%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU162+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n017.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 08:01:01 PM UTC 2025 % Result : Theorem 5.75s 5.93s % Output : Proof 5.80s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SEU162+1 : TPTP v9.2.0. Released v3.3.0. % 0.07/0.14 % Command : duper %s % 0.14/0.36 % Computer : n017.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 : Fri Oct 3 06:12:38 EDT 2025 % 0.14/0.36 % CPUTime : % 5.75/5.93 SZS status Theorem for theBenchmark.p % 5.75/5.93 SZS output start Proof for theBenchmark.p % 5.75/5.93 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Not (And (disjoint (singleton A) B) (in A B))) True % 5.75/5.93 Clause #3 (by assumption #[]): Eq (∀ (A B : Iota), Not (in A B) → disjoint (singleton A) B) True % 5.75/5.93 Clause #4 (by assumption #[]): Eq (∀ (A B : Iota), disjoint A B → disjoint B A) True % 5.75/5.93 Clause #5 (by assumption #[]): Eq (Not (∀ (A B : Iota), Iff (Eq (set_difference A (singleton B)) A) (Not (in B A)))) True % 5.75/5.93 Clause #6 (by assumption #[]): Eq (∀ (A B : Iota), Iff (disjoint A B) (Eq (set_difference A B) A)) True % 5.75/5.93 Clause #7 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B : Iota), disjoint a B → disjoint B a) True % 5.75/5.93 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Eq (disjoint a a_1 → disjoint a_1 a) True % 5.75/5.93 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) False) (Eq (disjoint a_1 a) True) % 5.75/5.93 Clause #10 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B : Iota), Not (in a B) → disjoint (singleton a) B) True % 5.75/5.93 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (Not (in a a_1) → disjoint (singleton a) a_1) True % 5.75/5.93 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (Not (in a a_1)) False) (Eq (disjoint (singleton a) a_1) True) % 5.75/5.93 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (disjoint (singleton a) a_1) True) (Eq (in a a_1) True) % 5.75/5.93 Clause #21 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Not (And (disjoint (singleton a) B) (in a B))) True % 5.75/5.93 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (Not (And (disjoint (singleton a) a_1) (in a a_1))) True % 5.75/5.93 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (And (disjoint (singleton a) a_1) (in a a_1)) False % 5.75/5.93 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (disjoint (singleton a) a_1) False) (Eq (in a a_1) False) % 5.75/5.93 Clause #40 (by clausification #[5]): Eq (∀ (A B : Iota), Iff (Eq (set_difference A (singleton B)) A) (Not (in B A))) False % 5.75/5.93 Clause #41 (by clausification #[40]): ∀ (a : Iota), % 5.75/5.93 Eq (Not (∀ (B : Iota), Iff (Eq (set_difference (skS.0 0 a) (singleton B)) (skS.0 0 a)) (Not (in B (skS.0 0 a))))) True % 5.75/5.93 Clause #42 (by clausification #[41]): ∀ (a : Iota), % 5.75/5.93 Eq (∀ (B : Iota), Iff (Eq (set_difference (skS.0 0 a) (singleton B)) (skS.0 0 a)) (Not (in B (skS.0 0 a)))) False % 5.75/5.93 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), % 5.75/5.93 Eq % 5.75/5.93 (Not % 5.75/5.93 (Iff (Eq (set_difference (skS.0 0 a) (singleton (skS.0 1 a a_1))) (skS.0 0 a)) % 5.75/5.93 (Not (in (skS.0 1 a a_1) (skS.0 0 a))))) % 5.75/5.93 True % 5.75/5.93 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), % 5.75/5.93 Eq % 5.75/5.93 (Iff (Eq (set_difference (skS.0 0 a) (singleton (skS.0 1 a a_1))) (skS.0 0 a)) % 5.75/5.93 (Not (in (skS.0 1 a a_1) (skS.0 0 a)))) % 5.75/5.93 False % 5.75/5.93 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), % 5.75/5.93 Or (Eq (Eq (set_difference (skS.0 0 a) (singleton (skS.0 1 a a_1))) (skS.0 0 a)) False) % 5.75/5.93 (Eq (Not (in (skS.0 1 a a_1) (skS.0 0 a))) False) % 5.75/5.93 Clause #46 (by clausification #[44]): ∀ (a a_1 : Iota), % 5.75/5.93 Or (Eq (Eq (set_difference (skS.0 0 a) (singleton (skS.0 1 a a_1))) (skS.0 0 a)) True) % 5.75/5.93 (Eq (Not (in (skS.0 1 a a_1) (skS.0 0 a))) True) % 5.75/5.93 Clause #47 (by clausification #[45]): ∀ (a a_1 : Iota), % 5.75/5.93 Or (Eq (Not (in (skS.0 1 a a_1) (skS.0 0 a))) False) % 5.75/5.93 (Ne (set_difference (skS.0 0 a) (singleton (skS.0 1 a a_1))) (skS.0 0 a)) % 5.75/5.93 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), % 5.75/5.93 Or (Ne (set_difference (skS.0 0 