%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE148+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n021.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 01:51:36 EDT 2022

% Result   : Theorem 3.97s 1.69s
% Output   : Proof 7.04s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : KLE148+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.35  % Computer : n021.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 16:20:00 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.59/0.60          ____       _                          
% 0.59/0.60    ___  / __ \_____(_)___  ________  __________
% 0.59/0.60   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.60  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.59/0.60  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.59/0.60  
% 0.59/0.60  A Theorem Prover for First-Order Logic
% 0.59/0.60  (ePrincess v.1.0)
% 0.59/0.60  
% 0.59/0.60  (c) Philipp Rümmer, 2009-2015
% 0.59/0.60  (c) Peter Backeman, 2014-2015
% 0.59/0.60  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.60  Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.60  Bug reports to peter@backeman.se
% 0.59/0.60  
% 0.59/0.60  For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.60  
% 0.59/0.60  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.73/0.65  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.62/0.98  Prover 0: Preprocessing ...
% 2.33/1.26  Prover 0: Constructing countermodel ...
% 3.97/1.68  Prover 0: proved (1031ms)
% 3.97/1.69  
% 3.97/1.69  No countermodel exists, formula is valid
% 3.97/1.69  % SZS status Theorem for theBenchmark
% 3.97/1.69  
% 3.97/1.69  Generating proof ... found it (size 57)
% 6.66/2.26  
% 6.66/2.26  % SZS output start Proof for theBenchmark
% 6.66/2.26  Assumed formulas after preprocessing and simplification: 
% 6.66/2.27  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : ( ~ (v3 = v0) & strong_iteration(v1) = v2 & multiplication(v0, v2) = v3 & multiplication(v0, v1) = zero &  ! [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)))
% 7.04/2.31  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 7.04/2.31  | (1)  ~ (all_0_0_0 = all_0_3_3) & strong_iteration(all_0_2_2) = all_0_1_1 & multiplication(all_0_3_3, all_0_1_1) = all_0_0_0 & multiplication(all_0_3_3, all_0_2_2) = zero &  ! [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))
% 7.04/2.32  |
% 7.04/2.32  | Applying alpha-rule on (1) yields:
% 7.04/2.32  | (2)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ~ leq(v0, v1))
% 7.04/2.32  | (3)  ! [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)))
% 7.04/2.32  | (4)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (strong_iteration(v2) = v1) |  ~ (strong_iteration(v2) = v0))
% 7.04/2.32  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 7.04/2.32  | (6)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (star(v0) = v1) |  ~ (multiplication(v0, v1) = v2) | addition(one, v2) = v1)
% 7.04/2.32  | (7)  ! [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))
