TSTP Solution File: ALG086+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG086+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 15:34:16 EDT 2022
% Result : Theorem 4.95s 1.72s
% Output : Proof 10.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG086+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n020.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 14:17:36 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
% 0.55/0.57 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
% 1.92/0.98 Prover 0: Preprocessing ...
% 2.96/1.26 Prover 0: Constructing countermodel ...
% 4.95/1.72 Prover 0: proved (1099ms)
% 4.95/1.72
% 4.95/1.72 No countermodel exists, formula is valid
% 4.95/1.72 % SZS status Theorem for theBenchmark
% 4.95/1.72
% 4.95/1.72 Generating proof ... found it (size 244)
% 10.22/2.91
% 10.22/2.91 % SZS output start Proof for theBenchmark
% 10.22/2.91 Assumed formulas after preprocessing and simplification:
% 10.22/2.91 | (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) = e21 & op2(e23, e23) = e24 & op2(e23, e22) = e20 & op2(e23, e20) = e23 & op2(e23, e21) = e22 & op2(e22, e24) = e23 & op2(e22, e23) = e21 & op2(e22, e22) = e24 & 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) = e22 & op2(e21, e23) = e20 & op2(e21, e22) = e23 & op2(e21, e20) = e21 & op2(e21, e21) = e24 & op1(v9, v9) = v5 & op1(v9, v8) = v7 & op1(v9, v7) = v6 & op1(v9, v6) = v8 & op1(v9, v5) = v9 & op1(v8, v9) = v6 & op1(v8, v8) = v9 & op1(v8, v7) = v5 & op1(v8, v6) = v7 & op1(v8, v5) = v8 & op1(v7, v9) = v8 & op1(v7, v8) = v6 & op1(v7, v7) = v9 & op1(v7, v6) = v5 & op1(v7, v5) = v7 & op1(v6, v9) = v7 & op1(v6, v8) = v5 & op1(v6, v7) = v8 & op1(v6, v6) = v9 & 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))
% 10.46/2.96 | 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:
% 10.46/2.96 | (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) = e21 & op2(e23, e23) = e24 & op2(e23, e22) = e20 & op2(e23, e20) = e23 & op2(e23, e21) = e22 & op2(e22, e24) = e23 & op2(e22, e23) = e21 & op2(e22, e22) = e24 & 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) = e22 & op2(e21, e23) = e20 & op2(e21, e22) = e23 & op2(e21, e20) = e21 & op2(e21, e21) = e24 & 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_3_3 & op1(all_0_1_1, all_0_1_1) = all_0_0_0 & op1(all_0_1_1, all_0_2_2) = all_0_4_4 & op1(all_0_1_1, all_0_3_3) = all_0_2_2 & op1(all_0_1_1, all_0_4_4) = all_0_1_1 & op1(all_0_2_2, all_0_0_0) = all_0_1_1 & op1(all_0_2_2, all_0_1_1) = all_0_3_3 & op1(all_0_2_2, all_0_2_2) = all_0_0_0 & 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_2_2 & op1(all_0_3_3, all_0_1_1) = all_0_4_4 & op1(all_0_3_3, all_0_2_2) = all_0_1_1 & op1(all_0_3_3, all_0_3_3) = all_0_0_0 & 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)
% 10.46/2.97 |
% 10.46/2.97 | Applying alpha-rule on (1) yields:
% 10.46/2.97 | (2) op1(e14, e11) = e13
% 10.46/2.97 | (3) op1(all_0_4_4, all_0_3_3) = all_0_3_3
% 10.46/2.97 | (4) j(all_0_8_8) = e11
% 10.46/2.97 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0))
% 10.46/2.97 | (6) op2(e23, e23) = e24
% 10.46/2.97 | (7) j(e23) = all_0_1_1
% 10.46/2.97 | (8) op1(e13, e10) = e13
% 10.46/2.97 | (9) ~ (e20 = e13)
% 10.46/2.97 | (10) op1(all_0_3_3, all_0_4_4) = all_0_3_3
% 10.46/2.97 | (11) ~ (e23 = e14)
% 10.46/2.97 | (12) op2(e20, e20) = e20
% 10.46/2.97 | (13) op2(e24, e24) = e20
% 10.46/2.97 | (14) h(all_0_1_1) = e23
% 10.46/2.97 | (15) op2(e22, e23) = e21
% 10.46/2.97 | (16) ~ (e14 = e12)
% 10.46/2.97 | (17) j(e20) = all_0_4_4
% 10.46/2.97 | (18) op1(e11, e10) = e11
% 10.46/2.97 | (19) ~ (e20 = e10)
% 10.46/2.97 | (20) op1(all_0_3_3, all_0_2_2) = all_0_1_1
% 10.46/2.97 | (21) op1(all_0_2_2, all_0_2_2) = all_0_0_0
% 10.46/2.97 | (22) h(all_0_2_2) = e22
% 10.46/2.97 | (23) op2(all_0_6_6, all_0_8_8) = all_0_7_7
% 10.46/2.97 | (24) ~ (e23 = e12)
% 10.46/2.97 | (25) op2(e21, e22) = e23
% 10.46/2.97 | (26) ~ (e24 = e10)
% 10.46/2.97 | (27) op2(e20, e21) = e21
% 10.46/2.97 | (28) h(all_0_4_4) = e20
% 10.46/2.97 | (29) op2(e23, e21) = e22
% 10.46/2.97 | (30) h(all_0_0_0) = e24
% 10.46/2.97 | (31) op1(all_0_1_1, all_0_0_0) = all_0_3_3
% 10.46/2.97 | (32) ~ (e22 = e14)
% 10.46/2.97 | (33) op2(e21, e24) = e22
% 10.46/2.97 | (34) 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
% 10.46/2.97 | (35) op2(e20, e23) = e23
% 10.46/2.97 | (36) ~ (e22 = e11)
% 10.46/2.97 | (37) op1(all_0_3_3, all_0_3_3) = all_0_0_0
% 10.46/2.97 | (38) op2(all_0_5_5, all_0_9_9) = all_0_5_5
% 10.46/2.97 | (39) op2(e23, e24) = e21
% 10.46/2.97 | (40) ~ (e23 = e11)
% 10.46/2.97 | (41) op1(e13, e14) = e11
% 10.46/2.97 | (42) 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
% 10.46/2.98 | (43) op1(all_0_4_4, all_0_2_2) = all_0_2_2
% 10.46/2.98 | (44) op1(all_0_2_2, all_0_0_0) = all_0_1_1
% 10.46/2.98 | (45) op1(e11, e14) = e12
% 10.46/2.98 | (46) h(e11) = all_0_8_8
% 10.46/2.98 | (47) op1(all_0_1_1, all_0_4_4) = all_0_1_1
% 10.46/2.98 | (48) ~ (e21 = e10)
% 10.46/2.98 | (49) op2(all_0_6_6, all_0_9_9) = all_0_6_6
% 10.46/2.98 | (50) ~ (e22 = e20)
% 10.46/2.98 | (51) op1(all_0_4_4, all_0_1_1) = all_0_1_1
% 10.46/2.98 | (52) ~ (e20 = e12)
% 10.46/2.98 | (53) 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
% 10.46/2.98 | (54) ~ (e12 = e11)
% 10.46/2.98 | (55) ~ (e22 = e10)
% 10.46/2.98 | (56) op1(e10, e13) = e13
% 10.46/2.98 | (57) all_0_1_1 = e14 | all_0_1_1 = e13 | all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11
% 10.46/2.98 | (58) ~ (e21 = e11)
% 10.46/2.98 | (59) ~ (e22 = e12)
% 10.46/2.98 | (60) op2(all_0_7_7, all_0_8_8) = all_0_5_5
% 10.46/2.98 | (61) op1(e10, e12) = e12
% 10.46/2.98 | (62) ~ (e22 = e21)
