TSTP Solution File: GEO204+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO204+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.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 03:48:40 EDT 2022
% Result : Theorem 3.99s 1.68s
% Output : Proof 6.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO204+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 05:41:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.56/0.60 ____ _
% 0.56/0.60 ___ / __ \_____(_)___ ________ __________
% 0.56/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.56/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.56/0.60
% 0.56/0.60 A Theorem Prover for First-Order Logic
% 0.56/0.60 (ePrincess v.1.0)
% 0.56/0.60
% 0.56/0.60 (c) Philipp Rümmer, 2009-2015
% 0.56/0.60 (c) Peter Backeman, 2014-2015
% 0.56/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.60 Bug reports to peter@backeman.se
% 0.56/0.60
% 0.56/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.60
% 0.56/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.58/0.96 Prover 0: Preprocessing ...
% 1.94/1.09 Prover 0: Warning: ignoring some quantifiers
% 1.94/1.11 Prover 0: Constructing countermodel ...
% 2.40/1.23 Prover 0: gave up
% 2.40/1.23 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.40/1.26 Prover 1: Preprocessing ...
% 2.72/1.35 Prover 1: Constructing countermodel ...
% 2.94/1.42 Prover 1: gave up
% 2.94/1.42 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.94/1.44 Prover 2: Preprocessing ...
% 3.56/1.55 Prover 2: Warning: ignoring some quantifiers
% 3.56/1.56 Prover 2: Constructing countermodel ...
% 3.99/1.68 Prover 2: proved (260ms)
% 3.99/1.68
% 3.99/1.68 No countermodel exists, formula is valid
% 3.99/1.68 % SZS status Theorem for theBenchmark
% 3.99/1.68
% 3.99/1.68 Generating proof ... Warning: ignoring some quantifiers
% 5.58/2.06 found it (size 72)
% 5.58/2.06
% 5.58/2.06 % SZS output start Proof for theBenchmark
% 5.58/2.06 Assumed formulas after preprocessing and simplification:
% 5.58/2.06 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v3 = 0) & distinct_points(v1, v2) = v3 & distinct_points(v0, v1) = 0 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = 0 | ~ (apart_point_and_line(v9, v11) = v13) | ~ (apart_point_and_line(v9, v10) = v12) | ~ (distinct_points(v8, v9) = 0) | ? [v14] : ((v14 = 0 & apart_point_and_line(v8, v11) = 0) | (v14 = 0 & apart_point_and_line(v8, v10) = 0) | ( ~ (v14 = 0) & distinct_lines(v10, v11) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = 0 | ~ (apart_point_and_line(v9, v11) = v13) | ~ (apart_point_and_line(v8, v11) = v12) | ~ (distinct_lines(v10, v11) = 0) | ? [v14] : ((v14 = 0 & apart_point_and_line(v9, v10) = 0) | (v14 = 0 & apart_point_and_line(v8, v10) = 0) | ( ~ (v14 = 0) & distinct_points(v8, v9) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = 0 | ~ (apart_point_and_line(v9, v11) = v13) | ~ (apart_point_and_line(v8, v10) = v12) | ? [v14] : ((v14 = 0 & apart_point_and_line(v9, v10) = 0) | (v14 = 0 & apart_point_and_line(v8, v11) = 0) | ( ~ (v14 = 0) & distinct_lines(v10, v11) = v14) | ( ~ (v14 = 0) & distinct_points(v8, v9) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = 0 | ~ (apart_point_and_line(v9, v10) = v13) | ~ (apart_point_and_line(v8, v11) = v12) | ? [v14] : ((v14 = 0 & apart_point_and_line(v9, v11) = 0) | (v14 = 0 & apart_point_and_line(v8, v10) = 0) | ( ~ (v14 = 0) & distinct_lines(v10, v11) = v14) | ( ~ (v14 = 0) & distinct_points(v8, v9) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = 0 | ~ (apart_point_and_line(v9, v10) = v13) | ~ (apart_point_and_line(v8, v10) = v12) | ~ (distinct_lines(v10, v11) = 0) | ? [v14] : ((v14 = 0 & apart_point_and_line(v9, v11) = 0) | (v14 = 0 & apart_point_and_line(v8, v11) = 0) | ( ~ (v14 = 0) & distinct_points(v8, v9) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = 0 | ~ (apart_point_and_line(v8, v11) = v13) | ~ (apart_point_and_line(v8, v10) = v12) | ~ (distinct_points(v8, v9) = 0) | ? [v14] : ((v14 = 0 & apart_point_and_line(v9, v11) = 0) | (v14 = 0 & apart_point_and_line(v9, v10) = 0) | ( ~ (v14 = 0) & distinct_lines(v10, v11) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (apart_point_and_line(v10, v9) = v12) | ~ (distinct_points(v8, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & apart_point_and_line(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (apart_point_and_line(v8, v10) = v12) | ~ (distinct_lines(v9, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & apart_point_and_line(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (convergent_lines(v9, v10) = v12) | ~ (convergent_lines(v8, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & convergent_lines(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (distinct_lines(v9, v10) = v12) | ~ (distinct_lines(v8, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & distinct_lines(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (distinct_points(v9, v10) = v12) | ~ (distinct_points(v8, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & distinct_points(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (intersection_point(v8, v9) = v11) | ~ (distinct_points(v10, v11) = v12) | ? [v13] : ? [v14] : (( ~ (v14 = 0) & ~ (v13 = 0) & apart_point_and_line(v10, v9) = v14 & apart_point_and_line(v10, v8) = v13) | ( ~ (v13 = 0) & convergent_lines(v8, v9) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (apart_point_and_line(v10, v9) = v11) | ~ (apart_point_and_line(v8, v9) = 0) | distinct_points(v8, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (apart_point_and_line(v8, v10) = v11) | ~ (apart_point_and_line(v8, v9) = 0) | distinct_lines(v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (apart_point_and_line(v8, v9) = 0) | ~ (distinct_lines(v9, v10) = v11) | apart_point_and_line(v8, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (apart_point_and_line(v8, v9) = 0) | ~ (distinct_points(v8, v10) = v11) | apart_point_and_line(v10, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (convergent_lines(v9, v10) = v11) | ~ (convergent_lines(v8, v9) = 0) | convergent_lines(v8, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (convergent_lines(v8, v10) = v11) | ~ (convergent_lines(v8, v9) = 0) | convergent_lines(v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (distinct_lines(v9, v10) = v11) | ~ (distinct_lines(v8, v9) = 0) | distinct_lines(v8, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (distinct_lines(v8, v10) = v11) | ~ (distinct_lines(v8, v9) = 0) | distinct_lines(v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (distinct_points(v9, v10) = v11) | ~ (distinct_points(v8, v9) = 0) | distinct_points(v8, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (distinct_points(v8, v10) = v11) | ~ (distinct_points(v8, v9) = 0) | distinct_points(v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (intersection_point(v11, v10) = v9) | ~ (intersection_point(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (line_connecting(v11, v10) = v9) | ~ (line_connecting(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (apart_point_and_line(v11, v10) = v9) | ~ (apart_point_and_line(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (convergent_lines(v11, v10) = v9) | ~ (convergent_lines(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (distinct_lines(v11, v10) = v9) | ~ (distinct_lines(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (distinct_points(v11, v10) = v9) | ~ (distinct_points(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (line_connecting(v8, v9) = v11) | ~ (apart_point_and_line(v10, v11) = 0) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & distinct_points(v10, v9) = 0 & distinct_points(v10, v8) = 0) | ( ~ (v12 = 0) & distinct_points(v8, v9) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (distinct_lines(v10, v11) = 0) | ~ (distinct_points(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v9, v11) = 0) | (v12 = 0 & apart_point_and_line(v9, v10) = 0) | (v12 = 0 & apart_point_and_line(v8, v11) = 0) | (v12 = 0 & apart_point_and_line(v8, v10) = 0))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (distinct_lines(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11)) & ! [v8] : ! [v9] : ( ~ (convergent_lines(v8, v9) = 0) | distinct_lines(v8, v9) = 0) & ! [v8] : ~ (convergent_lines(v8, v8) = 0) & ! [v8] : ~ (distinct_lines(v8, v8) = 0) & ! [v8] : ~ (distinct_points(v8, v8) = 0) & ? [v8] : ? [v9] : ? [v10] : intersection_point(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : line_connecting(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : apart_point_and_line(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : convergent_lines(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : distinct_lines(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : distinct_points(v9, v8) = v10 & ((v7 = 0 & line_connecting(v0, v2) = v6 & line_connecting(v0, v1) = v5 & distinct_lines(v5, v6) = 0) | ( ~ (v4 = 0) & distinct_points(v0, v2) = v4)))
% 6.07/2.10 | 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, all_0_7_7 yields:
% 6.07/2.10 | (1) ~ (all_0_4_4 = 0) & distinct_points(all_0_6_6, all_0_5_5) = all_0_4_4 & distinct_points(all_0_7_7, all_0_6_6) = 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 & ((all_0_0_0 = 0 & line_connecting(all_0_7_7, all_0_5_5) = all_0_1_1 & line_connecting(all_0_7_7, all_0_6_6) = all_0_2_2 & distinct_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (all_0_3_3 = 0) & distinct_points(all_0_7_7, all_0_5_5) = all_0_3_3))
% 6.14/2.12 |
% 6.14/2.12 | Applying alpha-rule on (1) yields:
% 6.14/2.12 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 6.14/2.12 | (3) ! [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)))
% 6.14/2.12 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 6.14/2.12 | (5) ! [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)
% 6.14/2.12 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 6.14/2.12 | (7) ! [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)
% 6.14/2.12 | (8) ! [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)
% 6.14/2.12 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 6.14/2.12 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 6.14/2.12 | (11) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 6.14/2.12 | (12) ! [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))
% 6.14/2.12 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 6.14/2.12 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 6.14/2.12 | (15) ! [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)))
% 6.14/2.12 | (16) ! [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))
% 6.14/2.12 | (17) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 6.14/2.12 | (18) (all_0_0_0 = 0 & line_connecting(all_0_7_7, all_0_5_5) = all_0_1_1 & line_connecting(all_0_7_7, all_0_6_6) = all_0_2_2 & distinct_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (all_0_3_3 = 0) & distinct_points(all_0_7_7, all_0_5_5) = all_0_3_3)
% 6.14/2.12 | (19) ! [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)))
% 6.14/2.13 | (20) ! [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)))
% 6.14/2.13 | (21) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 6.14/2.13 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 6.14/2.13 | (23) ! [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)))
% 6.14/2.13 | (24) ! [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))
% 6.14/2.13 | (25) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 6.14/2.13 | (26) ~ (all_0_4_4 = 0)
% 6.14/2.13 | (27) distinct_points(all_0_7_7, all_0_6_6) = 0
% 6.14/2.13 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 6.14/2.13 | (29) ! [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))
% 6.14/2.13 | (30) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 6.14/2.13 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 6.14/2.13 | (32) ! [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))
% 6.14/2.13 | (33) distinct_points(all_0_6_6, all_0_5_5) = all_0_4_4
% 6.14/2.13 | (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)))
% 6.14/2.13 | (35) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 6.14/2.13 | (36) ! [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)
% 6.14/2.13 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 6.14/2.13 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 6.14/2.13 | (39) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0)
% 6.14/2.13 | (40) ! [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)))
% 6.14/2.14 | (41) ! [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)))
% 6.14/2.14 | (42) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 6.14/2.14 | (43) ! [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)))
% 6.14/2.14 | (44) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 6.14/2.14 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 6.14/2.14 | (46) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 6.14/2.14 |
% 6.14/2.14 | Instantiating formula (32) with all_0_4_4, all_0_4_4, all_0_5_5, all_0_6_6, all_0_6_6 and discharging atoms distinct_points(all_0_6_6, all_0_5_5) = all_0_4_4, yields:
% 6.14/2.14 | (47) all_0_4_4 = 0 | ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0)
% 6.14/2.14 |
% 6.14/2.14 | Instantiating formula (31) with all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms distinct_points(all_0_6_6, all_0_5_5) = all_0_4_4, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 6.14/2.14 | (48) all_0_4_4 = 0 | distinct_points(all_0_7_7, all_0_5_5) = 0
% 6.14/2.14 |
% 6.14/2.14 +-Applying beta-rule and splitting (18), into two cases.
