%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO217+2 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 07:48:15 PM UTC 2025 % Result : Theorem 4.94s 5.18s % Output : Proof 5.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO217+2 : TPTP v9.2.0. Released v3.3.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n003.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 11:43:38 EDT 2025 % 0.13/0.34 % CPUTime : % 4.94/5.18 SZS status Theorem for theBenchmark.p % 4.94/5.18 SZS output start Proof for theBenchmark.p % 4.94/5.18 Clause #2 (by assumption #[]): Eq (∀ (X : Iota), Not (convergent_lines X X)) True % 4.94/5.18 Clause #5 (by assumption #[]): Eq (∀ (X Y Z : Iota), convergent_lines X Y → Or (convergent_lines X Z) (convergent_lines Y Z)) True % 4.94/5.18 Clause #15 (by assumption #[]): Eq (Not (∀ (L M N : Iota), And (Not (convergent_lines L M)) (Not (convergent_lines L N)) → Not (convergent_lines M N))) % 4.94/5.18 True % 4.94/5.18 Clause #16 (by clausification #[2]): ∀ (a : Iota), Eq (Not (convergent_lines a a)) True % 4.94/5.18 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (convergent_lines a a) False % 4.94/5.18 Clause #38 (by clausification #[15]): Eq (∀ (L M N : Iota), And (Not (convergent_lines L M)) (Not (convergent_lines L N)) → Not (convergent_lines M N)) False % 4.94/5.18 Clause #39 (by clausification #[38]): ∀ (a : Iota), % 4.94/5.18 Eq % 4.94/5.18 (Not % 4.94/5.18 (∀ (M N : Iota), % 4.94/5.18 And (Not (convergent_lines (skS.0 0 a) M)) (Not (convergent_lines (skS.0 0 a) N)) → Not (convergent_lines M N))) % 4.94/5.18 True % 4.94/5.18 Clause #40 (by clausification #[39]): ∀ (a : Iota), % 4.94/5.18 Eq % 4.94/5.18 (∀ (M N : Iota), % 4.94/5.18 And (Not (convergent_lines (skS.0 0 a) M)) (Not (convergent_lines (skS.0 0 a) N)) → Not (convergent_lines M N)) % 4.94/5.18 False % 4.94/5.18 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), % 4.94/5.18 Eq % 4.94/5.18 (Not % 4.94/5.18 (∀ (N : Iota), % 4.94/5.18 And (Not (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) (Not (convergent_lines (skS.0 0 a) N)) → % 4.94/5.18 Not (convergent_lines (skS.0 1 a a_1) N))) % 4.94/5.18 True % 4.94/5.18 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), % 4.94/5.18 Eq % 4.94/5.18 (∀ (N : Iota), % 4.94/5.18 And (Not (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) (Not (convergent_lines (skS.0 0 a) N)) → % 4.94/5.18 Not (convergent_lines (skS.0 1 a a_1) N)) % 4.94/5.18 False % 4.94/5.18 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), % 4.94/5.18 Eq % 4.94/5.18 (Not % 4.94/5.18 (And (Not (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) % 4.94/5.18 (Not (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) → % 4.94/5.18 Not (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))) % 4.94/5.18 True % 4.94/5.18 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), % 4.94/5.18 Eq % 4.94/5.18 (And (Not (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) (Not (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2))) → % 4.94/5.18 Not (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 4.94/5.18 False % 4.94/5.18 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), % 4.94/5.18 Eq (And (Not (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) (Not (convergent_lines (skS.0 0 a) (skS.0 2 a a_1 a_2)))) % 4.94/5.18 True % 4.94/5.18 Clause #46 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Eq (Not (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) False % 4.94/5.18 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 % 4.94/5.18 Clause #48 