% 10.46/2.98 | (63) ~ (e14 = e13)
% 10.46/2.98 | (64) 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
% 10.46/2.98 | (65) ~ (e24 = e22)
% 10.46/2.98 | (66) op2(e22, e21) = e20
% 10.46/2.98 | (67) j(all_0_7_7) = e12
% 10.46/2.98 | (68) ~ (e24 = e23)
% 10.46/2.98 | (69) op2(e24, e23) = e22
% 10.46/2.98 | (70) op1(all_0_2_2, all_0_3_3) = all_0_4_4
% 10.46/2.98 | (71) ~ (e21 = e12)
% 10.46/2.98 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0))
% 10.46/2.98 | (73) op2(all_0_5_5, all_0_7_7) = all_0_8_8
% 10.46/2.98 | (74) op1(all_0_4_4, all_0_4_4) = all_0_4_4
% 10.46/2.98 | (75) ~ (e23 = e20)
% 10.46/2.98 | (76) op1(all_0_3_3, all_0_0_0) = all_0_2_2
% 10.46/2.98 | (77) j(all_0_6_6) = e13
% 10.46/2.98 | (78) ~ (e24 = e14)
% 10.46/2.98 | (79) ~ (e13 = e11)
% 10.46/2.98 | (80) op1(e14, e10) = e14
% 10.46/2.98 | (81) op2(all_0_8_8, all_0_6_6) = all_0_5_5
% 10.46/2.98 | (82) ~ (e14 = e10)
% 10.46/2.98 | (83) ~ (e23 = e13)
% 10.46/2.98 | (84) op2(all_0_8_8, all_0_8_8) = all_0_9_9
% 10.46/2.98 | (85) ~ (e22 = e13)
% 10.46/2.98 | (86) op1(all_0_4_4, all_0_0_0) = all_0_0_0
% 10.46/2.98 | (87) op2(all_0_5_5, all_0_5_5) = all_0_9_9
% 10.46/2.98 | (88) op2(e21, e20) = e21
% 10.46/2.98 | (89) 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
% 10.46/2.98 | (90) op1(e10, e10) = e10
% 10.46/2.98 | (91) op2(all_0_9_9, all_0_6_6) = all_0_6_6
% 10.46/2.98 | (92) op1(e10, e11) = e11
% 10.46/2.98 | (93) op2(all_0_9_9, all_0_9_9) = all_0_9_9
% 10.46/2.98 | (94) op2(all_0_7_7, all_0_5_5) = all_0_6_6
% 10.46/2.98 | (95) op1(e12, e10) = e12
% 10.46/2.98 | (96) op1(all_0_0_0, all_0_4_4) = all_0_0_0
% 10.46/2.98 | (97) op1(e12, e13) = e11
% 10.46/2.98 | (98) op1(all_0_1_1, all_0_3_3) = all_0_2_2
% 10.46/2.98 | (99) 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
% 10.46/2.98 | (100) op1(e13, e13) = e10
% 10.46/2.98 | (101) 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
% 10.46/2.98 | (102) 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
% 10.46/2.98 | (103) op1(e14, e13) = e12
% 10.46/2.98 | (104) op1(e14, e14) = e10
% 10.46/2.98 | (105) op2(all_0_9_9, all_0_5_5) = all_0_5_5
% 10.46/2.98 | (106) h(all_0_3_3) = e21
% 10.46/2.98 | (107) op2(e22, e22) = e24
% 10.46/2.98 | (108) ~ (e24 = e21)
% 10.46/2.98 | (109) ~ (e24 = e11)
% 10.46/2.98 | (110) op2(all_0_8_8, all_0_5_5) = all_0_7_7
% 10.46/2.99 | (111) ~ (e23 = e22)
% 10.46/2.99 | (112) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0))
% 10.46/2.99 | (113) op2(e21, e21) = e24
% 10.46/2.99 | (114) ~ (e24 = e20)
% 10.46/2.99 | (115) op1(e13, e12) = e14
% 10.46/2.99 | (116) h(e13) = all_0_6_6
% 10.46/2.99 | (117) op2(all_0_9_9, all_0_8_8) = all_0_8_8
% 10.46/2.99 | (118) ~ (e14 = e11)
% 10.46/2.99 | (119) op1(e12, e12) = e10
% 10.46/2.99 | (120) j(all_0_5_5) = e14
% 10.46/2.99 | (121) ~ (e10 = e11)
% 10.46/2.99 | (122) op2(e23, e20) = e23
% 10.46/2.99 | (123) op2(all_0_5_5, all_0_6_6) = all_0_7_7
% 10.46/2.99 | (124) op1(e13, e11) = e12
% 10.46/2.99 | (125) ~ (e24 = e12)
% 10.46/2.99 | (126) ~ (e13 = e12)
% 10.46/2.99 | (127) op2(all_0_7_7, all_0_9_9) = all_0_7_7
% 10.46/2.99 | (128) ~ (e24 = e13)
% 10.46/2.99 | (129) op1(all_0_0_0, all_0_2_2) = all_0_3_3
% 10.46/2.99 | (130) op1(all_0_3_3, all_0_1_1) = all_0_4_4
% 10.46/2.99 | (131) op1(e11, e13) = e14
% 10.46/2.99 | (132) h(e10) = all_0_9_9
% 10.46/2.99 | (133) op2(all_0_6_6, all_0_5_5) = all_0_8_8
% 10.46/2.99 | (134) op1(e12, e11) = e14
% 10.46/2.99 | (135) op1(all_0_0_0, all_0_0_0) = all_0_4_4
% 10.46/2.99 | (136) ~ (e21 = e13)
% 10.46/2.99 | (137) op2(e20, e24) = e24
% 10.46/2.99 | (138) j(e21) = all_0_3_3
% 10.46/2.99 | (139) ~ (e21 = e14)
% 10.46/2.99 | (140) ~ (e23 = e21)
% 10.46/2.99 | (141) ~ (e12 = e10)
% 10.46/2.99 | (142) j(all_0_9_9) = e10
% 10.46/2.99 | (143) op1(e11, e11) = e10
% 10.46/2.99 | (144) op2(all_0_8_8, all_0_7_7) = all_0_6_6
% 10.46/2.99 | (145) op2(e20, e22) = e22
% 10.46/2.99 | (146) op1(all_0_1_1, all_0_2_2) = all_0_4_4
% 10.46/2.99 | (147) op1(e12, e14) = e13
% 10.46/2.99 | (148) op1(all_0_1_1, all_0_1_1) = all_0_0_0
% 10.46/2.99 | (149) op2(e24, e21) = e23
% 10.46/2.99 | (150) op2(all_0_6_6, all_0_7_7) = all_0_5_5
% 10.46/2.99 | (151) op2(e24, e22) = e21
% 10.46/2.99 | (152) j(e24) = all_0_0_0
% 10.46/2.99 | (153) op1(e10, e14) = e14
% 10.46/2.99 | (154) ~ (e20 = e11)
% 10.46/2.99 | (155) op1(all_0_2_2, all_0_4_4) = all_0_2_2
% 10.46/2.99 | (156) op2(e24, e20) = e24
% 10.46/2.99 | (157) op1(all_0_0_0, all_0_3_3) = all_0_1_1
% 10.46/2.99 | (158) h(e12) = all_0_7_7
% 10.46/2.99 | (159) op2(e23, e22) = e20
% 10.46/2.99 | (160) ~ (e20 = e14)
% 10.46/2.99 | (161) op2(all_0_7_7, all_0_6_6) = all_0_8_8
% 10.46/2.99 | (162) ~ (e23 = e10)
% 10.46/2.99 | (163) op2(all_0_5_5, all_0_8_8) = all_0_6_6
% 10.46/2.99 | (164) op2(all_0_6_6, all_0_6_6) = all_0_9_9
% 10.46/2.99 | (165) op2(e22, e24) = e23
% 10.46/2.99 | (166) op1(all_0_0_0, all_0_1_1) = all_0_2_2
% 10.46/2.99 | (167) op2(e22, e20) = e22
% 10.46/2.99 | (168) op1(e14, e12) = e11
% 10.46/2.99 | (169) 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
% 10.46/2.99 | (170) j(e22) = all_0_2_2
% 10.46/3.00 | (171) op2(e21, e23) = e20
% 10.46/3.00 | (172) h(e14) = all_0_5_5
% 10.46/3.00 | (173) op1(all_0_2_2, all_0_1_1) = all_0_3_3
% 10.46/3.00 | (174) ~ (e13 = e10)
% 10.46/3.00 | (175) op2(all_0_9_9, all_0_7_7) = all_0_7_7
% 10.46/3.00 | (176) op2(all_0_7_7, all_0_7_7) = all_0_9_9
% 10.46/3.00 | (177) ~ (e20 = e21)
% 10.46/3.00 | (178) op2(all_0_8_8, all_0_9_9) = all_0_8_8
% 10.46/3.00 | (179) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0))
% 10.46/3.00 | (180) op1(e11, e12) = e13
% 10.46/3.00 |
% 10.46/3.00 +-Applying beta-rule and splitting (169), into two cases.
