TSTP Solution File: GEO198+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO198+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n023.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 03:48:34 EDT 2022
% Result : Theorem 14.85s 4.45s
% Output : Proof 15.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GEO198+2 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n023.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 07:31:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.48/0.58 ____ _
% 0.48/0.58 ___ / __ \_____(_)___ ________ __________
% 0.48/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.48/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.48/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.48/0.58
% 0.48/0.58 A Theorem Prover for First-Order Logic
% 0.48/0.58 (ePrincess v.1.0)
% 0.48/0.58
% 0.48/0.58 (c) Philipp Rümmer, 2009-2015
% 0.48/0.58 (c) Peter Backeman, 2014-2015
% 0.48/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.48/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.48/0.58 Bug reports to peter@backeman.se
% 0.48/0.58
% 0.48/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.48/0.58
% 0.48/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.73/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.67/0.94 Prover 0: Preprocessing ...
% 1.97/1.07 Prover 0: Warning: ignoring some quantifiers
% 2.04/1.09 Prover 0: Constructing countermodel ...
% 14.85/4.45 Prover 0: proved (3817ms)
% 14.85/4.45
% 14.85/4.45 No countermodel exists, formula is valid
% 14.85/4.45 % SZS status Theorem for theBenchmark
% 14.85/4.45
% 14.85/4.45 Generating proof ... Warning: ignoring some quantifiers
% 15.85/4.65 found it (size 16)
% 15.85/4.65
% 15.85/4.65 % SZS output start Proof for theBenchmark
% 15.85/4.65 Assumed formulas after preprocessing and simplification:
% 15.85/4.65 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (intersection_point(v0, v2) = v4 & intersection_point(v0, v1) = v3 & apart_point_and_line(v4, v1) & convergent_lines(v2, v1) & convergent_lines(v0, v2) & convergent_lines(v0, v1) & ~ apart_point_and_line(v3, v2) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersection_point(v8, v7) = v6) | ~ (intersection_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (line_connecting(v8, v7) = v6) | ~ (line_connecting(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v5, v6) = v8) | ~ apart_point_and_line(v7, v6) | ~ convergent_lines(v5, v6) | distinct_points(v7, v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v5, v6) = v8) | ~ apart_point_and_line(v7, v5) | ~ convergent_lines(v5, v6) | distinct_points(v7, v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v5, v6) = v8) | ~ apart_point_and_line(v7, v8) | ~ distinct_points(v5, v6) | distinct_points(v7, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v5, v6) = v8) | ~ apart_point_and_line(v7, v8) | ~ distinct_points(v5, v6) | distinct_points(v7, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ distinct_lines(v7, v8) | ~ distinct_points(v5, v6) | apart_point_and_line(v6, v8) | apart_point_and_line(v6, v7) | apart_point_and_line(v5, v8) | apart_point_and_line(v5, v7)) & ? [v5] : ! [v6] : ! [v7] : ( ~ apart_point_and_line(v6, v7) | apart_point_and_line(v6, v5) | distinct_lines(v7, v5)) & ? [v5] : ! [v6] : ! [v7] : ( ~ apart_point_and_line(v6, v7) | apart_point_and_line(v5, v7) | distinct_points(v6, v5)) & ? [v5] : ! [v6] : ! [v7] : ( ~ convergent_lines(v6, v7) | convergent_lines(v7, v5) | convergent_lines(v6, v5)) & ? [v5] : ! [v6] : ! [v7] : ( ~ distinct_lines(v6, v7) | distinct_lines(v7, v5) | distinct_lines(v6, v5)) & ? [v5] : ! [v6] : ! [v7] : ( ~ distinct_points(v6, v7) | distinct_points(v7, v5) | distinct_points(v6, v5)) & ! [v5] : ! [v6] : ( ~ convergent_lines(v5, v6) | distinct_lines(v5, v6)) & ! [v5] : ~ convergent_lines(v5, v5) & ! [v5] : ~ distinct_lines(v5, v5) & ! [v5] : ~ distinct_points(v5, v5))
