%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : REL008+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 19:14:07 EDT 2022

% Result   : Theorem 2.83s 1.35s
% Output   : Proof 4.78s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : REL008+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % 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 12:07:22 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.52/0.58          ____       _                          
% 0.52/0.58    ___  / __ \_____(_)___  ________  __________
% 0.52/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.52/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.52/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.52/0.58  
% 0.52/0.58  A Theorem Prover for First-Order Logic
% 0.52/0.58  (ePrincess v.1.0)
% 0.52/0.58  
% 0.52/0.58  (c) Philipp Rümmer, 2009-2015
% 0.52/0.58  (c) Peter Backeman, 2014-2015
% 0.52/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.52/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.52/0.58  Bug reports to peter@backeman.se
% 0.52/0.58  
% 0.52/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.52/0.58  
% 0.52/0.58  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.52/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.44/0.90  Prover 0: Preprocessing ...
% 2.13/1.16  Prover 0: Constructing countermodel ...
% 2.83/1.35  Prover 0: proved (717ms)
% 2.83/1.35  
% 2.83/1.35  No countermodel exists, formula is valid
% 2.83/1.35  % SZS status Theorem for theBenchmark
% 2.83/1.35  
% 2.83/1.35  Generating proof ... found it (size 53)
% 4.34/1.69  
% 4.34/1.69  % SZS output start Proof for theBenchmark
% 4.34/1.69  Assumed formulas after preprocessing and simplification: 
% 4.34/1.69  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : ( ~ (v7 = v4) & composition(v0, v3) = v4 & composition(v0, v2) = v6 & composition(v0, v1) = v5 & join(v5, v6) = v7 & join(v1, v2) = v3 &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] : (v16 = v8 |  ~ (complement(v14) = v15) |  ~ (complement(v12) = v13) |  ~ (complement(v9) = v11) |  ~ (complement(v8) = v10) |  ~ (join(v13, v15) = v16) |  ~ (join(v10, v11) = v12) |  ~ (join(v10, v9) = v14)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v15 = v14 |  ~ (converse(v8) = v10) |  ~ (composition(v10, v12) = v13) |  ~ (composition(v8, v9) = v11) |  ~ (complement(v11) = v12) |  ~ (complement(v9) = v14) |  ~ (join(v13, v14) = v15)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (composition(v9, v10) = v12) |  ~ (composition(v8, v10) = v11) |  ~ (join(v11, v12) = v13) |  ? [v14] : (composition(v14, v10) = v13 & join(v8, v9) = v14)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (converse(v9) = v11) |  ~ (converse(v8) = v10) |  ~ (join(v10, v11) = v12) |  ? [v13] : (converse(v13) = v12 & join(v8, v9) = v13)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (converse(v9) = v10) |  ~ (converse(v8) = v11) |  ~ (composition(v10, v11) = v12) |  ? [v13] : (converse(v13) = v12 & composition(v8, v9) = v13)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (composition(v11, v10) = v12) |  ~ (composition(v8, v9) = v11) |  ? [v13] : (composition(v9, v10) = v13 & composition(v8, v13) = v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (composition(v11, v10) = v12) |  ~ (join(v8, v9) = v11) |  ? [v13] :  ? [v14] : (composition(v9, v10) = v14 & composition(v8, v10) = v13 & join(v13, v14) = v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (composition(v9, v10) = v11) |  ~ (composition(v8, v11) = v12) |  ? [v13] : (composition(v13, v10) = v12 & composition(v8, v9) = v13)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (complement(v9) = v11) |  ~ (complement(v8) = v10) |  ~ (join(v10, v11) = v12) |  ? [v13] : (meet(v8, v9) = v13 & complement(v12) = v13)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (join(v11, v10) = v12) |  ~ (join(v8, v9) = v11) |  ? [v13] : (join(v9, v10) = v13 & join(v8, v13) = v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (join(v9, v10) = v11) |  ~ (join(v8, v11) = v12) |  ? [v13] : (join(v13, v10) = v12 & join(v8, v9) = v13)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (composition(v11, v10) = v9) |  ~ (composition(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (meet(v11, v10) = v9) |  ~ (meet(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (join(v11, v10) = v9) |  ~ (join(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = zero |  ~ (meet(v8, v9) = v10) |  ~ (complement(v8) = v9)) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = top |  ~ (complement(v8) = v9) |  ~ (join(v8, v9) = v10)) &  ! [v8] :  ! [v9] :  ! [v10] : (v9 = v8 |  ~ (converse(v10) = v9) |  ~ (converse(v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] : (v9 = v8 |  ~ (complement(v10) = v9) |  ~ (complement(v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (composition(v8, v9) = v10) |  ? [v11] :  ? [v12] :  ? [v13] : (converse(v10) = v11 & converse(v9) = v12 & converse(v8) = v13 & composition(v12, v13) = v11)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (meet(v8, v9) = v10) |  ? [v11] :  ? [v12] :  ? [v13] : (complement(v13) = v10 & complement(v9) = v12 & complement(v8) = v11 & join(v11, v12) = v13)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (join(v9, v8) = v10) | join(v8, v9) = v10) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (join(v8, v9) = v10) | join(v9, v8) = v10) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (join(v8, v9) = v10) |  ? [v11] :  ? [v12] :  ? [v13] : (converse(v10) = v11 & converse(v9) = v13 & converse(v8) = v12 & join(v12, v13) = v11)) &  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (composition(v8, one) = v9)) &  ! [v8] :  ! [v9] : ( ~ (converse(v8) = v9) | converse(v9) = v8))
% 4.34/1.73  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields:
% 4.34/1.73  | (1)  ~ (all_0_0_0 = all_0_3_3) & composition(all_0_7_7, all_0_4_4) = all_0_3_3 & composition(all_0_7_7, all_0_5_5) = all_0_1_1 & composition(all_0_7_7, all_0_6_6) = all_0_2_2 & join(all_0_2_2, all_0_1_1) = all_0_0_0 & join(all_0_6_6, all_0_5_5) = all_0_4_4 &  ! [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)
% 4.34/1.74  |
% 4.34/1.74  | Applying alpha-rule on (1) yields:
% 4.34/1.74  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (converse(v1) = v2) |  ~ (converse(v0) = v3) |  ~ (composition(v2, v3) = v4) |  ? [v5] : (converse(v5) = v4 & composition(v0, v1) = v5))
