TSTP Solution File: ALG080+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG080+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 15:34:15 EDT 2022
% Result : Theorem 4.22s 1.61s
% Output : Proof 8.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG080+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 14:54:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.55/0.57 ____ _
% 0.55/0.57 ___ / __ \_____(_)___ ________ __________
% 0.55/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.57
% 0.55/0.57 A Theorem Prover for First-Order Logic
% 0.55/0.57 (ePrincess v.1.0)
% 0.55/0.57
% 0.55/0.57 (c) Philipp Rümmer, 2009-2015
% 0.55/0.57 (c) Peter Backeman, 2014-2015
% 0.55/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.57 Bug reports to peter@backeman.se
% 0.55/0.57
% 0.55/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.57
% 0.55/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.55/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.85/1.00 Prover 0: Preprocessing ...
% 2.81/1.29 Prover 0: Constructing countermodel ...
% 4.22/1.61 Prover 0: proved (988ms)
% 4.22/1.61
% 4.22/1.61 No countermodel exists, formula is valid
% 4.22/1.61 % SZS status Theorem for theBenchmark
% 4.22/1.61
% 4.22/1.61 Generating proof ... found it (size 136)
% 7.83/2.43
% 7.83/2.43 % SZS output start Proof for theBenchmark
% 7.83/2.43 Assumed formulas after preprocessing and simplification:
% 7.83/2.43 | (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) = v2 & op2(v4, v3) = v1 & op2(v4, v2) = v0 & op2(v4, v1) = v3 & op2(v4, v0) = v4 & op2(v3, v4) = v0 & op2(v3, v3) = v4 & op2(v3, v2) = v1 & op2(v3, v1) = v2 & op2(v3, v0) = v3 & op2(v2, v4) = v1 & op2(v2, v3) = v0 & op2(v2, v2) = v3 & op2(v2, v1) = v4 & op2(v2, v0) = v2 & op2(v1, v4) = v3 & op2(v1, v3) = v2 & op2(v1, v2) = v4 & 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) = e12 & op1(e14, e13) = e11 & op1(e14, e12) = e10 & op1(e14, e10) = e14 & op1(e14, e11) = e13 & op1(e13, e14) = e10 & op1(e13, e13) = e14 & op1(e13, e12) = e11 & op1(e13, e10) = e13 & op1(e13, e11) = e12 & op1(e12, e14) = e11 & op1(e12, e13) = e10 & op1(e12, e12) = e13 & 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) = e13 & op1(e11, e13) = e12 & op1(e11, e12) = e14 & 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))
% 8.42/2.50 | 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:
% 8.42/2.50 | (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_7_7 & op2(all_0_5_5, all_0_6_6) = all_0_8_8 & op2(all_0_5_5, all_0_7_7) = all_0_9_9 & 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_9_9 & op2(all_0_6_6, all_0_6_6) = all_0_5_5 & op2(all_0_6_6, all_0_7_7) = all_0_8_8 & 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_8_8 & op2(all_0_7_7, all_0_6_6) = all_0_9_9 & op2(all_0_7_7, all_0_7_7) = all_0_6_6 & 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_6_6 & op2(all_0_8_8, all_0_6_6) = all_0_7_7 & op2(all_0_8_8, all_0_7_7) = all_0_5_5 & 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) = e12 & op1(e14, e13) = e11 & op1(e14, e12) = e10 & op1(e14, e10) = e14 & op1(e14, e11) = e13 & op1(e13, e14) = e10 & op1(e13, e13) = e14 & op1(e13, e12) = e11 & op1(e13, e10) = e13 & op1(e13, e11) = e12 & op1(e12, e14) = e11 & op1(e12, e13) = e10 & op1(e12, e12) = e13 & 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) = e13 & op1(e11, e13) = e12 & op1(e11, e12) = e14 & 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)
% 8.42/2.52 |
% 8.42/2.52 | Applying alpha-rule on (1) yields:
% 8.42/2.52 | (2) op2(all_0_8_8, all_0_8_8) = all_0_9_9
% 8.42/2.52 | (3) ~ (e21 = e12)
% 8.42/2.52 | (4) op1(all_0_4_4, all_0_1_1) = all_0_1_1
% 8.42/2.52 | (5) ~ (e20 = e21)
% 8.42/2.52 | (6) ~ (e20 = e14)
% 8.42/2.52 | (7) op2(e23, e21) = e24
% 8.42/2.52 | (8) op1(all_0_2_2, all_0_2_2) = all_0_1_1
% 8.42/2.52 | (9) op1(e12, e12) = e13
% 8.42/2.52 | (10) op2(e20, e23) = e23