% 7.04/2.32  | (8)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 7.04/2.32  | (9)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 7.04/2.32  | (10)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strong_iteration(v0) = v1) |  ~ (multiplication(v0, v1) = v2) | addition(v2, one) = v1)
% 7.04/2.32  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v1 |  ~ (strong_iteration(v0) = v1) |  ~ (star(v0) = v2) |  ~ (multiplication(v1, zero) = v3) |  ~ (addition(v2, v3) = v4))
% 7.04/2.32  | (12)  ! [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))
% 7.04/2.32  | (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))
% 7.04/2.32  | (14)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 7.04/2.32  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 7.04/2.32  | (16)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (star(v2) = v1) |  ~ (star(v2) = v0))
% 7.04/2.32  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 7.04/2.32  | (18)  ! [v0] :  ! [v1] : ( ~ (star(v0) = v1) |  ? [v2] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1))
% 7.04/2.32  | (19)  ! [v0] :  ! [v1] : ( ~ (star(v0) = v1) |  ? [v2] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1))
% 7.04/2.32  | (20)  ! [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)))
% 7.04/2.32  | (21)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (star(v0) = v1) |  ~ (multiplication(v1, v0) = v2) | addition(one, v2) = v1)
% 7.04/2.32  | (22)  ~ (all_0_0_0 = all_0_3_3)
% 7.04/2.32  | (23) multiplication(all_0_3_3, all_0_2_2) = zero
% 7.04/2.32  | (24)  ! [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))
% 7.04/2.32  | (25)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 7.04/2.32  | (26)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 7.04/2.32  | (27) strong_iteration(all_0_2_2) = all_0_1_1
% 7.04/2.32  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 7.04/2.32  | (29)  ! [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)))
% 7.04/2.32  | (30) multiplication(all_0_3_3, all_0_1_1) = all_0_0_0
% 7.04/2.32  | (31)  ! [v0] :  ! [v1] : ( ~ (strong_iteration(v0) = v1) |  ? [v2] :  ? [v3] : (star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1))
% 7.04/2.33  | (32)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 7.04/2.33  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 7.04/2.33  | (34)  ! [v0] :  ! [v1] : ( ~ (strong_iteration(v0) = v1) |  ? [v2] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1))
% 7.04/2.33  | (35)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 7.04/2.33  | (36)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 7.04/2.33  | (37)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 7.04/2.33  |
% 7.04/2.33  | Instantiating formula (31) with all_0_1_1, all_0_2_2 and discharging atoms strong_iteration(all_0_2_2) = all_0_1_1, yields:
% 7.04/2.33  | (38)  ? [v0] :  ? [v1] : (star(all_0_2_2) = v0 & multiplication(all_0_1_1, zero) = v1 & addition(v0, v1) = all_0_1_1)
% 7.04/2.33  |
% 7.04/2.33  | Instantiating formula (34) with all_0_1_1, all_0_2_2 and discharging atoms strong_iteration(all_0_2_2) = all_0_1_1, yields:
% 7.04/2.33  | (39)  ? [v0] : (multiplication(all_0_2_2, all_0_1_1) = v0 & addition(v0, one) = all_0_1_1)
