TSTP Solution File: ALG185+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG185+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n022.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 15:37:06 EDT 2022
% Result : Theorem 6.75s 2.19s
% Output : Proof 16.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG185+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 04:01:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.58/0.57 ____ _
% 0.58/0.57 ___ / __ \_____(_)___ ________ __________
% 0.58/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.57
% 0.58/0.57 A Theorem Prover for First-Order Logic
% 0.58/0.57 (ePrincess v.1.0)
% 0.58/0.57
% 0.58/0.57 (c) Philipp Rümmer, 2009-2015
% 0.58/0.57 (c) Peter Backeman, 2014-2015
% 0.58/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.57 Bug reports to peter@backeman.se
% 0.58/0.57
% 0.58/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.57
% 0.58/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.58/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.83/0.99 Prover 0: Preprocessing ...
% 2.82/1.28 Prover 0: Constructing countermodel ...
% 6.75/2.19 Prover 0: proved (1574ms)
% 6.75/2.19
% 6.75/2.19 No countermodel exists, formula is valid
% 6.75/2.19 % SZS status Theorem for theBenchmark
% 6.75/2.20
% 6.75/2.20 Generating proof ... found it (size 681)
% 15.40/4.17
% 15.40/4.17 % SZS output start Proof for theBenchmark
% 15.40/4.17 Assumed formulas after preprocessing and simplification:
% 15.40/4.17 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (e24 = e23) & ~ (e24 = e22) & ~ (e24 = e20) & ~ (e24 = e21) & ~ (e24 = e14) & ~ (e24 = e13) & ~ (e24 = e12) & ~ (e24 = e10) & ~ (e24 = e11) & ~ (e23 = e22) & ~ (e23 = e20) & ~ (e23 = e21) & ~ (e23 = e14) & ~ (e23 = e13) & ~ (e23 = e12) & ~ (e23 = e10) & ~ (e23 = e11) & ~ (e22 = e20) & ~ (e22 = e21) & ~ (e22 = e14) & ~ (e22 = e13) & ~ (e22 = e12) & ~ (e22 = e10) & ~ (e22 = e11) & ~ (e20 = e21) & ~ (e20 = e14) & ~ (e20 = e13) & ~ (e20 = e12) & ~ (e20 = e10) & ~ (e20 = e11) & ~ (e21 = e14) & ~ (e21 = e13) & ~ (e21 = e12) & ~ (e21 = e10) & ~ (e21 = e11) & ~ (e14 = e13) & ~ (e14 = e12) & ~ (e14 = e10) & ~ (e14 = e11) & ~ (e13 = e12) & ~ (e13 = e10) & ~ (e13 = e11) & ~ (e12 = e10) & ~ (e12 = e11) & ~ (e10 = e11) & op2(v4, v4) = v4 & op2(v4, v3) = v0 & op2(v4, v2) = v1 & op2(v4, v1) = v2 & op2(v4, v0) = v3 & op2(v3, v4) = v1 & op2(v3, v3) = v3 & op2(v3, v2) = v0 & op2(v3, v1) = v4 & op2(v3, v0) = v2 & op2(v2, v4) = v3 & op2(v2, v3) = v4 & op2(v2, v2) = v2 & op2(v2, v1) = v0 & op2(v2, v0) = v1 & op2(v1, v4) = v0 & op2(v1, v3) = v2 & op2(v1, v2) = v3 & op2(v1, v1) = v1 & op2(v1, v0) = v4 & op2(v0, v4) = v2 & op2(v0, v3) = v1 & op2(v0, v2) = v4 & op2(v0, v1) = v3 & op2(v0, v0) = v0 & op2(e24, e24) = e24 & op2(e24, e23) = e21 & op2(e24, e22) = e20 & op2(e24, e20) = e23 & op2(e24, e21) = e22 & op2(e23, e24) = e22 & op2(e23, e23) = e23 & op2(e23, e22) = e21 & op2(e23, e20) = e24 & op2(e23, e21) = e20 & op2(e22, e24) = e23 & op2(e22, e23) = e20 & op2(e22, e22) = e22 & op2(e22, e20) = e21 & op2(e22, e21) = e24 & op2(e20, e24) = e21 & op2(e20, e23) = e22 & op2(e20, e22) = e24 & op2(e20, e20) = e20 & op2(e20, e21) = e23 & op2(e21, e24) = e20 & op2(e21, e23) = e24 & op2(e21, e22) = e23 & op2(e21, e20) = e22 & op2(e21, e21) = e21 & op1(v9, v9) = v9 & op1(v9, v8) = v6 & op1(v9, v7) = v5 & op1(v9, v6) = v7 & op1(v9, v5) = v8 & op1(v8, v9) = v7 & op1(v8, v8) = v8 & op1(v8, v7) = v6 & op1(v8, v6) = v5 & op1(v8, v5) = v9 & op1(v7, v9) = v8 & op1(v7, v8) = v5 & op1(v7, v7) = v7 & op1(v7, v6) = v9 & op1(v7, v5) = v6 & op1(v6, v9) = v5 & op1(v6, v8) = v9 & op1(v6, v7) = v8 & op1(v6, v6) = v6 & op1(v6, v5) = v7 & op1(v5, v9) = v6 & op1(v5, v8) = v7 & op1(v5, v7) = v9 & op1(v5, v6) = v8 & op1(v5, v5) = v5 & op1(e14, e14) = e14 & op1(e14, e13) = e10 & op1(e14, e12) = e11 & op1(e14, e10) = e13 & op1(e14, e11) = e12 & op1(e13, e14) = e11 & op1(e13, e13) = e13 & op1(e13, e12) = e10 & op1(e13, e10) = e12 & op1(e13, e11) = e14 & op1(e12, e14) = e13 & op1(e12, e13) = e14 & op1(e12, e12) = e12 & op1(e12, e10) = e11 & op1(e12, e11) = e10 & op1(e10, e14) = e12 & op1(e10, e13) = e11 & op1(e10, e12) = e14 & op1(e10, e10) = e10 & op1(e10, e11) = e13 & op1(e11, e14) = e10 & op1(e11, e13) = e12 & op1(e11, e12) = e13 & op1(e11, e10) = e14 & op1(e11, e11) = e11 & h(v9) = e24 & h(v8) = e23 & h(v7) = e22 & h(v6) = e21 & h(v5) = e20 & h(e14) = v4 & h(e13) = v3 & h(e12) = v2 & h(e10) = v0 & h(e11) = v1 & j(v4) = e14 & j(v3) = e13 & j(v2) = e12 & j(v1) = e11 & j(v0) = e10 & j(e24) = v9 & j(e23) = v8 & j(e22) = v7 & j(e20) = v5 & j(e21) = v6 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (op2(v13, v12) = v11) | ~ (op2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (op1(v13, v12) = v11) | ~ (op1(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (h(v12) = v11) | ~ (h(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (j(v12) = v11) | ~ (j(v12) = v10)) & (v9 = e14 | v9 = e13 | v9 = e12 | v9 = e10 | v9 = e11) & (v8 = e14 | v8 = e13 | v8 = e12 | v8 = e10 | v8 = e11) & (v7 = e14 | v7 = e13 | v7 = e12 | v7 = e10 | v7 = e11) & (v6 = e14 | v6 = e13 | v6 = e12 | v6 = e10 | v6 = e11) & (v5 = e14 | v5 = e13 | v5 = e12 | v5 = e10 | v5 = e11) & (v4 = e24 | v4 = e23 | v4 = e22 | v4 = e20 | v4 = e21) & (v3 = e24 | v3 = e23 | v3 = e22 | v3 = e20 | v3 = e21) & (v2 = e24 | v2 = e23 | v2 = e22 | v2 = e20 | v2 = e21) & (v1 = e24 | v1 = e23 | v1 = e22 | v1 = e20 | v1 = e21) & (v0 = e24 | v0 = e23 | v0 = e22 | v0 = e20 | v0 = e21))
% 15.40/4.22 | 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 yields:
% 15.40/4.22 | (1) ~ (e24 = e23) & ~ (e24 = e22) & ~ (e24 = e20) & ~ (e24 = e21) & ~ (e24 = e14) & ~ (e24 = e13) & ~ (e24 = e12) & ~ (e24 = e10) & ~ (e24 = e11) & ~ (e23 = e22) & ~ (e23 = e20) & ~ (e23 = e21) & ~ (e23 = e14) & ~ (e23 = e13) & ~ (e23 = e12) & ~ (e23 = e10) & ~ (e23 = e11) & ~ (e22 = e20) & ~ (e22 = e21) & ~ (e22 = e14) & ~ (e22 = e13) & ~ (e22 = e12) & ~ (e22 = e10) & ~ (e22 = e11) & ~ (e20 = e21) & ~ (e20 = e14) & ~ (e20 = e13) & ~ (e20 = e12) & ~ (e20 = e10) & ~ (e20 = e11) & ~ (e21 = e14) & ~ (e21 = e13) & ~ (e21 = e12) & ~ (e21 = e10) & ~ (e21 = e11) & ~ (e14 = e13) & ~ (e14 = e12) & ~ (e14 = e10) & ~ (e14 = e11) & ~ (e13 = e12) & ~ (e13 = e10) & ~ (e13 = e11) & ~ (e12 = e10) & ~ (e12 = e11) & ~ (e10 = e11) & op2(all_0_5_5, all_0_5_5) = all_0_5_5 & op2(all_0_5_5, all_0_6_6) = all_0_9_9 & op2(all_0_5_5, all_0_7_7) = all_0_8_8 & op2(all_0_5_5, all_0_8_8) = all_0_7_7 & op2(all_0_5_5, all_0_9_9) = all_0_6_6 & op2(all_0_6_6, all_0_5_5) = all_0_8_8 & op2(all_0_6_6, all_0_6_6) = all_0_6_6 & op2(all_0_6_6, all_0_7_7) = all_0_9_9 & op2(all_0_6_6, all_0_8_8) = all_0_5_5 & op2(all_0_6_6, all_0_9_9) = all_0_7_7 & op2(all_0_7_7, all_0_5_5) = all_0_6_6 & op2(all_0_7_7, all_0_6_6) = all_0_5_5 & op2(all_0_7_7, all_0_7_7) = all_0_7_7 & op2(all_0_7_7, all_0_8_8) = all_0_9_9 & op2(all_0_7_7, all_0_9_9) = all_0_8_8 & op2(all_0_8_8, all_0_5_5) = all_0_9_9 & op2(all_0_8_8, all_0_6_6) = all_0_7_7 & op2(all_0_8_8, all_0_7_7) = all_0_6_6 & op2(all_0_8_8, all_0_8_8) = all_0_8_8 & op2(all_0_8_8, all_0_9_9) = all_0_5_5 & op2(all_0_9_9, all_0_5_5) = all_0_7_7 & op2(all_0_9_9, all_0_6_6) = all_0_8_8 & op2(all_0_9_9, all_0_7_7) = all_0_5_5 & op2(all_0_9_9, all_0_8_8) = all_0_6_6 & op2(all_0_9_9, all_0_9_9) = all_0_9_9 & op2(e24, e24) = e24 & op2(e24, e23) = e21 & op2(e24, e22) = e20 & op2(e24, e20) = e23 & op2(e24, e21) = e22 & op2(e23, e24) = e22 & op2(e23, e23) = e23 & op2(e23, e22) = e21 & op2(e23, e20) = e24 & op2(e23, e21) = e20 & op2(e22, e24) = e23 & op2(e22, e23) = e20 & op2(e22, e22) = e22 & op2(e22, e20) = e21 & op2(e22, e21) = e24 & op2(e20, e24) = e21 & op2(e20, e23) = e22 & op2(e20, e22) = e24 & op2(e20, e20) = e20 & op2(e20, e21) = e23 & op2(e21, e24) = e20 & op2(e21, e23) = e24 & op2(e21, e22) = e23 & op2(e21, e20) = e22 & op2(e21, e21) = e21 & op1(all_0_0_0, all_0_0_0) = all_0_0_0 & op1(all_0_0_0, all_0_1_1) = all_0_3_3 & op1(all_0_0_0, all_0_2_2) = all_0_4_4 & op1(all_0_0_0, all_0_3_3) = all_0_2_2 & op1(all_0_0_0, all_0_4_4) = all_0_1_1 & op1(all_0_1_1, all_0_0_0) = all_0_2_2 & op1(all_0_1_1, all_0_1_1) = all_0_1_1 & op1(all_0_1_1, all_0_2_2) = all_0_3_3 & op1(all_0_1_1, all_0_3_3) = all_0_4_4 & op1(all_0_1_1, all_0_4_4) = all_0_0_0 & op1(all_0_2_2, all_0_0_0) = all_0_1_1 & op1(all_0_2_2, all_0_1_1) = all_0_4_4 & op1(all_0_2_2, all_0_2_2) = all_0_2_2 & op1(all_0_2_2, all_0_3_3) = all_0_0_0 & op1(all_0_2_2, all_0_4_4) = all_0_3_3 & op1(all_0_3_3, all_0_0_0) = all_0_4_4 & op1(all_0_3_3, all_0_1_1) = all_0_0_0 & op1(all_0_3_3, all_0_2_2) = all_0_1_1 & op1(all_0_3_3, all_0_3_3) = all_0_3_3 & op1(all_0_3_3, all_0_4_4) = all_0_2_2 & op1(all_0_4_4, all_0_0_0) = all_0_3_3 & op1(all_0_4_4, all_0_1_1) = all_0_2_2 & op1(all_0_4_4, all_0_2_2) = all_0_0_0 & op1(all_0_4_4, all_0_3_3) = all_0_1_1 & op1(all_0_4_4, all_0_4_4) = all_0_4_4 & op1(e14, e14) = e14 & op1(e14, e13) = e10 & op1(e14, e12) = e11 & op1(e14, e10) = e13 & op1(e14, e11) = e12 & op1(e13, e14) = e11 & op1(e13, e13) = e13 & op1(e13, e12) = e10 & op1(e13, e10) = e12 & op1(e13, e11) = e14 & op1(e12, e14) = e13 & op1(e12, e13) = e14 & op1(e12, e12) = e12 & op1(e12, e10) = e11 & op1(e12, e11) = e10 & op1(e10, e14) = e12 & op1(e10, e13) = e11 & op1(e10, e12) = e14 & op1(e10, e10) = e10 & op1(e10, e11) = e13 & op1(e11, e14) = e10 & op1(e11, e13) = e12 & op1(e11, e12) = e13 & op1(e11, e10) = e14 & op1(e11, e11) = e11 & h(all_0_0_0) = e24 & h(all_0_1_1) = e23 & h(all_0_2_2) = e22 & h(all_0_3_3) = e21 & h(all_0_4_4) = e20 & h(e14) = all_0_5_5 & h(e13) = all_0_6_6 & h(e12) = all_0_7_7 & h(e10) = all_0_9_9 & h(e11) = all_0_8_8 & j(all_0_5_5) = e14 & j(all_0_6_6) = e13 & j(all_0_7_7) = e12 & j(all_0_8_8) = e11 & j(all_0_9_9) = e10 & j(e24) = all_0_0_0 & j(e23) = all_0_1_1 & j(e22) = all_0_2_2 & j(e20) = all_0_4_4 & j(e21) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0)) & (all_0_0_0 = e14 | all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11) & (all_0_1_1 = e14 | all_0_1_1 = e13 | all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11) & (all_0_2_2 = e14 | all_0_2_2 = e13 | all_0_2_2 = e12 | all_0_2_2 = e10 | all_0_2_2 = e11) & (all_0_3_3 = e14 | all_0_3_3 = e13 | all_0_3_3 = e12 | all_0_3_3 = e10 | all_0_3_3 = e11) & (all_0_4_4 = e14 | all_0_4_4 = e13 | all_0_4_4 = e12 | all_0_4_4 = e10 | all_0_4_4 = e11) & (all_0_5_5 = e24 | all_0_5_5 = e23 | all_0_5_5 = e22 | all_0_5_5 = e20 | all_0_5_5 = e21) & (all_0_6_6 = e24 | all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21) & (all_0_7_7 = e24 | all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21) & (all_0_8_8 = e24 | all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21) & (all_0_9_9 = e24 | all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21)
% 15.73/4.24 |
% 15.73/4.24 | Applying alpha-rule on (1) yields:
% 15.73/4.24 | (2) ~ (e21 = e12)
% 15.73/4.24 | (3) op2(e20, e22) = e24
% 15.73/4.24 | (4) op1(e13, e14) = e11
% 15.73/4.24 | (5) op2(all_0_7_7, all_0_8_8) = all_0_9_9
% 15.73/4.24 | (6) op2(e21, e21) = e21
% 15.73/4.24 | (7) ~ (e20 = e21)
% 15.73/4.24 | (8) ~ (e20 = e14)
% 15.73/4.24 | (9) op1(e11, e11) = e11
% 15.73/4.24 | (10) op2(all_0_5_5, all_0_9_9) = all_0_6_6
% 15.73/4.24 | (11) op2(e24, e20) = e23
% 15.73/4.24 | (12) ~ (e24 = e11)
% 15.73/4.24 | (13) op2(all_0_9_9, all_0_6_6) = all_0_8_8
% 15.73/4.24 | (14) ~ (e12 = e11)
% 15.73/4.24 | (15) op2(all_0_6_6, all_0_7_7) = all_0_9_9
% 15.73/4.24 | (16) h(e12) = all_0_7_7
% 15.73/4.24 | (17) op2(all_0_7_7, all_0_7_7) = all_0_7_7
% 15.73/4.24 | (18) h(all_0_0_0) = e24
% 15.73/4.24 | (19) h(e13) = all_0_6_6
% 15.73/4.24 | (20) ~ (e14 = e12)
% 15.73/4.24 | (21) ~ (e24 = e12)
% 15.73/4.24 | (22) op1(e12, e14) = e13
% 15.73/4.24 | (23) op1(all_0_0_0, all_0_4_4) = all_0_1_1
% 15.73/4.24 | (24) j(e22) = all_0_2_2
% 15.73/4.24 | (25) op2(e20, e23) = e22
% 15.73/4.24 | (26) j(e21) = all_0_3_3
% 15.73/4.24 | (27) op1(all_0_1_1, all_0_2_2) = all_0_3_3
% 15.73/4.24 | (28) j(all_0_8_8) = e11
% 15.73/4.24 | (29) ~ (e22 = e13)
% 15.73/4.24 | (30) op2(all_0_8_8, all_0_7_7) = all_0_6_6
% 15.73/4.24 | (31) op1(e13, e11) = e14
% 15.73/4.24 | (32) op2(all_0_8_8, all_0_6_6) = all_0_7_7
% 15.73/4.24 | (33) op2(e24, e21) = e22
% 15.73/4.24 | (34) op1(e11, e12) = e13
% 15.73/4.24 | (35) op2(all_0_6_6, all_0_9_9) = all_0_7_7
% 15.73/4.24 | (36) j(all_0_6_6) = e13
% 15.73/4.24 | (37) op2(e23, e23) = e23
% 15.73/4.24 | (38) op2(all_0_5_5, all_0_7_7) = all_0_8_8
% 15.73/4.24 | (39) op2(e20, e21) = e23
% 15.73/4.24 | (40) op2(e23, e20) = e24
% 15.73/4.25 | (41) h(all_0_4_4) = e20
% 15.73/4.25 | (42) op1(all_0_2_2, all_0_0_0) = all_0_1_1
% 15.73/4.25 | (43) op2(all_0_5_5, all_0_5_5) = all_0_5_5
% 15.73/4.25 | (44) op2(e22, e20) = e21
% 15.73/4.25 | (45) op1(e10, e14) = e12
% 15.73/4.25 | (46) op1(all_0_2_2, all_0_2_2) = all_0_2_2
% 15.73/4.25 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0))
% 15.73/4.25 | (48) op2(e21, e22) = e23
% 15.73/4.25 | (49) ~ (e23 = e13)
% 15.73/4.25 | (50) op2(e24, e22) = e20
% 15.73/4.25 | (51) all_0_5_5 = e24 | all_0_5_5 = e23 | all_0_5_5 = e22 | all_0_5_5 = e20 | all_0_5_5 = e21
% 15.73/4.25 | (52) op2(e23, e22) = e21
% 15.73/4.25 | (53) ~ (e23 = e12)
% 15.73/4.25 | (54) ~ (e24 = e14)
% 15.73/4.25 | (55) h(all_0_3_3) = e21
% 15.73/4.25 | (56) ~ (e23 = e21)
% 15.73/4.25 | (57) all_0_1_1 = e14 | all_0_1_1 = e13 | all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11
% 15.73/4.25 | (58) op1(e11, e10) = e14
% 15.73/4.25 | (59) ~ (e22 = e21)
% 15.73/4.25 | (60) ~ (e20 = e11)
% 15.73/4.25 | (61) j(all_0_9_9) = e10
% 15.73/4.25 | (62) op2(e24, e24) = e24
% 15.73/4.25 | (63) ~ (e14 = e10)
% 15.73/4.25 | (64) ~ (e22 = e10)
% 15.73/4.25 | (65) op1(e14, e12) = e11
% 15.73/4.25 | (66) h(all_0_1_1) = e23
% 15.73/4.25 | (67) op2(all_0_9_9, all_0_9_9) = all_0_9_9
% 15.73/4.25 | (68) op1(e10, e12) = e14
% 15.73/4.25 | (69) ~ (e12 = e10)
% 15.73/4.25 | (70) ~ (e24 = e22)
% 15.73/4.25 | (71) op2(all_0_9_9, all_0_7_7) = all_0_5_5
% 15.73/4.25 | (72) op2(e21, e24) = e20
% 15.73/4.25 | (73) op1(all_0_3_3, all_0_0_0) = all_0_4_4
