%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU747^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.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 08:02:21 PM UTC 2025 % Result : Theorem 4.00s 4.19s % Output : Proof 4.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU747^2 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.14 % Command : duper %s % 0.13/0.35 % Computer : n015.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 05:16:08 EDT 2025 % 0.13/0.35 % CPUTime : % 4.00/4.19 SZS status Theorem for theBenchmark.p % 4.00/4.19 SZS output start Proof for theBenchmark.p % 4.00/4.19 Clause #0 (by assumption #[]): Eq (Eq binunionE (∀ (A B Xx : Iota), in Xx (binunion A B) → Or (in Xx A) (in Xx B))) True % 4.00/4.19 Clause #1 (by assumption #[]): Eq % 4.00/4.19 (Not % 4.00/4.19 (binunionE → % 4.00/4.19 ∀ (A X : Iota), % 4.00/4.19 in X (powerset A) → % 4.00/4.19 ∀ (Y : Iota), % 4.00/4.19 in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx X) → Not (in Xx Y) → Not (in Xx (binunion X Y)))) % 4.00/4.19 True % 4.00/4.19 Clause #2 (by clausification #[0]): Eq binunionE (∀ (A B Xx : Iota), in Xx (binunion A B) → Or (in Xx A) (in Xx B)) % 4.00/4.19 Clause #19 (by clausification #[1]): Eq % 4.00/4.19 (binunionE → % 4.00/4.19 ∀ (A X : Iota), % 4.00/4.19 in X (powerset A) → % 4.00/4.19 ∀ (Y : Iota), % 4.00/4.19 in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx X) → Not (in Xx Y) → Not (in Xx (binunion X Y))) % 4.00/4.19 False % 4.00/4.19 Clause #20 (by clausification #[19]): Eq binunionE True % 4.00/4.19 Clause #21 (by clausification #[19]): Eq % 4.00/4.19 (∀ (A X : Iota), % 4.00/4.19 in X (powerset A) → % 4.00/4.19 ∀ (Y : Iota), % 4.00/4.19 in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx X) → Not (in Xx Y) → Not (in Xx (binunion X Y))) % 4.00/4.19 False % 4.00/4.19 Clause #22 (by backward demodulation #[20, 2]): Eq True (∀ (A B Xx : Iota), in Xx (binunion A B) → Or (in Xx A) (in Xx B)) % 4.00/4.19 Clause #28 (by clausification #[22]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (binunion a B) → Or (in Xx a) (in Xx B)) True % 4.00/4.19 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (binunion a a_1) → Or (in Xx a) (in Xx a_1)) True % 4.00/4.19 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Eq (in a (binunion a_1 a_2) → Or (in a a_1) (in a a_2)) True % 4.00/4.19 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (binunion a_1 a_2)) False) (Eq (Or (in a a_1) (in a a_2)) True) % 4.00/4.19 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (binunion a_1 a_2)) False) (Or (Eq (in a a_1) True) (Eq (in a a_2) True)) % 4.00/4.19 Clause #33 (by clausification #[21]): ∀ (a : Iota), % 4.00/4.19 Eq % 4.00/4.19 (Not % 4.00/4.19 (∀ (X : Iota), % 4.00/4.19 in X (powerset (skS.0 3 a)) → % 4.00/4.19 ∀ (Y : Iota), % 4.00/4.19 in Y (powerset (skS.0 3 a)) → % 4.00/4.19 ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx X) → Not (in Xx Y) → Not (in Xx (binunion X Y)))) % 4.00/4.19 True % 4.00/4.19 Clause #34 (by clausification #[33]): ∀ (a : Iota), % 4.00/4.19 Eq % 4.00/4.19 (∀ (X : Iota), % 4.00/4.19 in X (powerset (skS.0 3 a)) → % 4.00/4.19 ∀ (Y : Iota), % 4.00/4.19 in Y (powerset (skS.0 3 a)) → % 4.00/4.19 ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx X) → Not (in Xx Y) → Not (in Xx (binunion X Y))) % 4.00/4.19 False % 4.00/4.19 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), % 4.00/4.19 Eq % 4.00/4.19 (Not % 4.00/4.19 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) → % 4.00/4.19 ∀ (Y : Iota), % 4.00/4.19 in Y (powerset (skS.0 3 a)) → % 4.00/4.19 ∀ (Xx : Iota), % 4.00/4.19 in Xx (skS.0 3 a) → % 4.00/4.19 Not (in Xx (skS.0 4 a a_1)) → Not (in Xx Y) → Not (in Xx (binunion (skS.0 4 a a_1) Y)))) % 4.00/4.19 True % 4.00/4.19 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), % 4.00/4.19 Eq % 4.00/4.19 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) → % 4.00/4.19 ∀ (Y : Iota), % 4.00/4.19 in Y (powerset (skS.0 3 a)) → % 4.00/4.19 ∀ (Xx : Iota), % 4.00/4.19 in Xx (skS.0 3 a) → Not (in Xx (skS.0 4 a a_1)) → Not (in Xx Y) → Not (in Xx (binunion (skS.0 4 a a_1) Y))) % 4.00/4.19 False % 4.00/4.19 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota), % 4.00/4.19 Eq % 4.00/4.19 (∀ (Y : Iota), % 