TSTP Solution File: GEO181+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO181+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n009.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 03:48:18 EDT 2022
% Result : Theorem 13.04s 3.79s
% Output : Proof 23.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO181+2 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 10:54:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.54/0.62 ____ _
% 0.54/0.62 ___ / __ \_____(_)___ ________ __________
% 0.54/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.62
% 0.54/0.62 A Theorem Prover for First-Order Logic
% 0.54/0.62 (ePrincess v.1.0)
% 0.54/0.62
% 0.54/0.62 (c) Philipp Rümmer, 2009-2015
% 0.54/0.62 (c) Peter Backeman, 2014-2015
% 0.54/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.62 Bug reports to peter@backeman.se
% 0.54/0.62
% 0.54/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.62
% 0.54/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.70/0.97 Prover 0: Preprocessing ...
% 2.02/1.11 Prover 0: Warning: ignoring some quantifiers
% 2.02/1.13 Prover 0: Constructing countermodel ...
% 2.68/1.33 Prover 0: gave up
% 2.68/1.34 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.68/1.36 Prover 1: Preprocessing ...
% 2.92/1.45 Prover 1: Constructing countermodel ...
% 3.38/1.51 Prover 1: gave up
% 3.38/1.51 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.48/1.53 Prover 2: Preprocessing ...
% 3.91/1.64 Prover 2: Warning: ignoring some quantifiers
% 3.91/1.65 Prover 2: Constructing countermodel ...
% 4.84/1.89 Prover 2: gave up
% 4.84/1.89 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 5.23/1.90 Prover 3: Preprocessing ...
% 5.23/1.92 Prover 3: Warning: ignoring some quantifiers
% 5.23/1.92 Prover 3: Constructing countermodel ...
% 5.23/1.96 Prover 3: gave up
% 5.23/1.96 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 5.23/1.98 Prover 4: Preprocessing ...
% 5.63/2.04 Prover 4: Warning: ignoring some quantifiers
% 5.63/2.05 Prover 4: Constructing countermodel ...
% 10.44/3.17 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 10.44/3.19 Prover 5: Preprocessing ...
% 11.01/3.27 Prover 5: Constructing countermodel ...
% 13.04/3.79 Prover 5: proved (619ms)
% 13.04/3.79 Prover 4: stopped
% 13.04/3.79
% 13.04/3.79 No countermodel exists, formula is valid
% 13.04/3.79 % SZS status Theorem for theBenchmark
% 13.04/3.79
% 13.04/3.79 Generating proof ... found it (size 426)
% 23.07/6.13
% 23.07/6.13 % SZS output start Proof for theBenchmark
% 23.07/6.13 Assumed formulas after preprocessing and simplification:
% 23.07/6.13 | (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] : ( ~ (v5 = 0) & line_connecting(v0, v2) = v4 & line_connecting(v0, v1) = v3 & apart_point_and_line(v2, v3) = 0 & apart_point_and_line(v1, v4) = v5 & distinct_points(v0, v1) = 0)
% 23.07/6.18 | Applying alpha-rule on (0) yields:
% 23.07/6.18 | (1) ! [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)))
% 23.07/6.18 | (2) ! [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))
% 23.07/6.18 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 23.07/6.18 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 23.07/6.18 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 23.07/6.18 | (6) ! [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))))
% 23.07/6.18 | (7) ! [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)))
% 23.07/6.18 | (8) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 23.07/6.18 | (9) ! [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)))))
% 23.07/6.18 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 23.07/6.18 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 23.07/6.18 | (12) ! [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)
% 23.07/6.18 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 23.07/6.18 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 23.07/6.18 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 23.07/6.18 | (16) ! [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))
% 23.07/6.18 | (17) ! [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)
% 23.07/6.18 | (18) ! [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)
% 23.07/6.19 | (19) ! [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)))
% 23.07/6.19 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 23.07/6.19 | (21) ! [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))
% 23.07/6.19 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 23.07/6.19 | (23) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 23.07/6.19 | (24) ! [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))
% 23.07/6.19 | (25) ! [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))
% 23.07/6.19 | (26) ! [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)
% 23.07/6.19 | (27) ! [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)))
% 23.07/6.19 | (28) ! [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)))
% 23.07/6.19 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 23.07/6.19 | (30) ! [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)))
% 23.07/6.19 | (31) ! [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))))
% 23.07/6.19 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 23.07/6.19 | (33) ! [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)))))
% 23.07/6.19 | (34) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 23.07/6.19 | (35) ! [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)))))
% 23.07/6.19 | (36) ! [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))))
% 23.07/6.19 | (37) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & line_connecting(v0, v2) = v4 & line_connecting(v0, v1) = v3 & apart_point_and_line(v2, v3) = 0 & apart_point_and_line(v1, v4) = v5 & distinct_points(v0, v1) = 0)
% 23.07/6.19 | (38) ! [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))
% 23.07/6.19 | (39) ! [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))))
% 23.07/6.20 | (40) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0)
% 23.07/6.20 | (41) ! [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)))))
% 23.07/6.20 | (42) ! [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)))
% 23.07/6.20 | (43) ! [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))))
% 23.07/6.20 | (44) ! [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)))))
% 23.07/6.20 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 23.07/6.20 | (46) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 23.07/6.20 |
% 23.07/6.20 | Instantiating (37) 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:
% 23.07/6.20 | (47) ~ (all_1_0_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 & apart_point_and_line(all_1_3_3, all_1_2_2) = 0 & apart_point_and_line(all_1_4_4, all_1_1_1) = all_1_0_0 & distinct_points(all_1_5_5, all_1_4_4) = 0
% 23.07/6.20 |
% 23.07/6.20 | Applying alpha-rule on (47) yields:
% 23.07/6.20 | (48) line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2
% 23.07/6.20 | (49) apart_point_and_line(all_1_4_4, all_1_1_1) = all_1_0_0
% 23.07/6.20 | (50) apart_point_and_line(all_1_3_3, all_1_2_2) = 0
% 23.07/6.20 | (51) line_connecting(all_1_5_5, all_1_3_3) = all_1_1_1
% 23.07/6.20 | (52) distinct_points(all_1_5_5, all_1_4_4) = 0
% 23.07/6.20 | (53) ~ (all_1_0_0 = 0)
% 23.07/6.20 |
% 23.07/6.20 | Instantiating formula (46) with all_1_5_5 yields:
% 23.07/6.20 | (54) ~ (distinct_points(all_1_5_5, all_1_5_5) = 0)
% 23.07/6.20 |
% 23.07/6.20 | Instantiating formula (19) with 0, 0, all_1_3_3, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = 0, yields:
% 23.07/6.20 | (55) ? [v0] : ? [v1] : ? [v2] : (intersection_point(all_1_2_2, all_1_2_2) = v1 & convergent_lines(all_1_2_2, all_1_2_2) = v0 & distinct_points(all_1_3_3, v1) = v2 & ( ~ (v0 = 0) | v2 = 0))
% 23.07/6.20 |
% 23.07/6.20 | Instantiating formula (31) with all_1_2_2, all_1_3_3, all_1_4_4, all_1_5_5 and discharging atoms line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2, apart_point_and_line(all_1_3_3, all_1_2_2) = 0, yields:
% 23.07/6.20 | (56) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_1_3_3, all_1_4_4) = v2 & distinct_points(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))
% 23.07/6.20 |
% 23.07/6.20 | Instantiating formula (1) with all_1_0_0, all_1_0_0, all_1_1_1, all_1_1_1, all_1_4_4, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_1_0_0, yields:
% 23.07/6.20 | (57) all_1_0_0 = 0 | ? [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_1_1) = v2 & distinct_lines(all_1_1_1, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.07/6.20 |
% 23.07/6.20 | Instantiating formula (39) 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:
% 23.07/6.20 | (58) ? [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))
% 23.07/6.20 |
% 23.07/6.20 | Instantiating formula (6) 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:
% 23.07/6.20 | (59) ? [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))
% 23.07/6.20 |
% 23.07/6.20 | Instantiating formula (7) with all_1_0_0, all_1_0_0, 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_4_4, all_1_1_1) = all_1_0_0, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 23.07/6.20 | (60) all_1_0_0 = 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))
% 23.07/6.20 |
% 23.07/6.20 | Instantiating (59) with all_16_0_6, all_16_1_7, all_16_2_8 yields:
% 23.07/6.20 | (61) apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7 & distinct_points(all_1_5_5, all_1_4_4) = all_16_2_8 & distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6 & ( ~ (all_16_1_7 = 0) | ~ (all_16_2_8 = 0) | all_16_0_6 = 0)
% 23.07/6.21 |
% 23.07/6.21 | Applying alpha-rule on (61) yields:
% 23.07/6.21 | (62) apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7
% 23.07/6.21 | (63) distinct_points(all_1_5_5, all_1_4_4) = all_16_2_8
% 23.07/6.21 | (64) distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6
% 23.07/6.21 | (65) ~ (all_16_1_7 = 0) | ~ (all_16_2_8 = 0) | all_16_0_6 = 0
% 23.07/6.21 |
% 23.07/6.21 | Instantiating (58) with all_18_0_9, all_18_1_10, all_18_2_11 yields:
% 23.07/6.21 | (66) line_connecting(all_1_5_5, all_1_4_4) = all_18_2_11 & apart_point_and_line(all_1_5_5, all_18_2_11) = all_18_1_10 & distinct_points(all_1_5_5, all_1_5_5) = all_18_0_9 & ( ~ (all_18_1_10 = 0) | all_18_0_9 = 0)
% 23.07/6.21 |
% 23.07/6.21 | Applying alpha-rule on (66) yields:
% 23.07/6.21 | (67) line_connecting(all_1_5_5, all_1_4_4) = all_18_2_11
% 23.07/6.21 | (68) apart_point_and_line(all_1_5_5, all_18_2_11) = all_18_1_10
% 23.07/6.21 | (69) distinct_points(all_1_5_5, all_1_5_5) = all_18_0_9
% 23.07/6.21 | (70) ~ (all_18_1_10 = 0) | all_18_0_9 = 0
% 23.07/6.21 |
% 23.07/6.21 | Instantiating (56) with all_20_0_12, all_20_1_13, all_20_2_14 yields:
% 23.07/6.21 | (71) distinct_points(all_1_3_3, all_1_4_4) = all_20_0_12 & distinct_points(all_1_3_3, all_1_5_5) = all_20_1_13 & distinct_points(all_1_5_5, all_1_4_4) = all_20_2_14 & ( ~ (all_20_2_14 = 0) | (all_20_0_12 = 0 & all_20_1_13 = 0))
% 23.07/6.21 |
% 23.07/6.21 | Applying alpha-rule on (71) yields:
% 23.07/6.21 | (72) distinct_points(all_1_3_3, all_1_4_4) = all_20_0_12
% 23.07/6.21 | (73) distinct_points(all_1_3_3, all_1_5_5) = all_20_1_13
% 23.07/6.21 | (74) distinct_points(all_1_5_5, all_1_4_4) = all_20_2_14
% 23.07/6.21 | (75) ~ (all_20_2_14 = 0) | (all_20_0_12 = 0 & all_20_1_13 = 0)
% 23.07/6.21 |
% 23.07/6.21 | Instantiating (55) with all_22_0_15, all_22_1_16, all_22_2_17 yields:
% 23.07/6.21 | (76) intersection_point(all_1_2_2, all_1_2_2) = all_22_1_16 & convergent_lines(all_1_2_2, all_1_2_2) = all_22_2_17 & distinct_points(all_1_3_3, all_22_1_16) = all_22_0_15 & ( ~ (all_22_2_17 = 0) | all_22_0_15 = 0)
% 23.07/6.21 |
% 23.07/6.21 | Applying alpha-rule on (76) yields:
% 23.07/6.21 | (77) intersection_point(all_1_2_2, all_1_2_2) = all_22_1_16
% 23.07/6.21 | (78) convergent_lines(all_1_2_2, all_1_2_2) = all_22_2_17
% 23.07/6.21 | (79) distinct_points(all_1_3_3, all_22_1_16) = all_22_0_15
% 23.07/6.21 | (80) ~ (all_22_2_17 = 0) | all_22_0_15 = 0
% 23.07/6.21 |
% 23.07/6.21 +-Applying beta-rule and splitting (57), into two cases.
% 23.07/6.21 |-Branch one:
% 23.07/6.21 | (81) all_1_0_0 = 0
% 23.07/6.21 |
% 23.07/6.21 | Equations (81) can reduce 53 to:
% 23.07/6.21 | (82) $false
% 23.07/6.21 |
% 23.07/6.21 |-The branch is then unsatisfiable
% 23.07/6.21 |-Branch two:
% 23.07/6.21 | (53) ~ (all_1_0_0 = 0)
% 23.07/6.21 | (84) ? [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_1_1) = v2 & distinct_lines(all_1_1_1, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.07/6.21 |
% 23.07/6.21 | Instantiating (84) with all_28_0_18, all_28_1_19, all_28_2_20, all_28_3_21 yields:
% 23.07/6.21 | (85) apart_point_and_line(all_1_4_4, all_1_1_1) = all_28_0_18 & apart_point_and_line(all_1_4_4, all_1_1_1) = all_28_1_19 & distinct_lines(all_1_1_1, all_1_1_1) = all_28_2_20 & distinct_points(all_1_4_4, all_1_4_4) = all_28_3_21 & ( ~ (all_28_2_20 = 0) | ~ (all_28_3_21 = 0) | all_28_0_18 = 0 | all_28_1_19 = 0)
% 23.07/6.21 |
% 23.07/6.21 | Applying alpha-rule on (85) yields:
% 23.07/6.21 | (86) distinct_lines(all_1_1_1, all_1_1_1) = all_28_2_20
% 23.07/6.21 | (87) apart_point_and_line(all_1_4_4, all_1_1_1) = all_28_1_19
% 23.07/6.21 | (88) ~ (all_28_2_20 = 0) | ~ (all_28_3_21 = 0) | all_28_0_18 = 0 | all_28_1_19 = 0
% 23.07/6.21 | (89) distinct_points(all_1_4_4, all_1_4_4) = all_28_3_21
% 23.07/6.21 | (90) apart_point_and_line(all_1_4_4, all_1_1_1) = all_28_0_18
% 23.07/6.21 |
% 23.07/6.21 +-Applying beta-rule and splitting (60), into two cases.
