%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO219+2 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n009.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 : Fri Oct 3 07:48:16 PM UTC 2025 % Result : Theorem 75.58s 75.76s % Output : Proof 75.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO219+2 : TPTP v9.2.0. Released v3.3.0. % 0.03/0.13 % Command : duper %s % 0.12/0.34 % Computer : n009.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 11:26:08 EDT 2025 % 0.12/0.34 % CPUTime : % 75.58/75.76 SZS status Theorem for theBenchmark.p % 75.58/75.76 SZS output start Proof for theBenchmark.p % 75.58/75.76 Clause #5 (by assumption #[]): Eq (∀ (X Y Z : Iota), convergent_lines X Y → Or (convergent_lines X Z) (convergent_lines Y Z)) True % 75.58/75.76 Clause #12 (by assumption #[]): Eq (∀ (L M : Iota), Not (And (Not (convergent_lines L M)) (Not (unorthogonal_lines L M)))) True % 75.58/75.76 Clause #13 (by assumption #[]): Eq % 75.58/75.76 (∀ (L M N : Iota), % 75.58/75.76 And (Or (Not (convergent_lines L M)) (Not (unorthogonal_lines L M))) % 75.58/75.76 (Or (Not (convergent_lines L N)) (Not (unorthogonal_lines L N))) → % 75.58/75.76 Or (Not (convergent_lines M N)) (Not (unorthogonal_lines M N))) % 75.58/75.76 True % 75.58/75.76 Clause #15 (by assumption #[]): Eq % 75.58/75.76 (Not % 75.58/75.76 (∀ (L M N : Iota), And (Not (unorthogonal_lines L M)) (Not (convergent_lines L N)) → Not (unorthogonal_lines M N))) % 75.58/75.76 True % 75.58/75.76 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)) % 75.58/75.76 False % 75.58/75.76 Clause #39 (by clausification #[38]): ∀ (a : Iota), % 75.58/75.76 Eq % 75.58/75.76 (Not % 75.58/75.76 (∀ (M N : Iota), % 75.58/75.76 And (Not (unorthogonal_lines (skS.0 0 a) M)) (Not (convergent_lines (skS.0 0 a) N)) → % 75.58/75.76 Not (unorthogonal_lines M N))) % 75.58/75.76 True % 75.58/75.76 Clause #40 (by clausification #[39]): ∀ (a : Iota), % 75.58/75.76 Eq % 75.58/75.76 (∀ (M N : Iota), % 75.58/75.76 And (Not (unorthogonal_lines (skS.0 0 a) M)) (Not (convergent_lines (skS.0 0 a) N)) → % 75.58/75.76 Not (unorthogonal_lines M N)) % 75.58/75.76 False % 75.58/75.76 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), % 75.58/75.76 Eq % 75.58/75.76 (Not % 75.58/75.76 (∀ (N : Iota), % 75.58/75.76 And (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1))) (Not (convergent_lines (skS.0 0 a) N)) → % 75.58/75.76 Not (unorthogonal_lines (skS.0 1 a a_1) N))) % 75.58/75.76 True % 75.58/75.76 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), % 75.58/75.76 Eq % 75.58/75.76 (∀ (N : Iota), % 75.58/75.76 And (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1))) (Not (convergent_lines (skS.0 0 a) N)) → % 75.58/75.76 Not (unorthogonal_lines (skS.0 1 a a_1) N)) % 75.58/75.76 False % 75.58/75.76 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), % 75.58/75.76 Eq % 75.58/75.76 (Not % 75.58/75.76 (And (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1))) % 75.58/75.76 (Not (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) → % 75.58/75.76 Not (unorthogonal_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))) % 75.58/75.76 True % 75.58/75.76 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), % 75.58/75.76 Eq % 75.58/75.76 (And (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1))) % 75.58/75.76 (Not (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) → % 75.58/75.76 Not (unorthogonal_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 75.58/75.76 False % 75.58/75.76 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), % 75.58/75.76 Eq % 75.58/75.76 (And (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1))) % 75.58/75.76 (Not (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)))) % 75.58/75.76 True % 75.58/75.76 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 % 75.58/75.76 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 % 75.58/75.76 Clause #48 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (Not (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1))) True % 75.58/75.76 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 % 75.58/75.76 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 % 75.58/75.76 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 % 75.58/75.76 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 % 75.58/75.76 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 : Iota), % 75.58/75.76 Or (Eq (convergent_lines a a_1) False) (Eq (Or (convergent_lines a a_2) (convergent_lines a_1 a_2)) True) % 75.58/75.76 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), % 75.58/75.76 Or (Eq (convergent_lines a a_1) False) (Or (Eq (convergent_lines a a_2) True) (Eq (convergent_lines a_1 a_2) True)) % 75.58/75.76 Clause #84 (by clausification #[12]): ∀ (a : Iota), Eq (∀ (M : Iota), Not (And (Not (convergent_lines a M)) (Not (unorthogonal_lines a M)))) True % 75.58/75.78 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 % 75.58/75.78 Clause #86 (by clausification #[85]): ∀ (a a_1 : Iota), Eq (And (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) False % 75.58/75.78 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) % 75.58/75.78 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) % 75.58/75.78 Clause #89 (by clausification #[88]): ∀ (a a_1 : Iota), Or (Eq (convergent_lines a a_1) True) (Eq (unorthogonal_lines a a_1) True) % 75.58/75.78 Clause #90 (by clausification #[13]): ∀ (a : Iota), % 75.58/75.78 Eq % 75.58/75.78 (∀ (M N : Iota), % 75.58/75.78 And (Or (Not (convergent_lines a M)) (Not (unorthogonal_lines a M))) % 75.58/75.78 (Or (Not (convergent_lines a N)) (Not (unorthogonal_lines a N))) → % 75.58/75.78 Or (Not (convergent_lines M N)) (Not (unorthogonal_lines M N))) % 75.58/75.78 True % 75.58/75.78 Clause #91 (by clausification #[90]): ∀ (a a_1 : Iota), % 75.58/75.78 Eq % 75.58/75.78 (∀ (N : Iota), % 75.58/75.78 And (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) % 75.58/75.78 (Or (Not (convergent_lines a N)) (Not (unorthogonal_lines a N))) → % 75.58/75.78 Or (Not (convergent_lines a_1 N)) (Not (unorthogonal_lines a_1 N))) % 75.58/75.78 True % 75.58/75.78 Clause #92 (by clausification #[91]): ∀ (a a_1 a_2 : Iota), % 75.58/75.78 Eq % 75.58/75.78 (And (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) % 75.58/75.78 (Or (Not (convergent_lines a a_2)) (Not (unorthogonal_lines a a_2))) → % 75.58/75.78 Or (Not (convergent_lines a_1 a_2)) (Not (unorthogonal_lines a_1 a_2))) % 75.58/75.78 True % 75.58/75.78 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 : Iota), % 75.58/75.78 Or % 75.58/75.78 (Eq % 75.58/75.78 (And (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) % 75.58/75.78 (Or (Not (convergent_lines a a_2)) (Not (unorthogonal_lines a a_2)))) % 75.58/75.78 False) % 75.58/75.78 (Eq (Or (Not (convergent_lines a_1 a_2)) (Not (unorthogonal_lines a_1 a_2))) True) % 75.58/75.78 Clause #94 (by clausification #[93]): ∀ (a a_1 a_2 : Iota), % 75.58/75.78 Or (Eq (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) True) % 75.58/75.78 (Or (Eq (Or (Not (convergent_lines a_2 a)) (Not (unorthogonal_lines a_2 a))) False) % 75.58/75.78 (Eq (Or (Not (convergent_lines a_2 a_1)) (Not (unorthogonal_lines a_2 a_1))) False)) % 75.58/75.78 Clause #95 (by clausification #[94]): ∀ (a a_1 a_2 : Iota), % 75.58/75.78 Or (Eq (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) False) % 75.58/75.78 (Or (Eq (Or (Not (convergent_lines a a_2)) (Not (unorthogonal_lines a a_2))) False) % 75.58/75.78 (Or (Eq (Not (convergent_lines a_1 a_2)) True) (Eq (Not (unorthogonal_lines a_1 a_2)) True))) % 75.58/75.78 Clause #96 (by clausification #[95]): ∀ (a a_1 a_2 : Iota), % 75.58/75.78 Or (Eq (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) False) % 75.58/75.78 (Or (Eq (Not (convergent_lines a_2 a_1)) True) % 75.58/75.78 (Or (Eq (Not (unorthogonal_lines a_2 a_1)) True) (Eq (Not (unorthogonal_lines a a_2)) False))) % 75.58/75.78 Clause #99 (by clausification #[96]): ∀ (a a_1 a_2 : Iota), % 75.58/75.78 Or (Eq (Not (convergent_lines