TSTP Solution File: ALG076+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG076+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n032.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 15:34:15 EDT 2022
% Result : Theorem 4.49s 1.54s
% Output : Proof 8.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : ALG076+1 : TPTP v8.1.0. Released v2.7.0.
% 0.00/0.08 % Command : ePrincess-casc -timeout=%d %s
% 0.07/0.26 % Computer : n032.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 600
% 0.07/0.26 % DateTime : Wed Jun 8 04:14:36 EDT 2022
% 0.07/0.27 % CPUTime :
% 0.10/0.48 ____ _
% 0.10/0.48 ___ / __ \_____(_)___ ________ __________
% 0.10/0.48 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.10/0.48 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.10/0.48 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.10/0.48
% 0.10/0.48 A Theorem Prover for First-Order Logic
% 0.10/0.48 (ePrincess v.1.0)
% 0.10/0.48
% 0.10/0.48 (c) Philipp Rümmer, 2009-2015
% 0.10/0.48 (c) Peter Backeman, 2014-2015
% 0.10/0.48 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.10/0.48 Free software under GNU Lesser General Public License (LGPL).
% 0.10/0.48 Bug reports to peter@backeman.se
% 0.10/0.48
% 0.10/0.48 For more information, visit http://user.uu.se/~petba168/breu/
% 0.10/0.48
% 0.10/0.48 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.10/0.53 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.75/0.89 Prover 0: Preprocessing ...
% 2.97/1.18 Prover 0: Constructing countermodel ...
% 4.49/1.54 Prover 0: proved (1013ms)
% 4.49/1.54
% 4.49/1.54 No countermodel exists, formula is valid
% 4.49/1.54 % SZS status Theorem for theBenchmark
% 4.49/1.54
% 4.49/1.54 Generating proof ... found it (size 103)
% 7.97/2.34
% 7.97/2.34 % SZS output start Proof for theBenchmark
% 7.97/2.34 Assumed formulas after preprocessing and simplification:
% 7.97/2.34 | (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) = v4 & op2(v3, v2) = v0 & op2(v3, v1) = v2 & op2(v3, v0) = v3 & op2(v2, v4) = v3 & op2(v2, v3) = v1 & op2(v2, v2) = v4 & op2(v2, v1) = v0 & op2(v2, v0) = v2 & op2(v1, v4) = v2 & op2(v1, v3) = v0 & op2(v1, v2) = v3 & op2(v1, v1) = v4 & 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) = e14 & op1(e13, e12) = e10 & op1(e13, e10) = e13 & op1(e13, e11) = e12 & op1(e12, e14) = e13 & op1(e12, e13) = e11 & op1(e12, e12) = e14 & op1(e12, e10) = e12 & op1(e12, e11) = e10 & 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) = e10 & op1(e11, e12) = e13 & op1(e11, e10) = e11 & op1(e11, e11) = e14 & 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))
% 7.97/2.38 | 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:
% 7.97/2.38 | (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_5_5 & op2(all_0_6_6, all_0_7_7) = all_0_9_9 & 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_5_5 & op2(all_0_7_7, all_0_8_8) = all_0_9_9 & 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_9_9 & op2(all_0_8_8, all_0_7_7) = all_0_6_6 & op2(all_0_8_8, all_0_8_8) = all_0_5_5 & 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) = e14 & op1(e13, e12) = e10 & op1(e13, e10) = e13 & op1(e13, e11) = e12 & op1(e12, e14) = e13 & op1(e12, e13) = e11 & op1(e12, e12) = e14 & op1(e12, e10) = e12 & op1(e12, e11) = e10 & 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) = e10 & op1(e11, e12) = e13 & op1(e11, e10) = e11 & op1(e11, e11) = e14 & 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)
