TSTP Solution File: GEO188+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO188+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n027.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 03:48:25 EDT 2022
% Result : Theorem 11.40s 3.35s
% Output : Proof 23.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO188+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 14:15:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.59/0.57 ____ _
% 0.59/0.57 ___ / __ \_____(_)___ ________ __________
% 0.59/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.57
% 0.59/0.57 A Theorem Prover for First-Order Logic
% 0.59/0.58 (ePrincess v.1.0)
% 0.59/0.58
% 0.59/0.58 (c) Philipp Rümmer, 2009-2015
% 0.59/0.58 (c) Peter Backeman, 2014-2015
% 0.59/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.58 Bug reports to peter@backeman.se
% 0.59/0.58
% 0.59/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.58
% 0.59/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.62/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.56/0.93 Prover 0: Preprocessing ...
% 1.86/1.06 Prover 0: Warning: ignoring some quantifiers
% 1.86/1.08 Prover 0: Constructing countermodel ...
% 2.60/1.26 Prover 0: gave up
% 2.60/1.26 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.60/1.29 Prover 1: Preprocessing ...
% 2.94/1.37 Prover 1: Constructing countermodel ...
% 3.16/1.43 Prover 1: gave up
% 3.16/1.43 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.16/1.45 Prover 2: Preprocessing ...
% 3.75/1.56 Prover 2: Warning: ignoring some quantifiers
% 3.75/1.57 Prover 2: Constructing countermodel ...
% 4.58/1.72 Prover 2: gave up
% 4.58/1.72 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.58/1.73 Prover 3: Preprocessing ...
% 4.58/1.75 Prover 3: Warning: ignoring some quantifiers
% 4.58/1.75 Prover 3: Constructing countermodel ...
% 4.97/1.80 Prover 3: gave up
% 4.97/1.80 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 5.04/1.81 Prover 4: Preprocessing ...
% 5.10/1.88 Prover 4: Warning: ignoring some quantifiers
% 5.10/1.88 Prover 4: Constructing countermodel ...
% 10.07/3.02 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 10.07/3.04 Prover 5: Preprocessing ...
% 10.54/3.12 Prover 5: Constructing countermodel ...
% 11.40/3.35 Prover 5: proved (331ms)
% 11.40/3.35 Prover 4: stopped
% 11.40/3.35
% 11.40/3.35 No countermodel exists, formula is valid
% 11.40/3.35 % SZS status Theorem for theBenchmark
% 11.40/3.35
% 11.40/3.35 Generating proof ... found it (size 718)
% 22.41/5.95
% 22.41/5.95 % SZS output start Proof for theBenchmark
% 22.41/5.95 Assumed formulas after preprocessing and simplification:
% 22.41/5.95 | (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] : ( ~ (v4 = 0) & line_connecting(v2, v1) = v5 & line_connecting(v0, v1) = v3 & apart_point_and_line(v2, v3) = v4 & apart_point_and_line(v0, v5) = 0 & distinct_points(v1, v2) = 0 & distinct_points(v0, v2) = 0 & distinct_points(v0, v1) = 0)
% 22.86/6.00 | Applying alpha-rule on (0) yields:
% 22.86/6.01 | (1) ! [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)))))
% 22.86/6.01 | (2) ! [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)))
% 22.86/6.01 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 22.86/6.01 | (4) ! [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))
% 22.86/6.01 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 22.86/6.01 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 22.86/6.01 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 22.86/6.01 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 22.86/6.01 | (9) ! [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)
% 22.86/6.01 | (10) ! [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))))
% 22.86/6.01 | (11) ! [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))
% 22.86/6.01 | (12) ! [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))))
% 22.86/6.01 | (13) ! [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))))
% 22.86/6.01 | (14) ! [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)))
% 22.86/6.01 | (15) ! [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)))
% 22.86/6.01 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0)
% 22.86/6.01 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apart_point_and_line(v2, v1) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (intersection_point(v0, v1) = v5 & apart_point_and_line(v2, v0) = v4 & distinct_points(v2, v5) = v6 & (v6 = 0 | ( ~ (v4 = 0) & ~ (v3 = 0)))))
% 22.86/6.02 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 22.86/6.02 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 22.86/6.02 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 22.86/6.02 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 22.86/6.02 | (22) ! [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)))))
% 22.86/6.02 | (23) ! [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)))
% 22.86/6.02 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 22.86/6.02 | (25) ! [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))
% 22.86/6.02 | (26) ! [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)))
% 22.86/6.02 | (27) ! [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)
% 22.86/6.02 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 22.86/6.02 | (29) ! [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))
% 22.86/6.02 | (30) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v4 = 0) & line_connecting(v2, v1) = v5 & line_connecting(v0, v1) = v3 & apart_point_and_line(v2, v3) = v4 & apart_point_and_line(v0, v5) = 0 & distinct_points(v1, v2) = 0 & distinct_points(v0, v2) = 0 & distinct_points(v0, v1) = 0)
% 22.86/6.02 | (31) ! [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)
% 22.86/6.02 | (32) ! [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)))))
% 22.86/6.02 | (33) ! [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)))))
% 22.86/6.02 | (34) ! [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))
% 22.86/6.02 | (35) ! [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)))
% 22.86/6.02 | (36) ! [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))))
% 22.86/6.02 | (37) ! [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))))
% 22.86/6.03 | (38) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0)
% 22.86/6.03 | (39) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 22.86/6.03 | (40) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 22.86/6.03 | (41) ! [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))
% 22.86/6.03 | (42) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 22.86/6.03 | (43) ! [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)))
% 22.86/6.03 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 22.86/6.03 | (45) ! [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)))
% 22.86/6.03 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 22.86/6.03 |
% 22.86/6.03 | Instantiating (30) 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:
% 22.86/6.03 | (47) ~ (all_1_1_1 = 0) & line_connecting(all_1_3_3, all_1_4_4) = all_1_0_0 & line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2 & apart_point_and_line(all_1_3_3, all_1_2_2) = all_1_1_1 & apart_point_and_line(all_1_5_5, all_1_0_0) = 0 & distinct_points(all_1_4_4, all_1_3_3) = 0 & distinct_points(all_1_5_5, all_1_3_3) = 0 & distinct_points(all_1_5_5, all_1_4_4) = 0
% 22.86/6.03 |
% 22.86/6.03 | Applying alpha-rule on (47) yields:
% 22.86/6.03 | (48) ~ (all_1_1_1 = 0)
% 22.86/6.03 | (49) distinct_points(all_1_5_5, all_1_3_3) = 0
% 22.86/6.03 | (50) line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2
% 22.86/6.03 | (51) distinct_points(all_1_4_4, all_1_3_3) = 0
% 22.86/6.03 | (52) apart_point_and_line(all_1_3_3, all_1_2_2) = all_1_1_1
% 22.86/6.03 | (53) distinct_points(all_1_5_5, all_1_4_4) = 0
% 22.86/6.03 | (54) line_connecting(all_1_3_3, all_1_4_4) = all_1_0_0
% 22.86/6.03 | (55) apart_point_and_line(all_1_5_5, all_1_0_0) = 0
% 22.86/6.03 |
% 22.86/6.03 | Instantiating formula (39) with all_1_4_4 yields:
% 22.86/6.03 | (56) ~ (distinct_points(all_1_4_4, all_1_4_4) = 0)
% 22.86/6.03 |
% 22.86/6.03 | Instantiating formula (39) with all_1_5_5 yields:
% 22.86/6.03 | (57) ~ (distinct_points(all_1_5_5, all_1_5_5) = 0)
% 22.86/6.03 |
% 22.86/6.03 | Instantiating formula (43) with all_1_1_1, all_1_1_1, all_1_2_2, all_1_2_2, all_1_3_3, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = all_1_1_1, yields:
% 22.86/6.03 | (58) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v3 & apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 22.86/6.03 |
% 22.86/6.03 | Instantiating formula (13) with all_1_0_0, all_1_5_5, all_1_4_4, all_1_3_3 and discharging atoms line_connecting(all_1_3_3, all_1_4_4) = all_1_0_0, apart_point_and_line(all_1_5_5, all_1_0_0) = 0, yields:
% 22.86/6.03 | (59) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_1_3_3, all_1_4_4) = v0 & distinct_points(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v2 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))
% 22.86/6.03 |
% 22.86/6.03 | Instantiating formula (13) with all_1_2_2, all_1_5_5, all_1_4_4, all_1_5_5 and discharging atoms line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2, yields:
% 22.86/6.03 | (60) ~ (apart_point_and_line(all_1_5_5, all_1_2_2) = 0) | ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_1_5_5, all_1_4_4) = v2 & distinct_points(all_1_5_5, all_1_4_4) = v0 & distinct_points(all_1_5_5, all_1_5_5) = v1 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))
% 22.86/6.03 |
% 22.86/6.03 | Instantiating formula (36) with 0, all_1_4_4, all_1_3_3, all_1_4_4 and discharging atoms distinct_points(all_1_4_4, all_1_3_3) = 0, yields:
% 22.86/6.04 | (61) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_4_4, all_1_3_3) = v0 & apart_point_and_line(all_1_4_4, v0) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 22.86/6.04 |
% 22.86/6.04 | Instantiating formula (12) with 0, all_1_0_0, all_1_4_4, all_1_4_4, all_1_3_3 and discharging atoms line_connecting(all_1_3_3, all_1_4_4) = all_1_0_0, distinct_points(all_1_4_4, all_1_3_3) = 0, yields:
% 22.86/6.04 | (62) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_0_0) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & distinct_points(all_1_4_4, all_1_4_4) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 22.86/6.04 |
% 22.86/6.04 | Instantiating formula (15) with all_1_1_1, all_1_1_1, all_1_2_2, all_1_2_2, all_1_3_3, all_1_4_4 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = all_1_1_1, distinct_points(all_1_4_4, all_1_3_3) = 0, yields:
% 22.86/6.04 | (63) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 22.86/6.04 |
% 22.86/6.04 | Instantiating formula (36) with 0, all_1_5_5, all_1_3_3, all_1_4_4 and discharging atoms distinct_points(all_1_4_4, all_1_3_3) = 0, distinct_points(all_1_5_5, all_1_3_3) = 0, yields:
% 22.86/6.04 | (64) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_4_4, all_1_3_3) = v0 & apart_point_and_line(all_1_5_5, v0) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 22.86/6.04 |
% 22.86/6.04 | Instantiating formula (36) with 0, all_1_5_5, all_1_3_3, all_1_5_5 and discharging atoms distinct_points(all_1_5_5, all_1_3_3) = 0, yields:
% 22.86/6.04 | (65) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_3_3) = v0 & apart_point_and_line(all_1_5_5, v0) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 22.86/6.04 |
% 22.86/6.04 | Instantiating formula (12) with 0, all_1_0_0, all_1_5_5, all_1_4_4, all_1_3_3 and discharging atoms line_connecting(all_1_3_3, all_1_4_4) = all_1_0_0, distinct_points(all_1_5_5, all_1_3_3) = 0, yields:
% 22.86/6.04 | (66) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_1_0_0) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & distinct_points(all_1_5_5, all_1_4_4) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 22.86/6.04 |
% 22.86/6.04 | Instantiating formula (15) with all_1_1_1, all_1_1_1, all_1_2_2, all_1_2_2, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = all_1_1_1, distinct_points(all_1_5_5, all_1_3_3) = 0, yields:
% 22.86/6.04 | (67) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 22.86/6.04 |
% 22.86/6.04 | Instantiating formula (36) with 0, all_1_4_4, all_1_3_3, all_1_5_5 and discharging atoms distinct_points(all_1_4_4, all_1_3_3) = 0, distinct_points(all_1_5_5, all_1_3_3) = 0, yields:
% 22.86/6.04 | (68) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_3_3) = v0 & apart_point_and_line(all_1_4_4, v0) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 22.86/6.04 |
% 22.86/6.04 | Instantiating formula (37) with 0, all_1_5_5, all_1_3_3, all_1_4_4 and discharging atoms distinct_points(all_1_4_4, all_1_3_3) = 0, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 22.86/6.04 | (69) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_4_4, all_1_3_3) = v0 & apart_point_and_line(all_1_5_5, v0) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 22.86/6.04 |
% 22.86/6.04 | Instantiating formula (36) with 0, all_1_5_5, all_1_4_4, all_1_5_5 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 22.86/6.04 | (70) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_4_4) = v0 & apart_point_and_line(all_1_5_5, v0) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 22.86/6.04 |
% 22.86/6.04 | Instantiating formula (10) with 0, all_1_0_0, all_1_5_5, all_1_4_4, all_1_3_3 and discharging atoms line_connecting(all_1_3_3, all_1_4_4) = all_1_0_0, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 22.86/6.04 | (71) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_1_0_0) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & distinct_points(all_1_5_5, all_1_3_3) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 22.86/6.04 |
% 22.86/6.04 | Instantiating formula (10) with 0, all_1_2_2, all_1_5_5, all_1_4_4, all_1_5_5 and discharging atoms line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 22.86/6.04 | (72) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & distinct_points(all_1_5_5, all_1_5_5) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 22.86/6.04 |
% 22.86/6.04 | Instantiating (72) with all_16_0_6, all_16_1_7, all_16_2_8 yields:
% 22.86/6.04 | (73) apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7 & distinct_points(all_1_5_5, all_1_4_4) = all_16_2_8 & distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6 & ( ~ (all_16_1_7 = 0) | ~ (all_16_2_8 = 0) | all_16_0_6 = 0)
% 22.86/6.04 |
% 22.86/6.04 | Applying alpha-rule on (73) yields:
% 22.86/6.04 | (74) apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7
% 22.86/6.04 | (75) distinct_points(all_1_5_5, all_1_4_4) = all_16_2_8
% 22.86/6.04 | (76) distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6
% 22.86/6.04 | (77) ~ (all_16_1_7 = 0) | ~ (all_16_2_8 = 0) | all_16_0_6 = 0
% 22.86/6.04 |
% 22.86/6.04 | Instantiating (71) with all_18_0_9, all_18_1_10, all_18_2_11 yields:
% 22.86/6.04 | (78) apart_point_and_line(all_1_5_5, all_1_0_0) = all_18_1_10 & distinct_points(all_1_3_3, all_1_4_4) = all_18_2_11 & distinct_points(all_1_5_5, all_1_3_3) = all_18_0_9 & ( ~ (all_18_1_10 = 0) | ~ (all_18_2_11 = 0) | all_18_0_9 = 0)
% 22.86/6.04 |
% 22.86/6.04 | Applying alpha-rule on (78) yields:
% 22.86/6.04 | (79) apart_point_and_line(all_1_5_5, all_1_0_0) = all_18_1_10
% 22.86/6.04 | (80) distinct_points(all_1_3_3, all_1_4_4) = all_18_2_11
% 22.86/6.04 | (81) distinct_points(all_1_5_5, all_1_3_3) = all_18_0_9
% 22.86/6.04 | (82) ~ (all_18_1_10 = 0) | ~ (all_18_2_11 = 0) | all_18_0_9 = 0
% 22.86/6.04 |
% 22.86/6.04 | Instantiating (69) with all_20_0_12, all_20_1_13, all_20_2_14 yields:
% 22.86/6.04 | (83) line_connecting(all_1_4_4, all_1_3_3) = all_20_2_14 & apart_point_and_line(all_1_5_5, all_20_2_14) = all_20_1_13 & distinct_points(all_1_5_5, all_1_3_3) = all_20_0_12 & ( ~ (all_20_1_13 = 0) | all_20_0_12 = 0)
% 22.86/6.04 |
% 22.86/6.04 | Applying alpha-rule on (83) yields:
% 22.86/6.04 | (84) line_connecting(all_1_4_4, all_1_3_3) = all_20_2_14
% 22.86/6.04 | (85) apart_point_and_line(all_1_5_5, all_20_2_14) = all_20_1_13
% 22.86/6.05 | (86) distinct_points(all_1_5_5, all_1_3_3) = all_20_0_12
% 22.86/6.05 | (87) ~ (all_20_1_13 = 0) | all_20_0_12 = 0
% 22.86/6.05 |
% 22.86/6.05 | Instantiating (62) with all_22_0_15, all_22_1_16, all_22_2_17 yields:
% 22.86/6.05 | (88) apart_point_and_line(all_1_4_4, all_1_0_0) = all_22_1_16 & distinct_points(all_1_3_3, all_1_4_4) = all_22_2_17 & distinct_points(all_1_4_4, all_1_4_4) = all_22_0_15 & ( ~ (all_22_1_16 = 0) | ~ (all_22_2_17 = 0) | all_22_0_15 = 0)
% 22.86/6.05 |
% 22.86/6.05 | Applying alpha-rule on (88) yields:
% 22.86/6.05 | (89) apart_point_and_line(all_1_4_4, all_1_0_0) = all_22_1_16
% 22.86/6.05 | (90) distinct_points(all_1_3_3, all_1_4_4) = all_22_2_17
% 22.86/6.05 | (91) distinct_points(all_1_4_4, all_1_4_4) = all_22_0_15
% 22.86/6.05 | (92) ~ (all_22_1_16 = 0) | ~ (all_22_2_17 = 0) | all_22_0_15 = 0
% 22.86/6.05 |
% 22.86/6.05 | Instantiating (61) with all_24_0_18, all_24_1_19, all_24_2_20 yields:
% 22.86/6.05 | (93) line_connecting(all_1_4_4, all_1_3_3) = all_24_2_20 & apart_point_and_line(all_1_4_4, all_24_2_20) = all_24_1_19 & distinct_points(all_1_4_4, all_1_4_4) = all_24_0_18 & ( ~ (all_24_1_19 = 0) | all_24_0_18 = 0)
% 22.86/6.05 |
% 22.86/6.05 | Applying alpha-rule on (93) yields:
% 22.86/6.05 | (94) line_connecting(all_1_4_4, all_1_3_3) = all_24_2_20
% 22.86/6.05 | (95) apart_point_and_line(all_1_4_4, all_24_2_20) = all_24_1_19
% 22.86/6.05 | (96) distinct_points(all_1_4_4, all_1_4_4) = all_24_0_18
% 22.86/6.05 | (97) ~ (all_24_1_19 = 0) | all_24_0_18 = 0
% 22.86/6.05 |
% 22.86/6.05 | Instantiating (59) with all_26_0_21, all_26_1_22, all_26_2_23 yields:
% 22.86/6.05 | (98) distinct_points(all_1_3_3, all_1_4_4) = all_26_2_23 & distinct_points(all_1_5_5, all_1_3_3) = all_26_1_22 & distinct_points(all_1_5_5, all_1_4_4) = all_26_0_21 & ( ~ (all_26_2_23 = 0) | (all_26_0_21 = 0 & all_26_1_22 = 0))
% 22.86/6.05 |
% 22.86/6.05 | Applying alpha-rule on (98) yields:
% 22.86/6.05 | (99) distinct_points(all_1_3_3, all_1_4_4) = all_26_2_23
% 22.86/6.05 | (100) distinct_points(all_1_5_5, all_1_3_3) = all_26_1_22
% 22.86/6.05 | (101) distinct_points(all_1_5_5, all_1_4_4) = all_26_0_21
% 22.86/6.05 | (102) ~ (all_26_2_23 = 0) | (all_26_0_21 = 0 & all_26_1_22 = 0)
% 22.86/6.05 |
% 22.86/6.05 | Instantiating (68) with all_28_0_24, all_28_1_25, all_28_2_26 yields:
% 22.86/6.05 | (103) line_connecting(all_1_5_5, all_1_3_3) = all_28_2_26 & apart_point_and_line(all_1_4_4, all_28_2_26) = all_28_1_25 & distinct_points(all_1_4_4, all_1_5_5) = all_28_0_24 & ( ~ (all_28_1_25 = 0) | all_28_0_24 = 0)
% 22.86/6.05 |
% 22.86/6.05 | Applying alpha-rule on (103) yields:
% 22.86/6.05 | (104) line_connecting(all_1_5_5, all_1_3_3) = all_28_2_26
% 22.86/6.05 | (105) apart_point_and_line(all_1_4_4, all_28_2_26) = all_28_1_25
% 22.86/6.05 | (106) distinct_points(all_1_4_4, all_1_5_5) = all_28_0_24
% 22.86/6.05 | (107) ~ (all_28_1_25 = 0) | all_28_0_24 = 0
% 22.86/6.05 |
% 22.86/6.05 | Instantiating (70) with all_30_0_27, all_30_1_28, all_30_2_29 yields:
% 22.86/6.05 | (108) line_connecting(all_1_5_5, all_1_4_4) = all_30_2_29 & apart_point_and_line(all_1_5_5, all_30_2_29) = all_30_1_28 & distinct_points(all_1_5_5, all_1_5_5) = all_30_0_27 & ( ~ (all_30_1_28 = 0) | all_30_0_27 = 0)
% 22.86/6.05 |
% 22.86/6.05 | Applying alpha-rule on (108) yields:
% 22.86/6.05 | (109) line_connecting(all_1_5_5, all_1_4_4) = all_30_2_29
% 22.86/6.05 | (110) apart_point_and_line(all_1_5_5, all_30_2_29) = all_30_1_28
% 22.86/6.05 | (111) distinct_points(all_1_5_5, all_1_5_5) = all_30_0_27
% 22.86/6.05 | (112) ~ (all_30_1_28 = 0) | all_30_0_27 = 0
% 22.86/6.05 |
% 22.86/6.05 | Instantiating (66) with all_34_0_33, all_34_1_34, all_34_2_35 yields:
% 22.86/6.05 | (113) apart_point_and_line(all_1_5_5, all_1_0_0) = all_34_1_34 & distinct_points(all_1_3_3, all_1_4_4) = all_34_2_35 & distinct_points(all_1_5_5, all_1_4_4) = all_34_0_33 & ( ~ (all_34_1_34 = 0) | ~ (all_34_2_35 = 0) | all_34_0_33 = 0)
% 22.86/6.05 |
% 22.86/6.05 | Applying alpha-rule on (113) yields:
% 22.86/6.05 | (114) apart_point_and_line(all_1_5_5, all_1_0_0) = all_34_1_34
% 22.86/6.05 | (115) distinct_points(all_1_3_3, all_1_4_4) = all_34_2_35
% 22.86/6.05 | (116) distinct_points(all_1_5_5, all_1_4_4) = all_34_0_33
% 22.86/6.05 | (117) ~ (all_34_1_34 = 0) | ~ (all_34_2_35 = 0) | all_34_0_33 = 0
% 22.86/6.05 |
% 22.86/6.05 | Instantiating (65) with all_36_0_36, all_36_1_37, all_36_2_38 yields:
% 22.86/6.05 | (118) line_connecting(all_1_5_5, all_1_3_3) = all_36_2_38 & apart_point_and_line(all_1_5_5, all_36_2_38) = all_36_1_37 & distinct_points(all_1_5_5, all_1_5_5) = all_36_0_36 & ( ~ (all_36_1_37 = 0) | all_36_0_36 = 0)
% 22.86/6.05 |
% 22.86/6.05 | Applying alpha-rule on (118) yields:
% 22.86/6.05 | (119) line_connecting(all_1_5_5, all_1_3_3) = all_36_2_38
% 22.86/6.05 | (120) apart_point_and_line(all_1_5_5, all_36_2_38) = all_36_1_37
% 22.86/6.05 | (121) distinct_points(all_1_5_5, all_1_5_5) = all_36_0_36
% 22.86/6.05 | (122) ~ (all_36_1_37 = 0) | all_36_0_36 = 0
% 22.86/6.05 |
% 22.86/6.05 | Instantiating (64) with all_38_0_39, all_38_1_40, all_38_2_41 yields:
% 22.86/6.05 | (123) line_connecting(all_1_4_4, all_1_3_3) = all_38_2_41 & apart_point_and_line(all_1_5_5, all_38_2_41) = all_38_1_40 & distinct_points(all_1_5_5, all_1_4_4) = all_38_0_39 & ( ~ (all_38_1_40 = 0) | all_38_0_39 = 0)
% 22.86/6.05 |
% 22.86/6.05 | Applying alpha-rule on (123) yields:
% 22.86/6.05 | (124) line_connecting(all_1_4_4, all_1_3_3) = all_38_2_41
% 22.86/6.05 | (125) apart_point_and_line(all_1_5_5, all_38_2_41) = all_38_1_40
% 22.86/6.05 | (126) distinct_points(all_1_5_5, all_1_4_4) = all_38_0_39
% 22.86/6.05 | (127) ~ (all_38_1_40 = 0) | all_38_0_39 = 0
% 22.86/6.05 |
% 22.86/6.05 +-Applying beta-rule and splitting (67), into two cases.
% 22.86/6.05 |-Branch one:
% 22.86/6.05 | (128) all_1_1_1 = 0
% 22.86/6.05 |
% 22.86/6.05 | Equations (128) can reduce 48 to:
% 22.86/6.05 | (129) $false
% 22.86/6.05 |
% 22.86/6.05 |-The branch is then unsatisfiable
% 22.86/6.05 |-Branch two:
% 22.86/6.05 | (48) ~ (all_1_1_1 = 0)
% 22.86/6.05 | (131) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 22.86/6.06 |
% 22.86/6.06 | Instantiating (131) with all_44_0_42, all_44_1_43, all_44_2_44 yields:
% 22.86/6.06 | (132) apart_point_and_line(all_1_5_5, all_1_2_2) = all_44_0_42 & apart_point_and_line(all_1_5_5, all_1_2_2) = all_44_1_43 & distinct_lines(all_1_2_2, all_1_2_2) = all_44_2_44 & ( ~ (all_44_2_44 = 0) | all_44_0_42 = 0 | all_44_1_43 = 0)
% 22.86/6.06 |
% 22.86/6.06 | Applying alpha-rule on (132) yields:
% 22.86/6.06 | (133) apart_point_and_line(all_1_5_5, all_1_2_2) = all_44_0_42
% 22.86/6.06 | (134) apart_point_and_line(all_1_5_5, all_1_2_2) = all_44_1_43
% 22.86/6.06 | (135) distinct_lines(all_1_2_2, all_1_2_2) = all_44_2_44
% 22.86/6.06 | (136) ~ (all_44_2_44 = 0) | all_44_0_42 = 0 | all_44_1_43 = 0
% 22.86/6.06 |
% 22.86/6.06 +-Applying beta-rule and splitting (58), into two cases.
% 22.86/6.06 |-Branch one:
% 22.86/6.06 | (128) all_1_1_1 = 0
% 22.86/6.06 |
% 22.86/6.06 | Equations (128) can reduce 48 to:
% 22.86/6.06 | (129) $false
% 22.86/6.06 |
% 22.86/6.06 |-The branch is then unsatisfiable
% 22.86/6.06 |-Branch two:
% 22.86/6.06 | (48) ~ (all_1_1_1 = 0)
% 22.86/6.06 | (140) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v3 & apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 22.86/6.06 |
% 22.86/6.06 | Instantiating (140) with all_49_0_45, all_49_1_46, all_49_2_47, all_49_3_48 yields:
% 22.86/6.06 | (141) apart_point_and_line(all_1_3_3, all_1_2_2) = all_49_0_45 & apart_point_and_line(all_1_3_3, all_1_2_2) = all_49_1_46 & distinct_lines(all_1_2_2, all_1_2_2) = all_49_2_47 & distinct_points(all_1_3_3, all_1_3_3) = all_49_3_48 & ( ~ (all_49_2_47 = 0) | ~ (all_49_3_48 = 0) | all_49_0_45 = 0 | all_49_1_46 = 0)
% 22.86/6.06 |
% 22.86/6.06 | Applying alpha-rule on (141) yields:
% 22.86/6.06 | (142) distinct_points(all_1_3_3, all_1_3_3) = all_49_3_48
% 22.86/6.06 | (143) ~ (all_49_2_47 = 0) | ~ (all_49_3_48 = 0) | all_49_0_45 = 0 | all_49_1_46 = 0
% 22.86/6.06 | (144) apart_point_and_line(all_1_3_3, all_1_2_2) = all_49_1_46
% 22.86/6.06 | (145) distinct_lines(all_1_2_2, all_1_2_2) = all_49_2_47
% 22.86/6.06 | (146) apart_point_and_line(all_1_3_3, all_1_2_2) = all_49_0_45
% 22.86/6.06 |
% 22.86/6.06 +-Applying beta-rule and splitting (63), into two cases.
