%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET885+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 4.93s 5.12s % Output : Proof 4.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET885+1 : TPTP v9.2.0. Released v3.2.0. % 0.12/0.14 % Command : duper %s % 0.15/0.35 % Computer : n031.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Thu Oct 2 13:46:08 EDT 2025 % 0.15/0.35 % CPUTime : % 4.93/5.12 SZS status Theorem for theBenchmark.p % 4.93/5.12 SZS output start Proof for theBenchmark.p % 4.93/5.12 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True % 4.93/5.12 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True % 4.93/5.12 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 % 4.93/5.12 Clause #4 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True % 4.93/5.12 Clause #8 (by assumption #[]): Eq (Not (∀ (A B C : Iota), subset (unordered_pair A B) (singleton C) → Eq A C)) True % 4.93/5.12 Clause #19 (by clausification #[8]): Eq (∀ (A B C : Iota), subset (unordered_pair A B) (singleton C) → Eq A C) False % 4.93/5.12 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (Not (∀ (B C : Iota), subset (unordered_pair (skS.0 2 a) B) (singleton C) → Eq (skS.0 2 a) C)) True % 4.93/5.12 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (∀ (B C : Iota), subset (unordered_pair (skS.0 2 a) B) (singleton C) → Eq (skS.0 2 a) C) False % 4.93/5.12 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), % 4.93/5.12 Eq (Not (∀ (C : Iota), subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton C) → Eq (skS.0 2 a) C)) True % 4.93/5.12 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), % 4.93/5.12 Eq (∀ (C : Iota), subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton C) → Eq (skS.0 2 a) C) False % 4.93/5.12 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), % 4.93/5.12 Eq % 4.93/5.12 (Not % 4.93/5.12 (subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton (skS.0 4 a a_1 a_2)) → % 4.93/5.12 Eq (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 4.93/5.12 True % 4.93/5.12 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), % 4.93/5.12 Eq % 4.93/5.12 (subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton (skS.0 4 a a_1 a_2)) → % 4.93/5.12 Eq (skS.0 2 a) (skS.0 4 a a_1 a_2)) % 4.93/5.12 False % 4.93/5.12 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Eq (subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton (skS.0 4 a a_1 a_2))) True % 4.93/5.12 Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Eq (Eq (skS.0 2 a) (skS.0 4 a a_1 a_2)) False % 4.93/5.12 Clause #28 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True % 4.93/5.12 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True % 4.93/5.12 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a) % 4.93/5.12 Clause #31 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True % 4.93/5.12 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (C : Iota), in C a → in C a_1)) True % 4.93/5.12 Clause #34 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (∀ (C : Iota), in C a → in C a_1) True) % 4.93/5.12 Clause #40 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True) % 4.93/5.12 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 a_1) True)) % 4.93/5.12 Clause #42 (by superposition #[41, 26]): ∀ (a a_1 a_2 a_3 : Iota), % 4.93/5.12 Or (Eq (in a (unordered_pair (skS.0 2 a_1) (skS.0 3 a_1 a_2))) False) % 4.93/5.12 (Or (Eq (in a (singleton (skS.0 4 a_1 a_2 a_3))) True) (Eq False True)) % 4.93/5.12 Clause #48 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True % 4.93/5.12 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True % 4.93/5.12 Clause #51 (by clausification #[49]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) % 4.93/5.12 Clause #58 (by clausification #[51]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1)) % 4.93/5.12 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True) % 4.93/5.16 Clause #61 (by clausification #[59]): ∀ (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)) % 4.93/5.16 Clause #67 (by clausification #[61]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq a_2 a_1)) % 4.93/5.16 Clause #68 (by destructive equality resolution #[67]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) False) (Eq a a_1) % 4.93/5.16 Clause #72 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Ne (skS.0 2 a) (skS.0 4 a a_1 a_2) % 4.93/5.16 Clause #73 (by clausification #[3]): ∀ (a : Iota), % 4.93/5.16 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 % 4.93/5.16 Clause #74 (by clausification #[73]): ∀ (a a_1 : Iota), % 4.93/5.16 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 % 4.93/5.16 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 : Iota), % 4.93/5.16 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 % 4.93/5.16 Clause #77 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), % 4.93/5.16 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) % 4.93/5.16 Clause #97 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), % 4.93/5.16 Or (Eq (in a (unordered_pair (skS.0 2 a_1) (skS.0 3 a_1 a_2))) False) % 4.93/5.16 (Eq (in a (singleton (skS.0 4 a_1 a_2 a_3))) True) % 4.93/5.16 Clause #104 (by clausification #[77]): ∀ (a a_1 a_2 : Iota), % 4.93/5.16 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)) % 4.93/5.16 Clause #105 (by clausification #[104]): ∀ (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) % 4.93/5.16 Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 a_3 : Iota), % 4.93/5.16 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)) % 4.93/5.16 Clause #108 (by clausification #[106]): ∀ (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)) % 4.93/5.16 Clause #110 (by clausification #[108]): ∀ (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)) % 4.93/5.16 Clause #111 (by destructive equality resolution #[110]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (unordered_pair a_1 a_2)) True) (Ne a a_2) % 4.93/5.16 Clause #112 (by destructive equality resolution #[111]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a_1 a)) True % 4.93/5.16 Clause #116 (by superposition #[112, 30]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a a_1)) True % 4.93/5.16 Clause #117 (by superposition #[116, 97]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (in (skS.0 2 a) (singleton (skS.0 4 a a_1 a_2))) True) % 4.93/5.16 Clause #407 (by clausification #[117]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a) (singleton (skS.0 4 a a_1 a_2))) True % 4.93/5.16 Clause #408 (by superposition #[407, 68]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (skS.0 2 a) (skS.0 4 a a_1 a_2)) % 4.93/5.16 Clause #456 (by clausification #[408]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 2 a) (skS.0 4 a a_1 a_2) % 4.93/5.16 Clause #457 (by forward contextual literal cutting #[456, 72]): False % 4.93/5.16 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------