%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO081+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n007.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 19.05s 6.19s
% Output   : Proof 20.54s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : GEO081+1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n007.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 : Sat Jun 18 00:44:27 EDT 2022
% 0.12/0.34  % 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 ...
% 0.71/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.64/0.97  Prover 0: Preprocessing ...
% 2.26/1.20  Prover 0: Warning: ignoring some quantifiers
% 2.38/1.23  Prover 0: Constructing countermodel ...
% 17.80/5.93  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 17.80/5.98  Prover 1: Preprocessing ...
% 18.56/6.10  Prover 1: Warning: ignoring some quantifiers
% 18.56/6.11  Prover 1: Constructing countermodel ...
% 19.05/6.19  Prover 1: proved (255ms)
% 19.05/6.19  Prover 0: stopped
% 19.05/6.19  
% 19.05/6.19  No countermodel exists, formula is valid
% 19.05/6.19  % SZS status Theorem for theBenchmark
% 19.05/6.19  
% 19.05/6.19  Generating proof ... Warning: ignoring some quantifiers
% 20.06/6.47  found it (size 23)
% 20.06/6.47  
% 20.06/6.47  % SZS output start Proof for theBenchmark
% 20.06/6.47  Assumed formulas after preprocessing and simplification: 
% 20.06/6.47  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & part_of(v1, v2) = 0 & part_of(v0, v2) = v3 & part_of(v0, v1) = 0 &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v9 = 0 | v8 = 0 |  ~ (end_point(v10, v5) = 0) |  ~ (part_of(v5, v7) = v9) |  ~ (part_of(v5, v6) = v8) |  ~ (part_of(v5, v4) = 0) |  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] :  ? [v16] : ((end_point(v10, v7) = v12 & end_point(v10, v6) = v11 & ( ~ (v12 = 0) |  ~ (v11 = 0))) | (part_of(v7, v6) = v14 & part_of(v7, v5) = v16 & part_of(v7, v4) = v12 & part_of(v6, v7) = v13 & part_of(v6, v5) = v15 & part_of(v6, v4) = v11 & ( ~ (v12 = 0) |  ~ (v11 = 0) | v16 = 0 | v15 = 0 | v14 = 0 | v13 = 0)))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (closed(v4) = 0) |  ~ (meet(v8, v5, v6) = v9) |  ~ (meet(v7, v5, v6) = 0) |  ? [v10] : (( ~ (v10 = v4) & sum(v5, v6) = v10) | ( ~ (v10 = 0) & end_point(v8, v5) = v10))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (sum(v5, v6) = v4) |  ~ (incident_c(v7, v4) = v8) |  ? [v9] :  ? [v10] : ( ~ (v10 = 0) &  ~ (v9 = 0) & incident_c(v7, v6) = v10 & incident_c(v7, v5) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v5 = v4 |  ~ (meet(v8, v7, v6) = v5) |  ~ (meet(v8, v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (meet(v4, v5, v6) = 0) |  ~ (end_point(v7, v5) = v8) |  ? [v9] :  ? [v10] :  ? [v11] : (end_point(v7, v6) = v11 & incident_c(v7, v6) = v10 & incident_c(v7, v5) = v9 & ( ~ (v10 = 0) |  ~ (v9 = 0) | (v11 = 0 & v8 = 0)))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = v6 | v7 = v5 | v6 = v5 |  ~ (end_point(v7, v4) = 0) |  ~ (end_point(v6, v4) = 0) |  ~ (end_point(v5, v4) = 0)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (meet(v4, v5, v6) = v7) |  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] : ((v10 = 0 & v9 = 0 & end_point(v8, v6) = v12 & end_point(v8, v5) = v11 & incident_c(v8, v6) = 0 & incident_c(v8, v5) = 0 & ( ~ (v12 = 0) |  ~ (v11 = 0))) | (incident_c(v4, v6) = v9 & incident_c(v4, v5) = v8 & ( ~ (v9 = 0) |  ~ (v8 = 0))))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (part_of(v5, v4) = 0) |  ~ (incident_c(v6, v4) = v7) |  ? [v8] : ( ~ (v8 = 0) & incident_c(v6, v5) = v8)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (inner_point(v7, v6) = v5) |  ~ (inner_point(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (end_point(v7, v6) = v5) |  ~ (end_point(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (sum(v7, v6) = v5) |  ~ (sum(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (part_of(v7, v6) = v5) |  ~ (part_of(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (incident_c(v7, v6) = v5) |  ~ (incident_c(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (end_point(v4, v5) = 0) |  ~ (part_of(v7, v5) = 0) |  ~ (part_of(v6, v5) = 0) |  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] : (part_of(v7, v6) = v11 & part_of(v6, v7) = v10 & incident_c(v4, v7) = v9 & incident_c(v4, v6) = v8 & ( ~ (v9 = 0) |  ~ (v8 = 0) | v11 = 0 | v10 = 0))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (sum(v5, v6) = v4) |  ~ (incident_c(v7, v4) = 0) |  ? [v8] :  ? [v9] : (incident_c(v7, v6) = v9 & incident_c(v7, v5) = v8 & (v9 = 0 | v8 = 0))) &  ? [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = v4 |  ~ (sum(v5, v6) = v7) |  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] : (incident_c(v8, v6) = v11 & incident_c(v8, v5) = v10 & incident_c(v8, v4) = v9 & ( ~ (v9 = 0) | ( ~ (v11 = 0) &  ~ (v10 = 0))) & (v11 = 0 | v10 = 0 | v9 = 0))) &  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (inner_point(v4, v5) = v6) |  ? [v7] :  ? [v8] : (end_point(v4, v5) = v8 & incident_c(v4, v5) = v7 & ( ~ (v7 = 0) | v8 = 0))) &  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (end_point(v4, v5) = v6) |  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : ((v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 &  ~ (v14 = 0) &  ~ (v13 = 0) & part_of(v8, v7) = v14 & part_of(v8, v5) = 0 & part_of(v7, v8) = v13 & part_of(v7, v5) = 0 & incident_c(v4, v8) = 0 & incident_c(v4, v7) = 0) | ( ~ (v7 = 0) & incident_c(v4, v5) = v7))) &  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (part_of(v5, v4) = v6) |  ? [v7] :  ? [v8] : ( ~ (v8 = 0) & incident_c(v7, v5) = 0 & incident_c(v7, v4) = v8)) &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (open(v6) = v5) |  ~ (open(v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (closed(v6) = v5) |  ~ (closed(v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = 0 |  ~ (open(v4) = v5) |  ~ (end_point(v6, v4) = 0)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (meet(v4, v5, v6) = 0) | (incident_c(v4, v6) = 0 & incident_c(v4, v5) = 0)) &  ! [v4] :  ! [v5] : (v5 = v4 |  ~ (part_of(v5, v4) = 0) | open(v5) = 0) &  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (closed(v4) = v5) |  ? [v6] : end_point(v6, v4) = 0) &  ! [v4] :  ! [v5] : ( ~ (closed(v4) = 0) |  ~ (end_point(v5, v4) = 0)) &  ! [v4] :  ! [v5] : ( ~ (inner_point(v5, v4) = 0) |  ? [v6] :  ? [v7] : (meet(v5, v6, v7) = 0 & sum(v6, v7) = v4)) &  ! [v4] :  ! [v5] : ( ~ (inner_point(v4, v5) = 0) |  ? [v6] : ( ~ (v6 = 0) & end_point(v4, v5) = v6 & incident_c(v4, v5) = 0)) &  ! [v4] :  ! [v5] : ( ~ (end_point(v5, v4) = 0) |  ? [v6] : ( ~ (v6 = v5) & end_point(v6, v4) = 0)) &  ! [v4] :  ! [v5] : ( ~ (end_point(v4, v5) = 0) | incident_c(v4, v5) = 0) &  ! [v4] : ( ~ (open(v4) = 0) |  ? [v5] : end_point(v5, v4) = 0) &  ? [v4] :  ? [v5] : (v5 = v4 |  ? [v6] :  ? [v7] :  ? [v8] : (incident_c(v6, v5) = v8 & incident_c(v6, v4) = v7 & ( ~ (v8 = 0) |  ~ (v7 = 0)) & (v8 = 0 | v7 = 0))) &  ? [v4] :  ? [v5] : inner_point(v5, v4) = 0)
% 20.54/6.51  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 20.54/6.51  | (1)  ~ (all_0_0_0 = 0) & part_of(all_0_2_2, all_0_1_1) = 0 & part_of(all_0_3_3, all_0_1_1) = all_0_0_0 & part_of(all_0_3_3, all_0_2_2) = 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
% 20.54/6.53  |
% 20.54/6.53  | Applying alpha-rule on (1) yields:
% 20.54/6.53  | (2)  ! [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)))
% 20.54/6.53  | (3) part_of(all_0_3_3, all_0_1_1) = all_0_0_0
% 20.54/6.53  | (4)  ? [v0] :  ? [v1] : inner_point(v1, v0) = 0
% 20.54/6.53  | (5)  ! [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))))
% 20.54/6.53  | (6)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (meet(v0, v1, v2) = 0) | (incident_c(v0, v2) = 0 & incident_c(v0, v1) = 0))
% 20.54/6.53  | (7)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (part_of(v1, v0) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4))
% 20.54/6.53  | (8)  ? [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)))
% 20.54/6.53  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (part_of(v1, v0) = 0) |  ~ (incident_c(v2, v0) = v3) |  ? [v4] : ( ~ (v4 = 0) & incident_c(v2, v1) = v4))
% 20.54/6.53  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (part_of(v3, v2) = v1) |  ~ (part_of(v3, v2) = v0))
% 20.54/6.53  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (incident_c(v3, v2) = v1) |  ~ (incident_c(v3, v2) = v0))
% 20.54/6.53  | (12)  ! [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)))
% 20.54/6.53  | (13)  ! [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)))
% 20.54/6.53  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (inner_point(v3, v2) = v1) |  ~ (inner_point(v3, v2) = v0))
% 20.54/6.53  | (15)  ! [v0] : ( ~ (open(v0) = 0) |  ? [v1] : end_point(v1, v0) = 0)
% 20.54/6.53  | (16)  ~ (all_0_0_0 = 0)
% 20.54/6.53  | (17)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (open(v2) = v1) |  ~ (open(v2) = v0))
% 20.54/6.53  | (18) part_of(all_0_3_3, all_0_2_2) = 0
% 20.54/6.53  | (19)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (closed(v0) = v1) |  ? [v2] : end_point(v2, v0) = 0)
% 20.54/6.53  | (20) part_of(all_0_2_2, all_0_1_1) = 0
% 20.54/6.53  | (21)  ! [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))
% 20.54/6.53  | (22)  ! [v0] :  ! [v1] : ( ~ (end_point(v0, v1) = 0) | incident_c(v0, v1) = 0)
% 20.54/6.53  | (23)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = 0 |  ~ (open(v0) = v1) |  ~ (end_point(v2, v0) = 0))
% 20.54/6.53  | (24)  ! [v0] :  ! [v1] : ( ~ (end_point(v1, v0) = 0) |  ? [v2] : ( ~ (v2 = v1) & end_point(v2, v0) = 0))
