TSTP Solution File: ALG183+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG183+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 15:37:06 EDT 2022
% Result : Theorem 4.65s 1.74s
% Output : Proof 9.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : ALG183+1 : TPTP v8.1.0. Released v2.7.0.
% 0.08/0.15 % Command : ePrincess-casc -timeout=%d %s
% 0.15/0.37 % Computer : n020.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Wed Jun 8 16:02:51 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.58/0.62 ____ _
% 0.58/0.62 ___ / __ \_____(_)___ ________ __________
% 0.58/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.62
% 0.58/0.62 A Theorem Prover for First-Order Logic
% 0.64/0.62 (ePrincess v.1.0)
% 0.64/0.62
% 0.64/0.62 (c) Philipp Rümmer, 2009-2015
% 0.64/0.62 (c) Peter Backeman, 2014-2015
% 0.64/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.64/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.64/0.62 Bug reports to peter@backeman.se
% 0.64/0.62
% 0.64/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.64/0.62
% 0.64/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.92/1.06 Prover 0: Preprocessing ...
% 3.02/1.35 Prover 0: Constructing countermodel ...
% 4.65/1.74 Prover 0: proved (1068ms)
% 4.65/1.74
% 4.65/1.74 No countermodel exists, formula is valid
% 4.65/1.74 % SZS status Theorem for theBenchmark
% 4.65/1.74
% 4.65/1.74 Generating proof ... found it (size 67)
% 8.55/2.67
% 8.55/2.67 % SZS output start Proof for theBenchmark
% 8.55/2.67 Assumed formulas after preprocessing and simplification:
% 8.55/2.67 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (e24 = e23) & ~ (e24 = e22) & ~ (e24 = e20) & ~ (e24 = e21) & ~ (e24 = e14) & ~ (e24 = e13) & ~ (e24 = e12) & ~ (e24 = e10) & ~ (e24 = e11) & ~ (e23 = e22) & ~ (e23 = e20) & ~ (e23 = e21) & ~ (e23 = e14) & ~ (e23 = e13) & ~ (e23 = e12) & ~ (e23 = e10) & ~ (e23 = e11) & ~ (e22 = e20) & ~ (e22 = e21) & ~ (e22 = e14) & ~ (e22 = e13) & ~ (e22 = e12) & ~ (e22 = e10) & ~ (e22 = e11) & ~ (e20 = e21) & ~ (e20 = e14) & ~ (e20 = e13) & ~ (e20 = e12) & ~ (e20 = e10) & ~ (e20 = e11) & ~ (e21 = e14) & ~ (e21 = e13) & ~ (e21 = e12) & ~ (e21 = e10) & ~ (e21 = e11) & ~ (e14 = e13) & ~ (e14 = e12) & ~ (e14 = e10) & ~ (e14 = e11) & ~ (e13 = e12) & ~ (e13 = e10) & ~ (e13 = e11) & ~ (e12 = e10) & ~ (e12 = e11) & ~ (e10 = e11) & op2(v4, v4) = v0 & op2(v4, v3) = v4 & op2(v4, v2) = v1 & op2(v4, v1) = v3 & op2(v4, v0) = v2 & op2(v3, v4) = v1 & op2(v3, v3) = v2 & op2(v3, v2) = v4 & op2(v3, v1) = v0 & op2(v3, v0) = v3 & op2(v2, v4) = v2 & op2(v2, v3) = v0 & op2(v2, v2) = v3 & op2(v2, v1) = v4 & op2(v2, v0) = v1 & op2(v1, v4) = v4 & op2(v1, v3) = v3 & op2(v1, v2) = v2 & op2(v1, v1) = v1 & op2(v1, v0) = v0 & op2(v0, v4) = v3 & op2(v0, v3) = v1 & op2(v0, v2) = v0 & op2(v0, v1) = v2 & op2(v0, v0) = v4 & op2(e24, e24) = e24 & op2(e24, e23) = e20 & op2(e24, e22) = e21 & op2(e24, e20) = e23 & op2(e24, e21) = e22 & op2(e23, e24) = e21 & op2(e23, e23) = e23 & op2(e23, e22) = e20 & op2(e23, e20) = e22 & op2(e23, e21) = e24 & op2(e22, e24) = e23 & op2(e22, e23) = e24 & op2(e22, e22) = e22 & op2(e22, e20) = e21 & op2(e22, e21) = e20 & op2(e20, e24) = e22 & op2(e20, e23) = e21 & op2(e20, e22) = e24 & op2(e20, e20) = e20 & op2(e20, e21) = e23 & op2(e21, e24) = e20 & op2(e21, e23) = e22 & op2(e21, e22) = e23 & op2(e21, e20) = e24 & op2(e21, e21) = e21 & op1(v9, v9) = v9 & op1(v9, v8) = v5 & op1(v9, v7) = v6 & op1(v9, v6) = v7 & op1(v9, v5) = v8 & op1(v8, v9) = v6 & op1(v8, v8) = v8 & op1(v8, v7) = v5 & op1(v8, v6) = v9 & op1(v8, v5) = v7 & op1(v7, v9) = v8 & op1(v7, v8) = v9 & op1(v7, v7) = v7 & op1(v7, v6) = v5 & op1(v7, v5) = v6 & op1(v6, v9) = v5 & op1(v6, v8) = v7 & op1(v6, v7) = v8 & op1(v6, v6) = v6 & op1(v6, v5) = v9 & op1(v5, v9) = v7 & op1(v5, v8) = v6 & op1(v5, v7) = v9 & op1(v5, v6) = v8 & op1(v5, v5) = v5 & op1(e14, e14) = e10 & op1(e14, e13) = e14 & op1(e14, e12) = e11 & op1(e14, e10) = e12 & op1(e14, e11) = e13 & op1(e13, e14) = e11 & op1(e13, e13) = e12 & op1(e13, e12) = e14 & op1(e13, e10) = e13 & op1(e13, e11) = e10 & op1(e12, e14) = e12 & op1(e12, e13) = e10 & op1(e12, e12) = e13 & op1(e12, e10) = e11 & op1(e12, e11) = e14 & op1(e10, e14) = e13 & op1(e10, e13) = e11 & op1(e10, e12) = e10 & op1(e10, e10) = e14 & op1(e10, e11) = e12 & op1(e11, e14) = e14 & op1(e11, e13) = e13 & op1(e11, e12) = e12 & op1(e11, e10) = e10 & op1(e11, e11) = e11 & 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))
% 9.09/2.72 | 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:
% 9.09/2.72 | (1) ~ (e24 = e23) & ~ (e24 = e22) & ~ (e24 = e20) & ~ (e24 = e21) & ~ (e24 = e14) & ~ (e24 = e13) & ~ (e24 = e12) & ~ (e24 = e10) & ~ (e24 = e11) & ~ (e23 = e22) & ~ (e23 = e20) & ~ (e23 = e21) & ~ (e23 = e14) & ~ (e23 = e13) & ~ (e23 = e12) & ~ (e23 = e10) & ~ (e23 = e11) & ~ (e22 = e20) & ~ (e22 = e21) & ~ (e22 = e14) & ~ (e22 = e13) & ~ (e22 = e12) & ~ (e22 = e10) & ~ (e22 = e11) & ~ (e20 = e21) & ~ (e20 = e14) & ~ (e20 = e13) & ~ (e20 = e12) & ~ (e20 = e10) & ~ (e20 = e11) & ~ (e21 = e14) & ~ (e21 = e13) & ~ (e21 = e12) & ~ (e21 = e10) & ~ (e21 = e11) & ~ (e14 = e13) & ~ (e14 = e12) & ~ (e14 = e10) & ~ (e14 = e11) & ~ (e13 = e12) & ~ (e13 = e10) & ~ (e13 = e11) & ~ (e12 = e10) & ~ (e12 = e11) & ~ (e10 = e11) & op2(all_0_5_5, all_0_5_5) = all_0_9_9 & op2(all_0_5_5, all_0_6_6) = all_0_5_5 & op2(all_0_5_5, all_0_7_7) = all_0_8_8 & op2(all_0_5_5, all_0_8_8) = all_0_6_6 & op2(all_0_5_5, all_0_9_9) = all_0_7_7 & op2(all_0_6_6, all_0_5_5) = all_0_8_8 & op2(all_0_6_6, all_0_6_6) = all_0_7_7 & op2(all_0_6_6, all_0_7_7) = all_0_5_5 & op2(all_0_6_6, all_0_8_8) = all_0_9_9 & op2(all_0_6_6, all_0_9_9) = all_0_6_6 & op2(all_0_7_7, all_0_5_5) = all_0_7_7 & 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_8_8 & op2(all_0_8_8, all_0_5_5) = all_0_5_5 & op2(all_0_8_8, all_0_6_6) = all_0_6_6 & op2(all_0_8_8, all_0_7_7) = all_0_7_7 & op2(all_0_8_8, all_0_8_8) = all_0_8_8 & op2(all_0_8_8, all_0_9_9) = all_0_9_9 & op2(all_0_9_9, all_0_5_5) = all_0_6_6 & 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_5_5 & op2(e24, e24) = e24 & op2(e24, e23) = e20 & op2(e24, e22) = e21 & op2(e24, e20) = e23 & op2(e24, e21) = e22 & op2(e23, e24) = e21 & op2(e23, e23) = e23 & op2(e23, e22) = e20 & op2(e23, e20) = e22 & op2(e23, e21) = e24 & op2(e22, e24) = e23 & op2(e22, e23) = e24 & op2(e22, e22) = e22 & op2(e22, e20) = e21 & op2(e22, e21) = e20 & op2(e20, e24) = e22 & op2(e20, e23) = e21 & op2(e20, e22) = e24 & op2(e20, e20) = e20 & op2(e20, e21) = e23 & op2(e21, e24) = e20 & op2(e21, e23) = e22 & op2(e21, e22) = e23 & op2(e21, e20) = e24 & 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_4_4 & op1(all_0_0_0, all_0_2_2) = all_0_3_3 & 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_3_3 & op1(all_0_1_1, all_0_1_1) = all_0_1_1 & op1(all_0_1_1, all_0_2_2) = all_0_4_4 & op1(all_0_1_1, all_0_3_3) = all_0_0_0 & op1(all_0_1_1, all_0_4_4) = all_0_2_2 & op1(all_0_2_2, all_0_0_0) = all_0_1_1 & op1(all_0_2_2, all_0_1_1) = all_0_0_0 & op1(all_0_2_2, all_0_2_2) = all_0_2_2 & op1(all_0_2_2, all_0_3_3) = all_0_4_4 & 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_2_2 & 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_0_0 & op1(all_0_4_4, all_0_0_0) = all_0_2_2 & op1(all_0_4_4, all_0_1_1) = all_0_3_3 & 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) = e10 & op1(e14, e13) = e14 & op1(e14, e12) = e11 & op1(e14, e10) = e12 & op1(e14, e11) = e13 & op1(e13, e14) = e11 & op1(e13, e13) = e12 & op1(e13, e12) = e14 & op1(e13, e10) = e13 & op1(e13, e11) = e10 & op1(e12, e14) = e12 & op1(e12, e13) = e10 & op1(e12, e12) = e13 & op1(e12, e10) = e11 & op1(e12, e11) = e14 & op1(e10, e14) = e13 & op1(e10, e13) = e11 & op1(e10, e12) = e10 & op1(e10, e10) = e14 & op1(e10, e11) = e12 & op1(e11, e14) = e14 & op1(e11, e13) = e13 & op1(e11, e12) = e12 & op1(e11, e10) = e10 & op1(e11, e11) = e11 & 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)
% 9.21/2.73 |
% 9.21/2.73 | Applying alpha-rule on (1) yields:
% 9.21/2.73 | (2) ~ (e21 = e12)
% 9.21/2.73 | (3) op1(all_0_0_0, all_0_1_1) = all_0_4_4
% 9.21/2.73 | (4) op2(e20, e22) = e24
% 9.21/2.73 | (5) op1(e13, e14) = e11
% 9.21/2.73 | (6) op2(e21, e21) = e21
% 9.21/2.73 | (7) op1(e13, e12) = e14
% 9.21/2.73 | (8) op1(e10, e14) = e13
% 9.21/2.73 | (9) ~ (e20 = e21)
% 9.21/2.73 | (10) ~ (e20 = e14)
% 9.21/2.73 | (11) op1(all_0_4_4, all_0_0_0) = all_0_2_2
% 9.21/2.73 | (12) op2(e23, e21) = e24
% 9.21/2.73 | (13) op1(e11, e10) = e10
% 9.21/2.73 | (14) op1(e11, e11) = e11
% 9.21/2.73 | (15) op1(e12, e12) = e13
% 9.21/2.73 | (16) op1(e14, e10) = e12
% 9.21/2.73 | (17) op2(e24, e20) = e23
% 9.21/2.73 | (18) ~ (e24 = e11)
% 9.21/2.73 | (19) op2(all_0_9_9, all_0_6_6) = all_0_8_8
% 9.21/2.73 | (20) ~ (e12 = e11)
% 9.21/2.73 | (21) h(e12) = all_0_7_7
% 9.21/2.73 | (22) h(all_0_0_0) = e24
% 9.21/2.73 | (23) h(e13) = all_0_6_6
% 9.21/2.73 | (24) op2(all_0_5_5, all_0_8_8) = all_0_6_6
% 9.21/2.73 | (25) ~ (e14 = e12)
% 9.21/2.73 | (26) ~ (e24 = e12)
% 9.21/2.73 | (27) op1(all_0_0_0, all_0_4_4) = all_0_1_1
% 9.21/2.73 | (28) op2(all_0_6_6, all_0_6_6) = all_0_7_7
% 9.21/2.73 | (29) j(e22) = all_0_2_2
% 9.21/2.73 | (30) op1(e12, e11) = e14
% 9.21/2.73 | (31) j(e21) = all_0_3_3
% 9.21/2.73 | (32) op2(e23, e20) = e22
% 9.21/2.73 | (33) j(all_0_8_8) = e11
% 9.21/2.73 | (34) ~ (e22 = e13)
% 9.21/2.73 | (35) op2(all_0_6_6, all_0_9_9) = all_0_6_6
% 9.21/2.73 | (36) op2(e24, e21) = e22
% 9.21/2.73 | (37) op2(e20, e23) = e21
% 9.21/2.73 | (38) j(all_0_6_6) = e13
% 9.21/2.73 | (39) op2(e24, e22) = e21
% 9.21/2.73 | (40) op2(e23, e23) = e23
% 9.21/2.73 | (41) op2(all_0_5_5, all_0_7_7) = all_0_8_8
% 9.21/2.73 | (42) op2(e21, e20) = e24
% 9.21/2.73 | (43) op2(e20, e21) = e23
