TSTP Solution File: GEO226+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO226+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n009.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 03:48:58 EDT 2022
% Result : Theorem 4.22s 1.66s
% Output : Proof 6.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO226+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 10:19:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.50/0.57 ____ _
% 0.50/0.57 ___ / __ \_____(_)___ ________ __________
% 0.50/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.57
% 0.50/0.57 A Theorem Prover for First-Order Logic
% 0.50/0.57 (ePrincess v.1.0)
% 0.50/0.57
% 0.50/0.57 (c) Philipp Rümmer, 2009-2015
% 0.50/0.57 (c) Peter Backeman, 2014-2015
% 0.50/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.57 Bug reports to peter@backeman.se
% 0.50/0.57
% 0.50/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.57
% 0.50/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.50/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.55/0.90 Prover 0: Preprocessing ...
% 1.98/1.04 Prover 0: Warning: ignoring some quantifiers
% 2.16/1.06 Prover 0: Constructing countermodel ...
% 2.76/1.25 Prover 0: gave up
% 2.76/1.25 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.87/1.27 Prover 1: Preprocessing ...
% 3.30/1.38 Prover 1: Constructing countermodel ...
% 3.30/1.41 Prover 1: gave up
% 3.30/1.41 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.56/1.43 Prover 2: Preprocessing ...
% 4.04/1.57 Prover 2: Warning: ignoring some quantifiers
% 4.22/1.58 Prover 2: Constructing countermodel ...
% 4.22/1.65 Prover 2: proved (245ms)
% 4.22/1.66
% 4.22/1.66 No countermodel exists, formula is valid
% 4.22/1.66 % SZS status Theorem for theBenchmark
% 4.22/1.66
% 4.22/1.66 Generating proof ... Warning: ignoring some quantifiers
% 6.15/1.99 found it (size 56)
% 6.15/1.99
% 6.15/1.99 % SZS output start Proof for theBenchmark
% 6.15/1.99 Assumed formulas after preprocessing and simplification:
% 6.15/1.99 | (0) ? [v0] : ? [v1] : (line(v1) = 0 & line(v0) = 0 & convergent_lines(v0, v1) = 0 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v3, v5) = v7) | ~ (apart_point_and_line(v3, v4) = v6) | ~ (distinct_points(v2, v3) = 0) | ? [v8] : ((v8 = 0 & apart_point_and_line(v2, v5) = 0) | (v8 = 0 & apart_point_and_line(v2, v4) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v3, v5) = v7) | ~ (apart_point_and_line(v2, v5) = v6) | ~ (distinct_lines(v4, v5) = 0) | ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v4) = 0) | (v8 = 0 & apart_point_and_line(v2, v4) = 0) | ( ~ (v8 = 0) & distinct_points(v2, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v3, v5) = v7) | ~ (apart_point_and_line(v2, v4) = v6) | ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v4) = 0) | (v8 = 0 & apart_point_and_line(v2, v5) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8) | ( ~ (v8 = 0) & distinct_points(v2, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v3, v4) = v7) | ~ (apart_point_and_line(v2, v5) = v6) | ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v5) = 0) | (v8 = 0 & apart_point_and_line(v2, v4) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8) | ( ~ (v8 = 0) & distinct_points(v2, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v3, v4) = v7) | ~ (apart_point_and_line(v2, v4) = v6) | ~ (distinct_lines(v4, v5) = 0) | ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v5) = 0) | (v8 = 0 & apart_point_and_line(v2, v5) = 0) | ( ~ (v8 = 0) & distinct_points(v2, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (apart_point_and_line(v2, v5) = v7) | ~ (apart_point_and_line(v2, v4) = v6) | ~ (distinct_points(v2, v3) = 0) | ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v5) = 0) | (v8 = 0 & apart_point_and_line(v3, v4) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (apart_point_and_line(v4, v3) = v6) | ~ (distinct_points(v2, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & apart_point_and_line(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (apart_point_and_line(v2, v4) = v6) | ~ (distinct_lines(v3, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & apart_point_and_line(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (convergent_lines(v3, v4) = v6) | ~ (convergent_lines(v2, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & convergent_lines(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (convergent_lines(v2, v4) = v6) | ~ (distinct_lines(v3, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & convergent_lines(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_lines(v3, v4) = v6) | ~ (distinct_lines(v2, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_points(v3, v4) = v6) | ~ (distinct_points(v2, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & distinct_points(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apart_point_and_line(v4, v3) = v5) | ~ (apart_point_and_line(v2, v3) = 0) | distinct_points(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apart_point_and_line(v2, v4) = v5) | ~ (apart_point_and_line(v2, v3) = 0) | distinct_lines(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apart_point_and_line(v2, v3) = 0) | ~ (distinct_lines(v3, v4) = v5) | apart_point_and_line(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apart_point_and_line(v2, v3) = 0) | ~ (distinct_points(v2, v4) = v5) | apart_point_and_line(v4, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (convergent_lines(v3, v4) = v5) | ~ (convergent_lines(v2, v3) = 0) | convergent_lines(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (convergent_lines(v2, v4) = v5) | ~ (convergent_lines(v2, v3) = 0) | convergent_lines(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (convergent_lines(v2, v4) = v5) | ~ (convergent_lines(v2, v3) = 0) | distinct_lines(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (convergent_lines(v2, v3) = 0) | ~ (distinct_lines(v3, v4) = v5) | convergent_lines(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (distinct_lines(v3, v4) = v5) | ~ (distinct_lines(v2, v3) = 0) | distinct_lines(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (distinct_lines(v2, v4) = v5) | ~ (distinct_lines(v2, v3) = 0) | distinct_lines(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (distinct_points(v3, v4) = v5) | ~ (distinct_points(v2, v3) = 0) | distinct_points(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (distinct_points(v2, v4) = v5) | ~ (distinct_points(v2, v3) = 0) | distinct_points(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (orthogonal_through_point(v5, v4) = v3) | ~ (orthogonal_through_point(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (parallel_through_point(v5, v4) = v3) | ~ (parallel_through_point(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (intersection_point(v5, v4) = v3) | ~ (intersection_point(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (line_connecting(v5, v4) = v3) | ~ (line_connecting(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (apart_point_and_line(v5, v4) = v3) | ~ (apart_point_and_line(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (convergent_lines(v5, v4) = v3) | ~ (convergent_lines(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (distinct_lines(v5, v4) = v3) | ~ (distinct_lines(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (distinct_points(v5, v4) = v3) | ~ (distinct_points(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (distinct_lines(v4, v5) = 0) | ~ (distinct_points(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v3, v5) = 0) | (v6 = 0 & apart_point_and_line(v3, v4) = 0) | (v6 = 0 & apart_point_and_line(v2, v5) = 0) | (v6 = 0 & apart_point_and_line(v2, v4) = 0))) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (point(v4) = v3) | ~ (point(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (line(v4) = v3) | ~ (line(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (orthogonal_through_point(v2, v3) = v4) | ? [v5] : ((v5 = 0 & line(v4) = 0) | ( ~ (v5 = 0) & point(v3) = v5) | ( ~ (v5 = 0) & line(v2) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (parallel_through_point(v2, v3) = v4) | ? [v5] : ((v5 = 0 & line(v4) = 0) | ( ~ (v5 = 0) & point(v3) = v5) | ( ~ (v5 = 0) & line(v2) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v2, v3) = v4) | ? [v5] : ((v5 = 0 & point(v4) = 0) | ( ~ (v5 = 0) & line(v3) = v5) | ( ~ (v5 = 0) & line(v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & apart_point_and_line(v4, v3) = v5) | ( ~ (v5 = 0) & convergent_lines(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & apart_point_and_line(v4, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v2, v3) = v4) | ? [v5] : ((v5 = 0 & line(v4) = 0) | ( ~ (v5 = 0) & point(v3) = v5) | ( ~ (v5 = 0) & point(v2) = v5) | ( ~ (v5 = 0) & distinct_points(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & apart_point_and_line(v3, v4) = v5) | ( ~ (v5 = 0) & distinct_points(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & apart_point_and_line(v2, v4) = v5) | ( ~ (v5 = 0) & distinct_points(v2, v3) = v5))) & ! [v2] : ! [v3] : (v3 = 0 | ~ (point(v2) = v3)) & ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | apart_point_and_line(v2, v0) = 0) & ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v0) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v2] : ! [v3] : ( ~ (convergent_lines(v2, v3) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & intersection_point(v2, v3) = v4 & apart_point_and_line(v4, v3) = v5)) & ! [v2] : ! [v3] : ( ~ (convergent_lines(v2, v3) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & intersection_point(v2, v3) = v4 & apart_point_and_line(v4, v2) = v5)) & ! [v2] : ! [v3] : ( ~ (convergent_lines(v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & point(v4) = 0 & intersection_point(v2, v3) = v4) | ( ~ (v4 = 0) & line(v3) = v4) | ( ~ (v4 = 0) & line(v2) = v4))) & ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v3) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & line_connecting(v2, v3) = v4 & apart_point_and_line(v3, v4) = v5)) & ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v3) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & line_connecting(v2, v3) = v4 & apart_point_and_line(v2, v4) = v5)) & ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & line(v4) = 0 & line_connecting(v2, v3) = v4) | ( ~ (v4 = 0) & point(v3) = v4) | ( ~ (v4 = 0) & point(v2) = v4))) & ! [v2] : ~ (convergent_lines(v2, v2) = 0) & ! [v2] : ~ (distinct_lines(v2, v2) = 0) & ! [v2] : ~ (distinct_points(v2, v2) = 0) & ? [v2] : ? [v3] : ? [v4] : orthogonal_through_point(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : parallel_through_point(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : intersection_point(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : line_connecting(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : apart_point_and_line(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : convergent_lines(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : distinct_lines(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : distinct_points(v3, v2) = v4 & ? [v2] : ? [v3] : point(v2) = v3 & ? [v2] : ? [v3] : line(v2) = v3)
% 6.15/2.04 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 6.15/2.04 | (1) line(all_0_0_0) = 0 & line(all_0_1_1) = 0 & convergent_lines(all_0_1_1, all_0_0_0) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (point(v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (apart_point_and_line(v0, all_0_0_0) = v1) | apart_point_and_line(v0, all_0_1_1) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (apart_point_and_line(v0, all_0_1_1) = v1) | apart_point_and_line(v0, all_0_0_0) = 0) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2))) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 & ? [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 & ? [v0] : ? [v1] : point(v0) = v1 & ? [v0] : ? [v1] : line(v0) = v1
% 6.48/2.06 |
% 6.48/2.06 | Applying alpha-rule on (1) yields:
% 6.48/2.06 | (2) ! [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)))
% 6.48/2.06 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0)
% 6.48/2.07 | (4) ! [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)))
% 6.48/2.07 | (5) ! [v0] : ! [v1] : (v1 = 0 | ~ (point(v0) = v1))
% 6.48/2.07 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 6.48/2.07 | (7) ! [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)
% 6.48/2.07 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 6.48/2.07 | (9) ? [v0] : ? [v1] : line(v0) = v1
% 6.48/2.07 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 6.48/2.07 | (11) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 6.48/2.07 | (12) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 6.48/2.07 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3)))
% 6.48/2.07 | (14) ! [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))
% 6.48/2.07 | (15) ! [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)
% 6.48/2.07 | (16) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2)))
% 6.48/2.07 | (17) ! [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)))
% 6.48/2.07 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 6.48/2.07 | (19) ! [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))
% 6.48/2.07 | (20) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 6.48/2.07 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 6.48/2.07 | (22) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 6.48/2.07 | (23) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 6.48/2.07 | (24) ! [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))
% 6.48/2.07 | (25) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 6.48/2.07 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 6.48/2.07 | (27) ? [v0] : ? [v1] : point(v0) = v1
% 6.48/2.07 | (28) line(all_0_0_0) = 0
% 6.48/2.07 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 6.48/2.07 | (30) ! [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))
% 6.48/2.07 | (31) ! [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)
% 6.48/2.07 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 6.48/2.07 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 6.48/2.08 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 6.48/2.08 | (35) ! [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)))
