%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO080+1 : TPTP v8.1.0. Released v2.4.0.
% 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 : Sat Jul 16 03:47:28 EDT 2022

% Result   : Theorem 20.73s 6.20s
% Output   : Proof 21.92s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GEO080+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.34  % Computer : n019.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sat Jun 18 11:25:09 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.21/0.60          ____       _                          
% 0.21/0.60    ___  / __ \_____(_)___  ________  __________
% 0.21/0.60   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.21/0.60  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.21/0.60  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.21/0.60  
% 0.21/0.60  A Theorem Prover for First-Order Logic
% 0.21/0.60  (ePrincess v.1.0)
% 0.21/0.60  
% 0.21/0.60  (c) Philipp Rümmer, 2009-2015
% 0.21/0.60  (c) Peter Backeman, 2014-2015
% 0.21/0.60  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.21/0.60  Free software under GNU Lesser General Public License (LGPL).
% 0.21/0.60  Bug reports to peter@backeman.se
% 0.21/0.60  
% 0.21/0.60  For more information, visit http://user.uu.se/~petba168/breu/
% 0.21/0.60  
% 0.21/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.65  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.76/0.95  Prover 0: Preprocessing ...
% 2.12/1.15  Prover 0: Warning: ignoring some quantifiers
% 2.12/1.17  Prover 0: Constructing countermodel ...
% 19.54/5.94  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.86/5.99  Prover 1: Preprocessing ...
% 20.40/6.17  Prover 1: Warning: ignoring some quantifiers
% 20.40/6.18  Prover 1: Constructing countermodel ...
% 20.73/6.20  Prover 1: proved (256ms)
% 20.73/6.20  Prover 0: stopped
% 20.73/6.20  
% 20.73/6.20  No countermodel exists, formula is valid
% 20.73/6.20  % SZS status Theorem for theBenchmark
% 20.73/6.20  
% 20.73/6.20  Generating proof ... Warning: ignoring some quantifiers
% 21.46/6.37  found it (size 11)
% 21.46/6.37  
% 21.46/6.37  % SZS output start Proof for theBenchmark
% 21.46/6.37  Assumed formulas after preprocessing and simplification: 
% 21.46/6.37  | (0)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & part_of(v0, v0) = v1 &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v7 = 0 | v6 = 0 |  ~ (end_point(v8, v3) = 0) |  ~ (part_of(v3, v5) = v7) |  ~ (part_of(v3, v4) = v6) |  ~ (part_of(v3, v2) = 0) |  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : ((end_point(v8, v5) = v10 & end_point(v8, v4) = v9 & ( ~ (v10 = 0) |  ~ (v9 = 0))) | (part_of(v5, v4) = v12 & part_of(v5, v3) = v14 & part_of(v5, v2) = v10 & part_of(v4, v5) = v11 & part_of(v4, v3) = v13 & part_of(v4, v2) = v9 & ( ~ (v10 = 0) |  ~ (v9 = 0) | v14 = 0 | v13 = 0 | v12 = 0 | v11 = 0)))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (closed(v2) = 0) |  ~ (meet(v6, v3, v4) = v7) |  ~ (meet(v5, v3, v4) = 0) |  ? [v8] : (( ~ (v8 = v2) & sum(v3, v4) = v8) | ( ~ (v8 = 0) & end_point(v6, v3) = v8))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (sum(v3, v4) = v2) |  ~ (incident_c(v5, v2) = v6) |  ? [v7] :  ? [v8] : ( ~ (v8 = 0) &  ~ (v7 = 0) & incident_c(v5, v4) = v8 & incident_c(v5, v3) = v7)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v3 = v2 |  ~ (meet(v6, v5, v4) = v3) |  ~ (meet(v6, v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (meet(v2, v3, v4) = 0) |  ~ (end_point(v5, v3) = v6) |  ? [v7] :  ? [v8] :  ? [v9] : (end_point(v5, v4) = v9 & incident_c(v5, v4) = v8 & incident_c(v5, v3) = v7 & ( ~ (v8 = 0) |  ~ (v7 = 0) | (v9 = 0 & v6 = 0)))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = v4 | v5 = v3 | v4 = v3 |  ~ (end_point(v5, v2) = 0) |  ~ (end_point(v4, v2) = 0) |  ~ (end_point(v3, v2) = 0)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (meet(v2, v3, v4) = v5) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : ((v8 = 0 & v7 = 0 & end_point(v6, v4) = v10 & end_point(v6, v3) = v9 & incident_c(v6, v4) = 0 & incident_c(v6, v3) = 0 & ( ~ (v10 = 0) |  ~ (v9 = 0))) | (incident_c(v2, v4) = v7 & incident_c(v2, v3) = v6 & ( ~ (v7 = 0) |  ~ (v6 = 0))))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (part_of(v3, v2) = 0) |  ~ (incident_c(v4, v2) = v5) |  ? [v6] : ( ~ (v6 = 0) & incident_c(v4, v3) = v6)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (inner_point(v5, v4) = v3) |  ~ (inner_point(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (end_point(v5, v4) = v3) |  ~ (end_point(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (sum(v5, v4) = v3) |  ~ (sum(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (part_of(v5, v4) = v3) |  ~ (part_of(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (incident_c(v5, v4) = v3) |  ~ (incident_c(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (end_point(v2, v3) = 0) |  ~ (part_of(v5, v3) = 0) |  ~ (part_of(v4, v3) = 0) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (part_of(v5, v4) = v9 & part_of(v4, v5) = v8 & incident_c(v2, v5) = v7 & incident_c(v2, v4) = v6 & ( ~ (v7 = 0) |  ~ (v6 = 0) | v9 = 0 | v8 = 0))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (sum(v3, v4) = v2) |  ~ (incident_c(v5, v2) = 0) |  ? [v6] :  ? [v7] : (incident_c(v5, v4) = v7 & incident_c(v5, v3) = v6 & (v7 = 0 | v6 = 0))) &  ? [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = v2 |  ~ (sum(v3, v4) = v5) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (incident_c(v6, v4) = v9 & incident_c(v6, v3) = v8 & incident_c(v6, v2) = v7 & ( ~ (v7 = 0) | ( ~ (v9 = 0) &  ~ (v8 = 0))) & (v9 = 0 | v8 = 0 | v7 = 0))) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (inner_point(v2, v3) = v4) |  ? [v5] :  ? [v6] : (end_point(v2, v3) = v6 & incident_c(v2, v3) = v5 & ( ~ (v5 = 0) | v6 = 0))) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (end_point(v2, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 &  ~ (v12 = 0) &  ~ (v11 = 0) & part_of(v6, v5) = v12 & part_of(v6, v3) = 0 & part_of(v5, v6) = v11 & part_of(v5, v3) = 0 & incident_c(v2, v6) = 0 & incident_c(v2, v5) = 0) | ( ~ (v5 = 0) & incident_c(v2, v3) = v5))) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (part_of(v3, v2) = v4) |  ? [v5] :  ? [v6] : ( ~ (v6 = 0) & incident_c(v5, v3) = 0 & incident_c(v5, v2) = v6)) &  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (open(v4) = v3) |  ~ (open(v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (closed(v4) = v3) |  ~ (closed(v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] : (v3 = 0 |  ~ (open(v2) = v3) |  ~ (end_point(v4, v2) = 0)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (meet(v2, v3, v4) = 0) | (incident_c(v2, v4) = 0 & incident_c(v2, v3) = 0)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (part_of(v3, v2) = 0) | open(v3) = 0) &  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (closed(v2) = v3) |  ? [v4] : end_point(v4, v2) = 0) &  ! [v2] :  ! [v3] : ( ~ (closed(v2) = 0) |  ~ (end_point(v3, v2) = 0)) &  ! [v2] :  ! [v3] : ( ~ (inner_point(v3, v2) = 