%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU758^2 : 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 08:02:23 PM UTC 2025 % Result : Theorem 3.79s 4.00s % Output : Proof 3.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU758^2 : TPTP v9.2.0. Released v3.7.0. % 0.12/0.13 % Command : duper %s % 0.13/0.34 % Computer : n013.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 06:40:53 EDT 2025 % 0.13/0.34 % CPUTime : % 3.79/4.00 SZS status Theorem for theBenchmark.p % 3.79/4.00 SZS output start Proof for theBenchmark.p % 3.79/4.00 Clause #0 (by assumption #[]): Eq (Eq powersetE (∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A)) True % 3.79/4.00 Clause #1 (by assumption #[]): Eq (Eq binintersectEL (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx A)) True % 3.79/4.00 Clause #2 (by assumption #[]): Eq % 3.79/4.00 (Not % 3.79/4.00 (powersetE → % 3.79/4.00 binintersectEL → % 3.79/4.00 ∀ (A X : Iota), % 3.79/4.00 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx (binintersect X Y) → in Xx A)) % 3.79/4.00 True % 3.79/4.00 Clause #3 (by clausification #[1]): Eq binintersectEL (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx A) % 3.79/4.00 Clause #19 (by clausification #[0]): Eq powersetE (∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A) % 3.79/4.00 Clause #23 (by clausification #[2]): Eq % 3.79/4.00 (powersetE → % 3.79/4.00 binintersectEL → % 3.79/4.00 ∀ (A X : Iota), % 3.79/4.00 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx (binintersect X Y) → in Xx A) % 3.79/4.00 False % 3.79/4.00 Clause #24 (by clausification #[23]): Eq powersetE True % 3.79/4.00 Clause #25 (by clausification #[23]): Eq % 3.79/4.00 (binintersectEL → % 3.79/4.00 ∀ (A X : Iota), % 3.79/4.00 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx (binintersect X Y) → in Xx A) % 3.79/4.00 False % 3.79/4.00 Clause #26 (by backward demodulation #[24, 19]): Eq True (∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A) % 3.79/4.00 Clause #27 (by clausification #[26]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in B (powerset a) → in Xx B → in Xx a) True % 3.79/4.00 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in a (powerset a_1) → in Xx a → in Xx a_1) True % 3.79/4.00 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Eq (in a (powerset a_1) → in a_2 a → in a_2 a_1) True % 3.79/4.00 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) False) (Eq (in a_2 a → in a_2 a_1) True) % 3.79/4.00 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 a_1) True)) % 3.79/4.00 Clause #47 (by clausification #[25]): Eq binintersectEL True % 3.79/4.00 Clause #48 (by clausification #[25]): Eq % 3.79/4.00 (∀ (A X : Iota), % 3.79/4.00 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx (binintersect X Y) → in Xx A) % 3.79/4.00 False % 3.79/4.00 Clause #49 (by backward demodulation #[47, 3]): Eq True (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx A) % 3.79/4.00 Clause #53 (by clausification #[49]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (binintersect a B) → in Xx a) True % 3.79/4.00 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (binintersect a a_1) → in Xx a) True % 3.79/4.00 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), Eq (in a (binintersect a_1 a_2) → in a a_1) True % 3.79/4.00 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (binintersect a_1 a_2)) False) (Eq (in a a_1) True) % 3.79/4.00 Clause #57 (by clausification #[48]): ∀ (a : Iota), % 3.79/4.00 Eq % 3.79/4.00 (Not % 3.79/4.00 (∀ (X : Iota), % 3.79/4.00 in X (powerset (skS.0 6 a)) → % 3.79/4.00 ∀ (Y : Iota), in Y (powerset (skS.0 6 a)) → ∀ (Xx : Iota), in Xx (binintersect X Y) → in Xx (skS.0 6 a))) % 3.79/4.00 True % 3.79/4.00 Clause #58 (by clausification #[57]): ∀ (a : Iota), % 3.79/4.00 Eq % 3.79/4.00 (∀ (X : Iota), % 3.79/4.00 in X (powerset (skS.0 6 a)) → % 3.79/4.00 ∀ (Y : Iota), in Y (powerset (skS.0 6 a)) → ∀ (Xx : Iota), in Xx (binintersect X Y) → in Xx (skS.0 6 a)) % 3.79/4.00 False % 3.79/4.00 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota), % 3.79/4.00 Eq % 3.79/4.00 (Not % 3.79/4.00 (in (skS.0 7 a a_1) (powerset (skS.0 6 a)) → % 3.79/4.00 ∀ (Y : Iota), % 3.79/4.00 in Y (powerset (skS.0 6 a)) → ∀ (Xx : Iota), in Xx (binintersect (skS.0 7 a a_1) Y) → in Xx (skS.0 6 a))) % 3.79/4.00 True % 3.79/4.00 Clause #60 (by clausification #[59]): ∀ (a a_1 : Iota), % 3.79/4.00 Eq % 3.79/4.00 (in (skS.0 7 a a_1) (powerset (skS.0 6 a)) → % 3.79/4.00 ∀ (Y : Iota), % 3.79/4.00 in Y (powerset (skS.0 6 a)) → ∀ (Xx : Iota), in Xx (binintersect (skS.0 7 a a_1) Y) → in Xx (skS.0 6 a)) % 3.79/4.00 False % 3.79/4.00 Clause #61 (by clausification #[60]): ∀ (a a_1 : Iota), Eq (in (skS.0 7 a a_1) (powerset (skS.0 6 a))) True % 3.79/4.00 Clause #62 (by clausification #[60]): ∀ (a a_1 : Iota), % 3.79/4.02 Eq % 3.79/4.02 (∀ (Y : Iota), % 3.79/4.02 in Y (powerset (skS.0 6 a)) → ∀ (Xx : Iota), in Xx (binintersect (skS.0 7 a a_1) Y) → in Xx (skS.0 6 a)) % 3.79/4.02 False % 3.79/4.02 Clause #63 (by superposition #[61, 31]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (in a (skS.0 7 a_1 a_2)) False) (Eq (in a (skS.0 6 a_1)) True)) % 3.79/4.02 Clause #64 (by clausification #[62]): ∀ (a a_1 a_2 : Iota), % 3.79/4.02 Eq % 3.79/4.02 (Not % 3.79/4.02 (in (skS.0 8 a a_1 a_2) (powerset (skS.0 6 a)) → % 3.79/4.02 ∀ (Xx : Iota), in Xx (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → in Xx (skS.0 6 a))) % 3.79/4.02 True % 3.79/4.02 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), % 3.79/4.02 Eq % 3.79/4.02 (in (skS.0 8 a a_1 a_2) (powerset (skS.0 6 a)) → % 3.79/4.02 ∀ (Xx : Iota), in Xx (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → in Xx (skS.0 6 a)) % 3.79/4.02 False % 3.79/4.02 Clause #67 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), % 3.79/4.02 Eq (∀ (Xx : Iota), in Xx (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → in Xx (skS.0 6 a)) False % 3.79/4.02 Clause #69 (by clausification #[67]): ∀ (a a_1 a_2 a_3 : Iota), % 3.79/4.02 Eq % 3.79/4.02 (Not % 3.79/4.02 (in (skS.0 9 a a_1 a_2 a_3) (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → % 3.79/4.02 in (skS.0 9 a a_1 a_2 a_3) (skS.0 6 a))) % 3.79/4.02 True % 3.79/4.02 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 a_3 : Iota), % 3.79/4.02 Eq % 3.79/4.02 (in (skS.0 9 a a_1 a_2 a_3) (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → % 3.79/4.02 in (skS.0 9 a a_1 a_2 a_3) (skS.0 6 a)) % 3.79/4.02 False % 3.79/4.02 Clause #71 (by clausification #[70]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 9 a a_1 a_2 a_3) (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2))) True % 3.79/4.02 Clause #72 (by clausification #[70]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 6 a)) False % 3.79/4.02 Clause #73 (by superposition #[71, 56]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 7 a a_1)) True) % 3.79/4.02 Clause #78 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 7 a_1 a_2)) False) (Eq (in a (skS.0 6 a_1)) True) % 3.79/4.02 Clause #80 (by clausification #[73]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 7 a a_1)) True % 3.79/4.02 Clause #81 (by superposition #[80, 78]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 6 a)) True) % 3.79/4.02 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 6 a)) True % 3.79/4.02 Clause #83 (by superposition #[82, 72]): Eq True False % 3.79/4.02 Clause #84 (by clausification #[83]): False % 3.79/4.02 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------