%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE058+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n007.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 01:51:11 EDT 2022

% Result   : Theorem 19.03s 6.32s
% Output   : Proof 19.94s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : KLE058+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n007.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 14:06:41 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.58/0.61          ____       _                          
% 0.58/0.61    ___  / __ \_____(_)___  ________  __________
% 0.58/0.61   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.61  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.58/0.61  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.58/0.61  
% 0.58/0.61  A Theorem Prover for First-Order Logic
% 0.58/0.61  (ePrincess v.1.0)
% 0.58/0.61  
% 0.58/0.61  (c) Philipp Rümmer, 2009-2015
% 0.58/0.61  (c) Peter Backeman, 2014-2015
% 0.58/0.61  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.61  Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.61  Bug reports to peter@backeman.se
% 0.58/0.61  
% 0.58/0.61  For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.61  
% 0.58/0.61  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.67  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.54/0.96  Prover 0: Preprocessing ...
% 2.21/1.22  Prover 0: Constructing countermodel ...
% 17.36/5.96  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 17.53/6.00  Prover 1: Preprocessing ...
% 17.53/6.07  Prover 1: Constructing countermodel ...
% 18.56/6.21  Prover 1: gave up
% 18.56/6.21  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 18.56/6.23  Prover 2: Preprocessing ...
% 18.56/6.27  Prover 2: Warning: ignoring some quantifiers
% 18.56/6.27  Prover 2: Constructing countermodel ...
% 18.56/6.31  Prover 2: proved (93ms)
% 19.03/6.31  Prover 0: stopped
% 19.03/6.31  
% 19.03/6.32  No countermodel exists, formula is valid
% 19.03/6.32  % SZS status Theorem for theBenchmark
% 19.03/6.32  
% 19.03/6.32  Generating proof ... Warning: ignoring some quantifiers
% 19.94/6.53  found it (size 24)
% 19.94/6.53  
% 19.94/6.53  % SZS output start Proof for theBenchmark
% 19.94/6.53  Assumed formulas after preprocessing and simplification: 
% 19.94/6.54  | (0)  ? [v0] : ( ~ (v0 = one) & domain(one) = v0 & domain(zero) = zero &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (multiplication(v2, v3) = v5) |  ~ (multiplication(v1, v3) = v4) |  ~ (addition(v4, v5) = v6) |  ? [v7] : (multiplication(v7, v3) = v6 & addition(v1, v2) = v7)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (multiplication(v1, v3) = v5) |  ~ (multiplication(v1, v2) = v4) |  ~ (addition(v4, v5) = v6) |  ? [v7] : (multiplication(v1, v7) = v6 & addition(v2, v3) = v7)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (domain(v2) = v4) |  ~ (domain(v1) = v3) |  ~ (addition(v3, v4) = v5) |  ? [v6] : (domain(v6) = v5 & addition(v1, v2) = v6)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v4, v3) = v5) |  ~ (multiplication(v1, v2) = v4) |  ? [v6] : (multiplication(v2, v3) = v6 & multiplication(v1, v6) = v5)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v4, v3) = v5) |  ~ (addition(v1, v2) = v4) |  ? [v6] :  ? [v7] : (multiplication(v2, v3) = v7 & multiplication(v1, v3) = v6 & addition(v6, v7) = v5)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v2, v3) = v4) |  ~ (multiplication(v1, v4) = v5) |  ? [v6] : (multiplication(v6, v3) = v5 & multiplication(v1, v2) = v6)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v1, v4) = v5) |  ~ (addition(v2, v3) = v4) |  ? [v6] :  ? [v7] : (multiplication(v1, v3) = v7 & multiplication(v1, v2) = v6 & addition(v6, v7) = v5)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (addition(v4, v1) = v5) |  ~ (addition(v3, v2) = v4) |  ? [v6] : (addition(v3, v6) = v5 & addition(v2, v1) = v6)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (addition(v3, v4) = v5) |  ~ (addition(v2, v1) = v4) |  ? [v6] : (addition(v6, v1) = v5 & addition(v3, v2) = v6)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (leq(v4, v3) = v2) |  ~ (leq(v4, v3) = v1)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (multiplication(v4, v3) = v2) |  ~ (multiplication(v4, v3) = v1)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (addition(v4, v3) = v2) |  ~ (addition(v4, v3) = v1)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (domain(v2) = v3) |  ~ (multiplication(v1, v3) = v4) |  ? [v5] :  ? [v6] : (domain(v5) = v6 & domain(v4) = v6 & multiplication(v1, v2) = v5)) &  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (addition(v1, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & leq(v1, v2) = v4)) &  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (leq(v1, v2) = v3) |  ? [v4] : ( ~ (v4 = v2) & addition(v1, v2) = v4)) &  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 |  ~ (domain(v3) = v2) |  ~ (domain(v3) = v1)) &  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (multiplication(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] : (domain(v6) = v4 & domain(v3) = v4 & domain(v2) = v5 & multiplication(v1, v5) = v6)) &  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (addition(v2, v1) = v3) | addition(v1, v2) = v3) &  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (addition(v1, v2) = v3) | addition(v2, v1) = v3) &  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (addition(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] : (domain(v3) = v4 & domain(v2) = v6 & domain(v1) = v5 & addition(v5, v6) = v4)) &  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (multiplication(v1, one) = v2)) &  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (multiplication(one, v1) = v2)) &  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v1, v1) = v2)) &  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v1, zero) = v2)) &  ! [v1] :  ! [v2] : (v2 = zero |  ~ (multiplication(v1, zero) = v2)) &  ! [v1] :  ! [v2] : (v2 = zero |  ~ (multiplication(zero, v1) = v2)) &  ! [v1] :  ! [v2] : ( ~ (domain(v1) = v2) | addition(v2, one) = one) &  ! [v1] :  ! [v2] : ( ~ (domain(v1) = v2) |  ? [v3] : (multiplication(v2, v1) = v3 & addition(v1, v3) = v3)) &  ! [v1] :  ! [v2] : ( ~ (leq(v1, v2) = 0) | addition(v1, v2) = v2) &  ! [v1] :  ! [v2] : ( ~ (addition(v1, v2) = v2) | leq(v1, v2) = 0) &  ? [v1] :  ? [v2] :  ? [v3] : leq(v2, v1) = v3 &  ? [v1] :  ? [v2] :  ? [v3] : multiplication(v2, v1) = v3 &  ? [v1] :  ? [v2] :  ? [v3] : addition(v2, v1) = v3 &  ? [v1] :  ? [v2] : domain(v1) = v2)
% 19.94/6.57  | Instantiating (0) with all_0_0_0 yields:
% 19.94/6.57  | (1)  ~ (all_0_0_0 = one) & domain(one) = all_0_0_0 & domain(zero) = zero &  ! [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] : ( ~ (domain(v1) = v3) |  ~ (domain(v0) = v2) |  ~ (addition(v2, v3) = v4) |  ? [v5] : (domain(v5) = v4 & addition(v0, v1) = v5)) &  ! [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] :  ! [v3] : ( ~ (domain(v1) = v2) |  ~ (multiplication(v0, v2) = v3) |  ? [v4] :  ? [v5] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = v4)) &  ! [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 |  ~ (domain(v2) = v1) |  ~ (domain(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & multiplication(v0, v4) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4, v5) = v3)) &  ! [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] : ( ~ (domain(v0) = v1) | addition(v1, one) = one) &  ! [v0] :  ! [v1] : ( ~ (domain(v0) = v1) |  ? [v2] : (multiplication(v1, v0) = v2 & addition(v0, v2) = v2)) &  ! [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] : domain(v0) = v1
