%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE089+1 : TPTP v6.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n049.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-573.1.1.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Oct  8 13:58:51 EDT 2015

% Result   : Theorem 10.32s
% Output   : Proof 12.57s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : KLE089+1 : TPTP v6.2.0. Released v4.0.0.
% 0.00/0.02  % Command  : ePrincess-casc -timeout=%d %s
% 0.02/1.07  % Computer : n049.star.cs.uiowa.edu
% 0.02/1.07  % Model    : x86_64 x86_64
% 0.02/1.07  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/1.07  % Memory   : 32286.75MB
% 0.02/1.07  % OS       : Linux 2.6.32-573.1.1.el6.x86_64
% 0.02/1.07  % CPULimit : 300
% 0.02/1.07  % DateTime : Tue Oct  6 22:02:56 CDT 2015
% 0.02/1.07  % CPUTime  : 
% 0.02/1.31          ____       _                          
% 0.02/1.31    ___  / __ \_____(_)___  ________  __________
% 0.02/1.31   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.02/1.31  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.02/1.31  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.02/1.31  
% 0.02/1.31  A Theorem Prover for First-Order Logic
% 0.02/1.32  (ePrincess v.1.0)
% 0.02/1.32  
% 0.02/1.32  (c) Philipp Rümmer, 2009-2015
% 0.02/1.32  (c) Peter Backeman, 2014-2015
% 0.02/1.32  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.02/1.32  Free software under GNU Lesser General Public License (LGPL).
% 0.02/1.32  Bug reports to peter@backeman.se
% 0.02/1.32  
% 0.02/1.32  For more information, visit http://user.uu.se/~petba168/breu/
% 0.02/1.32  
% 0.02/1.32  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.02/1.38  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 0.02/2.04  Prover 0: Preprocessing ...
% 2.26/2.71  Prover 0: Constructing countermodel ...
% 7.98/6.68  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 8.12/6.79  Prover 1: Preprocessing ...
% 8.45/6.95  Prover 1: Constructing countermodel ...
% 9.08/7.33  Prover 1: gave up
% 9.08/7.33  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 9.28/7.42  Prover 2: Preprocessing ...
% 9.50/7.59  Prover 2: Warning: ignoring some quantifiers
% 9.71/7.61  Prover 2: Constructing countermodel ...
% 10.09/7.89  Prover 2: proved (560ms)
% 10.32/7.90  Prover 0: stopped
% 10.32/7.90  
% 10.32/7.90  No countermodel exists, formula is valid
% 10.32/7.90  % SZS status Theorem for theBenchmark
% 10.32/7.90  
% 10.32/7.90  Generating proof ... Warning: ignoring some quantifiers
% 11.95/8.59  found it (size 37)
% 11.95/8.59  
% 11.95/8.59  % SZS output start Proof for theBenchmark
% 11.95/8.59  Assumed formulas after preprocessing and simplification: 
% 11.95/8.60  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : ( ~ (v4 = zero) & domain(v0) = v2 & antidomain(v1) = v3 & multiplication(v2, v1) = v4 & addition(v2, v3) = v3 &  ! [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] : ( ~ (coantidomain(v7) = v8) |  ~ (coantidomain(v5) = v7) |  ~ (multiplication(v8, v6) = v9) |  ? [v10] :  ? [v11] :  ? [v12] : (coantidomain(v10) = v11 & coantidomain(v9) = v12 & multiplication(v5, v6) = v10 & addition(v11, v12) = v12)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (antidomain(v7) = v8) |  ~ 
