TSTP Solution File: GEO203+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO203+2 : TPTP v8.1.0. Released v3.3.0.
% 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 03:48:39 EDT 2022
% Result : Theorem 85.23s 51.34s
% Output : Proof 88.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GEO203+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Fri Jun 17 15:15:42 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.53/0.59 ____ _
% 0.53/0.59 ___ / __ \_____(_)___ ________ __________
% 0.53/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.53/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.53/0.59
% 0.53/0.59 A Theorem Prover for First-Order Logic
% 0.53/0.59 (ePrincess v.1.0)
% 0.53/0.59
% 0.53/0.59 (c) Philipp Rümmer, 2009-2015
% 0.53/0.59 (c) Peter Backeman, 2014-2015
% 0.53/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.59 Bug reports to peter@backeman.se
% 0.53/0.59
% 0.53/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.59
% 0.53/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.53/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.65/0.97 Prover 0: Preprocessing ...
% 1.91/1.11 Prover 0: Warning: ignoring some quantifiers
% 1.91/1.13 Prover 0: Constructing countermodel ...
% 19.85/5.94 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 20.17/5.97 Prover 1: Preprocessing ...
% 20.62/6.09 Prover 1: Constructing countermodel ...
% 21.19/6.18 Prover 1: gave up
% 21.19/6.18 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 21.19/6.20 Prover 2: Preprocessing ...
% 21.54/6.29 Prover 2: Warning: ignoring some quantifiers
% 21.54/6.29 Prover 2: Constructing countermodel ...
% 22.08/6.36 Prover 2: gave up
% 22.08/6.37 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 22.08/6.38 Prover 3: Preprocessing ...
% 22.08/6.40 Prover 3: Warning: ignoring some quantifiers
% 22.08/6.40 Prover 3: Constructing countermodel ...
% 78.59/49.79 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 78.59/49.82 Prover 4: Preprocessing ...
% 78.98/49.92 Prover 4: Warning: ignoring some quantifiers
% 78.98/49.92 Prover 4: Constructing countermodel ...
% 83.11/50.85 Prover 3: stopped
% 83.99/51.05 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 83.99/51.08 Prover 5: Preprocessing ...
% 84.27/51.14 Prover 5: Constructing countermodel ...
% 85.23/51.34 Prover 5: proved (285ms)
% 85.23/51.34 Prover 0: stopped
% 85.23/51.34 Prover 4: stopped
% 85.23/51.34
% 85.23/51.34 No countermodel exists, formula is valid
% 85.23/51.34 % SZS status Theorem for theBenchmark
% 85.23/51.34
% 85.23/51.34 Generating proof ... found it (size 269)
% 87.89/51.93
% 87.89/51.93 % SZS output start Proof for theBenchmark
% 87.89/51.93 Assumed formulas after preprocessing and simplification:
% 87.89/51.93 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v2) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v2) = v9 & apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection_point(v0, v1) = v3) | ~ (distinct_points(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v0, v1) = v4) | ~ (apart_point_and_line(v2, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v4) = v7 & ( ~ (v5 = 0) | v7 = 0 | ( ~ (v6 = 0) & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v0, v1) = v4) | ~ (apart_point_and_line(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v4) = v7 & ( ~ (v5 = 0) | v7 = 0 | ( ~ (v6 = 0) & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v0, v1) = v3) | ~ (distinct_points(v2, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v3) = v6 & distinct_points(v2, v0) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v7 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v0, v1) = v3) | ~ (distinct_points(v2, v0) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v3) = v6 & distinct_points(v2, v1) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v7 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apart_point_and_line(v2, v1) = v4) | ~ (apart_point_and_line(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (intersection_point(v0, v1) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v6) = v7 & ( ~ (v5 = 0) | v7 = 0)) | ( ~ (v4 = 0) & ~ (v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (distinct_points(v2, v1) = v4) | ~ (distinct_points(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (line_connecting(v0, v1) = v6 & apart_point_and_line(v2, v6) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0))) | (v4 = 0 & v3 = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apart_point_and_line(v2, v1) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (intersection_point(v0, v1) = v5 & apart_point_and_line(v2, v0) = v4 & distinct_points(v2, v5) = v6 & (v6 = 0 | ( ~ (v4 = 0) & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apart_point_and_line(v2, v0) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (intersection_point(v0, v1) = v5 & apart_point_and_line(v2, v1) = v4 & distinct_points(v2, v5) = v6 & (v6 = 0 | ( ~ (v4 = 0) & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v1) = v3) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (line_connecting(v0, v1) = v4 & apart_point_and_line(v2, v4) = v5 & distinct_points(v2, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v0) = v3) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (line_connecting(v0, v1) = v4 & apart_point_and_line(v2, v4) = v5 & distinct_points(v2, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (intersection_point(v0, v2) = v4 & intersection_point(v0, v1) = v3 & line_connecting(v3, v4) = v5 & convergent_lines(v0, v2) = 0 & convergent_lines(v0, v1) = 0 & distinct_lines(v5, v0) = 0 & distinct_points(v3, v4) = 0)
% 87.95/51.98 | Applying alpha-rule on (0) yields:
% 87.95/51.98 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 87.95/51.98 | (2) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 87.95/51.98 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 87.95/51.98 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 87.95/51.98 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 87.95/51.98 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection_point(v0, v1) = v3) | ~ (distinct_points(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0)))))
% 87.95/51.98 | (7) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0)
% 87.95/51.98 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0)))
% 87.95/51.98 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 87.95/51.98 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 87.95/51.98 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v0, v1) = v4) | ~ (apart_point_and_line(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v4) = v7 & ( ~ (v5 = 0) | v7 = 0 | ( ~ (v6 = 0) & ~ (v3 = 0)))))
% 87.95/51.98 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apart_point_and_line(v2, v0) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (intersection_point(v0, v1) = v5 & apart_point_and_line(v2, v1) = v4 & distinct_points(v2, v5) = v6 & (v6 = 0 | ( ~ (v4 = 0) & ~ (v3 = 0)))))
% 87.95/51.98 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 87.95/51.98 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0))))
% 87.95/51.98 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 87.95/51.99 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0)
% 87.95/51.99 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apart_point_and_line(v2, v1) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (intersection_point(v0, v1) = v5 & apart_point_and_line(v2, v0) = v4 & distinct_points(v2, v5) = v6 & (v6 = 0 | ( ~ (v4 = 0) & ~ (v3 = 0)))))
% 87.95/51.99 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (distinct_points(v2, v1) = v4) | ~ (distinct_points(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (line_connecting(v0, v1) = v6 & apart_point_and_line(v2, v6) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0))) | (v4 = 0 & v3 = 0))
% 87.95/51.99 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 87.95/51.99 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 87.95/51.99 | (21) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 87.95/51.99 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 87.95/51.99 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 87.95/51.99 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v2) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 87.95/51.99 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 87.95/51.99 | (26) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 87.95/51.99 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5))
% 87.95/51.99 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 87.95/51.99 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v0, v1) = v3) | ~ (distinct_points(v2, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v3) = v6 & distinct_points(v2, v0) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v7 = 0 & v4 = 0))))
% 87.95/51.99 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v0) = v3) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (line_connecting(v0, v1) = v4 & apart_point_and_line(v2, v4) = v5 & distinct_points(v2, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v3 = 0))))
% 87.95/51.99 | (31) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (intersection_point(v0, v2) = v4 & intersection_point(v0, v1) = v3 & line_connecting(v3, v4) = v5 & convergent_lines(v0, v2) = 0 & convergent_lines(v0, v1) = 0 & distinct_lines(v5, v0) = 0 & distinct_points(v3, v4) = 0)
% 87.95/51.99 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 87.95/51.99 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 87.95/51.99 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 87.95/51.99 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v1) = v3) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (line_connecting(v0, v1) = v4 & apart_point_and_line(v2, v4) = v5 & distinct_points(v2, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v3 = 0))))