% 20.54/6.53  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (meet(v4, v3, v2) = v1) |  ~ (meet(v4, v3, v2) = v0))
% 20.54/6.53  | (26)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (part_of(v1, v0) = 0) | open(v1) = 0)
% 20.54/6.53  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (end_point(v3, v2) = v1) |  ~ (end_point(v3, v2) = v0))
% 20.54/6.53  | (28)  ! [v0] :  ! [v1] : ( ~ (closed(v0) = 0) |  ~ (end_point(v1, v0) = 0))
% 20.54/6.53  | (29)  ! [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)))
% 20.54/6.54  | (30)  ! [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)))))
% 20.54/6.54  | (31)  ! [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)))
% 20.54/6.54  | (32)  ! [v0] :  ! [v1] : ( ~ (inner_point(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & end_point(v0, v1) = v2 & incident_c(v0, v1) = 0))
% 20.54/6.54  | (33)  ? [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)))
% 20.54/6.54  | (34)  ! [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))))
% 20.54/6.54  | (35)  ! [v0] :  ! [v1] : ( ~ (inner_point(v1, v0) = 0) |  ? [v2] :  ? [v3] : (meet(v1, v2, v3) = 0 & sum(v2, v3) = v0))
% 20.54/6.54  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sum(v3, v2) = v1) |  ~ (sum(v3, v2) = v0))
% 20.54/6.54  | (37)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (closed(v2) = v1) |  ~ (closed(v2) = v0))
% 20.54/6.54  | (38)  ! [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))
% 20.54/6.54  |
% 20.54/6.54  | Instantiating formula (7) with all_0_0_0, all_0_3_3, all_0_1_1 and discharging atoms part_of(all_0_3_3, all_0_1_1) = all_0_0_0, yields:
% 20.54/6.54  | (39) all_0_0_0 = 0 |  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & incident_c(v0, all_0_1_1) = v1 & incident_c(v0, all_0_3_3) = 0)
% 20.54/6.54  |
% 20.54/6.54  +-Applying beta-rule and splitting (39), into two cases.
% 20.54/6.54  |-Branch one:
% 20.54/6.54  | (40) all_0_0_0 = 0
% 20.54/6.54  |
% 20.54/6.54  	| Equations (40) can reduce 16 to:
% 20.54/6.54  	| (41) $false
% 20.54/6.54  	|
% 20.54/6.54  	|-The branch is then unsatisfiable
% 20.54/6.54  |-Branch two:
% 20.54/6.54  | (16)  ~ (all_0_0_0 = 0)
% 20.54/6.54  | (43)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & incident_c(v0, all_0_1_1) = v1 & incident_c(v0, all_0_3_3) = 0)
% 20.54/6.54  |
% 20.54/6.54  	| Instantiating (43) with all_21_0_12, all_21_1_13 yields:
% 20.54/6.54  	| (44)  ~ (all_21_0_12 = 0) & incident_c(all_21_1_13, all_0_1_1) = all_21_0_12 & incident_c(all_21_1_13, all_0_3_3) = 0
% 20.54/6.54  	|
% 20.54/6.54  	| Applying alpha-rule on (44) yields:
% 20.54/6.54  	| (45)  ~ (all_21_0_12 = 0)
% 20.54/6.54  	| (46) incident_c(all_21_1_13, all_0_1_1) = all_21_0_12
% 20.54/6.54  	| (47) incident_c(all_21_1_13, all_0_3_3) = 0
% 20.54/6.54  	|
% 20.54/6.54  	| Instantiating formula (9) with all_21_0_12, all_21_1_13, all_0_2_2, all_0_1_1 and discharging atoms part_of(all_0_2_2, all_0_1_1) = 0, incident_c(all_21_1_13, all_0_1_1) = all_21_0_12, yields:
% 20.54/6.54  	| (48) all_21_0_12 = 0 |  ? [v0] : ( ~ (v0 = 0) & incident_c(all_21_1_13, all_0_2_2) = v0)
% 20.54/6.54  	|
% 20.54/6.54  	+-Applying beta-rule and splitting (48), into two cases.