% 9.21/2.73 | (44) h(all_0_4_4) = e20
% 9.21/2.73 | (45) op2(e23, e22) = e20
% 9.21/2.73 | (46) op1(all_0_2_2, all_0_0_0) = all_0_1_1
% 9.21/2.73 | (47) op2(e22, e20) = e21
% 9.21/2.73 | (48) op1(all_0_2_2, all_0_2_2) = all_0_2_2
% 9.21/2.73 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0))
% 9.21/2.73 | (50) op2(e21, e22) = e23
% 9.21/2.73 | (51) op1(all_0_1_1, all_0_3_3) = all_0_0_0
% 9.21/2.73 | (52) ~ (e23 = e13)
% 9.21/2.73 | (53) 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
% 9.21/2.73 | (54) ~ (e23 = e12)
% 9.21/2.73 | (55) ~ (e24 = e14)
% 9.21/2.73 | (56) h(all_0_3_3) = e21
% 9.21/2.73 | (57) ~ (e23 = e21)
% 9.21/2.73 | (58) op1(e11, e12) = e12
% 9.21/2.73 | (59) 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
% 9.21/2.73 | (60) op2(e23, e24) = e21
% 9.21/2.73 | (61) ~ (e22 = e21)
% 9.21/2.73 | (62) ~ (e20 = e11)
% 9.21/2.73 | (63) j(all_0_9_9) = e10
% 9.21/2.73 | (64) op2(e24, e24) = e24
% 9.21/2.73 | (65) op2(all_0_9_9, all_0_8_8) = all_0_7_7
% 9.21/2.73 | (66) ~ (e14 = e10)
% 9.21/2.73 | (67) ~ (e22 = e10)
% 9.21/2.73 | (68) op1(e14, e12) = e11
% 9.21/2.73 | (69) h(all_0_1_1) = e23
% 9.21/2.74 | (70) op2(all_0_9_9, all_0_7_7) = all_0_9_9
% 9.21/2.74 | (71) ~ (e12 = e10)
% 9.21/2.74 | (72) ~ (e24 = e22)
% 9.21/2.74 | (73) op1(e14, e14) = e10
% 9.21/2.74 | (74) op2(all_0_8_8, all_0_9_9) = all_0_9_9
% 9.21/2.74 | (75) op2(e21, e24) = e20
% 9.21/2.74 | (76) op1(all_0_3_3, all_0_0_0) = all_0_4_4
% 9.21/2.74 | (77) 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
% 9.21/2.74 | (78) op2(all_0_8_8, all_0_8_8) = all_0_8_8
% 9.21/2.74 | (79) op2(e20, e20) = e20
% 9.21/2.74 | (80) op2(all_0_5_5, all_0_9_9) = all_0_7_7
% 9.21/2.74 | (81) op1(e10, e12) = e10
% 9.21/2.74 | (82) op2(e22, e21) = e20
% 9.21/2.74 | (83) 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
% 9.21/2.74 | (84) j(all_0_7_7) = e12
% 9.21/2.74 | (85) op2(all_0_5_5, all_0_6_6) = all_0_5_5
% 9.21/2.74 | (86) op1(all_0_4_4, all_0_3_3) = all_0_1_1
% 9.21/2.74 | (87) op1(e12, e14) = e12
% 9.21/2.74 | (88) op2(all_0_9_9, all_0_9_9) = all_0_5_5
% 9.21/2.74 | (89) h(all_0_2_2) = e22
% 9.21/2.74 | (90) ~ (e14 = e13)
% 9.21/2.74 | (91) ~ (e21 = e11)
% 9.21/2.74 | (92) h(e14) = all_0_5_5
% 9.21/2.74 | (93) ~ (e24 = e20)
% 9.21/2.74 | (94) op1(e11, e14) = e14
% 9.21/2.74 | (95) op2(all_0_7_7, all_0_5_5) = all_0_7_7
% 9.21/2.74 | (96) ~ (e13 = e12)
% 9.21/2.74 | (97) op2(all_0_6_6, all_0_7_7) = all_0_5_5
% 9.21/2.74 | (98) 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
% 9.21/2.74 | (99) op1(all_0_2_2, all_0_3_3) = all_0_4_4
% 9.21/2.74 | (100) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0))
% 9.21/2.74 | (101) op1(all_0_2_2, all_0_4_4) = all_0_3_3
% 9.21/2.74 | (102) ~ (e14 = e11)
% 9.21/2.74 | (103) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0))
% 9.21/2.74 | (104) op1(all_0_3_3, all_0_3_3) = all_0_3_3
% 9.21/2.74 | (105) op1(all_0_3_3, all_0_4_4) = all_0_0_0
% 9.21/2.74 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0))
% 9.21/2.74 | (107) 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
% 9.21/2.74 | (108) op2(e24, e23) = e20
% 9.21/2.74 | (109) op1(all_0_1_1, all_0_2_2) = all_0_4_4
% 9.21/2.74 | (110) op1(e13, e10) = e13
% 9.21/2.74 | (111) ~ (e23 = e10)