% 87.95/51.99 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 87.95/51.99 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5))
% 87.95/51.99 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v0, v1) = v4) | ~ (apart_point_and_line(v2, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v4) = v7 & ( ~ (v5 = 0) | v7 = 0 | ( ~ (v6 = 0) & ~ (v3 = 0)))))
% 87.95/51.99 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v0, v1) = v3) | ~ (distinct_points(v2, v0) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v3) = v6 & distinct_points(v2, v1) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v7 = 0 & v4 = 0))))
% 87.95/51.99 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5))
% 87.95/51.99 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0)
% 87.95/52.00 | (42) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 87.95/52.00 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apart_point_and_line(v2, v1) = v4) | ~ (apart_point_and_line(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (intersection_point(v0, v1) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v6) = v7 & ( ~ (v5 = 0) | v7 = 0)) | ( ~ (v4 = 0) & ~ (v3 = 0)))
% 87.95/52.00 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v2) = v9 & apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0)))
% 87.95/52.00 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5))
% 87.95/52.00 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 87.95/52.00 |
% 87.95/52.00 | Instantiating (31) with all_1_0_0, all_1_1_1, all_1_2_2, all_1_3_3, all_1_4_4, all_1_5_5 yields:
% 87.95/52.00 | (47) intersection_point(all_1_5_5, all_1_3_3) = all_1_1_1 & intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2 & line_connecting(all_1_2_2, all_1_1_1) = all_1_0_0 & convergent_lines(all_1_5_5, all_1_3_3) = 0 & convergent_lines(all_1_5_5, all_1_4_4) = 0 & distinct_lines(all_1_0_0, all_1_5_5) = 0 & distinct_points(all_1_2_2, all_1_1_1) = 0
% 87.95/52.00 |
% 87.95/52.00 | Applying alpha-rule on (47) yields:
% 87.95/52.00 | (48) line_connecting(all_1_2_2, all_1_1_1) = all_1_0_0
% 87.95/52.00 | (49) distinct_lines(all_1_0_0, all_1_5_5) = 0
% 87.95/52.00 | (50) intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2
% 87.95/52.00 | (51) convergent_lines(all_1_5_5, all_1_3_3) = 0
% 87.95/52.00 | (52) distinct_points(all_1_2_2, all_1_1_1) = 0
% 87.95/52.00 | (53) convergent_lines(all_1_5_5, all_1_4_4) = 0
% 87.95/52.00 | (54) intersection_point(all_1_5_5, all_1_3_3) = all_1_1_1
% 87.95/52.00 |
% 87.95/52.00 | Instantiating formula (21) with all_1_2_2 yields:
% 87.95/52.00 | (55) ~ (distinct_points(all_1_2_2, all_1_2_2) = 0)
% 87.95/52.00 |
% 87.95/52.00 | Instantiating formula (7) with all_1_3_3, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 87.95/52.00 | (56) distinct_lines(all_1_5_5, all_1_3_3) = 0
% 87.95/52.00 |
% 87.95/52.00 | Instantiating formula (35) with 0, all_1_2_2, all_1_1_1, all_1_2_2 and discharging atoms distinct_points(all_1_2_2, all_1_1_1) = 0, yields:
% 87.95/52.00 | (57) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_2_2, all_1_1_1) = v0 & apart_point_and_line(all_1_2_2, v0) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 87.95/52.00 |
% 87.95/52.00 | Instantiating formula (29) with 0, all_1_0_0, all_1_2_2, all_1_1_1, all_1_2_2 and discharging atoms line_connecting(all_1_2_2, all_1_1_1) = all_1_0_0, distinct_points(all_1_2_2, all_1_1_1) = 0, yields:
% 87.95/52.00 | (58) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_2_2, all_1_0_0) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & distinct_points(all_1_2_2, all_1_2_2) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 87.95/52.00 |
% 87.95/52.00 | Instantiating formula (36) with all_1_5_5, all_1_0_0, all_1_1_1, all_1_2_2 and discharging atoms distinct_lines(all_1_0_0, all_1_5_5) = 0, distinct_points(all_1_2_2, all_1_1_1) = 0, yields:
% 87.95/52.00 | (59) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_0_0) = v2 & apart_point_and_line(all_1_1_1, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_0_0) = v0 & apart_point_and_line(all_1_2_2, all_1_5_5) = v1 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0))
% 87.95/52.00 |
% 87.95/52.00 | Instantiating (59) with all_17_0_6, all_17_1_7, all_17_2_8, all_17_3_9 yields:
% 87.95/52.00 | (60) apart_point_and_line(all_1_1_1, all_1_0_0) = all_17_1_7 & apart_point_and_line(all_1_1_1, all_1_5_5) = all_17_0_6 & apart_point_and_line(all_1_2_2, all_1_0_0) = all_17_3_9 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_17_2_8 & (all_17_0_6 = 0 | all_17_1_7 = 0 | all_17_2_8 = 0 | all_17_3_9 = 0)
% 87.95/52.00 |
% 87.95/52.00 | Applying alpha-rule on (60) yields:
% 87.95/52.00 | (61) apart_point_and_line(all_1_1_1, all_1_5_5) = all_17_0_6
% 87.95/52.00 | (62) apart_point_and_line(all_1_2_2, all_1_0_0) = all_17_3_9
% 87.95/52.00 | (63) apart_point_and_line(all_1_2_2, all_1_5_5) = all_17_2_8
% 87.95/52.00 | (64) all_17_0_6 = 0 | all_17_1_7 = 0 | all_17_2_8 = 0 | all_17_3_9 = 0
% 87.95/52.00 | (65) apart_point_and_line(all_1_1_1, all_1_0_0) = all_17_1_7
% 87.95/52.00 |
% 87.95/52.00 | Instantiating (57) with all_19_0_10, all_19_1_11, all_19_2_12 yields:
% 87.95/52.00 | (66) line_connecting(all_1_2_2, all_1_1_1) = all_19_2_12 & apart_point_and_line(all_1_2_2, all_19_2_12) = all_19_1_11 & distinct_points(all_1_2_2, all_1_2_2) = all_19_0_10 & ( ~ (all_19_1_11 = 0) | all_19_0_10 = 0)
% 87.95/52.00 |
% 87.95/52.00 | Applying alpha-rule on (66) yields:
% 87.95/52.00 | (67) line_connecting(all_1_2_2, all_1_1_1) = all_19_2_12
% 87.95/52.00 | (68) apart_point_and_line(all_1_2_2, all_19_2_12) = all_19_1_11
% 87.95/52.00 | (69) distinct_points(all_1_2_2, all_1_2_2) = all_19_0_10
% 87.95/52.00 | (70) ~ (all_19_1_11 = 0) | all_19_0_10 = 0
% 87.95/52.00 |
% 87.95/52.00 | Instantiating (58) with all_21_0_13, all_21_1_14, all_21_2_15 yields:
% 87.95/52.00 | (71) apart_point_and_line(all_1_2_2, all_1_0_0) = all_21_1_14 & distinct_points(all_1_2_2, all_1_1_1) = all_21_2_15 & distinct_points(all_1_2_2, all_1_2_2) = all_21_0_13 & ( ~ (all_21_1_14 = 0) | ~ (all_21_2_15 = 0) | all_21_0_13 = 0)
% 87.95/52.00 |
% 87.95/52.00 | Applying alpha-rule on (71) yields:
% 87.95/52.00 | (72) apart_point_and_line(all_1_2_2, all_1_0_0) = all_21_1_14
% 87.95/52.00 | (73) distinct_points(all_1_2_2, all_1_1_1) = all_21_2_15
% 87.95/52.00 | (74) distinct_points(all_1_2_2, all_1_2_2) = all_21_0_13
% 87.95/52.00 | (75) ~ (all_21_1_14 = 0) | ~ (all_21_2_15 = 0) | all_21_0_13 = 0
% 87.95/52.00 |
% 87.95/52.00 | Instantiating formula (9) with all_1_2_2, all_1_1_1, all_19_2_12, all_1_0_0 and discharging atoms line_connecting(all_1_2_2, all_1_1_1) = all_19_2_12, line_connecting(all_1_2_2, all_1_1_1) = all_1_0_0, yields:
% 87.95/52.00 | (76) all_19_2_12 = all_1_0_0
% 87.95/52.00 |
% 87.95/52.00 | Instantiating formula (20) with all_1_2_2, all_1_0_0, all_17_3_9, all_19_1_11 and discharging atoms apart_point_and_line(all_1_2_2, all_1_0_0) = all_17_3_9, yields:
% 87.95/52.00 | (77) all_19_1_11 = all_17_3_9 | ~ (apart_point_and_line(all_1_2_2, all_1_0_0) = all_19_1_11)
% 87.95/52.00 |
% 87.95/52.00 | Instantiating formula (20) with all_1_2_2, all_1_0_0, all_17_3_9, all_21_1_14 and discharging atoms apart_point_and_line(all_1_2_2, all_1_0_0) = all_21_1_14, apart_point_and_line(all_1_2_2, all_1_0_0) = all_17_3_9, yields:
% 87.95/52.00 | (78) all_21_1_14 = all_17_3_9
% 87.95/52.00 |
% 87.95/52.00 | Instantiating formula (32) with all_1_2_2, all_1_1_1, all_21_2_15, 0 and discharging atoms distinct_points(all_1_2_2, all_1_1_1) = all_21_2_15, distinct_points(all_1_2_2, all_1_1_1) = 0, yields:
% 87.95/52.00 | (79) all_21_2_15 = 0
% 87.95/52.00 |
% 87.95/52.00 | Using (74) and (55) yields:
% 87.95/52.00 | (80) ~ (all_21_0_13 = 0)
% 87.95/52.00 |
% 87.95/52.00 | Instantiating formula (32) with all_1_2_2, all_1_2_2, all_19_0_10, all_21_0_13 and discharging atoms distinct_points(all_1_2_2, all_1_2_2) = all_21_0_13, distinct_points(all_1_2_2, all_1_2_2) = all_19_0_10, yields:
% 87.95/52.00 | (81) all_21_0_13 = all_19_0_10
% 87.95/52.00 |
% 87.95/52.01 | Equations (81) can reduce 80 to:
% 87.95/52.01 | (82) ~ (all_19_0_10 = 0)
% 87.95/52.01 |
% 87.95/52.01 | From (76) and (67) follows:
% 87.95/52.01 | (48) line_connecting(all_1_2_2, all_1_1_1) = all_1_0_0
% 87.95/52.01 |
% 87.95/52.01 | From (76) and (68) follows:
% 87.95/52.01 | (84) apart_point_and_line(all_1_2_2, all_1_0_0) = all_19_1_11
% 87.95/52.01 |
% 87.95/52.01 | From (79) and (73) follows:
% 87.95/52.01 | (52) distinct_points(all_1_2_2, all_1_1_1) = 0
% 87.95/52.01 |
% 87.95/52.01 | From (81) and (74) follows:
% 87.95/52.01 | (69) distinct_points(all_1_2_2, all_1_2_2) = all_19_0_10
% 87.95/52.01 |
% 87.95/52.01 +-Applying beta-rule and splitting (75), into two cases.
% 87.95/52.01 |-Branch one:
% 87.95/52.01 | (87) ~ (all_21_1_14 = 0)
% 87.95/52.01 |
% 87.95/52.01 | Equations (78) can reduce 87 to:
% 87.95/52.01 | (88) ~ (all_17_3_9 = 0)
% 87.95/52.01 |
% 87.95/52.01 +-Applying beta-rule and splitting (77), into two cases.
% 87.95/52.01 |-Branch one:
% 87.95/52.01 | (89) ~ (apart_point_and_line(all_1_2_2, all_1_0_0) = all_19_1_11)
% 87.95/52.01 |
% 87.95/52.01 | Using (84) and (89) yields:
% 87.95/52.01 | (90) $false
% 87.95/52.01 |
% 87.95/52.01 |-The branch is then unsatisfiable
% 87.95/52.01 |-Branch two:
% 87.95/52.01 | (84) apart_point_and_line(all_1_2_2, all_1_0_0) = all_19_1_11
% 87.95/52.01 | (92) all_19_1_11 = all_17_3_9
% 87.95/52.01 |
% 87.95/52.01 | From (92) and (84) follows:
% 87.95/52.01 | (62) apart_point_and_line(all_1_2_2, all_1_0_0) = all_17_3_9
% 87.95/52.01 |
% 87.95/52.01 | Instantiating formula (14) with all_1_0_0, all_1_1_1, all_1_1_1, all_1_2_2 and discharging atoms line_connecting(all_1_2_2, all_1_1_1) = all_1_0_0, yields:
% 87.95/52.01 | (94) ~ (apart_point_and_line(all_1_1_1, all_1_0_0) = 0) | ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_1_1_1, all_1_1_1) = v2 & distinct_points(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))
% 87.95/52.01 |
