%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU740^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n013.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 4.83s 5.01s % Output : Proof 4.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SEU740^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.14 % Command : duper %s % 0.14/0.36 % Computer : n013.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Fri Oct 3 06:24:53 EDT 2025 % 0.14/0.36 % CPUTime : % 4.83/5.01 SZS status Theorem for theBenchmark.p % 4.83/5.01 SZS output start Proof for theBenchmark.p % 4.83/5.01 Clause #0 (by assumption #[]): Eq (Eq binunionIL (∀ (A B Xx : Iota), in Xx A → in Xx (binunion A B))) True % 4.83/5.01 Clause #1 (by assumption #[]): Eq (Eq binintersectEL (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx A)) True % 4.83/5.01 Clause #2 (by assumption #[]): Eq % 4.83/5.01 (Not % 4.83/5.01 (binunionIL → % 4.83/5.01 binintersectEL → % 4.83/5.01 ∀ (A X : Iota), % 4.83/5.01 in X (powerset A) → % 4.83/5.01 ∀ (Y : Iota), % 4.83/5.01 in Y (powerset A) → % 4.83/5.01 ∀ (Z : Iota), % 4.83/5.01 in Z (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (binintersect X Y) → in Xx (binunion X Z))) % 4.83/5.01 True % 4.83/5.01 Clause #3 (by clausification #[1]): Eq binintersectEL (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx A) % 4.83/5.01 Clause #19 (by clausification #[0]): Eq binunionIL (∀ (A B Xx : Iota), in Xx A → in Xx (binunion A B)) % 4.83/5.01 Clause #23 (by clausification #[2]): Eq % 4.83/5.01 (binunionIL → % 4.83/5.01 binintersectEL → % 4.83/5.01 ∀ (A X : Iota), % 4.83/5.01 in X (powerset A) → % 4.83/5.01 ∀ (Y : Iota), % 4.83/5.01 in Y (powerset A) → % 4.83/5.01 ∀ (Z : Iota), % 4.83/5.01 in Z (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (binintersect X Y) → in Xx (binunion X Z)) % 4.83/5.01 False % 4.83/5.01 Clause #24 (by clausification #[23]): Eq binunionIL True % 4.83/5.01 Clause #25 (by clausification #[23]): Eq % 4.83/5.01 (binintersectEL → % 4.83/5.01 ∀ (A X : Iota), % 4.83/5.01 in X (powerset A) → % 4.83/5.01 ∀ (Y : Iota), % 4.83/5.01 in Y (powerset A) → % 4.83/5.01 ∀ (Z : Iota), in Z (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (binintersect X Y) → in Xx (binunion X Z)) % 4.83/5.01 False % 4.83/5.01 Clause #26 (by backward demodulation #[24, 19]): Eq True (∀ (A B Xx : Iota), in Xx A → in Xx (binunion A B)) % 4.83/5.01 Clause #27 (by clausification #[26]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx a → in Xx (binunion a B)) True % 4.83/5.01 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx a → in Xx (binunion a a_1)) True % 4.83/5.01 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → in a (binunion a_1 a_2)) True % 4.83/5.01 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) % 4.83/5.01 Clause #46 (by clausification #[25]): Eq binintersectEL True % 4.83/5.01 Clause #47 (by clausification #[25]): Eq % 4.83/5.01 (∀ (A X : Iota), % 4.83/5.01 in X (powerset A) → % 4.83/5.01 ∀ (Y : Iota), % 4.83/5.01 in Y (powerset A) → % 4.83/5.01 ∀ (Z : Iota), in Z (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (binintersect X Y) → in Xx (binunion X Z)) % 4.83/5.01 False % 4.83/5.01 Clause #48 (by backward demodulation #[46, 3]): Eq True (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx A) % 4.83/5.01 Clause #52 (by clausification #[48]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (binintersect