TSTP Solution File: ALG031+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG031+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n024.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 15:33:50 EDT 2022
% Result : Theorem 6.11s 1.96s
% Output : Proof 13.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG031+1 : TPTP v8.1.0. Released v2.7.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n024.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 18:14:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.57 ____ _
% 0.18/0.57 ___ / __ \_____(_)___ ________ __________
% 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.57
% 0.18/0.57 A Theorem Prover for First-Order Logic
% 0.18/0.58 (ePrincess v.1.0)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2015
% 0.18/0.58 (c) Peter Backeman, 2014-2015
% 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58 Bug reports to peter@backeman.se
% 0.18/0.58
% 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58
% 0.18/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.09/1.04 Prover 0: Preprocessing ...
% 3.25/1.35 Prover 0: Constructing countermodel ...
% 6.11/1.96 Prover 0: proved (1334ms)
% 6.11/1.96
% 6.11/1.96 No countermodel exists, formula is valid
% 6.11/1.96 % SZS status Theorem for theBenchmark
% 6.11/1.96
% 6.11/1.96 Generating proof ... found it (size 202)
% 12.50/3.49
% 12.50/3.49 % SZS output start Proof for theBenchmark
% 12.50/3.49 Assumed formulas after preprocessing and simplification:
% 12.50/3.49 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (e25 = e24) & ~ (e25 = e23) & ~ (e25 = e22) & ~ (e25 = e20) & ~ (e25 = e21) & ~ (e25 = e15) & ~ (e25 = e14) & ~ (e25 = e13) & ~ (e25 = e12) & ~ (e25 = e10) & ~ (e25 = e11) & ~ (e24 = e23) & ~ (e24 = e22) & ~ (e24 = e20) & ~ (e24 = e21) & ~ (e24 = e15) & ~ (e24 = e14) & ~ (e24 = e13) & ~ (e24 = e12) & ~ (e24 = e10) & ~ (e24 = e11) & ~ (e23 = e22) & ~ (e23 = e20) & ~ (e23 = e21) & ~ (e23 = e15) & ~ (e23 = e14) & ~ (e23 = e13) & ~ (e23 = e12) & ~ (e23 = e10) & ~ (e23 = e11) & ~ (e22 = e20) & ~ (e22 = e21) & ~ (e22 = e15) & ~ (e22 = e14) & ~ (e22 = e13) & ~ (e22 = e12) & ~ (e22 = e10) & ~ (e22 = e11) & ~ (e20 = e21) & ~ (e20 = e15) & ~ (e20 = e14) & ~ (e20 = e13) & ~ (e20 = e12) & ~ (e20 = e10) & ~ (e20 = e11) & ~ (e21 = e15) & ~ (e21 = e14) & ~ (e21 = e13) & ~ (e21 = e12) & ~ (e21 = e10) & ~ (e21 = e11) & ~ (e15 = e14) & ~ (e15 = e13) & ~ (e15 = e12) & ~ (e15 = e10) & ~ (e15 = e11) & ~ (e14 = e13) & ~ (e14 = e12) & ~ (e14 = e10) & ~ (e14 = e11) & ~ (e13 = e12) & ~ (e13 = e10) & ~ (e13 = e11) & ~ (e12 = e10) & ~ (e12 = e11) & ~ (e10 = e11) & op2(v5, v5) = v2 & op2(v5, v4) = v0 & op2(v5, v3) = v4 & op2(v5, v2) = v1 & op2(v5, v1) = v3 & op2(v5, v0) = v5 & op2(v4, v5) = v0 & op2(v4, v4) = v3 & op2(v4, v3) = v1 & op2(v4, v2) = v5 & op2(v4, v1) = v2 & op2(v4, v0) = v4 & op2(v3, v5) = v4 & op2(v3, v4) = v1 & op2(v3, v3) = v2 & op2(v3, v2) = v0 & op2(v3, v1) = v5 & op2(v3, v0) = v3 & op2(v2, v5) = v1 & op2(v2, v4) = v5 & op2(v2, v3) = v0 & op2(v2, v2) = v3 & op2(v2, v1) = v4 & op2(v2, v0) = v2 & op2(v1, v5) = v3 & op2(v1, v4) = v2 & op2(v1, v3) = v5 & op2(v1, v2) = v4 & op2(v1, v1) = v0 & op2(v1, v0) = v1 & op2(v0, v5) = v5 & op2(v0, v4) = v4 & op2(v0, v3) = v3 & op2(v0, v2) = v2 & op2(v0, v1) = v1 & op2(v0, v0) = v0 & op2(e25, e25) = e20 & op2(e25, e24) = e22 & op2(e25, e23) = e21 & op2(e25, e22) = e24 & op2(e25, e20) = e25 & op2(e25, e21) = e23 & op2(e24, e25) = e21 & op2(e24, e24) = e23 & op2(e24, e23) = e20 & op2(e24, e22) = e25 & op2(e24, e20) = e24 & op2(e24, e21) = e22 & op2(e23, e25) = e22 & op2(e23, e24) = e20 & op2(e23, e23) = e24 & op2(e23, e22) = e21 & op2(e23, e20) = e23 & op2(e23, e21) = e25 & op2(e22, e25) = e23 & op2(e22, e24) = e21 & op2(e22, e23) = e25 & op2(e22, e22) = e20 & op2(e22, e20) = e22 & op2(e22, e21) = e24 & op2(e20, e25) = e25 & op2(e20, e24) = e24 & op2(e20, e23) = e23 & op2(e20, e22) = e22 & op2(e20, e20) = e20 & op2(e20, e21) = e21 & op2(e21, e25) = e24 & op2(e21, e24) = e25 & op2(e21, e23) = e22 & op2(e21, e22) = e23 & op2(e21, e20) = e21 & op2(e21, e21) = e20 & op1(v11, v11) = v6 & op1(v11, v10) = v8 & op1(v11, v9) = v7 & op1(v11, v8) = v10 & op1(v11, v7) = v9 & op1(v11, v6) = v11 & op1(v10, v11) = v7 & op1(v10, v10) = v9 & op1(v10, v9) = v6 & op1(v10, v8) = v11 & op1(v10, v7) = v8 & op1(v10, v6) = v10 & op1(v9, v11) = v8 & op1(v9, v10) = v6 & op1(v9, v9) = v10 & op1(v9, v8) = v7 & op1(v9, v7) = v11 & op1(v9, v6) = v9 & op1(v8, v11) = v9 & op1(v8, v10) = v7 & op1(v8, v9) = v11 & op1(v8, v8) = v6 & op1(v8, v7) = v10 & op1(v8, v6) = v8 & op1(v7, v11) = v10 & op1(v7, v10) = v11 & op1(v7, v9) = v8 & op1(v7, v8) = v9 & op1(v7, v7) = v6 & op1(v7, v6) = v7 & op1(v6, v11) = v11 & op1(v6, v10) = v10 & op1(v6, v9) = v9 & op1(v6, v8) = v8 & op1(v6, v7) = v7 & op1(v6, v6) = v6 & op1(e15, e15) = e12 & op1(e15, e14) = e10 & op1(e15, e13) = e14 & op1(e15, e12) = e11 & op1(e15, e10) = e15 & op1(e15, e11) = e13 & op1(e14, e15) = e10 & op1(e14, e14) = e13 & op1(e14, e13) = e11 & op1(e14, e12) = e15 & op1(e14, e10) = e14 & op1(e14, e11) = e12 & op1(e13, e15) = e14 & op1(e13, e14) = e11 & op1(e13, e13) = e12 & op1(e13, e12) = e10 & op1(e13, e10) = e13 & op1(e13, e11) = e15 & op1(e12, e15) = e11 & op1(e12, e14) = e15 & op1(e12, e13) = e10 & op1(e12, e12) = e13 & op1(e12, e10) = e12 & op1(e12, e11) = e14 & op1(e10, e15) = e15 & op1(e10, e14) = e14 & op1(e10, e13) = e13 & op1(e10, e12) = e12 & op1(e10, e10) = e10 & op1(e10, e11) = e11 & op1(e11, e15) = e13 & op1(e11, e14) = e12 & op1(e11, e13) = e15 & op1(e11, e12) = e14 & op1(e11, e10) = e11 & op1(e11, e11) = e10 & h(v11) = e25 & h(v10) = e24 & h(v9) = e23 & h(v8) = e22 & h(v7) = e21 & h(v6) = e20 & h(e15) = v5 & h(e14) = v4 & h(e13) = v3 & h(e12) = v2 & h(e10) = v0 & h(e11) = v1 & j(v5) = e15 & j(v4) = e14 & j(v3) = e13 & j(v2) = e12 & j(v1) = e11 & j(v0) = e10 & j(e25) = v11 & j(e24) = v10 & j(e23) = v9 & j(e22) = v8 & j(e20) = v6 & j(e21) = v7 & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (op2(v15, v14) = v13) | ~ (op2(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (op1(v15, v14) = v13) | ~ (op1(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (h(v14) = v13) | ~ (h(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (j(v14) = v13) | ~ (j(v14) = v12)) & (v11 = e15 | v11 = e14 | v11 = e13 | v11 = e12 | v11 = e10 | v11 = e11) & (v10 = e15 | v10 = e14 | v10 = e13 | v10 = e12 | v10 = e10 | v10 = e11) & (v9 = e15 | v9 = e14 | v9 = e13 | v9 = e12 | v9 = e10 | v9 = e11) & (v8 = e15 | v8 = e14 | v8 = e13 | v8 = e12 | v8 = e10 | v8 = e11) & (v7 = e15 | v7 = e14 | v7 = e13 | v7 = e12 | v7 = e10 | v7 = e11) & (v6 = e15 | v6 = e14 | v6 = e13 | v6 = e12 | v6 = e10 | v6 = e11) & (v5 = e25 | v5 = e24 | v5 = e23 | v5 = e22 | v5 = e20 | v5 = e21) & (v4 = e25 | v4 = e24 | v4 = e23 | v4 = e22 | v4 = e20 | v4 = e21) & (v3 = e25 | v3 = e24 | v3 = e23 | v3 = e22 | v3 = e20 | v3 = e21) & (v2 = e25 | v2 = e24 | v2 = e23 | v2 = e22 | v2 = e20 | v2 = e21) & (v1 = e25 | v1 = e24 | v1 = e23 | v1 = e22 | v1 = e20 | v1 = e21) & (v0 = e25 | v0 = e24 | v0 = e23 | v0 = e22 | v0 = e20 | v0 = e21))
