TSTP Solution File: GEO185+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : GEO185+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n031.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 82.11s 82.28s
% Output : Proof 82.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO185+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n031.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 : 300
% 0.13/0.34 % DateTime : Wed Aug 30 00:14:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 82.11/82.28 SZS status Theorem for theBenchmark.p
% 82.11/82.28 SZS output start Proof for theBenchmark.p
% 82.11/82.28 Clause #8 (by assumption #[]): Eq (∀ (X Y : Iota), convergent_lines X Y → Not (apart_point_and_line (intersection_point X Y) X)) True
% 82.11/82.28 Clause #9 (by assumption #[]): Eq (∀ (X Y : Iota), convergent_lines X Y → Not (apart_point_and_line (intersection_point X Y) Y)) True
% 82.11/82.28 Clause #11 (by assumption #[]): Eq (∀ (X Y Z : Iota), apart_point_and_line X Y → Or (distinct_points X Z) (apart_point_and_line Z Y)) True
% 82.11/82.28 Clause #14 (by assumption #[]): Eq
% 82.11/82.28 (Not
% 82.11/82.28 (∀ (X Y U V : Iota),
% 82.11/82.28 And (And (distinct_points X Y) (convergent_lines U V)) (Not (distinct_points X (intersection_point U V))) →
% 82.11/82.28 And (Not (apart_point_and_line X U)) (Not (apart_point_and_line X V))))
% 82.11/82.28 True
% 82.11/82.28 Clause #34 (by clausification #[9]): ∀ (a : Iota), Eq (∀ (Y : Iota), convergent_lines a Y → Not (apart_point_and_line (intersection_point a Y) Y)) True
% 82.11/82.28 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Eq (convergent_lines a a_1 → Not (apart_point_and_line (intersection_point a a_1) a_1)) True
% 82.11/82.28 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota),
% 82.11/82.28 Or (Eq (convergent_lines a a_1) False) (Eq (Not (apart_point_and_line (intersection_point a a_1) a_1)) True)
% 82.11/82.28 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota),
% 82.11/82.28 Or (Eq (convergent_lines a a_1) False) (Eq (apart_point_and_line (intersection_point a a_1) a_1) False)
% 82.11/82.28 Clause #38 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (Y : Iota), convergent_lines a Y → Not (apart_point_and_line (intersection_point a Y) a)) True
% 82.11/82.28 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (convergent_lines a a_1 → Not (apart_point_and_line (intersection_point a a_1) a)) True
% 82.11/82.28 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota),
% 82.11/82.28 Or (Eq (convergent_lines a a_1) False) (Eq (Not (apart_point_and_line (intersection_point a a_1) a)) True)
% 82.11/82.28 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Or (Eq (convergent_lines a a_1) False) (Eq (apart_point_and_line (intersection_point a a_1) a) False)
% 82.11/82.28 Clause #52 (by clausification #[11]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), apart_point_and_line a Y → Or (distinct_points a Z) (apart_point_and_line Z Y)) True
% 82.11/82.28 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota),
% 82.11/82.28 Eq (∀ (Z : Iota), apart_point_and_line a a_1 → Or (distinct_points a Z) (apart_point_and_line Z a_1)) True
% 82.11/82.28 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), Eq (apart_point_and_line a a_1 → Or (distinct_points a a_2) (apart_point_and_line a_2 a_1)) True
% 82.11/82.28 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 : Iota),
% 82.11/82.28 Or (Eq (apart_point_and_line a a_1) False) (Eq (Or (distinct_points a a_2) (apart_point_and_line a_2 a_1)) True)
% 82.11/82.28 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 : Iota),
% 82.11/82.28 Or (Eq (apart_point_and_line a a_1) False)
% 82.11/82.28 (Or (Eq (distinct_points a a_2) True) (Eq (apart_point_and_line a_2 a_1) True))
% 82.11/82.28 Clause #67 (by clausification #[14]): Eq
% 82.11/82.28 (∀ (X Y U V : Iota),
% 82.11/82.28 And (And (distinct_points X Y) (convergent_lines U V)) (Not (distinct_points X (intersection_point U V))) →
% 82.11/82.28 And (Not (apart_point_and_line X U)) (Not (apart_point_and_line X V)))
% 82.11/82.28 False
% 82.11/82.28 Clause #68 (by clausification #[67]): ∀ (a : Iota),
% 82.11/82.28 Eq
% 82.11/82.28 (Not
% 82.11/82.28 (∀ (Y U V : Iota),
