%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET923+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.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 08:00:41 PM UTC 2025 % Result : Theorem 3.45s 3.66s % Output : Proof 3.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SET923+1 : TPTP v9.2.0. Released v3.2.0. % 0.07/0.14 % Command : duper %s % 0.14/0.35 % Computer : n010.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Thu Oct 2 14:32:08 EDT 2025 % 0.14/0.35 % CPUTime : % 3.45/3.66 SZS status Theorem for theBenchmark.p % 3.45/3.66 SZS output start Proof for theBenchmark.p % 3.45/3.66 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A (singleton B)) (Or (Eq A empty_set) (Eq A (singleton B)))) True % 3.45/3.66 Clause #5 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (set_difference A B) empty_set) (subset A B)) True % 3.45/3.66 Clause #6 (by assumption #[]): Eq % 3.45/3.66 (Not % 3.45/3.66 (∀ (A B : Iota), % 3.45/3.66 Not (And (And (Eq (set_difference A (singleton B)) empty_set) (Ne A empty_set)) (Ne A (singleton B))))) % 3.45/3.66 True % 3.45/3.66 Clause #13 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (set_difference a B) empty_set) (subset a B)) True % 3.45/3.66 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (Iff (Eq (set_difference a a_1) empty_set) (subset a a_1)) True % 3.45/3.66 Clause #16 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference a a_1) empty_set) False) (Eq (subset a a_1) True) % 3.45/3.66 Clause #19 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a (singleton B)) (Or (Eq a empty_set) (Eq a (singleton B)))) True % 3.45/3.66 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (Iff (subset a (singleton a_1)) (Or (Eq a empty_set) (Eq a (singleton a_1)))) True % 3.45/3.66 Clause #22 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) False) (Eq (Or (Eq a empty_set) (Eq a (singleton a_1))) True) % 3.45/3.66 Clause #32 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Ne (set_difference a a_1) empty_set) % 3.45/3.66 Clause #36 (by clausification #[6]): Eq % 3.45/3.66 (∀ (A B : Iota), % 3.45/3.66 Not (And (And (Eq (set_difference A (singleton B)) empty_set) (Ne A empty_set)) (Ne A (singleton B)))) % 3.45/3.66 False % 3.45/3.66 Clause #37 (by clausification #[36]): ∀ (a : Iota), % 3.45/3.66 Eq % 3.45/3.66 (Not % 3.45/3.66 (∀ (B : Iota), % 3.45/3.66 Not % 3.45/3.66 (And (And (Eq (set_difference (skS.0 2 a) (singleton B)) empty_set) (Ne (skS.0 2 a) empty_set)) % 3.45/3.66 (Ne (skS.0 2 a) (singleton B))))) % 3.45/3.66 True % 3.45/3.66 Clause #38 (by clausification #[37]): ∀ (a : Iota), % 3.45/3.66 Eq % 3.45/3.66 (∀ (B : Iota), % 3.45/3.66 Not % 3.45/3.66 (And (And (Eq (set_difference (skS.0 2 a) (singleton B)) empty_set) (Ne (skS.0 2 a) empty_set)) % 3.45/3.66 (Ne (skS.0 2 a) (singleton B)))) % 3.45/3.66 False % 3.45/3.66 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), % 3.45/3.66 Eq % 3.45/3.66 (Not % 3.45/3.66 (Not % 3.45/3.66 (And (And (Eq (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) empty_set) (Ne (skS.0 2 a) empty_set)) % 3.45/3.66 (Ne (skS.0 2 a) (singleton (skS.0 3 a a_1)))))) % 3.45/3.66 True % 3.45/3.66 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 3.45/3.66 Eq % 3.45/3.66 (Not % 3.45/3.66 (And (And (Eq (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) empty_set) (Ne (skS.0 2 a) empty_set)) % 3.45/3.66 (Ne (skS.0 2 a) (singleton (skS.0 3 a a_1))))) % 3.45/3.66 False % 3.45/3.66 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), % 3.45/3.66 Eq % 3.45/3.66 (And (And (Eq (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) empty_set) (Ne (skS.0 2 a) empty_set)) % 3.45/3.66 (Ne (skS.0 2 a) (singleton (skS.0 3 a a_1)))) % 3.45/3.66 True % 3.45/3.66 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Eq (Ne (skS.0 2 a) (singleton (skS.0 3 a a_1))) True % 3.45/3.66 Clause #43 (by clausification #[41]): ∀ (a a_1 : Iota), % 3.45/3.66 Eq (And (Eq (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) empty_set) (Ne (skS.0 2 a) empty_set)) True % 3.45/3.66 Clause #44 (by clausification #[42]): ∀ (a a_1 : Iota), Ne (skS.0 2 a) (singleton (skS.0 3 a a_1)) % 3.45/3.66 Clause #45 (by clausification #[22]): ∀ (a a_1 : Iota), % 3.45/3.66 Or (Eq (subset a (singleton a_1)) False) (Or (Eq (Eq a empty_set) True) (Eq (Eq a (singleton a_1)) True)) % 3.45/3.66 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) False) (Or (Eq (Eq a (singleton a_1)) True) (Eq a empty_set)) % 3.45/3.66 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) False) (Or (Eq a empty_set) (Eq a (singleton a_1))) % 3.45/3.66 Clause #52 (by clausification #[43]): ∀ (a : Iota), Eq (Ne (skS.0 2 a) empty_set) True % 3.45/3.66 Clause #53 (by clausification #[43]): ∀ (a a_1 : Iota), Eq (Eq (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) empty_set) True % 3.45/3.66 Clause #54 (by clausification #[52]): ∀ (a : Iota), Ne (skS.0 2 a) empty_set % 3.45/3.66 Clause #55 (by clausification #[53]): ∀ (a a_1 : Iota), Eq (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) empty_set % 3.45/3.66 Clause #56 (by superposition #[55, 32]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) (Ne empty_set empty_set) % 3.45/3.66 Clause #57 (by eliminate resolved literals #[56]): ∀ (a a_1 : Iota), Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) True % 3.45/3.66 Clause #58 (by superposition #[57, 47]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))) % 3.45/3.66 Clause #60 (by clausification #[58]): ∀ (a a_1 : Iota), Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 3.45/3.66 Clause #61 (by forward contextual literal cutting #[60, 54]): ∀ (a a_1 : Iota), Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)) % 3.45/3.66 Clause #62 (by forward contextual literal cutting #[61, 44]): False % 3.45/3.66 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------