% 4.34/1.74  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (join(v1, v2) = v3) |  ~ (join(v0, v3) = v4) |  ? [v5] : (join(v5, v2) = v4 & join(v0, v1) = v5))
% 4.34/1.74  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (composition(v3, v2) = v4) |  ~ (join(v0, v1) = v3) |  ? [v5] :  ? [v6] : (composition(v1, v2) = v6 & composition(v0, v2) = v5 & join(v5, v6) = v4))
% 4.34/1.74  | (5)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (composition(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (converse(v2) = v3 & converse(v1) = v4 & converse(v0) = v5 & composition(v4, v5) = v3))
% 4.34/1.74  | (6)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = top |  ~ (complement(v0) = v1) |  ~ (join(v0, v1) = v2))
% 4.34/1.74  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (composition(v3, v2) = v4) |  ~ (composition(v0, v1) = v3) |  ? [v5] : (composition(v1, v2) = v5 & composition(v0, v5) = v4))
% 4.34/1.74  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (join(v0, v1) = v2) | join(v1, v0) = v2)
% 4.34/1.74  | (9)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (join(v1, v0) = v2) | join(v0, v1) = v2)
% 4.34/1.74  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (converse(v1) = v3) |  ~ (converse(v0) = v2) |  ~ (join(v2, v3) = v4) |  ? [v5] : (converse(v5) = v4 & join(v0, v1) = v5))
% 4.34/1.74  | (11) join(all_0_2_2, all_0_1_1) = all_0_0_0
% 4.34/1.74  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (composition(v3, v2) = v1) |  ~ (composition(v3, v2) = v0))
% 4.34/1.74  | (13)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (complement(v2) = v1) |  ~ (complement(v2) = v0))
% 4.34/1.74  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (join(v3, v2) = v4) |  ~ (join(v0, v1) = v3) |  ? [v5] : (join(v1, v2) = v5 & join(v0, v5) = v4))
% 4.34/1.74  | (15) composition(all_0_7_7, all_0_5_5) = all_0_1_1
% 4.34/1.74  | (16)  ! [v0] :  ! [v1] : ( ~ (converse(v0) = v1) | converse(v1) = v0)
% 4.34/1.74  | (17)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (converse(v2) = v1) |  ~ (converse(v2) = v0))
% 4.34/1.74  | (18) composition(all_0_7_7, all_0_4_4) = all_0_3_3
% 4.34/1.74  | (19)  ! [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))
% 4.34/1.74  | (20)  ! [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))
% 4.34/1.74  | (21)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (meet(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (complement(v5) = v2 & complement(v1) = v4 & complement(v0) = v3 & join(v3, v4) = v5))
% 4.34/1.75  | (22)  ~ (all_0_0_0 = all_0_3_3)
% 4.34/1.75  | (23)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (composition(v0, one) = v1))
% 4.34/1.75  | (24)  ! [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))
% 4.34/1.75  | (25) composition(all_0_7_7, all_0_6_6) = all_0_2_2
% 4.34/1.75  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (join(v3, v2) = v1) |  ~ (join(v3, v2) = v0))
% 4.34/1.75  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (meet(v3, v2) = v1) |  ~ (meet(v3, v2) = v0))
% 4.34/1.75  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (complement(v1) = v3) |  ~ (complement(v0) = v2) |  ~ (join(v2, v3) = v4) |  ? [v5] : (meet(v0, v1) = v5 & complement(v4) = v5))
