TSTP Solution File: GEO203+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO203+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 03:48:38 EDT 2022
% Result : Theorem 20.60s 6.15s
% Output : Proof 21.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO203+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n012.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 06:11:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.47/0.59 ____ _
% 0.47/0.59 ___ / __ \_____(_)___ ________ __________
% 0.47/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.47/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.47/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.47/0.59
% 0.47/0.59 A Theorem Prover for First-Order Logic
% 0.47/0.59 (ePrincess v.1.0)
% 0.47/0.59
% 0.47/0.59 (c) Philipp Rümmer, 2009-2015
% 0.47/0.59 (c) Peter Backeman, 2014-2015
% 0.47/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.47/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.47/0.59 Bug reports to peter@backeman.se
% 0.47/0.59
% 0.47/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.47/0.59
% 0.47/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.39/0.92 Prover 0: Preprocessing ...
% 1.82/1.05 Prover 0: Warning: ignoring some quantifiers
% 1.98/1.07 Prover 0: Constructing countermodel ...
% 19.60/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.78/5.97 Prover 1: Preprocessing ...
% 20.13/6.09 Prover 1: Constructing countermodel ...
% 20.60/6.14 Prover 1: proved (213ms)
% 20.60/6.14 Prover 0: stopped
% 20.60/6.15
% 20.60/6.15 No countermodel exists, formula is valid
% 20.60/6.15 % SZS status Theorem for theBenchmark
% 20.60/6.15
% 20.60/6.15 Generating proof ... found it (size 48)
% 21.18/6.31
% 21.18/6.31 % SZS output start Proof for theBenchmark
% 21.18/6.31 Assumed formulas after preprocessing and simplification:
% 21.18/6.31 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (intersection_point(v0, v2) = v4 & intersection_point(v0, v1) = v3 & line_connecting(v3, v4) = v5 & convergent_lines(v0, v2) = 0 & convergent_lines(v0, v1) = 0 & distinct_lines(v5, v0) = 0 & distinct_points(v3, v4) = 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(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | convergent_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(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] : ( ~ (distinct_lines(v8, v9) = 0) | ~ (distinct_points(v6, v7) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (apart_point_and_line(v7, v9) = v13 & apart_point_and_line(v7, v8) = v12 & apart_point_and_line(v6, v9) = v11 & apart_point_and_line(v6, v8) = v10 & (v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ~ (apart_point_and_line(v8, v7) = 0) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ~ (apart_point_and_line(v8, v6) = 0) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ~ (apart_point_and_line(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & distinct_points(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ~ (apart_point_and_line(v6, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & distinct_points(v6, v7) = v9)) & ! [v6] : ~ (convergent_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_points(v6, v6) = 0))
% 21.18/6.34 | 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:
% 21.18/6.34 | (1) intersection_point(all_0_5_5, all_0_3_3) = all_0_1_1 & intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2 & line_connecting(all_0_2_2, all_0_1_1) = all_0_0_0 & convergent_lines(all_0_5_5, all_0_3_3) = 0 & convergent_lines(all_0_5_5, all_0_4_4) = 0 & distinct_lines(all_0_0_0, all_0_5_5) = 0 & distinct_points(all_0_2_2, all_0_1_1) = 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(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_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(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 21.18/6.35 |
% 21.18/6.35 | Applying alpha-rule on (1) yields:
% 21.18/6.35 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 21.18/6.35 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 21.18/6.35 | (4) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 21.18/6.35 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 21.18/6.35 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 21.18/6.35 | (7) convergent_lines(all_0_5_5, all_0_4_4) = 0
