TSTP Solution File: GEO186+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO186+1 : 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 03:48:22 EDT 2022
% Result : Theorem 5.54s 1.96s
% Output : Proof 9.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GEO186+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Fri Jun 17 16:57:23 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.63/0.62 ____ _
% 0.63/0.62 ___ / __ \_____(_)___ ________ __________
% 0.63/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.63/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.63/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.63/0.62
% 0.63/0.62 A Theorem Prover for First-Order Logic
% 0.63/0.62 (ePrincess v.1.0)
% 0.63/0.62
% 0.63/0.62 (c) Philipp Rümmer, 2009-2015
% 0.63/0.62 (c) Peter Backeman, 2014-2015
% 0.63/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.63/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.63/0.62 Bug reports to peter@backeman.se
% 0.63/0.62
% 0.63/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.63/0.62
% 0.63/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.72/0.96 Prover 0: Preprocessing ...
% 2.03/1.09 Prover 0: Warning: ignoring some quantifiers
% 2.03/1.11 Prover 0: Constructing countermodel ...
% 3.01/1.40 Prover 0: gave up
% 3.01/1.40 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.01/1.42 Prover 1: Preprocessing ...
% 3.55/1.51 Prover 1: Constructing countermodel ...
% 3.82/1.55 Prover 1: gave up
% 3.82/1.55 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.82/1.57 Prover 2: Preprocessing ...
% 4.13/1.68 Prover 2: Warning: ignoring some quantifiers
% 4.46/1.68 Prover 2: Constructing countermodel ...
% 5.54/1.96 Prover 2: proved (407ms)
% 5.54/1.96
% 5.54/1.96 No countermodel exists, formula is valid
% 5.54/1.96 % SZS status Theorem for theBenchmark
% 5.54/1.96
% 5.54/1.96 Generating proof ... Warning: ignoring some quantifiers
% 9.50/2.84 found it (size 82)
% 9.50/2.84
% 9.50/2.84 % SZS output start Proof for theBenchmark
% 9.50/2.84 Assumed formulas after preprocessing and simplification:
% 9.50/2.84 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v5 = 0) & ~ (v4 = 0) & intersection_point(v2, v3) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & convergent_lines(v2, v3) = 0 & distinct_points(v0, v6) = 0 & distinct_points(v0, v1) = 0 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (apart_point_and_line(v8, v10) = v12) | ~ (apart_point_and_line(v8, v9) = v11) | ~ (distinct_points(v7, v8) = 0) | ? [v13] : ((v13 = 0 & apart_point_and_line(v7, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v9) = 0) | ( ~ (v13 = 0) & distinct_lines(v9, v10) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (apart_point_and_line(v8, v10) = v12) | ~ (apart_point_and_line(v7, v10) = v11) | ~ (distinct_lines(v9, v10) = 0) | ? [v13] : ((v13 = 0 & apart_point_and_line(v8, v9) = 0) | (v13 = 0 & apart_point_and_line(v7, v9) = 0) | ( ~ (v13 = 0) & distinct_points(v7, v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (apart_point_and_line(v8, v10) = v12) | ~ (apart_point_and_line(v7, v9) = v11) | ? [v13] : ((v13 = 0 & apart_point_and_line(v8, v9) = 0) | (v13 = 0 & apart_point_and_line(v7, v10) = 0) | ( ~ (v13 = 0) & distinct_lines(v9, v10) = v13) | ( ~ (v13 = 0) & distinct_points(v7, v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (apart_point_and_line(v8, v9) = v12) | ~ (apart_point_and_line(v7, v10) = v11) | ? [v13] : ((v13 = 0 & apart_point_and_line(v8, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v9) = 0) | ( ~ (v13 = 0) & distinct_lines(v9, v10) = v13) | ( ~ (v13 = 0) & distinct_points(v7, v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (apart_point_and_line(v8, v9) = v12) | ~ (apart_point_and_line(v7, v9) = v11) | ~ (distinct_lines(v9, v10) = 0) | ? [v13] : ((v13 = 0 & apart_point_and_line(v8, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v10) = 0) | ( ~ (v13 = 0) & distinct_points(v7, v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (apart_point_and_line(v7, v10) = v12) | ~ (apart_point_and_line(v7, v9) = v11) | ~ (distinct_points(v7, v8) = 0) | ? [v13] : ((v13 = 0 & apart_point_and_line(v8, v10) = 0) | (v13 = 0 & apart_point_and_line(v8, v9) = 0) | ( ~ (v13 = 0) & distinct_lines(v9, v10) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v9, v8) = v11) | ~ (distinct_points(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & apart_point_and_line(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (distinct_lines(v8, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & apart_point_and_line(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (convergent_lines(v8, v9) = v11) | ~ (convergent_lines(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & convergent_lines(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (convergent_lines(v7, v9) = v11) | ~ (distinct_lines(v8, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & convergent_lines(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (distinct_lines(v8, v9) = v11) | ~ (distinct_lines(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (distinct_points(v8, v9) = v11) | ~ (distinct_points(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & distinct_points(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (apart_point_and_line(v9, v8) = v10) | ~ (apart_point_and_line(v7, v8) = 0) | distinct_points(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (apart_point_and_line(v7, v9) = v10) | ~ (apart_point_and_line(v7, v8) = 0) | distinct_lines(v8, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (apart_point_and_line(v7, v8) = 0) | ~ (distinct_lines(v8, v9) = v10) | apart_point_and_line(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (apart_point_and_line(v7, v8) = 0) | ~ (distinct_points(v7, v9) = v10) | apart_point_and_line(v9, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (convergent_lines(v8, v9) = v10) | ~ (convergent_lines(v7, v8) = 0) | convergent_lines(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (convergent_lines(v7, v9) = v10) | ~ (convergent_lines(v7, v8) = 0) | convergent_lines(v8, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (convergent_lines(v7, v9) = v10) | ~ (convergent_lines(v7, v8) = 0) | distinct_lines(v8, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (convergent_lines(v7, v8) = 0) | ~ (distinct_lines(v8, v9) = v10) | convergent_lines(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (distinct_lines(v8, v9) = v10) | ~ (distinct_lines(v7, v8) = 0) | distinct_lines(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (distinct_lines(v7, v9) = v10) | ~ (distinct_lines(v7, v8) = 0) | distinct_lines(v8, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (distinct_points(v8, v9) = v10) | ~ (distinct_points(v7, v8) = 0) | distinct_points(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (distinct_points(v7, v9) = v10) | ~ (distinct_points(v7, v8) = 0) | distinct_points(v8, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (intersection_point(v10, v9) = v8) | ~ (intersection_point(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (line_connecting(v10, v9) = v8) | ~ (line_connecting(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (apart_point_and_line(v10, v9) = v8) | ~ (apart_point_and_line(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (convergent_lines(v10, v9) = v8) | ~ (convergent_lines(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (distinct_lines(v10, v9) = v8) | ~ (distinct_lines(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (distinct_points(v10, v9) = v8) | ~ (distinct_points(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (distinct_lines(v9, v10) = 0) | ~ (distinct_points(v7, v8) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v8, v10) = 0) | (v11 = 0 & apart_point_and_line(v8, v9) = 0) | (v11 = 0 & apart_point_and_line(v7, v10) = 0) | (v11 = 0 & apart_point_and_line(v7, v9) = 0))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection_point(v7, v8) = v9) | ? [v10] : (( ~ (v10 = 0) & apart_point_and_line(v9, v8) = v10) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection_point(v7, v8) = v9) | ? [v10] : (( ~ (v10 = 0) & apart_point_and_line(v9, v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v7, v8) = v9) | ? [v10] : (( ~ (v10 = 0) & apart_point_and_line(v8, v9) = v10) | ( ~ (v10 = 0) & distinct_points(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v7, v8) = v9) | ? [v10] : (( ~ (v10 = 0) & apart_point_and_line(v7, v9) = v10) | ( ~ (v10 = 0) & distinct_points(v7, v8) = v10))) & ! [v7] : ! [v8] : ( ~ (convergent_lines(v7, v8) = 0) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & intersection_point(v7, v8) = v9 & apart_point_and_line(v9, v8) = v10)) & ! [v7] : ! [v8] : ( ~ (convergent_lines(v7, v8) = 0) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & intersection_point(v7, v8) = v9 & apart_point_and_line(v9, v7) = v10)) & ! [v7] : ! [v8] : ( ~ (distinct_points(v7, v8) = 0) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & line_connecting(v7, v8) = v9 & apart_point_and_line(v8, v9) = v10)) & ! [v7] : ! [v8] : ( ~ (distinct_points(v7, v8) = 0) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & line_connecting(v7, v8) = v9 & apart_point_and_line(v7, v9) = v10)) & ! [v7] : ~ (convergent_lines(v7, v7) = 0) & ! [v7] : ~ (distinct_lines(v7, v7) = 0) & ! [v7] : ~ (distinct_points(v7, v7) = 0) & ? [v7] : ? [v8] : ? [v9] : intersection_point(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : line_connecting(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : apart_point_and_line(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : convergent_lines(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : distinct_lines(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : distinct_points(v8, v7) = v9)
% 9.50/2.89 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields:
