%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE065+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n028.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 01:51:13 EDT 2022

% Result   : Theorem 27.36s 8.71s
% Output   : Proof 28.50s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : KLE065+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n028.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 07:46:11 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.55/0.60          ____       _                          
% 0.55/0.60    ___  / __ \_____(_)___  ________  __________
% 0.55/0.60   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.60  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.55/0.60  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.55/0.60  
% 0.55/0.60  A Theorem Prover for First-Order Logic
% 0.62/0.60  (ePrincess v.1.0)
% 0.62/0.60  
% 0.62/0.60  (c) Philipp Rümmer, 2009-2015
% 0.62/0.60  (c) Peter Backeman, 2014-2015
% 0.62/0.60  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.62/0.60  Free software under GNU Lesser General Public License (LGPL).
% 0.62/0.60  Bug reports to peter@backeman.se
% 0.62/0.60  
% 0.62/0.60  For more information, visit http://user.uu.se/~petba168/breu/
% 0.62/0.60  
% 0.62/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.65  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.39/0.94  Prover 0: Preprocessing ...
% 2.22/1.21  Prover 0: Constructing countermodel ...
% 18.25/5.94  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 18.25/5.97  Prover 1: Preprocessing ...
% 18.68/6.06  Prover 1: Constructing countermodel ...
% 26.69/8.54  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 26.71/8.56  Prover 2: Preprocessing ...
% 27.02/8.63  Prover 2: Warning: ignoring some quantifiers
% 27.02/8.64  Prover 2: Constructing countermodel ...
% 27.36/8.70  Prover 2: proved (165ms)
% 27.36/8.71  Prover 1: stopped
% 27.36/8.71  Prover 0: stopped
% 27.36/8.71  
% 27.36/8.71  No countermodel exists, formula is valid
% 27.36/8.71  % SZS status Theorem for theBenchmark
% 27.36/8.71  
% 27.36/8.71  Generating proof ... Warning: ignoring some quantifiers
% 28.07/8.86  found it (size 37)
% 28.07/8.86  
% 28.07/8.86  % SZS output start Proof for theBenchmark
% 28.07/8.86  Assumed formulas after preprocessing and simplification: 
% 28.07/8.87  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : ( ~ (v3 = zero) & domain(v1) = v2 & domain(zero) = zero & multiplication(v0, v2) = v3 & multiplication(v0, v1) = zero &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (multiplication(v5, v6) = v8) |  ~ (multiplication(v4, v6) = v7) |  ~ (addition(v7, v8) = v9) |  ? [v10] : (multiplication(v10, v6) = v9 & addition(v4, v5) = v10)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (multiplication(v4, v6) = v8) |  ~ (multiplication(v4, v5) = v7) |  ~ (addition(v7, v8) = v9) |  ? [v10] : (multiplication(v4, v10) = v9 & addition(v5, v6) = v10)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (domain(v5) = v7) |  ~ (domain(v4) = v6) |  ~ (addition(v6, v7) = v8) |  ? [v9] : (domain(v9) = v8 & addition(v4, v5) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v7, v6) = v8) |  ~ (multiplication(v4, v5) = v7) |  ? [v9] : (multiplication(v5, v6) = v9 & multiplication(v4, v9) = v8)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v7, v6) = v8) |  ~ (addition(v4, v5) = v7) |  ? [v9] :  ? [v10] : (multiplication(v5, v6) = v10 & multiplication(v4, v6) = v9 & addition(v9, v10) = v8)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v5, v6) = v7) |  ~ (multiplication(v4, v7) = v8) |  ? [v9] : (multiplication(v9, v6) = v8 & multiplication(v4, v5) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v4, v7) = v8) |  ~ (addition(v5, v6) = v7) |  ? [v9] :  ? [v10] : (multiplication(v4, v6) = v10 & multiplication(v4, v5) = v9 & addition(v9, v10) = v8)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (addition(v7, v4) = v8) |  ~ (addition(v6, v5) = v7) |  ? [v9] : (addition(v6, v9) = v8 & addition(v5, v4) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (addition(v6, v7) = v8) |  ~ (addition(v5, v4) = v7) |  ? [v9] : (addition(v9, v4) = v8 & addition(v6, v5) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (leq(v7, v6) = v5) |  ~ (leq(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (multiplication(v7, v6) = v5) |  ~ (multiplication(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (addition(v7, v6) = v5) |  ~ (addition(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (domain(v5) = v6) |  ~ (multiplication(v4, v6) = v7) |  ? [v8] :  ? [v9] : (domain(v8) = v9 & domain(v7) = v9 & multiplication(v4, v5) = v8)) &  ! [v4] :  ! [v5] :  ! [v6] : (v6 = v5 |  ~ (addition(v4, v5) = v6) |  ? [v7] : ( ~ (v7 = 0) & leq(v4, v5) = v7)) &  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (leq(v4, v5) = v6) |  ? [v7] : ( ~ (v7 = v5) & addition(v4, v5) = v7)) &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (domain(v6) = v5) |  ~ (domain(v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (multiplication(v4, v5) = v6) |  ? [v7] :  ? [v8] :  ? [v9] : (domain(v9) = v7 & domain(v6) = v7 & domain(v5) = v8 & multiplication(v4, v8) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (addition(v5, v4) = v6) | addition(v4, v5) = v6) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (addition(v4, v5) = v6) | addition(v5, v4) = v6) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (addition(v4, v5) = v6) |  ? [v7] :  ? [v8] :  ? [v9] : (domain(v6) = v7 & domain(v5) = v9 & domain(v4) = v8 & addition(v8, v9) = v7)) &  ! [v4] :  ! [v5] : (v5 = v4 |  ~ (multiplication(v4, one) = v5)) &  ! [v4] :  ! [v5] : (v5 = v4 |  ~ (multiplication(one, v4) = v5)) &  ! [v4] :  ! [v5] : (v5 = v4 |  ~ (addition(v4, v4) = v5)) &  ! [v4] :  ! [v5] : (v5 = v4 |  ~ (addition(v4, zero) = v5)) &  ! [v4] :  ! [v5] : (v5 = zero |  ~ (multiplication(v4, zero) = v5)) &  ! [v4] :  ! [v5] : (v5 = zero |  ~ (multiplication(zero, v4) = v5)) &  ! [v4] :  ! [v5] : ( ~ (domain(v4) = v5) | addition(v5, one) = one) &  ! [v4] :  ! [v5] : ( ~ (domain(v4) = v5) |  ? [v6] : (multiplication(v5, v4) = v6 & addition(v4, v6) = v6)) &  ! [v4] :  ! [v5] : ( ~ (leq(v4, v5) = 0) | addition(v4, v5) = v5) &  ! [v4] :  ! [v5] : ( ~ (addition(v4, v5) = v5) | leq(v4, v5) = 0) &  ? [v4] :  ? [v5] :  ? [v6] : leq(v5, v4) = v6 &  ? [v4] :  ? [v5] :  ? [v6] : multiplication(v5, v4) = v6 &  ? [v4] :  ? [v5] :  ? [v6] : addition(v5, v4) = v6 &  ? [v4] :  ? [v5] : domain(v4) = v5)
% 28.07/8.90  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 28.07/8.90  | (1)  ~ (all_0_0_0 = zero) & domain(all_0_2_2) = all_0_1_1 & domain(zero) = zero & multiplication(all_0_3_3, all_0_1_1) = all_0_0_0 & multiplication(all_0_3_3, all_0_2_2) = 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
% 28.07/8.91  |
% 28.07/8.91  | Applying alpha-rule on (1) yields:
% 28.07/8.91  | (2) domain(all_0_2_2) = all_0_1_1
% 28.07/8.91  | (3)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(v0, zero) = v1))
