TSTP Solution File: ALG079+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG079+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 15:34:15 EDT 2022
% Result : Theorem 4.17s 1.55s
% Output : Proof 8.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ALG079+1 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jun 8 23:07:34 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.52/0.57 ____ _
% 0.52/0.57 ___ / __ \_____(_)___ ________ __________
% 0.52/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.52/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.52/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.52/0.57
% 0.52/0.57 A Theorem Prover for First-Order Logic
% 0.52/0.58 (ePrincess v.1.0)
% 0.52/0.58
% 0.52/0.58 (c) Philipp Rümmer, 2009-2015
% 0.52/0.58 (c) Peter Backeman, 2014-2015
% 0.52/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.52/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.52/0.58 Bug reports to peter@backeman.se
% 0.52/0.58
% 0.52/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.52/0.58
% 0.52/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.52/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.93/1.00 Prover 0: Preprocessing ...
% 2.95/1.28 Prover 0: Constructing countermodel ...
% 4.17/1.55 Prover 0: proved (922ms)
% 4.17/1.55
% 4.17/1.55 No countermodel exists, formula is valid
% 4.17/1.55 % SZS status Theorem for theBenchmark
% 4.17/1.55
% 4.17/1.55 Generating proof ... found it (size 111)
% 7.57/2.32
% 7.57/2.32 % SZS output start Proof for theBenchmark
% 7.57/2.32 Assumed formulas after preprocessing and simplification:
% 7.57/2.32 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (e24 = e23) & ~ (e24 = e22) & ~ (e24 = e20) & ~ (e24 = e21) & ~ (e24 = e14) & ~ (e24 = e13) & ~ (e24 = e12) & ~ (e24 = e10) & ~ (e24 = e11) & ~ (e23 = e22) & ~ (e23 = e20) & ~ (e23 = e21) & ~ (e23 = e14) & ~ (e23 = e13) & ~ (e23 = e12) & ~ (e23 = e10) & ~ (e23 = e11) & ~ (e22 = e20) & ~ (e22 = e21) & ~ (e22 = e14) & ~ (e22 = e13) & ~ (e22 = e12) & ~ (e22 = e10) & ~ (e22 = e11) & ~ (e20 = e21) & ~ (e20 = e14) & ~ (e20 = e13) & ~ (e20 = e12) & ~ (e20 = e10) & ~ (e20 = e11) & ~ (e21 = e14) & ~ (e21 = e13) & ~ (e21 = e12) & ~ (e21 = e10) & ~ (e21 = e11) & ~ (e14 = e13) & ~ (e14 = e12) & ~ (e14 = e10) & ~ (e14 = e11) & ~ (e13 = e12) & ~ (e13 = e10) & ~ (e13 = e11) & ~ (e12 = e10) & ~ (e12 = e11) & ~ (e10 = e11) & op2(v4, v4) = v2 & op2(v4, v3) = v1 & op2(v4, v2) = v0 & op2(v4, v1) = v3 & op2(v4, v0) = v4 & op2(v3, v4) = v0 & op2(v3, v3) = v4 & op2(v3, v2) = v1 & op2(v3, v1) = v2 & op2(v3, v0) = v3 & op2(v2, v4) = v1 & op2(v2, v3) = v0 & op2(v2, v2) = v3 & op2(v2, v1) = v4 & op2(v2, v0) = v2 & op2(v1, v4) = v3 & op2(v1, v3) = v2 & op2(v1, v2) = v4 & op2(v1, v1) = v0 & op2(v1, v0) = v1 & op2(v0, v4) = v4 & op2(v0, v3) = v3 & op2(v0, v2) = v2 & op2(v0, v1) = v1 & op2(v0, v0) = v0 & op2(e24, e24) = e21 & op2(e24, e23) = e22 & op2(e24, e22) = e20 & op2(e24, e20) = e24 & op2(e24, e21) = e23 & op2(e23, e24) = e22 & op2(e23, e23) = e21 & op2(e23, e22) = e24 & op2(e23, e20) = e23 & op2(e23, e21) = e20 & op2(e22, e24) = e23 & op2(e22, e23) = e20 & op2(e22, e22) = e21 & op2(e22, e20) = e22 & op2(e22, e21) = e24 & op2(e20, e24) = e24 & op2(e20, e23) = e23 & op2(e20, e22) = e22 & op2(e20, e20) = e20 & op2(e20, e21) = e21 & op2(e21, e24) = e20 & op2(e21, e23) = e24 & op2(e21, e22) = e23 & op2(e21, e20) = e21 & op2(e21, e21) = e22 & op1(v9, v9) = v6 & op1(v9, v8) = v7 & op1(v9, v7) = v5 & op1(v9, v6) = v8 & op1(v9, v5) = v9 & op1(v8, v9) = v7 & op1(v8, v8) = v6 & op1(v8, v7) = v9 & op1(v8, v6) = v5 & op1(v8, v5) = v8 & op1(v7, v9) = v8 & op1(v7, v8) = v5 & op1(v7, v7) = v6 & op1(v7, v6) = v9 & op1(v7, v5) = v7 & op1(v6, v9) = v5 & op1(v6, v8) = v9 & op1(v6, v7) = v8 & op1(v6, v6) = v7 & op1(v6, v5) = v6 & op1(v5, v9) = v9 & op1(v5, v8) = v8 & op1(v5, v7) = v7 & op1(v5, v6) = v6 & op1(v5, v5) = v5 & op1(e14, e14) = e12 & op1(e14, e13) = e11 & op1(e14, e12) = e10 & op1(e14, e10) = e14 & op1(e14, e11) = e13 & op1(e13, e14) = e10 & op1(e13, e13) = e14 & op1(e13, e12) = e11 & op1(e13, e10) = e13 & op1(e13, e11) = e12 & op1(e12, e14) = e11 & op1(e12, e13) = e10 & op1(e12, e12) = e13 & op1(e12, e10) = e12 & op1(e12, e11) = e14 & op1(e10, e14) = e14 & op1(e10, e13) = e13 & op1(e10, e12) = e12 & op1(e10, e10) = e10 & op1(e10, e11) = e11 & op1(e11, e14) = e13 & op1(e11, e13) = e12 & op1(e11, e12) = e14 & op1(e11, e10) = e11 & op1(e11, e11) = e10 & h(v9) = e24 & h(v8) = e23 & h(v7) = e22 & h(v6) = e21 & h(v5) = e20 & h(e14) = v4 & h(e13) = v3 & h(e12) = v2 & h(e10) = v0 & h(e11) = v1 & j(v4) = e14 & j(v3) = e13 & j(v2) = e12 & j(v1) = e11 & j(v0) = e10 & j(e24) = v9 & j(e23) = v8 & j(e22) = v7 & j(e20) = v5 & j(e21) = v6 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (op2(v13, v12) = v11) | ~ (op2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (op1(v13, v12) = v11) | ~ (op1(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (h(v12) = v11) | ~ (h(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (j(v12) = v11) | ~ (j(v12) = v10)) & (v9 = e14 | v9 = e13 | v9 = e12 | v9 = e10 | v9 = e11) & (v8 = e14 | v8 = e13 | v8 = e12 | v8 = e10 | v8 = e11) & (v7 = e14 | v7 = e13 | v7 = e12 | v7 = e10 | v7 = e11) & (v6 = e14 | v6 = e13 | v6 = e12 | v6 = e10 | v6 = e11) & (v5 = e14 | v5 = e13 | v5 = e12 | v5 = e10 | v5 = e11) & (v4 = e24 | v4 = e23 | v4 = e22 | v4 = e20 | v4 = e21) & (v3 = e24 | v3 = e23 | v3 = e22 | v3 = e20 | v3 = e21) & (v2 = e24 | v2 = e23 | v2 = e22 | v2 = e20 | v2 = e21) & (v1 = e24 | v1 = e23 | v1 = e22 | v1 = e20 | v1 = e21) & (v0 = e24 | v0 = e23 | v0 = e22 | v0 = e20 | v0 = e21))
% 7.78/2.36 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 yields:
% 7.78/2.36 | (1) ~ (e24 = e23) & ~ (e24 = e22) & ~ (e24 = e20) & ~ (e24 = e21) & ~ (e24 = e14) & ~ (e24 = e13) & ~ (e24 = e12) & ~ (e24 = e10) & ~ (e24 = e11) & ~ (e23 = e22) & ~ (e23 = e20) & ~ (e23 = e21) & ~ (e23 = e14) & ~ (e23 = e13) & ~ (e23 = e12) & ~ (e23 = e10) & ~ (e23 = e11) & ~ (e22 = e20) & ~ (e22 = e21) & ~ (e22 = e14) & ~ (e22 = e13) & ~ (e22 = e12) & ~ (e22 = e10) & ~ (e22 = e11) & ~ (e20 = e21) & ~ (e20 = e14) & ~ (e20 = e13) & ~ (e20 = e12) & ~ (e20 = e10) & ~ (e20 = e11) & ~ (e21 = e14) & ~ (e21 = e13) & ~ (e21 = e12) & ~ (e21 = e10) & ~ (e21 = e11) & ~ (e14 = e13) & ~ (e14 = e12) & ~ (e14 = e10) & ~ (e14 = e11) & ~ (e13 = e12) & ~ (e13 = e10) & ~ (e13 = e11) & ~ (e12 = e10) & ~ (e12 = e11) & ~ (e10 = e11) & op2(all_0_5_5, all_0_5_5) = all_0_7_7 & op2(all_0_5_5, all_0_6_6) = all_0_8_8 & op2(all_0_5_5, all_0_7_7) = all_0_9_9 & op2(all_0_5_5, all_0_8_8) = all_0_6_6 & op2(all_0_5_5, all_0_9_9) = all_0_5_5 & op2(all_0_6_6, all_0_5_5) = all_0_9_9 & op2(all_0_6_6, all_0_6_6) = all_0_5_5 & op2(all_0_6_6, all_0_7_7) = all_0_8_8 & op2(all_0_6_6, all_0_8_8) = all_0_7_7 & op2(all_0_6_6, all_0_9_9) = all_0_6_6 & op2(all_0_7_7, all_0_5_5) = all_0_8_8 & op2(all_0_7_7, all_0_6_6) = all_0_9_9 & op2(all_0_7_7, all_0_7_7) = all_0_6_6 & op2(all_0_7_7, all_0_8_8) = all_0_5_5 & op2(all_0_7_7, all_0_9_9) = all_0_7_7 & op2(all_0_8_8, all_0_5_5) = all_0_6_6 & op2(all_0_8_8, all_0_6_6) = all_0_7_7 & op2(all_0_8_8, all_0_7_7) = all_0_5_5 & op2(all_0_8_8, all_0_8_8) = all_0_9_9 & op2(all_0_8_8, all_0_9_9) = all_0_8_8 & op2(all_0_9_9, all_0_5_5) = all_0_5_5 & op2(all_0_9_9, all_0_6_6) = all_0_6_6 & op2(all_0_9_9, all_0_7_7) = all_0_7_7 & op2(all_0_9_9, all_0_8_8) = all_0_8_8 & op2(all_0_9_9, all_0_9_9) = all_0_9_9 & op2(e24, e24) = e21 & op2(e24, e23) = e22 & op2(e24, e22) = e20 & op2(e24, e20) = e24 & op2(e24, e21) = e23 & op2(e23, e24) = e22 & op2(e23, e23) = e21 & op2(e23, e22) = e24 & op2(e23, e20) = e23 & op2(e23, e21) = e20 & op2(e22, e24) = e23 & op2(e22, e23) = e20 & op2(e22, e22) = e21 & op2(e22, e20) = e22 & op2(e22, e21) = e24 & op2(e20, e24) = e24 & op2(e20, e23) = e23 & op2(e20, e22) = e22 & op2(e20, e20) = e20 & op2(e20, e21) = e21 & op2(e21, e24) = e20 & op2(e21, e23) = e24 & op2(e21, e22) = e23 & op2(e21, e20) = e21 & op2(e21, e21) = e22 & op1(all_0_0_0, all_0_0_0) = all_0_3_3 & op1(all_0_0_0, all_0_1_1) = all_0_2_2 & op1(all_0_0_0, all_0_2_2) = all_0_4_4 & op1(all_0_0_0, all_0_3_3) = all_0_1_1 & op1(all_0_0_0, all_0_4_4) = all_0_0_0 & op1(all_0_1_1, all_0_0_0) = all_0_2_2 & op1(all_0_1_1, all_0_1_1) = all_0_3_3 & op1(all_0_1_1, all_0_2_2) = all_0_0_0 & op1(all_0_1_1, all_0_3_3) = all_0_4_4 & 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_4_4 & op1(all_0_2_2, all_0_2_2) = all_0_3_3 & op1(all_0_2_2, all_0_3_3) = all_0_0_0 & op1(all_0_2_2, all_0_4_4) = all_0_2_2 & op1(all_0_3_3, all_0_0_0) = all_0_4_4 & op1(all_0_3_3, all_0_1_1) = all_0_0_0 & op1(all_0_3_3, all_0_2_2) = all_0_1_1 & op1(all_0_3_3, all_0_3_3) = all_0_2_2 & op1(all_0_3_3, all_0_4_4) = all_0_3_3 & op1(all_0_4_4, all_0_0_0) = all_0_0_0 & op1(all_0_4_4, all_0_1_1) = all_0_1_1 & op1(all_0_4_4, all_0_2_2) = all_0_2_2 & op1(all_0_4_4, all_0_3_3) = all_0_3_3 & op1(all_0_4_4, all_0_4_4) = all_0_4_4 & op1(e14, e14) = e12 & op1(e14, e13) = e11 & op1(e14, e12) = e10 & op1(e14, e10) = e14 & op1(e14, e11) = e13 & op1(e13, e14) = e10 & op1(e13, e13) = e14 & op1(e13, e12) = e11 & op1(e13, e10) = e13 & op1(e13, e11) = e12 & op1(e12, e14) = e11 & op1(e12, e13) = e10 & op1(e12, e12) = e13 & op1(e12, e10) = e12 & op1(e12, e11) = e14 & op1(e10, e14) = e14 & op1(e10, e13) = e13 & op1(e10, e12) = e12 & op1(e10, e10) = e10 & op1(e10, e11) = e11 & op1(e11, e14) = e13 & op1(e11, e13) = e12 & op1(e11, e12) = e14 & op1(e11, e10) = e11 & op1(e11, e11) = e10 & h(all_0_0_0) = e24 & h(all_0_1_1) = e23 & h(all_0_2_2) = e22 & h(all_0_3_3) = e21 & h(all_0_4_4) = e20 & h(e14) = all_0_5_5 & h(e13) = all_0_6_6 & h(e12) = all_0_7_7 & h(e10) = all_0_9_9 & h(e11) = all_0_8_8 & j(all_0_5_5) = e14 & j(all_0_6_6) = e13 & j(all_0_7_7) = e12 & j(all_0_8_8) = e11 & j(all_0_9_9) = e10 & j(e24) = all_0_0_0 & j(e23) = all_0_1_1 & j(e22) = all_0_2_2 & j(e20) = all_0_4_4 & j(e21) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0)) & (all_0_0_0 = e14 | all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11) & (all_0_1_1 = e14 | all_0_1_1 = e13 | all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11) & (all_0_2_2 = e14 | all_0_2_2 = e13 | all_0_2_2 = e12 | all_0_2_2 = e10 | all_0_2_2 = e11) & (all_0_3_3 = e14 | all_0_3_3 = e13 | all_0_3_3 = e12 | all_0_3_3 = e10 | all_0_3_3 = e11) & (all_0_4_4 = e14 | all_0_4_4 = e13 | all_0_4_4 = e12 | all_0_4_4 = e10 | all_0_4_4 = e11) & (all_0_5_5 = e24 | all_0_5_5 = e23 | all_0_5_5 = e22 | all_0_5_5 = e20 | all_0_5_5 = e21) & (all_0_6_6 = e24 | all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21) & (all_0_7_7 = e24 | all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21) & (all_0_8_8 = e24 | all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21) & (all_0_9_9 = e24 | all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21)
% 7.78/2.37 |
% 7.78/2.37 | Applying alpha-rule on (1) yields:
% 7.78/2.37 | (2) op2(all_0_8_8, all_0_8_8) = all_0_9_9
% 7.78/2.37 | (3) ~ (e21 = e12)
% 7.78/2.37 | (4) op1(all_0_4_4, all_0_1_1) = all_0_1_1
% 7.78/2.37 | (5) ~ (e20 = e21)
% 7.78/2.37 | (6) ~ (e20 = e14)
% 7.78/2.37 | (7) op1(e12, e12) = e13
% 7.78/2.37 | (8) op2(e20, e23) = e23
% 7.78/2.37 | (9) op1(all_0_4_4, all_0_2_2) = all_0_2_2
% 7.78/2.37 | (10) ~ (e24 = e11)
% 7.78/2.37 | (11) op1(e11, e11) = e10
% 7.78/2.37 | (12) ~ (e12 = e11)
% 7.78/2.37 | (13) h(e12) = all_0_7_7
% 7.78/2.37 | (14) h(all_0_0_0) = e24
% 7.78/2.37 | (15) h(e13) = all_0_6_6
% 7.78/2.37 | (16) op2(all_0_5_5, all_0_8_8) = all_0_6_6
% 7.78/2.37 | (17) ~ (e14 = e12)
% 7.78/2.37 | (18) ~ (e24 = e12)
% 7.78/2.37 | (19) op1(all_0_0_0, all_0_0_0) = all_0_3_3
% 7.78/2.37 | (20) op1(e10, e11) = e11
% 7.78/2.37 | (21) j(e22) = all_0_2_2
% 7.78/2.37 | (22) op1(e12, e11) = e14
% 7.78/2.37 | (23) op2(all_0_9_9, all_0_8_8) = all_0_8_8
% 7.78/2.37 | (24) j(e21) = all_0_3_3
% 7.78/2.37 | (25) j(all_0_8_8) = e11
% 7.78/2.37 | (26) ~ (e22 = e13)
