TSTP Solution File: GEO200+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : GEO200+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n018.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 22:55:35 EDT 2023
% Result : Theorem 57.13s 57.35s
% Output : Proof 57.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO200+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n018.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 : Tue Aug 29 19:04:03 EDT 2023
% 0.13/0.35 % CPUTime :
% 57.13/57.35 SZS status Theorem for theBenchmark.p
% 57.13/57.35 SZS output start Proof for theBenchmark.p
% 57.13/57.35 Clause #0 (by assumption #[]): Eq (∀ (X : Iota), Not (distinct_points X X)) True
% 57.13/57.35 Clause #3 (by assumption #[]): Eq (∀ (X Y Z : Iota), distinct_points X Y → Or (distinct_points X Z) (distinct_points Y Z)) True
% 57.13/57.35 Clause #6 (by assumption #[]): Eq (∀ (X Y : Iota), distinct_points X Y → Not (apart_point_and_line X (line_connecting X Y))) True
% 57.13/57.35 Clause #7 (by assumption #[]): Eq (∀ (X Y : Iota), distinct_points X Y → Not (apart_point_and_line Y (line_connecting X Y))) True
% 57.13/57.35 Clause #10 (by assumption #[]): Eq
% 57.13/57.35 (∀ (X Y U V : Iota),
% 57.13/57.35 And (distinct_points X Y) (distinct_lines U V) →
% 57.13/57.35 Or (Or (Or (apart_point_and_line X U) (apart_point_and_line X V)) (apart_point_and_line Y U))
% 57.13/57.35 (apart_point_and_line Y V))
% 57.13/57.35 True
% 57.13/57.35 Clause #14 (by assumption #[]): Eq (Not (∀ (X Y : Iota), distinct_points X Y → Not (distinct_lines (line_connecting X Y) (line_connecting Y X)))) True
% 57.13/57.35 Clause #19 (by clausification #[0]): ∀ (a : Iota), Eq (Not (distinct_points a a)) True
% 57.13/57.35 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (distinct_points a a) False
% 57.13/57.35 Clause #21 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (Y : Iota), distinct_points a Y → Not (apart_point_and_line Y (line_connecting a Y))) True
% 57.13/57.35 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (distinct_points a a_1 → Not (apart_point_and_line a_1 (line_connecting a a_1))) True
% 57.13/57.35 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota),
% 57.13/57.35 Or (Eq (distinct_points a a_1) False) (Eq (Not (apart_point_and_line a_1 (line_connecting a a_1))) True)
% 57.13/57.35 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (distinct_points a a_1) False) (Eq (apart_point_and_line a_1 (line_connecting a a_1)) False)
% 57.13/57.35 Clause #25 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (Y : Iota), distinct_points a Y → Not (apart_point_and_line a (line_connecting a Y))) True
% 57.13/57.35 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (distinct_points a a_1 → Not (apart_point_and_line a (line_connecting a a_1))) True
% 57.13/57.35 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq (distinct_points a a_1) False) (Eq (Not (apart_point_and_line a (line_connecting a a_1))) True)
% 57.13/57.35 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (distinct_points a a_1) False) (Eq (apart_point_and_line a (line_connecting a a_1)) False)
