TSTP Solution File: ALG085+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG085+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 15:34:16 EDT 2022
% Result : Theorem 3.88s 1.60s
% Output : Proof 8.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG085+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 9 06:05:02 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.56/0.60 ____ _
% 0.56/0.60 ___ / __ \_____(_)___ ________ __________
% 0.56/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.56/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.56/0.60
% 0.56/0.60 A Theorem Prover for First-Order Logic
% 0.62/0.60 (ePrincess v.1.0)
% 0.62/0.60
% 0.62/0.60 (c) Philipp Rümmer, 2009-2015
% 0.62/0.60 (c) Peter Backeman, 2014-2015
% 0.62/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.62/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.62/0.60 Bug reports to peter@backeman.se
% 0.62/0.60
% 0.62/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.62/0.60
% 0.62/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.70/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.92/1.03 Prover 0: Preprocessing ...
% 2.95/1.32 Prover 0: Constructing countermodel ...
% 3.88/1.60 Prover 0: proved (942ms)
% 3.88/1.60
% 3.88/1.60 No countermodel exists, formula is valid
% 3.88/1.60 % SZS status Theorem for theBenchmark
% 3.88/1.60
% 3.88/1.60 Generating proof ... found it (size 61)
% 7.76/2.42
% 7.76/2.42 % SZS output start Proof for theBenchmark
% 7.76/2.43 Assumed formulas after preprocessing and simplification:
% 7.76/2.43 | (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) = v0 & op2(v4, v2) = v1 & op2(v4, v1) = v3 & op2(v4, v0) = v4 & op2(v3, v4) = v0 & op2(v3, v3) = v1 & op2(v3, v2) = v4 & op2(v3, v1) = v2 & op2(v3, v0) = v3 & op2(v2, v4) = v1 & op2(v2, v3) = v4 & op2(v2, v2) = v3 & op2(v2, v1) = v0 & op2(v2, v0) = v2 & op2(v1, v4) = v3 & op2(v1, v3) = v2 & op2(v1, v2) = v0 & op2(v1, v1) = v4 & op2(v1, v0) = v1 & op2(v0, v4) = v4 & op2(v0, v3) = v3 & op2(v0, v2) = v2 & op2(v0, v1) = v1 & op2(v0, v0) = v0 & op2(e24, e24) = e20 & op2(e24, e23) = e22 & op2(e24, e22) = e21 & op2(e24, e20) = e24 & op2(e24, e21) = e23 & op2(e23, e24) = e22 & op2(e23, e23) = e21 & op2(e23, e22) = e20 & op2(e23, e20) = e23 & op2(e23, e21) = e24 & op2(e22, e24) = e21 & op2(e22, e23) = e24 & op2(e22, e22) = e23 & op2(e22, e20) = e22 & op2(e22, e21) = e20 & op2(e20, e24) = e24 & op2(e20, e23) = e23 & op2(e20, e22) = e22 & op2(e20, e20) = e20 & op2(e20, e21) = e21 & op2(e21, e24) = e23 & op2(e21, e23) = e20 & op2(e21, e22) = e24 & op2(e21, e20) = e21 & op2(e21, e21) = e22 & op1(v9, v9) = v5 & op1(v9, v8) = v7 & op1(v9, v7) = v6 & op1(v9, v6) = v8 & op1(v9, v5) = v9 & op1(v8, v9) = v7 & op1(v8, v8) = v6 & op1(v8, v7) = v5 & op1(v8, v6) = v9 & op1(v8, v5) = v8 & op1(v7, v9) = v6 & op1(v7, v8) = v9 & op1(v7, v7) = v8 & op1(v7, v6) = v5 & op1(v7, v5) = v7 & op1(v6, v9) = v8 & op1(v6, v8) = v5 & op1(v6, v7) = v9 & 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) = e10 & op1(e14, e12) = e11 & op1(e14, e10) = e14 & op1(e14, e11) = e13 & op1(e13, e14) = e10 & op1(e13, e13) = e11 & op1(e13, e12) = e14 & op1(e13, e10) = e13 & op1(e13, e11) = e12 & op1(e12, e14) = e11 & op1(e12, e13) = e14 & op1(e12, e12) = e13 & op1(e12, e10) = e12 & op1(e12, e11) = e10 & 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) = e10 & op1(e11, e10) = e11 & 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))
% 7.76/2.47 | 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:
% 7.76/2.47 | (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_9_9 & op2(all_0_5_5, all_0_7_7) = all_0_8_8 & op2(all_0_5_5, all_0_8_8) = all_0_6_6 & op2(all_0_5_5, all_0_9_9) = all_0_5_5 & op2(all_0_6_6, all_0_5_5) = all_0_9_9 & op2(all_0_6_6, all_0_6_6) = all_0_8_8 & op2(all_0_6_6, all_0_7_7) = all_0_5_5 & op2(all_0_6_6, all_0_8_8) = all_0_7_7 & op2(all_0_6_6, all_0_9_9) = all_0_6_6 & op2(all_0_7_7, all_0_5_5) = all_0_8_8 & op2(all_0_7_7, all_0_6_6) = all_0_5_5 & op2(all_0_7_7, all_0_7_7) = all_0_6_6 & op2(all_0_7_7, all_0_8_8) = all_0_9_9 & 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_9_9 & op2(all_0_8_8, all_0_8_8) = all_0_5_5 & op2(all_0_8_8, all_0_9_9) = all_0_8_8 & op2(all_0_9_9, all_0_5_5) = all_0_5_5 & op2(all_0_9_9, all_0_6_6) = all_0_6_6 & op2(all_0_9_9, all_0_7_7) = all_0_7_7 & op2(all_0_9_9, all_0_8_8) = all_0_8_8 & op2(all_0_9_9, all_0_9_9) = all_0_9_9 & op2(e24, e24) = e20 & op2(e24, e23) = e22 & op2(e24, e22) = e21 & op2(e24, e20) = e24 & op2(e24, e21) = e23 & op2(e23, e24) = e22 & op2(e23, e23) = e21 & op2(e23, e22) = e20 & op2(e23, e20) = e23 & op2(e23, e21) = e24 & op2(e22, e24) = e21 & op2(e22, e23) = e24 & op2(e22, e22) = e23 & op2(e22, e20) = e22 & op2(e22, e21) = e20 & op2(e20, e24) = e24 & op2(e20, e23) = e23 & op2(e20, e22) = e22 & op2(e20, e20) = e20 & op2(e20, e21) = e21 & op2(e21, e24) = e23 & op2(e21, e23) = e20 & op2(e21, e22) = e24 & op2(e21, e20) = e21 & op2(e21, e21) = e22 & op1(all_0_0_0, all_0_0_0) = all_0_4_4 & op1(all_0_0_0, all_0_1_1) = all_0_2_2 & op1(all_0_0_0, all_0_2_2) = all_0_3_3 & op1(all_0_0_0, all_0_3_3) = all_0_1_1 & op1(all_0_0_0, all_0_4_4) = all_0_0_0 & op1(all_0_1_1, all_0_0_0) = all_0_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_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_1_1 & op1(all_0_2_2, all_0_0_0) = all_0_3_3 & op1(all_0_2_2, all_0_1_1) = all_0_0_0 & op1(all_0_2_2, all_0_2_2) = all_0_1_1 & op1(all_0_2_2, all_0_3_3) = all_0_4_4 & op1(all_0_2_2, all_0_4_4) = all_0_2_2 & op1(all_0_3_3, all_0_0_0) = all_0_1_1 & op1(all_0_3_3, all_0_1_1) = all_0_4_4 & op1(all_0_3_3, all_0_2_2) = all_0_0_0 & op1(all_0_3_3, all_0_3_3) = all_0_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) = e10 & op1(e14, e12) = e11 & op1(e14, e10) = e14 & op1(e14, e11) = e13 & op1(e13, e14) = e10 & op1(e13, e13) = e11 & op1(e13, e12) = e14 & op1(e13, e10) = e13 & op1(e13, e11) = e12 & op1(e12, e14) = e11 & op1(e12, e13) = e14 & op1(e12, e12) = e13 & op1(e12, e10) = e12 & op1(e12, e11) = e10 & 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) = e10 & op1(e11, e10) = e11 & 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)
