TSTP Solution File: GEO202+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO202+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.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 03:48:38 EDT 2022
% Result : Theorem 84.69s 51.27s
% Output : Proof 90.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO202+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n025.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 00:42:27 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.55/0.58 ____ _
% 0.55/0.58 ___ / __ \_____(_)___ ________ __________
% 0.55/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.58
% 0.55/0.58 A Theorem Prover for First-Order Logic
% 0.55/0.58 (ePrincess v.1.0)
% 0.55/0.58
% 0.55/0.58 (c) Philipp Rümmer, 2009-2015
% 0.55/0.58 (c) Peter Backeman, 2014-2015
% 0.55/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.58 Bug reports to peter@backeman.se
% 0.55/0.58
% 0.55/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.58
% 0.55/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.47/0.92 Prover 0: Preprocessing ...
% 1.90/1.05 Prover 0: Warning: ignoring some quantifiers
% 2.01/1.08 Prover 0: Constructing countermodel ...
% 19.18/5.92 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.23/5.96 Prover 1: Preprocessing ...
% 19.84/6.08 Prover 1: Constructing countermodel ...
% 19.84/6.14 Prover 1: gave up
% 19.84/6.14 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 20.27/6.16 Prover 2: Preprocessing ...
% 20.66/6.24 Prover 2: Warning: ignoring some quantifiers
% 20.66/6.25 Prover 2: Constructing countermodel ...
% 21.19/6.36 Prover 2: gave up
% 21.19/6.36 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 21.19/6.37 Prover 3: Preprocessing ...
% 21.19/6.39 Prover 3: Warning: ignoring some quantifiers
% 21.19/6.39 Prover 3: Constructing countermodel ...
% 78.41/49.78 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 78.41/49.81 Prover 4: Preprocessing ...
% 78.91/49.91 Prover 4: Warning: ignoring some quantifiers
% 78.91/49.91 Prover 4: Constructing countermodel ...
% 82.82/50.85 Prover 3: stopped
% 83.78/51.05 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 83.78/51.07 Prover 5: Preprocessing ...
% 84.06/51.13 Prover 5: Constructing countermodel ...
% 84.69/51.27 Prover 5: proved (218ms)
% 84.69/51.27 Prover 0: stopped
% 84.69/51.27 Prover 4: stopped
% 84.69/51.27
% 84.69/51.27 No countermodel exists, formula is valid
% 84.69/51.27 % SZS status Theorem for theBenchmark
% 84.69/51.27
% 84.69/51.27 Generating proof ... found it (size 432)
% 90.18/52.53
% 90.18/52.53 % SZS output start Proof for theBenchmark
% 90.18/52.53 Assumed formulas after preprocessing and simplification:
% 90.18/52.53 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v2) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v2) = v9 & apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection_point(v0, v1) = v3) | ~ (distinct_points(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v0, v1) = v4) | ~ (apart_point_and_line(v2, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v4) = v7 & ( ~ (v5 = 0) | v7 = 0 | ( ~ (v6 = 0) & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v0, v1) = v4) | ~ (apart_point_and_line(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v4) = v7 & ( ~ (v5 = 0) | v7 = 0 | ( ~ (v6 = 0) & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v0, v1) = v3) | ~ (distinct_points(v2, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v3) = v6 & distinct_points(v2, v0) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v7 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v0, v1) = v3) | ~ (distinct_points(v2, v0) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v3) = v6 & distinct_points(v2, v1) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v7 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apart_point_and_line(v2, v1) = v4) | ~ (apart_point_and_line(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (intersection_point(v0, v1) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v6) = v7 & ( ~ (v5 = 0) | v7 = 0)) | ( ~ (v4 = 0) & ~ (v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (distinct_points(v2, v1) = v4) | ~ (distinct_points(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (line_connecting(v0, v1) = v6 & apart_point_and_line(v2, v6) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0))) | (v4 = 0 & v3 = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apart_point_and_line(v2, v1) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (intersection_point(v0, v1) = v5 & apart_point_and_line(v2, v0) = v4 & distinct_points(v2, v5) = v6 & (v6 = 0 | ( ~ (v4 = 0) & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apart_point_and_line(v2, v0) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (intersection_point(v0, v1) = v5 & apart_point_and_line(v2, v1) = v4 & distinct_points(v2, v5) = v6 & (v6 = 0 | ( ~ (v4 = 0) & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v1) = v3) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (line_connecting(v0, v1) = v4 & apart_point_and_line(v2, v4) = v5 & distinct_points(v2, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v0) = v3) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (line_connecting(v0, v1) = v4 & apart_point_and_line(v2, v4) = v5 & distinct_points(v2, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (intersection_point(v3, v4) = v5 & line_connecting(v0, v2) = v4 & line_connecting(v0, v1) = v3 & convergent_lines(v3, v4) = 0 & distinct_points(v5, v0) = 0 & distinct_points(v0, v2) = 0 & distinct_points(v0, v1) = 0)
% 90.18/52.58 | Applying alpha-rule on (0) yields:
% 90.18/52.58 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 90.18/52.58 | (2) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 90.18/52.58 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 90.18/52.58 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 90.18/52.58 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 90.18/52.58 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection_point(v0, v1) = v3) | ~ (distinct_points(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0)))))
% 90.47/52.58 | (7) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0)
% 90.47/52.58 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0)))
% 90.47/52.58 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 90.47/52.58 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 90.47/52.58 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v0, v1) = v4) | ~ (apart_point_and_line(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v1) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v4) = v7 & ( ~ (v5 = 0) | v7 = 0 | ( ~ (v6 = 0) & ~ (v3 = 0)))))
% 90.47/52.58 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apart_point_and_line(v2, v0) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (intersection_point(v0, v1) = v5 & apart_point_and_line(v2, v1) = v4 & distinct_points(v2, v5) = v6 & (v6 = 0 | ( ~ (v4 = 0) & ~ (v3 = 0)))))
% 90.47/52.58 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 90.47/52.58 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0))))
% 90.47/52.58 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 90.47/52.58 | (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)
% 90.47/52.58 | (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)))))
% 90.47/52.59 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (distinct_points(v2, v1) = v4) | ~ (distinct_points(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (line_connecting(v0, v1) = v6 & apart_point_and_line(v2, v6) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0))) | (v4 = 0 & v3 = 0))
% 90.47/52.59 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 90.47/52.59 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 90.47/52.59 | (21) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 90.47/52.59 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 90.47/52.59 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 90.47/52.59 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v2) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 90.47/52.59 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 90.47/52.59 | (26) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 90.47/52.59 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5))
% 90.47/52.59 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 90.47/52.59 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v0, v1) = v3) | ~ (distinct_points(v2, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v2, v3) = v6 & distinct_points(v2, v0) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v7 = 0 & v4 = 0))))
% 90.47/52.59 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v0) = v3) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (line_connecting(v0, v1) = v4 & apart_point_and_line(v2, v4) = v5 & distinct_points(v2, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v3 = 0))))
% 90.47/52.59 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 90.47/52.59 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 90.47/52.59 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 90.47/52.59 | (34) ! [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))))
% 90.47/52.59 | (35) ! [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)))
% 90.47/52.59 | (36) ! [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))
% 90.47/52.59 | (37) ! [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)))))
% 90.47/52.59 | (38) ! [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))))
% 90.47/52.60 | (39) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (intersection_point(v3, v4) = v5 & line_connecting(v0, v2) = v4 & line_connecting(v0, v1) = v3 & convergent_lines(v3, v4) = 0 & distinct_points(v5, v0) = 0 & distinct_points(v0, v2) = 0 & distinct_points(v0, v1) = 0)
% 90.47/52.60 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5))
% 90.47/52.60 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0)
% 90.47/52.60 | (42) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 90.47/52.60 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apart_point_and_line(v2, v1) = v4) | ~ (apart_point_and_line(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (intersection_point(v0, v1) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v6) = v7 & ( ~ (v5 = 0) | v7 = 0)) | ( ~ (v4 = 0) & ~ (v3 = 0)))
% 90.47/52.60 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apart_point_and_line(v1, v2) = v9 & apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0)))
% 90.47/52.60 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5))
% 90.47/52.60 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 90.47/52.60 |
% 90.47/52.60 | Instantiating (39) 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:
% 90.47/52.60 | (47) intersection_point(all_1_2_2, all_1_1_1) = all_1_0_0 & line_connecting(all_1_5_5, all_1_3_3) = all_1_1_1 & line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2 & convergent_lines(all_1_2_2, all_1_1_1) = 0 & distinct_points(all_1_0_0, all_1_5_5) = 0 & distinct_points(all_1_5_5, all_1_3_3) = 0 & distinct_points(all_1_5_5, all_1_4_4) = 0
% 90.47/52.60 |
% 90.47/52.60 | Applying alpha-rule on (47) yields:
% 90.47/52.60 | (48) intersection_point(all_1_2_2, all_1_1_1) = all_1_0_0
% 90.47/52.60 | (49) distinct_points(all_1_0_0, all_1_5_5) = 0
% 90.47/52.60 | (50) distinct_points(all_1_5_5, all_1_3_3) = 0
% 90.47/52.60 | (51) line_connecting(all_1_5_5, all_1_3_3) = all_1_1_1
% 90.47/52.60 | (52) distinct_points(all_1_5_5, all_1_4_4) = 0
% 90.47/52.60 | (53) convergent_lines(all_1_2_2, all_1_1_1) = 0
% 90.47/52.60 | (54) line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2
% 90.47/52.60 |
% 90.47/52.60 | Instantiating formula (21) with all_1_5_5 yields:
% 90.47/52.60 | (55) ~ (distinct_points(all_1_5_5, all_1_5_5) = 0)
% 90.47/52.60 |
% 90.47/52.60 | Instantiating formula (7) with all_1_1_1, all_1_2_2 and discharging atoms convergent_lines(all_1_2_2, all_1_1_1) = 0, yields:
% 90.47/52.60 | (56) distinct_lines(all_1_2_2, all_1_1_1) = 0
% 90.47/52.60 |
% 90.47/52.60 | Instantiating formula (34) with 0, all_1_0_0, all_1_5_5, all_1_0_0 and discharging atoms distinct_points(all_1_0_0, all_1_5_5) = 0, yields:
% 90.47/52.60 | (57) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_0_0, all_1_5_5) = v0 & apart_point_and_line(all_1_0_0, v0) = v1 & distinct_points(all_1_0_0, all_1_0_0) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 90.47/52.60 |
% 90.47/52.60 | Instantiating formula (38) with 0, all_1_1_1, all_1_0_0, all_1_3_3, all_1_5_5 and discharging atoms line_connecting(all_1_5_5, all_1_3_3) = all_1_1_1, distinct_points(all_1_0_0, all_1_5_5) = 0, yields:
% 90.47/52.60 | (58) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_1_1) = v1 & distinct_points(all_1_0_0, all_1_3_3) = v2 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 90.47/52.60 |
% 90.47/52.60 | Instantiating formula (38) with 0, all_1_2_2, all_1_0_0, 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_0_0, all_1_5_5) = 0, yields:
% 90.47/52.60 | (59) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_2_2) = v1 & distinct_points(all_1_0_0, all_1_4_4) = v2 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 90.47/52.60 |
% 90.47/52.60 | Instantiating formula (34) 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:
% 90.47/52.60 | (60) ? [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))
% 90.47/52.60 |
% 90.47/52.60 | Instantiating formula (29) with 0, all_1_1_1, all_1_5_5, all_1_3_3, all_1_5_5 and discharging atoms line_connecting(all_1_5_5, all_1_3_3) = all_1_1_1, distinct_points(all_1_5_5, all_1_3_3) = 0, yields:
% 90.47/52.60 | (61) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v0 & distinct_points(all_1_5_5, all_1_5_5) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 90.47/52.60 |
% 90.47/52.60 | Instantiating formula (29) 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:
% 90.47/52.60 | (62) ? [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))
% 90.47/52.61 |
% 90.47/52.61 | Instantiating formula (30) with 0, all_1_0_0, all_1_3_3, all_1_5_5 and discharging atoms distinct_points(all_1_0_0, all_1_5_5) = 0, distinct_points(all_1_5_5, all_1_3_3) = 0, yields:
% 90.47/52.61 | (63) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_3_3) = v0 & apart_point_and_line(all_1_0_0, v0) = v1 & distinct_points(all_1_0_0, all_1_3_3) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 90.47/52.61 |
% 90.47/52.61 | Instantiating formula (34) 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:
% 90.47/52.61 | (64) ? [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))
% 90.47/52.61 |
% 90.47/52.61 | Instantiating formula (30) with 0, all_1_0_0, all_1_4_4, all_1_5_5 and discharging atoms distinct_points(all_1_0_0, all_1_5_5) = 0, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 90.47/52.61 | (65) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_4_4) = v0 & apart_point_and_line(all_1_0_0, v0) = v1 & distinct_points(all_1_0_0, all_1_4_4) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 90.47/52.61 |
% 90.47/52.61 | Instantiating (65) with all_17_0_6, all_17_1_7, all_17_2_8 yields:
