%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : REL046+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 : Mon Jul 18 19:15:02 EDT 2022

% Result   : Theorem 28.97s 9.31s
% Output   : Proof 49.36s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : REL046+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % 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 : Fri Jul  8 10:36:22 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.55/0.58          ____       _                          
% 0.55/0.58    ___  / __ \_____(_)___  ________  __________
% 0.55/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.55/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.55/0.58  
% 0.55/0.58  A Theorem Prover for First-Order Logic
% 0.55/0.58  (ePrincess v.1.0)
% 0.55/0.58  
% 0.55/0.58  (c) Philipp Rümmer, 2009-2015
% 0.55/0.58  (c) Peter Backeman, 2014-2015
% 0.55/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.58  Bug reports to peter@backeman.se
% 0.55/0.58  
% 0.55/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.58  
% 0.55/0.58  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.55/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.49/0.89  Prover 0: Preprocessing ...
% 2.22/1.15  Prover 0: Constructing countermodel ...
% 18.34/5.92  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 18.56/5.95  Prover 1: Preprocessing ...
% 18.91/6.03  Prover 1: Constructing countermodel ...
% 25.77/8.54  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 25.77/8.56  Prover 2: Preprocessing ...
% 26.02/8.63  Prover 2: Warning: ignoring some quantifiers
% 26.02/8.63  Prover 2: Constructing countermodel ...
% 28.97/9.31  Prover 2: proved (765ms)
% 28.97/9.31  Prover 1: stopped
% 28.97/9.31  Prover 0: stopped
% 28.97/9.31  
% 28.97/9.31  No countermodel exists, formula is valid
% 28.97/9.31  % SZS status Theorem for theBenchmark
% 28.97/9.31  
% 28.97/9.31  Generating proof ... Warning: ignoring some quantifiers
% 48.20/19.10  found it (size 350)
% 48.20/19.10  
% 48.20/19.10  % SZS output start Proof for theBenchmark
% 48.20/19.10  Assumed formulas after preprocessing and simplification: 
% 48.20/19.10  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : (meet(v1, v2) = v3 & join(v0, v3) = v3 &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (composition(v7, v8) = v10) |  ~ (composition(v6, v8) = v9) |  ~ (join(v9, v10) = v11) |  ? [v12] : (composition(v12, v8) = v11 & join(v6, v7) = v12)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (converse(v7) = v9) |  ~ (converse(v6) = v8) |  ~ (join(v8, v9) = v10) |  ? [v11] : (converse(v11) = v10 & join(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (converse(v7) = v8) |  ~ (converse(v6) = v9) |  ~ (composition(v8, v9) = v10) |  ? [v11] : (converse(v11) = v10 & composition(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (composition(v9, v8) = v10) |  ~ (composition(v6, v7) = v9) |  ? [v11] : (composition(v7, v8) = v11 & composition(v6, v11) = v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (composition(v9, v8) = v10) |  ~ (join(v6, v7) = v9) |  ? [v11] :  ? [v12] : (composition(v7, v8) = v12 & composition(v6, v8) = v11 & join(v11, v12) = v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (composition(v7, v8) = v9) |  ~ (composition(v6, v9) = v10) |  ? [v11] : (composition(v11, v8) = v10 & composition(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (complement(v7) = v9) |  ~ (complement(v6) = v8) |  ~ (join(v8, v9) = v10) |  ? [v11] :  ? [v12] :  ? [v13] : (complement(v12) = v13 & complement(v10) = v11 & join(v11, v13) = v6 & join(v8, v7) = v12)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (complement(v7) = v9) |  ~ (complement(v6) = v8) |  ~ (join(v8, v9) = v10) |  ? [v11] : (meet(v6, v7) = v11 & complement(v10) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (join(v9, v8) = v10) |  ~ (join(v6, v7) = v9) |  ? [v11] : (join(v7, v8) = v11 & join(v6, v11) = v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (join(v7, v8) = v9) |  ~ (join(v6, v9) = v10) |  ? [v11] : (join(v11, v8) = v10 & join(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (composition(v9, v8) = v7) |  ~ (composition(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (meet(v9, v8) = v7) |  ~ (meet(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (join(v9, v8) = v7) |  ~ (join(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (complement(v6) = v8) |  ~ (join(v8, v7) = v9) |  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] : (complement(v11) = v12 & complement(v9) = v13 & complement(v7) = v10 & join(v12, v13) = v6 & join(v8, v10) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] : (v7 = v6 |  ~ (converse(v8) = v7) |  ~ (converse(v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] : (v7 = v6 |  ~ (complement(v8) = v7) |  ~ (complement(v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (composition(v6, v7) = v8) |  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] : (converse(v6) = v9 & composition(v9, v10) = v11 & complement(v8) = v10 & complement(v7) = v12 & join(v11, v12) = v12)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (composition(v6, v7) = v8) |  ? [v9] :  ? [v10] :  ? [v11] : (converse(v8) = v9 & converse(v7) = v10 & converse(v6) = v11 & composition(v10, v11) = v9)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (meet(v6, v7) = v8) |  ? [v9] :  ? [v10] :  ? [v11] : (complement(v11) = v8 & complement(v7) = v10 & complement(v6) = v9 & join(v9, v10) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (join(v7, v6) = v8) | join(v6, v7) = v8) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (join(v6, v7) = v8) | join(v7, v6) = v8) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (join(v6, v7) = v8) |  ? [v9] :  ? [v10] :  ? [v11] : (converse(v8) = v9 & converse(v7) = v11 & converse(v6) = v10 & join(v10, v11) = v9)) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (composition(v6, one) = v7)) &  ! [v6] :  ! [v7] : ( ~ (converse(v6) = v7) | converse(v7) = v6) &  ! [v6] :  ! [v7] : ( ~ (complement(v6) = v7) | meet(v6, v7) = zero) &  ! [v6] :  ! [v7] : ( ~ (complement(v6) = v7) | join(v6, v7) = top) &  ? [v6] :  ? [v7] :  ? [v8] : composition(v7, v6) = v8 &  ? [v6] :  ? [v7] :  ? [v8] : meet(v7, v6) = v8 &  ? [v6] :  ? [v7] :  ? [v8] : join(v7, v6) = v8 &  ? [v6] :  ? [v7] : converse(v6) = v7 &  ? [v6] :  ? [v7] : complement(v6) = v7 & (( ~ (v5 = v2) & join(v0, v2) = v5) | ( ~ (v4 = v1) & join(v0, v1) = v4)))
% 48.48/19.14  | 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 yields:
% 48.48/19.14  | (1) meet(all_0_4_4, all_0_3_3) = all_0_2_2 & join(all_0_5_5, all_0_2_2) = all_0_2_2 &  ! [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] :  ? [v6] :  ? [v7] : (complement(v6) = v7 & complement(v4) = v5 & join(v5, v7) = v0 & join(v2, v1) = v6)) &  ! [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] :  ! [v3] : ( ~ (complement(v0) = v2) |  ~ (join(v2, v1) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (complement(v5) = v6 & complement(v3) = v7 & complement(v1) = v4 & join(v6, v7) = v0 & join(v2, v4) = v5)) &  ! [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] :  ? [v6] : (converse(v0) = v3 & composition(v3, v4) = v5 & complement(v2) = v4 & complement(v1) = v6 & join(v5, v6) = v6)) &  ! [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) &  ! [v0] :  ! [v1] : ( ~ (complement(v0) = v1) | meet(v0, v1) = zero) &  ! [v0] :  ! [v1] : ( ~ (complement(v0) = v1) | join(v0, v1) = top) &  ? [v0] :  ? [v1] :  ? [v2] : composition(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : meet(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : join(v1, v0) = v2 &  ? [v0] :  ? [v1] : converse(v0) = v1 &  ? [v0] :  ? [v1] : complement(v0) = v1 & (( ~ (all_0_0_0 = all_0_3_3) & join(all_0_5_5, all_0_3_3) = all_0_0_0) | ( ~ (all_0_1_1 = all_0_4_4) & join(all_0_5_5, all_0_4_4) = all_0_1_1))
% 48.48/19.16  |
% 48.48/19.16  | Applying alpha-rule on (1) yields:
% 48.48/19.16  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (join(v3, v2) = v4) |  ~ (join(v0, v1) = v3) |  ? [v5] : (join(v1, v2) = v5 & join(v0, v5) = v4))
% 48.48/19.16  | (3)  ! [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))
% 48.48/19.16  | (4)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (join(v0, v1) = v2) | join(v1, v0) = v2)
% 48.48/19.16  | (5)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (join(v1, v0) = v2) | join(v0, v1) = v2)
% 48.48/19.16  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (join(v3, v2) = v1) |  ~ (join(v3, v2) = v0))
% 48.48/19.16  | (7)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (composition(v0, one) = v1))
% 48.48/19.16  | (8)  ? [v0] :  ? [v1] : complement(v0) = v1
% 48.48/19.16  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (meet(v3, v2) = v1) |  ~ (meet(v3, v2) = v0))
% 48.48/19.16  | (10)  ! [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))
% 48.48/19.16  | (11)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (meet(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (complement(v5) = v2 & complement(v1) = v4 & complement(v0) = v3 & join(v3, v4) = v5))
% 48.48/19.16  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (composition(v1, v2) = v3) |  ~ (composition(v0, v3) = v4) |  ? [v5] : (composition(v5, v2) = v4 & composition(v0, v1) = v5))
% 48.48/19.16  | (13)  ! [v0] :  ! [v1] : ( ~ (complement(v0) = v1) | meet(v0, v1) = zero)
% 48.48/19.16  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (complement(v0) = v2) |  ~ (join(v2, v1) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (complement(v5) = v6 & complement(v3) = v7 & complement(v1) = v4 & join(v6, v7) = v0 & join(v2, v4) = v5))
% 48.48/19.16  | (15)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (join(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (converse(v2) = v3 & converse(v1) = v5 & converse(v0) = v4 & join(v4, v5) = v3))
% 48.48/19.16  | (16)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (converse(v2) = v1) |  ~ (converse(v2) = v0))
% 48.48/19.16  | (17)  ? [v0] :  ? [v1] :  ? [v2] : composition(v1, v0) = v2
% 48.48/19.16  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (complement(v1) = v3) |  ~ (complement(v0) = v2) |  ~ (join(v2, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (complement(v6) = v7 & complement(v4) = v5 & join(v5, v7) = v0 & join(v2, v1) = v6))
% 48.48/19.16  | (19)  ! [v0] :  ! [v1] : ( ~ (complement(v0) = v1) | join(v0, v1) = top)
% 48.48/19.16  | (20) join(all_0_5_5, all_0_2_2) = all_0_2_2
% 48.48/19.16  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (converse(v1) = v3) |  ~ (converse(v0) = v2) |  ~ (join(v2, v3) = v4) |  ? [v5] : (converse(v5) = v4 & join(v0, v1) = v5))
% 48.48/19.16  | (22)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (complement(v2) = v1) |  ~ (complement(v2) = v0))
% 48.48/19.16  | (23)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (composition(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (converse(v0) = v3 & composition(v3, v4) = v5 & complement(v2) = v4 & complement(v1) = v6 & join(v5, v6) = v6))
% 48.48/19.16  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (composition(v3, v2) = v4) |  ~ (composition(v0, v1) = v3) |  ? [v5] : (composition(v1, v2) = v5 & composition(v0, v5) = v4))
% 48.48/19.16  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (join(v1, v2) = v3) |  ~ (join(v0, v3) = v4) |  ? [v5] : (join(v5, v2) = v4 & join(v0, v1) = v5))