% 7.04/2.33  |
% 7.04/2.33  | Instantiating (39) with all_8_0_4 yields:
% 7.04/2.33  | (40) multiplication(all_0_2_2, all_0_1_1) = all_8_0_4 & addition(all_8_0_4, one) = all_0_1_1
% 7.04/2.33  |
% 7.04/2.33  | Applying alpha-rule on (40) yields:
% 7.04/2.33  | (41) multiplication(all_0_2_2, all_0_1_1) = all_8_0_4
% 7.04/2.33  | (42) addition(all_8_0_4, one) = all_0_1_1
% 7.04/2.33  |
% 7.04/2.33  | Instantiating (38) with all_10_0_5, all_10_1_6 yields:
% 7.04/2.33  | (43) star(all_0_2_2) = all_10_1_6 & multiplication(all_0_1_1, zero) = all_10_0_5 & addition(all_10_1_6, all_10_0_5) = all_0_1_1
% 7.04/2.33  |
% 7.04/2.33  | Applying alpha-rule on (43) yields:
% 7.04/2.33  | (44) star(all_0_2_2) = all_10_1_6
% 7.04/2.33  | (45) multiplication(all_0_1_1, zero) = all_10_0_5
% 7.04/2.33  | (46) addition(all_10_1_6, all_10_0_5) = all_0_1_1
% 7.04/2.33  |
% 7.04/2.33  | Instantiating formula (19) with all_10_1_6, all_0_2_2 and discharging atoms star(all_0_2_2) = all_10_1_6, yields:
% 7.04/2.33  | (47)  ? [v0] : (multiplication(all_0_2_2, all_10_1_6) = v0 & addition(one, v0) = all_10_1_6)
% 7.04/2.33  |
% 7.04/2.33  | Instantiating formula (24) with all_0_0_0, all_0_1_1, all_10_0_5, all_10_1_6, all_0_3_3 and discharging atoms multiplication(all_0_3_3, all_0_1_1) = all_0_0_0, addition(all_10_1_6, all_10_0_5) = all_0_1_1, yields:
% 7.04/2.33  | (48)  ? [v0] :  ? [v1] : (multiplication(all_0_3_3, all_10_0_5) = v1 & multiplication(all_0_3_3, all_10_1_6) = v0 & addition(v0, v1) = all_0_0_0)
% 7.04/2.33  |
% 7.04/2.33  | Instantiating formula (24) with all_8_0_4, all_0_1_1, all_10_0_5, all_10_1_6, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_8_0_4, addition(all_10_1_6, all_10_0_5) = all_0_1_1, yields:
% 7.04/2.33  | (49)  ? [v0] :  ? [v1] : (multiplication(all_0_2_2, all_10_0_5) = v1 & multiplication(all_0_2_2, all_10_1_6) = v0 & addition(v0, v1) = all_8_0_4)
% 7.04/2.33  |
% 7.04/2.33  | Instantiating formula (24) with all_0_0_0, all_0_1_1, one, all_8_0_4, all_0_3_3 and discharging atoms multiplication(all_0_3_3, all_0_1_1) = all_0_0_0, addition(all_8_0_4, one) = all_0_1_1, yields:
% 7.04/2.33  | (50)  ? [v0] :  ? [v1] : (multiplication(all_0_3_3, all_8_0_4) = v0 & multiplication(all_0_3_3, one) = v1 & addition(v0, v1) = all_0_0_0)
% 7.04/2.33  |
% 7.04/2.33  | Instantiating formula (12) with all_10_0_5, all_0_1_1, zero, one, all_8_0_4 and discharging atoms multiplication(all_0_1_1, zero) = all_10_0_5, addition(all_8_0_4, one) = all_0_1_1, yields:
% 7.04/2.33  | (51)  ? [v0] :  ? [v1] : (multiplication(all_8_0_4, zero) = v0 & multiplication(one, zero) = v1 & addition(v0, v1) = all_10_0_5)
% 7.04/2.33  |
% 7.04/2.33  | Instantiating formula (37) with all_0_1_1, all_8_0_4, one and discharging atoms addition(all_8_0_4, one) = all_0_1_1, yields:
% 7.04/2.33  | (52) addition(one, all_8_0_4) = all_0_1_1
% 7.04/2.33  |
% 7.04/2.33  | Instantiating (49) with all_18_0_7, all_18_1_8 yields:
% 7.04/2.33  | (53) multiplication(all_0_2_2, all_10_0_5) = all_18_0_7 & multiplication(all_0_2_2, all_10_1_6) = all_18_1_8 & addition(all_18_1_8, all_18_0_7) = all_8_0_4
% 7.04/2.33  |