% 8.36/2.39 |
% 8.36/2.39 | Applying alpha-rule on (1) yields:
% 8.36/2.39 | (2) op1(all_0_2_2, all_0_1_1) = all_0_4_4
% 8.36/2.39 | (3) op2(all_0_6_6, all_0_6_6) = all_0_5_5
% 8.36/2.39 | (4) op1(all_0_3_3, all_0_0_0) = all_0_1_1
% 8.36/2.39 | (5) op1(e13, e11) = e12
% 8.36/2.39 | (6) ~ (e22 = e13)
% 8.36/2.39 | (7) ~ (e24 = e23)
% 8.36/2.39 | (8) j(e21) = all_0_3_3
% 8.36/2.39 | (9) h(all_0_2_2) = e22
% 8.36/2.39 | (10) ~ (e22 = e11)
% 8.36/2.39 | (11) ~ (e24 = e10)
% 8.36/2.39 | (12) op2(e20, e24) = e24
% 8.36/2.39 | (13) op1(e13, e13) = e14
% 8.36/2.39 | (14) ~ (e21 = e11)
% 8.36/2.39 | (15) op1(e11, e12) = e13
% 8.36/2.39 | (16) op2(e20, e23) = e23
% 8.36/2.39 | (17) op2(all_0_5_5, all_0_8_8) = all_0_6_6
% 8.36/2.39 | (18) ~ (e21 = e12)
% 8.36/2.39 | (19) ~ (e24 = e12)
% 8.36/2.39 | (20) op2(all_0_8_8, all_0_8_8) = all_0_5_5
% 8.36/2.39 | (21) op2(e23, e23) = e24
% 8.36/2.39 | (22) ~ (e24 = e21)
% 8.36/2.39 | (23) op1(all_0_4_4, all_0_2_2) = all_0_2_2
% 8.36/2.39 | (24) op1(all_0_1_1, all_0_1_1) = all_0_0_0
% 8.36/2.39 | (25) j(e20) = all_0_4_4
% 8.36/2.39 | (26) op1(e13, e12) = e10
% 8.36/2.39 | (27) op2(e22, e20) = e22
% 8.36/2.39 | (28) ~ (e14 = e11)
% 8.36/2.39 | (29) op2(e21, e22) = e24
% 8.36/2.39 | (30) op2(e22, e21) = e24
% 8.36/2.39 | (31) ~ (e20 = e10)
% 8.36/2.39 | (32) op2(all_0_8_8, all_0_9_9) = all_0_8_8
% 8.36/2.39 | (33) op1(all_0_3_3, all_0_2_2) = all_0_0_0
% 8.36/2.39 | (34) op1(e13, e14) = e11
% 8.36/2.40 | (35) op2(all_0_9_9, all_0_6_6) = all_0_6_6
% 8.36/2.40 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0))
% 8.36/2.40 | (37) op1(all_0_2_2, all_0_2_2) = all_0_1_1
% 8.36/2.40 | (38) ~ (e23 = e10)
% 8.36/2.40 | (39) op1(all_0_3_3, all_0_4_4) = all_0_3_3
% 8.36/2.40 | (40) op1(e10, e11) = e11
% 8.36/2.40 | (41) op1(all_0_2_2, all_0_4_4) = all_0_2_2
% 8.36/2.40 | (42) op2(all_0_6_6, all_0_7_7) = all_0_9_9
% 8.36/2.40 | (43) ~ (e23 = e22)
% 8.36/2.40 | (44) op1(all_0_0_0, all_0_2_2) = all_0_4_4
% 8.36/2.40 | (45) op2(all_0_7_7, all_0_7_7) = all_0_5_5
% 8.36/2.40 | (46) op2(all_0_5_5, all_0_7_7) = all_0_8_8
% 8.36/2.40 | (47) op1(e12, e11) = e10
% 8.36/2.40 | (48) op2(all_0_9_9, all_0_8_8) = all_0_8_8
% 8.36/2.40 | (49) ~ (e22 = e12)
% 8.40/2.40 | (50) op2(e22, e24) = e21
% 8.40/2.40 | (51) ~ (e23 = e20)
% 8.40/2.40 | (52) op1(e11, e14) = e12
% 8.40/2.40 | (53) h(e14) = all_0_5_5
% 8.40/2.40 | (54) ~ (e22 = e10)
% 8.40/2.40 | (55) op1(all_0_0_0, all_0_1_1) = all_0_3_3
% 8.40/2.40 | (56) op1(e14, e14) = e10
% 8.40/2.40 | (57) op1(all_0_0_0, all_0_0_0) = all_0_2_2
% 8.40/2.40 | (58) op2(all_0_6_6, all_0_5_5) = all_0_8_8
% 8.40/2.40 | (59) op2(all_0_7_7, all_0_9_9) = all_0_7_7
% 8.40/2.40 | (60) op2(e20, e22) = e22
% 8.40/2.40 | (61) ~ (e14 = e10)
% 8.40/2.40 | (62) op2(e23, e20) = e23
% 8.40/2.40 | (63) ~ (e14 = e12)
% 8.40/2.40 | (64) ~ (e13 = e11)
% 8.40/2.40 | (65) op1(all_0_2_2, all_0_3_3) = all_0_0_0
% 8.40/2.40 | (66) j(all_0_6_6) = e13
% 8.40/2.40 | (67) ~ (e20 = e13)
% 8.40/2.40 | (68) j(e23) = all_0_1_1
% 8.40/2.40 | (69) j(all_0_5_5) = e14
% 8.40/2.40 | (70) op2(e24, e21) = e23
% 8.40/2.40 | (71) op1(e11, e10) = e11
% 8.40/2.40 | (72) ~ (e12 = e10)
% 8.40/2.40 | (73) op2(all_0_5_5, all_0_9_9) = all_0_5_5
% 8.40/2.40 | (74) ~ (e20 = e11)
% 8.40/2.40 | (75) h(all_0_1_1) = e23
% 8.40/2.40 | (76) op1(all_0_0_0, all_0_3_3) = all_0_1_1
% 8.40/2.40 | (77) op2(e23, e22) = e21
% 8.40/2.40 | (78) j(e24) = all_0_0_0
