TSTP Solution File: GEO183+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO183+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 03:48:19 EDT 2022
% Result : Theorem 3.57s 1.48s
% Output : Proof 4.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO183+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n004.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 10:51:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.50/0.58 ____ _
% 0.50/0.58 ___ / __ \_____(_)___ ________ __________
% 0.50/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.59
% 0.50/0.59 A Theorem Prover for First-Order Logic
% 0.50/0.59 (ePrincess v.1.0)
% 0.50/0.59
% 0.50/0.59 (c) Philipp Rümmer, 2009-2015
% 0.50/0.59 (c) Peter Backeman, 2014-2015
% 0.50/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.59 Bug reports to peter@backeman.se
% 0.50/0.59
% 0.50/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.59
% 0.50/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.74/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.50/0.90 Prover 0: Preprocessing ...
% 1.82/1.03 Prover 0: Warning: ignoring some quantifiers
% 1.82/1.04 Prover 0: Constructing countermodel ...
% 2.83/1.30 Prover 0: gave up
% 2.83/1.30 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.83/1.33 Prover 1: Preprocessing ...
% 3.22/1.42 Prover 1: Constructing countermodel ...
% 3.57/1.48 Prover 1: proved (184ms)
% 3.57/1.48
% 3.57/1.48 No countermodel exists, formula is valid
% 3.57/1.48 % SZS status Theorem for theBenchmark
% 3.57/1.48
% 3.57/1.48 Generating proof ... found it (size 31)
% 4.41/1.67
% 4.41/1.67 % SZS output start Proof for theBenchmark
% 4.41/1.67 Assumed formulas after preprocessing and simplification:
% 4.41/1.67 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v5 = 0) & line_connecting(v0, v1) = v4 & apart_point_and_line(v1, v2) = v7 & apart_point_and_line(v0, v2) = v6 & convergent_lines(v2, v3) = 0 & distinct_lines(v2, v4) = v5 & distinct_points(v0, v1) = 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(v8, v10) = v11) | ~ (convergent_lines(v8, v9) = 0) | convergent_lines(v9, v10) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (convergent_lines(v8, v9) = 0) | ~ (distinct_lines(v9, v10) = v11) | convergent_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(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] : ( ~ (distinct_lines(v10, v11) = 0) | ~ (distinct_points(v8, v9) = 0) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (apart_point_and_line(v9, v11) = v15 & apart_point_and_line(v9, v10) = v14 & apart_point_and_line(v8, v11) = v13 & apart_point_and_line(v8, v10) = v12 & (v15 = 0 | v14 = 0 | v13 = 0 | v12 = 0))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection_point(v8, v9) = v10) | ~ (apart_point_and_line(v10, v9) = 0) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection_point(v8, v9) = v10) | ~ (apart_point_and_line(v10, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v8, v9) = v10) | ~ (apart_point_and_line(v9, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & distinct_points(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v8, v9) = v10) | ~ (apart_point_and_line(v8, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & distinct_points(v8, v9) = v11)) & ! [v8] : ~ (convergent_lines(v8, v8) = 0) & ! [v8] : ~ (distinct_lines(v8, v8) = 0) & ! [v8] : ~ (distinct_points(v8, v8) = 0) & (v7 = 0 | v6 = 0))
% 4.55/1.72 | 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:
% 4.55/1.72 | (1) ~ (all_0_2_2 = 0) & line_connecting(all_0_7_7, all_0_6_6) = all_0_3_3 & apart_point_and_line(all_0_6_6, all_0_5_5) = all_0_0_0 & apart_point_and_line(all_0_7_7, all_0_5_5) = all_0_1_1 & convergent_lines(all_0_5_5, all_0_4_4) = 0 & distinct_lines(all_0_5_5, all_0_3_3) = all_0_2_2 & distinct_points(all_0_7_7, all_0_6_6) = 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)
% 4.55/1.74 |
% 4.55/1.74 | Applying alpha-rule on (1) yields:
% 4.55/1.74 | (2) ! [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)
% 4.55/1.74 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 4.55/1.74 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 4.55/1.74 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 4.55/1.74 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 4.55/1.74 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 4.55/1.74 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 4.55/1.74 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 4.55/1.74 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 4.55/1.74 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 4.55/1.74 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 4.55/1.74 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ~ (apart_point_and_line(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 4.55/1.74 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 4.79/1.74 | (15) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 4.79/1.75 | (16) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 4.79/1.75 | (17) all_0_0_0 = 0 | all_0_1_1 = 0
% 4.79/1.75 | (18) line_connecting(all_0_7_7, all_0_6_6) = all_0_3_3
% 4.79/1.75 | (19) apart_point_and_line(all_0_6_6, all_0_5_5) = all_0_0_0
% 4.79/1.75 | (20) ! [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)
% 4.79/1.75 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 4.79/1.75 | (22) distinct_lines(all_0_5_5, all_0_3_3) = all_0_2_2
% 4.79/1.75 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 4.79/1.75 | (24) distinct_points(all_0_7_7, all_0_6_6) = 0
% 4.79/1.75 | (25) apart_point_and_line(all_0_7_7, all_0_5_5) = all_0_1_1
% 4.79/1.75 | (26) ! [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)))
% 4.79/1.75 | (27) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 4.79/1.75 | (28) convergent_lines(all_0_5_5, all_0_4_4) = 0
% 4.79/1.75 | (29) ~ (all_0_2_2 = 0)
% 4.79/1.75 |
% 4.79/1.75 | Instantiating formula (20) with all_0_2_2, all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms distinct_lines(all_0_5_5, all_0_3_3) = all_0_2_2, yields:
% 4.79/1.75 | (30) all_0_2_2 = 0 | ~ (apart_point_and_line(all_0_6_6, all_0_5_5) = 0) | apart_point_and_line(all_0_6_6, all_0_3_3) = 0
% 4.79/1.75 |
% 4.79/1.75 | Instantiating formula (20) with all_0_2_2, all_0_3_3, all_0_5_5, all_0_7_7 and discharging atoms distinct_lines(all_0_5_5, all_0_3_3) = all_0_2_2, yields:
% 4.79/1.75 | (31) all_0_2_2 = 0 | ~ (apart_point_and_line(all_0_7_7, all_0_5_5) = 0) | apart_point_and_line(all_0_7_7, all_0_3_3) = 0
% 4.79/1.75 |
% 4.79/1.75 +-Applying beta-rule and splitting (17), into two cases.
% 4.79/1.75 |-Branch one:
% 4.79/1.75 | (32) all_0_0_0 = 0
% 4.79/1.75 |
% 4.79/1.75 | From (32) and (19) follows:
% 4.79/1.75 | (33) apart_point_and_line(all_0_6_6, all_0_5_5) = 0
% 4.79/1.75 |
% 4.79/1.75 +-Applying beta-rule and splitting (30), into two cases.
% 4.79/1.75 |-Branch one:
% 4.79/1.75 | (34) ~ (apart_point_and_line(all_0_6_6, all_0_5_5) = 0)
% 4.79/1.75 |
% 4.79/1.75 | Using (33) and (34) yields:
% 4.79/1.75 | (35) $false
% 4.79/1.75 |
% 4.79/1.75 |-The branch is then unsatisfiable
% 4.79/1.75 |-Branch two:
% 4.79/1.75 | (33) apart_point_and_line(all_0_6_6, all_0_5_5) = 0
% 4.79/1.76 | (37) all_0_2_2 = 0 | apart_point_and_line(all_0_6_6, all_0_3_3) = 0
% 4.79/1.76 |
% 4.79/1.76 +-Applying beta-rule and splitting (37), into two cases.