% 90.47/52.61 | (66) line_connecting(all_1_5_5, all_1_4_4) = all_17_2_8 & apart_point_and_line(all_1_0_0, all_17_2_8) = all_17_1_7 & distinct_points(all_1_0_0, all_1_4_4) = all_17_0_6 & ( ~ (all_17_1_7 = 0) | all_17_0_6 = 0)
% 90.47/52.61 |
% 90.47/52.61 | Applying alpha-rule on (66) yields:
% 90.47/52.61 | (67) line_connecting(all_1_5_5, all_1_4_4) = all_17_2_8
% 90.47/52.61 | (68) apart_point_and_line(all_1_0_0, all_17_2_8) = all_17_1_7
% 90.47/52.61 | (69) distinct_points(all_1_0_0, all_1_4_4) = all_17_0_6
% 90.47/52.61 | (70) ~ (all_17_1_7 = 0) | all_17_0_6 = 0
% 90.47/52.61 |
% 90.47/52.61 | Instantiating (58) with all_19_0_9, all_19_1_10, all_19_2_11 yields:
% 90.47/52.61 | (71) apart_point_and_line(all_1_0_0, all_1_1_1) = all_19_1_10 & distinct_points(all_1_0_0, all_1_3_3) = all_19_0_9 & distinct_points(all_1_5_5, all_1_3_3) = all_19_2_11 & ( ~ (all_19_1_10 = 0) | ~ (all_19_2_11 = 0) | all_19_0_9 = 0)
% 90.47/52.61 |
% 90.47/52.61 | Applying alpha-rule on (71) yields:
% 90.47/52.61 | (72) apart_point_and_line(all_1_0_0, all_1_1_1) = all_19_1_10
% 90.47/52.61 | (73) distinct_points(all_1_0_0, all_1_3_3) = all_19_0_9
% 90.47/52.61 | (74) distinct_points(all_1_5_5, all_1_3_3) = all_19_2_11
% 90.47/52.61 | (75) ~ (all_19_1_10 = 0) | ~ (all_19_2_11 = 0) | all_19_0_9 = 0
% 90.47/52.61 |
% 90.47/52.61 | Instantiating (64) with all_21_0_12, all_21_1_13, all_21_2_14 yields:
% 90.47/52.61 | (76) line_connecting(all_1_5_5, all_1_4_4) = all_21_2_14 & apart_point_and_line(all_1_5_5, all_21_2_14) = all_21_1_13 & distinct_points(all_1_5_5, all_1_5_5) = all_21_0_12 & ( ~ (all_21_1_13 = 0) | all_21_0_12 = 0)
% 90.47/52.61 |
% 90.47/52.61 | Applying alpha-rule on (76) yields:
% 90.47/52.61 | (77) line_connecting(all_1_5_5, all_1_4_4) = all_21_2_14
% 90.47/52.61 | (78) apart_point_and_line(all_1_5_5, all_21_2_14) = all_21_1_13
% 90.47/52.61 | (79) distinct_points(all_1_5_5, all_1_5_5) = all_21_0_12
% 90.47/52.61 | (80) ~ (all_21_1_13 = 0) | all_21_0_12 = 0
% 90.47/52.61 |
% 90.47/52.61 | Instantiating (61) with all_23_0_15, all_23_1_16, all_23_2_17 yields:
% 90.47/52.61 | (81) apart_point_and_line(all_1_5_5, all_1_1_1) = all_23_1_16 & distinct_points(all_1_5_5, all_1_3_3) = all_23_2_17 & distinct_points(all_1_5_5, all_1_5_5) = all_23_0_15 & ( ~ (all_23_1_16 = 0) | ~ (all_23_2_17 = 0) | all_23_0_15 = 0)
% 90.47/52.61 |
% 90.47/52.61 | Applying alpha-rule on (81) yields:
% 90.47/52.61 | (82) apart_point_and_line(all_1_5_5, all_1_1_1) = all_23_1_16
% 90.47/52.61 | (83) distinct_points(all_1_5_5, all_1_3_3) = all_23_2_17
% 90.47/52.61 | (84) distinct_points(all_1_5_5, all_1_5_5) = all_23_0_15
% 90.47/52.61 | (85) ~ (all_23_1_16 = 0) | ~ (all_23_2_17 = 0) | all_23_0_15 = 0
% 90.47/52.61 |
% 90.47/52.61 | Instantiating (60) with all_25_0_18, all_25_1_19, all_25_2_20 yields:
% 90.47/52.61 | (86) line_connecting(all_1_5_5, all_1_3_3) = all_25_2_20 & apart_point_and_line(all_1_5_5, all_25_2_20) = all_25_1_19 & distinct_points(all_1_5_5, all_1_5_5) = all_25_0_18 & ( ~ (all_25_1_19 = 0) | all_25_0_18 = 0)
% 90.47/52.61 |
% 90.47/52.61 | Applying alpha-rule on (86) yields:
% 90.47/52.61 | (87) line_connecting(all_1_5_5, all_1_3_3) = all_25_2_20
% 90.47/52.61 | (88) apart_point_and_line(all_1_5_5, all_25_2_20) = all_25_1_19
% 90.47/52.61 | (89) distinct_points(all_1_5_5, all_1_5_5) = all_25_0_18
% 90.47/52.61 | (90) ~ (all_25_1_19 = 0) | all_25_0_18 = 0
% 90.47/52.61 |
% 90.47/52.61 | Instantiating (59) with all_27_0_21, all_27_1_22, all_27_2_23 yields:
% 90.47/52.61 | (91) apart_point_and_line(all_1_0_0, all_1_2_2) = all_27_1_22 & distinct_points(all_1_0_0, all_1_4_4) = all_27_0_21 & distinct_points(all_1_5_5, all_1_4_4) = all_27_2_23 & ( ~ (all_27_1_22 = 0) | ~ (all_27_2_23 = 0) | all_27_0_21 = 0)
% 90.47/52.61 |
% 90.47/52.61 | Applying alpha-rule on (91) yields:
% 90.47/52.61 | (92) apart_point_and_line(all_1_0_0, all_1_2_2) = all_27_1_22
% 90.47/52.61 | (93) distinct_points(all_1_0_0, all_1_4_4) = all_27_0_21
% 90.47/52.61 | (94) distinct_points(all_1_5_5, all_1_4_4) = all_27_2_23
% 90.47/52.61 | (95) ~ (all_27_1_22 = 0) | ~ (all_27_2_23 = 0) | all_27_0_21 = 0
% 90.47/52.61 |
% 90.47/52.61 | Instantiating (63) with all_29_0_24, all_29_1_25, all_29_2_26 yields:
% 90.47/52.61 | (96) line_connecting(all_1_5_5, all_1_3_3) = all_29_2_26 & apart_point_and_line(all_1_0_0, all_29_2_26) = all_29_1_25 & distinct_points(all_1_0_0, all_1_3_3) = all_29_0_24 & ( ~ (all_29_1_25 = 0) | all_29_0_24 = 0)
% 90.47/52.61 |
% 90.47/52.61 | Applying alpha-rule on (96) yields:
% 90.47/52.61 | (97) line_connecting(all_1_5_5, all_1_3_3) = all_29_2_26
% 90.47/52.61 | (98) apart_point_and_line(all_1_0_0, all_29_2_26) = all_29_1_25
% 90.47/52.61 | (99) distinct_points(all_1_0_0, all_1_3_3) = all_29_0_24
% 90.47/52.61 | (100) ~ (all_29_1_25 = 0) | all_29_0_24 = 0
% 90.47/52.61 |
% 90.47/52.61 | Instantiating (62) with all_31_0_27, all_31_1_28, all_31_2_29 yields:
% 90.47/52.61 | (101) apart_point_and_line(all_1_5_5, all_1_2_2) = all_31_1_28 & distinct_points(all_1_5_5, all_1_4_4) = all_31_2_29 & distinct_points(all_1_5_5, all_1_5_5) = all_31_0_27 & ( ~ (all_31_1_28 = 0) | ~ (all_31_2_29 = 0) | all_31_0_27 = 0)
% 90.47/52.61 |
% 90.47/52.61 | Applying alpha-rule on (101) yields:
% 90.47/52.61 | (102) apart_point_and_line(all_1_5_5, all_1_2_2) = all_31_1_28
% 90.47/52.61 | (103) distinct_points(all_1_5_5, all_1_4_4) = all_31_2_29
% 90.47/52.61 | (104) distinct_points(all_1_5_5, all_1_5_5) = all_31_0_27
% 90.47/52.61 | (105) ~ (all_31_1_28 = 0) | ~ (all_31_2_29 = 0) | all_31_0_27 = 0
% 90.47/52.61 |
% 90.47/52.62 | Instantiating (57) with all_33_0_30, all_33_1_31, all_33_2_32 yields:
% 90.47/52.62 | (106) line_connecting(all_1_0_0, all_1_5_5) = all_33_2_32 & apart_point_and_line(all_1_0_0, all_33_2_32) = all_33_1_31 & distinct_points(all_1_0_0, all_1_0_0) = all_33_0_30 & ( ~ (all_33_1_31 = 0) | all_33_0_30 = 0)
% 90.47/52.62 |
% 90.47/52.62 | Applying alpha-rule on (106) yields:
% 90.47/52.62 | (107) line_connecting(all_1_0_0, all_1_5_5) = all_33_2_32
% 90.47/52.62 | (108) apart_point_and_line(all_1_0_0, all_33_2_32) = all_33_1_31
% 90.47/52.62 | (109) distinct_points(all_1_0_0, all_1_0_0) = all_33_0_30
% 90.47/52.62 | (110) ~ (all_33_1_31 = 0) | all_33_0_30 = 0
% 90.47/52.62 |
% 90.47/52.62 | Instantiating formula (9) with all_1_5_5, all_1_3_3, all_29_2_26, all_1_1_1 and discharging atoms line_connecting(all_1_5_5, all_1_3_3) = all_29_2_26, line_connecting(all_1_5_5, all_1_3_3) = all_1_1_1, yields:
% 90.47/52.62 | (111) all_29_2_26 = all_1_1_1
% 90.47/52.62 |
% 90.47/52.62 | Instantiating formula (9) with all_1_5_5, all_1_3_3, all_25_2_20, all_29_2_26 and discharging atoms line_connecting(all_1_5_5, all_1_3_3) = all_29_2_26, line_connecting(all_1_5_5, all_1_3_3) = all_25_2_20, yields:
% 90.47/52.62 | (112) all_29_2_26 = all_25_2_20
% 90.47/52.62 |
% 90.47/52.62 | Instantiating formula (9) with all_1_5_5, all_1_4_4, all_21_2_14, all_1_2_2 and discharging atoms line_connecting(all_1_5_5, all_1_4_4) = all_21_2_14, line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2, yields:
% 90.47/52.62 | (113) all_21_2_14 = all_1_2_2
% 90.47/52.62 |
% 90.47/52.62 | Instantiating formula (9) with all_1_5_5, all_1_4_4, all_17_2_8, all_21_2_14 and discharging atoms line_connecting(all_1_5_5, all_1_4_4) = all_21_2_14, line_connecting(all_1_5_5, all_1_4_4) = all_17_2_8, yields:
% 90.47/52.62 | (114) all_21_2_14 = all_17_2_8
% 90.47/52.62 |
% 90.47/52.62 | Instantiating formula (20) with all_1_0_0, all_1_1_1, all_19_1_10, all_29_1_25 and discharging atoms apart_point_and_line(all_1_0_0, all_1_1_1) = all_19_1_10, yields:
% 90.47/52.62 | (115) all_29_1_25 = all_19_1_10 | ~ (apart_point_and_line(all_1_0_0, all_1_1_1) = all_29_1_25)
% 90.47/52.62 |
% 90.47/52.62 | Instantiating formula (20) with all_1_0_0, all_1_2_2, all_27_1_22, all_17_1_7 and discharging atoms apart_point_and_line(all_1_0_0, all_1_2_2) = all_27_1_22, yields:
% 90.47/52.62 | (116) all_27_1_22 = all_17_1_7 | ~ (apart_point_and_line(all_1_0_0, all_1_2_2) = all_17_1_7)
% 90.47/52.62 |
% 90.47/52.62 | Instantiating formula (20) with all_1_5_5, all_1_1_1, all_23_1_16, all_25_1_19 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_23_1_16, yields:
% 90.47/52.62 | (117) all_25_1_19 = all_23_1_16 | ~ (apart_point_and_line(all_1_5_5, all_1_1_1) = all_25_1_19)
% 90.47/52.62 |
% 90.47/52.62 | Instantiating formula (20) with all_1_5_5, all_1_2_2, all_31_1_28, all_21_1_13 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_31_1_28, yields:
% 90.47/52.62 | (118) all_31_1_28 = all_21_1_13 | ~ (apart_point_and_line(all_1_5_5, all_1_2_2) = all_21_1_13)
% 90.47/52.62 |
% 90.47/52.62 | Instantiating formula (21) with all_1_0_0 yields:
% 90.47/52.62 | (119) ~ (distinct_points(all_1_0_0, all_1_0_0) = 0)
% 90.47/52.62 |
% 90.47/52.62 | Instantiating formula (31) with all_1_0_0, all_1_3_3, all_19_0_9, all_29_0_24 and discharging atoms distinct_points(all_1_0_0, all_1_3_3) = all_29_0_24, distinct_points(all_1_0_0, all_1_3_3) = all_19_0_9, yields:
% 90.47/52.62 | (120) all_29_0_24 = all_19_0_9
% 90.47/52.62 |
% 90.47/52.62 | Instantiating formula (31) with all_1_0_0, all_1_4_4, all_17_0_6, all_27_0_21 and discharging atoms distinct_points(all_1_0_0, all_1_4_4) = all_27_0_21, distinct_points(all_1_0_0, all_1_4_4) = all_17_0_6, yields:
% 90.47/52.62 | (121) all_27_0_21 = all_17_0_6
% 90.47/52.62 |
% 90.47/52.62 | Instantiating formula (31) with all_1_5_5, all_1_3_3, all_23_2_17, 0 and discharging atoms distinct_points(all_1_5_5, all_1_3_3) = all_23_2_17, distinct_points(all_1_5_5, all_1_3_3) = 0, yields:
% 90.47/52.62 | (122) all_23_2_17 = 0
% 90.47/52.62 |
% 90.47/52.62 | Instantiating formula (31) with all_1_5_5, all_1_3_3, all_19_2_11, all_23_2_17 and discharging atoms distinct_points(all_1_5_5, all_1_3_3) = all_23_2_17, distinct_points(all_1_5_5, all_1_3_3) = all_19_2_11, yields:
% 90.47/52.62 | (123) all_23_2_17 = all_19_2_11
% 90.47/52.62 |
% 90.47/52.62 | Instantiating formula (31) with all_1_5_5, all_1_4_4, all_31_2_29, 0 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = all_31_2_29, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 90.47/52.62 | (124) all_31_2_29 = 0
% 90.47/52.62 |
% 90.47/52.62 | Instantiating formula (31) with all_1_5_5, all_1_4_4, all_27_2_23, all_31_2_29 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = all_31_2_29, distinct_points(all_1_5_5, all_1_4_4) = all_27_2_23, yields:
% 90.47/52.62 | (125) all_31_2_29 = all_27_2_23
% 90.47/52.62 |
% 90.47/52.62 | Instantiating formula (31) with all_1_5_5, all_1_5_5, all_25_0_18, all_31_0_27 and discharging atoms distinct_points(all_1_5_5, all_1_5_5) = all_31_0_27, distinct_points(all_1_5_5, all_1_5_5) = all_25_0_18, yields:
% 90.47/52.62 | (126) all_31_0_27 = all_25_0_18
% 90.47/52.62 |
% 90.47/52.62 | Instantiating formula (31) with all_1_5_5, all_1_5_5, all_23_0_15, all_25_0_18 and discharging atoms distinct_points(all_1_5_5, all_1_5_5) = all_25_0_18, distinct_points(all_1_5_5, all_1_5_5) = all_23_0_15, yields:
% 90.47/52.62 | (127) all_25_0_18 = all_23_0_15
% 90.47/52.62 |
% 90.47/52.62 | Using (84) and (55) yields:
% 90.47/52.62 | (128) ~ (all_23_0_15 = 0)
% 90.47/52.62 |
% 90.47/52.62 | Instantiating formula (31) with all_1_5_5, all_1_5_5, all_21_0_12, all_31_0_27 and discharging atoms distinct_points(all_1_5_5, all_1_5_5) = all_31_0_27, distinct_points(all_1_5_5, all_1_5_5) = all_21_0_12, yields:
% 90.47/52.62 | (129) all_31_0_27 = all_21_0_12
% 90.47/52.62 |
% 90.47/52.62 | Combining equations (126,129) yields a new equation:
% 90.47/52.62 | (130) all_25_0_18 = all_21_0_12
% 90.47/52.62 |
% 90.47/52.62 | Simplifying 130 yields:
% 90.47/52.62 | (131) all_25_0_18 = all_21_0_12
% 90.47/52.62 |
% 90.47/52.62 | Combining equations (125,124) yields a new equation:
% 90.47/52.62 | (132) all_27_2_23 = 0
% 90.47/52.62 |
% 90.47/52.62 | Simplifying 132 yields:
% 90.47/52.62 | (133) all_27_2_23 = 0
% 90.47/52.62 |
% 90.47/52.62 | Combining equations (112,111) yields a new equation:
% 90.47/52.62 | (134) all_25_2_20 = all_1_1_1
% 90.47/52.62 |
% 90.47/52.62 | Simplifying 134 yields:
% 90.47/52.62 | (135) all_25_2_20 = all_1_1_1
% 90.47/52.62 |
% 90.47/52.62 | Combining equations (131,127) yields a new equation:
% 90.47/52.62 | (136) all_23_0_15 = all_21_0_12
% 90.47/52.62 |
% 90.47/52.62 | Combining equations (122,123) yields a new equation:
% 90.47/52.62 | (137) all_19_2_11 = 0
% 90.47/52.62 |
% 90.47/52.62 | Combining equations (113,114) yields a new equation:
% 90.47/52.62 | (138) all_17_2_8 = all_1_2_2
% 90.47/52.62 |
% 90.47/52.62 | Combining equations (138,114) yields a new equation:
% 90.47/52.62 | (113) all_21_2_14 = all_1_2_2
% 90.47/52.62 |
% 90.47/52.62 | Combining equations (136,127) yields a new equation:
% 90.47/52.62 | (131) all_25_0_18 = all_21_0_12
% 90.47/52.62 |
% 90.47/52.62 | Equations (136) can reduce 128 to:
% 90.47/52.62 | (141) ~ (all_21_0_12 = 0)
% 90.47/52.62 |
% 90.47/52.62 | From (135) and (87) follows:
% 90.47/52.62 | (51) line_connecting(all_1_5_5, all_1_3_3) = all_1_1_1
% 90.47/52.63 |
% 90.47/52.63 | From (138) and (67) follows:
% 90.47/52.63 | (54) line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2
% 90.47/52.63 |
% 90.47/52.63 | From (111) and (98) follows:
% 90.47/52.63 | (144) apart_point_and_line(all_1_0_0, all_1_1_1) = all_29_1_25
% 90.47/52.63 |
% 90.47/52.63 | From (138) and (68) follows:
% 90.47/52.63 | (145) apart_point_and_line(all_1_0_0, all_1_2_2) = all_17_1_7
% 90.47/52.63 |
% 90.47/52.63 | From (135) and (88) follows:
% 90.47/52.63 | (146) apart_point_and_line(all_1_5_5, all_1_1_1) = all_25_1_19
% 90.47/52.63 |
% 90.47/52.63 | From (113) and (78) follows:
% 90.47/52.63 | (147) apart_point_and_line(all_1_5_5, all_1_2_2) = all_21_1_13
% 90.47/52.63 |
% 90.47/52.63 | From (120) and (99) follows:
% 90.47/52.63 | (73) distinct_points(all_1_0_0, all_1_3_3) = all_19_0_9
% 90.47/52.63 |
% 90.47/52.63 | From (121) and (93) follows:
% 90.47/52.63 | (69) distinct_points(all_1_0_0, all_1_4_4) = all_17_0_6
% 90.47/52.63 |
% 90.47/52.63 | From (137) and (74) follows:
% 90.47/52.63 | (50) distinct_points(all_1_5_5, all_1_3_3) = 0
% 90.47/52.63 |
% 90.47/52.63 | From (133) and (94) follows:
% 90.47/52.63 | (52) distinct_points(all_1_5_5, all_1_4_4) = 0
% 90.47/52.63 |
% 90.47/52.63 +-Applying beta-rule and splitting (90), into two cases.
% 90.47/52.63 |-Branch one:
% 90.47/52.63 | (152) ~ (all_25_1_19 = 0)
% 90.47/52.63 |
% 90.47/52.63 +-Applying beta-rule and splitting (105), into two cases.
% 90.47/52.63 |-Branch one:
% 90.47/52.63 | (153) ~ (all_31_1_28 = 0)
% 90.47/52.63 |
% 90.47/52.63 +-Applying beta-rule and splitting (116), into two cases.
% 90.47/52.63 |-Branch one:
% 90.47/52.63 | (154) ~ (apart_point_and_line(all_1_0_0, all_1_2_2) = all_17_1_7)
% 90.47/52.63 |
% 90.47/52.63 | Using (145) and (154) yields:
% 90.47/52.63 | (155) $false
% 90.47/52.63 |
% 90.47/52.63 |-The branch is then unsatisfiable
% 90.47/52.63 |-Branch two:
% 90.47/52.63 | (145) apart_point_and_line(all_1_0_0, all_1_2_2) = all_17_1_7
% 90.47/52.63 | (157) all_27_1_22 = all_17_1_7
% 90.47/52.63 |
% 90.47/52.63 | From (157) and (92) follows:
% 90.47/52.63 | (145) apart_point_and_line(all_1_0_0, all_1_2_2) = all_17_1_7
% 90.47/52.63 |
% 90.47/52.63 +-Applying beta-rule and splitting (115), into two cases.
