TSTP Solution File: ALG089+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG089+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n018.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 5.00s 1.76s
% Output : Proof 10.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG089+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 10:33:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.52/0.58 ____ _
% 0.52/0.58 ___ / __ \_____(_)___ ________ __________
% 0.52/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.52/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.52/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.52/0.58
% 0.52/0.58 A Theorem Prover for First-Order Logic
% 0.52/0.58 (ePrincess v.1.0)
% 0.52/0.58
% 0.52/0.58 (c) Philipp Rümmer, 2009-2015
% 0.52/0.58 (c) Peter Backeman, 2014-2015
% 0.52/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.52/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.52/0.58 Bug reports to peter@backeman.se
% 0.52/0.58
% 0.52/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.52/0.58
% 0.52/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.52/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.81/1.03 Prover 0: Preprocessing ...
% 2.77/1.31 Prover 0: Constructing countermodel ...
% 5.00/1.76 Prover 0: proved (1130ms)
% 5.00/1.76
% 5.00/1.76 No countermodel exists, formula is valid
% 5.00/1.76 % SZS status Theorem for theBenchmark
% 5.00/1.76
% 5.00/1.76 Generating proof ... found it (size 257)
% 9.69/2.82
% 9.69/2.82 % SZS output start Proof for theBenchmark
% 9.69/2.82 Assumed formulas after preprocessing and simplification:
% 9.69/2.82 | (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) = e20 & op2(e24, e23) = e22 & op2(e24, e22) = e21 & op2(e24, e20) = e24 & op2(e24, e21) = e23 & op2(e23, e24) = e22 & op2(e23, e23) = e21 & op2(e23, e22) = e20 & op2(e23, e20) = e23 & op2(e23, e21) = e24 & op2(e22, e24) = e21 & op2(e22, e23) = e24 & op2(e22, e22) = e23 & op2(e22, e20) = e22 & op2(e22, e21) = e20 & 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) = e20 & op2(e21, e22) = e24 & op2(e21, e20) = e21 & op2(e21, e21) = e22 & op1(v9, v9) = v5 & op1(v9, v8) = v7 & op1(v9, v7) = v6 & op1(v9, v6) = v8 & op1(v9, v5) = v9 & op1(v8, v9) = v7 & op1(v8, v8) = v6 & op1(v8, v7) = v5 & op1(v8, v6) = v9 & op1(v8, v5) = v8 & op1(v7, v9) = v6 & op1(v7, v8) = v9 & op1(v7, v7) = v8 & op1(v7, v6) = v5 & op1(v7, v5) = v7 & op1(v6, v9) = v8 & op1(v6, v8) = v5 & op1(v6, v7) = v9 & op1(v6, v6) = v7 & 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))
% 9.93/2.87 | 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:
% 9.93/2.87 | (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) = e20 & op2(e24, e23) = e22 & op2(e24, e22) = e21 & op2(e24, e20) = e24 & op2(e24, e21) = e23 & op2(e23, e24) = e22 & op2(e23, e23) = e21 & op2(e23, e22) = e20 & op2(e23, e20) = e23 & op2(e23, e21) = e24 & op2(e22, e24) = e21 & op2(e22, e23) = e24 & op2(e22, e22) = e23 & op2(e22, e20) = e22 & op2(e22, e21) = e20 & 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) = e20 & op2(e21, e22) = e24 & op2(e21, e20) = e21 & op2(e21, e21) = e22 & op1(all_0_0_0, all_0_0_0) = all_0_4_4 & op1(all_0_0_0, all_0_1_1) = all_0_2_2 & op1(all_0_0_0, all_0_2_2) = all_0_3_3 & 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_2_2 & op1(all_0_1_1, all_0_1_1) = all_0_3_3 & op1(all_0_1_1, all_0_2_2) = all_0_4_4 & op1(all_0_1_1, all_0_3_3) = all_0_0_0 & 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_0_0 & op1(all_0_2_2, all_0_2_2) = all_0_1_1 & op1(all_0_2_2, all_0_3_3) = all_0_4_4 & 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_4_4 & op1(all_0_3_3, all_0_2_2) = all_0_0_0 & op1(all_0_3_3, all_0_3_3) = all_0_2_2 & 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)
% 9.93/2.88 |
% 9.93/2.88 | Applying alpha-rule on (1) yields:
% 9.93/2.89 | (2) op2(all_0_8_8, all_0_8_8) = all_0_9_9
% 9.93/2.89 | (3) ~ (e21 = e12)
% 9.93/2.89 | (4) op1(all_0_4_4, all_0_1_1) = all_0_1_1
% 9.93/2.89 | (5) op1(e13, e14) = e11
% 9.93/2.89 | (6) op1(e13, e12) = e14
% 9.93/2.89 | (7) ~ (e20 = e21)
% 9.93/2.89 | (8) ~ (e20 = e14)
% 9.93/2.89 | (9) op2(e23, e21) = e24
% 9.93/2.89 | (10) op1(all_0_2_2, all_0_2_2) = all_0_1_1
% 9.93/2.89 | (11) op2(e20, e23) = e23
% 9.93/2.89 | (12) op1(all_0_4_4, all_0_2_2) = all_0_2_2
% 9.93/2.89 | (13) ~ (e24 = e11)
% 9.93/2.89 | (14) op1(e11, e11) = e10
% 9.93/2.89 | (15) ~ (e12 = e11)
% 9.93/2.89 | (16) h(e12) = all_0_7_7
% 9.93/2.89 | (17) h(all_0_0_0) = e24
% 9.93/2.89 | (18) h(e13) = all_0_6_6
% 9.93/2.89 | (19) op2(all_0_5_5, all_0_8_8) = all_0_6_6
% 9.93/2.89 | (20) ~ (e14 = e12)
% 9.93/2.89 | (21) ~ (e24 = e12)
% 9.93/2.89 | (22) op2(all_0_6_6, all_0_6_6) = all_0_9_9
% 9.93/2.89 | (23) op1(e12, e14) = e13
% 9.93/2.89 | (24) op1(e10, e11) = e11
% 9.93/2.89 | (25) j(e22) = all_0_2_2
% 9.93/2.89 | (26) op1(e12, e11) = e14
% 9.93/2.89 | (27) op2(all_0_9_9, all_0_8_8) = all_0_8_8
% 9.93/2.89 | (28) j(e21) = all_0_3_3
% 9.93/2.89 | (29) j(all_0_8_8) = e11
% 9.93/2.89 | (30) ~ (e22 = e13)
% 9.93/2.89 | (31) op2(all_0_6_6, all_0_9_9) = all_0_6_6
% 9.93/2.89 | (32) op2(all_0_8_8, all_0_7_7) = all_0_6_6
% 9.93/2.89 | (33) op1(e13, e13) = e10
% 9.93/2.89 | (34) op2(e24, e21) = e23
% 9.93/2.89 | (35) op1(all_0_3_3, all_0_4_4) = all_0_3_3
% 9.93/2.89 | (36) op1(e11, e12) = e13
% 9.93/2.89 | (37) j(all_0_6_6) = e13
% 9.93/2.89 | (38) op2(e24, e22) = e21
% 9.93/2.89 | (39) op2(all_0_5_5, all_0_7_7) = all_0_8_8
% 9.93/2.89 | (40) h(all_0_4_4) = e20
% 9.93/2.89 | (41) op2(e23, e22) = e20
% 9.93/2.89 | (42) op2(all_0_7_7, all_0_7_7) = all_0_9_9
% 9.93/2.89 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0))
% 9.93/2.89 | (44) op1(all_0_3_3, all_0_2_2) = all_0_0_0
% 9.93/2.89 | (45) op1(all_0_1_1, all_0_3_3) = all_0_0_0
% 9.93/2.89 | (46) ~ (e23 = e13)
% 9.93/2.89 | (47) op1(all_0_0_0, all_0_4_4) = all_0_0_0
% 9.93/2.89 | (48) op2(all_0_9_9, all_0_6_6) = all_0_6_6
% 9.93/2.89 | (49) op2(e22, e20) = e22
% 9.93/2.89 | (50) 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
