%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN399+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 08:07:36 PM UTC 2025 % Result : Theorem 4.70s 4.91s % Output : Proof 4.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SYN399+1 : TPTP v9.2.0. Released v2.0.0. % 0.12/0.13 % Command : duper %s % 0.13/0.34 % Computer : n031.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 : Thu Oct 2 15:40:38 EDT 2025 % 0.13/0.34 % CPUTime : % 4.70/4.91 SZS status Theorem for theBenchmark.p % 4.70/4.91 SZS output start Proof for theBenchmark.p % 4.70/4.91 Clause #0 (by assumption #[]): Eq (Not ((∀ (X : Iota), Iff (f X) p) → Iff (∀ (Y : Iota), f Y) p)) True % 4.70/4.91 Clause #1 (by clausification #[0]): Eq ((∀ (X : Iota), Iff (f X) p) → Iff (∀ (Y : Iota), f Y) p) False % 4.70/4.91 Clause #2 (by clausification #[1]): Eq (∀ (X : Iota), Iff (f X) p) True % 4.70/4.91 Clause #3 (by clausification #[1]): Eq (Iff (∀ (Y : Iota), f Y) p) False % 4.70/4.91 Clause #4 (by clausification #[2]): ∀ (a : Iota), Eq (Iff (f a) p) True % 4.70/4.91 Clause #5 (by clausification #[4]): ∀ (a : Iota), Or (Eq (f a) True) (Eq p False) % 4.70/4.91 Clause #6 (by clausification #[4]): ∀ (a : Iota), Or (Eq (f a) False) (Eq p True) % 4.70/4.91 Clause #7 (by clausification #[3]): Or (Eq (∀ (Y : Iota), f Y) False) (Eq p False) % 4.70/4.91 Clause #8 (by clausification #[3]): Or (Eq (∀ (Y : Iota), f Y) True) (Eq p True) % 4.70/4.91 Clause #9 (by clausification #[7]): ∀ (a : Iota), Or (Eq p False) (Eq (Not (f (skS.0 0 a))) True) % 4.70/4.91 Clause #10 (by clausification #[9]): ∀ (a : Iota), Or (Eq p False) (Eq (f (skS.0 0 a)) False) % 4.70/4.91 Clause #11 (by clausification #[8]): ∀ (a : Iota), Or (Eq p True) (Eq (f a) True) % 4.70/4.91 Clause #12 (by superposition #[11, 6]): Or (Eq p True) (Or (Eq True False) (Eq p True)) % 4.70/4.91 Clause #13 (by clausification #[12]): Or (Eq p True) (Eq p True) % 4.70/4.91 Clause #14 (by eliminate duplicate literals #[13]): Eq p True % 4.70/4.91 Clause #15 (by backward demodulation #[14, 5]): ∀ (a : Iota), Or (Eq (f a) True) (Eq True False) % 4.70/4.91 Clause #17 (by backward demodulation #[14, 10]): ∀ (a : Iota), Or (Eq True False) (Eq (f (skS.0 0 a)) False) % 4.70/4.91 Clause #19 (by clausification #[15]): ∀ (a : Iota), Eq (f a) True % 4.70/4.91 Clause #20 (by clausification #[17]): ∀ (a : Iota), Eq (f (skS.0 0 a)) False % 4.70/4.91 Clause #21 (by superposition #[20, 19]): Eq False True % 4.70/4.91 Clause #22 (by clausification #[21]): False % 4.70/4.91 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------