% 90.47/52.63 |-Branch one:
% 90.47/52.63 | (159) ~ (apart_point_and_line(all_1_0_0, all_1_1_1) = all_29_1_25)
% 90.47/52.63 |
% 90.47/52.63 | Using (144) and (159) yields:
% 90.47/52.63 | (155) $false
% 90.47/52.63 |
% 90.47/52.63 |-The branch is then unsatisfiable
% 90.47/52.63 |-Branch two:
% 90.47/52.63 | (144) apart_point_and_line(all_1_0_0, all_1_1_1) = all_29_1_25
% 90.47/52.63 | (162) all_29_1_25 = all_19_1_10
% 90.47/52.63 |
% 90.47/52.63 | From (162) and (144) follows:
% 90.47/52.63 | (72) apart_point_and_line(all_1_0_0, all_1_1_1) = all_19_1_10
% 90.47/52.63 |
% 90.47/52.63 +-Applying beta-rule and splitting (118), into two cases.
% 90.47/52.63 |-Branch one:
% 90.47/52.63 | (164) ~ (apart_point_and_line(all_1_5_5, all_1_2_2) = all_21_1_13)
% 90.47/52.63 |
% 90.47/52.63 | Using (147) and (164) yields:
% 90.47/52.63 | (155) $false
% 90.47/52.63 |
% 90.47/52.63 |-The branch is then unsatisfiable
% 90.47/52.63 |-Branch two:
% 90.47/52.63 | (147) apart_point_and_line(all_1_5_5, all_1_2_2) = all_21_1_13
% 90.47/52.63 | (167) all_31_1_28 = all_21_1_13
% 90.47/52.63 |
% 90.47/52.63 | Equations (167) can reduce 153 to:
% 90.47/52.63 | (168) ~ (all_21_1_13 = 0)
% 90.47/52.63 |
% 90.47/52.63 | From (167) and (102) follows:
% 90.47/52.63 | (147) apart_point_and_line(all_1_5_5, all_1_2_2) = all_21_1_13
% 90.47/52.63 |
% 90.47/52.63 +-Applying beta-rule and splitting (117), into two cases.
% 90.47/52.63 |-Branch one:
% 90.47/52.63 | (170) ~ (apart_point_and_line(all_1_5_5, all_1_1_1) = all_25_1_19)
% 90.47/52.63 |
% 90.47/52.63 | Using (146) and (170) yields:
% 90.47/52.63 | (155) $false
% 90.47/52.63 |
% 90.47/52.63 |-The branch is then unsatisfiable
% 90.47/52.63 |-Branch two:
% 90.47/52.63 | (146) apart_point_and_line(all_1_5_5, all_1_1_1) = all_25_1_19
% 90.47/52.63 | (173) all_25_1_19 = all_23_1_16
% 90.47/52.63 |
% 90.47/52.63 | Equations (173) can reduce 152 to:
% 90.47/52.63 | (174) ~ (all_23_1_16 = 0)
% 90.47/52.63 |
% 90.47/52.63 | From (173) and (146) follows:
% 90.47/52.63 | (82) apart_point_and_line(all_1_5_5, all_1_1_1) = all_23_1_16
% 90.47/52.63 |
% 90.47/52.63 | Using (109) and (119) yields:
% 90.47/52.63 | (176) ~ (all_33_0_30 = 0)
% 90.47/52.63 |
% 90.47/52.63 +-Applying beta-rule and splitting (110), into two cases.
% 90.47/52.63 |-Branch one:
% 90.47/52.63 | (177) ~ (all_33_1_31 = 0)
% 90.47/52.63 |
% 90.47/52.63 | Instantiating formula (19) with all_33_1_31, all_33_1_31, all_33_2_32, all_33_2_32, all_1_5_5, all_1_0_0 and discharging atoms apart_point_and_line(all_1_0_0, all_33_2_32) = all_33_1_31, distinct_points(all_1_0_0, all_1_5_5) = 0, yields:
% 90.47/52.63 | (178) all_33_1_31 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_33_2_32) = v2 & apart_point_and_line(all_1_5_5, all_33_2_32) = v1 & distinct_lines(all_33_2_32, all_33_2_32) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 90.47/52.63 |
% 90.47/52.63 | Instantiating formula (44) with all_33_1_31, all_33_1_31, all_33_2_32, all_33_2_32, all_1_0_0, all_1_0_0 and discharging atoms apart_point_and_line(all_1_0_0, all_33_2_32) = all_33_1_31, yields:
% 90.47/52.63 | (179) all_33_1_31 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_33_2_32) = v3 & apart_point_and_line(all_1_0_0, all_33_2_32) = v2 & distinct_lines(all_33_2_32, all_33_2_32) = v1 & distinct_points(all_1_0_0, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.47/52.63 |
% 90.47/52.63 | Instantiating formula (19) with all_19_1_10, all_19_1_10, all_1_1_1, all_1_1_1, all_1_5_5, all_1_0_0 and discharging atoms apart_point_and_line(all_1_0_0, all_1_1_1) = all_19_1_10, distinct_points(all_1_0_0, all_1_5_5) = 0, yields:
% 90.47/52.63 | (180) all_19_1_10 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 90.47/52.63 |
% 90.47/52.63 | Instantiating formula (37) with all_1_0_0, all_19_1_10, all_1_0_0, all_1_1_1, all_1_2_2 and discharging atoms intersection_point(all_1_2_2, all_1_1_1) = all_1_0_0, apart_point_and_line(all_1_0_0, all_1_1_1) = all_19_1_10, yields:
% 90.47/52.63 | (181) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_2_2) = v1 & convergent_lines(all_1_2_2, all_1_1_1) = v0 & distinct_points(all_1_0_0, all_1_0_0) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_19_1_10 = 0))))
% 90.47/52.63 |
% 90.47/52.63 | Instantiating formula (17) with all_19_1_10, all_1_0_0, all_1_1_1, all_1_2_2 and discharging atoms apart_point_and_line(all_1_0_0, all_1_1_1) = all_19_1_10, convergent_lines(all_1_2_2, all_1_1_1) = 0, yields:
% 90.47/52.64 | (182) ? [v0] : ? [v1] : ? [v2] : (intersection_point(all_1_2_2, all_1_1_1) = v1 & apart_point_and_line(all_1_0_0, all_1_2_2) = v0 & distinct_points(all_1_0_0, v1) = v2 & (v2 = 0 | ( ~ (v0 = 0) & ~ (all_19_1_10 = 0))))
% 90.47/52.64 |
% 90.47/52.64 | Instantiating formula (19) with all_17_1_7, all_17_1_7, all_1_2_2, all_1_2_2, all_1_5_5, all_1_0_0 and discharging atoms apart_point_and_line(all_1_0_0, all_1_2_2) = all_17_1_7, distinct_points(all_1_0_0, all_1_5_5) = 0, yields:
% 90.47/52.64 | (183) all_17_1_7 = 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))
% 90.47/52.64 |
% 90.47/52.64 | Instantiating formula (11) with all_1_0_0, all_17_1_7, all_1_0_0, all_1_1_1, all_1_2_2 and discharging atoms intersection_point(all_1_2_2, all_1_1_1) = all_1_0_0, apart_point_and_line(all_1_0_0, all_1_2_2) = all_17_1_7, yields:
% 90.47/52.64 | (184) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_1_1) = v1 & convergent_lines(all_1_2_2, all_1_1_1) = v0 & distinct_points(all_1_0_0, all_1_0_0) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_17_1_7 = 0))))
% 90.47/52.64 |
% 90.47/52.64 | Instantiating formula (12) with all_17_1_7, all_1_0_0, all_1_1_1, all_1_2_2 and discharging atoms apart_point_and_line(all_1_0_0, all_1_2_2) = all_17_1_7, convergent_lines(all_1_2_2, all_1_1_1) = 0, yields:
% 90.47/52.64 | (185) ? [v0] : ? [v1] : ? [v2] : (intersection_point(all_1_2_2, all_1_1_1) = v1 & apart_point_and_line(all_1_0_0, all_1_1_1) = v0 & distinct_points(all_1_0_0, v1) = v2 & (v2 = 0 | ( ~ (v0 = 0) & ~ (all_17_1_7 = 0))))
% 90.47/52.64 |
% 90.47/52.64 | Instantiating formula (44) with all_23_1_16, all_33_1_31, all_1_1_1, all_33_2_32, all_1_5_5, all_1_0_0 and discharging atoms apart_point_and_line(all_1_0_0, all_33_2_32) = all_33_1_31, apart_point_and_line(all_1_5_5, all_1_1_1) = all_23_1_16, yields:
% 90.47/52.64 | (186) all_33_1_31 = 0 | all_23_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_33_2_32) = v3 & distinct_lines(all_33_2_32, all_1_1_1) = v1 & distinct_points(all_1_0_0, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.47/52.64 |
% 90.47/52.64 | Instantiating formula (44) with all_33_1_31, all_23_1_16, all_33_2_32, all_1_1_1, all_1_0_0, all_1_5_5 and discharging atoms apart_point_and_line(all_1_0_0, all_33_2_32) = all_33_1_31, apart_point_and_line(all_1_5_5, all_1_1_1) = all_23_1_16, yields:
% 90.47/52.64 | (187) all_33_1_31 = 0 | all_23_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_33_2_32) = v2 & distinct_lines(all_1_1_1, all_33_2_32) = v1 & distinct_points(all_1_5_5, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.47/52.64 |
% 90.47/52.64 | Instantiating formula (8) with all_23_1_16, all_33_1_31, all_33_2_32, all_1_1_1, all_1_5_5, all_1_0_0 and discharging atoms apart_point_and_line(all_1_0_0, all_33_2_32) = all_33_1_31, apart_point_and_line(all_1_5_5, all_1_1_1) = all_23_1_16, yields:
% 90.47/52.64 | (188) all_33_1_31 = 0 | all_23_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_33_2_32) = v3 & distinct_lines(all_1_1_1, all_33_2_32) = v1 & distinct_points(all_1_0_0, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.47/52.64 |
% 90.47/52.64 | Instantiating formula (19) with all_23_1_16, all_23_1_16, all_1_1_1, all_1_1_1, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_23_1_16, distinct_points(all_1_5_5, all_1_3_3) = 0, yields:
% 90.47/52.64 | (189) all_23_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_3_3, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 90.47/52.64 |
% 90.47/52.64 | Instantiating formula (19) with all_23_1_16, all_23_1_16, all_1_1_1, all_1_1_1, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_23_1_16, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 90.47/52.64 | (190) all_23_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 90.47/52.64 |
% 90.47/52.64 | Instantiating formula (37) with all_1_0_0, all_23_1_16, all_1_5_5, all_1_1_1, all_1_2_2 and discharging atoms intersection_point(all_1_2_2, all_1_1_1) = all_1_0_0, apart_point_and_line(all_1_5_5, all_1_1_1) = all_23_1_16, yields:
% 90.47/52.64 | (191) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_1_2_2) = v1 & convergent_lines(all_1_2_2, all_1_1_1) = v0 & distinct_points(all_1_5_5, all_1_0_0) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_23_1_16 = 0))))
% 90.47/52.64 |
% 90.47/52.64 | Instantiating formula (17) with all_23_1_16, all_1_5_5, all_1_1_1, all_1_2_2 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_23_1_16, convergent_lines(all_1_2_2, all_1_1_1) = 0, yields:
% 90.47/52.64 | (192) ? [v0] : ? [v1] : ? [v2] : (intersection_point(all_1_2_2, all_1_1_1) = v1 & apart_point_and_line(all_1_5_5, all_1_2_2) = v0 & distinct_points(all_1_5_5, v1) = v2 & (v2 = 0 | ( ~ (v0 = 0) & ~ (all_23_1_16 = 0))))
% 90.47/52.64 |
% 90.47/52.64 | Instantiating formula (44) with all_33_1_31, all_21_1_13, all_33_2_32, all_1_2_2, all_1_0_0, all_1_5_5 and discharging atoms apart_point_and_line(all_1_0_0, all_33_2_32) = all_33_1_31, apart_point_and_line(all_1_5_5, all_1_2_2) = all_21_1_13, yields:
% 90.47/52.64 | (193) all_33_1_31 = 0 | all_21_1_13 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_33_2_32) = v2 & distinct_lines(all_1_2_2, all_33_2_32) = v1 & distinct_points(all_1_5_5, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.47/52.64 |
% 90.47/52.64 | Instantiating formula (8) with all_21_1_13, all_33_1_31, all_33_2_32, all_1_2_2, all_1_5_5, all_1_0_0 and discharging atoms apart_point_and_line(all_1_0_0, all_33_2_32) = all_33_1_31, apart_point_and_line(all_1_5_5, all_1_2_2) = all_21_1_13, yields:
% 90.47/52.64 | (194) all_33_1_31 = 0 | all_21_1_13 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_33_2_32) = v3 & distinct_lines(all_1_2_2, all_33_2_32) = v1 & distinct_points(all_1_0_0, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.47/52.64 |
% 90.47/52.64 | Instantiating formula (8) with all_33_1_31, all_21_1_13, all_1_2_2, all_33_2_32, all_1_0_0, all_1_5_5 and discharging atoms apart_point_and_line(all_1_0_0, all_33_2_32) = all_33_1_31, apart_point_and_line(all_1_5_5, all_1_2_2) = all_21_1_13, yields:
% 90.47/52.64 | (195) all_33_1_31 = 0 | all_21_1_13 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_33_2_32) = v2 & distinct_lines(all_33_2_32, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.47/52.65 |
% 90.47/52.65 | Instantiating formula (4) with all_21_1_13, all_23_1_16, all_1_2_2, all_1_1_1, all_1_5_5, all_1_0_0 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_23_1_16, apart_point_and_line(all_1_5_5, all_1_2_2) = all_21_1_13, distinct_points(all_1_0_0, all_1_5_5) = 0, yields:
% 90.47/52.65 | (196) all_23_1_16 = 0 | all_21_1_13 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_1_1) = v1 & apart_point_and_line(all_1_0_0, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 90.47/52.65 |
% 90.47/52.65 | Instantiating formula (19) with all_21_1_13, all_23_1_16, all_1_2_2, all_1_1_1, all_1_3_3, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_23_1_16, apart_point_and_line(all_1_5_5, all_1_2_2) = all_21_1_13, distinct_points(all_1_5_5, all_1_3_3) = 0, yields:
% 90.47/52.65 | (197) all_23_1_16 = 0 | all_21_1_13 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v1 & apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 90.47/52.65 |
% 90.47/52.65 | Instantiating formula (19) with all_21_1_13, all_23_1_16, all_1_2_2, all_1_1_1, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_23_1_16, apart_point_and_line(all_1_5_5, all_1_2_2) = all_21_1_13, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 90.47/52.65 | (198) all_23_1_16 = 0 | all_21_1_13 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 90.47/52.65 |
% 90.47/52.65 | Instantiating formula (44) with all_21_1_13, all_23_1_16, all_1_2_2, all_1_1_1, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_23_1_16, apart_point_and_line(all_1_5_5, all_1_2_2) = all_21_1_13, yields:
% 90.47/52.65 | (199) all_23_1_16 = 0 | all_21_1_13 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.47/52.65 |
% 90.47/52.65 | Instantiating formula (8) with all_23_1_16, all_21_1_13, all_1_2_2, all_1_1_1, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_23_1_16, apart_point_and_line(all_1_5_5, all_1_2_2) = all_21_1_13, yields:
% 90.47/52.65 | (200) all_23_1_16 = 0 | all_21_1_13 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.47/52.65 |
% 90.47/52.65 | Instantiating formula (4) with all_21_1_13, all_21_1_13, all_1_2_2, all_1_2_2, all_1_5_5, all_1_0_0 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_21_1_13, distinct_points(all_1_0_0, all_1_5_5) = 0, yields:
% 90.47/52.65 | (201) all_21_1_13 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_2_2) = v2 & apart_point_and_line(all_1_0_0, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 90.47/52.65 |
% 90.47/52.65 | Instantiating formula (44) with all_21_1_13, all_21_1_13, all_1_2_2, all_1_2_2, all_1_5_5, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_21_1_13, yields:
% 90.47/52.65 | (202) all_21_1_13 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.47/52.65 |
