TSTP Solution File: GEO186+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO186+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n010.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 3.28s 1.41s
% Output : Proof 3.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO186+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n010.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 13:00:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.59 ____ _
% 0.18/0.59 ___ / __ \_____(_)___ ________ __________
% 0.18/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.59
% 0.18/0.59 A Theorem Prover for First-Order Logic
% 0.18/0.59 (ePrincess v.1.0)
% 0.18/0.59
% 0.18/0.59 (c) Philipp Rümmer, 2009-2015
% 0.18/0.59 (c) Peter Backeman, 2014-2015
% 0.18/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.59 Bug reports to peter@backeman.se
% 0.18/0.59
% 0.18/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.59
% 0.18/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.56/0.91 Prover 0: Preprocessing ...
% 1.86/1.04 Prover 0: Warning: ignoring some quantifiers
% 1.86/1.06 Prover 0: Constructing countermodel ...
% 3.28/1.41 Prover 0: proved (772ms)
% 3.28/1.41
% 3.28/1.41 No countermodel exists, formula is valid
% 3.28/1.41 % SZS status Theorem for theBenchmark
% 3.28/1.41
% 3.28/1.41 Generating proof ... Warning: ignoring some quantifiers
% 3.90/1.56 found it (size 11)
% 3.90/1.56
% 3.90/1.56 % SZS output start Proof for theBenchmark
% 3.90/1.56 Assumed formulas after preprocessing and simplification:
% 3.90/1.56 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (intersection_point(v2, v3) = v4 & convergent_lines(v2, v3) & distinct_points(v0, v4) & distinct_points(v0, v1) & ~ apart_point_and_line(v0, v3) & ~ apart_point_and_line(v0, 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))
% 3.90/1.60 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 3.90/1.60 | (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_0_0) & distinct_points(all_0_4_4, all_0_3_3) & ~ apart_point_and_line(all_0_4_4, all_0_1_1) & ~ apart_point_and_line(all_0_4_4, 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)
% 3.90/1.61 |
% 3.90/1.61 | Applying alpha-rule on (1) yields:
% 3.90/1.61 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v0, v1) = v3) | ~ apart_point_and_line(v2, v0) | ~ convergent_lines(v0, v1) | distinct_points(v2, v3))
% 3.90/1.61 | (3) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0))
% 3.90/1.61 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) | distinct_points(v2, v1))
% 3.90/1.61 | (5) distinct_points(all_0_4_4, all_0_3_3)
% 3.90/1.61 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) | distinct_points(v2, v0))
% 3.90/1.61 | (7) convergent_lines(all_0_2_2, all_0_1_1)
% 3.90/1.62 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 3.90/1.62 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 3.90/1.62 | (10) ! [v0] : ~ convergent_lines(v0, v0)
% 3.90/1.62 | (11) ~ apart_point_and_line(all_0_4_4, all_0_1_1)
% 3.90/1.62 | (12) ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v1, v0) | distinct_lines(v2, v0))
% 3.90/1.62 | (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))
% 3.90/1.62 | (14) ~ apart_point_and_line(all_0_4_4, all_0_2_2)
% 3.90/1.62 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection_point(v0, v1) = v3) | ~ apart_point_and_line(v2, v1) | ~ convergent_lines(v0, v1) | distinct_points(v2, v3))
% 3.90/1.62 | (16) ! [v0] : ~ distinct_points(v0, v0)
% 3.90/1.62 | (17) distinct_points(all_0_4_4, all_0_0_0)
% 3.90/1.62 | (18) intersection_point(all_0_2_2, all_0_1_1) = all_0_0_0
% 3.90/1.62 | (19) ! [v0] : ~ distinct_lines(v0, v0)
% 3.90/1.62 | (20) ? [v0] : ! [v1] : ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0))
% 3.90/1.62 | (21) ? [v0] : ! [v1] : ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v0, v2) | distinct_points(v1, v0))
% 3.90/1.62 | (22) ? [v0] : ! [v1] : ! [v2] : ( ~ convergent_lines(v1, v2) | convergent_lines(v2, v0) | convergent_lines(v1, v0))
% 3.90/1.62 | (23) ! [v0] : ! [v1] : ( ~ convergent_lines(v0, v1) | distinct_lines(v0, v1))
% 3.90/1.62 |
% 3.90/1.62 | Instantiating formula (23) with all_0_1_1, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1), yields:
% 3.90/1.62 | (24) distinct_lines(all_0_2_2, all_0_1_1)
% 3.90/1.62 |
% 3.90/1.62 | Instantiating formula (13) with all_0_1_1, all_0_2_2, all_0_0_0, all_0_4_4 and discharging atoms distinct_lines(all_0_2_2, all_0_1_1), distinct_points(all_0_4_4, all_0_0_0), ~ apart_point_and_line(all_0_4_4, all_0_1_1), ~ apart_point_and_line(all_0_4_4, all_0_2_2), yields:
% 3.90/1.62 | (25) apart_point_and_line(all_0_0_0, all_0_1_1) | apart_point_and_line(all_0_0_0, all_0_2_2)
% 3.90/1.62 |
% 3.90/1.62 +-Applying beta-rule and splitting (25), into two cases.
% 3.90/1.62 |-Branch one:
% 3.90/1.62 | (26) apart_point_and_line(all_0_0_0, all_0_1_1)
% 3.90/1.62 |
% 3.90/1.62 | Instantiating formula (15) with all_0_0_0, all_0_0_0, 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_0_0, all_0_1_1), convergent_lines(all_0_2_2, all_0_1_1), yields:
% 3.90/1.62 | (27) distinct_points(all_0_0_0, all_0_0_0)
% 3.90/1.62 |
% 3.90/1.62 | Instantiating formula (16) with all_0_0_0 and discharging atoms distinct_points(all_0_0_0, all_0_0_0), yields:
% 3.90/1.62 | (28) $false
% 3.90/1.62 |
% 3.90/1.62 |-The branch is then unsatisfiable
% 3.90/1.62 |-Branch two:
% 3.90/1.62 | (29) ~ apart_point_and_line(all_0_0_0, all_0_1_1)
% 3.90/1.62 | (30) apart_point_and_line(all_0_0_0, all_0_2_2)
% 3.90/1.62 |
% 3.90/1.62 | Instantiating formula (2) with all_0_0_0, all_0_0_0, 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_0_0, all_0_2_2), convergent_lines(all_0_2_2, all_0_1_1), yields:
% 3.90/1.62 | (27) distinct_points(all_0_0_0, all_0_0_0)
% 3.90/1.62 |
% 3.90/1.62 | Instantiating formula (16) with all_0_0_0 and discharging atoms distinct_points(all_0_0_0, all_0_0_0), yields:
% 3.90/1.62 | (28) $false
% 3.90/1.62 |
% 3.90/1.62 |-The branch is then unsatisfiable
% 3.90/1.62 % SZS output end Proof for theBenchmark
% 3.90/1.62
% 3.90/1.62 1027ms
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