% 22.86/6.06 |-Branch one:
% 22.86/6.06 | (128) all_1_1_1 = 0
% 22.86/6.06 |
% 22.86/6.06 | Equations (128) can reduce 48 to:
% 22.86/6.06 | (129) $false
% 22.86/6.06 |
% 22.86/6.06 |-The branch is then unsatisfiable
% 22.86/6.06 |-Branch two:
% 22.86/6.06 | (48) ~ (all_1_1_1 = 0)
% 22.86/6.06 | (150) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 22.86/6.06 |
% 22.86/6.06 | Instantiating (150) with all_54_0_49, all_54_1_50, all_54_2_51 yields:
% 22.86/6.06 | (151) apart_point_and_line(all_1_4_4, all_1_2_2) = all_54_0_49 & apart_point_and_line(all_1_4_4, all_1_2_2) = all_54_1_50 & distinct_lines(all_1_2_2, all_1_2_2) = all_54_2_51 & ( ~ (all_54_2_51 = 0) | all_54_0_49 = 0 | all_54_1_50 = 0)
% 22.86/6.06 |
% 22.86/6.06 | Applying alpha-rule on (151) yields:
% 22.86/6.06 | (152) apart_point_and_line(all_1_4_4, all_1_2_2) = all_54_0_49
% 22.86/6.06 | (153) apart_point_and_line(all_1_4_4, all_1_2_2) = all_54_1_50
% 22.86/6.06 | (154) distinct_lines(all_1_2_2, all_1_2_2) = all_54_2_51
% 22.86/6.06 | (155) ~ (all_54_2_51 = 0) | all_54_0_49 = 0 | all_54_1_50 = 0
% 22.86/6.06 |
% 22.86/6.06 | Instantiating formula (8) with all_1_4_4, all_1_3_3, all_24_2_20, all_38_2_41 and discharging atoms line_connecting(all_1_4_4, all_1_3_3) = all_38_2_41, line_connecting(all_1_4_4, all_1_3_3) = all_24_2_20, yields:
% 22.86/6.06 | (156) all_38_2_41 = all_24_2_20
% 22.86/6.06 |
% 22.86/6.06 | Instantiating formula (8) with all_1_4_4, all_1_3_3, all_20_2_14, all_38_2_41 and discharging atoms line_connecting(all_1_4_4, all_1_3_3) = all_38_2_41, line_connecting(all_1_4_4, all_1_3_3) = all_20_2_14, yields:
% 22.86/6.06 | (157) all_38_2_41 = all_20_2_14
% 22.86/6.06 |
% 22.86/6.06 | Instantiating formula (8) with all_1_5_5, all_1_3_3, all_28_2_26, all_36_2_38 and discharging atoms line_connecting(all_1_5_5, all_1_3_3) = all_36_2_38, line_connecting(all_1_5_5, all_1_3_3) = all_28_2_26, yields:
% 22.86/6.06 | (158) all_36_2_38 = all_28_2_26
% 22.86/6.06 |
% 22.86/6.06 | Instantiating formula (8) with all_1_5_5, all_1_4_4, all_30_2_29, all_1_2_2 and discharging atoms line_connecting(all_1_5_5, all_1_4_4) = all_30_2_29, line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2, yields:
% 22.86/6.06 | (159) all_30_2_29 = all_1_2_2
% 22.86/6.06 |
% 22.86/6.06 | Instantiating formula (20) with all_1_3_3, all_1_2_2, all_49_0_45, all_1_1_1 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = all_49_0_45, apart_point_and_line(all_1_3_3, all_1_2_2) = all_1_1_1, yields:
% 22.86/6.06 | (160) all_49_0_45 = all_1_1_1
% 22.86/6.06 |
% 22.86/6.06 | Instantiating formula (20) with all_1_3_3, all_1_2_2, all_49_1_46, all_49_0_45 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = all_49_0_45, apart_point_and_line(all_1_3_3, all_1_2_2) = all_49_1_46, yields:
% 22.86/6.06 | (161) all_49_0_45 = all_49_1_46
% 22.86/6.06 |
% 22.86/6.06 | Instantiating formula (20) with all_1_4_4, all_1_2_2, all_54_1_50, all_54_0_49 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_54_0_49, apart_point_and_line(all_1_4_4, all_1_2_2) = all_54_1_50, yields:
% 22.86/6.06 | (162) all_54_0_49 = all_54_1_50
% 22.86/6.06 |
% 22.86/6.06 | Instantiating formula (20) with all_1_5_5, all_20_2_14, all_20_1_13, all_38_1_40 and discharging atoms apart_point_and_line(all_1_5_5, all_20_2_14) = all_20_1_13, yields:
% 22.86/6.06 | (163) all_38_1_40 = all_20_1_13 | ~ (apart_point_and_line(all_1_5_5, all_20_2_14) = all_38_1_40)
% 22.86/6.06 |
% 22.86/6.06 | Instantiating formula (20) with all_1_5_5, all_1_0_0, all_34_1_34, 0 and discharging atoms apart_point_and_line(all_1_5_5, all_1_0_0) = all_34_1_34, apart_point_and_line(all_1_5_5, all_1_0_0) = 0, yields:
% 22.86/6.06 | (164) all_34_1_34 = 0
% 22.86/6.06 |
% 22.86/6.06 | Instantiating formula (20) with all_1_5_5, all_1_0_0, all_18_1_10, all_34_1_34 and discharging atoms apart_point_and_line(all_1_5_5, all_1_0_0) = all_34_1_34, apart_point_and_line(all_1_5_5, all_1_0_0) = all_18_1_10, yields:
% 22.86/6.06 | (165) all_34_1_34 = all_18_1_10
% 22.86/6.06 |
% 22.86/6.06 | Instantiating formula (20) with all_1_5_5, all_1_2_2, all_44_0_42, all_30_1_28 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_44_0_42, yields:
% 22.86/6.06 | (166) all_44_0_42 = all_30_1_28 | ~ (apart_point_and_line(all_1_5_5, all_1_2_2) = all_30_1_28)
% 22.86/6.06 |
% 22.86/6.06 | Instantiating formula (20) with all_1_5_5, all_1_2_2, all_44_1_43, all_18_1_10 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_44_1_43, yields:
% 22.86/6.06 | (167) all_44_1_43 = all_18_1_10 | ~ (apart_point_and_line(all_1_5_5, all_1_2_2) = all_18_1_10)
% 22.86/6.06 |
% 22.86/6.06 | Instantiating formula (20) with all_1_5_5, all_1_2_2, all_44_1_43, all_44_0_42 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_44_0_42, apart_point_and_line(all_1_5_5, all_1_2_2) = all_44_1_43, yields:
% 22.86/6.06 | (168) all_44_0_42 = all_44_1_43
% 22.86/6.06 |
% 22.86/6.06 | Instantiating formula (20) with all_1_5_5, all_1_2_2, all_16_1_7, all_30_1_28 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 22.86/6.06 | (169) all_30_1_28 = all_16_1_7 | ~ (apart_point_and_line(all_1_5_5, all_1_2_2) = all_30_1_28)
% 22.86/6.06 |
% 22.86/6.06 | Instantiating formula (20) with all_1_5_5, all_1_2_2, all_16_1_7, all_44_0_42 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_44_0_42, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 22.86/6.07 | (170) all_44_0_42 = all_16_1_7
% 22.86/6.07 |
% 22.86/6.07 | Instantiating formula (39) with all_1_3_3 yields:
% 22.86/6.07 | (171) ~ (distinct_points(all_1_3_3, all_1_3_3) = 0)
% 22.86/6.07 |
% 22.86/6.07 | Instantiating formula (46) with all_1_3_3, all_1_4_4, all_26_2_23, all_34_2_35 and discharging atoms distinct_points(all_1_3_3, all_1_4_4) = all_34_2_35, distinct_points(all_1_3_3, all_1_4_4) = all_26_2_23, yields:
% 22.86/6.07 | (172) all_34_2_35 = all_26_2_23
% 22.86/6.07 |
% 22.86/6.07 | Instantiating formula (46) with all_1_3_3, all_1_4_4, all_22_2_17, all_34_2_35 and discharging atoms distinct_points(all_1_3_3, all_1_4_4) = all_34_2_35, distinct_points(all_1_3_3, all_1_4_4) = all_22_2_17, yields:
% 22.86/6.07 | (173) all_34_2_35 = all_22_2_17
% 22.86/6.07 |
% 22.86/6.07 | Instantiating formula (46) with all_1_3_3, all_1_4_4, all_18_2_11, all_34_2_35 and discharging atoms distinct_points(all_1_3_3, all_1_4_4) = all_34_2_35, distinct_points(all_1_3_3, all_1_4_4) = all_18_2_11, yields:
% 22.86/6.07 | (174) all_34_2_35 = all_18_2_11
% 22.86/6.07 |
% 22.86/6.07 | Using (96) and (56) yields:
% 22.86/6.07 | (175) ~ (all_24_0_18 = 0)
% 22.86/6.07 |
% 22.86/6.07 | Instantiating formula (46) with all_1_4_4, all_1_4_4, all_22_0_15, all_24_0_18 and discharging atoms distinct_points(all_1_4_4, all_1_4_4) = all_24_0_18, distinct_points(all_1_4_4, all_1_4_4) = all_22_0_15, yields:
% 22.86/6.07 | (176) all_24_0_18 = all_22_0_15
% 22.86/6.07 |
% 22.86/6.07 | Instantiating formula (46) with all_1_5_5, all_1_3_3, all_26_1_22, 0 and discharging atoms distinct_points(all_1_5_5, all_1_3_3) = all_26_1_22, distinct_points(all_1_5_5, all_1_3_3) = 0, yields:
% 22.86/6.07 | (177) all_26_1_22 = 0
% 22.86/6.07 |
% 22.86/6.07 | Instantiating formula (46) with all_1_5_5, all_1_3_3, all_20_0_12, all_26_1_22 and discharging atoms distinct_points(all_1_5_5, all_1_3_3) = all_26_1_22, distinct_points(all_1_5_5, all_1_3_3) = all_20_0_12, yields:
% 22.86/6.07 | (178) all_26_1_22 = all_20_0_12
% 22.86/6.07 |
% 22.86/6.07 | Instantiating formula (46) with all_1_5_5, all_1_3_3, all_18_0_9, all_20_0_12 and discharging atoms distinct_points(all_1_5_5, all_1_3_3) = all_20_0_12, distinct_points(all_1_5_5, all_1_3_3) = all_18_0_9, yields:
% 22.86/6.07 | (179) all_20_0_12 = all_18_0_9
% 22.86/6.07 |
% 22.86/6.07 | Instantiating formula (46) with all_1_5_5, all_1_4_4, all_38_0_39, 0 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = all_38_0_39, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 22.86/6.07 | (180) all_38_0_39 = 0
% 22.86/6.07 |
% 22.86/6.07 | Instantiating formula (46) with all_1_5_5, all_1_4_4, all_34_0_33, all_38_0_39 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = all_38_0_39, distinct_points(all_1_5_5, all_1_4_4) = all_34_0_33, yields:
% 22.86/6.07 | (181) all_38_0_39 = all_34_0_33
% 22.86/6.07 |
% 22.86/6.07 | Instantiating formula (46) with all_1_5_5, all_1_4_4, all_26_0_21, all_38_0_39 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = all_38_0_39, distinct_points(all_1_5_5, all_1_4_4) = all_26_0_21, yields:
% 22.86/6.07 | (182) all_38_0_39 = all_26_0_21
% 22.86/6.07 |
% 22.86/6.07 | Instantiating formula (46) with all_1_5_5, all_1_4_4, all_16_2_8, all_38_0_39 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = all_38_0_39, distinct_points(all_1_5_5, all_1_4_4) = all_16_2_8, yields:
% 22.86/6.07 | (183) all_38_0_39 = all_16_2_8
% 22.86/6.07 |
% 22.86/6.07 | Instantiating formula (46) with all_1_5_5, all_1_5_5, all_30_0_27, all_36_0_36 and discharging atoms distinct_points(all_1_5_5, all_1_5_5) = all_36_0_36, distinct_points(all_1_5_5, all_1_5_5) = all_30_0_27, yields:
% 22.86/6.07 | (184) all_36_0_36 = all_30_0_27
% 22.86/6.07 |
% 22.86/6.07 | Using (111) and (57) yields:
% 22.86/6.07 | (185) ~ (all_30_0_27 = 0)
% 22.86/6.07 |
% 22.86/6.07 | Instantiating formula (46) with all_1_5_5, all_1_5_5, all_16_0_6, all_36_0_36 and discharging atoms distinct_points(all_1_5_5, all_1_5_5) = all_36_0_36, distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6, yields:
% 22.86/6.07 | (186) all_36_0_36 = all_16_0_6
% 22.86/6.07 |
% 22.86/6.07 | Combining equations (160,161) yields a new equation:
% 22.86/6.07 | (187) all_49_1_46 = all_1_1_1
% 22.86/6.07 |
% 22.86/6.07 | Combining equations (170,168) yields a new equation:
% 22.86/6.07 | (188) all_44_1_43 = all_16_1_7
% 22.86/6.07 |
% 22.86/6.07 | Combining equations (180,181) yields a new equation:
% 22.86/6.07 | (189) all_34_0_33 = 0
% 22.86/6.07 |
% 22.86/6.07 | Combining equations (183,181) yields a new equation:
% 22.86/6.07 | (190) all_34_0_33 = all_16_2_8
% 22.86/6.07 |
% 22.86/6.07 | Combining equations (182,181) yields a new equation:
% 22.86/6.07 | (191) all_34_0_33 = all_26_0_21
% 22.86/6.07 |
% 22.86/6.07 | Combining equations (156,157) yields a new equation:
% 22.86/6.07 | (192) all_24_2_20 = all_20_2_14
% 22.86/6.07 |
% 22.86/6.07 | Simplifying 192 yields:
% 22.86/6.07 | (193) all_24_2_20 = all_20_2_14
% 22.86/6.07 |
% 22.86/6.07 | Combining equations (186,184) yields a new equation:
% 22.86/6.07 | (194) all_30_0_27 = all_16_0_6
% 22.86/6.07 |
% 22.86/6.07 | Combining equations (190,191) yields a new equation:
% 22.86/6.07 | (195) all_26_0_21 = all_16_2_8
% 22.86/6.07 |
% 22.86/6.07 | Combining equations (189,191) yields a new equation:
% 22.86/6.07 | (196) all_26_0_21 = 0
% 22.86/6.07 |
% 22.86/6.07 | Combining equations (164,165) yields a new equation:
% 22.86/6.07 | (197) all_18_1_10 = 0
% 22.86/6.07 |
% 22.86/6.07 | Combining equations (174,172) yields a new equation:
% 22.86/6.07 | (198) all_26_2_23 = all_18_2_11
% 22.86/6.07 |
% 22.86/6.07 | Combining equations (173,172) yields a new equation:
% 22.86/6.07 | (199) all_26_2_23 = all_22_2_17
% 22.86/6.07 |
% 22.86/6.07 | Combining equations (196,195) yields a new equation:
% 22.86/6.07 | (200) all_16_2_8 = 0
% 22.86/6.07 |
% 22.86/6.07 | Combining equations (178,177) yields a new equation:
% 22.86/6.07 | (201) all_20_0_12 = 0
% 22.86/6.07 |
% 22.86/6.07 | Simplifying 201 yields:
% 22.86/6.07 | (202) all_20_0_12 = 0
% 22.86/6.07 |
% 22.86/6.07 | Combining equations (198,199) yields a new equation:
% 22.86/6.07 | (203) all_22_2_17 = all_18_2_11
% 22.86/6.07 |
% 22.86/6.07 | Combining equations (179,202) yields a new equation:
% 22.86/6.07 | (204) all_18_0_9 = 0
% 22.86/6.07 |
% 22.86/6.07 | Simplifying 204 yields:
% 22.86/6.07 | (205) all_18_0_9 = 0
% 22.86/6.07 |
% 22.86/6.07 | Combining equations (194,184) yields a new equation:
% 22.86/6.07 | (186) all_36_0_36 = all_16_0_6
% 22.86/6.07 |
% 22.86/6.07 | Combining equations (188,168) yields a new equation:
% 22.86/6.07 | (170) all_44_0_42 = all_16_1_7
% 22.86/6.07 |
% 22.86/6.07 | Equations (194) can reduce 185 to:
% 22.86/6.07 | (208) ~ (all_16_0_6 = 0)
% 22.86/6.07 |
% 22.86/6.07 | Equations (176) can reduce 175 to:
% 22.86/6.07 | (209) ~ (all_22_0_15 = 0)
% 22.86/6.07 |
% 22.86/6.07 | From (193) and (94) follows:
% 22.86/6.08 | (84) line_connecting(all_1_4_4, all_1_3_3) = all_20_2_14
% 22.86/6.08 |
% 22.86/6.08 | From (158) and (119) follows:
% 22.86/6.08 | (104) line_connecting(all_1_5_5, all_1_3_3) = all_28_2_26
% 22.86/6.08 |
% 22.86/6.08 | From (159) and (109) follows:
% 22.86/6.08 | (50) line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2
% 22.86/6.08 |
% 22.86/6.08 | From (187) and (144) follows:
% 22.86/6.08 | (52) apart_point_and_line(all_1_3_3, all_1_2_2) = all_1_1_1
% 22.86/6.08 |
% 22.86/6.08 | From (193) and (95) follows:
% 22.86/6.08 | (214) apart_point_and_line(all_1_4_4, all_20_2_14) = all_24_1_19
% 22.86/6.08 |
% 22.86/6.08 | From (162) and (152) follows:
% 22.86/6.08 | (153) apart_point_and_line(all_1_4_4, all_1_2_2) = all_54_1_50
% 22.86/6.08 |
% 22.86/6.08 | From (157) and (125) follows:
% 22.86/6.08 | (216) apart_point_and_line(all_1_5_5, all_20_2_14) = all_38_1_40
% 22.86/6.08 |
% 22.86/6.08 | From (158) and (120) follows:
% 22.86/6.08 | (217) apart_point_and_line(all_1_5_5, all_28_2_26) = all_36_1_37
% 22.86/6.08 |
% 22.86/6.08 | From (159) and (110) follows:
% 22.86/6.08 | (218) apart_point_and_line(all_1_5_5, all_1_2_2) = all_30_1_28
% 22.86/6.08 |
% 22.86/6.08 | From (197) and (79) follows:
% 22.86/6.08 | (55) apart_point_and_line(all_1_5_5, all_1_0_0) = 0
% 22.86/6.08 |
% 22.86/6.08 | From (203) and (90) follows:
% 22.86/6.08 | (80) distinct_points(all_1_3_3, all_1_4_4) = all_18_2_11
% 22.86/6.08 |
% 22.86/6.08 | From (176) and (96) follows:
% 22.86/6.08 | (91) distinct_points(all_1_4_4, all_1_4_4) = all_22_0_15
% 22.86/6.08 |
% 22.86/6.08 | From (205) and (81) follows:
% 22.86/6.08 | (49) distinct_points(all_1_5_5, all_1_3_3) = 0
% 22.86/6.08 |
% 22.86/6.08 | From (200) and (75) follows:
% 22.86/6.08 | (53) distinct_points(all_1_5_5, all_1_4_4) = 0
% 22.86/6.08 |
% 22.86/6.08 | From (194) and (111) follows:
% 22.86/6.08 | (76) distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6
% 22.86/6.08 |
% 22.86/6.08 +-Applying beta-rule and splitting (122), into two cases.
% 22.86/6.08 |-Branch one:
% 22.86/6.08 | (225) ~ (all_36_1_37 = 0)
% 22.86/6.08 |
% 22.86/6.08 +-Applying beta-rule and splitting (60), into two cases.
% 22.86/6.08 |-Branch one:
% 22.86/6.08 | (226) ~ (apart_point_and_line(all_1_5_5, all_1_2_2) = 0)
% 22.86/6.08 |
% 22.86/6.08 +-Applying beta-rule and splitting (112), into two cases.
% 22.86/6.08 |-Branch one:
% 22.86/6.08 | (227) ~ (all_30_1_28 = 0)
% 22.86/6.08 |
% 22.86/6.08 +-Applying beta-rule and splitting (97), into two cases.
% 22.86/6.08 |-Branch one:
% 22.86/6.08 | (228) ~ (all_24_1_19 = 0)
% 22.86/6.08 |
% 22.86/6.08 +-Applying beta-rule and splitting (166), into two cases.
% 22.86/6.08 |-Branch one:
% 22.86/6.08 | (229) ~ (apart_point_and_line(all_1_5_5, all_1_2_2) = all_30_1_28)
% 22.86/6.08 |
% 22.86/6.08 | Using (218) and (229) yields:
% 22.86/6.08 | (230) $false
% 22.86/6.08 |
% 22.86/6.08 |-The branch is then unsatisfiable
% 22.86/6.08 |-Branch two:
% 22.86/6.08 | (218) apart_point_and_line(all_1_5_5, all_1_2_2) = all_30_1_28
% 22.86/6.08 | (232) all_44_0_42 = all_30_1_28
% 22.86/6.08 |
% 22.86/6.08 | Combining equations (232,170) yields a new equation:
% 22.86/6.08 | (233) all_30_1_28 = all_16_1_7
% 22.86/6.08 |
% 22.86/6.08 | Simplifying 233 yields:
% 22.86/6.08 | (234) all_30_1_28 = all_16_1_7
% 22.86/6.08 |
% 22.86/6.08 | Equations (234) can reduce 227 to:
% 22.86/6.08 | (235) ~ (all_16_1_7 = 0)
% 22.86/6.08 |
% 22.86/6.08 | From (234) and (218) follows:
% 22.86/6.08 | (74) apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7
% 22.86/6.08 |
% 22.86/6.08 +-Applying beta-rule and splitting (163), into two cases.