% 10.46/3.00 |-Branch one:
% 10.46/3.00 | (181) all_0_0_0 = e14
% 10.46/3.00 |
% 10.46/3.00 | From (181)(181) and (135) follows:
% 10.46/3.00 | (182) op1(e14, e14) = all_0_4_4
% 10.46/3.00 |
% 10.46/3.00 | From (181) and (129) follows:
% 10.46/3.00 | (183) op1(e14, all_0_2_2) = all_0_3_3
% 10.46/3.00 |
% 10.46/3.00 | From (181) and (44) follows:
% 10.46/3.00 | (184) op1(all_0_2_2, e14) = all_0_1_1
% 10.46/3.00 |
% 10.46/3.00 | From (181) and (21) follows:
% 10.46/3.00 | (185) op1(all_0_2_2, all_0_2_2) = e14
% 10.46/3.00 |
% 10.46/3.00 | From (181)(181) and (86) follows:
% 10.46/3.00 | (186) op1(all_0_4_4, e14) = e14
% 10.46/3.00 |
% 10.46/3.00 | Instantiating formula (72) with e14, e14, all_0_4_4, e10 and discharging atoms op1(e14, e14) = all_0_4_4, op1(e14, e14) = e10, yields:
% 10.46/3.00 | (187) all_0_4_4 = e10
% 10.46/3.00 |
% 10.46/3.00 | From (187) and (70) follows:
% 10.46/3.00 | (188) op1(all_0_2_2, all_0_3_3) = e10
% 10.46/3.00 |
% 10.46/3.00 | From (187) and (51) follows:
% 10.46/3.00 | (189) op1(e10, all_0_1_1) = all_0_1_1
% 10.46/3.00 |
% 10.46/3.00 | From (187) and (3) follows:
% 10.46/3.00 | (190) op1(e10, all_0_3_3) = all_0_3_3
% 10.46/3.00 |
% 10.46/3.00 | From (187) and (186) follows:
% 10.46/3.00 | (153) op1(e10, e14) = e14
% 10.46/3.00 |
% 10.46/3.00 | From (187) and (182) follows:
% 10.46/3.00 | (104) op1(e14, e14) = e10
% 10.46/3.00 |
% 10.46/3.00 +-Applying beta-rule and splitting (42), into two cases.
% 10.46/3.00 |-Branch one:
% 10.46/3.00 | (193) all_0_2_2 = e14
% 10.46/3.00 |
% 10.46/3.00 | From (193)(193) and (185) follows:
% 10.46/3.00 | (194) op1(e14, e14) = e14
% 10.46/3.00 |
% 10.46/3.00 | From (193) and (184) follows:
% 10.46/3.00 | (195) op1(e14, e14) = all_0_1_1
% 10.46/3.00 |
% 10.46/3.00 | From (193) and (183) follows:
% 10.46/3.00 | (196) op1(e14, e14) = all_0_3_3
% 10.46/3.00 |
% 10.46/3.00 | Instantiating formula (72) with e14, e14, all_0_1_1, e10 and discharging atoms op1(e14, e14) = all_0_1_1, op1(e14, e14) = e10, yields:
% 10.46/3.00 | (197) all_0_1_1 = e10
% 10.46/3.00 |
% 10.46/3.00 | Instantiating formula (72) with e14, e14, all_0_3_3, all_0_1_1 and discharging atoms op1(e14, e14) = all_0_1_1, op1(e14, e14) = all_0_3_3, yields:
% 10.46/3.01 | (198) all_0_1_1 = all_0_3_3
% 10.46/3.01 |
% 10.46/3.01 | Instantiating formula (72) with e14, e14, e14, all_0_1_1 and discharging atoms op1(e14, e14) = all_0_1_1, op1(e14, e14) = e14, yields:
% 10.46/3.01 | (199) all_0_1_1 = e14
% 10.46/3.01 |
% 10.46/3.01 | Combining equations (197,198) yields a new equation:
% 10.46/3.01 | (200) all_0_3_3 = e10
% 10.46/3.01 |
% 10.46/3.01 | Combining equations (199,198) yields a new equation:
% 10.46/3.01 | (201) all_0_3_3 = e14
% 10.46/3.01 |
% 10.46/3.01 | Combining equations (200,201) yields a new equation:
% 10.46/3.01 | (202) e14 = e10
% 10.46/3.01 |
% 10.46/3.01 | Equations (202) can reduce 82 to:
% 10.46/3.01 | (203) $false
% 10.46/3.01 |
% 10.46/3.01 |-The branch is then unsatisfiable
% 10.46/3.01 |-Branch two:
% 10.46/3.01 | (204) ~ (all_0_2_2 = e14)
% 10.46/3.01 | (205) all_0_2_2 = e13 | all_0_2_2 = e12 | all_0_2_2 = e10 | all_0_2_2 = e11
% 10.46/3.01 |
% 10.46/3.01 +-Applying beta-rule and splitting (205), into two cases.
% 10.46/3.01 |-Branch one:
% 10.46/3.01 | (206) all_0_2_2 = e13
% 10.46/3.01 |
% 10.46/3.01 | From (206)(206) and (185) follows:
% 10.46/3.01 | (207) op1(e13, e13) = e14
% 10.46/3.01 |
% 10.46/3.01 | Instantiating formula (72) with e13, e13, e14, e10 and discharging atoms op1(e13, e13) = e14, op1(e13, e13) = e10, yields:
% 10.46/3.01 | (202) e14 = e10
% 10.46/3.01 |
% 10.46/3.01 | Equations (202) can reduce 82 to:
% 10.46/3.01 | (203) $false
% 10.46/3.01 |
% 10.46/3.01 |-The branch is then unsatisfiable
% 10.46/3.01 |-Branch two:
% 10.46/3.01 | (210) ~ (all_0_2_2 = e13)
% 10.46/3.01 | (211) all_0_2_2 = e12 | all_0_2_2 = e10 | all_0_2_2 = e11
% 10.46/3.01 |
% 10.46/3.01 +-Applying beta-rule and splitting (211), into two cases.
% 10.46/3.01 |-Branch one:
% 10.46/3.01 | (212) all_0_2_2 = e12
% 10.46/3.01 |
% 10.46/3.01 | From (212)(212) and (185) follows:
% 10.46/3.01 | (213) op1(e12, e12) = e14
% 10.46/3.01 |
% 10.46/3.01 | Instantiating formula (72) with e12, e12, e14, e10 and discharging atoms op1(e12, e12) = e14, op1(e12, e12) = e10, yields:
% 10.46/3.01 | (202) e14 = e10
% 10.46/3.01 |
% 10.46/3.01 | Equations (202) can reduce 82 to:
% 10.46/3.01 | (203) $false
% 10.46/3.01 |
% 10.46/3.01 |-The branch is then unsatisfiable
% 10.46/3.01 |-Branch two:
% 10.46/3.01 | (216) ~ (all_0_2_2 = e12)
% 10.46/3.01 | (217) all_0_2_2 = e10 | all_0_2_2 = e11
% 10.46/3.01 |
% 10.46/3.01 +-Applying beta-rule and splitting (217), into two cases.
