%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO218+2 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 36.95s 37.11s % Output : Proof 36.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO218+2 : TPTP v9.2.0. Released v3.3.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n031.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 : Fri Oct 3 11:28:23 EDT 2025 % 0.13/0.35 % CPUTime : % 36.95/37.11 SZS status Theorem for theBenchmark.p % 36.95/37.11 SZS output start Proof for theBenchmark.p % 36.95/37.11 Clause #2 (by assumption #[]): Eq (∀ (X : Iota), Not (convergent_lines X X)) True % 36.95/37.11 Clause #5 (by assumption #[]): Eq (∀ (X Y Z : Iota), convergent_lines X Y → Or (convergent_lines X Z) (convergent_lines Y Z)) True % 36.95/37.11 Clause #12 (by assumption #[]): Eq (∀ (L M : Iota), Not (And (Not (convergent_lines L M)) (Not (unorthogonal_lines L M)))) True % 36.95/37.11 Clause #13 (by assumption #[]): Eq % 36.95/37.11 (∀ (L M N : Iota), % 36.95/37.11 And (Or (Not (convergent_lines L M)) (Not (unorthogonal_lines L M))) % 36.95/37.11 (Or (Not (convergent_lines L N)) (Not (unorthogonal_lines L N))) → % 36.95/37.11 Or (Not (convergent_lines M N)) (Not (unorthogonal_lines M N))) % 36.95/37.11 True % 36.95/37.11 Clause #15 (by assumption #[]): Eq % 36.95/37.11 (Not % 36.95/37.11 (∀ (L M N : Iota), And (Not (convergent_lines L M)) (Not (unorthogonal_lines L N)) → Not (unorthogonal_lines M N))) % 36.95/37.11 True % 36.95/37.11 Clause #16 (by clausification #[2]): ∀ (a : Iota), Eq (Not (convergent_lines a a)) True % 36.95/37.11 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (convergent_lines a a) False % 36.95/37.11 Clause #38 (by clausification #[15]): Eq (∀ (L M N : Iota), And (Not (convergent_lines L M)) (Not (unorthogonal_lines L N)) → Not (unorthogonal_lines M N)) % 36.95/37.11 False % 36.95/37.11 Clause #39 (by clausification #[38]): ∀ (a : Iota), % 36.95/37.11 Eq % 36.95/37.11 (Not % 36.95/37.11 (∀ (M N : Iota), % 36.95/37.11 And (Not (convergent_lines (skS.0 0 a) M)) (Not (unorthogonal_lines (skS.0 0 a) N)) → % 36.95/37.11 Not (unorthogonal_lines M N))) % 36.95/37.11 True % 36.95/37.11 Clause #40 (by clausification #[39]): ∀ (a : Iota), % 36.95/37.11 Eq % 36.95/37.11 (∀ (M N : Iota), % 36.95/37.11 And (Not (convergent_lines (skS.0 0 a) M)) (Not (unorthogonal_lines (skS.0 0 a) N)) → % 36.95/37.11 Not (unorthogonal_lines M N)) % 36.95/37.11 False % 36.95/37.11 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), % 36.95/37.11 Eq % 36.95/37.11 (Not % 36.95/37.11 (∀ (N : Iota), % 36.95/37.11 And (Not (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) (Not (unorthogonal_lines (skS.0 0 a) N)) → % 36.95/37.11 Not (unorthogonal_lines (skS.0 1 a a_1) N))) % 36.95/37.11 True % 36.95/37.11 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), % 36.95/37.11 Eq % 36.95/37.11 (∀ (N : Iota), % 36.95/37.11 And (Not (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) (Not (unorthogonal_lines (skS.0 0 a) N)) → % 36.95/37.11 Not (unorthogonal_lines (skS.0 1 a a_1) N)) % 36.95/37.11 False % 36.95/37.11 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), % 36.95/37.11 Eq % 36.95/37.11 (Not % 36.95/37.11 (And (Not (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 36.95/37.11 (Not (unorthogonal_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) → % 36.95/37.11 Not (unorthogonal_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))) % 36.95/37.11 True % 36.95/37.11 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), % 36.95/37.11 Eq % 36.95/37.11 (And (Not (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 36.95/37.11 (Not (unorthogonal_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) → % 36.95/37.11 Not (unorthogonal_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 36.95/37.11 False % 36.95/37.11 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), % 