% 23.07/6.21 |-Branch one:
% 23.07/6.21 | (81) all_1_0_0 = 0
% 23.07/6.21 |
% 23.07/6.21 | Equations (81) can reduce 53 to:
% 23.07/6.21 | (82) $false
% 23.07/6.21 |
% 23.07/6.21 |-The branch is then unsatisfiable
% 23.07/6.21 |-Branch two:
% 23.07/6.21 | (53) ~ (all_1_0_0 = 0)
% 23.54/6.21 | (94) ? [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))
% 23.54/6.21 |
% 23.54/6.21 | Instantiating (94) with all_33_0_22, all_33_1_23, all_33_2_24 yields:
% 23.54/6.21 | (95) apart_point_and_line(all_1_5_5, all_1_1_1) = all_33_0_22 & apart_point_and_line(all_1_5_5, all_1_1_1) = all_33_1_23 & distinct_lines(all_1_1_1, all_1_1_1) = all_33_2_24 & ( ~ (all_33_2_24 = 0) | all_33_0_22 = 0 | all_33_1_23 = 0)
% 23.54/6.21 |
% 23.54/6.21 | Applying alpha-rule on (95) yields:
% 23.54/6.21 | (96) apart_point_and_line(all_1_5_5, all_1_1_1) = all_33_0_22
% 23.54/6.21 | (97) apart_point_and_line(all_1_5_5, all_1_1_1) = all_33_1_23
% 23.54/6.21 | (98) distinct_lines(all_1_1_1, all_1_1_1) = all_33_2_24
% 23.54/6.21 | (99) ~ (all_33_2_24 = 0) | all_33_0_22 = 0 | all_33_1_23 = 0
% 23.54/6.21 |
% 23.54/6.21 | Instantiating formula (5) with all_1_5_5, all_1_4_4, all_18_2_11, all_1_2_2 and discharging atoms line_connecting(all_1_5_5, all_1_4_4) = all_18_2_11, line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2, yields:
% 23.54/6.21 | (100) all_18_2_11 = all_1_2_2
% 23.54/6.21 |
% 23.54/6.21 | Instantiating formula (15) with all_1_4_4, all_1_1_1, all_28_0_18, all_1_0_0 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_28_0_18, apart_point_and_line(all_1_4_4, all_1_1_1) = all_1_0_0, yields:
% 23.54/6.21 | (101) all_28_0_18 = all_1_0_0
% 23.54/6.21 |
% 23.54/6.21 | Instantiating formula (15) with all_1_4_4, all_1_1_1, all_28_1_19, all_28_0_18 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_28_0_18, apart_point_and_line(all_1_4_4, all_1_1_1) = all_28_1_19, yields:
% 23.54/6.21 | (102) all_28_0_18 = all_28_1_19
% 23.54/6.21 |
% 23.54/6.21 | Instantiating formula (15) with all_1_5_5, all_1_1_1, all_33_1_23, all_33_0_22 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_33_0_22, apart_point_and_line(all_1_5_5, all_1_1_1) = all_33_1_23, yields:
% 23.54/6.21 | (103) all_33_0_22 = all_33_1_23
% 23.54/6.22 |
% 23.54/6.22 | Instantiating formula (15) with all_1_5_5, all_1_2_2, all_16_1_7, all_18_1_10 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 23.54/6.22 | (104) all_18_1_10 = all_16_1_7 | ~ (apart_point_and_line(all_1_5_5, all_1_2_2) = all_18_1_10)
% 23.54/6.22 |
% 23.54/6.22 | Instantiating formula (46) with all_1_4_4 yields:
% 23.54/6.22 | (105) ~ (distinct_points(all_1_4_4, all_1_4_4) = 0)
% 23.54/6.22 |
% 23.54/6.22 | Instantiating formula (32) with all_1_5_5, all_1_4_4, all_20_2_14, 0 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = all_20_2_14, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 23.54/6.22 | (106) all_20_2_14 = 0
% 23.54/6.22 |
% 23.54/6.22 | Instantiating formula (32) with all_1_5_5, all_1_4_4, all_16_2_8, all_20_2_14 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = all_20_2_14, distinct_points(all_1_5_5, all_1_4_4) = all_16_2_8, yields:
% 23.54/6.22 | (107) all_20_2_14 = all_16_2_8
% 23.54/6.22 |
% 23.54/6.22 | Using (69) and (54) yields:
% 23.54/6.22 | (108) ~ (all_18_0_9 = 0)
% 23.54/6.22 |
% 23.54/6.22 | Instantiating formula (32) with all_1_5_5, all_1_5_5, all_16_0_6, all_18_0_9 and discharging atoms distinct_points(all_1_5_5, all_1_5_5) = all_18_0_9, distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6, yields:
% 23.54/6.22 | (109) all_18_0_9 = all_16_0_6
% 23.54/6.22 |
% 23.54/6.22 | Combining equations (102,101) yields a new equation:
% 23.54/6.22 | (110) all_28_1_19 = all_1_0_0
% 23.54/6.22 |
% 23.54/6.22 | Simplifying 110 yields:
% 23.54/6.22 | (111) all_28_1_19 = all_1_0_0
% 23.54/6.22 |
% 23.54/6.22 | Combining equations (107,106) yields a new equation:
% 23.54/6.22 | (112) all_16_2_8 = 0
% 23.54/6.22 |
% 23.54/6.22 | Simplifying 112 yields:
% 23.54/6.22 | (113) all_16_2_8 = 0
% 23.54/6.22 |
% 23.54/6.22 | Equations (109) can reduce 108 to:
% 23.54/6.22 | (114) ~ (all_16_0_6 = 0)
% 23.54/6.22 |
% 23.54/6.22 | From (100) and (67) follows:
% 23.54/6.22 | (48) line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2
% 23.54/6.22 |
% 23.54/6.22 | From (111) and (87) follows:
% 23.54/6.22 | (49) apart_point_and_line(all_1_4_4, all_1_1_1) = all_1_0_0
% 23.54/6.22 |
% 23.54/6.22 | From (100) and (68) follows:
% 23.54/6.22 | (117) apart_point_and_line(all_1_5_5, all_1_2_2) = all_18_1_10
% 23.54/6.22 |
% 23.54/6.22 | From (103) and (96) follows:
% 23.54/6.22 | (97) apart_point_and_line(all_1_5_5, all_1_1_1) = all_33_1_23
% 23.54/6.22 |
% 23.54/6.22 | From (113) and (63) follows:
% 23.54/6.22 | (52) distinct_points(all_1_5_5, all_1_4_4) = 0
% 23.54/6.22 |
% 23.54/6.22 | From (109) and (69) follows:
% 23.54/6.22 | (64) distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6
% 23.54/6.22 |
% 23.54/6.22 +-Applying beta-rule and splitting (104), into two cases.
% 23.54/6.22 |-Branch one:
% 23.54/6.22 | (121) ~ (apart_point_and_line(all_1_5_5, all_1_2_2) = all_18_1_10)
% 23.54/6.22 |
% 23.54/6.22 | Using (117) and (121) yields:
% 23.54/6.22 | (122) $false
% 23.54/6.22 |
% 23.54/6.22 |-The branch is then unsatisfiable
% 23.54/6.22 |-Branch two:
% 23.54/6.22 | (117) apart_point_and_line(all_1_5_5, all_1_2_2) = all_18_1_10
% 23.54/6.22 | (124) all_18_1_10 = all_16_1_7
% 23.54/6.22 |
% 23.54/6.22 | From (124) and (117) follows:
% 23.54/6.22 | (62) apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7
% 23.54/6.22 |
% 23.54/6.22 +-Applying beta-rule and splitting (65), into two cases.
% 23.54/6.22 |-Branch one:
% 23.54/6.22 | (126) ~ (all_16_1_7 = 0)
% 23.54/6.22 |
% 23.54/6.22 +-Applying beta-rule and splitting (75), into two cases.
% 23.54/6.22 |-Branch one:
% 23.54/6.22 | (127) ~ (all_20_2_14 = 0)
% 23.54/6.22 |
% 23.54/6.22 | Equations (106) can reduce 127 to:
% 23.54/6.22 | (82) $false
% 23.54/6.22 |
% 23.54/6.22 |-The branch is then unsatisfiable
% 23.54/6.22 |-Branch two:
% 23.54/6.22 | (106) all_20_2_14 = 0
% 23.54/6.22 | (130) all_20_0_12 = 0 & all_20_1_13 = 0
% 23.54/6.22 |
% 23.54/6.22 | Applying alpha-rule on (130) yields:
% 23.54/6.22 | (131) all_20_0_12 = 0
% 23.54/6.22 | (132) all_20_1_13 = 0
% 23.54/6.22 |
% 23.54/6.22 | From (131) and (72) follows:
% 23.54/6.22 | (133) distinct_points(all_1_3_3, all_1_4_4) = 0
% 23.54/6.22 |
% 23.54/6.22 | From (132) and (73) follows:
% 23.54/6.22 | (134) distinct_points(all_1_3_3, all_1_5_5) = 0
% 23.54/6.22 |
% 23.54/6.22 | Using (89) and (105) yields:
% 23.54/6.22 | (135) ~ (all_28_3_21 = 0)
% 23.54/6.22 |
% 23.54/6.22 | Instantiating formula (1) with all_16_1_7, all_1_0_0, all_1_2_2, all_1_1_1, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_1_0_0, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 23.54/6.22 | (136) all_16_1_7 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.22 |
% 23.54/6.22 | Instantiating formula (1) with all_1_0_0, all_16_1_7, all_1_1_1, all_1_2_2, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_1_0_0, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 23.54/6.22 | (137) all_16_1_7 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.22 |
% 23.54/6.22 | Instantiating formula (28) with all_16_1_7, all_1_0_0, all_1_1_1, all_1_2_2, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_1_1_1) = all_1_0_0, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 23.54/6.22 | (138) all_16_1_7 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.22 |
% 23.54/6.22 | Instantiating formula (28) with all_1_0_0, all_16_1_7, 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_4_4, all_1_1_1) = all_1_0_0, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 23.54/6.22 | (139) all_16_1_7 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.23 |
% 23.54/6.23 | Instantiating formula (42) with all_16_1_7, all_16_1_7, all_1_2_2, all_1_2_2, all_1_4_4, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 23.54/6.23 | (140) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.54/6.23 |
% 23.54/6.23 | Instantiating formula (33) with all_22_1_16, all_16_1_7, all_1_5_5, all_1_2_2, all_1_2_2 and discharging atoms intersection_point(all_1_2_2, all_1_2_2) = all_22_1_16, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 23.54/6.23 | (141) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_1_2_2) = v1 & convergent_lines(all_1_2_2, all_1_2_2) = v0 & distinct_points(all_1_5_5, all_22_1_16) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) & ~ (all_16_1_7 = 0))))
% 23.54/6.23 |
% 23.54/6.23 | Instantiating formula (39) with 0, all_1_3_3, all_1_4_4, all_1_3_3 and discharging atoms distinct_points(all_1_3_3, all_1_4_4) = 0, yields:
% 23.54/6.23 | (142) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_3_3, all_1_4_4) = v0 & apart_point_and_line(all_1_3_3, v0) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 23.54/6.23 |
% 23.54/6.23 | Instantiating formula (39) with 0, all_1_5_5, all_1_4_4, all_1_3_3 and discharging atoms distinct_points(all_1_3_3, all_1_4_4) = 0, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 23.54/6.23 | (143) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_3_3, all_1_4_4) = v0 & apart_point_and_line(all_1_5_5, v0) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 23.54/6.23 |
% 23.54/6.23 | Instantiating formula (39) with 0, all_1_3_3, all_1_5_5, all_1_3_3 and discharging atoms distinct_points(all_1_3_3, all_1_5_5) = 0, yields:
% 23.54/6.23 | (144) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_3_3, all_1_5_5) = v0 & apart_point_and_line(all_1_3_3, v0) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 23.54/6.23 |
% 23.54/6.23 | Instantiating formula (43) with 0, all_1_1_1, all_1_3_3, 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_3_3, all_1_5_5) = 0, yields:
% 23.54/6.23 | (145) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_1_1) = v1 & distinct_points(all_1_3_3, all_1_3_3) = v2 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 23.54/6.23 |
% 23.54/6.23 | Instantiating formula (7) with all_16_1_7, all_16_1_7, all_1_2_2, all_1_2_2, all_1_5_5, all_1_3_3 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, distinct_points(all_1_3_3, all_1_5_5) = 0, yields:
% 23.54/6.23 | (146) all_16_1_7 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_3_3, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.54/6.23 |
% 23.54/6.23 | Instantiating formula (39) with all_28_3_21, all_1_4_4, all_1_4_4, all_1_5_5 and discharging atoms distinct_points(all_1_4_4, all_1_4_4) = all_28_3_21, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 23.54/6.23 | (147) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_4_4) = v0 & apart_point_and_line(all_1_4_4, v0) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_28_3_21 = 0)))
% 23.54/6.23 |
% 23.54/6.23 | Instantiating formula (39) with all_28_3_21, all_1_4_4, all_1_4_4, all_1_3_3 and discharging atoms distinct_points(all_1_3_3, all_1_4_4) = 0, distinct_points(all_1_4_4, all_1_4_4) = all_28_3_21, yields:
% 23.54/6.23 | (148) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_3_3, all_1_4_4) = v0 & apart_point_and_line(all_1_4_4, v0) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_28_3_21 = 0)))
% 23.54/6.23 |
% 23.54/6.23 | Instantiating formula (6) with all_28_3_21, all_1_2_2, all_1_4_4, all_1_4_4, all_1_5_5 and discharging atoms line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2, distinct_points(all_1_4_4, all_1_4_4) = all_28_3_21, yields:
% 23.54/6.23 | (149) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v2 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & all_28_3_21 = 0)))
% 23.54/6.23 |
% 23.54/6.23 | Instantiating formula (3) with all_16_0_6, 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, distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6, yields:
% 23.54/6.23 | (150) all_16_0_6 = 0 | distinct_points(all_1_4_4, all_1_5_5) = 0
% 23.54/6.23 |
% 23.54/6.23 | Instantiating formula (38) with all_16_0_6, 0, all_1_5_5, all_1_5_5, all_1_4_4 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = 0, distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6, yields:
% 23.54/6.23 | (151) all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_4_4, all_1_5_5) = v1 & apart_point_and_line(all_1_5_5, v1) = v2 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 23.54/6.23 |
% 23.54/6.23 | Instantiating formula (39) with all_16_0_6, all_1_5_5, all_1_5_5, all_1_3_3 and discharging atoms distinct_points(all_1_3_3, all_1_5_5) = 0, distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6, yields:
% 23.54/6.23 | (152) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_3_3, all_1_5_5) = v0 & apart_point_and_line(all_1_5_5, v0) = v1 & distinct_points(all_1_5_5, all_1_3_3) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_16_0_6 = 0)))
% 23.54/6.23 |
% 23.54/6.23 | Instantiating formula (38) with all_16_0_6, all_16_0_6, all_1_5_5, all_1_5_5, all_1_5_5 and discharging atoms distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6, yields:
