%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN398+1 : TPTP v9.2.0. Released v2.0.0. % 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 08:07:35 PM UTC 2025 % Result : Theorem 5.62s 5.85s % Output : Proof 5.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.10 % Problem : SYN398+1 : TPTP v9.2.0. Released v2.0.0. % 0.02/0.11 % Command : duper %s % 0.10/0.31 % Computer : n022.cluster.edu % 0.10/0.31 % Model : x86_64 x86_64 % 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.31 % Memory : 8042.1875MB % 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.31 % CPULimit : 300 % 0.10/0.31 % WCLimit : 300 % 0.10/0.31 % DateTime : Thu Oct 2 15:40:23 EDT 2025 % 0.10/0.31 % CPUTime : % 5.62/5.85 SZS status Theorem for theBenchmark.p % 5.62/5.85 SZS output start Proof for theBenchmark.p % 5.62/5.85 Clause #0 (by assumption #[]): Eq (Not (Iff (∀ (X : Iota), And p (f X)) (And p (∀ (Y : Iota), f Y)))) True % 5.62/5.85 Clause #1 (by clausification #[0]): Eq (Iff (∀ (X : Iota), And p (f X)) (And p (∀ (Y : Iota), f Y))) False % 5.62/5.85 Clause #2 (by clausification #[1]): Or (Eq (∀ (X : Iota), And p (f X)) False) (Eq (And p (∀ (Y : Iota), f Y)) False) % 5.62/5.85 Clause #3 (by clausification #[1]): Or (Eq (∀ (X : Iota), And p (f X)) True) (Eq (And p (∀ (Y : Iota), f Y)) True) % 5.62/5.85 Clause #4 (by clausification #[2]): ∀ (a : Iota), Or (Eq (And p (∀ (Y : Iota), f Y)) False) (Eq (Not (And p (f (skS.0 0 a)))) True) % 5.62/5.85 Clause #5 (by clausification #[4]): ∀ (a : Iota), Or (Eq (Not (And p (f (skS.0 0 a)))) True) (Or (Eq p False) (Eq (∀ (Y : Iota), f Y) False)) % 5.62/5.85 Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq p False) (Or (Eq (∀ (Y : Iota), f Y) False) (Eq (And p (f (skS.0 0 a))) False)) % 5.62/5.85 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Or (Eq p False) (Or (Eq (And p (f (skS.0 0 a))) False) (Eq (Not (f (skS.0 1 a_1))) True)) % 5.62/5.85 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq p False) (Or (Eq (Not (f (skS.0 1 a))) True) (Or (Eq p False) (Eq (f (skS.0 0 a_1)) False))) % 5.62/5.85 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq p False) (Or (Eq p False) (Or (Eq (f (skS.0 0 a)) False) (Eq (f (skS.0 1 a_1)) False))) % 5.62/5.85 Clause #10 (by eliminate duplicate literals #[9]): ∀ (a a_1 : Iota), Or (Eq p False) (Or (Eq (f (skS.0 0 a)) False) (Eq (f (skS.0 1 a_1)) False)) % 5.62/5.85 Clause #11 (by clausification #[3]): ∀ (a : Iota), Or (Eq (And p (∀ (Y : Iota), f Y)) True) (Eq (And p (f a)) True) % 5.62/5.85 Clause #12 (by clausification #[11]): ∀ (a : Iota), Or (Eq (And p (f a)) True) (Eq (∀ (Y : Iota), f Y) True) % 5.62/5.85 Clause #13 (by clausification #[11]): ∀ (a : Iota), Or (Eq (And p (f a)) True) (Eq p True) % 5.62/5.85 Clause #14 (by clausification #[12]): ∀ (a : Iota), Or (Eq (∀ (Y : Iota), f Y) True) (Eq (f a) True) % 5.62/5.85 Clause #16 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (f a) True) (Eq (f a_1) True) % 5.62/5.85 Clause #17 (by equality factoring #[16]): ∀ (a : Iota), Or (Ne True True) (Eq (f a) True) % 5.62/5.85 Clause #18 (by clausification #[17]): ∀ (a : Iota), Or (Eq (f a) True) (Or (Eq True False) (Eq True False)) % 5.62/5.85 Clause #20 (by clausification #[18]): ∀ (a : Iota), Or (Eq (f a) True) (Eq True False) % 5.62/5.85 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (f a) True % 5.62/5.85 Clause #23 (by clausification #[13]): Or (Eq p True) (Eq p True) % 5.62/5.85 Clause #24 (by eliminate duplicate literals #[23]): Eq p True % 5.62/5.85 Clause #25 (by backward demodulation #[24, 10]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (f (skS.0 0 a)) False) (Eq (f (skS.0 1 a_1)) False)) % 5.62/5.85 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 0 a)) False) (Eq (f (skS.0 1 a_1)) False) % 5.62/5.85 Clause #27 (by superposition #[26, 21]): ∀ (a : Iota), Or (Eq (f (skS.0 1 a)) False) (Eq False True) % 5.62/5.85 Clause #28 (by clausification #[27]): ∀ (a : Iota), Eq (f (skS.0 1 a)) False % 5.62/5.85 Clause #29 (by superposition #[28, 21]): Eq False True % 5.62/5.85 Clause #30 (by clausification #[29]): False % 5.62/5.85 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------