%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE146+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n006.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 01:51:35 EDT 2022

% Result   : Theorem 12.68s 3.74s
% Output   : Proof 25.91s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : KLE146+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.35  % Computer : n006.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Thu Jun 16 16:30:11 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.52/0.60          ____       _                          
% 0.52/0.60    ___  / __ \_____(_)___  ________  __________
% 0.52/0.60   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.52/0.60  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.52/0.60  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.52/0.60  
% 0.52/0.60  A Theorem Prover for First-Order Logic
% 0.52/0.60  (ePrincess v.1.0)
% 0.52/0.60  
% 0.52/0.60  (c) Philipp Rümmer, 2009-2015
% 0.52/0.60  (c) Peter Backeman, 2014-2015
% 0.52/0.60  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.52/0.60  Free software under GNU Lesser General Public License (LGPL).
% 0.52/0.60  Bug reports to peter@backeman.se
% 0.52/0.60  
% 0.52/0.60  For more information, visit http://user.uu.se/~petba168/breu/
% 0.52/0.60  
% 0.52/0.60  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.69/0.65  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.58/0.95  Prover 0: Preprocessing ...
% 2.24/1.21  Prover 0: Constructing countermodel ...
% 12.68/3.74  Prover 0: proved (3094ms)
% 12.68/3.74  
% 12.68/3.74  No countermodel exists, formula is valid
% 12.68/3.74  % SZS status Theorem for theBenchmark
% 12.68/3.74  
% 12.68/3.74  Generating proof ... found it (size 131)
% 25.44/7.06  
% 25.44/7.06  % SZS output start Proof for theBenchmark
% 25.44/7.06  Assumed formulas after preprocessing and simplification: 
% 25.44/7.06  | (0)  ? [v0] :  ? [v1] : (strong_iteration(v0) = v1 &  ~ leq(one, v1) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (multiplication(v3, v4) = v6) |  ~ (multiplication(v2, v4) = v5) |  ~ (addition(v5, v6) = v7) |  ? [v8] : (multiplication(v8, v4) = v7 & addition(v2, v3) = v8)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (multiplication(v2, v4) = v6) |  ~ (multiplication(v2, v3) = v5) |  ~ (addition(v5, v6) = v7) |  ? [v8] : (multiplication(v2, v8) = v7 & addition(v3, v4) = v8)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = v3 |  ~ (strong_iteration(v2) = v3) |  ~ (star(v2) = v4) |  ~ (multiplication(v3, zero) = v5) |  ~ (addition(v4, v5) = v6)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (multiplication(v5, v4) = v6) |  ~ (multiplication(v2, v3) = v5) |  ? [v7] : (multiplication(v3, v4) = v7 & multiplication(v2, v7) = v6)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (multiplication(v5, v4) = v6) |  ~ (addition(v2, v3) = v5) |  ? [v7] :  ? [v8] : (multiplication(v3, v4) = v8 & multiplication(v2, v4) = v7 & addition(v7, v8) = v6)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (multiplication(v4, v2) = v5) |  ~ (addition(v5, v3) = v6) |  ~ leq(v6, v4) |  ? [v7] :  ? [v8] : (star(v2) = v7 & multiplication(v3, v7) = v8 & leq(v8, v4))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (multiplication(v3, v4) = v5) |  ~ (multiplication(v2, v5) = v6) |  ? [v7] : (multiplication(v7, v4) = v6 & multiplication(v2, v3) = v7)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (multiplication(v2, v5) = v6) |  ~ (addition(v3, v4) = v5) |  ? [v7] :  ? [v8] : (multiplication(v2, v4) = v8 & multiplication(v2, v3) = v7 & addition(v7, v8) = v6)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (multiplication(v2, v4) = v5) |  ~ (addition(v5, v3) = v6) |  ~ leq(v6, v4) |  ? [v7] :  ? [v8] : (star(v2) = v7 & multiplication(v7, v3) = v8 & leq(v8, v4))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (multiplication(v2, v4) = v5) |  ~ (addition(v5, v3) = v6) |  ~ leq(v4, v6) |  ? [v7] :  ? [v8] : (strong_iteration(v2) = v7 & multiplication(v7, v3) = v8 & leq(v4, v8))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (addition(v5, v2) = v6) |  ~ (addition(v4, v3) = v5) |  ? [v7] : (addition(v4, v7) = v6 & addition(v3, v2) = v7)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (addition(v4, v5) = v6) |  ~ (addition(v3, v2) = v5) |  ? [v7] : (addition(v7, v2) = v6 & addition(v4, v3) = v7)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (multiplication(v5, v4) = v3) |  ~ (multiplication(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (addition(v5, v4) = v3) |  ~ (addition(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (addition(v2, v3) = v4) |  ~ leq(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (strong_iteration(v4) = v3) |  ~ (strong_iteration(v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (star(v4) = v3) |  ~ (star(v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (strong_iteration(v2) = v3) |  ~ (multiplication(v2, v3) = v4) | addition(v4, one) = v3) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (star(v2) = v3) |  ~ (multiplication(v3, v2) = v4) | addition(one, v4) = v3) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (star(v2) = v3) |  ~ (multiplication(v2, v3) = v4) | addition(one, v4) = v3) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v2) = v4) | addition(v2, v3) = v4) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) | addition(v3, v2) = v4) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (multiplication(v2, one) = v3)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (multiplication(one, v2) = v3)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (addition(v2, v2) = v3)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (addition(v2, zero) = v3)) &  ! [v2] :  ! [v3] : (v3 = zero |  ~ (multiplication(zero, v2) = v3)) &  ! [v2] :  ! [v3] : ( ~ (strong_iteration(v2) = v3) |  ? [v4] :  ? [v5] : (star(v2) = v4 & multiplication(v3, zero) = v5 & addition(v4, v5) = v3)) &  ! [v2] :  ! [v3] : ( ~ (strong_iteration(v2) = v3) |  ? [v4] : (multiplication(v2, v3) = v4 & addition(v4, one) = v3)) &  ! [v2] :  ! [v3] : ( ~ (star(v2) = v3) |  ? [v4] : (multiplication(v3, v2) = v4 & addition(one, v4) = v3)) &  ! [v2] :  ! [v3] : ( ~ (star(v2) = v3) |  ? [v4] : (multiplication(v2, v3) = v4 & addition(one, v4) = v3)) &  ! [v2] :  ! [v3] : ( ~ (addition(v2, v3) = v3) | leq(v2, v3)))
% 25.67/7.11  | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 25.67/7.11  | (1) strong_iteration(all_0_1_1) = all_0_0_0 &  ~ leq(one, 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))
% 25.67/7.12  |
% 25.67/7.12  | Applying alpha-rule on (1) yields:
% 25.67/7.12  | (2)  ! [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)))
% 25.67/7.12  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 25.67/7.13  | (4)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 25.67/7.13  | (5)  ! [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)))
% 25.67/7.13  | (6)  ! [v0] :  ! [v1] : ( ~ (strong_iteration(v0) = v1) |  ? [v2] :  ? [v3] : (star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1))
% 25.67/7.13  | (7)  ! [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))
% 25.67/7.13  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (star(v0) = v1) |  ~ (multiplication(v1, v0) = v2) | addition(one, v2) = v1)
% 25.67/7.13  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 25.67/7.13  | (10) strong_iteration(all_0_1_1) = all_0_0_0
% 25.67/7.13  | (11)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 25.67/7.13  | (12)  ! [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))
% 25.67/7.13  | (13)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strong_iteration(v0) = v1) |  ~ (multiplication(v0, v1) = v2) | addition(v2, one) = v1)
% 25.67/7.13  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 25.67/7.13  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 25.67/7.13  | (16)  ! [v0] :  ! [v1] : ( ~ (star(v0) = v1) |  ? [v2] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1))
% 25.67/7.13  | (17)  ~ leq(one, all_0_0_0)
% 25.67/7.13  | (18)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 25.67/7.13  | (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)))
% 25.67/7.13  | (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))
% 25.67/7.13  | (21)  ! [v0] :  ! [v1] : ( ~ (star(v0) = v1) |  ? [v2] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1))
% 25.67/7.13  | (22)  ! [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))
% 25.67/7.13  | (23)  ! [v0] :  ! [v1] : ( ~ (strong_iteration(v0) = v1) |  ? [v2] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1))
% 25.67/7.13  | (24)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (star(v2) = v1) |  ~ (star(v2) = v0))
% 25.67/7.13  | (25)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 25.67/7.13  | (26)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 25.67/7.13  | (27)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (strong_iteration(v2) = v1) |  ~ (strong_iteration(v2) = v0))
% 25.67/7.13  | (28)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ~ leq(v0, v1))
% 25.67/7.13  | (29)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 25.67/7.13  | (30)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (star(v0) = v1) |  ~ (multiplication(v0, v1) = v2) | addition(one, v2) = v1)
% 25.67/7.13  | (31)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 25.67/7.13  | (32)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 25.67/7.13  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 25.67/7.14  | (34)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v1 |  ~ (strong_iteration(v0) = v1) |  ~ (star(v0) = v2) |  ~ (multiplication(v1, zero) = v3) |  ~ (addition(v2, v3) = v4))
