%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GEO247+3 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 07:48:21 PM UTC 2025 % Result : Theorem 3.63s 3.80s % Output : Proof 3.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : GEO247+3 : TPTP v9.2.0. Released v4.0.0. % 0.04/0.13 % Command : duper %s % 0.13/0.34 % Computer : n005.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 11:58:23 EDT 2025 % 0.13/0.34 % CPUTime : % 3.63/3.80 SZS status Theorem for theBenchmark.p % 3.63/3.80 SZS output start Proof for theBenchmark.p % 3.63/3.80 Clause #19 (by assumption #[]): Eq (∀ (A L : Iota), Not (Or (left_apart_point A L) (left_apart_point A (reverse_line L)))) True % 3.63/3.80 Clause #36 (by assumption #[]): Eq % 3.63/3.80 (Not % 3.63/3.80 (∀ (A B C D L M : Iota), % 3.63/3.80 And % 3.63/3.80 (And % 3.63/3.80 (And % 3.63/3.80 (And % 3.63/3.80 (And (And (And (left_apart_point A L) (left_apart_point A M)) (right_apart_point B L)) % 3.63/3.80 (right_apart_point B M)) % 3.63/3.80 (left_apart_point C L)) % 3.63/3.80 (right_apart_point C M)) % 3.63/3.80 (right_apart_point D L)) % 3.63/3.80 (left_apart_point D M) → % 3.63/3.80 convergent_lines L M)) % 3.63/3.80 True % 3.63/3.80 Clause #163 (by clausification #[19]): ∀ (a : Iota), Eq (∀ (L : Iota), Not (Or (left_apart_point a L) (left_apart_point a (reverse_line L)))) True % 3.63/3.80 Clause #164 (by clausification #[163]): ∀ (a a_1 : Iota), Eq (Not (Or (left_apart_point a a_1) (left_apart_point a (reverse_line a_1)))) True % 3.63/3.80 Clause #165 (by clausification #[164]): ∀ (a a_1 : Iota), Eq (Or (left_apart_point a a_1) (left_apart_point a (reverse_line a_1))) False % 3.63/3.80 Clause #167 (by clausification #[165]): ∀ (a a_1 : Iota), Eq (left_apart_point a a_1) False % 3.63/3.80 Clause #258 (by clausification #[36]): Eq % 3.63/3.80 (∀ (A B C D L M : Iota), % 3.63/3.80 And % 3.63/3.80 (And % 3.63/3.80 (And % 3.63/3.80 (And % 3.63/3.80 (And (And (And (left_apart_point A L) (left_apart_point A M)) (right_apart_point B L)) % 3.63/3.80 (right_apart_point B M)) % 3.63/3.80 (left_apart_point C L)) % 3.63/3.80 (right_apart_point C M)) % 3.63/3.80 (right_apart_point D L)) % 3.63/3.80 (left_apart_point D M) → % 3.63/3.80 convergent_lines L M) % 3.63/3.80 False % 3.63/3.80 Clause #259 (by clausification #[258]): ∀ (a : Iota), % 3.63/3.80 Eq % 3.63/3.80 (Not % 3.63/3.80 (∀ (B C D L M : Iota), % 3.63/3.80 And % 3.63/3.80 (And % 3.63/3.80 (And % 3.63/3.80 (And % 3.63/3.80 (And % 3.63/3.80 (And (And (left_apart_point (skS.0 0 a) L) (left_apart_point (skS.0 0 a) M)) % 3.63/3.80 (right_apart_point B L)) % 3.63/3.80 (right_apart_point B M)) % 3.63/3.80 (left_apart_point C L)) % 3.63/3.80 (right_apart_point C M)) % 3.63/3.80 (right_apart_point D L)) % 3.63/3.80 (left_apart_point D M) → % 3.63/3.80 convergent_lines L M)) % 3.63/3.80 True % 3.63/3.80 Clause #260 (by clausification #[259]): ∀ (a : Iota), % 3.63/3.80 Eq % 3.63/3.80 (∀ (B C D L M : Iota), % 3.63/3.80 And % 3.63/3.80 (And % 3.63/3.80 (And % 3.63/3.80 (And % 3.63/3.80 (And % 3.63/3.80 (And (And (left_apart_point (skS.0 0 a) L) (left_apart_point (skS.0 0 a) M)) (right_apart_point B L)) % 3.63/3.80 (right_apart_point B M)) % 3.63/3.80 (left_apart_point C L)) % 3.63/3.80 (right_apart_point C M)) % 3.63/3.80 (right_apart_point D L)) % 3.63/3.80 (left_apart_point D M) → % 3.63/3.80 convergent_lines L M) % 3.63/3.80 False % 3.63/3.80 Clause #261 (by clausification #[260]): ∀ (a a_1 : Iota), % 3.63/3.80 Eq % 3.63/3.80 (Not % 3.63/3.80 (∀ (C D L M : Iota), % 3.63/3.80 And % 3.63/3.80 (And % 3.63/3.80 (And % 3.63/3.80 (And % 3.63/3.80 (And % 3.63/3.80 (And (And (left_apart_point (skS.0 0 a) L) (left_apart_point (skS.0 0 a) M)) % 3.63/3.80 (right_apart_point (skS.0 1 a a_1) L)) % 3.63/3.80 (right_apart_point (skS.0 1 a a_1) M)) % 3.63/3.80 (left_apart_point C L)) % 3.63/3.80 (right_apart_point C M)) % 3.63/3.80 (right_apart_point D L)) % 3.63/3.80 (left_apart_point D M) → % 3.63/3.80 convergent_lines L M)) % 3.63/3.80 True % 3.63/3.80 Clause #262 (by clausification #[261]): ∀ (a a_1 : Iota), % 3.63/3.80 Eq % 3.63/3.80 (∀ (C D L M : Iota), % 3.63/3.80 And % 3.63/3.80 (And % 3.63/3.80 (And % 3.63/3.80 (And % 3.63/3.80 (And % 3.63/3.80 (And (And (left_apart_point (skS.0 0 a) L) (left_apart_point (skS.0 0 a) M)) % 3.63/3.80 (right_apart_point (skS.0 1 a a_1) L)) % 3.63/3.80 (right_apart_point (skS.0 1 a a_1) M)) % 3.63/3.80 (left_apart_point C L)) % 3.63/3.80 (right_apart_point C M)) % 3.63/3.80 (right_apart_point D L)) % 3.63/3.80 (left_apart_point D M) → % 3.63/3.80 convergent_lines L M) % 3.63/3.80 False % 3.63/3.80 Clause #263 (by clausification #[262]): ∀ (a a_1 a_2 : Iota), % 3.63/3.80 Eq % 3.63/3.80 (Not % 3.63/3.80 (∀ (D L M : Iota), % 3.63/3.80 And % 3.63/3.80 (And % 3.63/3.82 (And % 3.63/3.82 (And % 3.63/3.82 (And % 3.63/3.82 (And (And (left_apart_point (skS.0 0 a) L) (left_apart_point (skS.0 0 a) M)) % 3.63/3.82 (right_apart_point (skS.0 1 a a_1) L)) % 3.63/3.82 (right_apart_point (skS.0 1 a a_1) M)) % 3.63/3.82 (left_apart_point (skS.0 2 a a_1 a_2) L)) % 3.63/3.82 (right_apart_point (skS.0 2 a a_1 a_2) M)) % 3.63/3.82 (right_apart_point D L)) % 3.63/3.82 (left_apart_point D M) → % 3.63/3.82 convergent_lines L M)) % 3.63/3.82 True % 3.63/3.82 Clause #264 (by clausification #[263]): ∀ (a a_1 a_2 : Iota), % 3.63/3.82 Eq % 3.63/3.82 (∀ (D L M : Iota), % 3.63/3.82 And % 3.63/3.82 (And % 3.63/3.82 (And % 3.63/3.82 (And % 3.63/3.82 (And % 3.63/3.82 (And (And (left_apart_point (skS.0 0 a) L) (left_apart_point (skS.0 0 a) M)) % 3.63/3.82 (right_apart_point (skS.0 1 a a_1) L)) % 3.63/3.82 (right_apart_point (skS.0 1 a a_1) M)) % 3.63/3.82 (left_apart_point (skS.0 2 a a_1 a_2) L)) % 3.63/3.82 (right_apart_point (skS.0 2 a a_1 a_2) M)) % 3.63/3.82 (right_apart_point D L)) % 3.63/3.82 (left_apart_point D M) → % 3.63/3.82 convergent_lines L M) % 3.63/3.82 False % 3.63/3.82 Clause #265 (by clausification #[264]): ∀ (a a_1 a_2 a_3 : Iota), % 3.63/3.82 Eq % 3.63/3.82 (Not % 3.63/3.82 (∀ (L M : Iota), % 3.63/3.82 And % 3.63/3.82 (And % 3.63/3.82 (And % 3.63/3.82 (And % 3.63/3.82 (And % 3.63/3.82 (And (And (left_apart_point (skS.0 0 a) L) (left_apart_point (skS.0 0 a) M)) % 3.63/3.82 (right_apart_point (skS.0 1 a a_1) L)) % 3.63/3.82 (right_apart_point (skS.0 1 a a_1) M)) % 3.63/3.82 (left_apart_point (skS.0 2 a a_1 a_2) L)) % 3.63/3.82 (right_apart_point (skS.0 2 a a_1 a_2) M)) % 3.63/3.82 (right_apart_point (skS.0 3 a a_1 a_2 a_3) L)) % 3.63/3.82 (left_apart_point (skS.0 3 a a_1 a_2 a_3) M) → % 3.63/3.82 convergent_lines L M)) % 3.63/3.82 True % 3.63/3.82 Clause #266 (by clausification #[265]): ∀ (a a_1 a_2 a_3 : Iota), % 3.63/3.82 Eq % 3.63/3.82 (∀ (L M : Iota), % 3.63/3.82 And % 3.63/3.82 (And % 3.63/3.82 (And % 3.63/3.82 (And % 3.63/3.82 (And % 3.63/3.82 (And (And (left_apart_point (skS.0 0 a) L) (left_apart_point (skS.0 0 a) M)) % 3.63/3.82 (right_apart_point (skS.0 1 a a_1) L)) % 3.63/3.82 (right_apart_point (skS.0 1 a a_1) M)) % 3.63/3.82 (left_apart_point (skS.0 2 a a_1 a_2) L)) % 3.63/3.82 (right_apart_point (skS.0 2 a a_1 a_2) M)) % 3.63/3.82 (right_apart_point (skS.0 3 a a_1 a_2 a_3) L)) % 3.63/3.82 (left_apart_point (skS.0 3 a a_1 a_2 a_3) M) → % 3.63/3.82 convergent_lines L M) % 3.63/3.82 False % 3.63/3.82 Clause #267 (by clausification #[266]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.63/3.82 Eq % 3.63/3.82 (Not % 3.63/3.82 (∀ (M : Iota), % 3.63/3.82 And % 3.63/3.82 (And % 3.63/3.82 (And % 3.63/3.82 (And % 3.63/3.82 (And % 3.63/3.82 (And % 3.63/3.82 (And (left_apart_point (skS.0 0 a) (skS.0 4 a a_1 a_2 a_3 a_4)) (left_apart_point (skS.0 0 a) M)) % 3.63/3.82 (right_apart_point (skS.0 1 a a_1) (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.63/3.82 (right_apart_point (skS.0 1 a a_1) M)) % 3.63/3.82 (left_apart_point (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.63/3.82 (right_apart_point (skS.0 2 a a_1 a_2) M)) % 3.63/3.82 (right_apart_point (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.63/3.82 (left_apart_point (skS.0 3 a a_1 a_2 a_3) M) → % 3.63/3.82 convergent_lines (skS.0 4 a a_1 a_2 a_3 a_4) M)) % 3.63/3.82 True % 3.63/3.82 Clause #268 (by clausification #[267]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.63/3.82 Eq % 3.63/3.82 (∀ (M : Iota), % 3.63/3.82 And % 3.63/3.82 (And % 3.63/3.82 (And % 3.63/3.82 (And % 3.63/3.82 (And % 3.63/3.82 (And (And (left_apart_point (skS.0 0 a) (skS.0 4 a a_1 a_2 a_3 a_4)) (left_apart_point (skS.0 0 a) M)) % 3.63/3.82 (right_apart_point (skS.0 1 a a_1) (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.63/3.82 (right_apart_point (skS.0 1 a a_1) M)) % 3.63/3.82 (left_apart_point (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.63/3.82 (right_apart_point (skS.0 2 a a_1 a_2) M)) % 3.63/3.82 (right_apart_point (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.63/3.82 (left_apart_point (skS.0 3 a a_1 a_2 a_3) M) → % 3.63/3.82 convergent_lines (skS.0 4 a a_1 a_2 a_3 a_4) M) % 3.63/3.83 False % 3.63/3.83 Clause #269 (by clausification #[268]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.63/3.83 Eq % 3.63/3.83 (Not % 3.63/3.83 (And % 3.63/3.83 (And % 3.63/3.83 (And % 3.63/3.83 (And % 3.63/3.83 (And % 3.63/3.83 (And % 3.63/3.83 (And (left_apart_point (skS.0 0 a) (skS.0 4 a a_1 a_2 a_3 a_4)) % 3.63/3.83 (left_apart_point (skS.0 0 