a) (singleton (skS.0 1 a a_1))) (skS.0 0 a)) % 5.75/5.93 (Eq (in (skS.0 1 a a_1) (skS.0 0 a)) True) % 5.75/5.93 Clause #53 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (disjoint a B) (Eq (set_difference a B) a)) True % 5.75/5.93 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), Eq (Iff (disjoint a a_1) (Eq (set_difference a a_1) a)) True % 5.75/5.93 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) True) (Eq (Eq (set_difference a a_1) a) False) % 5.75/5.93 Clause #56 (by clausification #[54]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) False) (Eq (Eq (set_difference a a_1) a) True) % 5.75/5.93 Clause #57 (by clausification #[55]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) True) (Ne (set_difference a a_1) a) % 5.80/5.96 Clause #58 (by clausification #[56]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) False) (Eq (set_difference a a_1) a) % 5.80/5.96 Clause #87 (by clausification #[46]): ∀ (a a_1 : Iota), % 5.80/5.96 Or (Eq (Not (in (skS.0 1 a a_1) (skS.0 0 a))) True) % 5.80/5.96 (Eq (set_difference (skS.0 0 a) (singleton (skS.0 1 a a_1))) (skS.0 0 a)) % 5.80/5.96 Clause #88 (by clausification #[87]): ∀ (a a_1 : Iota), % 5.80/5.96 Or (Eq (set_difference (skS.0 0 a) (singleton (skS.0 1 a a_1))) (skS.0 0 a)) % 5.80/5.96 (Eq (in (skS.0 1 a a_1) (skS.0 0 a)) False) % 5.80/5.96 Clause #89 (by superposition #[88, 13]): ∀ (a a_1 : Iota), % 5.80/5.96 Or (Eq (set_difference (skS.0 0 a) (singleton (skS.0 1 a a_1))) (skS.0 0 a)) % 5.80/5.96 (Or (Eq (disjoint (singleton (skS.0 1 a a_1)) (skS.0 0 a)) True) (Eq False True)) % 5.80/5.96 Clause #121 (by clausification #[89]): ∀ (a a_1 : Iota), % 5.80/5.96 Or (Eq (set_difference (skS.0 0 a) (singleton (skS.0 1 a a_1))) (skS.0 0 a)) % 5.80/5.96 (Eq (disjoint (singleton (skS.0 1 a a_1)) (skS.0 0 a)) True) % 5.80/5.96 Clause #123 (by superposition #[121, 57]): ∀ (a a_1 : Iota), % 5.80/5.96 Or (Eq (disjoint (singleton (skS.0 1 a a_1)) (skS.0 0 a)) True) % 5.80/5.96 (Or (Eq (disjoint (skS.0 0 a) (singleton (skS.0 1 a a_1))) True) (Ne (skS.0 0 a) (skS.0 0 a))) % 5.80/5.96 Clause #153 (by eliminate resolved literals #[123]): ∀ (a a_1 : Iota), % 5.80/5.96 Or (Eq (disjoint (singleton (skS.0 1 a a_1)) (skS.0 0 a)) True) % 5.80/5.96 (Eq (disjoint (skS.0 0 a) (singleton (skS.0 1 a a_1))) True) % 5.80/5.96 Clause #155 (by superposition #[153, 9]): ∀ (a a_1 : Iota), % 5.80/5.96 Or (Eq (disjoint (skS.0 0 a) (singleton (skS.0 1 a a_1))) True) % 5.80/5.96 (Or (Eq True False) (Eq (disjoint (skS.0 0 a) (singleton (skS.0 1 a a_1))) True)) % 5.80/5.96 Clause #159 (by clausification #[155]): ∀ (a a_1 : Iota), % 5.80/5.96 Or (Eq (disjoint (skS.0 0 a) (singleton (skS.0 1 a a_1))) True) % 5.80/5.96 (Eq (disjoint (skS.0 0 a) (singleton (skS.0 1 a a_1))) True) % 5.80/5.96 Clause #160 (by eliminate duplicate literals #[159]): ∀ (a a_1 : Iota), Eq (disjoint (skS.0 0 a) (singleton (skS.0 1 a a_1))) True % 5.80/5.96 Clause #163 (by superposition #[160, 9]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (disjoint (singleton (skS.0 1 a a_1)) (skS.0 0 a)) True) % 5.80/5.96 Clause #164 (by superposition #[160, 58]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (set_difference (skS.0 0 a) (singleton (skS.0 1 a a_1))) (skS.0 0 a)) % 5.80/5.96 Clause #167 (by clausification #[163]): ∀ (a a_1 : Iota), Eq (disjoint (singleton (skS.0 1 a a_1)) (skS.0 0 a)) True % 5.80/5.96 Clause #169 (by superposition #[167, 24]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (in (skS.0 1 a a_1) (skS.0 0 a)) False) % 5.80/5.96 Clause #172 (by clausification #[169]): ∀ (a a_1 : Iota), Eq (in (skS.0 1 a a_1) (skS.0 0 a)) False % 5.80/5.96 Clause #173 (by backward demodulation #[172, 48]): ∀ (a a_1 : Iota), Or (Ne (set_difference (skS.0 0 a) (singleton (skS.0 1 a a_1))) (skS.0 0 a)) (Eq False True) % 5.80/5.96 Clause #178 (by clausification #[164]): ∀ (a a_1 : Iota), Eq (set_difference (skS.0 0 a) (singleton (skS.0 1 a a_1))) (skS.0 0 a) % 5.80/5.96 Clause #180 (by clausification #[173]): ∀ (a a_1 : Iota), Ne (set_difference (skS.0 0 a) (singleton (skS.0 1 a a_1))) (skS.0 0 a) % 5.80/5.96 Clause #181 (by forward demodulation #[180, 178]): ∀ (a : Iota), Ne (skS.0 0 a) (skS.0 0 a) % 5.80/5.96 Clause #182 (by eliminate resolved literals #[181]): False % 5.80/5.96 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------