%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : NUM839+1 : TPTP v8.1.0. Released v4.1.0.
% 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 : Mon Jul 18 08:49:02 EDT 2022

% Result   : Theorem 20.77s 6.13s
% Output   : Proof 22.28s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM839+1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n010.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 : Wed Jul  6 08:48:32 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.43/0.62          ____       _                          
% 0.43/0.62    ___  / __ \_____(_)___  ________  __________
% 0.43/0.62   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.43/0.62  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.43/0.62  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.43/0.62  
% 0.43/0.62  A Theorem Prover for First-Order Logic
% 0.67/0.62  (ePrincess v.1.0)
% 0.67/0.62  
% 0.67/0.62  (c) Philipp Rümmer, 2009-2015
% 0.67/0.62  (c) Peter Backeman, 2014-2015
% 0.67/0.62  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.67/0.62  Free software under GNU Lesser General Public License (LGPL).
% 0.67/0.62  Bug reports to peter@backeman.se
% 0.67/0.62  
% 0.67/0.62  For more information, visit http://user.uu.se/~petba168/breu/
% 0.67/0.62  
% 0.67/0.63  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.67  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.70/0.97  Prover 0: Preprocessing ...
% 2.47/1.23  Prover 0: Warning: ignoring some quantifiers
% 2.47/1.25  Prover 0: Constructing countermodel ...
% 20.04/5.96  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 20.04/5.99  Prover 1: Preprocessing ...
% 20.43/6.07  Prover 1: Warning: ignoring some quantifiers
% 20.43/6.08  Prover 1: Constructing countermodel ...
% 20.77/6.12  Prover 1: proved (158ms)
% 20.77/6.13  Prover 0: stopped
% 20.77/6.13  
% 20.77/6.13  No countermodel exists, formula is valid
% 20.77/6.13  % SZS status Theorem for theBenchmark
% 20.77/6.13  
% 20.77/6.13  Generating proof ... Warning: ignoring some quantifiers
% 21.87/6.39  found it (size 34)
% 21.87/6.39  
% 21.87/6.39  % SZS output start Proof for theBenchmark
% 21.87/6.39  Assumed formulas after preprocessing and simplification: 
% 21.87/6.39  | (0)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & greater(v0, v1) = 0 & greater(vd328, vd329) = v2 & vplus(vd329, vd330) = v1 & vplus(vd328, vd330) = v0 &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (greater(v6, v7) = v8) |  ~ (vplus(v4, v5) = v7) |  ~ (vplus(v3, v5) = v6) |  ? [v9] : ( ~ (v9 = 0) & greater(v3, v4) = v9)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (vplus(v4, v5) = v7) |  ~ (vplus(v3, v5) = v6) |  ~ (less(v6, v7) = v8) |  ? [v9] : ( ~ (v9 = 0) & less(v3, v4) = v9)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (leq(v4, v5) = v7) |  ~ (leq(v3, v4) = v6) |  ? [v8] :  ? [v9] :  ? [v10] : (less(v4, v5) = v8 & less(v3, v5) = v10 & less(v3, v4) = v9 & (v10 = 0 | (( ~ (v9 = 0) |  ~ (v7 = 0)) & ( ~ (v8 = 0) |  ~ (v6 = 0)))))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (vplus(v6, v5) = v7) |  ~ (vplus(v3, v4) = v6) |  ? [v8] : (vplus(v4, v5) = v8 & vplus(v3, v8) = v7)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = v5 |  ~ (vplus(v3, v4) = v6) |  ~ (vplus(v3, v4) = v5)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (leq(v3, v5) = v6) |  ~ (leq(v3, v4) = 0) |  ? [v7] : ( ~ (v7 = 