%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO183^5 : TPTP v9.2.0. Released v4.0.0. % 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 : Fri Oct 3 08:08:42 PM UTC 2025 % Result : Theorem 3.65s 3.84s % Output : Proof 3.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYO183^5 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n022.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 13:34:08 EDT 2025 % 0.13/0.34 % CPUTime : % 3.65/3.84 SZS status Theorem for theBenchmark.p % 3.65/3.84 SZS output start Proof for theBenchmark.p % 3.65/3.84 Clause #0 (by assumption #[]): Eq (Not (Exists fun Xp => Xp a)) True % 3.65/3.84 Clause #1 (by clausification #[0]): Eq (Exists fun Xp => Xp a) False % 3.65/3.84 Clause #2 (by clausification #[1]): ∀ (a_1 : Prop → Prop), Eq (a_1 a) False % 3.65/3.84 Clause #3 (by identity loobHoist #[2]): ∀ (a_1 : Prop → Prop), Or (Eq (a_1 True) False) (Eq a False) % 3.65/3.84 Clause #4 (by identity boolHoist #[2]): ∀ (a_1 : Prop → Prop), Or (Eq (a_1 False) False) (Eq a True) % 3.65/3.84 Clause #9 (by fluidLoobHoist #[3]): ∀ (a_1 : Prop → Prop), Or (Eq a False) (Or (Eq True False) (Eq (a_1 True) False)) % 3.65/3.84 Clause #12 (by neHoist #[4]): ∀ (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (x : Prop) → a_1 x), % 3.65/3.84 Or (Eq a True) (Or (Eq True False) (Eq (a_2 False) (a_3 False))) % 3.65/3.84 Clause #17 (by clausification #[9]): ∀ (a_1 : Prop → Prop), Or (Eq a False) (Eq (a_1 True) False) % 3.65/3.84 Clause #21 (by clausification #[12]): ∀ (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (x : Prop) → a_1 x), Or (Eq a True) (Eq (a_2 False) (a_3 False)) % 3.65/3.84 Clause #28 (by equality factoring #[21]): ∀ (a_1 : (x : Prop) → (fun x => Prop) x), Or (Ne (a_1 False) a) (Eq a True) % 3.65/3.84 Clause #39 (by betaEtaReduce #[28]): ∀ (a_1 : (x : Prop) → (fun x => Prop) x), Or (Ne (a_1 False) a) (Eq a True) % 3.65/3.84 Clause #41 (by clausification #[39]): ∀ (a_1 : (x : Prop) → (fun x => Prop) x), Or (Eq a True) (Or (Eq (a_1 False) True) (Eq a True)) % 3.65/3.84 Clause #51 (by eliminate duplicate literals #[41]): ∀ (a_1 : (x : Prop) → (fun x => Prop) x), Or (Eq a True) (Eq (a_1 False) True) % 3.65/3.84 Clause #54 (by equality factoring #[51]): Or (Ne True True) (Eq a True) % 3.65/3.84 Clause #72 (by clausification #[54]): Or (Eq a True) (Or (Eq True False) (Eq True False)) % 3.65/3.84 Clause #74 (by clausification #[72]): Or (Eq a True) (Eq True False) % 3.65/3.84 Clause #75 (by clausification #[74]): Eq a True % 3.65/3.84 Clause #76 (by superposition #[75, 17]): ∀ (a : Prop → Prop), Or (Eq True False) (Eq (a True) False) % 3.65/3.84 Clause #78 (by clausification #[76]): ∀ (a : Prop → Prop), Eq (a True) False % 3.65/3.84 Clause #79 (by superposition #[78, 75]): Eq False True % 3.65/3.84 Clause #84 (by clausification #[79]): False % 3.65/3.84 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------