TSTP Solution File: GEO182+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO182+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 03:48:19 EDT 2022
% Result : Theorem 6.07s 2.02s
% Output : Proof 8.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GEO182+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.33 % Computer : n012.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sat Jun 18 01:04:38 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.18/0.57 ____ _
% 0.18/0.57 ___ / __ \_____(_)___ ________ __________
% 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.57
% 0.18/0.57 A Theorem Prover for First-Order Logic
% 0.18/0.57 (ePrincess v.1.0)
% 0.18/0.57
% 0.18/0.57 (c) Philipp Rümmer, 2009-2015
% 0.18/0.57 (c) Peter Backeman, 2014-2015
% 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.57 Bug reports to peter@backeman.se
% 0.18/0.57
% 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.57
% 0.18/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.61/0.89 Prover 0: Preprocessing ...
% 1.93/1.02 Prover 0: Warning: ignoring some quantifiers
% 1.93/1.03 Prover 0: Constructing countermodel ...
% 2.58/1.23 Prover 0: gave up
% 2.58/1.23 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.66/1.25 Prover 1: Preprocessing ...
% 3.02/1.34 Prover 1: Constructing countermodel ...
% 3.02/1.39 Prover 1: gave up
% 3.02/1.39 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.23/1.41 Prover 2: Preprocessing ...
% 3.55/1.52 Prover 2: Warning: ignoring some quantifiers
% 3.55/1.53 Prover 2: Constructing countermodel ...
% 6.07/2.02 Prover 2: proved (631ms)
% 6.07/2.02
% 6.07/2.02 No countermodel exists, formula is valid
% 6.07/2.02 % SZS status Theorem for theBenchmark
% 6.07/2.02
% 6.07/2.02 Generating proof ... Warning: ignoring some quantifiers
% 7.83/2.49 found it (size 65)
% 7.83/2.49
% 7.83/2.49 % SZS output start Proof for theBenchmark
% 7.83/2.49 Assumed formulas after preprocessing and simplification:
% 7.83/2.49 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & line_connecting(v1, v0) = v4 & line_connecting(v0, v1) = v3 & apart_point_and_line(v2, v4) = v5 & apart_point_and_line(v2, v3) = 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)
% 8.20/2.53 | 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:
% 8.20/2.53 | (1) ~ (all_0_0_0 = 0) & line_connecting(all_0_4_4, all_0_5_5) = all_0_1_1 & line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2 & apart_point_and_line(all_0_3_3, all_0_1_1) = all_0_0_0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 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
% 8.20/2.54 |
% 8.20/2.54 | Applying alpha-rule on (1) yields:
% 8.20/2.54 | (2) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 8.20/2.54 | (3) ! [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))
% 8.20/2.54 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 8.20/2.54 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 8.20/2.54 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 8.20/2.54 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 8.20/2.54 | (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))
% 8.20/2.54 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 8.20/2.54 | (10) ! [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)))
% 8.20/2.55 | (11) ! [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))
% 8.20/2.55 | (12) ! [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)
% 8.20/2.55 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 8.20/2.55 | (14) ! [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)
% 8.20/2.55 | (15) ! [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)))
% 8.20/2.55 | (16) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 8.20/2.55 | (17) ! [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)))
% 8.20/2.55 | (18) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 8.20/2.55 | (19) ! [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)))
% 8.20/2.55 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 8.20/2.55 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 8.20/2.55 | (22) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 8.20/2.55 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 8.20/2.55 | (24) line_connecting(all_0_4_4, all_0_5_5) = all_0_1_1
% 8.20/2.55 | (25) ! [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))
% 8.20/2.55 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 8.20/2.55 | (27) ! [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)))
% 8.20/2.55 | (28) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 8.20/2.55 | (29) ! [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)))
% 8.20/2.55 | (30) ! [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)
% 8.20/2.55 | (31) distinct_points(all_0_5_5, all_0_4_4) = 0
% 8.20/2.55 | (32) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0)
% 8.20/2.55 | (33) ! [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)))
% 8.20/2.56 | (34) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 8.20/2.56 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 8.20/2.56 | (36) ! [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)))
% 8.20/2.56 | (37) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 8.20/2.56 | (38) ! [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))
% 8.20/2.56 | (39) apart_point_and_line(all_0_3_3, all_0_1_1) = all_0_0_0
% 8.20/2.56 | (40) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 8.20/2.56 | (41) line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2
% 8.20/2.56 | (42) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 8.20/2.56 | (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)))
% 8.20/2.56 | (44) ~ (all_0_0_0 = 0)
% 8.20/2.56 | (45) ! [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)
% 8.20/2.56 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 8.20/2.56 | (47) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 8.20/2.56 | (48) apart_point_and_line(all_0_3_3, all_0_2_2) = 0
% 8.20/2.56 |
% 8.20/2.56 | Instantiating formula (43) with all_0_0_0, all_0_0_0, all_0_1_1, all_0_1_1, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_0_0_0, yields:
% 8.20/2.56 | (49) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 8.20/2.56 |
% 8.20/2.56 | Instantiating formula (14) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_0_0_0, apart_point_and_line(all_0_3_3, all_0_2_2) = 0, yields:
% 8.20/2.56 | (50) all_0_0_0 = 0 | distinct_lines(all_0_2_2, all_0_1_1) = 0
% 8.20/2.56 |
% 8.20/2.56 +-Applying beta-rule and splitting (49), into two cases.