% 48.48/19.17  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (composition(v3, v2) = v1) |  ~ (composition(v3, v2) = v0))
% 48.48/19.17  | (27) ( ~ (all_0_0_0 = all_0_3_3) & join(all_0_5_5, all_0_3_3) = all_0_0_0) | ( ~ (all_0_1_1 = all_0_4_4) & join(all_0_5_5, all_0_4_4) = all_0_1_1)
% 48.48/19.17  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (converse(v1) = v2) |  ~ (converse(v0) = v3) |  ~ (composition(v2, v3) = v4) |  ? [v5] : (converse(v5) = v4 & composition(v0, v1) = v5))
% 48.48/19.17  | (29)  ? [v0] :  ? [v1] :  ? [v2] : join(v1, v0) = v2
% 48.48/19.17  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (complement(v1) = v3) |  ~ (complement(v0) = v2) |  ~ (join(v2, v3) = v4) |  ? [v5] : (meet(v0, v1) = v5 & complement(v4) = v5))
% 48.48/19.17  | (31)  ! [v0] :  ! [v1] : ( ~ (converse(v0) = v1) | converse(v1) = v0)
% 48.48/19.17  | (32)  ? [v0] :  ? [v1] : converse(v0) = v1
% 48.48/19.17  | (33)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (composition(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (converse(v2) = v3 & converse(v1) = v4 & converse(v0) = v5 & composition(v4, v5) = v3))
% 48.48/19.17  | (34) meet(all_0_4_4, all_0_3_3) = all_0_2_2
% 48.48/19.17  | (35)  ? [v0] :  ? [v1] :  ? [v2] : meet(v1, v0) = v2
% 48.48/19.17  |
% 48.48/19.17  | Instantiating formula (11) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms meet(all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 48.48/19.17  | (36)  ? [v0] :  ? [v1] :  ? [v2] : (complement(v2) = all_0_2_2 & complement(all_0_3_3) = v1 & complement(all_0_4_4) = v0 & join(v0, v1) = v2)
% 48.48/19.17  |
% 48.48/19.17  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_0_5_5, all_0_5_5 and discharging atoms join(all_0_5_5, all_0_2_2) = all_0_2_2, yields:
% 48.48/19.17  | (37)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_0_5_5, all_0_5_5) = v0)
% 48.48/19.17  |
% 48.48/19.17  | Instantiating formula (5) with all_0_2_2, all_0_5_5, all_0_2_2 and discharging atoms join(all_0_5_5, all_0_2_2) = all_0_2_2, yields:
% 48.48/19.17  | (38) join(all_0_2_2, all_0_5_5) = all_0_2_2
% 48.48/19.17  |
% 48.48/19.17  | Instantiating formula (15) with all_0_2_2, all_0_2_2, all_0_5_5 and discharging atoms join(all_0_5_5, all_0_2_2) = all_0_2_2, yields:
% 48.48/19.17  | (39)  ? [v0] :  ? [v1] :  ? [v2] : (converse(all_0_2_2) = v2 & converse(all_0_2_2) = v0 & converse(all_0_5_5) = v1 & join(v1, v2) = v0)
% 48.48/19.17  |
% 48.48/19.17  | Instantiating (39) with all_19_0_19, all_19_1_20, all_19_2_21 yields:
% 48.48/19.17  | (40) converse(all_0_2_2) = all_19_0_19 & converse(all_0_2_2) = all_19_2_21 & converse(all_0_5_5) = all_19_1_20 & join(all_19_1_20, all_19_0_19) = all_19_2_21
% 48.48/19.17  |
% 48.48/19.17  | Applying alpha-rule on (40) yields:
% 48.48/19.17  | (41) converse(all_0_2_2) = all_19_0_19
% 48.48/19.17  | (42) converse(all_0_2_2) = all_19_2_21
% 48.48/19.17  | (43) converse(all_0_5_5) = all_19_1_20
% 48.48/19.17  | (44) join(all_19_1_20, all_19_0_19) = all_19_2_21
% 48.48/19.17  |
% 48.48/19.17  | Instantiating (37) with all_21_0_22 yields:
% 48.48/19.17  | (45) join(all_21_0_22, all_0_2_2) = all_0_2_2 & join(all_0_5_5, all_0_5_5) = all_21_0_22
% 48.48/19.17  |
% 48.48/19.17  | Applying alpha-rule on (45) yields:
% 48.48/19.17  | (46) join(all_21_0_22, all_0_2_2) = all_0_2_2
% 48.48/19.17  | (47) join(all_0_5_5, all_0_5_5) = all_21_0_22
% 48.48/19.17  |
% 48.48/19.17  | Instantiating (36) with all_23_0_23, all_23_1_24, all_23_2_25 yields:
% 48.48/19.17  | (48) complement(all_23_0_23) = all_0_2_2 & complement(all_0_3_3) = all_23_1_24 & complement(all_0_4_4) = all_23_2_25 & join(all_23_2_25, all_23_1_24) = all_23_0_23
% 48.48/19.17  |
% 48.48/19.17  | Applying alpha-rule on (48) yields:
% 48.48/19.17  | (49) complement(all_23_0_23) = all_0_2_2
% 48.48/19.17  | (50) complement(all_0_3_3) = all_23_1_24
% 48.48/19.17  | (51) complement(all_0_4_4) = all_23_2_25
% 48.48/19.17  | (52) join(all_23_2_25, all_23_1_24) = all_23_0_23
% 48.48/19.17  |
% 48.48/19.17  | Instantiating formula (16) with all_0_2_2, all_19_2_21, all_19_0_19 and discharging atoms converse(all_0_2_2) = all_19_0_19, converse(all_0_2_2) = all_19_2_21, yields:
% 48.48/19.17  | (53) all_19_0_19 = all_19_2_21
% 48.48/19.17  |
% 48.48/19.17  | From (53) and (41) follows:
% 48.48/19.17  | (42) converse(all_0_2_2) = all_19_2_21
% 48.48/19.17  |
% 48.48/19.17  | From (53) and (44) follows:
% 48.48/19.17  | (55) join(all_19_1_20, all_19_2_21) = all_19_2_21
% 48.48/19.17  |
% 48.48/19.17  | Instantiating formula (31) with all_19_2_21, all_0_2_2 and discharging atoms converse(all_0_2_2) = all_19_2_21, yields:
% 48.48/19.17  | (56) converse(all_19_2_21) = all_0_2_2
% 48.48/19.17  |
% 48.48/19.18  | Instantiating formula (31) with all_19_1_20, all_0_5_5 and discharging atoms converse(all_0_5_5) = all_19_1_20, yields:
% 48.48/19.18  | (57) converse(all_19_1_20) = all_0_5_5
% 48.48/19.18  |
% 48.48/19.18  | Instantiating formula (13) with all_0_2_2, all_23_0_23 and discharging atoms complement(all_23_0_23) = all_0_2_2, yields:
% 48.48/19.18  | (58) meet(all_23_0_23, all_0_2_2) = zero
% 48.48/19.18  |
% 48.48/19.18  | Instantiating formula (18) with all_23_0_23, all_23_1_24, all_23_2_25, all_0_3_3, all_0_4_4 and discharging atoms complement(all_0_3_3) = all_23_1_24, complement(all_0_4_4) = all_23_2_25, join(all_23_2_25, all_23_1_24) = all_23_0_23, yields:
% 48.48/19.18  | (59)  ? [v0] :  ? [v1] :  ? [v2] : (complement(v1) = v2 & complement(all_23_0_23) = v0 & join(v0, v2) = all_0_4_4 & join(all_23_2_25, all_0_3_3) = v1)
% 48.48/19.18  |
% 48.48/19.18  | Instantiating formula (14) with all_23_0_23, all_23_2_25, all_23_1_24, all_0_4_4 and discharging atoms complement(all_0_4_4) = all_23_2_25, join(all_23_2_25, all_23_1_24) = all_23_0_23, yields:
% 48.48/19.18  | (60)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (complement(v1) = v2 & complement(all_23_0_23) = v3 & complement(all_23_1_24) = v0 & join(v2, v3) = all_0_4_4 & join(all_23_2_25, v0) = v1)
% 48.48/19.18  |
% 48.48/19.18  | Instantiating formula (5) with all_23_0_23, all_23_2_25, all_23_1_24 and discharging atoms join(all_23_2_25, all_23_1_24) = all_23_0_23, yields:
% 48.48/19.18  | (61) join(all_23_1_24, all_23_2_25) = all_23_0_23
% 48.48/19.18  |
% 48.48/19.18  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_21_0_22, all_0_5_5 and discharging atoms join(all_21_0_22, all_0_2_2) = all_0_2_2, join(all_0_5_5, all_0_2_2) = all_0_2_2, yields:
% 48.48/19.18  | (62)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_0_5_5, all_21_0_22) = v0)
% 48.48/19.18  |
% 48.48/19.18  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_0_5_5, all_21_0_22 and discharging atoms join(all_21_0_22, all_0_2_2) = all_0_2_2, join(all_0_5_5, all_0_2_2) = all_0_2_2, yields:
% 48.48/19.18  | (63)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_21_0_22, all_0_5_5) = v0)
% 48.48/19.18  |
% 48.48/19.18  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_21_0_22, all_21_0_22 and discharging atoms join(all_21_0_22, all_0_2_2) = all_0_2_2, yields:
% 48.48/19.18  | (64)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_21_0_22, all_21_0_22) = v0)
% 48.48/19.18  |
% 48.48/19.18  | Instantiating formula (15) with all_0_2_2, all_0_2_2, all_21_0_22 and discharging atoms join(all_21_0_22, all_0_2_2) = all_0_2_2, yields:
% 48.48/19.18  | (65)  ? [v0] :  ? [v1] :  ? [v2] : (converse(all_21_0_22) = v1 & converse(all_0_2_2) = v2 & converse(all_0_2_2) = v0 & join(v1, v2) = v0)
% 48.48/19.18  |
% 48.48/19.18  | Instantiating formula (25) with all_19_2_21, all_19_2_21, all_19_2_21, all_19_1_20, all_19_1_20 and discharging atoms join(all_19_1_20, all_19_2_21) = all_19_2_21, yields:
% 48.48/19.18  | (66)  ? [v0] : (join(v0, all_19_2_21) = all_19_2_21 & join(all_19_1_20, all_19_1_20) = v0)
% 48.48/19.18  |
% 48.48/19.18  | Instantiating formula (15) with all_19_2_21, all_19_2_21, all_19_1_20 and discharging atoms join(all_19_1_20, all_19_2_21) = all_19_2_21, yields:
% 48.48/19.18  | (67)  ? [v0] :  ? [v1] :  ? [v2] : (converse(all_19_1_20) = v1 & converse(all_19_2_21) = v2 & converse(all_19_2_21) = v0 & join(v1, v2) = v0)
% 48.48/19.18  |
% 48.48/19.18  | Instantiating formula (14) with all_0_2_2, all_0_2_2, all_0_5_5, all_23_0_23 and discharging atoms complement(all_23_0_23) = all_0_2_2, join(all_0_2_2, all_0_5_5) = all_0_2_2, yields:
% 48.48/19.18  | (68)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (complement(v1) = v2 & complement(all_0_2_2) = v3 & complement(all_0_5_5) = v0 & join(v2, v3) = all_23_0_23 & join(all_0_2_2, v0) = v1)
% 48.87/19.18  |
% 48.87/19.18  | Instantiating formula (2) with all_0_2_2, all_0_2_2, all_0_5_5, all_0_5_5, all_0_2_2 and discharging atoms join(all_0_2_2, all_0_5_5) = all_0_2_2, yields:
% 48.87/19.18  | (69)  ? [v0] : (join(all_0_2_2, v0) = all_0_2_2 & join(all_0_5_5, all_0_5_5) = v0)
% 48.87/19.18  |
% 48.87/19.18  | Instantiating formula (15) with all_0_2_2, all_0_5_5, all_0_2_2 and discharging atoms join(all_0_2_2, all_0_5_5) = all_0_2_2, yields:
% 48.87/19.18  | (70)  ? [v0] :  ? [v1] :  ? [v2] : (converse(all_0_2_2) = v1 & converse(all_0_2_2) = v0 & converse(all_0_5_5) = v2 & join(v1, v2) = v0)
% 48.87/19.18  |
% 48.87/19.18  | Instantiating formula (15) with all_21_0_22, all_0_5_5, all_0_5_5 and discharging atoms join(all_0_5_5, all_0_5_5) = all_21_0_22, yields:
% 48.87/19.18  | (71)  ? [v0] :  ? [v1] :  ? [v2] : (converse(all_21_0_22) = v0 & converse(all_0_5_5) = v2 & converse(all_0_5_5) = v1 & join(v1, v2) = v0)
% 48.87/19.18  |
% 48.87/19.18  | Instantiating (59) with all_35_0_26, all_35_1_27, all_35_2_28 yields:
% 48.87/19.18  | (72) complement(all_35_1_27) = all_35_0_26 & complement(all_23_0_23) = all_35_2_28 & join(all_35_2_28, all_35_0_26) = all_0_4_4 & join(all_23_2_25, all_0_3_3) = all_35_1_27
% 48.87/19.18  |
% 48.87/19.18  | Applying alpha-rule on (72) yields:
% 48.87/19.18  | (73) complement(all_35_1_27) = all_35_0_26
% 48.87/19.18  | (74) complement(all_23_0_23) = all_35_2_28
% 48.87/19.18  | (75) join(all_35_2_28, all_35_0_26) = all_0_4_4
% 48.87/19.18  | (76) join(all_23_2_25, all_0_3_3) = all_35_1_27
% 48.87/19.18  |
% 48.87/19.18  | Instantiating (65) with all_37_0_29, all_37_1_30, all_37_2_31 yields:
% 48.87/19.18  | (77) converse(all_21_0_22) = all_37_1_30 & converse(all_0_2_2) = all_37_0_29 & converse(all_0_2_2) = all_37_2_31 & join(all_37_1_30, all_37_0_29) = all_37_2_31
% 48.87/19.18  |
% 48.87/19.18  | Applying alpha-rule on (77) yields:
% 48.87/19.18  | (78) converse(all_21_0_22) = all_37_1_30
% 48.87/19.18  | (79) converse(all_0_2_2) = all_37_0_29
% 48.87/19.18  | (80) converse(all_0_2_2) = all_37_2_31
% 48.87/19.18  | (81) join(all_37_1_30, all_37_0_29) = all_37_2_31
% 48.87/19.18  |
% 48.87/19.18  | Instantiating (71) with all_39_0_32, all_39_1_33, all_39_2_34 yields:
% 48.87/19.18  | (82) converse(all_21_0_22) = all_39_2_34 & converse(all_0_5_5) = all_39_0_32 & converse(all_0_5_5) = all_39_1_33 & join(all_39_1_33, all_39_0_32) = all_39_2_34
% 48.87/19.18  |
% 48.87/19.18  | Applying alpha-rule on (82) yields:
% 48.87/19.18  | (83) converse(all_21_0_22) = all_39_2_34
% 48.87/19.18  | (84) converse(all_0_5_5) = all_39_0_32
% 48.87/19.19  | (85) converse(all_0_5_5) = all_39_1_33
% 48.87/19.19  | (86) join(all_39_1_33, all_39_0_32) = all_39_2_34