a) (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.63/3.83 (right_apart_point (skS.0 1 a a_1) (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.63/3.83 (right_apart_point (skS.0 1 a a_1) (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.63/3.83 (left_apart_point (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.63/3.83 (right_apart_point (skS.0 2 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.63/3.83 (right_apart_point (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.63/3.83 (left_apart_point (skS.0 3 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) → % 3.63/3.83 convergent_lines (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.63/3.83 True % 3.63/3.83 Clause #270 (by clausification #[269]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.63/3.83 Eq % 3.63/3.83 (And % 3.63/3.83 (And % 3.63/3.83 (And % 3.63/3.83 (And % 3.63/3.83 (And % 3.63/3.83 (And % 3.63/3.83 (And (left_apart_point (skS.0 0 a) (skS.0 4 a a_1 a_2 a_3 a_4)) % 3.63/3.83 (left_apart_point (skS.0 0 a) (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.63/3.83 (right_apart_point (skS.0 1 a a_1) (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.63/3.83 (right_apart_point (skS.0 1 a a_1) (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.63/3.83 (left_apart_point (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.63/3.83 (right_apart_point (skS.0 2 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.63/3.83 (right_apart_point (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.63/3.83 (left_apart_point (skS.0 3 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) → % 3.63/3.83 convergent_lines (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) % 3.63/3.83 False % 3.63/3.83 Clause #271 (by clausification #[270]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 3.63/3.83 Eq % 3.63/3.83 (And % 3.63/3.83 (And % 3.63/3.83 (And % 3.63/3.83 (And % 3.63/3.83 (And % 3.63/3.83 (And % 3.63/3.83 (And (left_apart_point (skS.0 0 a) (skS.0 4 a a_1 a_2 a_3 a_4)) % 3.63/3.83 (left_apart_point (skS.0 0 a) (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.63/3.83 (right_apart_point (skS.0 1 a a_1) (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.63/3.83 (right_apart_point (skS.0 1 a a_1) (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.63/3.83 (left_apart_point (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.63/3.83 (right_apart_point (skS.0 2 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.63/3.83 (right_apart_point (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.63/3.83 (left_apart_point (skS.0 3 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2 a_3 a_4 a_5))) % 3.63/3.83 True % 3.63/3.83 Clause #273 (by clausification #[271]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Eq (left_apart_point (skS.0 3 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2 a_3 a_4 a_5)) True % 3.63/3.83 Clause #275 (by superposition #[273, 167]): Eq True False % 3.63/3.83 Clause #276 (by clausification #[275]): False % 3.63/3.83 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------