%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO882^1 : TPTP v9.2.0. Released v7.5.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.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 08:09:37 PM UTC 2025 % Result : Unsatisfiable 3.88s 4.05s % Output : Proof 3.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SYO882^1 : TPTP v9.2.0. Released v7.5.0. % 0.10/0.13 % Command : duper %s % 0.14/0.34 % Computer : n018.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 13:14:38 EDT 2025 % 0.14/0.34 % CPUTime : % 3.88/4.05 SZS status Theorem for theBenchmark.p % 3.88/4.05 SZS output start Proof for theBenchmark.p % 3.88/4.05 Clause #0 (by assumption #[]): Eq (∀ (Y : Iota → Iota), Or (Ne (h (Y b)) (h (g False))) (Ne (h (Y a)) (h (g True)))) True % 3.88/4.05 Clause #1 (by assumption #[]): Eq (Ne a b) True % 3.88/4.05 Clause #2 (by clausification #[1]): Ne a b % 3.88/4.05 Clause #3 (by clausification #[0]): ∀ (a_1 : Iota → Iota), Eq (Or (Ne (h (a_1 b)) (h (g False))) (Ne (h (a_1 a)) (h (g True)))) True % 3.88/4.05 Clause #4 (by clausification #[3]): ∀ (a_1 : Iota → Iota), Or (Eq (Ne (h (a_1 b)) (h (g False))) True) (Eq (Ne (h (a_1 a)) (h (g True))) True) % 3.88/4.05 Clause #5 (by clausification #[4]): ∀ (a_1 : Iota → Iota), Or (Eq (Ne (h (a_1 a)) (h (g True))) True) (Ne (h (a_1 b)) (h (g False))) % 3.88/4.05 Clause #6 (by clausification #[5]): ∀ (a_1 : Iota → Iota), Or (Ne (h (a_1 b)) (h (g False))) (Ne (h (a_1 a)) (h (g True))) % 3.88/4.05 Clause #10 (by fluidBoolHoist #[6]): ∀ (a_1 : (x : Iota) → (_ : Prop) → (fun x _ => Iota) x _) (a_2 : Iota → Prop), % 3.88/4.05 Or (Ne (h ((fun x => a_1 x (a_2 x)) a)) (h (g True))) (Or (Ne (h (a_1 b False)) (h (g False))) (Eq (a_2 b) True)) % 3.88/4.05 Clause #11 (by betaEtaReduce #[10]): ∀ (a_1 : (x : Iota) → (_ : Prop) → (fun x _ => Iota) x _) (a_2 : Iota → Prop), % 3.88/4.05 Or (Ne (h (a_1 a (a_2 a))) (h (g True))) (Or (Ne (h (a_1 b False)) (h (g False))) (Eq (a_2 b) True)) % 3.88/4.05 Clause #12 (by identity loobHoist #[11]): ∀ (a_1 : (x : Iota) → (_ : Prop) → (fun x _ => Iota) x _) (a_2 : Iota → Prop), % 3.88/4.05 Or (Ne (h (a_1 b False)) (h (g False))) % 3.88/4.05 (Or (Eq (a_2 b) True) (Or (Ne (h (a_1 a True)) (h (g True))) (Eq (a_2 a) False))) % 3.88/4.05 Clause #15 (by equality resolution #[12]): ∀ (a_1 : Iota → Prop), Or (Eq (a_1 b) True) (Or (Ne (h ((fun x _ => g _) a True)) (h (g True))) (Eq (a_1 a) False)) % 3.88/4.05 Clause #17 (by betaEtaReduce #[15]): ∀ (a_1 : Iota → Prop), Or (Eq (a_1 b) True) (Or (Ne (h (g True)) (h (g True))) (Eq (a_1 a) False)) % 3.88/4.05 Clause #18 (by eliminate resolved literals #[17]): ∀ (a_1 : Iota → Prop), Or (Eq (a_1 b) True) (Eq (a_1 a) False) % 3.88/4.05 Clause #20 (by neHoist #[18]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x), % 3.88/4.05 Or (Eq ((fun x => Ne (a_2 x) (a_3 x)) b) True) (Or (Eq True False) (Eq (a_2 a) (a_3 a))) % 3.88/4.05 Clause #54 (by betaEtaReduce #[20]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x), % 3.88/4.05 Or (Eq (Ne (a_2 b) (a_3 b)) True) (Or (Eq True False) (Eq (a_2 a) (a_3 a))) % 3.88/4.05 Clause #55 (by clausification #[54]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x), % 3.88/4.05 Or (Eq True False) (Or (Eq (a_2 a) (a_3 a)) (Ne (a_2 b) (a_3 b))) % 3.88/4.05 Clause #56 (by clausification #[55]): ∀ (a_1 : Iota → Sort _abstMVar.0) (a_2 a_3 : (x : Iota) → a_1 x), Or (Eq (a_2 a) (a_3 a)) (Ne (a_2 b) (a_3 b)) % 3.88/4.05 Clause #57 (by equality resolution #[56]): Eq ((fun x => x) a) ((fun x => b) a) % 3.88/4.05 Clause #64 (by betaEtaReduce #[57]): Eq a b % 3.88/4.05 Clause #65 (by forward contextual literal cutting #[64, 2]): False % 3.88/4.05 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------