% 13.05/3.56 | 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, all_0_10_10, all_0_11_11 yields:
% 13.05/3.56 | (1) ~ (e25 = e24) & ~ (e25 = e23) & ~ (e25 = e22) & ~ (e25 = e20) & ~ (e25 = e21) & ~ (e25 = e15) & ~ (e25 = e14) & ~ (e25 = e13) & ~ (e25 = e12) & ~ (e25 = e10) & ~ (e25 = e11) & ~ (e24 = e23) & ~ (e24 = e22) & ~ (e24 = e20) & ~ (e24 = e21) & ~ (e24 = e15) & ~ (e24 = e14) & ~ (e24 = e13) & ~ (e24 = e12) & ~ (e24 = e10) & ~ (e24 = e11) & ~ (e23 = e22) & ~ (e23 = e20) & ~ (e23 = e21) & ~ (e23 = e15) & ~ (e23 = e14) & ~ (e23 = e13) & ~ (e23 = e12) & ~ (e23 = e10) & ~ (e23 = e11) & ~ (e22 = e20) & ~ (e22 = e21) & ~ (e22 = e15) & ~ (e22 = e14) & ~ (e22 = e13) & ~ (e22 = e12) & ~ (e22 = e10) & ~ (e22 = e11) & ~ (e20 = e21) & ~ (e20 = e15) & ~ (e20 = e14) & ~ (e20 = e13) & ~ (e20 = e12) & ~ (e20 = e10) & ~ (e20 = e11) & ~ (e21 = e15) & ~ (e21 = e14) & ~ (e21 = e13) & ~ (e21 = e12) & ~ (e21 = e10) & ~ (e21 = e11) & ~ (e15 = e14) & ~ (e15 = e13) & ~ (e15 = e12) & ~ (e15 = e10) & ~ (e15 = e11) & ~ (e14 = e13) & ~ (e14 = e12) & ~ (e14 = e10) & ~ (e14 = e11) & ~ (e13 = e12) & ~ (e13 = e10) & ~ (e13 = e11) & ~ (e12 = e10) & ~ (e12 = e11) & ~ (e10 = e11) & op2(all_0_6_6, all_0_6_6) = all_0_9_9 & op2(all_0_6_6, all_0_7_7) = all_0_11_11 & op2(all_0_6_6, all_0_8_8) = all_0_7_7 & op2(all_0_6_6, all_0_9_9) = all_0_10_10 & op2(all_0_6_6, all_0_10_10) = all_0_8_8 & op2(all_0_6_6, all_0_11_11) = all_0_6_6 & op2(all_0_7_7, all_0_6_6) = all_0_11_11 & op2(all_0_7_7, all_0_7_7) = all_0_8_8 & op2(all_0_7_7, all_0_8_8) = all_0_10_10 & op2(all_0_7_7, all_0_9_9) = all_0_6_6 & op2(all_0_7_7, all_0_10_10) = all_0_9_9 & op2(all_0_7_7, all_0_11_11) = all_0_7_7 & op2(all_0_8_8, all_0_6_6) = all_0_7_7 & op2(all_0_8_8, all_0_7_7) = all_0_10_10 & op2(all_0_8_8, all_0_8_8) = all_0_9_9 & op2(all_0_8_8, all_0_9_9) = all_0_11_11 & op2(all_0_8_8, all_0_10_10) = all_0_6_6 & op2(all_0_8_8, all_0_11_11) = all_0_8_8 & op2(all_0_9_9, all_0_6_6) = all_0_10_10 & op2(all_0_9_9, all_0_7_7) = all_0_6_6 & op2(all_0_9_9, all_0_8_8) = all_0_11_11 & op2(all_0_9_9, all_0_9_9) = all_0_8_8 & op2(all_0_9_9, all_0_10_10) = all_0_7_7 & op2(all_0_9_9, all_0_11_11) = all_0_9_9 & op2(all_0_10_10, all_0_6_6) = all_0_8_8 & op2(all_0_10_10, all_0_7_7) = all_0_9_9 & op2(all_0_10_10, all_0_8_8) = all_0_6_6 & op2(all_0_10_10, all_0_9_9) = all_0_7_7 & op2(all_0_10_10, all_0_10_10) = all_0_11_11 & op2(all_0_10_10, all_0_11_11) = all_0_10_10 & op2(all_0_11_11, all_0_6_6) = all_0_6_6 & op2(all_0_11_11, all_0_7_7) = all_0_7_7 & op2(all_0_11_11, all_0_8_8) = all_0_8_8 & op2(all_0_11_11, all_0_9_9) = all_0_9_9 & op2(all_0_11_11, all_0_10_10) = all_0_10_10 & op2(all_0_11_11, all_0_11_11) = all_0_11_11 & op2(e25, e25) = e20 & op2(e25, e24) = e22 & op2(e25, e23) = e21 & op2(e25, e22) = e24 & op2(e25, e20) = e25 & op2(e25, e21) = e23 & op2(e24, e25) = e21 & op2(e24, e24) = e23 & op2(e24, e23) = e20 & op2(e24, e22) = e25 & op2(e24, e20) = e24 & op2(e24, e21) = e22 & op2(e23, e25) = e22 & op2(e23, e24) = e20 & op2(e23, e23) = e24 & op2(e23, e22) = e21 & op2(e23, e20) = e23 & op2(e23, e21) = e25 & op2(e22, e25) = e23 & op2(e22, e24) = e21 & op2(e22, e23) = e25 & op2(e22, e22) = e20 & op2(e22, e20) = e22 & op2(e22, e21) = e24 & op2(e20, e25) = e25 & op2(e20, e24) = e24 & op2(e20, e23) = e23 & op2(e20, e22) = e22 & op2(e20, e20) = e20 & op2(e20, e21) = e21 & op2(e21, e25) = e24 & op2(e21, e24) = e25 & op2(e21, e23) = e22 & op2(e21, e22) = e23 & op2(e21, e20) = e21 & op2(e21, e21) = e20 & op1(all_0_0_0, all_0_0_0) = all_0_5_5 & op1(all_0_0_0, all_0_1_1) = all_0_3_3 & op1(all_0_0_0, all_0_2_2) = all_0_4_4 & op1(all_0_0_0, all_0_3_3) = all_0_1_1 & op1(all_0_0_0, all_0_4_4) = all_0_2_2 & op1(all_0_0_0, all_0_5_5) = all_0_0_0 & op1(all_0_1_1, all_0_0_0) = all_0_4_4 & op1(all_0_1_1, all_0_1_1) = all_0_2_2 & op1(all_0_1_1, all_0_2_2) = all_0_5_5 & op1(all_0_1_1, all_0_3_3) = all_0_0_0 & op1(all_0_1_1, all_0_4_4) = all_0_3_3 & op1(all_0_1_1, all_0_5_5) = 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_5_5 & 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_0_0 & op1(all_0_2_2, all_0_5_5) = 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_0_0 & op1(all_0_3_3, all_0_3_3) = all_0_5_5 & op1(all_0_3_3, all_0_4_4) = all_0_1_1 & op1(all_0_3_3, all_0_5_5) = all_0_3_3 & op1(all_0_4_4, all_0_0_0) = all_0_1_1 & op1(all_0_4_4, all_0_1_1) = all_0_0_0 & op1(all_0_4_4, all_0_2_2) = all_0_3_3 & op1(all_0_4_4, all_0_3_3) = all_0_2_2 & op1(all_0_4_4, all_0_4_4) = all_0_5_5 & op1(all_0_4_4, all_0_5_5) = all_0_4_4 & op1(all_0_5_5, all_0_0_0) = all_0_0_0 & op1(all_0_5_5, all_0_1_1) = all_0_1_1 & op1(all_0_5_5, all_0_2_2) = all_0_2_2 & op1(all_0_5_5, all_0_3_3) = all_0_3_3 & op1(all_0_5_5, all_0_4_4) = all_0_4_4 & op1(all_0_5_5, all_0_5_5) = all_0_5_5 & op1(e15, e15) = e12 & op1(e15, e14) = e10 & op1(e15, e13) = e14 & op1(e15, e12) = e11 & op1(e15, e10) = e15 & op1(e15, e11) = e13 & op1(e14, e15) = e10 & op1(e14, e14) = e13 & op1(e14, e13) = e11 & op1(e14, e12) = e15 & op1(e14, e10) = e14 & op1(e14, e11) = e12 & op1(e13, e15) = e14 & op1(e13, e14) = e11 & op1(e13, e13) = e12 & op1(e13, e12) = e10 & op1(e13, e10) = e13 & op1(e13, e11) = e15 & op1(e12, e15) = e11 & op1(e12, e14) = e15 & op1(e12, e13) = e10 & op1(e12, e12) = e13 & op1(e12, e10) = e12 & op1(e12, e11) = e14 & op1(e10, e15) = e15 & op1(e10, e14) = e14 & op1(e10, e13) = e13 & op1(e10, e12) = e12 & op1(e10, e10) = e10 & op1(e10, e11) = e11 & op1(e11, e15) = e13 & op1(e11, e14) = e12 & op1(e11, e13) = e15 & op1(e11, e12) = e14 & op1(e11, e10) = e11 & op1(e11, e11) = e10 & h(all_0_0_0) = e25 & h(all_0_1_1) = e24 & h(all_0_2_2) = e23 & h(all_0_3_3) = e22 & h(all_0_4_4) = e21 & h(all_0_5_5) = e20 & h(e15) = all_0_6_6 & h(e14) = all_0_7_7 & h(e13) = all_0_8_8 & h(e12) = all_0_9_9 & h(e10) = all_0_11_11 & h(e11) = all_0_10_10 & j(all_0_6_6) = e15 & j(all_0_7_7) = e14 & j(all_0_8_8) = e13 & j(all_0_9_9) = e12 & j(all_0_10_10) = e11 & j(all_0_11_11) = e10 & j(e25) = all_0_0_0 & j(e24) = all_0_1_1 & j(e23) = all_0_2_2 & j(e22) = all_0_3_3 & j(e20) = all_0_5_5 & j(e21) = all_0_4_4 & ! [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 = e15 | 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 = e15 | 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 = e15 | 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 = e15 | 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 = e15 | 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 = e15 | all_0_5_5 = e14 | all_0_5_5 = e13 | all_0_5_5 = e12 | all_0_5_5 = e10 | all_0_5_5 = e11) & (all_0_6_6 = e25 | 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 = e25 | 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 = e25 | 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 = e25 | 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) & (all_0_10_10 = e25 | all_0_10_10 = e24 | all_0_10_10 = e23 | all_0_10_10 = e22 | all_0_10_10 = e20 | all_0_10_10 = e21) & (all_0_11_11 = e25 | all_0_11_11 = e24 | all_0_11_11 = e23 | all_0_11_11 = e22 | all_0_11_11 = e20 | all_0_11_11 = e21)
% 13.05/3.59 |
% 13.05/3.59 | Applying alpha-rule on (1) yields:
% 13.05/3.59 | (2) op1(e11, e15) = e13
% 13.05/3.59 | (3) all_0_7_7 = e25 | 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
% 13.05/3.59 | (4) ~ (e25 = e13)
% 13.05/3.59 | (5) op2(e21, e25) = e24
% 13.05/3.59 | (6) ~ (e21 = e12)
% 13.05/3.59 | (7) ~ (e23 = e21)
% 13.05/3.59 | (8) op2(all_0_6_6, all_0_10_10) = all_0_8_8
% 13.05/3.59 | (9) ~ (e23 = e13)
% 13.05/3.59 | (10) op1(all_0_3_3, all_0_5_5) = all_0_3_3
% 13.05/3.59 | (11) op1(all_0_1_1, all_0_0_0) = all_0_4_4
% 13.05/3.59 | (12) op1(all_0_3_3, all_0_3_3) = all_0_5_5
% 13.05/3.59 | (13) op2(e21, e22) = e23
% 13.05/3.59 | (14) op1(e10, e11) = e11
% 13.05/3.59 | (15) op1(e14, e10) = e14
% 13.05/3.59 | (16) op2(e24, e25) = e21
% 13.05/3.59 | (17) op2(all_0_6_6, all_0_7_7) = all_0_11_11
% 13.05/3.59 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0))
% 13.05/3.59 | (19) op1(e12, e14) = e15
% 13.05/3.59 | (20) op2(e22, e23) = e25
% 13.05/3.59 | (21) op1(all_0_4_4, all_0_4_4) = all_0_5_5
% 13.05/3.59 | (22) op1(all_0_2_2, all_0_1_1) = all_0_5_5
% 13.05/3.59 | (23) ~ (e12 = e11)
% 13.05/3.59 | (24) j(e24) = all_0_1_1
% 13.05/3.59 | (25) ~ (e25 = e12)
% 13.05/3.59 | (26) ~ (e14 = e12)
% 13.05/3.59 | (27) op1(e11, e12) = e14
% 13.05/3.59 | (28) op1(e12, e13) = e10
% 13.05/3.59 | (29) op2(all_0_11_11, all_0_6_6) = all_0_6_6
% 13.05/3.59 | (30) op2(all_0_7_7, all_0_10_10) = all_0_9_9
% 13.05/3.59 | (31) ~ (e20 = e12)
% 13.05/3.59 | (32) op1(all_0_5_5, all_0_5_5) = all_0_5_5
% 13.05/3.59 | (33) ~ (e24 = e14)
% 13.05/3.59 | (34) h(e13) = all_0_8_8
% 13.05/3.59 | (35) ~ (e21 = e15)
% 13.05/3.59 | (36) op1(all_0_1_1, all_0_5_5) = all_0_1_1
% 13.05/3.59 | (37) op1(e13, e15) = e14
% 13.05/3.59 | (38) op1(all_0_3_3, all_0_0_0) = all_0_2_2
% 13.05/3.59 | (39) op1(all_0_2_2, all_0_0_0) = all_0_3_3
% 13.05/3.59 | (40) op2(all_0_11_11, all_0_7_7) = all_0_7_7
% 13.05/3.59 | (41) ~ (e25 = e22)
% 13.05/3.59 | (42) ~ (e23 = e10)
% 13.05/3.59 | (43) op2(all_0_8_8, all_0_10_10) = all_0_6_6
% 13.05/3.59 | (44) op2(e20, e23) = e23
% 13.05/3.59 | (45) op2(e23, e24) = e20
% 13.05/3.59 | (46) h(all_0_5_5) = e20
% 13.05/3.59 | (47) op1(all_0_1_1, all_0_4_4) = all_0_3_3
% 13.05/3.59 | (48) op1(e10, e15) = e15
% 13.05/3.59 | (49) op1(e14, e12) = e15
% 13.05/3.59 | (50) h(all_0_2_2) = e23
% 13.05/3.59 | (51) ~ (e24 = e20)
% 13.05/3.59 | (52) ~ (e23 = e22)
% 13.05/3.60 | (53) op1(all_0_0_0, all_0_3_3) = all_0_1_1
% 13.05/3.60 | (54) all_0_11_11 = e25 | all_0_11_11 = e24 | all_0_11_11 = e23 | all_0_11_11 = e22 | all_0_11_11 = e20 | all_0_11_11 = e21
% 13.05/3.60 | (55) op1(all_0_4_4, all_0_5_5) = all_0_4_4
% 13.05/3.60 | (56) ~ (e25 = e24)
% 13.05/3.60 | (57) ~ (e20 = e21)
% 13.05/3.60 | (58) op2(all_0_9_9, all_0_6_6) = all_0_10_10
% 13.05/3.60 | (59) op1(e15, e14) = e10
% 13.05/3.60 | (60) ~ (e22 = e14)
% 13.05/3.60 | (61) ~ (e15 = e14)
% 13.05/3.60 | (62) all_0_8_8 = e25 | 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
% 13.05/3.60 | (63) op1(all_0_5_5, all_0_2_2) = all_0_2_2
% 13.05/3.60 | (64) op2(all_0_8_8, all_0_8_8) = all_0_9_9
% 13.05/3.60 | (65) j(all_0_8_8) = e13
% 13.05/3.60 | (66) op1(e11, e13) = e15
% 13.05/3.60 | (67) ~ (e15 = e12)
% 13.05/3.60 | (68) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0))
% 13.05/3.60 | (69) op1(all_0_2_2, all_0_4_4) = all_0_0_0
% 13.05/3.60 | (70) op2(e22, e20) = e22
% 13.05/3.60 | (71) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0))
% 13.05/3.60 | (72) op2(e24, e20) = e24
% 13.05/3.60 | (73) all_0_6_6 = e25 | 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
% 13.05/3.60 | (74) op2(all_0_9_9, all_0_11_11) = all_0_9_9
% 13.05/3.60 | (75) op2(all_0_9_9, all_0_8_8) = all_0_11_11
% 13.05/3.60 | (76) op1(e14, e13) = e11
% 13.05/3.60 | (77) ~ (e21 = e13)
% 13.05/3.60 | (78) op1(all_0_2_2, all_0_5_5) = all_0_2_2
% 13.05/3.60 | (79) ~ (e14 = e10)
% 13.05/3.60 | (80) ~ (e23 = e20)
% 13.05/3.60 | (81) ~ (e22 = e15)
% 13.05/3.60 | (82) op1(e12, e10) = e12
% 13.05/3.60 | (83) op1(all_0_4_4, all_0_3_3) = all_0_2_2
% 13.05/3.60 | (84) op2(e20, e20) = e20
% 13.05/3.60 | (85) ~ (e24 = e10)
% 13.05/3.60 | (86) ~ (e22 = e12)
% 13.05/3.60 | (87) ~ (e12 = e10)
% 13.05/3.60 | (88) ~ (e15 = e10)
% 13.05/3.60 | (89) op2(e25, e24) = e22
% 13.05/3.60 | (90) op2(e25, e23) = e21
% 13.05/3.60 | (91) ~ (e25 = e21)
% 13.05/3.60 | (92) h(e10) = all_0_11_11
% 13.05/3.60 | (93) op2(all_0_8_8, all_0_9_9) = all_0_11_11
% 13.05/3.60 | (94) op2(e25, e25) = e20
% 13.05/3.60 | (95) op1(e13, e12) = e10
% 13.05/3.60 | (96) all_0_4_4 = e15 | 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
% 13.05/3.60 | (97) op1(e13, e13) = e12
% 13.05/3.60 | (98) j(all_0_6_6) = e15
% 13.05/3.60 | (99) op2(all_0_10_10, all_0_9_9) = all_0_7_7
% 13.05/3.60 | (100) ~ (e24 = e13)
% 13.05/3.60 | (101) op1(e14, e11) = e12
% 13.05/3.60 | (102) ~ (e20 = e15)
% 13.05/3.60 | (103) op1(all_0_0_0, all_0_1_1) = all_0_3_3
% 13.05/3.60 | (104) op2(e23, e20) = e23
% 13.05/3.60 | (105) ~ (e24 = e11)
% 13.05/3.60 | (106) op2(all_0_6_6, all_0_8_8) = all_0_7_7
% 13.05/3.60 | (107) op1(e13, e11) = e15
% 13.05/3.60 | (108) ~ (e25 = e20)
% 13.05/3.60 | (109) op2(all_0_11_11, all_0_11_11) = all_0_11_11
% 13.05/3.60 | (110) op1(e14, e15) = e10
% 13.05/3.60 | (111) ~ (e21 = e14)
% 13.05/3.60 | (112) op1(all_0_1_1, all_0_2_2) = all_0_5_5
% 13.05/3.60 | (113) ~ (e24 = e21)
% 13.05/3.60 | (114) op2(e24, e22) = e25
% 13.05/3.60 | (115) op2(e23, e21) = e25
% 13.05/3.60 | (116) ~ (e22 = e13)
% 13.05/3.60 | (117) j(all_0_10_10) = e11
% 13.05/3.60 | (118) ~ (e15 = e11)
% 13.05/3.60 | (119) ~ (e24 = e15)
