%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET882+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n014.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 08:00:38 PM UTC 2025 % Result : Theorem 3.94s 4.16s % Output : Proof 4.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET882+1 : TPTP v9.2.0. Released v3.2.0. % 0.07/0.13 % Command : duper %s % 0.14/0.34 % Computer : n014.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Thu Oct 2 14:28:53 EDT 2025 % 0.14/0.34 % CPUTime : % 3.94/4.16 SZS status Theorem for theBenchmark.p % 3.94/4.16 SZS output start Proof for theBenchmark.p % 3.94/4.16 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True % 3.94/4.16 Clause #3 (by assumption #[]): Eq % 3.94/4.16 (∀ (A B C : Iota), % 3.94/4.16 Iff (Eq (set_difference (unordered_pair A B) C) (singleton A)) (And (Not (in A C)) (Or (in B C) (Eq A B)))) % 3.94/4.16 True % 3.94/4.16 Clause #6 (by assumption #[]): Eq (Not (∀ (A B : Iota), Ne A B → Eq (set_difference (unordered_pair A B) (singleton B)) (singleton A))) True % 3.94/4.16 Clause #18 (by clausification #[6]): Eq (∀ (A B : Iota), Ne A B → Eq (set_difference (unordered_pair A B) (singleton B)) (singleton A)) False % 3.94/4.16 Clause #19 (by clausification #[18]): ∀ (a : Iota), % 3.94/4.16 Eq % 3.94/4.16 (Not % 3.94/4.16 (∀ (B : Iota), % 3.94/4.16 Ne (skS.0 2 a) B → Eq (set_difference (unordered_pair (skS.0 2 a) B) (singleton B)) (singleton (skS.0 2 a)))) % 3.94/4.16 True % 3.94/4.16 Clause #20 (by clausification #[19]): ∀ (a : Iota), % 3.94/4.16 Eq % 3.94/4.16 (∀ (B : Iota), % 3.94/4.16 Ne (skS.0 2 a) B → Eq (set_difference (unordered_pair (skS.0 2 a) B) (singleton B)) (singleton (skS.0 2 a))) % 3.94/4.16 False % 3.94/4.16 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), % 3.94/4.16 Eq % 3.94/4.16 (Not % 3.94/4.16 (Ne (skS.0 2 a) (skS.0 3 a a_1) → % 3.94/4.16 Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton (skS.0 3 a a_1))) % 3.94/4.16 (singleton (skS.0 2 a)))) % 3.94/4.16 True % 3.94/4.16 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), % 3.94/4.16 Eq % 3.94/4.16 (Ne (skS.0 2 a) (skS.0 3 a a_1) → % 3.94/4.16 Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton (skS.0 3 a a_1))) % 3.94/4.16 (singleton (skS.0 2 a))) % 3.94/4.16 False % 3.94/4.16 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (Ne (skS.0 2 a) (skS.0 3 a a_1)) True % 3.94/4.16 Clause #24 (by clausification #[22]): ∀ (a a_1 : Iota), % 3.94/4.16 Eq % 3.94/4.16 (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton (skS.0 3 a a_1))) % 3.94/4.16 (singleton (skS.0 2 a))) % 3.94/4.16 False % 3.94/4.16 Clause #25 (by clausification #[23]): ∀ (a a_1 : Iota), Ne (skS.0 2 a) (skS.0 3 a a_1) % 3.94/4.16 Clause #26 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True % 3.94/4.16 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True % 3.94/4.16 Clause #29 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) % 3.94/4.16 Clause #36 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1)) % 3.94/4.16 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True) % 3.94/4.16 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Eq (Eq a_2 a_1) False)) % 3.94/4.16 Clause #39 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq (Eq a_2 a_1) True)) % 3.94/4.16 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Ne a_2 a_1)) % 3.94/4.16 Clause #41 (by destructive equality resolution #[40]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) True) (Ne a a_1) % 3.94/4.16 