% 87.95/52.01 | Instantiating formula (11) with all_1_1_1, all_17_0_6, all_1_1_1, all_1_3_3, all_1_5_5 and discharging atoms intersection_point(all_1_5_5, all_1_3_3) = all_1_1_1, apart_point_and_line(all_1_1_1, all_1_5_5) = all_17_0_6, yields:
% 87.95/52.01 | (95) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_3_3) = v1 & convergent_lines(all_1_5_5, all_1_3_3) = v0 & distinct_points(all_1_1_1, all_1_1_1) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_17_0_6 = 0))))
% 87.95/52.01 |
% 87.95/52.01 | Instantiating formula (11) with all_1_2_2, all_17_0_6, all_1_1_1, all_1_4_4, all_1_5_5 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2, apart_point_and_line(all_1_1_1, all_1_5_5) = all_17_0_6, yields:
% 88.31/52.01 | (96) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v1 & convergent_lines(all_1_5_5, all_1_4_4) = v0 & distinct_points(all_1_1_1, all_1_2_2) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_17_0_6 = 0))))
% 88.31/52.01 |
% 88.31/52.01 | Instantiating formula (12) with all_17_0_6, all_1_1_1, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_17_0_6, convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 88.31/52.01 | (97) ? [v0] : ? [v1] : ? [v2] : (intersection_point(all_1_5_5, all_1_3_3) = v1 & apart_point_and_line(all_1_1_1, all_1_3_3) = v0 & distinct_points(all_1_1_1, v1) = v2 & (v2 = 0 | ( ~ (v0 = 0) & ~ (all_17_0_6 = 0))))
% 88.31/52.01 |
% 88.31/52.01 | Instantiating formula (12) with all_17_0_6, all_1_1_1, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_17_0_6, convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 88.31/52.01 | (98) ? [v0] : ? [v1] : ? [v2] : (intersection_point(all_1_5_5, all_1_4_4) = v1 & apart_point_and_line(all_1_1_1, all_1_4_4) = v0 & distinct_points(all_1_1_1, v1) = v2 & (v2 = 0 | ( ~ (v0 = 0) & ~ (all_17_0_6 = 0))))
% 88.31/52.01 |
% 88.31/52.01 | Instantiating formula (8) with all_17_3_9, all_17_0_6, all_1_5_5, all_1_0_0, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_17_0_6, apart_point_and_line(all_1_2_2, all_1_0_0) = all_17_3_9, yields:
% 88.31/52.01 | (99) all_17_0_6 = 0 | all_17_3_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_0_0) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_0_0, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 88.31/52.01 |
% 88.31/52.01 | Instantiating formula (19) with all_17_3_9, all_17_3_9, all_1_0_0, all_1_0_0, all_1_1_1, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_0_0) = all_17_3_9, distinct_points(all_1_2_2, all_1_1_1) = 0, yields:
% 88.31/52.01 | (100) all_17_3_9 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_0_0) = v2 & apart_point_and_line(all_1_1_1, all_1_0_0) = v1 & distinct_lines(all_1_0_0, all_1_0_0) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 88.31/52.01 |
% 88.31/52.01 | Instantiating formula (44) with all_17_3_9, all_17_3_9, all_1_0_0, all_1_0_0, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_0_0) = all_17_3_9, yields:
% 88.31/52.01 | (101) all_17_3_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_0_0) = v3 & apart_point_and_line(all_1_2_2, all_1_0_0) = v2 & distinct_lines(all_1_0_0, all_1_0_0) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 88.31/52.01 |
% 88.31/52.01 | Instantiating formula (24) with all_17_0_6, all_17_2_8, all_1_5_5, all_1_0_0, all_1_1_1, all_1_2_2 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_17_0_6, apart_point_and_line(all_1_2_2, all_1_5_5) = all_17_2_8, distinct_lines(all_1_0_0, all_1_5_5) = 0, yields:
% 88.31/52.01 | (102) all_17_0_6 = 0 | all_17_2_8 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_0_0) = v2 & apart_point_and_line(all_1_2_2, all_1_0_0) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 88.31/52.01 |
% 88.31/52.01 | Instantiating formula (19) with all_17_3_9, all_17_2_8, all_1_0_0, all_1_5_5, all_1_1_1, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_0_0) = all_17_3_9, apart_point_and_line(all_1_2_2, all_1_5_5) = all_17_2_8, distinct_points(all_1_2_2, all_1_1_1) = 0, yields:
% 88.31/52.01 | (103) all_17_2_8 = 0 | all_17_3_9 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_0_0) = v2 & apart_point_and_line(all_1_1_1, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_0_0) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 88.31/52.01 |
% 88.31/52.01 | Instantiating formula (8) with all_17_2_8, all_17_3_9, all_1_0_0, all_1_5_5, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_0_0) = all_17_3_9, apart_point_and_line(all_1_2_2, all_1_5_5) = all_17_2_8, yields:
% 88.31/52.01 | (104) all_17_2_8 = 0 | all_17_3_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_0_0) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_0_0) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 88.31/52.01 |
% 88.31/52.01 | Instantiating formula (19) with all_17_2_8, all_17_2_8, all_1_5_5, all_1_5_5, all_1_1_1, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_17_2_8, distinct_points(all_1_2_2, all_1_1_1) = 0, yields:
% 88.31/52.01 | (105) all_17_2_8 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & apart_point_and_line(all_1_1_1, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 88.31/52.01 |
% 88.31/52.01 | Instantiating formula (11) with all_1_1_1, all_17_2_8, all_1_2_2, all_1_3_3, all_1_5_5 and discharging atoms intersection_point(all_1_5_5, all_1_3_3) = all_1_1_1, apart_point_and_line(all_1_2_2, all_1_5_5) = all_17_2_8, yields:
% 88.31/52.01 | (106) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_2_2, all_1_3_3) = v1 & convergent_lines(all_1_5_5, all_1_3_3) = v0 & distinct_points(all_1_2_2, all_1_1_1) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_17_2_8 = 0))))
% 88.31/52.02 |
% 88.31/52.02 | Instantiating formula (11) with all_1_2_2, all_17_2_8, all_1_2_2, all_1_4_4, all_1_5_5 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2, apart_point_and_line(all_1_2_2, all_1_5_5) = all_17_2_8, yields:
% 88.31/52.02 | (107) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v1 & convergent_lines(all_1_5_5, all_1_4_4) = v0 & distinct_points(all_1_2_2, all_1_2_2) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_17_2_8 = 0))))
% 88.31/52.02 |
% 88.31/52.02 | Instantiating formula (12) with all_17_2_8, all_1_2_2, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_17_2_8, convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 88.31/52.02 | (108) ? [v0] : ? [v1] : ? [v2] : (intersection_point(all_1_5_5, all_1_3_3) = v1 & apart_point_and_line(all_1_2_2, all_1_3_3) = v0 & distinct_points(all_1_2_2, v1) = v2 & (v2 = 0 | ( ~ (v0 = 0) & ~ (all_17_2_8 = 0))))
% 88.31/52.02 |
% 88.31/52.02 | Instantiating formula (12) with all_17_2_8, all_1_2_2, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_17_2_8, convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 88.31/52.02 | (109) ? [v0] : ? [v1] : ? [v2] : (intersection_point(all_1_5_5, all_1_4_4) = v1 & apart_point_and_line(all_1_2_2, all_1_4_4) = v0 & distinct_points(all_1_2_2, v1) = v2 & (v2 = 0 | ( ~ (v0 = 0) & ~ (all_17_2_8 = 0))))
% 88.31/52.02 |
% 88.31/52.02 | Instantiating formula (28) with all_17_0_6, all_17_0_6, all_1_3_3, all_1_5_5, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_17_0_6, distinct_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 88.31/52.02 | (110) all_17_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 88.31/52.02 |
% 88.31/52.02 | Instantiating formula (28) with all_17_2_8, all_17_0_6, all_1_3_3, all_1_5_5, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_17_0_6, apart_point_and_line(all_1_2_2, all_1_5_5) = all_17_2_8, distinct_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 88.31/52.02 | (111) all_17_0_6 = 0 | all_17_2_8 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_3_3) = v1 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 88.31/52.02 |
% 88.31/52.02 | Instantiating formula (36) with all_1_3_3, all_1_5_5, all_1_1_1, all_1_2_2 and discharging atoms distinct_lines(all_1_5_5, all_1_3_3) = 0, distinct_points(all_1_2_2, all_1_1_1) = 0, yields:
% 88.31/52.02 | (112) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v1 & apart_point_and_line(all_1_2_2, all_1_5_5) = v0 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0))
% 88.31/52.02 |
% 88.31/52.02 | Instantiating formula (10) with all_19_0_10, all_1_2_2, all_1_1_1, all_1_2_2 and discharging atoms distinct_points(all_1_2_2, all_1_1_1) = 0, distinct_points(all_1_2_2, all_1_2_2) = all_19_0_10, yields:
% 88.31/52.02 | (113) all_19_0_10 = 0 | distinct_points(all_1_1_1, all_1_2_2) = 0
% 88.31/52.02 |
% 88.31/52.02 | Instantiating formula (18) with all_19_0_10, 0, all_1_2_2, all_1_2_2, all_1_1_1 and discharging atoms distinct_points(all_1_2_2, all_1_1_1) = 0, distinct_points(all_1_2_2, all_1_2_2) = all_19_0_10, yields:
% 88.31/52.02 | (114) all_19_0_10 = 0 | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_1_1, all_1_2_2) = v1 & apart_point_and_line(all_1_2_2, v1) = v2 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 88.31/52.02 |
% 88.31/52.02 | Instantiating formula (18) with all_19_0_10, all_19_0_10, all_1_2_2, all_1_2_2, all_1_2_2 and discharging atoms distinct_points(all_1_2_2, all_1_2_2) = all_19_0_10, yields:
% 88.31/52.02 | (115) all_19_0_10 = 0 | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_2_2, all_1_2_2) = v1 & apart_point_and_line(all_1_2_2, v1) = v2 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 88.31/52.02 |
% 88.31/52.02 | Instantiating formula (6) with all_19_0_10, all_1_2_2, all_1_2_2, all_1_4_4, all_1_5_5 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2, distinct_points(all_1_2_2, all_1_2_2) = all_19_0_10, yields:
% 88.31/52.02 | (116) all_19_0_10 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v1 & convergent_lines(all_1_5_5, all_1_4_4) = v0 & ( ~ (v0 = 0) | ( ~ (v2 = 0) & ~ (v1 = 0))))
% 88.31/52.02 |
% 88.31/52.02 | Instantiating (112) with all_42_0_20, all_42_1_21, all_42_2_22, all_42_3_23 yields:
% 88.31/52.02 | (117) apart_point_and_line(all_1_1_1, all_1_3_3) = all_42_0_20 & apart_point_and_line(all_1_1_1, all_1_5_5) = all_42_1_21 & apart_point_and_line(all_1_2_2, all_1_3_3) = all_42_2_22 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_42_3_23 & (all_42_0_20 = 0 | all_42_1_21 = 0 | all_42_2_22 = 0 | all_42_3_23 = 0)
% 88.31/52.02 |
% 88.31/52.02 | Applying alpha-rule on (117) yields:
% 88.31/52.02 | (118) apart_point_and_line(all_1_1_1, all_1_5_5) = all_42_1_21
% 88.31/52.02 | (119) apart_point_and_line(all_1_1_1, all_1_3_3) = all_42_0_20
% 88.31/52.02 | (120) apart_point_and_line(all_1_2_2, all_1_3_3) = all_42_2_22
% 88.31/52.02 | (121) all_42_0_20 = 0 | all_42_1_21 = 0 | all_42_2_22 = 0 | all_42_3_23 = 0
% 88.31/52.02 | (122) apart_point_and_line(all_1_2_2, all_1_5_5) = all_42_3_23
% 88.31/52.02 |
% 88.31/52.02 | Instantiating (109) with all_44_0_24, all_44_1_25, all_44_2_26 yields:
% 88.31/52.02 | (123) intersection_point(all_1_5_5, all_1_4_4) = all_44_1_25 & apart_point_and_line(all_1_2_2, all_1_4_4) = all_44_2_26 & distinct_points(all_1_2_2, all_44_1_25) = all_44_0_24 & (all_44_0_24 = 0 | ( ~ (all_44_2_26 = 0) & ~ (all_17_2_8 = 0)))
% 88.31/52.02 |
% 88.31/52.02 | Applying alpha-rule on (123) yields:
% 88.31/52.02 | (124) intersection_point(all_1_5_5, all_1_4_4) = all_44_1_25
% 88.31/52.02 | (125) apart_point_and_line(all_1_2_2, all_1_4_4) = all_44_2_26
% 88.31/52.02 | (126) distinct_points(all_1_2_2, all_44_1_25) = all_44_0_24
% 88.31/52.02 | (127) all_44_0_24 = 0 | ( ~ (all_44_2_26 = 0) & ~ (all_17_2_8 = 0))
% 88.31/52.02 |
% 88.31/52.02 | Instantiating (108) with all_46_0_27, all_46_1_28, all_46_2_29 yields:
% 88.31/52.02 | (128) intersection_point(all_1_5_5, all_1_3_3) = all_46_1_28 & apart_point_and_line(all_1_2_2, all_1_3_3) = all_46_2_29 & distinct_points(all_1_2_2, all_46_1_28) = all_46_0_27 & (all_46_0_27 = 0 | ( ~ (all_46_2_29 = 0) & ~ (all_17_2_8 = 0)))
% 88.31/52.02 |
% 88.31/52.02 | Applying alpha-rule on (128) yields:
% 88.31/52.02 | (129) intersection_point(all_1_5_5, all_1_3_3) = all_46_1_28
% 88.31/52.02 | (130) apart_point_and_line(all_1_2_2, all_1_3_3) = all_46_2_29
% 88.31/52.02 | (131) distinct_points(all_1_2_2, all_46_1_28) = all_46_0_27
% 88.31/52.02 | (132) all_46_0_27 = 0 | ( ~ (all_46_2_29 = 0) & ~ (all_17_2_8 = 0))
% 88.31/52.02 |
% 88.31/52.02 | Instantiating (107) with all_48_0_30, all_48_1_31, all_48_2_32 yields:
% 88.31/52.02 | (133) apart_point_and_line(all_1_2_2, all_1_4_4) = all_48_1_31 & convergent_lines(all_1_5_5, all_1_4_4) = all_48_2_32 & distinct_points(all_1_2_2, all_1_2_2) = all_48_0_30 & ( ~ (all_48_2_32 = 0) | all_48_0_30 = 0 | ( ~ (all_48_1_31 = 0) & ~ (all_17_2_8 = 0)))
% 88.31/52.02 |
% 88.31/52.02 | Applying alpha-rule on (133) yields:
% 88.31/52.02 | (134) apart_point_and_line(all_1_2_2, all_1_4_4) = all_48_1_31
% 88.31/52.02 | (135) convergent_lines(all_1_5_5, all_1_4_4) = all_48_2_32
% 88.31/52.02 | (136) distinct_points(all_1_2_2, all_1_2_2) = all_48_0_30
% 88.31/52.02 | (137) ~ (all_48_2_32 = 0) | all_48_0_30 = 0 | ( ~ (all_48_1_31 = 0) & ~ (all_17_2_8 = 0))
% 88.31/52.02 |
% 88.31/52.02 | Instantiating (106) with all_50_0_33, all_50_1_34, all_50_2_35 yields:
% 88.31/52.02 | (138) apart_point_and_line(all_1_2_2, all_1_3_3) = all_50_1_34 & convergent_lines(all_1_5_5, all_1_3_3) = all_50_2_35 & distinct_points(all_1_2_2, all_1_1_1) = all_50_0_33 & ( ~ (all_50_2_35 = 0) | all_50_0_33 = 0 | ( ~ (all_50_1_34 = 0) & ~ (all_17_2_8 = 0)))
% 88.31/52.02 |
% 88.31/52.02 | Applying alpha-rule on (138) yields:
% 88.31/52.02 | (139) apart_point_and_line(all_1_2_2, all_1_3_3) = all_50_1_34
% 88.31/52.02 | (140) convergent_lines(all_1_5_5, all_1_3_3) = all_50_2_35
% 88.31/52.02 | (141) distinct_points(all_1_2_2, all_1_1_1) = all_50_0_33
% 88.31/52.02 | (142) ~ (all_50_2_35 = 0) | all_50_0_33 = 0 | ( ~ (all_50_1_34 = 0) & ~ (all_17_2_8 = 0))
% 88.31/52.02 |
% 88.31/52.02 | Instantiating (98) with all_52_0_36, all_52_1_37, all_52_2_38 yields:
% 88.31/52.02 | (143) intersection_point(all_1_5_5, all_1_4_4) = all_52_1_37 & apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_2_38 & distinct_points(all_1_1_1, all_52_1_37) = all_52_0_36 & (all_52_0_36 = 0 | ( ~ (all_52_2_38 = 0) & ~ (all_17_0_6 = 0)))
% 88.31/52.03 |
% 88.31/52.03 | Applying alpha-rule on (143) yields:
% 88.31/52.03 | (144) intersection_point(all_1_5_5, all_1_4_4) = all_52_1_37
% 88.31/52.03 | (145) apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_2_38
% 88.31/52.03 | (146) distinct_points(all_1_1_1, all_52_1_37) = all_52_0_36
% 88.31/52.03 | (147) all_52_0_36 = 0 | ( ~ (all_52_2_38 = 0) & ~ (all_17_0_6 = 0))
% 88.31/52.03 |
% 88.31/52.03 | Instantiating (97) with all_54_0_39, all_54_1_40, all_54_2_41 yields:
% 88.31/52.03 | (148) intersection_point(all_1_5_5, all_1_3_3) = all_54_1_40 & apart_point_and_line(all_1_1_1, all_1_3_3) = all_54_2_41 & distinct_points(all_1_1_1, all_54_1_40) = all_54_0_39 & (all_54_0_39 = 0 | ( ~ (all_54_2_41 = 0) & ~ (all_17_0_6 = 0)))
% 88.31/52.03 |
% 88.31/52.03 | Applying alpha-rule on (148) yields:
% 88.31/52.03 | (149) intersection_point(all_1_5_5, all_1_3_3) = all_54_1_40
% 88.31/52.03 | (150) apart_point_and_line(all_1_1_1, all_1_3_3) = all_54_2_41
% 88.31/52.03 | (151) distinct_points(all_1_1_1, all_54_1_40) = all_54_0_39
% 88.31/52.03 | (152) all_54_0_39 = 0 | ( ~ (all_54_2_41 = 0) & ~ (all_17_0_6 = 0))
% 88.31/52.03 |
% 88.31/52.03 | Instantiating (95) with all_56_0_42, all_56_1_43, all_56_2_44 yields:
% 88.31/52.03 | (153) apart_point_and_line(all_1_1_1, all_1_3_3) = all_56_1_43 & convergent_lines(all_1_5_5, all_1_3_3) = all_56_2_44 & distinct_points(all_1_1_1, all_1_1_1) = all_56_0_42 & ( ~ (all_56_2_44 = 0) | all_56_0_42 = 0 | ( ~ (all_56_1_43 = 0) & ~ (all_17_0_6 = 0)))
% 88.31/52.03 |
% 88.31/52.03 | Applying alpha-rule on (153) yields:
% 88.31/52.03 | (154) apart_point_and_line(all_1_1_1, all_1_3_3) = all_56_1_43
% 88.31/52.03 | (155) convergent_lines(all_1_5_5, all_1_3_3) = all_56_2_44
% 88.31/52.03 | (156) distinct_points(all_1_1_1, all_1_1_1) = all_56_0_42
% 88.31/52.03 | (157) ~ (all_56_2_44 = 0) | all_56_0_42 = 0 | ( ~ (all_56_1_43 = 0) & ~ (all_17_0_6 = 0))
% 88.31/52.03 |
% 88.31/52.03 | Instantiating (96) with all_58_0_45, all_58_1_46, all_58_2_47 yields:
% 88.31/52.03 | (158) apart_point_and_line(all_1_1_1, all_1_4_4) = all_58_1_46 & convergent_lines(all_1_5_5, all_1_4_4) = all_58_2_47 & distinct_points(all_1_1_1, all_1_2_2) = all_58_0_45 & ( ~ (all_58_2_47 = 0) | all_58_0_45 = 0 | ( ~ (all_58_1_46 = 0) & ~ (all_17_0_6 = 0)))
% 88.31/52.03 |
% 88.31/52.03 | Applying alpha-rule on (158) yields:
% 88.31/52.03 | (159) apart_point_and_line(all_1_1_1, all_1_4_4) = all_58_1_46
% 88.31/52.03 | (160) convergent_lines(all_1_5_5, all_1_4_4) = all_58_2_47
% 88.31/52.03 | (161) distinct_points(all_1_1_1, all_1_2_2) = all_58_0_45
% 88.31/52.03 | (162) ~ (all_58_2_47 = 0) | all_58_0_45 = 0 | ( ~ (all_58_1_46 = 0) & ~ (all_17_0_6 = 0))
% 88.31/52.03 |
% 88.31/52.03 +-Applying beta-rule and splitting (113), into two cases.
% 88.31/52.03 |-Branch one:
% 88.31/52.03 | (163) distinct_points(all_1_1_1, all_1_2_2) = 0
% 88.31/52.03 |
% 88.31/52.03 +-Applying beta-rule and splitting (100), into two cases.
% 88.31/52.03 |-Branch one:
% 88.31/52.03 | (164) all_17_3_9 = 0
% 88.31/52.03 |
% 88.31/52.03 | Equations (164) can reduce 88 to:
% 88.31/52.03 | (165) $false
% 88.31/52.03 |
% 88.31/52.03 |-The branch is then unsatisfiable
% 88.31/52.03 |-Branch two:
% 88.31/52.03 | (88) ~ (all_17_3_9 = 0)
% 88.31/52.03 | (167) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_0_0) = v2 & apart_point_and_line(all_1_1_1, all_1_0_0) = v1 & distinct_lines(all_1_0_0, all_1_0_0) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 88.31/52.03 |
% 88.31/52.03 | Instantiating (167) with all_72_0_48, all_72_1_49, all_72_2_50 yields:
% 88.31/52.03 | (168) apart_point_and_line(all_1_1_1, all_1_0_0) = all_72_0_48 & apart_point_and_line(all_1_1_1, all_1_0_0) = all_72_1_49 & distinct_lines(all_1_0_0, all_1_0_0) = all_72_2_50 & ( ~ (all_72_2_50 = 0) | all_72_0_48 = 0 | all_72_1_49 = 0)
% 88.31/52.03 |
% 88.31/52.03 | Applying alpha-rule on (168) yields:
% 88.31/52.03 | (169) apart_point_and_line(all_1_1_1, all_1_0_0) = all_72_0_48
% 88.31/52.03 | (170) apart_point_and_line(all_1_1_1, all_1_0_0) = all_72_1_49
% 88.31/52.03 | (171) distinct_lines(all_1_0_0, all_1_0_0) = all_72_2_50
% 88.31/52.03 | (172) ~ (all_72_2_50 = 0) | all_72_0_48 = 0 | all_72_1_49 = 0
% 88.31/52.03 |
% 88.31/52.03 +-Applying beta-rule and splitting (101), into two cases.
% 88.31/52.03 |-Branch one:
% 88.31/52.03 | (164) all_17_3_9 = 0
% 88.31/52.03 |
% 88.31/52.03 | Equations (164) can reduce 88 to:
% 88.31/52.03 | (165) $false
% 88.31/52.03 |
% 88.31/52.03 |-The branch is then unsatisfiable
% 88.31/52.03 |-Branch two:
% 88.31/52.03 | (88) ~ (all_17_3_9 = 0)
% 88.31/52.03 | (176) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_0_0) = v3 & apart_point_and_line(all_1_2_2, all_1_0_0) = v2 & distinct_lines(all_1_0_0, all_1_0_0) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 88.31/52.03 |
% 88.31/52.03 | Instantiating (176) with all_77_0_51, all_77_1_52, all_77_2_53, all_77_3_54 yields:
% 88.31/52.03 | (177) apart_point_and_line(all_1_2_2, all_1_0_0) = all_77_0_51 & apart_point_and_line(all_1_2_2, all_1_0_0) = all_77_1_52 & distinct_lines(all_1_0_0, all_1_0_0) = all_77_2_53 & distinct_points(all_1_2_2, all_1_2_2) = all_77_3_54 & ( ~ (all_77_2_53 = 0) | ~ (all_77_3_54 = 0) | all_77_0_51 = 0 | all_77_1_52 = 0)
% 88.31/52.03 |
% 88.31/52.03 | Applying alpha-rule on (177) yields:
% 88.31/52.03 | (178) distinct_points(all_1_2_2, all_1_2_2) = all_77_3_54
% 88.31/52.03 | (179) distinct_lines(all_1_0_0, all_1_0_0) = all_77_2_53
% 88.31/52.03 | (180) apart_point_and_line(all_1_2_2, all_1_0_0) = all_77_1_52
% 88.31/52.03 | (181) apart_point_and_line(all_1_2_2, all_1_0_0) = all_77_0_51
% 88.31/52.03 | (182) ~ (all_77_2_53 = 0) | ~ (all_77_3_54 = 0) | all_77_0_51 = 0 | all_77_1_52 = 0
% 88.31/52.03 |
% 88.31/52.03 +-Applying beta-rule and splitting (114), into two cases.
