TSTP Solution File: GEO219+1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : GEO219+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n013.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 22:55:43 EDT 2023
% Result : Theorem 44.61s 44.85s
% Output : Proof 44.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO219+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 23:03:46 EDT 2023
% 0.14/0.35 % CPUTime :
% 44.61/44.85 SZS status Theorem for theBenchmark.p
% 44.61/44.85 SZS output start Proof for theBenchmark.p
% 44.61/44.85 Clause #5 (by assumption #[]): Eq (∀ (X Y Z : Iota), convergent_lines X Y → Or (convergent_lines X Z) (convergent_lines Y Z)) True
% 44.61/44.85 Clause #14 (by assumption #[]): Eq (∀ (L M : Iota), Not (And (Not (convergent_lines L M)) (Not (unorthogonal_lines L M)))) True
% 44.61/44.85 Clause #15 (by assumption #[]): Eq
% 44.61/44.85 (∀ (L M N : Iota),
% 44.61/44.85 And (Or (Not (convergent_lines L M)) (Not (unorthogonal_lines L M)))
% 44.61/44.85 (Or (Not (convergent_lines L N)) (Not (unorthogonal_lines L N))) →
% 44.61/44.85 Or (Not (convergent_lines M N)) (Not (unorthogonal_lines M N)))
% 44.61/44.85 True
% 44.61/44.85 Clause #17 (by assumption #[]): Eq
% 44.61/44.85 (Not
% 44.61/44.85 (∀ (L M N : Iota), And (Not (unorthogonal_lines L M)) (Not (convergent_lines L N)) → Not (unorthogonal_lines M N)))
% 44.61/44.85 True
% 44.61/44.85 Clause #32 (by clausification #[17]): Eq (∀ (L M N : Iota), And (Not (unorthogonal_lines L M)) (Not (convergent_lines L N)) → Not (unorthogonal_lines M N))
% 44.61/44.85 False
% 44.61/44.85 Clause #33 (by clausification #[32]): ∀ (a : Iota),
% 44.61/44.86 Eq
% 44.61/44.86 (Not
% 44.61/44.86 (∀ (M N : Iota),
% 44.61/44.86 And (Not (unorthogonal_lines (skS.0 0 a) M)) (Not (convergent_lines (skS.0 0 a) N)) →
% 44.61/44.86 Not (unorthogonal_lines M N)))
% 44.61/44.86 True
% 44.61/44.86 Clause #34 (by clausification #[33]): ∀ (a : Iota),
% 44.61/44.86 Eq
% 44.61/44.86 (∀ (M N : Iota),
% 44.61/44.86 And (Not (unorthogonal_lines (skS.0 0 a) M)) (Not (convergent_lines (skS.0 0 a) N)) →
% 44.61/44.86 Not (unorthogonal_lines M N))
% 44.61/44.86 False
% 44.61/44.86 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota),
% 44.61/44.86 Eq
% 44.61/44.86 (Not
% 44.61/44.86 (∀ (N : Iota),
% 44.61/44.86 And (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1))) (Not (convergent_lines (skS.0 0 a) N)) →
% 44.61/44.86 Not (unorthogonal_lines (skS.0 1 a a_1) N)))
% 44.61/44.86 True
% 44.61/44.86 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota),
% 44.61/44.86 Eq
% 44.61/44.86 (∀ (N : Iota),
% 44.61/44.86 And (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1))) (Not (convergent_lines (skS.0 0 a) N)) →
% 44.61/44.86 Not (unorthogonal_lines (skS.0 1 a a_1) N))
% 44.61/44.86 False
% 44.61/44.86 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota),
% 44.61/44.86 Eq
% 44.61/44.86 (Not
% 44.61/44.86 (And (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1)))
% 44.61/44.86 (Not (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) →
% 44.61/44.86 Not (unorthogonal_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))))
% 44.61/44.86 True
% 44.61/44.86 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota),
% 44.61/44.86 Eq
% 44.61/44.86 (And (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1)))