% (antidomain(v6) = v7) |  ~ (multiplication(v5, v8) = v9) |  ? [v10] :  ? [v11] :  ? [v12] : (antidomain(v10) = v11 & antidomain(v9) = v12 & multiplication(v5, v6) = v10 & addition(v11, v12) = v12)) &  ! [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] : (v6 = v5 |  ~ (leq(v8, v7) = v6) |  ~ (leq(v8, v7) = v5)) &  ! [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] : (v7 = v6 |  ~ (addition(v5, v6) = v7) |  ? [v8] : ( ~ (v8 = 0) & leq(v5, v6) = v8)) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (leq(v5, v6) = v7) |  ? [v8] : ( ~ (v8 = v6) & addition(v5, v6) = v8)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (codomain(v7) = v6) |  ~ (codomain(v7) = 
% v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (coantidomain(v7) = v6) |  ~ (coantidomain(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (domain(v7) = v6) |  ~ (domain(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (antidomain(v7) = v6) |  ~ (antidomain(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (multiplication(v5, v6) = v7) |  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] : (coantidomain(v11) = v12 & coantidomain(v9) = v10 & coantidomain(v7) = v8 & coantidomain(v5) = v9 & multiplication(v10, v6) = v11 & addition(v8, v12) = v12)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (multiplication(v5, v6) = v7) |  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] : (antidomain(v11) = v12 & antidomain(v9) = v10 & antidomain(v7) = v8 & antidomain(v6) = v9 & multiplication(v5, v10) = v11 & addition(v8, v12) = v12)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (addition(v6, v5) = v7) | addition(v5, v6) = v7) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (addition(v5, v6) = v7) | addition(v6, v5) = v7) &  ! [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] : ( ~ (codomain(v5) = v6) |  ? [v7] : (coantidomain(v7) = v6 & coantidomain(v5) = v7)) &  ! [v5] :  ! [v6] : ( ~ (coantidomain(v5) = v6) | multiplication(v5, v6) = zero) &  ! [v5] :  ! [v6] : ( ~ (coantidomain(v5) = v6) |  ? [v7] : (codomain(v5) = v7 & coantidomain(v6) = v7)) &  ! [v5] :  ! [v6] : ( ~ (coantidomain(v5) = v6) |  ? [v7] : (coantidomain(v6) = v7 & addition(v7, v6) = one)) &  ! [v5] :  ! [v6] : ( ~ (domain(v5) = v6) |  ? [v7] : (antidomain(v7) = v6 & antidomain(v5) = v7)) &  ! [v5] :  ! [v6] : ( ~ (antidomain(v5) = v6) | multiplication(v6, v5) = zero) &  ! [v5] :  ! [v6] : ( ~ (antidomain(v5) = 
% v6) |  ? [v7] : (domain(v5) = v7 & antidomain(v6) = v7)) &  ! [v5] :  ! [v6] : ( ~ (antidomain(v5) = v6) |  ? [v7] : (antidomain(v6) = v7 & addition(v7, v6) = one)) &  ! [v5] :  ! [v6] : ( ~ (leq(v5, v6) = 0) | addition(v5, v6) = v6) &  ! [v5] :  ! [v6] : ( ~ (addition(v5, v6) = v6) | leq(v5, v6) = 0) &  ? [v5] :  ? [v6] :  ? [v7] : leq(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : multiplication(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : addition(v6, v5) = v7 &  ? [v5] :  ? [v6] : codomain(v5) = v6 &  ? [v5] :  ? [v6] : coantidomain(v5) = v6 &  ? [v5] :  ? [v6] : domain(v5) = v6 &  ? [v5] :  ? [v6] : antidomain(v5) = v6)
