%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE139+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n010.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 3.59s 1.59s
% Output   : Proof 6.68s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KLE139+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.14/0.34  % Computer : n010.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Thu Jun 16 08:54:23 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.60/0.61          ____       _                          
% 0.60/0.61    ___  / __ \_____(_)___  ________  __________
% 0.60/0.61   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.60/0.61  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.60/0.61  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.60/0.61  
% 0.60/0.61  A Theorem Prover for First-Order Logic
% 0.60/0.61  (ePrincess v.1.0)
% 0.60/0.61  
% 0.60/0.61  (c) Philipp Rümmer, 2009-2015
% 0.60/0.61  (c) Peter Backeman, 2014-2015
% 0.60/0.61  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.60/0.61  Free software under GNU Lesser General Public License (LGPL).
% 0.60/0.61  Bug reports to peter@backeman.se
% 0.60/0.61  
% 0.60/0.61  For more information, visit http://user.uu.se/~petba168/breu/
% 0.60/0.61  
% 0.60/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.66/0.66  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.56/0.95  Prover 0: Preprocessing ...
% 2.23/1.20  Prover 0: Constructing countermodel ...
% 3.59/1.59  Prover 0: proved (927ms)
% 3.59/1.59  
% 3.59/1.59  No countermodel exists, formula is valid
% 3.59/1.59  % SZS status Theorem for theBenchmark
% 3.59/1.59  
% 3.59/1.59  Generating proof ... found it (size 43)
% 6.27/2.15  
% 6.27/2.15  % SZS output start Proof for theBenchmark
% 6.27/2.15  Assumed formulas after preprocessing and simplification: 
% 6.27/2.15  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : ( ~ (v3 = v1) & strong_iteration(v0) = v1 & multiplication(v1, v0) = v2 & addition(v2, one) = v3 &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (multiplication(v5, v6) = v8) |  ~ (multiplication(v4, v6) = v7) |  ~ (addition(v7, v8) = v9) |  ? [v10] : (multiplication(v10, v6) = v9 & addition(v4, v5) = v10)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (multiplication(v4, v6) = v8) |  ~ (multiplication(v4, v5) = v7) |  ~ (addition(v7, v8) = v9) |  ? [v10] : (multiplication(v4, v10) = v9 & addition(v5, v6) = v10)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = v5 |  ~ (strong_iteration(v4) = v5) |  ~ (star(v4) = v6) |  ~ (multiplication(v5, zero) = v7) |  ~ (addition(v6, v7) = v8)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v7, v6) = v8) |  ~ (multiplication(v4, v5) = v7) |  ? [v9] : (multiplication(v5, v6) = v9 & multiplication(v4, v9) = v8)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v7, v6) = v8) |  ~ (addition(v4, v5) = v7) |  ? [v9] :  ? [v10] : (multiplication(v5, v6) = v10 & multiplication(v4, v6) = v9 & addition(v9, v10) = v8)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v6, v4) = v7) |  ~ (addition(v7, v5) = v8) |  ~ leq(v8, v6) |  ? [v9] :  ? [v10] : (star(v4) = v9 & multiplication(v5, v9) = v10 & leq(v10, v6))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v5, v6) = v7) |  ~ (multiplication(v4, v7) = v8) |  ? [v9] : (multiplication(v9, v6) = v8 & multiplication(v4, v5) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v4, v7) = v8) |  ~ (addition(v5, v6) = v7) |  ? [v9] :  ? [v10] : (multiplication(v4, v6) = v10 & multiplication(v4, v5) = v9 & addition(v9, v10) = v8)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v4, v6) = v7) |  ~ (addition(v7, v5) = v8) |  ~ leq(v8, v6) |  ? [v9] :  ? [v10] : (star(v4) = v9 & multiplication(v9, v5) = v10 & leq(v10, v6))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v4, v6) = v7) |  ~ (addition(v7, v5) = v8) |  ~ leq(v6, v8) |  ? [v9] :  ? [v10] : (strong_iteration(v4) = v9 & multiplication(v9, v5) = v10 & leq(v6, v10))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (addition(v7, v4) = v8) |  ~ (addition(v6, v5) = v7) |  ? [v9] : (addition(v6, v9) = v8 & addition(v5, v4) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (addition(v6, v7) = v8) |  ~ (addition(v5, v4) = v7) |  ? [v9] : (addition(v9, v4) = v8 & addition(v6, v5) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (multiplication(v7, v6) = v5) |  ~ (multiplication(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (addition(v7, v6) = v5) |  ~ (addition(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : (v6 = v5 |  ~ (addition(v4, v5) = v6) |  ~ leq(v4, v5)) &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (strong_iteration(v6) = v5) |  ~ (strong_iteration(v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (star(v6) = v5) |  ~ (star(v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (strong_iteration(v4) = v5) |  ~ (multiplication(v4, v5) = v6) | addition(v6, one) = v5) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (star(v4) = v5) |  ~ (multiplication(v5, v4) = v6) | addition(one, v6) = v5) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (star(v4) = v5) |  ~ (multiplication(v4, v5) = v6) | addition(one, v6) = v5) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (addition(v5, v4) = v6) | addition(v4, v5) = v6) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (addition(v4, v5) = v6) | addition(v5, v4) = v6) &  ! [v4] :  ! [v5] : (v5 = v4 |  ~ (multiplication(v4, one) = v5)) &  ! [v4] :  ! [v5] : (v5 = v4 |  ~ (multiplication(one, v4) = v5)) &  ! [v4] :  ! [v5] : (v5 = v4 |  ~ (addition(v4, v4) = v5)) &  ! [v4] :  ! [v5] : (v5 = v4 |  ~ (addition(v4, zero) = v5)) &  ! [v4] :  ! [v5] : (v5 = zero |  ~ (multiplication(zero, v4) = v5)) &  ! [v4] :  ! [v5] : ( ~ (strong_iteration(v4) = v5) |  ? [v6] :  ? [v7] : (star(v4) = v6 & multiplication(v5, zero) = v7 & addition(v6, v7) = v5)) &  ! [v4] :  ! [v5] : ( ~ (strong_iteration(v4) = v5) |  ? [v6] : (multiplication(v4, v5) = v6 & addition(v6, one) = v5)) &  ! [v4] :  ! [v5] : ( ~ (star(v4) = v5) |  ? [v6] : (multiplication(v5, v4) = v6 & addition(one, v6) = v5)) &  ! [v4] :  ! [v5] : ( ~ (star(v4) = v5) |  ? [v6] : (multiplication(v4, v5) = v6 & addition(one, v6) = v5)) &  ! [v4] :  ! [v5] : ( ~ (addition(v4, v5) = v5) | leq(v4, v5)))
