%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE006+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n014.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 01:50:47 EDT 2022

% Result   : Theorem 2.73s 1.30s
% Output   : Proof 3.67s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KLE006+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n014.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Thu Jun 16 10:30:05 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.49/0.58          ____       _                          
% 0.49/0.58    ___  / __ \_____(_)___  ________  __________
% 0.49/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.49/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.49/0.58  
% 0.49/0.58  A Theorem Prover for First-Order Logic
% 0.49/0.58  (ePrincess v.1.0)
% 0.49/0.58  
% 0.49/0.58  (c) Philipp Rümmer, 2009-2015
% 0.49/0.58  (c) Peter Backeman, 2014-2015
% 0.49/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.58  Bug reports to peter@backeman.se
% 0.49/0.58  
% 0.49/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.58  
% 0.49/0.58  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.76/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.69/0.94  Prover 0: Preprocessing ...
% 2.33/1.20  Prover 0: Constructing countermodel ...
% 2.73/1.30  Prover 0: proved (669ms)
% 2.73/1.30  
% 2.73/1.30  No countermodel exists, formula is valid
% 2.73/1.30  % SZS status Theorem for theBenchmark
% 2.73/1.30  
% 2.73/1.30  Generating proof ... found it (size 7)
% 3.47/1.47  
% 3.47/1.47  % SZS output start Proof for theBenchmark
% 3.47/1.47  Assumed formulas after preprocessing and simplification: 
% 3.47/1.47  | (0)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = one) & c(v0) = v1 & addition(v0, v1) = v2 & test(v0) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v4, v5) = v7) |  ~ (multiplication(v3, v5) = v6) |  ~ (addition(v6, v7) = v8) |  ? [v9] : (multiplication(v9, v5) = v8 & addition(v3, v4) = v9)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v3, v5) = v7) |  ~ (multiplication(v3, v4) = v6) |  ~ (addition(v6, v7) = v8) |  ? [v9] : (multiplication(v3, v9) = v8 & addition(v4, v5) = v9)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (multiplication(v6, v5) = v7) |  ~ (multiplication(v3, v4) = v6) |  ? [v8] : (multiplication(v4, v5) = v8 & multiplication(v3, v8) = v7)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (multiplication(v6, v5) = v7) |  ~ (addition(v3, v4) = v6) |  ? [v8] :  ? [v9] : (multiplication(v4, v5) = v9 & multiplication(v3, v5) = v8 & addition(v8, v9) = v7)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (multiplication(v4, v5) = v6) |  ~ (multiplication(v3, v6) = v7) |  ? [v8] : (multiplication(v8, v5) = v7 & multiplication(v3, v4) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (multiplication(v3, v6) = v7) |  ~ (addition(v4, v5) = v6) |  ? [v8] :  ? [v9] : (multiplication(v3, v5) = v9 & multiplication(v3, v4) = v8 & addition(v8, v9) = v7)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (addition(v6, v3) = v7) |  ~ (addition(v5, v4) = v6) |  ? [v8] : (addition(v5, v8) = v7 & addition(v4, v3) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (addition(v5, v6) = v7) |  ~ (addition(v4, v3) = v6) |  ? [v8] : (addition(v8, v3) = v7 & addition(v5, v4) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (multiplication(v6, v5) = v4) |  ~ (multiplication(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (addition(v6, v5) = v4) |  ~ (addition(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = v4 |  ~ (c(v3) = v5) |  ~ complement(v3, v4) |  ~ test(v3)) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = v4 |  ~ (addition(v3, v4) = v5) |  ~ leq(v3, v4)) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = one |  ~ (addition(v3, v4) = v5) |  ~ complement(v4, v3)) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = zero |  ~ (multiplication(v4, v3) = v5) |  ~ complement(v4, v3)) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = zero |  ~ (multiplication(v3, v4) = v5) |  ~ complement(v4, v3)) &  ! [v3] :  ! [v4] :  ! [v5] : (v4 = v3 |  ~ (c(v5) = v4) |  ~ (c(v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v4, v3) = v5) |  ~ complement(v4, v3) | (multiplication(v3, v4) = zero & addition(v3, v4) = one)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v3, v4) = v5) |  ~ complement(v4, v3) | (multiplication(v4, v3) = zero & addition(v3, v4) = one)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (addition(v4, v3) = v5) | addition(v3, v4) = v5) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (addition(v3, v4) = v5) |  ~ complement(v4, v3) | (multiplication(v4, v3) = zero & multiplication(v3, v4) = zero)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (addition(v3, v4) = v5) | addition(v4, v3) = v5) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (multiplication(v3, one) = v4)) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (multiplication(one, v3) = v4)) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (addition(v3, v3) = v4)) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (addition(v3, zero) = v4)) &  ! [v3] :  ! [v4] : (v4 = zero |  ~ (c(v3) = v4) | test(v3)) &  ! [v3] :  ! [v4] : (v4 = zero |  ~ (multiplication(v3, zero) = v4)) &  ! [v3] :  ! [v4] : (v4 = zero |  ~ (multiplication(zero, v3) = v4)) &  ! [v3] :  ! [v4] : ( ~ (c(v3) = v4) |  ~ test(v3) | complement(v3, v4)) &  ! [v3] :  ! [v4] : ( ~ (multiplication(v4, v3) = zero) | complement(v4, v3) |  ? [v5] :  ? [v6] : (multiplication(v3, v4) = v5 & addition(v3, v4) = v6 & ( ~ (v6 = one) |  ~ (v5 = zero)))) &  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v4) = zero) | complement(v4, v3) |  ? [v5] :  ? [v6] : (multiplication(v4, v3) = v5 & addition(v3, v4) = v6 & ( ~ (v6 = one) |  ~ (v5 = zero)))) &  ! [v3] :  ! [v4] : ( ~ (addition(v3, v4) = v4) | leq(v3, v4)) &  ! [v3] :  ! [v4] : ( ~ (addition(v3, v4) = one) | complement(v4, v3) |  ? [v5] :  ? [v6] : (multiplication(v4, v3) = v6 & multiplication(v3, v4) = v5 & ( ~ (v6 = zero) |  ~ (v5 = zero)))) &  ! [v3] :  ! [v4] : ( ~ complement(v4, v3) | test(v3)) &  ! [v3] : ( ~ test(v3) |  ? [v4] : complement(v4, v3)))
% 3.67/1.51  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 3.67/1.51  | (1)  ~ (all_0_0_0 = one) & c(all_0_2_2) = all_0_1_1 & addition(all_0_2_2, all_0_1_1) = all_0_0_0 & test(all_0_2_2) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v1, v2) = v4) |  ~ (multiplication(v0, v2) = v3) |  ~ (addition(v3, v4) = v5) |  ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v0, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ~ (addition(v3, v4) = v5) |  ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (addition(v0, v1) = v3) |  ? [v5] :  ? [v6] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(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] : ( ~ (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 |  ~ (c(v0) = v2) |  ~ complement(v0, v1) |  ~ test(v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ~ leq(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = one |  ~ (addition(v0, v1) = v2) |  ~ complement(v1, v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = zero |  ~ (multiplication(v1, v0) = v2) |  ~ complement(v1, v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = zero |  ~ (multiplication(v0, v1) = v2) |  ~ complement(v1, v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (c(v2) = v1) |  ~ (c(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v1, v0) = v2) |  ~ complement(v1, v0) | (multiplication(v0, v1) = zero & addition(v0, v1) = one)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ~ complement(v1, v0) | (multiplication(v1, v0) = zero & addition(v0, v1) = one)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) |  ~ complement(v1, v0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero)) &  ! [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 |  ~ (c(v0) = v1) | test(v0)) &  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(v0, zero) = v1)) &  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1)) &  ! [v0] :  ! [v1] : ( ~ (c(v0) = v1) |  ~ test(v0) | complement(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ (multiplication(v1, v0) = zero) | complement(v1, v0) |  ? [v2] :  ? [v3] : (multiplication(v0, v1) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) |  ~ (v2 = zero)))) &  ! [v0] :  ! [v1] : ( ~ (multiplication(v0, v1) = zero) | complement(v1, v0) |  ? [v2] :  ? [v3] : (multiplication(v1, v0) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) |  ~ (v2 = zero)))) &  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = one) | complement(v1, v0) |  ? [v2] :  ? [v3] : (multiplication(v1, v0) = v3 & multiplication(v0, v1) = v2 & ( ~ (v3 = zero) |  ~ (v2 = zero)))) &  ! [v0] :  ! [v1] : ( ~ complement(v1, v0) | test(v0)) &  ! [v0] : ( ~ test(v0) |  ? [v1] : complement(v1, v0))
% 3.67/1.52  |
% 3.67/1.52  | Applying alpha-rule on (1) yields:
% 3.67/1.52  | (2)  ! [v0] :  ! [v1] : ( ~ complement(v1, v0) | test(v0))
% 3.67/1.52  | (3)  ! [v0] : ( ~ test(v0) |  ? [v1] : complement(v1, v0))
