%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU741^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n028.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 5.16s 5.33s % Output : Proof 5.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SEU741^2 : TPTP v9.2.0. Released v3.7.0. % 0.10/0.13 % Command : duper %s % 0.13/0.34 % Computer : n028.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 05:07:53 EDT 2025 % 0.13/0.34 % CPUTime : % 5.16/5.33 SZS status Theorem for theBenchmark.p % 5.16/5.33 SZS output start Proof for theBenchmark.p % 5.16/5.33 Clause #0 (by assumption #[]): Eq (Eq binunionIL (∀ (A B Xx : Iota), in Xx A → in Xx (binunion A B))) True % 5.16/5.33 Clause #1 (by assumption #[]): Eq (Eq binintersectER (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx B)) True % 5.16/5.33 Clause #2 (by assumption #[]): Eq % 5.16/5.33 (Not % 5.16/5.33 (binunionIL → % 5.16/5.33 binintersectER → % 5.16/5.33 ∀ (A X : Iota), % 5.16/5.33 in X (powerset A) → % 5.16/5.33 ∀ (Y : Iota), % 5.16/5.33 in Y (powerset A) → % 5.16/5.33 ∀ (Z : Iota), % 5.16/5.33 in Z (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (binintersect X Y) → in Xx (binunion Y Z))) % 5.16/5.33 True % 5.16/5.33 Clause #3 (by clausification #[1]): Eq binintersectER (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx B) % 5.16/5.33 Clause #19 (by clausification #[0]): Eq binunionIL (∀ (A B Xx : Iota), in Xx A → in Xx (binunion A B)) % 5.16/5.33 Clause #23 (by clausification #[2]): Eq % 5.16/5.33 (binunionIL → % 5.16/5.33 binintersectER → % 5.16/5.33 ∀ (A X : Iota), % 5.16/5.33 in X (powerset A) → % 5.16/5.33 ∀ (Y : Iota), % 5.16/5.33 in Y (powerset A) → % 5.16/5.33 ∀ (Z : Iota), % 5.16/5.33 in Z (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (binintersect X Y) → in Xx (binunion Y Z)) % 5.16/5.33 False % 5.16/5.33 Clause #24 (by clausification #[23]): Eq binunionIL True % 5.16/5.33 Clause #25 (by clausification #[23]): Eq % 5.16/5.33 (binintersectER → % 5.16/5.33 ∀ (A X : Iota), % 5.16/5.33 in X (powerset A) → % 5.16/5.33 ∀ (Y : Iota), % 5.16/5.33 in Y (powerset A) → % 5.16/5.33 ∀ (Z : Iota), in Z (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (binintersect X Y) → in Xx (binunion Y Z)) % 5.16/5.33 False % 5.16/5.33 Clause #26 (by backward demodulation #[24, 19]): Eq True (∀ (A B Xx : Iota), in Xx A → in Xx (binunion A B)) % 5.16/5.33 Clause #27 (by clausification #[26]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx a → in Xx (binunion a B)) True % 5.16/5.33 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx a → in Xx (binunion a a_1)) True % 5.16/5.33 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → in a (binunion a_1 a_2)) True % 5.16/5.33 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (in a (binunion a_1 a_2)) True) % 5.16/5.33 Clause #46 (by clausification #[25]): Eq binintersectER True % 5.16/5.33 Clause #47 (by clausification #[25]): Eq % 5.16/5.33 (∀ (A X : Iota), % 5.16/5.33 in X (powerset A) → % 5.16/5.33 ∀ (Y : Iota), % 5.16/5.33 in Y (powerset A) → % 5.16/5.33 ∀ (Z : Iota), in Z (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (binintersect X Y) → in Xx (binunion Y Z)) % 5.16/5.33 False % 5.16/5.33 Clause #48 (by backward demodulation #[46, 3]): Eq True (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx B) % 5.16/5.33 Clause #52 (by clausification #[48]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (binintersect a B) → in Xx B) True % 5.16/5.33 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (binintersect a a_1) → in Xx