% 8.42/2.52 | (11) op1(all_0_4_4, all_0_2_2) = all_0_2_2
% 8.42/2.52 | (12) ~ (e24 = e11)
% 8.42/2.52 | (13) op1(e11, e11) = e10
% 8.42/2.52 | (14) ~ (e12 = e11)
% 8.42/2.52 | (15) h(e12) = all_0_7_7
% 8.42/2.52 | (16) h(all_0_0_0) = e24
% 8.42/2.52 | (17) h(e13) = all_0_6_6
% 8.42/2.52 | (18) op2(all_0_5_5, all_0_8_8) = all_0_6_6
% 8.42/2.52 | (19) ~ (e14 = e12)
% 8.42/2.52 | (20) ~ (e24 = e12)
% 8.42/2.52 | (21) op1(e10, e11) = e11
% 8.42/2.52 | (22) j(e22) = all_0_2_2
% 8.42/2.52 | (23) op1(e12, e11) = e14
% 8.42/2.52 | (24) op2(all_0_9_9, all_0_8_8) = all_0_8_8
% 8.42/2.52 | (25) j(e21) = all_0_3_3
% 8.42/2.52 | (26) j(all_0_8_8) = e11
% 8.42/2.52 | (27) ~ (e22 = e13)
% 8.42/2.52 | (28) op2(all_0_6_6, all_0_9_9) = all_0_6_6
% 8.42/2.52 | (29) op2(all_0_8_8, all_0_6_6) = all_0_7_7
% 8.42/2.52 | (30) op1(e12, e14) = e11
% 8.42/2.52 | (31) op2(e24, e21) = e23
% 8.42/2.52 | (32) op1(all_0_3_3, all_0_4_4) = all_0_3_3
% 8.42/2.52 | (33) j(all_0_6_6) = e13
% 8.42/2.52 | (34) op2(e24, e22) = e21
% 8.42/2.52 | (35) h(all_0_4_4) = e20
% 8.42/2.52 | (36) op2(e23, e22) = e20
% 8.42/2.53 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0))
% 8.42/2.53 | (38) op1(all_0_3_3, all_0_2_2) = all_0_0_0
% 8.42/2.53 | (39) op2(all_0_5_5, all_0_5_5) = all_0_7_7
% 8.42/2.53 | (40) op1(e14, e14) = e12
% 8.42/2.53 | (41) op1(all_0_1_1, all_0_3_3) = all_0_0_0
% 8.42/2.53 | (42) ~ (e23 = e13)
% 8.42/2.53 | (43) op1(all_0_0_0, all_0_4_4) = all_0_0_0
% 8.42/2.53 | (44) op2(all_0_9_9, all_0_6_6) = all_0_6_6
% 8.42/2.53 | (45) op2(e22, e20) = e22
% 8.42/2.53 | (46) 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
% 8.42/2.53 | (47) op1(e14, e12) = e10
% 8.42/2.53 | (48) ~ (e23 = e12)
% 8.42/2.53 | (49) op1(e11, e10) = e11
% 8.42/2.53 | (50) op2(e21, e24) = e23
% 8.42/2.53 | (51) op2(e21, e21) = e22
% 8.42/2.53 | (52) ~ (e24 = e14)
% 8.42/2.53 | (53) h(all_0_3_3) = e21
% 8.42/2.53 | (54) ~ (e23 = e21)
% 8.42/2.53 | (55) op1(e13, e11) = e12
% 8.42/2.53 | (56) 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
% 8.42/2.53 | (57) ~ (e22 = e21)
% 8.42/2.53 | (58) ~ (e20 = e11)
% 8.42/2.53 | (59) j(all_0_9_9) = e10
% 8.42/2.53 | (60) op1(all_0_3_3, all_0_3_3) = all_0_2_2
% 8.42/2.53 | (61) ~ (e14 = e10)
% 8.42/2.53 | (62) ~ (e22 = e10)
% 8.42/2.53 | (63) op1(all_0_0_0, all_0_0_0) = all_0_4_4
% 8.42/2.53 | (64) h(all_0_1_1) = e23
% 8.42/2.53 | (65) op2(all_0_9_9, all_0_9_9) = all_0_9_9
% 8.42/2.53 | (66) op2(all_0_9_9, all_0_7_7) = all_0_7_7
% 8.42/2.53 | (67) op1(e12, e10) = e12
% 8.58/2.53 | (68) ~ (e12 = e10)
% 8.58/2.53 | (69) ~ (e24 = e22)
% 8.58/2.53 | (70) op1(all_0_1_1, all_0_4_4) = all_0_1_1
% 8.58/2.53 | (71) 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
% 8.58/2.53 | (72) op2(e20, e24) = e24
% 8.58/2.53 | (73) op2(e20, e20) = e20
% 8.58/2.53 | (74) op2(e22, e21) = e20
% 8.58/2.53 | (75) 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
% 8.58/2.54 | (76) op2(all_0_6_6, all_0_5_5) = all_0_9_9
% 8.58/2.54 | (77) op1(all_0_1_1, all_0_0_0) = all_0_2_2
% 8.58/2.54 | (78) op2(all_0_7_7, all_0_9_9) = all_0_7_7
% 8.58/2.54 | (79) op1(all_0_0_0, all_0_1_1) = all_0_2_2
% 8.58/2.54 | (80) j(all_0_7_7) = e12
% 8.58/2.54 | (81) op2(all_0_8_8, all_0_5_5) = all_0_6_6
% 8.58/2.54 | (82) op2(all_0_5_5, all_0_9_9) = all_0_5_5
% 8.58/2.54 | (83) h(all_0_2_2) = e22
% 8.58/2.54 | (84) ~ (e14 = e13)
% 8.58/2.54 | (85) ~ (e21 = e11)
% 8.58/2.54 | (86) h(e14) = all_0_5_5
% 8.58/2.54 | (87) ~ (e24 = e20)
% 8.58/2.54 | (88) op2(e23, e23) = e21
% 8.58/2.54 | (89) ~ (e13 = e12)
% 8.58/2.54 | (90) 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
% 8.58/2.54 | (91) op1(all_0_2_2, all_0_3_3) = all_0_4_4
% 8.58/2.54 | (92) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0))
% 8.58/2.54 | (93) ~ (e14 = e11)
% 8.58/2.54 | (94) op2(e22, e24) = e21
% 8.58/2.54 | (95) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0))
% 8.58/2.54 | (96) op1(all_0_2_2, all_0_4_4) = all_0_2_2
