%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : REL003+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n019.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 19:14:01 EDT 2022

% Result   : Theorem 2.42s 1.29s
% Output   : Proof 4.00s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12  % Problem  : REL003+1 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n019.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Fri Jul  8 13:21:08 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.58/0.59          ____       _                          
% 0.58/0.59    ___  / __ \_____(_)___  ________  __________
% 0.58/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.58/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.58/0.59  
% 0.58/0.59  A Theorem Prover for First-Order Logic
% 0.58/0.59  (ePrincess v.1.0)
% 0.58/0.59  
% 0.58/0.59  (c) Philipp Rümmer, 2009-2015
% 0.58/0.59  (c) Peter Backeman, 2014-2015
% 0.58/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.59  Bug reports to peter@backeman.se
% 0.58/0.59  
% 0.58/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.59  
% 0.58/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.50/0.92  Prover 0: Preprocessing ...
% 1.94/1.16  Prover 0: Constructing countermodel ...
% 2.42/1.29  Prover 0: proved (652ms)
% 2.42/1.29  
% 2.42/1.29  No countermodel exists, formula is valid
% 2.42/1.29  % SZS status Theorem for theBenchmark
% 2.42/1.29  
% 2.42/1.29  Generating proof ... found it (size 38)
% 3.68/1.57  
% 3.68/1.57  % SZS output start Proof for theBenchmark
% 3.68/1.57  Assumed formulas after preprocessing and simplification: 
% 3.68/1.57  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : (converse(v1) = v4 & converse(v0) = v3 & join(v3, v4) = v5 & join(v0, v1) = v2 &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = v6 |  ~ (complement(v12) = v13) |  ~ (complement(v10) = v11) |  ~ (complement(v7) = v9) |  ~ (complement(v6) = v8) |  ~ (join(v11, v13) = v14) |  ~ (join(v8, v9) = v10) |  ~ (join(v8, v7) = v12)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = v12 |  ~ (converse(v6) = v8) |  ~ (composition(v8, v10) = v11) |  ~ (composition(v6, v7) = v9) |  ~ (complement(v9) = v10) |  ~ (complement(v7) = v12) |  ~ (join(v11, v12) = v13)) &  ! [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] : (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] : (v8 = zero |  ~ (meet(v6, v7) = v8) |  ~ (complement(v6) = v7)) &  ! [v6] :  ! [v7] :  ! [v8] : (v8 = top |  ~ (complement(v6) = v7) |  ~ (join(v6, v7) = v8)) &  ! [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] : (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) & ((v5 = v4 &  ~ (v2 = v1)) | (v2 = v1 &  ~ (v5 = v4))))
% 3.68/1.62  | 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:
% 3.68/1.62  | (1) converse(all_0_4_4) = all_0_1_1 & converse(all_0_5_5) = all_0_2_2 & join(all_0_2_2, all_0_1_1) = all_0_0_0 & join(all_0_5_5, all_0_4_4) = all_0_3_3 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = v0 |  ~ (complement(v6) = v7) |  ~ (complement(v4) = v5) |  ~ (complement(v1) = v3) |  ~ (complement(v0) = v2) |  ~ (join(v5, v7) = v8) |  ~ (join(v2, v3) = v4) |  ~ (join(v2, v1) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (converse(v0) = v2) |  ~ (composition(v2, v4) = v5) |  ~ (composition(v0, v1) = v3) |  ~ (complement(v3) = v4) |  ~ (complement(v1) = v6) |  ~ (join(v5, v6) = v7)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (composition(v1, v2) = v4) |  ~ (composition(v0, v2) = v3) |  ~ (join(v3, v4) = v5) |  ? [v6] : (composition(v6, v2) = v5 & join(v0, v1) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (converse(v1) = v3) |  ~ (converse(v0) = v2) |  ~ (join(v2, v3) = v4) |  ? [v5] : (converse(v5) = v4 & join(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (converse(v1) = v2) |  ~ (converse(v0) = v3) |  ~ (composition(v2, v3) = v4) |  ? [v5] : (converse(v5) = v4 & composition(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (composition(v3, v2) = v4) |  ~ (composition(v0, v1) = v3) |  ? [v5] : (composition(v1, v2) = v5 & composition(v0, v5) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (composition(v3, v2) = v4) |  ~ (join(v0, v1) = v3) |  ? [v5] :  ? [v6] : (composition(v1, v2) = v6 & composition(v0, v2) = v5 & join(v5, v6) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (composition(v1, v2) = v3) |  ~ (composition(v0, v3) = v4) |  ? [v5] : (composition(v5, v2) = v4 & composition(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (complement(v1) = v3) |  ~ (complement(v0) = v2) |  ~ (join(v2, v3) = v4) |  ? [v5] : (meet(v0, v1) = v5 & complement(v4) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (join(v3, v2) = v4) |  ~ (join(v0, v1) = v3) |  ? [v5] : (join(v1, v2) = v5 & join(v0, v5) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (join(v1, v2) = v3) |  ~ (join(v0, v3) = v4) |  ? [v5] : (join(v5, v2) = v4 & join(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (composition(v3, v2) = v1) |  ~ (composition(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (meet(v3, v2) = v1) |  ~ (meet(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (join(v3, v2) = v1) |  ~ (join(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = zero |  ~ (meet(v0, v1) = v2) |  ~ (complement(v0) = v1)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = top |  ~ (complement(v0) = v1) |  ~ (join(v0, v1) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (converse(v2) = v1) |  ~ (converse(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (complement(v2) = v1) |  ~ (complement(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (composition(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (converse(v2) = v3 & converse(v1) = v4 & converse(v0) = v5 & composition(v4, v5) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (meet(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (complement(v5) = v2 & complement(v1) = v4 & complement(v0) = v3 & join(v3, v4) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (join(v1, v0) = v2) | join(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (join(v0, v1) = v2) | join(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (join(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (converse(v2) = v3 & converse(v1) = v5 & converse(v0) = v4 & join(v4, v5) = v3)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (composition(v0, one) = v1)) &  ! [v0] :  ! [v1] : ( ~ (converse(v0) = v1) | converse(v1) = v0) & ((all_0_0_0 = all_0_1_1 &  ~ (all_0_3_3 = all_0_4_4)) | (all_0_3_3 = all_0_4_4 &  ~ (all_0_0_0 = all_0_1_1)))
% 4.00/1.63  |
% 4.00/1.63  | Applying alpha-rule on (1) yields:
% 4.00/1.63  | (2)  ! [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))
% 4.00/1.63  | (3)  ! [v0] :  ! [v1] : ( ~ (converse(v0) = v1) | converse(v1) = v0)
% 4.00/1.63  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (composition(v3, v2) = v4) |  ~ (composition(v0, v1) = v3) |  ? [v5] : (composition(v1, v2) = v5 & composition(v0, v5) = v4))
% 4.00/1.63  | (5)  ! [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))
% 4.00/1.63  | (6) converse(all_0_5_5) = all_0_2_2
% 4.00/1.63  | (7)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = top |  ~ (complement(v0) = v1) |  ~ (join(v0, v1) = v2))