% 6.27/2.19  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 6.27/2.19  | (1)  ~ (all_0_0_0 = all_0_2_2) & strong_iteration(all_0_3_3) = all_0_2_2 & multiplication(all_0_2_2, all_0_3_3) = all_0_1_1 & addition(all_0_1_1, 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))
% 6.27/2.20  |
% 6.27/2.20  | Applying alpha-rule on (1) yields:
% 6.27/2.20  | (2) multiplication(all_0_2_2, all_0_3_3) = all_0_1_1
% 6.27/2.20  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 6.27/2.20  | (4)  ! [v0] :  ! [v1] : ( ~ (strong_iteration(v0) = v1) |  ? [v2] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1))
% 6.27/2.20  | (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)))
% 6.27/2.20  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 6.27/2.20  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 6.27/2.20  | (8)  ! [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))
% 6.27/2.21  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 6.27/2.21  | (10)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strong_iteration(v0) = v1) |  ~ (multiplication(v0, v1) = v2) | addition(v2, one) = v1)
% 6.27/2.21  | (11)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (star(v0) = v1) |  ~ (multiplication(v1, v0) = v2) | addition(one, v2) = v1)
% 6.27/2.21  | (12)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ~ leq(v0, v1))
% 6.27/2.21  | (13)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 6.27/2.21  | (14)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 6.27/2.21  | (15)  ! [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)))
% 6.27/2.21  | (16)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 6.27/2.21  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v0, v3) = v4) |  ~ (addition(v1, v2) = v3) |  ? [v5] :  ? [v6] : (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4))
% 6.27/2.21  | (18)  ! [v0] :  ! [v1] : ( ~ (strong_iteration(v0) = v1) |  ? [v2] :  ? [v3] : (star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1))
% 6.68/2.21  | (19)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 6.68/2.21  | (20)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 6.68/2.21  | (21)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (strong_iteration(v2) = v1) |  ~ (strong_iteration(v2) = v0))
% 6.68/2.21  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 6.68/2.21  | (23)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (star(v2) = v1) |  ~ (star(v2) = v0))
% 6.68/2.21  | (24)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 6.68/2.21  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 6.68/2.21  | (26)  ! [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))
% 6.68/2.21  | (27)  ! [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))
% 6.68/2.21  | (28) strong_iteration(all_0_3_3) = all_0_2_2
% 6.68/2.21  | (29)  ~ (all_0_0_0 = all_0_2_2)
% 6.68/2.21  | (30)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (star(v0) = v1) |  ~ (multiplication(v0, v1) = v2) | addition(one, v2) = v1)
% 6.68/2.21  | (31)  ! [v0] :  ! [v1] : ( ~ (star(v0) = v1) |  ? [v2] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1))
% 6.68/2.21  | (32) addition(all_0_1_1, one) = all_0_0_0
% 6.68/2.21  | (33)  ! [v0] :  ! [v1] : ( ~ (star(v0) = v1) |  ? [v2] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1))