% 6.48/2.08 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 6.48/2.08 | (37) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 6.48/2.08 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 6.48/2.08 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 6.48/2.08 | (40) ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2
% 6.48/2.08 | (41) ! [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)))
% 6.48/2.08 | (42) ! [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))
% 6.48/2.08 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 6.48/2.08 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 6.48/2.08 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 6.48/2.08 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 6.48/2.08 | (47) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2)))
% 6.48/2.08 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0))
% 6.48/2.08 | (49) ! [v0] : ! [v1] : (v1 = 0 | ~ (apart_point_and_line(v0, all_0_1_1) = v1) | apart_point_and_line(v0, all_0_0_0) = 0)
% 6.48/2.08 | (50) ! [v0] : ! [v1] : (v1 = 0 | ~ (apart_point_and_line(v0, all_0_0_0) = v1) | apart_point_and_line(v0, all_0_1_1) = 0)
% 6.48/2.08 | (51) ! [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)))
% 6.48/2.08 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 6.48/2.08 | (53) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 6.48/2.08 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 6.48/2.08 | (55) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 6.48/2.08 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 6.48/2.08 | (57) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 6.48/2.08 | (58) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 6.48/2.09 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 6.48/2.09 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3)))
% 6.48/2.09 | (61) convergent_lines(all_0_1_1, all_0_0_0) = 0
% 6.48/2.09 | (62) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 6.48/2.09 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 6.48/2.09 | (64) ! [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)))
% 6.48/2.09 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 6.48/2.09 | (66) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2
% 6.48/2.09 | (67) line(all_0_1_1) = 0
% 6.48/2.09 | (68) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 6.48/2.09 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 6.48/2.09 |
% 6.48/2.09 | Instantiating formula (37) with all_0_0_0, all_0_1_1 and discharging atoms convergent_lines(all_0_1_1, all_0_0_0) = 0, yields:
% 6.48/2.09 | (70) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_1_1, all_0_0_0) = v0 & apart_point_and_line(v0, all_0_0_0) = v1)
% 6.48/2.09 |
% 6.48/2.09 | Instantiating formula (25) with all_0_0_0, all_0_1_1 and discharging atoms convergent_lines(all_0_1_1, all_0_0_0) = 0, yields:
% 6.48/2.09 | (71) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_1_1, all_0_0_0) = v0 & apart_point_and_line(v0, all_0_1_1) = v1)
% 6.48/2.09 |
% 6.48/2.09 | Instantiating formula (47) with all_0_0_0, all_0_1_1 and discharging atoms convergent_lines(all_0_1_1, all_0_0_0) = 0, yields:
% 6.48/2.09 | (72) ? [v0] : ? [v1] : ((v1 = 0 & point(v0) = 0 & intersection_point(all_0_1_1, all_0_0_0) = v0) | ( ~ (v0 = 0) & line(all_0_0_0) = v0) | ( ~ (v0 = 0) & line(all_0_1_1) = v0))
% 6.48/2.09 |
% 6.48/2.09 | Instantiating (72) with all_32_0_30, all_32_1_31 yields:
% 6.48/2.09 | (73) (all_32_0_30 = 0 & point(all_32_1_31) = 0 & intersection_point(all_0_1_1, all_0_0_0) = all_32_1_31) | ( ~ (all_32_1_31 = 0) & line(all_0_0_0) = all_32_1_31) | ( ~ (all_32_1_31 = 0) & line(all_0_1_1) = all_32_1_31)
% 6.48/2.09 |
% 6.48/2.09 | Instantiating (71) with all_33_0_32, all_33_1_33 yields:
% 6.48/2.09 | (74) ~ (all_33_0_32 = 0) & intersection_point(all_0_1_1, all_0_0_0) = all_33_1_33 & apart_point_and_line(all_33_1_33, all_0_1_1) = all_33_0_32
% 6.48/2.09 |
% 6.48/2.09 | Applying alpha-rule on (74) yields:
% 6.48/2.09 | (75) ~ (all_33_0_32 = 0)
% 6.48/2.09 | (76) intersection_point(all_0_1_1, all_0_0_0) = all_33_1_33
% 6.48/2.09 | (77) apart_point_and_line(all_33_1_33, all_0_1_1) = all_33_0_32
% 6.48/2.09 |
% 6.48/2.09 | Instantiating (70) with all_35_0_34, all_35_1_35 yields:
% 6.48/2.09 | (78) ~ (all_35_0_34 = 0) & intersection_point(all_0_1_1, all_0_0_0) = all_35_1_35 & apart_point_and_line(all_35_1_35, all_0_0_0) = all_35_0_34
% 6.48/2.09 |
% 6.48/2.09 | Applying alpha-rule on (78) yields:
% 6.48/2.09 | (79) ~ (all_35_0_34 = 0)
% 6.48/2.09 | (80) intersection_point(all_0_1_1, all_0_0_0) = all_35_1_35
% 6.48/2.09 | (81) apart_point_and_line(all_35_1_35, all_0_0_0) = all_35_0_34
% 6.48/2.09 |
% 6.48/2.09 +-Applying beta-rule and splitting (73), into two cases.
