%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU634^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n011.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 08:02:06 PM UTC 2025 % Result : Theorem 4.49s 4.69s % Output : Proof 4.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU634^2 : TPTP v9.2.0. Released v3.7.0. % 0.12/0.14 % Command : duper %s % 0.15/0.35 % Computer : n011.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Fri Oct 3 06:06:08 EDT 2025 % 0.15/0.35 % CPUTime : % 4.49/4.69 SZS status Theorem for theBenchmark.p % 4.49/4.69 SZS output start Proof for theBenchmark.p % 4.49/4.69 Clause #0 (by assumption #[]): Eq (Eq uniqinunit (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy)) True % 4.49/4.69 Clause #1 (by assumption #[]): Eq (Eq subsetI2 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)) True % 4.49/4.69 Clause #2 (by assumption #[]): Eq (Eq setunionE2 (∀ (A Xx : Iota), in Xx (setunion A) → Exists fun X => And (in X A) (in Xx X))) True % 4.49/4.69 Clause #3 (by assumption #[]): Eq (Not (uniqinunit → subsetI2 → setunionE2 → ∀ (A : Iota), subset (setunion (setadjoin A emptyset)) A)) True % 4.49/4.69 Clause #4 (by clausification #[1]): Eq subsetI2 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 4.49/4.69 Clause #23 (by clausification #[0]): Eq uniqinunit (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy) % 4.49/4.69 Clause #27 (by clausification #[2]): Eq setunionE2 (∀ (A Xx : Iota), in Xx (setunion A) → Exists fun X => And (in X A) (in Xx X)) % 4.49/4.69 Clause #41 (by clausification #[3]): Eq (uniqinunit → subsetI2 → setunionE2 → ∀ (A : Iota), subset (setunion (setadjoin A emptyset)) A) False % 4.49/4.69 Clause #42 (by clausification #[41]): Eq uniqinunit True % 4.49/4.69 Clause #43 (by clausification #[41]): Eq (subsetI2 → setunionE2 → ∀ (A : Iota), subset (setunion (setadjoin A emptyset)) A) False % 4.49/4.69 Clause #44 (by backward demodulation #[42, 23]): Eq True (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy) % 4.49/4.69 Clause #47 (by clausification #[44]): ∀ (a : Iota), Eq (∀ (Xy : Iota), in a (setadjoin Xy emptyset) → Eq a Xy) True % 4.49/4.69 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a_1 emptyset) → Eq a a_1) True % 4.49/4.69 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) False) (Eq (Eq a a_1) True) % 4.49/4.69 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) False) (Eq a a_1) % 4.49/4.69 Clause #51 (by clausification #[43]): Eq subsetI2 True % 4.49/4.69 Clause #52 (by clausification #[43]): Eq (setunionE2 → ∀ (A : Iota), subset (setunion (setadjoin A emptyset)) A) False % 4.49/4.69 Clause #53 (by backward demodulation #[51, 4]): Eq True (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 4.49/4.69 Clause #57 (by clausification #[53]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx a → in Xx B) → subset a B) True % 4.49/4.69 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota), Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → subset a a_1) True % 4.49/4.69 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota), Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (subset a a_1) True) % 4.49/4.69 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 : Iota), % 4.49/4.69 Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 5 a a_1 a_2) a → in (skS.0 5 a a_1 a_2) a_1)) True) % 4.49/4.69 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 5 a a_1 a_2) a → in (skS.0 5 a a_1 a_2) a_1) False) % 4.49/4.69 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 5 a a_1 a_2) a) True) % 4.49/4.69 Clause #63 (by clausification #[61]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 5 a a_1 a_2) a_1) False) % 4.49/4.69 Clause #65 (by clausification #[52]): Eq setunionE2 True % 4.49/4.69 Clause #66 (by clausification #[52]): Eq (∀ (A : Iota), subset (setunion (setadjoin A emptyset)) A) False % 4.49/4.69 Clause #67 (by backward demodulation #[65, 27]): Eq True (∀ (A Xx : Iota), in Xx (setunion A) → Exists