% 15.73/4.25 | (74) all_0_9_9 = e24 | all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21
% 15.73/4.25 | (75) op2(e22, e21) = e24
% 15.73/4.25 | (76) op2(all_0_8_8, all_0_8_8) = all_0_8_8
% 15.73/4.25 | (77) op2(e20, e20) = e20
% 15.73/4.25 | (78) op2(e21, e20) = e22
% 15.73/4.25 | (79) all_0_2_2 = e14 | all_0_2_2 = e13 | all_0_2_2 = e12 | all_0_2_2 = e10 | all_0_2_2 = e11
% 15.73/4.25 | (80) op2(all_0_5_5, all_0_8_8) = all_0_7_7
% 15.73/4.25 | (81) op1(all_0_1_1, all_0_0_0) = all_0_2_2
% 15.73/4.25 | (82) j(all_0_7_7) = e12
% 15.73/4.25 | (83) op1(all_0_4_4, all_0_3_3) = all_0_1_1
% 15.73/4.25 | (84) op2(all_0_7_7, all_0_5_5) = all_0_6_6
% 15.73/4.25 | (85) h(all_0_2_2) = e22
% 15.73/4.25 | (86) op1(e12, e13) = e14
% 15.73/4.25 | (87) op2(e20, e24) = e21
% 15.73/4.25 | (88) ~ (e14 = e13)
% 15.73/4.25 | (89) ~ (e21 = e11)
% 15.73/4.25 | (90) h(e14) = all_0_5_5
% 15.73/4.25 | (91) ~ (e24 = e20)
% 15.73/4.25 | (92) op2(all_0_8_8, all_0_5_5) = all_0_9_9
% 15.73/4.25 | (93) op1(all_0_4_4, all_0_0_0) = all_0_3_3
% 15.73/4.25 | (94) ~ (e13 = e12)
% 15.73/4.25 | (95) all_0_7_7 = e24 | all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 15.73/4.25 | (96) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0))
% 15.73/4.25 | (97) op1(all_0_2_2, all_0_4_4) = all_0_3_3
% 15.73/4.25 | (98) ~ (e14 = e11)
% 15.73/4.26 | (99) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0))
% 15.73/4.26 | (100) op1(all_0_3_3, all_0_3_3) = all_0_3_3
% 15.73/4.26 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0))
% 15.73/4.26 | (102) all_0_4_4 = e14 | all_0_4_4 = e13 | all_0_4_4 = e12 | all_0_4_4 = e10 | all_0_4_4 = e11
% 15.73/4.26 | (103) op1(e14, e10) = e13
% 15.73/4.26 | (104) op2(all_0_6_6, all_0_6_6) = all_0_6_6
% 15.73/4.26 | (105) op1(all_0_3_3, all_0_4_4) = all_0_2_2
% 15.73/4.26 | (106) op1(e10, e10) = e10
% 15.73/4.26 | (107) ~ (e23 = e10)
% 15.73/4.26 | (108) op1(all_0_4_4, all_0_4_4) = all_0_4_4
% 15.73/4.26 | (109) op1(all_0_1_1, all_0_3_3) = all_0_4_4
% 15.73/4.26 | (110) ~ (e13 = e10)
% 15.73/4.26 | (111) op1(all_0_1_1, all_0_1_1) = all_0_1_1
% 15.73/4.26 | (112) all_0_6_6 = e24 | all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21
% 15.73/4.26 | (113) all_0_0_0 = e14 | all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 15.73/4.26 | (114) ~ (e23 = e22)
% 15.73/4.26 | (115) op2(e22, e22) = e22
% 15.73/4.26 | (116) op2(all_0_5_5, all_0_6_6) = all_0_9_9
% 15.73/4.26 | (117) ~ (e20 = e10)
% 15.73/4.26 | (118) ~ (e22 = e11)
% 15.73/4.26 | (119) op2(e22, e23) = e20
% 15.73/4.26 | (120) op2(all_0_8_8, all_0_9_9) = all_0_5_5
% 15.73/4.26 | (121) ~ (e20 = e12)
% 15.73/4.26 | (122) op1(all_0_0_0, all_0_2_2) = all_0_4_4
% 15.73/4.26 | (123) op1(e14, e14) = e14
% 15.73/4.26 | (124) op1(all_0_4_4, all_0_1_1) = all_0_2_2
% 15.73/4.26 | (125) op2(all_0_6_6, all_0_8_8) = all_0_5_5
% 15.73/4.26 | (126) op1(e10, e11) = e13
% 15.73/4.26 | (127) op1(e13, e10) = e12
% 15.73/4.26 | (128) all_0_8_8 = e24 | all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 15.73/4.26 | (129) ~ (e10 = e11)
% 15.73/4.26 | (130) op1(all_0_3_3, all_0_2_2) = all_0_1_1
% 15.73/4.26 | (131) ~ (e23 = e14)
% 15.73/4.26 | (132) h(e11) = all_0_8_8
% 15.73/4.26 | (133) op1(e10, e13) = e11
% 15.73/4.26 | (134) op1(all_0_0_0, all_0_0_0) = all_0_0_0
% 15.73/4.26 | (135) op2(e23, e24) = e22
% 15.73/4.26 | (136) j(e23) = all_0_1_1
% 15.73/4.26 | (137) ~ (e23 = e20)
% 15.73/4.26 | (138) ~ (e21 = e14)
% 15.73/4.26 | (139) op1(e12, e12) = e12
% 15.73/4.26 | (140) op1(e11, e14) = e10
% 15.73/4.26 | (141) j(e24) = all_0_0_0
% 15.73/4.26 | (142) op2(all_0_7_7, all_0_6_6) = all_0_5_5
% 15.73/4.26 | (143) op1(e12, e11) = e10
% 15.73/4.26 | (144) op1(all_0_3_3, all_0_1_1) = all_0_0_0
% 15.73/4.26 | (145) op1(all_0_2_2, all_0_1_1) = all_0_4_4
% 15.73/4.26 | (146) ~ (e24 = e21)
% 15.73/4.26 | (147) op1(all_0_0_0, all_0_3_3) = all_0_2_2
% 15.73/4.26 | (148) op2(e23, e21) = e20
% 15.73/4.26 | (149) j(all_0_5_5) = e14
% 15.73/4.26 | (150) op1(e14, e11) = e12
% 15.73/4.26 | (151) op1(all_0_1_1, all_0_4_4) = all_0_0_0
% 15.73/4.26 | (152) op1(e13, e13) = e13
% 15.73/4.26 | (153) ~ (e22 = e20)
% 15.73/4.26 | (154) ~ (e23 = e11)
% 15.73/4.26 | (155) op2(e21, e23) = e24
% 15.73/4.26 | (156) op2(all_0_9_9, all_0_5_5) = all_0_7_7
% 15.73/4.26 | (157) op1(all_0_2_2, all_0_3_3) = all_0_0_0
% 15.73/4.27 | (158) ~ (e24 = e10)
% 15.73/4.27 | (159) ~ (e24 = e23)
% 15.73/4.27 | (160) op1(e11, e13) = e12
% 15.73/4.27 | (161) ~ (e20 = e13)
% 15.73/4.27 | (162) ~ (e24 = e13)
% 15.73/4.27 | (163) op2(all_0_7_7, all_0_9_9) = all_0_8_8
% 15.88/4.27 | (164) ~ (e21 = e10)
% 15.88/4.27 | (165) ~ (e21 = e13)
% 15.88/4.27 | (166) j(e20) = all_0_4_4
% 15.88/4.27 | (167) ~ (e22 = e12)
% 15.88/4.27 | (168) op1(all_0_0_0, all_0_1_1) = all_0_3_3
% 15.88/4.27 | (169) op1(e13, e12) = e10
% 15.88/4.27 | (170) all_0_3_3 = e14 | all_0_3_3 = e13 | all_0_3_3 = e12 | all_0_3_3 = e10 | all_0_3_3 = e11
% 15.88/4.27 | (171) op2(e22, e24) = e23
% 15.88/4.27 | (172) op2(all_0_6_6, all_0_5_5) = all_0_8_8
% 15.88/4.27 | (173) op1(e12, e10) = e11
% 15.88/4.27 | (174) op1(e14, e13) = e10
% 15.88/4.27 | (175) h(e10) = all_0_9_9
% 15.88/4.27 | (176) ~ (e22 = e14)
% 15.88/4.27 | (177) op2(e24, e23) = e21
% 15.88/4.27 | (178) op1(all_0_4_4, all_0_2_2) = all_0_0_0
% 15.88/4.27 | (179) ~ (e13 = e11)
% 15.88/4.27 | (180) op2(all_0_9_9, all_0_8_8) = all_0_6_6
% 15.88/4.27 |
% 15.88/4.27 +-Applying beta-rule and splitting (113), into two cases.
% 15.88/4.27 |-Branch one:
% 15.88/4.27 | (181) all_0_0_0 = e14
% 15.88/4.27 |
% 15.88/4.27 | From (181) and (168) follows:
% 15.88/4.27 | (182) op1(e14, all_0_1_1) = all_0_3_3
% 15.88/4.27 |
% 15.88/4.27 | From (181) and (147) follows:
% 15.88/4.27 | (183) op1(e14, all_0_3_3) = all_0_2_2
% 15.88/4.27 |
% 15.88/4.27 | From (181) and (81) follows:
% 15.88/4.27 | (184) op1(all_0_1_1, e14) = all_0_2_2
% 15.88/4.27 |
% 15.88/4.27 | From (181) and (42) follows:
% 15.88/4.27 | (185) op1(all_0_2_2, e14) = all_0_1_1
% 15.88/4.27 |
% 15.88/4.27 | From (181) and (18) follows:
% 15.88/4.27 | (186) h(e14) = e24
% 15.88/4.27 |
% 15.88/4.27 | Instantiating formula (96) with e14, e24, all_0_5_5 and discharging atoms h(e14) = all_0_5_5, h(e14) = e24, yields:
% 15.88/4.27 | (187) all_0_5_5 = e24
% 15.88/4.27 |
% 15.88/4.27 | From (187) and (116) follows:
% 15.88/4.27 | (188) op2(e24, all_0_6_6) = all_0_9_9
% 15.88/4.27 |
% 15.88/4.27 | From (187) and (38) follows:
% 15.88/4.27 | (189) op2(e24, all_0_7_7) = all_0_8_8
% 15.88/4.27 |
% 15.88/4.27 | From (187) and (80) follows:
% 15.88/4.27 | (190) op2(e24, all_0_8_8) = all_0_7_7
% 15.88/4.27 |
% 15.88/4.27 | From (187) and (10) follows:
% 15.88/4.27 | (191) op2(e24, all_0_9_9) = all_0_6_6
% 15.88/4.27 |
% 15.88/4.27 | From (187) and (172) follows:
% 15.88/4.27 | (192) op2(all_0_6_6, e24) = all_0_8_8
% 15.88/4.27 |
% 15.88/4.27 | From (187) and (84) follows:
% 15.88/4.27 | (193) op2(all_0_7_7, e24) = all_0_6_6
% 15.88/4.27 |
% 15.88/4.27 | From (187) and (92) follows:
% 15.88/4.27 | (194) op2(all_0_8_8, e24) = all_0_9_9
% 15.88/4.27 |
% 15.88/4.27 | From (187) and (156) follows:
% 15.88/4.27 | (195) op2(all_0_9_9, e24) = all_0_7_7
% 15.88/4.27 |
% 15.88/4.27 | From (187) and (90) follows:
% 15.88/4.27 | (186) h(e14) = e24
% 15.88/4.27 |
% 15.88/4.27 | From (187) and (149) follows:
% 15.88/4.27 | (197) j(e24) = e14
% 15.88/4.27 |
% 15.88/4.27 +-Applying beta-rule and splitting (57), into two cases.
% 15.88/4.27 |-Branch one:
% 15.88/4.27 | (198) all_0_1_1 = e14
% 15.88/4.27 |
% 15.88/4.27 | From (198) and (66) follows:
% 15.88/4.27 | (199) h(e14) = e23
% 15.88/4.27 |
% 15.88/4.27 | Instantiating formula (96) with e14, e23, e24 and discharging atoms h(e14) = e24, h(e14) = e23, yields:
% 15.88/4.28 | (200) e24 = e23
% 15.88/4.28 |
% 15.88/4.28 | Equations (200) can reduce 159 to:
% 15.88/4.28 | (201) $false
% 15.88/4.28 |
% 15.88/4.28 |-The branch is then unsatisfiable
% 15.88/4.28 |-Branch two:
% 15.88/4.28 | (202) ~ (all_0_1_1 = e14)
% 15.88/4.28 | (203) all_0_1_1 = e13 | all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11
% 15.88/4.28 |
% 15.88/4.28 +-Applying beta-rule and splitting (74), into two cases.
% 15.88/4.28 |-Branch one:
% 15.88/4.28 | (204) all_0_9_9 = e24
% 15.88/4.28 |
% 15.88/4.28 | From (204) and (61) follows:
% 15.88/4.28 | (205) j(e24) = e10
% 15.88/4.28 |
% 15.88/4.28 | Instantiating formula (99) with e24, e10, e14 and discharging atoms j(e24) = e14, j(e24) = e10, yields:
% 15.88/4.28 | (206) e14 = e10
% 15.88/4.28 |
% 15.88/4.28 | Equations (206) can reduce 63 to:
% 15.88/4.28 | (201) $false
% 15.88/4.28 |
% 15.88/4.28 |-The branch is then unsatisfiable
% 15.88/4.28 |-Branch two:
% 15.88/4.28 | (208) ~ (all_0_9_9 = e24)
% 15.88/4.28 | (209) all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21
% 15.88/4.28 |
% 15.88/4.28 +-Applying beta-rule and splitting (128), into two cases.
% 15.88/4.28 |-Branch one:
% 15.88/4.28 | (210) all_0_8_8 = e24
% 15.88/4.28 |
% 15.88/4.28 | From (210) and (28) follows:
% 15.88/4.28 | (211) j(e24) = e11
% 15.88/4.28 |
% 15.88/4.28 | Instantiating formula (99) with e24, e11, e14 and discharging atoms j(e24) = e14, j(e24) = e11, yields:
% 15.88/4.28 | (212) e14 = e11
% 15.88/4.28 |
% 15.88/4.28 | Equations (212) can reduce 98 to:
% 15.88/4.28 | (201) $false
% 15.88/4.28 |
% 15.88/4.28 |-The branch is then unsatisfiable
% 15.88/4.28 |-Branch two:
% 15.88/4.28 | (214) ~ (all_0_8_8 = e24)
% 15.88/4.28 | (215) all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 15.88/4.28 |
% 15.88/4.28 +-Applying beta-rule and splitting (95), into two cases.
% 15.88/4.28 |-Branch one:
% 15.88/4.28 | (216) all_0_7_7 = e24
% 15.88/4.28 |
% 15.88/4.28 | From (216) and (82) follows:
% 15.88/4.28 | (217) j(e24) = e12
% 15.88/4.28 |
% 15.88/4.28 | Instantiating formula (99) with e24, e12, e14 and discharging atoms j(e24) = e14, j(e24) = e12, yields:
% 15.88/4.28 | (218) e14 = e12
% 15.88/4.28 |
% 15.88/4.28 | Equations (218) can reduce 20 to:
% 15.88/4.28 | (201) $false
% 15.88/4.28 |
% 15.88/4.28 |-The branch is then unsatisfiable
% 15.88/4.28 |-Branch two:
% 15.88/4.28 | (220) ~ (all_0_7_7 = e24)
% 15.88/4.28 | (221) all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 15.88/4.28 |
% 15.88/4.28 +-Applying beta-rule and splitting (203), into two cases.
% 15.88/4.28 |-Branch one:
% 15.88/4.28 | (222) all_0_1_1 = e13
% 15.88/4.28 |
% 15.88/4.28 | From (222) and (184) follows:
% 15.88/4.28 | (223) op1(e13, e14) = all_0_2_2
% 15.88/4.28 |
% 15.88/4.28 | From (222) and (185) follows:
% 15.88/4.28 | (224) op1(all_0_2_2, e14) = e13
% 15.88/4.28 |
% 15.88/4.28 | From (222) and (182) follows:
% 15.88/4.28 | (225) op1(e14, e13) = all_0_3_3
% 15.88/4.28 |
% 15.88/4.28 | Instantiating formula (101) with e14, e13, all_0_3_3, e10 and discharging atoms op1(e14, e13) = all_0_3_3, op1(e14, e13) = e10, yields:
% 15.88/4.28 | (226) all_0_3_3 = e10
% 15.88/4.28 |
% 15.88/4.28 | Instantiating formula (101) with e13, e14, all_0_2_2, e11 and discharging atoms op1(e13, e14) = all_0_2_2, op1(e13, e14) = e11, yields:
% 15.88/4.28 | (227) all_0_2_2 = e11
% 15.88/4.28 |
% 15.88/4.28 | From (227) and (224) follows:
% 15.88/4.28 | (228) op1(e11, e14) = e13
% 15.88/4.28 |
% 15.88/4.28 | From (226)(227) and (183) follows:
% 15.88/4.28 | (229) op1(e14, e10) = e11
% 15.88/4.28 |
% 15.88/4.28 | Instantiating formula (101) with e14, e10, e11, e13 and discharging atoms op1(e14, e10) = e13, op1(e14, e10) = e11, yields:
% 15.88/4.28 | (230) e13 = e11
% 15.88/4.28 |
% 15.88/4.28 | Instantiating formula (101) with e11, e14, e13, e10 and discharging atoms op1(e11, e14) = e13, op1(e11, e14) = e10, yields:
% 15.88/4.28 | (231) e13 = e10
% 15.88/4.28 |
% 15.88/4.28 | Combining equations (230,231) yields a new equation:
% 15.88/4.28 | (232) e10 = e11
% 15.88/4.28 |
% 15.88/4.28 | Equations (232) can reduce 129 to:
% 15.88/4.28 | (201) $false
% 15.88/4.28 |
% 15.88/4.28 |-The branch is then unsatisfiable
% 15.88/4.28 |-Branch two:
% 15.88/4.28 | (234) ~ (all_0_1_1 = e13)
% 15.88/4.28 | (235) all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11
% 15.88/4.28 |
% 15.88/4.28 +-Applying beta-rule and splitting (209), into two cases.
% 15.88/4.28 |-Branch one:
% 15.88/4.28 | (236) all_0_9_9 = e23
% 15.88/4.28 |
% 15.88/4.28 | From (236) and (195) follows:
% 15.88/4.28 | (237) op2(e23, e24) = all_0_7_7
% 15.88/4.29 |
% 15.88/4.29 | From (236) and (188) follows:
% 15.88/4.29 | (238) op2(e24, all_0_6_6) = e23
% 15.88/4.29 |
% 15.88/4.29 | From (236) and (191) follows:
% 15.88/4.29 | (239) op2(e24, e23) = all_0_6_6
% 15.88/4.29 |
% 15.88/4.29 | Instantiating formula (47) with e24, e23, all_0_6_6, e21 and discharging atoms op2(e24, e23) = all_0_6_6, op2(e24, e23) = e21, yields:
% 15.88/4.29 | (240) all_0_6_6 = e21
% 15.88/4.29 |
% 15.88/4.29 | Instantiating formula (47) with e23, e24, all_0_7_7, e22 and discharging atoms op2(e23, e24) = all_0_7_7, op2(e23, e24) = e22, yields:
% 15.88/4.29 | (241) all_0_7_7 = e22
% 15.88/4.29 |
% 15.88/4.29 | From (241)(240) and (193) follows:
% 15.88/4.29 | (242) op2(e22, e24) = e21
% 15.88/4.29 |
% 15.88/4.29 | From (240) and (238) follows:
% 15.88/4.29 | (243) op2(e24, e21) = e23
% 15.88/4.29 |
% 15.88/4.29 | Instantiating formula (47) with e24, e21, e23, e22 and discharging atoms op2(e24, e21) = e23, op2(e24, e21) = e22, yields:
% 15.88/4.29 | (244) e23 = e22
% 15.88/4.29 |
% 15.88/4.29 | Instantiating formula (47) with e22, e24, e21, e23 and discharging atoms op2(e22, e24) = e23, op2(e22, e24) = e21, yields:
% 15.88/4.29 | (245) e23 = e21
% 15.88/4.29 |
% 15.88/4.29 | Combining equations (244,245) yields a new equation:
% 15.88/4.29 | (246) e22 = e21
% 15.88/4.29 |
% 15.88/4.29 | Simplifying 246 yields:
% 15.88/4.29 | (247) e22 = e21
% 15.88/4.29 |
% 15.88/4.29 | Equations (247) can reduce 59 to:
% 15.88/4.29 | (201) $false
% 15.88/4.29 |
% 15.88/4.29 |-The branch is then unsatisfiable
% 15.88/4.29 |-Branch two:
% 15.88/4.29 | (249) ~ (all_0_9_9 = e23)
% 15.88/4.29 | (250) all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21
% 15.88/4.29 |
% 15.88/4.29 +-Applying beta-rule and splitting (215), into two cases.
