TSTP Solution File: ALG204+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG204+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 15:37:31 EDT 2022
% Result : Theorem 5.53s 1.83s
% Output : Proof 11.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG204+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.32 % Computer : n025.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Thu Jun 9 06:16:50 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.54/0.57 ____ _
% 0.54/0.57 ___ / __ \_____(_)___ ________ __________
% 0.54/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.57
% 0.54/0.57 A Theorem Prover for First-Order Logic
% 0.54/0.57 (ePrincess v.1.0)
% 0.54/0.57
% 0.54/0.57 (c) Philipp Rümmer, 2009-2015
% 0.54/0.57 (c) Peter Backeman, 2014-2015
% 0.54/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.57 Bug reports to peter@backeman.se
% 0.54/0.57
% 0.54/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.57
% 0.54/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.59/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.15/1.06 Prover 0: Preprocessing ...
% 3.54/1.41 Prover 0: Constructing countermodel ...
% 5.53/1.83 Prover 0: proved (1210ms)
% 5.53/1.83
% 5.53/1.83 No countermodel exists, formula is valid
% 5.53/1.83 % SZS status Theorem for theBenchmark
% 5.53/1.83
% 5.53/1.83 Generating proof ... found it (size 44)
% 10.89/3.05
% 10.89/3.05 % SZS output start Proof for theBenchmark
% 10.89/3.05 Assumed formulas after preprocessing and simplification:
% 10.89/3.06 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ( ~ (e26 = e25) & ~ (e26 = e24) & ~ (e26 = e23) & ~ (e26 = e22) & ~ (e26 = e20) & ~ (e26 = e21) & ~ (e26 = e16) & ~ (e26 = e15) & ~ (e26 = e14) & ~ (e26 = e13) & ~ (e26 = e12) & ~ (e26 = e10) & ~ (e26 = e11) & ~ (e25 = e24) & ~ (e25 = e23) & ~ (e25 = e22) & ~ (e25 = e20) & ~ (e25 = e21) & ~ (e25 = e16) & ~ (e25 = e15) & ~ (e25 = e14) & ~ (e25 = e13) & ~ (e25 = e12) & ~ (e25 = e10) & ~ (e25 = e11) & ~ (e24 = e23) & ~ (e24 = e22) & ~ (e24 = e20) & ~ (e24 = e21) & ~ (e24 = e16) & ~ (e24 = e15) & ~ (e24 = e14) & ~ (e24 = e13) & ~ (e24 = e12) & ~ (e24 = e10) & ~ (e24 = e11) & ~ (e23 = e22) & ~ (e23 = e20) & ~ (e23 = e21) & ~ (e23 = e16) & ~ (e23 = e15) & ~ (e23 = e14) & ~ (e23 = e13) & ~ (e23 = e12) & ~ (e23 = e10) & ~ (e23 = e11) & ~ (e22 = e20) & ~ (e22 = e21) & ~ (e22 = e16) & ~ (e22 = e15) & ~ (e22 = e14) & ~ (e22 = e13) & ~ (e22 = e12) & ~ (e22 = e10) & ~ (e22 = e11) & ~ (e20 = e21) & ~ (e20 = e16) & ~ (e20 = e15) & ~ (e20 = e14) & ~ (e20 = e13) & ~ (e20 = e12) & ~ (e20 = e10) & ~ (e20 = e11) & ~ (e21 = e16) & ~ (e21 = e15) & ~ (e21 = e14) & ~ (e21 = e13) & ~ (e21 = e12) & ~ (e21 = e10) & ~ (e21 = e11) & ~ (e16 = e15) & ~ (e16 = e14) & ~ (e16 = e13) & ~ (e16 = e12) & ~ (e16 = e10) & ~ (e16 = e11) & ~ (e15 = e14) & ~ (e15 = e13) & ~ (e15 = e12) & ~ (e15 = e10) & ~ (e15 = e11) & ~ (e14 = e13) & ~ (e14 = e12) & ~ (e14 = e10) & ~ (e14 = e11) & ~ (e13 = e12) & ~ (e13 = e10) & ~ (e13 = e11) & ~ (e12 = e10) & ~ (e12 = e11) & ~ (e10 = e11) & op2(v6, v6) = v0 & op2(v6, v5) = v6 & op2(v6, v4) = v1 & op2(v6, v3) = v3 & op2(v6, v2) = v4 & op2(v6, v1) = v2 & op2(v6, v0) = v5 & op2(v5, v6) = v6 & op2(v5, v5) = v1 & op2(v5, v4) = v5 & op2(v5, v3) = v0 & op2(v5, v2) = v3 & op2(v5, v1) = v4 & op2(v5, v0) = v2 & op2(v4, v6) = v1 & op2(v4, v5) = v5 & op2(v4, v4) = v2 & op2(v4, v3) = v6 & op2(v4, v2) = v0 & op2(v4, v1) = v3 & op2(v4, v0) = v4 & op2(v3, v6) = v3 & op2(v3, v5) = v0 & op2(v3, v4) = v6 & op2(v3, v3) = v4 & op2(v3, v2) = v2 & op2(v3, v1) = v5 & op2(v3, v0) = v1 & op2(v2, v6) = v4 & op2(v2, v5) = v3 & op2(v2, v4) = v0 & op2(v2, v3) = v2 & op2(v2, v2) = v5 & op2(v2, v1) = v1 & op2(v2, v0) = v6 & op2(v1, v6) = v2 & op2(v1, v5) = v4 & op2(v1, v4) = v3 & op2(v1, v3) = v5 & op2(v1, v2) = v1 & op2(v1, v1) = v6 & op2(v1, v0) = v0 & op2(v0, v6) = v5 & op2(v0, v5) = v2 & op2(v0, v4) = v4 & op2(v0, v3) = v1 & op2(v0, v2) = v6 & op2(v0, v1) = v0 & op2(v0, v0) = v3 & op2(e26, e26) = e26 & op2(e26, e25) = e22 & op2(e26, e24) = e23 & op2(e26, e23) = e21 & op2(e26, e22) = e20 & op2(e26, e20) = e25 & op2(e26, e21) = e24 & op2(e25, e26) = e22 & op2(e25, e25) = e25 & op2(e25, e24) = e21 & op2(e25, e23) = e26 & op2(e25, e22) = e23 & op2(e25, e20) = e24 & op2(e25, e21) = e20 & op2(e24, e26) = e23 & op2(e24, e25) = e21 & op2(e24, e24) = e24 & op2(e24, e23) = e20 & op2(e24, e22) = e25 & op2(e24, e20) = e26 & op2(e24, e21) = e22 & op2(e23, e26) = e21 & op2(e23, e25) = e26 & op2(e23, e24) = e20 & op2(e23, e23) = e23 & op2(e23, e22) = e24 & op2(e23, e20) = e22 & op2(e23, e21) = e25 & op2(e22, e26) = e20 & op2(e22, e25) = e23 & op2(e22, e24) = e25 & op2(e22, e23) = e24 & op2(e22, e22) = e22 & op2(e22, e20) = e21 & op2(e22, e21) = e26 & op2(e20, e26) = e25 & op2(e20, e25) = e24 & op2(e20, e24) = e26 & op2(e20, e23) = e22 & op2(e20, e22) = e21 & op2(e20, e20) = e20 & op2(e20, e21) = e23 & op2(e21, e26) = e24 & op2(e21, e25) = e20 & op2(e21, e24) = e22 & op2(e21, e23) = e25 & op2(e21, e22) = e26 & op2(e21, e20) = e23 & op2(e21, e21) = e21 & op1(v13, v13) = v13 & op1(v13, v12) = v9 & op1(v13, v11) = v10 & op1(v13, v10) = v8 & op1(v13, v9) = v7 & op1(v13, v8) = v11 & op1(v13, v7) = v12 & op1(v12, v13) = v9 & op1(v12, v12) = v12 & op1(v12, v11) = v8 & op1(v12, v10) = v13 & op1(v12, v9) = v10 & op1(v12, v8) = v7 & op1(v12, v7) = v11 & op1(v11, v13) = v10 & op1(v11, v12) = v8 & op1(v11, v11) = v11 & op1(v11, v10) = v7 & op1(v11, v9) = v12 & op1(v11, v8) = v9 & op1(v11, v7) = v13 & op1(v10, v13) = v8 & op1(v10, v12) = v13 & op1(v10, v11) = v7 & op1(v10, v10) = v10 & op1(v10, v9) = v11 & op1(v10, v8) = v12 & op1(v10, v7) = v9 & op1(v9, v13) = v7 & op1(v9, v12) = v10 & op1(v9, v11) = v12 & op1(v9, v10) = v11 & op1(v9, v9) = v9 & op1(v9, v8) = v13 & op1(v9, v7) = v8 & op1(v8, v13) = v11 & op1(v8, v12) = v7 & op1(v8, v11) = v9 & op1(v8, v10) = v12 & op1(v8, v9) = v13 & op1(v8, v8) = v8 & op1(v8, v7) = v10 & op1(v7, v13) = v12 & op1(v7, v12) = v11 & op1(v7, v11) = v13 & op1(v7, v10) = v9 & op1(v7, v9) = v8 & op1(v7, v8) = v10 & op1(v7, v7) = v7 & op1(e16, e16) = e10 & op1(e16, e15) = e16 & op1(e16, e14) = e11 & op1(e16, e13) = e13 & op1(e16, e12) = e14 & op1(e16, e10) = e15 & op1(e16, e11) = e12 & op1(e15, e16) = e16 & op1(e15, e15) = e11 & op1(e15, e14) = e15 & op1(e15, e13) = e10 & op1(e15, e12) = e13 & op1(e15, e10) = e12 & op1(e15, e11) = e14 & op1(e14, e16) = e11 & op1(e14, e15) = e15 & op1(e14, e14) = e12 & op1(e14, e13) = e16 & op1(e14, e12) = e10 & op1(e14, e10) = e14 & op1(e14, e11) = e13 & op1(e13, e16) = e13 & op1(e13, e15) = e10 & op1(e13, e14) = e16 & op1(e13, e13) = e14 & op1(e13, e12) = e12 & op1(e13, e10) = e11 & op1(e13, e11) = e15 & op1(e12, e16) = e14 & op1(e12, e15) = e13 & op1(e12, e14) = e10 & op1(e12, e13) = e12 & op1(e12, e12) = e15 & op1(e12, e10) = e16 & op1(e12, e11) = e11 & op1(e10, e16) = e15 & op1(e10, e15) = e12 & op1(e10, e14) = e14 & op1(e10, e13) = e11 & op1(e10, e12) = e16 & op1(e10, e10) = e13 & op1(e10, e11) = e10 & op1(e11, e16) = e12 & op1(e11, e15) = e14 & op1(e11, e14) = e13 & op1(e11, e13) = e15 & op1(e11, e12) = e11 & op1(e11, e10) = e10 & op1(e11, e11) = e16 & h(v13) = e26 & h(v12) = e25 & h(v11) = e24 & h(v10) = e23 & h(v9) = e22 & h(v8) = e21 & h(v7) = e20 & h(e16) = v6 & h(e15) = v5 & h(e14) = v4 & h(e13) = v3 & h(e12) = v2 & h(e10) = v0 & h(e11) = v1 & j(v6) = e16 & j(v5) = e15 & j(v4) = e14 & j(v3) = e13 & j(v2) = e12 & j(v1) = e11 & j(v0) = e10 & j(e26) = v13 & j(e25) = v12 & j(e24) = v11 & j(e23) = v10 & j(e22) = v9 & j(e20) = v7 & j(e21) = v8 & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (op2(v17, v16) = v15) | ~ (op2(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (op1(v17, v16) = v15) | ~ (op1(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (h(v16) = v15) | ~ (h(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (j(v16) = v15) | ~ (j(v16) = v14)) & (v13 = e16 | v13 = e15 | v13 = e14 | v13 = e13 | v13 = e12 | v13 = e10 | v13 = e11) & (v12 = e16 | v12 = e15 | v12 = e14 | v12 = e13 | v12 = e12 | v12 = e10 | v12 = e11) & (v11 = e16 | v11 = e15 | v11 = e14 | v11 = e13 | v11 = e12 | v11 = e10 | v11 = e11) & (v10 = e16 | v10 = e15 | v10 = e14 | v10 = e13 | v10 = e12 | v10 = e10 | v10 = e11) & (v9 = e16 | v9 = e15 | v9 = e14 | v9 = e13 | v9 = e12 | v9 = e10 | v9 = e11) & (v8 = e16 | v8 = e15 | v8 = e14 | v8 = e13 | v8 = e12 | v8 = e10 | v8 = e11) & (v7 = e16 | v7 = e15 | v7 = e14 | v7 = e13 | v7 = e12 | v7 = e10 | v7 = e11) & (v6 = e26 | v6 = e25 | v6 = e24 | v6 = e23 | v6 = e22 | v6 = e20 | v6 = e21) & (v5 = e26 | v5 = e25 | v5 = e24 | v5 = e23 | v5 = e22 | v5 = e20 | v5 = e21) & (v4 = e26 | v4 = e25 | v4 = e24 | v4 = e23 | v4 = e22 | v4 = e20 | v4 = e21) & (v3 = e26 | v3 = e25 | v3 = e24 | v3 = e23 | v3 = e22 | v3 = e20 | v3 = e21) & (v2 = e26 | v2 = e25 | v2 = e24 | v2 = e23 | v2 = e22 | v2 = e20 | v2 = e21) & (v1 = e26 | v1 = e25 | v1 = e24 | v1 = e23 | v1 = e22 | v1 = e20 | v1 = e21) & (v0 = e26 | v0 = e25 | v0 = e24 | v0 = e23 | v0 = e22 | v0 = e20 | v0 = e21))
% 11.09/3.12 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13 yields:
% 11.09/3.12 | (1) ~ (e26 = e25) & ~ (e26 = e24) & ~ (e26 = e23) & ~ (e26 = e22) & ~ (e26 = e20) & ~ (e26 = e21) & ~ (e26 = e16) & ~ (e26 = e15) & ~ (e26 = e14) & ~ (e26 = e13) & ~ (e26 = e12) & ~ (e26 = e10) & ~ (e26 = e11) & ~ (e25 = e24) & ~ (e25 = e23) & ~ (e25 = e22) & ~ (e25 = e20) & ~ (e25 = e21) & ~ (e25 = e16) & ~ (e25 = e15) & ~ (e25 = e14) & ~ (e25 = e13) & ~ (e25 = e12) & ~ (e25 = e10) & ~ (e25 = e11) & ~ (e24 = e23) & ~ (e24 = e22) & ~ (e24 = e20) & ~ (e24 = e21) & ~ (e24 = e16) & ~ (e24 = e15) & ~ (e24 = e14) & ~ (e24 = e13) & ~ (e24 = e12) & ~ (e24 = e10) & ~ (e24 = e11) & ~ (e23 = e22) & ~ (e23 = e20) & ~ (e23 = e21) & ~ (e23 = e16) & ~ (e23 = e15) & ~ (e23 = e14) & ~ (e23 = e13) & ~ (e23 = e12) & ~ (e23 = e10) & ~ (e23 = e11) & ~ (e22 = e20) & ~ (e22 = e21) & ~ (e22 = e16) & ~ (e22 = e15) & ~ (e22 = e14) & ~ (e22 = e13) & ~ (e22 = e12) & ~ (e22 = e10) & ~ (e22 = e11) & ~ (e20 = e21) & ~ (e20 = e16) & ~ (e20 = e15) & ~ (e20 = e14) & ~ (e20 = e13) & ~ (e20 = e12) & ~ (e20 = e10) & ~ (e20 = e11) & ~ (e21 = e16) & ~ (e21 = e15) & ~ (e21 = e14) & ~ (e21 = e13) & ~ (e21 = e12) & ~ (e21 = e10) & ~ (e21 = e11) & ~ (e16 = e15) & ~ (e16 = e14) & ~ (e16 = e13) & ~ (e16 = e12) & ~ (e16 = e10) & ~ (e16 = e11) & ~ (e15 = e14) & ~ (e15 = e13) & ~ (e15 = e12) & ~ (e15 = e10) & ~ (e15 = e11) & ~ (e14 = e13) & ~ (e14 = e12) & ~ (e14 = e10) & ~ (e14 = e11) & ~ (e13 = e12) & ~ (e13 = e10) & ~ (e13 = e11) & ~ (e12 = e10) & ~ (e12 = e11) & ~ (e10 = e11) & op2(all_0_7_7, all_0_7_7) = all_0_13_13 & op2(all_0_7_7, all_0_8_8) = all_0_7_7 & op2(all_0_7_7, all_0_9_9) = all_0_12_12 & op2(all_0_7_7, all_0_10_10) = all_0_10_10 & op2(all_0_7_7, all_0_11_11) = all_0_9_9 & op2(all_0_7_7, all_0_12_12) = all_0_11_11 & op2(all_0_7_7, all_0_13_13) = all_0_8_8 & op2(all_0_8_8, all_0_7_7) = all_0_7_7 & op2(all_0_8_8, all_0_8_8) = all_0_12_12 & op2(all_0_8_8, all_0_9_9) = all_0_8_8 & op2(all_0_8_8, all_0_10_10) = all_0_13_13 & op2(all_0_8_8, all_0_11_11) = all_0_10_10 & op2(all_0_8_8, all_0_12_12) = all_0_9_9 & op2(all_0_8_8, all_0_13_13) = all_0_11_11 & op2(all_0_9_9, all_0_7_7) = all_0_12_12 & op2(all_0_9_9, all_0_8_8) = all_0_8_8 & op2(all_0_9_9, all_0_9_9) = all_0_11_11 & op2(all_0_9_9, all_0_10_10) = all_0_7_7 & op2(all_0_9_9, all_0_11_11) = all_0_13_13 & op2(all_0_9_9, all_0_12_12) = all_0_10_10 & op2(all_0_9_9, all_0_13_13) = all_0_9_9 & op2(all_0_10_10, all_0_7_7) = all_0_10_10 & op2(all_0_10_10, all_0_8_8) = all_0_13_13 & op2(all_0_10_10, all_0_9_9) = all_0_7_7 & op2(all_0_10_10, all_0_10_10) = all_0_9_9 & op2(all_0_10_10, all_0_11_11) = all_0_11_11 & op2(all_0_10_10, all_0_12_12) = all_0_8_8 & op2(all_0_10_10, all_0_13_13) = all_0_12_12 & op2(all_0_11_11, all_0_7_7) = all_0_9_9 & op2(all_0_11_11, all_0_8_8) = all_0_10_10 & op2(all_0_11_11, all_0_9_9) = all_0_13_13 & op2(all_0_11_11, all_0_10_10) = all_0_11_11 & op2(all_0_11_11, all_0_11_11) = all_0_8_8 & op2(all_0_11_11, all_0_12_12) = all_0_12_12 & op2(all_0_11_11, all_0_13_13) = all_0_7_7 & op2(all_0_12_12, all_0_7_7) = all_0_11_11 & op2(all_0_12_12, all_0_8_8) = all_0_9_9 & op2(all_0_12_12, all_0_9_9) = all_0_10_10 & op2(all_0_12_12, all_0_10_10) = all_0_8_8 & op2(all_0_12_12, all_0_11_11) = all_0_12_12 & op2(all_0_12_12, all_0_12_12) = all_0_7_7 & op2(all_0_12_12, all_0_13_13) = all_0_13_13 & op2(all_0_13_13, all_0_7_7) = all_0_8_8 & op2(all_0_13_13, all_0_8_8) = all_0_11_11 & op2(all_0_13_13, all_0_9_9) = all_0_9_9 & op2(all_0_13_13, all_0_10_10) = all_0_12_12 & op2(all_0_13_13, all_0_11_11) = all_0_7_7 & op2(all_0_13_13, all_0_12_12) = all_0_13_13 & op2(all_0_13_13, all_0_13_13) = all_0_10_10 & op2(e26, e26) = e26 & op2(e26, e25) = e22 & op2(e26, e24) = e23 & op2(e26, e23) = e21 & op2(e26, e22) = e20 & op2(e26, e20) = e25 & op2(e26, e21) = e24 & op2(e25, e26) = e22 & op2(e25, e25) = e25 & op2(e25, e24) = e21 & op2(e25, e23) = e26 & op2(e25, e22) = e23 & op2(e25, e20) = e24 & op2(e25, e21) = e20 & op2(e24, e26) = e23 & op2(e24, e25) = e21 & op2(e24, e24) = e24 & op2(e24, e23) = e20 & op2(e24, e22) = e25 & op2(e24, e20) = e26 & op2(e24, e21) = e22 & op2(e23, e26) = e21 & op2(e23, e25) = e26 & op2(e23, e24) = e20 & op2(e23, e23) = e23 & op2(e23, e22) = e24 & op2(e23, e20) = e22 & op2(e23, e21) = e25 & op2(e22, e26) = e20 & op2(e22, e25) = e23 & op2(e22, e24) = e25 & op2(e22, e23) = e24 & op2(e22, e22) = e22 & op2(e22, e20) = e21 & op2(e22, e21) = e26 & op2(e20, e26) = e25 & op2(e20, e25) = e24 & op2(e20, e24) = e26 & op2(e20, e23) = e22 & op2(e20, e22) = e21 & op2(e20, e20) = e20 & op2(e20, e21) = e23 & op2(e21, e26) = e24 & op2(e21, e25) = e20 & op2(e21, e24) = e22 & op2(e21, e23) = e25 & op2(e21, e22) = e26 & op2(e21, e20) = e23 & 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_5_5 & op1(all_0_0_0, all_0_4_4) = all_0_6_6 & op1(all_0_0_0, all_0_5_5) = all_0_2_2 & op1(all_0_0_0, all_0_6_6) = all_0_1_1 & op1(all_0_1_1, all_0_0_0) = all_0_4_4 & op1(all_0_1_1, all_0_1_1) = all_0_1_1 & op1(all_0_1_1, all_0_2_2) = all_0_5_5 & op1(all_0_1_1, all_0_3_3) = all_0_0_0 & op1(all_0_1_1, all_0_4_4) = all_0_3_3 & op1(all_0_1_1, all_0_5_5) = all_0_6_6 & op1(all_0_1_1, all_0_6_6) = all_0_2_2 & op1(all_0_2_2, all_0_0_0) = all_0_3_3 & op1(all_0_2_2, all_0_1_1) = all_0_5_5 & op1(all_0_2_2, all_0_2_2) = all_0_2_2 & op1(all_0_2_2, all_0_3_3) = all_0_6_6 & op1(all_0_2_2, all_0_4_4) = all_0_1_1 & op1(all_0_2_2, all_0_5_5) = all_0_4_4 & op1(all_0_2_2, all_0_6_6) = all_0_0_0 & op1(all_0_3_3, all_0_0_0) = all_0_5_5 & op1(all_0_3_3, all_0_1_1) = all_0_0_0 & op1(all_0_3_3, all_0_2_2) = all_0_6_6 & 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_3_3, all_0_5_5) = all_0_1_1 & op1(all_0_3_3, all_0_6_6) = all_0_4_4 & op1(all_0_4_4, all_0_0_0) = all_0_6_6 & op1(all_0_4_4, all_0_1_1) = all_0_3_3 & op1(all_0_4_4, all_0_2_2) = all_0_1_1 & op1(all_0_4_4, all_0_3_3) = all_0_2_2 & op1(all_0_4_4, all_0_4_4) = all_0_4_4 & op1(all_0_4_4, all_0_5_5) = all_0_0_0 & op1(all_0_4_4, all_0_6_6) = all_0_5_5 & op1(all_0_5_5, all_0_0_0) = all_0_2_2 & op1(all_0_5_5, all_0_1_1) = all_0_6_6 & op1(all_0_5_5, all_0_2_2) = all_0_4_4 & op1(all_0_5_5, all_0_3_3) = all_0_1_1 & op1(all_0_5_5, all_0_4_4) = all_0_0_0 & op1(all_0_5_5, all_0_5_5) = all_0_5_5 & op1(all_0_5_5, all_0_6_6) = all_0_3_3 & op1(all_0_6_6, all_0_0_0) = all_0_1_1 & op1(all_0_6_6, all_0_1_1) = all_0_2_2 & op1(all_0_6_6, all_0_2_2) = all_0_0_0 & op1(all_0_6_6, all_0_3_3) = all_0_4_4 & op1(all_0_6_6, all_0_4_4) = all_0_5_5 & op1(all_0_6_6, all_0_5_5) = all_0_3_3 & op1(all_0_6_6, all_0_6_6) = all_0_6_6 & op1(e16, e16) = e10 & op1(e16, e15) = e16 & op1(e16, e14) = e11 & op1(e16, e13) = e13 & op1(e16, e12) = e14 & op1(e16, e10) = e15 & op1(e16, e11) = e12 & op1(e15, e16) = e16 & op1(e15, e15) = e11 & op1(e15, e14) = e15 & op1(e15, e13) = e10 & op1(e15, e12) = e13 & op1(e15, e10) = e12 & op1(e15, e11) = e14 & op1(e14, e16) = e11 & op1(e14, e15) = e15 & op1(e14, e14) = e12 & op1(e14, e13) = e16 & op1(e14, e12) = e10 & op1(e14, e10) = e14 & op1(e14, e11) = e13 & op1(e13, e16) = e13 & op1(e13, e15) = e10 & op1(e13, e14) = e16 & op1(e13, e13) = e14 & op1(e13, e12) = e12 & op1(e13, e10) = e11 & op1(e13, e11) = e15 & op1(e12, e16) = e14 & op1(e12, e15) = e13 & op1(e12, e14) = e10 & op1(e12, e13) = e12 & op1(e12, e12) = e15 & op1(e12, e10) = e16 & op1(e12, e11) = e11 & op1(e10, e16) = e15 & op1(e10, e15) = e12 & op1(e10, e14) = e14 & op1(e10, e13) = e11 & op1(e10, e12) = e16 & op1(e10, e10) = e13 & op1(e10, e11) = e10 & op1(e11, e16) = e12 & op1(e11, e15) = e14 & op1(e11, e14) = e13 & op1(e11, e13) = e15 & op1(e11, e12) = e11 & op1(e11, e10) = e10 & op1(e11, e11) = e16 & h(all_0_0_0) = e26 & h(all_0_1_1) = e25 & h(all_0_2_2) = e24 & h(all_0_3_3) = e23 & h(all_0_4_4) = e22 & h(all_0_5_5) = e21 & h(all_0_6_6) = e20 & h(e16) = all_0_7_7 & h(e15) = all_0_8_8 & h(e14) = all_0_9_9 & h(e13) = all_0_10_10 & h(e12) = all_0_11_11 & h(e10) = all_0_13_13 & h(e11) = all_0_12_12 & j(all_0_7_7) = e16 & j(all_0_8_8) = e15 & j(all_0_9_9) = e14 & j(all_0_10_10) = e13 & j(all_0_11_11) = e12 & j(all_0_12_12) = e11 & j(all_0_13_13) = e10 & j(e26) = all_0_0_0 & j(e25) = all_0_1_1 & j(e24) = all_0_2_2 & j(e23) = all_0_3_3 & j(e22) = all_0_4_4 & j(e20) = all_0_6_6 & j(e21) = all_0_5_5 & ! [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 = e16 | all_0_0_0 = e15 | all_0_0_0 = e14 | all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11) & (all_0_1_1 = e16 | all_0_1_1 = e15 | all_0_1_1 = e14 | all_0_1_1 = e13 | all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11) & (all_0_2_2 = e16 | all_0_2_2 = e15 | all_0_2_2 = e14 | all_0_2_2 = e13 | all_0_2_2 = e12 | all_0_2_2 = e10 | all_0_2_2 = e11) & (all_0_3_3 = e16 | all_0_3_3 = e15 | all_0_3_3 = e14 | all_0_3_3 = e13 | all_0_3_3 = e12 | all_0_3_3 = e10 | all_0_3_3 = e11) & (all_0_4_4 = e16 | all_0_4_4 = e15 | all_0_4_4 = e14 | all_0_4_4 = e13 | all_0_4_4 = e12 | all_0_4_4 = e10 | all_0_4_4 = e11) & (all_0_5_5 = e16 | all_0_5_5 = e15 | all_0_5_5 = e14 | all_0_5_5 = e13 | all_0_5_5 = e12 | all_0_5_5 = e10 | all_0_5_5 = e11) & (all_0_6_6 = e16 | all_0_6_6 = e15 | all_0_6_6 = e14 | all_0_6_6 = e13 | all_0_6_6 = e12 | all_0_6_6 = e10 | all_0_6_6 = e11) & (all_0_7_7 = e26 | all_0_7_7 = e25 | all_0_7_7 = e24 | all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21) & (all_0_8_8 = e26 | all_0_8_8 = e25 | all_0_8_8 = e24 | all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21) & (all_0_9_9 = e26 | all_0_9_9 = e25 | all_0_9_9 = e24 | all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21) & (all_0_10_10 = e26 | all_0_10_10 = e25 | all_0_10_10 = e24 | all_0_10_10 = e23 | all_0_10_10 = e22 | all_0_10_10 = e20 | all_0_10_10 = e21) & (all_0_11_11 = e26 | all_0_11_11 = e25 | all_0_11_11 = e24 | all_0_11_11 = e23 | all_0_11_11 = e22 | all_0_11_11 = e20 | all_0_11_11 = e21) & (all_0_12_12 = e26 | all_0_12_12 = e25 | all_0_12_12 = e24 | all_0_12_12 = e23 | all_0_12_12 = e22 | all_0_12_12 = e20 | all_0_12_12 = e21) & (all_0_13_13 = e26 | all_0_13_13 = e25 | all_0_13_13 = e24 | all_0_13_13 = e23 | all_0_13_13 = e22 | all_0_13_13 = e20 | all_0_13_13 = e21)
% 11.31/3.14 |
% 11.31/3.14 | Applying alpha-rule on (1) yields:
% 11.31/3.14 | (2) ~ (e21 = e13)
% 11.31/3.14 | (3) ~ (e24 = e10)
% 11.31/3.14 | (4) op1(e10, e12) = e16
% 11.31/3.14 | (5) ~ (e21 = e16)
% 11.31/3.14 | (6) ~ (e16 = e14)
% 11.31/3.14 | (7) j(all_0_10_10) = e13
% 11.31/3.14 | (8) op1(all_0_0_0, all_0_5_5) = all_0_2_2
% 11.31/3.14 | (9) op2(all_0_11_11, all_0_13_13) = all_0_7_7
% 11.31/3.14 | (10) op1(e15, e14) = e15
% 11.31/3.14 | (11) op2(all_0_10_10, all_0_12_12) = all_0_8_8
% 11.31/3.14 | (12) op1(e11, e15) = e14
% 11.31/3.14 | (13) op1(all_0_4_4, all_0_0_0) = all_0_6_6
% 11.31/3.14 | (14) j(e26) = all_0_0_0
% 11.31/3.14 | (15) all_0_3_3 = e16 | all_0_3_3 = e15 | all_0_3_3 = e14 | all_0_3_3 = e13 | all_0_3_3 = e12 | all_0_3_3 = e10 | all_0_3_3 = e11
% 11.31/3.14 | (16) op1(e10, e13) = e11
% 11.31/3.14 | (17) ~ (e25 = e24)
% 11.31/3.15 | (18) op1(e13, e14) = e16
% 11.31/3.15 | (19) j(e22) = all_0_4_4
% 11.31/3.15 | (20) op2(e24, e23) = e20
% 11.31/3.15 | (21) all_0_0_0 = e16 | all_0_0_0 = e15 | all_0_0_0 = e14 | all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 11.31/3.15 | (22) ~ (e23 = e16)
% 11.31/3.15 | (23) op2(all_0_9_9, all_0_11_11) = all_0_13_13
% 11.31/3.15 | (24) op2(e21, e23) = e25
% 11.31/3.15 | (25) ~ (e12 = e11)
% 11.31/3.15 | (26) op1(e14, e10) = e14
% 11.31/3.15 | (27) ~ (e20 = e21)
% 11.31/3.15 | (28) ~ (e21 = e12)