% 13.05/3.60 | (120) op1(all_0_0_0, all_0_0_0) = all_0_5_5
% 13.05/3.60 | (121) ~ (e14 = e13)
% 13.05/3.61 | (122) op2(e20, e24) = e24
% 13.05/3.61 | (123) op2(all_0_6_6, all_0_6_6) = all_0_9_9
% 13.05/3.61 | (124) all_0_5_5 = e15 | all_0_5_5 = e14 | all_0_5_5 = e13 | all_0_5_5 = e12 | all_0_5_5 = e10 | all_0_5_5 = e11
% 13.05/3.61 | (125) op2(all_0_11_11, all_0_8_8) = all_0_8_8
% 13.05/3.61 | (126) ~ (e24 = e23)
% 13.05/3.61 | (127) ~ (e13 = e12)
% 13.05/3.61 | (128) ~ (e22 = e11)
% 13.05/3.61 | (129) op1(e11, e10) = e11
% 13.05/3.61 | (130) op2(all_0_10_10, all_0_6_6) = all_0_8_8
% 13.05/3.61 | (131) op2(all_0_8_8, all_0_6_6) = all_0_7_7
% 13.05/3.61 | (132) h(all_0_1_1) = e24
% 13.05/3.61 | (133) op1(all_0_0_0, all_0_2_2) = all_0_4_4
% 13.05/3.61 | (134) ~ (e14 = e11)
% 13.05/3.61 | (135) h(e15) = all_0_6_6
% 13.05/3.61 | (136) op2(all_0_11_11, all_0_10_10) = all_0_10_10
% 13.05/3.61 | (137) op2(e21, e23) = e22
% 13.05/3.61 | (138) op2(e22, e21) = e24
% 13.05/3.61 | (139) j(all_0_9_9) = e12
% 13.05/3.61 | (140) ~ (e25 = e23)
% 13.05/3.61 | (141) ~ (e21 = e10)
% 13.05/3.61 | (142) op1(all_0_5_5, all_0_3_3) = all_0_3_3
% 13.05/3.61 | (143) j(all_0_11_11) = e10
% 13.05/3.61 | (144) op1(all_0_5_5, all_0_4_4) = all_0_4_4
% 13.05/3.61 | (145) op2(e20, e22) = e22
% 13.05/3.61 | (146) all_0_2_2 = e15 | 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
% 13.05/3.61 | (147) op2(e24, e23) = e20
% 13.05/3.61 | (148) op2(all_0_6_6, all_0_9_9) = all_0_10_10
% 13.05/3.61 | (149) all_0_1_1 = e15 | 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
% 13.05/3.61 | (150) op2(all_0_9_9, all_0_10_10) = all_0_7_7
% 13.05/3.61 | (151) op2(all_0_7_7, all_0_7_7) = all_0_8_8
% 13.05/3.61 | (152) ~ (e25 = e15)
% 13.05/3.61 | (153) ~ (e23 = e14)
% 13.05/3.61 | (154) ~ (e24 = e12)
% 13.05/3.61 | (155) ~ (e20 = e14)
% 13.05/3.61 | (156) ~ (e23 = e12)
% 13.05/3.61 | (157) ~ (e13 = e10)
% 13.05/3.61 | (158) op1(e15, e13) = e14
% 13.05/3.61 | (159) ~ (e25 = e10)
% 13.05/3.61 | (160) op2(all_0_7_7, all_0_8_8) = all_0_10_10
% 13.05/3.61 | (161) j(e22) = all_0_3_3
% 13.05/3.61 | (162) op2(all_0_10_10, all_0_8_8) = all_0_6_6
% 13.05/3.61 | (163) op1(all_0_1_1, all_0_1_1) = all_0_2_2
% 13.05/3.61 | (164) op2(all_0_7_7, all_0_9_9) = all_0_6_6
% 13.05/3.61 | (165) h(all_0_4_4) = e21
% 13.05/3.61 | (166) op2(e24, e21) = e22
% 13.05/3.61 | (167) op2(e23, e22) = e21
% 13.05/3.61 | (168) op1(all_0_0_0, all_0_4_4) = all_0_2_2
% 13.05/3.61 | (169) op2(e23, e23) = e24
% 13.05/3.61 | (170) op1(all_0_4_4, all_0_0_0) = all_0_1_1
% 13.05/3.61 | (171) ~ (e20 = e10)
% 13.05/3.61 | (172) op1(e12, e12) = e13
% 13.05/3.61 | (173) ~ (e25 = e11)
% 13.05/3.61 | (174) op2(e22, e24) = e21
% 13.05/3.61 | (175) ~ (e20 = e11)
% 13.05/3.61 | (176) ~ (e21 = e11)
% 13.05/3.61 | (177) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0))
% 13.05/3.61 | (178) op1(all_0_3_3, all_0_4_4) = all_0_1_1
% 13.05/3.61 | (179) op1(e15, e11) = e13
% 13.05/3.61 | (180) ~ (e10 = e11)
% 13.05/3.61 | (181) h(e14) = all_0_7_7
% 13.05/3.61 | (182) op1(all_0_4_4, all_0_1_1) = all_0_0_0
% 13.05/3.61 | (183) op2(all_0_8_8, all_0_7_7) = all_0_10_10
% 13.05/3.61 | (184) all_0_10_10 = e25 | all_0_10_10 = e24 | all_0_10_10 = e23 | all_0_10_10 = e22 | all_0_10_10 = e20 | all_0_10_10 = e21
% 13.05/3.61 | (185) op2(e20, e25) = e25
% 13.05/3.61 | (186) op1(all_0_0_0, all_0_5_5) = all_0_0_0
% 13.05/3.61 | (187) op1(all_0_4_4, all_0_2_2) = all_0_3_3
% 13.05/3.61 | (188) op1(all_0_1_1, all_0_3_3) = all_0_0_0
% 13.05/3.61 | (189) op1(e13, e10) = e13
% 13.05/3.61 | (190) op2(e24, e24) = e23
% 13.05/3.61 | (191) op2(e20, e21) = e21
% 13.05/3.61 | (192) op1(e10, e12) = e12
% 13.05/3.61 | (193) op2(all_0_6_6, all_0_11_11) = all_0_6_6
% 13.05/3.62 | (194) ~ (e22 = e10)
% 13.05/3.62 | (195) op2(e22, e25) = e23
% 13.05/3.62 | (196) op2(all_0_9_9, all_0_7_7) = all_0_6_6
% 13.05/3.62 | (197) op1(all_0_3_3, all_0_2_2) = all_0_0_0
% 13.05/3.62 | (198) op1(e15, e10) = e15
% 13.05/3.62 | (199) op2(all_0_7_7, all_0_11_11) = all_0_7_7
% 13.05/3.62 | (200) op2(all_0_8_8, all_0_11_11) = all_0_8_8
% 13.05/3.62 | (201) ~ (e25 = e14)
% 13.05/3.62 | (202) op2(e21, e21) = e20
% 13.05/3.62 | (203) ~ (e22 = e21)
% 13.05/3.62 | (204) op1(e11, e14) = e12
% 13.05/3.62 | (205) ~ (e23 = e11)
% 13.05/3.62 | (206) op2(all_0_10_10, all_0_11_11) = all_0_10_10
% 13.05/3.62 | (207) j(e25) = all_0_0_0
% 13.05/3.62 | (208) ~ (e24 = e22)
% 13.05/3.62 | (209) all_0_3_3 = e15 | 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
% 13.05/3.62 | (210) op1(e10, e13) = e13
% 13.05/3.62 | (211) all_0_9_9 = e25 | 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
% 13.05/3.62 | (212) ~ (e20 = e13)
% 13.05/3.62 | (213) op2(e25, e21) = e23
% 13.05/3.62 | (214) op2(all_0_11_11, all_0_9_9) = all_0_9_9
% 13.05/3.62 | (215) op1(e12, e11) = e14
% 13.05/3.62 | (216) h(e12) = all_0_9_9
% 13.05/3.62 | (217) op1(all_0_3_3, all_0_1_1) = all_0_4_4
% 13.05/3.62 | (218) op1(e11, e11) = e10
% 13.05/3.62 | (219) op2(e25, e22) = e24
% 13.05/3.62 | (220) ~ (e15 = e13)
% 13.05/3.62 | (221) op2(all_0_7_7, all_0_6_6) = all_0_11_11
% 13.05/3.62 | (222) ~ (e22 = e20)
% 13.05/3.62 | (223) h(all_0_0_0) = e25
% 13.05/3.62 | (224) op1(e12, e15) = e11
% 13.44/3.62 | (225) op1(all_0_5_5, all_0_1_1) = all_0_1_1
% 13.44/3.62 | (226) ~ (e23 = e15)
% 13.44/3.62 | (227) j(all_0_7_7) = e14
% 13.44/3.62 | (228) j(e21) = all_0_4_4
% 13.44/3.62 | (229) op1(e13, e14) = e11
% 13.44/3.62 | (230) h(e11) = all_0_10_10
% 13.44/3.62 | (231) all_0_0_0 = e15 | 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
% 13.44/3.62 | (232) op1(e14, e14) = e13
% 13.44/3.62 | (233) op2(e21, e24) = e25
% 13.44/3.62 | (234) op1(all_0_2_2, all_0_3_3) = all_0_4_4
% 13.44/3.62 | (235) op2(e25, e20) = e25
% 13.44/3.62 | (236) op2(e21, e20) = e21
% 13.44/3.62 | (237) j(e23) = all_0_2_2
% 13.44/3.62 | (238) op1(e15, e15) = e12
% 13.44/3.62 | (239) op1(all_0_5_5, all_0_0_0) = all_0_0_0
% 13.44/3.62 | (240) op1(e10, e10) = e10
% 13.44/3.62 | (241) op1(all_0_2_2, all_0_2_2) = all_0_1_1
% 13.44/3.62 | (242) op2(all_0_10_10, all_0_7_7) = all_0_9_9
% 13.44/3.62 | (243) op2(e22, e22) = e20
% 13.44/3.62 | (244) j(e20) = all_0_5_5
% 13.44/3.62 | (245) op2(all_0_9_9, all_0_9_9) = all_0_8_8
% 13.44/3.62 | (246) h(all_0_3_3) = e22
% 13.44/3.62 | (247) op2(e23, e25) = e22
% 13.44/3.62 | (248) op1(e15, e12) = e11
% 13.44/3.62 | (249) ~ (e13 = e11)
% 13.44/3.62 | (250) op2(all_0_10_10, all_0_10_10) = all_0_11_11
% 13.44/3.62 | (251) op1(e10, e14) = e14
% 13.44/3.62 |
% 13.44/3.62 +-Applying beta-rule and splitting (62), into two cases.
