%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN373+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n028.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 08:07:31 PM UTC 2025 % Result : Theorem 3.51s 3.72s % Output : Proof 3.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN373+1 : TPTP v9.2.0. Released v2.0.0. % 0.07/0.14 % Command : duper %s % 0.13/0.33 % Computer : n028.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Thu Oct 2 15:36:53 EDT 2025 % 0.13/0.33 % CPUTime : % 3.51/3.72 SZS status Theorem for theBenchmark.p % 3.51/3.72 SZS output start Proof for theBenchmark.p % 3.51/3.72 Clause #0 (by assumption #[]): Eq (Not (Iff (Exists fun X => big_p X → big_q X) ((∀ (X : Iota), big_p X) → Exists fun X => big_q X))) True % 3.51/3.72 Clause #1 (by betaEtaReduce #[0]): Eq (Not (Iff (Exists fun X => big_p X → big_q X) ((∀ (X : Iota), big_p X) → Exists big_q))) True % 3.51/3.72 Clause #2 (by clausification #[1]): Eq (Iff (Exists fun X => big_p X → big_q X) ((∀ (X : Iota), big_p X) → Exists big_q)) False % 3.51/3.72 Clause #3 (by clausification #[2]): Or (Eq (Exists fun X => big_p X → big_q X) False) (Eq ((∀ (X : Iota), big_p X) → Exists big_q) False) % 3.51/3.72 Clause #4 (by clausification #[2]): Or (Eq (Exists fun X => big_p X → big_q X) True) (Eq ((∀ (X : Iota), big_p X) → Exists big_q) True) % 3.51/3.72 Clause #5 (by clausification #[3]): ∀ (a : Iota), Or (Eq ((∀ (X : Iota), big_p X) → Exists big_q) False) (Eq (big_p a → big_q a) False) % 3.51/3.72 Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq (big_p a → big_q a) False) (Eq (∀ (X : Iota), big_p X) True) % 3.51/3.72 Clause #7 (by clausification #[5]): ∀ (a : Iota), Or (Eq (big_p a → big_q a) False) (Eq (Exists big_q) False) % 3.51/3.72 Clause #8 (by clausification #[6]): ∀ (a : Iota), Or (Eq (∀ (X : Iota), big_p X) True) (Eq (big_p a) True) % 3.51/3.72 Clause #10 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Eq (big_p a_1) True) % 3.51/3.72 Clause #11 (by equality factoring #[10]): ∀ (a : Iota), Or (Ne True True) (Eq (big_p a) True) % 3.51/3.72 Clause #12 (by clausification #[11]): ∀ (a : Iota), Or (Eq (big_p a) True) (Or (Eq True False) (Eq True False)) % 3.51/3.72 Clause #14 (by clausification #[12]): ∀ (a : Iota), Or (Eq (big_p a) True) (Eq True False) % 3.51/3.72 Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (big_p a) True % 3.51/3.72 Clause #18 (by clausification #[7]): ∀ (a : Iota), Or (Eq (Exists big_q) False) (Eq (big_q a) False) % 3.51/3.72 Clause #20 (by clausification #[4]): ∀ (a : Iota), Or (Eq ((∀ (X : Iota), big_p X) → Exists big_q) True) (Eq (big_p (skS.0 0 a) → big_q (skS.0 0 a)) True) % 3.51/3.72 Clause #21 (by clausification #[20]): ∀ (a : Iota), % 3.51/3.72 Or (Eq (big_p (skS.0 0 a) → big_q (skS.0 0 a)) True) (Or (Eq (∀ (X : Iota), big_p X) False) (Eq (Exists big_q) True)) % 3.51/3.72 Clause #22 (by clausification #[21]): ∀ (a : Iota), % 3.51/3.72 Or (Eq (∀ (X : Iota), big_p X) False) % 3.51/3.72 (Or (Eq (Exists big_q) True) (Or (Eq (big_p (skS.0 0 a)) False) (Eq (big_q (skS.0 0 a)) True))) % 3.51/3.72 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), % 3.51/3.72 Or (Eq (Exists big_q) True) % 3.51/3.72 (Or (Eq (big_p (skS.0 0 a)) False) (Or (Eq (big_q (skS.0 0 a)) True) (Eq (Not (big_p (skS.0 1 a_1))) True))) % 3.51/3.72 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), % 3.51/3.72 Or (Eq (big_p (skS.0 0 a)) False) % 3.51/3.72 (Or (Eq (big_q (skS.0 0 a)) True) (Or (Eq (Not (big_p (skS.0 1 a_1))) True) (Eq (big_q (skS.0 2 a_2)) True))) % 3.51/3.72 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), % 3.51/3.72 Or (Eq (big_p (skS.0 0 a)) False) % 3.51/3.72 (Or (Eq (big_q (skS.0 0 a)) True) (Or (Eq (big_q (skS.0 2 a_1)) True) (Eq (big_p (skS.0 1 a_2)) False))) % 3.51/3.72 Clause #26 (by superposition #[25, 15]): ∀ (a a_1 a_2 : Iota), % 3.51/3.72 Or (Eq (big_q (skS.0 0 a)) True) % 3.51/3.72 (Or (Eq (big_q (skS.0 2 a_1)) True) (Or (Eq (big_p (skS.0 1 a_2)) False) (Eq False True))) % 3.51/3.72 Clause #27 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (big_q a) False) (Eq (big_q a_1) False) % 3.51/3.72 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), % 3.51/3.72 Or (Eq (big_q (skS.0 0 a)) True) (Or (Eq (big_q (skS.0 2 a_1)) True) (Eq (big_p (skS.0 1 a_2)) False)) % 3.51/3.72 Clause #29 (by superposition #[28, 15]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 0 a)) True) (Or (Eq (big_q (skS.0 2 a_1)) True) (Eq False True)) % 3.51/3.72 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 0 a)) True) (Eq (big_q (skS.0 2 a_1)) True) % 3.51/3.72 Clause #31 (by superposition #[30, 27]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 2 a)) True) (Or (Eq True False) (Eq (big_q a_1) False)) % 3.51/3.72 Clause #36 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 2 a)) True) (Eq (big_q a_1) False) % 3.51/3.72 Clause #37 (by superposition #[36, 30]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 2 a)) True) (Or (Eq False True) (Eq (big_q (skS.0 2 a_1)) True)) % 3.51/3.72 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 2 a)) True) (Eq (big_q (skS.0 2 a_1)) True) % 3.51/3.72 Clause #42 (by equality factoring #[39]): ∀ (a : Iota), Or (Ne True True) (Eq (big_q (skS.0 2 a)) True) % 3.51/3.72 Clause #43 (by clausification #[42]): ∀ (a : Iota), Or (Eq (big_q (skS.0 2 a)) True) (Or (Eq True False) (Eq True False)) % 3.51/3.72 Clause #45 (by clausification #[43]): ∀ (a : Iota), Or (Eq (big_q (skS.0 2 a)) True) (Eq True False) % 3.51/3.72 Clause #46 (by clausification #[45]): ∀ (a : Iota), Eq (big_q (skS.0 2 a)) True % 3.51/3.72 Clause #47 (by superposition #[46, 27]): ∀ (a : Iota), Or (Eq True False) (Eq (big_q a) False) % 3.51/3.72 Clause #49 (by clausification #[47]): ∀ (a : Iota), Eq (big_q a) False % 3.51/3.72 Clause #50 (by superposition #[49, 46]): Eq False True % 3.51/3.72 Clause #51 (by clausification #[50]): False % 3.51/3.72 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------