% 8.58/2.54 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0))
% 8.58/2.54 | (98) 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
% 8.58/2.54 | (99) op1(all_0_1_1, all_0_1_1) = all_0_3_3
% 8.58/2.54 | (100) op2(all_0_6_6, all_0_8_8) = all_0_7_7
% 8.58/2.54 | (101) op1(all_0_1_1, all_0_2_2) = all_0_4_4
% 8.58/2.54 | (102) op1(e13, e10) = e13
% 8.58/2.54 | (103) op2(all_0_6_6, all_0_6_6) = all_0_5_5
% 8.58/2.54 | (104) op1(e10, e10) = e10
% 8.58/2.54 | (105) op1(all_0_0_0, all_0_3_3) = all_0_1_1
% 8.58/2.54 | (106) ~ (e23 = e10)
% 8.58/2.54 | (107) op2(all_0_7_7, all_0_6_6) = all_0_9_9
% 8.58/2.54 | (108) op1(all_0_4_4, all_0_4_4) = all_0_4_4
% 8.58/2.55 | (109) op2(e21, e23) = e20
% 8.58/2.55 | (110) op1(all_0_2_2, all_0_1_1) = all_0_0_0
% 8.58/2.55 | (111) ~ (e13 = e10)
% 8.58/2.55 | (112) op1(e10, e12) = e12
% 8.58/2.55 | (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
% 8.58/2.55 | (114) 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
% 8.58/2.55 | (115) ~ (e23 = e22)
% 8.58/2.55 | (116) ~ (e20 = e10)
% 8.58/2.55 | (117) ~ (e22 = e11)
% 8.58/2.55 | (118) op1(e13, e14) = e10
% 8.58/2.55 | (119) op2(e22, e22) = e23
% 8.58/2.55 | (120) ~ (e20 = e12)
% 8.58/2.55 | (121) op2(e22, e23) = e24
% 8.58/2.55 | (122) op2(all_0_7_7, all_0_5_5) = all_0_8_8
% 8.58/2.55 | (123) op1(all_0_0_0, all_0_2_2) = all_0_3_3
% 8.58/2.55 | (124) op1(all_0_3_3, all_0_0_0) = all_0_1_1
% 8.58/2.55 | (125) op1(e14, e11) = e13
% 8.58/2.55 | (126) op2(e24, e20) = e24
% 8.58/2.55 | (127) op1(all_0_4_4, all_0_0_0) = all_0_0_0
% 8.58/2.55 | (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
% 8.58/2.55 | (129) ~ (e10 = e11)
% 8.58/2.55 | (130) op1(all_0_2_2, all_0_0_0) = all_0_3_3
% 8.58/2.55 | (131) op2(all_0_6_6, all_0_7_7) = all_0_8_8
% 8.58/2.55 | (132) ~ (e23 = e14)
% 8.58/2.55 | (133) h(e11) = all_0_8_8
% 8.58/2.55 | (134) op1(e10, e13) = e13
% 8.58/2.55 | (135) op1(e12, e13) = e10
% 8.58/2.55 | (136) op2(all_0_7_7, all_0_8_8) = all_0_5_5
% 8.58/2.55 | (137) op1(e11, e12) = e14
% 8.58/2.55 | (138) op1(e14, e10) = e14
% 8.58/2.55 | (139) op2(e23, e24) = e22
% 8.58/2.56 | (140) j(e23) = all_0_1_1
% 8.58/2.56 | (141) ~ (e23 = e20)
% 8.58/2.56 | (142) op2(e21, e20) = e21
% 8.58/2.56 | (143) ~ (e21 = e14)
% 8.58/2.56 | (144) j(e24) = all_0_0_0
% 8.58/2.56 | (145) op2(e24, e24) = e20
% 8.58/2.56 | (146) op1(e10, e14) = e14
% 8.58/2.56 | (147) ~ (e24 = e21)
% 8.58/2.56 | (148) op1(e11, e14) = e13
% 8.58/2.56 | (149) op2(all_0_8_8, all_0_9_9) = all_0_8_8
% 8.58/2.56 | (150) j(all_0_5_5) = e14
% 8.58/2.56 | (151) op2(all_0_5_5, all_0_7_7) = all_0_9_9
% 8.58/2.56 | (152) op2(e23, e20) = e23
% 8.58/2.56 | (153) ~ (e22 = e20)
% 8.58/2.56 | (154) ~ (e23 = e11)
% 8.58/2.56 | (155) op2(all_0_7_7, all_0_7_7) = all_0_6_6
% 8.58/2.56 | (156) op2(all_0_8_8, all_0_7_7) = all_0_5_5
% 8.58/2.56 | (157) op1(e14, e13) = e11
% 8.58/2.56 | (158) ~ (e24 = e10)
% 8.58/2.56 | (159) ~ (e24 = e23)
% 8.58/2.56 | (160) op1(e11, e13) = e12
% 8.58/2.56 | (161) ~ (e20 = e13)
% 8.58/2.56 | (162) ~ (e24 = e13)
% 8.58/2.56 | (163) op1(all_0_4_4, all_0_3_3) = all_0_3_3
% 8.58/2.56 | (164) ~ (e21 = e10)
% 8.58/2.56 | (165) op1(e13, e13) = e14
% 8.58/2.56 | (166) ~ (e21 = e13)
% 8.58/2.56 | (167) j(e20) = all_0_4_4
% 8.58/2.56 | (168) ~ (e22 = e12)
% 8.58/2.56 | (169) op2(e24, e23) = e22
% 8.58/2.56 | (170) op2(e20, e22) = e22
% 8.58/2.56 | (171) 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
% 8.58/2.57 | (172) h(e10) = all_0_9_9
% 8.58/2.57 | (173) op2(all_0_5_5, all_0_6_6) = all_0_8_8
% 8.58/2.57 | (174) ~ (e22 = e14)
% 8.58/2.57 | (175) op1(all_0_3_3, all_0_1_1) = all_0_4_4
% 8.58/2.57 | (176) op2(e20, e21) = e21
% 8.58/2.57 | (177) op2(all_0_9_9, all_0_5_5) = all_0_5_5
% 8.58/2.57 | (178) op2(e21, e22) = e24
% 8.58/2.57 | (179) ~ (e13 = e11)
% 8.58/2.57 | (180) op1(e13, e12) = e11
% 8.58/2.57 |
% 8.58/2.57 +-Applying beta-rule and splitting (114), into two cases.