% 4.34/1.75  | (29)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = zero |  ~ (meet(v0, v1) = v2) |  ~ (complement(v0) = v1))
% 4.34/1.75  | (30) join(all_0_6_6, all_0_5_5) = all_0_4_4
% 4.34/1.75  | (31)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (composition(v1, v2) = v3) |  ~ (composition(v0, v3) = v4) |  ? [v5] : (composition(v5, v2) = v4 & composition(v0, v1) = v5))
% 4.34/1.75  | (32)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (join(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (converse(v2) = v3 & converse(v1) = v5 & converse(v0) = v4 & join(v4, v5) = v3))
% 4.34/1.75  |
% 4.34/1.75  | Instantiating formula (5) with all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms composition(all_0_7_7, all_0_4_4) = all_0_3_3, yields:
% 4.34/1.75  | (33)  ? [v0] :  ? [v1] :  ? [v2] : (converse(all_0_3_3) = v0 & converse(all_0_4_4) = v1 & converse(all_0_7_7) = v2 & composition(v1, v2) = v0)
% 4.34/1.75  |
% 4.34/1.75  | Instantiating formula (5) with all_0_1_1, all_0_5_5, all_0_7_7 and discharging atoms composition(all_0_7_7, all_0_5_5) = all_0_1_1, yields:
% 4.34/1.75  | (34)  ? [v0] :  ? [v1] :  ? [v2] : (converse(all_0_1_1) = v0 & converse(all_0_5_5) = v1 & converse(all_0_7_7) = v2 & composition(v1, v2) = v0)
% 4.34/1.75  |
% 4.34/1.75  | Instantiating formula (5) with all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms composition(all_0_7_7, all_0_6_6) = all_0_2_2, yields:
% 4.34/1.75  | (35)  ? [v0] :  ? [v1] :  ? [v2] : (converse(all_0_2_2) = v0 & converse(all_0_6_6) = v1 & converse(all_0_7_7) = v2 & composition(v1, v2) = v0)
% 4.34/1.75  |
% 4.34/1.75  | Instantiating formula (32) 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:
% 4.34/1.75  | (36)  ? [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)
% 4.34/1.75  |
% 4.34/1.75  | Instantiating formula (32) with all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms join(all_0_6_6, all_0_5_5) = all_0_4_4, yields:
% 4.34/1.75  | (37)  ? [v0] :  ? [v1] :  ? [v2] : (converse(all_0_4_4) = v0 & converse(all_0_5_5) = v2 & converse(all_0_6_6) = v1 & join(v1, v2) = v0)
% 4.34/1.75  |
% 4.34/1.75  | Instantiating (34) with all_9_0_8, all_9_1_9, all_9_2_10 yields:
% 4.34/1.75  | (38) converse(all_0_1_1) = all_9_2_10 & converse(all_0_5_5) = all_9_1_9 & converse(all_0_7_7) = all_9_0_8 & composition(all_9_1_9, all_9_0_8) = all_9_2_10
% 4.34/1.75  |
% 4.34/1.75  | Applying alpha-rule on (38) yields:
% 4.34/1.75  | (39) converse(all_0_1_1) = all_9_2_10
% 4.34/1.75  | (40) converse(all_0_5_5) = all_9_1_9
% 4.34/1.75  | (41) converse(all_0_7_7) = all_9_0_8
% 4.34/1.75  | (42) composition(all_9_1_9, all_9_0_8) = all_9_2_10
% 4.34/1.75  |
% 4.34/1.75  | Instantiating (37) with all_11_0_11, all_11_1_12, all_11_2_13 yields:
% 4.34/1.75  | (43) converse(all_0_4_4) = all_11_2_13 & converse(all_0_5_5) = all_11_0_11 & converse(all_0_6_6) = all_11_1_12 & join(all_11_1_12, all_11_0_11) = all_11_2_13
% 4.34/1.75  |
% 4.34/1.75  | Applying alpha-rule on (43) yields:
% 4.34/1.75  | (44) converse(all_0_4_4) = all_11_2_13
% 4.34/1.75  | (45) converse(all_0_5_5) = all_11_0_11
% 4.34/1.75  | (46) converse(all_0_6_6) = all_11_1_12
% 4.34/1.75  | (47) join(all_11_1_12, all_11_0_11) = all_11_2_13