% 8.40/2.40 | (79) op1(all_0_1_1, all_0_0_0) = all_0_4_4
% 8.40/2.40 | (80) op1(e11, e13) = e10
% 8.40/2.40 | (81) op2(e22, e23) = e20
% 8.40/2.40 | (82) op2(all_0_7_7, all_0_5_5) = all_0_6_6
% 8.40/2.40 | (83) ~ (e23 = e13)
% 8.40/2.40 | (84) ~ (e13 = e10)
% 8.40/2.40 | (85) op2(e23, e21) = e22
% 8.40/2.40 | (86) op2(all_0_8_8, all_0_5_5) = all_0_7_7
% 8.40/2.40 | (87) h(e12) = all_0_7_7
% 8.40/2.40 | (88) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0))
% 8.40/2.40 | (89) op1(e10, e10) = e10
% 8.40/2.40 | (90) ~ (e20 = e21)
% 8.40/2.40 | (91) op1(e14, e12) = e11
% 8.40/2.40 | (92) op2(e24, e20) = e24
% 8.40/2.40 | (93) j(e22) = all_0_2_2
% 8.43/2.40 | (94) ~ (e22 = e14)
% 8.43/2.40 | (95) ~ (e24 = e13)
% 8.43/2.40 | (96) op1(all_0_3_3, all_0_3_3) = all_0_4_4
% 8.43/2.40 | (97) j(all_0_8_8) = e11
% 8.43/2.40 | (98) op2(e20, e20) = e20
% 8.43/2.40 | (99) ~ (e24 = e14)
% 8.43/2.40 | (100) op2(all_0_9_9, all_0_5_5) = all_0_5_5
% 8.43/2.40 | (101) op1(e10, e12) = e12
% 8.43/2.41 | (102) op2(e24, e23) = e21
% 8.43/2.41 | (103) op2(e21, e23) = e22
% 8.43/2.41 | (104) op1(e14, e11) = e13
% 8.43/2.41 | (105) ~ (e24 = e11)
% 8.43/2.41 | (106) op2(all_0_6_6, all_0_8_8) = all_0_7_7
% 8.43/2.41 | (107) op1(all_0_1_1, all_0_2_2) = all_0_3_3
% 8.43/2.41 | (108) op1(all_0_4_4, all_0_0_0) = all_0_0_0
% 8.43/2.41 | (109) op2(all_0_5_5, all_0_5_5) = all_0_9_9
% 8.43/2.41 | (110) ~ (e20 = e12)
% 8.43/2.41 | (111) ~ (e12 = e11)
% 8.43/2.41 | (112) 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
% 8.43/2.41 | (113) op2(all_0_8_8, all_0_6_6) = all_0_9_9
% 8.43/2.41 | (114) 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
% 8.43/2.41 | (115) ~ (e21 = e10)
% 8.43/2.41 | (116) 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
% 8.43/2.41 | (117) h(all_0_4_4) = e20
% 8.43/2.41 | (118) h(all_0_3_3) = e21
% 8.43/2.41 | (119) ~ (e24 = e20)
% 8.43/2.41 | (120) ~ (e13 = e12)
% 8.43/2.41 | (121) op2(e23, e24) = e20
% 8.43/2.41 | (122) op1(all_0_2_2, all_0_0_0) = all_0_3_3
% 8.43/2.41 | (123) 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
% 8.43/2.41 | (124) 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
% 8.43/2.41 | (125) op1(all_0_4_4, all_0_4_4) = all_0_4_4
% 8.43/2.41 | (126) ~ (e22 = e20)
% 8.43/2.41 | (127) op2(all_0_5_5, all_0_6_6) = all_0_7_7
% 8.43/2.41 | (128) op1(all_0_4_4, all_0_3_3) = all_0_3_3
% 8.43/2.41 | (129) ~ (e22 = e21)
% 8.43/2.41 | (130) op1(all_0_1_1, all_0_3_3) = all_0_2_2
% 8.43/2.41 | (131) op1(e10, e13) = e13
% 8.43/2.41 | (132) op1(e11, e11) = e14
% 8.43/2.41 | (133) ~ (e23 = e12)
% 8.43/2.41 | (134) 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
% 8.43/2.41 | (135) op1(e10, e14) = e14
% 8.43/2.41 | (136) op2(all_0_6_6, all_0_9_9) = all_0_6_6
% 8.43/2.41 | (137) op1(e12, e12) = e14
% 8.43/2.41 | (138) op1(all_0_1_1, all_0_4_4) = all_0_1_1
% 8.43/2.41 | (139) ~ (e23 = e11)
% 8.43/2.41 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0))
% 8.43/2.41 | (141) ~ (e23 = e21)
% 8.43/2.41 | (142) h(e10) = all_0_9_9
% 8.43/2.41 | (143) op2(all_0_7_7, all_0_8_8) = all_0_9_9
% 8.43/2.41 | (144) h(e13) = all_0_6_6
% 8.43/2.41 | (145) op1(e14, e13) = e12
% 8.43/2.41 | (146) ~ (e14 = e13)
% 8.43/2.41 | (147) ~ (e23 = e14)
% 8.43/2.41 | (148) op2(e21, e24) = e23
% 8.43/2.41 | (149) 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
% 8.43/2.41 | (150) ~ (e21 = e13)
% 8.43/2.41 | (151) ~ (e21 = e14)