a B) → in Xx a) True % 4.83/5.01 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (binintersect a a_1) → in Xx a) True % 4.83/5.01 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), Eq (in a (binintersect a_1 a_2) → in a a_1) True % 4.83/5.01 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_1) True) % 4.83/5.01 Clause #56 (by clausification #[47]): ∀ (a : Iota), % 4.83/5.01 Eq % 4.83/5.01 (Not % 4.83/5.01 (∀ (X : Iota), % 4.83/5.01 in X (powerset (skS.0 6 a)) → % 4.83/5.01 ∀ (Y : Iota), % 4.83/5.01 in Y (powerset (skS.0 6 a)) → % 4.83/5.01 ∀ (Z : Iota), % 4.83/5.01 in Z (powerset (skS.0 6 a)) → % 4.83/5.01 ∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (binintersect X Y) → in Xx (binunion X Z))) % 4.83/5.01 True % 4.83/5.01 Clause #57 (by clausification #[56]): ∀ (a : Iota), % 4.83/5.01 Eq % 4.83/5.01 (∀ (X : Iota), % 4.83/5.01 in X (powerset (skS.0 6 a)) → % 4.83/5.01 ∀ (Y : Iota), % 4.83/5.01 in Y (powerset (skS.0 6 a)) → % 4.83/5.01 ∀ (Z : Iota), % 4.83/5.01 in Z (powerset (skS.0 6 a)) → % 4.83/5.01 ∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (binintersect X Y) → in Xx (binunion X Z)) % 4.83/5.01 False % 4.83/5.01 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota), % 4.83/5.01 Eq % 4.83/5.01 (Not % 4.83/5.01 (in (skS.0 7 a a_1) (powerset (skS.0 6 a)) → % 4.83/5.01 ∀ (Y : Iota), % 4.83/5.01 in Y (powerset (skS.0 6 a)) → % 4.83/5.01 ∀ (Z : Iota), % 4.83/5.04 in Z (powerset (skS.0 6 a)) → % 4.83/5.04 ∀ (Xx : Iota), % 4.83/5.04 in Xx (skS.0 6 a) → in Xx (binintersect (skS.0 7 a a_1) Y) → in Xx (binunion (skS.0 7 a a_1) Z))) % 4.83/5.04 True % 4.83/5.04 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota), % 4.83/5.04 Eq % 4.83/5.04 (in (skS.0 7 a a_1) (powerset (skS.0 6 a)) → % 4.83/5.04 ∀ (Y : Iota), % 4.83/5.04 in Y (powerset (skS.0 6 a)) → % 4.83/5.04 ∀ (Z : Iota), % 4.83/5.04 in Z (powerset (skS.0 6 a)) → % 4.83/5.04 ∀ (Xx : Iota), % 4.83/5.04 in Xx (skS.0 6 a) → in Xx (binintersect (skS.0 7 a a_1) Y) → in Xx (binunion (skS.0 7 a a_1) Z)) % 4.83/5.04 False % 4.83/5.04 Clause #61 (by clausification #[59]): ∀ (a a_1 : Iota), % 4.83/5.04 Eq % 4.83/5.04 (∀ (Y : Iota), % 4.83/5.04 in Y (powerset (skS.0 6 a)) → % 4.83/5.04 ∀ (Z : Iota), % 4.83/5.04 in Z (powerset (skS.0 6 a)) → % 4.83/5.04 ∀ (Xx : Iota), % 4.83/5.04 in Xx (skS.0 6 a) → in Xx (binintersect (skS.0 7 a a_1) Y) → in Xx (binunion (skS.0 7 a a_1) Z)) % 4.83/5.04 False % 4.83/5.04 Clause #63 (by clausification #[61]): ∀ (a a_1 a_2 : Iota), % 4.83/5.04 Eq % 4.83/5.04 (Not % 4.83/5.04 (in (skS.0 8 a a_1 a_2) (powerset (skS.0 6 a)) → % 4.83/5.04 ∀ (Z : Iota), % 4.83/5.04 in Z (powerset (skS.0 6 a)) → % 4.83/5.04 ∀ (Xx : Iota), % 4.83/5.04 in Xx (skS.0 6 a) → % 4.83/5.04 in Xx (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → in Xx (binunion (skS.0 7 a a_1) Z))) % 4.83/5.04 True % 4.83/5.04 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), % 4.83/5.04 Eq % 4.83/5.04 (in (skS.0 8 a a_1 a_2) (powerset (skS.0 6 a)) → % 4.83/5.04 ∀ (Z : Iota), % 4.83/5.04 in Z (powerset (skS.0 6 a)) → % 4.83/5.04 ∀ (Xx : Iota), % 4.83/5.04 in Xx (skS.0 6 a) → % 4.83/5.04 in Xx (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → in Xx (binunion (skS.0 7 a a_1) Z)) % 4.83/5.04 False % 4.83/5.04 Clause #66 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), % 4.83/5.04 Eq % 4.83/5.04 (∀ (Z : Iota), % 4.83/5.04 in Z (powerset (skS.0 6 a)) → % 