% 8.58/2.57 |-Branch one:
% 8.58/2.57 | (181) all_0_0_0 = e14
% 8.58/2.57 |
% 8.58/2.57 | From (181)(181) and (63) follows:
% 8.58/2.57 | (182) op1(e14, e14) = all_0_4_4
% 8.58/2.57 |
% 8.58/2.57 | From (181)(181) and (43) follows:
% 8.58/2.57 | (183) op1(e14, all_0_4_4) = e14
% 8.58/2.57 |
% 8.58/2.57 | From (181)(181) and (127) follows:
% 8.58/2.57 | (184) op1(all_0_4_4, e14) = e14
% 8.58/2.57 |
% 8.58/2.58 | Instantiating formula (97) with e14, e14, all_0_4_4, e12 and discharging atoms op1(e14, e14) = all_0_4_4, op1(e14, e14) = e12, yields:
% 8.58/2.58 | (185) all_0_4_4 = e12
% 8.58/2.58 |
% 8.58/2.58 | From (185) and (184) follows:
% 8.58/2.58 | (186) op1(e12, e14) = e14
% 8.58/2.58 |
% 8.58/2.58 | From (185) and (183) follows:
% 8.58/2.58 | (187) op1(e14, e12) = e14
% 8.58/2.58 |
% 8.58/2.58 | Instantiating formula (97) with e14, e12, e14, e10 and discharging atoms op1(e14, e12) = e14, op1(e14, e12) = e10, yields:
% 8.58/2.58 | (188) e14 = e10
% 8.58/2.58 |
% 8.58/2.58 | Instantiating formula (97) with e12, e14, e14, e11 and discharging atoms op1(e12, e14) = e14, op1(e12, e14) = e11, yields:
% 8.58/2.58 | (189) e14 = e11
% 8.58/2.58 |
% 8.58/2.58 | Combining equations (188,189) yields a new equation:
% 8.58/2.58 | (190) e10 = e11
% 8.58/2.58 |
% 8.58/2.58 | Simplifying 190 yields:
% 8.58/2.58 | (191) e10 = e11
% 8.58/2.58 |
% 8.58/2.58 | Equations (191) can reduce 129 to:
% 8.58/2.58 | (192) $false
% 8.58/2.58 |
% 8.58/2.58 |-The branch is then unsatisfiable
% 8.58/2.58 |-Branch two:
% 8.58/2.58 | (193) ~ (all_0_0_0 = e14)
% 8.58/2.58 | (194) all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 8.58/2.58 |
% 8.58/2.58 +-Applying beta-rule and splitting (71), into two cases.
% 8.58/2.58 |-Branch one:
% 8.58/2.58 | (195) all_0_9_9 = e24
% 8.58/2.58 |
% 8.58/2.58 | From (195)(195)(195) and (65) follows:
% 8.58/2.58 | (196) op2(e24, e24) = e24
% 8.58/2.58 |
% 8.58/2.58 | Instantiating formula (37) with e24, e24, e24, e20 and discharging atoms op2(e24, e24) = e24, op2(e24, e24) = e20, yields:
% 8.58/2.58 | (197) e24 = e20
% 8.58/2.58 |
% 8.58/2.58 | Equations (197) can reduce 87 to:
% 8.58/2.58 | (192) $false
% 8.58/2.58 |
% 8.58/2.58 |-The branch is then unsatisfiable
% 8.58/2.58 |-Branch two:
% 8.58/2.58 | (199) ~ (all_0_9_9 = e24)
% 8.58/2.58 | (200) all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21
% 8.58/2.58 |
% 8.58/2.58 +-Applying beta-rule and splitting (56), into two cases.
% 8.58/2.58 |-Branch one:
% 8.58/2.58 | (201) all_0_1_1 = e14
% 8.58/2.58 |
% 8.58/2.58 | From (201)(201) and (99) follows:
% 8.58/2.58 | (202) op1(e14, e14) = all_0_3_3
% 8.58/2.58 |
% 8.58/2.58 | From (201) and (175) follows:
% 8.58/2.58 | (203) op1(all_0_3_3, e14) = all_0_4_4
% 8.58/2.58 |
% 8.58/2.58 | Instantiating formula (97) with e14, e14, all_0_3_3, e12 and discharging atoms op1(e14, e14) = all_0_3_3, op1(e14, e14) = e12, yields:
% 8.58/2.58 | (204) all_0_3_3 = e12
% 8.58/2.58 |
% 8.58/2.58 | From (204) and (203) follows:
% 8.58/2.58 | (205) op1(e12, e14) = all_0_4_4
% 8.58/2.58 |
% 8.58/2.58 | Instantiating formula (97) with e12, e14, all_0_4_4, e11 and discharging atoms op1(e12, e14) = all_0_4_4, op1(e12, e14) = e11, yields:
% 8.58/2.58 | (206) all_0_4_4 = e11
% 8.58/2.59 |
% 8.58/2.59 | From (206)(206)(206) and (108) follows:
% 8.58/2.59 | (207) op1(e11, e11) = e11
% 8.58/2.59 |
% 8.58/2.59 | Instantiating formula (97) with e11, e11, e11, e10 and discharging atoms op1(e11, e11) = e10, op1(e11, e11) = e11, yields:
% 8.58/2.59 | (191) e10 = e11
% 8.58/2.59 |
% 8.58/2.59 | Equations (191) can reduce 129 to:
% 8.58/2.59 | (192) $false
% 8.58/2.59 |
% 8.58/2.59 |-The branch is then unsatisfiable
% 8.58/2.59 |-Branch two:
% 8.58/2.59 | (210) ~ (all_0_1_1 = e14)
% 8.58/2.59 | (211) all_0_1_1 = e13 | all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11
% 8.58/2.59 |
% 8.58/2.59 +-Applying beta-rule and splitting (90), into two cases.
