%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE151+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n028.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 01:51:38 EDT 2022

% Result   : Theorem 28.73s 8.70s
% Output   : Proof 30.11s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : KLE151+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.34  % Computer : n028.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Thu Jun 16 07:23:11 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.58          ____       _                          
% 0.19/0.58    ___  / __ \_____(_)___  ________  __________
% 0.19/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.19/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.19/0.58  
% 0.19/0.58  A Theorem Prover for First-Order Logic
% 0.19/0.58  (ePrincess v.1.0)
% 0.19/0.58  
% 0.19/0.58  (c) Philipp Rümmer, 2009-2015
% 0.19/0.58  (c) Peter Backeman, 2014-2015
% 0.19/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58  Bug reports to peter@backeman.se
% 0.19/0.58  
% 0.19/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58  
% 0.19/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.69/0.66  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.55/0.96  Prover 0: Preprocessing ...
% 2.24/1.21  Prover 0: Constructing countermodel ...
% 17.68/5.96  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 17.75/5.99  Prover 1: Preprocessing ...
% 18.05/6.09  Prover 1: Constructing countermodel ...
% 28.01/8.56  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 28.06/8.57  Prover 2: Preprocessing ...
% 28.06/8.61  Prover 2: Warning: ignoring some quantifiers
% 28.06/8.61  Prover 2: Constructing countermodel ...
% 28.73/8.70  Prover 2: proved (143ms)
% 28.73/8.70  Prover 1: stopped
% 28.73/8.70  Prover 0: stopped
% 28.73/8.70  
% 28.73/8.70  No countermodel exists, formula is valid
% 28.73/8.70  % SZS status Theorem for theBenchmark
% 28.73/8.70  
% 28.73/8.70  Generating proof ... Warning: ignoring some quantifiers
% 29.55/8.93  found it (size 40)
% 29.55/8.93  
% 29.55/8.93  % SZS output start Proof for theBenchmark
% 29.55/8.93  Assumed formulas after preprocessing and simplification: 
% 29.55/8.93  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : ( ~ (v8 = 0) & strong_iteration(v5) = v6 & strong_iteration(v2) = v3 & leq(v4, v7) = v8 & multiplication(v6, v0) = v7 & multiplication(v1, v0) = v2 & multiplication(v0, v3) = v4 & multiplication(v0, v1) = v5 &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 |  ~ (strong_iteration(v9) = v12) |  ~ (leq(v11, v13) = v14) |  ~ (multiplication(v12, v10) = v13) |  ? [v15] :  ? [v16] :  ? [v17] : ( ~ (v17 = 0) & leq(v11, v16) = v17 & multiplication(v9, v11) = v15 & addition(v15, v10) = v16)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 |  ~ (leq(v13, v11) = v14) |  ~ (star(v9) = v12) |  ~ (multiplication(v12, v10) = v13) |  ? [v15] :  ? [v16] :  ? [v17] : ( ~ (v17 = 0) & leq(v16, v11) = v17 & multiplication(v9, v11) = v15 & addition(v15, v10) = v16)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 |  ~ (leq(v13, v11) = v14) |  ~ (star(v9) = v12) |  ~ (multiplication(v10, v12) = v13) |  ? [v15] :  ? [v16] :  ? [v17] : ( ~ (v17 = 0) & leq(v16, v11) = v17 & multiplication(v11, v9) = v15 & addition(v15, v10) = v16)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (multiplication(v10, v11) = v13) |  ~ (multiplication(v9, v11) = v12) |  ~ (addition(v12, v13) = v14) |  ? [v15] : (multiplication(v15, v11) = v14 & addition(v9, v10) = v15)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (multiplication(v9, v11) = v13) |  ~ (multiplication(v9, v10) = v12) |  ~ (addition(v12, v13) = v14) |  ? [v15] : (multiplication(v9, v15) = v14 & addition(v10, v11) = v15)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (multiplication(v12, v11) = v13) |  ~ (multiplication(v9, v10) = v12) |  ? [v14] : (multiplication(v10, v11) = v14 & multiplication(v9, v14) = v13)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (multiplication(v12, v11) = v13) |  ~ (addition(v9, v10) = v12) |  ? [v14] :  ? [v15] : (multiplication(v10, v11) = v15 & multiplication(v9, v11) = v14 & addition(v14, v15) = v13)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (multiplication(v11, v9) = v12) |  ~ (addition(v12, v10) = v13) |  ? [v14] :  ? [v15] :  ? [v16] : ((v16 = 0 & leq(v15, v11) = 0 & star(v9) = v14 & multiplication(v10, v14) = v15) | ( ~ (v14 = 0) & leq(v13, v11) = v14))) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (multiplication(v10, v11) = v12) |  ~ (multiplication(v9, v12) = v13) |  ? [v14] : (multiplication(v14, v11) = v13 & multiplication(v9, v10) = v14)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (multiplication(v9, v12) = v13) |  ~ (addition(v10, v11) = v12) |  ? [v14] :  ? [v15] : (multiplication(v9, v11) = v15 & multiplication(v9, v10) = v14 & addition(v14, v15) = v13)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (multiplication(v9, v11) = v12) |  ~ (addition(v12, v10) = v13) |  ? [v14] :  ? [v15] :  ? [v16] : ((v16 = 0 & strong_iteration(v9) = v14 & leq(v11, v15) = 0 & multiplication(v14, v10) = v15) | ( ~ (v14 = 0) & leq(v11, v13) = v14))) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (multiplication(v9, v11) = v12) |  ~ (addition(v12, v10) = v13) |  ? [v14] :  ? [v15] :  ? [v16] : ((v16 = 0 & leq(v15, v11) = 0 & star(v9) = v14 & multiplication(v14, v10) = v15) | ( ~ (v14 = 0) & leq(v13, v11) = v14))) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (addition(v12, v9) = v13) |  ~ (addition(v11, v10) = v12) |  ? [v14] : (addition(v11, v14) = v13 & addition(v10, v9) = v14)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (addition(v11, v12) = v13) |  ~ (addition(v10, v9) = v12) |  ? [v14] : (addition(v14, v9) = v13 & addition(v11, v10) = v14)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v10 = v9 |  ~ (leq(v12, v11) = v10) |  ~ (leq(v12, v11) = v9)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v10 = v9 |  ~ (multiplication(v12, v11) = v10) |  ~ (multiplication(v12, v11) = v9)) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v10 = v9 |  ~ (addition(v12, v11) = v10) |  ~ (addition(v12, v11) = v9)) &  ! [v9] :  ! [v10] :  ! [v11] : (v11 = v10 |  ~ (addition(v9, v10) = v11) |  ? [v12] : ( ~ (v12 = 0) & leq(v9, v10) = v12)) &  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (leq(v9, v10) = v11) |  ? [v12] : ( ~ (v12 = v10) & addition(v9, v10) = v12)) &  ! [v9] :  ! [v10] :  ! [v11] : (v10 = v9 |  ~ (strong_iteration(v11) = v10) |  ~ (strong_iteration(v11) = v9)) &  ! [v9] :  ! [v10] :  ! [v11] : (v10 = v9 |  ~ (star(v11) = v10) |  ~ (star(v11) = v9)) &  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (addition(v10, v9) = v11) | addition(v9, v10) = v11) &  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (addition(v9, v10) = v11) | addition(v10, v9) = v11) &  ! [v9] :  ! [v10] : (v10 = v9 |  ~ (multiplication(v9, one) = v10)) &  ! [v9] :  ! [v10] : (v10 = v9 |  ~ (multiplication(one, v9) = v10)) &  ! [v9] :  ! [v10] : (v10 = v9 |  ~ (addition(v9, v9) = v10)) &  ! [v9] :  ! [v10] : (v10 = v9 |  ~ (addition(v9, zero) = v10)) &  ! [v9] :  ! [v10] : (v10 = zero |  ~ (multiplication(zero, v9) = v10)) &  ! [v9] :  ! [v10] : ( ~ (strong_iteration(v9) = v10) |  ? [v11] :  ? [v12] : (star(v9) = v11 & multiplication(v10, zero) = v12 & addition(v11, v12) = v10)) &  ! [v9] :  ! [v10] : ( ~ (strong_iteration(v9) = v10) |  ? [v11] : (multiplication(v9, v10) = v11 & addition(v11, one) = v10)) &  ! [v9] :  ! [v10] : ( ~ (leq(v9, v10) = 0) | addition(v9, v10) = v10) &  ! [v9] :  ! [v10] : ( ~ (star(v9) = v10) |  ? [v11] :  ? [v12] : (strong_iteration(v9) = v11 & multiplication(v11, zero) = v12 & addition(v10, v12) = v11)) &  ! [v9] :  ! [v10] : ( ~ (star(v9) = v10) |  ? [v11] : (multiplication(v10, v9) = v11 & addition(one, v11) = v10)) &  ! [v9] :  ! [v10] : ( ~ (star(v9) = v10) |  ? [v11] : (multiplication(v9, v10) = v11 & addition(one, v11) = v10)) &  ! [v9] :  ! [v10] : ( ~ (addition(v9, v10) = v10) | leq(v9, v10) = 0) &  ? [v9] :  ? [v10] :  ? [v11] : leq(v10, v9) = v11 &  ? [v9] :  ? [v10] :  ? [v11] : multiplication(v10, v9) = v11 &  ? [v9] :  ? [v10] :  ? [v11] : addition(v10, v9) = v11 &  ? [v9] :  ? [v10] : strong_iteration(v9) = v10 &  ? [v9] :  ? [v10] : star(v9) = v10)
