%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU722^2 : 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 08:02:17 PM UTC 2025 % Result : Theorem 3.69s 3.89s % Output : Proof 3.69s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SEU722^2 : TPTP v9.2.0. Released v3.7.0. % 0.10/0.13 % Command : duper %s % 0.14/0.34 % Computer : n029.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 06:31:08 EDT 2025 % 0.14/0.34 % CPUTime : % 3.69/3.89 SZS status Theorem for theBenchmark.p % 3.69/3.89 SZS output start Proof for theBenchmark.p % 3.69/3.89 Clause #0 (by assumption #[]): Eq (Eq binintersectER (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx B)) True % 3.69/3.89 Clause #1 (by assumption #[]): Eq % 3.69/3.89 (Not % 3.69/3.89 (binintersectER → % 3.69/3.89 ∀ (A X : Iota), % 3.69/3.89 in X (powerset A) → % 3.69/3.89 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx Y) → Not (in Xx (binintersect X Y)))) % 3.69/3.89 True % 3.69/3.89 Clause #2 (by clausification #[0]): Eq binintersectER (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx B) % 3.69/3.89 Clause #18 (by clausification #[1]): Eq % 3.69/3.89 (binintersectER → % 3.69/3.89 ∀ (A X : Iota), % 3.69/3.89 in X (powerset A) → % 3.69/3.89 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx Y) → Not (in Xx (binintersect X Y))) % 3.69/3.89 False % 3.69/3.89 Clause #19 (by clausification #[18]): Eq binintersectER True % 3.69/3.89 Clause #20 (by clausification #[18]): Eq % 3.69/3.89 (∀ (A X : Iota), % 3.69/3.89 in X (powerset A) → % 3.69/3.89 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx Y) → Not (in Xx (binintersect X Y))) % 3.69/3.89 False % 3.69/3.89 Clause #21 (by backward demodulation #[19, 2]): Eq True (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx B) % 3.69/3.89 Clause #25 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (binintersect a B) → in Xx B) True % 3.69/3.89 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (binintersect a a_1) → in Xx a_1) True % 3.69/3.89 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Eq (in a (binintersect a_1 a_2) → in a a_2) True % 3.69/3.89 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_2) True) % 3.69/3.89 Clause #29 (by clausification #[20]): ∀ (a : Iota), % 3.69/3.89 Eq % 3.69/3.89 (Not % 3.69/3.89 (∀ (X : Iota), % 3.69/3.89 in X (powerset (skS.0 3 a)) → % 3.69/3.89 ∀ (Y : Iota), % 3.69/3.89 in Y (powerset (skS.0 3 a)) → % 3.69/3.89 ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx Y) → Not (in Xx (binintersect X Y)))) % 3.69/3.89 True % 3.69/3.89 Clause #30 (by clausification #[29]): ∀ (a : Iota), % 3.69/3.89 Eq % 3.69/3.89 (∀ (X : Iota), % 3.69/3.89 in X (powerset (skS.0 3 a)) → % 3.69/3.89 ∀ (Y : Iota), % 3.69/3.89 in Y (powerset (skS.0 3 a)) → % 3.69/3.89 ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx Y) → Not (in Xx (binintersect X Y))) % 3.69/3.89 False % 3.69/3.89 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), % 3.69/3.89 Eq % 3.69/3.89 (Not % 3.69/3.89 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) → % 3.69/3.89 ∀ (Y : Iota), % 3.69/3.89 in Y (powerset (skS.0 3 a)) → % 3.69/3.89 ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx Y) → Not (in Xx (binintersect (skS.0 4 a a_1) Y)))) % 3.69/3.89 True % 3.69/3.89 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), % 3.69/3.89 Eq % 3.69/3.89 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) → % 3.69/3.89 ∀ (Y : Iota), % 3.69/3.89 in Y (powerset (skS.0 3 a)) → % 3.69/3.89 ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx Y) → Not (in Xx (binintersect (skS.0 4 a a_1) Y))) % 3.69/3.89 False % 3.69/3.89 Clause #34 (by clausification #[32]): ∀ (a a_1 : Iota), % 3.69/3.89 Eq % 3.69/3.89 (∀ (Y : Iota), % 3.69/3.89 in Y (powerset (skS.0 3 a)) → % 3.69/3.89 ∀ (Xx : Iota), in Xx (skS.0 3 a) → Not (in Xx Y) → Not (in Xx (binintersect (skS.0 4 a a_1) Y))) % 3.69/3.89 False % 3.69/3.89 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), % 3.69/3.89 Eq % 3.69/3.89 (Not % 3.69/3.89 (in (skS.0 5 a a_1 a_2) (powerset (skS.0 3 a)) → % 3.69/3.89 ∀ (Xx : Iota), % 3.69/3.89 in Xx (skS.0 3 a) → % 3.69/3.89 Not (in Xx (skS.0 5 a a_1 a_2)) → Not (in Xx (binintersect (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))))) % 3.69/3.89 True % 3.69/3.89 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), % 3.69/3.89 Eq % 3.69/3.89 (in (skS.0 5 a a_1 a_2) (powerset (skS.0 3 a)) → % 3.69/3.89 ∀ (Xx : Iota), % 3.69/3.89 in Xx (skS.0 3 a) → % 3.69/3.89 Not (in Xx (skS.0 5 a a_1 a_2)) → Not (in Xx (binintersect (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))) % 3.69/3.89 False % 3.69/3.89 Clause #38 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), % 3.69/3.89 Eq % 3.69/3.89 (∀ (Xx : Iota), % 3.69/3.89 in Xx (skS.0 3 a) → % 3.69/3.89 Not (in Xx (skS.0 5 a a_1 a_2)) → Not (in Xx (binintersect (skS.0 4 a a_1) (skS.0 5 a a_1 a_2)))) % 3.69/3.89 False % 3.69/3.89 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 a_3 : Iota), % 3.69/3.89 Eq % 3.69/3.89 (Not % 3.69/3.89 (in (skS.0 6 a a_1 a_2 a_3) (skS.0 3 a) → % 3.69/3.90 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) → % 3.69/3.90 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))))) % 3.69/3.90 True % 3.69/3.90 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : Iota), % 3.69/3.90 Eq % 3.69/3.90 (in (skS.0 6 a a_1 a_2 a_3) (skS.0 3 a) → % 3.69/3.90 Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) → % 3.69/3.90 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)))) % 3.69/3.90 False % 3.69/3.90 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota), % 3.69/3.90 Eq % 3.69/3.90 (Not (in (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2)) → % 3.69/3.90 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)))) % 3.69/3.90 False % 3.69/3.90 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 5 a a_1 a_2))) True % 3.69/3.90 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 % 3.69/3.90 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 5 a a_1 a_2)) False % 3.69/3.90 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 % 3.69/3.90 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 5 a a_1 a_2)) True) % 3.69/3.90 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 5 a a_1 a_2)) True % 3.69/3.90 Clause #49 (by superposition #[48, 45]): Eq True False % 3.69/3.90 Clause #50 (by clausification #[49]): False % 3.69/3.90 SZS output end Proof for theBenchmark.p 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