TSTP Solution File: GEO219+2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : GEO219+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n022.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 22:55:44 EDT 2023
% Result : Theorem 95.78s 96.11s
% Output : Proof 95.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO219+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n022.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 21:19:23 EDT 2023
% 0.14/0.36 % CPUTime :
% 95.78/96.11 SZS status Theorem for theBenchmark.p
% 95.78/96.11 SZS output start Proof for theBenchmark.p
% 95.78/96.11 Clause #5 (by assumption #[]): Eq (∀ (X Y Z : Iota), convergent_lines X Y → Or (convergent_lines X Z) (convergent_lines Y Z)) True
% 95.78/96.11 Clause #12 (by assumption #[]): Eq (∀ (L M : Iota), Not (And (Not (convergent_lines L M)) (Not (unorthogonal_lines L M)))) True
% 95.78/96.11 Clause #13 (by assumption #[]): Eq
% 95.78/96.11 (∀ (L M N : Iota),
% 95.78/96.11 And (Or (Not (convergent_lines L M)) (Not (unorthogonal_lines L M)))
% 95.78/96.11 (Or (Not (convergent_lines L N)) (Not (unorthogonal_lines L N))) →
% 95.78/96.11 Or (Not (convergent_lines M N)) (Not (unorthogonal_lines M N)))
% 95.78/96.11 True
% 95.78/96.11 Clause #15 (by assumption #[]): Eq
% 95.78/96.11 (Not
% 95.78/96.11 (∀ (L M N : Iota), And (Not (unorthogonal_lines L M)) (Not (convergent_lines L N)) → Not (unorthogonal_lines M N)))
% 95.78/96.11 True
% 95.78/96.11 Clause #38 (by clausification #[15]): Eq (∀ (L M N : Iota), And (Not (unorthogonal_lines L M)) (Not (convergent_lines L N)) → Not (unorthogonal_lines M N))
% 95.78/96.11 False
% 95.78/96.11 Clause #39 (by clausification #[38]): ∀ (a : Iota),
% 95.78/96.11 Eq
% 95.78/96.11 (Not
% 95.78/96.11 (∀ (M N : Iota),
% 95.78/96.11 And (Not (unorthogonal_lines (skS.0 0 a) M)) (Not (convergent_lines (skS.0 0 a) N)) →
% 95.78/96.11 Not (unorthogonal_lines M N)))
% 95.78/96.11 True
% 95.78/96.11 Clause #40 (by clausification #[39]): ∀ (a : Iota),
% 95.78/96.11 Eq
% 95.78/96.11 (∀ (M N : Iota),
% 95.78/96.11 And (Not (unorthogonal_lines (skS.0 0 a) M)) (Not (convergent_lines (skS.0 0 a) N)) →
% 95.78/96.11 Not (unorthogonal_lines M N))
% 95.78/96.11 False
% 95.78/96.11 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota),
% 95.78/96.11 Eq
% 95.78/96.11 (Not
% 95.78/96.11 (∀ (N : Iota),
% 95.78/96.11 And (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1))) (Not (convergent_lines (skS.0 0 a) N)) →
% 95.78/96.11 Not (unorthogonal_lines (skS.0 1 a a_1) N)))
% 95.78/96.11 True
% 95.78/96.11 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota),
% 95.78/96.11 Eq
% 95.78/96.11 (∀ (N : Iota),
% 95.78/96.11 And (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1))) (Not (convergent_lines (skS.0 0 a) N)) →
% 95.78/96.11 Not (unorthogonal_lines (skS.0 1 a a_1) N))
% 95.78/96.11 False
% 95.78/96.11 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota),
% 95.78/96.11 Eq
% 95.78/96.11 (Not
% 95.78/96.11 (And (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1)))
% 95.78/96.11 (Not (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) →
% 95.78/96.11 Not (unorthogonal_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))))
% 95.78/96.11 True