% 11.31/3.15 | (29) op2(all_0_7_7, all_0_8_8) = all_0_7_7
% 11.31/3.15 | (30) all_0_13_13 = e26 | all_0_13_13 = e25 | all_0_13_13 = e24 | all_0_13_13 = e23 | all_0_13_13 = e22 | all_0_13_13 = e20 | all_0_13_13 = e21
% 11.31/3.15 | (31) ~ (e14 = e12)
% 11.31/3.15 | (32) op1(all_0_4_4, all_0_4_4) = all_0_4_4
% 11.31/3.15 | (33) op1(all_0_6_6, all_0_5_5) = all_0_3_3
% 11.31/3.15 | (34) ~ (e25 = e14)
% 11.31/3.15 | (35) ~ (e24 = e20)
% 11.31/3.15 | (36) op2(e26, e21) = e24
% 11.31/3.15 | (37) h(e16) = all_0_7_7
% 11.31/3.15 | (38) op2(all_0_12_12, all_0_12_12) = all_0_7_7
% 11.31/3.15 | (39) ~ (e26 = e10)
% 11.31/3.15 | (40) ~ (e26 = e25)
% 11.31/3.15 | (41) op1(e13, e11) = e15
% 11.31/3.15 | (42) ~ (e16 = e13)
% 11.31/3.15 | (43) op1(all_0_6_6, all_0_1_1) = all_0_2_2
% 11.31/3.15 | (44) op2(all_0_7_7, all_0_12_12) = all_0_11_11
% 11.31/3.15 | (45) j(all_0_11_11) = e12
% 11.31/3.15 | (46) ~ (e24 = e23)
% 11.31/3.15 | (47) op2(all_0_13_13, all_0_7_7) = all_0_8_8
% 11.31/3.15 | (48) op1(e15, e15) = e11
% 11.31/3.15 | (49) op2(e24, e21) = e22
% 11.31/3.15 | (50) op1(e11, e11) = e16
% 11.31/3.15 | (51) op1(all_0_6_6, all_0_2_2) = all_0_0_0
% 11.31/3.15 | (52) op2(all_0_11_11, all_0_11_11) = all_0_8_8
% 11.31/3.15 | (53) ~ (e26 = e14)
% 11.31/3.15 | (54) op2(e23, e25) = e26
% 11.31/3.15 | (55) op2(e26, e26) = e26
% 11.31/3.15 | (56) op1(e10, e11) = e10
% 11.31/3.15 | (57) ~ (e22 = e21)
% 11.31/3.15 | (58) op2(e22, e21) = e26
% 11.31/3.15 | (59) ~ (e24 = e22)
% 11.31/3.15 | (60) op1(e10, e16) = e15
% 11.31/3.15 | (61) op1(all_0_1_1, all_0_3_3) = all_0_0_0
% 11.31/3.15 | (62) op1(all_0_2_2, all_0_1_1) = all_0_5_5
% 11.31/3.15 | (63) op2(e21, e22) = e26
% 11.31/3.15 | (64) op2(e23, e24) = e20
% 11.31/3.15 | (65) ~ (e20 = e14)
% 11.31/3.15 | (66) ~ (e16 = e10)
% 11.31/3.15 | (67) op2(e20, e22) = e21
% 11.31/3.15 | (68) op1(all_0_5_5, all_0_5_5) = all_0_5_5
% 11.31/3.15 | (69) ~ (e25 = e20)
% 11.31/3.15 | (70) op1(all_0_2_2, all_0_3_3) = all_0_6_6
% 11.31/3.15 | (71) h(all_0_4_4) = e22
% 11.31/3.15 | (72) op2(all_0_9_9, all_0_9_9) = all_0_11_11
% 11.31/3.15 | (73) h(all_0_2_2) = e24
% 11.31/3.15 | (74) op1(e14, e14) = e12
% 11.31/3.15 | (75) op2(all_0_13_13, all_0_12_12) = all_0_13_13
% 11.31/3.15 | (76) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0))
% 11.31/3.15 | (77) ~ (e24 = e14)
% 11.31/3.15 | (78) h(e15) = all_0_8_8
% 11.31/3.15 | (79) op1(e15, e11) = e14
% 11.31/3.15 | (80) ~ (e20 = e10)
% 11.31/3.15 | (81) op1(all_0_1_1, all_0_1_1) = all_0_1_1
% 11.31/3.15 | (82) op2(e20, e20) = e20
% 11.31/3.15 | (83) j(all_0_9_9) = e14
% 11.31/3.15 | (84) op1(e12, e14) = e10
% 11.31/3.15 | (85) ~ (e26 = e24)
% 11.31/3.15 | (86) op2(all_0_13_13, all_0_13_13) = all_0_10_10
% 11.31/3.15 | (87) op2(e22, e26) = e20
% 11.31/3.15 | (88) op2(e22, e22) = e22
% 11.31/3.15 | (89) h(all_0_6_6) = e20
% 11.31/3.15 | (90) op1(e12, e16) = e14
% 11.31/3.15 | (91) ~ (e22 = e14)
% 11.31/3.15 | (92) op2(all_0_12_12, all_0_9_9) = all_0_10_10
% 11.31/3.15 | (93) op2(all_0_12_12, all_0_7_7) = all_0_11_11
% 11.31/3.15 | (94) op2(e23, e21) = e25
% 11.31/3.15 | (95) op2(all_0_10_10, all_0_13_13) = all_0_12_12
% 11.31/3.15 | (96) op1(all_0_6_6, all_0_6_6) = all_0_6_6
% 11.31/3.15 | (97) op1(all_0_5_5, all_0_3_3) = all_0_1_1
% 11.31/3.15 | (98) ~ (e25 = e13)
% 11.31/3.15 | (99) h(all_0_0_0) = e26
% 11.31/3.15 | (100) ~ (e15 = e14)
% 11.31/3.15 | (101) op1(all_0_1_1, all_0_0_0) = all_0_4_4
% 11.31/3.15 | (102) op2(e20, e23) = e22
% 11.31/3.15 | (103) op1(e15, e10) = e12
% 11.31/3.15 | (104) op2(e25, e26) = e22
% 11.31/3.15 | (105) ~ (e20 = e16)
% 11.31/3.15 | (106) ~ (e22 = e20)
% 11.31/3.16 | (107) ~ (e25 = e11)
% 11.31/3.16 | (108) ~ (e16 = e12)
% 11.31/3.16 | (109) op1(all_0_1_1, all_0_5_5) = all_0_6_6
% 11.31/3.16 | (110) ~ (e24 = e15)
% 11.31/3.16 | (111) op2(e25, e22) = e23
% 11.31/3.16 | (112) op2(e23, e26) = e21
% 11.31/3.16 | (113) op2(e21, e25) = e20
% 11.31/3.16 | (114) ~ (e15 = e12)
% 11.31/3.16 | (115) op1(all_0_0_0, all_0_0_0) = all_0_0_0
% 11.31/3.16 | (116) op2(all_0_10_10, all_0_8_8) = all_0_13_13
% 11.31/3.16 | (117) ~ (e26 = e20)
% 11.31/3.16 | (118) j(all_0_8_8) = e15
% 11.31/3.16 | (119) op2(all_0_13_13, all_0_9_9) = all_0_9_9
% 11.31/3.16 | (120) j(e23) = all_0_3_3
% 11.31/3.16 | (121) op2(all_0_13_13, all_0_8_8) = all_0_11_11
% 11.31/3.16 | (122) op2(e25, e25) = e25
% 11.31/3.16 | (123) op2(all_0_9_9, all_0_8_8) = all_0_8_8
% 11.31/3.16 | (124) j(e25) = all_0_1_1
% 11.31/3.16 | (125) op1(all_0_4_4, all_0_6_6) = all_0_5_5
% 11.31/3.16 | (126) ~ (e25 = e22)
% 11.31/3.16 | (127) ~ (e24 = e13)
% 11.31/3.16 | (128) ~ (e22 = e10)
% 11.31/3.16 | (129) op1(all_0_2_2, all_0_2_2) = all_0_2_2
% 11.31/3.16 | (130) ~ (e14 = e10)
% 11.31/3.16 | (131) op1(all_0_3_3, all_0_4_4) = all_0_2_2
% 11.31/3.16 | (132) op1(all_0_3_3, all_0_6_6) = all_0_4_4
% 11.31/3.16 | (133) op1(e15, e12) = e13
% 11.31/3.16 | (134) op1(all_0_2_2, all_0_6_6) = all_0_0_0
% 11.31/3.16 | (135) op1(all_0_2_2, all_0_0_0) = all_0_3_3
% 11.31/3.16 | (136) op2(e24, e22) = e25
% 11.31/3.16 | (137) all_0_9_9 = e26 | all_0_9_9 = e25 | all_0_9_9 = e24 | all_0_9_9 = e23 | all_0_9_9 = e22 | all_0_9_9 = e20 | all_0_9_9 = e21
