%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE072+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n032.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 01:51:14 EDT 2022

% Result   : Theorem 2.04s 1.16s
% Output   : Proof 4.01s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : KLE072+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.10  % Command  : ePrincess-casc -timeout=%d %s
% 0.09/0.29  % Computer : n032.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 600
% 0.09/0.29  % DateTime : Thu Jun 16 09:02:14 EDT 2022
% 0.09/0.29  % CPUTime  : 
% 0.14/0.48          ____       _                          
% 0.14/0.48    ___  / __ \_____(_)___  ________  __________
% 0.14/0.48   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.14/0.48  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.14/0.48  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.14/0.48  
% 0.14/0.48  A Theorem Prover for First-Order Logic
% 0.14/0.48  (ePrincess v.1.0)
% 0.14/0.48  
% 0.14/0.48  (c) Philipp Rümmer, 2009-2015
% 0.14/0.48  (c) Peter Backeman, 2014-2015
% 0.14/0.48  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.14/0.48  Free software under GNU Lesser General Public License (LGPL).
% 0.14/0.48  Bug reports to peter@backeman.se
% 0.14/0.48  
% 0.14/0.48  For more information, visit http://user.uu.se/~petba168/breu/
% 0.14/0.48  
% 0.14/0.48  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.14/0.53  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.17/0.76  Prover 0: Preprocessing ...
% 1.77/1.01  Prover 0: Constructing countermodel ...
% 2.04/1.16  Prover 0: proved (630ms)
% 2.04/1.16  
% 2.04/1.16  No countermodel exists, formula is valid
% 2.04/1.16  % SZS status Theorem for theBenchmark
% 2.04/1.16  
% 2.04/1.16  Generating proof ... found it (size 26)
% 3.39/1.45  
% 3.39/1.45  % SZS output start Proof for theBenchmark
% 3.39/1.45  Assumed formulas after preprocessing and simplification: 
% 3.39/1.46  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] : ( ~ (v11 = v6) & domain(v9) = v10 & domain(v7) = v8 & domain(v5) = v6 & domain(v2) = v4 & domain(zero) = zero & multiplication(v3, v4) = v5 & multiplication(v1, v4) = v9 & multiplication(v0, v4) = v7 & addition(v8, v10) = v11 & addition(v0, v1) = v3 &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (multiplication(v13, v14) = v16) |  ~ (multiplication(v12, v14) = v15) |  ~ (addition(v15, v16) = v17) |  ? [v18] : (multiplication(v18, v14) = v17 & addition(v12, v13) = v18)) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : ( ~ (multiplication(v12, v14) = v16) |  ~ (multiplication(v12, v13) = v15) |  ~ (addition(v15, v16) = v17) |  ? [v18] : (multiplication(v12, v18) = v17 & addition(v13, v14) = v18)) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (domain(v13) = v15) |  ~ (domain(v12) = v14) |  ~ (addition(v14, v15) = v16) |  ? [v17] : (domain(v17) = v16 & addition(v12, v13) = v17)) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (multiplication(v15, v14) = v16) |  ~ (multiplication(v12, v13) = v15) |  ? [v17] : (multiplication(v13, v14) = v17 & multiplication(v12, v17) = v16)) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (multiplication(v15, v14) = v16) |  ~ (addition(v12, v13) = v15) |  ? [v17] :  ? [v18] : (multiplication(v13, v14) = v18 & multiplication(v12, v14) = v17 & addition(v17, v18) = v16)) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (multiplication(v13, v14) = v15) |  ~ (multiplication(v12, v15) = v16) |  ? [v17] : (multiplication(v17, v14) = v16 & multiplication(v12, v13) = v17)) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (multiplication(v12, v15) = v16) |  ~ (addition(v13, v14) = v15) |  ? [v17] :  ? [v18] : (multiplication(v12, v14) = v18 & multiplication(v12, v13) = v17 & addition(v17, v18) = v16)) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (addition(v15, v12) = v16) |  ~ (addition(v14, v13) = v15) |  ? [v17] : (addition(v14, v17) = v16 & addition(v13, v12) = v17)) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (addition(v14, v15) = v16) |  ~ (addition(v13, v12) = v15) |  ? [v17] : (addition(v17, v12) = v16 & addition(v14, v13) = v17)) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v15 = v14 |  ~ (domain(v12) = v13) |  ~ (multiplication(v13, v12) = v14) |  ~ (addition(v12, v14) = v15)) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v13 = v12 |  ~ (multiplication(v15, v14) = v13) |  ~ (multiplication(v15, v14) = v12)) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v13 = v12 |  ~ (addition(v15, v14) = v13) |  ~ (addition(v15, v14) = v12)) &  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ (domain(v13) = v14) |  ~ (multiplication(v12, v14) = v15) |  ? [v16] :  ? [v17] : (domain(v16) = v17 & domain(v15) = v17 & multiplication(v12, v13) = v16)) &  ! [v12] :  ! [v13] :  ! [v14] : (v14 = v13 |  ~ (addition(v12, v13) = v14) |  ~ leq(v12, v13)) &  ! [v12] :  ! [v13] :  ! [v14] : (v13 = v12 |  ~ (domain(v14) = v13) |  ~ (domain(v14) = v12)) &  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (domain(v12) = v13) |  ~ (multiplication(v13, v12) = v14) | addition(v12, v14) = v14) &  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (multiplication(v12, v13) = v14) |  ? [v15] :  ? [v16] :  ? [v17] : (domain(v17) = v15 & domain(v14) = v15 & domain(v13) = v16 & multiplication(v12, v16) = v17)) &  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (addition(v13, v12) = v14) | addition(v12, v13) = v14) &  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (addition(v12, v13) = v14) | addition(v13, v12) = v14) &  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (addition(v12, v13) = v14) |  ? [v15] :  ? [v16] :  ? [v17] : (domain(v14) = v15 & domain(v13) = v17 & domain(v12) = v16 & addition(v16, v17) = v15)) &  ! [v12] :  ! [v13] : (v13 = v12 |  ~ (multiplication(v12, one) = v13)) &  ! [v12] :  ! [v13] : (v13 = v12 |  ~ (multiplication(one, v12) = v13)) &  ! [v12] :  ! [v13] : (v13 = v12 |  ~ (addition(v12, v12) = v13)) &  ! [v12] :  ! [v13] : (v13 = v12 |  ~ (addition(v12, zero) = v13)) &  ! [v12] :  ! [v13] : (v13 = zero |  ~ (multiplication(v12, zero) = v13)) &  ! [v12] :  ! [v13] : (v13 = zero |  ~ (multiplication(zero, v12) = v13)) &  ! [v12] :  ! [v13] : ( ~ (domain(v12) = v13) | addition(v13, one) = one) &  ! [v12] :  ! [v13] : ( ~ (addition(v12, v13) = v13) | leq(v12, v13)))
% 3.72/1.50  | 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, all_0_11_11 yields:
% 3.72/1.50  | (1)  ~ (all_0_0_0 = all_0_5_5) & domain(all_0_2_2) = all_0_1_1 & domain(all_0_4_4) = all_0_3_3 & domain(all_0_6_6) = all_0_5_5 & domain(all_0_9_9) = all_0_7_7 & domain(zero) = zero & multiplication(all_0_8_8, all_0_7_7) = all_0_6_6 & multiplication(all_0_10_10, all_0_7_7) = all_0_2_2 & multiplication(all_0_11_11, all_0_7_7) = all_0_4_4 & addition(all_0_3_3, all_0_1_1) = all_0_0_0 & addition(all_0_11_11, all_0_10_10) = all_0_8_8 &  ! [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))
% 3.87/1.51  |
% 3.87/1.51  | Applying alpha-rule on (1) yields:
% 3.87/1.51  | (2)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 3.87/1.51  | (3)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4, v5) = v3))
% 3.87/1.51  | (4)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 3.87/1.51  | (5) multiplication(all_0_8_8, all_0_7_7) = all_0_6_6
% 3.87/1.51  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 3.87/1.51  | (7)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (domain(v0) = v1) |  ~ (multiplication(v1, v0) = v2) | addition(v0, v2) = v2)
% 3.87/1.51  | (8)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 3.87/1.51  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 3.87/1.51  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (domain(v1) = v2) |  ~ (multiplication(v0, v2) = v3) |  ? [v4] :  ? [v5] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = v4))
% 3.87/1.52  | (11)  ! [v0] :  ! [v1] : ( ~ (domain(v0) = v1) | addition(v1, one) = one)