% 9.93/2.89 | (51) ~ (e23 = e12)
% 9.93/2.89 | (52) op1(e11, e10) = e11
% 9.93/2.89 | (53) op2(e21, e24) = e23
% 9.93/2.89 | (54) op2(e21, e21) = e22
% 9.93/2.89 | (55) ~ (e24 = e14)
% 9.93/2.89 | (56) h(all_0_3_3) = e21
% 9.93/2.89 | (57) ~ (e23 = e21)
% 9.93/2.89 | (58) op1(e13, e11) = e12
% 9.93/2.89 | (59) 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
% 9.93/2.89 | (60) ~ (e22 = e21)
% 9.93/2.89 | (61) ~ (e20 = e11)
% 9.93/2.89 | (62) j(all_0_9_9) = e10
% 9.93/2.89 | (63) op1(e11, e13) = e14
% 9.93/2.89 | (64) op1(all_0_3_3, all_0_3_3) = all_0_2_2
% 9.93/2.89 | (65) ~ (e14 = e10)
% 9.93/2.89 | (66) ~ (e22 = e10)
% 9.93/2.89 | (67) op1(all_0_0_0, all_0_0_0) = all_0_4_4
% 9.93/2.89 | (68) op1(e14, e12) = e11
% 9.93/2.89 | (69) h(all_0_1_1) = e23
% 9.93/2.89 | (70) op2(all_0_9_9, all_0_9_9) = all_0_9_9
% 9.93/2.90 | (71) op2(all_0_9_9, all_0_7_7) = all_0_7_7
% 9.93/2.90 | (72) op1(e12, e10) = e12
% 9.93/2.90 | (73) ~ (e12 = e10)
% 9.93/2.90 | (74) ~ (e24 = e22)
% 9.93/2.90 | (75) op1(all_0_1_1, all_0_4_4) = all_0_1_1
% 9.93/2.90 | (76) op1(e14, e14) = e10
% 9.93/2.90 | (77) 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
% 9.93/2.90 | (78) op2(e20, e24) = e24
% 9.93/2.90 | (79) op2(e20, e20) = e20
% 9.93/2.90 | (80) op2(e22, e21) = e20
% 9.93/2.90 | (81) 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
% 9.93/2.90 | (82) op1(all_0_1_1, all_0_0_0) = all_0_2_2
% 9.93/2.90 | (83) op2(all_0_7_7, all_0_9_9) = all_0_7_7
% 9.93/2.90 | (84) op1(all_0_0_0, all_0_1_1) = all_0_2_2
% 9.93/2.90 | (85) j(all_0_7_7) = e12
% 9.93/2.90 | (86) op1(e12, e13) = e11
% 9.93/2.90 | (87) op2(all_0_7_7, all_0_5_5) = all_0_6_6
% 9.93/2.90 | (88) op2(all_0_5_5, all_0_9_9) = all_0_5_5
% 9.93/2.90 | (89) h(all_0_2_2) = e22
% 9.93/2.90 | (90) ~ (e14 = e13)
% 9.93/2.90 | (91) ~ (e21 = e11)
% 9.93/2.90 | (92) h(e14) = all_0_5_5
% 9.93/2.90 | (93) ~ (e24 = e20)
% 9.93/2.90 | (94) op2(e23, e23) = e21
% 9.93/2.90 | (95) ~ (e13 = e12)
% 9.93/2.90 | (96) op2(all_0_6_6, all_0_7_7) = all_0_5_5
% 9.93/2.90 | (97) 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
% 9.93/2.90 | (98) op1(all_0_2_2, all_0_3_3) = all_0_4_4
% 9.93/2.90 | (99) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0))
% 9.93/2.90 | (100) ~ (e14 = e11)
% 9.93/2.90 | (101) op2(e22, e24) = e21
% 9.93/2.90 | (102) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0))
% 9.93/2.90 | (103) op1(all_0_2_2, all_0_4_4) = all_0_2_2
% 9.93/2.90 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0))
% 9.93/2.90 | (105) 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
% 9.93/2.90 | (106) op1(all_0_1_1, all_0_1_1) = all_0_3_3
% 9.93/2.90 | (107) op2(all_0_6_6, all_0_8_8) = all_0_7_7
% 9.93/2.90 | (108) op1(all_0_1_1, all_0_2_2) = all_0_4_4
% 9.93/2.90 | (109) op1(e13, e10) = e13
% 9.93/2.90 | (110) op1(e10, e10) = e10
% 9.93/2.90 | (111) op1(all_0_0_0, all_0_3_3) = all_0_1_1
% 9.93/2.90 | (112) ~ (e23 = e10)
% 9.93/2.90 | (113) op1(all_0_4_4, all_0_4_4) = all_0_4_4
% 9.93/2.90 | (114) op2(e21, e23) = e20
% 9.93/2.90 | (115) op1(all_0_2_2, all_0_1_1) = all_0_0_0
% 9.93/2.90 | (116) ~ (e13 = e10)
% 9.93/2.90 | (117) op1(e14, e13) = e12
% 9.93/2.90 | (118) op1(e10, e12) = e12
% 9.93/2.90 | (119) 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
% 9.93/2.90 | (120) op2(all_0_7_7, all_0_6_6) = all_0_8_8
% 9.93/2.90 | (121) 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
% 9.93/2.90 | (122) ~ (e23 = e22)
% 9.93/2.91 | (123) ~ (e20 = e10)
% 9.93/2.91 | (124) ~ (e22 = e11)
% 9.93/2.91 | (125) op2(e22, e22) = e23
% 9.93/2.91 | (126) ~ (e20 = e12)
% 9.93/2.91 | (127) op2(e22, e23) = e24
% 9.93/2.91 | (128) op1(all_0_0_0, all_0_2_2) = all_0_3_3
% 9.93/2.91 | (129) op1(e12, e12) = e10
% 9.93/2.91 | (130) op1(all_0_3_3, all_0_0_0) = all_0_1_1
% 9.93/2.91 | (131) op1(e14, e11) = e13
% 9.93/2.91 | (132) op2(e24, e20) = e24
% 9.93/2.91 | (133) op1(all_0_4_4, all_0_0_0) = all_0_0_0
% 9.93/2.91 | (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
% 9.93/2.91 | (135) ~ (e10 = e11)
% 9.93/2.91 | (136) op1(all_0_2_2, all_0_0_0) = all_0_3_3
% 9.93/2.91 | (137) ~ (e23 = e14)
% 9.93/2.91 | (138) h(e11) = all_0_8_8
% 9.93/2.91 | (139) op1(e10, e13) = e13
% 9.93/2.91 | (140) op2(all_0_7_7, all_0_8_8) = all_0_5_5
% 9.93/2.91 | (141) op1(e14, e10) = e14
% 9.93/2.91 | (142) op2(e23, e24) = e22
% 9.93/2.91 | (143) j(e23) = all_0_1_1
% 9.93/2.91 | (144) ~ (e23 = e20)
% 9.93/2.91 | (145) op2(e21, e20) = e21
% 9.93/2.91 | (146) ~ (e21 = e14)
% 9.93/2.91 | (147) op2(all_0_8_8, all_0_6_6) = all_0_5_5
% 9.93/2.91 | (148) j(e24) = all_0_0_0
% 9.93/2.91 | (149) op2(all_0_5_5, all_0_6_6) = all_0_7_7
% 9.93/2.91 | (150) op2(e24, e24) = e20
% 9.93/2.91 | (151) op1(e10, e14) = e14
% 9.93/2.91 | (152) ~ (e24 = e21)
% 9.93/2.91 | (153) op2(all_0_8_8, all_0_9_9) = all_0_8_8
% 9.93/2.91 | (154) j(all_0_5_5) = e14
% 9.93/2.91 | (155) op2(all_0_8_8, all_0_5_5) = all_0_7_7
% 9.93/2.91 | (156) op1(e11, e14) = e12
% 9.93/2.91 | (157) op2(e23, e20) = e23
% 9.93/2.91 | (158) ~ (e22 = e20)
% 9.93/2.91 | (159) ~ (e23 = e11)
% 9.93/2.91 | (160) ~ (e24 = e10)
% 9.93/2.91 | (161) ~ (e24 = e23)
% 9.93/2.91 | (162) ~ (e20 = e13)
% 9.93/2.91 | (163) ~ (e24 = e13)
% 9.93/2.91 | (164) op1(all_0_4_4, all_0_3_3) = all_0_3_3
% 9.93/2.91 | (165) ~ (e21 = e10)
% 9.93/2.91 | (166) ~ (e21 = e13)
% 9.93/2.91 | (167) j(e20) = all_0_4_4
% 9.93/2.91 | (168) op2(all_0_5_5, all_0_5_5) = all_0_9_9
% 9.93/2.91 | (169) ~ (e22 = e12)
% 9.93/2.91 | (170) op2(e24, e23) = e22
% 9.93/2.91 | (171) op2(e20, e22) = e22
% 9.93/2.91 | (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
% 9.93/2.92 | (173) op2(all_0_6_6, all_0_5_5) = all_0_8_8
% 9.93/2.92 | (174) h(e10) = all_0_9_9
% 9.93/2.92 | (175) ~ (e22 = e14)
% 9.93/2.92 | (176) op1(all_0_3_3, all_0_1_1) = all_0_4_4
% 9.93/2.92 | (177) op2(e20, e21) = e21
% 9.93/2.92 | (178) op2(all_0_9_9, all_0_5_5) = all_0_5_5
% 9.93/2.92 | (179) op2(e21, e22) = e24
% 9.93/2.92 | (180) ~ (e13 = e11)
% 9.93/2.92 |
% 9.93/2.92 +-Applying beta-rule and splitting (121), into two cases.
