.66 | (427) all_0_16_16 = e3
% 13.01/3.66 |
% 13.01/3.66 | Equations (427) can reduce 298 to:
% 13.01/3.66 | (202) $false
% 13.01/3.66 |
% 13.01/3.66 |-The branch is then unsatisfiable
% 13.01/3.66 |-Branch two:
% 13.01/3.66 | (298) ~ (all_0_16_16 = e3)
% 13.01/3.66 | (434) all_0_20_20 = e3
% 13.01/3.66 |
% 13.01/3.66 | Combining equations (434,213) yields a new equation:
% 13.01/3.66 | (277) e3 = e0
% 13.01/3.66 |
% 13.01/3.66 | Simplifying 277 yields:
% 13.01/3.66 | (278) e3 = e0
% 13.01/3.66 |
% 13.01/3.66 | Equations (278) can reduce 136 to:
% 13.01/3.66 | (202) $false
% 13.01/3.66 |
% 13.01/3.66 |-The branch is then unsatisfiable
% 13.01/3.66 |-Branch two:
% 13.01/3.66 | (319) ~ (all_0_14_14 = e1)
% 13.01/3.66 | (443) all_0_22_22 = e1
% 13.01/3.66 |
% 13.01/3.66 | Equations (443) can reduce 309 to:
% 13.01/3.66 | (202) $false
% 13.01/3.66 |
% 13.01/3.66 |-The branch is then unsatisfiable
% 13.01/3.66 |-Branch two:
% 13.01/3.66 | (212) ~ (all_0_9_9 = e3)
% 13.01/3.66 | (229) all_0_10_10 = e3 | all_0_11_11 = e3
% 13.01/3.66 |
% 13.01/3.66 +-Applying beta-rule and splitting (15), into two cases.
% 13.01/3.66 |-Branch one:
% 13.01/3.66 | (226) all_0_9_9 = e3
% 13.01/3.66 |
% 13.01/3.66 | Equations (226) can reduce 212 to:
% 13.01/3.66 | (202) $false
% 13.01/3.66 |
% 13.01/3.66 |-The branch is then unsatisfiable
% 13.01/3.66 |-Branch two:
% 13.01/3.66 | (212) ~ (all_0_9_9 = e3)
% 13.01/3.66 | (2858) all_0_13_13 = e3 | all_0_17_17 = e3 | all_0_21_21 = e3
% 13.01/3.66 |
% 13.01/3.66 +-Applying beta-rule and splitting (2858), into two cases.
% 13.01/3.66 |-Branch one:
% 13.01/3.66 | (311) all_0_13_13 = e3
% 13.01/3.66 |
% 13.01/3.66 | Combining equations (449,311) yields a new equation:
% 13.01/3.66 | (278) e3 = e0
% 13.01/3.66 |
% 13.01/3.66 | Equations (278) can reduce 136 to:
% 13.01/3.66 | (202) $false
% 13.01/3.66 |
% 13.01/3.66 |-The branch is then unsatisfiable
% 13.01/3.66 |-Branch two:
% 13.01/3.66 | (219) ~ (all_0_13_13 = e3)
% 13.01/3.66 | (2862) all_0_17_17 = e3 | all_0_21_21 = e3
% 13.01/3.66 |
% 13.01/3.66 +-Applying beta-rule and splitting (2217), into two cases.
% 13.01/3.66 |-Branch one:
% 13.01/3.66 | (339) all_0_14_14 = e1
% 13.01/3.66 |
% 13.01/3.66 +-Applying beta-rule and splitting (2862), into two cases.
% 13.01/3.66 |-Branch one:
% 13.01/3.66 | (295) all_0_17_17 = e3
% 13.01/3.66 |
% 13.01/3.66 | Combining equations (415,295) yields a new equation:
% 13.01/3.66 | (417) e3 = e1
% 13.01/3.66 |
% 13.01/3.66 | Equations (417) can reduce 137 to:
% 13.01/3.66 | (202) $false
% 13.01/3.66 |
% 13.01/3.66 |-The branch is then unsatisfiable
% 13.01/3.66 |-Branch two:
% 13.01/3.66 | (451) ~ (all_0_17_17 = e3)
% 13.01/3.66 | (1666) all_0_21_21 = e3
% 13.01/3.66 |
% 13.01/3.66 | Equations (1666) can reduce 27 to:
% 13.01/3.66 | (561) ~ (all_0_22_22 = e3)
% 13.01/3.66 |
% 13.01/3.66 | Simplifying 561 yields:
% 13.01/3.66 | (360) ~ (all_0_22_22 = e3)
% 13.01/3.66 |
% 13.01/3.66 | Equations (1666) can reduce 1688 to:
% 13.01/3.66 | (137) ~ (e3 = e1)
% 13.01/3.66 |
% 13.01/3.66 | Equations (1666) can reduce 204 to:
% 13.01/3.66 | (136) ~ (e3 = e0)
% 13.01/3.66 |
% 13.01/3.66 +-Applying beta-rule and splitting (67), into two cases.
% 13.01/3.66 |-Branch one:
% 13.01/3.66 | (230) all_0_10_10 = e3
% 13.01/3.66 |
% 13.01/3.66 | Equations (230) can reduce 225 to:
% 13.01/3.66 | (202) $false
% 13.01/3.66 |
% 13.01/3.66 |-The branch is then unsatisfiable
% 13.01/3.66 |-Branch two:
% 13.01/3.66 | (225) ~ (all_0_10_10 = e3)
% 13.01/3.66 | (401) all_0_14_14 = e3 | all_0_18_18 = e3 | all_0_22_22 = e3
% 13.01/3.66 |
% 13.01/3.66 +-Applying beta-rule and splitting (401), into two cases.