% 22.86/6.08 |-Branch one:
% 22.86/6.08 | (237) ~ (apart_point_and_line(all_1_5_5, all_20_2_14) = all_38_1_40)
% 22.86/6.08 |
% 22.86/6.08 | Using (216) and (237) yields:
% 22.86/6.08 | (230) $false
% 22.86/6.08 |
% 22.86/6.08 |-The branch is then unsatisfiable
% 22.86/6.08 |-Branch two:
% 22.86/6.08 | (216) apart_point_and_line(all_1_5_5, all_20_2_14) = all_38_1_40
% 22.86/6.08 | (240) all_38_1_40 = all_20_1_13
% 22.86/6.08 |
% 22.86/6.08 | From (240) and (216) follows:
% 22.86/6.08 | (85) apart_point_and_line(all_1_5_5, all_20_2_14) = all_20_1_13
% 22.86/6.08 |
% 22.86/6.08 | Using (142) and (171) yields:
% 22.86/6.08 | (242) ~ (all_49_3_48 = 0)
% 22.86/6.08 |
% 22.86/6.08 | Instantiating formula (43) with all_24_1_19, all_1_1_1, all_20_2_14, all_1_2_2, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = all_1_1_1, apart_point_and_line(all_1_4_4, all_20_2_14) = all_24_1_19, yields:
% 22.86/6.08 | (243) all_24_1_19 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_20_2_14) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 22.86/6.08 |
% 22.86/6.08 | Instantiating formula (43) with all_1_1_1, all_24_1_19, all_1_2_2, all_20_2_14, all_1_3_3, all_1_4_4 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = all_1_1_1, apart_point_and_line(all_1_4_4, all_20_2_14) = all_24_1_19, yields:
% 22.86/6.08 | (244) all_24_1_19 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v3 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_20_2_14, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 22.86/6.08 |
% 22.86/6.08 | Instantiating formula (23) with all_24_1_19, all_1_1_1, all_1_2_2, all_20_2_14, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = all_1_1_1, apart_point_and_line(all_1_4_4, all_20_2_14) = all_24_1_19, yields:
% 22.86/6.08 | (245) all_24_1_19 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & distinct_lines(all_20_2_14, all_1_2_2) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 22.86/6.08 |
% 22.86/6.08 | Instantiating formula (23) with all_1_1_1, all_24_1_19, all_20_2_14, all_1_2_2, all_1_3_3, all_1_4_4 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = all_1_1_1, apart_point_and_line(all_1_4_4, all_20_2_14) = all_24_1_19, yields:
% 22.86/6.08 | (246) all_24_1_19 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v3 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_20_2_14) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 22.86/6.09 |
% 22.86/6.09 | Instantiating formula (43) with all_24_1_19, all_24_1_19, all_20_2_14, all_20_2_14, all_1_4_4, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_20_2_14) = all_24_1_19, yields:
% 22.86/6.09 | (247) all_24_1_19 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_20_2_14) = v3 & apart_point_and_line(all_1_4_4, all_20_2_14) = v2 & distinct_lines(all_20_2_14, all_20_2_14) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 22.86/6.09 |
% 22.86/6.09 | Instantiating formula (2) with all_24_1_19, all_22_1_16, all_20_2_14, all_1_0_0, all_1_3_3, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_20_2_14) = all_24_1_19, apart_point_and_line(all_1_4_4, all_1_0_0) = all_22_1_16, distinct_points(all_1_4_4, all_1_3_3) = 0, yields:
% 22.86/6.09 | (248) all_24_1_19 = 0 | all_22_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v2 & apart_point_and_line(all_1_3_3, all_1_0_0) = v1 & distinct_lines(all_1_0_0, all_20_2_14) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 22.86/6.09 |
% 22.86/6.09 | Instantiating formula (15) with all_22_1_16, all_24_1_19, all_1_0_0, all_20_2_14, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_1_4_4, all_20_2_14) = all_24_1_19, apart_point_and_line(all_1_4_4, all_1_0_0) = all_22_1_16, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 22.86/6.09 | (249) all_24_1_19 = 0 | all_22_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_20_2_14) = v1 & apart_point_and_line(all_1_5_5, all_1_0_0) = v2 & distinct_lines(all_20_2_14, all_1_0_0) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 22.86/6.09 |
% 22.86/6.09 | Instantiating formula (15) with all_24_1_19, all_22_1_16, all_20_2_14, all_1_0_0, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_1_4_4, all_20_2_14) = all_24_1_19, apart_point_and_line(all_1_4_4, all_1_0_0) = all_22_1_16, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 22.86/6.09 | (250) all_24_1_19 = 0 | all_22_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_20_2_14) = v2 & apart_point_and_line(all_1_5_5, all_1_0_0) = v1 & distinct_lines(all_1_0_0, all_20_2_14) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 22.86/6.09 |
% 22.86/6.09 | Instantiating formula (43) with all_24_1_19, all_22_1_16, all_20_2_14, all_1_0_0, all_1_4_4, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_20_2_14) = all_24_1_19, apart_point_and_line(all_1_4_4, all_1_0_0) = all_22_1_16, yields:
% 22.86/6.09 | (251) all_24_1_19 = 0 | all_22_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_20_2_14) = v2 & apart_point_and_line(all_1_4_4, all_1_0_0) = v3 & distinct_lines(all_1_0_0, all_20_2_14) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 22.86/6.09 |
% 22.86/6.09 | Instantiating formula (23) with all_22_1_16, all_24_1_19, all_20_2_14, all_1_0_0, all_1_4_4, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_20_2_14) = all_24_1_19, apart_point_and_line(all_1_4_4, all_1_0_0) = all_22_1_16, yields:
% 22.86/6.09 | (252) all_24_1_19 = 0 | all_22_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_20_2_14) = v3 & apart_point_and_line(all_1_4_4, all_1_0_0) = v2 & distinct_lines(all_1_0_0, all_20_2_14) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 22.86/6.09 |
% 22.86/6.09 | Instantiating formula (43) with all_36_1_37, all_1_1_1, all_28_2_26, all_1_2_2, all_1_5_5, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = all_1_1_1, apart_point_and_line(all_1_5_5, all_28_2_26) = all_36_1_37, yields:
% 22.86/6.09 | (253) all_36_1_37 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_28_2_26) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_28_2_26) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 22.86/6.09 |
% 22.86/6.09 | Instantiating formula (43) with all_1_1_1, all_36_1_37, all_1_2_2, all_28_2_26, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = all_1_1_1, apart_point_and_line(all_1_5_5, all_28_2_26) = all_36_1_37, yields:
% 22.86/6.09 | (254) all_36_1_37 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_28_2_26) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_28_2_26, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 22.86/6.09 |
% 22.86/6.09 | Instantiating formula (23) with all_36_1_37, all_1_1_1, all_1_2_2, all_28_2_26, all_1_5_5, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = all_1_1_1, apart_point_and_line(all_1_5_5, all_28_2_26) = all_36_1_37, yields:
% 22.86/6.09 | (255) all_36_1_37 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_28_2_26) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_28_2_26, all_1_2_2) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 22.86/6.09 |
% 22.86/6.09 | Instantiating formula (23) with all_1_1_1, all_36_1_37, all_28_2_26, all_1_2_2, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = all_1_1_1, apart_point_and_line(all_1_5_5, all_28_2_26) = all_36_1_37, yields:
% 22.86/6.09 | (256) all_36_1_37 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_28_2_26) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_28_2_26) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 22.86/6.09 |
% 22.86/6.09 | Instantiating formula (43) with all_36_1_37, all_24_1_19, all_28_2_26, all_20_2_14, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_20_2_14) = all_24_1_19, apart_point_and_line(all_1_5_5, all_28_2_26) = all_36_1_37, yields:
% 22.86/6.09 | (257) all_36_1_37 = 0 | all_24_1_19 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_28_2_26) = v2 & apart_point_and_line(all_1_5_5, all_20_2_14) = v3 & distinct_lines(all_20_2_14, all_28_2_26) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 22.86/6.09 |
% 22.86/6.09 | Instantiating formula (43) with all_24_1_19, all_36_1_37, all_20_2_14, all_28_2_26, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_1_4_4, all_20_2_14) = all_24_1_19, apart_point_and_line(all_1_5_5, all_28_2_26) = all_36_1_37, yields:
% 23.32/6.09 | (258) all_36_1_37 = 0 | all_24_1_19 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_28_2_26) = v3 & apart_point_and_line(all_1_5_5, all_20_2_14) = v2 & distinct_lines(all_28_2_26, all_20_2_14) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.09 |
% 23.32/6.09 | Instantiating formula (23) with all_36_1_37, all_24_1_19, all_20_2_14, all_28_2_26, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_20_2_14) = all_24_1_19, apart_point_and_line(all_1_5_5, all_28_2_26) = all_36_1_37, yields:
% 23.32/6.10 | (259) all_36_1_37 = 0 | all_24_1_19 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_28_2_26) = v2 & apart_point_and_line(all_1_5_5, all_20_2_14) = v3 & distinct_lines(all_28_2_26, all_20_2_14) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.10 |
% 23.32/6.10 | Instantiating formula (43) with all_22_1_16, all_36_1_37, all_1_0_0, all_28_2_26, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_1_4_4, all_1_0_0) = all_22_1_16, apart_point_and_line(all_1_5_5, all_28_2_26) = all_36_1_37, yields:
% 23.32/6.10 | (260) all_36_1_37 = 0 | all_22_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_28_2_26) = v3 & apart_point_and_line(all_1_5_5, all_1_0_0) = v2 & distinct_lines(all_28_2_26, all_1_0_0) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.10 |
% 23.32/6.10 | Instantiating formula (31) with all_20_1_13, all_20_2_14, all_1_0_0, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_20_2_14) = all_20_1_13, apart_point_and_line(all_1_5_5, all_1_0_0) = 0, yields:
% 23.32/6.10 | (261) all_20_1_13 = 0 | distinct_lines(all_1_0_0, all_20_2_14) = 0
% 23.32/6.10 |
% 23.32/6.10 | Instantiating formula (43) with all_24_1_19, all_16_1_7, all_20_2_14, all_1_2_2, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_1_4_4, all_20_2_14) = all_24_1_19, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 23.32/6.10 | (262) all_24_1_19 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_20_2_14) = v2 & distinct_lines(all_1_2_2, all_20_2_14) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.10 |
% 23.32/6.10 | Instantiating formula (23) with all_16_1_7, all_24_1_19, all_20_2_14, all_1_2_2, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_20_2_14) = all_24_1_19, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 23.32/6.10 | (263) all_24_1_19 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_20_2_14) = v3 & distinct_lines(all_1_2_2, all_20_2_14) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.10 |
% 23.32/6.10 | Instantiating formula (23) with all_16_1_7, all_22_1_16, all_1_0_0, all_1_2_2, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_1_0_0) = all_22_1_16, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 23.32/6.10 | (264) all_22_1_16 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_1_0_0) = v3 & distinct_lines(all_1_2_2, all_1_0_0) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.10 |
% 23.32/6.10 | Instantiating formula (23) with all_22_1_16, all_16_1_7, all_1_2_2, all_1_0_0, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_1_4_4, all_1_0_0) = all_22_1_16, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 23.32/6.10 | (265) all_22_1_16 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_1_0_0) = v2 & distinct_lines(all_1_0_0, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.10 |
% 23.32/6.10 | Instantiating formula (31) with all_16_1_7, all_1_2_2, all_20_2_14, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 23.32/6.10 | (266) all_16_1_7 = 0 | ~ (apart_point_and_line(all_1_5_5, all_20_2_14) = 0) | distinct_lines(all_20_2_14, all_1_2_2) = 0
% 23.32/6.10 |
% 23.32/6.10 | Instantiating formula (36) with all_49_3_48, all_1_3_3, all_1_3_3, all_1_4_4 and discharging atoms distinct_points(all_1_3_3, all_1_3_3) = all_49_3_48, distinct_points(all_1_4_4, all_1_3_3) = 0, yields:
% 23.32/6.10 | (267) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_4_4, all_1_3_3) = v0 & apart_point_and_line(all_1_3_3, v0) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_49_3_48 = 0)))
% 23.32/6.10 |
% 23.32/6.10 | Instantiating formula (41) with all_49_3_48, all_49_3_48, all_1_3_3, all_1_3_3, all_1_3_3 and discharging atoms distinct_points(all_1_3_3, all_1_3_3) = all_49_3_48, yields:
% 23.32/6.10 | (268) all_49_3_48 = 0 | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_3_3, all_1_3_3) = v1 & apart_point_and_line(all_1_3_3, v1) = v2 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 23.32/6.10 |
% 23.32/6.10 | Instantiating formula (12) with all_49_3_48, all_1_0_0, all_1_3_3, all_1_4_4, all_1_3_3 and discharging atoms line_connecting(all_1_3_3, all_1_4_4) = all_1_0_0, distinct_points(all_1_3_3, all_1_3_3) = all_49_3_48, yields:
% 23.32/6.10 | (269) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_0_0) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v2 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & all_49_3_48 = 0)))
% 23.32/6.10 |
% 23.32/6.10 | Instantiating formula (10) with all_49_3_48, all_20_2_14, all_1_3_3, all_1_3_3, all_1_4_4 and discharging atoms line_connecting(all_1_4_4, all_1_3_3) = all_20_2_14, distinct_points(all_1_3_3, all_1_3_3) = all_49_3_48, yields:
% 23.32/6.10 | (270) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v2 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & all_49_3_48 = 0)))
% 23.32/6.11 |
% 23.32/6.11 | Instantiating formula (18) with all_18_2_11, all_1_4_4, all_1_3_3, all_1_4_4 and discharging atoms distinct_points(all_1_3_3, all_1_4_4) = all_18_2_11, distinct_points(all_1_4_4, all_1_3_3) = 0, ~ (distinct_points(all_1_4_4, all_1_4_4) = 0), yields:
% 23.32/6.11 | (271) all_18_2_11 = 0
% 23.32/6.11 |
% 23.32/6.11 | Instantiating formula (37) with all_18_2_11, all_1_3_3, all_1_3_3, all_1_4_4 and discharging atoms distinct_points(all_1_3_3, all_1_4_4) = all_18_2_11, distinct_points(all_1_4_4, all_1_3_3) = 0, yields:
% 23.32/6.11 | (272) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_4_4, all_1_3_3) = v0 & apart_point_and_line(all_1_3_3, v0) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_18_2_11 = 0)))
% 23.32/6.11 |
% 23.32/6.11 | Instantiating formula (10) with all_18_2_11, all_1_0_0, all_1_3_3, all_1_4_4, all_1_3_3 and discharging atoms line_connecting(all_1_3_3, all_1_4_4) = all_1_0_0, distinct_points(all_1_3_3, all_1_4_4) = all_18_2_11, yields:
% 23.32/6.11 | (273) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_0_0) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v2 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & all_18_2_11 = 0)))
% 23.32/6.11 |
% 23.32/6.11 | Instantiating formula (10) with all_18_2_11, all_1_2_2, all_1_3_3, all_1_4_4, all_1_5_5 and discharging atoms line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2, distinct_points(all_1_3_3, all_1_4_4) = all_18_2_11, yields:
% 23.32/6.11 | (274) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v2 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & all_18_2_11 = 0)))
% 23.32/6.11 |
% 23.32/6.11 | Instantiating formula (12) with all_18_2_11, all_20_2_14, all_1_3_3, all_1_3_3, all_1_4_4 and discharging atoms line_connecting(all_1_4_4, all_1_3_3) = all_20_2_14, distinct_points(all_1_3_3, all_1_4_4) = all_18_2_11, yields:
% 23.32/6.11 | (275) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v2 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & all_18_2_11 = 0)))
% 23.32/6.11 |
% 23.32/6.11 | Instantiating formula (15) with all_24_1_19, all_24_1_19, all_20_2_14, all_20_2_14, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_4_4, all_20_2_14) = all_24_1_19, yields:
% 23.32/6.11 | (276) all_24_1_19 = 0 | ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v2 & apart_point_and_line(all_1_3_3, all_20_2_14) = v1 & distinct_lines(all_20_2_14, all_20_2_14) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.11 |
% 23.32/6.11 | Instantiating formula (15) with all_22_1_16, all_24_1_19, all_1_0_0, all_20_2_14, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_4_4, all_20_2_14) = all_24_1_19, apart_point_and_line(all_1_4_4, all_1_0_0) = all_22_1_16, yields:
% 23.32/6.11 | (277) all_24_1_19 = 0 | all_22_1_16 = 0 | ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v1 & apart_point_and_line(all_1_3_3, all_1_0_0) = v2 & distinct_lines(all_20_2_14, all_1_0_0) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.11 |
% 23.32/6.11 | Instantiating formula (15) with all_22_1_16, all_22_1_16, all_1_0_0, all_1_0_0, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_4_4, all_1_0_0) = all_22_1_16, yields:
% 23.32/6.11 | (278) all_22_1_16 = 0 | ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_0_0) = v2 & apart_point_and_line(all_1_3_3, all_1_0_0) = v1 & distinct_lines(all_1_0_0, all_1_0_0) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.11 |
% 23.32/6.11 | Instantiating formula (37) with 0, all_1_4_4, all_1_4_4, all_1_3_3 and discharging atoms distinct_points(all_1_4_4, all_1_3_3) = 0, yields:
% 23.32/6.11 | (279) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_3_3, all_1_4_4) = v0 & apart_point_and_line(all_1_4_4, v0) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 23.32/6.11 |
% 23.32/6.11 | Instantiating formula (37) with all_49_3_48, all_1_3_3, all_1_4_4, all_1_3_3 and discharging atoms distinct_points(all_1_3_3, all_1_3_3) = all_49_3_48, yields:
% 23.32/6.11 | (280) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_3_3, all_1_4_4) = v0 & apart_point_and_line(all_1_3_3, v0) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_49_3_48 = 0)))
% 23.32/6.11 |
% 23.32/6.11 | Instantiating formula (41) with all_22_0_15, 0, all_1_4_4, all_1_4_4, all_1_3_3 and discharging atoms distinct_points(all_1_4_4, all_1_3_3) = 0, distinct_points(all_1_4_4, all_1_4_4) = all_22_0_15, yields:
% 23.32/6.11 | (281) all_22_0_15 = 0 | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_3_3, all_1_4_4) = v1 & apart_point_and_line(all_1_4_4, v1) = v2 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 23.32/6.11 |
% 23.32/6.11 | Instantiating formula (36) with all_22_0_15, all_1_4_4, all_1_4_4, all_1_3_3 and discharging atoms distinct_points(all_1_4_4, all_1_4_4) = all_22_0_15, yields:
% 23.32/6.11 | (282) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0) | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_3_3, all_1_4_4) = v0 & apart_point_and_line(all_1_4_4, v0) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_22_0_15 = 0)))
% 23.32/6.11 |
% 23.32/6.11 | Instantiating formula (41) with all_22_0_15, all_22_0_15, all_1_4_4, all_1_4_4, all_1_4_4 and discharging atoms distinct_points(all_1_4_4, all_1_4_4) = all_22_0_15, yields:
% 23.32/6.11 | (283) all_22_0_15 = 0 | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_4_4, all_1_4_4) = v1 & apart_point_and_line(all_1_4_4, v1) = v2 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 23.32/6.11 |
% 23.32/6.11 | Instantiating formula (10) with all_22_0_15, all_1_0_0, all_1_4_4, all_1_4_4, all_1_3_3 and discharging atoms line_connecting(all_1_3_3, all_1_4_4) = all_1_0_0, distinct_points(all_1_4_4, all_1_4_4) = all_22_0_15, yields:
% 23.32/6.11 | (284) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_0_0) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & distinct_points(all_1_4_4, all_1_3_3) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & all_22_0_15 = 0)))
% 23.32/6.11 |
% 23.32/6.11 | Instantiating formula (10) with all_22_0_15, all_1_2_2, all_1_4_4, all_1_4_4, all_1_5_5 and discharging atoms line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2, distinct_points(all_1_4_4, all_1_4_4) = all_22_0_15, yields:
% 23.32/6.11 | (285) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v2 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & all_22_0_15 = 0)))
% 23.32/6.11 |
% 23.32/6.11 | Instantiating formula (37) with all_28_0_24, all_1_4_4, all_1_3_3, all_1_5_5 and discharging atoms distinct_points(all_1_4_4, all_1_5_5) = all_28_0_24, distinct_points(all_1_5_5, all_1_3_3) = 0, yields:
% 23.32/6.11 | (286) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_3_3) = v0 & apart_point_and_line(all_1_4_4, v0) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_28_0_24 = 0)))
% 23.32/6.11 |
% 23.32/6.11 | Instantiating formula (18) with all_28_0_24, all_1_5_5, all_1_4_4, all_1_5_5 and discharging atoms distinct_points(all_1_4_4, all_1_5_5) = all_28_0_24, distinct_points(all_1_5_5, all_1_4_4) = 0, ~ (distinct_points(all_1_5_5, all_1_5_5) = 0), yields:
% 23.32/6.11 | (287) all_28_0_24 = 0
% 23.32/6.11 |
% 23.32/6.11 | Instantiating formula (37) with all_28_0_24, all_1_4_4, all_1_4_4, all_1_5_5 and discharging atoms distinct_points(all_1_4_4, all_1_5_5) = all_28_0_24, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 23.32/6.11 | (288) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_4_4) = v0 & apart_point_and_line(all_1_4_4, v0) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_28_0_24 = 0)))
% 23.32/6.12 |
% 23.32/6.12 | Instantiating formula (41) with all_22_0_15, all_28_0_24, all_1_4_4, all_1_4_4, all_1_5_5 and discharging atoms distinct_points(all_1_4_4, all_1_4_4) = all_22_0_15, distinct_points(all_1_4_4, all_1_5_5) = all_28_0_24, yields:
% 23.32/6.12 | (289) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_4_4) = v1 & apart_point_and_line(all_1_4_4, v1) = v2 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0))) | (all_28_0_24 = 0 & all_22_0_15 = 0)
% 23.32/6.12 |
% 23.32/6.12 | Instantiating formula (12) with all_28_0_24, all_1_2_2, all_1_4_4, all_1_4_4, all_1_5_5 and discharging atoms line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2, distinct_points(all_1_4_4, all_1_5_5) = all_28_0_24, yields:
% 23.32/6.12 | (290) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v2 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & all_28_0_24 = 0)))
% 23.32/6.12 |
% 23.32/6.12 | Instantiating formula (12) with all_28_0_24, all_28_2_26, all_1_4_4, all_1_3_3, all_1_5_5 and discharging atoms line_connecting(all_1_5_5, all_1_3_3) = all_28_2_26, distinct_points(all_1_4_4, all_1_5_5) = all_28_0_24, yields:
% 23.32/6.12 | (291) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_28_2_26) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v2 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & all_28_0_24 = 0)))
% 23.32/6.12 |
% 23.32/6.12 | Instantiating formula (2) with all_24_1_19, all_24_1_19, all_20_2_14, all_20_2_14, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_20_2_14) = all_24_1_19, yields:
% 23.32/6.12 | (292) all_24_1_19 = 0 | ~ (distinct_points(all_1_4_4, all_1_5_5) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_20_2_14) = v2 & apart_point_and_line(all_1_5_5, all_20_2_14) = v1 & distinct_lines(all_20_2_14, all_20_2_14) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.12 |
% 23.32/6.12 | Instantiating formula (2) with all_22_1_16, all_22_1_16, all_1_0_0, all_1_0_0, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_1_0_0) = all_22_1_16, yields:
% 23.32/6.12 | (293) all_22_1_16 = 0 | ~ (distinct_points(all_1_4_4, all_1_5_5) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_1_0_0) = v2 & apart_point_and_line(all_1_5_5, all_1_0_0) = v1 & distinct_lines(all_1_0_0, all_1_0_0) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.12 |
% 23.32/6.12 | Instantiating formula (15) with all_36_1_37, all_36_1_37, all_28_2_26, all_28_2_26, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_5_5, all_28_2_26) = all_36_1_37, yields:
% 23.32/6.12 | (294) all_36_1_37 = 0 | ~ (distinct_points(all_1_4_4, all_1_5_5) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_28_2_26) = v2 & apart_point_and_line(all_1_4_4, all_28_2_26) = v1 & distinct_lines(all_28_2_26, all_28_2_26) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.12 |
% 23.32/6.12 | Instantiating formula (15) with all_36_1_37, all_16_1_7, all_28_2_26, all_1_2_2, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_5_5, all_28_2_26) = all_36_1_37, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 23.32/6.12 | (295) all_36_1_37 = 0 | all_16_1_7 = 0 | ~ (distinct_points(all_1_4_4, all_1_5_5) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_28_2_26) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_28_2_26) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.12 |
% 23.32/6.12 | Instantiating formula (15) with all_16_1_7, all_36_1_37, all_1_2_2, all_28_2_26, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_5_5, all_28_2_26) = all_36_1_37, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 23.32/6.12 | (296) all_36_1_37 = 0 | all_16_1_7 = 0 | ~ (distinct_points(all_1_4_4, all_1_5_5) = 0) | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_28_2_26) = v1 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_28_2_26, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.12 |
% 23.32/6.12 | Instantiating formula (37) with 0, all_1_5_5, all_1_5_5, all_1_4_4 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 23.32/6.12 | (297) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0) | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_4_4, all_1_5_5) = v0 & apart_point_and_line(all_1_5_5, v0) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 23.32/6.12 |
% 23.32/6.12 | Instantiating formula (37) with all_18_2_11, all_1_3_3, all_1_5_5, all_1_4_4 and discharging atoms distinct_points(all_1_3_3, all_1_4_4) = all_18_2_11, yields:
% 23.32/6.12 | (298) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0) | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_4_4, all_1_5_5) = v0 & apart_point_and_line(all_1_3_3, v0) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_18_2_11 = 0)))
% 23.32/6.12 |
% 23.32/6.12 | Instantiating formula (37) with all_22_0_15, all_1_4_4, all_1_5_5, all_1_4_4 and discharging atoms distinct_points(all_1_4_4, all_1_4_4) = all_22_0_15, yields:
% 23.32/6.12 | (299) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0) | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_4_4, all_1_5_5) = v0 & apart_point_and_line(all_1_4_4, v0) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_22_0_15 = 0)))
% 23.32/6.12 |
% 23.32/6.12 | Instantiating formula (36) with all_16_0_6, all_1_5_5, all_1_5_5, all_1_4_4 and discharging atoms distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6, yields:
% 23.32/6.12 | (300) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0) | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_4_4, all_1_5_5) = v0 & apart_point_and_line(all_1_5_5, v0) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_16_0_6 = 0)))
% 23.32/6.12 |
% 23.32/6.12 | Combining equations (271,203) yields a new equation:
% 23.32/6.12 | (301) all_22_2_17 = 0
% 23.32/6.12 |
% 23.32/6.12 | Instantiating (288) with all_98_0_52, all_98_1_53, all_98_2_54 yields:
% 23.32/6.12 | (302) line_connecting(all_1_5_5, all_1_4_4) = all_98_2_54 & apart_point_and_line(all_1_4_4, all_98_2_54) = all_98_1_53 & distinct_points(all_1_4_4, all_1_4_4) = all_98_0_52 & ( ~ (all_98_1_53 = 0) | (all_98_0_52 = 0 & all_28_0_24 = 0))
% 23.32/6.12 |
% 23.32/6.12 | Applying alpha-rule on (302) yields:
% 23.32/6.12 | (303) line_connecting(all_1_5_5, all_1_4_4) = all_98_2_54
% 23.32/6.12 | (304) apart_point_and_line(all_1_4_4, all_98_2_54) = all_98_1_53
% 23.32/6.12 | (305) distinct_points(all_1_4_4, all_1_4_4) = all_98_0_52
% 23.32/6.12 | (306) ~ (all_98_1_53 = 0) | (all_98_0_52 = 0 & all_28_0_24 = 0)
% 23.32/6.12 |
% 23.32/6.12 | Instantiating (285) with all_100_0_55, all_100_1_56, all_100_2_57 yields:
% 23.32/6.12 | (307) apart_point_and_line(all_1_4_4, all_1_2_2) = all_100_1_56 & distinct_points(all_1_4_4, all_1_5_5) = all_100_0_55 & distinct_points(all_1_5_5, all_1_4_4) = all_100_2_57 & ( ~ (all_100_1_56 = 0) | ~ (all_100_2_57 = 0) | (all_100_0_55 = 0 & all_22_0_15 = 0))
% 23.32/6.12 |
% 23.32/6.12 | Applying alpha-rule on (307) yields:
% 23.32/6.12 | (308) apart_point_and_line(all_1_4_4, all_1_2_2) = all_100_1_56
% 23.32/6.12 | (309) distinct_points(all_1_4_4, all_1_5_5) = all_100_0_55
% 23.32/6.12 | (310) distinct_points(all_1_5_5, all_1_4_4) = all_100_2_57
% 23.32/6.12 | (311) ~ (all_100_1_56 = 0) | ~ (all_100_2_57 = 0) | (all_100_0_55 = 0 & all_22_0_15 = 0)
% 23.32/6.12 |
% 23.32/6.12 | Instantiating (284) with all_102_0_58, all_102_1_59, all_102_2_60 yields:
% 23.32/6.12 | (312) apart_point_and_line(all_1_4_4, all_1_0_0) = all_102_1_59 & distinct_points(all_1_3_3, all_1_4_4) = all_102_2_60 & distinct_points(all_1_4_4, all_1_3_3) = all_102_0_58 & ( ~ (all_102_1_59 = 0) | ~ (all_102_2_60 = 0) | (all_102_0_58 = 0 & all_22_0_15 = 0))
% 23.32/6.12 |
% 23.32/6.12 | Applying alpha-rule on (312) yields:
% 23.32/6.12 | (313) apart_point_and_line(all_1_4_4, all_1_0_0) = all_102_1_59
% 23.32/6.12 | (314) distinct_points(all_1_3_3, all_1_4_4) = all_102_2_60
% 23.32/6.12 | (315) distinct_points(all_1_4_4, all_1_3_3) = all_102_0_58
% 23.32/6.12 | (316) ~ (all_102_1_59 = 0) | ~ (all_102_2_60 = 0) | (all_102_0_58 = 0 & all_22_0_15 = 0)
% 23.32/6.12 |
% 23.32/6.12 | Instantiating (275) with all_104_0_61, all_104_1_62, all_104_2_63 yields:
% 23.32/6.12 | (317) apart_point_and_line(all_1_3_3, all_20_2_14) = all_104_1_62 & distinct_points(all_1_3_3, all_1_3_3) = all_104_0_61 & distinct_points(all_1_4_4, all_1_3_3) = all_104_2_63 & ( ~ (all_104_1_62 = 0) | ~ (all_104_2_63 = 0) | (all_104_0_61 = 0 & all_18_2_11 = 0))
% 23.32/6.12 |
% 23.32/6.12 | Applying alpha-rule on (317) yields:
% 23.32/6.12 | (318) apart_point_and_line(all_1_3_3, all_20_2_14) = all_104_1_62
% 23.32/6.12 | (319) distinct_points(all_1_3_3, all_1_3_3) = all_104_0_61
% 23.32/6.12 | (320) distinct_points(all_1_4_4, all_1_3_3) = all_104_2_63
% 23.32/6.12 | (321) ~ (all_104_1_62 = 0) | ~ (all_104_2_63 = 0) | (all_104_0_61 = 0 & all_18_2_11 = 0)
% 23.32/6.12 |
% 23.32/6.12 | Instantiating (273) with all_106_0_64, all_106_1_65, all_106_2_66 yields:
% 23.32/6.12 | (322) apart_point_and_line(all_1_3_3, all_1_0_0) = all_106_1_65 & distinct_points(all_1_3_3, all_1_3_3) = all_106_0_64 & distinct_points(all_1_3_3, all_1_4_4) = all_106_2_66 & ( ~ (all_106_1_65 = 0) | ~ (all_106_2_66 = 0) | (all_106_0_64 = 0 & all_18_2_11 = 0))
% 23.32/6.13 |
% 23.32/6.13 | Applying alpha-rule on (322) yields:
% 23.32/6.13 | (323) apart_point_and_line(all_1_3_3, all_1_0_0) = all_106_1_65
% 23.32/6.13 | (324) distinct_points(all_1_3_3, all_1_3_3) = all_106_0_64
% 23.32/6.13 | (325) distinct_points(all_1_3_3, all_1_4_4) = all_106_2_66
% 23.32/6.13 | (326) ~ (all_106_1_65 = 0) | ~ (all_106_2_66 = 0) | (all_106_0_64 = 0 & all_18_2_11 = 0)
% 23.32/6.13 |
% 23.32/6.13 | Instantiating (267) with all_112_0_73, all_112_1_74, all_112_2_75 yields:
% 23.32/6.13 | (327) line_connecting(all_1_4_4, all_1_3_3) = all_112_2_75 & apart_point_and_line(all_1_3_3, all_112_2_75) = all_112_1_74 & distinct_points(all_1_3_3, all_1_4_4) = all_112_0_73 & ( ~ (all_112_1_74 = 0) | (all_112_0_73 = 0 & all_49_3_48 = 0))
% 23.32/6.13 |
% 23.32/6.13 | Applying alpha-rule on (327) yields:
% 23.32/6.13 | (328) line_connecting(all_1_4_4, all_1_3_3) = all_112_2_75
% 23.32/6.13 | (329) apart_point_and_line(all_1_3_3, all_112_2_75) = all_112_1_74
% 23.32/6.13 | (330) distinct_points(all_1_3_3, all_1_4_4) = all_112_0_73
% 23.32/6.13 | (331) ~ (all_112_1_74 = 0) | (all_112_0_73 = 0 & all_49_3_48 = 0)
% 23.32/6.13 |
% 23.32/6.13 | Instantiating (270) with all_122_0_88, all_122_1_89, all_122_2_90 yields:
% 23.32/6.13 | (332) apart_point_and_line(all_1_3_3, all_20_2_14) = all_122_1_89 & distinct_points(all_1_3_3, all_1_4_4) = all_122_0_88 & distinct_points(all_1_4_4, all_1_3_3) = all_122_2_90 & ( ~ (all_122_1_89 = 0) | ~ (all_122_2_90 = 0) | (all_122_0_88 = 0 & all_49_3_48 = 0))
% 23.32/6.13 |
% 23.32/6.13 | Applying alpha-rule on (332) yields:
% 23.32/6.13 | (333) apart_point_and_line(all_1_3_3, all_20_2_14) = all_122_1_89
% 23.32/6.13 | (334) distinct_points(all_1_3_3, all_1_4_4) = all_122_0_88
% 23.32/6.13 | (335) distinct_points(all_1_4_4, all_1_3_3) = all_122_2_90
% 23.32/6.13 | (336) ~ (all_122_1_89 = 0) | ~ (all_122_2_90 = 0) | (all_122_0_88 = 0 & all_49_3_48 = 0)
% 23.32/6.13 |
% 23.32/6.13 | Instantiating (269) with all_124_0_91, all_124_1_92, all_124_2_93 yields:
% 23.32/6.13 | (337) apart_point_and_line(all_1_3_3, all_1_0_0) = all_124_1_92 & distinct_points(all_1_3_3, all_1_4_4) = all_124_0_91 & distinct_points(all_1_3_3, all_1_4_4) = all_124_2_93 & ( ~ (all_124_1_92 = 0) | ~ (all_124_2_93 = 0) | (all_124_0_91 = 0 & all_49_3_48 = 0))
% 23.32/6.13 |
% 23.32/6.13 | Applying alpha-rule on (337) yields:
% 23.32/6.13 | (338) apart_point_and_line(all_1_3_3, all_1_0_0) = all_124_1_92
% 23.32/6.13 | (339) distinct_points(all_1_3_3, all_1_4_4) = all_124_0_91
% 23.32/6.13 | (340) distinct_points(all_1_3_3, all_1_4_4) = all_124_2_93
% 23.32/6.13 | (341) ~ (all_124_1_92 = 0) | ~ (all_124_2_93 = 0) | (all_124_0_91 = 0 & all_49_3_48 = 0)
% 23.32/6.13 |
% 23.32/6.13 | Instantiating (274) with all_138_0_112, all_138_1_113, all_138_2_114 yields:
% 23.32/6.13 | (342) apart_point_and_line(all_1_3_3, all_1_2_2) = all_138_1_113 & distinct_points(all_1_3_3, all_1_5_5) = all_138_0_112 & distinct_points(all_1_5_5, all_1_4_4) = all_138_2_114 & ( ~ (all_138_1_113 = 0) | ~ (all_138_2_114 = 0) | (all_138_0_112 = 0 & all_18_2_11 = 0))
% 23.32/6.13 |
% 23.32/6.13 | Applying alpha-rule on (342) yields:
% 23.32/6.13 | (343) apart_point_and_line(all_1_3_3, all_1_2_2) = all_138_1_113
% 23.32/6.13 | (344) distinct_points(all_1_3_3, all_1_5_5) = all_138_0_112
% 23.32/6.13 | (345) distinct_points(all_1_5_5, all_1_4_4) = all_138_2_114
% 23.32/6.13 | (346) ~ (all_138_1_113 = 0) | ~ (all_138_2_114 = 0) | (all_138_0_112 = 0 & all_18_2_11 = 0)
% 23.32/6.13 |
% 23.32/6.13 | Instantiating (291) with all_140_0_115, all_140_1_116, all_140_2_117 yields:
% 23.32/6.13 | (347) apart_point_and_line(all_1_4_4, all_28_2_26) = all_140_1_116 & distinct_points(all_1_4_4, all_1_3_3) = all_140_0_115 & distinct_points(all_1_5_5, all_1_3_3) = all_140_2_117 & ( ~ (all_140_1_116 = 0) | ~ (all_140_2_117 = 0) | (all_140_0_115 = 0 & all_28_0_24 = 0))
% 23.32/6.13 |
% 23.32/6.13 | Applying alpha-rule on (347) yields:
% 23.32/6.13 | (348) apart_point_and_line(all_1_4_4, all_28_2_26) = all_140_1_116
% 23.32/6.13 | (349) distinct_points(all_1_4_4, all_1_3_3) = all_140_0_115
% 23.32/6.13 | (350) distinct_points(all_1_5_5, all_1_3_3) = all_140_2_117
% 23.32/6.13 | (351) ~ (all_140_1_116 = 0) | ~ (all_140_2_117 = 0) | (all_140_0_115 = 0 & all_28_0_24 = 0)
% 23.32/6.13 |
% 23.32/6.13 | Instantiating (290) with all_142_0_118, all_142_1_119, all_142_2_120 yields:
% 23.32/6.13 | (352) apart_point_and_line(all_1_4_4, all_1_2_2) = all_142_1_119 & distinct_points(all_1_4_4, all_1_4_4) = all_142_0_118 & distinct_points(all_1_5_5, all_1_4_4) = all_142_2_120 & ( ~ (all_142_1_119 = 0) | ~ (all_142_2_120 = 0) | (all_142_0_118 = 0 & all_28_0_24 = 0))
% 23.32/6.13 |
% 23.32/6.13 | Applying alpha-rule on (352) yields:
% 23.32/6.13 | (353) apart_point_and_line(all_1_4_4, all_1_2_2) = all_142_1_119
% 23.32/6.13 | (354) distinct_points(all_1_4_4, all_1_4_4) = all_142_0_118
% 23.32/6.13 | (355) distinct_points(all_1_5_5, all_1_4_4) = all_142_2_120
% 23.32/6.13 | (356) ~ (all_142_1_119 = 0) | ~ (all_142_2_120 = 0) | (all_142_0_118 = 0 & all_28_0_24 = 0)
% 23.32/6.13 |
% 23.32/6.13 | Instantiating (286) with all_144_0_121, all_144_1_122, all_144_2_123 yields:
% 23.32/6.13 | (357) line_connecting(all_1_5_5, all_1_3_3) = all_144_2_123 & apart_point_and_line(all_1_4_4, all_144_2_123) = all_144_1_122 & distinct_points(all_1_4_4, all_1_3_3) = all_144_0_121 & ( ~ (all_144_1_122 = 0) | (all_144_0_121 = 0 & all_28_0_24 = 0))
% 23.32/6.13 |
% 23.32/6.13 | Applying alpha-rule on (357) yields:
% 23.32/6.13 | (358) line_connecting(all_1_5_5, all_1_3_3) = all_144_2_123
% 23.32/6.13 | (359) apart_point_and_line(all_1_4_4, all_144_2_123) = all_144_1_122
% 23.32/6.13 | (360) distinct_points(all_1_4_4, all_1_3_3) = all_144_0_121
% 23.32/6.13 | (361) ~ (all_144_1_122 = 0) | (all_144_0_121 = 0 & all_28_0_24 = 0)
% 23.32/6.13 |
% 23.32/6.13 | Instantiating (272) with all_146_0_124, all_146_1_125, all_146_2_126 yields:
% 23.32/6.13 | (362) line_connecting(all_1_4_4, all_1_3_3) = all_146_2_126 & apart_point_and_line(all_1_3_3, all_146_2_126) = all_146_1_125 & distinct_points(all_1_3_3, all_1_3_3) = all_146_0_124 & ( ~ (all_146_1_125 = 0) | (all_146_0_124 = 0 & all_18_2_11 = 0))
% 23.32/6.13 |
% 23.32/6.13 | Applying alpha-rule on (362) yields:
% 23.32/6.13 | (363) line_connecting(all_1_4_4, all_1_3_3) = all_146_2_126
% 23.32/6.13 | (364) apart_point_and_line(all_1_3_3, all_146_2_126) = all_146_1_125
% 23.32/6.13 | (365) distinct_points(all_1_3_3, all_1_3_3) = all_146_0_124
% 23.32/6.13 | (366) ~ (all_146_1_125 = 0) | (all_146_0_124 = 0 & all_18_2_11 = 0)
% 23.32/6.13 |
% 23.32/6.13 | From (271) and (80) follows:
% 23.32/6.13 | (367) distinct_points(all_1_3_3, all_1_4_4) = 0
% 23.32/6.13 |
% 23.32/6.13 | From (287) and (106) follows:
% 23.32/6.13 | (368) distinct_points(all_1_4_4, all_1_5_5) = 0
% 23.32/6.13 |
% 23.32/6.13 +-Applying beta-rule and splitting (300), into two cases.
% 23.32/6.13 |-Branch one:
% 23.32/6.13 | (369) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0)
% 23.32/6.13 |
% 23.32/6.13 | Using (368) and (369) yields:
% 23.32/6.13 | (230) $false
% 23.32/6.13 |
% 23.32/6.13 |-The branch is then unsatisfiable
% 23.32/6.13 |-Branch two:
% 23.32/6.13 | (368) distinct_points(all_1_4_4, all_1_5_5) = 0
% 23.32/6.13 | (372) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_4_4, all_1_5_5) = v0 & apart_point_and_line(all_1_5_5, v0) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_16_0_6 = 0)))
% 23.32/6.13 |
% 23.32/6.13 | Instantiating (372) with all_155_0_127, all_155_1_128, all_155_2_129 yields:
% 23.32/6.13 | (373) line_connecting(all_1_4_4, all_1_5_5) = all_155_2_129 & apart_point_and_line(all_1_5_5, all_155_2_129) = all_155_1_128 & distinct_points(all_1_5_5, all_1_4_4) = all_155_0_127 & ( ~ (all_155_1_128 = 0) | (all_155_0_127 = 0 & all_16_0_6 = 0))
% 23.32/6.13 |
% 23.32/6.13 | Applying alpha-rule on (373) yields:
% 23.32/6.13 | (374) line_connecting(all_1_4_4, all_1_5_5) = all_155_2_129
% 23.32/6.13 | (375) apart_point_and_line(all_1_5_5, all_155_2_129) = all_155_1_128
% 23.32/6.13 | (376) distinct_points(all_1_5_5, all_1_4_4) = all_155_0_127
% 23.32/6.13 | (377) ~ (all_155_1_128 = 0) | (all_155_0_127 = 0 & all_16_0_6 = 0)
% 23.32/6.13 |
% 23.32/6.13 +-Applying beta-rule and splitting (297), into two cases.
% 23.32/6.13 |-Branch one:
% 23.32/6.13 | (369) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0)
% 23.32/6.13 |
% 23.32/6.13 | Using (368) and (369) yields:
% 23.32/6.13 | (230) $false
% 23.32/6.13 |
% 23.32/6.13 |-The branch is then unsatisfiable
% 23.32/6.13 |-Branch two:
% 23.32/6.13 | (368) distinct_points(all_1_4_4, all_1_5_5) = 0
% 23.32/6.13 | (381) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_4_4, all_1_5_5) = v0 & apart_point_and_line(all_1_5_5, v0) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 23.32/6.13 |
% 23.32/6.13 +-Applying beta-rule and splitting (298), into two cases.
% 23.32/6.13 |-Branch one:
% 23.32/6.13 | (369) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0)
% 23.32/6.13 |
% 23.32/6.13 | Using (368) and (369) yields:
% 23.32/6.14 | (230) $false
% 23.32/6.14 |
% 23.32/6.14 |-The branch is then unsatisfiable
% 23.32/6.14 |-Branch two:
% 23.32/6.14 | (368) distinct_points(all_1_4_4, all_1_5_5) = 0
% 23.32/6.14 | (385) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_4_4, all_1_5_5) = v0 & apart_point_and_line(all_1_3_3, v0) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_18_2_11 = 0)))
% 23.32/6.14 |
% 23.32/6.14 +-Applying beta-rule and splitting (299), into two cases.
% 23.32/6.14 |-Branch one:
% 23.32/6.14 | (369) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0)
% 23.32/6.14 |
% 23.32/6.14 | Using (368) and (369) yields:
% 23.32/6.14 | (230) $false
% 23.32/6.14 |
% 23.32/6.14 |-The branch is then unsatisfiable
% 23.32/6.14 |-Branch two:
% 23.32/6.14 | (368) distinct_points(all_1_4_4, all_1_5_5) = 0
% 23.32/6.14 | (389) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_4_4, all_1_5_5) = v0 & apart_point_and_line(all_1_4_4, v0) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_22_0_15 = 0)))
% 23.32/6.14 |
% 23.32/6.14 +-Applying beta-rule and splitting (296), into two cases.
% 23.32/6.14 |-Branch one:
% 23.32/6.14 | (369) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0)
% 23.32/6.14 |
% 23.32/6.14 | Using (368) and (369) yields:
% 23.32/6.14 | (230) $false
% 23.32/6.14 |
% 23.32/6.14 |-The branch is then unsatisfiable
% 23.32/6.14 |-Branch two:
% 23.32/6.14 | (368) distinct_points(all_1_4_4, all_1_5_5) = 0
% 23.32/6.14 | (393) all_36_1_37 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_28_2_26) = v1 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_28_2_26, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.14 |
% 23.32/6.14 +-Applying beta-rule and splitting (393), into two cases.
% 23.32/6.14 |-Branch one:
% 23.32/6.14 | (394) all_36_1_37 = 0
% 23.32/6.14 |
% 23.32/6.14 | Equations (394) can reduce 225 to:
% 23.32/6.14 | (129) $false
% 23.32/6.14 |
% 23.32/6.14 |-The branch is then unsatisfiable
% 23.32/6.14 |-Branch two:
% 23.32/6.14 | (225) ~ (all_36_1_37 = 0)
% 23.32/6.14 | (397) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_28_2_26) = v1 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_28_2_26, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.14 |
% 23.32/6.14 +-Applying beta-rule and splitting (92), into two cases.
% 23.32/6.14 |-Branch one:
% 23.32/6.14 | (398) ~ (all_22_1_16 = 0)
% 23.32/6.14 |
% 23.32/6.14 +-Applying beta-rule and splitting (283), into two cases.
% 23.32/6.14 |-Branch one:
% 23.32/6.14 | (399) all_22_0_15 = 0
% 23.32/6.14 |
% 23.32/6.14 | Equations (399) can reduce 209 to:
% 23.32/6.14 | (129) $false
% 23.32/6.14 |
% 23.32/6.14 |-The branch is then unsatisfiable
% 23.32/6.14 |-Branch two:
% 23.32/6.14 | (209) ~ (all_22_0_15 = 0)
% 23.32/6.14 | (402) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_4_4, all_1_4_4) = v1 & apart_point_and_line(all_1_4_4, v1) = v2 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 23.32/6.14 |
% 23.32/6.14 | Instantiating (402) with all_194_0_139, all_194_1_140, all_194_2_141 yields:
% 23.32/6.14 | (403) line_connecting(all_1_4_4, all_1_4_4) = all_194_1_140 & apart_point_and_line(all_1_4_4, all_194_1_140) = all_194_0_139 & distinct_points(all_1_4_4, all_1_4_4) = all_194_2_141 & ( ~ (all_194_0_139 = 0) | ~ (all_194_2_141 = 0))
% 23.32/6.14 |
% 23.32/6.14 | Applying alpha-rule on (403) yields:
% 23.32/6.14 | (404) line_connecting(all_1_4_4, all_1_4_4) = all_194_1_140
% 23.32/6.14 | (405) apart_point_and_line(all_1_4_4, all_194_1_140) = all_194_0_139
% 23.32/6.14 | (406) distinct_points(all_1_4_4, all_1_4_4) = all_194_2_141
% 23.32/6.14 | (407) ~ (all_194_0_139 = 0) | ~ (all_194_2_141 = 0)
% 23.32/6.14 |
% 23.32/6.14 +-Applying beta-rule and splitting (255), into two cases.
% 23.32/6.14 |-Branch one:
% 23.32/6.14 | (394) all_36_1_37 = 0
% 23.32/6.14 |
% 23.32/6.14 | Equations (394) can reduce 225 to:
% 23.32/6.14 | (129) $false
% 23.32/6.14 |
% 23.32/6.14 |-The branch is then unsatisfiable
% 23.32/6.14 |-Branch two:
% 23.32/6.14 | (225) ~ (all_36_1_37 = 0)
% 23.32/6.14 | (411) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_28_2_26) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_28_2_26, all_1_2_2) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.14 |
% 23.32/6.14 +-Applying beta-rule and splitting (256), into two cases.
% 23.32/6.14 |-Branch one:
% 23.32/6.14 | (394) all_36_1_37 = 0
% 23.32/6.14 |
% 23.32/6.14 | Equations (394) can reduce 225 to:
% 23.32/6.14 | (129) $false
% 23.32/6.14 |
% 23.32/6.14 |-The branch is then unsatisfiable
% 23.32/6.14 |-Branch two:
% 23.32/6.14 | (225) ~ (all_36_1_37 = 0)
% 23.32/6.14 | (415) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_28_2_26) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_28_2_26) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.14 |
% 23.32/6.14 +-Applying beta-rule and splitting (243), into two cases.
% 23.32/6.14 |-Branch one:
% 23.32/6.14 | (416) all_24_1_19 = 0
% 23.32/6.14 |
% 23.32/6.14 | Equations (416) can reduce 228 to:
% 23.32/6.14 | (129) $false
% 23.32/6.14 |
% 23.32/6.14 |-The branch is then unsatisfiable
% 23.32/6.14 |-Branch two:
% 23.32/6.14 | (228) ~ (all_24_1_19 = 0)
% 23.32/6.14 | (419) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_20_2_14) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.14 |
% 23.32/6.14 +-Applying beta-rule and splitting (246), into two cases.
% 23.32/6.14 |-Branch one:
% 23.32/6.14 | (416) all_24_1_19 = 0
% 23.32/6.14 |
% 23.32/6.14 | Equations (416) can reduce 228 to:
% 23.32/6.14 | (129) $false
% 23.32/6.14 |
% 23.32/6.14 |-The branch is then unsatisfiable
% 23.32/6.14 |-Branch two:
% 23.32/6.14 | (228) ~ (all_24_1_19 = 0)
% 23.32/6.14 | (423) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v3 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_20_2_14) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.14 |
% 23.32/6.14 +-Applying beta-rule and splitting (244), into two cases.
% 23.32/6.14 |-Branch one:
% 23.32/6.14 | (416) all_24_1_19 = 0
% 23.32/6.14 |
% 23.32/6.14 | Equations (416) can reduce 228 to:
% 23.32/6.14 | (129) $false
% 23.32/6.14 |
% 23.32/6.14 |-The branch is then unsatisfiable
% 23.32/6.14 |-Branch two:
% 23.32/6.14 | (228) ~ (all_24_1_19 = 0)
% 23.32/6.14 | (427) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v3 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_20_2_14, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.14 |
% 23.32/6.14 +-Applying beta-rule and splitting (245), into two cases.
% 23.32/6.14 |-Branch one:
% 23.32/6.14 | (416) all_24_1_19 = 0
% 23.32/6.14 |
% 23.32/6.14 | Equations (416) can reduce 228 to:
% 23.32/6.14 | (129) $false
% 23.32/6.14 |
% 23.32/6.14 |-The branch is then unsatisfiable
% 23.32/6.14 |-Branch two:
% 23.32/6.14 | (228) ~ (all_24_1_19 = 0)
% 23.32/6.14 | (431) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & distinct_lines(all_20_2_14, all_1_2_2) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.14 |
% 23.32/6.14 +-Applying beta-rule and splitting (253), into two cases.
% 23.32/6.14 |-Branch one:
% 23.32/6.14 | (394) all_36_1_37 = 0
% 23.32/6.14 |
% 23.32/6.14 | Equations (394) can reduce 225 to:
% 23.32/6.14 | (129) $false
% 23.32/6.14 |
% 23.32/6.14 |-The branch is then unsatisfiable
% 23.32/6.14 |-Branch two:
% 23.32/6.14 | (225) ~ (all_36_1_37 = 0)
% 23.32/6.14 | (435) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_28_2_26) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_28_2_26) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.14 |
% 23.32/6.14 +-Applying beta-rule and splitting (254), into two cases.
% 23.32/6.14 |-Branch one:
% 23.32/6.14 | (394) all_36_1_37 = 0
% 23.32/6.14 |
% 23.32/6.14 | Equations (394) can reduce 225 to:
% 23.32/6.14 | (129) $false
% 23.32/6.14 |
% 23.32/6.14 |-The branch is then unsatisfiable
% 23.32/6.14 |-Branch two:
% 23.32/6.14 | (225) ~ (all_36_1_37 = 0)
% 23.32/6.14 | (439) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_28_2_26) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_28_2_26, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.14 |
% 23.32/6.14 +-Applying beta-rule and splitting (293), into two cases.
% 23.32/6.14 |-Branch one:
% 23.32/6.14 | (369) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0)
% 23.32/6.14 |
% 23.32/6.14 | Using (368) and (369) yields:
% 23.32/6.14 | (230) $false
% 23.32/6.14 |
% 23.32/6.14 |-The branch is then unsatisfiable
% 23.32/6.14 |-Branch two:
% 23.32/6.14 | (368) distinct_points(all_1_4_4, all_1_5_5) = 0
% 23.32/6.14 | (443) all_22_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_1_0_0) = v2 & apart_point_and_line(all_1_5_5, all_1_0_0) = v1 & distinct_lines(all_1_0_0, all_1_0_0) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.14 |
% 23.32/6.14 +-Applying beta-rule and splitting (294), into two cases.
% 23.32/6.14 |-Branch one:
% 23.32/6.14 | (369) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0)
% 23.32/6.14 |
% 23.32/6.14 | Using (368) and (369) yields:
% 23.32/6.14 | (230) $false
% 23.32/6.14 |
% 23.32/6.14 |-The branch is then unsatisfiable
% 23.32/6.14 |-Branch two:
% 23.32/6.14 | (368) distinct_points(all_1_4_4, all_1_5_5) = 0
% 23.32/6.15 | (447) all_36_1_37 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_28_2_26) = v2 & apart_point_and_line(all_1_4_4, all_28_2_26) = v1 & distinct_lines(all_28_2_26, all_28_2_26) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.15 |
% 23.32/6.15 +-Applying beta-rule and splitting (295), into two cases.
% 23.32/6.15 |-Branch one:
% 23.32/6.15 | (369) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0)
% 23.32/6.15 |
% 23.32/6.15 | Using (368) and (369) yields:
% 23.32/6.15 | (230) $false
% 23.32/6.15 |
% 23.32/6.15 |-The branch is then unsatisfiable
% 23.32/6.15 |-Branch two:
% 23.32/6.15 | (368) distinct_points(all_1_4_4, all_1_5_5) = 0
% 23.32/6.15 | (451) all_36_1_37 = 0 | all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_28_2_26) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_28_2_26) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.15 |
% 23.32/6.15 +-Applying beta-rule and splitting (427), into two cases.
% 23.32/6.15 |-Branch one:
% 23.32/6.15 | (128) all_1_1_1 = 0
% 23.32/6.15 |
% 23.32/6.15 | Equations (128) can reduce 48 to:
% 23.32/6.15 | (129) $false
% 23.32/6.15 |
% 23.32/6.15 |-The branch is then unsatisfiable
% 23.32/6.15 |-Branch two:
% 23.32/6.15 | (48) ~ (all_1_1_1 = 0)
% 23.32/6.15 | (455) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v3 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_20_2_14, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.15 |
% 23.32/6.15 | Instantiating (455) with all_236_0_142, all_236_1_143, all_236_2_144, all_236_3_145 yields:
% 23.32/6.15 | (456) apart_point_and_line(all_1_3_3, all_20_2_14) = all_236_0_142 & apart_point_and_line(all_1_4_4, all_1_2_2) = all_236_1_143 & distinct_lines(all_20_2_14, all_1_2_2) = all_236_2_144 & distinct_points(all_1_4_4, all_1_3_3) = all_236_3_145 & ( ~ (all_236_2_144 = 0) | ~ (all_236_3_145 = 0) | all_236_0_142 = 0 | all_236_1_143 = 0)
% 23.32/6.15 |
% 23.32/6.15 | Applying alpha-rule on (456) yields:
% 23.32/6.15 | (457) apart_point_and_line(all_1_3_3, all_20_2_14) = all_236_0_142
% 23.32/6.15 | (458) ~ (all_236_2_144 = 0) | ~ (all_236_3_145 = 0) | all_236_0_142 = 0 | all_236_1_143 = 0
% 23.32/6.15 | (459) distinct_points(all_1_4_4, all_1_3_3) = all_236_3_145
% 23.32/6.15 | (460) distinct_lines(all_20_2_14, all_1_2_2) = all_236_2_144
% 23.32/6.15 | (461) apart_point_and_line(all_1_4_4, all_1_2_2) = all_236_1_143
% 23.32/6.15 |
% 23.32/6.15 +-Applying beta-rule and splitting (435), into two cases.
