%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE059+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n015.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 01:51:11 EDT 2022

% Result   : Theorem 2.58s 1.31s
% Output   : Proof 3.95s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KLE059+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.34  % Computer : n015.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Thu Jun 16 08:30:41 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.58          ____       _                          
% 0.19/0.58    ___  / __ \_____(_)___  ________  __________
% 0.19/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.19/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.19/0.58  
% 0.19/0.58  A Theorem Prover for First-Order Logic
% 0.19/0.58  (ePrincess v.1.0)
% 0.19/0.58  
% 0.19/0.58  (c) Philipp Rümmer, 2009-2015
% 0.19/0.58  (c) Peter Backeman, 2014-2015
% 0.19/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58  Bug reports to peter@backeman.se
% 0.19/0.58  
% 0.19/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58  
% 0.19/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.75/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.65/0.93  Prover 0: Preprocessing ...
% 2.32/1.21  Prover 0: Constructing countermodel ...
% 2.58/1.31  Prover 0: proved (675ms)
% 2.58/1.31  
% 2.58/1.31  No countermodel exists, formula is valid
% 2.58/1.31  % SZS status Theorem for theBenchmark
% 2.58/1.31  
% 2.58/1.31  Generating proof ... found it (size 14)
% 3.79/1.52  
% 3.79/1.52  % SZS output start Proof for theBenchmark
% 3.79/1.52  Assumed formulas after preprocessing and simplification: 
% 3.79/1.52  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : ( ~ (v4 = v3) & domain(v1) = v3 & domain(v0) = v2 & domain(zero) = zero & addition(v2, v3) = v4 & addition(v0, v1) = v1 &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (multiplication(v6, v7) = v9) |  ~ (multiplication(v5, v7) = v8) |  ~ (addition(v8, v9) = v10) |  ? [v11] : (multiplication(v11, v7) = v10 & addition(v5, v6) = v11)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (multiplication(v5, v7) = v9) |  ~ (multiplication(v5, v6) = v8) |  ~ (addition(v8, v9) = v10) |  ? [v11] : (multiplication(v5, v11) = v10 & addition(v6, v7) = v11)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (domain(v6) = v8) |  ~ (domain(v5) = v7) |  ~ (addition(v7, v8) = v9) |  ? [v10] : (domain(v10) = v9 & addition(v5, v6) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (multiplication(v8, v7) = v9) |  ~ (multiplication(v5, v6) = v8) |  ? [v10] : (multiplication(v6, v7) = v10 & multiplication(v5, v10) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (multiplication(v8, v7) = v9) |  ~ (addition(v5, v6) = v8) |  ? [v10] :  ? [v11] : (multiplication(v6, v7) = v11 & multiplication(v5, v7) = v10 & addition(v10, v11) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (multiplication(v6, v7) = v8) |  ~ (multiplication(v5, v8) = v9) |  ? [v10] : (multiplication(v10, v7) = v9 & multiplication(v5, v6) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (multiplication(v5, v8) = v9) |  ~ (addition(v6, v7) = v8) |  ? [v10] :  ? [v11] : (multiplication(v5, v7) = v11 & multiplication(v5, v6) = v10 & addition(v10, v11) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (addition(v8, v5) = v9) |  ~ (addition(v7, v6) = v8) |  ? [v10] : (addition(v7, v10) = v9 & addition(v6, v5) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (addition(v7, v8) = v9) |  ~ (addition(v6, v5) = v8) |  ? [v10] : (addition(v10, v5) = v9 & addition(v7, v6) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = v7 |  ~ (domain(v5) = v6) |  ~ (multiplication(v6, v5) = v7) |  ~ (addition(v5, v7) = v8)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (multiplication(v8, v7) = v6) |  ~ (multiplication(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (addition(v8, v7) = v6) |  ~ (addition(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (domain(v6) = v7) |  ~ (multiplication(v5, v7) = v8) |  ? [v9] :  ? [v10] : (domain(v9) = v10 & domain(v8) = v10 & multiplication(v5, v6) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (addition(v5, v6) = v7) |  ~ leq(v5, v6)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (domain(v7) = v6) |  ~ (domain(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (domain(v5) = v6) |  ~ (multiplication(v6, v5) = v7) | addition(v5, v7) = v7) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (multiplication(v5, v6) = v7) |  ? [v8] :  ? [v9] :  ? [v10] : (domain(v10) = v8 & domain(v7) = v8 & domain(v6) = v9 & multiplication(v5, v9) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (addition(v6, v5) = v7) | addition(v5, v6) = v7) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (addition(v5, v6) = v7) | addition(v6, v5) = v7) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (addition(v5, v6) = v7) |  ? [v8] :  ? [v9] :  ? [v10] : (domain(v7) = v8 & domain(v6) = v10 & domain(v5) = v9 & addition(v9, v10) = v8)) &  ! [v5] :  ! [v6] : (v6 = v5 |  ~ (multiplication(v5, one) = v6)) &  ! [v5] :  ! [v6] : (v6 = v5 |  ~ (multiplication(one, v5) = v6)) &  ! [v5] :  ! [v6] : (v6 = v5 |  ~ (addition(v5, v5) = v6)) &  ! [v5] :  ! [v6] : (v6 = v5 |  ~ (addition(v5, zero) = v6)) &  ! [v5] :  ! [v6] : (v6 = zero |  ~ (multiplication(v5, zero) = v6)) &  ! [v5] :  ! [v6] : (v6 = zero |  ~ (multiplication(zero, v5) = v6)) &  ! [v5] :  ! [v6] : ( ~ (domain(v5) = v6) | addition(v6, one) = one) &  ! [v5] :  ! [v6] : ( ~ (addition(v5, v6) = v6) | leq(v5, v6)))
% 3.95/1.57  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 3.95/1.57  | (1)  ~ (all_0_0_0 = all_0_1_1) & domain(all_0_3_3) = all_0_1_1 & domain(all_0_4_4) = all_0_2_2 & domain(zero) = zero & addition(all_0_2_2, all_0_1_1) = all_0_0_0 & addition(all_0_4_4, all_0_3_3) = all_0_3_3 &  ! [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] : ( ~ (domain(v1) = v3) |  ~ (domain(v0) = v2) |  ~ (addition(v2, v3) = v4) |  ? [v5] : (domain(v5) = v4 & addition(v0, v1) = v5)) &  ! [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] : (v3 = v2 |  ~ (domain(v0) = v1) |  ~ (multiplication(v1, v0) = v2) |  ~ (addition(v0, v2) = v3)) &  ! [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] :  ! [v3] : ( ~ (domain(v1) = v2) |  ~ (multiplication(v0, v2) = v3) |  ? [v4] :  ? [v5] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ~ leq(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (domain(v2) = v1) |  ~ (domain(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (domain(v0) = v1) |  ~ (multiplication(v1, v0) = v2) | addition(v0, v2) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & multiplication(v0, v4) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4, v5) = v3)) &  ! [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(v0, zero) = v1)) &  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1)) &  ! [v0] :  ! [v1] : ( ~ (domain(v0) = v1) | addition(v1, one) = one) &  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 3.95/1.58  |
% 3.95/1.58  | Applying alpha-rule on (1) yields:
% 3.95/1.58  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (domain(v0) = v1) |  ~ (multiplication(v1, v0) = v2) |  ~ (addition(v0, v2) = v3))
% 3.95/1.58  | (3)  ! [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))
% 3.95/1.58  | (4)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 3.95/1.58  | (5)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(v0, zero) = v1))
% 3.95/1.58  | (6)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 3.95/1.58  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 3.95/1.58  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & multiplication(v0, v4) = v5))
% 3.95/1.58  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (domain(v1) = v2) |  ~ (multiplication(v0, v2) = v3) |  ? [v4] :  ? [v5] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = v4))
% 3.95/1.58  | (10) domain(all_0_4_4) = all_0_2_2
% 3.95/1.58  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 3.95/1.58  | (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))
% 3.95/1.58  | (13)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (domain(v2) = v1) |  ~ (domain(v2) = v0))
% 3.95/1.58  | (14)  ! [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))