% 9.50/2.89 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_2_2 = 0) & intersection_point(all_0_4_4, all_0_3_3) = all_0_0_0 & apart_point_and_line(all_0_6_6, all_0_3_3) = all_0_1_1 & apart_point_and_line(all_0_6_6, all_0_4_4) = all_0_2_2 & convergent_lines(all_0_4_4, all_0_3_3) = 0 & distinct_points(all_0_6_6, all_0_0_0) = 0 & distinct_points(all_0_6_6, all_0_5_5) = 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] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [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] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [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] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [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] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [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] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [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] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [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 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, 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] : (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 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, 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] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 9.50/2.90 |
% 9.50/2.90 | Applying alpha-rule on (1) yields:
% 9.50/2.90 | (2) ! [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)
% 9.50/2.90 | (3) ! [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)
% 9.50/2.90 | (4) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 9.50/2.91 | (5) apart_point_and_line(all_0_6_6, all_0_4_4) = all_0_2_2
% 9.50/2.91 | (6) ! [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))
% 9.50/2.91 | (7) ! [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] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 9.50/2.91 | (8) ! [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))
% 9.50/2.91 | (9) ! [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] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 9.50/2.91 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 9.50/2.91 | (11) distinct_points(all_0_6_6, all_0_0_0) = 0
% 9.50/2.91 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 9.50/2.91 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 9.50/2.91 | (14) ! [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] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 9.50/2.91 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 9.50/2.91 | (16) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 9.92/2.91 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 9.92/2.91 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 9.92/2.91 | (19) ~ (all_0_2_2 = 0)
% 9.92/2.91 | (20) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 9.92/2.91 | (21) ! [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)
% 9.92/2.91 | (22) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 9.92/2.91 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 9.92/2.91 | (24) apart_point_and_line(all_0_6_6, all_0_3_3) = all_0_1_1
% 9.92/2.91 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 9.92/2.91 | (26) ! [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] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 9.92/2.91 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 9.92/2.91 | (28) distinct_points(all_0_6_6, all_0_5_5) = 0
% 9.92/2.91 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 9.92/2.92 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 9.92/2.92 | (31) ! [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))
% 9.92/2.92 | (32) ! [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))
% 9.92/2.92 | (33) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 9.92/2.92 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0)))
% 9.92/2.92 | (35) ! [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))
% 9.92/2.92 | (36) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 9.92/2.92 | (37) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 9.92/2.92 | (38) ! [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)
% 9.92/2.92 | (39) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 9.92/2.92 | (40) ! [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] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 9.92/2.92 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 9.92/2.92 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 9.92/2.92 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 9.92/2.92 | (44) ~ (all_0_1_1 = 0)