% 57.13/57.35 Clause #29 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), distinct_points a Y → Or (distinct_points a Z) (distinct_points Y Z)) True
% 57.13/57.35 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), distinct_points a a_1 → Or (distinct_points a Z) (distinct_points a_1 Z)) True
% 57.13/57.35 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Eq (distinct_points a a_1 → Or (distinct_points a a_2) (distinct_points a_1 a_2)) True
% 57.13/57.35 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota),
% 57.13/57.35 Or (Eq (distinct_points a a_1) False) (Eq (Or (distinct_points a a_2) (distinct_points a_1 a_2)) True)
% 57.13/57.35 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota),
% 57.13/57.35 Or (Eq (distinct_points a a_1) False) (Or (Eq (distinct_points a a_2) True) (Eq (distinct_points a_1 a_2) True))
% 57.13/57.35 Clause #67 (by clausification #[14]): Eq (∀ (X Y : Iota), distinct_points X Y → Not (distinct_lines (line_connecting X Y) (line_connecting Y X))) False
% 57.13/57.35 Clause #68 (by clausification #[67]): ∀ (a : Iota),
% 57.13/57.35 Eq
% 57.13/57.35 (Not
% 57.13/57.35 (∀ (Y : Iota),
% 57.13/57.35 distinct_points (skS.0 0 a) Y →
% 57.13/57.35 Not (distinct_lines (line_connecting (skS.0 0 a) Y) (line_connecting Y (skS.0 0 a)))))
% 57.13/57.35 True
% 57.13/57.35 Clause #69 (by clausification #[68]): ∀ (a : Iota),
% 57.13/57.35 Eq
% 57.13/57.35 (∀ (Y : Iota),
% 57.13/57.35 distinct_points (skS.0 0 a) Y →
% 57.13/57.35 Not (distinct_lines (line_connecting (skS.0 0 a) Y) (line_connecting Y (skS.0 0 a))))
% 57.13/57.35 False
% 57.13/57.35 Clause #70 (by clausification #[69]): ∀ (a a_1 : Iota),
% 57.13/57.35 Eq
% 57.13/57.35 (Not
% 57.13/57.35 (distinct_points (skS.0 0 a) (skS.0 1 a a_1) →
% 57.13/57.35 Not
% 57.13/57.35 (distinct_lines (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) (line_connecting (skS.0 1 a a_1) (skS.0 0 a)))))
% 57.13/57.35 True
% 57.13/57.35 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota),
% 57.21/57.37 Eq
% 57.21/57.37 (distinct_points (skS.0 0 a) (skS.0 1 a a_1) →
% 57.21/57.37 Not (distinct_lines (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) (line_connecting (skS.0 1 a a_1) (skS.0 0 a))))
% 57.21/57.37 False
% 57.21/57.37 Clause #72 (by clausification #[71]): ∀ (a a_1 : Iota), Eq (distinct_points (skS.0 0 a) (skS.0 1 a a_1)) True
% 57.21/57.37 Clause #73 (by clausification #[71]): ∀ (a a_1 : Iota),
% 57.21/57.37 Eq (Not (distinct_lines (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) (line_connecting (skS.0 1 a a_1) (skS.0 0 a))))
% 57.21/57.37 False
% 57.21/57.37 Clause #74 (by superposition #[72, 24]): ∀ (a a_1 : Iota),
% 57.21/57.37 Or (Eq True False) (Eq (apart_point_and_line (skS.0 1 a a_1) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) False)
% 57.21/57.37 Clause #75 (by superposition #[72, 28]): ∀ (a a_1 : Iota),
% 57.21/57.37 Or (Eq True False) (Eq (apart_point_and_line (skS.0 0 a) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) False)
