%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE009+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n006.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 01:50:49 EDT 2022

% Result   : Theorem 3.46s 1.52s
% Output   : Proof 5.48s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : KLE009+2 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n006.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
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Thu Jun 16 15:26:41 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.46/0.62          ____       _                          
% 0.46/0.62    ___  / __ \_____(_)___  ________  __________
% 0.46/0.62   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.46/0.62  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.46/0.62  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.46/0.62  
% 0.46/0.62  A Theorem Prover for First-Order Logic
% 0.46/0.62  (ePrincess v.1.0)
% 0.46/0.62  
% 0.46/0.62  (c) Philipp Rümmer, 2009-2015
% 0.46/0.62  (c) Peter Backeman, 2014-2015
% 0.46/0.62  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.46/0.62  Free software under GNU Lesser General Public License (LGPL).
% 0.46/0.62  Bug reports to peter@backeman.se
% 0.46/0.62  
% 0.46/0.62  For more information, visit http://user.uu.se/~petba168/breu/
% 0.46/0.62  
% 0.46/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.68  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.56/0.98  Prover 0: Preprocessing ...
% 2.36/1.27  Prover 0: Constructing countermodel ...
% 3.46/1.52  Prover 0: proved (837ms)
% 3.46/1.52  
% 3.46/1.52  No countermodel exists, formula is valid
% 3.46/1.52  % SZS status Theorem for theBenchmark
% 3.46/1.52  
% 3.46/1.52  Generating proof ... found it (size 39)
% 5.14/1.87  
% 5.14/1.87  % SZS output start Proof for theBenchmark
% 5.14/1.87  Assumed formulas after preprocessing and simplification: 
% 5.14/1.87  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : ( ~ (v10 = one) & c(v1) = v3 & c(v0) = v6 & multiplication(v6, v3) = v9 & multiplication(v6, v1) = v7 & multiplication(v0, v3) = v4 & multiplication(v0, v1) = v2 & addition(v8, v9) = v10 & addition(v5, v7) = v8 & addition(v2, v4) = v5 & test(v1) & test(v0) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (multiplication(v12, v13) = v15) |  ~ (multiplication(v11, v13) = v14) |  ~ (addition(v14, v15) = v16) |  ? [v17] : (multiplication(v17, v13) = v16 & addition(v11, v12) = v17)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (multiplication(v11, v13) = v15) |  ~ (multiplication(v11, v12) = v14) |  ~ (addition(v14, v15) = v16) |  ? [v17] : (multiplication(v11, v17) = v16 & addition(v12, v13) = v17)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ (c(v12) = v14) |  ~ (c(v11) = v13) |  ~ (multiplication(v13, v14) = v15) |  ~ test(v12) |  ~ test(v11) |  ? [v16] : (c(v16) = v15 & addition(v11, v12) = v16)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ (c(v12) = v14) |  ~ (c(v11) = v13) |  ~ (addition(v13, v14) = v15) |  ~ test(v12) |  ~ test(v11) |  ? [v16] : (c(v16) = v15 & multiplication(v11, v12) = v16)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ (multiplication(v14, v13) = v15) |  ~ (multiplication(v11, v12) = v14) |  ? [v16] : (multiplication(v12, v13) = v16 & multiplication(v11, v16) = v15)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ (multiplication(v14, v13) = v15) |  ~ (addition(v11, v12) = v14) |  ? [v16] :  ? [v17] : (multiplication(v12, v13) = v17 & multiplication(v11, v13) = v16 & addition(v16, v17) = v15)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ (multiplication(v12, v13) = v14) |  ~ (multiplication(v11, v14) = v15) |  ? [v16] : (multiplication(v16, v13) = v15 & multiplication(v11, v12) = v16)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ (multiplication(v11, v14) = v15) |  ~ (addition(v12, v13) = v14) |  ? [v16] :  ? [v17] : (multiplication(v11, v13) = v17 & multiplication(v11, v12) = v16 & addition(v16, v17) = v15)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ (addition(v14, v11) = v15) |  ~ (addition(v13, v12) = v14) |  ? [v16] : (addition(v13, v16) = v15 & addition(v12, v11) = v16)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ (addition(v13, v14) = v15) |  ~ (addition(v12, v11) = v14) |  ? [v16] : (addition(v16, v11) = v15 & addition(v13, v12) = v16)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (multiplication(v14, v13) = v12) |  ~ (multiplication(v14, v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (addition(v14, v13) = v12) |  ~ (addition(v14, v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = v12 |  ~ (c(v11) = v13) |  ~ complement(v11, v12) |  ~ test(v11)) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = v12 |  ~ (addition(v11, v12) = v13) |  ~ leq(v11, v12)) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = one |  ~ (addition(v11, v12) = v13) |  ~ complement(v12, v11)) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = zero |  ~ (multiplication(v12, v11) = v13) |  ~ complement(v12, v11)) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = zero |  ~ (multiplication(v11, v12) = v13) |  ~ complement(v12, v11)) &  ! [v11] :  ! [v12] :  ! [v13] : (v12 = v11 |  ~ (c(v13) = v12) |  ~ (c(v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (multiplication(v12, v11) = v13) |  ~ complement(v12, v11) | (multiplication(v11, v12) = zero & addition(v11, v12) = one)) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (multiplication(v11, v12) = v13) |  ~ complement(v12, v11) | (multiplication(v12, v11) = zero & addition(v11, v12) = one)) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (multiplication(v11, v12) = v13) |  ~ test(v12) |  ~ test(v11) |  ? [v14] :  ? [v15] :  ? [v16] : (c(v13) = v14 & c(v12) = v16 & c(v11) = v15 & addition(v15, v16) = v14)) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (addition(v12, v11) = v13) | addition(v11, v12) = v13) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (addition(v11, v12) = v13) |  ~ complement(v12, v11) | (multiplication(v12, v11) = zero & multiplication(v11, v12) = zero)) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (addition(v11, v12) = v13) |  ~ test(v12) |  ~ test(v11) |  ? [v14] :  ? [v15] :  ? [v16] : (c(v13) = v14 & c(v12) = v16 & c(v11) = v15 & multiplication(v15, v16) = v14)) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (addition(v11, v12) = v13) | addition(v12, v11) = v13) &  ! [v11] :  ! [v12] : (v12 = v11 |  ~ (multiplication(v11, one) = v12)) &  ! [v11] :  ! [v12] : (v12 = v11 |  ~ (multiplication(one, v11) = v12)) &  ! [v11] :  ! [v12] : (v12 = v11 |  ~ (addition(v11, v11) = v12)) &  ! [v11] :  ! [v12] : (v12 = v11 |  ~ (addition(v11, zero) = v12)) &  ! [v11] :  ! [v12] : (v12 = zero |  ~ (c(v11) = v12) | test(v11)) &  ! [v11] :  ! [v12] : (v12 = zero |  ~ (multiplication(v11, zero) = v12)) &  ! [v11] :  ! [v12] : (v12 = zero |  ~ (multiplication(zero, v11) = v12)) &  ! [v11] :  ! [v12] : ( ~ (c(v11) = v12) |  ~ test(v11) | complement(v11, v12)) &  ! [v11] :  ! [v12] : ( ~ (multiplication(v12, v11) = zero) | complement(v12, v11) |  ? [v13] :  ? [v14] : (multiplication(v11, v12) = v13 & addition(v11, v12) = v14 & ( ~ (v14 = one) |  ~ (v13 = zero)))) &  ! [v11] :  ! [v12] : ( ~ (multiplication(v11, v12) = zero) | complement(v12, v11) |  ? [v13] :  ? [v14] : (multiplication(v12, v11) = v13 & addition(v11, v12) = v14 & ( ~ (v14 = one) |  ~ (v13 = zero)))) &  ! [v11] :  ! [v12] : ( ~ (addition(v11, v12) = v12) | leq(v11, v12)) &  ! [v11] :  ! [v12] : ( ~ (addition(v11, v12) = one) | complement(v12, v11) |  ? [v13] :  ? [v14] : (multiplication(v12, v11) = v14 & multiplication(v11, v12) = v13 & ( ~ (v14 = zero) |  ~ (v13 = zero)))) &  ! [v11] :  ! [v12] : ( ~ complement(v12, v11) | test(v11)) &  ! [v11] : ( ~ test(v11) |  ? [v12] : complement(v12, v11)))
% 5.25/1.92  | 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, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10 yields:
% 5.25/1.92  | (1)  ~ (all_0_0_0 = one) & c(all_0_9_9) = all_0_7_7 & c(all_0_10_10) = all_0_4_4 & multiplication(all_0_4_4, all_0_7_7) = all_0_1_1 & multiplication(all_0_4_4, all_0_9_9) = all_0_3_3 & multiplication(all_0_10_10, all_0_7_7) = all_0_6_6 & multiplication(all_0_10_10, all_0_9_9) = all_0_8_8 & addition(all_0_2_2, all_0_1_1) = all_0_0_0 & addition(all_0_5_5, all_0_3_3) = all_0_2_2 & addition(all_0_8_8, all_0_6_6) = all_0_5_5 & test(all_0_9_9) & test(all_0_10_10) &  ! [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] : ( ~ (c(v1) = v3) |  ~ (c(v0) = v2) |  ~ (multiplication(v2, v3) = v4) |  ~ test(v1) |  ~ test(v0) |  ? [v5] : (c(v5) = v4 & addition(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (c(v1) = v3) |  ~ (c(v0) = v2) |  ~ (addition(v2, v3) = v4) |  ~ test(v1) |  ~ test(v0) |  ? [v5] : (c(v5) = v4 & multiplication(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 |  ~ (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] : ( ~ (multiplication(v0, v1) = v2) |  ~ test(v1) |  ~ test(v0) |  ? [v3] :  ? [v4] :  ? [v5] : (c(v2) = v3 & c(v1) = v5 & c(v0) = v4 & addition(v4, v5) = v3)) &  ! [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) |  ~ test(v1) |  ~ test(v0) |  ? [v3] :  ? [v4] :  ? [v5] : (c(v2) = v3 & c(v1) = v5 & c(v0) = v4 & multiplication(v4, v5) = v3)) &  ! [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))
% 5.43/1.93  |
% 5.43/1.93  | Applying alpha-rule on (1) yields:
% 5.43/1.93  | (2)  ! [v0] :  ! [v1] : ( ~ complement(v1, v0) | test(v0))
% 5.43/1.93  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 5.43/1.93  | (4)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ~ leq(v0, v1))
% 5.43/1.93  | (5)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) |  ~ test(v1) |  ~ test(v0) |  ? [v3] :  ? [v4] :  ? [v5] : (c(v2) = v3 & c(v1) = v5 & c(v0) = v4 & multiplication(v4, v5) = v3))
