%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : REL049+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n004.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 : Mon Jul 18 19:15:04 EDT 2022

% Result   : Theorem 2.59s 1.26s
% Output   : Proof 3.98s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : REL049+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n004.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Fri Jul  8 15:34:52 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.58          ____       _                          
% 0.19/0.58    ___  / __ \_____(_)___  ________  __________
% 0.19/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.59/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.59/0.58  
% 0.59/0.58  A Theorem Prover for First-Order Logic
% 0.59/0.58  (ePrincess v.1.0)
% 0.59/0.58  
% 0.59/0.58  (c) Philipp Rümmer, 2009-2015
% 0.59/0.58  (c) Peter Backeman, 2014-2015
% 0.59/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.58  Bug reports to peter@backeman.se
% 0.59/0.58  
% 0.59/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.58  
% 0.59/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.63/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.49/0.89  Prover 0: Preprocessing ...
% 2.11/1.15  Prover 0: Constructing countermodel ...
% 2.59/1.26  Prover 0: proved (629ms)
% 2.59/1.26  
% 2.59/1.26  No countermodel exists, formula is valid
% 2.59/1.26  % SZS status Theorem for theBenchmark
% 2.59/1.26  
% 2.59/1.26  Generating proof ... found it (size 10)
% 3.98/1.55  
% 3.98/1.55  % SZS output start Proof for theBenchmark
% 3.98/1.55  Assumed formulas after preprocessing and simplification: 
% 3.98/1.55  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : ( ~ (v4 = v1) & join(v3, v1) = v4 & join(v2, v1) = v1 & join(v0, v2) = v3 & join(v0, v1) = v1 &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = v5 |  ~ (complement(v11) = v12) |  ~ (complement(v9) = v10) |  ~ (complement(v6) = v8) |  ~ (complement(v5) = v7) |  ~ (join(v10, v12) = v13) |  ~ (join(v7, v8) = v9) |  ~ (join(v7, v6) = v11)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = v11 |  ~ (converse(v5) = v7) |  ~ (composition(v7, v9) = v10) |  ~ (composition(v5, v6) = v8) |  ~ (complement(v8) = v9) |  ~ (complement(v6) = v11) |  ~ (join(v10, v11) = v12)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (composition(v6, v7) = v9) |  ~ (composition(v5, v7) = v8) |  ~ (join(v8, v9) = v10) |  ? [v11] : (composition(v11, v7) = v10 & join(v5, v6) = v11)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (converse(v6) = v8) |  ~ (converse(v5) = v7) |  ~ (join(v7, v8) = v9) |  ? [v10] : (converse(v10) = v9 & join(v5, v6) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (converse(v6) = v7) |  ~ (converse(v5) = v8) |  ~ (composition(v7, v8) = v9) |  ? [v10] : (converse(v10) = v9 & composition(v5, v6) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (composition(v8, v7) = v9) |  ~ (composition(v5, v6) = v8) |  ? [v10] : (composition(v6, v7) = v10 & composition(v5, v10) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (composition(v8, v7) = v9) |  ~ (join(v5, v6) = v8) |  ? [v10] :  ? [v11] : (composition(v6, v7) = v11 & composition(v5, v7) = v10 & join(v10, v11) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (composition(v6, v7) = v8) |  ~ (composition(v5, v8) = v9) |  ? [v10] : (composition(v10, v7) = v9 & composition(v5, v6) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (complement(v6) = v8) |  ~ (complement(v5) = v7) |  ~ (join(v7, v8) = v9) |  ? [v10] : (meet(v5, v6) = v10 & complement(v9) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (join(v8, v7) = v9) |  ~ (join(v5, v6) = v8) |  ? [v10] : (join(v6, v7) = v10 & join(v5, v10) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (join(v6, v7) = v8) |  ~ (join(v5, v8) = v9) |  ? [v10] : (join(v10, v7) = v9 & join(v5, v6) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (composition(v8, v7) = v6) |  ~ (composition(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (meet(v8, v7) = v6) |  ~ (meet(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (join(v8, v7) = v6) |  ~ (join(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = zero |  ~ (meet(v5, v6) = v7) |  ~ (complement(v5) = v6)) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = top |  ~ (complement(v5) = v6) |  ~ (join(v5, v6) = v7)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (converse(v7) = v6) |  ~ (converse(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (complement(v7) = v6) |  ~ (complement(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (composition(v5, v6) = v7) |  ? [v8] :  ? [v9] :  ? [v10] : (converse(v7) = v8 & converse(v6) = v9 & converse(v5) = v10 & composition(v9, v10) = v8)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (meet(v5, v6) = v7) |  ? [v8] :  ? [v9] :  ? [v10] : (complement(v10) = v7 & complement(v6) = v9 & complement(v5) = v8 & join(v8, v9) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (join(v6, v5) = v7) | join(v5, v6) = v7) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (join(v5, v6) = v7) | join(v6, v5) = v7) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (join(v5, v6) = v7) |  ? [v8] :  ? [v9] :  ? [v10] : (converse(v7) = v8 & converse(v6) = v10 & converse(v5) = v9 & join(v9, v10) = v8)) &  ! [v5] :  ! [v6] : (v6 = v5 |  ~ (composition(v5, one) = v6)) &  ! [v5] :  ! [v6] : ( ~ (converse(v5) = v6) | converse(v6) = v5))
% 3.98/1.59  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 3.98/1.59  | (1)  ~ (all_0_0_0 = all_0_3_3) & join(all_0_1_1, all_0_3_3) = all_0_0_0 & join(all_0_2_2, all_0_3_3) = all_0_3_3 & join(all_0_4_4, all_0_2_2) = all_0_1_1 & join(all_0_4_4, all_0_3_3) = all_0_3_3 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = v0 |  ~ (complement(v6) = v7) |  ~ (complement(v4) = v5) |  ~ (complement(v1) = v3) |  ~ (complement(v0) = v2) |  ~ (join(v5, v7) = v8) |  ~ (join(v2, v3) = v4) |  ~ (join(v2, v1) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (converse(v0) = v2) |  ~ (composition(v2, v4) = v5) |  ~ (composition(v0, v1) = v3) |  ~ (complement(v3) = v4) |  ~ (complement(v1) = v6) |  ~ (join(v5, v6) = v7)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (composition(v1, v2) = v4) |  ~ (composition(v0, v2) = v3) |  ~ (join(v3, v4) = v5) |  ? [v6] : (composition(v6, v2) = v5 & join(v0, v1) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (converse(v1) = v3) |  ~ (converse(v0) = v2) |  ~ (join(v2, v3) = v4) |  ? [v5] : (converse(v5) = v4 & join(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (converse(v1) = v2) |  ~ (converse(v0) = v3) |  ~ (composition(v2, v3) = v4) |  ? [v5] : (converse(v5) = v4 & composition(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (composition(v3, v2) = v4) |  ~ (composition(v0, v1) = v3) |  ? [v5] : (composition(v1, v2) = v5 & composition(v0, v5) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (composition(v3, v2) = v4) |  ~ (join(v0, v1) = v3) |  ? [v5] :  ? [v6] : (composition(v1, v2) = v6 & composition(v0, v2) = v5 & join(v5, v6) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (composition(v1, v2) = v3) |  ~ (composition(v0, v3) = v4) |  ? [v5] : (composition(v5, v2) = v4 & composition(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (complement(v1) = v3) |  ~ (complement(v0) = v2) |  ~ (join(v2, v3) = v4) |  ? [v5] : (meet(v0, v1) = v5 & complement(v4) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (join(v3, v2) = v4) |  ~ (join(v0, v1) = v3) |  ? [v5] : (join(v1, v2) = v5 & join(v0, v5) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (join(v1, v2) = v3) |  ~ (join(v0, v3) = v4) |  ? [v5] : (join(v5, v2) = v4 & join(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (composition(v3, v2) = v1) |  ~ (composition(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (meet(v3, v2) = v1) |  ~ (meet(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (join(v3, v2) = v1) |  ~ (join(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = zero |  ~ (meet(v0, v1) = v2) |  ~ (complement(v0) = v1)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = top |  ~ (complement(v0) = v1) |  ~ (join(v0, v1) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (converse(v2) = v1) |  ~ (converse(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (complement(v2) = v1) |  ~ (complement(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (composition(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (converse(v2) = v3 & converse(v1) = v4 & converse(v0) = v5 & composition(v4, v5) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (meet(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (complement(v5) = v2 & complement(v1) = v4 & complement(v0) = v3 & join(v3, v4) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (join(v1, v0) = v2) | join(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (join(v0, v1) = v2) | join(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (join(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (converse(v2) = v3 & converse(v1) = v5 & converse(v0) = v4 & join(v4, v5) = v3)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (composition(v0, one) = v1)) &  ! [v0] :  ! [v1] : ( ~ (converse(v0) = v1) | converse(v1) = v0)
% 3.98/1.60  |
% 3.98/1.60  | Applying alpha-rule on (1) yields:
% 3.98/1.60  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (converse(v1) = v2) |  ~ (converse(v0) = v3) |  ~ (composition(v2, v3) = v4) |  ? [v5] : (converse(v5) = v4 & composition(v0, v1) = v5))
% 3.98/1.60  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (join(v1, v2) = v3) |  ~ (join(v0, v3) = v4) |  ? [v5] : (join(v5, v2) = v4 & join(v0, v1) = v5))
% 3.98/1.61  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (composition(v3, v2) = v4) |  ~ (join(v0, v1) = v3) |  ? [v5] :  ? [v6] : (composition(v1, v2) = v6 & composition(v0, v2) = v5 & join(v5, v6) = v4))
% 3.98/1.61  | (5)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (composition(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (converse(v2) = v3 & converse(v1) = v4 & converse(v0) = v5 & composition(v4, v5) = v3))
% 3.98/1.61  | (6)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = top |  ~ (complement(v0) = v1) |  ~ (join(v0, v1) = v2))
% 3.98/1.61  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (composition(v3, v2) = v4) |  ~ (composition(v0, v1) = v3) |  ? [v5] : (composition(v1, v2) = v5 & composition(v0, v5) = v4))
% 3.98/1.61  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (join(v0, v1) = v2) | join(v1, v0) = v2)
% 3.98/1.61  | (9)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (join(v1, v0) = v2) | join(v0, v1) = v2)
% 3.98/1.61  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (converse(v1) = v3) |  ~ (converse(v0) = v2) |  ~ (join(v2, v3) = v4) |  ? [v5] : (converse(v5) = v4 & join(v0, v1) = v5))
% 3.98/1.61  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (composition(v3, v2) = v1) |  ~ (composition(v3, v2) = v0))
% 3.98/1.61  | (12)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (complement(v2) = v1) |  ~ (complement(v2) = v0))
% 3.98/1.61  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (join(v3, v2) = v4) |  ~ (join(v0, v1) = v3) |  ? [v5] : (join(v1, v2) = v5 & join(v0, v5) = v4))
% 3.98/1.61  | (14) join(all_0_2_2, all_0_3_3) = all_0_3_3
% 3.98/1.61  | (15)  ! [v0] :  ! [v1] : ( ~ (converse(v0) = v1) | converse(v1) = v0)
% 3.98/1.61  | (16)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (converse(v2) = v1) |  ~ (converse(v2) = v0))