% 95.78/96.11 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 : Iota),
% 95.78/96.11 Eq
% 95.78/96.11 (And (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1)))
% 95.78/96.11 (Not (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) →
% 95.78/96.11 Not (unorthogonal_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 95.78/96.11 False
% 95.78/96.11 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota),
% 95.78/96.11 Eq
% 95.78/96.11 (And (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1)))
% 95.78/96.11 (Not (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))))
% 95.78/96.11 True
% 95.78/96.11 Clause #46 (by clausification #[44]): ∀ (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
% 95.78/96.11 Clause #47 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), Eq (Not (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) True
% 95.78/96.11 Clause #48 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1))) True
% 95.78/96.11 Clause #49 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Eq (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) False
% 95.78/96.11 Clause #57 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), convergent_lines a Y → Or (convergent_lines a Z) (convergent_lines Y Z)) True
% 95.78/96.11 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), convergent_lines a a_1 → Or (convergent_lines a Z) (convergent_lines a_1 Z)) True
% 95.78/96.11 Clause #59 (by clausification #[58]): ∀ (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
% 95.78/96.11 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 : Iota),
% 95.78/96.11 Or (Eq (convergent_lines a a_1) False) (Eq (Or (convergent_lines a a_2) (convergent_lines a_1 a_2)) True)
% 95.78/96.11 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 : Iota),
% 95.78/96.11 Or (Eq (convergent_lines a a_1) False) (Or (Eq (convergent_lines a a_2) True) (Eq (convergent_lines a_1 a_2) True))
% 95.78/96.11 Clause #84 (by clausification #[12]): ∀ (a : Iota), Eq (∀ (M : Iota), Not (And (Not (convergent_lines a M)) (Not (unorthogonal_lines a M)))) True
% 95.88/96.13 Clause #85 (by clausification #[84]): ∀ (a a_1 : Iota), Eq (Not (And (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1)))) True
% 95.88/96.13 Clause #86 (by clausification #[85]): ∀ (a a_1 : Iota), Eq (And (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) False
% 95.88/96.13 Clause #87 (by clausification #[86]): ∀ (a a_1 : Iota), Or (Eq (Not (convergent_lines a a_1)) False) (Eq (Not (unorthogonal_lines a a_1)) False)
% 95.88/96.13 Clause #88 (by clausification #[87]): ∀ (a a_1 : Iota), Or (Eq (Not (unorthogonal_lines a a_1)) False) (Eq (convergent_lines a a_1) True)
% 95.88/96.13 Clause #89 (by clausification #[88]): ∀ (a a_1 : Iota), Or (Eq (convergent_lines a a_1) True) (Eq (unorthogonal_lines a a_1) True)
% 95.88/96.13 Clause #90 (by clausification #[13]): ∀ (a : Iota),
% 95.88/96.13 Eq
% 95.88/96.13 (∀ (M N : Iota),
% 95.88/96.13 And (Or (Not (convergent_lines a M)) (Not (unorthogonal_lines a M)))
% 95.88/96.13 (Or (Not (convergent_lines a N)) (Not (unorthogonal_lines a N))) →
% 95.88/96.13 Or (Not (convergent_lines M N)) (Not (unorthogonal_lines M N)))
% 95.88/96.13 True
% 95.88/96.13 Clause #91 (by clausification #[90]): ∀ (a a_1 : Iota),
% 95.88/96.13 Eq