% 3.87/1.52  | (12)  ! [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))
% 3.87/1.52  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (domain(v1) = v3) |  ~ (domain(v0) = v2) |  ~ (addition(v2, v3) = v4) |  ? [v5] : (domain(v5) = v4 & addition(v0, v1) = v5))
% 3.87/1.52  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 3.87/1.52  | (15) domain(all_0_2_2) = all_0_1_1
% 3.87/1.52  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 3.87/1.52  | (17)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 3.87/1.52  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 3.87/1.52  | (19)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 3.87/1.52  | (20)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 3.87/1.52  | (21)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 3.87/1.52  | (22)  ! [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))
% 3.87/1.52  | (23) domain(all_0_6_6) = all_0_5_5
% 3.87/1.52  | (24)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ~ leq(v0, v1))
% 3.87/1.52  | (25) domain(all_0_9_9) = all_0_7_7
% 3.87/1.52  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 3.87/1.52  | (27)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & multiplication(v0, v4) = v5))
% 3.87/1.52  | (28) domain(all_0_4_4) = all_0_3_3
% 3.87/1.52  | (29)  ~ (all_0_0_0 = all_0_5_5)
% 3.87/1.52  | (30)  ! [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))
% 3.87/1.52  | (31)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (domain(v0) = v1) |  ~ (multiplication(v1, v0) = v2) |  ~ (addition(v0, v2) = v3))
% 3.87/1.52  | (32) domain(zero) = zero
% 3.87/1.52  | (33) addition(all_0_11_11, all_0_10_10) = all_0_8_8
% 3.87/1.52  | (34) multiplication(all_0_10_10, all_0_7_7) = all_0_2_2
% 3.87/1.52  | (35) addition(all_0_3_3, all_0_1_1) = all_0_0_0
% 3.87/1.52  | (36) multiplication(all_0_11_11, all_0_7_7) = all_0_4_4
% 3.87/1.52  | (37)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (domain(v2) = v1) |  ~ (domain(v2) = v0))
% 3.87/1.52  | (38)  ! [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))
% 3.87/1.53  | (39)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 3.87/1.53  | (40)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(v0, zero) = v1))
% 3.87/1.53  |
% 3.87/1.53  | Instantiating formula (10) with all_0_6_6, all_0_7_7, all_0_9_9, all_0_8_8 and discharging atoms domain(all_0_9_9) = all_0_7_7, multiplication(all_0_8_8, all_0_7_7) = all_0_6_6, yields:
% 3.87/1.53  | (41)  ? [v0] :  ? [v1] : (domain(v0) = v1 & domain(all_0_6_6) = v1 & multiplication(all_0_8_8, all_0_9_9) = v0)
% 3.87/1.53  |
% 3.87/1.53  | Instantiating formula (27) with all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms multiplication(all_0_8_8, all_0_7_7) = all_0_6_6, yields:
% 3.87/1.53  | (42)  ? [v0] :  ? [v1] :  ? [v2] : (domain(v2) = v0 & domain(all_0_6_6) = v0 & domain(all_0_7_7) = v1 & multiplication(all_0_8_8, v1) = v2)
% 3.87/1.53  |
% 3.87/1.53  | Instantiating formula (13) with all_0_0_0, all_0_1_1, all_0_3_3, all_0_2_2, all_0_4_4 and discharging atoms domain(all_0_2_2) = all_0_1_1, domain(all_0_4_4) = all_0_3_3, addition(all_0_3_3, all_0_1_1) = all_0_0_0, yields:
% 3.87/1.53  | (43)  ? [v0] : (domain(v0) = all_0_0_0 & addition(all_0_4_4, all_0_2_2) = v0)
% 3.87/1.53  |
% 3.87/1.53  | Instantiating formula (30) with all_0_6_6, all_0_8_8, all_0_7_7, all_0_10_10, all_0_11_11 and discharging atoms multiplication(all_0_8_8, all_0_7_7) = all_0_6_6, addition(all_0_11_11, all_0_10_10) = all_0_8_8, yields:
% 3.87/1.53  | (44)  ? [v0] :  ? [v1] : (multiplication(all_0_10_10, all_0_7_7) = v1 & multiplication(all_0_11_11, all_0_7_7) = v0 & addition(v0, v1) = all_0_6_6)
% 3.87/1.53  |
% 3.87/1.53  | Instantiating (44) with all_15_0_20, all_15_1_21 yields:
% 3.87/1.53  | (45) multiplication(all_0_10_10, all_0_7_7) = all_15_0_20 & multiplication(all_0_11_11, all_0_7_7) = all_15_1_21 & addition(all_15_1_21, all_15_0_20) = all_0_6_6
% 3.87/1.53  |
