%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET899+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 08:00:39 PM UTC 2025 % Result : Theorem 3.94s 4.15s % Output : Proof 3.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SET899+1 : TPTP v9.2.0. Released v3.2.0. % 0.11/0.12 % Command : duper %s % 0.12/0.33 % Computer : n003.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Thu Oct 2 13:42:53 EDT 2025 % 0.12/0.33 % CPUTime : % 3.94/4.15 SZS status Theorem for theBenchmark.p % 3.94/4.15 SZS output start Proof for theBenchmark.p % 3.94/4.15 Clause #4 (by assumption #[]): Eq (Not (∀ (A B C : Iota), subset A B → Or (in C A) (subset A (set_difference B (singleton C))))) True % 3.94/4.15 Clause #5 (by assumption #[]): Eq (∀ (A B C : Iota), subset A B → Or (in C A) (subset A (set_difference B (singleton C)))) True % 3.94/4.15 Clause #16 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B C : Iota), subset a B → Or (in C a) (subset a (set_difference B (singleton C)))) True % 3.94/4.15 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), subset a a_1 → Or (in C a) (subset a (set_difference a_1 (singleton C)))) True % 3.94/4.15 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Eq (subset a a_1 → Or (in a_2 a) (subset a (set_difference a_1 (singleton a_2)))) True % 3.94/4.15 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), % 3.94/4.15 Or (Eq (subset a a_1) False) (Eq (Or (in a_2 a) (subset a (set_difference a_1 (singleton a_2)))) True) % 3.94/4.15 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), % 3.94/4.15 Or (Eq (subset a a_1) False) (Or (Eq (in a_2 a) True) (Eq (subset a (set_difference a_1 (singleton a_2))) True)) % 3.94/4.15 Clause #22 (by clausification #[4]): Eq (∀ (A B C : Iota), subset A B → Or (in C A) (subset A (set_difference B (singleton C)))) False % 3.94/4.15 Clause #23 (by clausification #[22]): ∀ (a : Iota), % 3.94/4.15 Eq % 3.94/4.15 (Not % 3.94/4.15 (∀ (B C : Iota), % 3.94/4.15 subset (skS.0 2 a) B → Or (in C (skS.0 2 a)) (subset (skS.0 2 a) (set_difference B (singleton C))))) % 3.94/4.15 True % 3.94/4.15 Clause #24 (by clausification #[23]): ∀ (a : Iota), % 3.94/4.15 Eq % 3.94/4.15 (∀ (B C : Iota), subset (skS.0 2 a) B → Or (in C (skS.0 2 a)) (subset (skS.0 2 a) (set_difference B (singleton C)))) % 3.94/4.15 False % 3.94/4.15 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), % 3.94/4.15 Eq % 3.94/4.15 (Not % 3.94/4.15 (∀ (C : Iota), % 3.94/4.15 subset (skS.0 2 a) (skS.0 3 a a_1) → % 3.94/4.15 Or (in C (skS.0 2 a)) (subset (skS.0 2 a) (set_difference (skS.0 3 a a_1) (singleton C))))) % 3.94/4.15 True % 3.94/4.15 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), % 3.94/4.15 Eq % 3.94/4.15 (∀ (C : Iota), % 3.94/4.15 subset (skS.0 2 a) (skS.0 3 a a_1) → % 3.94/4.15 Or (in C (skS.0 2 a)) (subset (skS.0 2 a) (set_difference (skS.0 3 a a_1) (singleton C)))) % 3.94/4.15 False % 3.94/4.15 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), % 3.94/4.15 Eq % 3.94/4.15 (Not % 3.94/4.15 (subset (skS.0 2 a) (skS.0 3 a a_1) → % 3.94/4.15 Or (in (skS.0 4 a a_1 a_2) (skS.0 2 a)) % 3.94/4.15 (subset (skS.0 2 a) (set_difference (skS.0 3 a a_1) (singleton (skS.0 4 a a_1 a_2)))))) % 3.94/4.15 True % 3.94/4.15 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 3.94/4.15 Eq % 3.94/4.15 (subset (skS.0 2 a) (skS.0 3 a a_1) → % 3.94/4.15 Or (in (skS.0 4 a a_1 a_2) (skS.0 2 a)) % 3.94/4.15 (subset (skS.0 2 a) (set_difference (skS.0 3 a a_1) (singleton (skS.0 4 a a_1 a_2))))) % 3.94/4.15 False % 3.94/4.15 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (subset (skS.0 2 a) (skS.0 3 a a_1)) True % 3.94/4.15 Clause #30 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), % 3.94/4.15 Eq % 3.94/4.15 (Or (in (skS.0 4 a a_1 a_2) (skS.0 2 a)) % 3.94/4.15 (subset (skS.0 2 a) (set_difference (skS.0 3 a a_1) (singleton (skS.0 4 a a_1 a_2))))) % 3.94/4.15 False % 3.94/4.15 Clause #31 (by superposition #[29, 20]): ∀ (a a_1 a_2 : Iota), % 3.94/4.15 Or (Eq True False) % 3.94/4.15 (Or (Eq (in a (skS.0 2 a_1)) True) % 3.94/4.15 (Eq (subset (skS.0 2 a_1) (set_difference (skS.0 3 a_1 a_2) (singleton a))) True)) % 3.94/4.15 Clause #38 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), % 3.94/4.15 Or (Eq (in a (skS.0 2 a_1)) True) (Eq (subset (skS.0 2 a_1) (set_difference (skS.0 3 a_1 a_2) (singleton a))) True) % 3.94/4.15 Clause #42 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 2 a) (set_difference (skS.0 3 a a_1) (singleton (skS.0 4 a a_1 a_2)))) False % 3.94/4.15 Clause #43 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 4 a a_1 a_2) (skS.0 2 a)) False % 3.94/4.15 Clause #44 (by superposition #[42, 38]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 4 a a_1 a_2) (skS.0 2 a)) True) (Eq False True) % 3.94/4.15 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 4 a a_1 a_2) (skS.0 2 a)) True % 3.94/4.15 Clause #46 (by superposition #[45, 43]): Eq True False % 3.94/4.15 Clause #48 (by clausification #[46]): False % 3.94/4.15 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------