% 23.54/6.23 | (153) all_16_0_6 = 0 | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_5_5) = v1 & apart_point_and_line(all_1_5_5, v1) = v2 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 23.54/6.23 |
% 23.54/6.23 | Instantiating formula (43) with all_16_0_6, 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_5_5) = all_16_0_6, yields:
% 23.54/6.23 | (154) ? [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) = v2 & distinct_points(all_1_5_5, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & all_16_0_6 = 0)))
% 23.54/6.23 |
% 23.54/6.23 | Instantiating (154) with all_60_0_25, all_60_1_26, all_60_2_27 yields:
% 23.54/6.23 | (155) apart_point_and_line(all_1_5_5, all_1_1_1) = all_60_1_26 & distinct_points(all_1_5_5, all_1_3_3) = all_60_0_25 & distinct_points(all_1_5_5, all_1_3_3) = all_60_2_27 & ( ~ (all_60_1_26 = 0) | ~ (all_60_2_27 = 0) | (all_60_0_25 = 0 & all_16_0_6 = 0))
% 23.54/6.24 |
% 23.54/6.24 | Applying alpha-rule on (155) yields:
% 23.54/6.24 | (156) apart_point_and_line(all_1_5_5, all_1_1_1) = all_60_1_26
% 23.54/6.24 | (157) distinct_points(all_1_5_5, all_1_3_3) = all_60_0_25
% 23.54/6.24 | (158) distinct_points(all_1_5_5, all_1_3_3) = all_60_2_27
% 23.54/6.24 | (159) ~ (all_60_1_26 = 0) | ~ (all_60_2_27 = 0) | (all_60_0_25 = 0 & all_16_0_6 = 0)
% 23.54/6.24 |
% 23.54/6.24 | Instantiating (141) with all_62_0_28, all_62_1_29, all_62_2_30 yields:
% 23.54/6.24 | (160) apart_point_and_line(all_1_5_5, all_1_2_2) = all_62_1_29 & convergent_lines(all_1_2_2, all_1_2_2) = all_62_2_30 & distinct_points(all_1_5_5, all_22_1_16) = all_62_0_28 & ( ~ (all_62_2_30 = 0) | all_62_0_28 = 0 | ( ~ (all_62_1_29 = 0) & ~ (all_16_1_7 = 0)))
% 23.54/6.24 |
% 23.54/6.24 | Applying alpha-rule on (160) yields:
% 23.54/6.24 | (161) apart_point_and_line(all_1_5_5, all_1_2_2) = all_62_1_29
% 23.54/6.24 | (162) convergent_lines(all_1_2_2, all_1_2_2) = all_62_2_30
% 23.54/6.24 | (163) distinct_points(all_1_5_5, all_22_1_16) = all_62_0_28
% 23.54/6.24 | (164) ~ (all_62_2_30 = 0) | all_62_0_28 = 0 | ( ~ (all_62_1_29 = 0) & ~ (all_16_1_7 = 0))
% 23.54/6.24 |
% 23.54/6.24 | Instantiating (152) with all_64_0_31, all_64_1_32, all_64_2_33 yields:
% 23.54/6.24 | (165) line_connecting(all_1_3_3, all_1_5_5) = all_64_2_33 & apart_point_and_line(all_1_5_5, all_64_2_33) = all_64_1_32 & distinct_points(all_1_5_5, all_1_3_3) = all_64_0_31 & ( ~ (all_64_1_32 = 0) | (all_64_0_31 = 0 & all_16_0_6 = 0))
% 23.54/6.24 |
% 23.54/6.24 | Applying alpha-rule on (165) yields:
% 23.54/6.24 | (166) line_connecting(all_1_3_3, all_1_5_5) = all_64_2_33
% 23.54/6.24 | (167) apart_point_and_line(all_1_5_5, all_64_2_33) = all_64_1_32
% 23.54/6.24 | (168) distinct_points(all_1_5_5, all_1_3_3) = all_64_0_31
% 23.54/6.24 | (169) ~ (all_64_1_32 = 0) | (all_64_0_31 = 0 & all_16_0_6 = 0)
% 23.54/6.24 |
% 23.54/6.24 | Instantiating (149) with all_66_0_34, all_66_1_35, all_66_2_36 yields:
% 23.54/6.24 | (170) apart_point_and_line(all_1_4_4, all_1_2_2) = all_66_1_35 & distinct_points(all_1_4_4, all_1_5_5) = all_66_0_34 & distinct_points(all_1_5_5, all_1_4_4) = all_66_2_36 & ( ~ (all_66_1_35 = 0) | ~ (all_66_2_36 = 0) | (all_66_0_34 = 0 & all_28_3_21 = 0))
% 23.54/6.24 |
% 23.54/6.24 | Applying alpha-rule on (170) yields:
% 23.54/6.24 | (171) apart_point_and_line(all_1_4_4, all_1_2_2) = all_66_1_35
% 23.54/6.24 | (172) distinct_points(all_1_4_4, all_1_5_5) = all_66_0_34
% 23.54/6.24 | (173) distinct_points(all_1_5_5, all_1_4_4) = all_66_2_36
% 23.54/6.24 | (174) ~ (all_66_1_35 = 0) | ~ (all_66_2_36 = 0) | (all_66_0_34 = 0 & all_28_3_21 = 0)
% 23.54/6.24 |
% 23.54/6.24 | Instantiating (145) with all_68_0_37, all_68_1_38, all_68_2_39 yields:
% 23.54/6.24 | (175) apart_point_and_line(all_1_3_3, all_1_1_1) = all_68_1_38 & distinct_points(all_1_3_3, all_1_3_3) = all_68_0_37 & distinct_points(all_1_5_5, all_1_3_3) = all_68_2_39 & ( ~ (all_68_1_38 = 0) | ~ (all_68_2_39 = 0) | all_68_0_37 = 0)
% 23.54/6.24 |
% 23.54/6.24 | Applying alpha-rule on (175) yields:
% 23.54/6.24 | (176) apart_point_and_line(all_1_3_3, all_1_1_1) = all_68_1_38
% 23.54/6.24 | (177) distinct_points(all_1_3_3, all_1_3_3) = all_68_0_37
% 23.54/6.24 | (178) distinct_points(all_1_5_5, all_1_3_3) = all_68_2_39
% 23.54/6.24 | (179) ~ (all_68_1_38 = 0) | ~ (all_68_2_39 = 0) | all_68_0_37 = 0
% 23.54/6.24 |
% 23.54/6.24 | Instantiating (144) with all_70_0_40, all_70_1_41, all_70_2_42 yields:
% 23.54/6.24 | (180) line_connecting(all_1_3_3, all_1_5_5) = all_70_2_42 & apart_point_and_line(all_1_3_3, all_70_2_42) = all_70_1_41 & distinct_points(all_1_3_3, all_1_3_3) = all_70_0_40 & ( ~ (all_70_1_41 = 0) | all_70_0_40 = 0)
% 23.54/6.24 |
% 23.54/6.24 | Applying alpha-rule on (180) yields:
% 23.54/6.24 | (181) line_connecting(all_1_3_3, all_1_5_5) = all_70_2_42
% 23.54/6.24 | (182) apart_point_and_line(all_1_3_3, all_70_2_42) = all_70_1_41
% 23.54/6.24 | (183) distinct_points(all_1_3_3, all_1_3_3) = all_70_0_40
% 23.54/6.24 | (184) ~ (all_70_1_41 = 0) | all_70_0_40 = 0
% 23.54/6.24 |
% 23.54/6.24 | Instantiating (148) with all_72_0_43, all_72_1_44, all_72_2_45 yields:
% 23.54/6.24 | (185) line_connecting(all_1_3_3, all_1_4_4) = all_72_2_45 & apart_point_and_line(all_1_4_4, all_72_2_45) = all_72_1_44 & distinct_points(all_1_4_4, all_1_3_3) = all_72_0_43 & ( ~ (all_72_1_44 = 0) | (all_72_0_43 = 0 & all_28_3_21 = 0))
% 23.54/6.24 |
% 23.54/6.24 | Applying alpha-rule on (185) yields:
% 23.54/6.24 | (186) line_connecting(all_1_3_3, all_1_4_4) = all_72_2_45
% 23.54/6.24 | (187) apart_point_and_line(all_1_4_4, all_72_2_45) = all_72_1_44
% 23.54/6.24 | (188) distinct_points(all_1_4_4, all_1_3_3) = all_72_0_43
% 23.54/6.24 | (189) ~ (all_72_1_44 = 0) | (all_72_0_43 = 0 & all_28_3_21 = 0)
% 23.54/6.24 |
% 23.54/6.24 | Instantiating (147) with all_74_0_46, all_74_1_47, all_74_2_48 yields:
% 23.54/6.24 | (190) line_connecting(all_1_5_5, all_1_4_4) = all_74_2_48 & apart_point_and_line(all_1_4_4, all_74_2_48) = all_74_1_47 & distinct_points(all_1_4_4, all_1_5_5) = all_74_0_46 & ( ~ (all_74_1_47 = 0) | (all_74_0_46 = 0 & all_28_3_21 = 0))
% 23.54/6.24 |
% 23.54/6.24 | Applying alpha-rule on (190) yields:
% 23.54/6.24 | (191) line_connecting(all_1_5_5, all_1_4_4) = all_74_2_48
% 23.54/6.24 | (192) apart_point_and_line(all_1_4_4, all_74_2_48) = all_74_1_47
% 23.54/6.24 | (193) distinct_points(all_1_4_4, all_1_5_5) = all_74_0_46
% 23.54/6.24 | (194) ~ (all_74_1_47 = 0) | (all_74_0_46 = 0 & all_28_3_21 = 0)
% 23.54/6.24 |
% 23.54/6.24 | Instantiating (143) with all_76_0_49, all_76_1_50, all_76_2_51 yields:
% 23.54/6.24 | (195) line_connecting(all_1_3_3, all_1_4_4) = all_76_2_51 & apart_point_and_line(all_1_5_5, all_76_2_51) = all_76_1_50 & distinct_points(all_1_5_5, all_1_3_3) = all_76_0_49 & ( ~ (all_76_1_50 = 0) | all_76_0_49 = 0)
% 23.54/6.24 |
% 23.54/6.24 | Applying alpha-rule on (195) yields:
% 23.54/6.24 | (196) line_connecting(all_1_3_3, all_1_4_4) = all_76_2_51
% 23.54/6.25 | (197) apart_point_and_line(all_1_5_5, all_76_2_51) = all_76_1_50
% 23.54/6.25 | (198) distinct_points(all_1_5_5, all_1_3_3) = all_76_0_49
% 23.54/6.25 | (199) ~ (all_76_1_50 = 0) | all_76_0_49 = 0
% 23.54/6.25 |
% 23.54/6.25 | Instantiating (142) with all_78_0_52, all_78_1_53, all_78_2_54 yields:
% 23.54/6.25 | (200) line_connecting(all_1_3_3, all_1_4_4) = all_78_2_54 & apart_point_and_line(all_1_3_3, all_78_2_54) = all_78_1_53 & distinct_points(all_1_3_3, all_1_3_3) = all_78_0_52 & ( ~ (all_78_1_53 = 0) | all_78_0_52 = 0)
% 23.54/6.25 |
% 23.54/6.25 | Applying alpha-rule on (200) yields:
% 23.54/6.25 | (201) line_connecting(all_1_3_3, all_1_4_4) = all_78_2_54
% 23.54/6.25 | (202) apart_point_and_line(all_1_3_3, all_78_2_54) = all_78_1_53
% 23.54/6.25 | (203) distinct_points(all_1_3_3, all_1_3_3) = all_78_0_52
% 23.54/6.25 | (204) ~ (all_78_1_53 = 0) | all_78_0_52 = 0
% 23.54/6.25 |
% 23.54/6.25 +-Applying beta-rule and splitting (189), into two cases.
% 23.54/6.25 |-Branch one:
% 23.54/6.25 | (205) ~ (all_72_1_44 = 0)
% 23.54/6.25 |
% 23.54/6.25 +-Applying beta-rule and splitting (150), into two cases.
% 23.54/6.25 |-Branch one:
% 23.54/6.25 | (206) distinct_points(all_1_4_4, all_1_5_5) = 0
% 23.54/6.25 |
% 23.54/6.25 +-Applying beta-rule and splitting (194), into two cases.
% 23.54/6.25 |-Branch one:
% 23.54/6.25 | (207) ~ (all_74_1_47 = 0)
% 23.54/6.25 |
% 23.54/6.25 +-Applying beta-rule and splitting (146), into two cases.
% 23.54/6.25 |-Branch one:
% 23.54/6.25 | (208) all_16_1_7 = 0
% 23.54/6.25 |
% 23.54/6.25 | Equations (208) can reduce 126 to:
% 23.54/6.25 | (82) $false
% 23.54/6.25 |
% 23.54/6.25 |-The branch is then unsatisfiable
% 23.54/6.25 |-Branch two:
% 23.54/6.25 | (126) ~ (all_16_1_7 = 0)
% 23.54/6.25 | (211) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_3_3, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.54/6.25 |
% 23.54/6.25 | Instantiating (211) with all_100_0_56, all_100_1_57, all_100_2_58 yields:
% 23.54/6.25 | (212) apart_point_and_line(all_1_3_3, all_1_2_2) = all_100_0_56 & apart_point_and_line(all_1_3_3, all_1_2_2) = all_100_1_57 & distinct_lines(all_1_2_2, all_1_2_2) = all_100_2_58 & ( ~ (all_100_2_58 = 0) | all_100_0_56 = 0 | all_100_1_57 = 0)
% 23.54/6.25 |
% 23.54/6.25 | Applying alpha-rule on (212) yields:
% 23.54/6.25 | (213) apart_point_and_line(all_1_3_3, all_1_2_2) = all_100_0_56
% 23.54/6.25 | (214) apart_point_and_line(all_1_3_3, all_1_2_2) = all_100_1_57
% 23.54/6.25 | (215) distinct_lines(all_1_2_2, all_1_2_2) = all_100_2_58
% 23.54/6.25 | (216) ~ (all_100_2_58 = 0) | all_100_0_56 = 0 | all_100_1_57 = 0
% 23.54/6.25 |
% 23.54/6.25 +-Applying beta-rule and splitting (151), into two cases.
% 23.54/6.25 |-Branch one:
% 23.54/6.25 | (217) all_16_0_6 = 0
% 23.54/6.25 |
% 23.54/6.25 | Equations (217) can reduce 114 to:
% 23.54/6.25 | (82) $false
% 23.54/6.25 |
% 23.54/6.25 |-The branch is then unsatisfiable
% 23.54/6.25 |-Branch two:
% 23.54/6.25 | (114) ~ (all_16_0_6 = 0)
% 23.54/6.25 | (220) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_4_4, all_1_5_5) = v1 & apart_point_and_line(all_1_5_5, v1) = v2 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 23.54/6.25 |
% 23.54/6.25 | Instantiating (220) with all_105_0_59, all_105_1_60, all_105_2_61 yields:
% 23.54/6.25 | (221) line_connecting(all_1_4_4, all_1_5_5) = all_105_1_60 & apart_point_and_line(all_1_5_5, all_105_1_60) = all_105_0_59 & distinct_points(all_1_4_4, all_1_5_5) = all_105_2_61 & ( ~ (all_105_0_59 = 0) | ~ (all_105_2_61 = 0))
% 23.54/6.25 |
% 23.54/6.25 | Applying alpha-rule on (221) yields:
% 23.54/6.25 | (222) line_connecting(all_1_4_4, all_1_5_5) = all_105_1_60
% 23.54/6.25 | (223) apart_point_and_line(all_1_5_5, all_105_1_60) = all_105_0_59
% 23.54/6.25 | (224) distinct_points(all_1_4_4, all_1_5_5) = all_105_2_61
% 23.54/6.25 | (225) ~ (all_105_0_59 = 0) | ~ (all_105_2_61 = 0)
% 23.54/6.25 |
% 23.54/6.25 +-Applying beta-rule and splitting (153), into two cases.
% 23.54/6.25 |-Branch one:
% 23.54/6.25 | (217) all_16_0_6 = 0
% 23.54/6.25 |
% 23.54/6.25 | Equations (217) can reduce 114 to:
% 23.54/6.25 | (82) $false
% 23.54/6.25 |
% 23.54/6.25 |-The branch is then unsatisfiable
% 23.54/6.25 |-Branch two:
% 23.54/6.25 | (114) ~ (all_16_0_6 = 0)
% 23.54/6.25 | (229) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_5_5, all_1_5_5) = v1 & apart_point_and_line(all_1_5_5, v1) = v2 & distinct_points(all_1_5_5, all_1_5_5) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 23.54/6.25 |
% 23.54/6.25 | Instantiating (229) with all_114_0_62, all_114_1_63, all_114_2_64 yields:
% 23.54/6.25 | (230) line_connecting(all_1_5_5, all_1_5_5) = all_114_1_63 & apart_point_and_line(all_1_5_5, all_114_1_63) = all_114_0_62 & distinct_points(all_1_5_5, all_1_5_5) = all_114_2_64 & ( ~ (all_114_0_62 = 0) | ~ (all_114_2_64 = 0))
% 23.54/6.25 |
% 23.54/6.25 | Applying alpha-rule on (230) yields:
% 23.54/6.25 | (231) line_connecting(all_1_5_5, all_1_5_5) = all_114_1_63
% 23.54/6.25 | (232) apart_point_and_line(all_1_5_5, all_114_1_63) = all_114_0_62
% 23.54/6.25 | (233) distinct_points(all_1_5_5, all_1_5_5) = all_114_2_64
% 23.54/6.25 | (234) ~ (all_114_0_62 = 0) | ~ (all_114_2_64 = 0)
% 23.54/6.25 |
% 23.54/6.25 +-Applying beta-rule and splitting (136), into two cases.
% 23.54/6.25 |-Branch one:
% 23.54/6.25 | (208) all_16_1_7 = 0
% 23.54/6.25 |
% 23.54/6.25 | Equations (208) can reduce 126 to:
% 23.54/6.25 | (82) $false
% 23.54/6.25 |
% 23.54/6.25 |-The branch is then unsatisfiable
% 23.54/6.25 |-Branch two:
% 23.54/6.25 | (126) ~ (all_16_1_7 = 0)
% 23.54/6.25 | (238) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.26 |
% 23.54/6.26 +-Applying beta-rule and splitting (137), into two cases.
% 23.54/6.26 |-Branch one:
% 23.54/6.26 | (208) all_16_1_7 = 0
% 23.54/6.26 |
% 23.54/6.26 | Equations (208) can reduce 126 to:
% 23.54/6.26 | (82) $false
% 23.54/6.26 |
% 23.54/6.26 |-The branch is then unsatisfiable
% 23.54/6.26 |-Branch two:
% 23.54/6.26 | (126) ~ (all_16_1_7 = 0)
% 23.54/6.26 | (242) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.26 |
% 23.54/6.26 +-Applying beta-rule and splitting (138), into two cases.