% 48.87/19.19  |
% 48.87/19.19  | Instantiating (70) with all_41_0_35, all_41_1_36, all_41_2_37 yields:
% 48.87/19.19  | (87) converse(all_0_2_2) = all_41_1_36 & converse(all_0_2_2) = all_41_2_37 & converse(all_0_5_5) = all_41_0_35 & join(all_41_1_36, all_41_0_35) = all_41_2_37
% 48.87/19.19  |
% 48.87/19.19  | Applying alpha-rule on (87) yields:
% 48.87/19.19  | (88) converse(all_0_2_2) = all_41_1_36
% 48.87/19.19  | (89) converse(all_0_2_2) = all_41_2_37
% 48.87/19.19  | (90) converse(all_0_5_5) = all_41_0_35
% 48.87/19.19  | (91) join(all_41_1_36, all_41_0_35) = all_41_2_37
% 48.87/19.19  |
% 48.87/19.19  | Instantiating (69) with all_43_0_38 yields:
% 48.87/19.19  | (92) join(all_0_2_2, all_43_0_38) = all_0_2_2 & join(all_0_5_5, all_0_5_5) = all_43_0_38
% 48.87/19.19  |
% 48.87/19.19  | Applying alpha-rule on (92) yields:
% 48.87/19.19  | (93) join(all_0_2_2, all_43_0_38) = all_0_2_2
% 48.87/19.19  | (94) join(all_0_5_5, all_0_5_5) = all_43_0_38
% 48.87/19.19  |
% 48.87/19.19  | Instantiating (66) with all_45_0_39 yields:
% 48.87/19.19  | (95) join(all_45_0_39, all_19_2_21) = all_19_2_21 & join(all_19_1_20, all_19_1_20) = all_45_0_39
% 48.87/19.19  |
% 48.87/19.19  | Applying alpha-rule on (95) yields:
% 48.87/19.19  | (96) join(all_45_0_39, all_19_2_21) = all_19_2_21
% 48.87/19.19  | (97) join(all_19_1_20, all_19_1_20) = all_45_0_39
% 48.87/19.19  |
% 48.87/19.19  | Instantiating (68) with all_47_0_40, all_47_1_41, all_47_2_42, all_47_3_43 yields:
% 48.87/19.19  | (98) complement(all_47_2_42) = all_47_1_41 & complement(all_0_2_2) = all_47_0_40 & complement(all_0_5_5) = all_47_3_43 & join(all_47_1_41, all_47_0_40) = all_23_0_23 & join(all_0_2_2, all_47_3_43) = all_47_2_42
% 48.87/19.19  |
% 48.87/19.19  | Applying alpha-rule on (98) yields:
% 48.87/19.19  | (99) complement(all_47_2_42) = all_47_1_41
% 48.87/19.19  | (100) complement(all_0_5_5) = all_47_3_43
% 48.87/19.19  | (101) join(all_47_1_41, all_47_0_40) = all_23_0_23
% 48.87/19.19  | (102) join(all_0_2_2, all_47_3_43) = all_47_2_42
% 48.87/19.19  | (103) complement(all_0_2_2) = all_47_0_40
% 48.87/19.19  |
% 48.87/19.19  | Instantiating (64) with all_49_0_44 yields:
% 48.87/19.19  | (104) join(all_49_0_44, all_0_2_2) = all_0_2_2 & join(all_21_0_22, all_21_0_22) = all_49_0_44
% 48.87/19.19  |
% 48.87/19.19  | Applying alpha-rule on (104) yields:
% 48.87/19.19  | (105) join(all_49_0_44, all_0_2_2) = all_0_2_2
% 48.87/19.19  | (106) join(all_21_0_22, all_21_0_22) = all_49_0_44
% 48.87/19.19  |
% 48.87/19.19  | Instantiating (62) with all_51_0_45 yields:
% 48.87/19.19  | (107) join(all_51_0_45, all_0_2_2) = all_0_2_2 & join(all_0_5_5, all_21_0_22) = all_51_0_45
% 48.87/19.19  |
% 48.87/19.19  | Applying alpha-rule on (107) yields:
% 48.87/19.19  | (108) join(all_51_0_45, all_0_2_2) = all_0_2_2
% 48.87/19.19  | (109) join(all_0_5_5, all_21_0_22) = all_51_0_45
% 48.87/19.19  |
% 48.87/19.19  | Instantiating (67) with all_55_0_49, all_55_1_50, all_55_2_51 yields:
% 48.87/19.19  | (110) converse(all_19_1_20) = all_55_1_50 & converse(all_19_2_21) = all_55_0_49 & converse(all_19_2_21) = all_55_2_51 & join(all_55_1_50, all_55_0_49) = all_55_2_51
% 48.87/19.19  |
% 48.87/19.19  | Applying alpha-rule on (110) yields:
% 48.87/19.19  | (111) converse(all_19_1_20) = all_55_1_50
% 48.87/19.19  | (112) converse(all_19_2_21) = all_55_0_49
% 48.87/19.19  | (113) converse(all_19_2_21) = all_55_2_51
% 48.87/19.19  | (114) join(all_55_1_50, all_55_0_49) = all_55_2_51
% 48.87/19.19  |
% 48.87/19.19  | Instantiating (63) with all_57_0_52 yields:
% 48.87/19.19  | (115) join(all_57_0_52, all_0_2_2) = all_0_2_2 & join(all_21_0_22, all_0_5_5) = all_57_0_52
% 48.87/19.19  |
% 48.87/19.19  | Applying alpha-rule on (115) yields:
% 48.87/19.19  | (116) join(all_57_0_52, all_0_2_2) = all_0_2_2
% 48.87/19.19  | (117) join(all_21_0_22, all_0_5_5) = all_57_0_52
% 48.87/19.19  |
% 48.87/19.19  | Instantiating (60) with all_59_0_53, all_59_1_54, all_59_2_55, all_59_3_56 yields:
% 48.87/19.19  | (118) complement(all_59_2_55) = all_59_1_54 & complement(all_23_0_23) = all_59_0_53 & complement(all_23_1_24) = all_59_3_56 & join(all_59_1_54, all_59_0_53) = all_0_4_4 & join(all_23_2_25, all_59_3_56) = all_59_2_55
% 48.87/19.19  |
% 48.87/19.19  | Applying alpha-rule on (118) yields:
% 48.87/19.19  | (119) complement(all_23_1_24) = all_59_3_56
% 48.87/19.19  | (120) complement(all_59_2_55) = all_59_1_54
% 48.87/19.19  | (121) complement(all_23_0_23) = all_59_0_53
% 48.87/19.19  | (122) join(all_59_1_54, all_59_0_53) = all_0_4_4
% 48.87/19.19  | (123) join(all_23_2_25, all_59_3_56) = all_59_2_55
% 48.87/19.19  |
% 48.87/19.19  | Instantiating formula (16) with all_21_0_22, all_37_1_30, all_39_2_34 and discharging atoms converse(all_21_0_22) = all_39_2_34, converse(all_21_0_22) = all_37_1_30, yields:
% 48.87/19.19  | (124) all_39_2_34 = all_37_1_30
% 48.87/19.19  |
% 48.87/19.19  | Instantiating formula (16) with all_19_1_20, all_0_5_5, all_55_1_50 and discharging atoms converse(all_19_1_20) = all_55_1_50, converse(all_19_1_20) = all_0_5_5, yields:
% 48.87/19.19  | (125) all_55_1_50 = all_0_5_5
% 48.87/19.19  |
% 48.87/19.19  | Instantiating formula (16) with all_19_2_21, all_55_2_51, all_55_0_49 and discharging atoms converse(all_19_2_21) = all_55_0_49, converse(all_19_2_21) = all_55_2_51, yields:
% 48.87/19.19  | (126) all_55_0_49 = all_55_2_51
% 48.87/19.19  |
% 48.87/19.19  | Instantiating formula (16) with all_19_2_21, all_0_2_2, all_55_0_49 and discharging atoms converse(all_19_2_21) = all_55_0_49, converse(all_19_2_21) = all_0_2_2, yields:
% 48.87/19.20  | (127) all_55_0_49 = all_0_2_2
% 48.87/19.20  |
% 48.87/19.20  | Instantiating formula (16) with all_0_5_5, all_41_0_35, all_19_1_20 and discharging atoms converse(all_0_5_5) = all_41_0_35, converse(all_0_5_5) = all_19_1_20, yields:
% 48.87/19.20  | (128) all_41_0_35 = all_19_1_20
% 48.87/19.20  |
% 48.87/19.20  | Instantiating formula (16) with all_0_5_5, all_39_0_32, all_41_0_35 and discharging atoms converse(all_0_5_5) = all_41_0_35, converse(all_0_5_5) = all_39_0_32, yields:
% 48.87/19.20  | (129) all_41_0_35 = all_39_0_32
% 48.87/19.20  |
% 48.87/19.20  | Instantiating formula (16) with all_0_5_5, all_39_1_33, all_41_0_35 and discharging atoms converse(all_0_5_5) = all_41_0_35, converse(all_0_5_5) = all_39_1_33, yields:
% 48.87/19.20  | (130) all_41_0_35 = all_39_1_33
% 48.87/19.20  |
% 48.87/19.20  | Instantiating formula (22) with all_23_0_23, all_59_0_53, all_0_2_2 and discharging atoms complement(all_23_0_23) = all_59_0_53, complement(all_23_0_23) = all_0_2_2, yields:
% 48.87/19.20  | (131) all_59_0_53 = all_0_2_2
% 48.87/19.20  |
% 48.87/19.20  | Instantiating formula (22) with all_23_0_23, all_35_2_28, all_59_0_53 and discharging atoms complement(all_23_0_23) = all_59_0_53, complement(all_23_0_23) = all_35_2_28, yields:
% 48.87/19.20  | (132) all_59_0_53 = all_35_2_28
% 48.87/19.20  |
% 48.87/19.20  | Instantiating formula (6) with all_0_5_5, all_0_5_5, all_43_0_38, all_21_0_22 and discharging atoms join(all_0_5_5, all_0_5_5) = all_43_0_38, join(all_0_5_5, all_0_5_5) = all_21_0_22, yields:
% 48.87/19.20  | (133) all_43_0_38 = all_21_0_22
% 48.87/19.20  |
% 48.87/19.20  | Combining equations (131,132) yields a new equation:
% 48.87/19.20  | (134) all_35_2_28 = all_0_2_2
% 48.87/19.20  |
% 48.87/19.20  | Combining equations (126,127) yields a new equation:
% 48.87/19.20  | (135) all_55_2_51 = all_0_2_2
% 48.87/19.20  |
% 48.87/19.20  | Simplifying 135 yields:
% 48.87/19.20  | (136) all_55_2_51 = all_0_2_2
% 48.87/19.20  |
% 48.87/19.20  | Combining equations (128,129) yields a new equation:
% 48.87/19.20  | (137) all_39_0_32 = all_19_1_20
% 48.87/19.20  |
% 48.87/19.20  | Combining equations (130,129) yields a new equation:
% 48.87/19.20  | (138) all_39_0_32 = all_39_1_33
% 48.87/19.20  |
% 48.87/19.20  | Combining equations (138,137) yields a new equation:
% 48.87/19.20  | (139) all_39_1_33 = all_19_1_20
% 48.87/19.20  |
% 48.87/19.20  | Simplifying 139 yields:
% 48.87/19.20  | (140) all_39_1_33 = all_19_1_20
% 48.87/19.20  |
% 48.87/19.20  | From (124) and (83) follows:
% 48.87/19.20  | (78) converse(all_21_0_22) = all_37_1_30
% 48.87/19.20  |
% 48.87/19.20  | From (136) and (113) follows:
% 48.87/19.20  | (56) converse(all_19_2_21) = all_0_2_2
% 48.87/19.20  |
% 48.87/19.20  | From (134) and (74) follows:
% 48.87/19.20  | (49) complement(all_23_0_23) = all_0_2_2
% 48.87/19.20  |
% 48.87/19.20  | From (125)(127)(136) and (114) follows:
% 48.87/19.20  | (20) join(all_0_5_5, all_0_2_2) = all_0_2_2
% 48.87/19.20  |
% 48.87/19.20  | From (140)(137)(124) and (86) follows:
% 48.87/19.20  | (145) join(all_19_1_20, all_19_1_20) = all_37_1_30
% 48.87/19.20  |
% 48.87/19.20  | From (134) and (75) follows:
% 48.87/19.20  | (146) join(all_0_2_2, all_35_0_26) = all_0_4_4
% 48.87/19.20  |
% 48.87/19.20  | From (133) and (93) follows:
% 48.87/19.20  | (147) join(all_0_2_2, all_21_0_22) = all_0_2_2
% 48.87/19.20  |
% 48.87/19.20  | From (133) and (94) follows:
% 48.87/19.20  | (47) join(all_0_5_5, all_0_5_5) = all_21_0_22
% 48.87/19.20  |
% 48.87/19.20  | Instantiating formula (6) with all_19_1_20, all_19_1_20, all_37_1_30, all_45_0_39 and discharging atoms join(all_19_1_20, all_19_1_20) = all_45_0_39, join(all_19_1_20, all_19_1_20) = all_37_1_30, yields:
% 48.87/19.20  | (149) all_45_0_39 = all_37_1_30
% 48.87/19.20  |
% 48.87/19.20  | From (149) and (96) follows:
% 48.87/19.20  | (150) join(all_37_1_30, all_19_2_21) = all_19_2_21
% 48.87/19.20  |
% 48.87/19.20  | Instantiating formula (31) with all_37_1_30, all_21_0_22 and discharging atoms converse(all_21_0_22) = all_37_1_30, yields:
% 48.87/19.20  | (151) converse(all_37_1_30) = all_21_0_22
% 48.87/19.20  |
% 48.87/19.20  | Instantiating formula (11) with zero, all_0_2_2, all_23_0_23 and discharging atoms meet(all_23_0_23, all_0_2_2) = zero, yields:
% 48.87/19.20  | (152)  ? [v0] :  ? [v1] :  ? [v2] : (complement(v2) = zero & complement(all_23_0_23) = v0 & complement(all_0_2_2) = v1 & join(v0, v1) = v2)
% 48.87/19.20  |
% 48.87/19.20  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_57_0_52, all_21_0_22 and discharging atoms join(all_57_0_52, all_0_2_2) = all_0_2_2, join(all_21_0_22, all_0_2_2) = all_0_2_2, yields:
% 48.87/19.20  | (153)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_21_0_22, all_57_0_52) = v0)
% 48.87/19.20  |
% 48.87/19.20  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_21_0_22, all_57_0_52 and discharging atoms join(all_57_0_52, all_0_2_2) = all_0_2_2, join(all_21_0_22, all_0_2_2) = all_0_2_2, yields:
% 48.87/19.20  | (154)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_57_0_52, all_21_0_22) = v0)
% 48.87/19.20  |
% 48.87/19.20  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_57_0_52, all_0_5_5 and discharging atoms join(all_57_0_52, all_0_2_2) = all_0_2_2, join(all_0_5_5, all_0_2_2) = all_0_2_2, yields:
% 48.87/19.21  | (155)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_0_5_5, all_57_0_52) = v0)
% 48.87/19.21  |
% 48.87/19.21  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_57_0_52, all_57_0_52 and discharging atoms join(all_57_0_52, all_0_2_2) = all_0_2_2, yields:
% 48.87/19.21  | (156)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_57_0_52, all_57_0_52) = v0)
% 48.87/19.21  |
