%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE056+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 01:51:10 EDT 2022

% Result   : Theorem 19.79s 6.27s
% Output   : Proof 20.80s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KLE056+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.14/0.34  % Computer : n014.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 14:01:20 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.20/0.59          ____       _                          
% 0.20/0.59    ___  / __ \_____(_)___  ________  __________
% 0.20/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.20/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.20/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.20/0.59  
% 0.20/0.59  A Theorem Prover for First-Order Logic
% 0.20/0.59  (ePrincess v.1.0)
% 0.20/0.59  
% 0.20/0.59  (c) Philipp Rümmer, 2009-2015
% 0.20/0.59  (c) Peter Backeman, 2014-2015
% 0.20/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.20/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.20/0.59  Bug reports to peter@backeman.se
% 0.20/0.59  
% 0.20/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.20/0.59  
% 0.20/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.67  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.57/0.95  Prover 0: Preprocessing ...
% 2.31/1.22  Prover 0: Constructing countermodel ...
% 18.63/5.96  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 18.63/5.99  Prover 1: Preprocessing ...
% 19.00/6.08  Prover 1: Constructing countermodel ...
% 19.43/6.18  Prover 1: gave up
% 19.43/6.18  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 19.79/6.20  Prover 2: Preprocessing ...
% 19.79/6.25  Prover 2: Warning: ignoring some quantifiers
% 19.79/6.25  Prover 2: Constructing countermodel ...
% 19.79/6.27  Prover 2: proved (86ms)
% 19.79/6.27  Prover 0: stopped
% 19.79/6.27  
% 19.79/6.27  No countermodel exists, formula is valid
% 19.79/6.27  % SZS status Theorem for theBenchmark
% 19.79/6.27  
% 19.79/6.27  Generating proof ... Warning: ignoring some quantifiers
% 20.41/6.40  found it (size 10)
% 20.41/6.40  
% 20.41/6.40  % SZS output start Proof for theBenchmark
% 20.41/6.40  Assumed formulas after preprocessing and simplification: 
% 20.41/6.40  | (0)  ? [v0] : ( ~ (v0 = zero) & domain(v0) = zero & domain(zero) = zero &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (multiplication(v2, v3) = v5) |  ~ (multiplication(v1, v3) = v4) |  ~ (addition(v4, v5) = v6) |  ? [v7] : (multiplication(v7, v3) = v6 & addition(v1, v2) = v7)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (multiplication(v1, v3) = v5) |  ~ (multiplication(v1, v2) = v4) |  ~ (addition(v4, v5) = v6) |  ? [v7] : (multiplication(v1, v7) = v6 & addition(v2, v3) = v7)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (domain(v2) = v4) |  ~ (domain(v1) = v3) |  ~ (addition(v3, v4) = v5) |  ? [v6] : (domain(v6) = v5 & addition(v1, v2) = v6)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v4, v3) = v5) |  ~ (multiplication(v1, v2) = v4) |  ? [v6] : (multiplication(v2, v3) = v6 & multiplication(v1, v6) = v5)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v4, v3) = v5) |  ~ (addition(v1, v2) = v4) |  ? [v6] :  ? [v7] : (multiplication(v2, v3) = v7 & multiplication(v1, v3) = v6 & addition(v6, v7) = v5)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v2, v3) = v4) |  ~ (multiplication(v1, v4) = v5) |  ? [v6] : (multiplication(v6, v3) = v5 & multiplication(v1, v2) = v6)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v1, v4) = v5) |  ~ (addition(v2, v3) = v4) |  ? [v6] :  ? [v7] : (multiplication(v1, v3) = v7 & multiplication(v1, v2) = v6 & addition(v6, v7) = v5)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (addition(v4, v1) = v5) |  ~ (addition(v3, v2) = v4) |  ? [v6] : (addition(v3, v6) = v5 & addition(v2, v1) = v6)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (addition(v3, v4) = v5) |  ~ (addition(v2, v1) = v4) |  ? [v6] : (addition(v6, v1) = v5 & addition(v3, v2) = v6)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (leq(v4, v3) = v2) |  ~ (leq(v4, v3) = v1)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (multiplication(v4, v3) = v2) |  ~ (multiplication(v4, v3) = v1)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (addition(v4, v3) = v2) |  ~ (addition(v4, v3) = v1)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (domain(v2) = v3) |  ~ (multiplication(v1, v3) = v4) |  ? [v5] :  ? [v6] : (domain(v5) = v6 & domain(v4) = v6 & multiplication(v1, v2) = v5)) &  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (addition(v1, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & leq(v1, v2) = v4)) &  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (leq(v1, v2) = v3) |  ? [v4] : ( ~ (v4 = v2) & addition(v1, v2) = v4)) &  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 |  ~ (domain(v3) = v2) |  ~ (domain(v3) = v1)) &  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (multiplication(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] : (domain(v6) = v4 & domain(v3) = v4 & domain(v2) = v5 & multiplication(v1, v5) = v6)) &  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (addition(v2, v1) = v3) | addition(v1, v2) = v3) &  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (addition(v1, v2) = v3) | addition(v2, v1) = v3) &  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (addition(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] : (domain(v3) = v4 & domain(v2) = v6 & domain(v1) = v5 & addition(v5, v6) = v4)) &  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (multiplication(v1, one) = v2)) &  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (multiplication(one, v1) = v2)) &  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v1, v1) = v2)) &  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v1, zero) = v2)) &  ! [v1] :  ! [v2] : (v2 = zero |  ~ (multiplication(v1, zero) = v2)) &  ! [v1] :  ! [v2] : (v2 = zero |  ~ (multiplication(zero, v1) = v2)) &  ! [v1] :  ! [v2] : ( ~ (domain(v1) = v2) | addition(v2, one) = one) &  ! [v1] :  ! [v2] : ( ~ (domain(v1) = v2) |  ? [v3] : (multiplication(v2, v1) = v3 & addition(v1, v3) = v3)) &  ! [v1] :  ! [v2] : ( ~ (leq(v1, v2) = 0) | addition(v1, v2) = v2) &  ! [v1] :  ! [v2] : ( ~ (addition(v1, v2) = v2) | leq(v1, v2) = 0) &  ? [v1] :  ? [v2] :  ? [v3] : leq(v2, v1) = v3 &  ? [v1] :  ? [v2] :  ? [v3] : multiplication(v2, v1) = v3 &  ? [v1] :  ? [v2] :  ? [v3] : addition(v2, v1) = v3 &  ? [v1] :  ? [v2] : domain(v1) = v2)
% 20.80/6.43  | Instantiating (0) with all_0_0_0 yields:
% 20.80/6.43  | (1)  ~ (all_0_0_0 = zero) & domain(all_0_0_0) = zero & domain(zero) = 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] : ( ~ (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] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0)) &  ! [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) |  ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (leq(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (domain(v2) = v1) |  ~ (domain(v2) = v0)) &  ! [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] : ( ~ (domain(v0) = v1) |  ? [v2] : (multiplication(v1, v0) = v2 & addition(v0, v2) = v2)) &  ! [v0] :  ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1) &  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0) &  ? [v0] :  ? [v1] :  ? [v2] : leq(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : multiplication(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : addition(v1, v0) = v2 &  ? [v0] :  ? [v1] : domain(v0) = v1
% 20.80/6.44  |
% 20.80/6.44  | Applying alpha-rule on (1) yields:
% 20.80/6.44  | (2)  ! [v0] :  ! [v1] : ( ~ (domain(v0) = v1) |  ? [v2] : (multiplication(v1, v0) = v2 & addition(v0, v2) = v2))
% 20.80/6.44  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (domain(v1) = v3) |  ~ (domain(v0) = v2) |  ~ (addition(v2, v3) = v4) |  ? [v5] : (domain(v5) = v4 & addition(v0, v1) = v5))
% 20.80/6.44  | (4)  ? [v0] :  ? [v1] :  ? [v2] : addition(v1, v0) = v2
% 20.80/6.44  | (5)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(v0, zero) = v1))