% 9.93/2.92 |-Branch one:
% 9.93/2.92 | (181) all_0_0_0 = e14
% 9.93/2.92 |
% 9.93/2.92 | From (181)(181) and (67) follows:
% 9.93/2.92 | (182) op1(e14, e14) = all_0_4_4
% 9.93/2.92 |
% 9.93/2.92 | From (181) and (128) follows:
% 9.93/2.92 | (183) op1(e14, all_0_2_2) = all_0_3_3
% 9.93/2.92 |
% 9.93/2.92 | From (181) and (136) follows:
% 9.93/2.92 | (184) op1(all_0_2_2, e14) = all_0_3_3
% 9.93/2.92 |
% 9.93/2.92 | From (181) and (130) follows:
% 9.93/2.92 | (185) op1(all_0_3_3, e14) = all_0_1_1
% 9.93/2.92 |
% 9.93/2.92 | From (181) and (44) follows:
% 9.93/2.92 | (186) op1(all_0_3_3, all_0_2_2) = e14
% 9.93/2.92 |
% 9.93/2.92 | From (181)(181) and (133) follows:
% 9.93/2.92 | (187) op1(all_0_4_4, e14) = e14
% 9.93/2.92 |
% 9.93/2.92 | Instantiating formula (104) with e14, e14, all_0_4_4, e10 and discharging atoms op1(e14, e14) = all_0_4_4, op1(e14, e14) = e10, yields:
% 9.93/2.92 | (188) all_0_4_4 = e10
% 9.93/2.92 |
% 9.93/2.92 | From (188) and (98) follows:
% 9.93/2.92 | (189) op1(all_0_2_2, all_0_3_3) = e10
% 9.93/2.92 |
% 9.93/2.92 | From (188) and (164) follows:
% 9.93/2.92 | (190) op1(e10, all_0_3_3) = all_0_3_3
% 9.93/2.92 |
% 9.93/2.92 | From (188) and (187) follows:
% 9.93/2.92 | (151) op1(e10, e14) = e14
% 9.93/2.92 |
% 9.93/2.92 | From (188) and (182) follows:
% 9.93/2.92 | (76) op1(e14, e14) = e10
% 9.93/2.92 |
% 9.93/2.92 +-Applying beta-rule and splitting (81), into two cases.
% 9.93/2.92 |-Branch one:
% 9.93/2.92 | (193) all_0_2_2 = e14
% 9.93/2.92 |
% 9.93/2.92 | From (193)(193) and (10) follows:
% 9.93/2.92 | (194) op1(e14, e14) = all_0_1_1
% 9.93/2.92 |
% 9.93/2.92 | From (193) and (186) follows:
% 9.93/2.92 | (195) op1(all_0_3_3, e14) = e14
% 9.93/2.92 |
% 9.93/2.92 | Instantiating formula (104) with all_0_3_3, e14, e14, all_0_1_1 and discharging atoms op1(all_0_3_3, e14) = all_0_1_1, op1(all_0_3_3, e14) = e14, yields:
% 9.93/2.92 | (196) all_0_1_1 = e14
% 9.93/2.92 |
% 9.93/2.92 | Instantiating formula (104) with e14, e14, all_0_1_1, e10 and discharging atoms op1(e14, e14) = all_0_1_1, op1(e14, e14) = e10, yields:
% 9.93/2.93 | (197) all_0_1_1 = e10
% 9.93/2.93 |
% 9.93/2.93 | Combining equations (196,197) yields a new equation:
% 9.93/2.93 | (198) e14 = e10
% 9.93/2.93 |
% 9.93/2.93 | Simplifying 198 yields:
% 9.93/2.93 | (199) e14 = e10
% 9.93/2.93 |
% 9.93/2.93 | Equations (199) can reduce 65 to:
% 9.93/2.93 | (200) $false
% 9.93/2.93 |
% 9.93/2.93 |-The branch is then unsatisfiable
% 9.93/2.93 |-Branch two:
% 9.93/2.93 | (201) ~ (all_0_2_2 = e14)
% 9.93/2.93 | (202) all_0_2_2 = e13 | all_0_2_2 = e12 | all_0_2_2 = e10 | all_0_2_2 = e11
% 9.93/2.93 |
% 9.93/2.93 +-Applying beta-rule and splitting (202), into two cases.
% 9.93/2.93 |-Branch one:
% 9.93/2.93 | (203) all_0_2_2 = e13
% 9.93/2.93 |
% 9.93/2.93 | From (203) and (184) follows:
% 9.93/2.93 | (204) op1(e13, e14) = all_0_3_3
% 9.93/2.93 |
% 9.93/2.93 | From (203) and (183) follows:
% 9.93/2.93 | (205) op1(e14, e13) = all_0_3_3
% 9.93/2.93 |
% 9.93/2.93 | Instantiating formula (104) with e14, e13, all_0_3_3, e12 and discharging atoms op1(e14, e13) = all_0_3_3, op1(e14, e13) = e12, yields:
% 9.93/2.93 | (206) all_0_3_3 = e12
% 9.93/2.93 |
% 9.93/2.93 | Instantiating formula (104) with e13, e14, all_0_3_3, e11 and discharging atoms op1(e13, e14) = all_0_3_3, op1(e13, e14) = e11, yields:
% 9.93/2.93 | (207) all_0_3_3 = e11
% 9.93/2.93 |
% 9.93/2.93 | Combining equations (206,207) yields a new equation:
% 9.93/2.93 | (208) e12 = e11
% 9.93/2.93 |
% 9.93/2.93 | Simplifying 208 yields:
% 9.93/2.93 | (209) e12 = e11
% 9.93/2.93 |
% 9.93/2.93 | Equations (209) can reduce 15 to:
% 9.93/2.93 | (200) $false
% 9.93/2.93 |
% 9.93/2.93 |-The branch is then unsatisfiable
% 9.93/2.93 |-Branch two:
% 9.93/2.93 | (211) ~ (all_0_2_2 = e13)
% 9.93/2.93 | (212) all_0_2_2 = e12 | all_0_2_2 = e10 | all_0_2_2 = e11
% 9.93/2.93 |
% 9.93/2.93 +-Applying beta-rule and splitting (212), into two cases.
% 9.93/2.93 |-Branch one:
% 9.93/2.93 | (213) all_0_2_2 = e12
% 9.93/2.93 |
% 9.93/2.93 | From (213) and (184) follows:
% 9.93/2.93 | (214) op1(e12, e14) = all_0_3_3
% 9.93/2.93 |
% 9.93/2.93 | From (213) and (183) follows:
% 9.93/2.93 | (215) op1(e14, e12) = all_0_3_3
% 9.93/2.93 |
% 9.93/2.93 | Instantiating formula (104) with e14, e12, all_0_3_3, e11 and discharging atoms op1(e14, e12) = all_0_3_3, op1(e14, e12) = e11, yields:
% 9.93/2.93 | (207) all_0_3_3 = e11
% 9.93/2.93 |
% 9.93/2.93 | Instantiating formula (104) with e12, e14, all_0_3_3, e13 and discharging atoms op1(e12, e14) = all_0_3_3, op1(e12, e14) = e13, yields:
% 9.93/2.93 | (217) all_0_3_3 = e13
% 9.93/2.93 |
% 9.93/2.93 | Combining equations (207,217) yields a new equation:
% 9.93/2.93 | (218) e13 = e11
% 9.93/2.93 |
% 9.93/2.93 | Equations (218) can reduce 180 to:
% 9.93/2.93 | (200) $false
% 9.93/2.93 |
% 9.93/2.93 |-The branch is then unsatisfiable
% 9.93/2.93 |-Branch two:
% 9.93/2.93 | (220) ~ (all_0_2_2 = e12)
% 9.93/2.93 | (221) all_0_2_2 = e10 | all_0_2_2 = e11
% 9.93/2.93 |
% 9.93/2.93 +-Applying beta-rule and splitting (221), into two cases.
