%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU133+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n029.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 08:00:55 PM UTC 2025 % Result : Theorem 3.85s 4.02s % Output : Proof 3.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : SEU133+1 : TPTP v9.2.0. Released v3.3.0. % 0.03/0.14 % Command : duper %s % 0.14/0.35 % Computer : n029.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % 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 : Fri Oct 3 04:58:23 EDT 2025 % 0.14/0.36 % CPUTime : % 3.85/4.02 SZS status Theorem for theBenchmark.p % 3.85/4.02 SZS output start Proof for theBenchmark.p % 3.85/4.02 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True % 3.85/4.02 Clause #2 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (Eq C (set_difference A B)) (∀ (D : Iota), Iff (in D C) (And (in D A) (Not (in D B))))) True % 3.85/4.02 Clause #8 (by assumption #[]): Eq (Not (∀ (A B : Iota), subset (set_difference A B) A)) True % 3.85/4.02 Clause #34 (by clausification #[8]): Eq (∀ (A B : Iota), subset (set_difference A B) A) False % 3.85/4.02 Clause #35 (by clausification #[34]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), subset (set_difference (skS.0 2 a) B) (skS.0 2 a))) True % 3.85/4.02 Clause #36 (by clausification #[35]): ∀ (a : Iota), Eq (∀ (B : Iota), subset (set_difference (skS.0 2 a) B) (skS.0 2 a)) False % 3.85/4.02 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (Not (subset (set_difference (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 2 a))) True % 3.85/4.02 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (subset (set_difference (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 2 a)) False % 3.85/4.02 Clause #39 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True % 3.85/4.02 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (C : Iota), in C a → in C a_1)) True % 3.85/4.02 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (C : Iota), in C a → in C a_1) False) % 3.85/4.02 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 3.85/4.02 Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 4 a a_1 a_2) a → in (skS.0 4 a a_1 a_2) a_1)) True) % 3.85/4.02 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 4 a a_1 a_2) a → in (skS.0 4 a a_1 a_2) a_1) False) % 3.85/4.02 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 4 a a_1 a_2) a) True) % 3.85/4.02 Clause #46 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 4 a a_1 a_2) a_1) False) % 3.85/4.02 Clause #61 (by clausification #[2]): ∀ (a : Iota), % 3.85/4.02 Eq (∀ (B C : Iota), Iff (Eq C (set_difference a B)) (∀ (D : Iota), Iff (in D C) (And (in D a) (Not (in D B))))) True % 3.85/4.02 Clause #62 (by clausification #[61]): ∀ (a a_1 : Iota), % 3.85/4.02 Eq (∀ (C : Iota), Iff (Eq C (set_difference a a_1)) (∀ (D : Iota), Iff (in D C) (And (in D a) (Not (in D a_1))))) True % 3.85/4.02 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 : Iota), % 3.85/4.02 Eq (Iff (Eq a (set_difference a_1 a_2)) (∀ (D : Iota), Iff (in D a) (And (in D a_1) (Not (in D a_2))))) True % 3.85/4.02 Clause #65 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), % 3.85/4.02 Or (Eq (Eq a (set_difference a_1 a_2)) False) (Eq (∀ (D : Iota), Iff (in D a) (And (in D a_1) (Not (in D a_2)))) True) % 3.85/4.02 Clause #89 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), % 3.85/4.02 Or (Eq (∀ (D : Iota), Iff (in D a) (And (in D a_1) (Not (in D a_2)))) True) (Ne a (set_difference a_1 a_2)) % 3.85/4.02 Clause #90 (by clausification #[89]): ∀ (a a_1 a_2 a_3 : Iota), % 3.85/4.02 Or (Ne a (set_difference a_1 a_2)) (Eq (Iff (in a_3 a) (And (in a_3 a_1) (Not (in a_3 a_2)))) True) % 3.85/4.02 Clause #92 (by clausification #[90]): ∀ (a a_1 a_2 a_3 : Iota), % 3.85/4.02 Or (Ne a (set_difference a_1 a_2)) (Or (Eq (in a_3 a) False) (Eq (And (in a_3 a_1) (Not (in a_3 a_2))) True)) % 3.85/4.02 Clause #98 (by clausification #[92]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (set_difference a_1 a_2)) (Or (Eq (in a_3 a) False) (Eq (in a_3 a_1) True)) % 3.85/4.02 Clause #108 (by destructive equality resolution #[98]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (set_difference a_1 a_2)) False) (Eq (in a a_1) True) % 3.85/4.02 Clause #109 (by superposition #[108, 45]): ∀ (a a_1 a_2 a_3 : Iota), % 3.85/4.02 Or (Eq (in (skS.0 4 (set_difference a a_1) a_2 a_3) a) True) % 3.85/4.02 (Or (Eq (subset (set_difference a a_1) a_2) True) (Eq False True)) % 3.85/4.02 Clause #113 (by clausification #[109]): ∀ (a a_1 a_2 a_3 : Iota), % 3.85/4.02 Or (Eq (in (skS.0 4 (set_difference a a_1) a_2 a_3) a) True) (Eq (subset (set_difference a a_1) a_2) True) % 3.85/4.02 Clause #118 (by superposition #[113, 46]): ∀ (a a_1 : Iota), % 3.85/4.02 Or (Eq (subset (set_difference a a_1) a) True) (Or (Eq (subset (set_difference a a_1) a) True) (Eq True False)) % 3.85/4.02 Clause #136 (by clausification #[118]): ∀ (a a_1 : Iota), Or (Eq (subset (set_difference a a_1) a) True) (Eq (subset (set_difference a a_1) a) True) % 3.85/4.02 Clause #137 (by eliminate duplicate literals #[136]): ∀ (a a_1 : Iota), Eq (subset (set_difference a a_1) a) True % 3.85/4.02 Clause #138 (by superposition #[137, 38]): Eq True False % 3.85/4.02 Clause #141 (by clausification #[138]): False % 3.85/4.02 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------