% 9.21/2.74 | (112) op2(all_0_7_7, all_0_6_6) = all_0_9_9
% 9.21/2.74 | (113) op1(all_0_4_4, all_0_4_4) = all_0_4_4
% 9.21/2.74 | (114) op2(all_0_8_8, all_0_6_6) = all_0_6_6
% 9.21/2.74 | (115) op1(all_0_2_2, all_0_1_1) = all_0_0_0
% 9.21/2.74 | (116) ~ (e13 = e10)
% 9.21/2.74 | (117) op1(all_0_1_1, all_0_1_1) = all_0_1_1
% 9.21/2.74 | (118) 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
% 9.21/2.74 | (119) 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
% 9.21/2.74 | (120) ~ (e23 = e22)
% 9.21/2.74 | (121) op2(e22, e22) = e22
% 9.21/2.74 | (122) ~ (e20 = e10)
% 9.21/2.74 | (123) ~ (e22 = e11)
% 9.21/2.75 | (124) op1(e11, e13) = e13
% 9.21/2.75 | (125) ~ (e20 = e12)
% 9.21/2.75 | (126) op1(e10, e10) = e14
% 9.21/2.75 | (127) op2(e22, e23) = e24
% 9.21/2.75 | (128) op1(all_0_0_0, all_0_2_2) = all_0_3_3
% 9.21/2.75 | (129) op1(e13, e13) = e12
% 9.21/2.75 | (130) op1(e14, e11) = e13
% 9.21/2.75 | (131) 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
% 9.21/2.75 | (132) ~ (e10 = e11)
% 9.21/2.75 | (133) op1(all_0_3_3, all_0_2_2) = all_0_1_1
% 9.21/2.75 | (134) ~ (e23 = e14)
% 9.21/2.75 | (135) h(e11) = all_0_8_8
% 9.21/2.75 | (136) op1(e10, e13) = e11
% 9.21/2.75 | (137) op1(all_0_1_1, all_0_4_4) = all_0_2_2
% 9.21/2.75 | (138) op1(e12, e13) = e10
% 9.21/2.75 | (139) op2(all_0_8_8, all_0_7_7) = all_0_7_7
% 9.21/2.75 | (140) op2(all_0_7_7, all_0_8_8) = all_0_5_5
% 9.21/2.75 | (141) op2(all_0_8_8, all_0_5_5) = all_0_5_5
% 9.21/2.75 | (142) op1(all_0_0_0, all_0_0_0) = all_0_0_0
% 9.21/2.75 | (143) j(e23) = all_0_1_1
% 9.21/2.75 | (144) ~ (e23 = e20)
% 9.21/2.75 | (145) ~ (e21 = e14)
% 9.21/2.75 | (146) op1(all_0_4_4, all_0_1_1) = all_0_3_3
% 9.21/2.75 | (147) op1(all_0_1_1, all_0_0_0) = all_0_3_3
% 9.21/2.75 | (148) j(e24) = all_0_0_0
% 9.21/2.75 | (149) ~ (e24 = e21)
% 9.21/2.75 | (150) op1(all_0_0_0, all_0_3_3) = all_0_2_2
% 9.21/2.75 | (151) j(all_0_5_5) = e14
% 9.21/2.75 | (152) ~ (e22 = e20)
% 9.21/2.75 | (153) ~ (e23 = e11)
% 9.21/2.75 | (154) op2(all_0_6_6, all_0_8_8) = all_0_9_9
% 9.21/2.75 | (155) op2(e21, e23) = e22
% 9.21/2.75 | (156) op1(all_0_3_3, all_0_1_1) = all_0_2_2
% 9.21/2.75 | (157) op2(all_0_7_7, all_0_7_7) = all_0_6_6
% 9.21/2.75 | (158) ~ (e24 = e10)
% 9.21/2.75 | (159) ~ (e24 = e23)
% 9.21/2.75 | (160) ~ (e20 = e13)
% 9.21/2.75 | (161) op1(e10, e11) = e12
% 9.21/2.75 | (162) ~ (e24 = e13)
% 9.21/2.75 | (163) op1(e13, e11) = e10
% 9.21/2.75 | (164) op2(all_0_7_7, all_0_9_9) = all_0_8_8
% 9.21/2.75 | (165) ~ (e21 = e10)
% 9.21/2.75 | (166) ~ (e21 = e13)
% 9.21/2.75 | (167) j(e20) = all_0_4_4
% 9.21/2.75 | (168) op2(all_0_5_5, all_0_5_5) = all_0_9_9
% 9.21/2.75 | (169) ~ (e22 = e12)
% 9.21/2.75 | (170) op1(e14, e13) = e14
% 9.21/2.75 | (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
% 9.21/2.75 | (172) op2(e22, e24) = e23
% 9.21/2.75 | (173) op2(all_0_6_6, all_0_5_5) = all_0_8_8
% 9.21/2.75 | (174) op1(e12, e10) = e11
% 9.21/2.75 | (175) op2(all_0_9_9, all_0_5_5) = all_0_6_6
% 9.21/2.75 | (176) h(e10) = all_0_9_9
% 9.21/2.75 | (177) op2(e20, e24) = e22
% 9.21/2.76 | (178) ~ (e22 = e14)
% 9.21/2.76 | (179) op1(all_0_4_4, all_0_2_2) = all_0_0_0
% 9.21/2.76 | (180) ~ (e13 = e11)
% 9.21/2.76 |
% 9.21/2.76 +-Applying beta-rule and splitting (119), into two cases.