% 23.32/6.15 |-Branch one:
% 23.32/6.15 | (128) all_1_1_1 = 0
% 23.32/6.15 |
% 23.32/6.15 | Equations (128) can reduce 48 to:
% 23.32/6.15 | (129) $false
% 23.32/6.15 |
% 23.32/6.15 |-The branch is then unsatisfiable
% 23.32/6.15 |-Branch two:
% 23.32/6.15 | (48) ~ (all_1_1_1 = 0)
% 23.32/6.15 | (465) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_28_2_26) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_28_2_26) = v1 & distinct_points(all_1_3_3, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.15 |
% 23.32/6.15 | Instantiating (465) with all_241_0_146, all_241_1_147, all_241_2_148, all_241_3_149 yields:
% 23.32/6.15 | (466) apart_point_and_line(all_1_3_3, all_28_2_26) = all_241_1_147 & apart_point_and_line(all_1_5_5, all_1_2_2) = all_241_0_146 & distinct_lines(all_1_2_2, all_28_2_26) = all_241_2_148 & distinct_points(all_1_3_3, all_1_5_5) = all_241_3_149 & ( ~ (all_241_2_148 = 0) | ~ (all_241_3_149 = 0) | all_241_0_146 = 0 | all_241_1_147 = 0)
% 23.32/6.15 |
% 23.32/6.15 | Applying alpha-rule on (466) yields:
% 23.32/6.15 | (467) apart_point_and_line(all_1_5_5, all_1_2_2) = all_241_0_146
% 23.32/6.15 | (468) distinct_points(all_1_3_3, all_1_5_5) = all_241_3_149
% 23.32/6.15 | (469) distinct_lines(all_1_2_2, all_28_2_26) = all_241_2_148
% 23.32/6.15 | (470) ~ (all_241_2_148 = 0) | ~ (all_241_3_149 = 0) | all_241_0_146 = 0 | all_241_1_147 = 0
% 23.32/6.15 | (471) apart_point_and_line(all_1_3_3, all_28_2_26) = all_241_1_147
% 23.32/6.15 |
% 23.32/6.15 +-Applying beta-rule and splitting (439), into two cases.
% 23.32/6.15 |-Branch one:
% 23.32/6.15 | (128) all_1_1_1 = 0
% 23.32/6.15 |
% 23.32/6.15 | Equations (128) can reduce 48 to:
% 23.32/6.15 | (129) $false
% 23.32/6.15 |
% 23.32/6.15 |-The branch is then unsatisfiable
% 23.32/6.15 |-Branch two:
% 23.32/6.15 | (48) ~ (all_1_1_1 = 0)
% 23.32/6.15 | (475) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_28_2_26) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_28_2_26, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.15 |
% 23.32/6.15 | Instantiating (475) with all_246_0_150, all_246_1_151, all_246_2_152, all_246_3_153 yields:
% 23.32/6.15 | (476) apart_point_and_line(all_1_3_3, all_28_2_26) = all_246_0_150 & apart_point_and_line(all_1_5_5, all_1_2_2) = all_246_1_151 & distinct_lines(all_28_2_26, all_1_2_2) = all_246_2_152 & distinct_points(all_1_5_5, all_1_3_3) = all_246_3_153 & ( ~ (all_246_2_152 = 0) | ~ (all_246_3_153 = 0) | all_246_0_150 = 0 | all_246_1_151 = 0)
% 23.32/6.15 |
% 23.32/6.15 | Applying alpha-rule on (476) yields:
% 23.32/6.15 | (477) ~ (all_246_2_152 = 0) | ~ (all_246_3_153 = 0) | all_246_0_150 = 0 | all_246_1_151 = 0
% 23.32/6.15 | (478) apart_point_and_line(all_1_3_3, all_28_2_26) = all_246_0_150
% 23.32/6.15 | (479) distinct_points(all_1_5_5, all_1_3_3) = all_246_3_153
% 23.32/6.15 | (480) apart_point_and_line(all_1_5_5, all_1_2_2) = all_246_1_151
% 23.32/6.15 | (481) distinct_lines(all_28_2_26, all_1_2_2) = all_246_2_152
% 23.32/6.15 |
% 23.32/6.15 +-Applying beta-rule and splitting (280), into two cases.
% 23.32/6.15 |-Branch one:
% 23.32/6.15 | (482) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0)
% 23.32/6.15 |
% 23.32/6.15 | Using (367) and (482) yields:
% 23.32/6.15 | (230) $false
% 23.32/6.15 |
% 23.32/6.15 |-The branch is then unsatisfiable
% 23.32/6.15 |-Branch two:
% 23.32/6.15 | (367) distinct_points(all_1_3_3, all_1_4_4) = 0
% 23.32/6.15 | (485) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_3_3, all_1_4_4) = v0 & apart_point_and_line(all_1_3_3, v0) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_49_3_48 = 0)))
% 23.32/6.15 |
% 23.32/6.15 | Instantiating (485) with all_252_0_154, all_252_1_155, all_252_2_156 yields:
% 23.32/6.15 | (486) line_connecting(all_1_3_3, all_1_4_4) = all_252_2_156 & apart_point_and_line(all_1_3_3, all_252_2_156) = all_252_1_155 & distinct_points(all_1_3_3, all_1_4_4) = all_252_0_154 & ( ~ (all_252_1_155 = 0) | (all_252_0_154 = 0 & all_49_3_48 = 0))
% 23.32/6.15 |
% 23.32/6.15 | Applying alpha-rule on (486) yields:
% 23.32/6.15 | (487) line_connecting(all_1_3_3, all_1_4_4) = all_252_2_156
% 23.32/6.15 | (488) apart_point_and_line(all_1_3_3, all_252_2_156) = all_252_1_155
% 23.32/6.15 | (489) distinct_points(all_1_3_3, all_1_4_4) = all_252_0_154
% 23.32/6.15 | (490) ~ (all_252_1_155 = 0) | (all_252_0_154 = 0 & all_49_3_48 = 0)
% 23.32/6.15 |
% 23.32/6.15 +-Applying beta-rule and splitting (278), into two cases.
% 23.32/6.15 |-Branch one:
% 23.32/6.15 | (482) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0)
% 23.32/6.15 |
% 23.32/6.15 | Using (367) and (482) yields:
% 23.32/6.15 | (230) $false
% 23.32/6.15 |
% 23.32/6.15 |-The branch is then unsatisfiable
% 23.32/6.15 |-Branch two:
% 23.32/6.15 | (367) distinct_points(all_1_3_3, all_1_4_4) = 0
% 23.32/6.15 | (494) all_22_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_0_0) = v2 & apart_point_and_line(all_1_3_3, all_1_0_0) = v1 & distinct_lines(all_1_0_0, all_1_0_0) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.15 |
% 23.32/6.15 +-Applying beta-rule and splitting (277), into two cases.
% 23.32/6.15 |-Branch one:
% 23.32/6.15 | (482) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0)
% 23.32/6.15 |
% 23.32/6.15 | Using (367) and (482) yields:
% 23.32/6.15 | (230) $false
% 23.32/6.15 |
% 23.32/6.15 |-The branch is then unsatisfiable
% 23.32/6.15 |-Branch two:
% 23.32/6.15 | (367) distinct_points(all_1_3_3, all_1_4_4) = 0
% 23.32/6.15 | (498) all_24_1_19 = 0 | all_22_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v1 & apart_point_and_line(all_1_3_3, all_1_0_0) = v2 & distinct_lines(all_20_2_14, all_1_0_0) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.15 |
% 23.32/6.15 +-Applying beta-rule and splitting (264), into two cases.
% 23.32/6.15 |-Branch one:
% 23.32/6.15 | (499) all_22_1_16 = 0
% 23.32/6.15 |
% 23.32/6.15 | Equations (499) can reduce 398 to:
% 23.32/6.15 | (129) $false
% 23.32/6.15 |
% 23.32/6.15 |-The branch is then unsatisfiable
% 23.32/6.15 |-Branch two:
% 23.32/6.15 | (398) ~ (all_22_1_16 = 0)
% 23.32/6.15 | (502) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_1_0_0) = v3 & distinct_lines(all_1_2_2, all_1_0_0) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.15 |
% 23.32/6.15 +-Applying beta-rule and splitting (265), into two cases.
% 23.32/6.15 |-Branch one:
% 23.32/6.15 | (499) all_22_1_16 = 0
% 23.32/6.15 |
% 23.32/6.15 | Equations (499) can reduce 398 to:
% 23.32/6.15 | (129) $false
% 23.32/6.15 |
% 23.32/6.15 |-The branch is then unsatisfiable
% 23.32/6.15 |-Branch two:
% 23.32/6.15 | (398) ~ (all_22_1_16 = 0)
% 23.32/6.15 | (506) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_1_0_0) = v2 & distinct_lines(all_1_0_0, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.15 |
% 23.32/6.15 +-Applying beta-rule and splitting (268), into two cases.
% 23.32/6.15 |-Branch one:
% 23.32/6.15 | (507) all_49_3_48 = 0
% 23.32/6.15 |
% 23.32/6.15 | Equations (507) can reduce 242 to:
% 23.32/6.15 | (129) $false
% 23.32/6.15 |
% 23.32/6.15 |-The branch is then unsatisfiable
% 23.32/6.15 |-Branch two:
% 23.32/6.15 | (242) ~ (all_49_3_48 = 0)
% 23.32/6.15 | (510) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_3_3, all_1_3_3) = v1 & apart_point_and_line(all_1_3_3, v1) = v2 & distinct_points(all_1_3_3, all_1_3_3) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 23.32/6.15 |
% 23.32/6.15 +-Applying beta-rule and splitting (447), into two cases.
% 23.32/6.15 |-Branch one:
% 23.32/6.15 | (394) all_36_1_37 = 0
% 23.32/6.15 |
% 23.32/6.15 | Equations (394) can reduce 225 to:
% 23.32/6.15 | (129) $false
% 23.32/6.15 |
% 23.32/6.15 |-The branch is then unsatisfiable
% 23.32/6.15 |-Branch two:
% 23.32/6.15 | (225) ~ (all_36_1_37 = 0)
% 23.32/6.15 | (514) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_28_2_26) = v2 & apart_point_and_line(all_1_4_4, all_28_2_26) = v1 & distinct_lines(all_28_2_26, all_28_2_26) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.16 |
% 23.32/6.16 +-Applying beta-rule and splitting (490), into two cases.
% 23.32/6.16 |-Branch one:
% 23.32/6.16 | (515) ~ (all_252_1_155 = 0)
% 23.32/6.16 |
% 23.32/6.16 +-Applying beta-rule and splitting (276), into two cases.
% 23.32/6.16 |-Branch one:
% 23.32/6.16 | (482) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0)
% 23.32/6.16 |
% 23.32/6.16 | Using (367) and (482) yields:
% 23.32/6.16 | (230) $false
% 23.32/6.16 |
% 23.32/6.16 |-The branch is then unsatisfiable
% 23.32/6.16 |-Branch two:
% 23.32/6.16 | (367) distinct_points(all_1_3_3, all_1_4_4) = 0
% 23.32/6.16 | (519) all_24_1_19 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v2 & apart_point_and_line(all_1_3_3, all_20_2_14) = v1 & distinct_lines(all_20_2_14, all_20_2_14) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.16 |
% 23.32/6.16 +-Applying beta-rule and splitting (494), into two cases.
% 23.32/6.16 |-Branch one:
% 23.32/6.16 | (499) all_22_1_16 = 0
% 23.32/6.16 |
% 23.32/6.16 | Equations (499) can reduce 398 to:
% 23.32/6.16 | (129) $false
% 23.32/6.16 |
% 23.32/6.16 |-The branch is then unsatisfiable
% 23.32/6.16 |-Branch two:
% 23.32/6.16 | (398) ~ (all_22_1_16 = 0)
% 23.32/6.16 | (523) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_0_0) = v2 & apart_point_and_line(all_1_3_3, all_1_0_0) = v1 & distinct_lines(all_1_0_0, all_1_0_0) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.16 |
% 23.32/6.16 | Instantiating (523) with all_302_0_163, all_302_1_164, all_302_2_165 yields:
% 23.32/6.16 | (524) apart_point_and_line(all_1_3_3, all_1_0_0) = all_302_0_163 & apart_point_and_line(all_1_3_3, all_1_0_0) = all_302_1_164 & distinct_lines(all_1_0_0, all_1_0_0) = all_302_2_165 & ( ~ (all_302_2_165 = 0) | all_302_0_163 = 0 | all_302_1_164 = 0)
% 23.32/6.16 |
% 23.32/6.16 | Applying alpha-rule on (524) yields:
% 23.32/6.16 | (525) apart_point_and_line(all_1_3_3, all_1_0_0) = all_302_0_163
% 23.32/6.16 | (526) apart_point_and_line(all_1_3_3, all_1_0_0) = all_302_1_164
% 23.32/6.16 | (527) distinct_lines(all_1_0_0, all_1_0_0) = all_302_2_165
% 23.32/6.16 | (528) ~ (all_302_2_165 = 0) | all_302_0_163 = 0 | all_302_1_164 = 0
% 23.32/6.16 |
% 23.32/6.16 +-Applying beta-rule and splitting (252), into two cases.
% 23.32/6.16 |-Branch one:
% 23.32/6.16 | (416) all_24_1_19 = 0
% 23.32/6.16 |
% 23.32/6.16 | Equations (416) can reduce 228 to:
% 23.32/6.16 | (129) $false
% 23.32/6.16 |
% 23.32/6.16 |-The branch is then unsatisfiable
% 23.32/6.16 |-Branch two:
% 23.32/6.16 | (228) ~ (all_24_1_19 = 0)
% 23.32/6.16 | (532) all_22_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_20_2_14) = v3 & apart_point_and_line(all_1_4_4, all_1_0_0) = v2 & distinct_lines(all_1_0_0, all_20_2_14) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.16 |
% 23.32/6.16 +-Applying beta-rule and splitting (251), into two cases.
% 23.32/6.16 |-Branch one:
% 23.32/6.16 | (416) all_24_1_19 = 0
% 23.32/6.16 |
% 23.32/6.16 | Equations (416) can reduce 228 to:
% 23.32/6.16 | (129) $false
% 23.32/6.16 |
% 23.32/6.16 |-The branch is then unsatisfiable
% 23.32/6.16 |-Branch two:
% 23.32/6.16 | (228) ~ (all_24_1_19 = 0)
% 23.32/6.16 | (536) all_22_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_20_2_14) = v2 & apart_point_and_line(all_1_4_4, all_1_0_0) = v3 & distinct_lines(all_1_0_0, all_20_2_14) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.16 |
% 23.32/6.16 +-Applying beta-rule and splitting (249), into two cases.
% 23.32/6.16 |-Branch one:
% 23.32/6.16 | (416) all_24_1_19 = 0
% 23.32/6.16 |
% 23.32/6.16 | Equations (416) can reduce 228 to:
% 23.32/6.16 | (129) $false
% 23.32/6.16 |
% 23.32/6.16 |-The branch is then unsatisfiable
% 23.32/6.16 |-Branch two:
% 23.32/6.16 | (228) ~ (all_24_1_19 = 0)
% 23.32/6.16 | (540) all_22_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_20_2_14) = v1 & apart_point_and_line(all_1_5_5, all_1_0_0) = v2 & distinct_lines(all_20_2_14, all_1_0_0) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.16 |
% 23.32/6.16 +-Applying beta-rule and splitting (248), into two cases.
% 23.32/6.16 |-Branch one:
% 23.32/6.16 | (416) all_24_1_19 = 0
% 23.32/6.16 |
% 23.32/6.16 | Equations (416) can reduce 228 to:
% 23.32/6.16 | (129) $false
% 23.32/6.16 |
% 23.32/6.16 |-The branch is then unsatisfiable
% 23.32/6.16 |-Branch two:
% 23.32/6.16 | (228) ~ (all_24_1_19 = 0)
% 23.32/6.16 | (544) all_22_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v2 & apart_point_and_line(all_1_3_3, all_1_0_0) = v1 & distinct_lines(all_1_0_0, all_20_2_14) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.16 |
% 23.32/6.16 +-Applying beta-rule and splitting (498), into two cases.
% 23.32/6.16 |-Branch one:
% 23.32/6.16 | (416) all_24_1_19 = 0
% 23.32/6.16 |
% 23.32/6.16 | Equations (416) can reduce 228 to:
% 23.32/6.16 | (129) $false
% 23.32/6.16 |
% 23.32/6.16 |-The branch is then unsatisfiable
% 23.32/6.16 |-Branch two:
% 23.32/6.16 | (228) ~ (all_24_1_19 = 0)
% 23.32/6.16 | (548) all_22_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v1 & apart_point_and_line(all_1_3_3, all_1_0_0) = v2 & distinct_lines(all_20_2_14, all_1_0_0) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.16 |
% 23.32/6.16 +-Applying beta-rule and splitting (250), into two cases.
% 23.32/6.16 |-Branch one:
% 23.32/6.16 | (416) all_24_1_19 = 0
% 23.32/6.16 |
% 23.32/6.16 | Equations (416) can reduce 228 to:
% 23.32/6.16 | (129) $false
% 23.32/6.16 |
% 23.32/6.16 |-The branch is then unsatisfiable
% 23.32/6.16 |-Branch two:
% 23.32/6.16 | (228) ~ (all_24_1_19 = 0)
% 23.32/6.16 | (552) all_22_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_20_2_14) = v2 & apart_point_and_line(all_1_5_5, all_1_0_0) = v1 & distinct_lines(all_1_0_0, all_20_2_14) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.16 |
% 23.32/6.16 +-Applying beta-rule and splitting (494), into two cases.
% 23.32/6.16 |-Branch one:
% 23.32/6.16 | (499) all_22_1_16 = 0
% 23.32/6.16 |
% 23.32/6.16 | Equations (499) can reduce 398 to:
% 23.32/6.16 | (129) $false
% 23.32/6.16 |
% 23.32/6.16 |-The branch is then unsatisfiable
% 23.32/6.16 |-Branch two:
% 23.32/6.16 | (398) ~ (all_22_1_16 = 0)
% 23.32/6.16 | (523) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_0_0) = v2 & apart_point_and_line(all_1_3_3, all_1_0_0) = v1 & distinct_lines(all_1_0_0, all_1_0_0) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.16 |
% 23.32/6.16 | Instantiating (523) with all_325_0_166, all_325_1_167, all_325_2_168 yields:
% 23.32/6.16 | (557) apart_point_and_line(all_1_3_3, all_1_0_0) = all_325_0_166 & apart_point_and_line(all_1_3_3, all_1_0_0) = all_325_1_167 & distinct_lines(all_1_0_0, all_1_0_0) = all_325_2_168 & ( ~ (all_325_2_168 = 0) | all_325_0_166 = 0 | all_325_1_167 = 0)
% 23.32/6.16 |
% 23.32/6.16 | Applying alpha-rule on (557) yields:
% 23.32/6.16 | (558) apart_point_and_line(all_1_3_3, all_1_0_0) = all_325_0_166
% 23.32/6.16 | (559) apart_point_and_line(all_1_3_3, all_1_0_0) = all_325_1_167
% 23.32/6.16 | (560) distinct_lines(all_1_0_0, all_1_0_0) = all_325_2_168
% 23.32/6.16 | (561) ~ (all_325_2_168 = 0) | all_325_0_166 = 0 | all_325_1_167 = 0
% 23.32/6.16 |
% 23.32/6.16 +-Applying beta-rule and splitting (498), into two cases.
% 23.32/6.16 |-Branch one:
% 23.32/6.16 | (416) all_24_1_19 = 0
% 23.32/6.16 |
% 23.32/6.16 | Equations (416) can reduce 228 to:
% 23.32/6.16 | (129) $false
% 23.32/6.16 |
% 23.32/6.16 |-The branch is then unsatisfiable
% 23.32/6.16 |-Branch two:
% 23.32/6.16 | (228) ~ (all_24_1_19 = 0)
% 23.32/6.16 | (548) all_22_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v1 & apart_point_and_line(all_1_3_3, all_1_0_0) = v2 & distinct_lines(all_20_2_14, all_1_0_0) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.16 |
% 23.32/6.16 +-Applying beta-rule and splitting (502), into two cases.
% 23.32/6.16 |-Branch one:
% 23.32/6.16 | (566) all_16_1_7 = 0
% 23.32/6.16 |
% 23.32/6.16 | Equations (566) can reduce 235 to:
% 23.32/6.16 | (129) $false
% 23.32/6.16 |
% 23.32/6.16 |-The branch is then unsatisfiable
% 23.32/6.16 |-Branch two:
% 23.32/6.16 | (235) ~ (all_16_1_7 = 0)
% 23.32/6.16 | (569) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_1_0_0) = v3 & distinct_lines(all_1_2_2, all_1_0_0) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.16 |
% 23.32/6.16 | Instantiating (569) with all_333_0_169, all_333_1_170, all_333_2_171, all_333_3_172 yields:
% 23.32/6.16 | (570) apart_point_and_line(all_1_4_4, all_1_2_2) = all_333_1_170 & apart_point_and_line(all_1_5_5, all_1_0_0) = all_333_0_169 & distinct_lines(all_1_2_2, all_1_0_0) = all_333_2_171 & distinct_points(all_1_4_4, all_1_5_5) = all_333_3_172 & ( ~ (all_333_2_171 = 0) | ~ (all_333_3_172 = 0) | all_333_0_169 = 0 | all_333_1_170 = 0)
% 23.32/6.16 |
% 23.32/6.16 | Applying alpha-rule on (570) yields:
% 23.32/6.16 | (571) ~ (all_333_2_171 = 0) | ~ (all_333_3_172 = 0) | all_333_0_169 = 0 | all_333_1_170 = 0
% 23.32/6.16 | (572) distinct_points(all_1_4_4, all_1_5_5) = all_333_3_172
% 23.32/6.16 | (573) distinct_lines(all_1_2_2, all_1_0_0) = all_333_2_171
% 23.32/6.16 | (574) apart_point_and_line(all_1_4_4, all_1_2_2) = all_333_1_170
% 23.32/6.16 | (575) apart_point_and_line(all_1_5_5, all_1_0_0) = all_333_0_169
% 23.32/6.16 |
% 23.32/6.16 +-Applying beta-rule and splitting (548), into two cases.
% 23.32/6.16 |-Branch one:
% 23.32/6.16 | (499) all_22_1_16 = 0
% 23.32/6.16 |
% 23.32/6.16 | Equations (499) can reduce 398 to:
% 23.32/6.16 | (129) $false
% 23.32/6.16 |
% 23.32/6.16 |-The branch is then unsatisfiable
% 23.32/6.16 |-Branch two:
% 23.32/6.16 | (398) ~ (all_22_1_16 = 0)
% 23.32/6.16 | (579) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v1 & apart_point_and_line(all_1_3_3, all_1_0_0) = v2 & distinct_lines(all_20_2_14, all_1_0_0) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.16 |
% 23.32/6.17 | Instantiating (579) with all_342_0_173, all_342_1_174, all_342_2_175 yields:
% 23.32/6.17 | (580) apart_point_and_line(all_1_3_3, all_20_2_14) = all_342_1_174 & apart_point_and_line(all_1_3_3, all_1_0_0) = all_342_0_173 & distinct_lines(all_20_2_14, all_1_0_0) = all_342_2_175 & ( ~ (all_342_2_175 = 0) | all_342_0_173 = 0 | all_342_1_174 = 0)
% 23.32/6.17 |
% 23.32/6.17 | Applying alpha-rule on (580) yields:
% 23.32/6.17 | (581) apart_point_and_line(all_1_3_3, all_20_2_14) = all_342_1_174
% 23.32/6.17 | (582) apart_point_and_line(all_1_3_3, all_1_0_0) = all_342_0_173
% 23.32/6.17 | (583) distinct_lines(all_20_2_14, all_1_0_0) = all_342_2_175
% 23.32/6.17 | (584) ~ (all_342_2_175 = 0) | all_342_0_173 = 0 | all_342_1_174 = 0
% 23.32/6.17 |
% 23.32/6.17 +-Applying beta-rule and splitting (536), into two cases.
% 23.32/6.17 |-Branch one:
% 23.32/6.17 | (499) all_22_1_16 = 0
% 23.32/6.17 |
% 23.32/6.17 | Equations (499) can reduce 398 to:
% 23.32/6.17 | (129) $false
% 23.32/6.17 |
% 23.32/6.17 |-The branch is then unsatisfiable
% 23.32/6.17 |-Branch two:
% 23.32/6.17 | (398) ~ (all_22_1_16 = 0)
% 23.32/6.17 | (588) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_20_2_14) = v2 & apart_point_and_line(all_1_4_4, all_1_0_0) = v3 & distinct_lines(all_1_0_0, all_20_2_14) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.17 |
% 23.32/6.17 | Instantiating (588) with all_351_0_176, all_351_1_177, all_351_2_178, all_351_3_179 yields:
% 23.32/6.17 | (589) apart_point_and_line(all_1_4_4, all_20_2_14) = all_351_1_177 & apart_point_and_line(all_1_4_4, all_1_0_0) = all_351_0_176 & distinct_lines(all_1_0_0, all_20_2_14) = all_351_2_178 & distinct_points(all_1_4_4, all_1_4_4) = all_351_3_179 & ( ~ (all_351_2_178 = 0) | ~ (all_351_3_179 = 0) | all_351_0_176 = 0 | all_351_1_177 = 0)
% 23.32/6.17 |
% 23.32/6.17 | Applying alpha-rule on (589) yields:
% 23.32/6.17 | (590) apart_point_and_line(all_1_4_4, all_20_2_14) = all_351_1_177
% 23.32/6.17 | (591) distinct_lines(all_1_0_0, all_20_2_14) = all_351_2_178
% 23.32/6.17 | (592) ~ (all_351_2_178 = 0) | ~ (all_351_3_179 = 0) | all_351_0_176 = 0 | all_351_1_177 = 0
% 23.32/6.17 | (593) distinct_points(all_1_4_4, all_1_4_4) = all_351_3_179
% 23.32/6.17 | (594) apart_point_and_line(all_1_4_4, all_1_0_0) = all_351_0_176
% 23.32/6.17 |
% 23.32/6.17 +-Applying beta-rule and splitting (544), into two cases.
% 23.32/6.17 |-Branch one:
% 23.32/6.17 | (499) all_22_1_16 = 0
% 23.32/6.17 |
% 23.32/6.17 | Equations (499) can reduce 398 to:
% 23.32/6.17 | (129) $false
% 23.32/6.17 |
% 23.32/6.17 |-The branch is then unsatisfiable
% 23.32/6.17 |-Branch two:
% 23.32/6.17 | (398) ~ (all_22_1_16 = 0)
% 23.32/6.17 | (598) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v2 & apart_point_and_line(all_1_3_3, all_1_0_0) = v1 & distinct_lines(all_1_0_0, all_20_2_14) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.17 |
% 23.32/6.17 | Instantiating (598) with all_356_0_180, all_356_1_181, all_356_2_182 yields:
% 23.32/6.17 | (599) apart_point_and_line(all_1_3_3, all_20_2_14) = all_356_0_180 & apart_point_and_line(all_1_3_3, all_1_0_0) = all_356_1_181 & distinct_lines(all_1_0_0, all_20_2_14) = all_356_2_182 & ( ~ (all_356_2_182 = 0) | all_356_0_180 = 0 | all_356_1_181 = 0)
% 23.32/6.17 |
% 23.32/6.17 | Applying alpha-rule on (599) yields:
% 23.32/6.17 | (600) apart_point_and_line(all_1_3_3, all_20_2_14) = all_356_0_180
% 23.32/6.17 | (601) apart_point_and_line(all_1_3_3, all_1_0_0) = all_356_1_181
% 23.32/6.17 | (602) distinct_lines(all_1_0_0, all_20_2_14) = all_356_2_182
% 23.32/6.17 | (603) ~ (all_356_2_182 = 0) | all_356_0_180 = 0 | all_356_1_181 = 0
% 23.32/6.17 |
% 23.32/6.17 +-Applying beta-rule and splitting (331), into two cases.
% 23.32/6.17 |-Branch one:
% 23.32/6.17 | (604) ~ (all_112_1_74 = 0)
% 23.32/6.17 |
% 23.32/6.17 +-Applying beta-rule and splitting (279), into two cases.