0) |  ? [v4] :  ? [v5] : (meet(v3, v4, v5) = 0 & sum(v4, v5) = v2)) &  ! [v2] :  ! [v3] : ( ~ (inner_point(v2, v3) = 0) |  ? [v4] : ( ~ (v4 = 0) & end_point(v2, v3) = v4 & incident_c(v2, v3) = 0)) &  ! [v2] :  ! [v3] : ( ~ (end_point(v3, v2) = 0) |  ? [v4] : ( ~ (v4 = v3) & end_point(v4, v2) = 0)) &  ! [v2] :  ! [v3] : ( ~ (end_point(v2, v3) = 0) | incident_c(v2, v3) = 0) &  ! [v2] : ( ~ (open(v2) = 0) |  ? [v3] : end_point(v3, v2) = 0) &  ? [v2] :  ? [v3] : (v3 = v2 |  ? [v4] :  ? [v5] :  ? [v6] : (incident_c(v4, v3) = v6 & incident_c(v4, v2) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0)) & (v6 = 0 | v5 = 0))) &  ? [v2] :  ? [v3] : inner_point(v3, v2) = 0)
% 21.46/6.41  | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 21.46/6.41  | (1)  ~ (all_0_0_0 = 0) & part_of(all_0_1_1, all_0_1_1) = all_0_0_0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v5 = 0 | v4 = 0 |  ~ (end_point(v6, v1) = 0) |  ~ (part_of(v1, v3) = v5) |  ~ (part_of(v1, v2) = v4) |  ~ (part_of(v1, v0) = 0) |  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] : ((end_point(v6, v3) = v8 & end_point(v6, v2) = v7 & ( ~ (v8 = 0) |  ~ (v7 = 0))) | (part_of(v3, v2) = v10 & part_of(v3, v1) = v12 & part_of(v3, v0) = v8 & part_of(v2, v3) = v9 & part_of(v2, v1) = v11 & part_of(v2, v0) = v7 & ( ~ (v8 = 0) |  ~ (v7 = 0) | v12 = 0 | v11 = 0 | v10 = 0 | v9 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (closed(v0) = 0) |  ~ (meet(v4, v1, v2) = v5) |  ~ (meet(v3, v1, v2) = 0) |  ? [v6] : (( ~ (v6 = v0) & sum(v1, v2) = v6) | ( ~ (v6 = 0) & end_point(v4, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (sum(v1, v2) = v0) |  ~ (incident_c(v3, v0) = v4) |  ? [v5] :  ? [v6] : ( ~ (v6 = 0) &  ~ (v5 = 0) & incident_c(v3, v2) = v6 & incident_c(v3, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (meet(v4, v3, v2) = v1) |  ~ (meet(v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (meet(v0, v1, v2) = 0) |  ~ (end_point(v3, v1) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (end_point(v3, v2) = v7 & incident_c(v3, v2) = v6 & incident_c(v3, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0) | (v7 = 0 & v4 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 | v3 = v1 | v2 = v1 |  ~ (end_point(v3, v0) = 0) |  ~ (end_point(v2, v0) = 0) |  ~ (end_point(v1, v0) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (meet(v0, v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : ((v6 = 0 & v5 = 0 & end_point(v4, v2) = v8 & end_point(v4, v1) = v7 & incident_c(v4, v2) = 0 & incident_c(v4, v1) = 0 & ( ~ (v8 = 0) |  ~ (v7 = 0))) | (incident_c(v0, v2) = v5 & incident_c(v0, v1) = v4 & ( ~ (v5 = 0) |  ~ (v4 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (part_of(v1, v0) = 0) |  ~ (incident_c(v2, v0) = v3) |  ? [v4] : ( ~ (v4 = 0) & incident_c(v2, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (inner_point(v3, v2) = v1) |  ~ (inner_point(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (end_point(v3, v2) = v1) |  ~ (end_point(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sum(v3, v2) = v1) |  ~ (sum(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (part_of(v3, v2) = v1) |  ~ (part_of(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (incident_c(v3, v2) = v1) |  ~ (incident_c(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (end_point(v0, v1) = 0) |  ~ (part_of(v3, v1) = 0) |  ~ (part_of(v2, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (part_of(v3, v2) = v7 & part_of(v2, v3) = v6 & incident_c(v0, v3) = v5 & incident_c(v0, v2) = v4 & ( ~ (v5 = 0) |  ~ (v4 = 0) | v7 = 0 | v6 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sum(v1, v2) = v0) |  ~ (incident_c(v3, v0) = 0) |  ? [v4] :  ? [v5] : (incident_c(v3, v2) = v5 & incident_c(v3, v1) = v4 & (v5 = 0 | v4 = 0))) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (sum(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (incident_c(v4, v2) = v7 & incident_c(v4, v1) = v6 & incident_c(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) &  ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (inner_point(v0, v1) = v2) |  ? [v3] :  ? [v4] : (end_point(v0, v1) = v4 & incident_c(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (end_point(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : ((v8 = 0 & v7 = 0 & v6 = 0 & v5 = 0 &  ~ (v10 = 0) &  ~ (v9 = 0) & part_of(v4, v3) = v10 & part_of(v4, v1) = 0 & part_of(v3, v4) = v9 & part_of(v3, v1) = 0 & incident_c(v0, v4) = 0 & incident_c(v0, v3) = 0) | ( ~ (v3 = 0) & incident_c(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (part_of(v1, v0) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (open(v2) = v1) |  ~ (open(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (closed(v2) = v1) |  ~ (closed(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = 0 |  ~ (open(v0) = v1) |  ~ (end_point(v2, v0) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (meet(v0, v1, v2) = 0) | (incident_c(v0, v2) = 0 & incident_c(v0, v1) = 0)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (part_of(v1, v0) = 0) | open(v1) = 0) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (closed(v0) = v1) |  ? [v2] : end_point(v2, v0) = 0) &  ! [v0] :  ! [v1] : ( ~ (closed(v0) = 0) |  ~ (end_point(v1, v0) = 0)) &  ! [v0] :  ! [v1] : ( ~ (inner_point(v1, v0) = 0) |  ? [v2] :  ? [v3] : (meet(v1, v2, v3) = 0 & sum(v2, v3) = v0)) &  ! [v0] :  ! [v1] : ( ~ (inner_point(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & end_point(v0, v1) = v2 & incident_c(v0, v1) = 0)) &  ! [v0] :  ! [v1] : ( ~ (end_point(v1, v0) = 0) |  ? [v2] : ( ~ (v2 = v1) & end_point(v2, v0) = 0)) &  ! [v0] :  ! [v1] : ( ~ (end_point(v0, v1) = 0) | incident_c(v0, v1) = 0) &  ! [v0] : ( ~ (open(v0) = 0) |  ? [v1] : end_point(v1, v0) = 0) &  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] :  ? [v3] :  ? [v4] : (incident_c(v2, v1) = v4 & incident_c(v2, v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) &  ? [v0] :  ? [v1] : inner_point(v1, v0) = 0
% 21.46/6.42  |
% 21.46/6.42  | Applying alpha-rule on (1) yields:
% 21.46/6.42  | (2)  ! [v0] :  ! [v1] : ( ~ (inner_point(v1, v0) = 0) |  ? [v2] :  ? [v3] : (meet(v1, v2, v3) = 0 & sum(v2, v3) = v0))
% 21.46/6.42  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v5 = 0 | v4 = 0 |  ~ (end_point(v6, v1) = 0) |  ~ (part_of(v1, v3) = v5) |  ~ (part_of(v1, v2) = v4) |  ~ (part_of(v1, v0) = 0) |  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] : ((end_point(v6, v3) = v8 & end_point(v6, v2) = v7 & ( ~ (v8 = 0) |  ~ (v7 = 0))) | (part_of(v3, v2) = v10 & part_of(v3, v1) = v12 & part_of(v3, v0) = v8 & part_of(v2, v3) = v9 & part_of(v2, v1) = v11 & part_of(v2, v0) = v7 & ( ~ (v8 = 0) |  ~ (v7 = 0) | v12 = 0 | v11 = 0 | v10 = 0 | v9 = 0))))
% 21.46/6.42  | (4) part_of(all_0_1_1, all_0_1_1) = all_0_0_0
% 21.46/6.42  | (5)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = 0 |  ~ (open(v0) = v1) |  ~ (end_point(v2, v0) = 0))
% 21.46/6.42  | (6)  ! [v0] :  ! [v1] : ( ~ (inner_point(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & end_point(v0, v1) = v2 & incident_c(v0, v1) = 0))