4.00/4.19 in Y (powerset (skS.0 3 a)) → % 4.00/4.19 ∀ (Xx : Iota), % 4.00/4.19 in Xx (skS.0 3 a) → Not (in Xx (skS.0 4 a a_1)) → Not (in Xx Y) → Not (in Xx (binunion (skS.0 4 a a_1) Y))) % 4.00/4.19 False % 4.00/4.19 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), % 4.00/4.19 Eq % 4.00/4.19 (Not % 4.00/4.19 (in (skS.0 5 a a_1 a_2) (powerset (skS.0 3 a)) → % 4.00/4.19 ∀ (Xx : Iota), % 4.00/4.19 in Xx (skS.0 3 a) → % 4.00/4.19 Not (in Xx (skS.0 4 a a_1)) → % 4.00/4.19 Not (in Xx (skS.0 5 a a_1 a_2)) → Not (in Xx (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))))) % 4.00/4.19 True % 4.00/4.19 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 4.00/4.19 Eq % 4.00/4.19 (in (skS.0 5 a a_1 a_2) (powerset (skS.0 3 a)) → % 4.00/4.19 ∀ (Xx : Iota), % 4.00/4.21 in Xx (skS.0 3 a) → % 4.00/4.21 Not (in Xx (skS.0 4 a a_1)) → % 4.00/4.21 Not (in Xx (skS.0 5 a a_1 a_2)) → Not (in Xx (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))) % 4.00/4.21 False % 4.00/4.21 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 4.00/4.21 Eq % 4.00/4.21 (∀ (Xx : Iota), % 4.00/4.21 in Xx (skS.0 3 a) → % 4.00/4.21 Not (in Xx (skS.0 4 a a_1)) → % 4.00/4.21 Not (in Xx (skS.0 5 a a_1 a_2)) → Not (in Xx (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))) % 4.00/4.21 False % 4.00/4.21 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), % 4.00/4.21 Eq % 4.00/4.21 (Not % 4.00/4.21 (in (skS.0 6 a a_1 a_2 a_3) (skS.0 3 a) → % 4.00/4.21 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1)) → % 4.00/4.21 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) → % 4.00/4.21 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))))) % 4.00/4.21 True % 4.00/4.21 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), % 4.00/4.21 Eq % 4.00/4.21 (in (skS.0 6 a a_1 a_2 a_3) (skS.0 3 a) → % 4.00/4.21 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1)) → % 4.00/4.21 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) → % 4.00/4.21 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)))) % 4.00/4.21 False % 4.00/4.21 Clause #47 (by clausification #[45]): ∀ (a a_1 a_2 a_3 : Iota), % 4.00/4.21 Eq % 4.00/4.21 (Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1)) → % 4.00/4.21 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) → % 4.00/4.21 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)))) % 4.00/4.21 False % 4.00/4.21 Clause #48 (by clausification #[47]): ∀ (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))) True % 4.00/4.21 Clause #49 (by clausification #[47]): ∀ (a a_1 a_2 a_3 : Iota), % 4.00/4.21 Eq % 4.00/4.21 (Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) → % 4.00/4.21 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)))) % 4.00/4.21 False % 4.00/4.21 Clause #50 (by clausification #[48]): ∀ (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)) False % 4.00/4.21 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 % 4.00/4.21 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) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))) False % 4.00/4.21 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 % 4.00/4.21 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) (binunion (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) True % 4.00/4.21 Clause #55 (by superposition #[54, 32]): ∀ (a a_1 a_2 a_3 : Iota), % 4.00/4.21 Or (Eq True False) % 4.00/4.21 (Or (Eq (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1)) True) % 4.00/4.21 (Eq (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) True)) % 4.00/4.21 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 a_3 : Iota), % 4.00/4.21 Or (Eq (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1)) True) (Eq (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) True) % 4.00/4.21 Clause #57 (by forward demodulation #[56, 50]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq False True) (Eq (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) True) % 4.00/4.21 Clause #58 (by clausification #[57]): ∀ (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)) True % 4.00/4.21 Clause #59 (by superposition #[58, 53]): Eq True False % 4.00/4.21 Clause #60 (by clausification #[59]): False % 4.00/4.21 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------