% 90.47/52.65 | Instantiating formula (11) with all_1_0_0, all_21_1_13, all_1_5_5, all_1_1_1, all_1_2_2 and discharging atoms intersection_point(all_1_2_2, all_1_1_1) = all_1_0_0, apart_point_and_line(all_1_5_5, all_1_2_2) = all_21_1_13, yields:
% 90.47/52.65 | (203) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v1 & convergent_lines(all_1_2_2, all_1_1_1) = v0 & distinct_points(all_1_5_5, all_1_0_0) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_21_1_13 = 0))))
% 90.47/52.65 |
% 90.47/52.65 | Instantiating formula (35) with all_1_1_1, all_1_2_2, all_1_5_5, all_1_0_0 and discharging atoms distinct_lines(all_1_2_2, all_1_1_1) = 0, distinct_points(all_1_0_0, all_1_5_5) = 0, yields:
% 90.47/52.65 | (204) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_1_1) = v1 & apart_point_and_line(all_1_0_0, all_1_2_2) = v0 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0))
% 90.47/52.65 |
% 90.47/52.65 | Instantiating formula (35) with all_1_1_1, all_1_2_2, all_1_3_3, all_1_5_5 and discharging atoms distinct_lines(all_1_2_2, all_1_1_1) = 0, distinct_points(all_1_5_5, all_1_3_3) = 0, yields:
% 90.47/52.65 | (205) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v3 & apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v1 & apart_point_and_line(all_1_5_5, all_1_2_2) = v0 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0))
% 90.47/52.65 |
% 90.47/52.65 | Instantiating formula (35) with all_1_1_1, all_1_2_2, all_1_4_4, all_1_5_5 and discharging atoms distinct_lines(all_1_2_2, all_1_1_1) = 0, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 90.47/52.65 | (206) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v3 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v1 & apart_point_and_line(all_1_5_5, all_1_2_2) = v0 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0))
% 90.47/52.65 |
% 90.47/52.65 | Instantiating formula (18) with all_33_0_30, all_33_0_30, all_1_0_0, all_1_0_0, all_1_0_0 and discharging atoms distinct_points(all_1_0_0, all_1_0_0) = all_33_0_30, yields:
% 90.47/52.65 | (207) all_33_0_30 = 0 | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_0_0, all_1_0_0) = v1 & apart_point_and_line(all_1_0_0, v1) = v2 & distinct_points(all_1_0_0, all_1_0_0) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 90.47/52.65 |
% 90.47/52.65 | Instantiating formula (6) with all_33_0_30, all_1_0_0, all_1_0_0, all_1_1_1, all_1_2_2 and discharging atoms intersection_point(all_1_2_2, all_1_1_1) = all_1_0_0, distinct_points(all_1_0_0, all_1_0_0) = all_33_0_30, yields:
% 90.47/52.65 | (208) all_33_0_30 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_1_1) = v2 & apart_point_and_line(all_1_0_0, all_1_2_2) = v1 & convergent_lines(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | ( ~ (v2 = 0) & ~ (v1 = 0))))
% 90.47/52.65 |
% 90.47/52.65 | Instantiating formula (29) with all_19_0_9, all_1_1_1, all_1_0_0, all_1_3_3, all_1_5_5 and discharging atoms line_connecting(all_1_5_5, all_1_3_3) = all_1_1_1, distinct_points(all_1_0_0, all_1_3_3) = all_19_0_9, yields:
% 90.47/52.65 | (209) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_1_1) = v1 & distinct_points(all_1_0_0, all_1_5_5) = v2 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & all_19_0_9 = 0)))
% 90.47/52.66 |
% 90.47/52.66 | Instantiating formula (29) with all_17_0_6, all_1_2_2, all_1_0_0, 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_0_0, all_1_4_4) = all_17_0_6, yields:
% 90.47/52.66 | (210) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_2_2) = v1 & distinct_points(all_1_0_0, all_1_5_5) = v2 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & all_17_0_6 = 0)))
% 90.47/52.66 |
% 90.47/52.66 | Instantiating (192) with all_92_0_39, all_92_1_40, all_92_2_41 yields:
% 90.47/52.66 | (211) intersection_point(all_1_2_2, all_1_1_1) = all_92_1_40 & apart_point_and_line(all_1_5_5, all_1_2_2) = all_92_2_41 & distinct_points(all_1_5_5, all_92_1_40) = all_92_0_39 & (all_92_0_39 = 0 | ( ~ (all_92_2_41 = 0) & ~ (all_23_1_16 = 0)))
% 90.47/52.66 |
% 90.47/52.66 | Applying alpha-rule on (211) yields:
% 90.47/52.66 | (212) intersection_point(all_1_2_2, all_1_1_1) = all_92_1_40
% 90.47/52.66 | (213) apart_point_and_line(all_1_5_5, all_1_2_2) = all_92_2_41
% 90.85/52.66 | (214) distinct_points(all_1_5_5, all_92_1_40) = all_92_0_39
% 90.85/52.66 | (215) all_92_0_39 = 0 | ( ~ (all_92_2_41 = 0) & ~ (all_23_1_16 = 0))
% 90.85/52.66 |
% 90.85/52.66 | Instantiating (182) with all_94_0_42, all_94_1_43, all_94_2_44 yields:
% 90.85/52.66 | (216) intersection_point(all_1_2_2, all_1_1_1) = all_94_1_43 & apart_point_and_line(all_1_0_0, all_1_2_2) = all_94_2_44 & distinct_points(all_1_0_0, all_94_1_43) = all_94_0_42 & (all_94_0_42 = 0 | ( ~ (all_94_2_44 = 0) & ~ (all_19_1_10 = 0)))
% 90.85/52.66 |
% 90.85/52.66 | Applying alpha-rule on (216) yields:
% 90.85/52.66 | (217) intersection_point(all_1_2_2, all_1_1_1) = all_94_1_43
% 90.85/52.66 | (218) apart_point_and_line(all_1_0_0, all_1_2_2) = all_94_2_44
% 90.85/52.66 | (219) distinct_points(all_1_0_0, all_94_1_43) = all_94_0_42
% 90.85/52.66 | (220) all_94_0_42 = 0 | ( ~ (all_94_2_44 = 0) & ~ (all_19_1_10 = 0))
% 90.85/52.66 |
% 90.85/52.66 | Instantiating (191) with all_96_0_45, all_96_1_46, all_96_2_47 yields:
% 90.85/52.66 | (221) apart_point_and_line(all_1_5_5, all_1_2_2) = all_96_1_46 & convergent_lines(all_1_2_2, all_1_1_1) = all_96_2_47 & distinct_points(all_1_5_5, all_1_0_0) = all_96_0_45 & ( ~ (all_96_2_47 = 0) | all_96_0_45 = 0 | ( ~ (all_96_1_46 = 0) & ~ (all_23_1_16 = 0)))
% 90.85/52.66 |
% 90.85/52.66 | Applying alpha-rule on (221) yields:
% 90.85/52.66 | (222) apart_point_and_line(all_1_5_5, all_1_2_2) = all_96_1_46
% 90.85/52.66 | (223) convergent_lines(all_1_2_2, all_1_1_1) = all_96_2_47
% 90.85/52.66 | (224) distinct_points(all_1_5_5, all_1_0_0) = all_96_0_45
% 90.85/52.66 | (225) ~ (all_96_2_47 = 0) | all_96_0_45 = 0 | ( ~ (all_96_1_46 = 0) & ~ (all_23_1_16 = 0))
% 90.85/52.66 |
% 90.85/52.66 | Instantiating (185) with all_98_0_48, all_98_1_49, all_98_2_50 yields:
% 90.85/52.66 | (226) intersection_point(all_1_2_2, all_1_1_1) = all_98_1_49 & apart_point_and_line(all_1_0_0, all_1_1_1) = all_98_2_50 & distinct_points(all_1_0_0, all_98_1_49) = all_98_0_48 & (all_98_0_48 = 0 | ( ~ (all_98_2_50 = 0) & ~ (all_17_1_7 = 0)))
% 90.85/52.66 |
% 90.85/52.66 | Applying alpha-rule on (226) yields:
% 90.85/52.66 | (227) intersection_point(all_1_2_2, all_1_1_1) = all_98_1_49
% 90.85/52.66 | (228) apart_point_and_line(all_1_0_0, all_1_1_1) = all_98_2_50
% 90.85/52.66 | (229) distinct_points(all_1_0_0, all_98_1_49) = all_98_0_48
% 90.85/52.66 | (230) all_98_0_48 = 0 | ( ~ (all_98_2_50 = 0) & ~ (all_17_1_7 = 0))
% 90.85/52.66 |
% 90.85/52.66 | Instantiating (181) with all_100_0_51, all_100_1_52, all_100_2_53 yields:
% 90.85/52.66 | (231) apart_point_and_line(all_1_0_0, all_1_2_2) = all_100_1_52 & convergent_lines(all_1_2_2, all_1_1_1) = all_100_2_53 & distinct_points(all_1_0_0, all_1_0_0) = all_100_0_51 & ( ~ (all_100_2_53 = 0) | all_100_0_51 = 0 | ( ~ (all_100_1_52 = 0) & ~ (all_19_1_10 = 0)))
% 90.85/52.66 |
% 90.85/52.66 | Applying alpha-rule on (231) yields:
% 90.85/52.66 | (232) apart_point_and_line(all_1_0_0, all_1_2_2) = all_100_1_52
% 90.85/52.66 | (233) convergent_lines(all_1_2_2, all_1_1_1) = all_100_2_53
% 90.85/52.66 | (234) distinct_points(all_1_0_0, all_1_0_0) = all_100_0_51
% 90.85/52.66 | (235) ~ (all_100_2_53 = 0) | all_100_0_51 = 0 | ( ~ (all_100_1_52 = 0) & ~ (all_19_1_10 = 0))
% 90.85/52.66 |
% 90.85/52.66 | Instantiating (184) with all_102_0_54, all_102_1_55, all_102_2_56 yields:
% 90.85/52.66 | (236) apart_point_and_line(all_1_0_0, all_1_1_1) = all_102_1_55 & convergent_lines(all_1_2_2, all_1_1_1) = all_102_2_56 & distinct_points(all_1_0_0, all_1_0_0) = all_102_0_54 & ( ~ (all_102_2_56 = 0) | all_102_0_54 = 0 | ( ~ (all_102_1_55 = 0) & ~ (all_17_1_7 = 0)))
% 90.85/52.66 |
% 90.85/52.66 | Applying alpha-rule on (236) yields:
% 90.85/52.66 | (237) apart_point_and_line(all_1_0_0, all_1_1_1) = all_102_1_55
% 90.85/52.66 | (238) convergent_lines(all_1_2_2, all_1_1_1) = all_102_2_56
% 90.85/52.66 | (239) distinct_points(all_1_0_0, all_1_0_0) = all_102_0_54
% 90.85/52.66 | (240) ~ (all_102_2_56 = 0) | all_102_0_54 = 0 | ( ~ (all_102_1_55 = 0) & ~ (all_17_1_7 = 0))
% 90.85/52.66 |
% 90.85/52.66 | Instantiating (210) with all_104_0_57, all_104_1_58, all_104_2_59 yields:
% 90.85/52.66 | (241) apart_point_and_line(all_1_0_0, all_1_2_2) = all_104_1_58 & distinct_points(all_1_0_0, all_1_5_5) = all_104_0_57 & distinct_points(all_1_5_5, all_1_4_4) = all_104_2_59 & ( ~ (all_104_1_58 = 0) | ~ (all_104_2_59 = 0) | (all_104_0_57 = 0 & all_17_0_6 = 0))
% 90.85/52.66 |
% 90.85/52.66 | Applying alpha-rule on (241) yields:
% 90.85/52.66 | (242) apart_point_and_line(all_1_0_0, all_1_2_2) = all_104_1_58
% 90.85/52.66 | (243) distinct_points(all_1_0_0, all_1_5_5) = all_104_0_57
% 90.85/52.66 | (244) distinct_points(all_1_5_5, all_1_4_4) = all_104_2_59
% 90.85/52.66 | (245) ~ (all_104_1_58 = 0) | ~ (all_104_2_59 = 0) | (all_104_0_57 = 0 & all_17_0_6 = 0)
% 90.85/52.66 |
% 90.85/52.66 | Instantiating (209) with all_106_0_60, all_106_1_61, all_106_2_62 yields:
% 90.85/52.66 | (246) apart_point_and_line(all_1_0_0, all_1_1_1) = all_106_1_61 & distinct_points(all_1_0_0, all_1_5_5) = all_106_0_60 & distinct_points(all_1_5_5, all_1_3_3) = all_106_2_62 & ( ~ (all_106_1_61 = 0) | ~ (all_106_2_62 = 0) | (all_106_0_60 = 0 & all_19_0_9 = 0))
% 90.85/52.66 |
% 90.85/52.66 | Applying alpha-rule on (246) yields:
% 90.85/52.66 | (247) apart_point_and_line(all_1_0_0, all_1_1_1) = all_106_1_61
% 90.85/52.66 | (248) distinct_points(all_1_0_0, all_1_5_5) = all_106_0_60
% 90.85/52.66 | (249) distinct_points(all_1_5_5, all_1_3_3) = all_106_2_62
% 90.85/52.66 | (250) ~ (all_106_1_61 = 0) | ~ (all_106_2_62 = 0) | (all_106_0_60 = 0 & all_19_0_9 = 0)
% 90.85/52.66 |
% 90.85/52.66 | Instantiating (206) with all_112_0_69, all_112_1_70, all_112_2_71, all_112_3_72 yields:
% 90.85/52.66 | (251) apart_point_and_line(all_1_4_4, all_1_1_1) = all_112_0_69 & apart_point_and_line(all_1_4_4, all_1_2_2) = all_112_1_70 & apart_point_and_line(all_1_5_5, all_1_1_1) = all_112_2_71 & apart_point_and_line(all_1_5_5, all_1_2_2) = all_112_3_72 & (all_112_0_69 = 0 | all_112_1_70 = 0 | all_112_2_71 = 0 | all_112_3_72 = 0)
% 90.85/52.66 |
% 90.85/52.66 | Applying alpha-rule on (251) yields:
% 90.85/52.66 | (252) all_112_0_69 = 0 | all_112_1_70 = 0 | all_112_2_71 = 0 | all_112_3_72 = 0
% 90.85/52.67 | (253) apart_point_and_line(all_1_5_5, all_1_2_2) = all_112_3_72
% 90.85/52.67 | (254) apart_point_and_line(all_1_4_4, all_1_2_2) = all_112_1_70
% 90.85/52.67 | (255) apart_point_and_line(all_1_5_5, all_1_1_1) = all_112_2_71
% 90.85/52.67 | (256) apart_point_and_line(all_1_4_4, all_1_1_1) = all_112_0_69
% 90.85/52.67 |
% 90.85/52.67 | Instantiating (204) with all_114_0_73, all_114_1_74, all_114_2_75, all_114_3_76 yields:
% 90.85/52.67 | (257) apart_point_and_line(all_1_0_0, all_1_1_1) = all_114_2_75 & apart_point_and_line(all_1_0_0, all_1_2_2) = all_114_3_76 & apart_point_and_line(all_1_5_5, all_1_1_1) = all_114_0_73 & apart_point_and_line(all_1_5_5, all_1_2_2) = all_114_1_74 & (all_114_0_73 = 0 | all_114_1_74 = 0 | all_114_2_75 = 0 | all_114_3_76 = 0)
% 90.85/52.67 |
% 90.85/52.67 | Applying alpha-rule on (257) yields:
% 90.85/52.67 | (258) apart_point_and_line(all_1_0_0, all_1_1_1) = all_114_2_75
% 90.85/52.67 | (259) apart_point_and_line(all_1_5_5, all_1_2_2) = all_114_1_74
% 90.85/52.67 | (260) apart_point_and_line(all_1_0_0, all_1_2_2) = all_114_3_76
% 90.85/52.67 | (261) all_114_0_73 = 0 | all_114_1_74 = 0 | all_114_2_75 = 0 | all_114_3_76 = 0
% 90.85/52.67 | (262) apart_point_and_line(all_1_5_5, all_1_1_1) = all_114_0_73
% 90.85/52.67 |
% 90.85/52.67 | Instantiating (205) with all_116_0_77, all_116_1_78, all_116_2_79, all_116_3_80 yields:
% 90.85/52.67 | (263) apart_point_and_line(all_1_3_3, all_1_1_1) = all_116_0_77 & apart_point_and_line(all_1_3_3, all_1_2_2) = all_116_1_78 & apart_point_and_line(all_1_5_5, all_1_1_1) = all_116_2_79 & apart_point_and_line(all_1_5_5, all_1_2_2) = all_116_3_80 & (all_116_0_77 = 0 | all_116_1_78 = 0 | all_116_2_79 = 0 | all_116_3_80 = 0)
% 90.85/52.67 |
% 90.85/52.67 | Applying alpha-rule on (263) yields:
% 90.85/52.67 | (264) apart_point_and_line(all_1_3_3, all_1_1_1) = all_116_0_77
% 90.85/52.67 | (265) apart_point_and_line(all_1_3_3, all_1_2_2) = all_116_1_78
% 90.85/52.67 | (266) all_116_0_77 = 0 | all_116_1_78 = 0 | all_116_2_79 = 0 | all_116_3_80 = 0
% 90.85/52.67 | (267) apart_point_and_line(all_1_5_5, all_1_2_2) = all_116_3_80
% 90.85/52.67 | (268) apart_point_and_line(all_1_5_5, all_1_1_1) = all_116_2_79
% 90.85/52.67 |
% 90.85/52.67 | Instantiating (203) with all_120_0_84, all_120_1_85, all_120_2_86 yields:
% 90.85/52.67 | (269) apart_point_and_line(all_1_5_5, all_1_1_1) = all_120_1_85 & convergent_lines(all_1_2_2, all_1_1_1) = all_120_2_86 & distinct_points(all_1_5_5, all_1_0_0) = all_120_0_84 & ( ~ (all_120_2_86 = 0) | all_120_0_84 = 0 | ( ~ (all_120_1_85 = 0) & ~ (all_21_1_13 = 0)))
% 90.85/52.67 |
% 90.85/52.67 | Applying alpha-rule on (269) yields:
% 90.85/52.67 | (270) apart_point_and_line(all_1_5_5, all_1_1_1) = all_120_1_85
% 90.85/52.67 | (271) convergent_lines(all_1_2_2, all_1_1_1) = all_120_2_86
% 90.85/52.67 | (272) distinct_points(all_1_5_5, all_1_0_0) = all_120_0_84
% 90.85/52.67 | (273) ~ (all_120_2_86 = 0) | all_120_0_84 = 0 | ( ~ (all_120_1_85 = 0) & ~ (all_21_1_13 = 0))
% 90.85/52.67 |
% 90.85/52.67 +-Applying beta-rule and splitting (201), into two cases.