% 25.67/7.14  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 25.67/7.14  |
% 25.67/7.14  | Instantiating formula (6) with all_0_0_0, all_0_1_1 and discharging atoms strong_iteration(all_0_1_1) = all_0_0_0, yields:
% 25.67/7.14  | (36)  ? [v0] :  ? [v1] : (star(all_0_1_1) = v0 & multiplication(all_0_0_0, zero) = v1 & addition(v0, v1) = all_0_0_0)
% 25.67/7.14  |
% 25.67/7.14  | Instantiating formula (23) with all_0_0_0, all_0_1_1 and discharging atoms strong_iteration(all_0_1_1) = all_0_0_0, yields:
% 25.67/7.14  | (37)  ? [v0] : (multiplication(all_0_1_1, all_0_0_0) = v0 & addition(v0, one) = all_0_0_0)
% 25.67/7.14  |
% 25.67/7.14  | Instantiating (37) with all_8_0_2 yields:
% 25.67/7.14  | (38) multiplication(all_0_1_1, all_0_0_0) = all_8_0_2 & addition(all_8_0_2, one) = all_0_0_0
% 25.67/7.14  |
% 25.67/7.14  | Applying alpha-rule on (38) yields:
% 25.67/7.14  | (39) multiplication(all_0_1_1, all_0_0_0) = all_8_0_2
% 25.67/7.14  | (40) addition(all_8_0_2, one) = all_0_0_0
% 25.67/7.14  |
% 25.67/7.14  | Instantiating (36) with all_10_0_3, all_10_1_4 yields:
% 25.67/7.14  | (41) star(all_0_1_1) = all_10_1_4 & multiplication(all_0_0_0, zero) = all_10_0_3 & addition(all_10_1_4, all_10_0_3) = all_0_0_0
% 25.67/7.14  |
% 25.67/7.14  | Applying alpha-rule on (41) yields:
% 25.67/7.14  | (42) star(all_0_1_1) = all_10_1_4
% 25.67/7.14  | (43) multiplication(all_0_0_0, zero) = all_10_0_3
% 25.67/7.14  | (44) addition(all_10_1_4, all_10_0_3) = all_0_0_0
% 25.67/7.14  |
% 25.67/7.14  | Instantiating formula (16) with all_10_1_4, all_0_1_1 and discharging atoms star(all_0_1_1) = all_10_1_4, yields:
% 25.67/7.14  | (45)  ? [v0] : (multiplication(all_10_1_4, all_0_1_1) = v0 & addition(one, v0) = all_10_1_4)
% 25.67/7.14  |
% 25.67/7.14  | Instantiating formula (21) with all_10_1_4, all_0_1_1 and discharging atoms star(all_0_1_1) = all_10_1_4, yields:
% 25.67/7.14  | (46)  ? [v0] : (multiplication(all_0_1_1, all_10_1_4) = v0 & addition(one, v0) = all_10_1_4)
% 25.67/7.14  |
% 25.67/7.14  | Instantiating formula (20) with all_10_0_3, all_0_0_0, zero, all_10_0_3, all_10_1_4 and discharging atoms multiplication(all_0_0_0, zero) = all_10_0_3, addition(all_10_1_4, all_10_0_3) = all_0_0_0, yields:
% 25.67/7.14  | (47)  ? [v0] :  ? [v1] : (multiplication(all_10_0_3, zero) = v1 & multiplication(all_10_1_4, zero) = v0 & addition(v0, v1) = all_10_0_3)
% 25.67/7.14  |
% 25.67/7.14  | Instantiating formula (7) with all_8_0_2, all_0_0_0, all_10_0_3, all_10_1_4, all_0_1_1 and discharging atoms multiplication(all_0_1_1, all_0_0_0) = all_8_0_2, addition(all_10_1_4, all_10_0_3) = all_0_0_0, yields:
% 25.67/7.14  | (48)  ? [v0] :  ? [v1] : (multiplication(all_0_1_1, all_10_0_3) = v1 & multiplication(all_0_1_1, all_10_1_4) = v0 & addition(v0, v1) = all_8_0_2)
% 25.67/7.14  |
% 25.67/7.14  | Instantiating formula (20) with all_10_0_3, all_0_0_0, zero, one, all_8_0_2 and discharging atoms multiplication(all_0_0_0, zero) = all_10_0_3, addition(all_8_0_2, one) = all_0_0_0, yields:
% 25.67/7.14  | (49)  ? [v0] :  ? [v1] : (multiplication(all_8_0_2, zero) = v0 & multiplication(one, zero) = v1 & addition(v0, v1) = all_10_0_3)
% 25.67/7.14  |
% 25.67/7.14  | Instantiating formula (26) with all_0_0_0, all_8_0_2, one and discharging atoms addition(all_8_0_2, one) = all_0_0_0, yields:
% 25.67/7.14  | (50) addition(one, all_8_0_2) = all_0_0_0
% 25.67/7.14  |
% 25.67/7.14  | Instantiating (48) with all_20_0_7, all_20_1_8 yields:
% 25.67/7.14  | (51) multiplication(all_0_1_1, all_10_0_3) = all_20_0_7 & multiplication(all_0_1_1, all_10_1_4) = all_20_1_8 & addition(all_20_1_8, all_20_0_7) = all_8_0_2
% 25.67/7.14  |
% 25.67/7.14  | Applying alpha-rule on (51) yields:
% 25.67/7.14  | (52) multiplication(all_0_1_1, all_10_0_3) = all_20_0_7
% 25.67/7.14  | (53) multiplication(all_0_1_1, all_10_1_4) = all_20_1_8
% 25.67/7.14  | (54) addition(all_20_1_8, all_20_0_7) = all_8_0_2
% 25.67/7.14  |
% 25.67/7.14  | Instantiating (47) with all_22_0_9, all_22_1_10 yields:
% 25.67/7.14  | (55) multiplication(all_10_0_3, zero) = all_22_0_9 & multiplication(all_10_1_4, zero) = all_22_1_10 & addition(all_22_1_10, all_22_0_9) = all_10_0_3
% 25.67/7.14  |
% 25.67/7.14  | Applying alpha-rule on (55) yields:
% 25.67/7.14  | (56) multiplication(all_10_0_3, zero) = all_22_0_9
% 25.67/7.14  | (57) multiplication(all_10_1_4, zero) = all_22_1_10
% 25.67/7.14  | (58) addition(all_22_1_10, all_22_0_9) = all_10_0_3
% 25.67/7.14  |
% 25.67/7.14  | Instantiating (46) with all_24_0_11 yields:
% 25.67/7.14  | (59) multiplication(all_0_1_1, all_10_1_4) = all_24_0_11 & addition(one, all_24_0_11) = all_10_1_4