% 88.31/52.03 |-Branch one:
% 88.31/52.03 | (183) all_19_0_10 = 0
% 88.31/52.03 |
% 88.31/52.03 | Equations (183) can reduce 82 to:
% 88.31/52.03 | (165) $false
% 88.31/52.03 |
% 88.31/52.03 |-The branch is then unsatisfiable
% 88.31/52.03 |-Branch two:
% 88.31/52.03 | (82) ~ (all_19_0_10 = 0)
% 88.31/52.03 | (186) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_1_1, all_1_2_2) = v1 & apart_point_and_line(all_1_2_2, v1) = v2 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 88.31/52.03 |
% 88.31/52.03 +-Applying beta-rule and splitting (115), into two cases.
% 88.31/52.03 |-Branch one:
% 88.31/52.03 | (183) all_19_0_10 = 0
% 88.31/52.03 |
% 88.31/52.03 | Equations (183) can reduce 82 to:
% 88.31/52.03 | (165) $false
% 88.31/52.03 |
% 88.31/52.03 |-The branch is then unsatisfiable
% 88.31/52.03 |-Branch two:
% 88.31/52.03 | (82) ~ (all_19_0_10 = 0)
% 88.31/52.03 | (190) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_2_2, all_1_2_2) = v1 & apart_point_and_line(all_1_2_2, v1) = v2 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 88.31/52.03 |
% 88.31/52.03 | Instantiating (190) with all_87_0_58, all_87_1_59, all_87_2_60 yields:
% 88.31/52.03 | (191) line_connecting(all_1_2_2, all_1_2_2) = all_87_1_59 & apart_point_and_line(all_1_2_2, all_87_1_59) = all_87_0_58 & distinct_points(all_1_2_2, all_1_2_2) = all_87_2_60 & ( ~ (all_87_0_58 = 0) | ~ (all_87_2_60 = 0))
% 88.31/52.03 |
% 88.31/52.03 | Applying alpha-rule on (191) yields:
% 88.31/52.03 | (192) line_connecting(all_1_2_2, all_1_2_2) = all_87_1_59
% 88.31/52.03 | (193) apart_point_and_line(all_1_2_2, all_87_1_59) = all_87_0_58
% 88.31/52.03 | (194) distinct_points(all_1_2_2, all_1_2_2) = all_87_2_60
% 88.31/52.03 | (195) ~ (all_87_0_58 = 0) | ~ (all_87_2_60 = 0)
% 88.31/52.03 |
% 88.31/52.03 | Instantiating formula (34) with all_1_5_5, all_1_3_3, all_54_1_40, all_1_1_1 and discharging atoms intersection_point(all_1_5_5, all_1_3_3) = all_54_1_40, intersection_point(all_1_5_5, all_1_3_3) = all_1_1_1, yields:
% 88.31/52.04 | (196) all_54_1_40 = all_1_1_1
% 88.31/52.04 |
% 88.31/52.04 | Instantiating formula (34) with all_1_5_5, all_1_3_3, all_46_1_28, all_54_1_40 and discharging atoms intersection_point(all_1_5_5, all_1_3_3) = all_54_1_40, intersection_point(all_1_5_5, all_1_3_3) = all_46_1_28, yields:
% 88.31/52.04 | (197) all_54_1_40 = all_46_1_28
% 88.31/52.04 |
% 88.31/52.04 | Instantiating formula (34) with all_1_5_5, all_1_4_4, all_52_1_37, all_1_2_2 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_52_1_37, intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2, yields:
% 88.31/52.04 | (198) all_52_1_37 = all_1_2_2
% 88.31/52.04 |
% 88.31/52.04 | Instantiating formula (34) with all_1_5_5, all_1_4_4, all_44_1_25, all_52_1_37 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_52_1_37, intersection_point(all_1_5_5, all_1_4_4) = all_44_1_25, yields:
% 88.31/52.04 | (199) all_52_1_37 = all_44_1_25
% 88.31/52.04 |
% 88.31/52.04 | Instantiating formula (20) with all_1_1_1, all_1_0_0, all_72_0_48, all_17_1_7 and discharging atoms apart_point_and_line(all_1_1_1, all_1_0_0) = all_72_0_48, apart_point_and_line(all_1_1_1, all_1_0_0) = all_17_1_7, yields:
% 88.31/52.04 | (200) all_72_0_48 = all_17_1_7
% 88.31/52.04 |
% 88.31/52.04 | Instantiating formula (20) with all_1_1_1, all_1_0_0, all_72_1_49, all_72_0_48 and discharging atoms apart_point_and_line(all_1_1_1, all_1_0_0) = all_72_0_48, apart_point_and_line(all_1_1_1, all_1_0_0) = all_72_1_49, yields:
% 88.31/52.04 | (201) all_72_0_48 = all_72_1_49
% 88.31/52.04 |
% 88.31/52.04 | Instantiating formula (20) with all_1_1_1, all_1_3_3, all_54_2_41, all_56_1_43 and discharging atoms apart_point_and_line(all_1_1_1, all_1_3_3) = all_56_1_43, apart_point_and_line(all_1_1_1, all_1_3_3) = all_54_2_41, yields:
% 88.31/52.04 | (202) all_56_1_43 = all_54_2_41
% 88.31/52.04 |
% 88.31/52.04 | Instantiating formula (20) with all_1_1_1, all_1_3_3, all_42_0_20, all_56_1_43 and discharging atoms apart_point_and_line(all_1_1_1, all_1_3_3) = all_56_1_43, apart_point_and_line(all_1_1_1, all_1_3_3) = all_42_0_20, yields:
% 88.31/52.04 | (203) all_56_1_43 = all_42_0_20
% 88.31/52.04 |
% 88.31/52.04 | Instantiating formula (20) with all_1_1_1, all_1_5_5, all_42_1_21, all_17_0_6 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_42_1_21, apart_point_and_line(all_1_1_1, all_1_5_5) = all_17_0_6, yields:
% 88.31/52.04 | (204) all_42_1_21 = all_17_0_6
% 88.31/52.04 |
% 88.31/52.04 | Instantiating formula (3) with all_1_5_5, all_1_3_3, all_56_2_44, 0 and discharging atoms convergent_lines(all_1_5_5, all_1_3_3) = all_56_2_44, convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 88.31/52.04 | (205) all_56_2_44 = 0
% 88.31/52.04 |
% 88.31/52.04 | Instantiating formula (3) with all_1_5_5, all_1_3_3, all_50_2_35, all_56_2_44 and discharging atoms convergent_lines(all_1_5_5, all_1_3_3) = all_56_2_44, convergent_lines(all_1_5_5, all_1_3_3) = all_50_2_35, yields:
% 88.31/52.04 | (206) all_56_2_44 = all_50_2_35
% 88.31/52.04 |
% 88.31/52.04 | Instantiating formula (3) with all_1_5_5, all_1_4_4, all_58_2_47, 0 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = all_58_2_47, convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 88.31/52.04 | (207) all_58_2_47 = 0
% 88.31/52.04 |
% 88.31/52.04 | Instantiating formula (3) with all_1_5_5, all_1_4_4, all_48_2_32, all_58_2_47 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = all_58_2_47, convergent_lines(all_1_5_5, all_1_4_4) = all_48_2_32, yields:
% 88.31/52.04 | (208) all_58_2_47 = all_48_2_32
% 88.31/52.04 |
% 88.31/52.04 | Instantiating formula (32) with all_1_1_1, all_52_1_37, all_52_0_36, all_54_0_39 and discharging atoms distinct_points(all_1_1_1, all_52_1_37) = all_52_0_36, yields:
% 88.31/52.04 | (209) all_54_0_39 = all_52_0_36 | ~ (distinct_points(all_1_1_1, all_52_1_37) = all_54_0_39)
% 88.31/52.04 |
% 88.31/52.04 | Instantiating formula (32) with all_1_1_1, all_1_1_1, all_56_0_42, all_54_0_39 and discharging atoms distinct_points(all_1_1_1, all_1_1_1) = all_56_0_42, yields:
% 88.31/52.04 | (210) all_56_0_42 = all_54_0_39 | ~ (distinct_points(all_1_1_1, all_1_1_1) = all_54_0_39)
% 88.31/52.04 |
% 88.31/52.04 | Instantiating formula (21) with all_1_1_1 yields:
% 88.31/52.04 | (211) ~ (distinct_points(all_1_1_1, all_1_1_1) = 0)
% 88.31/52.04 |
% 88.31/52.04 | Instantiating formula (32) with all_1_1_1, all_1_2_2, 0, all_52_0_36 and discharging atoms distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 88.31/52.04 | (212) all_52_0_36 = 0 | ~ (distinct_points(all_1_1_1, all_1_2_2) = all_52_0_36)
% 88.31/52.04 |
% 88.31/52.04 | Instantiating formula (32) with all_1_2_2, all_1_1_1, all_50_0_33, 0 and discharging atoms distinct_points(all_1_2_2, all_1_1_1) = all_50_0_33, distinct_points(all_1_2_2, all_1_1_1) = 0, yields:
% 88.31/52.04 | (213) all_50_0_33 = 0
% 88.31/52.04 |
% 88.31/52.04 | Instantiating formula (32) with all_1_2_2, all_1_1_1, all_50_0_33, all_46_0_27 and discharging atoms distinct_points(all_1_2_2, all_1_1_1) = all_50_0_33, yields:
% 88.31/52.04 | (214) all_50_0_33 = all_46_0_27 | ~ (distinct_points(all_1_2_2, all_1_1_1) = all_46_0_27)
% 88.31/52.04 |
% 88.31/52.04 | Instantiating formula (32) with all_1_2_2, all_1_2_2, all_87_2_60, all_19_0_10 and discharging atoms distinct_points(all_1_2_2, all_1_2_2) = all_87_2_60, distinct_points(all_1_2_2, all_1_2_2) = all_19_0_10, yields:
% 88.31/52.04 | (215) all_87_2_60 = all_19_0_10
% 88.31/52.04 |
% 88.31/52.04 | Instantiating formula (32) with all_1_2_2, all_1_2_2, all_77_3_54, all_87_2_60 and discharging atoms distinct_points(all_1_2_2, all_1_2_2) = all_87_2_60, distinct_points(all_1_2_2, all_1_2_2) = all_77_3_54, yields:
% 88.31/52.04 | (216) all_87_2_60 = all_77_3_54
% 88.31/52.04 |
% 88.31/52.04 | Instantiating formula (32) with all_1_2_2, all_1_2_2, all_48_0_30, all_87_2_60 and discharging atoms distinct_points(all_1_2_2, all_1_2_2) = all_87_2_60, distinct_points(all_1_2_2, all_1_2_2) = all_48_0_30, yields:
% 88.31/52.04 | (217) all_87_2_60 = all_48_0_30
% 88.31/52.04 |
% 88.31/52.04 | Using (136) and (55) yields:
% 88.31/52.04 | (218) ~ (all_48_0_30 = 0)
% 88.31/52.04 |
% 88.31/52.04 | Combining equations (217,216) yields a new equation:
% 88.31/52.04 | (219) all_77_3_54 = all_48_0_30
% 88.31/52.04 |
% 88.31/52.04 | Combining equations (215,216) yields a new equation:
% 88.31/52.04 | (220) all_77_3_54 = all_19_0_10
% 88.31/52.04 |
% 88.31/52.04 | Combining equations (219,220) yields a new equation:
% 88.31/52.04 | (221) all_48_0_30 = all_19_0_10
% 88.31/52.04 |
% 88.31/52.04 | Simplifying 221 yields:
% 88.31/52.04 | (222) all_48_0_30 = all_19_0_10
% 88.31/52.04 |
% 88.31/52.04 | Combining equations (201,200) yields a new equation:
% 88.31/52.04 | (223) all_72_1_49 = all_17_1_7
% 88.31/52.04 |
% 88.31/52.04 | Simplifying 223 yields:
% 88.31/52.04 | (224) all_72_1_49 = all_17_1_7
% 88.31/52.04 |
% 88.31/52.04 | Combining equations (208,207) yields a new equation:
% 88.31/52.04 | (225) all_48_2_32 = 0
% 88.31/52.04 |
% 88.31/52.04 | Simplifying 225 yields:
% 88.31/52.04 | (226) all_48_2_32 = 0
% 88.31/52.04 |
% 88.31/52.04 | Combining equations (203,202) yields a new equation:
% 88.31/52.04 | (227) all_54_2_41 = all_42_0_20
% 88.31/52.04 |
% 88.31/52.04 | Combining equations (205,206) yields a new equation:
% 88.31/52.04 | (228) all_50_2_35 = 0
% 88.31/52.04 |
% 88.31/52.04 | Combining equations (196,197) yields a new equation:
% 88.31/52.04 | (229) all_46_1_28 = all_1_1_1
% 88.31/52.04 |
% 88.31/52.04 | Combining equations (198,199) yields a new equation:
% 88.31/52.04 | (230) all_44_1_25 = all_1_2_2
% 88.31/52.04 |
% 88.31/52.04 | Combining equations (230,199) yields a new equation:
% 88.31/52.04 | (198) all_52_1_37 = all_1_2_2
% 88.31/52.04 |
% 88.31/52.04 | Combining equations (229,197) yields a new equation:
% 88.31/52.04 | (196) all_54_1_40 = all_1_1_1
% 88.31/52.04 |
% 88.31/52.04 | Combining equations (228,206) yields a new equation:
% 88.31/52.04 | (205) all_56_2_44 = 0
% 88.31/52.04 |
% 88.31/52.04 | Combining equations (227,202) yields a new equation:
% 88.31/52.04 | (203) all_56_1_43 = all_42_0_20
% 88.31/52.04 |
% 88.31/52.04 | Equations (222) can reduce 218 to:
% 88.31/52.04 | (82) ~ (all_19_0_10 = 0)
% 88.31/52.04 |
% 88.31/52.04 | From (224) and (170) follows:
% 88.31/52.05 | (65) apart_point_and_line(all_1_1_1, all_1_0_0) = all_17_1_7
% 88.31/52.05 |
% 88.31/52.05 | From (196) and (151) follows:
% 88.31/52.05 | (237) distinct_points(all_1_1_1, all_1_1_1) = all_54_0_39
% 88.31/52.05 |
% 88.31/52.05 | From (198) and (146) follows:
% 88.31/52.05 | (238) distinct_points(all_1_1_1, all_1_2_2) = all_52_0_36
% 88.31/52.05 |
% 88.31/52.05 | From (229) and (131) follows:
% 88.31/52.05 | (239) distinct_points(all_1_2_2, all_1_1_1) = all_46_0_27
% 88.31/52.05 |
% 88.31/52.05 +-Applying beta-rule and splitting (214), into two cases.