% 7.04/2.33  | Applying alpha-rule on (53) yields:
% 7.04/2.33  | (54) multiplication(all_0_2_2, all_10_0_5) = all_18_0_7
% 7.04/2.33  | (55) multiplication(all_0_2_2, all_10_1_6) = all_18_1_8
% 7.04/2.33  | (56) addition(all_18_1_8, all_18_0_7) = all_8_0_4
% 7.04/2.33  |
% 7.04/2.33  | Instantiating (51) with all_22_0_11, all_22_1_12 yields:
% 7.04/2.33  | (57) multiplication(all_8_0_4, zero) = all_22_1_12 & multiplication(one, zero) = all_22_0_11 & addition(all_22_1_12, all_22_0_11) = all_10_0_5
% 7.04/2.33  |
% 7.04/2.33  | Applying alpha-rule on (57) yields:
% 7.04/2.33  | (58) multiplication(all_8_0_4, zero) = all_22_1_12
% 7.04/2.33  | (59) multiplication(one, zero) = all_22_0_11
% 7.04/2.33  | (60) addition(all_22_1_12, all_22_0_11) = all_10_0_5
% 7.04/2.33  |
% 7.04/2.33  | Instantiating (50) with all_26_0_15, all_26_1_16 yields:
% 7.04/2.33  | (61) multiplication(all_0_3_3, all_8_0_4) = all_26_1_16 & multiplication(all_0_3_3, one) = all_26_0_15 & addition(all_26_1_16, all_26_0_15) = all_0_0_0
% 7.04/2.33  |
% 7.04/2.33  | Applying alpha-rule on (61) yields:
% 7.04/2.33  | (62) multiplication(all_0_3_3, all_8_0_4) = all_26_1_16
% 7.04/2.33  | (63) multiplication(all_0_3_3, one) = all_26_0_15
% 7.04/2.33  | (64) addition(all_26_1_16, all_26_0_15) = all_0_0_0
% 7.04/2.33  |
% 7.04/2.33  | Instantiating (48) with all_28_0_17, all_28_1_18 yields:
% 7.04/2.33  | (65) multiplication(all_0_3_3, all_10_0_5) = all_28_0_17 & multiplication(all_0_3_3, all_10_1_6) = all_28_1_18 & addition(all_28_1_18, all_28_0_17) = all_0_0_0
% 7.04/2.33  |
% 7.04/2.33  | Applying alpha-rule on (65) yields:
% 7.04/2.33  | (66) multiplication(all_0_3_3, all_10_0_5) = all_28_0_17
% 7.04/2.33  | (67) multiplication(all_0_3_3, all_10_1_6) = all_28_1_18
% 7.04/2.33  | (68) addition(all_28_1_18, all_28_0_17) = all_0_0_0
% 7.04/2.34  |
% 7.04/2.34  | Instantiating (47) with all_32_0_20 yields:
% 7.04/2.34  | (69) multiplication(all_0_2_2, all_10_1_6) = all_32_0_20 & addition(one, all_32_0_20) = all_10_1_6
% 7.04/2.34  |
% 7.04/2.34  | Applying alpha-rule on (69) yields:
% 7.04/2.34  | (70) multiplication(all_0_2_2, all_10_1_6) = all_32_0_20
% 7.04/2.34  | (71) addition(one, all_32_0_20) = all_10_1_6
% 7.04/2.34  |
% 7.04/2.34  | Instantiating formula (28) with all_0_2_2, all_10_1_6, all_18_1_8, all_32_0_20 and discharging atoms multiplication(all_0_2_2, all_10_1_6) = all_32_0_20, multiplication(all_0_2_2, all_10_1_6) = all_18_1_8, yields:
% 7.04/2.34  | (72) all_32_0_20 = all_18_1_8
% 7.04/2.34  |
% 7.04/2.34  | Instantiating formula (14) with all_22_0_11, zero and discharging atoms multiplication(one, zero) = all_22_0_11, yields:
% 7.04/2.34  | (73) all_22_0_11 = zero
% 7.04/2.34  |
% 7.04/2.34  | From (73) and (60) follows:
% 7.04/2.34  | (74) addition(all_22_1_12, zero) = all_10_0_5
% 7.04/2.34  |
% 7.04/2.34  | From (72) and (71) follows:
% 7.04/2.34  | (75) addition(one, all_18_1_8) = all_10_1_6
% 7.04/2.34  |
% 7.04/2.34  | Instantiating formula (25) with all_10_0_5, all_22_1_12 and discharging atoms addition(all_22_1_12, zero) = all_10_0_5, yields:
% 7.04/2.34  | (76) all_22_1_12 = all_10_0_5
% 7.04/2.34  |
