TSTP Solution File: GEO262+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : GEO262+1 : TPTP v8.1.2. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n014.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 22:56:00 EDT 2023
% Result : Theorem 4.16s 4.32s
% Output : Proof 4.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO262+1 : TPTP v8.1.2. Bugfixed v6.4.0.
% 0.00/0.14 % Command : duper %s
% 0.15/0.35 % Computer : n014.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Aug 29 22:54:44 EDT 2023
% 0.15/0.35 % CPUTime :
% 4.16/4.32 SZS status Theorem for theBenchmark.p
% 4.16/4.32 SZS output start Proof for theBenchmark.p
% 4.16/4.32 Clause #1 (by assumption #[]): Eq
% 4.16/4.32 (∀ (L M : Iota),
% 4.16/4.32 Iff (convergent_lines L M) (And (unequally_directed_lines L M) (unequally_directed_lines L (reverse_line M))))
% 4.16/4.32 True
% 4.16/4.32 Clause #13 (by assumption #[]): Eq
% 4.16/4.32 (∀ (L M : Iota),
% 4.16/4.32 And (unequally_directed_lines L M) (unequally_directed_lines L (reverse_line M)) →
% 4.16/4.32 Or (left_convergent_lines L M) (left_convergent_lines L (reverse_line M)))
% 4.16/4.32 True
% 4.16/4.32 Clause #15 (by assumption #[]): Eq (∀ (L M : Iota), Not (Or (left_convergent_lines L M) (left_convergent_lines L (reverse_line M)))) True
% 4.16/4.32 Clause #31 (by assumption #[]): Eq
% 4.16/4.32 (Not
% 4.16/4.32 (∀ (L M N A B C : Iota),
% 4.16/4.32 And
% 4.16/4.32 (And
% 4.16/4.32 (And (And (And (between_on_line L A B C) (convergent_lines L M)) (Not (apart_point_and_line B M)))
% 4.16/4.32 (convergent_lines L N))
% 4.16/4.32 (convergent_lines M N))
% 4.16/4.32 (Not (apart_point_and_line B N)) →
% 4.16/4.32 between_on_line M (intersection_point M (parallel_through_point N A)) B
% 4.16/4.32 (intersection_point M (parallel_through_point N C))))
% 4.16/4.32 True
% 4.16/4.32 Clause #66 (by clausification #[1]): ∀ (a : Iota),
% 4.16/4.32 Eq
% 4.16/4.32 (∀ (M : Iota),
% 4.16/4.32 Iff (convergent_lines a M) (And (unequally_directed_lines a M) (unequally_directed_lines a (reverse_line M))))
% 4.16/4.32 True
% 4.16/4.32 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota),
% 4.16/4.32 Eq
% 4.16/4.32 (Iff (convergent_lines a a_1)
% 4.16/4.32 (And (unequally_directed_lines a a_1) (unequally_directed_lines a (reverse_line a_1))))
% 4.16/4.32 True
% 4.16/4.32 Clause #69 (by clausification #[67]): ∀ (a a_1 : Iota),
% 4.16/4.32 Or (Eq (convergent_lines a a_1) False)
% 4.16/4.32 (Eq (And (unequally_directed_lines a a_1) (unequally_directed_lines a (reverse_line a_1))) True)
% 4.16/4.32 Clause #74 (by clausification #[15]): ∀ (a : Iota), Eq (∀ (M : Iota), Not (Or (left_convergent_lines a M) (left_convergent_lines a (reverse_line M)))) True
% 4.16/4.32 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), Eq (Not (Or (left_convergent_lines a a_1) (left_convergent_lines a (reverse_line a_1)))) True
% 4.16/4.32 Clause #76 (by clausification #[75]): ∀ (a a_1 : Iota), Eq (Or (left_convergent_lines a a_1) (left_convergent_lines a (reverse_line a_1))) False
% 4.16/4.32 Clause #78 (by clausification #[76]): ∀ (a a_1 : Iota), Eq (left_convergent_lines a a_1) False
% 4.16/4.32 Clause #97 (by clausification #[13]): ∀ (a : Iota),
% 4.16/4.32 Eq
