%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET918+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.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 200.54s 200.71s % Output : Proof 200.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET918+1 : TPTP v9.2.0. Released v3.2.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n006.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 : Thu Oct 2 14:40:38 EDT 2025 % 0.13/0.35 % CPUTime : % 200.54/200.71 SZS status Theorem for theBenchmark.p % 200.54/200.71 SZS output start Proof for theBenchmark.p % 200.54/200.71 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True % 200.54/200.71 Clause #3 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True % 200.54/200.71 Clause #4 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (Eq C (unordered_pair A B)) (∀ (D : Iota), Iff (in D C) (Or (Eq D A) (Eq D B)))) True % 200.54/200.71 Clause #5 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (Eq C (set_intersection2 A B)) (∀ (D : Iota), Iff (in D C) (And (in D A) (in D B)))) True % 200.54/200.71 Clause #9 (by assumption #[]): Eq % 200.54/200.71 (Not % 200.54/200.71 (∀ (A B C : Iota), Not (And (And (Eq (set_intersection2 (unordered_pair A B) C) (singleton A)) (in B C)) (Ne A B)))) % 200.54/200.71 True % 200.54/200.71 Clause #21 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True % 200.54/200.71 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True % 200.54/200.71 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a) % 200.54/200.71 Clause #27 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True % 200.54/200.71 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True % 200.54/200.71 Clause #30 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) % 200.54/200.71 Clause #37 (by clausification #[30]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1)) % 200.54/200.71 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True) % 200.54/200.71 Clause #40 (by clausification #[38]): ∀ (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)) % 200.54/200.71 Clause #46 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq a_2 a_1)) % 200.54/200.71 Clause #47 (by destructive equality resolution #[46]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) False) (Eq a a_1) % 200.54/200.71 Clause #50 (by clausification #[4]): ∀ (a : Iota), % 200.54/200.71 Eq (∀ (B C : Iota), Iff (Eq C (unordered_pair a B)) (∀ (D : Iota), Iff (in D C) (Or (Eq D a) (Eq D B)))) True % 200.54/200.71 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), % 200.54/200.71 Eq (∀ (C : Iota), Iff (Eq C (unordered_pair a a_1)) (∀ (D : Iota), Iff (in D C) (Or (Eq D a) (Eq D a_1)))) True % 200.54/200.71 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), % 200.54/200.71 Eq (Iff (Eq a (unordered_pair a_1 a_2)) (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2)))) True % 200.54/200.71 Clause #54 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), % 200.54/200.71 Or (Eq (Eq a (unordered_pair a_1 a_2)) False) (Eq (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2))) True) % 200.54/200.71 Clause #63 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), % 200.54/200.71 Or (Eq (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2))) True) (Ne a (unordered_pair a_1 a_2)) % 200.54/200.71 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (unordered_pair a_1 a_2)) (Eq (Iff (in a_3 a) (Or (Eq a_3 a_1) (Eq a_3 a_2))) True) % 200.54/200.71 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 a_3 : Iota), % 200.54/200.71 Or (Ne a (unordered_pair a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (Or (Eq a_3 a_1) (Eq a_3 a_2)) False)) % 200.54/200.71 Clause #67 (by clausification #[65]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (unordered_pair a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (Eq a_3 a_2) False)) % 200.54/200.71 Clause #69 (by clausification #[67]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (unordered_pair a_1 a_2)) (Or (Eq (in a_3 a) True) (Ne a_3 a_2)) % 200.54/200.71 Clause #70 (by destructive equality resolution #[69]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (unordered_pair a_1 a_2)) True) (Ne a a_2) % 200.54/200.71 Clause #71 (by destructive equality resolution #[70]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a_1 a)) True % 200.54/200.71 Clause #73 (by superposition #[71, 23]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a a_1)) True % 200.54/200.71 Clause #77 (by clausification #[5]): ∀ (a : Iota), % 200.54/200.71 Eq (∀ (B C : Iota), Iff (Eq C (set_intersection2 a B)) (∀ (D : Iota), Iff (in D C) (And (in D a) (in D B)))) True % 200.54/200.73 Clause #78 (by clausification #[77]): ∀ (a a_1 : Iota), % 200.54/200.73 Eq (∀ (C : Iota), Iff (Eq C (set_intersection2 a a_1)) (∀ (D : Iota), Iff (in D C) (And (in D a) (in D a_1)))) True % 200.54/200.73 Clause #79 (by clausification #[78]): ∀ (a a_1 a_2 : Iota), % 200.54/200.73 Eq (Iff (Eq a (set_intersection2 a_1 a_2)) (∀ (D : Iota), Iff (in D a) (And (in D a_1) (in D a_2)))) True % 200.54/200.73 Clause #81 (by clausification #[79]): ∀ (a a_1 a_2 : Iota), % 200.54/200.73 Or (Eq (Eq a (set_intersection2 a_1 a_2)) False) (Eq (∀ (D : Iota), Iff (in D a) (And (in D a_1) (in D a_2))) True) % 200.54/200.73 Clause #99 (by clausification #[9]): Eq (∀ (A B C : Iota), Not (And (And (Eq (set_intersection2 (unordered_pair A B) C) (singleton A)) (in B C)) (Ne A B))) % 200.54/200.73 False % 200.54/200.73 Clause #100 (by clausification #[99]): ∀ (a : Iota), % 200.54/200.73 Eq % 200.54/200.73 (Not % 200.54/200.73 (∀ (B C : Iota), % 200.54/200.73 Not % 200.54/200.73 (And (And (Eq (set_intersection2 (unordered_pair (skS.0 5 a) B) C) (singleton (skS.0 5 a))) (in B C)) % 200.54/200.73 (Ne (skS.0 5 a) B)))) % 200.54/200.73 True % 200.54/200.73 Clause #101 (by clausification #[100]): ∀ (a : Iota), % 200.54/200.73 Eq % 200.54/200.73 (∀ (B C : Iota), % 200.54/200.73 Not % 200.54/200.73 (And (And (Eq (set_intersection2 (unordered_pair (skS.0 5 a) B) C) (singleton (skS.0 5 a))) (in B C)) % 200.54/200.73 (Ne (skS.0 5 a) B))) % 200.54/200.73 False % 200.54/200.73 Clause #102 (by clausification #[101]): ∀ (a a_1 : Iota), % 200.54/200.73 Eq % 200.54/200.73 (Not % 200.54/200.73 (∀ (C : Iota), % 200.54/200.73 Not % 200.54/200.73 (And % 200.54/200.73 (And (Eq (set_intersection2 (unordered_pair (skS.0 5 a) (skS.0 6 a a_1)) C) (singleton (skS.0 5 a))) % 200.54/200.73 (in (skS.0 6 a a_1) C)) % 200.54/200.73 (Ne (skS.0 5 a) (skS.0 6 a a_1))))) % 200.54/200.73 True % 200.54/200.73 Clause #103 (by clausification #[102]): ∀ (a a_1 : Iota), % 200.54/200.73 Eq % 200.54/200.73 (∀ (C : Iota), % 200.54/200.73 Not % 200.54/200.73 (And % 200.54/200.73 (And (Eq (set_intersection2 (unordered_pair (skS.0 5 a) (skS.0 6 a a_1)) C) (singleton (skS.0 5 a))) % 200.54/200.73 (in (skS.0 6 a a_1) C)) % 200.54/200.73 (Ne (skS.0 5 a) (skS.0 6 a a_1)))) % 200.54/200.73 False % 200.54/200.73 Clause #104 (by clausification #[103]): ∀ (a a_1 a_2 : Iota), % 200.54/200.73 Eq % 200.54/200.73 (Not % 200.54/200.73 (Not % 200.54/200.73 (And % 200.54/200.73 (And % 200.54/200.73 (Eq (set_intersection2 (unordered_pair (skS.0 5 a) (skS.0 6 a a_1)) (skS.0 7 a a_1 a_2)) % 200.54/200.73 (singleton (skS.0 5 a))) % 200.54/200.73 (in (skS.0 6 a a_1) (skS.0 7 a a_1 a_2))) % 200.54/200.73 (Ne (skS.0 5 a) (skS.0 6 a a_1))))) % 200.54/200.73 True % 200.54/200.73 Clause #105 (by clausification #[104]): ∀ (a a_1 a_2 : Iota), % 200.54/200.73 Eq % 200.54/200.73 (Not % 200.54/200.73 (And % 200.54/200.73 (And % 200.54/200.73 (Eq (set_intersection2 (unordered_pair (skS.0 5 a) (skS.0 6 a a_1)) (skS.0 7 a a_1 a_2)) % 200.54/200.73 (singleton (skS.0 5 a))) % 200.54/200.73 (in (skS.0 6 a a_1) (skS.0 7 a a_1 a_2))) % 200.54/200.73 (Ne (skS.0 5 a) (skS.0 6 a a_1)))) % 200.54/200.73 False % 200.54/200.73 Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 : Iota), % 200.54/200.73 Eq % 200.54/200.73 (And % 200.54/200.73 (And % 200.54/200.73 (Eq (set_intersection2 (unordered_pair (skS.0 5 a) (skS.0 6 a a_1)) (skS.0 7 a a_1 a_2)) % 200.54/200.73 (singleton (skS.0 5 a))) % 200.54/200.73 (in (skS.0 6 a a_1) (skS.0 7 a a_1 a_2))) % 200.54/200.73 (Ne (skS.0 5 a) (skS.0 6 a a_1))) % 200.54/200.73 True % 200.54/200.73 Clause #107 (by clausification #[106]): ∀ (a a_1 : Iota), Eq (Ne (skS.0 5 a) (skS.0 6 a a_1)) True % 200.54/200.73 Clause #108 (by clausification #[106]): ∀ (a a_1 a_2 : Iota), % 200.54/200.73 Eq % 200.54/200.73 (And % 200.54/200.73 (Eq (set_intersection2 (unordered_pair (skS.0 5 a) (skS.0 6 a a_1)) (skS.0 7 a a_1 a_2)) (singleton (skS.0 5 a))) % 200.54/200.73 (in (skS.0 6 a a_1) (skS.0 7 a a_1 a_2))) % 200.54/200.73 True % 200.54/200.73 Clause #109 (by clausification #[107]): ∀ (a a_1 : Iota), Ne (skS.0 5 a) (skS.0 6 a a_1) % 200.54/200.73 Clause #110 (by clausification #[81]): ∀ (a a_1 a_2 : Iota), % 200.54/200.73 Or (Eq (∀ (D : Iota), Iff (in D a) (And (in D a_1) (in D a_2))) True) (Ne a (set_intersection2 a_1 a_2)) % 200.54/200.73 Clause #111 (by clausification #[110]): ∀ (a a_1 a_2 a_3 : Iota), % 200.54/200.73 Or (Ne a (set_intersection2 a_1 a_2)) (Eq (Iff (in a_3 a) (And (in a_3 a_1) (in a_3 a_2))) True) % 200.54/200.73 Clause #112 (by clausification #[111]): ∀ (a a_1 a_2 a_3 : Iota), % 200.54/200.73 Or (Ne a (set_intersection2 a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (And (in a_3 a_1) (in a_3 a_2)) False)) % 200.54/200.73 Clause #114 (by clausification #[112]): ∀ (a a_1 a_2 a_3 : Iota), % 200.54/200.73 Or (Ne a (set_intersection2 a_1 a_2)) (Or (Eq (in a_3 a) True) (Or (Eq (in a_3 a_1) False) (Eq (in a_3 a_2) False))) % 200.94/201.12 Clause #115 (by destructive equality resolution #[114]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (set_intersection2 a_1 a_2)) True) (Or (Eq (in a a_1) False) (Eq (in a a_2) False)) % 200.94/201.12 Clause #118 (by superposition #[115, 73]): ∀ (a a_1 a_2 : Iota), % 200.94/201.12 Or (Eq (in a (set_intersection2 (unordered_pair a a_1) a_2)) True) (Or (Eq (in a a_2) False) (Eq False True)) % 200.94/201.12 Clause #149 (by clausification #[118]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (set_intersection2 (unordered_pair a a_1) a_2)) True) (Eq (in a a_2) False) % 200.94/201.12 Clause #257 (by clausification #[108]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 6 a a_1) (skS.0 7 a a_1 a_2)) True % 200.94/201.12 Clause #258 (by clausification #[108]): ∀ (a a_1 a_2 : Iota), % 200.94/201.12 Eq (Eq (set_intersection2 (unordered_pair (skS.0 5 a) (skS.0 6 a a_1)) (skS.0 7 a a_1 a_2)) (singleton (skS.0 5 a))) % 200.94/201.12 True % 200.94/201.12 Clause #262 (by superposition #[257, 149]): ∀ (a a_1 a_2 a_3 : Iota), % 200.94/201.12 Or (Eq (in (skS.0 6 a a_1) (set_intersection2 (unordered_pair (skS.0 6 a a_1) a_2) (skS.0 7 a a_1 a_3))) True) % 200.94/201.12 (Eq True False) % 200.94/201.12 Clause #29829 (by clausification #[258]): ∀ (a a_1 a_2 : Iota), % 200.94/201.12 Eq (set_intersection2 (unordered_pair (skS.0 5 a) (skS.0 6 a a_1)) (skS.0 7 a a_1 a_2)) (singleton (skS.0 5 a)) % 200.94/201.12 Clause #31912 (by clausification #[262]): ∀ (a a_1 a_2 a_3 : Iota), % 200.94/201.12 Eq (in (skS.0 6 a a_1) (set_intersection2 (unordered_pair (skS.0 6 a a_1) a_2) (skS.0 7 a a_1 a_3))) True % 200.94/201.12 Clause #31963 (by superposition #[31912, 23]): ∀ (a a_1 a_2 a_3 : Iota), % 200.94/201.12 Eq (in (skS.0 6 a a_1) (set_intersection2 (unordered_pair a_2 (skS.0 6 a a_1)) (skS.0 7 a a_1 a_3))) True % 200.94/201.12 Clause #39791 (by superposition #[31963, 29829]): ∀ (a a_1 : Iota), Eq (in (skS.0 6 a a_1) (singleton (skS.0 5 a))) True % 200.94/201.12 Clause #39835 (by superposition #[39791, 47]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 6 a a_1) (skS.0 5 a)) % 200.94/201.12 Clause #39897 (by clausification #[39835]): ∀ (a a_1 : Iota), Eq (skS.0 6 a a_1) (skS.0 5 a) % 200.94/201.12 Clause #39898 (by forward contextual literal cutting #[39897, 109]): False % 200.94/201.12 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------