% 48.87/19.21  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_51_0_45, all_21_0_22 and discharging atoms join(all_51_0_45, all_0_2_2) = all_0_2_2, join(all_21_0_22, all_0_2_2) = all_0_2_2, yields:
% 48.87/19.21  | (157)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_21_0_22, all_51_0_45) = v0)
% 48.87/19.21  |
% 48.87/19.21  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_21_0_22, all_51_0_45 and discharging atoms join(all_51_0_45, all_0_2_2) = all_0_2_2, join(all_21_0_22, all_0_2_2) = all_0_2_2, yields:
% 48.87/19.21  | (158)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_51_0_45, all_21_0_22) = v0)
% 48.87/19.21  |
% 48.87/19.21  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_51_0_45, all_0_5_5 and discharging atoms join(all_51_0_45, all_0_2_2) = all_0_2_2, join(all_0_5_5, all_0_2_2) = all_0_2_2, yields:
% 48.87/19.21  | (159)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_0_5_5, all_51_0_45) = v0)
% 48.87/19.21  |
% 48.87/19.21  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_51_0_45, all_57_0_52 and discharging atoms join(all_57_0_52, all_0_2_2) = all_0_2_2, join(all_51_0_45, all_0_2_2) = all_0_2_2, yields:
% 48.87/19.21  | (160)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_57_0_52, all_51_0_45) = v0)
% 48.87/19.21  |
% 48.87/19.21  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_57_0_52, all_51_0_45 and discharging atoms join(all_57_0_52, all_0_2_2) = all_0_2_2, join(all_51_0_45, all_0_2_2) = all_0_2_2, yields:
% 48.87/19.21  | (161)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_51_0_45, all_57_0_52) = v0)
% 48.87/19.21  |
% 48.87/19.21  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_51_0_45, all_51_0_45 and discharging atoms join(all_51_0_45, all_0_2_2) = all_0_2_2, yields:
% 48.87/19.21  | (162)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_51_0_45, all_51_0_45) = v0)
% 48.87/19.21  |
% 48.87/19.21  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_49_0_44, all_21_0_22 and discharging atoms join(all_49_0_44, all_0_2_2) = all_0_2_2, join(all_21_0_22, all_0_2_2) = all_0_2_2, yields:
% 48.87/19.21  | (163)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_21_0_22, all_49_0_44) = v0)
% 48.87/19.21  |
% 48.87/19.21  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_21_0_22, all_49_0_44 and discharging atoms join(all_49_0_44, all_0_2_2) = all_0_2_2, join(all_21_0_22, all_0_2_2) = all_0_2_2, yields:
% 48.87/19.21  | (164)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_49_0_44, all_21_0_22) = v0)
% 48.87/19.21  |
% 48.87/19.21  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_49_0_44, all_0_5_5 and discharging atoms join(all_49_0_44, all_0_2_2) = all_0_2_2, join(all_0_5_5, all_0_2_2) = all_0_2_2, yields:
% 48.87/19.21  | (165)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_0_5_5, all_49_0_44) = v0)
% 48.87/19.21  |
% 48.87/19.21  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_0_5_5, all_49_0_44 and discharging atoms join(all_49_0_44, all_0_2_2) = all_0_2_2, join(all_0_5_5, all_0_2_2) = all_0_2_2, yields:
% 48.87/19.21  | (166)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_49_0_44, all_0_5_5) = v0)
% 48.87/19.21  |
% 48.87/19.21  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_49_0_44, all_57_0_52 and discharging atoms join(all_57_0_52, all_0_2_2) = all_0_2_2, join(all_49_0_44, all_0_2_2) = all_0_2_2, yields:
% 48.87/19.21  | (167)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_57_0_52, all_49_0_44) = v0)
% 48.87/19.21  |
% 48.87/19.21  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_57_0_52, all_49_0_44 and discharging atoms join(all_57_0_52, all_0_2_2) = all_0_2_2, join(all_49_0_44, all_0_2_2) = all_0_2_2, yields:
% 48.87/19.21  | (168)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_49_0_44, all_57_0_52) = v0)
% 48.87/19.21  |
% 48.87/19.21  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_49_0_44, all_51_0_45 and discharging atoms join(all_51_0_45, all_0_2_2) = all_0_2_2, join(all_49_0_44, all_0_2_2) = all_0_2_2, yields:
% 48.87/19.21  | (169)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_51_0_45, all_49_0_44) = v0)
% 48.87/19.21  |
% 48.87/19.21  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_51_0_45, all_49_0_44 and discharging atoms join(all_51_0_45, all_0_2_2) = all_0_2_2, join(all_49_0_44, all_0_2_2) = all_0_2_2, yields:
% 48.87/19.21  | (170)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_49_0_44, all_51_0_45) = v0)
% 48.87/19.21  |
% 48.87/19.21  | Instantiating formula (25) with all_0_2_2, all_0_2_2, all_0_2_2, all_49_0_44, all_49_0_44 and discharging atoms join(all_49_0_44, all_0_2_2) = all_0_2_2, yields:
% 48.87/19.21  | (171)  ? [v0] : (join(v0, all_0_2_2) = all_0_2_2 & join(all_49_0_44, all_49_0_44) = v0)
% 48.87/19.21  |
% 48.87/19.21  | Instantiating formula (14) with all_23_0_23, all_47_1_41, all_47_0_40, all_47_2_42 and discharging atoms complement(all_47_2_42) = all_47_1_41, join(all_47_1_41, all_47_0_40) = all_23_0_23, yields:
% 48.87/19.21  | (172)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (complement(v1) = v2 & complement(all_47_0_40) = v0 & complement(all_23_0_23) = v3 & join(v2, v3) = all_47_2_42 & join(all_47_1_41, v0) = v1)
% 48.87/19.21  |
% 48.87/19.21  | Instantiating formula (18) with all_23_0_23, all_47_0_40, all_47_1_41, all_0_2_2, all_47_2_42 and discharging atoms complement(all_47_2_42) = all_47_1_41, complement(all_0_2_2) = all_47_0_40, join(all_47_1_41, all_47_0_40) = all_23_0_23, yields:
% 48.87/19.21  | (173)  ? [v0] :  ? [v1] :  ? [v2] : (complement(v1) = v2 & complement(all_23_0_23) = v0 & join(v0, v2) = all_47_2_42 & join(all_47_1_41, all_0_2_2) = v1)
% 48.87/19.22  |
% 48.87/19.22  | Instantiating formula (30) with all_23_0_23, all_47_0_40, all_47_1_41, all_0_2_2, all_47_2_42 and discharging atoms complement(all_47_2_42) = all_47_1_41, complement(all_0_2_2) = all_47_0_40, join(all_47_1_41, all_47_0_40) = all_23_0_23, yields:
% 48.87/19.22  | (174)  ? [v0] : (meet(all_47_2_42, all_0_2_2) = v0 & complement(all_23_0_23) = v0)
% 48.87/19.22  |
% 48.87/19.22  | Instantiating formula (15) with all_19_2_21, all_19_2_21, all_37_1_30 and discharging atoms join(all_37_1_30, all_19_2_21) = all_19_2_21, yields:
% 48.87/19.22  | (175)  ? [v0] :  ? [v1] :  ? [v2] : (converse(all_37_1_30) = v1 & converse(all_19_2_21) = v2 & converse(all_19_2_21) = v0 & join(v1, v2) = v0)
% 48.87/19.22  |
% 48.87/19.22  | Instantiating formula (18) with all_23_0_23, all_23_2_25, all_23_1_24, all_0_4_4, all_0_3_3 and discharging atoms complement(all_0_3_3) = all_23_1_24, complement(all_0_4_4) = all_23_2_25, join(all_23_1_24, all_23_2_25) = all_23_0_23, yields:
% 48.87/19.22  | (176)  ? [v0] :  ? [v1] :  ? [v2] : (complement(v1) = v2 & complement(all_23_0_23) = v0 & join(v0, v2) = all_0_3_3 & join(all_23_1_24, all_0_4_4) = v1)
% 48.87/19.22  |
% 48.87/19.22  | Instantiating formula (2) with all_49_0_44, all_21_0_22, all_21_0_22, all_0_5_5, all_0_5_5 and discharging atoms join(all_21_0_22, all_21_0_22) = all_49_0_44, join(all_0_5_5, all_0_5_5) = all_21_0_22, yields:
% 48.87/19.22  | (177)  ? [v0] : (join(all_0_5_5, v0) = all_49_0_44 & join(all_0_5_5, all_21_0_22) = v0)
% 48.87/19.22  |
% 48.87/19.22  | Instantiating formula (25) with all_49_0_44, all_21_0_22, all_0_5_5, all_0_5_5, all_21_0_22 and discharging atoms join(all_21_0_22, all_21_0_22) = all_49_0_44, join(all_0_5_5, all_0_5_5) = all_21_0_22, yields:
% 48.87/19.22  | (178)  ? [v0] : (join(v0, all_0_5_5) = all_49_0_44 & join(all_21_0_22, all_0_5_5) = v0)
% 48.87/19.22  |
% 48.87/19.22  | Instantiating formula (5) with all_57_0_52, all_21_0_22, all_0_5_5 and discharging atoms join(all_21_0_22, all_0_5_5) = all_57_0_52, yields:
% 48.87/19.22  | (179) join(all_0_5_5, all_21_0_22) = all_57_0_52
% 48.87/19.22  |
% 48.87/19.22  | Instantiating formula (2) with all_0_4_4, all_0_2_2, all_35_0_26, all_0_2_2, all_21_0_22 and discharging atoms join(all_21_0_22, all_0_2_2) = all_0_2_2, join(all_0_2_2, all_35_0_26) = all_0_4_4, yields:
% 48.87/19.22  | (180)  ? [v0] : (join(all_21_0_22, v0) = all_0_4_4 & join(all_0_2_2, all_35_0_26) = v0)
% 48.87/19.22  |
% 48.87/19.22  | Instantiating formula (2) with all_0_4_4, all_0_2_2, all_35_0_26, all_0_2_2, all_0_5_5 and discharging atoms join(all_0_2_2, all_35_0_26) = all_0_4_4, join(all_0_5_5, all_0_2_2) = all_0_2_2, yields:
% 48.87/19.22  | (181)  ? [v0] : (join(all_0_2_2, all_35_0_26) = v0 & join(all_0_5_5, v0) = all_0_4_4)
% 48.87/19.22  |
% 48.87/19.22  | Instantiating formula (2) with all_0_4_4, all_0_2_2, all_35_0_26, all_0_2_2, all_57_0_52 and discharging atoms join(all_57_0_52, all_0_2_2) = all_0_2_2, join(all_0_2_2, all_35_0_26) = all_0_4_4, yields:
% 48.87/19.22  | (182)  ? [v0] : (join(all_57_0_52, v0) = all_0_4_4 & join(all_0_2_2, all_35_0_26) = v0)
% 48.87/19.22  |
% 48.87/19.22  | Instantiating formula (2) with all_0_4_4, all_0_2_2, all_35_0_26, all_0_2_2, all_51_0_45 and discharging atoms join(all_51_0_45, all_0_2_2) = all_0_2_2, join(all_0_2_2, all_35_0_26) = all_0_4_4, yields:
% 48.87/19.22  | (183)  ? [v0] : (join(all_51_0_45, v0) = all_0_4_4 & join(all_0_2_2, all_35_0_26) = v0)
% 48.87/19.22  |
% 48.87/19.22  | Instantiating formula (2) with all_0_4_4, all_0_2_2, all_35_0_26, all_0_2_2, all_49_0_44 and discharging atoms join(all_49_0_44, all_0_2_2) = all_0_2_2, join(all_0_2_2, all_35_0_26) = all_0_4_4, yields:
% 48.87/19.22  | (184)  ? [v0] : (join(all_49_0_44, v0) = all_0_4_4 & join(all_0_2_2, all_35_0_26) = v0)
% 48.87/19.22  |
% 48.87/19.22  | Instantiating formula (2) with all_0_2_2, all_0_2_2, all_0_5_5, all_21_0_22, all_0_2_2 and discharging atoms join(all_0_2_2, all_21_0_22) = all_0_2_2, join(all_0_2_2, all_0_5_5) = all_0_2_2, yields:
% 48.87/19.22  | (185)  ? [v0] : (join(all_21_0_22, all_0_5_5) = v0 & join(all_0_2_2, v0) = all_0_2_2)
% 48.87/19.22  |
% 48.87/19.22  | Instantiating formula (5) with all_51_0_45, all_0_5_5, all_21_0_22 and discharging atoms join(all_0_5_5, all_21_0_22) = all_51_0_45, yields:
% 48.87/19.22  | (186) join(all_21_0_22, all_0_5_5) = all_51_0_45
% 48.87/19.22  |
% 48.87/19.22  | Instantiating (176) with all_91_0_75, all_91_1_76, all_91_2_77 yields:
% 48.87/19.22  | (187) complement(all_91_1_76) = all_91_0_75 & complement(all_23_0_23) = all_91_2_77 & join(all_91_2_77, all_91_0_75) = all_0_3_3 & join(all_23_1_24, all_0_4_4) = all_91_1_76
% 48.87/19.22  |
% 48.87/19.22  | Applying alpha-rule on (187) yields:
% 48.87/19.22  | (188) complement(all_91_1_76) = all_91_0_75
% 48.87/19.22  | (189) complement(all_23_0_23) = all_91_2_77
% 48.87/19.22  | (190) join(all_91_2_77, all_91_0_75) = all_0_3_3
% 48.87/19.22  | (191) join(all_23_1_24, all_0_4_4) = all_91_1_76
% 48.87/19.22  |
% 48.87/19.22  | Instantiating (156) with all_101_0_88 yields:
% 48.87/19.22  | (192) join(all_101_0_88, all_0_2_2) = all_0_2_2 & join(all_57_0_52, all_57_0_52) = all_101_0_88
% 48.87/19.22  |
% 48.87/19.22  | Applying alpha-rule on (192) yields:
% 48.87/19.22  | (193) join(all_101_0_88, all_0_2_2) = all_0_2_2
% 48.87/19.22  | (194) join(all_57_0_52, all_57_0_52) = all_101_0_88
% 48.87/19.22  |
% 48.87/19.22  | Instantiating (184) with all_105_0_92 yields:
% 48.87/19.22  | (195) join(all_49_0_44, all_105_0_92) = all_0_4_4 & join(all_0_2_2, all_35_0_26) = all_105_0_92
% 48.87/19.22  |
% 48.87/19.22  | Applying alpha-rule on (195) yields:
% 48.87/19.22  | (196) join(all_49_0_44, all_105_0_92) = all_0_4_4