% 6.14/2.14 |-Branch one:
% 6.14/2.14 | (49) all_0_0_0 = 0 & line_connecting(all_0_7_7, all_0_5_5) = all_0_1_1 & line_connecting(all_0_7_7, all_0_6_6) = all_0_2_2 & distinct_lines(all_0_2_2, all_0_1_1) = 0
% 6.14/2.14 |
% 6.14/2.14 | Applying alpha-rule on (49) yields:
% 6.14/2.14 | (50) all_0_0_0 = 0
% 6.14/2.14 | (51) line_connecting(all_0_7_7, all_0_5_5) = all_0_1_1
% 6.14/2.14 | (52) line_connecting(all_0_7_7, all_0_6_6) = all_0_2_2
% 6.14/2.14 | (53) distinct_lines(all_0_2_2, all_0_1_1) = 0
% 6.14/2.14 |
% 6.14/2.14 +-Applying beta-rule and splitting (48), into two cases.
% 6.14/2.14 |-Branch one:
% 6.14/2.14 | (54) distinct_points(all_0_7_7, all_0_5_5) = 0
% 6.14/2.14 |
% 6.14/2.14 +-Applying beta-rule and splitting (47), into two cases.
% 6.14/2.14 |-Branch one:
% 6.14/2.14 | (55) all_0_4_4 = 0
% 6.14/2.14 |
% 6.14/2.14 | Equations (55) can reduce 26 to:
% 6.14/2.14 | (56) $false
% 6.14/2.14 |
% 6.14/2.14 |-The branch is then unsatisfiable
% 6.14/2.14 |-Branch two:
% 6.14/2.14 | (26) ~ (all_0_4_4 = 0)
% 6.14/2.14 | (58) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0)
% 6.14/2.14 |
% 6.14/2.14 | Instantiating formula (34) with all_0_1_1, all_0_2_2, all_0_5_5, all_0_7_7 and discharging atoms distinct_lines(all_0_2_2, all_0_1_1) = 0, distinct_points(all_0_7_7, all_0_5_5) = 0, yields:
% 6.14/2.14 | (59) ? [v0] : ((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) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0))
% 6.14/2.14 |
% 6.14/2.14 | Instantiating (59) with all_37_0_27 yields:
% 6.14/2.14 | (60) (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) | (all_37_0_27 = 0 & apart_point_and_line(all_0_7_7, all_0_1_1) = 0) | (all_37_0_27 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0)
% 6.14/2.15 |
% 6.14/2.15 +-Applying beta-rule and splitting (60), into two cases.
% 6.14/2.15 |-Branch one:
% 6.14/2.15 | (61) (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) | (all_37_0_27 = 0 & apart_point_and_line(all_0_7_7, all_0_1_1) = 0)
% 6.14/2.15 |
% 6.14/2.15 +-Applying beta-rule and splitting (61), into two cases.
% 6.14/2.15 |-Branch one:
% 6.14/2.15 | (62) (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)
% 6.14/2.15 |
% 6.14/2.15 +-Applying beta-rule and splitting (62), into two cases.
% 6.14/2.15 |-Branch one:
% 6.14/2.15 | (63) all_37_0_27 = 0 & apart_point_and_line(all_0_5_5, all_0_1_1) = 0
% 6.14/2.15 |
% 6.14/2.15 | Applying alpha-rule on (63) yields:
% 6.14/2.15 | (64) all_37_0_27 = 0
% 6.14/2.15 | (65) apart_point_and_line(all_0_5_5, all_0_1_1) = 0
% 6.14/2.15 |
% 6.14/2.15 | Instantiating formula (20) with all_0_1_1, all_0_5_5, all_0_5_5, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_5_5) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_1_1) = 0, yields:
% 6.14/2.15 | (66) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & distinct_points(all_0_5_5, all_0_5_5) = 0 & distinct_points(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_5_5) = v0))
% 6.14/2.15 |
% 6.14/2.15 | Instantiating (66) with all_46_0_29, all_46_1_30 yields:
% 6.14/2.15 | (67) (all_46_0_29 = 0 & all_46_1_30 = 0 & distinct_points(all_0_5_5, all_0_5_5) = 0 & distinct_points(all_0_5_5, all_0_7_7) = 0) | ( ~ (all_46_1_30 = 0) & distinct_points(all_0_7_7, all_0_5_5) = all_46_1_30)
% 6.14/2.15 |
% 6.14/2.15 +-Applying beta-rule and splitting (67), into two cases.