% 9.92/2.92 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 9.92/2.92 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 9.92/2.92 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 9.92/2.92 | (48) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 9.92/2.92 | (49) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 9.92/2.92 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 9.92/2.92 | (51) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 9.92/2.92 | (52) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 9.92/2.92 | (53) ! [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] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 9.92/2.93 | (54) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 9.92/2.93 | (55) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 9.92/2.93 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 9.92/2.93 | (57) intersection_point(all_0_4_4, all_0_3_3) = all_0_0_0
% 9.92/2.93 |
% 9.92/2.93 | Instantiating formula (45) with all_0_0_0, all_0_3_3, all_0_4_4 and discharging atoms intersection_point(all_0_4_4, all_0_3_3) = all_0_0_0, yields:
% 9.92/2.93 | (58) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_0_0, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 9.92/2.93 |
% 9.92/2.93 | Instantiating formula (41) with all_0_0_0, all_0_3_3, all_0_4_4 and discharging atoms intersection_point(all_0_4_4, all_0_3_3) = all_0_0_0, yields:
% 9.92/2.93 | (59) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_0_0, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 9.92/2.93 |
% 9.92/2.93 | Instantiating formula (7) with all_0_1_1, all_0_1_1, all_0_3_3, all_0_3_3, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_0_1_1, yields:
% 9.92/2.93 | (60) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 9.92/2.93 |
% 9.92/2.93 | Instantiating formula (7) with all_0_2_2, all_0_1_1, all_0_4_4, all_0_3_3, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_0_1_1, apart_point_and_line(all_0_6_6, all_0_4_4) = all_0_2_2, yields:
% 9.92/2.93 | (61) all_0_1_1 = 0 | all_0_2_2 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 9.92/2.93 |
% 9.92/2.93 | Instantiating formula (7) with all_0_2_2, all_0_2_2, all_0_4_4, all_0_4_4, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_4_4) = all_0_2_2, yields:
% 9.92/2.93 | (62) all_0_2_2 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 9.92/2.93 |
% 9.92/2.93 | Instantiating formula (53) with all_0_1_1, all_0_1_1, all_0_3_3, all_0_3_3, all_0_0_0, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_0_1_1, distinct_points(all_0_6_6, all_0_0_0) = 0, yields:
% 9.92/2.93 | (63) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 9.92/2.93 |
% 9.92/2.93 | Instantiating formula (53) with all_0_2_2, all_0_1_1, all_0_4_4, all_0_3_3, all_0_0_0, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_0_1_1, apart_point_and_line(all_0_6_6, all_0_4_4) = all_0_2_2, distinct_points(all_0_6_6, all_0_0_0) = 0, yields:
% 9.92/2.93 | (64) all_0_1_1 = 0 | all_0_2_2 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 9.92/2.93 |
% 9.92/2.93 | Instantiating formula (53) with all_0_2_2, all_0_2_2, all_0_4_4, all_0_4_4, all_0_0_0, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_4_4) = all_0_2_2, distinct_points(all_0_6_6, all_0_0_0) = 0, yields:
% 9.92/2.93 | (65) all_0_2_2 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0))
% 9.92/2.93 |
% 9.92/2.93 | Instantiating formula (53) with all_0_1_1, all_0_1_1, all_0_3_3, all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_0_1_1, distinct_points(all_0_6_6, all_0_5_5) = 0, yields:
% 9.92/2.93 | (66) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 9.92/2.93 |
% 9.92/2.93 | Instantiating formula (53) with all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_0_1_1, apart_point_and_line(all_0_6_6, all_0_4_4) = all_0_2_2, distinct_points(all_0_6_6, all_0_5_5) = 0, yields:
% 9.92/2.93 | (67) all_0_1_1 = 0 | all_0_2_2 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0))
% 9.92/2.93 |
% 9.92/2.93 | Instantiating formula (53) with all_0_2_2, all_0_1_1, all_0_4_4, all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_0_1_1, apart_point_and_line(all_0_6_6, all_0_4_4) = all_0_2_2, distinct_points(all_0_6_6, all_0_5_5) = 0, yields:
% 9.92/2.93 | (68) all_0_1_1 = 0 | all_0_2_2 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 9.92/2.93 |
% 9.92/2.93 | Instantiating formula (53) with all_0_2_2, all_0_2_2, all_0_4_4, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_4_4) = all_0_2_2, distinct_points(all_0_6_6, all_0_5_5) = 0, yields:
% 9.92/2.94 | (69) all_0_2_2 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0))
% 9.92/2.94 |
% 9.92/2.94 | Instantiating (59) with all_32_0_37 yields:
% 9.92/2.94 | (70) ( ~ (all_32_0_37 = 0) & apart_point_and_line(all_0_0_0, all_0_4_4) = all_32_0_37) | ( ~ (all_32_0_37 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_32_0_37)
% 9.92/2.94 |
% 9.92/2.94 | Instantiating (58) with all_33_0_38 yields:
% 9.92/2.94 | (71) ( ~ (all_33_0_38 = 0) & apart_point_and_line(all_0_0_0, all_0_3_3) = all_33_0_38) | ( ~ (all_33_0_38 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_33_0_38)
% 9.92/2.94 |
% 9.92/2.94 +-Applying beta-rule and splitting (70), into two cases.