% 15.88/4.29 |-Branch one:
% 15.88/4.29 | (251) all_0_8_8 = e23
% 15.88/4.29 |
% 15.88/4.29 | From (251) and (194) follows:
% 15.88/4.29 | (252) op2(e23, e24) = all_0_9_9
% 15.88/4.29 |
% 15.88/4.29 | From (251) and (189) follows:
% 15.88/4.29 | (253) op2(e24, all_0_7_7) = e23
% 15.88/4.29 |
% 15.88/4.29 | From (251) and (190) follows:
% 15.88/4.29 | (254) op2(e24, e23) = all_0_7_7
% 15.88/4.29 |
% 15.88/4.29 | Instantiating formula (47) with e24, e23, all_0_7_7, e21 and discharging atoms op2(e24, e23) = all_0_7_7, op2(e24, e23) = e21, yields:
% 15.88/4.29 | (255) all_0_7_7 = e21
% 15.88/4.29 |
% 15.88/4.29 | Instantiating formula (47) with e23, e24, all_0_9_9, e22 and discharging atoms op2(e23, e24) = all_0_9_9, op2(e23, e24) = e22, yields:
% 15.88/4.29 | (256) all_0_9_9 = e22
% 15.88/4.29 |
% 15.88/4.29 | From (256)(255) and (195) follows:
% 15.88/4.29 | (242) op2(e22, e24) = e21
% 15.88/4.29 |
% 15.88/4.29 | From (255) and (253) follows:
% 15.88/4.29 | (243) op2(e24, e21) = e23
% 15.88/4.29 |
% 15.88/4.29 | Instantiating formula (47) with e24, e21, e23, e22 and discharging atoms op2(e24, e21) = e23, op2(e24, e21) = e22, yields:
% 15.88/4.29 | (244) e23 = e22
% 15.88/4.29 |
% 15.88/4.29 | Instantiating formula (47) with e22, e24, e21, e23 and discharging atoms op2(e22, e24) = e23, op2(e22, e24) = e21, yields:
% 15.88/4.29 | (245) e23 = e21
% 15.88/4.29 |
% 15.88/4.29 | Combining equations (244,245) yields a new equation:
% 15.88/4.29 | (246) e22 = e21
% 15.88/4.29 |
% 15.88/4.29 | Simplifying 246 yields:
% 15.88/4.29 | (247) e22 = e21
% 15.88/4.29 |
% 15.88/4.29 | Equations (247) can reduce 59 to:
% 15.88/4.29 | (201) $false
% 15.88/4.29 |
% 15.88/4.29 |-The branch is then unsatisfiable
% 15.88/4.29 |-Branch two:
% 15.88/4.29 | (264) ~ (all_0_8_8 = e23)
% 15.88/4.29 | (265) all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 15.88/4.29 |
% 15.88/4.29 +-Applying beta-rule and splitting (221), into two cases.
% 15.88/4.29 |-Branch one:
% 15.88/4.29 | (266) all_0_7_7 = e23
% 15.88/4.29 |
% 15.88/4.29 | From (266) and (193) follows:
% 15.88/4.29 | (267) op2(e23, e24) = all_0_6_6
% 15.88/4.29 |
% 15.88/4.29 | From (266) and (189) follows:
% 15.88/4.29 | (268) op2(e24, e23) = all_0_8_8
% 15.88/4.29 |
% 15.88/4.29 | From (266) and (190) follows:
% 15.88/4.29 | (269) op2(e24, all_0_8_8) = e23
% 15.88/4.29 |
% 15.88/4.29 | Instantiating formula (47) with e24, e23, all_0_8_8, e21 and discharging atoms op2(e24, e23) = all_0_8_8, op2(e24, e23) = e21, yields:
% 15.88/4.29 | (270) all_0_8_8 = e21
% 15.88/4.29 |
% 15.88/4.29 | Instantiating formula (47) with e23, e24, all_0_6_6, e22 and discharging atoms op2(e23, e24) = all_0_6_6, op2(e23, e24) = e22, yields:
% 15.88/4.29 | (271) all_0_6_6 = e22
% 15.88/4.29 |
% 15.88/4.29 | From (271)(270) and (192) follows:
% 15.88/4.30 | (242) op2(e22, e24) = e21
% 15.88/4.30 |
% 15.88/4.30 | From (270) and (269) follows:
% 15.88/4.30 | (243) op2(e24, e21) = e23
% 15.88/4.30 |
% 15.88/4.30 | Instantiating formula (47) with e24, e21, e23, e22 and discharging atoms op2(e24, e21) = e23, op2(e24, e21) = e22, yields:
% 15.88/4.30 | (244) e23 = e22
% 15.88/4.30 |
% 15.88/4.30 | Instantiating formula (47) with e22, e24, e21, e23 and discharging atoms op2(e22, e24) = e23, op2(e22, e24) = e21, yields:
% 15.88/4.30 | (245) e23 = e21
% 15.88/4.30 |
% 15.88/4.30 | Combining equations (245,244) yields a new equation:
% 15.88/4.30 | (247) e22 = e21
% 15.88/4.30 |
% 15.88/4.30 | Equations (247) can reduce 59 to:
% 15.88/4.30 | (201) $false
% 15.88/4.30 |
% 15.88/4.30 |-The branch is then unsatisfiable
% 15.88/4.30 |-Branch two:
% 15.88/4.30 | (278) ~ (all_0_7_7 = e23)
% 15.88/4.30 | (279) all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 15.88/4.30 |
% 15.88/4.30 +-Applying beta-rule and splitting (235), into two cases.
% 15.88/4.30 |-Branch one:
% 15.88/4.30 | (280) all_0_1_1 = e12
% 15.88/4.30 |
% 15.88/4.30 | From (280) and (66) follows:
% 15.88/4.30 | (281) h(e12) = e23
% 15.88/4.30 |
% 15.88/4.30 | Instantiating formula (96) with e12, e23, all_0_7_7 and discharging atoms h(e12) = all_0_7_7, h(e12) = e23, yields:
% 15.88/4.30 | (266) all_0_7_7 = e23
% 15.88/4.30 |
% 15.88/4.30 | Equations (266) can reduce 278 to:
% 15.88/4.30 | (201) $false
% 15.88/4.30 |
% 15.88/4.30 |-The branch is then unsatisfiable
% 15.88/4.30 |-Branch two:
% 15.88/4.30 | (284) ~ (all_0_1_1 = e12)
% 15.88/4.30 | (285) all_0_1_1 = e10 | all_0_1_1 = e11
% 15.88/4.30 |
% 15.88/4.30 +-Applying beta-rule and splitting (285), into two cases.
% 15.88/4.30 |-Branch one:
% 15.88/4.30 | (286) all_0_1_1 = e10
% 15.88/4.30 |
% 15.88/4.30 | From (286) and (66) follows:
% 15.88/4.30 | (287) h(e10) = e23
% 15.88/4.30 |
% 15.88/4.30 | Instantiating formula (96) with e10, e23, all_0_9_9 and discharging atoms h(e10) = all_0_9_9, h(e10) = e23, yields:
% 15.88/4.30 | (236) all_0_9_9 = e23
% 15.88/4.30 |
% 15.88/4.30 | Equations (236) can reduce 249 to:
% 15.88/4.30 | (201) $false
% 15.88/4.30 |
% 15.88/4.30 |-The branch is then unsatisfiable
% 15.88/4.30 |-Branch two:
% 15.88/4.30 | (290) ~ (all_0_1_1 = e10)
% 15.88/4.30 | (291) all_0_1_1 = e11
% 15.88/4.30 |
% 15.88/4.30 | From (291) and (66) follows:
% 15.88/4.30 | (292) h(e11) = e23
% 15.88/4.30 |
% 15.88/4.30 | Instantiating formula (96) with e11, e23, all_0_8_8 and discharging atoms h(e11) = all_0_8_8, h(e11) = e23, yields:
% 15.88/4.30 | (251) all_0_8_8 = e23
% 15.88/4.30 |
% 15.88/4.30 | Equations (251) can reduce 264 to:
% 15.88/4.30 | (201) $false
% 15.88/4.30 |
% 15.88/4.30 |-The branch is then unsatisfiable
% 15.88/4.30 |-Branch two:
% 15.88/4.30 | (295) ~ (all_0_0_0 = e14)
% 15.88/4.30 | (296) all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 15.88/4.30 |
% 15.88/4.30 +-Applying beta-rule and splitting (74), into two cases.
% 15.88/4.30 |-Branch one:
% 15.88/4.30 | (204) all_0_9_9 = e24
% 15.88/4.30 |
% 15.88/4.30 | From (204) and (10) follows:
% 15.88/4.30 | (298) op2(all_0_5_5, e24) = all_0_6_6
% 15.88/4.30 |
% 15.88/4.30 | From (204) and (163) follows:
% 15.88/4.30 | (299) op2(all_0_7_7, e24) = all_0_8_8
% 15.88/4.30 |
% 15.88/4.30 | From (204) and (120) follows:
% 15.88/4.30 | (300) op2(all_0_8_8, e24) = all_0_5_5
% 15.88/4.30 |
% 15.88/4.30 | From (204) and (156) follows:
% 15.88/4.30 | (301) op2(e24, all_0_5_5) = all_0_7_7
% 15.88/4.30 |
% 15.88/4.30 | From (204) and (13) follows:
% 15.88/4.30 | (302) op2(e24, all_0_6_6) = all_0_8_8
% 15.88/4.30 |
% 15.88/4.30 | From (204) and (71) follows:
% 15.88/4.30 | (303) op2(e24, all_0_7_7) = all_0_5_5
% 15.88/4.30 |
% 15.88/4.30 | From (204) and (180) follows:
% 15.88/4.30 | (304) op2(e24, all_0_8_8) = all_0_6_6
% 15.88/4.30 |
% 15.88/4.30 | From (204) and (61) follows:
% 15.88/4.30 | (205) j(e24) = e10
% 15.88/4.30 |
% 15.88/4.30 | Instantiating formula (99) with e24, e10, all_0_0_0 and discharging atoms j(e24) = all_0_0_0, j(e24) = e10, yields:
% 15.88/4.30 | (306) all_0_0_0 = e10
% 15.88/4.31 |
% 15.88/4.31 | Equations (306) can reduce 295 to:
% 15.88/4.31 | (307) ~ (e14 = e10)
% 15.88/4.31 |
% 15.88/4.31 | Simplifying 307 yields:
% 15.88/4.31 | (63) ~ (e14 = e10)
% 15.88/4.31 |
% 15.88/4.31 | From (306) and (168) follows:
% 15.88/4.31 | (309) op1(e10, all_0_1_1) = all_0_3_3
% 15.88/4.31 |
% 15.88/4.31 | From (306) and (147) follows:
% 15.88/4.31 | (310) op1(e10, all_0_3_3) = all_0_2_2
% 15.88/4.31 |
% 15.88/4.31 | From (306) and (81) follows:
% 15.88/4.31 | (311) op1(all_0_1_1, e10) = all_0_2_2
% 15.88/4.31 |
% 15.88/4.31 | From (306) and (42) follows:
% 15.88/4.31 | (312) op1(all_0_2_2, e10) = all_0_1_1
% 15.88/4.31 |
% 15.88/4.31 | From (306) and (144) follows:
% 15.88/4.31 | (313) op1(all_0_3_3, all_0_1_1) = e10
% 15.88/4.31 |
% 15.88/4.31 | From (306) and (141) follows:
% 15.88/4.31 | (205) j(e24) = e10
% 15.88/4.31 |
% 15.88/4.31 +-Applying beta-rule and splitting (95), into two cases.
% 15.88/4.31 |-Branch one:
% 15.88/4.31 | (216) all_0_7_7 = e24
% 15.88/4.31 |
% 15.88/4.31 | From (216) and (82) follows:
% 15.88/4.31 | (217) j(e24) = e12
% 15.88/4.31 |
% 15.88/4.31 | Instantiating formula (99) with e24, e12, e10 and discharging atoms j(e24) = e12, j(e24) = e10, yields:
% 15.88/4.31 | (317) e12 = e10
% 15.88/4.31 |
% 15.88/4.31 | Equations (317) can reduce 69 to:
% 15.88/4.31 | (201) $false
% 15.88/4.31 |
% 15.88/4.31 |-The branch is then unsatisfiable
% 15.88/4.31 |-Branch two:
% 15.88/4.31 | (220) ~ (all_0_7_7 = e24)
% 15.88/4.31 | (221) all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 15.88/4.31 |
% 15.88/4.31 +-Applying beta-rule and splitting (57), into two cases.
% 15.88/4.31 |-Branch one:
% 15.88/4.31 | (198) all_0_1_1 = e14
% 15.88/4.31 |
% 15.88/4.31 | From (198) and (311) follows:
% 15.88/4.31 | (322) op1(e14, e10) = all_0_2_2
% 15.88/4.31 |
% 15.88/4.31 | From (198) and (312) follows:
% 15.88/4.31 | (323) op1(all_0_2_2, e10) = e14
% 15.88/4.31 |
% 15.88/4.31 | From (198) and (313) follows:
% 15.88/4.31 | (324) op1(all_0_3_3, e14) = e10
% 15.88/4.31 |
% 15.88/4.31 | From (198) and (309) follows:
% 15.88/4.31 | (325) op1(e10, e14) = all_0_3_3
% 15.88/4.31 |
% 15.88/4.31 | Instantiating formula (101) with e14, e10, all_0_2_2, e13 and discharging atoms op1(e14, e10) = all_0_2_2, op1(e14, e10) = e13, yields:
% 15.88/4.31 | (326) all_0_2_2 = e13
% 15.88/4.31 |
% 15.88/4.31 | Instantiating formula (101) with e10, e14, all_0_3_3, e12 and discharging atoms op1(e10, e14) = all_0_3_3, op1(e10, e14) = e12, yields:
% 15.88/4.31 | (327) all_0_3_3 = e12
% 15.88/4.31 |
% 15.88/4.31 | From (326) and (323) follows:
% 15.88/4.31 | (328) op1(e13, e10) = e14
% 15.88/4.31 |
% 15.88/4.31 | From (327) and (324) follows:
% 15.88/4.31 | (329) op1(e12, e14) = e10
% 15.88/4.31 |
% 15.88/4.31 | From (327)(326) and (310) follows:
% 15.88/4.31 | (330) op1(e10, e12) = e13
% 15.88/4.31 |
% 15.88/4.31 | Instantiating formula (101) with e13, e10, e14, e12 and discharging atoms op1(e13, e10) = e14, op1(e13, e10) = e12, yields:
% 15.88/4.31 | (218) e14 = e12
% 15.88/4.31 |
% 15.88/4.31 | Instantiating formula (101) with e12, e14, e10, e13 and discharging atoms op1(e12, e14) = e13, op1(e12, e14) = e10, yields:
% 15.88/4.31 | (231) e13 = e10
% 15.88/4.31 |
% 15.88/4.31 | Instantiating formula (101) with e10, e12, e13, e14 and discharging atoms op1(e10, e12) = e14, op1(e10, e12) = e13, yields:
% 15.88/4.31 | (333) e14 = e13
% 15.88/4.31 |
% 15.88/4.31 | Combining equations (333,218) yields a new equation:
% 15.88/4.31 | (334) e13 = e12
% 15.88/4.31 |
% 15.88/4.31 | Simplifying 334 yields:
% 15.88/4.31 | (335) e13 = e12
% 15.88/4.31 |
% 15.88/4.31 | Combining equations (335,231) yields a new equation:
% 15.88/4.31 | (336) e12 = e10
% 15.88/4.31 |
% 15.88/4.31 | Simplifying 336 yields:
% 15.88/4.31 | (317) e12 = e10
% 15.88/4.31 |
% 15.88/4.31 | Equations (317) can reduce 69 to:
% 15.88/4.31 | (201) $false
% 15.88/4.31 |
% 15.88/4.31 |-The branch is then unsatisfiable
% 15.88/4.31 |-Branch two:
% 15.88/4.31 | (202) ~ (all_0_1_1 = e14)
% 15.88/4.31 | (203) all_0_1_1 = e13 | all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11
% 15.88/4.31 |
% 15.88/4.31 +-Applying beta-rule and splitting (128), into two cases.
% 15.88/4.31 |-Branch one:
% 15.88/4.31 | (210) all_0_8_8 = e24
% 15.88/4.32 |
% 15.88/4.32 | From (210) and (28) follows:
% 15.88/4.32 | (211) j(e24) = e11
% 15.88/4.32 |
% 15.88/4.32 | Instantiating formula (99) with e24, e11, e10 and discharging atoms j(e24) = e10, j(e24) = e11, yields:
% 15.88/4.32 | (232) e10 = e11
% 15.88/4.32 |
% 15.88/4.32 | Equations (232) can reduce 129 to:
% 15.88/4.32 | (201) $false
% 15.88/4.32 |
% 15.88/4.32 |-The branch is then unsatisfiable
% 15.88/4.32 |-Branch two:
% 15.88/4.32 | (214) ~ (all_0_8_8 = e24)
% 15.88/4.32 | (215) all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 15.88/4.32 |
% 15.88/4.32 +-Applying beta-rule and splitting (51), into two cases.
% 15.88/4.32 |-Branch one:
% 15.88/4.32 | (187) all_0_5_5 = e24
% 15.88/4.32 |
% 15.88/4.32 | From (187) and (149) follows:
% 15.88/4.32 | (197) j(e24) = e14
% 15.88/4.32 |
% 15.88/4.32 | Instantiating formula (99) with e24, e14, e10 and discharging atoms j(e24) = e14, j(e24) = e10, yields:
% 15.88/4.32 | (206) e14 = e10
% 15.88/4.32 |
% 15.88/4.32 | Equations (206) can reduce 63 to:
% 15.88/4.32 | (201) $false
% 15.88/4.32 |
% 15.88/4.32 |-The branch is then unsatisfiable
% 15.88/4.32 |-Branch two:
% 15.88/4.32 | (351) ~ (all_0_5_5 = e24)
% 15.88/4.32 | (352) all_0_5_5 = e23 | all_0_5_5 = e22 | all_0_5_5 = e20 | all_0_5_5 = e21
% 15.88/4.32 |
% 15.88/4.32 +-Applying beta-rule and splitting (112), into two cases.
% 15.88/4.32 |-Branch one:
% 15.88/4.32 | (353) all_0_6_6 = e24
% 15.88/4.32 |
% 15.88/4.32 | From (353) and (36) follows:
% 15.88/4.32 | (354) j(e24) = e13
% 15.88/4.32 |
% 15.88/4.32 | Instantiating formula (99) with e24, e13, e10 and discharging atoms j(e24) = e13, j(e24) = e10, yields:
% 15.88/4.32 | (231) e13 = e10
% 15.88/4.32 |
% 15.88/4.32 | Equations (231) can reduce 110 to:
% 15.88/4.32 | (201) $false
% 15.88/4.32 |
% 15.88/4.32 |-The branch is then unsatisfiable
% 15.88/4.32 |-Branch two:
% 15.88/4.32 | (357) ~ (all_0_6_6 = e24)
% 15.88/4.32 | (358) all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21
% 15.88/4.32 |
% 15.88/4.32 +-Applying beta-rule and splitting (221), into two cases.