% 4.00/1.63  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (meet(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (complement(v5) = v2 & complement(v1) = v4 & complement(v0) = v3 & join(v3, v4) = v5))
% 4.00/1.63  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (converse(v1) = v3) |  ~ (converse(v0) = v2) |  ~ (join(v2, v3) = v4) |  ? [v5] : (converse(v5) = v4 & join(v0, v1) = v5))
% 4.00/1.63  | (10)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (join(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (converse(v2) = v3 & converse(v1) = v5 & converse(v0) = v4 & join(v4, v5) = v3))
% 4.00/1.63  | (11)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (join(v0, v1) = v2) | join(v1, v0) = v2)
% 4.00/1.63  | (12)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (join(v1, v0) = v2) | join(v0, v1) = v2)
% 4.00/1.63  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (join(v3, v2) = v1) |  ~ (join(v3, v2) = v0))
% 4.00/1.63  | (14) (all_0_0_0 = all_0_1_1 &  ~ (all_0_3_3 = all_0_4_4)) | (all_0_3_3 = all_0_4_4 &  ~ (all_0_0_0 = all_0_1_1))
% 4.00/1.63  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = v0 |  ~ (complement(v6) = v7) |  ~ (complement(v4) = v5) |  ~ (complement(v1) = v3) |  ~ (complement(v0) = v2) |  ~ (join(v5, v7) = v8) |  ~ (join(v2, v3) = v4) |  ~ (join(v2, v1) = v6))
% 4.00/1.63  | (16)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = zero |  ~ (meet(v0, v1) = v2) |  ~ (complement(v0) = v1))
% 4.00/1.63  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (converse(v1) = v2) |  ~ (converse(v0) = v3) |  ~ (composition(v2, v3) = v4) |  ? [v5] : (converse(v5) = v4 & composition(v0, v1) = v5))
% 4.00/1.64  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (meet(v3, v2) = v1) |  ~ (meet(v3, v2) = v0))
% 4.00/1.64  | (19)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (converse(v2) = v1) |  ~ (converse(v2) = v0))
% 4.00/1.64  | (20) converse(all_0_4_4) = all_0_1_1
% 4.00/1.64  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (composition(v3, v2) = v1) |  ~ (composition(v3, v2) = v0))
% 4.00/1.64  | (22)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (composition(v0, one) = v1))
% 4.00/1.64  | (23) join(all_0_2_2, all_0_1_1) = all_0_0_0
% 4.00/1.64  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (composition(v1, v2) = v3) |  ~ (composition(v0, v3) = v4) |  ? [v5] : (composition(v5, v2) = v4 & composition(v0, v1) = v5))
% 4.00/1.64  | (25) join(all_0_5_5, all_0_4_4) = all_0_3_3
% 4.00/1.64  | (26)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (complement(v2) = v1) |  ~ (complement(v2) = v0))
% 4.00/1.64  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (converse(v0) = v2) |  ~ (composition(v2, v4) = v5) |  ~ (composition(v0, v1) = v3) |  ~ (complement(v3) = v4) |  ~ (complement(v1) = v6) |  ~ (join(v5, v6) = v7))
% 4.00/1.64  | (28)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (composition(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (converse(v2) = v3 & converse(v1) = v4 & converse(v0) = v5 & composition(v4, v5) = v3))
% 4.00/1.64  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (complement(v1) = v3) |  ~ (complement(v0) = v2) |  ~ (join(v2, v3) = v4) |  ? [v5] : (meet(v0, v1) = v5 & complement(v4) = v5))
% 4.00/1.64  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (join(v1, v2) = v3) |  ~ (join(v0, v3) = v4) |  ? [v5] : (join(v5, v2) = v4 & join(v0, v1) = v5))
% 4.00/1.64  | (31)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (join(v3, v2) = v4) |  ~ (join(v0, v1) = v3) |  ? [v5] : (join(v1, v2) = v5 & join(v0, v5) = v4))