% 23.32/6.17 |-Branch one:
% 23.32/6.17 | (482) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0)
% 23.32/6.17 |
% 23.32/6.17 | Using (367) and (482) yields:
% 23.32/6.17 | (230) $false
% 23.32/6.17 |
% 23.32/6.17 |-The branch is then unsatisfiable
% 23.32/6.17 |-Branch two:
% 23.32/6.17 | (367) distinct_points(all_1_3_3, all_1_4_4) = 0
% 23.32/6.17 | (608) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_3_3, all_1_4_4) = v0 & apart_point_and_line(all_1_4_4, v0) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 23.32/6.17 |
% 23.32/6.17 | Instantiating (608) with all_365_0_183, all_365_1_184, all_365_2_185 yields:
% 23.32/6.17 | (609) line_connecting(all_1_3_3, all_1_4_4) = all_365_2_185 & apart_point_and_line(all_1_4_4, all_365_2_185) = all_365_1_184 & distinct_points(all_1_4_4, all_1_4_4) = all_365_0_183 & ( ~ (all_365_1_184 = 0) | all_365_0_183 = 0)
% 23.32/6.17 |
% 23.32/6.17 | Applying alpha-rule on (609) yields:
% 23.32/6.17 | (610) line_connecting(all_1_3_3, all_1_4_4) = all_365_2_185
% 23.32/6.17 | (611) apart_point_and_line(all_1_4_4, all_365_2_185) = all_365_1_184
% 23.32/6.17 | (612) distinct_points(all_1_4_4, all_1_4_4) = all_365_0_183
% 23.32/6.17 | (613) ~ (all_365_1_184 = 0) | all_365_0_183 = 0
% 23.32/6.17 |
% 23.32/6.17 +-Applying beta-rule and splitting (282), into two cases.
% 23.32/6.17 |-Branch one:
% 23.32/6.17 | (482) ~ (distinct_points(all_1_3_3, all_1_4_4) = 0)
% 23.32/6.17 |
% 23.32/6.17 | Using (367) and (482) yields:
% 23.32/6.17 | (230) $false
% 23.32/6.17 |
% 23.32/6.17 |-The branch is then unsatisfiable
% 23.32/6.17 |-Branch two:
% 23.32/6.17 | (367) distinct_points(all_1_3_3, all_1_4_4) = 0
% 23.32/6.17 | (617) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_3_3, all_1_4_4) = v0 & apart_point_and_line(all_1_4_4, v0) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_22_0_15 = 0)))
% 23.32/6.17 |
% 23.32/6.17 | Instantiating (617) with all_370_0_186, all_370_1_187, all_370_2_188 yields:
% 23.32/6.17 | (618) line_connecting(all_1_3_3, all_1_4_4) = all_370_2_188 & apart_point_and_line(all_1_4_4, all_370_2_188) = all_370_1_187 & distinct_points(all_1_4_4, all_1_3_3) = all_370_0_186 & ( ~ (all_370_1_187 = 0) | (all_370_0_186 = 0 & all_22_0_15 = 0))
% 23.32/6.17 |
% 23.32/6.17 | Applying alpha-rule on (618) yields:
% 23.32/6.17 | (619) line_connecting(all_1_3_3, all_1_4_4) = all_370_2_188
% 23.32/6.17 | (620) apart_point_and_line(all_1_4_4, all_370_2_188) = all_370_1_187
% 23.32/6.17 | (621) distinct_points(all_1_4_4, all_1_3_3) = all_370_0_186
% 23.32/6.17 | (622) ~ (all_370_1_187 = 0) | (all_370_0_186 = 0 & all_22_0_15 = 0)
% 23.32/6.17 |
% 23.32/6.17 +-Applying beta-rule and splitting (292), into two cases.
% 23.32/6.17 |-Branch one:
% 23.32/6.17 | (369) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0)
% 23.32/6.17 |
% 23.32/6.17 | Using (368) and (369) yields:
% 23.32/6.17 | (230) $false
% 23.32/6.17 |
% 23.32/6.17 |-The branch is then unsatisfiable
% 23.32/6.17 |-Branch two:
% 23.32/6.17 | (368) distinct_points(all_1_4_4, all_1_5_5) = 0
% 23.32/6.17 | (626) all_24_1_19 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_20_2_14) = v2 & apart_point_and_line(all_1_5_5, all_20_2_14) = v1 & distinct_lines(all_20_2_14, all_20_2_14) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.17 |
% 23.32/6.17 +-Applying beta-rule and splitting (281), into two cases.
% 23.32/6.17 |-Branch one:
% 23.32/6.17 | (399) all_22_0_15 = 0
% 23.32/6.17 |
% 23.32/6.17 | Equations (399) can reduce 209 to:
% 23.32/6.17 | (129) $false
% 23.32/6.17 |
% 23.32/6.17 |-The branch is then unsatisfiable
% 23.32/6.17 |-Branch two:
% 23.32/6.17 | (209) ~ (all_22_0_15 = 0)
% 23.32/6.17 | (630) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_3_3, all_1_4_4) = v1 & apart_point_and_line(all_1_4_4, v1) = v2 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 23.32/6.17 |
% 23.32/6.17 | Instantiating (630) with all_378_0_189, all_378_1_190, all_378_2_191 yields:
% 23.32/6.17 | (631) line_connecting(all_1_3_3, all_1_4_4) = all_378_1_190 & apart_point_and_line(all_1_4_4, all_378_1_190) = all_378_0_189 & distinct_points(all_1_3_3, all_1_4_4) = all_378_2_191 & ( ~ (all_378_0_189 = 0) | ~ (all_378_2_191 = 0))
% 23.32/6.17 |
% 23.32/6.17 | Applying alpha-rule on (631) yields:
% 23.32/6.17 | (632) line_connecting(all_1_3_3, all_1_4_4) = all_378_1_190
% 23.32/6.17 | (633) apart_point_and_line(all_1_4_4, all_378_1_190) = all_378_0_189
% 23.32/6.17 | (634) distinct_points(all_1_3_3, all_1_4_4) = all_378_2_191
% 23.32/6.17 | (635) ~ (all_378_0_189 = 0) | ~ (all_378_2_191 = 0)
% 23.32/6.17 |
% 23.32/6.17 +-Applying beta-rule and splitting (247), into two cases.
% 23.32/6.17 |-Branch one:
% 23.32/6.17 | (416) all_24_1_19 = 0
% 23.32/6.17 |
% 23.32/6.17 | Equations (416) can reduce 228 to:
% 23.32/6.17 | (129) $false
% 23.32/6.17 |
% 23.32/6.17 |-The branch is then unsatisfiable
% 23.32/6.17 |-Branch two:
% 23.32/6.17 | (228) ~ (all_24_1_19 = 0)
% 23.32/6.17 | (639) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_20_2_14) = v3 & apart_point_and_line(all_1_4_4, all_20_2_14) = v2 & distinct_lines(all_20_2_14, all_20_2_14) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.17 |
% 23.32/6.17 | Instantiating (639) with all_406_0_207, all_406_1_208, all_406_2_209, all_406_3_210 yields:
% 23.32/6.17 | (640) apart_point_and_line(all_1_4_4, all_20_2_14) = all_406_0_207 & apart_point_and_line(all_1_4_4, all_20_2_14) = all_406_1_208 & distinct_lines(all_20_2_14, all_20_2_14) = all_406_2_209 & distinct_points(all_1_4_4, all_1_4_4) = all_406_3_210 & ( ~ (all_406_2_209 = 0) | ~ (all_406_3_210 = 0) | all_406_0_207 = 0 | all_406_1_208 = 0)
% 23.32/6.17 |
% 23.32/6.18 | Applying alpha-rule on (640) yields:
% 23.32/6.18 | (641) distinct_points(all_1_4_4, all_1_4_4) = all_406_3_210
% 23.32/6.18 | (642) apart_point_and_line(all_1_4_4, all_20_2_14) = all_406_1_208
% 23.32/6.18 | (643) apart_point_and_line(all_1_4_4, all_20_2_14) = all_406_0_207
% 23.32/6.18 | (644) ~ (all_406_2_209 = 0) | ~ (all_406_3_210 = 0) | all_406_0_207 = 0 | all_406_1_208 = 0
% 23.32/6.18 | (645) distinct_lines(all_20_2_14, all_20_2_14) = all_406_2_209
% 23.32/6.18 |
% 23.32/6.18 +-Applying beta-rule and splitting (519), into two cases.
% 23.32/6.18 |-Branch one:
% 23.32/6.18 | (416) all_24_1_19 = 0
% 23.32/6.18 |
% 23.32/6.18 | Equations (416) can reduce 228 to:
% 23.32/6.18 | (129) $false
% 23.32/6.18 |
% 23.32/6.18 |-The branch is then unsatisfiable
% 23.32/6.18 |-Branch two:
% 23.32/6.18 | (228) ~ (all_24_1_19 = 0)
% 23.32/6.18 | (649) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v2 & apart_point_and_line(all_1_3_3, all_20_2_14) = v1 & distinct_lines(all_20_2_14, all_20_2_14) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.18 |
% 23.32/6.18 | Instantiating (649) with all_411_0_211, all_411_1_212, all_411_2_213 yields:
% 23.32/6.18 | (650) apart_point_and_line(all_1_3_3, all_20_2_14) = all_411_0_211 & apart_point_and_line(all_1_3_3, all_20_2_14) = all_411_1_212 & distinct_lines(all_20_2_14, all_20_2_14) = all_411_2_213 & ( ~ (all_411_2_213 = 0) | all_411_0_211 = 0 | all_411_1_212 = 0)
% 23.32/6.18 |
% 23.32/6.18 | Applying alpha-rule on (650) yields:
% 23.32/6.18 | (651) apart_point_and_line(all_1_3_3, all_20_2_14) = all_411_0_211
% 23.32/6.18 | (652) apart_point_and_line(all_1_3_3, all_20_2_14) = all_411_1_212
% 23.32/6.18 | (653) distinct_lines(all_20_2_14, all_20_2_14) = all_411_2_213
% 23.32/6.18 | (654) ~ (all_411_2_213 = 0) | all_411_0_211 = 0 | all_411_1_212 = 0
% 23.32/6.18 |
% 23.32/6.18 +-Applying beta-rule and splitting (626), into two cases.
% 23.32/6.18 |-Branch one:
% 23.32/6.18 | (416) all_24_1_19 = 0
% 23.32/6.18 |
% 23.32/6.18 | Equations (416) can reduce 228 to:
% 23.32/6.18 | (129) $false
% 23.32/6.18 |
% 23.32/6.18 |-The branch is then unsatisfiable
% 23.32/6.18 |-Branch two:
% 23.32/6.18 | (228) ~ (all_24_1_19 = 0)
% 23.32/6.18 | (658) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_20_2_14) = v2 & apart_point_and_line(all_1_5_5, all_20_2_14) = v1 & distinct_lines(all_20_2_14, all_20_2_14) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.32/6.18 |
% 23.32/6.18 | Instantiating (658) with all_416_0_214, all_416_1_215, all_416_2_216 yields:
% 23.32/6.18 | (659) apart_point_and_line(all_1_5_5, all_20_2_14) = all_416_0_214 & apart_point_and_line(all_1_5_5, all_20_2_14) = all_416_1_215 & distinct_lines(all_20_2_14, all_20_2_14) = all_416_2_216 & ( ~ (all_416_2_216 = 0) | all_416_0_214 = 0 | all_416_1_215 = 0)
% 23.32/6.18 |
% 23.32/6.18 | Applying alpha-rule on (659) yields:
% 23.32/6.18 | (660) apart_point_and_line(all_1_5_5, all_20_2_14) = all_416_0_214
% 23.32/6.18 | (661) apart_point_and_line(all_1_5_5, all_20_2_14) = all_416_1_215
% 23.32/6.18 | (662) distinct_lines(all_20_2_14, all_20_2_14) = all_416_2_216
% 23.32/6.18 | (663) ~ (all_416_2_216 = 0) | all_416_0_214 = 0 | all_416_1_215 = 0
% 23.32/6.18 |
% 23.32/6.18 +-Applying beta-rule and splitting (289), into two cases.
% 23.32/6.18 |-Branch one:
% 23.32/6.18 | (664) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_4_4) = v1 & apart_point_and_line(all_1_4_4, v1) = v2 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 23.32/6.18 |
% 23.32/6.18 | Instantiating (664) with all_420_0_217, all_420_1_218, all_420_2_219 yields:
% 23.32/6.18 | (665) line_connecting(all_1_5_5, all_1_4_4) = all_420_1_218 & apart_point_and_line(all_1_4_4, all_420_1_218) = all_420_0_217 & distinct_points(all_1_5_5, all_1_4_4) = all_420_2_219 & ( ~ (all_420_0_217 = 0) | ~ (all_420_2_219 = 0))
% 23.32/6.18 |
% 23.32/6.18 | Applying alpha-rule on (665) yields:
% 23.32/6.18 | (666) line_connecting(all_1_5_5, all_1_4_4) = all_420_1_218
% 23.32/6.18 | (667) apart_point_and_line(all_1_4_4, all_420_1_218) = all_420_0_217
% 23.32/6.18 | (668) distinct_points(all_1_5_5, all_1_4_4) = all_420_2_219
% 23.32/6.18 | (669) ~ (all_420_0_217 = 0) | ~ (all_420_2_219 = 0)
% 23.32/6.18 |
% 23.32/6.18 +-Applying beta-rule and splitting (263), into two cases.
% 23.32/6.18 |-Branch one:
% 23.32/6.18 | (416) all_24_1_19 = 0
% 23.32/6.18 |
% 23.32/6.18 | Equations (416) can reduce 228 to:
% 23.32/6.18 | (129) $false
% 23.32/6.18 |
% 23.32/6.18 |-The branch is then unsatisfiable
% 23.32/6.18 |-Branch two:
% 23.32/6.18 | (228) ~ (all_24_1_19 = 0)
% 23.32/6.18 | (673) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_20_2_14) = v3 & distinct_lines(all_1_2_2, all_20_2_14) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.18 |
% 23.32/6.18 +-Applying beta-rule and splitting (262), into two cases.
% 23.32/6.18 |-Branch one:
% 23.32/6.18 | (416) all_24_1_19 = 0
% 23.32/6.18 |
% 23.32/6.18 | Equations (416) can reduce 228 to:
% 23.32/6.18 | (129) $false
% 23.32/6.18 |
% 23.32/6.18 |-The branch is then unsatisfiable
% 23.32/6.18 |-Branch two:
% 23.32/6.18 | (228) ~ (all_24_1_19 = 0)
% 23.32/6.18 | (677) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_20_2_14) = v2 & distinct_lines(all_1_2_2, all_20_2_14) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.18 |
% 23.32/6.18 +-Applying beta-rule and splitting (257), into two cases.
% 23.32/6.18 |-Branch one:
% 23.32/6.18 | (394) all_36_1_37 = 0
% 23.32/6.18 |
% 23.32/6.18 | Equations (394) can reduce 225 to:
% 23.32/6.18 | (129) $false
% 23.32/6.18 |
% 23.32/6.18 |-The branch is then unsatisfiable
% 23.32/6.18 |-Branch two:
% 23.32/6.18 | (225) ~ (all_36_1_37 = 0)
% 23.32/6.18 | (681) all_24_1_19 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_28_2_26) = v2 & apart_point_and_line(all_1_5_5, all_20_2_14) = v3 & distinct_lines(all_20_2_14, all_28_2_26) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.18 |
% 23.32/6.18 +-Applying beta-rule and splitting (258), into two cases.
% 23.32/6.18 |-Branch one:
% 23.32/6.18 | (394) all_36_1_37 = 0
% 23.32/6.18 |
% 23.32/6.18 | Equations (394) can reduce 225 to:
% 23.32/6.18 | (129) $false
% 23.32/6.18 |
% 23.32/6.18 |-The branch is then unsatisfiable
% 23.32/6.18 |-Branch two:
% 23.32/6.18 | (225) ~ (all_36_1_37 = 0)
% 23.32/6.18 | (685) all_24_1_19 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_28_2_26) = v3 & apart_point_and_line(all_1_5_5, all_20_2_14) = v2 & distinct_lines(all_28_2_26, all_20_2_14) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.18 |
% 23.32/6.18 +-Applying beta-rule and splitting (259), into two cases.
% 23.32/6.18 |-Branch one:
% 23.32/6.18 | (394) all_36_1_37 = 0
% 23.32/6.18 |
% 23.32/6.18 | Equations (394) can reduce 225 to:
% 23.32/6.18 | (129) $false
% 23.32/6.18 |
% 23.32/6.18 |-The branch is then unsatisfiable
% 23.32/6.18 |-Branch two:
% 23.32/6.18 | (225) ~ (all_36_1_37 = 0)
% 23.32/6.18 | (689) all_24_1_19 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_28_2_26) = v2 & apart_point_and_line(all_1_5_5, all_20_2_14) = v3 & distinct_lines(all_28_2_26, all_20_2_14) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.18 |
% 23.32/6.18 +-Applying beta-rule and splitting (260), into two cases.
% 23.32/6.18 |-Branch one:
% 23.32/6.18 | (394) all_36_1_37 = 0
% 23.32/6.18 |
% 23.32/6.18 | Equations (394) can reduce 225 to:
% 23.32/6.18 | (129) $false
% 23.32/6.18 |
% 23.32/6.18 |-The branch is then unsatisfiable
% 23.32/6.18 |-Branch two:
% 23.32/6.18 | (225) ~ (all_36_1_37 = 0)
% 23.32/6.18 | (693) all_22_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_28_2_26) = v3 & apart_point_and_line(all_1_5_5, all_1_0_0) = v2 & distinct_lines(all_28_2_26, all_1_0_0) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.18 |
% 23.32/6.18 +-Applying beta-rule and splitting (419), into two cases.
% 23.32/6.18 |-Branch one:
% 23.32/6.18 | (128) all_1_1_1 = 0
% 23.32/6.18 |
% 23.32/6.18 | Equations (128) can reduce 48 to:
% 23.32/6.18 | (129) $false
% 23.32/6.18 |
% 23.32/6.18 |-The branch is then unsatisfiable
% 23.32/6.18 |-Branch two:
% 23.32/6.18 | (48) ~ (all_1_1_1 = 0)
% 23.32/6.18 | (697) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_20_2_14) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_20_2_14) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.18 |
% 23.32/6.18 | Instantiating (697) with all_454_0_221, all_454_1_222, all_454_2_223, all_454_3_224 yields:
% 23.32/6.18 | (698) apart_point_and_line(all_1_3_3, all_20_2_14) = all_454_1_222 & apart_point_and_line(all_1_4_4, all_1_2_2) = all_454_0_221 & distinct_lines(all_1_2_2, all_20_2_14) = all_454_2_223 & distinct_points(all_1_3_3, all_1_4_4) = all_454_3_224 & ( ~ (all_454_2_223 = 0) | ~ (all_454_3_224 = 0) | all_454_0_221 = 0 | all_454_1_222 = 0)
% 23.32/6.18 |
% 23.32/6.18 | Applying alpha-rule on (698) yields:
% 23.32/6.18 | (699) ~ (all_454_2_223 = 0) | ~ (all_454_3_224 = 0) | all_454_0_221 = 0 | all_454_1_222 = 0
% 23.32/6.18 | (700) distinct_lines(all_1_2_2, all_20_2_14) = all_454_2_223
% 23.32/6.18 | (701) distinct_points(all_1_3_3, all_1_4_4) = all_454_3_224
% 23.32/6.18 | (702) apart_point_and_line(all_1_3_3, all_20_2_14) = all_454_1_222
% 23.32/6.18 | (703) apart_point_and_line(all_1_4_4, all_1_2_2) = all_454_0_221
% 23.32/6.18 |
% 23.32/6.18 +-Applying beta-rule and splitting (681), into two cases.
% 23.32/6.18 |-Branch one:
% 23.32/6.18 | (416) all_24_1_19 = 0
% 23.32/6.18 |
% 23.32/6.18 | Equations (416) can reduce 228 to:
% 23.32/6.18 | (129) $false
% 23.32/6.18 |
% 23.32/6.18 |-The branch is then unsatisfiable
% 23.32/6.18 |-Branch two:
% 23.32/6.18 | (228) ~ (all_24_1_19 = 0)
% 23.32/6.18 | (707) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_28_2_26) = v2 & apart_point_and_line(all_1_5_5, all_20_2_14) = v3 & distinct_lines(all_20_2_14, all_28_2_26) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.19 |
% 23.32/6.19 | Instantiating (707) with all_463_0_225, all_463_1_226, all_463_2_227, all_463_3_228 yields:
% 23.32/6.19 | (708) apart_point_and_line(all_1_4_4, all_28_2_26) = all_463_1_226 & apart_point_and_line(all_1_5_5, all_20_2_14) = all_463_0_225 & distinct_lines(all_20_2_14, all_28_2_26) = all_463_2_227 & distinct_points(all_1_4_4, all_1_5_5) = all_463_3_228 & ( ~ (all_463_2_227 = 0) | ~ (all_463_3_228 = 0) | all_463_0_225 = 0 | all_463_1_226 = 0)
% 23.32/6.19 |
% 23.32/6.19 | Applying alpha-rule on (708) yields:
% 23.32/6.19 | (709) distinct_lines(all_20_2_14, all_28_2_26) = all_463_2_227
% 23.32/6.19 | (710) ~ (all_463_2_227 = 0) | ~ (all_463_3_228 = 0) | all_463_0_225 = 0 | all_463_1_226 = 0
% 23.32/6.19 | (711) distinct_points(all_1_4_4, all_1_5_5) = all_463_3_228
% 23.32/6.19 | (712) apart_point_and_line(all_1_5_5, all_20_2_14) = all_463_0_225
% 23.32/6.19 | (713) apart_point_and_line(all_1_4_4, all_28_2_26) = all_463_1_226
% 23.32/6.19 |
% 23.32/6.19 +-Applying beta-rule and splitting (685), into two cases.
% 23.32/6.19 |-Branch one:
% 23.32/6.19 | (416) all_24_1_19 = 0
% 23.32/6.19 |
% 23.32/6.19 | Equations (416) can reduce 228 to:
% 23.32/6.19 | (129) $false
% 23.32/6.19 |
% 23.32/6.19 |-The branch is then unsatisfiable
% 23.32/6.19 |-Branch two:
% 23.32/6.19 | (228) ~ (all_24_1_19 = 0)
% 23.32/6.19 | (717) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_28_2_26) = v3 & apart_point_and_line(all_1_5_5, all_20_2_14) = v2 & distinct_lines(all_28_2_26, all_20_2_14) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.19 |
% 23.32/6.19 | Instantiating (717) with all_468_0_229, all_468_1_230, all_468_2_231, all_468_3_232 yields:
% 23.32/6.19 | (718) apart_point_and_line(all_1_4_4, all_28_2_26) = all_468_0_229 & apart_point_and_line(all_1_5_5, all_20_2_14) = all_468_1_230 & distinct_lines(all_28_2_26, all_20_2_14) = all_468_2_231 & distinct_points(all_1_5_5, all_1_4_4) = all_468_3_232 & ( ~ (all_468_2_231 = 0) | ~ (all_468_3_232 = 0) | all_468_0_229 = 0 | all_468_1_230 = 0)
% 23.32/6.19 |
% 23.32/6.19 | Applying alpha-rule on (718) yields:
% 23.32/6.19 | (719) apart_point_and_line(all_1_5_5, all_20_2_14) = all_468_1_230
% 23.32/6.19 | (720) apart_point_and_line(all_1_4_4, all_28_2_26) = all_468_0_229
% 23.32/6.19 | (721) distinct_lines(all_28_2_26, all_20_2_14) = all_468_2_231
% 23.32/6.19 | (722) distinct_points(all_1_5_5, all_1_4_4) = all_468_3_232
% 23.32/6.19 | (723) ~ (all_468_2_231 = 0) | ~ (all_468_3_232 = 0) | all_468_0_229 = 0 | all_468_1_230 = 0
% 23.32/6.19 |
% 23.32/6.19 +-Applying beta-rule and splitting (693), into two cases.