% 4.34/1.75  |
% 4.34/1.75  | Instantiating (33) with all_13_0_14, all_13_1_15, all_13_2_16 yields:
% 4.34/1.75  | (48) converse(all_0_3_3) = all_13_2_16 & converse(all_0_4_4) = all_13_1_15 & converse(all_0_7_7) = all_13_0_14 & composition(all_13_1_15, all_13_0_14) = all_13_2_16
% 4.69/1.76  |
% 4.69/1.76  | Applying alpha-rule on (48) yields:
% 4.69/1.76  | (49) converse(all_0_3_3) = all_13_2_16
% 4.69/1.76  | (50) converse(all_0_4_4) = all_13_1_15
% 4.69/1.76  | (51) converse(all_0_7_7) = all_13_0_14
% 4.69/1.76  | (52) composition(all_13_1_15, all_13_0_14) = all_13_2_16
% 4.69/1.76  |
% 4.69/1.76  | Instantiating (36) with all_15_0_17, all_15_1_18, all_15_2_19 yields:
% 4.69/1.76  | (53) converse(all_0_0_0) = all_15_2_19 & converse(all_0_1_1) = all_15_0_17 & converse(all_0_2_2) = all_15_1_18 & join(all_15_1_18, all_15_0_17) = all_15_2_19
% 4.69/1.76  |
% 4.69/1.76  | Applying alpha-rule on (53) yields:
% 4.69/1.76  | (54) converse(all_0_0_0) = all_15_2_19
% 4.69/1.76  | (55) converse(all_0_1_1) = all_15_0_17
% 4.69/1.76  | (56) converse(all_0_2_2) = all_15_1_18
% 4.69/1.76  | (57) join(all_15_1_18, all_15_0_17) = all_15_2_19
% 4.69/1.76  |
% 4.69/1.76  | Instantiating (35) with all_17_0_20, all_17_1_21, all_17_2_22 yields:
% 4.69/1.76  | (58) converse(all_0_2_2) = all_17_2_22 & converse(all_0_6_6) = all_17_1_21 & converse(all_0_7_7) = all_17_0_20 & composition(all_17_1_21, all_17_0_20) = all_17_2_22
% 4.69/1.76  |
% 4.69/1.76  | Applying alpha-rule on (58) yields:
% 4.69/1.76  | (59) converse(all_0_2_2) = all_17_2_22
% 4.69/1.76  | (60) converse(all_0_6_6) = all_17_1_21
% 4.69/1.76  | (61) converse(all_0_7_7) = all_17_0_20
% 4.69/1.76  | (62) composition(all_17_1_21, all_17_0_20) = all_17_2_22
% 4.69/1.76  |
% 4.69/1.76  | Instantiating formula (17) with all_0_1_1, all_9_2_10, all_15_0_17 and discharging atoms converse(all_0_1_1) = all_15_0_17, converse(all_0_1_1) = all_9_2_10, yields:
% 4.69/1.76  | (63) all_15_0_17 = all_9_2_10
% 4.69/1.76  |
% 4.69/1.76  | Instantiating formula (17) with all_0_2_2, all_15_1_18, all_17_2_22 and discharging atoms converse(all_0_2_2) = all_17_2_22, converse(all_0_2_2) = all_15_1_18, yields:
% 4.69/1.76  | (64) all_17_2_22 = all_15_1_18
% 4.69/1.76  |
% 4.69/1.76  | Instantiating formula (17) with all_0_4_4, all_11_2_13, all_13_1_15 and discharging atoms converse(all_0_4_4) = all_13_1_15, converse(all_0_4_4) = all_11_2_13, yields:
% 4.69/1.76  | (65) all_13_1_15 = all_11_2_13
% 4.69/1.76  |
% 4.69/1.76  | Instantiating formula (17) with all_0_5_5, all_9_1_9, all_11_0_11 and discharging atoms converse(all_0_5_5) = all_11_0_11, converse(all_0_5_5) = all_9_1_9, yields:
% 4.69/1.76  | (66) all_11_0_11 = all_9_1_9
% 4.69/1.76  |
% 4.69/1.76  | Instantiating formula (17) with all_0_6_6, all_11_1_12, all_17_1_21 and discharging atoms converse(all_0_6_6) = all_17_1_21, converse(all_0_6_6) = all_11_1_12, yields:
% 4.69/1.76  | (67) all_17_1_21 = all_11_1_12
% 4.69/1.76  |
% 4.69/1.76  | Instantiating formula (17) with all_0_7_7, all_13_0_14, all_17_0_20 and discharging atoms converse(all_0_7_7) = all_17_0_20, converse(all_0_7_7) = all_13_0_14, yields:
% 4.69/1.76  | (68) all_17_0_20 = all_13_0_14
% 4.69/1.76  |