% 8.43/2.41 | (152) op1(e14, e10) = e14
% 8.43/2.41 | (153) h(all_0_0_0) = e24
% 8.43/2.41 | (154) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0))
% 8.43/2.41 | (155) 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
% 8.43/2.42 | (156) op1(all_0_4_4, all_0_1_1) = all_0_1_1
% 8.43/2.42 | (157) op1(e12, e14) = e13
% 8.43/2.42 | (158) op2(e24, e22) = e20
% 8.43/2.42 | (159) op2(all_0_8_8, all_0_7_7) = all_0_6_6
% 8.43/2.42 | (160) op2(e21, e20) = e21
% 8.43/2.42 | (161) op1(e13, e10) = e13
% 8.43/2.42 | (162) op1(e12, e10) = e12
% 8.43/2.42 | (163) op2(e21, e21) = e20
% 8.43/2.42 | (164) ~ (e10 = e11)
% 8.43/2.42 | (165) 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
% 8.43/2.42 | (166) op1(all_0_0_0, all_0_4_4) = all_0_0_0
% 8.43/2.42 | (167) op2(all_0_9_9, all_0_9_9) = all_0_9_9
% 8.43/2.42 | (168) ~ (e20 = e14)
% 8.43/2.42 | (169) ~ (e24 = e22)
% 8.43/2.42 | (170) op2(all_0_9_9, all_0_7_7) = all_0_7_7
% 8.43/2.42 | (171) op2(all_0_7_7, all_0_6_6) = all_0_8_8
% 8.43/2.42 | (172) op1(e12, e13) = e11
% 8.43/2.42 | (173) op2(e20, e21) = e21
% 8.43/2.42 | (174) op2(e22, e22) = e23
% 8.43/2.42 | (175) 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
% 8.43/2.42 | (176) j(all_0_9_9) = e10
% 8.43/2.42 | (177) h(e11) = all_0_8_8
% 8.43/2.42 | (178) op2(e24, e24) = e22
% 8.43/2.42 | (179) j(all_0_7_7) = e12
% 8.43/2.42 | (180) op1(all_0_3_3, all_0_1_1) = all_0_2_2
% 8.43/2.42 |
% 8.43/2.42 +-Applying beta-rule and splitting (116), into two cases.
% 8.43/2.42 |-Branch one:
% 8.43/2.42 | (181) all_0_0_0 = e14
% 8.43/2.42 |
% 8.43/2.42 | From (181)(181) and (57) follows:
% 8.43/2.42 | (182) op1(e14, e14) = all_0_2_2
% 8.43/2.42 |
% 8.43/2.42 | From (181) and (44) follows:
% 8.43/2.42 | (183) op1(e14, all_0_2_2) = all_0_4_4
% 8.43/2.42 |
% 8.43/2.42 | Instantiating formula (36) with e14, e14, all_0_2_2, e10 and discharging atoms op1(e14, e14) = all_0_2_2, op1(e14, e14) = e10, yields:
% 8.43/2.42 | (184) all_0_2_2 = e10
% 8.43/2.42 |
% 8.43/2.42 | From (184) and (2) follows:
% 8.43/2.42 | (185) op1(e10, all_0_1_1) = all_0_4_4
% 8.43/2.42 |
% 8.43/2.42 | From (184)(184) and (37) follows:
% 8.43/2.42 | (186) op1(e10, e10) = all_0_1_1
% 8.43/2.42 |
% 8.43/2.42 | From (184) and (183) follows:
% 8.43/2.42 | (187) op1(e14, e10) = all_0_4_4
% 8.43/2.42 |
% 8.43/2.42 | Instantiating formula (36) with e14, e10, all_0_4_4, e14 and discharging atoms op1(e14, e10) = all_0_4_4, op1(e14, e10) = e14, yields:
% 8.43/2.43 | (188) all_0_4_4 = e14
% 8.43/2.43 |
% 8.43/2.43 | Instantiating formula (36) with e10, e10, all_0_1_1, e10 and discharging atoms op1(e10, e10) = all_0_1_1, op1(e10, e10) = e10, yields:
% 8.43/2.43 | (189) all_0_1_1 = e10
% 8.43/2.43 |
% 8.43/2.43 | From (189)(188) and (185) follows:
% 8.43/2.43 | (190) op1(e10, e10) = e14
% 8.43/2.43 |
% 8.43/2.43 | From (189) and (186) follows:
% 8.43/2.43 | (89) op1(e10, e10) = e10
% 8.43/2.43 |
% 8.43/2.43 | Instantiating formula (36) with e10, e10, e14, e10 and discharging atoms op1(e10, e10) = e14, op1(e10, e10) = e10, yields:
% 8.43/2.43 | (192) e14 = e10
% 8.43/2.43 |
% 8.43/2.43 | Equations (192) can reduce 61 to:
% 8.43/2.43 | (193) $false
% 8.43/2.43 |
% 8.43/2.43 |-The branch is then unsatisfiable
% 8.43/2.43 |-Branch two:
% 8.43/2.43 | (194) ~ (all_0_0_0 = e14)
% 8.43/2.43 | (195) all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 8.43/2.43 |
% 8.43/2.43 +-Applying beta-rule and splitting (165), into two cases.
