%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU522^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n017.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 08:01:49 PM UTC 2025 % Result : Theorem 3.62s 3.79s % Output : Proof 3.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU522^2 : TPTP v9.2.0. Released v3.7.0. % 0.06/0.13 % Command : duper %s % 0.12/0.34 % Computer : n017.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 05:38:23 EDT 2025 % 0.12/0.34 % CPUTime : % 3.62/3.79 SZS status Theorem for theBenchmark.p % 3.62/3.79 SZS output start Proof for theBenchmark.p % 3.62/3.79 Clause #0 (by assumption #[]): Eq (Eq setunionAx (∀ (A Xx : Iota), Iff (in Xx (setunion A)) (Exists fun B => And (in Xx B) (in B A)))) True % 3.62/3.79 Clause #1 (by assumption #[]): Eq (Not (setunionAx → ∀ (A Xx B : Iota), in Xx B → in B A → in Xx (setunion A))) True % 3.62/3.79 Clause #2 (by clausification #[1]): Eq (setunionAx → ∀ (A Xx B : Iota), in Xx B → in B A → in Xx (setunion A)) False % 3.62/3.79 Clause #3 (by clausification #[2]): Eq setunionAx True % 3.62/3.79 Clause #4 (by clausification #[2]): Eq (∀ (A Xx B : Iota), in Xx B → in B A → in Xx (setunion A)) False % 3.62/3.79 Clause #5 (by clausification #[4]): ∀ (a : Iota), Eq (Not (∀ (Xx B : Iota), in Xx B → in B (skS.0 0 a) → in Xx (setunion (skS.0 0 a)))) True % 3.62/3.79 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (Xx B : Iota), in Xx B → in B (skS.0 0 a) → in Xx (setunion (skS.0 0 a))) False % 3.62/3.79 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 3.62/3.79 Eq (Not (∀ (B : Iota), in (skS.0 1 a a_1) B → in B (skS.0 0 a) → in (skS.0 1 a a_1) (setunion (skS.0 0 a)))) True % 3.62/3.79 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 3.62/3.79 Eq (∀ (B : Iota), in (skS.0 1 a a_1) B → in B (skS.0 0 a) → in (skS.0 1 a a_1) (setunion (skS.0 0 a))) False % 3.62/3.79 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), % 3.62/3.79 Eq % 3.62/3.79 (Not % 3.62/3.79 (in (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) → % 3.62/3.79 in (skS.0 2 a a_1 a_2) (skS.0 0 a) → in (skS.0 1 a a_1) (setunion (skS.0 0 a)))) % 3.62/3.79 True % 3.62/3.79 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 3.62/3.79 Eq % 3.62/3.79 (in (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) → % 3.62/3.79 in (skS.0 2 a a_1 a_2) (skS.0 0 a) → in (skS.0 1 a a_1) (setunion (skS.0 0 a))) % 3.62/3.79 False % 3.62/3.79 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) True % 3.62/3.79 Clause #12 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 0 a) → in (skS.0 1 a a_1) (setunion (skS.0 0 a))) False % 3.62/3.79 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 0 a)) True % 3.62/3.79 Clause #14 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (in (skS.0 1 a a_1) (setunion (skS.0 0 a))) False % 3.62/3.79 Clause #15 (by clausification #[0]): Eq setunionAx (∀ (A Xx : Iota), Iff (in Xx (setunion A)) (Exists fun B => And (in Xx B) (in B A))) % 3.62/3.79 Clause #16 (by forward demodulation #[15, 3]): Eq True (∀ (A Xx : Iota), Iff (in Xx (setunion A)) (Exists fun B => And (in Xx B) (in B A))) % 3.62/3.79 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (Xx : Iota), Iff (in Xx (setunion a)) (Exists fun B => And (in Xx B) (in B a))) True % 3.62/3.79 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (Iff (in a (setunion a_1)) (Exists fun B => And (in a B) (in B a_1))) True % 3.62/3.79 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (in a (setunion a_1)) True) (Eq (Exists fun B => And (in a B) (in B a_1)) False) % 3.62/3.79 Clause #21 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setunion a_1)) True) (Eq (And (in a a_2) (in a_2 a_1)) False) % 3.62/3.79 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setunion a_1)) True) (Or (Eq (in a a_2) False) (Eq (in a_2 a_1) False)) % 3.62/3.79 Clause #23 (by superposition #[22, 11]): ∀ (a a_1 a_2 a_3 : Iota), % 3.62/3.79 Or (Eq (in (skS.0 1 a a_1) (setunion a_2)) True) (Or (Eq (in (skS.0 2 a a_1 a_3) a_2) False) (Eq False True)) % 3.62/3.79 Clause #29 (by clausification #[23]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in (skS.0 1 a a_1) (setunion a_2)) True) (Eq (in (skS.0 2 a a_1 a_3) a_2) False) % 3.62/3.79 Clause #30 (by superposition #[29, 13]): ∀ (a a_1 : Iota), Or (Eq (in (skS.0 1 a a_1) (setunion (skS.0 0 a))) True) (Eq False True) % 3.62/3.79 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (in (skS.0 1 a a_1) (setunion (skS.0 0 a))) True % 3.62/3.79 Clause #32 (by superposition #[31, 14]): Eq True False % 3.62/3.79 Clause #36 (by clausification #[32]): False % 3.62/3.79 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------