%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET891+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.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 08:00:39 PM UTC 2025 % Result : Theorem 3.94s 4.16s % Output : Proof 3.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SET891+1 : TPTP v9.2.0. Released v3.2.0. % 0.08/0.14 % Command : duper %s % 0.14/0.36 % Computer : n010.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 14:59:08 EDT 2025 % 0.14/0.36 % CPUTime : % 3.94/4.16 SZS status Theorem for theBenchmark.p % 3.94/4.16 SZS output start Proof for theBenchmark.p % 3.94/4.16 Clause #5 (by assumption #[]): Eq (∀ (A B : Iota), Eq (union (unordered_pair A B)) (set_union2 A B)) True % 3.94/4.16 Clause #8 (by assumption #[]): Eq (Not (∀ (A B : Iota), Eq (union (unordered_pair (singleton A) (singleton B))) (unordered_pair A B))) True % 3.94/4.16 Clause #9 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (set_union2 (singleton A) (singleton B))) True % 3.94/4.16 Clause #34 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (union (unordered_pair a B)) (set_union2 a B)) True % 3.94/4.16 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Eq (Eq (union (unordered_pair a a_1)) (set_union2 a a_1)) True % 3.94/4.16 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (union (unordered_pair a a_1)) (set_union2 a a_1) % 3.94/4.16 Clause #38 (by clausification #[9]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (set_union2 (singleton a) (singleton B))) True % 3.94/4.16 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (set_union2 (singleton a) (singleton a_1))) True % 3.94/4.16 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (set_union2 (singleton a) (singleton a_1)) % 3.94/4.16 Clause #46 (by clausification #[8]): Eq (∀ (A B : Iota), Eq (union (unordered_pair (singleton A) (singleton B))) (unordered_pair A B)) False % 3.94/4.16 Clause #47 (by clausification #[46]): ∀ (a : Iota), % 3.94/4.16 Eq % 3.94/4.16 (Not % 3.94/4.16 (∀ (B : Iota), Eq (union (unordered_pair (singleton (skS.0 2 a)) (singleton B))) (unordered_pair (skS.0 2 a) B))) % 3.94/4.16 True % 3.94/4.16 Clause #48 (by clausification #[47]): ∀ (a : Iota), % 3.94/4.16 Eq (∀ (B : Iota), Eq (union (unordered_pair (singleton (skS.0 2 a)) (singleton B))) (unordered_pair (skS.0 2 a) B)) % 3.94/4.16 False % 3.94/4.16 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), % 3.94/4.16 Eq % 3.94/4.16 (Not % 3.94/4.16 (Eq (union (unordered_pair (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1)))) % 3.94/4.16 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)))) % 3.94/4.16 True % 3.94/4.16 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), % 3.94/4.16 Eq % 3.94/4.16 (Eq (union (unordered_pair (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1)))) % 3.94/4.16 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1))) % 3.94/4.16 False % 3.94/4.16 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), % 3.94/4.16 Ne (union (unordered_pair (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1)))) % 3.94/4.16 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) % 3.94/4.16 Clause #52 (by forward demodulation #[51, 36]): ∀ (a a_1 : Iota), % 3.94/4.16 Ne (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) % 3.94/4.16 Clause #53 (by forward demodulation #[52, 40]): ∀ (a a_1 : Iota), Ne (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) % 3.94/4.16 Clause #54 (by eliminate resolved literals #[53]): False % 3.94/4.16 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------