TSTP Solution File: GEO206+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : GEO206+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n004.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 22:55:37 EDT 2023
% Result : Theorem 239.94s 240.56s
% Output : Proof 240.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.20 % Problem : GEO206+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.21 % Command : duper %s
% 0.13/0.51 % Computer : n004.cluster.edu
% 0.13/0.51 % Model : x86_64 x86_64
% 0.13/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.51 % Memory : 8042.1875MB
% 0.13/0.51 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.51 % CPULimit : 300
% 0.13/0.51 % WCLimit : 300
% 0.13/0.51 % DateTime : Tue Aug 29 20:55:52 EDT 2023
% 0.13/0.51 % CPUTime :
% 239.94/240.56 SZS status Theorem for theBenchmark.p
% 239.94/240.56 SZS output start Proof for theBenchmark.p
% 239.94/240.56 Clause #1 (by assumption #[]): Eq (∀ (X : Iota), Not (distinct_lines X X)) True
% 239.94/240.56 Clause #4 (by assumption #[]): Eq (∀ (X Y Z : Iota), distinct_lines X Y → Or (distinct_lines X Z) (distinct_lines Y Z)) True
% 239.94/240.56 Clause #5 (by assumption #[]): Eq (∀ (X Y Z : Iota), convergent_lines X Y → Or (convergent_lines X Z) (convergent_lines Y Z)) True
% 239.94/240.56 Clause #14 (by assumption #[]): Eq (∀ (X Y : Iota), Not (convergent_lines (parallel_through_point Y X) Y)) True
% 239.94/240.56 Clause #15 (by assumption #[]): Eq (∀ (X Y : Iota), Not (apart_point_and_line X (parallel_through_point Y X))) True
% 239.94/240.56 Clause #16 (by assumption #[]): Eq
% 239.94/240.56 (∀ (X Y Z : Iota),
% 239.94/240.56 distinct_lines Y Z → Or (Or (apart_point_and_line X Y) (apart_point_and_line X Z)) (convergent_lines Y Z))
% 239.94/240.56 True
% 239.94/240.56 Clause #17 (by assumption #[]): Eq
% 239.94/240.56 (Not
% 239.94/240.56 (∀ (X Y Z : Iota),
% 239.94/240.56 And (Not (apart_point_and_line X Y)) (Not (convergent_lines Y Z)) →
% 239.94/240.56 Not (distinct_lines Y (parallel_through_point Z X))))
% 239.94/240.56 True
% 239.94/240.56 Clause #20 (by clausification #[1]): ∀ (a : Iota), Eq (Not (distinct_lines a a)) True
% 239.94/240.56 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (distinct_lines a a) False
% 239.94/240.56 Clause #24 (by clausification #[15]): ∀ (a : Iota), Eq (∀ (Y : Iota), Not (apart_point_and_line a (parallel_through_point Y a))) True
% 239.94/240.56 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (Not (apart_point_and_line a (parallel_through_point a_1 a))) True
% 239.94/240.56 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (apart_point_and_line a (parallel_through_point a_1 a)) False
% 239.94/240.56 Clause #27 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (Y : Iota), Not (convergent_lines (parallel_through_point Y a) Y)) True
% 239.94/240.56 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (Not (convergent_lines (parallel_through_point a a_1) a)) True
% 239.94/240.56 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (convergent_lines (parallel_through_point a a_1) a) False
% 239.94/240.56 Clause #56 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), distinct_lines a Y → Or (distinct_lines a Z) (distinct_lines Y Z)) True
% 239.94/240.56 Clause #57 (by clausification #[56]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), distinct_lines a a_1 → Or (distinct_lines a Z) (distinct_lines a_1 Z)) True
% 239.94/240.56 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), Eq (distinct_lines a a_1 → Or (distinct_lines a a_2) (distinct_lines a_1 a_2)) True
% 239.94/240.56 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 : Iota),
% 239.94/240.56 Or (Eq (distinct_lines a a_1) False) (Eq (Or (distinct_lines a a_2) (distinct_lines a_1 a_2)) True)
% 239.94/240.56 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 : Iota),
% 239.94/240.56 Or (Eq (distinct_lines a a_1) False) (Or (Eq (distinct_lines a a_2) True) (Eq (distinct_lines a_1 a_2) True))
% 239.94/240.56 Clause #66 (by clausification #[17]): Eq
