%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE089+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n003.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 01:51:19 EDT 2022

% Result   : Theorem 12.46s 6.36s
% Output   : Proof 14.27s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KLE089+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.34  % Computer : n003.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 : Thu Jun 16 10:01:41 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.60/0.59          ____       _                          
% 0.60/0.59    ___  / __ \_____(_)___  ________  __________
% 0.60/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.60/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.60/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.60/0.59  
% 0.60/0.59  A Theorem Prover for First-Order Logic
% 0.60/0.59  (ePrincess v.1.0)
% 0.60/0.59  
% 0.60/0.59  (c) Philipp Rümmer, 2009-2015
% 0.60/0.59  (c) Peter Backeman, 2014-2015
% 0.60/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.60/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.60/0.59  Bug reports to peter@backeman.se
% 0.60/0.59  
% 0.60/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.60/0.59  
% 0.60/0.59  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.74/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.55/0.93  Prover 0: Preprocessing ...
% 2.49/1.21  Prover 0: Constructing countermodel ...
% 10.69/5.93  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 10.69/5.96  Prover 1: Preprocessing ...
% 11.07/6.05  Prover 1: Constructing countermodel ...
% 11.47/6.18  Prover 1: gave up
% 11.86/6.18  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 11.86/6.20  Prover 2: Preprocessing ...
% 11.86/6.26  Prover 2: Warning: ignoring some quantifiers
% 11.86/6.26  Prover 2: Constructing countermodel ...
% 12.46/6.36  Prover 2: proved (176ms)
% 12.46/6.36  Prover 0: stopped
% 12.46/6.36  
% 12.46/6.36  No countermodel exists, formula is valid
% 12.46/6.36  % SZS status Theorem for theBenchmark
% 12.46/6.36  
% 12.46/6.36  Generating proof ... Warning: ignoring some quantifiers
% 13.80/6.63  found it (size 37)
% 13.80/6.63  
% 13.80/6.63  % SZS output start Proof for theBenchmark
% 13.80/6.63  Assumed formulas after preprocessing and simplification: 
% 13.80/6.64  | (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)
% 13.80/6.67  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 13.80/6.67  | (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
% 13.80/6.68  |
% 13.80/6.68  | Applying alpha-rule on (1) yields:
% 13.80/6.68  | (2)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (codomain(v2) = v1) |  ~ (codomain(v2) = v0))
% 13.80/6.68  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 13.80/6.68  | (4)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3))
% 13.80/6.68  | (5)  ? [v0] :  ? [v1] :  ? [v2] : leq(v1, v0) = v2
% 13.80/6.68  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 13.80/6.68  | (7)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 13.80/6.68  | (8)  ? [v0] :  ? [v1] : antidomain(v0) = v1
% 13.80/6.68  | (9)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 13.80/6.68  | (10)  ~ (all_0_0_0 = zero)
% 13.80/6.68  | (11)  ! [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))
% 13.80/6.68  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 13.80/6.68  | (13)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 13.80/6.68  | (14)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 13.80/6.68  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 13.80/6.68  | (16)  ! [v0] :  ! [v1] : ( ~ (coantidomain(v0) = v1) |  ? [v2] : (codomain(v0) = v2 & coantidomain(v1) = v2))
% 13.80/6.68  | (17)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (leq(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3))
% 13.80/6.68  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 13.80/6.68  | (19)  ! [v0] :  ! [v1] : ( ~ (antidomain(v0) = v1) | multiplication(v1, v0) = zero)
% 13.80/6.68  | (20) addition(all_0_2_2, all_0_1_1) = all_0_1_1
% 13.80/6.68  | (21)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (domain(v2) = v1) |  ~ (domain(v2) = v0))