% 7.78/2.37 | (27) op2(all_0_6_6, all_0_9_9) = all_0_6_6
% 7.78/2.37 | (28) op2(all_0_8_8, all_0_6_6) = all_0_7_7
% 7.78/2.37 | (29) op1(e12, e14) = e11
% 7.78/2.37 | (30) op2(e24, e21) = e23
% 7.78/2.37 | (31) op1(all_0_3_3, all_0_4_4) = all_0_3_3
% 7.78/2.37 | (32) j(all_0_6_6) = e13
% 7.78/2.37 | (33) h(all_0_4_4) = e20
% 7.78/2.37 | (34) op1(all_0_2_2, all_0_0_0) = all_0_1_1
% 7.78/2.37 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0))
% 7.78/2.37 | (36) op2(all_0_5_5, all_0_5_5) = all_0_7_7
% 7.78/2.37 | (37) op1(e14, e14) = e12
% 7.78/2.37 | (38) op2(e21, e22) = e23
% 7.78/2.37 | (39) ~ (e23 = e13)
% 7.78/2.37 | (40) op1(all_0_0_0, all_0_4_4) = all_0_0_0
% 7.78/2.37 | (41) op2(all_0_9_9, all_0_6_6) = all_0_6_6
% 7.78/2.37 | (42) op2(e24, e22) = e20
% 7.78/2.37 | (43) op2(e22, e20) = e22
% 7.78/2.37 | (44) 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
% 7.78/2.37 | (45) op1(e14, e12) = e10
% 7.78/2.37 | (46) ~ (e23 = e12)
% 7.78/2.37 | (47) op1(e11, e10) = e11
% 7.78/2.37 | (48) op2(e21, e21) = e22
% 7.78/2.37 | (49) ~ (e24 = e14)
% 7.78/2.37 | (50) h(all_0_3_3) = e21
% 7.78/2.37 | (51) ~ (e23 = e21)
% 7.78/2.37 | (52) op1(e13, e11) = e12
% 7.78/2.37 | (53) 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
% 7.78/2.37 | (54) ~ (e22 = e21)
% 7.78/2.37 | (55) ~ (e20 = e11)
% 7.78/2.37 | (56) j(all_0_9_9) = e10
% 7.78/2.37 | (57) op1(all_0_3_3, all_0_3_3) = all_0_2_2
% 7.78/2.37 | (58) op1(all_0_2_2, all_0_2_2) = all_0_3_3
% 7.78/2.37 | (59) ~ (e14 = e10)
% 7.78/2.38 | (60) ~ (e22 = e10)
% 7.78/2.38 | (61) h(all_0_1_1) = e23
% 7.78/2.38 | (62) op2(all_0_9_9, all_0_9_9) = all_0_9_9
% 7.78/2.38 | (63) op2(all_0_9_9, all_0_7_7) = all_0_7_7
% 7.78/2.38 | (64) op1(e12, e10) = e12
% 7.78/2.38 | (65) ~ (e12 = e10)
% 7.78/2.38 | (66) ~ (e24 = e22)
% 7.78/2.38 | (67) op1(all_0_1_1, all_0_4_4) = all_0_1_1
% 7.78/2.38 | (68) op2(e21, e24) = e20
% 7.78/2.38 | (69) op1(all_0_3_3, all_0_0_0) = all_0_4_4
% 7.78/2.38 | (70) 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
% 7.78/2.38 | (71) op2(e20, e24) = e24
% 7.78/2.38 | (72) op2(e22, e21) = e24
% 7.78/2.38 | (73) op2(e20, e20) = e20
% 7.78/2.38 | (74) 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
% 7.78/2.38 | (75) op2(all_0_6_6, all_0_5_5) = all_0_9_9
% 7.78/2.38 | (76) op1(all_0_1_1, all_0_0_0) = all_0_2_2
% 7.78/2.38 | (77) op2(all_0_7_7, all_0_9_9) = all_0_7_7
% 7.78/2.38 | (78) op1(all_0_0_0, all_0_1_1) = all_0_2_2
% 7.78/2.38 | (79) j(all_0_7_7) = e12
% 7.78/2.38 | (80) op2(all_0_8_8, all_0_5_5) = all_0_6_6
% 7.78/2.38 | (81) op2(all_0_5_5, all_0_9_9) = all_0_5_5
% 7.78/2.38 | (82) h(all_0_2_2) = e22
% 7.78/2.38 | (83) ~ (e14 = e13)
% 7.78/2.38 | (84) ~ (e21 = e11)
% 7.78/2.38 | (85) h(e14) = all_0_5_5
% 7.78/2.38 | (86) ~ (e24 = e20)
% 7.78/2.38 | (87) op2(e23, e23) = e21
% 7.78/2.38 | (88) ~ (e13 = e12)
% 7.78/2.38 | (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
% 7.78/2.38 | (90) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0))
% 7.78/2.38 | (91) ~ (e14 = e11)
% 7.78/2.38 | (92) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0))
% 7.78/2.38 | (93) op1(all_0_2_2, all_0_4_4) = all_0_2_2
% 7.78/2.38 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0))
% 7.78/2.38 | (95) 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
% 7.78/2.38 | (96) op1(all_0_1_1, all_0_1_1) = all_0_3_3
% 7.78/2.38 | (97) op2(all_0_6_6, all_0_8_8) = all_0_7_7
% 7.78/2.38 | (98) op1(e13, e10) = e13
% 7.78/2.38 | (99) op2(all_0_6_6, all_0_6_6) = all_0_5_5
% 7.78/2.38 | (100) op1(e10, e10) = e10
% 7.78/2.38 | (101) op1(all_0_0_0, all_0_3_3) = all_0_1_1
% 7.78/2.38 | (102) ~ (e23 = e10)
% 7.78/2.38 | (103) op2(all_0_7_7, all_0_6_6) = all_0_9_9
% 7.78/2.38 | (104) op1(all_0_4_4, all_0_4_4) = all_0_4_4
% 7.78/2.38 | (105) op1(all_0_1_1, all_0_3_3) = all_0_4_4
% 7.78/2.38 | (106) ~ (e13 = e10)
% 7.78/2.38 | (107) op1(e10, e12) = e12
% 7.78/2.38 | (108) 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