% 239.94/240.56 (∀ (X Y Z : Iota),
% 239.94/240.56 And (Not (apart_point_and_line X Y)) (Not (convergent_lines Y Z)) →
% 239.94/240.56 Not (distinct_lines Y (parallel_through_point Z X)))
% 239.94/240.56 False
% 239.94/240.56 Clause #67 (by clausification #[66]): ∀ (a : Iota),
% 239.94/240.56 Eq
% 239.94/240.56 (Not
% 239.94/240.56 (∀ (Y Z : Iota),
% 239.94/240.56 And (Not (apart_point_and_line (skS.0 0 a) Y)) (Not (convergent_lines Y Z)) →
% 239.94/240.56 Not (distinct_lines Y (parallel_through_point Z (skS.0 0 a)))))
% 239.94/240.56 True
% 239.94/240.56 Clause #68 (by clausification #[67]): ∀ (a : Iota),
% 239.94/240.56 Eq
% 239.94/240.56 (∀ (Y Z : Iota),
% 239.94/240.56 And (Not (apart_point_and_line (skS.0 0 a) Y)) (Not (convergent_lines Y Z)) →
% 239.94/240.56 Not (distinct_lines Y (parallel_through_point Z (skS.0 0 a))))
% 239.94/240.56 False
% 239.94/240.56 Clause #69 (by clausification #[68]): ∀ (a a_1 : Iota),
% 239.94/240.56 Eq
% 239.94/240.56 (Not
% 239.94/240.56 (∀ (Z : Iota),
% 239.94/240.56 And (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1))) (Not (convergent_lines (skS.0 1 a a_1) Z)) →
% 239.94/240.56 Not (distinct_lines (skS.0 1 a a_1) (parallel_through_point Z (skS.0 0 a)))))
% 239.94/240.56 True
% 239.94/240.56 Clause #70 (by clausification #[69]): ∀ (a a_1 : Iota),
% 239.94/240.56 Eq
% 239.94/240.56 (∀ (Z : Iota),
% 239.94/240.56 And (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1))) (Not (convergent_lines (skS.0 1 a a_1) Z)) →
% 239.94/240.56 Not (distinct_lines (skS.0 1 a a_1) (parallel_through_point Z (skS.0 0 a))))
% 239.94/240.56 False
% 239.94/240.58 Clause #71 (by clausification #[70]): ∀ (a a_1 a_2 : Iota),
% 239.94/240.58 Eq
% 239.94/240.58 (Not
% 239.94/240.58 (And (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1)))
% 239.94/240.58 (Not (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) →
% 239.94/240.58 Not (distinct_lines (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 0 a)))))
% 239.94/240.58 True
% 239.94/240.58 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota),
% 239.94/240.58 Eq
% 239.94/240.58 (And (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1)))
% 239.94/240.58 (Not (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) →
% 239.94/240.58 Not (distinct_lines (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 0 a))))
% 239.94/240.58 False
% 239.94/240.58 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota),
% 239.94/240.58 Eq
% 239.94/240.58 (And (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1)))
% 239.94/240.58 (Not (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))))
% 239.94/240.58 True
% 239.94/240.58 Clause #74 (by clausification #[72]): ∀ (a a_1 a_2 : Iota),
% 239.94/240.58 Eq (Not (distinct_lines (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 0 a)))) False
% 239.94/240.58 Clause #75 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), Eq (Not (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) True
% 239.94/240.58 Clause #76 (by clausification #[73]): ∀ (a a_1 : Iota), Eq (Not (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1))) True
% 239.94/240.58 Clause #77 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), Eq (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) False
% 239.94/240.58 Clause #78 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), convergent_lines a Y → Or (convergent_lines a Z) (convergent_lines Y Z)) True
% 239.94/240.58 Clause #79 (by clausification #[78]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), convergent_lines a a_1 → Or (convergent_lines a Z) (convergent_lines a_1 Z)) True
% 239.94/240.58 Clause #80 (by clausification #[79]): ∀ (a a_1 a_2 : Iota), Eq (convergent_lines a a_1 → Or (convergent_lines a a_2) (convergent_lines a_1 a_2)) True
% 239.94/240.58 Clause #81 (by clausification #[80]): ∀ (a a_1 a_2 : Iota),
% 239.94/240.58 Or (Eq (convergent_lines a a_1) False) (Eq (Or (convergent_lines a a_2) (convergent_lines a_1 a_2)) True)
