%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET987+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.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 08:00:46 PM UTC 2025 % Result : Theorem 3.63s 3.80s % Output : Proof 3.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SET987+1 : TPTP v9.2.0. Released v3.2.0. % 0.10/0.13 % Command : duper %s % 0.14/0.34 % Computer : n004.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 13:51:53 EDT 2025 % 0.14/0.34 % CPUTime : % 3.63/3.80 SZS status Theorem for theBenchmark.p % 3.63/3.80 SZS output start Proof for theBenchmark.p % 3.63/3.80 Clause #7 (by assumption #[]): Eq (Not (∀ (A B : Iota), Not (in A B) → Eq (set_difference (set_union2 B (singleton A)) (singleton A)) B)) True % 3.63/3.80 Clause #8 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_difference (set_union2 A B) B) (set_difference A B)) True % 3.63/3.80 Clause #9 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (set_difference A (singleton B)) A) (Not (in B A))) True % 3.63/3.80 Clause #35 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_difference (set_union2 a B) B) (set_difference a B)) True % 3.63/3.80 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (Eq (set_difference (set_union2 a a_1) a_1) (set_difference a a_1)) True % 3.63/3.80 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (set_difference (set_union2 a a_1) a_1) (set_difference a a_1) % 3.63/3.80 Clause #39 (by clausification #[9]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (set_difference a (singleton B)) a) (Not (in B a))) True % 3.63/3.80 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (Iff (Eq (set_difference a (singleton a_1)) a) (Not (in a_1 a))) True % 3.63/3.80 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference a (singleton a_1)) a) True) (Eq (Not (in a_1 a)) False) % 3.63/3.80 Clause #43 (by clausification #[41]): ∀ (a a_1 : Iota), Or (Eq (Not (in a a_1)) False) (Eq (set_difference a_1 (singleton a)) a_1) % 3.63/3.80 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Or (Eq (set_difference a (singleton a_1)) a) (Eq (in a_1 a) True) % 3.63/3.80 Clause #46 (by clausification #[7]): Eq (∀ (A B : Iota), Not (in A B) → Eq (set_difference (set_union2 B (singleton A)) (singleton A)) B) False % 3.63/3.80 Clause #47 (by clausification #[46]): ∀ (a : Iota), % 3.63/3.80 Eq % 3.63/3.80 (Not % 3.63/3.80 (∀ (B : Iota), % 3.63/3.80 Not (in (skS.0 2 a) B) → Eq (set_difference (set_union2 B (singleton (skS.0 2 a))) (singleton (skS.0 2 a))) B)) % 3.63/3.80 True % 3.63/3.80 Clause #48 (by clausification #[47]): ∀ (a : Iota), % 3.63/3.80 Eq % 3.63/3.80 (∀ (B : Iota), % 3.63/3.80 Not (in (skS.0 2 a) B) → Eq (set_difference (set_union2 B (singleton (skS.0 2 a))) (singleton (skS.0 2 a))) B) % 3.63/3.80 False % 3.63/3.80 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), % 3.63/3.80 Eq % 3.63/3.80 (Not % 3.63/3.80 (Not (in (skS.0 2 a) (skS.0 3 a a_1)) → % 3.63/3.80 Eq (set_difference (set_union2 (skS.0 3 a a_1) (singleton (skS.0 2 a))) (singleton (skS.0 2 a))) % 3.63/3.80 (skS.0 3 a a_1))) % 3.63/3.80 True % 3.63/3.80 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), % 3.63/3.80 Eq % 3.63/3.80 (Not (in (skS.0 2 a) (skS.0 3 a a_1)) → % 3.63/3.80 Eq (set_difference (set_union2 (skS.0 3 a a_1) (singleton (skS.0 2 a))) (singleton (skS.0 2 a))) (skS.0 3 a a_1)) % 3.63/3.80 False % 3.63/3.80 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), Eq (Not (in (skS.0 2 a) (skS.0 3 a a_1))) True % 3.63/3.80 Clause #52 (by clausification #[50]): ∀ (a a_1 : Iota), % 3.63/3.80 Eq (Eq (set_difference (set_union2 (skS.0 3 a a_1) (singleton (skS.0 2 a))) (singleton (skS.0 2 a))) (skS.0 3 a a_1)) % 3.63/3.80 False % 3.63/3.80 Clause #53 (by clausification #[51]): ∀ (a a_1 : Iota), Eq (in (skS.0 2 a) (skS.0 3 a a_1)) False % 3.63/3.80 Clause #54 (by superposition #[53, 44]): ∀ (a a_1 : Iota), Or (Eq (set_difference (skS.0 3 a a_1) (singleton (skS.0 2 a))) (skS.0 3 a a_1)) (Eq False True) % 3.63/3.80 Clause #71 (by clausification #[52]): ∀ (a a_1 : Iota), % 3.63/3.80 Ne (set_difference (set_union2 (skS.0 3 a a_1) (singleton (skS.0 2 a))) (singleton (skS.0 2 a))) (skS.0 3 a a_1) % 3.63/3.80 Clause #72 (by forward demodulation #[71, 37]): ∀ (a a_1 : Iota), Ne (set_difference (skS.0 3 a a_1) (singleton (skS.0 2 a))) (skS.0 3 a a_1) % 3.63/3.80 Clause #81 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (set_difference (skS.0 3 a a_1) (singleton (skS.0 2 a))) (skS.0 3 a a_1) % 3.63/3.80 Clause #82 (by forward contextual literal cutting #[81, 72]): False % 3.63/3.80 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------