TSTP Solution File: GEO176+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : GEO176+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n022.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 22:55:24 EDT 2023
% Result : Theorem 46.43s 46.65s
% Output : Proof 46.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO176+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n022.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 22:38:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 46.43/46.65 SZS status Theorem for theBenchmark.p
% 46.43/46.65 SZS output start Proof for theBenchmark.p
% 46.43/46.65 Clause #8 (by assumption #[]): Eq (∀ (X Y : Iota), convergent_lines X Y → Not (apart_point_and_line (intersection_point X Y) X)) True
% 46.43/46.65 Clause #9 (by assumption #[]): Eq (∀ (X Y : Iota), convergent_lines X Y → Not (apart_point_and_line (intersection_point X Y) Y)) True
% 46.43/46.65 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
% 46.43/46.65 Clause #14 (by assumption #[]): Eq
% 46.43/46.65 (Not
% 46.43/46.65 (∀ (X Y U V : Iota),
% 46.43/46.65 And (And (distinct_points X Y) (convergent_lines U V))
% 46.43/46.65 (Or (apart_point_and_line X U) (apart_point_and_line X V)) →
% 46.43/46.65 distinct_points X (intersection_point U V)))
% 46.43/46.65 True
% 46.43/46.65 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
% 46.43/46.65 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
% 46.43/46.65 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota),
% 46.43/46.65 Or (Eq (convergent_lines a a_1) False) (Eq (Not (apart_point_and_line (intersection_point a a_1) a_1)) True)
% 46.43/46.65 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota),
% 46.43/46.65 Or (Eq (convergent_lines a a_1) False) (Eq (apart_point_and_line (intersection_point a a_1) a_1) False)
% 46.43/46.65 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
% 46.43/46.65 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
% 46.43/46.65 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota),
% 46.43/46.65 Or (Eq (convergent_lines a a_1) False) (Eq (Not (apart_point_and_line (intersection_point a a_1) a)) True)
% 46.43/46.65 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)
% 46.43/46.65 Clause #52 (by clausification #[14]): Eq
% 46.43/46.65 (∀ (X Y U V : Iota),
% 46.43/46.65 And (And (distinct_points X Y) (convergent_lines U V)) (Or (apart_point_and_line X U) (apart_point_and_line X V)) →
% 46.43/46.65 distinct_points X (intersection_point U V))
% 46.43/46.65 False
% 46.43/46.65 Clause #53 (by clausification #[52]): ∀ (a : Iota),
% 46.43/46.65 Eq
% 46.43/46.65 (Not
% 46.43/46.65 (∀ (Y U V : Iota),
% 46.43/46.65 And (And (distinct_points (skS.0 0 a) Y) (convergent_lines U V))
% 46.43/46.65 (Or (apart_point_and_line (skS.0 0 a) U) (apart_point_and_line (skS.0 0 a) V)) →
% 46.43/46.65 distinct_points (skS.0 0 a) (intersection_point U V)))
% 46.43/46.65 True
% 46.43/46.65 Clause #54 (by clausification #[53]): ∀ (a : Iota),
% 46.43/46.65 Eq
% 46.43/46.65 (∀ (Y U V : Iota),
% 46.43/46.65 And (And (distinct_points (skS.0 0 a) Y) (convergent_lines U V))
% 46.43/46.65 (Or (apart_point_and_line (skS.0 0 a) U) (apart_point_and_line (skS.0 0 a) V)) →
% 46.43/46.65 distinct_points (skS.0 0 a) (intersection_point U V))
% 46.43/46.65 False
% 46.43/46.65 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota),
% 46.43/46.65 Eq
% 46.43/46.65 (Not
% 46.43/46.65 (∀ (U V : Iota),
% 46.43/46.65 And (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines U V))
% 46.43/46.65 (Or (apart_point_and_line (skS.0 0 a) U) (apart_point_and_line (skS.0 0 a) V)) →
% 46.43/46.65 distinct_points (skS.0 0 a) (intersection_point U V)))
% 46.43/46.65 True
% 46.43/46.65 Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota),
% 46.43/46.65 Eq
% 46.43/46.65 (∀ (U V : Iota),
% 46.43/46.65 And (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines U V))
% 46.43/46.65 (Or (apart_point_and_line (skS.0 0 a) U) (apart_point_and_line (skS.0 0 a) V)) →
% 46.43/46.65 distinct_points (skS.0 0 a) (intersection_point U V))
% 46.43/46.65 False
% 46.43/46.65 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota),
% 46.43/46.65 Eq
% 46.43/46.65 (Not
% 46.43/46.65 (∀ (V : Iota),
% 46.43/46.65 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))
% 46.43/46.65 (Or (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) (apart_point_and_line (skS.0 0 a) V)) →
% 46.43/46.65 distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) V)))
% 46.43/46.65 True
% 46.43/46.65 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota),
% 46.51/46.68 Eq
% 46.51/46.68 (∀ (V : Iota),
% 46.51/46.68 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))
% 46.51/46.68 (Or (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) (apart_point_and_line (skS.0 0 a) V)) →
% 46.51/46.68 distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) V))
% 46.51/46.68 False
% 46.51/46.68 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 a_3 : Iota),
% 46.51/46.68 Eq
% 46.51/46.68 (Not
% 46.51/46.68 (And
% 46.51/46.68 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1))
% 46.51/46.68 (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))
% 46.51/46.68 (Or (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))
% 46.51/46.68 (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))) →
% 46.51/46.68 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))))
% 46.51/46.68 True
% 46.51/46.68 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 a_3 : Iota),
