TSTP Solution File: GEO172+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO172+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n015.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 03:48:08 EDT 2022
% Result : Theorem 2.75s 1.26s
% Output : Proof 3.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO172+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n015.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 04:11:13 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.58 ____ _
% 0.19/0.58 ___ / __ \_____(_)___ ________ __________
% 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic
% 0.19/0.58 (ePrincess v.1.0)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2015
% 0.19/0.58 (c) Peter Backeman, 2014-2015
% 0.19/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.59 Bug reports to peter@backeman.se
% 0.19/0.59
% 0.19/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.66/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.63/0.90 Prover 0: Preprocessing ...
% 1.97/1.03 Prover 0: Warning: ignoring some quantifiers
% 1.97/1.05 Prover 0: Constructing countermodel ...
% 2.75/1.26 Prover 0: proved (630ms)
% 2.75/1.26
% 2.75/1.26 No countermodel exists, formula is valid
% 2.75/1.26 % SZS status Theorem for theBenchmark
% 2.75/1.26
% 2.75/1.26 Generating proof ... Warning: ignoring some quantifiers
% 3.22/1.45 found it (size 11)
% 3.22/1.45
% 3.22/1.45 % SZS output start Proof for theBenchmark
% 3.22/1.45 Assumed formulas after preprocessing and simplification:
% 3.22/1.45 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (intersection_point(v0, v1) = v3 & convergent_lines(v0, v1) & distinct_points(v2, v3) & ~ apart_point_and_line(v2, v1) & ~ apart_point_and_line(v2, v0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (intersection_point(v7, v6) = v5) | ~ (intersection_point(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (line_connecting(v7, v6) = v5) | ~ (line_connecting(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v4, v5) = v7) | ~ apart_point_and_line(v6, v5) | ~ convergent_lines(v4, v5) | distinct_points(v6, v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v4, v5) = v7) | ~ apart_point_and_line(v6, v4) | ~ convergent_lines(v4, v5) | distinct_points(v6, v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v4, v5) = v7) | ~ apart_point_and_line(v6, v7) | ~ distinct_points(v4, v5) | distinct_points(v6, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v4, v5) = v7) | ~ apart_point_and_line(v6, v7) | ~ distinct_points(v4, v5) | distinct_points(v6, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ distinct_lines(v6, v7) | ~ distinct_points(v4, v5) | apart_point_and_line(v5, v7) | apart_point_and_line(v5, v6) | apart_point_and_line(v4, v7) | apart_point_and_line(v4, v6)) & ? [v4] : ! [v5] : ! [v6] : ( ~ apart_point_and_line(v5, v6) | apart_point_and_line(v5, v4) | distinct_lines(v6, v4)) & ? [v4] : ! [v5] : ! [v6] : ( ~ apart_point_and_line(v5, v6) | apart_point_and_line(v4, v6) | distinct_points(v5, v4)) & ? [v4] : ! [v5] : ! [v6] : ( ~ convergent_lines(v5, v6) | convergent_lines(v6, v4) | convergent_lines(v5, v4)) & ? [v4] : ! [v5] : ! [v6] : ( ~ distinct_lines(v5, v6) | distinct_lines(v6, v4) | distinct_lines(v5, v4)) & ? [v4] : ! [v5] : ! [v6] : ( ~ distinct_points(v5, v6) | distinct_points(v6, v4) | distinct_points(v5, v4)) & ! [v4] : ! [v5] : ( ~ convergent_lines(v4, v5) | distinct_lines(v4, v5)) & ! [v4] : ~ convergent_lines(v4, v4) & ! [v4] : ~ distinct_lines(v4, v4) & ! [v4] : ~ distinct_points(v4, v4))
% 3.48/1.49 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 3.48/1.49 | (1) intersection_point(all_0_3_3, all_0_2_2) = all_0_0_0 & convergent_lines(all_0_3_3, all_0_2_2) & distinct_points(all_0_1_1, all_0_0_0) & ~ 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)
