%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET045+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.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 07:59:28 PM UTC 2025 % Result : Theorem 3.46s 3.64s % Output : Proof 3.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SET045+1 : TPTP v9.2.0. Released v2.0.0. % 0.04/0.13 % Command : duper %s % 0.13/0.34 % Computer : n004.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 14:11:23 EDT 2025 % 0.13/0.34 % CPUTime : % 3.46/3.64 SZS status Theorem for theBenchmark.p % 3.46/3.64 SZS output start Proof for theBenchmark.p % 3.46/3.64 Clause #0 (by assumption #[]): Eq (∀ (Z : Iota), Exists fun Y => ∀ (X : Iota), Iff (element X Y) (And (element X Z) (Not (element X X)))) True % 3.46/3.64 Clause #1 (by assumption #[]): Eq (Not (Not (Exists fun Z => ∀ (X : Iota), element X Z))) True % 3.46/3.64 Clause #2 (by clausification #[1]): Eq (Not (Exists fun Z => ∀ (X : Iota), element X Z)) False % 3.46/3.64 Clause #3 (by clausification #[2]): Eq (Exists fun Z => ∀ (X : Iota), element X Z) True % 3.46/3.64 Clause #4 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (X : Iota), element X (skS.0 0 a)) True % 3.46/3.64 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Eq (element a (skS.0 0 a_1)) True % 3.46/3.64 Clause #6 (by clausification #[0]): ∀ (a : Iota), Eq (Exists fun Y => ∀ (X : Iota), Iff (element X Y) (And (element X a) (Not (element X X)))) True % 3.46/3.64 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (∀ (X : Iota), Iff (element X (skS.0 1 a a_1)) (And (element X a) (Not (element X X)))) True % 3.46/3.64 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Eq (Iff (element a (skS.0 1 a_1 a_2)) (And (element a a_1) (Not (element a a)))) True % 3.46/3.64 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 1 a_1 a_2)) True) (Eq (And (element a a_1) (Not (element a a))) False) % 3.46/3.64 Clause #10 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 1 a_1 a_2)) False) (Eq (And (element a a_1) (Not (element a a))) True) % 3.46/3.64 Clause #11 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 3.46/3.64 Or (Eq (element a (skS.0 1 a_1 a_2)) True) (Or (Eq (element a a_1) False) (Eq (Not (element a a)) False)) % 3.46/3.64 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 1 a_1 a_2)) True) (Or (Eq (element a a_1) False) (Eq (element a a) True)) % 3.46/3.64 Clause #13 (by superposition #[12, 5]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 1 (skS.0 0 a_1) a_2)) True) (Or (Eq (element a a) True) (Eq False True)) % 3.46/3.64 Clause #14 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 1 a_1 a_2)) False) (Eq (Not (element a a)) True) % 3.46/3.64 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 1 a_1 a_2)) False) (Eq (element a a) False) % 3.46/3.64 Clause #17 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 1 (skS.0 0 a_1) a_2)) True) (Eq (element a a) True) % 3.46/3.64 Clause #21 (by superposition #[17, 16]): ∀ (a a_1 a_2 a_3 : Iota), % 3.46/3.64 Or (Eq (element (skS.0 1 a a_1) (skS.0 1 (skS.0 0 a_2) a_3)) True) (Or (Eq True False) (Eq True False)) % 3.46/3.64 Clause #26 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (element (skS.0 1 a a_1) (skS.0 1 (skS.0 0 a_2) a_3)) True) (Eq True False) % 3.46/3.64 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 a_3 : Iota), Eq (element (skS.0 1 a a_1) (skS.0 1 (skS.0 0 a_2) a_3)) True % 3.46/3.64 Clause #28 (by superposition #[27, 16]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (element (skS.0 1 a a_1) (skS.0 1 a a_1)) False) % 3.46/3.64 Clause #32 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (element (skS.0 1 a a_1) (skS.0 1 a a_1)) False % 3.46/3.64 Clause #33 (by superposition #[32, 27]): Eq False True % 3.46/3.64 Clause #35 (by clausification #[33]): False % 3.46/3.64 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------