TSTP Solution File: ALG182+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG182+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.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 15:37:06 EDT 2022
% Result : Theorem 6.06s 2.05s
% Output : Proof 12.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : ALG182+1 : TPTP v8.1.0. Released v2.7.0.
% 0.00/0.09 % Command : ePrincess-casc -timeout=%d %s
% 0.08/0.28 % Computer : n025.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Wed Jun 8 02:00:49 EDT 2022
% 0.12/0.28 % CPUTime :
% 0.12/0.51 ____ _
% 0.12/0.51 ___ / __ \_____(_)___ ________ __________
% 0.12/0.51 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.12/0.51 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.12/0.51 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.12/0.51
% 0.12/0.51 A Theorem Prover for First-Order Logic
% 0.12/0.51 (ePrincess v.1.0)
% 0.12/0.51
% 0.12/0.51 (c) Philipp Rümmer, 2009-2015
% 0.12/0.51 (c) Peter Backeman, 2014-2015
% 0.12/0.51 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.12/0.51 Free software under GNU Lesser General Public License (LGPL).
% 0.12/0.51 Bug reports to peter@backeman.se
% 0.12/0.51
% 0.12/0.51 For more information, visit http://user.uu.se/~petba168/breu/
% 0.12/0.51
% 0.12/0.52 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.12/0.57 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.74/0.99 Prover 0: Preprocessing ...
% 3.29/1.39 Prover 0: Constructing countermodel ...
% 6.06/2.05 Prover 0: proved (1475ms)
% 6.06/2.05
% 6.06/2.05 No countermodel exists, formula is valid
% 6.06/2.05 % SZS status Theorem for theBenchmark
% 6.06/2.05
% 6.06/2.05 Generating proof ... found it (size 65)
% 11.71/3.38
% 11.71/3.38 % SZS output start Proof for theBenchmark
% 11.71/3.38 Assumed formulas after preprocessing and simplification:
% 11.71/3.38 | (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) = v1 & op2(v4, v3) = v3 & op2(v4, v2) = v4 & op2(v4, v1) = v0 & op2(v4, v0) = v2 & op2(v3, v4) = v2 & op2(v3, v3) = v0 & op2(v3, v2) = v3 & op2(v3, v1) = v1 & op2(v3, v0) = v4 & op2(v2, v4) = v0 & op2(v2, v3) = v4 & op2(v2, v2) = v2 & op2(v2, v1) = v3 & op2(v2, v0) = v1 & op2(v1, v4) = v3 & op2(v1, v3) = v2 & op2(v1, v2) = v1 & op2(v1, v1) = v4 & op2(v1, v0) = v0 & op2(v0, v4) = v4 & op2(v0, v3) = v1 & op2(v0, v2) = v0 & op2(v0, v1) = v2 & op2(v0, v0) = v3 & op2(e24, e24) = e24 & op2(e24, e23) = e21 & op2(e24, e22) = e20 & op2(e24, e20) = e23 & op2(e24, e21) = e22 & op2(e23, e24) = e22 & op2(e23, e23) = e23 & op2(e23, e22) = e21 & op2(e23, e20) = e24 & op2(e23, e21) = e20 & op2(e22, e24) = e23 & op2(e22, e23) = e20 & op2(e22, e22) = e22 & op2(e22, e20) = e21 & op2(e22, e21) = e24 & op2(e20, e24) = e21 & op2(e20, e23) = e22 & op2(e20, e22) = e24 & op2(e20, e20) = e20 & op2(e20, e21) = e23 & op2(e21, e24) = e20 & op2(e21, e23) = e24 & op2(e21, e22) = e23 & op2(e21, e20) = e22 & op2(e21, e21) = e21 & op1(v9, v9) = v9 & op1(v9, v8) = v6 & op1(v9, v7) = v5 & op1(v9, v6) = v7 & op1(v9, v5) = v8 & op1(v8, v9) = v7 & op1(v8, v8) = v8 & op1(v8, v7) = v6 & op1(v8, v6) = v5 & op1(v8, v5) = v9 & op1(v7, v9) = v8 & op1(v7, v8) = v5 & op1(v7, v7) = v7 & op1(v7, v6) = v9 & op1(v7, v5) = v6 & op1(v6, v9) = v5 & op1(v6, v8) = v9 & op1(v6, v7) = v8 & op1(v6, v6) = v6 & op1(v6, v5) = v7 & op1(v5, v9) = v6 & op1(v5, v8) = v7 & op1(v5, v7) = v9 & op1(v5, v6) = v8 & op1(v5, v5) = v5 & op1(e14, e14) = e11 & op1(e14, e13) = e13 & op1(e14, e12) = e14 & op1(e14, e10) = e12 & op1(e14, e11) = e10 & op1(e13, e14) = e12 & op1(e13, e13) = e10 & op1(e13, e12) = e13 & op1(e13, e10) = e14 & op1(e13, e11) = e11 & op1(e12, e14) = e10 & op1(e12, e13) = e14 & op1(e12, e12) = e12 & op1(e12, e10) = e11 & op1(e12, e11) = e13 & op1(e10, e14) = e14 & op1(e10, e13) = e11 & op1(e10, e12) = e10 & op1(e10, e10) = e13 & op1(e10, e11) = e12 & op1(e11, e14) = e13 & op1(e11, e13) = e12 & op1(e11, e12) = e11 & op1(e11, e10) = e10 & op1(e11, e11) = e14 & 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))
% 12.14/3.44 | 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:
% 12.14/3.44 | (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_8_8 & op2(all_0_5_5, all_0_6_6) = all_0_6_6 & op2(all_0_5_5, all_0_7_7) = all_0_5_5 & op2(all_0_5_5, all_0_8_8) = all_0_9_9 & op2(all_0_5_5, all_0_9_9) = all_0_7_7 & op2(all_0_6_6, all_0_5_5) = all_0_7_7 & op2(all_0_6_6, all_0_6_6) = all_0_9_9 & op2(all_0_6_6, all_0_7_7) = all_0_6_6 & op2(all_0_6_6, all_0_8_8) = all_0_8_8 & op2(all_0_6_6, all_0_9_9) = all_0_5_5 & op2(all_0_7_7, all_0_5_5) = all_0_9_9 & op2(all_0_7_7, all_0_6_6) = all_0_5_5 & op2(all_0_7_7, all_0_7_7) = all_0_7_7 & op2(all_0_7_7, all_0_8_8) = all_0_6_6 & op2(all_0_7_7, all_0_9_9) = all_0_8_8 & 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_8_8 & op2(all_0_8_8, all_0_8_8) = all_0_5_5 & op2(all_0_8_8, all_0_9_9) = all_0_9_9 & op2(all_0_9_9, all_0_5_5) = all_0_5_5 & op2(all_0_9_9, all_0_6_6) = all_0_8_8 & op2(all_0_9_9, all_0_7_7) = all_0_9_9 & op2(all_0_9_9, all_0_8_8) = all_0_7_7 & op2(all_0_9_9, all_0_9_9) = all_0_6_6 & op2(e24, e24) = e24 & op2(e24, e23) = e21 & op2(e24, e22) = e20 & op2(e24, e20) = e23 & op2(e24, e21) = e22 & op2(e23, e24) = e22 & op2(e23, e23) = e23 & op2(e23, e22) = e21 & op2(e23, e20) = e24 & op2(e23, e21) = e20 & op2(e22, e24) = e23 & op2(e22, e23) = e20 & op2(e22, e22) = e22 & op2(e22, e20) = e21 & op2(e22, e21) = e24 & op2(e20, e24) = e21 & op2(e20, e23) = e22 & op2(e20, e22) = e24 & op2(e20, e20) = e20 & op2(e20, e21) = e23 & op2(e21, e24) = e20 & op2(e21, e23) = e24 & op2(e21, e22) = e23 & op2(e21, e20) = e22 & op2(e21, e21) = e21 & op1(all_0_0_0, all_0_0_0) = all_0_0_0 & 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_2_2 & op1(all_0_0_0, all_0_4_4) = all_0_1_1 & op1(all_0_1_1, all_0_0_0) = all_0_2_2 & op1(all_0_1_1, all_0_1_1) = all_0_1_1 & op1(all_0_1_1, all_0_2_2) = all_0_3_3 & op1(all_0_1_1, all_0_3_3) = all_0_4_4 & op1(all_0_1_1, all_0_4_4) = all_0_0_0 & 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_2_2 & op1(all_0_2_2, all_0_3_3) = all_0_0_0 & op1(all_0_2_2, all_0_4_4) = all_0_3_3 & 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_3_3 & op1(all_0_3_3, all_0_4_4) = all_0_2_2 & op1(all_0_4_4, all_0_0_0) = all_0_3_3 & op1(all_0_4_4, all_0_1_1) = all_0_2_2 & op1(all_0_4_4, all_0_2_2) = all_0_0_0 & op1(all_0_4_4, all_0_3_3) = all_0_1_1 & op1(all_0_4_4, all_0_4_4) = all_0_4_4 & op1(e14, e14) = e11 & op1(e14, e13) = e13 & op1(e14, e12) = e14 & op1(e14, e10) = e12 & op1(e14, e11) = e10 & op1(e13, e14) = e12 & op1(e13, e13) = e10 & op1(e13, e12) = e13 & op1(e13, e10) = e14 & op1(e13, e11) = e11 & op1(e12, e14) = e10 & op1(e12, e13) = e14 & op1(e12, e12) = e12 & op1(e12, e10) = e11 & op1(e12, e11) = e13 & op1(e10, e14) = e14 & op1(e10, e13) = e11 & op1(e10, e12) = e10 & op1(e10, e10) = e13 & op1(e10, e11) = e12 & op1(e11, e14) = e13 & op1(e11, e13) = e12 & op1(e11, e12) = e11 & op1(e11, e10) = e10 & op1(e11, e11) = e14 & 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)
% 12.14/3.45 |
% 12.14/3.45 | Applying alpha-rule on (1) yields:
% 12.14/3.45 | (2) op2(all_0_5_5, all_0_5_5) = all_0_8_8
% 12.14/3.45 | (3) op2(e22, e20) = e21
% 12.14/3.45 | (4) op1(all_0_2_2, all_0_2_2) = all_0_2_2
% 12.14/3.45 | (5) j(all_0_8_8) = e11
% 12.14/3.45 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0))
% 12.14/3.45 | (7) j(e23) = all_0_1_1
% 12.14/3.45 | (8) ~ (e20 = e13)
% 12.14/3.45 | (9) ~ (e23 = e14)
% 12.14/3.45 | (10) op2(e20, e20) = e20
% 12.14/3.45 | (11) op2(all_0_5_5, all_0_9_9) = all_0_7_7
% 12.14/3.45 | (12) h(all_0_1_1) = e23
% 12.14/3.46 | (13) ~ (e14 = e12)
% 12.14/3.46 | (14) j(e20) = all_0_4_4
% 12.14/3.46 | (15) op2(e22, e22) = e22
% 12.14/3.46 | (16) op1(e12, e10) = e11
% 12.14/3.46 | (17) op1(e11, e12) = e11
% 12.14/3.46 | (18) ~ (e20 = e10)
% 12.14/3.46 | (19) op1(all_0_3_3, all_0_2_2) = all_0_1_1
% 12.14/3.46 | (20) op2(all_0_9_9, all_0_8_8) = all_0_7_7
% 12.14/3.46 | (21) h(all_0_2_2) = e22
% 12.14/3.46 | (22) op1(e14, e13) = e13
% 12.14/3.46 | (23) op1(e13, e14) = e12
% 12.14/3.46 | (24) ~ (e23 = e12)
% 12.14/3.46 | (25) op1(e11, e10) = e10
% 12.14/3.46 | (26) op2(e21, e22) = e23
% 12.14/3.46 | (27) ~ (e24 = e10)
% 12.14/3.46 | (28) op1(all_0_0_0, all_0_2_2) = all_0_4_4
% 12.14/3.46 | (29) h(all_0_4_4) = e20
% 12.14/3.46 | (30) op2(e24, e21) = e22
% 12.14/3.46 | (31) h(all_0_0_0) = e24
% 12.14/3.46 | (32) op1(e11, e11) = e14
% 12.14/3.46 | (33) ~ (e22 = e14)
% 12.14/3.46 | (34) all_0_6_6 = e24 | all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21
% 12.14/3.46 | (35) ~ (e22 = e11)
% 12.14/3.46 | (36) op1(all_0_3_3, all_0_3_3) = all_0_3_3
% 12.14/3.46 | (37) op1(e13, e11) = e11
% 12.14/3.46 | (38) op2(all_0_8_8, all_0_8_8) = all_0_5_5
% 12.14/3.46 | (39) op2(e21, e20) = e22
% 12.14/3.46 | (40) ~ (e23 = e11)
% 12.14/3.46 | (41) 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
% 12.14/3.46 | (42) op2(e21, e21) = e21
% 12.14/3.46 | (43) op2(all_0_7_7, all_0_7_7) = all_0_7_7
% 12.14/3.46 | (44) op1(all_0_0_0, all_0_4_4) = all_0_1_1
% 12.14/3.46 | (45) op1(all_0_1_1, all_0_2_2) = all_0_3_3
% 12.14/3.46 | (46) op2(e23, e24) = e22
% 12.14/3.46 | (47) op1(all_0_2_2, all_0_0_0) = all_0_1_1
% 12.14/3.46 | (48) op2(e21, e24) = e20
% 12.14/3.46 | (49) h(e11) = all_0_8_8
% 12.14/3.46 | (50) ~ (e21 = e10)