% 23.54/6.26 |-Branch one:
% 23.54/6.26 | (208) all_16_1_7 = 0
% 23.54/6.26 |
% 23.54/6.26 | Equations (208) can reduce 126 to:
% 23.54/6.26 | (82) $false
% 23.54/6.26 |
% 23.54/6.26 |-The branch is then unsatisfiable
% 23.54/6.26 |-Branch two:
% 23.54/6.26 | (126) ~ (all_16_1_7 = 0)
% 23.54/6.26 | (246) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.26 |
% 23.54/6.26 +-Applying beta-rule and splitting (139), into two cases.
% 23.54/6.26 |-Branch one:
% 23.54/6.26 | (208) all_16_1_7 = 0
% 23.54/6.26 |
% 23.54/6.26 | Equations (208) can reduce 126 to:
% 23.54/6.26 | (82) $false
% 23.54/6.26 |
% 23.54/6.26 |-The branch is then unsatisfiable
% 23.54/6.26 |-Branch two:
% 23.54/6.26 | (126) ~ (all_16_1_7 = 0)
% 23.54/6.26 | (250) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.26 |
% 23.54/6.26 +-Applying beta-rule and splitting (238), into two cases.
% 23.54/6.26 |-Branch one:
% 23.54/6.26 | (81) all_1_0_0 = 0
% 23.54/6.26 |
% 23.54/6.26 | Equations (81) can reduce 53 to:
% 23.54/6.26 | (82) $false
% 23.54/6.26 |
% 23.54/6.26 |-The branch is then unsatisfiable
% 23.54/6.26 |-Branch two:
% 23.54/6.26 | (53) ~ (all_1_0_0 = 0)
% 23.54/6.26 | (254) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.26 |
% 23.54/6.26 | Instantiating (254) with all_138_0_68, all_138_1_69, all_138_2_70, all_138_3_71 yields:
% 23.54/6.26 | (255) apart_point_and_line(all_1_4_4, all_1_2_2) = all_138_1_69 & apart_point_and_line(all_1_5_5, all_1_1_1) = all_138_0_68 & distinct_lines(all_1_1_1, all_1_2_2) = all_138_2_70 & distinct_points(all_1_4_4, all_1_5_5) = all_138_3_71 & ( ~ (all_138_2_70 = 0) | ~ (all_138_3_71 = 0) | all_138_0_68 = 0 | all_138_1_69 = 0)
% 23.54/6.26 |
% 23.54/6.26 | Applying alpha-rule on (255) yields:
% 23.54/6.26 | (256) distinct_lines(all_1_1_1, all_1_2_2) = all_138_2_70
% 23.54/6.26 | (257) ~ (all_138_2_70 = 0) | ~ (all_138_3_71 = 0) | all_138_0_68 = 0 | all_138_1_69 = 0
% 23.54/6.26 | (258) distinct_points(all_1_4_4, all_1_5_5) = all_138_3_71
% 23.54/6.26 | (259) apart_point_and_line(all_1_4_4, all_1_2_2) = all_138_1_69
% 23.54/6.26 | (260) apart_point_and_line(all_1_5_5, all_1_1_1) = all_138_0_68
% 23.54/6.26 |
% 23.54/6.26 +-Applying beta-rule and splitting (242), into two cases.
% 23.54/6.26 |-Branch one:
% 23.54/6.26 | (81) all_1_0_0 = 0
% 23.54/6.26 |
% 23.54/6.26 | Equations (81) can reduce 53 to:
% 23.54/6.26 | (82) $false
% 23.54/6.26 |
% 23.54/6.26 |-The branch is then unsatisfiable
% 23.54/6.26 |-Branch two:
% 23.54/6.26 | (53) ~ (all_1_0_0 = 0)
% 23.54/6.26 | (264) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.26 |
% 23.54/6.26 | Instantiating (264) with all_143_0_72, all_143_1_73, all_143_2_74, all_143_3_75 yields:
% 23.54/6.26 | (265) apart_point_and_line(all_1_4_4, all_1_2_2) = all_143_0_72 & apart_point_and_line(all_1_5_5, all_1_1_1) = all_143_1_73 & distinct_lines(all_1_2_2, all_1_1_1) = all_143_2_74 & distinct_points(all_1_5_5, all_1_4_4) = all_143_3_75 & ( ~ (all_143_2_74 = 0) | ~ (all_143_3_75 = 0) | all_143_0_72 = 0 | all_143_1_73 = 0)
% 23.54/6.26 |
% 23.54/6.26 | Applying alpha-rule on (265) yields:
% 23.54/6.26 | (266) apart_point_and_line(all_1_4_4, all_1_2_2) = all_143_0_72
% 23.54/6.26 | (267) ~ (all_143_2_74 = 0) | ~ (all_143_3_75 = 0) | all_143_0_72 = 0 | all_143_1_73 = 0
% 23.54/6.26 | (268) distinct_points(all_1_5_5, all_1_4_4) = all_143_3_75
% 23.54/6.26 | (269) apart_point_and_line(all_1_5_5, all_1_1_1) = all_143_1_73
% 23.54/6.26 | (270) distinct_lines(all_1_2_2, all_1_1_1) = all_143_2_74
% 23.54/6.26 |
% 23.54/6.26 +-Applying beta-rule and splitting (246), into two cases.
% 23.54/6.26 |-Branch one:
% 23.54/6.26 | (81) all_1_0_0 = 0
% 23.54/6.26 |
% 23.54/6.26 | Equations (81) can reduce 53 to:
% 23.54/6.26 | (82) $false
% 23.54/6.26 |
% 23.54/6.26 |-The branch is then unsatisfiable
% 23.54/6.26 |-Branch two:
% 23.54/6.26 | (53) ~ (all_1_0_0 = 0)
% 23.54/6.26 | (274) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v3 & distinct_lines(all_1_2_2, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.26 |
% 23.54/6.26 | Instantiating (274) with all_148_0_76, all_148_1_77, all_148_2_78, all_148_3_79 yields:
% 23.54/6.26 | (275) apart_point_and_line(all_1_4_4, all_1_2_2) = all_148_1_77 & apart_point_and_line(all_1_5_5, all_1_1_1) = all_148_0_76 & distinct_lines(all_1_2_2, all_1_1_1) = all_148_2_78 & distinct_points(all_1_4_4, all_1_5_5) = all_148_3_79 & ( ~ (all_148_2_78 = 0) | ~ (all_148_3_79 = 0) | all_148_0_76 = 0 | all_148_1_77 = 0)
% 23.54/6.26 |
% 23.54/6.26 | Applying alpha-rule on (275) yields:
% 23.54/6.26 | (276) distinct_lines(all_1_2_2, all_1_1_1) = all_148_2_78
% 23.54/6.26 | (277) distinct_points(all_1_4_4, all_1_5_5) = all_148_3_79
% 23.54/6.26 | (278) ~ (all_148_2_78 = 0) | ~ (all_148_3_79 = 0) | all_148_0_76 = 0 | all_148_1_77 = 0
% 23.54/6.26 | (279) apart_point_and_line(all_1_4_4, all_1_2_2) = all_148_1_77
% 23.54/6.26 | (280) apart_point_and_line(all_1_5_5, all_1_1_1) = all_148_0_76
% 23.54/6.26 |
% 23.54/6.26 +-Applying beta-rule and splitting (250), into two cases.
% 23.54/6.26 |-Branch one:
% 23.54/6.26 | (81) all_1_0_0 = 0
% 23.54/6.26 |
% 23.54/6.27 | Equations (81) can reduce 53 to:
% 23.54/6.27 | (82) $false
% 23.54/6.27 |
% 23.54/6.27 |-The branch is then unsatisfiable
% 23.54/6.27 |-Branch two:
% 23.54/6.27 | (53) ~ (all_1_0_0 = 0)
% 23.54/6.27 | (284) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v3 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_1_2_2) = v1 & distinct_points(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.27 |
% 23.54/6.27 | Instantiating (284) with all_153_0_80, all_153_1_81, all_153_2_82, all_153_3_83 yields:
% 23.54/6.27 | (285) apart_point_and_line(all_1_4_4, all_1_2_2) = all_153_0_80 & apart_point_and_line(all_1_5_5, all_1_1_1) = all_153_1_81 & distinct_lines(all_1_1_1, all_1_2_2) = all_153_2_82 & distinct_points(all_1_5_5, all_1_4_4) = all_153_3_83 & ( ~ (all_153_2_82 = 0) | ~ (all_153_3_83 = 0) | all_153_0_80 = 0 | all_153_1_81 = 0)
% 23.54/6.27 |
% 23.54/6.27 | Applying alpha-rule on (285) yields:
% 23.54/6.27 | (286) apart_point_and_line(all_1_5_5, all_1_1_1) = all_153_1_81
% 23.54/6.27 | (287) apart_point_and_line(all_1_4_4, all_1_2_2) = all_153_0_80
% 23.54/6.27 | (288) distinct_points(all_1_5_5, all_1_4_4) = all_153_3_83
% 23.54/6.27 | (289) ~ (all_153_2_82 = 0) | ~ (all_153_3_83 = 0) | all_153_0_80 = 0 | all_153_1_81 = 0
% 23.54/6.27 | (290) distinct_lines(all_1_1_1, all_1_2_2) = all_153_2_82
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (5) with all_1_3_3, all_1_5_5, all_64_2_33, all_70_2_42 and discharging atoms line_connecting(all_1_3_3, all_1_5_5) = all_70_2_42, line_connecting(all_1_3_3, all_1_5_5) = all_64_2_33, yields:
% 23.54/6.27 | (291) all_70_2_42 = all_64_2_33
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (5) with all_1_5_5, all_1_4_4, all_74_2_48, all_1_2_2 and discharging atoms line_connecting(all_1_5_5, all_1_4_4) = all_74_2_48, line_connecting(all_1_5_5, all_1_4_4) = all_1_2_2, yields:
% 23.54/6.27 | (292) all_74_2_48 = all_1_2_2
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (15) with all_1_3_3, all_1_2_2, all_100_0_56, 0 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = all_100_0_56, apart_point_and_line(all_1_3_3, all_1_2_2) = 0, yields:
% 23.54/6.27 | (293) all_100_0_56 = 0
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (15) with all_1_3_3, all_1_2_2, all_100_1_57, all_100_0_56 and discharging atoms apart_point_and_line(all_1_3_3, all_1_2_2) = all_100_0_56, apart_point_and_line(all_1_3_3, all_1_2_2) = all_100_1_57, yields:
% 23.54/6.27 | (294) all_100_0_56 = all_100_1_57
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (15) with all_1_4_4, all_1_2_2, all_153_0_80, all_74_1_47 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_153_0_80, yields:
% 23.54/6.27 | (295) all_153_0_80 = all_74_1_47 | ~ (apart_point_and_line(all_1_4_4, all_1_2_2) = all_74_1_47)
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (15) with all_1_4_4, all_1_2_2, all_66_1_35, all_153_0_80 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_153_0_80, apart_point_and_line(all_1_4_4, all_1_2_2) = all_66_1_35, yields:
% 23.54/6.27 | (296) all_153_0_80 = all_66_1_35
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (15) with all_1_5_5, all_1_1_1, all_148_0_76, all_153_1_81 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_153_1_81, apart_point_and_line(all_1_5_5, all_1_1_1) = all_148_0_76, yields:
% 23.54/6.27 | (297) all_153_1_81 = all_148_0_76
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (15) with all_1_5_5, all_1_1_1, all_143_1_73, all_33_1_23 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_143_1_73, apart_point_and_line(all_1_5_5, all_1_1_1) = all_33_1_23, yields:
% 23.54/6.27 | (298) all_143_1_73 = all_33_1_23
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (15) with all_1_5_5, all_1_1_1, all_143_1_73, all_148_0_76 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_148_0_76, apart_point_and_line(all_1_5_5, all_1_1_1) = all_143_1_73, yields:
% 23.54/6.27 | (299) all_148_0_76 = all_143_1_73
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (15) with all_1_5_5, all_1_1_1, all_138_0_68, all_153_1_81 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_153_1_81, apart_point_and_line(all_1_5_5, all_1_1_1) = all_138_0_68, yields:
% 23.54/6.27 | (300) all_153_1_81 = all_138_0_68
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (15) with all_1_5_5, all_1_1_1, all_60_1_26, all_143_1_73 and discharging atoms apart_point_and_line(all_1_5_5, all_1_1_1) = all_143_1_73, apart_point_and_line(all_1_5_5, all_1_1_1) = all_60_1_26, yields:
% 23.54/6.27 | (301) all_143_1_73 = all_60_1_26
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (15) with all_1_5_5, all_1_2_2, all_62_1_29, all_16_1_7 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_62_1_29, apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, yields:
% 23.54/6.27 | (302) all_62_1_29 = all_16_1_7
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (13) with all_1_1_1, all_1_2_2, all_138_2_70, all_153_2_82 and discharging atoms distinct_lines(all_1_1_1, all_1_2_2) = all_153_2_82, distinct_lines(all_1_1_1, all_1_2_2) = all_138_2_70, yields:
% 23.54/6.27 | (303) all_153_2_82 = all_138_2_70
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (13) with all_1_2_2, all_1_1_1, all_143_2_74, all_148_2_78 and discharging atoms distinct_lines(all_1_2_2, all_1_1_1) = all_148_2_78, distinct_lines(all_1_2_2, all_1_1_1) = all_143_2_74, yields:
% 23.54/6.27 | (304) all_148_2_78 = all_143_2_74
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (34) with all_1_2_2 yields:
% 23.54/6.27 | (305) ~ (distinct_lines(all_1_2_2, all_1_2_2) = 0)
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (46) with all_1_3_3 yields:
% 23.54/6.27 | (306) ~ (distinct_points(all_1_3_3, all_1_3_3) = 0)
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (32) with all_1_3_3, all_1_3_3, all_70_0_40, all_78_0_52 and discharging atoms distinct_points(all_1_3_3, all_1_3_3) = all_78_0_52, distinct_points(all_1_3_3, all_1_3_3) = all_70_0_40, yields:
% 23.54/6.27 | (307) all_78_0_52 = all_70_0_40
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (32) with all_1_3_3, all_1_3_3, all_68_0_37, all_78_0_52 and discharging atoms distinct_points(all_1_3_3, all_1_3_3) = all_78_0_52, distinct_points(all_1_3_3, all_1_3_3) = all_68_0_37, yields:
% 23.54/6.27 | (308) all_78_0_52 = all_68_0_37
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (32) with all_1_4_4, all_1_5_5, all_138_3_71, all_148_3_79 and discharging atoms distinct_points(all_1_4_4, all_1_5_5) = all_148_3_79, distinct_points(all_1_4_4, all_1_5_5) = all_138_3_71, yields:
% 23.54/6.27 | (309) all_148_3_79 = all_138_3_71
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (32) with all_1_4_4, all_1_5_5, all_105_2_61, all_148_3_79 and discharging atoms distinct_points(all_1_4_4, all_1_5_5) = all_148_3_79, distinct_points(all_1_4_4, all_1_5_5) = all_105_2_61, yields:
% 23.54/6.27 | (310) all_148_3_79 = all_105_2_61
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (32) with all_1_4_4, all_1_5_5, all_74_0_46, all_138_3_71 and discharging atoms distinct_points(all_1_4_4, all_1_5_5) = all_138_3_71, distinct_points(all_1_4_4, all_1_5_5) = all_74_0_46, yields:
% 23.54/6.27 | (311) all_138_3_71 = all_74_0_46
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (32) with all_1_4_4, all_1_5_5, all_66_0_34, all_138_3_71 and discharging atoms distinct_points(all_1_4_4, all_1_5_5) = all_138_3_71, distinct_points(all_1_4_4, all_1_5_5) = all_66_0_34, yields:
% 23.54/6.27 | (312) all_138_3_71 = all_66_0_34
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (32) with all_1_4_4, all_1_5_5, 0, all_138_3_71 and discharging atoms distinct_points(all_1_4_4, all_1_5_5) = all_138_3_71, distinct_points(all_1_4_4, all_1_5_5) = 0, yields:
% 23.54/6.27 | (313) all_138_3_71 = 0
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (32) with all_1_5_5, all_1_3_3, all_68_2_39, all_76_0_49 and discharging atoms distinct_points(all_1_5_5, all_1_3_3) = all_76_0_49, distinct_points(all_1_5_5, all_1_3_3) = all_68_2_39, yields:
% 23.54/6.27 | (314) all_76_0_49 = all_68_2_39
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (32) with all_1_5_5, all_1_3_3, all_64_0_31, all_76_0_49 and discharging atoms distinct_points(all_1_5_5, all_1_3_3) = all_76_0_49, distinct_points(all_1_5_5, all_1_3_3) = all_64_0_31, yields:
% 23.54/6.27 | (315) all_76_0_49 = all_64_0_31
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (32) with all_1_5_5, all_1_3_3, all_60_0_25, all_68_2_39 and discharging atoms distinct_points(all_1_5_5, all_1_3_3) = all_68_2_39, distinct_points(all_1_5_5, all_1_3_3) = all_60_0_25, yields:
% 23.54/6.27 | (316) all_68_2_39 = all_60_0_25
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (32) with all_1_5_5, all_1_3_3, all_60_2_27, all_68_2_39 and discharging atoms distinct_points(all_1_5_5, all_1_3_3) = all_68_2_39, distinct_points(all_1_5_5, all_1_3_3) = all_60_2_27, yields:
% 23.54/6.27 | (317) all_68_2_39 = all_60_2_27
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (32) with all_1_5_5, all_1_4_4, all_153_3_83, 0 and discharging atoms distinct_points(all_1_5_5, all_1_4_4) = all_153_3_83, distinct_points(all_1_5_5, all_1_4_4) = 0, yields:
% 23.54/6.27 | (318) all_153_3_83 = 0
% 23.54/6.27 |
% 23.54/6.27 | Instantiating formula (32) with all_1_5_5, all_1_5_5, all_114_2_64, all_16_0_6 and discharging atoms distinct_points(all_1_5_5, all_1_5_5) = all_114_2_64, distinct_points(all_1_5_5, all_1_5_5) = all_16_0_6, yields:
% 23.54/6.27 | (319) all_114_2_64 = all_16_0_6
% 23.54/6.27 |
% 23.54/6.27 | Using (233) and (54) yields:
% 23.54/6.27 | (320) ~ (all_114_2_64 = 0)
% 23.54/6.27 |
% 23.54/6.27 | Combining equations (297,300) yields a new equation:
% 23.54/6.27 | (321) all_148_0_76 = all_138_0_68
% 23.54/6.27 |
% 23.54/6.27 | Simplifying 321 yields:
% 23.54/6.27 | (322) all_148_0_76 = all_138_0_68
% 23.54/6.27 |
% 23.54/6.27 | Combining equations (299,322) yields a new equation:
% 23.54/6.27 | (323) all_143_1_73 = all_138_0_68
% 23.54/6.27 |
% 23.54/6.28 | Simplifying 323 yields:
% 23.54/6.28 | (324) all_143_1_73 = all_138_0_68
% 23.54/6.28 |
% 23.54/6.28 | Combining equations (309,310) yields a new equation:
% 23.54/6.28 | (325) all_138_3_71 = all_105_2_61
% 23.54/6.28 |
% 23.54/6.28 | Simplifying 325 yields:
% 23.54/6.28 | (326) all_138_3_71 = all_105_2_61
% 23.54/6.28 |
% 23.54/6.28 | Combining equations (301,324) yields a new equation:
% 23.54/6.28 | (327) all_138_0_68 = all_60_1_26
% 23.54/6.28 |
% 23.54/6.28 | Combining equations (298,324) yields a new equation:
% 23.54/6.28 | (328) all_138_0_68 = all_33_1_23
% 23.54/6.28 |
% 23.54/6.28 | Combining equations (328,327) yields a new equation:
% 23.54/6.28 | (329) all_60_1_26 = all_33_1_23
% 23.54/6.28 |
% 23.54/6.28 | Combining equations (312,326) yields a new equation:
% 23.54/6.28 | (330) all_105_2_61 = all_66_0_34
% 23.54/6.28 |
% 23.54/6.28 | Combining equations (311,326) yields a new equation:
% 23.54/6.28 | (331) all_105_2_61 = all_74_0_46
% 23.54/6.28 |
% 23.54/6.28 | Combining equations (313,326) yields a new equation:
% 23.54/6.28 | (332) all_105_2_61 = 0
% 23.54/6.28 |
% 23.54/6.28 | Combining equations (330,331) yields a new equation:
% 23.54/6.28 | (333) all_74_0_46 = all_66_0_34
% 23.54/6.28 |
% 23.54/6.28 | Combining equations (332,331) yields a new equation:
% 23.54/6.28 | (334) all_74_0_46 = 0
% 23.54/6.28 |
% 23.54/6.28 | Combining equations (294,293) yields a new equation:
% 23.54/6.28 | (335) all_100_1_57 = 0
% 23.54/6.28 |
% 23.54/6.28 | Simplifying 335 yields:
% 23.54/6.28 | (336) all_100_1_57 = 0
% 23.54/6.28 |
% 23.54/6.28 | Combining equations (307,308) yields a new equation:
% 23.54/6.28 | (337) all_70_0_40 = all_68_0_37
% 23.54/6.28 |
% 23.54/6.28 | Simplifying 337 yields:
% 23.54/6.28 | (338) all_70_0_40 = all_68_0_37
% 23.54/6.28 |
% 23.54/6.28 | Combining equations (314,315) yields a new equation:
% 23.54/6.28 | (339) all_68_2_39 = all_64_0_31
% 23.54/6.28 |
% 23.54/6.28 | Simplifying 339 yields:
% 23.54/6.28 | (340) all_68_2_39 = all_64_0_31
% 23.54/6.28 |
% 23.54/6.28 | Combining equations (334,333) yields a new equation:
% 23.54/6.28 | (341) all_66_0_34 = 0
% 23.54/6.28 |
% 23.54/6.28 | Combining equations (317,340) yields a new equation:
% 23.54/6.28 | (342) all_64_0_31 = all_60_2_27
% 23.54/6.28 |
% 23.54/6.28 | Combining equations (316,340) yields a new equation:
% 23.54/6.28 | (343) all_64_0_31 = all_60_0_25
% 23.54/6.28 |
% 23.54/6.28 | Combining equations (343,342) yields a new equation:
% 23.54/6.28 | (344) all_60_0_25 = all_60_2_27
% 23.54/6.28 |
% 23.54/6.28 | Simplifying 344 yields:
% 23.54/6.28 | (345) all_60_0_25 = all_60_2_27
% 23.54/6.28 |
% 23.54/6.28 | Combining equations (342,340) yields a new equation:
% 23.54/6.28 | (317) all_68_2_39 = all_60_2_27
% 23.54/6.28 |
% 23.54/6.28 | Combining equations (329,327) yields a new equation:
% 23.54/6.28 | (328) all_138_0_68 = all_33_1_23
% 23.54/6.28 |
% 23.54/6.28 | Combining equations (328,300) yields a new equation:
% 23.54/6.28 | (348) all_153_1_81 = all_33_1_23
% 23.54/6.28 |
% 23.54/6.28 | Equations (319) can reduce 320 to:
% 23.54/6.28 | (114) ~ (all_16_0_6 = 0)
% 23.54/6.28 |
% 23.54/6.28 | From (291) and (182) follows:
% 23.54/6.28 | (350) apart_point_and_line(all_1_3_3, all_64_2_33) = all_70_1_41
% 23.54/6.28 |
% 23.54/6.28 | From (336) and (214) follows:
% 23.54/6.28 | (50) apart_point_and_line(all_1_3_3, all_1_2_2) = 0
% 23.54/6.28 |
% 23.54/6.28 | From (292) and (192) follows:
% 23.54/6.28 | (352) apart_point_and_line(all_1_4_4, all_1_2_2) = all_74_1_47
% 23.54/6.28 |
% 23.54/6.28 | From (302) and (161) follows:
% 23.54/6.28 | (62) apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7
% 23.54/6.28 |
% 23.54/6.28 | From (303) and (290) follows:
% 23.54/6.28 | (256) distinct_lines(all_1_1_1, all_1_2_2) = all_138_2_70
% 23.54/6.28 |
% 23.54/6.28 | From (304) and (276) follows:
% 23.54/6.28 | (270) distinct_lines(all_1_2_2, all_1_1_1) = all_143_2_74
% 23.54/6.28 |
% 23.54/6.28 | From (338) and (183) follows:
% 23.54/6.28 | (177) distinct_points(all_1_3_3, all_1_3_3) = all_68_0_37
% 23.54/6.28 |
% 23.54/6.28 | From (341) and (172) follows:
% 23.54/6.28 | (206) distinct_points(all_1_4_4, all_1_5_5) = 0
% 23.54/6.28 |
% 23.54/6.28 | From (345) and (157) follows:
% 23.54/6.28 | (158) distinct_points(all_1_5_5, all_1_3_3) = all_60_2_27
% 23.54/6.28 |
% 23.54/6.28 +-Applying beta-rule and splitting (295), into two cases.
% 23.54/6.28 |-Branch one:
% 23.54/6.28 | (359) ~ (apart_point_and_line(all_1_4_4, all_1_2_2) = all_74_1_47)
% 23.54/6.28 |
% 23.54/6.28 | Using (352) and (359) yields:
% 23.54/6.28 | (122) $false
% 23.54/6.28 |
% 23.54/6.28 |-The branch is then unsatisfiable
% 23.54/6.28 |-Branch two:
% 23.54/6.28 | (352) apart_point_and_line(all_1_4_4, all_1_2_2) = all_74_1_47
% 23.54/6.28 | (362) all_153_0_80 = all_74_1_47
% 23.54/6.28 |
% 23.54/6.28 | Combining equations (362,296) yields a new equation:
% 23.54/6.28 | (363) all_74_1_47 = all_66_1_35
% 23.54/6.28 |
% 23.54/6.28 | Simplifying 363 yields:
% 23.54/6.28 | (364) all_74_1_47 = all_66_1_35
% 23.54/6.28 |
% 23.54/6.28 | Equations (364) can reduce 207 to:
% 23.54/6.28 | (365) ~ (all_66_1_35 = 0)
% 23.54/6.28 |
% 23.54/6.28 | From (364) and (352) follows:
% 23.54/6.28 | (171) apart_point_and_line(all_1_4_4, all_1_2_2) = all_66_1_35
% 23.54/6.28 |
% 23.54/6.28 +-Applying beta-rule and splitting (140), into two cases.
% 23.54/6.28 |-Branch one:
% 23.54/6.28 | (208) all_16_1_7 = 0
% 23.54/6.28 |
% 23.54/6.28 | Equations (208) can reduce 126 to:
% 23.54/6.28 | (82) $false
% 23.54/6.28 |
% 23.54/6.28 |-The branch is then unsatisfiable
% 23.54/6.28 |-Branch two:
% 23.54/6.28 | (126) ~ (all_16_1_7 = 0)
% 23.54/6.28 | (370) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & apart_point_and_line(all_1_4_4, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.54/6.28 |
% 23.54/6.28 | Instantiating (370) with all_167_0_84, all_167_1_85, all_167_2_86 yields:
% 23.54/6.28 | (371) apart_point_and_line(all_1_4_4, all_1_2_2) = all_167_0_84 & apart_point_and_line(all_1_4_4, all_1_2_2) = all_167_1_85 & distinct_lines(all_1_2_2, all_1_2_2) = all_167_2_86 & ( ~ (all_167_2_86 = 0) | all_167_0_84 = 0 | all_167_1_85 = 0)
% 23.54/6.28 |
% 23.54/6.28 | Applying alpha-rule on (371) yields:
% 23.54/6.28 | (372) apart_point_and_line(all_1_4_4, all_1_2_2) = all_167_0_84
% 23.54/6.28 | (373) apart_point_and_line(all_1_4_4, all_1_2_2) = all_167_1_85
% 23.54/6.28 | (374) distinct_lines(all_1_2_2, all_1_2_2) = all_167_2_86
% 23.54/6.28 | (375) ~ (all_167_2_86 = 0) | all_167_0_84 = 0 | all_167_1_85 = 0
% 23.54/6.28 |
% 23.54/6.28 | Instantiating formula (15) with all_1_4_4, all_1_2_2, all_167_0_84, all_66_1_35 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_167_0_84, apart_point_and_line(all_1_4_4, all_1_2_2) = all_66_1_35, yields:
% 23.54/6.28 | (376) all_167_0_84 = all_66_1_35
% 23.54/6.28 |
% 23.54/6.28 | Instantiating formula (15) with all_1_4_4, all_1_2_2, all_167_1_85, all_167_0_84 and discharging atoms apart_point_and_line(all_1_4_4, all_1_2_2) = all_167_0_84, apart_point_and_line(all_1_4_4, all_1_2_2) = all_167_1_85, yields:
% 23.54/6.28 | (377) all_167_0_84 = all_167_1_85
% 23.54/6.28 |
% 23.54/6.28 | Using (177) and (306) yields:
% 23.54/6.28 | (378) ~ (all_68_0_37 = 0)
% 23.54/6.28 |
% 23.54/6.28 | Combining equations (376,377) yields a new equation:
% 23.54/6.28 | (379) all_167_1_85 = all_66_1_35
% 23.54/6.28 |
% 23.54/6.28 | From (379) and (373) follows:
% 23.54/6.28 | (171) apart_point_and_line(all_1_4_4, all_1_2_2) = all_66_1_35
% 23.54/6.28 |
% 23.54/6.28 +-Applying beta-rule and splitting (184), into two cases.