% 9.92/2.94 |-Branch one:
% 9.92/2.94 | (72) ~ (all_32_0_37 = 0) & apart_point_and_line(all_0_0_0, all_0_4_4) = all_32_0_37
% 9.92/2.94 |
% 9.92/2.94 | Applying alpha-rule on (72) yields:
% 9.92/2.94 | (73) ~ (all_32_0_37 = 0)
% 9.92/2.94 | (74) apart_point_and_line(all_0_0_0, all_0_4_4) = all_32_0_37
% 9.92/2.94 |
% 9.92/2.94 +-Applying beta-rule and splitting (60), into two cases.
% 9.92/2.94 |-Branch one:
% 9.92/2.94 | (75) all_0_1_1 = 0
% 9.92/2.94 |
% 9.92/2.94 | Equations (75) can reduce 44 to:
% 9.92/2.94 | (76) $false
% 9.92/2.94 |
% 9.92/2.94 |-The branch is then unsatisfiable
% 9.92/2.94 |-Branch two:
% 9.92/2.94 | (44) ~ (all_0_1_1 = 0)
% 9.92/2.94 | (78) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 9.92/2.94 |
% 9.92/2.94 +-Applying beta-rule and splitting (71), into two cases.
% 9.92/2.94 |-Branch one:
% 9.92/2.94 | (79) ~ (all_33_0_38 = 0) & apart_point_and_line(all_0_0_0, all_0_3_3) = all_33_0_38
% 9.92/2.94 |
% 9.92/2.94 | Applying alpha-rule on (79) yields:
% 9.92/2.94 | (80) ~ (all_33_0_38 = 0)
% 9.92/2.94 | (81) apart_point_and_line(all_0_0_0, all_0_3_3) = all_33_0_38
% 9.92/2.94 |
% 9.92/2.94 +-Applying beta-rule and splitting (62), into two cases.
% 9.92/2.94 |-Branch one:
% 9.92/2.94 | (82) all_0_2_2 = 0
% 9.92/2.94 |
% 9.92/2.94 | Equations (82) can reduce 19 to:
% 9.92/2.94 | (76) $false
% 9.92/2.94 |
% 9.92/2.94 |-The branch is then unsatisfiable
% 9.92/2.94 |-Branch two:
% 9.92/2.94 | (19) ~ (all_0_2_2 = 0)
% 9.92/2.94 | (85) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 9.92/2.94 |
% 9.92/2.94 +-Applying beta-rule and splitting (63), into two cases.
% 9.92/2.94 |-Branch one:
% 9.92/2.94 | (75) all_0_1_1 = 0
% 9.92/2.94 |
% 9.92/2.94 | Equations (75) can reduce 44 to:
% 9.92/2.94 | (76) $false
% 9.92/2.94 |
% 9.92/2.94 |-The branch is then unsatisfiable
% 9.92/2.94 |-Branch two:
% 9.92/2.94 | (44) ~ (all_0_1_1 = 0)
% 9.92/2.94 | (89) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 9.92/2.94 |
% 9.92/2.94 +-Applying beta-rule and splitting (65), into two cases.
