%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN323+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n027.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 08:07:23 PM UTC 2025 % Result : Theorem 3.37s 3.55s % Output : Proof 3.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SYN323+1 : TPTP v9.2.0. Released v2.0.0. % 0.12/0.14 % Command : duper %s % 0.13/0.35 % Computer : n027.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Thu Oct 2 15:47:53 EDT 2025 % 0.13/0.35 % CPUTime : % 3.37/3.55 SZS status Theorem for theBenchmark.p % 3.37/3.55 SZS output start Proof for theBenchmark.p % 3.37/3.55 Clause #0 (by assumption #[]): Eq % 3.37/3.55 (Not % 3.37/3.55 (Exists fun Y => % 3.37/3.55 (∀ (X : Iota), (big_f X Y → big_f Y X) → big_g X Y) → % 3.37/3.55 Not (∀ (X : Iota), (big_f X Y → big_f Y X) → Not (big_g X Y)))) % 3.37/3.55 True % 3.37/3.55 Clause #1 (by clausification #[0]): Eq % 3.37/3.55 (Exists fun Y => % 3.37/3.55 (∀ (X : Iota), (big_f X Y → big_f Y X) → big_g X Y) → Not (∀ (X : Iota), (big_f X Y → big_f Y X) → Not (big_g X Y))) % 3.37/3.55 False % 3.37/3.55 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 3.37/3.55 Eq % 3.37/3.55 ((∀ (X : Iota), (big_f X a → big_f a X) → big_g X a) → % 3.37/3.55 Not (∀ (X : Iota), (big_f X a → big_f a X) → Not (big_g X a))) % 3.37/3.55 False % 3.37/3.55 Clause #3 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (X : Iota), (big_f X a → big_f a X) → big_g X a) True % 3.37/3.55 Clause #4 (by clausification #[2]): ∀ (a : Iota), Eq (Not (∀ (X : Iota), (big_f X a → big_f a X) → Not (big_g X a))) False % 3.37/3.55 Clause #5 (by clausification #[3]): ∀ (a a_1 : Iota), Eq ((big_f a a_1 → big_f a_1 a) → big_g a a_1) True % 3.37/3.55 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1 → big_f a_1 a) False) (Eq (big_g a a_1) True) % 3.37/3.55 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Or (Eq (big_g a a_1) True) (Eq (big_f a a_1) True) % 3.37/3.55 Clause #8 (by clausification #[6]): ∀ (a a_1 : Iota), Or (Eq (big_g a a_1) True) (Eq (big_f a_1 a) False) % 3.37/3.55 Clause #9 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (X : Iota), (big_f X a → big_f a X) → Not (big_g X a)) True % 3.37/3.55 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq ((big_f a a_1 → big_f a_1 a) → Not (big_g a a_1)) True % 3.37/3.55 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1 → big_f a_1 a) False) (Eq (Not (big_g a a_1)) True) % 3.37/3.55 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (Not (big_g a a_1)) True) (Eq (big_f a a_1) True) % 3.37/3.55 Clause #13 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (Not (big_g a a_1)) True) (Eq (big_f a_1 a) False) % 3.37/3.55 Clause #14 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Eq (big_g a a_1) False) % 3.37/3.55 Clause #15 (by superposition #[14, 7]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Or (Eq False True) (Eq (big_f a a_1) True)) % 3.37/3.55 Clause #16 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) False) (Eq (big_g a_1 a) False) % 3.37/3.55 Clause #17 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Eq (big_f a a_1) True) % 3.37/3.55 Clause #18 (by eliminate duplicate literals #[17]): ∀ (a a_1 : Iota), Eq (big_f a a_1) True % 3.37/3.55 Clause #20 (by backward demodulation #[18, 8]): ∀ (a a_1 : Iota), Or (Eq (big_g a a_1) True) (Eq True False) % 3.37/3.55 Clause #22 (by backward demodulation #[18, 16]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (big_g a a_1) False) % 3.37/3.55 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (big_g a a_1) False % 3.37/3.55 Clause #24 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (big_g a a_1) True % 3.37/3.55 Clause #25 (by superposition #[24, 23]): Eq True False % 3.37/3.55 Clause #26 (by clausification #[25]): False % 3.37/3.55 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------