0) & leq(v4, v5) = v7)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (greater(v5, v3) = v6) |  ~ (vplus(v3, v4) = v5)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (less(v3, v5) = v6) |  ~ (less(v3, v4) = 0) |  ? [v7] : ( ~ (v7 = 0) & less(v4, v5) = v7)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v5 = 0 |  ~ (greater(v4, v3) = v5) |  ~ (vplus(v3, v6) = v4)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v5 = 0 |  ~ (vplus(v4, v6) = v3) |  ~ (less(v4, v3) = v5)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (geq(v6, v5) = v4) |  ~ (geq(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (leq(v6, v5) = v4) |  ~ (leq(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (greater(v6, v5) = v4) |  ~ (greater(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (vplus(v6, v5) = v4) |  ~ (vplus(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (less(v6, v5) = v4) |  ~ (less(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (vsucc(v4) = v5) |  ~ (vplus(v3, v5) = v6) |  ? [v7] : (vsucc(v7) = v6 & vplus(v3, v4) = v7)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (vsucc(v3) = v5) |  ~ (vplus(v5, v4) = v6) |  ? [v7] : (vsucc(v7) = v6 & vplus(v3, v4) = v7)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (vplus(v4, v6) = v3) |  ~ (vplus(v3, v5) = v4)) &  ? [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (vplus(v5, v4) = v6) |  ? [v7] : ( ~ (v7 = v6) & vplus(v5, v3) = v7)) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = v3 |  ~ (greater(v3, v4) = v5) | less(v3, v4) = 0) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (geq(v4, v3) = v5) |  ? [v6] : ( ~ (v6 = 0) & leq(v3, v4) = v6)) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (geq(v4, v3) = v5) |  ? [v6] : ( ~ (v6 = 0) & greater(v4, v3) = v6)) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (leq(v4, v3) = v5) |  ? [v6] : ( ~ (v6 = 0) & less(v4, v3) = v6)) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (greater(v4, v3) = v5) |  ? [v6] : ( ~ (v6 = 0) & less(v3, v4) = v6)) &  ! [v3] :  ! [v4] :  ! [v5] : (v4 = v3 |  ~ (vskolem2(v5) = v4) |  ~ (vskolem2(v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] : (v4 = v3 |  ~ (vsucc(v5) = v4) |  ~ (vsucc(v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] : (v4 = v3 |  ~ (vsucc(v4) = v5) |  ~ (vsucc(v3) = v5)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (vplus(v3, v4) = v5) | vplus(v4, v3) = v5) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (geq(v4, v3) = 0) | greater(v4, v3) = 0) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (leq(v4, v3) = 0) | less(v4, v3) = 0) &  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (geq(v3, v3) = v4)) &  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (leq(v3, v3) = v4)) &  ! [v3] :  ! [v4] : (v3 = v1 |  ~ (vskolem2(v3) = v4) | vsucc(v4) = v3) &  ! [v3] :  ! [v4] : ( ~ (geq(v3, v4) = 0) | leq(v4, v3) = 0) &  ! [v3] :  ! [v4] : ( ~ (greater(v4, v3) = 0) |  ? [v5] : vplus(v3, v5) = v4) &  ! [v3] :  ! [v4] : ( ~ (greater(v3, v4) = 0) | less(v4, v3) = 0) &  ! [v3] :  ! [v4] : ( ~ (greater(v3, v4) = 0) |  ? [v5] : ( ~ (v5 = 0) & less(v3, v4) = v5)) &  ! [v3] :  ! [v4] :  ~ (vplus(v3, v4) = v4) &  ! [v3] :  ! [v4] :  ~ (vplus(v3, v4) = v3) &  ! [v3] :  ! [v4] : ( ~ (vplus(v3, v1) = v4) | vsucc(v3) = v4) &  ! [v3] :  ! [v4] : ( ~ (vplus(v1, v3) = v4) | vsucc(v3) = v4) &  ! [v3] :  ! [v4] : ( ~ (less(v4, v3) = 0) |  ? [v5] : vplus(v4, v5) = v3) &  ! [v3] :  ~ (vsucc(v3) = v3) &  ! [v3] :  ~ (vsucc(v3) = v1) &  ! [v3] :  ~ (greater(v3, v3) = 0) &  ! [v3] :  ~ (less(v3, v3) = 0) &  ? [v3] :  ? [v4] : (v4 = v3 |  ? [v5] :  ? [v6] : ((v6 = v4 & vplus(v3, v5) = v4) | (v6 = v3 & vplus(v4, v5) = v3))))