% 8.58/2.59 |-Branch one:
% 8.58/2.59 | (212) all_0_7_7 = e24
% 8.58/2.59 |
% 8.58/2.59 | From (212) and (107) follows:
% 8.58/2.59 | (213) op2(e24, all_0_6_6) = all_0_9_9
% 8.58/2.59 |
% 8.58/2.59 | From (212)(212) and (155) follows:
% 8.58/2.59 | (214) op2(e24, e24) = all_0_6_6
% 8.58/2.59 |
% 8.58/2.59 | Instantiating formula (37) with e24, e24, all_0_6_6, e20 and discharging atoms op2(e24, e24) = all_0_6_6, op2(e24, e24) = e20, yields:
% 8.58/2.59 | (215) all_0_6_6 = e20
% 8.58/2.59 |
% 8.58/2.59 | From (215) and (213) follows:
% 8.58/2.59 | (216) op2(e24, e20) = all_0_9_9
% 8.58/2.59 |
% 8.58/2.59 | Instantiating formula (37) with e24, e20, all_0_9_9, e24 and discharging atoms op2(e24, e20) = all_0_9_9, op2(e24, e20) = e24, yields:
% 8.58/2.59 | (195) all_0_9_9 = e24
% 8.58/2.59 |
% 8.58/2.59 | Equations (195) can reduce 199 to:
% 8.58/2.59 | (192) $false
% 8.58/2.59 |
% 8.58/2.59 |-The branch is then unsatisfiable
% 8.58/2.59 |-Branch two:
% 8.58/2.59 | (219) ~ (all_0_7_7 = e24)
% 8.58/2.59 | (220) all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 8.58/2.59 |
% 8.58/2.59 +-Applying beta-rule and splitting (113), into two cases.
% 8.58/2.59 |-Branch one:
% 8.58/2.59 | (221) all_0_6_6 = e24
% 8.58/2.59 |
% 8.58/2.59 | From (221) and (76) follows:
% 8.58/2.59 | (222) op2(e24, all_0_5_5) = all_0_9_9
% 8.58/2.59 |
% 8.58/2.59 | From (221)(221) and (103) follows:
% 8.58/2.59 | (223) op2(e24, e24) = all_0_5_5
% 8.58/2.59 |
% 8.58/2.59 | Instantiating formula (37) with e24, e24, all_0_5_5, e20 and discharging atoms op2(e24, e24) = all_0_5_5, op2(e24, e24) = e20, yields:
% 8.58/2.59 | (224) all_0_5_5 = e20
% 8.58/2.59 |
% 8.58/2.59 | From (224) and (222) follows:
% 8.58/2.59 | (216) op2(e24, e20) = all_0_9_9
% 8.58/2.59 |
% 8.58/2.59 | Instantiating formula (37) with e24, e20, all_0_9_9, e24 and discharging atoms op2(e24, e20) = all_0_9_9, op2(e24, e20) = e24, yields:
% 8.58/2.59 | (195) all_0_9_9 = e24
% 8.58/2.59 |
% 8.58/2.59 | Equations (195) can reduce 199 to:
% 8.58/2.59 | (192) $false
% 8.58/2.59 |
% 8.58/2.59 |-The branch is then unsatisfiable
% 8.58/2.59 |-Branch two:
% 8.58/2.59 | (228) ~ (all_0_6_6 = e24)
% 8.58/2.59 | (229) all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21
% 8.58/2.59 |
% 8.58/2.59 +-Applying beta-rule and splitting (171), into two cases.
% 8.58/2.59 |-Branch one:
% 8.58/2.59 | (230) all_0_3_3 = e14
% 8.58/2.59 |
% 8.58/2.59 | From (230) and (91) follows:
% 8.58/2.59 | (231) op1(all_0_2_2, e14) = all_0_4_4
% 8.58/2.59 |
% 8.58/2.59 | From (230)(230) and (60) follows:
% 8.58/2.59 | (232) op1(e14, e14) = all_0_2_2
% 8.58/2.59 |
% 8.58/2.59 | Instantiating formula (97) with e14, e14, all_0_2_2, e12 and discharging atoms op1(e14, e14) = all_0_2_2, op1(e14, e14) = e12, yields:
% 8.58/2.59 | (233) all_0_2_2 = e12
% 8.58/2.59 |
% 8.58/2.59 | From (233) and (231) follows:
% 8.58/2.59 | (205) op1(e12, e14) = all_0_4_4
% 8.58/2.59 |
% 8.58/2.59 | Instantiating formula (97) with e12, e14, all_0_4_4, e11 and discharging atoms op1(e12, e14) = all_0_4_4, op1(e12, e14) = e11, yields:
% 8.58/2.59 | (206) all_0_4_4 = e11
% 8.58/2.59 |
% 8.58/2.59 | From (206)(206)(206) and (108) follows:
% 8.58/2.59 | (207) op1(e11, e11) = e11
% 8.58/2.59 |
% 8.58/2.59 | Instantiating formula (97) with e11, e11, e11, e10 and discharging atoms op1(e11, e11) = e10, op1(e11, e11) = e11, yields:
% 8.58/2.59 | (191) e10 = e11
% 8.58/2.59 |
% 8.58/2.59 | Equations (191) can reduce 129 to:
% 8.58/2.59 | (192) $false
% 8.58/2.59 |
% 8.58/2.59 |-The branch is then unsatisfiable
% 8.58/2.59 |-Branch two:
% 8.58/2.59 | (239) ~ (all_0_3_3 = e14)
% 8.58/2.59 | (240) all_0_3_3 = e13 | all_0_3_3 = e12 | all_0_3_3 = e10 | all_0_3_3 = e11
% 8.58/2.59 |
% 8.58/2.59 +-Applying beta-rule and splitting (128), into two cases.