% 9.93/2.93 |-Branch one:
% 9.93/2.93 | (222) all_0_2_2 = e10
% 9.93/2.93 |
% 9.93/2.93 | Equations (222) can reduce 201 to:
% 9.93/2.93 | (223) ~ (e14 = e10)
% 9.93/2.93 |
% 9.93/2.94 | Simplifying 223 yields:
% 9.93/2.94 | (65) ~ (e14 = e10)
% 9.93/2.94 |
% 9.93/2.94 | From (222) and (189) follows:
% 9.93/2.94 | (225) op1(e10, all_0_3_3) = e10
% 9.93/2.94 |
% 9.93/2.94 | From (222) and (184) follows:
% 9.93/2.94 | (226) op1(e10, e14) = all_0_3_3
% 9.93/2.94 |
% 9.93/2.94 | Instantiating formula (104) with e10, all_0_3_3, e10, all_0_3_3 and discharging atoms op1(e10, all_0_3_3) = all_0_3_3, op1(e10, all_0_3_3) = e10, yields:
% 9.93/2.94 | (227) all_0_3_3 = e10
% 9.93/2.94 |
% 9.93/2.94 | Instantiating formula (104) with e10, e14, all_0_3_3, e14 and discharging atoms op1(e10, e14) = all_0_3_3, op1(e10, e14) = e14, yields:
% 9.93/2.94 | (228) all_0_3_3 = e14
% 9.93/2.94 |
% 9.93/2.94 | Combining equations (227,228) yields a new equation:
% 9.93/2.94 | (199) e14 = e10
% 9.93/2.94 |
% 9.93/2.94 | Equations (199) can reduce 65 to:
% 9.93/2.94 | (200) $false
% 9.93/2.94 |
% 9.93/2.94 |-The branch is then unsatisfiable
% 9.93/2.94 |-Branch two:
% 9.93/2.94 | (231) ~ (all_0_2_2 = e10)
% 9.93/2.94 | (232) all_0_2_2 = e11
% 9.93/2.94 |
% 9.93/2.94 | From (232) and (184) follows:
% 9.93/2.94 | (233) op1(e11, e14) = all_0_3_3
% 9.93/2.94 |
% 9.93/2.94 | From (232) and (183) follows:
% 9.93/2.94 | (234) op1(e14, e11) = all_0_3_3
% 9.93/2.94 |
% 9.93/2.94 | Instantiating formula (104) with e14, e11, all_0_3_3, e13 and discharging atoms op1(e14, e11) = all_0_3_3, op1(e14, e11) = e13, yields:
% 9.93/2.94 | (217) all_0_3_3 = e13
% 9.93/2.94 |
% 9.93/2.94 | Instantiating formula (104) with e11, e14, all_0_3_3, e12 and discharging atoms op1(e11, e14) = all_0_3_3, op1(e11, e14) = e12, yields:
% 9.93/2.94 | (206) all_0_3_3 = e12
% 9.93/2.94 |
% 9.93/2.94 | Combining equations (217,206) yields a new equation:
% 9.93/2.94 | (237) e13 = e12
% 9.93/2.94 |
% 9.93/2.94 | Simplifying 237 yields:
% 9.93/2.94 | (238) e13 = e12
% 9.93/2.94 |
% 9.93/2.94 | Equations (238) can reduce 95 to:
% 9.93/2.94 | (200) $false
% 9.93/2.94 |
% 9.93/2.94 |-The branch is then unsatisfiable
% 9.93/2.94 |-Branch two:
% 9.93/2.94 | (240) ~ (all_0_0_0 = e14)
% 9.93/2.94 | (241) all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 9.93/2.94 |
% 9.93/2.94 +-Applying beta-rule and splitting (77), into two cases.
% 9.93/2.94 |-Branch one:
% 9.93/2.94 | (242) all_0_9_9 = e24
% 9.93/2.94 |
% 9.93/2.94 | From (242)(242)(242) and (70) follows:
% 9.93/2.94 | (243) op2(e24, e24) = e24
% 9.93/2.94 |
% 9.93/2.94 | Instantiating formula (43) with e24, e24, e24, e20 and discharging atoms op2(e24, e24) = e24, op2(e24, e24) = e20, yields:
% 9.93/2.94 | (244) e24 = e20
% 9.93/2.94 |
% 9.93/2.94 | Equations (244) can reduce 93 to:
% 9.93/2.94 | (200) $false
% 9.93/2.94 |
% 9.93/2.94 |-The branch is then unsatisfiable
% 9.93/2.94 |-Branch two:
% 9.93/2.94 | (246) ~ (all_0_9_9 = e24)
% 9.93/2.94 | (247) all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21
% 9.93/2.94 |
% 9.93/2.94 +-Applying beta-rule and splitting (59), into two cases.
% 9.93/2.94 |-Branch one:
% 9.93/2.94 | (196) all_0_1_1 = e14
% 9.93/2.94 |
% 9.93/2.94 | From (196)(196) and (106) follows:
% 9.93/2.95 | (249) op1(e14, e14) = all_0_3_3
% 9.93/2.95 |
% 9.93/2.95 | From (196) and (45) follows:
% 9.93/2.95 | (250) op1(e14, all_0_3_3) = all_0_0_0
% 9.93/2.95 |
% 9.93/2.95 | Instantiating formula (104) with e14, e14, all_0_3_3, e10 and discharging atoms op1(e14, e14) = all_0_3_3, op1(e14, e14) = e10, yields:
% 9.93/2.95 | (227) all_0_3_3 = e10
% 9.93/2.95 |
% 9.93/2.95 | From (227) and (250) follows:
% 9.93/2.95 | (252) op1(e14, e10) = all_0_0_0
% 9.93/2.95 |
% 9.93/2.95 | Instantiating formula (104) with e14, e10, all_0_0_0, e14 and discharging atoms op1(e14, e10) = all_0_0_0, op1(e14, e10) = e14, yields:
% 9.93/2.95 | (181) all_0_0_0 = e14
% 9.93/2.95 |
% 9.93/2.95 | Equations (181) can reduce 240 to:
% 9.93/2.95 | (200) $false
% 9.93/2.95 |
% 9.93/2.95 |-The branch is then unsatisfiable
% 9.93/2.95 |-Branch two:
% 9.93/2.95 | (255) ~ (all_0_1_1 = e14)
% 9.93/2.95 | (256) all_0_1_1 = e13 | all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11
% 9.93/2.95 |
% 9.93/2.95 +-Applying beta-rule and splitting (97), into two cases.
% 9.93/2.95 |-Branch one:
% 9.93/2.95 | (257) all_0_7_7 = e24
% 9.93/2.95 |
% 9.93/2.95 | From (257)(257) and (42) follows:
% 9.93/2.95 | (258) op2(e24, e24) = all_0_9_9
% 9.93/2.95 |
% 9.93/2.95 | From (257) and (85) follows:
% 9.93/2.95 | (259) j(e24) = e12
% 9.93/2.95 |
% 9.93/2.95 | Instantiating formula (43) with e24, e24, all_0_9_9, e20 and discharging atoms op2(e24, e24) = all_0_9_9, op2(e24, e24) = e20, yields:
% 9.93/2.95 | (260) all_0_9_9 = e20
% 9.93/2.95 |
% 9.93/2.95 | Instantiating formula (102) with e24, e12, all_0_0_0 and discharging atoms j(e24) = all_0_0_0, j(e24) = e12, yields:
% 9.93/2.95 | (261) all_0_0_0 = e12
% 9.93/2.95 |
% 9.93/2.95 | From (261)(261) and (67) follows:
% 9.93/2.95 | (262) op1(e12, e12) = all_0_4_4
% 9.93/2.95 |
% 9.93/2.95 | From (261) and (84) follows:
% 9.93/2.95 | (263) op1(e12, all_0_1_1) = all_0_2_2
% 9.93/2.95 |
% 9.93/2.95 | From (261) and (82) follows:
% 9.93/2.95 | (264) op1(all_0_1_1, e12) = all_0_2_2
% 9.93/2.95 |
% 9.93/2.95 | From (261) and (45) follows:
% 9.93/2.95 | (265) op1(all_0_1_1, all_0_3_3) = e12
% 9.93/2.95 |
% 9.93/2.95 | From (261) and (136) follows:
% 9.93/2.95 | (266) op1(all_0_2_2, e12) = all_0_3_3
% 9.93/2.95 |
% 9.93/2.95 | From (261) and (115) follows:
% 9.93/2.95 | (267) op1(all_0_2_2, all_0_1_1) = e12
% 9.93/2.95 |
% 9.93/2.95 | From (260) and (62) follows:
% 9.93/2.95 | (268) j(e20) = e10
% 9.93/2.95 |
% 9.93/2.95 | Instantiating formula (102) with e20, e10, all_0_4_4 and discharging atoms j(e20) = all_0_4_4, j(e20) = e10, yields:
% 9.93/2.95 | (188) all_0_4_4 = e10
% 9.93/2.95 |
% 9.93/2.95 | From (188) and (4) follows:
% 9.93/2.95 | (270) op1(e10, all_0_1_1) = all_0_1_1
% 9.93/2.95 |
% 9.93/2.95 | From (188) and (164) follows:
% 9.93/2.95 | (190) op1(e10, all_0_3_3) = all_0_3_3
% 9.93/2.95 |
% 9.93/2.95 | From (188) and (262) follows:
% 9.93/2.95 | (129) op1(e12, e12) = e10
% 9.93/2.95 |
% 9.93/2.95 +-Applying beta-rule and splitting (256), into two cases.