% 8.20/2.56 |-Branch one:
% 8.20/2.56 | (51) all_0_0_0 = 0
% 8.20/2.56 |
% 8.20/2.56 | Equations (51) can reduce 44 to:
% 8.20/2.56 | (52) $false
% 8.20/2.56 |
% 8.20/2.56 |-The branch is then unsatisfiable
% 8.20/2.56 |-Branch two:
% 8.20/2.56 | (44) ~ (all_0_0_0 = 0)
% 8.20/2.56 | (54) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 8.20/2.56 |
% 8.20/2.56 +-Applying beta-rule and splitting (50), into two cases.
% 8.20/2.56 |-Branch one:
% 8.20/2.56 | (55) distinct_lines(all_0_2_2, all_0_1_1) = 0
% 8.20/2.56 |
% 8.20/2.56 | Instantiating formula (10) with all_0_1_1, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms distinct_lines(all_0_2_2, all_0_1_1) = 0, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 8.20/2.56 | (56) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 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_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0))
% 8.20/2.56 |
% 8.20/2.56 | Instantiating (56) with all_37_0_27 yields:
% 8.20/2.56 | (57) (all_37_0_27 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (all_37_0_27 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (all_37_0_27 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0) | (all_37_0_27 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0)
% 8.20/2.56 |
% 8.20/2.56 +-Applying beta-rule and splitting (57), into two cases.
% 8.20/2.56 |-Branch one:
% 8.20/2.56 | (58) (all_37_0_27 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (all_37_0_27 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (all_37_0_27 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0)
% 8.20/2.56 |
% 8.20/2.56 +-Applying beta-rule and splitting (58), into two cases.
% 8.20/2.56 |-Branch one:
% 8.20/2.56 | (59) (all_37_0_27 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0) | (all_37_0_27 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0)
% 8.20/2.57 |
% 8.20/2.57 +-Applying beta-rule and splitting (59), into two cases.
% 8.20/2.57 |-Branch one:
% 8.20/2.57 | (60) all_37_0_27 = 0 & apart_point_and_line(all_0_4_4, all_0_1_1) = 0
% 8.20/2.57 |
% 8.20/2.57 | Applying alpha-rule on (60) yields:
% 8.20/2.57 | (61) all_37_0_27 = 0
% 8.20/2.57 | (62) apart_point_and_line(all_0_4_4, all_0_1_1) = 0
% 8.20/2.57 |
% 8.20/2.57 | Instantiating formula (19) with all_0_1_1, 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_1_1, apart_point_and_line(all_0_4_4, all_0_1_1) = 0, yields:
% 8.20/2.57 | (63) ? [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))
% 8.20/2.57 |
% 8.20/2.57 | Instantiating (63) with all_82_0_64, all_82_1_65 yields:
% 8.20/2.57 | (64) (all_82_0_64 = 0 & all_82_1_65 = 0 & distinct_points(all_0_4_4, all_0_4_4) = 0 & distinct_points(all_0_4_4, all_0_5_5) = 0) | ( ~ (all_82_1_65 = 0) & distinct_points(all_0_4_4, all_0_5_5) = all_82_1_65)
% 8.20/2.57 |
% 8.20/2.57 +-Applying beta-rule and splitting (64), into two cases.