36.95/37.11 Eq % 36.95/37.11 (And (Not (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 36.95/37.11 (Not (unorthogonal_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)))) % 36.95/37.11 True % 36.95/37.11 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 % 36.95/37.11 Clause #47 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), Eq (Not (unorthogonal_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) True % 36.95/37.11 Clause #48 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (Not (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) True % 36.95/37.11 Clause #49 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Eq (unorthogonal_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) False % 36.95/37.11 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 % 36.95/37.11 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 % 36.95/37.11 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 % 36.95/37.11 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 : Iota), % 36.95/37.11 Or (Eq (convergent_lines a a_1) False) (Eq (Or (convergent_lines a a_2) (convergent_lines a_1 a_2)) True) % 36.95/37.13 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), % 36.95/37.13 Or (Eq (convergent_lines a a_1) False) (Or (Eq (convergent_lines a a_2) True) (Eq (convergent_lines a_1 a_2) True)) % 36.95/37.13 Clause #84 (by clausification #[12]): ∀ (a : Iota), Eq (∀ (M : Iota), Not (And (Not (convergent_lines a M)) (Not (unorthogonal_lines a M)))) True % 36.95/37.13 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 % 36.95/37.13 Clause #86 (by clausification #[85]): ∀ (a a_1 : Iota), Eq (And (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) False % 36.95/37.13 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) % 36.95/37.13 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) % 36.95/37.13 Clause #89 (by clausification #[88]): ∀ (a a_1 : Iota), Or (Eq (convergent_lines a a_1) True) (Eq (unorthogonal_lines a a_1) True) % 36.95/37.13 Clause #90 (by superposition #[89, 49]): ∀ (a a_1 a_2 : Iota), Or (Eq (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) True) (Eq True False) % 36.95/37.13 Clause #91 (by clausification #[13]): ∀ (a : Iota), % 36.95/37.13 Eq % 36.95/37.13 (∀ (M N : Iota), % 36.95/37.13 And (Or (Not (convergent_lines a M)) (Not (unorthogonal_lines a M))) % 36.95/37.13 (Or (Not (convergent_lines a N)) (Not (unorthogonal_lines a N))) → % 36.95/37.13 Or (Not (convergent_lines M N)) (Not (unorthogonal_lines M N))) % 36.95/37.13 True % 36.95/37.13 Clause #92 (by clausification #[91]): ∀ (a a_1 : Iota), % 36.95/37.13 Eq % 36.95/37.13 (∀ (N : Iota), % 36.95/37.13 And (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) % 36.95/37.13 (Or (Not (convergent_lines a N)) (Not (unorthogonal_lines a N))) → % 36.95/37.13 Or (Not (convergent_lines a_1 N)) (Not (unorthogonal_lines a_1 N))) % 36.95/37.13 True % 36.95/37.13 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 : Iota), % 36.95/37.13 Eq % 36.95/37.13 (And (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) % 36.95/37.13 (Or (Not (convergent_lines a a_2)) (Not (unorthogonal_lines a a_2))) → % 36.95/37.13 Or (Not (convergent_lines a_1 a_2)) (Not (unorthogonal_lines a_1 a_2))) % 36.95/37.13 True % 36.95/37.13 Clause #94 (by clausification #[93]): ∀ (a a_1 a_2 : Iota), % 36.95/37.13 Or % 36.95/37.13 (Eq % 36.95/37.13 (And (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) % 36.95/37.13 (Or (Not (convergent_lines a a_2)) (Not (unorthogonal_lines a a_2)))) % 36.95/37.13 False) % 36.95/37.13 (Eq (Or (Not (convergent_lines a_1 a_2)) (Not (unorthogonal_lines a_1 a_2))) True) % 36.95/37.13 Clause #95 (by clausification #[94]): ∀ (a a_1 a_2 : Iota), % 36.95/37.13 Or (Eq (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) True) % 36.95/37.13 (Or (Eq (Or (Not (convergent_lines