% 82.11/82.28 And (And (distinct_points (skS.0 0 a) Y) (convergent_lines U V))
% 82.11/82.28 (Not (distinct_points (skS.0 0 a) (intersection_point U V))) →
% 82.11/82.28 And (Not (apart_point_and_line (skS.0 0 a) U)) (Not (apart_point_and_line (skS.0 0 a) V))))
% 82.11/82.28 True
% 82.11/82.28 Clause #69 (by clausification #[68]): ∀ (a : Iota),
% 82.11/82.28 Eq
% 82.11/82.28 (∀ (Y U V : Iota),
% 82.11/82.28 And (And (distinct_points (skS.0 0 a) Y) (convergent_lines U V))
% 82.11/82.28 (Not (distinct_points (skS.0 0 a) (intersection_point U V))) →
% 82.11/82.28 And (Not (apart_point_and_line (skS.0 0 a) U)) (Not (apart_point_and_line (skS.0 0 a) V)))
% 82.11/82.28 False
% 82.11/82.28 Clause #70 (by clausification #[69]): ∀ (a a_1 : Iota),
% 82.11/82.28 Eq
% 82.11/82.28 (Not
% 82.11/82.28 (∀ (U V : Iota),
% 82.11/82.28 And (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines U V))
% 82.11/82.28 (Not (distinct_points (skS.0 0 a) (intersection_point U V))) →
% 82.13/82.30 And (Not (apart_point_and_line (skS.0 0 a) U)) (Not (apart_point_and_line (skS.0 0 a) V))))
% 82.13/82.30 True
% 82.13/82.30 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota),
% 82.13/82.30 Eq
% 82.13/82.30 (∀ (U V : Iota),
% 82.13/82.30 And (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines U V))
% 82.13/82.30 (Not (distinct_points (skS.0 0 a) (intersection_point U V))) →
% 82.13/82.30 And (Not (apart_point_and_line (skS.0 0 a) U)) (Not (apart_point_and_line (skS.0 0 a) V)))
% 82.13/82.30 False
% 82.13/82.30 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota),
% 82.13/82.30 Eq
% 82.13/82.30 (Not
% 82.13/82.30 (∀ (V : Iota),
% 82.13/82.30 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))
% 82.13/82.30 (Not (distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) V))) →
% 82.13/82.30 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))))
% 82.13/82.30 True
% 82.13/82.30 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota),
% 82.13/82.30 Eq
% 82.13/82.30 (∀ (V : Iota),
% 82.13/82.30 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))
% 82.13/82.30 (Not (distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) V))) →
% 82.13/82.30 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)))
% 82.13/82.30 False
% 82.13/82.30 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 a_3 : Iota),
% 82.13/82.30 Eq
% 82.13/82.30 (Not
% 82.13/82.30 (And
% 82.13/82.30 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1))
% 82.13/82.30 (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))
% 82.13/82.30 (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)))) →
% 82.13/82.30 And (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)))
% 82.13/82.30 (Not (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3)))))
% 82.13/82.30 True
% 82.13/82.30 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 a_3 : Iota),
% 82.13/82.30 Eq
% 82.13/82.30 (And
% 82.13/82.30 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1))
% 82.13/82.30 (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))
% 82.13/82.30 (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)))) →
% 82.13/82.30 And (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)))
% 82.13/82.30 (Not (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))))
% 82.13/82.30 False
% 82.13/82.30 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 a_3 : Iota),
% 82.13/82.30 Eq
% 82.13/82.30 (And
% 82.13/82.30 (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)))
% 82.13/82.30 (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)))))
% 82.13/82.30 True
% 82.13/82.30 Clause #77 (by clausification #[75]): ∀ (a a_1 a_2 a_3 : Iota),
% 82.13/82.30 Eq
% 82.13/82.30 (And (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)))
% 82.13/82.30 (Not (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))))
% 82.13/82.30 False
% 82.13/82.30 Clause #78 (by clausification #[76]): ∀ (a a_1 a_2 a_3 : Iota),
% 82.13/82.30 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
% 82.13/82.30 Clause #79 (by clausification #[76]): ∀ (a a_1 a_2 a_3 : Iota),
% 82.13/82.30 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)))
% 82.13/82.30 True
% 82.13/82.30 Clause #80 (by clausification #[78]): ∀ (a a_1 a_2 a_3 : Iota),