% 46.51/46.68 Eq
% 46.51/46.68 (And
% 46.51/46.68 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1))
% 46.51/46.68 (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))
% 46.51/46.68 (Or (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))
% 46.51/46.68 (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))) →
% 46.51/46.68 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)))
% 46.51/46.68 False
% 46.51/46.68 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 a_3 : Iota),
% 46.51/46.68 Eq
% 46.51/46.68 (And
% 46.51/46.68 (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)))
% 46.51/46.68 (Or (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))
% 46.51/46.68 (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))))
% 46.51/46.68 True
% 46.51/46.68 Clause #62 (by clausification #[60]): ∀ (a a_1 a_2 a_3 : Iota),
% 46.51/46.68 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
% 46.51/46.68 Clause #63 (by clausification #[61]): ∀ (a a_1 a_2 a_3 : Iota),
% 46.51/46.68 Eq
% 46.51/46.68 (Or (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))
% 46.51/46.68 (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3)))
% 46.51/46.68 True
% 46.51/46.68 Clause #64 (by clausification #[61]): ∀ (a a_1 a_2 a_3 : Iota),
% 46.51/46.68 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)))
% 46.51/46.68 True
% 46.51/46.68 Clause #65 (by clausification #[63]): ∀ (a a_1 a_2 a_3 : Iota),
% 46.51/46.68 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True)
% 46.51/46.68 (Eq (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3)) True)
% 46.51/46.68 Clause #72 (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
% 46.51/46.68 Clause #73 (by clausification #[72]): ∀ (a a_1 : Iota),
% 46.51/46.68 Eq (∀ (Z : Iota), apart_point_and_line a a_1 → Or (distinct_points a Z) (apart_point_and_line Z a_1)) True
% 46.51/46.68 Clause #74 (by clausification #[73]): ∀ (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
% 46.51/46.68 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 : Iota),
% 46.51/46.68 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)
% 46.51/46.68 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 : Iota),
% 46.51/46.68 Or (Eq (apart_point_and_line a a_1) False)
% 46.51/46.68 (Or (Eq (distinct_points a a_2) True) (Eq (apart_point_and_line a_2 a_1) True))
% 46.51/46.68 Clause #77 (by superposition #[76, 65]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 46.51/46.68 Or (Eq (distinct_points (skS.0 0 a) a_1) True)
% 46.51/46.68 (Or (Eq (apart_point_and_line a_1 (skS.0 3 a a_2 a_3 a_4)) True)
% 46.51/46.68 (Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_2 a_3)) True) (Eq False True)))
% 46.51/46.68 Clause #92 (by clausification #[64]): ∀ (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
% 46.51/46.68 Clause #94 (by superposition #[92, 37]): ∀ (a a_1 a_2 a_3 : Iota),
% 46.51/46.68 Or (Eq True False)
% 46.51/46.68 (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))
% 46.51/46.68 False)
% 46.51/46.68 Clause #95 (by superposition #[92, 41]): ∀ (a a_1 a_2 a_3 : Iota),
% 46.51/46.68 Or (Eq True False)
% 46.51/46.68 (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))
% 46.58/46.79 False)
% 46.58/46.79 Clause #115 (by clausification #[77]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 46.58/46.79 Or (Eq (distinct_points (skS.0 0 a) a_1) True)
% 46.58/46.79 (Or (Eq (apart_point_and_line a_1 (skS.0 3 a a_2 a_3 a_4)) True)
% 46.58/46.79 (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_2 a_3)) True))
% 46.58/46.79 Clause #146 (by clausification #[94]): ∀ (a a_1 a_2 a_3 : Iota),
% 46.58/46.79 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))
% 46.58/46.79 False
% 46.58/46.79 Clause #147 (by superposition #[146, 115]): ∀ (a a_1 a_2 a_3 : Iota),
% 46.58/46.79 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)
% 46.58/46.79 (Or (Eq False True) (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True))
% 46.58/46.79 Clause #153 (by clausification #[95]): ∀ (a a_1 a_2 a_3 : Iota),
% 46.58/46.79 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
% 46.58/46.79 Clause #911 (by clausification #[147]): ∀ (a a_1 a_2 a_3 : Iota),
% 46.58/46.79 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)
% 46.58/46.79 (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True)
% 46.58/46.79 Clause #912 (by superposition #[911, 62]): ∀ (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)
% 46.58/46.79 Clause #917 (by clausification #[912]): ∀ (a a_1 a_2 : Iota), Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True
% 46.58/46.79 Clause #921 (by superposition #[917, 76]): ∀ (a a_1 a_2 a_3 : Iota),
% 46.58/46.79 Or (Eq True False)
% 46.58/46.79 (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))
% 46.58/46.79 Clause #922 (by clausification #[921]): ∀ (a a_1 a_2 a_3 : Iota),
% 46.58/46.79 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)
% 46.58/46.79 Clause #923 (by superposition #[922, 153]): ∀ (a a_1 a_2 a_3 : Iota),
% 46.58/46.79 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)
% 46.58/46.79 (Eq True False)
% 46.58/46.79 Clause #8390 (by clausification #[923]): ∀ (a a_1 a_2 a_3 : Iota),
% 46.58/46.79 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
% 46.58/46.79 Clause #8391 (by superposition #[8390, 62]): Eq True False
% 46.58/46.79 Clause #8396 (by clausification #[8391]): False
% 46.58/46.79 SZS output end Proof for theBenchmark.p
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