% 4.16/4.32 (∀ (M : Iota),
% 4.16/4.32 And (unequally_directed_lines a M) (unequally_directed_lines a (reverse_line M)) →
% 4.16/4.32 Or (left_convergent_lines a M) (left_convergent_lines a (reverse_line M)))
% 4.16/4.32 True
% 4.16/4.32 Clause #98 (by clausification #[97]): ∀ (a a_1 : Iota),
% 4.16/4.32 Eq
% 4.16/4.32 (And (unequally_directed_lines a a_1) (unequally_directed_lines a (reverse_line a_1)) →
% 4.16/4.32 Or (left_convergent_lines a a_1) (left_convergent_lines a (reverse_line a_1)))
% 4.16/4.32 True
% 4.16/4.32 Clause #99 (by clausification #[98]): ∀ (a a_1 : Iota),
% 4.16/4.32 Or (Eq (And (unequally_directed_lines a a_1) (unequally_directed_lines a (reverse_line a_1))) False)
% 4.16/4.32 (Eq (Or (left_convergent_lines a a_1) (left_convergent_lines a (reverse_line a_1))) True)
% 4.16/4.32 Clause #100 (by clausification #[99]): ∀ (a a_1 : Iota),
% 4.16/4.32 Or (Eq (Or (left_convergent_lines a a_1) (left_convergent_lines a (reverse_line a_1))) True)
% 4.16/4.32 (Or (Eq (unequally_directed_lines a a_1) False) (Eq (unequally_directed_lines a (reverse_line a_1)) False))
% 4.16/4.32 Clause #101 (by clausification #[100]): ∀ (a a_1 : Iota),
% 4.16/4.32 Or (Eq (unequally_directed_lines a a_1) False)
% 4.16/4.32 (Or (Eq (unequally_directed_lines a (reverse_line a_1)) False)
% 4.16/4.32 (Or (Eq (left_convergent_lines a a_1) True) (Eq (left_convergent_lines a (reverse_line a_1)) True)))
% 4.16/4.32 Clause #102 (by forward demodulation #[101, 78]): ∀ (a a_1 : Iota),
% 4.16/4.32 Or (Eq (unequally_directed_lines a a_1) False)
% 4.16/4.32 (Or (Eq (unequally_directed_lines a (reverse_line a_1)) False)
% 4.16/4.32 (Or (Eq False True) (Eq (left_convergent_lines a (reverse_line a_1)) True)))
% 4.16/4.32 Clause #103 (by clausification #[102]): ∀ (a a_1 : Iota),
% 4.16/4.32 Or (Eq (unequally_directed_lines a a_1) False)
% 4.16/4.32 (Or (Eq (unequally_directed_lines a (reverse_line a_1)) False)
% 4.16/4.32 (Eq (left_convergent_lines a (reverse_line a_1)) True))
% 4.16/4.34 Clause #155 (by clausification #[69]): ∀ (a a_1 : Iota), Or (Eq (convergent_lines a a_1) False) (Eq (unequally_directed_lines a (reverse_line a_1)) True)
% 4.16/4.34 Clause #156 (by clausification #[69]): ∀ (a a_1 : Iota), Or (Eq (convergent_lines a a_1) False) (Eq (unequally_directed_lines a a_1) True)
% 4.16/4.34 Clause #233 (by clausification #[31]): Eq
% 4.16/4.34 (∀ (L M N A B C : Iota),
% 4.16/4.34 And
% 4.16/4.34 (And
% 4.16/4.34 (And (And (And (between_on_line L A B C) (convergent_lines L M)) (Not (apart_point_and_line B M)))
% 4.16/4.34 (convergent_lines L N))
% 4.16/4.34 (convergent_lines M N))
% 4.16/4.34 (Not (apart_point_and_line B N)) →
% 4.16/4.34 between_on_line M (intersection_point M (parallel_through_point N A)) B
% 4.16/4.34 (intersection_point M (parallel_through_point N C)))
% 4.16/4.34 False
% 4.16/4.34 Clause #234 (by clausification #[233]): ∀ (a : Iota),
% 4.16/4.34 Eq
% 4.16/4.34 (Not
% 4.16/4.34 (∀ (M N A B C : Iota),
% 4.16/4.34 And
% 4.16/4.34 (And
% 4.16/4.34 (And
% 4.16/4.34 (And (And (between_on_line (skS.0 0 a) A B C) (convergent_lines (skS.0 0 a) M))
% 4.16/4.34 (Not (apart_point_and_line B M)))
% 4.16/4.34 (convergent_lines (skS.0 0 a) N))
% 4.16/4.34 (convergent_lines M N))