% 13.44/3.62 |-Branch one:
% 13.44/3.62 | (252) all_0_8_8 = e25
% 13.44/3.62 |
% 13.44/3.62 | From (252)(252) and (64) follows:
% 13.44/3.62 | (253) op2(e25, e25) = all_0_9_9
% 13.44/3.62 |
% 13.44/3.62 | From (252) and (245) follows:
% 13.44/3.63 | (254) op2(all_0_9_9, all_0_9_9) = e25
% 13.44/3.63 |
% 13.44/3.63 | Instantiating formula (18) with e25, e25, all_0_9_9, e20 and discharging atoms op2(e25, e25) = all_0_9_9, op2(e25, e25) = e20, yields:
% 13.44/3.63 | (255) all_0_9_9 = e20
% 13.44/3.63 |
% 13.44/3.63 | From (255)(255) and (254) follows:
% 13.44/3.63 | (256) op2(e20, e20) = e25
% 13.44/3.63 |
% 13.44/3.63 | Instantiating formula (18) with e20, e20, e25, e20 and discharging atoms op2(e20, e20) = e25, op2(e20, e20) = e20, yields:
% 13.44/3.63 | (257) e25 = e20
% 13.44/3.63 |
% 13.44/3.63 | Equations (257) can reduce 108 to:
% 13.44/3.63 | (258) $false
% 13.44/3.63 |
% 13.44/3.63 |-The branch is then unsatisfiable
% 13.44/3.63 |-Branch two:
% 13.44/3.63 | (259) ~ (all_0_8_8 = e25)
% 13.44/3.63 | (260) 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
% 13.44/3.63 |
% 13.44/3.63 +-Applying beta-rule and splitting (3), into two cases.
% 13.44/3.63 |-Branch one:
% 13.44/3.63 | (261) all_0_7_7 = e25
% 13.44/3.63 |
% 13.44/3.63 | From (261)(261) and (151) follows:
% 13.44/3.63 | (262) op2(e25, e25) = all_0_8_8
% 13.44/3.63 |
% 13.44/3.63 | Instantiating formula (18) with e25, e25, all_0_8_8, e20 and discharging atoms op2(e25, e25) = all_0_8_8, op2(e25, e25) = e20, yields:
% 13.44/3.63 | (263) all_0_8_8 = e20
% 13.44/3.63 |
% 13.44/3.63 | From (263)(263) and (64) follows:
% 13.44/3.63 | (264) op2(e20, e20) = all_0_9_9
% 13.44/3.63 |
% 13.44/3.63 | From (263) and (65) follows:
% 13.44/3.63 | (265) j(e20) = e13
% 13.44/3.63 |
% 13.44/3.63 | Instantiating formula (18) with e20, e20, all_0_9_9, e20 and discharging atoms op2(e20, e20) = all_0_9_9, op2(e20, e20) = e20, yields:
% 13.44/3.63 | (255) all_0_9_9 = e20
% 13.44/3.63 |
% 13.44/3.63 | Instantiating formula (68) with e20, e13, all_0_5_5 and discharging atoms j(e20) = all_0_5_5, j(e20) = e13, yields:
% 13.44/3.63 | (267) all_0_5_5 = e13
% 13.44/3.63 |
% 13.44/3.63 | From (255) and (139) follows:
% 13.44/3.63 | (268) j(e20) = e12
% 13.44/3.63 |
% 13.44/3.63 | From (267) and (244) follows:
% 13.44/3.63 | (265) j(e20) = e13
% 13.44/3.63 |
% 13.44/3.63 | Instantiating formula (68) with e20, e12, e13 and discharging atoms j(e20) = e13, j(e20) = e12, yields:
% 13.44/3.63 | (270) e13 = e12
% 13.44/3.63 |
% 13.44/3.63 | Equations (270) can reduce 127 to:
% 13.44/3.63 | (258) $false
% 13.44/3.63 |
% 13.44/3.63 |-The branch is then unsatisfiable
% 13.44/3.63 |-Branch two:
% 13.44/3.63 | (272) ~ (all_0_7_7 = e25)
% 13.44/3.63 | (273) 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
% 13.44/3.63 |
% 13.44/3.63 +-Applying beta-rule and splitting (211), into two cases.
% 13.44/3.63 |-Branch one:
% 13.44/3.63 | (274) all_0_9_9 = e25
% 13.44/3.63 |
% 13.44/3.63 | From (274) and (64) follows:
% 13.44/3.63 | (275) op2(all_0_8_8, all_0_8_8) = e25
% 13.44/3.63 |
% 13.44/3.63 | From (274)(274) and (245) follows:
% 13.44/3.63 | (262) op2(e25, e25) = all_0_8_8
% 13.44/3.63 |
% 13.44/3.63 | Instantiating formula (18) with e25, e25, all_0_8_8, e20 and discharging atoms op2(e25, e25) = all_0_8_8, op2(e25, e25) = e20, yields:
% 13.44/3.63 | (263) all_0_8_8 = e20
% 13.44/3.63 |
% 13.44/3.63 | Equations (263) can reduce 259 to:
% 13.44/3.63 | (278) ~ (e25 = e20)
% 13.44/3.63 |
% 13.44/3.63 | Simplifying 278 yields:
% 13.44/3.63 | (108) ~ (e25 = e20)
% 13.44/3.63 |
% 13.44/3.63 | From (263)(263) and (275) follows:
% 13.44/3.63 | (256) op2(e20, e20) = e25
% 13.44/3.63 |
% 13.44/3.63 | Instantiating formula (18) with e20, e20, e25, e20 and discharging atoms op2(e20, e20) = e25, op2(e20, e20) = e20, yields:
% 13.44/3.63 | (257) e25 = e20
% 13.44/3.63 |
% 13.44/3.63 | Equations (257) can reduce 108 to:
% 13.44/3.63 | (258) $false
% 13.44/3.63 |
% 13.44/3.63 |-The branch is then unsatisfiable
% 13.44/3.63 |-Branch two:
% 13.44/3.63 | (283) ~ (all_0_9_9 = e25)
% 13.44/3.63 | (284) 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
% 13.44/3.63 |
% 13.44/3.63 +-Applying beta-rule and splitting (96), into two cases.
% 13.44/3.63 |-Branch one:
% 13.44/3.63 | (285) all_0_4_4 = e15
% 13.44/3.63 |
% 13.44/3.63 | From (285)(285) and (21) follows:
% 13.44/3.63 | (286) op1(e15, e15) = all_0_5_5
% 13.44/3.63 |
% 13.44/3.64 | Instantiating formula (177) with e15, e15, all_0_5_5, e12 and discharging atoms op1(e15, e15) = all_0_5_5, op1(e15, e15) = e12, yields:
% 13.44/3.64 | (287) all_0_5_5 = e12
% 13.44/3.64 |
% 13.44/3.64 | From (287)(287)(287) and (32) follows:
% 13.44/3.64 | (288) op1(e12, e12) = e12
% 13.44/3.64 |
% 13.44/3.64 | Instantiating formula (177) with e12, e12, e12, e13 and discharging atoms op1(e12, e12) = e13, op1(e12, e12) = e12, yields:
% 13.44/3.64 | (270) e13 = e12
% 13.44/3.64 |
% 13.44/3.64 | Equations (270) can reduce 127 to:
% 13.44/3.64 | (258) $false
% 13.44/3.64 |
% 13.44/3.64 |-The branch is then unsatisfiable
% 13.44/3.64 |-Branch two:
% 13.44/3.64 | (291) ~ (all_0_4_4 = e15)
% 13.44/3.64 | (292) 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
% 13.44/3.64 |
% 13.44/3.64 +-Applying beta-rule and splitting (209), into two cases.
% 13.44/3.64 |-Branch one:
% 13.44/3.64 | (293) all_0_3_3 = e15
% 13.44/3.64 |
% 13.44/3.64 | From (293)(293) and (12) follows:
% 13.44/3.64 | (286) op1(e15, e15) = all_0_5_5
% 13.44/3.64 |
% 13.44/3.64 | Instantiating formula (177) with e15, e15, all_0_5_5, e12 and discharging atoms op1(e15, e15) = all_0_5_5, op1(e15, e15) = e12, yields:
% 13.44/3.64 | (287) all_0_5_5 = e12
% 13.44/3.64 |
% 13.44/3.64 | From (287)(287)(287) and (32) follows:
% 13.44/3.64 | (288) op1(e12, e12) = e12
% 13.44/3.64 |
% 13.44/3.64 | Instantiating formula (177) with e12, e12, e12, e13 and discharging atoms op1(e12, e12) = e13, op1(e12, e12) = e12, yields:
% 13.44/3.64 | (270) e13 = e12
% 13.44/3.64 |
% 13.44/3.64 | Equations (270) can reduce 127 to:
% 13.44/3.64 | (258) $false
% 13.44/3.64 |
% 13.44/3.64 |-The branch is then unsatisfiable
% 13.44/3.64 |-Branch two:
% 13.44/3.64 | (299) ~ (all_0_3_3 = e15)
% 13.44/3.64 | (300) 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
% 13.44/3.64 |
% 13.44/3.64 +-Applying beta-rule and splitting (124), into two cases.
% 13.44/3.64 |-Branch one:
% 13.44/3.64 | (301) all_0_5_5 = e15
% 13.44/3.64 |
% 13.44/3.64 | From (301)(301)(301) and (32) follows:
% 13.44/3.64 | (302) op1(e15, e15) = e15
% 13.44/3.64 |
% 13.44/3.64 | Instantiating formula (177) with e15, e15, e15, e12 and discharging atoms op1(e15, e15) = e15, op1(e15, e15) = e12, yields:
% 13.44/3.64 | (303) e15 = e12
% 13.44/3.64 |
% 13.44/3.64 | Equations (303) can reduce 67 to:
% 13.44/3.64 | (258) $false
% 13.44/3.64 |
% 13.44/3.64 |-The branch is then unsatisfiable
% 13.44/3.64 |-Branch two:
% 13.44/3.64 | (305) ~ (all_0_5_5 = e15)
% 13.44/3.64 | (306) all_0_5_5 = e14 | all_0_5_5 = e13 | all_0_5_5 = e12 | all_0_5_5 = e10 | all_0_5_5 = e11
% 13.44/3.64 |
% 13.44/3.64 +-Applying beta-rule and splitting (260), into two cases.
