TSTP Solution File: GEO192+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO192+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n005.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 03:48:28 EDT 2022
% Result : Theorem 14.76s 4.11s
% Output : Proof 28.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO192+2 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jun 17 16:00:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.57 ____ _
% 0.18/0.58 ___ / __ \_____(_)___ ________ __________
% 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.58
% 0.18/0.58 A Theorem Prover for First-Order Logic
% 0.18/0.58 (ePrincess v.1.0)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2015
% 0.18/0.58 (c) Peter Backeman, 2014-2015
% 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58 Bug reports to peter@backeman.se
% 0.18/0.58
% 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58
% 0.18/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.67/0.89 Prover 0: Preprocessing ...
% 1.98/1.02 Prover 0: Warning: ignoring some quantifiers
% 1.98/1.05 Prover 0: Constructing countermodel ...
% 2.78/1.25 Prover 0: gave up
% 2.78/1.25 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.78/1.30 Prover 1: Preprocessing ...
% 3.28/1.41 Prover 1: Constructing countermodel ...
% 3.46/1.49 Prover 1: gave up
% 3.46/1.49 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.58/1.52 Prover 2: Preprocessing ...
% 3.78/1.64 Prover 2: Warning: ignoring some quantifiers
% 4.26/1.65 Prover 2: Constructing countermodel ...
% 4.80/1.80 Prover 2: gave up
% 4.80/1.80 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 5.03/1.81 Prover 3: Preprocessing ...
% 5.03/1.83 Prover 3: Warning: ignoring some quantifiers
% 5.03/1.83 Prover 3: Constructing countermodel ...
% 5.19/1.88 Prover 3: gave up
% 5.19/1.89 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 5.19/1.90 Prover 4: Preprocessing ...
% 5.59/1.97 Prover 4: Warning: ignoring some quantifiers
% 5.59/1.98 Prover 4: Constructing countermodel ...
% 10.25/3.09 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 10.25/3.11 Prover 5: Preprocessing ...
% 10.65/3.17 Prover 5: Constructing countermodel ...
% 14.76/4.11 Prover 5: proved (1015ms)
% 14.76/4.11 Prover 4: stopped
% 14.76/4.11
% 14.76/4.11 No countermodel exists, formula is valid
% 14.76/4.11 % SZS status Theorem for theBenchmark
% 14.76/4.11
% 14.76/4.11 Generating proof ... found it (size 818)
% 27.20/7.14
% 27.20/7.14 % SZS output start Proof for theBenchmark
% 27.20/7.14 Assumed formulas after preprocessing and simplification:
% 27.20/7.14 | (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, v1) = v3 & apart_point_and_line(v3, v2) = 0 & convergent_lines(v0, v1) = 0 & distinct_lines(v1, v2) = v5 & distinct_lines(v0, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))
% 27.20/7.19 | Applying alpha-rule on (0) yields:
% 27.20/7.19 | (1) ! [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)))
% 27.20/7.19 | (2) ! [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)))))
% 27.20/7.19 | (3) ! [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)))
% 27.20/7.19 | (4) ! [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))))
% 27.20/7.19 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 27.20/7.19 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 27.20/7.19 | (7) ! [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))
% 27.20/7.19 | (8) ! [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))))
% 27.20/7.19 | (9) ! [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))
% 27.20/7.19 | (10) ! [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))))
% 27.20/7.19 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 27.20/7.19 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 27.20/7.19 | (13) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 27.20/7.19 | (14) ! [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)))
% 27.20/7.19 | (15) ! [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))))
% 27.20/7.19 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 27.20/7.19 | (17) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 27.20/7.19 | (18) ! [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)))
% 27.20/7.19 | (19) ! [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)))))
% 27.20/7.19 | (20) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 27.20/7.20 | (21) ! [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)))))
% 27.20/7.20 | (22) ! [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)))))
% 27.20/7.20 | (23) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0)
% 27.20/7.20 | (24) ! [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))
% 27.20/7.20 | (25) ! [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)))
% 27.20/7.20 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 27.20/7.20 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 27.20/7.20 | (28) ! [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))
% 27.20/7.20 | (29) ! [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)
% 27.20/7.20 | (30) ! [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)
% 27.20/7.20 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 27.20/7.20 | (32) ! [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))))
% 27.20/7.20 | (33) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (intersection_point(v0, v1) = v3 & apart_point_and_line(v3, v2) = 0 & convergent_lines(v0, v1) = 0 & distinct_lines(v1, v2) = v5 & distinct_lines(v0, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))
% 27.20/7.20 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 27.20/7.20 | (35) ! [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)))
% 27.20/7.20 | (36) ! [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)))
% 27.20/7.20 | (37) ! [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)
% 27.20/7.20 | (38) ! [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)))
% 27.20/7.20 | (39) ! [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)
% 27.20/7.20 | (40) ! [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))
% 27.20/7.20 | (41) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 27.20/7.20 | (42) ! [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))
% 27.20/7.20 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 27.20/7.21 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 27.20/7.21 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 27.20/7.21 | (46) ! [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)))))
% 27.20/7.21 |
% 27.20/7.21 | Instantiating (33) 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:
% 27.20/7.21 | (47) intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2 & apart_point_and_line(all_1_2_2, all_1_3_3) = 0 & convergent_lines(all_1_5_5, all_1_4_4) = 0 & distinct_lines(all_1_4_4, all_1_3_3) = all_1_0_0 & distinct_lines(all_1_5_5, all_1_3_3) = all_1_1_1 & ( ~ (all_1_0_0 = 0) | ~ (all_1_1_1 = 0))
% 27.20/7.21 |
% 27.20/7.21 | Applying alpha-rule on (47) yields:
% 27.20/7.21 | (48) ~ (all_1_0_0 = 0) | ~ (all_1_1_1 = 0)
% 27.20/7.21 | (49) intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2
% 27.20/7.21 | (50) distinct_lines(all_1_5_5, all_1_3_3) = all_1_1_1
% 27.20/7.21 | (51) apart_point_and_line(all_1_2_2, all_1_3_3) = 0
% 27.20/7.21 | (52) convergent_lines(all_1_5_5, all_1_4_4) = 0
% 27.20/7.21 | (53) distinct_lines(all_1_4_4, all_1_3_3) = all_1_0_0
% 27.20/7.21 |
% 27.20/7.21 | Instantiating formula (41) with all_1_5_5 yields:
% 27.20/7.21 | (54) ~ (convergent_lines(all_1_5_5, all_1_5_5) = 0)
% 27.20/7.21 |
% 27.20/7.21 | Instantiating formula (5) with all_1_5_5, all_1_3_3, all_1_1_1, all_1_0_0 and discharging atoms distinct_lines(all_1_5_5, all_1_3_3) = all_1_1_1, yields:
% 27.20/7.21 | (55) all_1_0_0 = all_1_1_1 | ~ (distinct_lines(all_1_5_5, all_1_3_3) = all_1_0_0)
% 27.20/7.21 |
% 27.20/7.21 | Instantiating formula (25) with 0, 0, all_1_2_2, all_1_3_3, all_1_3_3 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = 0, yields:
% 27.20/7.21 | (56) ? [v0] : ? [v1] : ? [v2] : (intersection_point(all_1_3_3, all_1_3_3) = v1 & convergent_lines(all_1_3_3, all_1_3_3) = v0 & distinct_points(all_1_2_2, v1) = v2 & ( ~ (v0 = 0) | v2 = 0))
% 27.20/7.21 |
% 27.20/7.21 | Instantiating formula (2) with all_1_2_2, 0, 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, yields:
% 27.20/7.21 | (57) ~ (apart_point_and_line(all_1_2_2, all_1_4_4) = 0) | ? [v0] : ? [v1] : ? [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 & distinct_points(all_1_2_2, all_1_2_2) = v2 & ( ~ (v0 = 0) | v2 = 0))
% 27.20/7.21 |
% 27.20/7.21 | Instantiating formula (46) with 0, all_1_2_2, all_1_4_4, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 27.20/7.21 | (58) ~ (apart_point_and_line(all_1_2_2, all_1_4_4) = 0) | ? [v0] : ? [v1] : (intersection_point(all_1_5_5, all_1_4_4) = v1 & apart_point_and_line(all_1_2_2, all_1_5_5) = v0 & distinct_points(all_1_2_2, v1) = 0)
% 27.20/7.21 |
% 27.20/7.21 | Instantiating formula (21) with 0, all_1_2_2, all_1_4_4, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 27.20/7.21 | (59) ~ (apart_point_and_line(all_1_2_2, all_1_5_5) = 0) | ? [v0] : ? [v1] : (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) = 0)
% 27.20/7.21 |
% 27.20/7.21 | Instantiating formula (23) with all_1_4_4, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 27.20/7.21 | (60) distinct_lines(all_1_5_5, all_1_4_4) = 0
% 27.20/7.21 |
% 27.20/7.21 | Instantiating formula (9) with all_1_0_0, all_1_0_0, all_1_3_3, all_1_4_4, all_1_4_4 and discharging atoms distinct_lines(all_1_4_4, all_1_3_3) = all_1_0_0, yields:
% 27.20/7.21 | (61) all_1_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_4_4, all_1_4_4) = v0)
% 27.20/7.21 |
% 27.20/7.21 | Instantiating formula (13) with all_1_0_0, all_1_3_3, all_1_4_4 and discharging atoms distinct_lines(all_1_4_4, all_1_3_3) = all_1_0_0, yields:
% 27.20/7.21 | (62) all_1_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_1_4_4, all_1_3_3) = v0)
% 27.20/7.21 |
% 27.20/7.21 | Instantiating formula (9) with all_1_1_1, all_1_0_0, all_1_3_3, all_1_5_5, all_1_4_4 and discharging atoms distinct_lines(all_1_4_4, all_1_3_3) = all_1_0_0, distinct_lines(all_1_5_5, all_1_3_3) = all_1_1_1, yields:
% 27.20/7.21 | (63) all_1_0_0 = 0 | all_1_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_4_4, all_1_5_5) = v0)
% 27.20/7.21 |
% 27.20/7.21 | Instantiating formula (9) with all_1_0_0, all_1_1_1, all_1_3_3, all_1_4_4, all_1_5_5 and discharging atoms distinct_lines(all_1_4_4, all_1_3_3) = all_1_0_0, distinct_lines(all_1_5_5, all_1_3_3) = all_1_1_1, yields:
% 27.20/7.21 | (64) all_1_0_0 = 0 | all_1_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_5_5, all_1_4_4) = v0)
% 27.20/7.21 |
% 27.20/7.21 | Instantiating formula (9) with all_1_1_1, all_1_1_1, all_1_3_3, all_1_5_5, all_1_5_5 and discharging atoms distinct_lines(all_1_5_5, all_1_3_3) = all_1_1_1, yields:
% 27.20/7.21 | (65) all_1_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_5_5, all_1_5_5) = v0)
% 27.20/7.21 |
% 27.20/7.21 | Instantiating formula (13) with all_1_1_1, all_1_3_3, all_1_5_5 and discharging atoms distinct_lines(all_1_5_5, all_1_3_3) = all_1_1_1, yields:
% 27.20/7.21 | (66) all_1_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_1_5_5, all_1_3_3) = v0)
% 27.20/7.21 |
% 27.20/7.21 | Instantiating (56) with all_17_0_6, all_17_1_7, all_17_2_8 yields:
% 27.20/7.21 | (67) intersection_point(all_1_3_3, all_1_3_3) = all_17_1_7 & convergent_lines(all_1_3_3, all_1_3_3) = all_17_2_8 & distinct_points(all_1_2_2, all_17_1_7) = all_17_0_6 & ( ~ (all_17_2_8 = 0) | all_17_0_6 = 0)
% 27.20/7.21 |
% 27.20/7.21 | Applying alpha-rule on (67) yields:
% 27.20/7.21 | (68) intersection_point(all_1_3_3, all_1_3_3) = all_17_1_7
% 27.20/7.21 | (69) convergent_lines(all_1_3_3, all_1_3_3) = all_17_2_8
% 27.20/7.21 | (70) distinct_points(all_1_2_2, all_17_1_7) = all_17_0_6
% 27.20/7.21 | (71) ~ (all_17_2_8 = 0) | all_17_0_6 = 0
% 27.20/7.21 |
% 27.20/7.21 | Instantiating formula (41) with all_1_3_3 yields:
% 27.20/7.21 | (72) ~ (convergent_lines(all_1_3_3, all_1_3_3) = 0)
% 27.20/7.21 |
% 27.20/7.22 | Using (69) and (72) yields:
% 27.20/7.22 | (73) ~ (all_17_2_8 = 0)
% 27.20/7.22 |
% 27.20/7.22 | Instantiating formula (12) with all_1_0_0, all_1_3_3, all_1_4_4, all_1_5_5 and discharging atoms distinct_lines(all_1_4_4, all_1_3_3) = all_1_0_0, distinct_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 27.20/7.22 | (74) all_1_0_0 = 0 | distinct_lines(all_1_5_5, all_1_3_3) = 0
% 27.20/7.22 |
% 27.20/7.22 +-Applying beta-rule and splitting (55), into two cases.
% 27.20/7.22 |-Branch one:
% 27.20/7.22 | (75) ~ (distinct_lines(all_1_5_5, all_1_3_3) = all_1_0_0)
% 27.20/7.22 |
% 27.20/7.22 | Using (50) and (75) yields:
% 27.20/7.22 | (76) ~ (all_1_0_0 = all_1_1_1)
% 27.20/7.22 |
% 27.20/7.22 +-Applying beta-rule and splitting (48), into two cases.
% 27.20/7.22 |-Branch one:
% 27.20/7.22 | (77) ~ (all_1_0_0 = 0)
% 27.20/7.22 |
% 27.20/7.22 +-Applying beta-rule and splitting (64), into two cases.
% 27.20/7.22 |-Branch one:
% 27.20/7.22 | (78) all_1_0_0 = 0
% 27.20/7.22 |
% 27.20/7.22 | Equations (78) can reduce 77 to:
% 27.20/7.22 | (79) $false
% 27.20/7.22 |
% 27.20/7.22 |-The branch is then unsatisfiable
% 27.20/7.22 |-Branch two:
% 27.20/7.22 | (77) ~ (all_1_0_0 = 0)
% 27.20/7.22 | (81) all_1_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_5_5, all_1_4_4) = v0)
% 27.20/7.22 |
% 27.20/7.22 +-Applying beta-rule and splitting (62), into two cases.
% 27.20/7.22 |-Branch one:
% 27.20/7.22 | (78) all_1_0_0 = 0
% 27.20/7.22 |
% 27.20/7.22 | Equations (78) can reduce 77 to:
% 27.20/7.22 | (79) $false
% 27.20/7.22 |
% 27.20/7.22 |-The branch is then unsatisfiable
% 27.20/7.22 |-Branch two:
% 27.20/7.22 | (77) ~ (all_1_0_0 = 0)
% 27.20/7.22 | (85) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_1_4_4, all_1_3_3) = v0)
% 27.20/7.22 |
% 27.20/7.22 | Instantiating (85) with all_52_0_9 yields:
% 27.20/7.22 | (86) ~ (all_52_0_9 = 0) & convergent_lines(all_1_4_4, all_1_3_3) = all_52_0_9
% 27.20/7.22 |
% 27.20/7.22 | Applying alpha-rule on (86) yields:
% 27.20/7.22 | (87) ~ (all_52_0_9 = 0)
% 27.20/7.22 | (88) convergent_lines(all_1_4_4, all_1_3_3) = all_52_0_9
% 27.20/7.22 |
% 27.20/7.22 +-Applying beta-rule and splitting (81), into two cases.
% 27.20/7.22 |-Branch one:
% 27.20/7.22 | (89) all_1_1_1 = 0
% 27.20/7.22 |
% 27.20/7.22 | Equations (89) can reduce 76 to:
% 27.20/7.22 | (77) ~ (all_1_0_0 = 0)
% 27.20/7.22 |
% 27.20/7.22 | From (89) and (50) follows:
% 27.20/7.22 | (91) distinct_lines(all_1_5_5, all_1_3_3) = 0
% 27.20/7.22 |
% 27.20/7.22 +-Applying beta-rule and splitting (61), into two cases.
% 27.20/7.22 |-Branch one:
% 27.20/7.22 | (78) all_1_0_0 = 0
% 27.20/7.22 |
% 27.67/7.22 | Equations (78) can reduce 77 to:
% 27.67/7.22 | (79) $false
% 27.67/7.22 |
% 27.67/7.22 |-The branch is then unsatisfiable
% 27.67/7.22 |-Branch two:
% 27.67/7.22 | (77) ~ (all_1_0_0 = 0)
% 27.67/7.22 | (95) ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_4_4, all_1_4_4) = v0)
% 27.67/7.22 |
% 27.67/7.22 | Instantiating formula (34) with all_52_0_9, all_1_3_3, all_1_4_4, all_1_5_5 and discharging atoms convergent_lines(all_1_4_4, all_1_3_3) = all_52_0_9, convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 27.67/7.22 | (96) all_52_0_9 = 0 | convergent_lines(all_1_5_5, all_1_3_3) = 0
% 27.67/7.22 |
% 27.67/7.22 +-Applying beta-rule and splitting (59), into two cases.
% 27.67/7.22 |-Branch one:
% 27.67/7.22 | (97) ~ (apart_point_and_line(all_1_2_2, all_1_5_5) = 0)
% 27.67/7.22 |
% 27.67/7.22 +-Applying beta-rule and splitting (96), into two cases.
% 27.67/7.22 |-Branch one:
% 27.67/7.22 | (98) convergent_lines(all_1_5_5, all_1_3_3) = 0
% 27.67/7.22 |
% 27.67/7.22 | Instantiating formula (46) with 0, 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_3_3) = 0, convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 27.67/7.22 | (99) ? [v0] : ? [v1] : (intersection_point(all_1_5_5, all_1_3_3) = v1 & apart_point_and_line(all_1_2_2, all_1_5_5) = v0 & distinct_points(all_1_2_2, v1) = 0)
% 27.67/7.22 |
% 27.67/7.22 | Instantiating (99) with all_112_0_14, all_112_1_15 yields:
% 27.67/7.22 | (100) intersection_point(all_1_5_5, all_1_3_3) = all_112_0_14 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_112_1_15 & distinct_points(all_1_2_2, all_112_0_14) = 0
% 27.67/7.22 |
% 27.67/7.22 | Applying alpha-rule on (100) yields:
% 27.67/7.22 | (101) intersection_point(all_1_5_5, all_1_3_3) = all_112_0_14
% 27.67/7.22 | (102) apart_point_and_line(all_1_2_2, all_1_5_5) = all_112_1_15
% 27.67/7.22 | (103) distinct_points(all_1_2_2, all_112_0_14) = 0
% 27.67/7.22 |
% 27.67/7.22 | Using (102) and (97) yields:
% 27.67/7.22 | (104) ~ (all_112_1_15 = 0)
% 27.67/7.22 |
% 27.67/7.22 | Instantiating formula (20) with all_1_2_2 yields:
% 27.67/7.22 | (105) ~ (distinct_points(all_1_2_2, all_1_2_2) = 0)
% 27.67/7.22 |
% 27.67/7.22 +-Applying beta-rule and splitting (57), into two cases.
% 27.67/7.22 |-Branch one:
% 27.67/7.22 | (106) ~ (apart_point_and_line(all_1_2_2, all_1_4_4) = 0)
% 27.67/7.22 |
% 27.67/7.22 | Instantiating formula (39) with all_112_1_15, all_1_5_5, all_1_3_3, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = 0, apart_point_and_line(all_1_2_2, all_1_5_5) = all_112_1_15, yields:
% 27.67/7.22 | (107) all_112_1_15 = 0 | distinct_lines(all_1_3_3, all_1_5_5) = 0
% 27.67/7.22 |
% 27.67/7.22 | Instantiating formula (25) with all_112_1_15, 0, all_1_2_2, all_1_5_5, all_1_3_3 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = 0, apart_point_and_line(all_1_2_2, all_1_5_5) = all_112_1_15, yields:
% 27.67/7.22 | (108) ? [v0] : ? [v1] : ? [v2] : (intersection_point(all_1_3_3, all_1_5_5) = v1 & convergent_lines(all_1_3_3, all_1_5_5) = v0 & distinct_points(all_1_2_2, v1) = v2 & ( ~ (v0 = 0) | v2 = 0))
% 27.67/7.22 |
% 27.67/7.22 | Instantiating formula (38) with all_112_1_15, all_112_1_15, all_1_4_4, 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_5_5) = all_112_1_15, distinct_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 27.67/7.22 | (109) all_112_1_15 = 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_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.22 |
% 27.67/7.22 | Instantiating formula (14) with all_112_1_15, all_112_1_15, all_1_5_5, 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_5_5) = all_112_1_15, yields:
% 27.67/7.23 | (110) all_112_1_15 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.23 |
% 27.67/7.23 | Instantiating formula (19) with all_1_2_2, all_112_1_15, 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_112_1_15, yields:
% 27.67/7.23 | (111) ? [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_112_1_15 = 0))))
% 27.67/7.23 |
% 27.67/7.23 | Instantiating formula (21) with all_112_1_15, 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_112_1_15, convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 27.67/7.23 | (112) ? [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_112_1_15 = 0))))
% 27.67/7.23 |
% 27.67/7.23 | Instantiating formula (10) with 0, all_1_2_2, all_112_0_14, all_1_2_2 and discharging atoms distinct_points(all_1_2_2, all_112_0_14) = 0, yields:
% 27.67/7.23 | (113) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_2_2, all_112_0_14) = 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))
% 27.67/7.23 |
% 27.67/7.23 | Instantiating formula (3) with all_1_3_3, all_1_5_5, all_112_0_14, 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_112_0_14) = 0, yields:
% 27.67/7.23 | (114) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_112_0_14, all_1_3_3) = v3 & apart_point_and_line(all_112_0_14, 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))
% 27.67/7.23 |
% 27.67/7.23 | Instantiating formula (3) with all_1_4_4, all_1_5_5, all_112_0_14, all_1_2_2 and discharging atoms distinct_lines(all_1_5_5, all_1_4_4) = 0, distinct_points(all_1_2_2, all_112_0_14) = 0, yields:
% 27.67/7.23 | (115) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_112_0_14, all_1_4_4) = v3 & apart_point_and_line(all_112_0_14, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v1 & apart_point_and_line(all_1_2_2, all_1_5_5) = v0 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0))
% 27.67/7.23 |
% 27.67/7.23 | Instantiating (115) with all_131_0_16, all_131_1_17, all_131_2_18, all_131_3_19 yields:
% 27.67/7.23 | (116) apart_point_and_line(all_112_0_14, all_1_4_4) = all_131_0_16 & apart_point_and_line(all_112_0_14, all_1_5_5) = all_131_1_17 & apart_point_and_line(all_1_2_2, all_1_4_4) = all_131_2_18 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_131_3_19 & (all_131_0_16 = 0 | all_131_1_17 = 0 | all_131_2_18 = 0 | all_131_3_19 = 0)
% 27.67/7.23 |
% 27.67/7.23 | Applying alpha-rule on (116) yields:
% 27.67/7.23 | (117) apart_point_and_line(all_112_0_14, all_1_5_5) = all_131_1_17
% 27.67/7.23 | (118) apart_point_and_line(all_112_0_14, all_1_4_4) = all_131_0_16
% 27.67/7.23 | (119) all_131_0_16 = 0 | all_131_1_17 = 0 | all_131_2_18 = 0 | all_131_3_19 = 0
% 27.67/7.23 | (120) apart_point_and_line(all_1_2_2, all_1_4_4) = all_131_2_18
% 27.67/7.23 | (121) apart_point_and_line(all_1_2_2, all_1_5_5) = all_131_3_19
% 27.67/7.23 |
% 27.67/7.23 | Instantiating (114) with all_133_0_20, all_133_1_21, all_133_2_22, all_133_3_23 yields:
% 27.67/7.23 | (122) apart_point_and_line(all_112_0_14, all_1_3_3) = all_133_0_20 & apart_point_and_line(all_112_0_14, all_1_5_5) = all_133_1_21 & apart_point_and_line(all_1_2_2, all_1_3_3) = all_133_2_22 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_133_3_23 & (all_133_0_20 = 0 | all_133_1_21 = 0 | all_133_2_22 = 0 | all_133_3_23 = 0)
% 27.67/7.23 |
% 27.67/7.23 | Applying alpha-rule on (122) yields:
% 27.67/7.23 | (123) apart_point_and_line(all_112_0_14, all_1_3_3) = all_133_0_20
% 27.67/7.23 | (124) apart_point_and_line(all_1_2_2, all_1_5_5) = all_133_3_23
% 27.67/7.23 | (125) all_133_0_20 = 0 | all_133_1_21 = 0 | all_133_2_22 = 0 | all_133_3_23 = 0
% 27.67/7.23 | (126) apart_point_and_line(all_112_0_14, all_1_5_5) = all_133_1_21
% 27.67/7.23 | (127) apart_point_and_line(all_1_2_2, all_1_3_3) = all_133_2_22
% 27.67/7.23 |
% 27.67/7.23 | Instantiating (113) with all_135_0_24, all_135_1_25, all_135_2_26 yields:
% 27.67/7.23 | (128) line_connecting(all_1_2_2, all_112_0_14) = all_135_2_26 & apart_point_and_line(all_1_2_2, all_135_2_26) = all_135_1_25 & distinct_points(all_1_2_2, all_1_2_2) = all_135_0_24 & ( ~ (all_135_1_25 = 0) | all_135_0_24 = 0)
% 27.67/7.23 |
% 27.67/7.23 | Applying alpha-rule on (128) yields:
% 27.67/7.23 | (129) line_connecting(all_1_2_2, all_112_0_14) = all_135_2_26
% 27.67/7.23 | (130) apart_point_and_line(all_1_2_2, all_135_2_26) = all_135_1_25
% 27.67/7.23 | (131) distinct_points(all_1_2_2, all_1_2_2) = all_135_0_24
% 27.67/7.23 | (132) ~ (all_135_1_25 = 0) | all_135_0_24 = 0
% 27.67/7.23 |
% 27.67/7.23 | Instantiating (112) with all_137_0_27, all_137_1_28, all_137_2_29 yields:
% 27.67/7.23 | (133) intersection_point(all_1_5_5, all_1_4_4) = all_137_1_28 & apart_point_and_line(all_1_2_2, all_1_4_4) = all_137_2_29 & distinct_points(all_1_2_2, all_137_1_28) = all_137_0_27 & (all_137_0_27 = 0 | ( ~ (all_137_2_29 = 0) & ~ (all_112_1_15 = 0)))
% 27.67/7.23 |
% 27.67/7.23 | Applying alpha-rule on (133) yields:
% 27.67/7.23 | (134) intersection_point(all_1_5_5, all_1_4_4) = all_137_1_28
% 27.67/7.23 | (135) apart_point_and_line(all_1_2_2, all_1_4_4) = all_137_2_29
% 27.67/7.23 | (136) distinct_points(all_1_2_2, all_137_1_28) = all_137_0_27
% 27.67/7.23 | (137) all_137_0_27 = 0 | ( ~ (all_137_2_29 = 0) & ~ (all_112_1_15 = 0))
% 27.67/7.23 |
% 27.67/7.23 | Instantiating (111) with all_139_0_30, all_139_1_31, all_139_2_32 yields:
% 27.67/7.23 | (138) apart_point_and_line(all_1_2_2, all_1_4_4) = all_139_1_31 & convergent_lines(all_1_5_5, all_1_4_4) = all_139_2_32 & distinct_points(all_1_2_2, all_1_2_2) = all_139_0_30 & ( ~ (all_139_2_32 = 0) | all_139_0_30 = 0 | ( ~ (all_139_1_31 = 0) & ~ (all_112_1_15 = 0)))
% 27.67/7.23 |
% 27.67/7.23 | Applying alpha-rule on (138) yields:
% 27.67/7.23 | (139) apart_point_and_line(all_1_2_2, all_1_4_4) = all_139_1_31
% 27.67/7.23 | (140) convergent_lines(all_1_5_5, all_1_4_4) = all_139_2_32
% 27.67/7.23 | (141) distinct_points(all_1_2_2, all_1_2_2) = all_139_0_30
% 27.67/7.23 | (142) ~ (all_139_2_32 = 0) | all_139_0_30 = 0 | ( ~ (all_139_1_31 = 0) & ~ (all_112_1_15 = 0))
% 27.67/7.23 |
% 27.67/7.23 | Instantiating (108) with all_141_0_33, all_141_1_34, all_141_2_35 yields:
% 27.67/7.23 | (143) intersection_point(all_1_3_3, all_1_5_5) = all_141_1_34 & convergent_lines(all_1_3_3, all_1_5_5) = all_141_2_35 & distinct_points(all_1_2_2, all_141_1_34) = all_141_0_33 & ( ~ (all_141_2_35 = 0) | all_141_0_33 = 0)
% 27.67/7.23 |
% 27.67/7.23 | Applying alpha-rule on (143) yields:
% 27.67/7.23 | (144) intersection_point(all_1_3_3, all_1_5_5) = all_141_1_34
% 27.67/7.23 | (145) convergent_lines(all_1_3_3, all_1_5_5) = all_141_2_35
% 27.67/7.24 | (146) distinct_points(all_1_2_2, all_141_1_34) = all_141_0_33
% 27.67/7.24 | (147) ~ (all_141_2_35 = 0) | all_141_0_33 = 0
% 27.67/7.24 |
% 27.67/7.24 +-Applying beta-rule and splitting (110), into two cases.
% 27.67/7.24 |-Branch one:
% 27.67/7.24 | (148) all_112_1_15 = 0
% 27.67/7.24 |
% 27.67/7.24 | Equations (148) can reduce 104 to:
% 27.67/7.24 | (79) $false
% 27.67/7.24 |
% 27.67/7.24 |-The branch is then unsatisfiable
% 27.67/7.24 |-Branch two:
% 27.67/7.24 | (104) ~ (all_112_1_15 = 0)
% 27.67/7.24 | (151) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.24 |
% 27.67/7.24 | Instantiating (151) with all_150_0_36, all_150_1_37, all_150_2_38, all_150_3_39 yields:
% 27.67/7.24 | (152) apart_point_and_line(all_1_2_2, all_1_5_5) = all_150_0_36 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_150_1_37 & distinct_lines(all_1_5_5, all_1_5_5) = all_150_2_38 & distinct_points(all_1_2_2, all_1_2_2) = all_150_3_39 & ( ~ (all_150_2_38 = 0) | ~ (all_150_3_39 = 0) | all_150_0_36 = 0 | all_150_1_37 = 0)
% 27.67/7.24 |
% 27.67/7.24 | Applying alpha-rule on (152) yields:
% 27.67/7.24 | (153) distinct_points(all_1_2_2, all_1_2_2) = all_150_3_39
% 27.67/7.24 | (154) ~ (all_150_2_38 = 0) | ~ (all_150_3_39 = 0) | all_150_0_36 = 0 | all_150_1_37 = 0
% 27.67/7.24 | (155) apart_point_and_line(all_1_2_2, all_1_5_5) = all_150_1_37
% 27.67/7.24 | (156) apart_point_and_line(all_1_2_2, all_1_5_5) = all_150_0_36
% 27.67/7.24 | (157) distinct_lines(all_1_5_5, all_1_5_5) = all_150_2_38
% 27.67/7.24 |
% 27.67/7.24 +-Applying beta-rule and splitting (107), into two cases.