% 15.88/4.32 |-Branch one:
% 15.88/4.32 | (266) all_0_7_7 = e23
% 15.88/4.32 |
% 15.88/4.32 | From (266) and (299) follows:
% 15.88/4.32 | (360) op2(e23, e24) = all_0_8_8
% 15.88/4.32 |
% 15.88/4.32 | From (266) and (301) follows:
% 15.88/4.32 | (361) op2(e24, all_0_5_5) = e23
% 15.88/4.32 |
% 15.88/4.32 | From (266) and (303) follows:
% 15.88/4.32 | (362) op2(e24, e23) = all_0_5_5
% 15.88/4.32 |
% 15.88/4.32 | Instantiating formula (47) with e24, e23, all_0_5_5, e21 and discharging atoms op2(e24, e23) = all_0_5_5, op2(e24, e23) = e21, yields:
% 15.88/4.32 | (363) all_0_5_5 = e21
% 15.88/4.32 |
% 15.88/4.32 | Instantiating formula (47) with e23, e24, all_0_8_8, e22 and discharging atoms op2(e23, e24) = all_0_8_8, op2(e23, e24) = e22, yields:
% 15.88/4.32 | (364) all_0_8_8 = e22
% 15.88/4.32 |
% 15.88/4.32 | From (364)(363) and (300) follows:
% 15.88/4.32 | (242) op2(e22, e24) = e21
% 15.88/4.32 |
% 15.88/4.32 | From (363) and (361) follows:
% 15.88/4.32 | (243) op2(e24, e21) = e23
% 15.88/4.32 |
% 15.88/4.32 | Instantiating formula (47) with e24, e21, e23, e22 and discharging atoms op2(e24, e21) = e23, op2(e24, e21) = e22, yields:
% 15.88/4.32 | (244) e23 = e22
% 15.88/4.32 |
% 15.88/4.32 | Instantiating formula (47) with e22, e24, e21, e23 and discharging atoms op2(e22, e24) = e23, op2(e22, e24) = e21, yields:
% 15.88/4.32 | (245) e23 = e21
% 15.88/4.32 |
% 15.88/4.32 | Combining equations (244,245) yields a new equation:
% 15.88/4.33 | (246) e22 = e21
% 15.88/4.33 |
% 15.88/4.33 | Simplifying 246 yields:
% 15.88/4.33 | (247) e22 = e21
% 15.88/4.33 |
% 15.88/4.33 | Equations (247) can reduce 59 to:
% 15.88/4.33 | (201) $false
% 15.88/4.33 |
% 15.88/4.33 |-The branch is then unsatisfiable
% 15.88/4.33 |-Branch two:
% 15.88/4.33 | (278) ~ (all_0_7_7 = e23)
% 15.88/4.33 | (279) all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 15.88/4.33 |
% 15.88/4.33 +-Applying beta-rule and splitting (203), into two cases.
% 15.88/4.33 |-Branch one:
% 15.88/4.33 | (222) all_0_1_1 = e13
% 15.88/4.33 |
% 15.88/4.33 | From (222) and (311) follows:
% 15.88/4.33 | (375) op1(e13, e10) = all_0_2_2
% 15.88/4.33 |
% 15.88/4.33 | From (222) and (312) follows:
% 15.88/4.33 | (376) op1(all_0_2_2, e10) = e13
% 15.88/4.33 |
% 15.88/4.33 | From (222) and (313) follows:
% 15.88/4.33 | (377) op1(all_0_3_3, e13) = e10
% 15.88/4.33 |
% 15.88/4.33 | From (222) and (309) follows:
% 15.88/4.33 | (378) op1(e10, e13) = all_0_3_3
% 16.19/4.33 |
% 16.19/4.33 | Instantiating formula (101) with e13, e10, all_0_2_2, e12 and discharging atoms op1(e13, e10) = all_0_2_2, op1(e13, e10) = e12, yields:
% 16.19/4.33 | (379) all_0_2_2 = e12
% 16.19/4.33 |
% 16.19/4.33 | Instantiating formula (101) with e10, e13, all_0_3_3, e11 and discharging atoms op1(e10, e13) = all_0_3_3, op1(e10, e13) = e11, yields:
% 16.19/4.33 | (380) all_0_3_3 = e11
% 16.19/4.33 |
% 16.19/4.33 | From (379) and (376) follows:
% 16.19/4.33 | (381) op1(e12, e10) = e13
% 16.19/4.33 |
% 16.19/4.33 | From (380) and (377) follows:
% 16.19/4.33 | (382) op1(e11, e13) = e10
% 16.19/4.33 |
% 16.19/4.33 | From (380)(379) and (310) follows:
% 16.19/4.33 | (383) op1(e10, e11) = e12
% 16.19/4.33 |
% 16.19/4.33 | Instantiating formula (101) with e12, e10, e13, e11 and discharging atoms op1(e12, e10) = e13, op1(e12, e10) = e11, yields:
% 16.19/4.33 | (230) e13 = e11
% 16.19/4.33 |
% 16.19/4.33 | Instantiating formula (101) with e10, e11, e12, e13 and discharging atoms op1(e10, e11) = e13, op1(e10, e11) = e12, yields:
% 16.19/4.33 | (335) e13 = e12
% 16.19/4.33 |
% 16.19/4.33 | Instantiating formula (101) with e11, e13, e10, e12 and discharging atoms op1(e11, e13) = e12, op1(e11, e13) = e10, yields:
% 16.19/4.33 | (317) e12 = e10
% 16.19/4.33 |
% 16.19/4.33 | Combining equations (335,230) yields a new equation:
% 16.19/4.33 | (387) e12 = e11
% 16.19/4.33 |
% 16.19/4.33 | Simplifying 387 yields:
% 16.19/4.33 | (388) e12 = e11
% 16.19/4.33 |
% 16.19/4.33 | Combining equations (388,317) yields a new equation:
% 16.19/4.33 | (232) e10 = e11
% 16.19/4.33 |
% 16.19/4.33 | Equations (232) can reduce 129 to:
% 16.19/4.33 | (201) $false
% 16.19/4.33 |
% 16.19/4.33 |-The branch is then unsatisfiable
% 16.19/4.33 |-Branch two:
% 16.19/4.33 | (234) ~ (all_0_1_1 = e13)
% 16.19/4.33 | (235) all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11
% 16.19/4.33 |
% 16.19/4.33 +-Applying beta-rule and splitting (215), into two cases.
% 16.19/4.33 |-Branch one:
% 16.19/4.33 | (251) all_0_8_8 = e23
% 16.19/4.33 |
% 16.19/4.33 | From (251) and (300) follows:
% 16.19/4.33 | (394) op2(e23, e24) = all_0_5_5
% 16.19/4.33 |
% 16.19/4.33 | From (251) and (302) follows:
% 16.19/4.33 | (238) op2(e24, all_0_6_6) = e23
% 16.19/4.33 |
% 16.19/4.33 | From (251) and (304) follows:
% 16.19/4.33 | (239) op2(e24, e23) = all_0_6_6
% 16.19/4.33 |
% 16.19/4.33 | Instantiating formula (47) with e24, e23, all_0_6_6, e21 and discharging atoms op2(e24, e23) = all_0_6_6, op2(e24, e23) = e21, yields:
% 16.19/4.33 | (240) all_0_6_6 = e21
% 16.19/4.33 |
% 16.19/4.33 | Instantiating formula (47) with e23, e24, all_0_5_5, e22 and discharging atoms op2(e23, e24) = all_0_5_5, op2(e23, e24) = e22, yields:
% 16.19/4.33 | (398) all_0_5_5 = e22
% 16.19/4.33 |
% 16.19/4.33 | From (398)(240) and (298) follows:
% 16.19/4.33 | (242) op2(e22, e24) = e21
% 16.19/4.33 |
% 16.19/4.33 | From (240) and (238) follows:
% 16.19/4.34 | (243) op2(e24, e21) = e23
% 16.19/4.34 |
% 16.19/4.34 | Instantiating formula (47) with e24, e21, e23, e22 and discharging atoms op2(e24, e21) = e23, op2(e24, e21) = e22, yields:
% 16.19/4.34 | (244) e23 = e22
% 16.19/4.34 |
% 16.19/4.34 | Instantiating formula (47) with e22, e24, e21, e23 and discharging atoms op2(e22, e24) = e23, op2(e22, e24) = e21, yields:
% 16.19/4.34 | (245) e23 = e21
% 16.19/4.34 |
% 16.19/4.34 | Combining equations (244,245) yields a new equation:
% 16.19/4.34 | (246) e22 = e21
% 16.19/4.34 |
% 16.19/4.34 | Simplifying 246 yields:
% 16.19/4.34 | (247) e22 = e21
% 16.19/4.34 |
% 16.19/4.34 | Equations (247) can reduce 59 to:
% 16.19/4.34 | (201) $false
% 16.19/4.34 |
% 16.19/4.34 |-The branch is then unsatisfiable
% 16.19/4.34 |-Branch two:
% 16.19/4.34 | (264) ~ (all_0_8_8 = e23)
% 16.19/4.34 | (265) all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 16.19/4.34 |
% 16.19/4.34 +-Applying beta-rule and splitting (352), into two cases.
% 16.19/4.34 |-Branch one:
% 16.19/4.34 | (408) all_0_5_5 = e23
% 16.19/4.34 |
% 16.19/4.34 | From (408) and (149) follows:
% 16.19/4.34 | (409) j(e23) = e14
% 16.19/4.34 |
% 16.19/4.34 | Instantiating formula (99) with e23, e14, all_0_1_1 and discharging atoms j(e23) = all_0_1_1, j(e23) = e14, yields:
% 16.19/4.34 | (198) all_0_1_1 = e14
% 16.19/4.34 |
% 16.19/4.34 | Equations (198) can reduce 202 to:
% 16.19/4.34 | (201) $false
% 16.19/4.34 |
% 16.19/4.34 |-The branch is then unsatisfiable
% 16.19/4.34 |-Branch two:
% 16.19/4.34 | (412) ~ (all_0_5_5 = e23)
% 16.19/4.34 | (413) all_0_5_5 = e22 | all_0_5_5 = e20 | all_0_5_5 = e21
% 16.19/4.34 |
% 16.19/4.34 +-Applying beta-rule and splitting (358), into two cases.
% 16.19/4.34 |-Branch one:
% 16.19/4.34 | (414) all_0_6_6 = e23
% 16.19/4.34 |
% 16.19/4.34 | From (414) and (36) follows:
% 16.19/4.34 | (415) j(e23) = e13
% 16.19/4.34 |
% 16.19/4.34 | Instantiating formula (99) with e23, e13, all_0_1_1 and discharging atoms j(e23) = all_0_1_1, j(e23) = e13, yields:
% 16.19/4.34 | (222) all_0_1_1 = e13
% 16.19/4.34 |
% 16.19/4.34 | Equations (222) can reduce 234 to:
% 16.19/4.34 | (201) $false
% 16.19/4.34 |
% 16.19/4.34 |-The branch is then unsatisfiable
% 16.19/4.34 |-Branch two:
% 16.19/4.34 | (418) ~ (all_0_6_6 = e23)
% 16.19/4.34 | (419) all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21
% 16.19/4.34 |
% 16.19/4.34 +-Applying beta-rule and splitting (279), into two cases.
% 16.19/4.34 |-Branch one:
% 16.19/4.34 | (241) all_0_7_7 = e22
% 16.19/4.34 |
% 16.19/4.34 | From (241) and (299) follows:
% 16.19/4.34 | (421) op2(e22, e24) = all_0_8_8
% 16.19/4.34 |
% 16.19/4.34 | Instantiating formula (47) with e22, e24, all_0_8_8, e23 and discharging atoms op2(e22, e24) = all_0_8_8, op2(e22, e24) = e23, yields:
% 16.19/4.34 | (251) all_0_8_8 = e23
% 16.19/4.34 |
% 16.19/4.34 | Equations (251) can reduce 264 to:
% 16.19/4.34 | (201) $false
% 16.19/4.34 |
% 16.19/4.34 |-The branch is then unsatisfiable
% 16.19/4.34 |-Branch two:
% 16.19/4.34 | (424) ~ (all_0_7_7 = e22)
% 16.19/4.34 | (425) all_0_7_7 = e20 | all_0_7_7 = e21
% 16.19/4.34 |
% 16.19/4.34 +-Applying beta-rule and splitting (413), into two cases.
% 16.19/4.34 |-Branch one:
% 16.19/4.34 | (398) all_0_5_5 = e22
% 16.19/4.34 |
% 16.19/4.34 | From (398) and (298) follows:
% 16.19/4.34 | (427) op2(e22, e24) = all_0_6_6
% 16.19/4.34 |
% 16.19/4.34 | Instantiating formula (47) with e22, e24, all_0_6_6, e23 and discharging atoms op2(e22, e24) = all_0_6_6, op2(e22, e24) = e23, yields:
% 16.19/4.34 | (414) all_0_6_6 = e23
% 16.19/4.34 |
% 16.19/4.34 | Equations (414) can reduce 418 to:
% 16.19/4.34 | (201) $false
% 16.19/4.34 |
% 16.19/4.34 |-The branch is then unsatisfiable
% 16.19/4.34 |-Branch two:
% 16.19/4.34 | (430) ~ (all_0_5_5 = e22)
% 16.19/4.34 | (431) all_0_5_5 = e20 | all_0_5_5 = e21
% 16.19/4.34 |
% 16.19/4.34 +-Applying beta-rule and splitting (425), into two cases.
% 16.19/4.34 |-Branch one:
% 16.19/4.34 | (432) all_0_7_7 = e20
% 16.19/4.34 |
% 16.19/4.34 | From (432) and (303) follows:
% 16.19/4.34 | (433) op2(e24, e20) = all_0_5_5
% 16.19/4.34 |
% 16.19/4.34 | Instantiating formula (47) with e24, e20, all_0_5_5, e23 and discharging atoms op2(e24, e20) = all_0_5_5, op2(e24, e20) = e23, yields:
% 16.19/4.34 | (408) all_0_5_5 = e23
% 16.19/4.34 |
% 16.19/4.34 | Equations (408) can reduce 412 to:
% 16.19/4.34 | (201) $false
% 16.19/4.34 |
% 16.19/4.34 |-The branch is then unsatisfiable
% 16.19/4.34 |-Branch two:
% 16.19/4.34 | (436) ~ (all_0_7_7 = e20)
% 16.19/4.34 | (255) all_0_7_7 = e21
% 16.19/4.34 |
% 16.19/4.34 | From (255) and (303) follows:
% 16.19/4.34 | (438) op2(e24, e21) = all_0_5_5
% 16.19/4.34 |
% 16.19/4.34 | Instantiating formula (47) with e24, e21, all_0_5_5, e22 and discharging atoms op2(e24, e21) = all_0_5_5, op2(e24, e21) = e22, yields:
% 16.19/4.35 | (398) all_0_5_5 = e22
% 16.19/4.35 |
% 16.19/4.35 | Equations (398) can reduce 430 to:
% 16.19/4.35 | (201) $false
% 16.19/4.35 |
% 16.19/4.35 |-The branch is then unsatisfiable
% 16.19/4.35 |-Branch two:
% 16.19/4.35 | (208) ~ (all_0_9_9 = e24)
% 16.19/4.35 | (209) all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21
% 16.19/4.35 |
% 16.19/4.35 +-Applying beta-rule and splitting (57), into two cases.
% 16.19/4.35 |-Branch one:
% 16.19/4.35 | (198) all_0_1_1 = e14
% 16.19/4.35 |
% 16.19/4.35 | From (198) and (66) follows:
% 16.19/4.35 | (199) h(e14) = e23
% 16.19/4.35 |
% 16.19/4.35 | Instantiating formula (96) with e14, e23, all_0_5_5 and discharging atoms h(e14) = all_0_5_5, h(e14) = e23, yields:
% 16.19/4.35 | (408) all_0_5_5 = e23
% 16.19/4.35 |
% 16.19/4.35 | From (408) and (116) follows:
% 16.19/4.35 | (446) op2(e23, all_0_6_6) = all_0_9_9
% 16.19/4.35 |
% 16.19/4.35 | From (408) and (38) follows:
% 16.19/4.35 | (447) op2(e23, all_0_7_7) = all_0_8_8
% 16.19/4.35 |
% 16.19/4.35 | From (408) and (80) follows:
% 16.19/4.35 | (448) op2(e23, all_0_8_8) = all_0_7_7
% 16.19/4.35 |
% 16.19/4.35 | From (408) and (172) follows:
% 16.19/4.35 | (449) op2(all_0_6_6, e23) = all_0_8_8
% 16.19/4.35 |
% 16.19/4.35 | From (408) and (125) follows:
% 16.19/4.35 | (450) op2(all_0_6_6, all_0_8_8) = e23
% 16.19/4.35 |
% 16.19/4.35 | From (408) and (84) follows:
% 16.19/4.35 | (451) op2(all_0_7_7, e23) = all_0_6_6
% 16.19/4.35 |
% 16.19/4.35 | From (408) and (142) follows:
% 16.19/4.35 | (452) op2(all_0_7_7, all_0_6_6) = e23
% 16.19/4.35 |
% 16.19/4.35 | From (408) and (92) follows:
% 16.19/4.35 | (453) op2(all_0_8_8, e23) = all_0_9_9
% 16.19/4.35 |
% 16.19/4.35 | From (408) and (120) follows:
% 16.19/4.35 | (454) op2(all_0_8_8, all_0_9_9) = e23
% 16.19/4.35 |
% 16.19/4.35 +-Applying beta-rule and splitting (128), into two cases.
% 16.19/4.35 |-Branch one:
% 16.19/4.35 | (210) all_0_8_8 = e24
% 16.19/4.35 |
% 16.19/4.35 | From (210) and (5) follows:
% 16.19/4.35 | (456) op2(all_0_7_7, e24) = all_0_9_9
% 16.19/4.35 |
% 16.19/4.35 | From (210) and (454) follows:
% 16.19/4.35 | (457) op2(e24, all_0_9_9) = e23
% 16.19/4.35 |
% 16.19/4.35 | From (210) and (453) follows:
% 16.19/4.35 | (458) op2(e24, e23) = all_0_9_9
% 16.19/4.35 |
% 16.19/4.35 | From (210) and (448) follows:
% 16.19/4.35 | (237) op2(e23, e24) = all_0_7_7
% 16.19/4.35 |
% 16.19/4.35 | Instantiating formula (47) with e24, e23, all_0_9_9, e21 and discharging atoms op2(e24, e23) = all_0_9_9, op2(e24, e23) = e21, yields:
% 16.19/4.35 | (460) all_0_9_9 = e21
% 16.19/4.35 |
% 16.19/4.35 | Instantiating formula (47) with e23, e24, all_0_7_7, e22 and discharging atoms op2(e23, e24) = all_0_7_7, op2(e23, e24) = e22, yields:
% 16.19/4.35 | (241) all_0_7_7 = e22
% 16.19/4.35 |
% 16.19/4.35 | From (241)(460) and (456) follows:
% 16.19/4.35 | (242) op2(e22, e24) = e21
% 16.19/4.35 |
% 16.19/4.35 | From (460) and (457) follows:
% 16.19/4.35 | (243) op2(e24, e21) = e23
% 16.19/4.35 |
% 16.19/4.35 | Instantiating formula (47) with e24, e21, e23, e22 and discharging atoms op2(e24, e21) = e23, op2(e24, e21) = e22, yields:
% 16.19/4.35 | (244) e23 = e22
% 16.19/4.35 |
% 16.19/4.35 | Instantiating formula (47) with e22, e24, e21, e23 and discharging atoms op2(e22, e24) = e23, op2(e22, e24) = e21, yields:
% 16.19/4.35 | (245) e23 = e21
% 16.19/4.35 |
% 16.19/4.35 | Combining equations (244,245) yields a new equation:
% 16.19/4.35 | (246) e22 = e21
% 16.19/4.35 |
% 16.19/4.35 | Simplifying 246 yields:
% 16.19/4.35 | (247) e22 = e21
% 16.19/4.35 |
% 16.19/4.36 | Equations (247) can reduce 59 to:
% 16.19/4.36 | (201) $false
% 16.19/4.36 |
% 16.19/4.36 |-The branch is then unsatisfiable
% 16.19/4.36 |-Branch two:
% 16.19/4.36 | (214) ~ (all_0_8_8 = e24)
% 16.19/4.36 | (215) all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 16.19/4.36 |
% 16.19/4.36 +-Applying beta-rule and splitting (112), into two cases.
