%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE139+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n009.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 : Sun Jul 17 01:51:31 EDT 2022

% Result   : Theorem 34.49s 9.94s
% Output   : Proof 47.63s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KLE139+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Thu Jun 16 12:01:23 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.52/0.59          ____       _                          
% 0.52/0.59    ___  / __ \_____(_)___  ________  __________
% 0.52/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.52/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.52/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.52/0.59  
% 0.52/0.59  A Theorem Prover for First-Order Logic
% 0.52/0.59  (ePrincess v.1.0)
% 0.52/0.59  
% 0.52/0.59  (c) Philipp Rümmer, 2009-2015
% 0.52/0.59  (c) Peter Backeman, 2014-2015
% 0.52/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.52/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.52/0.59  Bug reports to peter@backeman.se
% 0.52/0.59  
% 0.52/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.52/0.59  
% 0.52/0.59  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.74/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.49/0.92  Prover 0: Preprocessing ...
% 2.18/1.16  Prover 0: Constructing countermodel ...
% 18.97/5.93  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.15/5.97  Prover 1: Preprocessing ...
% 19.46/6.06  Prover 1: Constructing countermodel ...
% 21.76/6.64  Prover 1: gave up
% 21.76/6.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 22.21/6.66  Prover 2: Preprocessing ...
% 22.45/6.70  Prover 2: Warning: ignoring some quantifiers
% 22.45/6.71  Prover 2: Constructing countermodel ...
% 29.03/8.35  Prover 3: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 29.20/8.38  Prover 3: Preprocessing ...
% 29.20/8.43  Prover 3: Constructing countermodel ...
% 29.73/8.52  Prover 3: gave up
% 29.73/8.52  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 29.96/8.54  Prover 4: Preprocessing ...
% 30.04/8.58  Prover 4: Warning: ignoring some quantifiers
% 30.04/8.58  Prover 4: Constructing countermodel ...
% 34.49/9.94  Prover 4: proved (1016ms)
% 34.49/9.94  Prover 0: stopped
% 34.49/9.94  Prover 2: stopped
% 34.49/9.94  
% 34.49/9.94  No countermodel exists, formula is valid
% 34.49/9.94  % SZS status Theorem for theBenchmark
% 34.49/9.94  
% 34.49/9.94  Generating proof ... Warning: ignoring some quantifiers
% 46.97/14.99  found it (size 293)
% 46.97/14.99  
% 46.97/14.99  % SZS output start Proof for theBenchmark
% 46.97/14.99  Assumed formulas after preprocessing and simplification: 
% 46.97/14.99  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : (strong_iteration(v0) = v1 & leq(v3, v1) = v5 & leq(v1, v3) = v4 & multiplication(v1, v0) = v2 & addition(v2, one) = v3 &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (strong_iteration(v6) = v9) |  ~ (leq(v8, v10) = v11) |  ~ (multiplication(v9, v7) = v10) |  ? [v12] :  ? [v13] :  ? [v14] : ( ~ (v14 = 0) & leq(v8, v13) = v14 & multiplication(v6, v8) = v12 & addition(v12, v7) = v13)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (leq(v10, v8) = v11) |  ~ (star(v6) = v9) |  ~ (multiplication(v9, v7) = v10) |  ? [v12] :  ? [v13] :  ? [v14] : ( ~ (v14 = 0) & leq(v13, v8) = v14 & multiplication(v6, v8) = v12 & addition(v12, v7) = v13)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (leq(v10, v8) = v11) |  ~ (star(v6) = v9) |  ~ (multiplication(v7, v9) = v10) |  ? [v12] :  ? [v13] :  ? [v14] : ( ~ (v14 = 0) & leq(v13, v8) = v14 & multiplication(v8, v6) = v12 & addition(v12, v7) = v13)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (multiplication(v7, v8) = v10) |  ~ (multiplication(v6, v8) = v9) |  ~ (addition(v9, v10) = v11) |  ? [v12] : (multiplication(v12, v8) = v11 & addition(v6, v7) = v12)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (multiplication(v6, v8) = v10) |  ~ (multiplication(v6, v7) = v9) |  ~ (addition(v9, v10) = v11) |  ? [v12] : (multiplication(v6, v12) = v11 & addition(v7, v8) = v12)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (multiplication(v9, v8) = v10) |  ~ (multiplication(v6, v7) = v9) |  ? [v11] : (multiplication(v7, v8) = v11 & multiplication(v6, v11) = v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (multiplication(v9, v8) = v10) |  ~ (addition(v6, v7) = v9) |  ? [v11] :  ? [v12] : (multiplication(v7, v8) = v12 & multiplication(v6, v8) = v11 & addition(v11, v12) = v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (multiplication(v8, v6) = v9) |  ~ (addition(v9, v7) = v10) |  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (leq(v13, v8) = v14 & leq(v10, v8) = v11 & star(v6) = v12 & multiplication(v7, v12) = v13 & ( ~ (v11 = 0) | v14 = 0))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (multiplication(v7, v8) = v9) |  ~ (multiplication(v6, v9) = v10) |  ? [v11] : (multiplication(v11, v8) = v10 & multiplication(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (multiplication(v6, v9) = v10) |  ~ (addition(v7, v8) = v9) |  ? [v11] :  ? [v12] : (multiplication(v6, v8) = v12 & multiplication(v6, v7) = v11 & addition(v11, v12) = v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (multiplication(v6, v8) = v9) |  ~ (addition(v9, v7) = v10) |  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (strong_iteration(v6) = v12 & leq(v8, v13) = v14 & leq(v8, v10) = v11 & multiplication(v12, v7) = v13 & ( ~ (v11 = 0) | v14 = 0))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (multiplication(v6, v8) = v9) |  ~ (addition(v9, v7) = v10) |  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (leq(v13, v8) = v14 & leq(v10, v8) = v11 & star(v6) = v12 & multiplication(v12, v7) = v13 & ( ~ (v11 = 0) | v14 = 0))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (addition(v9, v6) = v10) |  ~ (addition(v8, v7) = v9) |  ? [v11] : (addition(v8, v11) = v10 & addition(v7, v6) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (addition(v8, v9) = v10) |  ~ (addition(v7, v6) = v9) |  ? [v11] : (addition(v11, v6) = v10 & addition(v8, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (leq(v9, v8) = v7) |  ~ (leq(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (multiplication(v9, v8) = v7) |  ~ (multiplication(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (addition(v9, v8) = v7) |  ~ (addition(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] : (v8 = v7 |  ~ (addition(v6, v7) = v8) |  ? [v9] : ( ~ (v9 = 0) & leq(v6, v7) = v9)) &  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (leq(v6, v7) = v8) |  ? [v9] : ( ~ (v9 = v7) & addition(v6, v7) = v9)) &  ! [v6] :  ! [v7] :  ! [v8] : (v7 = v6 |  ~ (strong_iteration(v8) = v7) |  ~ (strong_iteration(v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] : (v7 = v6 |  ~ (star(v8) = v7) |  ~ (star(v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (addition(v7, v6) = v8) | addition(v6, v7) = v8) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (addition(v6, v7) = v8) | addition(v7, v6) = v8) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (multiplication(v6, one) = v7)) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (multiplication(one, v6) = v7)) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (addition(v6, v6) = v7)) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (addition(v6, zero) = v7)) &  ! [v6] :  ! [v7] : (v7 = zero |  ~ (multiplication(zero, v6) = v7)) &  ! [v6] :  ! [v7] : ( ~ (strong_iteration(v6) = v7) |  ? [v8] :  ? [v9] : (star(v6) = v8 & multiplication(v7, zero) = v9 & addition(v8, v9) = v7)) &  ! [v6] :  ! [v7] : ( ~ (strong_iteration(v6) = v7) |  ? [v8] : (multiplication(v6, v7) = v8 & addition(v8, one) = v7)) &  ! [v6] :  ! [v7] : ( ~ (leq(v6, v7) = 0) | addition(v6, v7) = v7) &  ! [v6] :  ! [v7] : ( ~ (star(v6) = v7) |  ? [v8] :  ? [v9] : (strong_iteration(v6) = v8 & multiplication(v8, zero) = v9 & addition(v7, v9) = v8)) &  ! [v6] :  ! [v7] : ( ~ (star(v6) = v7) |  ? [v8] : (multiplication(v7, v6) = v8 & addition(one, v8) = v7)) &  ! [v6] :  ! [v7] : ( ~ (star(v6) = v7) |  ? [v8] : (multiplication(v6, v7) = v8 & addition(one, v8) = v7)) &  ! [v6] :  ! [v7] : ( ~ (addition(v6, v7) = v7) | leq(v6, v7) = 0) &  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (strong_iteration(v6) = v12 & leq(v8, v13) = v14 & leq(v8, v10) = v11 & multiplication(v12, v7) = v13 & multiplication(v6, v8) = v9 & addition(v9, v7) = v10 & ( ~ (v11 = 0) | v14 = 0)) &  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (strong_iteration(v6) = v7 & star(v6) = v8 & multiplication(v7, zero) = v9 & addition(v8, v9) = v7) &  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (leq(v6, v7) = v9 & addition(v6, v7) = v8 & ( ~ (v8 = v7) | v9 = 0)) & ( ~ (v5 = 0) |  ~ (v4 = 0)))
% 46.97/15.03  | 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 yields:
% 46.97/15.03  | (1) strong_iteration(all_0_5_5) = all_0_4_4 & leq(all_0_2_2, all_0_4_4) = all_0_0_0 & leq(all_0_4_4, all_0_2_2) = all_0_1_1 & multiplication(all_0_4_4, all_0_5_5) = all_0_3_3 & addition(all_0_3_3, one) = all_0_2_2 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (strong_iteration(v0) = v3) |  ~ (leq(v2, v4) = v5) |  ~ (multiplication(v3, v1) = v4) |  ? [v6] :  ? [v7] :  ? [v8] : ( ~ (v8 = 0) & leq(v2, v7) = v8 & multiplication(v0, v2) = v6 & addition(v6, v1) = v7)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (leq(v4, v2) = v5) |  ~ (star(v0) = v3) |  ~ (multiplication(v3, v1) = v4) |  ? [v6] :  ? [v7] :  ? [v8] : ( ~ (v8 = 0) & leq(v7, v2) = v8 & multiplication(v0, v2) = v6 & addition(v6, v1) = v7)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (leq(v4, v2) = v5) |  ~ (star(v0) = v3) |  ~ (multiplication(v1, v3) = v4) |  ? [v6] :  ? [v7] :  ? [v8] : ( ~ (v8 = 0) & leq(v7, v2) = v8 & multiplication(v2, v0) = v6 & addition(v6, v1) = v7)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v1, v2) = v4) |  ~ (multiplication(v0, v2) = v3) |  ~ (addition(v3, v4) = v5) |  ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v0, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ~ (addition(v3, v4) = v5) |  ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (addition(v0, v1) = v3) |  ? [v5] :  ? [v6] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v2, v0) = v3) |  ~ (addition(v3, v1) = v4) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (leq(v7, v2) = v8 & leq(v4, v2) = v5 & star(v0) = v6 & multiplication(v1, v6) = v7 & ( ~ (v5 = 0) | v8 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v0, v3) = v4) |  ~ (addition(v1, v2) = v3) |  ? [v5] :  ? [v6] : (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v0, v2) = v3) |  ~ (addition(v3, v1) = v4) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (strong_iteration(v0) = v6 & leq(v2, v7) = v8 & leq(v2, v4) = v5 & multiplication(v6, v1) = v7 & ( ~ (v5 = 0) | v8 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v0, v2) = v3) |  ~ (addition(v3, v1) = v4) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (leq(v7, v2) = v8 & leq(v4, v2) = v5 & star(v0) = v6 & multiplication(v6, v1) = v7 & ( ~ (v5 = 0) | v8 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (leq(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (strong_iteration(v2) = v1) |  ~ (strong_iteration(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (star(v2) = v1) |  ~ (star(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1)) &  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1)) &  ! [v0] :  ! [v1] : ( ~ (strong_iteration(v0) = v1) |  ? [v2] :  ? [v3] : (star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1)) &  ! [v0] :  ! [v1] : ( ~ (strong_iteration(v0) = v1) |  ? [v2] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1)) &  ! [v0] :  ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1) &  ! [v0] :  ! [v1] : ( ~ (star(v0) = v1) |  ? [v2] :  ? [v3] : (strong_iteration(v0) = v2 & multiplication(v2, zero) = v3 & addition(v1, v3) = v2)) &  ! [v0] :  ! [v1] : ( ~ (star(v0) = v1) |  ? [v2] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1)) &  ! [v0] :  ! [v1] : ( ~ (star(v0) = v1) |  ? [v2] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1)) &  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0) &  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (strong_iteration(v0) = v6 & leq(v2, v7) = v8 & leq(v2, v4) = v5 & multiplication(v6, v1) = v7 & multiplication(v0, v2) = v3 & addition(v3, v1) = v4 & ( ~ (v5 = 0) | v8 = 0)) &  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (strong_iteration(v0) = v1 & star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1) &  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (leq(v0, v1) = v3 & addition(v0, v1) = v2 & ( ~ (v2 = v1) | v3 = 0)) & ( ~ (all_0_0_0 = 0) |  ~ (all_0_1_1 = 0))
% 47.33/15.05  |
% 47.33/15.05  | Applying alpha-rule on (1) yields:
% 47.33/15.05  | (2)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 47.33/15.05  | (3)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 47.33/15.05  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 47.33/15.05  | (5)  ! [v0] :  ! [v1] : ( ~ (star(v0) = v1) |  ? [v2] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1))
% 47.33/15.05  | (6)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (star(v2) = v1) |  ~ (star(v2) = v0))
% 47.33/15.05  | (7)  ~ (all_0_0_0 = 0) |  ~ (all_0_1_1 = 0)
% 47.33/15.05  | (8)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (leq(v0, v1) = v3 & addition(v0, v1) = v2 & ( ~ (v2 = v1) | v3 = 0))
% 47.33/15.05  | (9)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0)
% 47.33/15.05  | (10)  ! [v0] :  ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1)
% 47.33/15.05  | (11) leq(all_0_4_4, all_0_2_2) = all_0_1_1
% 47.33/15.05  | (12)  ! [v0] :  ! [v1] : ( ~ (strong_iteration(v0) = v1) |  ? [v2] :  ? [v3] : (star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1))
% 47.33/15.05  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 47.33/15.05  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v0, v2) = v3) |  ~ (addition(v3, v1) = v4) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (strong_iteration(v0) = v6 & leq(v2, v7) = v8 & leq(v2, v4) = v5 & multiplication(v6, v1) = v7 & ( ~ (v5 = 0) | v8 = 0)))
% 47.33/15.05  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v0, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ~ (addition(v3, v4) = v5) |  ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6))
% 47.33/15.05  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 47.33/15.05  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v0, v3) = v4) |  ~ (addition(v1, v2) = v3) |  ? [v5] :  ? [v6] : (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4))
% 47.33/15.05  | (18)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (strong_iteration(v2) = v1) |  ~ (strong_iteration(v2) = v0))
% 47.33/15.05  | (19)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (strong_iteration(v0) = v6 & leq(v2, v7) = v8 & leq(v2, v4) = v5 & multiplication(v6, v1) = v7 & multiplication(v0, v2) = v3 & addition(v3, v1) = v4 & ( ~ (v5 = 0) | v8 = 0))
% 47.33/15.05  | (20)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (leq(v4, v2) = v5) |  ~ (star(v0) = v3) |  ~ (multiplication(v3, v1) = v4) |  ? [v6] :  ? [v7] :  ? [v8] : ( ~ (v8 = 0) & leq(v7, v2) = v8 & multiplication(v0, v2) = v6 & addition(v6, v1) = v7))
% 47.33/15.05  | (21)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (leq(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3))
% 47.33/15.05  | (22)  ! [v0] :  ! [v1] : ( ~ (star(v0) = v1) |  ? [v2] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1))
% 47.33/15.05  | (23) addition(all_0_3_3, one) = all_0_2_2
% 47.33/15.05  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v1, v2) = v4) |  ~ (multiplication(v0, v2) = v3) |  ~ (addition(v3, v4) = v5) |  ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6))
% 47.33/15.05  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (addition(v0, v1) = v3) |  ? [v5] :  ? [v6] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4))
% 47.33/15.06  | (26)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 47.33/15.06  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (leq(v4, v2) = v5) |  ~ (star(v0) = v3) |  ~ (multiplication(v1, v3) = v4) |  ? [v6] :  ? [v7] :  ? [v8] : ( ~ (v8 = 0) & leq(v7, v2) = v8 & multiplication(v2, v0) = v6 & addition(v6, v1) = v7))
% 47.33/15.06  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v0, v2) = v3) |  ~ (addition(v3, v1) = v4) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (leq(v7, v2) = v8 & leq(v4, v2) = v5 & star(v0) = v6 & multiplication(v6, v1) = v7 & ( ~ (v5 = 0) | v8 = 0)))
% 47.33/15.06  | (29) strong_iteration(all_0_5_5) = all_0_4_4
% 47.33/15.06  | (30)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 47.33/15.06  | (31)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (strong_iteration(v0) = v1 & star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1)
% 47.33/15.06  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0))
% 47.33/15.06  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (strong_iteration(v0) = v3) |  ~ (leq(v2, v4) = v5) |  ~ (multiplication(v3, v1) = v4) |  ? [v6] :  ? [v7] :  ? [v8] : ( ~ (v8 = 0) & leq(v2, v7) = v8 & multiplication(v0, v2) = v6 & addition(v6, v1) = v7))
% 47.33/15.06  | (34)  ! [v0] :  ! [v1] : ( ~ (strong_iteration(v0) = v1) |  ? [v2] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1))
% 47.33/15.06  | (35)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3))
% 47.33/15.06  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 47.33/15.06  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v2, v0) = v3) |  ~ (addition(v3, v1) = v4) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (leq(v7, v2) = v8 & leq(v4, v2) = v5 & star(v0) = v6 & multiplication(v1, v6) = v7 & ( ~ (v5 = 0) | v8 = 0)))
% 47.33/15.06  | (38)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 47.33/15.06  | (39) multiplication(all_0_4_4, all_0_5_5) = all_0_3_3
% 47.33/15.06  | (40)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 47.33/15.06  | (41)  ! [v0] :  ! [v1] : ( ~ (star(v0) = v1) |  ? [v2] :  ? [v3] : (strong_iteration(v0) = v2 & multiplication(v2, zero) = v3 & addition(v1, v3) = v2))
% 47.33/15.06  | (42) leq(all_0_2_2, all_0_4_4) = all_0_0_0
% 47.33/15.06  | (43)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 47.33/15.06  | (44)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 47.33/15.06  | (45)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 47.33/15.06  |
% 47.33/15.06  | Instantiating (31) with all_5_0_10, all_5_1_11, all_5_2_12, all_5_3_13 yields:
% 47.33/15.06  | (46) strong_iteration(all_5_3_13) = all_5_2_12 & star(all_5_3_13) = all_5_1_11 & multiplication(all_5_2_12, zero) = all_5_0_10 & addition(all_5_1_11, all_5_0_10) = all_5_2_12
% 47.33/15.06  |
% 47.33/15.06  | Applying alpha-rule on (46) yields:
% 47.33/15.06  | (47) strong_iteration(all_5_3_13) = all_5_2_12
% 47.33/15.06  | (48) star(all_5_3_13) = all_5_1_11
% 47.33/15.06  | (49) multiplication(all_5_2_12, zero) = all_5_0_10
% 47.33/15.06  | (50) addition(all_5_1_11, all_5_0_10) = all_5_2_12
% 47.33/15.06  |
% 47.33/15.06  | Instantiating (19) with all_7_0_14, all_7_1_15, all_7_2_16, all_7_3_17, all_7_4_18, all_7_5_19, all_7_6_20, all_7_7_21, all_7_8_22 yields:
% 47.33/15.06  | (51) strong_iteration(all_7_8_22) = all_7_2_16 & leq(all_7_6_20, all_7_1_15) = all_7_0_14 & leq(all_7_6_20, all_7_4_18) = all_7_3_17 & multiplication(all_7_2_16, all_7_7_21) = all_7_1_15 & multiplication(all_7_8_22, all_7_6_20) = all_7_5_19 & addition(all_7_5_19, all_7_7_21) = all_7_4_18 & ( ~ (all_7_3_17 = 0) | all_7_0_14 = 0)
% 47.33/15.06  |
% 47.33/15.06  | Applying alpha-rule on (51) yields:
% 47.33/15.06  | (52) multiplication(all_7_8_22, all_7_6_20) = all_7_5_19
% 47.33/15.06  | (53) leq(all_7_6_20, all_7_4_18) = all_7_3_17
% 47.33/15.06  | (54) strong_iteration(all_7_8_22) = all_7_2_16
% 47.33/15.06  | (55) addition(all_7_5_19, all_7_7_21) = all_7_4_18
% 47.33/15.06  | (56)  ~ (all_7_3_17 = 0) | all_7_0_14 = 0
% 47.33/15.06  | (57) leq(all_7_6_20, all_7_1_15) = all_7_0_14
% 47.33/15.06  | (58) multiplication(all_7_2_16, all_7_7_21) = all_7_1_15
% 47.33/15.06  |
% 47.33/15.06  | Instantiating formula (12) with all_7_2_16, all_7_8_22 and discharging atoms strong_iteration(all_7_8_22) = all_7_2_16, yields:
% 47.33/15.06  | (59)  ? [v0] :  ? [v1] : (star(all_7_8_22) = v0 & multiplication(all_7_2_16, zero) = v1 & addition(v0, v1) = all_7_2_16)
% 47.33/15.06  |
% 47.33/15.07  | Instantiating formula (34) with all_7_2_16, all_7_8_22 and discharging atoms strong_iteration(all_7_8_22) = all_7_2_16, yields:
% 47.33/15.07  | (60)  ? [v0] : (multiplication(all_7_8_22, all_7_2_16) = v0 & addition(v0, one) = all_7_2_16)
% 47.33/15.07  |
% 47.33/15.07  | Instantiating formula (34) with all_5_2_12, all_5_3_13 and discharging atoms strong_iteration(all_5_3_13) = all_5_2_12, yields:
% 47.33/15.07  | (61)  ? [v0] : (multiplication(all_5_3_13, all_5_2_12) = v0 & addition(v0, one) = all_5_2_12)
% 47.33/15.07  |
% 47.33/15.07  | Instantiating formula (12) with all_0_4_4, all_0_5_5 and discharging atoms strong_iteration(all_0_5_5) = all_0_4_4, yields:
% 47.33/15.07  | (62)  ? [v0] :  ? [v1] : (star(all_0_5_5) = v0 & multiplication(all_0_4_4, zero) = v1 & addition(v0, v1) = all_0_4_4)
% 47.33/15.07  |
% 47.33/15.07  | Instantiating formula (34) with all_0_4_4, all_0_5_5 and discharging atoms strong_iteration(all_0_5_5) = all_0_4_4, yields:
% 47.33/15.07  | (63)  ? [v0] : (multiplication(all_0_5_5, all_0_4_4) = v0 & addition(v0, one) = all_0_4_4)
% 47.33/15.07  |
% 47.33/15.07  | Instantiating formula (21) with all_0_0_0, all_0_4_4, all_0_2_2 and discharging atoms leq(all_0_2_2, all_0_4_4) = all_0_0_0, yields:
% 47.33/15.07  | (64) all_0_0_0 = 0 |  ? [v0] : ( ~ (v0 = all_0_4_4) & addition(all_0_2_2, all_0_4_4) = v0)
% 47.33/15.07  |
% 47.33/15.07  | Instantiating formula (21) with all_0_1_1, all_0_2_2, all_0_4_4 and discharging atoms leq(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 47.33/15.07  | (65) all_0_1_1 = 0 |  ? [v0] : ( ~ (v0 = all_0_2_2) & addition(all_0_4_4, all_0_2_2) = v0)
% 47.33/15.07  |
% 47.33/15.07  | Instantiating formula (5) with all_5_1_11, all_5_3_13 and discharging atoms star(all_5_3_13) = all_5_1_11, yields:
% 47.33/15.07  | (66)  ? [v0] : (multiplication(all_5_1_11, all_5_3_13) = v0 & addition(one, v0) = all_5_1_11)
% 47.33/15.07  |
% 47.33/15.07  | Instantiating formula (22) with all_5_1_11, all_5_3_13 and discharging atoms star(all_5_3_13) = all_5_1_11, yields:
% 47.33/15.07  | (67)  ? [v0] : (multiplication(all_5_3_13, all_5_1_11) = v0 & addition(one, v0) = all_5_1_11)
% 47.33/15.07  |
% 47.33/15.07  | Instantiating formula (28) with all_7_4_18, all_7_5_19, all_7_6_20, all_7_7_21, all_7_8_22 and discharging atoms multiplication(all_7_8_22, all_7_6_20) = all_7_5_19, addition(all_7_5_19, all_7_7_21) = all_7_4_18, yields:
% 47.33/15.07  | (68)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (leq(v2, all_7_6_20) = v3 & leq(all_7_4_18, all_7_6_20) = v0 & star(all_7_8_22) = v1 & multiplication(v1, all_7_7_21) = v2 & ( ~ (v0 = 0) | v3 = 0))
% 47.33/15.07  |
% 47.33/15.07  | Instantiating formula (25) with all_5_0_10, all_5_2_12, zero, all_5_0_10, all_5_1_11 and discharging atoms multiplication(all_5_2_12, zero) = all_5_0_10, addition(all_5_1_11, all_5_0_10) = all_5_2_12, yields:
% 47.33/15.07  | (69)  ? [v0] :  ? [v1] : (multiplication(all_5_0_10, zero) = v1 & multiplication(all_5_1_11, zero) = v0 & addition(v0, v1) = all_5_0_10)
% 47.33/15.07  |
% 47.33/15.07  | Instantiating formula (3) with all_5_2_12, all_5_1_11, all_5_0_10 and discharging atoms addition(all_5_1_11, all_5_0_10) = all_5_2_12, yields:
% 47.33/15.07  | (70) addition(all_5_0_10, all_5_1_11) = all_5_2_12
% 47.33/15.07  |
% 47.33/15.07  | Instantiating formula (37) with all_0_2_2, all_0_3_3, all_0_4_4, one, all_0_5_5 and discharging atoms multiplication(all_0_4_4, all_0_5_5) = all_0_3_3, addition(all_0_3_3, one) = all_0_2_2, yields:
% 47.33/15.07  | (71)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (leq(v2, all_0_4_4) = v3 & leq(all_0_2_2, all_0_4_4) = v0 & star(all_0_5_5) = v1 & multiplication(one, v1) = v2 & ( ~ (v0 = 0) | v3 = 0))
% 47.33/15.07  |
% 47.33/15.07  | Instantiating formula (3) with all_0_2_2, all_0_3_3, one and discharging atoms addition(all_0_3_3, one) = all_0_2_2, yields:
% 47.33/15.07  | (72) addition(one, all_0_3_3) = all_0_2_2
% 47.33/15.07  |
% 47.33/15.07  | Instantiating (67) with all_15_0_23 yields:
% 47.33/15.07  | (73) multiplication(all_5_3_13, all_5_1_11) = all_15_0_23 & addition(one, all_15_0_23) = all_5_1_11
% 47.33/15.07  |
% 47.33/15.07  | Applying alpha-rule on (73) yields:
% 47.33/15.07  | (74) multiplication(all_5_3_13, all_5_1_11) = all_15_0_23
% 47.33/15.07  | (75) addition(one, all_15_0_23) = all_5_1_11
% 47.33/15.07  |
% 47.33/15.07  | Instantiating (66) with all_17_0_24 yields:
% 47.33/15.07  | (76) multiplication(all_5_1_11, all_5_3_13) = all_17_0_24 & addition(one, all_17_0_24) = all_5_1_11
% 47.33/15.07  |
% 47.33/15.07  | Applying alpha-rule on (76) yields:
% 47.33/15.07  | (77) multiplication(all_5_1_11, all_5_3_13) = all_17_0_24
% 47.33/15.07  | (78) addition(one, all_17_0_24) = all_5_1_11
% 47.33/15.07  |
% 47.33/15.07  | Instantiating (68) with all_19_0_25, all_19_1_26, all_19_2_27, all_19_3_28 yields:
% 47.33/15.07  | (79) leq(all_19_1_26, all_7_6_20) = all_19_0_25 & leq(all_7_4_18, all_7_6_20) = all_19_3_28 & star(all_7_8_22) = all_19_2_27 & multiplication(all_19_2_27, all_7_7_21) = all_19_1_26 & ( ~ (all_19_3_28 = 0) | all_19_0_25 = 0)
% 47.33/15.07  |
% 47.33/15.07  | Applying alpha-rule on (79) yields:
% 47.33/15.07  | (80) star(all_7_8_22) = all_19_2_27
% 47.33/15.07  | (81) leq(all_19_1_26, all_7_6_20) = all_19_0_25
% 47.33/15.07  | (82) multiplication(all_19_2_27, all_7_7_21) = all_19_1_26
% 47.33/15.07  | (83) leq(all_7_4_18, all_7_6_20) = all_19_3_28
% 47.33/15.07  | (84)  ~ (all_19_3_28 = 0) | all_19_0_25 = 0
% 47.33/15.07  |
% 47.33/15.07  | Instantiating (63) with all_23_0_33 yields:
% 47.33/15.07  | (85) multiplication(all_0_5_5, all_0_4_4) = all_23_0_33 & addition(all_23_0_33, one) = all_0_4_4
% 47.33/15.07  |
% 47.33/15.07  | Applying alpha-rule on (85) yields:
% 47.33/15.07  | (86) multiplication(all_0_5_5, all_0_4_4) = all_23_0_33
% 47.33/15.07  | (87) addition(all_23_0_33, one) = all_0_4_4
% 47.33/15.07  |
% 47.33/15.07  | Instantiating (71) with all_25_0_34, all_25_1_35, all_25_2_36, all_25_3_37 yields:
% 47.33/15.07  | (88) leq(all_25_1_35, all_0_4_4) = all_25_0_34 & leq(all_0_2_2, all_0_4_4) = all_25_3_37 & star(all_0_5_5) = all_25_2_36 & multiplication(one, all_25_2_36) = all_25_1_35 & ( ~ (all_25_3_37 = 0) | all_25_0_34 = 0)
% 47.33/15.07  |
% 47.33/15.07  | Applying alpha-rule on (88) yields:
% 47.33/15.07  | (89) multiplication(one, all_25_2_36) = all_25_1_35
% 47.33/15.07  | (90) leq(all_0_2_2, all_0_4_4) = all_25_3_37
% 47.33/15.07  | (91)  ~ (all_25_3_37 = 0) | all_25_0_34 = 0
% 47.33/15.07  | (92) leq(all_25_1_35, all_0_4_4) = all_25_0_34
% 47.33/15.07  | (93) star(all_0_5_5) = all_25_2_36
% 47.33/15.07  |
% 47.33/15.07  | Instantiating (62) with all_29_0_42, all_29_1_43 yields:
% 47.33/15.07  | (94) star(all_0_5_5) = all_29_1_43 & multiplication(all_0_4_4, zero) = all_29_0_42 & addition(all_29_1_43, all_29_0_42) = all_0_4_4
% 47.33/15.07  |
% 47.33/15.07  | Applying alpha-rule on (94) yields:
% 47.33/15.07  | (95) star(all_0_5_5) = all_29_1_43
% 47.33/15.07  | (96) multiplication(all_0_4_4, zero) = all_29_0_42
% 47.33/15.07  | (97) addition(all_29_1_43, all_29_0_42) = all_0_4_4
% 47.33/15.07  |
% 47.33/15.07  | Instantiating (61) with all_31_0_44 yields:
% 47.33/15.07  | (98) multiplication(all_5_3_13, all_5_2_12) = all_31_0_44 & addition(all_31_0_44, one) = all_5_2_12
% 47.33/15.07  |
% 47.33/15.07  | Applying alpha-rule on (98) yields:
% 47.33/15.07  | (99) multiplication(all_5_3_13, all_5_2_12) = all_31_0_44
% 47.33/15.07  | (100) addition(all_31_0_44, one) = all_5_2_12
% 47.33/15.07  |
% 47.33/15.07  | Instantiating (69) with all_37_0_53, all_37_1_54 yields:
% 47.33/15.07  | (101) multiplication(all_5_0_10, zero) = all_37_0_53 & multiplication(all_5_1_11, zero) = all_37_1_54 & addition(all_37_1_54, all_37_0_53) = all_5_0_10
% 47.33/15.08  |
% 47.33/15.08  | Applying alpha-rule on (101) yields:
% 47.33/15.08  | (102) multiplication(all_5_0_10, zero) = all_37_0_53
% 47.33/15.08  | (103) multiplication(all_5_1_11, zero) = all_37_1_54
% 47.33/15.08  | (104) addition(all_37_1_54, all_37_0_53) = all_5_0_10
% 47.33/15.08  |
% 47.33/15.08  | Instantiating (60) with all_39_0_55 yields:
% 47.33/15.08  | (105) multiplication(all_7_8_22, all_7_2_16) = all_39_0_55 & addition(all_39_0_55, one) = all_7_2_16
% 47.33/15.08  |
% 47.33/15.08  | Applying alpha-rule on (105) yields:
% 47.33/15.08  | (106) multiplication(all_7_8_22, all_7_2_16) = all_39_0_55
% 47.33/15.08  | (107) addition(all_39_0_55, one) = all_7_2_16
% 47.33/15.08  |
% 47.33/15.08  | Instantiating (59) with all_41_0_56, all_41_1_57 yields:
% 47.33/15.08  | (108) star(all_7_8_22) = all_41_1_57 & multiplication(all_7_2_16, zero) = all_41_0_56 & addition(all_41_1_57, all_41_0_56) = all_7_2_16
% 47.33/15.08  |
% 47.33/15.08  | Applying alpha-rule on (108) yields:
% 47.33/15.08  | (109) star(all_7_8_22) = all_41_1_57
% 47.33/15.08  | (110) multiplication(all_7_2_16, zero) = all_41_0_56
% 47.33/15.08  | (111) addition(all_41_1_57, all_41_0_56) = all_7_2_16
% 47.33/15.08  |
% 47.33/15.08  | Instantiating formula (32) with all_0_2_2, all_0_4_4, all_25_3_37, all_0_0_0 and discharging atoms leq(all_0_2_2, all_0_4_4) = all_25_3_37, leq(all_0_2_2, all_0_4_4) = all_0_0_0, yields:
% 47.33/15.08  | (112) all_25_3_37 = all_0_0_0
% 47.33/15.08  |
% 47.33/15.08  | Instantiating formula (6) with all_7_8_22, all_19_2_27, all_41_1_57 and discharging atoms star(all_7_8_22) = all_41_1_57, star(all_7_8_22) = all_19_2_27, yields:
% 47.33/15.08  | (113) all_41_1_57 = all_19_2_27
% 47.33/15.08  |
% 47.33/15.08  | Instantiating formula (6) with all_0_5_5, all_25_2_36, all_29_1_43 and discharging atoms star(all_0_5_5) = all_29_1_43, star(all_0_5_5) = all_25_2_36, yields:
% 47.33/15.08  | (114) all_29_1_43 = all_25_2_36
% 47.33/15.08  |
% 47.33/15.08  | Instantiating formula (30) with all_25_1_35, all_25_2_36 and discharging atoms multiplication(one, all_25_2_36) = all_25_1_35, yields:
% 47.33/15.08  | (115) all_25_1_35 = all_25_2_36
% 47.33/15.08  |
% 47.33/15.08  | From (112) and (90) follows:
% 47.33/15.08  | (42) leq(all_0_2_2, all_0_4_4) = all_0_0_0
% 47.33/15.08  |
% 47.33/15.08  | From (114) and (95) follows:
% 47.33/15.08  | (93) star(all_0_5_5) = all_25_2_36
% 47.33/15.08  |
% 47.33/15.08  | From (115) and (89) follows:
% 47.33/15.08  | (118) multiplication(one, all_25_2_36) = all_25_2_36
% 47.33/15.08  |
% 47.33/15.08  | From (113) and (111) follows:
% 47.33/15.08  | (119) addition(all_19_2_27, all_41_0_56) = all_7_2_16
% 47.33/15.08  |
% 47.33/15.08  | From (114) and (97) follows:
% 47.33/15.08  | (120) addition(all_25_2_36, all_29_0_42) = all_0_4_4
% 47.33/15.08  |
% 47.33/15.08  | Instantiating formula (5) with all_25_2_36, all_0_5_5 and discharging atoms star(all_0_5_5) = all_25_2_36, yields:
% 47.33/15.08  | (121)  ? [v0] : (multiplication(all_25_2_36, all_0_5_5) = v0 & addition(one, v0) = all_25_2_36)
% 47.33/15.08  |
% 47.33/15.08  | Instantiating formula (22) with all_25_2_36, all_0_5_5 and discharging atoms star(all_0_5_5) = all_25_2_36, yields:
% 47.33/15.08  | (122)  ? [v0] : (multiplication(all_0_5_5, all_25_2_36) = v0 & addition(one, v0) = all_25_2_36)
% 47.33/15.08  |
% 47.33/15.08  | Instantiating formula (43) with all_37_0_53, all_5_0_10, zero, zero, all_5_2_12 and discharging atoms multiplication(all_5_0_10, zero) = all_37_0_53, multiplication(all_5_2_12, zero) = all_5_0_10, yields:
% 47.33/15.08  | (123)  ? [v0] : (multiplication(all_5_2_12, v0) = all_37_0_53 & multiplication(zero, zero) = v0)
% 47.33/15.08  |
% 47.33/15.08  | Instantiating formula (25) with all_41_0_56, all_7_2_16, zero, one, all_39_0_55 and discharging atoms multiplication(all_7_2_16, zero) = all_41_0_56, addition(all_39_0_55, one) = all_7_2_16, yields:
% 47.33/15.08  | (124)  ? [v0] :  ? [v1] : (multiplication(all_39_0_55, zero) = v0 & multiplication(one, zero) = v1 & addition(v0, v1) = all_41_0_56)
% 47.33/15.08  |
% 47.33/15.08  | Instantiating formula (25) with all_37_0_53, all_5_0_10, zero, all_37_0_53, all_37_1_54 and discharging atoms multiplication(all_5_0_10, zero) = all_37_0_53, addition(all_37_1_54, all_37_0_53) = all_5_0_10, yields:
% 47.33/15.08  | (125)  ? [v0] :  ? [v1] : (multiplication(all_37_0_53, zero) = v1 & multiplication(all_37_1_54, zero) = v0 & addition(v0, v1) = all_37_0_53)