% 8.58/2.59 |-Branch one:
% 8.58/2.59 | (241) all_0_8_8 = e24
% 8.58/2.59 |
% 8.58/2.59 | From (241) and (136) follows:
% 8.58/2.59 | (242) op2(all_0_7_7, e24) = all_0_5_5
% 8.58/2.59 |
% 8.58/2.59 | From (241)(241) and (2) follows:
% 8.58/2.59 | (243) op2(e24, e24) = all_0_9_9
% 8.58/2.59 |
% 8.58/2.59 | From (241) and (26) follows:
% 8.58/2.59 | (244) j(e24) = e11
% 8.58/2.59 |
% 8.58/2.59 | Instantiating formula (37) with e24, e24, all_0_9_9, e20 and discharging atoms op2(e24, e24) = all_0_9_9, op2(e24, e24) = e20, yields:
% 8.58/2.59 | (245) all_0_9_9 = e20
% 8.58/2.59 |
% 8.58/2.59 | Instantiating formula (95) with e24, e11, all_0_0_0 and discharging atoms j(e24) = all_0_0_0, j(e24) = e11, yields:
% 8.58/2.59 | (246) all_0_0_0 = e11
% 8.58/2.59 |
% 8.58/2.59 | Equations (245) can reduce 199 to:
% 8.58/2.59 | (247) ~ (e24 = e20)
% 8.58/2.59 |
% 8.58/2.59 | Simplifying 247 yields:
% 8.58/2.59 | (87) ~ (e24 = e20)
% 8.58/2.59 |
% 8.58/2.59 | From (245) and (76) follows:
% 8.58/2.59 | (249) op2(all_0_6_6, all_0_5_5) = e20
% 8.58/2.59 |
% 8.58/2.59 | From (246)(246) and (63) follows:
% 8.58/2.59 | (250) op1(e11, e11) = all_0_4_4
% 8.58/2.59 |
% 8.58/2.59 | From (246) and (79) follows:
% 8.58/2.59 | (251) op1(e11, all_0_1_1) = all_0_2_2
% 8.58/2.59 |
% 8.58/2.59 | From (246) and (41) follows:
% 8.58/2.59 | (252) op1(all_0_1_1, all_0_3_3) = e11
% 8.58/2.59 |
% 8.58/2.59 | From (246) and (130) follows:
% 8.58/2.60 | (253) op1(all_0_2_2, e11) = all_0_3_3
% 8.58/2.60 |
% 8.58/2.60 | From (246) and (110) follows:
% 8.58/2.60 | (254) op1(all_0_2_2, all_0_1_1) = e11
% 8.58/2.60 |
% 8.58/2.60 | From (245) and (59) follows:
% 8.58/2.60 | (255) j(e20) = e10
% 8.58/2.60 |
% 8.58/2.60 | Instantiating formula (95) with e20, e10, all_0_4_4 and discharging atoms j(e20) = all_0_4_4, j(e20) = e10, yields:
% 8.58/2.60 | (256) all_0_4_4 = e10
% 8.58/2.60 |
% 8.58/2.60 | From (256) and (4) follows:
% 8.58/2.60 | (257) op1(e10, all_0_1_1) = all_0_1_1
% 8.58/2.60 |
% 8.58/2.60 | From (256) and (163) follows:
% 8.58/2.60 | (258) op1(e10, all_0_3_3) = all_0_3_3
% 8.58/2.60 |
% 8.58/2.60 | From (256) and (250) follows:
% 8.58/2.60 | (13) op1(e11, e11) = e10
% 8.58/2.60 |
% 8.58/2.60 +-Applying beta-rule and splitting (211), into two cases.
% 8.58/2.60 |-Branch one:
% 8.58/2.60 | (260) all_0_1_1 = e13
% 8.58/2.60 |
% 8.58/2.60 | From (260)(260) and (99) follows:
% 8.58/2.60 | (261) op1(e13, e13) = all_0_3_3
% 8.58/2.60 |
% 8.58/2.60 | Instantiating formula (97) with e13, e13, all_0_3_3, e14 and discharging atoms op1(e13, e13) = all_0_3_3, op1(e13, e13) = e14, yields:
% 8.58/2.60 | (230) all_0_3_3 = e14
% 8.58/2.60 |
% 8.58/2.60 | Equations (230) can reduce 239 to:
% 8.58/2.60 | (192) $false
% 8.58/2.60 |
% 8.58/2.60 |-The branch is then unsatisfiable
% 8.58/2.60 |-Branch two:
% 8.58/2.60 | (264) ~ (all_0_1_1 = e13)
% 8.58/2.60 | (265) all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11
% 8.58/2.60 |
% 8.58/2.60 +-Applying beta-rule and splitting (220), into two cases.