% 22.28/6.43  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 22.28/6.43  | (1)  ~ (all_0_0_0 = 0) & greater(all_0_2_2, all_0_1_1) = 0 & greater(vd328, vd329) = all_0_0_0 & vplus(vd329, vd330) = all_0_1_1 & vplus(vd328, vd330) = all_0_2_2 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (greater(v3, v4) = v5) |  ~ (vplus(v1, v2) = v4) |  ~ (vplus(v0, v2) = v3) |  ? [v6] : ( ~ (v6 = 0) & greater(v0, v1) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (vplus(v1, v2) = v4) |  ~ (vplus(v0, v2) = v3) |  ~ (less(v3, v4) = v5) |  ? [v6] : ( ~ (v6 = 0) & less(v0, v1) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (leq(v1, v2) = v4) |  ~ (leq(v0, v1) = v3) |  ? [v5] :  ? [v6] :  ? [v7] : (less(v1, v2) = v5 & less(v0, v2) = v7 & less(v0, v1) = v6 & (v7 = 0 | (( ~ (v6 = 0) |  ~ (v4 = 0)) & ( ~ (v5 = 0) |  ~ (v3 = 0)))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (vplus(v3, v2) = v4) |  ~ (vplus(v0, v1) = v3) |  ? [v5] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (vplus(v0, v1) = v3) |  ~ (vplus(v0, v1) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (leq(v0, v2) = v3) |  ~ (leq(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & leq(v1, v2) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (greater(v2, v0) = v3) |  ~ (vplus(v0, v1) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (less(v0, v2) = v3) |  ~ (less(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & less(v1, v2) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = 0 |  ~ (greater(v1, v0) = v2) |  ~ (vplus(v0, v3) = v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = 0 |  ~ (vplus(v1, v3) = v0) |  ~ (less(v1, v0) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (geq(v3, v2) = v1) |  ~ (geq(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (greater(v3, v2) = v1) |  ~ (greater(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (vplus(v3, v2) = v1) |  ~ (vplus(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (less(v3, v2) = v1) |  ~ (less(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (vsucc(v1) = v2) |  ~ (vplus(v0, v2) = v3) |  ? [v4] : (vsucc(v4) = v3 & vplus(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (vsucc(v0) = v2) |  ~ (vplus(v2, v1) = v3) |  ? [v4] : (vsucc(v4) = v3 & vplus(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (vplus(v1, v3) = v0) |  ~ (vplus(v0, v2) = v1)) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (vplus(v2, v1) = v3) |  ? [v4] : ( ~ (v4 = v3) & vplus(v2, v0) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 | v1 = v0 |  ~ (greater(v0, v1) = v2) | less(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (geq(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (geq(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & greater(v1, v0) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (leq(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & less(v1, v0) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (greater(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & less(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (vskolem2(v2) = v1) |  ~ (vskolem2(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (vsucc(v2) = v1) |  ~ (vsucc(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (vsucc(v1) = v2) |  ~ (vsucc(v0) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (vplus(v0, v1) = v2) | vplus(v1, v0) = v2) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (geq(v1, v0) = 0) | greater(v1, v0) = 0) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (leq(v1, v0) = 0) | less(v1, v0) = 0) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (geq(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (leq(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v0 = v1 |  ~ (vskolem2(v0) = v1) | vsucc(v1) = v0) &  ! [v0] :  ! [v1] : ( ~ (geq(v0, v1) = 0) | leq(v1, v0) = 0) &  ! [v0] :  ! [v1] : ( ~ (greater(v1, v0) = 0) |  ? [v2] : vplus(v0, v2) = v1) &  ! [v0] :  ! [v1] : ( ~ (greater(v0, v1) = 0) | less(v1, v0) = 0) &  ! [v0] :  ! [v1] : ( ~ (greater(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & less(v0, v1) = v2)) &  ! [v0] :  ! [v1] :  ~ (vplus(v0, v1) = v1) &  ! [v0] :  ! [v1] :  ~ (vplus(v0, v1) = v0) &  ! [v0] :  ! [v1] : ( ~ (vplus(v0, v1) = v1) | vsucc(v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (vplus(v1, v0) = v1) | vsucc(v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (less(v1, v0) = 0) |  ? [v2] : vplus(v1, v2) = v0) &  ! [v0] :  ~ (vsucc(v0) = v0) &  ! [v0] :  ~ (vsucc(v0) = v1) &  ! [v0] :  ~ (greater(v0, v0) = 0) &  ! [v0] :  ~ (less(v0, v0) = 0) &  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] :  ? [v3] : ((v3 = v1 & vplus(v0, v2) = v1) | (v3 = v0 & vplus(v1, v2) = v0)))
% 22.28/6.44  |
% 22.28/6.45  | Applying alpha-rule on (1) yields:
% 22.28/6.45  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (geq(v3, v2) = v1) |  ~ (geq(v3, v2) = v0))
% 22.28/6.45  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (leq(v0, v2) = v3) |  ~ (leq(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & leq(v1, v2) = v4))
% 22.28/6.45  | (4)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (leq(v0, v0) = v1))
% 22.28/6.45  | (5)  ! [v0] :  ~ (vsucc(v0) = v1)
% 22.28/6.45  | (6)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (vplus(v2, v1) = v3) |  ? [v4] : ( ~ (v4 = v3) & vplus(v2, v0) = v4))
% 22.28/6.45  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (vplus(v0, v1) = v3) |  ~ (vplus(v0, v1) = v2))
% 22.28/6.45  | (8)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (greater(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & less(v0, v1) = v3))
% 22.28/6.45  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (vsucc(v1) = v2) |  ~ (vplus(v0, v2) = v3) |  ? [v4] : (vsucc(v4) = v3 & vplus(v0, v1) = v4))
% 22.28/6.45  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (leq(v1, v2) = v4) |  ~ (leq(v0, v1) = v3) |  ? [v5] :  ? [v6] :  ? [v7] : (less(v1, v2) = v5 & less(v0, v2) = v7 & less(v0, v1) = v6 & (v7 = 0 | (( ~ (v6 = 0) |  ~ (v4 = 0)) & ( ~ (v5 = 0) |  ~ (v3 = 0))))))
% 22.28/6.45  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (greater(v3, v4) = v5) |  ~ (vplus(v1, v2) = v4) |  ~ (vplus(v0, v2) = v3) |  ? [v6] : ( ~ (v6 = 0) & greater(v0, v1) = v6))
% 22.28/6.45  | (12)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (geq(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & greater(v1, v0) = v3))
% 22.28/6.45  | (13)  ! [v0] :  ! [v1] : ( ~ (less(v1, v0) = 0) |  ? [v2] : vplus(v1, v2) = v0)
% 22.28/6.45  | (14)  ! [v0] :  ! [v1] : ( ~ (geq(v0, v1) = 0) | leq(v1, v0) = 0)
% 22.28/6.45  | (15)  ! [v0] :  ~ (greater(v0, v0) = 0)
% 22.28/6.45  | (16)  ~ (all_0_0_0 = 0)
