%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE085+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n024.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 01:51:18 EDT 2022

% Result   : Theorem 13.26s 6.30s
% Output   : Proof 15.15s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : KLE085+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n024.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Thu Jun 16 15:56:03 EDT 2022
% 0.13/0.34  % 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/sandbox2/benchmark/theBenchmark.p ...
% 0.73/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.51/0.94  Prover 0: Preprocessing ...
% 2.28/1.22  Prover 0: Constructing countermodel ...
% 12.01/5.93  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 12.01/5.96  Prover 1: Preprocessing ...
% 12.38/6.06  Prover 1: Constructing countermodel ...
% 12.78/6.15  Prover 1: gave up
% 12.78/6.15  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 12.78/6.17  Prover 2: Preprocessing ...
% 13.26/6.22  Prover 2: Warning: ignoring some quantifiers
% 13.26/6.23  Prover 2: Constructing countermodel ...
% 13.26/6.30  Prover 2: proved (147ms)
% 13.26/6.30  Prover 0: stopped
% 13.26/6.30  
% 13.26/6.30  No countermodel exists, formula is valid
% 13.26/6.30  % SZS status Theorem for theBenchmark
% 13.26/6.30  
% 13.26/6.30  Generating proof ... Warning: ignoring some quantifiers
% 14.55/6.55  found it (size 31)
% 14.55/6.55  
% 14.55/6.55  % SZS output start Proof for theBenchmark
% 14.55/6.55  Assumed formulas after preprocessing and simplification: 
% 14.55/6.55  | (0)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = one) & domain(v0) = v1 & addition(v1, one) = v2 &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v4, v5) = v7) |  ~ (multiplication(v3, v5) = v6) |  ~ (addition(v6, v7) = v8) |  ? [v9] : (multiplication(v9, v5) = v8 & addition(v3, v4) = v9)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v3, v5) = v7) |  ~ (multiplication(v3, v4) = v6) |  ~ (addition(v6, v7) = v8) |  ? [v9] : (multiplication(v3, v9) = v8 & addition(v4, v5) = v9)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (coantidomain(v5) = v6) |  ~ (coantidomain(v3) = v5) |  ~ (multiplication(v6, v4) = v7) |  ? [v8] :  ? [v9] :  ? [v10] : (coantidomain(v8) = v9 & coantidomain(v7) = v10 & multiplication(v3, v4) = v8 & addition(v9, v10) = v10)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (antidomain(v5) = v6) |  ~ (antidomain(v4) = v5) |  ~ (multiplication(v3, v6) = v7) |  ? [v8] :  ? [v9] :  ? [v10] : (antidomain(v8) = v9 & antidomain(v7) = v10 & multiplication(v3, v4) = v8 & addition(v9, v10) = v10)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (multiplication(v6, v5) = v7) |  ~ (multiplication(v3, v4) = v6) |  ? [v8] : (multiplication(v4, v5) = v8 & multiplication(v3, v8) = v7)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (multiplication(v6, v5) = v7) |  ~ (addition(v3, v4) = v6) |  ? [v8] :  ? [v9] : (multiplication(v4, v5) = v9 & multiplication(v3, v5) = v8 & addition(v8, v9) = v7)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (multiplication(v4, v5) = v6) |  ~ (multiplication(v3, v6) = v7) |  ? [v8] : (multiplication(v8, v5) = v7 & multiplication(v3, v4) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (multiplication(v3, v6) = v7) |  ~ (addition(v4, v5) = v6) |  ? [v8] :  ? [v9] : (multiplication(v3, v5) = v9 & multiplication(v3, v4) = v8 & addition(v8, v9) = v7)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (addition(v6, v3) = v7) |  ~ (addition(v5, v4) = v6) |  ? [v8] : (addition(v5, v8) = v7 & addition(v4, v3) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (addition(v5, v6) = v7) |  ~ (addition(v4, v3) = v6) |  ? [v8] : (addition(v8, v3) = v7 & addition(v5, v4) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (leq(v6, v5) = v4) |  ~ (leq(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (multiplication(v6, v5) = v4) |  ~ (multiplication(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (addition(v6, v5) = v4) |  ~ (addition(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = v4 |  ~ (addition(v3, v4) = v5) |  ? [v6] : ( ~ (v6 = 0) & leq(v3, v4) = v6)) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (leq(v3, v4) = v5) |  ? [v6] : ( ~ (v6 = v4) & addition(v3, v4) = v6)) &  ! [v3] :  ! [v4] :  ! [v5] : (v4 = v3 |  ~ (codomain(v5) = v4) |  ~ (codomain(v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] : (v4 = v3 |  ~ (coantidomain(v5) = v4) |  ~ (coantidomain(v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] : (v4 = v3 |  ~ (domain(v5) = v4) |  ~ (domain(v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] : (v4 = v3 |  ~ (antidomain(v5) = v4) |  ~ (antidomain(v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v3, v4) = v5) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : (coantidomain(v9) = v10 & coantidomain(v7) = v8 & coantidomain(v5) = v6 & coantidomain(v3) = v7 & multiplication(v8, v4) = v9 & addition(v6, v10) = v10)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v3, v4) = v5) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : (antidomain(v9) = v10 & antidomain(v7) = v8 & antidomain(v5) = v6 & antidomain(v4) = v7 & multiplication(v3, v8) = v9 & addition(v6, v10) = v10)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (addition(v4, v3) = v5) | addition(v3, v4) = v5) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (addition(v3, v4) = v5) | addition(v4, v3) = v5) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (multiplication(v3, one) = v4)) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (multiplication(one, v3) = v4)) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (addition(v3, v3) = v4)) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (addition(v3, zero) = v4)) &  ! [v3] :  ! [v4] : (v4 = zero |  ~ (multiplication(v3, zero) = v4)) &  ! [v3] :  ! [v4] : (v4 = zero |  ~ (multiplication(zero, v3) = v4)) &  ! [v3] :  ! [v4] : ( ~ (codomain(v3) = v4) |  ? [v5] : (coantidomain(v5) = v4 & coantidomain(v3) = v5)) &  ! [v3] :  ! [v4] : ( ~ (coantidomain(v3) = v4) | multiplication(v3, v4) = zero) &  ! [v3] :  ! [v4] : ( ~ (coantidomain(v3) = v4) |  ? [v5] : (codomain(v3) = v5 & coantidomain(v4) = v5)) &  ! [v3] :  ! [v4] : ( ~ (coantidomain(v3) = v4) |  ? [v5] : (coantidomain(v4) = v5 & addition(v5, v4) = one)) &  ! [v3] :  ! [v4] : ( ~ (domain(v3) = v4) |  ? [v5] : (antidomain(v5) = v4 & antidomain(v3) = v5)) &  ! [v3] :  ! [v4] : ( ~ (antidomain(v3) = v4) | multiplication(v4, v3) = zero) &  ! [v3] :  ! [v4] : ( ~ (antidomain(v3) = v4) |  ? [v5] : (domain(v3) = v5 & antidomain(v4) = v5)) &  ! [v3] :  ! [v4] : ( ~ (antidomain(v3) = v4) |  ? [v5] : (antidomain(v4) = v5 & addition(v5, v4) = one)) &  ! [v3] :  ! [v4] : ( ~ (leq(v3, v4) = 0) | addition(v3, v4) = v4) &  ! [v3] :  ! [v4] : ( ~ (addition(v3, v4) = v4) | leq(v3, v4) = 0) &  ? [v3] :  ? [v4] :  ? [v5] : leq(v4, v3) = v5 &  ? [v3] :  ? [v4] :  ? [v5] : multiplication(v4, v3) = v5 &  ? [v3] :  ? [v4] :  ? [v5] : addition(v4, v3) = v5 &  ? [v3] :  ? [v4] : codomain(v3) = v4 &  ? [v3] :  ? [v4] : coantidomain(v3) = v4 &  ? [v3] :  ? [v4] : domain(v3) = v4 &  ? [v3] :  ? [v4] : antidomain(v3) = v4)
