%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE064+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n016.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 01:51:12 EDT 2022

% Result   : Theorem 3.38s 1.46s
% Output   : Proof 5.71s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : KLE064+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n016.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % 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 10:03:04 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.53/0.59          ____       _                          
% 0.53/0.59    ___  / __ \_____(_)___  ________  __________
% 0.53/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.53/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.53/0.59  
% 0.53/0.59  A Theorem Prover for First-Order Logic
% 0.53/0.59  (ePrincess v.1.0)
% 0.53/0.59  
% 0.53/0.59  (c) Philipp Rümmer, 2009-2015
% 0.53/0.59  (c) Peter Backeman, 2014-2015
% 0.53/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.59  Bug reports to peter@backeman.se
% 0.53/0.59  
% 0.53/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.59  
% 0.53/0.59  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
% 1.47/0.92  Prover 0: Preprocessing ...
% 2.32/1.18  Prover 0: Constructing countermodel ...
% 3.38/1.45  Prover 0: proved (814ms)
% 3.38/1.46  
% 3.38/1.46  No countermodel exists, formula is valid
% 3.38/1.46  % SZS status Theorem for theBenchmark
% 3.38/1.46  
% 3.38/1.46  Generating proof ... found it (size 28)
% 5.39/1.95  
% 5.39/1.95  % SZS output start Proof for theBenchmark
% 5.39/1.95  Assumed formulas after preprocessing and simplification: 
% 5.39/1.95  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v5 = v4) & domain(v1) = v3 & domain(v0) = v2 & domain(zero) = zero & multiplication(v3, v0) = v4 & addition(v2, v3) = v3 & addition(v0, v4) = v5 &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (multiplication(v7, v8) = v10) |  ~ (multiplication(v6, v8) = v9) |  ~ (addition(v9, v10) = v11) |  ? [v12] : (multiplication(v12, v8) = v11 & addition(v6, v7) = v12)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (multiplication(v6, v8) = v10) |  ~ (multiplication(v6, v7) = v9) |  ~ (addition(v9, v10) = v11) |  ? [v12] : (multiplication(v6, v12) = v11 & addition(v7, v8) = v12)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (domain(v7) = v9) |  ~ (domain(v6) = v8) |  ~ (addition(v8, v9) = v10) |  ? [v11] : (domain(v11) = v10 & addition(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (multiplication(v9, v8) = v10) |  ~ (multiplication(v6, v7) = v9) |  ? [v11] : (multiplication(v7, v8) = v11 & multiplication(v6, v11) = v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (multiplication(v9, v8) = v10) |  ~ (addition(v6, v7) = v9) |  ? [v11] :  ? [v12] : (multiplication(v7, v8) = v12 & multiplication(v6, v8) = v11 & addition(v11, v12) = v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (multiplication(v7, v8) = v9) |  ~ (multiplication(v6, v9) = v10) |  ? [v11] : (multiplication(v11, v8) = v10 & multiplication(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (multiplication(v6, v9) = v10) |  ~ (addition(v7, v8) = v9) |  ? [v11] :  ? [v12] : (multiplication(v6, v8) = v12 & multiplication(v6, v7) = v11 & addition(v11, v12) = v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (addition(v9, v6) = v10) |  ~ (addition(v8, v7) = v9) |  ? [v11] : (addition(v8, v11) = v10 & addition(v7, v6) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (addition(v8, v9) = v10) |  ~ (addition(v7, v6) = v9) |  ? [v11] : (addition(v11, v6) = v10 & addition(v8, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (domain(v6) = v7) |  ~ (multiplication(v7, v6) = v8) |  ~ (addition(v6, v8) = v9)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (multiplication(v9, v8) = v7) |  ~ (multiplication(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (addition(v9, v8) = v7) |  ~ (addition(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (domain(v7) = v8) |  ~ (multiplication(v6, v8) = v9) |  ? [v10] :  ? [v11] : (domain(v10) = v11 & domain(v9) = v11 & multiplication(v6, v7) = v10)) &  ! [v6] :  ! [v7] :  ! [v8] : (v8 = v7 |  ~ (addition(v6, v7) = v8) |  ~ leq(v6, v7)) &  ! [v6] :  ! [v7] :  ! [v8] : (v7 = v6 |  ~ (domain(v8) = v7) |  ~ (domain(v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (domain(v6) = v7) |  ~ (multiplication(v7, v6) = v8) | addition(v6, v8) = v8) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v6, v7) = v8) |  ? [v9] :  ? [v10] :  ? [v11] : (domain(v11) = v9 & domain(v8) = v9 & domain(v7) = v10 & multiplication(v6, v10) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (addition(v7, v6) = v8) | addition(v6, v7) = v8) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (addition(v6, v7) = v8) | addition(v7, v6) = v8) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (addition(v6, v7) = v8) |  ? [v9] :  ? [v10] :  ? [v11] : (domain(v8) = v9 & domain(v7) = v11 & domain(v6) = v10 & addition(v10, v11) = v9)) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (multiplication(v6, one) = v7)) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (multiplication(one, v6) = v7)) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (addition(v6, v6) = v7)) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (addition(v6, zero) = v7)) &  ! [v6] :  ! [v7] : (v7 = zero |  ~ (multiplication(v6, zero) = v7)) &  ! [v6] :  ! [v7] : (v7 = zero |  ~ (multiplication(zero, v6) = v7)) &  ! [v6] :  ! [v7] : ( ~ (domain(v6) = v7) | addition(v7, one) = one) &  ! [v6] :  ! [v7] : ( ~ (addition(v6, v7) = v7) | leq(v6, v7)))
% 5.71/1.99  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 5.71/1.99  | (1)  ~ (all_0_0_0 = all_0_1_1) & domain(all_0_4_4) = all_0_2_2 & domain(all_0_5_5) = all_0_3_3 & domain(zero) = zero & multiplication(all_0_2_2, all_0_5_5) = all_0_1_1 & addition(all_0_3_3, all_0_2_2) = all_0_2_2 & addition(all_0_5_5, all_0_1_1) = 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] : ( ~ (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] : (v3 = v2 |  ~ (domain(v0) = v1) |  ~ (multiplication(v1, v0) = v2) |  ~ (addition(v0, v2) = v3)) &  ! [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) |  ~ leq(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (domain(v2) = v1) |  ~ (domain(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (domain(v0) = v1) |  ~ (multiplication(v1, v0) = v2) | addition(v0, v2) = v2) &  ! [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] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 5.71/2.00  |
% 5.71/2.00  | Applying alpha-rule on (1) yields:
% 5.71/2.00  | (2)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4, v5) = v3))
% 5.71/2.00  | (3)  ~ (all_0_0_0 = all_0_1_1)
% 5.71/2.00  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 5.71/2.00  | (5)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 5.71/2.00  | (6) domain(zero) = zero
% 5.71/2.00  | (7) domain(all_0_5_5) = all_0_3_3
% 5.71/2.00  | (8) domain(all_0_4_4) = all_0_2_2
% 5.71/2.00  | (9)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 5.71/2.00  | (10) addition(all_0_3_3, all_0_2_2) = all_0_2_2
% 5.71/2.00  | (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))
% 5.71/2.00  | (12)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 5.71/2.00  | (13)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(v0, zero) = v1))
% 5.71/2.00  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 5.71/2.01  | (15) addition(all_0_5_5, all_0_1_1) = all_0_0_0
% 5.71/2.01  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 5.71/2.01  | (17)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 5.71/2.01  | (18)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (domain(v2) = v1) |  ~ (domain(v2) = v0))