% 29.92/8.97  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 yields:
% 29.92/8.97  | (1)  ~ (all_0_0_0 = 0) & strong_iteration(all_0_3_3) = all_0_2_2 & strong_iteration(all_0_6_6) = all_0_5_5 & leq(all_0_4_4, all_0_1_1) = all_0_0_0 & multiplication(all_0_2_2, all_0_8_8) = all_0_1_1 & multiplication(all_0_7_7, all_0_8_8) = all_0_6_6 & multiplication(all_0_8_8, all_0_5_5) = all_0_4_4 & multiplication(all_0_8_8, all_0_7_7) = all_0_3_3 &  ! [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] : ((v7 = 0 & leq(v6, v2) = 0 & star(v0) = v5 & multiplication(v1, v5) = v6) | ( ~ (v5 = 0) & leq(v4, v2) = v5))) &  ! [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] : ((v7 = 0 & strong_iteration(v0) = v5 & leq(v2, v6) = 0 & multiplication(v5, v1) = v6) | ( ~ (v5 = 0) & leq(v2, v4) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v0, v2) = v3) |  ~ (addition(v3, v1) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : ((v7 = 0 & leq(v6, v2) = 0 & star(v0) = v5 & multiplication(v5, v1) = v6) | ( ~ (v5 = 0) & leq(v4, v2) = v5))) &  ! [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] : leq(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : multiplication(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : addition(v1, v0) = v2 &  ? [v0] :  ? [v1] : strong_iteration(v0) = v1 &  ? [v0] :  ? [v1] : star(v0) = v1
% 30.11/8.98  |
% 30.11/8.98  | Applying alpha-rule on (1) yields:
% 30.11/8.98  | (2)  ! [v0] :  ! [v1] : ( ~ (star(v0) = v1) |  ? [v2] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1))
% 30.11/8.98  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 30.11/8.98  | (4)  ! [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))
% 30.11/8.99  | (5)  ! [v0] :  ! [v1] : ( ~ (star(v0) = v1) |  ? [v2] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1))
% 30.11/8.99  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v0, v2) = v3) |  ~ (addition(v3, v1) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : ((v7 = 0 & leq(v6, v2) = 0 & star(v0) = v5 & multiplication(v5, v1) = v6) | ( ~ (v5 = 0) & leq(v4, v2) = v5)))
% 30.11/8.99  | (7) multiplication(all_0_8_8, all_0_7_7) = all_0_3_3
% 30.11/8.99  | (8)  ! [v0] :  ! [v1] : ( ~ (star(v0) = v1) |  ? [v2] :  ? [v3] : (strong_iteration(v0) = v2 & multiplication(v2, zero) = v3 & addition(v1, v3) = v2))
% 30.11/8.99  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v0, v2) = v3) |  ~ (addition(v3, v1) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : ((v7 = 0 & strong_iteration(v0) = v5 & leq(v2, v6) = 0 & multiplication(v5, v1) = v6) | ( ~ (v5 = 0) & leq(v2, v4) = v5)))
% 30.11/8.99  | (10) strong_iteration(all_0_3_3) = all_0_2_2
% 30.11/8.99  | (11)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 30.11/8.99  | (12)  ! [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))
% 30.11/8.99  | (13)  ! [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))
% 30.11/8.99  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 30.11/8.99  | (15) leq(all_0_4_4, all_0_1_1) = all_0_0_0
% 30.11/8.99  | (16)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 30.11/8.99  | (17) multiplication(all_0_7_7, all_0_8_8) = all_0_6_6
% 30.11/8.99  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 30.11/8.99  | (19)  ! [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))