% 27.67/7.24 |-Branch one:
% 27.67/7.24 | (158) distinct_lines(all_1_3_3, all_1_5_5) = 0
% 27.67/7.24 |
% 27.67/7.24 | Instantiating formula (45) with all_1_5_5, all_1_4_4, all_137_1_28, all_1_2_2 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_137_1_28, intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2, yields:
% 27.67/7.24 | (159) all_137_1_28 = all_1_2_2
% 27.67/7.24 |
% 27.67/7.24 | Instantiating formula (26) with all_112_0_14, all_1_5_5, all_131_1_17, all_133_1_21 and discharging atoms apart_point_and_line(all_112_0_14, all_1_5_5) = all_133_1_21, apart_point_and_line(all_112_0_14, all_1_5_5) = all_131_1_17, yields:
% 27.67/7.24 | (160) all_133_1_21 = all_131_1_17
% 27.67/7.24 |
% 27.67/7.24 | Instantiating formula (26) with all_1_2_2, all_1_3_3, all_133_2_22, 0 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = all_133_2_22, apart_point_and_line(all_1_2_2, all_1_3_3) = 0, yields:
% 27.67/7.24 | (161) all_133_2_22 = 0
% 27.67/7.24 |
% 27.67/7.24 | Instantiating formula (26) with all_1_2_2, all_1_4_4, all_137_2_29, all_139_1_31 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_139_1_31, apart_point_and_line(all_1_2_2, all_1_4_4) = all_137_2_29, yields:
% 27.67/7.24 | (162) all_139_1_31 = all_137_2_29
% 27.67/7.24 |
% 27.67/7.24 | Instantiating formula (26) with all_1_2_2, all_1_4_4, all_131_2_18, all_139_1_31 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_139_1_31, apart_point_and_line(all_1_2_2, all_1_4_4) = all_131_2_18, yields:
% 27.67/7.24 | (163) all_139_1_31 = all_131_2_18
% 27.67/7.24 |
% 27.67/7.24 | Instantiating formula (26) with all_1_2_2, all_1_5_5, all_150_0_36, all_112_1_15 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_150_0_36, apart_point_and_line(all_1_2_2, all_1_5_5) = all_112_1_15, yields:
% 27.67/7.24 | (164) all_150_0_36 = all_112_1_15
% 27.67/7.24 |
% 27.67/7.24 | Instantiating formula (26) with all_1_2_2, all_1_5_5, all_133_3_23, all_150_0_36 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_150_0_36, apart_point_and_line(all_1_2_2, all_1_5_5) = all_133_3_23, yields:
% 27.67/7.24 | (165) all_150_0_36 = all_133_3_23
% 27.67/7.24 |
% 27.67/7.24 | Instantiating formula (26) with all_1_2_2, all_1_5_5, all_133_3_23, all_150_1_37 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_150_1_37, apart_point_and_line(all_1_2_2, all_1_5_5) = all_133_3_23, yields:
% 27.67/7.24 | (166) all_150_1_37 = all_133_3_23
% 27.67/7.24 |
% 27.67/7.24 | Instantiating formula (26) with all_1_2_2, all_1_5_5, all_131_3_19, all_150_1_37 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_150_1_37, apart_point_and_line(all_1_2_2, all_1_5_5) = all_131_3_19, yields:
% 27.67/7.24 | (167) all_150_1_37 = all_131_3_19
% 27.67/7.24 |
% 27.67/7.24 | Using (121) and (97) yields:
% 27.67/7.24 | (168) ~ (all_131_3_19 = 0)
% 27.67/7.24 |
% 27.67/7.24 | Instantiating formula (27) with all_1_5_5, all_1_4_4, all_139_2_32, 0 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = all_139_2_32, convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 27.67/7.24 | (169) all_139_2_32 = 0
% 27.67/7.24 |
% 27.67/7.24 | Instantiating formula (16) with all_1_2_2, all_1_2_2, all_150_3_39, all_137_0_27 and discharging atoms distinct_points(all_1_2_2, all_1_2_2) = all_150_3_39, yields:
% 27.67/7.24 | (170) all_150_3_39 = all_137_0_27 | ~ (distinct_points(all_1_2_2, all_1_2_2) = all_137_0_27)
% 27.67/7.24 |
% 27.67/7.24 | Instantiating formula (16) with all_1_2_2, all_1_2_2, all_139_0_30, all_150_3_39 and discharging atoms distinct_points(all_1_2_2, all_1_2_2) = all_150_3_39, distinct_points(all_1_2_2, all_1_2_2) = all_139_0_30, yields:
% 27.67/7.24 | (171) all_150_3_39 = all_139_0_30
% 27.67/7.24 |
% 27.67/7.24 | Using (141) and (105) yields:
% 27.67/7.24 | (172) ~ (all_139_0_30 = 0)
% 27.67/7.24 |
% 27.67/7.24 | Instantiating formula (16) with all_1_2_2, all_1_2_2, all_135_0_24, all_150_3_39 and discharging atoms distinct_points(all_1_2_2, all_1_2_2) = all_150_3_39, distinct_points(all_1_2_2, all_1_2_2) = all_135_0_24, yields:
% 27.67/7.24 | (173) all_150_3_39 = all_135_0_24
% 27.67/7.24 |
% 27.67/7.24 | Combining equations (165,164) yields a new equation:
% 27.67/7.24 | (174) all_133_3_23 = all_112_1_15
% 27.67/7.24 |
% 27.67/7.24 | Simplifying 174 yields:
% 27.67/7.24 | (175) all_133_3_23 = all_112_1_15
% 27.67/7.24 |
% 27.67/7.24 | Combining equations (166,167) yields a new equation:
% 27.67/7.24 | (176) all_133_3_23 = all_131_3_19
% 27.67/7.24 |
% 27.67/7.24 | Simplifying 176 yields:
% 27.67/7.24 | (177) all_133_3_23 = all_131_3_19
% 27.67/7.24 |
% 27.67/7.24 | Combining equations (173,171) yields a new equation:
% 27.67/7.24 | (178) all_139_0_30 = all_135_0_24
% 27.67/7.24 |
% 27.67/7.24 | Combining equations (163,162) yields a new equation:
% 27.67/7.24 | (179) all_137_2_29 = all_131_2_18
% 27.67/7.24 |
% 27.67/7.24 | Combining equations (175,177) yields a new equation:
% 27.67/7.24 | (180) all_131_3_19 = all_112_1_15
% 27.67/7.24 |
% 27.67/7.24 | Combining equations (178,171) yields a new equation:
% 27.67/7.24 | (173) all_150_3_39 = all_135_0_24
% 27.67/7.24 |
% 27.67/7.24 | Equations (178) can reduce 172 to:
% 27.67/7.24 | (182) ~ (all_135_0_24 = 0)
% 27.67/7.24 |
% 27.67/7.24 | Equations (180) can reduce 168 to:
% 27.67/7.24 | (104) ~ (all_112_1_15 = 0)
% 27.67/7.24 |
% 27.67/7.24 | From (159) and (134) follows:
% 27.67/7.24 | (49) intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2
% 27.67/7.24 |
% 27.67/7.24 | From (160) and (126) follows:
% 27.67/7.24 | (117) apart_point_and_line(all_112_0_14, all_1_5_5) = all_131_1_17
% 27.67/7.24 |
% 27.67/7.24 | From (161) and (127) follows:
% 27.67/7.24 | (51) apart_point_and_line(all_1_2_2, all_1_3_3) = 0
% 27.67/7.24 |
% 27.67/7.24 | From (179) and (135) follows:
% 27.67/7.24 | (120) apart_point_and_line(all_1_2_2, all_1_4_4) = all_131_2_18
% 27.67/7.24 |
% 27.67/7.24 | From (180) and (121) follows:
% 27.67/7.24 | (102) apart_point_and_line(all_1_2_2, all_1_5_5) = all_112_1_15
% 27.67/7.24 |
% 27.67/7.24 | From (169) and (140) follows:
% 27.67/7.24 | (52) convergent_lines(all_1_5_5, all_1_4_4) = 0
% 27.67/7.24 |
% 27.67/7.24 | From (159) and (136) follows:
% 27.67/7.24 | (190) distinct_points(all_1_2_2, all_1_2_2) = all_137_0_27
% 27.67/7.24 |
% 27.67/7.24 +-Applying beta-rule and splitting (132), into two cases.
% 27.67/7.24 |-Branch one:
% 27.67/7.24 | (191) ~ (all_135_1_25 = 0)
% 27.67/7.24 |
% 27.67/7.24 +-Applying beta-rule and splitting (109), into two cases.
% 27.67/7.24 |-Branch one:
% 27.67/7.24 | (148) all_112_1_15 = 0
% 27.67/7.24 |
% 27.67/7.24 | Equations (148) can reduce 104 to:
% 27.67/7.24 | (79) $false
% 27.67/7.24 |
% 27.67/7.24 |-The branch is then unsatisfiable
% 27.67/7.24 |-Branch two:
% 27.67/7.24 | (104) ~ (all_112_1_15 = 0)
% 27.67/7.24 | (195) ? [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_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.25 |
% 27.67/7.25 | Instantiating (195) with all_168_0_40, all_168_1_41, all_168_2_42 yields:
% 27.67/7.25 | (196) apart_point_and_line(all_1_2_2, all_1_4_4) = all_168_0_40 & apart_point_and_line(all_1_2_2, all_1_4_4) = all_168_1_41 & distinct_points(all_1_2_2, all_1_2_2) = all_168_2_42 & ( ~ (all_168_2_42 = 0) | all_168_0_40 = 0 | all_168_1_41 = 0)
% 27.67/7.25 |
% 27.67/7.25 | Applying alpha-rule on (196) yields:
% 27.67/7.25 | (197) apart_point_and_line(all_1_2_2, all_1_4_4) = all_168_0_40
% 27.67/7.25 | (198) apart_point_and_line(all_1_2_2, all_1_4_4) = all_168_1_41
% 27.67/7.25 | (199) distinct_points(all_1_2_2, all_1_2_2) = all_168_2_42
% 27.67/7.25 | (200) ~ (all_168_2_42 = 0) | all_168_0_40 = 0 | all_168_1_41 = 0
% 27.67/7.25 |
% 27.67/7.25 +-Applying beta-rule and splitting (170), into two cases.
% 27.67/7.25 |-Branch one:
% 27.67/7.25 | (201) ~ (distinct_points(all_1_2_2, all_1_2_2) = all_137_0_27)
% 27.67/7.25 |
% 27.67/7.25 | Using (190) and (201) yields:
% 27.67/7.25 | (202) $false
% 27.67/7.25 |
% 27.67/7.25 |-The branch is then unsatisfiable
% 27.67/7.25 |-Branch two:
% 27.67/7.25 | (190) distinct_points(all_1_2_2, all_1_2_2) = all_137_0_27
% 27.67/7.25 | (204) all_150_3_39 = all_137_0_27
% 27.67/7.25 |
% 27.67/7.25 | Combining equations (204,173) yields a new equation:
% 27.67/7.25 | (205) all_137_0_27 = all_135_0_24
% 27.67/7.25 |
% 27.67/7.25 | Simplifying 205 yields:
% 27.67/7.25 | (206) all_137_0_27 = all_135_0_24
% 27.67/7.25 |
% 27.67/7.25 | From (206) and (190) follows:
% 27.67/7.25 | (131) distinct_points(all_1_2_2, all_1_2_2) = all_135_0_24
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (26) with all_1_2_2, all_1_4_4, all_168_0_40, all_131_2_18 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_168_0_40, apart_point_and_line(all_1_2_2, all_1_4_4) = all_131_2_18, yields:
% 27.67/7.25 | (208) all_168_0_40 = all_131_2_18
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (26) with all_1_2_2, all_1_4_4, all_168_1_41, all_168_0_40 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_168_0_40, apart_point_and_line(all_1_2_2, all_1_4_4) = all_168_1_41, yields:
% 27.67/7.25 | (209) all_168_0_40 = all_168_1_41
% 27.67/7.25 |
% 27.67/7.25 | Using (198) and (106) yields:
% 27.67/7.25 | (210) ~ (all_168_1_41 = 0)
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (16) with all_1_2_2, all_1_2_2, all_168_2_42, all_135_0_24 and discharging atoms distinct_points(all_1_2_2, all_1_2_2) = all_168_2_42, distinct_points(all_1_2_2, all_1_2_2) = all_135_0_24, yields:
% 27.67/7.25 | (211) all_168_2_42 = all_135_0_24
% 27.67/7.25 |
% 27.67/7.25 | Combining equations (208,209) yields a new equation:
% 27.67/7.25 | (212) all_168_1_41 = all_131_2_18
% 27.67/7.25 |
% 27.67/7.25 | Equations (212) can reduce 210 to:
% 27.67/7.25 | (213) ~ (all_131_2_18 = 0)
% 27.67/7.25 |
% 27.67/7.25 | From (212) and (198) follows:
% 27.67/7.25 | (120) apart_point_and_line(all_1_2_2, all_1_4_4) = all_131_2_18
% 27.67/7.25 |
% 27.67/7.25 | From (211) and (199) follows:
% 27.67/7.25 | (131) distinct_points(all_1_2_2, all_1_2_2) = all_135_0_24
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (19) with all_141_1_34, 0, all_1_2_2, all_1_5_5, all_1_3_3 and discharging atoms intersection_point(all_1_3_3, all_1_5_5) = all_141_1_34, apart_point_and_line(all_1_2_2, all_1_3_3) = 0, yields:
% 27.67/7.25 | (216) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_2_2, all_1_5_5) = v1 & convergent_lines(all_1_3_3, all_1_5_5) = v0 & distinct_points(all_1_2_2, all_141_1_34) = v2 & ( ~ (v0 = 0) | v2 = 0))
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (14) with all_112_1_15, all_131_0_16, all_1_5_5, all_1_4_4, all_1_2_2, all_112_0_14 and discharging atoms apart_point_and_line(all_112_0_14, all_1_4_4) = all_131_0_16, apart_point_and_line(all_1_2_2, all_1_5_5) = all_112_1_15, yields:
% 27.67/7.25 | (217) all_131_0_16 = 0 | all_112_1_15 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_112_0_14, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_112_0_14, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (37) with all_1_0_0, all_1_3_3, all_1_4_4, all_112_0_14 and discharging atoms distinct_lines(all_1_4_4, all_1_3_3) = all_1_0_0, yields:
% 27.67/7.25 | (218) all_1_0_0 = 0 | ~ (apart_point_and_line(all_112_0_14, all_1_4_4) = 0) | apart_point_and_line(all_112_0_14, all_1_3_3) = 0
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (19) with all_112_0_14, all_131_1_17, all_112_0_14, all_1_3_3, all_1_5_5 and discharging atoms intersection_point(all_1_5_5, all_1_3_3) = all_112_0_14, apart_point_and_line(all_112_0_14, all_1_5_5) = all_131_1_17, yields:
% 27.67/7.25 | (219) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_112_0_14, all_1_3_3) = v1 & convergent_lines(all_1_5_5, all_1_3_3) = v0 & distinct_points(all_112_0_14, all_112_0_14) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_131_1_17 = 0))))
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (19) with all_1_2_2, all_131_1_17, all_112_0_14, 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_112_0_14, all_1_5_5) = all_131_1_17, yields:
% 27.67/7.25 | (220) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_112_0_14, all_1_4_4) = v1 & convergent_lines(all_1_5_5, all_1_4_4) = v0 & distinct_points(all_112_0_14, all_1_2_2) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_131_1_17 = 0))))
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (2) with all_141_1_34, all_131_1_17, all_112_0_14, all_1_5_5, all_1_3_3 and discharging atoms intersection_point(all_1_3_3, all_1_5_5) = all_141_1_34, apart_point_and_line(all_112_0_14, all_1_5_5) = all_131_1_17, yields:
% 27.67/7.25 | (221) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_112_0_14, all_1_3_3) = v1 & convergent_lines(all_1_3_3, all_1_5_5) = v0 & distinct_points(all_112_0_14, all_141_1_34) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_131_1_17 = 0))))
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (21) with all_131_1_17, all_112_0_14, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_112_0_14, all_1_5_5) = all_131_1_17, convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 27.67/7.25 | (222) ? [v0] : ? [v1] : ? [v2] : (intersection_point(all_1_5_5, all_1_3_3) = v1 & apart_point_and_line(all_112_0_14, all_1_3_3) = v0 & distinct_points(all_112_0_14, v1) = v2 & (v2 = 0 | ( ~ (v0 = 0) & ~ (all_131_1_17 = 0))))
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (21) with all_131_1_17, all_112_0_14, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_112_0_14, all_1_5_5) = all_131_1_17, convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 27.67/7.25 | (223) ? [v0] : ? [v1] : ? [v2] : (intersection_point(all_1_5_5, all_1_4_4) = v1 & apart_point_and_line(all_112_0_14, all_1_4_4) = v0 & distinct_points(all_112_0_14, v1) = v2 & (v2 = 0 | ( ~ (v0 = 0) & ~ (all_131_1_17 = 0))))
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (36) with all_135_1_25, all_112_1_15, all_135_2_26, all_1_5_5, all_112_0_14, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_135_2_26) = all_135_1_25, apart_point_and_line(all_1_2_2, all_1_5_5) = all_112_1_15, distinct_points(all_1_2_2, all_112_0_14) = 0, yields:
% 27.67/7.25 | (224) all_135_1_25 = 0 | all_112_1_15 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_112_0_14, all_135_2_26) = v2 & apart_point_and_line(all_112_0_14, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_135_2_26) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (36) with all_112_1_15, all_135_1_25, all_1_5_5, all_135_2_26, all_112_0_14, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_135_2_26) = all_135_1_25, apart_point_and_line(all_1_2_2, all_1_5_5) = all_112_1_15, distinct_points(all_1_2_2, all_112_0_14) = 0, yields:
% 27.67/7.25 | (225) all_135_1_25 = 0 | all_112_1_15 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_112_0_14, all_135_2_26) = v1 & apart_point_and_line(all_112_0_14, all_1_5_5) = v2 & distinct_lines(all_135_2_26, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (14) with all_135_1_25, all_112_1_15, all_135_2_26, all_1_5_5, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_135_2_26) = all_135_1_25, apart_point_and_line(all_1_2_2, all_1_5_5) = all_112_1_15, yields:
% 27.67/7.25 | (226) all_135_1_25 = 0 | all_112_1_15 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_135_2_26) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_135_2_26) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (14) with all_112_1_15, all_135_1_25, all_1_5_5, all_135_2_26, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_135_2_26) = all_135_1_25, apart_point_and_line(all_1_2_2, all_1_5_5) = all_112_1_15, yields:
% 27.67/7.25 | (227) all_135_1_25 = 0 | all_112_1_15 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_135_2_26) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_135_2_26, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (1) with all_135_1_25, all_112_1_15, all_1_5_5, all_135_2_26, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_135_2_26) = all_135_1_25, apart_point_and_line(all_1_2_2, all_1_5_5) = all_112_1_15, yields:
% 27.67/7.25 | (228) all_135_1_25 = 0 | all_112_1_15 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_135_2_26) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_135_2_26, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (1) with all_112_1_15, all_135_1_25, all_135_2_26, all_1_5_5, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_135_2_26) = all_135_1_25, apart_point_and_line(all_1_2_2, all_1_5_5) = all_112_1_15, yields:
% 27.67/7.25 | (229) all_135_1_25 = 0 | all_112_1_15 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_135_2_26) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_135_2_26) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (14) with all_131_1_17, all_131_2_18, all_1_5_5, all_1_4_4, all_112_0_14, all_1_2_2 and discharging atoms apart_point_and_line(all_112_0_14, all_1_5_5) = all_131_1_17, apart_point_and_line(all_1_2_2, all_1_4_4) = all_131_2_18, yields:
% 27.67/7.25 | (230) all_131_1_17 = 0 | all_131_2_18 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_112_0_14, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_112_0_14) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (36) with all_135_1_25, all_131_2_18, all_135_2_26, all_1_4_4, all_112_0_14, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_135_2_26) = all_135_1_25, apart_point_and_line(all_1_2_2, all_1_4_4) = all_131_2_18, distinct_points(all_1_2_2, all_112_0_14) = 0, yields:
% 27.67/7.25 | (231) all_135_1_25 = 0 | all_131_2_18 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_112_0_14, all_135_2_26) = v2 & apart_point_and_line(all_112_0_14, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_135_2_26) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (14) with all_135_1_25, all_131_2_18, all_135_2_26, all_1_4_4, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_135_2_26) = all_135_1_25, apart_point_and_line(all_1_2_2, all_1_4_4) = all_131_2_18, yields:
% 27.67/7.25 | (232) all_135_1_25 = 0 | all_131_2_18 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_135_2_26) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_135_2_26) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (1) with all_131_2_18, all_135_1_25, all_135_2_26, all_1_4_4, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_135_2_26) = all_135_1_25, apart_point_and_line(all_1_2_2, all_1_4_4) = all_131_2_18, yields:
% 27.67/7.25 | (233) all_135_1_25 = 0 | all_131_2_18 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_135_2_26) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_135_2_26) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (1) with all_135_1_25, all_131_2_18, all_1_4_4, all_135_2_26, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_135_2_26) = all_135_1_25, apart_point_and_line(all_1_2_2, all_1_4_4) = all_131_2_18, yields:
% 27.67/7.25 | (234) all_135_1_25 = 0 | all_131_2_18 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_135_2_26) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_135_2_26, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (34) with all_141_2_35, all_1_5_5, all_1_3_3, all_1_5_5 and discharging atoms convergent_lines(all_1_3_3, all_1_5_5) = all_141_2_35, convergent_lines(all_1_5_5, all_1_3_3) = 0, ~ (convergent_lines(all_1_5_5, all_1_5_5) = 0), yields:
% 27.67/7.25 | (235) all_141_2_35 = 0
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (3) with all_1_5_5, all_1_3_3, all_112_0_14, all_1_2_2 and discharging atoms distinct_lines(all_1_3_3, all_1_5_5) = 0, distinct_points(all_1_2_2, all_112_0_14) = 0, yields:
% 27.67/7.25 | (236) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_112_0_14, all_1_3_3) = v2 & apart_point_and_line(all_112_0_14, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v0 & apart_point_and_line(all_1_2_2, all_1_5_5) = v1 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0))
% 27.67/7.25 |
% 27.67/7.25 | Instantiating formula (36) with all_112_1_15, all_112_1_15, all_1_5_5, all_1_5_5, all_141_1_34, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_112_1_15, yields:
% 27.67/7.25 | (237) all_112_1_15 = 0 | ~ (distinct_points(all_1_2_2, all_141_1_34) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_141_1_34, all_1_5_5) = v2 & apart_point_and_line(all_141_1_34, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.25 |
% 27.67/7.26 | Instantiating formula (36) with all_112_1_15, all_135_1_25, all_1_5_5, all_135_2_26, all_141_1_34, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_135_2_26) = all_135_1_25, apart_point_and_line(all_1_2_2, all_1_5_5) = all_112_1_15, yields:
% 27.67/7.26 | (238) all_135_1_25 = 0 | all_112_1_15 = 0 | ~ (distinct_points(all_1_2_2, all_141_1_34) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_141_1_34, all_135_2_26) = v1 & apart_point_and_line(all_141_1_34, all_1_5_5) = v2 & distinct_lines(all_135_2_26, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.26 |
% 27.67/7.26 | Instantiating formula (36) with all_112_1_15, all_131_2_18, all_1_5_5, all_1_4_4, all_141_1_34, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_131_2_18, apart_point_and_line(all_1_2_2, all_1_5_5) = all_112_1_15, yields:
% 27.67/7.26 | (239) all_131_2_18 = 0 | all_112_1_15 = 0 | ~ (distinct_points(all_1_2_2, all_141_1_34) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_141_1_34, all_1_4_4) = v1 & apart_point_and_line(all_141_1_34, all_1_5_5) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.26 |
% 27.67/7.26 | Instantiating formula (36) with all_135_1_25, all_112_1_15, all_135_2_26, all_1_5_5, all_141_1_34, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_135_2_26) = all_135_1_25, apart_point_and_line(all_1_2_2, all_1_5_5) = all_112_1_15, yields:
% 27.67/7.26 | (240) all_135_1_25 = 0 | all_112_1_15 = 0 | ~ (distinct_points(all_1_2_2, all_141_1_34) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_141_1_34, all_135_2_26) = v2 & apart_point_and_line(all_141_1_34, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_135_2_26) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.26 |
% 27.67/7.26 | Instantiating formula (36) with all_135_1_25, all_135_1_25, all_135_2_26, all_135_2_26, all_141_1_34, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_135_2_26) = all_135_1_25, yields:
% 27.67/7.26 | (241) all_135_1_25 = 0 | ~ (distinct_points(all_1_2_2, all_141_1_34) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_141_1_34, all_135_2_26) = v2 & apart_point_and_line(all_141_1_34, all_135_2_26) = v1 & distinct_lines(all_135_2_26, all_135_2_26) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.26 |
% 27.67/7.26 | Instantiating formula (36) with all_135_1_25, all_131_2_18, all_135_2_26, all_1_4_4, all_141_1_34, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_135_2_26) = all_135_1_25, apart_point_and_line(all_1_2_2, all_1_4_4) = all_131_2_18, yields:
% 27.67/7.26 | (242) all_135_1_25 = 0 | all_131_2_18 = 0 | ~ (distinct_points(all_1_2_2, all_141_1_34) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_141_1_34, all_135_2_26) = v2 & apart_point_and_line(all_141_1_34, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_135_2_26) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.26 |
% 27.67/7.26 | Instantiating formula (36) with all_131_2_18, all_131_2_18, all_1_4_4, all_1_4_4, all_141_1_34, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_131_2_18, yields:
% 27.67/7.26 | (243) all_131_2_18 = 0 | ~ (distinct_points(all_1_2_2, all_141_1_34) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_141_1_34, all_1_4_4) = v2 & apart_point_and_line(all_141_1_34, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_1_4_4) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.26 |
% 27.67/7.26 | Instantiating formula (31) with all_135_0_24, all_1_2_2, all_141_1_34, all_1_2_2 and discharging atoms distinct_points(all_1_2_2, all_1_2_2) = all_135_0_24, yields:
% 27.67/7.26 | (244) all_135_0_24 = 0 | ~ (distinct_points(all_1_2_2, all_141_1_34) = 0) | distinct_points(all_141_1_34, all_1_2_2) = 0
% 27.67/7.26 |
% 27.67/7.26 | Instantiating formula (32) with all_135_0_24, all_1_2_2, all_141_1_34, all_1_2_2 and discharging atoms distinct_points(all_1_2_2, all_1_2_2) = all_135_0_24, yields:
% 27.67/7.26 | (245) ~ (distinct_points(all_1_2_2, all_141_1_34) = 0) | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_2_2, all_141_1_34) = v0 & apart_point_and_line(all_1_2_2, v0) = v1 & distinct_points(all_1_2_2, all_141_1_34) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_135_0_24 = 0)))
% 27.67/7.26 |
% 27.67/7.26 | Instantiating (236) with all_204_0_55, all_204_1_56, all_204_2_57, all_204_3_58 yields:
% 27.67/7.26 | (246) apart_point_and_line(all_112_0_14, all_1_3_3) = all_204_1_56 & apart_point_and_line(all_112_0_14, all_1_5_5) = all_204_0_55 & apart_point_and_line(all_1_2_2, all_1_3_3) = all_204_3_58 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_204_2_57 & (all_204_0_55 = 0 | all_204_1_56 = 0 | all_204_2_57 = 0 | all_204_3_58 = 0)
% 27.67/7.26 |
% 27.67/7.26 | Applying alpha-rule on (246) yields:
% 27.67/7.26 | (247) apart_point_and_line(all_1_2_2, all_1_5_5) = all_204_2_57
% 27.67/7.26 | (248) all_204_0_55 = 0 | all_204_1_56 = 0 | all_204_2_57 = 0 | all_204_3_58 = 0
% 27.67/7.26 | (249) apart_point_and_line(all_112_0_14, all_1_3_3) = all_204_1_56
% 27.67/7.26 | (250) apart_point_and_line(all_112_0_14, all_1_5_5) = all_204_0_55
% 27.67/7.26 | (251) apart_point_and_line(all_1_2_2, all_1_3_3) = all_204_3_58
% 27.67/7.26 |
% 27.67/7.26 | Instantiating (223) with all_206_0_59, all_206_1_60, all_206_2_61 yields:
% 27.67/7.26 | (252) intersection_point(all_1_5_5, all_1_4_4) = all_206_1_60 & apart_point_and_line(all_112_0_14, all_1_4_4) = all_206_2_61 & distinct_points(all_112_0_14, all_206_1_60) = all_206_0_59 & (all_206_0_59 = 0 | ( ~ (all_206_2_61 = 0) & ~ (all_131_1_17 = 0)))
% 27.67/7.26 |
% 27.67/7.26 | Applying alpha-rule on (252) yields:
% 27.67/7.26 | (253) intersection_point(all_1_5_5, all_1_4_4) = all_206_1_60
% 27.67/7.26 | (254) apart_point_and_line(all_112_0_14, all_1_4_4) = all_206_2_61
% 27.67/7.26 | (255) distinct_points(all_112_0_14, all_206_1_60) = all_206_0_59
% 27.67/7.26 | (256) all_206_0_59 = 0 | ( ~ (all_206_2_61 = 0) & ~ (all_131_1_17 = 0))
% 27.67/7.26 |
% 27.67/7.26 | Instantiating (222) with all_208_0_62, all_208_1_63, all_208_2_64 yields:
% 27.67/7.26 | (257) intersection_point(all_1_5_5, all_1_3_3) = all_208_1_63 & apart_point_and_line(all_112_0_14, all_1_3_3) = all_208_2_64 & distinct_points(all_112_0_14, all_208_1_63) = all_208_0_62 & (all_208_0_62 = 0 | ( ~ (all_208_2_64 = 0) & ~ (all_131_1_17 = 0)))
% 27.67/7.26 |
% 27.67/7.26 | Applying alpha-rule on (257) yields:
% 27.67/7.26 | (258) intersection_point(all_1_5_5, all_1_3_3) = all_208_1_63
% 27.67/7.26 | (259) apart_point_and_line(all_112_0_14, all_1_3_3) = all_208_2_64
% 27.67/7.26 | (260) distinct_points(all_112_0_14, all_208_1_63) = all_208_0_62
% 27.67/7.26 | (261) all_208_0_62 = 0 | ( ~ (all_208_2_64 = 0) & ~ (all_131_1_17 = 0))
% 27.67/7.26 |
% 27.67/7.26 | Instantiating (219) with all_210_0_65, all_210_1_66, all_210_2_67 yields:
% 27.67/7.26 | (262) apart_point_and_line(all_112_0_14, all_1_3_3) = all_210_1_66 & convergent_lines(all_1_5_5, all_1_3_3) = all_210_2_67 & distinct_points(all_112_0_14, all_112_0_14) = all_210_0_65 & ( ~ (all_210_2_67 = 0) | all_210_0_65 = 0 | ( ~ (all_210_1_66 = 0) & ~ (all_131_1_17 = 0)))
% 27.67/7.26 |
% 27.67/7.26 | Applying alpha-rule on (262) yields:
% 27.67/7.26 | (263) apart_point_and_line(all_112_0_14, all_1_3_3) = all_210_1_66
% 27.67/7.26 | (264) convergent_lines(all_1_5_5, all_1_3_3) = all_210_2_67
% 27.67/7.26 | (265) distinct_points(all_112_0_14, all_112_0_14) = all_210_0_65
% 27.67/7.26 | (266) ~ (all_210_2_67 = 0) | all_210_0_65 = 0 | ( ~ (all_210_1_66 = 0) & ~ (all_131_1_17 = 0))
% 27.67/7.26 |
% 27.67/7.26 | Instantiating (221) with all_214_0_71, all_214_1_72, all_214_2_73 yields:
% 27.67/7.26 | (267) apart_point_and_line(all_112_0_14, all_1_3_3) = all_214_1_72 & convergent_lines(all_1_3_3, all_1_5_5) = all_214_2_73 & distinct_points(all_112_0_14, all_141_1_34) = all_214_0_71 & ( ~ (all_214_2_73 = 0) | all_214_0_71 = 0 | ( ~ (all_214_1_72 = 0) & ~ (all_131_1_17 = 0)))
% 27.67/7.26 |
% 27.67/7.26 | Applying alpha-rule on (267) yields:
% 27.67/7.26 | (268) apart_point_and_line(all_112_0_14, all_1_3_3) = all_214_1_72
% 27.67/7.26 | (269) convergent_lines(all_1_3_3, all_1_5_5) = all_214_2_73
% 27.67/7.26 | (270) distinct_points(all_112_0_14, all_141_1_34) = all_214_0_71
% 27.67/7.26 | (271) ~ (all_214_2_73 = 0) | all_214_0_71 = 0 | ( ~ (all_214_1_72 = 0) & ~ (all_131_1_17 = 0))
% 27.67/7.26 |
% 27.67/7.26 | Instantiating (220) with all_216_0_74, all_216_1_75, all_216_2_76 yields:
% 27.67/7.26 | (272) apart_point_and_line(all_112_0_14, all_1_4_4) = all_216_1_75 & convergent_lines(all_1_5_5, all_1_4_4) = all_216_2_76 & distinct_points(all_112_0_14, all_1_2_2) = all_216_0_74 & ( ~ (all_216_2_76 = 0) | all_216_0_74 = 0 | ( ~ (all_216_1_75 = 0) & ~ (all_131_1_17 = 0)))
% 27.67/7.26 |
% 27.67/7.26 | Applying alpha-rule on (272) yields:
% 27.67/7.26 | (273) apart_point_and_line(all_112_0_14, all_1_4_4) = all_216_1_75
% 27.67/7.26 | (274) convergent_lines(all_1_5_5, all_1_4_4) = all_216_2_76
% 27.67/7.26 | (275) distinct_points(all_112_0_14, all_1_2_2) = all_216_0_74
% 27.67/7.26 | (276) ~ (all_216_2_76 = 0) | all_216_0_74 = 0 | ( ~ (all_216_1_75 = 0) & ~ (all_131_1_17 = 0))
% 27.67/7.26 |
% 27.67/7.26 | Instantiating (216) with all_222_0_83, all_222_1_84, all_222_2_85 yields:
% 27.67/7.26 | (277) apart_point_and_line(all_1_2_2, all_1_5_5) = all_222_1_84 & convergent_lines(all_1_3_3, all_1_5_5) = all_222_2_85 & distinct_points(all_1_2_2, all_141_1_34) = all_222_0_83 & ( ~ (all_222_2_85 = 0) | all_222_0_83 = 0)
% 27.67/7.26 |
% 27.67/7.26 | Applying alpha-rule on (277) yields:
% 27.67/7.26 | (278) apart_point_and_line(all_1_2_2, all_1_5_5) = all_222_1_84
% 27.67/7.26 | (279) convergent_lines(all_1_3_3, all_1_5_5) = all_222_2_85
% 27.67/7.26 | (280) distinct_points(all_1_2_2, all_141_1_34) = all_222_0_83
% 27.67/7.26 | (281) ~ (all_222_2_85 = 0) | all_222_0_83 = 0
% 27.67/7.26 |
% 27.67/7.26 +-Applying beta-rule and splitting (147), into two cases.
