%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE074+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n027.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 01:51:15 EDT 2022

% Result   : Theorem 2.59s 1.27s
% Output   : Proof 4.24s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : KLE074+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n027.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 09:46:50 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.58          ____       _                          
% 0.18/0.58    ___  / __ \_____(_)___  ________  __________
% 0.18/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.18/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.18/0.58  
% 0.18/0.58  A Theorem Prover for First-Order Logic
% 0.18/0.58  (ePrincess v.1.0)
% 0.18/0.58  
% 0.18/0.58  (c) Philipp Rümmer, 2009-2015
% 0.18/0.58  (c) Peter Backeman, 2014-2015
% 0.18/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58  Bug reports to peter@backeman.se
% 0.18/0.58  
% 0.18/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58  
% 0.18/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.54/0.89  Prover 0: Preprocessing ...
% 2.01/1.15  Prover 0: Constructing countermodel ...
% 2.59/1.27  Prover 0: proved (639ms)
% 2.59/1.27  
% 2.59/1.27  No countermodel exists, formula is valid
% 2.59/1.27  % SZS status Theorem for theBenchmark
% 2.59/1.27  
% 2.59/1.27  Generating proof ... found it (size 32)
% 3.86/1.57  
% 3.86/1.57  % SZS output start Proof for theBenchmark
% 3.86/1.57  Assumed formulas after preprocessing and simplification: 
% 3.86/1.57  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : ( ~ (v10 = v6) & domain(v9) = v10 & domain(v7) = v8 & domain(v5) = v6 & domain(v2) = v4 & domain(zero) = zero & multiplication(v3, v4) = v5 & multiplication(v1, v4) = v7 & multiplication(v0, v8) = v9 & multiplication(v0, v1) = v3 &  ! [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] : ( ~ (domain(v12) = v14) |  ~ (domain(v11) = v13) |  ~ (addition(v13, v14) = v15) |  ? [v16] : (domain(v16) = v15 & addition(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] : (v14 = v13 |  ~ (domain(v11) = v12) |  ~ (multiplication(v12, v11) = v13) |  ~ (addition(v11, v13) = v14)) &  ! [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] :  ! [v14] : ( ~ (domain(v12) = v13) |  ~ (multiplication(v11, v13) = v14) |  ? [v15] :  ? [v16] : (domain(v15) = v16 & domain(v14) = v16 & multiplication(v11, v12) = v15)) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = v12 |  ~ (addition(v11, v12) = v13) |  ~ leq(v11, v12)) &  ! [v11] :  ! [v12] :  ! [v13] : (v12 = v11 |  ~ (domain(v13) = v12) |  ~ (domain(v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (domain(v11) = v12) |  ~ (multiplication(v12, v11) = v13) | addition(v11, v13) = v13) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (multiplication(v11, v12) = v13) |  ? [v14] :  ? [v15] :  ? [v16] : (domain(v16) = v14 & domain(v13) = v14 & domain(v12) = v15 & multiplication(v11, v15) = v16)) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (addition(v12, v11) = v13) | addition(v11, v12) = v13) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (addition(v11, v12) = v13) | addition(v12, v11) = v13) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (addition(v11, v12) = v13) |  ? [v14] :  ? [v15] :  ? [v16] : (domain(v13) = v14 & domain(v12) = v16 & domain(v11) = v15 & addition(v15, v16) = v14)) &  ! [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 |  ~ (multiplication(v11, zero) = v12)) &  ! [v11] :  ! [v12] : (v12 = zero |  ~ (multiplication(zero, v11) = v12)) &  ! [v11] :  ! [v12] : ( ~ (domain(v11) = v12) | addition(v12, one) = one) &  ! [v11] :  ! [v12] : ( ~ (addition(v11, v12) = v12) | leq(v11, v12)))