% 7.04/2.34  | From (76) and (58) follows:
% 7.04/2.34  | (77) multiplication(all_8_0_4, zero) = all_10_0_5
% 7.04/2.34  |
% 7.04/2.34  | Instantiating formula (5) with all_28_0_17, all_10_0_5, zero, all_8_0_4, all_0_3_3 and discharging atoms multiplication(all_8_0_4, zero) = all_10_0_5, multiplication(all_0_3_3, all_10_0_5) = all_28_0_17, yields:
% 7.04/2.34  | (78)  ? [v0] : (multiplication(v0, zero) = all_28_0_17 & multiplication(all_0_3_3, all_8_0_4) = v0)
% 7.04/2.34  |
% 7.04/2.34  | Instantiating formula (5) with all_26_1_16, all_8_0_4, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_8_0_4, multiplication(all_0_3_3, all_8_0_4) = all_26_1_16, yields:
% 7.04/2.34  | (79)  ? [v0] : (multiplication(v0, all_0_1_1) = all_26_1_16 & multiplication(all_0_3_3, all_0_2_2) = v0)
% 7.04/2.34  |
% 7.04/2.34  | Instantiating formula (24) with all_28_1_18, all_10_1_6, all_18_1_8, one, all_0_3_3 and discharging atoms multiplication(all_0_3_3, all_10_1_6) = all_28_1_18, addition(one, all_18_1_8) = all_10_1_6, yields:
% 7.04/2.34  | (80)  ? [v0] :  ? [v1] : (multiplication(all_0_3_3, all_18_1_8) = v1 & multiplication(all_0_3_3, one) = v0 & addition(v0, v1) = all_28_1_18)
% 7.04/2.34  |
% 7.04/2.34  | Instantiating formula (24) with all_0_0_0, all_0_1_1, all_8_0_4, one, all_0_3_3 and discharging atoms multiplication(all_0_3_3, all_0_1_1) = all_0_0_0, addition(one, all_8_0_4) = all_0_1_1, yields:
% 7.04/2.34  | (81)  ? [v0] :  ? [v1] : (multiplication(all_0_3_3, all_8_0_4) = v1 & multiplication(all_0_3_3, one) = v0 & addition(v0, v1) = all_0_0_0)
% 7.04/2.34  |
% 7.04/2.34  | Instantiating (79) with all_72_0_37 yields:
% 7.04/2.34  | (82) multiplication(all_72_0_37, all_0_1_1) = all_26_1_16 & multiplication(all_0_3_3, all_0_2_2) = all_72_0_37
% 7.04/2.34  |
% 7.04/2.34  | Applying alpha-rule on (82) yields:
% 7.04/2.34  | (83) multiplication(all_72_0_37, all_0_1_1) = all_26_1_16
% 7.04/2.34  | (84) multiplication(all_0_3_3, all_0_2_2) = all_72_0_37
% 7.04/2.34  |
% 7.04/2.34  | Instantiating (78) with all_88_0_47 yields:
% 7.04/2.34  | (85) multiplication(all_88_0_47, zero) = all_28_0_17 & multiplication(all_0_3_3, all_8_0_4) = all_88_0_47
% 7.04/2.34  |
% 7.04/2.34  | Applying alpha-rule on (85) yields:
% 7.04/2.34  | (86) multiplication(all_88_0_47, zero) = all_28_0_17
% 7.04/2.34  | (87) multiplication(all_0_3_3, all_8_0_4) = all_88_0_47
% 7.04/2.34  |
% 7.04/2.34  | Instantiating (81) with all_152_0_91, all_152_1_92 yields:
% 7.04/2.34  | (88) multiplication(all_0_3_3, all_8_0_4) = all_152_0_91 & multiplication(all_0_3_3, one) = all_152_1_92 & addition(all_152_1_92, all_152_0_91) = all_0_0_0
% 7.04/2.34  |
% 7.04/2.34  | Applying alpha-rule on (88) yields:
% 7.04/2.34  | (89) multiplication(all_0_3_3, all_8_0_4) = all_152_0_91
% 7.04/2.34  | (90) multiplication(all_0_3_3, one) = all_152_1_92
% 7.04/2.34  | (91) addition(all_152_1_92, all_152_0_91) = all_0_0_0
% 7.04/2.34  |
% 7.04/2.34  | Instantiating (80) with all_158_0_95, all_158_1_96 yields:
% 7.04/2.34  | (92) multiplication(all_0_3_3, all_18_1_8) = all_158_0_95 & multiplication(all_0_3_3, one) = all_158_1_96 & addition(all_158_1_96, all_158_0_95) = all_28_1_18
