TSTP Solution File: GEO185+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO185+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n007.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 03:48:22 EDT 2022
% Result : Theorem 2.32s 1.22s
% Output : Proof 3.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO185+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 17:51:43 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.51/0.60 ____ _
% 0.51/0.60 ___ / __ \_____(_)___ ________ __________
% 0.51/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.60
% 0.51/0.60 A Theorem Prover for First-Order Logic
% 0.51/0.60 (ePrincess v.1.0)
% 0.51/0.60
% 0.51/0.60 (c) Philipp Rümmer, 2009-2015
% 0.51/0.60 (c) Peter Backeman, 2014-2015
% 0.51/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.60 Bug reports to peter@backeman.se
% 0.51/0.60
% 0.51/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.60
% 0.51/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.67/0.95 Prover 0: Preprocessing ...
% 2.01/1.08 Prover 0: Warning: ignoring some quantifiers
% 2.01/1.11 Prover 0: Constructing countermodel ...
% 2.32/1.22 Prover 0: proved (571ms)
% 2.32/1.22
% 2.32/1.22 No countermodel exists, formula is valid
% 2.32/1.22 % SZS status Theorem for theBenchmark
% 2.32/1.22
% 2.32/1.22 Generating proof ... Warning: ignoring some quantifiers
% 2.92/1.41 found it (size 7)
% 2.92/1.41
% 2.92/1.41 % SZS output start Proof for theBenchmark
% 2.92/1.41 Assumed formulas after preprocessing and simplification:
% 2.92/1.41 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (intersection_point(v2, v3) = v4 & convergent_lines(v2, v3) & distinct_points(v0, v1) & ~ distinct_points(v0, v4) & ! [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) & (apart_point_and_line(v0, v3) | apart_point_and_line(v0, v2)))
% 3.18/1.45 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 3.18/1.45 | (1) intersection_point(all_0_2_2, all_0_1_1) = all_0_0_0 & convergent_lines(all_0_2_2, all_0_1_1) & distinct_points(all_0_4_4, all_0_3_3) & ~ distinct_points(all_0_4_4, all_0_0_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] : ( ~ (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) & (apart_point_and_line(all_0_4_4, all_0_1_1) | apart_point_and_line(all_0_4_4, all_0_2_2))
% 3.18/1.46 |
% 3.18/1.46 | Applying alpha-rule on (1) yields:
% 3.18/1.46 | (2) ! [v0] : ~ convergent_lines(v0, v0)
% 3.18/1.46 | (3) ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v1, v0) | distinct_lines(v2, v0))
% 3.18/1.46 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 3.18/1.46 | (5) convergent_lines(all_0_2_2, all_0_1_1)
% 3.18/1.46 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) | distinct_points(v2, v0))
% 3.18/1.46 | (7) ~ distinct_points(all_0_4_4, all_0_0_0)
% 3.18/1.46 | (8) intersection_point(all_0_2_2, all_0_1_1) = all_0_0_0
% 3.18/1.46 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 3.18/1.46 | (10) ! [v0] : ~ distinct_lines(v0, v0)
% 3.18/1.47 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v0, v1) = v3) | ~ apart_point_and_line(v2, v0) | ~ convergent_lines(v0, v1) | distinct_points(v2, v3))
% 3.18/1.47 | (12) distinct_points(all_0_4_4, all_0_3_3)
% 3.18/1.47 | (13) ? [v0] : ! [v1] : ! [v2] : ( ~ convergent_lines(v1, v2) | convergent_lines(v2, v0) | convergent_lines(v1, v0))
% 3.18/1.47 | (14) ! [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))
% 3.18/1.47 | (15) apart_point_and_line(all_0_4_4, all_0_1_1) | apart_point_and_line(all_0_4_4, all_0_2_2)
% 3.18/1.47 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v0, v1) = v3) | ~ apart_point_and_line(v2, v1) | ~ convergent_lines(v0, v1) | distinct_points(v2, v3))
% 3.18/1.47 | (17) ! [v0] : ~ distinct_points(v0, v0)
% 3.18/1.47 | (18) ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v0, v2) | distinct_points(v1, v0))
% 3.18/1.47 | (19) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0))
% 3.18/1.47 | (20) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0))
% 3.18/1.47 | (21) ! [v0] : ! [v1] : ( ~ convergent_lines(v0, v1) | distinct_lines(v0, v1))
% 3.18/1.47 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) | distinct_points(v2, v1))
% 3.18/1.47 |
% 3.18/1.47 +-Applying beta-rule and splitting (15), into two cases.
% 3.18/1.47 |-Branch one:
% 3.18/1.47 | (23) apart_point_and_line(all_0_4_4, all_0_1_1)
% 3.18/1.47 |
% 3.18/1.47 | Instantiating formula (16) with all_0_0_0, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms intersection_point(all_0_2_2, all_0_1_1) = all_0_0_0, apart_point_and_line(all_0_4_4, all_0_1_1), convergent_lines(all_0_2_2, all_0_1_1), ~ distinct_points(all_0_4_4, all_0_0_0), yields:
% 3.18/1.47 | (24) $false
% 3.18/1.47 |
% 3.18/1.47 |-The branch is then unsatisfiable
% 3.18/1.47 |-Branch two:
% 3.18/1.47 | (25) ~ apart_point_and_line(all_0_4_4, all_0_1_1)
% 3.18/1.47 | (26) apart_point_and_line(all_0_4_4, all_0_2_2)
% 3.18/1.47 |
% 3.18/1.47 | Instantiating formula (11) with all_0_0_0, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms intersection_point(all_0_2_2, all_0_1_1) = all_0_0_0, apart_point_and_line(all_0_4_4, all_0_2_2), convergent_lines(all_0_2_2, all_0_1_1), ~ distinct_points(all_0_4_4, all_0_0_0), yields:
% 3.18/1.47 | (24) $false
% 3.18/1.47 |
% 3.18/1.47 |-The branch is then unsatisfiable
% 3.18/1.47 % SZS output end Proof for theBenchmark
% 3.18/1.47
% 3.18/1.47 865ms
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