% 12.14/3.46 | (51) op2(all_0_9_9, all_0_9_9) = all_0_6_6
% 12.14/3.46 | (52) ~ (e22 = e20)
% 12.14/3.46 | (53) ~ (e20 = e12)
% 12.14/3.46 | (54) op2(e24, e23) = e21
% 12.14/3.46 | (55) op2(e20, e24) = e21
% 12.14/3.46 | (56) op1(e14, e10) = e12
% 12.14/3.46 | (57) op2(all_0_7_7, all_0_8_8) = all_0_6_6
% 12.14/3.46 | (58) op1(all_0_4_4, all_0_0_0) = all_0_3_3
% 12.14/3.46 | (59) 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
% 12.14/3.46 | (60) op1(all_0_4_4, all_0_3_3) = all_0_1_1
% 12.14/3.46 | (61) op2(e22, e21) = e24
% 12.14/3.46 | (62) op2(e24, e24) = e24
% 12.14/3.46 | (63) ~ (e12 = e11)
% 12.14/3.46 | (64) op1(all_0_3_3, all_0_0_0) = all_0_4_4
% 12.14/3.46 | (65) ~ (e22 = e10)
% 12.14/3.46 | (66) op2(all_0_8_8, all_0_7_7) = all_0_8_8
% 12.14/3.46 | (67) 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
% 12.14/3.47 | (68) ~ (e21 = e11)
% 12.14/3.47 | (69) ~ (e22 = e12)
% 12.14/3.47 | (70) op2(all_0_7_7, all_0_9_9) = all_0_8_8
% 12.14/3.47 | (71) op2(e22, e23) = e20
% 12.14/3.47 | (72) op2(e23, e22) = e21
% 12.14/3.47 | (73) op2(e23, e23) = e23
% 12.14/3.47 | (74) op1(e13, e10) = e14
% 12.14/3.47 | (75) op1(e11, e14) = e13
% 12.14/3.47 | (76) ~ (e22 = e21)
% 12.14/3.47 | (77) ~ (e14 = e13)
% 12.14/3.47 | (78) 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
% 12.14/3.47 | (79) ~ (e24 = e22)
% 12.14/3.47 | (80) op1(e10, e10) = e13
% 12.14/3.47 | (81) j(all_0_7_7) = e12
% 12.14/3.47 | (82) ~ (e24 = e23)
% 12.14/3.47 | (83) op1(e12, e14) = e10
% 12.14/3.47 | (84) op1(all_0_3_3, all_0_1_1) = all_0_0_0
% 12.14/3.47 | (85) op1(e14, e11) = e10
% 12.14/3.47 | (86) ~ (e21 = e12)
% 12.14/3.47 | (87) op2(all_0_7_7, all_0_5_5) = all_0_9_9
% 12.14/3.47 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0))
% 12.14/3.47 | (89) op1(e14, e12) = e14
% 12.14/3.47 | (90) op1(all_0_4_4, all_0_4_4) = all_0_4_4
% 12.14/3.47 | (91) ~ (e23 = e20)
% 12.14/3.47 | (92) j(all_0_6_6) = e13
% 12.14/3.47 | (93) op1(e10, e11) = e12
% 12.14/3.47 | (94) ~ (e24 = e14)
% 12.14/3.47 | (95) ~ (e13 = e11)
% 12.14/3.47 | (96) ~ (e14 = e10)
% 12.14/3.47 | (97) ~ (e23 = e13)
% 12.14/3.47 | (98) op1(e14, e14) = e11
% 12.14/3.47 | (99) op2(all_0_8_8, all_0_9_9) = all_0_9_9
% 12.14/3.47 | (100) ~ (e22 = e13)
% 12.14/3.47 | (101) op2(e20, e23) = e22
% 12.14/3.47 | (102) op2(e23, e21) = e20
% 12.14/3.47 | (103) op2(all_0_6_6, all_0_8_8) = all_0_8_8
% 12.14/3.47 | (104) op1(e12, e13) = e14
% 12.14/3.47 | (105) op2(all_0_5_5, all_0_8_8) = all_0_9_9
% 12.14/3.47 | (106) op1(e12, e11) = e13
% 12.14/3.47 | (107) 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
% 12.14/3.47 | (108) op1(all_0_1_1, all_0_3_3) = all_0_4_4
% 12.14/3.47 | (109) op2(all_0_6_6, all_0_9_9) = all_0_5_5
% 12.14/3.47 | (110) 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
% 12.14/3.47 | (111) op1(e13, e13) = e10
% 12.14/3.48 | (112) 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
% 12.14/3.48 | (113) 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
% 12.14/3.48 | (114) op2(all_0_9_9, all_0_5_5) = all_0_5_5
% 12.14/3.48 | (115) h(all_0_3_3) = e21
% 12.14/3.48 | (116) ~ (e24 = e21)