% 5.71/2.01  | (19)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 5.71/2.01  | (20)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 5.71/2.01  | (21)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & multiplication(v0, v4) = v5))
% 5.71/2.01  | (22) multiplication(all_0_2_2, all_0_5_5) = all_0_1_1
% 5.71/2.01  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 5.71/2.01  | (24)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 5.71/2.01  | (25)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 5.71/2.01  | (26)  ! [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))
% 5.71/2.01  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (domain(v1) = v2) |  ~ (multiplication(v0, v2) = v3) |  ? [v4] :  ? [v5] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = v4))
% 5.71/2.01  | (28)  ! [v0] :  ! [v1] : ( ~ (domain(v0) = v1) | addition(v1, one) = one)
% 5.71/2.01  | (29)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ~ leq(v0, v1))
% 5.71/2.01  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (domain(v1) = v3) |  ~ (domain(v0) = v2) |  ~ (addition(v2, v3) = v4) |  ? [v5] : (domain(v5) = v4 & addition(v0, v1) = v5))
% 5.71/2.01  | (31)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (domain(v0) = v1) |  ~ (multiplication(v1, v0) = v2) | addition(v0, v2) = v2)
% 5.71/2.01  | (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))
% 5.71/2.01  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (domain(v0) = v1) |  ~ (multiplication(v1, v0) = v2) |  ~ (addition(v0, v2) = v3))
% 5.71/2.01  | (34)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 5.71/2.01  | (35)  ! [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))
% 5.71/2.01  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 5.71/2.01  |
% 5.71/2.01  | Instantiating formula (21) with all_0_1_1, all_0_5_5, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_5_5) = all_0_1_1, yields:
% 5.71/2.01  | (37)  ? [v0] :  ? [v1] :  ? [v2] : (domain(v2) = v0 & domain(all_0_1_1) = v0 & domain(all_0_5_5) = v1 & multiplication(all_0_2_2, v1) = v2)
% 5.71/2.01  |
% 5.71/2.01  | Instantiating formula (11) with all_0_1_1, all_0_2_2, all_0_5_5, all_0_2_2, all_0_3_3 and discharging atoms multiplication(all_0_2_2, all_0_5_5) = all_0_1_1, addition(all_0_3_3, all_0_2_2) = all_0_2_2, yields:
% 5.71/2.01  | (38)  ? [v0] :  ? [v1] : (multiplication(all_0_2_2, all_0_5_5) = v1 & multiplication(all_0_3_3, all_0_5_5) = v0 & addition(v0, v1) = all_0_1_1)
% 5.71/2.02  |
% 5.71/2.02  | Instantiating formula (2) with all_0_0_0, all_0_1_1, all_0_5_5 and discharging atoms addition(all_0_5_5, all_0_1_1) = all_0_0_0, yields:
% 5.71/2.02  | (39)  ? [v0] :  ? [v1] :  ? [v2] : (domain(all_0_0_0) = v0 & domain(all_0_1_1) = v2 & domain(all_0_5_5) = v1 & addition(v1, v2) = v0)
% 5.71/2.02  |
% 5.71/2.02  | Instantiating (39) with all_11_0_7, all_11_1_8, all_11_2_9 yields:
% 5.71/2.02  | (40) domain(all_0_0_0) = all_11_2_9 & domain(all_0_1_1) = all_11_0_7 & domain(all_0_5_5) = all_11_1_8 & addition(all_11_1_8, all_11_0_7) = all_11_2_9
% 5.71/2.02  |
% 5.71/2.02  | Applying alpha-rule on (40) yields:
% 5.71/2.02  | (41) domain(all_0_0_0) = all_11_2_9
% 5.71/2.02  | (42) domain(all_0_1_1) = all_11_0_7
% 5.71/2.02  | (43) domain(all_0_5_5) = all_11_1_8
% 5.71/2.02  | (44) addition(all_11_1_8, all_11_0_7) = all_11_2_9
% 5.71/2.02  |
% 5.71/2.02  | Instantiating (38) with all_15_0_11, all_15_1_12 yields:
% 5.71/2.02  | (45) multiplication(all_0_2_2, all_0_5_5) = all_15_0_11 & multiplication(all_0_3_3, all_0_5_5) = all_15_1_12 & addition(all_15_1_12, all_15_0_11) = all_0_1_1
% 5.71/2.02  |
% 5.71/2.02  | Applying alpha-rule on (45) yields:
% 5.71/2.02  | (46) multiplication(all_0_2_2, all_0_5_5) = all_15_0_11
% 5.71/2.02  | (47) multiplication(all_0_3_3, all_0_5_5) = all_15_1_12
% 5.71/2.02  | (48) addition(all_15_1_12, all_15_0_11) = all_0_1_1
% 5.71/2.02  |
% 5.71/2.02  | Instantiating (37) with all_17_0_13, all_17_1_14, all_17_2_15 yields:
% 5.71/2.02  | (49) domain(all_17_0_13) = all_17_2_15 & domain(all_0_1_1) = all_17_2_15 & domain(all_0_5_5) = all_17_1_14 & multiplication(all_0_2_2, all_17_1_14) = all_17_0_13
% 5.71/2.02  |
% 5.71/2.02  | Applying alpha-rule on (49) yields:
% 5.71/2.02  | (50) domain(all_17_0_13) = all_17_2_15
% 5.71/2.02  | (51) domain(all_0_1_1) = all_17_2_15
% 5.71/2.02  | (52) domain(all_0_5_5) = all_17_1_14
% 5.71/2.02  | (53) multiplication(all_0_2_2, all_17_1_14) = all_17_0_13
% 5.71/2.02  |
% 5.71/2.02  | Instantiating formula (18) with all_0_5_5, all_17_1_14, all_0_3_3 and discharging atoms domain(all_0_5_5) = all_17_1_14, domain(all_0_5_5) = all_0_3_3, yields:
% 5.71/2.02  | (54) all_17_1_14 = all_0_3_3
% 5.71/2.02  |
% 5.71/2.02  | Instantiating formula (18) with all_0_5_5, all_11_1_8, all_17_1_14 and discharging atoms domain(all_0_5_5) = all_17_1_14, domain(all_0_5_5) = all_11_1_8, yields:
% 5.71/2.02  | (55) all_17_1_14 = all_11_1_8
% 5.71/2.02  |
% 5.71/2.02  | Instantiating formula (16) with all_0_2_2, all_0_5_5, all_15_0_11, all_0_1_1 and discharging atoms multiplication(all_0_2_2, all_0_5_5) = all_15_0_11, multiplication(all_0_2_2, all_0_5_5) = all_0_1_1, yields:
% 5.71/2.02  | (56) all_15_0_11 = all_0_1_1
% 5.71/2.02  |
% 5.71/2.02  | Combining equations (55,54) yields a new equation:
% 5.71/2.02  | (57) all_11_1_8 = all_0_3_3
% 5.71/2.02  |
% 5.71/2.02  | Simplifying 57 yields:
% 5.71/2.02  | (58) all_11_1_8 = all_0_3_3
% 5.71/2.02  |
% 5.71/2.02  | From (58) and (43) follows:
% 5.71/2.02  | (7) domain(all_0_5_5) = all_0_3_3
% 5.71/2.02  |
% 5.71/2.02  | From (56) and (48) follows:
% 5.71/2.02  | (60) addition(all_15_1_12, all_0_1_1) = all_0_1_1
% 5.71/2.02  |
% 5.71/2.02  | Instantiating formula (31) with all_15_1_12, all_0_3_3, all_0_5_5 and discharging atoms domain(all_0_5_5) = all_0_3_3, multiplication(all_0_3_3, all_0_5_5) = all_15_1_12, yields:
% 5.71/2.02  | (61) addition(all_0_5_5, all_15_1_12) = all_15_1_12
% 5.71/2.02  |
% 5.71/2.02  | Instantiating formula (23) with all_0_0_0, all_0_1_1, all_0_5_5, all_15_1_12, all_0_1_1 and discharging atoms addition(all_15_1_12, all_0_1_1) = all_0_1_1, addition(all_0_5_5, all_0_1_1) = all_0_0_0, yields:
% 5.71/2.02  | (62)  ? [v0] : (addition(v0, all_0_1_1) = all_0_0_0 & addition(all_0_5_5, all_15_1_12) = v0)
% 5.71/2.02  |
% 5.71/2.02  | Instantiating formula (25) with all_0_1_1, all_15_1_12 and discharging atoms addition(all_15_1_12, all_0_1_1) = all_0_1_1, yields:
% 5.71/2.02  | (63) leq(all_15_1_12, all_0_1_1)
% 5.71/2.02  |
% 5.71/2.02  | Instantiating (62) with all_71_0_56 yields:
% 5.71/2.02  | (64) addition(all_71_0_56, all_0_1_1) = all_0_0_0 & addition(all_0_5_5, all_15_1_12) = all_71_0_56
% 5.71/2.02  |
% 5.71/2.02  | Applying alpha-rule on (64) yields:
% 5.71/2.02  | (65) addition(all_71_0_56, all_0_1_1) = all_0_0_0
% 5.71/2.02  | (66) addition(all_0_5_5, all_15_1_12) = all_71_0_56
% 5.71/2.02  |
% 5.71/2.02  | Instantiating formula (4) with all_0_5_5, all_15_1_12, all_15_1_12, all_71_0_56 and discharging atoms addition(all_0_5_5, all_15_1_12) = all_71_0_56, addition(all_0_5_5, all_15_1_12) = all_15_1_12, yields:
% 5.71/2.02  | (67) all_71_0_56 = all_15_1_12
% 5.71/2.02  |
% 5.71/2.02  | From (67) and (65) follows:
% 5.71/2.02  | (68) addition(all_15_1_12, all_0_1_1) = all_0_0_0
% 5.71/2.02  |
% 5.71/2.02  | Instantiating formula (29) with all_0_0_0, all_0_1_1, all_15_1_12 and discharging atoms addition(all_15_1_12, all_0_1_1) = all_0_0_0, leq(all_15_1_12, all_0_1_1), yields:
% 5.71/2.02  | (69) all_0_0_0 = all_0_1_1
% 5.71/2.02  |
% 5.71/2.02  | Equations (69) can reduce 3 to:
% 5.71/2.02  | (70) $false
% 5.71/2.02  |
% 5.71/2.03  |-The branch is then unsatisfiable
% 5.71/2.03  % SZS output end Proof for theBenchmark
% 5.71/2.03  
% 5.71/2.03  1424ms
%------------------------------------------------------------------------------