%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU724^2 : TPTP v9.2.0. Released v3.7.0. % 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 08:02:18 PM UTC 2025 % Result : Theorem 3.56s 3.75s % Output : Proof 3.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SEU724^2 : TPTP v9.2.0. Released v3.7.0. % 0.08/0.13 % 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 : Fri Oct 3 04:57:53 EDT 2025 % 0.14/0.34 % CPUTime : % 3.56/3.75 SZS status Theorem for theBenchmark.p % 3.56/3.75 SZS output start Proof for theBenchmark.p % 3.56/3.75 Clause #0 (by assumption #[]): Eq (Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)) True % 3.56/3.75 Clause #1 (by assumption #[]): Eq % 3.56/3.75 (Not % 3.56/3.75 (subsetE → % 3.56/3.75 ∀ (A X : Iota), % 3.56/3.75 in X (powerset A) → % 3.56/3.75 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → subset X Y → Not (in Xx Y) → Not (in Xx X))) % 3.56/3.75 True % 3.56/3.75 Clause #2 (by clausification #[0]): Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) % 3.56/3.75 Clause #19 (by clausification #[1]): Eq % 3.56/3.75 (subsetE → % 3.56/3.75 ∀ (A X : Iota), % 3.56/3.75 in X (powerset A) → % 3.56/3.75 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → subset X Y → Not (in Xx Y) → Not (in Xx X)) % 3.56/3.75 False % 3.56/3.75 Clause #20 (by clausification #[19]): Eq subsetE True % 3.56/3.75 Clause #21 (by clausification #[19]): Eq % 3.56/3.75 (∀ (A X : Iota), % 3.56/3.75 in X (powerset A) → % 3.56/3.75 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → subset X Y → Not (in Xx Y) → Not (in Xx X)) % 3.56/3.75 False % 3.56/3.75 Clause #22 (by backward demodulation #[20, 2]): Eq True (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) % 3.56/3.75 Clause #28 (by clausification #[22]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), subset a B → in Xx a → in Xx B) True % 3.56/3.75 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), subset a a_1 → in Xx a → in Xx a_1) True % 3.56/3.75 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Eq (subset a a_1 → in a_2 a → in a_2 a_1) True % 3.56/3.75 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True) % 3.56/3.75 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 a_1) True)) % 3.56/3.75 Clause #33 (by clausification #[21]): ∀ (a : Iota), % 3.56/3.75 Eq % 3.56/3.75 (Not % 3.56/3.75 (∀ (X : Iota), % 3.56/3.75 in X (powerset (skS.0 3 a)) → % 3.56/3.75 ∀ (Y : Iota), % 3.56/3.75 in Y (powerset (skS.0 3 a)) → % 3.56/3.75 ∀ (Xx : Iota), in Xx (skS.0 3 a) → subset X Y → Not (in Xx Y) → Not (in Xx X))) % 3.56/3.75 True % 3.56/3.75 Clause #34 (by clausification #[33]): ∀ (a : Iota), % 3.56/3.75 Eq % 3.56/3.75 (∀ (X : Iota), % 3.56/3.75 in X (powerset (skS.0 3 a)) → % 3.56/3.75 ∀ (Y : Iota), % 3.56/3.75 in Y (powerset (skS.0 3 a)) → ∀ (Xx : Iota), in Xx (skS.0 3 a) → subset X Y → Not (in Xx Y) → Not (in Xx X)) % 3.56/3.75 False % 3.56/3.75 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), % 3.56/3.75 Eq % 3.56/3.75 (Not % 3.56/3.75 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) → % 3.56/3.75 ∀ (Y : Iota), % 3.56/3.75 in Y (powerset (skS.0 3 a)) → % 3.56/3.75 ∀ (Xx : Iota), in Xx (skS.0 3 a) → subset (skS.0 4 a a_1) Y → Not (in Xx Y) → Not (in Xx (skS.0 4 a a_1)))) % 3.56/3.75 True % 3.56/3.75 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), % 3.56/3.75 Eq % 3.56/3.75 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) → % 3.56/3.75 ∀ (Y : Iota), % 3.56/3.75 in Y (powerset (skS.0 3 a)) → % 3.56/3.75 ∀ (Xx : Iota), in Xx (skS.0 3 a) → subset (skS.0 4 a a_1) Y → Not (in Xx Y) → Not (in Xx (skS.0 4 a a_1))) % 3.56/3.75 False % 3.56/3.75 