% 20.80/6.44  | (6)  ? [v0] :  ? [v1] :  ? [v2] : leq(v1, v0) = v2
% 20.80/6.44  | (7)  ? [v0] :  ? [v1] :  ? [v2] : multiplication(v1, v0) = v2
% 20.80/6.44  | (8)  ! [v0] :  ! [v1] : ( ~ (domain(v0) = v1) | addition(v1, one) = one)
% 20.80/6.44  | (9)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 20.80/6.44  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 20.80/6.44  | (11) domain(all_0_0_0) = zero
% 20.80/6.44  | (12)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 20.80/6.44  | (13)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 20.80/6.44  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 20.80/6.44  | (15)  ? [v0] :  ? [v1] : domain(v0) = v1
% 20.80/6.44  | (16)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0)
% 20.80/6.44  | (17)  ! [v0] :  ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1)
% 20.80/6.44  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (domain(v1) = v2) |  ~ (multiplication(v0, v2) = v3) |  ? [v4] :  ? [v5] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = v4))
% 20.80/6.44  | (19)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & multiplication(v0, v4) = v5))
% 20.80/6.44  | (20)  ~ (all_0_0_0 = zero)
% 20.80/6.44  | (21)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 20.80/6.44  | (22)  ! [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))
% 20.80/6.44  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0))
% 20.80/6.44  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 20.80/6.44  | (25)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 20.80/6.44  | (26)  ! [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))
% 20.80/6.44  | (27)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 20.80/6.44  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 20.80/6.44  | (29)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4, v5) = v3))
% 20.80/6.44  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 20.80/6.44  | (31) domain(zero) = zero
% 20.80/6.44  | (32)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (domain(v2) = v1) |  ~ (domain(v2) = v0))
% 20.80/6.44  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 20.80/6.45  | (34)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (leq(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3))
% 20.80/6.45  | (35)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 20.80/6.45  | (36)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3))
% 20.80/6.45  | (37)  ! [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))
% 20.80/6.45  | (38)  ! [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))
% 20.80/6.45  |
% 20.80/6.45  | Instantiating formula (2) with zero, all_0_0_0 and discharging atoms domain(all_0_0_0) = zero, yields:
% 20.80/6.45  | (39)  ? [v0] : (multiplication(zero, all_0_0_0) = v0 & addition(all_0_0_0, v0) = v0)
% 20.80/6.45  |
% 20.80/6.45  | Instantiating (39) with all_19_0_13 yields:
% 20.80/6.45  | (40) multiplication(zero, all_0_0_0) = all_19_0_13 & addition(all_0_0_0, all_19_0_13) = all_19_0_13
% 20.80/6.45  |
% 20.80/6.45  | Applying alpha-rule on (40) yields:
% 20.80/6.45  | (41) multiplication(zero, all_0_0_0) = all_19_0_13
% 20.80/6.45  | (42) addition(all_0_0_0, all_19_0_13) = all_19_0_13
% 20.80/6.45  |
% 20.80/6.45  | Instantiating formula (27) with all_19_0_13, all_0_0_0 and discharging atoms multiplication(zero, all_0_0_0) = all_19_0_13, yields:
% 20.80/6.45  | (43) all_19_0_13 = zero
% 20.80/6.45  |
% 20.80/6.45  | From (43)(43) and (42) follows:
% 20.80/6.45  | (44) addition(all_0_0_0, zero) = zero
% 20.80/6.45  |
% 20.80/6.45  | Instantiating formula (35) with zero, all_0_0_0 and discharging atoms addition(all_0_0_0, zero) = zero, yields:
% 20.80/6.45  | (45) all_0_0_0 = zero
% 20.80/6.45  |
% 20.80/6.45  | Equations (45) can reduce 20 to:
% 20.80/6.45  | (46) $false
% 20.80/6.45  |
% 20.80/6.45  |-The branch is then unsatisfiable
% 20.80/6.45  % SZS output end Proof for theBenchmark
% 20.80/6.45  
% 20.80/6.45  5842ms
%------------------------------------------------------------------------------