% 4.16/4.34 (Not (apart_point_and_line B N)) →
% 4.16/4.34 between_on_line M (intersection_point M (parallel_through_point N A)) B
% 4.16/4.34 (intersection_point M (parallel_through_point N C))))
% 4.16/4.34 True
% 4.16/4.34 Clause #235 (by clausification #[234]): ∀ (a : Iota),
% 4.16/4.34 Eq
% 4.16/4.34 (∀ (M N A B C : Iota),
% 4.16/4.34 And
% 4.16/4.34 (And
% 4.16/4.34 (And
% 4.16/4.34 (And (And (between_on_line (skS.0 0 a) A B C) (convergent_lines (skS.0 0 a) M))
% 4.16/4.34 (Not (apart_point_and_line B M)))
% 4.16/4.34 (convergent_lines (skS.0 0 a) N))
% 4.16/4.34 (convergent_lines M N))
% 4.16/4.34 (Not (apart_point_and_line B N)) →
% 4.16/4.34 between_on_line M (intersection_point M (parallel_through_point N A)) B
% 4.16/4.34 (intersection_point M (parallel_through_point N C)))
% 4.16/4.34 False
% 4.16/4.34 Clause #236 (by clausification #[235]): ∀ (a a_1 : Iota),
% 4.16/4.34 Eq
% 4.16/4.34 (Not
% 4.16/4.34 (∀ (N A B C : Iota),
% 4.16/4.34 And
% 4.16/4.34 (And
% 4.16/4.34 (And
% 4.16/4.34 (And (And (between_on_line (skS.0 0 a) A B C) (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)))
% 4.16/4.34 (Not (apart_point_and_line B (skS.0 1 a a_1))))
% 4.16/4.34 (convergent_lines (skS.0 0 a) N))
% 4.16/4.34 (convergent_lines (skS.0 1 a a_1) N))
% 4.16/4.34 (Not (apart_point_and_line B N)) →
% 4.16/4.34 between_on_line (skS.0 1 a a_1) (intersection_point (skS.0 1 a a_1) (parallel_through_point N A)) B
% 4.16/4.34 (intersection_point (skS.0 1 a a_1) (parallel_through_point N C))))
% 4.16/4.34 True
% 4.16/4.34 Clause #237 (by clausification #[236]): ∀ (a a_1 : Iota),
% 4.16/4.34 Eq
% 4.16/4.34 (∀ (N A B C : Iota),
% 4.16/4.34 And
% 4.16/4.34 (And
% 4.16/4.34 (And
% 4.16/4.34 (And (And (between_on_line (skS.0 0 a) A B C) (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)))
% 4.16/4.34 (Not (apart_point_and_line B (skS.0 1 a a_1))))
% 4.16/4.34 (convergent_lines (skS.0 0 a) N))
% 4.16/4.34 (convergent_lines (skS.0 1 a a_1) N))
% 4.16/4.34 (Not (apart_point_and_line B N)) →
% 4.16/4.34 between_on_line (skS.0 1 a a_1) (intersection_point (skS.0 1 a a_1) (parallel_through_point N A)) B
% 4.16/4.34 (intersection_point (skS.0 1 a a_1) (parallel_through_point N C)))
% 4.16/4.34 False
% 4.16/4.34 Clause #238 (by clausification #[237]): ∀ (a a_1 a_2 : Iota),
% 4.16/4.34 Eq
% 4.16/4.34 (Not
% 4.16/4.34 (∀ (A B C : Iota),
% 4.16/4.34 And
% 4.16/4.34 (And
% 4.16/4.34 (And
% 4.16/4.34 (And (And (between_on_line (skS.0 0 a) A B C) (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)))
% 4.16/4.34 (Not (apart_point_and_line B (skS.0 1 a a_1))))
% 4.16/4.34 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)))
% 4.16/4.34 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 4.16/4.34 (Not (apart_point_and_line B (skS.0 2 a a_1 a_2))) →
% 4.16/4.34 between_on_line (skS.0 1 a a_1)
% 4.16/4.34 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) A)) B
% 4.16/4.34 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) C))))
% 4.16/4.34 True
% 4.16/4.34 Clause #239 (by clausification #[238]): ∀ (a a_1 a_2 : Iota),
% 4.16/4.34 Eq
% 4.16/4.34 (∀ (A B C : Iota),
% 4.16/4.35 And
% 4.16/4.35 (And
% 4.16/4.35 (And
