%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU596^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n026.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 08:02:00 PM UTC 2025 % Result : Theorem 18.51s 18.68s % Output : Proof 18.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU596^2 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n026.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 05:25:23 EDT 2025 % 0.13/0.35 % CPUTime : % 18.51/18.68 SZS status Theorem for theBenchmark.p % 18.51/18.68 SZS output start Proof for theBenchmark.p % 18.51/18.68 Clause #0 (by assumption #[]): Eq (Eq emptyI (∀ (A : Iota), (∀ (Xx : Iota), Not (in Xx A)) → Eq A emptyset)) True % 18.51/18.68 Clause #1 (by assumption #[]): Eq (Eq binintersectEL (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx A)) True % 18.51/18.68 Clause #2 (by assumption #[]): Eq (Eq binintersectER (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx B)) True % 18.51/18.68 Clause #3 (by assumption #[]): Eq % 18.51/18.68 (Not % 18.51/18.68 (emptyI → % 18.51/18.68 binintersectEL → % 18.51/18.68 binintersectER → % 18.51/18.68 ∀ (A B : Iota), Not (Exists fun Xx => And (in Xx A) (in Xx B)) → Eq (binintersect A B) emptyset)) % 18.51/18.68 True % 18.51/18.68 Clause #4 (by clausification #[0]): Eq emptyI (∀ (A : Iota), (∀ (Xx : Iota), Not (in Xx A)) → Eq A emptyset) % 18.51/18.68 Clause #20 (by clausification #[2]): Eq binintersectER (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx B) % 18.51/18.68 Clause #24 (by clausification #[1]): Eq binintersectEL (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx A) % 18.51/18.68 Clause #52 (by clausification #[3]): Eq % 18.51/18.68 (emptyI → % 18.51/18.68 binintersectEL → % 18.51/18.68 binintersectER → ∀ (A B : Iota), Not (Exists fun Xx => And (in Xx A) (in Xx B)) → Eq (binintersect A B) emptyset) % 18.51/18.68 False % 18.51/18.68 Clause #53 (by clausification #[52]): Eq emptyI True % 18.51/18.68 Clause #54 (by clausification #[52]): Eq % 18.51/18.68 (binintersectEL → % 18.51/18.68 binintersectER → ∀ (A B : Iota), Not (Exists fun Xx => And (in Xx A) (in Xx B)) → Eq (binintersect A B) emptyset) % 18.51/18.68 False % 18.51/18.68 Clause #55 (by backward demodulation #[53, 4]): Eq True (∀ (A : Iota), (∀ (Xx : Iota), Not (in Xx A)) → Eq A emptyset) % 18.51/18.68 Clause #58 (by clausification #[55]): ∀ (a : Iota), Eq ((∀ (Xx : Iota), Not (in Xx a)) → Eq a emptyset) True % 18.51/18.68 Clause #59 (by clausification #[58]): ∀ (a : Iota), Or (Eq (∀ (Xx : Iota), Not (in Xx a)) False) (Eq (Eq a emptyset) True) % 18.51/18.68 Clause #60 (by clausification #[59]): ∀ (a a_1 : Iota), Or (Eq (Eq a emptyset) True) (Eq (Not (Not (in (skS.0 8 a a_1) a))) True) % 18.51/18.68 Clause #61 (by clausification #[60]): ∀ (a a_1 : Iota), Or (Eq (Not (Not (in (skS.0 8 a a_1) a))) True) (Eq a emptyset) % 18.51/18.68 Clause #62 (by clausification #[61]): ∀ (a a_1 : Iota), Or (Eq a emptyset) (Eq (Not (in (skS.0 8 a a_1) a)) False) % 18.51/18.68 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), Or (Eq a emptyset) (Eq (in (skS.0 8 a a_1) a) True) % 18.51/18.68 Clause #65 (by clausification #[54]): Eq binintersectEL True % 18.51/18.68 Clause #66 (by clausification #[54]): Eq (binintersectER → ∀ (A B : Iota), Not (Exists fun Xx => And (in Xx A) (in Xx B)) → Eq (binintersect A B) emptyset) % 18.51/18.68 False % 18.51/18.68 Clause #67 (by backward demodulation #[65, 24]): Eq True (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx A) % 18.51/18.68 Clause #70 (by clausification #[67]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (binintersect a B) → in Xx a) True % 18.51/18.68 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (binintersect a a_1) → in Xx a) True % 18.51/18.68 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), Eq (in a (binintersect a_1 a_2) → in a a_1) True % 18.51/18.68 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (binintersect a_1 a_2)) False) (Eq (in a a_1) True) % 18.51/18.68 Clause #75 (by superposition #[73, 63]): ∀ (a a_1 a_2 : Iota), % 18.51/18.68 Or (Eq (in (skS.0 8 (binintersect a a_1) a_2) a) True) (Or (Eq (binintersect a a_1) emptyset) (Eq False True)) % 18.51/18.68 Clause #78 (by clausification #[66]): Eq binintersectER True % 18.51/18.68 Clause #79 (by clausification #[66]): Eq (∀ (A B : Iota), Not (Exists fun Xx => And (in Xx A) (in Xx