%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO118+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n009.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 03:47:45 EDT 2022

% Result   : Theorem 3.62s 1.44s
% Output   : Proof 5.38s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO118+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n009.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 : Sat Jun 18 03:14:08 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.51/0.59          ____       _                          
% 0.51/0.59    ___  / __ \_____(_)___  ________  __________
% 0.51/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.51/0.60  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.51/0.60  
% 0.51/0.60  A Theorem Prover for First-Order Logic
% 0.51/0.60  (ePrincess v.1.0)
% 0.51/0.60  
% 0.51/0.60  (c) Philipp Rümmer, 2009-2015
% 0.51/0.60  (c) Peter Backeman, 2014-2015
% 0.51/0.60  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.60  Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.60  Bug reports to peter@backeman.se
% 0.51/0.60  
% 0.51/0.60  For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.60  
% 0.51/0.60  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.65  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.78/0.96  Prover 0: Preprocessing ...
% 2.72/1.24  Prover 0: Warning: ignoring some quantifiers
% 2.80/1.27  Prover 0: Constructing countermodel ...
% 3.62/1.44  Prover 0: proved (794ms)
% 3.62/1.44  
% 3.62/1.44  No countermodel exists, formula is valid
% 3.62/1.44  % SZS status Theorem for theBenchmark
% 3.62/1.44  
% 3.62/1.44  Generating proof ... Warning: ignoring some quantifiers
% 5.08/1.76  found it (size 8)
% 5.08/1.76  
% 5.08/1.76  % SZS output start Proof for theBenchmark
% 5.08/1.76  Assumed formulas after preprocessing and simplification: 
% 5.08/1.76  | (0)  ? [v0] :  ? [v1] :  ? [v2] : (ordered_by(v0, v2, v1) & ordered_by(v0, v1, v2) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v4 |  ~ inner_point(v5, v7) |  ~ end_point(v6, v7) |  ~ end_point(v4, v7) |  ~ part_of(v7, v3) | between_c(v3, v4, v5, v6)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (sum(v4, v5) = v3) |  ~ closed(v3) |  ~ meet(v6, v4, v5) |  ~ end_point(v7, v4) | meet(v7, v4, v5)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ end_point(v7, v6) |  ~ end_point(v7, v5) |  ~ end_point(v7, v4) |  ~ part_of(v6, v3) |  ~ part_of(v5, v3) |  ~ part_of(v4, v3) | part_of(v6, v5) | part_of(v6, v4) | part_of(v5, v6) | part_of(v5, v4) | part_of(v4, v6) | part_of(v4, v5)) &  ? [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ between_c(v7, v4, v5, v6) | between_o(v3, v4, v5, v6) |  ? [v8] : (( ~ incident_o(v8, v3) |  ~ incident_c(v8, v7)) & (incident_o(v8, v3) | incident_c(v8, v7)))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = v5 | v6 = v4 | v5 = v4 |  ~ end_point(v6, v3) |  ~ end_point(v5, v3) |  ~ end_point(v4, v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (sum(v6, v5) = v4) |  ~ (sum(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (sum(v4, v5) = v3) |  ~ incident_c(v6, v5) | incident_c(v6, v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (sum(v4, v5) = v3) |  ~ incident_c(v6, v4) | incident_c(v6, v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (sum(v4, v5) = v3) |  ~ incident_c(v6, v3) | incident_c(v6, v5) | incident_c(v6, v4)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ ordered_by(v3, v6, v5) |  ~ ordered_by(v3, v5, v4) | between_o(v3, v4, v5, v6)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ ordered_by(v3, v5, v6) |  ~ ordered_by(v3, v4, v5) | between_o(v3, v4, v5, v6)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ between_o(v6, v3, v4, v5) |  ? [v7] : (between_c(v7, v3, v4, v5) &  ! [v8] : ( ~ incident_o(v8, v6) | incident_c(v8, v7)) &  ! [v8] : ( ~ incident_c(v8, v7) | incident_o(v8, v6)))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ between_o(v3, v4, v5, v6) | ordered_by(v3, v6, v5) | ordered_by(v3, v5, v6)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ between_o(v3, v4, v5, v6) | ordered_by(v3, v6, v5) | ordered_by(v3, v4, v5)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ between_o(v3, v4, v5, v6) | ordered_by(v3, v5, v6) | ordered_by(v3, v5, v4)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ between_o(v3, v4, v5, v6) | ordered_by(v3, v5, v4) | ordered_by(v3, v4, v5)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ between_c(v3, v4, v5, v6) |  ? [v7] : (inner_point(v5, v7) & end_point(v6, v7) & end_point(v4, v7) & part_of(v7, v3))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ meet(v3, v4, v5) |  ~ incident_c(v6, v5) |  ~ incident_c(v6, v4) | end_point(v6, v5)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ meet(v3, v4, v5) |  ~ incident_c(v6, v5) |  ~ incident_c(v6, v4) | end_point(v6, v4)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ end_point(v3, v4) |  ~ incident_c(v3, v6) |  ~ incident_c(v3, v5) |  ~ part_of(v6, v4) |  ~ part_of(v5, v4) | part_of(v6, v5) | part_of(v5, v6)) &  ? [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = v3 |  ~ (sum(v4, v5) = v6) |  ? [v7] : (( ~ incident_c(v7, v3) | ( ~ incident_c(v7, v5) &  ~ incident_c(v7, v4))) & (incident_c(v7, v5) | incident_c(v7, v4) | incident_c(v7, v3)))) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = v3 |  ~ finish_point(v3, v4) |  ~ incident_o(v5, v4) | ordered_by(v4, v5, v3)) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = v3 |  ~ incident_o(v5, v4) |  ~ start_point(v3, v4) | ordered_by(v4, v3, v5)) &  ! [v3] :  ! [v4] :  ! [v5] : (v4 = v3 |  ~ (underlying_curve(v5) = v4) |  ~ (underlying_curve(v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] : (v4 = v3 |  ~ open(v5) |  ~ incident_c(v4, v5) |  ~ incident_c(v3, v5) |  ? [v6] : (ordered_by(v6, v3, v4) &  ! [v7] : ( ~ incident_o(v7, v6) | incident_c(v7, v5)) &  ! [v7] : ( ~ incident_c(v7, v5) | incident_o(v7, v6)))) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (underlying_curve(v4) = v3) |  ~ incident_o(v5, v4) | incident_c(v5, v3)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (underlying_curve(v4) = v3) |  ~ incident_c(v5, v3) | incident_o(v5, v4)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ ordered_by(v3, v4, v5) | incident_o(v5, v3)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ ordered_by(v3, v4, v5) | incident_o(v4, v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ~ between_c(v3, v4, v5, v4) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ meet(v3, v4, v5) | incident_c(v3, v5)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ meet(v3, v4, v5) | incident_c(v3, v4)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ incident_c(v5, v4) |  ~ part_of(v4, v3) | incident_c(v5, v3)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ incident_c(v3, v5) |  ~ incident_c(v3, v4) | meet(v3, v4, v5) |  ? [v6] : (incident_c(v6, v5) & incident_c(v6, v4) & ( ~ end_point(v6, v5) |  ~ end_point(v6, v4)))) &  ? [v3] :  ! [v4] :  ! [v5] : (v5 = v3 |  ~ (underlying_curve(v4) = v5) |  ? [v6] : (( ~ incident_o(v6, v4) |  ~ incident_c(v6, v3)) & (incident_o(v6, v4) | incident_c(v6, v3)))) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ part_of(v4, v3) | open(v4)) &  ! [v3] :  ! [v4] : ( ~ finish_point(v3, v4) | incident_o(v3, v4)) &  ! [v3] :  ! [v4] : ( ~ incident_o(v3, v4) | finish_point(v3, v4) |  ? [v5] : ( ~ (v5 = v3) & incident_o(v5, v4) &  ~ ordered_by(v4, v5, v3))) &  ! [v3] :  ! [v4] : ( ~ incident_o(v3, v4) | start_point(v3, v4) |  ? [v5] : ( ~ (v5 = v3) & incident_o(v5, v4) &  ~ ordered_by(v4, v3, v5))) &  ! [v3] :  ! [v4] : ( ~ start_point(v3, v4) | incident_o(v3, v4)) &  ! [v3] :  ! [v4] : ( ~ closed(v3) |  ~ end_point(v4, v3)) &  ! [v3] :  ! [v4] : ( ~ inner_point(v4, v3) |  ? [v5] :  ? [v6] : (sum(v5, v6) = v3 & meet(v4, v5, v6))) &  ! [v3] :  ! [v4] : ( ~ inner_point(v3, v4) |  ~ end_point(v3, v4)) &  ! [v3] :  ! [v4] : ( ~ inner_point(v3, v4) | incident_c(v3, v4)) &  ! [v3] :  ! [v4] : ( ~ end_point(v4, v3) | open(v3)) &  ! [v3] :  ! [v4] : ( ~ end_point(v4, v3) |  ? [v5] : ( ~ (v5 = v4) & end_point(v5, v3))) &  ! [v3] :  ! [v4] : ( ~ end_point(v3, v4) | incident_c(v3, v4)) &  ! [v3] :  ! [v4] : ( ~ incident_c(v3, v4) | inner_point(v3, v4) | end_point(v3, v4)) &  ! [v3] :  ! [v4] : ( ~ incident_c(v3, v4) | end_point(v3, v4) |  ? [v5] :  ? [v6] : (incident_c(v3, v6) & incident_c(v3, v5) & part_of(v6, v4) & part_of(v5, v4) &  ~ part_of(v6, v5) &  ~ part_of(v5, v6))) &  ! [v3] : ( ~ open(v3) |  ? [v4] : end_point(v4, v3)) &  ? [v3] :  ? [v4] : (v4 = v3 |  ? [v5] :  ? [v6] : (( ~ ordered_by(v4, v5, v6) |  ~ ordered_by(v3, v5, v6)) & (ordered_by(v4, v5, v6) | ordered_by(v3, v5, v6)))) &  ? [v3] :  ? [v4] : (v4 = v3 |  ? [v5] : (( ~ incident_c(v5, v4) |  ~ incident_c(v5, v3)) & (incident_c(v5, v4) | incident_c(v5, v3)))) &  ? [v3] :  ? [v4] : start_point(v4, v3) &  ? [v3] :  ? [v4] : inner_point(v4, v3) &  ? [v3] :  ? [v4] : (part_of(v4, v3) |  ? [v5] : (incident_c(v5, v4) &  ~ incident_c(v5, v3))) &  ? [v3] :  ? [v4] : (open(v4) &  ! [v5] : ( ~ incident_o(v5, v3) | incident_c(v5, v4)) &  ! [v5] : ( ~ incident_c(v5, v4) | incident_o(v5, v3))) &  ? [v3] : (closed(v3) |  ? [v4] : end_point(v4, v3)))
% 5.28/1.82  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 5.28/1.82  | (1) ordered_by(all_0_2_2, all_0_0_0, all_0_1_1) & ordered_by(all_0_2_2, all_0_1_1, all_0_0_0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v1 |  ~ inner_point(v2, v4) |  ~ end_point(v3, v4) |  ~ end_point(v1, v4) |  ~ part_of(v4, v0) | between_c(v0, v1, v2, v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sum(v1, v2) = v0) |  ~ closed(v0) |  ~ meet(v3, v1, v2) |  ~ end_point(v4, v1) | meet(v4, v1, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ end_point(v4, v3) |  ~ end_point(v4, v2) |  ~ end_point(v4, v1) |  ~ part_of(v3, v0) |  ~ part_of(v2, v0) |  ~ part_of(v1, v0) | part_of(v3, v2) | part_of(v3, v1) | part_of(v2, v3) | part_of(v2, v1) | part_of(v1, v3) | part_of(v1, v2)) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ between_c(v4, v1, v2, v3) | between_o(v0, v1, v2, v3) |  ? [v5] : (( ~ incident_o(v5, v0) |  ~ incident_c(v5, v4)) & (incident_o(v5, v0) | incident_c(v5, v4)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 | v3 = v1 | v2 = v1 |  ~ end_point(v3, v0) |  ~ end_point(v2, v0) |  ~ end_point(v1, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sum(v3, v2) = v1) |  ~ (sum(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sum(v1, v2) = v0) |  ~ incident_c(v3, v2) | incident_c(v3, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sum(v1, v2) = v0) |  ~ incident_c(v3, v1) | incident_c(v3, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sum(v1, v2) = v0) |  ~ incident_c(v3, v0) | incident_c(v3, v2) | incident_c(v3, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ ordered_by(v0, v3, v2) |  ~ ordered_by(v0, v2, v1) | between_o(v0, v1, v2, v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ ordered_by(v0, v2, v3) |  ~ ordered_by(v0, v1, v2) | between_o(v0, v1, v2, v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_o(v3, v0, v1, v2) |  ? [v4] : (between_c(v4, v0, v1, v2) &  ! [v5] : ( ~ incident_o(v5, v3) | incident_c(v5, v4)) &  ! [v5] : ( ~ incident_c(v5, v4) | incident_o(v5, v3)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v3, v2) | ordered_by(v0, v2, v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v3, v2) | ordered_by(v0, v1, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v2, v3) | ordered_by(v0, v2, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v2, v1) | ordered_by(v0, v1, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_c(v0, v1, v2, v3) |  ? [v4] : (inner_point(v2, v4) & end_point(v3, v4) & end_point(v1, v4) & part_of(v4, v0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ meet(v0, v1, v2) |  ~ incident_c(v3, v2) |  ~ incident_c(v3, v1) | end_point(v3, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ meet(v0, v1, v2) |  ~ incident_c(v3, v2) |  ~ incident_c(v3, v1) | end_point(v3, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ end_point(v0, v1) |  ~ incident_c(v0, v3) |  ~ incident_c(v0, v2) |  ~ part_of(v3, v1) |  ~ part_of(v2, v1) | part_of(v3, v2) | part_of(v2, v3)) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (sum(v1, v2) = v3) |  ? [v4] : (( ~ incident_c(v4, v0) | ( ~ incident_c(v4, v2) &  ~ incident_c(v4, v1))) & (incident_c(v4, v2) | incident_c(v4, v1) | incident_c(v4, v0)))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ finish_point(v0, v1) |  ~ incident_o(v2, v1) | ordered_by(v1, v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ incident_o(v2, v1) |  ~ start_point(v0, v1) | ordered_by(v1, v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (underlying_curve(v2) = v1) |  ~ (underlying_curve(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ open(v2) |  ~ incident_c(v1, v2) |  ~ incident_c(v0, v2) |  ? [v3] : (ordered_by(v3, v0, v1) &  ! [v4] : ( ~ incident_o(v4, v3) | incident_c(v4, v2)) &  ! [v4] : ( ~ incident_c(v4, v2) | incident_o(v4, v3)))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (underlying_curve(v1) = v0) |  ~ incident_o(v2, v1) | incident_c(v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (underlying_curve(v1) = v0) |  ~ incident_c(v2, v0) | incident_o(v2, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ ordered_by(v0, v1, v2) | incident_o(v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ ordered_by(v0, v1, v2) | incident_o(v1, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ~ between_c(v0, v1, v2, v1) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ meet(v0, v1, v2) | incident_c(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ meet(v0, v1, v2) | incident_c(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ incident_c(v2, v1) |  ~ part_of(v1, v0) | incident_c(v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ incident_c(v0, v2) |  ~ incident_c(v0, v1) | meet(v0, v1, v2) |  ? [v3] : (incident_c(v3, v2) & incident_c(v3, v1) & ( ~ end_point(v3, v2) |  ~ end_point(v3, v1)))) &  ? [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (underlying_curve(v1) = v2) |  ? [v3] : (( ~ incident_o(v3, v1) |  ~ incident_c(v3, v0)) & (incident_o(v3, v1) | incident_c(v3, v0)))) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ part_of(v1, v0) | open(v1)) &  ! [v0] :  ! [v1] : ( ~ finish_point(v0, v1) | incident_o(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ incident_o(v0, v1) | finish_point(v0, v1) |  ? [v2] : ( ~ (v2 = v0) & incident_o(v2, v1) &  ~ ordered_by(v1, v2, v0))) &  ! [v0] :  ! [v1] : ( ~ incident_o(v0, v1) | start_point(v0, v1) |  ? [v2] : ( ~ (v2 = v0) & incident_o(v2, v1) &  ~ ordered_by(v1, v0, v2))) &  ! [v0] :  ! [v1] : ( ~ start_point(v0, v1) | incident_o(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ closed(v0) |  ~ end_point(v1, v0)) &  ! [v0] :  ! [v1] : ( ~ inner_point(v1, v0) |  ? [v2] :  ? [v3] : (sum(v2, v3) = v0 & meet(v1, v2, v3))) &  ! [v0] :  ! [v1] : ( ~ inner_point(v0, v1) |  ~ end_point(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ inner_point(v0, v1) | incident_c(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ end_point(v1, v0) | open(v0)) &  ! [v0] :  ! [v1] : ( ~ end_point(v1, v0) |  ? [v2] : ( ~ (v2 = v1) & end_point(v2, v0))) &  ! [v0] :  ! [v1] : ( ~ end_point(v0, v1) | incident_c(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ incident_c(v0, v1) | inner_point(v0, v1) | end_point(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ incident_c(v0, v1) | end_point(v0, v1) |  ? [v2] :  ? [v3] : (incident_c(v0, v3) & incident_c(v0, v2) & part_of(v3, v1) & part_of(v2, v1) &  ~ part_of(v3, v2) &  ~ part_of(v2, v3))) &  ! [v0] : ( ~ open(v0) |  ? [v1] : end_point(v1, v0)) &  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] :  ? [v3] : (( ~ ordered_by(v1, v2, v3) |  ~ ordered_by(v0, v2, v3)) & (ordered_by(v1, v2, v3) | ordered_by(v0, v2, v3)))) &  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] : (( ~ incident_c(v2, v1) |  ~ incident_c(v2, v0)) & (incident_c(v2, v1) | incident_c(v2, v0)))) &  ? [v0] :  ? [v1] : start_point(v1, v0) &  ? [v0] :  ? [v1] : inner_point(v1, v0) &  ? [v0] :  ? [v1] : (part_of(v1, v0) |  ? [v2] : (incident_c(v2, v1) &  ~ incident_c(v2, v0))) &  ? [v0] :  ? [v1] : (open(v1) &  ! [v2] : ( ~ incident_o(v2, v0) | incident_c(v2, v1)) &  ! [v2] : ( ~ incident_c(v2, v1) | incident_o(v2, v0))) &  ? [v0] : (closed(v0) |  ? [v1] : end_point(v1, v0))
% 5.38/1.84  |
% 5.38/1.84  | Applying alpha-rule on (1) yields:
% 5.38/1.84  | (2) ordered_by(all_0_2_2, all_0_1_1, all_0_0_0)