% 13.44/3.64 |-Branch one:
% 13.44/3.64 | (307) all_0_8_8 = e24
% 13.44/3.64 |
% 13.44/3.64 | From (307) and (151) follows:
% 13.44/3.64 | (308) op2(all_0_7_7, all_0_7_7) = e24
% 13.44/3.64 |
% 13.44/3.64 | From (307)(307) and (64) follows:
% 13.44/3.64 | (309) op2(e24, e24) = all_0_9_9
% 13.44/3.64 |
% 13.44/3.64 | From (307) and (75) follows:
% 13.44/3.64 | (310) op2(all_0_9_9, e24) = all_0_11_11
% 13.44/3.64 |
% 13.44/3.64 | From (307) and (65) follows:
% 13.44/3.64 | (311) j(e24) = e13
% 13.44/3.64 |
% 13.44/3.64 | Instantiating formula (18) with e24, e24, all_0_9_9, e23 and discharging atoms op2(e24, e24) = all_0_9_9, op2(e24, e24) = e23, yields:
% 13.44/3.64 | (312) all_0_9_9 = e23
% 13.44/3.64 |
% 13.44/3.64 | Instantiating formula (68) with e24, e13, all_0_1_1 and discharging atoms j(e24) = all_0_1_1, j(e24) = e13, yields:
% 13.44/3.64 | (313) all_0_1_1 = e13
% 13.44/3.64 |
% 13.44/3.64 | From (312) and (310) follows:
% 13.44/3.64 | (314) op2(e23, e24) = all_0_11_11
% 13.44/3.64 |
% 13.44/3.64 | From (312) and (139) follows:
% 13.44/3.64 | (315) j(e23) = e12
% 13.44/3.64 |
% 13.44/3.64 | From (313) and (24) follows:
% 13.44/3.64 | (311) j(e24) = e13
% 13.44/3.64 |
% 13.44/3.64 | Instantiating formula (18) with e23, e24, all_0_11_11, e20 and discharging atoms op2(e23, e24) = all_0_11_11, op2(e23, e24) = e20, yields:
% 13.44/3.64 | (317) all_0_11_11 = e20
% 13.44/3.64 |
% 13.44/3.64 | Instantiating formula (68) with e23, e12, all_0_2_2 and discharging atoms j(e23) = all_0_2_2, j(e23) = e12, yields:
% 13.44/3.64 | (318) all_0_2_2 = e12
% 13.44/3.64 |
% 13.44/3.64 | From (317) and (143) follows:
% 13.44/3.64 | (319) j(e20) = e10
% 13.44/3.64 |
% 13.44/3.64 | From (318) and (237) follows:
% 13.44/3.64 | (315) j(e23) = e12
% 13.44/3.64 |
% 13.44/3.64 | Instantiating formula (68) with e20, e10, all_0_5_5 and discharging atoms j(e20) = all_0_5_5, j(e20) = e10, yields:
% 13.44/3.64 | (321) all_0_5_5 = e10
% 13.44/3.64 |
% 13.44/3.64 | From (321) and (244) follows:
% 13.44/3.65 | (319) j(e20) = e10
% 13.44/3.65 |
% 13.44/3.65 +-Applying beta-rule and splitting (273), into two cases.
% 13.44/3.65 |-Branch one:
% 13.44/3.65 | (323) all_0_7_7 = e24
% 13.44/3.65 |
% 13.44/3.65 | From (323) and (227) follows:
% 13.44/3.65 | (324) j(e24) = e14
% 13.44/3.65 |
% 13.44/3.65 | Instantiating formula (68) with e24, e14, e13 and discharging atoms j(e24) = e14, j(e24) = e13, yields:
% 13.44/3.65 | (325) e14 = e13
% 13.44/3.65 |
% 13.44/3.65 | Equations (325) can reduce 121 to:
% 13.44/3.65 | (258) $false
% 13.44/3.65 |
% 13.44/3.65 |-The branch is then unsatisfiable
% 13.44/3.65 |-Branch two:
% 13.44/3.65 | (327) ~ (all_0_7_7 = e24)
% 13.44/3.65 | (328) all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 13.44/3.65 |
% 13.44/3.65 +-Applying beta-rule and splitting (328), into two cases.
% 13.44/3.65 |-Branch one:
% 13.44/3.65 | (329) all_0_7_7 = e23
% 13.44/3.65 |
% 13.44/3.65 | From (329) and (227) follows:
% 13.44/3.65 | (330) j(e23) = e14
% 13.44/3.65 |
% 13.44/3.65 | Instantiating formula (68) with e23, e14, e12 and discharging atoms j(e23) = e14, j(e23) = e12, yields:
% 13.44/3.65 | (331) e14 = e12
% 13.44/3.65 |
% 13.44/3.65 | Equations (331) can reduce 26 to:
% 13.44/3.65 | (258) $false
% 13.44/3.65 |
% 13.44/3.65 |-The branch is then unsatisfiable
% 13.44/3.65 |-Branch two:
% 13.44/3.65 | (333) ~ (all_0_7_7 = e23)
% 13.44/3.65 | (334) all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 13.44/3.65 |
% 13.44/3.65 +-Applying beta-rule and splitting (334), into two cases.
% 13.44/3.65 |-Branch one:
% 13.44/3.65 | (335) all_0_7_7 = e22
% 13.44/3.65 |
% 13.44/3.65 | From (335)(335) and (308) follows:
% 13.44/3.65 | (336) op2(e22, e22) = e24
% 13.44/3.65 |
% 13.44/3.65 | Instantiating formula (18) with e22, e22, e24, e20 and discharging atoms op2(e22, e22) = e24, op2(e22, e22) = e20, yields:
% 13.44/3.65 | (337) e24 = e20
% 13.44/3.65 |
% 13.44/3.65 | Equations (337) can reduce 51 to:
% 13.44/3.65 | (258) $false
% 13.44/3.65 |
% 13.44/3.65 |-The branch is then unsatisfiable
% 13.44/3.65 |-Branch two:
% 13.44/3.65 | (339) ~ (all_0_7_7 = e22)
% 13.44/3.65 | (340) all_0_7_7 = e20 | all_0_7_7 = e21
% 13.44/3.65 |
% 13.44/3.65 +-Applying beta-rule and splitting (340), into two cases.
% 13.44/3.65 |-Branch one:
% 13.44/3.65 | (341) all_0_7_7 = e20
% 13.44/3.65 |
% 13.44/3.65 | From (341) and (227) follows:
% 13.44/3.65 | (342) j(e20) = e14
% 13.44/3.65 |
% 13.44/3.65 | Instantiating formula (68) with e20, e14, e10 and discharging atoms j(e20) = e14, j(e20) = e10, yields:
% 13.44/3.65 | (343) e14 = e10
% 13.44/3.65 |
% 13.44/3.65 | Equations (343) can reduce 79 to:
% 13.44/3.65 | (258) $false
% 13.44/3.65 |
% 13.44/3.65 |-The branch is then unsatisfiable
% 13.44/3.65 |-Branch two:
% 13.44/3.65 | (345) ~ (all_0_7_7 = e20)
% 13.44/3.65 | (346) all_0_7_7 = e21
% 13.44/3.65 |
% 13.44/3.65 | From (346)(346) and (308) follows:
% 13.44/3.65 | (347) op2(e21, e21) = e24
% 13.44/3.65 |
% 13.44/3.65 | Instantiating formula (18) with e21, e21, e24, e20 and discharging atoms op2(e21, e21) = e24, op2(e21, e21) = e20, yields:
% 13.44/3.65 | (337) e24 = e20
% 13.44/3.65 |
% 13.44/3.65 | Equations (337) can reduce 51 to:
% 13.44/3.65 | (258) $false
% 13.44/3.65 |
% 13.44/3.65 |-The branch is then unsatisfiable
% 13.44/3.65 |-Branch two:
% 13.44/3.65 | (350) ~ (all_0_8_8 = e24)
% 13.44/3.65 | (351) all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 13.44/3.65 |
% 13.44/3.65 +-Applying beta-rule and splitting (273), into two cases.
% 13.44/3.65 |-Branch one:
% 13.44/3.65 | (323) all_0_7_7 = e24
% 13.44/3.65 |
% 13.44/3.65 | From (323)(323) and (151) follows:
% 13.44/3.65 | (353) op2(e24, e24) = all_0_8_8
% 13.44/3.65 |
% 13.44/3.65 | From (323) and (227) follows:
% 13.44/3.65 | (324) j(e24) = e14
% 13.44/3.65 |
% 13.44/3.65 | Instantiating formula (18) with e24, e24, all_0_8_8, e23 and discharging atoms op2(e24, e24) = all_0_8_8, op2(e24, e24) = e23, yields:
% 13.44/3.65 | (355) all_0_8_8 = e23
% 13.44/3.65 |
% 13.44/3.65 | Instantiating formula (68) with e24, e14, all_0_1_1 and discharging atoms j(e24) = all_0_1_1, j(e24) = e14, yields:
% 13.44/3.65 | (356) all_0_1_1 = e14
% 13.44/3.65 |
% 13.44/3.65 | From (355)(355) and (64) follows:
% 13.44/3.65 | (357) op2(e23, e23) = all_0_9_9
% 13.44/3.65 |
% 13.44/3.65 | From (356) and (24) follows:
% 13.44/3.65 | (324) j(e24) = e14
% 13.44/3.65 |
% 13.44/3.65 | Instantiating formula (18) with e23, e23, all_0_9_9, e24 and discharging atoms op2(e23, e23) = all_0_9_9, op2(e23, e23) = e24, yields:
% 13.44/3.65 | (359) all_0_9_9 = e24
% 13.44/3.65 |
% 13.44/3.65 | From (359) and (139) follows:
% 13.44/3.65 | (360) j(e24) = e12
% 13.44/3.65 |
% 13.44/3.65 | Instantiating formula (68) with e24, e12, e14 and discharging atoms j(e24) = e14, j(e24) = e12, yields:
% 13.44/3.65 | (331) e14 = e12
% 13.44/3.65 |
% 13.44/3.65 | Equations (331) can reduce 26 to:
% 13.44/3.65 | (258) $false
% 13.44/3.65 |
% 13.44/3.65 |-The branch is then unsatisfiable
% 13.44/3.65 |-Branch two:
% 13.44/3.65 | (327) ~ (all_0_7_7 = e24)
% 13.44/3.65 | (328) all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 13.44/3.66 |
% 13.44/3.66 +-Applying beta-rule and splitting (284), into two cases.