% 12.25/8.66  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 12.25/8.66  | (1)  ~ (all_0_0_0 = zero) & domain(all_0_4_4) = all_0_2_2 & antidomain(all_0_3_3) = all_0_1_1 & multiplication(all_0_2_2, all_0_3_3) = all_0_0_0 & addition(all_0_2_2, all_0_1_1) = all_0_1_1 &  ! [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] : ( ~ (coantidomain(v2) = v3) |  ~ (coantidomain(v0) = v2) |  ~ (multiplication(v3, v1) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (coantidomain(v5) = v6 & coantidomain(v4) = v7 & multiplication(v0, v1) = v5 & addition(v6, v7) = v7)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (antidomain(v2) = v3) |  ~ 
% (antidomain(v1) = v2) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (antidomain(v5) = v6 & antidomain(v4) = v7 & multiplication(v0, v1) = v5 & addition(v6, v7) = v7)) &  ! [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] : (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 |  ~ (codomain(v2) = v1) |  ~ (codomain(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] 
% : (v1 = v0 |  ~ (coantidomain(v2) = v1) |  ~ (coantidomain(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (domain(v2) = v1) |  ~ (domain(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (antidomain(v2) = v1) |  ~ (antidomain(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (coantidomain(v6) = v7 & coantidomain(v4) = v5 & coantidomain(v2) = v3 & coantidomain(v0) = v4 & multiplication(v5, v1) = v6 & addition(v3, v7) = v7)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (antidomain(v6) = v7 & antidomain(v4) = v5 & antidomain(v2) = v3 & antidomain(v1) = v4 & multiplication(v0, v5) = v6 & addition(v3, v7) = v7)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) &  ! [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 |  ~ (multiplication(v0, zero) = v1)) &  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1)) &  ! [v0] :  ! [v1] : ( ~ (codomain(v0) = v1) |  ? [v2] : (coantidomain(v2) = v1 & coantidomain(v0) = v2)) &  ! [v0] :  ! [v1] : ( ~ (coantidomain(v0) = v1) | multiplication(v0, v1) = zero) &  ! [v0] :  ! [v1] : ( ~ (coantidomain(v0) = v1) |  ? [v2] : (codomain(v0) = v2 & coantidomain(v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (coantidomain(v0) = v1) |  ? [v2] : (coantidomain(v1) = v2 & addition(v2, v1) = one)) &  ! [v0] :  ! [v1] : ( ~ (domain(v0) = v1) |  ? [v2] : (antidomain(v2) = v1 & antidomain(v0) = v2)) &  ! [v0] :  ! [v1] : ( ~ (antidomain(v0) = v1) | multiplication(v1, v0) = zero) &  ! [v0] :  ! [v1] : ( ~ (antidomain(v0) = v1) |  ? [v2] : (domain(v0) = v2 & antidomain(v1) = v2)) 
% &  ! [v0] :  ! [v1] : ( ~ (antidomain(v0) = v1) |  ? [v2] : (antidomain(v1) = v2 & addition(v2, v1) = one)) &  ! [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] : codomain(v0) = v1 &  ? [v0] :  ? [v1] : coantidomain(v0) = v1 &  ? [v0] :  ? [v1] : domain(v0) = v1 &  ? [v0] :  ? [v1] : antidomain(v0) = v1
% 12.25/8.70  |
% 12.25/8.70  | Applying alpha-rule on (1) yields:
% 12.25/8.70  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 12.25/8.70  | (3)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (domain(v2) = v1) |  ~ (domain(v2) = v0))