% 27.67/7.26 |-Branch one:
% 27.67/7.26 | (282) ~ (all_141_2_35 = 0)
% 27.67/7.26 |
% 27.67/7.26 | Equations (235) can reduce 282 to:
% 27.67/7.26 | (79) $false
% 27.67/7.26 |
% 27.67/7.26 |-The branch is then unsatisfiable
% 27.67/7.26 |-Branch two:
% 27.67/7.26 | (235) all_141_2_35 = 0
% 27.67/7.26 | (285) all_141_0_33 = 0
% 27.67/7.26 |
% 27.67/7.26 | From (285) and (146) follows:
% 27.67/7.26 | (286) distinct_points(all_1_2_2, all_141_1_34) = 0
% 27.67/7.26 |
% 27.67/7.26 +-Applying beta-rule and splitting (234), into two cases.
% 27.67/7.26 |-Branch one:
% 27.67/7.26 | (287) all_135_1_25 = 0
% 27.67/7.26 |
% 27.67/7.26 | Equations (287) can reduce 191 to:
% 27.67/7.26 | (79) $false
% 27.67/7.26 |
% 27.67/7.26 |-The branch is then unsatisfiable
% 27.67/7.26 |-Branch two:
% 27.67/7.26 | (191) ~ (all_135_1_25 = 0)
% 27.67/7.26 | (290) all_131_2_18 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_135_2_26) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_135_2_26, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.26 |
% 27.67/7.26 +-Applying beta-rule and splitting (224), into two cases.
% 27.67/7.26 |-Branch one:
% 27.67/7.26 | (287) all_135_1_25 = 0
% 27.67/7.26 |
% 27.67/7.26 | Equations (287) can reduce 191 to:
% 27.67/7.26 | (79) $false
% 27.67/7.26 |
% 27.67/7.26 |-The branch is then unsatisfiable
% 27.67/7.26 |-Branch two:
% 27.67/7.26 | (191) ~ (all_135_1_25 = 0)
% 27.67/7.26 | (294) all_112_1_15 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_112_0_14, all_135_2_26) = v2 & apart_point_and_line(all_112_0_14, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_135_2_26) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.26 |
% 27.67/7.26 +-Applying beta-rule and splitting (244), into two cases.
% 27.67/7.26 |-Branch one:
% 27.67/7.26 | (295) ~ (distinct_points(all_1_2_2, all_141_1_34) = 0)
% 27.67/7.26 |
% 27.67/7.26 | Using (286) and (295) yields:
% 27.67/7.26 | (202) $false
% 27.67/7.26 |
% 27.67/7.26 |-The branch is then unsatisfiable
% 27.67/7.26 |-Branch two:
% 27.67/7.26 | (286) distinct_points(all_1_2_2, all_141_1_34) = 0
% 27.67/7.26 | (298) all_135_0_24 = 0 | distinct_points(all_141_1_34, all_1_2_2) = 0
% 27.67/7.26 |
% 27.67/7.26 +-Applying beta-rule and splitting (245), into two cases.
% 27.67/7.26 |-Branch one:
% 27.67/7.26 | (295) ~ (distinct_points(all_1_2_2, all_141_1_34) = 0)
% 27.67/7.26 |
% 27.67/7.26 | Using (286) and (295) yields:
% 27.67/7.26 | (202) $false
% 27.67/7.26 |
% 27.67/7.26 |-The branch is then unsatisfiable
% 27.67/7.26 |-Branch two:
% 27.67/7.26 | (286) distinct_points(all_1_2_2, all_141_1_34) = 0
% 27.67/7.26 | (302) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_2_2, all_141_1_34) = v0 & apart_point_and_line(all_1_2_2, v0) = v1 & distinct_points(all_1_2_2, all_141_1_34) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_135_0_24 = 0)))
% 27.67/7.26 |
% 27.67/7.26 +-Applying beta-rule and splitting (225), into two cases.
% 27.67/7.26 |-Branch one:
% 27.67/7.26 | (287) all_135_1_25 = 0
% 27.67/7.26 |
% 27.67/7.26 | Equations (287) can reduce 191 to:
% 27.67/7.26 | (79) $false
% 27.67/7.26 |
% 27.67/7.26 |-The branch is then unsatisfiable
% 27.67/7.26 |-Branch two:
% 27.67/7.26 | (191) ~ (all_135_1_25 = 0)
% 27.67/7.26 | (306) all_112_1_15 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_112_0_14, all_135_2_26) = v1 & apart_point_and_line(all_112_0_14, all_1_5_5) = v2 & distinct_lines(all_135_2_26, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.26 |
% 27.67/7.26 +-Applying beta-rule and splitting (226), into two cases.
% 27.67/7.26 |-Branch one:
% 27.67/7.26 | (287) all_135_1_25 = 0
% 27.67/7.26 |
% 27.67/7.26 | Equations (287) can reduce 191 to:
% 27.67/7.26 | (79) $false
% 27.67/7.26 |
% 27.67/7.26 |-The branch is then unsatisfiable
% 27.67/7.26 |-Branch two:
% 27.67/7.26 | (191) ~ (all_135_1_25 = 0)
% 27.67/7.26 | (310) all_112_1_15 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_135_2_26) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_135_2_26) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.26 |
% 27.67/7.26 +-Applying beta-rule and splitting (290), into two cases.
% 27.67/7.26 |-Branch one:
% 27.67/7.26 | (311) all_131_2_18 = 0
% 27.67/7.26 |
% 27.67/7.26 | Equations (311) can reduce 213 to:
% 27.67/7.26 | (79) $false
% 27.67/7.26 |
% 27.67/7.26 |-The branch is then unsatisfiable
% 27.67/7.26 |-Branch two:
% 27.67/7.26 | (213) ~ (all_131_2_18 = 0)
% 27.67/7.26 | (314) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_135_2_26) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_135_2_26, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.26 |
% 27.67/7.26 | Instantiating (314) with all_269_0_95, all_269_1_96, all_269_2_97, all_269_3_98 yields:
% 27.67/7.26 | (315) apart_point_and_line(all_1_2_2, all_135_2_26) = all_269_1_96 & apart_point_and_line(all_1_2_2, all_1_4_4) = all_269_0_95 & distinct_lines(all_135_2_26, all_1_4_4) = all_269_2_97 & distinct_points(all_1_2_2, all_1_2_2) = all_269_3_98 & ( ~ (all_269_2_97 = 0) | ~ (all_269_3_98 = 0) | all_269_0_95 = 0 | all_269_1_96 = 0)
% 27.67/7.27 |
% 27.67/7.27 | Applying alpha-rule on (315) yields:
% 27.67/7.27 | (316) apart_point_and_line(all_1_2_2, all_1_4_4) = all_269_0_95
% 27.67/7.27 | (317) distinct_points(all_1_2_2, all_1_2_2) = all_269_3_98
% 27.67/7.27 | (318) distinct_lines(all_135_2_26, all_1_4_4) = all_269_2_97
% 27.67/7.27 | (319) ~ (all_269_2_97 = 0) | ~ (all_269_3_98 = 0) | all_269_0_95 = 0 | all_269_1_96 = 0
% 27.67/7.27 | (320) apart_point_and_line(all_1_2_2, all_135_2_26) = all_269_1_96
% 27.67/7.27 |
% 27.67/7.27 +-Applying beta-rule and splitting (237), into two cases.
% 27.67/7.27 |-Branch one:
% 27.67/7.27 | (295) ~ (distinct_points(all_1_2_2, all_141_1_34) = 0)
% 27.67/7.27 |
% 27.67/7.27 | Using (286) and (295) yields:
% 27.67/7.27 | (202) $false
% 27.67/7.27 |
% 27.67/7.27 |-The branch is then unsatisfiable
% 27.67/7.27 |-Branch two:
% 27.67/7.27 | (286) distinct_points(all_1_2_2, all_141_1_34) = 0
% 27.67/7.27 | (324) all_112_1_15 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_141_1_34, all_1_5_5) = v2 & apart_point_and_line(all_141_1_34, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.27 |
% 27.67/7.27 +-Applying beta-rule and splitting (241), into two cases.
% 27.67/7.27 |-Branch one:
% 27.67/7.27 | (295) ~ (distinct_points(all_1_2_2, all_141_1_34) = 0)
% 27.67/7.27 |
% 27.67/7.27 | Using (286) and (295) yields:
% 27.67/7.27 | (202) $false
% 27.67/7.27 |
% 27.67/7.27 |-The branch is then unsatisfiable
% 27.67/7.27 |-Branch two:
% 27.67/7.27 | (286) distinct_points(all_1_2_2, all_141_1_34) = 0
% 27.67/7.27 | (328) all_135_1_25 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_141_1_34, all_135_2_26) = v2 & apart_point_and_line(all_141_1_34, all_135_2_26) = v1 & distinct_lines(all_135_2_26, all_135_2_26) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.27 |
% 27.67/7.27 +-Applying beta-rule and splitting (238), into two cases.
% 27.67/7.27 |-Branch one:
% 27.67/7.27 | (295) ~ (distinct_points(all_1_2_2, all_141_1_34) = 0)
% 27.67/7.27 |
% 27.67/7.27 | Using (286) and (295) yields:
% 27.67/7.27 | (202) $false
% 27.67/7.27 |
% 27.67/7.27 |-The branch is then unsatisfiable
% 27.67/7.27 |-Branch two:
% 27.67/7.27 | (286) distinct_points(all_1_2_2, all_141_1_34) = 0
% 27.67/7.27 | (332) all_135_1_25 = 0 | all_112_1_15 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_141_1_34, all_135_2_26) = v1 & apart_point_and_line(all_141_1_34, all_1_5_5) = v2 & distinct_lines(all_135_2_26, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.27 |
% 27.67/7.27 +-Applying beta-rule and splitting (242), into two cases.
% 27.67/7.27 |-Branch one:
% 27.67/7.27 | (295) ~ (distinct_points(all_1_2_2, all_141_1_34) = 0)
% 27.67/7.27 |
% 27.67/7.27 | Using (286) and (295) yields:
% 27.67/7.27 | (202) $false
% 27.67/7.27 |
% 27.67/7.27 |-The branch is then unsatisfiable
% 27.67/7.27 |-Branch two:
% 27.67/7.27 | (286) distinct_points(all_1_2_2, all_141_1_34) = 0
% 27.67/7.27 | (336) all_135_1_25 = 0 | all_131_2_18 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_141_1_34, all_135_2_26) = v2 & apart_point_and_line(all_141_1_34, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_135_2_26) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.27 |
% 27.67/7.27 +-Applying beta-rule and splitting (239), into two cases.
% 27.67/7.27 |-Branch one:
% 27.67/7.27 | (295) ~ (distinct_points(all_1_2_2, all_141_1_34) = 0)
% 27.67/7.27 |
% 27.67/7.27 | Using (286) and (295) yields:
% 27.67/7.27 | (202) $false
% 27.67/7.27 |
% 27.67/7.27 |-The branch is then unsatisfiable
% 27.67/7.27 |-Branch two:
% 27.67/7.27 | (286) distinct_points(all_1_2_2, all_141_1_34) = 0
% 27.67/7.27 | (340) all_131_2_18 = 0 | all_112_1_15 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_141_1_34, all_1_4_4) = v1 & apart_point_and_line(all_141_1_34, all_1_5_5) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.27 |
% 27.67/7.27 +-Applying beta-rule and splitting (240), into two cases.
% 27.67/7.27 |-Branch one:
% 27.67/7.27 | (295) ~ (distinct_points(all_1_2_2, all_141_1_34) = 0)
% 27.67/7.27 |
% 27.67/7.27 | Using (286) and (295) yields:
% 27.67/7.27 | (202) $false
% 27.67/7.27 |
% 27.67/7.27 |-The branch is then unsatisfiable
% 27.67/7.27 |-Branch two:
% 27.67/7.27 | (286) distinct_points(all_1_2_2, all_141_1_34) = 0
% 27.67/7.27 | (344) all_135_1_25 = 0 | all_112_1_15 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_141_1_34, all_135_2_26) = v2 & apart_point_and_line(all_141_1_34, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_135_2_26) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.27 |
% 27.67/7.27 +-Applying beta-rule and splitting (227), into two cases.
% 27.67/7.27 |-Branch one:
% 27.67/7.27 | (287) all_135_1_25 = 0
% 27.67/7.27 |
% 27.67/7.27 | Equations (287) can reduce 191 to:
% 27.67/7.27 | (79) $false
% 27.67/7.27 |
% 27.67/7.27 |-The branch is then unsatisfiable
% 27.67/7.27 |-Branch two:
% 27.67/7.27 | (191) ~ (all_135_1_25 = 0)
% 27.67/7.27 | (348) all_112_1_15 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_135_2_26) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_135_2_26, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.27 |
% 27.67/7.27 +-Applying beta-rule and splitting (228), into two cases.
% 27.67/7.27 |-Branch one:
% 27.67/7.27 | (287) all_135_1_25 = 0
% 27.67/7.27 |
% 27.67/7.27 | Equations (287) can reduce 191 to:
% 27.67/7.27 | (79) $false
% 27.67/7.27 |
% 27.67/7.27 |-The branch is then unsatisfiable
% 27.67/7.27 |-Branch two:
% 27.67/7.27 | (191) ~ (all_135_1_25 = 0)
% 27.67/7.27 | (352) all_112_1_15 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_135_2_26) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_135_2_26, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.27 |
% 27.67/7.27 +-Applying beta-rule and splitting (229), into two cases.
% 27.67/7.27 |-Branch one:
% 27.67/7.27 | (287) all_135_1_25 = 0
% 27.67/7.27 |
% 27.67/7.27 | Equations (287) can reduce 191 to:
% 27.67/7.27 | (79) $false
% 27.67/7.27 |
% 27.67/7.27 |-The branch is then unsatisfiable
% 27.67/7.27 |-Branch two:
% 27.67/7.27 | (191) ~ (all_135_1_25 = 0)
% 27.67/7.27 | (356) all_112_1_15 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_135_2_26) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_135_2_26) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.27 |
% 27.67/7.27 +-Applying beta-rule and splitting (294), into two cases.
% 27.67/7.27 |-Branch one:
% 27.67/7.27 | (148) all_112_1_15 = 0
% 27.67/7.27 |
% 27.67/7.27 | Equations (148) can reduce 104 to:
% 27.67/7.27 | (79) $false
% 27.67/7.27 |
% 27.67/7.27 |-The branch is then unsatisfiable
% 27.67/7.27 |-Branch two:
% 27.67/7.27 | (104) ~ (all_112_1_15 = 0)
% 27.67/7.27 | (360) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_112_0_14, all_135_2_26) = v2 & apart_point_and_line(all_112_0_14, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_135_2_26) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.27 |
% 27.67/7.27 +-Applying beta-rule and splitting (306), into two cases.
% 27.67/7.27 |-Branch one:
% 27.67/7.27 | (148) all_112_1_15 = 0
% 27.67/7.27 |
% 27.67/7.27 | Equations (148) can reduce 104 to:
% 27.67/7.27 | (79) $false
% 27.67/7.27 |
% 27.67/7.27 |-The branch is then unsatisfiable
% 27.67/7.27 |-Branch two:
% 27.67/7.27 | (104) ~ (all_112_1_15 = 0)
% 27.67/7.27 | (364) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_112_0_14, all_135_2_26) = v1 & apart_point_and_line(all_112_0_14, all_1_5_5) = v2 & distinct_lines(all_135_2_26, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.27 |
% 27.67/7.27 +-Applying beta-rule and splitting (324), into two cases.
% 27.67/7.27 |-Branch one:
% 27.67/7.27 | (148) all_112_1_15 = 0
% 27.67/7.27 |
% 27.67/7.27 | Equations (148) can reduce 104 to:
% 27.67/7.27 | (79) $false
% 27.67/7.27 |
% 27.67/7.27 |-The branch is then unsatisfiable
% 27.67/7.27 |-Branch two:
% 27.67/7.27 | (104) ~ (all_112_1_15 = 0)
% 27.67/7.27 | (368) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_141_1_34, all_1_5_5) = v2 & apart_point_and_line(all_141_1_34, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.27 |
% 27.67/7.27 +-Applying beta-rule and splitting (328), into two cases.
% 27.67/7.27 |-Branch one:
% 27.67/7.27 | (287) all_135_1_25 = 0
% 27.67/7.27 |
% 27.67/7.27 | Equations (287) can reduce 191 to:
% 27.67/7.27 | (79) $false
% 27.67/7.27 |
% 27.67/7.27 |-The branch is then unsatisfiable
% 27.67/7.27 |-Branch two:
% 27.67/7.27 | (191) ~ (all_135_1_25 = 0)
% 27.67/7.27 | (372) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_141_1_34, all_135_2_26) = v2 & apart_point_and_line(all_141_1_34, all_135_2_26) = v1 & distinct_lines(all_135_2_26, all_135_2_26) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.27 |
% 27.67/7.27 +-Applying beta-rule and splitting (332), into two cases.
% 27.67/7.27 |-Branch one:
% 27.67/7.27 | (287) all_135_1_25 = 0
% 27.67/7.27 |
% 27.67/7.27 | Equations (287) can reduce 191 to:
% 27.67/7.27 | (79) $false
% 27.67/7.27 |
% 27.67/7.27 |-The branch is then unsatisfiable
% 27.67/7.27 |-Branch two:
% 27.67/7.27 | (191) ~ (all_135_1_25 = 0)
% 27.67/7.27 | (376) all_112_1_15 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_141_1_34, all_135_2_26) = v1 & apart_point_and_line(all_141_1_34, all_1_5_5) = v2 & distinct_lines(all_135_2_26, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.27 |
% 27.67/7.27 +-Applying beta-rule and splitting (344), into two cases.
% 27.67/7.27 |-Branch one:
% 27.67/7.27 | (287) all_135_1_25 = 0
% 27.67/7.27 |
% 27.67/7.27 | Equations (287) can reduce 191 to:
% 27.67/7.27 | (79) $false
% 27.67/7.27 |
% 27.67/7.27 |-The branch is then unsatisfiable
% 27.67/7.27 |-Branch two:
% 27.67/7.27 | (191) ~ (all_135_1_25 = 0)
% 27.67/7.27 | (380) all_112_1_15 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_141_1_34, all_135_2_26) = v2 & apart_point_and_line(all_141_1_34, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_135_2_26) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.27 |
% 27.67/7.27 +-Applying beta-rule and splitting (352), into two cases.
% 27.67/7.27 |-Branch one:
% 27.67/7.27 | (148) all_112_1_15 = 0
% 27.67/7.27 |
% 27.67/7.27 | Equations (148) can reduce 104 to:
% 27.67/7.27 | (79) $false
% 27.67/7.27 |
% 27.67/7.27 |-The branch is then unsatisfiable
% 27.67/7.27 |-Branch two:
% 27.67/7.27 | (104) ~ (all_112_1_15 = 0)
% 27.67/7.27 | (384) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_135_2_26) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_135_2_26, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.27 |
% 27.67/7.27 | Instantiating (384) with all_344_0_114, all_344_1_115, all_344_2_116, all_344_3_117 yields:
% 27.67/7.27 | (385) apart_point_and_line(all_1_2_2, all_135_2_26) = all_344_1_115 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_344_0_114 & distinct_lines(all_135_2_26, all_1_5_5) = all_344_2_116 & distinct_points(all_1_2_2, all_1_2_2) = all_344_3_117 & ( ~ (all_344_2_116 = 0) | ~ (all_344_3_117 = 0) | all_344_0_114 = 0 | all_344_1_115 = 0)
% 27.67/7.27 |
% 27.67/7.27 | Applying alpha-rule on (385) yields:
% 27.67/7.27 | (386) distinct_points(all_1_2_2, all_1_2_2) = all_344_3_117
% 27.67/7.27 | (387) distinct_lines(all_135_2_26, all_1_5_5) = all_344_2_116
% 27.67/7.27 | (388) ~ (all_344_2_116 = 0) | ~ (all_344_3_117 = 0) | all_344_0_114 = 0 | all_344_1_115 = 0
% 27.67/7.27 | (389) apart_point_and_line(all_1_2_2, all_1_5_5) = all_344_0_114
% 27.67/7.27 | (390) apart_point_and_line(all_1_2_2, all_135_2_26) = all_344_1_115
% 27.67/7.27 |
% 27.67/7.27 +-Applying beta-rule and splitting (356), into two cases.
% 27.67/7.27 |-Branch one:
% 27.67/7.27 | (148) all_112_1_15 = 0
% 27.67/7.27 |
% 27.67/7.27 | Equations (148) can reduce 104 to:
% 27.67/7.27 | (79) $false
% 27.67/7.27 |
% 27.67/7.27 |-The branch is then unsatisfiable
% 27.67/7.27 |-Branch two:
% 27.67/7.27 | (104) ~ (all_112_1_15 = 0)
% 27.67/7.27 | (394) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_135_2_26) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_135_2_26) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.27 |
% 27.67/7.27 | Instantiating (394) with all_349_0_118, all_349_1_119, all_349_2_120, all_349_3_121 yields:
% 27.67/7.27 | (395) apart_point_and_line(all_1_2_2, all_135_2_26) = all_349_0_118 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_349_1_119 & distinct_lines(all_1_5_5, all_135_2_26) = all_349_2_120 & distinct_points(all_1_2_2, all_1_2_2) = all_349_3_121 & ( ~ (all_349_2_120 = 0) | ~ (all_349_3_121 = 0) | all_349_0_118 = 0 | all_349_1_119 = 0)
% 27.67/7.27 |
% 27.67/7.27 | Applying alpha-rule on (395) yields:
% 27.67/7.27 | (396) apart_point_and_line(all_1_2_2, all_1_5_5) = all_349_1_119
% 27.67/7.27 | (397) distinct_lines(all_1_5_5, all_135_2_26) = all_349_2_120
% 27.67/7.27 | (398) distinct_points(all_1_2_2, all_1_2_2) = all_349_3_121
% 27.67/7.27 | (399) apart_point_and_line(all_1_2_2, all_135_2_26) = all_349_0_118
% 27.67/7.27 | (400) ~ (all_349_2_120 = 0) | ~ (all_349_3_121 = 0) | all_349_0_118 = 0 | all_349_1_119 = 0
% 27.67/7.27 |
% 27.67/7.27 +-Applying beta-rule and splitting (243), into two cases.
% 27.67/7.27 |-Branch one:
% 27.67/7.27 | (295) ~ (distinct_points(all_1_2_2, all_141_1_34) = 0)
% 27.67/7.27 |
% 27.67/7.27 | Using (286) and (295) yields:
% 27.67/7.27 | (202) $false
% 27.67/7.27 |
% 27.67/7.27 |-The branch is then unsatisfiable
% 27.67/7.27 |-Branch two:
% 27.67/7.27 | (286) distinct_points(all_1_2_2, all_141_1_34) = 0
% 27.67/7.27 | (404) all_131_2_18 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_141_1_34, all_1_4_4) = v2 & apart_point_and_line(all_141_1_34, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_1_4_4) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.27 |
% 27.67/7.27 +-Applying beta-rule and splitting (232), into two cases.
% 27.67/7.27 |-Branch one:
% 27.67/7.27 | (287) all_135_1_25 = 0
% 27.67/7.27 |
% 27.67/7.27 | Equations (287) can reduce 191 to:
% 27.67/7.27 | (79) $false
% 27.67/7.27 |
% 27.67/7.27 |-The branch is then unsatisfiable
% 27.67/7.27 |-Branch two:
% 27.67/7.27 | (191) ~ (all_135_1_25 = 0)
% 27.67/7.27 | (408) all_131_2_18 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_135_2_26) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_135_2_26) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.28 |
% 27.67/7.28 +-Applying beta-rule and splitting (231), into two cases.
% 27.67/7.28 |-Branch one:
% 27.67/7.28 | (287) all_135_1_25 = 0
% 27.67/7.28 |
% 27.67/7.28 | Equations (287) can reduce 191 to:
% 27.67/7.28 | (79) $false
% 27.67/7.28 |
% 27.67/7.28 |-The branch is then unsatisfiable
% 27.67/7.28 |-Branch two:
% 27.67/7.28 | (191) ~ (all_135_1_25 = 0)
% 27.67/7.28 | (412) all_131_2_18 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_112_0_14, all_135_2_26) = v2 & apart_point_and_line(all_112_0_14, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_135_2_26) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.28 |
% 27.67/7.28 +-Applying beta-rule and splitting (233), into two cases.
% 27.67/7.28 |-Branch one:
% 27.67/7.28 | (287) all_135_1_25 = 0
% 27.67/7.28 |
% 27.67/7.28 | Equations (287) can reduce 191 to:
% 27.67/7.28 | (79) $false
% 27.67/7.28 |
% 27.67/7.28 |-The branch is then unsatisfiable
% 27.67/7.28 |-Branch two:
% 27.67/7.28 | (191) ~ (all_135_1_25 = 0)
% 27.67/7.28 | (416) all_131_2_18 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_135_2_26) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_135_2_26) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.28 |
% 27.67/7.28 +-Applying beta-rule and splitting (340), into two cases.
% 27.67/7.28 |-Branch one:
% 27.67/7.28 | (311) all_131_2_18 = 0
% 27.67/7.28 |
% 27.67/7.28 | Equations (311) can reduce 213 to:
% 27.67/7.28 | (79) $false
% 27.67/7.28 |
% 27.67/7.28 |-The branch is then unsatisfiable
% 27.67/7.28 |-Branch two:
% 27.67/7.28 | (213) ~ (all_131_2_18 = 0)
% 27.67/7.28 | (420) all_112_1_15 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_141_1_34, all_1_4_4) = v1 & apart_point_and_line(all_141_1_34, all_1_5_5) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.28 |
% 27.67/7.28 +-Applying beta-rule and splitting (404), into two cases.
% 27.67/7.28 |-Branch one:
% 27.67/7.28 | (311) all_131_2_18 = 0
% 27.67/7.28 |
% 27.67/7.28 | Equations (311) can reduce 213 to:
% 27.67/7.28 | (79) $false
% 27.67/7.28 |
% 27.67/7.28 |-The branch is then unsatisfiable
% 27.67/7.28 |-Branch two:
% 27.67/7.28 | (213) ~ (all_131_2_18 = 0)
% 27.67/7.28 | (424) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_141_1_34, all_1_4_4) = v2 & apart_point_and_line(all_141_1_34, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_1_4_4) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.28 |
% 27.67/7.28 +-Applying beta-rule and splitting (408), into two cases.
% 27.67/7.28 |-Branch one:
% 27.67/7.28 | (311) all_131_2_18 = 0
% 27.67/7.28 |
% 27.67/7.28 | Equations (311) can reduce 213 to:
% 27.67/7.28 | (79) $false
% 27.67/7.28 |
% 27.67/7.28 |-The branch is then unsatisfiable
% 27.67/7.28 |-Branch two:
% 27.67/7.28 | (213) ~ (all_131_2_18 = 0)
% 27.67/7.28 | (428) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_135_2_26) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_135_2_26) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.28 |
% 27.67/7.28 | Instantiating (428) with all_405_0_129, all_405_1_130, all_405_2_131, all_405_3_132 yields:
% 27.67/7.28 | (429) apart_point_and_line(all_1_2_2, all_135_2_26) = all_405_1_130 & apart_point_and_line(all_1_2_2, all_1_4_4) = all_405_0_129 & distinct_lines(all_1_4_4, all_135_2_26) = all_405_2_131 & distinct_points(all_1_2_2, all_1_2_2) = all_405_3_132 & ( ~ (all_405_2_131 = 0) | ~ (all_405_3_132 = 0) | all_405_0_129 = 0 | all_405_1_130 = 0)
% 27.67/7.28 |
% 27.67/7.28 | Applying alpha-rule on (429) yields:
% 27.67/7.28 | (430) apart_point_and_line(all_1_2_2, all_1_4_4) = all_405_0_129
% 27.67/7.28 | (431) apart_point_and_line(all_1_2_2, all_135_2_26) = all_405_1_130
% 27.67/7.28 | (432) ~ (all_405_2_131 = 0) | ~ (all_405_3_132 = 0) | all_405_0_129 = 0 | all_405_1_130 = 0
% 27.67/7.28 | (433) distinct_points(all_1_2_2, all_1_2_2) = all_405_3_132
% 27.67/7.28 | (434) distinct_lines(all_1_4_4, all_135_2_26) = all_405_2_131
% 27.67/7.28 |
% 27.67/7.28 +-Applying beta-rule and splitting (412), into two cases.