% 21.46/6.42  | (7)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (end_point(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : ((v8 = 0 & v7 = 0 & v6 = 0 & v5 = 0 &  ~ (v10 = 0) &  ~ (v9 = 0) & part_of(v4, v3) = v10 & part_of(v4, v1) = 0 & part_of(v3, v4) = v9 & part_of(v3, v1) = 0 & incident_c(v0, v4) = 0 & incident_c(v0, v3) = 0) | ( ~ (v3 = 0) & incident_c(v0, v1) = v3)))
% 21.46/6.42  | (8)  ~ (all_0_0_0 = 0)
% 21.46/6.42  | (9)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (sum(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (incident_c(v4, v2) = v7 & incident_c(v4, v1) = v6 & incident_c(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) &  ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0)))
% 21.46/6.42  | (10)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (meet(v0, v1, v2) = 0) | (incident_c(v0, v2) = 0 & incident_c(v0, v1) = 0))
% 21.46/6.42  | (11)  ! [v0] :  ! [v1] : ( ~ (end_point(v0, v1) = 0) | incident_c(v0, v1) = 0)
% 21.46/6.42  | (12)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (closed(v0) = v1) |  ? [v2] : end_point(v2, v0) = 0)
% 21.46/6.42  | (13)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (part_of(v1, v0) = 0) | open(v1) = 0)
% 21.46/6.42  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 | v3 = v1 | v2 = v1 |  ~ (end_point(v3, v0) = 0) |  ~ (end_point(v2, v0) = 0) |  ~ (end_point(v1, v0) = 0))
% 21.46/6.42  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (inner_point(v3, v2) = v1) |  ~ (inner_point(v3, v2) = v0))
% 21.46/6.42  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (incident_c(v3, v2) = v1) |  ~ (incident_c(v3, v2) = v0))
% 21.46/6.42  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (meet(v0, v1, v2) = 0) |  ~ (end_point(v3, v1) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (end_point(v3, v2) = v7 & incident_c(v3, v2) = v6 & incident_c(v3, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0) | (v7 = 0 & v4 = 0))))
% 21.46/6.42  | (18)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (inner_point(v0, v1) = v2) |  ? [v3] :  ? [v4] : (end_point(v0, v1) = v4 & incident_c(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 21.46/6.42  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sum(v3, v2) = v1) |  ~ (sum(v3, v2) = v0))
% 21.46/6.42  | (20)  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] :  ? [v3] :  ? [v4] : (incident_c(v2, v1) = v4 & incident_c(v2, v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 21.46/6.43  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sum(v1, v2) = v0) |  ~ (incident_c(v3, v0) = 0) |  ? [v4] :  ? [v5] : (incident_c(v3, v2) = v5 & incident_c(v3, v1) = v4 & (v5 = 0 | v4 = 0)))
% 21.46/6.43  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (closed(v0) = 0) |  ~ (meet(v4, v1, v2) = v5) |  ~ (meet(v3, v1, v2) = 0) |  ? [v6] : (( ~ (v6 = v0) & sum(v1, v2) = v6) | ( ~ (v6 = 0) & end_point(v4, v1) = v6)))
% 21.46/6.43  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (meet(v4, v3, v2) = v1) |  ~ (meet(v4, v3, v2) = v0))
% 21.46/6.43  | (24)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (part_of(v1, v0) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4))
% 21.46/6.43  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (end_point(v3, v2) = v1) |  ~ (end_point(v3, v2) = v0))
% 21.46/6.43  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (part_of(v3, v2) = v1) |  ~ (part_of(v3, v2) = v0))
% 21.46/6.43  | (27)  ! [v0] :  ! [v1] : ( ~ (end_point(v1, v0) = 0) |  ? [v2] : ( ~ (v2 = v1) & end_point(v2, v0) = 0))