% 90.85/52.67 |-Branch one:
% 90.85/52.67 | (274) all_21_1_13 = 0
% 90.85/52.67 |
% 90.85/52.67 | Equations (274) can reduce 168 to:
% 90.85/52.67 | (275) $false
% 90.85/52.67 |
% 90.85/52.67 |-The branch is then unsatisfiable
% 90.85/52.67 |-Branch two:
% 90.85/52.67 | (168) ~ (all_21_1_13 = 0)
% 90.85/52.67 | (277) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_2_2) = v2 & apart_point_and_line(all_1_0_0, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 90.85/52.67 |
% 90.85/52.67 | Instantiating (277) with all_129_0_87, all_129_1_88, all_129_2_89 yields:
% 90.85/52.67 | (278) apart_point_and_line(all_1_0_0, all_1_2_2) = all_129_0_87 & apart_point_and_line(all_1_0_0, all_1_2_2) = all_129_1_88 & distinct_lines(all_1_2_2, all_1_2_2) = all_129_2_89 & ( ~ (all_129_2_89 = 0) | all_129_0_87 = 0 | all_129_1_88 = 0)
% 90.85/52.67 |
% 90.85/52.67 | Applying alpha-rule on (278) yields:
% 90.85/52.67 | (279) apart_point_and_line(all_1_0_0, all_1_2_2) = all_129_0_87
% 90.85/52.67 | (280) apart_point_and_line(all_1_0_0, all_1_2_2) = all_129_1_88
% 90.85/52.67 | (281) distinct_lines(all_1_2_2, all_1_2_2) = all_129_2_89
% 90.85/52.67 | (282) ~ (all_129_2_89 = 0) | all_129_0_87 = 0 | all_129_1_88 = 0
% 90.85/52.67 |
% 90.85/52.67 +-Applying beta-rule and splitting (202), into two cases.
% 90.85/52.67 |-Branch one:
% 90.85/52.67 | (274) all_21_1_13 = 0
% 90.85/52.67 |
% 90.85/52.67 | Equations (274) can reduce 168 to:
% 90.85/52.67 | (275) $false
% 90.85/52.67 |
% 90.85/52.67 |-The branch is then unsatisfiable
% 90.85/52.67 |-Branch two:
% 90.85/52.67 | (168) ~ (all_21_1_13 = 0)
% 90.85/52.67 | (286) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.85/52.67 |
% 90.85/52.67 | Instantiating (286) with all_134_0_90, all_134_1_91, all_134_2_92, all_134_3_93 yields:
% 90.85/52.67 | (287) apart_point_and_line(all_1_5_5, all_1_2_2) = all_134_0_90 & apart_point_and_line(all_1_5_5, all_1_2_2) = all_134_1_91 & distinct_lines(all_1_2_2, all_1_2_2) = all_134_2_92 & distinct_points(all_1_5_5, all_1_5_5) = all_134_3_93 & ( ~ (all_134_2_92 = 0) | ~ (all_134_3_93 = 0) | all_134_0_90 = 0 | all_134_1_91 = 0)
% 90.85/52.67 |
% 90.85/52.67 | Applying alpha-rule on (287) yields:
% 90.85/52.67 | (288) apart_point_and_line(all_1_5_5, all_1_2_2) = all_134_0_90
% 90.85/52.67 | (289) apart_point_and_line(all_1_5_5, all_1_2_2) = all_134_1_91
% 90.85/52.67 | (290) distinct_points(all_1_5_5, all_1_5_5) = all_134_3_93
% 90.85/52.67 | (291) ~ (all_134_2_92 = 0) | ~ (all_134_3_93 = 0) | all_134_0_90 = 0 | all_134_1_91 = 0
% 90.85/52.67 | (292) distinct_lines(all_1_2_2, all_1_2_2) = all_134_2_92
% 90.85/52.67 |
% 90.85/52.67 +-Applying beta-rule and splitting (178), into two cases.
% 90.85/52.67 |-Branch one:
% 90.85/52.67 | (293) all_33_1_31 = 0
% 90.85/52.67 |
% 90.85/52.67 | Equations (293) can reduce 177 to:
% 90.85/52.67 | (275) $false
% 90.85/52.67 |
% 90.85/52.67 |-The branch is then unsatisfiable
% 90.85/52.67 |-Branch two:
% 90.85/52.67 | (177) ~ (all_33_1_31 = 0)
% 90.85/52.67 | (296) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_33_2_32) = v2 & apart_point_and_line(all_1_5_5, all_33_2_32) = v1 & distinct_lines(all_33_2_32, all_33_2_32) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 90.85/52.67 |
% 90.85/52.67 +-Applying beta-rule and splitting (179), into two cases.
% 90.85/52.67 |-Branch one:
% 90.85/52.67 | (293) all_33_1_31 = 0
% 90.85/52.67 |
% 90.85/52.67 | Equations (293) can reduce 177 to:
% 90.85/52.67 | (275) $false
% 90.85/52.67 |
% 90.85/52.67 |-The branch is then unsatisfiable
% 90.85/52.67 |-Branch two:
% 90.85/52.67 | (177) ~ (all_33_1_31 = 0)
% 90.85/52.67 | (300) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_33_2_32) = v3 & apart_point_and_line(all_1_0_0, all_33_2_32) = v2 & distinct_lines(all_33_2_32, all_33_2_32) = v1 & distinct_points(all_1_0_0, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.85/52.67 |
% 90.85/52.67 | Instantiating (300) with all_148_0_100, all_148_1_101, all_148_2_102, all_148_3_103 yields:
% 90.85/52.67 | (301) apart_point_and_line(all_1_0_0, all_33_2_32) = all_148_0_100 & apart_point_and_line(all_1_0_0, all_33_2_32) = all_148_1_101 & distinct_lines(all_33_2_32, all_33_2_32) = all_148_2_102 & distinct_points(all_1_0_0, all_1_0_0) = all_148_3_103 & ( ~ (all_148_2_102 = 0) | ~ (all_148_3_103 = 0) | all_148_0_100 = 0 | all_148_1_101 = 0)
% 90.85/52.67 |
% 90.85/52.67 | Applying alpha-rule on (301) yields:
% 90.85/52.67 | (302) ~ (all_148_2_102 = 0) | ~ (all_148_3_103 = 0) | all_148_0_100 = 0 | all_148_1_101 = 0
% 90.85/52.67 | (303) distinct_points(all_1_0_0, all_1_0_0) = all_148_3_103
% 90.85/52.67 | (304) distinct_lines(all_33_2_32, all_33_2_32) = all_148_2_102
% 90.85/52.67 | (305) apart_point_and_line(all_1_0_0, all_33_2_32) = all_148_1_101
% 90.85/52.67 | (306) apart_point_and_line(all_1_0_0, all_33_2_32) = all_148_0_100
% 90.85/52.67 |
% 90.85/52.67 +-Applying beta-rule and splitting (189), into two cases.
% 90.85/52.67 |-Branch one:
% 90.85/52.67 | (307) all_23_1_16 = 0
% 90.85/52.67 |
% 90.85/52.67 | Equations (307) can reduce 174 to:
% 90.85/52.67 | (275) $false
% 90.85/52.67 |
% 90.85/52.67 |-The branch is then unsatisfiable
% 90.85/52.67 |-Branch two:
% 90.85/52.67 | (174) ~ (all_23_1_16 = 0)
% 90.85/52.67 | (310) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & apart_point_and_line(all_1_3_3, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 90.85/52.67 |
% 90.85/52.67 +-Applying beta-rule and splitting (190), into two cases.
% 90.85/52.67 |-Branch one:
% 90.85/52.67 | (307) all_23_1_16 = 0
% 90.85/52.67 |
% 90.85/52.67 | Equations (307) can reduce 174 to:
% 90.85/52.67 | (275) $false
% 90.85/52.67 |
% 90.85/52.67 |-The branch is then unsatisfiable
% 90.85/52.67 |-Branch two:
% 90.85/52.67 | (174) ~ (all_23_1_16 = 0)
% 90.85/52.67 | (314) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 90.85/52.67 |
% 90.85/52.67 +-Applying beta-rule and splitting (197), into two cases.
% 90.85/52.67 |-Branch one:
% 90.85/52.67 | (307) all_23_1_16 = 0
% 90.85/52.67 |
% 90.85/52.67 | Equations (307) can reduce 174 to:
% 90.85/52.67 | (275) $false
% 90.85/52.67 |
% 90.85/52.67 |-The branch is then unsatisfiable
% 90.85/52.67 |-Branch two:
% 90.85/52.67 | (174) ~ (all_23_1_16 = 0)
% 90.85/52.67 | (318) all_21_1_13 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v1 & apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 90.85/52.67 |
% 90.85/52.67 +-Applying beta-rule and splitting (198), into two cases.
% 90.85/52.67 |-Branch one:
% 90.85/52.67 | (307) all_23_1_16 = 0
% 90.85/52.67 |
% 90.85/52.67 | Equations (307) can reduce 174 to:
% 90.85/52.67 | (275) $false
% 90.85/52.67 |
% 90.85/52.67 |-The branch is then unsatisfiable
% 90.85/52.67 |-Branch two:
% 90.85/52.67 | (174) ~ (all_23_1_16 = 0)
% 90.85/52.67 | (322) all_21_1_13 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 90.85/52.67 |
% 90.85/52.67 +-Applying beta-rule and splitting (200), into two cases.
% 90.85/52.67 |-Branch one:
% 90.85/52.67 | (307) all_23_1_16 = 0
% 90.85/52.67 |
% 90.85/52.67 | Equations (307) can reduce 174 to:
% 90.85/52.67 | (275) $false
% 90.85/52.68 |
% 90.85/52.68 |-The branch is then unsatisfiable
% 90.85/52.68 |-Branch two:
% 90.85/52.68 | (174) ~ (all_23_1_16 = 0)
% 90.85/52.68 | (326) all_21_1_13 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.85/52.68 |
% 90.85/52.68 +-Applying beta-rule and splitting (199), into two cases.
% 90.85/52.68 |-Branch one:
% 90.85/52.68 | (307) all_23_1_16 = 0
% 90.85/52.68 |
% 90.85/52.68 | Equations (307) can reduce 174 to:
% 90.85/52.68 | (275) $false
% 90.85/52.68 |
% 90.85/52.68 |-The branch is then unsatisfiable
% 90.85/52.68 |-Branch two:
% 90.85/52.68 | (174) ~ (all_23_1_16 = 0)
% 90.85/52.68 | (330) all_21_1_13 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.85/52.68 |
% 90.85/52.68 +-Applying beta-rule and splitting (193), into two cases.
% 90.85/52.68 |-Branch one:
% 90.85/52.68 | (293) all_33_1_31 = 0
% 90.85/52.68 |
% 90.85/52.68 | Equations (293) can reduce 177 to:
% 90.85/52.68 | (275) $false
% 90.85/52.68 |
% 90.85/52.68 |-The branch is then unsatisfiable
% 90.85/52.68 |-Branch two:
% 90.85/52.68 | (177) ~ (all_33_1_31 = 0)
% 90.85/52.68 | (334) all_21_1_13 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_33_2_32) = v2 & distinct_lines(all_1_2_2, all_33_2_32) = v1 & distinct_points(all_1_5_5, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.85/52.68 |
% 90.85/52.68 +-Applying beta-rule and splitting (194), into two cases.
% 90.85/52.68 |-Branch one:
% 90.85/52.68 | (293) all_33_1_31 = 0
% 90.85/52.68 |
% 90.85/52.68 | Equations (293) can reduce 177 to:
% 90.85/52.68 | (275) $false
% 90.85/52.68 |
% 90.85/52.68 |-The branch is then unsatisfiable
% 90.85/52.68 |-Branch two:
% 90.85/52.68 | (177) ~ (all_33_1_31 = 0)
% 90.85/52.68 | (338) all_21_1_13 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_33_2_32) = v3 & distinct_lines(all_1_2_2, all_33_2_32) = v1 & distinct_points(all_1_0_0, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.85/52.68 |
% 90.85/52.68 +-Applying beta-rule and splitting (188), into two cases.
% 90.85/52.68 |-Branch one:
% 90.85/52.68 | (293) all_33_1_31 = 0
% 90.85/52.68 |
% 90.85/52.68 | Equations (293) can reduce 177 to:
% 90.85/52.68 | (275) $false
% 90.85/52.68 |
% 90.85/52.68 |-The branch is then unsatisfiable
% 90.85/52.68 |-Branch two:
% 90.85/52.68 | (177) ~ (all_33_1_31 = 0)
% 90.85/52.68 | (342) all_23_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_33_2_32) = v3 & distinct_lines(all_1_1_1, all_33_2_32) = v1 & distinct_points(all_1_0_0, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.85/52.68 |
% 90.85/52.68 +-Applying beta-rule and splitting (195), into two cases.
% 90.85/52.68 |-Branch one:
% 90.85/52.68 | (293) all_33_1_31 = 0
% 90.85/52.68 |
% 90.85/52.68 | Equations (293) can reduce 177 to:
% 90.85/52.68 | (275) $false
% 90.85/52.68 |
% 90.85/52.68 |-The branch is then unsatisfiable
% 90.85/52.68 |-Branch two:
% 90.85/52.68 | (177) ~ (all_33_1_31 = 0)
% 90.85/52.68 | (346) all_21_1_13 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_33_2_32) = v2 & distinct_lines(all_33_2_32, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.85/52.68 |
% 90.85/52.68 +-Applying beta-rule and splitting (196), into two cases.
% 90.85/52.68 |-Branch one:
% 90.85/52.68 | (307) all_23_1_16 = 0
% 90.85/52.68 |
% 90.85/52.68 | Equations (307) can reduce 174 to:
% 90.85/52.68 | (275) $false
% 90.85/52.68 |
% 90.85/52.68 |-The branch is then unsatisfiable
% 90.85/52.68 |-Branch two:
% 90.85/52.68 | (174) ~ (all_23_1_16 = 0)
% 90.85/52.68 | (350) all_21_1_13 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_1_1) = v1 & apart_point_and_line(all_1_0_0, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 90.85/52.68 |
% 90.85/52.68 +-Applying beta-rule and splitting (186), into two cases.
% 90.85/52.68 |-Branch one:
% 90.85/52.68 | (293) all_33_1_31 = 0
% 90.85/52.68 |
% 90.85/52.68 | Equations (293) can reduce 177 to:
% 90.85/52.68 | (275) $false
% 90.85/52.68 |
% 90.85/52.68 |-The branch is then unsatisfiable
% 90.85/52.68 |-Branch two:
% 90.85/52.68 | (177) ~ (all_33_1_31 = 0)
% 90.85/52.68 | (354) all_23_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_33_2_32) = v3 & distinct_lines(all_33_2_32, all_1_1_1) = v1 & distinct_points(all_1_0_0, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.85/52.68 |
% 90.85/52.68 +-Applying beta-rule and splitting (187), into two cases.
% 90.85/52.68 |-Branch one:
% 90.85/52.68 | (293) all_33_1_31 = 0
% 90.85/52.68 |
% 90.85/52.68 | Equations (293) can reduce 177 to:
% 90.85/52.68 | (275) $false
% 90.85/52.68 |
% 90.85/52.68 |-The branch is then unsatisfiable
% 90.85/52.68 |-Branch two:
% 90.85/52.68 | (177) ~ (all_33_1_31 = 0)
% 90.85/52.68 | (358) all_23_1_16 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_33_2_32) = v2 & distinct_lines(all_1_1_1, all_33_2_32) = v1 & distinct_points(all_1_5_5, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.85/52.68 |
% 90.85/52.68 +-Applying beta-rule and splitting (318), into two cases.
% 90.85/52.68 |-Branch one:
% 90.85/52.68 | (274) all_21_1_13 = 0
% 90.85/52.68 |
% 90.85/52.68 | Equations (274) can reduce 168 to:
% 90.85/52.68 | (275) $false
% 90.85/52.68 |
% 90.85/52.68 |-The branch is then unsatisfiable
% 90.85/52.68 |-Branch two:
% 90.85/52.68 | (168) ~ (all_21_1_13 = 0)
% 90.85/52.68 | (362) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v1 & apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 90.85/52.68 |
% 90.85/52.68 +-Applying beta-rule and splitting (322), into two cases.
% 90.85/52.68 |-Branch one:
% 90.85/52.68 | (274) all_21_1_13 = 0
% 90.85/52.68 |
% 90.85/52.68 | Equations (274) can reduce 168 to:
% 90.85/52.68 | (275) $false
% 90.85/52.68 |
% 90.85/52.68 |-The branch is then unsatisfiable
% 90.85/52.68 |-Branch two:
% 90.85/52.68 | (168) ~ (all_21_1_13 = 0)
% 90.85/52.68 | (366) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 90.85/52.68 |
% 90.85/52.68 +-Applying beta-rule and splitting (326), into two cases.
% 90.85/52.68 |-Branch one:
% 90.85/52.68 | (274) all_21_1_13 = 0
% 90.85/52.68 |
% 90.85/52.68 | Equations (274) can reduce 168 to:
% 90.85/52.68 | (275) $false
% 90.85/52.68 |
% 90.85/52.68 |-The branch is then unsatisfiable
% 90.85/52.68 |-Branch two:
% 90.85/52.68 | (168) ~ (all_21_1_13 = 0)
% 90.85/52.68 | (370) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v3 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.85/52.68 |
% 90.85/52.68 | Instantiating (370) with all_215_0_119, all_215_1_120, all_215_2_121, all_215_3_122 yields:
% 90.85/52.68 | (371) apart_point_and_line(all_1_5_5, all_1_1_1) = all_215_1_120 & apart_point_and_line(all_1_5_5, all_1_2_2) = all_215_0_119 & distinct_lines(all_1_1_1, all_1_2_2) = all_215_2_121 & distinct_points(all_1_5_5, all_1_5_5) = all_215_3_122 & ( ~ (all_215_2_121 = 0) | ~ (all_215_3_122 = 0) | all_215_0_119 = 0 | all_215_1_120 = 0)
% 90.85/52.68 |
% 90.85/52.68 | Applying alpha-rule on (371) yields:
% 90.85/52.68 | (372) distinct_points(all_1_5_5, all_1_5_5) = all_215_3_122
% 90.85/52.68 | (373) ~ (all_215_2_121 = 0) | ~ (all_215_3_122 = 0) | all_215_0_119 = 0 | all_215_1_120 = 0
% 90.85/52.68 | (374) apart_point_and_line(all_1_5_5, all_1_1_1) = all_215_1_120
% 90.85/52.68 | (375) distinct_lines(all_1_1_1, all_1_2_2) = all_215_2_121
% 90.85/52.68 | (376) apart_point_and_line(all_1_5_5, all_1_2_2) = all_215_0_119
% 90.85/52.68 |
% 90.85/52.68 +-Applying beta-rule and splitting (330), into two cases.