% 47.33/15.08  |
% 47.33/15.08  | Instantiating formula (25) with all_5_0_10, all_5_2_12, zero, one, all_31_0_44 and discharging atoms multiplication(all_5_2_12, zero) = all_5_0_10, addition(all_31_0_44, one) = all_5_2_12, yields:
% 47.33/15.08  | (126)  ? [v0] :  ? [v1] : (multiplication(all_31_0_44, zero) = v0 & multiplication(one, zero) = v1 & addition(v0, v1) = all_5_0_10)
% 47.33/15.08  |
% 47.33/15.08  | Instantiating formula (25) with all_0_3_3, all_0_4_4, all_0_5_5, all_29_0_42, all_25_2_36 and discharging atoms multiplication(all_0_4_4, all_0_5_5) = all_0_3_3, addition(all_25_2_36, all_29_0_42) = all_0_4_4, yields:
% 47.33/15.08  | (127)  ? [v0] :  ? [v1] : (multiplication(all_29_0_42, all_0_5_5) = v1 & multiplication(all_25_2_36, all_0_5_5) = v0 & addition(v0, v1) = all_0_3_3)
% 47.33/15.08  |
% 47.33/15.08  | Instantiating formula (25) with all_29_0_42, all_0_4_4, zero, all_29_0_42, all_25_2_36 and discharging atoms multiplication(all_0_4_4, zero) = all_29_0_42, addition(all_25_2_36, all_29_0_42) = all_0_4_4, yields:
% 47.33/15.08  | (128)  ? [v0] :  ? [v1] : (multiplication(all_29_0_42, zero) = v1 & multiplication(all_25_2_36, zero) = v0 & addition(v0, v1) = all_29_0_42)
% 47.33/15.08  |
% 47.33/15.08  | Instantiating formula (17) with all_23_0_33, all_0_4_4, all_29_0_42, all_25_2_36, all_0_5_5 and discharging atoms multiplication(all_0_5_5, all_0_4_4) = all_23_0_33, addition(all_25_2_36, all_29_0_42) = all_0_4_4, yields:
% 47.33/15.08  | (129)  ? [v0] :  ? [v1] : (multiplication(all_0_5_5, all_29_0_42) = v1 & multiplication(all_0_5_5, all_25_2_36) = v0 & addition(v0, v1) = all_23_0_33)
% 47.33/15.08  |
% 47.33/15.08  | Instantiating formula (37) with all_0_4_4, all_25_2_36, one, all_29_0_42, all_25_2_36 and discharging atoms multiplication(one, all_25_2_36) = all_25_2_36, addition(all_25_2_36, all_29_0_42) = all_0_4_4, yields:
% 47.33/15.08  | (130)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (leq(v2, one) = v3 & leq(all_0_4_4, one) = v0 & star(all_25_2_36) = v1 & multiplication(all_29_0_42, v1) = v2 & ( ~ (v0 = 0) | v3 = 0))
% 47.33/15.08  |
% 47.33/15.08  | Instantiating formula (3) with all_0_4_4, all_25_2_36, all_29_0_42 and discharging atoms addition(all_25_2_36, all_29_0_42) = all_0_4_4, yields:
% 47.33/15.08  | (131) addition(all_29_0_42, all_25_2_36) = all_0_4_4
% 47.33/15.08  |
% 47.33/15.08  | Instantiating formula (25) with all_29_0_42, all_0_4_4, zero, one, all_23_0_33 and discharging atoms multiplication(all_0_4_4, zero) = all_29_0_42, addition(all_23_0_33, one) = all_0_4_4, yields:
% 47.33/15.09  | (132)  ? [v0] :  ? [v1] : (multiplication(all_23_0_33, zero) = v0 & multiplication(one, zero) = v1 & addition(v0, v1) = all_29_0_42)
% 47.33/15.09  |
% 47.33/15.09  | Instantiating formula (14) with all_0_4_4, all_23_0_33, all_0_4_4, one, all_0_5_5 and discharging atoms multiplication(all_0_5_5, all_0_4_4) = all_23_0_33, addition(all_23_0_33, one) = all_0_4_4, yields:
% 47.33/15.09  | (133)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (strong_iteration(all_0_5_5) = v1 & leq(all_0_4_4, v2) = v3 & leq(all_0_4_4, all_0_4_4) = v0 & multiplication(v1, one) = v2 & ( ~ (v0 = 0) | v3 = 0))
% 47.33/15.09  |
% 47.33/15.09  | Instantiating formula (28) with all_0_4_4, all_23_0_33, all_0_4_4, one, all_0_5_5 and discharging atoms multiplication(all_0_5_5, all_0_4_4) = all_23_0_33, addition(all_23_0_33, one) = all_0_4_4, yields:
% 47.33/15.09  | (134)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (leq(v2, all_0_4_4) = v3 & leq(all_0_4_4, all_0_4_4) = v0 & star(all_0_5_5) = v1 & multiplication(v1, one) = v2 & ( ~ (v0 = 0) | v3 = 0))
% 47.33/15.09  |
% 47.33/15.09  | Instantiating formula (3) with all_0_4_4, all_23_0_33, one and discharging atoms addition(all_23_0_33, one) = all_0_4_4, yields:
% 47.33/15.09  | (135) addition(one, all_23_0_33) = all_0_4_4
% 47.33/15.09  |
% 47.33/15.09  | Instantiating formula (25) with all_41_0_56, all_7_2_16, zero, all_41_0_56, all_19_2_27 and discharging atoms multiplication(all_7_2_16, zero) = all_41_0_56, addition(all_19_2_27, all_41_0_56) = all_7_2_16, yields:
% 47.33/15.09  | (136)  ? [v0] :  ? [v1] : (multiplication(all_41_0_56, zero) = v1 & multiplication(all_19_2_27, zero) = v0 & addition(v0, v1) = all_41_0_56)
% 47.33/15.09  |
% 47.33/15.09  | Instantiating formula (25) with all_5_0_10, all_5_2_12, zero, all_5_1_11, all_5_0_10 and discharging atoms multiplication(all_5_2_12, zero) = all_5_0_10, addition(all_5_0_10, all_5_1_11) = all_5_2_12, yields:
% 47.33/15.09  | (137)  ? [v0] :  ? [v1] : (multiplication(all_5_0_10, zero) = v0 & multiplication(all_5_1_11, zero) = v1 & addition(v0, v1) = all_5_0_10)
% 47.33/15.09  |
% 47.33/15.09  | Instantiating formula (25) with all_37_1_54, all_5_1_11, zero, all_17_0_24, one and discharging atoms multiplication(all_5_1_11, zero) = all_37_1_54, addition(one, all_17_0_24) = all_5_1_11, yields:
% 47.33/15.09  | (138)  ? [v0] :  ? [v1] : (multiplication(all_17_0_24, zero) = v1 & multiplication(one, zero) = v0 & addition(v0, v1) = all_37_1_54)
% 47.33/15.09  |
% 47.33/15.09  | Instantiating formula (25) with all_37_1_54, all_5_1_11, zero, all_15_0_23, one and discharging atoms multiplication(all_5_1_11, zero) = all_37_1_54, addition(one, all_15_0_23) = all_5_1_11, yields:
% 47.33/15.09  | (139)  ? [v0] :  ? [v1] : (multiplication(all_15_0_23, zero) = v1 & multiplication(one, zero) = v0 & addition(v0, v1) = all_37_1_54)
% 47.33/15.09  |
% 47.33/15.09  | Instantiating (125) with all_63_0_62, all_63_1_63 yields:
% 47.33/15.09  | (140) multiplication(all_37_0_53, zero) = all_63_0_62 & multiplication(all_37_1_54, zero) = all_63_1_63 & addition(all_63_1_63, all_63_0_62) = all_37_0_53
% 47.33/15.09  |
% 47.33/15.09  | Applying alpha-rule on (140) yields:
% 47.33/15.09  | (141) multiplication(all_37_0_53, zero) = all_63_0_62
% 47.33/15.09  | (142) multiplication(all_37_1_54, zero) = all_63_1_63
% 47.33/15.09  | (143) addition(all_63_1_63, all_63_0_62) = all_37_0_53
% 47.33/15.09  |
% 47.33/15.09  | Instantiating (129) with all_67_0_68, all_67_1_69 yields:
% 47.33/15.09  | (144) multiplication(all_0_5_5, all_29_0_42) = all_67_0_68 & multiplication(all_0_5_5, all_25_2_36) = all_67_1_69 & addition(all_67_1_69, all_67_0_68) = all_23_0_33
% 47.33/15.09  |
% 47.33/15.09  | Applying alpha-rule on (144) yields:
% 47.33/15.09  | (145) multiplication(all_0_5_5, all_29_0_42) = all_67_0_68
% 47.33/15.09  | (146) multiplication(all_0_5_5, all_25_2_36) = all_67_1_69
% 47.33/15.09  | (147) addition(all_67_1_69, all_67_0_68) = all_23_0_33
% 47.33/15.09  |
% 47.33/15.09  | Instantiating (128) with all_69_0_70, all_69_1_71 yields:
% 47.33/15.09  | (148) multiplication(all_29_0_42, zero) = all_69_0_70 & multiplication(all_25_2_36, zero) = all_69_1_71 & addition(all_69_1_71, all_69_0_70) = all_29_0_42
% 47.33/15.09  |
% 47.33/15.09  | Applying alpha-rule on (148) yields:
% 47.33/15.09  | (149) multiplication(all_29_0_42, zero) = all_69_0_70
% 47.33/15.09  | (150) multiplication(all_25_2_36, zero) = all_69_1_71
% 47.33/15.09  | (151) addition(all_69_1_71, all_69_0_70) = all_29_0_42
% 47.33/15.09  |
% 47.33/15.09  | Instantiating (139) with all_81_0_88, all_81_1_89 yields:
% 47.33/15.09  | (152) multiplication(all_15_0_23, zero) = all_81_0_88 & multiplication(one, zero) = all_81_1_89 & addition(all_81_1_89, all_81_0_88) = all_37_1_54
% 47.33/15.09  |
% 47.33/15.09  | Applying alpha-rule on (152) yields:
% 47.33/15.09  | (153) multiplication(all_15_0_23, zero) = all_81_0_88
% 47.33/15.09  | (154) multiplication(one, zero) = all_81_1_89
% 47.33/15.09  | (155) addition(all_81_1_89, all_81_0_88) = all_37_1_54
% 47.33/15.09  |
% 47.33/15.09  | Instantiating (138) with all_89_0_95, all_89_1_96 yields:
% 47.33/15.09  | (156) multiplication(all_17_0_24, zero) = all_89_0_95 & multiplication(one, zero) = all_89_1_96 & addition(all_89_1_96, all_89_0_95) = all_37_1_54
% 47.33/15.09  |
% 47.33/15.09  | Applying alpha-rule on (156) yields:
% 47.33/15.09  | (157) multiplication(all_17_0_24, zero) = all_89_0_95
% 47.33/15.09  | (158) multiplication(one, zero) = all_89_1_96
% 47.33/15.09  | (159) addition(all_89_1_96, all_89_0_95) = all_37_1_54
% 47.33/15.09  |
% 47.33/15.09  | Instantiating (127) with all_91_0_97, all_91_1_98 yields:
% 47.33/15.09  | (160) multiplication(all_29_0_42, all_0_5_5) = all_91_0_97 & multiplication(all_25_2_36, all_0_5_5) = all_91_1_98 & addition(all_91_1_98, all_91_0_97) = all_0_3_3
% 47.33/15.09  |
% 47.33/15.09  | Applying alpha-rule on (160) yields:
% 47.33/15.09  | (161) multiplication(all_29_0_42, all_0_5_5) = all_91_0_97
% 47.33/15.09  | (162) multiplication(all_25_2_36, all_0_5_5) = all_91_1_98
% 47.33/15.09  | (163) addition(all_91_1_98, all_91_0_97) = all_0_3_3
% 47.33/15.09  |
% 47.33/15.09  | Instantiating (130) with all_95_0_103, all_95_1_104, all_95_2_105, all_95_3_106 yields:
% 47.33/15.09  | (164) leq(all_95_1_104, one) = all_95_0_103 & leq(all_0_4_4, one) = all_95_3_106 & star(all_25_2_36) = all_95_2_105 & multiplication(all_29_0_42, all_95_2_105) = all_95_1_104 & ( ~ (all_95_3_106 = 0) | all_95_0_103 = 0)
% 47.33/15.09  |
% 47.33/15.09  | Applying alpha-rule on (164) yields:
% 47.33/15.09  | (165) leq(all_95_1_104, one) = all_95_0_103
% 47.33/15.09  | (166) star(all_25_2_36) = all_95_2_105
% 47.33/15.09  | (167) multiplication(all_29_0_42, all_95_2_105) = all_95_1_104
% 47.33/15.09  | (168) leq(all_0_4_4, one) = all_95_3_106
% 47.33/15.10  | (169)  ~ (all_95_3_106 = 0) | all_95_0_103 = 0
% 47.33/15.10  |
% 47.33/15.10  | Instantiating (136) with all_113_0_126, all_113_1_127 yields:
% 47.33/15.10  | (170) multiplication(all_41_0_56, zero) = all_113_0_126 & multiplication(all_19_2_27, zero) = all_113_1_127 & addition(all_113_1_127, all_113_0_126) = all_41_0_56
% 47.33/15.10  |
% 47.33/15.10  | Applying alpha-rule on (170) yields:
% 47.33/15.10  | (171) multiplication(all_41_0_56, zero) = all_113_0_126
% 47.33/15.10  | (172) multiplication(all_19_2_27, zero) = all_113_1_127
% 47.33/15.10  | (173) addition(all_113_1_127, all_113_0_126) = all_41_0_56
% 47.33/15.10  |
% 47.33/15.10  | Instantiating (124) with all_117_0_132, all_117_1_133 yields:
% 47.33/15.10  | (174) multiplication(all_39_0_55, zero) = all_117_1_133 & multiplication(one, zero) = all_117_0_132 & addition(all_117_1_133, all_117_0_132) = all_41_0_56
% 47.33/15.10  |
% 47.33/15.10  | Applying alpha-rule on (174) yields:
% 47.33/15.10  | (175) multiplication(all_39_0_55, zero) = all_117_1_133
% 47.33/15.10  | (176) multiplication(one, zero) = all_117_0_132
% 47.33/15.10  | (177) addition(all_117_1_133, all_117_0_132) = all_41_0_56
% 47.63/15.10  |
% 47.63/15.10  | Instantiating (132) with all_123_0_140, all_123_1_141 yields:
% 47.63/15.10  | (178) multiplication(all_23_0_33, zero) = all_123_1_141 & multiplication(one, zero) = all_123_0_140 & addition(all_123_1_141, all_123_0_140) = all_29_0_42