% 7.76/2.49 |
% 7.76/2.49 | Applying alpha-rule on (1) yields:
% 7.76/2.49 | (2) ~ (e21 = e12)
% 7.76/2.49 | (3) op1(all_0_4_4, all_0_1_1) = all_0_1_1
% 7.76/2.49 | (4) op2(all_0_7_7, all_0_8_8) = all_0_9_9
% 7.76/2.49 | (5) op1(e13, e12) = e14
% 7.76/2.49 | (6) ~ (e20 = e21)
% 7.76/2.49 | (7) ~ (e20 = e14)
% 7.76/2.49 | (8) op2(e23, e21) = e24
% 7.76/2.49 | (9) op1(all_0_2_2, all_0_2_2) = all_0_1_1
% 7.76/2.49 | (10) op1(e12, e12) = e13
% 7.76/2.49 | (11) op2(e20, e23) = e23
% 7.76/2.49 | (12) op1(all_0_4_4, all_0_2_2) = all_0_2_2
% 7.76/2.49 | (13) ~ (e24 = e11)
% 7.76/2.49 | (14) ~ (e12 = e11)
% 7.76/2.49 | (15) h(e12) = all_0_7_7
% 7.76/2.49 | (16) h(all_0_0_0) = e24
% 7.76/2.49 | (17) h(e13) = all_0_6_6
% 7.76/2.49 | (18) op2(all_0_5_5, all_0_8_8) = all_0_6_6
% 7.76/2.49 | (19) ~ (e14 = e12)
% 7.76/2.49 | (20) ~ (e24 = e12)
% 7.76/2.49 | (21) op1(e10, e11) = e11
% 7.76/2.49 | (22) j(e22) = all_0_2_2
% 7.76/2.49 | (23) op2(all_0_9_9, all_0_8_8) = all_0_8_8
% 7.76/2.49 | (24) j(e21) = all_0_3_3
% 8.22/2.51 | (25) j(all_0_8_8) = e11
% 8.22/2.51 | (26) ~ (e22 = e13)
% 8.22/2.51 | (27) op2(all_0_6_6, all_0_9_9) = all_0_6_6
% 8.22/2.51 | (28) op2(all_0_8_8, all_0_6_6) = all_0_7_7
% 8.22/2.51 | (29) op1(e12, e14) = e11
% 8.22/2.51 | (30) op2(e24, e21) = e23
% 8.22/2.51 | (31) op1(all_0_3_3, all_0_4_4) = all_0_3_3
% 8.22/2.51 | (32) j(all_0_6_6) = e13
% 8.22/2.51 | (33) op2(e24, e22) = e21
% 8.22/2.51 | (34) op2(all_0_5_5, all_0_7_7) = all_0_8_8
% 8.22/2.51 | (35) h(all_0_4_4) = e20
% 8.22/2.51 | (36) op2(e23, e22) = e20
% 8.22/2.51 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0))
% 8.22/2.51 | (38) op1(all_0_3_3, all_0_2_2) = all_0_0_0
% 8.22/2.51 | (39) op2(all_0_5_5, all_0_5_5) = all_0_7_7
% 8.22/2.51 | (40) op1(e14, e14) = e12
% 8.22/2.51 | (41) op1(all_0_1_1, all_0_3_3) = all_0_0_0
% 8.22/2.51 | (42) ~ (e23 = e13)
% 8.22/2.51 | (43) op1(all_0_0_0, all_0_4_4) = all_0_0_0
% 8.22/2.51 | (44) op2(all_0_9_9, all_0_6_6) = all_0_6_6
% 8.22/2.51 | (45) op2(e22, e20) = e22
% 8.22/2.51 | (46) 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
% 8.22/2.51 | (47) ~ (e23 = e12)
% 8.22/2.51 | (48) op1(e11, e10) = e11
% 8.22/2.51 | (49) op2(e21, e24) = e23
% 8.22/2.51 | (50) op2(e21, e21) = e22
% 8.22/2.51 | (51) ~ (e24 = e14)
% 8.22/2.51 | (52) h(all_0_3_3) = e21
% 8.22/2.51 | (53) ~ (e23 = e21)
% 8.22/2.51 | (54) op1(e13, e11) = e12
% 8.22/2.51 | (55) 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
% 8.22/2.51 | (56) ~ (e22 = e21)
% 8.22/2.51 | (57) ~ (e20 = e11)
