%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU721^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.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 08:02:17 PM UTC 2025 % Result : Theorem 3.77s 3.96s % Output : Proof 3.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU721^2 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.13 % Command : duper %s % 0.12/0.34 % Computer : n010.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 04:47:53 EDT 2025 % 0.12/0.34 % CPUTime : % 3.77/3.96 SZS status Theorem for theBenchmark.p % 3.77/3.96 SZS output start Proof for theBenchmark.p % 3.77/3.96 Clause #0 (by assumption #[]): Eq (Eq binintersectEL (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx A)) True % 3.77/3.96 Clause #1 (by assumption #[]): Eq % 3.77/3.96 (Not % 3.77/3.96 (binintersectEL → % 3.77/3.96 ∀ (A X : Iota), % 3.77/3.96 in X (powerset A) → % 3.77/3.96 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx X) → Not (in Xx (binintersect X Y)))) % 3.77/3.96 True % 3.77/3.96 Clause #2 (by clausification #[0]): Eq binintersectEL (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx A) % 3.77/3.96 Clause #18 (by clausification #[1]): Eq % 3.77/3.96 (binintersectEL → % 3.77/3.96 ∀ (A X : Iota), % 3.77/3.96 in X (powerset A) → % 3.77/3.96 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx X) → Not (in Xx (binintersect X Y))) % 3.77/3.96 False % 3.77/3.96 Clause #19 (by clausification #[18]): Eq binintersectEL True % 3.77/3.96 Clause #20 (by clausification #[18]): Eq % 3.77/3.96 (∀ (A X : Iota), % 3.77/3.96 in X (powerset A) → % 3.77/3.96 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx X) → Not (in Xx (binintersect X Y))) % 3.77/3.96 False % 3.77/3.96 Clause #21 (by backward demodulation #[19, 2]): Eq True (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx A) % 3.77/3.96 Clause #25 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (binintersect a B) → in Xx a) True % 3.77/3.96 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (binintersect a a_1) → in Xx a) True % 3.77/3.96 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Eq (in a (binintersect a_1 a_2) → in a a_1) True % 3.77/3.96 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (binintersect a_1 a_2)) False) (Eq (in a a_1) True) % 3.77/3.96 Clause #29 (by clausification #[20]): ∀ (a : Iota), % 3.77/3.96 Eq % 3.77/3.96 (Not % 3.77/3.96 (∀ (X : Iota), % 3.77/3.96 in X (powerset (skS.0 3 a)) → % 3.77/3.96 ∀ (Y : Iota), % 3.77/3.96 in Y (powerset (skS.0 3 a)) → % 3.77/3.96 ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx X) → Not (in Xx (binintersect X Y)))) % 3.77/3.96 True % 3.77/3.96 Clause #30 (by clausification #[29]): ∀ (a : Iota), % 3.77/3.96 Eq % 3.77/3.96 (∀ (X : Iota), % 3.77/3.96 in X (powerset (skS.0 3 a)) → % 3.77/3.96 ∀ (Y : Iota), % 3.77/3.96 in Y (powerset (skS.0 3 a)) → % 3.77/3.96 ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx X) → Not (in Xx (binintersect X Y))) % 3.77/3.96 False % 3.77/3.96 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), % 3.77/3.96 Eq % 3.77/3.96 (Not % 3.77/3.96 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) → % 3.77/3.96 ∀ (Y : Iota), % 3.77/3.96 in Y (powerset (skS.0 3 a)) → % 3.77/3.96 ∀ (Xx : Iota), % 3.77/3.96 in Xx (skS.0 3 a) → Not (in Xx (skS.0 4 a a_1)) → Not (in Xx (binintersect (skS.0 4 a a_1) Y)))) % 3.77/3.96 True % 3.77/3.96 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), % 3.77/3.96 Eq % 3.77/3.96 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) → % 3.77/3.96 ∀ (Y : Iota), % 3.77/3.96 in Y (powerset (skS.0 3 a)) → % 3.77/3.96 ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx (skS.0 4 a a_1)) → Not (in Xx (binintersect (skS.0 4 a a_1) Y))) % 3.77/3.96 False % 3.77/3.96 Clause #34 (by clausification #[32]): ∀ (a a_1 : Iota), % 3.77/3.96 Eq % 3.77/3.96 (∀ (Y : Iota), % 3.77/3.96 in Y (powerset (skS.0 3 a)) → % 3.77/3.96 ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx (skS.0 4 a a_1)) → Not (in Xx (binintersect (skS.0 4 a a_1) Y))) % 3.77/3.96 False % 3.77/3.96 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), % 3.77/3.96 Eq % 3.77/3.96 (Not % 3.77/3.96 (in (skS.0 5 a a_1 a_2) (powerset (skS.0 3 a)) → % 3.77/3.96 ∀ (Xx : Iota), % 3.77/3.96 in Xx (skS.0 3 a) → % 3.77/3.96 Not (in Xx (skS.0 4 a a_1)) → Not (in Xx (binintersect (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))))) % 3.77/3.96 True % 3.77/3.96 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), % 3.77/3.96 Eq % 3.77/3.96 (in (skS.0 5 a a_1 a_2) (powerset (skS.0 3 a)) → % 3.77/3.96 ∀ (Xx : Iota), % 3.77/3.96 in Xx (skS.0 3 a) → % 3.77/3.96 Not (in Xx (skS.0 4 a a_1)) → Not (in Xx (binintersect (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))) % 3.77/3.96 False % 3.77/3.96 Clause #38 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), % 3.77/3.96 Eq % 3.77/3.96 (∀ (Xx : Iota), % 3.77/3.96 in Xx (skS.0 3 a) → Not (in Xx (skS.0 4 a a_1)) → Not (in Xx (binintersect (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))) % 3.77/3.96 False % 3.77/3.96 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/3.97 Eq % 3.77/3.97 (Not % 3.77/3.97 (in (skS.0 6 a a_1 a_2 a_3) (skS.0 3 a) → % 3.77/3.97 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1)) → % 3.77/3.97 Not (in (skS.0 6 a a_1 a_2 a_3) (binintersect (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))))) % 3.77/3.97 True % 3.77/3.97 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/3.97 Eq % 3.77/3.97 (in (skS.0 6 a a_1 a_2 a_3) (skS.0 3 a) → % 3.77/3.97 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1)) → % 3.77/3.97 Not (in (skS.0 6 a a_1 a_2 a_3) (binintersect (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))) % 3.77/3.97 False % 3.77/3.97 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/3.97 Eq % 3.77/3.97 (Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1)) → % 3.77/3.97 Not (in (skS.0 6 a a_1 a_2 a_3) (binintersect (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))) % 3.77/3.97 False % 3.77/3.97 Clause #43 (by clausification #[42]): ∀ (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 % 3.77/3.97 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Not (in (skS.0 6 a a_1 a_2 a_3) (binintersect (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))) False % 3.77/3.97 Clause #45 (by clausification #[43]): ∀ (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 % 3.77/3.97 Clause #46 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 6 a a_1 a_2 a_3) (binintersect (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) True % 3.77/3.97 Clause #47 (by superposition #[46, 28]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (in (skS.0 6 a a_1 a_2 a_3) (skS.0 4 a a_1)) True) % 3.77/3.97 Clause #48 (by clausification #[47]): ∀ (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 % 3.77/3.97 Clause #49 (by superposition #[48, 45]): Eq True False % 3.77/3.97 Clause #50 (by clausification #[49]): False % 3.77/3.97 SZS output end Proof for theBenchmark.p 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