%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET881+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n025.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 5.47s 5.64s % Output : Proof 5.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET881+1 : TPTP v9.2.0. Released v3.2.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n025.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 14:37:23 EDT 2025 % 0.13/0.35 % CPUTime : % 5.47/5.64 SZS status Theorem for theBenchmark.p % 5.47/5.64 SZS output start Proof for theBenchmark.p % 5.47/5.64 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True % 5.47/5.64 Clause #2 (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 % 5.47/5.64 Clause #4 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (set_difference (singleton A) B) empty_set) (in A B)) True % 5.47/5.64 Clause #7 (by assumption #[]): Eq (Not (∀ (A B : Iota), Eq (set_difference (singleton A) (unordered_pair A B)) empty_set)) True % 5.47/5.64 Clause #16 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True % 5.47/5.64 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True % 5.47/5.64 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a) % 5.47/5.64 Clause #19 (by clausification #[2]): ∀ (a : Iota), % 5.47/5.64 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 % 5.47/5.64 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), % 5.47/5.64 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 % 5.47/5.64 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), % 5.47/5.64 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 % 5.47/5.64 Clause #23 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), % 5.47/5.64 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) % 5.47/5.64 Clause #32 (by clausification #[7]): Eq (∀ (A B : Iota), Eq (set_difference (singleton A) (unordered_pair A B)) empty_set) False % 5.47/5.64 Clause #33 (by clausification #[32]): ∀ (a : Iota), % 5.47/5.64 Eq (Not (∀ (B : Iota), Eq (set_difference (singleton (skS.0 3 a)) (unordered_pair (skS.0 3 a) B)) empty_set)) True % 5.47/5.64 Clause #34 (by clausification #[33]): ∀ (a : Iota), % 5.47/5.64 Eq (∀ (B : Iota), Eq (set_difference (singleton (skS.0 3 a)) (unordered_pair (skS.0 3 a) B)) empty_set) False % 5.47/5.64 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), % 5.47/5.64 Eq (Not (Eq (set_difference (singleton (skS.0 3 a)) (unordered_pair (skS.0 3 a) (skS.0 4 a a_1))) empty_set)) True % 5.47/5.64 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), % 5.47/5.64 Eq (Eq (set_difference (singleton (skS.0 3 a)) (unordered_pair (skS.0 3 a) (skS.0 4 a a_1))) empty_set) False % 5.47/5.64 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Ne (set_difference (singleton (skS.0 3 a)) (unordered_pair (skS.0 3 a) (skS.0 4 a a_1))) empty_set % 5.47/5.64 Clause #38 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (set_difference (singleton a) B) empty_set) (in a B)) True % 5.47/5.64 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (Iff (Eq (set_difference (singleton a) a_1) empty_set) (in a a_1)) True % 5.47/5.64 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference (singleton a) a_1) empty_set) True) (Eq (in a a_1) False) % 5.47/5.64 Clause #42 (by clausification #[40]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (set_difference (singleton a) a_1) empty_set) % 5.47/5.64 Clause #44 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), % 5.47/5.64 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)) % 5.47/5.64 Clause #45 (by clausification #[44]): ∀ (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) % 5.47/5.64 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 a_3 : Iota), % 5.47/5.64 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)) % 5.47/5.64 Clause #48 (by clausification #[46]): ∀ (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)) % 5.47/5.64 Clause #50 (by clausification #[48]): ∀ (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)) % 5.47/5.64 Clause #51 (by destructive equality resolution #[50]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (unordered_pair a_1 a_2)) True) (Ne a a_2) % 5.47/5.64 Clause #52 (by destructive equality resolution #[51]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a_1 a)) True % 5.47/5.64 Clause #54 (by superposition #[52, 42]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (set_difference (singleton a) (unordered_pair a_1 a)) empty_set) % 5.47/5.64 Clause #78 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (set_difference (singleton a) (unordered_pair a_1 a)) empty_set % 5.47/5.64 Clause #80 (by superposition #[78, 18]): ∀ (a a_1 : Iota), Eq (set_difference (singleton a) (unordered_pair a a_1)) empty_set % 5.47/5.64 Clause #83 (by backward contextual literal cutting #[80, 37]): False % 5.47/5.64 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------