% 4.69/1.76  | Instantiating formula (17) with all_0_7_7, all_9_0_8, all_17_0_20 and discharging atoms converse(all_0_7_7) = all_17_0_20, converse(all_0_7_7) = all_9_0_8, yields:
% 4.69/1.76  | (69) all_17_0_20 = all_9_0_8
% 4.69/1.76  |
% 4.69/1.76  | Combining equations (68,69) yields a new equation:
% 4.69/1.76  | (70) all_13_0_14 = all_9_0_8
% 4.69/1.76  |
% 4.69/1.76  | Simplifying 70 yields:
% 4.69/1.76  | (71) all_13_0_14 = all_9_0_8
% 4.69/1.76  |
% 4.69/1.76  | From (67)(69)(64) and (62) follows:
% 4.69/1.76  | (72) composition(all_11_1_12, all_9_0_8) = all_15_1_18
% 4.69/1.76  |
% 4.69/1.76  | From (65)(71) and (52) follows:
% 4.69/1.76  | (73) composition(all_11_2_13, all_9_0_8) = all_13_2_16
% 4.69/1.76  |
% 4.69/1.76  | From (63) and (57) follows:
% 4.69/1.76  | (74) join(all_15_1_18, all_9_2_10) = all_15_2_19
% 4.69/1.76  |
% 4.69/1.76  | From (66) and (47) follows:
% 4.69/1.76  | (75) join(all_11_1_12, all_9_1_9) = all_11_2_13
% 4.69/1.76  |
% 4.69/1.76  | Instantiating formula (16) with all_15_2_19, all_0_0_0 and discharging atoms converse(all_0_0_0) = all_15_2_19, yields:
% 4.69/1.76  | (76) converse(all_15_2_19) = all_0_0_0
% 4.69/1.76  |
% 4.69/1.76  | Instantiating formula (16) with all_13_2_16, all_0_3_3 and discharging atoms converse(all_0_3_3) = all_13_2_16, yields:
% 4.69/1.76  | (77) converse(all_13_2_16) = all_0_3_3
% 4.69/1.76  |
% 4.69/1.76  | Instantiating formula (5) with all_13_2_16, all_9_0_8, all_11_2_13 and discharging atoms composition(all_11_2_13, all_9_0_8) = all_13_2_16, yields:
% 4.69/1.77  | (78)  ? [v0] :  ? [v1] :  ? [v2] : (converse(all_13_2_16) = v0 & converse(all_11_2_13) = v2 & converse(all_9_0_8) = v1 & composition(v1, v2) = v0)
% 4.69/1.77  |
% 4.69/1.77  | Instantiating formula (32) with all_15_2_19, all_9_2_10, all_15_1_18 and discharging atoms join(all_15_1_18, all_9_2_10) = all_15_2_19, yields:
% 4.69/1.77  | (79)  ? [v0] :  ? [v1] :  ? [v2] : (converse(all_15_1_18) = v1 & converse(all_15_2_19) = v0 & converse(all_9_2_10) = v2 & join(v1, v2) = v0)
% 4.69/1.77  |
% 4.69/1.77  | Instantiating formula (4) with all_13_2_16, all_11_2_13, all_9_0_8, all_9_1_9, all_11_1_12 and discharging atoms composition(all_11_2_13, all_9_0_8) = all_13_2_16, join(all_11_1_12, all_9_1_9) = all_11_2_13, yields:
% 4.69/1.77  | (80)  ? [v0] :  ? [v1] : (composition(all_11_1_12, all_9_0_8) = v0 & composition(all_9_1_9, all_9_0_8) = v1 & join(v0, v1) = all_13_2_16)
% 4.69/1.77  |
% 4.69/1.77  | Instantiating (80) with all_31_0_26, all_31_1_27 yields:
% 4.69/1.77  | (81) composition(all_11_1_12, all_9_0_8) = all_31_1_27 & composition(all_9_1_9, all_9_0_8) = all_31_0_26 & join(all_31_1_27, all_31_0_26) = all_13_2_16
% 4.69/1.77  |
% 4.69/1.77  | Applying alpha-rule on (81) yields:
% 4.69/1.77  | (82) composition(all_11_1_12, all_9_0_8) = all_31_1_27
% 4.69/1.77  | (83) composition(all_9_1_9, all_9_0_8) = all_31_0_26
% 4.69/1.77  | (84) join(all_31_1_27, all_31_0_26) = all_13_2_16
% 4.69/1.77  |
% 4.69/1.77  | Instantiating (79) with all_35_0_31, all_35_1_32, all_35_2_33 yields:
% 4.69/1.77  | (85) converse(all_15_1_18) = all_35_1_32 & converse(all_15_2_19) = all_35_2_33 & converse(all_9_2_10) = all_35_0_31 & join(all_35_1_32, all_35_0_31) = all_35_2_33
% 4.69/1.77  |