% 239.94/240.58 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 : Iota),
% 239.94/240.58 Or (Eq (convergent_lines a a_1) False) (Or (Eq (convergent_lines a a_2) True) (Eq (convergent_lines a_1 a_2) True))
% 239.94/240.58 Clause #88 (by clausification #[16]): ∀ (a : Iota),
% 239.94/240.58 Eq
% 239.94/240.58 (∀ (Y Z : Iota),
% 239.94/240.58 distinct_lines Y Z → Or (Or (apart_point_and_line a Y) (apart_point_and_line a Z)) (convergent_lines Y Z))
% 239.94/240.58 True
% 239.94/240.58 Clause #89 (by clausification #[88]): ∀ (a a_1 : Iota),
% 239.94/240.58 Eq
% 239.94/240.58 (∀ (Z : Iota),
% 239.94/240.58 distinct_lines a Z → Or (Or (apart_point_and_line a_1 a) (apart_point_and_line a_1 Z)) (convergent_lines a Z))
% 239.94/240.58 True
% 239.94/240.58 Clause #90 (by clausification #[89]): ∀ (a a_1 a_2 : Iota),
% 239.94/240.58 Eq
% 239.94/240.58 (distinct_lines a a_1 →
% 239.94/240.58 Or (Or (apart_point_and_line a_2 a) (apart_point_and_line a_2 a_1)) (convergent_lines a a_1))
% 239.94/240.58 True
% 239.94/240.58 Clause #91 (by clausification #[90]): ∀ (a a_1 a_2 : Iota),
% 239.94/240.58 Or (Eq (distinct_lines a a_1) False)
% 239.94/240.58 (Eq (Or (Or (apart_point_and_line a_2 a) (apart_point_and_line a_2 a_1)) (convergent_lines a a_1)) True)
% 239.94/240.58 Clause #92 (by clausification #[91]): ∀ (a a_1 a_2 : Iota),
% 239.94/240.58 Or (Eq (distinct_lines a a_1) False)
% 239.94/240.58 (Or (Eq (Or (apart_point_and_line a_2 a) (apart_point_and_line a_2 a_1)) True) (Eq (convergent_lines a a_1) True))
% 239.94/240.58 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 : Iota),
% 239.94/240.58 Or (Eq (distinct_lines a a_1) False)
% 239.94/240.58 (Or (Eq (convergent_lines a a_1) True)
% 239.94/240.58 (Or (Eq (apart_point_and_line a_2 a) True) (Eq (apart_point_and_line a_2 a_1) True)))
% 239.94/240.58 Clause #103 (by clausification #[76]): ∀ (a a_1 : Iota), Eq (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1)) False
% 239.94/240.58 Clause #104 (by clausification #[74]): ∀ (a a_1 a_2 : Iota), Eq (distinct_lines (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 0 a))) True
% 239.94/240.58 Clause #105 (by superposition #[104, 60]): ∀ (a a_1 a_2 a_3 : Iota),
% 239.94/240.58 Or (Eq True False)
% 239.94/240.58 (Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True)
% 239.94/240.58 (Eq (distinct_lines (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a)) a_2) True))
% 239.94/240.58 Clause #107 (by clausification #[105]): ∀ (a a_1 a_2 a_3 : Iota),
% 239.94/240.60 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True)
% 239.94/240.60 (Eq (distinct_lines (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a)) a_2) True)
% 239.94/240.60 Clause #109 (by superposition #[107, 60]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 239.94/240.60 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True)
% 239.94/240.60 (Or (Eq True False)
% 239.94/240.60 (Or (Eq (distinct_lines (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a)) a_4) True)
% 239.94/240.60 (Eq (distinct_lines a_2 a_4) True)))
% 239.94/240.60 Clause #111 (by clausification #[109]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 239.94/240.60 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True)
% 239.94/240.60 (Or (Eq (distinct_lines (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a)) a_4) True)
% 239.94/240.60 (Eq (distinct_lines a_2 a_4) True))
% 239.94/240.60 Clause #115 (by superposition #[111, 21]): ∀ (a a_1 a_2 a_3 : Iota),
% 239.94/240.60 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True)
% 239.94/240.60 (Or (Eq (distinct_lines a_2 (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a))) True) (Eq True False))
% 239.94/240.60 Clause #129 (by clausification #[115]): ∀ (a a_1 a_2 a_3 : Iota),
% 239.94/240.60 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True)
% 239.94/240.60 (Eq (distinct_lines a_2 (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a))) True)
% 239.94/240.60 Clause #131 (by superposition #[129, 93]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 239.94/240.60 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True)
