%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU636^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.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 3.64s 3.85s % Output : Proof 3.64s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU636^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n006.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 06:06:23 EDT 2025 % 0.13/0.34 % CPUTime : % 3.64/3.85 SZS status Theorem for theBenchmark.p % 3.64/3.85 SZS output start Proof for theBenchmark.p % 3.64/3.85 Clause #0 (by assumption #[]): Eq (Eq setextsub (∀ (A B : Iota), subset A B → subset B A → Eq A B)) True % 3.64/3.85 Clause #1 (by assumption #[]): Eq (Eq setunionsingleton1 (∀ (A : Iota), subset (setunion (setadjoin A emptyset)) A)) True % 3.64/3.85 Clause #2 (by assumption #[]): Eq (Eq setunionsingleton2 (∀ (A : Iota), subset A (setunion (setadjoin A emptyset)))) True % 3.64/3.85 Clause #3 (by assumption #[]): Eq (Not (setextsub → setunionsingleton1 → setunionsingleton2 → ∀ (Xx : Iota), Eq (setunion (setadjoin Xx emptyset)) Xx)) % 3.64/3.85 True % 3.64/3.85 Clause #4 (by clausification #[2]): Eq setunionsingleton2 (∀ (A : Iota), subset A (setunion (setadjoin A emptyset))) % 3.64/3.85 Clause #11 (by clausification #[1]): Eq setunionsingleton1 (∀ (A : Iota), subset (setunion (setadjoin A emptyset)) A) % 3.64/3.85 Clause #15 (by clausification #[0]): Eq setextsub (∀ (A B : Iota), subset A B → subset B A → Eq A B) % 3.64/3.85 Clause #33 (by clausification #[3]): Eq (setextsub → setunionsingleton1 → setunionsingleton2 → ∀ (Xx : Iota), Eq (setunion (setadjoin Xx emptyset)) Xx) False % 3.64/3.85 Clause #34 (by clausification #[33]): Eq setextsub True % 3.64/3.85 Clause #35 (by clausification #[33]): Eq (setunionsingleton1 → setunionsingleton2 → ∀ (Xx : Iota), Eq (setunion (setadjoin Xx emptyset)) Xx) False % 3.64/3.85 Clause #36 (by backward demodulation #[34, 15]): Eq True (∀ (A B : Iota), subset A B → subset B A → Eq A B) % 3.64/3.85 Clause #39 (by clausification #[36]): ∀ (a : Iota), Eq (∀ (B : Iota), subset a B → subset B a → Eq a B) True % 3.64/3.85 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (subset a a_1 → subset a_1 a → Eq a a_1) True % 3.64/3.85 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (subset a_1 a → Eq a a_1) True) % 3.64/3.85 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (subset a_1 a) False) (Eq (Eq a a_1) True)) % 3.64/3.85 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (subset a_1 a) False) (Eq a a_1)) % 3.64/3.85 Clause #44 (by clausification #[35]): Eq setunionsingleton1 True % 3.64/3.85 Clause #45 (by clausification #[35]): Eq (setunionsingleton2 → ∀ (Xx : Iota), Eq (setunion (setadjoin Xx emptyset)) Xx) False % 3.64/3.85 Clause #46 (by backward demodulation #[44, 11]): Eq True (∀ (A : Iota), subset (setunion (setadjoin A emptyset)) A) % 3.64/3.85 Clause #49 (by clausification #[46]): ∀ (a : Iota), Eq (subset (setunion (setadjoin a emptyset)) a) True % 3.64/3.85 Clause #50 (by superposition #[49, 43]): ∀ (a : Iota), % 3.64/3.85 Or (Eq True False) % 3.64/3.85 (Or (Eq (subset a (setunion (setadjoin a emptyset))) False) (Eq (setunion (setadjoin a emptyset)) a)) % 3.64/3.85 Clause #51 (by clausification #[45]): Eq setunionsingleton2 True % 3.64/3.85 Clause #52 (by clausification #[45]): Eq (∀ (Xx : Iota), Eq (setunion (setadjoin Xx emptyset)) Xx) False % 3.64/3.85 Clause #53 (by backward demodulation #[51, 4]): Eq True (∀ (A : Iota), subset A (setunion (setadjoin A emptyset))) % 3.64/3.85 Clause #56 (by clausification #[53]): ∀ (a : Iota), Eq (subset a (setunion (setadjoin a emptyset))) True % 3.64/3.85 Clause #58 (by clausification #[52]): ∀ (a : Iota), Eq (Not (Eq (setunion (setadjoin (skS.0 4 a) emptyset)) (skS.0 4 a))) True % 3.64/3.85 Clause #59 (by clausification #[58]): ∀ (a : Iota), Eq (Eq (setunion (setadjoin (skS.0 4 a) emptyset)) (skS.0 4 a)) False % 3.64/3.85 Clause #60 (by clausification #[59]): ∀ (a : Iota), Ne (setunion (setadjoin (skS.0 4 a) emptyset)) (skS.0 4 a) % 3.64/3.85 Clause #61 (by clausification #[50]): ∀ (a : Iota), Or (Eq (subset a (setunion (setadjoin a emptyset))) False) (Eq (setunion (setadjoin a emptyset)) a) % 3.64/3.85 Clause #62 (by superposition #[61, 56]): ∀ (a : Iota), Or (Eq (setunion (setadjoin a emptyset)) a) (Eq False True) % 3.64/3.85 Clause #66 (by clausification #[62]): ∀ (a : Iota), Eq (setunion (setadjoin a emptyset)) a % 3.64/3.85 Clause #70 (by backward contextual literal cutting #[66, 60]): False % 3.64/3.85 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------