TSTP Solution File: GEO125+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO125+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n004.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 03:47:48 EDT 2022
% Result : Theorem 4.01s 1.58s
% Output : Proof 6.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : GEO125+1 : TPTP v8.1.0. Released v2.4.0.
% 0.14/0.15 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Fri Jun 17 20:44:53 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.52/0.62 ____ _
% 0.52/0.62 ___ / __ \_____(_)___ ________ __________
% 0.52/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.52/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.52/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.52/0.62
% 0.52/0.62 A Theorem Prover for First-Order Logic
% 0.52/0.62 (ePrincess v.1.0)
% 0.52/0.62
% 0.52/0.62 (c) Philipp Rümmer, 2009-2015
% 0.52/0.62 (c) Peter Backeman, 2014-2015
% 0.52/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.52/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.52/0.62 Bug reports to peter@backeman.se
% 0.52/0.62
% 0.52/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.52/0.62
% 0.52/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.75/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.87/1.00 Prover 0: Preprocessing ...
% 2.72/1.29 Prover 0: Warning: ignoring some quantifiers
% 2.97/1.32 Prover 0: Constructing countermodel ...
% 4.01/1.58 Prover 0: proved (903ms)
% 4.01/1.58
% 4.01/1.58 No countermodel exists, formula is valid
% 4.01/1.58 % SZS status Theorem for theBenchmark
% 4.01/1.58
% 4.01/1.58 Generating proof ... Warning: ignoring some quantifiers
% 5.96/1.99 found it (size 18)
% 5.96/1.99
% 5.96/1.99 % SZS output start Proof for theBenchmark
% 5.96/1.99 Assumed formulas after preprocessing and simplification:
% 5.96/1.99 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & finish_point(v2, v0) & finish_point(v1, v0) & ! [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)))
% 5.96/2.04 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 5.96/2.04 | (1) ~ (all_0_0_0 = all_0_1_1) & finish_point(all_0_0_0, all_0_2_2) & finish_point(all_0_1_1, all_0_2_2) & ! [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))
% 5.96/2.05 |
% 5.96/2.06 | Applying alpha-rule on (1) yields:
% 5.96/2.06 | (2) ? [v0] : ? [v1] : inner_point(v1, v0)
% 5.96/2.06 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v3, v2) | ordered_by(v0, v1, v2))
% 5.96/2.06 | (4) ! [v0] : ! [v1] : ( ~ start_point(v0, v1) | incident_o(v0, v1))
% 5.96/2.06 | (5) ? [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))))
% 5.96/2.06 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v2, v1) | ordered_by(v0, v1, v2))
% 5.96/2.06 | (7) ! [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))
% 5.96/2.06 | (8) ! [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)))
% 5.96/2.06 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ meet(v0, v1, v2) | ~ incident_c(v3, v2) | ~ incident_c(v3, v1) | end_point(v3, v1))
% 5.96/2.06 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0))
% 5.96/2.06 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v3, v2) | ordered_by(v0, v2, v3))
% 5.96/2.06 | (12) ! [v0] : ! [v1] : ( ~ end_point(v1, v0) | open(v0))
% 5.96/2.06 | (13) ? [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))))
% 5.96/2.06 | (14) ! [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))))
% 5.96/2.06 | (15) ! [v0] : ! [v1] : ( ~ end_point(v0, v1) | incident_c(v0, v1))
% 5.96/2.06 | (16) finish_point(all_0_0_0, all_0_2_2)
% 5.96/2.06 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sum(v1, v2) = v0) | ~ closed(v0) | ~ meet(v3, v1, v2) | ~ end_point(v4, v1) | meet(v4, v1, v2))
% 5.96/2.06 | (18) ! [v0] : ! [v1] : ( ~ incident_o(v0, v1) | finish_point(v0, v1) | ? [v2] : ( ~ (v2 = v0) & incident_o(v2, v1) & ~ ordered_by(v1, v2, v0)))