% 8.20/2.57 |-Branch one:
% 8.20/2.57 | (65) all_82_0_64 = 0 & all_82_1_65 = 0 & distinct_points(all_0_4_4, all_0_4_4) = 0 & distinct_points(all_0_4_4, all_0_5_5) = 0
% 8.20/2.57 |
% 8.20/2.57 | Applying alpha-rule on (65) yields:
% 8.20/2.57 | (66) all_82_0_64 = 0
% 8.20/2.57 | (67) all_82_1_65 = 0
% 8.20/2.57 | (68) distinct_points(all_0_4_4, all_0_4_4) = 0
% 8.20/2.57 | (69) distinct_points(all_0_4_4, all_0_5_5) = 0
% 8.20/2.57 |
% 8.20/2.57 | Instantiating formula (2) with all_0_4_4 and discharging atoms distinct_points(all_0_4_4, all_0_4_4) = 0, yields:
% 8.20/2.57 | (70) $false
% 8.20/2.57 |
% 8.20/2.57 |-The branch is then unsatisfiable
% 8.20/2.57 |-Branch two:
% 8.20/2.57 | (71) ~ (all_82_1_65 = 0) & distinct_points(all_0_4_4, all_0_5_5) = all_82_1_65
% 8.20/2.57 |
% 8.20/2.57 | Applying alpha-rule on (71) yields:
% 8.20/2.57 | (72) ~ (all_82_1_65 = 0)
% 8.20/2.57 | (73) distinct_points(all_0_4_4, all_0_5_5) = all_82_1_65
% 8.20/2.57 |
% 8.20/2.57 | Instantiating formula (7) with all_82_1_65, 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_82_1_65, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 8.20/2.57 | (74) all_82_1_65 = 0 | distinct_points(all_0_5_5, all_0_5_5) = 0
% 8.20/2.57 |
% 8.20/2.57 +-Applying beta-rule and splitting (74), into two cases.
% 8.20/2.57 |-Branch one:
% 8.20/2.57 | (75) distinct_points(all_0_5_5, all_0_5_5) = 0
% 8.20/2.57 |
% 8.20/2.57 | Instantiating formula (2) with all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_5_5) = 0, yields:
% 8.20/2.57 | (70) $false
% 8.20/2.57 |
% 8.20/2.57 |-The branch is then unsatisfiable
% 8.20/2.57 |-Branch two:
% 8.20/2.57 | (77) ~ (distinct_points(all_0_5_5, all_0_5_5) = 0)
% 8.20/2.57 | (67) all_82_1_65 = 0
% 8.20/2.57 |
% 8.20/2.57 | Equations (67) can reduce 72 to:
% 8.20/2.57 | (52) $false
% 8.20/2.57 |
% 8.20/2.57 |-The branch is then unsatisfiable
% 8.20/2.57 |-Branch two:
% 8.20/2.57 | (80) all_37_0_27 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 8.20/2.57 |
% 8.20/2.57 | Applying alpha-rule on (80) yields:
% 8.20/2.57 | (61) all_37_0_27 = 0
% 8.20/2.57 | (82) apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 8.20/2.57 |
% 8.20/2.57 | Instantiating formula (19) 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:
% 8.20/2.57 | (83) ? [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))
% 8.20/2.57 |
% 8.20/2.57 | Instantiating (83) with all_82_0_74, all_82_1_75 yields:
% 8.20/2.57 | (84) (all_82_0_74 = 0 & all_82_1_75 = 0 & distinct_points(all_0_4_4, all_0_4_4) = 0 & distinct_points(all_0_4_4, all_0_5_5) = 0) | ( ~ (all_82_1_75 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_82_1_75)
% 8.20/2.57 |
% 8.20/2.57 +-Applying beta-rule and splitting (84), into two cases.