% 4.16/4.35 (And (And (between_on_line (skS.0 0 a) A B C) (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)))
% 4.16/4.35 (Not (apart_point_and_line B (skS.0 1 a a_1))))
% 4.16/4.35 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)))
% 4.16/4.35 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 4.16/4.35 (Not (apart_point_and_line B (skS.0 2 a a_1 a_2))) →
% 4.16/4.35 between_on_line (skS.0 1 a a_1)
% 4.16/4.35 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) A)) B
% 4.16/4.35 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) C)))
% 4.16/4.35 False
% 4.16/4.35 Clause #240 (by clausification #[239]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.16/4.35 Eq
% 4.16/4.35 (Not
% 4.16/4.35 (∀ (B C : Iota),
% 4.16/4.35 And
% 4.16/4.35 (And
% 4.16/4.35 (And
% 4.16/4.35 (And
% 4.16/4.35 (And (between_on_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) B C)
% 4.16/4.35 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)))
% 4.16/4.35 (Not (apart_point_and_line B (skS.0 1 a a_1))))
% 4.16/4.35 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)))
% 4.16/4.35 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 4.16/4.35 (Not (apart_point_and_line B (skS.0 2 a a_1 a_2))) →
% 4.16/4.35 between_on_line (skS.0 1 a a_1)
% 4.16/4.35 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) B
% 4.16/4.35 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) C))))
% 4.16/4.35 True
% 4.16/4.35 Clause #241 (by clausification #[240]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.16/4.35 Eq
% 4.16/4.35 (∀ (B C : Iota),
% 4.16/4.35 And
% 4.16/4.35 (And
% 4.16/4.35 (And
% 4.16/4.35 (And
% 4.16/4.35 (And (between_on_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) B C)
% 4.16/4.35 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)))
% 4.16/4.35 (Not (apart_point_and_line B (skS.0 1 a a_1))))
% 4.16/4.35 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)))
% 4.16/4.35 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 4.16/4.35 (Not (apart_point_and_line B (skS.0 2 a a_1 a_2))) →
% 4.16/4.35 between_on_line (skS.0 1 a a_1)
% 4.16/4.35 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) B
% 4.16/4.35 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) C)))
% 4.16/4.35 False
% 4.16/4.35 Clause #242 (by clausification #[241]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.16/4.35 Eq
% 4.16/4.35 (Not
% 4.16/4.35 (∀ (C : Iota),
% 4.16/4.35 And
% 4.16/4.35 (And
% 4.16/4.35 (And
% 4.16/4.35 (And
% 4.16/4.35 (And (between_on_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4) C)
% 4.16/4.35 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)))
% 4.16/4.35 (Not (apart_point_and_line (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 1 a a_1))))
% 4.16/4.35 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)))
% 4.16/4.35 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 4.16/4.35 (Not (apart_point_and_line (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2))) →
% 4.16/4.35 between_on_line (skS.0 1 a a_1)
% 4.16/4.35 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))
% 4.16/4.35 (skS.0 4 a a_1 a_2 a_3 a_4)
% 4.16/4.35 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) C))))
% 4.16/4.35 True