% 6.14/2.15 |-Branch one:
% 6.14/2.15 | (68) all_46_0_29 = 0 & all_46_1_30 = 0 & distinct_points(all_0_5_5, all_0_5_5) = 0 & distinct_points(all_0_5_5, all_0_7_7) = 0
% 6.14/2.15 |
% 6.14/2.15 | Applying alpha-rule on (68) yields:
% 6.14/2.15 | (69) all_46_0_29 = 0
% 6.14/2.15 | (70) all_46_1_30 = 0
% 6.14/2.15 | (71) distinct_points(all_0_5_5, all_0_5_5) = 0
% 6.14/2.15 | (72) distinct_points(all_0_5_5, all_0_7_7) = 0
% 6.14/2.15 |
% 6.14/2.15 | Instantiating formula (25) with all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_5_5) = 0, yields:
% 6.14/2.15 | (73) $false
% 6.14/2.15 |
% 6.14/2.15 |-The branch is then unsatisfiable
% 6.14/2.15 |-Branch two:
% 6.14/2.15 | (74) ~ (all_46_1_30 = 0) & distinct_points(all_0_7_7, all_0_5_5) = all_46_1_30
% 6.14/2.15 |
% 6.14/2.15 | Applying alpha-rule on (74) yields:
% 6.14/2.15 | (75) ~ (all_46_1_30 = 0)
% 6.14/2.15 | (76) distinct_points(all_0_7_7, all_0_5_5) = all_46_1_30
% 6.14/2.15 |
% 6.14/2.15 | Instantiating formula (4) with all_0_7_7, all_0_5_5, all_46_1_30, 0 and discharging atoms distinct_points(all_0_7_7, all_0_5_5) = all_46_1_30, distinct_points(all_0_7_7, all_0_5_5) = 0, yields:
% 6.14/2.15 | (70) all_46_1_30 = 0
% 6.14/2.15 |
% 6.14/2.15 | Equations (70) can reduce 75 to:
% 6.14/2.15 | (56) $false
% 6.14/2.15 |
% 6.14/2.15 |-The branch is then unsatisfiable
% 6.14/2.15 |-Branch two:
% 6.14/2.15 | (79) all_37_0_27 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0
% 6.14/2.15 |
% 6.14/2.15 | Applying alpha-rule on (79) yields:
% 6.14/2.15 | (64) all_37_0_27 = 0
% 6.14/2.15 | (81) apart_point_and_line(all_0_5_5, all_0_2_2) = 0
% 6.14/2.15 |
% 6.14/2.15 | Instantiating formula (20) with all_0_2_2, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_0_2_2, apart_point_and_line(all_0_5_5, all_0_2_2) = 0, yields:
% 6.14/2.16 | (82) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & distinct_points(all_0_5_5, all_0_6_6) = 0 & distinct_points(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 6.14/2.16 |
% 6.14/2.16 | Instantiating (82) with all_46_0_31, all_46_1_32 yields:
% 6.14/2.16 | (83) (all_46_0_31 = 0 & all_46_1_32 = 0 & distinct_points(all_0_5_5, all_0_6_6) = 0 & distinct_points(all_0_5_5, all_0_7_7) = 0) | ( ~ (all_46_1_32 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_46_1_32)
% 6.14/2.16 |
% 6.14/2.16 +-Applying beta-rule and splitting (83), into two cases.