% 15.97/4.69 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 15.97/4.69 | (1) intersection_point(all_0_4_4, all_0_2_2) = all_0_0_0 & intersection_point(all_0_4_4, all_0_3_3) = all_0_1_1 & apart_point_and_line(all_0_0_0, all_0_3_3) & convergent_lines(all_0_2_2, all_0_3_3) & convergent_lines(all_0_4_4, all_0_2_2) & convergent_lines(all_0_4_4, all_0_3_3) & ~ apart_point_and_line(all_0_1_1, all_0_2_2) & ! [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] : ( ~ (intersection_point(v0, v1) = v3) | ~ apart_point_and_line(v2, v1) | ~ convergent_lines(v0, v1) | distinct_points(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v0, v1) = v3) | ~ apart_point_and_line(v2, v0) | ~ convergent_lines(v0, v1) | distinct_points(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) | distinct_points(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) | distinct_points(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ distinct_lines(v2, v3) | ~ distinct_points(v0, v1) | apart_point_and_line(v1, v3) | apart_point_and_line(v1, v2) | apart_point_and_line(v0, v3) | apart_point_and_line(v0, v2)) & ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v1, v0) | distinct_lines(v2, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v0, v2) | distinct_points(v1, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ convergent_lines(v1, v2) | convergent_lines(v2, v0) | convergent_lines(v1, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0)) & ! [v0] : ! [v1] : ( ~ convergent_lines(v0, v1) | distinct_lines(v0, v1)) & ! [v0] : ~ convergent_lines(v0, v0) & ! [v0] : ~ distinct_lines(v0, v0) & ! [v0] : ~ distinct_points(v0, v0)
% 15.97/4.70 |
% 15.97/4.70 | Applying alpha-rule on (1) yields:
% 15.97/4.70 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v0, v1) = v3) | ~ apart_point_and_line(v2, v0) | ~ convergent_lines(v0, v1) | distinct_points(v2, v3))
% 15.97/4.70 | (3) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0))
% 15.97/4.70 | (4) convergent_lines(all_0_4_4, all_0_3_3)
% 15.97/4.70 | (5) convergent_lines(all_0_2_2, all_0_3_3)
% 15.97/4.70 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) | distinct_points(v2, v1))
% 15.97/4.70 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) | distinct_points(v2, v0))
% 15.97/4.70 | (8) intersection_point(all_0_4_4, all_0_3_3) = all_0_1_1
% 15.97/4.70 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 15.97/4.70 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 15.97/4.70 | (11) ! [v0] : ~ convergent_lines(v0, v0)
% 15.97/4.70 | (12) ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v1, v0) | distinct_lines(v2, v0))
% 15.97/4.70 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ distinct_lines(v2, v3) | ~ distinct_points(v0, v1) | apart_point_and_line(v1, v3) | apart_point_and_line(v1, v2) | apart_point_and_line(v0, v3) | apart_point_and_line(v0, v2))
% 15.97/4.70 | (14) apart_point_and_line(all_0_0_0, all_0_3_3)
% 15.97/4.70 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v0, v1) = v3) | ~ apart_point_and_line(v2, v1) | ~ convergent_lines(v0, v1) | distinct_points(v2, v3))
% 15.97/4.70 | (16) ! [v0] : ~ distinct_points(v0, v0)
% 15.97/4.70 | (17) intersection_point(all_0_4_4, all_0_2_2) = all_0_0_0
% 15.97/4.70 | (18) ! [v0] : ~ distinct_lines(v0, v0)
% 15.97/4.71 | (19) ~ apart_point_and_line(all_0_1_1, all_0_2_2)
% 15.97/4.71 | (20) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0))
% 15.97/4.71 | (21) ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v0, v2) | distinct_points(v1, v0))
% 15.97/4.71 | (22) ? [v0] : ! [v1] : ! [v2] : ( ~ convergent_lines(v1, v2) | convergent_lines(v2, v0) | convergent_lines(v1, v0))
% 15.97/4.71 | (23) ! [v0] : ! [v1] : ( ~ convergent_lines(v0, v1) | distinct_lines(v0, v1))
% 15.97/4.71 | (24) convergent_lines(all_0_4_4, all_0_2_2)
% 15.97/4.71 |
% 15.97/4.71 | Instantiating formula (23) with all_0_2_2, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2), yields:
% 15.97/4.71 | (25) distinct_lines(all_0_4_4, all_0_2_2)
% 15.97/4.71 |
% 15.97/4.71 | Instantiating formula (15) with all_0_1_1, all_0_0_0, all_0_3_3, all_0_4_4 and discharging atoms intersection_point(all_0_4_4, all_0_3_3) = all_0_1_1, apart_point_and_line(all_0_0_0, all_0_3_3), convergent_lines(all_0_4_4, all_0_3_3), yields:
% 15.97/4.71 | (26) distinct_points(all_0_0_0, all_0_1_1)
% 15.97/4.71 |
% 15.97/4.71 | Instantiating formula (13) with all_0_2_2, all_0_4_4, all_0_1_1, all_0_0_0 and discharging atoms distinct_lines(all_0_4_4, all_0_2_2), distinct_points(all_0_0_0, all_0_1_1), ~ apart_point_and_line(all_0_1_1, all_0_2_2), yields:
% 15.97/4.71 | (27) apart_point_and_line(all_0_0_0, all_0_2_2) | apart_point_and_line(all_0_0_0, all_0_4_4) | apart_point_and_line(all_0_1_1, all_0_4_4)
% 15.97/4.71 |
% 15.97/4.71 +-Applying beta-rule and splitting (27), into two cases.
