%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU147+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n028.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 08:00:57 PM UTC 2025 % Result : Theorem 3.98s 4.21s % Output : Proof 3.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU147+1 : TPTP v9.2.0. Released v3.3.0. % 0.07/0.13 % Command : duper %s % 0.12/0.33 % Computer : n028.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Fri Oct 3 06:09:08 EDT 2025 % 0.12/0.34 % CPUTime : % 3.98/4.21 SZS status Theorem for theBenchmark.p % 3.98/4.21 SZS output start Proof for theBenchmark.p % 3.98/4.21 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True % 3.98/4.21 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (powerset A)) (∀ (C : Iota), Iff (in C B) (subset C A))) True % 3.98/4.21 Clause #7 (by assumption #[]): Eq (∀ (A : Iota), Iota → subset A A) True % 3.98/4.21 Clause #8 (by assumption #[]): Eq (Not (Eq (powerset empty_set) (singleton empty_set))) True % 3.98/4.21 Clause #10 (by assumption #[]): Eq (∀ (A : Iota), subset A empty_set → Eq A empty_set) True % 3.98/4.21 Clause #13 (by clausification #[7]): ∀ (a : Iota), Eq (Iota → subset a a) True % 3.98/4.21 Clause #14 (by clausification #[13]): ∀ (a : Iota), Iota → Eq (subset a a) True % 3.98/4.21 Clause #21 (by clausification #[10]): ∀ (a : Iota), Eq (subset a empty_set → Eq a empty_set) True % 3.98/4.21 Clause #22 (by clausification #[21]): ∀ (a : Iota), Or (Eq (subset a empty_set) False) (Eq (Eq a empty_set) True) % 3.98/4.21 Clause #23 (by clausification #[22]): ∀ (a : Iota), Or (Eq (subset a empty_set) False) (Eq a empty_set) % 3.98/4.21 Clause #34 (by clausification #[8]): Eq (Eq (powerset empty_set) (singleton empty_set)) False % 3.98/4.21 Clause #35 (by clausification #[34]): Ne (powerset empty_set) (singleton empty_set) % 3.98/4.21 Clause #36 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (powerset a)) (∀ (C : Iota), Iff (in C B) (subset C a))) True % 3.98/4.21 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (powerset a_1)) (∀ (C : Iota), Iff (in C a) (subset C a_1))) True % 3.98/4.21 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (Eq a (powerset a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (subset C a_1)) True) % 3.98/4.21 Clause #45 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True % 3.98/4.21 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True % 3.98/4.21 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) True) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) False) % 3.98/4.21 Clause #49 (by clausification #[47]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) False) (Eq a (singleton a_1)) % 3.98/4.21 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), % 3.98/4.21 Or (Eq a (singleton a_1)) (Eq (Not (Iff (in (skS.0 4 a a_1 a_2) a) (Eq (skS.0 4 a a_1 a_2) a_1))) True) % 3.98/4.21 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), Or (Eq a (singleton a_1)) (Eq (Iff (in (skS.0 4 a a_1 a_2) a) (Eq (skS.0 4 a a_1 a_2) a_1)) False) % 3.98/4.21 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), % 3.98/4.21 Or (Eq a (singleton a_1)) (Or (Eq (in (skS.0 4 a a_1 a_2) a) False) (Eq (Eq (skS.0 4 a a_1 a_2) a_1) False)) % 3.98/4.21 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), % 3.98/4.21 Or (Eq a (singleton a_1)) (Or (Eq (in (skS.0 4 a a_1 a_2) a) True) (Eq (Eq (skS.0 4 a a_1 a_2) a_1) True)) % 3.98/4.21 Clause #54 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), Or (Eq a (singleton a_1)) (Or (Eq (in (skS.0 4 a a_1 a_2) a) False) (Ne (skS.0 4 a a_1 a_2) a_1)) % 3.98/4.21 Clause #55 (by clausification #[39]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (subset C a_1)) True) (Ne