a_2 a)) (Not (unorthogonal_lines a_2 a))) False) % 36.95/37.13 (Eq (Or (Not (convergent_lines a_2 a_1)) (Not (unorthogonal_lines a_2 a_1))) False)) % 36.95/37.13 Clause #96 (by clausification #[95]): ∀ (a a_1 a_2 : Iota), % 36.95/37.13 Or (Eq (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) False) % 36.95/37.13 (Or (Eq (Or (Not (convergent_lines a a_2)) (Not (unorthogonal_lines a a_2))) False) % 36.95/37.13 (Or (Eq (Not (convergent_lines a_1 a_2)) True) (Eq (Not (unorthogonal_lines a_1 a_2)) True))) % 36.95/37.13 Clause #97 (by clausification #[96]): ∀ (a a_1 a_2 : Iota), % 36.95/37.13 Or (Eq (Or (Not (convergent_lines a a_1)) (Not (unorthogonal_lines a a_1))) False) % 36.95/37.13 (Or (Eq (Not (convergent_lines a_2 a_1)) True) % 36.95/37.13 (Or (Eq (Not (unorthogonal_lines a_2 a_1)) True) (Eq (Not (unorthogonal_lines a a_2)) False))) % 36.95/37.13 Clause #100 (by clausification #[97]): ∀ (a a_1 a_2 : Iota), % 36.95/37.13 Or (Eq (Not (convergent_lines a a_1)) True) % 36.95/37.13 (Or (Eq (Not (unorthogonal_lines a a_1)) True) % 36.95/37.13 (Or (Eq (Not (unorthogonal_lines a_2 a)) False) (Eq (Not (convergent_lines a_2 a_1)) False))) % 36.95/37.13 Clause #114 (by clausification #[48]): ∀ (a a_1 : Iota), Eq (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)) False % 36.95/37.13 Clause #115 (by clausification #[90]): ∀ (a a_1 a_2 : Iota), Eq (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)) True % 36.95/37.13 Clause #119 (by superposition #[115, 61]): ∀ (a a_1 a_2 a_3 : Iota), % 36.95/37.13 Or (Eq True False) % 36.95/37.13 (Or (Eq (convergent_lines (skS.0 0 a) a_1) True) (Eq (convergent_lines (skS.0 2 a a_2 a_3) a_1) True)) % 36.95/37.15 Clause #123 (by clausification #[100]): ∀ (a a_1 a_2 : Iota), % 36.95/37.15 Or (Eq (Not (unorthogonal_lines a a_1)) True) % 36.95/37.15 (Or (Eq (Not (unorthogonal_lines a_2 a)) False) % 36.95/37.15 (Or (Eq (Not (convergent_lines a_2 a_1)) False) (Eq (convergent_lines a a_1) False))) % 36.95/37.15 Clause #124 (by clausification #[123]): ∀ (a a_1 a_2 : Iota), % 36.95/37.15 Or (Eq (Not (unorthogonal_lines a a_1)) False) % 36.95/37.15 (Or (Eq (Not (convergent_lines a a_2)) False) % 36.95/37.15 (Or (Eq (convergent_lines a_1 a_2) False) (Eq (unorthogonal_lines a_1 a_2) False))) % 36.95/37.15 Clause #125 (by clausification #[124]): ∀ (a a_1 a_2 : Iota), % 36.95/37.15 Or (Eq (Not (convergent_lines a a_1)) False) % 36.95/37.15 (Or (Eq (convergent_lines a_2 a_1) False) % 36.95/37.15 (Or (Eq (unorthogonal_lines a_2 a_1) False) (Eq (unorthogonal_lines a a_2) True))) % 36.95/37.15 Clause #126 (by clausification #[125]): ∀ (a a_1 a_2 : Iota), % 36.95/37.15 Or (Eq (convergent_lines a a_1) False) % 36.95/37.15 (Or (Eq (unorthogonal_lines a a_1) False) % 36.95/37.15 (Or (Eq (unorthogonal_lines a_2 a) True) (Eq (convergent_lines a_2 a_1) True))) % 36.95/37.15 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 % 36.95/37.15 Clause #148 (by clausification #[119]): ∀ (a a_1 a_2 a_3 : Iota), % 36.95/37.15 Or (Eq (convergent_lines (skS.0 0 a) a_1) True) (Eq (convergent_lines (skS.0 2 a a_2 a_3) a_1) True) % 36.95/37.15 Clause #152 (by superposition #[148, 61]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 36.95/37.15 Or (Eq (convergent_lines (skS.0 0 a) a_1) True) % 36.95/37.15 (Or (Eq True False) (Or (Eq (convergent_lines (skS.0 2 a a_2 a_3) a_4) True) (Eq (convergent_lines a_1 a_4) True))) % 36.95/37.15 Clause #171 (by clausification #[152]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 36.95/37.15 Or (Eq (convergent_lines (skS.0 0 a) a_1) True) % 36.95/37.15 (Or (Eq (convergent_lines (skS.0 2 a a_2 a_3) a_4) True) (Eq (convergent_lines a_1 a_4) True)) % 36.95/37.15 Clause #172 (by superposition #[171, 114]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 36.95/37.15 Or (Eq (convergent_lines (skS.0 2 a a_1 a_2) a_3) True) % 36.95/37.15 (Or (Eq (convergent_lines (skS.0 1 a a_4) a_3) True) (Eq True False)) % 36.95/37.15 Clause #215 (by clausification #[172]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 36.95/37.15 Or (Eq (convergent_lines (skS.0 2 a a_1 a_2) a_3) True) (Eq (convergent_lines (skS.0 1 a a_4) a_3) True) % 36.95/37.15 Clause #216 (by superposition #[215, 17]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_2 a_3)) True) (Eq True False) % 36.95/37.15 Clause #225 (by superposition #[215, 17]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 1 a a_3)) True) (Eq True False) % 36.95/37.15 Clause #234 (by clausification #[225]): ∀ (a a_1 a_2 a_3 : Iota), Eq (convergent_lines (skS.0 2 a a_1 a_2) (skS.0 1 a a_3)) True % 36.95/37.15 Clause #240 (by superposition #[234, 126]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 36.95/37.15 Or (Eq True False) % 36.95/37.15 (Or (Eq (unorthogonal_lines (skS.0 2 a a_1 a_2) (skS.0 1 a a_3)) False) % 36.95/37.15 (Or (Eq (unorthogonal_lines a_4 (skS.0 2 a a_1 a_2)) True) (Eq (convergent_lines a_4 (skS.0 1 a a_3)) True))) % 36.95/37.15 Clause #245 (by clausification #[216]): ∀ (a a_1 a_2 a_3 : Iota), Eq (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_2 a_3)) True % 36.95/37.15 Clause #251 (by superposition #[245, 126]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 36.95/37.15 Or (Eq True False) % 36.95/37.15 (Or (Eq (unorthogonal_lines (skS.0 1 a a_1) (skS.0 2 a a_2 a_3)) False) % 36.95/37.15 (Or (Eq (unorthogonal_lines a_4 (skS.0 1 a a_1)) True) (Eq (convergent_lines a_4 (skS.0 2 a a_2 a_3)) True))) % 36.95/37.15 Clause #3325 (by clausification #[240]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 36.95/37.15 Or (Eq (unorthogonal_lines (skS.0 2 a a_1 a_2) (skS.0 1 a a_3)) False) % 36.95/37.15 (Or (Eq (unorthogonal_lines a_4 (skS.0 2 a a_1 a_2)) True) (Eq (convergent_lines a_4 (skS.0 1 a a_3)) True)) % 36.95/37.15 Clause #3477 (by clausification #[251]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 36.95/37.15 Or (Eq (unorthogonal_lines (skS.0 1 a a_1) (skS.0 2 a a_2 a_3)) False) % 36.95/37.15 (Or (Eq (unorthogonal_lines a_4 (skS.0 1 a a_1)) True) (Eq (convergent_lines a_4 (skS.0 2 a a_2 a_3)) True)) % 36.95/37.15 Clause #3478 (by superposition #[3477, 128]): ∀ (a a_1 a_2 a_3 : Iota), % 36.95/37.15 Or (Eq (unorthogonal_lines a (skS.0 1 a_1 a_2)) True) % 36.95/37.15 (Or (Eq (convergent_lines a (skS.0 2 a_1 a_2 a_3)) True) (Eq False True)) % 36.95/37.15 Clause #3509 (by clausification #[3478]): ∀ (a a_1 a_2 a_3 : Iota), % 36.95/37.20 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) % 36.95/37.20 Clause #3510 (by superposition #[3509, 17]): ∀ (a a_1 a_2 : Iota), Or (Eq (unorthogonal_lines (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True) (Eq True False) % 36.95/37.20 Clause #3519 (by clausification #[3510]): ∀ (a a_1 a_2 : Iota), Eq (unorthogonal_lines (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True % 36.95/37.20 Clause #3520 (by superposition #[3519, 3325]): ∀ (a a_1 a_2 a_3 : Iota), % 36.95/37.20 Or (Eq True False) % 36.95/37.20 (Or (Eq (unorthogonal_lines a (skS.0 2 a_1 a_2 a_3)) True) (Eq (convergent_lines a (skS.0 1 a_1 a_2)) True)) % 36.95/37.20 Clause #3535 (by clausification #[3520]): ∀ (a a_1 a_2 a_3 : Iota), % 36.95/37.20 Or (Eq (unorthogonal_lines a (skS.0 2 a_1 a_2 a_3)) True) (Eq (convergent_lines a (skS.0 1 a_1 a_2)) True) % 36.95/37.20 Clause #3536 (by superposition #[3535, 49]): ∀ (a a_1 : Iota), Or (Eq (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq True False) % 36.95/37.20 Clause #3589 (by clausification #[3536]): ∀ (a a_1 : Iota), Eq (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)) True % 36.95/37.20 Clause #3590 (by superposition #[3589, 114]): Eq True False % 36.95/37.20 Clause #3599 (by clausification #[3590]): False % 36.95/37.20 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------