% 3.67/1.52  | (4)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = zero |  ~ (multiplication(v0, v1) = v2) |  ~ complement(v1, v0))
% 3.67/1.52  | (5)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = one |  ~ (addition(v0, v1) = v2) |  ~ complement(v1, v0))
% 3.67/1.52  | (6)  ! [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))
% 3.67/1.52  | (7)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 3.67/1.52  | (8)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 3.67/1.52  | (9)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ~ complement(v1, v0) | (multiplication(v1, v0) = zero & addition(v0, v1) = one))
% 3.67/1.52  | (10)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v1, v0) = v2) |  ~ complement(v1, v0) | (multiplication(v0, v1) = zero & addition(v0, v1) = one))
% 3.67/1.53  | (11)  ! [v0] :  ! [v1] : ( ~ (multiplication(v0, v1) = zero) | complement(v1, v0) |  ? [v2] :  ? [v3] : (multiplication(v1, v0) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) |  ~ (v2 = zero))))
% 3.67/1.53  | (12)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 3.67/1.53  | (13)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(v0, zero) = v1))
% 3.67/1.53  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 3.67/1.53  | (15)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 3.67/1.53  | (16)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = zero |  ~ (multiplication(v1, v0) = v2) |  ~ complement(v1, v0))
% 3.67/1.53  | (17)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ~ leq(v0, v1))
% 3.67/1.53  | (18)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (c(v0) = v2) |  ~ complement(v0, v1) |  ~ test(v0))
% 3.67/1.53  | (19)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (c(v0) = v1) | test(v0))
% 3.67/1.53  | (20)  ~ (all_0_0_0 = one)
% 3.67/1.53  | (21)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) |  ~ complement(v1, v0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero))
% 3.67/1.53  | (22) test(all_0_2_2)
% 3.67/1.53  | (23)  ! [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))
% 3.67/1.53  | (24)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 3.67/1.53  | (25)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 3.67/1.53  | (26) addition(all_0_2_2, all_0_1_1) = all_0_0_0
% 3.67/1.53  | (27)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 3.67/1.53  | (28)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 3.67/1.53  | (29)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = one) | complement(v1, v0) |  ? [v2] :  ? [v3] : (multiplication(v1, v0) = v3 & multiplication(v0, v1) = v2 & ( ~ (v3 = zero) |  ~ (v2 = zero))))
% 3.67/1.53  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 3.67/1.53  | (31) c(all_0_2_2) = all_0_1_1
% 3.67/1.53  | (32)  ! [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))
% 3.67/1.53  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 3.67/1.53  | (34)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 3.67/1.53  | (35)  ! [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))
% 3.67/1.53  | (36)  ! [v0] :  ! [v1] : ( ~ (multiplication(v1, v0) = zero) | complement(v1, v0) |  ? [v2] :  ? [v3] : (multiplication(v0, v1) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) |  ~ (v2 = zero))))
% 3.67/1.53  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 3.67/1.54  | (38)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 3.67/1.54  | (39)  ! [v0] :  ! [v1] : ( ~ (c(v0) = v1) |  ~ test(v0) | complement(v0, v1))
% 3.67/1.54  | (40)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (c(v2) = v1) |  ~ (c(v2) = v0))
% 3.67/1.54  |
% 3.67/1.54  | Instantiating formula (25) with all_0_0_0, all_0_2_2, all_0_1_1 and discharging atoms addition(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 3.67/1.54  | (41) addition(all_0_1_1, all_0_2_2) = all_0_0_0
% 3.67/1.54  |
% 3.67/1.54  | Instantiating formula (39) with all_0_1_1, all_0_2_2 and discharging atoms c(all_0_2_2) = all_0_1_1, test(all_0_2_2), yields:
% 3.67/1.54  | (42) complement(all_0_2_2, all_0_1_1)
% 3.67/1.54  |
% 3.67/1.54  | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_0_1_1 and discharging atoms addition(all_0_1_1, all_0_2_2) = all_0_0_0, complement(all_0_2_2, all_0_1_1), yields:
% 3.67/1.54  | (43) all_0_0_0 = one
% 3.67/1.54  |
% 3.67/1.54  | Equations (43) can reduce 20 to:
% 3.67/1.54  | (44) $false
% 3.67/1.54  |
% 3.67/1.54  |-The branch is then unsatisfiable
% 3.67/1.54  % SZS output end Proof for theBenchmark
% 3.67/1.54  
% 3.67/1.54  947ms
%------------------------------------------------------------------------------