% 48.87/19.23  | (197) join(all_0_2_2, all_35_0_26) = all_105_0_92
% 48.87/19.23  |
% 48.87/19.23  | Instantiating (181) with all_107_0_93 yields:
% 48.87/19.23  | (198) join(all_0_2_2, all_35_0_26) = all_107_0_93 & join(all_0_5_5, all_107_0_93) = all_0_4_4
% 48.87/19.23  |
% 48.87/19.23  | Applying alpha-rule on (198) yields:
% 48.87/19.23  | (199) join(all_0_2_2, all_35_0_26) = all_107_0_93
% 48.87/19.23  | (200) join(all_0_5_5, all_107_0_93) = all_0_4_4
% 48.87/19.23  |
% 48.87/19.23  | Instantiating (155) with all_111_0_95 yields:
% 48.87/19.23  | (201) join(all_111_0_95, all_0_2_2) = all_0_2_2 & join(all_0_5_5, all_57_0_52) = all_111_0_95
% 48.87/19.23  |
% 48.87/19.23  | Applying alpha-rule on (201) yields:
% 48.87/19.23  | (202) join(all_111_0_95, all_0_2_2) = all_0_2_2
% 48.87/19.23  | (203) join(all_0_5_5, all_57_0_52) = all_111_0_95
% 48.87/19.23  |
% 48.87/19.23  | Instantiating (153) with all_113_0_96 yields:
% 48.87/19.23  | (204) join(all_113_0_96, all_0_2_2) = all_0_2_2 & join(all_21_0_22, all_57_0_52) = all_113_0_96
% 48.87/19.23  |
% 48.87/19.23  | Applying alpha-rule on (204) yields:
% 48.87/19.23  | (205) join(all_113_0_96, all_0_2_2) = all_0_2_2
% 48.87/19.23  | (206) join(all_21_0_22, all_57_0_52) = all_113_0_96
% 48.87/19.23  |
% 48.87/19.23  | Instantiating (154) with all_117_0_100 yields:
% 48.87/19.23  | (207) join(all_117_0_100, all_0_2_2) = all_0_2_2 & join(all_57_0_52, all_21_0_22) = all_117_0_100
% 48.87/19.23  |
% 48.87/19.23  | Applying alpha-rule on (207) yields:
% 48.87/19.23  | (208) join(all_117_0_100, all_0_2_2) = all_0_2_2
% 48.87/19.23  | (209) join(all_57_0_52, all_21_0_22) = all_117_0_100
% 48.87/19.23  |
% 48.87/19.23  | Instantiating (180) with all_119_0_101 yields:
% 48.87/19.23  | (210) join(all_21_0_22, all_119_0_101) = all_0_4_4 & join(all_0_2_2, all_35_0_26) = all_119_0_101
% 48.87/19.23  |
% 48.87/19.23  | Applying alpha-rule on (210) yields:
% 48.87/19.23  | (211) join(all_21_0_22, all_119_0_101) = all_0_4_4
% 48.87/19.23  | (212) join(all_0_2_2, all_35_0_26) = all_119_0_101
% 48.87/19.23  |
% 48.87/19.23  | Instantiating (152) with all_123_0_103, all_123_1_104, all_123_2_105 yields:
% 48.87/19.23  | (213) complement(all_123_0_103) = zero & complement(all_23_0_23) = all_123_2_105 & complement(all_0_2_2) = all_123_1_104 & join(all_123_2_105, all_123_1_104) = all_123_0_103
% 48.87/19.23  |
% 48.87/19.23  | Applying alpha-rule on (213) yields:
% 48.87/19.23  | (214) complement(all_123_0_103) = zero
% 48.87/19.23  | (215) complement(all_23_0_23) = all_123_2_105
% 48.87/19.23  | (216) complement(all_0_2_2) = all_123_1_104
% 48.87/19.23  | (217) join(all_123_2_105, all_123_1_104) = all_123_0_103
% 48.87/19.23  |
% 48.87/19.23  | Instantiating (161) with all_141_0_125 yields:
% 48.87/19.23  | (218) join(all_141_0_125, all_0_2_2) = all_0_2_2 & join(all_51_0_45, all_57_0_52) = all_141_0_125
% 48.87/19.23  |
% 48.87/19.23  | Applying alpha-rule on (218) yields:
% 48.87/19.23  | (219) join(all_141_0_125, all_0_2_2) = all_0_2_2
% 48.87/19.23  | (220) join(all_51_0_45, all_57_0_52) = all_141_0_125
% 48.87/19.23  |
% 48.87/19.23  | Instantiating (157) with all_143_0_126 yields:
% 48.87/19.23  | (221) join(all_143_0_126, all_0_2_2) = all_0_2_2 & join(all_21_0_22, all_51_0_45) = all_143_0_126
% 48.87/19.23  |
% 48.87/19.23  | Applying alpha-rule on (221) yields:
% 48.87/19.23  | (222) join(all_143_0_126, all_0_2_2) = all_0_2_2
% 48.87/19.23  | (223) join(all_21_0_22, all_51_0_45) = all_143_0_126
% 48.87/19.23  |
% 48.87/19.23  | Instantiating (160) with all_147_0_130 yields:
% 48.87/19.23  | (224) join(all_147_0_130, all_0_2_2) = all_0_2_2 & join(all_57_0_52, all_51_0_45) = all_147_0_130
% 48.87/19.23  |
% 48.87/19.23  | Applying alpha-rule on (224) yields:
% 48.87/19.23  | (225) join(all_147_0_130, all_0_2_2) = all_0_2_2
% 48.87/19.23  | (226) join(all_57_0_52, all_51_0_45) = all_147_0_130
% 48.87/19.23  |
% 48.87/19.23  | Instantiating (185) with all_163_0_140 yields:
% 48.87/19.23  | (227) join(all_21_0_22, all_0_5_5) = all_163_0_140 & join(all_0_2_2, all_163_0_140) = all_0_2_2
% 48.87/19.23  |
% 48.87/19.23  | Applying alpha-rule on (227) yields:
% 48.87/19.24  | (228) join(all_21_0_22, all_0_5_5) = all_163_0_140
% 48.87/19.24  | (229) join(all_0_2_2, all_163_0_140) = all_0_2_2
% 48.87/19.24  |
% 48.87/19.24  | Instantiating (170) with all_187_0_165 yields:
% 48.87/19.24  | (230) join(all_187_0_165, all_0_2_2) = all_0_2_2 & join(all_49_0_44, all_51_0_45) = all_187_0_165
% 48.87/19.24  |
% 48.87/19.24  | Applying alpha-rule on (230) yields:
% 48.87/19.24  | (231) join(all_187_0_165, all_0_2_2) = all_0_2_2
% 48.87/19.24  | (232) join(all_49_0_44, all_51_0_45) = all_187_0_165
% 48.87/19.24  |
% 48.87/19.24  | Instantiating (169) with all_189_0_166 yields:
% 48.87/19.24  | (233) join(all_189_0_166, all_0_2_2) = all_0_2_2 & join(all_51_0_45, all_49_0_44) = all_189_0_166
% 48.87/19.24  |
% 48.87/19.24  | Applying alpha-rule on (233) yields:
% 48.87/19.24  | (234) join(all_189_0_166, all_0_2_2) = all_0_2_2
% 48.87/19.24  | (235) join(all_51_0_45, all_49_0_44) = all_189_0_166
% 48.87/19.24  |
% 48.87/19.24  | Instantiating (183) with all_195_0_169 yields:
% 48.87/19.24  | (236) join(all_51_0_45, all_195_0_169) = all_0_4_4 & join(all_0_2_2, all_35_0_26) = all_195_0_169
% 48.87/19.24  |
% 48.87/19.24  | Applying alpha-rule on (236) yields:
% 48.87/19.24  | (237) join(all_51_0_45, all_195_0_169) = all_0_4_4
% 48.87/19.24  | (238) join(all_0_2_2, all_35_0_26) = all_195_0_169
% 48.87/19.24  |
% 48.87/19.24  | Instantiating (182) with all_197_0_170 yields:
% 48.87/19.24  | (239) join(all_57_0_52, all_197_0_170) = all_0_4_4 & join(all_0_2_2, all_35_0_26) = all_197_0_170
% 48.87/19.24  |
% 48.87/19.24  | Applying alpha-rule on (239) yields:
% 48.87/19.24  | (240) join(all_57_0_52, all_197_0_170) = all_0_4_4
% 48.87/19.24  | (241) join(all_0_2_2, all_35_0_26) = all_197_0_170
% 48.87/19.24  |
% 48.87/19.24  | Instantiating (168) with all_199_0_171 yields:
% 48.87/19.24  | (242) join(all_199_0_171, all_0_2_2) = all_0_2_2 & join(all_49_0_44, all_57_0_52) = all_199_0_171
% 48.87/19.24  |
% 48.87/19.24  | Applying alpha-rule on (242) yields:
% 48.87/19.24  | (243) join(all_199_0_171, all_0_2_2) = all_0_2_2
% 48.87/19.24  | (244) join(all_49_0_44, all_57_0_52) = all_199_0_171
% 48.87/19.24  |
% 48.87/19.24  | Instantiating (167) with all_201_0_172 yields:
% 48.87/19.24  | (245) join(all_201_0_172, all_0_2_2) = all_0_2_2 & join(all_57_0_52, all_49_0_44) = all_201_0_172
% 48.87/19.24  |
% 48.87/19.24  | Applying alpha-rule on (245) yields:
% 48.87/19.24  | (246) join(all_201_0_172, all_0_2_2) = all_0_2_2
% 48.87/19.24  | (247) join(all_57_0_52, all_49_0_44) = all_201_0_172
% 48.87/19.24  |
% 48.87/19.24  | Instantiating (165) with all_203_0_173 yields:
% 48.87/19.24  | (248) join(all_203_0_173, all_0_2_2) = all_0_2_2 & join(all_0_5_5, all_49_0_44) = all_203_0_173
% 48.87/19.24  |
% 48.87/19.24  | Applying alpha-rule on (248) yields:
% 48.87/19.24  | (249) join(all_203_0_173, all_0_2_2) = all_0_2_2
% 48.87/19.24  | (250) join(all_0_5_5, all_49_0_44) = all_203_0_173
% 48.87/19.24  |
% 48.87/19.24  | Instantiating (163) with all_205_0_174 yields:
% 48.87/19.24  | (251) join(all_205_0_174, all_0_2_2) = all_0_2_2 & join(all_21_0_22, all_49_0_44) = all_205_0_174
% 48.87/19.24  |
% 48.87/19.24  | Applying alpha-rule on (251) yields:
% 48.87/19.24  | (252) join(all_205_0_174, all_0_2_2) = all_0_2_2
% 48.87/19.24  | (253) join(all_21_0_22, all_49_0_44) = all_205_0_174
% 48.87/19.24  |
% 48.87/19.24  | Instantiating (164) with all_217_0_188 yields:
% 48.87/19.24  | (254) join(all_217_0_188, all_0_2_2) = all_0_2_2 & join(all_49_0_44, all_21_0_22) = all_217_0_188
% 48.87/19.24  |
% 48.87/19.24  | Applying alpha-rule on (254) yields:
% 48.87/19.24  | (255) join(all_217_0_188, all_0_2_2) = all_0_2_2
% 48.87/19.24  | (256) join(all_49_0_44, all_21_0_22) = all_217_0_188
% 48.87/19.24  |
% 48.87/19.24  | Instantiating (166) with all_221_0_190 yields:
% 48.87/19.24  | (257) join(all_221_0_190, all_0_2_2) = all_0_2_2 & join(all_49_0_44, all_0_5_5) = all_221_0_190
% 48.87/19.25  |
% 48.87/19.25  | Applying alpha-rule on (257) yields:
% 48.87/19.25  | (258) join(all_221_0_190, all_0_2_2) = all_0_2_2
% 48.87/19.25  | (259) join(all_49_0_44, all_0_5_5) = all_221_0_190
% 48.87/19.25  |
% 48.87/19.25  | Instantiating (175) with all_233_0_196, all_233_1_197, all_233_2_198 yields:
% 48.87/19.25  | (260) converse(all_37_1_30) = all_233_1_197 & converse(all_19_2_21) = all_233_0_196 & converse(all_19_2_21) = all_233_2_198 & join(all_233_1_197, all_233_0_196) = all_233_2_198
% 48.87/19.25  |
% 48.87/19.25  | Applying alpha-rule on (260) yields:
% 48.87/19.25  | (261) converse(all_37_1_30) = all_233_1_197
% 48.87/19.25  | (262) converse(all_19_2_21) = all_233_0_196
% 48.87/19.25  | (263) converse(all_19_2_21) = all_233_2_198
% 48.87/19.25  | (264) join(all_233_1_197, all_233_0_196) = all_233_2_198
% 48.87/19.25  |
% 48.87/19.25  | Instantiating (178) with all_239_0_201 yields:
% 48.87/19.25  | (265) join(all_239_0_201, all_0_5_5) = all_49_0_44 & join(all_21_0_22, all_0_5_5) = all_239_0_201
% 48.87/19.25  |
% 48.87/19.25  | Applying alpha-rule on (265) yields:
% 48.87/19.25  | (266) join(all_239_0_201, all_0_5_5) = all_49_0_44
% 48.87/19.25  | (267) join(all_21_0_22, all_0_5_5) = all_239_0_201
% 48.87/19.25  |
% 48.87/19.25  | Instantiating (174) with all_255_0_213 yields:
% 48.87/19.25  | (268) meet(all_47_2_42, all_0_2_2) = all_255_0_213 & complement(all_23_0_23) = all_255_0_213
% 48.87/19.25  |
% 48.87/19.25  | Applying alpha-rule on (268) yields:
% 48.87/19.25  | (269) meet(all_47_2_42, all_0_2_2) = all_255_0_213
% 48.87/19.25  | (270) complement(all_23_0_23) = all_255_0_213
% 48.87/19.25  |
% 48.87/19.25  | Instantiating (173) with all_257_0_214, all_257_1_215, all_257_2_216 yields:
% 48.87/19.25  | (271) complement(all_257_1_215) = all_257_0_214 & complement(all_23_0_23) = all_257_2_216 & join(all_257_2_216, all_257_0_214) = all_47_2_42 & join(all_47_1_41, all_0_2_2) = all_257_1_215
% 48.87/19.25  |
% 48.87/19.25  | Applying alpha-rule on (271) yields:
% 48.87/19.25  | (272) complement(all_257_1_215) = all_257_0_214
% 48.87/19.25  | (273) complement(all_23_0_23) = all_257_2_216
% 48.87/19.25  | (274) join(all_257_2_216, all_257_0_214) = all_47_2_42
% 48.87/19.25  | (275) join(all_47_1_41, all_0_2_2) = all_257_1_215
% 48.87/19.25  |
% 48.87/19.25  | Instantiating (171) with all_259_0_217 yields:
% 48.87/19.25  | (276) join(all_259_0_217, all_0_2_2) = all_0_2_2 & join(all_49_0_44, all_49_0_44) = all_259_0_217
% 48.87/19.25  |
% 48.87/19.25  | Applying alpha-rule on (276) yields:
% 48.87/19.25  | (277) join(all_259_0_217, all_0_2_2) = all_0_2_2
% 48.87/19.25  | (278) join(all_49_0_44, all_49_0_44) = all_259_0_217
% 48.87/19.25  |
% 48.87/19.25  | Instantiating (172) with all_261_0_218, all_261_1_219, all_261_2_220, all_261_3_221 yields:
% 48.87/19.25  | (279) complement(all_261_2_220) = all_261_1_219 & complement(all_47_0_40) = all_261_3_221 & complement(all_23_0_23) = all_261_0_218 & join(all_261_1_219, all_261_0_218) = all_47_2_42 & join(all_47_1_41, all_261_3_221) = all_261_2_220
% 48.87/19.25  |
% 48.87/19.25  | Applying alpha-rule on (279) yields:
% 48.87/19.25  | (280) join(all_261_1_219, all_261_0_218) = all_47_2_42
% 48.87/19.25  | (281) complement(all_23_0_23) = all_261_0_218
