TSTP Solution File: ALG087+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG087+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 15:34:17 EDT 2022
% Result : Theorem 4.56s 1.66s
% Output : Proof 8.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ALG087+1 : TPTP v8.1.0. Released v2.7.0.
% 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 8 03:33:21 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.51/0.60 ____ _
% 0.51/0.60 ___ / __ \_____(_)___ ________ __________
% 0.51/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.60
% 0.51/0.60 A Theorem Prover for First-Order Logic
% 0.51/0.60 (ePrincess v.1.0)
% 0.51/0.60
% 0.51/0.60 (c) Philipp Rümmer, 2009-2015
% 0.51/0.60 (c) Peter Backeman, 2014-2015
% 0.51/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.60 Bug reports to peter@backeman.se
% 0.51/0.60
% 0.51/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.60
% 0.51/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.73/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.87/1.02 Prover 0: Preprocessing ...
% 2.84/1.29 Prover 0: Constructing countermodel ...
% 4.56/1.66 Prover 0: proved (1014ms)
% 4.56/1.66
% 4.56/1.66 No countermodel exists, formula is valid
% 4.56/1.66 % SZS status Theorem for theBenchmark
% 4.56/1.66
% 4.56/1.66 Generating proof ... found it (size 76)
% 8.54/2.54
% 8.54/2.54 % SZS output start Proof for theBenchmark
% 8.54/2.54 Assumed formulas after preprocessing and simplification:
% 8.54/2.54 | (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) = v0 & op2(v4, v3) = v2 & op2(v4, v2) = v1 & op2(v4, v1) = v3 & op2(v4, v0) = v4 & op2(v3, v4) = v1 & op2(v3, v3) = v0 & op2(v3, v2) = v4 & op2(v3, v1) = v2 & op2(v3, v0) = v3 & op2(v2, v4) = v3 & op2(v2, v3) = v1 & op2(v2, v2) = v0 & op2(v2, v1) = v4 & op2(v2, v0) = v2 & op2(v1, v4) = v2 & op2(v1, v3) = v4 & op2(v1, v2) = v3 & op2(v1, v1) = v0 & op2(v1, v0) = v1 & op2(v0, v4) = v4 & op2(v0, v3) = v3 & op2(v0, v2) = v2 & op2(v0, v1) = v1 & op2(v0, v0) = v0 & op2(e24, e24) = e22 & op2(e24, e23) = e21 & op2(e24, e22) = e20 & op2(e24, e20) = e24 & op2(e24, e21) = e23 & op2(e23, e24) = e20 & op2(e23, e23) = e24 & op2(e23, e22) = e21 & op2(e23, e20) = e23 & op2(e23, e21) = e22 & op2(e22, e24) = e21 & op2(e22, e23) = e20 & op2(e22, e22) = e23 & op2(e22, e20) = e22 & op2(e22, e21) = e24 & op2(e20, e24) = e24 & op2(e20, e23) = e23 & op2(e20, e22) = e22 & op2(e20, e20) = e20 & op2(e20, e21) = e21 & op2(e21, e24) = e23 & op2(e21, e23) = e22 & op2(e21, e22) = e24 & op2(e21, e20) = e21 & op2(e21, e21) = e20 & op1(v9, v9) = v7 & op1(v9, v8) = v6 & op1(v9, v7) = v5 & op1(v9, v6) = v8 & op1(v9, v5) = v9 & op1(v8, v9) = v5 & op1(v8, v8) = v9 & op1(v8, v7) = v6 & op1(v8, v6) = v7 & op1(v8, v5) = v8 & op1(v7, v9) = v6 & op1(v7, v8) = v5 & op1(v7, v7) = v8 & op1(v7, v6) = v9 & op1(v7, v5) = v7 & op1(v6, v9) = v8 & op1(v6, v8) = v7 & op1(v6, v7) = v9 & op1(v6, v6) = v5 & op1(v6, v5) = v6 & op1(v5, v9) = v9 & op1(v5, v8) = v8 & op1(v5, v7) = v7 & op1(v5, v6) = v6 & op1(v5, v5) = v5 & op1(e14, e14) = e10 & op1(e14, e13) = e12 & op1(e14, e12) = e11 & op1(e14, e10) = e14 & op1(e14, e11) = e13 & op1(e13, e14) = e11 & op1(e13, e13) = e10 & op1(e13, e12) = e14 & op1(e13, e10) = e13 & op1(e13, e11) = e12 & op1(e12, e14) = e13 & op1(e12, e13) = e11 & op1(e12, e12) = e10 & op1(e12, e10) = e12 & op1(e12, e11) = e14 & op1(e10, e14) = e14 & op1(e10, e13) = e13 & op1(e10, e12) = e12 & op1(e10, e10) = e10 & op1(e10, e11) = e11 & op1(e11, e14) = e12 & op1(e11, e13) = e14 & op1(e11, e12) = e13 & op1(e11, e10) = e11 & op1(e11, e11) = e10 & 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))
% 8.54/2.59 | 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:
% 8.54/2.59 | (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_9_9 & op2(all_0_5_5, all_0_6_6) = all_0_7_7 & op2(all_0_5_5, all_0_7_7) = all_0_8_8 & op2(all_0_5_5, all_0_8_8) = all_0_6_6 & op2(all_0_5_5, all_0_9_9) = all_0_5_5 & op2(all_0_6_6, all_0_5_5) = all_0_8_8 & op2(all_0_6_6, all_0_6_6) = all_0_9_9 & op2(all_0_6_6, all_0_7_7) = all_0_5_5 & op2(all_0_6_6, all_0_8_8) = all_0_7_7 & op2(all_0_6_6, all_0_9_9) = all_0_6_6 & op2(all_0_7_7, all_0_5_5) = all_0_6_6 & op2(all_0_7_7, all_0_6_6) = all_0_8_8 & op2(all_0_7_7, all_0_7_7) = all_0_9_9 & op2(all_0_7_7, all_0_8_8) = all_0_5_5 & op2(all_0_7_7, all_0_9_9) = all_0_7_7 & op2(all_0_8_8, all_0_5_5) = all_0_7_7 & op2(all_0_8_8, all_0_6_6) = all_0_5_5 & op2(all_0_8_8, all_0_7_7) = all_0_6_6 & op2(all_0_8_8, all_0_8_8) = all_0_9_9 & op2(all_0_8_8, all_0_9_9) = all_0_8_8 & op2(all_0_9_9, all_0_5_5) = all_0_5_5 & op2(all_0_9_9, all_0_6_6) = all_0_6_6 & op2(all_0_9_9, all_0_7_7) = all_0_7_7 & op2(all_0_9_9, all_0_8_8) = all_0_8_8 & op2(all_0_9_9, all_0_9_9) = all_0_9_9 & op2(e24, e24) = e22 & op2(e24, e23) = e21 & op2(e24, e22) = e20 & op2(e24, e20) = e24 & op2(e24, e21) = e23 & op2(e23, e24) = e20 & op2(e23, e23) = e24 & op2(e23, e22) = e21 & op2(e23, e20) = e23 & op2(e23, e21) = e22 & op2(e22, e24) = e21 & op2(e22, e23) = e20 & op2(e22, e22) = e23 & op2(e22, e20) = e22 & op2(e22, e21) = e24 & op2(e20, e24) = e24 & op2(e20, e23) = e23 & op2(e20, e22) = e22 & op2(e20, e20) = e20 & op2(e20, e21) = e21 & op2(e21, e24) = e23 & op2(e21, e23) = e22 & op2(e21, e22) = e24 & op2(e21, e20) = e21 & op2(e21, e21) = e20 & op1(all_0_0_0, all_0_0_0) = all_0_2_2 & 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_1_1 & op1(all_0_0_0, all_0_4_4) = all_0_0_0 & op1(all_0_1_1, all_0_0_0) = all_0_4_4 & op1(all_0_1_1, all_0_1_1) = all_0_0_0 & op1(all_0_1_1, all_0_2_2) = all_0_3_3 & op1(all_0_1_1, all_0_3_3) = all_0_2_2 & op1(all_0_1_1, all_0_4_4) = all_0_1_1 & op1(all_0_2_2, all_0_0_0) = all_0_3_3 & op1(all_0_2_2, all_0_1_1) = all_0_4_4 & op1(all_0_2_2, all_0_2_2) = all_0_1_1 & op1(all_0_2_2, all_0_3_3) = all_0_0_0 & op1(all_0_2_2, all_0_4_4) = all_0_2_2 & op1(all_0_3_3, all_0_0_0) = all_0_1_1 & op1(all_0_3_3, all_0_1_1) = all_0_2_2 & op1(all_0_3_3, all_0_2_2) = all_0_0_0 & op1(all_0_3_3, all_0_3_3) = all_0_4_4 & op1(all_0_3_3, all_0_4_4) = all_0_3_3 & op1(all_0_4_4, all_0_0_0) = all_0_0_0 & op1(all_0_4_4, all_0_1_1) = all_0_1_1 & op1(all_0_4_4, all_0_2_2) = all_0_2_2 & op1(all_0_4_4, all_0_3_3) = all_0_3_3 & op1(all_0_4_4, all_0_4_4) = all_0_4_4 & op1(e14, e14) = e10 & op1(e14, e13) = e12 & op1(e14, e12) = e11 & op1(e14, e10) = e14 & op1(e14, e11) = e13 & op1(e13, e14) = e11 & op1(e13, e13) = e10 & op1(e13, e12) = e14 & op1(e13, e10) = e13 & op1(e13, e11) = e12 & op1(e12, e14) = e13 & op1(e12, e13) = e11 & op1(e12, e12) = e10 & op1(e12, e10) = e12 & op1(e12, e11) = e14 & op1(e10, e14) = e14 & op1(e10, e13) = e13 & op1(e10, e12) = e12 & op1(e10, e10) = e10 & op1(e10, e11) = e11 & op1(e11, e14) = e12 & op1(e11, e13) = e14 & op1(e11, e12) = e13 & op1(e11, e10) = e11 & op1(e11, e11) = e10 & 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)
% 8.81/2.59 |
% 8.81/2.59 | Applying alpha-rule on (1) yields:
% 8.81/2.59 | (2) op2(all_0_8_8, all_0_8_8) = all_0_9_9
% 8.81/2.59 | (3) ~ (e21 = e12)
% 8.81/2.59 | (4) op1(all_0_4_4, all_0_1_1) = all_0_1_1
% 8.81/2.59 | (5) op1(e13, e14) = e11
% 8.81/2.59 | (6) op1(e13, e12) = e14
% 8.81/2.59 | (7) ~ (e20 = e21)
% 8.81/2.59 | (8) ~ (e20 = e14)
% 8.81/2.59 | (9) op1(all_0_2_2, all_0_2_2) = all_0_1_1
% 8.81/2.59 | (10) op2(e20, e23) = e23
% 8.81/2.59 | (11) op1(all_0_4_4, all_0_2_2) = all_0_2_2
% 8.81/2.59 | (12) ~ (e24 = e11)
% 8.81/2.59 | (13) op1(e11, e11) = e10
% 8.81/2.60 | (14) ~ (e12 = e11)
% 8.81/2.60 | (15) h(e12) = all_0_7_7
% 8.81/2.60 | (16) h(all_0_0_0) = e24
% 8.81/2.60 | (17) h(e13) = all_0_6_6
% 8.81/2.60 | (18) op2(e24, e24) = e22
% 8.81/2.60 | (19) op2(all_0_5_5, all_0_8_8) = all_0_6_6
% 8.81/2.60 | (20) ~ (e14 = e12)
% 8.81/2.60 | (21) op2(e23, e21) = e22
% 8.81/2.60 | (22) ~ (e24 = e12)
% 8.81/2.60 | (23) op2(all_0_6_6, all_0_6_6) = all_0_9_9
% 8.81/2.60 | (24) op1(all_0_1_1, all_0_0_0) = all_0_4_4
% 8.81/2.60 | (25) op1(e12, e14) = e13
% 8.81/2.60 | (26) op1(e10, e11) = e11
% 8.81/2.60 | (27) j(e22) = all_0_2_2
% 8.81/2.60 | (28) op1(e12, e11) = e14
% 8.81/2.60 | (29) op2(all_0_9_9, all_0_8_8) = all_0_8_8
% 8.81/2.60 | (30) j(e21) = all_0_3_3
% 8.81/2.60 | (31) op1(all_0_1_1, all_0_2_2) = all_0_3_3
% 8.81/2.60 | (32) j(all_0_8_8) = e11
% 8.81/2.60 | (33) ~ (e22 = e13)
% 8.81/2.60 | (34) op2(all_0_6_6, all_0_9_9) = all_0_6_6
% 8.81/2.60 | (35) op2(all_0_8_8, all_0_7_7) = all_0_6_6
% 8.81/2.60 | (36) op1(e13, e13) = e10
% 8.81/2.60 | (37) op2(e24, e21) = e23
% 8.81/2.60 | (38) op1(all_0_3_3, all_0_4_4) = all_0_3_3
% 8.81/2.60 | (39) op1(e11, e12) = e13
% 8.81/2.60 | (40) j(all_0_6_6) = e13
% 8.81/2.60 | (41) op2(all_0_5_5, all_0_7_7) = all_0_8_8
% 8.81/2.60 | (42) h(all_0_4_4) = e20
% 8.81/2.60 | (43) op2(all_0_7_7, all_0_7_7) = all_0_9_9
% 8.81/2.60 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0))
% 8.81/2.60 | (45) op1(all_0_3_3, all_0_2_2) = all_0_0_0
% 8.81/2.60 | (46) op2(e23, e23) = e24
% 8.81/2.60 | (47) ~ (e23 = e13)
% 8.81/2.60 | (48) op1(all_0_0_0, all_0_4_4) = all_0_0_0
% 8.81/2.60 | (49) op2(all_0_9_9, all_0_6_6) = all_0_6_6
% 8.81/2.60 | (50) op2(e24, e22) = e20