% 6.48/2.09 |-Branch one:
% 6.48/2.09 | (82) (all_32_0_30 = 0 & point(all_32_1_31) = 0 & intersection_point(all_0_1_1, all_0_0_0) = all_32_1_31) | ( ~ (all_32_1_31 = 0) & line(all_0_0_0) = all_32_1_31)
% 6.48/2.09 |
% 6.48/2.09 +-Applying beta-rule and splitting (82), into two cases.
% 6.48/2.09 |-Branch one:
% 6.48/2.09 | (83) all_32_0_30 = 0 & point(all_32_1_31) = 0 & intersection_point(all_0_1_1, all_0_0_0) = all_32_1_31
% 6.48/2.09 |
% 6.48/2.09 | Applying alpha-rule on (83) yields:
% 6.48/2.09 | (84) all_32_0_30 = 0
% 6.48/2.09 | (85) point(all_32_1_31) = 0
% 6.48/2.09 | (86) intersection_point(all_0_1_1, all_0_0_0) = all_32_1_31
% 6.48/2.09 |
% 6.48/2.09 | Instantiating formula (54) with all_0_1_1, all_0_0_0, all_33_1_33, all_35_1_35 and discharging atoms intersection_point(all_0_1_1, all_0_0_0) = all_35_1_35, intersection_point(all_0_1_1, all_0_0_0) = all_33_1_33, yields:
% 6.48/2.09 | (87) all_35_1_35 = all_33_1_33
% 6.48/2.09 |
% 6.48/2.09 | Instantiating formula (54) with all_0_1_1, all_0_0_0, all_32_1_31, all_35_1_35 and discharging atoms intersection_point(all_0_1_1, all_0_0_0) = all_35_1_35, intersection_point(all_0_1_1, all_0_0_0) = all_32_1_31, yields:
% 6.48/2.10 | (88) all_35_1_35 = all_32_1_31
% 6.48/2.10 |
% 6.48/2.10 | Combining equations (88,87) yields a new equation:
% 6.48/2.10 | (89) all_33_1_33 = all_32_1_31
% 6.48/2.10 |
% 6.48/2.10 | Combining equations (89,87) yields a new equation:
% 6.48/2.10 | (88) all_35_1_35 = all_32_1_31
% 6.48/2.10 |
% 6.48/2.10 | From (88) and (81) follows:
% 6.48/2.10 | (91) apart_point_and_line(all_32_1_31, all_0_0_0) = all_35_0_34
% 6.48/2.10 |
% 6.48/2.10 | From (89) and (77) follows:
% 6.48/2.10 | (92) apart_point_and_line(all_32_1_31, all_0_1_1) = all_33_0_32
% 6.48/2.10 |
% 6.48/2.10 | Instantiating formula (64) with all_35_0_34, all_35_0_34, all_0_0_0, all_0_0_0, all_32_1_31, all_32_1_31 and discharging atoms apart_point_and_line(all_32_1_31, all_0_0_0) = all_35_0_34, yields:
% 6.48/2.10 | (93) all_35_0_34 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_32_1_31, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_32_1_31, all_32_1_31) = v0))
% 6.48/2.10 |
% 6.48/2.10 | Instantiating formula (50) with all_35_0_34, all_32_1_31 and discharging atoms apart_point_and_line(all_32_1_31, all_0_0_0) = all_35_0_34, yields:
% 6.48/2.10 | (94) all_35_0_34 = 0 | apart_point_and_line(all_32_1_31, all_0_1_1) = 0
% 6.48/2.10 |
% 6.48/2.10 | Instantiating formula (64) with all_33_0_32, all_35_0_34, all_0_1_1, all_0_0_0, all_32_1_31, all_32_1_31 and discharging atoms apart_point_and_line(all_32_1_31, all_0_0_0) = all_35_0_34, apart_point_and_line(all_32_1_31, all_0_1_1) = all_33_0_32, yields:
% 6.48/2.10 | (95) all_35_0_34 = 0 | all_33_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_32_1_31, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_32_1_31, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_32_1_31, all_32_1_31) = v0))
% 6.48/2.10 |
% 6.48/2.10 | Instantiating formula (64) with all_35_0_34, all_33_0_32, all_0_0_0, all_0_1_1, all_32_1_31, all_32_1_31 and discharging atoms apart_point_and_line(all_32_1_31, all_0_0_0) = all_35_0_34, apart_point_and_line(all_32_1_31, all_0_1_1) = all_33_0_32, yields:
% 6.48/2.10 | (96) all_35_0_34 = 0 | all_33_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_32_1_31, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_32_1_31, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_32_1_31, all_32_1_31) = v0))
% 6.48/2.10 |
% 6.48/2.10 | Instantiating formula (64) with all_33_0_32, all_33_0_32, all_0_1_1, all_0_1_1, all_32_1_31, all_32_1_31 and discharging atoms apart_point_and_line(all_32_1_31, all_0_1_1) = all_33_0_32, yields:
% 6.48/2.10 | (97) all_33_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_32_1_31, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_32_1_31, all_32_1_31) = v0))
% 6.48/2.10 |
% 6.48/2.10 +-Applying beta-rule and splitting (94), into two cases.