% 5.38/1.84  | (3)  ! [v0] :  ! [v1] : ( ~ end_point(v0, v1) | incident_c(v0, v1))
% 5.38/1.84  | (4)  ! [v0] :  ! [v1] : ( ~ inner_point(v0, v1) |  ~ end_point(v0, v1))
% 5.38/1.84  | (5) ordered_by(all_0_2_2, all_0_0_0, all_0_1_1)
% 5.38/1.84  | (6)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ part_of(v1, v0) | open(v1))
% 5.38/1.84  | (7)  ! [v0] :  ! [v1] : ( ~ finish_point(v0, v1) | incident_o(v0, v1))
% 5.38/1.84  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ meet(v0, v1, v2) | incident_c(v0, v2))
% 5.38/1.84  | (9)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ ordered_by(v0, v1, v2) | incident_o(v1, v0))
% 5.38/1.84  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sum(v1, v2) = v0) |  ~ incident_c(v3, v2) | incident_c(v3, v0))
% 5.38/1.84  | (11)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ ordered_by(v0, v1, v2) | incident_o(v2, v0))
% 5.38/1.84  | (12)  ! [v0] :  ! [v1] : ( ~ closed(v0) |  ~ end_point(v1, v0))
% 5.38/1.84  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v3, v2) | ordered_by(v0, v1, v2))
% 5.38/1.84  | (14)  ! [v0] :  ! [v1] : ( ~ start_point(v0, v1) | incident_o(v0, v1))
% 5.38/1.84  | (15)  ! [v0] :  ! [v1] : ( ~ inner_point(v1, v0) |  ? [v2] :  ? [v3] : (sum(v2, v3) = v0 & meet(v1, v2, v3)))
% 5.38/1.84  | (16)  ! [v0] :  ! [v1] : ( ~ inner_point(v0, v1) | incident_c(v0, v1))
% 5.38/1.84  | (17)  ! [v0] :  ! [v1] : ( ~ incident_o(v0, v1) | start_point(v0, v1) |  ? [v2] : ( ~ (v2 = v0) & incident_o(v2, v1) &  ~ ordered_by(v1, v0, v2)))
% 5.38/1.84  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sum(v1, v2) = v0) |  ~ incident_c(v3, v0) | incident_c(v3, v2) | incident_c(v3, v1))
% 5.38/1.84  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v2, v1) | ordered_by(v0, v1, v2))
% 5.38/1.85  | (20)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ open(v2) |  ~ incident_c(v1, v2) |  ~ incident_c(v0, v2) |  ? [v3] : (ordered_by(v3, v0, v1) &  ! [v4] : ( ~ incident_o(v4, v3) | incident_c(v4, v2)) &  ! [v4] : ( ~ incident_c(v4, v2) | incident_o(v4, v3))))
% 5.38/1.85  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 | v3 = v1 | v2 = v1 |  ~ end_point(v3, v0) |  ~ end_point(v2, v0) |  ~ end_point(v1, v0))
% 5.38/1.85  | (22)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ incident_c(v2, v1) |  ~ part_of(v1, v0) | incident_c(v2, v0))
% 5.38/1.85  | (23)  ? [v0] :  ? [v1] : (open(v1) &  ! [v2] : ( ~ incident_o(v2, v0) | incident_c(v2, v1)) &  ! [v2] : ( ~ incident_c(v2, v1) | incident_o(v2, v0)))
% 5.38/1.85  | (24)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ between_c(v4, v1, v2, v3) | between_o(v0, v1, v2, v3) |  ? [v5] : (( ~ incident_o(v5, v0) |  ~ incident_c(v5, v4)) & (incident_o(v5, v0) | incident_c(v5, v4))))
% 5.38/1.85  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sum(v1, v2) = v0) |  ~ incident_c(v3, v1) | incident_c(v3, v0))
% 5.38/1.85  | (26)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (sum(v1, v2) = v3) |  ? [v4] : (( ~ incident_c(v4, v0) | ( ~ incident_c(v4, v2) &  ~ incident_c(v4, v1))) & (incident_c(v4, v2) | incident_c(v4, v1) | incident_c(v4, v0))))
% 5.38/1.85  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ end_point(v0, v1) |  ~ incident_c(v0, v3) |  ~ incident_c(v0, v2) |  ~ part_of(v3, v1) |  ~ part_of(v2, v1) | part_of(v3, v2) | part_of(v2, v3))