% 16.19/4.36 |-Branch one:
% 16.19/4.36 | (353) all_0_6_6 = e24
% 16.19/4.36 |
% 16.19/4.36 | From (353) and (450) follows:
% 16.19/4.36 | (269) op2(e24, all_0_8_8) = e23
% 16.19/4.36 |
% 16.19/4.36 | From (353) and (449) follows:
% 16.19/4.36 | (268) op2(e24, e23) = all_0_8_8
% 16.19/4.36 |
% 16.19/4.36 | From (353) and (13) follows:
% 16.19/4.36 | (474) op2(all_0_9_9, e24) = all_0_8_8
% 16.19/4.36 |
% 16.19/4.36 | From (353) and (446) follows:
% 16.19/4.36 | (252) op2(e23, e24) = all_0_9_9
% 16.19/4.36 |
% 16.19/4.36 | Instantiating formula (47) with e24, e23, all_0_8_8, e21 and discharging atoms op2(e24, e23) = all_0_8_8, op2(e24, e23) = e21, yields:
% 16.19/4.36 | (270) all_0_8_8 = e21
% 16.19/4.36 |
% 16.19/4.36 | Instantiating formula (47) with e23, e24, all_0_9_9, e22 and discharging atoms op2(e23, e24) = all_0_9_9, op2(e23, e24) = e22, yields:
% 16.19/4.36 | (256) all_0_9_9 = e22
% 16.19/4.36 |
% 16.19/4.36 | From (256)(270) and (474) follows:
% 16.19/4.36 | (242) op2(e22, e24) = e21
% 16.19/4.36 |
% 16.19/4.36 | From (270) and (269) follows:
% 16.19/4.36 | (243) op2(e24, e21) = e23
% 16.19/4.36 |
% 16.19/4.36 | Instantiating formula (47) with e24, e21, e23, e22 and discharging atoms op2(e24, e21) = e23, op2(e24, e21) = e22, yields:
% 16.19/4.36 | (244) e23 = e22
% 16.19/4.36 |
% 16.19/4.36 | Instantiating formula (47) with e22, e24, e21, e23 and discharging atoms op2(e22, e24) = e23, op2(e22, e24) = e21, yields:
% 16.19/4.36 | (245) e23 = e21
% 16.35/4.36 |
% 16.35/4.36 | Combining equations (244,245) yields a new equation:
% 16.35/4.36 | (246) e22 = e21
% 16.35/4.36 |
% 16.35/4.36 | Simplifying 246 yields:
% 16.35/4.36 | (247) e22 = e21
% 16.35/4.36 |
% 16.35/4.36 | Equations (247) can reduce 59 to:
% 16.35/4.36 | (201) $false
% 16.35/4.36 |
% 16.35/4.36 |-The branch is then unsatisfiable
% 16.35/4.36 |-Branch two:
% 16.35/4.36 | (357) ~ (all_0_6_6 = e24)
% 16.35/4.36 | (358) all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21
% 16.35/4.36 |
% 16.35/4.36 +-Applying beta-rule and splitting (95), into two cases.
% 16.35/4.36 |-Branch one:
% 16.35/4.36 | (216) all_0_7_7 = e24
% 16.35/4.36 |
% 16.35/4.36 | From (216) and (452) follows:
% 16.35/4.36 | (238) op2(e24, all_0_6_6) = e23
% 16.35/4.36 |
% 16.35/4.36 | From (216) and (451) follows:
% 16.35/4.36 | (239) op2(e24, e23) = all_0_6_6
% 16.35/4.36 |
% 16.35/4.36 | From (216) and (30) follows:
% 16.35/4.36 | (490) op2(all_0_8_8, e24) = all_0_6_6
% 16.35/4.36 |
% 16.35/4.36 | From (216) and (447) follows:
% 16.35/4.36 | (360) op2(e23, e24) = all_0_8_8
% 16.35/4.36 |
% 16.35/4.36 | Instantiating formula (47) with e24, e23, all_0_6_6, e21 and discharging atoms op2(e24, e23) = all_0_6_6, op2(e24, e23) = e21, yields:
% 16.35/4.36 | (240) all_0_6_6 = e21
% 16.35/4.36 |
% 16.35/4.36 | Instantiating formula (47) with e23, e24, all_0_8_8, e22 and discharging atoms op2(e23, e24) = all_0_8_8, op2(e23, e24) = e22, yields:
% 16.35/4.36 | (364) all_0_8_8 = e22
% 16.35/4.36 |
% 16.35/4.36 | From (364)(240) and (490) follows:
% 16.35/4.36 | (242) op2(e22, e24) = e21
% 16.35/4.36 |
% 16.35/4.36 | From (240) and (238) follows:
% 16.35/4.36 | (243) op2(e24, e21) = e23
% 16.35/4.36 |
% 16.35/4.36 | Instantiating formula (47) with e24, e21, e23, e22 and discharging atoms op2(e24, e21) = e23, op2(e24, e21) = e22, yields:
% 16.35/4.36 | (244) e23 = e22
% 16.35/4.36 |
% 16.35/4.36 | Instantiating formula (47) with e22, e24, e21, e23 and discharging atoms op2(e22, e24) = e23, op2(e22, e24) = e21, yields:
% 16.35/4.36 | (245) e23 = e21
% 16.35/4.36 |
% 16.35/4.36 | Combining equations (244,245) yields a new equation:
% 16.35/4.36 | (246) e22 = e21
% 16.35/4.36 |
% 16.35/4.36 | Simplifying 246 yields:
% 16.35/4.36 | (247) e22 = e21
% 16.35/4.36 |
% 16.35/4.36 | Equations (247) can reduce 59 to:
% 16.35/4.36 | (201) $false
% 16.35/4.36 |
% 16.35/4.36 |-The branch is then unsatisfiable
% 16.35/4.36 |-Branch two:
% 16.35/4.36 | (220) ~ (all_0_7_7 = e24)
% 16.35/4.36 | (221) all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 16.35/4.36 |
% 16.35/4.36 +-Applying beta-rule and splitting (296), into two cases.
% 16.35/4.36 |-Branch one:
% 16.35/4.36 | (503) all_0_0_0 = e13
% 16.35/4.36 |
% 16.35/4.36 | From (503) and (18) follows:
% 16.35/4.36 | (504) h(e13) = e24
% 16.35/4.36 |
% 16.35/4.36 | Instantiating formula (96) with e13, e24, all_0_6_6 and discharging atoms h(e13) = all_0_6_6, h(e13) = e24, yields:
% 16.35/4.36 | (353) all_0_6_6 = e24
% 16.35/4.36 |
% 16.35/4.36 | Equations (353) can reduce 357 to:
% 16.35/4.37 | (201) $false
% 16.35/4.37 |
% 16.35/4.37 |-The branch is then unsatisfiable
% 16.35/4.37 |-Branch two:
% 16.35/4.37 | (507) ~ (all_0_0_0 = e13)
% 16.35/4.37 | (508) all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 16.35/4.37 |
% 16.35/4.37 +-Applying beta-rule and splitting (508), into two cases.
% 16.35/4.37 |-Branch one:
% 16.35/4.37 | (509) all_0_0_0 = e12
% 16.35/4.37 |
% 16.35/4.37 | From (509) and (18) follows:
% 16.35/4.37 | (510) h(e12) = e24
% 16.35/4.37 |
% 16.35/4.37 | Instantiating formula (96) with e12, e24, all_0_7_7 and discharging atoms h(e12) = all_0_7_7, h(e12) = e24, yields:
% 16.35/4.37 | (216) all_0_7_7 = e24
% 16.35/4.37 |
% 16.35/4.37 | Equations (216) can reduce 220 to:
% 16.35/4.37 | (201) $false
% 16.35/4.37 |
% 16.35/4.37 |-The branch is then unsatisfiable
% 16.35/4.37 |-Branch two:
% 16.35/4.37 | (513) ~ (all_0_0_0 = e12)
% 16.35/4.37 | (514) all_0_0_0 = e10 | all_0_0_0 = e11
% 16.35/4.37 |
% 16.35/4.37 +-Applying beta-rule and splitting (514), into two cases.
% 16.35/4.37 |-Branch one:
% 16.35/4.37 | (306) all_0_0_0 = e10
% 16.35/4.37 |
% 16.35/4.37 | From (306) and (18) follows:
% 16.35/4.37 | (516) h(e10) = e24
% 16.35/4.37 |
% 16.35/4.37 | Instantiating formula (96) with e10, e24, all_0_9_9 and discharging atoms h(e10) = all_0_9_9, h(e10) = e24, yields:
% 16.35/4.37 | (204) all_0_9_9 = e24
% 16.35/4.37 |
% 16.35/4.37 | Equations (204) can reduce 208 to:
% 16.35/4.37 | (201) $false
% 16.35/4.37 |
% 16.35/4.37 |-The branch is then unsatisfiable
% 16.35/4.37 |-Branch two:
% 16.35/4.37 | (519) ~ (all_0_0_0 = e10)
% 16.35/4.37 | (520) all_0_0_0 = e11
% 16.35/4.37 |
% 16.35/4.37 | From (520) and (18) follows:
% 16.35/4.37 | (521) h(e11) = e24
% 16.35/4.37 |
% 16.35/4.37 | Instantiating formula (96) with e11, e24, all_0_8_8 and discharging atoms h(e11) = all_0_8_8, h(e11) = e24, yields:
% 16.35/4.37 | (210) all_0_8_8 = e24
% 16.35/4.37 |
% 16.35/4.37 | Equations (210) can reduce 214 to:
% 16.35/4.37 | (201) $false
% 16.35/4.37 |
% 16.35/4.37 |-The branch is then unsatisfiable
% 16.35/4.37 |-Branch two:
% 16.35/4.37 | (202) ~ (all_0_1_1 = e14)
% 16.35/4.37 | (203) all_0_1_1 = e13 | all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11
% 16.35/4.37 |
% 16.35/4.37 +-Applying beta-rule and splitting (95), into two cases.
% 16.35/4.37 |-Branch one:
% 16.35/4.37 | (216) all_0_7_7 = e24
% 16.35/4.37 |
% 16.35/4.37 | From (216) and (38) follows:
% 16.35/4.37 | (527) op2(all_0_5_5, e24) = all_0_8_8
% 16.35/4.37 |
% 16.35/4.37 | From (216) and (15) follows:
% 16.35/4.37 | (528) op2(all_0_6_6, e24) = all_0_9_9
% 16.35/4.37 |
% 16.35/4.37 | From (216) and (5) follows:
% 16.35/4.37 | (529) op2(e24, all_0_8_8) = all_0_9_9
% 16.35/4.37 |
% 16.35/4.37 | From (216) and (163) follows:
% 16.35/4.37 | (530) op2(e24, all_0_9_9) = all_0_8_8
% 16.35/4.37 |
% 16.35/4.37 | From (216) and (30) follows:
% 16.35/4.37 | (490) op2(all_0_8_8, e24) = all_0_6_6
% 16.35/4.37 |
% 16.35/4.37 | From (216) and (71) follows:
% 16.35/4.37 | (532) op2(all_0_9_9, e24) = all_0_5_5
% 16.35/4.37 |
% 16.35/4.37 | From (216) and (82) follows:
% 16.35/4.37 | (217) j(e24) = e12
% 16.35/4.37 |
% 16.35/4.37 | Instantiating formula (99) with e24, e12, all_0_0_0 and discharging atoms j(e24) = all_0_0_0, j(e24) = e12, yields:
% 16.35/4.37 | (509) all_0_0_0 = e12
% 16.35/4.37 |
% 16.35/4.37 | Equations (509) can reduce 295 to:
% 16.35/4.37 | (535) ~ (e14 = e12)
% 16.35/4.37 |
% 16.35/4.37 | Simplifying 535 yields:
% 16.35/4.37 | (20) ~ (e14 = e12)
% 16.35/4.37 |
% 16.35/4.37 | From (509) and (168) follows:
% 16.35/4.37 | (537) op1(e12, all_0_1_1) = all_0_3_3
% 16.35/4.37 |
% 16.35/4.37 | From (509) and (122) follows:
% 16.35/4.37 | (538) op1(e12, all_0_2_2) = all_0_4_4
% 16.35/4.37 |
% 16.35/4.37 | From (509) and (147) follows:
% 16.35/4.37 | (539) op1(e12, all_0_3_3) = all_0_2_2
% 16.35/4.37 |
% 16.35/4.37 | From (509) and (73) follows:
% 16.35/4.37 | (540) op1(all_0_3_3, e12) = all_0_4_4
% 16.35/4.37 |
% 16.35/4.37 | From (509) and (93) follows:
% 16.35/4.37 | (541) op1(all_0_4_4, e12) = all_0_3_3
% 16.35/4.38 |
% 16.35/4.38 | From (509) and (141) follows:
% 16.35/4.38 | (217) j(e24) = e12
% 16.35/4.38 |
% 16.35/4.38 +-Applying beta-rule and splitting (112), into two cases.
% 16.35/4.38 |-Branch one:
% 16.35/4.38 | (353) all_0_6_6 = e24
% 16.35/4.38 |
% 16.35/4.38 | From (353) and (36) follows:
% 16.35/4.38 | (354) j(e24) = e13
% 16.35/4.38 |
% 16.35/4.38 | Instantiating formula (99) with e24, e13, e12 and discharging atoms j(e24) = e13, j(e24) = e12, yields:
% 16.35/4.38 | (335) e13 = e12
% 16.35/4.38 |
% 16.35/4.38 | Equations (335) can reduce 94 to:
% 16.35/4.38 | (201) $false
% 16.35/4.38 |
% 16.35/4.38 |-The branch is then unsatisfiable
% 16.35/4.38 |-Branch two:
% 16.35/4.38 | (357) ~ (all_0_6_6 = e24)
% 16.35/4.38 | (358) all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21
% 16.35/4.38 |
% 16.35/4.38 +-Applying beta-rule and splitting (170), into two cases.
% 16.35/4.38 |-Branch one:
% 16.35/4.38 | (549) all_0_3_3 = e14
% 16.35/4.38 |
% 16.35/4.38 | From (549) and (105) follows:
% 16.35/4.38 | (550) op1(e14, all_0_4_4) = all_0_2_2
% 16.35/4.38 |
% 16.35/4.38 | From (549) and (540) follows:
% 16.35/4.38 | (551) op1(e14, e12) = all_0_4_4
% 16.35/4.38 |
% 16.35/4.38 | From (549) and (541) follows:
% 16.35/4.38 | (552) op1(all_0_4_4, e12) = e14
% 16.35/4.38 |
% 16.35/4.38 | From (549) and (539) follows:
% 16.35/4.38 | (553) op1(e12, e14) = all_0_2_2
% 16.35/4.38 |
% 16.35/4.38 | Instantiating formula (101) with e14, e12, all_0_4_4, e11 and discharging atoms op1(e14, e12) = all_0_4_4, op1(e14, e12) = e11, yields:
% 16.35/4.38 | (554) all_0_4_4 = e11
% 16.35/4.38 |
% 16.35/4.38 | Instantiating formula (101) with e12, e14, all_0_2_2, e13 and discharging atoms op1(e12, e14) = all_0_2_2, op1(e12, e14) = e13, yields:
% 16.35/4.38 | (326) all_0_2_2 = e13
% 16.35/4.38 |
% 16.35/4.38 | From (554) and (552) follows:
% 16.35/4.38 | (556) op1(e11, e12) = e14
% 16.35/4.38 |
% 16.35/4.38 | From (554)(326) and (550) follows:
% 16.35/4.38 | (557) op1(e14, e11) = e13
% 16.35/4.38 |
% 16.35/4.38 | From (326)(554) and (538) follows:
% 16.35/4.38 | (558) op1(e12, e13) = e11
% 16.35/4.38 |
% 16.35/4.38 | Instantiating formula (101) with e14, e11, e13, e12 and discharging atoms op1(e14, e11) = e13, op1(e14, e11) = e12, yields:
% 16.35/4.38 | (335) e13 = e12
% 16.35/4.38 |
% 16.35/4.38 | Instantiating formula (101) with e12, e13, e11, e14 and discharging atoms op1(e12, e13) = e14, op1(e12, e13) = e11, yields:
% 16.35/4.38 | (212) e14 = e11
% 16.35/4.38 |
% 16.35/4.38 | Instantiating formula (101) with e11, e12, e14, e13 and discharging atoms op1(e11, e12) = e14, op1(e11, e12) = e13, yields:
% 16.35/4.38 | (333) e14 = e13
% 16.35/4.38 |
% 16.35/4.38 | Combining equations (333,212) yields a new equation:
% 16.35/4.38 | (562) e13 = e11
% 16.35/4.38 |
% 16.35/4.38 | Simplifying 562 yields:
% 16.35/4.38 | (230) e13 = e11
% 16.35/4.38 |
% 16.35/4.38 | Combining equations (230,335) yields a new equation:
% 16.35/4.38 | (388) e12 = e11
% 16.35/4.38 |
% 16.35/4.38 | Equations (388) can reduce 14 to:
% 16.35/4.38 | (201) $false
% 16.35/4.38 |
% 16.35/4.38 |-The branch is then unsatisfiable
% 16.35/4.38 |-Branch two:
% 16.35/4.38 | (566) ~ (all_0_3_3 = e14)
% 16.35/4.38 | (567) all_0_3_3 = e13 | all_0_3_3 = e12 | all_0_3_3 = e10 | all_0_3_3 = e11
% 16.35/4.38 |
% 16.35/4.38 +-Applying beta-rule and splitting (51), into two cases.
% 16.35/4.38 |-Branch one:
% 16.35/4.38 | (187) all_0_5_5 = e24
% 16.35/4.38 |
% 16.35/4.38 | From (187) and (149) follows:
% 16.35/4.38 | (197) j(e24) = e14
% 16.35/4.38 |
% 16.35/4.38 | Instantiating formula (99) with e24, e14, e12 and discharging atoms j(e24) = e14, j(e24) = e12, yields:
% 16.35/4.38 | (218) e14 = e12
% 16.35/4.38 |
% 16.35/4.38 | Equations (218) can reduce 20 to:
% 16.35/4.38 | (201) $false
% 16.35/4.38 |
% 16.35/4.38 |-The branch is then unsatisfiable
% 16.35/4.38 |-Branch two:
% 16.35/4.38 | (351) ~ (all_0_5_5 = e24)
% 16.35/4.38 | (352) all_0_5_5 = e23 | all_0_5_5 = e22 | all_0_5_5 = e20 | all_0_5_5 = e21
% 16.35/4.38 |
% 16.35/4.38 +-Applying beta-rule and splitting (128), into two cases.
% 16.35/4.38 |-Branch one:
% 16.35/4.38 | (210) all_0_8_8 = e24
% 16.35/4.38 |
% 16.35/4.38 | From (210) and (28) follows:
% 16.35/4.38 | (211) j(e24) = e11
% 16.35/4.38 |
% 16.35/4.38 | Instantiating formula (99) with e24, e11, e12 and discharging atoms j(e24) = e12, j(e24) = e11, yields:
% 16.35/4.38 | (388) e12 = e11
% 16.35/4.38 |
% 16.35/4.38 | Equations (388) can reduce 14 to:
% 16.35/4.38 | (201) $false
% 16.35/4.38 |
% 16.35/4.38 |-The branch is then unsatisfiable
% 16.35/4.38 |-Branch two:
% 16.35/4.38 | (214) ~ (all_0_8_8 = e24)
% 16.35/4.38 | (215) all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 16.35/4.38 |
% 16.35/4.38 +-Applying beta-rule and splitting (209), into two cases.
% 16.35/4.38 |-Branch one:
% 16.35/4.38 | (236) all_0_9_9 = e23
% 16.35/4.38 |
% 16.35/4.38 | From (236) and (532) follows:
% 16.35/4.38 | (394) op2(e23, e24) = all_0_5_5
% 16.35/4.38 |
% 16.35/4.39 | From (236) and (529) follows:
% 16.35/4.39 | (269) op2(e24, all_0_8_8) = e23
% 16.35/4.39 |
% 16.35/4.39 | From (236) and (530) follows:
% 16.35/4.39 | (268) op2(e24, e23) = all_0_8_8
% 16.35/4.39 |
% 16.35/4.39 | Instantiating formula (47) with e24, e23, all_0_8_8, e21 and discharging atoms op2(e24, e23) = all_0_8_8, op2(e24, e23) = e21, yields:
% 16.35/4.39 | (270) all_0_8_8 = e21
% 16.35/4.39 |
% 16.35/4.39 | Instantiating formula (47) with e23, e24, all_0_5_5, e22 and discharging atoms op2(e23, e24) = all_0_5_5, op2(e23, e24) = e22, yields:
% 16.35/4.39 | (398) all_0_5_5 = e22
% 16.35/4.39 |
% 16.35/4.39 | From (398)(270) and (527) follows:
% 16.35/4.39 | (242) op2(e22, e24) = e21
% 16.35/4.39 |
% 16.35/4.39 | From (270) and (269) follows:
% 16.35/4.39 | (243) op2(e24, e21) = e23
% 16.35/4.39 |
% 16.35/4.39 | Instantiating formula (47) with e24, e21, e23, e22 and discharging atoms op2(e24, e21) = e23, op2(e24, e21) = e22, yields:
% 16.35/4.39 | (244) e23 = e22
% 16.35/4.39 |
% 16.35/4.39 | Instantiating formula (47) with e22, e24, e21, e23 and discharging atoms op2(e22, e24) = e23, op2(e22, e24) = e21, yields:
% 16.35/4.39 | (245) e23 = e21
% 16.35/4.39 |
% 16.35/4.39 | Combining equations (244,245) yields a new equation:
% 16.35/4.39 | (246) e22 = e21
% 16.35/4.39 |
% 16.35/4.39 | Simplifying 246 yields:
% 16.35/4.39 | (247) e22 = e21
% 16.35/4.39 |
% 16.35/4.39 | Equations (247) can reduce 59 to:
% 16.35/4.39 | (201) $false
% 16.35/4.39 |
% 16.35/4.39 |-The branch is then unsatisfiable
% 16.35/4.39 |-Branch two:
% 16.35/4.39 | (249) ~ (all_0_9_9 = e23)
% 16.35/4.39 | (250) all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21
% 16.35/4.39 |
% 16.35/4.39 +-Applying beta-rule and splitting (203), into two cases.