% 3.86/1.61  | 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:
% 3.86/1.61  | (1)  ~ (all_0_0_0 = all_0_4_4) & domain(all_0_1_1) = all_0_0_0 & domain(all_0_3_3) = all_0_2_2 & domain(all_0_5_5) = all_0_4_4 & domain(all_0_8_8) = all_0_6_6 & domain(zero) = zero & multiplication(all_0_7_7, all_0_6_6) = all_0_5_5 & multiplication(all_0_9_9, all_0_6_6) = all_0_3_3 & multiplication(all_0_10_10, all_0_2_2) = all_0_1_1 & multiplication(all_0_10_10, all_0_9_9) = 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] : ( ~ (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))
% 3.86/1.63  |
% 3.86/1.63  | Applying alpha-rule on (1) yields:
% 3.86/1.63  | (2) domain(all_0_5_5) = all_0_4_4
% 3.86/1.63  | (3)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 3.86/1.63  | (4) multiplication(all_0_7_7, all_0_6_6) = all_0_5_5
% 3.86/1.63  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 3.86/1.63  | (6)  ! [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))
% 4.24/1.63  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (domain(v1) = v3) |  ~ (domain(v0) = v2) |  ~ (addition(v2, v3) = v4) |  ? [v5] : (domain(v5) = v4 & addition(v0, v1) = v5))
% 4.24/1.63  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (domain(v0) = v1) |  ~ (multiplication(v1, v0) = v2) | addition(v0, v2) = v2)
% 4.24/1.63  | (9)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 4.24/1.63  | (10)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 4.24/1.63  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 4.24/1.63  | (12)  ! [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))
% 4.24/1.63  | (13) multiplication(all_0_9_9, all_0_6_6) = all_0_3_3
% 4.24/1.64  | (14)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 4.24/1.64  | (15) domain(zero) = zero
% 4.24/1.64  | (16)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4, v5) = v3))
% 4.24/1.64  | (17)  ~ (all_0_0_0 = all_0_4_4)
% 4.24/1.64  | (18)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 4.24/1.64  | (19)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 4.24/1.64  | (20) multiplication(all_0_10_10, all_0_2_2) = all_0_1_1
% 4.24/1.64  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 4.24/1.64  | (22)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 4.24/1.64  | (23)  ! [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))
% 4.24/1.64  | (24) domain(all_0_8_8) = all_0_6_6
% 4.24/1.64  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 4.24/1.64  | (26)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(v0, zero) = v1))
% 4.24/1.64  | (27)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (domain(v2) = v1) |  ~ (domain(v2) = v0))
% 4.24/1.64  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (domain(v1) = v2) |  ~ (multiplication(v0, v2) = v3) |  ? [v4] :  ? [v5] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = v4))
% 4.24/1.64  | (29)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & multiplication(v0, v4) = v5))
% 4.24/1.64  | (30)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ~ leq(v0, v1))
% 4.24/1.64  | (31) multiplication(all_0_10_10, all_0_9_9) = all_0_7_7
% 4.24/1.64  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 4.24/1.64  | (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))
% 4.24/1.64  | (34) domain(all_0_3_3) = all_0_2_2
% 4.24/1.65  | (35)  ! [v0] :  ! [v1] : ( ~ (domain(v0) = v1) | addition(v1, one) = one)