% 22.28/6.45  | (17)  ! [v0] :  ~ (vsucc(v0) = v0)
% 22.28/6.45  | (18)  ! [v0] :  ! [v1] : (v0 = v1 |  ~ (vskolem2(v0) = v1) | vsucc(v1) = v0)
% 22.28/6.45  | (19)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 | v1 = v0 |  ~ (greater(v0, v1) = v2) | less(v0, v1) = 0)
% 22.28/6.45  | (20)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (geq(v1, v0) = 0) | greater(v1, v0) = 0)
% 22.28/6.45  | (21)  ! [v0] :  ! [v1] : ( ~ (greater(v0, v1) = 0) | less(v1, v0) = 0)
% 22.28/6.45  | (22)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (leq(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & less(v1, v0) = v3))
% 22.28/6.45  | (23)  ! [v0] :  ! [v1] :  ~ (vplus(v0, v1) = v1)
% 22.28/6.45  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0))
% 22.28/6.45  | (25)  ! [v0] :  ! [v1] : ( ~ (vplus(v0, v1) = v1) | vsucc(v0) = v1)
% 22.28/6.45  | (26)  ! [v0] :  ! [v1] :  ~ (vplus(v0, v1) = v0)
% 22.28/6.45  | (27)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (vsucc(v1) = v2) |  ~ (vsucc(v0) = v2))
% 22.28/6.45  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (less(v3, v2) = v1) |  ~ (less(v3, v2) = v0))
% 22.28/6.45  | (29)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (geq(v0, v0) = v1))
% 22.28/6.45  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (less(v0, v2) = v3) |  ~ (less(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & less(v1, v2) = v4))
% 22.28/6.45  | (31)  ! [v0] :  ! [v1] : ( ~ (greater(v1, v0) = 0) |  ? [v2] : vplus(v0, v2) = v1)
% 22.28/6.45  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (vplus(v3, v2) = v4) |  ~ (vplus(v0, v1) = v3) |  ? [v5] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4))
% 22.28/6.46  | (33)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (leq(v1, v0) = 0) | less(v1, v0) = 0)
% 22.28/6.46  | (34)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = 0 |  ~ (vplus(v1, v3) = v0) |  ~ (less(v1, v0) = v2))
% 22.28/6.46  | (35) greater(vd328, vd329) = all_0_0_0
% 22.28/6.46  | (36)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (vskolem2(v2) = v1) |  ~ (vskolem2(v2) = v0))
% 22.28/6.46  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (vplus(v3, v2) = v1) |  ~ (vplus(v3, v2) = v0))
% 22.28/6.46  | (38)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (vsucc(v0) = v2) |  ~ (vplus(v2, v1) = v3) |  ? [v4] : (vsucc(v4) = v3 & vplus(v0, v1) = v4))
% 22.28/6.46  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = 0 |  ~ (greater(v1, v0) = v2) |  ~ (vplus(v0, v3) = v1))
% 22.28/6.46  | (40)  ! [v0] :  ! [v1] : ( ~ (greater(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & less(v0, v1) = v2))
% 22.28/6.46  | (41)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (vplus(v0, v1) = v2) | vplus(v1, v0) = v2)
% 22.28/6.46  | (42)  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] :  ? [v3] : ((v3 = v1 & vplus(v0, v2) = v1) | (v3 = v0 & vplus(v1, v2) = v0)))
% 22.28/6.46  | (43)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (greater(v2, v0) = v3) |  ~ (vplus(v0, v1) = v2))
% 22.28/6.46  | (44)  ! [v0] :  ! [v1] : ( ~ (vplus(v1, v0) = v1) | vsucc(v0) = v1)
% 22.28/6.46  | (45)  ! [v0] :  ~ (less(v0, v0) = 0)
% 22.28/6.46  | (46)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (vplus(v1, v3) = v0) |  ~ (vplus(v0, v2) = v1))
% 22.28/6.46  | (47) greater(all_0_2_2, all_0_1_1) = 0