% 4.16/4.35 Clause #243 (by clausification #[242]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.16/4.35 Eq
% 4.16/4.35 (∀ (C : Iota),
% 4.16/4.35 And
% 4.16/4.35 (And
% 4.16/4.35 (And
% 4.16/4.35 (And
% 4.16/4.35 (And (between_on_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4) C)
% 4.16/4.35 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)))
% 4.16/4.35 (Not (apart_point_and_line (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 1 a a_1))))
% 4.16/4.35 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)))
% 4.16/4.35 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 4.16/4.35 (Not (apart_point_and_line (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2))) →
% 4.16/4.35 between_on_line (skS.0 1 a a_1)
% 4.16/4.35 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))
% 4.16/4.37 (skS.0 4 a a_1 a_2 a_3 a_4)
% 4.16/4.37 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) C)))
% 4.16/4.37 False
% 4.16/4.37 Clause #244 (by clausification #[243]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.16/4.37 Eq
% 4.16/4.37 (Not
% 4.16/4.37 (And
% 4.16/4.37 (And
% 4.16/4.37 (And
% 4.16/4.37 (And
% 4.16/4.37 (And
% 4.16/4.37 (between_on_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)
% 4.16/4.37 (skS.0 5 a a_1 a_2 a_3 a_4 a_5))
% 4.16/4.37 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)))
% 4.16/4.37 (Not (apart_point_and_line (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 1 a a_1))))
% 4.16/4.37 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)))
% 4.16/4.37 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 4.16/4.37 (Not (apart_point_and_line (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2))) →
% 4.16/4.37 between_on_line (skS.0 1 a a_1)
% 4.16/4.37 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))
% 4.16/4.37 (skS.0 4 a a_1 a_2 a_3 a_4)
% 4.16/4.37 (intersection_point (skS.0 1 a a_1)
% 4.16/4.37 (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3 a_4 a_5)))))
% 4.16/4.37 True
% 4.16/4.37 Clause #245 (by clausification #[244]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.16/4.37 Eq
% 4.16/4.37 (And
% 4.16/4.37 (And
% 4.16/4.37 (And
% 4.16/4.37 (And
% 4.16/4.37 (And
% 4.16/4.37 (between_on_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)
% 4.16/4.37 (skS.0 5 a a_1 a_2 a_3 a_4 a_5))
% 4.16/4.37 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)))
% 4.16/4.37 (Not (apart_point_and_line (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 1 a a_1))))
% 4.16/4.37 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)))
% 4.16/4.37 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 4.16/4.37 (Not (apart_point_and_line (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2))) →
% 4.16/4.37 between_on_line (skS.0 1 a a_1)
% 4.16/4.37 (intersection_point (skS.0 1 a a_1) (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))
% 4.16/4.37 (skS.0 4 a a_1 a_2 a_3 a_4)
% 4.16/4.37 (intersection_point (skS.0 1 a a_1)
% 4.16/4.37 (parallel_through_point (skS.0 2 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3 a_4 a_5))))
% 4.16/4.37 False
% 4.16/4.37 Clause #246 (by clausification #[245]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.16/4.37 Eq
% 4.16/4.37 (And
% 4.16/4.37 (And
% 4.16/4.37 (And