% 4.24/1.65  | (36)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 4.24/1.65  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 4.24/1.65  | (38)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (domain(v0) = v1) |  ~ (multiplication(v1, v0) = v2) |  ~ (addition(v0, v2) = v3))
% 4.24/1.65  | (39) domain(all_0_1_1) = all_0_0_0
% 4.24/1.65  |
% 4.24/1.65  | Instantiating formula (28) with all_0_5_5, all_0_6_6, all_0_8_8, all_0_7_7 and discharging atoms domain(all_0_8_8) = all_0_6_6, multiplication(all_0_7_7, all_0_6_6) = all_0_5_5, yields:
% 4.24/1.65  | (40)  ? [v0] :  ? [v1] : (domain(v0) = v1 & domain(all_0_5_5) = v1 & multiplication(all_0_7_7, all_0_8_8) = v0)
% 4.24/1.65  |
% 4.24/1.65  | Instantiating formula (29) with all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms multiplication(all_0_7_7, all_0_6_6) = all_0_5_5, yields:
% 4.24/1.65  | (41)  ? [v0] :  ? [v1] :  ? [v2] : (domain(v2) = v0 & domain(all_0_5_5) = v0 & domain(all_0_6_6) = v1 & multiplication(all_0_7_7, v1) = v2)
% 4.24/1.65  |
% 4.24/1.65  | Instantiating formula (28) with all_0_1_1, all_0_2_2, all_0_3_3, all_0_10_10 and discharging atoms domain(all_0_3_3) = all_0_2_2, multiplication(all_0_10_10, all_0_2_2) = all_0_1_1, yields:
% 4.24/1.65  | (42)  ? [v0] :  ? [v1] : (domain(v0) = v1 & domain(all_0_1_1) = v1 & multiplication(all_0_10_10, all_0_3_3) = v0)
% 4.24/1.65  |
% 4.24/1.65  | Instantiating formula (29) with all_0_1_1, all_0_2_2, all_0_10_10 and discharging atoms multiplication(all_0_10_10, all_0_2_2) = all_0_1_1, yields:
% 4.24/1.65  | (43)  ? [v0] :  ? [v1] :  ? [v2] : (domain(v2) = v0 & domain(all_0_1_1) = v0 & domain(all_0_2_2) = v1 & multiplication(all_0_10_10, v1) = v2)
% 4.24/1.65  |
% 4.24/1.65  | Instantiating formula (11) with all_0_5_5, all_0_7_7, all_0_6_6, all_0_9_9, all_0_10_10 and discharging atoms multiplication(all_0_7_7, all_0_6_6) = all_0_5_5, multiplication(all_0_10_10, all_0_9_9) = all_0_7_7, yields:
% 4.24/1.65  | (44)  ? [v0] : (multiplication(all_0_9_9, all_0_6_6) = v0 & multiplication(all_0_10_10, v0) = all_0_5_5)
% 4.24/1.65  |
% 4.24/1.65  | Instantiating (44) with all_11_0_14 yields:
% 4.24/1.65  | (45) multiplication(all_0_9_9, all_0_6_6) = all_11_0_14 & multiplication(all_0_10_10, all_11_0_14) = all_0_5_5
% 4.24/1.65  |
% 4.24/1.65  | Applying alpha-rule on (45) yields:
% 4.24/1.65  | (46) multiplication(all_0_9_9, all_0_6_6) = all_11_0_14
% 4.24/1.65  | (47) multiplication(all_0_10_10, all_11_0_14) = all_0_5_5
% 4.24/1.65  |
% 4.24/1.65  | Instantiating (42) with all_13_0_15, all_13_1_16 yields:
% 4.24/1.65  | (48) domain(all_13_1_16) = all_13_0_15 & domain(all_0_1_1) = all_13_0_15 & multiplication(all_0_10_10, all_0_3_3) = all_13_1_16
% 4.24/1.65  |
% 4.24/1.65  | Applying alpha-rule on (48) yields:
% 4.24/1.65  | (49) domain(all_13_1_16) = all_13_0_15
% 4.24/1.65  | (50) domain(all_0_1_1) = all_13_0_15
% 4.24/1.65  | (51) multiplication(all_0_10_10, all_0_3_3) = all_13_1_16
% 4.24/1.65  |
% 4.24/1.65  | Instantiating (41) with all_17_0_19, all_17_1_20, all_17_2_21 yields:
% 4.24/1.65  | (52) domain(all_17_0_19) = all_17_2_21 & domain(all_0_5_5) = all_17_2_21 & domain(all_0_6_6) = all_17_1_20 & multiplication(all_0_7_7, all_17_1_20) = all_17_0_19
% 4.24/1.66  |
% 4.24/1.66  | Applying alpha-rule on (52) yields:
% 4.24/1.66  | (53) domain(all_17_0_19) = all_17_2_21
% 4.24/1.66  | (54) domain(all_0_5_5) = all_17_2_21
% 4.24/1.66  | (55) domain(all_0_6_6) = all_17_1_20
% 4.24/1.66  | (56) multiplication(all_0_7_7, all_17_1_20) = all_17_0_19
% 4.24/1.66  |
% 4.24/1.66  | Instantiating (40) with all_19_0_22, all_19_1_23 yields:
% 4.24/1.66  | (57) domain(all_19_1_23) = all_19_0_22 & domain(all_0_5_5) = all_19_0_22 & multiplication(all_0_7_7, all_0_8_8) = all_19_1_23