% 15.07/6.60  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 15.07/6.60  | (1)  ~ (all_0_0_0 = one) & domain(all_0_2_2) = all_0_1_1 & addition(all_0_1_1, one) = all_0_0_0 &  ! [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
% 15.07/6.61  |
% 15.07/6.61  | Applying alpha-rule on (1) yields:
% 15.07/6.61  | (2)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (codomain(v2) = v1) |  ~ (codomain(v2) = v0))
% 15.14/6.61  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 15.15/6.61  | (4)  ? [v0] :  ? [v1] : antidomain(v0) = v1
% 15.15/6.61  | (5)  ? [v0] :  ? [v1] :  ? [v2] : multiplication(v1, v0) = v2
% 15.15/6.61  | (6)  ! [v0] :  ! [v1] : ( ~ (coantidomain(v0) = v1) | multiplication(v0, v1) = zero)
% 15.15/6.61  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 15.15/6.61  | (8)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 15.15/6.61  | (9)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3))
% 15.15/6.61  | (10)  ! [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))
% 15.15/6.61  | (11)  ? [v0] :  ? [v1] :  ? [v2] : leq(v1, v0) = v2
% 15.15/6.61  | (12)  ! [v0] :  ! [v1] : ( ~ (antidomain(v0) = v1) |  ? [v2] : (domain(v0) = v2 & antidomain(v1) = v2))
% 15.15/6.61  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 15.15/6.61  | (14)  ! [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))
% 15.15/6.61  | (15)  ! [v0] :  ! [v1] : ( ~ (coantidomain(v0) = v1) |  ? [v2] : (coantidomain(v1) = v2 & addition(v2, v1) = one))
% 15.15/6.61  | (16)  ? [v0] :  ? [v1] :  ? [v2] : addition(v1, v0) = v2
% 15.15/6.61  | (17)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 15.15/6.61  | (18)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 15.15/6.62  | (19)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(v0, zero) = v1))
% 15.15/6.62  | (20)  ! [v0] :  ! [v1] : ( ~ (antidomain(v0) = v1) | multiplication(v1, v0) = zero)
% 15.15/6.62  | (21)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 15.15/6.62  | (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))
% 15.15/6.62  | (23)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (coantidomain(v2) = v1) |  ~ (coantidomain(v2) = v0))
% 15.15/6.62  | (24)  ! [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))
% 15.15/6.62  | (25)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 15.15/6.62  | (26)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 15.15/6.62  | (27)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0)
% 15.15/6.62  | (28)  ! [v0] :  ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1)
% 15.15/6.62  | (29)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (antidomain(v2) = v1) |  ~ (antidomain(v2) = v0))
% 15.15/6.62  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 15.15/6.62  | (31)  ? [v0] :  ? [v1] : codomain(v0) = v1
% 15.15/6.62  | (32)  ! [v0] :  ! [v1] : ( ~ (antidomain(v0) = v1) |  ? [v2] : (antidomain(v1) = v2 & addition(v2, v1) = one))
% 15.15/6.62  | (33)  ? [v0] :  ? [v1] : domain(v0) = v1
% 15.15/6.62  | (34)  ! [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))
% 15.15/6.62  | (35)  ! [v0] :  ! [v1] : ( ~ (coantidomain(v0) = v1) |  ? [v2] : (codomain(v0) = v2 & coantidomain(v1) = v2))
% 15.15/6.62  | (36)  ! [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))
% 15.15/6.62  | (37)  ! [v0] :  ! [v1] : ( ~ (domain(v0) = v1) |  ? [v2] : (antidomain(v2) = v1 & antidomain(v0) = v2))