% 88.31/52.05 |-Branch one:
% 88.31/52.05 | (240) ~ (distinct_points(all_1_2_2, all_1_1_1) = all_46_0_27)
% 88.31/52.05 |
% 88.31/52.05 | Using (239) and (240) yields:
% 88.31/52.05 | (90) $false
% 88.31/52.05 |
% 88.31/52.05 |-The branch is then unsatisfiable
% 88.31/52.05 |-Branch two:
% 88.31/52.05 | (239) distinct_points(all_1_2_2, all_1_1_1) = all_46_0_27
% 88.31/52.05 | (243) all_50_0_33 = all_46_0_27
% 88.31/52.05 |
% 88.31/52.05 | Combining equations (213,243) yields a new equation:
% 88.31/52.05 | (244) all_46_0_27 = 0
% 88.31/52.05 |
% 88.31/52.05 | From (244) and (239) follows:
% 88.31/52.05 | (52) distinct_points(all_1_2_2, all_1_1_1) = 0
% 88.31/52.05 |
% 88.31/52.05 +-Applying beta-rule and splitting (116), into two cases.
% 88.31/52.05 |-Branch one:
% 88.31/52.05 | (183) all_19_0_10 = 0
% 88.31/52.05 |
% 88.31/52.05 | Equations (183) can reduce 82 to:
% 88.31/52.05 | (165) $false
% 88.31/52.05 |
% 88.31/52.05 |-The branch is then unsatisfiable
% 88.31/52.05 |-Branch two:
% 88.31/52.05 | (82) ~ (all_19_0_10 = 0)
% 88.31/52.05 | (249) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v1 & convergent_lines(all_1_5_5, all_1_4_4) = v0 & ( ~ (v0 = 0) | ( ~ (v2 = 0) & ~ (v1 = 0))))
% 88.31/52.05 |
% 88.31/52.05 +-Applying beta-rule and splitting (137), into two cases.
% 88.31/52.05 |-Branch one:
% 88.31/52.05 | (250) ~ (all_48_2_32 = 0)
% 88.31/52.05 |
% 88.31/52.05 | Equations (226) can reduce 250 to:
% 88.31/52.05 | (165) $false
% 88.31/52.05 |
% 88.31/52.05 |-The branch is then unsatisfiable
% 88.31/52.05 |-Branch two:
% 88.31/52.05 | (226) all_48_2_32 = 0
% 88.31/52.05 | (253) all_48_0_30 = 0 | ( ~ (all_48_1_31 = 0) & ~ (all_17_2_8 = 0))
% 88.31/52.05 |
% 88.31/52.05 +-Applying beta-rule and splitting (253), into two cases.
% 88.31/52.05 |-Branch one:
% 88.31/52.05 | (254) all_48_0_30 = 0
% 88.31/52.05 |
% 88.31/52.05 | Combining equations (222,254) yields a new equation:
% 88.31/52.05 | (255) all_19_0_10 = 0
% 88.31/52.05 |
% 88.31/52.05 | Simplifying 255 yields:
% 88.31/52.05 | (183) all_19_0_10 = 0
% 88.31/52.05 |
% 88.31/52.05 | Equations (183) can reduce 82 to:
% 88.31/52.05 | (165) $false
% 88.31/52.05 |
% 88.31/52.05 |-The branch is then unsatisfiable
% 88.31/52.05 |-Branch two:
% 88.31/52.05 | (218) ~ (all_48_0_30 = 0)
% 88.31/52.05 | (259) ~ (all_48_1_31 = 0) & ~ (all_17_2_8 = 0)
% 88.31/52.05 |
% 88.31/52.05 | Applying alpha-rule on (259) yields:
% 88.31/52.05 | (260) ~ (all_48_1_31 = 0)
% 88.31/52.05 | (261) ~ (all_17_2_8 = 0)
% 88.31/52.05 |
% 88.31/52.05 +-Applying beta-rule and splitting (212), into two cases.
% 88.31/52.05 |-Branch one:
% 88.31/52.05 | (262) ~ (distinct_points(all_1_1_1, all_1_2_2) = all_52_0_36)
% 88.31/52.05 |
% 88.31/52.05 | Using (238) and (262) yields:
% 88.31/52.05 | (90) $false
% 88.31/52.05 |
% 88.31/52.05 |-The branch is then unsatisfiable
% 88.31/52.05 |-Branch two:
% 88.31/52.05 | (238) distinct_points(all_1_1_1, all_1_2_2) = all_52_0_36
% 88.31/52.05 | (265) all_52_0_36 = 0
% 88.31/52.05 |
% 88.31/52.05 | From (265) and (238) follows:
% 88.31/52.05 | (163) distinct_points(all_1_1_1, all_1_2_2) = 0
% 88.31/52.05 |
% 88.31/52.05 +-Applying beta-rule and splitting (105), into two cases.
% 88.31/52.05 |-Branch one:
% 88.31/52.05 | (267) all_17_2_8 = 0
% 88.31/52.05 |
% 88.31/52.05 | Equations (267) can reduce 261 to:
% 88.31/52.05 | (165) $false
% 88.31/52.05 |
% 88.31/52.05 |-The branch is then unsatisfiable
% 88.31/52.05 |-Branch two:
% 88.31/52.05 | (261) ~ (all_17_2_8 = 0)
% 88.31/52.05 | (270) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & apart_point_and_line(all_1_1_1, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 88.31/52.05 |
% 88.31/52.05 +-Applying beta-rule and splitting (104), into two cases.
% 88.31/52.05 |-Branch one:
% 88.31/52.05 | (267) all_17_2_8 = 0
% 88.31/52.05 |
% 88.31/52.05 | Equations (267) can reduce 261 to:
% 88.31/52.05 | (165) $false
% 88.31/52.05 |
% 88.31/52.05 |-The branch is then unsatisfiable
% 88.31/52.05 |-Branch two:
% 88.31/52.05 | (261) ~ (all_17_2_8 = 0)
% 88.31/52.05 | (274) all_17_3_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_0_0) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_0_0) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 88.31/52.05 |
% 88.31/52.05 +-Applying beta-rule and splitting (103), into two cases.
% 88.31/52.05 |-Branch one:
% 88.31/52.05 | (267) all_17_2_8 = 0
% 88.31/52.05 |
% 88.31/52.05 | Equations (267) can reduce 261 to:
% 88.31/52.05 | (165) $false
% 88.31/52.05 |
% 88.31/52.05 |-The branch is then unsatisfiable
% 88.31/52.05 |-Branch two:
% 88.31/52.05 | (261) ~ (all_17_2_8 = 0)
% 88.31/52.05 | (278) all_17_3_9 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_0_0) = v2 & apart_point_and_line(all_1_1_1, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_0_0) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 88.31/52.05 |
% 88.31/52.05 +-Applying beta-rule and splitting (274), into two cases.
% 88.31/52.05 |-Branch one:
% 88.31/52.05 | (164) all_17_3_9 = 0
% 88.31/52.05 |
% 88.31/52.05 | Equations (164) can reduce 88 to:
% 88.31/52.05 | (165) $false
% 88.31/52.05 |
% 88.31/52.05 |-The branch is then unsatisfiable
% 88.31/52.05 |-Branch two:
% 88.31/52.05 | (88) ~ (all_17_3_9 = 0)
% 88.31/52.05 | (282) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_0_0) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_0_0) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 88.31/52.05 |
% 88.31/52.05 +-Applying beta-rule and splitting (278), into two cases.
% 88.31/52.05 |-Branch one:
% 88.31/52.05 | (164) all_17_3_9 = 0
% 88.31/52.05 |
% 88.31/52.05 | Equations (164) can reduce 88 to:
% 88.31/52.05 | (165) $false
% 88.31/52.05 |
% 88.31/52.05 |-The branch is then unsatisfiable
% 88.31/52.05 |-Branch two:
% 88.31/52.05 | (88) ~ (all_17_3_9 = 0)
% 88.31/52.05 | (286) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_0_0) = v2 & apart_point_and_line(all_1_1_1, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_0_0) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 88.31/52.05 |
% 88.31/52.05 | Instantiating (286) with all_142_0_71, all_142_1_72, all_142_2_73 yields:
% 88.31/52.05 | (287) apart_point_and_line(all_1_1_1, all_1_0_0) = all_142_0_71 & apart_point_and_line(all_1_1_1, all_1_5_5) = all_142_1_72 & distinct_lines(all_1_5_5, all_1_0_0) = all_142_2_73 & ( ~ (all_142_2_73 = 0) | all_142_0_71 = 0 | all_142_1_72 = 0)
% 88.31/52.05 |
% 88.31/52.05 | Applying alpha-rule on (287) yields:
% 88.31/52.05 | (288) apart_point_and_line(all_1_1_1, all_1_0_0) = all_142_0_71
% 88.31/52.05 | (289) apart_point_and_line(all_1_1_1, all_1_5_5) = all_142_1_72
% 88.31/52.05 | (290) distinct_lines(all_1_5_5, all_1_0_0) = all_142_2_73
% 88.31/52.05 | (291) ~ (all_142_2_73 = 0) | all_142_0_71 = 0 | all_142_1_72 = 0
% 88.31/52.05 |
% 88.31/52.05 +-Applying beta-rule and splitting (210), into two cases.