% 8.81/2.60 | (51) op2(e22, e20) = e22
% 8.81/2.60 | (52) 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
% 8.81/2.60 | (53) op2(e23, e22) = e21
% 8.81/2.60 | (54) ~ (e23 = e12)
% 8.81/2.60 | (55) op1(e11, e10) = e11
% 8.81/2.60 | (56) op2(e21, e24) = e23
% 8.81/2.60 | (57) ~ (e24 = e14)
% 8.81/2.60 | (58) h(all_0_3_3) = e21
% 8.81/2.60 | (59) ~ (e23 = e21)
% 8.81/2.60 | (60) op1(e13, e11) = e12
% 8.81/2.60 | (61) 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
% 8.81/2.60 | (62) ~ (e22 = e21)
% 8.81/2.60 | (63) ~ (e20 = e11)
% 8.81/2.60 | (64) j(all_0_9_9) = e10
% 8.81/2.60 | (65) op1(e11, e13) = e14
% 8.81/2.60 | (66) op1(all_0_0_0, all_0_0_0) = all_0_2_2
% 8.81/2.60 | (67) ~ (e14 = e10)
% 8.81/2.60 | (68) ~ (e22 = e10)
% 8.81/2.60 | (69) op1(e14, e12) = e11
% 8.81/2.60 | (70) h(all_0_1_1) = e23
% 8.81/2.60 | (71) op2(all_0_9_9, all_0_9_9) = all_0_9_9
% 8.81/2.60 | (72) op2(all_0_9_9, all_0_7_7) = all_0_7_7
% 8.81/2.60 | (73) op1(e12, e10) = e12
% 8.81/2.60 | (74) ~ (e12 = e10)
% 8.81/2.60 | (75) ~ (e24 = e22)
% 8.81/2.60 | (76) op1(all_0_1_1, all_0_4_4) = all_0_1_1
% 8.81/2.60 | (77) op1(e14, e14) = e10
% 8.81/2.60 | (78) 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
% 8.81/2.60 | (79) op2(e20, e24) = e24
% 8.81/2.60 | (80) op2(e22, e21) = e24
% 8.81/2.60 | (81) op2(e20, e20) = e20
% 8.81/2.60 | (82) 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
% 8.81/2.60 | (83) op2(all_0_7_7, all_0_9_9) = all_0_7_7
% 8.81/2.60 | (84) j(all_0_7_7) = e12
% 8.81/2.60 | (85) op1(e12, e13) = e11
% 8.81/2.60 | (86) op2(all_0_7_7, all_0_5_5) = all_0_6_6
% 8.81/2.60 | (87) op2(all_0_5_5, all_0_9_9) = all_0_5_5
% 8.81/2.60 | (88) h(all_0_2_2) = e22
% 8.81/2.60 | (89) ~ (e14 = e13)
% 8.81/2.60 | (90) ~ (e21 = e11)
% 8.81/2.60 | (91) h(e14) = all_0_5_5
% 8.81/2.61 | (92) ~ (e24 = e20)
% 8.81/2.61 | (93) ~ (e13 = e12)
% 8.81/2.61 | (94) op2(all_0_6_6, all_0_7_7) = all_0_5_5
% 8.81/2.61 | (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
% 8.81/2.61 | (96) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0))
% 8.81/2.61 | (97) ~ (e14 = e11)
% 8.81/2.61 | (98) op2(e22, e24) = e21
% 8.81/2.61 | (99) op2(e21, e21) = e20
% 8.81/2.61 | (100) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0))
% 8.81/2.61 | (101) op1(all_0_2_2, all_0_4_4) = all_0_2_2
% 8.81/2.61 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0))
% 8.81/2.61 | (103) 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
% 8.81/2.61 | (104) op2(all_0_6_6, all_0_8_8) = all_0_7_7
% 8.81/2.61 | (105) op1(e13, e10) = e13
% 8.81/2.61 | (106) op1(e10, e10) = e10
% 8.81/2.61 | (107) op1(all_0_0_0, all_0_3_3) = all_0_1_1
% 8.81/2.61 | (108) ~ (e23 = e10)
% 8.81/2.61 | (109) op1(all_0_4_4, all_0_4_4) = all_0_4_4
% 8.81/2.61 | (110) ~ (e13 = e10)
% 8.81/2.61 | (111) op1(e14, e13) = e12
% 8.81/2.61 | (112) op1(e10, e12) = e12
% 8.81/2.61 | (113) 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
% 8.81/2.61 | (114) op2(all_0_7_7, all_0_6_6) = all_0_8_8