% 9.93/2.95 |-Branch one:
% 9.93/2.95 | (273) all_0_1_1 = e13
% 9.93/2.95 |
% 9.93/2.95 | From (273) and (264) follows:
% 9.93/2.95 | (274) op1(e13, e12) = all_0_2_2
% 9.93/2.95 |
% 9.93/2.95 | From (273) and (263) follows:
% 9.93/2.95 | (275) op1(e12, e13) = all_0_2_2
% 9.93/2.95 |
% 9.93/2.95 | Instantiating formula (104) with e13, e12, all_0_2_2, e14 and discharging atoms op1(e13, e12) = all_0_2_2, op1(e13, e12) = e14, yields:
% 9.93/2.96 | (193) all_0_2_2 = e14
% 9.93/2.96 |
% 9.93/2.96 | Instantiating formula (104) with e12, e13, all_0_2_2, e11 and discharging atoms op1(e12, e13) = all_0_2_2, op1(e12, e13) = e11, yields:
% 9.93/2.96 | (232) all_0_2_2 = e11
% 9.93/2.96 |
% 9.93/2.96 | Combining equations (232,193) yields a new equation:
% 9.93/2.96 | (278) e14 = e11
% 9.93/2.96 |
% 9.93/2.96 | Equations (278) can reduce 100 to:
% 9.93/2.96 | (200) $false
% 9.93/2.96 |
% 9.93/2.96 |-The branch is then unsatisfiable
% 9.93/2.96 |-Branch two:
% 9.93/2.96 | (280) ~ (all_0_1_1 = e13)
% 9.93/2.96 | (281) all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11
% 9.93/2.96 |
% 9.93/2.96 +-Applying beta-rule and splitting (281), into two cases.
% 9.93/2.96 |-Branch one:
% 9.93/2.96 | (282) all_0_1_1 = e12
% 9.93/2.96 |
% 9.93/2.96 | From (282)(282) and (106) follows:
% 9.93/2.96 | (283) op1(e12, e12) = all_0_3_3
% 9.93/2.96 |
% 9.93/2.96 | From (282) and (267) follows:
% 9.93/2.96 | (284) op1(all_0_2_2, e12) = e12
% 9.93/2.96 |
% 9.93/2.96 | From (282) and (263) follows:
% 9.93/2.96 | (285) op1(e12, e12) = all_0_2_2
% 9.93/2.96 |
% 9.93/2.96 | Instantiating formula (104) with all_0_2_2, e12, e12, all_0_3_3 and discharging atoms op1(all_0_2_2, e12) = all_0_3_3, op1(all_0_2_2, e12) = e12, yields:
% 9.93/2.96 | (206) all_0_3_3 = e12
% 9.93/2.96 |
% 9.93/2.96 | Instantiating formula (104) with e12, e12, all_0_2_2, e10 and discharging atoms op1(e12, e12) = all_0_2_2, op1(e12, e12) = e10, yields:
% 9.93/2.96 | (222) all_0_2_2 = e10
% 9.93/2.96 |
% 9.93/2.96 | Instantiating formula (104) with e12, e12, all_0_3_3, all_0_2_2 and discharging atoms op1(e12, e12) = all_0_2_2, op1(e12, e12) = all_0_3_3, yields:
% 9.93/2.96 | (288) all_0_2_2 = all_0_3_3
% 9.93/2.96 |
% 9.93/2.96 | Combining equations (288,222) yields a new equation:
% 9.93/2.96 | (289) all_0_3_3 = e10
% 9.93/2.96 |
% 9.93/2.96 | Simplifying 289 yields:
% 9.93/2.96 | (227) all_0_3_3 = e10
% 9.93/2.96 |
% 9.93/2.96 | Combining equations (206,227) yields a new equation:
% 9.93/2.96 | (291) e12 = e10
% 9.93/2.96 |
% 9.93/2.96 | Simplifying 291 yields:
% 9.93/2.96 | (292) e12 = e10
% 9.93/2.96 |
% 9.93/2.96 | Equations (292) can reduce 73 to:
% 9.93/2.96 | (200) $false
% 9.93/2.96 |
% 9.93/2.96 |-The branch is then unsatisfiable
% 9.93/2.96 |-Branch two:
% 9.93/2.96 | (294) ~ (all_0_1_1 = e12)
% 9.93/2.96 | (295) all_0_1_1 = e10 | all_0_1_1 = e11
% 9.93/2.96 |
% 9.93/2.96 +-Applying beta-rule and splitting (295), into two cases.
% 9.93/2.96 |-Branch one:
% 9.93/2.96 | (197) all_0_1_1 = e10
% 9.93/2.96 |
% 9.93/2.96 | Equations (197) can reduce 294 to:
% 9.93/2.96 | (297) ~ (e12 = e10)
% 9.93/2.96 |
% 9.93/2.96 | Simplifying 297 yields:
% 9.93/2.96 | (73) ~ (e12 = e10)
% 9.93/2.96 |
% 9.93/2.96 | From (197)(197) and (106) follows:
% 9.93/2.96 | (299) op1(e10, e10) = all_0_3_3
% 9.93/2.96 |
% 9.93/2.96 | From (197) and (265) follows:
% 9.93/2.96 | (300) op1(e10, all_0_3_3) = e12
% 9.93/2.96 |
% 9.93/2.96 | From (197)(197) and (270) follows:
% 9.93/2.96 | (110) op1(e10, e10) = e10
% 9.93/2.96 |
% 9.93/2.96 | Instantiating formula (104) with e10, all_0_3_3, e12, all_0_3_3 and discharging atoms op1(e10, all_0_3_3) = all_0_3_3, op1(e10, all_0_3_3) = e12, yields:
% 9.93/2.96 | (206) all_0_3_3 = e12
% 9.93/2.96 |
% 9.93/2.96 | Instantiating formula (104) with e10, e10, all_0_3_3, e10 and discharging atoms op1(e10, e10) = all_0_3_3, op1(e10, e10) = e10, yields:
% 9.93/2.96 | (227) all_0_3_3 = e10
% 9.93/2.96 |
% 9.93/2.96 | Combining equations (227,206) yields a new equation:
% 9.93/2.96 | (292) e12 = e10
% 9.93/2.96 |
% 9.93/2.96 | Equations (292) can reduce 73 to:
% 9.93/2.96 | (200) $false
% 9.93/2.96 |
% 9.93/2.96 |-The branch is then unsatisfiable
% 9.93/2.96 |-Branch two:
% 9.93/2.96 | (306) ~ (all_0_1_1 = e10)
% 9.93/2.96 | (307) all_0_1_1 = e11
% 9.93/2.96 |
% 9.93/2.96 | From (307) and (264) follows:
% 9.93/2.96 | (308) op1(e11, e12) = all_0_2_2
% 9.93/2.96 |
% 9.93/2.96 | From (307) and (263) follows:
% 9.93/2.96 | (309) op1(e12, e11) = all_0_2_2
% 9.93/2.96 |
% 9.93/2.96 | Instantiating formula (104) with e12, e11, all_0_2_2, e14 and discharging atoms op1(e12, e11) = all_0_2_2, op1(e12, e11) = e14, yields:
% 10.43/2.96 | (193) all_0_2_2 = e14
% 10.43/2.96 |
% 10.43/2.96 | Instantiating formula (104) with e11, e12, all_0_2_2, e13 and discharging atoms op1(e11, e12) = all_0_2_2, op1(e11, e12) = e13, yields:
% 10.43/2.96 | (203) all_0_2_2 = e13
% 10.43/2.96 |
% 10.43/2.96 | Combining equations (203,193) yields a new equation:
% 10.43/2.96 | (312) e14 = e13
% 10.43/2.96 |
% 10.43/2.96 | Equations (312) can reduce 90 to:
% 10.43/2.96 | (200) $false
% 10.43/2.96 |
% 10.43/2.96 |-The branch is then unsatisfiable
% 10.43/2.96 |-Branch two:
% 10.43/2.96 | (314) ~ (all_0_7_7 = e24)
% 10.43/2.96 | (315) all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 10.43/2.96 |
% 10.43/2.96 +-Applying beta-rule and splitting (119), into two cases.