% 27.67/7.28 |-Branch one:
% 27.67/7.28 | (311) all_131_2_18 = 0
% 27.67/7.28 |
% 27.67/7.28 | Equations (311) can reduce 213 to:
% 27.67/7.28 | (79) $false
% 27.67/7.28 |
% 27.67/7.28 |-The branch is then unsatisfiable
% 27.67/7.28 |-Branch two:
% 27.67/7.28 | (213) ~ (all_131_2_18 = 0)
% 27.67/7.28 | (438) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_112_0_14, all_135_2_26) = v2 & apart_point_and_line(all_112_0_14, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_135_2_26) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 27.67/7.28 |
% 27.67/7.28 | Instantiating (438) with all_410_0_133, all_410_1_134, all_410_2_135 yields:
% 27.67/7.28 | (439) apart_point_and_line(all_112_0_14, all_135_2_26) = all_410_0_133 & apart_point_and_line(all_112_0_14, all_1_4_4) = all_410_1_134 & distinct_lines(all_1_4_4, all_135_2_26) = all_410_2_135 & ( ~ (all_410_2_135 = 0) | all_410_0_133 = 0 | all_410_1_134 = 0)
% 27.67/7.28 |
% 27.67/7.28 | Applying alpha-rule on (439) yields:
% 27.67/7.28 | (440) apart_point_and_line(all_112_0_14, all_135_2_26) = all_410_0_133
% 27.67/7.28 | (441) apart_point_and_line(all_112_0_14, all_1_4_4) = all_410_1_134
% 27.67/7.28 | (442) distinct_lines(all_1_4_4, all_135_2_26) = all_410_2_135
% 27.67/7.28 | (443) ~ (all_410_2_135 = 0) | all_410_0_133 = 0 | all_410_1_134 = 0
% 27.67/7.28 |
% 27.67/7.28 +-Applying beta-rule and splitting (416), into two cases.
% 27.67/7.28 |-Branch one:
% 27.67/7.28 | (311) all_131_2_18 = 0
% 27.67/7.28 |
% 27.67/7.28 | Equations (311) can reduce 213 to:
% 27.67/7.28 | (79) $false
% 27.67/7.28 |
% 27.67/7.28 |-The branch is then unsatisfiable
% 27.67/7.28 |-Branch two:
% 27.67/7.28 | (213) ~ (all_131_2_18 = 0)
% 27.67/7.28 | (447) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_135_2_26) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_135_2_26) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.28 |
% 27.67/7.28 | Instantiating (447) with all_415_0_136, all_415_1_137, all_415_2_138, all_415_3_139 yields:
% 27.67/7.28 | (448) apart_point_and_line(all_1_2_2, all_135_2_26) = all_415_0_136 & apart_point_and_line(all_1_2_2, all_1_4_4) = all_415_1_137 & distinct_lines(all_1_4_4, all_135_2_26) = all_415_2_138 & distinct_points(all_1_2_2, all_1_2_2) = all_415_3_139 & ( ~ (all_415_2_138 = 0) | ~ (all_415_3_139 = 0) | all_415_0_136 = 0 | all_415_1_137 = 0)
% 27.67/7.28 |
% 27.67/7.28 | Applying alpha-rule on (448) yields:
% 27.67/7.28 | (449) apart_point_and_line(all_1_2_2, all_135_2_26) = all_415_0_136
% 27.67/7.28 | (450) distinct_lines(all_1_4_4, all_135_2_26) = all_415_2_138
% 27.67/7.28 | (451) ~ (all_415_2_138 = 0) | ~ (all_415_3_139 = 0) | all_415_0_136 = 0 | all_415_1_137 = 0
% 27.67/7.28 | (452) distinct_points(all_1_2_2, all_1_2_2) = all_415_3_139
% 27.67/7.28 | (453) apart_point_and_line(all_1_2_2, all_1_4_4) = all_415_1_137
% 27.67/7.28 |
% 27.67/7.28 | Instantiating formula (45) with all_1_5_5, all_1_3_3, all_208_1_63, all_112_0_14 and discharging atoms intersection_point(all_1_5_5, all_1_3_3) = all_208_1_63, intersection_point(all_1_5_5, all_1_3_3) = all_112_0_14, yields:
% 27.67/7.28 | (454) all_208_1_63 = all_112_0_14
% 27.67/7.28 |
% 27.67/7.28 | Instantiating formula (26) with all_112_0_14, all_1_3_3, all_210_1_66, all_214_1_72 and discharging atoms apart_point_and_line(all_112_0_14, all_1_3_3) = all_214_1_72, apart_point_and_line(all_112_0_14, all_1_3_3) = all_210_1_66, yields:
% 27.67/7.28 | (455) all_214_1_72 = all_210_1_66
% 27.67/7.28 |
% 27.67/7.28 | Instantiating formula (26) with all_112_0_14, all_1_3_3, all_208_2_64, all_210_1_66 and discharging atoms apart_point_and_line(all_112_0_14, all_1_3_3) = all_210_1_66, apart_point_and_line(all_112_0_14, all_1_3_3) = all_208_2_64, yields:
% 27.67/7.28 | (456) all_210_1_66 = all_208_2_64
% 27.67/7.28 |
% 27.67/7.28 | Instantiating formula (26) with all_112_0_14, all_1_3_3, all_204_1_56, all_214_1_72 and discharging atoms apart_point_and_line(all_112_0_14, all_1_3_3) = all_214_1_72, apart_point_and_line(all_112_0_14, all_1_3_3) = all_204_1_56, yields:
% 27.67/7.28 | (457) all_214_1_72 = all_204_1_56
% 27.67/7.28 |
% 27.67/7.28 | Instantiating formula (26) with all_112_0_14, all_1_4_4, all_410_1_134, all_131_0_16 and discharging atoms apart_point_and_line(all_112_0_14, all_1_4_4) = all_410_1_134, apart_point_and_line(all_112_0_14, all_1_4_4) = all_131_0_16, yields:
% 27.67/7.28 | (458) all_410_1_134 = all_131_0_16
% 27.67/7.28 |
% 27.67/7.28 | Instantiating formula (26) with all_112_0_14, all_1_4_4, all_216_1_75, all_410_1_134 and discharging atoms apart_point_and_line(all_112_0_14, all_1_4_4) = all_410_1_134, apart_point_and_line(all_112_0_14, all_1_4_4) = all_216_1_75, yields:
% 27.67/7.28 | (459) all_410_1_134 = all_216_1_75
% 27.67/7.28 |
% 27.67/7.28 | Instantiating formula (26) with all_112_0_14, all_1_4_4, all_206_2_61, all_216_1_75 and discharging atoms apart_point_and_line(all_112_0_14, all_1_4_4) = all_216_1_75, apart_point_and_line(all_112_0_14, all_1_4_4) = all_206_2_61, yields:
% 27.67/7.28 | (460) all_216_1_75 = all_206_2_61
% 27.67/7.28 |
% 27.67/7.28 | Instantiating formula (26) with all_1_2_2, all_1_4_4, all_405_0_129, all_131_2_18 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_405_0_129, apart_point_and_line(all_1_2_2, all_1_4_4) = all_131_2_18, yields:
% 27.67/7.28 | (461) all_405_0_129 = all_131_2_18
% 27.67/7.28 |
% 27.67/7.28 | Instantiating formula (26) with all_1_2_2, all_1_4_4, all_405_0_129, all_415_1_137 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_415_1_137, apart_point_and_line(all_1_2_2, all_1_4_4) = all_405_0_129, yields:
% 27.67/7.28 | (462) all_415_1_137 = all_405_0_129
% 27.67/7.28 |
% 27.67/7.28 | Instantiating formula (26) with all_1_2_2, all_1_4_4, all_269_0_95, all_415_1_137 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_415_1_137, apart_point_and_line(all_1_2_2, all_1_4_4) = all_269_0_95, yields:
% 27.67/7.28 | (463) all_415_1_137 = all_269_0_95
% 27.67/7.28 |
% 27.67/7.28 | Using (316) and (106) yields:
% 27.67/7.28 | (464) ~ (all_269_0_95 = 0)
% 27.67/7.28 |
% 27.67/7.28 | Instantiating formula (26) with all_1_2_2, all_1_5_5, all_349_1_119, all_112_1_15 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_349_1_119, apart_point_and_line(all_1_2_2, all_1_5_5) = all_112_1_15, yields:
% 27.67/7.28 | (465) all_349_1_119 = all_112_1_15
% 27.67/7.28 |
% 27.67/7.28 | Instantiating formula (26) with all_1_2_2, all_1_5_5, all_344_0_114, all_349_1_119 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_349_1_119, apart_point_and_line(all_1_2_2, all_1_5_5) = all_344_0_114, yields:
% 27.67/7.28 | (466) all_349_1_119 = all_344_0_114
% 27.67/7.28 |
% 27.67/7.28 | Instantiating formula (26) with all_1_2_2, all_1_5_5, all_222_1_84, all_344_0_114 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_344_0_114, apart_point_and_line(all_1_2_2, all_1_5_5) = all_222_1_84, yields:
% 27.67/7.28 | (467) all_344_0_114 = all_222_1_84
% 27.67/7.28 |
% 27.67/7.28 | Instantiating formula (26) with all_1_2_2, all_1_5_5, all_204_2_57, all_222_1_84 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_222_1_84, apart_point_and_line(all_1_2_2, all_1_5_5) = all_204_2_57, yields:
% 27.67/7.28 | (468) all_222_1_84 = all_204_2_57
% 27.67/7.28 |
% 27.67/7.28 | Using (247) and (97) yields:
% 27.67/7.28 | (469) ~ (all_204_2_57 = 0)
% 27.67/7.28 |
% 27.67/7.28 | Instantiating formula (16) with all_112_0_14, all_112_0_14, all_210_0_65, all_208_0_62 and discharging atoms distinct_points(all_112_0_14, all_112_0_14) = all_210_0_65, yields:
% 27.67/7.28 | (470) all_210_0_65 = all_208_0_62 | ~ (distinct_points(all_112_0_14, all_112_0_14) = all_208_0_62)
% 27.67/7.28 |
% 27.67/7.28 | Instantiating formula (20) with all_112_0_14 yields:
% 27.67/7.28 | (471) ~ (distinct_points(all_112_0_14, all_112_0_14) = 0)
% 27.67/7.28 |
% 27.67/7.28 | Combining equations (462,463) yields a new equation:
% 27.67/7.28 | (472) all_405_0_129 = all_269_0_95
% 27.67/7.28 |
% 27.67/7.28 | Simplifying 472 yields:
% 27.67/7.28 | (473) all_405_0_129 = all_269_0_95
% 27.67/7.28 |
% 27.67/7.28 | Combining equations (459,458) yields a new equation:
% 27.67/7.28 | (474) all_216_1_75 = all_131_0_16
% 27.67/7.28 |
% 27.67/7.28 | Simplifying 474 yields:
% 27.67/7.28 | (475) all_216_1_75 = all_131_0_16
% 27.67/7.28 |
% 27.67/7.28 | Combining equations (461,473) yields a new equation:
% 27.67/7.28 | (476) all_269_0_95 = all_131_2_18
% 27.67/7.28 |
% 27.67/7.28 | Combining equations (466,465) yields a new equation:
% 27.67/7.28 | (477) all_344_0_114 = all_112_1_15
% 27.67/7.28 |
% 27.67/7.28 | Simplifying 477 yields:
% 27.67/7.28 | (478) all_344_0_114 = all_112_1_15
% 27.67/7.28 |
% 27.67/7.28 | Combining equations (467,478) yields a new equation:
% 27.67/7.28 | (479) all_222_1_84 = all_112_1_15
% 27.67/7.28 |
% 27.67/7.28 | Simplifying 479 yields:
% 27.67/7.28 | (480) all_222_1_84 = all_112_1_15
% 27.67/7.28 |
% 27.67/7.28 | Combining equations (468,480) yields a new equation:
% 27.67/7.28 | (481) all_204_2_57 = all_112_1_15
% 27.67/7.28 |
% 27.67/7.28 | Simplifying 481 yields:
% 27.67/7.28 | (482) all_204_2_57 = all_112_1_15
% 27.67/7.28 |
% 27.67/7.28 | Combining equations (475,460) yields a new equation:
% 27.67/7.28 | (483) all_206_2_61 = all_131_0_16
% 27.67/7.28 |
% 27.67/7.28 | Combining equations (455,457) yields a new equation:
% 27.67/7.28 | (484) all_210_1_66 = all_204_1_56
% 27.67/7.28 |
% 27.67/7.28 | Simplifying 484 yields:
% 27.67/7.28 | (485) all_210_1_66 = all_204_1_56
% 27.67/7.28 |
% 27.67/7.28 | Combining equations (485,456) yields a new equation:
% 27.67/7.28 | (486) all_208_2_64 = all_204_1_56
% 27.67/7.28 |
% 27.67/7.28 | Equations (476) can reduce 464 to:
% 27.67/7.28 | (213) ~ (all_131_2_18 = 0)
% 27.67/7.28 |
% 27.67/7.28 | Equations (482) can reduce 469 to:
% 27.67/7.28 | (104) ~ (all_112_1_15 = 0)
% 27.67/7.28 |
% 27.67/7.28 | From (486) and (259) follows:
% 27.67/7.28 | (249) apart_point_and_line(all_112_0_14, all_1_3_3) = all_204_1_56
% 27.67/7.29 |
% 27.67/7.29 | From (483) and (254) follows:
% 27.67/7.29 | (118) apart_point_and_line(all_112_0_14, all_1_4_4) = all_131_0_16
% 27.67/7.29 |
% 27.67/7.29 | From (454) and (260) follows:
% 27.67/7.29 | (491) distinct_points(all_112_0_14, all_112_0_14) = all_208_0_62
% 27.67/7.29 |
% 27.67/7.29 +-Applying beta-rule and splitting (470), into two cases.
% 27.67/7.29 |-Branch one:
% 27.67/7.29 | (492) ~ (distinct_points(all_112_0_14, all_112_0_14) = all_208_0_62)
% 27.67/7.29 |
% 27.67/7.29 | Using (491) and (492) yields:
% 27.67/7.29 | (202) $false
% 27.67/7.29 |
% 27.67/7.29 |-The branch is then unsatisfiable
% 27.67/7.29 |-Branch two:
% 27.67/7.29 | (491) distinct_points(all_112_0_14, all_112_0_14) = all_208_0_62
% 27.67/7.29 | (495) all_210_0_65 = all_208_0_62
% 27.67/7.29 |
% 27.67/7.29 | From (495) and (265) follows:
% 27.67/7.29 | (491) distinct_points(all_112_0_14, all_112_0_14) = all_208_0_62
% 27.67/7.29 |
% 27.67/7.29 | Using (491) and (471) yields:
% 27.67/7.29 | (497) ~ (all_208_0_62 = 0)
% 27.67/7.29 |
% 27.67/7.29 +-Applying beta-rule and splitting (261), into two cases.
% 27.67/7.29 |-Branch one:
% 27.67/7.29 | (498) all_208_0_62 = 0
% 27.67/7.29 |
% 27.67/7.29 | Equations (498) can reduce 497 to:
% 27.67/7.29 | (79) $false
% 27.67/7.29 |
% 27.67/7.29 |-The branch is then unsatisfiable
% 27.67/7.29 |-Branch two:
% 27.67/7.29 | (497) ~ (all_208_0_62 = 0)
% 27.67/7.29 | (501) ~ (all_208_2_64 = 0) & ~ (all_131_1_17 = 0)
% 27.67/7.29 |
% 27.67/7.29 | Applying alpha-rule on (501) yields:
% 27.67/7.29 | (502) ~ (all_208_2_64 = 0)
% 27.67/7.29 | (503) ~ (all_131_1_17 = 0)
% 27.67/7.29 |
% 27.67/7.29 | Equations (486) can reduce 502 to:
% 27.67/7.29 | (504) ~ (all_204_1_56 = 0)
% 27.67/7.29 |
% 27.67/7.29 +-Applying beta-rule and splitting (119), into two cases.
% 27.67/7.29 |-Branch one:
% 27.67/7.29 | (505) all_131_0_16 = 0
% 27.67/7.29 |
% 27.67/7.29 | From (505) and (118) follows:
% 27.67/7.29 | (506) apart_point_and_line(all_112_0_14, all_1_4_4) = 0
% 27.67/7.29 |
% 27.67/7.29 +-Applying beta-rule and splitting (218), into two cases.
% 27.67/7.29 |-Branch one:
% 27.67/7.29 | (507) ~ (apart_point_and_line(all_112_0_14, all_1_4_4) = 0)
% 27.67/7.29 |
% 27.67/7.29 | Using (506) and (507) yields:
% 27.67/7.29 | (202) $false
% 27.67/7.29 |
% 27.67/7.29 |-The branch is then unsatisfiable
% 27.67/7.29 |-Branch two:
% 27.67/7.29 | (506) apart_point_and_line(all_112_0_14, all_1_4_4) = 0
% 27.67/7.29 | (510) all_1_0_0 = 0 | apart_point_and_line(all_112_0_14, all_1_3_3) = 0
% 27.67/7.29 |
% 27.67/7.29 +-Applying beta-rule and splitting (510), into two cases.
% 27.67/7.29 |-Branch one:
% 27.67/7.29 | (511) apart_point_and_line(all_112_0_14, all_1_3_3) = 0
% 27.67/7.29 |
% 27.67/7.29 | Instantiating formula (26) with all_112_0_14, all_1_3_3, 0, all_204_1_56 and discharging atoms apart_point_and_line(all_112_0_14, all_1_3_3) = all_204_1_56, apart_point_and_line(all_112_0_14, all_1_3_3) = 0, yields:
% 27.67/7.29 | (512) all_204_1_56 = 0
% 27.67/7.29 |
% 27.67/7.29 | Equations (512) can reduce 504 to:
% 27.67/7.29 | (79) $false
% 27.67/7.29 |
% 27.67/7.29 |-The branch is then unsatisfiable
% 27.67/7.29 |-Branch two:
% 27.67/7.29 | (514) ~ (apart_point_and_line(all_112_0_14, all_1_3_3) = 0)
% 27.67/7.29 | (78) all_1_0_0 = 0
% 27.67/7.29 |
% 27.67/7.29 | Equations (78) can reduce 77 to:
% 27.67/7.29 | (79) $false
% 27.67/7.29 |
% 27.67/7.29 |-The branch is then unsatisfiable
% 27.67/7.29 |-Branch two:
% 27.67/7.29 | (517) ~ (all_131_0_16 = 0)
% 27.67/7.29 | (518) all_131_1_17 = 0 | all_131_2_18 = 0 | all_131_3_19 = 0
% 27.67/7.29 |
% 27.67/7.29 +-Applying beta-rule and splitting (230), into two cases.
% 27.67/7.29 |-Branch one:
% 27.67/7.29 | (519) all_131_1_17 = 0
% 27.67/7.29 |
% 27.67/7.29 | Equations (519) can reduce 503 to:
% 27.67/7.29 | (79) $false
% 27.67/7.29 |
% 27.67/7.29 |-The branch is then unsatisfiable
% 27.67/7.29 |-Branch two:
% 27.67/7.29 | (503) ~ (all_131_1_17 = 0)
% 27.67/7.29 | (522) all_131_2_18 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_112_0_14, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_112_0_14) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.29 |
% 27.67/7.29 +-Applying beta-rule and splitting (518), into two cases.
% 27.67/7.29 |-Branch one:
% 27.67/7.29 | (519) all_131_1_17 = 0
% 27.67/7.29 |
% 27.67/7.29 | Equations (519) can reduce 503 to:
% 27.67/7.29 | (79) $false
% 27.67/7.29 |
% 27.67/7.29 |-The branch is then unsatisfiable
% 27.67/7.29 |-Branch two:
% 27.67/7.29 | (503) ~ (all_131_1_17 = 0)
% 27.67/7.29 | (526) all_131_2_18 = 0 | all_131_3_19 = 0
% 27.67/7.29 |
% 27.67/7.29 +-Applying beta-rule and splitting (217), into two cases.
% 27.67/7.29 |-Branch one:
% 27.67/7.29 | (505) all_131_0_16 = 0
% 27.67/7.29 |
% 27.67/7.29 | Equations (505) can reduce 517 to:
% 27.67/7.29 | (79) $false
% 27.67/7.29 |
% 27.67/7.29 |-The branch is then unsatisfiable
% 27.67/7.29 |-Branch two:
% 27.67/7.29 | (517) ~ (all_131_0_16 = 0)
% 27.67/7.29 | (530) all_112_1_15 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_112_0_14, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_112_0_14, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.29 |
% 27.67/7.29 +-Applying beta-rule and splitting (530), into two cases.
% 27.67/7.29 |-Branch one:
% 27.67/7.29 | (148) all_112_1_15 = 0
% 27.67/7.29 |
% 27.67/7.29 | Equations (148) can reduce 104 to:
% 27.67/7.29 | (79) $false
% 27.67/7.29 |
% 27.67/7.29 |-The branch is then unsatisfiable
% 27.67/7.29 |-Branch two:
% 27.67/7.29 | (104) ~ (all_112_1_15 = 0)
% 27.67/7.29 | (534) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_112_0_14, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_112_0_14, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 27.67/7.29 |
% 27.67/7.29 +-Applying beta-rule and splitting (526), into two cases.
% 27.67/7.29 |-Branch one:
% 27.67/7.29 | (311) all_131_2_18 = 0
% 27.67/7.29 |
% 27.67/7.29 | Equations (311) can reduce 213 to:
% 27.67/7.29 | (79) $false
% 27.67/7.29 |
% 27.67/7.29 |-The branch is then unsatisfiable
% 27.67/7.29 |-Branch two:
% 27.67/7.29 | (213) ~ (all_131_2_18 = 0)
% 27.67/7.29 | (538) all_131_3_19 = 0
% 27.67/7.29 |
% 27.67/7.29 | Combining equations (538,180) yields a new equation:
% 27.67/7.29 | (148) all_112_1_15 = 0
% 27.67/7.29 |
% 27.67/7.29 | Equations (148) can reduce 104 to:
% 27.67/7.29 | (79) $false
% 27.67/7.29 |
% 27.67/7.29 |-The branch is then unsatisfiable
% 27.67/7.29 |-Branch two:
% 27.67/7.29 | (287) all_135_1_25 = 0
% 27.67/7.29 | (542) all_135_0_24 = 0
% 27.67/7.29 |
% 27.67/7.29 | Equations (542) can reduce 182 to:
% 27.67/7.29 | (79) $false
% 27.67/7.29 |
% 27.67/7.29 |-The branch is then unsatisfiable
% 27.67/7.29 |-Branch two:
% 27.67/7.29 | (544) ~ (distinct_lines(all_1_3_3, all_1_5_5) = 0)
% 27.67/7.29 | (148) all_112_1_15 = 0
% 27.67/7.29 |
% 27.67/7.29 | Equations (148) can reduce 104 to:
% 27.67/7.29 | (79) $false
% 27.67/7.29 |
% 27.67/7.29 |-The branch is then unsatisfiable
% 27.67/7.29 |-Branch two:
% 27.67/7.29 | (547) apart_point_and_line(all_1_2_2, all_1_4_4) = 0
% 27.67/7.29 | (548) ? [v0] : ? [v1] : ? [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 & distinct_points(all_1_2_2, all_1_2_2) = v2 & ( ~ (v0 = 0) | v2 = 0))
% 27.67/7.29 |
% 27.67/7.29 +-Applying beta-rule and splitting (58), into two cases.
% 27.67/7.29 |-Branch one:
% 27.67/7.29 | (106) ~ (apart_point_and_line(all_1_2_2, all_1_4_4) = 0)
% 27.67/7.29 |
% 27.67/7.29 | Using (547) and (106) yields:
% 27.67/7.29 | (202) $false
% 27.67/7.29 |
% 27.67/7.29 |-The branch is then unsatisfiable
% 27.67/7.29 |-Branch two:
% 27.67/7.29 | (547) apart_point_and_line(all_1_2_2, all_1_4_4) = 0
% 27.67/7.29 | (552) ? [v0] : ? [v1] : (intersection_point(all_1_5_5, all_1_4_4) = v1 & apart_point_and_line(all_1_2_2, all_1_5_5) = v0 & distinct_points(all_1_2_2, v1) = 0)
% 27.67/7.29 |
% 27.67/7.29 | Instantiating (552) with all_128_0_147, all_128_1_148 yields:
% 27.67/7.29 | (553) intersection_point(all_1_5_5, all_1_4_4) = all_128_0_147 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_128_1_148 & distinct_points(all_1_2_2, all_128_0_147) = 0
% 27.67/7.29 |
% 27.67/7.29 | Applying alpha-rule on (553) yields:
% 27.67/7.29 | (554) intersection_point(all_1_5_5, all_1_4_4) = all_128_0_147
% 27.67/7.29 | (555) apart_point_and_line(all_1_2_2, all_1_5_5) = all_128_1_148
% 27.67/7.29 | (556) distinct_points(all_1_2_2, all_128_0_147) = 0
% 27.67/7.29 |
% 27.67/7.29 | Instantiating formula (45) with all_1_5_5, all_1_4_4, all_128_0_147, all_1_2_2 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_128_0_147, intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2, yields:
% 27.67/7.29 | (557) all_128_0_147 = all_1_2_2
% 27.67/7.29 |
% 27.67/7.29 | Using (556) and (105) yields:
% 27.67/7.30 | (558) ~ (all_128_0_147 = all_1_2_2)
% 27.67/7.30 |
% 28.03/7.30 | Equations (557) can reduce 558 to:
% 28.03/7.30 | (79) $false
% 28.03/7.30 |
% 28.03/7.30 |-The branch is then unsatisfiable
% 28.03/7.30 |-Branch two:
% 28.03/7.30 | (560) ~ (convergent_lines(all_1_5_5, all_1_3_3) = 0)
% 28.03/7.30 | (561) all_52_0_9 = 0
% 28.03/7.30 |
% 28.03/7.30 | Equations (561) can reduce 87 to:
% 28.03/7.30 | (79) $false
% 28.03/7.30 |
% 28.03/7.30 |-The branch is then unsatisfiable
% 28.03/7.30 |-Branch two:
% 28.03/7.30 | (563) apart_point_and_line(all_1_2_2, all_1_5_5) = 0
% 28.03/7.30 | (564) ? [v0] : ? [v1] : (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) = 0)
% 28.03/7.30 |
% 28.03/7.30 | Instantiating (564) with all_79_0_149, all_79_1_150 yields:
% 28.03/7.30 | (565) intersection_point(all_1_5_5, all_1_4_4) = all_79_0_149 & apart_point_and_line(all_1_2_2, all_1_4_4) = all_79_1_150 & distinct_points(all_1_2_2, all_79_0_149) = 0
% 28.03/7.30 |
% 28.03/7.30 | Applying alpha-rule on (565) yields:
% 28.03/7.30 | (566) intersection_point(all_1_5_5, all_1_4_4) = all_79_0_149
% 28.03/7.30 | (567) apart_point_and_line(all_1_2_2, all_1_4_4) = all_79_1_150
% 28.03/7.30 | (568) distinct_points(all_1_2_2, all_79_0_149) = 0
% 28.03/7.30 |
% 28.03/7.30 | Instantiating formula (45) with all_1_5_5, all_1_4_4, all_79_0_149, all_1_2_2 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_79_0_149, intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2, yields:
% 28.03/7.30 | (569) all_79_0_149 = all_1_2_2
% 28.03/7.30 |
% 28.03/7.30 | Instantiating formula (20) with all_1_2_2 yields:
% 28.03/7.30 | (105) ~ (distinct_points(all_1_2_2, all_1_2_2) = 0)
% 28.03/7.30 |
% 28.03/7.30 | From (569) and (568) follows:
% 28.03/7.30 | (571) distinct_points(all_1_2_2, all_1_2_2) = 0
% 28.03/7.30 |
% 28.03/7.30 | Using (571) and (105) yields:
% 28.03/7.30 | (202) $false
% 28.03/7.30 |
% 28.03/7.30 |-The branch is then unsatisfiable
% 28.03/7.30 |-Branch two:
% 28.03/7.30 | (573) ~ (all_1_1_1 = 0)
% 28.03/7.30 | (574) ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_5_5, all_1_4_4) = v0)
% 28.03/7.30 |
% 28.03/7.30 +-Applying beta-rule and splitting (65), into two cases.
% 28.03/7.30 |-Branch one:
% 28.03/7.30 | (89) all_1_1_1 = 0
% 28.03/7.30 |
% 28.03/7.30 | Equations (89) can reduce 573 to:
% 28.03/7.30 | (79) $false
% 28.03/7.30 |
% 28.03/7.30 |-The branch is then unsatisfiable
% 28.03/7.30 |-Branch two:
% 28.03/7.30 | (573) ~ (all_1_1_1 = 0)
% 28.03/7.30 | (578) ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_5_5, all_1_5_5) = v0)
% 28.03/7.30 |
% 28.03/7.30 +-Applying beta-rule and splitting (61), into two cases.
% 28.03/7.30 |-Branch one:
% 28.03/7.30 | (78) all_1_0_0 = 0
% 28.03/7.30 |
% 28.03/7.30 | Equations (78) can reduce 77 to:
% 28.03/7.30 | (79) $false
% 28.03/7.30 |
% 28.03/7.30 |-The branch is then unsatisfiable
% 28.03/7.30 |-Branch two:
% 28.03/7.30 | (77) ~ (all_1_0_0 = 0)
% 28.03/7.30 | (95) ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_4_4, all_1_4_4) = v0)
% 28.03/7.30 |
% 28.03/7.30 +-Applying beta-rule and splitting (63), into two cases.
% 28.03/7.30 |-Branch one:
% 28.03/7.30 | (78) all_1_0_0 = 0
% 28.03/7.30 |
% 28.03/7.30 | Equations (78) can reduce 77 to:
% 28.03/7.30 | (79) $false
% 28.03/7.30 |
% 28.03/7.30 |-The branch is then unsatisfiable
% 28.03/7.30 |-Branch two:
% 28.03/7.30 | (77) ~ (all_1_0_0 = 0)
% 28.03/7.30 | (586) all_1_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_4_4, all_1_5_5) = v0)
% 28.03/7.30 |
% 28.03/7.30 +-Applying beta-rule and splitting (74), into two cases.
% 28.03/7.30 |-Branch one:
% 28.03/7.30 | (91) distinct_lines(all_1_5_5, all_1_3_3) = 0
% 28.03/7.30 |
% 28.03/7.30 +-Applying beta-rule and splitting (66), into two cases.
% 28.03/7.30 |-Branch one:
% 28.03/7.30 | (89) all_1_1_1 = 0
% 28.03/7.30 |
% 28.03/7.30 | Equations (89) can reduce 573 to:
% 28.03/7.30 | (79) $false
% 28.03/7.30 |
% 28.03/7.30 |-The branch is then unsatisfiable
% 28.03/7.30 |-Branch two:
% 28.03/7.30 | (573) ~ (all_1_1_1 = 0)
% 28.03/7.30 | (591) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_1_5_5, all_1_3_3) = v0)
% 28.03/7.30 |
% 28.03/7.30 +-Applying beta-rule and splitting (586), into two cases.