% 23.54/6.28 |-Branch one:
% 23.54/6.28 | (381) ~ (all_70_1_41 = 0)
% 23.54/6.28 |
% 23.54/6.28 | Instantiating formula (17) with all_68_1_38, all_1_1_1, all_1_2_2, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_68_1_38, apart_point_and_line(all_1_3_3, all_1_2_2) = 0, yields:
% 23.54/6.28 | (382) all_68_1_38 = 0 | distinct_lines(all_1_2_2, all_1_1_1) = 0
% 23.54/6.28 |
% 23.54/6.28 | Instantiating formula (42) with all_70_1_41, all_68_1_38, all_64_2_33, all_1_1_1, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_64_2_33) = all_70_1_41, apart_point_and_line(all_1_3_3, all_1_1_1) = all_68_1_38, distinct_points(all_1_3_3, all_1_4_4) = 0, yields:
% 23.54/6.28 | (383) all_70_1_41 = 0 | all_68_1_38 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_64_2_33) = v2 & apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_64_2_33) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.54/6.28 |
% 23.54/6.28 | Instantiating formula (7) with all_72_1_44, all_1_0_0, all_72_2_45, all_1_1_1, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_4_4, all_72_2_45) = all_72_1_44, apart_point_and_line(all_1_4_4, all_1_1_1) = all_1_0_0, distinct_points(all_1_3_3, all_1_4_4) = 0, yields:
% 23.54/6.28 | (384) all_72_1_44 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_72_2_45) = v2 & apart_point_and_line(all_1_3_3, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_72_2_45) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.54/6.29 |
% 23.54/6.29 | Instantiating formula (7) with all_1_0_0, all_72_1_44, all_1_1_1, all_72_2_45, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_4_4, all_72_2_45) = all_72_1_44, apart_point_and_line(all_1_4_4, all_1_1_1) = all_1_0_0, distinct_points(all_1_3_3, all_1_4_4) = 0, yields:
% 23.54/6.29 | (385) all_72_1_44 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_72_2_45) = v1 & apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & distinct_lines(all_72_2_45, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.54/6.29 |
% 23.54/6.29 | Instantiating formula (1) with all_72_1_44, all_1_0_0, all_72_2_45, all_1_1_1, all_1_4_4, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_72_2_45) = all_72_1_44, apart_point_and_line(all_1_4_4, all_1_1_1) = all_1_0_0, yields:
% 23.54/6.29 | (386) all_72_1_44 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_72_2_45) = v2 & apart_point_and_line(all_1_4_4, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_72_2_45) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.29 |
% 23.54/6.29 | Instantiating formula (1) with all_1_0_0, all_72_1_44, all_1_1_1, all_72_2_45, all_1_4_4, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_72_2_45) = all_72_1_44, apart_point_and_line(all_1_4_4, all_1_1_1) = all_1_0_0, yields:
% 23.54/6.29 | (387) all_72_1_44 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_72_2_45) = v3 & apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & distinct_lines(all_72_2_45, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.29 |
% 23.54/6.29 | Instantiating formula (28) with all_72_1_44, all_1_0_0, all_1_1_1, all_72_2_45, all_1_4_4, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_72_2_45) = all_72_1_44, apart_point_and_line(all_1_4_4, all_1_1_1) = all_1_0_0, yields:
% 23.54/6.29 | (388) all_72_1_44 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_72_2_45) = v2 & apart_point_and_line(all_1_4_4, all_1_1_1) = v3 & distinct_lines(all_72_2_45, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.29 |
% 23.54/6.29 | Instantiating formula (28) with all_1_0_0, all_72_1_44, all_72_2_45, all_1_1_1, all_1_4_4, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_72_2_45) = all_72_1_44, apart_point_and_line(all_1_4_4, all_1_1_1) = all_1_0_0, yields:
% 23.54/6.29 | (389) all_72_1_44 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_72_2_45) = v3 & apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_72_2_45) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.29 |
% 23.54/6.29 | Instantiating formula (1) with all_72_1_44, all_70_1_41, all_72_2_45, all_64_2_33, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_64_2_33) = all_70_1_41, apart_point_and_line(all_1_4_4, all_72_2_45) = all_72_1_44, yields:
% 23.54/6.29 | (390) all_72_1_44 = 0 | all_70_1_41 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_72_2_45) = v2 & apart_point_and_line(all_1_4_4, all_64_2_33) = v3 & distinct_lines(all_64_2_33, all_72_2_45) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.29 |
% 23.54/6.29 | Instantiating formula (1) with all_70_1_41, all_72_1_44, all_64_2_33, all_72_2_45, all_1_3_3, all_1_4_4 and discharging atoms apart_point_and_line(all_1_3_3, all_64_2_33) = all_70_1_41, apart_point_and_line(all_1_4_4, all_72_2_45) = all_72_1_44, yields:
% 23.54/6.29 | (391) all_72_1_44 = 0 | all_70_1_41 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_72_2_45) = v3 & apart_point_and_line(all_1_4_4, all_64_2_33) = v2 & distinct_lines(all_72_2_45, all_64_2_33) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.29 |
% 23.54/6.29 | Instantiating formula (28) with all_72_1_44, all_70_1_41, all_64_2_33, all_72_2_45, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_64_2_33) = all_70_1_41, apart_point_and_line(all_1_4_4, all_72_2_45) = all_72_1_44, yields:
% 23.54/6.29 | (392) all_72_1_44 = 0 | all_70_1_41 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_72_2_45) = v2 & apart_point_and_line(all_1_4_4, all_64_2_33) = v3 & distinct_lines(all_72_2_45, all_64_2_33) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.29 |
% 23.54/6.29 | Instantiating formula (28) with all_70_1_41, all_72_1_44, all_72_2_45, all_64_2_33, all_1_3_3, all_1_4_4 and discharging atoms apart_point_and_line(all_1_3_3, all_64_2_33) = all_70_1_41, apart_point_and_line(all_1_4_4, all_72_2_45) = all_72_1_44, yields:
% 23.54/6.29 | (393) all_72_1_44 = 0 | all_70_1_41 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_72_2_45) = v3 & apart_point_and_line(all_1_4_4, all_64_2_33) = v2 & distinct_lines(all_64_2_33, all_72_2_45) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.29 |
% 23.54/6.29 | Instantiating formula (1) with all_66_1_35, all_70_1_41, all_1_2_2, all_64_2_33, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_64_2_33) = all_70_1_41, apart_point_and_line(all_1_4_4, all_1_2_2) = all_66_1_35, yields:
% 23.54/6.29 | (394) all_70_1_41 = 0 | all_66_1_35 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_4_4, all_64_2_33) = v3 & distinct_lines(all_64_2_33, all_1_2_2) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.29 |
% 23.54/6.29 | Instantiating formula (28) with all_70_1_41, all_66_1_35, all_1_2_2, all_64_2_33, all_1_3_3, all_1_4_4 and discharging atoms apart_point_and_line(all_1_3_3, all_64_2_33) = all_70_1_41, apart_point_and_line(all_1_4_4, all_1_2_2) = all_66_1_35, yields:
% 23.54/6.29 | (395) all_70_1_41 = 0 | all_66_1_35 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v3 & apart_point_and_line(all_1_4_4, all_64_2_33) = v2 & distinct_lines(all_64_2_33, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.29 |
% 23.54/6.29 | Instantiating formula (7) with all_66_1_35, all_72_1_44, all_1_2_2, all_72_2_45, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_4_4, all_72_2_45) = all_72_1_44, apart_point_and_line(all_1_4_4, all_1_2_2) = all_66_1_35, distinct_points(all_1_3_3, all_1_4_4) = 0, yields:
% 23.54/6.29 | (396) all_72_1_44 = 0 | all_66_1_35 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_72_2_45) = v1 & apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & distinct_lines(all_72_2_45, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.54/6.29 |
% 23.54/6.29 | Instantiating formula (7) with all_72_1_44, all_66_1_35, all_72_2_45, all_1_2_2, all_1_4_4, all_1_3_3 and discharging atoms apart_point_and_line(all_1_4_4, all_72_2_45) = all_72_1_44, apart_point_and_line(all_1_4_4, all_1_2_2) = all_66_1_35, distinct_points(all_1_3_3, all_1_4_4) = 0, yields:
% 23.54/6.29 | (397) all_72_1_44 = 0 | all_66_1_35 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_72_2_45) = v2 & apart_point_and_line(all_1_3_3, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_72_2_45) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.54/6.29 |
% 23.54/6.29 | Instantiating formula (1) with all_66_1_35, all_72_1_44, all_1_2_2, all_72_2_45, all_1_4_4, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_72_2_45) = all_72_1_44, apart_point_and_line(all_1_4_4, all_1_2_2) = all_66_1_35, yields:
% 23.54/6.29 | (398) all_72_1_44 = 0 | all_66_1_35 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_72_2_45) = v3 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_72_2_45, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.54/6.29 |
% 23.54/6.29 | Instantiating formula (2) with all_16_1_7, all_138_2_70, all_1_2_2, all_1_1_1, all_1_5_5 and discharging atoms apart_point_and_line(all_1_5_5, all_1_2_2) = all_16_1_7, distinct_lines(all_1_1_1, all_1_2_2) = all_138_2_70, yields:
% 23.54/6.29 | (399) all_138_2_70 = 0 | all_16_1_7 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_1_5_5, all_1_1_1) = v0)
% 23.54/6.29 |
% 23.95/6.29 | Instantiating formula (23) with all_138_2_70, all_1_2_2, all_1_1_1 and discharging atoms distinct_lines(all_1_1_1, all_1_2_2) = all_138_2_70, yields:
% 23.95/6.29 | (400) all_138_2_70 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_1_1_1, all_1_2_2) = v0)
% 23.95/6.29 |
% 23.95/6.29 | Instantiating formula (2) with all_68_1_38, all_143_2_74, all_1_1_1, all_1_2_2, all_1_3_3 and discharging atoms apart_point_and_line(all_1_3_3, all_1_1_1) = all_68_1_38, distinct_lines(all_1_2_2, all_1_1_1) = all_143_2_74, yields:
% 23.95/6.30 | (401) all_143_2_74 = 0 | all_68_1_38 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_1_3_3, all_1_2_2) = v0)
% 23.95/6.30 |
% 23.95/6.30 | Instantiating formula (29) with all_138_2_70, all_1_2_2, all_1_1_1, all_1_2_2 and discharging atoms distinct_lines(all_1_1_1, all_1_2_2) = all_138_2_70, ~ (distinct_lines(all_1_2_2, all_1_2_2) = 0), yields:
% 23.95/6.30 | (402) all_138_2_70 = 0 | ~ (distinct_lines(all_1_2_2, all_1_1_1) = 0)
% 23.95/6.30 |
% 23.95/6.30 | Instantiating formula (23) with all_143_2_74, all_1_1_1, all_1_2_2 and discharging atoms distinct_lines(all_1_2_2, all_1_1_1) = all_143_2_74, yields:
% 23.95/6.30 | (403) all_143_2_74 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_1_2_2, all_1_1_1) = v0)
% 23.95/6.30 |
% 23.95/6.30 | Instantiating formula (42) with all_1_0_0, all_72_1_44, all_1_1_1, all_72_2_45, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_72_2_45) = all_72_1_44, apart_point_and_line(all_1_4_4, all_1_1_1) = all_1_0_0, distinct_points(all_1_4_4, all_1_5_5) = 0, yields:
% 23.95/6.30 | (404) all_72_1_44 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_72_2_45) = v1 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_72_2_45, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.95/6.30 |
% 23.95/6.30 | Instantiating formula (42) with all_72_1_44, all_1_0_0, all_72_2_45, all_1_1_1, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_72_2_45) = all_72_1_44, apart_point_and_line(all_1_4_4, all_1_1_1) = all_1_0_0, distinct_points(all_1_4_4, all_1_5_5) = 0, yields:
% 23.95/6.30 | (405) all_72_1_44 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_72_2_45) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_72_2_45) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.95/6.30 |
% 23.95/6.30 | Instantiating formula (42) with all_72_1_44, all_66_1_35, all_72_2_45, all_1_2_2, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_72_2_45) = all_72_1_44, apart_point_and_line(all_1_4_4, all_1_2_2) = all_66_1_35, distinct_points(all_1_4_4, all_1_5_5) = 0, yields:
% 23.95/6.30 | (406) all_72_1_44 = 0 | all_66_1_35 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_72_2_45) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_72_2_45) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.95/6.30 |
% 23.95/6.30 | Instantiating formula (42) with all_66_1_35, all_72_1_44, all_1_2_2, all_72_2_45, all_1_5_5, all_1_4_4 and discharging atoms apart_point_and_line(all_1_4_4, all_72_2_45) = all_72_1_44, apart_point_and_line(all_1_4_4, all_1_2_2) = all_66_1_35, distinct_points(all_1_4_4, all_1_5_5) = 0, yields:
% 23.95/6.30 | (407) all_72_1_44 = 0 | all_66_1_35 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_72_2_45) = v1 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_72_2_45, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.95/6.30 |
% 23.95/6.30 | Instantiating formula (10) with all_60_2_27, all_1_3_3, all_1_5_5, all_1_3_3 and discharging atoms distinct_points(all_1_3_3, all_1_5_5) = 0, distinct_points(all_1_5_5, all_1_3_3) = all_60_2_27, ~ (distinct_points(all_1_3_3, all_1_3_3) = 0), yields:
% 23.95/6.30 | (408) all_60_2_27 = 0
% 23.95/6.30 |
% 23.95/6.30 | Combining equations (408,317) yields a new equation:
% 23.95/6.30 | (409) all_68_2_39 = 0
% 23.95/6.30 |
% 23.95/6.30 +-Applying beta-rule and splitting (396), into two cases.
% 23.95/6.30 |-Branch one:
% 23.95/6.30 | (410) all_72_1_44 = 0
% 23.95/6.30 |
% 23.95/6.30 | Equations (410) can reduce 205 to:
% 23.95/6.30 | (82) $false
% 23.95/6.30 |
% 23.95/6.30 |-The branch is then unsatisfiable
% 23.95/6.30 |-Branch two:
% 23.95/6.30 | (205) ~ (all_72_1_44 = 0)
% 23.95/6.30 | (413) all_66_1_35 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_72_2_45) = v1 & apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & distinct_lines(all_72_2_45, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.95/6.30 |
% 23.95/6.30 +-Applying beta-rule and splitting (406), into two cases.
% 23.95/6.30 |-Branch one:
% 23.95/6.30 | (410) all_72_1_44 = 0
% 23.95/6.30 |
% 23.95/6.30 | Equations (410) can reduce 205 to:
% 23.95/6.30 | (82) $false
% 23.95/6.30 |
% 23.95/6.30 |-The branch is then unsatisfiable
% 23.95/6.30 |-Branch two:
% 23.95/6.30 | (205) ~ (all_72_1_44 = 0)
% 23.95/6.30 | (417) all_66_1_35 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_72_2_45) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_72_2_45) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.95/6.30 |
% 23.95/6.30 +-Applying beta-rule and splitting (397), into two cases.
% 23.95/6.30 |-Branch one:
% 23.95/6.30 | (410) all_72_1_44 = 0
% 23.95/6.30 |
% 23.95/6.30 | Equations (410) can reduce 205 to:
% 23.95/6.30 | (82) $false
% 23.95/6.30 |
% 23.95/6.30 |-The branch is then unsatisfiable
% 23.95/6.30 |-Branch two:
% 23.95/6.30 | (205) ~ (all_72_1_44 = 0)
% 23.95/6.30 | (421) all_66_1_35 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_72_2_45) = v2 & apart_point_and_line(all_1_3_3, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_72_2_45) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.95/6.30 |
% 23.95/6.30 +-Applying beta-rule and splitting (407), into two cases.
% 23.95/6.30 |-Branch one:
% 23.95/6.30 | (410) all_72_1_44 = 0
% 23.95/6.30 |
% 23.95/6.30 | Equations (410) can reduce 205 to:
% 23.95/6.30 | (82) $false
% 23.95/6.30 |
% 23.95/6.30 |-The branch is then unsatisfiable
% 23.95/6.30 |-Branch two:
% 23.95/6.30 | (205) ~ (all_72_1_44 = 0)
% 23.95/6.30 | (425) all_66_1_35 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_72_2_45) = v1 & apart_point_and_line(all_1_5_5, all_1_2_2) = v2 & distinct_lines(all_72_2_45, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.95/6.30 |
% 23.95/6.30 +-Applying beta-rule and splitting (398), into two cases.
% 23.95/6.30 |-Branch one:
% 23.95/6.30 | (410) all_72_1_44 = 0
% 23.95/6.30 |
% 23.95/6.30 | Equations (410) can reduce 205 to:
% 23.95/6.30 | (82) $false
% 23.95/6.30 |
% 23.95/6.30 |-The branch is then unsatisfiable
% 23.95/6.30 |-Branch two:
% 23.95/6.30 | (205) ~ (all_72_1_44 = 0)
% 23.95/6.30 | (429) all_66_1_35 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_72_2_45) = v3 & apart_point_and_line(all_1_4_4, all_1_2_2) = v2 & distinct_lines(all_72_2_45, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.95/6.30 |
% 23.95/6.30 +-Applying beta-rule and splitting (413), into two cases.
% 23.95/6.30 |-Branch one:
% 23.95/6.30 | (430) all_66_1_35 = 0
% 23.95/6.30 |
% 23.95/6.30 | Equations (430) can reduce 365 to:
% 23.95/6.30 | (82) $false
% 23.95/6.30 |
% 23.95/6.30 |-The branch is then unsatisfiable
% 23.95/6.30 |-Branch two:
% 23.95/6.30 | (365) ~ (all_66_1_35 = 0)
% 23.95/6.30 | (433) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_72_2_45) = v1 & apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & distinct_lines(all_72_2_45, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.95/6.30 |
% 23.95/6.30 +-Applying beta-rule and splitting (417), into two cases.
% 23.95/6.30 |-Branch one:
% 23.95/6.30 | (430) all_66_1_35 = 0
% 23.95/6.30 |
% 23.95/6.30 | Equations (430) can reduce 365 to:
% 23.95/6.30 | (82) $false
% 23.95/6.30 |
% 23.95/6.30 |-The branch is then unsatisfiable
% 23.95/6.30 |-Branch two:
% 23.95/6.30 | (365) ~ (all_66_1_35 = 0)
% 23.95/6.30 | (437) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_72_2_45) = v2 & apart_point_and_line(all_1_5_5, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_72_2_45) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.95/6.30 |
% 23.95/6.30 +-Applying beta-rule and splitting (394), into two cases.