% 22.28/6.46  | (48)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (greater(v3, v2) = v1) |  ~ (greater(v3, v2) = v0))
% 22.28/6.46  | (49) vplus(vd328, vd330) = all_0_2_2
% 22.28/6.46  | (50) vplus(vd329, vd330) = all_0_1_1
% 22.28/6.46  | (51)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (vsucc(v2) = v1) |  ~ (vsucc(v2) = v0))
% 22.28/6.46  | (52)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (geq(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3))
% 22.28/6.46  | (53)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (vplus(v1, v2) = v4) |  ~ (vplus(v0, v2) = v3) |  ~ (less(v3, v4) = v5) |  ? [v6] : ( ~ (v6 = 0) & less(v0, v1) = v6))
% 22.28/6.46  |
% 22.28/6.46  | Instantiating formula (15) with all_0_2_2 yields:
% 22.28/6.46  | (54)  ~ (greater(all_0_2_2, all_0_2_2) = 0)
% 22.28/6.46  |
% 22.28/6.46  | Using (47) and (54) yields:
% 22.28/6.46  | (55)  ~ (all_0_1_1 = all_0_2_2)
% 22.28/6.46  |
% 22.28/6.46  | Instantiating formula (40) with all_0_1_1, all_0_2_2 and discharging atoms greater(all_0_2_2, all_0_1_1) = 0, yields:
% 22.28/6.46  | (56)  ? [v0] : ( ~ (v0 = 0) & less(all_0_2_2, all_0_1_1) = v0)
% 22.28/6.46  |
% 22.28/6.46  | Instantiating formula (19) with all_0_0_0, vd329, vd328 and discharging atoms greater(vd328, vd329) = all_0_0_0, yields:
% 22.28/6.46  | (57) all_0_0_0 = 0 | vd329 = vd328 | less(vd328, vd329) = 0
% 22.28/6.46  |
% 22.28/6.46  | Instantiating formula (8) with all_0_0_0, vd328, vd329 and discharging atoms greater(vd328, vd329) = all_0_0_0, yields:
% 22.28/6.46  | (58) all_0_0_0 = 0 |  ? [v0] : ( ~ (v0 = 0) & less(vd329, vd328) = v0)
% 22.28/6.46  |
% 22.28/6.47  | Instantiating formula (41) with all_0_1_1, vd330, vd329 and discharging atoms vplus(vd329, vd330) = all_0_1_1, yields:
% 22.28/6.47  | (59) vplus(vd330, vd329) = all_0_1_1
% 22.28/6.47  |
% 22.28/6.47  | Instantiating formula (41) with all_0_2_2, vd330, vd328 and discharging atoms vplus(vd328, vd330) = all_0_2_2, yields:
% 22.28/6.47  | (60) vplus(vd330, vd328) = all_0_2_2
% 22.28/6.47  |
% 22.28/6.47  | Instantiating (56) with all_24_0_6 yields:
% 22.28/6.47  | (61)  ~ (all_24_0_6 = 0) & less(all_0_2_2, all_0_1_1) = all_24_0_6
% 22.28/6.47  |
% 22.28/6.47  | Applying alpha-rule on (61) yields:
% 22.28/6.47  | (62)  ~ (all_24_0_6 = 0)
% 22.28/6.47  | (63) less(all_0_2_2, all_0_1_1) = all_24_0_6
% 22.28/6.47  |
% 22.28/6.47  +-Applying beta-rule and splitting (58), into two cases.
% 22.28/6.47  |-Branch one:
% 22.28/6.47  | (64) all_0_0_0 = 0
% 22.28/6.47  |
% 22.28/6.47  	| Equations (64) can reduce 16 to:
% 22.28/6.47  	| (65) $false
% 22.28/6.47  	|
% 22.28/6.47  	|-The branch is then unsatisfiable
% 22.28/6.47  |-Branch two:
% 22.28/6.47  | (16)  ~ (all_0_0_0 = 0)
% 22.28/6.47  | (67)  ? [v0] : ( ~ (v0 = 0) & less(vd329, vd328) = v0)
% 22.28/6.47  |
% 22.28/6.47  	| Instantiating formula (7) with all_0_2_2, all_0_1_1, vd328, vd330 and discharging atoms vplus(vd330, vd328) = all_0_2_2, yields:
% 22.28/6.47  	| (68) all_0_1_1 = all_0_2_2 |  ~ (vplus(vd330, vd328) = all_0_1_1)
% 22.28/6.47  	|
% 22.28/6.47  	| Instantiating formula (53) with all_24_0_6, all_0_1_1, all_0_2_2, vd330, vd329, vd328 and discharging atoms vplus(vd329, vd330) = all_0_1_1, vplus(vd328, vd330) = all_0_2_2, less(all_0_2_2, all_0_1_1) = all_24_0_6, yields:
% 22.28/6.47  	| (69) all_24_0_6 = 0 |  ? [v0] : ( ~ (v0 = 0) & less(vd328, vd329) = v0)
% 22.28/6.47  	|
% 22.28/6.47  	+-Applying beta-rule and splitting (69), into two cases.