% 4.00/1.64  |
% 4.00/1.64  | Instantiating formula (3) with all_0_1_1, all_0_4_4 and discharging atoms converse(all_0_4_4) = all_0_1_1, yields:
% 4.00/1.64  | (32) converse(all_0_1_1) = all_0_4_4
% 4.00/1.64  |
% 4.00/1.64  | Instantiating formula (3) with all_0_2_2, all_0_5_5 and discharging atoms converse(all_0_5_5) = all_0_2_2, yields:
% 4.00/1.64  | (33) converse(all_0_2_2) = all_0_5_5
% 4.00/1.64  |
% 4.00/1.64  | Instantiating formula (9) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms converse(all_0_4_4) = all_0_1_1, converse(all_0_5_5) = all_0_2_2, join(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 4.00/1.64  | (34)  ? [v0] : (converse(v0) = all_0_0_0 & join(all_0_5_5, all_0_4_4) = v0)
% 4.00/1.64  |
% 4.00/1.64  | Instantiating formula (10) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms join(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 4.00/1.64  | (35)  ? [v0] :  ? [v1] :  ? [v2] : (converse(all_0_0_0) = v0 & converse(all_0_1_1) = v2 & converse(all_0_2_2) = v1 & join(v1, v2) = v0)
% 4.00/1.64  |
% 4.00/1.64  | Instantiating formula (10) with all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms join(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 4.00/1.64  | (36)  ? [v0] :  ? [v1] :  ? [v2] : (converse(all_0_3_3) = v0 & converse(all_0_4_4) = v2 & converse(all_0_5_5) = v1 & join(v1, v2) = v0)
% 4.00/1.65  |
% 4.00/1.65  | Instantiating (36) with all_9_0_6, all_9_1_7, all_9_2_8 yields:
% 4.00/1.65  | (37) converse(all_0_3_3) = all_9_2_8 & converse(all_0_4_4) = all_9_0_6 & converse(all_0_5_5) = all_9_1_7 & join(all_9_1_7, all_9_0_6) = all_9_2_8
% 4.00/1.65  |
% 4.00/1.65  | Applying alpha-rule on (37) yields:
% 4.00/1.65  | (38) converse(all_0_3_3) = all_9_2_8
% 4.00/1.65  | (39) converse(all_0_4_4) = all_9_0_6
% 4.00/1.65  | (40) converse(all_0_5_5) = all_9_1_7
% 4.00/1.65  | (41) join(all_9_1_7, all_9_0_6) = all_9_2_8
% 4.00/1.65  |
% 4.00/1.65  | Instantiating (34) with all_11_0_9 yields:
% 4.00/1.65  | (42) converse(all_11_0_9) = all_0_0_0 & join(all_0_5_5, all_0_4_4) = all_11_0_9
% 4.00/1.65  |
% 4.00/1.65  | Applying alpha-rule on (42) yields:
% 4.00/1.65  | (43) converse(all_11_0_9) = all_0_0_0
% 4.00/1.65  | (44) join(all_0_5_5, all_0_4_4) = all_11_0_9
% 4.00/1.65  |
% 4.00/1.65  | Instantiating (35) with all_13_0_10, all_13_1_11, all_13_2_12 yields:
% 4.00/1.65  | (45) converse(all_0_0_0) = all_13_2_12 & converse(all_0_1_1) = all_13_0_10 & converse(all_0_2_2) = all_13_1_11 & join(all_13_1_11, all_13_0_10) = all_13_2_12
% 4.00/1.65  |
% 4.00/1.65  | Applying alpha-rule on (45) yields:
% 4.00/1.65  | (46) converse(all_0_0_0) = all_13_2_12
% 4.00/1.65  | (47) converse(all_0_1_1) = all_13_0_10
% 4.00/1.65  | (48) converse(all_0_2_2) = all_13_1_11
% 4.00/1.65  | (49) join(all_13_1_11, all_13_0_10) = all_13_2_12
% 4.00/1.65  |
% 4.00/1.65  | Instantiating formula (19) with all_0_1_1, all_0_4_4, all_13_0_10 and discharging atoms converse(all_0_1_1) = all_13_0_10, converse(all_0_1_1) = all_0_4_4, yields:
% 4.00/1.65  | (50) all_13_0_10 = all_0_4_4
% 4.00/1.65  |
% 4.00/1.65  | Instantiating formula (19) with all_0_2_2, all_0_5_5, all_13_1_11 and discharging atoms converse(all_0_2_2) = all_13_1_11, converse(all_0_2_2) = all_0_5_5, yields:
% 4.00/1.65  | (51) all_13_1_11 = all_0_5_5
% 4.00/1.65  |
% 4.00/1.65  | Instantiating formula (19) with all_0_4_4, all_9_0_6, all_0_1_1 and discharging atoms converse(all_0_4_4) = all_9_0_6, converse(all_0_4_4) = all_0_1_1, yields:
% 4.00/1.65  | (52) all_9_0_6 = all_0_1_1
% 4.00/1.65  |