% 95.88/96.13 (∀ (N : Iota),
% 95.88/96.13 And (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1)))
% 95.88/96.13 (Or (Not (convergent_lines a N)) (Not (unorthogonal_lines a N))) →
% 95.88/96.13 Or (Not (convergent_lines a_1 N)) (Not (unorthogonal_lines a_1 N)))
% 95.88/96.13 True
% 95.88/96.13 Clause #92 (by clausification #[91]): ∀ (a a_1 a_2 : Iota),
% 95.88/96.13 Eq
% 95.88/96.13 (And (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1)))
% 95.88/96.13 (Or (Not (convergent_lines a a_2)) (Not (unorthogonal_lines a a_2))) →
% 95.88/96.13 Or (Not (convergent_lines a_1 a_2)) (Not (unorthogonal_lines a_1 a_2)))
% 95.88/96.13 True
% 95.88/96.13 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 : Iota),
% 95.88/96.13 Or
% 95.88/96.13 (Eq
% 95.88/96.13 (And (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1)))
% 95.88/96.13 (Or (Not (convergent_lines a a_2)) (Not (unorthogonal_lines a a_2))))
% 95.88/96.13 False)
% 95.88/96.13 (Eq (Or (Not (convergent_lines a_1 a_2)) (Not (unorthogonal_lines a_1 a_2))) True)
% 95.88/96.13 Clause #94 (by clausification #[93]): ∀ (a a_1 a_2 : Iota),
% 95.88/96.13 Or (Eq (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) True)
% 95.88/96.13 (Or (Eq (Or (Not (convergent_lines a_2 a)) (Not (unorthogonal_lines a_2 a))) False)
% 95.88/96.13 (Eq (Or (Not (convergent_lines a_2 a_1)) (Not (unorthogonal_lines a_2 a_1))) False))
% 95.88/96.13 Clause #95 (by clausification #[94]): ∀ (a a_1 a_2 : Iota),
% 95.88/96.13 Or (Eq (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) False)
% 95.88/96.13 (Or (Eq (Or (Not (convergent_lines a a_2)) (Not (unorthogonal_lines a a_2))) False)
% 95.88/96.13 (Or (Eq (Not (convergent_lines a_1 a_2)) True) (Eq (Not (unorthogonal_lines a_1 a_2)) True)))
% 95.88/96.13 Clause #96 (by clausification #[95]): ∀ (a a_1 a_2 : Iota),
% 95.88/96.13 Or (Eq (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) False)
% 95.88/96.13 (Or (Eq (Not (convergent_lines a_2 a_1)) True)
% 95.88/96.13 (Or (Eq (Not (unorthogonal_lines a_2 a_1)) True) (Eq (Not (unorthogonal_lines a a_2)) False)))
% 95.88/96.13 Clause #99 (by clausification #[96]): ∀ (a a_1 a_2 : Iota),
% 95.88/96.13 Or (Eq (Not (convergent_lines a a_1)) True)
% 95.88/96.13 (Or (Eq (Not (unorthogonal_lines a a_1)) True)
% 95.88/96.13 (Or (Eq (Not (unorthogonal_lines a_2 a)) False) (Eq (Not (convergent_lines a_2 a_1)) False)))
% 95.88/96.13 Clause #113 (by clausification #[48]): ∀ (a a_1 : Iota), Eq (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1)) False
% 95.88/96.13 Clause #114 (by superposition #[113, 89]): ∀ (a a_1 : Iota), Or (Eq (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq False True)
% 95.88/96.13 Clause #115 (by clausification #[114]): ∀ (a a_1 : Iota), Eq (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)) True
% 95.88/96.13 Clause #119 (by superposition #[115, 61]): ∀ (a a_1 a_2 : Iota),
% 95.88/96.13 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))
% 95.88/96.13 Clause #123 (by clausification #[99]): ∀ (a a_1 a_2 : Iota),
% 95.88/96.13 Or (Eq (Not (unorthogonal_lines a a_1)) True)
% 95.88/96.13 (Or (Eq (Not (unorthogonal_lines a_2 a)) False)
% 95.88/96.13 (Or (Eq (Not (convergent_lines a_2 a_1)) False) (Eq (convergent_lines a a_1) False)))