% 4.16/4.37 (And
% 4.16/4.37 (And
% 4.16/4.37 (between_on_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)
% 4.16/4.37 (skS.0 5 a a_1 a_2 a_3 a_4 a_5))
% 4.16/4.37 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)))
% 4.16/4.37 (Not (apart_point_and_line (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 1 a a_1))))
% 4.16/4.37 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)))
% 4.16/4.37 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 4.16/4.37 (Not (apart_point_and_line (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2))))
% 4.16/4.37 True
% 4.16/4.37 Clause #249 (by clausification #[246]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.16/4.37 Eq
% 4.16/4.37 (And
% 4.16/4.37 (And
% 4.16/4.37 (And
% 4.16/4.37 (And
% 4.16/4.37 (between_on_line (skS.0 0 a) (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4)
% 4.16/4.37 (skS.0 5 a a_1 a_2 a_3 a_4 a_5))
% 4.16/4.37 (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)))
% 4.16/4.37 (Not (apart_point_and_line (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 1 a a_1))))
% 4.16/4.37 (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)))
% 4.16/4.37 (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 4.16/4.37 True
% 4.16/4.37 Clause #285 (by clausification #[249]): ∀ (a a_1 a_2 : Iota), Eq (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True
% 4.16/4.37 Clause #287 (by superposition #[285, 155]): ∀ (a a_1 a_2 : Iota),
% 4.16/4.37 Or (Eq True False) (Eq (unequally_directed_lines (skS.0 1 a a_1) (reverse_line (skS.0 2 a a_1 a_2))) True)
% 4.16/4.37 Clause #288 (by superposition #[285, 156]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (unequally_directed_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True)
% 4.16/4.37 Clause #289 (by clausification #[288]): ∀ (a a_1 a_2 : Iota), Eq (unequally_directed_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True
% 4.16/4.37 Clause #291 (by superposition #[289, 103]): ∀ (a a_1 a_2 : Iota),
% 4.16/4.38 Or (Eq True False)
% 4.16/4.38 (Or (Eq (unequally_directed_lines (skS.0 1 a a_1) (reverse_line (skS.0 2 a a_1 a_2))) False)
% 4.16/4.38 (Eq (left_convergent_lines (skS.0 1 a a_1) (reverse_line (skS.0 2 a a_1 a_2))) True))
% 4.16/4.38 Clause #297 (by clausification #[287]): ∀ (a a_1 a_2 : Iota), Eq (unequally_directed_lines (skS.0 1 a a_1) (reverse_line (skS.0 2 a a_1 a_2))) True
% 4.16/4.38 Clause #400 (by clausification #[291]): ∀ (a a_1 a_2 : Iota),
% 4.16/4.38 Or (Eq (unequally_directed_lines (skS.0 1 a a_1) (reverse_line (skS.0 2 a a_1 a_2))) False)
% 4.16/4.38 (Eq (left_convergent_lines (skS.0 1 a a_1) (reverse_line (skS.0 2 a a_1 a_2))) True)
% 4.16/4.38 Clause #401 (by forward demodulation #[400, 297]): ∀ (a a_1 a_2 : Iota),
% 4.16/4.38 Or (Eq True False) (Eq (left_convergent_lines (skS.0 1 a a_1) (reverse_line (skS.0 2 a a_1 a_2))) True)
% 4.16/4.38 Clause #402 (by clausification #[401]): ∀ (a a_1 a_2 : Iota), Eq (left_convergent_lines (skS.0 1 a a_1) (reverse_line (skS.0 2 a a_1 a_2))) True
% 4.16/4.38 Clause #403 (by superposition #[402, 78]): Eq True False
% 4.16/4.38 Clause #404 (by clausification #[403]): False
% 4.16/4.38 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------