Clause #42 (by destructive equality resolution #[41]): ∀ (a : Iota), Eq (in a (singleton a)) True % 3.94/4.16 Clause #45 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq a_2 a_1)) % 3.94/4.16 Clause #46 (by destructive equality resolution #[45]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) False) (Eq a a_1) % 3.94/4.16 Clause #49 (by clausification #[3]): ∀ (a : Iota), % 3.94/4.16 Eq % 3.94/4.16 (∀ (B C : Iota), % 3.94/4.16 Iff (Eq (set_difference (unordered_pair a B) C) (singleton a)) (And (Not (in a C)) (Or (in B C) (Eq a B)))) % 3.94/4.16 True % 3.94/4.16 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), % 3.94/4.16 Eq % 3.94/4.16 (∀ (C : Iota), % 3.94/4.16 Iff (Eq (set_difference (unordered_pair a a_1) C) (singleton a)) (And (Not (in a C)) (Or (in a_1 C) (Eq a a_1)))) % 3.94/4.16 True % 3.94/4.16 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), % 3.94/4.16 Eq % 3.94/4.16 (Iff (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a)) % 4.01/4.18 (And (Not (in a a_2)) (Or (in a_1 a_2) (Eq a a_1)))) % 4.01/4.18 True % 4.01/4.18 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), % 4.01/4.18 Or (Eq (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a)) True) % 4.01/4.18 (Eq (And (Not (in a a_2)) (Or (in a_1 a_2) (Eq a a_1))) False) % 4.01/4.18 Clause #54 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), % 4.01/4.18 Or (Eq (And (Not (in a a_1)) (Or (in a_2 a_1) (Eq a a_2))) False) % 4.01/4.18 (Eq (set_difference (unordered_pair a a_2) a_1) (singleton a)) % 4.01/4.18 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), % 4.01/4.18 Or (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a)) % 4.01/4.18 (Or (Eq (Not (in a a_2)) False) (Eq (Or (in a_1 a_2) (Eq a a_1)) False)) % 4.01/4.18 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), % 4.01/4.18 Or (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a)) % 4.01/4.18 (Or (Eq (Or (in a_1 a_2) (Eq a a_1)) False) (Eq (in a a_2) True)) % 4.01/4.18 Clause #58 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), % 4.01/4.18 Or (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a)) (Or (Eq (in a a_2) True) (Eq (in a_1 a_2) False)) % 4.01/4.18 Clause #61 (by clausification #[24]): ∀ (a a_1 : Iota), % 4.01/4.18 Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton (skS.0 3 a a_1))) (singleton (skS.0 2 a)) % 4.01/4.18 Clause #62 (by superposition #[58, 42]): ∀ (a a_1 : Iota), % 4.01/4.18 Or (Eq (set_difference (unordered_pair a a_1) (singleton a_1)) (singleton a)) % 4.01/4.18 (Or (Eq (in a (singleton a_1)) True) (Eq False True)) % 4.01/4.18 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), % 4.01/4.18 Or (Eq (set_difference (unordered_pair a a_1) (singleton a_1)) (singleton a)) (Eq (in a (singleton a_1)) True) % 4.01/4.18 Clause #64 (by superposition #[63, 61]): ∀ (a a_1 : Iota), % 4.01/4.18 Or (Eq (in (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) (Ne (singleton (skS.0 2 a)) (singleton (skS.0 2 a))) % 4.01/4.18 Clause #95 (by eliminate resolved literals #[64]): ∀ (a a_1 : Iota), Eq (in (skS.0 2 a) (singleton (skS.0 3 a a_1))) True % 4.01/4.18 Clause #96 (by superposition #[95, 46]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 2 a) (skS.0 3 a a_1)) % 4.01/4.18 Clause #100 (by clausification #[96]): ∀ (a a_1 : Iota), Eq (skS.0 2 a) (skS.0 3 a a_1) % 4.01/4.18 Clause #101 (by forward contextual literal cutting #[100, 25]): False % 4.01/4.18 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------