% 48.87/19.25  | (282) join(all_47_1_41, all_261_3_221) = all_261_2_220
% 48.87/19.25  | (283) complement(all_261_2_220) = all_261_1_219
% 48.87/19.25  | (284) complement(all_47_0_40) = all_261_3_221
% 48.87/19.25  |
% 48.87/19.25  | Instantiating (162) with all_265_0_225 yields:
% 48.87/19.25  | (285) join(all_265_0_225, all_0_2_2) = all_0_2_2 & join(all_51_0_45, all_51_0_45) = all_265_0_225
% 48.87/19.25  |
% 48.87/19.25  | Applying alpha-rule on (285) yields:
% 48.87/19.25  | (286) join(all_265_0_225, all_0_2_2) = all_0_2_2
% 48.87/19.25  | (287) join(all_51_0_45, all_51_0_45) = all_265_0_225
% 48.87/19.25  |
% 48.87/19.25  | Instantiating (159) with all_271_0_228 yields:
% 48.87/19.26  | (288) join(all_271_0_228, all_0_2_2) = all_0_2_2 & join(all_0_5_5, all_51_0_45) = all_271_0_228
% 48.87/19.26  |
% 48.87/19.26  | Applying alpha-rule on (288) yields:
% 48.87/19.26  | (289) join(all_271_0_228, all_0_2_2) = all_0_2_2
% 48.87/19.26  | (290) join(all_0_5_5, all_51_0_45) = all_271_0_228
% 48.87/19.26  |
% 48.87/19.26  | Instantiating (158) with all_275_0_230 yields:
% 48.87/19.26  | (291) join(all_275_0_230, all_0_2_2) = all_0_2_2 & join(all_51_0_45, all_21_0_22) = all_275_0_230
% 48.87/19.26  |
% 48.87/19.26  | Applying alpha-rule on (291) yields:
% 48.87/19.26  | (292) join(all_275_0_230, all_0_2_2) = all_0_2_2
% 48.87/19.26  | (293) join(all_51_0_45, all_21_0_22) = all_275_0_230
% 48.87/19.26  |
% 48.87/19.26  | Instantiating (177) with all_285_0_237 yields:
% 48.87/19.26  | (294) join(all_0_5_5, all_285_0_237) = all_49_0_44 & join(all_0_5_5, all_21_0_22) = all_285_0_237
% 48.87/19.26  |
% 48.87/19.26  | Applying alpha-rule on (294) yields:
% 48.87/19.26  | (295) join(all_0_5_5, all_285_0_237) = all_49_0_44
% 48.87/19.26  | (296) join(all_0_5_5, all_21_0_22) = all_285_0_237
% 48.87/19.26  |
% 48.87/19.26  | Instantiating formula (16) with all_37_1_30, all_21_0_22, all_233_1_197 and discharging atoms converse(all_37_1_30) = all_233_1_197, converse(all_37_1_30) = all_21_0_22, yields:
% 48.87/19.26  | (297) all_233_1_197 = all_21_0_22
% 48.87/19.26  |
% 48.87/19.26  | Instantiating formula (16) with all_19_2_21, all_233_0_196, all_0_2_2 and discharging atoms converse(all_19_2_21) = all_233_0_196, converse(all_19_2_21) = all_0_2_2, yields:
% 48.87/19.26  | (298) all_233_0_196 = all_0_2_2
% 48.87/19.26  |
% 48.87/19.26  | Instantiating formula (16) with all_19_2_21, all_233_2_198, all_233_0_196 and discharging atoms converse(all_19_2_21) = all_233_0_196, converse(all_19_2_21) = all_233_2_198, yields:
% 48.87/19.26  | (299) all_233_0_196 = all_233_2_198
% 48.87/19.26  |
% 48.87/19.26  | Instantiating formula (22) with all_23_0_23, all_261_0_218, all_0_2_2 and discharging atoms complement(all_23_0_23) = all_261_0_218, complement(all_23_0_23) = all_0_2_2, yields:
% 48.87/19.26  | (300) all_261_0_218 = all_0_2_2
% 48.87/19.26  |
% 48.87/19.26  | Instantiating formula (22) with all_23_0_23, all_257_2_216, all_261_0_218 and discharging atoms complement(all_23_0_23) = all_261_0_218, complement(all_23_0_23) = all_257_2_216, yields:
% 48.87/19.26  | (301) all_261_0_218 = all_257_2_216
% 48.87/19.26  |
% 48.87/19.26  | Instantiating formula (22) with all_23_0_23, all_123_2_105, all_261_0_218 and discharging atoms complement(all_23_0_23) = all_261_0_218, complement(all_23_0_23) = all_123_2_105, yields:
% 48.87/19.26  | (302) all_261_0_218 = all_123_2_105
% 48.87/19.26  |
% 48.87/19.26  | Instantiating formula (22) with all_23_0_23, all_123_2_105, all_255_0_213 and discharging atoms complement(all_23_0_23) = all_255_0_213, complement(all_23_0_23) = all_123_2_105, yields:
% 48.87/19.26  | (303) all_255_0_213 = all_123_2_105
% 48.87/19.26  |
% 48.87/19.26  | Instantiating formula (22) with all_23_0_23, all_91_2_77, all_255_0_213 and discharging atoms complement(all_23_0_23) = all_255_0_213, complement(all_23_0_23) = all_91_2_77, yields:
% 48.87/19.26  | (304) all_255_0_213 = all_91_2_77
% 48.87/19.26  |
% 48.87/19.26  | Instantiating formula (6) with all_21_0_22, all_0_5_5, all_239_0_201, all_57_0_52 and discharging atoms join(all_21_0_22, all_0_5_5) = all_239_0_201, join(all_21_0_22, all_0_5_5) = all_57_0_52, yields:
% 48.87/19.26  | (305) all_239_0_201 = all_57_0_52
% 48.87/19.26  |
% 48.87/19.26  | Instantiating formula (6) with all_21_0_22, all_0_5_5, all_163_0_140, all_239_0_201 and discharging atoms join(all_21_0_22, all_0_5_5) = all_239_0_201, join(all_21_0_22, all_0_5_5) = all_163_0_140, yields:
% 48.87/19.26  | (306) all_239_0_201 = all_163_0_140
% 48.87/19.26  |
% 48.87/19.26  | Instantiating formula (6) with all_21_0_22, all_0_5_5, all_51_0_45, all_163_0_140 and discharging atoms join(all_21_0_22, all_0_5_5) = all_163_0_140, join(all_21_0_22, all_0_5_5) = all_51_0_45, yields:
% 48.87/19.26  | (307) all_163_0_140 = all_51_0_45
% 48.87/19.26  |
% 48.87/19.26  | Instantiating formula (6) with all_0_2_2, all_35_0_26, all_195_0_169, all_0_4_4 and discharging atoms join(all_0_2_2, all_35_0_26) = all_195_0_169, join(all_0_2_2, all_35_0_26) = all_0_4_4, yields:
% 48.87/19.26  | (308) all_195_0_169 = all_0_4_4
% 48.87/19.26  |
% 48.87/19.26  | Instantiating formula (6) with all_0_2_2, all_35_0_26, all_195_0_169, all_197_0_170 and discharging atoms join(all_0_2_2, all_35_0_26) = all_197_0_170, join(all_0_2_2, all_35_0_26) = all_195_0_169, yields:
% 48.87/19.26  | (309) all_197_0_170 = all_195_0_169
% 48.87/19.26  |
% 48.87/19.26  | Instantiating formula (6) with all_0_2_2, all_35_0_26, all_119_0_101, all_197_0_170 and discharging atoms join(all_0_2_2, all_35_0_26) = all_197_0_170, join(all_0_2_2, all_35_0_26) = all_119_0_101, yields:
% 48.87/19.26  | (310) all_197_0_170 = all_119_0_101
% 48.87/19.26  |
% 48.87/19.26  | Instantiating formula (6) with all_0_2_2, all_35_0_26, all_107_0_93, all_195_0_169 and discharging atoms join(all_0_2_2, all_35_0_26) = all_195_0_169, join(all_0_2_2, all_35_0_26) = all_107_0_93, yields:
% 48.87/19.26  | (311) all_195_0_169 = all_107_0_93
% 48.87/19.26  |
% 48.87/19.26  | Instantiating formula (6) with all_0_2_2, all_35_0_26, all_105_0_92, all_195_0_169 and discharging atoms join(all_0_2_2, all_35_0_26) = all_195_0_169, join(all_0_2_2, all_35_0_26) = all_105_0_92, yields:
% 48.87/19.26  | (312) all_195_0_169 = all_105_0_92
% 48.87/19.26  |
% 48.87/19.26  | Instantiating formula (6) with all_0_5_5, all_21_0_22, all_57_0_52, all_285_0_237 and discharging atoms join(all_0_5_5, all_21_0_22) = all_285_0_237, join(all_0_5_5, all_21_0_22) = all_57_0_52, yields:
% 48.87/19.26  | (313) all_285_0_237 = all_57_0_52
% 48.87/19.26  |
% 48.87/19.26  | Combining equations (300,301) yields a new equation:
% 48.87/19.26  | (314) all_257_2_216 = all_0_2_2
% 48.87/19.26  |
% 48.87/19.26  | Combining equations (302,301) yields a new equation:
% 48.87/19.26  | (315) all_257_2_216 = all_123_2_105
% 48.87/19.26  |
% 48.87/19.26  | Combining equations (315,314) yields a new equation:
% 48.87/19.26  | (316) all_123_2_105 = all_0_2_2
% 48.87/19.26  |
% 48.87/19.26  | Simplifying 316 yields:
% 48.87/19.26  | (317) all_123_2_105 = all_0_2_2
% 48.87/19.26  |
% 48.87/19.26  | Combining equations (303,304) yields a new equation:
% 48.87/19.26  | (318) all_123_2_105 = all_91_2_77
% 48.87/19.26  |
% 48.87/19.26  | Simplifying 318 yields:
% 48.87/19.26  | (319) all_123_2_105 = all_91_2_77
% 48.87/19.26  |
% 48.87/19.26  | Combining equations (306,305) yields a new equation:
% 48.87/19.26  | (320) all_163_0_140 = all_57_0_52
% 48.87/19.26  |
% 48.87/19.26  | Simplifying 320 yields:
% 48.87/19.26  | (321) all_163_0_140 = all_57_0_52
% 48.87/19.26  |
% 48.87/19.26  | Combining equations (299,298) yields a new equation:
% 48.87/19.26  | (322) all_233_2_198 = all_0_2_2
% 48.87/19.26  |
% 48.87/19.26  | Simplifying 322 yields:
% 48.87/19.26  | (323) all_233_2_198 = all_0_2_2
% 48.87/19.26  |
% 48.87/19.26  | Combining equations (309,310) yields a new equation:
% 48.87/19.26  | (324) all_195_0_169 = all_119_0_101
% 48.87/19.26  |
% 48.87/19.26  | Simplifying 324 yields:
% 48.87/19.26  | (325) all_195_0_169 = all_119_0_101
% 48.87/19.26  |
% 48.87/19.26  | Combining equations (308,325) yields a new equation:
% 48.87/19.26  | (326) all_119_0_101 = all_0_4_4
% 48.87/19.26  |
% 48.87/19.26  | Combining equations (312,325) yields a new equation:
% 48.87/19.26  | (327) all_119_0_101 = all_105_0_92
% 48.87/19.26  |
% 48.87/19.26  | Combining equations (311,325) yields a new equation:
% 48.87/19.26  | (328) all_119_0_101 = all_107_0_93
% 48.87/19.26  |
% 48.87/19.26  | Combining equations (307,321) yields a new equation:
% 48.87/19.26  | (329) all_57_0_52 = all_51_0_45
% 48.87/19.26  |
% 48.87/19.26  | Combining equations (319,317) yields a new equation:
% 48.87/19.26  | (330) all_91_2_77 = all_0_2_2
% 48.87/19.26  |
% 48.87/19.26  | Simplifying 330 yields:
% 48.87/19.26  | (331) all_91_2_77 = all_0_2_2
% 48.87/19.26  |
% 48.87/19.26  | Combining equations (326,328) yields a new equation:
% 48.87/19.26  | (332) all_107_0_93 = all_0_4_4
% 48.87/19.26  |
% 48.87/19.26  | Combining equations (327,328) yields a new equation:
% 48.87/19.26  | (333) all_107_0_93 = all_105_0_92
% 48.87/19.26  |
% 48.87/19.26  | Combining equations (332,333) yields a new equation:
% 48.87/19.26  | (334) all_105_0_92 = all_0_4_4
% 48.87/19.26  |
% 48.87/19.26  | Combining equations (334,333) yields a new equation:
% 48.87/19.26  | (332) all_107_0_93 = all_0_4_4
% 48.87/19.26  |
% 48.87/19.26  | Combining equations (329,313) yields a new equation:
% 48.87/19.26  | (336) all_285_0_237 = all_51_0_45
% 48.87/19.26  |
% 48.87/19.26  | From (297)(298)(323) and (264) follows:
% 48.87/19.26  | (46) join(all_21_0_22, all_0_2_2) = all_0_2_2
% 48.87/19.26  |
% 48.87/19.26  | From (331) and (190) follows:
% 48.87/19.26  | (338) join(all_0_2_2, all_91_0_75) = all_0_3_3
% 48.87/19.26  |
% 48.87/19.26  | From (329)(329) and (194) follows:
% 48.87/19.26  | (339) join(all_51_0_45, all_51_0_45) = all_101_0_88
% 48.87/19.26  |
% 48.87/19.26  | From (329) and (226) follows:
% 48.87/19.26  | (340) join(all_51_0_45, all_51_0_45) = all_147_0_130
% 48.87/19.26  |
% 48.87/19.26  | From (329) and (247) follows:
% 48.87/19.26  | (341) join(all_51_0_45, all_49_0_44) = all_201_0_172
% 48.87/19.27  |
% 48.87/19.27  | From (329) and (209) follows:
% 48.87/19.27  | (342) join(all_51_0_45, all_21_0_22) = all_117_0_100
% 48.87/19.27  |
% 48.87/19.27  | From (329) and (116) follows:
% 48.87/19.27  | (108) join(all_51_0_45, all_0_2_2) = all_0_2_2
% 48.87/19.27  |
% 48.87/19.27  | From (329) and (220) follows:
% 48.87/19.27  | (344) join(all_51_0_45, all_51_0_45) = all_141_0_125
% 48.87/19.27  |
% 48.87/19.27  | From (329) and (244) follows:
% 48.87/19.27  | (345) join(all_49_0_44, all_51_0_45) = all_199_0_171
% 48.87/19.27  |
% 48.87/19.27  | From (329) and (206) follows:
% 48.87/19.27  | (346) join(all_21_0_22, all_51_0_45) = all_113_0_96
% 48.87/19.27  |
% 48.87/19.27  | From (336) and (295) follows:
% 48.87/19.27  | (347) join(all_0_5_5, all_51_0_45) = all_49_0_44
% 48.87/19.27  |
% 48.87/19.27  | From (332) and (200) follows:
% 48.87/19.27  | (348) join(all_0_5_5, all_0_4_4) = all_0_4_4
% 48.87/19.27  |
% 48.87/19.27  | From (329) and (203) follows:
% 48.87/19.27  | (349) join(all_0_5_5, all_51_0_45) = all_111_0_95
% 48.87/19.27  |
% 48.87/19.27  +-Applying beta-rule and splitting (27), into two cases.