% 9.92/2.94 |-Branch one:
% 9.92/2.94 | (82) all_0_2_2 = 0
% 9.92/2.94 |
% 9.92/2.94 | Equations (82) can reduce 19 to:
% 9.92/2.94 | (76) $false
% 9.92/2.94 |
% 9.92/2.94 |-The branch is then unsatisfiable
% 9.92/2.94 |-Branch two:
% 9.92/2.94 | (19) ~ (all_0_2_2 = 0)
% 9.92/2.94 | (93) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0))
% 9.92/2.94 |
% 9.92/2.94 +-Applying beta-rule and splitting (66), into two cases.
% 9.92/2.94 |-Branch one:
% 9.92/2.94 | (75) all_0_1_1 = 0
% 9.92/2.94 |
% 9.92/2.94 | Equations (75) can reduce 44 to:
% 9.92/2.94 | (76) $false
% 9.92/2.94 |
% 9.92/2.94 |-The branch is then unsatisfiable
% 9.92/2.94 |-Branch two:
% 9.92/2.94 | (44) ~ (all_0_1_1 = 0)
% 9.92/2.94 | (97) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 9.92/2.94 |
% 9.92/2.94 +-Applying beta-rule and splitting (69), into two cases.
% 9.92/2.94 |-Branch one:
% 9.92/2.94 | (82) all_0_2_2 = 0
% 9.92/2.94 |
% 9.92/2.94 | Equations (82) can reduce 19 to:
% 9.92/2.94 | (76) $false
% 9.92/2.94 |
% 9.92/2.94 |-The branch is then unsatisfiable
% 9.92/2.94 |-Branch two:
% 9.92/2.94 | (19) ~ (all_0_2_2 = 0)
% 9.92/2.95 | (101) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0))
% 9.92/2.95 |
% 9.92/2.95 +-Applying beta-rule and splitting (68), into two cases.
% 9.92/2.95 |-Branch one:
% 9.92/2.95 | (75) all_0_1_1 = 0
% 9.92/2.95 |
% 9.92/2.95 | Equations (75) can reduce 44 to:
% 9.92/2.95 | (76) $false
% 9.92/2.95 |
% 9.92/2.95 |-The branch is then unsatisfiable
% 9.92/2.95 |-Branch two:
% 9.92/2.95 | (44) ~ (all_0_1_1 = 0)
% 9.92/2.95 | (105) all_0_2_2 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 9.92/2.95 |
% 9.92/2.95 +-Applying beta-rule and splitting (61), into two cases.
% 9.92/2.95 |-Branch one:
% 9.92/2.95 | (75) all_0_1_1 = 0
% 9.92/2.95 |
% 9.92/2.95 | Equations (75) can reduce 44 to:
% 9.92/2.95 | (76) $false
% 9.92/2.95 |
% 9.92/2.95 |-The branch is then unsatisfiable
% 9.92/2.95 |-Branch two:
% 9.92/2.95 | (44) ~ (all_0_1_1 = 0)
% 9.92/2.95 | (109) all_0_2_2 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 9.92/2.95 |
% 9.92/2.95 +-Applying beta-rule and splitting (67), into two cases.
% 9.92/2.95 |-Branch one:
% 9.92/2.95 | (75) all_0_1_1 = 0
% 9.92/2.95 |
% 9.92/2.95 | Equations (75) can reduce 44 to:
% 9.92/2.95 | (76) $false
% 9.92/2.95 |
% 9.92/2.95 |-The branch is then unsatisfiable
% 9.92/2.95 |-Branch two:
% 9.92/2.95 | (44) ~ (all_0_1_1 = 0)
% 9.92/2.95 | (113) all_0_2_2 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0))
% 9.92/2.95 |
% 9.92/2.95 +-Applying beta-rule and splitting (64), into two cases.