% 88.31/52.05 |-Branch one:
% 88.31/52.05 | (292) ~ (distinct_points(all_1_1_1, all_1_1_1) = all_54_0_39)
% 88.31/52.05 |
% 88.31/52.05 | Using (237) and (292) yields:
% 88.31/52.05 | (90) $false
% 88.31/52.05 |
% 88.31/52.05 |-The branch is then unsatisfiable
% 88.31/52.05 |-Branch two:
% 88.31/52.05 | (237) distinct_points(all_1_1_1, all_1_1_1) = all_54_0_39
% 88.31/52.05 | (295) all_56_0_42 = all_54_0_39
% 88.31/52.05 |
% 88.31/52.05 | From (295) and (156) follows:
% 88.31/52.05 | (237) distinct_points(all_1_1_1, all_1_1_1) = all_54_0_39
% 88.31/52.05 |
% 88.31/52.05 | Instantiating formula (20) with all_1_1_1, all_1_0_0, all_142_0_71, all_17_1_7 and discharging atoms apart_point_and_line(all_1_1_1, all_1_0_0) = all_142_0_71, apart_point_and_line(all_1_1_1, all_1_0_0) = all_17_1_7, yields:
% 88.31/52.05 | (297) all_142_0_71 = all_17_1_7
% 88.31/52.05 |
% 88.31/52.05 | Using (237) and (211) yields:
% 88.31/52.05 | (298) ~ (all_54_0_39 = 0)
% 88.31/52.06 |
% 88.31/52.06 | From (297) and (288) follows:
% 88.31/52.06 | (65) apart_point_and_line(all_1_1_1, all_1_0_0) = all_17_1_7
% 88.31/52.06 |
% 88.31/52.06 +-Applying beta-rule and splitting (94), into two cases.
% 88.31/52.06 |-Branch one:
% 88.31/52.06 | (300) ~ (apart_point_and_line(all_1_1_1, all_1_0_0) = 0)
% 88.31/52.06 |
% 88.31/52.06 +-Applying beta-rule and splitting (152), into two cases.
% 88.31/52.06 |-Branch one:
% 88.31/52.06 | (301) all_54_0_39 = 0
% 88.31/52.06 |
% 88.31/52.06 | Equations (301) can reduce 298 to:
% 88.31/52.06 | (165) $false
% 88.31/52.06 |
% 88.31/52.06 |-The branch is then unsatisfiable
% 88.31/52.06 |-Branch two:
% 88.31/52.06 | (298) ~ (all_54_0_39 = 0)
% 88.31/52.06 | (304) ~ (all_54_2_41 = 0) & ~ (all_17_0_6 = 0)
% 88.31/52.06 |
% 88.31/52.06 | Applying alpha-rule on (304) yields:
% 88.31/52.06 | (305) ~ (all_54_2_41 = 0)
% 88.31/52.06 | (306) ~ (all_17_0_6 = 0)
% 88.31/52.06 |
% 88.31/52.06 +-Applying beta-rule and splitting (64), into two cases.
% 88.31/52.06 |-Branch one:
% 88.31/52.06 | (307) all_17_0_6 = 0
% 88.31/52.06 |
% 88.31/52.06 | Equations (307) can reduce 306 to:
% 88.31/52.06 | (165) $false
% 88.31/52.06 |
% 88.31/52.06 |-The branch is then unsatisfiable
% 88.31/52.06 |-Branch two:
% 88.31/52.06 | (306) ~ (all_17_0_6 = 0)
% 88.31/52.06 | (310) all_17_1_7 = 0 | all_17_2_8 = 0 | all_17_3_9 = 0
% 88.31/52.06 |
% 88.31/52.06 +-Applying beta-rule and splitting (111), into two cases.
% 88.31/52.06 |-Branch one:
% 88.31/52.06 | (307) all_17_0_6 = 0
% 88.31/52.06 |
% 88.31/52.06 | Equations (307) can reduce 306 to:
% 88.31/52.06 | (165) $false
% 88.31/52.06 |
% 88.31/52.06 |-The branch is then unsatisfiable
% 88.31/52.06 |-Branch two:
% 88.31/52.06 | (306) ~ (all_17_0_6 = 0)
% 88.31/52.06 | (314) all_17_2_8 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_3_3) = v1 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 88.31/52.06 |
% 88.31/52.06 +-Applying beta-rule and splitting (99), into two cases.
% 88.31/52.06 |-Branch one:
% 88.31/52.06 | (307) all_17_0_6 = 0
% 88.31/52.06 |
% 88.31/52.06 | Equations (307) can reduce 306 to:
% 88.31/52.06 | (165) $false
% 88.31/52.06 |
% 88.31/52.06 |-The branch is then unsatisfiable
% 88.31/52.06 |-Branch two:
% 88.31/52.06 | (306) ~ (all_17_0_6 = 0)
% 88.31/52.06 | (318) all_17_3_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_1_1, all_1_0_0) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_0_0, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 88.31/52.06 |
% 88.31/52.06 +-Applying beta-rule and splitting (314), into two cases.
% 88.31/52.06 |-Branch one:
% 88.31/52.06 | (267) all_17_2_8 = 0
% 88.31/52.06 |
% 88.31/52.06 | Equations (267) can reduce 261 to:
% 88.31/52.06 | (165) $false
% 88.31/52.06 |
% 88.31/52.06 |-The branch is then unsatisfiable
% 88.31/52.06 |-Branch two:
% 88.31/52.06 | (261) ~ (all_17_2_8 = 0)
% 88.31/52.06 | (322) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_3_3) = v1 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 88.31/52.06 |
% 88.31/52.06 +-Applying beta-rule and splitting (102), into two cases.
% 88.31/52.06 |-Branch one:
% 88.31/52.06 | (307) all_17_0_6 = 0
% 88.31/52.06 |
% 88.31/52.06 | Equations (307) can reduce 306 to:
% 88.31/52.06 | (165) $false
% 88.31/52.06 |
% 88.31/52.06 |-The branch is then unsatisfiable
% 88.31/52.06 |-Branch two:
% 88.31/52.06 | (306) ~ (all_17_0_6 = 0)
% 88.31/52.06 | (326) all_17_2_8 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_0_0) = v2 & apart_point_and_line(all_1_2_2, all_1_0_0) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 88.31/52.06 |
% 88.31/52.06 +-Applying beta-rule and splitting (326), into two cases.
% 88.31/52.06 |-Branch one:
% 88.31/52.06 | (267) all_17_2_8 = 0
% 88.31/52.06 |
% 88.31/52.06 | Equations (267) can reduce 261 to:
% 88.31/52.06 | (165) $false
% 88.31/52.06 |
% 88.31/52.06 |-The branch is then unsatisfiable
% 88.31/52.06 |-Branch two:
% 88.31/52.06 | (261) ~ (all_17_2_8 = 0)
% 88.31/52.06 | (330) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_0_0) = v2 & apart_point_and_line(all_1_2_2, all_1_0_0) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 88.31/52.06 |
% 88.31/52.06 +-Applying beta-rule and splitting (310), into two cases.
% 88.31/52.06 |-Branch one:
% 88.31/52.06 | (331) all_17_1_7 = 0
% 88.31/52.06 |
% 88.31/52.06 | From (331) and (65) follows:
% 88.31/52.06 | (332) apart_point_and_line(all_1_1_1, all_1_0_0) = 0
% 88.31/52.06 |
% 88.31/52.06 | Using (332) and (300) yields:
% 88.31/52.06 | (90) $false
% 88.31/52.06 |
% 88.31/52.06 |-The branch is then unsatisfiable
% 88.31/52.06 |-Branch two:
% 88.31/52.06 | (334) ~ (all_17_1_7 = 0)
% 88.31/52.06 | (335) all_17_2_8 = 0 | all_17_3_9 = 0
% 88.31/52.06 |
% 88.31/52.06 +-Applying beta-rule and splitting (335), into two cases.
% 88.31/52.06 |-Branch one:
% 88.31/52.06 | (267) all_17_2_8 = 0
% 88.31/52.06 |
% 88.31/52.06 | Equations (267) can reduce 261 to:
% 88.31/52.06 | (165) $false
% 88.31/52.06 |
% 88.31/52.06 |-The branch is then unsatisfiable
% 88.31/52.06 |-Branch two:
% 88.31/52.06 | (261) ~ (all_17_2_8 = 0)
% 88.31/52.06 | (164) all_17_3_9 = 0
% 88.31/52.06 |
% 88.31/52.06 | Equations (164) can reduce 88 to:
% 88.31/52.06 | (165) $false
% 88.31/52.06 |
% 88.31/52.06 |-The branch is then unsatisfiable
% 88.31/52.06 |-Branch two:
% 88.31/52.06 | (332) apart_point_and_line(all_1_1_1, all_1_0_0) = 0
% 88.31/52.06 | (342) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_1_1_1, all_1_1_1) = v2 & distinct_points(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))
% 88.31/52.06 |
% 88.31/52.06 | Instantiating (342) with all_156_0_80, all_156_1_81, all_156_2_82 yields:
% 88.31/52.06 | (343) distinct_points(all_1_1_1, all_1_1_1) = all_156_0_80 & distinct_points(all_1_1_1, all_1_2_2) = all_156_1_81 & distinct_points(all_1_2_2, all_1_1_1) = all_156_2_82 & ( ~ (all_156_2_82 = 0) | (all_156_0_80 = 0 & all_156_1_81 = 0))
% 88.31/52.06 |
% 88.31/52.06 | Applying alpha-rule on (343) yields:
% 88.31/52.06 | (344) distinct_points(all_1_1_1, all_1_1_1) = all_156_0_80
% 88.31/52.06 | (345) distinct_points(all_1_1_1, all_1_2_2) = all_156_1_81
% 88.31/52.06 | (346) distinct_points(all_1_2_2, all_1_1_1) = all_156_2_82
% 88.31/52.06 | (347) ~ (all_156_2_82 = 0) | (all_156_0_80 = 0 & all_156_1_81 = 0)
% 88.31/52.06 |
% 88.31/52.06 +-Applying beta-rule and splitting (209), into two cases.
% 88.31/52.06 |-Branch one:
% 88.31/52.06 | (348) ~ (distinct_points(all_1_1_1, all_52_1_37) = all_54_0_39)
% 88.31/52.06 |
% 88.31/52.06 | From (198) and (348) follows:
% 88.31/52.06 | (349) ~ (distinct_points(all_1_1_1, all_1_2_2) = all_54_0_39)
% 88.31/52.06 |
% 88.31/52.06 +-Applying beta-rule and splitting (157), into two cases.
% 88.31/52.06 |-Branch one:
% 88.31/52.06 | (350) ~ (all_56_2_44 = 0)
% 88.31/52.06 |
% 88.31/52.06 | Equations (205) can reduce 350 to:
% 88.31/52.06 | (165) $false
% 88.31/52.06 |
% 88.31/52.06 |-The branch is then unsatisfiable
% 88.31/52.06 |-Branch two:
% 88.31/52.06 | (205) all_56_2_44 = 0
% 88.31/52.06 | (353) all_56_0_42 = 0 | ( ~ (all_56_1_43 = 0) & ~ (all_17_0_6 = 0))
% 88.31/52.06 |
% 88.31/52.06 +-Applying beta-rule and splitting (353), into two cases.