% 8.43/2.43 |-Branch one:
% 8.43/2.43 | (196) all_0_9_9 = e24
% 8.43/2.43 |
% 8.43/2.43 | From (196)(196)(196) and (167) follows:
% 8.43/2.43 | (197) op2(e24, e24) = e24
% 8.43/2.43 |
% 8.43/2.43 | Instantiating formula (140) with e24, e24, e24, e22 and discharging atoms op2(e24, e24) = e24, op2(e24, e24) = e22, yields:
% 8.43/2.43 | (198) e24 = e22
% 8.43/2.43 |
% 8.43/2.43 | Equations (198) can reduce 169 to:
% 8.43/2.43 | (193) $false
% 8.43/2.43 |
% 8.43/2.43 |-The branch is then unsatisfiable
% 8.43/2.43 |-Branch two:
% 8.43/2.43 | (200) ~ (all_0_9_9 = e24)
% 8.43/2.43 | (201) all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21
% 8.43/2.43 |
% 8.43/2.43 +-Applying beta-rule and splitting (175), into two cases.
% 8.43/2.43 |-Branch one:
% 8.43/2.43 | (202) all_0_7_7 = e24
% 8.43/2.43 |
% 8.43/2.43 | From (202) and (127) follows:
% 8.43/2.43 | (203) op2(all_0_5_5, all_0_6_6) = e24
% 8.43/2.43 |
% 8.43/2.43 | From (202) and (46) follows:
% 8.43/2.43 | (204) op2(all_0_5_5, e24) = all_0_8_8
% 8.43/2.43 |
% 8.43/2.43 | From (202) and (42) follows:
% 8.43/2.43 | (205) op2(all_0_6_6, e24) = all_0_9_9
% 8.43/2.43 |
% 8.43/2.43 | From (202) and (106) follows:
% 8.43/2.43 | (206) op2(all_0_6_6, all_0_8_8) = e24
% 8.43/2.43 |
% 8.43/2.43 | From (202) and (82) follows:
% 8.43/2.43 | (207) op2(e24, all_0_5_5) = all_0_6_6
% 8.43/2.43 |
% 8.43/2.43 | From (202)(202) and (45) follows:
% 8.43/2.43 | (208) op2(e24, e24) = all_0_5_5
% 8.43/2.43 |
% 8.43/2.43 | From (202) and (159) follows:
% 8.43/2.43 | (209) op2(all_0_8_8, e24) = all_0_6_6
% 8.43/2.43 |
% 8.43/2.43 | Instantiating formula (140) with e24, e24, all_0_5_5, e22 and discharging atoms op2(e24, e24) = all_0_5_5, op2(e24, e24) = e22, yields:
% 8.43/2.43 | (210) all_0_5_5 = e22
% 8.43/2.43 |
% 8.43/2.43 | From (210)(210) and (109) follows:
% 8.43/2.43 | (211) op2(e22, e22) = all_0_9_9
% 8.43/2.43 |
% 8.43/2.43 | From (210) and (203) follows:
% 8.43/2.43 | (212) op2(e22, all_0_6_6) = e24
% 8.43/2.43 |
% 8.43/2.43 | From (210) and (204) follows:
% 8.43/2.43 | (213) op2(e22, e24) = all_0_8_8
% 8.43/2.43 |
% 8.43/2.43 | From (210) and (207) follows:
% 8.43/2.43 | (214) op2(e24, e22) = all_0_6_6
% 8.43/2.43 |
% 8.43/2.43 | Instantiating formula (140) with e24, e22, all_0_6_6, e20 and discharging atoms op2(e24, e22) = all_0_6_6, op2(e24, e22) = e20, yields:
% 8.43/2.43 | (215) all_0_6_6 = e20
% 8.43/2.43 |
% 8.43/2.43 | Instantiating formula (140) with e22, e24, all_0_8_8, e21 and discharging atoms op2(e22, e24) = all_0_8_8, op2(e22, e24) = e21, yields:
% 8.43/2.43 | (216) all_0_8_8 = e21
% 8.43/2.43 |
% 8.43/2.43 | Instantiating formula (140) with e22, e22, all_0_9_9, e23 and discharging atoms op2(e22, e22) = all_0_9_9, op2(e22, e22) = e23, yields:
% 8.43/2.43 | (217) all_0_9_9 = e23
% 8.43/2.43 |
% 8.43/2.43 | From (215)(216) and (206) follows:
% 8.43/2.43 | (218) op2(e20, e21) = e24
% 8.43/2.43 |
% 8.43/2.43 | From (215)(217) and (205) follows:
% 8.43/2.43 | (219) op2(e20, e24) = e23
% 8.43/2.43 |
% 8.43/2.43 | From (216)(215) and (209) follows:
% 8.43/2.43 | (220) op2(e21, e24) = e20
% 8.43/2.43 |
% 8.43/2.43 | From (215) and (212) follows:
% 8.43/2.43 | (221) op2(e22, e20) = e24
% 8.43/2.43 |
% 8.43/2.43 | Instantiating formula (140) with e22, e20, e24, e22 and discharging atoms op2(e22, e20) = e24, op2(e22, e20) = e22, yields:
% 8.43/2.43 | (198) e24 = e22
% 8.43/2.43 |
% 8.43/2.43 | Instantiating formula (140) with e20, e24, e23, e24 and discharging atoms op2(e20, e24) = e24, op2(e20, e24) = e23, yields:
% 8.43/2.43 | (223) e24 = e23
% 8.43/2.43 |
% 8.43/2.43 | Instantiating formula (140) with e20, e21, e24, e21 and discharging atoms op2(e20, e21) = e24, op2(e20, e21) = e21, yields:
% 8.43/2.43 | (224) e24 = e21
% 8.43/2.43 |
% 8.43/2.43 | Instantiating formula (140) with e21, e24, e20, e23 and discharging atoms op2(e21, e24) = e23, op2(e21, e24) = e20, yields:
% 8.43/2.43 | (225) e23 = e20
% 8.43/2.43 |
% 8.43/2.43 | Combining equations (223,198) yields a new equation:
% 8.43/2.43 | (226) e23 = e22
% 8.43/2.43 |
% 8.43/2.43 | Simplifying 226 yields:
% 8.43/2.43 | (227) e23 = e22
% 8.43/2.43 |
% 8.43/2.43 | Combining equations (224,198) yields a new equation:
% 8.43/2.43 | (228) e22 = e21
% 8.43/2.43 |
% 8.43/2.43 | Combining equations (227,225) yields a new equation:
% 8.43/2.43 | (229) e22 = e20
% 8.43/2.44 |
% 8.43/2.44 | Simplifying 229 yields:
% 8.43/2.44 | (230) e22 = e20
% 8.43/2.44 |
% 8.43/2.44 | Combining equations (230,228) yields a new equation:
% 8.43/2.44 | (231) e20 = e21
% 8.43/2.44 |
% 8.43/2.44 | Simplifying 231 yields:
% 8.43/2.44 | (232) e20 = e21
% 8.43/2.44 |
% 8.43/2.44 | Equations (232) can reduce 90 to:
% 8.43/2.44 | (193) $false
% 8.43/2.44 |
% 8.43/2.44 |-The branch is then unsatisfiable
% 8.43/2.44 |-Branch two:
% 8.43/2.44 | (234) ~ (all_0_7_7 = e24)
% 8.43/2.44 | (235) all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 8.43/2.44 |
% 8.43/2.44 +-Applying beta-rule and splitting (114), into two cases.