% 21.18/6.35 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 21.18/6.35 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 21.18/6.35 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 21.18/6.35 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 21.18/6.35 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 21.18/6.35 | (13) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 21.18/6.35 | (14) distinct_lines(all_0_0_0, all_0_5_5) = 0
% 21.18/6.35 | (15) intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2
% 21.18/6.35 | (16) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 21.18/6.35 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 21.18/6.35 | (18) convergent_lines(all_0_5_5, all_0_3_3) = 0
% 21.18/6.35 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 21.18/6.35 | (20) distinct_points(all_0_2_2, all_0_1_1) = 0
% 21.18/6.35 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 21.18/6.35 | (22) intersection_point(all_0_5_5, all_0_3_3) = all_0_1_1
% 21.18/6.35 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 21.18/6.35 | (24) line_connecting(all_0_2_2, all_0_1_1) = all_0_0_0
% 21.18/6.35 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 21.18/6.35 | (26) ! [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)
% 21.18/6.35 | (27) ! [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)
% 21.18/6.35 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 21.18/6.35 |
% 21.18/6.36 | Instantiating formula (25) with all_0_5_5, all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms distinct_lines(all_0_0_0, all_0_5_5) = 0, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 21.18/6.36 | (29) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apart_point_and_line(all_0_1_1, all_0_0_0) = v2 & apart_point_and_line(all_0_1_1, all_0_5_5) = v3 & apart_point_and_line(all_0_2_2, all_0_0_0) = v0 & apart_point_and_line(all_0_2_2, all_0_5_5) = v1 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0))
% 21.18/6.36 |
% 21.18/6.36 | Instantiating (29) with all_16_0_6, all_16_1_7, all_16_2_8, all_16_3_9 yields:
% 21.18/6.36 | (30) apart_point_and_line(all_0_1_1, all_0_0_0) = all_16_1_7 & apart_point_and_line(all_0_1_1, all_0_5_5) = all_16_0_6 & apart_point_and_line(all_0_2_2, all_0_0_0) = all_16_3_9 & apart_point_and_line(all_0_2_2, all_0_5_5) = all_16_2_8 & (all_16_0_6 = 0 | all_16_1_7 = 0 | all_16_2_8 = 0 | all_16_3_9 = 0)
% 21.18/6.36 |
% 21.18/6.36 | Applying alpha-rule on (30) yields:
% 21.18/6.36 | (31) all_16_0_6 = 0 | all_16_1_7 = 0 | all_16_2_8 = 0 | all_16_3_9 = 0
% 21.18/6.36 | (32) apart_point_and_line(all_0_2_2, all_0_5_5) = all_16_2_8
% 21.18/6.36 | (33) apart_point_and_line(all_0_1_1, all_0_5_5) = all_16_0_6
% 21.18/6.36 | (34) apart_point_and_line(all_0_2_2, all_0_0_0) = all_16_3_9
% 21.18/6.36 | (35) apart_point_and_line(all_0_1_1, all_0_0_0) = all_16_1_7
% 21.18/6.36 |
% 21.18/6.36 | Instantiating formula (17) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms line_connecting(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 21.66/6.36 | (36) ~ (apart_point_and_line(all_0_1_1, all_0_0_0) = 0) | ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)
% 21.66/6.36 |
% 21.66/6.36 | Instantiating formula (21) with all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_3_3) = all_0_1_1, yields:
% 21.66/6.36 | (37) ~ (apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_5_5, all_0_3_3) = v0)
% 21.66/6.36 |
% 21.66/6.36 | Instantiating formula (5) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms line_connecting(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 21.66/6.36 | (38) ~ (apart_point_and_line(all_0_2_2, all_0_0_0) = 0) | ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)
% 21.66/6.36 |
% 21.66/6.36 | Instantiating formula (21) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 21.66/6.36 | (39) ~ (apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = v0)
% 21.66/6.36 |
% 21.66/6.36 +-Applying beta-rule and splitting (39), into two cases.
% 21.66/6.36 |-Branch one:
% 21.66/6.36 | (40) ~ (apart_point_and_line(all_0_2_2, all_0_5_5) = 0)
% 21.66/6.36 |
% 21.66/6.36 +-Applying beta-rule and splitting (38), into two cases.
% 21.66/6.36 |-Branch one:
% 21.66/6.36 | (41) ~ (apart_point_and_line(all_0_2_2, all_0_0_0) = 0)
% 21.66/6.36 |
% 21.66/6.36 +-Applying beta-rule and splitting (37), into two cases.
% 21.66/6.36 |-Branch one:
% 21.66/6.36 | (42) ~ (apart_point_and_line(all_0_1_1, all_0_5_5) = 0)
% 21.66/6.36 |
% 21.66/6.36 +-Applying beta-rule and splitting (36), into two cases.