% 88.31/52.06 |-Branch one:
% 88.31/52.06 | (354) all_56_0_42 = 0
% 88.31/52.06 |
% 88.31/52.06 | Combining equations (354,295) yields a new equation:
% 88.31/52.06 | (301) all_54_0_39 = 0
% 88.31/52.06 |
% 88.31/52.06 | Equations (301) can reduce 298 to:
% 88.31/52.06 | (165) $false
% 88.31/52.06 |
% 88.31/52.06 |-The branch is then unsatisfiable
% 88.31/52.06 |-Branch two:
% 88.31/52.06 | (357) ~ (all_56_0_42 = 0)
% 88.31/52.06 | (358) ~ (all_56_1_43 = 0) & ~ (all_17_0_6 = 0)
% 88.31/52.06 |
% 88.31/52.06 | Applying alpha-rule on (358) yields:
% 88.31/52.06 | (359) ~ (all_56_1_43 = 0)
% 88.31/52.06 | (306) ~ (all_17_0_6 = 0)
% 88.31/52.06 |
% 88.31/52.06 | Equations (203) can reduce 359 to:
% 88.31/52.06 | (361) ~ (all_42_0_20 = 0)
% 88.31/52.06 |
% 88.31/52.06 +-Applying beta-rule and splitting (64), into two cases.
% 88.31/52.06 |-Branch one:
% 88.31/52.06 | (307) all_17_0_6 = 0
% 88.31/52.06 |
% 88.31/52.06 | Equations (307) can reduce 306 to:
% 88.31/52.06 | (165) $false
% 88.31/52.06 |
% 88.31/52.06 |-The branch is then unsatisfiable
% 88.31/52.06 |-Branch two:
% 88.31/52.06 | (306) ~ (all_17_0_6 = 0)
% 88.31/52.06 | (310) all_17_1_7 = 0 | all_17_2_8 = 0 | all_17_3_9 = 0
% 88.31/52.06 |
% 88.31/52.06 +-Applying beta-rule and splitting (121), into two cases.
% 88.31/52.06 |-Branch one:
% 88.31/52.06 | (366) all_42_0_20 = 0
% 88.31/52.06 |
% 88.31/52.06 | Equations (366) can reduce 361 to:
% 88.31/52.06 | (165) $false
% 88.31/52.06 |
% 88.31/52.06 |-The branch is then unsatisfiable
% 88.31/52.06 |-Branch two:
% 88.31/52.06 | (361) ~ (all_42_0_20 = 0)
% 88.31/52.06 | (369) all_42_1_21 = 0 | all_42_2_22 = 0 | all_42_3_23 = 0
% 88.31/52.06 |
% 88.31/52.06 +-Applying beta-rule and splitting (369), into two cases.
% 88.31/52.06 |-Branch one:
% 88.31/52.06 | (370) all_42_1_21 = 0
% 88.31/52.06 |
% 88.31/52.06 | Combining equations (204,370) yields a new equation:
% 88.31/52.06 | (371) all_17_0_6 = 0
% 88.31/52.06 |
% 88.31/52.06 | Simplifying 371 yields:
% 88.31/52.06 | (307) all_17_0_6 = 0
% 88.31/52.06 |
% 88.31/52.06 | Equations (307) can reduce 306 to:
% 88.31/52.06 | (165) $false
% 88.31/52.06 |
% 88.31/52.06 |-The branch is then unsatisfiable
% 88.31/52.06 |-Branch two:
% 88.31/52.06 | (374) ~ (all_42_1_21 = 0)
% 88.31/52.06 | (375) all_42_2_22 = 0 | all_42_3_23 = 0
% 88.31/52.06 |
% 88.31/52.06 | Equations (204) can reduce 374 to:
% 88.31/52.06 | (306) ~ (all_17_0_6 = 0)
% 88.31/52.06 |
% 88.31/52.06 +-Applying beta-rule and splitting (110), into two cases.
% 88.31/52.06 |-Branch one:
% 88.31/52.06 | (307) all_17_0_6 = 0
% 88.31/52.06 |
% 88.31/52.06 | Equations (307) can reduce 306 to:
% 88.31/52.06 | (165) $false
% 88.31/52.06 |
% 88.31/52.06 |-The branch is then unsatisfiable
% 88.31/52.06 |-Branch two:
% 88.31/52.06 | (306) ~ (all_17_0_6 = 0)
% 88.31/52.06 | (380) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 88.31/52.06 |
% 88.31/52.06 | Instantiating (380) with all_198_0_83, all_198_1_84, all_198_2_85 yields:
% 88.31/52.06 | (381) apart_point_and_line(all_1_1_1, all_1_3_3) = all_198_0_83 & apart_point_and_line(all_1_1_1, all_1_3_3) = all_198_1_84 & distinct_points(all_1_1_1, all_1_1_1) = all_198_2_85 & ( ~ (all_198_2_85 = 0) | all_198_0_83 = 0 | all_198_1_84 = 0)
% 88.31/52.06 |
% 88.31/52.06 | Applying alpha-rule on (381) yields:
% 88.31/52.06 | (382) apart_point_and_line(all_1_1_1, all_1_3_3) = all_198_0_83
% 88.31/52.06 | (383) apart_point_and_line(all_1_1_1, all_1_3_3) = all_198_1_84
% 88.31/52.06 | (384) distinct_points(all_1_1_1, all_1_1_1) = all_198_2_85
% 88.31/52.06 | (385) ~ (all_198_2_85 = 0) | all_198_0_83 = 0 | all_198_1_84 = 0
% 88.31/52.06 |
% 88.31/52.06 | Instantiating formula (32) with all_1_1_1, all_1_1_1, all_198_2_85, all_54_0_39 and discharging atoms distinct_points(all_1_1_1, all_1_1_1) = all_198_2_85, distinct_points(all_1_1_1, all_1_1_1) = all_54_0_39, yields:
% 88.31/52.07 | (386) all_198_2_85 = all_54_0_39
% 88.31/52.07 |
% 88.31/52.07 | Instantiating formula (32) with all_1_1_1, all_1_1_1, all_156_0_80, all_198_2_85 and discharging atoms distinct_points(all_1_1_1, all_1_1_1) = all_198_2_85, distinct_points(all_1_1_1, all_1_1_1) = all_156_0_80, yields:
% 88.31/52.07 | (387) all_198_2_85 = all_156_0_80
% 88.31/52.07 |
% 88.31/52.07 | Instantiating formula (32) with all_1_1_1, all_1_2_2, all_156_1_81, 0 and discharging atoms distinct_points(all_1_1_1, all_1_2_2) = all_156_1_81, distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 88.31/52.07 | (388) all_156_1_81 = 0
% 88.31/52.07 |
% 88.31/52.07 | Instantiating formula (32) with all_1_2_2, all_1_1_1, all_156_2_82, 0 and discharging atoms distinct_points(all_1_2_2, all_1_1_1) = all_156_2_82, distinct_points(all_1_2_2, all_1_1_1) = 0, yields:
% 88.31/52.07 | (389) all_156_2_82 = 0
% 88.31/52.07 |
% 88.31/52.07 | Using (345) and (349) yields:
% 88.31/52.07 | (390) ~ (all_156_1_81 = all_54_0_39)
% 88.31/52.07 |
% 88.31/52.07 | Combining equations (387,386) yields a new equation:
% 88.31/52.07 | (391) all_156_0_80 = all_54_0_39
% 88.31/52.07 |
% 88.31/52.07 | Simplifying 391 yields:
% 88.31/52.07 | (392) all_156_0_80 = all_54_0_39
% 88.31/52.07 |
% 88.31/52.07 | Equations (388) can reduce 390 to:
% 88.31/52.07 | (393) ~ (all_54_0_39 = 0)
% 88.31/52.07 |
% 88.31/52.07 | Simplifying 393 yields:
% 88.31/52.07 | (298) ~ (all_54_0_39 = 0)
% 88.31/52.07 |
% 88.31/52.07 +-Applying beta-rule and splitting (347), into two cases.
% 88.31/52.07 |-Branch one:
% 88.31/52.07 | (395) ~ (all_156_2_82 = 0)
% 88.31/52.07 |
% 88.31/52.07 | Equations (389) can reduce 395 to:
% 88.31/52.07 | (165) $false
% 88.31/52.07 |
% 88.31/52.07 |-The branch is then unsatisfiable
% 88.31/52.07 |-Branch two:
% 88.31/52.07 | (389) all_156_2_82 = 0
% 88.31/52.07 | (398) all_156_0_80 = 0 & all_156_1_81 = 0
% 88.31/52.07 |
% 88.31/52.07 | Applying alpha-rule on (398) yields:
% 88.31/52.07 | (399) all_156_0_80 = 0
% 88.31/52.07 | (388) all_156_1_81 = 0
% 88.31/52.07 |
% 88.31/52.07 | Combining equations (399,392) yields a new equation:
% 88.31/52.07 | (301) all_54_0_39 = 0
% 88.31/52.07 |
% 88.31/52.07 | Equations (301) can reduce 298 to:
% 88.31/52.07 | (165) $false
% 88.31/52.07 |
% 88.31/52.07 |-The branch is then unsatisfiable
% 88.31/52.07 |-Branch two:
% 88.31/52.07 | (403) distinct_points(all_1_1_1, all_52_1_37) = all_54_0_39
% 88.31/52.07 | (404) all_54_0_39 = all_52_0_36
% 88.31/52.07 |
% 88.31/52.07 | Combining equations (265,404) yields a new equation:
% 88.31/52.07 | (301) all_54_0_39 = 0
% 88.31/52.07 |
% 88.31/52.07 | Equations (301) can reduce 298 to:
% 88.31/52.07 | (165) $false
% 88.31/52.07 |
% 88.31/52.07 |-The branch is then unsatisfiable
% 88.60/52.07 |-Branch two:
% 88.60/52.07 | (407) ~ (distinct_points(all_1_1_1, all_1_2_2) = 0)
% 88.60/52.07 | (183) all_19_0_10 = 0
% 88.60/52.07 |
% 88.60/52.07 | Equations (183) can reduce 82 to:
% 88.60/52.07 | (165) $false
% 88.60/52.07 |
% 88.60/52.07 |-The branch is then unsatisfiable
% 88.60/52.07 |-Branch two:
% 88.60/52.07 | (410) all_21_1_14 = 0
% 88.60/52.07 | (411) ~ (all_21_2_15 = 0) | all_21_0_13 = 0
% 88.60/52.07 |
% 88.60/52.07 +-Applying beta-rule and splitting (411), into two cases.
% 88.60/52.07 |-Branch one:
% 88.60/52.07 | (412) ~ (all_21_2_15 = 0)
% 88.60/52.07 |
% 88.60/52.07 | Equations (79) can reduce 412 to:
% 88.60/52.07 | (165) $false
% 88.60/52.07 |
% 88.60/52.07 |-The branch is then unsatisfiable
% 88.60/52.07 |-Branch two:
% 88.60/52.07 | (79) all_21_2_15 = 0
% 88.60/52.07 | (415) all_21_0_13 = 0
% 88.60/52.07 |
% 88.60/52.07 | Combining equations (415,81) yields a new equation:
% 88.60/52.07 | (183) all_19_0_10 = 0
% 88.60/52.07 |
% 88.60/52.07 | Equations (183) can reduce 82 to:
% 88.60/52.07 | (165) $false
% 88.60/52.07 |
% 88.60/52.07 |-The branch is then unsatisfiable
% 88.60/52.07 % SZS output end Proof for theBenchmark
% 88.60/52.07
% 88.60/52.07 51466ms
%------------------------------------------------------------------------------