% 13.80/6.68  | (22)  ! [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))
% 13.80/6.68  | (23)  ? [v0] :  ? [v1] : domain(v0) = v1
% 13.80/6.68  | (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))
% 13.80/6.68  | (25)  ! [v0] :  ! [v1] : ( ~ (domain(v0) = v1) |  ? [v2] : (antidomain(v2) = v1 & antidomain(v0) = v2))
% 13.80/6.68  | (26)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (coantidomain(v2) = v1) |  ~ (coantidomain(v2) = v0))
% 13.80/6.68  | (27)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (antidomain(v2) = v1) |  ~ (antidomain(v2) = v0))
% 13.80/6.68  | (28)  ? [v0] :  ? [v1] : codomain(v0) = v1
% 13.80/6.68  | (29)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0)
% 13.80/6.68  | (30)  ! [v0] :  ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1)
% 13.80/6.68  | (31)  ? [v0] :  ? [v1] :  ? [v2] : multiplication(v1, v0) = v2
% 13.80/6.68  | (32)  ! [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))
% 13.80/6.68  | (33)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 13.80/6.68  | (34)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 13.80/6.68  | (35)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 13.80/6.68  | (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))
% 13.80/6.68  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0))
% 13.80/6.68  | (38)  ? [v0] :  ? [v1] : coantidomain(v0) = v1
% 13.80/6.68  | (39)  ! [v0] :  ! [v1] : ( ~ (codomain(v0) = v1) |  ? [v2] : (coantidomain(v2) = v1 & coantidomain(v0) = v2))
% 13.80/6.68  | (40)  ? [v0] :  ? [v1] :  ? [v2] : addition(v1, v0) = v2
% 13.80/6.68  | (41)  ! [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))
% 13.80/6.69  | (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))
% 13.80/6.69  | (43)  ! [v0] :  ! [v1] : ( ~ (antidomain(v0) = v1) |  ? [v2] : (domain(v0) = v2 & antidomain(v1) = v2))
% 13.80/6.69  | (44)  ! [v0] :  ! [v1] : ( ~ (antidomain(v0) = v1) |  ? [v2] : (antidomain(v1) = v2 & addition(v2, v1) = one))
% 13.80/6.69  | (45) antidomain(all_0_3_3) = all_0_1_1
% 13.80/6.69  | (46)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(v0, zero) = v1))
% 13.80/6.69  | (47)  ! [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))
% 13.80/6.69  | (48)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 13.80/6.69  | (49)  ! [v0] :  ! [v1] : ( ~ (coantidomain(v0) = v1) | multiplication(v0, v1) = zero)
% 13.80/6.69  | (50) multiplication(all_0_2_2, all_0_3_3) = all_0_0_0
% 13.80/6.69  | (51) domain(all_0_4_4) = all_0_2_2
% 13.80/6.69  | (52)  ! [v0] :  ! [v1] : ( ~ (coantidomain(v0) = v1) |  ? [v2] : (coantidomain(v1) = v2 & addition(v2, v1) = one))
% 13.80/6.69  |
% 13.80/6.69  | Instantiating formula (19) with all_0_1_1, all_0_3_3 and discharging atoms antidomain(all_0_3_3) = all_0_1_1, yields:
% 13.80/6.69  | (53) multiplication(all_0_1_1, all_0_3_3) = zero
% 13.80/6.69  |
% 13.80/6.69  | Instantiating formula (15) 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:
% 13.80/6.69  | (54)  ? [v0] : (addition(v0, all_0_1_1) = all_0_1_1 & addition(all_0_2_2, all_0_2_2) = v0)
% 13.80/6.69  |
% 13.80/6.69  | Instantiating formula (14) 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:
% 13.80/6.69  | (55) addition(all_0_1_1, all_0_2_2) = all_0_1_1
% 13.80/6.69  |
% 13.80/6.69  | Instantiating (54) with all_31_0_34 yields:
% 13.80/6.69  | (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
% 13.80/6.69  |
% 13.80/6.69  | Applying alpha-rule on (56) yields:
% 13.80/6.69  | (57) addition(all_31_0_34, all_0_1_1) = all_0_1_1
% 13.80/6.69  | (58) addition(all_0_2_2, all_0_2_2) = all_31_0_34
% 13.80/6.69  |
% 13.80/6.69  | Instantiating formula (48) 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:
% 13.80/6.69  | (59) all_31_0_34 = all_0_2_2
% 13.80/6.69  |
% 13.80/6.69  | From (59) and (57) follows:
% 13.80/6.69  | (20) addition(all_0_2_2, all_0_1_1) = all_0_1_1
% 13.80/6.69  |
% 13.80/6.69  | From (59) and (58) follows:
% 13.80/6.69  | (61) addition(all_0_2_2, all_0_2_2) = all_0_2_2
% 13.80/6.69  |
% 13.80/6.69  | Instantiating formula (11) 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:
% 13.80/6.69  | (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)
% 13.80/6.69  |