% 57.21/57.37 Clause #76 (by superposition #[72, 33]): ∀ (a a_1 a_2 : Iota),
% 57.21/57.37 Or (Eq True False) (Or (Eq (distinct_points (skS.0 0 a) a_1) True) (Eq (distinct_points (skS.0 1 a a_2) a_1) True))
% 57.21/57.37 Clause #77 (by clausification #[10]): ∀ (a : Iota),
% 57.21/57.37 Eq
% 57.21/57.37 (∀ (Y U V : Iota),
% 57.21/57.37 And (distinct_points a Y) (distinct_lines U V) →
% 57.21/57.37 Or (Or (Or (apart_point_and_line a U) (apart_point_and_line a V)) (apart_point_and_line Y U))
% 57.21/57.37 (apart_point_and_line Y V))
% 57.21/57.37 True
% 57.21/57.37 Clause #78 (by clausification #[77]): ∀ (a a_1 : Iota),
% 57.21/57.37 Eq
% 57.21/57.37 (∀ (U V : Iota),
% 57.21/57.37 And (distinct_points a a_1) (distinct_lines U V) →
% 57.21/57.37 Or (Or (Or (apart_point_and_line a U) (apart_point_and_line a V)) (apart_point_and_line a_1 U))
% 57.21/57.37 (apart_point_and_line a_1 V))
% 57.21/57.37 True
% 57.21/57.37 Clause #79 (by clausification #[78]): ∀ (a a_1 a_2 : Iota),
% 57.21/57.37 Eq
% 57.21/57.37 (∀ (V : Iota),
% 57.21/57.37 And (distinct_points a a_1) (distinct_lines a_2 V) →
% 57.21/57.37 Or (Or (Or (apart_point_and_line a a_2) (apart_point_and_line a V)) (apart_point_and_line a_1 a_2))
% 57.21/57.37 (apart_point_and_line a_1 V))
% 57.21/57.37 True
% 57.21/57.37 Clause #80 (by clausification #[79]): ∀ (a a_1 a_2 a_3 : Iota),
% 57.21/57.37 Eq
% 57.21/57.37 (And (distinct_points a a_1) (distinct_lines a_2 a_3) →
% 57.21/57.37 Or (Or (Or (apart_point_and_line a a_2) (apart_point_and_line a a_3)) (apart_point_and_line a_1 a_2))
% 57.21/57.37 (apart_point_and_line a_1 a_3))
% 57.21/57.37 True
% 57.21/57.37 Clause #81 (by clausification #[80]): ∀ (a a_1 a_2 a_3 : Iota),
% 57.21/57.37 Or (Eq (And (distinct_points a a_1) (distinct_lines a_2 a_3)) False)
% 57.21/57.37 (Eq
% 57.21/57.37 (Or (Or (Or (apart_point_and_line a a_2) (apart_point_and_line a a_3)) (apart_point_and_line a_1 a_2))
% 57.21/57.37 (apart_point_and_line a_1 a_3))
% 57.21/57.37 True)
% 57.21/57.37 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 a_3 : Iota),
% 57.21/57.37 Or
% 57.21/57.37 (Eq
% 57.21/57.37 (Or (Or (Or (apart_point_and_line a a_1) (apart_point_and_line a a_2)) (apart_point_and_line a_3 a_1))
% 57.21/57.37 (apart_point_and_line a_3 a_2))
% 57.21/57.37 True)
% 57.21/57.37 (Or (Eq (distinct_points a a_3) False) (Eq (distinct_lines a_1 a_2) False))
% 57.21/57.37 Clause #83 (by clausification #[82]): ∀ (a a_1 a_2 a_3 : Iota),
% 57.21/57.37 Or (Eq (distinct_points a a_1) False)
% 57.21/57.37 (Or (Eq (distinct_lines a_2 a_3) False)
% 57.21/57.37 (Or (Eq (Or (Or (apart_point_and_line a a_2) (apart_point_and_line a a_3)) (apart_point_and_line a_1 a_2)) True)
% 57.21/57.37 (Eq (apart_point_and_line a_1 a_3) True)))
% 57.21/57.37 Clause #84 (by clausification #[83]): ∀ (a a_1 a_2 a_3 : Iota),
% 57.21/57.37 Or (Eq (distinct_points a a_1) False)
% 57.21/57.37 (Or (Eq (distinct_lines a_2 a_3) False)
% 57.21/57.37 (Or (Eq (apart_point_and_line a_1 a_3) True)
% 57.21/57.37 (Or (Eq (Or (apart_point_and_line a a_2) (apart_point_and_line a a_3)) True)