% 12.25/8.70  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 12.25/8.71  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 12.25/8.71  | (6)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (antidomain(v2) = v1) |  ~ (antidomain(v2) = v0))
% 12.25/8.71  | (7)  ! [v0] :  ! [v1] : ( ~ (codomain(v0) = v1) |  ? [v2] : (coantidomain(v2) = v1 & coantidomain(v0) = v2))
% 12.25/8.71  | (8)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (codomain(v2) = v1) |  ~ (codomain(v2) = v0))
% 12.25/8.71  | (9)  ! [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))
% 12.25/8.71  | (10)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0)
% 12.25/8.71  | (11)  ! [v0] :  ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1)
% 12.25/8.71  | (12)  ~ (all_0_0_0 = zero)
% 12.25/8.71  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (antidomain(v2) = v3) |  ~ (antidomain(v1) = v2) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (antidomain(v5) = v6 & antidomain(v4) = v7 & multiplication(v0, v1) = v5 & addition(v6, v7) = v7))
% 12.57/8.72  | (14)  ! [v0] :  ! [v1] : ( ~ (coantidomain(v0) = v1) |  ? [v2] : (coantidomain(v1) = v2 & addition(v2, v1) = one))
% 12.57/8.72  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 12.57/8.72  | (16)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (antidomain(v6) = v7 & antidomain(v4) = v5 & antidomain(v2) = v3 & antidomain(v1) = v4 & multiplication(v0, v5) = v6 & addition(v3, v7) = v7))
% 12.57/8.72  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 12.57/8.72  | (18)  ! [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))
% 12.57/8.72  | (19)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3))
% 12.57/8.72  | (20)  ! [v0] :  ! [v1] : ( ~ (domain(v0) = v1) |  ? [v2] : (antidomain(v2) = v1 & antidomain(v0) = v2))
% 12.57/8.74  | (21)  ! [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))
% 12.57/8.74  | (22)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (coantidomain(v2) = v1) |  ~ (coantidomain(v2) = v0))
% 12.57/8.74  | (23)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 12.57/8.74  | (24)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 12.57/8.74  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0))
% 12.57/8.74  | (26)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (leq(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3))
% 12.57/8.74  | (27)  ! [v0] :  ! [v1] : ( ~ (antidomain(v0) = v1) |  ? [v2] : (antidomain(v1) = v2 & addition(v2, v1) = one))
% 12.57/8.74  | (28) antidomain(all_0_3_3) = all_0_1_1
% 12.57/8.74  | (29)  ! [v0] :  ! [v1] : ( ~ (coantidomain(v0) = v1) | multiplication(v0, v1) = zero)
% 12.57/8.74  | (30) domain(all_0_4_4) = all_0_2_2
% 12.57/8.74  | (31)  ? [v0] :  ? [v1] :  ? [v2] : addition(v1, v0) = v2
% 12.57/8.74  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (coantidomain(v2) = v3) |  ~ (coantidomain(v0) = v2) |  ~ (multiplication(v3, v1) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (coantidomain(v5) = v6 & coantidomain(v4) = v7 & multiplication(v0, v1) = v5 & addition(v6, v7) = v7))