% 3.87/1.53  | Applying alpha-rule on (45) yields:
% 3.87/1.53  | (46) multiplication(all_0_10_10, all_0_7_7) = all_15_0_20
% 3.87/1.53  | (47) multiplication(all_0_11_11, all_0_7_7) = all_15_1_21
% 4.01/1.53  | (48) addition(all_15_1_21, all_15_0_20) = all_0_6_6
% 4.01/1.53  |
% 4.01/1.53  | Instantiating (42) with all_17_0_22, all_17_1_23, all_17_2_24 yields:
% 4.01/1.53  | (49) domain(all_17_0_22) = all_17_2_24 & domain(all_0_6_6) = all_17_2_24 & domain(all_0_7_7) = all_17_1_23 & multiplication(all_0_8_8, all_17_1_23) = all_17_0_22
% 4.01/1.53  |
% 4.01/1.53  | Applying alpha-rule on (49) yields:
% 4.01/1.53  | (50) domain(all_17_0_22) = all_17_2_24
% 4.01/1.53  | (51) domain(all_0_6_6) = all_17_2_24
% 4.01/1.53  | (52) domain(all_0_7_7) = all_17_1_23
% 4.01/1.53  | (53) multiplication(all_0_8_8, all_17_1_23) = all_17_0_22
% 4.01/1.53  |
% 4.01/1.53  | Instantiating (41) with all_19_0_25, all_19_1_26 yields:
% 4.01/1.53  | (54) domain(all_19_1_26) = all_19_0_25 & domain(all_0_6_6) = all_19_0_25 & multiplication(all_0_8_8, all_0_9_9) = all_19_1_26
% 4.01/1.53  |
% 4.01/1.53  | Applying alpha-rule on (54) yields:
% 4.01/1.53  | (55) domain(all_19_1_26) = all_19_0_25
% 4.01/1.53  | (56) domain(all_0_6_6) = all_19_0_25
% 4.01/1.53  | (57) multiplication(all_0_8_8, all_0_9_9) = all_19_1_26
% 4.01/1.53  |
% 4.01/1.53  | Instantiating (43) with all_21_0_27 yields:
% 4.01/1.53  | (58) domain(all_21_0_27) = all_0_0_0 & addition(all_0_4_4, all_0_2_2) = all_21_0_27
% 4.01/1.53  |
% 4.01/1.53  | Applying alpha-rule on (58) yields:
% 4.01/1.53  | (59) domain(all_21_0_27) = all_0_0_0
% 4.01/1.53  | (60) addition(all_0_4_4, all_0_2_2) = all_21_0_27
% 4.01/1.53  |
% 4.01/1.53  | Instantiating formula (37) with all_0_6_6, all_19_0_25, all_0_5_5 and discharging atoms domain(all_0_6_6) = all_19_0_25, domain(all_0_6_6) = all_0_5_5, yields:
% 4.01/1.53  | (61) all_19_0_25 = all_0_5_5
% 4.01/1.53  |
% 4.01/1.53  | Instantiating formula (37) with all_0_6_6, all_17_2_24, all_19_0_25 and discharging atoms domain(all_0_6_6) = all_19_0_25, domain(all_0_6_6) = all_17_2_24, yields:
% 4.01/1.53  | (62) all_19_0_25 = all_17_2_24
% 4.01/1.53  |
% 4.01/1.53  | Instantiating formula (16) with all_0_10_10, all_0_7_7, all_15_0_20, all_0_2_2 and discharging atoms multiplication(all_0_10_10, all_0_7_7) = all_15_0_20, multiplication(all_0_10_10, all_0_7_7) = all_0_2_2, yields:
% 4.01/1.53  | (63) all_15_0_20 = all_0_2_2
% 4.01/1.53  |
% 4.01/1.53  | Instantiating formula (16) with all_0_11_11, all_0_7_7, all_15_1_21, all_0_4_4 and discharging atoms multiplication(all_0_11_11, all_0_7_7) = all_15_1_21, multiplication(all_0_11_11, all_0_7_7) = all_0_4_4, yields:
% 4.01/1.54  | (64) all_15_1_21 = all_0_4_4
% 4.01/1.54  |
% 4.01/1.54  | Combining equations (61,62) yields a new equation:
% 4.01/1.54  | (65) all_17_2_24 = all_0_5_5
% 4.01/1.54  |
% 4.01/1.54  | From (65) and (51) follows:
% 4.01/1.54  | (23) domain(all_0_6_6) = all_0_5_5
% 4.01/1.54  |
% 4.01/1.54  | From (64)(63) and (48) follows:
% 4.01/1.54  | (67) addition(all_0_4_4, all_0_2_2) = all_0_6_6
% 4.01/1.54  |
% 4.01/1.54  | Instantiating formula (18) with all_0_4_4, all_0_2_2, all_0_6_6, all_21_0_27 and discharging atoms addition(all_0_4_4, all_0_2_2) = all_21_0_27, addition(all_0_4_4, all_0_2_2) = all_0_6_6, yields:
% 4.01/1.54  | (68) all_21_0_27 = all_0_6_6
% 4.01/1.54  |
% 4.01/1.54  | From (68) and (59) follows:
% 4.01/1.54  | (69) domain(all_0_6_6) = all_0_0_0
% 4.01/1.54  |
% 4.01/1.54  | Instantiating formula (37) with all_0_6_6, all_0_0_0, all_0_5_5 and discharging atoms domain(all_0_6_6) = all_0_0_0, domain(all_0_6_6) = all_0_5_5, yields:
% 4.01/1.54  | (70) all_0_0_0 = all_0_5_5
% 4.01/1.54  |
% 4.01/1.54  | Equations (70) can reduce 29 to:
% 4.01/1.54  | (71) $false
% 4.01/1.54  |
% 4.01/1.54  |-The branch is then unsatisfiable
% 4.01/1.54  % SZS output end Proof for theBenchmark
% 4.01/1.54  
% 4.01/1.54  1050ms
%------------------------------------------------------------------------------