% 48.87/19.27  |-Branch one:
% 48.87/19.27  | (350)  ~ (all_0_0_0 = all_0_3_3) & join(all_0_5_5, all_0_3_3) = all_0_0_0
% 48.87/19.27  |
% 48.87/19.27  	| Applying alpha-rule on (350) yields:
% 48.87/19.27  	| (351)  ~ (all_0_0_0 = all_0_3_3)
% 48.87/19.27  	| (352) join(all_0_5_5, all_0_3_3) = all_0_0_0
% 48.87/19.27  	|
% 48.87/19.27  	| Instantiating formula (6) with all_51_0_45, all_51_0_45, all_147_0_130, all_265_0_225 and discharging atoms join(all_51_0_45, all_51_0_45) = all_265_0_225, join(all_51_0_45, all_51_0_45) = all_147_0_130, yields:
% 48.87/19.27  	| (353) all_265_0_225 = all_147_0_130
% 48.87/19.27  	|
% 48.87/19.27  	| Instantiating formula (6) with all_51_0_45, all_51_0_45, all_141_0_125, all_147_0_130 and discharging atoms join(all_51_0_45, all_51_0_45) = all_147_0_130, join(all_51_0_45, all_51_0_45) = all_141_0_125, yields:
% 48.87/19.27  	| (354) all_147_0_130 = all_141_0_125
% 48.87/19.27  	|
% 48.87/19.27  	| Instantiating formula (6) with all_51_0_45, all_51_0_45, all_101_0_88, all_265_0_225 and discharging atoms join(all_51_0_45, all_51_0_45) = all_265_0_225, join(all_51_0_45, all_51_0_45) = all_101_0_88, yields:
% 48.87/19.27  	| (355) all_265_0_225 = all_101_0_88
% 48.87/19.27  	|
% 48.87/19.27  	| Instantiating formula (6) with all_51_0_45, all_49_0_44, all_201_0_172, all_189_0_166 and discharging atoms join(all_51_0_45, all_49_0_44) = all_201_0_172, join(all_51_0_45, all_49_0_44) = all_189_0_166, yields:
% 48.87/19.27  	| (356) all_201_0_172 = all_189_0_166
% 48.87/19.27  	|
% 48.87/19.27  	| Instantiating formula (6) with all_51_0_45, all_21_0_22, all_117_0_100, all_275_0_230 and discharging atoms join(all_51_0_45, all_21_0_22) = all_275_0_230, join(all_51_0_45, all_21_0_22) = all_117_0_100, yields:
% 48.87/19.27  	| (357) all_275_0_230 = all_117_0_100
% 48.87/19.27  	|
% 48.87/19.27  	| Instantiating formula (6) with all_49_0_44, all_51_0_45, all_199_0_171, all_187_0_165 and discharging atoms join(all_49_0_44, all_51_0_45) = all_199_0_171, join(all_49_0_44, all_51_0_45) = all_187_0_165, yields:
% 48.87/19.27  	| (358) all_199_0_171 = all_187_0_165
% 48.87/19.27  	|
% 48.87/19.27  	| Instantiating formula (6) with all_21_0_22, all_51_0_45, all_113_0_96, all_143_0_126 and discharging atoms join(all_21_0_22, all_51_0_45) = all_143_0_126, join(all_21_0_22, all_51_0_45) = all_113_0_96, yields:
% 48.87/19.27  	| (359) all_143_0_126 = all_113_0_96
% 48.87/19.27  	|
% 48.87/19.27  	| Instantiating formula (6) with all_0_5_5, all_51_0_45, all_111_0_95, all_271_0_228 and discharging atoms join(all_0_5_5, all_51_0_45) = all_271_0_228, join(all_0_5_5, all_51_0_45) = all_111_0_95, yields:
% 48.87/19.27  	| (360) all_271_0_228 = all_111_0_95
% 48.87/19.27  	|
% 48.87/19.27  	| Instantiating formula (6) with all_0_5_5, all_51_0_45, all_49_0_44, all_271_0_228 and discharging atoms join(all_0_5_5, all_51_0_45) = all_271_0_228, join(all_0_5_5, all_51_0_45) = all_49_0_44, yields:
% 48.87/19.27  	| (361) all_271_0_228 = all_49_0_44
% 48.87/19.27  	|
% 48.87/19.27  	| Combining equations (360,361) yields a new equation:
% 48.87/19.27  	| (362) all_111_0_95 = all_49_0_44
% 48.87/19.27  	|
% 48.87/19.27  	| Simplifying 362 yields:
% 48.87/19.27  	| (363) all_111_0_95 = all_49_0_44
% 48.87/19.27  	|
% 48.87/19.27  	| Combining equations (353,355) yields a new equation:
% 48.87/19.27  	| (364) all_147_0_130 = all_101_0_88
% 48.87/19.27  	|
% 48.87/19.27  	| Simplifying 364 yields:
% 48.87/19.27  	| (365) all_147_0_130 = all_101_0_88
% 48.87/19.27  	|
% 48.87/19.27  	| Combining equations (354,365) yields a new equation:
% 48.87/19.27  	| (366) all_141_0_125 = all_101_0_88
% 48.87/19.27  	|
% 48.87/19.27  	| Simplifying 366 yields:
% 48.87/19.27  	| (367) all_141_0_125 = all_101_0_88
% 48.87/19.27  	|
% 48.87/19.27  	| From (357) and (292) follows:
% 48.87/19.27  	| (208) join(all_117_0_100, all_0_2_2) = all_0_2_2
% 48.87/19.27  	|
% 48.87/19.27  	| From (356) and (246) follows:
% 48.87/19.27  	| (234) join(all_189_0_166, all_0_2_2) = all_0_2_2
% 48.87/19.27  	|
% 48.87/19.27  	| From (358) and (243) follows:
% 48.87/19.27  	| (231) join(all_187_0_165, all_0_2_2) = all_0_2_2
% 48.87/19.27  	|
% 48.87/19.27  	| From (359) and (222) follows:
% 48.87/19.27  	| (205) join(all_113_0_96, all_0_2_2) = all_0_2_2
% 48.87/19.27  	|
% 48.87/19.27  	| From (367) and (219) follows:
% 48.87/19.27  	| (193) join(all_101_0_88, all_0_2_2) = all_0_2_2
% 48.87/19.27  	|
% 48.87/19.27  	| From (363) and (202) follows:
% 48.87/19.27  	| (105) join(all_49_0_44, all_0_2_2) = all_0_2_2
% 48.87/19.27  	|
% 48.87/19.27  	| Instantiating formula (2) with all_0_3_3, all_0_2_2, all_91_0_75, all_0_2_2, all_51_0_45 and discharging atoms join(all_51_0_45, all_0_2_2) = all_0_2_2, join(all_0_2_2, all_91_0_75) = all_0_3_3, yields:
% 48.87/19.27  	| (374)  ? [v0] : (join(all_51_0_45, v0) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = v0)
% 48.87/19.27  	|
% 48.87/19.27  	| Instantiating formula (2) with all_0_3_3, all_0_2_2, all_91_0_75, all_0_2_2, all_49_0_44 and discharging atoms join(all_49_0_44, all_0_2_2) = all_0_2_2, join(all_0_2_2, all_91_0_75) = all_0_3_3, yields:
% 48.87/19.27  	| (375)  ? [v0] : (join(all_49_0_44, v0) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = v0)
% 48.87/19.27  	|
% 48.87/19.27  	| Instantiating formula (2) with all_0_3_3, all_0_2_2, all_91_0_75, all_0_2_2, all_21_0_22 and discharging atoms join(all_21_0_22, all_0_2_2) = all_0_2_2, join(all_0_2_2, all_91_0_75) = all_0_3_3, yields:
% 48.87/19.27  	| (376)  ? [v0] : (join(all_21_0_22, v0) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = v0)
% 48.87/19.27  	|
% 48.87/19.27  	| Instantiating formula (2) with all_0_3_3, all_0_2_2, all_91_0_75, all_0_2_2, all_0_5_5 and discharging atoms join(all_0_2_2, all_91_0_75) = all_0_3_3, join(all_0_5_5, all_0_2_2) = all_0_2_2, yields:
% 48.87/19.27  	| (377)  ? [v0] : (join(all_0_2_2, all_91_0_75) = v0 & join(all_0_5_5, v0) = all_0_3_3)
% 48.87/19.27  	|
% 48.87/19.27  	| Instantiating formula (2) with all_0_3_3, all_0_2_2, all_91_0_75, all_0_2_2, all_259_0_217 and discharging atoms join(all_259_0_217, all_0_2_2) = all_0_2_2, join(all_0_2_2, all_91_0_75) = all_0_3_3, yields:
% 48.87/19.27  	| (378)  ? [v0] : (join(all_259_0_217, v0) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = v0)
% 48.87/19.27  	|
% 48.87/19.27  	| Instantiating formula (2) with all_0_3_3, all_0_2_2, all_91_0_75, all_0_2_2, all_221_0_190 and discharging atoms join(all_221_0_190, all_0_2_2) = all_0_2_2, join(all_0_2_2, all_91_0_75) = all_0_3_3, yields:
% 48.87/19.27  	| (379)  ? [v0] : (join(all_221_0_190, v0) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = v0)
% 48.87/19.27  	|
% 48.87/19.27  	| Instantiating formula (2) with all_0_3_3, all_0_2_2, all_91_0_75, all_0_2_2, all_217_0_188 and discharging atoms join(all_217_0_188, all_0_2_2) = all_0_2_2, join(all_0_2_2, all_91_0_75) = all_0_3_3, yields:
% 48.87/19.27  	| (380)  ? [v0] : (join(all_217_0_188, v0) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = v0)
% 48.87/19.27  	|
% 48.87/19.27  	| Instantiating formula (2) with all_0_3_3, all_0_2_2, all_91_0_75, all_0_2_2, all_205_0_174 and discharging atoms join(all_205_0_174, all_0_2_2) = all_0_2_2, join(all_0_2_2, all_91_0_75) = all_0_3_3, yields:
% 48.87/19.27  	| (381)  ? [v0] : (join(all_205_0_174, v0) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = v0)
% 48.87/19.27  	|
% 48.87/19.27  	| Instantiating formula (2) with all_0_3_3, all_0_2_2, all_91_0_75, all_0_2_2, all_203_0_173 and discharging atoms join(all_203_0_173, all_0_2_2) = all_0_2_2, join(all_0_2_2, all_91_0_75) = all_0_3_3, yields:
% 48.87/19.27  	| (382)  ? [v0] : (join(all_203_0_173, v0) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = v0)
% 48.87/19.27  	|
% 48.87/19.27  	| Instantiating formula (2) with all_0_3_3, all_0_2_2, all_91_0_75, all_0_2_2, all_189_0_166 and discharging atoms join(all_189_0_166, all_0_2_2) = all_0_2_2, join(all_0_2_2, all_91_0_75) = all_0_3_3, yields:
% 48.87/19.27  	| (383)  ? [v0] : (join(all_189_0_166, v0) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = v0)
% 48.87/19.27  	|
% 48.87/19.27  	| Instantiating formula (2) with all_0_3_3, all_0_2_2, all_91_0_75, all_0_2_2, all_187_0_165 and discharging atoms join(all_187_0_165, all_0_2_2) = all_0_2_2, join(all_0_2_2, all_91_0_75) = all_0_3_3, yields:
% 48.87/19.27  	| (384)  ? [v0] : (join(all_187_0_165, v0) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = v0)
% 48.87/19.27  	|
% 48.87/19.27  	| Instantiating formula (2) with all_0_3_3, all_0_2_2, all_91_0_75, all_0_2_2, all_117_0_100 and discharging atoms join(all_117_0_100, all_0_2_2) = all_0_2_2, join(all_0_2_2, all_91_0_75) = all_0_3_3, yields:
% 48.87/19.27  	| (385)  ? [v0] : (join(all_117_0_100, v0) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = v0)
% 48.87/19.27  	|
% 48.87/19.27  	| Instantiating formula (2) with all_0_3_3, all_0_2_2, all_91_0_75, all_0_2_2, all_113_0_96 and discharging atoms join(all_113_0_96, all_0_2_2) = all_0_2_2, join(all_0_2_2, all_91_0_75) = all_0_3_3, yields:
% 48.87/19.27  	| (386)  ? [v0] : (join(all_113_0_96, v0) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = v0)
% 48.87/19.28  	|
% 48.87/19.28  	| Instantiating formula (2) with all_0_3_3, all_0_2_2, all_91_0_75, all_0_2_2, all_101_0_88 and discharging atoms join(all_101_0_88, all_0_2_2) = all_0_2_2, join(all_0_2_2, all_91_0_75) = all_0_3_3, yields:
% 48.87/19.28  	| (387)  ? [v0] : (join(all_101_0_88, v0) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = v0)
% 48.87/19.28  	|
% 48.87/19.28  	| Instantiating (378) with all_2121_0_1458 yields:
% 48.87/19.28  	| (388) join(all_259_0_217, all_2121_0_1458) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = all_2121_0_1458
% 48.87/19.28  	|
% 48.87/19.28  	| Applying alpha-rule on (388) yields:
% 48.87/19.28  	| (389) join(all_259_0_217, all_2121_0_1458) = all_0_3_3
% 48.87/19.28  	| (390) join(all_0_2_2, all_91_0_75) = all_2121_0_1458
% 48.87/19.28  	|
% 48.87/19.28  	| Instantiating (377) with all_2123_0_1459 yields:
% 48.87/19.28  	| (391) join(all_0_2_2, all_91_0_75) = all_2123_0_1459 & join(all_0_5_5, all_2123_0_1459) = all_0_3_3
% 48.87/19.28  	|
% 48.87/19.28  	| Applying alpha-rule on (391) yields:
% 48.87/19.28  	| (392) join(all_0_2_2, all_91_0_75) = all_2123_0_1459
% 48.87/19.28  	| (393) join(all_0_5_5, all_2123_0_1459) = all_0_3_3
% 48.87/19.28  	|
% 48.87/19.28  	| Instantiating (375) with all_2133_0_1464 yields:
% 48.87/19.28  	| (394) join(all_49_0_44, all_2133_0_1464) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = all_2133_0_1464
% 49.36/19.28  	|
% 49.36/19.28  	| Applying alpha-rule on (394) yields:
% 49.36/19.28  	| (395) join(all_49_0_44, all_2133_0_1464) = all_0_3_3
% 49.36/19.28  	| (396) join(all_0_2_2, all_91_0_75) = all_2133_0_1464
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating (376) with all_2135_0_1465 yields:
% 49.36/19.28  	| (397) join(all_21_0_22, all_2135_0_1465) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = all_2135_0_1465
% 49.36/19.28  	|
% 49.36/19.28  	| Applying alpha-rule on (397) yields:
% 49.36/19.28  	| (398) join(all_21_0_22, all_2135_0_1465) = all_0_3_3
% 49.36/19.28  	| (399) join(all_0_2_2, all_91_0_75) = all_2135_0_1465
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating (374) with all_2155_0_1478 yields:
% 49.36/19.28  	| (400) join(all_51_0_45, all_2155_0_1478) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = all_2155_0_1478
% 49.36/19.28  	|
% 49.36/19.28  	| Applying alpha-rule on (400) yields:
% 49.36/19.28  	| (401) join(all_51_0_45, all_2155_0_1478) = all_0_3_3
% 49.36/19.28  	| (402) join(all_0_2_2, all_91_0_75) = all_2155_0_1478
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating (387) with all_2203_0_1515 yields:
% 49.36/19.28  	| (403) join(all_101_0_88, all_2203_0_1515) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = all_2203_0_1515
% 49.36/19.28  	|
% 49.36/19.28  	| Applying alpha-rule on (403) yields:
% 49.36/19.28  	| (404) join(all_101_0_88, all_2203_0_1515) = all_0_3_3
% 49.36/19.28  	| (405) join(all_0_2_2, all_91_0_75) = all_2203_0_1515
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating (386) with all_2225_0_1530 yields:
% 49.36/19.28  	| (406) join(all_113_0_96, all_2225_0_1530) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = all_2225_0_1530
% 49.36/19.28  	|
% 49.36/19.28  	| Applying alpha-rule on (406) yields:
% 49.36/19.28  	| (407) join(all_113_0_96, all_2225_0_1530) = all_0_3_3