% 4.24/1.66  |
% 4.24/1.66  | Applying alpha-rule on (57) yields:
% 4.24/1.66  | (58) domain(all_19_1_23) = all_19_0_22
% 4.24/1.66  | (59) domain(all_0_5_5) = all_19_0_22
% 4.24/1.66  | (60) multiplication(all_0_7_7, all_0_8_8) = all_19_1_23
% 4.24/1.66  |
% 4.24/1.66  | Instantiating (43) with all_23_0_27, all_23_1_28, all_23_2_29 yields:
% 4.24/1.66  | (61) domain(all_23_0_27) = all_23_2_29 & domain(all_0_1_1) = all_23_2_29 & domain(all_0_2_2) = all_23_1_28 & multiplication(all_0_10_10, all_23_1_28) = all_23_0_27
% 4.24/1.66  |
% 4.24/1.66  | Applying alpha-rule on (61) yields:
% 4.24/1.66  | (62) domain(all_23_0_27) = all_23_2_29
% 4.24/1.66  | (63) domain(all_0_1_1) = all_23_2_29
% 4.24/1.66  | (64) domain(all_0_2_2) = all_23_1_28
% 4.24/1.66  | (65) multiplication(all_0_10_10, all_23_1_28) = all_23_0_27
% 4.24/1.66  |
% 4.24/1.66  | Instantiating formula (27) with all_0_1_1, all_23_2_29, all_0_0_0 and discharging atoms domain(all_0_1_1) = all_23_2_29, domain(all_0_1_1) = all_0_0_0, yields:
% 4.24/1.66  | (66) all_23_2_29 = all_0_0_0
% 4.24/1.66  |
% 4.24/1.66  | Instantiating formula (27) with all_0_1_1, all_13_0_15, all_23_2_29 and discharging atoms domain(all_0_1_1) = all_23_2_29, domain(all_0_1_1) = all_13_0_15, yields:
% 4.24/1.66  | (67) all_23_2_29 = all_13_0_15
% 4.24/1.66  |
% 4.24/1.66  | Instantiating formula (27) with all_0_5_5, all_19_0_22, all_0_4_4 and discharging atoms domain(all_0_5_5) = all_19_0_22, domain(all_0_5_5) = all_0_4_4, yields:
% 4.24/1.66  | (68) all_19_0_22 = all_0_4_4
% 4.24/1.66  |
% 4.24/1.66  | Instantiating formula (27) with all_0_5_5, all_17_2_21, all_19_0_22 and discharging atoms domain(all_0_5_5) = all_19_0_22, domain(all_0_5_5) = all_17_2_21, yields:
% 4.24/1.66  | (69) all_19_0_22 = all_17_2_21
% 4.24/1.66  |
% 4.24/1.66  | Instantiating formula (21) with all_0_9_9, all_0_6_6, all_11_0_14, all_0_3_3 and discharging atoms multiplication(all_0_9_9, all_0_6_6) = all_11_0_14, multiplication(all_0_9_9, all_0_6_6) = all_0_3_3, yields:
% 4.24/1.66  | (70) all_11_0_14 = all_0_3_3
% 4.24/1.66  |
% 4.24/1.66  | Combining equations (66,67) yields a new equation:
% 4.24/1.66  | (71) all_13_0_15 = all_0_0_0
% 4.24/1.66  |
% 4.24/1.66  | Combining equations (68,69) yields a new equation:
% 4.24/1.66  | (72) all_17_2_21 = all_0_4_4
% 4.24/1.66  |
% 4.24/1.66  | From (71) and (49) follows:
% 4.24/1.66  | (73) domain(all_13_1_16) = all_0_0_0
% 4.24/1.66  |
% 4.24/1.66  | From (72) and (54) follows:
% 4.24/1.66  | (2) domain(all_0_5_5) = all_0_4_4
% 4.24/1.66  |
% 4.24/1.66  | From (70) and (47) follows:
% 4.24/1.66  | (75) multiplication(all_0_10_10, all_0_3_3) = all_0_5_5
% 4.24/1.67  |
% 4.24/1.67  | Instantiating formula (21) with all_0_10_10, all_0_3_3, all_0_5_5, all_13_1_16 and discharging atoms multiplication(all_0_10_10, all_0_3_3) = all_13_1_16, multiplication(all_0_10_10, all_0_3_3) = all_0_5_5, yields:
% 4.24/1.67  | (76) all_13_1_16 = all_0_5_5
% 4.24/1.67  |
% 4.24/1.67  | From (76) and (73) follows:
% 4.24/1.67  | (77) domain(all_0_5_5) = all_0_0_0
% 4.24/1.67  |
% 4.24/1.67  | Instantiating formula (27) with all_0_5_5, all_0_0_0, all_0_4_4 and discharging atoms domain(all_0_5_5) = all_0_0_0, domain(all_0_5_5) = all_0_4_4, yields:
% 4.24/1.67  | (78) all_0_0_0 = all_0_4_4
% 4.24/1.67  |
% 4.24/1.67  | Equations (78) can reduce 17 to:
% 4.24/1.67  | (79) $false
% 4.24/1.67  |
% 4.24/1.67  |-The branch is then unsatisfiable
% 4.24/1.67  % SZS output end Proof for theBenchmark
% 4.24/1.67  
% 4.24/1.67  1082ms
%------------------------------------------------------------------------------