% 8.81/2.61 | (115) 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
% 8.81/2.61 | (116) ~ (e23 = e22)
% 8.81/2.61 | (117) ~ (e20 = e10)
% 8.81/2.61 | (118) ~ (e22 = e11)
% 8.81/2.61 | (119) op2(e22, e23) = e20
% 8.81/2.61 | (120) op2(e22, e22) = e23
% 8.81/2.61 | (121) ~ (e20 = e12)
% 8.81/2.61 | (122) op1(all_0_0_0, all_0_2_2) = all_0_4_4
% 8.81/2.61 | (123) op1(e12, e12) = e10
% 8.81/2.61 | (124) op1(all_0_3_3, all_0_0_0) = all_0_1_1
% 8.81/2.61 | (125) op1(e14, e11) = e13
% 8.81/2.61 | (126) op2(e24, e20) = e24
% 8.81/2.61 | (127) op1(all_0_4_4, all_0_0_0) = all_0_0_0
% 8.81/2.61 | (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
% 8.81/2.61 | (129) ~ (e10 = e11)
% 8.81/2.61 | (130) op1(all_0_2_2, all_0_0_0) = all_0_3_3
% 8.81/2.61 | (131) ~ (e23 = e14)
% 8.81/2.61 | (132) h(e11) = all_0_8_8
% 8.81/2.61 | (133) op1(e10, e13) = e13
% 8.81/2.61 | (134) op2(e23, e24) = e20
% 8.81/2.61 | (135) op2(all_0_7_7, all_0_8_8) = all_0_5_5
% 8.81/2.61 | (136) op1(e14, e10) = e14
% 8.81/2.61 | (137) j(e23) = all_0_1_1
% 8.81/2.61 | (138) ~ (e23 = e20)
% 8.81/2.61 | (139) op2(e21, e20) = e21
% 8.81/2.61 | (140) ~ (e21 = e14)
% 8.81/2.61 | (141) op2(all_0_8_8, all_0_6_6) = all_0_5_5
% 8.81/2.61 | (142) j(e24) = all_0_0_0
% 8.81/2.61 | (143) op2(all_0_5_5, all_0_6_6) = all_0_7_7
% 8.81/2.61 | (144) op1(e10, e14) = e14
% 8.81/2.61 | (145) op1(all_0_2_2, all_0_1_1) = all_0_4_4
% 8.81/2.61 | (146) ~ (e24 = e21)
% 8.81/2.61 | (147) op2(all_0_8_8, all_0_9_9) = all_0_8_8
% 8.81/2.61 | (148) j(all_0_5_5) = e14
% 8.81/2.61 | (149) op2(all_0_8_8, all_0_5_5) = all_0_7_7
% 8.81/2.61 | (150) op1(e11, e14) = e12
% 8.81/2.61 | (151) op2(e23, e20) = e23
% 8.81/2.61 | (152) ~ (e22 = e20)
% 8.81/2.61 | (153) ~ (e23 = e11)
% 8.81/2.61 | (154) op2(e21, e23) = e22
% 8.81/2.62 | (155) op1(all_0_1_1, all_0_3_3) = all_0_2_2
% 8.81/2.62 | (156) op1(all_0_3_3, all_0_1_1) = all_0_2_2
% 8.81/2.62 | (157) op1(all_0_1_1, all_0_1_1) = all_0_0_0
% 8.81/2.62 | (158) op1(all_0_2_2, all_0_3_3) = all_0_0_0
% 8.81/2.62 | (159) ~ (e24 = e10)
% 8.81/2.62 | (160) ~ (e24 = e23)
% 8.81/2.62 | (161) ~ (e20 = e13)
% 8.81/2.62 | (162) ~ (e24 = e13)
% 8.81/2.62 | (163) op1(all_0_4_4, all_0_3_3) = all_0_3_3
% 8.81/2.62 | (164) ~ (e21 = e10)
% 8.81/2.62 | (165) ~ (e21 = e13)
% 8.81/2.62 | (166) j(e20) = all_0_4_4
% 8.81/2.62 | (167) op2(all_0_5_5, all_0_5_5) = all_0_9_9
% 8.81/2.62 | (168) ~ (e22 = e12)
% 8.81/2.62 | (169) op1(all_0_0_0, all_0_1_1) = all_0_3_3
% 8.81/2.62 | (170) op1(all_0_3_3, all_0_3_3) = all_0_4_4
% 8.81/2.62 | (171) op2(e20, e22) = e22
% 8.81/2.62 | (172) 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
% 8.81/2.62 | (173) op2(all_0_6_6, all_0_5_5) = all_0_8_8
% 8.81/2.62 | (174) h(e10) = all_0_9_9
% 8.81/2.62 | (175) ~ (e22 = e14)
% 8.81/2.62 | (176) op2(e24, e23) = e21
% 8.81/2.62 | (177) op2(e20, e21) = e21
% 8.81/2.62 | (178) op2(all_0_9_9, all_0_5_5) = all_0_5_5
% 8.81/2.62 | (179) op2(e21, e22) = e24
% 8.81/2.62 | (180) ~ (e13 = e11)
% 8.81/2.62 |
% 8.81/2.62 +-Applying beta-rule and splitting (115), into two cases.