% 8.20/2.57 |-Branch one:
% 8.20/2.57 | (85) all_82_0_74 = 0 & all_82_1_75 = 0 & distinct_points(all_0_4_4, all_0_4_4) = 0 & distinct_points(all_0_4_4, all_0_5_5) = 0
% 8.20/2.57 |
% 8.20/2.57 | Applying alpha-rule on (85) yields:
% 8.20/2.57 | (86) all_82_0_74 = 0
% 8.20/2.57 | (87) all_82_1_75 = 0
% 8.20/2.57 | (68) distinct_points(all_0_4_4, all_0_4_4) = 0
% 8.20/2.57 | (69) distinct_points(all_0_4_4, all_0_5_5) = 0
% 8.20/2.57 |
% 8.20/2.57 | Instantiating formula (2) with all_0_4_4 and discharging atoms distinct_points(all_0_4_4, all_0_4_4) = 0, yields:
% 8.20/2.57 | (70) $false
% 8.20/2.57 |
% 8.20/2.57 |-The branch is then unsatisfiable
% 8.20/2.57 |-Branch two:
% 8.20/2.57 | (91) ~ (all_82_1_75 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_82_1_75
% 8.20/2.57 |
% 8.20/2.57 | Applying alpha-rule on (91) yields:
% 8.20/2.57 | (92) ~ (all_82_1_75 = 0)
% 8.20/2.57 | (93) distinct_points(all_0_5_5, all_0_4_4) = all_82_1_75
% 8.20/2.57 |
% 8.20/2.57 | Instantiating formula (35) with all_0_5_5, all_0_4_4, all_82_1_75, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_82_1_75, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 8.20/2.57 | (87) all_82_1_75 = 0
% 8.20/2.57 |
% 8.20/2.57 | Equations (87) can reduce 92 to:
% 8.20/2.57 | (52) $false
% 8.20/2.57 |
% 8.20/2.57 |-The branch is then unsatisfiable
% 8.20/2.57 |-Branch two:
% 8.20/2.57 | (96) all_37_0_27 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0
% 8.20/2.57 |
% 8.20/2.57 | Applying alpha-rule on (96) yields:
% 8.20/2.57 | (61) all_37_0_27 = 0
% 8.20/2.57 | (98) apart_point_and_line(all_0_5_5, all_0_1_1) = 0
% 8.20/2.57 |
% 8.20/2.57 | Instantiating formula (19) with all_0_1_1, 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_1_1, apart_point_and_line(all_0_5_5, all_0_1_1) = 0, yields:
% 8.20/2.57 | (99) ? [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))
% 8.20/2.57 |
% 8.20/2.57 | Instantiating (99) with all_82_0_76, all_82_1_77 yields:
% 8.20/2.57 | (100) (all_82_0_76 = 0 & all_82_1_77 = 0 & distinct_points(all_0_5_5, all_0_4_4) = 0 & distinct_points(all_0_5_5, all_0_5_5) = 0) | ( ~ (all_82_1_77 = 0) & distinct_points(all_0_4_4, all_0_5_5) = all_82_1_77)
% 8.20/2.57 |
% 8.20/2.57 +-Applying beta-rule and splitting (100), into two cases.
% 8.20/2.57 |-Branch one:
% 8.20/2.57 | (101) all_82_0_76 = 0 & all_82_1_77 = 0 & distinct_points(all_0_5_5, all_0_4_4) = 0 & distinct_points(all_0_5_5, all_0_5_5) = 0
% 8.20/2.57 |
% 8.20/2.57 | Applying alpha-rule on (101) yields:
% 8.20/2.57 | (102) all_82_0_76 = 0
% 8.20/2.57 | (103) all_82_1_77 = 0
% 8.20/2.57 | (31) distinct_points(all_0_5_5, all_0_4_4) = 0
% 8.20/2.57 | (75) distinct_points(all_0_5_5, all_0_5_5) = 0
% 8.20/2.57 |
% 8.20/2.57 | Instantiating formula (2) with all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_5_5) = 0, yields:
% 8.20/2.57 | (70) $false
% 8.20/2.57 |
% 8.20/2.57 |-The branch is then unsatisfiable
% 8.20/2.57 |-Branch two:
% 8.20/2.57 | (107) ~ (all_82_1_77 = 0) & distinct_points(all_0_4_4, all_0_5_5) = all_82_1_77
% 8.20/2.57 |
% 8.20/2.57 | Applying alpha-rule on (107) yields:
% 8.20/2.57 | (108) ~ (all_82_1_77 = 0)
% 8.20/2.57 | (109) distinct_points(all_0_4_4, all_0_5_5) = all_82_1_77
% 8.20/2.57 |
% 8.20/2.57 | Instantiating formula (7) with all_82_1_77, 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_82_1_77, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 8.20/2.57 | (110) all_82_1_77 = 0 | distinct_points(all_0_5_5, all_0_5_5) = 0
% 8.20/2.57 |
% 8.20/2.57 +-Applying beta-rule and splitting (110), into two cases.