% 8.22/2.51 | (58) j(all_0_9_9) = e10
% 8.22/2.51 | (59) op1(all_0_3_3, all_0_3_3) = all_0_2_2
% 8.22/2.51 | (60) ~ (e14 = e10)
% 8.22/2.51 | (61) ~ (e22 = e10)
% 8.22/2.51 | (62) op1(all_0_0_0, all_0_0_0) = all_0_4_4
% 8.22/2.51 | (63) op1(e14, e12) = e11
% 8.22/2.51 | (64) h(all_0_1_1) = e23
% 8.22/2.51 | (65) op2(all_0_9_9, all_0_9_9) = all_0_9_9
% 8.22/2.51 | (66) op2(all_0_9_9, all_0_7_7) = all_0_7_7
% 8.22/2.51 | (67) op1(e12, e10) = e12
% 8.22/2.51 | (68) ~ (e12 = e10)
% 8.22/2.51 | (69) ~ (e24 = e22)
% 8.22/2.51 | (70) op1(all_0_1_1, all_0_4_4) = all_0_1_1
% 8.22/2.51 | (71) 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
% 8.22/2.51 | (72) op2(e20, e24) = e24
% 8.22/2.51 | (73) op2(e20, e20) = e20
% 8.22/2.51 | (74) op2(e22, e21) = e20
% 8.22/2.51 | (75) 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
% 8.22/2.51 | (76) op2(all_0_6_6, all_0_5_5) = all_0_9_9
% 8.22/2.51 | (77) op1(all_0_1_1, all_0_0_0) = all_0_2_2
% 8.22/2.51 | (78) op2(all_0_7_7, all_0_9_9) = all_0_7_7
% 8.22/2.51 | (79) op1(all_0_0_0, all_0_1_1) = all_0_2_2
% 8.22/2.51 | (80) j(all_0_7_7) = e12
% 8.22/2.51 | (81) op2(all_0_8_8, all_0_5_5) = all_0_6_6
% 8.22/2.51 | (82) op2(all_0_5_5, all_0_9_9) = all_0_5_5
% 8.22/2.51 | (83) h(all_0_2_2) = e22
% 8.22/2.51 | (84) op1(e12, e13) = e14
% 8.22/2.51 | (85) ~ (e14 = e13)
% 8.22/2.51 | (86) ~ (e21 = e11)
% 8.22/2.51 | (87) h(e14) = all_0_5_5
% 8.22/2.51 | (88) ~ (e24 = e20)
% 8.22/2.51 | (89) op2(e23, e23) = e21
% 8.22/2.51 | (90) ~ (e13 = e12)
% 8.22/2.51 | (91) op2(all_0_6_6, all_0_7_7) = all_0_5_5
% 8.22/2.51 | (92) 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
% 8.22/2.51 | (93) op1(all_0_2_2, all_0_3_3) = all_0_4_4
% 8.22/2.51 | (94) op2(all_0_8_8, all_0_8_8) = all_0_5_5
% 8.22/2.51 | (95) op1(e11, e12) = e10
% 8.22/2.51 | (96) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0))
% 8.22/2.51 | (97) ~ (e14 = e11)
% 8.22/2.51 | (98) op2(e22, e24) = e21
% 8.22/2.51 | (99) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0))
% 8.22/2.51 | (100) op1(all_0_2_2, all_0_4_4) = all_0_2_2
% 8.22/2.51 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0))
% 8.22/2.51 | (102) 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
% 8.22/2.51 | (103) op1(all_0_1_1, all_0_1_1) = all_0_3_3
% 8.22/2.51 | (104) op2(all_0_6_6, all_0_8_8) = all_0_7_7
% 8.22/2.51 | (105) op1(all_0_1_1, all_0_2_2) = all_0_4_4
% 8.22/2.51 | (106) op1(e13, e10) = e13
% 8.22/2.51 | (107) op1(e10, e10) = e10
% 8.22/2.51 | (108) op1(all_0_0_0, all_0_3_3) = all_0_1_1
% 8.22/2.51 | (109) ~ (e23 = e10)
% 8.22/2.51 | (110) op1(all_0_4_4, all_0_4_4) = all_0_4_4
% 8.22/2.51 | (111) op2(e21, e23) = e20
% 8.22/2.51 | (112) op1(all_0_2_2, all_0_1_1) = all_0_0_0
% 8.22/2.51 | (113) ~ (e13 = e10)
% 8.22/2.51 | (114) op1(e10, e12) = e12
% 8.22/2.51 | (115) 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