% 28.07/8.91  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 28.07/8.91  | (5)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & multiplication(v0, v4) = v5))
% 28.07/8.91  | (6)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0)
% 28.07/8.91  | (7)  ! [v0] :  ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1)
% 28.07/8.91  | (8)  ! [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))
% 28.07/8.91  | (9)  ! [v0] :  ! [v1] : ( ~ (domain(v0) = v1) |  ? [v2] : (multiplication(v1, v0) = v2 & addition(v0, v2) = v2))
% 28.07/8.91  | (10)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4, v5) = v3))
% 28.07/8.91  | (11)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 28.07/8.91  | (12)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 28.07/8.91  | (13)  ? [v0] :  ? [v1] :  ? [v2] : leq(v1, v0) = v2
% 28.07/8.91  | (14)  ! [v0] :  ! [v1] : ( ~ (domain(v0) = v1) | addition(v1, one) = one)
% 28.07/8.91  | (15)  ! [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))
% 28.07/8.91  | (16)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 28.07/8.91  | (17)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 28.07/8.91  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (domain(v1) = v3) |  ~ (domain(v0) = v2) |  ~ (addition(v2, v3) = v4) |  ? [v5] : (domain(v5) = v4 & addition(v0, v1) = v5))
% 28.07/8.91  | (19)  ? [v0] :  ? [v1] :  ? [v2] : addition(v1, v0) = v2
% 28.07/8.92  | (20) multiplication(all_0_3_3, all_0_2_2) = zero
% 28.07/8.92  | (21)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 28.07/8.92  | (22)  ? [v0] :  ? [v1] :  ? [v2] : multiplication(v1, v0) = v2
% 28.07/8.92  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (domain(v1) = v2) |  ~ (multiplication(v0, v2) = v3) |  ? [v4] :  ? [v5] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = v4))
% 28.07/8.92  | (24)  ! [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))
% 28.07/8.92  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 28.07/8.92  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 28.07/8.92  | (27)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3))
% 28.07/8.92  | (28) multiplication(all_0_3_3, all_0_1_1) = all_0_0_0
% 28.07/8.92  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 28.07/8.92  | (30)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 28.07/8.92  | (31)  ~ (all_0_0_0 = zero)
% 28.07/8.92  | (32)  ? [v0] :  ? [v1] : domain(v0) = v1
% 28.07/8.92  | (33)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 28.07/8.92  | (34)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (domain(v2) = v1) |  ~ (domain(v2) = v0))
% 28.07/8.92  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 28.07/8.92  | (36)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (leq(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3))
% 28.07/8.92  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0))
% 28.07/8.92  | (38) domain(zero) = zero
% 28.07/8.92  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 28.07/8.92  | (40)  ! [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))
% 28.07/8.92  |
% 28.07/8.92  | Instantiating formula (9) with zero, zero and discharging atoms domain(zero) = zero, yields:
% 28.07/8.92  | (41)  ? [v0] : (multiplication(zero, zero) = v0 & addition(zero, v0) = v0)
% 28.07/8.92  |
% 28.07/8.92  | Instantiating formula (23) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms domain(all_0_2_2) = all_0_1_1, multiplication(all_0_3_3, all_0_1_1) = all_0_0_0, yields:
% 28.07/8.92  | (42)  ? [v0] :  ? [v1] : (domain(v0) = v1 & domain(all_0_0_0) = v1 & multiplication(all_0_3_3, all_0_2_2) = v0)
% 28.07/8.92  |
% 28.07/8.92  | Instantiating formula (5) with all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms multiplication(all_0_3_3, all_0_1_1) = all_0_0_0, yields:
% 28.07/8.92  | (43)  ? [v0] :  ? [v1] :  ? [v2] : (domain(v2) = v0 & domain(all_0_0_0) = v0 & domain(all_0_1_1) = v1 & multiplication(all_0_3_3, v1) = v2)
% 28.07/8.92  |
% 28.07/8.92  | Instantiating formula (5) with zero, all_0_2_2, all_0_3_3 and discharging atoms multiplication(all_0_3_3, all_0_2_2) = zero, yields:
% 28.07/8.92  | (44)  ? [v0] :  ? [v1] :  ? [v2] : (domain(v2) = v0 & domain(all_0_2_2) = v1 & domain(zero) = v0 & multiplication(all_0_3_3, v1) = v2)
% 28.07/8.92  |
% 28.07/8.92  | Instantiating (44) with all_17_0_15, all_17_1_16, all_17_2_17 yields:
% 28.07/8.92  | (45) domain(all_17_0_15) = all_17_2_17 & domain(all_0_2_2) = all_17_1_16 & domain(zero) = all_17_2_17 & multiplication(all_0_3_3, all_17_1_16) = all_17_0_15
% 28.50/8.92  |
% 28.50/8.92  | Applying alpha-rule on (45) yields:
% 28.50/8.92  | (46) domain(all_17_0_15) = all_17_2_17
% 28.50/8.92  | (47) domain(all_0_2_2) = all_17_1_16
% 28.50/8.92  | (48) domain(zero) = all_17_2_17
% 28.50/8.92  | (49) multiplication(all_0_3_3, all_17_1_16) = all_17_0_15
% 28.50/8.92  |
% 28.50/8.92  | Instantiating (43) with all_19_0_18, all_19_1_19, all_19_2_20 yields:
% 28.50/8.92  | (50) domain(all_19_0_18) = all_19_2_20 & domain(all_0_0_0) = all_19_2_20 & domain(all_0_1_1) = all_19_1_19 & multiplication(all_0_3_3, all_19_1_19) = all_19_0_18
% 28.50/8.93  |
% 28.50/8.93  | Applying alpha-rule on (50) yields:
% 28.50/8.93  | (51) domain(all_19_0_18) = all_19_2_20
% 28.50/8.93  | (52) domain(all_0_0_0) = all_19_2_20
% 28.50/8.93  | (53) domain(all_0_1_1) = all_19_1_19
% 28.50/8.93  | (54) multiplication(all_0_3_3, all_19_1_19) = all_19_0_18
% 28.50/8.93  |
% 28.50/8.93  | Instantiating (42) with all_21_0_21, all_21_1_22 yields:
% 28.50/8.93  | (55) domain(all_21_1_22) = all_21_0_21 & domain(all_0_0_0) = all_21_0_21 & multiplication(all_0_3_3, all_0_2_2) = all_21_1_22
% 28.50/8.93  |
% 28.50/8.93  | Applying alpha-rule on (55) yields:
% 28.50/8.93  | (56) domain(all_21_1_22) = all_21_0_21
% 28.50/8.93  | (57) domain(all_0_0_0) = all_21_0_21
% 28.50/8.93  | (58) multiplication(all_0_3_3, all_0_2_2) = all_21_1_22
% 28.50/8.93  |
% 28.50/8.93  | Instantiating (41) with all_25_0_24 yields:
% 28.50/8.93  | (59) multiplication(zero, zero) = all_25_0_24 & addition(zero, all_25_0_24) = all_25_0_24
% 28.50/8.93  |
% 28.50/8.93  | Applying alpha-rule on (59) yields:
% 28.50/8.93  | (60) multiplication(zero, zero) = all_25_0_24
% 28.50/8.93  | (61) addition(zero, all_25_0_24) = all_25_0_24
% 28.50/8.93  |
% 28.50/8.93  | Instantiating formula (34) with all_0_0_0, all_19_2_20, all_21_0_21 and discharging atoms domain(all_0_0_0) = all_21_0_21, domain(all_0_0_0) = all_19_2_20, yields:
% 28.50/8.93  | (62) all_21_0_21 = all_19_2_20
% 28.50/8.93  |
% 28.50/8.93  | Instantiating formula (34) with zero, all_17_2_17, zero and discharging atoms domain(zero) = all_17_2_17, domain(zero) = zero, yields:
% 28.50/8.93  | (63) all_17_2_17 = zero
% 28.50/8.93  |
% 28.50/8.93  | Instantiating formula (35) with all_0_3_3, all_0_2_2, all_21_1_22, zero and discharging atoms multiplication(all_0_3_3, all_0_2_2) = all_21_1_22, multiplication(all_0_3_3, all_0_2_2) = zero, yields:
% 28.50/8.93  | (64) all_21_1_22 = zero
% 28.50/8.93  |