% 10.43/2.96 |-Branch one:
% 10.43/2.96 | (316) all_0_6_6 = e24
% 10.43/2.96 |
% 10.43/2.96 | From (316)(316) and (22) follows:
% 10.43/2.96 | (258) op2(e24, e24) = all_0_9_9
% 10.43/2.96 |
% 10.43/2.96 | From (316) and (37) follows:
% 10.43/2.96 | (318) j(e24) = e13
% 10.43/2.96 |
% 10.43/2.96 | Instantiating formula (43) with e24, e24, all_0_9_9, e20 and discharging atoms op2(e24, e24) = all_0_9_9, op2(e24, e24) = e20, yields:
% 10.43/2.96 | (260) all_0_9_9 = e20
% 10.43/2.96 |
% 10.43/2.96 | Instantiating formula (102) with e24, e13, all_0_0_0 and discharging atoms j(e24) = all_0_0_0, j(e24) = e13, yields:
% 10.43/2.96 | (320) all_0_0_0 = e13
% 10.43/2.96 |
% 10.43/2.96 | From (320)(320) and (67) follows:
% 10.43/2.96 | (321) op1(e13, e13) = all_0_4_4
% 10.43/2.96 |
% 10.43/2.96 | From (320) and (84) follows:
% 10.43/2.96 | (322) op1(e13, all_0_1_1) = all_0_2_2
% 10.43/2.96 |
% 10.43/2.96 | From (320) and (82) follows:
% 10.43/2.96 | (323) op1(all_0_1_1, e13) = all_0_2_2
% 10.43/2.96 |
% 10.43/2.96 | From (320) and (45) follows:
% 10.43/2.96 | (324) op1(all_0_1_1, all_0_3_3) = e13
% 10.43/2.96 |
% 10.43/2.96 | From (320) and (136) follows:
% 10.43/2.96 | (325) op1(all_0_2_2, e13) = all_0_3_3
% 10.43/2.96 |
% 10.43/2.96 | From (320) and (115) follows:
% 10.43/2.96 | (326) op1(all_0_2_2, all_0_1_1) = e13
% 10.43/2.96 |
% 10.43/2.96 | From (260) and (62) follows:
% 10.43/2.96 | (268) j(e20) = e10
% 10.43/2.96 |
% 10.43/2.96 | Instantiating formula (102) with e20, e10, all_0_4_4 and discharging atoms j(e20) = all_0_4_4, j(e20) = e10, yields:
% 10.43/2.96 | (188) all_0_4_4 = e10
% 10.43/2.96 |
% 10.43/2.96 | From (188) and (4) follows:
% 10.43/2.96 | (270) op1(e10, all_0_1_1) = all_0_1_1
% 10.43/2.96 |
% 10.43/2.96 | From (188) and (164) follows:
% 10.43/2.96 | (190) op1(e10, all_0_3_3) = all_0_3_3
% 10.43/2.96 |
% 10.43/2.96 | From (188) and (321) follows:
% 10.43/2.96 | (33) op1(e13, e13) = e10
% 10.43/2.96 |
% 10.43/2.96 +-Applying beta-rule and splitting (256), into two cases.
% 10.43/2.96 |-Branch one:
% 10.43/2.96 | (273) all_0_1_1 = e13
% 10.43/2.97 |
% 10.43/2.97 | From (273)(273) and (106) follows:
% 10.43/2.97 | (333) op1(e13, e13) = all_0_3_3
% 10.43/2.97 |
% 10.43/2.97 | From (273) and (326) follows:
% 10.43/2.97 | (334) op1(all_0_2_2, e13) = e13
% 10.43/2.97 |
% 10.43/2.97 | From (273) and (322) follows:
% 10.43/2.97 | (335) op1(e13, e13) = all_0_2_2
% 10.43/2.97 |
% 10.43/2.97 | Instantiating formula (104) with all_0_2_2, e13, e13, all_0_3_3 and discharging atoms op1(all_0_2_2, e13) = all_0_3_3, op1(all_0_2_2, e13) = e13, yields:
% 10.43/2.97 | (217) all_0_3_3 = e13
% 10.43/2.97 |
% 10.43/2.97 | Instantiating formula (104) with e13, e13, all_0_2_2, e10 and discharging atoms op1(e13, e13) = all_0_2_2, op1(e13, e13) = e10, yields:
% 10.43/2.97 | (222) all_0_2_2 = e10
% 10.43/2.97 |
% 10.43/2.97 | Instantiating formula (104) with e13, e13, all_0_3_3, all_0_2_2 and discharging atoms op1(e13, e13) = all_0_2_2, op1(e13, e13) = all_0_3_3, yields:
% 10.43/2.97 | (288) all_0_2_2 = all_0_3_3
% 10.43/2.97 |
% 10.43/2.97 | Combining equations (288,222) yields a new equation:
% 10.43/2.97 | (289) all_0_3_3 = e10
% 10.43/2.97 |
% 10.43/2.97 | Simplifying 289 yields:
% 10.43/2.97 | (227) all_0_3_3 = e10
% 10.43/2.97 |
% 10.43/2.97 | Combining equations (217,227) yields a new equation:
% 10.43/2.97 | (341) e13 = e10
% 10.43/2.97 |
% 10.43/2.97 | Simplifying 341 yields:
% 10.43/2.97 | (342) e13 = e10
% 10.43/2.97 |
% 10.43/2.97 | Equations (342) can reduce 116 to:
% 10.43/2.97 | (200) $false
% 10.43/2.97 |
% 10.43/2.97 |-The branch is then unsatisfiable
% 10.43/2.97 |-Branch two:
% 10.43/2.97 | (280) ~ (all_0_1_1 = e13)
% 10.43/2.97 | (281) all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11
% 10.43/2.97 |
% 10.43/2.97 +-Applying beta-rule and splitting (281), into two cases.
% 10.43/2.97 |-Branch one:
% 10.43/2.97 | (282) all_0_1_1 = e12
% 10.43/2.97 |
% 10.43/2.97 | From (282) and (323) follows:
% 10.43/2.97 | (275) op1(e12, e13) = all_0_2_2
% 10.43/2.97 |
% 10.43/2.97 | From (282) and (322) follows:
% 10.43/2.97 | (274) op1(e13, e12) = all_0_2_2
% 10.43/2.97 |
% 10.43/2.97 | Instantiating formula (104) with e13, e12, all_0_2_2, e14 and discharging atoms op1(e13, e12) = all_0_2_2, op1(e13, e12) = e14, yields:
% 10.43/2.97 | (193) all_0_2_2 = e14
% 10.43/2.97 |
% 10.43/2.97 | Instantiating formula (104) with e12, e13, all_0_2_2, e11 and discharging atoms op1(e12, e13) = all_0_2_2, op1(e12, e13) = e11, yields:
% 10.43/2.97 | (232) all_0_2_2 = e11
% 10.43/2.97 |
% 10.43/2.97 | Combining equations (232,193) yields a new equation:
% 10.43/2.97 | (278) e14 = e11
% 10.43/2.97 |
% 10.43/2.97 | Equations (278) can reduce 100 to:
% 10.43/2.97 | (200) $false
% 10.43/2.97 |
% 10.43/2.97 |-The branch is then unsatisfiable
% 10.43/2.97 |-Branch two:
% 10.43/2.97 | (294) ~ (all_0_1_1 = e12)
% 10.43/2.97 | (295) all_0_1_1 = e10 | all_0_1_1 = e11
% 10.43/2.97 |
% 10.43/2.97 +-Applying beta-rule and splitting (295), into two cases.
