%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN360+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n008.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 08:07:29 PM UTC 2025 % Result : Theorem 4.07s 4.23s % Output : Proof 4.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SYN360+1 : TPTP v9.2.0. Released v2.0.0. % 0.03/0.13 % Command : duper %s % 0.12/0.33 % Computer : n008.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Thu Oct 2 15:19:53 EDT 2025 % 0.12/0.33 % CPUTime : % 4.07/4.23 SZS status Theorem for theBenchmark.p % 4.07/4.23 SZS output start Proof for theBenchmark.p % 4.07/4.23 Clause #0 (by assumption #[]): Eq % 4.07/4.23 (Not % 4.07/4.23 (And (∀ (X : Iota), (Exists fun Y => big_p X Y) → ∀ (Y : Iota), big_q X Y) % 4.07/4.23 (∀ (Z : Iota), Exists fun Y => big_p Z Y) → % 4.07/4.23 ∀ (Y X : Iota), big_q X Y)) % 4.07/4.23 True % 4.07/4.23 Clause #1 (by betaEtaReduce #[0]): Eq % 4.07/4.23 (Not % 4.07/4.23 (And (∀ (X : Iota), Exists (big_p X) → ∀ (Y : Iota), big_q X Y) (∀ (Z : Iota), Exists (big_p Z)) → % 4.07/4.23 ∀ (Y X : Iota), big_q X Y)) % 4.07/4.23 True % 4.07/4.23 Clause #2 (by clausification #[1]): Eq % 4.07/4.23 (And (∀ (X : Iota), Exists (big_p X) → ∀ (Y : Iota), big_q X Y) (∀ (Z : Iota), Exists (big_p Z)) → % 4.07/4.23 ∀ (Y X : Iota), big_q X Y) % 4.07/4.23 False % 4.07/4.23 Clause #3 (by clausification #[2]): Eq (And (∀ (X : Iota), Exists (big_p X) → ∀ (Y : Iota), big_q X Y) (∀ (Z : Iota), Exists (big_p Z))) True % 4.07/4.23 Clause #4 (by clausification #[2]): Eq (∀ (Y X : Iota), big_q X Y) False % 4.07/4.23 Clause #5 (by clausification #[3]): Eq (∀ (Z : Iota), Exists (big_p Z)) True % 4.07/4.23 Clause #6 (by clausification #[3]): Eq (∀ (X : Iota), Exists (big_p X) → ∀ (Y : Iota), big_q X Y) True % 4.07/4.23 Clause #7 (by clausification #[5]): ∀ (a : Iota), Eq (Exists (big_p a)) True % 4.07/4.23 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Eq (big_p a (skS.0 0 a a_1)) True % 4.07/4.23 Clause #9 (by clausification #[4]): ∀ (a : Iota), Eq (Not (∀ (X : Iota), big_q X (skS.0 1 a))) True % 4.07/4.23 Clause #10 (by clausification #[9]): ∀ (a : Iota), Eq (∀ (X : Iota), big_q X (skS.0 1 a)) False % 4.07/4.23 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (Not (big_q (skS.0 2 a a_1) (skS.0 1 a))) True % 4.07/4.23 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (big_q (skS.0 2 a a_1) (skS.0 1 a)) False % 4.07/4.23 Clause #13 (by clausification #[6]): ∀ (a : Iota), Eq (Exists (big_p a) → ∀ (Y : Iota), big_q a Y) True % 4.07/4.23 Clause #14 (by clausification #[13]): ∀ (a : Iota), Or (Eq (Exists (big_p a)) False) (Eq (∀ (Y : Iota), big_q a Y) True) % 4.07/4.23 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (∀ (Y : Iota), big_q a Y) True) (Eq (big_p a a_1) False) % 4.07/4.23 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a a_1) False) (Eq (big_q a a_2) True) % 4.07/4.23 Clause #17 (by superposition #[16, 8]): ∀ (a a_1 : Iota), Or (Eq (big_q a a_1) True) (Eq False True) % 4.07/4.23 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (big_q a a_1) True % 4.07/4.23 Clause #19 (by superposition #[18, 12]): Eq True False % 4.07/4.23 Clause #20 (by clausification #[19]): False % 4.07/4.23 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------