% 57.21/57.37 (Eq (apart_point_and_line a_1 a_2) True))))
% 57.21/57.37 Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 a_3 : Iota),
% 57.21/57.37 Or (Eq (distinct_points a a_1) False)
% 57.21/57.37 (Or (Eq (distinct_lines a_2 a_3) False)
% 57.21/57.37 (Or (Eq (apart_point_and_line a_1 a_3) True)
% 57.21/57.37 (Or (Eq (apart_point_and_line a_1 a_2) True)
% 57.21/57.37 (Or (Eq (apart_point_and_line a a_2) True) (Eq (apart_point_and_line a a_3) True)))))
% 57.21/57.37 Clause #86 (by superposition #[85, 72]): ∀ (a a_1 a_2 a_3 : Iota),
% 57.21/57.37 Or (Eq (distinct_lines a a_1) False)
% 57.21/57.37 (Or (Eq (apart_point_and_line (skS.0 1 a_2 a_3) a_1) True)
% 57.21/57.37 (Or (Eq (apart_point_and_line (skS.0 1 a_2 a_3) a) True)
% 57.22/57.39 (Or (Eq (apart_point_and_line (skS.0 0 a_2) a) True)
% 57.22/57.39 (Or (Eq (apart_point_and_line (skS.0 0 a_2) a_1) True) (Eq False True)))))
% 57.22/57.39 Clause #87 (by clausification #[76]): ∀ (a a_1 a_2 : Iota), Or (Eq (distinct_points (skS.0 0 a) a_1) True) (Eq (distinct_points (skS.0 1 a a_2) a_1) True)
% 57.22/57.39 Clause #90 (by superposition #[87, 28]): ∀ (a a_1 a_2 : Iota),
% 57.22/57.39 Or (Eq (distinct_points (skS.0 0 a) a_1) True)
% 57.22/57.39 (Or (Eq True False) (Eq (apart_point_and_line (skS.0 1 a a_2) (line_connecting (skS.0 1 a a_2) a_1)) False))
% 57.22/57.39 Clause #91 (by superposition #[87, 33]): ∀ (a a_1 a_2 a_3 : Iota),
% 57.22/57.39 Or (Eq (distinct_points (skS.0 0 a) a_1) True)
% 57.22/57.39 (Or (Eq True False) (Or (Eq (distinct_points (skS.0 1 a a_2) a_3) True) (Eq (distinct_points a_1 a_3) True)))
% 57.22/57.39 Clause #93 (by clausification #[73]): ∀ (a a_1 : Iota),
% 57.22/57.39 Eq (distinct_lines (line_connecting (skS.0 0 a) (skS.0 1 a a_1)) (line_connecting (skS.0 1 a a_1) (skS.0 0 a))) True
% 57.22/57.39 Clause #96 (by clausification #[75]): ∀ (a a_1 : Iota), Eq (apart_point_and_line (skS.0 0 a) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) False
% 57.22/57.39 Clause #97 (by clausification #[91]): ∀ (a a_1 a_2 a_3 : Iota),
% 57.22/57.39 Or (Eq (distinct_points (skS.0 0 a) a_1) True)
% 57.22/57.39 (Or (Eq (distinct_points (skS.0 1 a a_2) a_3) True) (Eq (distinct_points a_1 a_3) True))
% 57.22/57.39 Clause #111 (by superposition #[97, 33]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 57.22/57.39 Or (Eq (distinct_points (skS.0 0 a) a_1) True)
% 57.22/57.39 (Or (Eq (distinct_points (skS.0 1 a a_2) a_3) True)
% 57.22/57.39 (Or (Eq True False) (Or (Eq (distinct_points a_1 a_4) True) (Eq (distinct_points a_3 a_4) True))))
% 57.22/57.39 Clause #119 (by clausification #[74]): ∀ (a a_1 : Iota), Eq (apart_point_and_line (skS.0 1 a a_1) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) False
% 57.22/57.39 Clause #125 (by clausification #[86]): ∀ (a a_1 a_2 a_3 : Iota),
% 57.22/57.39 Or (Eq (distinct_lines a a_1) False)
% 57.22/57.39 (Or (Eq (apart_point_and_line (skS.0 1 a_2 a_3) a_1) True)
% 57.22/57.39 (Or (Eq (apart_point_and_line (skS.0 1 a_2 a_3) a) True)
% 57.22/57.39 (Or (Eq (apart_point_and_line (skS.0 0 a_2) a) True) (Eq (apart_point_and_line (skS.0 0 a_2) a_1) True))))