% 9.92/2.95 |-Branch one:
% 9.92/2.95 | (75) all_0_1_1 = 0
% 9.92/2.95 |
% 9.92/2.95 | Equations (75) can reduce 44 to:
% 9.92/2.95 | (76) $false
% 9.92/2.95 |
% 9.92/2.95 |-The branch is then unsatisfiable
% 9.92/2.95 |-Branch two:
% 9.92/2.95 | (44) ~ (all_0_1_1 = 0)
% 9.92/2.95 | (117) all_0_2_2 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 9.92/2.95 |
% 9.92/2.95 +-Applying beta-rule and splitting (113), into two cases.
% 9.92/2.95 |-Branch one:
% 9.92/2.95 | (82) all_0_2_2 = 0
% 9.92/2.95 |
% 9.92/2.95 | Equations (82) can reduce 19 to:
% 9.92/2.95 | (76) $false
% 9.92/2.95 |
% 9.92/2.95 |-The branch is then unsatisfiable
% 9.92/2.95 |-Branch two:
% 9.92/2.95 | (19) ~ (all_0_2_2 = 0)
% 9.92/2.95 | (121) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0))
% 9.92/2.95 |
% 9.92/2.95 +-Applying beta-rule and splitting (117), into two cases.
% 9.92/2.95 |-Branch one:
% 9.92/2.95 | (82) all_0_2_2 = 0
% 9.92/2.95 |
% 9.92/2.95 | Equations (82) can reduce 19 to:
% 9.92/2.95 | (76) $false
% 9.92/2.95 |
% 9.92/2.95 |-The branch is then unsatisfiable
% 9.92/2.95 |-Branch two:
% 9.92/2.95 | (19) ~ (all_0_2_2 = 0)
% 9.92/2.95 | (125) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 9.92/2.95 |
% 9.92/2.95 | Instantiating (125) with all_99_0_64 yields:
% 9.92/2.95 | (126) (all_99_0_64 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (all_99_0_64 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (all_99_0_64 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = all_99_0_64)
% 9.92/2.95 |
% 9.92/2.95 +-Applying beta-rule and splitting (126), into two cases.
% 9.92/2.95 |-Branch one:
% 9.92/2.95 | (127) (all_99_0_64 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (all_99_0_64 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0)
% 9.92/2.95 |
% 9.92/2.95 +-Applying beta-rule and splitting (127), into two cases.
% 9.92/2.95 |-Branch one:
% 9.92/2.95 | (128) all_99_0_64 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0
% 9.92/2.95 |
% 9.92/2.95 | Applying alpha-rule on (128) yields:
% 9.92/2.95 | (129) all_99_0_64 = 0
% 9.92/2.95 | (130) apart_point_and_line(all_0_0_0, all_0_3_3) = 0
% 9.92/2.95 |
% 9.92/2.95 | Instantiating formula (17) with all_0_0_0, all_0_3_3, 0, all_33_0_38 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_33_0_38, apart_point_and_line(all_0_0_0, all_0_3_3) = 0, yields:
% 9.92/2.95 | (131) all_33_0_38 = 0
% 9.92/2.95 |
% 9.92/2.95 | Equations (131) can reduce 80 to:
% 9.92/2.95 | (76) $false
% 9.92/2.95 |
% 9.92/2.95 |-The branch is then unsatisfiable
% 9.92/2.95 |-Branch two:
% 9.92/2.95 | (133) all_99_0_64 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0
% 9.92/2.95 |
% 9.92/2.95 | Applying alpha-rule on (133) yields:
% 9.92/2.95 | (129) all_99_0_64 = 0
% 9.92/2.95 | (135) apart_point_and_line(all_0_0_0, all_0_4_4) = 0
% 9.92/2.95 |
% 9.92/2.95 | Instantiating formula (17) with all_0_0_0, all_0_4_4, 0, all_32_0_37 and discharging atoms apart_point_and_line(all_0_0_0, all_0_4_4) = all_32_0_37, apart_point_and_line(all_0_0_0, all_0_4_4) = 0, yields:
% 9.92/2.95 | (136) all_32_0_37 = 0
% 9.92/2.95 |
% 9.92/2.95 | Equations (136) can reduce 73 to:
% 9.92/2.95 | (76) $false
% 9.92/2.95 |
% 9.92/2.95 |-The branch is then unsatisfiable
% 9.92/2.95 |-Branch two:
% 9.92/2.95 | (138) ~ (all_99_0_64 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = all_99_0_64
% 9.92/2.95 |
% 9.92/2.95 | Applying alpha-rule on (138) yields:
% 9.92/2.95 | (139) ~ (all_99_0_64 = 0)
% 9.92/2.95 | (140) distinct_lines(all_0_3_3, all_0_4_4) = all_99_0_64
% 9.92/2.95 |
% 9.92/2.95 | Instantiating formula (10) with all_99_0_64, all_0_4_4, all_0_3_3, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = 0, distinct_lines(all_0_3_3, all_0_4_4) = all_99_0_64, yields:
% 9.92/2.95 | (141) all_99_0_64 = 0 | convergent_lines(all_0_4_4, all_0_4_4) = 0
% 9.92/2.95 |
% 9.92/2.95 +-Applying beta-rule and splitting (141), into two cases.
% 9.92/2.95 |-Branch one:
% 9.92/2.95 | (142) convergent_lines(all_0_4_4, all_0_4_4) = 0
% 9.92/2.95 |
% 9.92/2.95 | Instantiating formula (33) with all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 9.92/2.95 | (143) $false
% 9.92/2.95 |
% 9.92/2.95 |-The branch is then unsatisfiable
% 9.92/2.96 |-Branch two:
% 9.92/2.96 | (144) ~ (convergent_lines(all_0_4_4, all_0_4_4) = 0)
% 9.92/2.96 | (129) all_99_0_64 = 0
% 9.92/2.96 |
% 9.92/2.96 | Equations (129) can reduce 139 to:
% 9.92/2.96 | (76) $false
% 9.92/2.96 |
% 9.92/2.96 |-The branch is then unsatisfiable
% 9.92/2.96 |-Branch two:
% 9.92/2.96 | (147) ~ (all_33_0_38 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_33_0_38
% 9.92/2.96 |
% 9.92/2.96 | Applying alpha-rule on (147) yields:
% 9.92/2.96 | (80) ~ (all_33_0_38 = 0)
% 9.92/2.96 | (149) convergent_lines(all_0_4_4, all_0_3_3) = all_33_0_38
% 9.92/2.96 |
% 9.92/2.96 | Instantiating formula (13) with all_0_4_4, all_0_3_3, all_33_0_38, 0 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_33_0_38, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 9.92/2.96 | (131) all_33_0_38 = 0
% 9.92/2.96 |
% 9.92/2.96 | Equations (131) can reduce 80 to:
% 9.92/2.96 | (76) $false
% 9.92/2.96 |
% 9.92/2.96 |-The branch is then unsatisfiable
% 9.92/2.96 |-Branch two:
% 9.92/2.96 | (152) ~ (all_32_0_37 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_32_0_37
% 9.92/2.96 |
% 9.92/2.96 | Applying alpha-rule on (152) yields:
% 9.92/2.96 | (73) ~ (all_32_0_37 = 0)
% 9.92/2.96 | (154) convergent_lines(all_0_4_4, all_0_3_3) = all_32_0_37
% 9.92/2.96 |
% 9.92/2.96 | Instantiating formula (13) with all_0_4_4, all_0_3_3, all_32_0_37, 0 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_32_0_37, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 9.92/2.96 | (136) all_32_0_37 = 0
% 9.92/2.96 |
% 9.92/2.96 | Equations (136) can reduce 73 to:
% 9.92/2.96 | (76) $false
% 9.92/2.96 |
% 9.92/2.96 |-The branch is then unsatisfiable
% 9.92/2.96 % SZS output end Proof for theBenchmark
% 9.92/2.96
% 9.92/2.96 2329ms
%------------------------------------------------------------------------------