% 47.63/15.10  |
% 47.63/15.10  | Applying alpha-rule on (178) yields:
% 47.63/15.10  | (179) multiplication(all_23_0_33, zero) = all_123_1_141
% 47.63/15.10  | (180) multiplication(one, zero) = all_123_0_140
% 47.63/15.10  | (181) addition(all_123_1_141, all_123_0_140) = all_29_0_42
% 47.63/15.10  |
% 47.63/15.10  | Instantiating (121) with all_139_0_152 yields:
% 47.63/15.10  | (182) multiplication(all_25_2_36, all_0_5_5) = all_139_0_152 & addition(one, all_139_0_152) = all_25_2_36
% 47.63/15.10  |
% 47.63/15.10  | Applying alpha-rule on (182) yields:
% 47.63/15.10  | (183) multiplication(all_25_2_36, all_0_5_5) = all_139_0_152
% 47.63/15.10  | (184) addition(one, all_139_0_152) = all_25_2_36
% 47.63/15.10  |
% 47.63/15.10  | Instantiating (122) with all_147_0_157 yields:
% 47.63/15.10  | (185) multiplication(all_0_5_5, all_25_2_36) = all_147_0_157 & addition(one, all_147_0_157) = all_25_2_36
% 47.63/15.10  |
% 47.63/15.10  | Applying alpha-rule on (185) yields:
% 47.63/15.10  | (186) multiplication(all_0_5_5, all_25_2_36) = all_147_0_157
% 47.63/15.10  | (187) addition(one, all_147_0_157) = all_25_2_36
% 47.63/15.10  |
% 47.63/15.10  | Instantiating (123) with all_159_0_165 yields:
% 47.63/15.10  | (188) multiplication(all_5_2_12, all_159_0_165) = all_37_0_53 & multiplication(zero, zero) = all_159_0_165
% 47.63/15.10  |
% 47.63/15.10  | Applying alpha-rule on (188) yields:
% 47.63/15.10  | (189) multiplication(all_5_2_12, all_159_0_165) = all_37_0_53
% 47.63/15.10  | (190) multiplication(zero, zero) = all_159_0_165
% 47.63/15.10  |
% 47.63/15.10  | Instantiating (137) with all_169_0_172, all_169_1_173 yields:
% 47.63/15.10  | (191) multiplication(all_5_0_10, zero) = all_169_1_173 & multiplication(all_5_1_11, zero) = all_169_0_172 & addition(all_169_1_173, all_169_0_172) = all_5_0_10
% 47.63/15.10  |
% 47.63/15.10  | Applying alpha-rule on (191) yields:
% 47.63/15.10  | (192) multiplication(all_5_0_10, zero) = all_169_1_173
% 47.63/15.10  | (193) multiplication(all_5_1_11, zero) = all_169_0_172
% 47.63/15.10  | (194) addition(all_169_1_173, all_169_0_172) = all_5_0_10
% 47.63/15.10  |
% 47.63/15.10  | Instantiating (134) with all_179_0_185, all_179_1_186, all_179_2_187, all_179_3_188 yields:
% 47.63/15.10  | (195) leq(all_179_1_186, all_0_4_4) = all_179_0_185 & leq(all_0_4_4, all_0_4_4) = all_179_3_188 & star(all_0_5_5) = all_179_2_187 & multiplication(all_179_2_187, one) = all_179_1_186 & ( ~ (all_179_3_188 = 0) | all_179_0_185 = 0)
% 47.63/15.10  |
% 47.63/15.10  | Applying alpha-rule on (195) yields:
% 47.63/15.10  | (196) multiplication(all_179_2_187, one) = all_179_1_186
% 47.63/15.10  | (197)  ~ (all_179_3_188 = 0) | all_179_0_185 = 0
% 47.63/15.10  | (198) leq(all_179_1_186, all_0_4_4) = all_179_0_185
% 47.63/15.10  | (199) star(all_0_5_5) = all_179_2_187
% 47.63/15.10  | (200) leq(all_0_4_4, all_0_4_4) = all_179_3_188
% 47.63/15.10  |
% 47.63/15.10  | Instantiating (133) with all_181_0_189, all_181_1_190, all_181_2_191, all_181_3_192 yields:
% 47.63/15.10  | (201) strong_iteration(all_0_5_5) = all_181_2_191 & leq(all_0_4_4, all_181_1_190) = all_181_0_189 & leq(all_0_4_4, all_0_4_4) = all_181_3_192 & multiplication(all_181_2_191, one) = all_181_1_190 & ( ~ (all_181_3_192 = 0) | all_181_0_189 = 0)
% 47.63/15.10  |
% 47.63/15.10  | Applying alpha-rule on (201) yields:
% 47.63/15.10  | (202) leq(all_0_4_4, all_181_1_190) = all_181_0_189
% 47.63/15.10  | (203) multiplication(all_181_2_191, one) = all_181_1_190
% 47.63/15.10  | (204)  ~ (all_181_3_192 = 0) | all_181_0_189 = 0
% 47.63/15.10  | (205) strong_iteration(all_0_5_5) = all_181_2_191
% 47.63/15.10  | (206) leq(all_0_4_4, all_0_4_4) = all_181_3_192
% 47.63/15.10  |
% 47.63/15.10  | Instantiating (126) with all_187_0_201, all_187_1_202 yields:
% 47.63/15.10  | (207) multiplication(all_31_0_44, zero) = all_187_1_202 & multiplication(one, zero) = all_187_0_201 & addition(all_187_1_202, all_187_0_201) = all_5_0_10
% 47.63/15.10  |
% 47.63/15.10  | Applying alpha-rule on (207) yields:
% 47.63/15.10  | (208) multiplication(all_31_0_44, zero) = all_187_1_202
% 47.63/15.10  | (209) multiplication(one, zero) = all_187_0_201
% 47.63/15.10  | (210) addition(all_187_1_202, all_187_0_201) = all_5_0_10
% 47.63/15.10  |
% 47.63/15.10  | Instantiating formula (18) with all_0_5_5, all_181_2_191, all_0_4_4 and discharging atoms strong_iteration(all_0_5_5) = all_181_2_191, strong_iteration(all_0_5_5) = all_0_4_4, yields:
% 47.63/15.10  | (211) all_181_2_191 = all_0_4_4
% 47.63/15.10  |
% 47.63/15.10  | Instantiating formula (32) with all_0_4_4, all_0_4_4, all_179_3_188, all_181_3_192 and discharging atoms leq(all_0_4_4, all_0_4_4) = all_181_3_192, leq(all_0_4_4, all_0_4_4) = all_179_3_188, yields:
% 47.63/15.10  | (212) all_181_3_192 = all_179_3_188
% 47.63/15.10  |
% 47.63/15.10  | Instantiating formula (44) with all_181_1_190, all_181_2_191 and discharging atoms multiplication(all_181_2_191, one) = all_181_1_190, yields:
% 47.63/15.10  | (213) all_181_1_190 = all_181_2_191
% 47.63/15.10  |
% 47.63/15.10  | Instantiating formula (4) with all_25_2_36, all_0_5_5, all_91_1_98, all_139_0_152 and discharging atoms multiplication(all_25_2_36, all_0_5_5) = all_139_0_152, multiplication(all_25_2_36, all_0_5_5) = all_91_1_98, yields:
% 47.63/15.10  | (214) all_139_0_152 = all_91_1_98
% 47.63/15.11  |
% 47.63/15.11  | Instantiating formula (4) with all_5_1_11, zero, all_169_0_172, all_37_1_54 and discharging atoms multiplication(all_5_1_11, zero) = all_169_0_172, multiplication(all_5_1_11, zero) = all_37_1_54, yields:
% 47.63/15.11  | (215) all_169_0_172 = all_37_1_54
% 47.63/15.11  |
% 47.63/15.11  | Instantiating formula (4) with all_0_5_5, all_25_2_36, all_67_1_69, all_147_0_157 and discharging atoms multiplication(all_0_5_5, all_25_2_36) = all_147_0_157, multiplication(all_0_5_5, all_25_2_36) = all_67_1_69, yields:
% 47.63/15.11  | (216) all_147_0_157 = all_67_1_69
% 47.63/15.11  |
% 47.63/15.11  | Instantiating formula (30) with all_123_0_140, zero and discharging atoms multiplication(one, zero) = all_123_0_140, yields:
% 47.63/15.11  | (217) all_123_0_140 = zero
% 47.63/15.11  |
% 47.63/15.11  | Instantiating formula (4) with one, zero, all_117_0_132, all_187_0_201 and discharging atoms multiplication(one, zero) = all_187_0_201, multiplication(one, zero) = all_117_0_132, yields:
% 47.63/15.11  | (218) all_187_0_201 = all_117_0_132
% 47.63/15.11  |
% 47.63/15.11  | Instantiating formula (4) with one, zero, all_117_0_132, all_123_0_140 and discharging atoms multiplication(one, zero) = all_123_0_140, multiplication(one, zero) = all_117_0_132, yields:
% 47.63/15.11  | (219) all_123_0_140 = all_117_0_132
% 47.63/15.11  |
% 47.63/15.11  | Instantiating formula (4) with one, zero, all_89_1_96, all_187_0_201 and discharging atoms multiplication(one, zero) = all_187_0_201, multiplication(one, zero) = all_89_1_96, yields:
% 47.63/15.11  | (220) all_187_0_201 = all_89_1_96
% 47.63/15.11  |
% 47.63/15.11  | Instantiating formula (4) with one, zero, all_81_1_89, all_187_0_201 and discharging atoms multiplication(one, zero) = all_187_0_201, multiplication(one, zero) = all_81_1_89, yields:
% 47.63/15.11  | (221) all_187_0_201 = all_81_1_89
% 47.63/15.11  |
% 47.63/15.11  | Instantiating formula (45) with all_159_0_165, zero and discharging atoms multiplication(zero, zero) = all_159_0_165, yields:
% 47.63/15.11  | (222) all_159_0_165 = zero
% 47.63/15.11  |
% 47.63/15.11  | Combining equations (221,220) yields a new equation:
% 47.63/15.11  | (223) all_89_1_96 = all_81_1_89
% 47.63/15.11  |
% 47.63/15.11  | Combining equations (218,220) yields a new equation:
% 47.63/15.11  | (224) all_117_0_132 = all_89_1_96
% 47.63/15.11  |
% 47.63/15.11  | Simplifying 224 yields:
% 47.63/15.11  | (225) all_117_0_132 = all_89_1_96
% 47.63/15.11  |
% 47.63/15.11  | Combining equations (219,217) yields a new equation:
% 47.63/15.11  | (226) all_117_0_132 = zero
% 47.63/15.11  |
% 47.63/15.11  | Simplifying 226 yields:
% 47.63/15.11  | (227) all_117_0_132 = zero
% 47.63/15.11  |
% 47.63/15.11  | Combining equations (225,227) yields a new equation:
% 47.63/15.11  | (228) all_89_1_96 = zero
% 47.63/15.11  |
% 47.63/15.11  | Simplifying 228 yields:
% 47.63/15.11  | (229) all_89_1_96 = zero
% 47.63/15.11  |
% 47.63/15.11  | Combining equations (223,229) yields a new equation:
% 47.63/15.11  | (230) all_81_1_89 = zero
% 47.63/15.11  |
% 47.63/15.11  | Simplifying 230 yields:
% 47.63/15.11  | (231) all_81_1_89 = zero
% 47.63/15.11  |
% 47.63/15.11  | Combining equations (211,213) yields a new equation:
% 47.63/15.11  | (232) all_181_1_190 = all_0_4_4
% 47.63/15.11  |
% 47.63/15.11  | From (232) and (202) follows:
% 47.63/15.11  | (233) leq(all_0_4_4, all_0_4_4) = all_181_0_189
% 47.63/15.11  |
% 47.63/15.11  | From (212) and (206) follows:
% 47.63/15.11  | (200) leq(all_0_4_4, all_0_4_4) = all_179_3_188
% 47.63/15.11  |
% 47.63/15.11  | From (211)(232) and (203) follows:
% 47.63/15.11  | (235) multiplication(all_0_4_4, one) = all_0_4_4
% 47.63/15.11  |
% 47.63/15.11  | From (215) and (193) follows:
% 47.63/15.11  | (103) multiplication(all_5_1_11, zero) = all_37_1_54
% 47.63/15.11  |
% 47.63/15.11  | From (222) and (190) follows:
% 47.63/15.11  | (237) multiplication(zero, zero) = zero
% 47.63/15.11  |
% 47.63/15.11  | From (217) and (181) follows:
% 47.63/15.11  | (238) addition(all_123_1_141, zero) = all_29_0_42
% 47.63/15.11  |
% 47.63/15.11  | From (227) and (177) follows:
% 47.63/15.11  | (239) addition(all_117_1_133, zero) = all_41_0_56
% 47.63/15.11  |
% 47.63/15.11  | From (231) and (155) follows:
% 47.63/15.11  | (240) addition(zero, all_81_0_88) = all_37_1_54
% 47.63/15.11  |
% 47.63/15.11  | From (216) and (187) follows:
% 47.63/15.11  | (241) addition(one, all_67_1_69) = all_25_2_36
% 47.63/15.11  |
% 47.63/15.11  | From (214) and (184) follows:
% 47.63/15.11  | (242) addition(one, all_91_1_98) = all_25_2_36
% 47.63/15.11  |
% 47.63/15.11  | Instantiating formula (32) with all_0_4_4, all_0_4_4, all_181_0_189, all_179_3_188 and discharging atoms leq(all_0_4_4, all_0_4_4) = all_181_0_189, leq(all_0_4_4, all_0_4_4) = all_179_3_188, yields:
% 47.63/15.11  | (243) all_181_0_189 = all_179_3_188
% 47.63/15.11  |
% 47.63/15.11  | Instantiating formula (40) with all_29_0_42, all_123_1_141 and discharging atoms addition(all_123_1_141, zero) = all_29_0_42, yields:
% 47.63/15.11  | (244) all_123_1_141 = all_29_0_42
% 47.63/15.11  |
% 47.63/15.11  | Instantiating formula (40) with all_41_0_56, all_117_1_133 and discharging atoms addition(all_117_1_133, zero) = all_41_0_56, yields:
% 47.63/15.11  | (245) all_117_1_133 = all_41_0_56
% 47.63/15.11  |
% 47.63/15.11  | From (243) and (233) follows:
% 47.63/15.11  | (200) leq(all_0_4_4, all_0_4_4) = all_179_3_188
% 47.63/15.11  |
% 47.63/15.11  | From (245) and (175) follows:
% 47.63/15.11  | (247) multiplication(all_39_0_55, zero) = all_41_0_56