% 11.31/3.16 | (138) op1(e10, e15) = e12
% 11.31/3.16 | (139) ~ (e25 = e10)
% 11.31/3.16 | (140) op2(e22, e24) = e25
% 11.31/3.16 | (141) op2(all_0_8_8, all_0_10_10) = all_0_13_13
% 11.31/3.16 | (142) ~ (e12 = e10)
% 11.31/3.16 | (143) op1(all_0_3_3, all_0_3_3) = all_0_3_3
% 11.31/3.16 | (144) ~ (e15 = e10)
% 11.31/3.16 | (145) op2(all_0_11_11, all_0_9_9) = all_0_13_13
% 11.31/3.16 | (146) all_0_5_5 = e16 | all_0_5_5 = e15 | all_0_5_5 = e14 | all_0_5_5 = e13 | all_0_5_5 = e12 | all_0_5_5 = e10 | all_0_5_5 = e11
% 11.31/3.16 | (147) h(e13) = all_0_10_10
% 11.31/3.16 | (148) op2(all_0_8_8, all_0_12_12) = all_0_9_9
% 11.31/3.16 | (149) op2(e24, e24) = e24
% 11.31/3.16 | (150) op1(all_0_0_0, all_0_3_3) = all_0_5_5
% 11.31/3.16 | (151) op1(all_0_5_5, all_0_4_4) = all_0_0_0
% 11.31/3.16 | (152) op1(e14, e11) = e13
% 11.31/3.16 | (153) op1(all_0_3_3, all_0_1_1) = all_0_0_0
% 11.31/3.16 | (154) op1(e11, e13) = e15
% 11.31/3.16 | (155) op2(e20, e24) = e26
% 11.31/3.16 | (156) op2(e21, e24) = e22
% 11.31/3.16 | (157) op1(all_0_4_4, all_0_3_3) = all_0_2_2
% 11.31/3.16 | (158) op2(e24, e26) = e23
% 11.31/3.16 | (159) h(e14) = all_0_9_9
% 11.31/3.16 | (160) op2(e24, e20) = e26
% 11.31/3.16 | (161) op2(all_0_8_8, all_0_8_8) = all_0_12_12
% 11.31/3.16 | (162) ~ (e23 = e12)
% 11.31/3.16 | (163) all_0_11_11 = e26 | all_0_11_11 = e25 | all_0_11_11 = e24 | all_0_11_11 = e23 | all_0_11_11 = e22 | all_0_11_11 = e20 | all_0_11_11 = e21
% 11.31/3.16 | (164) op2(e21, e21) = e21
% 11.31/3.16 | (165) ~ (e23 = e20)
% 11.31/3.16 | (166) op2(all_0_9_9, all_0_13_13) = all_0_9_9
% 11.31/3.16 | (167) op1(e11, e16) = e12
% 11.31/3.16 | (168) ~ (e20 = e11)
% 11.31/3.16 | (169) op1(e12, e15) = e13
% 11.31/3.16 | (170) op1(e10, e10) = e13
% 11.31/3.16 | (171) ~ (e15 = e11)
% 11.31/3.16 | (172) ~ (e16 = e11)
% 11.31/3.16 | (173) j(e21) = all_0_5_5
% 11.31/3.16 | (174) op1(e16, e16) = e10
% 11.31/3.16 | (175) op2(all_0_13_13, all_0_11_11) = all_0_7_7
% 11.31/3.16 | (176) op1(all_0_1_1, all_0_6_6) = all_0_2_2
% 11.31/3.16 | (177) ~ (e14 = e13)
% 11.31/3.16 | (178) op1(e12, e13) = e12
% 11.31/3.16 | (179) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0))
% 11.31/3.16 | (180) ~ (e25 = e15)
% 11.31/3.16 | (181) h(all_0_3_3) = e23
% 11.31/3.16 | (182) op2(all_0_13_13, all_0_10_10) = all_0_12_12
% 11.31/3.16 | (183) op1(e13, e10) = e11
% 11.31/3.16 | (184) op2(all_0_12_12, all_0_11_11) = all_0_12_12
% 11.31/3.17 | (185) ~ (e13 = e12)
% 11.31/3.17 | (186) op2(all_0_7_7, all_0_7_7) = all_0_13_13
% 11.31/3.17 | (187) op2(e20, e21) = e23
% 11.31/3.17 | (188) op2(all_0_8_8, all_0_11_11) = all_0_10_10
% 11.31/3.17 | (189) j(e20) = all_0_6_6
% 11.31/3.17 | (190) op1(all_0_6_6, all_0_0_0) = all_0_1_1
% 11.31/3.17 | (191) h(all_0_5_5) = e21
% 11.31/3.17 | (192) ~ (e14 = e11)
% 11.31/3.17 | (193) ~ (e23 = e15)
% 11.31/3.17 | (194) op1(e12, e10) = e16
% 11.31/3.17 | (195) ~ (e26 = e11)
% 11.31/3.17 | (196) op1(all_0_6_6, all_0_4_4) = all_0_5_5
% 11.31/3.17 | (197) op2(all_0_7_7, all_0_11_11) = all_0_9_9
% 11.31/3.17 | (198) op2(e22, e20) = e21
% 11.31/3.17 | (199) ~ (e24 = e11)
% 11.31/3.17 | (200) op1(all_0_0_0, all_0_1_1) = all_0_4_4
% 11.31/3.17 | (201) ~ (e26 = e23)
% 11.31/3.17 | (202) op1(e12, e12) = e15
% 11.31/3.17 | (203) op2(e26, e20) = e25
% 11.31/3.17 | (204) op2(all_0_9_9, all_0_12_12) = all_0_10_10
% 11.31/3.17 | (205) op2(e26, e22) = e20
% 11.31/3.17 | (206) op1(e16, e15) = e16
% 11.31/3.17 | (207) op2(all_0_11_11, all_0_12_12) = all_0_12_12
% 11.31/3.17 | (208) h(e12) = all_0_11_11
% 11.31/3.17 | (209) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0))
% 11.31/3.17 | (210) op2(all_0_10_10, all_0_9_9) = all_0_7_7
% 11.31/3.17 | (211) op1(all_0_3_3, all_0_5_5) = all_0_1_1
% 11.31/3.17 | (212) op2(all_0_9_9, all_0_7_7) = all_0_12_12
% 11.31/3.17 | (213) op1(all_0_4_4, all_0_5_5) = all_0_0_0
% 11.31/3.17 | (214) op1(all_0_5_5, all_0_6_6) = all_0_3_3
% 11.31/3.17 | (215) ~ (e23 = e14)
% 11.31/3.17 | (216) ~ (e21 = e15)
% 11.31/3.17 | (217) h(all_0_1_1) = e25
% 11.31/3.17 | (218) ~ (e23 = e13)
% 11.31/3.17 | (219) op2(all_0_11_11, all_0_7_7) = all_0_9_9
% 11.31/3.17 | (220) j(e24) = all_0_2_2
% 11.31/3.17 | (221) op2(all_0_8_8, all_0_7_7) = all_0_7_7
% 11.31/3.17 | (222) ~ (e13 = e10)
% 11.31/3.17 | (223) ~ (e21 = e10)
% 11.31/3.17 | (224) all_0_4_4 = e16 | all_0_4_4 = e15 | all_0_4_4 = e14 | all_0_4_4 = e13 | all_0_4_4 = e12 | all_0_4_4 = e10 | all_0_4_4 = e11
% 11.31/3.17 | (225) ~ (e22 = e13)
% 11.31/3.17 | (226) op2(all_0_10_10, all_0_10_10) = all_0_9_9
% 11.31/3.17 | (227) ~ (e20 = e12)
% 11.31/3.17 | (228) op2(e23, e20) = e22
% 11.31/3.17 | (229) ~ (e22 = e15)
% 11.31/3.17 | (230) ~ (e25 = e21)
% 11.31/3.17 | (231) op1(all_0_0_0, all_0_4_4) = all_0_6_6
% 11.31/3.17 | (232) op1(all_0_4_4, all_0_1_1) = all_0_3_3
% 11.31/3.17 | (233) op2(all_0_12_12, all_0_13_13) = all_0_13_13
% 11.31/3.17 | (234) all_0_10_10 = e26 | all_0_10_10 = e25 | all_0_10_10 = e24 | all_0_10_10 = e23 | all_0_10_10 = e22 | all_0_10_10 = e20 | all_0_10_10 = e21
% 11.31/3.17 | (235) op2(all_0_12_12, all_0_8_8) = all_0_9_9