a a_1)) True) % 75.58/75.78 (Or (Eq (Not (unorthogonal_lines a a_1)) True) % 75.58/75.78 (Or (Eq (Not (unorthogonal_lines a_2 a)) False) (Eq (Not (convergent_lines a_2 a_1)) False))) % 75.58/75.78 Clause #113 (by clausification #[48]): ∀ (a a_1 : Iota), Eq (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1)) False % 75.58/75.78 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) % 75.58/75.78 Clause #115 (by clausification #[114]): ∀ (a a_1 : Iota), Eq (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)) True % 75.58/75.78 Clause #119 (by superposition #[115, 61]): ∀ (a a_1 a_2 : Iota), % 75.58/75.78 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)) % 75.58/75.78 Clause #123 (by clausification #[99]): ∀ (a a_1 a_2 : Iota), % 75.58/75.78 Or (Eq (Not (unorthogonal_lines a a_1)) True) % 75.58/75.78 (Or (Eq (Not (unorthogonal_lines a_2 a)) False) % 75.58/75.78 (Or (Eq (Not (convergent_lines a_2 a_1)) False) (Eq (convergent_lines a a_1) False))) % 75.72/75.91 Clause #124 (by clausification #[123]): ∀ (a a_1 a_2 : Iota), % 75.72/75.91 Or (Eq (Not (unorthogonal_lines a a_1)) False) % 75.72/75.91 (Or (Eq (Not (convergent_lines a a_2)) False) % 75.72/75.91 (Or (Eq (convergent_lines a_1 a_2) False) (Eq (unorthogonal_lines a_1 a_2) False))) % 75.72/75.91 Clause #125 (by clausification #[124]): ∀ (a a_1 a_2 : Iota), % 75.72/75.91 Or (Eq (Not (convergent_lines a a_1)) False) % 75.72/75.91 (Or (Eq (convergent_lines a_2 a_1) False) % 75.72/75.91 (Or (Eq (unorthogonal_lines a_2 a_1) False) (Eq (unorthogonal_lines a a_2) True))) % 75.72/75.91 Clause #126 (by clausification #[125]): ∀ (a a_1 a_2 : Iota), % 75.72/75.91 Or (Eq (convergent_lines a a_1) False) % 75.72/75.91 (Or (Eq (unorthogonal_lines a a_1) False) % 75.72/75.91 (Or (Eq (unorthogonal_lines a_2 a) True) (Eq (convergent_lines a_2 a_1) True))) % 75.72/75.91 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 % 75.72/75.91 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) % 75.72/75.91 Clause #155 (by superposition #[148, 126]): ∀ (a a_1 a_2 a_3 : Iota), % 75.72/75.91 Or (Eq (convergent_lines (skS.0 0 a) a_1) True) % 75.72/75.91 (Or (Eq True False) % 75.72/75.91 (Or (Eq (unorthogonal_lines (skS.0 1 a a_2) a_1) False) % 75.72/75.91 (Or (Eq (unorthogonal_lines a_3 (skS.0 1 a a_2)) True) (Eq (convergent_lines a_3 a_1) True)))) % 75.72/75.91 Clause #349 (by clausification #[155]): ∀ (a a_1 a_2 a_3 : Iota), % 75.72/75.91 Or (Eq (convergent_lines (skS.0 0 a) a_1) True) % 75.72/75.91 (Or (Eq (unorthogonal_lines (skS.0 1 a a_2) a_1) False) % 75.72/75.91 (Or (Eq (unorthogonal_lines a_3 (skS.0 1 a a_2)) True) (Eq (convergent_lines a_3 a_1) True))) % 75.72/75.91 Clause #350 (by superposition #[349, 128]): ∀ (a a_1 a_2 a_3 : Iota), % 75.72/75.91 Or (Eq (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 75.72/75.91 (Or (Eq (unorthogonal_lines a_3 (skS.0 1 a a_1)) True) % 75.72/75.91 (Or (Eq (convergent_lines a_3 (skS.0 2 a a_1 a_2)) True) (Eq False True))) % 75.72/75.91 Clause #7098 (by clausification #[350]): ∀ (a a_1 a_2 a_3 : Iota), % 75.72/75.91 Or (Eq (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) % 75.72/75.91 (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)) % 75.72/75.91 Clause #7099 (by superposition #[7098, 49]): ∀ (a a_1 a_2 a_3 : Iota), % 75.72/75.91 Or (Eq (unorthogonal_lines a (skS.0 1 a_1 a_2)) True) % 75.72/75.91 (Or (Eq (convergent_lines a (skS.0 2 a_1 a_2 a_3)) True) (Eq True False)) % 75.72/75.91 Clause #7118 (by clausification #[7099]): ∀ (a a_1 a_2 a_3 : Iota), % 75.72/75.91 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) % 75.72/75.91 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) % 75.72/75.91 Clause #7129 (by clausification #[7119]): ∀ (a a_1 : Iota), Eq (unorthogonal_lines (skS.0 0 a) (skS.0 1 a a_1)) True % 75.72/75.91 Clause #7130 (by superposition #[7129, 113]): Eq True False % 75.72/75.91 Clause #7152 (by clausification #[7130]): False % 75.72/75.91 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------