% 90.85/52.68 |-Branch one:
% 90.85/52.68 | (274) all_21_1_13 = 0
% 90.85/52.68 |
% 90.85/52.68 | Equations (274) can reduce 168 to:
% 90.85/52.68 | (275) $false
% 90.85/52.68 |
% 90.85/52.68 |-The branch is then unsatisfiable
% 90.85/52.68 |-Branch two:
% 90.85/52.68 | (168) ~ (all_21_1_13 = 0)
% 90.85/52.68 | (380) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.85/52.68 |
% 90.85/52.68 | Instantiating (380) with all_220_0_123, all_220_1_124, all_220_2_125, all_220_3_126 yields:
% 90.85/52.68 | (381) apart_point_and_line(all_1_5_5, all_1_1_1) = all_220_0_123 & apart_point_and_line(all_1_5_5, all_1_2_2) = all_220_1_124 & distinct_lines(all_1_1_1, all_1_2_2) = all_220_2_125 & distinct_points(all_1_5_5, all_1_5_5) = all_220_3_126 & ( ~ (all_220_2_125 = 0) | ~ (all_220_3_126 = 0) | all_220_0_123 = 0 | all_220_1_124 = 0)
% 90.85/52.68 |
% 90.85/52.68 | Applying alpha-rule on (381) yields:
% 90.85/52.68 | (382) ~ (all_220_2_125 = 0) | ~ (all_220_3_126 = 0) | all_220_0_123 = 0 | all_220_1_124 = 0
% 90.85/52.68 | (383) apart_point_and_line(all_1_5_5, all_1_2_2) = all_220_1_124
% 90.85/52.68 | (384) apart_point_and_line(all_1_5_5, all_1_1_1) = all_220_0_123
% 90.85/52.68 | (385) distinct_lines(all_1_1_1, all_1_2_2) = all_220_2_125
% 90.99/52.68 | (386) distinct_points(all_1_5_5, all_1_5_5) = all_220_3_126
% 90.99/52.68 |
% 90.99/52.68 +-Applying beta-rule and splitting (334), into two cases.
% 90.99/52.68 |-Branch one:
% 90.99/52.68 | (274) all_21_1_13 = 0
% 90.99/52.68 |
% 90.99/52.68 | Equations (274) can reduce 168 to:
% 90.99/52.68 | (275) $false
% 90.99/52.68 |
% 90.99/52.68 |-The branch is then unsatisfiable
% 90.99/52.68 |-Branch two:
% 90.99/52.68 | (168) ~ (all_21_1_13 = 0)
% 90.99/52.68 | (390) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_33_2_32) = v2 & distinct_lines(all_1_2_2, all_33_2_32) = v1 & distinct_points(all_1_5_5, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.99/52.68 |
% 90.99/52.68 | Instantiating (390) with all_225_0_127, all_225_1_128, all_225_2_129, all_225_3_130 yields:
% 90.99/52.68 | (391) apart_point_and_line(all_1_0_0, all_1_2_2) = all_225_0_127 & apart_point_and_line(all_1_5_5, all_33_2_32) = all_225_1_128 & distinct_lines(all_1_2_2, all_33_2_32) = all_225_2_129 & distinct_points(all_1_5_5, all_1_0_0) = all_225_3_130 & ( ~ (all_225_2_129 = 0) | ~ (all_225_3_130 = 0) | all_225_0_127 = 0 | all_225_1_128 = 0)
% 90.99/52.68 |
% 90.99/52.68 | Applying alpha-rule on (391) yields:
% 90.99/52.68 | (392) distinct_points(all_1_5_5, all_1_0_0) = all_225_3_130
% 90.99/52.68 | (393) apart_point_and_line(all_1_5_5, all_33_2_32) = all_225_1_128
% 90.99/52.68 | (394) ~ (all_225_2_129 = 0) | ~ (all_225_3_130 = 0) | all_225_0_127 = 0 | all_225_1_128 = 0
% 90.99/52.68 | (395) apart_point_and_line(all_1_0_0, all_1_2_2) = all_225_0_127
% 90.99/52.68 | (396) distinct_lines(all_1_2_2, all_33_2_32) = all_225_2_129
% 90.99/52.68 |
% 90.99/52.68 +-Applying beta-rule and splitting (338), into two cases.
% 90.99/52.68 |-Branch one:
% 90.99/52.68 | (274) all_21_1_13 = 0
% 90.99/52.68 |
% 90.99/52.68 | Equations (274) can reduce 168 to:
% 90.99/52.68 | (275) $false
% 90.99/52.68 |
% 90.99/52.68 |-The branch is then unsatisfiable
% 90.99/52.68 |-Branch two:
% 90.99/52.68 | (168) ~ (all_21_1_13 = 0)
% 90.99/52.69 | (400) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_33_2_32) = v3 & distinct_lines(all_1_2_2, all_33_2_32) = v1 & distinct_points(all_1_0_0, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.99/52.69 |
% 90.99/52.69 | Instantiating (400) with all_230_0_131, all_230_1_132, all_230_2_133, all_230_3_134 yields:
% 90.99/52.69 | (401) apart_point_and_line(all_1_0_0, all_1_2_2) = all_230_1_132 & apart_point_and_line(all_1_5_5, all_33_2_32) = all_230_0_131 & distinct_lines(all_1_2_2, all_33_2_32) = all_230_2_133 & distinct_points(all_1_0_0, all_1_5_5) = all_230_3_134 & ( ~ (all_230_2_133 = 0) | ~ (all_230_3_134 = 0) | all_230_0_131 = 0 | all_230_1_132 = 0)
% 90.99/52.69 |
% 90.99/52.69 | Applying alpha-rule on (401) yields:
% 90.99/52.69 | (402) distinct_lines(all_1_2_2, all_33_2_32) = all_230_2_133
% 90.99/52.69 | (403) distinct_points(all_1_0_0, all_1_5_5) = all_230_3_134
% 90.99/52.69 | (404) apart_point_and_line(all_1_5_5, all_33_2_32) = all_230_0_131
% 90.99/52.69 | (405) ~ (all_230_2_133 = 0) | ~ (all_230_3_134 = 0) | all_230_0_131 = 0 | all_230_1_132 = 0
% 90.99/52.69 | (406) apart_point_and_line(all_1_0_0, all_1_2_2) = all_230_1_132
% 90.99/52.69 |
% 90.99/52.69 +-Applying beta-rule and splitting (342), into two cases.
% 90.99/52.69 |-Branch one:
% 90.99/52.69 | (307) all_23_1_16 = 0
% 90.99/52.69 |
% 90.99/52.69 | Equations (307) can reduce 174 to:
% 90.99/52.69 | (275) $false
% 90.99/52.69 |
% 90.99/52.69 |-The branch is then unsatisfiable
% 90.99/52.69 |-Branch two:
% 90.99/52.69 | (174) ~ (all_23_1_16 = 0)
% 90.99/52.69 | (410) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_33_2_32) = v3 & distinct_lines(all_1_1_1, all_33_2_32) = v1 & distinct_points(all_1_0_0, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.99/52.69 |
% 90.99/52.69 | Instantiating (410) with all_235_0_135, all_235_1_136, all_235_2_137, all_235_3_138 yields:
% 90.99/52.69 | (411) apart_point_and_line(all_1_0_0, all_1_1_1) = all_235_1_136 & apart_point_and_line(all_1_5_5, all_33_2_32) = all_235_0_135 & distinct_lines(all_1_1_1, all_33_2_32) = all_235_2_137 & distinct_points(all_1_0_0, all_1_5_5) = all_235_3_138 & ( ~ (all_235_2_137 = 0) | ~ (all_235_3_138 = 0) | all_235_0_135 = 0 | all_235_1_136 = 0)
% 90.99/52.69 |
% 90.99/52.69 | Applying alpha-rule on (411) yields:
% 90.99/52.69 | (412) distinct_points(all_1_0_0, all_1_5_5) = all_235_3_138
% 90.99/52.69 | (413) apart_point_and_line(all_1_5_5, all_33_2_32) = all_235_0_135
% 90.99/52.69 | (414) apart_point_and_line(all_1_0_0, all_1_1_1) = all_235_1_136
% 90.99/52.69 | (415) ~ (all_235_2_137 = 0) | ~ (all_235_3_138 = 0) | all_235_0_135 = 0 | all_235_1_136 = 0
% 90.99/52.69 | (416) distinct_lines(all_1_1_1, all_33_2_32) = all_235_2_137
% 90.99/52.69 |
% 90.99/52.69 +-Applying beta-rule and splitting (346), into two cases.
% 90.99/52.69 |-Branch one:
% 90.99/52.69 | (274) all_21_1_13 = 0
% 90.99/52.69 |
% 90.99/52.69 | Equations (274) can reduce 168 to:
% 90.99/52.69 | (275) $false
% 90.99/52.69 |
% 90.99/52.69 |-The branch is then unsatisfiable
% 90.99/52.69 |-Branch two:
% 90.99/52.69 | (168) ~ (all_21_1_13 = 0)
% 90.99/52.69 | (420) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_33_2_32) = v2 & distinct_lines(all_33_2_32, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.99/52.69 |
% 90.99/52.69 | Instantiating (420) with all_240_0_139, all_240_1_140, all_240_2_141, all_240_3_142 yields:
% 90.99/52.69 | (421) apart_point_and_line(all_1_0_0, all_1_2_2) = all_240_0_139 & apart_point_and_line(all_1_5_5, all_33_2_32) = all_240_1_140 & distinct_lines(all_33_2_32, all_1_2_2) = all_240_2_141 & distinct_points(all_1_5_5, all_1_0_0) = all_240_3_142 & ( ~ (all_240_2_141 = 0) | ~ (all_240_3_142 = 0) | all_240_0_139 = 0 | all_240_1_140 = 0)
% 90.99/52.69 |
% 90.99/52.69 | Applying alpha-rule on (421) yields:
% 90.99/52.69 | (422) apart_point_and_line(all_1_0_0, all_1_2_2) = all_240_0_139
% 90.99/52.69 | (423) apart_point_and_line(all_1_5_5, all_33_2_32) = all_240_1_140
% 90.99/52.69 | (424) distinct_points(all_1_5_5, all_1_0_0) = all_240_3_142
% 90.99/52.69 | (425) ~ (all_240_2_141 = 0) | ~ (all_240_3_142 = 0) | all_240_0_139 = 0 | all_240_1_140 = 0
% 90.99/52.69 | (426) distinct_lines(all_33_2_32, all_1_2_2) = all_240_2_141
% 90.99/52.69 |
% 90.99/52.69 +-Applying beta-rule and splitting (350), into two cases.
% 90.99/52.69 |-Branch one:
% 90.99/52.69 | (274) all_21_1_13 = 0
% 90.99/52.69 |
% 90.99/52.69 | Equations (274) can reduce 168 to:
% 90.99/52.69 | (275) $false
% 90.99/52.69 |
% 90.99/52.69 |-The branch is then unsatisfiable
% 90.99/52.69 |-Branch two:
% 90.99/52.69 | (168) ~ (all_21_1_13 = 0)
% 90.99/52.69 | (430) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_1_1) = v1 & apart_point_and_line(all_1_0_0, all_1_2_2) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 90.99/52.69 |
% 90.99/52.69 | Instantiating (430) with all_245_0_143, all_245_1_144, all_245_2_145 yields:
% 90.99/52.69 | (431) apart_point_and_line(all_1_0_0, all_1_1_1) = all_245_1_144 & apart_point_and_line(all_1_0_0, all_1_2_2) = all_245_0_143 & distinct_lines(all_1_1_1, all_1_2_2) = all_245_2_145 & ( ~ (all_245_2_145 = 0) | all_245_0_143 = 0 | all_245_1_144 = 0)
% 90.99/52.69 |
% 90.99/52.69 | Applying alpha-rule on (431) yields:
% 90.99/52.69 | (432) apart_point_and_line(all_1_0_0, all_1_1_1) = all_245_1_144
% 90.99/52.69 | (433) apart_point_and_line(all_1_0_0, all_1_2_2) = all_245_0_143
% 90.99/52.69 | (434) distinct_lines(all_1_1_1, all_1_2_2) = all_245_2_145
% 90.99/52.69 | (435) ~ (all_245_2_145 = 0) | all_245_0_143 = 0 | all_245_1_144 = 0
% 90.99/52.69 |
% 90.99/52.69 +-Applying beta-rule and splitting (354), into two cases.
% 90.99/52.69 |-Branch one:
% 90.99/52.69 | (307) all_23_1_16 = 0
% 90.99/52.69 |
% 90.99/52.69 | Equations (307) can reduce 174 to:
% 90.99/52.69 | (275) $false
% 90.99/52.69 |
% 90.99/52.69 |-The branch is then unsatisfiable
% 90.99/52.69 |-Branch two:
% 90.99/52.69 | (174) ~ (all_23_1_16 = 0)
% 90.99/52.69 | (439) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_33_2_32) = v3 & distinct_lines(all_33_2_32, all_1_1_1) = v1 & distinct_points(all_1_0_0, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.99/52.69 |
% 90.99/52.69 | Instantiating (439) with all_250_0_146, all_250_1_147, all_250_2_148, all_250_3_149 yields:
% 90.99/52.69 | (440) apart_point_and_line(all_1_0_0, all_1_1_1) = all_250_1_147 & apart_point_and_line(all_1_5_5, all_33_2_32) = all_250_0_146 & distinct_lines(all_33_2_32, all_1_1_1) = all_250_2_148 & distinct_points(all_1_0_0, all_1_5_5) = all_250_3_149 & ( ~ (all_250_2_148 = 0) | ~ (all_250_3_149 = 0) | all_250_0_146 = 0 | all_250_1_147 = 0)
% 90.99/52.69 |
% 90.99/52.69 | Applying alpha-rule on (440) yields:
% 90.99/52.69 | (441) distinct_lines(all_33_2_32, all_1_1_1) = all_250_2_148
% 90.99/52.69 | (442) ~ (all_250_2_148 = 0) | ~ (all_250_3_149 = 0) | all_250_0_146 = 0 | all_250_1_147 = 0
% 90.99/52.69 | (443) apart_point_and_line(all_1_0_0, all_1_1_1) = all_250_1_147
% 90.99/52.69 | (444) distinct_points(all_1_0_0, all_1_5_5) = all_250_3_149
% 90.99/52.69 | (445) apart_point_and_line(all_1_5_5, all_33_2_32) = all_250_0_146
% 90.99/52.69 |
% 90.99/52.69 +-Applying beta-rule and splitting (358), into two cases.
% 90.99/52.69 |-Branch one:
% 90.99/52.69 | (307) all_23_1_16 = 0
% 90.99/52.69 |
% 90.99/52.69 | Equations (307) can reduce 174 to:
% 90.99/52.69 | (275) $false
% 90.99/52.69 |
% 90.99/52.69 |-The branch is then unsatisfiable
% 90.99/52.69 |-Branch two:
% 90.99/52.69 | (174) ~ (all_23_1_16 = 0)
% 90.99/52.69 | (449) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_0_0, all_1_1_1) = v3 & apart_point_and_line(all_1_5_5, all_33_2_32) = v2 & distinct_lines(all_1_1_1, all_33_2_32) = v1 & distinct_points(all_1_5_5, all_1_0_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 90.99/52.69 |
% 90.99/52.69 | Instantiating (449) with all_255_0_150, all_255_1_151, all_255_2_152, all_255_3_153 yields:
% 90.99/52.69 | (450) apart_point_and_line(all_1_0_0, all_1_1_1) = all_255_0_150 & apart_point_and_line(all_1_5_5, all_33_2_32) = all_255_1_151 & distinct_lines(all_1_1_1, all_33_2_32) = all_255_2_152 & distinct_points(all_1_5_5, all_1_0_0) = all_255_3_153 & ( ~ (all_255_2_152 = 0) | ~ (all_255_3_153 = 0) | all_255_0_150 = 0 | all_255_1_151 = 0)
% 90.99/52.69 |
% 90.99/52.69 | Applying alpha-rule on (450) yields:
% 90.99/52.69 | (451) apart_point_and_line(all_1_0_0, all_1_1_1) = all_255_0_150
% 90.99/52.69 | (452) distinct_points(all_1_5_5, all_1_0_0) = all_255_3_153
% 90.99/52.69 | (453) apart_point_and_line(all_1_5_5, all_33_2_32) = all_255_1_151
% 90.99/52.69 | (454) distinct_lines(all_1_1_1, all_33_2_32) = all_255_2_152
% 90.99/52.69 | (455) ~ (all_255_2_152 = 0) | ~ (all_255_3_153 = 0) | all_255_0_150 = 0 | all_255_1_151 = 0
% 90.99/52.69 |
% 90.99/52.69 +-Applying beta-rule and splitting (207), into two cases.