% 12.57/8.74  | (33) addition(all_0_2_2, all_0_1_1) = all_0_1_1
% 12.57/8.74  | (34)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 12.57/8.74  | (35)  ! [v0] :  ! [v1] : ( ~ (antidomain(v0) = v1) |  ? [v2] : (domain(v0) = v2 & antidomain(v1) = v2))
% 12.57/8.75  | (36)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 12.57/8.75  | (37)  ? [v0] :  ? [v1] : coantidomain(v0) = v1
% 12.57/8.75  | (38)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 12.57/8.75  | (39)  ? [v0] :  ? [v1] : domain(v0) = v1
% 12.57/8.75  | (40) multiplication(all_0_2_2, all_0_3_3) = all_0_0_0
% 12.57/8.75  | (41)  ? [v0] :  ? [v1] : antidomain(v0) = v1
% 12.57/8.75  | (42)  ! [v0] :  ! [v1] : ( ~ (coantidomain(v0) = v1) |  ? [v2] : (codomain(v0) = v2 & coantidomain(v1) = v2))
% 12.57/8.75  | (43)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (coantidomain(v6) = v7 & coantidomain(v4) = v5 & coantidomain(v2) = v3 & coantidomain(v0) = v4 & multiplication(v5, v1) = v6 & addition(v3, v7) = v7))
% 12.57/8.75  | (44)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(v0, zero) = v1))
% 12.57/8.75  | (45)  ! [v0] :  ! [v1] : ( ~ (antidomain(v0) = v1) | multiplication(v1, v0) = zero)
% 12.57/8.75  | (46)  ? [v0] :  ? [v1] :  ? [v2] : leq(v1, v0) = v2
% 12.57/8.75  | (47)  ? [v0] :  ? [v1] : codomain(v0) = v1
% 12.57/8.75  | (48)  ? [v0] :  ? [v1] :  ? [v2] : multiplication(v1, v0) = v2
% 12.57/8.75  | (49)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 12.57/8.75  | (50)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 12.57/8.75  | (51)  ! [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))
% 12.57/8.76  | (52)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 12.57/8.76  |
% 12.57/8.76  | Instantiating formula (45) with all_0_1_1, all_0_3_3 and discharging atoms antidomain(all_0_3_3) = all_0_1_1, yields:
% 12.57/8.76  | (53) multiplication(all_0_1_1, all_0_3_3) = zero
% 12.57/8.76  |
% 12.57/8.76  | Instantiating formula (5) with all_0_1_1, all_0_1_1, all_0_2_2, all_0_2_2, all_0_1_1 and discharging atoms addition(all_0_2_2, all_0_1_1) = all_0_1_1, yields:
% 12.57/8.76  | (54)  ? [v0] : (addition(v0, all_0_1_1) = all_0_1_1 & addition(all_0_2_2, all_0_2_2) = v0)
% 12.57/8.76  |
% 12.57/8.76  | Instantiating formula (50) with all_0_1_1, all_0_2_2, all_0_1_1 and discharging atoms addition(all_0_2_2, all_0_1_1) = all_0_1_1, yields:
% 12.57/8.76  | (55) addition(all_0_1_1, all_0_2_2) = all_0_1_1
% 12.57/8.76  |
% 12.57/8.76  | Instantiating (54) with all_31_0_34 yields:
% 12.57/8.76  | (56) addition(all_31_0_34, all_0_1_1) = all_0_1_1 & addition(all_0_2_2, all_0_2_2) = all_31_0_34
% 12.57/8.76  |
% 12.57/8.76  | Applying alpha-rule on (56) yields:
% 12.57/8.76  | (57) addition(all_31_0_34, all_0_1_1) = all_0_1_1
% 12.57/8.76  | (58) addition(all_0_2_2, all_0_2_2) = all_31_0_34
% 12.57/8.76  |
% 12.57/8.76  | Instantiating formula (23) with all_31_0_34, all_0_2_2 and discharging atoms addition(all_0_2_2, all_0_2_2) = all_31_0_34, yields:
% 12.57/8.76  | (59) all_31_0_34 = all_0_2_2
% 12.57/8.76  |
% 12.57/8.76  | From (59) and (57) follows:
% 12.57/8.76  | (33) addition(all_0_2_2, all_0_1_1) = all_0_1_1
% 12.57/8.76  |
% 12.57/8.76  | From (59) and (58) follows:
% 12.57/8.76  | (61) addition(all_0_2_2, all_0_2_2) = all_0_2_2
% 12.57/8.76  |
% 12.57/8.76  | Instantiating formula (18) with zero, all_0_1_1, all_0_3_3, all_0_1_1, all_0_2_2 and discharging atoms multiplication(all_0_1_1, all_0_3_3) = zero, addition(all_0_2_2, all_0_1_1) = all_0_1_1, yields:
% 12.57/8.76  | (62)  ? [v0] :  ? [v1] : (multiplication(all_0_1_1, all_0_3_3) = v1 & multiplication(all_0_2_2, all_0_3_3) = v0 & addition(v0, v1) = zero)
% 12.57/8.77  |
% 12.57/8.77  | Instantiating formula (18) with zero, all_0_1_1, all_0_3_3, all_0_2_2, all_0_1_1 and discharging atoms multiplication(all_0_1_1, all_0_3_3) = zero, addition(all_0_1_1, all_0_2_2) = all_0_1_1, yields:
% 12.57/8.77  | (63)  ? [v0] :  ? [v1] : (multiplication(all_0_1_1, all_0_3_3) = v0 & multiplication(all_0_2_2, all_0_3_3) = v1 & addition(v0, v1) = zero)
% 12.57/8.77  |
% 12.57/8.77  | Instantiating formula (18) with all_0_0_0, all_0_2_2, all_0_3_3, all_0_2_2, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_3_3) = all_0_0_0, addition(all_0_2_2, all_0_2_2) = all_0_2_2, yields:
% 12.57/8.77  | (64)  ? [v0] :  ? [v1] : (multiplication(all_0_2_2, all_0_3_3) = v1 & multiplication(all_0_2_2, all_0_3_3) = v0 & addition(v0, v1) = all_0_0_0)
% 12.57/8.77  |
% 12.57/8.77  | Instantiating (64) with all_53_0_39, all_53_1_40 yields:
% 12.57/8.77  | (65) multiplication(all_0_2_2, all_0_3_3) = all_53_0_39 & multiplication(all_0_2_2, all_0_3_3) = all_53_1_40 & addition(all_53_1_40, all_53_0_39) = all_0_0_0
% 12.57/8.77  |
% 12.57/8.77  | Applying alpha-rule on (65) yields:
% 12.57/8.77  | (66) multiplication(all_0_2_2, all_0_3_3) = all_53_0_39
% 12.57/8.77  | (67) multiplication(all_0_2_2, all_0_3_3) = all_53_1_40
% 12.57/8.77  | (68) addition(all_53_1_40, all_53_0_39) = all_0_0_0
% 12.57/8.77  |
% 12.57/8.77  | Instantiating (62) with all_67_0_59, all_67_1_60 yields:
% 12.57/8.77  | (69) multiplication(all_0_1_1, all_0_3_3) = all_67_0_59 & multiplication(all_0_2_2, all_0_3_3) = all_67_1_60 & addition(all_67_1_60, all_67_0_59) = zero
% 12.57/8.77  |
% 12.57/8.77  | Applying alpha-rule on (69) yields:
% 12.57/8.77  | (70) multiplication(all_0_1_1, all_0_3_3) = all_67_0_59
% 12.57/8.77  | (71) multiplication(all_0_2_2, all_0_3_3) = all_67_1_60
% 12.57/8.77  | (72) addition(all_67_1_60, all_67_0_59) = zero
% 12.57/8.77  |
% 12.57/8.77  | Instantiating (63) with all_83_0_72, all_83_1_73 yields:
% 12.57/8.77  | (73) multiplication(all_0_1_1, all_0_3_3) = all_83_1_73 & multiplication(all_0_2_2, all_0_3_3) = all_83_0_72 & addition(all_83_1_73, all_83_0_72) = zero
% 12.57/8.77  |
% 12.57/8.77  | Applying alpha-rule on (73) yields:
% 12.57/8.77  | (74) multiplication(all_0_1_1, all_0_3_3) = all_83_1_73
% 12.57/8.77  | (75) multiplication(all_0_2_2, all_0_3_3) = all_83_0_72
% 12.57/8.77  | (76) addition(all_83_1_73, all_83_0_72) = zero
% 12.57/8.77  |
% 12.57/8.77  | Instantiating formula (52) with all_0_1_1, all_0_3_3, all_83_1_73, zero and discharging atoms multiplication(all_0_1_1, all_0_3_3) = all_83_1_73, multiplication(all_0_1_1, all_0_3_3) = zero, yields:
% 12.57/8.77  | (77) all_83_1_73 = zero
% 12.57/8.78  |
% 12.57/8.78  | Instantiating formula (52) with all_0_1_1, all_0_3_3, all_67_0_59, all_83_1_73 and discharging atoms multiplication(all_0_1_1, all_0_3_3) = all_83_1_73, multiplication(all_0_1_1, all_0_3_3) = all_67_0_59, yields:
% 12.57/8.78  | (78) all_83_1_73 = all_67_0_59
% 12.57/8.78  |
% 12.57/8.78  | Instantiating formula (52) with all_0_2_2, all_0_3_3, all_67_1_60, all_0_0_0 and discharging atoms multiplication(all_0_2_2, all_0_3_3) = all_67_1_60, multiplication(all_0_2_2, all_0_3_3) = all_0_0_0, yields:
% 12.57/8.78  | (79) all_67_1_60 = all_0_0_0
% 12.57/8.78  |
% 12.57/8.78  | Instantiating formula (52) with all_0_2_2, all_0_3_3, all_67_1_60, all_83_0_72 and discharging atoms multiplication(all_0_2_2, all_0_3_3) = all_83_0_72, multiplication(all_0_2_2, all_0_3_3) = all_67_1_60, yields:
% 12.57/8.78  | (80) all_83_0_72 = all_67_1_60
% 12.57/8.78  |
% 12.57/8.78  | Instantiating formula (52) with all_0_2_2, all_0_3_3, all_53_0_39, all_67_1_60 and discharging atoms multiplication(all_0_2_2, all_0_3_3) = all_67_1_60, multiplication(all_0_2_2, all_0_3_3) = all_53_0_39, yields:
% 12.57/8.78  | (81) all_67_1_60 = all_53_0_39
% 12.57/8.78  |
% 12.57/8.78  | Instantiating formula (52) with all_0_2_2, all_0_3_3, all_53_1_40, all_83_0_72 and discharging atoms multiplication(all_0_2_2, all_0_3_3) = all_83_0_72, multiplication(all_0_2_2, all_0_3_3) = all_53_1_40, yields:
% 12.57/8.78  | (82) all_83_0_72 = all_53_1_40
% 12.57/8.78  |
% 12.57/8.78  | Combining equations (80,82) yields a new equation:
% 12.57/8.78  | (83) all_67_1_60 = all_53_1_40
% 12.57/8.78  |
% 12.57/8.78  | Simplifying 83 yields:
% 12.57/8.78  | (84) all_67_1_60 = all_53_1_40
% 12.57/8.78  |
% 12.57/8.78  | Combining equations (77,78) yields a new equation:
% 12.57/8.78  | (85) all_67_0_59 = zero
% 12.57/8.78  |
% 12.57/8.78  | Combining equations (79,81) yields a new equation:
% 12.57/8.78  | (86) all_53_0_39 = all_0_0_0
% 12.57/8.78  |
% 12.57/8.78  | Combining equations (84,81) yields a new equation:
% 12.57/8.78  | (87) all_53_0_39 = all_53_1_40
% 12.57/8.78  |
% 12.57/8.78  | Combining equations (86,87) yields a new equation:
% 12.57/8.78  | (88) all_53_1_40 = all_0_0_0
% 12.57/8.78  |
% 12.57/8.78  | Combining equations (88,87) yields a new equation:
% 12.57/8.78  | (86) all_53_0_39 = all_0_0_0
% 12.57/8.78  |
% 12.57/8.78  | Combining equations (86,81) yields a new equation:
% 12.57/8.78  | (79) all_67_1_60 = all_0_0_0
% 12.57/8.78  |
% 12.57/8.78  | From (79)(85) and (72) follows:
% 12.57/8.78  | (91) addition(all_0_0_0, zero) = zero
% 12.57/8.78  |
% 12.57/8.78  | Instantiating formula (36) with zero, all_0_0_0 and discharging atoms addition(all_0_0_0, zero) = zero, yields:
% 12.57/8.78  | (92) all_0_0_0 = zero
% 12.57/8.78  |
% 12.57/8.78  | Equations (92) can reduce 12 to:
% 12.57/8.78  | (93) $false
% 12.57/8.78  |
% 12.57/8.78  |-The branch is then unsatisfiable
% 12.57/8.78  % SZS output end Proof for theBenchmark
% 12.57/8.78  
% 12.57/8.78  7453ms
%------------------------------------------------------------------------------