%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET786+1 : TPTP v9.2.0. Released v2.5.0. % 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 08:00:29 PM UTC 2025 % Result : Theorem 4.47s 4.65s % Output : Proof 4.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET786+1 : TPTP v9.2.0. Released v2.5.0. % 0.03/0.13 % Command : duper %s % 0.14/0.34 % Computer : n008.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Thu Oct 2 13:35:38 EDT 2025 % 0.14/0.34 % CPUTime : % 4.47/4.65 SZS status Theorem for theBenchmark.p % 4.47/4.65 SZS output start Proof for theBenchmark.p % 4.47/4.65 Clause #0 (by assumption #[]): Eq (Not (Not (Exists fun Y => ∀ (X : Iota), Iff (element X Y) (Not (Exists fun Z => And (element X Z) (element Z X)))))) % 4.47/4.65 True % 4.47/4.65 Clause #1 (by clausification #[0]): Eq (Not (Exists fun Y => ∀ (X : Iota), Iff (element X Y) (Not (Exists fun Z => And (element X Z) (element Z X))))) False % 4.47/4.65 Clause #2 (by clausification #[1]): Eq (Exists fun Y => ∀ (X : Iota), Iff (element X Y) (Not (Exists fun Z => And (element X Z) (element Z X)))) True % 4.47/4.65 Clause #3 (by clausification #[2]): ∀ (a : Iota), % 4.47/4.65 Eq (∀ (X : Iota), Iff (element X (skS.0 0 a)) (Not (Exists fun Z => And (element X Z) (element Z X)))) True % 4.47/4.65 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), Eq (Iff (element a (skS.0 0 a_1)) (Not (Exists fun Z => And (element a Z) (element Z a)))) True % 4.47/4.65 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), % 4.47/4.65 Or (Eq (element a (skS.0 0 a_1)) True) (Eq (Not (Exists fun Z => And (element a Z) (element Z a))) False) % 4.47/4.65 Clause #6 (by clausification #[4]): ∀ (a a_1 : Iota), % 4.47/4.65 Or (Eq (element a (skS.0 0 a_1)) False) (Eq (Not (Exists fun Z => And (element a Z) (element Z a))) True) % 4.47/4.65 Clause #7 (by clausification #[5]): ∀ (a a_1 : Iota), Or (Eq (element a (skS.0 0 a_1)) True) (Eq (Exists fun Z => And (element a Z) (element Z a)) True) % 4.47/4.65 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), % 4.47/4.65 Or (Eq (element a (skS.0 0 a_1)) True) (Eq (And (element a (skS.0 1 a a_2)) (element (skS.0 1 a a_2) a)) True) % 4.47/4.65 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 0 a_1)) True) (Eq (element (skS.0 1 a a_2) a) True) % 4.47/4.65 Clause #10 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 0 a_1)) True) (Eq (element a (skS.0 1 a a_2)) True) % 4.47/4.65 Clause #11 (by clausification #[6]): ∀ (a a_1 : Iota), Or (Eq (element a (skS.0 0 a_1)) False) (Eq (Exists fun Z => And (element a Z) (element Z a)) False) % 4.47/4.65 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 0 a_1)) False) (Eq (And (element a a_2) (element a_2 a)) False) % 4.47/4.65 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 0 a_1)) False) (Or (Eq (element a a_2) False) (Eq (element a_2 a) False)) % 4.47/4.65 Clause #16 (by superposition #[13, 9]): ∀ (a a_1 a_2 a_3 : Iota), % 4.47/4.65 Or (Eq (element (skS.0 1 (skS.0 0 a) a_1) a_2) False) % 4.47/4.65 (Or (Eq (element a_2 (skS.0 1 (skS.0 0 a) a_1)) False) % 4.47/4.65 (Or (Eq (element (skS.0 0 a) (skS.0 0 a_3)) True) (Eq False True))) % 4.47/4.65 Clause #27 (by clausification #[16]): ∀ (a a_1 a_2 a_3 : Iota), % 4.47/4.65 Or (Eq (element (skS.0 1 (skS.0 0 a) a_1) a_2) False) % 4.47/4.65 (Or (Eq (element a_2 (skS.0 1 (skS.0 0 a) a_1)) False) (Eq (element (skS.0 0 a) (skS.0 0 a_3)) True)) % 4.47/4.65 Clause #31 (by superposition #[27, 9]): ∀ (a a_1 a_2 a_3 : Iota), % 4.47/4.65 Or (Eq (element (skS.0 0 a) (skS.0 1 (skS.0 0 a) a_1)) False) % 4.47/4.65 (Or (Eq (element (skS.0 0 a) (skS.0 0 a_2)) True) % 4.47/4.65 (Or (Eq (element (skS.0 0 a) (skS.0 0 a_3)) True) (Eq False True))) % 4.47/4.65 Clause #156 (by clausification #[31]): ∀ (a a_1 a_2 a_3 : Iota), % 4.47/4.65 Or (Eq (element (skS.0 0 a) (skS.0 1 (skS.0 0 a) a_1)) False) % 4.47/4.65 (Or (Eq (element (skS.0 0 a) (skS.0 0 a_2)) True) (Eq (element (skS.0 0 a) (skS.0 0 a_3)) True)) % 4.47/4.65 Clause #157 (by superposition #[156, 10]): ∀ (a a_1 a_2 a_3 : Iota), % 4.47/4.65 Or (Eq (element (skS.0 0 a) (skS.0 0 a_1)) True) % 4.47/4.65 (Or (Eq (element (skS.0 0 a) (skS.0 0 a_2)) True) % 4.47/4.65 (Or (Eq (element (skS.0 0 a) (skS.0 0 a_3)) True) (Eq False True))) % 4.47/4.65 Clause #158 (by clausification #[157]): ∀ (a a_1 a_2 a_3 : Iota), % 4.47/4.65 Or (Eq (element (skS.0 0 a) (skS.0 0 a_1)) True) % 4.47/4.65 (Or (Eq (element (skS.0 0 a) (skS.0 0 a_2)) True) (Eq (element (skS.0 0 a) (skS.0 0 a_3)) True)) % 4.47/4.65 Clause #171 (by equality factoring #[158]): ∀ (a a_1 a_2 : Iota), % 4.47/4.65 Or (Eq (element (skS.0 0 a) (skS.0 0 a_1)) True) (Or (Ne True True) (Eq (element (skS.0 0 a) (skS.0 0 a_2)) True)) % 4.47/4.65 Clause #172 (by clausification #[171]): ∀ (a a_1 a_2 : Iota), % 4.47/4.65 Or (Eq (element (skS.0 0 a) (skS.0 0 a_1)) True) % 4.47/4.65 (Or (Eq (element (skS.0 0 a) (skS.0 0 a_2)) True) (Or (Eq True False) (Eq True False))) % 4.52/4.67 Clause #174 (by clausification #[172]): ∀ (a a_1 a_2 : Iota), % 4.52/4.67 Or (Eq (element (skS.0 0 a) (skS.0 0 a_1)) True) (Or (Eq (element (skS.0 0 a) (skS.0 0 a_2)) True) (Eq True False)) % 4.52/4.67 Clause #175 (by clausification #[174]): ∀ (a a_1 a_2 : Iota), Or (Eq (element (skS.0 0 a) (skS.0 0 a_1)) True) (Eq (element (skS.0 0 a) (skS.0 0 a_2)) True) % 4.52/4.67 Clause #188 (by equality factoring #[175]): ∀ (a a_1 : Iota), Or (Ne True True) (Eq (element (skS.0 0 a) (skS.0 0 a_1)) True) % 4.52/4.67 Clause #189 (by clausification #[188]): ∀ (a a_1 : Iota), Or (Eq (element (skS.0 0 a) (skS.0 0 a_1)) True) (Or (Eq True False) (Eq True False)) % 4.52/4.67 Clause #191 (by clausification #[189]): ∀ (a a_1 : Iota), Or (Eq (element (skS.0 0 a) (skS.0 0 a_1)) True) (Eq True False) % 4.52/4.67 Clause #192 (by clausification #[191]): ∀ (a a_1 : Iota), Eq (element (skS.0 0 a) (skS.0 0 a_1)) True % 4.52/4.67 Clause #193 (by superposition #[192, 13]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (element (skS.0 0 a) a_1) False) (Eq (element a_1 (skS.0 0 a)) False)) % 4.52/4.67 Clause #218 (by clausification #[193]): ∀ (a a_1 : Iota), Or (Eq (element (skS.0 0 a) a_1) False) (Eq (element a_1 (skS.0 0 a)) False) % 4.52/4.67 Clause #219 (by superposition #[218, 192]): ∀ (a a_1 : Iota), Or (Eq (element (skS.0 0 a) (skS.0 0 a_1)) False) (Eq False True) % 4.52/4.67 Clause #225 (by clausification #[219]): ∀ (a a_1 : Iota), Eq (element (skS.0 0 a) (skS.0 0 a_1)) False % 4.52/4.67 Clause #226 (by superposition #[225, 192]): Eq False True % 4.52/4.67 Clause #231 (by clausification #[226]): False % 4.52/4.67 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------