% 10.43/2.97 |-Branch one:
% 10.43/2.97 | (197) all_0_1_1 = e10
% 10.43/2.97 |
% 10.43/2.97 | Equations (197) can reduce 280 to:
% 10.43/2.97 | (356) ~ (e13 = e10)
% 10.43/2.97 |
% 10.43/2.97 | Simplifying 356 yields:
% 10.43/2.97 | (116) ~ (e13 = e10)
% 10.43/2.97 |
% 10.43/2.97 | From (197)(197) and (106) follows:
% 10.43/2.97 | (299) op1(e10, e10) = all_0_3_3
% 10.43/2.97 |
% 10.43/2.97 | From (197) and (324) follows:
% 10.43/2.97 | (359) op1(e10, all_0_3_3) = e13
% 10.43/2.97 |
% 10.43/2.97 | From (197)(197) and (270) follows:
% 10.43/2.97 | (110) op1(e10, e10) = e10
% 10.43/2.97 |
% 10.43/2.97 | Instantiating formula (104) with e10, all_0_3_3, e13, all_0_3_3 and discharging atoms op1(e10, all_0_3_3) = all_0_3_3, op1(e10, all_0_3_3) = e13, yields:
% 10.43/2.97 | (217) all_0_3_3 = e13
% 10.43/2.97 |
% 10.43/2.97 | Instantiating formula (104) with e10, e10, all_0_3_3, e10 and discharging atoms op1(e10, e10) = all_0_3_3, op1(e10, e10) = e10, yields:
% 10.43/2.97 | (227) all_0_3_3 = e10
% 10.43/2.97 |
% 10.43/2.97 | Combining equations (227,217) yields a new equation:
% 10.43/2.97 | (342) e13 = e10
% 10.43/2.97 |
% 10.43/2.97 | Equations (342) can reduce 116 to:
% 10.43/2.97 | (200) $false
% 10.43/2.97 |
% 10.43/2.97 |-The branch is then unsatisfiable
% 10.43/2.97 |-Branch two:
% 10.43/2.97 | (306) ~ (all_0_1_1 = e10)
% 10.43/2.97 | (307) all_0_1_1 = e11
% 10.43/2.97 |
% 10.43/2.97 | From (307) and (323) follows:
% 10.43/2.97 | (367) op1(e11, e13) = all_0_2_2
% 10.43/2.97 |
% 10.43/2.97 | From (307) and (322) follows:
% 10.43/2.97 | (368) op1(e13, e11) = all_0_2_2
% 10.43/2.97 |
% 10.43/2.97 | Instantiating formula (104) with e13, e11, all_0_2_2, e12 and discharging atoms op1(e13, e11) = all_0_2_2, op1(e13, e11) = e12, yields:
% 10.43/2.97 | (213) all_0_2_2 = e12
% 10.43/2.97 |
% 10.43/2.97 | Instantiating formula (104) with e11, e13, all_0_2_2, e14 and discharging atoms op1(e11, e13) = all_0_2_2, op1(e11, e13) = e14, yields:
% 10.43/2.97 | (193) all_0_2_2 = e14
% 10.43/2.97 |
% 10.43/2.97 | Combining equations (193,213) yields a new equation:
% 10.43/2.97 | (371) e14 = e12
% 10.43/2.97 |
% 10.43/2.97 | Simplifying 371 yields:
% 10.43/2.97 | (372) e14 = e12
% 10.43/2.97 |
% 10.43/2.97 | Equations (372) can reduce 20 to:
% 10.43/2.97 | (200) $false
% 10.43/2.97 |
% 10.43/2.97 |-The branch is then unsatisfiable
% 10.43/2.97 |-Branch two:
% 10.43/2.97 | (374) ~ (all_0_6_6 = e24)
% 10.43/2.97 | (375) all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21
% 10.43/2.97 |
% 10.43/2.97 +-Applying beta-rule and splitting (134), into two cases.
% 10.43/2.97 |-Branch one:
% 10.43/2.97 | (376) all_0_8_8 = e24
% 10.43/2.97 |
% 10.43/2.97 | From (376)(376) and (2) follows:
% 10.43/2.97 | (258) op2(e24, e24) = all_0_9_9
% 10.43/2.97 |
% 10.43/2.97 | From (376) and (29) follows:
% 10.43/2.97 | (378) j(e24) = e11
% 10.43/2.97 |
% 10.43/2.97 | Instantiating formula (43) with e24, e24, all_0_9_9, e20 and discharging atoms op2(e24, e24) = all_0_9_9, op2(e24, e24) = e20, yields:
% 10.43/2.97 | (260) all_0_9_9 = e20
% 10.43/2.97 |
% 10.43/2.97 | Instantiating formula (102) with e24, e11, all_0_0_0 and discharging atoms j(e24) = all_0_0_0, j(e24) = e11, yields:
% 10.43/2.97 | (380) all_0_0_0 = e11
% 10.43/2.97 |
% 10.43/2.97 | From (380)(380) and (67) follows:
% 10.43/2.97 | (381) op1(e11, e11) = all_0_4_4
% 10.43/2.97 |
% 10.43/2.97 | From (380) and (84) follows:
% 10.43/2.97 | (382) op1(e11, all_0_1_1) = all_0_2_2
% 10.43/2.97 |
% 10.43/2.97 | From (380) and (82) follows:
% 10.43/2.97 | (383) op1(all_0_1_1, e11) = all_0_2_2
% 10.43/2.97 |
% 10.43/2.97 | From (380) and (45) follows:
% 10.43/2.97 | (384) op1(all_0_1_1, all_0_3_3) = e11
% 10.43/2.97 |
% 10.43/2.97 | From (380) and (136) follows:
% 10.43/2.97 | (385) op1(all_0_2_2, e11) = all_0_3_3
% 10.43/2.97 |
% 10.43/2.97 | From (380) and (115) follows:
% 10.43/2.97 | (386) op1(all_0_2_2, all_0_1_1) = e11
% 10.43/2.97 |
% 10.43/2.97 | From (260) and (62) follows:
% 10.43/2.97 | (268) j(e20) = e10
% 10.43/2.97 |
% 10.43/2.97 | Instantiating formula (102) with e20, e10, all_0_4_4 and discharging atoms j(e20) = all_0_4_4, j(e20) = e10, yields:
% 10.43/2.97 | (188) all_0_4_4 = e10
% 10.43/2.97 |
% 10.43/2.97 | From (188) and (4) follows:
% 10.43/2.97 | (270) op1(e10, all_0_1_1) = all_0_1_1
% 10.43/2.97 |
% 10.43/2.97 | From (188) and (164) follows:
% 10.43/2.98 | (190) op1(e10, all_0_3_3) = all_0_3_3
% 10.43/2.98 |
% 10.43/2.98 | From (188) and (381) follows:
% 10.43/2.98 | (14) op1(e11, e11) = e10
% 10.43/2.98 |
% 10.43/2.98 +-Applying beta-rule and splitting (256), into two cases.
% 10.43/2.98 |-Branch one:
% 10.43/2.98 | (273) all_0_1_1 = e13
% 10.43/2.98 |
% 10.43/2.98 | From (273) and (383) follows:
% 10.43/2.98 | (368) op1(e13, e11) = all_0_2_2
% 10.43/2.98 |
% 10.43/2.98 | From (273) and (382) follows:
% 10.43/2.98 | (367) op1(e11, e13) = all_0_2_2
% 10.43/2.98 |
% 10.43/2.98 | Instantiating formula (104) with e13, e11, all_0_2_2, e12 and discharging atoms op1(e13, e11) = all_0_2_2, op1(e13, e11) = e12, yields:
% 10.43/2.98 | (213) all_0_2_2 = e12
% 10.43/2.98 |
% 10.43/2.98 | Instantiating formula (104) with e11, e13, all_0_2_2, e14 and discharging atoms op1(e11, e13) = all_0_2_2, op1(e11, e13) = e14, yields:
% 10.43/2.98 | (193) all_0_2_2 = e14
% 10.43/2.98 |
% 10.43/2.98 | Combining equations (193,213) yields a new equation:
% 10.43/2.98 | (371) e14 = e12
% 10.43/2.98 |
% 10.43/2.98 | Simplifying 371 yields:
% 10.43/2.98 | (372) e14 = e12
% 10.43/2.98 |
% 10.43/2.98 | Equations (372) can reduce 20 to:
% 10.43/2.98 | (200) $false
% 10.43/2.98 |
% 10.43/2.98 |-The branch is then unsatisfiable
% 10.43/2.98 |-Branch two:
% 10.43/2.98 | (280) ~ (all_0_1_1 = e13)
% 10.43/2.98 | (281) all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11
% 10.43/2.98 |
% 10.43/2.98 +-Applying beta-rule and splitting (281), into two cases.
% 10.43/2.98 |-Branch one:
% 10.43/2.98 | (282) all_0_1_1 = e12
% 10.43/2.98 |
% 10.43/2.98 | From (282) and (383) follows:
% 10.43/2.98 | (309) op1(e12, e11) = all_0_2_2
% 10.43/2.98 |
% 10.43/2.98 | From (282) and (382) follows:
% 10.43/2.98 | (308) op1(e11, e12) = all_0_2_2
% 10.43/2.98 |
% 10.43/2.98 | Instantiating formula (104) with e12, e11, all_0_2_2, e14 and discharging atoms op1(e12, e11) = all_0_2_2, op1(e12, e11) = e14, yields:
% 10.43/2.98 | (193) all_0_2_2 = e14
% 10.43/2.98 |
% 10.43/2.98 | Instantiating formula (104) with e11, e12, all_0_2_2, e13 and discharging atoms op1(e11, e12) = all_0_2_2, op1(e11, e12) = e13, yields:
% 10.43/2.98 | (203) all_0_2_2 = e13
% 10.43/2.98 |
% 10.43/2.98 | Combining equations (203,193) yields a new equation:
% 10.43/2.98 | (312) e14 = e13
% 10.43/2.98 |
% 10.43/2.98 | Equations (312) can reduce 90 to:
% 10.43/2.98 | (200) $false
% 10.43/2.98 |
% 10.43/2.98 |-The branch is then unsatisfiable
% 10.43/2.98 |-Branch two:
% 10.43/2.98 | (294) ~ (all_0_1_1 = e12)
% 10.43/2.98 | (295) all_0_1_1 = e10 | all_0_1_1 = e11
% 10.43/2.98 |
% 10.43/2.98 +-Applying beta-rule and splitting (295), into two cases.