% 25.67/7.14  |
% 25.67/7.14  | Applying alpha-rule on (59) yields:
% 25.67/7.14  | (60) multiplication(all_0_1_1, all_10_1_4) = all_24_0_11
% 25.67/7.14  | (61) addition(one, all_24_0_11) = all_10_1_4
% 25.67/7.14  |
% 25.67/7.14  | Instantiating (49) with all_26_0_12, all_26_1_13 yields:
% 25.67/7.14  | (62) multiplication(all_8_0_2, zero) = all_26_1_13 & multiplication(one, zero) = all_26_0_12 & addition(all_26_1_13, all_26_0_12) = all_10_0_3
% 25.67/7.14  |
% 25.67/7.14  | Applying alpha-rule on (62) yields:
% 25.67/7.14  | (63) multiplication(all_8_0_2, zero) = all_26_1_13
% 25.67/7.14  | (64) multiplication(one, zero) = all_26_0_12
% 25.67/7.14  | (65) addition(all_26_1_13, all_26_0_12) = all_10_0_3
% 25.67/7.14  |
% 25.67/7.14  | Instantiating (45) with all_28_0_14 yields:
% 25.67/7.14  | (66) multiplication(all_10_1_4, all_0_1_1) = all_28_0_14 & addition(one, all_28_0_14) = all_10_1_4
% 25.67/7.14  |
% 25.67/7.14  | Applying alpha-rule on (66) yields:
% 25.67/7.14  | (67) multiplication(all_10_1_4, all_0_1_1) = all_28_0_14
% 25.67/7.14  | (68) addition(one, all_28_0_14) = all_10_1_4
% 25.67/7.14  |
% 25.67/7.14  | Instantiating formula (15) with all_0_1_1, all_10_1_4, all_20_1_8, all_24_0_11 and discharging atoms multiplication(all_0_1_1, all_10_1_4) = all_24_0_11, multiplication(all_0_1_1, all_10_1_4) = all_20_1_8, yields:
% 25.67/7.14  | (69) all_24_0_11 = all_20_1_8
% 25.67/7.15  |
% 25.67/7.15  | Instantiating formula (11) with all_26_0_12, zero and discharging atoms multiplication(one, zero) = all_26_0_12, yields:
% 25.67/7.15  | (70) all_26_0_12 = zero
% 25.67/7.15  |
% 25.67/7.15  | From (70) and (64) follows:
% 25.67/7.15  | (71) multiplication(one, zero) = zero
% 25.67/7.15  |
% 25.67/7.15  | From (70) and (65) follows:
% 25.67/7.15  | (72) addition(all_26_1_13, zero) = all_10_0_3
% 25.67/7.15  |
% 25.67/7.15  | From (69) and (61) follows:
% 25.67/7.15  | (73) addition(one, all_20_1_8) = all_10_1_4
% 25.67/7.15  |
% 25.67/7.15  | Instantiating formula (31) with all_10_0_3, all_26_1_13 and discharging atoms addition(all_26_1_13, zero) = all_10_0_3, yields:
% 25.67/7.15  | (74) all_26_1_13 = all_10_0_3
% 25.67/7.15  |
% 25.67/7.15  | From (74) and (63) follows:
% 25.67/7.15  | (75) multiplication(all_8_0_2, zero) = all_10_0_3
% 25.67/7.15  |
% 25.67/7.15  | From (74) and (72) follows:
% 25.67/7.15  | (76) addition(all_10_0_3, zero) = all_10_0_3
% 25.67/7.15  |
% 25.67/7.15  | Instantiating formula (35) with all_22_0_9, all_10_0_3, zero, zero, all_0_0_0 and discharging atoms multiplication(all_10_0_3, zero) = all_22_0_9, multiplication(all_0_0_0, zero) = all_10_0_3, yields:
% 25.67/7.15  | (77)  ? [v0] : (multiplication(all_0_0_0, v0) = all_22_0_9 & multiplication(zero, zero) = v0)
% 25.67/7.15  |
% 25.67/7.15  | Instantiating formula (35) with all_10_0_3, all_8_0_2, zero, all_0_0_0, all_0_1_1 and discharging atoms multiplication(all_8_0_2, zero) = all_10_0_3, multiplication(all_0_1_1, all_0_0_0) = all_8_0_2, yields:
% 25.67/7.15  | (78)  ? [v0] : (multiplication(all_0_0_0, zero) = v0 & multiplication(all_0_1_1, v0) = all_10_0_3)
% 25.67/7.15  |
% 25.67/7.15  | Instantiating formula (35) with all_22_0_9, all_10_0_3, zero, zero, all_8_0_2 and discharging atoms multiplication(all_10_0_3, zero) = all_22_0_9, multiplication(all_8_0_2, zero) = all_10_0_3, yields:
% 25.67/7.15  | (79)  ? [v0] : (multiplication(all_8_0_2, v0) = all_22_0_9 & multiplication(zero, zero) = v0)
% 25.67/7.15  |
% 25.67/7.15  | Instantiating formula (14) with all_20_0_7, all_10_0_3, zero, all_0_0_0, all_0_1_1 and discharging atoms multiplication(all_0_0_0, zero) = all_10_0_3, multiplication(all_0_1_1, all_10_0_3) = all_20_0_7, yields:
% 25.67/7.15  | (80)  ? [v0] : (multiplication(v0, zero) = all_20_0_7 & multiplication(all_0_1_1, all_0_0_0) = v0)
% 25.67/7.15  |
% 25.67/7.15  | Instantiating formula (20) with all_22_0_9, all_10_0_3, zero, zero, all_10_0_3 and discharging atoms multiplication(all_10_0_3, zero) = all_22_0_9, addition(all_10_0_3, zero) = all_10_0_3, yields:
% 25.67/7.15  | (81)  ? [v0] :  ? [v1] : (multiplication(all_10_0_3, zero) = v0 & multiplication(zero, zero) = v1 & addition(v0, v1) = all_22_0_9)
% 25.67/7.15  |
% 25.67/7.15  | Instantiating formula (12) with all_10_0_3, zero, all_10_0_3, zero, one, all_0_0_0 and discharging atoms multiplication(all_0_0_0, zero) = all_10_0_3, multiplication(one, zero) = zero, addition(all_10_0_3, zero) = all_10_0_3, yields:
% 25.67/7.15  | (82)  ? [v0] : (multiplication(v0, zero) = all_10_0_3 & addition(all_0_0_0, one) = v0)
% 25.67/7.15  |
% 25.67/7.15  | Instantiating formula (33) with all_10_0_3, all_10_0_3, all_10_0_3, zero, zero and discharging atoms addition(all_10_0_3, zero) = all_10_0_3, yields:
% 25.67/7.15  | (83)  ? [v0] : (addition(all_10_0_3, v0) = all_10_0_3 & addition(zero, zero) = v0)
% 25.67/7.15  |
% 25.67/7.15  | Instantiating formula (20) with all_22_1_10, all_10_1_4, zero, all_28_0_14, one and discharging atoms multiplication(all_10_1_4, zero) = all_22_1_10, addition(one, all_28_0_14) = all_10_1_4, yields:
% 25.67/7.15  | (84)  ? [v0] :  ? [v1] : (multiplication(all_28_0_14, zero) = v1 & multiplication(one, zero) = v0 & addition(v0, v1) = all_22_1_10)
% 25.67/7.15  |
% 25.67/7.15  | Instantiating formula (20) with all_22_1_10, all_10_1_4, zero, all_20_1_8, one and discharging atoms multiplication(all_10_1_4, zero) = all_22_1_10, addition(one, all_20_1_8) = all_10_1_4, yields:
% 25.67/7.15  | (85)  ? [v0] :  ? [v1] : (multiplication(all_20_1_8, zero) = v1 & multiplication(one, zero) = v0 & addition(v0, v1) = all_22_1_10)
% 25.67/7.15  |
% 25.67/7.15  | Instantiating formula (33) with all_0_0_0, all_10_1_4, one, all_20_1_8, all_10_0_3 and discharging atoms addition(all_10_1_4, all_10_0_3) = all_0_0_0, addition(one, all_20_1_8) = all_10_1_4, yields:
% 25.67/7.15  | (86)  ? [v0] : (addition(all_20_1_8, all_10_0_3) = v0 & addition(one, v0) = all_0_0_0)
% 25.67/7.15  |
% 25.67/7.15  | Instantiating formula (20) with all_10_0_3, all_0_0_0, zero, all_8_0_2, one and discharging atoms multiplication(all_0_0_0, zero) = all_10_0_3, addition(one, all_8_0_2) = all_0_0_0, yields:
% 25.67/7.15  | (87)  ? [v0] :  ? [v1] : (multiplication(all_8_0_2, zero) = v1 & multiplication(one, zero) = v0 & addition(v0, v1) = all_10_0_3)
% 25.67/7.15  |
% 25.67/7.15  | Instantiating (83) with all_46_0_17 yields:
% 25.67/7.15  | (88) addition(all_10_0_3, all_46_0_17) = all_10_0_3 & addition(zero, zero) = all_46_0_17
% 25.67/7.15  |
% 25.67/7.15  | Applying alpha-rule on (88) yields:
% 25.67/7.15  | (89) addition(all_10_0_3, all_46_0_17) = all_10_0_3
% 25.67/7.15  | (90) addition(zero, zero) = all_46_0_17
% 25.67/7.15  |
% 25.67/7.15  | Instantiating (85) with all_52_0_21, all_52_1_22 yields:
% 25.67/7.15  | (91) multiplication(all_20_1_8, zero) = all_52_0_21 & multiplication(one, zero) = all_52_1_22 & addition(all_52_1_22, all_52_0_21) = all_22_1_10
% 25.67/7.15  |
% 25.67/7.15  | Applying alpha-rule on (91) yields:
% 25.67/7.15  | (92) multiplication(all_20_1_8, zero) = all_52_0_21
% 25.67/7.15  | (93) multiplication(one, zero) = all_52_1_22
% 25.67/7.15  | (94) addition(all_52_1_22, all_52_0_21) = all_22_1_10
% 25.67/7.15  |
% 25.91/7.15  | Instantiating (81) with all_58_0_25, all_58_1_26 yields:
% 25.91/7.15  | (95) multiplication(all_10_0_3, zero) = all_58_1_26 & multiplication(zero, zero) = all_58_0_25 & addition(all_58_1_26, all_58_0_25) = all_22_0_9
% 25.91/7.15  |
% 25.91/7.15  | Applying alpha-rule on (95) yields:
% 25.91/7.16  | (96) multiplication(all_10_0_3, zero) = all_58_1_26
% 25.91/7.16  | (97) multiplication(zero, zero) = all_58_0_25
% 25.91/7.16  | (98) addition(all_58_1_26, all_58_0_25) = all_22_0_9
% 25.91/7.16  |
% 25.91/7.16  | Instantiating (82) with all_66_0_32 yields:
% 25.91/7.16  | (99) multiplication(all_66_0_32, zero) = all_10_0_3 & addition(all_0_0_0, one) = all_66_0_32
% 25.91/7.16  |
% 25.91/7.16  | Applying alpha-rule on (99) yields:
% 25.91/7.16  | (100) multiplication(all_66_0_32, zero) = all_10_0_3
% 25.91/7.16  | (101) addition(all_0_0_0, one) = all_66_0_32
% 25.91/7.16  |
% 25.91/7.16  | Instantiating (86) with all_82_0_44 yields:
% 25.91/7.16  | (102) addition(all_20_1_8, all_10_0_3) = all_82_0_44 & addition(one, all_82_0_44) = all_0_0_0
% 25.91/7.16  |
% 25.91/7.16  | Applying alpha-rule on (102) yields:
% 25.91/7.16  | (103) addition(all_20_1_8, all_10_0_3) = all_82_0_44
% 25.91/7.16  | (104) addition(one, all_82_0_44) = all_0_0_0
% 25.91/7.16  |
% 25.91/7.16  | Instantiating (84) with all_92_0_51, all_92_1_52 yields:
% 25.91/7.16  | (105) multiplication(all_28_0_14, zero) = all_92_0_51 & multiplication(one, zero) = all_92_1_52 & addition(all_92_1_52, all_92_0_51) = all_22_1_10
% 25.91/7.16  |
% 25.91/7.16  | Applying alpha-rule on (105) yields:
% 25.91/7.16  | (106) multiplication(all_28_0_14, zero) = all_92_0_51
% 25.91/7.16  | (107) multiplication(one, zero) = all_92_1_52
% 25.91/7.16  | (108) addition(all_92_1_52, all_92_0_51) = all_22_1_10
% 25.91/7.16  |
% 25.91/7.16  | Instantiating (87) with all_102_0_59, all_102_1_60 yields:
% 25.91/7.16  | (109) multiplication(all_8_0_2, zero) = all_102_0_59 & multiplication(one, zero) = all_102_1_60 & addition(all_102_1_60, all_102_0_59) = all_10_0_3
% 25.91/7.16  |
% 25.91/7.16  | Applying alpha-rule on (109) yields:
% 25.91/7.16  | (110) multiplication(all_8_0_2, zero) = all_102_0_59
% 25.91/7.16  | (111) multiplication(one, zero) = all_102_1_60
% 25.91/7.16  | (112) addition(all_102_1_60, all_102_0_59) = all_10_0_3
