TSTP Solution File: GEO177+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO177+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n012.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 03:48:12 EDT 2022
% Result : Theorem 14.09s 3.99s
% Output : Proof 34.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO177+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 17:40:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.50/0.60 ____ _
% 0.50/0.60 ___ / __ \_____(_)___ ________ __________
% 0.50/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.60
% 0.50/0.60 A Theorem Prover for First-Order Logic
% 0.50/0.60 (ePrincess v.1.0)
% 0.50/0.60
% 0.50/0.60 (c) Philipp Rümmer, 2009-2015
% 0.50/0.60 (c) Peter Backeman, 2014-2015
% 0.50/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.60 Bug reports to peter@backeman.se
% 0.50/0.60
% 0.50/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.60
% 0.50/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.65/0.96 Prover 0: Preprocessing ...
% 1.97/1.09 Prover 0: Warning: ignoring some quantifiers
% 1.97/1.11 Prover 0: Constructing countermodel ...
% 2.83/1.34 Prover 0: gave up
% 2.83/1.34 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.98/1.36 Prover 1: Preprocessing ...
% 3.26/1.44 Prover 1: Constructing countermodel ...
% 3.43/1.51 Prover 1: gave up
% 3.43/1.51 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.43/1.53 Prover 2: Preprocessing ...
% 3.83/1.64 Prover 2: Warning: ignoring some quantifiers
% 4.21/1.65 Prover 2: Constructing countermodel ...
% 4.99/1.82 Prover 2: gave up
% 4.99/1.82 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.99/1.84 Prover 3: Preprocessing ...
% 5.11/1.85 Prover 3: Warning: ignoring some quantifiers
% 5.11/1.86 Prover 3: Constructing countermodel ...
% 5.11/1.92 Prover 3: gave up
% 5.11/1.92 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 5.47/1.93 Prover 4: Preprocessing ...
% 5.72/1.99 Prover 4: Warning: ignoring some quantifiers
% 5.72/2.00 Prover 4: Constructing countermodel ...
% 10.21/3.13 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 10.21/3.15 Prover 5: Preprocessing ...
% 10.82/3.23 Prover 5: Constructing countermodel ...
% 14.09/3.99 Prover 5: proved (862ms)
% 14.09/3.99 Prover 4: stopped
% 14.09/3.99
% 14.09/3.99 No countermodel exists, formula is valid
% 14.09/3.99 % SZS status Theorem for theBenchmark
% 14.09/3.99
% 14.09/3.99 Generating proof ... found it (size 567)
% 32.98/9.77
% 32.98/9.77 % SZS output start Proof for theBenchmark
% 32.98/9.77 Assumed formulas after preprocessing and simplification:
% 32.98/9.77 | (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] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = 0) & ~ (v8 = 0) & line_connecting(v2, v3) = v4 & line_connecting(v0, v1) = v7 & apart_point_and_line(v3, v7) = v9 & apart_point_and_line(v2, v7) = v8 & apart_point_and_line(v1, v4) = v6 & apart_point_and_line(v0, v4) = v5 & distinct_points(v2, v3) = 0 & distinct_points(v0, v1) = 0 & (v6 = 0 | v5 = 0))
% 33.25/9.84 | Applying alpha-rule on (0) yields:
% 33.25/9.84 | (1) ! [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))))
% 33.25/9.84 | (2) ! [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)))
% 33.25/9.84 | (3) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 33.25/9.84 | (4) ! [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)))
% 33.25/9.85 | (5) ! [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)))))
% 33.25/9.85 | (6) ! [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))))
% 33.25/9.85 | (7) ! [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))
% 33.25/9.85 | (8) ! [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))))
% 33.25/9.85 | (9) ! [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)))
% 33.25/9.85 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 33.25/9.85 | (11) ! [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)))))
% 33.25/9.85 | (12) ! [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)))
% 33.25/9.86 | (13) ! [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))))
% 33.25/9.86 | (14) ! [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))
% 33.44/9.86 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 33.44/9.86 | (16) ! [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)
% 33.44/9.86 | (17) ! [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)))
% 33.44/9.86 | (18) ! [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))))
% 33.44/9.86 | (19) ! [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))
% 33.44/9.86 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 33.44/9.86 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 33.44/9.86 | (22) ! [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)))
% 33.44/9.87 | (23) ! [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)))))
% 33.44/9.87 | (24) ! [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)
% 33.44/9.87 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 33.44/9.87 | (26) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0)
% 33.44/9.87 | (27) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 33.44/9.87 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 33.44/9.87 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 33.44/9.87 | (30) ! [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)
% 33.44/9.87 | (31) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = 0) & ~ (v8 = 0) & line_connecting(v2, v3) = v4 & line_connecting(v0, v1) = v7 & apart_point_and_line(v3, v7) = v9 & apart_point_and_line(v2, v7) = v8 & apart_point_and_line(v1, v4) = v6 & apart_point_and_line(v0, v4) = v5 & distinct_points(v2, v3) = 0 & distinct_points(v0, v1) = 0 & (v6 = 0 | v5 = 0))
% 33.44/9.87 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 33.44/9.87 | (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)))))
% 33.44/9.87 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5))
% 33.44/9.88 | (35) ! [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)
% 33.44/9.88 | (36) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 33.44/9.88 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 33.44/9.88 | (38) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 33.44/9.88 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 33.44/9.88 | (40) ! [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))
% 33.44/9.88 | (41) ! [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)))
% 33.44/9.88 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 33.44/9.88 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 33.44/9.88 | (44) ! [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)))))
% 33.44/9.88 | (45) ! [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)))
% 33.44/9.88 | (46) ! [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))
% 33.44/9.88 |
% 33.44/9.88 | Instantiating (31) with all_1_0_0, all_1_1_1, all_1_2_2, all_1_3_3, all_1_4_4, all_1_5_5, all_1_6_6, all_1_7_7, all_1_8_8, all_1_9_9 yields:
% 33.44/9.88 | (47) ~ (all_1_0_0 = 0) & ~ (all_1_1_1 = 0) & line_connecting(all_1_7_7, all_1_6_6) = all_1_5_5 & line_connecting(all_1_9_9, all_1_8_8) = all_1_2_2 & apart_point_and_line(all_1_6_6, all_1_2_2) = all_1_0_0 & apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1 & apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4 & distinct_points(all_1_7_7, all_1_6_6) = 0 & distinct_points(all_1_9_9, all_1_8_8) = 0 & (all_1_3_3 = 0 | all_1_4_4 = 0)
% 33.44/9.89 |
% 33.44/9.89 | Applying alpha-rule on (47) yields:
% 33.44/9.89 | (48) apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1
% 33.44/9.89 | (49) apart_point_and_line(all_1_8_8, all_1_5_5) = all_1_3_3
% 33.44/9.89 | (50) distinct_points(all_1_9_9, all_1_8_8) = 0
% 33.44/9.89 | (51) ~ (all_1_0_0 = 0)
% 33.44/9.89 | (52) distinct_points(all_1_7_7, all_1_6_6) = 0
% 33.44/9.89 | (53) ~ (all_1_1_1 = 0)
% 33.44/9.89 | (54) line_connecting(all_1_9_9, all_1_8_8) = all_1_2_2
% 33.44/9.89 | (55) apart_point_and_line(all_1_6_6, all_1_2_2) = all_1_0_0
% 33.44/9.89 | (56) apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4
% 33.44/9.89 | (57) line_connecting(all_1_7_7, all_1_6_6) = all_1_5_5
% 33.44/9.89 | (58) all_1_3_3 = 0 | all_1_4_4 = 0
% 33.44/9.89 |
% 33.44/9.89 | Instantiating formula (36) with all_1_7_7 yields:
% 33.44/9.89 | (59) ~ (distinct_points(all_1_7_7, all_1_7_7) = 0)
% 33.44/9.89 |
% 33.44/9.89 | Instantiating formula (36) with all_1_9_9 yields:
% 33.44/9.89 | (60) ~ (distinct_points(all_1_9_9, all_1_9_9) = 0)
% 33.44/9.89 |
% 33.44/9.89 | Instantiating formula (12) with all_1_0_0, all_1_0_0, all_1_2_2, all_1_2_2, all_1_6_6, all_1_6_6 and discharging atoms apart_point_and_line(all_1_6_6, all_1_2_2) = all_1_0_0, yields:
% 33.44/9.89 | (61) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_2_2) = v3 & apart_point_and_line(all_1_6_6, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_6_6, all_1_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.44/9.89 |
% 33.44/9.89 | Instantiating formula (12) with all_1_1_1, all_1_0_0, all_1_2_2, all_1_2_2, all_1_7_7, all_1_6_6 and discharging atoms apart_point_and_line(all_1_6_6, all_1_2_2) = all_1_0_0, apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1, yields:
% 33.44/9.89 | (62) all_1_0_0 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_2_2) = v2 & apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_6_6, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.44/9.89 |
% 33.44/9.89 | Instantiating formula (12) with all_1_0_0, all_1_1_1, all_1_2_2, all_1_2_2, all_1_6_6, all_1_7_7 and discharging atoms apart_point_and_line(all_1_6_6, all_1_2_2) = all_1_0_0, apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1, yields:
% 33.44/9.89 | (63) all_1_0_0 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_2_2) = v3 & apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.44/9.90 |
% 33.44/9.90 | Instantiating formula (12) with all_1_1_1, all_1_1_1, all_1_2_2, all_1_2_2, all_1_7_7, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1, yields:
% 33.44/9.90 | (64) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.44/9.90 |
% 33.44/9.90 | Instantiating formula (6) with all_1_5_5, all_1_8_8, all_1_6_6, all_1_7_7 and discharging atoms line_connecting(all_1_7_7, all_1_6_6) = all_1_5_5, yields:
% 33.44/9.90 | (65) ~ (apart_point_and_line(all_1_8_8, all_1_5_5) = 0) | ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_1_7_7, all_1_6_6) = v0 & distinct_points(all_1_8_8, all_1_6_6) = v2 & distinct_points(all_1_8_8, all_1_7_7) = v1 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))
% 33.44/9.90 |
% 33.44/9.90 | Instantiating formula (18) with 0, all_1_7_7, all_1_6_6, all_1_7_7 and discharging atoms distinct_points(all_1_7_7, all_1_6_6) = 0, yields:
% 33.44/9.90 | (66) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_7_7, all_1_6_6) = v0 & apart_point_and_line(all_1_7_7, v0) = v1 & distinct_points(all_1_7_7, all_1_7_7) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 33.44/9.90 |
% 33.44/9.90 | Instantiating formula (13) with 0, all_1_5_5, all_1_7_7, all_1_6_6, all_1_7_7 and discharging atoms line_connecting(all_1_7_7, all_1_6_6) = all_1_5_5, distinct_points(all_1_7_7, all_1_6_6) = 0, yields:
% 33.44/9.90 | (67) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_6_6) = v0 & distinct_points(all_1_7_7, all_1_7_7) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 33.44/9.90 |
% 33.44/9.90 | Instantiating formula (17) with all_1_0_0, all_1_0_0, all_1_2_2, all_1_2_2, all_1_6_6, all_1_7_7 and discharging atoms apart_point_and_line(all_1_6_6, all_1_2_2) = all_1_0_0, distinct_points(all_1_7_7, all_1_6_6) = 0, yields:
% 33.44/9.90 | (68) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_7_7, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 33.44/9.90 |
% 33.44/9.90 | Instantiating formula (45) with all_1_1_1, all_1_1_1, all_1_2_2, all_1_2_2, all_1_6_6, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1, distinct_points(all_1_7_7, all_1_6_6) = 0, yields:
% 33.44/9.90 | (69) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_1_2_2) = v2 & apart_point_and_line(all_1_6_6, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 33.44/9.90 |
% 33.44/9.90 | Instantiating formula (8) with 0, all_1_9_9, all_1_6_6, all_1_8_8 and discharging atoms distinct_points(all_1_9_9, all_1_8_8) = 0, yields:
% 33.44/9.90 | (70) ~ (distinct_points(all_1_8_8, all_1_6_6) = 0) | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_8_8, all_1_6_6) = v0 & apart_point_and_line(all_1_9_9, v0) = v1 & distinct_points(all_1_9_9, all_1_6_6) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 33.44/9.90 |
% 33.44/9.90 | Instantiating formula (18) with 0, all_1_9_9, all_1_8_8, all_1_9_9 and discharging atoms distinct_points(all_1_9_9, all_1_8_8) = 0, yields:
% 33.44/9.90 | (71) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_9_9, all_1_8_8) = v0 & apart_point_and_line(all_1_9_9, v0) = v1 & distinct_points(all_1_9_9, all_1_9_9) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 33.44/9.90 |
% 33.44/9.90 | Instantiating formula (13) with 0, all_1_2_2, all_1_9_9, all_1_8_8, all_1_9_9 and discharging atoms line_connecting(all_1_9_9, all_1_8_8) = all_1_2_2, distinct_points(all_1_9_9, all_1_8_8) = 0, yields:
% 33.44/9.90 | (72) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_9_9, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_8_8) = v0 & distinct_points(all_1_9_9, all_1_9_9) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 33.44/9.91 |
% 33.44/9.91 | Instantiating (72) with all_16_0_10, all_16_1_11, all_16_2_12 yields:
% 33.44/9.91 | (73) apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11 & distinct_points(all_1_9_9, all_1_8_8) = all_16_2_12 & distinct_points(all_1_9_9, all_1_9_9) = all_16_0_10 & ( ~ (all_16_1_11 = 0) | ~ (all_16_2_12 = 0) | all_16_0_10 = 0)
% 33.44/9.91 |
% 33.44/9.91 | Applying alpha-rule on (73) yields:
% 33.44/9.91 | (74) apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11
% 33.44/9.91 | (75) distinct_points(all_1_9_9, all_1_8_8) = all_16_2_12
% 33.44/9.91 | (76) distinct_points(all_1_9_9, all_1_9_9) = all_16_0_10
% 33.44/9.91 | (77) ~ (all_16_1_11 = 0) | ~ (all_16_2_12 = 0) | all_16_0_10 = 0
% 33.44/9.91 |
% 33.44/9.91 | Instantiating (66) with all_18_0_13, all_18_1_14, all_18_2_15 yields:
% 33.44/9.91 | (78) line_connecting(all_1_7_7, all_1_6_6) = all_18_2_15 & apart_point_and_line(all_1_7_7, all_18_2_15) = all_18_1_14 & distinct_points(all_1_7_7, all_1_7_7) = all_18_0_13 & ( ~ (all_18_1_14 = 0) | all_18_0_13 = 0)
% 33.44/9.91 |
% 33.44/9.91 | Applying alpha-rule on (78) yields:
% 33.44/9.91 | (79) line_connecting(all_1_7_7, all_1_6_6) = all_18_2_15
% 33.44/9.91 | (80) apart_point_and_line(all_1_7_7, all_18_2_15) = all_18_1_14
% 33.44/9.91 | (81) distinct_points(all_1_7_7, all_1_7_7) = all_18_0_13
% 33.44/9.91 | (82) ~ (all_18_1_14 = 0) | all_18_0_13 = 0
% 33.44/9.91 |
% 33.44/9.91 | Instantiating (71) with all_20_0_16, all_20_1_17, all_20_2_18 yields:
% 33.44/9.91 | (83) line_connecting(all_1_9_9, all_1_8_8) = all_20_2_18 & apart_point_and_line(all_1_9_9, all_20_2_18) = all_20_1_17 & distinct_points(all_1_9_9, all_1_9_9) = all_20_0_16 & ( ~ (all_20_1_17 = 0) | all_20_0_16 = 0)
% 33.44/9.91 |
% 33.44/9.91 | Applying alpha-rule on (83) yields:
% 33.44/9.91 | (84) line_connecting(all_1_9_9, all_1_8_8) = all_20_2_18
% 33.44/9.91 | (85) apart_point_and_line(all_1_9_9, all_20_2_18) = all_20_1_17
% 33.44/9.91 | (86) distinct_points(all_1_9_9, all_1_9_9) = all_20_0_16
% 33.44/9.91 | (87) ~ (all_20_1_17 = 0) | all_20_0_16 = 0
% 33.44/9.91 |
% 33.44/9.91 | Instantiating (67) with all_22_0_19, all_22_1_20, all_22_2_21 yields:
% 33.44/9.91 | (88) apart_point_and_line(all_1_7_7, all_1_5_5) = all_22_1_20 & distinct_points(all_1_7_7, all_1_6_6) = all_22_2_21 & distinct_points(all_1_7_7, all_1_7_7) = all_22_0_19 & ( ~ (all_22_1_20 = 0) | ~ (all_22_2_21 = 0) | all_22_0_19 = 0)
% 33.44/9.91 |
% 33.44/9.91 | Applying alpha-rule on (88) yields:
% 33.44/9.91 | (89) apart_point_and_line(all_1_7_7, all_1_5_5) = all_22_1_20
% 33.44/9.91 | (90) distinct_points(all_1_7_7, all_1_6_6) = all_22_2_21
% 33.44/9.91 | (91) distinct_points(all_1_7_7, all_1_7_7) = all_22_0_19
% 33.44/9.92 | (92) ~ (all_22_1_20 = 0) | ~ (all_22_2_21 = 0) | all_22_0_19 = 0
% 33.44/9.92 |
% 33.44/9.92 +-Applying beta-rule and splitting (69), into two cases.
% 33.44/9.92 |-Branch one:
% 33.44/9.92 | (93) all_1_1_1 = 0
% 33.44/9.92 |
% 33.44/9.92 | Equations (93) can reduce 53 to:
% 33.44/9.92 | (94) $false
% 33.44/9.92 |
% 33.44/9.92 |-The branch is then unsatisfiable
% 33.44/9.92 |-Branch two:
% 33.44/9.92 | (53) ~ (all_1_1_1 = 0)
% 33.44/9.92 | (96) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_1_2_2) = v2 & apart_point_and_line(all_1_6_6, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 33.44/9.92 |
% 33.44/9.92 | Instantiating (96) with all_28_0_22, all_28_1_23, all_28_2_24 yields:
% 33.44/9.92 | (97) apart_point_and_line(all_1_6_6, all_1_2_2) = all_28_0_22 & apart_point_and_line(all_1_6_6, all_1_2_2) = all_28_1_23 & distinct_lines(all_1_2_2, all_1_2_2) = all_28_2_24 & ( ~ (all_28_2_24 = 0) | all_28_0_22 = 0 | all_28_1_23 = 0)
% 33.44/9.92 |
% 33.44/9.92 | Applying alpha-rule on (97) yields:
% 33.44/9.92 | (98) apart_point_and_line(all_1_6_6, all_1_2_2) = all_28_0_22
% 33.44/9.92 | (99) apart_point_and_line(all_1_6_6, all_1_2_2) = all_28_1_23
% 33.44/9.92 | (100) distinct_lines(all_1_2_2, all_1_2_2) = all_28_2_24
% 33.44/9.92 | (101) ~ (all_28_2_24 = 0) | all_28_0_22 = 0 | all_28_1_23 = 0
% 33.44/9.92 |
% 33.44/9.92 +-Applying beta-rule and splitting (68), into two cases.
% 33.44/9.92 |-Branch one:
% 33.44/9.92 | (102) all_1_0_0 = 0
% 33.44/9.92 |
% 33.44/9.92 | Equations (102) can reduce 51 to:
% 33.44/9.92 | (94) $false
% 33.44/9.92 |
% 33.44/9.92 |-The branch is then unsatisfiable
% 33.44/9.92 |-Branch two:
% 33.44/9.92 | (51) ~ (all_1_0_0 = 0)
% 33.44/9.92 | (105) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_7_7, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 33.44/9.92 |
% 33.44/9.92 | Instantiating (105) with all_33_0_25, all_33_1_26, all_33_2_27 yields:
% 33.44/9.92 | (106) apart_point_and_line(all_1_7_7, all_1_2_2) = all_33_0_25 & apart_point_and_line(all_1_7_7, all_1_2_2) = all_33_1_26 & distinct_lines(all_1_2_2, all_1_2_2) = all_33_2_27 & ( ~ (all_33_2_27 = 0) | all_33_0_25 = 0 | all_33_1_26 = 0)
% 33.44/9.92 |
% 33.44/9.92 | Applying alpha-rule on (106) yields:
% 33.44/9.92 | (107) apart_point_and_line(all_1_7_7, all_1_2_2) = all_33_0_25
% 33.44/9.92 | (108) apart_point_and_line(all_1_7_7, all_1_2_2) = all_33_1_26
% 33.44/9.92 | (109) distinct_lines(all_1_2_2, all_1_2_2) = all_33_2_27
% 33.44/9.92 | (110) ~ (all_33_2_27 = 0) | all_33_0_25 = 0 | all_33_1_26 = 0
% 33.44/9.92 |
% 33.44/9.92 +-Applying beta-rule and splitting (61), into two cases.
% 33.44/9.92 |-Branch one:
% 33.44/9.92 | (102) all_1_0_0 = 0
% 33.44/9.92 |
% 33.44/9.92 | Equations (102) can reduce 51 to:
% 33.44/9.92 | (94) $false
% 33.44/9.92 |
% 33.44/9.92 |-The branch is then unsatisfiable
% 33.44/9.92 |-Branch two:
% 33.44/9.92 | (51) ~ (all_1_0_0 = 0)
% 33.44/9.92 | (114) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_2_2) = v3 & apart_point_and_line(all_1_6_6, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_6_6, all_1_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.44/9.93 |
% 33.44/9.93 | Instantiating (114) with all_38_0_28, all_38_1_29, all_38_2_30, all_38_3_31 yields:
% 33.44/9.93 | (115) apart_point_and_line(all_1_6_6, all_1_2_2) = all_38_0_28 & apart_point_and_line(all_1_6_6, all_1_2_2) = all_38_1_29 & distinct_lines(all_1_2_2, all_1_2_2) = all_38_2_30 & distinct_points(all_1_6_6, all_1_6_6) = all_38_3_31 & ( ~ (all_38_2_30 = 0) | ~ (all_38_3_31 = 0) | all_38_0_28 = 0 | all_38_1_29 = 0)
% 33.44/9.93 |
% 33.44/9.93 | Applying alpha-rule on (115) yields:
% 33.44/9.93 | (116) ~ (all_38_2_30 = 0) | ~ (all_38_3_31 = 0) | all_38_0_28 = 0 | all_38_1_29 = 0
% 33.44/9.93 | (117) distinct_points(all_1_6_6, all_1_6_6) = all_38_3_31
% 33.44/9.93 | (118) apart_point_and_line(all_1_6_6, all_1_2_2) = all_38_1_29
% 33.44/9.93 | (119) apart_point_and_line(all_1_6_6, all_1_2_2) = all_38_0_28
% 33.44/9.93 | (120) distinct_lines(all_1_2_2, all_1_2_2) = all_38_2_30
% 33.44/9.93 |
% 33.44/9.93 +-Applying beta-rule and splitting (64), into two cases.