% 7.04/2.34  |
% 7.04/2.34  | Applying alpha-rule on (92) yields:
% 7.04/2.34  | (93) multiplication(all_0_3_3, all_18_1_8) = all_158_0_95
% 7.04/2.34  | (94) multiplication(all_0_3_3, one) = all_158_1_96
% 7.04/2.34  | (95) addition(all_158_1_96, all_158_0_95) = all_28_1_18
% 7.04/2.34  |
% 7.04/2.34  | Instantiating formula (28) with all_0_3_3, all_8_0_4, all_152_0_91, all_26_1_16 and discharging atoms multiplication(all_0_3_3, all_8_0_4) = all_152_0_91, multiplication(all_0_3_3, all_8_0_4) = all_26_1_16, yields:
% 7.04/2.34  | (96) all_152_0_91 = all_26_1_16
% 7.04/2.34  |
% 7.04/2.34  | Instantiating formula (28) with all_0_3_3, all_8_0_4, all_88_0_47, all_152_0_91 and discharging atoms multiplication(all_0_3_3, all_8_0_4) = all_152_0_91, multiplication(all_0_3_3, all_8_0_4) = all_88_0_47, yields:
% 7.04/2.34  | (97) all_152_0_91 = all_88_0_47
% 7.04/2.34  |
% 7.04/2.34  | Instantiating formula (28) with all_0_3_3, all_0_2_2, all_72_0_37, zero and discharging atoms multiplication(all_0_3_3, all_0_2_2) = all_72_0_37, multiplication(all_0_3_3, all_0_2_2) = zero, yields:
% 7.04/2.34  | (98) all_72_0_37 = zero
% 7.04/2.34  |
% 7.04/2.34  | Instantiating formula (32) with all_158_1_96, all_0_3_3 and discharging atoms multiplication(all_0_3_3, one) = all_158_1_96, yields:
% 7.04/2.34  | (99) all_158_1_96 = all_0_3_3
% 7.04/2.34  |
% 7.04/2.34  | Instantiating formula (28) with all_0_3_3, one, all_152_1_92, all_158_1_96 and discharging atoms multiplication(all_0_3_3, one) = all_158_1_96, multiplication(all_0_3_3, one) = all_152_1_92, yields:
% 7.04/2.35  | (100) all_158_1_96 = all_152_1_92
% 7.04/2.35  |
% 7.04/2.35  | Combining equations (99,100) yields a new equation:
% 7.04/2.35  | (101) all_152_1_92 = all_0_3_3
% 7.04/2.35  |
% 7.04/2.35  | Combining equations (96,97) yields a new equation:
% 7.04/2.35  | (102) all_88_0_47 = all_26_1_16
% 7.04/2.35  |
% 7.04/2.35  | Combining equations (102,97) yields a new equation:
% 7.04/2.35  | (96) all_152_0_91 = all_26_1_16
% 7.04/2.35  |
% 7.04/2.35  | From (98) and (83) follows:
% 7.04/2.35  | (104) multiplication(zero, all_0_1_1) = all_26_1_16
% 7.04/2.35  |
% 7.04/2.35  | From (101)(96) and (91) follows:
% 7.04/2.35  | (105) addition(all_0_3_3, all_26_1_16) = all_0_0_0
% 7.04/2.35  |
% 7.04/2.35  | Instantiating formula (9) with all_26_1_16, all_0_1_1 and discharging atoms multiplication(zero, all_0_1_1) = all_26_1_16, yields:
% 7.04/2.35  | (106) all_26_1_16 = zero
% 7.04/2.35  |
% 7.04/2.35  | From (106) and (105) follows:
% 7.04/2.35  | (107) addition(all_0_3_3, zero) = all_0_0_0
% 7.04/2.35  |
% 7.04/2.35  | Instantiating formula (25) with all_0_0_0, all_0_3_3 and discharging atoms addition(all_0_3_3, zero) = all_0_0_0, yields:
% 7.04/2.35  | (108) all_0_0_0 = all_0_3_3
% 7.04/2.35  |
% 7.04/2.35  | Equations (108) can reduce 22 to:
% 7.04/2.35  | (109) $false
% 7.04/2.35  |
% 7.04/2.35  |-The branch is then unsatisfiable
% 7.04/2.35  % SZS output end Proof for theBenchmark
% 7.04/2.35  
% 7.04/2.35  1737ms
%------------------------------------------------------------------------------