% 9.21/2.76 |-Branch one:
% 9.21/2.76 | (181) all_0_0_0 = e14
% 9.21/2.76 |
% 9.21/2.76 | From (181)(181)(181) and (142) follows:
% 9.21/2.76 | (182) op1(e14, e14) = e14
% 9.21/2.76 |
% 9.21/2.76 | Instantiating formula (106) with e14, e14, e14, e10 and discharging atoms op1(e14, e14) = e14, op1(e14, e14) = e10, yields:
% 9.21/2.76 | (183) e14 = e10
% 9.21/2.76 |
% 9.21/2.76 | Equations (183) can reduce 66 to:
% 9.21/2.76 | (184) $false
% 9.21/2.76 |
% 9.21/2.76 |-The branch is then unsatisfiable
% 9.21/2.76 |-Branch two:
% 9.21/2.76 | (185) ~ (all_0_0_0 = e14)
% 9.21/2.76 | (186) all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 9.21/2.76 |
% 9.21/2.76 +-Applying beta-rule and splitting (77), into two cases.
% 9.21/2.76 |-Branch one:
% 9.21/2.76 | (187) all_0_9_9 = e24
% 9.21/2.76 |
% 9.21/2.76 | From (187)(187) and (88) follows:
% 9.21/2.76 | (188) op2(e24, e24) = all_0_5_5
% 9.21/2.76 |
% 9.21/2.76 | From (187) and (63) follows:
% 9.21/2.76 | (189) j(e24) = e10
% 9.21/2.76 |
% 9.21/2.76 | Instantiating formula (49) with e24, e24, all_0_5_5, e24 and discharging atoms op2(e24, e24) = all_0_5_5, op2(e24, e24) = e24, yields:
% 9.21/2.76 | (190) all_0_5_5 = e24
% 9.21/2.76 |
% 9.21/2.76 | Instantiating formula (103) with e24, e10, all_0_0_0 and discharging atoms j(e24) = all_0_0_0, j(e24) = e10, yields:
% 9.21/2.76 | (191) all_0_0_0 = e10
% 9.21/2.76 |
% 9.21/2.76 | Equations (191) can reduce 185 to:
% 9.21/2.76 | (192) ~ (e14 = e10)
% 9.21/2.76 |
% 9.21/2.76 | Simplifying 192 yields:
% 9.21/2.76 | (66) ~ (e14 = e10)
% 9.21/2.76 |
% 9.21/2.76 | From (190) and (151) follows:
% 9.21/2.76 | (194) j(e24) = e14
% 9.21/2.76 |
% 9.21/2.76 | From (191) and (148) follows:
% 9.21/2.76 | (189) j(e24) = e10
% 9.21/2.76 |
% 9.21/2.76 | Instantiating formula (103) with e24, e14, e10 and discharging atoms j(e24) = e14, j(e24) = e10, yields:
% 9.21/2.76 | (183) e14 = e10
% 9.21/2.76 |
% 9.21/2.76 | Equations (183) can reduce 66 to:
% 9.21/2.76 | (184) $false
% 9.21/2.76 |
% 9.21/2.76 |-The branch is then unsatisfiable
% 9.21/2.76 |-Branch two:
% 9.21/2.76 | (198) ~ (all_0_9_9 = e24)
% 9.21/2.76 | (199) all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21
% 9.21/2.76 |
% 9.21/2.76 +-Applying beta-rule and splitting (131), into two cases.
