TSTP Solution File: GEO190+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO190+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n007.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 03:48:27 EDT 2022
% Result : Theorem 6.22s 2.18s
% Output : Proof 8.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO190+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 06:35:13 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.58 ____ _
% 0.20/0.58 ___ / __ \_____(_)___ ________ __________
% 0.20/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.20/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.20/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.20/0.58
% 0.20/0.58 A Theorem Prover for First-Order Logic
% 0.20/0.58 (ePrincess v.1.0)
% 0.20/0.58
% 0.20/0.58 (c) Philipp Rümmer, 2009-2015
% 0.20/0.58 (c) Peter Backeman, 2014-2015
% 0.20/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.20/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.20/0.58 Bug reports to peter@backeman.se
% 0.20/0.58
% 0.20/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.20/0.58
% 0.20/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.74/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.50/0.92 Prover 0: Preprocessing ...
% 1.76/1.05 Prover 0: Warning: ignoring some quantifiers
% 1.76/1.07 Prover 0: Constructing countermodel ...
% 2.50/1.25 Prover 0: gave up
% 2.50/1.25 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.50/1.28 Prover 1: Preprocessing ...
% 2.83/1.37 Prover 1: Constructing countermodel ...
% 3.36/1.50 Prover 1: gave up
% 3.36/1.50 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.36/1.52 Prover 2: Preprocessing ...
% 3.50/1.63 Prover 2: Warning: ignoring some quantifiers
% 3.50/1.63 Prover 2: Constructing countermodel ...
% 6.22/2.18 Prover 2: proved (668ms)
% 6.22/2.18
% 6.22/2.18 No countermodel exists, formula is valid
% 6.22/2.18 % SZS status Theorem for theBenchmark
% 6.22/2.18
% 6.22/2.18 Generating proof ... Warning: ignoring some quantifiers
% 7.90/2.58 found it (size 65)
% 7.90/2.58
% 7.90/2.58 % SZS output start Proof for theBenchmark
% 8.23/2.58 Assumed formulas after preprocessing and simplification:
% 8.23/2.58 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v4 = 0) & line_connecting(v1, v0) = v5 & line_connecting(v0, v1) = v3 & apart_point_and_line(v2, v5) = 0 & apart_point_and_line(v2, v3) = v4 & distinct_points(v1, v2) = 0 & distinct_points(v0, v2) = 0 & distinct_points(v0, v1) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v7, v8) = v10) | ~ (distinct_points(v6, v7) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v6, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v6, v9) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v11) | ~ (apart_point_and_line(v6, v9) = v10) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v6, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_points(v6, v7) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v7, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v8, v7) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (convergent_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = v10) | ~ (distinct_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_points(v7, v8) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_points(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (intersection_point(v6, v7) = v9) | ~ (distinct_points(v8, v9) = v10) | ? [v11] : ? [v12] : (( ~ (v12 = 0) & ~ (v11 = 0) & apart_point_and_line(v8, v7) = v12 & apart_point_and_line(v8, v6) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v8, v7) = v9) | ~ (apart_point_and_line(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (apart_point_and_line(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | apart_point_and_line(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_points(v6, v8) = v9) | apart_point_and_line(v8, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v7, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v6, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v7, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v6, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection_point(v9, v8) = v7) | ~ (intersection_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (line_connecting(v9, v8) = v7) | ~ (line_connecting(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (apart_point_and_line(v9, v8) = v7) | ~ (apart_point_and_line(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (convergent_lines(v9, v8) = v7) | ~ (convergent_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_lines(v9, v8) = v7) | ~ (distinct_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_points(v9, v8) = v7) | ~ (distinct_points(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v6, v7) = v9) | ~ (apart_point_and_line(v8, v9) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & distinct_points(v8, v7) = 0 & distinct_points(v8, v6) = 0) | ( ~ (v10 = 0) & distinct_points(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (distinct_lines(v8, v9) = 0) | ~ (distinct_points(v6, v7) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v7, v9) = 0) | (v10 = 0 & apart_point_and_line(v7, v8) = 0) | (v10 = 0 & apart_point_and_line(v6, v9) = 0) | (v10 = 0 & apart_point_and_line(v6, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | distinct_lines(v6, v7) = 0) & ! [v6] : ~ (convergent_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_points(v6, v6) = 0) & ? [v6] : ? [v7] : ? [v8] : intersection_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : line_connecting(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : apart_point_and_line(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : convergent_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_points(v7, v6) = v8)