% 6.48/2.10 |-Branch one:
% 6.48/2.10 | (98) apart_point_and_line(all_32_1_31, all_0_1_1) = 0
% 6.48/2.10 |
% 6.48/2.10 +-Applying beta-rule and splitting (97), into two cases.
% 6.48/2.10 |-Branch one:
% 6.48/2.10 | (99) all_33_0_32 = 0
% 6.48/2.10 |
% 6.48/2.10 | Equations (99) can reduce 75 to:
% 6.48/2.10 | (100) $false
% 6.48/2.10 |
% 6.48/2.10 |-The branch is then unsatisfiable
% 6.48/2.10 |-Branch two:
% 6.48/2.10 | (75) ~ (all_33_0_32 = 0)
% 6.48/2.10 | (102) ? [v0] : ((v0 = 0 & apart_point_and_line(all_32_1_31, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_32_1_31, all_32_1_31) = v0))
% 6.48/2.10 |
% 6.48/2.10 +-Applying beta-rule and splitting (93), into two cases.
% 6.48/2.10 |-Branch one:
% 6.48/2.10 | (103) all_35_0_34 = 0
% 6.48/2.10 |
% 6.48/2.10 | Equations (103) can reduce 79 to:
% 6.48/2.10 | (100) $false
% 6.48/2.10 |
% 6.48/2.10 |-The branch is then unsatisfiable
% 6.48/2.10 |-Branch two:
% 6.48/2.10 | (79) ~ (all_35_0_34 = 0)
% 6.48/2.10 | (106) ? [v0] : ((v0 = 0 & apart_point_and_line(all_32_1_31, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_32_1_31, all_32_1_31) = v0))
% 6.48/2.10 |
% 6.48/2.10 +-Applying beta-rule and splitting (95), into two cases.
% 6.48/2.10 |-Branch one:
% 6.48/2.10 | (103) all_35_0_34 = 0
% 6.48/2.10 |
% 6.48/2.10 | Equations (103) can reduce 79 to:
% 6.48/2.10 | (100) $false
% 6.48/2.10 |
% 6.48/2.10 |-The branch is then unsatisfiable
% 6.48/2.10 |-Branch two:
% 6.48/2.10 | (79) ~ (all_35_0_34 = 0)
% 6.48/2.10 | (110) all_33_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_32_1_31, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_32_1_31, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_32_1_31, all_32_1_31) = v0))
% 6.48/2.10 |
% 6.48/2.10 +-Applying beta-rule and splitting (96), into two cases.
% 6.48/2.10 |-Branch one:
% 6.48/2.11 | (103) all_35_0_34 = 0
% 6.48/2.11 |
% 6.48/2.11 | Equations (103) can reduce 79 to:
% 6.48/2.11 | (100) $false
% 6.48/2.11 |
% 6.48/2.11 |-The branch is then unsatisfiable
% 6.48/2.11 |-Branch two:
% 6.48/2.11 | (79) ~ (all_35_0_34 = 0)
% 6.48/2.11 | (114) all_33_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_32_1_31, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_32_1_31, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_32_1_31, all_32_1_31) = v0))
% 6.48/2.11 |
% 6.48/2.11 +-Applying beta-rule and splitting (110), into two cases.