% 57.22/57.39 Clause #126 (by superposition #[125, 93]): ∀ (a a_1 a_2 a_3 : Iota),
% 57.22/57.39 Or (Eq (apart_point_and_line (skS.0 1 a a_1) (line_connecting (skS.0 1 a_2 a_3) (skS.0 0 a_2))) True)
% 57.22/57.39 (Or (Eq (apart_point_and_line (skS.0 1 a a_1) (line_connecting (skS.0 0 a_2) (skS.0 1 a_2 a_3))) True)
% 57.22/57.39 (Or (Eq (apart_point_and_line (skS.0 0 a) (line_connecting (skS.0 0 a_2) (skS.0 1 a_2 a_3))) True)
% 57.22/57.39 (Or (Eq (apart_point_and_line (skS.0 0 a) (line_connecting (skS.0 1 a_2 a_3) (skS.0 0 a_2))) True)
% 57.22/57.39 (Eq False True))))
% 57.22/57.39 Clause #133 (by clausification #[111]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 57.22/57.39 Or (Eq (distinct_points (skS.0 0 a) a_1) True)
% 57.22/57.39 (Or (Eq (distinct_points (skS.0 1 a a_2) a_3) True)
% 57.22/57.39 (Or (Eq (distinct_points a_1 a_4) True) (Eq (distinct_points a_3 a_4) True)))
% 57.22/57.39 Clause #144 (by superposition #[133, 20]): ∀ (a a_1 a_2 a_3 : Iota),
% 57.22/57.39 Or (Eq (distinct_points (skS.0 0 a) a_1) True)
% 57.22/57.39 (Or (Eq (distinct_points (skS.0 1 a a_2) a_3) True) (Or (Eq (distinct_points a_3 a_1) True) (Eq True False)))
% 57.22/57.39 Clause #163 (by clausification #[90]): ∀ (a a_1 a_2 : Iota),
% 57.22/57.39 Or (Eq (distinct_points (skS.0 0 a) a_1) True)
% 57.22/57.39 (Eq (apart_point_and_line (skS.0 1 a a_2) (line_connecting (skS.0 1 a a_2) a_1)) False)
% 57.22/57.39 Clause #164 (by clausification #[144]): ∀ (a a_1 a_2 a_3 : Iota),
% 57.22/57.39 Or (Eq (distinct_points (skS.0 0 a) a_1) True)
% 57.22/57.39 (Or (Eq (distinct_points (skS.0 1 a a_2) a_3) True) (Eq (distinct_points a_3 a_1) True))
% 57.22/57.39 Clause #165 (by superposition #[164, 20]): ∀ (a a_1 a_2 : Iota),
% 57.22/57.39 Or (Eq (distinct_points (skS.0 1 a a_1) a_2) True) (Or (Eq (distinct_points a_2 (skS.0 0 a)) True) (Eq True False))
% 57.22/57.39 Clause #180 (by clausification #[165]): ∀ (a a_1 a_2 : Iota), Or (Eq (distinct_points (skS.0 1 a a_1) a_2) True) (Eq (distinct_points a_2 (skS.0 0 a)) True)
% 57.22/57.39 Clause #181 (by superposition #[180, 20]): ∀ (a a_1 : Iota), Or (Eq (distinct_points (skS.0 1 a a_1) (skS.0 0 a)) True) (Eq True False)
% 57.22/57.39 Clause #186 (by clausification #[181]): ∀ (a a_1 : Iota), Eq (distinct_points (skS.0 1 a a_1) (skS.0 0 a)) True
% 57.25/57.50 Clause #187 (by superposition #[186, 24]): ∀ (a a_1 : Iota),
% 57.25/57.50 Or (Eq True False) (Eq (apart_point_and_line (skS.0 0 a) (line_connecting (skS.0 1 a a_1) (skS.0 0 a))) False)
% 57.25/57.50 Clause #194 (by clausification #[187]): ∀ (a a_1 : Iota), Eq (apart_point_and_line (skS.0 0 a) (line_connecting (skS.0 1 a a_1) (skS.0 0 a))) False
% 57.25/57.50 Clause #414 (by clausification #[126]): ∀ (a a_1 a_2 a_3 : Iota),
% 57.25/57.50 Or (Eq (apart_point_and_line (skS.0 1 a a_1) (line_connecting (skS.0 1 a_2 a_3) (skS.0 0 a_2))) True)
% 57.25/57.50 (Or (Eq (apart_point_and_line (skS.0 1 a a_1) (line_connecting (skS.0 0 a_2) (skS.0 1 a_2 a_3))) True)
% 57.25/57.50 (Or (Eq (apart_point_and_line (skS.0 0 a) (line_connecting (skS.0 0 a_2) (skS.0 1 a_2 a_3))) True)