% 33.44/9.93 |-Branch one:
% 33.44/9.93 | (93) all_1_1_1 = 0
% 33.44/9.93 |
% 33.44/9.93 | Equations (93) can reduce 53 to:
% 33.44/9.93 | (94) $false
% 33.44/9.93 |
% 33.44/9.93 |-The branch is then unsatisfiable
% 33.44/9.93 |-Branch two:
% 33.44/9.93 | (53) ~ (all_1_1_1 = 0)
% 33.44/9.93 | (124) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.44/9.93 |
% 33.44/9.93 | Instantiating (124) with all_43_0_32, all_43_1_33, all_43_2_34, all_43_3_35 yields:
% 33.44/9.93 | (125) apart_point_and_line(all_1_7_7, all_1_2_2) = all_43_0_32 & apart_point_and_line(all_1_7_7, all_1_2_2) = all_43_1_33 & distinct_lines(all_1_2_2, all_1_2_2) = all_43_2_34 & distinct_points(all_1_7_7, all_1_7_7) = all_43_3_35 & ( ~ (all_43_2_34 = 0) | ~ (all_43_3_35 = 0) | all_43_0_32 = 0 | all_43_1_33 = 0)
% 33.44/9.93 |
% 33.44/9.93 | Applying alpha-rule on (125) yields:
% 33.44/9.93 | (126) apart_point_and_line(all_1_7_7, all_1_2_2) = all_43_1_33
% 33.44/9.93 | (127) distinct_lines(all_1_2_2, all_1_2_2) = all_43_2_34
% 33.44/9.93 | (128) apart_point_and_line(all_1_7_7, all_1_2_2) = all_43_0_32
% 33.44/9.93 | (129) ~ (all_43_2_34 = 0) | ~ (all_43_3_35 = 0) | all_43_0_32 = 0 | all_43_1_33 = 0
% 33.44/9.93 | (130) distinct_points(all_1_7_7, all_1_7_7) = all_43_3_35
% 33.44/9.93 |
% 33.44/9.93 +-Applying beta-rule and splitting (63), into two cases.
% 33.44/9.93 |-Branch one:
% 33.44/9.93 | (102) all_1_0_0 = 0
% 33.44/9.93 |
% 33.44/9.93 | Equations (102) can reduce 51 to:
% 33.44/9.93 | (94) $false
% 33.44/9.93 |
% 33.44/9.93 |-The branch is then unsatisfiable
% 33.44/9.93 |-Branch two:
% 33.44/9.93 | (51) ~ (all_1_0_0 = 0)
% 33.44/9.93 | (134) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_2_2) = v3 & apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.44/9.93 |
% 33.44/9.93 +-Applying beta-rule and splitting (62), into two cases.
% 33.44/9.93 |-Branch one:
% 33.44/9.93 | (102) all_1_0_0 = 0
% 33.44/9.93 |
% 33.44/9.93 | Equations (102) can reduce 51 to:
% 33.44/9.93 | (94) $false
% 33.44/9.93 |
% 33.44/9.93 |-The branch is then unsatisfiable
% 33.44/9.93 |-Branch two:
% 33.44/9.93 | (51) ~ (all_1_0_0 = 0)
% 33.44/9.93 | (138) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_2_2) = v2 & apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_6_6, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.44/9.93 |
% 33.44/9.93 +-Applying beta-rule and splitting (138), into two cases.
% 33.44/9.93 |-Branch one:
% 33.44/9.93 | (93) all_1_1_1 = 0
% 33.44/9.93 |
% 33.44/9.93 | Equations (93) can reduce 53 to:
% 33.44/9.93 | (94) $false
% 33.44/9.93 |
% 33.44/9.93 |-The branch is then unsatisfiable
% 33.44/9.93 |-Branch two:
% 33.44/9.93 | (53) ~ (all_1_1_1 = 0)
% 33.44/9.93 | (142) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_2_2) = v2 & apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_6_6, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.94 |
% 33.83/9.94 | Instantiating (142) with all_55_0_36, all_55_1_37, all_55_2_38, all_55_3_39 yields:
% 33.83/9.94 | (143) apart_point_and_line(all_1_6_6, all_1_2_2) = all_55_1_37 & apart_point_and_line(all_1_7_7, all_1_2_2) = all_55_0_36 & distinct_lines(all_1_2_2, all_1_2_2) = all_55_2_38 & distinct_points(all_1_6_6, all_1_7_7) = all_55_3_39 & ( ~ (all_55_2_38 = 0) | ~ (all_55_3_39 = 0) | all_55_0_36 = 0 | all_55_1_37 = 0)
% 33.83/9.94 |
% 33.83/9.94 | Applying alpha-rule on (143) yields:
% 33.83/9.94 | (144) apart_point_and_line(all_1_6_6, all_1_2_2) = all_55_1_37
% 33.83/9.94 | (145) ~ (all_55_2_38 = 0) | ~ (all_55_3_39 = 0) | all_55_0_36 = 0 | all_55_1_37 = 0
% 33.83/9.94 | (146) distinct_lines(all_1_2_2, all_1_2_2) = all_55_2_38
% 33.83/9.94 | (147) apart_point_and_line(all_1_7_7, all_1_2_2) = all_55_0_36
% 33.83/9.94 | (148) distinct_points(all_1_6_6, all_1_7_7) = all_55_3_39
% 33.83/9.94 |
% 33.83/9.94 | Instantiating formula (25) with all_1_7_7, all_1_6_6, all_18_2_15, all_1_5_5 and discharging atoms line_connecting(all_1_7_7, all_1_6_6) = all_18_2_15, line_connecting(all_1_7_7, all_1_6_6) = all_1_5_5, yields:
% 33.83/9.94 | (149) all_18_2_15 = all_1_5_5
% 33.83/9.94 |
% 33.83/9.94 | Instantiating formula (25) with all_1_9_9, all_1_8_8, all_20_2_18, all_1_2_2 and discharging atoms line_connecting(all_1_9_9, all_1_8_8) = all_20_2_18, line_connecting(all_1_9_9, all_1_8_8) = all_1_2_2, yields:
% 33.83/9.94 | (150) all_20_2_18 = all_1_2_2
% 33.83/9.94 |
% 33.83/9.94 | Instantiating formula (42) with all_1_6_6, all_1_2_2, all_38_0_28, all_55_1_37 and discharging atoms apart_point_and_line(all_1_6_6, all_1_2_2) = all_55_1_37, apart_point_and_line(all_1_6_6, all_1_2_2) = all_38_0_28, yields:
% 33.83/9.94 | (151) all_55_1_37 = all_38_0_28
% 33.83/9.94 |
% 33.83/9.94 | Instantiating formula (42) with all_1_6_6, all_1_2_2, all_38_1_29, all_55_1_37 and discharging atoms apart_point_and_line(all_1_6_6, all_1_2_2) = all_55_1_37, apart_point_and_line(all_1_6_6, all_1_2_2) = all_38_1_29, yields:
% 33.83/9.94 | (152) all_55_1_37 = all_38_1_29
% 33.83/9.94 |
% 33.83/9.94 | Instantiating formula (42) with all_1_6_6, all_1_2_2, all_28_0_22, all_1_0_0 and discharging atoms apart_point_and_line(all_1_6_6, all_1_2_2) = all_28_0_22, apart_point_and_line(all_1_6_6, all_1_2_2) = all_1_0_0, yields:
% 33.83/9.94 | (153) all_28_0_22 = all_1_0_0
% 33.83/9.94 |
% 33.83/9.94 | Instantiating formula (42) with all_1_6_6, all_1_2_2, all_28_0_22, all_38_0_28 and discharging atoms apart_point_and_line(all_1_6_6, all_1_2_2) = all_38_0_28, apart_point_and_line(all_1_6_6, all_1_2_2) = all_28_0_22, yields:
% 33.83/9.94 | (154) all_38_0_28 = all_28_0_22
% 33.83/9.94 |
% 33.83/9.94 | Instantiating formula (42) with all_1_6_6, all_1_2_2, all_28_1_23, all_38_0_28 and discharging atoms apart_point_and_line(all_1_6_6, all_1_2_2) = all_38_0_28, apart_point_and_line(all_1_6_6, all_1_2_2) = all_28_1_23, yields:
% 33.83/9.94 | (155) all_38_0_28 = all_28_1_23
% 33.83/9.94 |
% 33.83/9.94 | Instantiating formula (42) with all_1_7_7, all_1_2_2, all_43_0_32, all_55_0_36 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_55_0_36, apart_point_and_line(all_1_7_7, all_1_2_2) = all_43_0_32, yields:
% 33.83/9.94 | (156) all_55_0_36 = all_43_0_32
% 33.83/9.94 |
% 33.83/9.94 | Instantiating formula (42) with all_1_7_7, all_1_2_2, all_43_1_33, all_1_1_1 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_43_1_33, apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1, yields:
% 33.83/9.94 | (157) all_43_1_33 = all_1_1_1
% 33.83/9.94 |
% 33.83/9.94 | Instantiating formula (42) with all_1_7_7, all_1_2_2, all_43_1_33, all_43_0_32 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_43_0_32, apart_point_and_line(all_1_7_7, all_1_2_2) = all_43_1_33, yields:
% 33.83/9.94 | (158) all_43_0_32 = all_43_1_33
% 33.83/9.94 |
% 33.83/9.94 | Instantiating formula (42) with all_1_7_7, all_1_2_2, all_33_0_25, all_55_0_36 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_55_0_36, apart_point_and_line(all_1_7_7, all_1_2_2) = all_33_0_25, yields:
% 33.83/9.94 | (159) all_55_0_36 = all_33_0_25
% 33.83/9.94 |
% 33.83/9.94 | Instantiating formula (42) with all_1_7_7, all_1_2_2, all_33_1_26, all_43_0_32 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_43_0_32, apart_point_and_line(all_1_7_7, all_1_2_2) = all_33_1_26, yields:
% 33.83/9.94 | (160) all_43_0_32 = all_33_1_26
% 33.83/9.94 |
% 33.83/9.94 | Instantiating formula (42) with all_1_7_7, all_1_5_5, all_22_1_20, all_18_1_14 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_22_1_20, yields:
% 33.83/9.94 | (161) all_22_1_20 = all_18_1_14 | ~ (apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14)
% 33.83/9.94 |
% 33.83/9.94 | Instantiating formula (42) with all_1_9_9, all_1_2_2, all_16_1_11, all_20_1_17 and discharging atoms apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 33.83/9.94 | (162) all_20_1_17 = all_16_1_11 | ~ (apart_point_and_line(all_1_9_9, all_1_2_2) = all_20_1_17)
% 33.83/9.94 |
% 33.83/9.94 | Instantiating formula (36) with all_1_6_6 yields:
% 33.83/9.94 | (163) ~ (distinct_points(all_1_6_6, all_1_6_6) = 0)
% 33.83/9.94 |
% 33.83/9.94 | Instantiating formula (10) with all_1_7_7, all_1_6_6, all_22_2_21, 0 and discharging atoms distinct_points(all_1_7_7, all_1_6_6) = all_22_2_21, distinct_points(all_1_7_7, all_1_6_6) = 0, yields:
% 33.83/9.94 | (164) all_22_2_21 = 0
% 33.83/9.94 |
% 33.83/9.94 | Instantiating formula (10) with all_1_7_7, all_1_7_7, all_22_0_19, all_43_3_35 and discharging atoms distinct_points(all_1_7_7, all_1_7_7) = all_43_3_35, distinct_points(all_1_7_7, all_1_7_7) = all_22_0_19, yields:
% 33.83/9.94 | (165) all_43_3_35 = all_22_0_19
% 33.83/9.94 |
% 33.83/9.94 | Using (91) and (59) yields:
% 33.83/9.94 | (166) ~ (all_22_0_19 = 0)
% 33.83/9.94 |
% 33.83/9.94 | Instantiating formula (10) with all_1_7_7, all_1_7_7, all_18_0_13, all_43_3_35 and discharging atoms distinct_points(all_1_7_7, all_1_7_7) = all_43_3_35, distinct_points(all_1_7_7, all_1_7_7) = all_18_0_13, yields:
% 33.83/9.94 | (167) all_43_3_35 = all_18_0_13
% 33.83/9.94 |
% 33.83/9.94 | Instantiating formula (10) with all_1_9_9, all_1_8_8, all_16_2_12, 0 and discharging atoms distinct_points(all_1_9_9, all_1_8_8) = all_16_2_12, distinct_points(all_1_9_9, all_1_8_8) = 0, yields:
% 33.83/9.94 | (168) all_16_2_12 = 0
% 33.83/9.94 |
% 33.83/9.94 | Using (86) and (60) yields:
% 33.83/9.94 | (169) ~ (all_20_0_16 = 0)
% 33.83/9.94 |
% 33.83/9.94 | Instantiating formula (10) with all_1_9_9, all_1_9_9, all_16_0_10, all_20_0_16 and discharging atoms distinct_points(all_1_9_9, all_1_9_9) = all_20_0_16, distinct_points(all_1_9_9, all_1_9_9) = all_16_0_10, yields:
% 33.83/9.95 | (170) all_20_0_16 = all_16_0_10
% 33.83/9.95 |
% 33.83/9.95 | Combining equations (156,159) yields a new equation:
% 33.83/9.95 | (171) all_43_0_32 = all_33_0_25
% 33.83/9.95 |
% 33.83/9.95 | Simplifying 171 yields:
% 33.83/9.95 | (172) all_43_0_32 = all_33_0_25
% 33.83/9.95 |
% 33.83/9.95 | Combining equations (151,152) yields a new equation:
% 33.83/9.95 | (173) all_38_0_28 = all_38_1_29
% 33.83/9.95 |
% 33.83/9.95 | Simplifying 173 yields:
% 33.83/9.95 | (174) all_38_0_28 = all_38_1_29
% 33.83/9.95 |
% 33.83/9.95 | Combining equations (160,172) yields a new equation:
% 33.83/9.95 | (175) all_33_0_25 = all_33_1_26
% 33.83/9.95 |
% 33.83/9.95 | Combining equations (158,172) yields a new equation:
% 33.83/9.95 | (176) all_43_1_33 = all_33_0_25
% 33.83/9.95 |
% 33.83/9.95 | Simplifying 176 yields:
% 33.83/9.95 | (177) all_43_1_33 = all_33_0_25
% 33.83/9.95 |
% 33.83/9.95 | Combining equations (177,157) yields a new equation:
% 33.83/9.95 | (178) all_33_0_25 = all_1_1_1
% 33.83/9.95 |
% 33.83/9.95 | Simplifying 178 yields:
% 33.83/9.95 | (179) all_33_0_25 = all_1_1_1
% 33.83/9.95 |
% 33.83/9.95 | Combining equations (165,167) yields a new equation:
% 33.83/9.95 | (180) all_22_0_19 = all_18_0_13
% 33.83/9.95 |
% 33.83/9.95 | Simplifying 180 yields:
% 33.83/9.95 | (181) all_22_0_19 = all_18_0_13
% 33.83/9.95 |
% 33.83/9.95 | Combining equations (155,174) yields a new equation:
% 33.83/9.95 | (182) all_38_1_29 = all_28_1_23
% 33.83/9.95 |
% 33.83/9.95 | Combining equations (154,174) yields a new equation:
% 33.83/9.95 | (183) all_38_1_29 = all_28_0_22
% 33.83/9.95 |
% 33.83/9.95 | Combining equations (183,182) yields a new equation:
% 33.83/9.95 | (184) all_28_0_22 = all_28_1_23
% 33.83/9.95 |
% 33.83/9.95 | Simplifying 184 yields:
% 33.83/9.95 | (185) all_28_0_22 = all_28_1_23
% 33.83/9.95 |
% 33.83/9.95 | Combining equations (175,179) yields a new equation:
% 33.83/9.95 | (186) all_33_1_26 = all_1_1_1
% 33.83/9.95 |
% 33.83/9.95 | Simplifying 186 yields:
% 33.83/9.95 | (187) all_33_1_26 = all_1_1_1
% 33.83/9.95 |
% 33.83/9.95 | Combining equations (153,185) yields a new equation:
% 33.83/9.95 | (188) all_28_1_23 = all_1_0_0
% 33.83/9.95 |
% 33.83/9.95 | Equations (181) can reduce 166 to:
% 33.83/9.95 | (189) ~ (all_18_0_13 = 0)
% 33.83/9.95 |
% 33.83/9.95 | Equations (170) can reduce 169 to:
% 33.83/9.95 | (190) ~ (all_16_0_10 = 0)
% 33.83/9.95 |
% 33.83/9.95 | From (149) and (79) follows:
% 33.83/9.95 | (57) line_connecting(all_1_7_7, all_1_6_6) = all_1_5_5
% 33.83/9.95 |
% 33.83/9.95 | From (150) and (84) follows:
% 33.83/9.95 | (54) line_connecting(all_1_9_9, all_1_8_8) = all_1_2_2
% 33.83/9.95 |
% 33.83/9.95 | From (188) and (99) follows:
% 33.83/9.95 | (55) apart_point_and_line(all_1_6_6, all_1_2_2) = all_1_0_0
% 33.83/9.95 |
% 33.83/9.95 | From (149) and (80) follows:
% 33.83/9.95 | (194) apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14
% 33.83/9.95 |
% 33.83/9.95 | From (187) and (108) follows:
% 33.83/9.95 | (48) apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1
% 33.83/9.95 |
% 33.83/9.95 | From (150) and (85) follows:
% 33.83/9.95 | (196) apart_point_and_line(all_1_9_9, all_1_2_2) = all_20_1_17
% 33.83/9.95 |
% 33.83/9.95 | From (164) and (90) follows:
% 33.83/9.95 | (52) distinct_points(all_1_7_7, all_1_6_6) = 0
% 33.83/9.95 |
% 33.83/9.95 | From (168) and (75) follows:
% 33.83/9.95 | (50) distinct_points(all_1_9_9, all_1_8_8) = 0
% 33.83/9.95 |
% 33.83/9.95 | From (170) and (86) follows:
% 33.83/9.95 | (76) distinct_points(all_1_9_9, all_1_9_9) = all_16_0_10
% 33.83/9.95 |
% 33.83/9.95 +-Applying beta-rule and splitting (82), into two cases.
% 33.83/9.95 |-Branch one:
% 33.83/9.95 | (200) ~ (all_18_1_14 = 0)
% 33.83/9.95 |
% 33.83/9.95 +-Applying beta-rule and splitting (87), into two cases.
% 33.83/9.95 |-Branch one:
% 33.83/9.95 | (201) ~ (all_20_1_17 = 0)
% 33.83/9.95 |
% 33.83/9.95 +-Applying beta-rule and splitting (92), into two cases.
% 33.83/9.95 |-Branch one:
% 33.83/9.95 | (202) ~ (all_22_1_20 = 0)
% 33.83/9.95 |
% 33.83/9.95 +-Applying beta-rule and splitting (162), into two cases.
% 33.83/9.95 |-Branch one:
% 33.83/9.95 | (203) ~ (apart_point_and_line(all_1_9_9, all_1_2_2) = all_20_1_17)
% 33.83/9.95 |
% 33.83/9.95 | Using (196) and (203) yields:
% 33.83/9.95 | (204) $false
% 33.83/9.95 |
% 33.83/9.95 |-The branch is then unsatisfiable
% 33.83/9.95 |-Branch two:
% 33.83/9.95 | (196) apart_point_and_line(all_1_9_9, all_1_2_2) = all_20_1_17
% 33.83/9.95 | (206) all_20_1_17 = all_16_1_11
% 33.83/9.95 |
% 33.83/9.95 | Equations (206) can reduce 201 to:
% 33.83/9.95 | (207) ~ (all_16_1_11 = 0)
% 33.83/9.95 |
% 33.83/9.95 | From (206) and (196) follows:
% 33.83/9.95 | (74) apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11
% 33.83/9.95 |
% 33.83/9.95 +-Applying beta-rule and splitting (161), into two cases.
