%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE021+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n013.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 01:50:55 EDT 2022

% Result   : Theorem 2.78s 1.34s
% Output   : Proof 4.35s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : KLE021+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.14/0.35  % Computer : n013.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Thu Jun 16 15:10:14 EDT 2022
% 0.14/0.35  % 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 ...
% 0.69/0.66  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.60/0.93  Prover 0: Preprocessing ...
% 2.30/1.19  Prover 0: Constructing countermodel ...
% 2.78/1.34  Prover 0: proved (680ms)
% 2.78/1.34  
% 2.78/1.34  No countermodel exists, formula is valid
% 2.78/1.34  % SZS status Theorem for theBenchmark
% 2.78/1.34  
% 2.78/1.34  Generating proof ... found it (size 19)
% 4.04/1.61  
% 4.04/1.61  % SZS output start Proof for theBenchmark
% 4.04/1.61  Assumed formulas after preprocessing and simplification: 
% 4.04/1.61  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v5 = v0) & c(v1) = v3 & multiplication(v3, v0) = v4 & multiplication(v1, v0) = v2 & addition(v2, v4) = v5 & test(v1) &  ! [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] : ( ~ (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] : (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] : (v8 = v7 |  ~ (c(v6) = v8) |  ~ complement(v6, v7) |  ~ test(v6)) &  ! [v6] :  ! [v7] :  ! [v8] : (v8 = v7 |  ~ (addition(v6, v7) = v8) |  ~ leq(v6, v7)) &  ! [v6] :  ! [v7] :  ! [v8] : (v8 = one |  ~ (addition(v6, v7) = v8) |  ~ complement(v7, v6)) &  ! [v6] :  ! [v7] :  ! [v8] : (v8 = zero |  ~ (multiplication(v7, v6) = v8) |  ~ complement(v7, v6)) &  ! [v6] :  ! [v7] :  ! [v8] : (v8 = zero |  ~ (multiplication(v6, v7) = v8) |  ~ complement(v7, v6)) &  ! [v6] :  ! [v7] :  ! [v8] : (v7 = v6 |  ~ (c(v8) = v7) |  ~ (c(v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v7, v6) = v8) |  ~ complement(v7, v6) | (multiplication(v6, v7) = zero & addition(v6, v7) = one)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v6, v7) = v8) |  ~ complement(v7, v6) | (multiplication(v7, v6) = zero & addition(v6, v7) = one)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (addition(v7, v6) = v8) | addition(v6, v7) = v8) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (addition(v6, v7) = v8) |  ~ complement(v7, v6) | (multiplication(v7, v6) = zero & multiplication(v6, v7) = zero)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (addition(v6, v7) = v8) | addition(v7, v6) = v8) &  ! [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 |  ~ (c(v6) = v7) | test(v6)) &  ! [v6] :  ! [v7] : (v7 = zero |  ~ (multiplication(v6, zero) = v7)) &  ! [v6] :  ! [v7] : (v7 = zero |  ~ (multiplication(zero, v6) = v7)) &  ! [v6] :  ! [v7] : ( ~ (c(v6) = v7) |  ~ test(v6) | complement(v6, v7)) &  ! [v6] :  ! [v7] : ( ~ (multiplication(v7, v6) = zero) | complement(v7, v6) |  ? [v8] :  ? [v9] : (multiplication(v6, v7) = v8 & addition(v6, v7) = v9 & ( ~ (v9 = one) |  ~ (v8 = zero)))) &  ! [v6] :  ! [v7] : ( ~ (multiplication(v6, v7) = zero) | complement(v7, v6) |  ? [v8] :  ? [v9] : (multiplication(v7, v6) = v8 & addition(v6, v7) = v9 & ( ~ (v9 = one) |  ~ (v8 = zero)))) &  ! [v6] :  ! [v7] : ( ~ (addition(v6, v7) = v7) | leq(v6, v7)) &  ! [v6] :  ! [v7] : ( ~ (addition(v6, v7) = one) | complement(v7, v6) |  ? [v8] :  ? [v9] : (multiplication(v7, v6) = v9 & multiplication(v6, v7) = v8 & ( ~ (v9 = zero) |  ~ (v8 = zero)))) &  ! [v6] :  ! [v7] : ( ~ complement(v7, v6) | test(v6)) &  ! [v6] : ( ~ test(v6) |  ? [v7] : complement(v7, v6)))