% 4.79/1.76 |-Branch one:
% 4.79/1.76 | (38) apart_point_and_line(all_0_6_6, all_0_3_3) = 0
% 4.79/1.76 |
% 4.79/1.76 | Instantiating formula (3) with all_0_3_3, all_0_6_6, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_0_3_3, apart_point_and_line(all_0_6_6, all_0_3_3) = 0, yields:
% 4.79/1.76 | (39) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)
% 4.79/1.76 |
% 4.79/1.76 | Instantiating (39) with all_42_0_8 yields:
% 4.79/1.76 | (40) ~ (all_42_0_8 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_42_0_8
% 4.79/1.76 |
% 4.79/1.76 | Applying alpha-rule on (40) yields:
% 4.79/1.76 | (41) ~ (all_42_0_8 = 0)
% 4.79/1.76 | (42) distinct_points(all_0_7_7, all_0_6_6) = all_42_0_8
% 4.79/1.76 |
% 4.79/1.76 | Instantiating formula (23) with all_0_7_7, all_0_6_6, all_42_0_8, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_42_0_8, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 4.79/1.76 | (43) all_42_0_8 = 0
% 4.79/1.76 |
% 4.79/1.76 | Equations (43) can reduce 41 to:
% 4.79/1.76 | (44) $false
% 4.79/1.76 |
% 4.79/1.76 |-The branch is then unsatisfiable
% 4.79/1.76 |-Branch two:
% 4.79/1.76 | (45) ~ (apart_point_and_line(all_0_6_6, all_0_3_3) = 0)
% 4.79/1.76 | (46) all_0_2_2 = 0
% 4.79/1.76 |
% 4.86/1.76 | Equations (46) can reduce 29 to:
% 4.86/1.76 | (44) $false
% 4.86/1.76 |
% 4.86/1.76 |-The branch is then unsatisfiable
% 4.86/1.76 |-Branch two:
% 4.86/1.76 | (48) ~ (all_0_0_0 = 0)
% 4.86/1.76 | (49) all_0_1_1 = 0
% 4.86/1.76 |
% 4.86/1.76 | From (49) and (25) follows:
% 4.86/1.76 | (50) apart_point_and_line(all_0_7_7, all_0_5_5) = 0
% 4.86/1.76 |
% 4.86/1.76 +-Applying beta-rule and splitting (31), into two cases.
% 4.86/1.76 |-Branch one:
% 4.86/1.76 | (51) ~ (apart_point_and_line(all_0_7_7, all_0_5_5) = 0)
% 4.86/1.76 |
% 4.86/1.76 | Using (50) and (51) yields:
% 4.86/1.76 | (35) $false
% 4.86/1.76 |
% 4.86/1.76 |-The branch is then unsatisfiable
% 4.86/1.76 |-Branch two:
% 4.86/1.76 | (50) apart_point_and_line(all_0_7_7, all_0_5_5) = 0
% 4.86/1.76 | (54) all_0_2_2 = 0 | apart_point_and_line(all_0_7_7, all_0_3_3) = 0
% 4.86/1.76 |
% 4.86/1.76 +-Applying beta-rule and splitting (54), into two cases.
% 4.86/1.76 |-Branch one:
% 4.86/1.76 | (55) apart_point_and_line(all_0_7_7, all_0_3_3) = 0
% 4.86/1.76 |
% 4.86/1.76 | Instantiating formula (4) with all_0_3_3, all_0_6_6, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_0_3_3, apart_point_and_line(all_0_7_7, all_0_3_3) = 0, yields:
% 4.86/1.76 | (39) ? [v0] : ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0)
% 4.86/1.76 |
% 4.86/1.76 | Instantiating (39) with all_42_0_9 yields:
% 4.86/1.76 | (57) ~ (all_42_0_9 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_42_0_9
% 4.86/1.76 |
% 4.86/1.76 | Applying alpha-rule on (57) yields:
% 4.86/1.76 | (58) ~ (all_42_0_9 = 0)
% 4.86/1.76 | (59) distinct_points(all_0_7_7, all_0_6_6) = all_42_0_9
% 4.86/1.76 |
% 4.86/1.76 | Instantiating formula (23) with all_0_7_7, all_0_6_6, all_42_0_9, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_42_0_9, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 4.86/1.76 | (60) all_42_0_9 = 0
% 4.86/1.76 |
% 4.86/1.76 | Equations (60) can reduce 58 to:
% 4.86/1.76 | (44) $false
% 4.86/1.76 |
% 4.86/1.76 |-The branch is then unsatisfiable
% 4.86/1.76 |-Branch two:
% 4.86/1.76 | (62) ~ (apart_point_and_line(all_0_7_7, all_0_3_3) = 0)
% 4.86/1.76 | (46) all_0_2_2 = 0
% 4.86/1.76 |
% 4.86/1.76 | Equations (46) can reduce 29 to:
% 4.86/1.76 | (44) $false
% 4.86/1.77 |
% 4.86/1.77 |-The branch is then unsatisfiable
% 4.86/1.77 % SZS output end Proof for theBenchmark
% 4.86/1.77
% 4.86/1.77 1169ms
%------------------------------------------------------------------------------