% 3.59/1.50 |
% 3.59/1.50 | Applying alpha-rule on (1) yields:
% 3.59/1.50 | (2) ~ apart_point_and_line(all_0_1_1, all_0_2_2)
% 3.59/1.50 | (3) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0))
% 3.59/1.50 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v0, v1) = v3) | ~ apart_point_and_line(v2, v0) | ~ convergent_lines(v0, v1) | distinct_points(v2, v3))
% 3.59/1.51 | (5) ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v1, v0) | distinct_lines(v2, v0))
% 3.59/1.51 | (6) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0))
% 3.59/1.51 | (7) distinct_points(all_0_1_1, all_0_0_0)
% 3.59/1.51 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) | distinct_points(v2, v0))
% 3.59/1.51 | (9) ! [v0] : ~ distinct_lines(v0, v0)
% 3.59/1.51 | (10) convergent_lines(all_0_3_3, all_0_2_2)
% 3.59/1.51 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 3.59/1.51 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) | distinct_points(v2, v1))
% 3.59/1.51 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 3.59/1.51 | (14) ? [v0] : ! [v1] : ! [v2] : ( ~ convergent_lines(v1, v2) | convergent_lines(v2, v0) | convergent_lines(v1, v0))
% 3.59/1.51 | (15) ~ apart_point_and_line(all_0_1_1, all_0_3_3)
% 3.59/1.51 | (16) ! [v0] : ~ distinct_points(v0, v0)
% 3.59/1.51 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v0, v1) = v3) | ~ apart_point_and_line(v2, v1) | ~ convergent_lines(v0, v1) | distinct_points(v2, v3))
% 3.59/1.51 | (18) ! [v0] : ~ convergent_lines(v0, v0)
% 3.59/1.51 | (19) ! [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))
% 3.59/1.51 | (20) intersection_point(all_0_3_3, all_0_2_2) = all_0_0_0
% 3.59/1.51 | (21) ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v0, v2) | distinct_points(v1, v0))
% 3.59/1.51 | (22) ! [v0] : ! [v1] : ( ~ convergent_lines(v0, v1) | distinct_lines(v0, v1))
% 3.59/1.51 |
% 3.59/1.51 | Instantiating formula (22) with all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2), yields:
% 3.59/1.51 | (23) distinct_lines(all_0_3_3, all_0_2_2)
% 3.59/1.51 |
% 3.59/1.51 | Instantiating formula (19) with all_0_2_2, all_0_3_3, all_0_0_0, all_0_1_1 and discharging atoms distinct_lines(all_0_3_3, all_0_2_2), distinct_points(all_0_1_1, all_0_0_0), ~ 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:
% 3.59/1.51 | (24) apart_point_and_line(all_0_0_0, all_0_2_2) | apart_point_and_line(all_0_0_0, all_0_3_3)
% 3.59/1.51 |
% 3.59/1.51 +-Applying beta-rule and splitting (24), into two cases.
% 3.59/1.51 |-Branch one:
% 3.59/1.51 | (25) apart_point_and_line(all_0_0_0, all_0_2_2)
% 3.59/1.51 |
% 3.59/1.51 | Instantiating formula (17) 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:
% 3.59/1.51 | (26) distinct_points(all_0_0_0, all_0_0_0)
% 3.59/1.51 |
% 3.59/1.51 | Instantiating formula (16) with all_0_0_0 and discharging atoms distinct_points(all_0_0_0, all_0_0_0), yields:
% 3.59/1.51 | (27) $false
% 3.59/1.51 |
% 3.59/1.51 |-The branch is then unsatisfiable
% 3.59/1.51 |-Branch two:
% 3.59/1.51 | (28) ~ apart_point_and_line(all_0_0_0, all_0_2_2)
% 3.59/1.52 | (29) apart_point_and_line(all_0_0_0, all_0_3_3)
% 3.59/1.52 |
% 3.59/1.52 | Instantiating formula (4) 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:
% 3.59/1.52 | (26) distinct_points(all_0_0_0, all_0_0_0)
% 3.59/1.52 |
% 3.59/1.52 | Instantiating formula (16) with all_0_0_0 and discharging atoms distinct_points(all_0_0_0, all_0_0_0), yields:
% 3.59/1.52 | (27) $false
% 3.59/1.52 |
% 3.59/1.52 |-The branch is then unsatisfiable
% 3.59/1.52 % SZS output end Proof for theBenchmark
% 3.59/1.52
% 3.59/1.52 921ms
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