% 6.14/2.16 |-Branch one:
% 6.14/2.16 | (84) all_46_0_31 = 0 & all_46_1_32 = 0 & distinct_points(all_0_5_5, all_0_6_6) = 0 & distinct_points(all_0_5_5, all_0_7_7) = 0
% 6.14/2.16 |
% 6.14/2.16 | Applying alpha-rule on (84) yields:
% 6.14/2.16 | (85) all_46_0_31 = 0
% 6.14/2.16 | (86) all_46_1_32 = 0
% 6.14/2.16 | (87) distinct_points(all_0_5_5, all_0_6_6) = 0
% 6.14/2.16 | (72) distinct_points(all_0_5_5, all_0_7_7) = 0
% 6.14/2.16 |
% 6.14/2.16 | Instantiating formula (31) with all_0_4_4, all_0_5_5, all_0_6_6, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_6_6) = 0, distinct_points(all_0_6_6, all_0_5_5) = all_0_4_4, yields:
% 6.14/2.16 | (89) all_0_4_4 = 0 | distinct_points(all_0_5_5, all_0_5_5) = 0
% 6.14/2.16 |
% 6.14/2.16 +-Applying beta-rule and splitting (89), into two cases.
% 6.14/2.16 |-Branch one:
% 6.14/2.16 | (71) distinct_points(all_0_5_5, all_0_5_5) = 0
% 6.14/2.16 |
% 6.14/2.16 | Instantiating formula (25) with all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_5_5) = 0, yields:
% 6.14/2.16 | (73) $false
% 6.14/2.16 |
% 6.14/2.16 |-The branch is then unsatisfiable
% 6.14/2.16 |-Branch two:
% 6.14/2.16 | (92) ~ (distinct_points(all_0_5_5, all_0_5_5) = 0)
% 6.14/2.16 | (55) all_0_4_4 = 0
% 6.14/2.16 |
% 6.14/2.16 | Equations (55) can reduce 26 to:
% 6.14/2.16 | (56) $false
% 6.14/2.16 |
% 6.14/2.16 |-The branch is then unsatisfiable
% 6.14/2.16 |-Branch two:
% 6.14/2.16 | (95) ~ (all_46_1_32 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_46_1_32
% 6.14/2.16 |
% 6.14/2.16 | Applying alpha-rule on (95) yields:
% 6.14/2.16 | (96) ~ (all_46_1_32 = 0)
% 6.14/2.16 | (97) distinct_points(all_0_7_7, all_0_6_6) = all_46_1_32
% 6.14/2.16 |
% 6.14/2.16 | Instantiating formula (4) with all_0_7_7, all_0_6_6, all_46_1_32, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_46_1_32, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 6.14/2.16 | (86) all_46_1_32 = 0
% 6.14/2.16 |
% 6.14/2.16 | Equations (86) can reduce 96 to:
% 6.14/2.16 | (56) $false
% 6.14/2.16 |
% 6.14/2.16 |-The branch is then unsatisfiable
% 6.14/2.16 |-Branch two:
% 6.14/2.16 | (100) all_37_0_27 = 0 & apart_point_and_line(all_0_7_7, all_0_1_1) = 0
% 6.14/2.16 |
% 6.14/2.16 | Applying alpha-rule on (100) yields:
% 6.14/2.16 | (64) all_37_0_27 = 0
% 6.14/2.16 | (102) apart_point_and_line(all_0_7_7, all_0_1_1) = 0
% 6.14/2.16 |
% 6.14/2.16 | Instantiating formula (20) with all_0_1_1, all_0_7_7, all_0_5_5, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_5_5) = all_0_1_1, apart_point_and_line(all_0_7_7, all_0_1_1) = 0, yields:
% 6.14/2.16 | (103) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & distinct_points(all_0_7_7, all_0_5_5) = 0 & distinct_points(all_0_7_7, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_5_5) = v0))
% 6.14/2.16 |
% 6.14/2.16 | Instantiating (103) with all_50_0_39, all_50_1_40 yields:
% 6.14/2.16 | (104) (all_50_0_39 = 0 & all_50_1_40 = 0 & distinct_points(all_0_7_7, all_0_5_5) = 0 & distinct_points(all_0_7_7, all_0_7_7) = 0) | ( ~ (all_50_1_40 = 0) & distinct_points(all_0_7_7, all_0_5_5) = all_50_1_40)
% 6.14/2.16 |
% 6.14/2.16 +-Applying beta-rule and splitting (104), into two cases.
