TSTP Solution File: GEO178+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO178+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n020.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 03:48:13 EDT 2022
% Result : Theorem 3.18s 1.48s
% Output : Proof 4.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO178+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jun 17 21:57:04 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.63/0.65 ____ _
% 0.63/0.65 ___ / __ \_____(_)___ ________ __________
% 0.63/0.65 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.63/0.65 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.63/0.65 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.63/0.65
% 0.63/0.65 A Theorem Prover for First-Order Logic
% 0.63/0.65 (ePrincess v.1.0)
% 0.63/0.65
% 0.63/0.65 (c) Philipp Rümmer, 2009-2015
% 0.63/0.65 (c) Peter Backeman, 2014-2015
% 0.63/0.65 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.63/0.65 Free software under GNU Lesser General Public License (LGPL).
% 0.63/0.65 Bug reports to peter@backeman.se
% 0.63/0.65
% 0.63/0.65 For more information, visit http://user.uu.se/~petba168/breu/
% 0.63/0.65
% 0.63/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.81/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.76/1.00 Prover 0: Preprocessing ...
% 2.06/1.13 Prover 0: Warning: ignoring some quantifiers
% 2.14/1.15 Prover 0: Constructing countermodel ...
% 2.58/1.31 Prover 0: gave up
% 2.58/1.31 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.58/1.34 Prover 1: Preprocessing ...
% 3.09/1.43 Prover 1: Constructing countermodel ...
% 3.18/1.48 Prover 1: proved (168ms)
% 3.18/1.48
% 3.18/1.48 No countermodel exists, formula is valid
% 3.18/1.48 % SZS status Theorem for theBenchmark
% 3.18/1.48
% 3.18/1.48 Generating proof ... found it (size 29)
% 4.12/1.70
% 4.12/1.70 % SZS output start Proof for theBenchmark
% 4.12/1.70 Assumed formulas after preprocessing and simplification:
% 4.12/1.70 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (line_connecting(v0, v1) = v3 & apart_point_and_line(v2, v3) = 0 & distinct_points(v2, v1) = v5 & distinct_points(v2, v0) = v4 & distinct_points(v0, v1) = 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) & ( ~ (v5 = 0) | ~ (v4 = 0)))
% 4.12/1.73 | 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:
% 4.12/1.73 | (1) line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0 & distinct_points(all_0_3_3, all_0_4_4) = all_0_0_0 & distinct_points(all_0_3_3, all_0_5_5) = all_0_1_1 & distinct_points(all_0_5_5, all_0_4_4) = 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) & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0))
% 4.34/1.74 |
% 4.34/1.74 | Applying alpha-rule on (1) yields:
% 4.34/1.74 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 4.34/1.74 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 4.34/1.74 | (4) distinct_points(all_0_5_5, all_0_4_4) = 0
% 4.34/1.74 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 4.34/1.74 | (6) line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2
% 4.34/1.74 | (7) distinct_points(all_0_3_3, all_0_4_4) = all_0_0_0
% 4.34/1.74 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 4.34/1.74 | (9) ! [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)
% 4.34/1.74 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 4.34/1.74 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 4.34/1.74 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 4.34/1.74 | (13) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 4.34/1.74 | (14) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 4.34/1.74 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 4.34/1.75 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 4.34/1.75 | (17) ! [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)))
% 4.34/1.75 | (18) apart_point_and_line(all_0_3_3, all_0_2_2) = 0
% 4.34/1.75 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 4.34/1.75 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 4.34/1.75 | (21) distinct_points(all_0_3_3, all_0_5_5) = all_0_1_1
% 4.34/1.75 | (22) ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)
% 4.34/1.75 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 4.34/1.75 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 4.34/1.75 | (25) ! [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)
% 4.34/1.75 | (26) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 4.34/1.75 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 4.34/1.75 |
% 4.34/1.75 | Instantiating formula (16) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 4.34/1.75 | (28) ~ (apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)
% 4.34/1.75 |
% 4.34/1.75 | Instantiating formula (23) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 4.34/1.75 | (29) ~ (apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)
% 4.34/1.75 |
% 4.34/1.75 | Instantiating formula (9) with all_0_0_0, all_0_4_4, all_0_2_2, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = 0, distinct_points(all_0_3_3, all_0_4_4) = all_0_0_0, yields:
% 4.34/1.75 | (30) all_0_0_0 = 0 | apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 4.34/1.75 |
% 4.34/1.75 | Instantiating formula (9) with all_0_1_1, all_0_5_5, all_0_2_2, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = 0, distinct_points(all_0_3_3, all_0_5_5) = all_0_1_1, yields:
% 4.38/1.75 | (31) all_0_1_1 = 0 | apart_point_and_line(all_0_5_5, all_0_2_2) = 0
% 4.38/1.75 |
% 4.38/1.75 +-Applying beta-rule and splitting (29), into two cases.