fun X => And (in X A) (in Xx X)) % 4.49/4.69 Clause #68 (by clausification #[66]): ∀ (a : Iota), Eq (Not (subset (setunion (setadjoin (skS.0 6 a) emptyset)) (skS.0 6 a))) True % 4.49/4.69 Clause #69 (by clausification #[68]): ∀ (a : Iota), Eq (subset (setunion (setadjoin (skS.0 6 a) emptyset)) (skS.0 6 a)) False % 4.49/4.69 Clause #71 (by clausification #[67]): ∀ (a : Iota), Eq (∀ (Xx : Iota), in Xx (setunion a) → Exists fun X => And (in X a) (in Xx X)) True % 4.49/4.69 Clause #72 (by clausification #[71]): ∀ (a a_1 : Iota), Eq (in a (setunion a_1) → Exists fun X => And (in X a_1) (in a X)) True % 4.49/4.69 Clause #73 (by clausification #[72]): ∀ (a a_1 : Iota), Or (Eq (in a (setunion a_1)) False) (Eq (Exists fun X => And (in X a_1) (in a X)) True) % 4.49/4.71 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), % 4.49/4.71 Or (Eq (in a (setunion a_1)) False) (Eq (And (in (skS.0 7 a_1 a a_2) a_1) (in a (skS.0 7 a_1 a a_2))) True) % 4.49/4.71 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setunion a_1)) False) (Eq (in a (skS.0 7 a_1 a a_2)) True) % 4.49/4.71 Clause #76 (by clausification #[74]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setunion a_1)) False) (Eq (in (skS.0 7 a_1 a a_2) a_1) True) % 4.49/4.71 Clause #77 (by superposition #[75, 62]): ∀ (a a_1 a_2 a_3 : Iota), % 4.49/4.71 Or (Eq (in (skS.0 5 (setunion a) a_1 a_2) (skS.0 7 a (skS.0 5 (setunion a) a_1 a_2) a_3)) True) % 4.49/4.71 (Or (Eq (subset (setunion a) a_1) True) (Eq False True)) % 4.49/4.71 Clause #97 (by superposition #[76, 62]): ∀ (a a_1 a_2 a_3 : Iota), % 4.49/4.71 Or (Eq (in (skS.0 7 a (skS.0 5 (setunion a) a_1 a_2) a_3) a) True) % 4.49/4.71 (Or (Eq (subset (setunion a) a_1) True) (Eq False True)) % 4.49/4.71 Clause #127 (by clausification #[77]): ∀ (a a_1 a_2 a_3 : Iota), % 4.49/4.71 Or (Eq (in (skS.0 5 (setunion a) a_1 a_2) (skS.0 7 a (skS.0 5 (setunion a) a_1 a_2) a_3)) True) % 4.49/4.71 (Eq (subset (setunion a) a_1) True) % 4.49/4.71 Clause #143 (by clausification #[97]): ∀ (a a_1 a_2 a_3 : Iota), % 4.49/4.71 Or (Eq (in (skS.0 7 a (skS.0 5 (setunion a) a_1 a_2) a_3) a) True) (Eq (subset (setunion a) a_1) True) % 4.49/4.71 Clause #144 (by superposition #[143, 50]): ∀ (a a_1 a_2 a_3 : Iota), % 4.49/4.71 Or (Eq (subset (setunion (setadjoin a emptyset)) a_1) True) % 4.49/4.71 (Or (Eq True False) (Eq (skS.0 7 (setadjoin a emptyset) (skS.0 5 (setunion (setadjoin a emptyset)) a_1 a_2) a_3) a)) % 4.49/4.71 Clause #163 (by clausification #[144]): ∀ (a a_1 a_2 a_3 : Iota), % 4.49/4.71 Or (Eq (subset (setunion (setadjoin a emptyset)) a_1) True) % 4.49/4.71 (Eq (skS.0 7 (setadjoin a emptyset) (skS.0 5 (setunion (setadjoin a emptyset)) a_1 a_2) a_3) a) % 4.49/4.71 Clause #164 (by superposition #[163, 127]): ∀ (a a_1 a_2 : Iota), % 4.49/4.71 Or (Eq (subset (setunion (setadjoin a emptyset)) a_1) True) % 4.49/4.71 (Or (Eq (in (skS.0 5 (setunion (setadjoin a emptyset)) a_1 a_2) a) True) % 4.49/4.71 (Eq (subset (setunion (setadjoin a emptyset)) a_1) True)) % 4.49/4.71 Clause #176 (by eliminate duplicate literals #[164]): ∀ (a a_1 a_2 : Iota), % 4.49/4.71 Or (Eq (subset (setunion (setadjoin a emptyset)) a_1) True) % 4.49/4.71 (Eq (in (skS.0 5 (setunion (setadjoin a emptyset)) a_1 a_2) a) True) % 4.49/4.71 Clause #182 (by superposition #[176, 63]): ∀ (a : Iota), % 4.49/4.71 Or (Eq (subset (setunion (setadjoin a emptyset)) a) True) % 4.49/4.71 (Or (Eq (subset (setunion (setadjoin a emptyset)) a) True) (Eq True False)) % 4.49/4.71 Clause #186 (by clausification #[182]): ∀ (a : Iota), % 4.49/4.71 Or (Eq (subset (setunion (setadjoin a emptyset)) a) True) (Eq (subset (setunion (setadjoin a emptyset)) a) True) % 4.49/4.71 Clause #187 (by eliminate duplicate literals #[186]): ∀ (a : Iota), Eq (subset (setunion (setadjoin a emptyset)) a) True % 4.49/4.71 Clause #188 (by superposition #[187, 69]): Eq True False % 4.49/4.71 Clause #189 (by clausification #[188]): False % 4.49/4.71 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------