% 3.95/1.58  | (15) addition(all_0_2_2, all_0_1_1) = all_0_0_0
% 3.95/1.58  | (16)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 3.95/1.58  | (17)  ~ (all_0_0_0 = all_0_1_1)
% 3.95/1.58  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 3.95/1.58  | (19)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 3.95/1.58  | (20) domain(all_0_3_3) = all_0_1_1
% 3.95/1.58  | (21)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ~ leq(v0, v1))
% 3.95/1.58  | (22)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 3.95/1.58  | (23)  ! [v0] :  ! [v1] : ( ~ (domain(v0) = v1) | addition(v1, one) = one)
% 3.95/1.58  | (24)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 3.95/1.59  | (25)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 3.95/1.59  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 3.95/1.59  | (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))
% 3.95/1.59  | (28)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4, v5) = v3))
% 3.95/1.59  | (29) domain(zero) = zero
% 3.95/1.59  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 3.95/1.59  | (31) addition(all_0_4_4, all_0_3_3) = all_0_3_3
% 3.95/1.59  | (32)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 3.95/1.59  | (33)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (domain(v0) = v1) |  ~ (multiplication(v1, v0) = v2) | addition(v0, v2) = v2)
% 3.95/1.59  | (34)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (domain(v1) = v3) |  ~ (domain(v0) = v2) |  ~ (addition(v2, v3) = v4) |  ? [v5] : (domain(v5) = v4 & addition(v0, v1) = v5))
% 3.95/1.59  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 3.95/1.59  |
% 3.95/1.59  | Instantiating formula (28) with all_0_3_3, all_0_3_3, all_0_4_4 and discharging atoms addition(all_0_4_4, all_0_3_3) = all_0_3_3, yields:
% 3.95/1.59  | (36)  ? [v0] :  ? [v1] :  ? [v2] : (domain(all_0_3_3) = v2 & domain(all_0_3_3) = v0 & domain(all_0_4_4) = v1 & addition(v1, v2) = v0)
% 3.95/1.59  |
% 3.95/1.59  | Instantiating (36) with all_11_0_6, all_11_1_7, all_11_2_8 yields:
% 3.95/1.59  | (37) domain(all_0_3_3) = all_11_0_6 & domain(all_0_3_3) = all_11_2_8 & domain(all_0_4_4) = all_11_1_7 & addition(all_11_1_7, all_11_0_6) = all_11_2_8
% 3.95/1.59  |
% 3.95/1.59  | Applying alpha-rule on (37) yields:
% 3.95/1.59  | (38) domain(all_0_3_3) = all_11_0_6
% 3.95/1.59  | (39) domain(all_0_3_3) = all_11_2_8
% 3.95/1.59  | (40) domain(all_0_4_4) = all_11_1_7
% 3.95/1.59  | (41) addition(all_11_1_7, all_11_0_6) = all_11_2_8
% 3.95/1.59  |
% 3.95/1.59  | Instantiating formula (13) with all_0_3_3, all_11_0_6, all_0_1_1 and discharging atoms domain(all_0_3_3) = all_11_0_6, domain(all_0_3_3) = all_0_1_1, yields:
% 3.95/1.59  | (42) all_11_0_6 = all_0_1_1
% 3.95/1.59  |
% 3.95/1.59  | Instantiating formula (13) with all_0_3_3, all_11_2_8, all_11_0_6 and discharging atoms domain(all_0_3_3) = all_11_0_6, domain(all_0_3_3) = all_11_2_8, yields:
% 3.95/1.59  | (43) all_11_0_6 = all_11_2_8
% 3.95/1.59  |
% 3.95/1.59  | Instantiating formula (13) with all_0_4_4, all_11_1_7, all_0_2_2 and discharging atoms domain(all_0_4_4) = all_11_1_7, domain(all_0_4_4) = all_0_2_2, yields:
% 3.95/1.59  | (44) all_11_1_7 = all_0_2_2
% 3.95/1.59  |
% 3.95/1.59  | Combining equations (42,43) yields a new equation:
% 3.95/1.59  | (45) all_11_2_8 = all_0_1_1
% 3.95/1.59  |
% 3.95/1.59  | Combining equations (45,43) yields a new equation:
% 3.95/1.59  | (42) all_11_0_6 = all_0_1_1
% 3.95/1.59  |
% 3.95/1.59  | From (44)(42)(45) and (41) follows:
% 3.95/1.60  | (47) addition(all_0_2_2, all_0_1_1) = all_0_1_1
% 3.95/1.60  |
% 3.95/1.60  | Instantiating formula (7) with all_0_2_2, all_0_1_1, all_0_1_1, all_0_0_0 and discharging atoms addition(all_0_2_2, all_0_1_1) = all_0_0_0, addition(all_0_2_2, all_0_1_1) = all_0_1_1, yields:
% 3.95/1.60  | (48) all_0_0_0 = all_0_1_1
% 3.95/1.60  |
% 3.95/1.60  | Equations (48) can reduce 17 to:
% 3.95/1.60  | (49) $false
% 3.95/1.60  |
% 3.95/1.60  |-The branch is then unsatisfiable
% 3.95/1.60  % SZS output end Proof for theBenchmark
% 3.95/1.60  
% 3.95/1.60  1003ms
%------------------------------------------------------------------------------