% 8.22/2.51 | (116) 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
% 8.22/2.51 | (117) ~ (e23 = e22)
% 8.22/2.52 | (118) op2(all_0_5_5, all_0_6_6) = all_0_9_9
% 8.22/2.52 | (119) ~ (e20 = e10)
% 8.22/2.52 | (120) ~ (e22 = e11)
% 8.22/2.52 | (121) op1(e13, e14) = e10
% 8.22/2.52 | (122) op2(e22, e22) = e23
% 8.22/2.52 | (123) ~ (e20 = e12)
% 8.22/2.52 | (124) op2(e22, e23) = e24
% 8.22/2.52 | (125) op2(all_0_7_7, all_0_5_5) = all_0_8_8
% 8.22/2.52 | (126) op1(all_0_0_0, all_0_2_2) = all_0_3_3
% 8.22/2.52 | (127) op1(all_0_3_3, all_0_0_0) = all_0_1_1
% 8.22/2.52 | (128) op1(e14, e11) = e13
% 8.22/2.52 | (129) op2(e24, e20) = e24
% 8.22/2.52 | (130) op1(all_0_4_4, all_0_0_0) = all_0_0_0
% 8.22/2.52 | (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
% 8.22/2.52 | (132) ~ (e10 = e11)
% 8.22/2.52 | (133) op1(all_0_2_2, all_0_0_0) = all_0_3_3
% 8.22/2.52 | (134) ~ (e23 = e14)
% 8.22/2.52 | (135) h(e11) = all_0_8_8
% 8.22/2.52 | (136) op1(e10, e13) = e13
% 8.22/2.52 | (137) op1(e14, e10) = e14
% 8.22/2.52 | (138) op2(e23, e24) = e22
% 8.22/2.52 | (139) j(e23) = all_0_1_1
% 8.22/2.52 | (140) ~ (e23 = e20)
% 8.22/2.52 | (141) op2(e21, e20) = e21
% 8.22/2.52 | (142) ~ (e21 = e14)
% 8.22/2.52 | (143) j(e24) = all_0_0_0
% 8.22/2.52 | (144) op2(all_0_7_7, all_0_6_6) = all_0_5_5
% 8.22/2.52 | (145) op2(e24, e24) = e20
% 8.22/2.52 | (146) op1(e12, e11) = e10
% 8.22/2.52 | (147) op1(e10, e14) = e14
% 8.22/2.52 | (148) ~ (e24 = e21)
% 8.22/2.52 | (149) op1(e11, e14) = e13
% 8.22/2.52 | (150) op2(all_0_8_8, all_0_9_9) = all_0_8_8
% 8.22/2.52 | (151) j(all_0_5_5) = e14
% 8.22/2.52 | (152) op2(e23, e20) = e23
% 8.22/2.52 | (153) ~ (e22 = e20)
% 8.22/2.52 | (154) ~ (e23 = e11)
% 8.22/2.52 | (155) op2(all_0_6_6, all_0_6_6) = all_0_8_8
% 8.22/2.52 | (156) op2(all_0_7_7, all_0_7_7) = all_0_6_6
% 8.22/2.52 | (157) op1(e11, e11) = e14
% 8.22/2.52 | (158) op2(all_0_8_8, all_0_7_7) = all_0_9_9
% 8.22/2.53 | (159) ~ (e24 = e10)
% 8.22/2.53 | (160) ~ (e24 = e23)
% 8.22/2.53 | (161) op1(e11, e13) = e12
% 8.22/2.53 | (162) ~ (e20 = e13)
% 8.22/2.53 | (163) ~ (e24 = e13)
% 8.22/2.53 | (164) op1(all_0_4_4, all_0_3_3) = all_0_3_3
% 8.22/2.53 | (165) ~ (e21 = e10)
% 8.22/2.53 | (166) ~ (e21 = e13)
% 8.22/2.53 | (167) j(e20) = all_0_4_4
% 8.22/2.53 | (168) ~ (e22 = e12)
% 8.22/2.53 | (169) op2(e24, e23) = e22
% 8.22/2.53 | (170) op2(e20, e22) = e22
% 8.22/2.53 | (171) op1(e13, e13) = e11
% 8.22/2.53 | (172) 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
% 8.22/2.53 | (173) op1(e14, e13) = e10
% 8.22/2.53 | (174) h(e10) = all_0_9_9
% 8.22/2.53 | (175) ~ (e22 = e14)
% 8.22/2.53 | (176) op1(all_0_3_3, all_0_1_1) = all_0_4_4
% 8.22/2.53 | (177) op2(e20, e21) = e21
% 8.22/2.53 | (178) op2(all_0_9_9, all_0_5_5) = all_0_5_5
% 8.22/2.53 | (179) op2(e21, e22) = e24
% 8.22/2.53 | (180) ~ (e13 = e11)
% 8.22/2.53 |
% 8.22/2.53 +-Applying beta-rule and splitting (116), into two cases.
