%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : NUM840+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n017.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 19.64s 6.17s
% Output   : Proof 21.03s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : NUM840+1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.34  % Computer : n017.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 : Wed Jul  6 23:38:44 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.52/0.59          ____       _                          
% 0.52/0.59    ___  / __ \_____(_)___  ________  __________
% 0.52/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.52/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.52/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.52/0.59  
% 0.52/0.59  A Theorem Prover for First-Order Logic
% 0.52/0.59  (ePrincess v.1.0)
% 0.52/0.59  
% 0.52/0.59  (c) Philipp Rümmer, 2009-2015
% 0.52/0.59  (c) Peter Backeman, 2014-2015
% 0.52/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.52/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.52/0.59  Bug reports to peter@backeman.se
% 0.52/0.59  
% 0.52/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.52/0.59  
% 0.52/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.78/0.99  Prover 0: Preprocessing ...
% 2.59/1.26  Prover 0: Warning: ignoring some quantifiers
% 2.59/1.29  Prover 0: Constructing countermodel ...
% 18.51/5.93  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 18.64/5.98  Prover 1: Preprocessing ...
% 19.17/6.11  Prover 1: Warning: ignoring some quantifiers
% 19.17/6.12  Prover 1: Constructing countermodel ...
% 19.64/6.16  Prover 1: proved (234ms)
% 19.64/6.17  Prover 0: stopped
% 19.64/6.17  
% 19.64/6.17  No countermodel exists, formula is valid
% 19.64/6.17  % SZS status Theorem for theBenchmark
% 19.64/6.17  
% 19.64/6.17  Generating proof ... Warning: ignoring some quantifiers
% 20.57/6.41  found it (size 43)
% 20.57/6.41  
% 20.57/6.41  % SZS output start Proof for theBenchmark
% 20.57/6.41  Assumed formulas after preprocessing and simplification: 
% 20.57/6.41  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & greater(v0, v1) = v2 & greater(vd328, vd329) = v3 & vplus(vd329, vd330) = v1 & vplus(vd328, vd330) = v0 & less(v0, v1) = 0 & less(vd328, vd329) = v4 &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (greater(v8, v9) = v10) |  ~ (vplus(v6, v7) = v9) |  ~ (vplus(v5, v7) = v8) |  ? [v11] : ( ~ (v11 = 0) & greater(v5, v6) = v11)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (vplus(v6, v7) = v9) |  ~ (vplus(v5, v7) = v8) |  ~ (less(v8, v9) = v10) |  ? [v11] : ( ~ (v11 = 0) & less(v5, v6) = v11)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (leq(v6, v7) = v9) |  ~ (leq(v5, v6) = v8) |  ? [v10] :  ? [v11] :  ? [v12] : (less(v6, v7) = v10 & less(v5, v7) = v12 & less(v5, v6) = v11 & (v12 = 0 | (( ~ (v11 = 0) |  ~ (v9 = 0)) & ( ~ (v10 = 0) |  ~ (v8 = 0)))))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (vplus(v8, v7) = v9) |  ~ (vplus(v5, v6) = v8) |  ? [v10] : (vplus(v6, v7) = v10 & vplus(v5, v10) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = v7 |  ~ (vplus(v5, v6) = v8) |  ~ (vplus(v5, v6) = v7)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (leq(v5, v7) = v8) |  ~ (leq(v5, v6) = 0) |  ? [v9] : ( ~ (v9 = 0) & leq(v6, v7) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (greater(v7, v5) = v8) |  ~ (vplus(v5, v6) = v7)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (less(v5, v7) = v8) |  ~ (less(v5, v6) = 0) |  ? [v9] : ( ~ (v9 = 0) & less(v6, v7) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v7 = 0 |  ~ (greater(v6, v5) = v7) |  ~ (vplus(v5, v8) = v6)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v7 = 0 |  ~ (vplus(v6, v8) = v5) |  ~ (less(v6, v5) = v7)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (geq(v8, v7) = v6) |  ~ (geq(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (leq(v8, v7) = v6) |  ~ (leq(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (greater(v8, v7) = v6) |  ~ (greater(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (vplus(v8, v7) = v6) |  ~ (vplus(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (less(v8, v7) = v6) |  ~ (less(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (vsucc(v6) = v7) |  ~ (vplus(v5, v7) = v8) |  ? [v9] : (vsucc(v9) = v8 & vplus(v5, v6) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (vsucc(v5) = v7) |  ~ (vplus(v7, v6) = v8) |  ? [v9] : (vsucc(v9) = v8 & vplus(v5, v6) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (vplus(v6, v8) = v5) |  ~ (vplus(v5, v7) = v6)) &  ? [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (vplus(v7, v6) = v8) |  ? [v9] : ( ~ (v9 = v8) & vplus(v7, v5) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v6 = v5 |  ~ (greater(v5, v6) = v7) | less(v5, v6) = 0) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (geq(v6, v5) = v7) |  ? [v8] : ( ~ (v8 = 0) & leq(v5, v6) = v8)) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (geq(v6, v5) = v7) |  ? [v8] : ( ~ (v8 = 0) & greater(v6, v5) = v8)) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (leq(v6, v5) = v7) |  ? [v8] : ( ~ (v8 = 0) & less(v6, v5) = v8)) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (greater(v6, v5) = v7) |  ? [v8] : ( ~ (v8 = 0) & less(v5, v6) = v8)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (vskolem2(v7) = v6) |  ~ (vskolem2(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (vsucc(v7) = v6) |  ~ (vsucc(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (vsucc(v6) = v7) |  ~ (vsucc(v5) = v7)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (vplus(v5, v6) = v7) | vplus(v6, v5) = v7) &  ! [v5] :  ! [v6] : (v6 = v5 |  ~ (geq(v6, v5) = 0) | greater(v6, v5) = 0) &  ! [v5] :  ! [v6] : (v6 = v5 |  ~ (leq(v6, v5) = 0) | less(v6, v5) = 0) &  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (geq(v5, v5) = v6)) &  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (leq(v5, v5) = v6)) &  ! [v5] :  ! [v6] : (v5 = v1 |  ~ (vskolem2(v5) = v6) | vsucc(v6) = v5) &  ! [v5] :  ! [v6] : ( ~ (geq(v5, v6) = 0) | leq(v6, v5) = 0) &  ! [v5] :  ! [v6] : ( ~ (greater(v6, v5) = 0) |  ? [v7] : vplus(v5, v7) = v6) &  ! [v5] :  ! [v6] : ( ~ (greater(v5, v6) = 0) | less(v6, v5) = 0) &  ! [v5] :  ! [v6] : ( ~ (greater(v5, v6) = 0) |  ? [v7] : ( ~ (v7 = 0) & less(v5, v6) = v7)) &  ! [v5] :  ! [v6] :  ~ (vplus(v5, v6) = v6) &  ! [v5] :  ! [v6] :  ~ (vplus(v5, v6) = v5) &  ! [v5] :  ! [v6] : ( ~ (vplus(v5, v1) = v6) | vsucc(v5) = v6) &  ! [v5] :  ! [v6] : ( ~ (vplus(v1, v5) = v6) | vsucc(v5) = v6) &  ! [v5] :  ! [v6] : ( ~ (less(v6, v5) = 0) |  ? [v7] : vplus(v6, v7) = v5) &  ! [v5] :  ~ (vsucc(v5) = v5) &  ! [v5] :  ~ (vsucc(v5) = v1) &  ! [v5] :  ~ (greater(v5, v5) = 0) &  ! [v5] :  ~ (less(v5, v5) = 0) &  ? [v5] :  ? [v6] : (v6 = v5 |  ? [v7] :  ? [v8] : ((v8 = v6 & vplus(v5, v7) = v6) | (v8 = v5 & vplus(v6, v7) = v5))) & ( ~ (v2 = 0) | v3 = 0) & ( ~ (v1 = v0) | vd329 = vd328))
% 21.03/6.44  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 21.03/6.44  | (1)  ~ (all_0_0_0 = 0) & greater(all_0_4_4, all_0_3_3) = all_0_2_2 & greater(vd328, vd329) = all_0_1_1 & vplus(vd329, vd330) = all_0_3_3 & vplus(vd328, vd330) = all_0_4_4 & less(all_0_4_4, all_0_3_3) = 0 & less(vd328, vd329) = all_0_0_0 &  ! [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))) & ( ~ (all_0_2_2 = 0) | all_0_1_1 = 0) & ( ~ (all_0_3_3 = all_0_4_4) | vd329 = vd328)
% 21.03/6.45  |
% 21.03/6.45  | Applying alpha-rule on (1) yields:
% 21.03/6.45  | (2)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 | v1 = v0 |  ~ (greater(v0, v1) = v2) | less(v0, v1) = 0)
