%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU149+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.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 08:00:58 PM UTC 2025 % Result : Theorem 3.90s 4.10s % Output : Proof 3.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU149+1 : TPTP v9.2.0. Released v3.3.0. % 0.13/0.13 % Command : duper %s % 0.14/0.35 % Computer : n015.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 : Fri Oct 3 05:55:08 EDT 2025 % 0.14/0.35 % CPUTime : % 3.90/4.10 SZS status Theorem for theBenchmark.p % 3.90/4.10 SZS output start Proof for theBenchmark.p % 3.90/4.10 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True % 3.90/4.10 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True % 3.90/4.10 Clause #3 (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 % 3.90/4.10 Clause #5 (by assumption #[]): Eq (Not (∀ (A B C : Iota), Eq (singleton A) (unordered_pair B C) → Eq A B)) True % 3.90/4.10 Clause #10 (by clausification #[5]): Eq (∀ (A B C : Iota), Eq (singleton A) (unordered_pair B C) → Eq A B) False % 3.90/4.10 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (Not (∀ (B C : Iota), Eq (singleton (skS.0 0 a)) (unordered_pair B C) → Eq (skS.0 0 a) B)) True % 3.90/4.10 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (∀ (B C : Iota), Eq (singleton (skS.0 0 a)) (unordered_pair B C) → Eq (skS.0 0 a) B) False % 3.90/4.10 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), % 3.90/4.10 Eq % 3.90/4.10 (Not (∀ (C : Iota), Eq (singleton (skS.0 0 a)) (unordered_pair (skS.0 1 a a_1) C) → Eq (skS.0 0 a) (skS.0 1 a a_1))) % 3.90/4.10 True % 3.90/4.10 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), % 3.90/4.10 Eq (∀ (C : Iota), Eq (singleton (skS.0 0 a)) (unordered_pair (skS.0 1 a a_1) C) → Eq (skS.0 0 a) (skS.0 1 a a_1)) % 3.90/4.10 False % 3.90/4.10 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), % 3.90/4.10 Eq % 3.90/4.10 (Not % 3.90/4.10 (Eq (singleton (skS.0 0 a)) (unordered_pair (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → % 3.90/4.10 Eq (skS.0 0 a) (skS.0 1 a a_1))) % 3.90/4.10 True % 3.90/4.10 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), % 3.90/4.10 Eq (Eq (singleton (skS.0 0 a)) (unordered_pair (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) → Eq (skS.0 0 a) (skS.0 1 a a_1)) % 3.90/4.10 False % 3.90/4.10 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), Eq (Eq (singleton (skS.0 0 a)) (unordered_pair (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) True % 3.90/4.10 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 0 a) (skS.0 1 a a_1)) False % 3.90/4.10 Clause #19 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Eq (singleton (skS.0 0 a)) (unordered_pair (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) % 3.90/4.10 Clause #20 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True % 3.90/4.10 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True % 3.90/4.10 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a) % 3.90/4.10 Clause #23 (by clausification #[18]): ∀ (a a_1 : Iota), Ne (skS.0 0 a) (skS.0 1 a a_1) % 3.90/4.10 Clause #24 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True % 3.90/4.10 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True % 3.90/4.10 Clause #27 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) % 3.90/4.10 Clause #34 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1)) % 3.90/4.10 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True) % 3.90/4.10 Clause #37 (by clausification #[35]): ∀ (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)) % 3.90/4.10 Clause #43 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq a_2 a_1)) % 3.90/4.10 Clause #44 (by destructive equality resolution #[43]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) False) (Eq a a_1) % 3.90/4.10 Clause #47 (by clausification #[3]): ∀ (a : Iota), % 3.90/4.10 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 % 3.90/4.10 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), % 3.90/4.10 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 % 3.90/4.10 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 : Iota), % 3.90/4.11 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 % 3.90/4.11 Clause #51 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), % 3.90/4.11 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) % 3.90/4.11 Clause #69 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), % 3.90/4.11 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)) % 3.90/4.11 Clause #70 (by clausification #[69]): ∀ (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) % 3.90/4.11 Clause #71 (by clausification #[70]): ∀ (a a_1 a_2 a_3 : Iota), % 3.90/4.11 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)) % 3.90/4.11 Clause #73 (by clausification #[71]): ∀ (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)) % 3.90/4.11 Clause #75 (by clausification #[73]): ∀ (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)) % 3.90/4.11 Clause #76 (by destructive equality resolution #[75]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (unordered_pair a_1 a_2)) True) (Ne a a_2) % 3.90/4.11 Clause #77 (by destructive equality resolution #[76]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a_1 a)) True % 3.90/4.11 Clause #80 (by superposition #[77, 22]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a a_1)) True % 3.90/4.11 Clause #82 (by superposition #[80, 19]): ∀ (a a_1 : Iota), Eq (in (skS.0 1 a a_1) (singleton (skS.0 0 a))) True % 3.90/4.11 Clause #108 (by superposition #[82, 44]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 1 a a_1) (skS.0 0 a)) % 3.90/4.11 Clause #111 (by clausification #[108]): ∀ (a a_1 : Iota), Eq (skS.0 1 a a_1) (skS.0 0 a) % 3.90/4.11 Clause #112 (by forward contextual literal cutting #[111, 23]): False % 3.90/4.11 SZS output end Proof for theBenchmark.p 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