% 8.43/2.44 |-Branch one:
% 8.43/2.44 | (236) all_0_2_2 = e14
% 8.43/2.44 |
% 8.43/2.44 | From (236) and (2) follows:
% 8.43/2.44 | (237) op1(e14, all_0_1_1) = all_0_4_4
% 8.43/2.44 |
% 8.43/2.44 | From (236)(236) and (37) follows:
% 8.43/2.44 | (238) op1(e14, e14) = all_0_1_1
% 8.43/2.44 |
% 8.43/2.44 | Instantiating formula (36) with e14, e14, all_0_1_1, e10 and discharging atoms op1(e14, e14) = all_0_1_1, op1(e14, e14) = e10, yields:
% 8.43/2.44 | (189) all_0_1_1 = e10
% 8.43/2.44 |
% 8.43/2.44 | From (189) and (79) follows:
% 8.43/2.44 | (240) op1(e10, all_0_0_0) = all_0_4_4
% 8.43/2.44 |
% 8.43/2.44 | From (189)(189) and (24) follows:
% 8.43/2.44 | (241) op1(e10, e10) = all_0_0_0
% 8.43/2.44 |
% 8.43/2.44 | From (189) and (237) follows:
% 8.43/2.44 | (187) op1(e14, e10) = all_0_4_4
% 8.43/2.44 |
% 8.43/2.44 | Instantiating formula (36) with e14, e10, all_0_4_4, e14 and discharging atoms op1(e14, e10) = all_0_4_4, op1(e14, e10) = e14, yields:
% 8.43/2.44 | (188) all_0_4_4 = e14
% 8.43/2.44 |
% 8.43/2.44 | Instantiating formula (36) with e10, e10, all_0_0_0, e10 and discharging atoms op1(e10, e10) = all_0_0_0, op1(e10, e10) = e10, yields:
% 8.43/2.44 | (244) all_0_0_0 = e10
% 8.43/2.44 |
% 8.43/2.44 | Equations (244) can reduce 194 to:
% 8.43/2.44 | (245) ~ (e14 = e10)
% 8.43/2.44 |
% 8.43/2.44 | Simplifying 245 yields:
% 8.43/2.44 | (61) ~ (e14 = e10)
% 8.43/2.44 |
% 8.43/2.44 | From (244)(188) and (240) follows:
% 8.43/2.44 | (190) op1(e10, e10) = e14
% 8.43/2.44 |
% 8.43/2.44 | From (244) and (241) follows:
% 8.43/2.44 | (89) op1(e10, e10) = e10
% 8.43/2.44 |
% 8.43/2.44 | Instantiating formula (36) with e10, e10, e14, e10 and discharging atoms op1(e10, e10) = e14, op1(e10, e10) = e10, yields:
% 8.43/2.44 | (192) e14 = e10
% 8.43/2.44 |
% 8.43/2.44 | Equations (192) can reduce 61 to:
% 8.43/2.44 | (193) $false
% 8.43/2.44 |
% 8.43/2.44 |-The branch is then unsatisfiable
% 8.43/2.44 |-Branch two:
% 8.43/2.44 | (251) ~ (all_0_2_2 = e14)
% 8.43/2.44 | (252) all_0_2_2 = e13 | all_0_2_2 = e12 | all_0_2_2 = e10 | all_0_2_2 = e11
% 8.43/2.44 |
% 8.43/2.44 +-Applying beta-rule and splitting (124), into two cases.
% 8.43/2.44 |-Branch one:
% 8.43/2.44 | (253) all_0_6_6 = e24
% 8.43/2.44 |
% 8.43/2.44 | From (253)(253) and (3) follows:
% 8.43/2.44 | (208) op2(e24, e24) = all_0_5_5
% 8.43/2.44 |
% 8.43/2.44 | Instantiating formula (140) with e24, e24, all_0_5_5, e22 and discharging atoms op2(e24, e24) = all_0_5_5, op2(e24, e24) = e22, yields:
% 8.43/2.44 | (210) all_0_5_5 = e22
% 8.43/2.44 |
% 8.43/2.44 | From (210) and (69) follows:
% 8.43/2.44 | (256) j(e22) = e14
% 8.43/2.44 |
% 8.43/2.44 | Instantiating formula (88) with e22, e14, all_0_2_2 and discharging atoms j(e22) = all_0_2_2, j(e22) = e14, yields:
% 8.43/2.44 | (236) all_0_2_2 = e14
% 8.43/2.44 |
% 8.43/2.44 | Equations (236) can reduce 251 to:
% 8.43/2.44 | (193) $false
% 8.43/2.44 |
% 8.43/2.44 |-The branch is then unsatisfiable
% 8.43/2.44 |-Branch two:
% 8.43/2.44 | (259) ~ (all_0_6_6 = e24)
% 8.43/2.44 | (260) all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21
% 8.43/2.44 |
% 8.43/2.44 +-Applying beta-rule and splitting (134), into two cases.