% 5.43/1.93  | (6)  ~ (all_0_0_0 = one)
% 5.43/1.93  | (7) multiplication(all_0_10_10, all_0_7_7) = all_0_6_6
% 5.43/1.93  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ~ test(v1) |  ~ test(v0) |  ? [v3] :  ? [v4] :  ? [v5] : (c(v2) = v3 & c(v1) = v5 & c(v0) = v4 & addition(v4, v5) = v3))
% 5.43/1.94  | (9)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (c(v0) = v1) | test(v0))
% 5.43/1.94  | (10)  ! [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))
% 5.43/1.94  | (11)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ~ complement(v1, v0) | (multiplication(v1, v0) = zero & addition(v0, v1) = one))
% 5.43/1.94  | (12)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v1, v0) = v2) |  ~ complement(v1, v0) | (multiplication(v0, v1) = zero & addition(v0, v1) = one))
% 5.43/1.94  | (13) multiplication(all_0_10_10, all_0_9_9) = all_0_8_8
% 5.43/1.94  | (14)  ! [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))
% 5.43/1.94  | (15) c(all_0_10_10) = all_0_4_4
% 5.43/1.94  | (16)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = zero |  ~ (multiplication(v0, v1) = v2) |  ~ complement(v1, v0))
% 5.43/1.94  | (17) multiplication(all_0_4_4, all_0_9_9) = all_0_3_3
% 5.43/1.94  | (18)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 5.43/1.94  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 5.43/1.94  | (20) addition(all_0_8_8, all_0_6_6) = all_0_5_5
% 5.43/1.94  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (c(v1) = v3) |  ~ (c(v0) = v2) |  ~ (multiplication(v2, v3) = v4) |  ~ test(v1) |  ~ test(v0) |  ? [v5] : (c(v5) = v4 & addition(v0, v1) = v5))
% 5.43/1.94  | (22)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (c(v0) = v2) |  ~ complement(v0, v1) |  ~ test(v0))
% 5.43/1.94  | (23)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) |  ~ complement(v1, v0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero))
% 5.43/1.94  | (24)  ! [v0] :  ! [v1] : ( ~ (multiplication(v1, v0) = zero) | complement(v1, v0) |  ? [v2] :  ? [v3] : (multiplication(v0, v1) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) |  ~ (v2 = zero))))
% 5.43/1.94  | (25)  ! [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))
% 5.48/1.94  | (26) multiplication(all_0_4_4, all_0_7_7) = all_0_1_1
% 5.48/1.94  | (27)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 5.48/1.94  | (28)  ! [v0] :  ! [v1] : ( ~ (multiplication(v0, v1) = zero) | complement(v1, v0) |  ? [v2] :  ? [v3] : (multiplication(v1, v0) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) |  ~ (v2 = zero))))
% 5.48/1.94  | (29)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (c(v2) = v1) |  ~ (c(v2) = v0))
% 5.48/1.94  | (30) addition(all_0_5_5, all_0_3_3) = all_0_2_2
% 5.48/1.94  | (31)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 5.48/1.94  | (32)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = zero |  ~ (multiplication(v1, v0) = v2) |  ~ complement(v1, v0))
% 5.48/1.94  | (33)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = one |  ~ (addition(v0, v1) = v2) |  ~ complement(v1, v0))
% 5.48/1.95  | (34)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 5.48/1.95  | (35) test(all_0_9_9)