% 8.58/2.60 |-Branch one:
% 8.58/2.60 | (266) all_0_7_7 = e23
% 8.58/2.60 |
% 8.58/2.60 | From (266)(266) and (155) follows:
% 8.58/2.60 | (267) op2(e23, e23) = all_0_6_6
% 8.58/2.60 |
% 8.58/2.60 | From (266) and (242) follows:
% 8.58/2.60 | (268) op2(e23, e24) = all_0_5_5
% 8.58/2.60 |
% 8.58/2.60 | Instantiating formula (37) with e23, e24, all_0_5_5, e22 and discharging atoms op2(e23, e24) = all_0_5_5, op2(e23, e24) = e22, yields:
% 8.58/2.60 | (269) all_0_5_5 = e22
% 8.58/2.60 |
% 8.58/2.60 | Instantiating formula (37) with e23, e23, all_0_6_6, e21 and discharging atoms op2(e23, e23) = all_0_6_6, op2(e23, e23) = e21, yields:
% 8.58/2.60 | (270) all_0_6_6 = e21
% 8.58/2.60 |
% 8.58/2.60 | From (270)(269) and (249) follows:
% 8.58/2.60 | (271) op2(e21, e22) = e20
% 8.58/2.60 |
% 8.58/2.60 | Instantiating formula (37) with e21, e22, e20, e24 and discharging atoms op2(e21, e22) = e24, op2(e21, e22) = e20, yields:
% 8.58/2.60 | (197) e24 = e20
% 8.58/2.60 |
% 8.58/2.60 | Equations (197) can reduce 87 to:
% 8.58/2.60 | (192) $false
% 8.58/2.60 |
% 8.58/2.60 |-The branch is then unsatisfiable
% 8.58/2.60 |-Branch two:
% 8.58/2.60 | (274) ~ (all_0_7_7 = e23)
% 8.58/2.60 | (275) all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 8.58/2.60 |
% 8.58/2.60 +-Applying beta-rule and splitting (265), into two cases.
% 8.58/2.60 |-Branch one:
% 8.58/2.60 | (276) all_0_1_1 = e12
% 8.58/2.60 |
% 8.58/2.60 | From (276) and (64) follows:
% 8.58/2.60 | (277) h(e12) = e23
% 8.58/2.60 |
% 8.58/2.60 | Instantiating formula (92) with e12, e23, all_0_7_7 and discharging atoms h(e12) = all_0_7_7, h(e12) = e23, yields:
% 8.58/2.60 | (266) all_0_7_7 = e23
% 8.58/2.60 |
% 8.58/2.60 | Equations (266) can reduce 274 to:
% 8.58/2.60 | (192) $false
% 8.58/2.60 |
% 8.58/2.60 |-The branch is then unsatisfiable
% 8.58/2.60 |-Branch two:
% 8.58/2.60 | (280) ~ (all_0_1_1 = e12)
% 8.58/2.60 | (281) all_0_1_1 = e10 | all_0_1_1 = e11
% 8.58/2.60 |
% 8.58/2.60 +-Applying beta-rule and splitting (281), into two cases.
% 8.58/2.60 |-Branch one:
% 8.58/2.60 | (282) all_0_1_1 = e10
% 8.58/2.60 |
% 8.58/2.60 | From (282)(282) and (99) follows:
% 8.58/2.60 | (283) op1(e10, e10) = all_0_3_3
% 8.58/2.60 |
% 8.58/2.60 | From (282) and (252) follows:
% 8.58/2.60 | (284) op1(e10, all_0_3_3) = e11
% 8.58/2.60 |
% 8.58/2.60 | From (282)(282) and (257) follows:
% 8.58/2.60 | (104) op1(e10, e10) = e10
% 8.58/2.60 |
% 8.58/2.60 | Instantiating formula (97) 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:
% 8.58/2.60 | (286) all_0_3_3 = e11
% 8.58/2.60 |
% 8.58/2.60 | Instantiating formula (97) with e10, e10, all_0_3_3, e10 and discharging atoms op1(e10, e10) = all_0_3_3, op1(e10, e10) = e10, yields:
% 8.58/2.60 | (287) all_0_3_3 = e10
% 8.58/2.60 |
% 8.58/2.60 | Combining equations (287,286) yields a new equation:
% 8.58/2.60 | (190) e10 = e11
% 8.58/2.60 |
% 8.58/2.60 | Simplifying 190 yields:
% 8.58/2.60 | (191) e10 = e11
% 8.58/2.60 |
% 8.58/2.60 | Equations (191) can reduce 129 to:
% 8.58/2.60 | (192) $false
% 8.58/2.60 |
% 8.58/2.60 |-The branch is then unsatisfiable
% 8.58/2.60 |-Branch two:
% 8.58/2.60 | (291) ~ (all_0_1_1 = e10)
% 8.58/2.60 | (292) all_0_1_1 = e11
% 8.58/2.60 |
% 8.58/2.60 | Equations (292) can reduce 291 to:
% 8.58/2.60 | (293) ~ (e10 = e11)
% 8.58/2.60 |
% 8.58/2.60 | Simplifying 293 yields:
% 8.58/2.60 | (129) ~ (e10 = e11)
% 8.58/2.60 |
% 8.58/2.60 | From (292)(292) and (99) follows:
% 8.58/2.60 | (295) op1(e11, e11) = all_0_3_3
% 8.58/2.60 |
% 8.58/2.60 | From (292) and (254) follows:
% 8.58/2.60 | (296) op1(all_0_2_2, e11) = e11
% 8.58/2.60 |
% 8.58/2.60 | From (292) and (251) follows:
% 8.58/2.60 | (297) op1(e11, e11) = all_0_2_2
% 8.58/2.60 |