% 21.03/6.45  | (3)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (greater(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & less(v0, v1) = v3))
% 21.03/6.45  | (4)  ! [v0] :  ~ (vsucc(v0) = v1)
% 21.03/6.45  | (5)  ! [v0] :  ! [v1] : ( ~ (vplus(v1, v0) = v1) | vsucc(v0) = v1)
% 21.03/6.45  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (vsucc(v0) = v2) |  ~ (vplus(v2, v1) = v3) |  ? [v4] : (vsucc(v4) = v3 & vplus(v0, v1) = v4))
% 21.03/6.45  | (7)  ! [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))))))
% 21.03/6.45  | (8)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (vskolem2(v2) = v1) |  ~ (vskolem2(v2) = v0))
% 21.03/6.45  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (greater(v3, v2) = v1) |  ~ (greater(v3, v2) = v0))
% 21.03/6.45  | (10)  ! [v0] :  ! [v1] : ( ~ (greater(v0, v1) = 0) | less(v1, v0) = 0)
% 21.03/6.45  | (11)  ! [v0] :  ! [v1] :  ~ (vplus(v0, v1) = v1)
% 21.03/6.45  | (12)  ! [v0] :  ~ (less(v0, v0) = 0)
% 21.03/6.45  | (13)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (geq(v0, v0) = v1))
% 21.03/6.45  | (14)  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] :  ? [v3] : ((v3 = v1 & vplus(v0, v2) = v1) | (v3 = v0 & vplus(v1, v2) = v0)))
% 21.03/6.46  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (less(v0, v2) = v3) |  ~ (less(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & less(v1, v2) = v4))
% 21.03/6.46  | (16)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (leq(v1, v0) = 0) | less(v1, v0) = 0)
% 21.03/6.46  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (vplus(v3, v2) = v1) |  ~ (vplus(v3, v2) = v0))
% 21.03/6.46  | (18)  ! [v0] :  ~ (greater(v0, v0) = 0)
% 21.03/6.46  | (19)  ! [v0] :  ! [v1] : ( ~ (greater(v1, v0) = 0) |  ? [v2] : vplus(v0, v2) = v1)
% 21.03/6.46  | (20)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (vsucc(v1) = v2) |  ~ (vsucc(v0) = v2))
% 21.03/6.46  | (21)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (vplus(v0, v1) = v2) | vplus(v1, v0) = v2)
% 21.03/6.46  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (vplus(v1, v3) = v0) |  ~ (vplus(v0, v2) = v1))
% 21.03/6.46  | (23)  ~ (all_0_3_3 = all_0_4_4) | vd329 = vd328
% 21.03/6.46  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = 0 |  ~ (greater(v1, v0) = v2) |  ~ (vplus(v0, v3) = v1))
% 21.03/6.46  | (25)  ! [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))
% 21.03/6.46  | (26)  ~ (all_0_0_0 = 0)
% 21.03/6.46  | (27)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (geq(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & greater(v1, v0) = v3))
% 21.03/6.46  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0))
% 21.03/6.46  | (29)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (geq(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3))
% 21.03/6.46  | (30)  ! [v0] :  ~ (vsucc(v0) = v0)
% 21.03/6.46  | (31)  ! [v0] :  ! [v1] : ( ~ (less(v1, v0) = 0) |  ? [v2] : vplus(v1, v2) = v0)
% 21.03/6.46  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (greater(v2, v0) = v3) |  ~ (vplus(v0, v1) = v2))
% 21.03/6.46  | (33)  ! [v0] :  ! [v1] : ( ~ (vplus(v0, v1) = v1) | vsucc(v0) = v1)
% 21.03/6.46  | (34)  ! [v0] :  ! [v1] : (v0 = v1 |  ~ (vskolem2(v0) = v1) | vsucc(v1) = v0)
% 21.03/6.46  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (geq(v3, v2) = v1) |  ~ (geq(v3, v2) = v0))
% 21.03/6.46  | (36)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (geq(v1, v0) = 0) | greater(v1, v0) = 0)
% 21.03/6.46  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (vplus(v0, v1) = v3) |  ~ (vplus(v0, v1) = v2))
% 21.03/6.46  | (38)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (vsucc(v2) = v1) |  ~ (vsucc(v2) = v0))
% 21.03/6.46  | (39) greater(all_0_4_4, all_0_3_3) = all_0_2_2
% 21.03/6.46  | (40)  ! [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))
% 21.03/6.46  | (41) vplus(vd329, vd330) = all_0_3_3
