%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU112+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n001.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 08:00:53 PM UTC 2025 % Result : Theorem 5.65s 5.84s % Output : Proof 5.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.14 % Problem : SEU112+1 : TPTP v9.2.0. Released v3.2.0. % 0.14/0.15 % Command : duper %s % 0.16/0.37 % Computer : n001.cluster.edu % 0.16/0.37 % Model : x86_64 x86_64 % 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.37 % Memory : 8042.1875MB % 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.37 % CPULimit : 300 % 0.16/0.37 % WCLimit : 300 % 0.16/0.37 % DateTime : Fri Oct 3 04:51:23 EDT 2025 % 0.16/0.37 % CPUTime : % 5.65/5.84 SZS status Theorem for theBenchmark.p % 5.65/5.84 SZS output start Proof for theBenchmark.p % 5.65/5.84 Clause #6 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_union2 A B) (set_union2 B A)) True % 5.65/5.84 Clause #28 (by assumption #[]): Eq (∀ (A B : Iota), subset A B → subset (finite_subsets A) (finite_subsets B)) True % 5.65/5.84 Clause #29 (by assumption #[]): Eq (Not (∀ (A B : Iota), subset (set_union2 (finite_subsets A) (finite_subsets B)) (finite_subsets (set_union2 A B)))) % 5.65/5.84 True % 5.65/5.84 Clause #36 (by assumption #[]): Eq (∀ (A B : Iota), subset A (set_union2 A B)) True % 5.65/5.84 Clause #38 (by assumption #[]): Eq (∀ (A B C : Iota), And (subset A B) (subset C B) → subset (set_union2 A C) B) True % 5.65/5.84 Clause #91 (by clausification #[36]): ∀ (a : Iota), Eq (∀ (B : Iota), subset a (set_union2 a B)) True % 5.65/5.84 Clause #92 (by clausification #[91]): ∀ (a a_1 : Iota), Eq (subset a (set_union2 a a_1)) True % 5.65/5.84 Clause #94 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_union2 a B) (set_union2 B a)) True % 5.65/5.84 Clause #95 (by clausification #[94]): ∀ (a a_1 : Iota), Eq (Eq (set_union2 a a_1) (set_union2 a_1 a)) True % 5.65/5.84 Clause #96 (by clausification #[95]): ∀ (a a_1 : Iota), Eq (set_union2 a a_1) (set_union2 a_1 a) % 5.65/5.84 Clause #98 (by superposition #[96, 92]): ∀ (a a_1 : Iota), Eq (subset a (set_union2 a_1 a)) True % 5.65/5.84 Clause #143 (by clausification #[28]): ∀ (a : Iota), Eq (∀ (B : Iota), subset a B → subset (finite_subsets a) (finite_subsets B)) True % 5.65/5.84 Clause #144 (by clausification #[143]): ∀ (a a_1 : Iota), Eq (subset a a_1 → subset (finite_subsets a) (finite_subsets a_1)) True % 5.65/5.84 Clause #145 (by clausification #[144]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (subset (finite_subsets a) (finite_subsets a_1)) True) % 5.65/5.84 Clause #147 (by superposition #[145, 98]): ∀ (a a_1 : Iota), Or (Eq (subset (finite_subsets a) (finite_subsets (set_union2 a_1 a))) True) (Eq False True) % 5.65/5.84 Clause #180 (by clausification #[38]): ∀ (a : Iota), Eq (∀ (B C : Iota), And (subset a B) (subset C B) → subset (set_union2 a C) B) True % 5.65/5.84 Clause #181 (by clausification #[180]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), And (subset a a_1) (subset C a_1) → subset (set_union2 a C) a_1) True % 5.65/5.84 Clause #182 (by clausification #[181]): ∀ (a a_1 a_2 : Iota), Eq (And (subset a a_1) (subset a_2 a_1) → subset (set_union2 a a_2) a_1) True % 5.65/5.84 