% 12.14/3.48 | (117) op2(all_0_5_5, all_0_7_7) = all_0_5_5
% 12.14/3.48 | (118) ~ (e24 = e11)
% 12.14/3.48 | (119) op1(all_0_2_2, all_0_4_4) = all_0_3_3
% 12.14/3.48 | (120) ~ (e23 = e22)
% 12.14/3.48 | (121) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0))
% 12.14/3.48 | (122) ~ (e24 = e20)
% 12.14/3.48 | (123) op1(all_0_1_1, all_0_0_0) = all_0_2_2
% 12.14/3.48 | (124) op1(e13, e12) = e13
% 12.14/3.48 | (125) h(e13) = all_0_6_6
% 12.14/3.48 | (126) op2(e20, e22) = e24
% 12.14/3.48 | (127) ~ (e14 = e11)
% 12.14/3.48 | (128) j(all_0_5_5) = e14
% 12.14/3.48 | (129) ~ (e10 = e11)
% 12.14/3.48 | (130) op1(all_0_0_0, all_0_0_0) = all_0_0_0
% 12.14/3.48 | (131) op2(e20, e21) = e23
% 12.14/3.48 | (132) ~ (e24 = e12)
% 12.14/3.48 | (133) ~ (e13 = e12)
% 12.14/3.48 | (134) op1(all_0_2_2, all_0_3_3) = all_0_0_0
% 12.14/3.48 | (135) ~ (e24 = e13)
% 12.14/3.48 | (136) op2(all_0_5_5, all_0_6_6) = all_0_6_6
% 12.14/3.48 | (137) op1(e12, e12) = e12
% 12.14/3.48 | (138) h(e10) = all_0_9_9
% 12.14/3.48 | (139) op1(e11, e13) = e12
% 12.14/3.48 | (140) ~ (e21 = e13)
% 12.14/3.48 | (141) op1(all_0_4_4, all_0_1_1) = all_0_2_2
% 12.14/3.48 | (142) j(e21) = all_0_3_3
% 12.14/3.48 | (143) op2(all_0_9_9, all_0_7_7) = all_0_9_9
% 12.14/3.48 | (144) ~ (e21 = e14)
% 12.14/3.48 | (145) op1(all_0_1_1, all_0_1_1) = all_0_1_1
% 12.14/3.48 | (146) ~ (e23 = e21)
% 12.14/3.48 | (147) ~ (e12 = e10)
% 12.14/3.48 | (148) op1(all_0_1_1, all_0_4_4) = all_0_0_0
% 12.14/3.49 | (149) op2(e23, e20) = e24
% 12.14/3.49 | (150) j(all_0_9_9) = e10
% 12.14/3.49 | (151) op1(e10, e12) = e10
% 12.14/3.49 | (152) op1(all_0_0_0, all_0_1_1) = all_0_3_3
% 12.14/3.49 | (153) op2(all_0_8_8, all_0_5_5) = all_0_6_6
% 12.14/3.49 | (154) op2(all_0_7_7, all_0_6_6) = all_0_5_5
% 12.14/3.49 | (155) op2(e24, e20) = e23
% 12.14/3.49 | (156) op1(all_0_2_2, all_0_1_1) = all_0_4_4
% 12.14/3.49 | (157) j(e24) = all_0_0_0
% 12.14/3.49 | (158) op1(all_0_3_3, all_0_4_4) = all_0_2_2
% 12.14/3.49 | (159) op1(e10, e14) = e14
% 12.14/3.49 | (160) ~ (e20 = e11)
% 12.14/3.49 | (161) op2(e21, e23) = e24
% 12.14/3.49 | (162) h(e12) = all_0_7_7
% 12.14/3.49 | (163) ~ (e20 = e14)
% 12.14/3.49 | (164) op1(all_0_0_0, all_0_3_3) = all_0_2_2
% 12.14/3.49 | (165) ~ (e23 = e10)
% 12.14/3.49 | (166) op1(e10, e13) = e11
% 12.14/3.49 | (167) op2(all_0_9_9, all_0_6_6) = all_0_8_8
% 12.14/3.49 | (168) op2(all_0_6_6, all_0_5_5) = all_0_7_7
% 12.14/3.49 | (169) op2(all_0_6_6, all_0_6_6) = all_0_9_9
% 12.14/3.49 | (170) op2(e22, e24) = e23
% 12.14/3.49 | (171) 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
% 12.14/3.49 | (172) j(e22) = all_0_2_2
% 12.14/3.49 | (173) op1(all_0_4_4, all_0_2_2) = all_0_0_0
% 12.14/3.49 | (174) h(e14) = all_0_5_5
% 12.14/3.49 | (175) op2(all_0_6_6, all_0_7_7) = all_0_6_6
% 12.14/3.49 | (176) op2(all_0_8_8, all_0_6_6) = all_0_7_7
% 12.14/3.49 | (177) ~ (e13 = e10)
% 12.14/3.49 | (178) op2(e24, e22) = e20
% 12.14/3.49 | (179) ~ (e20 = e21)
% 12.14/3.49 | (180) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0))
% 12.14/3.49 |
% 12.14/3.49 +-Applying beta-rule and splitting (171), into two cases.
