%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN409+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 08:07:37 PM UTC 2025 % Result : Theorem 3.58s 3.76s % Output : Proof 3.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SYN409+1 : TPTP v9.2.0. Released v2.0.0. % 0.04/0.13 % Command : duper %s % 0.12/0.34 % Computer : n019.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Oct 2 15:44:23 EDT 2025 % 0.12/0.34 % CPUTime : % 3.58/3.76 SZS status Theorem for theBenchmark.p % 3.58/3.76 SZS output start Proof for theBenchmark.p % 3.58/3.76 Clause #0 (by assumption #[]): Eq (Not (Iff (∀ (X : Iota), f X) (∀ (Y Z : Iota), And (f Y) (f Z)))) True % 3.58/3.76 Clause #1 (by clausification #[0]): Eq (Iff (∀ (X : Iota), f X) (∀ (Y Z : Iota), And (f Y) (f Z))) False % 3.58/3.76 Clause #2 (by clausification #[1]): Or (Eq (∀ (X : Iota), f X) False) (Eq (∀ (Y Z : Iota), And (f Y) (f Z)) False) % 3.58/3.76 Clause #3 (by clausification #[1]): Or (Eq (∀ (X : Iota), f X) True) (Eq (∀ (Y Z : Iota), And (f Y) (f Z)) True) % 3.58/3.76 Clause #4 (by clausification #[2]): ∀ (a : Iota), Or (Eq (∀ (Y Z : Iota), And (f Y) (f Z)) False) (Eq (Not (f (skS.0 0 a))) True) % 3.58/3.76 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Or (Eq (Not (f (skS.0 0 a))) True) (Eq (Not (∀ (Z : Iota), And (f (skS.0 1 a_1)) (f Z))) True) % 3.58/3.76 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Or (Eq (Not (∀ (Z : Iota), And (f (skS.0 1 a)) (f Z))) True) (Eq (f (skS.0 0 a_1)) False) % 3.58/3.76 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 0 a)) False) (Eq (∀ (Z : Iota), And (f (skS.0 1 a_1)) (f Z)) False) % 3.58/3.76 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Or (Eq (f (skS.0 0 a)) False) (Eq (Not (And (f (skS.0 1 a_1)) (f (skS.0 2 a_1 a_2)))) True) % 3.58/3.76 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Or (Eq (f (skS.0 0 a)) False) (Eq (And (f (skS.0 1 a_1)) (f (skS.0 2 a_1 a_2))) False) % 3.58/3.76 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), Or (Eq (f (skS.0 0 a)) False) (Or (Eq (f (skS.0 1 a_1)) False) (Eq (f (skS.0 2 a_1 a_2)) False)) % 3.58/3.76 Clause #11 (by clausification #[3]): ∀ (a : Iota), Or (Eq (∀ (Y Z : Iota), And (f Y) (f Z)) True) (Eq (f a) True) % 3.58/3.76 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (f a) True) (Eq (∀ (Z : Iota), And (f a_1) (f Z)) True) % 3.58/3.76 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq (f a) True) (Eq (And (f a_1) (f a_2)) True) % 3.58/3.76 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (f a) True) (Eq (f a_1) True) % 3.58/3.76 Clause #16 (by equality factoring #[14]): ∀ (a : Iota), Or (Ne True True) (Eq (f a) True) % 3.58/3.76 Clause #17 (by clausification #[16]): ∀ (a : Iota), Or (Eq (f a) True) (Or (Eq True False) (Eq True False)) % 3.58/3.76 Clause #19 (by clausification #[17]): ∀ (a : Iota), Or (Eq (f a) True) (Eq True False) % 3.58/3.76 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (f a) True % 3.58/3.76 Clause #21 (by backward demodulation #[20, 10]): ∀ (a a_1 a_2 : Iota), Or (Eq (f (skS.0 0 a)) False) (Or (Eq True False) (Eq (f (skS.0 2 a_1 a_2)) False)) % 3.58/3.76 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Or (Eq (f (skS.0 0 a)) False) (Eq (f (skS.0 2 a_1 a_2)) False) % 3.58/3.76 Clause #23 (by superposition #[22, 20]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 2 a a_1)) False) (Eq False True) % 3.58/3.76 Clause #27 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (f (skS.0 2 a a_1)) False % 3.58/3.76 Clause #28 (by superposition #[27, 20]): Eq False True % 3.58/3.76 Clause #29 (by clausification #[28]): False % 3.58/3.76 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------