% 21.46/6.43  | (28)  ! [v0] :  ! [v1] : ( ~ (closed(v0) = 0) |  ~ (end_point(v1, v0) = 0))
% 21.92/6.43  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (part_of(v1, v0) = 0) |  ~ (incident_c(v2, v0) = v3) |  ? [v4] : ( ~ (v4 = 0) & incident_c(v2, v1) = v4))
% 21.92/6.43  | (30)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (open(v2) = v1) |  ~ (open(v2) = v0))
% 21.92/6.43  | (31)  ? [v0] :  ? [v1] : inner_point(v1, v0) = 0
% 21.92/6.43  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (end_point(v0, v1) = 0) |  ~ (part_of(v3, v1) = 0) |  ~ (part_of(v2, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (part_of(v3, v2) = v7 & part_of(v2, v3) = v6 & incident_c(v0, v3) = v5 & incident_c(v0, v2) = v4 & ( ~ (v5 = 0) |  ~ (v4 = 0) | v7 = 0 | v6 = 0)))
% 21.92/6.43  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (meet(v0, v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : ((v6 = 0 & v5 = 0 & end_point(v4, v2) = v8 & end_point(v4, v1) = v7 & incident_c(v4, v2) = 0 & incident_c(v4, v1) = 0 & ( ~ (v8 = 0) |  ~ (v7 = 0))) | (incident_c(v0, v2) = v5 & incident_c(v0, v1) = v4 & ( ~ (v5 = 0) |  ~ (v4 = 0)))))
% 21.92/6.43  | (34)  ! [v0] : ( ~ (open(v0) = 0) |  ? [v1] : end_point(v1, v0) = 0)
% 21.92/6.43  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (sum(v1, v2) = v0) |  ~ (incident_c(v3, v0) = v4) |  ? [v5] :  ? [v6] : ( ~ (v6 = 0) &  ~ (v5 = 0) & incident_c(v3, v2) = v6 & incident_c(v3, v1) = v5))
% 21.92/6.43  | (36)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (closed(v2) = v1) |  ~ (closed(v2) = v0))
% 21.92/6.43  |
% 21.92/6.43  | Instantiating formula (24) with all_0_0_0, all_0_1_1, all_0_1_1 and discharging atoms part_of(all_0_1_1, all_0_1_1) = all_0_0_0, yields:
% 21.92/6.43  | (37) all_0_0_0 = 0 |  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & incident_c(v0, all_0_1_1) = v1 & incident_c(v0, all_0_1_1) = 0)
% 21.92/6.43  |
% 21.92/6.43  +-Applying beta-rule and splitting (37), into two cases.
% 21.92/6.43  |-Branch one:
% 21.92/6.43  | (38) all_0_0_0 = 0
% 21.92/6.43  |
% 21.92/6.43  	| Equations (38) can reduce 8 to:
% 21.92/6.43  	| (39) $false
% 21.92/6.43  	|
% 21.92/6.43  	|-The branch is then unsatisfiable
% 21.92/6.43  |-Branch two:
% 21.92/6.43  | (8)  ~ (all_0_0_0 = 0)
% 21.92/6.43  | (41)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & incident_c(v0, all_0_1_1) = v1 & incident_c(v0, all_0_1_1) = 0)
% 21.92/6.43  |
% 21.92/6.43  	| Instantiating (41) with all_21_0_10, all_21_1_11 yields:
% 21.92/6.43  	| (42)  ~ (all_21_0_10 = 0) & incident_c(all_21_1_11, all_0_1_1) = all_21_0_10 & incident_c(all_21_1_11, all_0_1_1) = 0
% 21.92/6.43  	|
% 21.92/6.43  	| Applying alpha-rule on (42) yields:
% 21.92/6.43  	| (43)  ~ (all_21_0_10 = 0)
% 21.92/6.43  	| (44) incident_c(all_21_1_11, all_0_1_1) = all_21_0_10
% 21.92/6.43  	| (45) incident_c(all_21_1_11, all_0_1_1) = 0
% 21.92/6.43  	|
% 21.92/6.43  	| Instantiating formula (16) with all_21_1_11, all_0_1_1, 0, all_21_0_10 and discharging atoms incident_c(all_21_1_11, all_0_1_1) = all_21_0_10, incident_c(all_21_1_11, all_0_1_1) = 0, yields:
% 21.92/6.43  	| (46) all_21_0_10 = 0
% 21.92/6.43  	|
% 21.92/6.43  	| Equations (46) can reduce 43 to:
% 21.92/6.43  	| (39) $false
% 21.92/6.43  	|
% 21.92/6.43  	|-The branch is then unsatisfiable
% 21.92/6.43  % SZS output end Proof for theBenchmark
% 21.92/6.43  
% 21.92/6.43  5822ms
%------------------------------------------------------------------------------