% 21.66/6.36 |-Branch one:
% 21.66/6.36 | (43) ~ (apart_point_and_line(all_0_1_1, all_0_0_0) = 0)
% 21.66/6.36 |
% 21.66/6.36 | Using (35) and (43) yields:
% 21.66/6.36 | (44) ~ (all_16_1_7 = 0)
% 21.66/6.36 |
% 21.66/6.36 | Using (33) and (42) yields:
% 21.66/6.36 | (45) ~ (all_16_0_6 = 0)
% 21.66/6.36 |
% 21.66/6.36 | Using (34) and (41) yields:
% 21.66/6.36 | (46) ~ (all_16_3_9 = 0)
% 21.66/6.36 |
% 21.66/6.36 | Using (32) and (40) yields:
% 21.66/6.36 | (47) ~ (all_16_2_8 = 0)
% 21.66/6.36 |
% 21.66/6.36 +-Applying beta-rule and splitting (31), into two cases.
% 21.66/6.36 |-Branch one:
% 21.66/6.36 | (48) all_16_0_6 = 0
% 21.66/6.36 |
% 21.66/6.36 | Equations (48) can reduce 45 to:
% 21.66/6.36 | (49) $false
% 21.66/6.36 |
% 21.66/6.36 |-The branch is then unsatisfiable
% 21.66/6.36 |-Branch two:
% 21.66/6.36 | (45) ~ (all_16_0_6 = 0)
% 21.66/6.36 | (51) all_16_1_7 = 0 | all_16_2_8 = 0 | all_16_3_9 = 0
% 21.66/6.36 |
% 21.66/6.36 +-Applying beta-rule and splitting (51), into two cases.
% 21.66/6.36 |-Branch one:
% 21.66/6.36 | (52) all_16_1_7 = 0
% 21.66/6.36 |
% 21.66/6.36 | Equations (52) can reduce 44 to:
% 21.66/6.36 | (49) $false
% 21.66/6.36 |
% 21.66/6.36 |-The branch is then unsatisfiable
% 21.66/6.36 |-Branch two:
% 21.66/6.36 | (44) ~ (all_16_1_7 = 0)
% 21.66/6.36 | (55) all_16_2_8 = 0 | all_16_3_9 = 0
% 21.66/6.36 |
% 21.66/6.36 +-Applying beta-rule and splitting (55), into two cases.
% 21.66/6.36 |-Branch one:
% 21.66/6.36 | (56) all_16_2_8 = 0
% 21.66/6.36 |
% 21.66/6.36 | Equations (56) can reduce 47 to:
% 21.66/6.36 | (49) $false
% 21.66/6.36 |
% 21.66/6.36 |-The branch is then unsatisfiable
% 21.66/6.36 |-Branch two:
% 21.66/6.36 | (47) ~ (all_16_2_8 = 0)
% 21.66/6.36 | (59) all_16_3_9 = 0
% 21.66/6.36 |
% 21.66/6.36 | Equations (59) can reduce 46 to:
% 21.66/6.36 | (49) $false
% 21.66/6.36 |
% 21.66/6.36 |-The branch is then unsatisfiable
% 21.66/6.36 |-Branch two:
% 21.66/6.36 | (61) apart_point_and_line(all_0_1_1, all_0_0_0) = 0
% 21.66/6.36 | (62) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)
% 21.66/6.36 |
% 21.66/6.36 | Instantiating (62) with all_41_0_10 yields:
% 21.66/6.36 | (63) ~ (all_41_0_10 = 0) & distinct_points(all_0_2_2, all_0_1_1) = all_41_0_10
% 21.66/6.36 |
% 21.66/6.36 | Applying alpha-rule on (63) yields:
% 21.66/6.36 | (64) ~ (all_41_0_10 = 0)
% 21.66/6.37 | (65) distinct_points(all_0_2_2, all_0_1_1) = all_41_0_10
% 21.66/6.37 |
% 21.66/6.37 | Instantiating formula (3) with all_0_2_2, all_0_1_1, all_41_0_10, 0 and discharging atoms distinct_points(all_0_2_2, all_0_1_1) = all_41_0_10, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 21.66/6.37 | (66) all_41_0_10 = 0
% 21.66/6.37 |
% 21.66/6.37 | Equations (66) can reduce 64 to:
% 21.66/6.37 | (49) $false
% 21.66/6.37 |
% 21.66/6.37 |-The branch is then unsatisfiable
% 21.66/6.37 |-Branch two:
% 21.66/6.37 | (68) apart_point_and_line(all_0_1_1, all_0_5_5) = 0