% 8.23/2.63 | 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 yields:
% 8.23/2.63 | (1) ~ (all_0_1_1 = 0) & line_connecting(all_0_4_4, all_0_5_5) = all_0_0_0 & line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1 & distinct_points(all_0_4_4, all_0_3_3) = 0 & distinct_points(all_0_5_5, all_0_3_3) = 0 & distinct_points(all_0_5_5, all_0_4_4) = 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 | ~ (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] : (( ~ (v6 = 0) & ~ (v5 = 0) & apart_point_and_line(v2, v1) = v6 & apart_point_and_line(v2, v0) = v5) | ( ~ (v5 = 0) & convergent_lines(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 | ~ (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] : ((v5 = 0 & v4 = 0 & distinct_points(v2, v1) = 0 & distinct_points(v2, v0) = 0) | ( ~ (v4 = 0) & distinct_points(v0, v1) = v4))) & ! [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] : (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] : 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
% 8.23/2.66 |
% 8.23/2.66 | Applying alpha-rule on (1) yields:
% 8.23/2.66 | (2) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 8.23/2.66 | (3) ! [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)))
% 8.23/2.66 | (4) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0)
% 8.23/2.66 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 8.23/2.66 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 8.23/2.66 | (7) ! [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))
% 8.23/2.66 | (8) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 8.23/2.66 | (9) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 8.23/2.67 | (10) ! [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))
% 8.23/2.67 | (11) ! [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)))
% 8.23/2.67 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 8.23/2.67 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 8.23/2.67 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 8.23/2.67 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 8.23/2.67 | (16) distinct_points(all_0_4_4, all_0_3_3) = 0
% 8.23/2.67 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 8.23/2.67 | (18) ! [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)))
% 8.23/2.67 | (19) ! [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))
% 8.23/2.67 | (20) line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2
% 8.23/2.67 | (21) ! [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)
% 8.66/2.67 | (22) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 8.66/2.67 | (23) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 8.66/2.67 | (24) ! [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)))
% 8.66/2.67 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 8.66/2.67 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 8.66/2.67 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 8.66/2.68 | (28) ~ (all_0_1_1 = 0)
% 8.66/2.68 | (29) ! [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))
% 8.66/2.68 | (30) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 8.66/2.68 | (31) ! [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)))
% 8.66/2.68 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 8.66/2.68 | (33) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 8.66/2.68 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection_point(v0, v1) = v3) | ~ (distinct_points(v2, v3) = v4) | ? [v5] : ? [v6] : (( ~ (v6 = 0) & ~ (v5 = 0) & apart_point_and_line(v2, v1) = v6 & apart_point_and_line(v2, v0) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 8.66/2.68 | (35) ! [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)
% 8.66/2.68 | (36) distinct_points(all_0_5_5, all_0_4_4) = 0
% 8.66/2.68 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & distinct_points(v2, v1) = 0 & distinct_points(v2, v0) = 0) | ( ~ (v4 = 0) & distinct_points(v0, v1) = v4)))
% 8.66/2.68 | (38) ! [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))
% 8.66/2.68 | (39) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 8.66/2.68 | (40) ! [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)
% 8.66/2.68 | (41) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 8.66/2.68 | (42) line_connecting(all_0_4_4, all_0_5_5) = all_0_0_0
% 8.66/2.68 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((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)))
% 8.66/2.68 | (44) apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1
% 8.66/2.68 | (45) ! [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)))
% 8.66/2.68 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 8.66/2.68 | (47) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 8.66/2.68 | (48) distinct_points(all_0_5_5, all_0_3_3) = 0
% 8.66/2.68 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 8.66/2.68 | (50) apart_point_and_line(all_0_3_3, all_0_0_0) = 0
% 8.66/2.68 |
% 8.66/2.68 | Instantiating formula (15) with all_0_1_1, all_0_2_2, all_0_0_0, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = 0, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 8.66/2.68 | (51) all_0_1_1 = 0 | distinct_lines(all_0_0_0, all_0_2_2) = 0
% 8.66/2.68 |
% 8.66/2.68 | Instantiating formula (45) with all_0_1_1, all_0_1_1, all_0_2_2, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 8.66/2.68 | (52) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 8.66/2.68 |
% 8.66/2.68 +-Applying beta-rule and splitting (52), into two cases.
