%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO029^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n025.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 08:08:26 PM UTC 2025 % Result : Theorem 3.64s 3.81s % Output : Proof 3.64s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYO029^1 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.14 % Command : duper %s % 0.15/0.35 % Computer : n025.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Fri Oct 3 13:00:23 EDT 2025 % 0.15/0.35 % CPUTime : % 3.64/3.81 SZS status Theorem for theBenchmark.p % 3.64/3.81 SZS output start Proof for theBenchmark.p % 3.64/3.81 Clause #0 (by assumption #[]): Eq (Not (Exists fun N => ∀ (P : Prop), Iff (N P) (Not P))) True % 3.64/3.81 Clause #1 (by clausification #[0]): Eq (Exists fun N => ∀ (P : Prop), Iff (N P) (Not P)) False % 3.64/3.81 Clause #2 (by clausification #[1]): ∀ (a : Prop → Prop), Eq (∀ (P : Prop), Iff (a P) (Not P)) False % 3.64/3.81 Clause #3 (by clausification #[2]): ∀ (a : Prop → Prop) (a_1 : Prop), Eq (Not (Iff (a (skS.0 0 a a_1)) (Not (skS.0 0 a a_1)))) True % 3.64/3.81 Clause #4 (by clausification #[3]): ∀ (a : Prop → Prop) (a_1 : Prop), Eq (Iff (a (skS.0 0 a a_1)) (Not (skS.0 0 a a_1))) False % 3.64/3.81 Clause #5 (by clausification #[4]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (a (skS.0 0 a a_1)) False) (Eq (Not (skS.0 0 a a_1)) False) % 3.64/3.81 Clause #6 (by clausification #[4]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (a (skS.0 0 a a_1)) True) (Eq (Not (skS.0 0 a a_1)) True) % 3.64/3.81 Clause #7 (by clausification #[5]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (a (skS.0 0 a a_1)) False) (Eq (skS.0 0 a a_1) True) % 3.64/3.81 Clause #9 (by identity boolHoist #[7]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (skS.0 0 a a_1) True) (Or (Eq (a False) False) (Eq (skS.0 0 a a_1) True)) % 3.64/3.81 Clause #10 (by clausification #[6]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (a (skS.0 0 a a_1)) True) (Eq (skS.0 0 a a_1) False) % 3.64/3.81 Clause #11 (by identity loobHoist #[10]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (skS.0 0 a a_1) False) (Or (Eq (a True) True) (Eq (skS.0 0 a a_1) False)) % 3.64/3.81 Clause #13 (by eliminate duplicate literals #[11]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (skS.0 0 a a_1) False) (Eq (a True) True) % 3.64/3.81 Clause #14 (by identity loobHoist #[13]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (a True) True) (Or (Eq (skS.0 0 a True) False) (Eq a_1 False)) % 3.64/3.81 Clause #16 (by eliminate duplicate literals #[9]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (skS.0 0 a a_1) True) (Eq (a False) False) % 3.64/3.81 Clause #17 (by identity loobHoist #[16]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (a False) False) (Or (Eq (skS.0 0 a True) True) (Eq a_1 False)) % 3.64/3.81 Clause #23 (by fluidLoobHoist #[17]): ∀ (a : Prop → Prop) (a_1 : Prop), % 3.64/3.81 Or (Eq (skS.0 0 a True) True) (Or (Eq a_1 False) (Or (Eq True False) (Eq (a False) False))) % 3.64/3.81 Clause #32 (by clausification #[23]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (skS.0 0 a True) True) (Or (Eq a_1 False) (Eq (a False) False)) % 3.64/3.81 Clause #33 (by falseElim #[32]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 a True) True) (Eq (a False) False) % 3.64/3.81 Clause #36 (by neHoist #[33]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.64/3.81 Or (Eq (skS.0 0 (fun x => Ne (a_1 x) (a_2 x)) True) True) (Or (Eq True False) (Eq (a_1 False) (a_2 False))) % 3.64/3.81 Clause #42 (by clausification #[36]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.64/3.81 Or (Eq (skS.0 0 (fun x => Ne (a_1 x) (a_2 x)) True) True) (Eq (a_1 False) (a_2 False)) % 3.64/3.81 Clause #43 (by superposition #[42, 14]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x) (a_3 : Prop), % 3.64/3.81 Or (Eq (a_1 False) (a_2 False)) (Or (Eq (Ne (a_1 True) (a_2 True)) True) (Or (Eq True False) (Eq a_3 False))) % 3.64/3.81 Clause #78 (by clausification #[43]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x) (a_3 : Prop), % 3.64/3.81 Or (Eq (a_1 False) (a_2 False)) (Or (Eq True False) (Or (Eq a_3 False) (Ne (a_1 True) (a_2 True)))) % 3.64/3.81 Clause #79 (by clausification #[78]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x) (a_3 : Prop), % 3.64/3.81 Or (Eq (a_1 False) (a_2 False)) (Or (Eq a_3 False) (Ne (a_1 True) (a_2 True))) % 3.64/3.81 Clause #81 (by falseElim #[79]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), Or (Eq (a_1 False) (a_2 False)) (Ne (a_1 True) (a_2 True)) % 3.64/3.81 Clause #86 (by equality resolution #[81]): Eq ((fun x => x) False) ((fun x => True) False) % 3.64/3.81 Clause #91 (by betaEtaReduce #[86]): Eq False True % 3.64/3.81 Clause #92 (by clausification #[91]): False % 3.64/3.81 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------