% 8.58/2.60 | Instantiating formula (97) 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:
% 8.58/2.60 | (286) all_0_3_3 = e11
% 8.58/2.60 |
% 8.58/2.60 | Instantiating formula (97) with e11, e11, all_0_2_2, e10 and discharging atoms op1(e11, e11) = all_0_2_2, op1(e11, e11) = e10, yields:
% 8.58/2.60 | (299) all_0_2_2 = e10
% 8.58/2.60 |
% 8.58/2.60 | Instantiating formula (97) 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:
% 8.58/2.60 | (300) all_0_2_2 = all_0_3_3
% 8.58/2.60 |
% 8.58/2.60 | Combining equations (300,299) yields a new equation:
% 8.58/2.60 | (301) all_0_3_3 = e10
% 8.58/2.60 |
% 8.58/2.60 | Simplifying 301 yields:
% 8.58/2.60 | (287) all_0_3_3 = e10
% 8.58/2.60 |
% 8.58/2.60 | Combining equations (286,287) yields a new equation:
% 8.58/2.60 | (191) e10 = e11
% 8.58/2.60 |
% 8.58/2.60 | Equations (191) can reduce 129 to:
% 8.58/2.60 | (192) $false
% 8.58/2.60 |
% 8.58/2.60 |-The branch is then unsatisfiable
% 8.58/2.60 |-Branch two:
% 8.58/2.60 | (305) ~ (all_0_8_8 = e24)
% 8.58/2.60 | (306) all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 8.58/2.60 |
% 8.58/2.60 +-Applying beta-rule and splitting (194), into two cases.
% 8.58/2.61 |-Branch one:
% 8.58/2.61 | (307) all_0_0_0 = e13
% 8.58/2.61 |
% 8.58/2.61 | From (307) and (16) follows:
% 8.58/2.61 | (308) h(e13) = e24
% 8.58/2.61 |
% 8.58/2.61 | Instantiating formula (92) with e13, e24, all_0_6_6 and discharging atoms h(e13) = all_0_6_6, h(e13) = e24, yields:
% 8.58/2.61 | (221) all_0_6_6 = e24
% 8.58/2.61 |
% 8.58/2.61 | Equations (221) can reduce 228 to:
% 8.58/2.61 | (192) $false
% 8.58/2.61 |
% 8.58/2.61 |-The branch is then unsatisfiable
% 8.58/2.61 |-Branch two:
% 8.58/2.61 | (311) ~ (all_0_0_0 = e13)
% 8.58/2.61 | (312) all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 8.58/2.61 |
% 8.58/2.61 +-Applying beta-rule and splitting (312), into two cases.
% 8.58/2.61 |-Branch one:
% 8.58/2.61 | (313) all_0_0_0 = e12
% 8.58/2.61 |
% 8.58/2.61 | From (313) and (16) follows:
% 8.58/2.61 | (314) h(e12) = e24
% 8.58/2.61 |
% 8.58/2.61 | Instantiating formula (92) with e12, e24, all_0_7_7 and discharging atoms h(e12) = all_0_7_7, h(e12) = e24, yields:
% 8.58/2.61 | (212) all_0_7_7 = e24
% 8.58/2.61 |
% 8.58/2.61 | Equations (212) can reduce 219 to:
% 8.58/2.61 | (192) $false
% 8.58/2.61 |
% 8.58/2.61 |-The branch is then unsatisfiable
% 8.58/2.61 |-Branch two:
% 8.58/2.61 | (317) ~ (all_0_0_0 = e12)
% 8.58/2.61 | (318) all_0_0_0 = e10 | all_0_0_0 = e11
% 8.58/2.61 |
% 8.58/2.61 +-Applying beta-rule and splitting (318), into two cases.
% 8.58/2.61 |-Branch one:
% 8.58/2.61 | (319) all_0_0_0 = e10
% 8.58/2.61 |
% 8.58/2.61 | From (319) and (16) follows:
% 8.58/2.61 | (320) h(e10) = e24
% 8.58/2.61 |
% 8.58/2.61 | Instantiating formula (92) with e10, e24, all_0_9_9 and discharging atoms h(e10) = all_0_9_9, h(e10) = e24, yields:
% 8.58/2.61 | (195) all_0_9_9 = e24
% 8.58/2.61 |
% 8.58/2.61 | Equations (195) can reduce 199 to:
% 8.58/2.61 | (192) $false
% 8.58/2.61 |
% 8.58/2.61 |-The branch is then unsatisfiable
% 8.58/2.61 |-Branch two:
% 8.58/2.61 | (323) ~ (all_0_0_0 = e10)
% 8.58/2.61 | (246) all_0_0_0 = e11
% 8.58/2.61 |
% 8.58/2.61 | From (246) and (16) follows:
% 8.58/2.61 | (325) h(e11) = e24
% 8.58/2.61 |
% 8.58/2.61 | Instantiating formula (92) with e11, e24, all_0_8_8 and discharging atoms h(e11) = all_0_8_8, h(e11) = e24, yields:
% 8.58/2.61 | (241) all_0_8_8 = e24
% 8.58/2.61 |
% 8.58/2.61 | Equations (241) can reduce 305 to:
% 8.58/2.61 | (192) $false
% 8.58/2.61 |
% 8.58/2.61 |-The branch is then unsatisfiable
% 8.58/2.61 % SZS output end Proof for theBenchmark
% 8.58/2.61
% 8.58/2.61 2023ms
%------------------------------------------------------------------------------