% 3.98/1.61  | (17) join(all_0_4_4, all_0_2_2) = all_0_1_1
% 3.98/1.61  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = v0 |  ~ (complement(v6) = v7) |  ~ (complement(v4) = v5) |  ~ (complement(v1) = v3) |  ~ (complement(v0) = v2) |  ~ (join(v5, v7) = v8) |  ~ (join(v2, v3) = v4) |  ~ (join(v2, v1) = v6))
% 3.98/1.61  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (composition(v1, v2) = v4) |  ~ (composition(v0, v2) = v3) |  ~ (join(v3, v4) = v5) |  ? [v6] : (composition(v6, v2) = v5 & join(v0, v1) = v6))
% 3.98/1.61  | (20)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (meet(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (complement(v5) = v2 & complement(v1) = v4 & complement(v0) = v3 & join(v3, v4) = v5))
% 3.98/1.61  | (21) join(all_0_4_4, all_0_3_3) = all_0_3_3
% 3.98/1.61  | (22)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (composition(v0, one) = v1))
% 3.98/1.61  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (converse(v0) = v2) |  ~ (composition(v2, v4) = v5) |  ~ (composition(v0, v1) = v3) |  ~ (complement(v3) = v4) |  ~ (complement(v1) = v6) |  ~ (join(v5, v6) = v7))
% 3.98/1.61  | (24) join(all_0_1_1, all_0_3_3) = all_0_0_0
% 3.98/1.61  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (join(v3, v2) = v1) |  ~ (join(v3, v2) = v0))
% 3.98/1.61  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (meet(v3, v2) = v1) |  ~ (meet(v3, v2) = v0))
% 3.98/1.62  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (complement(v1) = v3) |  ~ (complement(v0) = v2) |  ~ (join(v2, v3) = v4) |  ? [v5] : (meet(v0, v1) = v5 & complement(v4) = v5))
% 3.98/1.62  | (28)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = zero |  ~ (meet(v0, v1) = v2) |  ~ (complement(v0) = v1))
% 3.98/1.62  | (29)  ~ (all_0_0_0 = all_0_3_3)
% 3.98/1.62  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (composition(v1, v2) = v3) |  ~ (composition(v0, v3) = v4) |  ? [v5] : (composition(v5, v2) = v4 & composition(v0, v1) = v5))
% 3.98/1.62  | (31)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (join(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (converse(v2) = v3 & converse(v1) = v5 & converse(v0) = v4 & join(v4, v5) = v3))
% 3.98/1.62  |
% 3.98/1.62  | 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 join(all_0_1_1, all_0_3_3) = all_0_0_0, join(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 3.98/1.62  | (32)  ? [v0] : (join(all_0_2_2, all_0_3_3) = v0 & join(all_0_4_4, v0) = all_0_0_0)
% 3.98/1.62  |
% 3.98/1.62  | Instantiating (32) with all_9_0_5 yields:
% 3.98/1.62  | (33) join(all_0_2_2, all_0_3_3) = all_9_0_5 & join(all_0_4_4, all_9_0_5) = all_0_0_0
% 3.98/1.62  |
% 3.98/1.62  | Applying alpha-rule on (33) yields:
% 3.98/1.62  | (34) join(all_0_2_2, all_0_3_3) = all_9_0_5
% 3.98/1.62  | (35) join(all_0_4_4, all_9_0_5) = all_0_0_0
% 3.98/1.62  |
% 3.98/1.62  | Instantiating formula (25) with all_0_2_2, all_0_3_3, all_9_0_5, all_0_3_3 and discharging atoms join(all_0_2_2, all_0_3_3) = all_9_0_5, join(all_0_2_2, all_0_3_3) = all_0_3_3, yields:
% 3.98/1.62  | (36) all_9_0_5 = all_0_3_3
% 3.98/1.62  |
% 3.98/1.62  | From (36) and (35) follows:
% 3.98/1.62  | (37) join(all_0_4_4, all_0_3_3) = all_0_0_0
% 3.98/1.62  |
% 3.98/1.62  | Instantiating formula (25) with all_0_4_4, all_0_3_3, all_0_0_0, all_0_3_3 and discharging atoms join(all_0_4_4, all_0_3_3) = all_0_0_0, join(all_0_4_4, all_0_3_3) = all_0_3_3, yields:
% 3.98/1.62  | (38) all_0_0_0 = all_0_3_3
% 3.98/1.62  |
% 3.98/1.62  | Equations (38) can reduce 29 to:
% 3.98/1.62  | (39) $false
% 3.98/1.62  |
% 3.98/1.62  |-The branch is then unsatisfiable
% 3.98/1.62  % SZS output end Proof for theBenchmark
% 3.98/1.62  
% 3.98/1.62  1029ms
%------------------------------------------------------------------------------