% 33.83/9.95 |-Branch one:
% 33.83/9.95 | (209) ~ (apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14)
% 33.83/9.95 |
% 33.83/9.95 | Using (194) and (209) yields:
% 33.83/9.95 | (204) $false
% 33.83/9.95 |
% 33.83/9.95 |-The branch is then unsatisfiable
% 33.83/9.95 |-Branch two:
% 33.83/9.95 | (194) apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14
% 33.83/9.95 | (212) all_22_1_20 = all_18_1_14
% 33.83/9.95 |
% 33.83/9.95 | Equations (212) can reduce 202 to:
% 33.83/9.95 | (200) ~ (all_18_1_14 = 0)
% 33.83/9.95 |
% 33.83/9.95 | From (212) and (89) follows:
% 33.83/9.95 | (194) apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14
% 33.83/9.95 |
% 33.83/9.95 | Using (117) and (163) yields:
% 33.83/9.95 | (215) ~ (all_38_3_31 = 0)
% 33.83/9.95 |
% 33.83/9.95 | Instantiating formula (12) with all_18_1_14, all_1_0_0, all_1_5_5, all_1_2_2, all_1_7_7, all_1_6_6 and discharging atoms apart_point_and_line(all_1_6_6, all_1_2_2) = all_1_0_0, apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, yields:
% 33.83/9.95 | (216) all_18_1_14 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_5_5) = v2 & apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_6_6, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.95 |
% 33.83/9.95 | Instantiating formula (12) with all_1_0_0, all_18_1_14, all_1_2_2, all_1_5_5, all_1_6_6, all_1_7_7 and discharging atoms apart_point_and_line(all_1_6_6, all_1_2_2) = all_1_0_0, apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, yields:
% 33.83/9.95 | (217) all_18_1_14 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_5_5) = v3 & apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.95 |
% 33.83/9.95 | Instantiating formula (4) with all_18_1_14, all_1_0_0, all_1_2_2, all_1_5_5, all_1_7_7, all_1_6_6 and discharging atoms apart_point_and_line(all_1_6_6, all_1_2_2) = all_1_0_0, apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, yields:
% 33.83/9.95 | (218) all_18_1_14 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_5_5) = v2 & apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_6_6, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.95 |
% 33.83/9.95 | Instantiating formula (4) with all_1_0_0, all_18_1_14, all_1_5_5, all_1_2_2, all_1_6_6, all_1_7_7 and discharging atoms apart_point_and_line(all_1_6_6, all_1_2_2) = all_1_0_0, apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, yields:
% 33.83/9.95 | (219) all_18_1_14 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_5_5) = v3 & apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.95 |
% 33.83/9.95 | Instantiating formula (45) with all_18_1_14, all_1_1_1, all_1_5_5, all_1_2_2, all_1_6_6, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1, apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, distinct_points(all_1_7_7, all_1_6_6) = 0, yields:
% 33.83/9.95 | (220) all_18_1_14 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_1_2_2) = v1 & apart_point_and_line(all_1_6_6, all_1_5_5) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 33.83/9.96 |
% 33.83/9.96 | Instantiating formula (45) with all_1_1_1, all_18_1_14, all_1_2_2, all_1_5_5, all_1_6_6, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1, apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, distinct_points(all_1_7_7, all_1_6_6) = 0, yields:
% 33.83/9.96 | (221) all_18_1_14 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_1_2_2) = v2 & apart_point_and_line(all_1_6_6, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 33.83/9.96 |
% 33.83/9.96 | Instantiating formula (12) with all_18_1_14, all_1_1_1, all_1_5_5, all_1_2_2, all_1_7_7, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1, apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, yields:
% 33.83/9.96 | (222) all_18_1_14 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_7_7, all_1_5_5) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.96 |
% 33.83/9.96 | Instantiating formula (12) with all_1_1_1, all_18_1_14, all_1_2_2, all_1_5_5, all_1_7_7, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1, apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, yields:
% 33.83/9.96 | (223) all_18_1_14 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_7_7, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.96 |
% 33.83/9.96 | Instantiating formula (4) with all_18_1_14, all_1_1_1, all_1_2_2, all_1_5_5, all_1_7_7, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1, apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, yields:
% 33.83/9.96 | (224) all_18_1_14 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_7_7, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.96 |
% 33.83/9.96 | Instantiating formula (4) with all_1_1_1, all_18_1_14, all_1_5_5, all_1_2_2, all_1_7_7, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1, apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, yields:
% 33.83/9.96 | (225) all_18_1_14 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_7_7, all_1_5_5) = v3 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.96 |
% 33.83/9.96 | Instantiating formula (35) with all_18_1_14, all_1_7_7, all_1_5_5, all_1_8_8 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, yields:
% 33.83/9.96 | (226) all_18_1_14 = 0 | ~ (apart_point_and_line(all_1_8_8, all_1_5_5) = 0) | distinct_points(all_1_8_8, all_1_7_7) = 0
% 33.83/9.96 |
% 33.83/9.96 | Instantiating formula (45) with all_18_1_14, all_18_1_14, all_1_5_5, all_1_5_5, all_1_6_6, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, distinct_points(all_1_7_7, all_1_6_6) = 0, yields:
% 33.83/9.96 | (227) all_18_1_14 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_1_5_5) = v2 & apart_point_and_line(all_1_6_6, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 33.83/9.96 |
% 33.83/9.96 | Instantiating formula (12) with all_18_1_14, all_18_1_14, all_1_5_5, all_1_5_5, all_1_7_7, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, yields:
% 33.83/9.96 | (228) all_18_1_14 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v3 & apart_point_and_line(all_1_7_7, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.96 |
% 33.83/9.96 | Instantiating formula (12) with all_16_1_11, all_1_0_0, all_1_2_2, all_1_2_2, all_1_9_9, all_1_6_6 and discharging atoms apart_point_and_line(all_1_6_6, all_1_2_2) = all_1_0_0, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 33.83/9.96 | (229) all_16_1_11 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_6_6, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.96 |
% 33.83/9.96 | Instantiating formula (12) with all_1_0_0, all_16_1_11, all_1_2_2, all_1_2_2, all_1_6_6, all_1_9_9 and discharging atoms apart_point_and_line(all_1_6_6, all_1_2_2) = all_1_0_0, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 33.83/9.96 | (230) all_16_1_11 = 0 | all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.96 |
% 33.83/9.96 | Instantiating formula (12) with all_16_1_11, all_1_1_1, all_1_2_2, all_1_2_2, all_1_9_9, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 33.83/9.96 | (231) all_16_1_11 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.96 |
% 33.83/9.96 | Instantiating formula (12) with all_1_1_1, all_16_1_11, all_1_2_2, all_1_2_2, all_1_7_7, all_1_9_9 and discharging atoms apart_point_and_line(all_1_7_7, all_1_2_2) = all_1_1_1, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 33.83/9.96 | (232) all_16_1_11 = 0 | all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.96 |
% 33.83/9.96 | Instantiating formula (16) with all_16_1_11, all_1_2_2, all_1_5_5, all_1_9_9 and discharging atoms apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 33.83/9.96 | (233) all_16_1_11 = 0 | ~ (apart_point_and_line(all_1_9_9, all_1_5_5) = 0) | distinct_lines(all_1_5_5, all_1_2_2) = 0
% 33.83/9.96 |
% 33.83/9.96 | Instantiating formula (12) with all_16_1_11, all_18_1_14, all_1_2_2, all_1_5_5, all_1_9_9, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 33.83/9.96 | (234) all_18_1_14 = 0 | all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.96 |
% 33.83/9.96 | Instantiating formula (12) with all_18_1_14, all_16_1_11, all_1_5_5, all_1_2_2, all_1_7_7, all_1_9_9 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 33.83/9.96 | (235) all_18_1_14 = 0 | all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.96 |
% 33.83/9.96 | Instantiating formula (4) with all_16_1_11, all_18_1_14, all_1_5_5, all_1_2_2, all_1_9_9, all_1_7_7 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 33.83/9.96 | (236) all_18_1_14 = 0 | all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.96 |
% 33.83/9.96 | Instantiating formula (4) with all_18_1_14, all_16_1_11, all_1_2_2, all_1_5_5, all_1_7_7, all_1_9_9 and discharging atoms apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14, apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, yields:
% 33.83/9.96 | (237) all_18_1_14 = 0 | all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.96 |
% 33.83/9.96 | Instantiating formula (45) with all_16_1_11, all_16_1_11, all_1_2_2, all_1_2_2, all_1_8_8, all_1_9_9 and discharging atoms apart_point_and_line(all_1_9_9, all_1_2_2) = all_16_1_11, distinct_points(all_1_9_9, all_1_8_8) = 0, yields:
% 33.83/9.96 | (238) all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v2 & apart_point_and_line(all_1_8_8, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 33.83/9.96 |
% 33.83/9.96 | Instantiating formula (18) with all_38_3_31, all_1_6_6, all_1_6_6, all_1_7_7 and discharging atoms distinct_points(all_1_6_6, all_1_6_6) = all_38_3_31, distinct_points(all_1_7_7, all_1_6_6) = 0, yields:
% 33.83/9.96 | (239) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_7_7, all_1_6_6) = v0 & apart_point_and_line(all_1_6_6, v0) = v1 & distinct_points(all_1_6_6, all_1_7_7) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_38_3_31 = 0)))
% 33.83/9.96 |
% 33.83/9.96 | Instantiating formula (13) with all_38_3_31, all_1_5_5, all_1_6_6, all_1_6_6, all_1_7_7 and discharging atoms line_connecting(all_1_7_7, all_1_6_6) = all_1_5_5, distinct_points(all_1_6_6, all_1_6_6) = all_38_3_31, yields:
% 33.83/9.96 | (240) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_1_5_5) = v1 & distinct_points(all_1_6_6, all_1_7_7) = v2 & distinct_points(all_1_7_7, all_1_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & all_38_3_31 = 0)))
% 33.83/9.96 |
% 33.83/9.96 | Instantiating formula (29) with all_16_0_10, all_1_9_9, all_1_8_8, all_1_9_9 and discharging atoms distinct_points(all_1_9_9, all_1_8_8) = 0, distinct_points(all_1_9_9, all_1_9_9) = all_16_0_10, yields:
% 33.83/9.96 | (241) all_16_0_10 = 0 | distinct_points(all_1_8_8, all_1_9_9) = 0
% 33.83/9.96 |
% 33.83/9.96 | Instantiating formula (19) with all_16_0_10, 0, all_1_9_9, all_1_9_9, all_1_8_8 and discharging atoms distinct_points(all_1_9_9, all_1_8_8) = 0, distinct_points(all_1_9_9, all_1_9_9) = all_16_0_10, yields:
% 33.83/9.96 | (242) all_16_0_10 = 0 | ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_8_8, all_1_9_9) = v1 & apart_point_and_line(all_1_9_9, v1) = v2 & distinct_points(all_1_8_8, all_1_9_9) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 33.83/9.97 |
% 33.83/9.97 | Instantiating (240) with all_98_0_40, all_98_1_41, all_98_2_42 yields:
% 33.83/9.97 | (243) apart_point_and_line(all_1_6_6, all_1_5_5) = all_98_1_41 & distinct_points(all_1_6_6, all_1_7_7) = all_98_0_40 & distinct_points(all_1_7_7, all_1_6_6) = all_98_2_42 & ( ~ (all_98_1_41 = 0) | ~ (all_98_2_42 = 0) | (all_98_0_40 = 0 & all_38_3_31 = 0))
% 33.83/9.97 |
% 33.83/9.97 | Applying alpha-rule on (243) yields:
% 33.83/9.97 | (244) apart_point_and_line(all_1_6_6, all_1_5_5) = all_98_1_41
% 33.83/9.97 | (245) distinct_points(all_1_6_6, all_1_7_7) = all_98_0_40
% 33.83/9.97 | (246) distinct_points(all_1_7_7, all_1_6_6) = all_98_2_42
% 33.83/9.97 | (247) ~ (all_98_1_41 = 0) | ~ (all_98_2_42 = 0) | (all_98_0_40 = 0 & all_38_3_31 = 0)
% 33.83/9.97 |
% 33.83/9.97 | Instantiating (239) with all_100_0_43, all_100_1_44, all_100_2_45 yields:
% 33.83/9.97 | (248) line_connecting(all_1_7_7, all_1_6_6) = all_100_2_45 & apart_point_and_line(all_1_6_6, all_100_2_45) = all_100_1_44 & distinct_points(all_1_6_6, all_1_7_7) = all_100_0_43 & ( ~ (all_100_1_44 = 0) | (all_100_0_43 = 0 & all_38_3_31 = 0))
% 33.83/9.97 |
% 33.83/9.97 | Applying alpha-rule on (248) yields:
% 33.83/9.97 | (249) line_connecting(all_1_7_7, all_1_6_6) = all_100_2_45
% 33.83/9.97 | (250) apart_point_and_line(all_1_6_6, all_100_2_45) = all_100_1_44
% 33.83/9.97 | (251) distinct_points(all_1_6_6, all_1_7_7) = all_100_0_43
% 33.83/9.97 | (252) ~ (all_100_1_44 = 0) | (all_100_0_43 = 0 & all_38_3_31 = 0)
% 33.83/9.97 |
% 33.83/9.97 +-Applying beta-rule and splitting (252), into two cases.
% 33.83/9.97 |-Branch one:
% 33.83/9.97 | (253) ~ (all_100_1_44 = 0)
% 33.83/9.97 |
% 33.83/9.97 +-Applying beta-rule and splitting (241), into two cases.
% 33.83/9.97 |-Branch one:
% 33.83/9.97 | (254) distinct_points(all_1_8_8, all_1_9_9) = 0
% 33.83/9.97 |
% 33.83/9.97 +-Applying beta-rule and splitting (242), into two cases.
% 33.83/9.97 |-Branch one:
% 33.83/9.97 | (255) all_16_0_10 = 0
% 33.83/9.97 |
% 33.83/9.97 | Equations (255) can reduce 190 to:
% 33.83/9.97 | (94) $false
% 33.83/9.97 |
% 33.83/9.97 |-The branch is then unsatisfiable
% 33.83/9.97 |-Branch two:
% 33.83/9.97 | (190) ~ (all_16_0_10 = 0)
% 33.83/9.97 | (258) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_8_8, all_1_9_9) = v1 & apart_point_and_line(all_1_9_9, v1) = v2 & distinct_points(all_1_8_8, all_1_9_9) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 33.83/9.97 |
% 33.83/9.97 | Instantiating (258) with all_118_0_46, all_118_1_47, all_118_2_48 yields:
% 33.83/9.97 | (259) line_connecting(all_1_8_8, all_1_9_9) = all_118_1_47 & apart_point_and_line(all_1_9_9, all_118_1_47) = all_118_0_46 & distinct_points(all_1_8_8, all_1_9_9) = all_118_2_48 & ( ~ (all_118_0_46 = 0) | ~ (all_118_2_48 = 0))
% 33.83/9.97 |
% 33.83/9.97 | Applying alpha-rule on (259) yields:
% 33.83/9.97 | (260) line_connecting(all_1_8_8, all_1_9_9) = all_118_1_47
% 33.83/9.97 | (261) apart_point_and_line(all_1_9_9, all_118_1_47) = all_118_0_46
% 33.83/9.97 | (262) distinct_points(all_1_8_8, all_1_9_9) = all_118_2_48
% 33.83/9.97 | (263) ~ (all_118_0_46 = 0) | ~ (all_118_2_48 = 0)
% 33.83/9.97 |
% 33.83/9.97 +-Applying beta-rule and splitting (227), into two cases.
% 33.83/9.97 |-Branch one:
% 33.83/9.97 | (264) all_18_1_14 = 0
% 33.83/9.97 |
% 33.83/9.97 | Equations (264) can reduce 200 to:
% 33.83/9.97 | (94) $false
% 33.83/9.97 |
% 33.83/9.97 |-The branch is then unsatisfiable
% 33.83/9.97 |-Branch two:
% 33.83/9.97 | (200) ~ (all_18_1_14 = 0)
% 33.83/9.97 | (267) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_1_5_5) = v2 & apart_point_and_line(all_1_6_6, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 33.83/9.97 |
% 33.83/9.97 | Instantiating (267) with all_133_0_55, all_133_1_56, all_133_2_57 yields:
% 33.83/9.97 | (268) apart_point_and_line(all_1_6_6, all_1_5_5) = all_133_0_55 & apart_point_and_line(all_1_6_6, all_1_5_5) = all_133_1_56 & distinct_lines(all_1_5_5, all_1_5_5) = all_133_2_57 & ( ~ (all_133_2_57 = 0) | all_133_0_55 = 0 | all_133_1_56 = 0)
% 33.83/9.97 |
% 33.83/9.97 | Applying alpha-rule on (268) yields:
% 33.83/9.97 | (269) apart_point_and_line(all_1_6_6, all_1_5_5) = all_133_0_55
% 33.83/9.97 | (270) apart_point_and_line(all_1_6_6, all_1_5_5) = all_133_1_56
% 33.83/9.97 | (271) distinct_lines(all_1_5_5, all_1_5_5) = all_133_2_57
% 33.83/9.97 | (272) ~ (all_133_2_57 = 0) | all_133_0_55 = 0 | all_133_1_56 = 0
% 33.83/9.97 |
% 33.83/9.97 +-Applying beta-rule and splitting (228), into two cases.
% 33.83/9.97 |-Branch one:
% 33.83/9.97 | (264) all_18_1_14 = 0
% 33.83/9.97 |
% 33.83/9.97 | Equations (264) can reduce 200 to:
% 33.83/9.97 | (94) $false
% 33.83/9.97 |
% 33.83/9.97 |-The branch is then unsatisfiable
% 33.83/9.97 |-Branch two:
% 33.83/9.97 | (200) ~ (all_18_1_14 = 0)
% 33.83/9.97 | (276) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_5_5) = v3 & apart_point_and_line(all_1_7_7, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.97 |
% 33.83/9.97 +-Applying beta-rule and splitting (238), into two cases.
% 33.83/9.97 |-Branch one:
% 33.83/9.97 | (277) all_16_1_11 = 0
% 33.83/9.97 |
% 33.83/9.97 | Equations (277) can reduce 207 to:
% 33.83/9.97 | (94) $false
% 33.83/9.97 |
% 33.83/9.97 |-The branch is then unsatisfiable
% 33.83/9.97 |-Branch two:
% 33.83/9.97 | (207) ~ (all_16_1_11 = 0)
% 33.83/9.97 | (280) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v2 & apart_point_and_line(all_1_8_8, all_1_2_2) = v1 & distinct_lines(all_1_2_2, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 33.83/9.97 |
% 33.83/9.97 | Instantiating (280) with all_148_0_65, all_148_1_66, all_148_2_67 yields:
% 33.83/9.97 | (281) apart_point_and_line(all_1_8_8, all_1_2_2) = all_148_0_65 & apart_point_and_line(all_1_8_8, all_1_2_2) = all_148_1_66 & distinct_lines(all_1_2_2, all_1_2_2) = all_148_2_67 & ( ~ (all_148_2_67 = 0) | all_148_0_65 = 0 | all_148_1_66 = 0)
% 33.83/9.97 |
% 33.83/9.97 | Applying alpha-rule on (281) yields:
% 33.83/9.97 | (282) apart_point_and_line(all_1_8_8, all_1_2_2) = all_148_0_65
% 33.83/9.97 | (283) apart_point_and_line(all_1_8_8, all_1_2_2) = all_148_1_66
% 33.83/9.97 | (284) distinct_lines(all_1_2_2, all_1_2_2) = all_148_2_67
% 33.83/9.97 | (285) ~ (all_148_2_67 = 0) | all_148_0_65 = 0 | all_148_1_66 = 0
% 33.83/9.97 |
% 33.83/9.97 +-Applying beta-rule and splitting (237), into two cases.
% 33.83/9.97 |-Branch one:
% 33.83/9.97 | (264) all_18_1_14 = 0
% 33.83/9.97 |
% 33.83/9.97 | Equations (264) can reduce 200 to:
% 33.83/9.97 | (94) $false
% 33.83/9.97 |
% 33.83/9.97 |-The branch is then unsatisfiable
% 33.83/9.97 |-Branch two:
% 33.83/9.97 | (200) ~ (all_18_1_14 = 0)
% 33.83/9.97 | (289) all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.97 |
% 33.83/9.97 +-Applying beta-rule and splitting (224), into two cases.
% 33.83/9.97 |-Branch one:
% 33.83/9.97 | (264) all_18_1_14 = 0
% 33.83/9.97 |
% 33.83/9.97 | Equations (264) can reduce 200 to:
% 33.83/9.97 | (94) $false
% 33.83/9.97 |
% 33.83/9.97 |-The branch is then unsatisfiable
% 33.83/9.97 |-Branch two:
% 33.83/9.97 | (200) ~ (all_18_1_14 = 0)
% 33.83/9.97 | (293) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_7_7, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.97 |
% 33.83/9.97 +-Applying beta-rule and splitting (216), into two cases.
% 33.83/9.97 |-Branch one:
% 33.83/9.97 | (264) all_18_1_14 = 0
% 33.83/9.97 |
% 33.83/9.97 | Equations (264) can reduce 200 to:
% 33.83/9.97 | (94) $false
% 33.83/9.97 |
% 33.83/9.97 |-The branch is then unsatisfiable
% 33.83/9.97 |-Branch two:
% 33.83/9.97 | (200) ~ (all_18_1_14 = 0)
% 33.83/9.97 | (297) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_5_5) = v2 & apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_6_6, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.97 |
% 33.83/9.97 +-Applying beta-rule and splitting (217), into two cases.
% 33.83/9.97 |-Branch one:
% 33.83/9.97 | (264) all_18_1_14 = 0
% 33.83/9.97 |
% 33.83/9.97 | Equations (264) can reduce 200 to:
% 33.83/9.97 | (94) $false
% 33.83/9.97 |
% 33.83/9.97 |-The branch is then unsatisfiable
% 33.83/9.97 |-Branch two:
% 33.83/9.97 | (200) ~ (all_18_1_14 = 0)
% 33.83/9.97 | (301) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_5_5) = v3 & apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.97 |
% 33.83/9.97 +-Applying beta-rule and splitting (218), into two cases.
% 33.83/9.97 |-Branch one:
% 33.83/9.97 | (264) all_18_1_14 = 0
% 33.83/9.97 |
% 33.83/9.97 | Equations (264) can reduce 200 to:
% 33.83/9.97 | (94) $false
% 33.83/9.97 |
% 33.83/9.97 |-The branch is then unsatisfiable
% 33.83/9.97 |-Branch two:
% 33.83/9.97 | (200) ~ (all_18_1_14 = 0)
% 33.83/9.97 | (305) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_5_5) = v2 & apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_6_6, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.97 |
% 33.83/9.97 +-Applying beta-rule and splitting (219), into two cases.
% 33.83/9.97 |-Branch one:
% 33.83/9.97 | (264) all_18_1_14 = 0
% 33.83/9.97 |
% 33.83/9.97 | Equations (264) can reduce 200 to:
% 33.83/9.97 | (94) $false
% 33.83/9.97 |
% 33.83/9.97 |-The branch is then unsatisfiable
% 33.83/9.97 |-Branch two:
% 33.83/9.97 | (200) ~ (all_18_1_14 = 0)
% 33.83/9.97 | (309) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_5_5) = v3 & apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.97 |
% 33.83/9.97 +-Applying beta-rule and splitting (225), into two cases.
% 33.83/9.97 |-Branch one:
% 33.83/9.97 | (264) all_18_1_14 = 0
% 33.83/9.97 |
% 33.83/9.97 | Equations (264) can reduce 200 to:
% 33.83/9.97 | (94) $false
% 33.83/9.97 |
% 33.83/9.97 |-The branch is then unsatisfiable
% 33.83/9.97 |-Branch two:
% 33.83/9.97 | (200) ~ (all_18_1_14 = 0)
% 33.83/9.97 | (313) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_7_7, all_1_5_5) = v3 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.97 |
% 33.83/9.97 +-Applying beta-rule and splitting (231), into two cases.
% 33.83/9.97 |-Branch one:
% 33.83/9.97 | (277) all_16_1_11 = 0
% 33.83/9.97 |
% 33.83/9.97 | Equations (277) can reduce 207 to:
% 33.83/9.97 | (94) $false
% 33.83/9.97 |
% 33.83/9.97 |-The branch is then unsatisfiable
% 33.83/9.97 |-Branch two:
% 33.83/9.97 | (207) ~ (all_16_1_11 = 0)
% 33.83/9.97 | (317) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.98 |
% 33.83/9.98 +-Applying beta-rule and splitting (232), into two cases.