% 8.66/2.68 |-Branch one:
% 8.66/2.68 | (53) all_0_1_1 = 0
% 8.66/2.68 |
% 8.66/2.69 | Equations (53) can reduce 28 to:
% 8.66/2.69 | (54) $false
% 8.66/2.69 |
% 8.66/2.69 |-The branch is then unsatisfiable
% 8.66/2.69 |-Branch two:
% 8.66/2.69 | (28) ~ (all_0_1_1 = 0)
% 8.66/2.69 | (56) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 8.66/2.69 |
% 8.66/2.69 +-Applying beta-rule and splitting (51), into two cases.
% 8.66/2.69 |-Branch one:
% 8.66/2.69 | (57) distinct_lines(all_0_0_0, all_0_2_2) = 0
% 8.66/2.69 |
% 8.66/2.69 | Instantiating formula (11) with all_0_2_2, all_0_0_0, all_0_4_4, all_0_5_5 and discharging atoms distinct_lines(all_0_0_0, all_0_2_2) = 0, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 8.66/2.69 | (58) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0))
% 8.66/2.69 |
% 8.66/2.69 | Instantiating (58) with all_41_0_29 yields:
% 8.66/2.69 | (59) (all_41_0_29 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (all_41_0_29 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (all_41_0_29 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | (all_41_0_29 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0)
% 8.66/2.69 |
% 8.66/2.69 +-Applying beta-rule and splitting (59), into two cases.
% 8.66/2.69 |-Branch one:
% 8.66/2.69 | (60) (all_41_0_29 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (all_41_0_29 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (all_41_0_29 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0)
% 8.66/2.69 |
% 8.66/2.69 +-Applying beta-rule and splitting (60), into two cases.
% 8.66/2.69 |-Branch one:
% 8.66/2.69 | (61) (all_41_0_29 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (all_41_0_29 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0)
% 8.66/2.69 |
% 8.66/2.69 +-Applying beta-rule and splitting (61), into two cases.
% 8.66/2.69 |-Branch one:
% 8.66/2.69 | (62) all_41_0_29 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0
% 8.66/2.69 |
% 8.66/2.69 | Applying alpha-rule on (62) yields:
% 8.66/2.69 | (63) all_41_0_29 = 0
% 8.66/2.69 | (64) apart_point_and_line(all_0_4_4, all_0_0_0) = 0
% 8.74/2.69 |
% 8.74/2.69 | Instantiating formula (37) with all_0_0_0, all_0_4_4, all_0_5_5, all_0_4_4 and discharging atoms line_connecting(all_0_4_4, all_0_5_5) = all_0_0_0, apart_point_and_line(all_0_4_4, all_0_0_0) = 0, yields:
% 8.74/2.69 | (65) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & distinct_points(all_0_4_4, all_0_4_4) = 0 & distinct_points(all_0_4_4, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 8.74/2.69 |
% 8.74/2.69 | Instantiating (65) with all_112_0_45, all_112_1_46 yields:
% 8.74/2.69 | (66) (all_112_0_45 = 0 & all_112_1_46 = 0 & distinct_points(all_0_4_4, all_0_4_4) = 0 & distinct_points(all_0_4_4, all_0_5_5) = 0) | ( ~ (all_112_1_46 = 0) & distinct_points(all_0_4_4, all_0_5_5) = all_112_1_46)
% 8.74/2.69 |
% 8.74/2.69 +-Applying beta-rule and splitting (66), into two cases.