% 16.35/4.39 |-Branch one:
% 16.35/4.39 | (222) all_0_1_1 = e13
% 16.35/4.39 |
% 16.35/4.39 | From (222) and (537) follows:
% 16.35/4.39 | (596) op1(e12, e13) = all_0_3_3
% 16.35/4.39 |
% 16.35/4.39 | Instantiating formula (101) with e12, e13, all_0_3_3, e14 and discharging atoms op1(e12, e13) = all_0_3_3, op1(e12, e13) = e14, yields:
% 16.35/4.39 | (549) all_0_3_3 = e14
% 16.35/4.39 |
% 16.35/4.39 | Equations (549) can reduce 566 to:
% 16.35/4.39 | (201) $false
% 16.35/4.39 |
% 16.35/4.39 |-The branch is then unsatisfiable
% 16.35/4.39 |-Branch two:
% 16.35/4.39 | (234) ~ (all_0_1_1 = e13)
% 16.35/4.39 | (235) all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11
% 16.35/4.39 |
% 16.35/4.39 +-Applying beta-rule and splitting (358), into two cases.
% 16.35/4.39 |-Branch one:
% 16.35/4.39 | (414) all_0_6_6 = e23
% 16.35/4.39 |
% 16.35/4.39 | From (414) and (36) follows:
% 16.35/4.39 | (415) j(e23) = e13
% 16.35/4.39 |
% 16.35/4.39 | Instantiating formula (99) with e23, e13, all_0_1_1 and discharging atoms j(e23) = all_0_1_1, j(e23) = e13, yields:
% 16.35/4.39 | (222) all_0_1_1 = e13
% 16.35/4.39 |
% 16.35/4.39 | Equations (222) can reduce 234 to:
% 16.35/4.39 | (201) $false
% 16.35/4.39 |
% 16.35/4.39 |-The branch is then unsatisfiable
% 16.35/4.39 |-Branch two:
% 16.35/4.39 | (418) ~ (all_0_6_6 = e23)
% 16.35/4.39 | (419) all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21
% 16.35/4.39 |
% 16.35/4.39 +-Applying beta-rule and splitting (352), into two cases.
% 16.35/4.39 |-Branch one:
% 16.35/4.39 | (408) all_0_5_5 = e23
% 16.35/4.39 |
% 16.35/4.39 | From (408) and (149) follows:
% 16.35/4.39 | (409) j(e23) = e14
% 16.35/4.39 |
% 16.35/4.39 | Instantiating formula (99) with e23, e14, all_0_1_1 and discharging atoms j(e23) = all_0_1_1, j(e23) = e14, yields:
% 16.35/4.39 | (198) all_0_1_1 = e14
% 16.35/4.39 |
% 16.35/4.39 | Equations (198) can reduce 202 to:
% 16.35/4.39 | (201) $false
% 16.35/4.39 |
% 16.35/4.39 |-The branch is then unsatisfiable
% 16.35/4.39 |-Branch two:
% 16.35/4.39 | (412) ~ (all_0_5_5 = e23)
% 16.35/4.39 | (413) all_0_5_5 = e22 | all_0_5_5 = e20 | all_0_5_5 = e21
% 16.35/4.39 |
% 16.35/4.39 +-Applying beta-rule and splitting (215), into two cases.
% 16.35/4.39 |-Branch one:
% 16.35/4.39 | (251) all_0_8_8 = e23
% 16.35/4.39 |
% 16.35/4.39 | From (251) and (490) follows:
% 16.35/4.39 | (267) op2(e23, e24) = all_0_6_6
% 16.35/4.39 |
% 16.35/4.39 | From (251) and (529) follows:
% 16.35/4.39 | (458) op2(e24, e23) = all_0_9_9
% 16.35/4.39 |
% 16.35/4.39 | From (251) and (530) follows:
% 16.35/4.39 | (457) op2(e24, all_0_9_9) = e23
% 16.35/4.39 |
% 16.35/4.39 | Instantiating formula (47) with e24, e23, all_0_9_9, e21 and discharging atoms op2(e24, e23) = all_0_9_9, op2(e24, e23) = e21, yields:
% 16.35/4.39 | (460) all_0_9_9 = e21
% 16.35/4.39 |
% 16.35/4.39 | Instantiating formula (47) with e23, e24, all_0_6_6, e22 and discharging atoms op2(e23, e24) = all_0_6_6, op2(e23, e24) = e22, yields:
% 16.35/4.39 | (271) all_0_6_6 = e22
% 16.35/4.39 |
% 16.35/4.39 | From (271)(460) and (528) follows:
% 16.35/4.39 | (242) op2(e22, e24) = e21
% 16.35/4.39 |
% 16.35/4.39 | From (460) and (457) follows:
% 16.35/4.39 | (243) op2(e24, e21) = e23
% 16.35/4.39 |
% 16.35/4.39 | Instantiating formula (47) with e24, e21, e23, e22 and discharging atoms op2(e24, e21) = e23, op2(e24, e21) = e22, yields:
% 16.35/4.39 | (244) e23 = e22
% 16.35/4.39 |
% 16.35/4.39 | Instantiating formula (47) with e22, e24, e21, e23 and discharging atoms op2(e22, e24) = e23, op2(e22, e24) = e21, yields:
% 16.35/4.39 | (245) e23 = e21
% 16.35/4.39 |
% 16.35/4.40 | Combining equations (244,245) yields a new equation:
% 16.35/4.40 | (246) e22 = e21
% 16.35/4.40 |
% 16.35/4.40 | Simplifying 246 yields:
% 16.35/4.40 | (247) e22 = e21
% 16.35/4.40 |
% 16.35/4.40 | Equations (247) can reduce 59 to:
% 16.35/4.40 | (201) $false
% 16.35/4.40 |
% 16.35/4.40 |-The branch is then unsatisfiable
% 16.35/4.40 |-Branch two:
% 16.35/4.40 | (264) ~ (all_0_8_8 = e23)
% 16.35/4.40 | (265) all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 16.35/4.40 |
% 16.35/4.40 +-Applying beta-rule and splitting (250), into two cases.
% 16.35/4.40 |-Branch one:
% 16.35/4.40 | (256) all_0_9_9 = e22
% 16.35/4.40 |
% 16.35/4.40 | From (256) and (532) follows:
% 16.35/4.40 | (629) op2(e22, e24) = all_0_5_5
% 16.35/4.40 |
% 16.35/4.40 | Instantiating formula (47) with e22, e24, all_0_5_5, e23 and discharging atoms op2(e22, e24) = all_0_5_5, op2(e22, e24) = e23, yields:
% 16.35/4.40 | (408) all_0_5_5 = e23
% 16.35/4.40 |
% 16.35/4.40 | Equations (408) can reduce 412 to:
% 16.35/4.40 | (201) $false
% 16.35/4.40 |
% 16.35/4.40 |-The branch is then unsatisfiable
% 16.35/4.40 |-Branch two:
% 16.35/4.40 | (632) ~ (all_0_9_9 = e22)
% 16.35/4.40 | (633) all_0_9_9 = e20 | all_0_9_9 = e21
% 16.35/4.40 |
% 16.35/4.40 +-Applying beta-rule and splitting (265), into two cases.
% 16.35/4.40 |-Branch one:
% 16.35/4.40 | (364) all_0_8_8 = e22
% 16.35/4.40 |
% 16.35/4.40 | From (364) and (490) follows:
% 16.35/4.40 | (427) op2(e22, e24) = all_0_6_6
% 16.35/4.40 |
% 16.35/4.40 | Instantiating formula (47) with e22, e24, all_0_6_6, e23 and discharging atoms op2(e22, e24) = all_0_6_6, op2(e22, e24) = e23, yields:
% 16.35/4.40 | (414) all_0_6_6 = e23
% 16.35/4.40 |
% 16.35/4.40 | Equations (414) can reduce 418 to:
% 16.35/4.40 | (201) $false
% 16.35/4.40 |
% 16.35/4.40 |-The branch is then unsatisfiable
% 16.35/4.40 |-Branch two:
% 16.35/4.40 | (638) ~ (all_0_8_8 = e22)
% 16.35/4.40 | (639) all_0_8_8 = e20 | all_0_8_8 = e21
% 16.35/4.40 |
% 16.35/4.40 +-Applying beta-rule and splitting (633), into two cases.
% 16.35/4.40 |-Branch one:
% 16.35/4.40 | (640) all_0_9_9 = e20
% 16.35/4.40 |
% 16.35/4.40 | From (640) and (530) follows:
% 16.35/4.40 | (641) op2(e24, e20) = all_0_8_8
% 16.35/4.40 |
% 16.35/4.40 | Instantiating formula (47) with e24, e20, all_0_8_8, e23 and discharging atoms op2(e24, e20) = all_0_8_8, op2(e24, e20) = e23, yields:
% 16.35/4.40 | (251) all_0_8_8 = e23
% 16.35/4.40 |
% 16.35/4.40 | Equations (251) can reduce 264 to:
% 16.35/4.40 | (201) $false
% 16.35/4.40 |
% 16.35/4.40 |-The branch is then unsatisfiable
% 16.35/4.40 |-Branch two:
% 16.35/4.40 | (644) ~ (all_0_9_9 = e20)
% 16.35/4.40 | (460) all_0_9_9 = e21
% 16.35/4.40 |
% 16.35/4.40 | From (460) and (530) follows:
% 16.35/4.40 | (646) op2(e24, e21) = all_0_8_8
% 16.35/4.40 |
% 16.35/4.40 | Instantiating formula (47) with e24, e21, all_0_8_8, e22 and discharging atoms op2(e24, e21) = all_0_8_8, op2(e24, e21) = e22, yields:
% 16.35/4.40 | (364) all_0_8_8 = e22
% 16.35/4.40 |
% 16.35/4.40 | Equations (364) can reduce 638 to:
% 16.35/4.40 | (201) $false
% 16.35/4.40 |
% 16.35/4.40 |-The branch is then unsatisfiable
% 16.35/4.40 |-Branch two:
% 16.35/4.40 | (220) ~ (all_0_7_7 = e24)
% 16.35/4.40 | (221) all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 16.35/4.40 |
% 16.35/4.40 +-Applying beta-rule and splitting (79), into two cases.
% 16.35/4.40 |-Branch one:
% 16.35/4.40 | (651) all_0_2_2 = e14
% 16.35/4.40 |
% 16.35/4.40 | From (651) and (85) follows:
% 16.35/4.40 | (652) h(e14) = e22
% 16.35/4.40 |
% 16.35/4.40 | Instantiating formula (96) with e14, e22, all_0_5_5 and discharging atoms h(e14) = all_0_5_5, h(e14) = e22, yields:
% 16.35/4.40 | (398) all_0_5_5 = e22
% 16.35/4.40 |
% 16.35/4.40 | From (398) and (116) follows:
% 16.35/4.40 | (654) op2(e22, all_0_6_6) = all_0_9_9
% 16.35/4.40 |
% 16.35/4.40 | From (398) and (38) follows:
% 16.35/4.40 | (655) op2(e22, all_0_7_7) = all_0_8_8
% 16.35/4.40 |
% 16.35/4.40 | From (398) and (80) follows:
% 16.35/4.41 | (656) op2(e22, all_0_8_8) = all_0_7_7
% 16.35/4.41 |
% 16.35/4.41 | From (398) and (10) follows:
% 16.35/4.41 | (657) op2(e22, all_0_9_9) = all_0_6_6
% 16.35/4.41 |
% 16.35/4.41 | From (398) and (172) follows:
% 16.35/4.41 | (658) op2(all_0_6_6, e22) = all_0_8_8
% 16.35/4.41 |
% 16.35/4.41 | From (398) and (125) follows:
% 16.35/4.41 | (659) op2(all_0_6_6, all_0_8_8) = e22
% 16.35/4.41 |
% 16.35/4.41 | From (398) and (92) follows:
% 16.35/4.41 | (660) op2(all_0_8_8, e22) = all_0_9_9
% 16.35/4.41 |
% 16.35/4.41 | From (398) and (120) follows:
% 16.35/4.41 | (661) op2(all_0_8_8, all_0_9_9) = e22
% 16.35/4.41 |
% 16.35/4.41 | From (398) and (156) follows:
% 16.35/4.41 | (662) op2(all_0_9_9, e22) = all_0_7_7
% 16.35/4.41 |
% 16.35/4.41 +-Applying beta-rule and splitting (112), into two cases.
% 16.35/4.41 |-Branch one:
% 16.35/4.41 | (353) all_0_6_6 = e24
% 16.35/4.41 |
% 16.35/4.41 | From (353) and (659) follows:
% 16.35/4.41 | (664) op2(e24, all_0_8_8) = e22
% 16.35/4.41 |
% 16.35/4.41 | From (353) and (658) follows:
% 16.35/4.41 | (665) op2(e24, e22) = all_0_8_8
% 16.35/4.41 |
% 16.35/4.41 | From (353) and (654) follows:
% 16.35/4.41 | (666) op2(e22, e24) = all_0_9_9
% 16.35/4.41 |
% 16.35/4.41 | From (353) and (657) follows:
% 16.35/4.41 | (667) op2(e22, all_0_9_9) = e24
% 16.35/4.41 |
% 16.35/4.41 | Instantiating formula (47) with e24, e22, all_0_8_8, e20 and discharging atoms op2(e24, e22) = all_0_8_8, op2(e24, e22) = e20, yields:
% 16.35/4.41 | (668) all_0_8_8 = e20
% 16.35/4.41 |
% 16.35/4.41 | Instantiating formula (47) with e22, e24, all_0_9_9, e23 and discharging atoms op2(e22, e24) = all_0_9_9, op2(e22, e24) = e23, yields:
% 16.35/4.41 | (236) all_0_9_9 = e23
% 16.35/4.41 |
% 16.35/4.41 | From (668)(236) and (660) follows:
% 16.35/4.41 | (670) op2(e20, e22) = e23
% 16.35/4.41 |
% 16.35/4.41 | From (668) and (664) follows:
% 16.35/4.41 | (671) op2(e24, e20) = e22
% 16.35/4.41 |
% 16.35/4.41 | From (236) and (667) follows:
% 16.35/4.41 | (672) op2(e22, e23) = e24
% 16.35/4.41 |
% 16.35/4.41 | Instantiating formula (47) with e24, e20, e22, e23 and discharging atoms op2(e24, e20) = e23, op2(e24, e20) = e22, yields:
% 16.35/4.41 | (244) e23 = e22
% 16.35/4.41 |
% 16.35/4.41 | Instantiating formula (47) with e22, e23, e24, e20 and discharging atoms op2(e22, e23) = e24, op2(e22, e23) = e20, yields:
% 16.35/4.41 | (674) e24 = e20
% 16.35/4.41 |
% 16.35/4.41 | Instantiating formula (47) with e20, e22, e23, e24 and discharging atoms op2(e20, e22) = e24, op2(e20, e22) = e23, yields:
% 16.35/4.41 | (200) e24 = e23
% 16.35/4.41 |
% 16.35/4.41 | Combining equations (200,674) yields a new equation:
% 16.35/4.41 | (676) e23 = e20
% 16.35/4.41 |
% 16.35/4.41 | Simplifying 676 yields:
% 16.35/4.41 | (677) e23 = e20
% 16.35/4.41 |
% 16.35/4.41 | Combining equations (677,244) yields a new equation:
% 16.35/4.41 | (678) e22 = e20
% 16.35/4.41 |
% 16.35/4.41 | Equations (678) can reduce 153 to:
% 16.35/4.41 | (201) $false
% 16.35/4.41 |
% 16.35/4.41 |-The branch is then unsatisfiable
% 16.35/4.41 |-Branch two:
% 16.35/4.41 | (357) ~ (all_0_6_6 = e24)
% 16.35/4.41 | (358) all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21
% 16.35/4.41 |
% 16.35/4.41 +-Applying beta-rule and splitting (128), into two cases.
% 16.35/4.41 |-Branch one:
% 16.35/4.41 | (210) all_0_8_8 = e24
% 16.35/4.41 |
% 16.35/4.41 | From (210) and (661) follows:
% 16.35/4.41 | (683) op2(e24, all_0_9_9) = e22
% 16.35/4.41 |
% 16.35/4.41 | From (210) and (660) follows:
% 16.35/4.41 | (684) op2(e24, e22) = all_0_9_9
% 16.35/4.41 |
% 16.35/4.41 | From (210) and (655) follows:
% 16.35/4.42 | (685) op2(e22, all_0_7_7) = e24
% 16.35/4.42 |
% 16.35/4.42 | From (210) and (656) follows:
% 16.35/4.42 | (686) op2(e22, e24) = all_0_7_7
% 16.35/4.42 |
% 16.35/4.42 | Instantiating formula (47) with e24, e22, all_0_9_9, e20 and discharging atoms op2(e24, e22) = all_0_9_9, op2(e24, e22) = e20, yields:
% 16.35/4.42 | (640) all_0_9_9 = e20
% 16.35/4.42 |
% 16.35/4.42 | Instantiating formula (47) with e22, e24, all_0_7_7, e23 and discharging atoms op2(e22, e24) = all_0_7_7, op2(e22, e24) = e23, yields:
% 16.35/4.42 | (266) all_0_7_7 = e23
% 16.35/4.42 |
% 16.35/4.42 | From (640)(266) and (662) follows:
% 16.35/4.42 | (670) op2(e20, e22) = e23
% 16.35/4.42 |
% 16.35/4.42 | From (640) and (683) follows:
% 16.35/4.42 | (671) op2(e24, e20) = e22
% 16.35/4.42 |
% 16.35/4.42 | From (266) and (685) follows:
% 16.35/4.42 | (672) op2(e22, e23) = e24
% 16.35/4.42 |
% 16.35/4.42 | Instantiating formula (47) with e24, e20, e22, e23 and discharging atoms op2(e24, e20) = e23, op2(e24, e20) = e22, yields:
% 16.35/4.42 | (244) e23 = e22
% 16.35/4.42 |
% 16.35/4.42 | Instantiating formula (47) with e22, e23, e24, e20 and discharging atoms op2(e22, e23) = e24, op2(e22, e23) = e20, yields:
% 16.35/4.42 | (674) e24 = e20
% 16.35/4.42 |
% 16.35/4.42 | Instantiating formula (47) with e20, e22, e23, e24 and discharging atoms op2(e20, e22) = e24, op2(e20, e22) = e23, yields:
% 16.35/4.42 | (200) e24 = e23
% 16.35/4.42 |
% 16.35/4.42 | Combining equations (200,674) yields a new equation:
% 16.35/4.42 | (676) e23 = e20
% 16.35/4.42 |
% 16.35/4.42 | Simplifying 676 yields:
% 16.35/4.42 | (677) e23 = e20
% 16.35/4.42 |
% 16.35/4.42 | Combining equations (677,244) yields a new equation:
% 16.35/4.42 | (678) e22 = e20
% 16.35/4.42 |
% 16.35/4.42 | Equations (678) can reduce 153 to:
% 16.35/4.42 | (201) $false
% 16.35/4.42 |
% 16.35/4.42 |-The branch is then unsatisfiable
% 16.35/4.42 |-Branch two:
% 16.35/4.42 | (214) ~ (all_0_8_8 = e24)
% 16.35/4.42 | (215) all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 16.35/4.42 |
% 16.35/4.42 +-Applying beta-rule and splitting (296), into two cases.
% 16.35/4.42 |-Branch one:
% 16.35/4.42 | (503) all_0_0_0 = e13
% 16.35/4.42 |
% 16.35/4.42 | From (503) and (18) follows:
% 16.35/4.42 | (504) h(e13) = e24
% 16.35/4.42 |
% 16.35/4.42 | Instantiating formula (96) with e13, e24, all_0_6_6 and discharging atoms h(e13) = all_0_6_6, h(e13) = e24, yields:
% 16.35/4.42 | (353) all_0_6_6 = e24
% 16.35/4.42 |
% 16.35/4.42 | Equations (353) can reduce 357 to:
% 16.35/4.42 | (201) $false
% 16.35/4.42 |
% 16.35/4.42 |-The branch is then unsatisfiable
% 16.35/4.42 |-Branch two:
% 16.35/4.42 | (507) ~ (all_0_0_0 = e13)
% 16.35/4.42 | (508) all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 16.35/4.42 |
% 16.35/4.42 +-Applying beta-rule and splitting (508), into two cases.