% 28.03/7.30 |-Branch one:
% 28.03/7.30 | (89) all_1_1_1 = 0
% 28.03/7.30 |
% 28.03/7.30 | Equations (89) can reduce 573 to:
% 28.03/7.30 | (79) $false
% 28.03/7.30 |
% 28.03/7.30 |-The branch is then unsatisfiable
% 28.03/7.30 |-Branch two:
% 28.03/7.30 | (573) ~ (all_1_1_1 = 0)
% 28.03/7.30 | (595) ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_4_4, all_1_5_5) = v0)
% 28.03/7.30 |
% 28.03/7.30 | Instantiating formula (5) with all_1_5_5, all_1_3_3, 0, all_1_1_1 and discharging atoms distinct_lines(all_1_5_5, all_1_3_3) = all_1_1_1, distinct_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 28.03/7.30 | (89) all_1_1_1 = 0
% 28.03/7.30 |
% 28.03/7.30 | Equations (89) can reduce 573 to:
% 28.03/7.30 | (79) $false
% 28.03/7.30 |
% 28.03/7.30 |-The branch is then unsatisfiable
% 28.03/7.30 |-Branch two:
% 28.03/7.30 | (598) ~ (distinct_lines(all_1_5_5, all_1_3_3) = 0)
% 28.03/7.30 | (78) all_1_0_0 = 0
% 28.03/7.30 |
% 28.03/7.30 | Equations (78) can reduce 77 to:
% 28.03/7.30 | (79) $false
% 28.03/7.30 |
% 28.03/7.30 |-The branch is then unsatisfiable
% 28.03/7.30 |-Branch two:
% 28.03/7.30 | (78) all_1_0_0 = 0
% 28.03/7.30 | (573) ~ (all_1_1_1 = 0)
% 28.03/7.30 |
% 28.03/7.30 | Equations (78) can reduce 76 to:
% 28.03/7.30 | (603) ~ (all_1_1_1 = 0)
% 28.03/7.30 |
% 28.03/7.30 | Simplifying 603 yields:
% 28.03/7.30 | (573) ~ (all_1_1_1 = 0)
% 28.03/7.30 |
% 28.03/7.30 | From (78) and (53) follows:
% 28.03/7.30 | (605) distinct_lines(all_1_4_4, all_1_3_3) = 0
% 28.03/7.30 |
% 28.03/7.30 +-Applying beta-rule and splitting (66), into two cases.
% 28.03/7.30 |-Branch one:
% 28.03/7.30 | (89) all_1_1_1 = 0
% 28.03/7.30 |
% 28.03/7.30 | Equations (89) can reduce 573 to:
% 28.03/7.30 | (79) $false
% 28.03/7.30 |
% 28.03/7.30 |-The branch is then unsatisfiable
% 28.03/7.30 |-Branch two:
% 28.03/7.30 | (573) ~ (all_1_1_1 = 0)
% 28.03/7.30 | (591) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_1_5_5, all_1_3_3) = v0)
% 28.03/7.30 |
% 28.03/7.30 | Instantiating (591) with all_49_0_162 yields:
% 28.03/7.30 | (610) ~ (all_49_0_162 = 0) & convergent_lines(all_1_5_5, all_1_3_3) = all_49_0_162
% 28.03/7.30 |
% 28.03/7.30 | Applying alpha-rule on (610) yields:
% 28.03/7.30 | (611) ~ (all_49_0_162 = 0)
% 28.03/7.30 | (612) convergent_lines(all_1_5_5, all_1_3_3) = all_49_0_162
% 28.03/7.30 |
% 28.03/7.30 +-Applying beta-rule and splitting (65), into two cases.
% 28.03/7.30 |-Branch one:
% 28.03/7.30 | (89) all_1_1_1 = 0
% 28.03/7.30 |
% 28.03/7.30 | Equations (89) can reduce 573 to:
% 28.03/7.30 | (79) $false
% 28.03/7.30 |
% 28.03/7.30 |-The branch is then unsatisfiable
% 28.03/7.30 |-Branch two:
% 28.03/7.30 | (573) ~ (all_1_1_1 = 0)
% 28.03/7.30 | (578) ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_5_5, all_1_5_5) = v0)
% 28.03/7.30 |
% 28.03/7.30 | Instantiating (578) with all_54_0_163 yields:
% 28.03/7.30 | (617) ~ (all_54_0_163 = 0) & distinct_lines(all_1_5_5, all_1_5_5) = all_54_0_163
% 28.03/7.30 |
% 28.03/7.30 | Applying alpha-rule on (617) yields:
% 28.03/7.30 | (618) ~ (all_54_0_163 = 0)
% 28.03/7.30 | (619) distinct_lines(all_1_5_5, all_1_5_5) = all_54_0_163
% 28.03/7.30 |
% 28.03/7.30 | Instantiating formula (28) with all_49_0_162, all_17_2_8, all_1_3_3, all_1_5_5, all_1_3_3 and discharging atoms convergent_lines(all_1_3_3, all_1_3_3) = all_17_2_8, convergent_lines(all_1_5_5, all_1_3_3) = all_49_0_162, yields:
% 28.03/7.30 | (620) all_49_0_162 = 0 | all_17_2_8 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_1_3_3, all_1_5_5) = v0)
% 28.03/7.30 |
% 28.03/7.30 | Instantiating formula (43) with all_49_0_162, all_1_3_3, all_1_4_4, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_3_3) = all_49_0_162, convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 28.03/7.30 | (621) all_49_0_162 = 0 | convergent_lines(all_1_4_4, all_1_3_3) = 0
% 28.03/7.30 |
% 28.03/7.30 | Instantiating formula (28) with all_49_0_162, all_49_0_162, all_1_3_3, all_1_5_5, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_3_3) = all_49_0_162, yields:
% 28.03/7.30 | (622) all_49_0_162 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_1_5_5, all_1_5_5) = v0)
% 28.03/7.30 |
% 28.03/7.30 | Instantiating formula (44) with all_54_0_163, all_1_5_5, all_1_4_4, all_1_5_5 and discharging atoms distinct_lines(all_1_5_5, all_1_4_4) = 0, distinct_lines(all_1_5_5, all_1_5_5) = all_54_0_163, yields:
% 28.03/7.30 | (623) all_54_0_163 = 0 | distinct_lines(all_1_4_4, all_1_5_5) = 0
% 28.03/7.30 |
% 28.03/7.30 +-Applying beta-rule and splitting (59), into two cases.
% 28.03/7.30 |-Branch one:
% 28.03/7.30 | (97) ~ (apart_point_and_line(all_1_2_2, all_1_5_5) = 0)
% 28.03/7.30 |
% 28.03/7.30 +-Applying beta-rule and splitting (623), into two cases.
% 28.03/7.30 |-Branch one:
% 28.03/7.30 | (625) distinct_lines(all_1_4_4, all_1_5_5) = 0
% 28.03/7.30 |
% 28.03/7.30 +-Applying beta-rule and splitting (621), into two cases.
% 28.03/7.30 |-Branch one:
% 28.03/7.30 | (626) convergent_lines(all_1_4_4, all_1_3_3) = 0
% 28.03/7.30 |
% 28.03/7.30 +-Applying beta-rule and splitting (622), into two cases.
% 28.03/7.30 |-Branch one:
% 28.03/7.30 | (627) all_49_0_162 = 0
% 28.03/7.30 |
% 28.03/7.30 | Equations (627) can reduce 611 to:
% 28.03/7.30 | (79) $false
% 28.03/7.30 |
% 28.03/7.30 |-The branch is then unsatisfiable
% 28.03/7.30 |-Branch two:
% 28.03/7.30 | (611) ~ (all_49_0_162 = 0)
% 28.03/7.30 | (630) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_1_5_5, all_1_5_5) = v0)
% 28.03/7.30 |
% 28.03/7.30 +-Applying beta-rule and splitting (620), into two cases.
% 28.03/7.30 |-Branch one:
% 28.03/7.30 | (627) all_49_0_162 = 0
% 28.03/7.30 |
% 28.03/7.30 | Equations (627) can reduce 611 to:
% 28.03/7.30 | (79) $false
% 28.03/7.30 |
% 28.03/7.30 |-The branch is then unsatisfiable
% 28.03/7.30 |-Branch two:
% 28.03/7.30 | (611) ~ (all_49_0_162 = 0)
% 28.03/7.30 | (634) all_17_2_8 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_1_3_3, all_1_5_5) = v0)
% 28.03/7.30 |
% 28.03/7.30 +-Applying beta-rule and splitting (634), into two cases.
% 28.03/7.30 |-Branch one:
% 28.03/7.30 | (635) all_17_2_8 = 0
% 28.03/7.30 |
% 28.03/7.30 | Equations (635) can reduce 73 to:
% 28.03/7.30 | (79) $false
% 28.03/7.30 |
% 28.03/7.30 |-The branch is then unsatisfiable
% 28.03/7.30 |-Branch two:
% 28.03/7.30 | (73) ~ (all_17_2_8 = 0)
% 28.03/7.30 | (638) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_1_3_3, all_1_5_5) = v0)
% 28.03/7.30 |
% 28.03/7.30 | Instantiating (638) with all_93_0_166 yields:
% 28.03/7.30 | (639) ~ (all_93_0_166 = 0) & convergent_lines(all_1_3_3, all_1_5_5) = all_93_0_166
% 28.03/7.30 |
% 28.03/7.30 | Applying alpha-rule on (639) yields:
% 28.03/7.30 | (640) ~ (all_93_0_166 = 0)
% 28.03/7.30 | (641) convergent_lines(all_1_3_3, all_1_5_5) = all_93_0_166
% 28.03/7.30 |
% 28.03/7.30 | Instantiating formula (34) with all_93_0_166, all_1_5_5, all_1_3_3, all_1_4_4 and discharging atoms convergent_lines(all_1_3_3, all_1_5_5) = all_93_0_166, convergent_lines(all_1_4_4, all_1_3_3) = 0, yields:
% 28.03/7.30 | (642) all_93_0_166 = 0 | convergent_lines(all_1_4_4, all_1_5_5) = 0
% 28.03/7.30 |
% 28.03/7.30 | Instantiating formula (46) with 0, all_1_2_2, all_1_3_3, all_1_4_4 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = 0, convergent_lines(all_1_4_4, all_1_3_3) = 0, yields:
% 28.03/7.31 | (643) ? [v0] : ? [v1] : (intersection_point(all_1_4_4, all_1_3_3) = v1 & apart_point_and_line(all_1_2_2, all_1_4_4) = v0 & distinct_points(all_1_2_2, v1) = 0)
% 28.03/7.31 |
% 28.03/7.31 | Instantiating (643) with all_104_0_167, all_104_1_168 yields:
% 28.03/7.31 | (644) intersection_point(all_1_4_4, all_1_3_3) = all_104_0_167 & apart_point_and_line(all_1_2_2, all_1_4_4) = all_104_1_168 & distinct_points(all_1_2_2, all_104_0_167) = 0
% 28.03/7.31 |
% 28.03/7.31 | Applying alpha-rule on (644) yields:
% 28.03/7.31 | (645) intersection_point(all_1_4_4, all_1_3_3) = all_104_0_167
% 28.03/7.31 | (646) apart_point_and_line(all_1_2_2, all_1_4_4) = all_104_1_168
% 28.03/7.31 | (647) distinct_points(all_1_2_2, all_104_0_167) = 0
% 28.03/7.31 |
% 28.03/7.31 +-Applying beta-rule and splitting (642), into two cases.
% 28.03/7.31 |-Branch one:
% 28.03/7.31 | (648) convergent_lines(all_1_4_4, all_1_5_5) = 0
% 28.03/7.31 |
% 28.03/7.31 | Instantiating formula (20) with all_1_2_2 yields:
% 28.03/7.31 | (105) ~ (distinct_points(all_1_2_2, all_1_2_2) = 0)
% 28.03/7.31 |
% 28.03/7.31 +-Applying beta-rule and splitting (58), into two cases.
% 28.03/7.31 |-Branch one:
% 28.03/7.31 | (106) ~ (apart_point_and_line(all_1_2_2, all_1_4_4) = 0)
% 28.03/7.31 |
% 28.03/7.31 | Using (646) and (106) yields:
% 28.03/7.31 | (651) ~ (all_104_1_168 = 0)
% 28.03/7.31 |
% 28.03/7.31 | Instantiating formula (39) with all_104_1_168, all_1_4_4, all_1_3_3, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = 0, apart_point_and_line(all_1_2_2, all_1_4_4) = all_104_1_168, yields:
% 28.03/7.31 | (652) all_104_1_168 = 0 | distinct_lines(all_1_3_3, all_1_4_4) = 0
% 28.03/7.31 |
% 28.03/7.31 | Instantiating formula (25) with all_104_1_168, 0, all_1_2_2, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = 0, apart_point_and_line(all_1_2_2, all_1_4_4) = all_104_1_168, yields:
% 28.03/7.31 | (653) ? [v0] : ? [v1] : ? [v2] : (intersection_point(all_1_3_3, all_1_4_4) = v1 & convergent_lines(all_1_3_3, all_1_4_4) = v0 & distinct_points(all_1_2_2, v1) = v2 & ( ~ (v0 = 0) | v2 = 0))
% 28.03/7.31 |
% 28.03/7.31 | Instantiating formula (14) with all_104_1_168, all_104_1_168, all_1_4_4, all_1_4_4, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_104_1_168, yields:
% 28.03/7.31 | (654) all_104_1_168 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.31 |
% 28.03/7.31 | Instantiating formula (2) with all_1_2_2, all_104_1_168, 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_4_4) = all_104_1_168, yields:
% 28.03/7.31 | (655) ? [v0] : ? [v1] : ? [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 & distinct_points(all_1_2_2, all_1_2_2) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_104_1_168 = 0))))
% 28.03/7.31 |
% 28.03/7.31 | Instantiating formula (46) with all_104_1_168, 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_4_4) = all_104_1_168, convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 28.03/7.31 | (656) ? [v0] : ? [v1] : ? [v2] : (intersection_point(all_1_5_5, all_1_4_4) = v1 & apart_point_and_line(all_1_2_2, all_1_5_5) = v0 & distinct_points(all_1_2_2, v1) = v2 & (v2 = 0 | ( ~ (v0 = 0) & ~ (all_104_1_168 = 0))))
% 28.03/7.31 |
% 28.03/7.31 | Instantiating formula (21) with all_104_1_168, all_1_2_2, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_104_1_168, convergent_lines(all_1_4_4, all_1_5_5) = 0, yields:
% 28.03/7.31 | (657) ? [v0] : ? [v1] : ? [v2] : (intersection_point(all_1_4_4, all_1_5_5) = v1 & apart_point_and_line(all_1_2_2, all_1_5_5) = v0 & distinct_points(all_1_2_2, v1) = v2 & (v2 = 0 | ( ~ (v0 = 0) & ~ (all_104_1_168 = 0))))
% 28.03/7.31 |
% 28.03/7.31 | Instantiating formula (10) with 0, all_1_2_2, all_104_0_167, all_1_2_2 and discharging atoms distinct_points(all_1_2_2, all_104_0_167) = 0, yields:
% 28.03/7.31 | (658) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_2_2, all_104_0_167) = 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))
% 28.03/7.31 |
% 28.03/7.31 | Instantiating formula (36) with all_104_1_168, all_104_1_168, all_1_4_4, all_1_4_4, all_104_0_167, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_104_1_168, distinct_points(all_1_2_2, all_104_0_167) = 0, yields:
% 28.03/7.31 | (659) all_104_1_168 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_104_0_167, all_1_4_4) = v2 & apart_point_and_line(all_104_0_167, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_1_4_4) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 28.03/7.31 |
% 28.03/7.31 | Instantiating formula (3) with all_1_3_3, all_1_4_4, all_104_0_167, all_1_2_2 and discharging atoms distinct_lines(all_1_4_4, all_1_3_3) = 0, distinct_points(all_1_2_2, all_104_0_167) = 0, yields:
% 28.03/7.31 | (660) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_104_0_167, all_1_3_3) = v3 & apart_point_and_line(all_104_0_167, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v1 & apart_point_and_line(all_1_2_2, all_1_4_4) = v0 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0))
% 28.03/7.31 |
% 28.03/7.31 | Instantiating formula (3) with all_1_5_5, all_1_4_4, all_104_0_167, all_1_2_2 and discharging atoms distinct_lines(all_1_4_4, all_1_5_5) = 0, distinct_points(all_1_2_2, all_104_0_167) = 0, yields:
% 28.03/7.31 | (661) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_104_0_167, all_1_4_4) = v2 & apart_point_and_line(all_104_0_167, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v0 & apart_point_and_line(all_1_2_2, all_1_5_5) = v1 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0))
% 28.03/7.31 |
% 28.03/7.31 | Instantiating formula (3) with all_1_4_4, all_1_5_5, all_104_0_167, all_1_2_2 and discharging atoms distinct_lines(all_1_5_5, all_1_4_4) = 0, distinct_points(all_1_2_2, all_104_0_167) = 0, yields:
% 28.03/7.31 | (662) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_104_0_167, all_1_4_4) = v3 & apart_point_and_line(all_104_0_167, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v1 & apart_point_and_line(all_1_2_2, all_1_5_5) = v0 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0))
% 28.03/7.31 |
% 28.03/7.31 | Instantiating (662) with all_127_0_169, all_127_1_170, all_127_2_171, all_127_3_172 yields:
% 28.03/7.31 | (663) apart_point_and_line(all_104_0_167, all_1_4_4) = all_127_0_169 & apart_point_and_line(all_104_0_167, all_1_5_5) = all_127_1_170 & apart_point_and_line(all_1_2_2, all_1_4_4) = all_127_2_171 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_127_3_172 & (all_127_0_169 = 0 | all_127_1_170 = 0 | all_127_2_171 = 0 | all_127_3_172 = 0)
% 28.03/7.31 |
% 28.03/7.31 | Applying alpha-rule on (663) yields:
% 28.03/7.31 | (664) apart_point_and_line(all_104_0_167, all_1_5_5) = all_127_1_170
% 28.03/7.31 | (665) apart_point_and_line(all_1_2_2, all_1_4_4) = all_127_2_171
% 28.03/7.31 | (666) apart_point_and_line(all_104_0_167, all_1_4_4) = all_127_0_169
% 28.03/7.31 | (667) all_127_0_169 = 0 | all_127_1_170 = 0 | all_127_2_171 = 0 | all_127_3_172 = 0
% 28.03/7.31 | (668) apart_point_and_line(all_1_2_2, all_1_5_5) = all_127_3_172
% 28.03/7.31 |
% 28.03/7.31 | Instantiating (661) with all_129_0_173, all_129_1_174, all_129_2_175, all_129_3_176 yields:
% 28.03/7.31 | (669) apart_point_and_line(all_104_0_167, all_1_4_4) = all_129_1_174 & apart_point_and_line(all_104_0_167, all_1_5_5) = all_129_0_173 & apart_point_and_line(all_1_2_2, all_1_4_4) = all_129_3_176 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_129_2_175 & (all_129_0_173 = 0 | all_129_1_174 = 0 | all_129_2_175 = 0 | all_129_3_176 = 0)
% 28.03/7.31 |
% 28.03/7.31 | Applying alpha-rule on (669) yields:
% 28.03/7.31 | (670) apart_point_and_line(all_1_2_2, all_1_4_4) = all_129_3_176
% 28.03/7.31 | (671) apart_point_and_line(all_1_2_2, all_1_5_5) = all_129_2_175
% 28.03/7.31 | (672) all_129_0_173 = 0 | all_129_1_174 = 0 | all_129_2_175 = 0 | all_129_3_176 = 0
% 28.03/7.31 | (673) apart_point_and_line(all_104_0_167, all_1_4_4) = all_129_1_174
% 28.03/7.31 | (674) apart_point_and_line(all_104_0_167, all_1_5_5) = all_129_0_173
% 28.03/7.31 |
% 28.03/7.31 | Instantiating (658) with all_131_0_177, all_131_1_178, all_131_2_179 yields:
% 28.03/7.31 | (675) line_connecting(all_1_2_2, all_104_0_167) = all_131_2_179 & apart_point_and_line(all_1_2_2, all_131_2_179) = all_131_1_178 & distinct_points(all_1_2_2, all_1_2_2) = all_131_0_177 & ( ~ (all_131_1_178 = 0) | all_131_0_177 = 0)
% 28.03/7.31 |
% 28.03/7.31 | Applying alpha-rule on (675) yields:
% 28.03/7.31 | (676) line_connecting(all_1_2_2, all_104_0_167) = all_131_2_179
% 28.03/7.31 | (677) apart_point_and_line(all_1_2_2, all_131_2_179) = all_131_1_178
% 28.03/7.31 | (678) distinct_points(all_1_2_2, all_1_2_2) = all_131_0_177
% 28.03/7.31 | (679) ~ (all_131_1_178 = 0) | all_131_0_177 = 0
% 28.03/7.31 |
% 28.03/7.31 | Instantiating (660) with all_133_0_180, all_133_1_181, all_133_2_182, all_133_3_183 yields:
% 28.03/7.31 | (680) apart_point_and_line(all_104_0_167, all_1_3_3) = all_133_0_180 & apart_point_and_line(all_104_0_167, all_1_4_4) = all_133_1_181 & apart_point_and_line(all_1_2_2, all_1_3_3) = all_133_2_182 & apart_point_and_line(all_1_2_2, all_1_4_4) = all_133_3_183 & (all_133_0_180 = 0 | all_133_1_181 = 0 | all_133_2_182 = 0 | all_133_3_183 = 0)
% 28.03/7.31 |
% 28.03/7.31 | Applying alpha-rule on (680) yields:
% 28.03/7.31 | (681) apart_point_and_line(all_1_2_2, all_1_3_3) = all_133_2_182
% 28.03/7.31 | (682) apart_point_and_line(all_1_2_2, all_1_4_4) = all_133_3_183
% 28.03/7.31 | (683) apart_point_and_line(all_104_0_167, all_1_3_3) = all_133_0_180
% 28.03/7.31 | (684) apart_point_and_line(all_104_0_167, all_1_4_4) = all_133_1_181
% 28.03/7.31 | (685) all_133_0_180 = 0 | all_133_1_181 = 0 | all_133_2_182 = 0 | all_133_3_183 = 0
% 28.03/7.31 |
% 28.03/7.31 | Instantiating (657) with all_135_0_184, all_135_1_185, all_135_2_186 yields:
% 28.03/7.31 | (686) intersection_point(all_1_4_4, all_1_5_5) = all_135_1_185 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_135_2_186 & distinct_points(all_1_2_2, all_135_1_185) = all_135_0_184 & (all_135_0_184 = 0 | ( ~ (all_135_2_186 = 0) & ~ (all_104_1_168 = 0)))
% 28.03/7.31 |
% 28.03/7.31 | Applying alpha-rule on (686) yields:
% 28.03/7.31 | (687) intersection_point(all_1_4_4, all_1_5_5) = all_135_1_185
% 28.03/7.31 | (688) apart_point_and_line(all_1_2_2, all_1_5_5) = all_135_2_186
% 28.03/7.31 | (689) distinct_points(all_1_2_2, all_135_1_185) = all_135_0_184
% 28.03/7.31 | (690) all_135_0_184 = 0 | ( ~ (all_135_2_186 = 0) & ~ (all_104_1_168 = 0))
% 28.03/7.31 |
% 28.03/7.31 | Instantiating (656) with all_137_0_187, all_137_1_188, all_137_2_189 yields:
% 28.03/7.31 | (691) intersection_point(all_1_5_5, all_1_4_4) = all_137_1_188 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_137_2_189 & distinct_points(all_1_2_2, all_137_1_188) = all_137_0_187 & (all_137_0_187 = 0 | ( ~ (all_137_2_189 = 0) & ~ (all_104_1_168 = 0)))
% 28.03/7.31 |
% 28.03/7.31 | Applying alpha-rule on (691) yields:
% 28.03/7.31 | (692) intersection_point(all_1_5_5, all_1_4_4) = all_137_1_188
% 28.03/7.31 | (693) apart_point_and_line(all_1_2_2, all_1_5_5) = all_137_2_189
% 28.03/7.31 | (694) distinct_points(all_1_2_2, all_137_1_188) = all_137_0_187
% 28.03/7.31 | (695) all_137_0_187 = 0 | ( ~ (all_137_2_189 = 0) & ~ (all_104_1_168 = 0))
% 28.03/7.31 |
% 28.03/7.31 | Instantiating (653) with all_139_0_190, all_139_1_191, all_139_2_192 yields:
% 28.03/7.31 | (696) intersection_point(all_1_3_3, all_1_4_4) = all_139_1_191 & convergent_lines(all_1_3_3, all_1_4_4) = all_139_2_192 & distinct_points(all_1_2_2, all_139_1_191) = all_139_0_190 & ( ~ (all_139_2_192 = 0) | all_139_0_190 = 0)
% 28.03/7.31 |
% 28.03/7.31 | Applying alpha-rule on (696) yields:
% 28.03/7.31 | (697) intersection_point(all_1_3_3, all_1_4_4) = all_139_1_191
% 28.03/7.31 | (698) convergent_lines(all_1_3_3, all_1_4_4) = all_139_2_192
% 28.03/7.31 | (699) distinct_points(all_1_2_2, all_139_1_191) = all_139_0_190
% 28.03/7.31 | (700) ~ (all_139_2_192 = 0) | all_139_0_190 = 0
% 28.03/7.31 |
% 28.03/7.31 | Instantiating (655) with all_141_0_193, all_141_1_194, all_141_2_195 yields:
% 28.03/7.31 | (701) apart_point_and_line(all_1_2_2, all_1_5_5) = all_141_1_194 & convergent_lines(all_1_5_5, all_1_4_4) = all_141_2_195 & distinct_points(all_1_2_2, all_1_2_2) = all_141_0_193 & ( ~ (all_141_2_195 = 0) | all_141_0_193 = 0 | ( ~ (all_141_1_194 = 0) & ~ (all_104_1_168 = 0)))
% 28.03/7.31 |
% 28.03/7.31 | Applying alpha-rule on (701) yields:
% 28.03/7.31 | (702) apart_point_and_line(all_1_2_2, all_1_5_5) = all_141_1_194
% 28.03/7.31 | (703) convergent_lines(all_1_5_5, all_1_4_4) = all_141_2_195
% 28.03/7.31 | (704) distinct_points(all_1_2_2, all_1_2_2) = all_141_0_193
% 28.03/7.31 | (705) ~ (all_141_2_195 = 0) | all_141_0_193 = 0 | ( ~ (all_141_1_194 = 0) & ~ (all_104_1_168 = 0))
% 28.03/7.32 |
% 28.03/7.32 +-Applying beta-rule and splitting (652), into two cases.
% 28.03/7.32 |-Branch one:
% 28.03/7.32 | (706) distinct_lines(all_1_3_3, all_1_4_4) = 0
% 28.03/7.32 |
% 28.03/7.32 +-Applying beta-rule and splitting (654), into two cases.
% 28.03/7.32 |-Branch one:
% 28.03/7.32 | (707) all_104_1_168 = 0
% 28.03/7.32 |
% 28.03/7.32 | Equations (707) can reduce 651 to:
% 28.03/7.32 | (79) $false
% 28.03/7.32 |
% 28.03/7.32 |-The branch is then unsatisfiable
% 28.03/7.32 |-Branch two:
% 28.03/7.32 | (651) ~ (all_104_1_168 = 0)
% 28.03/7.32 | (710) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.32 |
% 28.03/7.32 | Instantiating (710) with all_154_0_196, all_154_1_197, all_154_2_198, all_154_3_199 yields:
% 28.03/7.32 | (711) apart_point_and_line(all_1_2_2, all_1_4_4) = all_154_0_196 & apart_point_and_line(all_1_2_2, all_1_4_4) = all_154_1_197 & distinct_lines(all_1_4_4, all_1_4_4) = all_154_2_198 & distinct_points(all_1_2_2, all_1_2_2) = all_154_3_199 & ( ~ (all_154_2_198 = 0) | ~ (all_154_3_199 = 0) | all_154_0_196 = 0 | all_154_1_197 = 0)
% 28.03/7.32 |
% 28.03/7.32 | Applying alpha-rule on (711) yields:
% 28.03/7.32 | (712) apart_point_and_line(all_1_2_2, all_1_4_4) = all_154_0_196
% 28.03/7.32 | (713) apart_point_and_line(all_1_2_2, all_1_4_4) = all_154_1_197
% 28.03/7.32 | (714) distinct_points(all_1_2_2, all_1_2_2) = all_154_3_199
% 28.03/7.32 | (715) distinct_lines(all_1_4_4, all_1_4_4) = all_154_2_198
% 28.03/7.32 | (716) ~ (all_154_2_198 = 0) | ~ (all_154_3_199 = 0) | all_154_0_196 = 0 | all_154_1_197 = 0
% 28.03/7.32 |
% 28.03/7.32 +-Applying beta-rule and splitting (659), into two cases.