% 4.04/1.65  | 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:
% 4.04/1.65  | (1)  ~ (all_0_0_0 = all_0_5_5) & c(all_0_4_4) = all_0_2_2 & multiplication(all_0_2_2, all_0_5_5) = all_0_1_1 & multiplication(all_0_4_4, all_0_5_5) = all_0_3_3 & addition(all_0_3_3, all_0_1_1) = all_0_0_0 & test(all_0_4_4) &  ! [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] : ( ~ (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 |  ~ (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 |  ~ (c(v0) = v2) |  ~ complement(v0, v1) |  ~ test(v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ~ leq(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = one |  ~ (addition(v0, v1) = v2) |  ~ complement(v1, v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = zero |  ~ (multiplication(v1, v0) = v2) |  ~ complement(v1, v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = zero |  ~ (multiplication(v0, v1) = v2) |  ~ complement(v1, v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (c(v2) = v1) |  ~ (c(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v1, v0) = v2) |  ~ complement(v1, v0) | (multiplication(v0, v1) = zero & addition(v0, v1) = one)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ~ complement(v1, v0) | (multiplication(v1, v0) = zero & addition(v0, v1) = one)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) |  ~ complement(v1, v0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero)) &  ! [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 |  ~ (c(v0) = v1) | test(v0)) &  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(v0, zero) = v1)) &  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1)) &  ! [v0] :  ! [v1] : ( ~ (c(v0) = v1) |  ~ test(v0) | complement(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ (multiplication(v1, v0) = zero) | complement(v1, v0) |  ? [v2] :  ? [v3] : (multiplication(v0, v1) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) |  ~ (v2 = zero)))) &  ! [v0] :  ! [v1] : ( ~ (multiplication(v0, v1) = zero) | complement(v1, v0) |  ? [v2] :  ? [v3] : (multiplication(v1, v0) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) |  ~ (v2 = zero)))) &  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = one) | complement(v1, v0) |  ? [v2] :  ? [v3] : (multiplication(v1, v0) = v3 & multiplication(v0, v1) = v2 & ( ~ (v3 = zero) |  ~ (v2 = zero)))) &  ! [v0] :  ! [v1] : ( ~ complement(v1, v0) | test(v0)) &  ! [v0] : ( ~ test(v0) |  ? [v1] : complement(v1, v0))
% 4.04/1.66  |
% 4.04/1.66  | Applying alpha-rule on (1) yields:
% 4.04/1.66  | (2)  ! [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))
% 4.04/1.66  | (3)  ! [v0] :  ! [v1] : ( ~ (c(v0) = v1) |  ~ test(v0) | complement(v0, v1))
% 4.04/1.67  | (4)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ~ leq(v0, v1))
% 4.04/1.67  | (5)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (c(v0) = v1) | test(v0))
% 4.04/1.67  | (6) multiplication(all_0_4_4, all_0_5_5) = all_0_3_3
% 4.04/1.67  | (7)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (c(v2) = v1) |  ~ (c(v2) = v0))
% 4.04/1.67  | (8) test(all_0_4_4)
% 4.04/1.67  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 4.04/1.67  | (10) addition(all_0_3_3, all_0_1_1) = all_0_0_0
