TSTP Solution File: GEO176+2 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : GEO176+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n002.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 36.04s 36.22s
% Output : Proof 36.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO176+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13 % Command : duper %s
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 21:10:35 EDT 2023
% 0.12/0.34 % CPUTime :
% 36.04/36.22 SZS status Theorem for theBenchmark.p
% 36.04/36.22 SZS output start Proof for theBenchmark.p
% 36.04/36.22 Clause #7 (by assumption #[]): Eq
% 36.04/36.22 (∀ (X Y Z : Iota),
% 36.04/36.22 convergent_lines X Y →
% 36.04/36.22 Or (apart_point_and_line Z X) (apart_point_and_line Z Y) → distinct_points Z (intersection_point X Y))
% 36.04/36.22 True
% 36.04/36.22 Clause #12 (by assumption #[]): Eq
% 36.04/36.22 (Not
% 36.04/36.22 (∀ (X Y U V : Iota),
% 36.04/36.22 And (And (distinct_points X Y) (convergent_lines U V))
% 36.04/36.22 (Or (apart_point_and_line X U) (apart_point_and_line X V)) →
% 36.04/36.22 distinct_points X (intersection_point U V)))
% 36.04/36.22 True
% 36.04/36.22 Clause #22 (by clausification #[7]): ∀ (a : Iota),
% 36.04/36.22 Eq
% 36.04/36.22 (∀ (Y Z : Iota),
% 36.04/36.22 convergent_lines a Y →
% 36.04/36.22 Or (apart_point_and_line Z a) (apart_point_and_line Z Y) → distinct_points Z (intersection_point a Y))
% 36.04/36.22 True
% 36.04/36.22 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota),
% 36.04/36.22 Eq
% 36.04/36.22 (∀ (Z : Iota),
% 36.04/36.22 convergent_lines a a_1 →
% 36.04/36.22 Or (apart_point_and_line Z a) (apart_point_and_line Z a_1) → distinct_points Z (intersection_point a a_1))
% 36.04/36.22 True
% 36.04/36.22 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota),
% 36.04/36.22 Eq
% 36.04/36.22 (convergent_lines a a_1 →
% 36.04/36.22 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))
% 36.04/36.22 True
% 36.04/36.22 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota),
% 36.04/36.22 Or (Eq (convergent_lines a a_1) False)
% 36.04/36.22 (Eq
% 36.04/36.22 (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))
% 36.04/36.22 True)
% 36.04/36.22 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota),
% 36.04/36.22 Or (Eq (convergent_lines a a_1) False)
% 36.04/36.22 (Or (Eq (Or (apart_point_and_line a_2 a) (apart_point_and_line a_2 a_1)) False)
% 36.04/36.22 (Eq (distinct_points a_2 (intersection_point a a_1)) True))
% 36.04/36.22 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota),
% 36.04/36.22 Or (Eq (convergent_lines a a_1) False)
% 36.04/36.22 (Or (Eq (distinct_points a_2 (intersection_point a a_1)) True) (Eq (apart_point_and_line a_2 a_1) False))
% 36.04/36.22 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 : Iota),
% 36.04/36.22 Or (Eq (convergent_lines a a_1) False)
% 36.04/36.22 (Or (Eq (distinct_points a_2 (intersection_point a a_1)) True) (Eq (apart_point_and_line a_2 a) False))
% 36.04/36.22 Clause #54 (by clausification #[12]): Eq
% 36.04/36.22 (∀ (X Y U V : Iota),
% 36.04/36.22 And (And (distinct_points X Y) (convergent_lines U V)) (Or (apart_point_and_line X U) (apart_point_and_line X V)) →
% 36.04/36.22 distinct_points X (intersection_point U V))
% 36.04/36.22 False
% 36.04/36.22 Clause #55 (by clausification #[54]): ∀ (a : Iota),
% 36.04/36.22 Eq
% 36.04/36.22 (Not
% 36.04/36.22 (∀ (Y U V : Iota),
% 36.04/36.22 And (And (distinct_points (skS.0 0 a) Y) (convergent_lines U V))
% 36.04/36.22 (Or (apart_point_and_line (skS.0 0 a) U) (apart_point_and_line (skS.0 0 a) V)) →
% 36.04/36.22 distinct_points (skS.0 0 a) (intersection_point U V)))
% 36.04/36.22 True
% 36.04/36.22 Clause #56 (by clausification #[55]): ∀ (a : Iota),
% 36.04/36.22 Eq
% 36.04/36.22 (∀ (Y U V : Iota),
% 36.04/36.22 And (And (distinct_points (skS.0 0 a) Y) (convergent_lines U V))
% 36.04/36.22 (Or (apart_point_and_line (skS.0 0 a) U) (apart_point_and_line (skS.0 0 a) V)) →
% 36.04/36.22 distinct_points (skS.0 0 a) (intersection_point U V))
% 36.04/36.22 False
% 36.04/36.22 Clause #57 (by clausification #[56]): ∀ (a a_1 : Iota),
% 36.04/36.22 Eq
% 36.04/36.22 (Not
% 36.04/36.22 (∀ (U V : Iota),
% 36.04/36.22 And (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines U V))
% 36.04/36.22 (Or (apart_point_and_line (skS.0 0 a) U) (apart_point_and_line (skS.0 0 a) V)) →
% 36.04/36.22 distinct_points (skS.0 0 a) (intersection_point U V)))
% 36.04/36.22 True
% 36.04/36.22 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota),
% 36.04/36.22 Eq
% 36.04/36.22 (∀ (U V : Iota),
% 36.04/36.22 And (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) (convergent_lines U V))
% 36.04/36.22 (Or (apart_point_and_line (skS.0 0 a) U) (apart_point_and_line (skS.0 0 a) V)) →
% 36.04/36.22 distinct_points (skS.0 0 a) (intersection_point U V))
% 36.04/36.22 False
% 36.04/36.22 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 : Iota),
% 36.04/36.22 Eq
% 36.04/36.22 (Not
% 36.04/36.22 (∀ (V : Iota),
% 36.04/36.22 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))
% 36.04/36.22 (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)) →