% 44.61/44.86 (Not (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) →
% 44.61/44.86 Not (unorthogonal_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 44.61/44.86 False
% 44.61/44.86 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota),
% 44.61/44.86 Eq
% 44.61/44.86 (And (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1)))
% 44.61/44.86 (Not (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))))
% 44.61/44.86 True
% 44.61/44.86 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Eq (Not (unorthogonal_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) False
% 44.61/44.86 Clause #41 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), Eq (Not (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) True
% 44.61/44.86 Clause #42 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1))) True
% 44.61/44.86 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), Eq (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) False
% 44.61/44.86 Clause #80 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), convergent_lines a Y → Or (convergent_lines a Z) (convergent_lines Y Z)) True
% 44.61/44.86 Clause #81 (by clausification #[80]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), convergent_lines a a_1 → Or (convergent_lines a Z) (convergent_lines a_1 Z)) True
% 44.61/44.86 Clause #82 (by clausification #[81]): ∀ (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
% 44.61/44.86 Clause #83 (by clausification #[82]): ∀ (a a_1 a_2 : Iota),
% 44.61/44.86 Or (Eq (convergent_lines a a_1) False) (Eq (Or (convergent_lines a a_2) (convergent_lines a_1 a_2)) True)
% 44.61/44.86 Clause #84 (by clausification #[83]): ∀ (a a_1 a_2 : Iota),
% 44.61/44.86 Or (Eq (convergent_lines a a_1) False) (Or (Eq (convergent_lines a a_2) True) (Eq (convergent_lines a_1 a_2) True))
% 44.61/44.86 Clause #90 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (M : Iota), Not (And (Not (convergent_lines a M)) (Not (unorthogonal_lines a M)))) True
% 44.61/44.88 Clause #91 (by clausification #[90]): ∀ (a a_1 : Iota), Eq (Not (And (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1)))) True
% 44.61/44.88 Clause #92 (by clausification #[91]): ∀ (a a_1 : Iota), Eq (And (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) False
% 44.61/44.88 Clause #93 (by clausification #[92]): ∀ (a a_1 : Iota), Or (Eq (Not (convergent_lines a a_1)) False) (Eq (Not (unorthogonal_lines a a_1)) False)
% 44.61/44.88 Clause #94 (by clausification #[93]): ∀ (a a_1 : Iota), Or (Eq (Not (unorthogonal_lines a a_1)) False) (Eq (convergent_lines a a_1) True)
% 44.61/44.88 Clause #95 (by clausification #[94]): ∀ (a a_1 : Iota), Or (Eq (convergent_lines a a_1) True) (Eq (unorthogonal_lines a a_1) True)
% 44.61/44.88 Clause #96 (by clausification #[15]): ∀ (a : Iota),
% 44.61/44.88 Eq
% 44.61/44.88 (∀ (M N : Iota),
% 44.61/44.88 And (Or (Not (convergent_lines a M)) (Not (unorthogonal_lines a M)))
% 44.61/44.88 (Or (Not (convergent_lines a N)) (Not (unorthogonal_lines a N))) →
% 44.61/44.88 Or (Not (convergent_lines M N)) (Not (unorthogonal_lines M N)))
% 44.61/44.88 True
% 44.61/44.88 Clause #97 (by clausification #[96]): ∀ (a a_1 : Iota),
% 44.61/44.88 Eq
% 44.61/44.88 (∀ (N : Iota),
% 44.61/44.88 And (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1)))