% 13.01/3.66 |-Branch one:
% 13.01/3.66 | (331) all_0_14_14 = e3
% 13.01/3.66 |
% 13.01/3.66 | Combining equations (339,331) yields a new equation:
% 13.01/3.66 | (417) e3 = e1
% 13.01/3.66 |
% 13.01/3.66 | Equations (417) can reduce 137 to:
% 13.01/3.66 | (202) $false
% 13.01/3.66 |
% 13.01/3.66 |-The branch is then unsatisfiable
% 13.01/3.66 |-Branch two:
% 13.01/3.66 | (325) ~ (all_0_14_14 = e3)
% 13.01/3.66 | (406) all_0_18_18 = e3 | all_0_22_22 = e3
% 13.01/3.66 |
% 13.01/3.66 +-Applying beta-rule and splitting (406), into two cases.
% 13.01/3.66 |-Branch one:
% 13.01/3.66 | (250) all_0_18_18 = e3
% 13.01/3.66 |
% 13.01/3.66 | Combining equations (556,250) yields a new equation:
% 13.01/3.66 | (278) e3 = e0
% 13.01/3.66 |
% 13.01/3.66 | Equations (278) can reduce 136 to:
% 13.01/3.66 | (202) $false
% 13.01/3.66 |
% 13.01/3.66 |-The branch is then unsatisfiable
% 13.01/3.66 |-Branch two:
% 13.01/3.66 | (224) ~ (all_0_18_18 = e3)
% 13.01/3.66 | (344) all_0_22_22 = e3
% 13.01/3.66 |
% 13.01/3.66 | Equations (344) can reduce 360 to:
% 13.01/3.66 | (202) $false
% 13.01/3.66 |
% 13.01/3.66 |-The branch is then unsatisfiable
% 13.01/3.66 |-Branch two:
% 13.01/3.66 | (319) ~ (all_0_14_14 = e1)
% 13.01/3.66 | (443) all_0_22_22 = e1
% 13.01/3.66 |
% 13.01/3.66 | Equations (443) can reduce 309 to:
% 13.01/3.66 | (202) $false
% 13.01/3.66 |
% 13.01/3.66 |-The branch is then unsatisfiable
% 13.01/3.66 |-Branch two:
% 13.01/3.66 | (220) ~ (all_0_20_20 = e0)
% 13.01/3.66 | (828) all_0_21_21 = e0 | all_0_22_22 = e0
% 13.01/3.66 |
% 13.01/3.66 +-Applying beta-rule and splitting (828), into two cases.
% 13.01/3.66 |-Branch one:
% 13.01/3.66 | (829) all_0_21_21 = e0
% 13.01/3.66 |
% 13.01/3.66 | Equations (829) can reduce 204 to:
% 13.01/3.66 | (202) $false
% 13.01/3.66 |
% 13.01/3.66 |-The branch is then unsatisfiable
% 13.01/3.66 |-Branch two:
% 13.01/3.66 | (204) ~ (all_0_21_21 = e0)
% 13.01/3.66 | (446) all_0_22_22 = e0
% 13.01/3.66 |
% 13.01/3.66 | Equations (446) can reduce 194 to:
% 13.01/3.66 | (202) $false
% 13.01/3.66 |
% 13.01/3.66 |-The branch is then unsatisfiable
% 13.01/3.66 |-Branch two:
% 13.01/3.66 | (200) ~ (all_0_12_12 = e2)
% 13.01/3.66 | (263) all_0_14_14 = e2 | all_0_15_15 = e2
% 13.01/3.66 |
% 13.01/3.66 +-Applying beta-rule and splitting (263), into two cases.
% 13.01/3.66 |-Branch one:
% 13.01/3.66 | (264) all_0_14_14 = e2
% 13.01/3.66 |
% 13.01/3.66 | Equations (264) can reduce 255 to:
% 13.01/3.66 | (202) $false
% 13.01/3.66 |
% 13.01/3.66 |-The branch is then unsatisfiable
% 13.01/3.66 |-Branch two:
% 13.01/3.66 | (255) ~ (all_0_14_14 = e2)
% 13.01/3.66 | (267) all_0_15_15 = e2
% 13.01/3.66 |
% 13.01/3.66 | Equations (267) can reduce 576 to:
% 13.01/3.66 | (202) $false
% 13.01/3.66 |
% 13.01/3.66 |-The branch is then unsatisfiable
% 13.01/3.66 |-Branch two:
% 13.01/3.66 | (267) all_0_15_15 = e2
% 13.01/3.66 | (245) ~ (all_0_18_18 = e0)
% 13.01/3.66 |
% 13.01/3.66 | Equations (556) can reduce 245 to:
% 13.01/3.66 | (202) $false
% 13.01/3.66 |
% 13.01/3.66 |-The branch is then unsatisfiable
% 13.01/3.66 |-Branch two:
% 13.01/3.66 | (208) ~ (all_0_17_17 = e1)
% 13.01/3.66 | (420) all_0_19_19 = e1
% 13.01/3.66 |
% 13.01/3.66 | Equations (420) can reduce 622 to:
% 13.01/3.66 | (202) $false
% 13.01/3.66 |
% 13.01/3.66 |-The branch is then unsatisfiable
% 13.01/3.66 % SZS output end Proof for theBenchmark
% 13.01/3.66
% 13.01/3.66 3061ms
%------------------------------------------------------------------------------