% 25.91/7.16  |
% 25.91/7.16  | Instantiating (80) with all_124_0_73 yields:
% 25.91/7.16  | (113) multiplication(all_124_0_73, zero) = all_20_0_7 & multiplication(all_0_1_1, all_0_0_0) = all_124_0_73
% 25.91/7.16  |
% 25.91/7.16  | Applying alpha-rule on (113) yields:
% 25.91/7.16  | (114) multiplication(all_124_0_73, zero) = all_20_0_7
% 25.91/7.16  | (115) multiplication(all_0_1_1, all_0_0_0) = all_124_0_73
% 25.91/7.16  |
% 25.91/7.16  | Instantiating (78) with all_126_0_74 yields:
% 25.91/7.16  | (116) multiplication(all_0_0_0, zero) = all_126_0_74 & multiplication(all_0_1_1, all_126_0_74) = all_10_0_3
% 25.91/7.16  |
% 25.91/7.16  | Applying alpha-rule on (116) yields:
% 25.91/7.16  | (117) multiplication(all_0_0_0, zero) = all_126_0_74
% 25.91/7.16  | (118) multiplication(all_0_1_1, all_126_0_74) = all_10_0_3
% 25.91/7.16  |
% 25.91/7.16  | Instantiating (77) with all_134_0_78 yields:
% 25.91/7.16  | (119) multiplication(all_0_0_0, all_134_0_78) = all_22_0_9 & multiplication(zero, zero) = all_134_0_78
% 25.91/7.16  |
% 25.91/7.16  | Applying alpha-rule on (119) yields:
% 25.91/7.16  | (120) multiplication(all_0_0_0, all_134_0_78) = all_22_0_9
% 25.91/7.16  | (121) multiplication(zero, zero) = all_134_0_78
% 25.91/7.16  |
% 25.91/7.16  | Instantiating (79) with all_138_0_80 yields:
% 25.91/7.16  | (122) multiplication(all_8_0_2, all_138_0_80) = all_22_0_9 & multiplication(zero, zero) = all_138_0_80
% 25.91/7.16  |
% 25.91/7.16  | Applying alpha-rule on (122) yields:
% 25.91/7.16  | (123) multiplication(all_8_0_2, all_138_0_80) = all_22_0_9
% 25.91/7.16  | (124) multiplication(zero, zero) = all_138_0_80
% 25.91/7.16  |
% 25.91/7.16  | Instantiating formula (15) with all_8_0_2, zero, all_102_0_59, all_10_0_3 and discharging atoms multiplication(all_8_0_2, zero) = all_102_0_59, multiplication(all_8_0_2, zero) = all_10_0_3, yields:
% 25.91/7.16  | (125) all_102_0_59 = all_10_0_3
% 25.91/7.16  |
% 25.91/7.16  | Instantiating formula (15) with all_0_0_0, zero, all_126_0_74, all_10_0_3 and discharging atoms multiplication(all_0_0_0, zero) = all_126_0_74, multiplication(all_0_0_0, zero) = all_10_0_3, yields:
% 25.91/7.16  | (126) all_126_0_74 = all_10_0_3
% 25.91/7.16  |
% 25.91/7.16  | Instantiating formula (15) with all_0_1_1, all_0_0_0, all_124_0_73, all_8_0_2 and discharging atoms multiplication(all_0_1_1, all_0_0_0) = all_124_0_73, multiplication(all_0_1_1, all_0_0_0) = all_8_0_2, yields:
% 25.91/7.16  | (127) all_124_0_73 = all_8_0_2
% 25.91/7.16  |
% 25.91/7.16  | Instantiating formula (15) with one, zero, all_92_1_52, all_102_1_60 and discharging atoms multiplication(one, zero) = all_102_1_60, multiplication(one, zero) = all_92_1_52, yields:
% 25.91/7.16  | (128) all_102_1_60 = all_92_1_52
% 25.91/7.16  |
% 25.91/7.16  | Instantiating formula (11) with all_92_1_52, zero and discharging atoms multiplication(one, zero) = all_92_1_52, yields:
% 25.91/7.16  | (129) all_92_1_52 = zero
% 25.91/7.16  |
% 25.91/7.16  | Instantiating formula (15) with one, zero, all_52_1_22, all_102_1_60 and discharging atoms multiplication(one, zero) = all_102_1_60, multiplication(one, zero) = all_52_1_22, yields:
% 25.91/7.16  | (130) all_102_1_60 = all_52_1_22
% 25.91/7.16  |
% 25.91/7.16  | Instantiating formula (15) with zero, zero, all_134_0_78, all_138_0_80 and discharging atoms multiplication(zero, zero) = all_138_0_80, multiplication(zero, zero) = all_134_0_78, yields:
% 25.91/7.16  | (131) all_138_0_80 = all_134_0_78
% 25.91/7.16  |
% 25.91/7.16  | Instantiating formula (18) with all_134_0_78, zero and discharging atoms multiplication(zero, zero) = all_134_0_78, yields:
% 25.91/7.16  | (132) all_134_0_78 = zero
% 25.91/7.16  |
% 25.91/7.16  | Instantiating formula (15) with zero, zero, all_58_0_25, all_138_0_80 and discharging atoms multiplication(zero, zero) = all_138_0_80, multiplication(zero, zero) = all_58_0_25, yields:
% 25.91/7.16  | (133) all_138_0_80 = all_58_0_25
% 25.91/7.16  |
% 25.91/7.16  | Instantiating formula (4) with all_46_0_17, zero and discharging atoms addition(zero, zero) = all_46_0_17, yields:
% 25.91/7.16  | (134) all_46_0_17 = zero
% 25.91/7.16  |
% 25.91/7.17  | Combining equations (131,133) yields a new equation:
% 25.91/7.17  | (135) all_134_0_78 = all_58_0_25
% 25.91/7.17  |
% 25.91/7.17  | Simplifying 135 yields:
% 25.91/7.17  | (136) all_134_0_78 = all_58_0_25
% 25.91/7.17  |
% 25.91/7.17  | Combining equations (132,136) yields a new equation:
% 25.91/7.17  | (137) all_58_0_25 = zero
% 25.91/7.17  |
% 25.91/7.17  | Combining equations (128,130) yields a new equation:
% 25.91/7.17  | (138) all_92_1_52 = all_52_1_22
% 25.91/7.17  |
% 25.91/7.17  | Simplifying 138 yields:
% 25.91/7.17  | (139) all_92_1_52 = all_52_1_22
% 25.91/7.17  |