% 44.61/44.88 (Or (Not (convergent_lines a N)) (Not (unorthogonal_lines a N))) →
% 44.61/44.88 Or (Not (convergent_lines a_1 N)) (Not (unorthogonal_lines a_1 N)))
% 44.61/44.88 True
% 44.61/44.88 Clause #98 (by clausification #[97]): ∀ (a a_1 a_2 : Iota),
% 44.61/44.88 Eq
% 44.61/44.88 (And (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1)))
% 44.61/44.88 (Or (Not (convergent_lines a a_2)) (Not (unorthogonal_lines a a_2))) →
% 44.61/44.88 Or (Not (convergent_lines a_1 a_2)) (Not (unorthogonal_lines a_1 a_2)))
% 44.61/44.88 True
% 44.61/44.88 Clause #99 (by clausification #[98]): ∀ (a a_1 a_2 : Iota),
% 44.61/44.88 Or
% 44.61/44.88 (Eq
% 44.61/44.88 (And (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1)))
% 44.61/44.88 (Or (Not (convergent_lines a a_2)) (Not (unorthogonal_lines a a_2))))
% 44.61/44.88 False)
% 44.61/44.88 (Eq (Or (Not (convergent_lines a_1 a_2)) (Not (unorthogonal_lines a_1 a_2))) True)
% 44.61/44.88 Clause #100 (by clausification #[99]): ∀ (a a_1 a_2 : Iota),
% 44.61/44.88 Or (Eq (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) True)
% 44.61/44.88 (Or (Eq (Or (Not (convergent_lines a_2 a)) (Not (unorthogonal_lines a_2 a))) False)
% 44.61/44.88 (Eq (Or (Not (convergent_lines a_2 a_1)) (Not (unorthogonal_lines a_2 a_1))) False))
% 44.61/44.88 Clause #101 (by clausification #[100]): ∀ (a a_1 a_2 : Iota),
% 44.61/44.88 Or (Eq (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) False)
% 44.61/44.88 (Or (Eq (Or (Not (convergent_lines a a_2)) (Not (unorthogonal_lines a a_2))) False)
% 44.61/44.88 (Or (Eq (Not (convergent_lines a_1 a_2)) True) (Eq (Not (unorthogonal_lines a_1 a_2)) True)))
% 44.61/44.88 Clause #102 (by clausification #[101]): ∀ (a a_1 a_2 : Iota),
% 44.61/44.88 Or (Eq (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) False)
% 44.61/44.88 (Or (Eq (Not (convergent_lines a_2 a_1)) True)
% 44.61/44.88 (Or (Eq (Not (unorthogonal_lines a_2 a_1)) True) (Eq (Not (unorthogonal_lines a a_2)) False)))
% 44.61/44.88 Clause #105 (by clausification #[102]): ∀ (a a_1 a_2 : Iota),
% 44.61/44.88 Or (Eq (Not (convergent_lines a a_1)) True)
% 44.61/44.88 (Or (Eq (Not (unorthogonal_lines a a_1)) True)
% 44.61/44.88 (Or (Eq (Not (unorthogonal_lines a_2 a)) False) (Eq (Not (convergent_lines a_2 a_1)) False)))
% 44.61/44.88 Clause #119 (by clausification #[42]): ∀ (a a_1 : Iota), Eq (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1)) False
% 44.61/44.88 Clause #120 (by superposition #[119, 95]): ∀ (a a_1 : Iota), Or (Eq (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq False True)
% 44.61/44.88 Clause #121 (by clausification #[120]): ∀ (a a_1 : Iota), Eq (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)) True
% 44.61/44.88 Clause #126 (by superposition #[121, 84]): ∀ (a a_1 a_2 : Iota),
% 44.61/44.88 Or (Eq True False) (Or (Eq (convergent_lines (skS.0 0 a) a_1) True) (Eq (convergent_lines (skS.0 1 a a_2) a_1) True))
% 44.61/44.88 Clause #127 (by clausification #[105]): ∀ (a a_1 a_2 : Iota),
% 44.61/44.88 Or (Eq (Not (unorthogonal_lines a a_1)) True)
% 44.61/44.88 (Or (Eq (Not (unorthogonal_lines a_2 a)) False)
% 44.61/44.88 (Or (Eq (Not (convergent_lines a_2 a_1)) False) (Eq (convergent_lines a a_1) False)))
% 44.77/44.95 Clause #128 (by clausification #[127]): ∀ (a a_1 a_2 : Iota),