% 8.22/2.53 |-Branch one:
% 8.22/2.53 | (181) all_0_0_0 = e14
% 8.22/2.53 |
% 8.22/2.53 | From (181)(181) and (62) follows:
% 8.22/2.53 | (182) op1(e14, e14) = all_0_4_4
% 8.22/2.53 |
% 8.22/2.53 | Instantiating formula (101) with e14, e14, all_0_4_4, e12 and discharging atoms op1(e14, e14) = all_0_4_4, op1(e14, e14) = e12, yields:
% 8.22/2.53 | (183) all_0_4_4 = e12
% 8.22/2.53 |
% 8.22/2.53 | From (183)(183)(183) and (110) follows:
% 8.22/2.53 | (184) op1(e12, e12) = e12
% 8.22/2.53 |
% 8.22/2.53 | Instantiating formula (101) with e12, e12, e12, e13 and discharging atoms op1(e12, e12) = e13, op1(e12, e12) = e12, yields:
% 8.22/2.53 | (185) e13 = e12
% 8.22/2.54 |
% 8.22/2.54 | Equations (185) can reduce 90 to:
% 8.22/2.54 | (186) $false
% 8.22/2.54 |
% 8.22/2.54 |-The branch is then unsatisfiable
% 8.22/2.54 |-Branch two:
% 8.22/2.54 | (187) ~ (all_0_0_0 = e14)
% 8.22/2.54 | (188) all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 8.22/2.54 |
% 8.22/2.54 +-Applying beta-rule and splitting (71), into two cases.
% 8.22/2.54 |-Branch one:
% 8.22/2.54 | (189) all_0_9_9 = e24
% 8.22/2.54 |
% 8.22/2.54 | From (189)(189)(189) and (65) follows:
% 8.22/2.54 | (190) op2(e24, e24) = e24
% 8.22/2.54 |
% 8.22/2.54 | Instantiating formula (37) with e24, e24, e24, e20 and discharging atoms op2(e24, e24) = e24, op2(e24, e24) = e20, yields:
% 8.22/2.54 | (191) e24 = e20
% 8.22/2.54 |
% 8.22/2.54 | Equations (191) can reduce 88 to:
% 8.22/2.54 | (186) $false
% 8.22/2.54 |
% 8.22/2.54 |-The branch is then unsatisfiable
% 8.22/2.54 |-Branch two:
% 8.22/2.54 | (193) ~ (all_0_9_9 = e24)
% 8.22/2.54 | (194) all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21
% 8.22/2.54 |
% 8.22/2.54 +-Applying beta-rule and splitting (92), into two cases.
% 8.22/2.54 |-Branch one:
% 8.22/2.54 | (195) all_0_7_7 = e24
% 8.22/2.54 |
% 8.22/2.54 | From (195)(195) and (156) follows:
% 8.22/2.54 | (196) op2(e24, e24) = all_0_6_6
% 8.22/2.54 |
% 8.22/2.54 | Instantiating formula (37) with e24, e24, all_0_6_6, e20 and discharging atoms op2(e24, e24) = all_0_6_6, op2(e24, e24) = e20, yields:
% 8.22/2.54 | (197) all_0_6_6 = e20
% 8.22/2.54 |
% 8.22/2.54 | From (197)(197) and (155) follows:
% 8.22/2.54 | (198) op2(e20, e20) = all_0_8_8
% 8.22/2.54 |
% 8.22/2.54 | From (197) and (32) follows:
% 8.22/2.54 | (199) j(e20) = e13
% 8.22/2.54 |
% 8.22/2.54 | Instantiating formula (37) with e20, e20, all_0_8_8, e20 and discharging atoms op2(e20, e20) = all_0_8_8, op2(e20, e20) = e20, yields:
% 8.22/2.54 | (200) all_0_8_8 = e20
% 8.22/2.54 |
% 8.22/2.54 | Instantiating formula (99) with e20, e13, all_0_4_4 and discharging atoms j(e20) = all_0_4_4, j(e20) = e13, yields:
% 8.22/2.54 | (201) all_0_4_4 = e13
% 8.22/2.54 |
% 8.22/2.54 | From (200) and (25) follows:
% 8.22/2.54 | (202) j(e20) = e11
% 8.22/2.54 |
% 8.22/2.54 | From (201) and (167) follows:
% 8.22/2.54 | (199) j(e20) = e13
% 8.22/2.54 |
% 8.22/2.54 | Instantiating formula (99) with e20, e11, e13 and discharging atoms j(e20) = e13, j(e20) = e11, yields:
% 8.22/2.54 | (204) e13 = e11
% 8.22/2.54 |
% 8.22/2.54 | Equations (204) can reduce 180 to:
% 8.22/2.54 | (186) $false
% 8.22/2.54 |
% 8.22/2.54 |-The branch is then unsatisfiable
% 8.22/2.54 |-Branch two:
% 8.22/2.54 | (206) ~ (all_0_7_7 = e24)
% 8.22/2.54 | (207) all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 8.22/2.54 |
% 8.22/2.54 +-Applying beta-rule and splitting (115), into two cases.