% 4.04/1.67  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 4.04/1.67  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 4.04/1.67  | (13)  ! [v0] : ( ~ test(v0) |  ? [v1] : complement(v1, v0))
% 4.04/1.67  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 4.04/1.67  | (15)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 4.04/1.67  | (16)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 4.04/1.67  | (17)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) |  ~ complement(v1, v0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero))
% 4.04/1.67  | (18)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = one) | complement(v1, v0) |  ? [v2] :  ? [v3] : (multiplication(v1, v0) = v3 & multiplication(v0, v1) = v2 & ( ~ (v3 = zero) |  ~ (v2 = zero))))
% 4.04/1.67  | (19) multiplication(all_0_2_2, all_0_5_5) = all_0_1_1
% 4.04/1.67  | (20)  ! [v0] :  ! [v1] : ( ~ (multiplication(v1, v0) = zero) | complement(v1, v0) |  ? [v2] :  ? [v3] : (multiplication(v0, v1) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) |  ~ (v2 = zero))))
% 4.04/1.67  | (21)  ! [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))
% 4.04/1.67  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 4.04/1.67  | (23) c(all_0_4_4) = all_0_2_2
% 4.04/1.67  | (24)  ~ (all_0_0_0 = all_0_5_5)
% 4.04/1.67  | (25)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ~ complement(v1, v0) | (multiplication(v1, v0) = zero & addition(v0, v1) = one))
% 4.04/1.67  | (26)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v1, v0) = v2) |  ~ complement(v1, v0) | (multiplication(v0, v1) = zero & addition(v0, v1) = one))
% 4.04/1.67  | (27)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (c(v0) = v2) |  ~ complement(v0, v1) |  ~ test(v0))
% 4.04/1.67  | (28)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = one |  ~ (addition(v0, v1) = v2) |  ~ complement(v1, v0))
% 4.04/1.68  | (29)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 4.04/1.68  | (30)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 4.04/1.68  | (31)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(v0, zero) = v1))
% 4.04/1.68  | (32)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = zero |  ~ (multiplication(v1, v0) = v2) |  ~ complement(v1, v0))
% 4.04/1.68  | (33)  ! [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))
% 4.04/1.68  | (34)  ! [v0] :  ! [v1] : ( ~ (multiplication(v0, v1) = zero) | complement(v1, v0) |  ? [v2] :  ? [v3] : (multiplication(v1, v0) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) |  ~ (v2 = zero))))
% 4.35/1.68  | (35)  ! [v0] :  ! [v1] : ( ~ complement(v1, v0) | test(v0))
% 4.35/1.68  | (36)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 4.35/1.68  | (37)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 4.35/1.68  | (38)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 4.35/1.68  | (39)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = zero |  ~ (multiplication(v0, v1) = v2) |  ~ complement(v1, v0))
% 4.35/1.68  | (40)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 4.35/1.68  | (41)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v1, v2) = v4) |  ~ (multiplication(v0, v2) = v3) |  ~ (addition(v3, v4) = v5) |  ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6))
% 4.35/1.68  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 4.35/1.68  |
% 4.35/1.68  | Instantiating formula (41) with all_0_0_0, all_0_1_1, all_0_3_3, all_0_5_5, all_0_2_2, all_0_4_4 and discharging atoms multiplication(all_0_2_2, all_0_5_5) = all_0_1_1, multiplication(all_0_4_4, all_0_5_5) = all_0_3_3, addition(all_0_3_3, all_0_1_1) = all_0_0_0, yields:
% 4.35/1.68  | (43)  ? [v0] : (multiplication(v0, all_0_5_5) = all_0_0_0 & addition(all_0_4_4, all_0_2_2) = v0)
% 4.35/1.68  |
% 4.35/1.68  | Instantiating formula (37) with all_0_0_0, all_0_3_3, all_0_1_1 and discharging atoms addition(all_0_3_3, all_0_1_1) = all_0_0_0, yields:
% 4.35/1.68  | (44) addition(all_0_1_1, all_0_3_3) = all_0_0_0
% 4.35/1.68  |
% 4.35/1.68  | Instantiating formula (3) with all_0_2_2, all_0_4_4 and discharging atoms c(all_0_4_4) = all_0_2_2, test(all_0_4_4), yields:
% 4.35/1.68  | (45) complement(all_0_4_4, all_0_2_2)
% 4.35/1.68  |
% 4.35/1.68  | Instantiating (43) with all_11_0_7 yields:
% 4.35/1.68  | (46) multiplication(all_11_0_7, all_0_5_5) = all_0_0_0 & addition(all_0_4_4, all_0_2_2) = all_11_0_7
% 4.35/1.68  |
% 4.35/1.68  | Applying alpha-rule on (46) yields:
% 4.35/1.68  | (47) multiplication(all_11_0_7, all_0_5_5) = all_0_0_0
% 4.35/1.68  | (48) addition(all_0_4_4, all_0_2_2) = all_11_0_7
% 4.35/1.68  |
% 4.35/1.68  | Instantiating formula (41) with all_0_0_0, all_0_3_3, all_0_1_1, all_0_5_5, all_0_4_4, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_5_5) = all_0_1_1, multiplication(all_0_4_4, all_0_5_5) = all_0_3_3, addition(all_0_1_1, all_0_3_3) = all_0_0_0, yields:
% 4.35/1.68  | (49)  ? [v0] : (multiplication(v0, all_0_5_5) = all_0_0_0 & addition(all_0_2_2, all_0_4_4) = v0)
% 4.35/1.68  |
% 4.35/1.68  | Instantiating formula (37) with all_11_0_7, all_0_4_4, all_0_2_2 and discharging atoms addition(all_0_4_4, all_0_2_2) = all_11_0_7, yields:
% 4.35/1.69  | (50) addition(all_0_2_2, all_0_4_4) = all_11_0_7
% 4.35/1.69  |
% 4.35/1.69  | Instantiating (49) with all_19_0_8 yields:
% 4.35/1.69  | (51) multiplication(all_19_0_8, all_0_5_5) = all_0_0_0 & addition(all_0_2_2, all_0_4_4) = all_19_0_8
% 4.35/1.69  |
% 4.35/1.69  | Applying alpha-rule on (51) yields:
% 4.35/1.69  | (52) multiplication(all_19_0_8, all_0_5_5) = all_0_0_0
% 4.35/1.69  | (53) addition(all_0_2_2, all_0_4_4) = all_19_0_8
% 4.35/1.69  |
% 4.35/1.69  | Instantiating formula (28) with all_19_0_8, all_0_4_4, all_0_2_2 and discharging atoms addition(all_0_2_2, all_0_4_4) = all_19_0_8, complement(all_0_4_4, all_0_2_2), yields:
% 4.35/1.69  | (54) all_19_0_8 = one
% 4.35/1.69  |
% 4.35/1.69  | Instantiating formula (14) with all_0_2_2, all_0_4_4, all_11_0_7, all_19_0_8 and discharging atoms addition(all_0_2_2, all_0_4_4) = all_19_0_8, addition(all_0_2_2, all_0_4_4) = all_11_0_7, yields:
% 4.35/1.69  | (55) all_19_0_8 = all_11_0_7
% 4.35/1.69  |
% 4.35/1.69  | Combining equations (55,54) yields a new equation:
% 4.35/1.69  | (56) all_11_0_7 = one
% 4.35/1.69  |
% 4.35/1.69  | Simplifying 56 yields:
% 4.35/1.69  | (57) all_11_0_7 = one
% 4.35/1.69  |
% 4.35/1.69  | From (57) and (47) follows:
% 4.35/1.69  | (58) multiplication(one, all_0_5_5) = all_0_0_0
% 4.35/1.69  |
% 4.35/1.69  | Instantiating formula (16) with all_0_0_0, all_0_5_5 and discharging atoms multiplication(one, all_0_5_5) = all_0_0_0, yields:
% 4.35/1.69  | (59) all_0_0_0 = all_0_5_5
% 4.35/1.69  |
% 4.35/1.69  | Equations (59) can reduce 24 to:
% 4.35/1.69  | (60) $false
% 4.35/1.69  |
% 4.35/1.69  |-The branch is then unsatisfiable
% 4.35/1.69  % SZS output end Proof for theBenchmark
% 4.35/1.69  
% 4.35/1.69  1073ms
%------------------------------------------------------------------------------