% 30.11/8.99  | (20)  ! [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))
% 30.11/8.99  | (21)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (strong_iteration(v2) = v1) |  ~ (strong_iteration(v2) = v0))
% 30.11/8.99  | (22)  ! [v0] :  ! [v1] : ( ~ (strong_iteration(v0) = v1) |  ? [v2] :  ? [v3] : (star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1))
% 30.11/8.99  | (23)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (star(v2) = v1) |  ~ (star(v2) = v0))
% 30.11/8.99  | (24)  ? [v0] :  ? [v1] : star(v0) = v1
% 30.11/8.99  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v2, v0) = v3) |  ~ (addition(v3, v1) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : ((v7 = 0 & leq(v6, v2) = 0 & star(v0) = v5 & multiplication(v1, v5) = v6) | ( ~ (v5 = 0) & leq(v4, v2) = v5)))
% 30.11/8.99  | (26)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 30.11/8.99  | (27)  ! [v0] :  ! [v1] : ( ~ (strong_iteration(v0) = v1) |  ? [v2] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1))
% 30.11/8.99  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 30.11/8.99  | (29)  ! [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))
% 30.11/8.99  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 30.11/9.00  | (31) multiplication(all_0_8_8, all_0_5_5) = all_0_4_4
% 30.11/9.00  | (32)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 30.11/9.00  | (33)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 30.11/9.00  | (34)  ? [v0] :  ? [v1] :  ? [v2] : leq(v1, v0) = v2
% 30.11/9.00  | (35)  ! [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))
% 30.11/9.00  | (36)  ? [v0] :  ? [v1] : strong_iteration(v0) = v1
% 30.11/9.00  | (37) strong_iteration(all_0_6_6) = all_0_5_5
% 30.11/9.00  | (38)  ~ (all_0_0_0 = 0)
% 30.11/9.00  | (39)  ? [v0] :  ? [v1] :  ? [v2] : addition(v1, v0) = v2
% 30.11/9.00  | (40)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 30.11/9.00  | (41)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3))
% 30.11/9.00  | (42)  ? [v0] :  ? [v1] :  ? [v2] : multiplication(v1, v0) = v2
% 30.11/9.00  | (43)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (leq(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3))
% 30.11/9.00  | (44) multiplication(all_0_2_2, all_0_8_8) = all_0_1_1
% 30.11/9.00  | (45)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0))
% 30.11/9.00  | (46)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0)
% 30.11/9.00  | (47)  ! [v0] :  ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1)
% 30.11/9.00  | (48)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 30.11/9.00  | (49)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 30.11/9.00  |
% 30.11/9.00  | Instantiating formula (27) with all_0_5_5, all_0_6_6 and discharging atoms strong_iteration(all_0_6_6) = all_0_5_5, yields:
% 30.11/9.00  | (50)  ? [v0] : (multiplication(all_0_6_6, all_0_5_5) = v0 & addition(v0, one) = all_0_5_5)
% 30.11/9.00  |
% 30.11/9.00  | Instantiating formula (19) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_4_4, all_0_8_8, all_0_3_3 and discharging atoms strong_iteration(all_0_3_3) = all_0_2_2, leq(all_0_4_4, all_0_1_1) = all_0_0_0, multiplication(all_0_2_2, all_0_8_8) = all_0_1_1, yields:
% 30.11/9.00  | (51) all_0_0_0 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & leq(all_0_4_4, v1) = v2 & multiplication(all_0_3_3, all_0_4_4) = v0 & addition(v0, all_0_8_8) = v1)
% 30.11/9.00  |
% 30.11/9.00  | Instantiating (50) with all_18_0_22 yields:
% 30.11/9.00  | (52) multiplication(all_0_6_6, all_0_5_5) = all_18_0_22 & addition(all_18_0_22, one) = all_0_5_5
% 30.11/9.00  |
% 30.11/9.00  | Applying alpha-rule on (52) yields:
% 30.11/9.00  | (53) multiplication(all_0_6_6, all_0_5_5) = all_18_0_22
% 30.11/9.00  | (54) addition(all_18_0_22, one) = all_0_5_5
% 30.11/9.00  |
% 30.11/9.00  +-Applying beta-rule and splitting (51), into two cases.