% 12.14/3.49 |-Branch one:
% 12.14/3.49 | (181) all_0_0_0 = e14
% 12.14/3.49 |
% 12.59/3.49 | From (181)(181)(181) and (130) follows:
% 12.60/3.50 | (182) op1(e14, e14) = e14
% 12.60/3.50 |
% 12.60/3.50 | Instantiating formula (88) with e14, e14, e14, e11 and discharging atoms op1(e14, e14) = e14, op1(e14, e14) = e11, yields:
% 12.60/3.50 | (183) e14 = e11
% 12.60/3.50 |
% 12.60/3.50 | Equations (183) can reduce 127 to:
% 12.60/3.50 | (184) $false
% 12.61/3.50 |
% 12.61/3.50 |-The branch is then unsatisfiable
% 12.61/3.50 |-Branch two:
% 12.61/3.50 | (185) ~ (all_0_0_0 = e14)
% 12.61/3.50 | (186) all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 12.61/3.50 |
% 12.61/3.50 +-Applying beta-rule and splitting (113), into two cases.
% 12.61/3.50 |-Branch one:
% 12.61/3.50 | (187) all_0_9_9 = e24
% 12.61/3.50 |
% 12.61/3.50 | From (187)(187) and (51) follows:
% 12.61/3.50 | (188) op2(e24, e24) = all_0_6_6
% 12.61/3.50 |
% 12.61/3.50 | From (187) and (150) follows:
% 12.61/3.50 | (189) j(e24) = e10
% 12.61/3.50 |
% 12.61/3.50 | Instantiating formula (6) with e24, e24, all_0_6_6, e24 and discharging atoms op2(e24, e24) = all_0_6_6, op2(e24, e24) = e24, yields:
% 12.61/3.50 | (190) all_0_6_6 = e24
% 12.61/3.50 |
% 12.61/3.50 | Instantiating formula (180) with e24, e10, all_0_0_0 and discharging atoms j(e24) = all_0_0_0, j(e24) = e10, yields:
% 12.61/3.50 | (191) all_0_0_0 = e10
% 12.61/3.50 |
% 12.61/3.50 | From (190) and (92) follows:
% 12.61/3.50 | (192) j(e24) = e13
% 12.61/3.50 |
% 12.61/3.50 | From (191) and (157) follows:
% 12.61/3.50 | (189) j(e24) = e10
% 12.61/3.50 |
% 12.61/3.50 | Instantiating formula (180) with e24, e13, e10 and discharging atoms j(e24) = e13, j(e24) = e10, yields:
% 12.61/3.50 | (194) e13 = e10
% 12.61/3.50 |
% 12.61/3.50 | Equations (194) can reduce 177 to:
% 12.61/3.50 | (184) $false
% 12.61/3.50 |
% 12.61/3.50 |-The branch is then unsatisfiable
% 12.61/3.50 |-Branch two:
% 12.61/3.50 | (196) ~ (all_0_9_9 = e24)
% 12.61/3.50 | (197) all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21
% 12.61/3.50 |
% 12.61/3.50 +-Applying beta-rule and splitting (107), into two cases.
% 12.61/3.50 |-Branch one:
% 12.61/3.50 | (198) all_0_7_7 = e24
% 12.61/3.50 |
% 12.61/3.50 | From (198) and (143) follows:
% 12.61/3.50 | (199) op2(all_0_9_9, e24) = all_0_9_9
% 12.61/3.50 |
% 12.61/3.50 +-Applying beta-rule and splitting (197), into two cases.