% 11.31/3.17 | (236) ~ (e26 = e21)
% 11.31/3.17 | (237) op2(e23, e23) = e23
% 11.31/3.17 | (238) op1(e10, e14) = e14
% 11.31/3.17 | (239) ~ (e16 = e15)
% 11.31/3.17 | (240) op2(all_0_11_11, all_0_8_8) = all_0_10_10
% 11.31/3.17 | (241) op2(e20, e25) = e24
% 11.31/3.17 | (242) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0))
% 11.31/3.17 | (243) op1(e14, e12) = e10
% 11.31/3.17 | (244) ~ (e21 = e11)
% 11.31/3.17 | (245) ~ (e22 = e16)
% 11.31/3.17 | (246) op1(e16, e11) = e12
% 11.31/3.17 | (247) op2(e21, e26) = e24
% 11.31/3.17 | (248) j(all_0_12_12) = e11
% 11.31/3.17 | (249) ~ (e10 = e11)
% 11.31/3.17 | (250) op2(e25, e24) = e21
% 11.31/3.17 | (251) op2(e26, e24) = e23
% 11.31/3.18 | (252) op1(all_0_2_2, all_0_4_4) = all_0_1_1
% 11.31/3.18 | (253) ~ (e25 = e16)
% 11.31/3.18 | (254) op2(all_0_8_8, all_0_13_13) = all_0_11_11
% 11.31/3.18 | (255) ~ (e26 = e13)
% 11.31/3.18 | (256) op2(all_0_7_7, all_0_10_10) = all_0_10_10
% 11.31/3.18 | (257) all_0_6_6 = e16 | all_0_6_6 = e15 | all_0_6_6 = e14 | all_0_6_6 = e13 | all_0_6_6 = e12 | all_0_6_6 = e10 | all_0_6_6 = e11
% 11.31/3.18 | (258) h(e10) = all_0_13_13
% 11.31/3.18 | (259) ~ (e25 = e23)
% 11.31/3.18 | (260) ~ (e22 = e12)
% 11.31/3.18 | (261) op2(e26, e23) = e21
% 11.31/3.18 | (262) op1(all_0_0_0, all_0_6_6) = all_0_1_1
% 11.31/3.18 | (263) op1(e14, e13) = e16
% 11.31/3.18 | (264) ~ (e24 = e16)
% 11.31/3.18 | (265) op2(all_0_12_12, all_0_10_10) = all_0_8_8
% 11.31/3.18 | (266) op1(all_0_1_1, all_0_4_4) = all_0_3_3
% 11.31/3.18 | (267) j(all_0_7_7) = e16
% 11.31/3.18 | (268) op1(e11, e14) = e13
% 11.31/3.18 | (269) all_0_12_12 = e26 | all_0_12_12 = e25 | all_0_12_12 = e24 | all_0_12_12 = e23 | all_0_12_12 = e22 | all_0_12_12 = e20 | all_0_12_12 = e21
% 11.31/3.18 | (270) ~ (e23 = e22)
% 11.31/3.18 | (271) op1(all_0_2_2, all_0_5_5) = all_0_4_4
% 11.31/3.18 | (272) all_0_8_8 = e26 | all_0_8_8 = e25 | all_0_8_8 = e24 | all_0_8_8 = e23 | all_0_8_8 = e22 | all_0_8_8 = e20 | all_0_8_8 = e21
% 11.31/3.18 | (273) op1(e11, e12) = e11
% 11.31/3.18 | (274) all_0_7_7 = e26 | all_0_7_7 = e25 | all_0_7_7 = e24 | all_0_7_7 = e23 | all_0_7_7 = e22 | all_0_7_7 = e20 | all_0_7_7 = e21
% 11.31/3.18 | (275) op2(all_0_7_7, all_0_9_9) = all_0_12_12
% 11.31/3.18 | (276) op2(all_0_7_7, all_0_13_13) = all_0_8_8
% 11.31/3.18 | (277) op1(e14, e15) = e15
% 11.31/3.18 | (278) op1(e16, e14) = e11
% 11.31/3.18 | (279) ~ (e23 = e21)
% 11.31/3.18 | (280) ~ (e21 = e14)
% 11.31/3.18 | (281) op1(e15, e16) = e16
% 11.31/3.18 | (282) op1(e13, e12) = e12
% 11.31/3.18 | (283) ~ (e22 = e11)
% 11.31/3.18 | (284) op1(all_0_3_3, all_0_0_0) = all_0_5_5
% 11.31/3.18 | (285) ~ (e23 = e11)
% 11.31/3.18 | (286) op1(all_0_1_1, all_0_2_2) = all_0_5_5
% 11.31/3.18 | (287) j(all_0_13_13) = e10
% 11.31/3.18 | (288) op2(all_0_11_11, all_0_10_10) = all_0_11_11
% 11.31/3.18 | (289) op2(e20, e26) = e25
% 11.31/3.18 | (290) op2(e22, e23) = e24
% 11.31/3.18 | (291) op1(e16, e13) = e13
% 11.31/3.18 | (292) ~ (e26 = e15)
% 11.31/3.18 | (293) op2(all_0_8_8, all_0_9_9) = all_0_8_8
% 11.31/3.18 | (294) ~ (e26 = e22)
% 11.31/3.18 | (295) ~ (e15 = e13)
% 11.31/3.18 | (296) op1(e16, e12) = e14
% 11.31/3.18 | (297) all_0_1_1 = e16 | all_0_1_1 = e15 | all_0_1_1 = e14 | all_0_1_1 = e13 | all_0_1_1 = e12 | all_0_1_1 = e10 | all_0_1_1 = e11
% 11.31/3.18 | (298) op1(all_0_0_0, all_0_2_2) = all_0_3_3
% 11.31/3.18 | (299) op2(e25, e20) = e24
% 11.31/3.18 | (300) ~ (e20 = e13)
% 11.31/3.18 | (301) op2(all_0_9_9, all_0_10_10) = all_0_7_7
% 11.31/3.18 | (302) op1(all_0_5_5, all_0_2_2) = all_0_4_4
% 11.31/3.18 | (303) op2(e24, e25) = e21
% 11.31/3.18 | (304) ~ (e25 = e12)
% 11.31/3.18 | (305) h(e11) = all_0_12_12
% 11.31/3.18 | (306) op1(e12, e11) = e11
% 11.31/3.18 | (307) op2(e26, e25) = e22
% 11.31/3.18 | (308) op1(e14, e16) = e11
% 11.31/3.18 | (309) op1(e13, e13) = e14
% 11.31/3.18 | (310) op2(e21, e20) = e23
% 11.31/3.18 | (311) ~ (e20 = e15)
% 11.31/3.18 | (312) op1(all_0_5_5, all_0_0_0) = all_0_2_2
% 11.31/3.19 | (313) op1(e16, e10) = e15
% 11.31/3.19 | (314) op1(e11, e10) = e10
% 11.31/3.19 | (315) op1(all_0_5_5, all_0_1_1) = all_0_6_6
% 11.31/3.19 | (316) op1(e15, e13) = e10
% 11.31/3.19 | (317) op2(all_0_10_10, all_0_11_11) = all_0_11_11
% 11.31/3.19 | (318) op1(e13, e15) = e10
% 11.31/3.19 | (319) ~ (e26 = e12)
% 11.31/3.19 | (320) op2(all_0_10_10, all_0_7_7) = all_0_10_10
% 11.31/3.19 | (321) ~ (e24 = e12)
% 11.31/3.19 | (322) ~ (e26 = e16)
% 11.31/3.19 | (323) ~ (e24 = e21)
% 11.31/3.19 | (324) op1(all_0_6_6, all_0_3_3) = all_0_4_4
% 11.31/3.19 | (325) op2(e23, e22) = e24
% 11.31/3.19 | (326) op1(e13, e16) = e13
% 11.31/3.19 | (327) op2(e22, e25) = e23
% 11.31/3.19 | (328) op1(all_0_3_3, all_0_2_2) = all_0_6_6
% 11.31/3.19 | (329) op2(e25, e21) = e20
% 11.31/3.19 | (330) ~ (e23 = e10)
% 11.31/3.19 | (331) ~ (e13 = e11)
% 11.31/3.19 | (332) all_0_2_2 = e16 | all_0_2_2 = e15 | all_0_2_2 = e14 | all_0_2_2 = e13 | all_0_2_2 = e12 | all_0_2_2 = e10 | all_0_2_2 = e11
% 11.31/3.19 | (333) op1(all_0_4_4, all_0_2_2) = all_0_1_1
% 11.31/3.19 | (334) op2(e25, e23) = e26
% 11.31/3.19 |
% 11.31/3.19 +-Applying beta-rule and splitting (21), into two cases.