% 23.95/6.30 |-Branch one:
% 23.95/6.30 | (438) all_70_1_41 = 0
% 23.95/6.30 |
% 23.95/6.30 | Equations (438) can reduce 381 to:
% 23.95/6.30 | (82) $false
% 23.95/6.30 |
% 23.95/6.30 |-The branch is then unsatisfiable
% 23.95/6.30 |-Branch two:
% 23.95/6.30 | (381) ~ (all_70_1_41 = 0)
% 23.95/6.30 | (441) all_66_1_35 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v2 & apart_point_and_line(all_1_4_4, all_64_2_33) = v3 & distinct_lines(all_64_2_33, all_1_2_2) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.95/6.30 |
% 23.95/6.30 +-Applying beta-rule and splitting (395), into two cases.
% 23.95/6.30 |-Branch one:
% 23.95/6.30 | (438) all_70_1_41 = 0
% 23.95/6.30 |
% 23.95/6.30 | Equations (438) can reduce 381 to:
% 23.95/6.30 | (82) $false
% 23.95/6.30 |
% 23.95/6.30 |-The branch is then unsatisfiable
% 23.95/6.30 |-Branch two:
% 23.95/6.30 | (381) ~ (all_70_1_41 = 0)
% 23.95/6.30 | (445) all_66_1_35 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_1_2_2) = v3 & apart_point_and_line(all_1_4_4, all_64_2_33) = v2 & distinct_lines(all_64_2_33, all_1_2_2) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.95/6.31 |
% 23.95/6.31 +-Applying beta-rule and splitting (384), into two cases.
% 23.95/6.31 |-Branch one:
% 23.95/6.31 | (410) all_72_1_44 = 0
% 23.95/6.31 |
% 23.95/6.31 | Equations (410) can reduce 205 to:
% 23.95/6.31 | (82) $false
% 23.95/6.31 |
% 23.95/6.31 |-The branch is then unsatisfiable
% 23.95/6.31 |-Branch two:
% 23.95/6.31 | (205) ~ (all_72_1_44 = 0)
% 23.95/6.31 | (449) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_72_2_45) = v2 & apart_point_and_line(all_1_3_3, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_72_2_45) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.95/6.31 |
% 23.95/6.31 +-Applying beta-rule and splitting (387), into two cases.
% 23.95/6.31 |-Branch one:
% 23.95/6.31 | (410) all_72_1_44 = 0
% 23.95/6.31 |
% 23.95/6.31 | Equations (410) can reduce 205 to:
% 23.95/6.31 | (82) $false
% 23.95/6.31 |
% 23.95/6.31 |-The branch is then unsatisfiable
% 23.95/6.31 |-Branch two:
% 23.95/6.31 | (205) ~ (all_72_1_44 = 0)
% 23.95/6.31 | (453) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_72_2_45) = v3 & apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & distinct_lines(all_72_2_45, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.95/6.31 |
% 23.95/6.31 +-Applying beta-rule and splitting (388), into two cases.
% 23.95/6.31 |-Branch one:
% 23.95/6.31 | (410) all_72_1_44 = 0
% 23.95/6.31 |
% 23.95/6.31 | Equations (410) can reduce 205 to:
% 23.95/6.31 | (82) $false
% 23.95/6.31 |
% 23.95/6.31 |-The branch is then unsatisfiable
% 23.95/6.31 |-Branch two:
% 23.95/6.31 | (205) ~ (all_72_1_44 = 0)
% 23.95/6.31 | (457) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_72_2_45) = v2 & apart_point_and_line(all_1_4_4, all_1_1_1) = v3 & distinct_lines(all_72_2_45, all_1_1_1) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.95/6.31 |
% 23.95/6.31 +-Applying beta-rule and splitting (389), into two cases.
% 23.95/6.31 |-Branch one:
% 23.95/6.31 | (410) all_72_1_44 = 0
% 23.95/6.31 |
% 23.95/6.31 | Equations (410) can reduce 205 to:
% 23.95/6.31 | (82) $false
% 23.95/6.31 |
% 23.95/6.31 |-The branch is then unsatisfiable
% 23.95/6.31 |-Branch two:
% 23.95/6.31 | (205) ~ (all_72_1_44 = 0)
% 23.95/6.31 | (461) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_72_2_45) = v3 & apart_point_and_line(all_1_4_4, all_1_1_1) = v2 & distinct_lines(all_1_1_1, all_72_2_45) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.95/6.31 |
% 23.95/6.31 +-Applying beta-rule and splitting (404), into two cases.
% 23.95/6.31 |-Branch one:
% 23.95/6.31 | (410) all_72_1_44 = 0
% 23.95/6.31 |
% 23.95/6.31 | Equations (410) can reduce 205 to:
% 23.95/6.31 | (82) $false
% 23.95/6.31 |
% 23.95/6.31 |-The branch is then unsatisfiable
% 23.95/6.31 |-Branch two:
% 23.95/6.31 | (205) ~ (all_72_1_44 = 0)
% 23.95/6.31 | (465) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_72_2_45) = v1 & apart_point_and_line(all_1_5_5, all_1_1_1) = v2 & distinct_lines(all_72_2_45, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.95/6.31 |
% 23.95/6.31 +-Applying beta-rule and splitting (385), into two cases.
% 23.95/6.31 |-Branch one:
% 23.95/6.31 | (410) all_72_1_44 = 0
% 23.95/6.31 |
% 23.95/6.31 | Equations (410) can reduce 205 to:
% 23.95/6.31 | (82) $false
% 23.95/6.31 |
% 23.95/6.31 |-The branch is then unsatisfiable
% 23.95/6.31 |-Branch two:
% 23.95/6.31 | (205) ~ (all_72_1_44 = 0)
% 23.95/6.31 | (469) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_3_3, all_72_2_45) = v1 & apart_point_and_line(all_1_3_3, all_1_1_1) = v2 & distinct_lines(all_72_2_45, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.95/6.31 |
% 23.95/6.31 +-Applying beta-rule and splitting (405), into two cases.
% 23.95/6.31 |-Branch one:
% 23.95/6.31 | (410) all_72_1_44 = 0
% 23.95/6.31 |
% 23.95/6.31 | Equations (410) can reduce 205 to:
% 23.95/6.31 | (82) $false
% 23.95/6.31 |
% 23.95/6.31 |-The branch is then unsatisfiable
% 23.95/6.31 |-Branch two:
% 23.95/6.31 | (205) ~ (all_72_1_44 = 0)
% 23.95/6.31 | (473) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_5_5, all_72_2_45) = v2 & apart_point_and_line(all_1_5_5, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_72_2_45) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.95/6.31 |
% 23.95/6.31 +-Applying beta-rule and splitting (386), into two cases.
% 23.95/6.31 |-Branch one:
% 23.95/6.31 | (410) all_72_1_44 = 0
% 23.95/6.31 |
% 23.95/6.31 | Equations (410) can reduce 205 to:
% 23.95/6.31 | (82) $false
% 23.95/6.31 |
% 23.95/6.31 |-The branch is then unsatisfiable
% 23.95/6.31 |-Branch two:
% 23.95/6.31 | (205) ~ (all_72_1_44 = 0)
% 23.95/6.31 | (477) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_4_4, all_72_2_45) = v2 & apart_point_and_line(all_1_4_4, all_1_1_1) = v3 & distinct_lines(all_1_1_1, all_72_2_45) = v1 & distinct_points(all_1_4_4, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.95/6.31 |
% 23.95/6.31 +-Applying beta-rule and splitting (393), into two cases.
% 23.95/6.31 |-Branch one:
% 23.95/6.31 | (410) all_72_1_44 = 0
% 23.95/6.31 |
% 23.95/6.31 | Equations (410) can reduce 205 to:
% 23.95/6.31 | (82) $false
% 23.95/6.31 |
% 23.95/6.31 |-The branch is then unsatisfiable
% 23.95/6.31 |-Branch two:
% 23.95/6.31 | (205) ~ (all_72_1_44 = 0)
% 23.95/6.31 | (481) all_70_1_41 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_72_2_45) = v3 & apart_point_and_line(all_1_4_4, all_64_2_33) = v2 & distinct_lines(all_64_2_33, all_72_2_45) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.95/6.31 |
% 23.95/6.31 +-Applying beta-rule and splitting (391), into two cases.
% 23.95/6.31 |-Branch one:
% 23.95/6.31 | (410) all_72_1_44 = 0
% 23.95/6.31 |
% 23.95/6.31 | Equations (410) can reduce 205 to:
% 23.95/6.31 | (82) $false
% 23.95/6.31 |
% 23.95/6.31 |-The branch is then unsatisfiable
% 23.95/6.31 |-Branch two:
% 23.95/6.31 | (205) ~ (all_72_1_44 = 0)
% 23.95/6.31 | (485) all_70_1_41 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_72_2_45) = v3 & apart_point_and_line(all_1_4_4, all_64_2_33) = v2 & distinct_lines(all_72_2_45, all_64_2_33) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.95/6.31 |
% 23.95/6.31 +-Applying beta-rule and splitting (390), into two cases.
% 23.95/6.31 |-Branch one:
% 23.95/6.31 | (410) all_72_1_44 = 0
% 23.95/6.31 |
% 23.95/6.31 | Equations (410) can reduce 205 to:
% 23.95/6.31 | (82) $false
% 23.95/6.31 |
% 23.95/6.31 |-The branch is then unsatisfiable
% 23.95/6.31 |-Branch two:
% 23.95/6.31 | (205) ~ (all_72_1_44 = 0)
% 23.95/6.31 | (489) all_70_1_41 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_72_2_45) = v2 & apart_point_and_line(all_1_4_4, all_64_2_33) = v3 & distinct_lines(all_64_2_33, all_72_2_45) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.95/6.31 |
% 23.95/6.31 +-Applying beta-rule and splitting (392), into two cases.
% 23.95/6.31 |-Branch one:
% 23.95/6.31 | (410) all_72_1_44 = 0
% 23.95/6.31 |
% 23.95/6.31 | Equations (410) can reduce 205 to:
% 23.95/6.31 | (82) $false
% 23.95/6.31 |
% 23.95/6.31 |-The branch is then unsatisfiable
% 23.95/6.31 |-Branch two:
% 23.95/6.31 | (205) ~ (all_72_1_44 = 0)
% 23.95/6.31 | (493) all_70_1_41 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_72_2_45) = v2 & apart_point_and_line(all_1_4_4, all_64_2_33) = v3 & distinct_lines(all_72_2_45, all_64_2_33) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.95/6.31 |
% 23.95/6.31 +-Applying beta-rule and splitting (159), into two cases.
% 23.95/6.31 |-Branch one:
% 23.95/6.31 | (494) ~ (all_60_1_26 = 0)
% 23.95/6.31 |
% 23.95/6.31 | Equations (329) can reduce 494 to:
% 23.95/6.31 | (495) ~ (all_33_1_23 = 0)
% 23.95/6.31 |
% 23.95/6.31 +-Applying beta-rule and splitting (481), into two cases.
% 23.95/6.31 |-Branch one:
% 23.95/6.31 | (438) all_70_1_41 = 0
% 23.95/6.31 |
% 23.95/6.31 | Equations (438) can reduce 381 to:
% 23.95/6.31 | (82) $false
% 23.95/6.31 |
% 23.95/6.31 |-The branch is then unsatisfiable
% 23.95/6.31 |-Branch two:
% 23.95/6.31 | (381) ~ (all_70_1_41 = 0)
% 23.95/6.31 | (499) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_72_2_45) = v3 & apart_point_and_line(all_1_4_4, all_64_2_33) = v2 & distinct_lines(all_64_2_33, all_72_2_45) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.95/6.31 |
% 23.95/6.31 +-Applying beta-rule and splitting (485), into two cases.
% 23.95/6.31 |-Branch one:
% 23.95/6.31 | (438) all_70_1_41 = 0
% 23.95/6.32 |
% 23.95/6.32 | Equations (438) can reduce 381 to:
% 23.95/6.32 | (82) $false
% 23.95/6.32 |
% 23.95/6.32 |-The branch is then unsatisfiable
% 23.95/6.32 |-Branch two:
% 23.95/6.32 | (381) ~ (all_70_1_41 = 0)
% 23.95/6.32 | (503) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_72_2_45) = v3 & apart_point_and_line(all_1_4_4, all_64_2_33) = v2 & distinct_lines(all_72_2_45, all_64_2_33) = v1 & distinct_points(all_1_4_4, all_1_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.95/6.32 |
% 23.95/6.32 +-Applying beta-rule and splitting (489), into two cases.
% 23.95/6.32 |-Branch one:
% 23.95/6.32 | (438) all_70_1_41 = 0
% 23.95/6.32 |
% 23.95/6.32 | Equations (438) can reduce 381 to:
% 23.95/6.32 | (82) $false
% 23.95/6.32 |
% 23.95/6.32 |-The branch is then unsatisfiable
% 23.95/6.32 |-Branch two:
% 23.95/6.32 | (381) ~ (all_70_1_41 = 0)
% 23.95/6.32 | (507) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_72_2_45) = v2 & apart_point_and_line(all_1_4_4, all_64_2_33) = v3 & distinct_lines(all_64_2_33, all_72_2_45) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.95/6.32 |
% 23.95/6.32 +-Applying beta-rule and splitting (493), into two cases.
% 23.95/6.32 |-Branch one:
% 23.95/6.32 | (438) all_70_1_41 = 0
% 23.95/6.32 |
% 23.95/6.32 | Equations (438) can reduce 381 to:
% 23.95/6.32 | (82) $false
% 23.95/6.32 |
% 23.95/6.32 |-The branch is then unsatisfiable
% 23.95/6.32 |-Branch two:
% 23.95/6.32 | (381) ~ (all_70_1_41 = 0)
% 23.95/6.32 | (511) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_3_3, all_72_2_45) = v2 & apart_point_and_line(all_1_4_4, all_64_2_33) = v3 & distinct_lines(all_72_2_45, all_64_2_33) = v1 & distinct_points(all_1_3_3, all_1_4_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 23.95/6.32 |
% 23.95/6.32 +-Applying beta-rule and splitting (257), into two cases.
% 23.95/6.32 |-Branch one:
% 23.95/6.32 | (512) ~ (all_138_2_70 = 0)
% 23.95/6.32 |
% 23.95/6.32 +-Applying beta-rule and splitting (400), into two cases.
% 23.95/6.32 |-Branch one:
% 23.95/6.32 | (513) all_138_2_70 = 0
% 23.95/6.32 |
% 23.95/6.32 | Equations (513) can reduce 512 to:
% 23.95/6.32 | (82) $false
% 23.95/6.32 |
% 23.95/6.32 |-The branch is then unsatisfiable
% 23.95/6.32 |-Branch two:
% 23.95/6.32 | (512) ~ (all_138_2_70 = 0)
% 23.95/6.32 | (516) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_1_1_1, all_1_2_2) = v0)
% 23.95/6.32 |
% 23.95/6.32 +-Applying beta-rule and splitting (179), into two cases.
% 23.95/6.32 |-Branch one:
% 23.95/6.32 | (517) ~ (all_68_1_38 = 0)
% 23.95/6.32 |
% 23.95/6.32 +-Applying beta-rule and splitting (383), into two cases.
% 23.95/6.32 |-Branch one:
% 23.95/6.32 | (438) all_70_1_41 = 0
% 23.95/6.32 |
% 23.95/6.32 | Equations (438) can reduce 381 to:
% 23.95/6.32 | (82) $false
% 23.95/6.32 |
% 23.95/6.32 |-The branch is then unsatisfiable
% 23.95/6.32 |-Branch two:
% 23.95/6.32 | (381) ~ (all_70_1_41 = 0)
% 23.95/6.32 | (521) all_68_1_38 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_64_2_33) = v2 & apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_64_2_33) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.95/6.32 |
% 23.95/6.32 +-Applying beta-rule and splitting (521), into two cases.