% 28.03/7.32 |-Branch one:
% 28.03/7.32 | (707) all_104_1_168 = 0
% 28.03/7.32 |
% 28.03/7.32 | Equations (707) can reduce 651 to:
% 28.03/7.32 | (79) $false
% 28.03/7.32 |
% 28.03/7.32 |-The branch is then unsatisfiable
% 28.03/7.32 |-Branch two:
% 28.03/7.32 | (651) ~ (all_104_1_168 = 0)
% 28.03/7.32 | (720) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_104_0_167, all_1_4_4) = v2 & apart_point_and_line(all_104_0_167, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_1_4_4) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 28.03/7.32 |
% 28.03/7.32 | Instantiating (720) with all_159_0_200, all_159_1_201, all_159_2_202 yields:
% 28.03/7.32 | (721) apart_point_and_line(all_104_0_167, all_1_4_4) = all_159_0_200 & apart_point_and_line(all_104_0_167, all_1_4_4) = all_159_1_201 & distinct_lines(all_1_4_4, all_1_4_4) = all_159_2_202 & ( ~ (all_159_2_202 = 0) | all_159_0_200 = 0 | all_159_1_201 = 0)
% 28.03/7.32 |
% 28.03/7.32 | Applying alpha-rule on (721) yields:
% 28.03/7.32 | (722) apart_point_and_line(all_104_0_167, all_1_4_4) = all_159_0_200
% 28.03/7.32 | (723) apart_point_and_line(all_104_0_167, all_1_4_4) = all_159_1_201
% 28.03/7.32 | (724) distinct_lines(all_1_4_4, all_1_4_4) = all_159_2_202
% 28.03/7.32 | (725) ~ (all_159_2_202 = 0) | all_159_0_200 = 0 | all_159_1_201 = 0
% 28.03/7.32 |
% 28.03/7.32 | Instantiating formula (45) with all_1_5_5, all_1_4_4, all_137_1_188, all_1_2_2 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_137_1_188, intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2, yields:
% 28.03/7.32 | (726) all_137_1_188 = all_1_2_2
% 28.03/7.32 |
% 28.03/7.32 | Instantiating formula (26) with all_104_0_167, all_1_4_4, all_159_1_201, all_159_0_200 and discharging atoms apart_point_and_line(all_104_0_167, all_1_4_4) = all_159_0_200, apart_point_and_line(all_104_0_167, all_1_4_4) = all_159_1_201, yields:
% 28.03/7.32 | (727) all_159_0_200 = all_159_1_201
% 28.03/7.32 |
% 28.03/7.32 | Instantiating formula (26) with all_104_0_167, all_1_4_4, all_133_1_181, all_159_1_201 and discharging atoms apart_point_and_line(all_104_0_167, all_1_4_4) = all_159_1_201, apart_point_and_line(all_104_0_167, all_1_4_4) = all_133_1_181, yields:
% 28.03/7.32 | (728) all_159_1_201 = all_133_1_181
% 28.03/7.32 |
% 28.03/7.32 | Instantiating formula (26) with all_104_0_167, all_1_4_4, all_129_1_174, all_133_1_181 and discharging atoms apart_point_and_line(all_104_0_167, all_1_4_4) = all_133_1_181, apart_point_and_line(all_104_0_167, all_1_4_4) = all_129_1_174, yields:
% 28.03/7.32 | (729) all_133_1_181 = all_129_1_174
% 28.03/7.32 |
% 28.03/7.32 | Instantiating formula (26) with all_104_0_167, all_1_4_4, all_127_0_169, all_159_0_200 and discharging atoms apart_point_and_line(all_104_0_167, all_1_4_4) = all_159_0_200, apart_point_and_line(all_104_0_167, all_1_4_4) = all_127_0_169, yields:
% 28.03/7.32 | (730) all_159_0_200 = all_127_0_169
% 28.03/7.32 |
% 28.03/7.32 | Instantiating formula (26) with all_104_0_167, all_1_5_5, all_127_1_170, all_129_0_173 and discharging atoms apart_point_and_line(all_104_0_167, all_1_5_5) = all_129_0_173, apart_point_and_line(all_104_0_167, all_1_5_5) = all_127_1_170, yields:
% 28.03/7.32 | (731) all_129_0_173 = all_127_1_170
% 28.03/7.32 |
% 28.03/7.32 | Instantiating formula (26) with all_1_2_2, all_1_3_3, all_133_2_182, 0 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = all_133_2_182, apart_point_and_line(all_1_2_2, all_1_3_3) = 0, yields:
% 28.03/7.32 | (732) all_133_2_182 = 0
% 28.03/7.32 |
% 28.03/7.32 | Instantiating formula (26) with all_1_2_2, all_1_4_4, all_154_0_196, all_104_1_168 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_154_0_196, apart_point_and_line(all_1_2_2, all_1_4_4) = all_104_1_168, yields:
% 28.03/7.32 | (733) all_154_0_196 = all_104_1_168
% 28.03/7.32 |
% 28.03/7.32 | Instantiating formula (26) with all_1_2_2, all_1_4_4, all_154_1_197, all_154_0_196 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_154_0_196, apart_point_and_line(all_1_2_2, all_1_4_4) = all_154_1_197, yields:
% 28.03/7.32 | (734) all_154_0_196 = all_154_1_197
% 28.03/7.32 |
% 28.03/7.32 | Instantiating formula (26) with all_1_2_2, all_1_4_4, all_133_3_183, all_154_1_197 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_154_1_197, apart_point_and_line(all_1_2_2, all_1_4_4) = all_133_3_183, yields:
% 28.03/7.32 | (735) all_154_1_197 = all_133_3_183
% 28.03/7.32 |
% 28.03/7.32 | Instantiating formula (26) with all_1_2_2, all_1_4_4, all_129_3_176, all_154_1_197 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_154_1_197, apart_point_and_line(all_1_2_2, all_1_4_4) = all_129_3_176, yields:
% 28.03/7.32 | (736) all_154_1_197 = all_129_3_176
% 28.03/7.32 |
% 28.03/7.32 | Instantiating formula (26) with all_1_2_2, all_1_4_4, all_127_2_171, all_133_3_183 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_133_3_183, apart_point_and_line(all_1_2_2, all_1_4_4) = all_127_2_171, yields:
% 28.03/7.32 | (737) all_133_3_183 = all_127_2_171
% 28.03/7.32 |
% 28.03/7.32 | Using (665) and (106) yields:
% 28.03/7.32 | (738) ~ (all_127_2_171 = 0)
% 28.03/7.32 |
% 28.03/7.32 | Instantiating formula (26) with all_1_2_2, all_1_5_5, all_137_2_189, all_141_1_194 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_141_1_194, apart_point_and_line(all_1_2_2, all_1_5_5) = all_137_2_189, yields:
% 28.03/7.32 | (739) all_141_1_194 = all_137_2_189
% 28.03/7.32 |
% 28.03/7.32 | Instantiating formula (26) with all_1_2_2, all_1_5_5, all_135_2_186, all_137_2_189 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_137_2_189, apart_point_and_line(all_1_2_2, all_1_5_5) = all_135_2_186, yields:
% 28.03/7.32 | (740) all_137_2_189 = all_135_2_186
% 28.03/7.32 |
% 28.03/7.32 | Instantiating formula (26) with all_1_2_2, all_1_5_5, all_129_2_175, all_141_1_194 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_141_1_194, apart_point_and_line(all_1_2_2, all_1_5_5) = all_129_2_175, yields:
% 28.03/7.32 | (741) all_141_1_194 = all_129_2_175
% 28.03/7.32 |
% 28.03/7.32 | Using (671) and (97) yields:
% 28.03/7.32 | (742) ~ (all_129_2_175 = 0)
% 28.03/7.32 |
% 28.03/7.32 | Instantiating formula (26) with all_1_2_2, all_1_5_5, all_127_3_172, all_135_2_186 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_135_2_186, apart_point_and_line(all_1_2_2, all_1_5_5) = all_127_3_172, yields:
% 28.03/7.32 | (743) all_135_2_186 = all_127_3_172
% 28.03/7.32 |
% 28.03/7.32 | Instantiating formula (27) with all_1_5_5, all_1_4_4, all_141_2_195, 0 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = all_141_2_195, convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 28.03/7.32 | (744) all_141_2_195 = 0
% 28.03/7.32 |
% 28.03/7.32 | Instantiating formula (16) with all_1_2_2, all_1_2_2, all_141_0_193, all_154_3_199 and discharging atoms distinct_points(all_1_2_2, all_1_2_2) = all_154_3_199, distinct_points(all_1_2_2, all_1_2_2) = all_141_0_193, yields:
% 28.03/7.32 | (745) all_154_3_199 = all_141_0_193
% 28.03/7.32 |
% 28.03/7.32 | Using (704) and (105) yields:
% 28.03/7.32 | (746) ~ (all_141_0_193 = 0)
% 28.03/7.32 |
% 28.03/7.32 | Instantiating formula (16) with all_1_2_2, all_1_2_2, all_131_0_177, all_154_3_199 and discharging atoms distinct_points(all_1_2_2, all_1_2_2) = all_154_3_199, distinct_points(all_1_2_2, all_1_2_2) = all_131_0_177, yields:
% 28.03/7.32 | (747) all_154_3_199 = all_131_0_177
% 28.03/7.32 |
% 28.03/7.32 | Combining equations (727,730) yields a new equation:
% 28.03/7.32 | (748) all_159_1_201 = all_127_0_169
% 28.03/7.32 |
% 28.03/7.32 | Simplifying 748 yields:
% 28.03/7.32 | (749) all_159_1_201 = all_127_0_169
% 28.03/7.32 |
% 28.03/7.32 | Combining equations (728,749) yields a new equation:
% 28.03/7.32 | (750) all_133_1_181 = all_127_0_169
% 28.03/7.32 |
% 28.03/7.32 | Simplifying 750 yields:
% 28.03/7.32 | (751) all_133_1_181 = all_127_0_169
% 28.03/7.32 |
% 28.03/7.32 | Combining equations (734,733) yields a new equation:
% 28.03/7.32 | (752) all_154_1_197 = all_104_1_168
% 28.03/7.32 |
% 28.03/7.32 | Simplifying 752 yields:
% 28.03/7.32 | (753) all_154_1_197 = all_104_1_168
% 28.03/7.32 |
% 28.03/7.32 | Combining equations (753,736) yields a new equation:
% 28.03/7.32 | (754) all_129_3_176 = all_104_1_168
% 28.03/7.32 |
% 28.03/7.32 | Combining equations (735,736) yields a new equation:
% 28.03/7.32 | (755) all_133_3_183 = all_129_3_176
% 28.03/7.32 |
% 28.03/7.32 | Simplifying 755 yields:
% 28.03/7.32 | (756) all_133_3_183 = all_129_3_176
% 28.03/7.32 |
% 28.03/7.32 | Combining equations (745,747) yields a new equation:
% 28.03/7.32 | (757) all_141_0_193 = all_131_0_177
% 28.03/7.32 |
% 28.03/7.32 | Simplifying 757 yields:
% 28.03/7.32 | (758) all_141_0_193 = all_131_0_177
% 28.03/7.32 |
% 28.03/7.32 | Combining equations (739,741) yields a new equation:
% 28.03/7.32 | (759) all_137_2_189 = all_129_2_175
% 28.03/7.32 |
% 28.03/7.32 | Simplifying 759 yields:
% 28.03/7.32 | (760) all_137_2_189 = all_129_2_175
% 28.03/7.32 |
% 28.03/7.32 | Combining equations (740,760) yields a new equation:
% 28.03/7.32 | (761) all_135_2_186 = all_129_2_175
% 28.03/7.32 |
% 28.03/7.32 | Simplifying 761 yields:
% 28.03/7.32 | (762) all_135_2_186 = all_129_2_175
% 28.03/7.32 |
% 28.03/7.32 | Combining equations (743,762) yields a new equation:
% 28.03/7.32 | (763) all_129_2_175 = all_127_3_172
% 28.03/7.32 |
% 28.03/7.32 | Combining equations (751,729) yields a new equation:
% 28.03/7.32 | (764) all_129_1_174 = all_127_0_169
% 28.03/7.32 |
% 28.03/7.32 | Combining equations (756,737) yields a new equation:
% 28.03/7.32 | (765) all_129_3_176 = all_127_2_171
% 28.03/7.32 |
% 28.03/7.32 | Simplifying 765 yields:
% 28.03/7.32 | (766) all_129_3_176 = all_127_2_171
% 28.03/7.32 |
% 28.03/7.32 | Combining equations (766,754) yields a new equation:
% 28.03/7.32 | (767) all_127_2_171 = all_104_1_168
% 28.03/7.32 |
% 28.03/7.32 | Simplifying 767 yields:
% 28.03/7.32 | (768) all_127_2_171 = all_104_1_168
% 28.03/7.32 |
% 28.03/7.32 | Equations (758) can reduce 746 to:
% 28.03/7.32 | (769) ~ (all_131_0_177 = 0)
% 28.03/7.33 |
% 28.03/7.33 | Equations (763) can reduce 742 to:
% 28.03/7.33 | (770) ~ (all_127_3_172 = 0)
% 28.03/7.33 |
% 28.03/7.33 | Equations (768) can reduce 738 to:
% 28.03/7.33 | (651) ~ (all_104_1_168 = 0)
% 28.03/7.33 |
% 28.03/7.33 | From (726) and (692) follows:
% 28.03/7.33 | (49) intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2
% 28.03/7.33 |
% 28.03/7.33 | From (764) and (673) follows:
% 28.03/7.33 | (666) apart_point_and_line(all_104_0_167, all_1_4_4) = all_127_0_169
% 28.03/7.33 |
% 28.03/7.33 | From (731) and (674) follows:
% 28.03/7.33 | (664) apart_point_and_line(all_104_0_167, all_1_5_5) = all_127_1_170
% 28.03/7.33 |
% 28.03/7.33 | From (732) and (681) follows:
% 28.03/7.33 | (51) apart_point_and_line(all_1_2_2, all_1_3_3) = 0
% 28.03/7.33 |
% 28.03/7.33 | From (768) and (665) follows:
% 28.03/7.33 | (646) apart_point_and_line(all_1_2_2, all_1_4_4) = all_104_1_168
% 28.03/7.33 |
% 28.03/7.33 | From (763) and (671) follows:
% 28.03/7.33 | (668) apart_point_and_line(all_1_2_2, all_1_5_5) = all_127_3_172
% 28.03/7.33 |
% 28.03/7.33 | From (744) and (703) follows:
% 28.03/7.33 | (52) convergent_lines(all_1_5_5, all_1_4_4) = 0
% 28.03/7.33 |
% 28.03/7.33 +-Applying beta-rule and splitting (679), into two cases.
% 28.03/7.33 |-Branch one:
% 28.03/7.33 | (779) ~ (all_131_1_178 = 0)
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (19) with all_139_1_191, 0, all_1_2_2, all_1_4_4, all_1_3_3 and discharging atoms intersection_point(all_1_3_3, all_1_4_4) = all_139_1_191, apart_point_and_line(all_1_2_2, all_1_3_3) = 0, yields:
% 28.03/7.33 | (780) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v1 & convergent_lines(all_1_3_3, all_1_4_4) = v0 & distinct_points(all_1_2_2, all_139_1_191) = v2 & ( ~ (v0 = 0) | v2 = 0))
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (19) with all_104_0_167, all_127_0_169, all_104_0_167, all_1_3_3, all_1_4_4 and discharging atoms intersection_point(all_1_4_4, all_1_3_3) = all_104_0_167, apart_point_and_line(all_104_0_167, all_1_4_4) = all_127_0_169, yields:
% 28.03/7.33 | (781) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_104_0_167, all_1_3_3) = v1 & convergent_lines(all_1_4_4, all_1_3_3) = v0 & distinct_points(all_104_0_167, all_104_0_167) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_127_0_169 = 0))))
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (2) with all_1_2_2, all_127_0_169, all_104_0_167, 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_104_0_167, all_1_4_4) = all_127_0_169, yields:
% 28.03/7.33 | (782) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_104_0_167, all_1_5_5) = v1 & convergent_lines(all_1_5_5, all_1_4_4) = v0 & distinct_points(all_104_0_167, all_1_2_2) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_127_0_169 = 0))))
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (2) with all_139_1_191, all_127_0_169, all_104_0_167, all_1_4_4, all_1_3_3 and discharging atoms intersection_point(all_1_3_3, all_1_4_4) = all_139_1_191, apart_point_and_line(all_104_0_167, all_1_4_4) = all_127_0_169, yields:
% 28.03/7.33 | (783) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_104_0_167, all_1_3_3) = v1 & convergent_lines(all_1_3_3, all_1_4_4) = v0 & distinct_points(all_104_0_167, all_139_1_191) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_127_0_169 = 0))))
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (19) with all_135_1_185, all_127_0_169, all_104_0_167, all_1_5_5, all_1_4_4 and discharging atoms intersection_point(all_1_4_4, all_1_5_5) = all_135_1_185, apart_point_and_line(all_104_0_167, all_1_4_4) = all_127_0_169, yields:
% 28.03/7.33 | (784) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_104_0_167, all_1_5_5) = v1 & convergent_lines(all_1_4_4, all_1_5_5) = v0 & distinct_points(all_104_0_167, all_135_1_185) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_127_0_169 = 0))))
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (21) with all_127_0_169, all_104_0_167, all_1_3_3, all_1_4_4 and discharging atoms apart_point_and_line(all_104_0_167, all_1_4_4) = all_127_0_169, convergent_lines(all_1_4_4, all_1_3_3) = 0, yields:
% 28.03/7.33 | (785) ? [v0] : ? [v1] : ? [v2] : (intersection_point(all_1_4_4, all_1_3_3) = v1 & apart_point_and_line(all_104_0_167, all_1_3_3) = v0 & distinct_points(all_104_0_167, v1) = v2 & (v2 = 0 | ( ~ (v0 = 0) & ~ (all_127_0_169 = 0))))
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (21) with all_127_0_169, all_104_0_167, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_104_0_167, all_1_4_4) = all_127_0_169, convergent_lines(all_1_4_4, all_1_5_5) = 0, yields:
% 28.03/7.33 | (786) ? [v0] : ? [v1] : ? [v2] : (intersection_point(all_1_4_4, all_1_5_5) = v1 & apart_point_and_line(all_104_0_167, all_1_5_5) = v0 & distinct_points(all_104_0_167, v1) = v2 & (v2 = 0 | ( ~ (v0 = 0) & ~ (all_127_0_169 = 0))))
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (46) with all_127_0_169, all_104_0_167, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_104_0_167, all_1_4_4) = all_127_0_169, convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 28.03/7.33 | (787) ? [v0] : ? [v1] : ? [v2] : (intersection_point(all_1_5_5, all_1_4_4) = v1 & apart_point_and_line(all_104_0_167, all_1_5_5) = v0 & distinct_points(all_104_0_167, v1) = v2 & (v2 = 0 | ( ~ (v0 = 0) & ~ (all_127_0_169 = 0))))
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (37) with all_1_1_1, all_1_3_3, all_1_5_5, all_104_0_167 and discharging atoms distinct_lines(all_1_5_5, all_1_3_3) = all_1_1_1, yields:
% 28.03/7.33 | (788) all_1_1_1 = 0 | ~ (apart_point_and_line(all_104_0_167, all_1_5_5) = 0) | apart_point_and_line(all_104_0_167, all_1_3_3) = 0
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (36) with all_131_1_178, all_104_1_168, all_131_2_179, all_1_4_4, all_104_0_167, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_131_2_179) = all_131_1_178, apart_point_and_line(all_1_2_2, all_1_4_4) = all_104_1_168, distinct_points(all_1_2_2, all_104_0_167) = 0, yields:
% 28.03/7.33 | (789) all_131_1_178 = 0 | all_104_1_168 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_104_0_167, all_131_2_179) = v2 & apart_point_and_line(all_104_0_167, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_131_2_179) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (36) with all_104_1_168, all_131_1_178, all_1_4_4, all_131_2_179, all_104_0_167, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_131_2_179) = all_131_1_178, apart_point_and_line(all_1_2_2, all_1_4_4) = all_104_1_168, distinct_points(all_1_2_2, all_104_0_167) = 0, yields:
% 28.03/7.33 | (790) all_131_1_178 = 0 | all_104_1_168 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_104_0_167, all_131_2_179) = v1 & apart_point_and_line(all_104_0_167, all_1_4_4) = v2 & distinct_lines(all_131_2_179, all_1_4_4) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (14) with all_131_1_178, all_104_1_168, all_131_2_179, all_1_4_4, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_131_2_179) = all_131_1_178, apart_point_and_line(all_1_2_2, all_1_4_4) = all_104_1_168, yields:
% 28.03/7.33 | (791) all_131_1_178 = 0 | all_104_1_168 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_131_2_179) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (14) with all_104_1_168, all_131_1_178, all_1_4_4, all_131_2_179, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_131_2_179) = all_131_1_178, apart_point_and_line(all_1_2_2, all_1_4_4) = all_104_1_168, yields:
% 28.03/7.33 | (792) all_131_1_178 = 0 | all_104_1_168 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_131_2_179, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (1) with all_131_1_178, all_104_1_168, all_1_4_4, all_131_2_179, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_131_2_179) = all_131_1_178, apart_point_and_line(all_1_2_2, all_1_4_4) = all_104_1_168, yields:
% 28.03/7.33 | (793) all_131_1_178 = 0 | all_104_1_168 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_131_2_179, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (1) with all_104_1_168, all_131_1_178, all_131_2_179, all_1_4_4, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_131_2_179) = all_131_1_178, apart_point_and_line(all_1_2_2, all_1_4_4) = all_104_1_168, yields:
% 28.03/7.33 | (794) all_131_1_178 = 0 | all_104_1_168 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_131_2_179) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (36) with all_131_1_178, all_131_1_178, all_131_2_179, all_131_2_179, all_104_0_167, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_131_2_179) = all_131_1_178, distinct_points(all_1_2_2, all_104_0_167) = 0, yields:
% 28.03/7.33 | (795) all_131_1_178 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_104_0_167, all_131_2_179) = v2 & apart_point_and_line(all_104_0_167, all_131_2_179) = v1 & distinct_lines(all_131_2_179, all_131_2_179) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (14) with all_131_1_178, all_131_1_178, all_131_2_179, all_131_2_179, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_131_2_179) = all_131_1_178, yields:
% 28.03/7.33 | (796) all_131_1_178 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v3 & apart_point_and_line(all_1_2_2, all_131_2_179) = v2 & distinct_lines(all_131_2_179, all_131_2_179) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (14) with all_127_3_172, all_131_1_178, all_1_5_5, all_131_2_179, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_131_2_179) = all_131_1_178, apart_point_and_line(all_1_2_2, all_1_5_5) = all_127_3_172, yields:
% 28.03/7.33 | (797) all_131_1_178 = 0 | all_127_3_172 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_131_2_179, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (14) with all_131_1_178, all_127_3_172, all_131_2_179, all_1_5_5, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_131_2_179) = all_131_1_178, apart_point_and_line(all_1_2_2, all_1_5_5) = all_127_3_172, yields:
% 28.03/7.33 | (798) all_131_1_178 = 0 | all_127_3_172 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_131_2_179) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (1) with all_127_3_172, all_131_1_178, all_131_2_179, all_1_5_5, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_131_2_179) = all_131_1_178, apart_point_and_line(all_1_2_2, all_1_5_5) = all_127_3_172, yields:
% 28.03/7.33 | (799) all_131_1_178 = 0 | all_127_3_172 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_131_2_179) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (1) with all_131_1_178, all_127_3_172, all_1_5_5, all_131_2_179, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_131_2_179) = all_131_1_178, apart_point_and_line(all_1_2_2, all_1_5_5) = all_127_3_172, yields:
% 28.03/7.33 | (800) all_131_1_178 = 0 | all_127_3_172 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_131_2_179, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (34) with all_139_2_192, all_1_4_4, all_1_3_3, all_1_4_4 and discharging atoms convergent_lines(all_1_3_3, all_1_4_4) = all_139_2_192, convergent_lines(all_1_4_4, all_1_3_3) = 0, yields:
% 28.03/7.33 | (801) all_139_2_192 = 0 | convergent_lines(all_1_4_4, all_1_4_4) = 0
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (21) with 0, all_1_2_2, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = 0, yields:
% 28.03/7.33 | (802) ~ (convergent_lines(all_1_3_3, all_1_4_4) = 0) | ? [v0] : ? [v1] : (intersection_point(all_1_3_3, 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) = 0)
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (46) with all_127_0_169, all_104_0_167, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_104_0_167, all_1_4_4) = all_127_0_169, yields:
% 28.03/7.33 | (803) ~ (convergent_lines(all_1_3_3, all_1_4_4) = 0) | ? [v0] : ? [v1] : ? [v2] : (intersection_point(all_1_3_3, all_1_4_4) = v1 & apart_point_and_line(all_104_0_167, all_1_3_3) = v0 & distinct_points(all_104_0_167, v1) = v2 & (v2 = 0 | ( ~ (v0 = 0) & ~ (all_127_0_169 = 0))))
% 28.03/7.33 |
% 28.03/7.33 | Instantiating formula (3) with all_1_4_4, all_1_3_3, all_104_0_167, all_1_2_2 and discharging atoms distinct_lines(all_1_3_3, all_1_4_4) = 0, distinct_points(all_1_2_2, all_104_0_167) = 0, yields:
% 28.03/7.33 | (804) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_104_0_167, all_1_3_3) = v2 & apart_point_and_line(all_104_0_167, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v0 & apart_point_and_line(all_1_2_2, all_1_4_4) = v1 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0))
% 28.03/7.33 |
% 28.03/7.33 | Instantiating (804) with all_184_0_203, all_184_1_204, all_184_2_205, all_184_3_206 yields:
% 28.03/7.33 | (805) apart_point_and_line(all_104_0_167, all_1_3_3) = all_184_1_204 & apart_point_and_line(all_104_0_167, all_1_4_4) = all_184_0_203 & apart_point_and_line(all_1_2_2, all_1_3_3) = all_184_3_206 & apart_point_and_line(all_1_2_2, all_1_4_4) = all_184_2_205 & (all_184_0_203 = 0 | all_184_1_204 = 0 | all_184_2_205 = 0 | all_184_3_206 = 0)
% 28.03/7.33 |
% 28.03/7.33 | Applying alpha-rule on (805) yields:
% 28.03/7.33 | (806) apart_point_and_line(all_1_2_2, all_1_4_4) = all_184_2_205
% 28.03/7.33 | (807) apart_point_and_line(all_104_0_167, all_1_3_3) = all_184_1_204
% 28.03/7.33 | (808) apart_point_and_line(all_1_2_2, all_1_3_3) = all_184_3_206
% 28.03/7.34 | (809) apart_point_and_line(all_104_0_167, all_1_4_4) = all_184_0_203
% 28.03/7.34 | (810) all_184_0_203 = 0 | all_184_1_204 = 0 | all_184_2_205 = 0 | all_184_3_206 = 0
% 28.03/7.34 |
% 28.03/7.34 | Instantiating (785) with all_202_0_231, all_202_1_232, all_202_2_233 yields:
% 28.03/7.34 | (811) intersection_point(all_1_4_4, all_1_3_3) = all_202_1_232 & apart_point_and_line(all_104_0_167, all_1_3_3) = all_202_2_233 & distinct_points(all_104_0_167, all_202_1_232) = all_202_0_231 & (all_202_0_231 = 0 | ( ~ (all_202_2_233 = 0) & ~ (all_127_0_169 = 0)))
% 28.03/7.34 |
% 28.03/7.34 | Applying alpha-rule on (811) yields:
% 28.03/7.34 | (812) intersection_point(all_1_4_4, all_1_3_3) = all_202_1_232
% 28.03/7.34 | (813) apart_point_and_line(all_104_0_167, all_1_3_3) = all_202_2_233
% 28.03/7.34 | (814) distinct_points(all_104_0_167, all_202_1_232) = all_202_0_231
% 28.03/7.34 | (815) all_202_0_231 = 0 | ( ~ (all_202_2_233 = 0) & ~ (all_127_0_169 = 0))
% 28.03/7.34 |
% 28.03/7.34 | Instantiating (784) with all_204_0_234, all_204_1_235, all_204_2_236 yields:
% 28.03/7.34 | (816) apart_point_and_line(all_104_0_167, all_1_5_5) = all_204_1_235 & convergent_lines(all_1_4_4, all_1_5_5) = all_204_2_236 & distinct_points(all_104_0_167, all_135_1_185) = all_204_0_234 & ( ~ (all_204_2_236 = 0) | all_204_0_234 = 0 | ( ~ (all_204_1_235 = 0) & ~ (all_127_0_169 = 0)))
% 28.03/7.34 |
% 28.03/7.34 | Applying alpha-rule on (816) yields:
% 28.03/7.34 | (817) apart_point_and_line(all_104_0_167, all_1_5_5) = all_204_1_235
% 28.03/7.34 | (818) convergent_lines(all_1_4_4, all_1_5_5) = all_204_2_236
% 28.03/7.34 | (819) distinct_points(all_104_0_167, all_135_1_185) = all_204_0_234
% 28.03/7.34 | (820) ~ (all_204_2_236 = 0) | all_204_0_234 = 0 | ( ~ (all_204_1_235 = 0) & ~ (all_127_0_169 = 0))
% 28.03/7.34 |
% 28.03/7.34 | Instantiating (781) with all_206_0_237, all_206_1_238, all_206_2_239 yields:
% 28.03/7.34 | (821) apart_point_and_line(all_104_0_167, all_1_3_3) = all_206_1_238 & convergent_lines(all_1_4_4, all_1_3_3) = all_206_2_239 & distinct_points(all_104_0_167, all_104_0_167) = all_206_0_237 & ( ~ (all_206_2_239 = 0) | all_206_0_237 = 0 | ( ~ (all_206_1_238 = 0) & ~ (all_127_0_169 = 0)))
% 28.03/7.34 |
% 28.03/7.34 | Applying alpha-rule on (821) yields:
% 28.03/7.34 | (822) apart_point_and_line(all_104_0_167, all_1_3_3) = all_206_1_238
% 28.03/7.34 | (823) convergent_lines(all_1_4_4, all_1_3_3) = all_206_2_239
% 28.03/7.34 | (824) distinct_points(all_104_0_167, all_104_0_167) = all_206_0_237
% 28.03/7.34 | (825) ~ (all_206_2_239 = 0) | all_206_0_237 = 0 | ( ~ (all_206_1_238 = 0) & ~ (all_127_0_169 = 0))
% 28.03/7.34 |
% 28.03/7.34 | Instantiating (783) with all_208_0_240, all_208_1_241, all_208_2_242 yields:
% 28.03/7.34 | (826) apart_point_and_line(all_104_0_167, all_1_3_3) = all_208_1_241 & convergent_lines(all_1_3_3, all_1_4_4) = all_208_2_242 & distinct_points(all_104_0_167, all_139_1_191) = all_208_0_240 & ( ~ (all_208_2_242 = 0) | all_208_0_240 = 0 | ( ~ (all_208_1_241 = 0) & ~ (all_127_0_169 = 0)))
% 28.03/7.34 |
% 28.03/7.34 | Applying alpha-rule on (826) yields:
% 28.03/7.34 | (827) apart_point_and_line(all_104_0_167, all_1_3_3) = all_208_1_241
% 28.03/7.34 | (828) convergent_lines(all_1_3_3, all_1_4_4) = all_208_2_242
% 28.03/7.34 | (829) distinct_points(all_104_0_167, all_139_1_191) = all_208_0_240
% 28.03/7.34 | (830) ~ (all_208_2_242 = 0) | all_208_0_240 = 0 | ( ~ (all_208_1_241 = 0) & ~ (all_127_0_169 = 0))
% 28.03/7.34 |
% 28.03/7.34 | Instantiating (787) with all_212_0_246, all_212_1_247, all_212_2_248 yields:
% 28.03/7.34 | (831) intersection_point(all_1_5_5, all_1_4_4) = all_212_1_247 & apart_point_and_line(all_104_0_167, all_1_5_5) = all_212_2_248 & distinct_points(all_104_0_167, all_212_1_247) = all_212_0_246 & (all_212_0_246 = 0 | ( ~ (all_212_2_248 = 0) & ~ (all_127_0_169 = 0)))
% 28.03/7.34 |
% 28.03/7.34 | Applying alpha-rule on (831) yields:
% 28.03/7.34 | (832) intersection_point(all_1_5_5, all_1_4_4) = all_212_1_247
% 28.03/7.34 | (833) apart_point_and_line(all_104_0_167, all_1_5_5) = all_212_2_248
% 28.03/7.34 | (834) distinct_points(all_104_0_167, all_212_1_247) = all_212_0_246
% 28.03/7.34 | (835) all_212_0_246 = 0 | ( ~ (all_212_2_248 = 0) & ~ (all_127_0_169 = 0))
% 28.03/7.34 |
% 28.03/7.34 | Instantiating (786) with all_214_0_249, all_214_1_250, all_214_2_251 yields:
% 28.03/7.34 | (836) intersection_point(all_1_4_4, all_1_5_5) = all_214_1_250 & apart_point_and_line(all_104_0_167, all_1_5_5) = all_214_2_251 & distinct_points(all_104_0_167, all_214_1_250) = all_214_0_249 & (all_214_0_249 = 0 | ( ~ (all_214_2_251 = 0) & ~ (all_127_0_169 = 0)))
% 28.03/7.34 |
% 28.03/7.34 | Applying alpha-rule on (836) yields:
% 28.03/7.34 | (837) intersection_point(all_1_4_4, all_1_5_5) = all_214_1_250
% 28.03/7.34 | (838) apart_point_and_line(all_104_0_167, all_1_5_5) = all_214_2_251
% 28.03/7.34 | (839) distinct_points(all_104_0_167, all_214_1_250) = all_214_0_249
% 28.03/7.34 | (840) all_214_0_249 = 0 | ( ~ (all_214_2_251 = 0) & ~ (all_127_0_169 = 0))
% 28.03/7.34 |
% 28.03/7.34 | Instantiating (780) with all_216_0_252, all_216_1_253, all_216_2_254 yields:
% 28.03/7.34 | (841) apart_point_and_line(all_1_2_2, all_1_4_4) = all_216_1_253 & convergent_lines(all_1_3_3, all_1_4_4) = all_216_2_254 & distinct_points(all_1_2_2, all_139_1_191) = all_216_0_252 & ( ~ (all_216_2_254 = 0) | all_216_0_252 = 0)
% 28.03/7.34 |
% 28.03/7.34 | Applying alpha-rule on (841) yields:
% 28.03/7.34 | (842) apart_point_and_line(all_1_2_2, all_1_4_4) = all_216_1_253
% 28.03/7.34 | (843) convergent_lines(all_1_3_3, all_1_4_4) = all_216_2_254
% 28.03/7.34 | (844) distinct_points(all_1_2_2, all_139_1_191) = all_216_0_252
% 28.03/7.34 | (845) ~ (all_216_2_254 = 0) | all_216_0_252 = 0
% 28.03/7.34 |
% 28.03/7.34 | Instantiating (782) with all_218_0_255, all_218_1_256, all_218_2_257 yields:
% 28.03/7.34 | (846) apart_point_and_line(all_104_0_167, all_1_5_5) = all_218_1_256 & convergent_lines(all_1_5_5, all_1_4_4) = all_218_2_257 & distinct_points(all_104_0_167, all_1_2_2) = all_218_0_255 & ( ~ (all_218_2_257 = 0) | all_218_0_255 = 0 | ( ~ (all_218_1_256 = 0) & ~ (all_127_0_169 = 0)))
% 28.03/7.34 |
% 28.03/7.34 | Applying alpha-rule on (846) yields:
% 28.03/7.34 | (847) apart_point_and_line(all_104_0_167, all_1_5_5) = all_218_1_256
% 28.03/7.34 | (848) convergent_lines(all_1_5_5, all_1_4_4) = all_218_2_257
% 28.03/7.34 | (849) distinct_points(all_104_0_167, all_1_2_2) = all_218_0_255
% 28.03/7.34 | (850) ~ (all_218_2_257 = 0) | all_218_0_255 = 0 | ( ~ (all_218_1_256 = 0) & ~ (all_127_0_169 = 0))
% 28.03/7.34 |
% 28.03/7.34 +-Applying beta-rule and splitting (795), into two cases.
