%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET872+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 08:00:37 PM UTC 2025 % Result : Theorem 3.85s 4.03s % Output : Proof 3.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET872+1 : TPTP v9.2.0. Released v3.2.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n031.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 13:36:53 EDT 2025 % 0.13/0.35 % CPUTime : % 3.85/4.03 SZS status Theorem for theBenchmark.p % 3.85/4.03 SZS output start Proof for theBenchmark.p % 3.85/4.03 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True % 3.85/4.03 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True % 3.85/4.03 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 % 3.85/4.03 Clause #4 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True % 3.85/4.03 Clause #8 (by assumption #[]): Eq (Not (∀ (A B : Iota), subset (singleton A) (unordered_pair A B))) True % 3.85/4.03 Clause #19 (by clausification #[8]): Eq (∀ (A B : Iota), subset (singleton A) (unordered_pair A B)) False % 3.85/4.03 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), subset (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) B))) True % 3.85/4.03 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (∀ (B : Iota), subset (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) B)) False % 3.85/4.03 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (Not (subset (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)))) True % 3.85/4.03 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (subset (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1))) False % 3.85/4.03 Clause #24 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True % 3.85/4.03 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True % 3.85/4.03 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a) % 3.85/4.03 Clause #27 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True % 3.85/4.03 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (C : Iota), in C a → in C a_1)) True % 3.85/4.03 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (C : Iota), in C a → in C a_1) False) % 3.85/4.03 Clause #31 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), % 3.85/4.03 Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 4 a a_1 a_2) a → in (skS.0 4 a a_1 a_2) a_1)) True) % 3.85/4.03 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 4 a a_1 a_2) a → in (skS.0 4 a a_1 a_2) a_1) False) % 3.85/4.03 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 4 a a_1 a_2) a) True) % 3.85/4.03 Clause #34 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 4 a a_1 a_2) a_1) False) % 3.85/4.03 Clause #43 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True % 3.85/4.03 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True % 3.85/4.03 Clause #46 (by clausification #[44]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) % 3.85/4.03 Clause #53 (by clausification #[46]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1)) % 3.85/4.03 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True) % 3.85/4.03 Clause #56 (by clausification #[54]): ∀ (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)) % 3.85/4.03 Clause #62 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq a_2 a_1)) % 3.85/4.03 Clause #63 (by destructive equality resolution #[62]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) False) (Eq a a_1) % 3.85/4.03 Clause #65 (by superposition #[63, 33]): ∀ (a a_1 a_2 : Iota), % 3.85/4.03 Or (Eq (skS.0 4 (singleton a) a_1 a_2) a) (Or (Eq (subset (singleton a) a_1) True) (Eq False True)) % 3.85/4.03 Clause #67 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), Or (Eq (skS.0 4 (singleton a) a_1 a_2) a) (Eq (subset (singleton a) a_1) True) % 3.85/4.03 Clause #69 (by superposition #[67, 34]): ∀ (a a_1 : Iota), % 3.85/4.04 Or (Eq (subset (singleton a) a_1) True) (Or (Eq (subset (singleton a) a_1) True) (Eq (in a a_1) False)) % 3.85/4.04 Clause #71 (by clausification #[3]): ∀ (a : Iota), % 3.85/4.04 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 % 3.85/4.04 Clause #72 (by clausification #[71]): ∀ (a a_1 : Iota), % 3.85/4.04 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 % 3.85/4.04 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota), % 3.85/4.04 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 % 3.85/4.04 Clause #75 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), % 3.85/4.04 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) % 3.85/4.04 Clause #84 (by eliminate duplicate literals #[69]): ∀ (a a_1 : Iota), Or (Eq (subset (singleton a) a_1) True) (Eq (in a a_1) False) % 3.85/4.04 Clause #109 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), % 3.85/4.04 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)) % 3.85/4.04 Clause #110 (by clausification #[109]): ∀ (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) % 3.85/4.04 Clause #111 (by clausification #[110]): ∀ (a a_1 a_2 a_3 : Iota), % 3.85/4.04 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)) % 3.85/4.04 Clause #113 (by clausification #[111]): ∀ (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)) % 3.85/4.04 Clause #115 (by clausification #[113]): ∀ (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)) % 3.85/4.04 Clause #116 (by destructive equality resolution #[115]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (unordered_pair a_1 a_2)) True) (Ne a a_2) % 3.85/4.04 Clause #117 (by destructive equality resolution #[116]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a_1 a)) True % 3.85/4.04 Clause #120 (by superposition #[117, 26]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a a_1)) True % 3.85/4.04 Clause #122 (by superposition #[120, 84]): ∀ (a a_1 : Iota), Or (Eq (subset (singleton a) (unordered_pair a a_1)) True) (Eq True False) % 3.85/4.04 Clause #130 (by clausification #[122]): ∀ (a a_1 : Iota), Eq (subset (singleton a) (unordered_pair a a_1)) True % 3.85/4.04 Clause #131 (by superposition #[130, 23]): Eq True False % 3.85/4.04 Clause #135 (by clausification #[131]): False % 3.85/4.04 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------