% 5.96/2.06 | (19) ! [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))
% 5.96/2.06 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ ordered_by(v0, v3, v2) | ~ ordered_by(v0, v2, v1) | between_o(v0, v1, v2, v3))
% 5.96/2.06 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (underlying_curve(v2) = v1) | ~ (underlying_curve(v2) = v0))
% 5.96/2.06 | (22) ! [v0] : ! [v1] : (v1 = v0 | ~ part_of(v1, v0) | open(v1))
% 5.96/2.06 | (23) ! [v0] : ! [v1] : ( ~ incident_c(v0, v1) | inner_point(v0, v1) | end_point(v0, v1))
% 5.96/2.06 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ ordered_by(v0, v2, v3) | ~ ordered_by(v0, v1, v2) | between_o(v0, v1, v2, v3))
% 5.96/2.06 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ incident_o(v2, v1) | ~ start_point(v0, v1) | ordered_by(v1, v0, v2))
% 5.96/2.06 | (26) ! [v0] : ( ~ open(v0) | ? [v1] : end_point(v1, v0))
% 5.96/2.06 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (underlying_curve(v1) = v0) | ~ incident_c(v2, v0) | incident_o(v2, v1))
% 5.96/2.06 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (underlying_curve(v1) = v0) | ~ incident_o(v2, v1) | incident_c(v2, v0))
% 5.96/2.07 | (29) ? [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))))
% 5.96/2.07 | (30) ? [v0] : ? [v1] : start_point(v1, v0)
% 5.96/2.07 | (31) ! [v0] : ! [v1] : ( ~ finish_point(v0, v1) | incident_o(v0, v1))
% 5.96/2.07 | (32) ! [v0] : ! [v1] : ( ~ inner_point(v1, v0) | ? [v2] : ? [v3] : (sum(v2, v3) = v0 & meet(v1, v2, v3)))
% 5.96/2.07 | (33) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ finish_point(v0, v1) | ~ incident_o(v2, v1) | ordered_by(v1, v2, v0))
% 5.96/2.07 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ meet(v0, v1, v2) | incident_c(v0, v1))
% 5.96/2.07 | (35) ? [v0] : ? [v1] : (part_of(v1, v0) | ? [v2] : (incident_c(v2, v1) & ~ incident_c(v2, v0)))
% 5.96/2.07 | (36) ! [v0] : ! [v1] : ( ~ incident_o(v0, v1) | start_point(v0, v1) | ? [v2] : ( ~ (v2 = v0) & incident_o(v2, v1) & ~ ordered_by(v1, v0, v2)))
% 5.96/2.07 | (37) ? [v0] : (closed(v0) | ? [v1] : end_point(v1, v0))
% 5.96/2.07 | (38) ~ (all_0_0_0 = all_0_1_1)
% 5.96/2.07 | (39) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ incident_c(v2, v1) | ~ incident_c(v2, v0)) & (incident_c(v2, v1) | incident_c(v2, v0))))
% 5.96/2.07 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | v2 = v1 | ~ end_point(v3, v0) | ~ end_point(v2, v0) | ~ end_point(v1, v0))
% 5.96/2.07 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ ordered_by(v0, v1, v2) | incident_o(v1, v0))
% 5.96/2.07 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v2, v3) | ordered_by(v0, v2, v1))
% 5.96/2.07 | (43) ! [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))
% 5.96/2.07 | (44) ! [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))))
% 5.96/2.07 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ meet(v0, v1, v2) | ~ incident_c(v3, v2) | ~ incident_c(v3, v1) | end_point(v3, v2))
% 5.96/2.07 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ meet(v0, v1, v2) | incident_c(v0, v2))
% 6.41/2.07 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ ordered_by(v0, v1, v2) | incident_o(v2, v0))
% 6.41/2.07 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1, v2) = v0) | ~ incident_c(v3, v0) | incident_c(v3, v2) | incident_c(v3, v1))
% 6.41/2.07 | (49) ! [v0] : ! [v1] : ( ~ end_point(v1, v0) | ? [v2] : ( ~ (v2 = v1) & end_point(v2, v0)))
% 6.41/2.07 | (50) ! [v0] : ! [v1] : ( ~ inner_point(v0, v1) | incident_c(v0, v1))
% 6.41/2.07 | (51) ! [v0] : ! [v1] : ! [v2] : ~ between_c(v0, v1, v2, v1)
% 6.41/2.07 | (52) ! [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)))
% 6.41/2.07 | (53) ? [v0] : ? [v1] : (open(v1) & ! [v2] : ( ~ incident_o(v2, v0) | incident_c(v2, v1)) & ! [v2] : ( ~ incident_c(v2, v1) | incident_o(v2, v0)))
% 6.41/2.07 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ incident_c(v2, v1) | ~ part_of(v1, v0) | incident_c(v2, v0))
