%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET878+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 3.74s 3.99s % Output : Proof 3.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SET878+1 : TPTP v9.2.0. Released v3.2.0. % 0.07/0.15 % Command : duper %s % 0.14/0.36 % Computer : n005.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Thu Oct 2 14:00:38 EDT 2025 % 0.14/0.36 % CPUTime : % 3.74/3.99 SZS status Theorem for theBenchmark.p % 3.74/3.99 SZS output start Proof for theBenchmark.p % 3.74/3.99 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True % 3.74/3.99 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_intersection2 A B) (set_intersection2 B A)) True % 3.74/3.99 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 % 3.74/3.99 Clause #5 (by assumption #[]): Eq (∀ (A B : Iota), in A B → Eq (set_intersection2 B (singleton A)) (singleton A)) True % 3.74/3.99 Clause #8 (by assumption #[]): Eq (Not (∀ (A B : Iota), Eq (set_intersection2 (singleton A) (unordered_pair A B)) (singleton A))) True % 3.74/3.99 Clause #20 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_intersection2 a B) (set_intersection2 B a)) True % 3.74/3.99 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Eq (set_intersection2 a a_1) (set_intersection2 a_1 a)) True % 3.74/3.99 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (set_intersection2 a a_1) (set_intersection2 a_1 a) % 3.74/3.99 Clause #23 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True % 3.74/3.99 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True % 3.74/3.99 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a) % 3.74/3.99 Clause #26 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B : Iota), in a B → Eq (set_intersection2 B (singleton a)) (singleton a)) True % 3.74/3.99 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (in a a_1 → Eq (set_intersection2 a_1 (singleton a)) (singleton a)) True % 3.74/3.99 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (Eq (set_intersection2 a_1 (singleton a)) (singleton a)) True) % 3.74/3.99 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (set_intersection2 a_1 (singleton a)) (singleton a)) % 3.74/3.99 Clause #30 (by clausification #[8]): Eq (∀ (A B : Iota), Eq (set_intersection2 (singleton A) (unordered_pair A B)) (singleton A)) False % 3.74/3.99 Clause #31 (by clausification #[30]): ∀ (a : Iota), % 3.74/3.99 Eq % 3.74/3.99 (Not % 3.74/3.99 (∀ (B : Iota), % 3.74/3.99 Eq (set_intersection2 (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) B)) (singleton (skS.0 2 a)))) % 3.74/3.99 True % 3.74/3.99 Clause #32 (by clausification #[31]): ∀ (a : Iota), % 3.74/3.99 Eq % 3.74/3.99 (∀ (B : Iota), % 3.74/3.99 Eq (set_intersection2 (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) B)) (singleton (skS.0 2 a))) % 3.74/3.99 False % 3.74/3.99 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), % 3.74/3.99 Eq % 3.74/3.99 (Not % 3.74/3.99 (Eq (set_intersection2 (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1))) % 3.74/3.99 (singleton (skS.0 2 a)))) % 3.74/3.99 True % 3.74/3.99 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), % 3.74/3.99 Eq % 3.74/3.99 (Eq (set_intersection2 (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1))) % 3.74/3.99 (singleton (skS.0 2 a))) % 3.74/3.99 False % 3.74/3.99 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), % 3.74/3.99 Ne (set_intersection2 (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1))) (singleton (skS.0 2 a)) % 3.74/3.99 Clause #36 (by clausification #[3]): ∀ (a : Iota), % 3.74/3.99 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 % 3.74/3.99 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), % 3.74/3.99 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 % 3.74/3.99 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), % 3.74/3.99 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 % 3.74/3.99 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), % 3.74/3.99 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) % 3.74/3.99 Clause #49 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 3.74/3.99 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)) % 3.74/3.99 Clause #50 (by clausification #[49]): ∀ (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) % 3.82/4.00 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 a_3 : Iota), % 3.82/4.00 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)) % 3.82/4.00 Clause #53 (by clausification #[51]): ∀ (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)) % 3.82/4.00 Clause #55 (by clausification #[53]): ∀ (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)) % 3.82/4.00 Clause #56 (by destructive equality resolution #[55]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (unordered_pair a_1 a_2)) True) (Ne a a_2) % 3.82/4.00 Clause #57 (by destructive equality resolution #[56]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a_1 a)) True % 3.82/4.00 Clause #59 (by superposition #[57, 29]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (set_intersection2 (unordered_pair a a_1) (singleton a_1)) (singleton a_1)) % 3.82/4.00 Clause #83 (by clausification #[59]): ∀ (a a_1 : Iota), Eq (set_intersection2 (unordered_pair a a_1) (singleton a_1)) (singleton a_1) % 3.82/4.00 Clause #86 (by superposition #[83, 25]): ∀ (a a_1 : Iota), Eq (set_intersection2 (unordered_pair a a_1) (singleton a)) (singleton a) % 3.82/4.00 Clause #89 (by superposition #[86, 22]): ∀ (a a_1 : Iota), Eq (set_intersection2 (singleton a) (unordered_pair a a_1)) (singleton a) % 3.82/4.00 Clause #96 (by backward contextual literal cutting #[89, 35]): False % 3.82/4.00 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------