% 13.80/6.69  | Instantiating formula (11) 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:
% 13.80/6.69  | (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)
% 13.80/6.69  |
% 13.80/6.69  | Instantiating formula (11) 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:
% 13.80/6.69  | (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)
% 13.80/6.69  |
% 13.80/6.69  | Instantiating (64) with all_53_0_39, all_53_1_40 yields:
% 13.80/6.69  | (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
% 13.80/6.69  |
% 13.80/6.69  | Applying alpha-rule on (65) yields:
% 13.80/6.69  | (66) multiplication(all_0_2_2, all_0_3_3) = all_53_0_39
% 13.80/6.69  | (67) multiplication(all_0_2_2, all_0_3_3) = all_53_1_40
% 13.80/6.69  | (68) addition(all_53_1_40, all_53_0_39) = all_0_0_0
% 13.80/6.69  |
% 13.80/6.69  | Instantiating (62) with all_67_0_59, all_67_1_60 yields:
% 13.80/6.69  | (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
% 13.80/6.69  |
% 13.80/6.69  | Applying alpha-rule on (69) yields:
% 13.80/6.69  | (70) multiplication(all_0_1_1, all_0_3_3) = all_67_0_59
% 13.80/6.69  | (71) multiplication(all_0_2_2, all_0_3_3) = all_67_1_60
% 13.80/6.69  | (72) addition(all_67_1_60, all_67_0_59) = zero
% 13.80/6.69  |
% 13.80/6.69  | Instantiating (63) with all_83_0_72, all_83_1_73 yields:
% 13.80/6.69  | (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
% 13.80/6.69  |
% 13.80/6.69  | Applying alpha-rule on (73) yields:
% 13.80/6.69  | (74) multiplication(all_0_1_1, all_0_3_3) = all_83_1_73
% 13.80/6.69  | (75) multiplication(all_0_2_2, all_0_3_3) = all_83_0_72
% 13.80/6.69  | (76) addition(all_83_1_73, all_83_0_72) = zero
% 13.80/6.69  |
% 13.80/6.69  | Instantiating formula (12) 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:
% 13.80/6.69  | (77) all_83_1_73 = zero
% 13.80/6.69  |
% 13.80/6.69  | Instantiating formula (12) 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:
% 13.80/6.69  | (78) all_83_1_73 = all_67_0_59
% 13.80/6.69  |
% 13.80/6.70  | Instantiating formula (12) 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:
% 13.80/6.70  | (79) all_67_1_60 = all_0_0_0
% 13.80/6.70  |
% 13.80/6.70  | Instantiating formula (12) 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:
% 13.80/6.70  | (80) all_83_0_72 = all_67_1_60
% 13.80/6.70  |
% 13.80/6.70  | Instantiating formula (12) 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:
% 13.80/6.70  | (81) all_67_1_60 = all_53_0_39
% 13.80/6.70  |
% 13.80/6.70  | Instantiating formula (12) 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:
% 13.80/6.70  | (82) all_83_0_72 = all_53_1_40
% 13.80/6.70  |
% 13.80/6.70  | Combining equations (80,82) yields a new equation:
% 13.80/6.70  | (83) all_67_1_60 = all_53_1_40
% 13.80/6.70  |
% 14.27/6.70  | Simplifying 83 yields:
% 14.27/6.70  | (84) all_67_1_60 = all_53_1_40
% 14.27/6.70  |
% 14.27/6.70  | Combining equations (77,78) yields a new equation:
% 14.27/6.70  | (85) all_67_0_59 = zero
% 14.27/6.70  |
% 14.27/6.70  | Combining equations (79,81) yields a new equation:
% 14.27/6.70  | (86) all_53_0_39 = all_0_0_0
% 14.27/6.70  |
% 14.27/6.70  | Combining equations (84,81) yields a new equation:
% 14.27/6.70  | (87) all_53_0_39 = all_53_1_40
% 14.27/6.70  |
% 14.27/6.70  | Combining equations (86,87) yields a new equation:
% 14.27/6.70  | (88) all_53_1_40 = all_0_0_0
% 14.27/6.70  |
% 14.27/6.70  | Combining equations (88,87) yields a new equation:
% 14.27/6.70  | (86) all_53_0_39 = all_0_0_0
% 14.27/6.70  |
% 14.27/6.70  | Combining equations (86,81) yields a new equation:
% 14.27/6.70  | (79) all_67_1_60 = all_0_0_0
% 14.27/6.70  |
% 14.27/6.70  | From (79)(85) and (72) follows:
% 14.27/6.70  | (91) addition(all_0_0_0, zero) = zero
% 14.27/6.70  |
% 14.27/6.70  | Instantiating formula (33) with zero, all_0_0_0 and discharging atoms addition(all_0_0_0, zero) = zero, yields:
% 14.27/6.70  | (92) all_0_0_0 = zero
% 14.27/6.70  |
% 14.27/6.70  | Equations (92) can reduce 10 to:
% 14.27/6.70  | (93) $false
% 14.27/6.70  |
% 14.27/6.70  |-The branch is then unsatisfiable
% 14.27/6.70  % SZS output end Proof for theBenchmark
% 14.27/6.70  
% 14.27/6.70  6100ms
%------------------------------------------------------------------------------