%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE138+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n011.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 2.90s 1.38s
% Output   : Proof 4.26s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : KLE138+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.14/0.35  % Computer : n011.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Thu Jun 16 12:45:36 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.58/0.60          ____       _                          
% 0.58/0.60    ___  / __ \_____(_)___  ________  __________
% 0.58/0.60   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.60  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.58/0.60  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.58/0.60  
% 0.58/0.60  A Theorem Prover for First-Order Logic
% 0.58/0.61  (ePrincess v.1.0)
% 0.58/0.61  
% 0.58/0.61  (c) Philipp Rümmer, 2009-2015
% 0.58/0.61  (c) Peter Backeman, 2014-2015
% 0.58/0.61  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.61  Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.61  Bug reports to peter@backeman.se
% 0.58/0.61  
% 0.58/0.61  For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.61  
% 0.58/0.61  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.66  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.56/0.95  Prover 0: Preprocessing ...
% 2.24/1.20  Prover 0: Constructing countermodel ...
% 2.90/1.38  Prover 0: proved (725ms)
% 2.90/1.38  
% 2.90/1.38  No countermodel exists, formula is valid
% 2.90/1.38  % SZS status Theorem for theBenchmark
% 2.90/1.38  
% 2.90/1.38  Generating proof ... found it (size 11)
% 4.26/1.68  
% 4.26/1.68  % SZS output start Proof for theBenchmark
% 4.26/1.68  Assumed formulas after preprocessing and simplification: 
% 4.26/1.68  | (0)  ? [v0] : ( ~ (v0 = one) & strong_iteration(zero) = v0 &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (multiplication(v2, v3) = v5) |  ~ (multiplication(v1, v3) = v4) |  ~ (addition(v4, v5) = v6) |  ? [v7] : (multiplication(v7, v3) = v6 & addition(v1, v2) = v7)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (multiplication(v1, v3) = v5) |  ~ (multiplication(v1, v2) = v4) |  ~ (addition(v4, v5) = v6) |  ? [v7] : (multiplication(v1, v7) = v6 & addition(v2, v3) = v7)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = v2 |  ~ (strong_iteration(v1) = v2) |  ~ (star(v1) = v3) |  ~ (multiplication(v2, zero) = v4) |  ~ (addition(v3, v4) = v5)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v4, v3) = v5) |  ~ (multiplication(v1, v2) = v4) |  ? [v6] : (multiplication(v2, v3) = v6 & multiplication(v1, v6) = v5)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v4, v3) = v5) |  ~ (addition(v1, v2) = v4) |  ? [v6] :  ? [v7] : (multiplication(v2, v3) = v7 & multiplication(v1, v3) = v6 & addition(v6, v7) = v5)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v3, v1) = v4) |  ~ (addition(v4, v2) = v5) |  ~ leq(v5, v3) |  ? [v6] :  ? [v7] : (star(v1) = v6 & multiplication(v2, v6) = v7 & leq(v7, v3))) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v2, v3) = v4) |  ~ (multiplication(v1, v4) = v5) |  ? [v6] : (multiplication(v6, v3) = v5 & multiplication(v1, v2) = v6)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v1, v4) = v5) |  ~ (addition(v2, v3) = v4) |  ? [v6] :  ? [v7] : (multiplication(v1, v3) = v7 & multiplication(v1, v2) = v6 & addition(v6, v7) = v5)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v1, v3) = v4) |  ~ (addition(v4, v2) = v5) |  ~ leq(v5, v3) |  ? [v6] :  ? [v7] : (star(v1) = v6 & multiplication(v6, v2) = v7 & leq(v7, v3))) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v1, v3) = v4) |  ~ (addition(v4, v2) = v5) |  ~ leq(v3, v5) |  ? [v6] :  ? [v7] : (strong_iteration(v1) = v6 & multiplication(v6, v2) = v7 & leq(v3, v7))) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (addition(v4, v1) = v5) |  ~ (addition(v3, v2) = v4) |  ? [v6] : (addition(v3, v6) = v5 & addition(v2, v1) = v6)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (addition(v3, v4) = v5) |  ~ (addition(v2, v1) = v4) |  ? [v6] : (addition(v6, v1) = v5 & addition(v3, v2) = v6)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (multiplication(v4, v3) = v2) |  ~ (multiplication(v4, v3) = v1)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (addition(v4, v3) = v2) |  ~ (addition(v4, v3) = v1)) &  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (addition(v1, v2) = v3) |  ~ leq(v1, v2)) &  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 |  ~ (strong_iteration(v3) = v2) |  ~ (strong_iteration(v3) = v1)) &  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 |  ~ (star(v3) = v2) |  ~ (star(v3) = v1)) &  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (strong_iteration(v1) = v2) |  ~ (multiplication(v1, v2) = v3) | addition(v3, one) = v2) &  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (star(v1) = v2) |  ~ (multiplication(v2, v1) = v3) | addition(one, v3) = v2) &  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (star(v1) = v2) |  ~ (multiplication(v1, v2) = v3) | addition(one, v3) = v2) &  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (addition(v2, v1) = v3) | addition(v1, v2) = v3) &  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (addition(v1, v2) = v3) | addition(v2, v1) = v3) &  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (multiplication(v1, one) = v2)) &  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (multiplication(one, v1) = v2)) &  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v1, v1) = v2)) &  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v1, zero) = v2)) &  ! [v1] :  ! [v2] : (v2 = zero |  ~ (multiplication(zero, v1) = v2)) &  ! [v1] :  ! [v2] : ( ~ (strong_iteration(v1) = v2) |  ? [v3] :  ? [v4] : (star(v1) = v3 & multiplication(v2, zero) = v4 & addition(v3, v4) = v2)) &  ! [v1] :  ! [v2] : ( ~ (strong_iteration(v1) = v2) |  ? [v3] : (multiplication(v1, v2) = v3 & addition(v3, one) = v2)) &  ! [v1] :  ! [v2] : ( ~ (star(v1) = v2) |  ? [v3] : (multiplication(v2, v1) = v3 & addition(one, v3) = v2)) &  ! [v1] :  ! [v2] : ( ~ (star(v1) = v2) |  ? [v3] : (multiplication(v1, v2) = v3 & addition(one, v3) = v2)) &  ! [v1] :  ! [v2] : ( ~ (addition(v1, v2) = v2) | leq(v1, v2)))
% 4.26/1.73  | Instantiating (0) with all_0_0_0 yields:
% 4.26/1.73  | (1)  ~ (all_0_0_0 = one) & strong_iteration(zero) = all_0_0_0 &  ! [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] : (v4 = v1 |  ~ (strong_iteration(v0) = v1) |  ~ (star(v0) = v2) |  ~ (multiplication(v1, zero) = v3) |  ~ (addition(v2, v3) = v4)) &  ! [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) |  ~ leq(v4, v2) |  ? [v5] :  ? [v6] : (star(v0) = v5 & multiplication(v1, v5) = v6 & leq(v6, v2))) &  ! [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) |  ~ leq(v4, v2) |  ? [v5] :  ? [v6] : (star(v0) = v5 & multiplication(v5, v1) = v6 & leq(v6, v2))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v0, v2) = v3) |  ~ (addition(v3, v1) = v4) |  ~ leq(v2, v4) |  ? [v5] :  ? [v6] : (strong_iteration(v0) = v5 & multiplication(v5, v1) = v6 & leq(v2, v6))) &  ! [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 |  ~ (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) |  ~ leq(v0, v1)) &  ! [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] : ( ~ (strong_iteration(v0) = v1) |  ~ (multiplication(v0, v1) = v2) | addition(v2, one) = v1) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (star(v0) = v1) |  ~ (multiplication(v1, v0) = v2) | addition(one, v2) = v1) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (star(v0) = v1) |  ~ (multiplication(v0, v1) = v2) | addition(one, v2) = v1) &  ! [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] : ( ~ (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))
% 4.26/1.74  |
% 4.26/1.74  | Applying alpha-rule on (1) yields:
% 4.26/1.74  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 4.26/1.74  | (3)  ! [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))
% 4.26/1.74  | (4)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 4.26/1.74  | (5)  ! [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))
% 4.26/1.74  | (6)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (star(v0) = v1) |  ~ (multiplication(v1, v0) = v2) | addition(one, v2) = v1)
% 4.26/1.74  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 4.26/1.74  | (8)  ! [v0] :  ! [v1] : ( ~ (star(v0) = v1) |  ? [v2] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1))
% 4.26/1.75  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 4.26/1.75  | (10)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ~ leq(v0, v1))
