%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU621^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n023.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 08:02:04 PM UTC 2025 % Result : Theorem 3.93s 4.14s % Output : Proof 3.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU621^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n023.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 06:10:23 EDT 2025 % 0.13/0.34 % CPUTime : % 3.93/4.14 SZS status Theorem for theBenchmark.p % 3.93/4.14 SZS output start Proof for theBenchmark.p % 3.93/4.14 Clause #0 (by assumption #[]): Eq (Eq uniqinunit (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy)) True % 3.93/4.14 Clause #1 (by assumption #[]): Eq (Eq subsetI2 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)) True % 3.93/4.14 Clause #2 (by assumption #[]): Eq (Not (uniqinunit → subsetI2 → ∀ (A Xx : Iota), in Xx A → subset (setadjoin Xx emptyset) A)) True % 3.93/4.14 Clause #3 (by clausification #[1]): Eq subsetI2 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 3.93/4.14 Clause #22 (by clausification #[0]): Eq uniqinunit (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy) % 3.93/4.14 Clause #26 (by clausification #[2]): Eq (uniqinunit → subsetI2 → ∀ (A Xx : Iota), in Xx A → subset (setadjoin Xx emptyset) A) False % 3.93/4.14 Clause #27 (by clausification #[26]): Eq uniqinunit True % 3.93/4.14 Clause #28 (by clausification #[26]): Eq (subsetI2 → ∀ (A Xx : Iota), in Xx A → subset (setadjoin Xx emptyset) A) False % 3.93/4.14 Clause #29 (by backward demodulation #[27, 22]): Eq True (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy) % 3.93/4.14 Clause #30 (by clausification #[29]): ∀ (a : Iota), Eq (∀ (Xy : Iota), in a (setadjoin Xy emptyset) → Eq a Xy) True % 3.93/4.14 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a_1 emptyset) → Eq a a_1) True % 3.93/4.14 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) False) (Eq (Eq a a_1) True) % 3.93/4.14 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) False) (Eq a a_1) % 3.93/4.14 Clause #34 (by clausification #[28]): Eq subsetI2 True % 3.93/4.14 Clause #35 (by clausification #[28]): Eq (∀ (A Xx : Iota), in Xx A → subset (setadjoin Xx emptyset) A) False % 3.93/4.14 Clause #36 (by backward demodulation #[34, 3]): Eq True (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 3.93/4.14 Clause #39 (by clausification #[36]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx a → in Xx B) → subset a B) True % 3.93/4.14 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → subset a a_1) True % 3.93/4.14 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (subset a a_1) True) % 3.93/4.14 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 3.93/4.14 Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 3 a a_1 a_2) a → in (skS.0 3 a a_1 a_2) a_1)) True) % 3.93/4.14 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 3 a a_1 a_2) a → in (skS.0 3 a a_1 a_2) a_1) False) % 3.93/4.14 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 3 a a_1 a_2) a) True) % 3.93/4.14 Clause #45 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 3 a a_1 a_2) a_1) False) % 3.93/4.14 Clause #46 (by superposition #[44, 33]): ∀ (a a_1 a_2 : Iota), % 3.93/4.14 Or (Eq (subset (setadjoin a emptyset) a_1) True) (Or (Eq True False) (Eq (skS.0 3 (setadjoin a emptyset) a_1 a_2) a)) % 3.93/4.14 Clause #47 (by clausification #[35]): ∀ (a : Iota), Eq (Not (∀ (Xx : Iota), in Xx (skS.0 4 a) → subset (setadjoin Xx emptyset) (skS.0 4 a))) True % 3.93/4.14 Clause #48 (by clausification #[47]): ∀ (a : Iota), Eq (∀ (Xx : Iota), in Xx (skS.0 4 a) → subset (setadjoin Xx emptyset) (skS.0 4 a)) False % 3.93/4.14 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), % 3.93/4.14 Eq (Not (in (skS.0 5 a a_1) (skS.0 4 a) → subset (setadjoin (skS.0 5 a a_1) emptyset) (skS.0 4 a))) True % 3.93/4.14 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), Eq (in (skS.0 5 a a_1) (skS.0 4 a) → subset (setadjoin (skS.0 5 a a_1) emptyset) (skS.0 4 a)) False % 3.93/4.14 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), Eq (in (skS.0 5 a a_1) (skS.0 4 a)) True % 3.93/4.14 Clause #52 (by clausification #[50]): ∀ (a a_1 : Iota), Eq (subset (setadjoin (skS.0 5 a a_1) emptyset) (skS.0 4 a)) False % 3.93/4.14 Clause #76 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (setadjoin a emptyset) a_1) True) (Eq (skS.0 3 (setadjoin a emptyset) a_1 a_2) a) % 3.93/4.14 Clause #78 (by superposition #[76, 45]): ∀ (a a_1 : Iota), % 3.93/4.14 Or (Eq (subset (setadjoin a emptyset) a_1) True) % 3.93/4.14 (Or (Eq (subset (setadjoin a emptyset) a_1) True) (Eq (in a a_1) False)) % 3.93/4.14 Clause #79 (by eliminate duplicate literals #[78]): ∀ (a a_1 : Iota), Or (Eq (subset (setadjoin a emptyset) a_1) True) (Eq (in a a_1) False) % 3.93/4.14 Clause #80 (by superposition #[79, 51]): ∀ (a a_1 : Iota), Or (Eq (subset (setadjoin (skS.0 5 a a_1) emptyset) (skS.0 4 a)) True) (Eq False True) % 3.93/4.14 Clause #86 (by clausification #[80]): ∀ (a a_1 : Iota), Eq (subset (setadjoin (skS.0 5 a a_1) emptyset) (skS.0 4 a)) True % 3.93/4.14 Clause #87 (by superposition #[86, 52]): Eq True False % 3.93/4.14 Clause #88 (by clausification #[87]): False % 3.93/4.14 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------