% 33.83/9.98 |-Branch one:
% 33.83/9.98 | (277) all_16_1_11 = 0
% 33.83/9.98 |
% 33.83/9.98 | Equations (277) can reduce 207 to:
% 33.83/9.98 | (94) $false
% 33.83/9.98 |
% 33.83/9.98 |-The branch is then unsatisfiable
% 33.83/9.98 |-Branch two:
% 33.83/9.98 | (207) ~ (all_16_1_11 = 0)
% 33.83/9.98 | (321) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.98 |
% 33.83/9.98 +-Applying beta-rule and splitting (222), into two cases.
% 33.83/9.98 |-Branch one:
% 33.83/9.98 | (264) all_18_1_14 = 0
% 33.83/9.98 |
% 33.83/9.98 | Equations (264) can reduce 200 to:
% 33.83/9.98 | (94) $false
% 33.83/9.98 |
% 33.83/9.98 |-The branch is then unsatisfiable
% 33.83/9.98 |-Branch two:
% 33.83/9.98 | (200) ~ (all_18_1_14 = 0)
% 33.83/9.98 | (325) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_7_7, all_1_5_5) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.98 |
% 33.83/9.98 +-Applying beta-rule and splitting (220), into two cases.
% 33.83/9.98 |-Branch one:
% 33.83/9.98 | (264) all_18_1_14 = 0
% 33.83/9.98 |
% 33.83/9.98 | Equations (264) can reduce 200 to:
% 33.83/9.98 | (94) $false
% 33.83/9.98 |
% 33.83/9.98 |-The branch is then unsatisfiable
% 33.83/9.98 |-Branch two:
% 33.83/9.98 | (200) ~ (all_18_1_14 = 0)
% 33.83/9.98 | (329) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_1_2_2) = v1 & apart_point_and_line(all_1_6_6, all_1_5_5) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 33.83/9.98 |
% 33.83/9.98 +-Applying beta-rule and splitting (234), into two cases.
% 33.83/9.98 |-Branch one:
% 33.83/9.98 | (264) all_18_1_14 = 0
% 33.83/9.98 |
% 33.83/9.98 | Equations (264) can reduce 200 to:
% 33.83/9.98 | (94) $false
% 33.83/9.98 |
% 33.83/9.98 |-The branch is then unsatisfiable
% 33.83/9.98 |-Branch two:
% 33.83/9.98 | (200) ~ (all_18_1_14 = 0)
% 33.83/9.98 | (333) all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.98 |
% 33.83/9.98 +-Applying beta-rule and splitting (235), into two cases.
% 33.83/9.98 |-Branch one:
% 33.83/9.98 | (264) all_18_1_14 = 0
% 33.83/9.98 |
% 33.83/9.98 | Equations (264) can reduce 200 to:
% 33.83/9.98 | (94) $false
% 33.83/9.98 |
% 33.83/9.98 |-The branch is then unsatisfiable
% 33.83/9.98 |-Branch two:
% 33.83/9.98 | (200) ~ (all_18_1_14 = 0)
% 33.83/9.98 | (337) all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.98 |
% 33.83/9.98 +-Applying beta-rule and splitting (236), into two cases.
% 33.83/9.98 |-Branch one:
% 33.83/9.98 | (264) all_18_1_14 = 0
% 33.83/9.98 |
% 33.83/9.98 | Equations (264) can reduce 200 to:
% 33.83/9.98 | (94) $false
% 33.83/9.98 |
% 33.83/9.98 |-The branch is then unsatisfiable
% 33.83/9.98 |-Branch two:
% 33.83/9.98 | (200) ~ (all_18_1_14 = 0)
% 33.83/9.98 | (341) all_16_1_11 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.98 |
% 33.83/9.98 +-Applying beta-rule and splitting (221), into two cases.
% 33.83/9.98 |-Branch one:
% 33.83/9.98 | (264) all_18_1_14 = 0
% 33.83/9.98 |
% 33.83/9.98 | Equations (264) can reduce 200 to:
% 33.83/9.98 | (94) $false
% 33.83/9.98 |
% 33.83/9.98 |-The branch is then unsatisfiable
% 33.83/9.98 |-Branch two:
% 33.83/9.98 | (200) ~ (all_18_1_14 = 0)
% 33.83/9.98 | (345) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_1_2_2) = v2 & apart_point_and_line(all_1_6_6, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 33.83/9.98 |
% 33.83/9.98 +-Applying beta-rule and splitting (223), into two cases.
% 33.83/9.98 |-Branch one:
% 33.83/9.98 | (264) all_18_1_14 = 0
% 33.83/9.98 |
% 33.83/9.98 | Equations (264) can reduce 200 to:
% 33.83/9.98 | (94) $false
% 33.83/9.98 |
% 33.83/9.98 |-The branch is then unsatisfiable
% 33.83/9.98 |-Branch two:
% 33.83/9.98 | (200) ~ (all_18_1_14 = 0)
% 33.83/9.98 | (349) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_7_7, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.98 |
% 33.83/9.98 +-Applying beta-rule and splitting (229), into two cases.
% 33.83/9.98 |-Branch one:
% 33.83/9.98 | (277) all_16_1_11 = 0
% 33.83/9.98 |
% 33.83/9.98 | Equations (277) can reduce 207 to:
% 33.83/9.98 | (94) $false
% 33.83/9.98 |
% 33.83/9.98 |-The branch is then unsatisfiable
% 33.83/9.98 |-Branch two:
% 33.83/9.98 | (207) ~ (all_16_1_11 = 0)
% 33.83/9.98 | (353) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_6_6, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.98 |
% 33.83/9.98 +-Applying beta-rule and splitting (230), into two cases.
% 33.83/9.98 |-Branch one:
% 33.83/9.98 | (277) all_16_1_11 = 0
% 33.83/9.98 |
% 33.83/9.98 | Equations (277) can reduce 207 to:
% 33.83/9.98 | (94) $false
% 33.83/9.98 |
% 33.83/9.98 |-The branch is then unsatisfiable
% 33.83/9.98 |-Branch two:
% 33.83/9.98 | (207) ~ (all_16_1_11 = 0)
% 33.83/9.98 | (357) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.98 |
% 33.83/9.98 +-Applying beta-rule and splitting (289), into two cases.
% 33.83/9.98 |-Branch one:
% 33.83/9.98 | (277) all_16_1_11 = 0
% 33.83/9.98 |
% 33.83/9.98 | Equations (277) can reduce 207 to:
% 33.83/9.98 | (94) $false
% 33.83/9.98 |
% 33.83/9.98 |-The branch is then unsatisfiable
% 33.83/9.98 |-Branch two:
% 33.83/9.98 | (207) ~ (all_16_1_11 = 0)
% 33.83/9.98 | (361) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.98 |
% 33.83/9.98 | Instantiating (361) with all_218_0_72, all_218_1_73, all_218_2_74, all_218_3_75 yields:
% 33.83/9.98 | (362) apart_point_and_line(all_1_7_7, all_1_2_2) = all_218_0_72 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_218_1_73 & distinct_lines(all_1_5_5, all_1_2_2) = all_218_2_74 & distinct_points(all_1_9_9, all_1_7_7) = all_218_3_75 & ( ~ (all_218_2_74 = 0) | ~ (all_218_3_75 = 0) | all_218_0_72 = 0 | all_218_1_73 = 0)
% 33.83/9.98 |
% 33.83/9.98 | Applying alpha-rule on (362) yields:
% 33.83/9.98 | (363) ~ (all_218_2_74 = 0) | ~ (all_218_3_75 = 0) | all_218_0_72 = 0 | all_218_1_73 = 0
% 33.83/9.98 | (364) apart_point_and_line(all_1_9_9, all_1_5_5) = all_218_1_73
% 33.83/9.98 | (365) apart_point_and_line(all_1_7_7, all_1_2_2) = all_218_0_72
% 33.83/9.98 | (366) distinct_points(all_1_9_9, all_1_7_7) = all_218_3_75
% 33.83/9.98 | (367) distinct_lines(all_1_5_5, all_1_2_2) = all_218_2_74
% 33.83/9.98 |
% 33.83/9.98 +-Applying beta-rule and splitting (293), into two cases.
% 33.83/9.98 |-Branch one:
% 33.83/9.98 | (93) all_1_1_1 = 0
% 33.83/9.98 |
% 33.83/9.98 | Equations (93) can reduce 53 to:
% 33.83/9.98 | (94) $false
% 33.83/9.98 |
% 33.83/9.98 |-The branch is then unsatisfiable
% 33.83/9.98 |-Branch two:
% 33.83/9.98 | (53) ~ (all_1_1_1 = 0)
% 33.83/9.98 | (371) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_7_7, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.98 |
% 33.83/9.98 | Instantiating (371) with all_223_0_76, all_223_1_77, all_223_2_78, all_223_3_79 yields:
% 33.83/9.98 | (372) apart_point_and_line(all_1_7_7, all_1_2_2) = all_223_0_76 & apart_point_and_line(all_1_7_7, all_1_5_5) = all_223_1_77 & distinct_lines(all_1_5_5, all_1_2_2) = all_223_2_78 & distinct_points(all_1_7_7, all_1_7_7) = all_223_3_79 & ( ~ (all_223_2_78 = 0) | ~ (all_223_3_79 = 0) | all_223_0_76 = 0 | all_223_1_77 = 0)
% 33.83/9.98 |
% 33.83/9.98 | Applying alpha-rule on (372) yields:
% 33.83/9.98 | (373) distinct_points(all_1_7_7, all_1_7_7) = all_223_3_79
% 33.83/9.98 | (374) ~ (all_223_2_78 = 0) | ~ (all_223_3_79 = 0) | all_223_0_76 = 0 | all_223_1_77 = 0
% 33.83/9.98 | (375) apart_point_and_line(all_1_7_7, all_1_2_2) = all_223_0_76
% 33.83/9.98 | (376) apart_point_and_line(all_1_7_7, all_1_5_5) = all_223_1_77
% 33.83/9.98 | (377) distinct_lines(all_1_5_5, all_1_2_2) = all_223_2_78
% 33.83/9.98 |
% 33.83/9.98 +-Applying beta-rule and splitting (297), into two cases.
% 33.83/9.98 |-Branch one:
% 33.83/9.98 | (102) all_1_0_0 = 0
% 33.83/9.98 |
% 33.83/9.98 | Equations (102) can reduce 51 to:
% 33.83/9.98 | (94) $false
% 33.83/9.98 |
% 33.83/9.98 |-The branch is then unsatisfiable
% 33.83/9.98 |-Branch two:
% 33.83/9.98 | (51) ~ (all_1_0_0 = 0)
% 33.83/9.98 | (381) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_5_5) = v2 & apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_6_6, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.98 |
% 33.83/9.98 | Instantiating (381) with all_228_0_80, all_228_1_81, all_228_2_82, all_228_3_83 yields:
% 33.83/9.98 | (382) apart_point_and_line(all_1_6_6, all_1_5_5) = all_228_1_81 & apart_point_and_line(all_1_7_7, all_1_2_2) = all_228_0_80 & distinct_lines(all_1_2_2, all_1_5_5) = all_228_2_82 & distinct_points(all_1_6_6, all_1_7_7) = all_228_3_83 & ( ~ (all_228_2_82 = 0) | ~ (all_228_3_83 = 0) | all_228_0_80 = 0 | all_228_1_81 = 0)
% 33.83/9.98 |
% 33.83/9.98 | Applying alpha-rule on (382) yields:
% 33.83/9.98 | (383) distinct_lines(all_1_2_2, all_1_5_5) = all_228_2_82
% 33.83/9.98 | (384) distinct_points(all_1_6_6, all_1_7_7) = all_228_3_83
% 33.83/9.98 | (385) ~ (all_228_2_82 = 0) | ~ (all_228_3_83 = 0) | all_228_0_80 = 0 | all_228_1_81 = 0
% 33.83/9.98 | (386) apart_point_and_line(all_1_7_7, all_1_2_2) = all_228_0_80
% 33.83/9.98 | (387) apart_point_and_line(all_1_6_6, all_1_5_5) = all_228_1_81
% 33.83/9.98 |
% 33.83/9.98 +-Applying beta-rule and splitting (301), into two cases.
% 33.83/9.98 |-Branch one:
% 33.83/9.98 | (102) all_1_0_0 = 0
% 33.83/9.98 |
% 33.83/9.98 | Equations (102) can reduce 51 to:
% 33.83/9.98 | (94) $false
% 33.83/9.98 |
% 33.83/9.98 |-The branch is then unsatisfiable
% 33.83/9.98 |-Branch two:
% 33.83/9.98 | (51) ~ (all_1_0_0 = 0)
% 33.83/9.98 | (391) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_5_5) = v3 & apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.98 |
% 33.83/9.98 | Instantiating (391) with all_233_0_84, all_233_1_85, all_233_2_86, all_233_3_87 yields:
% 33.83/9.98 | (392) apart_point_and_line(all_1_6_6, all_1_5_5) = all_233_0_84 & apart_point_and_line(all_1_7_7, all_1_2_2) = all_233_1_85 & distinct_lines(all_1_5_5, all_1_2_2) = all_233_2_86 & distinct_points(all_1_7_7, all_1_6_6) = all_233_3_87 & ( ~ (all_233_2_86 = 0) | ~ (all_233_3_87 = 0) | all_233_0_84 = 0 | all_233_1_85 = 0)
% 33.83/9.99 |
% 33.83/9.99 | Applying alpha-rule on (392) yields:
% 33.83/9.99 | (393) distinct_points(all_1_7_7, all_1_6_6) = all_233_3_87
% 33.83/9.99 | (394) apart_point_and_line(all_1_6_6, all_1_5_5) = all_233_0_84
% 33.83/9.99 | (395) distinct_lines(all_1_5_5, all_1_2_2) = all_233_2_86
% 33.83/9.99 | (396) ~ (all_233_2_86 = 0) | ~ (all_233_3_87 = 0) | all_233_0_84 = 0 | all_233_1_85 = 0
% 33.83/9.99 | (397) apart_point_and_line(all_1_7_7, all_1_2_2) = all_233_1_85
% 33.83/9.99 |
% 33.83/9.99 +-Applying beta-rule and splitting (305), into two cases.
% 33.83/9.99 |-Branch one:
% 33.83/9.99 | (102) all_1_0_0 = 0
% 33.83/9.99 |
% 33.83/9.99 | Equations (102) can reduce 51 to:
% 33.83/9.99 | (94) $false
% 33.83/9.99 |
% 33.83/9.99 |-The branch is then unsatisfiable
% 33.83/9.99 |-Branch two:
% 33.83/9.99 | (51) ~ (all_1_0_0 = 0)
% 33.83/9.99 | (401) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_5_5) = v2 & apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_6_6, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.99 |
% 33.83/9.99 | Instantiating (401) with all_238_0_88, all_238_1_89, all_238_2_90, all_238_3_91 yields:
% 33.83/9.99 | (402) apart_point_and_line(all_1_6_6, all_1_5_5) = all_238_1_89 & apart_point_and_line(all_1_7_7, all_1_2_2) = all_238_0_88 & distinct_lines(all_1_5_5, all_1_2_2) = all_238_2_90 & distinct_points(all_1_6_6, all_1_7_7) = all_238_3_91 & ( ~ (all_238_2_90 = 0) | ~ (all_238_3_91 = 0) | all_238_0_88 = 0 | all_238_1_89 = 0)
% 33.83/9.99 |
% 33.83/9.99 | Applying alpha-rule on (402) yields:
% 33.83/9.99 | (403) distinct_lines(all_1_5_5, all_1_2_2) = all_238_2_90
% 33.83/9.99 | (404) apart_point_and_line(all_1_6_6, all_1_5_5) = all_238_1_89
% 33.83/9.99 | (405) apart_point_and_line(all_1_7_7, all_1_2_2) = all_238_0_88
% 33.83/9.99 | (406) distinct_points(all_1_6_6, all_1_7_7) = all_238_3_91
% 33.83/9.99 | (407) ~ (all_238_2_90 = 0) | ~ (all_238_3_91 = 0) | all_238_0_88 = 0 | all_238_1_89 = 0
% 33.83/9.99 |
% 33.83/9.99 +-Applying beta-rule and splitting (309), into two cases.
% 33.83/9.99 |-Branch one:
% 33.83/9.99 | (102) all_1_0_0 = 0
% 33.83/9.99 |
% 33.83/9.99 | Equations (102) can reduce 51 to:
% 33.83/9.99 | (94) $false
% 33.83/9.99 |
% 33.83/9.99 |-The branch is then unsatisfiable
% 33.83/9.99 |-Branch two:
% 33.83/9.99 | (51) ~ (all_1_0_0 = 0)
% 33.83/9.99 | (411) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_5_5) = v3 & apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.99 |
% 33.83/9.99 | Instantiating (411) with all_243_0_92, all_243_1_93, all_243_2_94, all_243_3_95 yields:
% 33.83/9.99 | (412) apart_point_and_line(all_1_6_6, all_1_5_5) = all_243_0_92 & apart_point_and_line(all_1_7_7, all_1_2_2) = all_243_1_93 & distinct_lines(all_1_2_2, all_1_5_5) = all_243_2_94 & distinct_points(all_1_7_7, all_1_6_6) = all_243_3_95 & ( ~ (all_243_2_94 = 0) | ~ (all_243_3_95 = 0) | all_243_0_92 = 0 | all_243_1_93 = 0)
% 33.83/9.99 |
% 33.83/9.99 | Applying alpha-rule on (412) yields:
% 33.83/9.99 | (413) distinct_lines(all_1_2_2, all_1_5_5) = all_243_2_94
% 33.83/9.99 | (414) distinct_points(all_1_7_7, all_1_6_6) = all_243_3_95
% 33.83/9.99 | (415) ~ (all_243_2_94 = 0) | ~ (all_243_3_95 = 0) | all_243_0_92 = 0 | all_243_1_93 = 0
% 33.83/9.99 | (416) apart_point_and_line(all_1_6_6, all_1_5_5) = all_243_0_92
% 33.83/9.99 | (417) apart_point_and_line(all_1_7_7, all_1_2_2) = all_243_1_93
% 33.83/9.99 |
% 33.83/9.99 +-Applying beta-rule and splitting (313), into two cases.
% 33.83/9.99 |-Branch one:
% 33.83/9.99 | (93) all_1_1_1 = 0
% 33.83/9.99 |
% 33.83/9.99 | Equations (93) can reduce 53 to:
% 33.83/9.99 | (94) $false
% 33.83/9.99 |
% 33.83/9.99 |-The branch is then unsatisfiable
% 33.83/9.99 |-Branch two:
% 33.83/9.99 | (53) ~ (all_1_1_1 = 0)
% 33.83/9.99 | (421) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_7_7, all_1_5_5) = v3 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.99 |
% 33.83/9.99 +-Applying beta-rule and splitting (317), into two cases.
% 33.83/9.99 |-Branch one:
% 33.83/9.99 | (93) all_1_1_1 = 0
% 33.83/9.99 |
% 33.83/9.99 | Equations (93) can reduce 53 to:
% 33.83/9.99 | (94) $false
% 33.83/9.99 |
% 33.83/9.99 |-The branch is then unsatisfiable
% 33.83/9.99 |-Branch two:
% 33.83/9.99 | (53) ~ (all_1_1_1 = 0)
% 33.83/9.99 | (425) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.99 |
% 33.83/9.99 | Instantiating (425) with all_253_0_100, all_253_1_101, all_253_2_102, all_253_3_103 yields:
% 33.83/9.99 | (426) apart_point_and_line(all_1_7_7, all_1_2_2) = all_253_1_101 & apart_point_and_line(all_1_9_9, all_1_2_2) = all_253_0_100 & distinct_lines(all_1_2_2, all_1_2_2) = all_253_2_102 & distinct_points(all_1_7_7, all_1_9_9) = all_253_3_103 & ( ~ (all_253_2_102 = 0) | ~ (all_253_3_103 = 0) | all_253_0_100 = 0 | all_253_1_101 = 0)
% 33.83/9.99 |
% 33.83/9.99 | Applying alpha-rule on (426) yields:
% 33.83/9.99 | (427) apart_point_and_line(all_1_9_9, all_1_2_2) = all_253_0_100
% 33.83/9.99 | (428) distinct_points(all_1_7_7, all_1_9_9) = all_253_3_103
% 33.83/9.99 | (429) apart_point_and_line(all_1_7_7, all_1_2_2) = all_253_1_101
% 33.83/9.99 | (430) ~ (all_253_2_102 = 0) | ~ (all_253_3_103 = 0) | all_253_0_100 = 0 | all_253_1_101 = 0
% 33.83/9.99 | (431) distinct_lines(all_1_2_2, all_1_2_2) = all_253_2_102
% 33.83/9.99 |
% 33.83/9.99 +-Applying beta-rule and splitting (321), into two cases.
% 33.83/9.99 |-Branch one:
% 33.83/9.99 | (93) all_1_1_1 = 0
% 33.83/9.99 |
% 33.83/9.99 | Equations (93) can reduce 53 to:
% 33.83/9.99 | (94) $false
% 33.83/9.99 |
% 33.83/9.99 |-The branch is then unsatisfiable
% 33.83/9.99 |-Branch two:
% 33.83/9.99 | (53) ~ (all_1_1_1 = 0)
% 33.83/9.99 | (435) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.99 |
% 33.83/9.99 | Instantiating (435) with all_258_0_104, all_258_1_105, all_258_2_106, all_258_3_107 yields:
% 33.83/9.99 | (436) apart_point_and_line(all_1_7_7, all_1_2_2) = all_258_0_104 & apart_point_and_line(all_1_9_9, all_1_2_2) = all_258_1_105 & distinct_lines(all_1_2_2, all_1_2_2) = all_258_2_106 & distinct_points(all_1_9_9, all_1_7_7) = all_258_3_107 & ( ~ (all_258_2_106 = 0) | ~ (all_258_3_107 = 0) | all_258_0_104 = 0 | all_258_1_105 = 0)
% 33.83/9.99 |
% 33.83/9.99 | Applying alpha-rule on (436) yields:
% 33.83/9.99 | (437) apart_point_and_line(all_1_9_9, all_1_2_2) = all_258_1_105
% 33.83/9.99 | (438) ~ (all_258_2_106 = 0) | ~ (all_258_3_107 = 0) | all_258_0_104 = 0 | all_258_1_105 = 0
% 33.83/9.99 | (439) distinct_lines(all_1_2_2, all_1_2_2) = all_258_2_106
% 33.83/9.99 | (440) apart_point_and_line(all_1_7_7, all_1_2_2) = all_258_0_104
% 33.83/9.99 | (441) distinct_points(all_1_9_9, all_1_7_7) = all_258_3_107
% 33.83/9.99 |
% 33.83/9.99 +-Applying beta-rule and splitting (325), into two cases.