% 44.77/44.95 Or (Eq (Not (unorthogonal_lines a a_1)) False)
% 44.77/44.95 (Or (Eq (Not (convergent_lines a a_2)) False)
% 44.77/44.95 (Or (Eq (convergent_lines a_1 a_2) False) (Eq (unorthogonal_lines a_1 a_2) False)))
% 44.77/44.95 Clause #129 (by clausification #[128]): ∀ (a a_1 a_2 : Iota),
% 44.77/44.95 Or (Eq (Not (convergent_lines a a_1)) False)
% 44.77/44.95 (Or (Eq (convergent_lines a_2 a_1) False)
% 44.77/44.95 (Or (Eq (unorthogonal_lines a_2 a_1) False) (Eq (unorthogonal_lines a a_2) True)))
% 44.77/44.95 Clause #130 (by clausification #[129]): ∀ (a a_1 a_2 : Iota),
% 44.77/44.95 Or (Eq (convergent_lines a a_1) False)
% 44.77/44.95 (Or (Eq (unorthogonal_lines a a_1) False)
% 44.77/44.95 (Or (Eq (unorthogonal_lines a_2 a) True) (Eq (convergent_lines a_2 a_1) True)))
% 44.77/44.95 Clause #132 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Eq (unorthogonal_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True
% 44.77/44.95 Clause #133 (by clausification #[126]): ∀ (a a_1 a_2 : Iota), Or (Eq (convergent_lines (skS.0 0 a) a_1) True) (Eq (convergent_lines (skS.0 1 a a_2) a_1) True)
% 44.77/44.95 Clause #140 (by superposition #[133, 130]): ∀ (a a_1 a_2 a_3 : Iota),
% 44.77/44.95 Or (Eq (convergent_lines (skS.0 0 a) a_1) True)
% 44.77/44.95 (Or (Eq True False)
% 44.77/44.95 (Or (Eq (unorthogonal_lines (skS.0 1 a a_2) a_1) False)
% 44.77/44.95 (Or (Eq (unorthogonal_lines a_3 (skS.0 1 a a_2)) True) (Eq (convergent_lines a_3 a_1) True))))
% 44.77/44.95 Clause #279 (by clausification #[140]): ∀ (a a_1 a_2 a_3 : Iota),
% 44.77/44.95 Or (Eq (convergent_lines (skS.0 0 a) a_1) True)
% 44.77/44.95 (Or (Eq (unorthogonal_lines (skS.0 1 a a_2) a_1) False)
% 44.77/44.95 (Or (Eq (unorthogonal_lines a_3 (skS.0 1 a a_2)) True) (Eq (convergent_lines a_3 a_1) True)))
% 44.77/44.95 Clause #280 (by superposition #[279, 132]): ∀ (a a_1 a_2 a_3 : Iota),
% 44.77/44.95 Or (Eq (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) True)
% 44.77/44.95 (Or (Eq (unorthogonal_lines a_3 (skS.0 1 a a_1)) True)
% 44.77/44.95 (Or (Eq (convergent_lines a_3 (skS.0 2 a a_1 a_2)) True) (Eq False True)))
% 44.77/44.95 Clause #4600 (by clausification #[280]): ∀ (a a_1 a_2 a_3 : Iota),
% 44.77/44.95 Or (Eq (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) True)
% 44.77/44.95 (Or (Eq (unorthogonal_lines a_3 (skS.0 1 a a_1)) True) (Eq (convergent_lines a_3 (skS.0 2 a a_1 a_2)) True))
% 44.77/44.95 Clause #4601 (by superposition #[4600, 43]): ∀ (a a_1 a_2 a_3 : Iota),
% 44.77/44.95 Or (Eq (unorthogonal_lines a (skS.0 1 a_1 a_2)) True)
% 44.77/44.95 (Or (Eq (convergent_lines a (skS.0 2 a_1 a_2 a_3)) True) (Eq True False))
% 44.77/44.95 Clause #4620 (by clausification #[4601]): ∀ (a a_1 a_2 a_3 : Iota),
% 44.77/44.95 Or (Eq (unorthogonal_lines a (skS.0 1 a_1 a_2)) True) (Eq (convergent_lines a (skS.0 2 a_1 a_2 a_3)) True)
% 44.77/44.95 Clause #4621 (by superposition #[4620, 43]): ∀ (a a_1 : Iota), Or (Eq (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq True False)
% 44.77/44.95 Clause #4631 (by clausification #[4621]): ∀ (a a_1 : Iota), Eq (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1)) True
% 44.77/44.95 Clause #4632 (by superposition #[4631, 119]): Eq True False
% 44.77/44.95 Clause #4647 (by clausification #[4632]): False
% 44.77/44.95 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------