%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN081+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.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 08:07:09 PM UTC 2025 % Result : Theorem 3.48s 3.71s % Output : Proof 3.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SYN081+1 : TPTP v9.2.0. Released v2.0.0. % 0.03/0.12 % Command : duper %s % 0.11/0.33 % Computer : n006.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 300 % 0.11/0.33 % DateTime : Thu Oct 2 15:43:38 EDT 2025 % 0.11/0.33 % CPUTime : % 3.48/3.71 SZS status Theorem for theBenchmark.p % 3.48/3.71 SZS output start Proof for theBenchmark.p % 3.48/3.71 Clause #0 (by assumption #[]): Eq (∀ (X : Iota), Iff (big_f X) (Not (big_f (f X)))) True % 3.48/3.71 Clause #1 (by assumption #[]): Eq (Not (Exists fun X => And (big_f X) (Not (big_f (f X))))) True % 3.48/3.71 Clause #2 (by clausification #[0]): ∀ (a : Iota), Eq (Iff (big_f a) (Not (big_f (f a)))) True % 3.48/3.71 Clause #3 (by clausification #[2]): ∀ (a : Iota), Or (Eq (big_f a) True) (Eq (Not (big_f (f a))) False) % 3.48/3.71 Clause #4 (by clausification #[2]): ∀ (a : Iota), Or (Eq (big_f a) False) (Eq (Not (big_f (f a))) True) % 3.48/3.71 Clause #5 (by clausification #[3]): ∀ (a : Iota), Or (Eq (big_f a) True) (Eq (big_f (f a)) True) % 3.48/3.71 Clause #6 (by clausification #[4]): ∀ (a : Iota), Or (Eq (big_f a) False) (Eq (big_f (f a)) False) % 3.48/3.71 Clause #7 (by superposition #[6, 5]): ∀ (a : Iota), Or (Eq (big_f (f (f a))) False) (Or (Eq (big_f a) True) (Eq False True)) % 3.48/3.71 Clause #8 (by clausification #[7]): ∀ (a : Iota), Or (Eq (big_f (f (f a))) False) (Eq (big_f a) True) % 3.48/3.71 Clause #10 (by clausification #[1]): Eq (Exists fun X => And (big_f X) (Not (big_f (f X)))) False % 3.48/3.71 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (And (big_f a) (Not (big_f (f a)))) False % 3.48/3.71 Clause #12 (by clausification #[11]): ∀ (a : Iota), Or (Eq (big_f a) False) (Eq (Not (big_f (f a))) False) % 3.48/3.71 Clause #13 (by clausification #[12]): ∀ (a : Iota), Or (Eq (big_f a) False) (Eq (big_f (f a)) True) % 3.48/3.71 Clause #14 (by superposition #[13, 5]): ∀ (a : Iota), Or (Eq (big_f (f (f a))) True) (Or (Eq (big_f a) True) (Eq False True)) % 3.48/3.71 Clause #15 (by clausification #[14]): ∀ (a : Iota), Or (Eq (big_f (f (f a))) True) (Eq (big_f a) True) % 3.48/3.71 Clause #16 (by superposition #[15, 8]): ∀ (a : Iota), Or (Eq (big_f a) True) (Or (Eq True False) (Eq (big_f a) True)) % 3.48/3.71 Clause #19 (by clausification #[16]): ∀ (a : Iota), Or (Eq (big_f a) True) (Eq (big_f a) True) % 3.48/3.71 Clause #20 (by eliminate duplicate literals #[19]): ∀ (a : Iota), Eq (big_f a) True % 3.48/3.71 Clause #22 (by backward demodulation #[20, 6]): ∀ (a : Iota), Or (Eq True False) (Eq (big_f (f a)) False) % 3.48/3.71 Clause #27 (by clausification #[22]): ∀ (a : Iota), Eq (big_f (f a)) False % 3.48/3.71 Clause #28 (by superposition #[27, 20]): Eq False True % 3.48/3.71 Clause #29 (by clausification #[28]): False % 3.48/3.71 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------