% 12.61/3.50 |-Branch one:
% 12.61/3.50 | (200) all_0_9_9 = e23
% 12.61/3.50 |
% 12.61/3.50 | From (200)(200) and (199) follows:
% 12.61/3.50 | (201) op2(e23, e24) = e23
% 12.61/3.50 |
% 12.61/3.50 | Instantiating formula (6) with e23, e24, e23, e22 and discharging atoms op2(e23, e24) = e23, op2(e23, e24) = e22, yields:
% 12.61/3.50 | (202) e23 = e22
% 12.61/3.50 |
% 12.61/3.50 | Equations (202) can reduce 120 to:
% 12.61/3.50 | (184) $false
% 12.61/3.50 |
% 12.61/3.50 |-The branch is then unsatisfiable
% 12.61/3.50 |-Branch two:
% 12.61/3.50 | (204) ~ (all_0_9_9 = e23)
% 12.61/3.50 | (205) all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21
% 12.61/3.50 |
% 12.61/3.50 +-Applying beta-rule and splitting (205), into two cases.
% 12.61/3.50 |-Branch one:
% 12.61/3.50 | (206) all_0_9_9 = e22
% 12.61/3.50 |
% 12.61/3.50 | Equations (206) can reduce 204 to:
% 12.61/3.50 | (207) ~ (e23 = e22)
% 12.61/3.50 |
% 12.61/3.50 | Simplifying 207 yields:
% 12.61/3.50 | (120) ~ (e23 = e22)
% 12.61/3.50 |
% 12.61/3.50 | From (206)(206) and (199) follows:
% 12.61/3.50 | (209) op2(e22, e24) = e22
% 12.61/3.50 |
% 12.61/3.50 | Instantiating formula (6) with e22, e24, e22, e23 and discharging atoms op2(e22, e24) = e23, op2(e22, e24) = e22, yields:
% 12.61/3.50 | (202) e23 = e22
% 12.61/3.50 |
% 12.61/3.50 | Equations (202) can reduce 120 to:
% 12.61/3.50 | (184) $false
% 12.61/3.50 |
% 12.61/3.50 |-The branch is then unsatisfiable
% 12.61/3.50 |-Branch two:
% 12.61/3.50 | (212) ~ (all_0_9_9 = e22)
% 12.61/3.50 | (213) all_0_9_9 = e20 | all_0_9_9 = e21
% 12.61/3.50 |
% 12.61/3.50 +-Applying beta-rule and splitting (213), into two cases.
% 12.61/3.50 |-Branch one:
% 12.61/3.50 | (214) all_0_9_9 = e20
% 12.61/3.50 |
% 12.61/3.50 | From (214)(214) and (199) follows:
% 12.61/3.50 | (215) op2(e20, e24) = e20
% 12.61/3.50 |
% 12.61/3.50 | Instantiating formula (6) with e20, e24, e20, e21 and discharging atoms op2(e20, e24) = e20, op2(e20, e24) = e21, yields:
% 12.61/3.50 | (216) e20 = e21
% 12.61/3.50 |
% 12.61/3.50 | Equations (216) can reduce 179 to:
% 12.61/3.50 | (184) $false
% 12.61/3.50 |
% 12.61/3.50 |-The branch is then unsatisfiable
% 12.61/3.50 |-Branch two:
% 12.61/3.50 | (218) ~ (all_0_9_9 = e20)
% 12.61/3.50 | (219) all_0_9_9 = e21
% 12.61/3.51 |
% 12.61/3.51 | Equations (219) can reduce 218 to:
% 12.61/3.51 | (220) ~ (e20 = e21)
% 12.61/3.51 |
% 12.61/3.51 | Simplifying 220 yields:
% 12.61/3.51 | (179) ~ (e20 = e21)
% 12.61/3.51 |
% 12.61/3.51 | From (219)(219) and (199) follows:
% 12.61/3.51 | (222) op2(e21, e24) = e21
% 12.61/3.51 |
% 12.61/3.51 | Instantiating formula (6) with e21, e24, e21, e20 and discharging atoms op2(e21, e24) = e20, op2(e21, e24) = e21, yields:
% 12.61/3.51 | (216) e20 = e21
% 12.61/3.51 |
% 12.61/3.51 | Equations (216) can reduce 179 to:
% 12.61/3.51 | (184) $false
% 12.61/3.51 |
% 12.61/3.51 |-The branch is then unsatisfiable
% 12.61/3.51 |-Branch two:
% 12.61/3.51 | (225) ~ (all_0_7_7 = e24)
% 12.61/3.51 | (226) all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 12.61/3.51 |
% 12.61/3.51 +-Applying beta-rule and splitting (186), into two cases.