% 9.21/2.76 |-Branch one:
% 9.21/2.76 | (200) all_0_8_8 = e24
% 9.21/2.76 |
% 9.21/2.76 | From (200) and (74) follows:
% 9.21/2.76 | (201) op2(e24, all_0_9_9) = all_0_9_9
% 9.21/2.76 |
% 9.21/2.76 +-Applying beta-rule and splitting (199), into two cases.
% 9.21/2.76 |-Branch one:
% 9.21/2.76 | (202) all_0_9_9 = e23
% 9.21/2.76 |
% 9.21/2.76 | From (202)(202) and (201) follows:
% 9.21/2.76 | (203) op2(e24, e23) = e23
% 9.21/2.76 |
% 9.21/2.76 | Instantiating formula (49) with e24, e23, e23, e20 and discharging atoms op2(e24, e23) = e23, op2(e24, e23) = e20, yields:
% 9.21/2.76 | (204) e23 = e20
% 9.21/2.76 |
% 9.21/2.76 | Equations (204) can reduce 144 to:
% 9.21/2.76 | (184) $false
% 9.21/2.76 |
% 9.21/2.76 |-The branch is then unsatisfiable
% 9.21/2.76 |-Branch two:
% 9.21/2.76 | (206) ~ (all_0_9_9 = e23)
% 9.21/2.76 | (207) all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21
% 9.21/2.76 |
% 9.21/2.76 +-Applying beta-rule and splitting (207), into two cases.
% 9.21/2.76 |-Branch one:
% 9.21/2.76 | (208) all_0_9_9 = e22
% 9.21/2.76 |
% 9.21/2.76 | From (208)(208) and (201) follows:
% 9.21/2.76 | (209) op2(e24, e22) = e22
% 9.21/2.76 |
% 9.21/2.76 | Instantiating formula (49) with e24, e22, e22, e21 and discharging atoms op2(e24, e22) = e22, op2(e24, e22) = e21, yields:
% 9.21/2.76 | (210) e22 = e21
% 9.21/2.76 |
% 9.21/2.76 | Equations (210) can reduce 61 to:
% 9.21/2.76 | (184) $false
% 9.21/2.76 |
% 9.21/2.77 |-The branch is then unsatisfiable
% 9.21/2.77 |-Branch two:
% 9.21/2.77 | (212) ~ (all_0_9_9 = e22)
% 9.21/2.77 | (213) all_0_9_9 = e20 | all_0_9_9 = e21
% 9.21/2.77 |
% 9.21/2.77 +-Applying beta-rule and splitting (213), into two cases.
% 9.21/2.77 |-Branch one:
% 9.21/2.77 | (214) all_0_9_9 = e20
% 9.21/2.77 |
% 9.21/2.77 | Equations (214) can reduce 206 to:
% 9.21/2.77 | (215) ~ (e23 = e20)
% 9.21/2.77 |
% 9.21/2.77 | Simplifying 215 yields:
% 9.21/2.77 | (144) ~ (e23 = e20)
% 9.21/2.77 |
% 9.21/2.77 | From (214)(214) and (201) follows:
% 9.21/2.77 | (217) op2(e24, e20) = e20
% 9.21/2.77 |
% 9.21/2.77 | Instantiating formula (49) with e24, e20, e20, e23 and discharging atoms op2(e24, e20) = e23, op2(e24, e20) = e20, yields:
% 9.21/2.77 | (204) e23 = e20
% 9.21/2.77 |
% 9.21/2.77 | Equations (204) can reduce 144 to:
% 9.21/2.77 | (184) $false
% 9.21/2.77 |
% 9.21/2.77 |-The branch is then unsatisfiable
% 9.21/2.77 |-Branch two:
% 9.21/2.77 | (220) ~ (all_0_9_9 = e20)
% 9.21/2.77 | (221) all_0_9_9 = e21
% 9.21/2.77 |
% 9.21/2.77 | Equations (221) can reduce 212 to:
% 9.21/2.77 | (222) ~ (e22 = e21)
% 9.21/2.77 |
% 9.21/2.77 | Simplifying 222 yields:
% 9.21/2.77 | (61) ~ (e22 = e21)
% 9.21/2.77 |
% 9.21/2.77 | From (221)(221) and (201) follows:
% 9.21/2.77 | (224) op2(e24, e21) = e21
% 9.21/2.77 |
% 9.21/2.77 | Instantiating formula (49) with e24, e21, e21, e22 and discharging atoms op2(e24, e21) = e22, op2(e24, e21) = e21, yields:
% 9.21/2.77 | (210) e22 = e21
% 9.21/2.77 |
% 9.21/2.77 | Equations (210) can reduce 61 to:
% 9.21/2.77 | (184) $false
% 9.21/2.77 |
% 9.21/2.77 |-The branch is then unsatisfiable
% 9.21/2.77 |-Branch two:
% 9.21/2.77 | (227) ~ (all_0_8_8 = e24)
% 9.21/2.77 | (228) all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 9.21/2.77 |
% 9.21/2.77 +-Applying beta-rule and splitting (186), into two cases.