% 21.03/6.46  | (42)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (vplus(v2, v1) = v3) |  ? [v4] : ( ~ (v4 = v3) & vplus(v2, v0) = v4))
% 21.03/6.46  | (43)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (vsucc(v1) = v2) |  ~ (vplus(v0, v2) = v3) |  ? [v4] : (vsucc(v4) = v3 & vplus(v0, v1) = v4))
% 21.03/6.46  | (44)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (leq(v0, v2) = v3) |  ~ (leq(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & leq(v1, v2) = v4))
% 21.03/6.46  | (45)  ~ (all_0_2_2 = 0) | all_0_1_1 = 0
% 21.03/6.46  | (46) greater(vd328, vd329) = all_0_1_1
% 21.03/6.46  | (47) vplus(vd328, vd330) = all_0_4_4
% 21.03/6.46  | (48)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (leq(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & less(v1, v0) = v3))
% 21.03/6.46  | (49)  ! [v0] :  ! [v1] : ( ~ (geq(v0, v1) = 0) | leq(v1, v0) = 0)
% 21.03/6.46  | (50)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (less(v3, v2) = v1) |  ~ (less(v3, v2) = v0))
% 21.03/6.46  | (51)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (vplus(v3, v2) = v4) |  ~ (vplus(v0, v1) = v3) |  ? [v5] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4))
% 21.03/6.46  | (52)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = 0 |  ~ (vplus(v1, v3) = v0) |  ~ (less(v1, v0) = v2))
% 21.03/6.46  | (53) less(vd328, vd329) = all_0_0_0
% 21.03/6.46  | (54)  ! [v0] :  ! [v1] :  ~ (vplus(v0, v1) = v0)
% 21.03/6.46  | (55) less(all_0_4_4, all_0_3_3) = 0
% 21.03/6.46  | (56)  ! [v0] :  ! [v1] : ( ~ (greater(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & less(v0, v1) = v2))
% 21.03/6.46  | (57)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (leq(v0, v0) = v1))
% 21.03/6.46  |
% 21.03/6.46  | Instantiating formula (37) with all_0_4_4, all_0_3_3, vd330, vd328 and discharging atoms vplus(vd328, vd330) = all_0_4_4, yields:
% 21.03/6.46  | (58) all_0_3_3 = all_0_4_4 |  ~ (vplus(vd328, vd330) = all_0_3_3)
% 21.03/6.46  |
% 21.03/6.46  | Instantiating formula (12) with all_0_4_4 yields:
% 21.03/6.46  | (59)  ~ (less(all_0_4_4, all_0_4_4) = 0)
% 21.03/6.46  |
% 21.03/6.46  | Using (55) and (59) yields:
% 21.03/6.47  | (60)  ~ (all_0_3_3 = all_0_4_4)
% 21.03/6.47  |
% 21.03/6.47  | Instantiating formula (19) with all_0_4_4, all_0_3_3 yields:
% 21.03/6.47  | (61)  ~ (greater(all_0_4_4, all_0_3_3) = 0) |  ? [v0] : vplus(all_0_3_3, v0) = all_0_4_4
% 21.03/6.47  |
% 21.03/6.47  | Instantiating formula (56) with all_0_3_3, all_0_4_4 yields:
% 21.03/6.47  | (62)  ~ (greater(all_0_4_4, all_0_3_3) = 0) |  ? [v0] : ( ~ (v0 = 0) & less(all_0_4_4, all_0_3_3) = v0)
% 21.03/6.47  |
% 21.03/6.47  | Instantiating formula (2) with all_0_1_1, vd329, vd328 and discharging atoms greater(vd328, vd329) = all_0_1_1, yields:
% 21.03/6.47  | (63) all_0_1_1 = 0 | vd329 = vd328 | less(vd328, vd329) = 0
% 21.03/6.47  |
% 21.03/6.47  | Instantiating formula (3) with all_0_1_1, vd328, vd329 and discharging atoms greater(vd328, vd329) = all_0_1_1, yields:
% 21.03/6.47  | (64) all_0_1_1 = 0 |  ? [v0] : ( ~ (v0 = 0) & less(vd329, vd328) = v0)
% 21.03/6.47  |
% 21.03/6.47  | Instantiating formula (40) with all_0_2_2, all_0_3_3, all_0_4_4, vd330, vd329, vd328 and discharging atoms greater(all_0_4_4, all_0_3_3) = all_0_2_2, vplus(vd329, vd330) = all_0_3_3, vplus(vd328, vd330) = all_0_4_4, yields:
% 21.03/6.47  | (65) all_0_2_2 = 0 |  ? [v0] : ( ~ (v0 = 0) & greater(vd328, vd329) = v0)
% 21.03/6.47  |
% 21.03/6.47  | Instantiating formula (31) with all_0_4_4, all_0_3_3 and discharging atoms less(all_0_4_4, all_0_3_3) = 0, yields:
% 21.03/6.47  | (66)  ? [v0] : vplus(all_0_4_4, v0) = all_0_3_3
% 21.03/6.47  |
% 21.03/6.47  | Instantiating (66) with all_24_0_8 yields:
% 21.03/6.47  | (67) vplus(all_0_4_4, all_24_0_8) = all_0_3_3
% 21.03/6.47  |
% 21.03/6.47  +-Applying beta-rule and splitting (62), into two cases.