% 4.00/1.65  | Instantiating formula (19) with all_0_5_5, all_9_1_7, all_0_2_2 and discharging atoms converse(all_0_5_5) = all_9_1_7, converse(all_0_5_5) = all_0_2_2, yields:
% 4.00/1.65  | (53) all_9_1_7 = all_0_2_2
% 4.00/1.65  |
% 4.00/1.65  | Instantiating formula (13) with all_0_5_5, all_0_4_4, all_11_0_9, all_0_3_3 and discharging atoms join(all_0_5_5, all_0_4_4) = all_11_0_9, join(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 4.00/1.65  | (54) all_11_0_9 = all_0_3_3
% 4.00/1.65  |
% 4.00/1.65  | From (50) and (47) follows:
% 4.00/1.65  | (32) converse(all_0_1_1) = all_0_4_4
% 4.00/1.65  |
% 4.00/1.65  | From (52) and (39) follows:
% 4.00/1.65  | (20) converse(all_0_4_4) = all_0_1_1
% 4.00/1.65  |
% 4.00/1.65  | From (51)(50) and (49) follows:
% 4.00/1.65  | (57) join(all_0_5_5, all_0_4_4) = all_13_2_12
% 4.00/1.65  |
% 4.00/1.65  | From (53)(52) and (41) follows:
% 4.00/1.65  | (58) join(all_0_2_2, all_0_1_1) = all_9_2_8
% 4.00/1.65  |
% 4.00/1.65  | From (54) and (44) follows:
% 4.00/1.65  | (25) join(all_0_5_5, all_0_4_4) = all_0_3_3
% 4.00/1.65  |
% 4.00/1.65  | Instantiating formula (13) with all_0_2_2, all_0_1_1, all_9_2_8, all_0_0_0 and discharging atoms join(all_0_2_2, all_0_1_1) = all_9_2_8, join(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 4.00/1.65  | (60) all_9_2_8 = all_0_0_0
% 4.00/1.65  |
% 4.00/1.65  | Instantiating formula (13) with all_0_5_5, all_0_4_4, all_13_2_12, all_0_3_3 and discharging atoms join(all_0_5_5, all_0_4_4) = all_13_2_12, join(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 4.00/1.65  | (61) all_13_2_12 = all_0_3_3
% 4.00/1.65  |
% 4.00/1.65  | From (61) and (46) follows:
% 4.00/1.65  | (62) converse(all_0_0_0) = all_0_3_3
% 4.00/1.65  |
% 4.00/1.65  | From (60) and (38) follows:
% 4.00/1.66  | (63) converse(all_0_3_3) = all_0_0_0
% 4.00/1.66  |
% 4.00/1.66  +-Applying beta-rule and splitting (14), into two cases.
% 4.00/1.66  |-Branch one:
% 4.00/1.66  | (64) all_0_0_0 = all_0_1_1 &  ~ (all_0_3_3 = all_0_4_4)
% 4.00/1.66  |
% 4.00/1.66  	| Applying alpha-rule on (64) yields:
% 4.00/1.66  	| (65) all_0_0_0 = all_0_1_1
% 4.00/1.66  	| (66)  ~ (all_0_3_3 = all_0_4_4)
% 4.00/1.66  	|
% 4.00/1.66  	| From (65) and (62) follows:
% 4.00/1.66  	| (67) converse(all_0_1_1) = all_0_3_3
% 4.00/1.66  	|
% 4.00/1.66  	| Instantiating formula (19) with all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms converse(all_0_1_1) = all_0_3_3, converse(all_0_1_1) = all_0_4_4, yields:
% 4.00/1.66  	| (68) all_0_3_3 = all_0_4_4
% 4.00/1.66  	|
% 4.00/1.66  	| Equations (68) can reduce 66 to:
% 4.00/1.66  	| (69) $false
% 4.00/1.66  	|
% 4.00/1.66  	|-The branch is then unsatisfiable
% 4.00/1.66  |-Branch two:
% 4.00/1.66  | (70) all_0_3_3 = all_0_4_4 &  ~ (all_0_0_0 = all_0_1_1)
% 4.00/1.66  |
% 4.00/1.66  	| Applying alpha-rule on (70) yields:
% 4.00/1.66  	| (68) all_0_3_3 = all_0_4_4
% 4.00/1.66  	| (72)  ~ (all_0_0_0 = all_0_1_1)
% 4.00/1.66  	|
% 4.00/1.66  	| From (68) and (63) follows:
% 4.00/1.66  	| (73) converse(all_0_4_4) = all_0_0_0
% 4.00/1.66  	|
% 4.00/1.66  	| Instantiating formula (19) with all_0_4_4, all_0_0_0, all_0_1_1 and discharging atoms converse(all_0_4_4) = all_0_0_0, converse(all_0_4_4) = all_0_1_1, yields:
% 4.00/1.66  	| (65) all_0_0_0 = all_0_1_1
% 4.00/1.66  	|
% 4.00/1.66  	| Equations (65) can reduce 72 to:
% 4.00/1.66  	| (69) $false
% 4.00/1.66  	|
% 4.00/1.66  	|-The branch is then unsatisfiable
% 4.00/1.66  % SZS output end Proof for theBenchmark
% 4.00/1.66  
% 4.00/1.66  1059ms
%------------------------------------------------------------------------------