% 6.68/2.21  | (34)  ! [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)))
% 6.68/2.21  | (35)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 6.68/2.21  | (36)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 6.68/2.21  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v1 |  ~ (strong_iteration(v0) = v1) |  ~ (star(v0) = v2) |  ~ (multiplication(v1, zero) = v3) |  ~ (addition(v2, v3) = v4))
% 6.68/2.21  |
% 6.68/2.22  | Instantiating formula (18) with all_0_2_2, all_0_3_3 and discharging atoms strong_iteration(all_0_3_3) = all_0_2_2, yields:
% 6.68/2.22  | (38)  ? [v0] :  ? [v1] : (star(all_0_3_3) = v0 & multiplication(all_0_2_2, zero) = v1 & addition(v0, v1) = all_0_2_2)
% 6.68/2.22  |
% 6.68/2.22  | Instantiating formula (4) with all_0_2_2, all_0_3_3 and discharging atoms strong_iteration(all_0_3_3) = all_0_2_2, yields:
% 6.68/2.22  | (39)  ? [v0] : (multiplication(all_0_3_3, all_0_2_2) = v0 & addition(v0, one) = all_0_2_2)
% 6.68/2.22  |
% 6.68/2.22  | Instantiating formula (36) with all_0_0_0, all_0_1_1, one and discharging atoms addition(all_0_1_1, one) = all_0_0_0, yields:
% 6.68/2.22  | (40) addition(one, all_0_1_1) = all_0_0_0
% 6.68/2.22  |
% 6.68/2.22  | Instantiating (39) with all_9_0_4 yields:
% 6.68/2.22  | (41) multiplication(all_0_3_3, all_0_2_2) = all_9_0_4 & addition(all_9_0_4, one) = all_0_2_2
% 6.68/2.22  |
% 6.68/2.22  | Applying alpha-rule on (41) yields:
% 6.68/2.22  | (42) multiplication(all_0_3_3, all_0_2_2) = all_9_0_4
% 6.68/2.22  | (43) addition(all_9_0_4, one) = all_0_2_2
% 6.68/2.22  |
% 6.68/2.22  | Instantiating (38) with all_11_0_5, all_11_1_6 yields:
% 6.68/2.22  | (44) star(all_0_3_3) = all_11_1_6 & multiplication(all_0_2_2, zero) = all_11_0_5 & addition(all_11_1_6, all_11_0_5) = all_0_2_2
% 6.68/2.22  |
% 6.68/2.22  | Applying alpha-rule on (44) yields:
% 6.68/2.22  | (45) star(all_0_3_3) = all_11_1_6
% 6.68/2.22  | (46) multiplication(all_0_2_2, zero) = all_11_0_5
% 6.68/2.22  | (47) addition(all_11_1_6, all_11_0_5) = all_0_2_2
% 6.68/2.22  |
% 6.68/2.22  | Instantiating formula (33) with all_11_1_6, all_0_3_3 and discharging atoms star(all_0_3_3) = all_11_1_6, yields:
% 6.68/2.22  | (48)  ? [v0] : (multiplication(all_11_1_6, all_0_3_3) = v0 & addition(one, v0) = all_11_1_6)
% 6.68/2.22  |
% 6.68/2.22  | Instantiating formula (8) with all_0_1_1, all_0_2_2, all_0_3_3, all_11_0_5, all_11_1_6 and discharging atoms multiplication(all_0_2_2, all_0_3_3) = all_0_1_1, addition(all_11_1_6, all_11_0_5) = all_0_2_2, yields:
% 6.68/2.22  | (49)  ? [v0] :  ? [v1] : (multiplication(all_11_0_5, all_0_3_3) = v1 & multiplication(all_11_1_6, all_0_3_3) = v0 & addition(v0, v1) = all_0_1_1)
% 6.68/2.22  |
% 6.68/2.22  | Instantiating formula (8) with all_11_0_5, all_0_2_2, zero, one, all_9_0_4 and discharging atoms multiplication(all_0_2_2, zero) = all_11_0_5, addition(all_9_0_4, one) = all_0_2_2, yields:
% 6.68/2.22  | (50)  ? [v0] :  ? [v1] : (multiplication(all_9_0_4, zero) = v0 & multiplication(one, zero) = v1 & addition(v0, v1) = all_11_0_5)
% 6.68/2.22  |
% 6.68/2.22  | Instantiating (50) with all_19_0_7, all_19_1_8 yields:
% 6.68/2.22  | (51) multiplication(all_9_0_4, zero) = all_19_1_8 & multiplication(one, zero) = all_19_0_7 & addition(all_19_1_8, all_19_0_7) = all_11_0_5
