TSTP Solution File: GEO185+2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : GEO185+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n024.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 : 300s
% DateTime : Wed Aug 30 22:55:28 EDT 2023
% Result : Theorem 34.03s 34.31s
% Output : Proof 34.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO185+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : duper %s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 30 00:00:22 EDT 2023
% 0.20/0.35 % CPUTime :
% 34.03/34.31 SZS status Theorem for theBenchmark.p
% 34.03/34.31 SZS output start Proof for theBenchmark.p
% 34.03/34.31 Clause #7 (by assumption #[]): Eq
% 34.03/34.31 (∀ (X Y Z : Iota),
% 34.03/34.31 convergent_lines X Y →
% 34.03/34.31 Or (apart_point_and_line Z X) (apart_point_and_line Z Y) → distinct_points Z (intersection_point X Y))
% 34.03/34.31 True
% 34.03/34.31 Clause #12 (by assumption #[]): Eq
% 34.03/34.31 (Not
% 34.03/34.31 (∀ (X Y U V : Iota),
% 34.03/34.31 And (And (distinct_points X Y) (convergent_lines U V)) (Not (distinct_points X (intersection_point U V))) →
% 34.03/34.31 And (Not (apart_point_and_line X U)) (Not (apart_point_and_line X V))))
% 34.03/34.31 True
% 34.03/34.31 Clause #22 (by clausification #[7]): ∀ (a : Iota),
% 34.03/34.31 Eq
% 34.03/34.31 (∀ (Y Z : Iota),
% 34.03/34.31 convergent_lines a Y →
% 34.03/34.31 Or (apart_point_and_line Z a) (apart_point_and_line Z Y) → distinct_points Z (intersection_point a Y))
% 34.03/34.31 True
% 34.03/34.31 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota),
% 34.03/34.31 Eq
% 34.03/34.31 (∀ (Z : Iota),
% 34.03/34.31 convergent_lines a a_1 →
% 34.03/34.31 Or (apart_point_and_line Z a) (apart_point_and_line Z a_1) → distinct_points Z (intersection_point a a_1))
% 34.03/34.31 True
% 34.03/34.31 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota),
% 34.03/34.31 Eq
% 34.03/34.31 (convergent_lines a a_1 →
% 34.03/34.31 Or (apart_point_and_line a_2 a) (apart_point_and_line a_2 a_1) → distinct_points a_2 (intersection_point a a_1))
% 34.03/34.31 True
% 34.03/34.31 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota),
% 34.03/34.31 Or (Eq (convergent_lines a a_1) False)
% 34.03/34.31 (Eq
% 34.03/34.31 (Or (apart_point_and_line a_2 a) (apart_point_and_line a_2 a_1) → distinct_points a_2 (intersection_point a a_1))
% 34.03/34.31 True)
% 34.03/34.31 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota),
% 34.03/34.31 Or (Eq (convergent_lines a a_1) False)
% 34.03/34.31 (Or (Eq (Or (apart_point_and_line a_2 a) (apart_point_and_line a_2 a_1)) False)
% 34.03/34.31 (Eq (distinct_points a_2 (intersection_point a a_1)) True))
% 34.03/34.31 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota),
% 34.03/34.31 Or (Eq (convergent_lines a a_1) False)
% 34.03/34.31 (Or (Eq (distinct_points a_2 (intersection_point a a_1)) True) (Eq (apart_point_and_line a_2 a_1) False))
% 34.03/34.31 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 : Iota),
% 34.03/34.31 Or (Eq (convergent_lines a a_1) False)
% 34.03/34.31 (Or (Eq (distinct_points a_2 (intersection_point a a_1)) True) (Eq (apart_point_and_line a_2 a) False))
% 34.03/34.31 Clause #70 (by clausification #[12]): Eq
% 34.03/34.31 (∀ (X Y U V : Iota),
% 34.03/34.31 And (And (distinct_points X Y) (convergent_lines U V)) (Not (distinct_points X (intersection_point U V))) →
% 34.03/34.31 And (Not (apart_point_and_line X U)) (Not (apart_point_and_line X V)))
% 34.03/34.31 False
% 34.03/34.31 Clause #71 (by clausification #[70]): ∀ (a : Iota),
% 34.03/34.31 Eq
% 34.03/34.31 (Not
% 34.03/34.31 (∀ (Y U V : Iota),
% 34.03/34.31 And (And (distinct_points (skS.0 0 a) Y) (convergent_lines U V))
% 34.03/34.31 (Not (distinct_points (skS.0 0 a) (intersection_point U V))) →
% 34.03/34.31 And (Not (apart_point_and_line (skS.0 0 a) U)) (Not (apart_point_and_line (skS.0 0 a) V))))