% 11.31/3.19 |-Branch one:
% 11.31/3.19 | (335) all_0_0_0 = e16
% 11.31/3.19 |
% 11.31/3.19 | From (335)(335)(335) and (115) follows:
% 11.31/3.19 | (336) op1(e16, e16) = e16
% 11.31/3.19 |
% 11.31/3.19 | Instantiating formula (209) with e16, e16, e16, e10 and discharging atoms op1(e16, e16) = e16, op1(e16, e16) = e10, yields:
% 11.31/3.19 | (337) e16 = e10
% 11.31/3.19 |
% 11.31/3.19 | Equations (337) can reduce 66 to:
% 11.31/3.19 | (338) $false
% 11.31/3.19 |
% 11.31/3.19 |-The branch is then unsatisfiable
% 11.31/3.19 |-Branch two:
% 11.31/3.19 | (339) ~ (all_0_0_0 = e16)
% 11.31/3.19 | (340) all_0_0_0 = e15 | all_0_0_0 = e14 | all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 11.31/3.19 |
% 11.31/3.19 +-Applying beta-rule and splitting (340), into two cases.
% 11.31/3.19 |-Branch one:
% 11.31/3.19 | (341) all_0_0_0 = e15
% 11.31/3.19 |
% 11.31/3.19 | From (341)(341)(341) and (115) follows:
% 11.31/3.19 | (342) op1(e15, e15) = e15
% 11.31/3.19 |
% 11.31/3.19 | Instantiating formula (209) with e15, e15, e15, e11 and discharging atoms op1(e15, e15) = e15, op1(e15, e15) = e11, yields:
% 11.31/3.19 | (343) e15 = e11
% 11.31/3.19 |
% 11.31/3.19 | Equations (343) can reduce 171 to:
% 11.31/3.19 | (338) $false
% 11.31/3.19 |
% 11.31/3.19 |-The branch is then unsatisfiable
% 11.31/3.19 |-Branch two:
% 11.31/3.19 | (345) ~ (all_0_0_0 = e15)
% 11.31/3.19 | (346) 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
% 11.31/3.19 |
% 11.31/3.19 +-Applying beta-rule and splitting (346), into two cases.
% 11.31/3.19 |-Branch one:
% 11.31/3.19 | (347) all_0_0_0 = e14
% 11.31/3.19 |
% 11.31/3.19 | From (347)(347)(347) and (115) follows:
% 11.31/3.19 | (348) op1(e14, e14) = e14
% 11.31/3.19 |
% 11.31/3.19 | Instantiating formula (209) with e14, e14, e14, e12 and discharging atoms op1(e14, e14) = e14, op1(e14, e14) = e12, yields:
% 11.31/3.19 | (349) e14 = e12
% 11.31/3.19 |
% 11.31/3.19 | Equations (349) can reduce 31 to:
% 11.31/3.19 | (338) $false
% 11.31/3.19 |
% 11.31/3.19 |-The branch is then unsatisfiable
% 11.31/3.19 |-Branch two:
% 11.31/3.19 | (351) ~ (all_0_0_0 = e14)
% 11.31/3.19 | (352) all_0_0_0 = e13 | all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 11.31/3.19 |
% 11.31/3.19 +-Applying beta-rule and splitting (352), into two cases.
% 11.31/3.19 |-Branch one:
% 11.31/3.19 | (353) all_0_0_0 = e13
% 11.31/3.19 |
% 11.31/3.19 | Equations (353) can reduce 351 to:
% 11.31/3.19 | (354) ~ (e14 = e13)
% 11.31/3.19 |
% 11.31/3.19 | Simplifying 354 yields:
% 11.31/3.19 | (177) ~ (e14 = e13)
% 11.31/3.19 |
% 11.31/3.19 | From (353)(353)(353) and (115) follows:
% 11.31/3.19 | (356) op1(e13, e13) = e13
% 11.31/3.19 |
% 11.31/3.19 | Instantiating formula (209) with e13, e13, e13, e14 and discharging atoms op1(e13, e13) = e14, op1(e13, e13) = e13, yields:
% 11.31/3.20 | (357) e14 = e13
% 11.31/3.20 |
% 11.31/3.20 | Equations (357) can reduce 177 to:
% 11.31/3.20 | (338) $false
% 11.31/3.20 |
% 11.31/3.20 |-The branch is then unsatisfiable
% 11.31/3.20 |-Branch two:
% 11.31/3.20 | (359) ~ (all_0_0_0 = e13)
% 11.31/3.20 | (360) all_0_0_0 = e12 | all_0_0_0 = e10 | all_0_0_0 = e11
% 11.31/3.20 |
% 11.31/3.20 +-Applying beta-rule and splitting (360), into two cases.
% 11.31/3.20 |-Branch one:
% 11.31/3.20 | (361) all_0_0_0 = e12
% 11.31/3.20 |
% 11.31/3.20 | Equations (361) can reduce 345 to:
% 11.31/3.20 | (362) ~ (e15 = e12)
% 11.31/3.20 |
% 11.31/3.20 | Simplifying 362 yields:
% 11.31/3.20 | (114) ~ (e15 = e12)
% 11.31/3.20 |
% 11.31/3.20 | From (361)(361)(361) and (115) follows:
% 11.31/3.20 | (364) op1(e12, e12) = e12
% 11.31/3.20 |
% 11.31/3.20 | Instantiating formula (209) with e12, e12, e12, e15 and discharging atoms op1(e12, e12) = e15, op1(e12, e12) = e12, yields:
% 11.31/3.20 | (365) e15 = e12
% 11.31/3.20 |
% 11.31/3.20 | Equations (365) can reduce 114 to:
% 11.31/3.20 | (338) $false
% 11.31/3.20 |
% 11.31/3.20 |-The branch is then unsatisfiable
% 11.31/3.20 |-Branch two:
% 11.31/3.20 | (367) ~ (all_0_0_0 = e12)
% 11.31/3.20 | (368) all_0_0_0 = e10 | all_0_0_0 = e11
% 11.31/3.20 |
% 11.31/3.20 +-Applying beta-rule and splitting (368), into two cases.
% 11.31/3.20 |-Branch one:
% 11.31/3.20 | (369) all_0_0_0 = e10
% 11.31/3.20 |
% 11.31/3.20 | Equations (369) can reduce 359 to:
% 11.31/3.20 | (370) ~ (e13 = e10)
% 11.31/3.20 |
% 11.31/3.20 | Simplifying 370 yields:
% 11.31/3.20 | (222) ~ (e13 = e10)
% 11.31/3.20 |
% 11.31/3.20 | From (369)(369)(369) and (115) follows:
% 11.31/3.20 | (372) op1(e10, e10) = e10
% 11.31/3.20 |
% 11.31/3.20 | Instantiating formula (209) with e10, e10, e10, e13 and discharging atoms op1(e10, e10) = e13, op1(e10, e10) = e10, yields:
% 11.31/3.20 | (373) e13 = e10
% 11.31/3.20 |
% 11.31/3.20 | Equations (373) can reduce 222 to:
% 11.31/3.20 | (338) $false
% 11.31/3.20 |
% 11.31/3.20 |-The branch is then unsatisfiable
% 11.31/3.20 |-Branch two:
% 11.31/3.20 | (375) ~ (all_0_0_0 = e10)
% 11.31/3.20 | (376) all_0_0_0 = e11
% 11.31/3.20 |
% 11.31/3.20 | Equations (376) can reduce 339 to:
% 11.31/3.20 | (377) ~ (e16 = e11)
% 11.60/3.20 |
% 11.60/3.20 | Simplifying 377 yields:
% 11.60/3.20 | (172) ~ (e16 = e11)
% 11.60/3.20 |
% 11.60/3.20 | From (376)(376)(376) and (115) follows:
% 11.60/3.20 | (379) op1(e11, e11) = e11
% 11.60/3.20 |
% 11.60/3.20 | Instantiating formula (209) with e11, e11, e11, e16 and discharging atoms op1(e11, e11) = e16, op1(e11, e11) = e11, yields:
% 11.60/3.20 | (380) e16 = e11
% 11.60/3.20 |
% 11.60/3.20 | Equations (380) can reduce 172 to:
% 11.60/3.20 | (338) $false
% 11.60/3.20 |
% 11.60/3.20 |-The branch is then unsatisfiable
% 11.60/3.20 % SZS output end Proof for theBenchmark
% 11.60/3.20
% 11.60/3.20 2623ms
%------------------------------------------------------------------------------