% 8.74/2.69 |-Branch one:
% 8.74/2.69 | (67) all_112_0_45 = 0 & all_112_1_46 = 0 & distinct_points(all_0_4_4, all_0_4_4) = 0 & distinct_points(all_0_4_4, all_0_5_5) = 0
% 8.74/2.69 |
% 8.74/2.69 | Applying alpha-rule on (67) yields:
% 8.74/2.69 | (68) all_112_0_45 = 0
% 8.74/2.69 | (69) all_112_1_46 = 0
% 8.74/2.69 | (70) distinct_points(all_0_4_4, all_0_4_4) = 0
% 8.74/2.69 | (71) distinct_points(all_0_4_4, all_0_5_5) = 0
% 8.74/2.69 |
% 8.74/2.69 | Instantiating formula (8) with all_0_4_4 and discharging atoms distinct_points(all_0_4_4, all_0_4_4) = 0, yields:
% 8.74/2.69 | (72) $false
% 8.74/2.69 |
% 8.74/2.69 |-The branch is then unsatisfiable
% 8.74/2.69 |-Branch two:
% 8.74/2.69 | (73) ~ (all_112_1_46 = 0) & distinct_points(all_0_4_4, all_0_5_5) = all_112_1_46
% 8.74/2.69 |
% 8.74/2.69 | Applying alpha-rule on (73) yields:
% 8.74/2.69 | (74) ~ (all_112_1_46 = 0)
% 8.74/2.69 | (75) distinct_points(all_0_4_4, all_0_5_5) = all_112_1_46
% 8.74/2.69 |
% 8.74/2.69 | Instantiating formula (46) with all_112_1_46, all_0_5_5, all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_4_4, all_0_5_5) = all_112_1_46, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 8.74/2.69 | (76) all_112_1_46 = 0 | distinct_points(all_0_5_5, all_0_5_5) = 0
% 8.74/2.69 |
% 8.74/2.69 +-Applying beta-rule and splitting (76), into two cases.
% 8.74/2.69 |-Branch one:
% 8.74/2.69 | (77) distinct_points(all_0_5_5, all_0_5_5) = 0
% 8.74/2.69 |
% 8.74/2.69 | Instantiating formula (8) with all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_5_5) = 0, yields:
% 8.74/2.69 | (72) $false
% 8.74/2.69 |
% 8.74/2.69 |-The branch is then unsatisfiable
% 8.74/2.69 |-Branch two:
% 8.74/2.69 | (79) ~ (distinct_points(all_0_5_5, all_0_5_5) = 0)
% 8.74/2.69 | (69) all_112_1_46 = 0
% 8.74/2.69 |
% 8.74/2.69 | Equations (69) can reduce 74 to:
% 8.74/2.69 | (54) $false
% 8.74/2.69 |
% 8.74/2.69 |-The branch is then unsatisfiable
% 8.74/2.69 |-Branch two:
% 8.74/2.69 | (82) all_41_0_29 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 8.74/2.69 |
% 8.74/2.69 | Applying alpha-rule on (82) yields:
% 8.74/2.69 | (63) all_41_0_29 = 0
% 8.74/2.69 | (84) apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 8.74/2.69 |
% 8.74/2.69 | Instantiating formula (37) with all_0_2_2, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2, apart_point_and_line(all_0_4_4, all_0_2_2) = 0, yields:
% 8.74/2.69 | (85) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & distinct_points(all_0_4_4, all_0_4_4) = 0 & distinct_points(all_0_4_4, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 8.74/2.69 |
% 8.74/2.69 | Instantiating (85) with all_112_0_52, all_112_1_53 yields:
% 8.74/2.69 | (86) (all_112_0_52 = 0 & all_112_1_53 = 0 & distinct_points(all_0_4_4, all_0_4_4) = 0 & distinct_points(all_0_4_4, all_0_5_5) = 0) | ( ~ (all_112_1_53 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_112_1_53)
% 8.74/2.69 |
% 8.74/2.69 +-Applying beta-rule and splitting (86), into two cases.