% 7.78/2.38 | (109) 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
% 7.78/2.38 | (110) ~ (e23 = e22)
% 7.78/2.38 | (111) ~ (e20 = e10)
% 7.78/2.38 | (112) ~ (e22 = e11)
% 7.78/2.38 | (113) op2(e22, e23) = e20
% 7.78/2.39 | (114) op1(e13, e14) = e10
% 7.78/2.39 | (115) ~ (e20 = e12)
% 7.78/2.39 | (116) op2(e24, e24) = e21
% 7.78/2.39 | (117) op2(all_0_7_7, all_0_5_5) = all_0_8_8
% 7.78/2.39 | (118) op1(all_0_0_0, all_0_2_2) = all_0_4_4
% 7.78/2.39 | (119) op2(e23, e22) = e24
% 7.78/2.39 | (120) op1(e14, e11) = e13
% 7.78/2.39 | (121) op2(e24, e20) = e24
% 7.78/2.39 | (122) op1(all_0_4_4, all_0_0_0) = all_0_0_0
% 7.78/2.39 | (123) 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
% 7.78/2.39 | (124) ~ (e10 = e11)
% 7.78/2.39 | (125) op1(all_0_3_3, all_0_2_2) = all_0_1_1
% 7.78/2.39 | (126) op2(all_0_6_6, all_0_7_7) = all_0_8_8
% 7.78/2.39 | (127) ~ (e23 = e14)
% 7.78/2.39 | (128) h(e11) = all_0_8_8
% 7.78/2.39 | (129) op1(e10, e13) = e13
% 7.78/2.39 | (130) op1(e12, e13) = e10
% 7.78/2.39 | (131) op2(all_0_7_7, all_0_8_8) = all_0_5_5
% 7.78/2.39 | (132) op1(e11, e12) = e14
% 7.78/2.39 | (133) op1(e14, e10) = e14
% 7.78/2.39 | (134) op2(e23, e24) = e22
% 7.78/2.39 | (135) j(e23) = all_0_1_1
% 7.78/2.39 | (136) ~ (e23 = e20)
% 7.78/2.39 | (137) op2(e21, e20) = e21
% 7.78/2.39 | (138) ~ (e21 = e14)
% 7.78/2.39 | (139) j(e24) = all_0_0_0
% 7.78/2.39 | (140) op1(all_0_3_3, all_0_1_1) = all_0_0_0
% 7.78/2.39 | (141) op1(e10, e14) = e14
% 7.78/2.39 | (142) op1(all_0_2_2, all_0_1_1) = all_0_4_4
% 7.78/2.39 | (143) ~ (e24 = e21)
% 7.78/2.39 | (144) op1(e11, e14) = e13
% 7.78/2.39 | (145) op2(e23, e21) = e20
% 7.78/2.39 | (146) op2(all_0_8_8, all_0_9_9) = all_0_8_8
% 7.78/2.39 | (147) j(all_0_5_5) = e14
% 7.78/2.39 | (148) op2(all_0_5_5, all_0_7_7) = all_0_9_9
% 7.78/2.39 | (149) op2(e23, e20) = e23
% 7.78/2.39 | (150) op1(all_0_1_1, all_0_2_2) = all_0_0_0
% 7.78/2.39 | (151) ~ (e22 = e20)
% 7.78/2.39 | (152) ~ (e23 = e11)
% 7.78/2.39 | (153) op2(all_0_7_7, all_0_7_7) = all_0_6_6
% 7.78/2.39 | (154) op2(e21, e23) = e24
% 7.78/2.39 | (155) op2(all_0_8_8, all_0_7_7) = all_0_5_5
% 7.78/2.39 | (156) op1(all_0_2_2, all_0_3_3) = all_0_0_0
% 7.78/2.39 | (157) op1(e14, e13) = e11
% 7.78/2.39 | (158) ~ (e24 = e10)
% 7.78/2.39 | (159) ~ (e24 = e23)
% 7.78/2.39 | (160) op1(e11, e13) = e12
% 7.78/2.40 | (161) ~ (e20 = e13)
% 7.78/2.40 | (162) ~ (e24 = e13)
% 7.78/2.40 | (163) op1(all_0_4_4, all_0_3_3) = all_0_3_3
% 7.78/2.40 | (164) ~ (e21 = e10)
% 7.78/2.40 | (165) op1(e13, e13) = e14
% 7.78/2.40 | (166) ~ (e21 = e13)
% 7.78/2.40 | (167) j(e20) = all_0_4_4
% 7.78/2.40 | (168) ~ (e22 = e12)
% 7.78/2.40 | (169) op2(e24, e23) = e22
% 7.78/2.40 | (170) op2(e20, e22) = e22
% 7.78/2.40 | (171) all_0_3_3 = e14 | all_0_3_3 = e13 | all_0_3_3 = e12 | all_0_3_3 = e10 | all_0_3_3 = e11
% 7.78/2.40 | (172) op2(e22, e24) = e23
% 7.78/2.40 | (173) h(e10) = all_0_9_9
% 7.78/2.40 | (174) op2(all_0_5_5, all_0_6_6) = all_0_8_8
% 7.78/2.40 | (175) op2(e22, e22) = e21
% 7.78/2.40 | (176) ~ (e22 = e14)
% 7.78/2.40 | (177) op2(e20, e21) = e21
% 7.78/2.40 | (178) op2(all_0_9_9, all_0_5_5) = all_0_5_5
% 7.78/2.40 | (179) ~ (e13 = e11)
% 8.07/2.40 | (180) op1(e13, e12) = e11
% 8.07/2.40 |
% 8.07/2.40 +-Applying beta-rule and splitting (109), into two cases.
% 8.07/2.40 |-Branch one:
% 8.07/2.40 | (181) all_0_0_0 = e14
% 8.07/2.40 |
% 8.07/2.40 | From (181)(181) and (19) follows:
% 8.07/2.40 | (182) op1(e14, e14) = all_0_3_3
% 8.07/2.40 |
% 8.07/2.40 | From (181) and (101) follows:
% 8.07/2.40 | (183) op1(e14, all_0_3_3) = all_0_1_1
% 8.07/2.40 |
% 8.07/2.40 | From (181) and (156) follows:
% 8.07/2.40 | (184) op1(all_0_2_2, all_0_3_3) = e14
% 8.07/2.40 |
% 8.07/2.40 | From (181) and (69) follows:
% 8.07/2.40 | (185) op1(all_0_3_3, e14) = all_0_4_4
% 8.07/2.40 |
% 8.07/2.40 | From (181)(181) and (122) follows:
% 8.07/2.40 | (186) op1(all_0_4_4, e14) = e14
% 8.07/2.40 |
% 8.07/2.40 | Instantiating formula (94) with e14, e14, all_0_3_3, e12 and discharging atoms op1(e14, e14) = all_0_3_3, op1(e14, e14) = e12, yields:
% 8.07/2.40 | (187) all_0_3_3 = e12
% 8.07/2.40 |
% 8.07/2.40 | From (187) and (96) follows:
% 8.07/2.40 | (188) op1(all_0_1_1, all_0_1_1) = e12
% 8.07/2.40 |
% 8.07/2.40 | From (187) and (184) follows:
% 8.07/2.40 | (189) op1(all_0_2_2, e12) = e14
% 8.07/2.40 |
% 8.07/2.40 | From (187)(187) and (57) follows:
% 8.07/2.40 | (190) op1(e12, e12) = all_0_2_2
% 8.07/2.40 |
% 8.07/2.40 | From (187) and (185) follows:
% 8.07/2.40 | (191) op1(e12, e14) = all_0_4_4
% 8.07/2.40 |
% 8.07/2.40 | From (187) and (183) follows:
% 8.07/2.40 | (192) op1(e14, e12) = all_0_1_1
% 8.07/2.40 |
% 8.07/2.40 | Instantiating formula (94) with e14, e12, all_0_1_1, e10 and discharging atoms op1(e14, e12) = all_0_1_1, op1(e14, e12) = e10, yields:
% 8.07/2.40 | (193) all_0_1_1 = e10
% 8.07/2.40 |
% 8.07/2.40 | Instantiating formula (94) with e12, e14, all_0_4_4, e11 and discharging atoms op1(e12, e14) = all_0_4_4, op1(e12, e14) = e11, yields:
% 8.07/2.40 | (194) all_0_4_4 = e11
% 8.07/2.40 |
% 8.07/2.40 | Instantiating formula (94) with e12, e12, all_0_2_2, e13 and discharging atoms op1(e12, e12) = all_0_2_2, op1(e12, e12) = e13, yields:
% 8.07/2.41 | (195) all_0_2_2 = e13
% 8.07/2.41 |
% 8.07/2.41 | From (193)(193) and (188) follows:
% 8.07/2.41 | (196) op1(e10, e10) = e12
% 8.07/2.41 |
% 8.07/2.41 | From (195) and (189) follows:
% 8.07/2.41 | (197) op1(e13, e12) = e14
% 8.07/2.41 |
% 8.07/2.41 | From (194)(195)(195) and (9) follows:
% 8.07/2.41 | (198) op1(e11, e13) = e13
% 8.07/2.41 |
% 8.07/2.41 | From (194) and (186) follows:
% 8.07/2.41 | (199) op1(e11, e14) = e14
% 8.07/2.41 |
% 8.07/2.41 | Instantiating formula (94) with e13, e12, e14, e11 and discharging atoms op1(e13, e12) = e14, op1(e13, e12) = e11, yields:
% 8.07/2.41 | (200) e14 = e11
% 8.07/2.41 |
% 8.07/2.41 | Instantiating formula (94) with e10, e10, e12, e10 and discharging atoms op1(e10, e10) = e12, op1(e10, e10) = e10, yields:
% 8.07/2.41 | (201) e12 = e10
% 8.07/2.41 |
% 8.07/2.41 | Instantiating formula (94) with e11, e14, e14, e13 and discharging atoms op1(e11, e14) = e14, op1(e11, e14) = e13, yields:
% 8.07/2.41 | (202) e14 = e13
% 8.07/2.41 |
% 8.07/2.41 | Instantiating formula (94) with e11, e13, e13, e12 and discharging atoms op1(e11, e13) = e13, op1(e11, e13) = e12, yields:
% 8.07/2.41 | (203) e13 = e12
% 8.07/2.41 |
% 8.07/2.41 | Combining equations (202,200) yields a new equation:
% 8.07/2.41 | (204) e13 = e11
% 8.07/2.41 |
% 8.07/2.41 | Simplifying 204 yields:
% 8.07/2.41 | (205) e13 = e11
% 8.07/2.41 |
% 8.07/2.41 | Combining equations (203,205) yields a new equation:
% 8.07/2.41 | (206) e12 = e11
% 8.07/2.41 |
% 8.07/2.41 | Simplifying 206 yields:
% 8.07/2.41 | (207) e12 = e11
% 8.07/2.41 |
% 8.07/2.41 | Combining equations (207,201) yields a new equation:
% 8.07/2.41 | (208) e10 = e11
% 8.07/2.41 |
% 8.07/2.41 | Equations (208) can reduce 124 to:
% 8.07/2.41 | (209) $false
% 8.07/2.41 |
% 8.07/2.41 |-The branch is then unsatisfiable
% 8.07/2.41 |-Branch two:
% 8.07/2.41 | (210) ~ (all_0_0_0 = e14)
% 8.07/2.41 | (211) all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 8.07/2.41 |
% 8.07/2.41 +-Applying beta-rule and splitting (70), into two cases.
% 8.07/2.41 |-Branch one:
% 8.07/2.41 | (212) all_0_9_9 = e24
% 8.07/2.41 |
% 8.07/2.41 | From (212)(212)(212) and (62) follows:
% 8.07/2.41 | (213) op2(e24, e24) = e24
% 8.07/2.41 |
% 8.07/2.41 | Instantiating formula (35) with e24, e24, e24, e21 and discharging atoms op2(e24, e24) = e24, op2(e24, e24) = e21, yields:
% 8.07/2.41 | (214) e24 = e21
% 8.07/2.41 |
% 8.07/2.41 | Equations (214) can reduce 143 to:
% 8.07/2.41 | (209) $false
% 8.07/2.41 |
% 8.07/2.41 |-The branch is then unsatisfiable
% 8.07/2.41 |-Branch two:
% 8.07/2.41 | (216) ~ (all_0_9_9 = e24)
% 8.07/2.41 | (217) all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21
% 8.07/2.41 |
% 8.07/2.41 +-Applying beta-rule and splitting (89), into two cases.