% 4.26/1.75  | (11)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 4.26/1.75  | (12) strong_iteration(zero) = all_0_0_0
% 4.26/1.75  | (13)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 4.26/1.75  | (14)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (strong_iteration(v2) = v1) |  ~ (strong_iteration(v2) = v0))
% 4.26/1.75  | (15)  ! [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))
% 4.26/1.75  | (16)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strong_iteration(v0) = v1) |  ~ (multiplication(v0, v1) = v2) | addition(v2, one) = v1)
% 4.26/1.75  | (17)  ~ (all_0_0_0 = one)
% 4.26/1.75  | (18)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (star(v2) = v1) |  ~ (star(v2) = v0))
% 4.26/1.75  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v0, v2) = v3) |  ~ (addition(v3, v1) = v4) |  ~ leq(v4, v2) |  ? [v5] :  ? [v6] : (star(v0) = v5 & multiplication(v5, v1) = v6 & leq(v6, v2)))
% 4.26/1.75  | (20)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 4.26/1.75  | (21)  ! [v0] :  ! [v1] : ( ~ (strong_iteration(v0) = v1) |  ? [v2] :  ? [v3] : (star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1))
% 4.26/1.75  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 4.26/1.75  | (23)  ! [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))
% 4.26/1.75  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v1 |  ~ (strong_iteration(v0) = v1) |  ~ (star(v0) = v2) |  ~ (multiplication(v1, zero) = v3) |  ~ (addition(v2, v3) = v4))
% 4.26/1.75  | (25)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 4.26/1.75  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v0, v2) = v3) |  ~ (addition(v3, v1) = v4) |  ~ leq(v2, v4) |  ? [v5] :  ? [v6] : (strong_iteration(v0) = v5 & multiplication(v5, v1) = v6 & leq(v2, v6)))
% 4.26/1.75  | (27)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (star(v0) = v1) |  ~ (multiplication(v0, v1) = v2) | addition(one, v2) = v1)
% 4.26/1.75  | (28)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 4.26/1.75  | (29)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 4.26/1.75  | (30)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 4.26/1.76  | (31)  ! [v0] :  ! [v1] : ( ~ (star(v0) = v1) |  ? [v2] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1))
% 4.26/1.76  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 4.26/1.76  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v2, v0) = v3) |  ~ (addition(v3, v1) = v4) |  ~ leq(v4, v2) |  ? [v5] :  ? [v6] : (star(v0) = v5 & multiplication(v1, v5) = v6 & leq(v6, v2)))
% 4.26/1.76  | (34)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 4.26/1.76  | (35)  ! [v0] :  ! [v1] : ( ~ (strong_iteration(v0) = v1) |  ? [v2] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1))
% 4.26/1.76  |
% 4.26/1.76  | Instantiating formula (35) with all_0_0_0, zero and discharging atoms strong_iteration(zero) = all_0_0_0, yields:
% 4.26/1.76  | (36)  ? [v0] : (multiplication(zero, all_0_0_0) = v0 & addition(v0, one) = all_0_0_0)
% 4.26/1.76  |
% 4.26/1.76  | Instantiating (36) with all_8_0_1 yields:
% 4.26/1.76  | (37) multiplication(zero, all_0_0_0) = all_8_0_1 & addition(all_8_0_1, one) = all_0_0_0
% 4.26/1.76  |
% 4.26/1.76  | Applying alpha-rule on (37) yields:
% 4.26/1.76  | (38) multiplication(zero, all_0_0_0) = all_8_0_1
% 4.26/1.76  | (39) addition(all_8_0_1, one) = all_0_0_0
% 4.26/1.76  |
% 4.26/1.76  | Instantiating formula (11) with all_8_0_1, all_0_0_0 and discharging atoms multiplication(zero, all_0_0_0) = all_8_0_1, yields:
% 4.26/1.76  | (40) all_8_0_1 = zero
% 4.26/1.76  |
% 4.26/1.76  | From (40) and (39) follows:
% 4.26/1.76  | (41) addition(zero, one) = all_0_0_0
% 4.26/1.76  |
% 4.26/1.76  | Instantiating formula (30) with all_0_0_0, zero, one and discharging atoms addition(zero, one) = all_0_0_0, yields:
% 4.26/1.76  | (42) addition(one, zero) = all_0_0_0
% 4.26/1.76  |
% 4.26/1.76  | Instantiating formula (13) with all_0_0_0, one and discharging atoms addition(one, zero) = all_0_0_0, yields:
% 4.26/1.76  | (43) all_0_0_0 = one
% 4.26/1.76  |
% 4.26/1.76  | Equations (43) can reduce 17 to:
% 4.26/1.76  | (44) $false
% 4.26/1.76  |
% 4.26/1.76  |-The branch is then unsatisfiable
% 4.26/1.76  % SZS output end Proof for theBenchmark
% 4.26/1.76  
% 4.26/1.76  1147ms
%------------------------------------------------------------------------------