% 6.14/2.16 |-Branch one:
% 6.14/2.16 | (105) all_50_0_39 = 0 & all_50_1_40 = 0 & distinct_points(all_0_7_7, all_0_5_5) = 0 & distinct_points(all_0_7_7, all_0_7_7) = 0
% 6.14/2.16 |
% 6.14/2.16 | Applying alpha-rule on (105) yields:
% 6.14/2.16 | (106) all_50_0_39 = 0
% 6.14/2.16 | (107) all_50_1_40 = 0
% 6.14/2.16 | (54) distinct_points(all_0_7_7, all_0_5_5) = 0
% 6.14/2.16 | (109) distinct_points(all_0_7_7, all_0_7_7) = 0
% 6.14/2.16 |
% 6.14/2.16 | Instantiating formula (25) with all_0_7_7 and discharging atoms distinct_points(all_0_7_7, all_0_7_7) = 0, yields:
% 6.14/2.16 | (73) $false
% 6.14/2.16 |
% 6.14/2.16 |-The branch is then unsatisfiable
% 6.14/2.16 |-Branch two:
% 6.14/2.16 | (111) ~ (all_50_1_40 = 0) & distinct_points(all_0_7_7, all_0_5_5) = all_50_1_40
% 6.14/2.16 |
% 6.14/2.16 | Applying alpha-rule on (111) yields:
% 6.14/2.16 | (112) ~ (all_50_1_40 = 0)
% 6.14/2.16 | (113) distinct_points(all_0_7_7, all_0_5_5) = all_50_1_40
% 6.14/2.16 |
% 6.14/2.16 | Instantiating formula (4) with all_0_7_7, all_0_5_5, all_50_1_40, 0 and discharging atoms distinct_points(all_0_7_7, all_0_5_5) = all_50_1_40, distinct_points(all_0_7_7, all_0_5_5) = 0, yields:
% 6.14/2.16 | (107) all_50_1_40 = 0
% 6.14/2.16 |
% 6.14/2.16 | Equations (107) can reduce 112 to:
% 6.14/2.16 | (56) $false
% 6.14/2.16 |
% 6.14/2.16 |-The branch is then unsatisfiable
% 6.14/2.16 |-Branch two:
% 6.14/2.16 | (116) all_37_0_27 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0
% 6.14/2.16 |
% 6.14/2.16 | Applying alpha-rule on (116) yields:
% 6.14/2.16 | (64) all_37_0_27 = 0
% 6.14/2.16 | (118) apart_point_and_line(all_0_7_7, all_0_2_2) = 0
% 6.14/2.16 |
% 6.14/2.16 | Instantiating formula (20) with all_0_2_2, all_0_7_7, all_0_6_6, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_0_2_2, apart_point_and_line(all_0_7_7, all_0_2_2) = 0, yields:
% 6.14/2.16 | (119) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & distinct_points(all_0_7_7, all_0_6_6) = 0 & distinct_points(all_0_7_7, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 6.14/2.17 |
% 6.14/2.17 | Instantiating (119) with all_50_0_43, all_50_1_44 yields:
% 6.14/2.17 | (120) (all_50_0_43 = 0 & all_50_1_44 = 0 & distinct_points(all_0_7_7, all_0_6_6) = 0 & distinct_points(all_0_7_7, all_0_7_7) = 0) | ( ~ (all_50_1_44 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_50_1_44)
% 6.14/2.17 |
% 6.14/2.17 +-Applying beta-rule and splitting (120), into two cases.