% 8.07/2.41 |-Branch one:
% 8.07/2.41 | (218) all_0_7_7 = e24
% 8.07/2.41 |
% 8.07/2.41 | From (218) and (126) follows:
% 8.07/2.41 | (219) op2(all_0_6_6, e24) = all_0_8_8
% 8.07/2.41 |
% 8.07/2.41 | From (218) and (97) follows:
% 8.07/2.41 | (220) op2(all_0_6_6, all_0_8_8) = e24
% 8.07/2.41 |
% 8.07/2.41 | From (218)(218) and (153) follows:
% 8.07/2.41 | (221) op2(e24, e24) = all_0_6_6
% 8.07/2.41 |
% 8.07/2.41 | From (218) and (155) follows:
% 8.07/2.41 | (222) op2(all_0_8_8, e24) = all_0_5_5
% 8.07/2.41 |
% 8.07/2.41 | Instantiating formula (35) with e24, e24, all_0_6_6, e21 and discharging atoms op2(e24, e24) = all_0_6_6, op2(e24, e24) = e21, yields:
% 8.07/2.41 | (223) all_0_6_6 = e21
% 8.07/2.41 |
% 8.07/2.41 | From (223) and (174) follows:
% 8.07/2.41 | (224) op2(all_0_5_5, e21) = all_0_8_8
% 8.07/2.41 |
% 8.07/2.41 | From (223)(223) and (99) follows:
% 8.07/2.41 | (225) op2(e21, e21) = all_0_5_5
% 8.07/2.41 |
% 8.07/2.41 | From (223) and (220) follows:
% 8.07/2.41 | (226) op2(e21, all_0_8_8) = e24
% 8.07/2.41 |
% 8.07/2.41 | From (223) and (219) follows:
% 8.07/2.41 | (227) op2(e21, e24) = all_0_8_8
% 8.07/2.41 |
% 8.07/2.41 | Instantiating formula (35) with e21, e24, all_0_8_8, e20 and discharging atoms op2(e21, e24) = all_0_8_8, op2(e21, e24) = e20, yields:
% 8.07/2.41 | (228) all_0_8_8 = e20
% 8.07/2.41 |
% 8.07/2.41 | Instantiating formula (35) with e21, e21, all_0_5_5, e22 and discharging atoms op2(e21, e21) = all_0_5_5, op2(e21, e21) = e22, yields:
% 8.07/2.41 | (229) all_0_5_5 = e22
% 8.07/2.41 |
% 8.07/2.41 | From (229)(228) and (224) follows:
% 8.07/2.41 | (230) op2(e22, e21) = e20
% 8.07/2.41 |
% 8.07/2.41 | From (228)(229) and (222) follows:
% 8.07/2.41 | (231) op2(e20, e24) = e22
% 8.07/2.41 |
% 8.07/2.41 | From (228) and (226) follows:
% 8.07/2.41 | (232) op2(e21, e20) = e24
% 8.07/2.41 |
% 8.07/2.41 | Instantiating formula (35) with e22, e21, e20, e24 and discharging atoms op2(e22, e21) = e24, op2(e22, e21) = e20, yields:
% 8.07/2.41 | (233) e24 = e20
% 8.07/2.41 |
% 8.07/2.41 | Instantiating formula (35) with e20, e24, e22, e24 and discharging atoms op2(e20, e24) = e24, op2(e20, e24) = e22, yields:
% 8.07/2.41 | (234) e24 = e22
% 8.07/2.41 |
% 8.07/2.41 | Instantiating formula (35) with e21, e20, e24, e21 and discharging atoms op2(e21, e20) = e24, op2(e21, e20) = e21, yields:
% 8.07/2.41 | (214) e24 = e21
% 8.07/2.41 |
% 8.07/2.41 | Combining equations (214,234) yields a new equation:
% 8.07/2.41 | (236) e22 = e21
% 8.07/2.41 |
% 8.07/2.41 | Combining equations (233,234) yields a new equation:
% 8.07/2.41 | (237) e22 = e20
% 8.07/2.41 |
% 8.07/2.41 | Combining equations (237,236) yields a new equation:
% 8.07/2.41 | (238) e20 = e21
% 8.07/2.41 |
% 8.07/2.41 | Simplifying 238 yields:
% 8.07/2.41 | (239) e20 = e21
% 8.07/2.41 |
% 8.07/2.41 | Equations (239) can reduce 5 to:
% 8.07/2.41 | (209) $false
% 8.07/2.41 |
% 8.07/2.41 |-The branch is then unsatisfiable
% 8.07/2.41 |-Branch two:
% 8.07/2.41 | (241) ~ (all_0_7_7 = e24)
% 8.07/2.41 | (242) all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 8.07/2.41 |
% 8.07/2.41 +-Applying beta-rule and splitting (108), into two cases.
% 8.07/2.41 |-Branch one:
% 8.07/2.41 | (243) all_0_6_6 = e24
% 8.07/2.41 |
% 8.07/2.41 | From (243) and (174) follows:
% 8.07/2.41 | (244) op2(all_0_5_5, e24) = all_0_8_8
% 8.07/2.41 |
% 8.07/2.41 | From (243) and (16) follows:
% 8.07/2.41 | (245) op2(all_0_5_5, all_0_8_8) = e24
% 8.07/2.41 |
% 8.07/2.41 | From (243)(243) and (99) follows:
% 8.07/2.41 | (246) op2(e24, e24) = all_0_5_5
% 8.07/2.42 |
% 8.07/2.42 | From (243) and (28) follows:
% 8.07/2.42 | (247) op2(all_0_8_8, e24) = all_0_7_7
% 8.07/2.42 |
% 8.07/2.42 | Instantiating formula (35) with e24, e24, all_0_5_5, e21 and discharging atoms op2(e24, e24) = all_0_5_5, op2(e24, e24) = e21, yields:
% 8.07/2.42 | (248) all_0_5_5 = e21
% 8.07/2.42 |
% 8.07/2.42 | From (248)(248) and (36) follows:
% 8.07/2.42 | (249) op2(e21, e21) = all_0_7_7
% 8.07/2.42 |
% 8.07/2.42 | From (248) and (245) follows:
% 8.07/2.42 | (226) op2(e21, all_0_8_8) = e24
% 8.07/2.42 |
% 8.07/2.42 | From (248) and (244) follows:
% 8.07/2.42 | (227) op2(e21, e24) = all_0_8_8
% 8.07/2.42 |
% 8.07/2.42 | From (248) and (117) follows:
% 8.07/2.42 | (252) op2(all_0_7_7, e21) = all_0_8_8
% 8.07/2.42 |
% 8.07/2.42 | Instantiating formula (35) with e21, e24, all_0_8_8, e20 and discharging atoms op2(e21, e24) = all_0_8_8, op2(e21, e24) = e20, yields:
% 8.07/2.42 | (228) all_0_8_8 = e20
% 8.07/2.42 |
% 8.07/2.42 | Instantiating formula (35) with e21, e21, all_0_7_7, e22 and discharging atoms op2(e21, e21) = all_0_7_7, op2(e21, e21) = e22, yields:
% 8.07/2.42 | (254) all_0_7_7 = e22
% 8.07/2.42 |
% 8.07/2.42 | From (254)(228) and (252) follows:
% 8.07/2.42 | (230) op2(e22, e21) = e20
% 8.07/2.42 |
% 8.07/2.42 | From (228)(254) and (247) follows:
% 8.07/2.42 | (231) op2(e20, e24) = e22
% 8.07/2.42 |
% 8.07/2.42 | From (228) and (226) follows:
% 8.07/2.42 | (232) op2(e21, e20) = e24
% 8.07/2.42 |
% 8.07/2.42 | Instantiating formula (35) with e22, e21, e20, e24 and discharging atoms op2(e22, e21) = e24, op2(e22, e21) = e20, yields:
% 8.07/2.42 | (233) e24 = e20
% 8.07/2.42 |
% 8.07/2.42 | Instantiating formula (35) with e20, e24, e22, e24 and discharging atoms op2(e20, e24) = e24, op2(e20, e24) = e22, yields:
% 8.07/2.42 | (234) e24 = e22
% 8.07/2.42 |
% 8.07/2.42 | Instantiating formula (35) with e21, e20, e24, e21 and discharging atoms op2(e21, e20) = e24, op2(e21, e20) = e21, yields:
% 8.07/2.42 | (214) e24 = e21
% 8.07/2.42 |
% 8.07/2.42 | Combining equations (214,234) yields a new equation:
% 8.07/2.42 | (236) e22 = e21
% 8.07/2.42 |
% 8.07/2.42 | Combining equations (233,234) yields a new equation:
% 8.07/2.42 | (237) e22 = e20
% 8.07/2.42 |
% 8.07/2.42 | Combining equations (237,236) yields a new equation:
% 8.07/2.42 | (238) e20 = e21
% 8.07/2.42 |
% 8.07/2.42 | Simplifying 238 yields:
% 8.07/2.42 | (239) e20 = e21
% 8.07/2.42 |
% 8.07/2.42 | Equations (239) can reduce 5 to:
% 8.07/2.42 | (209) $false
% 8.07/2.42 |
% 8.07/2.42 |-The branch is then unsatisfiable
% 8.07/2.42 |-Branch two:
% 8.07/2.42 | (266) ~ (all_0_6_6 = e24)
% 8.07/2.42 | (267) all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21
% 8.07/2.42 |
% 8.07/2.42 +-Applying beta-rule and splitting (123), into two cases.