% 36.04/36.22 distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) V)))
% 36.04/36.24 True
% 36.04/36.24 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 : Iota),
% 36.04/36.24 Eq
% 36.04/36.24 (∀ (V : Iota),
% 36.04/36.24 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))
% 36.04/36.24 (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)) →
% 36.04/36.24 distinct_points (skS.0 0 a) (intersection_point (skS.0 2 a a_1 a_2) V))
% 36.04/36.24 False
% 36.04/36.24 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 a_3 : Iota),
% 36.04/36.24 Eq
% 36.04/36.24 (Not
% 36.04/36.24 (And
% 36.04/36.24 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1))
% 36.04/36.24 (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))
% 36.04/36.24 (Or (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))
% 36.04/36.24 (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))) →
% 36.04/36.24 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))))
% 36.04/36.24 True
% 36.04/36.24 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 a_3 : Iota),
% 36.04/36.24 Eq
% 36.04/36.24 (And
% 36.04/36.24 (And (distinct_points (skS.0 0 a) (skS.0 1 a a_1))
% 36.04/36.24 (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))
% 36.04/36.24 (Or (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))
% 36.04/36.24 (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))) →
% 36.04/36.24 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)))
% 36.04/36.24 False
% 36.04/36.24 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 a_3 : Iota),
% 36.04/36.24 Eq
% 36.04/36.24 (And
% 36.04/36.24 (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)))
% 36.04/36.24 (Or (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))
% 36.04/36.24 (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3))))
% 36.04/36.24 True
% 36.04/36.24 Clause #64 (by clausification #[62]): ∀ (a a_1 a_2 a_3 : Iota),
% 36.04/36.24 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
% 36.04/36.24 Clause #65 (by clausification #[63]): ∀ (a a_1 a_2 a_3 : Iota),
% 36.04/36.24 Eq
% 36.04/36.24 (Or (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2))
% 36.04/36.24 (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3)))
% 36.04/36.24 True
% 36.04/36.24 Clause #66 (by clausification #[63]): ∀ (a a_1 a_2 a_3 : Iota),
% 36.04/36.24 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)))
% 36.04/36.24 True
% 36.04/36.24 Clause #67 (by clausification #[65]): ∀ (a a_1 a_2 a_3 : Iota),
% 36.04/36.24 Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True)
% 36.04/36.24 (Eq (apart_point_and_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3)) True)
% 36.04/36.24 Clause #86 (by clausification #[66]): ∀ (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
% 36.04/36.24 Clause #89 (by superposition #[86, 27]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 36.04/36.24 Or (Eq True False)
% 36.04/36.24 (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)
% 36.04/36.24 (Eq (apart_point_and_line a (skS.0 3 a_1 a_2 a_3 a_4)) False))
% 36.04/36.24 Clause #91 (by superposition #[86, 28]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 36.04/36.24 Or (Eq True False)
% 36.04/36.24 (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)
% 36.04/36.24 (Eq (apart_point_and_line a (skS.0 2 a_1 a_2 a_3)) False))
% 36.04/36.24 Clause #141 (by clausification #[89]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 36.04/36.24 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)
% 36.04/36.24 (Eq (apart_point_and_line a (skS.0 3 a_1 a_2 a_3 a_4)) False)
% 36.04/36.24 Clause #142 (by superposition #[141, 67]): ∀ (a a_1 a_2 a_3 : Iota),
% 36.04/36.24 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)
% 36.04/36.24 (Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) (Eq False True))
% 36.04/36.24 Clause #217 (by clausification #[91]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 36.04/36.24 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)
% 36.04/36.24 (Eq (apart_point_and_line a (skS.0 2 a_1 a_2 a_3)) False)
% 36.04/36.24 Clause #1076 (by clausification #[142]): ∀ (a a_1 a_2 a_3 : Iota),
% 36.04/36.24 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)
% 36.04/36.30 (Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True)
% 36.04/36.30 Clause #1077 (by superposition #[1076, 64]): ∀ (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)
% 36.04/36.30 Clause #1082 (by clausification #[1077]): ∀ (a a_1 a_2 : Iota), Eq (apart_point_and_line (skS.0 0 a) (skS.0 2 a a_1 a_2)) True
% 36.04/36.30 Clause #1085 (by superposition #[1082, 217]): ∀ (a a_1 a_2 a_3 : Iota),
% 36.04/36.30 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)
% 36.04/36.30 (Eq True False)
% 36.04/36.30 Clause #5285 (by clausification #[1085]): ∀ (a a_1 a_2 a_3 : Iota),
% 36.04/36.30 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))) True
% 36.04/36.30 Clause #5286 (by superposition #[5285, 64]): Eq True False
% 36.04/36.30 Clause #5291 (by clausification #[5286]): False
% 36.04/36.30 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------