%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE007+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n005.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 01:50:48 EDT 2022

% Result   : Theorem 3.22s 1.40s
% Output   : Proof 4.44s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : KLE007+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n005.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 09:12:23 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.58          ____       _                          
% 0.19/0.58    ___  / __ \_____(_)___  ________  __________
% 0.19/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.19/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.19/0.58  
% 0.19/0.58  A Theorem Prover for First-Order Logic
% 0.19/0.58  (ePrincess v.1.0)
% 0.19/0.58  
% 0.19/0.58  (c) Philipp Rümmer, 2009-2015
% 0.19/0.58  (c) Peter Backeman, 2014-2015
% 0.19/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58  Bug reports to peter@backeman.se
% 0.19/0.58  
% 0.19/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58  
% 0.19/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.77/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.69/0.95  Prover 0: Preprocessing ...
% 2.57/1.23  Prover 0: Constructing countermodel ...
% 3.22/1.39  Prover 0: proved (763ms)
% 3.22/1.40  
% 3.22/1.40  No countermodel exists, formula is valid
% 3.22/1.40  % SZS status Theorem for theBenchmark
% 3.22/1.40  
% 3.22/1.40  Generating proof ... found it (size 15)
% 4.44/1.69  
% 4.44/1.69  % SZS output start Proof for theBenchmark
% 4.44/1.69  Assumed formulas after preprocessing and simplification: 
% 4.44/1.69  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : ( ~ (v7 = one) & c(v1) = v5 & c(v0) = v2 & multiplication(v3, v5) = v6 & multiplication(v3, v1) = v4 & addition(v4, v6) = v7 & addition(v0, v2) = v3 & test(v1) & test(v0) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (multiplication(v9, v10) = v12) |  ~ (multiplication(v8, v10) = v11) |  ~ (addition(v11, v12) = v13) |  ? [v14] : (multiplication(v14, v10) = v13 & addition(v8, v9) = v14)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (multiplication(v8, v10) = v12) |  ~ (multiplication(v8, v9) = v11) |  ~ (addition(v11, v12) = v13) |  ? [v14] : (multiplication(v8, v14) = v13 & addition(v9, v10) = v14)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (multiplication(v11, v10) = v12) |  ~ (multiplication(v8, v9) = v11) |  ? [v13] : (multiplication(v9, v10) = v13 & multiplication(v8, v13) = v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (multiplication(v11, v10) = v12) |  ~ (addition(v8, v9) = v11) |  ? [v13] :  ? [v14] : (multiplication(v9, v10) = v14 & multiplication(v8, v10) = v13 & addition(v13, v14) = v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (multiplication(v9, v10) = v11) |  ~ (multiplication(v8, v11) = v12) |  ? [v13] : (multiplication(v13, v10) = v12 & multiplication(v8, v9) = v13)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (multiplication(v8, v11) = v12) |  ~ (addition(v9, v10) = v11) |  ? [v13] :  ? [v14] : (multiplication(v8, v10) = v14 & multiplication(v8, v9) = v13 & addition(v13, v14) = v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (addition(v11, v8) = v12) |  ~ (addition(v10, v9) = v11) |  ? [v13] : (addition(v10, v13) = v12 & addition(v9, v8) = v13)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (addition(v10, v11) = v12) |  ~ (addition(v9, v8) = v11) |  ? [v13] : (addition(v13, v8) = v12 & addition(v10, v9) = v13)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (multiplication(v11, v10) = v9) |  ~ (multiplication(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (addition(v11, v10) = v9) |  ~ (addition(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = v9 |  ~ (c(v8) = v10) |  ~ complement(v8, v9) |  ~ test(v8)) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = v9 |  ~ (addition(v8, v9) = v10) |  ~ leq(v8, v9)) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = one |  ~ (addition(v8, v9) = v10) |  ~ complement(v9, v8)) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = zero |  ~ (multiplication(v9, v8) = v10) |  ~ complement(v9, v8)) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = zero |  ~ (multiplication(v8, v9) = v10) |  ~ complement(v9, v8)) &  ! [v8] :  ! [v9] :  ! [v10] : (v9 = v8 |  ~ (c(v10) = v9) |  ~ (c(v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (multiplication(v9, v8) = v10) |  ~ complement(v9, v8) | (multiplication(v8, v9) = zero & addition(v8, v9) = one)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (multiplication(v8, v9) = v10) |  ~ complement(v9, v8) | (multiplication(v9, v8) = zero & addition(v8, v9) = one)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (addition(v9, v8) = v10) | addition(v8, v9) = v10) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (addition(v8, v9) = v10) |  ~ complement(v9, v8) | (multiplication(v9, v8) = zero & multiplication(v8, v9) = zero)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (addition(v8, v9) = v10) | addition(v9, v8) = v10) &  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (multiplication(v8, one) = v9)) &  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (multiplication(one, v8) = v9)) &  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (addition(v8, v8) = v9)) &  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (addition(v8, zero) = v9)) &  ! [v8] :  ! [v9] : (v9 = zero |  ~ (c(v8) = v9) | test(v8)) &  ! [v8] :  ! [v9] : (v9 = zero |  ~ (multiplication(v8, zero) = v9)) &  ! [v8] :  ! [v9] : (v9 = zero |  ~ (multiplication(zero, v8) = v9)) &  ! [v8] :  ! [v9] : ( ~ (c(v8) = v9) |  ~ test(v8) | complement(v8, v9)) &  ! [v8] :  ! [v9] : ( ~ (multiplication(v9, v8) = zero) | complement(v9, v8) |  ? [v10] :  ? [v11] : (multiplication(v8, v9) = v10 & addition(v8, v9) = v11 & ( ~ (v11 = one) |  ~ (v10 = zero)))) &  ! [v8] :  ! [v9] : ( ~ (multiplication(v8, v9) = zero) | complement(v9, v8) |  ? [v10] :  ? [v11] : (multiplication(v9, v8) = v10 & addition(v8, v9) = v11 & ( ~ (v11 = one) |  ~ (v10 = zero)))) &  ! [v8] :  ! [v9] : ( ~ (addition(v8, v9) = v9) | leq(v8, v9)) &  ! [v8] :  ! [v9] : ( ~ (addition(v8, v9) = one) | complement(v9, v8) |  ? [v10] :  ? [v11] : (multiplication(v9, v8) = v11 & multiplication(v8, v9) = v10 & ( ~ (v11 = zero) |  ~ (v10 = zero)))) &  ! [v8] :  ! [v9] : ( ~ complement(v9, v8) | test(v8)) &  ! [v8] : ( ~ test(v8) |  ? [v9] : complement(v9, v8)))
% 4.44/1.73  | 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 yields:
% 4.44/1.73  | (1)  ~ (all_0_0_0 = one) & c(all_0_6_6) = all_0_2_2 & c(all_0_7_7) = all_0_5_5 & multiplication(all_0_4_4, all_0_2_2) = all_0_1_1 & multiplication(all_0_4_4, all_0_6_6) = all_0_3_3 & addition(all_0_3_3, all_0_1_1) = all_0_0_0 & addition(all_0_7_7, all_0_5_5) = all_0_4_4 & test(all_0_6_6) & test(all_0_7_7) &  ! [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))
% 4.44/1.74  |
% 4.44/1.74  | Applying alpha-rule on (1) yields:
% 4.44/1.74  | (2) addition(all_0_7_7, all_0_5_5) = all_0_4_4
% 4.44/1.74  | (3)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(v0, zero) = v1))
% 4.44/1.74  | (4) multiplication(all_0_4_4, all_0_2_2) = all_0_1_1
% 4.44/1.74  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 4.44/1.75  | (6) c(all_0_6_6) = all_0_2_2
% 4.44/1.75  | (7)  ~ (all_0_0_0 = one)
% 4.44/1.75  | (8) test(all_0_6_6)
% 4.44/1.75  | (9)  ! [v0] :  ! [v1] : ( ~ (multiplication(v0, v1) = zero) | complement(v1, v0) |  ? [v2] :  ? [v3] : (multiplication(v1, v0) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) |  ~ (v2 = zero))))
% 4.44/1.75  | (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))
% 4.44/1.75  | (11)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (c(v0) = v1) | test(v0))
% 4.44/1.75  | (12)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ~ complement(v1, v0) | (multiplication(v1, v0) = zero & addition(v0, v1) = one))
% 4.44/1.75  | (13)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v1, v0) = v2) |  ~ complement(v1, v0) | (multiplication(v0, v1) = zero & addition(v0, v1) = one))
% 4.44/1.75  | (14)  ! [v0] : ( ~ test(v0) |  ? [v1] : complement(v1, v0))
% 4.44/1.75  | (15) addition(all_0_3_3, all_0_1_1) = all_0_0_0
% 4.44/1.75  | (16)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 4.44/1.75  | (17)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 4.44/1.75  | (18)  ! [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))
% 4.44/1.75  | (19)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 4.44/1.75  | (20)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 4.44/1.75  | (21)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 4.44/1.75  | (22) multiplication(all_0_4_4, all_0_6_6) = all_0_3_3
% 4.44/1.75  | (23)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (c(v0) = v2) |  ~ complement(v0, v1) |  ~ test(v0))