% 21.03/6.47  |-Branch one:
% 21.03/6.47  | (68)  ~ (greater(all_0_4_4, all_0_3_3) = 0)
% 21.03/6.47  |
% 21.03/6.47  	| Using (39) and (68) yields:
% 21.03/6.47  	| (69)  ~ (all_0_2_2 = 0)
% 21.03/6.47  	|
% 21.03/6.47  	+-Applying beta-rule and splitting (65), into two cases.
% 21.03/6.47  	|-Branch one:
% 21.03/6.47  	| (70) all_0_2_2 = 0
% 21.03/6.47  	|
% 21.03/6.47  		| Equations (70) can reduce 69 to:
% 21.03/6.47  		| (71) $false
% 21.03/6.47  		|
% 21.03/6.47  		|-The branch is then unsatisfiable
% 21.03/6.47  	|-Branch two:
% 21.03/6.47  	| (69)  ~ (all_0_2_2 = 0)
% 21.03/6.47  	| (73)  ? [v0] : ( ~ (v0 = 0) & greater(vd328, vd329) = v0)
% 21.03/6.47  	|
% 21.03/6.47  		| Instantiating (73) with all_42_0_9 yields:
% 21.03/6.47  		| (74)  ~ (all_42_0_9 = 0) & greater(vd328, vd329) = all_42_0_9
% 21.03/6.47  		|
% 21.03/6.47  		| Applying alpha-rule on (74) yields:
% 21.03/6.47  		| (75)  ~ (all_42_0_9 = 0)
% 21.03/6.47  		| (76) greater(vd328, vd329) = all_42_0_9
% 21.03/6.47  		|
% 21.03/6.47  		| Instantiating formula (9) with vd328, vd329, all_42_0_9, all_0_1_1 and discharging atoms greater(vd328, vd329) = all_42_0_9, greater(vd328, vd329) = all_0_1_1, yields:
% 21.03/6.47  		| (77) all_42_0_9 = all_0_1_1
% 21.03/6.47  		|
% 21.03/6.47  		| Equations (77) can reduce 75 to:
% 21.03/6.47  		| (78)  ~ (all_0_1_1 = 0)
% 21.03/6.47  		|
% 21.03/6.47  		+-Applying beta-rule and splitting (64), into two cases.
% 21.03/6.47  		|-Branch one:
% 21.03/6.47  		| (79) all_0_1_1 = 0
% 21.03/6.47  		|
% 21.03/6.47  			| Equations (79) can reduce 78 to:
% 21.03/6.47  			| (71) $false
% 21.03/6.47  			|
% 21.03/6.47  			|-The branch is then unsatisfiable
% 21.03/6.47  		|-Branch two:
% 21.03/6.47  		| (78)  ~ (all_0_1_1 = 0)
% 21.03/6.47  		| (82)  ? [v0] : ( ~ (v0 = 0) & less(vd329, vd328) = v0)
% 21.03/6.47  		|
% 21.03/6.47  			+-Applying beta-rule and splitting (63), into two cases.