% 6.41/2.07 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1, v2) = v0) | ~ incident_c(v3, v1) | incident_c(v3, v0))
% 6.41/2.07 | (56) ! [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))))
% 6.41/2.07 | (57) ! [v0] : ! [v1] : ( ~ inner_point(v0, v1) | ~ end_point(v0, v1))
% 6.41/2.07 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1, v2) = v0) | ~ incident_c(v3, v2) | incident_c(v3, v0))
% 6.41/2.08 | (59) finish_point(all_0_1_1, all_0_2_2)
% 6.41/2.08 | (60) ! [v0] : ! [v1] : ( ~ closed(v0) | ~ end_point(v1, v0))
% 6.41/2.08 | (61) ? [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))))
% 6.41/2.08 |
% 6.41/2.08 | Instantiating formula (31) with all_0_2_2, all_0_0_0 and discharging atoms finish_point(all_0_0_0, all_0_2_2), yields:
% 6.41/2.08 | (62) incident_o(all_0_0_0, all_0_2_2)
% 6.41/2.08 |
% 6.41/2.08 | Instantiating formula (31) with all_0_2_2, all_0_1_1 and discharging atoms finish_point(all_0_1_1, all_0_2_2), yields:
% 6.41/2.08 | (63) incident_o(all_0_1_1, all_0_2_2)
% 6.41/2.08 |
% 6.41/2.08 | Instantiating formula (33) with all_0_0_0, all_0_2_2, all_0_1_1 and discharging atoms finish_point(all_0_1_1, all_0_2_2), incident_o(all_0_0_0, all_0_2_2), yields:
% 6.41/2.08 | (64) all_0_0_0 = all_0_1_1 | ordered_by(all_0_2_2, all_0_0_0, all_0_1_1)
% 6.41/2.08 |
% 6.41/2.08 | Instantiating formula (33) with all_0_1_1, all_0_2_2, all_0_0_0 and discharging atoms finish_point(all_0_0_0, all_0_2_2), incident_o(all_0_1_1, all_0_2_2), yields:
% 6.41/2.08 | (65) all_0_0_0 = all_0_1_1 | ordered_by(all_0_2_2, all_0_1_1, all_0_0_0)
% 6.41/2.08 |
% 6.41/2.08 +-Applying beta-rule and splitting (65), into two cases.
% 6.41/2.08 |-Branch one:
% 6.41/2.08 | (66) ordered_by(all_0_2_2, all_0_1_1, all_0_0_0)
% 6.41/2.08 |
% 6.41/2.08 +-Applying beta-rule and splitting (64), into two cases.
% 6.41/2.08 |-Branch one:
% 6.41/2.08 | (67) ordered_by(all_0_2_2, all_0_0_0, all_0_1_1)
% 6.41/2.08 |
% 6.41/2.08 | Instantiating formula (20) 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:
% 6.41/2.08 | (68) between_o(all_0_2_2, all_0_1_1, all_0_0_0, all_0_1_1)
% 6.41/2.08 |
% 6.41/2.08 | Instantiating formula (56) 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:
% 6.41/2.08 | (69) ? [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)))
% 6.41/2.08 |
% 6.41/2.08 | Instantiating (69) with all_62_0_25 yields:
% 6.41/2.08 | (70) between_c(all_62_0_25, all_0_1_1, all_0_0_0, all_0_1_1) & ! [v0] : ( ~ incident_o(v0, all_0_2_2) | incident_c(v0, all_62_0_25)) & ! [v0] : ( ~ incident_c(v0, all_62_0_25) | incident_o(v0, all_0_2_2))
% 6.41/2.08 |
% 6.41/2.08 | Applying alpha-rule on (70) yields:
% 6.41/2.08 | (71) between_c(all_62_0_25, all_0_1_1, all_0_0_0, all_0_1_1)
% 6.41/2.08 | (72) ! [v0] : ( ~ incident_o(v0, all_0_2_2) | incident_c(v0, all_62_0_25))
% 6.41/2.08 | (73) ! [v0] : ( ~ incident_c(v0, all_62_0_25) | incident_o(v0, all_0_2_2))
% 6.41/2.08 |
% 6.41/2.08 | Instantiating formula (51) with all_0_0_0, all_0_1_1, all_62_0_25 and discharging atoms between_c(all_62_0_25, all_0_1_1, all_0_0_0, all_0_1_1), yields:
% 6.41/2.08 | (74) $false
% 6.41/2.08 |
% 6.41/2.08 |-The branch is then unsatisfiable
% 6.41/2.08 |-Branch two:
% 6.41/2.08 | (75) ~ ordered_by(all_0_2_2, all_0_0_0, all_0_1_1)
% 6.41/2.08 | (76) all_0_0_0 = all_0_1_1
% 6.41/2.08 |
% 6.41/2.08 | Equations (76) can reduce 38 to:
% 6.41/2.08 | (77) $false
% 6.41/2.08 |
% 6.41/2.08 |-The branch is then unsatisfiable
% 6.41/2.08 |-Branch two:
% 6.41/2.08 | (78) ~ ordered_by(all_0_2_2, all_0_1_1, all_0_0_0)
% 6.41/2.08 | (76) all_0_0_0 = all_0_1_1
% 6.41/2.08 |
% 6.41/2.08 | Equations (76) can reduce 38 to:
% 6.41/2.08 | (77) $false
% 6.41/2.08 |
% 6.41/2.08 |-The branch is then unsatisfiable
% 6.41/2.08 % SZS output end Proof for theBenchmark
% 6.41/2.08
% 6.41/2.08 1450ms
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