% 33.83/9.99 |-Branch one:
% 33.83/9.99 | (93) all_1_1_1 = 0
% 33.83/9.99 |
% 33.83/9.99 | Equations (93) can reduce 53 to:
% 33.83/9.99 | (94) $false
% 33.83/9.99 |
% 33.83/9.99 |-The branch is then unsatisfiable
% 33.83/9.99 |-Branch two:
% 33.83/9.99 | (53) ~ (all_1_1_1 = 0)
% 33.83/9.99 | (445) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_7_7, all_1_5_5) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.99 |
% 33.83/9.99 +-Applying beta-rule and splitting (329), into two cases.
% 33.83/9.99 |-Branch one:
% 33.83/9.99 | (93) all_1_1_1 = 0
% 33.83/9.99 |
% 33.83/9.99 | Equations (93) can reduce 53 to:
% 33.83/9.99 | (94) $false
% 33.83/9.99 |
% 33.83/9.99 |-The branch is then unsatisfiable
% 33.83/9.99 |-Branch two:
% 33.83/9.99 | (53) ~ (all_1_1_1 = 0)
% 33.83/9.99 | (449) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_1_2_2) = v1 & apart_point_and_line(all_1_6_6, all_1_5_5) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 33.83/9.99 |
% 33.83/9.99 | Instantiating (449) with all_268_0_112, all_268_1_113, all_268_2_114 yields:
% 33.83/9.99 | (450) apart_point_and_line(all_1_6_6, all_1_2_2) = all_268_1_113 & apart_point_and_line(all_1_6_6, all_1_5_5) = all_268_0_112 & distinct_lines(all_1_2_2, all_1_5_5) = all_268_2_114 & ( ~ (all_268_2_114 = 0) | all_268_0_112 = 0 | all_268_1_113 = 0)
% 33.83/9.99 |
% 33.83/9.99 | Applying alpha-rule on (450) yields:
% 33.83/9.99 | (451) apart_point_and_line(all_1_6_6, all_1_2_2) = all_268_1_113
% 33.83/9.99 | (452) apart_point_and_line(all_1_6_6, all_1_5_5) = all_268_0_112
% 33.83/9.99 | (453) distinct_lines(all_1_2_2, all_1_5_5) = all_268_2_114
% 33.83/9.99 | (454) ~ (all_268_2_114 = 0) | all_268_0_112 = 0 | all_268_1_113 = 0
% 33.83/9.99 |
% 33.83/9.99 +-Applying beta-rule and splitting (333), into two cases.
% 33.83/9.99 |-Branch one:
% 33.83/9.99 | (277) all_16_1_11 = 0
% 33.83/9.99 |
% 33.83/9.99 | Equations (277) can reduce 207 to:
% 33.83/9.99 | (94) $false
% 33.83/9.99 |
% 33.83/9.99 |-The branch is then unsatisfiable
% 33.83/9.99 |-Branch two:
% 33.83/9.99 | (207) ~ (all_16_1_11 = 0)
% 33.83/9.99 | (458) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.99 |
% 33.83/9.99 | Instantiating (458) with all_273_0_115, all_273_1_116, all_273_2_117, all_273_3_118 yields:
% 33.83/9.99 | (459) apart_point_and_line(all_1_7_7, all_1_2_2) = all_273_1_116 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_273_0_115 & distinct_lines(all_1_5_5, all_1_2_2) = all_273_2_117 & distinct_points(all_1_7_7, all_1_9_9) = all_273_3_118 & ( ~ (all_273_2_117 = 0) | ~ (all_273_3_118 = 0) | all_273_0_115 = 0 | all_273_1_116 = 0)
% 33.83/9.99 |
% 33.83/9.99 | Applying alpha-rule on (459) yields:
% 33.83/9.99 | (460) ~ (all_273_2_117 = 0) | ~ (all_273_3_118 = 0) | all_273_0_115 = 0 | all_273_1_116 = 0
% 33.83/9.99 | (461) distinct_lines(all_1_5_5, all_1_2_2) = all_273_2_117
% 33.83/9.99 | (462) distinct_points(all_1_7_7, all_1_9_9) = all_273_3_118
% 33.83/9.99 | (463) apart_point_and_line(all_1_9_9, all_1_5_5) = all_273_0_115
% 33.83/9.99 | (464) apart_point_and_line(all_1_7_7, all_1_2_2) = all_273_1_116
% 33.83/9.99 |
% 33.83/9.99 +-Applying beta-rule and splitting (337), into two cases.
% 33.83/9.99 |-Branch one:
% 33.83/9.99 | (277) all_16_1_11 = 0
% 33.83/9.99 |
% 33.83/9.99 | Equations (277) can reduce 207 to:
% 33.83/9.99 | (94) $false
% 33.83/9.99 |
% 33.83/9.99 |-The branch is then unsatisfiable
% 33.83/9.99 |-Branch two:
% 33.83/9.99 | (207) ~ (all_16_1_11 = 0)
% 33.83/9.99 | (468) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_5_5) = v2 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_9_9, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/9.99 |
% 33.83/9.99 | Instantiating (468) with all_278_0_119, all_278_1_120, all_278_2_121, all_278_3_122 yields:
% 33.83/9.99 | (469) apart_point_and_line(all_1_7_7, all_1_2_2) = all_278_0_119 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_278_1_120 & distinct_lines(all_1_2_2, all_1_5_5) = all_278_2_121 & distinct_points(all_1_9_9, all_1_7_7) = all_278_3_122 & ( ~ (all_278_2_121 = 0) | ~ (all_278_3_122 = 0) | all_278_0_119 = 0 | all_278_1_120 = 0)
% 33.83/10.00 |
% 33.83/10.00 | Applying alpha-rule on (469) yields:
% 33.83/10.00 | (470) ~ (all_278_2_121 = 0) | ~ (all_278_3_122 = 0) | all_278_0_119 = 0 | all_278_1_120 = 0
% 33.83/10.00 | (471) apart_point_and_line(all_1_9_9, all_1_5_5) = all_278_1_120
% 33.83/10.00 | (472) distinct_points(all_1_9_9, all_1_7_7) = all_278_3_122
% 33.83/10.00 | (473) apart_point_and_line(all_1_7_7, all_1_2_2) = all_278_0_119
% 33.83/10.00 | (474) distinct_lines(all_1_2_2, all_1_5_5) = all_278_2_121
% 33.83/10.00 |
% 33.83/10.00 +-Applying beta-rule and splitting (341), into two cases.
% 33.83/10.00 |-Branch one:
% 33.83/10.00 | (277) all_16_1_11 = 0
% 33.83/10.00 |
% 33.83/10.00 | Equations (277) can reduce 207 to:
% 33.83/10.00 | (94) $false
% 33.83/10.00 |
% 33.83/10.00 |-The branch is then unsatisfiable
% 33.83/10.00 |-Branch two:
% 33.83/10.00 | (207) ~ (all_16_1_11 = 0)
% 33.83/10.00 | (478) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_5_5) = v3 & distinct_lines(all_1_2_2, all_1_5_5) = v1 & distinct_points(all_1_7_7, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 33.83/10.00 |
% 33.83/10.00 | Instantiating (478) with all_283_0_123, all_283_1_124, all_283_2_125, all_283_3_126 yields:
% 33.83/10.00 | (479) apart_point_and_line(all_1_7_7, all_1_2_2) = all_283_1_124 & apart_point_and_line(all_1_9_9, all_1_5_5) = all_283_0_123 & distinct_lines(all_1_2_2, all_1_5_5) = all_283_2_125 & distinct_points(all_1_7_7, all_1_9_9) = all_283_3_126 & ( ~ (all_283_2_125 = 0) | ~ (all_283_3_126 = 0) | all_283_0_123 = 0 | all_283_1_124 = 0)
% 33.83/10.00 |
% 33.83/10.00 | Applying alpha-rule on (479) yields:
% 33.83/10.00 | (480) distinct_points(all_1_7_7, all_1_9_9) = all_283_3_126
% 33.83/10.00 | (481) apart_point_and_line(all_1_9_9, all_1_5_5) = all_283_0_123
% 33.83/10.00 | (482) ~ (all_283_2_125 = 0) | ~ (all_283_3_126 = 0) | all_283_0_123 = 0 | all_283_1_124 = 0
% 33.83/10.00 | (483) apart_point_and_line(all_1_7_7, all_1_2_2) = all_283_1_124
% 33.83/10.00 | (484) distinct_lines(all_1_2_2, all_1_5_5) = all_283_2_125
% 33.83/10.00 |
% 33.83/10.00 +-Applying beta-rule and splitting (345), into two cases.
% 33.83/10.00 |-Branch one:
% 33.83/10.00 | (93) all_1_1_1 = 0
% 33.83/10.00 |
% 33.83/10.00 | Equations (93) can reduce 53 to:
% 33.83/10.00 | (94) $false
% 33.83/10.00 |
% 33.83/10.00 |-The branch is then unsatisfiable
% 33.83/10.00 |-Branch two:
% 33.83/10.00 | (53) ~ (all_1_1_1 = 0)
% 33.83/10.00 | (488) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_1_2_2) = v2 & apart_point_and_line(all_1_6_6, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 33.83/10.00 |
% 33.83/10.00 | Instantiating (488) with all_288_0_127, all_288_1_128, all_288_2_129 yields:
% 33.83/10.00 | (489) apart_point_and_line(all_1_6_6, all_1_2_2) = all_288_0_127 & apart_point_and_line(all_1_6_6, all_1_5_5) = all_288_1_128 & distinct_lines(all_1_5_5, all_1_2_2) = all_288_2_129 & ( ~ (all_288_2_129 = 0) | all_288_0_127 = 0 | all_288_1_128 = 0)
% 33.83/10.00 |
% 33.83/10.00 | Applying alpha-rule on (489) yields:
% 33.83/10.00 | (490) apart_point_and_line(all_1_6_6, all_1_2_2) = all_288_0_127
% 33.83/10.00 | (491) apart_point_and_line(all_1_6_6, all_1_5_5) = all_288_1_128
% 33.83/10.00 | (492) distinct_lines(all_1_5_5, all_1_2_2) = all_288_2_129
% 33.83/10.00 | (493) ~ (all_288_2_129 = 0) | all_288_0_127 = 0 | all_288_1_128 = 0
% 33.83/10.00 |
% 33.83/10.00 +-Applying beta-rule and splitting (349), into two cases.
% 33.83/10.00 |-Branch one:
% 33.83/10.00 | (93) all_1_1_1 = 0
% 33.83/10.00 |
% 33.83/10.00 | Equations (93) can reduce 53 to:
% 33.83/10.00 | (94) $false
% 33.83/10.00 |
% 33.83/10.00 |-The branch is then unsatisfiable
% 33.83/10.00 |-Branch two:
% 33.83/10.00 | (53) ~ (all_1_1_1 = 0)
% 33.83/10.00 | (497) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v2 & apart_point_and_line(all_1_7_7, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 34.10/10.00 |
% 34.10/10.00 | Instantiating (497) with all_293_0_130, all_293_1_131, all_293_2_132, all_293_3_133 yields:
% 34.10/10.00 | (498) apart_point_and_line(all_1_7_7, all_1_2_2) = all_293_1_131 & apart_point_and_line(all_1_7_7, all_1_5_5) = all_293_0_130 & distinct_lines(all_1_5_5, all_1_2_2) = all_293_2_132 & distinct_points(all_1_7_7, all_1_7_7) = all_293_3_133 & ( ~ (all_293_2_132 = 0) | ~ (all_293_3_133 = 0) | all_293_0_130 = 0 | all_293_1_131 = 0)
% 34.10/10.00 |
% 34.10/10.00 | Applying alpha-rule on (498) yields:
% 34.10/10.00 | (499) apart_point_and_line(all_1_7_7, all_1_2_2) = all_293_1_131
% 34.10/10.00 | (500) ~ (all_293_2_132 = 0) | ~ (all_293_3_133 = 0) | all_293_0_130 = 0 | all_293_1_131 = 0
% 34.10/10.00 | (501) distinct_points(all_1_7_7, all_1_7_7) = all_293_3_133
% 34.10/10.00 | (502) apart_point_and_line(all_1_7_7, all_1_5_5) = all_293_0_130
% 34.10/10.00 | (503) distinct_lines(all_1_5_5, all_1_2_2) = all_293_2_132
% 34.10/10.00 |
% 34.10/10.00 +-Applying beta-rule and splitting (353), into two cases.
% 34.10/10.00 |-Branch one:
% 34.10/10.00 | (102) all_1_0_0 = 0
% 34.10/10.00 |
% 34.10/10.00 | Equations (102) can reduce 51 to:
% 34.10/10.00 | (94) $false
% 34.10/10.00 |
% 34.10/10.00 |-The branch is then unsatisfiable
% 34.10/10.00 |-Branch two:
% 34.10/10.00 | (51) ~ (all_1_0_0 = 0)
% 34.10/10.00 | (507) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_2_2) = v2 & apart_point_and_line(all_1_9_9, all_1_2_2) = v3 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_6_6, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 34.10/10.00 |
% 34.10/10.00 | Instantiating (507) with all_298_0_134, all_298_1_135, all_298_2_136, all_298_3_137 yields:
% 34.10/10.00 | (508) apart_point_and_line(all_1_6_6, all_1_2_2) = all_298_1_135 & apart_point_and_line(all_1_9_9, all_1_2_2) = all_298_0_134 & distinct_lines(all_1_2_2, all_1_2_2) = all_298_2_136 & distinct_points(all_1_6_6, all_1_9_9) = all_298_3_137 & ( ~ (all_298_2_136 = 0) | ~ (all_298_3_137 = 0) | all_298_0_134 = 0 | all_298_1_135 = 0)
% 34.10/10.00 |
% 34.10/10.00 | Applying alpha-rule on (508) yields:
% 34.10/10.00 | (509) distinct_points(all_1_6_6, all_1_9_9) = all_298_3_137
% 34.10/10.00 | (510) apart_point_and_line(all_1_9_9, all_1_2_2) = all_298_0_134
% 34.10/10.00 | (511) ~ (all_298_2_136 = 0) | ~ (all_298_3_137 = 0) | all_298_0_134 = 0 | all_298_1_135 = 0
% 34.10/10.00 | (512) apart_point_and_line(all_1_6_6, all_1_2_2) = all_298_1_135
% 34.10/10.00 | (513) distinct_lines(all_1_2_2, all_1_2_2) = all_298_2_136
% 34.10/10.00 |
% 34.10/10.00 +-Applying beta-rule and splitting (357), into two cases.
% 34.10/10.00 |-Branch one:
% 34.10/10.00 | (102) all_1_0_0 = 0
% 34.10/10.00 |
% 34.10/10.00 | Equations (102) can reduce 51 to:
% 34.10/10.00 | (94) $false
% 34.10/10.00 |
% 34.10/10.00 |-The branch is then unsatisfiable
% 34.10/10.00 |-Branch two:
% 34.10/10.00 | (51) ~ (all_1_0_0 = 0)
% 34.10/10.00 | (517) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_1_6_6, all_1_2_2) = v3 & apart_point_and_line(all_1_9_9, all_1_2_2) = v2 & distinct_lines(all_1_2_2, all_1_2_2) = v1 & distinct_points(all_1_9_9, all_1_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 34.10/10.00 |
% 34.10/10.00 | Instantiating (517) with all_303_0_138, all_303_1_139, all_303_2_140, all_303_3_141 yields:
% 34.10/10.00 | (518) apart_point_and_line(all_1_6_6, all_1_2_2) = all_303_0_138 & apart_point_and_line(all_1_9_9, all_1_2_2) = all_303_1_139 & distinct_lines(all_1_2_2, all_1_2_2) = all_303_2_140 & distinct_points(all_1_9_9, all_1_6_6) = all_303_3_141 & ( ~ (all_303_2_140 = 0) | ~ (all_303_3_141 = 0) | all_303_0_138 = 0 | all_303_1_139 = 0)
% 34.10/10.00 |
% 34.10/10.00 | Applying alpha-rule on (518) yields:
% 34.10/10.00 | (519) distinct_points(all_1_9_9, all_1_6_6) = all_303_3_141
% 34.10/10.00 | (520) ~ (all_303_2_140 = 0) | ~ (all_303_3_141 = 0) | all_303_0_138 = 0 | all_303_1_139 = 0
% 34.10/10.00 | (521) apart_point_and_line(all_1_9_9, all_1_2_2) = all_303_1_139
% 34.10/10.00 | (522) apart_point_and_line(all_1_6_6, all_1_2_2) = all_303_0_138
% 34.10/10.00 | (523) distinct_lines(all_1_2_2, all_1_2_2) = all_303_2_140
% 34.10/10.00 |
% 34.10/10.00 | Instantiating formula (25) with all_1_7_7, all_1_6_6, all_100_2_45, all_1_5_5 and discharging atoms line_connecting(all_1_7_7, all_1_6_6) = all_100_2_45, line_connecting(all_1_7_7, all_1_6_6) = all_1_5_5, yields:
% 34.10/10.00 | (524) all_100_2_45 = all_1_5_5
% 34.10/10.00 |
% 34.10/10.00 | Instantiating formula (42) with all_1_6_6, all_1_2_2, all_303_0_138, all_1_0_0 and discharging atoms apart_point_and_line(all_1_6_6, all_1_2_2) = all_303_0_138, apart_point_and_line(all_1_6_6, all_1_2_2) = all_1_0_0, yields:
% 34.10/10.00 | (525) all_303_0_138 = all_1_0_0
% 34.10/10.00 |
% 34.10/10.00 | Instantiating formula (42) with all_1_6_6, all_1_2_2, all_298_1_135, all_303_0_138 and discharging atoms apart_point_and_line(all_1_6_6, all_1_2_2) = all_303_0_138, apart_point_and_line(all_1_6_6, all_1_2_2) = all_298_1_135, yields:
% 34.10/10.00 | (526) all_303_0_138 = all_298_1_135
% 34.10/10.00 |
% 34.10/10.00 | Instantiating formula (42) with all_1_6_6, all_1_2_2, all_288_0_127, all_298_1_135 and discharging atoms apart_point_and_line(all_1_6_6, all_1_2_2) = all_298_1_135, apart_point_and_line(all_1_6_6, all_1_2_2) = all_288_0_127, yields:
% 34.10/10.00 | (527) all_298_1_135 = all_288_0_127
% 34.10/10.00 |
% 34.10/10.00 | Instantiating formula (42) with all_1_6_6, all_1_5_5, all_268_0_112, all_100_1_44 and discharging atoms apart_point_and_line(all_1_6_6, all_1_5_5) = all_268_0_112, yields:
% 34.10/10.00 | (528) all_268_0_112 = all_100_1_44 | ~ (apart_point_and_line(all_1_6_6, all_1_5_5) = all_100_1_44)
% 34.10/10.00 |
% 34.10/10.00 | Instantiating formula (42) with all_1_6_6, all_1_5_5, all_268_0_112, all_288_1_128 and discharging atoms apart_point_and_line(all_1_6_6, all_1_5_5) = all_288_1_128, apart_point_and_line(all_1_6_6, all_1_5_5) = all_268_0_112, yields:
% 34.10/10.00 | (529) all_288_1_128 = all_268_0_112
% 34.10/10.00 |
% 34.10/10.00 | Instantiating formula (42) with all_1_6_6, all_1_5_5, all_238_1_89, all_268_0_112 and discharging atoms apart_point_and_line(all_1_6_6, all_1_5_5) = all_268_0_112, apart_point_and_line(all_1_6_6, all_1_5_5) = all_238_1_89, yields:
% 34.10/10.00 | (530) all_268_0_112 = all_238_1_89
% 34.10/10.00 |
% 34.10/10.00 | Instantiating formula (42) with all_1_6_6, all_1_5_5, all_233_0_84, all_243_0_92 and discharging atoms apart_point_and_line(all_1_6_6, all_1_5_5) = all_243_0_92, apart_point_and_line(all_1_6_6, all_1_5_5) = all_233_0_84, yields:
% 34.10/10.00 | (531) all_243_0_92 = all_233_0_84
% 34.10/10.00 |
% 34.10/10.00 | Instantiating formula (42) with all_1_6_6, all_1_5_5, all_228_1_81, all_268_0_112 and discharging atoms apart_point_and_line(all_1_6_6, all_1_5_5) = all_268_0_112, apart_point_and_line(all_1_6_6, all_1_5_5) = all_228_1_81, yields:
% 34.10/10.00 | (532) all_268_0_112 = all_228_1_81
% 34.10/10.00 |
% 34.10/10.00 | Instantiating formula (42) with all_1_6_6, all_1_5_5, all_228_1_81, all_243_0_92 and discharging atoms apart_point_and_line(all_1_6_6, all_1_5_5) = all_243_0_92, apart_point_and_line(all_1_6_6, all_1_5_5) = all_228_1_81, yields:
% 34.10/10.00 | (533) all_243_0_92 = all_228_1_81
% 34.10/10.00 |
% 34.10/10.00 | Instantiating formula (42) with all_1_6_6, all_1_5_5, all_133_0_55, all_268_0_112 and discharging atoms apart_point_and_line(all_1_6_6, all_1_5_5) = all_268_0_112, apart_point_and_line(all_1_6_6, all_1_5_5) = all_133_0_55, yields:
% 34.10/10.00 | (534) all_268_0_112 = all_133_0_55
% 34.10/10.00 |
% 34.10/10.00 | Instantiating formula (42) with all_1_6_6, all_1_5_5, all_133_1_56, all_288_1_128 and discharging atoms apart_point_and_line(all_1_6_6, all_1_5_5) = all_288_1_128, apart_point_and_line(all_1_6_6, all_1_5_5) = all_133_1_56, yields:
% 34.10/10.00 | (535) all_288_1_128 = all_133_1_56
% 34.10/10.00 |
% 34.10/10.00 | Instantiating formula (42) with all_1_6_6, all_1_5_5, all_98_1_41, all_243_0_92 and discharging atoms apart_point_and_line(all_1_6_6, all_1_5_5) = all_243_0_92, apart_point_and_line(all_1_6_6, all_1_5_5) = all_98_1_41, yields:
% 34.10/10.00 | (536) all_243_0_92 = all_98_1_41
% 34.10/10.00 |
% 34.10/10.00 | Instantiating formula (42) with all_1_8_8, all_1_2_2, all_148_1_66, all_148_0_65 and discharging atoms apart_point_and_line(all_1_8_8, all_1_2_2) = all_148_0_65, apart_point_and_line(all_1_8_8, all_1_2_2) = all_148_1_66, yields:
% 34.10/10.00 | (537) all_148_0_65 = all_148_1_66
% 34.10/10.00 |
% 34.10/10.00 | Instantiating formula (42) with all_1_9_9, all_1_5_5, all_283_0_123, all_1_4_4 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_283_0_123, apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4, yields:
% 34.10/10.00 | (538) all_283_0_123 = all_1_4_4
% 34.10/10.00 |
% 34.10/10.00 | Instantiating formula (42) with all_1_9_9, all_1_5_5, all_278_1_120, all_283_0_123 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_283_0_123, apart_point_and_line(all_1_9_9, all_1_5_5) = all_278_1_120, yields:
% 34.10/10.00 | (539) all_283_0_123 = all_278_1_120
% 34.10/10.00 |