% 34.03/34.31 True
% 34.03/34.31 Clause #72 (by clausification #[71]): ∀ (a : Iota),
% 34.03/34.31 Eq
% 34.03/34.31 (∀ (Y U V : Iota),
% 34.03/34.31 And (And (distinct_points (skS.0 0 a) Y) (convergent_lines U V))
% 34.03/34.31 (Not (distinct_points (skS.0 0 a) (intersection_point U V))) →
% 34.03/34.31 And (Not (apart_point_and_line (skS.0 0 a) U)) (Not (apart_point_and_line (skS.0 0 a) V)))
% 34.03/34.31 False
% 34.03/34.31 Clause #73 (by clausification #[72]): ∀ (a a_1 : Iota),
% 34.03/34.31 Eq
% 34.03/34.31 (Not
% 34.03/34.31 (∀ (U V : Iota),
% 34.03/34.31 And (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines U V))
% 34.03/34.31 (Not (distinct_points (skS.0 0 a) (intersection_point U V))) →
% 34.03/34.31 And (Not (apart_point_and_line (skS.0 0 a) U)) (Not (apart_point_and_line (skS.0 0 a) V))))
% 34.03/34.31 True
% 34.03/34.31 Clause #74 (by clausification #[73]): ∀ (a a_1 : Iota),
% 34.03/34.31 Eq
% 34.03/34.31 (∀ (U V : Iota),
% 34.03/34.31 And (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines U V))
% 34.03/34.31 (Not (distinct_points (skS.0 0 a) (intersection_point U V))) →
% 34.03/34.31 And (Not (apart_point_and_line (skS.0 0 a) U)) (Not (apart_point_and_line (skS.0 0 a) V)))
% 34.03/34.31 False
% 34.03/34.31 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 : Iota),
% 34.03/34.31 Eq
% 34.03/34.31 (Not
% 34.03/34.31 (∀ (V : Iota),
% 34.03/34.31 And (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines (skS.0 2 a a_1 a_2) V))
% 34.03/34.31 (Not (distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) V))) →
% 34.10/34.34 And (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))) (Not (apart_point_and_line (skS.0 0 a) V))))
% 34.10/34.34 True
% 34.10/34.34 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 : Iota),
% 34.10/34.34 Eq
% 34.10/34.34 (∀ (V : Iota),
% 34.10/34.34 And (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines (skS.0 2 a a_1 a_2) V))
% 34.10/34.34 (Not (distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) V))) →
% 34.10/34.34 And (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))) (Not (apart_point_and_line (skS.0 0 a) V)))
% 34.10/34.34 False
% 34.10/34.34 Clause #77 (by clausification #[76]): ∀ (a a_1 a_2 a_3 : Iota),
% 34.10/34.34 Eq
% 34.10/34.34 (Not
% 34.10/34.34 (And
% 34.10/34.34 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1))
% 34.10/34.34 (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))
% 34.10/34.34 (Not (distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))) →
% 34.10/34.34 And (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)))
% 34.10/34.34 (Not (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3)))))
% 34.10/34.34 True
% 34.10/34.34 Clause #78 (by clausification #[77]): ∀ (a a_1 a_2 a_3 : Iota),
% 34.10/34.34 Eq
% 34.10/34.34 (And
% 34.10/34.34 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1))
% 34.10/34.34 (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))
% 34.10/34.34 (Not (distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))) →
% 34.10/34.34 And (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)))
% 34.10/34.34 (Not (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))))
% 34.10/34.34 False
% 34.10/34.34 Clause #79 (by clausification #[78]): ∀ (a a_1 a_2 a_3 : Iota),
% 34.10/34.34 Eq
% 34.10/34.34 (And
% 34.10/34.34 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))
% 34.10/34.34 (Not (distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))))
% 34.10/34.34 True
% 34.10/34.34 Clause #80 (by clausification #[78]): ∀ (a a_1 a_2 a_3 : Iota),
% 34.10/34.34 Eq
% 34.10/34.34 (And (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)))
% 34.10/34.34 (Not (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))))
% 34.10/34.34 False
% 34.10/34.34 Clause #81 (by clausification #[79]): ∀ (a a_1 a_2 a_3 : Iota),