% 8.07/2.42 |-Branch one:
% 8.07/2.42 | (268) all_0_8_8 = e24
% 8.07/2.42 |
% 8.07/2.42 | From (268)(268) and (2) follows:
% 8.07/2.42 | (269) op2(e24, e24) = all_0_9_9
% 8.07/2.42 |
% 8.07/2.42 | Instantiating formula (35) with e24, e24, all_0_9_9, e21 and discharging atoms op2(e24, e24) = all_0_9_9, op2(e24, e24) = e21, yields:
% 8.07/2.42 | (270) all_0_9_9 = e21
% 8.07/2.42 |
% 8.07/2.42 | From (270)(270)(270) and (62) follows:
% 8.07/2.42 | (271) op2(e21, e21) = e21
% 8.07/2.42 |
% 8.07/2.42 | Instantiating formula (35) with e21, e21, e21, e22 and discharging atoms op2(e21, e21) = e22, op2(e21, e21) = e21, yields:
% 8.07/2.42 | (236) e22 = e21
% 8.07/2.42 |
% 8.07/2.42 | Equations (236) can reduce 54 to:
% 8.07/2.42 | (209) $false
% 8.07/2.42 |
% 8.07/2.42 |-The branch is then unsatisfiable
% 8.07/2.42 |-Branch two:
% 8.07/2.42 | (274) ~ (all_0_8_8 = e24)
% 8.07/2.42 | (275) all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 8.07/2.42 |
% 8.07/2.42 +-Applying beta-rule and splitting (211), into two cases.
% 8.07/2.42 |-Branch one:
% 8.07/2.42 | (276) all_0_0_0 = e13
% 8.07/2.42 |
% 8.07/2.42 | From (276) and (14) follows:
% 8.07/2.42 | (277) h(e13) = e24
% 8.07/2.42 |
% 8.07/2.42 | Instantiating formula (90) with e13, e24, all_0_6_6 and discharging atoms h(e13) = all_0_6_6, h(e13) = e24, yields:
% 8.07/2.42 | (243) all_0_6_6 = e24
% 8.07/2.42 |
% 8.07/2.42 | Equations (243) can reduce 266 to:
% 8.07/2.42 | (209) $false
% 8.07/2.42 |
% 8.07/2.42 |-The branch is then unsatisfiable
% 8.07/2.42 |-Branch two:
% 8.07/2.42 | (280) ~ (all_0_0_0 = e13)
% 8.07/2.42 | (281) all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 8.07/2.42 |
% 8.07/2.42 +-Applying beta-rule and splitting (281), into two cases.
% 8.07/2.42 |-Branch one:
% 8.07/2.42 | (282) all_0_0_0 = e12
% 8.07/2.42 |
% 8.07/2.42 | From (282) and (14) follows:
% 8.07/2.42 | (283) h(e12) = e24
% 8.07/2.42 |
% 8.07/2.42 | Instantiating formula (90) with e12, e24, all_0_7_7 and discharging atoms h(e12) = all_0_7_7, h(e12) = e24, yields:
% 8.07/2.42 | (218) all_0_7_7 = e24
% 8.07/2.42 |
% 8.07/2.42 | Equations (218) can reduce 241 to:
% 8.07/2.42 | (209) $false
% 8.07/2.42 |
% 8.07/2.42 |-The branch is then unsatisfiable
% 8.07/2.42 |-Branch two:
% 8.07/2.42 | (286) ~ (all_0_0_0 = e12)
% 8.07/2.42 | (287) all_0_0_0 = e10 | all_0_0_0 = e11
% 8.07/2.42 |
% 8.07/2.42 +-Applying beta-rule and splitting (287), into two cases.
% 8.07/2.42 |-Branch one:
% 8.07/2.42 | (288) all_0_0_0 = e10
% 8.07/2.42 |
% 8.07/2.42 | From (288) and (14) follows:
% 8.07/2.42 | (289) h(e10) = e24
% 8.07/2.42 |
% 8.07/2.42 | Instantiating formula (90) with e10, e24, all_0_9_9 and discharging atoms h(e10) = all_0_9_9, h(e10) = e24, yields:
% 8.07/2.42 | (212) all_0_9_9 = e24
% 8.07/2.42 |
% 8.07/2.42 | Equations (212) can reduce 216 to:
% 8.07/2.42 | (209) $false
% 8.07/2.42 |
% 8.07/2.42 |-The branch is then unsatisfiable
% 8.07/2.42 |-Branch two:
% 8.07/2.42 | (292) ~ (all_0_0_0 = e10)
% 8.07/2.42 | (293) all_0_0_0 = e11
% 8.07/2.42 |
% 8.07/2.42 | From (293) and (14) follows:
% 8.07/2.42 | (294) h(e11) = e24
% 8.07/2.42 |
% 8.07/2.42 | Instantiating formula (90) with e11, e24, all_0_8_8 and discharging atoms h(e11) = all_0_8_8, h(e11) = e24, yields:
% 8.07/2.42 | (268) all_0_8_8 = e24
% 8.07/2.42 |
% 8.07/2.42 | Equations (268) can reduce 274 to:
% 8.07/2.42 | (209) $false
% 8.07/2.42 |
% 8.07/2.42 |-The branch is then unsatisfiable
% 8.07/2.42 % SZS output end Proof for theBenchmark
% 8.07/2.42
% 8.07/2.42 1838ms
%------------------------------------------------------------------------------