% 95.98/96.25 Clause #124 (by clausification #[123]): ∀ (a a_1 a_2 : Iota),
% 95.98/96.25 Or (Eq (Not (unorthogonal_lines a a_1)) False)
% 95.98/96.25 (Or (Eq (Not (convergent_lines a a_2)) False)
% 95.98/96.25 (Or (Eq (convergent_lines a_1 a_2) False) (Eq (unorthogonal_lines a_1 a_2) False)))
% 95.98/96.25 Clause #125 (by clausification #[124]): ∀ (a a_1 a_2 : Iota),
% 95.98/96.25 Or (Eq (Not (convergent_lines a a_1)) False)
% 95.98/96.25 (Or (Eq (convergent_lines a_2 a_1) False)
% 95.98/96.25 (Or (Eq (unorthogonal_lines a_2 a_1) False) (Eq (unorthogonal_lines a a_2) True)))
% 95.98/96.25 Clause #126 (by clausification #[125]): ∀ (a a_1 a_2 : Iota),
% 95.98/96.25 Or (Eq (convergent_lines a a_1) False)
% 95.98/96.25 (Or (Eq (unorthogonal_lines a a_1) False)
% 95.98/96.25 (Or (Eq (unorthogonal_lines a_2 a) True) (Eq (convergent_lines a_2 a_1) True)))
% 95.98/96.25 Clause #128 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), Eq (unorthogonal_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True
% 95.98/96.25 Clause #148 (by clausification #[119]): ∀ (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)
% 95.98/96.25 Clause #155 (by superposition #[148, 126]): ∀ (a a_1 a_2 a_3 : Iota),
% 95.98/96.25 Or (Eq (convergent_lines (skS.0 0 a) a_1) True)
% 95.98/96.25 (Or (Eq True False)
% 95.98/96.25 (Or (Eq (unorthogonal_lines (skS.0 1 a a_2) a_1) False)
% 95.98/96.25 (Or (Eq (unorthogonal_lines a_3 (skS.0 1 a a_2)) True) (Eq (convergent_lines a_3 a_1) True))))
% 95.98/96.25 Clause #349 (by clausification #[155]): ∀ (a a_1 a_2 a_3 : Iota),
% 95.98/96.25 Or (Eq (convergent_lines (skS.0 0 a) a_1) True)
% 95.98/96.25 (Or (Eq (unorthogonal_lines (skS.0 1 a a_2) a_1) False)
% 95.98/96.25 (Or (Eq (unorthogonal_lines a_3 (skS.0 1 a a_2)) True) (Eq (convergent_lines a_3 a_1) True)))
% 95.98/96.25 Clause #350 (by superposition #[349, 128]): ∀ (a a_1 a_2 a_3 : Iota),
% 95.98/96.25 Or (Eq (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) True)
% 95.98/96.25 (Or (Eq (unorthogonal_lines a_3 (skS.0 1 a a_1)) True)
% 95.98/96.25 (Or (Eq (convergent_lines a_3 (skS.0 2 a a_1 a_2)) True) (Eq False True)))
% 95.98/96.25 Clause #7098 (by clausification #[350]): ∀ (a a_1 a_2 a_3 : Iota),
% 95.98/96.25 Or (Eq (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) True)
% 95.98/96.25 (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))
% 95.98/96.25 Clause #7099 (by superposition #[7098, 49]): ∀ (a a_1 a_2 a_3 : Iota),
% 95.98/96.25 Or (Eq (unorthogonal_lines a (skS.0 1 a_1 a_2)) True)
% 95.98/96.25 (Or (Eq (convergent_lines a (skS.0 2 a_1 a_2 a_3)) True) (Eq True False))
% 95.98/96.25 Clause #7118 (by clausification #[7099]): ∀ (a a_1 a_2 a_3 : Iota),
% 95.98/96.25 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)
% 95.98/96.25 Clause #7119 (by superposition #[7118, 49]): ∀ (a a_1 : Iota), Or (Eq (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq True False)
% 95.98/96.25 Clause #7129 (by clausification #[7119]): ∀ (a a_1 : Iota), Eq (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1)) True
% 95.98/96.25 Clause #7130 (by superposition #[7129, 113]): Eq True False
% 95.98/96.25 Clause #7152 (by clausification #[7130]): False
% 95.98/96.25 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------