% 10.46/3.01 |-Branch one:
% 10.46/3.01 | (218) all_0_2_2 = e10
% 10.46/3.01 |
% 10.46/3.01 | Equations (218) can reduce 204 to:
% 10.46/3.01 | (219) ~ (e14 = e10)
% 10.46/3.01 |
% 10.46/3.01 | Simplifying 219 yields:
% 10.46/3.01 | (82) ~ (e14 = e10)
% 10.46/3.01 |
% 10.46/3.01 | From (218) and (173) follows:
% 10.46/3.01 | (221) op1(e10, all_0_1_1) = all_0_3_3
% 10.46/3.01 |
% 10.46/3.01 | From (218) and (188) follows:
% 10.46/3.01 | (222) op1(e10, all_0_3_3) = e10
% 10.46/3.01 |
% 10.46/3.01 | From (218) and (184) follows:
% 10.46/3.01 | (223) op1(e10, e14) = all_0_1_1
% 10.46/3.01 |
% 10.46/3.01 | Instantiating formula (72) with e10, all_0_1_1, all_0_3_3, all_0_1_1 and discharging atoms op1(e10, all_0_1_1) = all_0_1_1, op1(e10, all_0_1_1) = all_0_3_3, yields:
% 10.46/3.01 | (198) all_0_1_1 = all_0_3_3
% 10.46/3.01 |
% 10.46/3.01 | Instantiating formula (72) 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:
% 10.46/3.01 | (200) all_0_3_3 = e10
% 10.46/3.01 |
% 10.46/3.01 | Instantiating formula (72) with e10, e14, all_0_1_1, e14 and discharging atoms op1(e10, e14) = all_0_1_1, op1(e10, e14) = e14, yields:
% 10.46/3.01 | (199) all_0_1_1 = e14
% 10.46/3.01 |
% 10.46/3.02 | Combining equations (198,199) yields a new equation:
% 10.46/3.02 | (227) all_0_3_3 = e14
% 10.46/3.02 |
% 10.46/3.02 | Simplifying 227 yields:
% 10.46/3.02 | (201) all_0_3_3 = e14
% 10.46/3.02 |
% 10.46/3.02 | Combining equations (200,201) yields a new equation:
% 10.46/3.02 | (202) e14 = e10
% 10.46/3.02 |
% 10.46/3.02 | Equations (202) can reduce 82 to:
% 10.46/3.02 | (203) $false
% 10.46/3.02 |
% 10.46/3.02 |-The branch is then unsatisfiable
% 10.46/3.02 |-Branch two:
% 10.46/3.02 | (231) ~ (all_0_2_2 = e10)
% 10.46/3.02 | (232) all_0_2_2 = e11
% 10.46/3.02 |
% 10.46/3.02 | From (232)(232) and (185) follows:
% 10.46/3.02 | (233) op1(e11, e11) = e14
% 10.46/3.02 |
% 10.46/3.02 | Instantiating formula (72) with e11, e11, e14, e10 and discharging atoms op1(e11, e11) = e14, op1(e11, e11) = e10, yields:
% 10.46/3.02 | (202) e14 = e10
% 10.46/3.02 |
% 10.46/3.02 | Equations (202) can reduce 82 to:
% 10.46/3.02 | (203) $false
% 10.46/3.02 |
% 10.46/3.02 |-The branch is then unsatisfiable
% 10.46/3.02 |-Branch two:
% 10.46/3.02 | (236) ~ (all_0_0_0 = e14)
% 10.46/3.02 | (237) all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 10.46/3.02 |
% 10.46/3.02 +-Applying beta-rule and splitting (102), into two cases.
% 10.46/3.02 |-Branch one:
% 10.46/3.02 | (238) all_0_9_9 = e24
% 10.46/3.02 |
% 10.46/3.02 | From (238)(238)(238) and (93) follows:
% 10.46/3.02 | (239) op2(e24, e24) = e24
% 10.46/3.02 |
% 10.46/3.02 | Instantiating formula (5) with e24, e24, e24, e20 and discharging atoms op2(e24, e24) = e24, op2(e24, e24) = e20, yields:
% 10.46/3.02 | (240) e24 = e20
% 10.46/3.02 |
% 10.46/3.02 | Equations (240) can reduce 114 to:
% 10.46/3.02 | (203) $false
% 10.46/3.02 |
% 10.46/3.02 |-The branch is then unsatisfiable
% 10.46/3.02 |-Branch two:
% 10.46/3.02 | (242) ~ (all_0_9_9 = e24)
% 10.46/3.02 | (243) all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21
% 10.46/3.02 |
% 10.46/3.02 +-Applying beta-rule and splitting (57), into two cases.
% 10.46/3.02 |-Branch one:
% 10.46/3.02 | (199) all_0_1_1 = e14
% 10.46/3.02 |
% 10.46/3.02 | From (199)(199) and (148) follows:
% 10.46/3.02 | (245) op1(e14, e14) = all_0_0_0
% 10.46/3.02 |
% 10.46/3.02 | Instantiating formula (72) with e14, e14, all_0_0_0, e10 and discharging atoms op1(e14, e14) = all_0_0_0, op1(e14, e14) = e10, yields:
% 10.46/3.02 | (246) all_0_0_0 = e10
% 10.46/3.02 |
% 10.46/3.02 | From (246) and (30) follows:
% 10.46/3.02 | (247) h(e10) = e24
% 10.46/3.02 |
% 10.46/3.02 | Instantiating formula (112) with e10, e24, all_0_9_9 and discharging atoms h(e10) = all_0_9_9, h(e10) = e24, yields:
% 10.46/3.02 | (238) all_0_9_9 = e24
% 10.46/3.02 |
% 10.46/3.02 | Equations (238) can reduce 242 to:
% 10.46/3.02 | (203) $false
% 10.46/3.02 |
% 10.46/3.02 |-The branch is then unsatisfiable
% 10.46/3.02 |-Branch two:
% 10.46/3.02 | (250) ~ (all_0_1_1 = e14)
% 10.46/3.02 | (251) all_0_1_1 = e13 | all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11
% 10.46/3.02 |
% 10.46/3.02 +-Applying beta-rule and splitting (89), into two cases.
% 10.46/3.02 |-Branch one:
% 10.46/3.02 | (252) all_0_7_7 = e24
% 10.46/3.02 |
% 10.46/3.02 | From (252)(252) and (176) follows:
% 10.46/3.02 | (253) op2(e24, e24) = all_0_9_9
% 10.46/3.02 |
% 10.46/3.02 | From (252) and (67) follows:
% 10.46/3.02 | (254) j(e24) = e12
% 10.46/3.02 |
% 10.46/3.02 | Instantiating formula (5) with e24, e24, all_0_9_9, e20 and discharging atoms op2(e24, e24) = all_0_9_9, op2(e24, e24) = e20, yields:
% 10.46/3.03 | (255) all_0_9_9 = e20
% 10.46/3.03 |
% 10.46/3.03 | Instantiating formula (179) with e24, e12, all_0_0_0 and discharging atoms j(e24) = all_0_0_0, j(e24) = e12, yields:
% 10.46/3.03 | (256) all_0_0_0 = e12
% 10.46/3.03 |
% 10.46/3.03 | From (256)(256) and (135) follows:
% 10.46/3.03 | (257) op1(e12, e12) = all_0_4_4
% 10.46/3.03 |
% 10.46/3.03 | From (256) and (166) follows:
% 10.46/3.03 | (258) op1(e12, all_0_1_1) = all_0_2_2
% 10.46/3.03 |
% 10.46/3.03 | From (256) and (31) follows:
% 10.46/3.03 | (259) op1(all_0_1_1, e12) = all_0_3_3
% 10.46/3.03 |
% 10.46/3.03 | From (256) and (148) follows:
% 10.46/3.03 | (260) op1(all_0_1_1, all_0_1_1) = e12
% 10.46/3.03 |
% 10.46/3.03 | From (256)(256) and (86) follows:
% 10.46/3.03 | (261) op1(all_0_4_4, e12) = e12
% 10.46/3.03 |
% 10.46/3.03 | From (255) and (142) follows:
% 10.46/3.03 | (262) j(e20) = e10
% 10.46/3.03 |
% 10.46/3.03 | Instantiating formula (179) with e20, e10, all_0_4_4 and discharging atoms j(e20) = all_0_4_4, j(e20) = e10, yields:
% 10.46/3.03 | (187) all_0_4_4 = e10
% 10.46/3.03 |
% 10.46/3.03 | From (187) and (146) follows:
% 10.46/3.03 | (264) op1(all_0_1_1, all_0_2_2) = e10
% 10.46/3.03 |
% 10.46/3.03 | From (187) and (43) follows:
% 10.46/3.03 | (265) op1(e10, all_0_2_2) = all_0_2_2
% 10.46/3.03 |
% 10.46/3.03 | From (187) and (3) follows:
% 10.46/3.03 | (190) op1(e10, all_0_3_3) = all_0_3_3
% 10.46/3.03 |
% 10.46/3.03 | From (187) and (261) follows:
% 10.46/3.03 | (61) op1(e10, e12) = e12
% 10.46/3.03 |
% 10.46/3.03 | From (187) and (257) follows:
% 10.46/3.03 | (119) op1(e12, e12) = e10
% 10.46/3.03 |
% 10.46/3.03 +-Applying beta-rule and splitting (251), into two cases.