% 239.94/240.60 (Or (Eq True False)
% 239.94/240.60 (Or (Eq (convergent_lines a_2 (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a))) True)
% 239.94/240.60 (Or (Eq (apart_point_and_line a_4 a_2) True)
% 239.94/240.60 (Eq (apart_point_and_line a_4 (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a))) True))))
% 239.94/240.60 Clause #571 (by clausification #[131]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 239.94/240.60 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True)
% 239.94/240.60 (Or (Eq (convergent_lines a_2 (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a))) True)
% 239.94/240.60 (Or (Eq (apart_point_and_line a_4 a_2) True)
% 239.94/240.60 (Eq (apart_point_and_line a_4 (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a))) True)))
% 239.94/240.60 Clause #584 (by superposition #[571, 26]): ∀ (a a_1 a_2 a_3 : Iota),
% 239.94/240.60 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True)
% 239.94/240.60 (Or (Eq (convergent_lines a_2 (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a))) True)
% 239.94/240.60 (Or (Eq (apart_point_and_line (skS.0 0 a) a_2) True) (Eq True False)))
% 239.94/240.60 Clause #936 (by clausification #[584]): ∀ (a a_1 a_2 a_3 : Iota),
% 239.94/240.60 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True)
% 239.94/240.60 (Or (Eq (convergent_lines a_2 (parallel_through_point (skS.0 2 a a_1 a_3) (skS.0 0 a))) True)
% 239.94/240.60 (Eq (apart_point_and_line (skS.0 0 a) a_2) True))
% 239.94/240.60 Clause #941 (by superposition #[936, 82]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 239.94/240.60 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True)
% 239.94/240.60 (Or (Eq (apart_point_and_line (skS.0 0 a) a_2) True)
% 239.94/240.60 (Or (Eq True False)
% 239.94/240.60 (Or (Eq (convergent_lines a_2 a_3) True)
% 239.94/240.60 (Eq (convergent_lines (parallel_through_point (skS.0 2 a a_1 a_4) (skS.0 0 a)) a_3) True))))
% 239.94/240.60 Clause #5354 (by clausification #[941]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 239.94/240.60 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True)
% 239.94/240.60 (Or (Eq (apart_point_and_line (skS.0 0 a) a_2) True)
% 239.94/240.60 (Or (Eq (convergent_lines a_2 a_3) True)
% 239.94/240.60 (Eq (convergent_lines (parallel_through_point (skS.0 2 a a_1 a_4) (skS.0 0 a)) a_3) True)))
% 239.94/240.60 Clause #5364 (by superposition #[5354, 29]): ∀ (a a_1 a_2 a_3 : Iota),
% 239.94/240.60 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True)
% 239.94/240.60 (Or (Eq (apart_point_and_line (skS.0 0 a) a_2) True)
% 239.94/240.60 (Or (Eq (convergent_lines a_2 (skS.0 2 a a_1 a_3)) True) (Eq True False)))
% 239.94/240.60 Clause #5371 (by clausification #[5364]): ∀ (a a_1 a_2 a_3 : Iota),
% 239.94/240.60 Or (Eq (distinct_lines (skS.0 1 a a_1) a_2) True)
% 239.94/240.60 (Or (Eq (apart_point_and_line (skS.0 0 a) a_2) True) (Eq (convergent_lines a_2 (skS.0 2 a a_1 a_3)) True))
% 239.94/240.60 Clause #5372 (by superposition #[5371, 77]): ∀ (a a_1 : Iota),
% 239.94/240.60 Or (Eq (distinct_lines (skS.0 1 a a_1) (skS.0 1 a a_1)) True)
% 239.94/240.60 (Or (Eq (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq True False))
% 239.94/240.60 Clause #5378 (by clausification #[5372]): ∀ (a a_1 : Iota),
% 239.94/240.60 Or (Eq (distinct_lines (skS.0 1 a a_1) (skS.0 1 a a_1)) True)
% 239.94/240.60 (Eq (apart_point_and_line (skS.0 0 a) (skS.0 1 a a_1)) True)
% 240.17/240.79 Clause #5379 (by forward demodulation #[5378, 103]): ∀ (a a_1 : Iota), Or (Eq (distinct_lines (skS.0 1 a a_1) (skS.0 1 a a_1)) True) (Eq False True)
% 240.17/240.79 Clause #5380 (by clausification #[5379]): ∀ (a a_1 : Iota), Eq (distinct_lines (skS.0 1 a a_1) (skS.0 1 a a_1)) True
% 240.17/240.79 Clause #5381 (by superposition #[5380, 21]): Eq True False
% 240.17/240.79 Clause #5428 (by clausification #[5381]): False
% 240.17/240.79 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------