a (powerset a_1)) % 3.98/4.21 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), Or (Ne a (powerset a_1)) (Eq (Iff (in a_2 a) (subset a_2 a_1)) True) % 3.98/4.21 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), Or (Ne a (powerset a_1)) (Or (Eq (in a_2 a) True) (Eq (subset a_2 a_1) False)) % 3.98/4.21 Clause #58 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), Or (Ne a (powerset a_1)) (Or (Eq (in a_2 a) False) (Eq (subset a_2 a_1) True)) % 3.98/4.21 Clause #59 (by destructive equality resolution #[57]): ∀ (a a_1 : Iota), Or (Eq (in a (powerset a_1)) True) (Eq (subset a a_1) False) % 3.98/4.21 Clause #60 (by superposition #[59, 14]): ∀ (a : Iota), Or (Eq (in a (powerset a)) True) (Eq False True) % 3.98/4.21 Clause #61 (by clausification #[60]): ∀ (a : Iota), Eq (in a (powerset a)) True % 3.98/4.21 Clause #64 (by destructive equality resolution #[58]): ∀ (a a_1 : Iota), Or (Eq (in a (powerset a_1)) False) (Eq (subset a a_1) True) % 3.98/4.22 Clause #160 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), Or (Eq a (singleton a_1)) (Or (Eq (in (skS.0 4 a a_1 a_2) a) True) (Eq (skS.0 4 a a_1 a_2) a_1)) % 3.98/4.22 Clause #170 (by superposition #[160, 54]): ∀ (a a_1 a_2 : Iota), % 3.98/4.22 Or (Eq a (singleton a_1)) % 3.98/4.22 (Or (Eq (in (skS.0 4 a a_1 a_2) a) True) (Or (Eq a (singleton a_1)) (Or (Eq (in a_1 a) False) (Ne a_1 a_1)))) % 3.98/4.22 Clause #173 (by eliminate duplicate literals #[170]): ∀ (a a_1 a_2 : Iota), % 3.98/4.22 Or (Eq a (singleton a_1)) (Or (Eq (in (skS.0 4 a a_1 a_2) a) True) (Or (Eq (in a_1 a) False) (Ne a_1 a_1))) % 3.98/4.22 Clause #174 (by eliminate resolved literals #[173]): ∀ (a a_1 a_2 : Iota), Or (Eq a (singleton a_1)) (Or (Eq (in (skS.0 4 a a_1 a_2) a) True) (Eq (in a_1 a) False)) % 3.98/4.22 Clause #177 (by superposition #[174, 61]): ∀ (a a_1 : Iota), % 3.98/4.22 Or (Eq (powerset a) (singleton a)) (Or (Eq (in (skS.0 4 (powerset a) a a_1) (powerset a)) True) (Eq False True)) % 3.98/4.22 Clause #186 (by clausification #[177]): ∀ (a a_1 : Iota), Or (Eq (powerset a) (singleton a)) (Eq (in (skS.0 4 (powerset a) a a_1) (powerset a)) True) % 3.98/4.22 Clause #187 (by superposition #[186, 64]): ∀ (a a_1 : Iota), % 3.98/4.22 Or (Eq (powerset a) (singleton a)) (Or (Eq True False) (Eq (subset (skS.0 4 (powerset a) a a_1) a) True)) % 3.98/4.22 Clause #197 (by clausification #[187]): ∀ (a a_1 : Iota), Or (Eq (powerset a) (singleton a)) (Eq (subset (skS.0 4 (powerset a) a a_1) a) True) % 3.98/4.22 Clause #198 (by superposition #[197, 23]): ∀ (a : Iota), % 3.98/4.22 Or (Eq (powerset empty_set) (singleton empty_set)) % 3.98/4.22 (Or (Eq True False) (Eq (skS.0 4 (powerset empty_set) empty_set a) empty_set)) % 3.98/4.22 Clause #206 (by clausification #[198]): ∀ (a : Iota), % 3.98/4.22 Or (Eq (powerset empty_set) (singleton empty_set)) (Eq (skS.0 4 (powerset empty_set) empty_set a) empty_set) % 3.98/4.22 Clause #207 (by forward contextual literal cutting #[206, 35]): ∀ (a : Iota), Eq (skS.0 4 (powerset empty_set) empty_set a) empty_set % 3.98/4.22 Clause #208 (by superposition #[207, 54]): Or (Eq (powerset empty_set) (singleton empty_set)) % 3.98/4.22 (Or (Eq (in empty_set (powerset empty_set)) False) (Ne empty_set empty_set)) % 3.98/4.22 Clause #219 (by eliminate resolved literals #[208]): Or (Eq (powerset empty_set) (singleton empty_set)) (Eq (in empty_set (powerset empty_set)) False) % 3.98/4.22 Clause #220 (by forward contextual literal cutting #[219, 35]): Eq (in empty_set (powerset empty_set)) False % 3.98/4.22 Clause #221 (by superposition #[220, 61]): Eq False True % 3.98/4.22 Clause #227 (by clausification #[221]): False % 3.98/4.22 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------