% 30.11/9.00  |-Branch one:
% 30.11/9.00  | (55) all_0_0_0 = 0
% 30.11/9.00  |
% 30.11/9.00  	| Equations (55) can reduce 38 to:
% 30.11/9.00  	| (56) $false
% 30.11/9.00  	|
% 30.11/9.00  	|-The branch is then unsatisfiable
% 30.11/9.00  |-Branch two:
% 30.11/9.00  | (38)  ~ (all_0_0_0 = 0)
% 30.11/9.00  | (58)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & leq(all_0_4_4, v1) = v2 & multiplication(all_0_3_3, all_0_4_4) = v0 & addition(v0, all_0_8_8) = v1)
% 30.11/9.00  |
% 30.11/9.00  	| Instantiating (58) with all_30_0_28, all_30_1_29, all_30_2_30 yields:
% 30.11/9.00  	| (59)  ~ (all_30_0_28 = 0) & leq(all_0_4_4, all_30_1_29) = all_30_0_28 & multiplication(all_0_3_3, all_0_4_4) = all_30_2_30 & addition(all_30_2_30, all_0_8_8) = all_30_1_29
% 30.11/9.00  	|
% 30.11/9.00  	| Applying alpha-rule on (59) yields:
% 30.11/9.00  	| (60)  ~ (all_30_0_28 = 0)
% 30.11/9.00  	| (61) leq(all_0_4_4, all_30_1_29) = all_30_0_28
% 30.11/9.00  	| (62) multiplication(all_0_3_3, all_0_4_4) = all_30_2_30
% 30.11/9.00  	| (63) addition(all_30_2_30, all_0_8_8) = all_30_1_29
% 30.11/9.00  	|
% 30.11/9.00  	| Instantiating formula (43) with all_30_0_28, all_30_1_29, all_0_4_4 and discharging atoms leq(all_0_4_4, all_30_1_29) = all_30_0_28, yields:
% 30.11/9.00  	| (64) all_30_0_28 = 0 |  ? [v0] : ( ~ (v0 = all_30_1_29) & addition(all_0_4_4, all_30_1_29) = v0)
% 30.11/9.00  	|
% 30.11/9.00  	| Instantiating formula (49) with all_30_2_30, all_0_3_3, all_0_4_4, all_0_7_7, all_0_8_8 and discharging atoms multiplication(all_0_3_3, all_0_4_4) = all_30_2_30, multiplication(all_0_8_8, all_0_7_7) = all_0_3_3, yields:
% 30.11/9.01  	| (65)  ? [v0] : (multiplication(all_0_7_7, all_0_4_4) = v0 & multiplication(all_0_8_8, v0) = all_30_2_30)
% 30.11/9.01  	|
% 30.11/9.01  	| Instantiating formula (49) with all_18_0_22, all_0_6_6, all_0_5_5, all_0_8_8, all_0_7_7 and discharging atoms multiplication(all_0_6_6, all_0_5_5) = all_18_0_22, multiplication(all_0_7_7, all_0_8_8) = all_0_6_6, yields:
% 30.11/9.01  	| (66)  ? [v0] : (multiplication(all_0_7_7, v0) = all_18_0_22 & multiplication(all_0_8_8, all_0_5_5) = v0)
% 30.11/9.01  	|
% 30.11/9.01  	| Instantiating formula (35) with all_0_4_4, all_0_5_5, one, all_18_0_22, all_0_8_8 and discharging atoms multiplication(all_0_8_8, all_0_5_5) = all_0_4_4, addition(all_18_0_22, one) = all_0_5_5, yields:
% 30.11/9.01  	| (67)  ? [v0] :  ? [v1] : (multiplication(all_0_8_8, all_18_0_22) = v0 & multiplication(all_0_8_8, one) = v1 & addition(v0, v1) = all_0_4_4)
% 30.11/9.01  	|
% 30.11/9.01  	| Instantiating (65) with all_50_0_45 yields:
% 30.11/9.01  	| (68) multiplication(all_0_7_7, all_0_4_4) = all_50_0_45 & multiplication(all_0_8_8, all_50_0_45) = all_30_2_30
% 30.11/9.01  	|
% 30.11/9.01  	| Applying alpha-rule on (68) yields:
% 30.11/9.01  	| (69) multiplication(all_0_7_7, all_0_4_4) = all_50_0_45
% 30.11/9.01  	| (70) multiplication(all_0_8_8, all_50_0_45) = all_30_2_30
% 30.11/9.01  	|
% 30.11/9.01  	| Instantiating (67) with all_80_0_81, all_80_1_82 yields:
% 30.11/9.01  	| (71) multiplication(all_0_8_8, all_18_0_22) = all_80_1_82 & multiplication(all_0_8_8, one) = all_80_0_81 & addition(all_80_1_82, all_80_0_81) = all_0_4_4
% 30.11/9.01  	|
% 30.11/9.01  	| Applying alpha-rule on (71) yields:
% 30.11/9.01  	| (72) multiplication(all_0_8_8, all_18_0_22) = all_80_1_82
% 30.11/9.01  	| (73) multiplication(all_0_8_8, one) = all_80_0_81
% 30.11/9.01  	| (74) addition(all_80_1_82, all_80_0_81) = all_0_4_4
% 30.11/9.01  	|
% 30.11/9.01  	| Instantiating (66) with all_92_0_96 yields:
% 30.11/9.01  	| (75) multiplication(all_0_7_7, all_92_0_96) = all_18_0_22 & multiplication(all_0_8_8, all_0_5_5) = all_92_0_96
% 30.11/9.01  	|
% 30.11/9.01  	| Applying alpha-rule on (75) yields:
% 30.11/9.01  	| (76) multiplication(all_0_7_7, all_92_0_96) = all_18_0_22
% 30.11/9.01  	| (77) multiplication(all_0_8_8, all_0_5_5) = all_92_0_96
% 30.11/9.01  	|
% 30.11/9.01  	+-Applying beta-rule and splitting (64), into two cases.