% 4.38/1.75 |-Branch one:
% 4.38/1.75 | (32) ~ (apart_point_and_line(all_0_5_5, all_0_2_2) = 0)
% 4.38/1.75 |
% 4.38/1.75 +-Applying beta-rule and splitting (31), into two cases.
% 4.38/1.75 |-Branch one:
% 4.38/1.75 | (33) apart_point_and_line(all_0_5_5, all_0_2_2) = 0
% 4.38/1.75 |
% 4.38/1.75 | Using (33) and (32) yields:
% 4.38/1.75 | (34) $false
% 4.38/1.75 |
% 4.38/1.75 |-The branch is then unsatisfiable
% 4.38/1.75 |-Branch two:
% 4.38/1.75 | (32) ~ (apart_point_and_line(all_0_5_5, all_0_2_2) = 0)
% 4.38/1.75 | (36) all_0_1_1 = 0
% 4.38/1.75 |
% 4.38/1.75 +-Applying beta-rule and splitting (22), into two cases.
% 4.38/1.75 |-Branch one:
% 4.38/1.75 | (37) ~ (all_0_0_0 = 0)
% 4.38/1.75 |
% 4.38/1.75 +-Applying beta-rule and splitting (28), into two cases.
% 4.38/1.75 |-Branch one:
% 4.38/1.75 | (38) ~ (apart_point_and_line(all_0_4_4, all_0_2_2) = 0)
% 4.38/1.75 |
% 4.38/1.75 +-Applying beta-rule and splitting (30), into two cases.
% 4.38/1.75 |-Branch one:
% 4.38/1.75 | (39) apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 4.38/1.75 |
% 4.38/1.75 | Using (39) and (38) yields:
% 4.38/1.75 | (34) $false
% 4.38/1.75 |
% 4.38/1.75 |-The branch is then unsatisfiable
% 4.38/1.75 |-Branch two:
% 4.38/1.75 | (38) ~ (apart_point_and_line(all_0_4_4, all_0_2_2) = 0)
% 4.38/1.75 | (42) all_0_0_0 = 0
% 4.38/1.75 |
% 4.38/1.75 | Equations (42) can reduce 37 to:
% 4.38/1.75 | (43) $false
% 4.38/1.75 |
% 4.38/1.75 |-The branch is then unsatisfiable
% 4.38/1.75 |-Branch two:
% 4.38/1.76 | (39) apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 4.38/1.76 | (45) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)
% 4.38/1.76 |
% 4.38/1.76 | Instantiating (45) with all_34_0_6 yields:
% 4.38/1.76 | (46) ~ (all_34_0_6 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_34_0_6
% 4.38/1.76 |
% 4.38/1.76 | Applying alpha-rule on (46) yields:
% 4.38/1.76 | (47) ~ (all_34_0_6 = 0)
% 4.38/1.76 | (48) distinct_points(all_0_5_5, all_0_4_4) = all_34_0_6
% 4.38/1.76 |
% 4.38/1.76 | Instantiating formula (3) with all_0_5_5, all_0_4_4, all_34_0_6, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_34_0_6, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 4.38/1.76 | (49) all_34_0_6 = 0
% 4.38/1.76 |
% 4.38/1.76 | Equations (49) can reduce 47 to:
% 4.38/1.76 | (43) $false
% 4.38/1.76 |
% 4.38/1.76 |-The branch is then unsatisfiable
% 4.38/1.76 |-Branch two:
% 4.38/1.76 | (42) all_0_0_0 = 0
% 4.38/1.76 | (52) ~ (all_0_1_1 = 0)
% 4.38/1.76 |
% 4.38/1.76 | Equations (36) can reduce 52 to:
% 4.38/1.76 | (43) $false
% 4.38/1.76 |
% 4.38/1.76 |-The branch is then unsatisfiable
% 4.38/1.76 |-Branch two:
% 4.38/1.76 | (33) apart_point_and_line(all_0_5_5, all_0_2_2) = 0
% 4.38/1.76 | (45) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0)
% 4.38/1.76 |
% 4.38/1.76 | Instantiating (45) with all_22_0_7 yields:
% 4.38/1.76 | (56) ~ (all_22_0_7 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_22_0_7
% 4.38/1.76 |
% 4.38/1.76 | Applying alpha-rule on (56) yields:
% 4.38/1.76 | (57) ~ (all_22_0_7 = 0)
% 4.38/1.76 | (58) distinct_points(all_0_5_5, all_0_4_4) = all_22_0_7
% 4.38/1.76 |
% 4.38/1.76 | Instantiating formula (3) with all_0_5_5, all_0_4_4, all_22_0_7, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_22_0_7, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 4.38/1.76 | (59) all_22_0_7 = 0
% 4.38/1.76 |
% 4.38/1.76 | Equations (59) can reduce 57 to:
% 4.38/1.76 | (43) $false
% 4.38/1.76 |
% 4.38/1.76 |-The branch is then unsatisfiable
% 4.38/1.76 % SZS output end Proof for theBenchmark
% 4.38/1.76
% 4.38/1.76 1096ms
%------------------------------------------------------------------------------