% 5.38/1.85  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v3, v2) | ordered_by(v0, v2, v3))
% 5.38/1.85  | (29)  ! [v0] :  ! [v1] : ( ~ incident_c(v0, v1) | inner_point(v0, v1) | end_point(v0, v1))
% 5.38/1.85  | (30)  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] : (( ~ incident_c(v2, v1) |  ~ incident_c(v2, v0)) & (incident_c(v2, v1) | incident_c(v2, v0))))
% 5.38/1.85  | (31)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (underlying_curve(v2) = v1) |  ~ (underlying_curve(v2) = v0))
% 5.38/1.85  | (32)  ! [v0] : ( ~ open(v0) |  ? [v1] : end_point(v1, v0))
% 5.38/1.85  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ meet(v0, v1, v2) |  ~ incident_c(v3, v2) |  ~ incident_c(v3, v1) | end_point(v3, v1))
% 5.38/1.85  | (34)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ ordered_by(v0, v3, v2) |  ~ ordered_by(v0, v2, v1) | between_o(v0, v1, v2, v3))
% 5.38/1.85  | (35)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (underlying_curve(v1) = v0) |  ~ incident_c(v2, v0) | incident_o(v2, v1))
% 5.38/1.85  | (36)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (underlying_curve(v1) = v0) |  ~ incident_o(v2, v1) | incident_c(v2, v0))
% 5.38/1.85  | (37)  ! [v0] :  ! [v1] : ( ~ end_point(v1, v0) | open(v0))
% 5.38/1.85  | (38)  ? [v0] : (closed(v0) |  ? [v1] : end_point(v1, v0))
% 5.38/1.85  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ meet(v0, v1, v2) |  ~ incident_c(v3, v2) |  ~ incident_c(v3, v1) | end_point(v3, v2))
% 5.38/1.85  | (40)  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] :  ? [v3] : (( ~ ordered_by(v1, v2, v3) |  ~ ordered_by(v0, v2, v3)) & (ordered_by(v1, v2, v3) | ordered_by(v0, v2, v3))))
% 5.38/1.85  | (41)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sum(v1, v2) = v0) |  ~ closed(v0) |  ~ meet(v3, v1, v2) |  ~ end_point(v4, v1) | meet(v4, v1, v2))
% 5.38/1.86  | (42)  ? [v0] :  ? [v1] : (part_of(v1, v0) |  ? [v2] : (incident_c(v2, v1) &  ~ incident_c(v2, v0)))
% 5.38/1.86  | (43)  ! [v0] :  ! [v1] :  ! [v2] :  ~ between_c(v0, v1, v2, v1)
% 5.38/1.86  | (44)  ! [v0] :  ! [v1] : ( ~ incident_o(v0, v1) | finish_point(v0, v1) |  ? [v2] : ( ~ (v2 = v0) & incident_o(v2, v1) &  ~ ordered_by(v1, v2, v0)))
% 5.38/1.86  | (45)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_c(v0, v1, v2, v3) |  ? [v4] : (inner_point(v2, v4) & end_point(v3, v4) & end_point(v1, v4) & part_of(v4, v0)))
% 5.38/1.86  | (46)  ? [v0] :  ? [v1] : start_point(v1, v0)
% 5.38/1.86  | (47)  ! [v0] :  ! [v1] : ( ~ incident_c(v0, v1) | end_point(v0, v1) |  ? [v2] :  ? [v3] : (incident_c(v0, v3) & incident_c(v0, v2) & part_of(v3, v1) & part_of(v2, v1) &  ~ part_of(v3, v2) &  ~ part_of(v2, v3)))
% 5.38/1.86  | (48)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ ordered_by(v0, v2, v3) |  ~ ordered_by(v0, v1, v2) | between_o(v0, v1, v2, v3))
% 5.38/1.86  | (49)  ? [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (underlying_curve(v1) = v2) |  ? [v3] : (( ~ incident_o(v3, v1) |  ~ incident_c(v3, v0)) & (incident_o(v3, v1) | incident_c(v3, v0))))
% 5.38/1.86  | (50)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ finish_point(v0, v1) |  ~ incident_o(v2, v1) | ordered_by(v1, v2, v0))