% 47.63/15.11  |
% 47.63/15.11  | From (244) and (179) follows:
% 47.63/15.11  | (248) multiplication(all_23_0_33, zero) = all_29_0_42
% 47.63/15.11  |
% 47.63/15.11  | From (244) and (238) follows:
% 47.63/15.11  | (249) addition(all_29_0_42, zero) = all_29_0_42
% 47.63/15.11  |
% 47.63/15.11  | Instantiating formula (21) with all_179_3_188, all_0_4_4, all_0_4_4 and discharging atoms leq(all_0_4_4, all_0_4_4) = all_179_3_188, yields:
% 47.63/15.11  | (250) all_179_3_188 = 0 |  ? [v0] : ( ~ (v0 = all_0_4_4) & addition(all_0_4_4, all_0_4_4) = v0)
% 47.63/15.11  |
% 47.63/15.11  | Instantiating formula (43) with all_113_0_126, all_41_0_56, zero, zero, all_7_2_16 and discharging atoms multiplication(all_41_0_56, zero) = all_113_0_126, multiplication(all_7_2_16, zero) = all_41_0_56, yields:
% 47.63/15.12  | (251)  ? [v0] : (multiplication(all_7_2_16, v0) = all_113_0_126 & multiplication(zero, zero) = v0)
% 47.63/15.12  |
% 47.63/15.12  | Instantiating formula (43) with all_113_0_126, all_41_0_56, zero, zero, all_39_0_55 and discharging atoms multiplication(all_41_0_56, zero) = all_113_0_126, multiplication(all_39_0_55, zero) = all_41_0_56, yields:
% 47.63/15.12  | (252)  ? [v0] : (multiplication(all_39_0_55, v0) = all_113_0_126 & multiplication(zero, zero) = v0)
% 47.63/15.12  |
% 47.63/15.12  | Instantiating formula (43) with all_63_1_63, all_37_1_54, zero, zero, all_5_1_11 and discharging atoms multiplication(all_37_1_54, zero) = all_63_1_63, multiplication(all_5_1_11, zero) = all_37_1_54, yields:
% 47.63/15.12  | (253)  ? [v0] : (multiplication(all_5_1_11, v0) = all_63_1_63 & multiplication(zero, zero) = v0)
% 47.63/15.12  |
% 47.63/15.12  | Instantiating formula (43) with all_95_1_104, all_29_0_42, all_95_2_105, zero, all_0_4_4 and discharging atoms multiplication(all_29_0_42, all_95_2_105) = all_95_1_104, multiplication(all_0_4_4, zero) = all_29_0_42, yields:
% 47.63/15.12  | (254)  ? [v0] : (multiplication(all_0_4_4, v0) = all_95_1_104 & multiplication(zero, all_95_2_105) = v0)
% 47.63/15.12  |
% 47.63/15.12  | Instantiating formula (43) with all_91_0_97, all_29_0_42, all_0_5_5, zero, all_0_4_4 and discharging atoms multiplication(all_29_0_42, all_0_5_5) = all_91_0_97, multiplication(all_0_4_4, zero) = all_29_0_42, yields:
% 47.63/15.12  | (255)  ? [v0] : (multiplication(all_0_4_4, v0) = all_91_0_97 & multiplication(zero, all_0_5_5) = v0)
% 47.63/15.12  |
% 47.63/15.12  | Instantiating formula (43) with all_69_0_70, all_29_0_42, zero, zero, all_0_4_4 and discharging atoms multiplication(all_29_0_42, zero) = all_69_0_70, multiplication(all_0_4_4, zero) = all_29_0_42, yields:
% 47.63/15.12  | (256)  ? [v0] : (multiplication(all_0_4_4, v0) = all_69_0_70 & multiplication(zero, zero) = v0)
% 47.63/15.12  |
% 47.63/15.12  | Instantiating formula (43) with all_29_0_42, all_23_0_33, zero, all_0_4_4, all_0_5_5 and discharging atoms multiplication(all_23_0_33, zero) = all_29_0_42, multiplication(all_0_5_5, all_0_4_4) = all_23_0_33, yields:
% 47.63/15.12  | (257)  ? [v0] : (multiplication(all_0_4_4, zero) = v0 & multiplication(all_0_5_5, v0) = all_29_0_42)
% 47.63/15.12  |
% 47.63/15.12  | Instantiating formula (43) with all_95_1_104, all_29_0_42, all_95_2_105, zero, all_23_0_33 and discharging atoms multiplication(all_29_0_42, all_95_2_105) = all_95_1_104, multiplication(all_23_0_33, zero) = all_29_0_42, yields:
% 47.63/15.12  | (258)  ? [v0] : (multiplication(all_23_0_33, v0) = all_95_1_104 & multiplication(zero, all_95_2_105) = v0)
% 47.63/15.12  |
% 47.63/15.12  | Instantiating formula (43) with all_69_0_70, all_29_0_42, zero, zero, all_23_0_33 and discharging atoms multiplication(all_29_0_42, zero) = all_69_0_70, multiplication(all_23_0_33, zero) = all_29_0_42, yields:
% 47.63/15.12  | (259)  ? [v0] : (multiplication(all_23_0_33, v0) = all_69_0_70 & multiplication(zero, zero) = v0)
% 47.63/15.12  |
% 47.63/15.12  | Instantiating formula (16) with all_23_0_33, all_0_4_4, one, all_0_4_4, all_0_5_5 and discharging atoms multiplication(all_0_4_4, one) = all_0_4_4, multiplication(all_0_5_5, all_0_4_4) = all_23_0_33, yields:
% 47.63/15.12  | (260)  ? [v0] : (multiplication(v0, one) = all_23_0_33 & multiplication(all_0_5_5, all_0_4_4) = v0)
% 47.63/15.12  |
% 47.63/15.12  | Instantiating formula (16) with all_67_0_68, all_29_0_42, zero, all_0_4_4, all_0_5_5 and discharging atoms multiplication(all_0_4_4, zero) = all_29_0_42, multiplication(all_0_5_5, all_29_0_42) = all_67_0_68, yields:
% 47.63/15.12  | (261)  ? [v0] : (multiplication(v0, zero) = all_67_0_68 & multiplication(all_0_5_5, all_0_4_4) = v0)
% 47.63/15.12  |
% 47.63/15.12  | Instantiating formula (16) with all_29_0_42, zero, zero, zero, all_0_4_4 and discharging atoms multiplication(all_0_4_4, zero) = all_29_0_42, multiplication(zero, zero) = zero, yields:
% 47.63/15.12  | (262)  ? [v0] : (multiplication(v0, zero) = all_29_0_42 & multiplication(all_0_4_4, zero) = v0)
% 47.63/15.12  |
% 47.63/15.12  | Instantiating formula (36) with all_0_2_2, all_0_3_3, one, all_91_1_98, all_91_0_97 and discharging atoms addition(all_91_1_98, all_91_0_97) = all_0_3_3, addition(one, all_0_3_3) = all_0_2_2, yields:
% 47.63/15.12  | (263)  ? [v0] : (addition(v0, all_91_0_97) = all_0_2_2 & addition(one, all_91_1_98) = v0)
% 47.63/15.12  |
% 47.63/15.12  | Instantiating formula (37) with all_0_4_4, all_29_0_42, all_0_4_4, all_25_2_36, zero and discharging atoms multiplication(all_0_4_4, zero) = all_29_0_42, addition(all_29_0_42, all_25_2_36) = all_0_4_4, yields:
% 47.63/15.12  | (264)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (leq(v2, all_0_4_4) = v3 & leq(all_0_4_4, all_0_4_4) = v0 & star(zero) = v1 & multiplication(all_25_2_36, v1) = v2 & ( ~ (v0 = 0) | v3 = 0))
% 47.63/15.12  |
% 47.63/15.12  | Instantiating formula (25) with all_69_0_70, all_29_0_42, zero, zero, all_29_0_42 and discharging atoms multiplication(all_29_0_42, zero) = all_69_0_70, addition(all_29_0_42, zero) = all_29_0_42, yields:
% 47.63/15.12  | (265)  ? [v0] :  ? [v1] : (multiplication(all_29_0_42, zero) = v0 & multiplication(zero, zero) = v1 & addition(v0, v1) = all_69_0_70)
% 47.63/15.12  |
% 47.63/15.12  | Instantiating formula (36) with all_0_4_4, all_23_0_33, one, all_67_1_69, all_67_0_68 and discharging atoms addition(all_67_1_69, all_67_0_68) = all_23_0_33, addition(one, all_23_0_33) = all_0_4_4, yields:
% 47.63/15.12  | (266)  ? [v0] : (addition(v0, all_67_0_68) = all_0_4_4 & addition(one, all_67_1_69) = v0)
% 47.63/15.12  |
% 47.63/15.12  | Instantiating formula (25) with all_63_1_63, all_37_1_54, zero, all_81_0_88, zero and discharging atoms multiplication(all_37_1_54, zero) = all_63_1_63, addition(zero, all_81_0_88) = all_37_1_54, yields:
% 47.63/15.12  | (267)  ? [v0] :  ? [v1] : (multiplication(all_81_0_88, zero) = v1 & multiplication(zero, zero) = v0 & addition(v0, v1) = all_63_1_63)
% 47.63/15.12  |
% 47.63/15.12  | Instantiating (263) with all_383_0_394 yields:
% 47.63/15.12  | (268) addition(all_383_0_394, all_91_0_97) = all_0_2_2 & addition(one, all_91_1_98) = all_383_0_394
% 47.63/15.12  |
% 47.63/15.12  | Applying alpha-rule on (268) yields:
% 47.63/15.12  | (269) addition(all_383_0_394, all_91_0_97) = all_0_2_2
% 47.63/15.12  | (270) addition(one, all_91_1_98) = all_383_0_394
% 47.63/15.13  |
% 47.63/15.13  | Instantiating (266) with all_661_0_773 yields:
% 47.63/15.13  | (271) addition(all_661_0_773, all_67_0_68) = all_0_4_4 & addition(one, all_67_1_69) = all_661_0_773
% 47.63/15.13  |
% 47.63/15.13  | Applying alpha-rule on (271) yields:
% 47.63/15.13  | (272) addition(all_661_0_773, all_67_0_68) = all_0_4_4
% 47.63/15.13  | (273) addition(one, all_67_1_69) = all_661_0_773
% 47.63/15.13  |
% 47.63/15.13  | Instantiating (262) with all_791_0_943 yields:
% 47.63/15.13  | (274) multiplication(all_791_0_943, zero) = all_29_0_42 & multiplication(all_0_4_4, zero) = all_791_0_943
% 47.63/15.13  |
% 47.63/15.13  | Applying alpha-rule on (274) yields:
% 47.63/15.13  | (275) multiplication(all_791_0_943, zero) = all_29_0_42
% 47.63/15.13  | (276) multiplication(all_0_4_4, zero) = all_791_0_943
% 47.63/15.13  |
% 47.63/15.13  | Instantiating (267) with all_815_0_963, all_815_1_964 yields:
% 47.63/15.13  | (277) multiplication(all_81_0_88, zero) = all_815_0_963 & multiplication(zero, zero) = all_815_1_964 & addition(all_815_1_964, all_815_0_963) = all_63_1_63
% 47.63/15.13  |
% 47.63/15.13  | Applying alpha-rule on (277) yields:
% 47.63/15.13  | (278) multiplication(all_81_0_88, zero) = all_815_0_963
% 47.63/15.13  | (279) multiplication(zero, zero) = all_815_1_964
% 47.63/15.13  | (280) addition(all_815_1_964, all_815_0_963) = all_63_1_63
% 47.63/15.13  |
% 47.63/15.13  | Instantiating (258) with all_893_0_1028 yields:
% 47.63/15.13  | (281) multiplication(all_23_0_33, all_893_0_1028) = all_95_1_104 & multiplication(zero, all_95_2_105) = all_893_0_1028
% 47.63/15.13  |
% 47.63/15.13  | Applying alpha-rule on (281) yields:
% 47.63/15.13  | (282) multiplication(all_23_0_33, all_893_0_1028) = all_95_1_104
% 47.63/15.13  | (283) multiplication(zero, all_95_2_105) = all_893_0_1028
% 47.63/15.13  |
% 47.63/15.13  | Instantiating (257) with all_899_0_1031 yields:
% 47.63/15.13  | (284) multiplication(all_0_4_4, zero) = all_899_0_1031 & multiplication(all_0_5_5, all_899_0_1031) = all_29_0_42
% 47.63/15.13  |
% 47.63/15.13  | Applying alpha-rule on (284) yields:
% 47.63/15.13  | (285) multiplication(all_0_4_4, zero) = all_899_0_1031
% 47.63/15.13  | (286) multiplication(all_0_5_5, all_899_0_1031) = all_29_0_42
% 47.63/15.13  |
% 47.63/15.13  | Instantiating (259) with all_903_0_1034 yields:
% 47.63/15.13  | (287) multiplication(all_23_0_33, all_903_0_1034) = all_69_0_70 & multiplication(zero, zero) = all_903_0_1034
% 47.63/15.13  |
% 47.63/15.13  | Applying alpha-rule on (287) yields:
% 47.63/15.13  | (288) multiplication(all_23_0_33, all_903_0_1034) = all_69_0_70
% 47.63/15.13  | (289) multiplication(zero, zero) = all_903_0_1034
% 47.63/15.13  |
% 47.63/15.13  | Instantiating (256) with all_917_0_1044 yields:
% 47.63/15.13  | (290) multiplication(all_0_4_4, all_917_0_1044) = all_69_0_70 & multiplication(zero, zero) = all_917_0_1044
% 47.63/15.13  |
% 47.63/15.13  | Applying alpha-rule on (290) yields:
% 47.63/15.13  | (291) multiplication(all_0_4_4, all_917_0_1044) = all_69_0_70
% 47.63/15.13  | (292) multiplication(zero, zero) = all_917_0_1044
% 47.63/15.13  |
% 47.63/15.13  | Instantiating (255) with all_919_0_1045 yields:
% 47.63/15.13  | (293) multiplication(all_0_4_4, all_919_0_1045) = all_91_0_97 & multiplication(zero, all_0_5_5) = all_919_0_1045
% 47.63/15.13  |
% 47.63/15.13  | Applying alpha-rule on (293) yields:
% 47.63/15.13  | (294) multiplication(all_0_4_4, all_919_0_1045) = all_91_0_97
% 47.63/15.13  | (295) multiplication(zero, all_0_5_5) = all_919_0_1045
% 47.63/15.13  |
% 47.63/15.13  | Instantiating (254) with all_929_0_1059 yields:
% 47.63/15.13  | (296) multiplication(all_0_4_4, all_929_0_1059) = all_95_1_104 & multiplication(zero, all_95_2_105) = all_929_0_1059
% 47.63/15.13  |
% 47.63/15.13  | Applying alpha-rule on (296) yields:
% 47.63/15.13  | (297) multiplication(all_0_4_4, all_929_0_1059) = all_95_1_104
% 47.63/15.13  | (298) multiplication(zero, all_95_2_105) = all_929_0_1059
% 47.63/15.13  |
% 47.63/15.13  | Instantiating (253) with all_933_0_1061 yields:
% 47.63/15.13  | (299) multiplication(all_5_1_11, all_933_0_1061) = all_63_1_63 & multiplication(zero, zero) = all_933_0_1061
% 47.63/15.13  |
% 47.63/15.13  | Applying alpha-rule on (299) yields:
% 47.63/15.13  | (300) multiplication(all_5_1_11, all_933_0_1061) = all_63_1_63
% 47.63/15.13  | (301) multiplication(zero, zero) = all_933_0_1061
% 47.63/15.13  |
% 47.63/15.13  | Instantiating (252) with all_943_0_1071 yields:
% 47.63/15.13  | (302) multiplication(all_39_0_55, all_943_0_1071) = all_113_0_126 & multiplication(zero, zero) = all_943_0_1071
% 47.63/15.13  |
% 47.63/15.13  | Applying alpha-rule on (302) yields:
% 47.63/15.13  | (303) multiplication(all_39_0_55, all_943_0_1071) = all_113_0_126
% 47.63/15.13  | (304) multiplication(zero, zero) = all_943_0_1071
% 47.63/15.13  |
% 47.63/15.13  | Instantiating (261) with all_977_0_1097 yields:
% 47.63/15.13  | (305) multiplication(all_977_0_1097, zero) = all_67_0_68 & multiplication(all_0_5_5, all_0_4_4) = all_977_0_1097
% 47.63/15.13  |
% 47.63/15.13  | Applying alpha-rule on (305) yields:
% 47.63/15.13  | (306) multiplication(all_977_0_1097, zero) = all_67_0_68
% 47.63/15.13  | (307) multiplication(all_0_5_5, all_0_4_4) = all_977_0_1097
% 47.63/15.13  |
% 47.63/15.13  | Instantiating (265) with all_1003_0_1120, all_1003_1_1121 yields:
% 47.63/15.13  | (308) multiplication(all_29_0_42, zero) = all_1003_1_1121 & multiplication(zero, zero) = all_1003_0_1120 & addition(all_1003_1_1121, all_1003_0_1120) = all_69_0_70
% 47.63/15.13  |
% 47.63/15.13  | Applying alpha-rule on (308) yields:
% 47.63/15.13  | (309) multiplication(all_29_0_42, zero) = all_1003_1_1121
% 47.63/15.13  | (310) multiplication(zero, zero) = all_1003_0_1120
% 47.63/15.13  | (311) addition(all_1003_1_1121, all_1003_0_1120) = all_69_0_70
% 47.63/15.13  |
% 47.63/15.13  | Instantiating (260) with all_1061_0_1186 yields:
% 47.63/15.13  | (312) multiplication(all_1061_0_1186, one) = all_23_0_33 & multiplication(all_0_5_5, all_0_4_4) = all_1061_0_1186
% 47.63/15.13  |
% 47.63/15.13  | Applying alpha-rule on (312) yields:
% 47.63/15.13  | (313) multiplication(all_1061_0_1186, one) = all_23_0_33
% 47.63/15.13  | (314) multiplication(all_0_5_5, all_0_4_4) = all_1061_0_1186
% 47.63/15.13  |
% 47.63/15.13  | Instantiating (251) with all_1073_0_1195 yields:
% 47.63/15.13  | (315) multiplication(all_7_2_16, all_1073_0_1195) = all_113_0_126 & multiplication(zero, zero) = all_1073_0_1195
% 47.63/15.13  |
% 47.63/15.13  | Applying alpha-rule on (315) yields:
% 47.63/15.13  | (316) multiplication(all_7_2_16, all_1073_0_1195) = all_113_0_126
% 47.63/15.13  | (317) multiplication(zero, zero) = all_1073_0_1195
% 47.63/15.13  |
% 47.63/15.13  | Instantiating (264) with all_1431_0_1566, all_1431_1_1567, all_1431_2_1568, all_1431_3_1569 yields:
% 47.63/15.13  | (318) leq(all_1431_1_1567, all_0_4_4) = all_1431_0_1566 & leq(all_0_4_4, all_0_4_4) = all_1431_3_1569 & star(zero) = all_1431_2_1568 & multiplication(all_25_2_36, all_1431_2_1568) = all_1431_1_1567 & ( ~ (all_1431_3_1569 = 0) | all_1431_0_1566 = 0)
% 47.63/15.13  |
% 47.63/15.13  | Applying alpha-rule on (318) yields:
% 47.63/15.13  | (319) star(zero) = all_1431_2_1568
% 47.63/15.13  | (320)  ~ (all_1431_3_1569 = 0) | all_1431_0_1566 = 0
% 47.63/15.13  | (321) multiplication(all_25_2_36, all_1431_2_1568) = all_1431_1_1567
% 47.63/15.13  | (322) leq(all_0_4_4, all_0_4_4) = all_1431_3_1569
% 47.63/15.13  | (323) leq(all_1431_1_1567, all_0_4_4) = all_1431_0_1566
% 47.63/15.13  |
% 47.63/15.13  | Instantiating formula (32) with all_0_4_4, all_0_4_4, all_1431_3_1569, all_179_3_188 and discharging atoms leq(all_0_4_4, all_0_4_4) = all_1431_3_1569, leq(all_0_4_4, all_0_4_4) = all_179_3_188, yields:
% 47.63/15.13  | (324) all_1431_3_1569 = all_179_3_188
% 47.63/15.13  |
% 47.63/15.13  | Instantiating formula (4) with all_0_4_4, zero, all_899_0_1031, all_29_0_42 and discharging atoms multiplication(all_0_4_4, zero) = all_899_0_1031, multiplication(all_0_4_4, zero) = all_29_0_42, yields:
% 47.63/15.14  | (325) all_899_0_1031 = all_29_0_42
% 47.63/15.14  |
% 47.63/15.14  | Instantiating formula (4) with all_0_4_4, zero, all_791_0_943, all_899_0_1031 and discharging atoms multiplication(all_0_4_4, zero) = all_899_0_1031, multiplication(all_0_4_4, zero) = all_791_0_943, yields:
% 47.63/15.14  | (326) all_899_0_1031 = all_791_0_943
% 47.63/15.14  |
% 47.63/15.14  | Instantiating formula (4) with all_0_5_5, all_0_4_4, all_1061_0_1186, all_23_0_33 and discharging atoms multiplication(all_0_5_5, all_0_4_4) = all_1061_0_1186, multiplication(all_0_5_5, all_0_4_4) = all_23_0_33, yields:
% 47.63/15.14  | (327) all_1061_0_1186 = all_23_0_33
% 47.63/15.14  |
% 47.63/15.14  | Instantiating formula (4) with all_0_5_5, all_0_4_4, all_977_0_1097, all_1061_0_1186 and discharging atoms multiplication(all_0_5_5, all_0_4_4) = all_1061_0_1186, multiplication(all_0_5_5, all_0_4_4) = all_977_0_1097, yields:
% 47.63/15.14  | (328) all_1061_0_1186 = all_977_0_1097
% 47.63/15.14  |
% 47.63/15.14  | Instantiating formula (45) with all_929_0_1059, all_95_2_105 and discharging atoms multiplication(zero, all_95_2_105) = all_929_0_1059, yields:
% 47.63/15.14  | (329) all_929_0_1059 = zero
% 47.63/15.14  |
% 47.63/15.14  | Instantiating formula (4) with zero, all_95_2_105, all_893_0_1028, all_929_0_1059 and discharging atoms multiplication(zero, all_95_2_105) = all_929_0_1059, multiplication(zero, all_95_2_105) = all_893_0_1028, yields:
% 47.63/15.14  | (330) all_929_0_1059 = all_893_0_1028
% 47.63/15.14  |
% 47.63/15.14  | Instantiating formula (45) with all_919_0_1045, all_0_5_5 and discharging atoms multiplication(zero, all_0_5_5) = all_919_0_1045, yields:
% 47.63/15.14  | (331) all_919_0_1045 = zero
% 47.63/15.14  |
% 47.63/15.14  | Instantiating formula (45) with all_1073_0_1195, zero and discharging atoms multiplication(zero, zero) = all_1073_0_1195, yields:
% 47.63/15.14  | (332) all_1073_0_1195 = zero
% 47.63/15.14  |
% 47.63/15.14  | Instantiating formula (4) with zero, zero, all_943_0_1071, all_1073_0_1195 and discharging atoms multiplication(zero, zero) = all_1073_0_1195, multiplication(zero, zero) = all_943_0_1071, yields:
% 47.63/15.14  | (333) all_1073_0_1195 = all_943_0_1071
% 47.63/15.14  |
% 47.63/15.14  | Instantiating formula (4) with zero, zero, all_933_0_1061, all_943_0_1071 and discharging atoms multiplication(zero, zero) = all_943_0_1071, multiplication(zero, zero) = all_933_0_1061, yields:
% 47.63/15.14  | (334) all_943_0_1071 = all_933_0_1061
% 47.63/15.14  |
% 47.63/15.14  | Instantiating formula (4) with zero, zero, all_917_0_1044, all_1003_0_1120 and discharging atoms multiplication(zero, zero) = all_1003_0_1120, multiplication(zero, zero) = all_917_0_1044, yields:
% 47.63/15.14  | (335) all_1003_0_1120 = all_917_0_1044
% 47.63/15.14  |
% 47.63/15.14  | Instantiating formula (4) with zero, zero, all_903_0_1034, all_1003_0_1120 and discharging atoms multiplication(zero, zero) = all_1003_0_1120, multiplication(zero, zero) = all_903_0_1034, yields:
% 47.63/15.14  | (336) all_1003_0_1120 = all_903_0_1034
% 47.63/15.14  |
% 47.63/15.14  | Instantiating formula (4) with zero, zero, all_903_0_1034, all_943_0_1071 and discharging atoms multiplication(zero, zero) = all_943_0_1071, multiplication(zero, zero) = all_903_0_1034, yields:
% 47.63/15.14  | (337) all_943_0_1071 = all_903_0_1034
% 47.63/15.14  |
% 47.63/15.14  | Instantiating formula (4) with zero, zero, all_815_1_964, all_1003_0_1120 and discharging atoms multiplication(zero, zero) = all_1003_0_1120, multiplication(zero, zero) = all_815_1_964, yields:
% 47.63/15.14  | (338) all_1003_0_1120 = all_815_1_964
% 47.63/15.14  |
% 47.63/15.14  | Instantiating formula (38) with one, all_91_1_98, all_383_0_394, all_25_2_36 and discharging atoms addition(one, all_91_1_98) = all_383_0_394, addition(one, all_91_1_98) = all_25_2_36, yields:
% 47.63/15.14  | (339) all_383_0_394 = all_25_2_36
% 47.63/15.14  |
% 47.63/15.14  | Instantiating formula (38) with one, all_67_1_69, all_661_0_773, all_25_2_36 and discharging atoms addition(one, all_67_1_69) = all_661_0_773, addition(one, all_67_1_69) = all_25_2_36, yields:
% 47.63/15.14  | (340) all_661_0_773 = all_25_2_36
% 47.63/15.14  |
% 47.63/15.14  | Combining equations (333,332) yields a new equation:
% 47.63/15.14  | (341) all_943_0_1071 = zero
% 47.63/15.14  |
% 47.63/15.14  | Simplifying 341 yields:
% 47.63/15.14  | (342) all_943_0_1071 = zero
% 47.63/15.14  |
% 47.63/15.14  | Combining equations (328,327) yields a new equation:
% 47.63/15.14  | (343) all_977_0_1097 = all_23_0_33
% 47.63/15.14  |
% 47.63/15.14  | Simplifying 343 yields:
% 47.63/15.14  | (344) all_977_0_1097 = all_23_0_33
% 47.63/15.14  |
% 47.63/15.14  | Combining equations (338,335) yields a new equation:
% 47.63/15.14  | (345) all_917_0_1044 = all_815_1_964
% 47.63/15.14  |
% 47.63/15.14  | Combining equations (336,335) yields a new equation:
% 47.63/15.14  | (346) all_917_0_1044 = all_903_0_1034
% 47.63/15.14  |
% 47.63/15.14  | Combining equations (342,334) yields a new equation:
% 47.63/15.14  | (347) all_933_0_1061 = zero
% 47.63/15.14  |
% 47.63/15.14  | Combining equations (337,334) yields a new equation:
% 47.63/15.14  | (348) all_933_0_1061 = all_903_0_1034
% 47.63/15.14  |
% 47.63/15.14  | Combining equations (348,347) yields a new equation:
% 47.63/15.14  | (349) all_903_0_1034 = zero
% 47.63/15.14  |
% 47.63/15.14  | Simplifying 349 yields:
% 47.63/15.14  | (350) all_903_0_1034 = zero
% 47.63/15.14  |
% 47.63/15.14  | Combining equations (329,330) yields a new equation:
% 47.63/15.14  | (351) all_893_0_1028 = zero
% 47.63/15.14  |
% 47.63/15.14  | Combining equations (346,345) yields a new equation:
% 47.63/15.14  | (352) all_903_0_1034 = all_815_1_964
% 47.63/15.14  |
% 47.63/15.14  | Simplifying 352 yields:
% 47.63/15.14  | (353) all_903_0_1034 = all_815_1_964
% 47.63/15.14  |
% 47.63/15.14  | Combining equations (353,350) yields a new equation:
% 47.63/15.14  | (354) all_815_1_964 = zero
% 47.63/15.14  |
% 47.63/15.14  | Simplifying 354 yields:
% 47.63/15.14  | (355) all_815_1_964 = zero
% 47.63/15.14  |
% 47.63/15.14  | Combining equations (326,325) yields a new equation:
% 47.63/15.14  | (356) all_791_0_943 = all_29_0_42
% 47.63/15.14  |
% 47.63/15.14  | Simplifying 356 yields:
% 47.63/15.14  | (357) all_791_0_943 = all_29_0_42
% 47.63/15.14  |
% 47.63/15.14  | Combining equations (355,345) yields a new equation:
% 47.63/15.14  | (358) all_917_0_1044 = zero
% 47.63/15.14  |
