TSTP Solution File: GEO196+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO196+2 : 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 03:48:32 EDT 2022
% Result : Theorem 7.44s 2.42s
% Output : Proof 8.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO196+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % 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 : Sat Jun 18 04:13:04 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.61/0.61 ____ _
% 0.61/0.61 ___ / __ \_____(_)___ ________ __________
% 0.61/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.61/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.61/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.61/0.61
% 0.61/0.61 A Theorem Prover for First-Order Logic
% 0.61/0.61 (ePrincess v.1.0)
% 0.61/0.61
% 0.61/0.61 (c) Philipp Rümmer, 2009-2015
% 0.61/0.61 (c) Peter Backeman, 2014-2015
% 0.61/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.61/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.61/0.61 Bug reports to peter@backeman.se
% 0.61/0.61
% 0.61/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.61/0.61
% 0.61/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.64/0.97 Prover 0: Preprocessing ...
% 1.99/1.11 Prover 0: Warning: ignoring some quantifiers
% 1.99/1.12 Prover 0: Constructing countermodel ...
% 7.44/2.42 Prover 0: proved (1728ms)
% 7.44/2.42
% 7.44/2.42 No countermodel exists, formula is valid
% 7.44/2.42 % SZS status Theorem for theBenchmark
% 7.44/2.42
% 7.44/2.42 Generating proof ... Warning: ignoring some quantifiers
% 8.27/2.62 found it (size 22)
% 8.27/2.62
% 8.27/2.62 % SZS output start Proof for theBenchmark
% 8.27/2.62 Assumed formulas after preprocessing and simplification:
% 8.27/2.63 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (intersection_point(v2, v3) = v5 & intersection_point(v0, v1) = v4 & convergent_lines(v2, v3) & convergent_lines(v0, v1) & ~ apart_point_and_line(v4, v3) & ~ apart_point_and_line(v4, v2) & ! [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] : ( ~ (intersection_point(v6, v7) = v9) | ~ apart_point_and_line(v8, v7) | ~ convergent_lines(v6, v7) | distinct_points(v8, v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection_point(v6, v7) = v9) | ~ apart_point_and_line(v8, v6) | ~ convergent_lines(v6, v7) | distinct_points(v8, v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v6, v7) = v9) | ~ apart_point_and_line(v8, v9) | ~ distinct_points(v6, v7) | distinct_points(v8, v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v6, v7) = v9) | ~ apart_point_and_line(v8, v9) | ~ distinct_points(v6, v7) | distinct_points(v8, v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ distinct_lines(v8, v9) | ~ distinct_points(v6, v7) | apart_point_and_line(v7, v9) | apart_point_and_line(v7, v8) | apart_point_and_line(v6, v9) | apart_point_and_line(v6, v8)) & ? [v6] : ! [v7] : ! [v8] : ( ~ apart_point_and_line(v7, v8) | apart_point_and_line(v7, v6) | distinct_lines(v8, v6)) & ? [v6] : ! [v7] : ! [v8] : ( ~ apart_point_and_line(v7, v8) | apart_point_and_line(v6, v8) | distinct_points(v7, v6)) & ? [v6] : ! [v7] : ! [v8] : ( ~ convergent_lines(v7, v8) | convergent_lines(v8, v6) | convergent_lines(v7, v6)) & ? [v6] : ! [v7] : ! [v8] : ( ~ distinct_lines(v7, v8) | distinct_lines(v8, v6) | distinct_lines(v7, v6)) & ? [v6] : ! [v7] : ! [v8] : ( ~ distinct_points(v7, v8) | distinct_points(v8, v6) | distinct_points(v7, v6)) & ! [v6] : ! [v7] : ( ~ convergent_lines(v6, v7) | distinct_lines(v6, v7)) & ! [v6] : ~ convergent_lines(v6, v6) & ! [v6] : ~ distinct_lines(v6, v6) & ! [v6] : ~ distinct_points(v6, v6) & (apart_point_and_line(v5, v1) | apart_point_and_line(v5, v0)))