% 16.35/4.42 |-Branch one:
% 16.35/4.42 | (509) all_0_0_0 = e12
% 16.35/4.42 |
% 16.35/4.42 | From (509) and (18) follows:
% 16.35/4.42 | (510) h(e12) = e24
% 16.35/4.42 |
% 16.35/4.42 | Instantiating formula (96) with e12, e24, all_0_7_7 and discharging atoms h(e12) = all_0_7_7, h(e12) = e24, yields:
% 16.35/4.42 | (216) all_0_7_7 = e24
% 16.35/4.42 |
% 16.35/4.42 | Equations (216) can reduce 220 to:
% 16.35/4.42 | (201) $false
% 16.35/4.42 |
% 16.35/4.42 |-The branch is then unsatisfiable
% 16.35/4.42 |-Branch two:
% 16.35/4.42 | (513) ~ (all_0_0_0 = e12)
% 16.35/4.42 | (514) all_0_0_0 = e10 | all_0_0_0 = e11
% 16.35/4.42 |
% 16.35/4.42 +-Applying beta-rule and splitting (514), into two cases.
% 16.35/4.42 |-Branch one:
% 16.35/4.42 | (306) all_0_0_0 = e10
% 16.35/4.42 |
% 16.35/4.42 | From (306) and (18) follows:
% 16.35/4.42 | (516) h(e10) = e24
% 16.35/4.42 |
% 16.35/4.42 | Instantiating formula (96) with e10, e24, all_0_9_9 and discharging atoms h(e10) = all_0_9_9, h(e10) = e24, yields:
% 16.35/4.42 | (204) all_0_9_9 = e24
% 16.35/4.42 |
% 16.35/4.42 | Equations (204) can reduce 208 to:
% 16.35/4.42 | (201) $false
% 16.35/4.42 |
% 16.35/4.42 |-The branch is then unsatisfiable
% 16.35/4.42 |-Branch two:
% 16.35/4.42 | (519) ~ (all_0_0_0 = e10)
% 16.35/4.42 | (520) all_0_0_0 = e11
% 16.35/4.42 |
% 16.35/4.42 | From (520) and (18) follows:
% 16.35/4.42 | (521) h(e11) = e24
% 16.35/4.42 |
% 16.35/4.42 | Instantiating formula (96) with e11, e24, all_0_8_8 and discharging atoms h(e11) = all_0_8_8, h(e11) = e24, yields:
% 16.35/4.42 | (210) all_0_8_8 = e24
% 16.35/4.42 |
% 16.35/4.42 | Equations (210) can reduce 214 to:
% 16.35/4.43 | (201) $false
% 16.35/4.43 |
% 16.35/4.43 |-The branch is then unsatisfiable
% 16.35/4.43 |-Branch two:
% 16.35/4.43 | (722) ~ (all_0_2_2 = e14)
% 16.35/4.43 | (723) all_0_2_2 = e13 | all_0_2_2 = e12 | all_0_2_2 = e10 | all_0_2_2 = e11
% 16.35/4.43 |
% 16.35/4.43 +-Applying beta-rule and splitting (112), into two cases.
% 16.35/4.43 |-Branch one:
% 16.35/4.43 | (353) all_0_6_6 = e24
% 16.35/4.43 |
% 16.35/4.43 | From (353) and (116) follows:
% 16.35/4.43 | (725) op2(all_0_5_5, e24) = all_0_9_9
% 16.35/4.43 |
% 16.35/4.43 | From (353) and (172) follows:
% 16.35/4.43 | (726) op2(e24, all_0_5_5) = all_0_8_8
% 16.35/4.43 |
% 16.35/4.43 | From (353) and (15) follows:
% 16.35/4.43 | (727) op2(e24, all_0_7_7) = all_0_9_9
% 16.35/4.43 |
% 16.35/4.43 | From (353) and (125) follows:
% 16.65/4.43 | (728) op2(e24, all_0_8_8) = all_0_5_5
% 16.65/4.43 |
% 16.65/4.43 | From (353) and (35) follows:
% 16.65/4.43 | (729) op2(e24, all_0_9_9) = all_0_7_7
% 16.65/4.43 |
% 16.65/4.43 | From (353) and (142) follows:
% 16.65/4.43 | (730) op2(all_0_7_7, e24) = all_0_5_5
% 16.65/4.43 |
% 16.65/4.43 | From (353) and (32) follows:
% 16.65/4.43 | (731) op2(all_0_8_8, e24) = all_0_7_7
% 16.65/4.43 |
% 16.65/4.43 | From (353) and (13) follows:
% 16.65/4.43 | (474) op2(all_0_9_9, e24) = all_0_8_8
% 16.65/4.43 |
% 16.65/4.43 | From (353) and (36) follows:
% 16.65/4.43 | (354) j(e24) = e13
% 16.65/4.43 |
% 16.65/4.43 | Instantiating formula (99) with e24, e13, all_0_0_0 and discharging atoms j(e24) = all_0_0_0, j(e24) = e13, yields:
% 16.65/4.43 | (503) all_0_0_0 = e13
% 16.65/4.43 |
% 16.65/4.43 | Equations (503) can reduce 295 to:
% 16.65/4.43 | (735) ~ (e14 = e13)
% 16.65/4.43 |
% 16.65/4.43 | Simplifying 735 yields:
% 16.65/4.43 | (88) ~ (e14 = e13)
% 16.65/4.43 |
% 16.65/4.43 | From (503) and (141) follows:
% 16.65/4.43 | (354) j(e24) = e13
% 16.65/4.43 |
% 16.65/4.43 +-Applying beta-rule and splitting (51), into two cases.
% 16.65/4.43 |-Branch one:
% 16.65/4.43 | (187) all_0_5_5 = e24
% 16.65/4.43 |
% 16.65/4.43 | From (187) and (149) follows:
% 16.65/4.43 | (197) j(e24) = e14
% 16.65/4.43 |
% 16.65/4.43 | Instantiating formula (99) with e24, e14, e13 and discharging atoms j(e24) = e14, j(e24) = e13, yields:
% 16.65/4.43 | (333) e14 = e13
% 16.65/4.43 |
% 16.65/4.43 | Equations (333) can reduce 88 to:
% 16.65/4.43 | (201) $false
% 16.65/4.43 |
% 16.65/4.43 |-The branch is then unsatisfiable
% 16.65/4.43 |-Branch two:
% 16.65/4.43 | (351) ~ (all_0_5_5 = e24)
% 16.65/4.43 | (352) all_0_5_5 = e23 | all_0_5_5 = e22 | all_0_5_5 = e20 | all_0_5_5 = e21
% 16.65/4.43 |
% 16.65/4.43 +-Applying beta-rule and splitting (128), into two cases.
% 16.65/4.43 |-Branch one:
% 16.65/4.43 | (210) all_0_8_8 = e24
% 16.65/4.43 |
% 16.65/4.43 | From (210) and (28) follows:
% 16.65/4.43 | (211) j(e24) = e11
% 16.65/4.43 |
% 16.65/4.43 | Instantiating formula (99) with e24, e11, e13 and discharging atoms j(e24) = e13, j(e24) = e11, yields:
% 16.65/4.43 | (230) e13 = e11
% 16.65/4.43 |
% 16.65/4.43 | Equations (230) can reduce 179 to:
% 16.65/4.43 | (201) $false
% 16.65/4.43 |
% 16.65/4.43 |-The branch is then unsatisfiable
% 16.65/4.43 |-Branch two:
% 16.65/4.43 | (214) ~ (all_0_8_8 = e24)
% 16.65/4.43 | (215) all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 16.65/4.43 |
% 16.65/4.43 +-Applying beta-rule and splitting (209), into two cases.
% 16.65/4.43 |-Branch one:
% 16.65/4.43 | (236) all_0_9_9 = e23
% 16.65/4.43 |
% 16.65/4.43 | From (236) and (474) follows:
% 16.65/4.43 | (360) op2(e23, e24) = all_0_8_8
% 16.65/4.43 |
% 16.65/4.43 | From (236) and (727) follows:
% 16.65/4.43 | (253) op2(e24, all_0_7_7) = e23
% 16.65/4.43 |
% 16.65/4.43 | From (236) and (729) follows:
% 16.65/4.43 | (254) op2(e24, e23) = all_0_7_7
% 16.65/4.43 |
% 16.65/4.43 | Instantiating formula (47) with e24, e23, all_0_7_7, e21 and discharging atoms op2(e24, e23) = all_0_7_7, op2(e24, e23) = e21, yields:
% 16.65/4.43 | (255) all_0_7_7 = e21
% 16.65/4.43 |
% 16.65/4.43 | Instantiating formula (47) with e23, e24, all_0_8_8, e22 and discharging atoms op2(e23, e24) = all_0_8_8, op2(e23, e24) = e22, yields:
% 16.65/4.44 | (364) all_0_8_8 = e22
% 16.65/4.44 |
% 16.65/4.44 | From (364)(255) and (731) follows:
% 16.65/4.44 | (242) op2(e22, e24) = e21
% 16.65/4.44 |
% 16.65/4.44 | From (255) and (253) follows:
% 16.65/4.44 | (243) op2(e24, e21) = e23
% 16.65/4.44 |
% 16.65/4.44 | Instantiating formula (47) with e24, e21, e23, e22 and discharging atoms op2(e24, e21) = e23, op2(e24, e21) = e22, yields:
% 16.65/4.44 | (244) e23 = e22
% 16.65/4.44 |
% 16.65/4.44 | Instantiating formula (47) with e22, e24, e21, e23 and discharging atoms op2(e22, e24) = e23, op2(e22, e24) = e21, yields:
% 16.65/4.44 | (245) e23 = e21
% 16.65/4.44 |
% 16.65/4.44 | Combining equations (244,245) yields a new equation:
% 16.65/4.44 | (246) e22 = e21
% 16.65/4.44 |
% 16.65/4.44 | Simplifying 246 yields:
% 16.65/4.44 | (247) e22 = e21
% 16.65/4.44 |
% 16.65/4.44 | Equations (247) can reduce 59 to:
% 16.65/4.44 | (201) $false
% 16.65/4.44 |
% 16.65/4.44 |-The branch is then unsatisfiable
% 16.65/4.44 |-Branch two:
% 16.65/4.44 | (249) ~ (all_0_9_9 = e23)
% 16.65/4.44 | (250) all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21
% 16.65/4.44 |
% 16.65/4.44 +-Applying beta-rule and splitting (221), into two cases.
% 16.65/4.44 |-Branch one:
% 16.65/4.44 | (266) all_0_7_7 = e23
% 16.65/4.44 |
% 16.65/4.44 | From (266) and (730) follows:
% 16.65/4.44 | (394) op2(e23, e24) = all_0_5_5
% 16.65/4.44 |
% 16.65/4.44 | From (266) and (727) follows:
% 16.65/4.44 | (458) op2(e24, e23) = all_0_9_9
% 16.65/4.44 |
% 16.65/4.44 | From (266) and (729) follows:
% 16.65/4.44 | (457) op2(e24, all_0_9_9) = e23
% 16.65/4.44 |
% 16.65/4.44 | Instantiating formula (47) with e24, e23, all_0_9_9, e21 and discharging atoms op2(e24, e23) = all_0_9_9, op2(e24, e23) = e21, yields:
% 16.65/4.44 | (460) all_0_9_9 = e21
% 16.65/4.44 |
% 16.65/4.44 | Instantiating formula (47) with e23, e24, all_0_5_5, e22 and discharging atoms op2(e23, e24) = all_0_5_5, op2(e23, e24) = e22, yields:
% 16.65/4.44 | (398) all_0_5_5 = e22
% 16.65/4.44 |
% 16.65/4.44 | From (398)(460) and (725) follows:
% 16.65/4.44 | (242) op2(e22, e24) = e21
% 16.65/4.44 |
% 16.65/4.44 | From (460) and (457) follows:
% 16.65/4.44 | (243) op2(e24, e21) = e23
% 16.65/4.44 |
% 16.65/4.44 | Instantiating formula (47) with e24, e21, e23, e22 and discharging atoms op2(e24, e21) = e23, op2(e24, e21) = e22, yields:
% 16.65/4.44 | (244) e23 = e22
% 16.65/4.44 |
% 16.65/4.44 | Instantiating formula (47) with e22, e24, e21, e23 and discharging atoms op2(e22, e24) = e23, op2(e22, e24) = e21, yields:
% 16.65/4.44 | (245) e23 = e21
% 16.65/4.44 |
% 16.65/4.44 | Combining equations (244,245) yields a new equation:
% 16.65/4.44 | (246) e22 = e21
% 16.65/4.44 |
% 16.65/4.44 | Simplifying 246 yields:
% 16.65/4.44 | (247) e22 = e21
% 16.65/4.44 |
% 16.65/4.44 | Equations (247) can reduce 59 to:
% 16.65/4.44 | (201) $false
% 16.65/4.44 |
% 16.65/4.44 |-The branch is then unsatisfiable
% 16.65/4.44 |-Branch two:
% 16.65/4.44 | (278) ~ (all_0_7_7 = e23)
% 16.65/4.44 | (279) all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 16.65/4.44 |
% 16.65/4.44 +-Applying beta-rule and splitting (352), into two cases.
% 16.65/4.44 |-Branch one:
% 16.65/4.44 | (408) all_0_5_5 = e23
% 16.65/4.44 |
% 16.65/4.44 | From (408) and (149) follows:
% 16.65/4.44 | (409) j(e23) = e14
% 16.65/4.44 |
% 16.65/4.44 | Instantiating formula (99) with e23, e14, all_0_1_1 and discharging atoms j(e23) = all_0_1_1, j(e23) = e14, yields:
% 16.65/4.44 | (198) all_0_1_1 = e14
% 16.65/4.44 |
% 16.65/4.44 | Equations (198) can reduce 202 to:
% 16.65/4.44 | (201) $false
% 16.65/4.44 |
% 16.65/4.44 |-The branch is then unsatisfiable
% 16.65/4.44 |-Branch two:
% 16.65/4.44 | (412) ~ (all_0_5_5 = e23)
% 16.65/4.44 | (413) all_0_5_5 = e22 | all_0_5_5 = e20 | all_0_5_5 = e21
% 16.65/4.44 |
% 16.65/4.44 +-Applying beta-rule and splitting (215), into two cases.
% 16.65/4.44 |-Branch one:
% 16.65/4.44 | (251) all_0_8_8 = e23
% 16.65/4.44 |
% 16.65/4.44 | From (251) and (731) follows:
% 16.65/4.44 | (237) op2(e23, e24) = all_0_7_7
% 16.65/4.44 |
% 16.65/4.44 | From (251) and (726) follows:
% 16.65/4.44 | (361) op2(e24, all_0_5_5) = e23
% 16.65/4.44 |
% 16.65/4.44 | From (251) and (728) follows:
% 16.65/4.44 | (362) op2(e24, e23) = all_0_5_5
% 16.65/4.44 |
% 16.65/4.44 | Instantiating formula (47) with e24, e23, all_0_5_5, e21 and discharging atoms op2(e24, e23) = all_0_5_5, op2(e24, e23) = e21, yields:
% 16.65/4.44 | (363) all_0_5_5 = e21
% 16.65/4.44 |
% 16.65/4.44 | Instantiating formula (47) with e23, e24, all_0_7_7, e22 and discharging atoms op2(e23, e24) = all_0_7_7, op2(e23, e24) = e22, yields:
% 16.65/4.44 | (241) all_0_7_7 = e22
% 16.65/4.44 |
% 16.65/4.44 | From (241)(363) and (730) follows:
% 16.65/4.44 | (242) op2(e22, e24) = e21
% 16.65/4.44 |
% 16.65/4.44 | From (363) and (361) follows:
% 16.65/4.44 | (243) op2(e24, e21) = e23
% 16.65/4.44 |
% 16.65/4.44 | Instantiating formula (47) with e24, e21, e23, e22 and discharging atoms op2(e24, e21) = e23, op2(e24, e21) = e22, yields:
% 16.65/4.44 | (244) e23 = e22
% 16.65/4.44 |
% 16.65/4.44 | Instantiating formula (47) with e22, e24, e21, e23 and discharging atoms op2(e22, e24) = e23, op2(e22, e24) = e21, yields:
% 16.65/4.45 | (245) e23 = e21
% 16.65/4.45 |
% 16.65/4.45 | Combining equations (245,244) yields a new equation:
% 16.65/4.45 | (247) e22 = e21
% 16.65/4.45 |
% 16.65/4.45 | Equations (247) can reduce 59 to:
% 16.65/4.45 | (201) $false
% 16.65/4.45 |
% 16.65/4.45 |-The branch is then unsatisfiable
% 16.65/4.45 |-Branch two:
% 16.65/4.45 | (264) ~ (all_0_8_8 = e23)
% 16.65/4.45 | (265) all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 16.65/4.45 |
% 16.65/4.45 +-Applying beta-rule and splitting (250), into two cases.
% 16.65/4.45 |-Branch one:
% 16.65/4.45 | (256) all_0_9_9 = e22
% 16.65/4.45 |
% 16.65/4.45 | From (256) and (474) follows:
% 16.65/4.45 | (421) op2(e22, e24) = all_0_8_8
% 16.65/4.45 |
% 16.65/4.45 | Instantiating formula (47) with e22, e24, all_0_8_8, e23 and discharging atoms op2(e22, e24) = all_0_8_8, op2(e22, e24) = e23, yields:
% 16.65/4.45 | (251) all_0_8_8 = e23
% 16.65/4.45 |
% 16.65/4.45 | Equations (251) can reduce 264 to:
% 16.65/4.45 | (201) $false
% 16.65/4.45 |
% 16.65/4.45 |-The branch is then unsatisfiable
% 16.65/4.45 |-Branch two:
% 16.65/4.45 | (632) ~ (all_0_9_9 = e22)
% 16.65/4.45 | (633) all_0_9_9 = e20 | all_0_9_9 = e21
% 16.65/4.45 |
% 16.65/4.45 +-Applying beta-rule and splitting (279), into two cases.
% 16.65/4.45 |-Branch one:
% 16.65/4.45 | (241) all_0_7_7 = e22
% 16.65/4.45 |
% 16.65/4.45 | From (241) and (730) follows:
% 16.65/4.45 | (629) op2(e22, e24) = all_0_5_5
% 16.65/4.45 |
% 16.65/4.45 | Instantiating formula (47) with e22, e24, all_0_5_5, e23 and discharging atoms op2(e22, e24) = all_0_5_5, op2(e22, e24) = e23, yields:
% 16.65/4.45 | (408) all_0_5_5 = e23
% 16.65/4.45 |
% 16.65/4.45 | Equations (408) can reduce 412 to:
% 16.65/4.45 | (201) $false
% 16.65/4.45 |
% 16.65/4.45 |-The branch is then unsatisfiable
% 16.65/4.45 |-Branch two:
% 16.65/4.45 | (424) ~ (all_0_7_7 = e22)
% 16.65/4.45 | (425) all_0_7_7 = e20 | all_0_7_7 = e21
% 16.65/4.45 |
% 16.65/4.45 +-Applying beta-rule and splitting (633), into two cases.
% 16.65/4.45 |-Branch one:
% 16.65/4.45 | (640) all_0_9_9 = e20
% 16.65/4.45 |
% 16.65/4.45 | From (640) and (729) follows:
% 16.65/4.45 | (813) op2(e24, e20) = all_0_7_7
% 16.65/4.45 |
% 16.65/4.45 | Instantiating formula (47) with e24, e20, all_0_7_7, e23 and discharging atoms op2(e24, e20) = all_0_7_7, op2(e24, e20) = e23, yields:
% 16.65/4.45 | (266) all_0_7_7 = e23
% 16.65/4.45 |
% 16.65/4.45 | Equations (266) can reduce 278 to:
% 16.65/4.45 | (201) $false
% 16.65/4.45 |
% 16.65/4.45 |-The branch is then unsatisfiable
% 16.65/4.45 |-Branch two:
% 16.65/4.45 | (644) ~ (all_0_9_9 = e20)
% 16.65/4.45 | (460) all_0_9_9 = e21
% 16.65/4.45 |
% 16.65/4.45 | From (460) and (729) follows:
% 16.65/4.45 | (818) op2(e24, e21) = all_0_7_7
% 16.65/4.45 |
% 16.65/4.45 | Instantiating formula (47) with e24, e21, all_0_7_7, e22 and discharging atoms op2(e24, e21) = all_0_7_7, op2(e24, e21) = e22, yields:
% 16.65/4.45 | (241) all_0_7_7 = e22
% 16.65/4.45 |
% 16.65/4.45 | Equations (241) can reduce 424 to:
% 16.65/4.45 | (201) $false
% 16.65/4.45 |
% 16.65/4.45 |-The branch is then unsatisfiable
% 16.65/4.45 |-Branch two:
% 16.65/4.45 | (357) ~ (all_0_6_6 = e24)
% 16.65/4.45 | (358) all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21
% 16.65/4.45 |
% 16.65/4.45 +-Applying beta-rule and splitting (51), into two cases.