% 34.10/34.34 Eq (Not (distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))) True
% 34.10/34.34 Clause #82 (by clausification #[79]): ∀ (a a_1 a_2 a_3 : Iota),
% 34.10/34.34 Eq (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))
% 34.10/34.34 True
% 34.10/34.34 Clause #83 (by clausification #[81]): ∀ (a a_1 a_2 a_3 : Iota),
% 34.10/34.34 Eq (distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) False
% 34.10/34.34 Clause #84 (by clausification #[82]): ∀ (a a_1 a_2 a_3 : Iota), Eq (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) True
% 34.10/34.34 Clause #87 (by superposition #[84, 27]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 34.10/34.34 Or (Eq True False)
% 34.10/34.34 (Or (Eq (distinct_points a (intersection_point (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4))) True)
% 34.10/34.34 (Eq (apart_point_and_line a (skS.0 3 a_1 a_2 a_3 a_4)) False))
% 34.10/34.34 Clause #89 (by superposition #[84, 28]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 34.10/34.34 Or (Eq True False)
% 34.10/34.34 (Or (Eq (distinct_points a (intersection_point (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4))) True)
% 34.10/34.34 (Eq (apart_point_and_line a (skS.0 2 a_1 a_2 a_3)) False))
% 34.10/34.34 Clause #94 (by clausification #[80]): ∀ (a a_1 a_2 a_3 : Iota),
% 34.10/34.34 Or (Eq (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))) False)
% 34.10/34.34 (Eq (Not (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))) False)
% 34.10/34.34 Clause #95 (by clausification #[94]): ∀ (a a_1 a_2 a_3 : Iota),
% 34.10/34.34 Or (Eq (Not (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))) False)
% 34.10/34.34 (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True)
% 34.10/34.34 Clause #96 (by clausification #[95]): ∀ (a a_1 a_2 a_3 : Iota),
% 34.10/34.34 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True)
% 34.10/34.34 (Eq (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3)) True)
% 34.10/34.34 Clause #126 (by clausification #[87]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 34.10/34.34 Or (Eq (distinct_points a (intersection_point (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4))) True)
% 34.10/34.40 (Eq (apart_point_and_line a (skS.0 3 a_1 a_2 a_3 a_4)) False)
% 34.10/34.40 Clause #127 (by superposition #[126, 96]): ∀ (a a_1 a_2 a_3 : Iota),
% 34.10/34.40 Or (Eq (distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) True)
% 34.10/34.40 (Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) (Eq False True))
% 34.10/34.40 Clause #151 (by clausification #[89]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 34.10/34.40 Or (Eq (distinct_points a (intersection_point (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4))) True)
% 34.10/34.40 (Eq (apart_point_and_line a (skS.0 2 a_1 a_2 a_3)) False)
% 34.10/34.40 Clause #800 (by clausification #[127]): ∀ (a a_1 a_2 a_3 : Iota),
% 34.10/34.40 Or (Eq (distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) True)
% 34.10/34.40 (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True)
% 34.10/34.40 Clause #801 (by superposition #[800, 83]): ∀ (a a_1 a_2 : Iota), Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) (Eq True False)
% 34.10/34.40 Clause #806 (by clausification #[801]): ∀ (a a_1 a_2 : Iota), Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True
% 34.10/34.40 Clause #809 (by superposition #[806, 151]): ∀ (a a_1 a_2 a_3 : Iota),
% 34.10/34.40 Or (Eq (distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) True)
% 34.10/34.40 (Eq True False)
% 34.10/34.40 Clause #4920 (by clausification #[809]): ∀ (a a_1 a_2 a_3 : Iota),
% 34.10/34.40 Eq (distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) True
% 34.10/34.40 Clause #4921 (by superposition #[4920, 83]): Eq True False
% 34.10/34.40 Clause #4926 (by clausification #[4921]): False
% 34.10/34.40 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------