% 30.11/9.01  	|-Branch one:
% 30.11/9.01  	| (78) all_30_0_28 = 0
% 30.11/9.01  	|
% 30.11/9.01  		| Equations (78) can reduce 60 to:
% 30.11/9.01  		| (56) $false
% 30.11/9.01  		|
% 30.11/9.01  		|-The branch is then unsatisfiable
% 30.11/9.01  	|-Branch two:
% 30.11/9.01  	| (60)  ~ (all_30_0_28 = 0)
% 30.11/9.01  	| (81)  ? [v0] : ( ~ (v0 = all_30_1_29) & addition(all_0_4_4, all_30_1_29) = v0)
% 30.11/9.01  	|
% 30.11/9.01  		| Instantiating (81) with all_98_0_97 yields:
% 30.11/9.01  		| (82)  ~ (all_98_0_97 = all_30_1_29) & addition(all_0_4_4, all_30_1_29) = all_98_0_97
% 30.11/9.01  		|
% 30.11/9.01  		| Applying alpha-rule on (82) yields:
% 30.11/9.01  		| (83)  ~ (all_98_0_97 = all_30_1_29)
% 30.11/9.01  		| (84) addition(all_0_4_4, all_30_1_29) = all_98_0_97
% 30.11/9.01  		|
% 30.11/9.01  		| Instantiating formula (3) with all_0_8_8, all_0_5_5, all_92_0_96, all_0_4_4 and discharging atoms multiplication(all_0_8_8, all_0_5_5) = all_92_0_96, multiplication(all_0_8_8, all_0_5_5) = all_0_4_4, yields:
% 30.11/9.01  		| (85) all_92_0_96 = all_0_4_4
% 30.11/9.01  		|
% 30.11/9.01  		| Instantiating formula (48) with all_80_0_81, all_0_8_8 and discharging atoms multiplication(all_0_8_8, one) = all_80_0_81, yields:
% 30.11/9.01  		| (86) all_80_0_81 = all_0_8_8
% 30.11/9.01  		|
% 30.11/9.01  		| From (85) and (76) follows:
% 30.11/9.01  		| (87) multiplication(all_0_7_7, all_0_4_4) = all_18_0_22
% 30.11/9.01  		|
% 30.11/9.01  		| From (86) and (74) follows:
% 30.11/9.01  		| (88) addition(all_80_1_82, all_0_8_8) = all_0_4_4
% 30.11/9.01  		|
% 30.11/9.01  		| Instantiating formula (3) with all_0_7_7, all_0_4_4, all_18_0_22, all_50_0_45 and discharging atoms multiplication(all_0_7_7, all_0_4_4) = all_50_0_45, multiplication(all_0_7_7, all_0_4_4) = all_18_0_22, yields:
% 30.11/9.01  		| (89) all_50_0_45 = all_18_0_22
% 30.11/9.01  		|
% 30.11/9.01  		| From (89) and (70) follows:
% 30.11/9.01  		| (90) multiplication(all_0_8_8, all_18_0_22) = all_30_2_30
% 30.11/9.01  		|
% 30.11/9.01  		| Instantiating formula (3) with all_0_8_8, all_18_0_22, all_30_2_30, all_80_1_82 and discharging atoms multiplication(all_0_8_8, all_18_0_22) = all_80_1_82, multiplication(all_0_8_8, all_18_0_22) = all_30_2_30, yields:
% 30.11/9.01  		| (91) all_80_1_82 = all_30_2_30
% 30.11/9.01  		|
% 30.11/9.01  		| From (91) and (88) follows:
% 30.11/9.01  		| (92) addition(all_30_2_30, all_0_8_8) = all_0_4_4
% 30.11/9.01  		|
% 30.11/9.01  		| Instantiating formula (14) with all_30_2_30, all_0_8_8, all_0_4_4, all_30_1_29 and discharging atoms addition(all_30_2_30, all_0_8_8) = all_30_1_29, addition(all_30_2_30, all_0_8_8) = all_0_4_4, yields:
% 30.11/9.01  		| (93) all_30_1_29 = all_0_4_4
% 30.11/9.01  		|
% 30.11/9.01  		| Equations (93) can reduce 83 to:
% 30.11/9.01  		| (94)  ~ (all_98_0_97 = all_0_4_4)
% 30.11/9.01  		|
% 30.11/9.01  		| From (93) and (84) follows:
% 30.11/9.01  		| (95) addition(all_0_4_4, all_0_4_4) = all_98_0_97
% 30.11/9.01  		|
% 30.11/9.01  		| Instantiating formula (26) with all_98_0_97, all_0_4_4 and discharging atoms addition(all_0_4_4, all_0_4_4) = all_98_0_97, yields:
% 30.11/9.01  		| (96) all_98_0_97 = all_0_4_4
% 30.11/9.01  		|
% 30.11/9.01  		| Equations (96) can reduce 94 to:
% 30.11/9.01  		| (56) $false
% 30.11/9.01  		|
% 30.11/9.01  		|-The branch is then unsatisfiable
% 30.11/9.01  % SZS output end Proof for theBenchmark
% 30.11/9.01  
% 30.11/9.01  8417ms
%------------------------------------------------------------------------------