% 20.54/6.54  	|-Branch one:
% 20.54/6.54  	| (49) all_21_0_12 = 0
% 20.54/6.54  	|
% 20.54/6.54  		| Equations (49) can reduce 45 to:
% 20.54/6.54  		| (41) $false
% 20.54/6.54  		|
% 20.54/6.54  		|-The branch is then unsatisfiable
% 20.54/6.54  	|-Branch two:
% 20.54/6.54  	| (45)  ~ (all_21_0_12 = 0)
% 20.54/6.54  	| (52)  ? [v0] : ( ~ (v0 = 0) & incident_c(all_21_1_13, all_0_2_2) = v0)
% 20.54/6.54  	|
% 20.54/6.54  		| Instantiating (52) with all_47_0_24 yields:
% 20.54/6.54  		| (53)  ~ (all_47_0_24 = 0) & incident_c(all_21_1_13, all_0_2_2) = all_47_0_24
% 20.54/6.54  		|
% 20.54/6.54  		| Applying alpha-rule on (53) yields:
% 20.54/6.54  		| (54)  ~ (all_47_0_24 = 0)
% 20.54/6.54  		| (55) incident_c(all_21_1_13, all_0_2_2) = all_47_0_24
% 20.54/6.54  		|
% 20.54/6.54  		| Instantiating formula (9) with all_47_0_24, all_21_1_13, all_0_3_3, all_0_2_2 and discharging atoms part_of(all_0_3_3, all_0_2_2) = 0, incident_c(all_21_1_13, all_0_2_2) = all_47_0_24, yields:
% 20.54/6.55  		| (56) all_47_0_24 = 0 |  ? [v0] : ( ~ (v0 = 0) & incident_c(all_21_1_13, all_0_3_3) = v0)
% 20.54/6.55  		|
% 20.54/6.55  		+-Applying beta-rule and splitting (56), into two cases.
% 20.54/6.55  		|-Branch one:
% 20.54/6.55  		| (57) all_47_0_24 = 0
% 20.54/6.55  		|
% 20.54/6.55  			| Equations (57) can reduce 54 to:
% 20.54/6.55  			| (41) $false
% 20.54/6.55  			|
% 20.54/6.55  			|-The branch is then unsatisfiable
% 20.54/6.55  		|-Branch two:
% 20.54/6.55  		| (54)  ~ (all_47_0_24 = 0)
% 20.54/6.55  		| (60)  ? [v0] : ( ~ (v0 = 0) & incident_c(all_21_1_13, all_0_3_3) = v0)
% 20.54/6.55  		|
% 20.54/6.55  			| Instantiating (60) with all_76_0_26 yields:
% 20.54/6.55  			| (61)  ~ (all_76_0_26 = 0) & incident_c(all_21_1_13, all_0_3_3) = all_76_0_26
% 20.54/6.55  			|
% 20.54/6.55  			| Applying alpha-rule on (61) yields:
% 20.54/6.55  			| (62)  ~ (all_76_0_26 = 0)
% 20.54/6.55  			| (63) incident_c(all_21_1_13, all_0_3_3) = all_76_0_26
% 20.54/6.55  			|
% 20.54/6.55  			| Instantiating formula (11) with all_21_1_13, all_0_3_3, all_76_0_26, 0 and discharging atoms incident_c(all_21_1_13, all_0_3_3) = all_76_0_26, incident_c(all_21_1_13, all_0_3_3) = 0, yields:
% 20.54/6.55  			| (64) all_76_0_26 = 0
% 20.54/6.55  			|
% 20.54/6.55  			| Equations (64) can reduce 62 to:
% 20.54/6.55  			| (41) $false
% 20.54/6.55  			|
% 20.54/6.55  			|-The branch is then unsatisfiable
% 20.54/6.55  % SZS output end Proof for theBenchmark
% 20.54/6.55  
% 20.54/6.55  5947ms
%------------------------------------------------------------------------------