% 25.91/7.17  | Combining equations (129,139) yields a new equation:
% 25.91/7.17  | (140) all_52_1_22 = zero
% 25.91/7.17  |
% 25.91/7.17  | Combining equations (140,130) yields a new equation:
% 25.91/7.17  | (141) all_102_1_60 = zero
% 25.91/7.17  |
% 25.91/7.17  | Combining equations (137,136) yields a new equation:
% 25.91/7.17  | (132) all_134_0_78 = zero
% 25.91/7.17  |
% 25.91/7.17  | Combining equations (137,133) yields a new equation:
% 25.91/7.17  | (143) all_138_0_80 = zero
% 25.91/7.17  |
% 25.91/7.17  | From (127) and (114) follows:
% 25.91/7.17  | (144) multiplication(all_8_0_2, zero) = all_20_0_7
% 25.91/7.17  |
% 25.91/7.17  | From (143) and (123) follows:
% 25.91/7.17  | (145) multiplication(all_8_0_2, zero) = all_22_0_9
% 25.91/7.17  |
% 25.91/7.17  | From (132) and (120) follows:
% 25.91/7.17  | (146) multiplication(all_0_0_0, zero) = all_22_0_9
% 25.91/7.17  |
% 25.91/7.17  | From (126) and (117) follows:
% 25.91/7.17  | (43) multiplication(all_0_0_0, zero) = all_10_0_3
% 25.91/7.17  |
% 25.91/7.17  | From (140) and (93) follows:
% 25.91/7.17  | (71) multiplication(one, zero) = zero
% 25.91/7.17  |
% 25.91/7.17  | From (141)(125) and (112) follows:
% 25.91/7.17  | (149) addition(zero, all_10_0_3) = all_10_0_3
% 25.91/7.17  |
% 25.91/7.17  | From (134) and (90) follows:
% 25.91/7.17  | (150) addition(zero, zero) = zero
% 25.91/7.17  |
% 25.91/7.17  | Instantiating formula (15) with all_8_0_2, zero, all_20_0_7, all_22_0_9 and discharging atoms multiplication(all_8_0_2, zero) = all_22_0_9, multiplication(all_8_0_2, zero) = all_20_0_7, yields:
% 25.91/7.17  | (151) all_22_0_9 = all_20_0_7
% 25.91/7.17  |
% 25.91/7.17  | Instantiating formula (15) with all_0_0_0, zero, all_22_0_9, all_10_0_3 and discharging atoms multiplication(all_0_0_0, zero) = all_22_0_9, multiplication(all_0_0_0, zero) = all_10_0_3, yields:
% 25.91/7.17  | (152) all_22_0_9 = all_10_0_3
% 25.91/7.17  |
% 25.91/7.17  | Combining equations (152,151) yields a new equation:
% 25.91/7.17  | (153) all_20_0_7 = all_10_0_3
% 25.91/7.17  |
% 25.91/7.17  | Combining equations (153,151) yields a new equation:
% 25.91/7.17  | (152) all_22_0_9 = all_10_0_3
% 25.91/7.17  |
% 25.91/7.17  | From (152) and (146) follows:
% 25.91/7.17  | (43) multiplication(all_0_0_0, zero) = all_10_0_3
% 25.91/7.17  |
% 25.91/7.17  | From (153) and (54) follows:
% 25.91/7.17  | (156) addition(all_20_1_8, all_10_0_3) = all_8_0_2
% 25.91/7.17  |
% 25.91/7.17  | Instantiating formula (3) with all_20_1_8, all_10_0_3, all_8_0_2, all_82_0_44 and discharging atoms addition(all_20_1_8, all_10_0_3) = all_82_0_44, addition(all_20_1_8, all_10_0_3) = all_8_0_2, yields:
% 25.91/7.17  | (157) all_82_0_44 = all_8_0_2
% 25.91/7.17  |
% 25.91/7.17  | From (157) and (104) follows:
% 25.91/7.17  | (50) addition(one, all_8_0_2) = all_0_0_0
% 25.91/7.17  |
% 25.91/7.17  | Instantiating formula (33) with all_66_0_32, all_0_0_0, all_8_0_2, one, one and discharging atoms addition(all_8_0_2, one) = all_0_0_0, addition(all_0_0_0, one) = all_66_0_32, yields:
% 25.91/7.17  | (159)  ? [v0] : (addition(all_8_0_2, v0) = all_66_0_32 & addition(one, one) = v0)
% 25.91/7.17  |
% 25.91/7.17  | Instantiating formula (33) with all_66_0_32, all_0_0_0, one, all_8_0_2, one and discharging atoms addition(all_0_0_0, one) = all_66_0_32, addition(one, all_8_0_2) = all_0_0_0, yields:
% 25.91/7.17  | (160)  ? [v0] : (addition(all_8_0_2, one) = v0 & addition(one, v0) = all_66_0_32)
% 25.91/7.17  |
% 25.91/7.17  | Instantiating formula (26) with all_66_0_32, all_0_0_0, one and discharging atoms addition(all_0_0_0, one) = all_66_0_32, yields:
% 25.91/7.17  | (161) addition(one, all_0_0_0) = all_66_0_32
% 25.91/7.17  |
% 25.91/7.17  | Instantiating formula (12) with all_10_0_3, all_10_0_3, zero, zero, all_0_0_0, one and discharging atoms multiplication(all_0_0_0, zero) = all_10_0_3, multiplication(one, zero) = zero, addition(zero, all_10_0_3) = all_10_0_3, yields:
% 25.91/7.17  | (162)  ? [v0] : (multiplication(v0, zero) = all_10_0_3 & addition(one, all_0_0_0) = v0)
% 25.91/7.17  |
% 25.91/7.17  | Instantiating formula (12) with all_10_0_3, all_10_0_3, zero, zero, all_66_0_32, one and discharging atoms multiplication(all_66_0_32, zero) = all_10_0_3, multiplication(one, zero) = zero, addition(zero, all_10_0_3) = all_10_0_3, yields:
% 25.91/7.17  | (163)  ? [v0] : (multiplication(v0, zero) = all_10_0_3 & addition(one, all_66_0_32) = v0)
% 25.91/7.17  |
% 25.91/7.17  | Instantiating formula (12) with zero, zero, zero, zero, one, one and discharging atoms multiplication(one, zero) = zero, addition(zero, zero) = zero, yields:
% 25.91/7.17  | (164)  ? [v0] : (multiplication(v0, zero) = zero & addition(one, one) = v0)
% 25.91/7.18  |
% 25.91/7.18  | Instantiating (164) with all_692_0_443 yields:
% 25.91/7.18  | (165) multiplication(all_692_0_443, zero) = zero & addition(one, one) = all_692_0_443
% 25.91/7.18  |
% 25.91/7.18  | Applying alpha-rule on (165) yields:
% 25.91/7.18  | (166) multiplication(all_692_0_443, zero) = zero
% 25.91/7.18  | (167) addition(one, one) = all_692_0_443
% 25.91/7.18  |
% 25.91/7.18  | Instantiating (160) with all_734_0_471 yields:
% 25.91/7.18  | (168) addition(all_8_0_2, one) = all_734_0_471 & addition(one, all_734_0_471) = all_66_0_32
% 25.91/7.18  |
% 25.91/7.18  | Applying alpha-rule on (168) yields:
% 25.91/7.18  | (169) addition(all_8_0_2, one) = all_734_0_471
% 25.91/7.18  | (170) addition(one, all_734_0_471) = all_66_0_32
% 25.91/7.18  |
% 25.91/7.18  | Instantiating (159) with all_742_0_475 yields:
% 25.91/7.18  | (171) addition(all_8_0_2, all_742_0_475) = all_66_0_32 & addition(one, one) = all_742_0_475
% 25.91/7.18  |
% 25.91/7.18  | Applying alpha-rule on (171) yields:
% 25.91/7.18  | (172) addition(all_8_0_2, all_742_0_475) = all_66_0_32
% 25.91/7.18  | (173) addition(one, one) = all_742_0_475
% 25.91/7.18  |
% 25.91/7.18  | Instantiating (162) with all_840_0_536 yields:
% 25.91/7.18  | (174) multiplication(all_840_0_536, zero) = all_10_0_3 & addition(one, all_0_0_0) = all_840_0_536
% 25.91/7.18  |
% 25.91/7.18  | Applying alpha-rule on (174) yields:
% 25.91/7.18  | (175) multiplication(all_840_0_536, zero) = all_10_0_3
% 25.91/7.18  | (176) addition(one, all_0_0_0) = all_840_0_536
% 25.91/7.18  |
% 25.91/7.18  | Instantiating (163) with all_842_0_537 yields:
% 25.91/7.18  | (177) multiplication(all_842_0_537, zero) = all_10_0_3 & addition(one, all_66_0_32) = all_842_0_537
% 25.91/7.18  |
% 25.91/7.18  | Applying alpha-rule on (177) yields:
% 25.91/7.18  | (178) multiplication(all_842_0_537, zero) = all_10_0_3
% 25.91/7.18  | (179) addition(one, all_66_0_32) = all_842_0_537
% 25.91/7.18  |
% 25.91/7.18  | Instantiating formula (3) with all_8_0_2, one, all_734_0_471, all_0_0_0 and discharging atoms addition(all_8_0_2, one) = all_734_0_471, addition(all_8_0_2, one) = all_0_0_0, yields:
% 25.91/7.18  | (180) all_734_0_471 = all_0_0_0
% 25.91/7.18  |
% 25.91/7.18  | Instantiating formula (3) with one, all_0_0_0, all_66_0_32, all_840_0_536 and discharging atoms addition(one, all_0_0_0) = all_840_0_536, addition(one, all_0_0_0) = all_66_0_32, yields:
% 25.91/7.18  | (181) all_840_0_536 = all_66_0_32
% 25.91/7.18  |
% 25.91/7.18  | Instantiating formula (4) with all_742_0_475, one and discharging atoms addition(one, one) = all_742_0_475, yields:
% 25.91/7.18  | (182) all_742_0_475 = one
% 25.91/7.18  |
% 25.91/7.18  | Instantiating formula (3) with one, one, all_692_0_443, all_742_0_475 and discharging atoms addition(one, one) = all_742_0_475, addition(one, one) = all_692_0_443, yields:
% 25.91/7.18  | (183) all_742_0_475 = all_692_0_443
% 25.91/7.18  |
% 25.91/7.18  | Combining equations (182,183) yields a new equation:
% 25.91/7.18  | (184) all_692_0_443 = one
% 25.91/7.18  |
% 25.91/7.18  | Combining equations (184,183) yields a new equation:
% 25.91/7.18  | (182) all_742_0_475 = one
% 25.91/7.18  |
% 25.91/7.18  | From (182) and (172) follows:
% 25.91/7.18  | (186) addition(all_8_0_2, one) = all_66_0_32
% 25.91/7.18  |
% 25.91/7.18  | From (180) and (169) follows:
% 25.91/7.18  | (40) addition(all_8_0_2, one) = all_0_0_0
% 25.91/7.18  |
% 25.91/7.18  | From (181) and (176) follows:
% 25.91/7.18  | (161) addition(one, all_0_0_0) = all_66_0_32
% 25.91/7.18  |
% 25.91/7.18  | Instantiating formula (3) with all_8_0_2, one, all_66_0_32, all_0_0_0 and discharging atoms addition(all_8_0_2, one) = all_66_0_32, addition(all_8_0_2, one) = all_0_0_0, yields:
% 25.91/7.18  | (189) all_66_0_32 = all_0_0_0
% 25.91/7.18  |
% 25.91/7.18  | From (189) and (179) follows:
% 25.91/7.18  | (190) addition(one, all_0_0_0) = all_842_0_537
% 25.91/7.18  |
% 25.91/7.18  | From (189) and (161) follows:
% 25.91/7.18  | (191) addition(one, all_0_0_0) = all_0_0_0
% 25.91/7.18  |
% 25.91/7.18  | Instantiating formula (3) with one, all_0_0_0, all_0_0_0, all_842_0_537 and discharging atoms addition(one, all_0_0_0) = all_842_0_537, addition(one, all_0_0_0) = all_0_0_0, yields:
% 25.91/7.18  | (192) all_842_0_537 = all_0_0_0
% 25.91/7.18  |
% 25.91/7.18  | From (192) and (190) follows:
% 25.91/7.18  | (191) addition(one, all_0_0_0) = all_0_0_0
% 25.91/7.18  |
% 25.91/7.18  | Instantiating formula (29) with all_0_0_0, one and discharging atoms addition(one, all_0_0_0) = all_0_0_0,  ~ leq(one, all_0_0_0), yields:
% 25.91/7.18  | (194) $false
% 25.91/7.18  |
% 25.91/7.19  |-The branch is then unsatisfiable
% 25.91/7.19  % SZS output end Proof for theBenchmark
% 25.91/7.19  
% 25.91/7.19  6578ms
%------------------------------------------------------------------------------