%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN053+1 : TPTP v9.2.0. Released v2.0.0. % 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 08:07:03 PM UTC 2025 % Result : Theorem 3.37s 3.58s % Output : Proof 3.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.13 % Problem : SYN053+1 : TPTP v9.2.0. Released v2.0.0. % 0.06/0.14 % Command : duper %s % 0.14/0.35 % Computer : n024.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Thu Oct 2 15:23:53 EDT 2025 % 0.14/0.35 % CPUTime : % 3.37/3.58 SZS status Theorem for theBenchmark.p % 3.37/3.58 SZS output start Proof for theBenchmark.p % 3.37/3.58 Clause #0 (by assumption #[]): Eq (Not (Iff (∀ (X : Iota), Or p (big_f X)) (Or p (∀ (X1 : Iota), big_f X1)))) True % 3.37/3.58 Clause #1 (by clausification #[0]): Eq (Iff (∀ (X : Iota), Or p (big_f X)) (Or p (∀ (X1 : Iota), big_f X1))) False % 3.37/3.58 Clause #2 (by clausification #[1]): Or (Eq (∀ (X : Iota), Or p (big_f X)) False) (Eq (Or p (∀ (X1 : Iota), big_f X1)) False) % 3.37/3.58 Clause #3 (by clausification #[1]): Or (Eq (∀ (X : Iota), Or p (big_f X)) True) (Eq (Or p (∀ (X1 : Iota), big_f X1)) True) % 3.37/3.58 Clause #4 (by clausification #[2]): ∀ (a : Iota), Or (Eq (Or p (∀ (X1 : Iota), big_f X1)) False) (Eq (Not (Or p (big_f (skS.0 0 a)))) True) % 3.37/3.58 Clause #5 (by clausification #[4]): ∀ (a : Iota), Or (Eq (Not (Or p (big_f (skS.0 0 a)))) True) (Eq (∀ (X1 : Iota), big_f X1) False) % 3.37/3.58 Clause #6 (by clausification #[4]): ∀ (a : Iota), Or (Eq (Not (Or p (big_f (skS.0 0 a)))) True) (Eq p False) % 3.37/3.58 Clause #7 (by clausification #[5]): ∀ (a : Iota), Or (Eq (∀ (X1 : Iota), big_f X1) False) (Eq (Or p (big_f (skS.0 0 a))) False) % 3.37/3.58 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (Or p (big_f (skS.0 0 a))) False) (Eq (Not (big_f (skS.0 1 a_1))) True) % 3.37/3.58 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (Not (big_f (skS.0 1 a))) True) (Eq (big_f (skS.0 0 a_1)) False) % 3.37/3.58 Clause #11 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 0 a)) False) (Eq (big_f (skS.0 1 a_1)) False) % 3.37/3.58 Clause #13 (by clausification #[3]): ∀ (a : Iota), Or (Eq (Or p (∀ (X1 : Iota), big_f X1)) True) (Eq (Or p (big_f a)) True) % 3.37/3.58 Clause #14 (by clausification #[13]): ∀ (a : Iota), Or (Eq (Or p (big_f a)) True) (Or (Eq p True) (Eq (∀ (X1 : Iota), big_f X1) True)) % 3.37/3.58 Clause #15 (by clausification #[14]): ∀ (a : Iota), Or (Eq p True) (Or (Eq (∀ (X1 : Iota), big_f X1) True) (Or (Eq p True) (Eq (big_f a) True))) % 3.37/3.58 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq p True) (Or (Eq p True) (Or (Eq (big_f a) True) (Eq (big_f a_1) True))) % 3.37/3.58 Clause #17 (by eliminate duplicate literals #[16]): ∀ (a a_1 : Iota), Or (Eq p True) (Or (Eq (big_f a) True) (Eq (big_f a_1) True)) % 3.37/3.58 Clause #19 (by equality factoring #[17]): ∀ (a : Iota), Or (Eq p True) (Or (Ne True True) (Eq (big_f a) True)) % 3.37/3.58 Clause #20 (by clausification #[19]): ∀ (a : Iota), Or (Eq p True) (Or (Eq (big_f a) True) (Or (Eq True False) (Eq True False))) % 3.37/3.58 Clause #22 (by clausification #[20]): ∀ (a : Iota), Or (Eq p True) (Or (Eq (big_f a) True) (Eq True False)) % 3.37/3.58 Clause #23 (by clausification #[22]): ∀ (a : Iota), Or (Eq p True) (Eq (big_f a) True) % 3.37/3.58 Clause #25 (by clausification #[6]): ∀ (a : Iota), Or (Eq p False) (Eq (Or p (big_f (skS.0 0 a))) False) % 3.37/3.58 Clause #27 (by clausification #[25]): Or (Eq p False) (Eq p False) % 3.37/3.58 Clause #28 (by eliminate duplicate literals #[27]): Eq p False % 3.37/3.58 Clause #30 (by backward demodulation #[28, 23]): ∀ (a : Iota), Or (Eq False True) (Eq (big_f a) True) % 3.37/3.58 Clause #32 (by clausification #[30]): ∀ (a : Iota), Eq (big_f a) True % 3.37/3.58 Clause #33 (by superposition #[32, 11]): ∀ (a : Iota), Or (Eq True False) (Eq (big_f (skS.0 1 a)) False) % 3.37/3.58 Clause #34 (by clausification #[33]): ∀ (a : Iota), Eq (big_f (skS.0 1 a)) False % 3.37/3.58 Clause #35 (by superposition #[34, 32]): Eq False True % 3.37/3.58 Clause #36 (by clausification #[35]): False % 3.37/3.58 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------