% 90.99/52.69 |-Branch one:
% 90.99/52.69 | (456) all_33_0_30 = 0
% 90.99/52.69 |
% 90.99/52.69 | Equations (456) can reduce 176 to:
% 90.99/52.69 | (275) $false
% 90.99/52.69 |
% 90.99/52.69 |-The branch is then unsatisfiable
% 90.99/52.69 |-Branch two:
% 90.99/52.69 | (176) ~ (all_33_0_30 = 0)
% 90.99/52.69 | (459) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_0_0, all_1_0_0) = v1 & apart_point_and_line(all_1_0_0, v1) = v2 & distinct_points(all_1_0_0, all_1_0_0) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 90.99/52.69 |
% 90.99/52.69 | Instantiating (459) with all_303_0_175, all_303_1_176, all_303_2_177 yields:
% 90.99/52.69 | (460) line_connecting(all_1_0_0, all_1_0_0) = all_303_1_176 & apart_point_and_line(all_1_0_0, all_303_1_176) = all_303_0_175 & distinct_points(all_1_0_0, all_1_0_0) = all_303_2_177 & ( ~ (all_303_0_175 = 0) | ~ (all_303_2_177 = 0))
% 90.99/52.69 |
% 90.99/52.69 | Applying alpha-rule on (460) yields:
% 90.99/52.69 | (461) line_connecting(all_1_0_0, all_1_0_0) = all_303_1_176
% 90.99/52.69 | (462) apart_point_and_line(all_1_0_0, all_303_1_176) = all_303_0_175
% 90.99/52.69 | (463) distinct_points(all_1_0_0, all_1_0_0) = all_303_2_177
% 90.99/52.69 | (464) ~ (all_303_0_175 = 0) | ~ (all_303_2_177 = 0)
% 90.99/52.69 |
% 90.99/52.69 | Instantiating formula (20) with all_1_0_0, all_1_1_1, all_250_1_147, all_255_0_150 and discharging atoms apart_point_and_line(all_1_0_0, all_1_1_1) = all_255_0_150, apart_point_and_line(all_1_0_0, all_1_1_1) = all_250_1_147, yields:
% 90.99/52.69 | (465) all_255_0_150 = all_250_1_147
% 90.99/52.69 |
% 90.99/52.69 | Instantiating formula (20) with all_1_0_0, all_1_1_1, all_245_1_144, all_255_0_150 and discharging atoms apart_point_and_line(all_1_0_0, all_1_1_1) = all_255_0_150, apart_point_and_line(all_1_0_0, all_1_1_1) = all_245_1_144, yields:
% 90.99/52.69 | (466) all_255_0_150 = all_245_1_144
% 90.99/52.69 |
% 90.99/52.69 | Instantiating formula (20) with all_1_0_0, all_1_1_1, all_235_1_136, all_255_0_150 and discharging atoms apart_point_and_line(all_1_0_0, all_1_1_1) = all_255_0_150, apart_point_and_line(all_1_0_0, all_1_1_1) = all_235_1_136, yields:
% 90.99/52.69 | (467) all_255_0_150 = all_235_1_136
% 90.99/52.69 |
% 90.99/52.69 | Instantiating formula (20) with all_1_0_0, all_1_1_1, all_114_2_75, all_235_1_136 and discharging atoms apart_point_and_line(all_1_0_0, all_1_1_1) = all_235_1_136, apart_point_and_line(all_1_0_0, all_1_1_1) = all_114_2_75, yields:
% 90.99/52.69 | (468) all_235_1_136 = all_114_2_75
% 90.99/52.69 |
% 90.99/52.69 | Instantiating formula (20) with all_1_0_0, all_1_1_1, all_106_1_61, all_114_2_75 and discharging atoms apart_point_and_line(all_1_0_0, all_1_1_1) = all_114_2_75, apart_point_and_line(all_1_0_0, all_1_1_1) = all_106_1_61, yields:
% 90.99/52.70 | (469) all_114_2_75 = all_106_1_61
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_0_0, all_1_1_1, all_102_1_55, all_19_1_10 and discharging atoms apart_point_and_line(all_1_0_0, all_1_1_1) = all_102_1_55, apart_point_and_line(all_1_0_0, all_1_1_1) = all_19_1_10, yields:
% 90.99/52.70 | (470) all_102_1_55 = all_19_1_10
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_0_0, all_1_1_1, all_102_1_55, all_106_1_61 and discharging atoms apart_point_and_line(all_1_0_0, all_1_1_1) = all_106_1_61, apart_point_and_line(all_1_0_0, all_1_1_1) = all_102_1_55, yields:
% 90.99/52.70 | (471) all_106_1_61 = all_102_1_55
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_0_0, all_1_1_1, all_98_2_50, all_250_1_147 and discharging atoms apart_point_and_line(all_1_0_0, all_1_1_1) = all_250_1_147, apart_point_and_line(all_1_0_0, all_1_1_1) = all_98_2_50, yields:
% 90.99/52.70 | (472) all_250_1_147 = all_98_2_50
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_0_0, all_1_2_2, all_230_1_132, all_245_0_143 and discharging atoms apart_point_and_line(all_1_0_0, all_1_2_2) = all_245_0_143, apart_point_and_line(all_1_0_0, all_1_2_2) = all_230_1_132, yields:
% 90.99/52.70 | (473) all_245_0_143 = all_230_1_132
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_0_0, all_1_2_2, all_230_1_132, all_240_0_139 and discharging atoms apart_point_and_line(all_1_0_0, all_1_2_2) = all_240_0_139, apart_point_and_line(all_1_0_0, all_1_2_2) = all_230_1_132, yields:
% 90.99/52.70 | (474) all_240_0_139 = all_230_1_132
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_0_0, all_1_2_2, all_225_0_127, all_245_0_143 and discharging atoms apart_point_and_line(all_1_0_0, all_1_2_2) = all_245_0_143, apart_point_and_line(all_1_0_0, all_1_2_2) = all_225_0_127, yields:
% 90.99/52.70 | (475) all_245_0_143 = all_225_0_127
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_0_0, all_1_2_2, all_129_0_87, all_240_0_139 and discharging atoms apart_point_and_line(all_1_0_0, all_1_2_2) = all_240_0_139, apart_point_and_line(all_1_0_0, all_1_2_2) = all_129_0_87, yields:
% 90.99/52.70 | (476) all_240_0_139 = all_129_0_87
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_0_0, all_1_2_2, all_129_1_88, all_240_0_139 and discharging atoms apart_point_and_line(all_1_0_0, all_1_2_2) = all_240_0_139, apart_point_and_line(all_1_0_0, all_1_2_2) = all_129_1_88, yields:
% 90.99/52.70 | (477) all_240_0_139 = all_129_1_88
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_0_0, all_1_2_2, all_114_3_76, all_129_1_88 and discharging atoms apart_point_and_line(all_1_0_0, all_1_2_2) = all_129_1_88, apart_point_and_line(all_1_0_0, all_1_2_2) = all_114_3_76, yields:
% 90.99/52.70 | (478) all_129_1_88 = all_114_3_76
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_0_0, all_1_2_2, all_104_1_58, all_230_1_132 and discharging atoms apart_point_and_line(all_1_0_0, all_1_2_2) = all_230_1_132, apart_point_and_line(all_1_0_0, all_1_2_2) = all_104_1_58, yields:
% 90.99/52.70 | (479) all_230_1_132 = all_104_1_58
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_0_0, all_1_2_2, all_100_1_52, all_17_1_7 and discharging atoms apart_point_and_line(all_1_0_0, all_1_2_2) = all_100_1_52, apart_point_and_line(all_1_0_0, all_1_2_2) = all_17_1_7, yields:
% 90.99/52.70 | (480) all_100_1_52 = all_17_1_7
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_0_0, all_1_2_2, all_100_1_52, all_114_3_76 and discharging atoms apart_point_and_line(all_1_0_0, all_1_2_2) = all_114_3_76, apart_point_and_line(all_1_0_0, all_1_2_2) = all_100_1_52, yields:
% 90.99/52.70 | (481) all_114_3_76 = all_100_1_52
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_0_0, all_1_2_2, all_94_2_44, all_114_3_76 and discharging atoms apart_point_and_line(all_1_0_0, all_1_2_2) = all_114_3_76, apart_point_and_line(all_1_0_0, all_1_2_2) = all_94_2_44, yields:
% 90.99/52.70 | (482) all_114_3_76 = all_94_2_44
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_5_5, all_1_1_1, all_215_1_120, all_220_0_123 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_220_0_123, apart_point_and_line(all_1_5_5, all_1_1_1) = all_215_1_120, yields:
% 90.99/52.70 | (483) all_220_0_123 = all_215_1_120
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_5_5, all_1_1_1, all_120_1_85, all_23_1_16 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_120_1_85, apart_point_and_line(all_1_5_5, all_1_1_1) = all_23_1_16, yields:
% 90.99/52.70 | (484) all_120_1_85 = all_23_1_16
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_5_5, all_1_1_1, all_120_1_85, all_215_1_120 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_215_1_120, apart_point_and_line(all_1_5_5, all_1_1_1) = all_120_1_85, yields:
% 90.99/52.70 | (485) all_215_1_120 = all_120_1_85
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_5_5, all_1_1_1, all_116_2_79, all_220_0_123 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_220_0_123, apart_point_and_line(all_1_5_5, all_1_1_1) = all_116_2_79, yields:
% 90.99/52.70 | (486) all_220_0_123 = all_116_2_79
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_5_5, all_1_1_1, all_114_0_73, all_120_1_85 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_120_1_85, apart_point_and_line(all_1_5_5, all_1_1_1) = all_114_0_73, yields:
% 90.99/52.70 | (487) all_120_1_85 = all_114_0_73
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_5_5, all_1_2_2, all_215_0_119, all_21_1_13 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_215_0_119, apart_point_and_line(all_1_5_5, all_1_2_2) = all_21_1_13, yields:
% 90.99/52.70 | (488) all_215_0_119 = all_21_1_13
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_5_5, all_1_2_2, all_134_0_90, all_215_0_119 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_215_0_119, apart_point_and_line(all_1_5_5, all_1_2_2) = all_134_0_90, yields:
% 90.99/52.70 | (489) all_215_0_119 = all_134_0_90
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_5_5, all_1_2_2, all_134_1_91, all_220_1_124 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_220_1_124, apart_point_and_line(all_1_5_5, all_1_2_2) = all_134_1_91, yields:
% 90.99/52.70 | (490) all_220_1_124 = all_134_1_91
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_5_5, all_1_2_2, all_116_3_80, all_220_1_124 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_220_1_124, apart_point_and_line(all_1_5_5, all_1_2_2) = all_116_3_80, yields:
% 90.99/52.70 | (491) all_220_1_124 = all_116_3_80
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_5_5, all_1_2_2, all_114_1_74, all_220_1_124 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_220_1_124, apart_point_and_line(all_1_5_5, all_1_2_2) = all_114_1_74, yields:
% 90.99/52.70 | (492) all_220_1_124 = all_114_1_74
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_5_5, all_1_2_2, all_114_1_74, all_134_0_90 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_134_0_90, apart_point_and_line(all_1_5_5, all_1_2_2) = all_114_1_74, yields:
% 90.99/52.70 | (493) all_134_0_90 = all_114_1_74
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_5_5, all_1_2_2, all_112_3_72, all_134_1_91 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_134_1_91, apart_point_and_line(all_1_5_5, all_1_2_2) = all_112_3_72, yields:
% 90.99/52.70 | (494) all_134_1_91 = all_112_3_72
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_5_5, all_1_2_2, all_96_1_46, all_134_0_90 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_134_0_90, apart_point_and_line(all_1_5_5, all_1_2_2) = all_96_1_46, yields:
% 90.99/52.70 | (495) all_134_0_90 = all_96_1_46
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (20) with all_1_5_5, all_1_2_2, all_92_2_41, all_114_1_74 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_114_1_74, apart_point_and_line(all_1_5_5, all_1_2_2) = all_92_2_41, yields:
% 90.99/52.70 | (496) all_114_1_74 = all_92_2_41
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (3) with all_1_2_2, all_1_1_1, all_102_2_56, all_120_2_86 and discharging atoms convergent_lines(all_1_2_2, all_1_1_1) = all_120_2_86, convergent_lines(all_1_2_2, all_1_1_1) = all_102_2_56, yields:
% 90.99/52.70 | (497) all_120_2_86 = all_102_2_56
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (3) with all_1_2_2, all_1_1_1, all_100_2_53, 0 and discharging atoms convergent_lines(all_1_2_2, all_1_1_1) = all_100_2_53, convergent_lines(all_1_2_2, all_1_1_1) = 0, yields:
% 90.99/52.70 | (498) all_100_2_53 = 0
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (3) with all_1_2_2, all_1_1_1, all_100_2_53, all_102_2_56 and discharging atoms convergent_lines(all_1_2_2, all_1_1_1) = all_102_2_56, convergent_lines(all_1_2_2, all_1_1_1) = all_100_2_53, yields:
% 90.99/52.70 | (499) all_102_2_56 = all_100_2_53
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (3) with all_1_2_2, all_1_1_1, all_96_2_47, all_120_2_86 and discharging atoms convergent_lines(all_1_2_2, all_1_1_1) = all_120_2_86, convergent_lines(all_1_2_2, all_1_1_1) = all_96_2_47, yields:
% 90.99/52.70 | (500) all_120_2_86 = all_96_2_47
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (31) with all_1_0_0, all_1_0_0, all_148_3_103, all_303_2_177 and discharging atoms distinct_points(all_1_0_0, all_1_0_0) = all_303_2_177, distinct_points(all_1_0_0, all_1_0_0) = all_148_3_103, yields:
% 90.99/52.70 | (501) all_303_2_177 = all_148_3_103
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (31) with all_1_0_0, all_1_0_0, all_102_0_54, all_33_0_30 and discharging atoms distinct_points(all_1_0_0, all_1_0_0) = all_102_0_54, distinct_points(all_1_0_0, all_1_0_0) = all_33_0_30, yields:
% 90.99/52.70 | (502) all_102_0_54 = all_33_0_30
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (31) with all_1_0_0, all_1_0_0, all_102_0_54, all_148_3_103 and discharging atoms distinct_points(all_1_0_0, all_1_0_0) = all_148_3_103, distinct_points(all_1_0_0, all_1_0_0) = all_102_0_54, yields:
% 90.99/52.70 | (503) all_148_3_103 = all_102_0_54
% 90.99/52.70 |
% 90.99/52.70 | Instantiating formula (31) with all_1_0_0, all_1_0_0, all_100_0_51, all_303_2_177 and discharging atoms distinct_points(all_1_0_0, all_1_0_0) = all_303_2_177, distinct_points(all_1_0_0, all_1_0_0) = all_100_0_51, yields:
% 90.99/52.70 | (504) all_303_2_177 = all_100_0_51
% 90.99/52.70 |
% 90.99/52.70 | Using (234) and (119) yields:
% 90.99/52.70 | (505) ~ (all_100_0_51 = 0)
% 90.99/52.70 |
% 90.99/52.70 | Combining equations (501,504) yields a new equation:
% 90.99/52.70 | (506) all_148_3_103 = all_100_0_51
% 90.99/52.70 |
% 90.99/52.70 | Simplifying 506 yields:
% 90.99/52.70 | (507) all_148_3_103 = all_100_0_51
% 90.99/52.70 |
% 90.99/52.70 | Combining equations (467,466) yields a new equation:
% 90.99/52.70 | (508) all_245_1_144 = all_235_1_136
% 90.99/52.70 |
% 90.99/52.70 | Combining equations (465,466) yields a new equation:
% 90.99/52.70 | (509) all_250_1_147 = all_245_1_144
% 90.99/52.70 |
% 90.99/52.70 | Simplifying 509 yields:
% 90.99/52.70 | (510) all_250_1_147 = all_245_1_144
% 90.99/52.70 |
% 90.99/52.70 | Combining equations (510,472) yields a new equation:
% 90.99/52.70 | (511) all_245_1_144 = all_98_2_50
% 90.99/52.70 |
% 90.99/52.70 | Simplifying 511 yields:
% 90.99/52.70 | (512) all_245_1_144 = all_98_2_50
% 90.99/52.70 |
% 90.99/52.70 | Combining equations (473,475) yields a new equation:
% 90.99/52.70 | (513) all_230_1_132 = all_225_0_127
% 90.99/52.70 |
% 90.99/52.70 | Simplifying 513 yields:
% 90.99/52.70 | (514) all_230_1_132 = all_225_0_127
% 90.99/52.70 |
% 90.99/52.70 | Combining equations (508,512) yields a new equation:
% 90.99/52.70 | (515) all_235_1_136 = all_98_2_50
% 90.99/52.70 |
% 90.99/52.70 | Simplifying 515 yields:
% 90.99/52.70 | (516) all_235_1_136 = all_98_2_50
% 90.99/52.70 |
% 90.99/52.70 | Combining equations (474,476) yields a new equation:
% 90.99/52.70 | (517) all_230_1_132 = all_129_0_87
% 90.99/52.70 |
% 90.99/52.70 | Simplifying 517 yields:
% 90.99/52.70 | (518) all_230_1_132 = all_129_0_87
% 90.99/52.70 |
% 90.99/52.70 | Combining equations (477,476) yields a new equation:
% 90.99/52.70 | (519) all_129_0_87 = all_129_1_88
