%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN965+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n016.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 08:08:19 PM UTC 2025 % Result : Theorem 3.56s 3.80s % Output : Proof 3.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SYN965+1 : TPTP v9.2.0. Released v3.1.0. % 0.12/0.14 % Command : duper %s % 0.13/0.35 % Computer : n016.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 15:47:08 EDT 2025 % 0.13/0.35 % CPUTime : % 3.56/3.80 SZS status Theorem for theBenchmark.p % 3.56/3.80 SZS output start Proof for theBenchmark.p % 3.56/3.80 Clause #0 (by assumption #[]): Eq % 3.56/3.80 (Not % 3.56/3.80 (Exists fun Z => ∀ (X : Iota), Exists fun Y => And (p Y X → Exists fun W => p W Y) (And (p Z Y) (p Y Z) → p Y X))) % 3.56/3.80 True % 3.56/3.80 Clause #1 (by clausification #[0]): Eq (Exists fun Z => ∀ (X : Iota), Exists fun Y => And (p Y X → Exists fun W => p W Y) (And (p Z Y) (p Y Z) → p Y X)) % 3.56/3.80 False % 3.56/3.80 Clause #2 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (X : Iota), Exists fun Y => And (p Y X → Exists fun W => p W Y) (And (p a Y) (p Y a) → p Y X)) False % 3.56/3.80 Clause #3 (by clausification #[2]): ∀ (a a_1 : Iota), % 3.56/3.80 Eq % 3.56/3.80 (Not % 3.56/3.80 (Exists fun Y => And (p Y (skS.0 0 a a_1) → Exists fun W => p W Y) (And (p a Y) (p Y a) → p Y (skS.0 0 a a_1)))) % 3.56/3.80 True % 3.56/3.80 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), % 3.56/3.80 Eq (Exists fun Y => And (p Y (skS.0 0 a a_1) → Exists fun W => p W Y) (And (p a Y) (p Y a) → p Y (skS.0 0 a a_1))) % 3.56/3.80 False % 3.56/3.80 Clause #5 (by clausification #[4]): ∀ (a a_1 a_2 : Iota), % 3.56/3.80 Eq (And (p a (skS.0 0 a_1 a_2) → Exists fun W => p W a) (And (p a_1 a) (p a a_1) → p a (skS.0 0 a_1 a_2))) False % 3.56/3.80 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), % 3.56/3.80 Or (Eq (p a (skS.0 0 a_1 a_2) → Exists fun W => p W a) False) % 3.56/3.80 (Eq (And (p a_1 a) (p a a_1) → p a (skS.0 0 a_1 a_2)) False) % 3.56/3.80 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (p a a_1) (p a_1 a) → p a_1 (skS.0 0 a a_2)) False) (Eq (p a_1 (skS.0 0 a a_2)) True) % 3.56/3.80 Clause #8 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), % 3.56/3.80 Or (Eq (And (p a a_1) (p a_1 a) → p a_1 (skS.0 0 a a_2)) False) (Eq (Exists fun W => p W a_1) False) % 3.56/3.80 Clause #9 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a (skS.0 0 a_1 a_2)) True) (Eq (And (p a_1 a) (p a a_1)) True) % 3.56/3.80 Clause #11 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a (skS.0 0 a_1 a_2)) True) (Eq (p a a_1) True) % 3.56/3.80 Clause #13 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (Exists fun W => p W a) False) (Eq (And (p a_1 a) (p a a_1)) True) % 3.56/3.80 Clause #14 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Or (Eq (Exists fun W => p W a) False) (Eq (p a (skS.0 0 a_1 a_2)) False) % 3.56/3.80 Clause #15 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (p a a_1) (p a_1 a)) True) (Eq (p a_2 a_1) False) % 3.56/3.80 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a_1) False) (Eq (p a_1 a_2) True) % 3.56/3.80 Clause #17 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Or (Eq (p a a_1) False) (Eq (p a_2 a_1) True) % 3.56/3.80 Clause #20 (by superposition #[17, 11]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (p a (skS.0 0 a_1 a_2)) True) (Or (Eq False True) (Eq (p a_3 a_1) True)) % 3.56/3.80 Clause #22 (by clausification #[20]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (p a (skS.0 0 a_1 a_2)) True) (Eq (p a_3 a_1) True) % 3.56/3.80 Clause #25 (by superposition #[22, 16]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (p a (skS.0 0 a_1 a_2)) True) (Or (Eq True False) (Eq (p a_1 a_3) True)) % 3.56/3.80 Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (p a (skS.0 0 a_1 a_2)) True) (Eq (p a_1 a_3) True) % 3.56/3.80 Clause #31 (by equality factoring #[27]): ∀ (a a_1 : Iota), Or (Ne True True) (Eq (p a (skS.0 0 a a_1)) True) % 3.56/3.80 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (p a (skS.0 0 a a_1)) True) (Or (Eq True False) (Eq True False)) % 3.56/3.80 Clause #34 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq (p a (skS.0 0 a a_1)) True) (Eq True False) % 3.56/3.80 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Eq (p a (skS.0 0 a a_1)) True % 3.56/3.80 Clause #37 (by superposition #[35, 17]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (p a (skS.0 0 a_1 a_2)) True) % 3.56/3.80 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), Eq (p a (skS.0 0 a_1 a_2)) True % 3.56/3.80 Clause #41 (by clausification #[14]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (p a (skS.0 0 a_1 a_2)) False) (Eq (p a_3 a) False) % 3.56/3.80 Clause #42 (by superposition #[41, 38]): ∀ (a a_1 : Iota), Or (Eq (p a a_1) False) (Eq False True) % 3.56/3.80 Clause #44 (by clausification #[42]): ∀ (a a_1 : Iota), Eq (p a a_1) False % 3.56/3.80 Clause #45 (by superposition #[44, 38]): Eq False True % 3.56/3.80 Clause #46 (by clausification #[45]): False % 3.56/3.80 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------