% 8.81/2.62 |-Branch one:
% 8.81/2.62 | (181) all_0_0_0 = e14
% 8.81/2.62 |
% 8.81/2.62 | From (181)(181) and (66) follows:
% 8.81/2.62 | (182) op1(e14, e14) = all_0_2_2
% 8.81/2.62 |
% 8.81/2.62 | From (181) and (122) follows:
% 8.81/2.62 | (183) op1(e14, all_0_2_2) = all_0_4_4
% 8.81/2.62 |
% 8.81/2.62 | Instantiating formula (102) with e14, e14, all_0_2_2, e10 and discharging atoms op1(e14, e14) = all_0_2_2, op1(e14, e14) = e10, yields:
% 8.81/2.62 | (184) all_0_2_2 = e10
% 8.81/2.62 |
% 8.81/2.62 | From (184) and (145) follows:
% 8.81/2.62 | (185) op1(e10, all_0_1_1) = all_0_4_4
% 8.81/2.62 |
% 8.81/2.62 | From (184)(184) and (9) follows:
% 8.81/2.62 | (186) op1(e10, e10) = all_0_1_1
% 8.81/2.62 |
% 8.81/2.62 | From (184) and (183) follows:
% 8.81/2.62 | (187) op1(e14, e10) = all_0_4_4
% 8.81/2.62 |
% 8.81/2.62 | Instantiating formula (102) with e14, e10, all_0_4_4, e14 and discharging atoms op1(e14, e10) = all_0_4_4, op1(e14, e10) = e14, yields:
% 8.81/2.62 | (188) all_0_4_4 = e14
% 8.81/2.62 |
% 8.81/2.62 | Instantiating formula (102) with e10, e10, all_0_1_1, e10 and discharging atoms op1(e10, e10) = all_0_1_1, op1(e10, e10) = e10, yields:
% 8.81/2.62 | (189) all_0_1_1 = e10
% 8.81/2.62 |
% 8.81/2.62 | From (189)(188) and (185) follows:
% 8.81/2.62 | (190) op1(e10, e10) = e14
% 8.81/2.62 |
% 8.81/2.62 | From (189) and (186) follows:
% 8.81/2.62 | (106) op1(e10, e10) = e10
% 8.81/2.62 |
% 8.81/2.62 | Instantiating formula (102) with e10, e10, e14, e10 and discharging atoms op1(e10, e10) = e14, op1(e10, e10) = e10, yields:
% 8.81/2.62 | (192) e14 = e10
% 8.81/2.62 |
% 8.81/2.63 | Equations (192) can reduce 67 to:
% 8.81/2.63 | (193) $false
% 8.81/2.63 |
% 8.81/2.63 |-The branch is then unsatisfiable
% 8.81/2.63 |-Branch two:
% 8.81/2.63 | (194) ~ (all_0_0_0 = e14)
% 8.81/2.63 | (195) all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 8.81/2.63 |
% 8.81/2.63 +-Applying beta-rule and splitting (78), into two cases.
% 8.81/2.63 |-Branch one:
% 8.81/2.63 | (196) all_0_9_9 = e24
% 8.81/2.63 |
% 8.81/2.63 | From (196)(196)(196) and (71) follows:
% 8.81/2.63 | (197) op2(e24, e24) = e24
% 8.81/2.63 |
% 8.81/2.63 | Instantiating formula (44) with e24, e24, e24, e22 and discharging atoms op2(e24, e24) = e24, op2(e24, e24) = e22, yields:
% 8.81/2.63 | (198) e24 = e22
% 8.81/2.63 |
% 8.81/2.63 | Equations (198) can reduce 75 to:
% 8.81/2.63 | (193) $false
% 8.81/2.63 |
% 8.81/2.63 |-The branch is then unsatisfiable
% 8.81/2.63 |-Branch two:
% 8.81/2.63 | (200) ~ (all_0_9_9 = e24)
% 8.81/2.63 | (201) all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21
% 8.81/2.63 |
% 8.81/2.63 +-Applying beta-rule and splitting (95), into two cases.
% 8.81/2.63 |-Branch one:
% 8.81/2.63 | (202) all_0_7_7 = e24
% 8.81/2.63 |
% 8.81/2.63 | From (202)(202) and (43) follows:
% 8.81/2.63 | (203) op2(e24, e24) = all_0_9_9
% 8.81/2.63 |
% 8.81/2.63 | From (202)(202) and (83) follows:
% 8.81/2.63 | (204) op2(e24, all_0_9_9) = e24
% 8.81/2.63 |
% 8.81/2.63 | From (202)(202) and (72) follows:
% 8.81/2.63 | (205) op2(all_0_9_9, e24) = e24
% 8.81/2.63 |
% 8.81/2.63 | Instantiating formula (44) with e24, e24, all_0_9_9, e22 and discharging atoms op2(e24, e24) = all_0_9_9, op2(e24, e24) = e22, yields:
% 8.81/2.63 | (206) all_0_9_9 = e22
% 8.81/2.63 |
% 8.81/2.63 | From (206) and (205) follows:
% 8.81/2.63 | (207) op2(e22, e24) = e24
% 8.81/2.63 |
% 8.81/2.63 | From (206) and (204) follows:
% 8.81/2.63 | (208) op2(e24, e22) = e24
% 8.81/2.63 |
% 8.81/2.63 | Instantiating formula (44) with e24, e22, e24, e20 and discharging atoms op2(e24, e22) = e24, op2(e24, e22) = e20, yields:
% 8.81/2.63 | (209) e24 = e20
% 8.81/2.63 |
% 8.81/2.63 | Instantiating formula (44) with e22, e24, e24, e21 and discharging atoms op2(e22, e24) = e24, op2(e22, e24) = e21, yields:
% 8.81/2.63 | (210) e24 = e21
% 8.81/2.63 |
% 8.81/2.63 | Combining equations (210,209) yields a new equation:
% 8.81/2.63 | (211) e20 = e21
% 8.81/2.63 |
% 8.81/2.63 | Equations (211) can reduce 7 to:
% 8.81/2.63 | (193) $false
% 8.81/2.63 |
% 8.81/2.63 |-The branch is then unsatisfiable
% 8.81/2.63 |-Branch two:
% 8.81/2.63 | (213) ~ (all_0_7_7 = e24)
% 8.81/2.63 | (214) all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 8.81/2.63 |
% 8.81/2.63 +-Applying beta-rule and splitting (113), into two cases.