% 15.97/4.71 |-Branch one:
% 15.97/4.71 | (28) apart_point_and_line(all_0_0_0, all_0_2_2)
% 15.97/4.71 |
% 15.97/4.71 | Instantiating formula (15) with all_0_0_0, all_0_0_0, all_0_2_2, all_0_4_4 and discharging atoms intersection_point(all_0_4_4, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_0_0, all_0_2_2), convergent_lines(all_0_4_4, all_0_2_2), yields:
% 15.97/4.71 | (29) distinct_points(all_0_0_0, all_0_0_0)
% 15.97/4.71 |
% 15.97/4.71 | Instantiating formula (16) with all_0_0_0 and discharging atoms distinct_points(all_0_0_0, all_0_0_0), yields:
% 15.97/4.71 | (30) $false
% 15.97/4.71 |
% 15.97/4.71 |-The branch is then unsatisfiable
% 15.97/4.71 |-Branch two:
% 15.97/4.71 | (31) ~ apart_point_and_line(all_0_0_0, all_0_2_2)
% 15.97/4.71 | (32) apart_point_and_line(all_0_0_0, all_0_4_4) | apart_point_and_line(all_0_1_1, all_0_4_4)
% 15.97/4.71 |
% 15.97/4.71 +-Applying beta-rule and splitting (32), into two cases.
% 15.97/4.71 |-Branch one:
% 15.97/4.71 | (33) apart_point_and_line(all_0_0_0, all_0_4_4)
% 15.97/4.71 |
% 15.97/4.71 | Instantiating formula (2) with all_0_0_0, all_0_0_0, all_0_2_2, all_0_4_4 and discharging atoms intersection_point(all_0_4_4, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_0_0, all_0_4_4), convergent_lines(all_0_4_4, all_0_2_2), yields:
% 15.97/4.71 | (29) distinct_points(all_0_0_0, all_0_0_0)
% 15.97/4.71 |
% 15.97/4.71 | Instantiating formula (16) with all_0_0_0 and discharging atoms distinct_points(all_0_0_0, all_0_0_0), yields:
% 15.97/4.71 | (30) $false
% 15.97/4.71 |
% 15.97/4.71 |-The branch is then unsatisfiable
% 15.97/4.71 |-Branch two:
% 15.97/4.71 | (36) ~ apart_point_and_line(all_0_0_0, all_0_4_4)
% 15.97/4.71 | (37) apart_point_and_line(all_0_1_1, all_0_4_4)
% 15.97/4.71 |
% 15.97/4.71 | Instantiating formula (2) with all_0_1_1, all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms intersection_point(all_0_4_4, all_0_3_3) = all_0_1_1, apart_point_and_line(all_0_1_1, all_0_4_4), convergent_lines(all_0_4_4, all_0_3_3), yields:
% 15.97/4.71 | (38) distinct_points(all_0_1_1, all_0_1_1)
% 15.97/4.71 |
% 15.97/4.71 | Instantiating formula (16) with all_0_1_1 and discharging atoms distinct_points(all_0_1_1, all_0_1_1), yields:
% 15.97/4.71 | (30) $false
% 15.97/4.71 |
% 15.97/4.71 |-The branch is then unsatisfiable
% 15.97/4.71 % SZS output end Proof for theBenchmark
% 15.97/4.71
% 15.97/4.71 4121ms
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