% 9.21/2.77 |-Branch one:
% 9.21/2.77 | (229) all_0_0_0 = e13
% 9.21/2.77 |
% 9.21/2.77 | From (229)(229)(229) and (142) follows:
% 9.21/2.77 | (230) op1(e13, e13) = e13
% 9.21/2.77 |
% 9.21/2.77 | Instantiating formula (106) with e13, e13, e13, e12 and discharging atoms op1(e13, e13) = e13, op1(e13, e13) = e12, yields:
% 9.21/2.77 | (231) e13 = e12
% 9.21/2.77 |
% 9.21/2.77 | Equations (231) can reduce 96 to:
% 9.21/2.77 | (184) $false
% 9.21/2.77 |
% 9.21/2.77 |-The branch is then unsatisfiable
% 9.21/2.77 |-Branch two:
% 9.21/2.77 | (233) ~ (all_0_0_0 = e13)
% 9.21/2.77 | (234) all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 9.21/2.77 |
% 9.21/2.77 +-Applying beta-rule and splitting (234), into two cases.
% 9.21/2.77 |-Branch one:
% 9.21/2.77 | (235) all_0_0_0 = e12
% 9.21/2.77 |
% 9.21/2.77 | Equations (235) can reduce 233 to:
% 9.21/2.77 | (236) ~ (e13 = e12)
% 9.21/2.77 |
% 9.21/2.77 | Simplifying 236 yields:
% 9.21/2.77 | (96) ~ (e13 = e12)
% 9.21/2.77 |
% 9.21/2.77 | From (235)(235)(235) and (142) follows:
% 9.21/2.77 | (238) op1(e12, e12) = e12
% 9.21/2.77 |
% 9.21/2.77 | Instantiating formula (106) with e12, e12, e12, e13 and discharging atoms op1(e12, e12) = e13, op1(e12, e12) = e12, yields:
% 9.21/2.77 | (231) e13 = e12
% 9.21/2.77 |
% 9.21/2.77 | Equations (231) can reduce 96 to:
% 9.21/2.77 | (184) $false
% 9.21/2.77 |
% 9.21/2.77 |-The branch is then unsatisfiable
% 9.21/2.77 |-Branch two:
% 9.21/2.77 | (241) ~ (all_0_0_0 = e12)
% 9.21/2.77 | (242) all_0_0_0 = e10 | all_0_0_0 = e11
% 9.21/2.77 |
% 9.21/2.77 +-Applying beta-rule and splitting (242), into two cases.
% 9.21/2.77 |-Branch one:
% 9.21/2.77 | (191) all_0_0_0 = e10
% 9.21/2.77 |
% 9.21/2.77 | Equations (191) can reduce 185 to:
% 9.21/2.77 | (192) ~ (e14 = e10)
% 9.21/2.77 |
% 9.21/2.77 | Simplifying 192 yields:
% 9.21/2.77 | (66) ~ (e14 = e10)
% 9.21/2.77 |
% 9.21/2.77 | From (191)(191)(191) and (142) follows:
% 9.21/2.77 | (246) op1(e10, e10) = e10
% 9.21/2.77 |
% 9.21/2.77 | Instantiating formula (106) with e10, e10, e10, e14 and discharging atoms op1(e10, e10) = e14, op1(e10, e10) = e10, yields:
% 9.21/2.77 | (183) e14 = e10
% 9.21/2.77 |
% 9.21/2.77 | Equations (183) can reduce 66 to:
% 9.21/2.77 | (184) $false
% 9.21/2.77 |
% 9.21/2.77 |-The branch is then unsatisfiable
% 9.21/2.77 |-Branch two:
% 9.21/2.77 | (249) ~ (all_0_0_0 = e10)
% 9.21/2.77 | (250) all_0_0_0 = e11
% 9.21/2.77 |
% 9.21/2.77 | From (250) and (22) follows:
% 9.21/2.77 | (251) h(e11) = e24
% 9.21/2.77 |
% 9.21/2.77 | Instantiating formula (100) with e11, e24, all_0_8_8 and discharging atoms h(e11) = all_0_8_8, h(e11) = e24, yields:
% 9.21/2.77 | (200) all_0_8_8 = e24
% 9.21/2.77 |
% 9.21/2.77 | Equations (200) can reduce 227 to:
% 9.21/2.77 | (184) $false
% 9.21/2.77 |
% 9.21/2.77 |-The branch is then unsatisfiable
% 9.21/2.77 % SZS output end Proof for theBenchmark
% 9.21/2.77
% 9.21/2.77 2140ms
%------------------------------------------------------------------------------