% 23.32/6.19 |-Branch one:
% 23.32/6.19 | (499) all_22_1_16 = 0
% 23.32/6.19 |
% 23.32/6.19 | Equations (499) can reduce 398 to:
% 23.32/6.19 | (129) $false
% 23.32/6.19 |
% 23.32/6.19 |-The branch is then unsatisfiable
% 23.32/6.19 |-Branch two:
% 23.32/6.19 | (398) ~ (all_22_1_16 = 0)
% 23.32/6.19 | (727) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_28_2_26) = v3 & apart_point_and_line(all_1_5_5, all_1_0_0) = v2 & distinct_lines(all_28_2_26, all_1_0_0) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.32/6.19 |
% 23.32/6.19 | Instantiating (727) with all_473_0_233, all_473_1_234, all_473_2_235, all_473_3_236 yields:
% 23.32/6.19 | (728) apart_point_and_line(all_1_4_4, all_28_2_26) = all_473_0_233 & apart_point_and_line(all_1_5_5, all_1_0_0) = all_473_1_234 & distinct_lines(all_28_2_26, all_1_0_0) = all_473_2_235 & distinct_points(all_1_5_5, all_1_4_4) = all_473_3_236 & ( ~ (all_473_2_235 = 0) | ~ (all_473_3_236 = 0) | all_473_0_233 = 0 | all_473_1_234 = 0)
% 23.32/6.19 |
% 23.32/6.19 | Applying alpha-rule on (728) yields:
% 23.32/6.19 | (729) ~ (all_473_2_235 = 0) | ~ (all_473_3_236 = 0) | all_473_0_233 = 0 | all_473_1_234 = 0
% 23.32/6.19 | (730) distinct_points(all_1_5_5, all_1_4_4) = all_473_3_236
% 23.32/6.19 | (731) apart_point_and_line(all_1_4_4, all_28_2_26) = all_473_0_233
% 23.32/6.19 | (732) apart_point_and_line(all_1_5_5, all_1_0_0) = all_473_1_234
% 23.32/6.19 | (733) distinct_lines(all_28_2_26, all_1_0_0) = all_473_2_235
% 23.32/6.19 |
% 23.32/6.19 | Instantiating formula (8) with all_1_3_3, all_1_4_4, all_370_2_188, all_1_0_0 and discharging atoms line_connecting(all_1_3_3, all_1_4_4) = all_370_2_188, line_connecting(all_1_3_3, all_1_4_4) = all_1_0_0, yields:
% 23.32/6.19 | (734) all_370_2_188 = all_1_0_0
% 23.32/6.19 |
% 23.32/6.19 | Instantiating formula (8) with all_1_3_3, all_1_4_4, all_370_2_188, all_378_1_190 and discharging atoms line_connecting(all_1_3_3, all_1_4_4) = all_378_1_190, line_connecting(all_1_3_3, all_1_4_4) = all_370_2_188, yields:
% 23.32/6.19 | (735) all_378_1_190 = all_370_2_188
% 23.32/6.19 |
% 23.32/6.19 | Instantiating formula (8) with all_1_3_3, all_1_4_4, all_365_2_185, all_378_1_190 and discharging atoms line_connecting(all_1_3_3, all_1_4_4) = all_378_1_190, line_connecting(all_1_3_3, all_1_4_4) = all_365_2_185, yields:
% 23.32/6.19 | (736) all_378_1_190 = all_365_2_185
% 23.32/6.19 |
% 23.32/6.19 | Instantiating formula (8) with all_1_3_3, all_1_4_4, all_252_2_156, all_370_2_188 and discharging atoms line_connecting(all_1_3_3, all_1_4_4) = all_370_2_188, line_connecting(all_1_3_3, all_1_4_4) = all_252_2_156, yields:
% 23.32/6.19 | (737) all_370_2_188 = all_252_2_156
% 23.32/6.19 |
% 23.32/6.19 | Instantiating formula (8) with all_1_4_4, all_1_3_3, all_146_2_126, all_20_2_14 and discharging atoms line_connecting(all_1_4_4, all_1_3_3) = all_146_2_126, line_connecting(all_1_4_4, all_1_3_3) = all_20_2_14, yields:
% 23.77/6.19 | (738) all_146_2_126 = all_20_2_14
% 23.77/6.19 |
% 23.77/6.19 | Instantiating formula (8) with all_1_4_4, all_1_3_3, all_112_2_75, all_146_2_126 and discharging atoms line_connecting(all_1_4_4, all_1_3_3) = all_146_2_126, line_connecting(all_1_4_4, all_1_3_3) = all_112_2_75, yields:
% 23.77/6.19 | (739) all_146_2_126 = all_112_2_75
% 23.77/6.19 |
% 23.77/6.19 | Instantiating formula (20) with all_1_3_3, all_20_2_14, all_411_0_211, all_454_1_222 and discharging atoms apart_point_and_line(all_1_3_3, all_20_2_14) = all_454_1_222, apart_point_and_line(all_1_3_3, all_20_2_14) = all_411_0_211, yields:
% 23.77/6.19 | (740) all_454_1_222 = all_411_0_211
% 23.77/6.19 |
% 23.77/6.19 | Instantiating formula (20) with all_1_3_3, all_20_2_14, all_356_0_180, all_146_1_125 and discharging atoms apart_point_and_line(all_1_3_3, all_20_2_14) = all_356_0_180, yields:
% 23.77/6.19 | (741) all_356_0_180 = all_146_1_125 | ~ (apart_point_and_line(all_1_3_3, all_20_2_14) = all_146_1_125)
% 23.77/6.19 |
% 23.77/6.19 | Instantiating formula (20) with all_1_3_3, all_20_2_14, all_356_0_180, all_112_1_74 and discharging atoms apart_point_and_line(all_1_3_3, all_20_2_14) = all_356_0_180, yields:
% 23.77/6.19 | (742) all_356_0_180 = all_112_1_74 | ~ (apart_point_and_line(all_1_3_3, all_20_2_14) = all_112_1_74)
% 23.77/6.19 |
% 23.77/6.19 | Instantiating formula (20) with all_1_3_3, all_20_2_14, all_356_0_180, all_411_1_212 and discharging atoms apart_point_and_line(all_1_3_3, all_20_2_14) = all_411_1_212, apart_point_and_line(all_1_3_3, all_20_2_14) = all_356_0_180, yields:
% 23.77/6.19 | (743) all_411_1_212 = all_356_0_180
% 23.77/6.19 |
% 23.77/6.19 | Instantiating formula (20) with all_1_3_3, all_20_2_14, all_342_1_174, all_411_0_211 and discharging atoms apart_point_and_line(all_1_3_3, all_20_2_14) = all_411_0_211, apart_point_and_line(all_1_3_3, all_20_2_14) = all_342_1_174, yields:
% 23.77/6.19 | (744) all_411_0_211 = all_342_1_174
% 23.77/6.19 |
% 23.77/6.19 | Instantiating formula (20) with all_1_3_3, all_20_2_14, all_342_1_174, all_356_0_180 and discharging atoms apart_point_and_line(all_1_3_3, all_20_2_14) = all_356_0_180, apart_point_and_line(all_1_3_3, all_20_2_14) = all_342_1_174, yields:
% 23.77/6.19 | (745) all_356_0_180 = all_342_1_174
% 23.77/6.19 |
% 23.77/6.19 | Instantiating formula (20) with all_1_3_3, all_20_2_14, all_236_0_142, all_454_1_222 and discharging atoms apart_point_and_line(all_1_3_3, all_20_2_14) = all_454_1_222, apart_point_and_line(all_1_3_3, all_20_2_14) = all_236_0_142, yields:
% 23.77/6.19 | (746) all_454_1_222 = all_236_0_142
% 23.77/6.19 |
% 23.77/6.19 | Instantiating formula (20) with all_1_3_3, all_20_2_14, all_104_1_62, all_411_1_212 and discharging atoms apart_point_and_line(all_1_3_3, all_20_2_14) = all_411_1_212, apart_point_and_line(all_1_3_3, all_20_2_14) = all_104_1_62, yields:
% 23.77/6.19 | (747) all_411_1_212 = all_104_1_62
% 23.77/6.19 |
% 23.77/6.19 | Instantiating formula (20) with all_1_3_3, all_1_0_0, all_356_1_181, all_252_1_155 and discharging atoms apart_point_and_line(all_1_3_3, all_1_0_0) = all_356_1_181, yields:
% 23.78/6.19 | (748) all_356_1_181 = all_252_1_155 | ~ (apart_point_and_line(all_1_3_3, all_1_0_0) = all_252_1_155)
% 23.78/6.19 |
% 23.78/6.19 | Instantiating formula (20) with all_1_3_3, all_1_0_0, all_325_0_166, all_356_1_181 and discharging atoms apart_point_and_line(all_1_3_3, all_1_0_0) = all_356_1_181, apart_point_and_line(all_1_3_3, all_1_0_0) = all_325_0_166, yields:
% 23.78/6.19 | (749) all_356_1_181 = all_325_0_166
% 23.78/6.19 |
% 23.78/6.19 | Instantiating formula (20) with all_1_3_3, all_1_0_0, all_325_1_167, all_356_1_181 and discharging atoms apart_point_and_line(all_1_3_3, all_1_0_0) = all_356_1_181, apart_point_and_line(all_1_3_3, all_1_0_0) = all_325_1_167, yields:
% 23.78/6.19 | (750) all_356_1_181 = all_325_1_167
% 23.78/6.19 |
% 23.78/6.19 | Instantiating formula (20) with all_1_3_3, all_1_0_0, all_325_1_167, all_342_0_173 and discharging atoms apart_point_and_line(all_1_3_3, all_1_0_0) = all_342_0_173, apart_point_and_line(all_1_3_3, all_1_0_0) = all_325_1_167, yields:
% 23.78/6.19 | (751) all_342_0_173 = all_325_1_167
% 23.78/6.19 |
% 23.78/6.19 | Instantiating formula (20) with all_1_3_3, all_1_0_0, all_302_0_163, all_325_1_167 and discharging atoms apart_point_and_line(all_1_3_3, all_1_0_0) = all_325_1_167, apart_point_and_line(all_1_3_3, all_1_0_0) = all_302_0_163, yields:
% 23.78/6.19 | (752) all_325_1_167 = all_302_0_163
% 23.78/6.19 |
% 23.78/6.19 | Instantiating formula (20) with all_1_3_3, all_1_0_0, all_302_1_164, all_342_0_173 and discharging atoms apart_point_and_line(all_1_3_3, all_1_0_0) = all_342_0_173, apart_point_and_line(all_1_3_3, all_1_0_0) = all_302_1_164, yields:
% 23.78/6.20 | (753) all_342_0_173 = all_302_1_164
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (20) with all_1_3_3, all_1_0_0, all_124_1_92, all_356_1_181 and discharging atoms apart_point_and_line(all_1_3_3, all_1_0_0) = all_356_1_181, apart_point_and_line(all_1_3_3, all_1_0_0) = all_124_1_92, yields:
% 23.78/6.20 | (754) all_356_1_181 = all_124_1_92
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (20) with all_1_3_3, all_1_0_0, all_106_1_65, all_342_0_173 and discharging atoms apart_point_and_line(all_1_3_3, all_1_0_0) = all_342_0_173, apart_point_and_line(all_1_3_3, all_1_0_0) = all_106_1_65, yields:
% 23.78/6.20 | (755) all_342_0_173 = all_106_1_65
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (20) with all_1_4_4, all_1_2_2, all_333_1_170, all_454_0_221 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_454_0_221, apart_point_and_line(all_1_4_4, all_1_2_2) = all_333_1_170, yields:
% 23.78/6.20 | (756) all_454_0_221 = all_333_1_170
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (20) with all_1_4_4, all_1_2_2, all_236_1_143, all_454_0_221 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_454_0_221, apart_point_and_line(all_1_4_4, all_1_2_2) = all_236_1_143, yields:
% 23.78/6.20 | (757) all_454_0_221 = all_236_1_143
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (20) with all_1_4_4, all_1_2_2, all_142_1_119, all_54_1_50 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_142_1_119, apart_point_and_line(all_1_4_4, all_1_2_2) = all_54_1_50, yields:
% 23.78/6.20 | (758) all_142_1_119 = all_54_1_50
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (20) with all_1_4_4, all_1_2_2, all_142_1_119, all_333_1_170 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_333_1_170, apart_point_and_line(all_1_4_4, all_1_2_2) = all_142_1_119, yields:
% 23.78/6.20 | (759) all_333_1_170 = all_142_1_119
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (20) with all_1_4_4, all_1_2_2, all_100_1_56, all_333_1_170 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_333_1_170, apart_point_and_line(all_1_4_4, all_1_2_2) = all_100_1_56, yields:
% 23.78/6.20 | (760) all_333_1_170 = all_100_1_56
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (20) with all_1_5_5, all_20_2_14, all_463_0_225, all_20_1_13 and discharging atoms apart_point_and_line(all_1_5_5, all_20_2_14) = all_463_0_225, apart_point_and_line(all_1_5_5, all_20_2_14) = all_20_1_13, yields:
% 23.78/6.20 | (761) all_463_0_225 = all_20_1_13
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (20) with all_1_5_5, all_20_2_14, all_463_0_225, all_468_1_230 and discharging atoms apart_point_and_line(all_1_5_5, all_20_2_14) = all_468_1_230, apart_point_and_line(all_1_5_5, all_20_2_14) = all_463_0_225, yields:
% 23.78/6.20 | (762) all_468_1_230 = all_463_0_225
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (20) with all_1_5_5, all_20_2_14, all_416_0_214, all_468_1_230 and discharging atoms apart_point_and_line(all_1_5_5, all_20_2_14) = all_468_1_230, apart_point_and_line(all_1_5_5, all_20_2_14) = all_416_0_214, yields:
% 23.78/6.20 | (763) all_468_1_230 = all_416_0_214
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (20) with all_1_5_5, all_20_2_14, all_416_1_215, all_463_0_225 and discharging atoms apart_point_and_line(all_1_5_5, all_20_2_14) = all_463_0_225, apart_point_and_line(all_1_5_5, all_20_2_14) = all_416_1_215, yields:
% 23.78/6.20 | (764) all_463_0_225 = all_416_1_215
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (20) with all_1_5_5, all_1_2_2, all_246_1_151, all_16_1_7 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_246_1_151, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 23.78/6.20 | (765) all_246_1_151 = all_16_1_7
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (20) with all_1_5_5, all_1_2_2, all_241_0_146, all_246_1_151 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_246_1_151, apart_point_and_line(all_1_5_5, all_1_2_2) = all_241_0_146, yields:
% 23.78/6.20 | (766) all_246_1_151 = all_241_0_146
% 23.78/6.20 |
% 23.78/6.20 | Using (467) and (226) yields:
% 23.78/6.20 | (767) ~ (all_241_0_146 = 0)
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (5) with all_1_0_0, all_20_2_14, all_351_2_178, 0 and discharging atoms distinct_lines(all_1_0_0, all_20_2_14) = all_351_2_178, yields:
% 23.78/6.20 | (768) all_351_2_178 = 0 | ~ (distinct_lines(all_1_0_0, all_20_2_14) = 0)
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (5) with all_1_0_0, all_20_2_14, all_351_2_178, all_356_2_182 and discharging atoms distinct_lines(all_1_0_0, all_20_2_14) = all_356_2_182, distinct_lines(all_1_0_0, all_20_2_14) = all_351_2_178, yields:
% 23.78/6.20 | (769) all_356_2_182 = all_351_2_178
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (46) with all_1_4_4, all_1_3_3, all_370_0_186, 0 and discharging atoms distinct_points(all_1_4_4, all_1_3_3) = all_370_0_186, distinct_points(all_1_4_4, all_1_3_3) = 0, yields:
% 23.78/6.20 | (770) all_370_0_186 = 0
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (46) with all_1_4_4, all_1_3_3, all_144_0_121, all_370_0_186 and discharging atoms distinct_points(all_1_4_4, all_1_3_3) = all_370_0_186, distinct_points(all_1_4_4, all_1_3_3) = all_144_0_121, yields:
% 23.78/6.20 | (771) all_370_0_186 = all_144_0_121
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (46) with all_1_4_4, all_1_3_3, all_144_0_121, all_236_3_145 and discharging atoms distinct_points(all_1_4_4, all_1_3_3) = all_236_3_145, distinct_points(all_1_4_4, all_1_3_3) = all_144_0_121, yields:
% 23.78/6.20 | (772) all_236_3_145 = all_144_0_121
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (46) with all_1_4_4, all_1_3_3, all_140_0_115, all_144_0_121 and discharging atoms distinct_points(all_1_4_4, all_1_3_3) = all_144_0_121, distinct_points(all_1_4_4, all_1_3_3) = all_140_0_115, yields:
% 23.78/6.20 | (773) all_144_0_121 = all_140_0_115
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (46) with all_1_4_4, all_1_3_3, all_122_2_90, all_370_0_186 and discharging atoms distinct_points(all_1_4_4, all_1_3_3) = all_370_0_186, distinct_points(all_1_4_4, all_1_3_3) = all_122_2_90, yields:
% 23.78/6.20 | (774) all_370_0_186 = all_122_2_90
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (46) with all_1_4_4, all_1_3_3, all_104_2_63, all_236_3_145 and discharging atoms distinct_points(all_1_4_4, all_1_3_3) = all_236_3_145, distinct_points(all_1_4_4, all_1_3_3) = all_104_2_63, yields:
% 23.78/6.20 | (775) all_236_3_145 = all_104_2_63
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (46) with all_1_4_4, all_1_3_3, all_102_0_58, all_370_0_186 and discharging atoms distinct_points(all_1_4_4, all_1_3_3) = all_370_0_186, distinct_points(all_1_4_4, all_1_3_3) = all_102_0_58, yields:
% 23.78/6.20 | (776) all_370_0_186 = all_102_0_58
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (46) with all_1_4_4, all_1_4_4, all_406_3_210, all_22_0_15 and discharging atoms distinct_points(all_1_4_4, all_1_4_4) = all_406_3_210, distinct_points(all_1_4_4, all_1_4_4) = all_22_0_15, yields:
% 23.78/6.20 | (777) all_406_3_210 = all_22_0_15
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (46) with all_1_4_4, all_1_4_4, all_365_0_183, all_406_3_210 and discharging atoms distinct_points(all_1_4_4, all_1_4_4) = all_406_3_210, distinct_points(all_1_4_4, all_1_4_4) = all_365_0_183, yields:
% 23.78/6.20 | (778) all_406_3_210 = all_365_0_183
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (46) with all_1_4_4, all_1_4_4, all_351_3_179, all_406_3_210 and discharging atoms distinct_points(all_1_4_4, all_1_4_4) = all_406_3_210, distinct_points(all_1_4_4, all_1_4_4) = all_351_3_179, yields:
% 23.78/6.20 | (779) all_406_3_210 = all_351_3_179
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (46) with all_1_4_4, all_1_4_4, all_194_2_141, all_406_3_210 and discharging atoms distinct_points(all_1_4_4, all_1_4_4) = all_406_3_210, distinct_points(all_1_4_4, all_1_4_4) = all_194_2_141, yields:
% 23.78/6.20 | (780) all_406_3_210 = all_194_2_141
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (46) with all_1_4_4, all_1_4_4, all_142_0_118, all_194_2_141 and discharging atoms distinct_points(all_1_4_4, all_1_4_4) = all_194_2_141, distinct_points(all_1_4_4, all_1_4_4) = all_142_0_118, yields:
% 23.78/6.20 | (781) all_194_2_141 = all_142_0_118
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (46) with all_1_4_4, all_1_4_4, all_98_0_52, all_142_0_118 and discharging atoms distinct_points(all_1_4_4, all_1_4_4) = all_142_0_118, distinct_points(all_1_4_4, all_1_4_4) = all_98_0_52, yields:
% 23.78/6.20 | (782) all_142_0_118 = all_98_0_52
% 23.78/6.20 |
% 23.78/6.20 | Using (305) and (56) yields:
% 23.78/6.20 | (783) ~ (all_98_0_52 = 0)
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (46) with all_1_5_5, all_1_4_4, all_468_3_232, 0 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = all_468_3_232, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 23.78/6.20 | (784) all_468_3_232 = 0
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (46) with all_1_5_5, all_1_4_4, all_468_3_232, all_473_3_236 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = all_473_3_236, distinct_points(all_1_5_5, all_1_4_4) = all_468_3_232, yields:
% 23.78/6.20 | (785) all_473_3_236 = all_468_3_232
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (46) with all_1_5_5, all_1_4_4, all_420_2_219, all_468_3_232 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = all_468_3_232, distinct_points(all_1_5_5, all_1_4_4) = all_420_2_219, yields:
% 23.78/6.20 | (786) all_468_3_232 = all_420_2_219
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (46) with all_1_5_5, all_1_4_4, all_155_0_127, all_473_3_236 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = all_473_3_236, distinct_points(all_1_5_5, all_1_4_4) = all_155_0_127, yields:
% 23.78/6.20 | (787) all_473_3_236 = all_155_0_127
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (46) with all_1_5_5, all_1_4_4, all_142_2_120, all_468_3_232 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = all_468_3_232, distinct_points(all_1_5_5, all_1_4_4) = all_142_2_120, yields:
% 23.78/6.20 | (788) all_468_3_232 = all_142_2_120
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (46) with all_1_5_5, all_1_4_4, all_138_2_114, all_468_3_232 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = all_468_3_232, distinct_points(all_1_5_5, all_1_4_4) = all_138_2_114, yields:
% 23.78/6.20 | (789) all_468_3_232 = all_138_2_114
% 23.78/6.20 |
% 23.78/6.20 | Instantiating formula (46) with all_1_5_5, all_1_4_4, all_100_2_57, all_138_2_114 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = all_138_2_114, distinct_points(all_1_5_5, all_1_4_4) = all_100_2_57, yields:
% 23.78/6.20 | (790) all_138_2_114 = all_100_2_57
% 23.78/6.20 |
% 23.78/6.20 | Combining equations (785,787) yields a new equation:
% 23.78/6.20 | (791) all_468_3_232 = all_155_0_127
% 23.78/6.20 |
% 23.78/6.20 | Simplifying 791 yields:
% 23.78/6.20 | (792) all_468_3_232 = all_155_0_127
% 23.78/6.20 |
% 23.78/6.20 | Combining equations (762,763) yields a new equation:
% 23.78/6.20 | (793) all_463_0_225 = all_416_0_214
% 23.78/6.20 |
% 23.78/6.20 | Simplifying 793 yields:
% 23.78/6.20 | (794) all_463_0_225 = all_416_0_214
% 23.78/6.20 |
% 23.78/6.20 | Combining equations (788,786) yields a new equation:
% 23.78/6.20 | (795) all_420_2_219 = all_142_2_120
% 23.78/6.20 |
% 23.78/6.20 | Combining equations (792,786) yields a new equation:
% 23.78/6.20 | (796) all_420_2_219 = all_155_0_127
% 23.78/6.20 |
% 23.78/6.20 | Combining equations (789,786) yields a new equation:
% 23.78/6.20 | (797) all_420_2_219 = all_138_2_114
% 23.78/6.20 |
% 23.78/6.20 | Combining equations (784,786) yields a new equation:
% 23.78/6.20 | (798) all_420_2_219 = 0
% 23.78/6.20 |
% 23.78/6.20 | Combining equations (761,794) yields a new equation:
% 23.78/6.20 | (799) all_416_0_214 = all_20_1_13
% 23.78/6.20 |
% 23.78/6.20 | Combining equations (764,794) yields a new equation:
% 23.78/6.20 | (800) all_416_0_214 = all_416_1_215
% 23.78/6.20 |
% 23.78/6.20 | Combining equations (756,757) yields a new equation:
% 23.78/6.20 | (801) all_333_1_170 = all_236_1_143
% 23.78/6.20 |
% 23.78/6.20 | Simplifying 801 yields:
% 23.78/6.20 | (802) all_333_1_170 = all_236_1_143
% 23.78/6.20 |
% 23.78/6.20 | Combining equations (740,746) yields a new equation:
% 23.78/6.20 | (803) all_411_0_211 = all_236_0_142
% 23.78/6.20 |
% 23.78/6.20 | Simplifying 803 yields:
% 23.78/6.20 | (804) all_411_0_211 = all_236_0_142
% 23.78/6.20 |
% 23.78/6.20 | Combining equations (798,796) yields a new equation:
% 23.78/6.20 | (805) all_155_0_127 = 0
% 23.78/6.20 |
% 23.78/6.20 | Combining equations (797,796) yields a new equation:
% 23.78/6.20 | (806) all_155_0_127 = all_138_2_114
% 23.78/6.20 |
% 23.78/6.20 | Combining equations (795,796) yields a new equation:
% 23.78/6.20 | (807) all_155_0_127 = all_142_2_120
% 23.78/6.20 |
% 23.78/6.20 | Combining equations (800,799) yields a new equation:
% 23.78/6.20 | (808) all_416_1_215 = all_20_1_13
% 23.78/6.20 |
% 23.78/6.20 | Simplifying 808 yields:
% 23.78/6.20 | (809) all_416_1_215 = all_20_1_13
% 23.78/6.20 |
% 23.78/6.20 | Combining equations (744,804) yields a new equation:
% 23.78/6.20 | (810) all_342_1_174 = all_236_0_142
% 23.78/6.20 |
% 23.78/6.20 | Simplifying 810 yields:
% 23.78/6.20 | (811) all_342_1_174 = all_236_0_142
% 23.78/6.20 |
% 23.78/6.20 | Combining equations (743,747) yields a new equation:
% 23.78/6.20 | (812) all_356_0_180 = all_104_1_62
% 23.78/6.20 |
% 23.78/6.20 | Simplifying 812 yields:
% 23.78/6.20 | (813) all_356_0_180 = all_104_1_62
% 23.78/6.20 |
% 23.78/6.20 | Combining equations (779,778) yields a new equation:
% 23.78/6.20 | (814) all_365_0_183 = all_351_3_179
% 23.78/6.20 |
% 23.78/6.20 | Combining equations (780,778) yields a new equation:
% 23.78/6.20 | (815) all_365_0_183 = all_194_2_141
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (777,778) yields a new equation:
% 23.78/6.21 | (816) all_365_0_183 = all_22_0_15
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (735,736) yields a new equation:
% 23.78/6.21 | (817) all_370_2_188 = all_365_2_185
% 23.78/6.21 |
% 23.78/6.21 | Simplifying 817 yields:
% 23.78/6.21 | (818) all_370_2_188 = all_365_2_185
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (771,774) yields a new equation:
% 23.78/6.21 | (819) all_144_0_121 = all_122_2_90
% 23.78/6.21 |
% 23.78/6.21 | Simplifying 819 yields:
% 23.78/6.21 | (820) all_144_0_121 = all_122_2_90
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (770,774) yields a new equation:
% 23.78/6.21 | (821) all_122_2_90 = 0
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (776,774) yields a new equation:
% 23.78/6.21 | (822) all_122_2_90 = all_102_0_58
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (734,818) yields a new equation:
% 23.78/6.21 | (823) all_365_2_185 = all_1_0_0
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (737,818) yields a new equation:
% 23.78/6.21 | (824) all_365_2_185 = all_252_2_156
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (816,814) yields a new equation:
% 23.78/6.21 | (825) all_351_3_179 = all_22_0_15
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (815,814) yields a new equation:
% 23.78/6.21 | (826) all_351_3_179 = all_194_2_141
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (823,824) yields a new equation:
% 23.78/6.21 | (827) all_252_2_156 = all_1_0_0
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (745,813) yields a new equation:
% 23.78/6.21 | (828) all_342_1_174 = all_104_1_62
% 23.78/6.21 |
% 23.78/6.21 | Simplifying 828 yields:
% 23.78/6.21 | (829) all_342_1_174 = all_104_1_62
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (750,749) yields a new equation:
% 23.78/6.21 | (830) all_325_0_166 = all_325_1_167
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (754,749) yields a new equation:
% 23.78/6.21 | (831) all_325_0_166 = all_124_1_92
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (826,825) yields a new equation:
% 23.78/6.21 | (832) all_194_2_141 = all_22_0_15
% 23.78/6.21 |
% 23.78/6.21 | Simplifying 832 yields:
% 23.78/6.21 | (833) all_194_2_141 = all_22_0_15
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (751,753) yields a new equation:
% 23.78/6.21 | (834) all_325_1_167 = all_302_1_164
% 23.78/6.21 |
% 23.78/6.21 | Simplifying 834 yields:
% 23.78/6.21 | (835) all_325_1_167 = all_302_1_164
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (755,753) yields a new equation:
% 23.78/6.21 | (836) all_302_1_164 = all_106_1_65
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (811,829) yields a new equation:
% 23.78/6.21 | (837) all_236_0_142 = all_104_1_62
% 23.78/6.21 |
% 23.78/6.21 | Simplifying 837 yields:
% 23.78/6.21 | (838) all_236_0_142 = all_104_1_62
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (760,802) yields a new equation:
% 23.78/6.21 | (839) all_236_1_143 = all_100_1_56
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (759,802) yields a new equation:
% 23.78/6.21 | (840) all_236_1_143 = all_142_1_119
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (830,831) yields a new equation:
% 23.78/6.21 | (841) all_325_1_167 = all_124_1_92
% 23.78/6.21 |
% 23.78/6.21 | Simplifying 841 yields:
% 23.78/6.21 | (842) all_325_1_167 = all_124_1_92
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (842,752) yields a new equation:
% 23.78/6.21 | (843) all_302_0_163 = all_124_1_92
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (835,752) yields a new equation:
% 23.78/6.21 | (844) all_302_0_163 = all_302_1_164
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (844,843) yields a new equation:
% 23.78/6.21 | (845) all_302_1_164 = all_124_1_92
% 23.78/6.21 |
% 23.78/6.21 | Simplifying 845 yields:
% 23.78/6.21 | (846) all_302_1_164 = all_124_1_92
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (836,846) yields a new equation:
% 23.78/6.21 | (847) all_124_1_92 = all_106_1_65
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (766,765) yields a new equation:
% 23.78/6.21 | (848) all_241_0_146 = all_16_1_7
% 23.78/6.21 |
% 23.78/6.21 | Simplifying 848 yields:
% 23.78/6.21 | (849) all_241_0_146 = all_16_1_7
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (840,839) yields a new equation:
% 23.78/6.21 | (850) all_142_1_119 = all_100_1_56
% 23.78/6.21 |
% 23.78/6.21 | Simplifying 850 yields:
% 23.78/6.21 | (851) all_142_1_119 = all_100_1_56
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (772,775) yields a new equation:
% 23.78/6.21 | (852) all_144_0_121 = all_104_2_63
% 23.78/6.21 |
% 23.78/6.21 | Simplifying 852 yields:
% 23.78/6.21 | (853) all_144_0_121 = all_104_2_63
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (781,833) yields a new equation:
% 23.78/6.21 | (854) all_142_0_118 = all_22_0_15
% 23.78/6.21 |
% 23.78/6.21 | Simplifying 854 yields:
% 23.78/6.21 | (855) all_142_0_118 = all_22_0_15
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (805,807) yields a new equation:
% 23.78/6.21 | (856) all_142_2_120 = 0
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (806,807) yields a new equation:
% 23.78/6.21 | (857) all_142_2_120 = all_138_2_114
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (738,739) yields a new equation:
% 23.78/6.21 | (858) all_112_2_75 = all_20_2_14
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (820,773) yields a new equation:
% 23.78/6.21 | (859) all_140_0_115 = all_122_2_90
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (853,773) yields a new equation:
% 23.78/6.21 | (860) all_140_0_115 = all_104_2_63
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (782,855) yields a new equation:
% 23.78/6.21 | (861) all_98_0_52 = all_22_0_15
% 23.78/6.21 |
% 23.78/6.21 | Simplifying 861 yields:
% 23.78/6.21 | (862) all_98_0_52 = all_22_0_15
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (758,851) yields a new equation:
% 23.78/6.21 | (863) all_100_1_56 = all_54_1_50
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (857,856) yields a new equation:
% 23.78/6.21 | (864) all_138_2_114 = 0
% 23.78/6.21 |
% 23.78/6.21 | Simplifying 864 yields:
% 23.78/6.21 | (865) all_138_2_114 = 0
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (859,860) yields a new equation:
% 23.78/6.21 | (866) all_122_2_90 = all_104_2_63
% 23.78/6.21 |
% 23.78/6.21 | Simplifying 866 yields:
% 23.78/6.21 | (867) all_122_2_90 = all_104_2_63
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (790,865) yields a new equation:
% 23.78/6.21 | (868) all_100_2_57 = 0
% 23.78/6.21 |
% 23.78/6.21 | Simplifying 868 yields:
% 23.78/6.21 | (869) all_100_2_57 = 0
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (822,867) yields a new equation:
% 23.78/6.21 | (870) all_104_2_63 = all_102_0_58
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (821,867) yields a new equation:
% 23.78/6.21 | (871) all_104_2_63 = 0
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (871,870) yields a new equation:
% 23.78/6.21 | (872) all_102_0_58 = 0
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (872,870) yields a new equation:
% 23.78/6.21 | (871) all_104_2_63 = 0
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (858,739) yields a new equation:
% 23.78/6.21 | (738) all_146_2_126 = all_20_2_14
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (871,775) yields a new equation:
% 23.78/6.21 | (875) all_236_3_145 = 0
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (863,839) yields a new equation:
% 23.78/6.21 | (876) all_236_1_143 = all_54_1_50
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (847,831) yields a new equation:
% 23.78/6.21 | (877) all_325_0_166 = all_106_1_65
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (877,749) yields a new equation:
% 23.78/6.21 | (878) all_356_1_181 = all_106_1_65
% 23.78/6.21 |
% 23.78/6.21 | Equations (849) can reduce 767 to:
% 23.78/6.21 | (235) ~ (all_16_1_7 = 0)
% 23.78/6.21 |
% 23.78/6.21 | Equations (862) can reduce 783 to:
% 23.78/6.21 | (209) ~ (all_22_0_15 = 0)
% 23.78/6.21 |
% 23.78/6.21 | From (827) and (488) follows:
% 23.78/6.21 | (881) apart_point_and_line(all_1_3_3, all_1_0_0) = all_252_1_155
% 23.78/6.21 |
% 23.78/6.21 | From (738) and (364) follows:
% 23.78/6.21 | (882) apart_point_and_line(all_1_3_3, all_20_2_14) = all_146_1_125
% 23.78/6.21 |
% 23.78/6.21 | From (858) and (329) follows:
% 23.78/6.21 | (883) apart_point_and_line(all_1_3_3, all_20_2_14) = all_112_1_74
% 23.78/6.21 |
% 23.78/6.21 | From (809) and (661) follows:
% 23.78/6.21 | (85) apart_point_and_line(all_1_5_5, all_20_2_14) = all_20_1_13
% 23.78/6.21 |
% 23.78/6.21 +-Applying beta-rule and splitting (748), into two cases.