a_1) True % 5.16/5.33 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), Eq (in a (binintersect a_1 a_2) → in a a_2) True % 5.16/5.33 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (binintersect a_1 a_2)) False) (Eq (in a a_2) True) % 5.16/5.33 Clause #56 (by clausification #[47]): ∀ (a : Iota), % 5.16/5.33 Eq % 5.16/5.33 (Not % 5.16/5.33 (∀ (X : Iota), % 5.16/5.33 in X (powerset (skS.0 6 a)) → % 5.16/5.33 ∀ (Y : Iota), % 5.16/5.33 in Y (powerset (skS.0 6 a)) → % 5.16/5.33 ∀ (Z : Iota), % 5.16/5.33 in Z (powerset (skS.0 6 a)) → % 5.16/5.33 ∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (binintersect X Y) → in Xx (binunion Y Z))) % 5.16/5.33 True % 5.16/5.33 Clause #57 (by clausification #[56]): ∀ (a : Iota), % 5.16/5.33 Eq % 5.16/5.33 (∀ (X : Iota), % 5.16/5.33 in X (powerset (skS.0 6 a)) → % 5.16/5.33 ∀ (Y : Iota), % 5.16/5.33 in Y (powerset (skS.0 6 a)) → % 5.16/5.33 ∀ (Z : Iota), % 5.16/5.33 in Z (powerset (skS.0 6 a)) → % 5.16/5.33 ∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (binintersect X Y) → in Xx (binunion Y Z)) % 5.16/5.33 False % 5.16/5.33 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota), % 5.16/5.33 Eq % 5.16/5.33 (Not % 5.16/5.33 (in (skS.0 7 a a_1) (powerset (skS.0 6 a)) → % 5.16/5.33 ∀ (Y : Iota), % 5.16/5.33 in Y (powerset (skS.0 6 a)) → % 5.16/5.36 ∀ (Z : Iota), % 5.16/5.36 in Z (powerset (skS.0 6 a)) → % 5.16/5.36 ∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (binintersect (skS.0 7 a a_1) Y) → in Xx (binunion Y Z))) % 5.16/5.36 True % 5.16/5.36 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota), % 5.16/5.36 Eq % 5.16/5.36 (in (skS.0 7 a a_1) (powerset (skS.0 6 a)) → % 5.16/5.36 ∀ (Y : Iota), % 5.16/5.36 in Y (powerset (skS.0 6 a)) → % 5.16/5.36 ∀ (Z : Iota), % 5.16/5.36 in Z (powerset (skS.0 6 a)) → % 5.16/5.36 ∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (binintersect (skS.0 7 a a_1) Y) → in Xx (binunion Y Z)) % 5.16/5.36 False % 5.16/5.36 Clause #61 (by clausification #[59]): ∀ (a a_1 : Iota), % 5.16/5.36 Eq % 5.16/5.36 (∀ (Y : Iota), % 5.16/5.36 in Y (powerset (skS.0 6 a)) → % 5.16/5.36 ∀ (Z : Iota), % 5.16/5.36 in Z (powerset (skS.0 6 a)) → % 5.16/5.36 ∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (binintersect (skS.0 7 a a_1) Y) → in Xx (binunion Y Z)) % 5.16/5.36 False % 5.16/5.36 Clause #63 (by clausification #[61]): ∀ (a a_1 a_2 : Iota), % 5.16/5.36 Eq % 5.16/5.36 (Not % 5.16/5.36 (in (skS.0 8 a a_1 a_2) (powerset (skS.0 6 a)) → % 5.16/5.36 ∀ (Z : Iota), % 5.16/5.36 in Z (powerset (skS.0 6 a)) → % 5.16/5.36 ∀ (Xx : Iota), % 5.16/5.36 in Xx (skS.0 6 a) → % 5.16/5.36 in Xx (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → in Xx (binunion (skS.0 8 a a_1 a_2) Z))) % 5.16/5.36 True % 5.16/5.36 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), % 5.16/5.36 Eq % 5.16/5.36 (in (skS.0 8 a a_1 a_2) (powerset (skS.0 6 a)) → % 5.16/5.36 ∀ (Z : Iota), % 5.16/5.36 in Z (powerset (skS.0 6 a)) → % 5.16/5.36 ∀ (Xx : Iota), % 5.16/5.36 in Xx (skS.0 6 a) → % 5.16/5.36 in Xx (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → in Xx (binunion (skS.0 8 a a_1 a_2) Z)) % 5.16/5.36 False % 5.16/5.36 Clause #66 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), % 5.16/5.36 Eq % 5.16/5.36 (∀ (Z : Iota), % 5.16/5.36 in Z (powerset (skS.0 6 a)) → % 5.16/5.36 ∀ (Xx : Iota), % 5.16/5.36 in Xx (skS.0 6 a) → % 5.16/5.36 in Xx (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → in Xx (binunion (skS.0 8 a a_1 a_2) Z)) % 5.16/5.36 False % 5.16/5.36 Clause #68 (by clausification #[66]): ∀ (a a_1 a_2 a_3 : Iota), % 5.16/5.36 Eq % 5.16/5.36 (Not % 5.16/5.36 (in (skS.0 9 a a_1 a_2 a_3) (powerset (skS.0 6 a)) → % 5.16/5.36 ∀ (Xx : Iota), % 5.16/5.36 in Xx (skS.0 6 a) → % 5.16/5.36 in Xx (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → % 5.16/5.36 in Xx (binunion (skS.0 8 a a_1 a_2) (skS.0 9 a a_1 a_2 a_3)))) % 5.16/5.36 True % 5.16/5.36 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 a_3 : Iota), % 5.16/5.36 Eq % 5.16/5.36 (in (skS.0 9 a a_1 a_2 a_3) (powerset (skS.0 6 a)) → % 5.16/5.36 ∀ (Xx : Iota), % 5.16/5.36 in Xx (skS.0 6 a) → % 5.16/5.36 in Xx (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → % 5.16/5.36 in Xx (binunion (skS.0 8 a a_1 a_2) (skS.0 9 a a_1 a_2 a_3))) % 5.16/5.36 False % 5.16/5.36 Clause #71 (by clausification #[69]): ∀ (a a_1 a_2 a_3 : Iota), % 5.16/5.36 Eq % 5.16/5.36 (∀ (Xx : Iota), % 5.16/5.36 in Xx (skS.0 6 a) → % 5.16/5.36 in Xx (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → % 5.16/5.36 in Xx (binunion (skS.0 8 a a_1 a_2) (skS.0 9 a a_1 a_2 a_3))) % 5.16/5.36 False % 5.16/5.36 Clause #100 (by clausification #[71]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.16/5.36 Eq % 5.16/5.36 (Not % 5.16/5.36 (in (skS.0 10 a a_1 a_2 a_3 a_4) (skS.0 6 a) → % 5.16/5.36 in (skS.0 10 a a_1 a_2 a_3 a_4) (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → % 5.16/5.36 in (skS.0 10 a a_1 a_2 a_3 a_4) (binunion (skS.0 8 a a_1 a_2) (skS.0 9 a a_1 a_2 a_3)))) % 5.16/5.36 True % 5.16/5.36 Clause #101 (by clausification #[100]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.16/5.36 Eq % 5.16/5.36 (in (skS.0 10 a a_1 a_2 a_3 a_4) (skS.0 6 a) → % 5.16/5.36 in (skS.0 10 a a_1 a_2 a_3 a_4) (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → % 5.16/5.36 in (skS.0 10 a a_1 a_2 a_3 a_4) (binunion (skS.0 8 a a_1 a_2) (skS.0 9 a a_1 a_2 a_3))) % 5.16/5.36 False % 5.16/5.36 Clause #103 (by clausification #[101]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.16/5.36 Eq % 5.16/5.36 (in (skS.0 10 a a_1 a_2 a_3 a_4) (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → % 5.16/5.36 in (skS.0 10 a a_1 a_2 a_3 a_4) (binunion (skS.0 8 a a_1 a_2) (skS.0 9 a a_1 a_2 a_3))) % 5.16/5.36 False % 5.16/5.36 Clause #121 (by clausification #[103]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.16/5.36 Eq (in (skS.0 10 a a_1 a_2 a_3 a_4) (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2))) True % 5.16/5.36 Clause #122 (by clausification #[103]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.16/5.36 Eq (in (skS.0 10 a a_1 a_2 a_3 a_4) (binunion (skS.0 8 a a_1 a_2) (skS.0 9 a a_1 a_2 a_3))) False % 5.16/5.36 Clause #123 (by superposition #[121, 55]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq True False) (Eq (in (skS.0 10 a a_1 a_2 a_3 a_4) (skS.0 8 a a_1 a_2)) True) % 5.16/5.36 Clause #125 (by clausification #[123]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (in (skS.0 10 a a_1 a_2 a_3 a_4) (skS.0 8 a a_1 a_2)) True % 5.16/5.36 Clause #126 (by superposition #[125, 30]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 5.16/5.36 Or (Eq True False) (Eq (in (skS.0 10 a a_1 a_2 a_3 a_4) (binunion (skS.0 8 a a_1 a_2) a_5)) True) % 5.16/5.36 Clause #127 (by clausification #[126]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Eq (in (skS.0 10 a a_1 a_2 a_3 a_4) (binunion (skS.0 8 a a_1 a_2) a_5)) True % 5.16/5.36 Clause #147 (by superposition #[122, 127]): Eq True False % 5.16/5.36 Clause #148 (by clausification #[147]): False % 5.16/5.36 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------