% 8.43/2.44 |-Branch one:
% 8.43/2.44 | (261) all_0_8_8 = e24
% 8.43/2.44 |
% 8.43/2.44 | From (261)(261) and (20) follows:
% 8.43/2.44 | (208) op2(e24, e24) = all_0_5_5
% 8.43/2.44 |
% 8.43/2.44 | Instantiating formula (140) with e24, e24, all_0_5_5, e22 and discharging atoms op2(e24, e24) = all_0_5_5, op2(e24, e24) = e22, yields:
% 8.43/2.44 | (210) all_0_5_5 = e22
% 8.43/2.44 |
% 8.43/2.44 | From (210) and (69) follows:
% 8.43/2.44 | (256) j(e22) = e14
% 8.43/2.44 |
% 8.43/2.44 | Instantiating formula (88) with e22, e14, all_0_2_2 and discharging atoms j(e22) = all_0_2_2, j(e22) = e14, yields:
% 8.43/2.44 | (236) all_0_2_2 = e14
% 8.43/2.44 |
% 8.43/2.44 | Equations (236) can reduce 251 to:
% 8.43/2.44 | (193) $false
% 8.43/2.44 |
% 8.43/2.44 |-The branch is then unsatisfiable
% 8.43/2.44 |-Branch two:
% 8.43/2.44 | (267) ~ (all_0_8_8 = e24)
% 8.43/2.44 | (268) all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 8.43/2.44 |
% 8.43/2.44 +-Applying beta-rule and splitting (195), into two cases.
% 8.43/2.44 |-Branch one:
% 8.43/2.44 | (269) all_0_0_0 = e13
% 8.43/2.44 |
% 8.43/2.44 | From (269) and (153) follows:
% 8.43/2.44 | (270) h(e13) = e24
% 8.43/2.44 |
% 8.43/2.44 | Instantiating formula (154) with e13, e24, all_0_6_6 and discharging atoms h(e13) = all_0_6_6, h(e13) = e24, yields:
% 8.43/2.44 | (253) all_0_6_6 = e24
% 8.43/2.44 |
% 8.43/2.44 | Equations (253) can reduce 259 to:
% 8.43/2.44 | (193) $false
% 8.43/2.44 |
% 8.43/2.44 |-The branch is then unsatisfiable
% 8.43/2.44 |-Branch two:
% 8.43/2.44 | (273) ~ (all_0_0_0 = e13)
% 8.43/2.44 | (274) all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 8.43/2.44 |
% 8.43/2.44 +-Applying beta-rule and splitting (274), into two cases.
% 8.43/2.44 |-Branch one:
% 8.43/2.44 | (275) all_0_0_0 = e12
% 8.43/2.44 |
% 8.43/2.44 | From (275) and (153) follows:
% 8.43/2.44 | (276) h(e12) = e24
% 8.43/2.44 |
% 8.43/2.44 | Instantiating formula (154) with e12, e24, all_0_7_7 and discharging atoms h(e12) = all_0_7_7, h(e12) = e24, yields:
% 8.43/2.44 | (202) all_0_7_7 = e24
% 8.43/2.44 |
% 8.43/2.44 | Equations (202) can reduce 234 to:
% 8.43/2.44 | (193) $false
% 8.43/2.44 |
% 8.43/2.44 |-The branch is then unsatisfiable
% 8.43/2.44 |-Branch two:
% 8.43/2.44 | (279) ~ (all_0_0_0 = e12)
% 8.43/2.44 | (280) all_0_0_0 = e10 | all_0_0_0 = e11
% 8.43/2.44 |
% 8.43/2.44 +-Applying beta-rule and splitting (280), into two cases.
% 8.43/2.44 |-Branch one:
% 8.43/2.44 | (244) all_0_0_0 = e10
% 8.43/2.44 |
% 8.43/2.44 | From (244) and (153) follows:
% 8.43/2.44 | (282) h(e10) = e24
% 8.43/2.44 |
% 8.43/2.44 | Instantiating formula (154) with e10, e24, all_0_9_9 and discharging atoms h(e10) = all_0_9_9, h(e10) = e24, yields:
% 8.43/2.44 | (196) all_0_9_9 = e24
% 8.43/2.44 |
% 8.43/2.44 | Equations (196) can reduce 200 to:
% 8.43/2.44 | (193) $false
% 8.43/2.44 |
% 8.43/2.44 |-The branch is then unsatisfiable
% 8.43/2.44 |-Branch two:
% 8.43/2.44 | (285) ~ (all_0_0_0 = e10)
% 8.43/2.44 | (286) all_0_0_0 = e11
% 8.43/2.44 |
% 8.43/2.44 | From (286) and (153) follows:
% 8.43/2.44 | (287) h(e11) = e24
% 8.43/2.44 |
% 8.43/2.44 | Instantiating formula (154) with e11, e24, all_0_8_8 and discharging atoms h(e11) = all_0_8_8, h(e11) = e24, yields:
% 8.43/2.44 | (261) all_0_8_8 = e24
% 8.43/2.44 |
% 8.43/2.44 | Equations (261) can reduce 267 to:
% 8.43/2.44 | (193) $false
% 8.43/2.44 |
% 8.43/2.44 |-The branch is then unsatisfiable
% 8.43/2.44 % SZS output end Proof for theBenchmark
% 8.43/2.44
% 8.43/2.44 1954ms
%------------------------------------------------------------------------------