% 28.50/8.93  | Instantiating formula (3) with all_25_0_24, zero and discharging atoms multiplication(zero, zero) = all_25_0_24, yields:
% 28.50/8.93  | (65) all_25_0_24 = zero
% 28.50/8.93  |
% 28.50/8.93  | From (64)(62) and (56) follows:
% 28.50/8.93  | (66) domain(zero) = all_19_2_20
% 28.50/8.93  |
% 28.50/8.93  | From (62) and (57) follows:
% 28.50/8.93  | (52) domain(all_0_0_0) = all_19_2_20
% 28.50/8.93  |
% 28.50/8.93  | From (63) and (48) follows:
% 28.50/8.93  | (38) domain(zero) = zero
% 28.50/8.93  |
% 28.50/8.93  | From (65) and (60) follows:
% 28.50/8.93  | (69) multiplication(zero, zero) = zero
% 28.50/8.93  |
% 28.50/8.93  | Instantiating formula (34) with zero, all_19_2_20, zero and discharging atoms domain(zero) = all_19_2_20, domain(zero) = zero, yields:
% 28.50/8.93  | (70) all_19_2_20 = zero
% 28.50/8.93  |
% 28.50/8.93  | From (70) and (52) follows:
% 28.50/8.93  | (71) domain(all_0_0_0) = zero
% 28.50/8.93  |
% 28.50/8.93  | Instantiating formula (9) with zero, all_0_0_0 and discharging atoms domain(all_0_0_0) = zero, yields:
% 28.50/8.93  | (72)  ? [v0] : (multiplication(zero, all_0_0_0) = v0 & addition(all_0_0_0, v0) = v0)
% 28.50/8.93  |
% 28.50/8.93  | Instantiating formula (23) with zero, zero, all_0_0_0, zero and discharging atoms domain(all_0_0_0) = zero, multiplication(zero, zero) = zero, yields:
% 28.50/8.93  | (73)  ? [v0] :  ? [v1] : (domain(v0) = v1 & domain(zero) = v1 & multiplication(zero, all_0_0_0) = v0)
% 28.50/8.93  |
% 28.50/8.93  | Instantiating (72) with all_63_0_40 yields:
% 28.50/8.93  | (74) multiplication(zero, all_0_0_0) = all_63_0_40 & addition(all_0_0_0, all_63_0_40) = all_63_0_40
% 28.50/8.93  |
% 28.50/8.93  | Applying alpha-rule on (74) yields:
% 28.50/8.93  | (75) multiplication(zero, all_0_0_0) = all_63_0_40
% 28.50/8.93  | (76) addition(all_0_0_0, all_63_0_40) = all_63_0_40
% 28.50/8.93  |
% 28.50/8.93  | Instantiating (73) with all_75_0_50, all_75_1_51 yields:
% 28.50/8.93  | (77) domain(all_75_1_51) = all_75_0_50 & domain(zero) = all_75_0_50 & multiplication(zero, all_0_0_0) = all_75_1_51
% 28.50/8.93  |
% 28.50/8.93  | Applying alpha-rule on (77) yields:
% 28.50/8.93  | (78) domain(all_75_1_51) = all_75_0_50
% 28.50/8.93  | (79) domain(zero) = all_75_0_50
% 28.50/8.93  | (80) multiplication(zero, all_0_0_0) = all_75_1_51
% 28.50/8.93  |
% 28.50/8.93  | Instantiating formula (11) with all_75_1_51, all_0_0_0 and discharging atoms multiplication(zero, all_0_0_0) = all_75_1_51, yields:
% 28.50/8.93  | (81) all_75_1_51 = zero
% 28.50/8.93  |
% 28.50/8.93  | Instantiating formula (35) with zero, all_0_0_0, all_63_0_40, all_75_1_51 and discharging atoms multiplication(zero, all_0_0_0) = all_75_1_51, multiplication(zero, all_0_0_0) = all_63_0_40, yields:
% 28.50/8.93  | (82) all_75_1_51 = all_63_0_40
% 28.50/8.93  |
% 28.50/8.93  | Combining equations (81,82) yields a new equation:
% 28.50/8.93  | (83) all_63_0_40 = zero
% 28.50/8.93  |
% 28.50/8.93  | From (83)(83) and (76) follows:
% 28.50/8.93  | (84) addition(all_0_0_0, zero) = zero
% 28.50/8.93  |
% 28.50/8.93  | Instantiating formula (33) with zero, all_0_0_0 and discharging atoms addition(all_0_0_0, zero) = zero, yields:
% 28.50/8.93  | (85) all_0_0_0 = zero
% 28.50/8.93  |
% 28.50/8.93  | Equations (85) can reduce 31 to:
% 28.50/8.93  | (86) $false
% 28.50/8.93  |
% 28.50/8.93  |-The branch is then unsatisfiable
% 28.50/8.93  % SZS output end Proof for theBenchmark
% 28.50/8.93  
% 28.50/8.93  8326ms
%------------------------------------------------------------------------------