% 90.99/52.70 |
% 90.99/52.70 | Combining equations (468,516) yields a new equation:
% 90.99/52.70 | (520) all_114_2_75 = all_98_2_50
% 90.99/52.70 |
% 90.99/52.70 | Simplifying 520 yields:
% 90.99/52.70 | (521) all_114_2_75 = all_98_2_50
% 90.99/52.70 |
% 90.99/52.70 | Combining equations (479,514) yields a new equation:
% 90.99/52.70 | (522) all_225_0_127 = all_104_1_58
% 90.99/52.70 |
% 90.99/52.70 | Combining equations (518,514) yields a new equation:
% 90.99/52.70 | (523) all_225_0_127 = all_129_0_87
% 90.99/52.70 |
% 90.99/52.70 | Combining equations (523,522) yields a new equation:
% 90.99/52.70 | (524) all_129_0_87 = all_104_1_58
% 90.99/52.70 |
% 90.99/52.70 | Simplifying 524 yields:
% 90.99/52.70 | (525) all_129_0_87 = all_104_1_58
% 90.99/52.70 |
% 90.99/52.70 | Combining equations (483,486) yields a new equation:
% 90.99/52.70 | (526) all_215_1_120 = all_116_2_79
% 90.99/52.70 |
% 90.99/52.70 | Simplifying 526 yields:
% 90.99/52.70 | (527) all_215_1_120 = all_116_2_79
% 90.99/52.70 |
% 90.99/52.70 | Combining equations (490,491) yields a new equation:
% 90.99/52.70 | (528) all_134_1_91 = all_116_3_80
% 90.99/52.70 |
% 90.99/52.70 | Simplifying 528 yields:
% 90.99/52.70 | (529) all_134_1_91 = all_116_3_80
% 90.99/52.70 |
% 90.99/52.70 | Combining equations (492,491) yields a new equation:
% 90.99/52.70 | (530) all_116_3_80 = all_114_1_74
% 90.99/52.70 |
% 90.99/52.70 | Combining equations (489,488) yields a new equation:
% 90.99/52.70 | (531) all_134_0_90 = all_21_1_13
% 90.99/52.70 |
% 90.99/52.71 | Simplifying 531 yields:
% 90.99/52.71 | (532) all_134_0_90 = all_21_1_13
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (485,527) yields a new equation:
% 90.99/52.71 | (533) all_120_1_85 = all_116_2_79
% 90.99/52.71 |
% 90.99/52.71 | Simplifying 533 yields:
% 90.99/52.71 | (534) all_120_1_85 = all_116_2_79
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (503,507) yields a new equation:
% 90.99/52.71 | (535) all_102_0_54 = all_100_0_51
% 90.99/52.71 |
% 90.99/52.71 | Simplifying 535 yields:
% 90.99/52.71 | (536) all_102_0_54 = all_100_0_51
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (532,495) yields a new equation:
% 90.99/52.71 | (537) all_96_1_46 = all_21_1_13
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (493,495) yields a new equation:
% 90.99/52.71 | (538) all_114_1_74 = all_96_1_46
% 90.99/52.71 |
% 90.99/52.71 | Simplifying 538 yields:
% 90.99/52.71 | (539) all_114_1_74 = all_96_1_46
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (529,494) yields a new equation:
% 90.99/52.71 | (540) all_116_3_80 = all_112_3_72
% 90.99/52.71 |
% 90.99/52.71 | Simplifying 540 yields:
% 90.99/52.71 | (541) all_116_3_80 = all_112_3_72
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (519,525) yields a new equation:
% 90.99/52.71 | (542) all_129_1_88 = all_104_1_58
% 90.99/52.71 |
% 90.99/52.71 | Simplifying 542 yields:
% 90.99/52.71 | (543) all_129_1_88 = all_104_1_58
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (478,543) yields a new equation:
% 90.99/52.71 | (544) all_114_3_76 = all_104_1_58
% 90.99/52.71 |
% 90.99/52.71 | Simplifying 544 yields:
% 90.99/52.71 | (545) all_114_3_76 = all_104_1_58
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (484,534) yields a new equation:
% 90.99/52.71 | (546) all_116_2_79 = all_23_1_16
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (487,534) yields a new equation:
% 90.99/52.71 | (547) all_116_2_79 = all_114_0_73
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (497,500) yields a new equation:
% 90.99/52.71 | (548) all_102_2_56 = all_96_2_47
% 90.99/52.71 |
% 90.99/52.71 | Simplifying 548 yields:
% 90.99/52.71 | (549) all_102_2_56 = all_96_2_47
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (547,546) yields a new equation:
% 90.99/52.71 | (550) all_114_0_73 = all_23_1_16
% 90.99/52.71 |
% 90.99/52.71 | Simplifying 550 yields:
% 90.99/52.71 | (551) all_114_0_73 = all_23_1_16
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (530,541) yields a new equation:
% 90.99/52.71 | (552) all_114_1_74 = all_112_3_72
% 90.99/52.71 |
% 90.99/52.71 | Simplifying 552 yields:
% 90.99/52.71 | (553) all_114_1_74 = all_112_3_72
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (539,553) yields a new equation:
% 90.99/52.71 | (554) all_112_3_72 = all_96_1_46
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (496,553) yields a new equation:
% 90.99/52.71 | (555) all_112_3_72 = all_92_2_41
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (469,521) yields a new equation:
% 90.99/52.71 | (556) all_106_1_61 = all_98_2_50
% 90.99/52.71 |
% 90.99/52.71 | Simplifying 556 yields:
% 90.99/52.71 | (557) all_106_1_61 = all_98_2_50
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (481,545) yields a new equation:
% 90.99/52.71 | (558) all_104_1_58 = all_100_1_52
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (482,545) yields a new equation:
% 90.99/52.71 | (559) all_104_1_58 = all_94_2_44
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (554,555) yields a new equation:
% 90.99/52.71 | (560) all_96_1_46 = all_92_2_41
% 90.99/52.71 |
% 90.99/52.71 | Simplifying 560 yields:
% 90.99/52.71 | (561) all_96_1_46 = all_92_2_41
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (471,557) yields a new equation:
% 90.99/52.71 | (562) all_102_1_55 = all_98_2_50
% 90.99/52.71 |
% 90.99/52.71 | Simplifying 562 yields:
% 90.99/52.71 | (563) all_102_1_55 = all_98_2_50
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (558,559) yields a new equation:
% 90.99/52.71 | (564) all_100_1_52 = all_94_2_44
% 90.99/52.71 |
% 90.99/52.71 | Simplifying 564 yields:
% 90.99/52.71 | (565) all_100_1_52 = all_94_2_44
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (502,536) yields a new equation:
% 90.99/52.71 | (566) all_100_0_51 = all_33_0_30
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (470,563) yields a new equation:
% 90.99/52.71 | (567) all_98_2_50 = all_19_1_10
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (499,549) yields a new equation:
% 90.99/52.71 | (568) all_100_2_53 = all_96_2_47
% 90.99/52.71 |
% 90.99/52.71 | Simplifying 568 yields:
% 90.99/52.71 | (569) all_100_2_53 = all_96_2_47
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (480,565) yields a new equation:
% 90.99/52.71 | (570) all_94_2_44 = all_17_1_7
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (498,569) yields a new equation:
% 90.99/52.71 | (571) all_96_2_47 = 0
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (561,537) yields a new equation:
% 90.99/52.71 | (572) all_92_2_41 = all_21_1_13
% 90.99/52.71 |
% 90.99/52.71 | Simplifying 572 yields:
% 90.99/52.71 | (573) all_92_2_41 = all_21_1_13
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (571,569) yields a new equation:
% 90.99/52.71 | (498) all_100_2_53 = 0
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (570,565) yields a new equation:
% 90.99/52.71 | (480) all_100_1_52 = all_17_1_7
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (570,559) yields a new equation:
% 90.99/52.71 | (576) all_104_1_58 = all_17_1_7
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (573,555) yields a new equation:
% 90.99/52.71 | (577) all_112_3_72 = all_21_1_13
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (576,545) yields a new equation:
% 90.99/52.71 | (578) all_114_3_76 = all_17_1_7
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (567,521) yields a new equation:
% 90.99/52.71 | (579) all_114_2_75 = all_19_1_10
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (577,553) yields a new equation:
% 90.99/52.71 | (580) all_114_1_74 = all_21_1_13
% 90.99/52.71 |
% 90.99/52.71 | Equations (566) can reduce 505 to:
% 90.99/52.71 | (176) ~ (all_33_0_30 = 0)
% 90.99/52.71 |
% 90.99/52.71 +-Applying beta-rule and splitting (208), into two cases.
% 90.99/52.71 |-Branch one:
% 90.99/52.71 | (456) all_33_0_30 = 0
% 90.99/52.71 |
% 90.99/52.71 | Equations (456) can reduce 176 to:
% 90.99/52.71 | (275) $false
% 90.99/52.71 |
% 90.99/52.71 |-The branch is then unsatisfiable
% 90.99/52.71 |-Branch two:
% 90.99/52.71 | (176) ~ (all_33_0_30 = 0)
% 90.99/52.71 | (585) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_0_0, all_1_1_1) = v2 & apart_point_and_line(all_1_0_0, all_1_2_2) = v1 & convergent_lines(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | ( ~ (v2 = 0) & ~ (v1 = 0))))
% 90.99/52.71 |
% 90.99/52.71 +-Applying beta-rule and splitting (235), into two cases.
% 90.99/52.71 |-Branch one:
% 90.99/52.71 | (586) ~ (all_100_2_53 = 0)
% 90.99/52.71 |
% 90.99/52.71 | Equations (498) can reduce 586 to:
% 90.99/52.71 | (275) $false
% 90.99/52.71 |
% 90.99/52.71 |-The branch is then unsatisfiable
% 90.99/52.71 |-Branch two:
% 90.99/52.71 | (498) all_100_2_53 = 0
% 90.99/52.71 | (589) all_100_0_51 = 0 | ( ~ (all_100_1_52 = 0) & ~ (all_19_1_10 = 0))
% 90.99/52.71 |
% 90.99/52.71 +-Applying beta-rule and splitting (589), into two cases.
% 90.99/52.71 |-Branch one:
% 90.99/52.71 | (590) all_100_0_51 = 0
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (566,590) yields a new equation:
% 90.99/52.71 | (591) all_33_0_30 = 0
% 90.99/52.71 |
% 90.99/52.71 | Simplifying 591 yields:
% 90.99/52.71 | (456) all_33_0_30 = 0
% 90.99/52.71 |
% 90.99/52.71 | Equations (456) can reduce 176 to:
% 90.99/52.71 | (275) $false
% 90.99/52.71 |
% 90.99/52.71 |-The branch is then unsatisfiable
% 90.99/52.71 |-Branch two:
% 90.99/52.71 | (505) ~ (all_100_0_51 = 0)
% 90.99/52.71 | (595) ~ (all_100_1_52 = 0) & ~ (all_19_1_10 = 0)
% 90.99/52.71 |
% 90.99/52.71 | Applying alpha-rule on (595) yields:
% 90.99/52.71 | (596) ~ (all_100_1_52 = 0)
% 90.99/52.71 | (597) ~ (all_19_1_10 = 0)
% 90.99/52.71 |
% 90.99/52.71 | Equations (480) can reduce 596 to:
% 90.99/52.71 | (598) ~ (all_17_1_7 = 0)
% 90.99/52.71 |
% 90.99/52.71 +-Applying beta-rule and splitting (183), into two cases.
% 90.99/52.71 |-Branch one:
% 90.99/52.71 | (599) all_17_1_7 = 0
% 90.99/52.71 |
% 90.99/52.71 | Equations (599) can reduce 598 to:
% 90.99/52.71 | (275) $false
% 90.99/52.71 |
% 90.99/52.71 |-The branch is then unsatisfiable
% 90.99/52.71 |-Branch two:
% 90.99/52.71 | (598) ~ (all_17_1_7 = 0)
% 90.99/52.71 | (602) ? [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))
% 90.99/52.71 |
% 90.99/52.71 +-Applying beta-rule and splitting (180), into two cases.
% 90.99/52.71 |-Branch one:
% 90.99/52.71 | (603) all_19_1_10 = 0
% 90.99/52.71 |
% 90.99/52.71 | Equations (603) can reduce 597 to:
% 90.99/52.71 | (275) $false
% 90.99/52.71 |
% 90.99/52.71 |-The branch is then unsatisfiable
% 90.99/52.71 |-Branch two:
% 90.99/52.71 | (597) ~ (all_19_1_10 = 0)
% 90.99/52.71 | (606) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 90.99/52.71 |
% 90.99/52.71 +-Applying beta-rule and splitting (261), into two cases.
% 90.99/52.71 |-Branch one:
% 90.99/52.71 | (607) all_114_0_73 = 0
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (551,607) yields a new equation:
% 90.99/52.71 | (608) all_23_1_16 = 0
% 90.99/52.71 |
% 90.99/52.71 | Simplifying 608 yields:
% 90.99/52.71 | (307) all_23_1_16 = 0
% 90.99/52.71 |
% 90.99/52.71 | Equations (307) can reduce 174 to:
% 90.99/52.71 | (275) $false
% 90.99/52.71 |
% 90.99/52.71 |-The branch is then unsatisfiable
% 90.99/52.71 |-Branch two:
% 90.99/52.71 | (611) ~ (all_114_0_73 = 0)
% 90.99/52.71 | (612) all_114_1_74 = 0 | all_114_2_75 = 0 | all_114_3_76 = 0
% 90.99/52.71 |
% 90.99/52.71 +-Applying beta-rule and splitting (612), into two cases.
% 90.99/52.71 |-Branch one:
% 90.99/52.71 | (613) all_114_1_74 = 0
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (580,613) yields a new equation:
% 90.99/52.71 | (614) all_21_1_13 = 0
% 90.99/52.71 |
% 90.99/52.71 | Simplifying 614 yields:
% 90.99/52.71 | (274) all_21_1_13 = 0
% 90.99/52.71 |
% 90.99/52.71 | Equations (274) can reduce 168 to:
% 90.99/52.71 | (275) $false
% 90.99/52.71 |
% 90.99/52.71 |-The branch is then unsatisfiable
% 90.99/52.71 |-Branch two:
% 90.99/52.71 | (617) ~ (all_114_1_74 = 0)
% 90.99/52.71 | (618) all_114_2_75 = 0 | all_114_3_76 = 0
% 90.99/52.71 |
% 90.99/52.71 +-Applying beta-rule and splitting (618), into two cases.
% 90.99/52.71 |-Branch one:
% 90.99/52.71 | (619) all_114_2_75 = 0
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (579,619) yields a new equation:
% 90.99/52.71 | (620) all_19_1_10 = 0
% 90.99/52.71 |
% 90.99/52.71 | Simplifying 620 yields:
% 90.99/52.71 | (603) all_19_1_10 = 0
% 90.99/52.71 |
% 90.99/52.71 | Equations (603) can reduce 597 to:
% 90.99/52.71 | (275) $false
% 90.99/52.71 |
% 90.99/52.71 |-The branch is then unsatisfiable
% 90.99/52.71 |-Branch two:
% 90.99/52.71 | (623) ~ (all_114_2_75 = 0)
% 90.99/52.71 | (624) all_114_3_76 = 0
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (578,624) yields a new equation:
% 90.99/52.71 | (625) all_17_1_7 = 0
% 90.99/52.71 |
% 90.99/52.71 | Simplifying 625 yields:
% 90.99/52.71 | (599) all_17_1_7 = 0
% 90.99/52.71 |
% 90.99/52.71 | Equations (599) can reduce 598 to:
% 90.99/52.71 | (275) $false
% 90.99/52.71 |
% 90.99/52.71 |-The branch is then unsatisfiable
% 90.99/52.71 |-Branch two:
% 90.99/52.71 | (293) all_33_1_31 = 0
% 90.99/52.71 | (456) all_33_0_30 = 0
% 90.99/52.71 |
% 90.99/52.71 | Equations (456) can reduce 176 to:
% 90.99/52.71 | (275) $false
% 90.99/52.71 |
% 90.99/52.71 |-The branch is then unsatisfiable
% 90.99/52.71 |-Branch two:
% 90.99/52.71 | (631) all_31_1_28 = 0
% 90.99/52.71 | (632) ~ (all_31_2_29 = 0) | all_31_0_27 = 0
% 90.99/52.71 |
% 90.99/52.71 +-Applying beta-rule and splitting (632), into two cases.
% 90.99/52.71 |-Branch one:
% 90.99/52.71 | (633) ~ (all_31_2_29 = 0)
% 90.99/52.71 |
% 90.99/52.71 | Equations (124) can reduce 633 to:
% 90.99/52.71 | (275) $false
% 90.99/52.71 |
% 90.99/52.71 |-The branch is then unsatisfiable
% 90.99/52.71 |-Branch two:
% 90.99/52.71 | (124) all_31_2_29 = 0
% 90.99/52.71 | (636) all_31_0_27 = 0
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (636,129) yields a new equation:
% 90.99/52.71 | (637) all_21_0_12 = 0
% 90.99/52.71 |
% 90.99/52.71 | Equations (637) can reduce 141 to:
% 90.99/52.71 | (275) $false
% 90.99/52.71 |
% 90.99/52.71 |-The branch is then unsatisfiable
% 90.99/52.71 |-Branch two:
% 90.99/52.71 | (639) all_25_1_19 = 0
% 90.99/52.71 | (640) all_25_0_18 = 0
% 90.99/52.71 |
% 90.99/52.71 | Combining equations (131,640) yields a new equation:
% 90.99/52.71 | (641) all_21_0_12 = 0
% 90.99/52.71 |
% 90.99/52.71 | Simplifying 641 yields:
% 90.99/52.71 | (637) all_21_0_12 = 0
% 90.99/52.71 |
% 90.99/52.71 | Equations (637) can reduce 141 to:
% 90.99/52.71 | (275) $false
% 90.99/52.71 |
% 90.99/52.71 |-The branch is then unsatisfiable
% 90.99/52.71 % SZS output end Proof for theBenchmark
% 90.99/52.71
% 90.99/52.71 52119ms
%------------------------------------------------------------------------------