% 15.15/6.62  | (38)  ~ (all_0_0_0 = one)
% 15.15/6.62  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 15.15/6.62  | (40)  ! [v0] :  ! [v1] : ( ~ (codomain(v0) = v1) |  ? [v2] : (coantidomain(v2) = v1 & coantidomain(v0) = v2))
% 15.15/6.62  | (41)  ! [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))
% 15.15/6.62  | (42)  ! [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))
% 15.15/6.62  | (43) addition(all_0_1_1, one) = all_0_0_0
% 15.15/6.62  | (44) domain(all_0_2_2) = all_0_1_1
% 15.15/6.62  | (45)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (leq(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3))
% 15.15/6.62  | (46)  ? [v0] :  ? [v1] : coantidomain(v0) = v1
% 15.15/6.62  | (47)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0))
% 15.15/6.62  | (48)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 15.15/6.62  | (49)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 15.15/6.62  | (50)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (domain(v2) = v1) |  ~ (domain(v2) = v0))
% 15.15/6.62  |
% 15.15/6.63  | Instantiating formula (37) with all_0_1_1, all_0_2_2 and discharging atoms domain(all_0_2_2) = all_0_1_1, yields:
% 15.15/6.63  | (51)  ? [v0] : (antidomain(v0) = all_0_1_1 & antidomain(all_0_2_2) = v0)
% 15.15/6.63  |
% 15.15/6.63  | Instantiating formula (9) with all_0_0_0, one, all_0_1_1 and discharging atoms addition(all_0_1_1, one) = all_0_0_0, yields:
% 15.15/6.63  | (52) all_0_0_0 = one |  ? [v0] : ( ~ (v0 = 0) & leq(all_0_1_1, one) = v0)
% 15.15/6.63  |
% 15.15/6.63  | Instantiating formula (49) with all_0_0_0, all_0_1_1, one and discharging atoms addition(all_0_1_1, one) = all_0_0_0, yields:
% 15.15/6.63  | (53) addition(one, all_0_1_1) = all_0_0_0
% 15.15/6.63  |
% 15.15/6.63  | Instantiating (51) with all_23_0_20 yields:
% 15.15/6.63  | (54) antidomain(all_23_0_20) = all_0_1_1 & antidomain(all_0_2_2) = all_23_0_20
% 15.15/6.63  |
% 15.15/6.63  | Applying alpha-rule on (54) yields:
% 15.15/6.63  | (55) antidomain(all_23_0_20) = all_0_1_1
% 15.15/6.63  | (56) antidomain(all_0_2_2) = all_23_0_20
% 15.15/6.63  |
% 15.15/6.63  +-Applying beta-rule and splitting (52), into two cases.
% 15.15/6.63  |-Branch one:
% 15.15/6.63  | (57) all_0_0_0 = one
% 15.15/6.63  |
% 15.15/6.63  	| Equations (57) can reduce 38 to:
% 15.15/6.63  	| (58) $false
% 15.15/6.63  	|
% 15.15/6.63  	|-The branch is then unsatisfiable
% 15.15/6.63  |-Branch two:
% 15.15/6.63  | (38)  ~ (all_0_0_0 = one)
% 15.15/6.63  | (60)  ? [v0] : ( ~ (v0 = 0) & leq(all_0_1_1, one) = v0)
% 15.15/6.63  |
% 15.15/6.63  	| Instantiating formula (32) with all_0_1_1, all_23_0_20 and discharging atoms antidomain(all_23_0_20) = all_0_1_1, yields:
% 15.15/6.63  	| (61)  ? [v0] : (antidomain(all_0_1_1) = v0 & addition(v0, all_0_1_1) = one)
% 15.15/6.63  	|
% 15.15/6.63  	| Instantiating formula (32) with all_23_0_20, all_0_2_2 and discharging atoms antidomain(all_0_2_2) = all_23_0_20, yields:
% 15.15/6.63  	| (62)  ? [v0] : (antidomain(all_23_0_20) = v0 & addition(v0, all_23_0_20) = one)
% 15.15/6.63  	|
% 15.15/6.63  	| Instantiating (62) with all_37_0_22 yields:
% 15.15/6.63  	| (63) antidomain(all_23_0_20) = all_37_0_22 & addition(all_37_0_22, all_23_0_20) = one
% 15.15/6.63  	|
% 15.15/6.63  	| Applying alpha-rule on (63) yields:
% 15.15/6.63  	| (64) antidomain(all_23_0_20) = all_37_0_22
% 15.15/6.63  	| (65) addition(all_37_0_22, all_23_0_20) = one
% 15.15/6.63  	|