% 8.20/2.57 |-Branch one:
% 8.20/2.57 | (75) distinct_points(all_0_5_5, all_0_5_5) = 0
% 8.20/2.57 |
% 8.20/2.57 | Instantiating formula (2) with all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_5_5) = 0, yields:
% 8.20/2.57 | (70) $false
% 8.20/2.57 |
% 8.20/2.57 |-The branch is then unsatisfiable
% 8.20/2.57 |-Branch two:
% 8.20/2.57 | (77) ~ (distinct_points(all_0_5_5, all_0_5_5) = 0)
% 8.20/2.57 | (103) all_82_1_77 = 0
% 8.20/2.57 |
% 8.20/2.57 | Equations (103) can reduce 108 to:
% 8.20/2.57 | (52) $false
% 8.20/2.57 |
% 8.20/2.57 |-The branch is then unsatisfiable
% 8.20/2.57 |-Branch two:
% 8.20/2.57 | (116) all_37_0_27 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0
% 8.20/2.57 |
% 8.20/2.57 | Applying alpha-rule on (116) yields:
% 8.20/2.57 | (61) all_37_0_27 = 0
% 8.20/2.57 | (118) apart_point_and_line(all_0_5_5, all_0_2_2) = 0
% 8.20/2.57 |
% 8.20/2.57 | Instantiating formula (19) 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:
% 8.20/2.57 | (119) ? [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))
% 8.20/2.57 |
% 8.20/2.57 | Instantiating (119) with all_82_0_80, all_82_1_81 yields:
% 8.20/2.57 | (120) (all_82_0_80 = 0 & all_82_1_81 = 0 & distinct_points(all_0_5_5, all_0_4_4) = 0 & distinct_points(all_0_5_5, all_0_5_5) = 0) | ( ~ (all_82_1_81 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_82_1_81)
% 8.20/2.57 |
% 8.20/2.57 +-Applying beta-rule and splitting (120), into two cases.
% 8.20/2.57 |-Branch one:
% 8.20/2.57 | (121) all_82_0_80 = 0 & all_82_1_81 = 0 & distinct_points(all_0_5_5, all_0_4_4) = 0 & distinct_points(all_0_5_5, all_0_5_5) = 0
% 8.20/2.57 |
% 8.20/2.57 | Applying alpha-rule on (121) yields:
% 8.20/2.57 | (122) all_82_0_80 = 0
% 8.20/2.57 | (123) all_82_1_81 = 0
% 8.20/2.57 | (31) distinct_points(all_0_5_5, all_0_4_4) = 0
% 8.20/2.58 | (75) distinct_points(all_0_5_5, all_0_5_5) = 0
% 8.20/2.58 |
% 8.20/2.58 | Instantiating formula (2) with all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_5_5) = 0, yields:
% 8.20/2.58 | (70) $false
% 8.20/2.58 |
% 8.20/2.58 |-The branch is then unsatisfiable
% 8.20/2.58 |-Branch two:
% 8.20/2.58 | (127) ~ (all_82_1_81 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_82_1_81
% 8.20/2.58 |
% 8.20/2.58 | Applying alpha-rule on (127) yields:
% 8.20/2.58 | (128) ~ (all_82_1_81 = 0)
% 8.20/2.58 | (129) distinct_points(all_0_5_5, all_0_4_4) = all_82_1_81
% 8.20/2.58 |
% 8.20/2.58 | Instantiating formula (35) with all_0_5_5, all_0_4_4, all_82_1_81, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_82_1_81, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 8.20/2.58 | (123) all_82_1_81 = 0
% 8.20/2.58 |
% 8.20/2.58 | Equations (123) can reduce 128 to:
% 8.20/2.58 | (52) $false
% 8.20/2.58 |
% 8.20/2.58 |-The branch is then unsatisfiable
% 8.20/2.58 |-Branch two:
% 8.20/2.58 | (132) ~ (distinct_lines(all_0_2_2, all_0_1_1) = 0)
% 8.20/2.58 | (51) all_0_0_0 = 0
% 8.20/2.58 |
% 8.20/2.58 | Equations (51) can reduce 44 to:
% 8.20/2.58 | (52) $false
% 8.20/2.58 |
% 8.20/2.58 |-The branch is then unsatisfiable
% 8.20/2.58 % SZS output end Proof for theBenchmark
% 8.20/2.58
% 8.20/2.58 1992ms
%------------------------------------------------------------------------------