Clause #183 (by clausification #[182]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (subset a a_1) (subset a_2 a_1)) False) (Eq (subset (set_union2 a a_2) a_1) True) % 5.65/5.84 Clause #184 (by clausification #[183]): ∀ (a a_1 a_2 : Iota), % 5.65/5.84 Or (Eq (subset (set_union2 a a_1) a_2) True) (Or (Eq (subset a a_2) False) (Eq (subset a_1 a_2) False)) % 5.65/5.84 Clause #196 (by clausification #[147]): ∀ (a a_1 : Iota), Eq (subset (finite_subsets a) (finite_subsets (set_union2 a_1 a))) True % 5.65/5.84 Clause #198 (by superposition #[196, 184]): ∀ (a a_1 a_2 : Iota), % 5.65/5.84 Or (Eq (subset (set_union2 (finite_subsets a) a_1) (finite_subsets (set_union2 a_2 a))) True) % 5.65/5.84 (Or (Eq True False) (Eq (subset a_1 (finite_subsets (set_union2 a_2 a))) False)) % 5.65/5.84 Clause #199 (by superposition #[196, 96]): ∀ (a a_1 : Iota), Eq (subset (finite_subsets a) (finite_subsets (set_union2 a a_1))) True % 5.65/5.84 Clause #254 (by clausification #[29]): Eq (∀ (A B : Iota), subset (set_union2 (finite_subsets A) (finite_subsets B)) (finite_subsets (set_union2 A B))) False % 5.65/5.84 Clause #255 (by clausification #[254]): ∀ (a : Iota), % 5.65/5.84 Eq % 5.65/5.84 (Not % 5.65/5.84 (∀ (B : Iota), % 5.65/5.84 subset (set_union2 (finite_subsets (skS.0 9 a)) (finite_subsets B)) % 5.65/5.84 (finite_subsets (set_union2 (skS.0 9 a) B)))) % 5.65/5.84 True % 5.65/5.84 Clause #256 (by clausification #[255]): ∀ (a : Iota), % 5.65/5.84 Eq % 5.65/5.84 (∀ (B : Iota), % 5.65/5.84 subset (set_union2 (finite_subsets (skS.0 9 a)) (finite_subsets B)) (finite_subsets (set_union2 (skS.0 9 a) B))) % 5.65/5.84 False % 5.65/5.84 Clause #257 (by clausification #[256]): ∀ (a a_1 : Iota), % 5.65/5.84 Eq % 5.65/5.84 (Not % 5.65/5.84 (subset (set_union2 (finite_subsets (skS.0 9 a)) (finite_subsets (skS.0 10 a a_1))) % 5.65/5.84 (finite_subsets (set_union2 (skS.0 9 a) (skS.0 10 a a_1))))) % 5.65/5.84 True % 5.65/5.84 Clause #258 (by clausification #[257]): ∀ (a a_1 : Iota), % 5.65/5.84 Eq % 5.65/5.84 (subset (set_union2 (finite_subsets (skS.0 9 a)) (finite_subsets (skS.0 10 a a_1))) % 5.65/5.85 (finite_subsets (set_union2 (skS.0 9 a) (skS.0 10 a a_1)))) % 5.65/5.85 False % 5.65/5.85 Clause #488 (by clausification #[198]): ∀ (a a_1 a_2 : Iota), % 5.65/5.85 Or (Eq (subset (set_union2 (finite_subsets a) a_1) (finite_subsets (set_union2 a_2 a))) True) % 5.65/5.85 (Eq (subset a_1 (finite_subsets (set_union2 a_2 a))) False) % 5.65/5.85 Clause #491 (by superposition #[488, 199]): ∀ (a a_1 : Iota), % 5.65/5.85 Or (Eq (subset (set_union2 (finite_subsets a) (finite_subsets a_1)) (finite_subsets (set_union2 a_1 a))) True) % 5.65/5.85 (Eq False True) % 5.65/5.85 Clause #655 (by clausification #[491]): ∀ (a a_1 : Iota), % 5.65/5.85 Eq (subset (set_union2 (finite_subsets a) (finite_subsets a_1)) (finite_subsets (set_union2 a_1 a))) True % 5.65/5.85 Clause #663 (by superposition #[655, 96]): ∀ (a a_1 : Iota), % 5.65/5.85 Eq (subset (set_union2 (finite_subsets a) (finite_subsets a_1)) (finite_subsets (set_union2 a a_1))) True % 5.65/5.85 Clause #666 (by superposition #[663, 258]): Eq True False % 5.65/5.85 Clause #674 (by clausification #[666]): False % 5.65/5.85 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------