% 8.81/2.63 |-Branch one:
% 8.81/2.63 | (215) all_0_6_6 = e24
% 8.81/2.63 |
% 8.81/2.63 | From (215)(215) and (23) follows:
% 8.81/2.63 | (203) op2(e24, e24) = all_0_9_9
% 8.81/2.63 |
% 8.81/2.63 | From (215)(215) and (34) follows:
% 8.81/2.63 | (204) op2(e24, all_0_9_9) = e24
% 8.81/2.63 |
% 8.81/2.63 | From (215)(215) and (49) follows:
% 8.81/2.63 | (205) op2(all_0_9_9, e24) = e24
% 8.81/2.63 |
% 8.81/2.63 | Instantiating formula (44) with e24, e24, all_0_9_9, e22 and discharging atoms op2(e24, e24) = all_0_9_9, op2(e24, e24) = e22, yields:
% 8.81/2.63 | (206) all_0_9_9 = e22
% 8.81/2.63 |
% 8.81/2.63 | From (206) and (205) follows:
% 8.81/2.63 | (207) op2(e22, e24) = e24
% 8.81/2.63 |
% 8.81/2.63 | From (206) and (204) follows:
% 8.81/2.63 | (208) op2(e24, e22) = e24
% 8.81/2.63 |
% 8.81/2.63 | Instantiating formula (44) with e24, e22, e24, e20 and discharging atoms op2(e24, e22) = e24, op2(e24, e22) = e20, yields:
% 8.81/2.63 | (209) e24 = e20
% 8.81/2.63 |
% 8.81/2.63 | Instantiating formula (44) with e22, e24, e24, e21 and discharging atoms op2(e22, e24) = e24, op2(e22, e24) = e21, yields:
% 8.81/2.63 | (210) e24 = e21
% 8.81/2.63 |
% 8.81/2.63 | Combining equations (210,209) yields a new equation:
% 8.81/2.63 | (211) e20 = e21
% 8.81/2.63 |
% 8.81/2.63 | Equations (211) can reduce 7 to:
% 8.81/2.63 | (193) $false
% 8.81/2.63 |
% 8.81/2.63 |-The branch is then unsatisfiable
% 8.81/2.63 |-Branch two:
% 8.81/2.63 | (226) ~ (all_0_6_6 = e24)
% 8.81/2.63 | (227) all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21
% 8.81/2.63 |
% 8.81/2.63 +-Applying beta-rule and splitting (128), into two cases.
% 8.81/2.63 |-Branch one:
% 8.81/2.63 | (228) all_0_8_8 = e24
% 8.81/2.63 |
% 8.81/2.63 | From (228)(228) and (2) follows:
% 8.81/2.63 | (203) op2(e24, e24) = all_0_9_9
% 8.81/2.63 |
% 8.81/2.63 | From (228)(228) and (147) follows:
% 8.81/2.63 | (204) op2(e24, all_0_9_9) = e24
% 8.81/2.63 |
% 8.81/2.63 | From (228)(228) and (29) follows:
% 8.81/2.63 | (205) op2(all_0_9_9, e24) = e24
% 8.81/2.63 |
% 8.81/2.63 | Instantiating formula (44) with e24, e24, all_0_9_9, e22 and discharging atoms op2(e24, e24) = all_0_9_9, op2(e24, e24) = e22, yields:
% 8.81/2.63 | (206) all_0_9_9 = e22
% 8.81/2.63 |
% 8.81/2.63 | From (206) and (205) follows:
% 8.81/2.63 | (207) op2(e22, e24) = e24
% 8.81/2.63 |
% 8.81/2.63 | From (206) and (204) follows:
% 8.81/2.63 | (208) op2(e24, e22) = e24
% 8.81/2.63 |
% 8.81/2.63 | Instantiating formula (44) with e24, e22, e24, e20 and discharging atoms op2(e24, e22) = e24, op2(e24, e22) = e20, yields:
% 8.81/2.63 | (209) e24 = e20
% 8.81/2.63 |
% 8.81/2.63 | Instantiating formula (44) with e22, e24, e24, e21 and discharging atoms op2(e22, e24) = e24, op2(e22, e24) = e21, yields:
% 8.81/2.63 | (210) e24 = e21
% 8.81/2.63 |
% 8.81/2.63 | Combining equations (210,209) yields a new equation:
% 8.81/2.63 | (211) e20 = e21
% 8.81/2.63 |
% 8.81/2.63 | Equations (211) can reduce 7 to:
% 8.81/2.63 | (193) $false
% 8.81/2.63 |
% 8.81/2.63 |-The branch is then unsatisfiable
% 8.81/2.63 |-Branch two:
% 8.81/2.63 | (239) ~ (all_0_8_8 = e24)
% 8.81/2.63 | (240) all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 8.81/2.63 |
% 8.81/2.63 +-Applying beta-rule and splitting (195), into two cases.