% 5.38/1.86  | (51)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_o(v3, v0, v1, v2) |  ? [v4] : (between_c(v4, v0, v1, v2) &  ! [v5] : ( ~ incident_o(v5, v3) | incident_c(v5, v4)) &  ! [v5] : ( ~ incident_c(v5, v4) | incident_o(v5, v3))))
% 5.38/1.86  | (52)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ incident_o(v2, v1) |  ~ start_point(v0, v1) | ordered_by(v1, v0, v2))
% 5.38/1.86  | (53)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v1 |  ~ inner_point(v2, v4) |  ~ end_point(v3, v4) |  ~ end_point(v1, v4) |  ~ part_of(v4, v0) | between_c(v0, v1, v2, v3))
% 5.38/1.86  | (54)  ? [v0] :  ? [v1] : inner_point(v1, v0)
% 5.38/1.86  | (55)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (sum(v3, v2) = v1) |  ~ (sum(v3, v2) = v0))
% 5.38/1.86  | (56)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v2, v3) | ordered_by(v0, v2, v1))
% 5.38/1.86  | (57)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ end_point(v4, v3) |  ~ end_point(v4, v2) |  ~ end_point(v4, v1) |  ~ part_of(v3, v0) |  ~ part_of(v2, v0) |  ~ part_of(v1, v0) | part_of(v3, v2) | part_of(v3, v1) | part_of(v2, v3) | part_of(v2, v1) | part_of(v1, v3) | part_of(v1, v2))
% 5.38/1.86  | (58)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ incident_c(v0, v2) |  ~ incident_c(v0, v1) | meet(v0, v1, v2) |  ? [v3] : (incident_c(v3, v2) & incident_c(v3, v1) & ( ~ end_point(v3, v2) |  ~ end_point(v3, v1))))
% 5.38/1.86  | (59)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ meet(v0, v1, v2) | incident_c(v0, v1))
% 5.38/1.86  | (60)  ! [v0] :  ! [v1] : ( ~ end_point(v1, v0) |  ? [v2] : ( ~ (v2 = v1) & end_point(v2, v0)))
% 5.38/1.86  |
% 5.38/1.86  | Instantiating formula (34) with all_0_1_1, all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms ordered_by(all_0_2_2, all_0_0_0, all_0_1_1), ordered_by(all_0_2_2, all_0_1_1, all_0_0_0), yields:
% 5.38/1.87  | (61) between_o(all_0_2_2, all_0_1_1, all_0_0_0, all_0_1_1)
% 5.38/1.87  |
% 5.38/1.87  | Instantiating formula (51) with all_0_2_2, all_0_1_1, all_0_0_0, all_0_1_1 and discharging atoms between_o(all_0_2_2, all_0_1_1, all_0_0_0, all_0_1_1), yields:
% 5.38/1.87  | (62)  ? [v0] : (between_c(v0, all_0_1_1, all_0_0_0, all_0_1_1) &  ! [v1] : ( ~ incident_o(v1, all_0_2_2) | incident_c(v1, v0)) &  ! [v1] : ( ~ incident_c(v1, v0) | incident_o(v1, all_0_2_2)))
% 5.38/1.87  |
% 5.38/1.87  | Instantiating (62) with all_38_0_23 yields:
% 5.38/1.87  | (63) between_c(all_38_0_23, all_0_1_1, all_0_0_0, all_0_1_1) &  ! [v0] : ( ~ incident_o(v0, all_0_2_2) | incident_c(v0, all_38_0_23)) &  ! [v0] : ( ~ incident_c(v0, all_38_0_23) | incident_o(v0, all_0_2_2))
% 5.38/1.87  |
% 5.38/1.87  | Applying alpha-rule on (63) yields:
% 5.38/1.87  | (64) between_c(all_38_0_23, all_0_1_1, all_0_0_0, all_0_1_1)
% 5.38/1.87  | (65)  ! [v0] : ( ~ incident_o(v0, all_0_2_2) | incident_c(v0, all_38_0_23))
% 5.38/1.87  | (66)  ! [v0] : ( ~ incident_c(v0, all_38_0_23) | incident_o(v0, all_0_2_2))
% 5.38/1.87  |
% 5.38/1.87  | Instantiating formula (43) with all_0_0_0, all_0_1_1, all_38_0_23 and discharging atoms between_c(all_38_0_23, all_0_1_1, all_0_0_0, all_0_1_1), yields:
% 5.38/1.87  | (67) $false
% 5.38/1.87  |
% 5.38/1.87  |-The branch is then unsatisfiable
% 5.38/1.87  % SZS output end Proof for theBenchmark
% 5.38/1.87  
% 5.38/1.87  1263ms
%------------------------------------------------------------------------------