% 8.22/2.54 |-Branch one:
% 8.22/2.54 | (208) all_0_6_6 = e24
% 8.22/2.54 |
% 8.22/2.54 | From (208)(208) and (155) follows:
% 8.22/2.54 | (209) op2(e24, e24) = all_0_8_8
% 8.22/2.54 |
% 8.22/2.54 | From (208) and (28) follows:
% 8.22/2.54 | (210) op2(all_0_8_8, e24) = all_0_7_7
% 8.22/2.54 |
% 8.22/2.54 | Instantiating formula (37) with e24, e24, all_0_8_8, e20 and discharging atoms op2(e24, e24) = all_0_8_8, op2(e24, e24) = e20, yields:
% 8.22/2.54 | (200) all_0_8_8 = e20
% 8.22/2.54 |
% 8.22/2.54 | From (200) and (210) follows:
% 8.22/2.54 | (212) op2(e20, e24) = all_0_7_7
% 8.22/2.54 |
% 8.22/2.54 | Instantiating formula (37) with e20, e24, all_0_7_7, e24 and discharging atoms op2(e20, e24) = all_0_7_7, op2(e20, e24) = e24, yields:
% 8.22/2.54 | (195) all_0_7_7 = e24
% 8.22/2.54 |
% 8.22/2.54 | Equations (195) can reduce 206 to:
% 8.22/2.54 | (186) $false
% 8.22/2.54 |
% 8.22/2.54 |-The branch is then unsatisfiable
% 8.22/2.54 |-Branch two:
% 8.22/2.54 | (215) ~ (all_0_6_6 = e24)
% 8.22/2.55 | (216) all_0_6_6 = e23 | all_0_6_6 = e22 | all_0_6_6 = e20 | all_0_6_6 = e21
% 8.22/2.55 |
% 8.22/2.55 +-Applying beta-rule and splitting (131), into two cases.
% 8.22/2.55 |-Branch one:
% 8.22/2.55 | (217) all_0_8_8 = e24
% 8.22/2.55 |
% 8.22/2.55 | From (217) and (18) follows:
% 8.22/2.55 | (218) op2(all_0_5_5, e24) = all_0_6_6
% 8.22/2.55 |
% 8.22/2.55 | From (217)(217) and (94) follows:
% 8.22/2.55 | (219) op2(e24, e24) = all_0_5_5
% 8.22/2.55 |
% 8.22/2.55 | Instantiating formula (37) with e24, e24, all_0_5_5, e20 and discharging atoms op2(e24, e24) = all_0_5_5, op2(e24, e24) = e20, yields:
% 8.22/2.55 | (220) all_0_5_5 = e20
% 8.22/2.55 |
% 8.22/2.55 | From (220) and (218) follows:
% 8.22/2.55 | (221) op2(e20, e24) = all_0_6_6
% 8.22/2.55 |
% 8.22/2.55 | Instantiating formula (37) with e20, e24, all_0_6_6, e24 and discharging atoms op2(e20, e24) = all_0_6_6, op2(e20, e24) = e24, yields:
% 8.22/2.55 | (208) all_0_6_6 = e24
% 8.22/2.55 |
% 8.22/2.55 | Equations (208) can reduce 215 to:
% 8.22/2.55 | (186) $false
% 8.22/2.55 |
% 8.22/2.55 |-The branch is then unsatisfiable
% 8.22/2.55 |-Branch two:
% 8.22/2.55 | (224) ~ (all_0_8_8 = e24)
% 8.22/2.55 | (225) all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 8.22/2.55 |
% 8.22/2.55 +-Applying beta-rule and splitting (188), into two cases.