% 21.66/6.37 | (69) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_5_5, all_0_3_3) = v0)
% 21.66/6.37 |
% 21.66/6.37 | Instantiating (69) with all_37_0_11 yields:
% 21.66/6.37 | (70) ~ (all_37_0_11 = 0) & convergent_lines(all_0_5_5, all_0_3_3) = all_37_0_11
% 21.66/6.37 |
% 21.66/6.37 | Applying alpha-rule on (70) yields:
% 21.66/6.37 | (71) ~ (all_37_0_11 = 0)
% 21.66/6.37 | (72) convergent_lines(all_0_5_5, all_0_3_3) = all_37_0_11
% 21.66/6.37 |
% 21.66/6.37 | Instantiating formula (9) with all_0_5_5, all_0_3_3, all_37_0_11, 0 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = all_37_0_11, convergent_lines(all_0_5_5, all_0_3_3) = 0, yields:
% 21.66/6.37 | (73) all_37_0_11 = 0
% 21.66/6.37 |
% 21.66/6.37 | Equations (73) can reduce 71 to:
% 21.66/6.37 | (49) $false
% 21.66/6.37 |
% 21.66/6.37 |-The branch is then unsatisfiable
% 21.66/6.37 |-Branch two:
% 21.66/6.37 | (75) apart_point_and_line(all_0_2_2, all_0_0_0) = 0
% 21.66/6.37 | (62) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)
% 21.66/6.37 |
% 21.66/6.37 | Instantiating (62) with all_33_0_12 yields:
% 21.66/6.37 | (77) ~ (all_33_0_12 = 0) & distinct_points(all_0_2_2, all_0_1_1) = all_33_0_12
% 21.66/6.37 |
% 21.66/6.37 | Applying alpha-rule on (77) yields:
% 21.66/6.37 | (78) ~ (all_33_0_12 = 0)
% 21.66/6.37 | (79) distinct_points(all_0_2_2, all_0_1_1) = all_33_0_12
% 21.66/6.37 |
% 21.66/6.37 | Instantiating formula (3) with all_0_2_2, all_0_1_1, all_33_0_12, 0 and discharging atoms distinct_points(all_0_2_2, all_0_1_1) = all_33_0_12, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 21.66/6.37 | (80) all_33_0_12 = 0
% 21.66/6.37 |
% 21.66/6.37 | Equations (80) can reduce 78 to:
% 21.66/6.37 | (49) $false
% 21.66/6.37 |
% 21.66/6.37 |-The branch is then unsatisfiable
% 21.66/6.37 |-Branch two:
% 21.66/6.37 | (82) apart_point_and_line(all_0_2_2, all_0_5_5) = 0
% 21.66/6.37 | (83) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = v0)
% 21.66/6.37 |
% 21.66/6.37 | Instantiating (83) with all_29_0_13 yields:
% 21.66/6.37 | (84) ~ (all_29_0_13 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_29_0_13
% 21.66/6.37 |
% 21.66/6.37 | Applying alpha-rule on (84) yields:
% 21.66/6.37 | (85) ~ (all_29_0_13 = 0)
% 21.66/6.37 | (86) convergent_lines(all_0_5_5, all_0_4_4) = all_29_0_13
% 21.66/6.37 |
% 21.66/6.37 | Instantiating formula (9) with all_0_5_5, all_0_4_4, all_29_0_13, 0 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = all_29_0_13, convergent_lines(all_0_5_5, all_0_4_4) = 0, yields:
% 21.66/6.37 | (87) all_29_0_13 = 0
% 21.66/6.37 |
% 21.66/6.37 | Equations (87) can reduce 85 to:
% 21.66/6.37 | (49) $false
% 21.66/6.37 |
% 21.66/6.37 |-The branch is then unsatisfiable
% 21.66/6.37 % SZS output end Proof for theBenchmark
% 21.66/6.37
% 21.66/6.37 5771ms
%------------------------------------------------------------------------------