% 15.15/6.63  	| Instantiating (61) with all_39_0_23 yields:
% 15.15/6.63  	| (66) antidomain(all_0_1_1) = all_39_0_23 & addition(all_39_0_23, all_0_1_1) = one
% 15.15/6.63  	|
% 15.15/6.63  	| Applying alpha-rule on (66) yields:
% 15.15/6.63  	| (67) antidomain(all_0_1_1) = all_39_0_23
% 15.15/6.63  	| (68) addition(all_39_0_23, all_0_1_1) = one
% 15.15/6.63  	|
% 15.15/6.63  	| Instantiating formula (29) with all_23_0_20, all_37_0_22, all_0_1_1 and discharging atoms antidomain(all_23_0_20) = all_37_0_22, antidomain(all_23_0_20) = all_0_1_1, yields:
% 15.15/6.63  	| (69) all_37_0_22 = all_0_1_1
% 15.15/6.63  	|
% 15.15/6.63  	| From (69) and (65) follows:
% 15.15/6.63  	| (70) addition(all_0_1_1, all_23_0_20) = one
% 15.15/6.63  	|
% 15.15/6.63  	| Instantiating formula (8) with all_0_0_0, one, all_39_0_23, all_0_1_1, all_0_1_1 and discharging atoms addition(all_39_0_23, all_0_1_1) = one, addition(one, all_0_1_1) = all_0_0_0, yields:
% 15.15/6.63  	| (71)  ? [v0] : (addition(all_39_0_23, v0) = all_0_0_0 & addition(all_0_1_1, all_0_1_1) = v0)
% 15.15/6.63  	|
% 15.15/6.63  	| Instantiating formula (7) with all_0_0_0, one, all_0_1_1, all_0_1_1, all_23_0_20 and discharging atoms addition(all_0_1_1, all_23_0_20) = one, addition(all_0_1_1, one) = all_0_0_0, yields:
% 15.15/6.63  	| (72)  ? [v0] : (addition(v0, all_23_0_20) = all_0_0_0 & addition(all_0_1_1, all_0_1_1) = v0)
% 15.15/6.63  	|
% 15.15/6.63  	| Instantiating (72) with all_55_0_26 yields:
% 15.15/6.63  	| (73) addition(all_55_0_26, all_23_0_20) = all_0_0_0 & addition(all_0_1_1, all_0_1_1) = all_55_0_26
% 15.15/6.63  	|
% 15.15/6.63  	| Applying alpha-rule on (73) yields:
% 15.15/6.63  	| (74) addition(all_55_0_26, all_23_0_20) = all_0_0_0
% 15.15/6.63  	| (75) addition(all_0_1_1, all_0_1_1) = all_55_0_26
% 15.15/6.63  	|
% 15.15/6.63  	| Instantiating (71) with all_65_0_39 yields:
% 15.15/6.63  	| (76) addition(all_39_0_23, all_65_0_39) = all_0_0_0 & addition(all_0_1_1, all_0_1_1) = all_65_0_39
% 15.15/6.63  	|
% 15.15/6.63  	| Applying alpha-rule on (76) yields:
% 15.15/6.63  	| (77) addition(all_39_0_23, all_65_0_39) = all_0_0_0
% 15.15/6.63  	| (78) addition(all_0_1_1, all_0_1_1) = all_65_0_39
% 15.15/6.64  	|
% 15.15/6.64  	| Instantiating formula (17) with all_65_0_39, all_0_1_1 and discharging atoms addition(all_0_1_1, all_0_1_1) = all_65_0_39, yields:
% 15.15/6.64  	| (79) all_65_0_39 = all_0_1_1
% 15.15/6.64  	|
% 15.15/6.64  	| Instantiating formula (39) with all_0_1_1, all_0_1_1, all_55_0_26, all_65_0_39 and discharging atoms addition(all_0_1_1, all_0_1_1) = all_65_0_39, addition(all_0_1_1, all_0_1_1) = all_55_0_26, yields:
% 15.15/6.64  	| (80) all_65_0_39 = all_55_0_26
% 15.15/6.64  	|
% 15.15/6.64  	| Combining equations (79,80) yields a new equation:
% 15.15/6.64  	| (81) all_55_0_26 = all_0_1_1
% 15.15/6.64  	|
% 15.15/6.64  	| From (81) and (74) follows:
% 15.15/6.64  	| (82) addition(all_0_1_1, all_23_0_20) = all_0_0_0
% 15.15/6.64  	|
% 15.15/6.64  	| Instantiating formula (39) with all_0_1_1, all_23_0_20, all_0_0_0, one and discharging atoms addition(all_0_1_1, all_23_0_20) = all_0_0_0, addition(all_0_1_1, all_23_0_20) = one, yields:
% 15.15/6.64  	| (57) all_0_0_0 = one
% 15.15/6.64  	|
% 15.15/6.64  	| Equations (57) can reduce 38 to:
% 15.15/6.64  	| (58) $false
% 15.15/6.64  	|
% 15.15/6.64  	|-The branch is then unsatisfiable
% 15.15/6.64  % SZS output end Proof for theBenchmark
% 15.15/6.64  
% 15.15/6.64  6038ms
%------------------------------------------------------------------------------