% 34.10/10.00 | Instantiating formula (42) with all_1_9_9, all_1_5_5, all_273_0_115, all_278_1_120 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_278_1_120, apart_point_and_line(all_1_9_9, all_1_5_5) = all_273_0_115, yields:
% 34.10/10.00 | (540) all_278_1_120 = all_273_0_115
% 34.10/10.00 |
% 34.10/10.00 | Instantiating formula (42) with all_1_9_9, all_1_5_5, all_218_1_73, all_273_0_115 and discharging atoms apart_point_and_line(all_1_9_9, all_1_5_5) = all_273_0_115, apart_point_and_line(all_1_9_9, all_1_5_5) = all_218_1_73, yields:
% 34.10/10.00 | (541) all_273_0_115 = all_218_1_73
% 34.10/10.00 |
% 34.10/10.00 | Instantiating formula (15) with all_1_5_5, all_1_2_2, all_288_2_129, all_293_2_132 and discharging atoms distinct_lines(all_1_5_5, all_1_2_2) = all_293_2_132, distinct_lines(all_1_5_5, all_1_2_2) = all_288_2_129, yields:
% 34.10/10.00 | (542) all_293_2_132 = all_288_2_129
% 34.10/10.00 |
% 34.10/10.00 | Instantiating formula (15) with all_1_5_5, all_1_2_2, all_273_2_117, all_288_2_129 and discharging atoms distinct_lines(all_1_5_5, all_1_2_2) = all_288_2_129, distinct_lines(all_1_5_5, all_1_2_2) = all_273_2_117, yields:
% 34.10/10.00 | (543) all_288_2_129 = all_273_2_117
% 34.10/10.00 |
% 34.10/10.00 | Instantiating formula (15) with all_1_5_5, all_1_2_2, all_238_2_90, all_288_2_129 and discharging atoms distinct_lines(all_1_5_5, all_1_2_2) = all_288_2_129, distinct_lines(all_1_5_5, all_1_2_2) = all_238_2_90, yields:
% 34.10/10.00 | (544) all_288_2_129 = all_238_2_90
% 34.10/10.01 |
% 34.10/10.01 | Instantiating formula (15) with all_1_5_5, all_1_2_2, all_233_2_86, all_288_2_129 and discharging atoms distinct_lines(all_1_5_5, all_1_2_2) = all_288_2_129, distinct_lines(all_1_5_5, all_1_2_2) = all_233_2_86, yields:
% 34.10/10.01 | (545) all_288_2_129 = all_233_2_86
% 34.10/10.01 |
% 34.10/10.01 | Instantiating formula (15) with all_1_5_5, all_1_2_2, all_223_2_78, all_293_2_132 and discharging atoms distinct_lines(all_1_5_5, all_1_2_2) = all_293_2_132, distinct_lines(all_1_5_5, all_1_2_2) = all_223_2_78, yields:
% 34.10/10.01 | (546) all_293_2_132 = all_223_2_78
% 34.10/10.01 |
% 34.10/10.01 | Instantiating formula (15) with all_1_5_5, all_1_2_2, all_218_2_74, all_233_2_86 and discharging atoms distinct_lines(all_1_5_5, all_1_2_2) = all_233_2_86, distinct_lines(all_1_5_5, all_1_2_2) = all_218_2_74, yields:
% 34.10/10.01 | (547) all_233_2_86 = all_218_2_74
% 34.10/10.01 |
% 34.10/10.01 | Instantiating formula (10) with all_1_7_7, all_1_6_6, all_243_3_95, 0 and discharging atoms distinct_points(all_1_7_7, all_1_6_6) = all_243_3_95, distinct_points(all_1_7_7, all_1_6_6) = 0, yields:
% 34.10/10.01 | (548) all_243_3_95 = 0
% 34.10/10.01 |
% 34.10/10.01 | Instantiating formula (10) with all_1_7_7, all_1_6_6, all_233_3_87, all_243_3_95 and discharging atoms distinct_points(all_1_7_7, all_1_6_6) = all_243_3_95, distinct_points(all_1_7_7, all_1_6_6) = all_233_3_87, yields:
% 34.10/10.01 | (549) all_243_3_95 = all_233_3_87
% 34.10/10.01 |
% 34.10/10.01 | Instantiating formula (10) with all_1_7_7, all_1_6_6, all_98_2_42, all_243_3_95 and discharging atoms distinct_points(all_1_7_7, all_1_6_6) = all_243_3_95, distinct_points(all_1_7_7, all_1_6_6) = all_98_2_42, yields:
% 34.10/10.01 | (550) all_243_3_95 = all_98_2_42
% 34.10/10.01 |
% 34.10/10.01 | Instantiating formula (10) with all_1_7_7, all_1_9_9, all_273_3_118, all_283_3_126 and discharging atoms distinct_points(all_1_7_7, all_1_9_9) = all_283_3_126, distinct_points(all_1_7_7, all_1_9_9) = all_273_3_118, yields:
% 34.10/10.01 | (551) all_283_3_126 = all_273_3_118
% 34.10/10.01 |
% 34.10/10.01 | Instantiating formula (10) with all_1_7_7, all_1_9_9, all_253_3_103, all_283_3_126 and discharging atoms distinct_points(all_1_7_7, all_1_9_9) = all_283_3_126, distinct_points(all_1_7_7, all_1_9_9) = all_253_3_103, yields:
% 34.10/10.01 | (552) all_283_3_126 = all_253_3_103
% 34.10/10.01 |
% 34.10/10.01 | Instantiating formula (10) with all_1_8_8, all_1_9_9, 0, all_118_2_48 and discharging atoms distinct_points(all_1_8_8, all_1_9_9) = all_118_2_48, distinct_points(all_1_8_8, all_1_9_9) = 0, yields:
% 34.10/10.01 | (553) all_118_2_48 = 0
% 34.10/10.01 |
% 34.10/10.01 | Instantiating formula (10) with all_1_9_9, all_1_7_7, all_258_3_107, all_278_3_122 and discharging atoms distinct_points(all_1_9_9, all_1_7_7) = all_278_3_122, distinct_points(all_1_9_9, all_1_7_7) = all_258_3_107, yields:
% 34.10/10.01 | (554) all_278_3_122 = all_258_3_107
% 34.10/10.01 |
% 34.10/10.01 | Instantiating formula (10) with all_1_9_9, all_1_7_7, all_218_3_75, all_278_3_122 and discharging atoms distinct_points(all_1_9_9, all_1_7_7) = all_278_3_122, distinct_points(all_1_9_9, all_1_7_7) = all_218_3_75, yields:
% 34.10/10.01 | (555) all_278_3_122 = all_218_3_75
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (526,525) yields a new equation:
% 34.10/10.01 | (556) all_298_1_135 = all_1_0_0
% 34.10/10.01 |
% 34.10/10.01 | Simplifying 556 yields:
% 34.10/10.01 | (557) all_298_1_135 = all_1_0_0
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (527,557) yields a new equation:
% 34.10/10.01 | (558) all_288_0_127 = all_1_0_0
% 34.10/10.01 |
% 34.10/10.01 | Simplifying 558 yields:
% 34.10/10.01 | (559) all_288_0_127 = all_1_0_0
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (542,546) yields a new equation:
% 34.10/10.01 | (560) all_288_2_129 = all_223_2_78
% 34.10/10.01 |
% 34.10/10.01 | Simplifying 560 yields:
% 34.10/10.01 | (561) all_288_2_129 = all_223_2_78
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (529,535) yields a new equation:
% 34.10/10.01 | (562) all_268_0_112 = all_133_1_56
% 34.10/10.01 |
% 34.10/10.01 | Simplifying 562 yields:
% 34.10/10.01 | (563) all_268_0_112 = all_133_1_56
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (545,543) yields a new equation:
% 34.10/10.01 | (564) all_273_2_117 = all_233_2_86
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (544,543) yields a new equation:
% 34.10/10.01 | (565) all_273_2_117 = all_238_2_90
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (561,543) yields a new equation:
% 34.10/10.01 | (566) all_273_2_117 = all_223_2_78
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (539,538) yields a new equation:
% 34.10/10.01 | (567) all_278_1_120 = all_1_4_4
% 34.10/10.01 |
% 34.10/10.01 | Simplifying 567 yields:
% 34.10/10.01 | (568) all_278_1_120 = all_1_4_4
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (552,551) yields a new equation:
% 34.10/10.01 | (569) all_273_3_118 = all_253_3_103
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (540,568) yields a new equation:
% 34.10/10.01 | (570) all_273_0_115 = all_1_4_4
% 34.10/10.01 |
% 34.10/10.01 | Simplifying 570 yields:
% 34.10/10.01 | (571) all_273_0_115 = all_1_4_4
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (554,555) yields a new equation:
% 34.10/10.01 | (572) all_258_3_107 = all_218_3_75
% 34.10/10.01 |
% 34.10/10.01 | Simplifying 572 yields:
% 34.10/10.01 | (573) all_258_3_107 = all_218_3_75
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (541,571) yields a new equation:
% 34.10/10.01 | (574) all_218_1_73 = all_1_4_4
% 34.10/10.01 |
% 34.10/10.01 | Simplifying 574 yields:
% 34.10/10.01 | (575) all_218_1_73 = all_1_4_4
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (564,565) yields a new equation:
% 34.10/10.01 | (576) all_238_2_90 = all_233_2_86
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (566,565) yields a new equation:
% 34.10/10.01 | (577) all_238_2_90 = all_223_2_78
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (532,530) yields a new equation:
% 34.10/10.01 | (578) all_238_1_89 = all_228_1_81
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (534,530) yields a new equation:
% 34.10/10.01 | (579) all_238_1_89 = all_133_0_55
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (563,530) yields a new equation:
% 34.10/10.01 | (580) all_238_1_89 = all_133_1_56
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (533,531) yields a new equation:
% 34.10/10.01 | (581) all_233_0_84 = all_228_1_81
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (536,531) yields a new equation:
% 34.10/10.01 | (582) all_233_0_84 = all_98_1_41
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (548,549) yields a new equation:
% 34.10/10.01 | (583) all_233_3_87 = 0
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (550,549) yields a new equation:
% 34.10/10.01 | (584) all_233_3_87 = all_98_2_42
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (580,579) yields a new equation:
% 34.10/10.01 | (585) all_133_0_55 = all_133_1_56
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (578,579) yields a new equation:
% 34.10/10.01 | (586) all_228_1_81 = all_133_0_55
% 34.10/10.01 |
% 34.10/10.01 | Simplifying 586 yields:
% 34.10/10.01 | (587) all_228_1_81 = all_133_0_55
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (576,577) yields a new equation:
% 34.10/10.01 | (588) all_233_2_86 = all_223_2_78
% 34.10/10.01 |
% 34.10/10.01 | Simplifying 588 yields:
% 34.10/10.01 | (589) all_233_2_86 = all_223_2_78
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (581,582) yields a new equation:
% 34.10/10.01 | (590) all_228_1_81 = all_98_1_41
% 34.10/10.01 |
% 34.10/10.01 | Simplifying 590 yields:
% 34.10/10.01 | (591) all_228_1_81 = all_98_1_41
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (547,589) yields a new equation:
% 34.10/10.01 | (592) all_223_2_78 = all_218_2_74
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (583,584) yields a new equation:
% 34.10/10.01 | (593) all_98_2_42 = 0
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (587,591) yields a new equation:
% 34.10/10.01 | (594) all_133_0_55 = all_98_1_41
% 34.10/10.01 |
% 34.10/10.01 | Simplifying 594 yields:
% 34.10/10.01 | (595) all_133_0_55 = all_98_1_41
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (585,595) yields a new equation:
% 34.10/10.01 | (596) all_133_1_56 = all_98_1_41
% 34.10/10.01 |
% 34.10/10.01 | Simplifying 596 yields:
% 34.10/10.01 | (597) all_133_1_56 = all_98_1_41
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (592,577) yields a new equation:
% 34.10/10.01 | (598) all_238_2_90 = all_218_2_74
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (595,579) yields a new equation:
% 34.10/10.01 | (599) all_238_1_89 = all_98_1_41
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (599,530) yields a new equation:
% 34.10/10.01 | (600) all_268_0_112 = all_98_1_41
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (598,565) yields a new equation:
% 34.10/10.01 | (601) all_273_2_117 = all_218_2_74
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (601,543) yields a new equation:
% 34.10/10.01 | (602) all_288_2_129 = all_218_2_74
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (597,535) yields a new equation:
% 34.10/10.01 | (603) all_288_1_128 = all_98_1_41
% 34.10/10.01 |
% 34.10/10.01 | From (524) and (250) follows:
% 34.10/10.01 | (604) apart_point_and_line(all_1_6_6, all_1_5_5) = all_100_1_44
% 34.10/10.01 |
% 34.10/10.01 | From (537) and (282) follows:
% 34.10/10.01 | (283) apart_point_and_line(all_1_8_8, all_1_2_2) = all_148_1_66
% 34.10/10.01 |
% 34.10/10.01 | From (575) and (364) follows:
% 34.10/10.01 | (56) apart_point_and_line(all_1_9_9, all_1_5_5) = all_1_4_4
% 34.10/10.01 |
% 34.10/10.01 | From (592) and (377) follows:
% 34.10/10.01 | (367) distinct_lines(all_1_5_5, all_1_2_2) = all_218_2_74
% 34.10/10.01 |
% 34.10/10.01 | From (593) and (246) follows:
% 34.10/10.01 | (52) distinct_points(all_1_7_7, all_1_6_6) = 0
% 34.10/10.01 |
% 34.10/10.01 | From (569) and (462) follows:
% 34.10/10.01 | (428) distinct_points(all_1_7_7, all_1_9_9) = all_253_3_103
% 34.10/10.01 |
% 34.10/10.01 | From (553) and (262) follows:
% 34.10/10.01 | (254) distinct_points(all_1_8_8, all_1_9_9) = 0
% 34.10/10.01 |
% 34.10/10.01 | From (573) and (441) follows:
% 34.10/10.01 | (366) distinct_points(all_1_9_9, all_1_7_7) = all_218_3_75
% 34.10/10.01 |
% 34.10/10.01 +-Applying beta-rule and splitting (528), into two cases.
% 34.10/10.01 |-Branch one:
% 34.10/10.01 | (612) ~ (apart_point_and_line(all_1_6_6, all_1_5_5) = all_100_1_44)
% 34.10/10.01 |
% 34.10/10.01 | Using (604) and (612) yields:
% 34.10/10.01 | (204) $false
% 34.10/10.01 |
% 34.10/10.01 |-The branch is then unsatisfiable
% 34.10/10.01 |-Branch two:
% 34.10/10.01 | (604) apart_point_and_line(all_1_6_6, all_1_5_5) = all_100_1_44
% 34.10/10.01 | (615) all_268_0_112 = all_100_1_44
% 34.10/10.01 |
% 34.10/10.01 | Combining equations (600,615) yields a new equation:
% 34.10/10.01 | (616) all_100_1_44 = all_98_1_41
% 34.10/10.01 |
% 34.10/10.01 | Equations (616) can reduce 253 to:
% 34.10/10.01 | (617) ~ (all_98_1_41 = 0)
% 34.10/10.01 |
% 34.10/10.01 +-Applying beta-rule and splitting (493), into two cases.
% 34.10/10.01 |-Branch one:
% 34.10/10.01 | (618) ~ (all_288_2_129 = 0)
% 34.10/10.01 |
% 34.10/10.01 | Equations (602) can reduce 618 to:
% 34.10/10.01 | (619) ~ (all_218_2_74 = 0)
% 34.10/10.01 |
% 34.10/10.01 +-Applying beta-rule and splitting (233), into two cases.
% 34.10/10.01 |-Branch one:
% 34.10/10.01 | (620) ~ (apart_point_and_line(all_1_9_9, all_1_5_5) = 0)
% 34.10/10.01 |
% 34.10/10.01 | Using (56) and (620) yields:
% 34.10/10.01 | (621) ~ (all_1_4_4 = 0)
% 34.10/10.01 |
% 34.10/10.01 +-Applying beta-rule and splitting (58), into two cases.
% 34.10/10.01 |-Branch one:
% 34.10/10.01 | (622) all_1_3_3 = 0
% 34.10/10.01 |
% 34.10/10.01 | From (622) and (49) follows:
% 34.10/10.01 | (623) apart_point_and_line(all_1_8_8, all_1_5_5) = 0
% 34.10/10.01 |
% 34.10/10.01 +-Applying beta-rule and splitting (226), into two cases.
% 34.10/10.01 |-Branch one:
% 34.10/10.01 | (624) ~ (apart_point_and_line(all_1_8_8, all_1_5_5) = 0)
% 34.10/10.01 |
% 34.10/10.01 | Using (623) and (624) yields:
% 34.10/10.01 | (204) $false
% 34.10/10.01 |
% 34.10/10.01 |-The branch is then unsatisfiable
% 34.10/10.01 |-Branch two:
% 34.10/10.01 | (623) apart_point_and_line(all_1_8_8, all_1_5_5) = 0
% 34.10/10.01 | (627) all_18_1_14 = 0 | distinct_points(all_1_8_8, all_1_7_7) = 0
% 34.10/10.01 |
% 34.10/10.01 +-Applying beta-rule and splitting (627), into two cases.
% 34.10/10.01 |-Branch one:
% 34.10/10.01 | (628) distinct_points(all_1_8_8, all_1_7_7) = 0
% 34.10/10.01 |
% 34.10/10.01 +-Applying beta-rule and splitting (65), into two cases.
% 34.10/10.01 |-Branch one:
% 34.10/10.01 | (624) ~ (apart_point_and_line(all_1_8_8, all_1_5_5) = 0)
% 34.10/10.01 |
% 34.10/10.01 | Using (623) and (624) yields:
% 34.10/10.01 | (204) $false
% 34.10/10.01 |
% 34.10/10.01 |-The branch is then unsatisfiable
% 34.10/10.01 |-Branch two:
% 34.10/10.01 | (623) apart_point_and_line(all_1_8_8, all_1_5_5) = 0
% 34.10/10.01 | (632) ? [v0] : ? [v1] : ? [v2] : (distinct_points(all_1_7_7, all_1_6_6) = v0 & distinct_points(all_1_8_8, all_1_6_6) = v2 & distinct_points(all_1_8_8, all_1_7_7) = v1 & ( ~ (v0 = 0) | (v2 = 0 & v1 = 0)))
% 34.10/10.01 |
% 34.10/10.01 | Instantiating (632) with all_357_0_142, all_357_1_143, all_357_2_144 yields:
% 34.10/10.01 | (633) distinct_points(all_1_7_7, all_1_6_6) = all_357_2_144 & distinct_points(all_1_8_8, all_1_6_6) = all_357_0_142 & distinct_points(all_1_8_8, all_1_7_7) = all_357_1_143 & ( ~ (all_357_2_144 = 0) | (all_357_0_142 = 0 & all_357_1_143 = 0))
% 34.10/10.01 |
% 34.10/10.01 | Applying alpha-rule on (633) yields:
% 34.10/10.01 | (634) distinct_points(all_1_7_7, all_1_6_6) = all_357_2_144
% 34.10/10.01 | (635) distinct_points(all_1_8_8, all_1_6_6) = all_357_0_142
% 34.10/10.01 | (636) distinct_points(all_1_8_8, all_1_7_7) = all_357_1_143
% 34.10/10.01 | (637) ~ (all_357_2_144 = 0) | (all_357_0_142 = 0 & all_357_1_143 = 0)
% 34.10/10.01 |
% 34.10/10.01 | Instantiating formula (10) with all_1_7_7, all_1_6_6, all_357_2_144, 0 and discharging atoms distinct_points(all_1_7_7, all_1_6_6) = all_357_2_144, distinct_points(all_1_7_7, all_1_6_6) = 0, yields:
% 34.10/10.01 | (638) all_357_2_144 = 0
% 34.10/10.01 |
% 34.10/10.01 | Instantiating formula (10) with all_1_8_8, all_1_7_7, all_357_1_143, 0 and discharging atoms distinct_points(all_1_8_8, all_1_7_7) = all_357_1_143, distinct_points(all_1_8_8, all_1_7_7) = 0, yields:
% 34.10/10.01 | (639) all_357_1_143 = 0
% 34.10/10.01 |
% 34.10/10.01 | Instantiating formula (36) with all_1_8_8 yields:
% 34.10/10.01 | (640) ~ (distinct_points(all_1_8_8, all_1_8_8) = 0)
% 34.10/10.01 |
% 34.10/10.01 | From (639) and (636) follows:
% 34.10/10.01 | (628) distinct_points(all_1_8_8, all_1_7_7) = 0
% 34.10/10.01 |
% 34.10/10.01 +-Applying beta-rule and splitting (637), into two cases.
% 34.10/10.01 |-Branch one:
% 34.10/10.01 | (642) ~ (all_357_2_144 = 0)
% 34.10/10.01 |
% 34.10/10.01 | Equations (638) can reduce 642 to:
% 34.10/10.01 | (94) $false
% 34.10/10.01 |
% 34.10/10.01 |-The branch is then unsatisfiable
% 34.10/10.01 |-Branch two:
% 34.10/10.01 | (638) all_357_2_144 = 0
% 34.10/10.01 | (645) all_357_0_142 = 0 & all_357_1_143 = 0
% 34.10/10.01 |
% 34.10/10.01 | Applying alpha-rule on (645) yields:
% 34.10/10.01 | (646) all_357_0_142 = 0
% 34.10/10.01 | (639) all_357_1_143 = 0
% 34.10/10.01 |
% 34.10/10.01 | From (646) and (635) follows:
% 34.10/10.01 | (648) distinct_points(all_1_8_8, all_1_6_6) = 0
% 34.10/10.02 |
% 34.10/10.02 +-Applying beta-rule and splitting (70), into two cases.