% 8.74/2.69 |-Branch one:
% 8.74/2.69 | (87) all_112_0_52 = 0 & all_112_1_53 = 0 & distinct_points(all_0_4_4, all_0_4_4) = 0 & distinct_points(all_0_4_4, all_0_5_5) = 0
% 8.74/2.69 |
% 8.74/2.69 | Applying alpha-rule on (87) yields:
% 8.74/2.69 | (88) all_112_0_52 = 0
% 8.74/2.69 | (89) all_112_1_53 = 0
% 8.74/2.69 | (70) distinct_points(all_0_4_4, all_0_4_4) = 0
% 8.74/2.69 | (71) distinct_points(all_0_4_4, all_0_5_5) = 0
% 8.74/2.69 |
% 8.74/2.69 | Instantiating formula (8) with all_0_4_4 and discharging atoms distinct_points(all_0_4_4, all_0_4_4) = 0, yields:
% 8.74/2.69 | (72) $false
% 8.74/2.69 |
% 8.74/2.69 |-The branch is then unsatisfiable
% 8.74/2.69 |-Branch two:
% 8.74/2.69 | (93) ~ (all_112_1_53 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_112_1_53
% 8.74/2.69 |
% 8.74/2.69 | Applying alpha-rule on (93) yields:
% 8.74/2.69 | (94) ~ (all_112_1_53 = 0)
% 8.74/2.69 | (95) distinct_points(all_0_5_5, all_0_4_4) = all_112_1_53
% 8.74/2.69 |
% 8.74/2.69 | Instantiating formula (25) with all_0_5_5, all_0_4_4, all_112_1_53, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_112_1_53, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 8.74/2.69 | (89) all_112_1_53 = 0
% 8.74/2.69 |
% 8.74/2.69 | Equations (89) can reduce 94 to:
% 8.74/2.69 | (54) $false
% 8.74/2.69 |
% 8.74/2.69 |-The branch is then unsatisfiable
% 8.74/2.69 |-Branch two:
% 8.74/2.69 | (98) all_41_0_29 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0
% 8.74/2.69 |
% 8.74/2.69 | Applying alpha-rule on (98) yields:
% 8.74/2.69 | (63) all_41_0_29 = 0
% 8.74/2.69 | (100) apart_point_and_line(all_0_5_5, all_0_0_0) = 0
% 8.74/2.69 |
% 8.74/2.69 | Instantiating formula (37) with all_0_0_0, all_0_5_5, all_0_5_5, all_0_4_4 and discharging atoms line_connecting(all_0_4_4, all_0_5_5) = all_0_0_0, apart_point_and_line(all_0_5_5, all_0_0_0) = 0, yields:
% 8.74/2.69 | (101) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & distinct_points(all_0_5_5, all_0_4_4) = 0 & distinct_points(all_0_5_5, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 8.74/2.69 |
% 8.74/2.69 | Instantiating (101) with all_112_0_54, all_112_1_55 yields:
% 8.74/2.69 | (102) (all_112_0_54 = 0 & all_112_1_55 = 0 & distinct_points(all_0_5_5, all_0_4_4) = 0 & distinct_points(all_0_5_5, all_0_5_5) = 0) | ( ~ (all_112_1_55 = 0) & distinct_points(all_0_4_4, all_0_5_5) = all_112_1_55)
% 8.74/2.69 |
% 8.74/2.69 +-Applying beta-rule and splitting (102), into two cases.
% 8.74/2.69 |-Branch one:
% 8.74/2.70 | (103) all_112_0_54 = 0 & all_112_1_55 = 0 & distinct_points(all_0_5_5, all_0_4_4) = 0 & distinct_points(all_0_5_5, all_0_5_5) = 0
% 8.74/2.70 |
% 8.74/2.70 | Applying alpha-rule on (103) yields:
% 8.74/2.70 | (104) all_112_0_54 = 0
% 8.74/2.70 | (105) all_112_1_55 = 0
% 8.74/2.70 | (36) distinct_points(all_0_5_5, all_0_4_4) = 0
% 8.74/2.70 | (77) distinct_points(all_0_5_5, all_0_5_5) = 0
% 8.74/2.70 |
% 8.74/2.70 | Instantiating formula (8) with all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_5_5) = 0, yields:
% 8.74/2.70 | (72) $false
% 8.74/2.70 |
% 8.74/2.70 |-The branch is then unsatisfiable
% 8.74/2.70 |-Branch two:
% 8.74/2.70 | (109) ~ (all_112_1_55 = 0) & distinct_points(all_0_4_4, all_0_5_5) = all_112_1_55
% 8.74/2.70 |
% 8.74/2.70 | Applying alpha-rule on (109) yields:
% 8.74/2.70 | (110) ~ (all_112_1_55 = 0)
% 8.74/2.70 | (111) distinct_points(all_0_4_4, all_0_5_5) = all_112_1_55
% 8.74/2.70 |
% 8.74/2.70 | Instantiating formula (46) with all_112_1_55, all_0_5_5, all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_4_4, all_0_5_5) = all_112_1_55, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 8.74/2.70 | (112) all_112_1_55 = 0 | distinct_points(all_0_5_5, all_0_5_5) = 0
% 8.74/2.70 |
% 8.74/2.70 +-Applying beta-rule and splitting (112), into two cases.