% 6.14/2.17 |-Branch one:
% 6.14/2.17 | (121) all_50_0_43 = 0 & all_50_1_44 = 0 & distinct_points(all_0_7_7, all_0_6_6) = 0 & distinct_points(all_0_7_7, all_0_7_7) = 0
% 6.14/2.17 |
% 6.14/2.17 | Applying alpha-rule on (121) yields:
% 6.14/2.17 | (122) all_50_0_43 = 0
% 6.14/2.17 | (123) all_50_1_44 = 0
% 6.14/2.17 | (27) distinct_points(all_0_7_7, all_0_6_6) = 0
% 6.14/2.17 | (109) distinct_points(all_0_7_7, all_0_7_7) = 0
% 6.14/2.17 |
% 6.14/2.17 | Instantiating formula (25) with all_0_7_7 and discharging atoms distinct_points(all_0_7_7, all_0_7_7) = 0, yields:
% 6.14/2.17 | (73) $false
% 6.14/2.17 |
% 6.14/2.17 |-The branch is then unsatisfiable
% 6.14/2.17 |-Branch two:
% 6.14/2.17 | (127) ~ (all_50_1_44 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_50_1_44
% 6.14/2.17 |
% 6.14/2.17 | Applying alpha-rule on (127) yields:
% 6.14/2.17 | (128) ~ (all_50_1_44 = 0)
% 6.14/2.17 | (129) distinct_points(all_0_7_7, all_0_6_6) = all_50_1_44
% 6.14/2.17 |
% 6.14/2.17 | Instantiating formula (4) with all_0_7_7, all_0_6_6, all_50_1_44, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_50_1_44, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 6.14/2.17 | (123) all_50_1_44 = 0
% 6.14/2.17 |
% 6.14/2.17 | Equations (123) can reduce 128 to:
% 6.14/2.17 | (56) $false
% 6.14/2.17 |
% 6.14/2.17 |-The branch is then unsatisfiable
% 6.14/2.17 |-Branch two:
% 6.14/2.17 | (132) ~ (distinct_points(all_0_7_7, all_0_5_5) = 0)
% 6.14/2.17 | (55) all_0_4_4 = 0
% 6.14/2.17 |
% 6.14/2.17 | Equations (55) can reduce 26 to:
% 6.14/2.17 | (56) $false
% 6.14/2.17 |
% 6.14/2.17 |-The branch is then unsatisfiable
% 6.14/2.17 |-Branch two:
% 6.14/2.17 | (135) ~ (all_0_3_3 = 0) & distinct_points(all_0_7_7, all_0_5_5) = all_0_3_3
% 6.14/2.17 |
% 6.14/2.17 | Applying alpha-rule on (135) yields:
% 6.14/2.17 | (136) ~ (all_0_3_3 = 0)
% 6.14/2.17 | (137) distinct_points(all_0_7_7, all_0_5_5) = all_0_3_3
% 6.14/2.17 |
% 6.14/2.17 +-Applying beta-rule and splitting (48), into two cases.
% 6.14/2.17 |-Branch one:
% 6.14/2.17 | (54) distinct_points(all_0_7_7, all_0_5_5) = 0
% 6.14/2.17 |
% 6.14/2.17 | Instantiating formula (4) with all_0_7_7, all_0_5_5, 0, all_0_3_3 and discharging atoms distinct_points(all_0_7_7, all_0_5_5) = all_0_3_3, distinct_points(all_0_7_7, all_0_5_5) = 0, yields:
% 6.14/2.17 | (139) all_0_3_3 = 0
% 6.14/2.17 |
% 6.14/2.17 | Equations (139) can reduce 136 to:
% 6.14/2.17 | (56) $false
% 6.14/2.17 |
% 6.14/2.17 |-The branch is then unsatisfiable
% 6.14/2.17 |-Branch two:
% 6.14/2.17 | (132) ~ (distinct_points(all_0_7_7, all_0_5_5) = 0)
% 6.14/2.17 | (55) all_0_4_4 = 0
% 6.14/2.17 |
% 6.14/2.17 | Equations (55) can reduce 26 to:
% 6.14/2.17 | (56) $false
% 6.14/2.17 |
% 6.14/2.17 |-The branch is then unsatisfiable
% 6.14/2.17 % SZS output end Proof for theBenchmark
% 6.14/2.17
% 6.14/2.17 1557ms
%------------------------------------------------------------------------------