% 6.48/2.11 |-Branch one:
% 6.48/2.11 | (99) all_33_0_32 = 0
% 6.48/2.11 |
% 6.48/2.11 | Equations (99) can reduce 75 to:
% 6.48/2.11 | (100) $false
% 6.70/2.11 |
% 6.70/2.11 |-The branch is then unsatisfiable
% 6.70/2.11 |-Branch two:
% 6.70/2.11 | (75) ~ (all_33_0_32 = 0)
% 6.70/2.11 | (118) ? [v0] : ((v0 = 0 & apart_point_and_line(all_32_1_31, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_32_1_31, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_32_1_31, all_32_1_31) = v0))
% 6.70/2.11 |
% 6.70/2.11 +-Applying beta-rule and splitting (114), into two cases.
% 6.70/2.11 |-Branch one:
% 6.70/2.11 | (99) all_33_0_32 = 0
% 6.70/2.11 |
% 6.70/2.11 | Equations (99) can reduce 75 to:
% 6.70/2.11 | (100) $false
% 6.70/2.11 |
% 6.70/2.11 |-The branch is then unsatisfiable
% 6.70/2.11 |-Branch two:
% 6.70/2.11 | (75) ~ (all_33_0_32 = 0)
% 6.70/2.11 | (122) ? [v0] : ((v0 = 0 & apart_point_and_line(all_32_1_31, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_32_1_31, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_32_1_31, all_32_1_31) = v0))
% 6.70/2.11 |
% 6.70/2.11 | Instantiating formula (45) with all_32_1_31, all_0_1_1, 0, all_33_0_32 and discharging atoms apart_point_and_line(all_32_1_31, all_0_1_1) = all_33_0_32, apart_point_and_line(all_32_1_31, all_0_1_1) = 0, yields:
% 6.70/2.11 | (99) all_33_0_32 = 0
% 6.70/2.11 |
% 6.70/2.11 | Equations (99) can reduce 75 to:
% 6.70/2.11 | (100) $false
% 6.70/2.11 |
% 6.70/2.11 |-The branch is then unsatisfiable
% 6.70/2.11 |-Branch two:
% 6.70/2.11 | (125) ~ (apart_point_and_line(all_32_1_31, all_0_1_1) = 0)
% 6.70/2.11 | (103) all_35_0_34 = 0
% 6.70/2.11 |
% 6.70/2.11 | Equations (103) can reduce 79 to:
% 6.70/2.11 | (100) $false
% 6.70/2.11 |
% 6.70/2.11 |-The branch is then unsatisfiable
% 6.70/2.11 |-Branch two:
% 6.70/2.11 | (128) ~ (all_32_1_31 = 0) & line(all_0_0_0) = all_32_1_31
% 6.70/2.11 |
% 6.70/2.11 | Applying alpha-rule on (128) yields:
% 6.70/2.11 | (129) ~ (all_32_1_31 = 0)
% 6.70/2.11 | (130) line(all_0_0_0) = all_32_1_31
% 6.70/2.11 |
% 6.70/2.11 | Instantiating formula (52) with all_0_0_0, all_32_1_31, 0 and discharging atoms line(all_0_0_0) = all_32_1_31, line(all_0_0_0) = 0, yields:
% 6.70/2.11 | (131) all_32_1_31 = 0
% 6.70/2.11 |
% 6.70/2.11 | Equations (131) can reduce 129 to:
% 6.70/2.11 | (100) $false
% 6.70/2.11 |
% 6.70/2.11 |-The branch is then unsatisfiable
% 6.70/2.11 |-Branch two:
% 6.70/2.11 | (133) ~ (all_32_1_31 = 0) & line(all_0_1_1) = all_32_1_31
% 6.70/2.11 |
% 6.70/2.11 | Applying alpha-rule on (133) yields:
% 6.70/2.11 | (129) ~ (all_32_1_31 = 0)
% 6.70/2.11 | (135) line(all_0_1_1) = all_32_1_31
% 6.70/2.11 |
% 6.70/2.11 | Instantiating formula (52) with all_0_1_1, all_32_1_31, 0 and discharging atoms line(all_0_1_1) = all_32_1_31, line(all_0_1_1) = 0, yields:
% 6.70/2.11 | (131) all_32_1_31 = 0
% 6.70/2.11 |
% 6.70/2.11 | Equations (131) can reduce 129 to:
% 6.70/2.11 | (100) $false
% 6.70/2.11 |
% 6.70/2.11 |-The branch is then unsatisfiable
% 6.70/2.11 % SZS output end Proof for theBenchmark
% 6.70/2.11
% 6.70/2.11 1530ms
%------------------------------------------------------------------------------