%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET906+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.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 08:00:40 PM UTC 2025 % Result : Theorem 23.59s 23.76s % Output : Proof 23.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SET906+1 : TPTP v9.2.0. Released v3.2.0. % 0.04/0.13 % Command : duper %s % 0.13/0.34 % Computer : n018.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 13:44:08 EDT 2025 % 0.13/0.34 % CPUTime : % 23.59/23.76 SZS status Theorem for theBenchmark.p % 23.59/23.76 SZS output start Proof for theBenchmark.p % 23.59/23.76 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True % 23.59/23.76 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 % 23.59/23.76 Clause #4 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (Eq C (set_union2 A B)) (∀ (D : Iota), Iff (in D C) (Or (in D A) (in D B)))) True % 23.59/23.76 Clause #5 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True % 23.59/23.76 Clause #12 (by assumption #[]): Eq (Not (∀ (A B C : Iota), subset (set_union2 (unordered_pair A B) C) C → in A C)) True % 23.59/23.76 Clause #28 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True % 23.59/23.76 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True % 23.59/23.76 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a) % 23.59/23.76 Clause #31 (by clausification #[12]): Eq (∀ (A B C : Iota), subset (set_union2 (unordered_pair A B) C) C → in A C) False % 23.59/23.76 Clause #32 (by clausification #[31]): ∀ (a : Iota), Eq (Not (∀ (B C : Iota), subset (set_union2 (unordered_pair (skS.0 2 a) B) C) C → in (skS.0 2 a) C)) True % 23.59/23.76 Clause #33 (by clausification #[32]): ∀ (a : Iota), Eq (∀ (B C : Iota), subset (set_union2 (unordered_pair (skS.0 2 a) B) C) C → in (skS.0 2 a) C) False % 23.59/23.76 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), % 23.59/23.76 Eq (Not (∀ (C : Iota), subset (set_union2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) C) C → in (skS.0 2 a) C)) True % 23.59/23.76 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), % 23.59/23.76 Eq (∀ (C : Iota), subset (set_union2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) C) C → in (skS.0 2 a) C) False % 23.59/23.76 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), % 23.59/23.76 Eq % 23.59/23.76 (Not % 23.59/23.76 (subset (set_union2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (skS.0 4 a a_1 a_2) → % 23.59/23.76 in (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 23.59/23.76 True % 23.59/23.76 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), % 23.59/23.76 Eq % 23.59/23.76 (subset (set_union2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (skS.0 4 a a_1 a_2) → % 23.59/23.76 in (skS.0 2 a) (skS.0 4 a a_1 a_2)) % 23.59/23.76 False % 23.59/23.76 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), % 23.59/23.76 Eq (subset (set_union2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (skS.0 4 a a_1 a_2)) True % 23.59/23.76 Clause #39 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) False % 23.59/23.76 Clause #53 (by clausification #[3]): ∀ (a : Iota), % 23.59/23.76 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 % 23.59/23.76 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), % 23.59/23.76 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 % 23.59/23.76 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), % 23.59/23.76 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 % 23.59/23.76 Clause #57 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), % 23.59/23.76 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) % 23.59/23.76 Clause #66 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True % 23.59/23.76 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (C : Iota), in C a → in C a_1)) True % 23.59/23.76 Clause #69 (by clausification #[67]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (∀ (C : Iota), in C a → in C a_1) True) % 23.59/23.76 Clause #75 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True) % 23.59/23.76 Clause #76 (by clausification #[75]): ∀ (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)) % 23.59/23.76 Clause #77 (by superposition #[76, 38]): ∀ (a a_1 a_2 a_3 : Iota), % 23.59/23.76 Or (Eq (in a (set_union2 (unordered_pair (skS.0 2 a_1) (skS.0 3 a_1 a_2)) (skS.0 4 a_1 a_2 a_3))) False) % 23.70/23.87 (Or (Eq (in a (skS.0 4 a_1 a_2 a_3)) True) (Eq False True)) % 23.70/23.87 Clause #83 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B C : Iota), Iff (Eq C (set_union2 a B)) (∀ (D : Iota), Iff (in D C) (Or (in D a) (in D B)))) True % 23.70/23.87 Clause #84 (by clausification #[83]): ∀ (a a_1 : Iota), % 23.70/23.87 Eq (∀ (C : Iota), Iff (Eq C (set_union2 a a_1)) (∀ (D : Iota), Iff (in D C) (Or (in D a) (in D a_1)))) True % 23.70/23.87 Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 : Iota), Eq (Iff (Eq a (set_union2 a_1 a_2)) (∀ (D : Iota), Iff (in D a) (Or (in D a_1) (in D a_2)))) True % 23.70/23.87 Clause #87 (by clausification #[85]): ∀ (a a_1 a_2 : Iota), % 23.70/23.87 Or (Eq (Eq a (set_union2 a_1 a_2)) False) (Eq (∀ (D : Iota), Iff (in D a) (Or (in D a_1) (in D a_2))) True) % 23.70/23.87 Clause #96 (by clausification #[87]): ∀ (a a_1 a_2 : Iota), Or (Eq (∀ (D : Iota), Iff (in D a) (Or (in D a_1) (in D a_2))) True) (Ne a (set_union2 a_1 a_2)) % 23.70/23.87 Clause #97 (by clausification #[96]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (set_union2 a_1 a_2)) (Eq (Iff (in a_3 a) (Or (in a_3 a_1) (in a_3 a_2))) True) % 23.70/23.87 Clause #98 (by clausification #[97]): ∀ (a a_1 a_2 a_3 : Iota), % 23.70/23.87 Or (Ne a (set_union2 a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (Or (in a_3 a_1) (in a_3 a_2)) False)) % 23.70/23.87 Clause #101 (by clausification #[98]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (set_union2 a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (in a_3 a_1) False)) % 23.70/23.87 Clause #104 (by destructive equality resolution #[101]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (set_union2 a_1 a_2)) True) (Eq (in a a_1) False) % 23.70/23.87 Clause #125 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), % 23.70/23.87 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)) % 23.70/23.87 Clause #126 (by clausification #[125]): ∀ (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) % 23.70/23.87 Clause #127 (by clausification #[126]): ∀ (a a_1 a_2 a_3 : Iota), % 23.70/23.87 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)) % 23.70/23.87 Clause #129 (by clausification #[127]): ∀ (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)) % 23.70/23.87 Clause #131 (by clausification #[129]): ∀ (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)) % 23.70/23.87 Clause #132 (by destructive equality resolution #[131]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (unordered_pair a_1 a_2)) True) (Ne a a_2) % 23.70/23.87 Clause #133 (by destructive equality resolution #[132]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a_1 a)) True % 23.70/23.87 Clause #136 (by superposition #[133, 104]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (set_union2 (unordered_pair a_1 a) a_2)) True) (Eq True False) % 23.70/23.87 Clause #143 (by clausification #[136]): ∀ (a a_1 a_2 : Iota), Eq (in a (set_union2 (unordered_pair a_1 a) a_2)) True % 23.70/23.87 Clause #148 (by superposition #[143, 30]): ∀ (a a_1 a_2 : Iota), Eq (in a (set_union2 (unordered_pair a a_1) a_2)) True % 23.70/23.87 Clause #195 (by clausification #[77]): ∀ (a a_1 a_2 a_3 : Iota), % 23.70/23.87 Or (Eq (in a (set_union2 (unordered_pair (skS.0 2 a_1) (skS.0 3 a_1 a_2)) (skS.0 4 a_1 a_2 a_3))) False) % 23.70/23.87 (Eq (in a (skS.0 4 a_1 a_2 a_3)) True) % 23.70/23.87 Clause #198 (by superposition #[195, 148]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) (Eq False True) % 23.70/23.87 Clause #3857 (by clausification #[198]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True % 23.70/23.87 Clause #3858 (by superposition #[3857, 39]): Eq True False % 23.70/23.87 Clause #3870 (by clausification #[3858]): False % 23.70/23.87 SZS output end Proof for theBenchmark.p 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