% 23.95/6.32 |-Branch one:
% 23.95/6.32 | (522) all_68_1_38 = 0
% 23.95/6.32 |
% 23.95/6.32 | Equations (522) can reduce 517 to:
% 23.95/6.32 | (82) $false
% 23.95/6.32 |
% 23.95/6.32 |-The branch is then unsatisfiable
% 23.95/6.32 |-Branch two:
% 23.95/6.32 | (517) ~ (all_68_1_38 = 0)
% 23.95/6.32 | (525) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_4_4, all_64_2_33) = v2 & apart_point_and_line(all_1_4_4, all_1_1_1) = v1 & distinct_lines(all_1_1_1, all_64_2_33) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 23.95/6.32 |
% 23.95/6.32 +-Applying beta-rule and splitting (278), into two cases.
% 23.95/6.32 |-Branch one:
% 23.95/6.32 | (526) ~ (all_148_2_78 = 0)
% 23.95/6.32 |
% 23.95/6.32 | Equations (304) can reduce 526 to:
% 23.95/6.32 | (527) ~ (all_143_2_74 = 0)
% 23.95/6.32 |
% 23.95/6.32 +-Applying beta-rule and splitting (403), into two cases.
% 23.95/6.32 |-Branch one:
% 23.95/6.32 | (528) all_143_2_74 = 0
% 23.95/6.32 |
% 23.95/6.32 | Equations (528) can reduce 527 to:
% 23.95/6.32 | (82) $false
% 23.95/6.32 |
% 23.95/6.32 |-The branch is then unsatisfiable
% 23.95/6.32 |-Branch two:
% 23.95/6.32 | (527) ~ (all_143_2_74 = 0)
% 23.95/6.32 | (531) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_1_2_2, all_1_1_1) = v0)
% 23.95/6.32 |
% 23.95/6.32 +-Applying beta-rule and splitting (399), into two cases.
% 23.95/6.32 |-Branch one:
% 23.95/6.32 | (513) all_138_2_70 = 0
% 23.95/6.32 |
% 23.95/6.32 | Equations (513) can reduce 512 to:
% 23.95/6.32 | (82) $false
% 23.95/6.32 |
% 23.95/6.32 |-The branch is then unsatisfiable
% 23.95/6.32 |-Branch two:
% 23.95/6.32 | (512) ~ (all_138_2_70 = 0)
% 23.95/6.32 | (535) all_16_1_7 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_1_5_5, all_1_1_1) = v0)
% 23.95/6.32 |
% 23.95/6.32 +-Applying beta-rule and splitting (401), into two cases.
% 23.95/6.32 |-Branch one:
% 23.95/6.32 | (528) all_143_2_74 = 0
% 23.95/6.32 |
% 23.95/6.32 | Equations (528) can reduce 527 to:
% 23.95/6.32 | (82) $false
% 23.95/6.32 |
% 23.95/6.32 |-The branch is then unsatisfiable
% 23.95/6.32 |-Branch two:
% 23.95/6.32 | (527) ~ (all_143_2_74 = 0)
% 23.95/6.32 | (539) all_68_1_38 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_1_3_3, all_1_2_2) = v0)
% 23.95/6.32 |
% 23.95/6.32 +-Applying beta-rule and splitting (539), into two cases.
% 23.95/6.32 |-Branch one:
% 23.95/6.32 | (522) all_68_1_38 = 0
% 23.95/6.32 |
% 23.95/6.32 | Equations (522) can reduce 517 to:
% 23.95/6.32 | (82) $false
% 23.95/6.32 |
% 23.95/6.32 |-The branch is then unsatisfiable
% 23.95/6.32 |-Branch two:
% 23.95/6.32 | (517) ~ (all_68_1_38 = 0)
% 23.95/6.32 | (543) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_1_3_3, all_1_2_2) = v0)
% 23.95/6.32 |
% 23.95/6.32 +-Applying beta-rule and splitting (382), into two cases.
% 23.95/6.32 |-Branch one:
% 23.95/6.32 | (544) distinct_lines(all_1_2_2, all_1_1_1) = 0
% 23.95/6.32 |
% 23.95/6.32 +-Applying beta-rule and splitting (402), into two cases.
% 23.95/6.32 |-Branch one:
% 23.95/6.32 | (545) ~ (distinct_lines(all_1_2_2, all_1_1_1) = 0)
% 23.95/6.32 |
% 23.95/6.32 | Using (544) and (545) yields:
% 23.95/6.32 | (122) $false
% 23.95/6.32 |
% 23.95/6.32 |-The branch is then unsatisfiable
% 23.95/6.32 |-Branch two:
% 23.95/6.32 | (544) distinct_lines(all_1_2_2, all_1_1_1) = 0
% 23.95/6.32 | (513) all_138_2_70 = 0
% 23.95/6.32 |
% 23.95/6.32 | Equations (513) can reduce 512 to:
% 23.95/6.32 | (82) $false
% 23.95/6.32 |
% 23.95/6.32 |-The branch is then unsatisfiable
% 23.95/6.32 |-Branch two:
% 23.95/6.32 | (545) ~ (distinct_lines(all_1_2_2, all_1_1_1) = 0)
% 23.95/6.32 | (522) all_68_1_38 = 0
% 23.95/6.32 |
% 23.95/6.32 | Equations (522) can reduce 517 to:
% 23.95/6.32 | (82) $false
% 23.95/6.32 |
% 23.95/6.32 |-The branch is then unsatisfiable
% 23.95/6.32 |-Branch two:
% 23.95/6.32 | (553) all_148_2_78 = 0
% 23.95/6.32 | (554) ~ (all_148_3_79 = 0) | all_148_0_76 = 0 | all_148_1_77 = 0
% 23.95/6.32 |
% 23.95/6.32 | Combining equations (553,304) yields a new equation:
% 23.95/6.32 | (528) all_143_2_74 = 0
% 23.95/6.32 |
% 23.95/6.32 | From (528) and (270) follows:
% 23.95/6.32 | (544) distinct_lines(all_1_2_2, all_1_1_1) = 0
% 23.95/6.32 |
% 23.95/6.32 +-Applying beta-rule and splitting (402), into two cases.
% 23.95/6.32 |-Branch one:
% 23.95/6.32 | (545) ~ (distinct_lines(all_1_2_2, all_1_1_1) = 0)
% 23.95/6.32 |
% 23.95/6.32 | Using (544) and (545) yields:
% 23.95/6.32 | (122) $false
% 23.95/6.32 |
% 23.95/6.32 |-The branch is then unsatisfiable
% 23.95/6.33 |-Branch two:
% 23.95/6.33 | (544) distinct_lines(all_1_2_2, all_1_1_1) = 0
% 23.95/6.33 | (513) all_138_2_70 = 0
% 23.95/6.33 |
% 23.95/6.33 | Equations (513) can reduce 512 to:
% 23.95/6.33 | (82) $false
% 23.95/6.33 |
% 23.95/6.33 |-The branch is then unsatisfiable
% 23.95/6.33 |-Branch two:
% 23.95/6.33 | (522) all_68_1_38 = 0
% 23.95/6.33 | (563) ~ (all_68_2_39 = 0) | all_68_0_37 = 0
% 23.95/6.33 |
% 23.95/6.33 +-Applying beta-rule and splitting (563), into two cases.
% 23.95/6.33 |-Branch one:
% 23.95/6.33 | (564) ~ (all_68_2_39 = 0)
% 23.95/6.33 |
% 23.95/6.33 | Equations (409) can reduce 564 to:
% 23.95/6.33 | (82) $false
% 23.95/6.33 |
% 23.95/6.33 |-The branch is then unsatisfiable
% 23.95/6.33 |-Branch two:
% 23.95/6.33 | (409) all_68_2_39 = 0
% 23.95/6.33 | (567) all_68_0_37 = 0
% 23.95/6.33 |
% 23.95/6.33 | Equations (567) can reduce 378 to:
% 23.95/6.33 | (82) $false
% 23.95/6.33 |
% 23.95/6.33 |-The branch is then unsatisfiable
% 23.95/6.33 |-Branch two:
% 23.95/6.33 | (513) all_138_2_70 = 0
% 23.95/6.33 | (570) ~ (all_138_3_71 = 0) | all_138_0_68 = 0 | all_138_1_69 = 0
% 23.95/6.33 |
% 23.95/6.33 | Combining equations (513,303) yields a new equation:
% 23.95/6.33 | (571) all_153_2_82 = 0
% 23.95/6.33 |
% 23.95/6.33 +-Applying beta-rule and splitting (289), into two cases.
% 23.95/6.33 |-Branch one:
% 23.95/6.33 | (572) ~ (all_153_2_82 = 0)
% 23.95/6.33 |
% 23.95/6.33 | Equations (571) can reduce 572 to:
% 23.95/6.33 | (82) $false
% 23.95/6.33 |
% 23.95/6.33 |-The branch is then unsatisfiable
% 23.95/6.33 |-Branch two:
% 23.95/6.33 | (571) all_153_2_82 = 0
% 23.95/6.33 | (575) ~ (all_153_3_83 = 0) | all_153_0_80 = 0 | all_153_1_81 = 0
% 23.95/6.33 |
% 23.95/6.33 +-Applying beta-rule and splitting (575), into two cases.
% 23.95/6.33 |-Branch one:
% 23.95/6.33 | (576) ~ (all_153_3_83 = 0)
% 23.95/6.33 |
% 23.95/6.33 | Equations (318) can reduce 576 to:
% 23.95/6.33 | (82) $false
% 23.95/6.33 |
% 23.95/6.33 |-The branch is then unsatisfiable
% 23.95/6.33 |-Branch two:
% 23.95/6.33 | (318) all_153_3_83 = 0
% 23.95/6.33 | (579) all_153_0_80 = 0 | all_153_1_81 = 0
% 23.95/6.33 |
% 23.95/6.33 +-Applying beta-rule and splitting (579), into two cases.
% 23.95/6.33 |-Branch one:
% 23.95/6.33 | (580) all_153_0_80 = 0
% 23.95/6.33 |
% 23.95/6.33 | Combining equations (580,296) yields a new equation:
% 23.95/6.33 | (430) all_66_1_35 = 0
% 23.95/6.33 |
% 23.95/6.33 | Equations (430) can reduce 365 to:
% 23.95/6.33 | (82) $false
% 23.95/6.33 |
% 23.95/6.33 |-The branch is then unsatisfiable
% 23.95/6.33 |-Branch two:
% 23.95/6.33 | (583) ~ (all_153_0_80 = 0)
% 23.95/6.33 | (584) all_153_1_81 = 0
% 23.95/6.33 |
% 23.95/6.33 | Combining equations (584,348) yields a new equation:
% 23.95/6.33 | (585) all_33_1_23 = 0
% 23.95/6.33 |
% 23.95/6.33 | Equations (585) can reduce 495 to:
% 23.95/6.33 | (82) $false
% 23.95/6.33 |
% 23.95/6.33 |-The branch is then unsatisfiable
% 23.95/6.33 |-Branch two:
% 23.95/6.33 | (587) all_60_1_26 = 0
% 23.95/6.33 | (588) ~ (all_60_2_27 = 0) | (all_60_0_25 = 0 & all_16_0_6 = 0)
% 23.95/6.33 |
% 23.95/6.33 +-Applying beta-rule and splitting (588), into two cases.
% 23.95/6.33 |-Branch one:
% 23.95/6.33 | (589) ~ (all_60_2_27 = 0)
% 23.95/6.33 |
% 23.95/6.33 | Equations (408) can reduce 589 to:
% 23.95/6.33 | (82) $false
% 23.95/6.33 |
% 23.95/6.33 |-The branch is then unsatisfiable
% 23.95/6.33 |-Branch two:
% 23.95/6.33 | (408) all_60_2_27 = 0
% 23.95/6.33 | (592) all_60_0_25 = 0 & all_16_0_6 = 0
% 23.95/6.33 |
% 23.95/6.33 | Applying alpha-rule on (592) yields:
% 23.95/6.33 | (593) all_60_0_25 = 0
% 23.95/6.33 | (217) all_16_0_6 = 0
% 23.95/6.33 |
% 23.95/6.33 | Equations (217) can reduce 114 to:
% 23.95/6.33 | (82) $false
% 23.95/6.33 |
% 23.95/6.33 |-The branch is then unsatisfiable
% 23.95/6.33 |-Branch two:
% 23.95/6.33 | (438) all_70_1_41 = 0
% 23.95/6.33 | (597) all_70_0_40 = 0
% 23.95/6.33 |
% 23.95/6.33 | Combining equations (338,597) yields a new equation:
% 23.95/6.33 | (598) all_68_0_37 = 0
% 23.95/6.33 |
% 23.95/6.33 | Simplifying 598 yields:
% 23.95/6.33 | (567) all_68_0_37 = 0
% 23.95/6.33 |
% 23.95/6.33 | Equations (567) can reduce 378 to:
% 23.95/6.33 | (82) $false
% 23.95/6.33 |
% 23.95/6.33 |-The branch is then unsatisfiable
% 23.95/6.33 |-Branch two:
% 23.95/6.33 | (601) all_74_1_47 = 0
% 23.95/6.33 | (602) all_74_0_46 = 0 & all_28_3_21 = 0
% 23.95/6.33 |
% 23.95/6.33 | Applying alpha-rule on (602) yields:
% 23.95/6.33 | (334) all_74_0_46 = 0
% 23.95/6.33 | (604) all_28_3_21 = 0
% 23.95/6.33 |
% 23.95/6.33 | Equations (604) can reduce 135 to:
% 23.95/6.33 | (82) $false
% 23.95/6.33 |
% 23.95/6.33 |-The branch is then unsatisfiable
% 23.95/6.33 |-Branch two:
% 23.95/6.33 | (606) ~ (distinct_points(all_1_4_4, all_1_5_5) = 0)
% 23.95/6.33 | (217) all_16_0_6 = 0
% 23.95/6.33 |
% 23.95/6.33 | Equations (217) can reduce 114 to:
% 23.95/6.33 | (82) $false
% 23.95/6.33 |
% 23.95/6.33 |-The branch is then unsatisfiable
% 23.95/6.33 |-Branch two:
% 23.95/6.33 | (410) all_72_1_44 = 0
% 23.95/6.33 | (610) all_72_0_43 = 0 & all_28_3_21 = 0
% 23.95/6.33 |
% 23.95/6.33 | Applying alpha-rule on (610) yields:
% 23.95/6.33 | (611) all_72_0_43 = 0
% 23.95/6.33 | (604) all_28_3_21 = 0
% 23.95/6.33 |
% 23.95/6.33 | Equations (604) can reduce 135 to:
% 23.95/6.33 | (82) $false
% 23.95/6.33 |
% 23.95/6.33 |-The branch is then unsatisfiable
% 23.95/6.33 |-Branch two:
% 23.95/6.33 | (208) all_16_1_7 = 0
% 23.95/6.33 | (615) ~ (all_16_2_8 = 0) | all_16_0_6 = 0
% 23.95/6.33 |
% 23.95/6.33 | Combining equations (208,124) yields a new equation:
% 23.95/6.34 | (616) all_18_1_10 = 0
% 23.95/6.34 |
% 23.95/6.34 +-Applying beta-rule and splitting (70), into two cases.
% 23.95/6.34 |-Branch one:
% 23.95/6.34 | (617) ~ (all_18_1_10 = 0)
% 23.95/6.34 |
% 23.95/6.34 | Equations (616) can reduce 617 to:
% 23.95/6.34 | (82) $false
% 23.95/6.34 |
% 23.95/6.34 |-The branch is then unsatisfiable
% 23.95/6.34 |-Branch two:
% 23.95/6.34 | (616) all_18_1_10 = 0
% 23.95/6.34 | (620) all_18_0_9 = 0
% 23.95/6.34 |
% 23.95/6.34 | Combining equations (109,620) yields a new equation:
% 23.95/6.34 | (621) all_16_0_6 = 0
% 23.95/6.34 |
% 23.95/6.34 | Simplifying 621 yields:
% 23.95/6.34 | (217) all_16_0_6 = 0
% 23.95/6.34 |
% 23.95/6.34 | Equations (217) can reduce 114 to:
% 23.95/6.34 | (82) $false
% 23.95/6.34 |
% 23.95/6.34 |-The branch is then unsatisfiable
% 23.95/6.34 % SZS output end Proof for theBenchmark
% 23.95/6.34
% 23.95/6.34 5707ms
%------------------------------------------------------------------------------