% 10.46/3.03 |-Branch one:
% 10.46/3.03 | (269) all_0_1_1 = e13
% 10.46/3.03 |
% 10.46/3.03 | From (269)(269) and (260) follows:
% 10.46/3.03 | (270) op1(e13, e13) = e12
% 10.46/3.03 |
% 10.46/3.03 | Instantiating formula (72) with e13, e13, e12, e10 and discharging atoms op1(e13, e13) = e12, op1(e13, e13) = e10, yields:
% 10.46/3.03 | (271) e12 = e10
% 10.46/3.03 |
% 10.46/3.03 | Equations (271) can reduce 141 to:
% 10.46/3.03 | (203) $false
% 10.46/3.03 |
% 10.46/3.03 |-The branch is then unsatisfiable
% 10.46/3.03 |-Branch two:
% 10.46/3.03 | (273) ~ (all_0_1_1 = e13)
% 10.46/3.03 | (274) all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11
% 10.46/3.03 |
% 10.46/3.03 +-Applying beta-rule and splitting (274), into two cases.
% 10.46/3.03 |-Branch one:
% 10.46/3.03 | (275) all_0_1_1 = e12
% 10.46/3.03 |
% 10.46/3.03 | From (275)(275) and (260) follows:
% 10.46/3.03 | (276) op1(e12, e12) = e12
% 10.46/3.03 |
% 10.46/3.03 | From (275) and (259) follows:
% 10.46/3.03 | (277) op1(e12, e12) = all_0_3_3
% 10.46/3.03 |
% 10.46/3.03 | From (275) and (258) follows:
% 10.46/3.03 | (278) op1(e12, e12) = all_0_2_2
% 10.46/3.03 |
% 10.46/3.03 | Instantiating formula (72) with e12, e12, all_0_2_2, e10 and discharging atoms op1(e12, e12) = all_0_2_2, op1(e12, e12) = e10, yields:
% 10.46/3.03 | (218) all_0_2_2 = e10
% 10.46/3.03 |
% 10.46/3.03 | Instantiating formula (72) 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:
% 10.46/3.03 | (280) all_0_2_2 = all_0_3_3
% 10.46/3.03 |
% 10.46/3.03 | Instantiating formula (72) with e12, e12, e12, all_0_2_2 and discharging atoms op1(e12, e12) = all_0_2_2, op1(e12, e12) = e12, yields:
% 10.46/3.03 | (212) all_0_2_2 = e12
% 10.46/3.03 |
% 10.46/3.03 | Combining equations (212,280) yields a new equation:
% 10.46/3.03 | (282) all_0_3_3 = e12
% 10.46/3.03 |
% 10.46/3.03 | Combining equations (218,280) yields a new equation:
% 10.46/3.03 | (200) all_0_3_3 = e10
% 10.46/3.03 |
% 10.46/3.03 | Combining equations (282,200) yields a new equation:
% 10.46/3.03 | (284) e12 = e10
% 10.46/3.03 |
% 10.46/3.03 | Simplifying 284 yields:
% 10.46/3.03 | (271) e12 = e10
% 10.46/3.03 |
% 10.46/3.03 | Equations (271) can reduce 141 to:
% 10.46/3.03 | (203) $false
% 10.46/3.03 |
% 10.46/3.03 |-The branch is then unsatisfiable
% 10.46/3.03 |-Branch two:
% 10.46/3.03 | (287) ~ (all_0_1_1 = e12)
% 10.46/3.03 | (288) all_0_1_1 = e10 | all_0_1_1 = e11
% 10.46/3.04 |
% 10.46/3.04 +-Applying beta-rule and splitting (288), into two cases.
% 10.46/3.04 |-Branch one:
% 10.46/3.04 | (197) all_0_1_1 = e10
% 10.46/3.04 |
% 10.46/3.04 | Equations (197) can reduce 287 to:
% 10.46/3.04 | (290) ~ (e12 = e10)
% 10.46/3.04 |
% 10.46/3.04 | Simplifying 290 yields:
% 10.46/3.04 | (141) ~ (e12 = e10)
% 10.46/3.04 |
% 10.46/3.04 | From (197) and (264) follows:
% 10.46/3.04 | (292) op1(e10, all_0_2_2) = e10
% 10.46/3.04 |
% 10.46/3.04 | From (197) and (98) follows:
% 10.46/3.04 | (293) op1(e10, all_0_3_3) = all_0_2_2
% 10.46/3.04 |
% 10.46/3.04 | From (197) and (259) follows:
% 10.46/3.04 | (294) op1(e10, e12) = all_0_3_3
% 10.46/3.04 |
% 10.46/3.04 | Instantiating formula (72) with e10, all_0_2_2, e10, all_0_2_2 and discharging atoms op1(e10, all_0_2_2) = all_0_2_2, op1(e10, all_0_2_2) = e10, yields:
% 10.46/3.04 | (218) all_0_2_2 = e10
% 10.46/3.04 |
% 10.46/3.04 | Instantiating formula (72) with e10, all_0_3_3, all_0_2_2, all_0_3_3 and discharging atoms op1(e10, all_0_3_3) = all_0_2_2, op1(e10, all_0_3_3) = all_0_3_3, yields:
% 10.46/3.04 | (280) all_0_2_2 = all_0_3_3
% 10.46/3.04 |
% 10.46/3.04 | Instantiating formula (72) with e10, e12, all_0_3_3, e12 and discharging atoms op1(e10, e12) = all_0_3_3, op1(e10, e12) = e12, yields:
% 10.46/3.04 | (282) all_0_3_3 = e12
% 10.46/3.04 |
% 10.46/3.04 | Combining equations (280,218) yields a new equation:
% 10.46/3.04 | (298) all_0_3_3 = e10
% 10.46/3.04 |
% 10.46/3.04 | Simplifying 298 yields:
% 10.46/3.04 | (200) all_0_3_3 = e10
% 10.46/3.04 |
% 10.46/3.04 | Combining equations (200,282) yields a new equation:
% 10.46/3.04 | (271) e12 = e10
% 10.46/3.04 |
% 10.46/3.04 | Equations (271) can reduce 141 to:
% 10.46/3.04 | (203) $false
% 10.46/3.04 |
% 10.46/3.04 |-The branch is then unsatisfiable
% 10.46/3.04 |-Branch two:
% 10.46/3.04 | (302) ~ (all_0_1_1 = e10)
% 10.46/3.04 | (303) all_0_1_1 = e11
% 10.46/3.04 |
% 10.46/3.04 | From (303)(303) and (260) follows:
% 10.46/3.04 | (304) op1(e11, e11) = e12
% 10.46/3.04 |
% 10.46/3.04 | Instantiating formula (72) with e11, e11, e12, e10 and discharging atoms op1(e11, e11) = e12, op1(e11, e11) = e10, yields:
% 10.46/3.04 | (271) e12 = e10
% 10.46/3.04 |
% 10.46/3.04 | Equations (271) can reduce 141 to:
% 10.46/3.04 | (203) $false
% 10.46/3.04 |
% 10.46/3.04 |-The branch is then unsatisfiable
% 10.46/3.04 |-Branch two:
% 10.46/3.04 | (307) ~ (all_0_7_7 = e24)
% 10.46/3.04 | (308) all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 10.46/3.04 |
% 10.46/3.04 +-Applying beta-rule and splitting (34), into two cases.