% 4.44/1.75  | (24)  ! [v0] :  ! [v1] : ( ~ (multiplication(v1, v0) = zero) | complement(v1, v0) |  ? [v2] :  ? [v3] : (multiplication(v0, v1) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) |  ~ (v2 = zero))))
% 4.44/1.75  | (25)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = one |  ~ (addition(v0, v1) = v2) |  ~ complement(v1, v0))
% 4.44/1.75  | (26) test(all_0_7_7)
% 4.44/1.75  | (27)  ! [v0] :  ! [v1] : ( ~ complement(v1, v0) | test(v0))
% 4.44/1.75  | (28)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = one) | complement(v1, v0) |  ? [v2] :  ? [v3] : (multiplication(v1, v0) = v3 & multiplication(v0, v1) = v2 & ( ~ (v3 = zero) |  ~ (v2 = zero))))
% 4.44/1.75  | (29)  ! [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))
% 4.44/1.75  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 4.44/1.75  | (31)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 4.44/1.76  | (32)  ! [v0] :  ! [v1] : ( ~ (c(v0) = v1) |  ~ test(v0) | complement(v0, v1))
% 4.44/1.76  | (33)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = zero |  ~ (multiplication(v0, v1) = v2) |  ~ complement(v1, v0))
% 4.44/1.76  | (34)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = zero |  ~ (multiplication(v1, v0) = v2) |  ~ complement(v1, v0))
% 4.44/1.76  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 4.44/1.76  | (36)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) |  ~ complement(v1, v0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero))
% 4.44/1.76  | (37)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 4.44/1.76  | (38)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 4.44/1.76  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 4.44/1.76  | (40)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 4.44/1.76  | (41)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (c(v2) = v1) |  ~ (c(v2) = v0))
% 4.44/1.76  | (42) c(all_0_7_7) = all_0_5_5
% 4.44/1.76  | (43)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 4.44/1.76  | (44)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ~ leq(v0, v1))
% 4.44/1.76  | (45)  ! [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))
% 4.44/1.76  |
% 4.44/1.76  | Instantiating formula (20) 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:
% 4.44/1.76  | (46) addition(all_0_1_1, all_0_3_3) = all_0_0_0
% 4.44/1.76  |
% 4.44/1.76  | Instantiating formula (20) with all_0_4_4, all_0_7_7, all_0_5_5 and discharging atoms addition(all_0_7_7, all_0_5_5) = all_0_4_4, yields:
% 4.44/1.76  | (47) addition(all_0_5_5, all_0_7_7) = all_0_4_4
% 4.44/1.76  |
% 4.44/1.76  | Instantiating formula (32) with all_0_2_2, all_0_6_6 and discharging atoms c(all_0_6_6) = all_0_2_2, test(all_0_6_6), yields:
% 4.44/1.76  | (48) complement(all_0_6_6, all_0_2_2)
% 4.44/1.76  |
% 4.44/1.76  | Instantiating formula (32) with all_0_5_5, all_0_7_7 and discharging atoms c(all_0_7_7) = all_0_5_5, test(all_0_7_7), yields:
% 4.44/1.76  | (49) complement(all_0_7_7, all_0_5_5)
% 4.44/1.76  |
% 4.44/1.76  | Instantiating formula (25) with all_0_4_4, all_0_7_7, all_0_5_5 and discharging atoms addition(all_0_5_5, all_0_7_7) = all_0_4_4, complement(all_0_7_7, all_0_5_5), yields:
% 4.44/1.76  | (50) all_0_4_4 = one
% 4.44/1.76  |
% 4.44/1.77  | From (50) and (4) follows:
% 4.44/1.77  | (51) multiplication(one, all_0_2_2) = all_0_1_1
% 4.44/1.77  |
% 4.44/1.77  | From (50) and (22) follows:
% 4.44/1.77  | (52) multiplication(one, all_0_6_6) = all_0_3_3
% 4.44/1.77  |
% 4.44/1.77  | Instantiating formula (17) with all_0_1_1, all_0_2_2 and discharging atoms multiplication(one, all_0_2_2) = all_0_1_1, yields:
% 4.44/1.77  | (53) all_0_1_1 = all_0_2_2
% 4.44/1.77  |
% 4.44/1.77  | Instantiating formula (17) with all_0_3_3, all_0_6_6 and discharging atoms multiplication(one, all_0_6_6) = all_0_3_3, yields:
% 4.44/1.77  | (54) all_0_3_3 = all_0_6_6
% 4.44/1.77  |
% 4.44/1.77  | From (53)(54) and (46) follows:
% 4.44/1.77  | (55) addition(all_0_2_2, all_0_6_6) = all_0_0_0
% 4.44/1.77  |
% 4.44/1.77  | Instantiating formula (25) with all_0_0_0, all_0_6_6, all_0_2_2 and discharging atoms addition(all_0_2_2, all_0_6_6) = all_0_0_0, complement(all_0_6_6, all_0_2_2), yields:
% 4.44/1.77  | (56) all_0_0_0 = one
% 4.44/1.77  |
% 4.44/1.77  | Equations (56) can reduce 7 to:
% 4.44/1.77  | (57) $false
% 4.44/1.77  |
% 4.44/1.77  |-The branch is then unsatisfiable
% 4.44/1.77  % SZS output end Proof for theBenchmark
% 4.44/1.77  
% 4.44/1.77  1179ms
%------------------------------------------------------------------------------