% 5.48/1.95  | (36) c(all_0_9_9) = all_0_7_7
% 5.48/1.95  | (37) test(all_0_10_10)
% 5.48/1.95  | (38)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 5.48/1.95  | (39)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(v0, zero) = v1))
% 5.48/1.95  | (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))
% 5.48/1.95  | (41)  ! [v0] :  ! [v1] : ( ~ (c(v0) = v1) |  ~ test(v0) | complement(v0, v1))
% 5.48/1.95  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (c(v1) = v3) |  ~ (c(v0) = v2) |  ~ (addition(v2, v3) = v4) |  ~ test(v1) |  ~ test(v0) |  ? [v5] : (c(v5) = v4 & multiplication(v0, v1) = v5))
% 5.48/1.95  | (43)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 5.48/1.95  | (44)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 5.48/1.95  | (45) addition(all_0_2_2, all_0_1_1) = all_0_0_0
% 5.48/1.95  | (46)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 5.48/1.95  | (47)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = one) | complement(v1, v0) |  ? [v2] :  ? [v3] : (multiplication(v1, v0) = v3 & multiplication(v0, v1) = v2 & ( ~ (v3 = zero) |  ~ (v2 = zero))))
% 5.48/1.95  | (48)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 5.48/1.95  | (49)  ! [v0] : ( ~ test(v0) |  ? [v1] : complement(v1, v0))
% 5.48/1.95  | (50)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 5.48/1.95  | (51)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 5.48/1.95  | (52)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 5.48/1.95  |
% 5.48/1.95  | Instantiating formula (52) with all_0_0_0, all_0_2_2, all_0_1_1 and discharging atoms addition(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 5.48/1.95  | (53) addition(all_0_1_1, all_0_2_2) = all_0_0_0
% 5.48/1.95  |
% 5.48/1.95  | Instantiating formula (46) with all_0_0_0, all_0_2_2, all_0_5_5, all_0_3_3, all_0_1_1 and discharging atoms addition(all_0_2_2, all_0_1_1) = all_0_0_0, addition(all_0_5_5, all_0_3_3) = all_0_2_2, yields:
% 5.48/1.95  | (54)  ? [v0] : (addition(all_0_3_3, all_0_1_1) = v0 & addition(all_0_5_5, v0) = all_0_0_0)
% 5.48/1.95  |
% 5.48/1.95  | Instantiating formula (52) with all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms addition(all_0_5_5, all_0_3_3) = all_0_2_2, yields:
% 5.48/1.95  | (55) addition(all_0_3_3, all_0_5_5) = all_0_2_2
% 5.48/1.95  |
% 5.48/1.95  | Instantiating formula (10) with all_0_5_5, all_0_6_6, all_0_8_8, all_0_7_7, all_0_9_9, all_0_10_10 and discharging atoms multiplication(all_0_10_10, all_0_7_7) = all_0_6_6, multiplication(all_0_10_10, all_0_9_9) = all_0_8_8, addition(all_0_8_8, all_0_6_6) = all_0_5_5, yields:
% 5.48/1.96  | (56)  ? [v0] : (multiplication(all_0_10_10, v0) = all_0_5_5 & addition(all_0_9_9, all_0_7_7) = v0)
% 5.48/1.96  |
% 5.48/1.96  | Instantiating formula (52) with all_0_5_5, all_0_8_8, all_0_6_6 and discharging atoms addition(all_0_8_8, all_0_6_6) = all_0_5_5, yields:
% 5.48/1.96  | (57) addition(all_0_6_6, all_0_8_8) = all_0_5_5
% 5.48/1.96  |
% 5.48/1.96  | Instantiating formula (41) with all_0_7_7, all_0_9_9 and discharging atoms c(all_0_9_9) = all_0_7_7, test(all_0_9_9), yields:
% 5.48/1.96  | (58) complement(all_0_9_9, all_0_7_7)
% 5.48/1.96  |
% 5.48/1.96  | Instantiating formula (41) with all_0_4_4, all_0_10_10 and discharging atoms c(all_0_10_10) = all_0_4_4, test(all_0_10_10), yields:
% 5.48/1.96  | (59) complement(all_0_10_10, all_0_4_4)
% 5.48/1.96  |
% 5.48/1.96  | Instantiating (56) with all_17_0_17 yields:
% 5.48/1.96  | (60) multiplication(all_0_10_10, all_17_0_17) = all_0_5_5 & addition(all_0_9_9, all_0_7_7) = all_17_0_17
% 5.48/1.96  |
% 5.48/1.96  | Applying alpha-rule on (60) yields:
% 5.48/1.96  | (61) multiplication(all_0_10_10, all_17_0_17) = all_0_5_5
% 5.48/1.96  | (62) addition(all_0_9_9, all_0_7_7) = all_17_0_17
% 5.48/1.96  |
% 5.48/1.96  | Instantiating (54) with all_21_0_19 yields:
% 5.48/1.96  | (63) addition(all_0_3_3, all_0_1_1) = all_21_0_19 & addition(all_0_5_5, all_21_0_19) = all_0_0_0
% 5.48/1.96  |
% 5.48/1.96  | Applying alpha-rule on (63) yields:
% 5.48/1.96  | (64) addition(all_0_3_3, all_0_1_1) = all_21_0_19
% 5.48/1.96  | (65) addition(all_0_5_5, all_21_0_19) = all_0_0_0
% 5.48/1.96  |
% 5.48/1.96  | Instantiating formula (10) with all_21_0_19, all_0_1_1, all_0_3_3, all_0_7_7, all_0_9_9, all_0_4_4 and discharging atoms multiplication(all_0_4_4, all_0_7_7) = all_0_1_1, multiplication(all_0_4_4, all_0_9_9) = all_0_3_3, addition(all_0_3_3, all_0_1_1) = all_21_0_19, yields:
% 5.48/1.96  | (66)  ? [v0] : (multiplication(all_0_4_4, v0) = all_21_0_19 & addition(all_0_9_9, all_0_7_7) = v0)
% 5.48/1.96  |
% 5.48/1.96  | Instantiating formula (52) with all_21_0_19, all_0_3_3, all_0_1_1 and discharging atoms addition(all_0_3_3, all_0_1_1) = all_21_0_19, yields:
% 5.48/1.96  | (67) addition(all_0_1_1, all_0_3_3) = all_21_0_19
% 5.48/1.96  |
% 5.48/1.96  | Instantiating formula (50) with all_0_0_0, all_0_2_2, all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms addition(all_0_1_1, all_0_2_2) = all_0_0_0, addition(all_0_3_3, all_0_5_5) = all_0_2_2, yields:
% 5.48/1.96  | (68)  ? [v0] : (addition(v0, all_0_5_5) = all_0_0_0 & addition(all_0_1_1, all_0_3_3) = v0)
% 5.48/1.96  |
% 5.48/1.96  | Instantiating formula (10) with all_0_5_5, all_0_8_8, all_0_6_6, all_0_9_9, all_0_7_7, all_0_10_10 and discharging atoms multiplication(all_0_10_10, all_0_7_7) = all_0_6_6, multiplication(all_0_10_10, all_0_9_9) = all_0_8_8, addition(all_0_6_6, all_0_8_8) = all_0_5_5, yields:
% 5.48/1.96  | (69)  ? [v0] : (multiplication(all_0_10_10, v0) = all_0_5_5 & addition(all_0_7_7, all_0_9_9) = v0)
% 5.48/1.96  |
% 5.48/1.96  | Instantiating formula (52) with all_17_0_17, all_0_9_9, all_0_7_7 and discharging atoms addition(all_0_9_9, all_0_7_7) = all_17_0_17, yields:
% 5.48/1.96  | (70) addition(all_0_7_7, all_0_9_9) = all_17_0_17
% 5.48/1.96  |
% 5.48/1.96  | Instantiating (66) with all_35_0_21 yields:
% 5.48/1.96  | (71) multiplication(all_0_4_4, all_35_0_21) = all_21_0_19 & addition(all_0_9_9, all_0_7_7) = all_35_0_21
% 5.48/1.96  |
% 5.48/1.96  | Applying alpha-rule on (71) yields:
% 5.48/1.96  | (72) multiplication(all_0_4_4, all_35_0_21) = all_21_0_19
% 5.48/1.96  | (73) addition(all_0_9_9, all_0_7_7) = all_35_0_21
% 5.48/1.96  |
% 5.48/1.96  | Instantiating (68) with all_39_0_23 yields:
% 5.48/1.96  | (74) addition(all_39_0_23, all_0_5_5) = all_0_0_0 & addition(all_0_1_1, all_0_3_3) = all_39_0_23
% 5.48/1.96  |
% 5.48/1.96  | Applying alpha-rule on (74) yields:
% 5.48/1.96  | (75) addition(all_39_0_23, all_0_5_5) = all_0_0_0