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota), % 3.56/3.75 Eq % 3.56/3.75 (∀ (Y : Iota), % 3.56/3.75 in Y (powerset (skS.0 3 a)) → % 3.56/3.75 ∀ (Xx : Iota), in Xx (skS.0 3 a) → subset (skS.0 4 a a_1) Y → Not (in Xx Y) → Not (in Xx (skS.0 4 a a_1))) % 3.56/3.75 False % 3.56/3.75 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), % 3.56/3.75 Eq % 3.56/3.75 (Not % 3.56/3.75 (in (skS.0 5 a a_1 a_2) (powerset (skS.0 3 a)) → % 3.56/3.75 ∀ (Xx : Iota), % 3.56/3.75 in Xx (skS.0 3 a) → % 3.56/3.75 subset (skS.0 4 a a_1) (skS.0 5 a a_1 a_2) → Not (in Xx (skS.0 5 a a_1 a_2)) → Not (in Xx (skS.0 4 a a_1)))) % 3.56/3.75 True % 3.56/3.75 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), % 3.56/3.75 Eq % 3.56/3.75 (in (skS.0 5 a a_1 a_2) (powerset (skS.0 3 a)) → % 3.56/3.75 ∀ (Xx : Iota), % 3.56/3.75 in Xx (skS.0 3 a) → % 3.56/3.75 subset (skS.0 4 a a_1) (skS.0 5 a a_1 a_2) → Not (in Xx (skS.0 5 a a_1 a_2)) → Not (in Xx (skS.0 4 a a_1))) % 3.56/3.75 False % 3.56/3.75 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 3.56/3.75 Eq % 3.56/3.75 (∀ (Xx : Iota), % 3.56/3.75 in Xx (skS.0 3 a) → % 3.56/3.75 subset (skS.0 4 a a_1) (skS.0 5 a a_1 a_2) → Not (in Xx (skS.0 5 a a_1 a_2)) → Not (in Xx (skS.0 4 a a_1))) % 3.56/3.76 False % 3.56/3.76 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), % 3.56/3.76 Eq % 3.56/3.76 (Not % 3.56/3.76 (in (skS.0 6 a a_1 a_2 a_3) (skS.0 3 a) → % 3.56/3.76 subset (skS.0 4 a a_1) (skS.0 5 a a_1 a_2) → % 3.56/3.76 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) → Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1)))) % 3.56/3.76 True % 3.56/3.76 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), % 3.56/3.76 Eq % 3.56/3.76 (in (skS.0 6 a a_1 a_2 a_3) (skS.0 3 a) → % 3.56/3.76 subset (skS.0 4 a a_1) (skS.0 5 a a_1 a_2) → % 3.56/3.76 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) → Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1))) % 3.56/3.76 False % 3.56/3.76 Clause #46 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), % 3.56/3.76 Eq % 3.56/3.76 (subset (skS.0 4 a a_1) (skS.0 5 a a_1 a_2) → % 3.56/3.76 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) → Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1))) % 3.56/3.76 False % 3.56/3.76 Clause #48 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)) True % 3.56/3.76 Clause #49 (by clausification #[46]): ∀ (a a_1 a_2 a_3 : Iota), % 3.56/3.76 Eq (Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) → Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1))) False % 3.56/3.76 Clause #50 (by superposition #[48, 32]): ∀ (a a_1 a_2 a_3 : Iota), % 3.56/3.76 Or (Eq True False) (Or (Eq (in a (skS.0 4 a_1 a_2)) False) (Eq (in a (skS.0 5 a_1 a_2 a_3)) True)) % 3.56/3.76 Clause #51 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2))) True % 3.56/3.76 Clause #52 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1))) False % 3.56/3.76 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) False % 3.56/3.76 Clause #54 (by clausification #[52]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1)) True % 3.56/3.76 Clause #55 (by clausification #[50]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a (skS.0 4 a_1 a_2)) False) (Eq (in a (skS.0 5 a_1 a_2 a_3)) True) % 3.56/3.76 Clause #56 (by superposition #[55, 54]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_4)) True) (Eq False True) % 3.56/3.76 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_4)) True % 3.56/3.76 Clause #58 (by superposition #[57, 53]): Eq True False % 3.56/3.76 Clause #59 (by clausification #[58]): False % 3.56/3.76 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------