%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU738^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n029.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 08:02:20 PM UTC 2025 % Result : Theorem 4.37s 4.52s % Output : Proof 4.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU738^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.13 % Command : duper %s % 0.13/0.35 % Computer : n029.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 : Fri Oct 3 04:51:08 EDT 2025 % 0.13/0.35 % CPUTime : % 4.37/4.52 SZS status Theorem for theBenchmark.p % 4.37/4.52 SZS output start Proof for theBenchmark.p % 4.37/4.52 Clause #0 (by assumption #[]): Eq (Eq binunionIL (∀ (A B Xx : Iota), in Xx A → in Xx (binunion A B))) True % 4.37/4.52 Clause #1 (by assumption #[]): Eq % 4.37/4.52 (Not % 4.37/4.52 (binunionIL → % 4.37/4.52 ∀ (A X : Iota), % 4.37/4.52 in X (powerset A) → % 4.37/4.52 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx (binunion X Y)) → Not (in Xx X))) % 4.37/4.52 True % 4.37/4.52 Clause #2 (by clausification #[0]): Eq binunionIL (∀ (A B Xx : Iota), in Xx A → in Xx (binunion A B)) % 4.37/4.52 Clause #18 (by clausification #[1]): Eq % 4.37/4.52 (binunionIL → % 4.37/4.52 ∀ (A X : Iota), % 4.37/4.52 in X (powerset A) → % 4.37/4.52 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx (binunion X Y)) → Not (in Xx X)) % 4.37/4.52 False % 4.37/4.52 Clause #19 (by clausification #[18]): Eq binunionIL True % 4.37/4.52 Clause #20 (by clausification #[18]): Eq % 4.37/4.52 (∀ (A X : Iota), % 4.37/4.52 in X (powerset A) → % 4.37/4.52 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx (binunion X Y)) → Not (in Xx X)) % 4.37/4.52 False % 4.37/4.52 Clause #21 (by backward demodulation #[19, 2]): Eq True (∀ (A B Xx : Iota), in Xx A → in Xx (binunion A B)) % 4.37/4.52 Clause #25 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx a → in Xx (binunion a B)) True % 4.37/4.52 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx a → in Xx (binunion a a_1)) True % 4.37/4.52 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → in a (binunion a_1 a_2)) True % 4.37/4.52 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (in a (binunion a_1 a_2)) True) % 4.37/4.52 Clause #29 (by clausification #[20]): ∀ (a : Iota), % 4.37/4.52 Eq % 4.37/4.52 (Not % 4.37/4.52 (∀ (X : Iota), % 4.37/4.52 in X (powerset (skS.0 3 a)) → % 4.37/4.52 ∀ (Y : Iota), % 4.37/4.52 in Y (powerset (skS.0 3 a)) → % 4.37/4.52 ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx (binunion X Y)) → Not (in Xx X))) % 4.37/4.52 True % 4.37/4.52 Clause #30 (by clausification #[29]): ∀ (a : Iota), % 4.37/4.52 Eq % 4.37/4.52 (∀ (X : Iota), % 4.37/4.52 in X (powerset (skS.0 3 a)) → % 4.37/4.52 ∀ (Y : Iota), % 4.37/4.52 in Y (powerset (skS.0 3 a)) → ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx (binunion X Y)) → Not (in Xx X)) % 4.37/4.52 False % 4.37/4.52 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), % 4.37/4.52 Eq % 4.37/4.52 (Not % 4.37/4.52 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) → % 4.37/4.52 ∀ (Y : Iota), % 4.37/4.52 in Y (powerset (skS.0 3 a)) → % 4.37/4.52 ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx (binunion (skS.0 4 a a_1) Y)) → Not (in Xx (skS.0 4 a a_1)))) % 4.37/4.52 True % 4.37/4.52 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), % 4.37/4.52 Eq % 4.37/4.52 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) → % 4.37/4.52 ∀ (Y : Iota), % 4.37/4.52 in Y (powerset (skS.0 3 a)) → % 4.37/4.52 ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx (binunion (skS.0 4 a a_1) Y)) → Not (in Xx (skS.0 4 a a_1))) % 4.37/4.52 False % 4.37/4.52 Clause #34 (by clausification #[32]): ∀ (a a_1 : Iota), % 4.37/4.52 Eq % 4.37/4.52 (∀ (Y : Iota), % 4.37/4.52 in Y (powerset (skS.0 3 a)) → % 4.37/4.52 ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx (binunion (skS.0 4 a a_1) Y)) → Not (in Xx (skS.0 4 a a_1))) % 4.37/4.52 False % 4.37/4.52 Clause #36 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), % 4.37/4.52 Eq % 4.37/4.52 (Not % 4.37/4.52 (in (skS.0 5 a a_1 a_2) (powerset (skS.0 3 a)) → % 4.37/4.52 ∀ (Xx : Iota), % 4.37/4.52 in Xx (skS.0 3 a) → Not (in Xx (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) → Not (in Xx (skS.0 4 a a_1)))) % 4.37/4.52 True % 4.37/4.52 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), % 4.37/4.52 Eq % 4.37/4.52 (in (skS.0 5 a a_1 a_2) (powerset (skS.0 3 a)) → % 4.37/4.52 ∀ (Xx : Iota), % 4.37/4.52 in Xx (skS.0 3 a) → Not (in Xx (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) → Not (in Xx (skS.0 4 a a_1))) % 4.37/4.52 False % 4.37/4.52 Clause #39 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), % 4.37/4.52 Eq % 4.37/4.52 (∀ (Xx : Iota), % 4.37/4.52 in Xx (skS.0 3 a) → Not (in Xx (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) → Not (in Xx (skS.0 4 a a_1))) % 4.37/4.52 False % 4.37/4.52 Clause #41 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : Iota), % 4.37/4.52 Eq % 4.37/4.52 (Not % 4.37/4.52 (in (skS.0 6 a a_1 a_2 a_3) (skS.0 3 a) → % 4.37/4.52 Not (in (skS.0 6 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) → % 4.37/4.53 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1)))) % 4.37/4.53 True % 4.37/4.53 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : Iota), % 4.37/4.53 Eq % 4.37/4.53 (in (skS.0 6 a a_1 a_2 a_3) (skS.0 3 a) → % 4.37/4.53 Not (in (skS.0 6 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) → % 4.37/4.53 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1))) % 4.37/4.53 False % 4.37/4.53 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), % 4.37/4.53 Eq % 4.37/4.53 (Not (in (skS.0 6 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) → % 4.37/4.53 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1))) % 4.37/4.53 False % 4.37/4.53 Clause #54 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Not (in (skS.0 6 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))) True % 4.37/4.53 Clause #55 (by clausification #[44]): ∀ (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 % 4.37/4.53 Clause #56 (by clausification #[54]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 6 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) False % 4.37/4.53 Clause #59 (by clausification #[55]): ∀ (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 % 4.37/4.53 Clause #60 (by superposition #[59, 28]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq True False) (Eq (in (skS.0 6 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) a_4)) True) % 4.37/4.53 Clause #65 (by clausification #[60]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (in (skS.0 6 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) a_4)) True % 4.37/4.53 Clause #66 (by superposition #[65, 56]): Eq True False % 4.37/4.53 Clause #68 (by clausification #[66]): False % 4.37/4.53 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------