B)) → Eq (binintersect A B) emptyset) False % 18.51/18.68 Clause #80 (by backward demodulation #[78, 20]): Eq True (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx B) % 18.51/18.68 Clause #83 (by clausification #[80]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (binintersect a B) → in Xx B) True % 18.51/18.68 Clause #84 (by clausification #[83]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (binintersect a a_1) → in Xx a_1) True % 18.51/18.68 Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 : Iota), Eq (in a (binintersect a_1 a_2) → in a a_2) True % 18.51/18.68 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (binintersect a_1 a_2)) False) (Eq (in a a_2) True) % 18.58/18.77 Clause #87 (by superposition #[86, 63]): ∀ (a a_1 a_2 : Iota), % 18.58/18.77 Or (Eq (in (skS.0 8 (binintersect a a_1) a_2) a_1) True) (Or (Eq (binintersect a a_1) emptyset) (Eq False True)) % 18.58/18.77 Clause #88 (by clausification #[79]): ∀ (a : Iota), % 18.58/18.77 Eq % 18.58/18.77 (Not % 18.58/18.77 (∀ (B : Iota), % 18.58/18.77 Not (Exists fun Xx => And (in Xx (skS.0 9 a)) (in Xx B)) → Eq (binintersect (skS.0 9 a) B) emptyset)) % 18.58/18.77 True % 18.58/18.77 Clause #89 (by clausification #[88]): ∀ (a : Iota), % 18.58/18.77 Eq (∀ (B : Iota), Not (Exists fun Xx => And (in Xx (skS.0 9 a)) (in Xx B)) → Eq (binintersect (skS.0 9 a) B) emptyset) % 18.58/18.77 False % 18.58/18.77 Clause #90 (by clausification #[89]): ∀ (a a_1 : Iota), % 18.58/18.77 Eq % 18.58/18.77 (Not % 18.58/18.77 (Not (Exists fun Xx => And (in Xx (skS.0 9 a)) (in Xx (skS.0 10 a a_1))) → % 18.58/18.77 Eq (binintersect (skS.0 9 a) (skS.0 10 a a_1)) emptyset)) % 18.58/18.77 True % 18.58/18.77 Clause #91 (by clausification #[90]): ∀ (a a_1 : Iota), % 18.58/18.77 Eq % 18.58/18.77 (Not (Exists fun Xx => And (in Xx (skS.0 9 a)) (in Xx (skS.0 10 a a_1))) → % 18.58/18.77 Eq (binintersect (skS.0 9 a) (skS.0 10 a a_1)) emptyset) % 18.58/18.77 False % 18.58/18.77 Clause #92 (by clausification #[91]): ∀ (a a_1 : Iota), Eq (Not (Exists fun Xx => And (in Xx (skS.0 9 a)) (in Xx (skS.0 10 a a_1)))) True % 18.58/18.77 Clause #93 (by clausification #[91]): ∀ (a a_1 : Iota), Eq (Eq (binintersect (skS.0 9 a) (skS.0 10 a a_1)) emptyset) False % 18.58/18.77 Clause #94 (by clausification #[92]): ∀ (a a_1 : Iota), Eq (Exists fun Xx => And (in Xx (skS.0 9 a)) (in Xx (skS.0 10 a a_1))) False % 18.58/18.77 Clause #95 (by clausification #[94]): ∀ (a a_1 a_2 : Iota), Eq (And (in a (skS.0 9 a_1)) (in a (skS.0 10 a_1 a_2))) False % 18.58/18.77 Clause #96 (by clausification #[95]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 9 a_1)) False) (Eq (in a (skS.0 10 a_1 a_2)) False) % 18.58/18.77 Clause #105 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 8 (binintersect a a_1) a_2) a) True) (Eq (binintersect a a_1) emptyset) % 18.58/18.77 Clause #108 (by superposition #[105, 96]): ∀ (a a_1 a_2 a_3 : Iota), % 18.58/18.77 Or (Eq (binintersect (skS.0 9 a) a_1) emptyset) % 18.58/18.77 (Or (Eq True False) (Eq (in (skS.0 8 (binintersect (skS.0 9 a) a_1) a_2) (skS.0 10 a a_3)) False)) % 18.58/18.77 Clause #117 (by clausification #[93]): ∀ (a a_1 : Iota), Ne (binintersect (skS.0 9 a) (skS.0 10 a a_1)) emptyset % 18.58/18.77 Clause #119 (by clausification #[87]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 8 (binintersect a a_1) a_2) a_1) True) (Eq (binintersect a a_1) emptyset) % 18.58/18.77 Clause #901 (by clausification #[108]): ∀ (a a_1 a_2 a_3 : Iota), % 18.58/18.77 Or (Eq (binintersect (skS.0 9 a) a_1) emptyset) % 18.58/18.77 (Eq (in (skS.0 8 (binintersect (skS.0 9 a) a_1) a_2) (skS.0 10 a a_3)) False) % 18.58/18.77 Clause #902 (by superposition #[901, 119]): ∀ (a a_1 : Iota), % 18.58/18.77 Or (Eq (binintersect (skS.0 9 a) (skS.0 10 a a_1)) emptyset) % 18.58/18.77 (Or (Eq False True) (Eq (binintersect (skS.0 9 a) (skS.0 10 a a_1)) emptyset)) % 18.58/18.77 Clause #9119 (by clausification #[902]): ∀ (a a_1 : Iota), % 18.58/18.77 Or (Eq (binintersect (skS.0 9 a) (skS.0 10 a a_1)) emptyset) (Eq (binintersect (skS.0 9 a) (skS.0 10 a a_1)) emptyset) % 18.58/18.77 Clause #9120 (by eliminate duplicate literals #[9119]): ∀ (a a_1 : Iota), Eq (binintersect (skS.0 9 a) (skS.0 10 a a_1)) emptyset % 18.58/18.77 Clause #9121 (by forward contextual literal cutting #[9120, 117]): False % 18.58/18.77 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------