% 16.65/4.45 |-Branch one:
% 16.65/4.45 | (187) all_0_5_5 = e24
% 16.65/4.45 |
% 16.65/4.45 | From (187) and (149) follows:
% 16.65/4.45 | (197) j(e24) = e14
% 16.65/4.45 |
% 16.65/4.45 | Instantiating formula (99) with e24, e14, all_0_0_0 and discharging atoms j(e24) = all_0_0_0, j(e24) = e14, yields:
% 16.65/4.45 | (181) all_0_0_0 = e14
% 16.65/4.45 |
% 16.65/4.45 | Equations (181) can reduce 295 to:
% 16.65/4.45 | (201) $false
% 16.65/4.45 |
% 16.65/4.45 |-The branch is then unsatisfiable
% 16.65/4.45 |-Branch two:
% 16.65/4.45 | (351) ~ (all_0_5_5 = e24)
% 16.65/4.45 | (352) all_0_5_5 = e23 | all_0_5_5 = e22 | all_0_5_5 = e20 | all_0_5_5 = e21
% 16.65/4.45 |
% 16.65/4.45 +-Applying beta-rule and splitting (128), into two cases.
% 16.65/4.45 |-Branch one:
% 16.65/4.45 | (210) all_0_8_8 = e24
% 16.65/4.45 |
% 16.65/4.45 | From (210) and (80) follows:
% 16.65/4.45 | (830) op2(all_0_5_5, e24) = all_0_7_7
% 16.65/4.45 |
% 16.65/4.45 | From (210) and (125) follows:
% 16.65/4.45 | (831) op2(all_0_6_6, e24) = all_0_5_5
% 16.65/4.45 |
% 16.65/4.45 | From (210) and (5) follows:
% 16.65/4.45 | (456) op2(all_0_7_7, e24) = all_0_9_9
% 16.65/4.45 |
% 16.65/4.45 | From (210) and (92) follows:
% 16.65/4.46 | (833) op2(e24, all_0_5_5) = all_0_9_9
% 16.65/4.46 |
% 16.65/4.46 | From (210) and (32) follows:
% 16.65/4.46 | (834) op2(e24, all_0_6_6) = all_0_7_7
% 16.65/4.46 |
% 16.65/4.46 | From (210) and (30) follows:
% 16.65/4.46 | (835) op2(e24, all_0_7_7) = all_0_6_6
% 16.65/4.46 |
% 16.65/4.46 | From (210) and (120) follows:
% 16.65/4.46 | (836) op2(e24, all_0_9_9) = all_0_5_5
% 16.65/4.46 |
% 16.65/4.46 | From (210) and (180) follows:
% 16.65/4.46 | (837) op2(all_0_9_9, e24) = all_0_6_6
% 16.65/4.46 |
% 16.65/4.46 | From (210) and (28) follows:
% 16.65/4.46 | (211) j(e24) = e11
% 16.65/4.46 |
% 16.65/4.46 | Instantiating formula (99) with e24, e11, all_0_0_0 and discharging atoms j(e24) = all_0_0_0, j(e24) = e11, yields:
% 16.65/4.46 | (520) all_0_0_0 = e11
% 16.65/4.46 |
% 16.65/4.46 | From (520) and (81) follows:
% 16.65/4.46 | (840) op1(all_0_1_1, e11) = all_0_2_2
% 16.65/4.46 |
% 16.65/4.46 +-Applying beta-rule and splitting (209), into two cases.
% 16.65/4.46 |-Branch one:
% 16.65/4.46 | (236) all_0_9_9 = e23
% 16.65/4.46 |
% 16.65/4.46 | From (236) and (837) follows:
% 16.65/4.46 | (267) op2(e23, e24) = all_0_6_6
% 16.65/4.46 |
% 16.65/4.46 | From (236) and (833) follows:
% 16.65/4.46 | (361) op2(e24, all_0_5_5) = e23
% 16.65/4.46 |
% 16.65/4.46 | From (236) and (836) follows:
% 16.65/4.46 | (362) op2(e24, e23) = all_0_5_5
% 16.65/4.46 |
% 16.65/4.46 | Instantiating formula (47) with e24, e23, all_0_5_5, e21 and discharging atoms op2(e24, e23) = all_0_5_5, op2(e24, e23) = e21, yields:
% 16.65/4.46 | (363) all_0_5_5 = e21
% 16.65/4.46 |
% 16.65/4.46 | Instantiating formula (47) with e23, e24, all_0_6_6, e22 and discharging atoms op2(e23, e24) = all_0_6_6, op2(e23, e24) = e22, yields:
% 16.65/4.46 | (271) all_0_6_6 = e22
% 16.65/4.46 |
% 16.65/4.46 | From (271)(363) and (831) follows:
% 16.65/4.46 | (242) op2(e22, e24) = e21
% 16.65/4.46 |
% 16.65/4.46 | From (363) and (361) follows:
% 16.65/4.46 | (243) op2(e24, e21) = e23
% 16.65/4.46 |
% 16.65/4.46 | Instantiating formula (47) with e24, e21, e23, e22 and discharging atoms op2(e24, e21) = e23, op2(e24, e21) = e22, yields:
% 16.65/4.46 | (244) e23 = e22
% 16.65/4.46 |
% 16.65/4.46 | Instantiating formula (47) with e22, e24, e21, e23 and discharging atoms op2(e22, e24) = e23, op2(e22, e24) = e21, yields:
% 16.65/4.46 | (245) e23 = e21
% 16.65/4.46 |
% 16.65/4.46 | Combining equations (244,245) yields a new equation:
% 16.65/4.46 | (246) e22 = e21
% 16.65/4.46 |
% 16.65/4.46 | Simplifying 246 yields:
% 16.65/4.46 | (247) e22 = e21
% 16.65/4.46 |
% 16.65/4.46 | Equations (247) can reduce 59 to:
% 16.65/4.46 | (201) $false
% 16.65/4.46 |
% 16.65/4.46 |-The branch is then unsatisfiable
% 16.65/4.46 |-Branch two:
% 16.65/4.46 | (249) ~ (all_0_9_9 = e23)
% 16.65/4.46 | (250) all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21
% 16.65/4.46 |
% 16.65/4.46 +-Applying beta-rule and splitting (203), into two cases.
% 16.65/4.46 |-Branch one:
% 16.65/4.46 | (222) all_0_1_1 = e13
% 16.65/4.46 |
% 16.65/4.46 | From (222) and (840) follows:
% 16.65/4.46 | (857) op1(e13, e11) = all_0_2_2
% 16.65/4.46 |
% 16.65/4.46 | Instantiating formula (101) with e13, e11, all_0_2_2, e14 and discharging atoms op1(e13, e11) = all_0_2_2, op1(e13, e11) = e14, yields:
% 16.65/4.46 | (651) all_0_2_2 = e14
% 16.65/4.46 |
% 16.65/4.46 | Equations (651) can reduce 722 to:
% 16.65/4.46 | (201) $false
% 16.65/4.46 |
% 16.65/4.46 |-The branch is then unsatisfiable
% 16.65/4.46 |-Branch two:
% 16.65/4.46 | (234) ~ (all_0_1_1 = e13)
% 16.65/4.46 | (235) all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11
% 16.65/4.46 |
% 16.65/4.46 +-Applying beta-rule and splitting (221), into two cases.
% 16.65/4.46 |-Branch one:
% 16.65/4.46 | (266) all_0_7_7 = e23
% 16.65/4.46 |
% 16.65/4.46 | From (266) and (456) follows:
% 16.65/4.46 | (252) op2(e23, e24) = all_0_9_9
% 16.65/4.46 |
% 16.65/4.46 | From (266) and (834) follows:
% 16.65/4.46 | (238) op2(e24, all_0_6_6) = e23
% 16.65/4.46 |
% 16.65/4.46 | From (266) and (835) follows:
% 16.65/4.46 | (239) op2(e24, e23) = all_0_6_6
% 16.65/4.46 |
% 16.65/4.46 | Instantiating formula (47) with e24, e23, all_0_6_6, e21 and discharging atoms op2(e24, e23) = all_0_6_6, op2(e24, e23) = e21, yields:
% 16.65/4.46 | (240) all_0_6_6 = e21
% 16.65/4.46 |
% 16.65/4.46 | Instantiating formula (47) with e23, e24, all_0_9_9, e22 and discharging atoms op2(e23, e24) = all_0_9_9, op2(e23, e24) = e22, yields:
% 16.65/4.46 | (256) all_0_9_9 = e22
% 16.65/4.46 |
% 16.65/4.46 | From (256)(240) and (837) follows:
% 16.65/4.46 | (242) op2(e22, e24) = e21
% 16.65/4.46 |
% 16.65/4.46 | From (240) and (238) follows:
% 16.65/4.47 | (243) op2(e24, e21) = e23
% 16.65/4.47 |
% 16.65/4.47 | Instantiating formula (47) with e24, e21, e23, e22 and discharging atoms op2(e24, e21) = e23, op2(e24, e21) = e22, yields:
% 16.65/4.47 | (244) e23 = e22
% 16.65/4.47 |
% 16.65/4.47 | Instantiating formula (47) with e22, e24, e21, e23 and discharging atoms op2(e22, e24) = e23, op2(e22, e24) = e21, yields:
% 16.65/4.47 | (245) e23 = e21
% 16.65/4.47 |
% 16.65/4.47 | Combining equations (244,245) yields a new equation:
% 16.65/4.47 | (246) e22 = e21
% 16.65/4.47 |
% 16.65/4.47 | Simplifying 246 yields:
% 16.65/4.47 | (247) e22 = e21
% 16.65/4.47 |
% 16.65/4.47 | Equations (247) can reduce 59 to:
% 16.65/4.47 | (201) $false
% 16.65/4.47 |
% 16.65/4.47 |-The branch is then unsatisfiable
% 16.65/4.47 |-Branch two:
% 16.65/4.47 | (278) ~ (all_0_7_7 = e23)
% 16.65/4.47 | (279) all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 16.65/4.47 |
% 16.65/4.47 +-Applying beta-rule and splitting (358), into two cases.
% 16.65/4.47 |-Branch one:
% 16.65/4.47 | (414) all_0_6_6 = e23
% 16.65/4.47 |
% 16.65/4.47 | From (414) and (36) follows:
% 16.65/4.47 | (415) j(e23) = e13
% 16.65/4.47 |
% 16.65/4.47 | Instantiating formula (99) with e23, e13, all_0_1_1 and discharging atoms j(e23) = all_0_1_1, j(e23) = e13, yields:
% 16.65/4.47 | (222) all_0_1_1 = e13
% 16.65/4.47 |
% 16.65/4.47 | Equations (222) can reduce 234 to:
% 16.65/4.47 | (201) $false
% 16.65/4.47 |
% 16.65/4.47 |-The branch is then unsatisfiable
% 16.65/4.47 |-Branch two:
% 16.65/4.47 | (418) ~ (all_0_6_6 = e23)
% 16.65/4.47 | (419) all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21
% 16.65/4.47 |
% 16.65/4.47 +-Applying beta-rule and splitting (352), into two cases.
% 16.65/4.47 |-Branch one:
% 16.65/4.47 | (408) all_0_5_5 = e23
% 16.65/4.47 |
% 16.65/4.47 | From (408) and (149) follows:
% 16.65/4.47 | (409) j(e23) = e14
% 16.65/4.47 |
% 16.65/4.47 | Instantiating formula (99) with e23, e14, all_0_1_1 and discharging atoms j(e23) = all_0_1_1, j(e23) = e14, yields:
% 16.65/4.47 | (198) all_0_1_1 = e14
% 16.65/4.47 |
% 16.65/4.47 | Equations (198) can reduce 202 to:
% 16.65/4.47 | (201) $false
% 16.65/4.47 |
% 16.65/4.47 |-The branch is then unsatisfiable
% 16.65/4.47 |-Branch two:
% 16.65/4.47 | (412) ~ (all_0_5_5 = e23)
% 16.65/4.47 | (413) all_0_5_5 = e22 | all_0_5_5 = e20 | all_0_5_5 = e21
% 16.65/4.47 |
% 16.65/4.47 +-Applying beta-rule and splitting (250), into two cases.
% 16.65/4.47 |-Branch one:
% 16.65/4.47 | (256) all_0_9_9 = e22
% 16.65/4.47 |
% 16.65/4.47 | From (256) and (837) follows:
% 16.65/4.47 | (427) op2(e22, e24) = all_0_6_6
% 16.65/4.47 |
% 16.65/4.47 | Instantiating formula (47) with e22, e24, all_0_6_6, e23 and discharging atoms op2(e22, e24) = all_0_6_6, op2(e22, e24) = e23, yields:
% 16.65/4.47 | (414) all_0_6_6 = e23
% 16.65/4.47 |
% 16.65/4.47 | Equations (414) can reduce 418 to:
% 16.65/4.47 | (201) $false
% 16.65/4.47 |
% 16.65/4.47 |-The branch is then unsatisfiable
% 16.65/4.47 |-Branch two:
% 16.65/4.47 | (632) ~ (all_0_9_9 = e22)
% 16.65/4.47 | (633) all_0_9_9 = e20 | all_0_9_9 = e21
% 16.65/4.47 |
% 16.65/4.47 +-Applying beta-rule and splitting (413), into two cases.
% 16.65/4.47 |-Branch one:
% 16.65/4.47 | (398) all_0_5_5 = e22
% 16.65/4.47 |
% 16.65/4.47 | From (398) and (830) follows:
% 16.65/4.47 | (686) op2(e22, e24) = all_0_7_7
% 16.65/4.47 |
% 16.65/4.47 | Instantiating formula (47) with e22, e24, all_0_7_7, e23 and discharging atoms op2(e22, e24) = all_0_7_7, op2(e22, e24) = e23, yields:
% 16.65/4.47 | (266) all_0_7_7 = e23
% 16.65/4.47 |
% 16.65/4.47 | Equations (266) can reduce 278 to:
% 16.65/4.47 | (201) $false
% 16.65/4.47 |
% 16.65/4.47 |-The branch is then unsatisfiable
% 16.65/4.47 |-Branch two:
% 16.65/4.47 | (430) ~ (all_0_5_5 = e22)
% 16.65/4.47 | (431) all_0_5_5 = e20 | all_0_5_5 = e21
% 16.65/4.47 |
% 16.65/4.47 +-Applying beta-rule and splitting (633), into two cases.
% 16.65/4.47 |-Branch one:
% 16.65/4.47 | (640) all_0_9_9 = e20
% 16.65/4.47 |
% 16.65/4.47 | From (640) and (836) follows:
% 16.65/4.47 | (433) op2(e24, e20) = all_0_5_5
% 16.65/4.47 |
% 16.65/4.47 | Instantiating formula (47) with e24, e20, all_0_5_5, e23 and discharging atoms op2(e24, e20) = all_0_5_5, op2(e24, e20) = e23, yields:
% 16.65/4.47 | (408) all_0_5_5 = e23
% 16.65/4.47 |
% 16.65/4.47 | Equations (408) can reduce 412 to:
% 16.65/4.47 | (201) $false
% 16.65/4.47 |
% 16.65/4.47 |-The branch is then unsatisfiable
% 16.65/4.47 |-Branch two:
% 16.65/4.47 | (644) ~ (all_0_9_9 = e20)
% 16.65/4.47 | (460) all_0_9_9 = e21
% 16.65/4.47 |
% 16.65/4.47 | From (460) and (836) follows:
% 16.65/4.47 | (438) op2(e24, e21) = all_0_5_5
% 16.65/4.47 |
% 16.65/4.47 | Instantiating formula (47) with e24, e21, all_0_5_5, e22 and discharging atoms op2(e24, e21) = all_0_5_5, op2(e24, e21) = e22, yields:
% 16.65/4.47 | (398) all_0_5_5 = e22
% 16.65/4.47 |
% 16.65/4.47 | Equations (398) can reduce 430 to:
% 16.65/4.47 | (201) $false
% 16.65/4.47 |
% 16.65/4.47 |-The branch is then unsatisfiable
% 16.65/4.48 |-Branch two:
% 16.65/4.48 | (214) ~ (all_0_8_8 = e24)
% 16.65/4.48 | (215) all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 16.65/4.48 |
% 16.65/4.48 +-Applying beta-rule and splitting (296), into two cases.
% 16.65/4.48 |-Branch one:
% 16.65/4.48 | (503) all_0_0_0 = e13
% 16.65/4.48 |
% 16.65/4.48 | From (503) and (18) follows:
% 16.65/4.48 | (504) h(e13) = e24
% 16.65/4.48 |
% 16.65/4.48 | Instantiating formula (96) with e13, e24, all_0_6_6 and discharging atoms h(e13) = all_0_6_6, h(e13) = e24, yields:
% 16.65/4.48 | (353) all_0_6_6 = e24
% 16.65/4.48 |
% 16.65/4.48 | Equations (353) can reduce 357 to:
% 16.65/4.48 | (201) $false
% 16.65/4.48 |
% 16.65/4.48 |-The branch is then unsatisfiable
% 16.65/4.48 |-Branch two:
% 16.65/4.48 | (507) ~ (all_0_0_0 = e13)
% 16.65/4.48 | (508) all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 16.65/4.48 |
% 16.65/4.48 +-Applying beta-rule and splitting (508), into two cases.
% 16.65/4.48 |-Branch one:
% 16.65/4.48 | (509) all_0_0_0 = e12
% 16.65/4.48 |
% 16.65/4.48 | From (509) and (18) follows:
% 16.65/4.48 | (510) h(e12) = e24
% 16.65/4.48 |
% 16.65/4.48 | Instantiating formula (96) with e12, e24, all_0_7_7 and discharging atoms h(e12) = all_0_7_7, h(e12) = e24, yields:
% 16.65/4.48 | (216) all_0_7_7 = e24
% 16.65/4.48 |
% 16.65/4.48 | Equations (216) can reduce 220 to:
% 16.65/4.48 | (201) $false
% 16.65/4.48 |
% 16.65/4.48 |-The branch is then unsatisfiable
% 16.65/4.48 |-Branch two:
% 16.65/4.48 | (513) ~ (all_0_0_0 = e12)
% 16.65/4.48 | (514) all_0_0_0 = e10 | all_0_0_0 = e11
% 16.65/4.48 |
% 16.65/4.48 +-Applying beta-rule and splitting (514), into two cases.
% 16.65/4.48 |-Branch one:
% 16.65/4.48 | (306) all_0_0_0 = e10
% 16.65/4.48 |
% 16.65/4.48 | From (306) and (18) follows:
% 16.65/4.48 | (516) h(e10) = e24
% 16.65/4.48 |
% 16.65/4.48 | Instantiating formula (96) with e10, e24, all_0_9_9 and discharging atoms h(e10) = all_0_9_9, h(e10) = e24, yields:
% 16.65/4.48 | (204) all_0_9_9 = e24
% 16.65/4.48 |
% 16.65/4.48 | Equations (204) can reduce 208 to:
% 16.65/4.48 | (201) $false
% 16.65/4.48 |
% 16.65/4.48 |-The branch is then unsatisfiable
% 16.65/4.48 |-Branch two:
% 16.65/4.48 | (519) ~ (all_0_0_0 = e10)
% 16.65/4.48 | (520) all_0_0_0 = e11
% 16.65/4.48 |
% 16.65/4.48 | From (520) and (18) follows:
% 16.65/4.48 | (521) h(e11) = e24
% 16.65/4.48 |
% 16.65/4.48 | Instantiating formula (96) with e11, e24, all_0_8_8 and discharging atoms h(e11) = all_0_8_8, h(e11) = e24, yields:
% 16.65/4.48 | (210) all_0_8_8 = e24
% 16.65/4.48 |
% 16.65/4.48 | Equations (210) can reduce 214 to:
% 16.65/4.48 | (201) $false
% 16.65/4.48 |
% 16.65/4.48 |-The branch is then unsatisfiable
% 16.87/4.48 % SZS output end Proof for theBenchmark
% 16.87/4.48
% 16.87/4.48 3904ms
%------------------------------------------------------------------------------