% 8.74/2.70 |-Branch one:
% 8.74/2.70 | (77) distinct_points(all_0_5_5, all_0_5_5) = 0
% 8.74/2.70 |
% 8.74/2.70 | Instantiating formula (8) with all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_5_5) = 0, yields:
% 8.74/2.70 | (72) $false
% 8.74/2.70 |
% 8.74/2.70 |-The branch is then unsatisfiable
% 8.74/2.70 |-Branch two:
% 8.74/2.70 | (79) ~ (distinct_points(all_0_5_5, all_0_5_5) = 0)
% 8.74/2.70 | (105) all_112_1_55 = 0
% 8.74/2.70 |
% 8.74/2.70 | Equations (105) can reduce 110 to:
% 8.74/2.70 | (54) $false
% 8.74/2.70 |
% 8.74/2.70 |-The branch is then unsatisfiable
% 8.74/2.70 |-Branch two:
% 8.74/2.70 | (118) all_41_0_29 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0
% 8.74/2.70 |
% 8.74/2.70 | Applying alpha-rule on (118) yields:
% 8.74/2.70 | (63) all_41_0_29 = 0
% 8.74/2.70 | (120) apart_point_and_line(all_0_5_5, all_0_2_2) = 0
% 8.74/2.70 |
% 8.74/2.70 | Instantiating formula (37) with all_0_2_2, all_0_5_5, all_0_4_4, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2, apart_point_and_line(all_0_5_5, all_0_2_2) = 0, yields:
% 8.74/2.70 | (121) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & distinct_points(all_0_5_5, all_0_4_4) = 0 & distinct_points(all_0_5_5, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 8.74/2.70 |
% 8.74/2.70 | Instantiating (121) with all_112_0_61, all_112_1_62 yields:
% 8.74/2.70 | (122) (all_112_0_61 = 0 & all_112_1_62 = 0 & distinct_points(all_0_5_5, all_0_4_4) = 0 & distinct_points(all_0_5_5, all_0_5_5) = 0) | ( ~ (all_112_1_62 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_112_1_62)
% 8.74/2.70 |
% 8.74/2.70 +-Applying beta-rule and splitting (122), into two cases.
% 8.74/2.70 |-Branch one:
% 8.74/2.70 | (123) all_112_0_61 = 0 & all_112_1_62 = 0 & distinct_points(all_0_5_5, all_0_4_4) = 0 & distinct_points(all_0_5_5, all_0_5_5) = 0
% 8.74/2.70 |
% 8.74/2.70 | Applying alpha-rule on (123) yields:
% 8.74/2.70 | (124) all_112_0_61 = 0
% 8.74/2.70 | (125) all_112_1_62 = 0
% 8.74/2.70 | (36) distinct_points(all_0_5_5, all_0_4_4) = 0
% 8.74/2.70 | (77) distinct_points(all_0_5_5, all_0_5_5) = 0
% 8.74/2.70 |
% 8.74/2.70 | Instantiating formula (8) with all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_5_5) = 0, yields:
% 8.74/2.70 | (72) $false
% 8.74/2.70 |
% 8.74/2.70 |-The branch is then unsatisfiable
% 8.74/2.70 |-Branch two:
% 8.74/2.70 | (129) ~ (all_112_1_62 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_112_1_62
% 8.74/2.70 |
% 8.74/2.70 | Applying alpha-rule on (129) yields:
% 8.74/2.70 | (130) ~ (all_112_1_62 = 0)
% 8.74/2.70 | (131) distinct_points(all_0_5_5, all_0_4_4) = all_112_1_62
% 8.74/2.70 |
% 8.74/2.70 | Instantiating formula (25) with all_0_5_5, all_0_4_4, all_112_1_62, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_112_1_62, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 8.74/2.70 | (125) all_112_1_62 = 0
% 8.74/2.70 |
% 8.74/2.70 | Equations (125) can reduce 130 to:
% 8.74/2.70 | (54) $false
% 8.74/2.70 |
% 8.74/2.70 |-The branch is then unsatisfiable
% 8.74/2.70 |-Branch two:
% 8.74/2.70 | (134) ~ (distinct_lines(all_0_0_0, all_0_2_2) = 0)
% 8.74/2.70 | (53) all_0_1_1 = 0
% 8.74/2.70 |
% 8.74/2.70 | Equations (53) can reduce 28 to:
% 8.74/2.70 | (54) $false
% 8.74/2.70 |
% 8.74/2.70 |-The branch is then unsatisfiable
% 8.74/2.70 % SZS output end Proof for theBenchmark
% 8.74/2.70
% 8.74/2.70 2108ms
%------------------------------------------------------------------------------