%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO034^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n024.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 08:08:27 PM UTC 2025 % Result : Theorem 4.83s 5.00s % Output : Proof 4.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYO034^1 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n024.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 13:27:08 EDT 2025 % 0.13/0.34 % CPUTime : % 4.83/5.00 SZS status Theorem for theBenchmark.p % 4.83/5.00 SZS output start Proof for theBenchmark.p % 4.83/5.00 Clause #0 (by assumption #[]): Eq (Not (Exists fun N => ∀ (P : Prop), Iff (N P) P)) True % 4.83/5.00 Clause #1 (by clausification #[0]): Eq (Exists fun N => ∀ (P : Prop), Iff (N P) P) False % 4.83/5.00 Clause #2 (by clausification #[1]): ∀ (a : Prop → Prop), Eq (∀ (P : Prop), Iff (a P) P) False % 4.83/5.00 Clause #3 (by clausification #[2]): ∀ (a : Prop → Prop) (a_1 : Prop), Eq (Not (Iff (a (skS.0 0 a a_1)) (skS.0 0 a a_1))) True % 4.83/5.00 Clause #4 (by clausification #[3]): ∀ (a : Prop → Prop) (a_1 : Prop), Eq (Iff (a (skS.0 0 a a_1)) (skS.0 0 a a_1)) False % 4.83/5.00 Clause #5 (by clausification #[4]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (a (skS.0 0 a a_1)) False) (Eq (skS.0 0 a a_1) False) % 4.83/5.00 Clause #6 (by clausification #[4]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (a (skS.0 0 a a_1)) True) (Eq (skS.0 0 a a_1) True) % 4.83/5.00 Clause #7 (by identity loobHoist #[5]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (skS.0 0 a a_1) False) (Or (Eq (a True) False) (Eq (skS.0 0 a a_1) False)) % 4.83/5.00 Clause #9 (by eliminate duplicate literals #[7]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (skS.0 0 a a_1) False) (Eq (a True) False) % 4.83/5.00 Clause #10 (by identity loobHoist #[9]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (a True) False) (Or (Eq (skS.0 0 a True) False) (Eq a_1 False)) % 4.83/5.00 Clause #13 (by neHoist #[10]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x) (a_3 : Prop), % 4.83/5.00 Or (Eq (skS.0 0 (fun x => Ne (a_1 x) (a_2 x)) True) False) % 4.83/5.00 (Or (Eq a_3 False) (Or (Eq True False) (Eq (a_1 True) (a_2 True)))) % 4.83/5.00 Clause #28 (by identity boolHoist #[6]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (skS.0 0 a a_1) True) (Or (Eq (a False) True) (Eq (skS.0 0 a a_1) True)) % 4.83/5.00 Clause #54 (by eliminate duplicate literals #[28]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (skS.0 0 a a_1) True) (Eq (a False) True) % 4.83/5.00 Clause #55 (by identity loobHoist #[54]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (a False) True) (Or (Eq (skS.0 0 a True) True) (Eq a_1 False)) % 4.83/5.00 Clause #57 (by falseElim #[55]): ∀ (a : Prop → Prop), Or (Eq (a False) True) (Eq (skS.0 0 a True) True) % 4.83/5.00 Clause #80 (by clausification #[13]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x) (a_3 : Prop), % 4.83/5.00 Or (Eq (skS.0 0 (fun x => Ne (a_1 x) (a_2 x)) True) False) (Or (Eq a_3 False) (Eq (a_1 True) (a_2 True))) % 4.83/5.00 Clause #81 (by superposition #[80, 57]): ∀ (a : Prop) (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (x : Prop) → a_1 x), % 4.83/5.00 Or (Eq a False) (Or (Eq (a_2 True) (a_3 True)) (Or (Eq (Ne (a_2 False) (a_3 False)) True) (Eq False True))) % 4.83/5.00 Clause #314 (by clausification #[81]): ∀ (a : Prop) (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (x : Prop) → a_1 x), % 4.83/5.00 Or (Eq a False) (Or (Eq (a_2 True) (a_3 True)) (Or (Eq False True) (Ne (a_2 False) (a_3 False)))) % 4.83/5.00 Clause #315 (by clausification #[314]): ∀ (a : Prop) (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (x : Prop) → a_1 x), % 4.83/5.00 Or (Eq a False) (Or (Eq (a_2 True) (a_3 True)) (Ne (a_2 False) (a_3 False))) % 4.83/5.00 Clause #317 (by falseElim #[315]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), Or (Eq (a_1 True) (a_2 True)) (Ne (a_1 False) (a_2 False)) % 4.83/5.00 Clause #332 (by equality resolution #[317]): Eq ((fun x => x) True) ((fun x => False) True) % 4.83/5.00 Clause #339 (by betaEtaReduce #[332]): Eq True False % 4.83/5.00 Clause #340 (by clausification #[339]): False % 4.83/5.00 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------