% 10.46/3.04 |-Branch one:
% 10.46/3.04 | (309) all_0_6_6 = e24
% 10.46/3.04 |
% 10.46/3.04 | From (309)(309) and (164) follows:
% 10.46/3.04 | (253) op2(e24, e24) = all_0_9_9
% 10.46/3.04 |
% 10.46/3.04 | From (309) and (77) follows:
% 10.46/3.04 | (311) j(e24) = e13
% 10.46/3.04 |
% 10.46/3.04 | Instantiating formula (5) with e24, e24, all_0_9_9, e20 and discharging atoms op2(e24, e24) = all_0_9_9, op2(e24, e24) = e20, yields:
% 10.46/3.04 | (255) all_0_9_9 = e20
% 10.46/3.04 |
% 10.46/3.04 | Instantiating formula (179) with e24, e13, all_0_0_0 and discharging atoms j(e24) = all_0_0_0, j(e24) = e13, yields:
% 10.46/3.04 | (313) all_0_0_0 = e13
% 10.46/3.04 |
% 10.46/3.04 | From (313)(313) and (135) follows:
% 10.46/3.04 | (314) op1(e13, e13) = all_0_4_4
% 10.46/3.04 |
% 10.46/3.04 | From (313) and (166) follows:
% 10.46/3.04 | (315) op1(e13, all_0_1_1) = all_0_2_2
% 10.46/3.04 |
% 10.46/3.04 | From (313) and (31) follows:
% 10.46/3.04 | (316) op1(all_0_1_1, e13) = all_0_3_3
% 10.46/3.04 |
% 10.46/3.04 | From (313) and (148) follows:
% 10.46/3.04 | (317) op1(all_0_1_1, all_0_1_1) = e13
% 10.46/3.04 |
% 10.46/3.04 | From (313)(313) and (86) follows:
% 10.46/3.04 | (318) op1(all_0_4_4, e13) = e13
% 10.46/3.04 |
% 10.46/3.04 | From (255) and (142) follows:
% 10.46/3.04 | (262) j(e20) = e10
% 10.46/3.04 |
% 10.46/3.04 | Instantiating formula (179) with e20, e10, all_0_4_4 and discharging atoms j(e20) = all_0_4_4, j(e20) = e10, yields:
% 10.46/3.04 | (187) all_0_4_4 = e10
% 10.46/3.04 |
% 10.46/3.04 | From (187) and (146) follows:
% 10.46/3.04 | (264) op1(all_0_1_1, all_0_2_2) = e10
% 10.46/3.04 |
% 10.46/3.04 | From (187) and (43) follows:
% 10.46/3.04 | (265) op1(e10, all_0_2_2) = all_0_2_2
% 10.46/3.04 |
% 10.46/3.04 | From (187) and (3) follows:
% 10.46/3.04 | (190) op1(e10, all_0_3_3) = all_0_3_3
% 10.46/3.04 |
% 10.46/3.04 | From (187) and (318) follows:
% 10.46/3.04 | (56) op1(e10, e13) = e13
% 10.46/3.04 |
% 10.46/3.04 | From (187) and (314) follows:
% 10.46/3.04 | (100) op1(e13, e13) = e10
% 10.46/3.04 |
% 10.46/3.04 +-Applying beta-rule and splitting (251), into two cases.
% 10.46/3.04 |-Branch one:
% 10.46/3.04 | (269) all_0_1_1 = e13
% 10.46/3.04 |
% 10.46/3.04 | From (269)(269) and (317) follows:
% 10.46/3.04 | (327) op1(e13, e13) = e13
% 10.46/3.04 |
% 10.46/3.04 | From (269) and (316) follows:
% 10.46/3.04 | (328) op1(e13, e13) = all_0_3_3
% 10.46/3.04 |
% 10.46/3.04 | From (269) and (315) follows:
% 10.46/3.04 | (329) op1(e13, e13) = all_0_2_2
% 10.46/3.04 |
% 10.46/3.04 | Instantiating formula (72) with e13, e13, all_0_2_2, e10 and discharging atoms op1(e13, e13) = all_0_2_2, op1(e13, e13) = e10, yields:
% 10.46/3.04 | (218) all_0_2_2 = e10
% 10.46/3.04 |
% 10.46/3.04 | Instantiating formula (72) 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:
% 10.46/3.04 | (280) all_0_2_2 = all_0_3_3
% 10.46/3.04 |
% 10.46/3.04 | Instantiating formula (72) with e13, e13, e13, all_0_2_2 and discharging atoms op1(e13, e13) = all_0_2_2, op1(e13, e13) = e13, yields:
% 10.46/3.04 | (206) all_0_2_2 = e13
% 10.46/3.04 |
% 10.46/3.04 | Combining equations (206,280) yields a new equation:
% 10.46/3.04 | (333) all_0_3_3 = e13
% 10.46/3.04 |
% 10.46/3.04 | Combining equations (218,280) yields a new equation:
% 10.46/3.04 | (200) all_0_3_3 = e10
% 10.46/3.04 |
% 10.46/3.04 | Combining equations (333,200) yields a new equation:
% 10.46/3.04 | (335) e13 = e10
% 10.46/3.04 |
% 10.46/3.04 | Simplifying 335 yields:
% 10.46/3.04 | (336) e13 = e10
% 10.46/3.04 |
% 10.46/3.04 | Equations (336) can reduce 174 to:
% 10.46/3.04 | (203) $false
% 10.46/3.04 |
% 10.46/3.04 |-The branch is then unsatisfiable
% 10.46/3.04 |-Branch two:
% 10.46/3.04 | (273) ~ (all_0_1_1 = e13)
% 10.46/3.04 | (274) all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11
% 10.46/3.04 |
% 10.46/3.04 +-Applying beta-rule and splitting (274), into two cases.
% 10.46/3.04 |-Branch one:
% 10.46/3.04 | (275) all_0_1_1 = e12
% 10.46/3.04 |
% 10.46/3.04 | From (275)(275) and (317) follows:
% 10.46/3.04 | (341) op1(e12, e12) = e13
% 10.46/3.04 |
% 10.46/3.04 | Instantiating formula (72) with e12, e12, e13, e10 and discharging atoms op1(e12, e12) = e13, op1(e12, e12) = e10, yields:
% 10.46/3.04 | (336) e13 = e10
% 10.46/3.04 |
% 10.46/3.04 | Equations (336) can reduce 174 to:
% 10.46/3.04 | (203) $false
% 10.46/3.04 |
% 10.46/3.04 |-The branch is then unsatisfiable
% 10.46/3.04 |-Branch two:
% 10.46/3.04 | (287) ~ (all_0_1_1 = e12)
% 10.46/3.04 | (288) all_0_1_1 = e10 | all_0_1_1 = e11
% 10.46/3.04 |
% 10.46/3.04 +-Applying beta-rule and splitting (288), into two cases.