% 12.61/3.51 |-Branch one:
% 12.61/3.51 | (227) all_0_0_0 = e13
% 12.61/3.51 |
% 12.61/3.51 | From (227)(227)(227) and (130) follows:
% 12.61/3.51 | (228) op1(e13, e13) = e13
% 12.61/3.51 |
% 12.61/3.51 | Instantiating formula (88) with e13, e13, e13, e10 and discharging atoms op1(e13, e13) = e13, op1(e13, e13) = e10, yields:
% 12.61/3.51 | (194) e13 = e10
% 12.61/3.51 |
% 12.61/3.51 | Equations (194) can reduce 177 to:
% 12.61/3.51 | (184) $false
% 12.61/3.51 |
% 12.61/3.51 |-The branch is then unsatisfiable
% 12.61/3.51 |-Branch two:
% 12.61/3.51 | (231) ~ (all_0_0_0 = e13)
% 12.61/3.51 | (232) all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 12.61/3.51 |
% 12.61/3.51 +-Applying beta-rule and splitting (232), into two cases.
% 12.61/3.51 |-Branch one:
% 12.61/3.51 | (233) all_0_0_0 = e12
% 12.61/3.51 |
% 12.61/3.51 | From (233) and (31) follows:
% 12.61/3.51 | (234) h(e12) = e24
% 12.61/3.51 |
% 12.61/3.51 | Instantiating formula (121) with e12, e24, all_0_7_7 and discharging atoms h(e12) = all_0_7_7, h(e12) = e24, yields:
% 12.61/3.51 | (198) all_0_7_7 = e24
% 12.61/3.51 |
% 12.61/3.51 | Equations (198) can reduce 225 to:
% 12.61/3.51 | (184) $false
% 12.61/3.51 |
% 12.61/3.51 |-The branch is then unsatisfiable
% 12.61/3.51 |-Branch two:
% 12.61/3.51 | (237) ~ (all_0_0_0 = e12)
% 12.61/3.51 | (238) all_0_0_0 = e10 | all_0_0_0 = e11
% 12.61/3.51 |
% 12.61/3.51 +-Applying beta-rule and splitting (238), into two cases.
% 12.61/3.51 |-Branch one:
% 12.61/3.51 | (191) all_0_0_0 = e10
% 12.61/3.51 |
% 12.61/3.51 | Equations (191) can reduce 231 to:
% 12.61/3.51 | (240) ~ (e13 = e10)
% 12.61/3.51 |
% 12.61/3.51 | Simplifying 240 yields:
% 12.61/3.51 | (177) ~ (e13 = e10)
% 12.61/3.51 |
% 12.61/3.51 | From (191)(191)(191) and (130) follows:
% 12.61/3.51 | (242) op1(e10, e10) = e10
% 12.61/3.51 |
% 12.61/3.51 | Instantiating formula (88) with e10, e10, e10, e13 and discharging atoms op1(e10, e10) = e13, op1(e10, e10) = e10, yields:
% 12.61/3.51 | (194) e13 = e10
% 12.61/3.51 |
% 12.61/3.51 | Equations (194) can reduce 177 to:
% 12.61/3.51 | (184) $false
% 12.61/3.51 |
% 12.61/3.51 |-The branch is then unsatisfiable
% 12.61/3.51 |-Branch two:
% 12.61/3.51 | (245) ~ (all_0_0_0 = e10)
% 12.61/3.51 | (246) all_0_0_0 = e11
% 12.61/3.51 |
% 12.61/3.51 | Equations (246) can reduce 185 to:
% 12.61/3.51 | (247) ~ (e14 = e11)
% 12.61/3.51 |
% 12.61/3.51 | Simplifying 247 yields:
% 12.61/3.51 | (127) ~ (e14 = e11)
% 12.61/3.51 |
% 12.61/3.51 | From (246)(246)(246) and (130) follows:
% 12.61/3.51 | (249) op1(e11, e11) = e11
% 12.61/3.51 |
% 12.61/3.51 | Instantiating formula (88) with e11, e11, e11, e14 and discharging atoms op1(e11, e11) = e14, op1(e11, e11) = e11, yields:
% 12.61/3.51 | (183) e14 = e11
% 12.61/3.51 |
% 12.61/3.51 | Equations (183) can reduce 127 to:
% 12.61/3.51 | (184) $false
% 12.61/3.51 |
% 12.61/3.51 |-The branch is then unsatisfiable
% 12.61/3.51 % SZS output end Proof for theBenchmark
% 12.61/3.51
% 12.61/3.51 2985ms
%------------------------------------------------------------------------------