% 13.44/3.66 |-Branch one:
% 13.44/3.66 | (359) all_0_9_9 = e24
% 13.44/3.66 |
% 13.44/3.66 | From (359) and (93) follows:
% 13.44/3.66 | (366) op2(all_0_8_8, e24) = all_0_11_11
% 13.44/3.66 |
% 13.44/3.66 | From (359)(359) and (245) follows:
% 13.44/3.66 | (353) op2(e24, e24) = all_0_8_8
% 13.44/3.66 |
% 13.44/3.66 | Instantiating formula (18) with e24, e24, all_0_8_8, e23 and discharging atoms op2(e24, e24) = all_0_8_8, op2(e24, e24) = e23, yields:
% 13.44/3.66 | (355) all_0_8_8 = e23
% 13.44/3.66 |
% 13.44/3.66 | From (355) and (151) follows:
% 13.44/3.66 | (369) op2(all_0_7_7, all_0_7_7) = e23
% 13.44/3.66 |
% 13.44/3.66 | From (355) and (366) follows:
% 13.44/3.66 | (314) op2(e23, e24) = all_0_11_11
% 13.44/3.66 |
% 13.44/3.66 | From (355) and (65) follows:
% 13.44/3.66 | (371) j(e23) = e13
% 13.44/3.66 |
% 13.44/3.66 | Instantiating formula (18) with e23, e24, all_0_11_11, e20 and discharging atoms op2(e23, e24) = all_0_11_11, op2(e23, e24) = e20, yields:
% 13.44/3.66 | (317) all_0_11_11 = e20
% 13.44/3.66 |
% 13.44/3.66 | Instantiating formula (68) with e23, e13, all_0_2_2 and discharging atoms j(e23) = all_0_2_2, j(e23) = e13, yields:
% 13.44/3.66 | (373) all_0_2_2 = e13
% 13.44/3.66 |
% 13.44/3.66 | From (317) and (143) follows:
% 13.44/3.66 | (319) j(e20) = e10
% 13.44/3.66 |
% 13.44/3.66 | From (373) and (237) follows:
% 13.44/3.66 | (371) j(e23) = e13
% 13.44/3.66 |
% 13.44/3.66 | Instantiating formula (68) with e20, e10, all_0_5_5 and discharging atoms j(e20) = all_0_5_5, j(e20) = e10, yields:
% 13.44/3.66 | (321) all_0_5_5 = e10
% 13.44/3.66 |
% 13.44/3.66 | From (321) and (244) follows:
% 13.44/3.66 | (319) j(e20) = e10
% 13.44/3.66 |
% 13.44/3.66 +-Applying beta-rule and splitting (328), into two cases.
% 13.44/3.66 |-Branch one:
% 13.44/3.66 | (329) all_0_7_7 = e23
% 13.44/3.66 |
% 13.44/3.66 | From (329) and (227) follows:
% 13.44/3.66 | (330) j(e23) = e14
% 13.44/3.66 |
% 13.44/3.66 | Instantiating formula (68) with e23, e14, e13 and discharging atoms j(e23) = e14, j(e23) = e13, yields:
% 13.44/3.66 | (325) e14 = e13
% 13.44/3.66 |
% 13.44/3.66 | Equations (325) can reduce 121 to:
% 13.44/3.66 | (258) $false
% 13.44/3.66 |
% 13.44/3.66 |-The branch is then unsatisfiable
% 13.44/3.66 |-Branch two:
% 13.44/3.66 | (333) ~ (all_0_7_7 = e23)
% 13.44/3.66 | (334) all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 13.44/3.66 |
% 13.44/3.66 +-Applying beta-rule and splitting (334), into two cases.
% 13.44/3.66 |-Branch one:
% 13.44/3.66 | (335) all_0_7_7 = e22
% 13.44/3.66 |
% 13.44/3.66 | From (335)(335) and (369) follows:
% 13.44/3.66 | (385) op2(e22, e22) = e23
% 13.44/3.66 |
% 13.44/3.66 | Instantiating formula (18) with e22, e22, e23, e20 and discharging atoms op2(e22, e22) = e23, op2(e22, e22) = e20, yields:
% 13.44/3.66 | (386) e23 = e20
% 13.44/3.66 |
% 13.44/3.66 | Equations (386) can reduce 80 to:
% 13.44/3.66 | (258) $false
% 13.44/3.66 |
% 13.44/3.66 |-The branch is then unsatisfiable
% 13.44/3.66 |-Branch two:
% 13.44/3.66 | (339) ~ (all_0_7_7 = e22)
% 13.44/3.66 | (340) all_0_7_7 = e20 | all_0_7_7 = e21
% 13.44/3.66 |
% 13.44/3.66 +-Applying beta-rule and splitting (340), into two cases.
% 13.44/3.66 |-Branch one:
% 13.44/3.66 | (341) all_0_7_7 = e20
% 13.44/3.66 |
% 13.44/3.66 | From (341) and (227) follows:
% 13.44/3.66 | (342) j(e20) = e14
% 13.44/3.66 |
% 13.44/3.66 | Instantiating formula (68) with e20, e14, e10 and discharging atoms j(e20) = e14, j(e20) = e10, yields:
% 13.44/3.66 | (343) e14 = e10
% 13.44/3.66 |
% 13.44/3.66 | Equations (343) can reduce 79 to:
% 13.44/3.66 | (258) $false
% 13.44/3.66 |
% 13.44/3.66 |-The branch is then unsatisfiable
% 13.44/3.66 |-Branch two:
% 13.44/3.66 | (345) ~ (all_0_7_7 = e20)
% 13.44/3.66 | (346) all_0_7_7 = e21
% 13.44/3.66 |
% 13.44/3.66 | From (346)(346) and (369) follows:
% 13.44/3.66 | (396) op2(e21, e21) = e23
% 13.44/3.66 |
% 13.44/3.66 | Instantiating formula (18) with e21, e21, e23, e20 and discharging atoms op2(e21, e21) = e23, op2(e21, e21) = e20, yields:
% 13.44/3.66 | (386) e23 = e20
% 13.44/3.66 |
% 13.44/3.66 | Equations (386) can reduce 80 to:
% 13.44/3.66 | (258) $false
% 13.44/3.66 |
% 13.44/3.66 |-The branch is then unsatisfiable
% 13.44/3.66 |-Branch two:
% 13.44/3.66 | (399) ~ (all_0_9_9 = e24)
% 13.44/3.66 | (400) all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21
% 13.44/3.66 |
% 13.44/3.66 +-Applying beta-rule and splitting (292), into two cases.
% 13.44/3.66 |-Branch one:
% 13.44/3.66 | (401) all_0_4_4 = e14
% 13.44/3.66 |
% 13.44/3.66 | From (401)(401) and (21) follows:
% 13.44/3.66 | (402) op1(e14, e14) = all_0_5_5
% 13.44/3.66 |
% 13.44/3.66 | Instantiating formula (177) with e14, e14, all_0_5_5, e13 and discharging atoms op1(e14, e14) = all_0_5_5, op1(e14, e14) = e13, yields:
% 13.44/3.66 | (267) all_0_5_5 = e13
% 13.44/3.66 |
% 13.44/3.66 | From (267)(267)(267) and (32) follows:
% 13.44/3.66 | (404) op1(e13, e13) = e13
% 13.44/3.66 |
% 13.44/3.66 | Instantiating formula (177) with e13, e13, e13, e12 and discharging atoms op1(e13, e13) = e13, op1(e13, e13) = e12, yields:
% 13.44/3.66 | (270) e13 = e12
% 13.44/3.66 |
% 13.44/3.66 | Equations (270) can reduce 127 to:
% 13.44/3.66 | (258) $false
% 13.44/3.66 |
% 13.44/3.66 |-The branch is then unsatisfiable
% 13.44/3.66 |-Branch two:
% 13.44/3.66 | (407) ~ (all_0_4_4 = e14)
% 13.44/3.66 | (408) all_0_4_4 = e13 | all_0_4_4 = e12 | all_0_4_4 = e10 | all_0_4_4 = e11
% 13.44/3.66 |
% 13.44/3.66 +-Applying beta-rule and splitting (300), into two cases.
% 13.44/3.66 |-Branch one:
% 13.44/3.66 | (409) all_0_3_3 = e14
% 13.44/3.66 |
% 13.44/3.66 | From (409)(409) and (12) follows:
% 13.44/3.66 | (402) op1(e14, e14) = all_0_5_5
% 13.44/3.66 |
% 13.44/3.66 | Instantiating formula (177) with e14, e14, all_0_5_5, e13 and discharging atoms op1(e14, e14) = all_0_5_5, op1(e14, e14) = e13, yields:
% 13.44/3.66 | (267) all_0_5_5 = e13
% 13.44/3.66 |
% 13.44/3.66 | From (267)(267)(267) and (32) follows:
% 13.44/3.66 | (404) op1(e13, e13) = e13
% 13.44/3.66 |
% 13.44/3.66 | Instantiating formula (177) with e13, e13, e13, e12 and discharging atoms op1(e13, e13) = e13, op1(e13, e13) = e12, yields:
% 13.44/3.66 | (270) e13 = e12
% 13.44/3.66 |
% 13.44/3.66 | Equations (270) can reduce 127 to:
% 13.44/3.66 | (258) $false
% 13.44/3.66 |
% 13.44/3.66 |-The branch is then unsatisfiable
% 13.44/3.66 |-Branch two:
% 13.44/3.66 | (415) ~ (all_0_3_3 = e14)
% 13.44/3.66 | (416) all_0_3_3 = e13 | all_0_3_3 = e12 | all_0_3_3 = e10 | all_0_3_3 = e11
% 13.44/3.66 |
% 13.44/3.66 +-Applying beta-rule and splitting (306), into two cases.
% 13.44/3.66 |-Branch one:
% 13.44/3.66 | (417) all_0_5_5 = e14
% 13.44/3.66 |
% 13.44/3.66 | From (417)(417)(417) and (32) follows:
% 13.44/3.66 | (418) op1(e14, e14) = e14
% 13.44/3.66 |
% 13.44/3.66 | Instantiating formula (177) with e14, e14, e14, e13 and discharging atoms op1(e14, e14) = e14, op1(e14, e14) = e13, yields:
% 13.44/3.66 | (325) e14 = e13
% 13.44/3.66 |
% 13.44/3.66 | Equations (325) can reduce 121 to:
% 13.44/3.66 | (258) $false
% 13.44/3.66 |
% 13.44/3.66 |-The branch is then unsatisfiable
% 13.44/3.66 |-Branch two:
% 13.44/3.66 | (421) ~ (all_0_5_5 = e14)
% 13.44/3.66 | (422) all_0_5_5 = e13 | all_0_5_5 = e12 | all_0_5_5 = e10 | all_0_5_5 = e11
% 13.44/3.66 |
% 13.44/3.66 +-Applying beta-rule and splitting (351), into two cases.