% 6.68/2.22  |
% 6.68/2.22  | Applying alpha-rule on (51) yields:
% 6.68/2.22  | (52) multiplication(all_9_0_4, zero) = all_19_1_8
% 6.68/2.22  | (53) multiplication(one, zero) = all_19_0_7
% 6.68/2.22  | (54) addition(all_19_1_8, all_19_0_7) = all_11_0_5
% 6.68/2.22  |
% 6.68/2.22  | Instantiating (49) with all_29_0_17, all_29_1_18 yields:
% 6.68/2.22  | (55) multiplication(all_11_0_5, all_0_3_3) = all_29_0_17 & multiplication(all_11_1_6, all_0_3_3) = all_29_1_18 & addition(all_29_1_18, all_29_0_17) = all_0_1_1
% 6.68/2.22  |
% 6.68/2.22  | Applying alpha-rule on (55) yields:
% 6.68/2.22  | (56) multiplication(all_11_0_5, all_0_3_3) = all_29_0_17
% 6.68/2.22  | (57) multiplication(all_11_1_6, all_0_3_3) = all_29_1_18
% 6.68/2.22  | (58) addition(all_29_1_18, all_29_0_17) = all_0_1_1
% 6.68/2.22  |
% 6.68/2.22  | Instantiating (48) with all_33_0_20 yields:
% 6.68/2.22  | (59) multiplication(all_11_1_6, all_0_3_3) = all_33_0_20 & addition(one, all_33_0_20) = all_11_1_6
% 6.68/2.22  |
% 6.68/2.22  | Applying alpha-rule on (59) yields:
% 6.68/2.22  | (60) multiplication(all_11_1_6, all_0_3_3) = all_33_0_20
% 6.68/2.22  | (61) addition(one, all_33_0_20) = all_11_1_6
% 6.68/2.22  |
% 6.68/2.22  | Instantiating formula (3) with all_11_1_6, all_0_3_3, all_29_1_18, all_33_0_20 and discharging atoms multiplication(all_11_1_6, all_0_3_3) = all_33_0_20, multiplication(all_11_1_6, all_0_3_3) = all_29_1_18, yields:
% 6.68/2.22  | (62) all_33_0_20 = all_29_1_18
% 6.68/2.22  |
% 6.68/2.22  | Instantiating formula (19) with all_19_0_7, zero and discharging atoms multiplication(one, zero) = all_19_0_7, yields:
% 6.68/2.22  | (63) all_19_0_7 = zero
% 6.68/2.22  |
% 6.68/2.22  | From (63) and (54) follows:
% 6.68/2.22  | (64) addition(all_19_1_8, zero) = all_11_0_5
% 6.68/2.22  |
% 6.68/2.22  | From (62) and (61) follows:
% 6.68/2.22  | (65) addition(one, all_29_1_18) = all_11_1_6
% 6.68/2.22  |
% 6.68/2.22  | Instantiating formula (20) with all_11_0_5, all_19_1_8 and discharging atoms addition(all_19_1_8, zero) = all_11_0_5, yields:
% 6.68/2.22  | (66) all_19_1_8 = all_11_0_5
% 6.68/2.22  |
% 6.68/2.22  | From (66) and (52) follows:
% 6.68/2.22  | (67) multiplication(all_9_0_4, zero) = all_11_0_5
% 6.68/2.22  |
% 6.68/2.22  | Instantiating formula (22) with all_29_0_17, all_11_0_5, all_0_3_3, zero, all_0_2_2 and discharging atoms multiplication(all_11_0_5, all_0_3_3) = all_29_0_17, multiplication(all_0_2_2, zero) = all_11_0_5, yields:
% 6.68/2.22  | (68)  ? [v0] : (multiplication(all_0_2_2, v0) = all_29_0_17 & multiplication(zero, all_0_3_3) = v0)
% 6.68/2.22  |
% 6.68/2.22  | Instantiating formula (22) with all_29_0_17, all_11_0_5, all_0_3_3, zero, all_9_0_4 and discharging atoms multiplication(all_11_0_5, all_0_3_3) = all_29_0_17, multiplication(all_9_0_4, zero) = all_11_0_5, yields:
% 6.68/2.22  | (69)  ? [v0] : (multiplication(all_9_0_4, v0) = all_29_0_17 & multiplication(zero, all_0_3_3) = v0)
% 6.68/2.23  |
% 6.68/2.23  | Instantiating formula (6) with all_0_0_0, all_0_1_1, one, all_29_1_18, all_29_0_17 and discharging atoms addition(all_29_1_18, all_29_0_17) = all_0_1_1, addition(one, all_0_1_1) = all_0_0_0, yields:
% 6.68/2.23  | (70)  ? [v0] : (addition(v0, all_29_0_17) = all_0_0_0 & addition(one, all_29_1_18) = v0)
% 6.68/2.23  |
% 6.68/2.23  | Instantiating (70) with all_153_0_96 yields:
% 6.68/2.23  | (71) addition(all_153_0_96, all_29_0_17) = all_0_0_0 & addition(one, all_29_1_18) = all_153_0_96
% 6.68/2.23  |
% 6.68/2.23  | Applying alpha-rule on (71) yields:
% 6.68/2.23  | (72) addition(all_153_0_96, all_29_0_17) = all_0_0_0
% 6.68/2.23  | (73) addition(one, all_29_1_18) = all_153_0_96
% 6.68/2.23  |
% 6.68/2.23  | Instantiating (68) with all_179_0_110 yields:
% 6.68/2.23  | (74) multiplication(all_0_2_2, all_179_0_110) = all_29_0_17 & multiplication(zero, all_0_3_3) = all_179_0_110
% 6.68/2.23  |
% 6.68/2.23  | Applying alpha-rule on (74) yields:
% 6.68/2.23  | (75) multiplication(all_0_2_2, all_179_0_110) = all_29_0_17
% 6.68/2.23  | (76) multiplication(zero, all_0_3_3) = all_179_0_110
% 6.68/2.23  |
% 6.68/2.23  | Instantiating (69) with all_195_0_118 yields:
% 6.68/2.23  | (77) multiplication(all_9_0_4, all_195_0_118) = all_29_0_17 & multiplication(zero, all_0_3_3) = all_195_0_118
% 6.68/2.23  |
% 6.68/2.23  | Applying alpha-rule on (77) yields:
% 6.68/2.23  | (78) multiplication(all_9_0_4, all_195_0_118) = all_29_0_17
% 6.68/2.23  | (79) multiplication(zero, all_0_3_3) = all_195_0_118
% 6.68/2.23  |
% 6.68/2.23  | Instantiating formula (14) with all_195_0_118, all_0_3_3 and discharging atoms multiplication(zero, all_0_3_3) = all_195_0_118, yields:
% 6.68/2.23  | (80) all_195_0_118 = zero
% 6.68/2.23  |
% 6.68/2.23  | Instantiating formula (3) with zero, all_0_3_3, all_179_0_110, all_195_0_118 and discharging atoms multiplication(zero, all_0_3_3) = all_195_0_118, multiplication(zero, all_0_3_3) = all_179_0_110, yields:
% 6.68/2.23  | (81) all_195_0_118 = all_179_0_110
% 6.68/2.23  |
% 6.68/2.23  | Instantiating formula (25) with one, all_29_1_18, all_153_0_96, all_11_1_6 and discharging atoms addition(one, all_29_1_18) = all_153_0_96, addition(one, all_29_1_18) = all_11_1_6, yields:
% 6.68/2.23  | (82) all_153_0_96 = all_11_1_6
% 6.68/2.23  |
% 6.68/2.23  | Combining equations (81,80) yields a new equation:
% 6.68/2.23  | (83) all_179_0_110 = zero
% 6.68/2.23  |
% 6.68/2.23  | Simplifying 83 yields:
% 6.68/2.23  | (84) all_179_0_110 = zero
% 6.68/2.23  |
% 6.68/2.23  | From (84) and (75) follows:
% 6.68/2.23  | (85) multiplication(all_0_2_2, zero) = all_29_0_17
% 6.68/2.23  |
% 6.68/2.23  | From (82) and (72) follows:
% 6.68/2.23  | (86) addition(all_11_1_6, all_29_0_17) = all_0_0_0
% 6.68/2.23  |
% 6.68/2.23  | Instantiating formula (37) with all_0_0_0, all_29_0_17, all_11_1_6, all_0_2_2, all_0_3_3 and discharging atoms strong_iteration(all_0_3_3) = all_0_2_2, star(all_0_3_3) = all_11_1_6, multiplication(all_0_2_2, zero) = all_29_0_17, addition(all_11_1_6, all_29_0_17) = all_0_0_0, yields:
% 6.68/2.23  | (87) all_0_0_0 = all_0_2_2
% 6.68/2.23  |
% 6.68/2.23  | Equations (87) can reduce 29 to:
% 6.68/2.23  | (88) $false
% 6.68/2.23  |
% 6.68/2.23  |-The branch is then unsatisfiable
% 6.68/2.23  % SZS output end Proof for theBenchmark
% 6.68/2.23  
% 6.68/2.23  1613ms
%------------------------------------------------------------------------------