% 22.28/6.47  	|-Branch one:
% 22.28/6.47  	| (70) all_24_0_6 = 0
% 22.28/6.47  	|
% 22.28/6.47  		| Equations (70) can reduce 62 to:
% 22.28/6.47  		| (65) $false
% 22.28/6.47  		|
% 22.28/6.47  		|-The branch is then unsatisfiable
% 22.28/6.47  	|-Branch two:
% 22.28/6.47  	| (62)  ~ (all_24_0_6 = 0)
% 22.28/6.47  	| (73)  ? [v0] : ( ~ (v0 = 0) & less(vd328, vd329) = v0)
% 22.28/6.47  	|
% 22.28/6.47  		| Instantiating (73) with all_62_0_12 yields:
% 22.28/6.47  		| (74)  ~ (all_62_0_12 = 0) & less(vd328, vd329) = all_62_0_12
% 22.28/6.47  		|
% 22.28/6.47  		| Applying alpha-rule on (74) yields:
% 22.28/6.47  		| (75)  ~ (all_62_0_12 = 0)
% 22.28/6.47  		| (76) less(vd328, vd329) = all_62_0_12
% 22.28/6.47  		|
% 22.28/6.47  		+-Applying beta-rule and splitting (57), into two cases.
% 22.28/6.47  		|-Branch one:
% 22.28/6.47  		| (77) less(vd328, vd329) = 0
% 22.28/6.47  		|
% 22.28/6.47  			| Instantiating formula (28) with vd328, vd329, 0, all_62_0_12 and discharging atoms less(vd328, vd329) = all_62_0_12, less(vd328, vd329) = 0, yields:
% 22.28/6.47  			| (78) all_62_0_12 = 0
% 22.28/6.47  			|
% 22.28/6.47  			| Equations (78) can reduce 75 to:
% 22.28/6.47  			| (65) $false
% 22.28/6.47  			|
% 22.28/6.47  			|-The branch is then unsatisfiable
% 22.28/6.47  		|-Branch two:
% 22.28/6.47  		| (80)  ~ (less(vd328, vd329) = 0)
% 22.28/6.47  		| (81) all_0_0_0 = 0 | vd329 = vd328
% 22.28/6.47  		|
% 22.28/6.47  			+-Applying beta-rule and splitting (81), into two cases.
% 22.28/6.47  			|-Branch one:
% 22.28/6.47  			| (64) all_0_0_0 = 0
% 22.28/6.47  			|
% 22.28/6.47  				| Equations (64) can reduce 16 to:
% 22.28/6.47  				| (65) $false
% 22.28/6.47  				|
% 22.28/6.47  				|-The branch is then unsatisfiable
% 22.28/6.47  			|-Branch two:
% 22.28/6.47  			| (16)  ~ (all_0_0_0 = 0)
% 22.28/6.47  			| (85) vd329 = vd328
% 22.28/6.47  			|
% 22.28/6.47  				| From (85) and (59) follows:
% 22.28/6.47  				| (86) vplus(vd330, vd328) = all_0_1_1
% 22.28/6.47  				|
% 22.28/6.47  				+-Applying beta-rule and splitting (68), into two cases.
% 22.28/6.47  				|-Branch one:
% 22.28/6.47  				| (87)  ~ (vplus(vd330, vd328) = all_0_1_1)
% 22.28/6.47  				|
% 22.28/6.47  					| Using (86) and (87) yields:
% 22.28/6.47  					| (88) $false
% 22.28/6.47  					|
% 22.28/6.47  					|-The branch is then unsatisfiable
% 22.28/6.47  				|-Branch two:
% 22.28/6.47  				| (86) vplus(vd330, vd328) = all_0_1_1
% 22.28/6.47  				| (90) all_0_1_1 = all_0_2_2
% 22.28/6.47  				|
% 22.28/6.47  					| Equations (90) can reduce 55 to:
% 22.28/6.47  					| (65) $false
% 22.28/6.47  					|
% 22.28/6.47  					|-The branch is then unsatisfiable
% 22.28/6.47  % SZS output end Proof for theBenchmark
% 22.28/6.48  
% 22.28/6.48  5840ms
%------------------------------------------------------------------------------