% 23.78/6.21 |-Branch one:
% 23.78/6.21 | (885) ~ (apart_point_and_line(all_1_3_3, all_1_0_0) = all_252_1_155)
% 23.78/6.21 |
% 23.78/6.21 | Using (881) and (885) yields:
% 23.78/6.21 | (230) $false
% 23.78/6.21 |
% 23.78/6.21 |-The branch is then unsatisfiable
% 23.78/6.21 |-Branch two:
% 23.78/6.21 | (881) apart_point_and_line(all_1_3_3, all_1_0_0) = all_252_1_155
% 23.78/6.21 | (888) all_356_1_181 = all_252_1_155
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (878,888) yields a new equation:
% 23.78/6.21 | (889) all_252_1_155 = all_106_1_65
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (889,888) yields a new equation:
% 23.78/6.21 | (878) all_356_1_181 = all_106_1_65
% 23.78/6.21 |
% 23.78/6.21 | Equations (889) can reduce 515 to:
% 23.78/6.21 | (891) ~ (all_106_1_65 = 0)
% 23.78/6.21 |
% 23.78/6.21 +-Applying beta-rule and splitting (742), into two cases.
% 23.78/6.21 |-Branch one:
% 23.78/6.21 | (892) ~ (apart_point_and_line(all_1_3_3, all_20_2_14) = all_112_1_74)
% 23.78/6.21 |
% 23.78/6.21 | Using (883) and (892) yields:
% 23.78/6.21 | (230) $false
% 23.78/6.21 |
% 23.78/6.21 |-The branch is then unsatisfiable
% 23.78/6.21 |-Branch two:
% 23.78/6.21 | (883) apart_point_and_line(all_1_3_3, all_20_2_14) = all_112_1_74
% 23.78/6.21 | (895) all_356_0_180 = all_112_1_74
% 23.78/6.21 |
% 23.78/6.21 | Combining equations (813,895) yields a new equation:
% 23.78/6.21 | (896) all_112_1_74 = all_104_1_62
% 23.78/6.21 |
% 23.78/6.22 | Combining equations (896,895) yields a new equation:
% 23.87/6.22 | (813) all_356_0_180 = all_104_1_62
% 23.87/6.22 |
% 23.87/6.22 | Equations (896) can reduce 604 to:
% 23.87/6.22 | (898) ~ (all_104_1_62 = 0)
% 23.87/6.22 |
% 23.87/6.22 +-Applying beta-rule and splitting (311), into two cases.
% 23.87/6.22 |-Branch one:
% 23.87/6.22 | (899) ~ (all_100_1_56 = 0)
% 23.87/6.22 |
% 23.87/6.22 | Equations (863) can reduce 899 to:
% 23.87/6.22 | (900) ~ (all_54_1_50 = 0)
% 23.87/6.22 |
% 23.87/6.22 +-Applying beta-rule and splitting (458), into two cases.
% 23.87/6.22 |-Branch one:
% 23.87/6.22 | (901) ~ (all_236_2_144 = 0)
% 23.87/6.22 |
% 23.87/6.22 +-Applying beta-rule and splitting (266), into two cases.
% 23.87/6.22 |-Branch one:
% 23.87/6.22 | (902) ~ (apart_point_and_line(all_1_5_5, all_20_2_14) = 0)
% 23.87/6.22 |
% 23.87/6.22 +-Applying beta-rule and splitting (741), into two cases.
% 23.87/6.22 |-Branch one:
% 23.87/6.22 | (903) ~ (apart_point_and_line(all_1_3_3, all_20_2_14) = all_146_1_125)
% 23.87/6.22 |
% 23.87/6.22 | Using (882) and (903) yields:
% 23.87/6.22 | (230) $false
% 23.87/6.22 |
% 23.87/6.22 |-The branch is then unsatisfiable
% 23.87/6.22 |-Branch two:
% 23.87/6.22 | (882) apart_point_and_line(all_1_3_3, all_20_2_14) = all_146_1_125
% 23.87/6.22 | (906) all_356_0_180 = all_146_1_125
% 23.87/6.22 |
% 23.87/6.22 | Combining equations (813,906) yields a new equation:
% 23.87/6.22 | (907) all_146_1_125 = all_104_1_62
% 23.87/6.22 |
% 23.87/6.22 | Combining equations (907,906) yields a new equation:
% 23.87/6.22 | (813) all_356_0_180 = all_104_1_62
% 23.87/6.22 |
% 23.87/6.22 +-Applying beta-rule and splitting (603), into two cases.
% 23.87/6.22 |-Branch one:
% 23.87/6.22 | (909) ~ (all_356_2_182 = 0)
% 23.87/6.22 |
% 23.87/6.22 | Equations (769) can reduce 909 to:
% 23.87/6.22 | (910) ~ (all_351_2_178 = 0)
% 23.87/6.22 |
% 23.87/6.22 +-Applying beta-rule and splitting (261), into two cases.
% 23.87/6.22 |-Branch one:
% 23.87/6.22 | (911) distinct_lines(all_1_0_0, all_20_2_14) = 0
% 23.87/6.22 |
% 23.87/6.22 +-Applying beta-rule and splitting (768), into two cases.
% 23.87/6.22 |-Branch one:
% 23.87/6.22 | (912) ~ (distinct_lines(all_1_0_0, all_20_2_14) = 0)
% 23.87/6.22 |
% 23.87/6.22 | Using (911) and (912) yields:
% 23.87/6.22 | (230) $false
% 23.87/6.22 |
% 23.87/6.22 |-The branch is then unsatisfiable
% 23.87/6.22 |-Branch two:
% 23.87/6.22 | (911) distinct_lines(all_1_0_0, all_20_2_14) = 0
% 23.87/6.22 | (915) all_351_2_178 = 0
% 23.87/6.22 |
% 23.87/6.22 | Equations (915) can reduce 910 to:
% 23.87/6.22 | (129) $false
% 23.87/6.22 |
% 23.87/6.22 |-The branch is then unsatisfiable
% 23.87/6.22 |-Branch two:
% 23.87/6.22 | (912) ~ (distinct_lines(all_1_0_0, all_20_2_14) = 0)
% 23.87/6.22 | (918) all_20_1_13 = 0
% 23.87/6.22 |
% 23.87/6.22 | From (918) and (85) follows:
% 23.87/6.22 | (919) apart_point_and_line(all_1_5_5, all_20_2_14) = 0
% 23.87/6.22 |
% 23.87/6.22 | Using (919) and (902) yields:
% 23.87/6.22 | (230) $false
% 23.87/6.22 |
% 23.87/6.22 |-The branch is then unsatisfiable
% 23.87/6.22 |-Branch two:
% 23.87/6.22 | (921) all_356_2_182 = 0
% 23.87/6.22 | (922) all_356_0_180 = 0 | all_356_1_181 = 0
% 23.89/6.22 |
% 23.89/6.22 +-Applying beta-rule and splitting (922), into two cases.
% 23.89/6.22 |-Branch one:
% 23.89/6.22 | (923) all_356_0_180 = 0
% 23.89/6.22 |
% 23.89/6.22 | Combining equations (813,923) yields a new equation:
% 23.89/6.22 | (924) all_104_1_62 = 0
% 23.89/6.22 |
% 23.89/6.22 | Simplifying 924 yields:
% 23.89/6.22 | (925) all_104_1_62 = 0
% 23.89/6.22 |
% 23.89/6.22 | Equations (925) can reduce 898 to:
% 23.89/6.22 | (129) $false
% 23.89/6.22 |
% 23.89/6.22 |-The branch is then unsatisfiable
% 23.89/6.22 |-Branch two:
% 23.89/6.22 | (927) ~ (all_356_0_180 = 0)
% 23.89/6.22 | (928) all_356_1_181 = 0
% 23.89/6.22 |
% 23.89/6.22 | Combining equations (878,928) yields a new equation:
% 23.89/6.22 | (929) all_106_1_65 = 0
% 23.89/6.22 |
% 23.89/6.22 | Simplifying 929 yields:
% 23.89/6.22 | (930) all_106_1_65 = 0
% 23.89/6.22 |
% 23.89/6.22 | Equations (930) can reduce 891 to:
% 23.89/6.22 | (129) $false
% 23.89/6.22 |
% 23.89/6.22 |-The branch is then unsatisfiable
% 23.89/6.22 |-Branch two:
% 23.89/6.22 | (919) apart_point_and_line(all_1_5_5, all_20_2_14) = 0
% 23.89/6.22 | (933) all_16_1_7 = 0 | distinct_lines(all_20_2_14, all_1_2_2) = 0
% 23.89/6.22 |
% 23.89/6.22 +-Applying beta-rule and splitting (933), into two cases.
% 23.89/6.22 |-Branch one:
% 23.89/6.22 | (934) distinct_lines(all_20_2_14, all_1_2_2) = 0
% 23.89/6.22 |
% 23.89/6.22 | Instantiating formula (5) with all_20_2_14, all_1_2_2, 0, all_236_2_144 and discharging atoms distinct_lines(all_20_2_14, all_1_2_2) = all_236_2_144, distinct_lines(all_20_2_14, all_1_2_2) = 0, yields:
% 23.89/6.22 | (935) all_236_2_144 = 0
% 23.89/6.22 |
% 23.89/6.22 | Equations (935) can reduce 901 to:
% 23.89/6.22 | (129) $false
% 23.89/6.22 |
% 23.89/6.22 |-The branch is then unsatisfiable
% 23.89/6.22 |-Branch two:
% 23.89/6.22 | (937) ~ (distinct_lines(all_20_2_14, all_1_2_2) = 0)
% 23.89/6.22 | (566) all_16_1_7 = 0
% 23.89/6.22 |
% 23.89/6.22 | Equations (566) can reduce 235 to:
% 23.89/6.22 | (129) $false
% 23.89/6.22 |
% 23.89/6.22 |-The branch is then unsatisfiable
% 23.89/6.22 |-Branch two:
% 23.89/6.22 | (935) all_236_2_144 = 0
% 23.89/6.22 | (941) ~ (all_236_3_145 = 0) | all_236_0_142 = 0 | all_236_1_143 = 0
% 23.89/6.22 |
% 23.89/6.22 +-Applying beta-rule and splitting (941), into two cases.
% 23.89/6.22 |-Branch one:
% 23.89/6.22 | (942) ~ (all_236_3_145 = 0)
% 23.89/6.22 |
% 23.89/6.22 | Equations (875) can reduce 942 to:
% 23.89/6.22 | (129) $false
% 23.89/6.22 |
% 23.89/6.22 |-The branch is then unsatisfiable
% 23.89/6.22 |-Branch two:
% 23.89/6.22 | (875) all_236_3_145 = 0
% 23.89/6.22 | (945) all_236_0_142 = 0 | all_236_1_143 = 0
% 23.89/6.22 |
% 23.89/6.22 +-Applying beta-rule and splitting (945), into two cases.
% 23.89/6.22 |-Branch one:
% 23.89/6.22 | (946) all_236_0_142 = 0
% 23.89/6.22 |
% 23.89/6.22 | Combining equations (946,838) yields a new equation:
% 23.89/6.22 | (925) all_104_1_62 = 0
% 23.89/6.22 |
% 23.89/6.22 | Equations (925) can reduce 898 to:
% 23.89/6.22 | (129) $false
% 23.89/6.22 |
% 23.89/6.22 |-The branch is then unsatisfiable
% 23.89/6.22 |-Branch two:
% 23.89/6.22 | (949) ~ (all_236_0_142 = 0)
% 23.89/6.22 | (950) all_236_1_143 = 0
% 23.89/6.22 |
% 23.89/6.22 | Combining equations (950,876) yields a new equation:
% 23.89/6.22 | (951) all_54_1_50 = 0
% 23.89/6.22 |
% 23.89/6.22 | Equations (951) can reduce 900 to:
% 23.89/6.22 | (129) $false
% 23.89/6.22 |
% 23.89/6.22 |-The branch is then unsatisfiable
% 23.89/6.22 |-Branch two:
% 23.89/6.22 | (953) all_100_1_56 = 0
% 23.89/6.22 | (954) ~ (all_100_2_57 = 0) | (all_100_0_55 = 0 & all_22_0_15 = 0)
% 23.89/6.22 |
% 23.89/6.22 +-Applying beta-rule and splitting (954), into two cases.
% 23.89/6.22 |-Branch one:
% 23.89/6.22 | (955) ~ (all_100_2_57 = 0)
% 23.89/6.22 |
% 23.89/6.22 | Equations (869) can reduce 955 to:
% 23.89/6.22 | (129) $false
% 23.89/6.22 |
% 23.89/6.22 |-The branch is then unsatisfiable
% 23.89/6.22 |-Branch two:
% 23.89/6.22 | (869) all_100_2_57 = 0
% 23.89/6.22 | (958) all_100_0_55 = 0 & all_22_0_15 = 0
% 23.89/6.22 |
% 23.89/6.22 | Applying alpha-rule on (958) yields:
% 23.89/6.22 | (959) all_100_0_55 = 0
% 23.89/6.22 | (399) all_22_0_15 = 0
% 23.89/6.22 |
% 23.89/6.22 | Equations (399) can reduce 209 to:
% 23.89/6.22 | (129) $false
% 23.89/6.22 |
% 23.89/6.22 |-The branch is then unsatisfiable
% 23.89/6.22 |-Branch two:
% 23.89/6.22 | (962) all_28_0_24 = 0 & all_22_0_15 = 0
% 23.89/6.22 |
% 23.89/6.22 | Applying alpha-rule on (962) yields:
% 23.89/6.22 | (287) all_28_0_24 = 0
% 23.89/6.22 | (399) all_22_0_15 = 0
% 23.89/6.22 |
% 23.89/6.22 | Equations (399) can reduce 209 to:
% 23.89/6.22 | (129) $false
% 23.89/6.22 |
% 23.89/6.22 |-The branch is then unsatisfiable
% 23.89/6.22 |-Branch two:
% 23.89/6.22 | (966) all_112_1_74 = 0
% 23.89/6.22 | (967) all_112_0_73 = 0 & all_49_3_48 = 0
% 23.89/6.22 |
% 23.89/6.22 | Applying alpha-rule on (967) yields:
% 23.89/6.22 | (968) all_112_0_73 = 0
% 23.89/6.22 | (507) all_49_3_48 = 0
% 23.89/6.22 |
% 23.89/6.22 | Equations (507) can reduce 242 to:
% 23.89/6.22 | (129) $false
% 23.89/6.22 |
% 23.89/6.22 |-The branch is then unsatisfiable
% 23.89/6.22 |-Branch two:
% 23.89/6.22 | (971) all_252_1_155 = 0
% 23.89/6.22 | (972) all_252_0_154 = 0 & all_49_3_48 = 0
% 23.89/6.23 |
% 23.89/6.23 | Applying alpha-rule on (972) yields:
% 23.89/6.23 | (973) all_252_0_154 = 0
% 23.89/6.23 | (507) all_49_3_48 = 0
% 23.89/6.23 |
% 23.89/6.23 | Equations (507) can reduce 242 to:
% 23.89/6.23 | (129) $false
% 23.89/6.23 |
% 23.89/6.23 |-The branch is then unsatisfiable
% 23.89/6.23 |-Branch two:
% 23.89/6.23 | (499) all_22_1_16 = 0
% 23.89/6.23 | (977) ~ (all_22_2_17 = 0) | all_22_0_15 = 0
% 23.89/6.23 |
% 23.89/6.23 +-Applying beta-rule and splitting (283), into two cases.
% 23.89/6.23 |-Branch one:
% 23.89/6.23 | (399) all_22_0_15 = 0
% 23.89/6.23 |
% 23.89/6.23 | Equations (399) can reduce 209 to:
% 23.89/6.23 | (129) $false
% 23.89/6.23 |
% 23.89/6.23 |-The branch is then unsatisfiable
% 23.89/6.23 |-Branch two:
% 23.89/6.23 | (209) ~ (all_22_0_15 = 0)
% 23.89/6.23 | (402) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_4_4, all_1_4_4) = v1 & apart_point_and_line(all_1_4_4, v1) = v2 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 23.89/6.23 |
% 23.89/6.23 +-Applying beta-rule and splitting (977), into two cases.
% 23.89/6.23 |-Branch one:
% 23.89/6.23 | (982) ~ (all_22_2_17 = 0)
% 23.89/6.23 |
% 23.89/6.23 | Equations (301) can reduce 982 to:
% 23.89/6.23 | (129) $false
% 23.89/6.23 |
% 23.89/6.23 |-The branch is then unsatisfiable
% 23.89/6.23 |-Branch two:
% 23.89/6.23 | (301) all_22_2_17 = 0
% 23.89/6.23 | (399) all_22_0_15 = 0
% 23.89/6.23 |
% 23.89/6.23 | Equations (399) can reduce 209 to:
% 23.89/6.23 | (129) $false
% 23.89/6.23 |
% 23.89/6.23 |-The branch is then unsatisfiable
% 23.89/6.23 |-Branch two:
% 23.89/6.23 | (416) all_24_1_19 = 0
% 23.89/6.23 | (988) all_24_0_18 = 0
% 23.89/6.23 |
% 23.89/6.23 | Combining equations (988,176) yields a new equation:
% 23.89/6.23 | (399) all_22_0_15 = 0
% 23.89/6.23 |
% 23.89/6.23 | Equations (399) can reduce 209 to:
% 23.89/6.23 | (129) $false
% 23.89/6.23 |
% 23.89/6.23 |-The branch is then unsatisfiable
% 23.89/6.23 |-Branch two:
% 23.89/6.23 | (991) all_30_1_28 = 0
% 23.89/6.23 | (992) all_30_0_27 = 0
% 23.89/6.23 |
% 23.89/6.23 | Combining equations (194,992) yields a new equation:
% 23.89/6.23 | (993) all_16_0_6 = 0
% 23.89/6.23 |
% 23.89/6.23 | Simplifying 993 yields:
% 23.89/6.23 | (994) all_16_0_6 = 0
% 23.89/6.23 |
% 23.89/6.23 | Equations (994) can reduce 208 to:
% 23.89/6.23 | (129) $false
% 23.89/6.23 |
% 23.89/6.23 |-The branch is then unsatisfiable
% 23.89/6.23 |-Branch two:
% 23.89/6.23 | (996) apart_point_and_line(all_1_5_5, all_1_2_2) = 0
% 23.89/6.23 | (997) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_1_5_5, all_1_4_4) = v2 & distinct_points(all_1_5_5, all_1_4_4) = v0 & distinct_points(all_1_5_5, all_1_5_5) = v1 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))
% 23.89/6.23 |
% 23.89/6.23 +-Applying beta-rule and splitting (112), into two cases.
% 23.89/6.23 |-Branch one:
% 23.89/6.23 | (227) ~ (all_30_1_28 = 0)
% 23.89/6.23 |
% 23.89/6.23 +-Applying beta-rule and splitting (167), into two cases.
% 23.89/6.23 |-Branch one:
% 23.89/6.23 | (999) ~ (apart_point_and_line(all_1_5_5, all_1_2_2) = all_18_1_10)
% 23.89/6.23 |
% 23.89/6.23 | From (197) and (999) follows:
% 23.89/6.23 | (226) ~ (apart_point_and_line(all_1_5_5, all_1_2_2) = 0)
% 23.89/6.23 |
% 23.89/6.23 | Using (996) and (226) yields:
% 23.89/6.23 | (230) $false
% 23.89/6.23 |
% 23.89/6.23 |-The branch is then unsatisfiable
% 23.89/6.23 |-Branch two:
% 23.89/6.23 | (1002) apart_point_and_line(all_1_5_5, all_1_2_2) = all_18_1_10
% 23.89/6.23 | (1003) all_44_1_43 = all_18_1_10
% 23.89/6.23 |
% 23.89/6.23 | Combining equations (188,1003) yields a new equation:
% 23.89/6.23 | (1004) all_18_1_10 = all_16_1_7
% 23.89/6.23 |
% 23.89/6.23 | Combining equations (1004,197) yields a new equation:
% 23.89/6.23 | (1005) all_16_1_7 = 0
% 23.89/6.23 |
% 23.89/6.23 | Simplifying 1005 yields:
% 23.89/6.23 | (566) all_16_1_7 = 0
% 23.89/6.23 |
% 23.89/6.23 +-Applying beta-rule and splitting (77), into two cases.
% 23.89/6.23 |-Branch one:
% 23.89/6.23 | (235) ~ (all_16_1_7 = 0)
% 23.89/6.23 |
% 23.89/6.23 | Equations (566) can reduce 235 to:
% 23.89/6.23 | (129) $false
% 23.89/6.23 |
% 23.89/6.23 |-The branch is then unsatisfiable
% 23.89/6.23 |-Branch two:
% 23.89/6.23 | (566) all_16_1_7 = 0
% 23.89/6.23 | (1010) ~ (all_16_2_8 = 0) | all_16_0_6 = 0
% 23.89/6.23 |
% 23.89/6.23 +-Applying beta-rule and splitting (169), into two cases.
% 23.89/6.23 |-Branch one:
% 23.89/6.23 | (229) ~ (apart_point_and_line(all_1_5_5, all_1_2_2) = all_30_1_28)
% 23.89/6.23 |
% 23.89/6.23 | Using (218) and (229) yields:
% 23.89/6.23 | (230) $false
% 23.89/6.23 |
% 23.89/6.23 |-The branch is then unsatisfiable
% 23.89/6.23 |-Branch two:
% 23.89/6.23 | (218) apart_point_and_line(all_1_5_5, all_1_2_2) = all_30_1_28
% 23.89/6.23 | (234) all_30_1_28 = all_16_1_7
% 23.89/6.23 |
% 23.89/6.23 | Combining equations (566,234) yields a new equation:
% 23.89/6.23 | (991) all_30_1_28 = 0
% 23.89/6.23 |
% 23.89/6.23 | Equations (991) can reduce 227 to:
% 23.89/6.23 | (129) $false
% 23.89/6.23 |
% 23.89/6.23 |-The branch is then unsatisfiable
% 23.89/6.23 |-Branch two:
% 23.89/6.23 | (991) all_30_1_28 = 0
% 23.89/6.23 | (992) all_30_0_27 = 0
% 23.89/6.23 |
% 23.89/6.23 | Combining equations (194,992) yields a new equation:
% 23.89/6.23 | (993) all_16_0_6 = 0
% 23.89/6.23 |
% 23.89/6.23 | Simplifying 993 yields:
% 23.89/6.23 | (994) all_16_0_6 = 0
% 23.89/6.23 |
% 23.89/6.23 | Equations (994) can reduce 208 to:
% 23.89/6.23 | (129) $false
% 23.89/6.23 |
% 23.89/6.23 |-The branch is then unsatisfiable
% 23.89/6.23 |-Branch two:
% 23.89/6.23 | (394) all_36_1_37 = 0
% 23.89/6.23 | (1023) all_36_0_36 = 0
% 23.89/6.23 |
% 23.89/6.23 | Combining equations (1023,186) yields a new equation:
% 23.89/6.23 | (994) all_16_0_6 = 0
% 23.89/6.23 |
% 23.89/6.23 | Equations (994) can reduce 208 to:
% 23.89/6.23 | (129) $false
% 23.89/6.23 |
% 23.89/6.23 |-The branch is then unsatisfiable
% 23.89/6.23 % SZS output end Proof for theBenchmark
% 23.89/6.23
% 23.89/6.23 5645ms
%------------------------------------------------------------------------------