% 4.69/1.77  | Applying alpha-rule on (85) yields:
% 4.69/1.77  | (86) converse(all_15_1_18) = all_35_1_32
% 4.69/1.77  | (87) converse(all_15_2_19) = all_35_2_33
% 4.69/1.77  | (88) converse(all_9_2_10) = all_35_0_31
% 4.69/1.77  | (89) join(all_35_1_32, all_35_0_31) = all_35_2_33
% 4.69/1.77  |
% 4.69/1.77  | Instantiating (78) with all_41_0_38, all_41_1_39, all_41_2_40 yields:
% 4.69/1.77  | (90) converse(all_13_2_16) = all_41_2_40 & converse(all_11_2_13) = all_41_0_38 & converse(all_9_0_8) = all_41_1_39 & composition(all_41_1_39, all_41_0_38) = all_41_2_40
% 4.69/1.77  |
% 4.69/1.77  | Applying alpha-rule on (90) yields:
% 4.69/1.77  | (91) converse(all_13_2_16) = all_41_2_40
% 4.69/1.77  | (92) converse(all_11_2_13) = all_41_0_38
% 4.69/1.77  | (93) converse(all_9_0_8) = all_41_1_39
% 4.69/1.77  | (94) composition(all_41_1_39, all_41_0_38) = all_41_2_40
% 4.69/1.77  |
% 4.69/1.77  | Instantiating formula (17) with all_15_2_19, all_0_0_0, all_35_2_33 and discharging atoms converse(all_15_2_19) = all_35_2_33, converse(all_15_2_19) = all_0_0_0, yields:
% 4.69/1.77  | (95) all_35_2_33 = all_0_0_0
% 4.69/1.77  |
% 4.69/1.77  | Instantiating formula (17) with all_13_2_16, all_0_3_3, all_41_2_40 and discharging atoms converse(all_13_2_16) = all_41_2_40, converse(all_13_2_16) = all_0_3_3, yields:
% 4.69/1.77  | (96) all_41_2_40 = all_0_3_3
% 4.69/1.77  |
% 4.69/1.77  | Instantiating formula (12) with all_11_1_12, all_9_0_8, all_31_1_27, all_15_1_18 and discharging atoms composition(all_11_1_12, all_9_0_8) = all_31_1_27, composition(all_11_1_12, all_9_0_8) = all_15_1_18, yields:
% 4.69/1.77  | (97) all_31_1_27 = all_15_1_18
% 4.69/1.77  |
% 4.69/1.77  | Instantiating formula (12) with all_9_1_9, all_9_0_8, all_31_0_26, all_9_2_10 and discharging atoms composition(all_9_1_9, all_9_0_8) = all_31_0_26, composition(all_9_1_9, all_9_0_8) = all_9_2_10, yields:
% 4.69/1.77  | (98) all_31_0_26 = all_9_2_10
% 4.69/1.77  |
% 4.69/1.77  | From (95) and (87) follows:
% 4.69/1.77  | (76) converse(all_15_2_19) = all_0_0_0
% 4.69/1.77  |
% 4.69/1.77  | From (96) and (91) follows:
% 4.69/1.77  | (77) converse(all_13_2_16) = all_0_3_3
% 4.69/1.77  |
% 4.69/1.77  | From (97)(98) and (84) follows:
% 4.69/1.77  | (101) join(all_15_1_18, all_9_2_10) = all_13_2_16
% 4.69/1.77  |
% 4.69/1.77  | Instantiating formula (26) with all_15_1_18, all_9_2_10, all_13_2_16, all_15_2_19 and discharging atoms join(all_15_1_18, all_9_2_10) = all_15_2_19, join(all_15_1_18, all_9_2_10) = all_13_2_16, yields:
% 4.78/1.77  | (102) all_15_2_19 = all_13_2_16
% 4.78/1.77  |
% 4.78/1.77  | From (102) and (76) follows:
% 4.78/1.77  | (103) converse(all_13_2_16) = all_0_0_0
% 4.78/1.77  |
% 4.78/1.77  | Instantiating formula (17) with all_13_2_16, all_0_0_0, all_0_3_3 and discharging atoms converse(all_13_2_16) = all_0_0_0, converse(all_13_2_16) = all_0_3_3, yields:
% 4.78/1.77  | (104) all_0_0_0 = all_0_3_3
% 4.78/1.77  |
% 4.78/1.77  | Equations (104) can reduce 22 to:
% 4.78/1.77  | (105) $false
% 4.78/1.77  |
% 4.78/1.78  |-The branch is then unsatisfiable
% 4.78/1.78  % SZS output end Proof for theBenchmark
% 4.78/1.78  
% 4.78/1.78  1185ms
%------------------------------------------------------------------------------