% 8.27/2.67 | 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:
% 8.27/2.67 | (1) intersection_point(all_0_3_3, all_0_2_2) = all_0_0_0 & intersection_point(all_0_5_5, all_0_4_4) = all_0_1_1 & convergent_lines(all_0_3_3, all_0_2_2) & convergent_lines(all_0_5_5, all_0_4_4) & ~ apart_point_and_line(all_0_1_1, all_0_2_2) & ~ apart_point_and_line(all_0_1_1, all_0_3_3) & ! [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_0_0, all_0_4_4) | apart_point_and_line(all_0_0_0, all_0_5_5))
% 8.72/2.67 |
% 8.72/2.67 | Applying alpha-rule on (1) yields:
% 8.72/2.67 | (2) ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v0, v2) | distinct_points(v1, v0))
% 8.72/2.67 | (3) apart_point_and_line(all_0_0_0, all_0_4_4) | apart_point_and_line(all_0_0_0, all_0_5_5)
% 8.72/2.67 | (4) ! [v0] : ~ distinct_points(v0, v0)
% 8.72/2.67 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) | distinct_points(v2, v1))
% 8.72/2.67 | (6) intersection_point(all_0_3_3, all_0_2_2) = all_0_0_0
% 8.72/2.67 | (7) ! [v0] : ! [v1] : ( ~ convergent_lines(v0, v1) | distinct_lines(v0, v1))
% 8.72/2.67 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v0, v1) = v3) | ~ apart_point_and_line(v2, v0) | ~ convergent_lines(v0, v1) | distinct_points(v2, v3))
% 8.72/2.67 | (9) convergent_lines(all_0_3_3, all_0_2_2)
% 8.72/2.67 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 8.72/2.67 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) | distinct_points(v2, v0))
% 8.72/2.67 | (12) ! [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))
% 8.72/2.67 | (13) ~ apart_point_and_line(all_0_1_1, all_0_2_2)
% 8.72/2.67 | (14) ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v1, v0) | distinct_lines(v2, v0))
% 8.72/2.68 | (15) convergent_lines(all_0_5_5, all_0_4_4)
% 8.72/2.68 | (16) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0))
% 8.72/2.68 | (17) ! [v0] : ~ distinct_lines(v0, v0)
% 8.72/2.68 | (18) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0))
% 8.72/2.68 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 8.72/2.68 | (20) ~ apart_point_and_line(all_0_1_1, all_0_3_3)
% 8.72/2.68 | (21) ! [v0] : ~ convergent_lines(v0, v0)
% 8.72/2.68 | (22) ? [v0] : ! [v1] : ! [v2] : ( ~ convergent_lines(v1, v2) | convergent_lines(v2, v0) | convergent_lines(v1, v0))
% 8.72/2.68 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v0, v1) = v3) | ~ apart_point_and_line(v2, v1) | ~ convergent_lines(v0, v1) | distinct_points(v2, v3))
% 8.72/2.68 | (24) intersection_point(all_0_5_5, all_0_4_4) = all_0_1_1
% 8.72/2.68 |
% 8.72/2.68 | Instantiating formula (7) with all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2), yields:
% 8.72/2.68 | (25) distinct_lines(all_0_3_3, all_0_2_2)
% 8.72/2.68 |
% 8.72/2.68 +-Applying beta-rule and splitting (3), into two cases.
% 8.72/2.68 |-Branch one:
% 8.72/2.68 | (26) apart_point_and_line(all_0_0_0, all_0_4_4)
% 8.72/2.68 |
% 8.72/2.68 | Instantiating formula (23) with all_0_1_1, all_0_0_0, all_0_4_4, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_0_1_1, apart_point_and_line(all_0_0_0, all_0_4_4), convergent_lines(all_0_5_5, all_0_4_4), yields:
% 8.72/2.68 | (27) distinct_points(all_0_0_0, all_0_1_1)
% 8.72/2.68 |
% 8.72/2.68 | Instantiating formula (12) with all_0_2_2, all_0_3_3, all_0_1_1, all_0_0_0 and discharging atoms distinct_lines(all_0_3_3, 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), ~ apart_point_and_line(all_0_1_1, all_0_3_3), yields:
% 8.72/2.68 | (28) apart_point_and_line(all_0_0_0, all_0_2_2) | apart_point_and_line(all_0_0_0, all_0_3_3)
% 8.72/2.68 |
% 8.72/2.68 +-Applying beta-rule and splitting (28), into two cases.
