%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET920+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n028.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 16.88s 17.09s % Output : Proof 16.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET920+1 : TPTP v9.2.0. Released v3.2.0. % 0.12/0.13 % Command : duper %s % 0.14/0.34 % Computer : n028.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Thu Oct 2 13:35:53 EDT 2025 % 0.14/0.34 % CPUTime : % 16.88/17.09 SZS status Theorem for theBenchmark.p % 16.88/17.09 SZS output start Proof for theBenchmark.p % 16.88/17.09 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True % 16.88/17.09 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 % 16.88/17.09 Clause #4 (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 % 16.88/17.09 Clause #8 (by assumption #[]): Eq (Not (∀ (A B C : Iota), Eq (set_intersection2 (unordered_pair A B) C) (unordered_pair A B) → in A C)) True % 16.88/17.09 Clause #17 (by clausification #[8]): Eq (∀ (A B C : Iota), Eq (set_intersection2 (unordered_pair A B) C) (unordered_pair A B) → in A C) False % 16.88/17.09 Clause #18 (by clausification #[17]): ∀ (a : Iota), % 16.88/17.09 Eq % 16.88/17.09 (Not % 16.88/17.09 (∀ (B C : Iota), % 16.88/17.09 Eq (set_intersection2 (unordered_pair (skS.0 2 a) B) C) (unordered_pair (skS.0 2 a) B) → in (skS.0 2 a) C)) % 16.88/17.09 True % 16.88/17.09 Clause #19 (by clausification #[18]): ∀ (a : Iota), % 16.88/17.09 Eq % 16.88/17.09 (∀ (B C : Iota), % 16.88/17.09 Eq (set_intersection2 (unordered_pair (skS.0 2 a) B) C) (unordered_pair (skS.0 2 a) B) → in (skS.0 2 a) C) % 16.88/17.09 False % 16.88/17.09 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), % 16.88/17.09 Eq % 16.88/17.09 (Not % 16.88/17.09 (∀ (C : Iota), % 16.88/17.09 Eq (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) C) % 16.88/17.09 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) → % 16.88/17.09 in (skS.0 2 a) C)) % 16.88/17.09 True % 16.88/17.09 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), % 16.88/17.09 Eq % 16.88/17.09 (∀ (C : Iota), % 16.88/17.09 Eq (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) C) % 16.88/17.09 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) → % 16.88/17.09 in (skS.0 2 a) C) % 16.88/17.09 False % 16.88/17.09 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), % 16.88/17.09 Eq % 16.88/17.09 (Not % 16.88/17.09 (Eq (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) % 16.88/17.09 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) → % 16.88/17.09 in (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 16.88/17.09 True % 16.88/17.09 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), % 16.88/17.09 Eq % 16.88/17.09 (Eq (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) % 16.88/17.09 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) → % 16.88/17.09 in (skS.0 2 a) (skS.0 4 a a_1 a_2)) % 16.88/17.09 False % 16.88/17.09 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), % 16.88/17.09 Eq % 16.88/17.09 (Eq (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) % 16.88/17.09 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1))) % 16.88/17.09 True % 16.88/17.09 Clause #25 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) False % 16.88/17.09 Clause #26 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), % 16.88/17.09 Eq (set_intersection2 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) % 16.88/17.09 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) % 16.88/17.09 Clause #30 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True % 16.88/17.09 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True % 16.88/17.09 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a) % 16.88/17.09 Clause #37 (by clausification #[4]): ∀ (a : Iota), % 16.88/17.09 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 % 16.88/17.09 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), % 16.88/17.09 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 % 16.88/17.09 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), % 16.88/17.09 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 % 16.88/17.09 Clause #41 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), % 16.88/17.09 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) % 16.88/17.09 Clause #48 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 16.88/17.09 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)) % 16.88/17.09 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 a_3 : Iota), % 16.96/17.15 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) % 16.96/17.15 Clause #51 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota), % 16.96/17.15 Or (Ne a (set_intersection2 a_1 a_2)) (Or (Eq (in a_3 a) False) (Eq (And (in a_3 a_1) (in a_3 a_2)) True)) % 16.96/17.15 Clause #54 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (set_intersection2 a_1 a_2)) (Or (Eq (in a_3 a) False) (Eq (in a_3 a_2) True)) % 16.96/17.15 Clause #56 (by destructive equality resolution #[54]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (set_intersection2 a_1 a_2)) False) (Eq (in a a_2) True) % 16.96/17.15 Clause #57 (by superposition #[56, 26]): ∀ (a a_1 a_2 a_3 : Iota), % 16.96/17.15 Or (Eq (in a (unordered_pair (skS.0 2 a_1) (skS.0 3 a_1 a_2))) False) (Eq (in a (skS.0 4 a_1 a_2 a_3)) True) % 16.96/17.15 Clause #60 (by clausification #[3]): ∀ (a : Iota), % 16.96/17.15 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 % 16.96/17.15 Clause #61 (by clausification #[60]): ∀ (a a_1 : Iota), % 16.96/17.15 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 % 16.96/17.15 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 : Iota), % 16.96/17.15 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 % 16.96/17.15 Clause #64 (by clausification #[62]): ∀ (a a_1 a_2 : Iota), % 16.96/17.15 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) % 16.96/17.15 Clause #74 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), % 16.96/17.15 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)) % 16.96/17.15 Clause #75 (by clausification #[74]): ∀ (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) % 16.96/17.15 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 a_3 : Iota), % 16.96/17.15 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)) % 16.96/17.15 Clause #78 (by clausification #[76]): ∀ (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)) % 16.96/17.15 Clause #80 (by clausification #[78]): ∀ (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)) % 16.96/17.15 Clause #81 (by destructive equality resolution #[80]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (unordered_pair a_1 a_2)) True) (Ne a a_2) % 16.96/17.15 Clause #82 (by destructive equality resolution #[81]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a_1 a)) True % 16.96/17.15 Clause #85 (by superposition #[82, 32]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a a_1)) True % 16.96/17.15 Clause #134 (by superposition #[57, 85]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) % 16.96/17.15 Clause #4834 (by clausification #[134]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True % 16.96/17.15 Clause #4835 (by superposition #[4834, 25]): Eq True False % 16.96/17.15 Clause #4854 (by clausification #[4835]): False % 16.96/17.15 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------