% 21.03/6.47  			|-Branch one:
% 21.03/6.47  			| (83) less(vd328, vd329) = 0
% 21.03/6.47  			|
% 21.03/6.47  				| Instantiating formula (50) with vd328, vd329, 0, all_0_0_0 and discharging atoms less(vd328, vd329) = all_0_0_0, less(vd328, vd329) = 0, yields:
% 21.03/6.47  				| (84) all_0_0_0 = 0
% 21.03/6.47  				|
% 21.03/6.47  				| Equations (84) can reduce 26 to:
% 21.03/6.47  				| (71) $false
% 21.03/6.47  				|
% 21.03/6.47  				|-The branch is then unsatisfiable
% 21.03/6.47  			|-Branch two:
% 21.03/6.47  			| (86)  ~ (less(vd328, vd329) = 0)
% 21.03/6.47  			| (87) all_0_1_1 = 0 | vd329 = vd328
% 21.03/6.47  			|
% 21.03/6.47  				+-Applying beta-rule and splitting (87), into two cases.
% 21.03/6.47  				|-Branch one:
% 21.03/6.47  				| (88) vd329 = vd328
% 21.03/6.47  				|
% 21.03/6.47  					| From (88) and (41) follows:
% 21.03/6.47  					| (89) vplus(vd328, vd330) = all_0_3_3
% 21.03/6.47  					|
% 21.03/6.47  					+-Applying beta-rule and splitting (58), into two cases.
% 21.03/6.47  					|-Branch one:
% 21.03/6.47  					| (90)  ~ (vplus(vd328, vd330) = all_0_3_3)
% 21.03/6.47  					|
% 21.03/6.47  						| Using (89) and (90) yields:
% 21.03/6.47  						| (91) $false
% 21.03/6.47  						|
% 21.03/6.47  						|-The branch is then unsatisfiable
% 21.03/6.47  					|-Branch two:
% 21.03/6.47  					| (89) vplus(vd328, vd330) = all_0_3_3
% 21.03/6.47  					| (93) all_0_3_3 = all_0_4_4
% 21.03/6.47  					|
% 21.03/6.47  						| Equations (93) can reduce 60 to:
% 21.03/6.47  						| (71) $false
% 21.03/6.47  						|
% 21.03/6.47  						|-The branch is then unsatisfiable
% 21.03/6.47  				|-Branch two:
% 21.03/6.47  				| (95)  ~ (vd329 = vd328)
% 21.03/6.47  				| (79) all_0_1_1 = 0
% 21.03/6.47  				|
% 21.03/6.47  					| Equations (79) can reduce 78 to:
% 21.03/6.47  					| (71) $false
% 21.03/6.47  					|
% 21.03/6.47  					|-The branch is then unsatisfiable
% 21.03/6.47  |-Branch two:
% 21.03/6.47  | (98) greater(all_0_4_4, all_0_3_3) = 0
% 21.03/6.47  | (99)  ? [v0] : ( ~ (v0 = 0) & less(all_0_4_4, all_0_3_3) = v0)
% 21.03/6.48  |
% 21.03/6.48  	+-Applying beta-rule and splitting (61), into two cases.
% 21.03/6.48  	|-Branch one:
% 21.03/6.48  	| (68)  ~ (greater(all_0_4_4, all_0_3_3) = 0)
% 21.03/6.48  	|
% 21.03/6.48  		| Using (98) and (68) yields:
% 21.03/6.48  		| (91) $false
% 21.03/6.48  		|
% 21.03/6.48  		|-The branch is then unsatisfiable
% 21.03/6.48  	|-Branch two:
% 21.03/6.48  	| (98) greater(all_0_4_4, all_0_3_3) = 0
% 21.03/6.48  	| (103)  ? [v0] : vplus(all_0_3_3, v0) = all_0_4_4
% 21.03/6.48  	|
% 21.03/6.48  		| Instantiating (103) with all_39_0_13 yields:
% 21.03/6.48  		| (104) vplus(all_0_3_3, all_39_0_13) = all_0_4_4
% 21.03/6.48  		|
% 21.03/6.48  		| Instantiating formula (22) with all_24_0_8, all_39_0_13, all_0_4_4, all_0_3_3 and discharging atoms vplus(all_0_3_3, all_39_0_13) = all_0_4_4, vplus(all_0_4_4, all_24_0_8) = all_0_3_3, yields:
% 21.03/6.48  		| (91) $false
% 21.03/6.48  		|
% 21.03/6.48  		|-The branch is then unsatisfiable
% 21.03/6.48  % SZS output end Proof for theBenchmark
% 21.03/6.48  
% 21.03/6.48  5877ms
%------------------------------------------------------------------------------