% 8.22/2.55 |-Branch one:
% 8.22/2.55 | (226) all_0_0_0 = e13
% 8.22/2.55 |
% 8.22/2.55 | From (226) and (16) follows:
% 8.22/2.55 | (227) h(e13) = e24
% 8.22/2.55 |
% 8.22/2.55 | Instantiating formula (96) with e13, e24, all_0_6_6 and discharging atoms h(e13) = all_0_6_6, h(e13) = e24, yields:
% 8.22/2.55 | (208) all_0_6_6 = e24
% 8.22/2.55 |
% 8.22/2.55 | Equations (208) can reduce 215 to:
% 8.22/2.55 | (186) $false
% 8.22/2.55 |
% 8.22/2.55 |-The branch is then unsatisfiable
% 8.22/2.55 |-Branch two:
% 8.22/2.55 | (230) ~ (all_0_0_0 = e13)
% 8.22/2.55 | (231) all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 8.22/2.55 |
% 8.22/2.55 +-Applying beta-rule and splitting (231), into two cases.
% 8.22/2.55 |-Branch one:
% 8.22/2.55 | (232) all_0_0_0 = e12
% 8.22/2.55 |
% 8.22/2.55 | From (232) and (16) follows:
% 8.22/2.55 | (233) h(e12) = e24
% 8.22/2.55 |
% 8.22/2.55 | Instantiating formula (96) with e12, e24, all_0_7_7 and discharging atoms h(e12) = all_0_7_7, h(e12) = e24, yields:
% 8.22/2.55 | (195) all_0_7_7 = e24
% 8.22/2.55 |
% 8.22/2.55 | Equations (195) can reduce 206 to:
% 8.22/2.55 | (186) $false
% 8.22/2.55 |
% 8.22/2.55 |-The branch is then unsatisfiable
% 8.22/2.55 |-Branch two:
% 8.22/2.55 | (236) ~ (all_0_0_0 = e12)
% 8.22/2.55 | (237) all_0_0_0 = e10 | all_0_0_0 = e11
% 8.22/2.55 |
% 8.22/2.55 +-Applying beta-rule and splitting (237), into two cases.
% 8.22/2.55 |-Branch one:
% 8.22/2.55 | (238) all_0_0_0 = e10
% 8.22/2.55 |
% 8.22/2.55 | From (238) and (16) follows:
% 8.22/2.55 | (239) h(e10) = e24
% 8.22/2.55 |
% 8.22/2.55 | Instantiating formula (96) with e10, e24, all_0_9_9 and discharging atoms h(e10) = all_0_9_9, h(e10) = e24, yields:
% 8.22/2.55 | (189) all_0_9_9 = e24
% 8.22/2.55 |
% 8.22/2.55 | Equations (189) can reduce 193 to:
% 8.22/2.55 | (186) $false
% 8.22/2.55 |
% 8.22/2.55 |-The branch is then unsatisfiable
% 8.22/2.55 |-Branch two:
% 8.22/2.55 | (242) ~ (all_0_0_0 = e10)
% 8.22/2.55 | (243) all_0_0_0 = e11
% 8.22/2.55 |
% 8.22/2.55 | From (243) and (16) follows:
% 8.22/2.55 | (244) h(e11) = e24
% 8.22/2.55 |
% 8.22/2.55 | Instantiating formula (96) with e11, e24, all_0_8_8 and discharging atoms h(e11) = all_0_8_8, h(e11) = e24, yields:
% 8.22/2.55 | (217) all_0_8_8 = e24
% 8.22/2.55 |
% 8.22/2.55 | Equations (217) can reduce 224 to:
% 8.22/2.55 | (186) $false
% 8.22/2.55 |
% 8.22/2.55 |-The branch is then unsatisfiable
% 8.22/2.55 % SZS output end Proof for theBenchmark
% 8.22/2.55
% 8.22/2.55 1936ms
%------------------------------------------------------------------------------