% 8.81/2.63 |-Branch one:
% 8.81/2.63 | (241) all_0_0_0 = e13
% 8.81/2.63 |
% 8.81/2.63 | From (241) and (16) follows:
% 8.81/2.63 | (242) h(e13) = e24
% 8.81/2.63 |
% 8.81/2.63 | Instantiating formula (96) with e13, e24, all_0_6_6 and discharging atoms h(e13) = all_0_6_6, h(e13) = e24, yields:
% 8.81/2.63 | (215) all_0_6_6 = e24
% 8.81/2.63 |
% 8.81/2.63 | Equations (215) can reduce 226 to:
% 8.81/2.63 | (193) $false
% 8.81/2.63 |
% 8.81/2.63 |-The branch is then unsatisfiable
% 8.81/2.63 |-Branch two:
% 8.81/2.63 | (245) ~ (all_0_0_0 = e13)
% 8.81/2.63 | (246) all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 8.81/2.63 |
% 8.81/2.63 +-Applying beta-rule and splitting (246), into two cases.
% 8.81/2.63 |-Branch one:
% 8.81/2.63 | (247) all_0_0_0 = e12
% 8.81/2.63 |
% 8.81/2.63 | From (247) and (16) follows:
% 8.81/2.63 | (248) h(e12) = e24
% 8.81/2.63 |
% 8.81/2.63 | Instantiating formula (96) with e12, e24, all_0_7_7 and discharging atoms h(e12) = all_0_7_7, h(e12) = e24, yields:
% 8.81/2.63 | (202) all_0_7_7 = e24
% 8.81/2.63 |
% 8.81/2.63 | Equations (202) can reduce 213 to:
% 8.81/2.63 | (193) $false
% 8.81/2.63 |
% 8.81/2.63 |-The branch is then unsatisfiable
% 8.81/2.63 |-Branch two:
% 8.81/2.63 | (251) ~ (all_0_0_0 = e12)
% 8.81/2.63 | (252) all_0_0_0 = e10 | all_0_0_0 = e11
% 8.81/2.63 |
% 8.81/2.63 +-Applying beta-rule and splitting (252), into two cases.
% 8.81/2.63 |-Branch one:
% 8.81/2.63 | (253) all_0_0_0 = e10
% 8.81/2.63 |
% 8.81/2.63 | From (253) and (16) follows:
% 8.81/2.63 | (254) h(e10) = e24
% 8.81/2.63 |
% 8.81/2.63 | Instantiating formula (96) with e10, e24, all_0_9_9 and discharging atoms h(e10) = all_0_9_9, h(e10) = e24, yields:
% 8.81/2.63 | (196) all_0_9_9 = e24
% 8.81/2.63 |
% 8.81/2.63 | Equations (196) can reduce 200 to:
% 8.81/2.63 | (193) $false
% 8.81/2.63 |
% 8.81/2.63 |-The branch is then unsatisfiable
% 8.81/2.63 |-Branch two:
% 8.81/2.63 | (257) ~ (all_0_0_0 = e10)
% 8.81/2.63 | (258) all_0_0_0 = e11
% 8.81/2.63 |
% 8.81/2.63 | From (258) and (16) follows:
% 8.81/2.63 | (259) h(e11) = e24
% 8.81/2.63 |
% 8.81/2.63 | Instantiating formula (96) with e11, e24, all_0_8_8 and discharging atoms h(e11) = all_0_8_8, h(e11) = e24, yields:
% 8.81/2.63 | (228) all_0_8_8 = e24
% 8.81/2.64 |
% 8.81/2.64 | Equations (228) can reduce 239 to:
% 8.81/2.64 | (193) $false
% 8.81/2.64 |
% 8.81/2.64 |-The branch is then unsatisfiable
% 8.81/2.64 % SZS output end Proof for theBenchmark
% 8.81/2.64
% 8.81/2.64 2027ms
%------------------------------------------------------------------------------