4.83/5.04 ∀ (Xx : Iota), % 4.83/5.04 in Xx (skS.0 6 a) → % 4.83/5.04 in Xx (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → in Xx (binunion (skS.0 7 a a_1) Z)) % 4.83/5.04 False % 4.83/5.04 Clause #68 (by clausification #[66]): ∀ (a a_1 a_2 a_3 : Iota), % 4.83/5.04 Eq % 4.83/5.04 (Not % 4.83/5.04 (in (skS.0 9 a a_1 a_2 a_3) (powerset (skS.0 6 a)) → % 4.83/5.04 ∀ (Xx : Iota), % 4.83/5.04 in Xx (skS.0 6 a) → % 4.83/5.04 in Xx (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → % 4.83/5.04 in Xx (binunion (skS.0 7 a a_1) (skS.0 9 a a_1 a_2 a_3)))) % 4.83/5.04 True % 4.83/5.04 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 a_3 : Iota), % 4.83/5.04 Eq % 4.83/5.04 (in (skS.0 9 a a_1 a_2 a_3) (powerset (skS.0 6 a)) → % 4.83/5.04 ∀ (Xx : Iota), % 4.83/5.04 in Xx (skS.0 6 a) → % 4.83/5.04 in Xx (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → % 4.83/5.04 in Xx (binunion (skS.0 7 a a_1) (skS.0 9 a a_1 a_2 a_3))) % 4.83/5.04 False % 4.83/5.04 Clause #71 (by clausification #[69]): ∀ (a a_1 a_2 a_3 : Iota), % 4.83/5.04 Eq % 4.83/5.04 (∀ (Xx : Iota), % 4.83/5.04 in Xx (skS.0 6 a) → % 4.83/5.04 in Xx (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → % 4.83/5.04 in Xx (binunion (skS.0 7 a a_1) (skS.0 9 a a_1 a_2 a_3))) % 4.83/5.04 False % 4.83/5.04 Clause #88 (by clausification #[71]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.83/5.04 Eq % 4.83/5.04 (Not % 4.83/5.04 (in (skS.0 10 a a_1 a_2 a_3 a_4) (skS.0 6 a) → % 4.83/5.04 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)) → % 4.83/5.04 in (skS.0 10 a a_1 a_2 a_3 a_4) (binunion (skS.0 7 a a_1) (skS.0 9 a a_1 a_2 a_3)))) % 4.83/5.04 True % 4.83/5.04 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.83/5.04 Eq % 4.83/5.04 (in (skS.0 10 a a_1 a_2 a_3 a_4) (skS.0 6 a) → % 4.83/5.04 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)) → % 4.83/5.04 in (skS.0 10 a a_1 a_2 a_3 a_4) (binunion (skS.0 7 a a_1) (skS.0 9 a a_1 a_2 a_3))) % 4.83/5.04 False % 4.83/5.04 Clause #91 (by clausification #[89]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.83/5.04 Eq % 4.83/5.04 (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)) → % 4.83/5.04 in (skS.0 10 a a_1 a_2 a_3 a_4) (binunion (skS.0 7 a a_1) (skS.0 9 a a_1 a_2 a_3))) % 4.83/5.04 False % 4.83/5.04 Clause #109 (by clausification #[91]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.83/5.04 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 % 4.83/5.04 Clause #110 (by clausification #[91]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.83/5.04 Eq (in (skS.0 10 a a_1 a_2 a_3 a_4) (binunion (skS.0 7 a a_1) (skS.0 9 a a_1 a_2 a_3))) False % 4.83/5.04 Clause #111 (by superposition #[109, 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 7 a a_1)) True) % 4.83/5.04 Clause #113 (by clausification #[111]): ∀ (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 7 a a_1)) True % 4.83/5.04 Clause #114 (by superposition #[113, 30]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.83/5.04 Or (Eq True False) (Eq (in (skS.0 10 a a_1 a_2 a_3 a_4) (binunion (skS.0 7 a a_1) a_5)) True) % 4.83/5.04 Clause #115 (by clausification #[114]): ∀ (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 7 a a_1) a_5)) True % 4.83/5.04 Clause #135 (by superposition #[110, 115]): Eq True False % 4.83/5.04 Clause #136 (by clausification #[135]): False % 4.83/5.04 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------