%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN066+1 : TPTP v9.2.0. Bugfixed v3.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n001.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 08:07:06 PM UTC 2025 % Result : Theorem 3.56s 3.74s % Output : Proof 3.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : SYN066+1 : TPTP v9.2.0. Bugfixed v3.0.0. % 0.12/0.14 % Command : duper %s % 0.12/0.35 % Computer : n001.cluster.edu % 0.12/0.35 % Model : x86_64 x86_64 % 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.35 % Memory : 8042.1875MB % 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.35 % CPULimit : 300 % 0.12/0.35 % WCLimit : 300 % 0.12/0.35 % DateTime : Thu Oct 2 15:32:23 EDT 2025 % 0.12/0.35 % CPUTime : % 3.56/3.74 SZS status Theorem for theBenchmark.p % 3.56/3.74 SZS output start Proof for theBenchmark.p % 3.56/3.74 Clause #0 (by assumption #[]): Eq % 3.56/3.74 (∀ (Z : Iota), % 3.56/3.74 Exists fun W => % 3.56/3.74 ∀ (X : Iota), % 3.56/3.74 Exists fun Y => And (And (big_p X Z → big_p Y W) (big_p Y Z)) (big_p Y W → Exists fun U => big_q U W)) % 3.56/3.74 True % 3.56/3.74 Clause #1 (by assumption #[]): Eq (∀ (X Z : Iota), Not (big_p X Z) → Exists fun Y => big_q Y Z) True % 3.56/3.74 Clause #2 (by assumption #[]): Eq ((Exists fun X => Exists fun Y => big_q X Y) → ∀ (Z : Iota), big_r Z Z) True % 3.56/3.74 Clause #3 (by assumption #[]): Eq (Not (∀ (X : Iota), Exists fun Y => big_r X Y)) True % 3.56/3.74 Clause #4 (by betaEtaReduce #[2]): Eq ((Exists fun X => Exists (big_q X)) → ∀ (Z : Iota), big_r Z Z) True % 3.56/3.74 Clause #5 (by clausification #[4]): Or (Eq (Exists fun X => Exists (big_q X)) False) (Eq (∀ (Z : Iota), big_r Z Z) True) % 3.56/3.74 Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq (∀ (Z : Iota), big_r Z Z) True) (Eq (Exists (big_q a)) False) % 3.56/3.74 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Or (Eq (Exists (big_q a)) False) (Eq (big_r a_1 a_1) True) % 3.56/3.74 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_r a a) True) (Eq (big_q a_1 a_2) False) % 3.56/3.74 Clause #9 (by betaEtaReduce #[3]): Eq (Not (∀ (X : Iota), Exists (big_r X))) True % 3.56/3.74 Clause #10 (by clausification #[9]): Eq (∀ (X : Iota), Exists (big_r X)) False % 3.56/3.74 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (Not (Exists (big_r (skS.0 0 a)))) True % 3.56/3.74 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (Exists (big_r (skS.0 0 a))) False % 3.56/3.74 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (big_r (skS.0 0 a) a_1) False % 3.56/3.74 Clause #14 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (Z : Iota), Not (big_p a Z) → Exists fun Y => big_q Y Z) True % 3.56/3.74 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (Not (big_p a a_1) → Exists fun Y => big_q Y a_1) True % 3.56/3.74 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (Not (big_p a a_1)) False) (Eq (Exists fun Y => big_q Y a_1) True) % 3.56/3.74 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (Exists fun Y => big_q Y a) True) (Eq (big_p a_1 a) True) % 3.56/3.74 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a a_1) True) (Eq (big_q (skS.0 1 a_1 a_2) a_1) True) % 3.56/3.74 Clause #19 (by superposition #[18, 8]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a a_1) True) (Or (Eq (big_r a_2 a_2) True) (Eq True False)) % 3.56/3.74 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a a_1) True) (Eq (big_r a_2 a_2) True) % 3.56/3.74 Clause #21 (by superposition #[20, 13]): ∀ (a a_1 : Iota), Or (Eq (big_p a a_1) True) (Eq True False) % 3.56/3.74 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (big_p a a_1) True % 3.56/3.74 Clause #23 (by clausification #[0]): ∀ (a : Iota), % 3.56/3.74 Eq % 3.56/3.74 (Exists fun W => % 3.56/3.74 ∀ (X : Iota), % 3.56/3.74 Exists fun Y => And (And (big_p X a → big_p Y W) (big_p Y a)) (big_p Y W → Exists fun U => big_q U W)) % 3.56/3.74 True % 3.56/3.74 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), % 3.56/3.74 Eq % 3.56/3.74 (∀ (X : Iota), % 3.56/3.74 Exists fun Y => % 3.56/3.74 And (And (big_p X a → big_p Y (skS.0 2 a a_1)) (big_p Y a)) % 3.56/3.74 (big_p Y (skS.0 2 a a_1) → Exists fun U => big_q U (skS.0 2 a a_1))) % 3.56/3.74 True % 3.56/3.74 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), % 3.56/3.74 Eq % 3.56/3.74 (Exists fun Y => % 3.56/3.74 And (And (big_p a a_1 → big_p Y (skS.0 2 a_1 a_2)) (big_p Y a_1)) % 3.56/3.74 (big_p Y (skS.0 2 a_1 a_2) → Exists fun U => big_q U (skS.0 2 a_1 a_2))) % 3.56/3.74 True % 3.56/3.74 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 a_3 : Iota), % 3.56/3.74 Eq % 3.56/3.74 (And (And (big_p a a_1 → big_p (skS.0 3 a a_1 a_2 a_3) (skS.0 2 a_1 a_2)) (big_p (skS.0 3 a a_1 a_2 a_3) a_1)) % 3.56/3.74 (big_p (skS.0 3 a a_1 a_2 a_3) (skS.0 2 a_1 a_2) → Exists fun U => big_q U (skS.0 2 a_1 a_2))) % 3.56/3.74 True % 3.56/3.74 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 a_3 : Iota), % 3.56/3.74 Eq (big_p (skS.0 3 a a_1 a_2 a_3) (skS.0 2 a_1 a_2) → Exists fun U => big_q U (skS.0 2 a_1 a_2)) True % 3.56/3.74 Clause #29 (by clausification #[27]): ∀ (a a_1 a_2 a_3 : Iota), % 3.56/3.74 Or (Eq (big_p (skS.0 3 a a_1 a_2 a_3) (skS.0 2 a_1 a_2)) False) (Eq (Exists fun U => big_q U (skS.0 2 a_1 a_2)) True) % 3.56/3.74 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 3.56/3.74 Or (Eq (big_p (skS.0 3 a a_1 a_2 a_3) (skS.0 2 a_1 a_2)) False) % 3.56/3.74 (Eq (big_q (skS.0 4 a_1 a_2 a_4) (skS.0 2 a_1 a_2)) True) % 3.56/3.74 Clause #31 (by superposition #[30, 22]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_q (skS.0 4 a a_1 a_2) (skS.0 2 a a_1)) True) (Eq False True) % 3.56/3.74 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Eq (big_q (skS.0 4 a a_1 a_2) (skS.0 2 a a_1)) True % 3.56/3.74 Clause #33 (by superposition #[32, 8]): ∀ (a : Iota), Or (Eq (big_r a a) True) (Eq True False) % 3.56/3.74 Clause #34 (by clausification #[33]): ∀ (a : Iota), Eq (big_r a a) True % 3.56/3.74 Clause #35 (by superposition #[34, 13]): Eq True False % 3.56/3.74 Clause #36 (by clausification #[35]): False % 3.56/3.74 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------