% 82.13/82.30 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
% 82.13/82.30 Clause #90 (by clausification #[79]): ∀ (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
% 82.13/82.30 Clause #92 (by superposition #[90, 37]): ∀ (a a_1 a_2 a_3 : Iota),
% 82.13/82.30 Or (Eq True False)
% 82.13/82.30 (Eq (apart_point_and_line (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (skS.0 3 a a_1 a_2 a_3))
% 82.13/82.30 False)
% 82.13/82.30 Clause #93 (by superposition #[90, 41]): ∀ (a a_1 a_2 a_3 : Iota),
% 82.13/82.30 Or (Eq True False)
% 82.13/82.30 (Eq (apart_point_and_line (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (skS.0 2 a a_1 a_2))
% 82.13/82.30 False)
% 82.13/82.30 Clause #100 (by clausification #[77]): ∀ (a a_1 a_2 a_3 : Iota),
% 82.13/82.30 Or (Eq (Not (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))) False)
% 82.25/82.45 (Eq (Not (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))) False)
% 82.25/82.45 Clause #101 (by clausification #[100]): ∀ (a a_1 a_2 a_3 : Iota),
% 82.25/82.45 Or (Eq (Not (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))) False)
% 82.25/82.45 (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True)
% 82.25/82.45 Clause #102 (by clausification #[101]): ∀ (a a_1 a_2 a_3 : Iota),
% 82.25/82.45 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True)
% 82.25/82.45 (Eq (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3)) True)
% 82.25/82.45 Clause #104 (by superposition #[102, 56]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 82.25/82.45 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True)
% 82.25/82.45 (Or (Eq True False)
% 82.25/82.45 (Or (Eq (distinct_points (skS.0 0 a) a_3) True) (Eq (apart_point_and_line a_3 (skS.0 3 a a_1 a_2 a_4)) True)))
% 82.25/82.45 Clause #132 (by clausification #[92]): ∀ (a a_1 a_2 a_3 : Iota),
% 82.25/82.45 Eq (apart_point_and_line (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (skS.0 3 a a_1 a_2 a_3))
% 82.25/82.45 False
% 82.25/82.45 Clause #141 (by clausification #[93]): ∀ (a a_1 a_2 a_3 : Iota),
% 82.25/82.45 Eq (apart_point_and_line (intersection_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (skS.0 2 a a_1 a_2)) False
% 82.25/82.45 Clause #282 (by clausification #[104]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 82.25/82.45 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True)
% 82.25/82.45 (Or (Eq (distinct_points (skS.0 0 a) a_3) True) (Eq (apart_point_and_line a_3 (skS.0 3 a a_1 a_2 a_4)) True))
% 82.25/82.45 Clause #285 (by superposition #[282, 132]): ∀ (a a_1 a_2 a_3 : Iota),
% 82.25/82.45 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True)
% 82.25/82.45 (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)
% 82.25/82.45 (Eq True False))
% 82.25/82.45 Clause #2531 (by clausification #[285]): ∀ (a a_1 a_2 a_3 : Iota),
% 82.25/82.45 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True)
% 82.25/82.45 (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)
% 82.25/82.45 Clause #2532 (by superposition #[2531, 80]): ∀ (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)
% 82.25/82.45 Clause #2537 (by clausification #[2532]): ∀ (a a_1 a_2 : Iota), Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True
% 82.25/82.45 Clause #2541 (by superposition #[2537, 56]): ∀ (a a_1 a_2 a_3 : Iota),
% 82.25/82.45 Or (Eq True False)
% 82.25/82.45 (Or (Eq (distinct_points (skS.0 0 a) a_1) True) (Eq (apart_point_and_line a_1 (skS.0 2 a a_2 a_3)) True))
% 82.25/82.45 Clause #2542 (by clausification #[2541]): ∀ (a a_1 a_2 a_3 : Iota),
% 82.25/82.45 Or (Eq (distinct_points (skS.0 0 a) a_1) True) (Eq (apart_point_and_line a_1 (skS.0 2 a a_2 a_3)) True)
% 82.25/82.45 Clause #2543 (by superposition #[2542, 141]): ∀ (a a_1 a_2 a_3 : Iota),
% 82.25/82.45 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)
% 82.25/82.45 (Eq True False)
% 82.25/82.45 Clause #11328 (by clausification #[2543]): ∀ (a a_1 a_2 a_3 : Iota),
% 82.25/82.45 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
% 82.25/82.45 Clause #11329 (by superposition #[11328, 80]): Eq True False
% 82.25/82.45 Clause #11370 (by clausification #[11329]): False
% 82.25/82.45 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------