% 28.03/7.34 |-Branch one:
% 28.03/7.34 | (851) all_131_1_178 = 0
% 28.03/7.34 |
% 28.03/7.34 | Equations (851) can reduce 779 to:
% 28.03/7.34 | (79) $false
% 28.03/7.34 |
% 28.03/7.34 |-The branch is then unsatisfiable
% 28.03/7.34 |-Branch two:
% 28.03/7.34 | (779) ~ (all_131_1_178 = 0)
% 28.03/7.34 | (854) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_104_0_167, all_131_2_179) = v2 & apart_point_and_line(all_104_0_167, all_131_2_179) = v1 & distinct_lines(all_131_2_179, all_131_2_179) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 28.03/7.34 |
% 28.03/7.34 +-Applying beta-rule and splitting (796), into two cases.
% 28.03/7.34 |-Branch one:
% 28.03/7.34 | (851) all_131_1_178 = 0
% 28.03/7.34 |
% 28.03/7.34 | Equations (851) can reduce 779 to:
% 28.03/7.34 | (79) $false
% 28.03/7.34 |
% 28.03/7.34 |-The branch is then unsatisfiable
% 28.03/7.34 |-Branch two:
% 28.03/7.34 | (779) ~ (all_131_1_178 = 0)
% 28.03/7.34 | (858) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v3 & apart_point_and_line(all_1_2_2, all_131_2_179) = v2 & distinct_lines(all_131_2_179, all_131_2_179) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.34 |
% 28.03/7.34 +-Applying beta-rule and splitting (789), into two cases.
% 28.03/7.34 |-Branch one:
% 28.03/7.34 | (851) all_131_1_178 = 0
% 28.03/7.34 |
% 28.03/7.34 | Equations (851) can reduce 779 to:
% 28.03/7.34 | (79) $false
% 28.03/7.34 |
% 28.03/7.34 |-The branch is then unsatisfiable
% 28.03/7.34 |-Branch two:
% 28.03/7.34 | (779) ~ (all_131_1_178 = 0)
% 28.03/7.34 | (862) all_104_1_168 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_104_0_167, all_131_2_179) = v2 & apart_point_and_line(all_104_0_167, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_131_2_179) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 28.03/7.34 |
% 28.03/7.34 +-Applying beta-rule and splitting (790), into two cases.
% 28.03/7.34 |-Branch one:
% 28.03/7.34 | (851) all_131_1_178 = 0
% 28.03/7.34 |
% 28.03/7.34 | Equations (851) can reduce 779 to:
% 28.03/7.34 | (79) $false
% 28.03/7.34 |
% 28.03/7.34 |-The branch is then unsatisfiable
% 28.03/7.34 |-Branch two:
% 28.03/7.34 | (779) ~ (all_131_1_178 = 0)
% 28.03/7.34 | (866) all_104_1_168 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_104_0_167, all_131_2_179) = v1 & apart_point_and_line(all_104_0_167, all_1_4_4) = v2 & distinct_lines(all_131_2_179, all_1_4_4) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 28.03/7.34 |
% 28.03/7.34 +-Applying beta-rule and splitting (791), into two cases.
% 28.03/7.34 |-Branch one:
% 28.03/7.34 | (851) all_131_1_178 = 0
% 28.03/7.34 |
% 28.03/7.34 | Equations (851) can reduce 779 to:
% 28.03/7.34 | (79) $false
% 28.03/7.34 |
% 28.03/7.34 |-The branch is then unsatisfiable
% 28.03/7.34 |-Branch two:
% 28.03/7.34 | (779) ~ (all_131_1_178 = 0)
% 28.03/7.34 | (870) all_104_1_168 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_131_2_179) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.34 |
% 28.03/7.34 +-Applying beta-rule and splitting (792), into two cases.
% 28.03/7.34 |-Branch one:
% 28.03/7.34 | (851) all_131_1_178 = 0
% 28.03/7.34 |
% 28.03/7.34 | Equations (851) can reduce 779 to:
% 28.03/7.34 | (79) $false
% 28.03/7.34 |
% 28.03/7.34 |-The branch is then unsatisfiable
% 28.03/7.34 |-Branch two:
% 28.03/7.34 | (779) ~ (all_131_1_178 = 0)
% 28.03/7.34 | (874) all_104_1_168 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_131_2_179, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.34 |
% 28.03/7.34 +-Applying beta-rule and splitting (793), into two cases.
% 28.03/7.34 |-Branch one:
% 28.03/7.34 | (851) all_131_1_178 = 0
% 28.03/7.34 |
% 28.03/7.34 | Equations (851) can reduce 779 to:
% 28.03/7.34 | (79) $false
% 28.03/7.34 |
% 28.03/7.34 |-The branch is then unsatisfiable
% 28.03/7.34 |-Branch two:
% 28.03/7.34 | (779) ~ (all_131_1_178 = 0)
% 28.03/7.34 | (878) all_104_1_168 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_131_2_179, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.34 |
% 28.03/7.35 +-Applying beta-rule and splitting (794), into two cases.
% 28.03/7.35 |-Branch one:
% 28.03/7.35 | (851) all_131_1_178 = 0
% 28.03/7.35 |
% 28.03/7.35 | Equations (851) can reduce 779 to:
% 28.03/7.35 | (79) $false
% 28.03/7.35 |
% 28.03/7.35 |-The branch is then unsatisfiable
% 28.03/7.35 |-Branch two:
% 28.03/7.35 | (779) ~ (all_131_1_178 = 0)
% 28.03/7.35 | (882) all_104_1_168 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_131_2_179) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.35 |
% 28.03/7.35 +-Applying beta-rule and splitting (797), into two cases.
% 28.03/7.35 |-Branch one:
% 28.03/7.35 | (851) all_131_1_178 = 0
% 28.03/7.35 |
% 28.03/7.35 | Equations (851) can reduce 779 to:
% 28.03/7.35 | (79) $false
% 28.03/7.35 |
% 28.03/7.35 |-The branch is then unsatisfiable
% 28.03/7.35 |-Branch two:
% 28.03/7.35 | (779) ~ (all_131_1_178 = 0)
% 28.03/7.35 | (886) all_127_3_172 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_131_2_179, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.35 |
% 28.03/7.35 +-Applying beta-rule and splitting (798), into two cases.
% 28.03/7.35 |-Branch one:
% 28.03/7.35 | (851) all_131_1_178 = 0
% 28.03/7.35 |
% 28.03/7.35 | Equations (851) can reduce 779 to:
% 28.03/7.35 | (79) $false
% 28.03/7.35 |
% 28.03/7.35 |-The branch is then unsatisfiable
% 28.03/7.35 |-Branch two:
% 28.03/7.35 | (779) ~ (all_131_1_178 = 0)
% 28.03/7.35 | (890) all_127_3_172 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_131_2_179) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.35 |
% 28.03/7.35 +-Applying beta-rule and splitting (799), into two cases.
% 28.03/7.35 |-Branch one:
% 28.03/7.35 | (851) all_131_1_178 = 0
% 28.03/7.35 |
% 28.03/7.35 | Equations (851) can reduce 779 to:
% 28.03/7.35 | (79) $false
% 28.03/7.35 |
% 28.03/7.35 |-The branch is then unsatisfiable
% 28.03/7.35 |-Branch two:
% 28.03/7.35 | (779) ~ (all_131_1_178 = 0)
% 28.03/7.35 | (894) all_127_3_172 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_131_2_179) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.35 |
% 28.03/7.35 +-Applying beta-rule and splitting (800), into two cases.
% 28.03/7.35 |-Branch one:
% 28.03/7.35 | (851) all_131_1_178 = 0
% 28.03/7.35 |
% 28.03/7.35 | Equations (851) can reduce 779 to:
% 28.03/7.35 | (79) $false
% 28.03/7.35 |
% 28.03/7.35 |-The branch is then unsatisfiable
% 28.03/7.35 |-Branch two:
% 28.03/7.35 | (779) ~ (all_131_1_178 = 0)
% 28.03/7.35 | (898) all_127_3_172 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_131_2_179, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.35 |
% 28.03/7.35 +-Applying beta-rule and splitting (801), into two cases.
% 28.03/7.35 |-Branch one:
% 28.03/7.35 | (899) convergent_lines(all_1_4_4, all_1_4_4) = 0
% 28.03/7.35 |
% 28.03/7.35 | Instantiating formula (41) with all_1_4_4 and discharging atoms convergent_lines(all_1_4_4, all_1_4_4) = 0, yields:
% 28.03/7.35 | (202) $false
% 28.03/7.35 |
% 28.03/7.35 |-The branch is then unsatisfiable
% 28.03/7.35 |-Branch two:
% 28.03/7.35 | (901) ~ (convergent_lines(all_1_4_4, all_1_4_4) = 0)
% 28.03/7.35 | (902) all_139_2_192 = 0
% 28.03/7.35 |
% 28.03/7.35 | From (902) and (698) follows:
% 28.03/7.35 | (903) convergent_lines(all_1_3_3, all_1_4_4) = 0
% 28.03/7.35 |
% 28.03/7.35 +-Applying beta-rule and splitting (862), into two cases.
% 28.03/7.35 |-Branch one:
% 28.03/7.35 | (707) all_104_1_168 = 0
% 28.03/7.35 |
% 28.03/7.35 | Equations (707) can reduce 651 to:
% 28.03/7.35 | (79) $false
% 28.03/7.35 |
% 28.03/7.35 |-The branch is then unsatisfiable
% 28.03/7.35 |-Branch two:
% 28.03/7.35 | (651) ~ (all_104_1_168 = 0)
% 28.03/7.35 | (907) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_104_0_167, all_131_2_179) = v2 & apart_point_and_line(all_104_0_167, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_131_2_179) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 28.03/7.35 |
% 28.03/7.35 +-Applying beta-rule and splitting (866), into two cases.
% 28.03/7.35 |-Branch one:
% 28.03/7.35 | (707) all_104_1_168 = 0
% 28.03/7.35 |
% 28.03/7.35 | Equations (707) can reduce 651 to:
% 28.03/7.35 | (79) $false
% 28.03/7.35 |
% 28.03/7.35 |-The branch is then unsatisfiable
% 28.03/7.35 |-Branch two:
% 28.03/7.35 | (651) ~ (all_104_1_168 = 0)
% 28.03/7.35 | (911) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_104_0_167, all_131_2_179) = v1 & apart_point_and_line(all_104_0_167, all_1_4_4) = v2 & distinct_lines(all_131_2_179, all_1_4_4) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 28.03/7.35 |
% 28.03/7.35 +-Applying beta-rule and splitting (870), into two cases.
% 28.03/7.35 |-Branch one:
% 28.03/7.35 | (707) all_104_1_168 = 0
% 28.03/7.35 |
% 28.03/7.35 | Equations (707) can reduce 651 to:
% 28.03/7.35 | (79) $false
% 28.03/7.35 |
% 28.03/7.35 |-The branch is then unsatisfiable
% 28.03/7.35 |-Branch two:
% 28.03/7.35 | (651) ~ (all_104_1_168 = 0)
% 28.03/7.35 | (915) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_131_2_179) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.35 |
% 28.03/7.35 | Instantiating (915) with all_334_0_319, all_334_1_320, all_334_2_321, all_334_3_322 yields:
% 28.03/7.35 | (916) apart_point_and_line(all_1_2_2, all_131_2_179) = all_334_1_320 & apart_point_and_line(all_1_2_2, all_1_4_4) = all_334_0_319 & distinct_lines(all_1_4_4, all_131_2_179) = all_334_2_321 & distinct_points(all_1_2_2, all_1_2_2) = all_334_3_322 & ( ~ (all_334_2_321 = 0) | ~ (all_334_3_322 = 0) | all_334_0_319 = 0 | all_334_1_320 = 0)
% 28.03/7.35 |
% 28.03/7.35 | Applying alpha-rule on (916) yields:
% 28.03/7.35 | (917) apart_point_and_line(all_1_2_2, all_131_2_179) = all_334_1_320
% 28.03/7.35 | (918) distinct_points(all_1_2_2, all_1_2_2) = all_334_3_322
% 28.03/7.35 | (919) ~ (all_334_2_321 = 0) | ~ (all_334_3_322 = 0) | all_334_0_319 = 0 | all_334_1_320 = 0
% 28.03/7.35 | (920) apart_point_and_line(all_1_2_2, all_1_4_4) = all_334_0_319
% 28.03/7.35 | (921) distinct_lines(all_1_4_4, all_131_2_179) = all_334_2_321
% 28.03/7.35 |
% 28.03/7.35 +-Applying beta-rule and splitting (874), into two cases.
% 28.03/7.35 |-Branch one:
% 28.03/7.35 | (707) all_104_1_168 = 0
% 28.03/7.35 |
% 28.03/7.35 | Equations (707) can reduce 651 to:
% 28.03/7.35 | (79) $false
% 28.03/7.35 |
% 28.03/7.35 |-The branch is then unsatisfiable
% 28.03/7.35 |-Branch two:
% 28.03/7.35 | (651) ~ (all_104_1_168 = 0)
% 28.03/7.35 | (925) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_131_2_179, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.35 |
% 28.03/7.35 | Instantiating (925) with all_339_0_323, all_339_1_324, all_339_2_325, all_339_3_326 yields:
% 28.03/7.35 | (926) apart_point_and_line(all_1_2_2, all_131_2_179) = all_339_0_323 & apart_point_and_line(all_1_2_2, all_1_4_4) = all_339_1_324 & distinct_lines(all_131_2_179, all_1_4_4) = all_339_2_325 & distinct_points(all_1_2_2, all_1_2_2) = all_339_3_326 & ( ~ (all_339_2_325 = 0) | ~ (all_339_3_326 = 0) | all_339_0_323 = 0 | all_339_1_324 = 0)
% 28.03/7.35 |
% 28.03/7.35 | Applying alpha-rule on (926) yields:
% 28.03/7.35 | (927) distinct_lines(all_131_2_179, all_1_4_4) = all_339_2_325
% 28.03/7.35 | (928) apart_point_and_line(all_1_2_2, all_131_2_179) = all_339_0_323
% 28.03/7.35 | (929) apart_point_and_line(all_1_2_2, all_1_4_4) = all_339_1_324
% 28.03/7.35 | (930) distinct_points(all_1_2_2, all_1_2_2) = all_339_3_326
% 28.03/7.35 | (931) ~ (all_339_2_325 = 0) | ~ (all_339_3_326 = 0) | all_339_0_323 = 0 | all_339_1_324 = 0
% 28.03/7.35 |
% 28.03/7.35 +-Applying beta-rule and splitting (890), into two cases.
% 28.03/7.35 |-Branch one:
% 28.03/7.35 | (932) all_127_3_172 = 0
% 28.03/7.35 |
% 28.03/7.35 | Equations (932) can reduce 770 to:
% 28.03/7.35 | (79) $false
% 28.03/7.35 |
% 28.03/7.35 |-The branch is then unsatisfiable
% 28.03/7.35 |-Branch two:
% 28.03/7.35 | (770) ~ (all_127_3_172 = 0)
% 28.03/7.35 | (935) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_131_2_179) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.35 |
% 28.03/7.35 | Instantiating (935) with all_344_0_327, all_344_1_328, all_344_2_329, all_344_3_330 yields:
% 28.03/7.35 | (936) apart_point_and_line(all_1_2_2, all_131_2_179) = all_344_1_328 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_344_0_327 & distinct_lines(all_1_5_5, all_131_2_179) = all_344_2_329 & distinct_points(all_1_2_2, all_1_2_2) = all_344_3_330 & ( ~ (all_344_2_329 = 0) | ~ (all_344_3_330 = 0) | all_344_0_327 = 0 | all_344_1_328 = 0)
% 28.03/7.35 |
% 28.03/7.35 | Applying alpha-rule on (936) yields:
% 28.03/7.35 | (937) distinct_lines(all_1_5_5, all_131_2_179) = all_344_2_329
% 28.03/7.36 | (938) distinct_points(all_1_2_2, all_1_2_2) = all_344_3_330
% 28.03/7.36 | (939) apart_point_and_line(all_1_2_2, all_1_5_5) = all_344_0_327
% 28.03/7.36 | (940) ~ (all_344_2_329 = 0) | ~ (all_344_3_330 = 0) | all_344_0_327 = 0 | all_344_1_328 = 0
% 28.03/7.36 | (941) apart_point_and_line(all_1_2_2, all_131_2_179) = all_344_1_328
% 28.03/7.36 |
% 28.03/7.36 +-Applying beta-rule and splitting (894), into two cases.
% 28.03/7.36 |-Branch one:
% 28.03/7.36 | (932) all_127_3_172 = 0
% 28.03/7.36 |
% 28.03/7.36 | Equations (932) can reduce 770 to:
% 28.03/7.36 | (79) $false
% 28.03/7.36 |
% 28.03/7.36 |-The branch is then unsatisfiable
% 28.03/7.36 |-Branch two:
% 28.03/7.36 | (770) ~ (all_127_3_172 = 0)
% 28.03/7.36 | (945) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_131_2_179) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.36 |
% 28.03/7.36 | Instantiating (945) with all_349_0_331, all_349_1_332, all_349_2_333, all_349_3_334 yields:
% 28.03/7.36 | (946) apart_point_and_line(all_1_2_2, all_131_2_179) = all_349_0_331 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_349_1_332 & distinct_lines(all_1_5_5, all_131_2_179) = all_349_2_333 & distinct_points(all_1_2_2, all_1_2_2) = all_349_3_334 & ( ~ (all_349_2_333 = 0) | ~ (all_349_3_334 = 0) | all_349_0_331 = 0 | all_349_1_332 = 0)
% 28.03/7.36 |
% 28.03/7.36 | Applying alpha-rule on (946) yields:
% 28.03/7.36 | (947) distinct_lines(all_1_5_5, all_131_2_179) = all_349_2_333
% 28.03/7.36 | (948) apart_point_and_line(all_1_2_2, all_131_2_179) = all_349_0_331
% 28.03/7.36 | (949) ~ (all_349_2_333 = 0) | ~ (all_349_3_334 = 0) | all_349_0_331 = 0 | all_349_1_332 = 0
% 28.03/7.36 | (950) distinct_points(all_1_2_2, all_1_2_2) = all_349_3_334
% 28.03/7.36 | (951) apart_point_and_line(all_1_2_2, all_1_5_5) = all_349_1_332
% 28.03/7.36 |
% 28.03/7.36 +-Applying beta-rule and splitting (898), into two cases.
% 28.03/7.36 |-Branch one:
% 28.03/7.36 | (932) all_127_3_172 = 0
% 28.03/7.36 |
% 28.03/7.36 | Equations (932) can reduce 770 to:
% 28.03/7.36 | (79) $false
% 28.03/7.36 |
% 28.03/7.36 |-The branch is then unsatisfiable
% 28.03/7.36 |-Branch two:
% 28.03/7.36 | (770) ~ (all_127_3_172 = 0)
% 28.03/7.36 | (955) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_2_2, all_131_2_179) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_131_2_179, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 28.03/7.36 |
% 28.03/7.36 | Instantiating (955) with all_354_0_335, all_354_1_336, all_354_2_337, all_354_3_338 yields:
% 28.03/7.36 | (956) apart_point_and_line(all_1_2_2, all_131_2_179) = all_354_1_336 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_354_0_335 & distinct_lines(all_131_2_179, all_1_5_5) = all_354_2_337 & distinct_points(all_1_2_2, all_1_2_2) = all_354_3_338 & ( ~ (all_354_2_337 = 0) | ~ (all_354_3_338 = 0) | all_354_0_335 = 0 | all_354_1_336 = 0)
% 28.03/7.36 |
% 28.03/7.36 | Applying alpha-rule on (956) yields:
% 28.03/7.36 | (957) apart_point_and_line(all_1_2_2, all_131_2_179) = all_354_1_336
% 28.03/7.36 | (958) ~ (all_354_2_337 = 0) | ~ (all_354_3_338 = 0) | all_354_0_335 = 0 | all_354_1_336 = 0
% 28.03/7.36 | (959) apart_point_and_line(all_1_2_2, all_1_5_5) = all_354_0_335
% 28.03/7.36 | (960) distinct_lines(all_131_2_179, all_1_5_5) = all_354_2_337
% 28.03/7.36 | (961) distinct_points(all_1_2_2, all_1_2_2) = all_354_3_338
% 28.03/7.36 |
% 28.03/7.36 +-Applying beta-rule and splitting (802), into two cases.
% 28.03/7.36 |-Branch one:
% 28.03/7.36 | (962) ~ (convergent_lines(all_1_3_3, all_1_4_4) = 0)
% 28.03/7.36 |
% 28.03/7.36 | Using (903) and (962) yields:
% 28.03/7.36 | (202) $false
% 28.03/7.36 |
% 28.03/7.36 |-The branch is then unsatisfiable
% 28.03/7.36 |-Branch two:
% 28.03/7.36 | (903) convergent_lines(all_1_3_3, all_1_4_4) = 0
% 28.03/7.36 | (965) ? [v0] : ? [v1] : (intersection_point(all_1_3_3, 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) = 0)
% 28.03/7.36 |
% 28.03/7.36 | Instantiating (965) with all_360_0_339, all_360_1_340 yields:
% 28.03/7.36 | (966) intersection_point(all_1_3_3, all_1_4_4) = all_360_0_339 & apart_point_and_line(all_1_2_2, all_1_4_4) = all_360_1_340 & distinct_points(all_1_2_2, all_360_0_339) = 0
% 28.03/7.36 |
% 28.03/7.36 | Applying alpha-rule on (966) yields:
% 28.03/7.36 | (967) intersection_point(all_1_3_3, all_1_4_4) = all_360_0_339
% 28.03/7.36 | (968) apart_point_and_line(all_1_2_2, all_1_4_4) = all_360_1_340
% 28.03/7.36 | (969) distinct_points(all_1_2_2, all_360_0_339) = 0
% 28.03/7.36 |
% 28.03/7.36 +-Applying beta-rule and splitting (803), into two cases.