% 49.36/19.28  	| (408) join(all_0_2_2, all_91_0_75) = all_2225_0_1530
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating (385) with all_2227_0_1531 yields:
% 49.36/19.28  	| (409) join(all_117_0_100, all_2227_0_1531) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = all_2227_0_1531
% 49.36/19.28  	|
% 49.36/19.28  	| Applying alpha-rule on (409) yields:
% 49.36/19.28  	| (410) join(all_117_0_100, all_2227_0_1531) = all_0_3_3
% 49.36/19.28  	| (411) join(all_0_2_2, all_91_0_75) = all_2227_0_1531
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating (382) with all_2229_0_1532 yields:
% 49.36/19.28  	| (412) join(all_203_0_173, all_2229_0_1532) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = all_2229_0_1532
% 49.36/19.28  	|
% 49.36/19.28  	| Applying alpha-rule on (412) yields:
% 49.36/19.28  	| (413) join(all_203_0_173, all_2229_0_1532) = all_0_3_3
% 49.36/19.28  	| (414) join(all_0_2_2, all_91_0_75) = all_2229_0_1532
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating (380) with all_2231_0_1533 yields:
% 49.36/19.28  	| (415) join(all_217_0_188, all_2231_0_1533) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = all_2231_0_1533
% 49.36/19.28  	|
% 49.36/19.28  	| Applying alpha-rule on (415) yields:
% 49.36/19.28  	| (416) join(all_217_0_188, all_2231_0_1533) = all_0_3_3
% 49.36/19.28  	| (417) join(all_0_2_2, all_91_0_75) = all_2231_0_1533
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating (379) with all_2239_0_1537 yields:
% 49.36/19.28  	| (418) join(all_221_0_190, all_2239_0_1537) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = all_2239_0_1537
% 49.36/19.28  	|
% 49.36/19.28  	| Applying alpha-rule on (418) yields:
% 49.36/19.28  	| (419) join(all_221_0_190, all_2239_0_1537) = all_0_3_3
% 49.36/19.28  	| (420) join(all_0_2_2, all_91_0_75) = all_2239_0_1537
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating (381) with all_2247_0_1541 yields:
% 49.36/19.28  	| (421) join(all_205_0_174, all_2247_0_1541) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = all_2247_0_1541
% 49.36/19.28  	|
% 49.36/19.28  	| Applying alpha-rule on (421) yields:
% 49.36/19.28  	| (422) join(all_205_0_174, all_2247_0_1541) = all_0_3_3
% 49.36/19.28  	| (423) join(all_0_2_2, all_91_0_75) = all_2247_0_1541
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating (384) with all_2249_0_1542 yields:
% 49.36/19.28  	| (424) join(all_187_0_165, all_2249_0_1542) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = all_2249_0_1542
% 49.36/19.28  	|
% 49.36/19.28  	| Applying alpha-rule on (424) yields:
% 49.36/19.28  	| (425) join(all_187_0_165, all_2249_0_1542) = all_0_3_3
% 49.36/19.28  	| (426) join(all_0_2_2, all_91_0_75) = all_2249_0_1542
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating (383) with all_2311_0_1580 yields:
% 49.36/19.28  	| (427) join(all_189_0_166, all_2311_0_1580) = all_0_3_3 & join(all_0_2_2, all_91_0_75) = all_2311_0_1580
% 49.36/19.28  	|
% 49.36/19.28  	| Applying alpha-rule on (427) yields:
% 49.36/19.28  	| (428) join(all_189_0_166, all_2311_0_1580) = all_0_3_3
% 49.36/19.28  	| (429) join(all_0_2_2, all_91_0_75) = all_2311_0_1580
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating formula (6) with all_0_2_2, all_91_0_75, all_2249_0_1542, all_2311_0_1580 and discharging atoms join(all_0_2_2, all_91_0_75) = all_2311_0_1580, join(all_0_2_2, all_91_0_75) = all_2249_0_1542, yields:
% 49.36/19.28  	| (430) all_2311_0_1580 = all_2249_0_1542
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating formula (6) with all_0_2_2, all_91_0_75, all_2239_0_1537, all_2247_0_1541 and discharging atoms join(all_0_2_2, all_91_0_75) = all_2247_0_1541, join(all_0_2_2, all_91_0_75) = all_2239_0_1537, yields:
% 49.36/19.28  	| (431) all_2247_0_1541 = all_2239_0_1537
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating formula (6) with all_0_2_2, all_91_0_75, all_2231_0_1533, all_2249_0_1542 and discharging atoms join(all_0_2_2, all_91_0_75) = all_2249_0_1542, join(all_0_2_2, all_91_0_75) = all_2231_0_1533, yields:
% 49.36/19.28  	| (432) all_2249_0_1542 = all_2231_0_1533
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating formula (6) with all_0_2_2, all_91_0_75, all_2229_0_1532, all_2239_0_1537 and discharging atoms join(all_0_2_2, all_91_0_75) = all_2239_0_1537, join(all_0_2_2, all_91_0_75) = all_2229_0_1532, yields:
% 49.36/19.28  	| (433) all_2239_0_1537 = all_2229_0_1532
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating formula (6) with all_0_2_2, all_91_0_75, all_2225_0_1530, all_2311_0_1580 and discharging atoms join(all_0_2_2, all_91_0_75) = all_2311_0_1580, join(all_0_2_2, all_91_0_75) = all_2225_0_1530, yields:
% 49.36/19.28  	| (434) all_2311_0_1580 = all_2225_0_1530
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating formula (6) with all_0_2_2, all_91_0_75, all_2203_0_1515, all_0_3_3 and discharging atoms join(all_0_2_2, all_91_0_75) = all_2203_0_1515, join(all_0_2_2, all_91_0_75) = all_0_3_3, yields:
% 49.36/19.28  	| (435) all_2203_0_1515 = all_0_3_3
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating formula (6) with all_0_2_2, all_91_0_75, all_2203_0_1515, all_2229_0_1532 and discharging atoms join(all_0_2_2, all_91_0_75) = all_2229_0_1532, join(all_0_2_2, all_91_0_75) = all_2203_0_1515, yields:
% 49.36/19.28  	| (436) all_2229_0_1532 = all_2203_0_1515
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating formula (6) with all_0_2_2, all_91_0_75, all_2155_0_1478, all_2247_0_1541 and discharging atoms join(all_0_2_2, all_91_0_75) = all_2247_0_1541, join(all_0_2_2, all_91_0_75) = all_2155_0_1478, yields:
% 49.36/19.28  	| (437) all_2247_0_1541 = all_2155_0_1478
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating formula (6) with all_0_2_2, all_91_0_75, all_2135_0_1465, all_2231_0_1533 and discharging atoms join(all_0_2_2, all_91_0_75) = all_2231_0_1533, join(all_0_2_2, all_91_0_75) = all_2135_0_1465, yields:
% 49.36/19.28  	| (438) all_2231_0_1533 = all_2135_0_1465
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating formula (6) with all_0_2_2, all_91_0_75, all_2135_0_1465, all_2203_0_1515 and discharging atoms join(all_0_2_2, all_91_0_75) = all_2203_0_1515, join(all_0_2_2, all_91_0_75) = all_2135_0_1465, yields:
% 49.36/19.28  	| (439) all_2203_0_1515 = all_2135_0_1465
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating formula (6) with all_0_2_2, all_91_0_75, all_2133_0_1464, all_2231_0_1533 and discharging atoms join(all_0_2_2, all_91_0_75) = all_2231_0_1533, join(all_0_2_2, all_91_0_75) = all_2133_0_1464, yields:
% 49.36/19.28  	| (440) all_2231_0_1533 = all_2133_0_1464
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating formula (6) with all_0_2_2, all_91_0_75, all_2123_0_1459, all_2227_0_1531 and discharging atoms join(all_0_2_2, all_91_0_75) = all_2227_0_1531, join(all_0_2_2, all_91_0_75) = all_2123_0_1459, yields:
% 49.36/19.28  	| (441) all_2227_0_1531 = all_2123_0_1459
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating formula (6) with all_0_2_2, all_91_0_75, all_2123_0_1459, all_2135_0_1465 and discharging atoms join(all_0_2_2, all_91_0_75) = all_2135_0_1465, join(all_0_2_2, all_91_0_75) = all_2123_0_1459, yields:
% 49.36/19.28  	| (442) all_2135_0_1465 = all_2123_0_1459
% 49.36/19.28  	|
% 49.36/19.28  	| Instantiating formula (6) with all_0_2_2, all_91_0_75, all_2121_0_1458, all_2227_0_1531 and discharging atoms join(all_0_2_2, all_91_0_75) = all_2227_0_1531, join(all_0_2_2, all_91_0_75) = all_2121_0_1458, yields:
% 49.36/19.28  	| (443) all_2227_0_1531 = all_2121_0_1458
% 49.36/19.28  	|
% 49.36/19.28  	| Combining equations (430,434) yields a new equation:
% 49.36/19.28  	| (444) all_2249_0_1542 = all_2225_0_1530
% 49.36/19.28  	|
% 49.36/19.28  	| Simplifying 444 yields:
% 49.36/19.28  	| (445) all_2249_0_1542 = all_2225_0_1530
% 49.36/19.28  	|
% 49.36/19.28  	| Combining equations (432,445) yields a new equation:
% 49.36/19.28  	| (446) all_2231_0_1533 = all_2225_0_1530
% 49.36/19.29  	|
% 49.36/19.29  	| Simplifying 446 yields:
% 49.36/19.29  	| (447) all_2231_0_1533 = all_2225_0_1530
% 49.36/19.29  	|
% 49.36/19.29  	| Combining equations (431,437) yields a new equation:
% 49.36/19.29  	| (448) all_2239_0_1537 = all_2155_0_1478
% 49.36/19.29  	|
% 49.36/19.29  	| Simplifying 448 yields:
% 49.36/19.29  	| (449) all_2239_0_1537 = all_2155_0_1478
% 49.36/19.29  	|
% 49.36/19.29  	| Combining equations (433,449) yields a new equation:
% 49.36/19.29  	| (450) all_2229_0_1532 = all_2155_0_1478
% 49.36/19.29  	|
% 49.36/19.29  	| Simplifying 450 yields:
% 49.36/19.29  	| (451) all_2229_0_1532 = all_2155_0_1478
% 49.36/19.29  	|
% 49.36/19.29  	| Combining equations (440,447) yields a new equation:
% 49.36/19.29  	| (452) all_2225_0_1530 = all_2133_0_1464
% 49.36/19.29  	|
% 49.36/19.29  	| Combining equations (438,447) yields a new equation:
% 49.36/19.29  	| (453) all_2225_0_1530 = all_2135_0_1465
% 49.36/19.29  	|
% 49.36/19.29  	| Combining equations (436,451) yields a new equation:
% 49.36/19.29  	| (454) all_2203_0_1515 = all_2155_0_1478
% 49.36/19.29  	|
% 49.36/19.29  	| Simplifying 454 yields:
% 49.36/19.29  	| (455) all_2203_0_1515 = all_2155_0_1478
% 49.36/19.29  	|
% 49.36/19.29  	| Combining equations (441,443) yields a new equation:
% 49.36/19.29  	| (456) all_2123_0_1459 = all_2121_0_1458
% 49.36/19.29  	|
% 49.36/19.29  	| Simplifying 456 yields:
% 49.36/19.29  	| (457) all_2123_0_1459 = all_2121_0_1458
% 49.36/19.29  	|
% 49.36/19.29  	| Combining equations (453,452) yields a new equation:
% 49.36/19.29  	| (458) all_2135_0_1465 = all_2133_0_1464
% 49.36/19.29  	|
% 49.36/19.29  	| Simplifying 458 yields:
% 49.36/19.29  	| (459) all_2135_0_1465 = all_2133_0_1464
% 49.36/19.29  	|
% 49.36/19.29  	| Combining equations (439,455) yields a new equation:
% 49.36/19.29  	| (460) all_2155_0_1478 = all_2135_0_1465
% 49.36/19.29  	|
% 49.36/19.29  	| Combining equations (435,455) yields a new equation:
% 49.36/19.29  	| (461) all_2155_0_1478 = all_0_3_3
% 49.36/19.29  	|
% 49.36/19.29  	| Combining equations (460,461) yields a new equation:
% 49.36/19.29  	| (462) all_2135_0_1465 = all_0_3_3
% 49.36/19.29  	|
% 49.36/19.29  	| Simplifying 462 yields:
% 49.36/19.29  	| (463) all_2135_0_1465 = all_0_3_3
% 49.36/19.29  	|
% 49.36/19.29  	| Combining equations (442,459) yields a new equation:
% 49.36/19.29  	| (464) all_2133_0_1464 = all_2123_0_1459
% 49.36/19.29  	|
% 49.36/19.29  	| Combining equations (463,459) yields a new equation:
% 49.36/19.29  	| (465) all_2133_0_1464 = all_0_3_3
% 49.36/19.29  	|
% 49.36/19.29  	| Combining equations (464,465) yields a new equation:
% 49.36/19.29  	| (466) all_2123_0_1459 = all_0_3_3
% 49.36/19.29  	|
% 49.36/19.29  	| Simplifying 466 yields:
% 49.36/19.29  	| (467) all_2123_0_1459 = all_0_3_3
% 49.36/19.29  	|
% 49.36/19.29  	| Combining equations (467,457) yields a new equation:
% 49.36/19.29  	| (468) all_2121_0_1458 = all_0_3_3
% 49.36/19.29  	|
% 49.36/19.29  	| Combining equations (468,457) yields a new equation:
% 49.36/19.29  	| (467) all_2123_0_1459 = all_0_3_3
% 49.36/19.29  	|
% 49.36/19.29  	| From (467) and (393) follows:
% 49.36/19.29  	| (470) join(all_0_5_5, all_0_3_3) = all_0_3_3
% 49.36/19.29  	|
% 49.36/19.29  	| Instantiating formula (6) with all_0_5_5, all_0_3_3, all_0_3_3, all_0_0_0 and discharging atoms join(all_0_5_5, all_0_3_3) = all_0_0_0, join(all_0_5_5, all_0_3_3) = all_0_3_3, yields:
% 49.36/19.29  	| (471) all_0_0_0 = all_0_3_3
% 49.36/19.29  	|
% 49.36/19.29  	| Equations (471) can reduce 351 to:
% 49.36/19.29  	| (472) $false
% 49.36/19.29  	|
% 49.36/19.29  	|-The branch is then unsatisfiable
% 49.36/19.29  |-Branch two:
% 49.36/19.29  | (473)  ~ (all_0_1_1 = all_0_4_4) & join(all_0_5_5, all_0_4_4) = all_0_1_1
% 49.36/19.29  |
% 49.36/19.29  	| Applying alpha-rule on (473) yields:
% 49.36/19.29  	| (474)  ~ (all_0_1_1 = all_0_4_4)
% 49.36/19.29  	| (475) join(all_0_5_5, all_0_4_4) = all_0_1_1
% 49.36/19.29  	|
% 49.36/19.29  	| Instantiating formula (6) with all_0_5_5, all_0_4_4, all_0_4_4, all_0_1_1 and discharging atoms join(all_0_5_5, all_0_4_4) = all_0_1_1, join(all_0_5_5, all_0_4_4) = all_0_4_4, yields:
% 49.36/19.29  	| (476) all_0_1_1 = all_0_4_4
% 49.36/19.29  	|
% 49.36/19.29  	| Equations (476) can reduce 474 to:
% 49.36/19.29  	| (472) $false
% 49.36/19.29  	|
% 49.36/19.29  	|-The branch is then unsatisfiable
% 49.36/19.29  % SZS output end Proof for theBenchmark
% 49.36/19.29  
% 49.36/19.29  18702ms
%------------------------------------------------------------------------------