% 13.44/3.66 |-Branch one:
% 13.44/3.66 | (355) all_0_8_8 = e23
% 13.44/3.66 |
% 13.44/3.66 | From (355)(355) and (64) follows:
% 13.44/3.66 | (357) op2(e23, e23) = all_0_9_9
% 13.44/3.66 |
% 13.44/3.66 | Instantiating formula (18) with e23, e23, all_0_9_9, e24 and discharging atoms op2(e23, e23) = all_0_9_9, op2(e23, e23) = e24, yields:
% 13.44/3.66 | (359) all_0_9_9 = e24
% 13.44/3.66 |
% 13.44/3.66 | Equations (359) can reduce 399 to:
% 13.44/3.66 | (258) $false
% 13.44/3.66 |
% 13.44/3.66 |-The branch is then unsatisfiable
% 13.44/3.66 |-Branch two:
% 13.44/3.66 | (427) ~ (all_0_8_8 = e23)
% 13.44/3.66 | (428) all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 13.44/3.66 |
% 13.44/3.66 +-Applying beta-rule and splitting (408), into two cases.
% 13.44/3.66 |-Branch one:
% 13.44/3.66 | (429) all_0_4_4 = e13
% 13.44/3.66 |
% 13.44/3.66 | From (429)(429) and (21) follows:
% 13.44/3.66 | (430) op1(e13, e13) = all_0_5_5
% 13.44/3.66 |
% 13.44/3.66 | From (429)(429) and (144) follows:
% 13.44/3.66 | (431) op1(all_0_5_5, e13) = e13
% 13.44/3.66 |
% 13.44/3.66 | Instantiating formula (177) with e13, e13, all_0_5_5, e12 and discharging atoms op1(e13, e13) = all_0_5_5, op1(e13, e13) = e12, yields:
% 13.44/3.66 | (287) all_0_5_5 = e12
% 13.44/3.67 |
% 13.44/3.67 | From (287)(287)(287) and (32) follows:
% 13.44/3.67 | (288) op1(e12, e12) = e12
% 13.44/3.67 |
% 13.44/3.67 | From (287) and (431) follows:
% 13.44/3.67 | (434) op1(e12, e13) = e13
% 13.44/3.67 |
% 13.44/3.67 | Instantiating formula (177) with e12, e13, e13, e10 and discharging atoms op1(e12, e13) = e13, op1(e12, e13) = e10, yields:
% 13.44/3.67 | (435) e13 = e10
% 13.44/3.67 |
% 13.44/3.67 | Instantiating formula (177) with e12, e12, e12, e13 and discharging atoms op1(e12, e12) = e13, op1(e12, e12) = e12, yields:
% 13.44/3.67 | (270) e13 = e12
% 13.44/3.67 |
% 13.44/3.67 | Combining equations (270,435) yields a new equation:
% 13.44/3.67 | (437) e12 = e10
% 13.44/3.67 |
% 13.44/3.67 | Simplifying 437 yields:
% 13.44/3.67 | (438) e12 = e10
% 13.44/3.67 |
% 13.44/3.67 | Equations (438) can reduce 87 to:
% 13.44/3.67 | (258) $false
% 13.44/3.67 |
% 13.44/3.67 |-The branch is then unsatisfiable
% 13.44/3.67 |-Branch two:
% 13.44/3.67 | (440) ~ (all_0_4_4 = e13)
% 13.44/3.67 | (441) all_0_4_4 = e12 | all_0_4_4 = e10 | all_0_4_4 = e11
% 13.44/3.67 |
% 13.44/3.67 +-Applying beta-rule and splitting (416), into two cases.
% 13.44/3.67 |-Branch one:
% 13.44/3.67 | (442) all_0_3_3 = e13
% 13.44/3.67 |
% 13.44/3.67 | From (442)(442) and (12) follows:
% 13.44/3.67 | (430) op1(e13, e13) = all_0_5_5
% 13.44/3.67 |
% 13.44/3.67 | From (442)(442) and (142) follows:
% 13.44/3.67 | (431) op1(all_0_5_5, e13) = e13
% 13.44/3.67 |
% 13.44/3.67 | Instantiating formula (177) with e13, e13, all_0_5_5, e12 and discharging atoms op1(e13, e13) = all_0_5_5, op1(e13, e13) = e12, yields:
% 13.44/3.67 | (287) all_0_5_5 = e12
% 13.44/3.67 |
% 13.44/3.67 | From (287)(287)(287) and (32) follows:
% 13.44/3.67 | (288) op1(e12, e12) = e12
% 13.44/3.67 |
% 13.44/3.67 | From (287) and (431) follows:
% 13.44/3.67 | (434) op1(e12, e13) = e13
% 13.44/3.67 |
% 13.44/3.67 | Instantiating formula (177) with e12, e13, e13, e10 and discharging atoms op1(e12, e13) = e13, op1(e12, e13) = e10, yields:
% 13.44/3.67 | (435) e13 = e10
% 13.44/3.67 |
% 13.44/3.67 | Instantiating formula (177) with e12, e12, e12, e13 and discharging atoms op1(e12, e12) = e13, op1(e12, e12) = e12, yields:
% 13.44/3.67 | (270) e13 = e12
% 13.44/3.67 |
% 13.44/3.67 | Combining equations (270,435) yields a new equation:
% 13.44/3.67 | (437) e12 = e10
% 13.44/3.67 |
% 13.44/3.67 | Simplifying 437 yields:
% 13.44/3.67 | (438) e12 = e10
% 13.44/3.67 |
% 13.44/3.67 | Equations (438) can reduce 87 to:
% 13.44/3.67 | (258) $false
% 13.44/3.67 |
% 13.44/3.67 |-The branch is then unsatisfiable
% 13.44/3.67 |-Branch two:
% 13.44/3.67 | (453) ~ (all_0_3_3 = e13)
% 13.44/3.67 | (454) all_0_3_3 = e12 | all_0_3_3 = e10 | all_0_3_3 = e11
% 13.44/3.67 |
% 13.44/3.67 +-Applying beta-rule and splitting (422), into two cases.
% 13.44/3.67 |-Branch one:
% 13.44/3.67 | (267) all_0_5_5 = e13
% 13.44/3.67 |
% 13.44/3.67 | From (267)(267)(267) and (32) follows:
% 13.44/3.67 | (404) op1(e13, e13) = e13
% 13.44/3.67 |
% 13.44/3.67 | Instantiating formula (177) with e13, e13, e13, e12 and discharging atoms op1(e13, e13) = e13, op1(e13, e13) = e12, yields:
% 13.44/3.67 | (270) e13 = e12
% 13.44/3.67 |
% 13.44/3.67 | Equations (270) can reduce 127 to:
% 13.44/3.67 | (258) $false
% 13.44/3.67 |
% 13.44/3.67 |-The branch is then unsatisfiable
% 13.44/3.67 |-Branch two:
% 13.44/3.67 | (459) ~ (all_0_5_5 = e13)
% 13.44/3.67 | (460) all_0_5_5 = e12 | all_0_5_5 = e10 | all_0_5_5 = e11
% 13.44/3.67 |
% 13.44/3.67 +-Applying beta-rule and splitting (428), into two cases.
% 13.44/3.67 |-Branch one:
% 13.44/3.67 | (461) all_0_8_8 = e22
% 13.44/3.67 |
% 13.44/3.67 | From (461) and (65) follows:
% 13.44/3.67 | (462) j(e22) = e13
% 13.44/3.67 |
% 13.44/3.67 | Instantiating formula (68) with e22, e13, all_0_3_3 and discharging atoms j(e22) = all_0_3_3, j(e22) = e13, yields:
% 13.44/3.67 | (442) all_0_3_3 = e13
% 13.44/3.67 |
% 13.44/3.67 | Equations (442) can reduce 453 to:
% 13.44/3.67 | (258) $false
% 13.44/3.67 |
% 13.44/3.67 |-The branch is then unsatisfiable
% 13.44/3.67 |-Branch two:
% 13.44/3.67 | (465) ~ (all_0_8_8 = e22)
% 13.44/3.67 | (466) all_0_8_8 = e20 | all_0_8_8 = e21
% 13.44/3.67 |
% 13.44/3.67 +-Applying beta-rule and splitting (466), into two cases.
% 13.44/3.67 |-Branch one:
% 13.44/3.67 | (263) all_0_8_8 = e20
% 13.44/3.67 |
% 13.44/3.67 | From (263) and (65) follows:
% 13.44/3.67 | (265) j(e20) = e13
% 13.44/3.67 |
% 13.44/3.67 | Instantiating formula (68) with e20, e13, all_0_5_5 and discharging atoms j(e20) = all_0_5_5, j(e20) = e13, yields:
% 13.44/3.67 | (267) all_0_5_5 = e13
% 13.44/3.67 |
% 13.44/3.67 | Equations (267) can reduce 459 to:
% 13.44/3.67 | (258) $false
% 13.44/3.67 |
% 13.44/3.67 |-The branch is then unsatisfiable
% 13.44/3.67 |-Branch two:
% 13.44/3.67 | (471) ~ (all_0_8_8 = e20)
% 13.44/3.67 | (472) all_0_8_8 = e21
% 13.44/3.67 |
% 13.44/3.67 | From (472) and (65) follows:
% 13.44/3.67 | (473) j(e21) = e13
% 13.44/3.67 |
% 13.44/3.67 | Instantiating formula (68) with e21, e13, all_0_4_4 and discharging atoms j(e21) = all_0_4_4, j(e21) = e13, yields:
% 13.44/3.67 | (429) all_0_4_4 = e13
% 13.44/3.67 |
% 13.44/3.67 | Equations (429) can reduce 440 to:
% 13.44/3.67 | (258) $false
% 13.44/3.67 |
% 13.44/3.67 |-The branch is then unsatisfiable
% 13.44/3.67 % SZS output end Proof for theBenchmark
% 13.44/3.67
% 13.44/3.67 3087ms
%------------------------------------------------------------------------------