% 28.03/7.36 |-Branch one:
% 28.03/7.36 | (962) ~ (convergent_lines(all_1_3_3, all_1_4_4) = 0)
% 28.03/7.36 |
% 28.03/7.36 | Using (903) and (962) yields:
% 28.03/7.36 | (202) $false
% 28.03/7.36 |
% 28.03/7.36 |-The branch is then unsatisfiable
% 28.03/7.36 |-Branch two:
% 28.03/7.36 | (903) convergent_lines(all_1_3_3, all_1_4_4) = 0
% 28.03/7.36 | (973) ? [v0] : ? [v1] : ? [v2] : (intersection_point(all_1_3_3, all_1_4_4) = v1 & apart_point_and_line(all_104_0_167, all_1_3_3) = v0 & distinct_points(all_104_0_167, v1) = v2 & (v2 = 0 | ( ~ (v0 = 0) & ~ (all_127_0_169 = 0))))
% 28.03/7.36 |
% 28.03/7.36 | Instantiating (973) with all_369_0_341, all_369_1_342, all_369_2_343 yields:
% 28.03/7.36 | (974) intersection_point(all_1_3_3, all_1_4_4) = all_369_1_342 & apart_point_and_line(all_104_0_167, all_1_3_3) = all_369_2_343 & distinct_points(all_104_0_167, all_369_1_342) = all_369_0_341 & (all_369_0_341 = 0 | ( ~ (all_369_2_343 = 0) & ~ (all_127_0_169 = 0)))
% 28.03/7.36 |
% 28.03/7.36 | Applying alpha-rule on (974) yields:
% 28.03/7.36 | (975) intersection_point(all_1_3_3, all_1_4_4) = all_369_1_342
% 28.03/7.36 | (976) apart_point_and_line(all_104_0_167, all_1_3_3) = all_369_2_343
% 28.03/7.36 | (977) distinct_points(all_104_0_167, all_369_1_342) = all_369_0_341
% 28.03/7.36 | (978) all_369_0_341 = 0 | ( ~ (all_369_2_343 = 0) & ~ (all_127_0_169 = 0))
% 28.03/7.36 |
% 28.03/7.36 | Instantiating formula (45) with all_1_4_4, all_1_3_3, all_202_1_232, all_104_0_167 and discharging atoms intersection_point(all_1_4_4, all_1_3_3) = all_202_1_232, intersection_point(all_1_4_4, all_1_3_3) = all_104_0_167, yields:
% 28.03/7.36 | (979) all_202_1_232 = all_104_0_167
% 28.03/7.36 |
% 28.03/7.36 | Instantiating formula (26) with all_104_0_167, all_1_3_3, all_206_1_238, all_369_2_343 and discharging atoms apart_point_and_line(all_104_0_167, all_1_3_3) = all_369_2_343, apart_point_and_line(all_104_0_167, all_1_3_3) = all_206_1_238, yields:
% 28.03/7.36 | (980) all_369_2_343 = all_206_1_238
% 28.03/7.36 |
% 28.03/7.36 | Instantiating formula (26) with all_104_0_167, all_1_3_3, all_206_1_238, all_208_1_241 and discharging atoms apart_point_and_line(all_104_0_167, all_1_3_3) = all_208_1_241, apart_point_and_line(all_104_0_167, all_1_3_3) = all_206_1_238, yields:
% 28.03/7.36 | (981) all_208_1_241 = all_206_1_238
% 28.03/7.36 |
% 28.03/7.36 | Instantiating formula (26) with all_104_0_167, all_1_3_3, all_202_2_233, all_369_2_343 and discharging atoms apart_point_and_line(all_104_0_167, all_1_3_3) = all_369_2_343, apart_point_and_line(all_104_0_167, all_1_3_3) = all_202_2_233, yields:
% 28.03/7.36 | (982) all_369_2_343 = all_202_2_233
% 28.03/7.36 |
% 28.03/7.36 | Instantiating formula (26) with all_104_0_167, all_1_3_3, all_184_1_204, all_208_1_241 and discharging atoms apart_point_and_line(all_104_0_167, all_1_3_3) = all_208_1_241, apart_point_and_line(all_104_0_167, all_1_3_3) = all_184_1_204, yields:
% 28.03/7.36 | (983) all_208_1_241 = all_184_1_204
% 28.03/7.36 |
% 28.03/7.36 | Instantiating formula (26) with all_104_0_167, all_1_5_5, all_218_1_256, all_127_1_170 and discharging atoms apart_point_and_line(all_104_0_167, all_1_5_5) = all_218_1_256, apart_point_and_line(all_104_0_167, all_1_5_5) = all_127_1_170, yields:
% 28.03/7.36 | (984) all_218_1_256 = all_127_1_170
% 28.03/7.36 |
% 28.03/7.36 | Instantiating formula (26) with all_104_0_167, all_1_5_5, all_214_2_251, all_218_1_256 and discharging atoms apart_point_and_line(all_104_0_167, all_1_5_5) = all_218_1_256, apart_point_and_line(all_104_0_167, all_1_5_5) = all_214_2_251, yields:
% 28.03/7.36 | (985) all_218_1_256 = all_214_2_251
% 28.03/7.36 |
% 28.03/7.36 | Instantiating formula (26) with all_104_0_167, all_1_5_5, all_212_2_248, all_214_2_251 and discharging atoms apart_point_and_line(all_104_0_167, all_1_5_5) = all_214_2_251, apart_point_and_line(all_104_0_167, all_1_5_5) = all_212_2_248, yields:
% 28.03/7.36 | (986) all_214_2_251 = all_212_2_248
% 28.03/7.36 |
% 28.03/7.36 | Instantiating formula (26) with all_104_0_167, all_1_5_5, all_204_1_235, all_214_2_251 and discharging atoms apart_point_and_line(all_104_0_167, all_1_5_5) = all_214_2_251, apart_point_and_line(all_104_0_167, all_1_5_5) = all_204_1_235, yields:
% 28.03/7.36 | (987) all_214_2_251 = all_204_1_235
% 28.03/7.36 |
% 28.03/7.36 | Instantiating formula (26) with all_1_2_2, all_1_4_4, all_339_1_324, all_360_1_340 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_360_1_340, apart_point_and_line(all_1_2_2, all_1_4_4) = all_339_1_324, yields:
% 28.03/7.36 | (988) all_360_1_340 = all_339_1_324
% 28.03/7.36 |
% 28.03/7.36 | Instantiating formula (26) with all_1_2_2, all_1_4_4, all_334_0_319, all_104_1_168 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_334_0_319, apart_point_and_line(all_1_2_2, all_1_4_4) = all_104_1_168, yields:
% 28.03/7.36 | (989) all_334_0_319 = all_104_1_168
% 28.03/7.36 |
% 28.03/7.36 | Instantiating formula (26) with all_1_2_2, all_1_4_4, all_334_0_319, all_339_1_324 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_339_1_324, apart_point_and_line(all_1_2_2, all_1_4_4) = all_334_0_319, yields:
% 28.03/7.36 | (990) all_339_1_324 = all_334_0_319
% 28.03/7.36 |
% 28.03/7.36 | Instantiating formula (26) with all_1_2_2, all_1_4_4, all_216_1_253, all_360_1_340 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_360_1_340, apart_point_and_line(all_1_2_2, all_1_4_4) = all_216_1_253, yields:
% 28.03/7.36 | (991) all_360_1_340 = all_216_1_253
% 28.03/7.36 |
% 28.03/7.36 | Instantiating formula (26) with all_1_2_2, all_1_4_4, all_184_2_205, all_339_1_324 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_339_1_324, apart_point_and_line(all_1_2_2, all_1_4_4) = all_184_2_205, yields:
% 28.03/7.36 | (992) all_339_1_324 = all_184_2_205
% 28.03/7.36 |
% 28.03/7.36 | Using (806) and (106) yields:
% 28.03/7.36 | (993) ~ (all_184_2_205 = 0)
% 28.03/7.36 |
% 28.03/7.36 | Instantiating formula (26) with all_1_2_2, all_1_5_5, all_349_1_332, all_127_3_172 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_349_1_332, apart_point_and_line(all_1_2_2, all_1_5_5) = all_127_3_172, yields:
% 28.03/7.36 | (994) all_349_1_332 = all_127_3_172
% 28.03/7.36 |
% 28.03/7.36 | Instantiating formula (26) with all_1_2_2, all_1_5_5, all_349_1_332, all_354_0_335 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_354_0_335, apart_point_and_line(all_1_2_2, all_1_5_5) = all_349_1_332, yields:
% 28.03/7.36 | (995) all_354_0_335 = all_349_1_332
% 28.03/7.36 |
% 28.03/7.36 | Instantiating formula (26) with all_1_2_2, all_1_5_5, all_344_0_327, all_354_0_335 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_354_0_335, apart_point_and_line(all_1_2_2, all_1_5_5) = all_344_0_327, yields:
% 28.03/7.36 | (996) all_354_0_335 = all_344_0_327
% 28.03/7.36 |
% 28.03/7.36 | Using (939) and (97) yields:
% 28.03/7.37 | (997) ~ (all_344_0_327 = 0)
% 28.03/7.37 |
% 28.03/7.37 | Instantiating formula (27) with all_1_4_4, all_1_3_3, all_206_2_239, 0 and discharging atoms convergent_lines(all_1_4_4, all_1_3_3) = all_206_2_239, convergent_lines(all_1_4_4, all_1_3_3) = 0, yields:
% 28.03/7.37 | (998) all_206_2_239 = 0
% 28.03/7.37 |
% 28.03/7.37 | Instantiating formula (16) with all_104_0_167, all_104_0_167, all_206_0_237, all_202_0_231 and discharging atoms distinct_points(all_104_0_167, all_104_0_167) = all_206_0_237, yields:
% 28.03/7.37 | (999) all_206_0_237 = all_202_0_231 | ~ (distinct_points(all_104_0_167, all_104_0_167) = all_202_0_231)
% 28.03/7.37 |
% 28.03/7.37 | Instantiating formula (20) with all_104_0_167 yields:
% 28.03/7.37 | (1000) ~ (distinct_points(all_104_0_167, all_104_0_167) = 0)
% 28.03/7.37 |
% 28.03/7.37 | Combining equations (980,982) yields a new equation:
% 28.03/7.37 | (1001) all_206_1_238 = all_202_2_233
% 28.03/7.37 |
% 28.03/7.37 | Simplifying 1001 yields:
% 28.03/7.37 | (1002) all_206_1_238 = all_202_2_233
% 28.03/7.37 |
% 28.03/7.37 | Combining equations (988,991) yields a new equation:
% 28.03/7.37 | (1003) all_339_1_324 = all_216_1_253
% 28.03/7.37 |
% 28.03/7.37 | Simplifying 1003 yields:
% 28.03/7.37 | (1004) all_339_1_324 = all_216_1_253
% 28.03/7.37 |
% 28.03/7.37 | Combining equations (995,996) yields a new equation:
% 28.03/7.37 | (1005) all_349_1_332 = all_344_0_327
% 28.03/7.37 |
% 28.03/7.37 | Simplifying 1005 yields:
% 28.03/7.37 | (1006) all_349_1_332 = all_344_0_327
% 28.03/7.37 |
% 28.03/7.37 | Combining equations (994,1006) yields a new equation:
% 28.03/7.37 | (1007) all_344_0_327 = all_127_3_172
% 28.03/7.37 |
% 28.03/7.37 | Combining equations (990,1004) yields a new equation:
% 28.03/7.37 | (1008) all_334_0_319 = all_216_1_253
% 28.03/7.37 |
% 28.03/7.37 | Simplifying 1008 yields:
% 28.03/7.37 | (1009) all_334_0_319 = all_216_1_253
% 28.03/7.37 |
% 28.03/7.37 | Combining equations (992,1004) yields a new equation:
% 28.03/7.37 | (1010) all_216_1_253 = all_184_2_205
% 28.03/7.37 |
% 28.03/7.37 | Combining equations (1009,989) yields a new equation:
% 28.03/7.37 | (1011) all_216_1_253 = all_104_1_168
% 28.03/7.37 |
% 28.03/7.37 | Simplifying 1011 yields:
% 28.03/7.37 | (1012) all_216_1_253 = all_104_1_168
% 28.03/7.37 |
% 28.03/7.37 | Combining equations (985,984) yields a new equation:
% 28.03/7.37 | (1013) all_214_2_251 = all_127_1_170
% 28.03/7.37 |
% 28.03/7.37 | Simplifying 1013 yields:
% 28.03/7.37 | (1014) all_214_2_251 = all_127_1_170
% 28.03/7.37 |
% 28.03/7.37 | Combining equations (1010,1012) yields a new equation:
% 28.03/7.37 | (1015) all_184_2_205 = all_104_1_168
% 28.03/7.37 |
% 28.03/7.37 | Simplifying 1015 yields:
% 28.03/7.37 | (1016) all_184_2_205 = all_104_1_168
% 28.03/7.37 |
% 28.03/7.37 | Combining equations (1014,986) yields a new equation:
% 28.03/7.37 | (1017) all_212_2_248 = all_127_1_170
% 28.03/7.37 |
% 28.03/7.37 | Combining equations (987,986) yields a new equation:
% 28.03/7.37 | (1018) all_212_2_248 = all_204_1_235
% 28.03/7.37 |
% 28.03/7.37 | Combining equations (1017,1018) yields a new equation:
% 28.03/7.37 | (1019) all_204_1_235 = all_127_1_170
% 28.03/7.37 |
% 28.03/7.37 | Combining equations (981,983) yields a new equation:
% 28.03/7.37 | (1020) all_206_1_238 = all_184_1_204
% 28.03/7.37 |
% 28.03/7.37 | Simplifying 1020 yields:
% 28.03/7.37 | (1021) all_206_1_238 = all_184_1_204
% 28.03/7.37 |
% 28.03/7.37 | Combining equations (1002,1021) yields a new equation:
% 28.03/7.37 | (1022) all_202_2_233 = all_184_1_204
% 28.03/7.37 |
% 28.03/7.37 | Simplifying 1022 yields:
% 28.03/7.37 | (1023) all_202_2_233 = all_184_1_204
% 28.03/7.37 |
% 28.03/7.37 | Equations (1007) can reduce 997 to:
% 28.03/7.37 | (770) ~ (all_127_3_172 = 0)
% 28.03/7.37 |
% 28.03/7.37 | Equations (1016) can reduce 993 to:
% 28.34/7.37 | (651) ~ (all_104_1_168 = 0)
% 28.34/7.37 |
% 28.34/7.37 | From (1023) and (813) follows:
% 28.34/7.37 | (807) apart_point_and_line(all_104_0_167, all_1_3_3) = all_184_1_204
% 28.34/7.37 |
% 28.34/7.37 | From (1019) and (817) follows:
% 28.34/7.37 | (664) apart_point_and_line(all_104_0_167, all_1_5_5) = all_127_1_170
% 28.34/7.37 |
% 28.34/7.37 | From (979) and (814) follows:
% 28.34/7.37 | (1028) distinct_points(all_104_0_167, all_104_0_167) = all_202_0_231
% 28.34/7.37 |
% 28.34/7.37 +-Applying beta-rule and splitting (999), into two cases.
% 28.34/7.37 |-Branch one:
% 28.34/7.37 | (1029) ~ (distinct_points(all_104_0_167, all_104_0_167) = all_202_0_231)
% 28.34/7.37 |
% 28.34/7.37 | Using (1028) and (1029) yields:
% 28.34/7.37 | (202) $false
% 28.34/7.37 |
% 28.34/7.37 |-The branch is then unsatisfiable
% 28.34/7.37 |-Branch two:
% 28.34/7.37 | (1028) distinct_points(all_104_0_167, all_104_0_167) = all_202_0_231
% 28.34/7.37 | (1032) all_206_0_237 = all_202_0_231
% 28.34/7.37 |
% 28.34/7.37 | From (1032) and (824) follows:
% 28.34/7.37 | (1028) distinct_points(all_104_0_167, all_104_0_167) = all_202_0_231
% 28.34/7.37 |
% 28.34/7.37 | Using (1028) and (1000) yields:
% 28.34/7.37 | (1034) ~ (all_202_0_231 = 0)
% 28.34/7.37 |
% 28.34/7.37 +-Applying beta-rule and splitting (825), into two cases.
% 28.34/7.37 |-Branch one:
% 28.34/7.37 | (1035) ~ (all_206_2_239 = 0)
% 28.34/7.37 |
% 28.34/7.37 | Equations (998) can reduce 1035 to:
% 28.34/7.37 | (79) $false
% 28.34/7.37 |
% 28.34/7.37 |-The branch is then unsatisfiable
% 28.34/7.37 |-Branch two:
% 28.34/7.37 | (998) all_206_2_239 = 0
% 28.34/7.37 | (1038) all_206_0_237 = 0 | ( ~ (all_206_1_238 = 0) & ~ (all_127_0_169 = 0))
% 28.34/7.37 |
% 28.34/7.37 +-Applying beta-rule and splitting (1038), into two cases.
% 28.34/7.37 |-Branch one:
% 28.34/7.37 | (1039) all_206_0_237 = 0
% 28.34/7.37 |
% 28.34/7.37 | Combining equations (1032,1039) yields a new equation:
% 28.34/7.37 | (1040) all_202_0_231 = 0
% 28.34/7.37 |
% 28.34/7.37 | Simplifying 1040 yields:
% 28.34/7.37 | (1041) all_202_0_231 = 0
% 28.34/7.37 |
% 28.34/7.37 | Equations (1041) can reduce 1034 to:
% 28.34/7.37 | (79) $false
% 28.34/7.37 |
% 28.34/7.37 |-The branch is then unsatisfiable
% 28.34/7.37 |-Branch two:
% 28.34/7.37 | (1043) ~ (all_206_0_237 = 0)
% 28.34/7.37 | (1044) ~ (all_206_1_238 = 0) & ~ (all_127_0_169 = 0)
% 28.34/7.37 |
% 28.34/7.38 | Applying alpha-rule on (1044) yields:
% 28.34/7.38 | (1045) ~ (all_206_1_238 = 0)
% 28.34/7.38 | (1046) ~ (all_127_0_169 = 0)
% 28.34/7.38 |
% 28.34/7.38 | Equations (1021) can reduce 1045 to:
% 28.34/7.38 | (1047) ~ (all_184_1_204 = 0)
% 28.34/7.38 |
% 28.34/7.38 +-Applying beta-rule and splitting (672), into two cases.
% 28.34/7.38 |-Branch one:
% 28.34/7.38 | (1048) all_129_0_173 = 0
% 28.34/7.38 |
% 28.34/7.38 | Combining equations (731,1048) yields a new equation:
% 28.34/7.38 | (1049) all_127_1_170 = 0
% 28.34/7.38 |
% 28.34/7.38 | Simplifying 1049 yields:
% 28.34/7.38 | (1050) all_127_1_170 = 0
% 28.34/7.38 |
% 28.34/7.38 | From (1050) and (664) follows:
% 28.34/7.38 | (1051) apart_point_and_line(all_104_0_167, all_1_5_5) = 0
% 28.34/7.38 |
% 28.34/7.38 +-Applying beta-rule and splitting (788), into two cases.
% 28.34/7.38 |-Branch one:
% 28.34/7.38 | (1052) ~ (apart_point_and_line(all_104_0_167, all_1_5_5) = 0)
% 28.34/7.38 |
% 28.34/7.38 | Using (1051) and (1052) yields:
% 28.34/7.38 | (202) $false
% 28.34/7.38 |
% 28.34/7.38 |-The branch is then unsatisfiable
% 28.34/7.38 |-Branch two:
% 28.34/7.38 | (1051) apart_point_and_line(all_104_0_167, all_1_5_5) = 0
% 28.34/7.38 | (1055) all_1_1_1 = 0 | apart_point_and_line(all_104_0_167, all_1_3_3) = 0
% 28.34/7.38 |
% 28.34/7.38 +-Applying beta-rule and splitting (1055), into two cases.
% 28.34/7.38 |-Branch one:
% 28.34/7.38 | (1056) apart_point_and_line(all_104_0_167, all_1_3_3) = 0
% 28.34/7.38 |
% 28.34/7.38 | Instantiating formula (26) with all_104_0_167, all_1_3_3, 0, all_184_1_204 and discharging atoms apart_point_and_line(all_104_0_167, all_1_3_3) = all_184_1_204, apart_point_and_line(all_104_0_167, all_1_3_3) = 0, yields:
% 28.34/7.38 | (1057) all_184_1_204 = 0
% 28.34/7.38 |
% 28.34/7.38 | Equations (1057) can reduce 1047 to:
% 28.34/7.38 | (79) $false
% 28.34/7.38 |
% 28.34/7.38 |-The branch is then unsatisfiable
% 28.34/7.38 |-Branch two:
% 28.34/7.38 | (1059) ~ (apart_point_and_line(all_104_0_167, all_1_3_3) = 0)
% 28.34/7.38 | (89) all_1_1_1 = 0
% 28.34/7.38 |
% 28.34/7.38 | Equations (89) can reduce 573 to:
% 28.34/7.38 | (79) $false
% 28.34/7.38 |
% 28.34/7.38 |-The branch is then unsatisfiable
% 28.34/7.38 |-Branch two:
% 28.34/7.38 | (1062) ~ (all_129_0_173 = 0)
% 28.34/7.38 | (1063) all_129_1_174 = 0 | all_129_2_175 = 0 | all_129_3_176 = 0
% 28.34/7.38 |
% 28.34/7.38 +-Applying beta-rule and splitting (1063), into two cases.
% 28.34/7.38 |-Branch one:
% 28.34/7.38 | (1064) all_129_1_174 = 0
% 28.34/7.38 |
% 28.34/7.38 | Combining equations (764,1064) yields a new equation:
% 28.34/7.38 | (1065) all_127_0_169 = 0
% 28.34/7.38 |
% 28.34/7.38 | Simplifying 1065 yields:
% 28.34/7.38 | (1066) all_127_0_169 = 0
% 28.34/7.38 |
% 28.34/7.38 | Equations (1066) can reduce 1046 to:
% 28.34/7.38 | (79) $false
% 28.34/7.38 |
% 28.34/7.38 |-The branch is then unsatisfiable
% 28.34/7.38 |-Branch two:
% 28.34/7.38 | (1068) ~ (all_129_1_174 = 0)
% 28.34/7.38 | (1069) all_129_2_175 = 0 | all_129_3_176 = 0
% 28.34/7.38 |
% 28.34/7.38 +-Applying beta-rule and splitting (1069), into two cases.
% 28.34/7.38 |-Branch one:
% 28.34/7.38 | (1070) all_129_2_175 = 0
% 28.34/7.38 |
% 28.34/7.38 | Combining equations (1070,763) yields a new equation:
% 28.34/7.38 | (932) all_127_3_172 = 0
% 28.34/7.38 |
% 28.34/7.38 | Equations (932) can reduce 770 to:
% 28.34/7.38 | (79) $false
% 28.34/7.38 |
% 28.34/7.38 |-The branch is then unsatisfiable
% 28.34/7.38 |-Branch two:
% 28.34/7.38 | (742) ~ (all_129_2_175 = 0)
% 28.34/7.38 | (1074) all_129_3_176 = 0
% 28.34/7.38 |
% 28.34/7.38 | Combining equations (1074,754) yields a new equation:
% 28.34/7.38 | (707) all_104_1_168 = 0
% 28.34/7.38 |
% 28.34/7.38 | Equations (707) can reduce 651 to:
% 28.34/7.38 | (79) $false
% 28.34/7.38 |
% 28.34/7.38 |-The branch is then unsatisfiable
% 28.34/7.38 |-Branch two:
% 28.34/7.38 | (851) all_131_1_178 = 0
% 28.34/7.38 | (1078) all_131_0_177 = 0
% 28.34/7.38 |
% 28.34/7.38 | Equations (1078) can reduce 769 to:
% 28.34/7.38 | (79) $false
% 28.34/7.38 |
% 28.34/7.38 |-The branch is then unsatisfiable
% 28.34/7.38 |-Branch two:
% 28.34/7.38 | (1080) ~ (distinct_lines(all_1_3_3, all_1_4_4) = 0)
% 28.34/7.38 | (707) all_104_1_168 = 0
% 28.34/7.38 |
% 28.34/7.38 | Equations (707) can reduce 651 to:
% 28.34/7.38 | (79) $false
% 28.34/7.38 |
% 28.34/7.38 |-The branch is then unsatisfiable
% 28.34/7.38 |-Branch two:
% 28.34/7.38 | (547) apart_point_and_line(all_1_2_2, all_1_4_4) = 0
% 28.34/7.38 | (552) ? [v0] : ? [v1] : (intersection_point(all_1_5_5, all_1_4_4) = v1 & apart_point_and_line(all_1_2_2, all_1_5_5) = v0 & distinct_points(all_1_2_2, v1) = 0)
% 28.34/7.39 |
% 28.34/7.39 | Instantiating (552) with all_118_0_356, all_118_1_357 yields:
% 28.34/7.39 | (1085) intersection_point(all_1_5_5, all_1_4_4) = all_118_0_356 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_118_1_357 & distinct_points(all_1_2_2, all_118_0_356) = 0
% 28.34/7.39 |
% 28.34/7.39 | Applying alpha-rule on (1085) yields:
% 28.34/7.39 | (1086) intersection_point(all_1_5_5, all_1_4_4) = all_118_0_356
% 28.34/7.39 | (1087) apart_point_and_line(all_1_2_2, all_1_5_5) = all_118_1_357
% 28.34/7.39 | (1088) distinct_points(all_1_2_2, all_118_0_356) = 0
% 28.34/7.39 |
% 28.34/7.39 | Instantiating formula (45) with all_1_5_5, all_1_4_4, all_118_0_356, all_1_2_2 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_118_0_356, intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2, yields:
% 28.34/7.39 | (1089) all_118_0_356 = all_1_2_2
% 28.34/7.39 |
% 28.34/7.39 | Using (1088) and (105) yields:
% 28.34/7.39 | (1090) ~ (all_118_0_356 = all_1_2_2)
% 28.34/7.39 |
% 28.34/7.39 | Equations (1089) can reduce 1090 to:
% 28.34/7.39 | (79) $false
% 28.34/7.39 |
% 28.34/7.39 |-The branch is then unsatisfiable
% 28.34/7.39 |-Branch two:
% 28.34/7.39 | (1092) ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0)
% 28.34/7.39 | (1093) all_93_0_166 = 0
% 28.34/7.39 |
% 28.34/7.39 | Equations (1093) can reduce 640 to:
% 28.34/7.39 | (79) $false
% 28.34/7.39 |
% 28.34/7.39 |-The branch is then unsatisfiable
% 28.34/7.39 |-Branch two:
% 28.34/7.39 | (1095) ~ (convergent_lines(all_1_4_4, all_1_3_3) = 0)
% 28.34/7.39 | (627) all_49_0_162 = 0
% 28.34/7.39 |
% 28.34/7.39 | Equations (627) can reduce 611 to:
% 28.34/7.39 | (79) $false
% 28.34/7.39 |
% 28.34/7.39 |-The branch is then unsatisfiable
% 28.34/7.39 |-Branch two:
% 28.34/7.39 | (1098) ~ (distinct_lines(all_1_4_4, all_1_5_5) = 0)
% 28.34/7.39 | (1099) all_54_0_163 = 0
% 28.34/7.39 |
% 28.34/7.39 | Equations (1099) can reduce 618 to:
% 28.34/7.39 | (79) $false
% 28.34/7.39 |
% 28.34/7.39 |-The branch is then unsatisfiable
% 28.34/7.39 |-Branch two:
% 28.34/7.39 | (563) apart_point_and_line(all_1_2_2, all_1_5_5) = 0
% 28.34/7.39 | (564) ? [v0] : ? [v1] : (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) = 0)
% 28.34/7.39 |
% 28.34/7.39 | Instantiating (564) with all_67_0_361, all_67_1_362 yields:
% 28.34/7.39 | (1103) intersection_point(all_1_5_5, all_1_4_4) = all_67_0_361 & apart_point_and_line(all_1_2_2, all_1_4_4) = all_67_1_362 & distinct_points(all_1_2_2, all_67_0_361) = 0
% 28.34/7.39 |
% 28.34/7.39 | Applying alpha-rule on (1103) yields:
% 28.34/7.39 | (1104) intersection_point(all_1_5_5, all_1_4_4) = all_67_0_361
% 28.34/7.39 | (1105) apart_point_and_line(all_1_2_2, all_1_4_4) = all_67_1_362
% 28.34/7.39 | (1106) distinct_points(all_1_2_2, all_67_0_361) = 0
% 28.34/7.39 |
% 28.34/7.39 | Instantiating formula (45) with all_1_5_5, all_1_4_4, all_67_0_361, all_1_2_2 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_67_0_361, intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2, yields:
% 28.34/7.39 | (1107) all_67_0_361 = all_1_2_2
% 28.34/7.39 |
% 28.34/7.39 | Instantiating formula (20) with all_1_2_2 yields:
% 28.34/7.39 | (105) ~ (distinct_points(all_1_2_2, all_1_2_2) = 0)
% 28.34/7.39 |
% 28.34/7.39 | From (1107) and (1106) follows:
% 28.34/7.39 | (571) distinct_points(all_1_2_2, all_1_2_2) = 0
% 28.34/7.39 |
% 28.34/7.39 | Using (571) and (105) yields:
% 28.34/7.39 | (202) $false
% 28.34/7.39 |
% 28.34/7.39 |-The branch is then unsatisfiable
% 28.34/7.39 |-Branch two:
% 28.34/7.39 | (1111) distinct_lines(all_1_5_5, all_1_3_3) = all_1_0_0
% 28.34/7.39 | (1112) all_1_0_0 = all_1_1_1
% 28.34/7.39 |
% 28.34/7.39 | From (1112) and (1111) follows:
% 28.34/7.39 | (50) distinct_lines(all_1_5_5, all_1_3_3) = all_1_1_1
% 28.34/7.39 |
% 28.34/7.39 +-Applying beta-rule and splitting (48), into two cases.
% 28.34/7.39 |-Branch one:
% 28.34/7.39 | (77) ~ (all_1_0_0 = 0)
% 28.34/7.39 |
% 28.34/7.39 | Equations (1112) can reduce 77 to:
% 28.34/7.39 | (573) ~ (all_1_1_1 = 0)
% 28.34/7.39 |
% 28.34/7.39 +-Applying beta-rule and splitting (64), into two cases.
% 28.34/7.39 |-Branch one:
% 28.34/7.39 | (78) all_1_0_0 = 0
% 28.34/7.39 |
% 28.34/7.39 | Combining equations (78,1112) yields a new equation:
% 28.34/7.39 | (89) all_1_1_1 = 0
% 28.34/7.39 |
% 28.34/7.39 | Equations (89) can reduce 573 to:
% 28.34/7.39 | (79) $false
% 28.34/7.39 |
% 28.34/7.39 |-The branch is then unsatisfiable
% 28.34/7.39 |-Branch two:
% 28.34/7.39 | (77) ~ (all_1_0_0 = 0)
% 28.34/7.39 | (81) all_1_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_5_5, all_1_4_4) = v0)
% 28.34/7.39 |
% 28.34/7.39 | Equations (1112) can reduce 77 to:
% 28.34/7.39 | (573) ~ (all_1_1_1 = 0)
% 28.34/7.39 |
% 28.34/7.39 +-Applying beta-rule and splitting (65), into two cases.
% 28.34/7.39 |-Branch one:
% 28.34/7.39 | (89) all_1_1_1 = 0
% 28.34/7.39 |
% 28.34/7.39 | Equations (89) can reduce 573 to:
% 28.34/7.39 | (79) $false
% 28.34/7.39 |
% 28.34/7.39 |-The branch is then unsatisfiable
% 28.34/7.39 |-Branch two:
% 28.34/7.39 | (573) ~ (all_1_1_1 = 0)
% 28.34/7.39 | (578) ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_5_5, all_1_5_5) = v0)
% 28.34/7.39 |
% 28.34/7.39 +-Applying beta-rule and splitting (61), into two cases.
% 28.34/7.39 |-Branch one:
% 28.34/7.39 | (78) all_1_0_0 = 0
% 28.34/7.39 |
% 28.34/7.39 | Combining equations (78,1112) yields a new equation:
% 28.34/7.39 | (89) all_1_1_1 = 0
% 28.34/7.39 |
% 28.34/7.39 | Equations (89) can reduce 573 to:
% 28.34/7.39 | (79) $false
% 28.34/7.39 |
% 28.34/7.39 |-The branch is then unsatisfiable
% 28.34/7.39 |-Branch two:
% 28.34/7.39 | (77) ~ (all_1_0_0 = 0)
% 28.34/7.39 | (95) ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_4_4, all_1_4_4) = v0)
% 28.34/7.39 |
% 28.34/7.39 | Equations (1112) can reduce 77 to:
% 28.34/7.39 | (573) ~ (all_1_1_1 = 0)
% 28.34/7.39 |
% 28.34/7.39 +-Applying beta-rule and splitting (74), into two cases.
% 28.34/7.39 |-Branch one:
% 28.34/7.39 | (91) distinct_lines(all_1_5_5, all_1_3_3) = 0
% 28.34/7.39 |
% 28.34/7.39 +-Applying beta-rule and splitting (62), into two cases.
% 28.34/7.39 |-Branch one:
% 28.34/7.39 | (78) all_1_0_0 = 0
% 28.34/7.39 |
% 28.34/7.39 | Combining equations (78,1112) yields a new equation:
% 28.34/7.39 | (89) all_1_1_1 = 0
% 28.34/7.39 |
% 28.34/7.39 | Equations (89) can reduce 573 to:
% 28.34/7.39 | (79) $false
% 28.34/7.39 |
% 28.34/7.39 |-The branch is then unsatisfiable
% 28.34/7.39 |-Branch two:
% 28.34/7.39 | (77) ~ (all_1_0_0 = 0)
% 28.34/7.39 | (85) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_1_4_4, all_1_3_3) = v0)
% 28.34/7.39 |
% 28.34/7.39 | Equations (1112) can reduce 77 to:
% 28.34/7.39 | (573) ~ (all_1_1_1 = 0)
% 28.34/7.39 |
% 28.34/7.39 +-Applying beta-rule and splitting (66), into two cases.
% 28.34/7.39 |-Branch one:
% 28.34/7.39 | (89) all_1_1_1 = 0
% 28.34/7.39 |
% 28.34/7.39 | Equations (89) can reduce 573 to:
% 28.34/7.39 | (79) $false
% 28.34/7.39 |
% 28.34/7.39 |-The branch is then unsatisfiable
% 28.34/7.39 |-Branch two:
% 28.34/7.39 | (573) ~ (all_1_1_1 = 0)
% 28.34/7.39 | (591) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_1_5_5, all_1_3_3) = v0)
% 28.34/7.39 |
% 28.34/7.39 +-Applying beta-rule and splitting (63), into two cases.
% 28.34/7.39 |-Branch one:
% 28.34/7.39 | (78) all_1_0_0 = 0
% 28.34/7.39 |
% 28.34/7.39 | Combining equations (78,1112) yields a new equation:
% 28.34/7.39 | (89) all_1_1_1 = 0
% 28.34/7.39 |
% 28.34/7.39 | Equations (89) can reduce 573 to:
% 28.34/7.39 | (79) $false
% 28.34/7.39 |
% 28.34/7.39 |-The branch is then unsatisfiable
% 28.34/7.39 |-Branch two:
% 28.34/7.39 | (77) ~ (all_1_0_0 = 0)
% 28.34/7.39 | (586) all_1_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_4_4, all_1_5_5) = v0)
% 28.34/7.39 |
% 28.34/7.39 | Equations (1112) can reduce 77 to:
% 28.34/7.39 | (573) ~ (all_1_1_1 = 0)
% 28.34/7.39 |
% 28.34/7.39 +-Applying beta-rule and splitting (81), into two cases.
% 28.34/7.39 |-Branch one:
% 28.34/7.39 | (89) all_1_1_1 = 0
% 28.34/7.39 |
% 28.34/7.39 | Equations (89) can reduce 573 to:
% 28.34/7.39 | (79) $false
% 28.34/7.39 |
% 28.34/7.39 |-The branch is then unsatisfiable
% 28.34/7.39 |-Branch two:
% 28.34/7.39 | (573) ~ (all_1_1_1 = 0)
% 28.34/7.39 | (574) ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_5_5, all_1_4_4) = v0)
% 28.34/7.39 |
% 28.34/7.39 +-Applying beta-rule and splitting (586), into two cases.
% 28.34/7.39 |-Branch one:
% 28.34/7.39 | (89) all_1_1_1 = 0
% 28.34/7.39 |
% 28.34/7.39 | Equations (89) can reduce 573 to:
% 28.34/7.39 | (79) $false
% 28.34/7.39 |
% 28.34/7.39 |-The branch is then unsatisfiable
% 28.34/7.39 |-Branch two:
% 28.34/7.39 | (573) ~ (all_1_1_1 = 0)
% 28.34/7.39 | (595) ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_4_4, all_1_5_5) = v0)
% 28.34/7.39 |
% 28.34/7.39 | Instantiating formula (5) with all_1_5_5, all_1_3_3, 0, all_1_1_1 and discharging atoms distinct_lines(all_1_5_5, all_1_3_3) = all_1_1_1, distinct_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 28.34/7.39 | (89) all_1_1_1 = 0
% 28.34/7.39 |
% 28.34/7.39 | Equations (89) can reduce 573 to:
% 28.34/7.39 | (79) $false
% 28.34/7.39 |
% 28.34/7.39 |-The branch is then unsatisfiable
% 28.34/7.39 |-Branch two:
% 28.34/7.39 | (598) ~ (distinct_lines(all_1_5_5, all_1_3_3) = 0)
% 28.34/7.39 | (78) all_1_0_0 = 0
% 28.34/7.39 |
% 28.34/7.39 | Combining equations (78,1112) yields a new equation:
% 28.34/7.39 | (89) all_1_1_1 = 0
% 28.34/7.39 |
% 28.34/7.39 | Equations (89) can reduce 573 to:
% 28.34/7.39 | (79) $false
% 28.34/7.39 |
% 28.34/7.39 |-The branch is then unsatisfiable
% 28.34/7.39 |-Branch two:
% 28.34/7.39 | (78) all_1_0_0 = 0
% 28.34/7.39 | (573) ~ (all_1_1_1 = 0)
% 28.34/7.39 |
% 28.34/7.39 | Combining equations (78,1112) yields a new equation:
% 28.34/7.39 | (89) all_1_1_1 = 0
% 28.34/7.39 |
% 28.34/7.39 | Equations (89) can reduce 573 to:
% 28.34/7.39 | (79) $false
% 28.34/7.39 |
% 28.34/7.39 |-The branch is then unsatisfiable
% 28.34/7.39 % SZS output end Proof for theBenchmark
% 28.34/7.40
% 28.34/7.40 6807ms
%------------------------------------------------------------------------------