% 8.72/2.68 |-Branch one:
% 8.72/2.68 | (29) apart_point_and_line(all_0_0_0, all_0_2_2)
% 8.72/2.68 |
% 8.72/2.68 | Instantiating formula (23) with all_0_0_0, all_0_0_0, all_0_2_2, all_0_3_3 and discharging atoms intersection_point(all_0_3_3, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_0_0, all_0_2_2), convergent_lines(all_0_3_3, all_0_2_2), yields:
% 8.72/2.68 | (30) distinct_points(all_0_0_0, all_0_0_0)
% 8.72/2.68 |
% 8.72/2.68 | Instantiating formula (4) with all_0_0_0 and discharging atoms distinct_points(all_0_0_0, all_0_0_0), yields:
% 8.72/2.68 | (31) $false
% 8.72/2.68 |
% 8.72/2.68 |-The branch is then unsatisfiable
% 8.72/2.68 |-Branch two:
% 8.72/2.68 | (32) ~ apart_point_and_line(all_0_0_0, all_0_2_2)
% 8.72/2.68 | (33) apart_point_and_line(all_0_0_0, all_0_3_3)
% 8.72/2.68 |
% 8.72/2.68 | Instantiating formula (8) with all_0_0_0, all_0_0_0, all_0_2_2, all_0_3_3 and discharging atoms intersection_point(all_0_3_3, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_0_0, all_0_3_3), convergent_lines(all_0_3_3, all_0_2_2), yields:
% 8.72/2.68 | (30) distinct_points(all_0_0_0, all_0_0_0)
% 8.72/2.68 |
% 8.72/2.68 | Instantiating formula (4) with all_0_0_0 and discharging atoms distinct_points(all_0_0_0, all_0_0_0), yields:
% 8.72/2.68 | (31) $false
% 8.72/2.68 |
% 8.72/2.68 |-The branch is then unsatisfiable
% 8.72/2.68 |-Branch two:
% 8.72/2.68 | (36) ~ apart_point_and_line(all_0_0_0, all_0_4_4)
% 8.72/2.68 | (37) apart_point_and_line(all_0_0_0, all_0_5_5)
% 8.72/2.68 |
% 8.72/2.68 | Instantiating formula (8) with all_0_1_1, all_0_0_0, all_0_4_4, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_0_1_1, apart_point_and_line(all_0_0_0, all_0_5_5), convergent_lines(all_0_5_5, all_0_4_4), yields:
% 8.72/2.68 | (27) distinct_points(all_0_0_0, all_0_1_1)
% 8.72/2.68 |
% 8.72/2.68 | Instantiating formula (12) with all_0_2_2, all_0_3_3, all_0_1_1, all_0_0_0 and discharging atoms distinct_lines(all_0_3_3, 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), ~ apart_point_and_line(all_0_1_1, all_0_3_3), yields:
% 8.72/2.68 | (28) apart_point_and_line(all_0_0_0, all_0_2_2) | apart_point_and_line(all_0_0_0, all_0_3_3)
% 8.72/2.68 |
% 8.72/2.68 +-Applying beta-rule and splitting (28), into two cases.
% 8.72/2.68 |-Branch one:
% 8.72/2.68 | (29) apart_point_and_line(all_0_0_0, all_0_2_2)
% 8.72/2.68 |
% 8.72/2.68 | Instantiating formula (23) with all_0_0_0, all_0_0_0, all_0_2_2, all_0_3_3 and discharging atoms intersection_point(all_0_3_3, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_0_0, all_0_2_2), convergent_lines(all_0_3_3, all_0_2_2), yields:
% 8.72/2.68 | (30) distinct_points(all_0_0_0, all_0_0_0)
% 8.72/2.68 |
% 8.72/2.68 | Instantiating formula (4) with all_0_0_0 and discharging atoms distinct_points(all_0_0_0, all_0_0_0), yields:
% 8.72/2.68 | (31) $false
% 8.72/2.68 |
% 8.72/2.68 |-The branch is then unsatisfiable
% 8.72/2.68 |-Branch two:
% 8.72/2.68 | (32) ~ apart_point_and_line(all_0_0_0, all_0_2_2)
% 8.72/2.68 | (33) apart_point_and_line(all_0_0_0, all_0_3_3)
% 8.72/2.68 |
% 8.72/2.68 | Instantiating formula (8) with all_0_0_0, all_0_0_0, all_0_2_2, all_0_3_3 and discharging atoms intersection_point(all_0_3_3, all_0_2_2) = all_0_0_0, apart_point_and_line(all_0_0_0, all_0_3_3), convergent_lines(all_0_3_3, all_0_2_2), yields:
% 8.72/2.69 | (30) distinct_points(all_0_0_0, all_0_0_0)
% 8.72/2.69 |
% 8.72/2.69 | Instantiating formula (4) with all_0_0_0 and discharging atoms distinct_points(all_0_0_0, all_0_0_0), yields:
% 8.72/2.69 | (31) $false
% 8.72/2.69 |
% 8.72/2.69 |-The branch is then unsatisfiable
% 8.72/2.69 % SZS output end Proof for theBenchmark
% 8.72/2.69
% 8.72/2.69 2056ms
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