% 10.46/3.04 |-Branch one:
% 10.46/3.04 | (197) all_0_1_1 = e10
% 10.46/3.04 |
% 10.46/3.04 | Equations (197) can reduce 273 to:
% 10.46/3.04 | (347) ~ (e13 = e10)
% 10.46/3.04 |
% 10.46/3.04 | Simplifying 347 yields:
% 10.46/3.04 | (174) ~ (e13 = e10)
% 10.46/3.04 |
% 10.46/3.04 | From (197) and (264) follows:
% 10.46/3.04 | (292) op1(e10, all_0_2_2) = e10
% 10.46/3.04 |
% 10.46/3.04 | From (197) and (98) follows:
% 10.46/3.04 | (293) op1(e10, all_0_3_3) = all_0_2_2
% 10.46/3.04 |
% 10.46/3.04 | From (197) and (316) follows:
% 10.46/3.04 | (351) op1(e10, e13) = all_0_3_3
% 10.46/3.04 |
% 10.46/3.04 | Instantiating formula (72) with e10, all_0_2_2, e10, all_0_2_2 and discharging atoms op1(e10, all_0_2_2) = all_0_2_2, op1(e10, all_0_2_2) = e10, yields:
% 10.46/3.04 | (218) all_0_2_2 = e10
% 10.46/3.04 |
% 10.46/3.04 | Instantiating formula (72) with e10, all_0_3_3, all_0_2_2, all_0_3_3 and discharging atoms op1(e10, all_0_3_3) = all_0_2_2, op1(e10, all_0_3_3) = all_0_3_3, yields:
% 10.46/3.05 | (280) all_0_2_2 = all_0_3_3
% 10.46/3.05 |
% 10.46/3.05 | Instantiating formula (72) with e10, e13, all_0_3_3, e13 and discharging atoms op1(e10, e13) = all_0_3_3, op1(e10, e13) = e13, yields:
% 10.46/3.05 | (333) all_0_3_3 = e13
% 10.46/3.05 |
% 10.46/3.05 | Combining equations (280,218) yields a new equation:
% 10.46/3.05 | (298) all_0_3_3 = e10
% 10.46/3.05 |
% 10.46/3.05 | Simplifying 298 yields:
% 10.46/3.05 | (200) all_0_3_3 = e10
% 10.46/3.05 |
% 10.46/3.05 | Combining equations (200,333) yields a new equation:
% 10.46/3.05 | (336) e13 = e10
% 10.46/3.05 |
% 10.46/3.05 | Equations (336) can reduce 174 to:
% 10.46/3.05 | (203) $false
% 10.46/3.05 |
% 10.46/3.05 |-The branch is then unsatisfiable
% 10.46/3.05 |-Branch two:
% 10.46/3.05 | (302) ~ (all_0_1_1 = e10)
% 10.46/3.05 | (303) all_0_1_1 = e11
% 10.46/3.05 |
% 10.46/3.05 | From (303)(303) and (317) follows:
% 10.46/3.05 | (361) op1(e11, e11) = e13
% 10.46/3.05 |
% 10.46/3.05 | Instantiating formula (72) with e11, e11, e13, e10 and discharging atoms op1(e11, e11) = e13, op1(e11, e11) = e10, yields:
% 10.46/3.05 | (336) e13 = e10
% 10.46/3.05 |
% 10.46/3.05 | Equations (336) can reduce 174 to:
% 10.46/3.05 | (203) $false
% 10.46/3.05 |
% 10.46/3.05 |-The branch is then unsatisfiable
% 10.46/3.05 |-Branch two:
% 10.46/3.05 | (364) ~ (all_0_6_6 = e24)
% 10.46/3.05 | (365) all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21
% 10.46/3.05 |
% 10.46/3.05 +-Applying beta-rule and splitting (99), into two cases.
% 10.46/3.05 |-Branch one:
% 10.46/3.05 | (366) all_0_8_8 = e24
% 10.46/3.05 |
% 10.46/3.05 | From (366)(366) and (84) follows:
% 10.46/3.05 | (253) op2(e24, e24) = all_0_9_9
% 10.46/3.05 |
% 10.46/3.05 | From (366) and (4) follows:
% 10.46/3.05 | (368) j(e24) = e11
% 10.46/3.05 |
% 10.46/3.05 | Instantiating formula (5) with e24, e24, all_0_9_9, e20 and discharging atoms op2(e24, e24) = all_0_9_9, op2(e24, e24) = e20, yields:
% 10.46/3.05 | (255) all_0_9_9 = e20
% 10.46/3.05 |
% 10.46/3.05 | Instantiating formula (179) with e24, e11, all_0_0_0 and discharging atoms j(e24) = all_0_0_0, j(e24) = e11, yields:
% 10.46/3.05 | (370) all_0_0_0 = e11
% 10.46/3.05 |
% 10.46/3.05 | From (370)(370) and (135) follows:
% 10.46/3.05 | (371) op1(e11, e11) = all_0_4_4
% 10.46/3.05 |
% 10.46/3.05 | From (370) and (166) follows:
% 10.46/3.05 | (372) op1(e11, all_0_1_1) = all_0_2_2
% 10.46/3.05 |
% 10.46/3.05 | From (370)(370) and (96) follows:
% 10.46/3.05 | (373) op1(e11, all_0_4_4) = e11
% 10.94/3.05 |
% 10.94/3.05 | From (370) and (31) follows:
% 10.94/3.05 | (374) op1(all_0_1_1, e11) = all_0_3_3
% 10.94/3.05 |
% 10.94/3.05 | From (370) and (148) follows:
% 10.94/3.05 | (375) op1(all_0_1_1, all_0_1_1) = e11
% 10.94/3.05 |
% 10.94/3.05 | From (255) and (142) follows:
% 10.94/3.05 | (262) j(e20) = e10
% 10.94/3.05 |
% 10.94/3.05 | Instantiating formula (179) with e20, e10, all_0_4_4 and discharging atoms j(e20) = all_0_4_4, j(e20) = e10, yields:
% 10.94/3.05 | (187) all_0_4_4 = e10
% 10.94/3.05 |
% 10.94/3.05 | From (187) and (146) follows:
% 10.94/3.05 | (264) op1(all_0_1_1, all_0_2_2) = e10
% 10.94/3.05 |
% 10.94/3.05 | From (187) and (43) follows:
% 10.94/3.05 | (265) op1(e10, all_0_2_2) = all_0_2_2
% 10.94/3.05 |
% 10.94/3.05 | From (187) and (3) follows:
% 10.94/3.05 | (190) op1(e10, all_0_3_3) = all_0_3_3
% 10.94/3.05 |
% 10.94/3.05 | From (187) and (373) follows:
% 10.94/3.05 | (18) op1(e11, e10) = e11
% 10.94/3.05 |
% 10.94/3.05 | From (187) and (371) follows:
% 10.94/3.05 | (143) op1(e11, e11) = e10
% 10.94/3.05 |
% 10.94/3.05 +-Applying beta-rule and splitting (251), into two cases.
% 10.94/3.05 |-Branch one:
% 10.94/3.05 | (269) all_0_1_1 = e13
% 10.94/3.05 |
% 10.94/3.05 | From (269)(269) and (375) follows:
% 10.94/3.05 | (384) op1(e13, e13) = e11
% 10.94/3.05 |
% 10.94/3.05 | Instantiating formula (72) with e13, e13, e11, e10 and discharging atoms op1(e13, e13) = e10, op1(e13, e13) = e11, yields:
% 10.94/3.05 | (385) e10 = e11
% 10.94/3.05 |
% 10.94/3.05 | Equations (385) can reduce 121 to:
% 10.94/3.05 | (203) $false
% 10.94/3.05 |
% 10.94/3.05 |-The branch is then unsatisfiable
% 10.94/3.05 |-Branch two:
% 10.94/3.05 | (273) ~ (all_0_1_1 = e13)
% 10.94/3.05 | (274) all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11
% 10.94/3.05 |
% 10.94/3.05 +-Applying beta-rule and splitting (274), into two cases.
% 10.94/3.05 |-Branch one:
% 10.94/3.05 | (275) all_0_1_1 = e12
% 10.94/3.05 |
% 10.94/3.05 | From (275)(275) and (375) follows:
% 10.94/3.05 | (390) op1(e12, e12) = e11
% 10.94/3.05 |
% 10.94/3.05 | Instantiating formula (72) with e12, e12, e11, e10 and discharging atoms op1(e12, e12) = e10, op1(e12, e12) = e11, yields:
% 10.94/3.05 | (385) e10 = e11
% 10.94/3.05 |
% 10.94/3.05 | Equations (385) can reduce 121 to:
% 10.94/3.05 | (203) $false
% 10.94/3.05 |
% 10.94/3.05 |-The branch is then unsatisfiable
% 10.94/3.05 |-Branch two:
% 10.94/3.05 | (287) ~ (all_0_1_1 = e12)
% 10.94/3.05 | (288) all_0_1_1 = e10 | all_0_1_1 = e11
% 10.94/3.05 |
% 10.94/3.05 +-Applying beta-rule and splitting (288), into two cases.