% 34.10/10.02 |-Branch one:
% 34.10/10.02 | (649) ~ (distinct_points(all_1_8_8, all_1_6_6) = 0)
% 34.10/10.02 |
% 34.10/10.02 | Using (648) and (649) yields:
% 34.10/10.02 | (204) $false
% 34.10/10.02 |
% 34.10/10.02 |-The branch is then unsatisfiable
% 34.10/10.02 |-Branch two:
% 34.10/10.02 | (648) distinct_points(all_1_8_8, all_1_6_6) = 0
% 34.10/10.02 | (652) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_8_8, all_1_6_6) = v0 & apart_point_and_line(all_1_9_9, v0) = v1 & distinct_points(all_1_9_9, all_1_6_6) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 34.10/10.02 |
% 34.10/10.02 | Instantiating (652) with all_371_0_145, all_371_1_146, all_371_2_147 yields:
% 34.10/10.02 | (653) line_connecting(all_1_8_8, all_1_6_6) = all_371_2_147 & apart_point_and_line(all_1_9_9, all_371_2_147) = all_371_1_146 & distinct_points(all_1_9_9, all_1_6_6) = all_371_0_145 & ( ~ (all_371_1_146 = 0) | all_371_0_145 = 0)
% 34.10/10.02 |
% 34.10/10.02 | Applying alpha-rule on (653) yields:
% 34.10/10.02 | (654) line_connecting(all_1_8_8, all_1_6_6) = all_371_2_147
% 34.10/10.02 | (655) apart_point_and_line(all_1_9_9, all_371_2_147) = all_371_1_146
% 34.10/10.02 | (656) distinct_points(all_1_9_9, all_1_6_6) = all_371_0_145
% 34.10/10.02 | (657) ~ (all_371_1_146 = 0) | all_371_0_145 = 0
% 34.10/10.02 |
% 34.10/10.02 | Instantiating formula (10) with all_1_9_9, all_1_6_6, all_371_0_145, all_303_3_141 and discharging atoms distinct_points(all_1_9_9, all_1_6_6) = all_371_0_145, distinct_points(all_1_9_9, all_1_6_6) = all_303_3_141, yields:
% 34.10/10.02 | (658) all_371_0_145 = all_303_3_141
% 34.10/10.02 |
% 34.10/10.02 | From (658) and (656) follows:
% 34.10/10.02 | (519) distinct_points(all_1_9_9, all_1_6_6) = all_303_3_141
% 34.10/10.02 |
% 34.10/10.02 | Instantiating formula (16) with all_148_1_66, all_1_2_2, all_1_5_5, all_1_8_8 and discharging atoms apart_point_and_line(all_1_8_8, all_1_2_2) = all_148_1_66, apart_point_and_line(all_1_8_8, all_1_5_5) = 0, yields:
% 34.10/10.02 | (660) all_148_1_66 = 0 | distinct_lines(all_1_5_5, all_1_2_2) = 0
% 34.10/10.02 |
% 34.10/10.02 | Instantiating formula (7) with all_148_1_66, all_218_2_74, all_1_2_2, all_1_5_5, all_1_8_8 and discharging atoms apart_point_and_line(all_1_8_8, all_1_2_2) = all_148_1_66, distinct_lines(all_1_5_5, all_1_2_2) = all_218_2_74, yields:
% 34.10/10.02 | (661) all_218_2_74 = 0 | all_148_1_66 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_1_8_8, all_1_5_5) = v0)
% 34.10/10.02 |
% 34.10/10.02 | Instantiating formula (27) with all_218_2_74, all_1_2_2, all_1_5_5 and discharging atoms distinct_lines(all_1_5_5, all_1_2_2) = all_218_2_74, yields:
% 34.10/10.02 | (662) all_218_2_74 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_1_5_5, all_1_2_2) = v0)
% 34.10/10.02 |
% 34.10/10.02 | Instantiating formula (1) with all_298_3_137, all_1_2_2, all_1_6_6, all_1_8_8, all_1_9_9 and discharging atoms line_connecting(all_1_9_9, all_1_8_8) = all_1_2_2, distinct_points(all_1_6_6, all_1_9_9) = all_298_3_137, yields:
% 34.10/10.02 | (663) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_6_6, all_1_2_2) = v1 & distinct_points(all_1_6_6, all_1_8_8) = v2 & distinct_points(all_1_9_9, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & all_298_3_137 = 0)))
% 34.10/10.02 |
% 34.10/10.02 | Instantiating formula (1) with all_253_3_103, all_1_2_2, all_1_7_7, all_1_8_8, all_1_9_9 and discharging atoms line_connecting(all_1_9_9, all_1_8_8) = all_1_2_2, distinct_points(all_1_7_7, all_1_9_9) = all_253_3_103, yields:
% 34.10/10.02 | (664) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_7_7, all_1_2_2) = v1 & distinct_points(all_1_7_7, all_1_8_8) = v2 & distinct_points(all_1_9_9, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & all_253_3_103 = 0)))
% 34.10/10.02 |
% 34.10/10.02 | Instantiating formula (8) with 0, all_1_8_8, all_1_8_8, all_1_9_9 and discharging atoms distinct_points(all_1_8_8, all_1_9_9) = 0, distinct_points(all_1_9_9, all_1_8_8) = 0, yields:
% 34.10/10.02 | (665) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_9_9, all_1_8_8) = v0 & apart_point_and_line(all_1_8_8, v0) = v1 & distinct_points(all_1_8_8, all_1_8_8) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 34.10/10.02 |
% 34.10/10.02 | Instantiating formula (18) with 0, all_1_8_8, all_1_6_6, all_1_8_8 and discharging atoms distinct_points(all_1_8_8, all_1_6_6) = 0, yields:
% 34.10/10.02 | (666) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_8_8, all_1_6_6) = v0 & apart_point_and_line(all_1_8_8, v0) = v1 & distinct_points(all_1_8_8, all_1_8_8) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 34.10/10.02 |
% 34.10/10.02 | Instantiating formula (1) with 0, all_1_2_2, all_1_8_8, all_1_8_8, all_1_9_9 and discharging atoms line_connecting(all_1_9_9, all_1_8_8) = all_1_2_2, distinct_points(all_1_8_8, all_1_9_9) = 0, yields:
% 34.10/10.02 | (667) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_1_2_2) = v1 & distinct_points(all_1_8_8, all_1_8_8) = v2 & distinct_points(all_1_9_9, all_1_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 34.10/10.02 |
% 34.10/10.02 | Instantiating formula (13) with 0, all_371_2_147, all_1_8_8, all_1_6_6, all_1_8_8 and discharging atoms line_connecting(all_1_8_8, all_1_6_6) = all_371_2_147, distinct_points(all_1_8_8, all_1_6_6) = 0, yields:
% 34.10/10.02 | (668) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_371_2_147) = v1 & distinct_points(all_1_8_8, all_1_6_6) = v0 & distinct_points(all_1_8_8, all_1_8_8) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 34.10/10.02 |
% 34.10/10.02 | Instantiating formula (13) with 0, all_118_1_47, all_1_8_8, all_1_9_9, all_1_8_8 and discharging atoms line_connecting(all_1_8_8, all_1_9_9) = all_118_1_47, distinct_points(all_1_8_8, all_1_9_9) = 0, yields:
% 34.10/10.02 | (669) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_8_8, all_118_1_47) = v1 & distinct_points(all_1_8_8, all_1_8_8) = v2 & distinct_points(all_1_8_8, all_1_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 34.10/10.02 |
% 34.10/10.02 | Instantiating formula (18) with 0, all_1_8_8, all_1_7_7, all_1_8_8 and discharging atoms distinct_points(all_1_8_8, all_1_7_7) = 0, yields:
% 34.10/10.02 | (670) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_8_8, all_1_7_7) = v0 & apart_point_and_line(all_1_8_8, v0) = v1 & distinct_points(all_1_8_8, all_1_8_8) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 34.10/10.02 |
% 34.10/10.02 | Instantiating formula (18) with 0, all_1_8_8, all_1_9_9, all_1_8_8 and discharging atoms distinct_points(all_1_8_8, all_1_9_9) = 0, yields:
% 34.10/10.02 | (671) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_8_8, all_1_9_9) = v0 & apart_point_and_line(all_1_8_8, v0) = v1 & distinct_points(all_1_8_8, all_1_8_8) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 34.10/10.02 |
% 34.10/10.02 | Instantiating formula (18) with all_303_3_141, all_1_9_9, all_1_6_6, all_1_8_8 and discharging atoms distinct_points(all_1_8_8, all_1_6_6) = 0, distinct_points(all_1_9_9, all_1_6_6) = all_303_3_141, yields:
% 34.10/10.02 | (672) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_8_8, all_1_6_6) = v0 & apart_point_and_line(all_1_9_9, v0) = v1 & distinct_points(all_1_9_9, all_1_8_8) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_303_3_141 = 0)))
% 34.10/10.02 |
% 34.10/10.02 | Instantiating formula (13) with all_303_3_141, all_371_2_147, all_1_9_9, all_1_6_6, all_1_8_8 and discharging atoms line_connecting(all_1_8_8, all_1_6_6) = all_371_2_147, distinct_points(all_1_9_9, all_1_6_6) = all_303_3_141, yields:
% 34.10/10.02 | (673) ? [v0] : ? [v1] : ? [v2] : (apart_point_and_line(all_1_9_9, all_371_2_147) = v1 & distinct_points(all_1_8_8, all_1_6_6) = v0 & distinct_points(all_1_9_9, all_1_8_8) = v2 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & all_303_3_141 = 0)))
% 34.10/10.02 |
% 34.10/10.02 | Instantiating formula (18) with all_218_3_75, all_1_9_9, all_1_7_7, all_1_8_8 and discharging atoms distinct_points(all_1_8_8, all_1_7_7) = 0, distinct_points(all_1_9_9, all_1_7_7) = all_218_3_75, yields:
% 34.10/10.02 | (674) ? [v0] : ? [v1] : ? [v2] : (line_connecting(all_1_8_8, all_1_7_7) = v0 & apart_point_and_line(all_1_9_9, v0) = v1 & distinct_points(all_1_9_9, all_1_8_8) = v2 & ( ~ (v1 = 0) | (v2 = 0 & all_218_3_75 = 0)))
% 34.10/10.02 |
% 34.10/10.02 | Instantiating (673) with all_386_0_154, all_386_1_155, all_386_2_156 yields:
% 34.10/10.02 | (675) apart_point_and_line(all_1_9_9, all_371_2_147) = all_386_1_155 & distinct_points(all_1_8_8, all_1_6_6) = all_386_2_156 & distinct_points(all_1_9_9, all_1_8_8) = all_386_0_154 & ( ~ (all_386_1_155 = 0) | ~ (all_386_2_156 = 0) | (all_386_0_154 = 0 & all_303_3_141 = 0))
% 34.10/10.02 |
% 34.10/10.02 | Applying alpha-rule on (675) yields:
% 34.10/10.02 | (676) apart_point_and_line(all_1_9_9, all_371_2_147) = all_386_1_155
% 34.10/10.02 | (677) distinct_points(all_1_8_8, all_1_6_6) = all_386_2_156
% 34.10/10.02 | (678) distinct_points(all_1_9_9, all_1_8_8) = all_386_0_154
% 34.10/10.02 | (679) ~ (all_386_1_155 = 0) | ~ (all_386_2_156 = 0) | (all_386_0_154 = 0 & all_303_3_141 = 0)
% 34.10/10.02 |
% 34.10/10.02 | Instantiating (674) with all_390_0_160, all_390_1_161, all_390_2_162 yields:
% 34.10/10.02 | (680) line_connecting(all_1_8_8, all_1_7_7) = all_390_2_162 & apart_point_and_line(all_1_9_9, all_390_2_162) = all_390_1_161 & distinct_points(all_1_9_9, all_1_8_8) = all_390_0_160 & ( ~ (all_390_1_161 = 0) | (all_390_0_160 = 0 & all_218_3_75 = 0))
% 34.10/10.02 |
% 34.10/10.02 | Applying alpha-rule on (680) yields:
% 34.10/10.02 | (681) line_connecting(all_1_8_8, all_1_7_7) = all_390_2_162
% 34.10/10.02 | (682) apart_point_and_line(all_1_9_9, all_390_2_162) = all_390_1_161
% 34.10/10.02 | (683) distinct_points(all_1_9_9, all_1_8_8) = all_390_0_160
% 34.10/10.02 | (684) ~ (all_390_1_161 = 0) | (all_390_0_160 = 0 & all_218_3_75 = 0)
% 34.10/10.02 |
% 34.10/10.02 | Instantiating (671) with all_392_0_163, all_392_1_164, all_392_2_165 yields:
% 34.10/10.02 | (685) line_connecting(all_1_8_8, all_1_9_9) = all_392_2_165 & apart_point_and_line(all_1_8_8, all_392_2_165) = all_392_1_164 & distinct_points(all_1_8_8, all_1_8_8) = all_392_0_163 & ( ~ (all_392_1_164 = 0) | all_392_0_163 = 0)
% 34.10/10.02 |
% 34.10/10.02 | Applying alpha-rule on (685) yields:
% 34.10/10.02 | (686) line_connecting(all_1_8_8, all_1_9_9) = all_392_2_165
% 34.10/10.02 | (687) apart_point_and_line(all_1_8_8, all_392_2_165) = all_392_1_164
% 34.10/10.02 | (688) distinct_points(all_1_8_8, all_1_8_8) = all_392_0_163
% 34.10/10.02 | (689) ~ (all_392_1_164 = 0) | all_392_0_163 = 0
% 34.10/10.02 |
% 34.10/10.02 | Instantiating (670) with all_408_0_187, all_408_1_188, all_408_2_189 yields:
% 34.10/10.02 | (690) line_connecting(all_1_8_8, all_1_7_7) = all_408_2_189 & apart_point_and_line(all_1_8_8, all_408_2_189) = all_408_1_188 & distinct_points(all_1_8_8, all_1_8_8) = all_408_0_187 & ( ~ (all_408_1_188 = 0) | all_408_0_187 = 0)
% 34.10/10.02 |
% 34.10/10.02 | Applying alpha-rule on (690) yields:
% 34.10/10.02 | (691) line_connecting(all_1_8_8, all_1_7_7) = all_408_2_189
% 34.10/10.02 | (692) apart_point_and_line(all_1_8_8, all_408_2_189) = all_408_1_188
% 34.10/10.02 | (693) distinct_points(all_1_8_8, all_1_8_8) = all_408_0_187
% 34.10/10.02 | (694) ~ (all_408_1_188 = 0) | all_408_0_187 = 0
% 34.10/10.02 |
% 34.10/10.02 | Instantiating (664) with all_428_0_217, all_428_1_218, all_428_2_219 yields:
% 34.10/10.02 | (695) apart_point_and_line(all_1_7_7, all_1_2_2) = all_428_1_218 & distinct_points(all_1_7_7, all_1_8_8) = all_428_0_217 & distinct_points(all_1_9_9, all_1_8_8) = all_428_2_219 & ( ~ (all_428_1_218 = 0) | ~ (all_428_2_219 = 0) | (all_428_0_217 = 0 & all_253_3_103 = 0))
% 34.10/10.02 |
% 34.10/10.02 | Applying alpha-rule on (695) yields:
% 34.10/10.02 | (696) apart_point_and_line(all_1_7_7, all_1_2_2) = all_428_1_218
% 34.10/10.02 | (697) distinct_points(all_1_7_7, all_1_8_8) = all_428_0_217
% 34.10/10.02 | (698) distinct_points(all_1_9_9, all_1_8_8) = all_428_2_219
% 34.10/10.02 | (699) ~ (all_428_1_218 = 0) | ~ (all_428_2_219 = 0) | (all_428_0_217 = 0 & all_253_3_103 = 0)
% 34.10/10.02 |
% 34.10/10.02 | Instantiating (672) with all_432_0_223, all_432_1_224, all_432_2_225 yields:
% 34.10/10.02 | (700) line_connecting(all_1_8_8, all_1_6_6) = all_432_2_225 & apart_point_and_line(all_1_9_9, all_432_2_225) = all_432_1_224 & distinct_points(all_1_9_9, all_1_8_8) = all_432_0_223 & ( ~ (all_432_1_224 = 0) | (all_432_0_223 = 0 & all_303_3_141 = 0))
% 34.10/10.02 |
% 34.10/10.02 | Applying alpha-rule on (700) yields:
% 34.10/10.02 | (701) line_connecting(all_1_8_8, all_1_6_6) = all_432_2_225
% 34.10/10.02 | (702) apart_point_and_line(all_1_9_9, all_432_2_225) = all_432_1_224
% 34.10/10.02 | (703) distinct_points(all_1_9_9, all_1_8_8) = all_432_0_223
% 34.10/10.02 | (704) ~ (all_432_1_224 = 0) | (all_432_0_223 = 0 & all_303_3_141 = 0)
% 34.10/10.02 |
% 34.10/10.02 | Instantiating (668) with all_436_0_229, all_436_1_230, all_436_2_231 yields:
% 34.10/10.02 | (705) apart_point_and_line(all_1_8_8, all_371_2_147) = all_436_1_230 & distinct_points(all_1_8_8, all_1_6_6) = all_436_2_231 & distinct_points(all_1_8_8, all_1_8_8) = all_436_0_229 & ( ~ (all_436_1_230 = 0) | ~ (all_436_2_231 = 0) | all_436_0_229 = 0)
% 34.10/10.02 |
% 34.10/10.02 | Applying alpha-rule on (705) yields:
% 34.10/10.02 | (706) apart_point_and_line(all_1_8_8, all_371_2_147) = all_436_1_230
% 34.10/10.02 | (707) distinct_points(all_1_8_8, all_1_6_6) = all_436_2_231
% 34.10/10.02 | (708) distinct_points(all_1_8_8, all_1_8_8) = all_436_0_229
% 34.10/10.02 | (709) ~ (all_436_1_230 = 0) | ~ (all_436_2_231 = 0) | all_436_0_229 = 0
% 34.10/10.03 |
% 34.10/10.03 | Instantiating (667) with all_440_0_235, all_440_1_236, all_440_2_237 yields:
% 34.10/10.03 | (710) apart_point_and_line(all_1_8_8, all_1_2_2) = all_440_1_236 & distinct_points(all_1_8_8, all_1_8_8) = all_440_0_235 & distinct_points(all_1_9_9, all_1_8_8) = all_440_2_237 & ( ~ (all_440_1_236 = 0) | ~ (all_440_2_237 = 0) | all_440_0_235 = 0)
% 34.10/10.03 |
% 34.10/10.03 | Applying alpha-rule on (710) yields:
% 34.10/10.03 | (711) apart_point_and_line(all_1_8_8, all_1_2_2) = all_440_1_236
% 34.10/10.03 | (712) distinct_points(all_1_8_8, all_1_8_8) = all_440_0_235
% 34.10/10.03 | (713) distinct_points(all_1_9_9, all_1_8_8) = all_440_2_237
% 34.10/10.03 | (714) ~ (all_440_1_236 = 0) | ~ (all_440_2_237 = 0) | all_440_0_235 = 0
% 34.10/10.03 |
% 34.10/10.03 | Instantiating (669) with all_446_0_244, all_446_1_245, all_446_2_246 yields:
% 34.10/10.03 | (715) apart_point_and_line(all_1_8_8, all_118_1_47) = all_446_1_245 & distinct_points(all_1_8_8, all_1_8_8) = all_446_0_244 & distinct_points(all_1_8_8, all_1_9_9) = all_446_2_246 & ( ~ (all_446_1_245 = 0) | ~ (all_446_2_246 = 0) | all_446_0_244 = 0)
% 34.10/10.03 |
% 34.10/10.03 | Applying alpha-rule on (715) yields:
% 34.10/10.03 | (716) apart_point_and_line(all_1_8_8, all_118_1_47) = all_446_1_245
% 34.10/10.03 | (717) distinct_points(all_1_8_8, all_1_8_8) = all_446_0_244
% 34.10/10.03 | (718) distinct_points(all_1_8_8, all_1_9_9) = all_446_2_246
% 34.10/10.03 | (719) ~ (all_446_1_245 = 0) | ~ (all_446_2_246 = 0) | all_446_0_244 = 0
% 34.10/10.03 |
% 34.10/10.03 | Instantiating (663) with all_458_0_262, all_458_1_263, all_458_2_264 yields:
% 34.10/10.03 | (720) apart_point_and_line(all_1_6_6, all_1_2_2) = all_458_1_263 & distinct_points(all_1_6_6, all_1_8_8) = all_458_0_262 & distinct_points(all_1_9_9, all_1_8_8) = all_458_2_264 & ( ~ (all_458_1_263 = 0) | ~ (all_458_2_264 = 0) | (all_458_0_262 = 0 & all_298_3_137 = 0))
% 34.10/10.03 |
% 34.10/10.03 | Applying alpha-rule on (720) yields:
% 34.10/10.03 | (721) apart_point_and_line(all_1_6_6, all_1_2_2) = all_458_1_263
% 34.10/10.03 | (722) distinct_points(all_1_6_6, all_1_8_8) = all_458_0_262
% 34.10/10.03 | (723) distinct_points(all_1_9_9, all_1_8_8) = all_458_2_264
% 34.10/10.03 | (724) ~ (all_458_1_263 = 0) | ~ (all_458_2_264 = 0) | (all_458_0_262 = 0 & all_298_3_137 = 0)
% 34.10/10.03 |
% 34.10/10.03 | Instantiating (666) with all_460_0_265, all_460_1_266, all_460_2_267 yields:
% 34.10/10.03 | (725) line_connecting(all_1_8_8, all_1_6_6) = all_460_2_267 & apart_point_and_line(all_1_8_8, all_460_2_267) = all_460_1_266 & distinct_points(all_1_8_8, all_1_8_8) = all_460_0_265 & ( ~ (all_460_1_266 = 0) | all_460_0_265 = 0)
% 34.10/10.03 |
% 34.10/10.03 | Applying alpha-rule on (725) yields:
% 34.10/10.03 | (726) line_connecting(all_1_8_8, all_1_6_6) = all_460_2_267
% 34.10/10.03 | (727) apart_point_and_line(all_1_8_8, all_460_2_267) = all_460_1_266
% 34.10/10.03 | (728) distinct_points(all_1_8_8, all_1_8_8) = all_460_0_265
% 34.10/10.03 | (729) ~ (all_460_1_266 = 0) | all_460_0_265 = 0
% 34.10/10.03 |
% 34.10/10.03 | Instantiating (665) with all_470_0_280, all_470_1_281, all_470_2_282 yields:
% 34.10/10.03 | (730) line_connecting(all_1_9_9, all_1_8_8) = all_470_2_282 & apart_point_and_line(all_1_8_8, all_470_2_282) = all_470_1_281 & distinct_points(all_1_8_8, all_1_8_8) = all_470_0_280 & ( ~ (all_470_1_281 = 0) | all_470_0_280 = 0)
% 34.10/10.03 |
% 34.10/10.03 | Applying alpha-rule on (730) yields:
% 34.10/10.03 | (731) line_connecting(all_1_9_9, all_1_8_8) = all_470_2_282
% 34.10/10.03 | (732) apart_point_and_line(all_1_8_8, all_470_2_282) = all_470_1_281
% 34.10/10.03 | (733) distinct_points(all_1_8_8, all_1_8_8) = all_470_0_280
% 34.10/10.03 | (734) ~ (all_470_1_281 = 0) | all_470_0_280 = 0
% 34.10/10.03 |
% 34.10/10.03 +-Applying beta-rule and splitting (661), into two cases.