% 5.48/1.96  | (76) addition(all_0_1_1, all_0_3_3) = all_39_0_23
% 5.48/1.96  |
% 5.48/1.96  | Instantiating (69) with all_55_0_31 yields:
% 5.48/1.96  | (77) multiplication(all_0_10_10, all_55_0_31) = all_0_5_5 & addition(all_0_7_7, all_0_9_9) = all_55_0_31
% 5.48/1.96  |
% 5.48/1.96  | Applying alpha-rule on (77) yields:
% 5.48/1.96  | (78) multiplication(all_0_10_10, all_55_0_31) = all_0_5_5
% 5.48/1.96  | (79) addition(all_0_7_7, all_0_9_9) = all_55_0_31
% 5.48/1.96  |
% 5.48/1.96  | Instantiating formula (19) with all_0_1_1, all_0_3_3, all_21_0_19, all_39_0_23 and discharging atoms addition(all_0_1_1, all_0_3_3) = all_39_0_23, addition(all_0_1_1, all_0_3_3) = all_21_0_19, yields:
% 5.48/1.96  | (80) all_39_0_23 = all_21_0_19
% 5.48/1.96  |
% 5.48/1.96  | Instantiating formula (33) with all_55_0_31, all_0_9_9, all_0_7_7 and discharging atoms addition(all_0_7_7, all_0_9_9) = all_55_0_31, complement(all_0_9_9, all_0_7_7), yields:
% 5.48/1.96  | (81) all_55_0_31 = one
% 5.48/1.96  |
% 5.48/1.96  | Instantiating formula (19) with all_0_7_7, all_0_9_9, all_17_0_17, all_55_0_31 and discharging atoms addition(all_0_7_7, all_0_9_9) = all_55_0_31, addition(all_0_7_7, all_0_9_9) = all_17_0_17, yields:
% 5.48/1.96  | (82) all_55_0_31 = all_17_0_17
% 5.48/1.96  |
% 5.48/1.96  | Instantiating formula (19) with all_0_9_9, all_0_7_7, all_35_0_21, all_17_0_17 and discharging atoms addition(all_0_9_9, all_0_7_7) = all_35_0_21, addition(all_0_9_9, all_0_7_7) = all_17_0_17, yields:
% 5.48/1.97  | (83) all_35_0_21 = all_17_0_17
% 5.48/1.97  |
% 5.48/1.97  | Combining equations (81,82) yields a new equation:
% 5.48/1.97  | (84) all_17_0_17 = one
% 5.48/1.97  |
% 5.48/1.97  | Combining equations (84,83) yields a new equation:
% 5.48/1.97  | (85) all_35_0_21 = one
% 5.48/1.97  |
% 5.48/1.97  | From (85) and (72) follows:
% 5.48/1.97  | (86) multiplication(all_0_4_4, one) = all_21_0_19
% 5.48/1.97  |
% 5.48/1.97  | From (84) and (61) follows:
% 5.48/1.97  | (87) multiplication(all_0_10_10, one) = all_0_5_5
% 5.48/1.97  |
% 5.48/1.97  | From (80) and (75) follows:
% 5.48/1.97  | (88) addition(all_21_0_19, all_0_5_5) = all_0_0_0
% 5.48/1.97  |
% 5.48/1.97  | Instantiating formula (18) with all_21_0_19, all_0_4_4 and discharging atoms multiplication(all_0_4_4, one) = all_21_0_19, yields:
% 5.48/1.97  | (89) all_21_0_19 = all_0_4_4
% 5.48/1.97  |
% 5.48/1.97  | Instantiating formula (18) with all_0_5_5, all_0_10_10 and discharging atoms multiplication(all_0_10_10, one) = all_0_5_5, yields:
% 5.48/1.97  | (90) all_0_5_5 = all_0_10_10
% 5.48/1.97  |
% 5.48/1.97  | From (89)(90) and (88) follows:
% 5.48/1.97  | (91) addition(all_0_4_4, all_0_10_10) = all_0_0_0
% 5.48/1.97  |
% 5.48/1.97  | Instantiating formula (33) with all_0_0_0, all_0_10_10, all_0_4_4 and discharging atoms addition(all_0_4_4, all_0_10_10) = all_0_0_0, complement(all_0_10_10, all_0_4_4), yields:
% 5.48/1.97  | (92) all_0_0_0 = one
% 5.48/1.97  |
% 5.48/1.97  | Equations (92) can reduce 6 to:
% 5.48/1.97  | (93) $false
% 5.48/1.97  |
% 5.48/1.97  |-The branch is then unsatisfiable
% 5.48/1.97  % SZS output end Proof for theBenchmark
% 5.48/1.97  
% 5.48/1.97  1337ms
%------------------------------------------------------------------------------