% 10.43/2.98 |-Branch one:
% 10.43/2.98 | (197) all_0_1_1 = e10
% 10.43/2.98 |
% 10.43/2.98 | From (197)(197) and (106) follows:
% 10.43/2.98 | (299) op1(e10, e10) = all_0_3_3
% 10.43/2.98 |
% 10.43/2.98 | From (197) and (384) follows:
% 10.43/2.98 | (413) op1(e10, all_0_3_3) = e11
% 10.43/2.98 |
% 10.43/2.98 | From (197)(197) and (270) follows:
% 10.43/2.98 | (110) op1(e10, e10) = e10
% 10.43/2.98 |
% 10.43/2.98 | Instantiating formula (104) with e10, all_0_3_3, e11, all_0_3_3 and discharging atoms op1(e10, all_0_3_3) = all_0_3_3, op1(e10, all_0_3_3) = e11, yields:
% 10.43/2.98 | (207) all_0_3_3 = e11
% 10.43/2.98 |
% 10.43/2.98 | Instantiating formula (104) with e10, e10, all_0_3_3, e10 and discharging atoms op1(e10, e10) = all_0_3_3, op1(e10, e10) = e10, yields:
% 10.43/2.98 | (227) all_0_3_3 = e10
% 10.43/2.98 |
% 10.43/2.98 | Combining equations (227,207) yields a new equation:
% 10.43/2.98 | (417) e10 = e11
% 10.43/2.98 |
% 10.43/2.98 | Simplifying 417 yields:
% 10.43/2.98 | (418) e10 = e11
% 10.43/2.98 |
% 10.43/2.98 | Equations (418) can reduce 135 to:
% 10.43/2.98 | (200) $false
% 10.43/2.98 |
% 10.43/2.98 |-The branch is then unsatisfiable
% 10.43/2.98 |-Branch two:
% 10.43/2.98 | (306) ~ (all_0_1_1 = e10)
% 10.43/2.98 | (307) all_0_1_1 = e11
% 10.43/2.98 |
% 10.43/2.98 | Equations (307) can reduce 306 to:
% 10.43/2.98 | (422) ~ (e10 = e11)
% 10.43/2.98 |
% 10.43/2.98 | Simplifying 422 yields:
% 10.43/2.98 | (135) ~ (e10 = e11)
% 10.43/2.98 |
% 10.43/2.98 | From (307)(307) and (106) follows:
% 10.43/2.98 | (424) op1(e11, e11) = all_0_3_3
% 10.43/2.98 |
% 10.43/2.98 | From (307) and (386) follows:
% 10.43/2.98 | (425) op1(all_0_2_2, e11) = e11
% 10.43/2.98 |
% 10.43/2.98 | From (307) and (382) follows:
% 10.43/2.98 | (426) op1(e11, e11) = all_0_2_2
% 10.43/2.98 |
% 10.43/2.98 | Instantiating formula (104) with all_0_2_2, e11, e11, all_0_3_3 and discharging atoms op1(all_0_2_2, e11) = all_0_3_3, op1(all_0_2_2, e11) = e11, yields:
% 10.43/2.98 | (207) all_0_3_3 = e11
% 10.43/2.98 |
% 10.43/2.98 | Instantiating formula (104) with e11, e11, all_0_2_2, e10 and discharging atoms op1(e11, e11) = all_0_2_2, op1(e11, e11) = e10, yields:
% 10.43/2.98 | (222) all_0_2_2 = e10
% 10.43/2.98 |
% 10.43/2.98 | Instantiating formula (104) with e11, e11, all_0_3_3, all_0_2_2 and discharging atoms op1(e11, e11) = all_0_2_2, op1(e11, e11) = all_0_3_3, yields:
% 10.43/2.98 | (288) all_0_2_2 = all_0_3_3
% 10.43/2.98 |
% 10.43/2.98 | Combining equations (288,222) yields a new equation:
% 10.43/2.98 | (289) all_0_3_3 = e10
% 10.43/2.98 |
% 10.43/2.98 | Simplifying 289 yields:
% 10.43/2.98 | (227) all_0_3_3 = e10
% 10.43/2.98 |
% 10.43/2.98 | Combining equations (207,227) yields a new equation:
% 10.43/2.98 | (418) e10 = e11
% 10.43/2.98 |
% 10.43/2.98 | Equations (418) can reduce 135 to:
% 10.43/2.98 | (200) $false
% 10.43/2.98 |
% 10.43/2.98 |-The branch is then unsatisfiable
% 10.43/2.98 |-Branch two:
% 10.43/2.98 | (434) ~ (all_0_8_8 = e24)
% 10.43/2.98 | (435) all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 10.43/2.98 |
% 10.43/2.98 +-Applying beta-rule and splitting (241), into two cases.
% 10.43/2.98 |-Branch one:
% 10.43/2.98 | (320) all_0_0_0 = e13
% 10.43/2.98 |
% 10.43/2.98 | From (320) and (17) follows:
% 10.43/2.98 | (437) h(e13) = e24
% 10.43/2.98 |
% 10.43/2.98 | Instantiating formula (99) with e13, e24, all_0_6_6 and discharging atoms h(e13) = all_0_6_6, h(e13) = e24, yields:
% 10.43/2.98 | (316) all_0_6_6 = e24
% 10.43/2.98 |
% 10.43/2.98 | Equations (316) can reduce 374 to:
% 10.43/2.98 | (200) $false
% 10.43/2.98 |
% 10.43/2.98 |-The branch is then unsatisfiable
% 10.43/2.98 |-Branch two:
% 10.43/2.98 | (440) ~ (all_0_0_0 = e13)
% 10.43/2.98 | (441) all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 10.43/2.98 |
% 10.43/2.98 +-Applying beta-rule and splitting (441), into two cases.
% 10.43/2.98 |-Branch one:
% 10.43/2.98 | (261) all_0_0_0 = e12
% 10.43/2.98 |
% 10.43/2.98 | From (261) and (17) follows:
% 10.43/2.98 | (443) h(e12) = e24
% 10.43/2.98 |
% 10.43/2.98 | Instantiating formula (99) with e12, e24, all_0_7_7 and discharging atoms h(e12) = all_0_7_7, h(e12) = e24, yields:
% 10.43/2.98 | (257) all_0_7_7 = e24
% 10.43/2.98 |
% 10.43/2.98 | Equations (257) can reduce 314 to:
% 10.43/2.98 | (200) $false
% 10.43/2.98 |
% 10.43/2.98 |-The branch is then unsatisfiable
% 10.43/2.98 |-Branch two:
% 10.43/2.98 | (446) ~ (all_0_0_0 = e12)
% 10.43/2.98 | (447) all_0_0_0 = e10 | all_0_0_0 = e11
% 10.43/2.98 |
% 10.43/2.98 +-Applying beta-rule and splitting (447), into two cases.
% 10.43/2.98 |-Branch one:
% 10.43/2.98 | (448) all_0_0_0 = e10
% 10.43/2.98 |
% 10.43/2.98 | From (448) and (17) follows:
% 10.43/2.98 | (449) h(e10) = e24
% 10.43/2.98 |
% 10.43/2.98 | Instantiating formula (99) with e10, e24, all_0_9_9 and discharging atoms h(e10) = all_0_9_9, h(e10) = e24, yields:
% 10.43/2.98 | (242) all_0_9_9 = e24
% 10.43/2.98 |
% 10.43/2.98 | Equations (242) can reduce 246 to:
% 10.43/2.98 | (200) $false
% 10.43/2.98 |
% 10.43/2.98 |-The branch is then unsatisfiable
% 10.43/2.98 |-Branch two:
% 10.43/2.98 | (452) ~ (all_0_0_0 = e10)
% 10.43/2.98 | (380) all_0_0_0 = e11
% 10.43/2.98 |
% 10.43/2.98 | From (380) and (17) follows:
% 10.43/2.99 | (454) h(e11) = e24
% 10.43/2.99 |
% 10.43/2.99 | Instantiating formula (99) with e11, e24, all_0_8_8 and discharging atoms h(e11) = all_0_8_8, h(e11) = e24, yields:
% 10.43/2.99 | (376) all_0_8_8 = e24
% 10.43/2.99 |
% 10.43/2.99 | Equations (376) can reduce 434 to:
% 10.43/2.99 | (200) $false
% 10.43/2.99 |
% 10.43/2.99 |-The branch is then unsatisfiable
% 10.43/2.99 % SZS output end Proof for theBenchmark
% 10.43/2.99
% 10.43/2.99 2396ms
%------------------------------------------------------------------------------