% 34.10/10.03 |-Branch one:
% 34.10/10.03 | (735) all_218_2_74 = 0
% 34.10/10.03 |
% 34.10/10.03 | Equations (735) can reduce 619 to:
% 34.10/10.03 | (94) $false
% 34.10/10.03 |
% 34.10/10.03 |-The branch is then unsatisfiable
% 34.10/10.03 |-Branch two:
% 34.10/10.03 | (619) ~ (all_218_2_74 = 0)
% 34.10/10.03 | (738) all_148_1_66 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_1_8_8, all_1_5_5) = v0)
% 34.10/10.03 |
% 34.10/10.03 +-Applying beta-rule and splitting (662), into two cases.
% 34.10/10.03 |-Branch one:
% 34.10/10.03 | (735) all_218_2_74 = 0
% 34.10/10.03 |
% 34.10/10.03 | Equations (735) can reduce 619 to:
% 34.10/10.03 | (94) $false
% 34.10/10.03 |
% 34.10/10.03 |-The branch is then unsatisfiable
% 34.10/10.03 |-Branch two:
% 34.10/10.03 | (619) ~ (all_218_2_74 = 0)
% 34.10/10.03 | (742) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_1_5_5, all_1_2_2) = v0)
% 34.10/10.03 |
% 34.10/10.03 +-Applying beta-rule and splitting (660), into two cases.
% 34.10/10.03 |-Branch one:
% 34.10/10.03 | (743) distinct_lines(all_1_5_5, all_1_2_2) = 0
% 34.10/10.03 |
% 34.10/10.03 | Instantiating formula (15) with all_1_5_5, all_1_2_2, 0, all_218_2_74 and discharging atoms distinct_lines(all_1_5_5, all_1_2_2) = all_218_2_74, distinct_lines(all_1_5_5, all_1_2_2) = 0, yields:
% 34.10/10.03 | (735) all_218_2_74 = 0
% 34.10/10.03 |
% 34.10/10.03 | Equations (735) can reduce 619 to:
% 34.10/10.03 | (94) $false
% 34.10/10.03 |
% 34.10/10.03 |-The branch is then unsatisfiable
% 34.10/10.03 |-Branch two:
% 34.10/10.03 | (746) ~ (distinct_lines(all_1_5_5, all_1_2_2) = 0)
% 34.10/10.03 | (747) all_148_1_66 = 0
% 34.10/10.03 |
% 34.10/10.03 | From (747) and (283) follows:
% 34.10/10.03 | (748) apart_point_and_line(all_1_8_8, all_1_2_2) = 0
% 34.10/10.03 |
% 34.10/10.03 | Instantiating formula (42) with all_1_8_8, all_1_2_2, 0, all_440_1_236 and discharging atoms apart_point_and_line(all_1_8_8, all_1_2_2) = all_440_1_236, apart_point_and_line(all_1_8_8, all_1_2_2) = 0, yields:
% 34.10/10.03 | (749) all_440_1_236 = 0
% 34.10/10.03 |
% 34.10/10.03 | Instantiating formula (10) with all_1_8_8, all_1_8_8, all_460_0_265, all_470_0_280 and discharging atoms distinct_points(all_1_8_8, all_1_8_8) = all_470_0_280, distinct_points(all_1_8_8, all_1_8_8) = all_460_0_265, yields:
% 34.10/10.03 | (750) all_470_0_280 = all_460_0_265
% 34.10/10.03 |
% 34.10/10.03 | Instantiating formula (10) with all_1_8_8, all_1_8_8, all_446_0_244, all_460_0_265 and discharging atoms distinct_points(all_1_8_8, all_1_8_8) = all_460_0_265, distinct_points(all_1_8_8, all_1_8_8) = all_446_0_244, yields:
% 34.10/10.03 | (751) all_460_0_265 = all_446_0_244
% 34.10/10.03 |
% 34.10/10.03 | Instantiating formula (10) with all_1_8_8, all_1_8_8, all_440_0_235, all_446_0_244 and discharging atoms distinct_points(all_1_8_8, all_1_8_8) = all_446_0_244, distinct_points(all_1_8_8, all_1_8_8) = all_440_0_235, yields:
% 34.10/10.03 | (752) all_446_0_244 = all_440_0_235
% 34.10/10.03 |
% 34.10/10.03 | Instantiating formula (10) with all_1_8_8, all_1_8_8, all_436_0_229, all_446_0_244 and discharging atoms distinct_points(all_1_8_8, all_1_8_8) = all_446_0_244, distinct_points(all_1_8_8, all_1_8_8) = all_436_0_229, yields:
% 34.10/10.03 | (753) all_446_0_244 = all_436_0_229
% 34.10/10.03 |
% 34.10/10.03 | Instantiating formula (10) with all_1_8_8, all_1_8_8, all_408_0_187, all_446_0_244 and discharging atoms distinct_points(all_1_8_8, all_1_8_8) = all_446_0_244, distinct_points(all_1_8_8, all_1_8_8) = all_408_0_187, yields:
% 34.10/10.03 | (754) all_446_0_244 = all_408_0_187
% 34.10/10.03 |
% 34.10/10.03 | Using (693) and (640) yields:
% 34.10/10.03 | (755) ~ (all_408_0_187 = 0)
% 34.10/10.03 |
% 34.10/10.03 | Instantiating formula (10) with all_1_8_8, all_1_8_8, all_392_0_163, all_470_0_280 and discharging atoms distinct_points(all_1_8_8, all_1_8_8) = all_470_0_280, distinct_points(all_1_8_8, all_1_8_8) = all_392_0_163, yields:
% 34.10/10.03 | (756) all_470_0_280 = all_392_0_163
% 34.10/10.03 |
% 34.10/10.03 | Instantiating formula (10) with all_1_9_9, all_1_8_8, all_440_2_237, all_458_2_264 and discharging atoms distinct_points(all_1_9_9, all_1_8_8) = all_458_2_264, distinct_points(all_1_9_9, all_1_8_8) = all_440_2_237, yields:
% 34.10/10.03 | (757) all_458_2_264 = all_440_2_237
% 34.10/10.03 |
% 34.10/10.03 | Instantiating formula (10) with all_1_9_9, all_1_8_8, all_432_0_223, all_440_2_237 and discharging atoms distinct_points(all_1_9_9, all_1_8_8) = all_440_2_237, distinct_points(all_1_9_9, all_1_8_8) = all_432_0_223, yields:
% 34.10/10.03 | (758) all_440_2_237 = all_432_0_223
% 34.10/10.03 |
% 34.10/10.03 | Instantiating formula (10) with all_1_9_9, all_1_8_8, all_428_2_219, 0 and discharging atoms distinct_points(all_1_9_9, all_1_8_8) = all_428_2_219, distinct_points(all_1_9_9, all_1_8_8) = 0, yields:
% 34.10/10.03 | (759) all_428_2_219 = 0
% 34.10/10.03 |
% 34.10/10.03 | Instantiating formula (10) with all_1_9_9, all_1_8_8, all_428_2_219, all_440_2_237 and discharging atoms distinct_points(all_1_9_9, all_1_8_8) = all_440_2_237, distinct_points(all_1_9_9, all_1_8_8) = all_428_2_219, yields:
% 34.10/10.03 | (760) all_440_2_237 = all_428_2_219
% 34.10/10.03 |
% 34.10/10.03 | Instantiating formula (10) with all_1_9_9, all_1_8_8, all_390_0_160, all_428_2_219 and discharging atoms distinct_points(all_1_9_9, all_1_8_8) = all_428_2_219, distinct_points(all_1_9_9, all_1_8_8) = all_390_0_160, yields:
% 34.10/10.03 | (761) all_428_2_219 = all_390_0_160
% 34.10/10.03 |
% 34.10/10.03 | Instantiating formula (10) with all_1_9_9, all_1_8_8, all_386_0_154, all_458_2_264 and discharging atoms distinct_points(all_1_9_9, all_1_8_8) = all_458_2_264, distinct_points(all_1_9_9, all_1_8_8) = all_386_0_154, yields:
% 34.10/10.03 | (762) all_458_2_264 = all_386_0_154
% 34.10/10.03 |
% 34.10/10.03 | Combining equations (750,756) yields a new equation:
% 34.10/10.03 | (763) all_460_0_265 = all_392_0_163
% 34.10/10.03 |
% 34.10/10.03 | Simplifying 763 yields:
% 34.10/10.03 | (764) all_460_0_265 = all_392_0_163
% 34.10/10.03 |
% 34.10/10.03 | Combining equations (751,764) yields a new equation:
% 34.10/10.03 | (765) all_446_0_244 = all_392_0_163
% 34.10/10.03 |
% 34.10/10.03 | Simplifying 765 yields:
% 34.10/10.03 | (766) all_446_0_244 = all_392_0_163
% 34.10/10.03 |
% 34.10/10.03 | Combining equations (757,762) yields a new equation:
% 34.10/10.03 | (767) all_440_2_237 = all_386_0_154
% 34.10/10.03 |
% 34.10/10.03 | Simplifying 767 yields:
% 34.10/10.03 | (768) all_440_2_237 = all_386_0_154
% 34.10/10.03 |
% 34.10/10.03 | Combining equations (753,752) yields a new equation:
% 34.10/10.03 | (769) all_440_0_235 = all_436_0_229
% 34.10/10.03 |
% 34.10/10.03 | Combining equations (754,752) yields a new equation:
% 34.10/10.03 | (770) all_440_0_235 = all_408_0_187
% 34.10/10.03 |
% 34.10/10.03 | Combining equations (766,752) yields a new equation:
% 34.10/10.03 | (771) all_440_0_235 = all_392_0_163
% 34.10/10.03 |
% 34.10/10.03 | Combining equations (770,769) yields a new equation:
% 34.10/10.03 | (772) all_436_0_229 = all_408_0_187
% 34.10/10.03 |
% 34.10/10.03 | Combining equations (771,769) yields a new equation:
% 34.10/10.03 | (773) all_436_0_229 = all_392_0_163
% 34.10/10.03 |
% 34.10/10.03 | Combining equations (760,758) yields a new equation:
% 34.10/10.03 | (774) all_432_0_223 = all_428_2_219
% 34.10/10.03 |
% 34.10/10.03 | Combining equations (768,758) yields a new equation:
% 34.10/10.03 | (775) all_432_0_223 = all_386_0_154
% 34.10/10.03 |
% 34.10/10.03 | Combining equations (772,773) yields a new equation:
% 34.10/10.03 | (776) all_408_0_187 = all_392_0_163
% 34.10/10.03 |
% 34.10/10.03 | Simplifying 776 yields:
% 34.10/10.03 | (777) all_408_0_187 = all_392_0_163
% 34.10/10.03 |
% 34.10/10.03 | Combining equations (774,775) yields a new equation:
% 34.10/10.03 | (778) all_428_2_219 = all_386_0_154
% 34.10/10.03 |
% 34.10/10.03 | Simplifying 778 yields:
% 34.10/10.03 | (779) all_428_2_219 = all_386_0_154
% 34.10/10.03 |
% 34.10/10.03 | Combining equations (759,761) yields a new equation:
% 34.10/10.03 | (780) all_390_0_160 = 0
% 34.10/10.03 |
% 34.10/10.03 | Combining equations (779,761) yields a new equation:
% 34.10/10.03 | (781) all_390_0_160 = all_386_0_154
% 34.10/10.03 |
% 34.10/10.03 | Combining equations (780,781) yields a new equation:
% 34.10/10.03 | (782) all_386_0_154 = 0
% 34.10/10.03 |
% 34.10/10.03 | Combining equations (782,775) yields a new equation:
% 34.10/10.03 | (783) all_432_0_223 = 0
% 34.10/10.03 |
% 34.10/10.03 | Combining equations (783,758) yields a new equation:
% 34.10/10.03 | (784) all_440_2_237 = 0
% 34.10/10.03 |
% 34.10/10.03 | Combining equations (773,769) yields a new equation:
% 34.10/10.03 | (771) all_440_0_235 = all_392_0_163
% 34.10/10.03 |
% 34.10/10.03 | Equations (777) can reduce 755 to:
% 34.10/10.03 | (786) ~ (all_392_0_163 = 0)
% 34.10/10.03 |
% 34.10/10.03 +-Applying beta-rule and splitting (714), into two cases.
% 34.10/10.03 |-Branch one:
% 34.10/10.03 | (787) ~ (all_440_1_236 = 0)
% 34.10/10.03 |
% 34.10/10.03 | Equations (749) can reduce 787 to:
% 34.10/10.03 | (94) $false
% 34.10/10.03 |
% 34.10/10.03 |-The branch is then unsatisfiable
% 34.10/10.03 |-Branch two:
% 34.10/10.03 | (749) all_440_1_236 = 0
% 34.10/10.03 | (790) ~ (all_440_2_237 = 0) | all_440_0_235 = 0
% 34.10/10.03 |
% 34.10/10.03 +-Applying beta-rule and splitting (790), into two cases.
% 34.10/10.03 |-Branch one:
% 34.10/10.03 | (791) ~ (all_440_2_237 = 0)
% 34.10/10.03 |
% 34.10/10.03 | Equations (784) can reduce 791 to:
% 34.10/10.03 | (94) $false
% 34.10/10.03 |
% 34.10/10.03 |-The branch is then unsatisfiable
% 34.10/10.03 |-Branch two:
% 34.10/10.03 | (784) all_440_2_237 = 0
% 34.10/10.03 | (794) all_440_0_235 = 0
% 34.10/10.03 |
% 34.10/10.03 | Combining equations (771,794) yields a new equation:
% 34.10/10.03 | (795) all_392_0_163 = 0
% 34.10/10.03 |
% 34.10/10.03 | Simplifying 795 yields:
% 34.10/10.03 | (796) all_392_0_163 = 0
% 34.10/10.03 |
% 34.10/10.03 | Equations (796) can reduce 786 to:
% 34.10/10.03 | (94) $false
% 34.10/10.03 |
% 34.10/10.03 |-The branch is then unsatisfiable
% 34.10/10.03 |-Branch two:
% 34.10/10.03 | (798) ~ (distinct_points(all_1_8_8, all_1_7_7) = 0)
% 34.10/10.03 | (264) all_18_1_14 = 0
% 34.10/10.03 |
% 34.10/10.03 | Equations (264) can reduce 200 to:
% 34.10/10.03 | (94) $false
% 34.10/10.03 |
% 34.10/10.03 |-The branch is then unsatisfiable
% 34.10/10.03 |-Branch two:
% 34.10/10.03 | (801) ~ (all_1_3_3 = 0)
% 34.10/10.03 | (802) all_1_4_4 = 0
% 34.10/10.03 |
% 34.10/10.03 | Equations (802) can reduce 621 to:
% 34.10/10.03 | (94) $false
% 34.10/10.03 |
% 34.10/10.03 |-The branch is then unsatisfiable
% 34.10/10.03 |-Branch two:
% 34.10/10.03 | (804) apart_point_and_line(all_1_9_9, all_1_5_5) = 0
% 34.10/10.03 | (805) all_16_1_11 = 0 | distinct_lines(all_1_5_5, all_1_2_2) = 0
% 34.10/10.03 |
% 34.10/10.03 +-Applying beta-rule and splitting (805), into two cases.
% 34.10/10.03 |-Branch one:
% 34.10/10.03 | (743) distinct_lines(all_1_5_5, all_1_2_2) = 0
% 34.10/10.04 |
% 34.10/10.04 | Instantiating formula (15) with all_1_5_5, all_1_2_2, 0, all_218_2_74 and discharging atoms distinct_lines(all_1_5_5, all_1_2_2) = all_218_2_74, distinct_lines(all_1_5_5, all_1_2_2) = 0, yields:
% 34.10/10.04 | (735) all_218_2_74 = 0
% 34.10/10.04 |
% 34.10/10.04 | Equations (735) can reduce 619 to:
% 34.10/10.04 | (94) $false
% 34.10/10.04 |
% 34.10/10.04 |-The branch is then unsatisfiable
% 34.10/10.04 |-Branch two:
% 34.10/10.04 | (746) ~ (distinct_lines(all_1_5_5, all_1_2_2) = 0)
% 34.10/10.04 | (277) all_16_1_11 = 0
% 34.10/10.04 |
% 34.10/10.04 | Equations (277) can reduce 207 to:
% 34.10/10.04 | (94) $false
% 34.10/10.04 |
% 34.10/10.04 |-The branch is then unsatisfiable
% 34.10/10.04 |-Branch two:
% 34.10/10.04 | (812) all_288_2_129 = 0
% 34.10/10.04 | (813) all_288_0_127 = 0 | all_288_1_128 = 0
% 34.10/10.04 |
% 34.10/10.04 +-Applying beta-rule and splitting (813), into two cases.
% 34.10/10.04 |-Branch one:
% 34.10/10.04 | (814) all_288_0_127 = 0
% 34.10/10.04 |
% 34.10/10.04 | Combining equations (814,559) yields a new equation:
% 34.10/10.04 | (102) all_1_0_0 = 0
% 34.10/10.04 |
% 34.10/10.04 | Equations (102) can reduce 51 to:
% 34.10/10.04 | (94) $false
% 34.10/10.04 |
% 34.10/10.04 |-The branch is then unsatisfiable
% 34.10/10.04 |-Branch two:
% 34.10/10.04 | (817) ~ (all_288_0_127 = 0)
% 34.10/10.04 | (818) all_288_1_128 = 0
% 34.10/10.04 |
% 34.10/10.04 | Combining equations (818,603) yields a new equation:
% 34.10/10.04 | (819) all_98_1_41 = 0
% 34.10/10.04 |
% 34.10/10.04 | Equations (819) can reduce 617 to:
% 34.10/10.04 | (94) $false
% 34.10/10.04 |
% 34.10/10.04 |-The branch is then unsatisfiable
% 34.10/10.04 |-Branch two:
% 34.10/10.04 | (821) ~ (distinct_points(all_1_8_8, all_1_9_9) = 0)
% 34.10/10.04 | (255) all_16_0_10 = 0
% 34.10/10.04 |
% 34.10/10.04 | Equations (255) can reduce 190 to:
% 34.10/10.04 | (94) $false
% 34.10/10.04 |
% 34.10/10.04 |-The branch is then unsatisfiable
% 34.10/10.04 |-Branch two:
% 34.10/10.04 | (824) all_100_1_44 = 0
% 34.10/10.04 | (825) all_100_0_43 = 0 & all_38_3_31 = 0
% 34.10/10.04 |
% 34.10/10.04 | Applying alpha-rule on (825) yields:
% 34.10/10.04 | (826) all_100_0_43 = 0
% 34.10/10.04 | (827) all_38_3_31 = 0
% 34.10/10.04 |
% 34.10/10.04 | Equations (827) can reduce 215 to:
% 34.10/10.04 | (94) $false
% 34.10/10.04 |
% 34.10/10.04 |-The branch is then unsatisfiable
% 34.10/10.04 |-Branch two:
% 34.10/10.04 | (829) all_22_1_20 = 0
% 34.10/10.04 | (830) ~ (all_22_2_21 = 0) | all_22_0_19 = 0
% 34.10/10.04 |
% 34.10/10.04 +-Applying beta-rule and splitting (161), into two cases.
% 34.10/10.04 |-Branch one:
% 34.10/10.04 | (209) ~ (apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14)
% 34.10/10.04 |
% 34.10/10.04 | Using (194) and (209) yields:
% 34.10/10.04 | (204) $false
% 34.10/10.04 |
% 34.10/10.04 |-The branch is then unsatisfiable
% 34.10/10.04 |-Branch two:
% 34.10/10.04 | (194) apart_point_and_line(all_1_7_7, all_1_5_5) = all_18_1_14
% 34.10/10.04 | (212) all_22_1_20 = all_18_1_14
% 34.10/10.04 |
% 34.10/10.04 | Combining equations (829,212) yields a new equation:
% 34.10/10.04 | (264) all_18_1_14 = 0
% 34.10/10.04 |
% 34.10/10.04 | Equations (264) can reduce 200 to:
% 34.10/10.04 | (94) $false
% 34.10/10.04 |
% 34.10/10.04 |-The branch is then unsatisfiable
% 34.10/10.04 |-Branch two:
% 34.10/10.04 | (837) all_20_1_17 = 0
% 34.10/10.04 | (838) all_20_0_16 = 0
% 34.10/10.04 |
% 34.10/10.04 | Combining equations (838,170) yields a new equation:
% 34.10/10.04 | (255) all_16_0_10 = 0
% 34.10/10.04 |
% 34.10/10.04 | Equations (255) can reduce 190 to:
% 34.10/10.04 | (94) $false
% 34.10/10.04 |
% 34.10/10.04 |-The branch is then unsatisfiable
% 34.10/10.04 |-Branch two:
% 34.10/10.04 | (264) all_18_1_14 = 0
% 34.10/10.04 | (842) all_18_0_13 = 0
% 34.10/10.04 |
% 34.10/10.04 | Equations (842) can reduce 189 to:
% 34.10/10.04 | (94) $false
% 34.10/10.04 |
% 34.10/10.04 |-The branch is then unsatisfiable
% 34.10/10.04 % SZS output end Proof for theBenchmark
% 34.10/10.04
% 34.10/10.04 9430ms
%------------------------------------------------------------------------------