% 19.94/6.58  |
% 19.94/6.58  | Applying alpha-rule on (1) yields:
% 19.94/6.58  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 19.94/6.58  | (3)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (domain(v2) = v1) |  ~ (domain(v2) = v0))
% 19.94/6.58  | (4)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3))
% 19.94/6.58  | (5)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4, v5) = v3))
% 19.94/6.58  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 19.94/6.58  | (7)  ! [v0] :  ! [v1] : ( ~ (domain(v0) = v1) | addition(v1, one) = one)
% 19.94/6.58  | (8) domain(zero) = zero
% 19.94/6.58  | (9)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0)
% 19.94/6.58  | (10)  ! [v0] :  ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1)
% 19.94/6.58  | (11)  ~ (all_0_0_0 = one)
% 19.94/6.58  | (12)  ! [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))
% 19.94/6.58  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 19.94/6.58  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 19.94/6.58  | (15)  ! [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))
% 19.94/6.58  | (16)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 19.94/6.58  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 19.94/6.58  | (18)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 19.94/6.58  | (19)  ? [v0] :  ? [v1] :  ? [v2] : leq(v1, v0) = v2
% 19.94/6.58  | (20)  ! [v0] :  ! [v1] : ( ~ (domain(v0) = v1) |  ? [v2] : (multiplication(v1, v0) = v2 & addition(v0, v2) = v2))
% 19.94/6.58  | (21)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 19.94/6.58  | (22)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 19.94/6.58  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (domain(v1) = v3) |  ~ (domain(v0) = v2) |  ~ (addition(v2, v3) = v4) |  ? [v5] : (domain(v5) = v4 & addition(v0, v1) = v5))
% 19.94/6.58  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 19.94/6.58  | (25)  ? [v0] :  ? [v1] :  ? [v2] : multiplication(v1, v0) = v2
% 19.94/6.59  | (26)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(v0, zero) = v1))
% 19.94/6.59  | (27)  ! [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))
% 19.94/6.59  | (28)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (leq(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3))
% 19.94/6.59  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0))
% 19.94/6.59  | (30)  ? [v0] :  ? [v1] : domain(v0) = v1
% 19.94/6.59  | (31)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & multiplication(v0, v4) = v5))
% 19.94/6.59  | (32)  ! [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))
% 19.94/6.59  | (33)  ? [v0] :  ? [v1] :  ? [v2] : addition(v1, v0) = v2
% 19.94/6.59  | (34)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 19.94/6.59  | (35)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 19.94/6.59  | (36)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 19.94/6.59  | (37) domain(one) = all_0_0_0
% 19.94/6.59  | (38)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (domain(v1) = v2) |  ~ (multiplication(v0, v2) = v3) |  ? [v4] :  ? [v5] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = v4))
% 19.94/6.59  |
% 19.94/6.59  | Instantiating formula (7) with all_0_0_0, one and discharging atoms domain(one) = all_0_0_0, yields:
% 19.94/6.59  | (39) addition(all_0_0_0, one) = one
% 19.94/6.59  |
% 19.94/6.59  | Instantiating formula (20) with all_0_0_0, one and discharging atoms domain(one) = all_0_0_0, yields:
% 19.94/6.59  | (40)  ? [v0] : (multiplication(all_0_0_0, one) = v0 & addition(one, v0) = v0)
% 19.94/6.59  |
% 19.94/6.59  | Instantiating formula (7) with zero, zero and discharging atoms domain(zero) = zero, yields:
% 19.94/6.59  | (41) addition(zero, one) = one
% 19.94/6.59  |
% 19.94/6.59  | Instantiating (40) with all_19_0_13 yields:
% 19.94/6.59  | (42) multiplication(all_0_0_0, one) = all_19_0_13 & addition(one, all_19_0_13) = all_19_0_13
% 19.94/6.59  |
% 19.94/6.59  | Applying alpha-rule on (42) yields:
% 19.94/6.59  | (43) multiplication(all_0_0_0, one) = all_19_0_13
% 19.94/6.59  | (44) addition(one, all_19_0_13) = all_19_0_13
% 19.94/6.59  |
% 19.94/6.59  | Instantiating formula (18) with all_19_0_13, all_0_0_0 and discharging atoms multiplication(all_0_0_0, one) = all_19_0_13, yields:
% 19.94/6.59  | (45) all_19_0_13 = all_0_0_0
% 19.94/6.59  |
% 19.94/6.59  | From (45)(45) and (44) follows:
% 19.94/6.59  | (46) addition(one, all_0_0_0) = all_0_0_0
% 19.94/6.59  |
% 19.94/6.59  | Instantiating formula (35) with one, all_0_0_0, one and discharging atoms addition(all_0_0_0, one) = one, yields:
% 19.94/6.59  | (47) addition(one, all_0_0_0) = one
% 19.94/6.59  |
% 19.94/6.59  | Instantiating formula (2) with all_0_0_0, one, all_0_0_0, one, all_0_0_0 and discharging atoms addition(all_0_0_0, one) = one, addition(one, all_0_0_0) = all_0_0_0, yields:
% 19.94/6.59  | (48)  ? [v0] : (addition(all_0_0_0, v0) = all_0_0_0 & addition(one, all_0_0_0) = v0)
% 19.94/6.59  |
% 19.94/6.59  | Instantiating formula (2) with all_0_0_0, one, zero, one, all_0_0_0 and discharging atoms addition(one, all_0_0_0) = all_0_0_0, addition(zero, one) = one, yields:
% 19.94/6.59  | (49)  ? [v0] : (addition(one, all_0_0_0) = v0 & addition(zero, v0) = all_0_0_0)
% 19.94/6.59  |
% 19.94/6.59  | Instantiating (49) with all_31_0_14 yields:
% 19.94/6.59  | (50) addition(one, all_0_0_0) = all_31_0_14 & addition(zero, all_31_0_14) = all_0_0_0
% 19.94/6.59  |
% 19.94/6.59  | Applying alpha-rule on (50) yields:
% 19.94/6.59  | (51) addition(one, all_0_0_0) = all_31_0_14
% 19.94/6.59  | (52) addition(zero, all_31_0_14) = all_0_0_0
% 19.94/6.59  |
% 19.94/6.59  | Instantiating (48) with all_49_0_29 yields:
% 19.94/6.59  | (53) addition(all_0_0_0, all_49_0_29) = all_0_0_0 & addition(one, all_0_0_0) = all_49_0_29
% 19.94/6.59  |
% 19.94/6.59  | Applying alpha-rule on (53) yields:
% 19.94/6.59  | (54) addition(all_0_0_0, all_49_0_29) = all_0_0_0
% 19.94/6.59  | (55) addition(one, all_0_0_0) = all_49_0_29
% 19.94/6.59  |
% 19.94/6.59  | Instantiating formula (17) with one, all_0_0_0, all_49_0_29, all_0_0_0 and discharging atoms addition(one, all_0_0_0) = all_49_0_29, addition(one, all_0_0_0) = all_0_0_0, yields:
% 19.94/6.59  | (56) all_49_0_29 = all_0_0_0
% 19.94/6.59  |
% 19.94/6.59  | Instantiating formula (17) with one, all_0_0_0, all_31_0_14, all_49_0_29 and discharging atoms addition(one, all_0_0_0) = all_49_0_29, addition(one, all_0_0_0) = all_31_0_14, yields:
% 19.94/6.59  | (57) all_49_0_29 = all_31_0_14
% 19.94/6.59  |
% 19.94/6.59  | Instantiating formula (17) with one, all_0_0_0, one, all_31_0_14 and discharging atoms addition(one, all_0_0_0) = all_31_0_14, addition(one, all_0_0_0) = one, yields:
% 19.94/6.59  | (58) all_31_0_14 = one
% 19.94/6.59  |
% 19.94/6.60  | Combining equations (57,56) yields a new equation:
% 19.94/6.60  | (59) all_31_0_14 = all_0_0_0
% 19.94/6.60  |
% 19.94/6.60  | Simplifying 59 yields:
% 19.94/6.60  | (60) all_31_0_14 = all_0_0_0
% 19.94/6.60  |
% 19.94/6.60  | Combining equations (58,60) yields a new equation:
% 19.94/6.60  | (61) all_0_0_0 = one
% 19.94/6.60  |
% 19.94/6.60  | Equations (61) can reduce 11 to:
% 19.94/6.60  | (62) $false
% 19.94/6.60  |
% 19.94/6.60  |-The branch is then unsatisfiable
% 19.94/6.60  % SZS output end Proof for theBenchmark
% 19.94/6.60  
% 20.40/6.60  5971ms
%------------------------------------------------------------------------------