% 47.63/15.14  | Combining equations (351,330) yields a new equation:
% 47.63/15.14  | (329) all_929_0_1059 = zero
% 47.63/15.14  |
% 47.63/15.14  | From (324) and (322) follows:
% 47.63/15.14  | (200) leq(all_0_4_4, all_0_4_4) = all_179_3_188
% 47.63/15.14  |
% 47.63/15.14  | From (344) and (306) follows:
% 47.63/15.14  | (361) multiplication(all_23_0_33, zero) = all_67_0_68
% 47.63/15.14  |
% 47.63/15.14  | From (350) and (288) follows:
% 47.63/15.14  | (362) multiplication(all_23_0_33, zero) = all_69_0_70
% 47.63/15.14  |
% 47.63/15.14  | From (329) and (297) follows:
% 47.63/15.14  | (363) multiplication(all_0_4_4, zero) = all_95_1_104
% 47.63/15.14  |
% 47.63/15.14  | From (331) and (294) follows:
% 47.63/15.14  | (364) multiplication(all_0_4_4, zero) = all_91_0_97
% 47.63/15.14  |
% 47.63/15.14  | From (358) and (291) follows:
% 47.63/15.14  | (365) multiplication(all_0_4_4, zero) = all_69_0_70
% 47.63/15.14  |
% 47.63/15.14  | From (357) and (276) follows:
% 47.63/15.14  | (96) multiplication(all_0_4_4, zero) = all_29_0_42
% 47.63/15.14  |
% 47.63/15.14  | From (340) and (272) follows:
% 47.63/15.14  | (367) addition(all_25_2_36, all_67_0_68) = all_0_4_4
% 47.63/15.14  |
% 47.63/15.14  | From (339) and (269) follows:
% 47.63/15.14  | (368) addition(all_25_2_36, all_91_0_97) = all_0_2_2
% 47.63/15.14  |
% 47.63/15.14  | Instantiating formula (4) with all_23_0_33, zero, all_67_0_68, all_69_0_70 and discharging atoms multiplication(all_23_0_33, zero) = all_69_0_70, multiplication(all_23_0_33, zero) = all_67_0_68, yields:
% 47.63/15.14  | (369) all_69_0_70 = all_67_0_68
% 47.63/15.14  |
% 47.63/15.14  | Instantiating formula (4) with all_0_4_4, zero, all_95_1_104, all_29_0_42 and discharging atoms multiplication(all_0_4_4, zero) = all_95_1_104, multiplication(all_0_4_4, zero) = all_29_0_42, yields:
% 47.63/15.14  | (370) all_95_1_104 = all_29_0_42
% 47.63/15.14  |
% 47.63/15.14  | Instantiating formula (4) with all_0_4_4, zero, all_91_0_97, all_95_1_104 and discharging atoms multiplication(all_0_4_4, zero) = all_95_1_104, multiplication(all_0_4_4, zero) = all_91_0_97, yields:
% 47.63/15.14  | (371) all_95_1_104 = all_91_0_97
% 47.63/15.14  |
% 47.63/15.14  | Instantiating formula (4) with all_0_4_4, zero, all_69_0_70, all_91_0_97 and discharging atoms multiplication(all_0_4_4, zero) = all_91_0_97, multiplication(all_0_4_4, zero) = all_69_0_70, yields:
% 47.63/15.14  | (372) all_91_0_97 = all_69_0_70
% 47.63/15.14  |
% 47.63/15.14  | Combining equations (371,370) yields a new equation:
% 47.63/15.14  | (373) all_91_0_97 = all_29_0_42
% 47.63/15.14  |
% 47.63/15.14  | Simplifying 373 yields:
% 47.63/15.14  | (374) all_91_0_97 = all_29_0_42
% 47.63/15.14  |
% 47.63/15.14  | Combining equations (372,374) yields a new equation:
% 47.63/15.14  | (375) all_69_0_70 = all_29_0_42
% 47.63/15.14  |
% 47.63/15.14  | Simplifying 375 yields:
% 47.63/15.14  | (376) all_69_0_70 = all_29_0_42
% 47.63/15.14  |
% 47.63/15.14  | Combining equations (376,369) yields a new equation:
% 47.63/15.14  | (377) all_67_0_68 = all_29_0_42
% 47.63/15.14  |
% 47.63/15.14  | From (374) and (368) follows:
% 47.63/15.14  | (378) addition(all_25_2_36, all_29_0_42) = all_0_2_2
% 47.63/15.14  |
% 47.63/15.14  | From (377) and (367) follows:
% 47.63/15.14  | (120) addition(all_25_2_36, all_29_0_42) = all_0_4_4
% 47.63/15.14  |
% 47.63/15.14  | Instantiating formula (38) with all_25_2_36, all_29_0_42, all_0_2_2, all_0_4_4 and discharging atoms addition(all_25_2_36, all_29_0_42) = all_0_2_2, addition(all_25_2_36, all_29_0_42) = all_0_4_4, yields:
% 47.63/15.14  | (380) all_0_2_2 = all_0_4_4
% 47.63/15.14  |
% 47.63/15.14  | From (380) and (42) follows:
% 47.63/15.14  | (381) leq(all_0_4_4, all_0_4_4) = all_0_0_0
% 47.63/15.14  |
% 47.63/15.14  | From (380) and (11) follows:
% 47.63/15.14  | (382) leq(all_0_4_4, all_0_4_4) = all_0_1_1
% 47.63/15.14  |
% 47.63/15.14  | Instantiating formula (32) with all_0_4_4, all_0_4_4, all_0_0_0, all_179_3_188 and discharging atoms leq(all_0_4_4, all_0_4_4) = all_179_3_188, leq(all_0_4_4, all_0_4_4) = all_0_0_0, yields:
% 47.63/15.14  | (383) all_179_3_188 = all_0_0_0
% 47.63/15.14  |
% 47.63/15.14  | Instantiating formula (32) with all_0_4_4, all_0_4_4, all_0_1_1, all_179_3_188 and discharging atoms leq(all_0_4_4, all_0_4_4) = all_179_3_188, leq(all_0_4_4, all_0_4_4) = all_0_1_1, yields:
% 47.63/15.14  | (384) all_179_3_188 = all_0_1_1
% 47.63/15.14  |
% 47.63/15.14  | Combining equations (383,384) yields a new equation:
% 47.63/15.14  | (385) all_0_0_0 = all_0_1_1
% 47.63/15.14  |
% 47.63/15.14  | Simplifying 385 yields:
% 47.63/15.14  | (386) all_0_0_0 = all_0_1_1
% 47.63/15.14  |
% 47.63/15.14  +-Applying beta-rule and splitting (7), into two cases.
% 47.63/15.14  |-Branch one:
% 47.63/15.14  | (387)  ~ (all_0_0_0 = 0)
% 47.63/15.14  |
% 47.63/15.14  	| Equations (386) can reduce 387 to:
% 47.63/15.14  	| (388)  ~ (all_0_1_1 = 0)
% 47.63/15.14  	|
% 47.63/15.14  	+-Applying beta-rule and splitting (65), into two cases.
% 47.63/15.14  	|-Branch one:
% 47.63/15.14  	| (389) all_0_1_1 = 0
% 47.63/15.14  	|
% 47.63/15.15  		| Equations (389) can reduce 388 to:
% 47.63/15.15  		| (390) $false
% 47.63/15.15  		|
% 47.63/15.15  		|-The branch is then unsatisfiable
% 47.63/15.15  	|-Branch two:
% 47.63/15.15  	| (388)  ~ (all_0_1_1 = 0)
% 47.63/15.15  	| (392)  ? [v0] : ( ~ (v0 = all_0_2_2) & addition(all_0_4_4, all_0_2_2) = v0)
% 47.63/15.15  	|
% 47.63/15.15  		| Instantiating (392) with all_1689_0_1772 yields:
% 47.63/15.15  		| (393)  ~ (all_1689_0_1772 = all_0_2_2) & addition(all_0_4_4, all_0_2_2) = all_1689_0_1772
% 47.63/15.15  		|
% 47.63/15.15  		| Applying alpha-rule on (393) yields:
% 47.63/15.15  		| (394)  ~ (all_1689_0_1772 = all_0_2_2)
% 47.63/15.15  		| (395) addition(all_0_4_4, all_0_2_2) = all_1689_0_1772
% 47.63/15.15  		|
% 47.63/15.15  		| Equations (380) can reduce 394 to:
% 47.63/15.15  		| (396)  ~ (all_1689_0_1772 = all_0_4_4)
% 47.63/15.15  		|
% 47.63/15.15  		| From (380) and (395) follows:
% 47.63/15.15  		| (397) addition(all_0_4_4, all_0_4_4) = all_1689_0_1772
% 47.63/15.15  		|
% 47.63/15.15  		+-Applying beta-rule and splitting (64), into two cases.
% 47.63/15.15  		|-Branch one:
% 47.63/15.15  		| (398) all_0_0_0 = 0
% 47.63/15.15  		|
% 47.63/15.15  			| Combining equations (386,398) yields a new equation:
% 47.63/15.15  			| (399) all_0_1_1 = 0
% 47.63/15.15  			|
% 47.63/15.15  			| Simplifying 399 yields:
% 47.63/15.15  			| (389) all_0_1_1 = 0
% 47.63/15.15  			|
% 47.63/15.15  			| Equations (389) can reduce 388 to:
% 47.63/15.15  			| (390) $false
% 47.63/15.15  			|
% 47.63/15.15  			|-The branch is then unsatisfiable
% 47.63/15.15  		|-Branch two:
% 47.63/15.15  		| (387)  ~ (all_0_0_0 = 0)
% 47.63/15.15  		| (403)  ? [v0] : ( ~ (v0 = all_0_4_4) & addition(all_0_2_2, all_0_4_4) = v0)
% 47.63/15.15  		|
% 47.63/15.15  			| Instantiating (403) with all_1694_0_1773 yields:
% 47.63/15.15  			| (404)  ~ (all_1694_0_1773 = all_0_4_4) & addition(all_0_2_2, all_0_4_4) = all_1694_0_1773
% 47.63/15.15  			|
% 47.63/15.15  			| Applying alpha-rule on (404) yields:
% 47.63/15.15  			| (405)  ~ (all_1694_0_1773 = all_0_4_4)
% 47.63/15.15  			| (406) addition(all_0_2_2, all_0_4_4) = all_1694_0_1773
% 47.63/15.15  			|
% 47.63/15.15  			| Equations (386) can reduce 387 to:
% 47.63/15.15  			| (388)  ~ (all_0_1_1 = 0)
% 47.63/15.15  			|
% 47.63/15.15  			| From (380) and (406) follows:
% 47.63/15.15  			| (408) addition(all_0_4_4, all_0_4_4) = all_1694_0_1773
% 47.63/15.15  			|
% 47.63/15.15  			+-Applying beta-rule and splitting (250), into two cases.
% 47.63/15.15  			|-Branch one:
% 47.63/15.15  			| (409) all_179_3_188 = 0
% 47.63/15.15  			|
% 47.63/15.15  				| Combining equations (384,409) yields a new equation:
% 47.63/15.15  				| (399) all_0_1_1 = 0
% 47.63/15.15  				|
% 47.63/15.15  				| Simplifying 399 yields:
% 47.63/15.15  				| (389) all_0_1_1 = 0
% 47.63/15.15  				|
% 47.63/15.15  				| Equations (389) can reduce 388 to:
% 47.63/15.15  				| (390) $false
% 47.63/15.15  				|
% 47.63/15.15  				|-The branch is then unsatisfiable
% 47.63/15.15  			|-Branch two:
% 47.63/15.15  			| (413)  ~ (all_179_3_188 = 0)
% 47.63/15.15  			| (414)  ? [v0] : ( ~ (v0 = all_0_4_4) & addition(all_0_4_4, all_0_4_4) = v0)
% 47.63/15.15  			|
% 47.63/15.15  				| Instantiating (414) with all_1699_0_1774 yields:
% 47.63/15.15  				| (415)  ~ (all_1699_0_1774 = all_0_4_4) & addition(all_0_4_4, all_0_4_4) = all_1699_0_1774
% 47.63/15.15  				|
% 47.63/15.15  				| Applying alpha-rule on (415) yields:
% 47.63/15.15  				| (416)  ~ (all_1699_0_1774 = all_0_4_4)
% 47.63/15.15  				| (417) addition(all_0_4_4, all_0_4_4) = all_1699_0_1774
% 47.63/15.15  				|
% 47.63/15.15  				| Instantiating formula (26) with all_1699_0_1774, all_0_4_4 and discharging atoms addition(all_0_4_4, all_0_4_4) = all_1699_0_1774, yields:
% 47.63/15.15  				| (418) all_1699_0_1774 = all_0_4_4
% 47.63/15.15  				|
% 47.63/15.15  				| Instantiating formula (38) with all_0_4_4, all_0_4_4, all_1694_0_1773, all_1699_0_1774 and discharging atoms addition(all_0_4_4, all_0_4_4) = all_1699_0_1774, addition(all_0_4_4, all_0_4_4) = all_1694_0_1773, yields:
% 47.63/15.15  				| (419) all_1699_0_1774 = all_1694_0_1773
% 47.63/15.15  				|
% 47.63/15.15  				| Instantiating formula (38) with all_0_4_4, all_0_4_4, all_1689_0_1772, all_1699_0_1774 and discharging atoms addition(all_0_4_4, all_0_4_4) = all_1699_0_1774, addition(all_0_4_4, all_0_4_4) = all_1689_0_1772, yields:
% 47.63/15.15  				| (420) all_1699_0_1774 = all_1689_0_1772
% 47.63/15.15  				|
% 47.63/15.15  				| Combining equations (418,419) yields a new equation:
% 47.63/15.15  				| (421) all_1694_0_1773 = all_0_4_4
% 47.63/15.15  				|
% 47.63/15.15  				| Combining equations (420,419) yields a new equation:
% 47.63/15.15  				| (422) all_1694_0_1773 = all_1689_0_1772
% 47.63/15.15  				|
% 47.63/15.15  				| Combining equations (421,422) yields a new equation:
% 47.63/15.15  				| (423) all_1689_0_1772 = all_0_4_4
% 47.63/15.15  				|
% 47.63/15.15  				| Equations (423) can reduce 396 to:
% 47.63/15.15  				| (390) $false
% 47.63/15.15  				|
% 47.63/15.15  				|-The branch is then unsatisfiable
% 47.63/15.15  |-Branch two:
% 47.63/15.15  | (398) all_0_0_0 = 0
% 47.63/15.15  | (388)  ~ (all_0_1_1 = 0)
% 47.63/15.15  |
% 47.63/15.15  	| Combining equations (386,398) yields a new equation:
% 47.63/15.15  	| (399) all_0_1_1 = 0
% 47.63/15.15  	|
% 47.63/15.15  	| Simplifying 399 yields:
% 47.63/15.15  	| (389) all_0_1_1 = 0
% 47.63/15.15  	|
% 47.63/15.15  	| Equations (389) can reduce 388 to:
% 47.63/15.15  	| (390) $false
% 47.63/15.15  	|
% 47.63/15.15  	|-The branch is then unsatisfiable
% 47.63/15.15  % SZS output end Proof for theBenchmark
% 47.63/15.15  
% 47.63/15.15  14546ms
%------------------------------------------------------------------------------