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (Not (convergent_lines (skS.0 0 a) (skS.0 1 a a_1))) True % 4.94/5.18 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 % 4.94/5.18 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 % 4.94/5.18 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 % 4.94/5.18 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 % 4.94/5.18 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 : Iota), % 4.94/5.18 Or (Eq (convergent_lines a a_1) False) (Eq (Or (convergent_lines a a_2) (convergent_lines a_1 a_2)) True) % 4.94/5.18 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), % 4.94/5.18 Or (Eq (convergent_lines a a_1) False) (Or (Eq (convergent_lines a a_2) True) (Eq (convergent_lines a_1 a_2) True)) % 4.94/5.18 Clause #113 (by clausification #[48]): ∀ (a a_1 : Iota), Eq (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)) False % 4.94/5.18 Clause #118 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), Eq (convergent_lines (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True % 4.94/5.18 Clause #122 (by superposition #[118, 61]): ∀ (a a_1 a_2 a_3 : Iota), % 5.03/5.20 Or (Eq True False) % 5.03/5.20 (Or (Eq (convergent_lines (skS.0 1 a a_1) a_2) True) (Eq (convergent_lines (skS.0 2 a a_1 a_3) a_2) True)) % 5.03/5.20 Clause #140 (by clausification #[122]): ∀ (a a_1 a_2 a_3 : Iota), % 5.03/5.20 Or (Eq (convergent_lines (skS.0 1 a a_1) a_2) True) (Eq (convergent_lines (skS.0 2 a a_1 a_3) a_2) True) % 5.03/5.20 Clause #145 (by superposition #[140, 61]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.03/5.20 Or (Eq (convergent_lines (skS.0 1 a a_1) a_2) True) % 5.03/5.20 (Or (Eq True False) (Or (Eq (convergent_lines (skS.0 2 a a_1 a_3) a_4) True) (Eq (convergent_lines a_2 a_4) True))) % 5.03/5.20 Clause #206 (by clausification #[145]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.03/5.20 Or (Eq (convergent_lines (skS.0 1 a a_1) a_2) True) % 5.03/5.20 (Or (Eq (convergent_lines (skS.0 2 a a_1 a_3) a_4) True) (Eq (convergent_lines a_2 a_4) True)) % 5.03/5.20 Clause #216 (by superposition #[206, 17]): ∀ (a a_1 a_2 a_3 : Iota), % 5.03/5.20 Or (Eq (convergent_lines (skS.0 1 a a_1) a_2) True) % 5.03/5.20 (Or (Eq (convergent_lines a_2 (skS.0 2 a a_1 a_3)) True) (Eq True False)) % 5.03/5.20 Clause #237 (by clausification #[216]): ∀ (a a_1 a_2 a_3 : Iota), % 5.03/5.20 Or (Eq (convergent_lines (skS.0 1 a a_1) a_2) True) (Eq (convergent_lines a_2 (skS.0 2 a a_1 a_3)) True) % 5.03/5.20 Clause #238 (by superposition #[237, 49]): ∀ (a a_1 : Iota), Or (Eq (convergent_lines (skS.0 1 a a_1) (skS.0 0 a)) True) (Eq True False) % 5.03/5.20 Clause #247 (by clausification #[238]): ∀ (a a_1 : Iota), Eq (convergent_lines (skS.0 1 a a_1) (skS.0 0 a)) True % 5.03/5.20 Clause #251 (by superposition #[247, 61]): ∀ (a a_1 a_2 : Iota), % 5.03/5.20 Or (Eq True False) (Or (Eq (convergent_lines (skS.0 1 a a_1) a_2) True) (Eq (convergent_lines (skS.0 0 a) a_2) True)) % 5.03/5.20 Clause #265 (by clausification #[251]): ∀ (a a_1 a_2 : Iota), Or (Eq (convergent_lines (skS.0 1 a a_1) a_2) True) (Eq (convergent_lines (skS.0 0 a) a_2) True) % 5.03/5.20 Clause #266 (by superposition #[265, 17]): ∀ (a a_1 : Iota), Or (Eq (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq True False) % 5.03/5.20 Clause #275 (by clausification #[266]): ∀ (a a_1 : Iota), Eq (convergent_lines (skS.0 0 a) (skS.0 1 a a_1)) True % 5.03/5.20 Clause #276 (by superposition #[275, 113]): Eq True False % 5.03/5.20 Clause #285 (by clausification #[276]): False % 5.03/5.20 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------