% 10.94/3.05 |-Branch one:
% 10.94/3.05 | (197) all_0_1_1 = e10
% 10.94/3.05 |
% 10.94/3.05 | From (197) and (264) follows:
% 10.94/3.05 | (292) op1(e10, all_0_2_2) = e10
% 10.94/3.05 |
% 10.94/3.05 | From (197) and (98) follows:
% 10.94/3.05 | (293) op1(e10, all_0_3_3) = all_0_2_2
% 10.94/3.05 |
% 10.94/3.05 | From (197) and (372) follows:
% 10.94/3.05 | (398) op1(e11, e10) = all_0_2_2
% 10.94/3.05 |
% 10.94/3.05 | Instantiating formula (72) with e10, all_0_2_2, e10, all_0_2_2 and discharging atoms op1(e10, all_0_2_2) = all_0_2_2, op1(e10, all_0_2_2) = e10, yields:
% 10.94/3.05 | (218) all_0_2_2 = e10
% 10.94/3.05 |
% 10.94/3.05 | Instantiating formula (72) with e10, all_0_3_3, all_0_2_2, all_0_3_3 and discharging atoms op1(e10, all_0_3_3) = all_0_2_2, op1(e10, all_0_3_3) = all_0_3_3, yields:
% 10.94/3.05 | (280) all_0_2_2 = all_0_3_3
% 10.94/3.05 |
% 10.94/3.05 | Instantiating formula (72) with e11, e10, all_0_2_2, e11 and discharging atoms op1(e11, e10) = all_0_2_2, op1(e11, e10) = e11, yields:
% 10.94/3.05 | (232) all_0_2_2 = e11
% 10.94/3.05 |
% 10.94/3.05 | Combining equations (232,280) yields a new equation:
% 10.94/3.05 | (402) all_0_3_3 = e11
% 10.94/3.05 |
% 10.94/3.05 | Combining equations (218,280) yields a new equation:
% 10.94/3.05 | (200) all_0_3_3 = e10
% 10.94/3.05 |
% 10.94/3.05 | Combining equations (200,402) yields a new equation:
% 10.94/3.05 | (404) e10 = e11
% 10.94/3.05 |
% 10.94/3.05 | Simplifying 404 yields:
% 10.94/3.05 | (385) e10 = e11
% 10.94/3.05 |
% 10.94/3.05 | Equations (385) can reduce 121 to:
% 10.94/3.05 | (203) $false
% 10.94/3.05 |
% 10.94/3.05 |-The branch is then unsatisfiable
% 10.94/3.05 |-Branch two:
% 10.94/3.05 | (302) ~ (all_0_1_1 = e10)
% 10.94/3.05 | (303) all_0_1_1 = e11
% 10.94/3.05 |
% 10.94/3.05 | Equations (303) can reduce 302 to:
% 10.94/3.05 | (409) ~ (e10 = e11)
% 10.94/3.05 |
% 10.94/3.05 | Simplifying 409 yields:
% 10.94/3.05 | (121) ~ (e10 = e11)
% 10.94/3.05 |
% 10.94/3.05 | From (303)(303) and (375) follows:
% 10.94/3.05 | (411) op1(e11, e11) = e11
% 10.94/3.05 |
% 10.94/3.05 | From (303) and (374) follows:
% 10.94/3.05 | (412) op1(e11, e11) = all_0_3_3
% 10.94/3.05 |
% 10.94/3.05 | From (303) and (372) follows:
% 10.94/3.05 | (413) op1(e11, e11) = all_0_2_2
% 10.94/3.05 |
% 10.94/3.05 | Instantiating formula (72) with e11, e11, all_0_2_2, e10 and discharging atoms op1(e11, e11) = all_0_2_2, op1(e11, e11) = e10, yields:
% 10.94/3.05 | (218) all_0_2_2 = e10
% 10.94/3.05 |
% 10.94/3.05 | Instantiating formula (72) 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:
% 10.94/3.05 | (280) all_0_2_2 = all_0_3_3
% 10.94/3.06 |
% 10.94/3.06 | Instantiating formula (72) with e11, e11, e11, all_0_2_2 and discharging atoms op1(e11, e11) = all_0_2_2, op1(e11, e11) = e11, yields:
% 10.94/3.06 | (232) all_0_2_2 = e11
% 10.94/3.06 |
% 10.94/3.06 | Combining equations (232,280) yields a new equation:
% 10.94/3.06 | (402) all_0_3_3 = e11
% 10.94/3.06 |
% 10.94/3.06 | Combining equations (218,280) yields a new equation:
% 10.94/3.06 | (200) all_0_3_3 = e10
% 10.94/3.06 |
% 10.94/3.06 | Combining equations (402,200) yields a new equation:
% 10.94/3.06 | (385) e10 = e11
% 10.94/3.06 |
% 10.94/3.06 | Equations (385) can reduce 121 to:
% 10.94/3.06 | (203) $false
% 10.94/3.06 |
% 10.94/3.06 |-The branch is then unsatisfiable
% 10.94/3.06 |-Branch two:
% 10.94/3.06 | (421) ~ (all_0_8_8 = e24)
% 10.94/3.06 | (422) all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 10.94/3.06 |
% 10.94/3.06 +-Applying beta-rule and splitting (237), into two cases.
% 10.94/3.06 |-Branch one:
% 10.94/3.06 | (313) all_0_0_0 = e13
% 10.94/3.06 |
% 10.94/3.06 | From (313) and (30) follows:
% 10.94/3.06 | (424) h(e13) = e24
% 10.94/3.06 |
% 10.94/3.06 | Instantiating formula (112) with e13, e24, all_0_6_6 and discharging atoms h(e13) = all_0_6_6, h(e13) = e24, yields:
% 10.94/3.06 | (309) all_0_6_6 = e24
% 10.94/3.06 |
% 10.94/3.06 | Equations (309) can reduce 364 to:
% 10.94/3.06 | (203) $false
% 10.94/3.06 |
% 10.94/3.06 |-The branch is then unsatisfiable
% 10.94/3.06 |-Branch two:
% 10.94/3.06 | (427) ~ (all_0_0_0 = e13)
% 10.94/3.06 | (428) all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 10.94/3.06 |
% 10.94/3.06 +-Applying beta-rule and splitting (428), into two cases.
% 10.94/3.06 |-Branch one:
% 10.94/3.06 | (256) all_0_0_0 = e12
% 10.94/3.06 |
% 10.94/3.06 | From (256) and (30) follows:
% 10.94/3.06 | (430) h(e12) = e24
% 10.94/3.06 |
% 10.94/3.06 | Instantiating formula (112) with e12, e24, all_0_7_7 and discharging atoms h(e12) = all_0_7_7, h(e12) = e24, yields:
% 10.94/3.06 | (252) all_0_7_7 = e24
% 10.94/3.06 |
% 10.94/3.06 | Equations (252) can reduce 307 to:
% 10.94/3.06 | (203) $false
% 10.94/3.06 |
% 10.94/3.06 |-The branch is then unsatisfiable
% 10.94/3.06 |-Branch two:
% 10.94/3.06 | (433) ~ (all_0_0_0 = e12)
% 10.94/3.06 | (434) all_0_0_0 = e10 | all_0_0_0 = e11
% 10.94/3.06 |
% 10.94/3.06 +-Applying beta-rule and splitting (434), into two cases.
% 10.94/3.06 |-Branch one:
% 10.94/3.06 | (246) all_0_0_0 = e10
% 10.94/3.06 |
% 10.94/3.06 | From (246) and (30) follows:
% 10.94/3.06 | (247) h(e10) = e24
% 10.94/3.06 |
% 10.94/3.06 | Instantiating formula (112) with e10, e24, all_0_9_9 and discharging atoms h(e10) = all_0_9_9, h(e10) = e24, yields:
% 10.94/3.06 | (238) all_0_9_9 = e24
% 10.94/3.06 |
% 10.94/3.06 | Equations (238) can reduce 242 to:
% 10.94/3.06 | (203) $false
% 10.94/3.06 |
% 10.94/3.06 |-The branch is then unsatisfiable
% 10.94/3.06 |-Branch two:
% 10.94/3.06 | (439) ~ (all_0_0_0 = e10)
% 10.94/3.06 | (370) all_0_0_0 = e11
% 10.94/3.06 |
% 10.94/3.06 | From (370) and (30) follows:
% 10.94/3.06 | (441) h(e11) = e24
% 10.94/3.06 |
% 10.94/3.06 | Instantiating formula (112) with e11, e24, all_0_8_8 and discharging atoms h(e11) = all_0_8_8, h(e11) = e24, yields:
% 10.94/3.06 | (366) all_0_8_8 = e24
% 10.94/3.06 |
% 10.94/3.06 | Equations (366) can reduce 421 to:
% 10.94/3.06 | (203) $false
% 10.94/3.06 |
% 10.94/3.06 |-The branch is then unsatisfiable
% 10.94/3.06 % SZS output end Proof for theBenchmark
% 10.94/3.06
% 10.94/3.06 2476ms
%------------------------------------------------------------------------------