% 57.25/57.50 (Eq (apart_point_and_line (skS.0 0 a) (line_connecting (skS.0 1 a_2 a_3) (skS.0 0 a_2))) True)))
% 57.25/57.50 Clause #415 (by superposition #[414, 163]): ∀ (a a_1 : Iota),
% 57.25/57.50 Or (Eq (apart_point_and_line (skS.0 1 a a_1) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True)
% 57.25/57.50 (Or (Eq (apart_point_and_line (skS.0 0 a) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True)
% 57.25/57.50 (Or (Eq (apart_point_and_line (skS.0 0 a) (line_connecting (skS.0 1 a a_1) (skS.0 0 a))) True)
% 57.25/57.50 (Or (Eq (distinct_points (skS.0 0 a) (skS.0 0 a)) True) (Eq True False))))
% 57.25/57.50 Clause #5968 (by clausification #[415]): ∀ (a a_1 : Iota),
% 57.25/57.50 Or (Eq (apart_point_and_line (skS.0 1 a a_1) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True)
% 57.25/57.50 (Or (Eq (apart_point_and_line (skS.0 0 a) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True)
% 57.25/57.50 (Or (Eq (apart_point_and_line (skS.0 0 a) (line_connecting (skS.0 1 a a_1) (skS.0 0 a))) True)
% 57.25/57.50 (Eq (distinct_points (skS.0 0 a) (skS.0 0 a)) True)))
% 57.25/57.50 Clause #5969 (by forward demodulation #[5968, 96]): ∀ (a a_1 : Iota),
% 57.25/57.50 Or (Eq (apart_point_and_line (skS.0 1 a a_1) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True)
% 57.25/57.50 (Or (Eq False True)
% 57.25/57.50 (Or (Eq (apart_point_and_line (skS.0 0 a) (line_connecting (skS.0 1 a a_1) (skS.0 0 a))) True)
% 57.25/57.50 (Eq (distinct_points (skS.0 0 a) (skS.0 0 a)) True)))
% 57.25/57.50 Clause #5970 (by clausification #[5969]): ∀ (a a_1 : Iota),
% 57.25/57.50 Or (Eq (apart_point_and_line (skS.0 1 a a_1) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True)
% 57.25/57.50 (Or (Eq (apart_point_and_line (skS.0 0 a) (line_connecting (skS.0 1 a a_1) (skS.0 0 a))) True)
% 57.25/57.50 (Eq (distinct_points (skS.0 0 a) (skS.0 0 a)) True))
% 57.25/57.50 Clause #5971 (by forward demodulation #[5970, 194]): ∀ (a a_1 : Iota),
% 57.25/57.50 Or (Eq (apart_point_and_line (skS.0 1 a a_1) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True)
% 57.25/57.50 (Or (Eq False True) (Eq (distinct_points (skS.0 0 a) (skS.0 0 a)) True))
% 57.25/57.50 Clause #5972 (by clausification #[5971]): ∀ (a a_1 : Iota),
% 57.25/57.50 Or (Eq (apart_point_and_line (skS.0 1 a a_1) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True)
% 57.25/57.50 (Eq (distinct_points (skS.0 0 a) (skS.0 0 a)) True)
% 57.25/57.50 Clause #5973 (by forward demodulation #[5972, 20]): ∀ (a a_1 : Iota),
% 57.25/57.50 Or (Eq (apart_point_and_line (skS.0 1 a a_1) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True) (Eq False True)
% 57.25/57.50 Clause #5974 (by clausification #[5973]): ∀ (a a_1 : Iota), Eq (apart_point_and_line (skS.0 1 a a_1) (line_connecting (skS.0 0 a) (skS.0 1 a a_1))) True
% 57.25/57.50 Clause #5975 (by superposition #[5974, 119]): Eq True False
% 57.25/57.50 Clause #6027 (by clausification #[5975]): False
% 57.25/57.50 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------