%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU113+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 08:00:53 PM UTC 2025 % Result : Theorem 13.42s 13.57s % Output : Proof 13.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU113+1 : TPTP v9.2.0. Released v3.2.0. % 0.13/0.13 % Command : duper %s % 0.14/0.34 % Computer : n019.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 : Fri Oct 3 05:22:23 EDT 2025 % 0.14/0.34 % CPUTime : % 13.42/13.57 SZS status Theorem for theBenchmark.p % 13.42/13.57 SZS output start Proof for theBenchmark.p % 13.42/13.57 Clause #6 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True % 13.42/13.57 Clause #7 (by assumption #[]): Eq % 13.42/13.57 (∀ (A B : Iota), % 13.42/13.57 preboolean B → Iff (Eq B (finite_subsets A)) (∀ (C : Iota), Iff (in C B) (And (subset C A) (finite C)))) % 13.42/13.57 True % 13.42/13.57 Clause #8 (by assumption #[]): Eq (∀ (A : Iota), preboolean (finite_subsets A)) True % 13.42/13.57 Clause #11 (by assumption #[]): Eq (∀ (A : Iota), Not (empty (powerset A))) True % 13.42/13.57 Clause #24 (by assumption #[]): Eq (Not (∀ (A : Iota), subset (finite_subsets A) (powerset A))) True % 13.42/13.57 Clause #25 (by assumption #[]): Eq (∀ (A B : Iota), element A B → Or (empty B) (in A B)) True % 13.42/13.57 Clause #26 (by assumption #[]): Eq (∀ (A B : Iota), Iff (element A (powerset B)) (subset A B)) True % 13.42/13.57 Clause #32 (by clausification #[8]): ∀ (a : Iota), Eq (preboolean (finite_subsets a)) True % 13.42/13.57 Clause #47 (by clausification #[11]): ∀ (a : Iota), Eq (Not (empty (powerset a))) True % 13.42/13.57 Clause #48 (by clausification #[47]): ∀ (a : Iota), Eq (empty (powerset a)) False % 13.42/13.57 Clause #87 (by clausification #[24]): Eq (∀ (A : Iota), subset (finite_subsets A) (powerset A)) False % 13.42/13.57 Clause #88 (by clausification #[87]): ∀ (a : Iota), Eq (Not (subset (finite_subsets (skS.0 3 a)) (powerset (skS.0 3 a)))) True % 13.42/13.57 Clause #89 (by clausification #[88]): ∀ (a : Iota), Eq (subset (finite_subsets (skS.0 3 a)) (powerset (skS.0 3 a))) False % 13.42/13.57 Clause #91 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True % 13.42/13.57 Clause #92 (by clausification #[91]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (C : Iota), in C a → in C a_1)) True % 13.42/13.57 Clause #93 (by clausification #[92]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (C : Iota), in C a → in C a_1) False) % 13.42/13.57 Clause #95 (by clausification #[93]): ∀ (a a_1 a_2 : Iota), % 13.42/13.57 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) % 13.42/13.57 Clause #96 (by clausification #[95]): ∀ (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) % 13.42/13.57 Clause #97 (by clausification #[96]): ∀ (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) % 13.42/13.57 Clause #98 (by clausification #[96]): ∀ (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) % 13.42/13.57 Clause #116 (by clausification #[7]): ∀ (a : Iota), % 13.42/13.57 Eq % 13.42/13.57 (∀ (B : Iota), % 13.42/13.57 preboolean B → Iff (Eq B (finite_subsets a)) (∀ (C : Iota), Iff (in C B) (And (subset C a) (finite C)))) % 13.42/13.57 True % 13.42/13.57 Clause #117 (by clausification #[116]): ∀ (a a_1 : Iota), % 13.42/13.57 Eq (preboolean a → Iff (Eq a (finite_subsets a_1)) (∀ (C : Iota), Iff (in C a) (And (subset C a_1) (finite C)))) True % 13.42/13.57 Clause #118 (by clausification #[117]): ∀ (a a_1 : Iota), % 13.42/13.57 Or (Eq (preboolean a) False) % 13.42/13.57 (Eq (Iff (Eq a (finite_subsets a_1)) (∀ (C : Iota), Iff (in C a) (And (subset C a_1) (finite C)))) True) % 13.42/13.57 Clause #120 (by clausification #[118]): ∀ (a a_1 : Iota), % 13.42/13.57 Or (Eq (preboolean a) False) % 13.42/13.57 (Or (Eq (Eq a (finite_subsets a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (And (subset C a_1) (finite C))) True)) % 13.42/13.57 Clause #150 (by clausification #[25]): ∀ (a : Iota), Eq (∀ (B : Iota), element a B → Or (empty B) (in a B)) True % 13.42/13.57 Clause #151 (by clausification #[150]): ∀ (a a_1 : Iota), Eq (element a a_1 → Or (empty a_1) (in a a_1)) True % 13.42/13.57 Clause #152 (by clausification #[151]): ∀ (a a_1 : Iota), Or (Eq (element a a_1) False) (Eq (Or (empty a_1) (in a a_1)) True) % 13.42/13.57 Clause #153 (by clausification #[152]): ∀ (a a_1 : Iota), Or (Eq (element a a_1) False) (Or (Eq (empty a_1) True) (Eq (in a a_1) True)) % 13.42/13.57 Clause #157 (by clausification #[26]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (element a (powerset B)) (subset a B)) True % 13.42/13.57 Clause #158 (by clausification #[157]): ∀ (a a_1 : Iota), Eq (Iff (element a (powerset a_1)) (subset a a_1)) True % 13.42/13.57 Clause #159 (by clausification #[158]): ∀ (a a_1 : Iota), Or (Eq (element a (powerset a_1)) True) (Eq (subset a a_1) False) % 13.42/13.60 Clause #319 (by clausification #[120]): ∀ (a a_1 : Iota), % 13.42/13.60 Or (Eq (preboolean a) False) % 13.42/13.60 (Or (Eq (∀ (C : Iota), Iff (in C a) (And (subset C a_1) (finite C))) True) (Ne a (finite_subsets a_1))) % 13.42/13.60 Clause #320 (by clausification #[319]): ∀ (a a_1 a_2 : Iota), % 13.42/13.60 Or (Eq (preboolean a) False) % 13.42/13.60 (Or (Ne a (finite_subsets a_1)) (Eq (Iff (in a_2 a) (And (subset a_2 a_1) (finite a_2))) True)) % 13.42/13.60 Clause #322 (by clausification #[320]): ∀ (a a_1 a_2 : Iota), % 13.42/13.60 Or (Eq (preboolean a) False) % 13.42/13.60 (Or (Ne a (finite_subsets a_1)) (Or (Eq (in a_2 a) False) (Eq (And (subset a_2 a_1) (finite a_2)) True))) % 13.42/13.60 Clause #403 (by clausification #[322]): ∀ (a a_1 a_2 : Iota), % 13.42/13.60 Or (Eq (preboolean a) False) (Or (Ne a (finite_subsets a_1)) (Or (Eq (in a_2 a) False) (Eq (subset a_2 a_1) True))) % 13.42/13.60 Clause #409 (by destructive equality resolution #[403]): ∀ (a a_1 : Iota), % 13.42/13.60 Or (Eq (preboolean (finite_subsets a)) False) (Or (Eq (in a_1 (finite_subsets a)) False) (Eq (subset a_1 a) True)) % 13.42/13.60 Clause #410 (by forward demodulation #[409, 32]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (in a (finite_subsets a_1)) False) (Eq (subset a a_1) True)) % 13.42/13.60 Clause #411 (by clausification #[410]): ∀ (a a_1 : Iota), Or (Eq (in a (finite_subsets a_1)) False) (Eq (subset a a_1) True) % 13.42/13.60 Clause #413 (by superposition #[411, 97]): ∀ (a a_1 a_2 : Iota), % 13.42/13.60 Or (Eq (subset (skS.0 4 (finite_subsets a) a_1 a_2) a) True) % 13.42/13.60 (Or (Eq (subset (finite_subsets a) a_1) True) (Eq False True)) % 13.42/13.60 Clause #784 (by clausification #[413]): ∀ (a a_1 a_2 : Iota), % 13.42/13.60 Or (Eq (subset (skS.0 4 (finite_subsets a) a_1 a_2) a) True) (Eq (subset (finite_subsets a) a_1) True) % 13.42/13.60 Clause #786 (by superposition #[784, 159]): ∀ (a a_1 a_2 : Iota), % 13.42/13.60 Or (Eq (subset (finite_subsets a) a_1) True) % 13.42/13.60 (Or (Eq (element (skS.0 4 (finite_subsets a) a_1 a_2) (powerset a)) True) (Eq True False)) % 13.42/13.60 Clause #805 (by clausification #[786]): ∀ (a a_1 a_2 : Iota), % 13.42/13.60 Or (Eq (subset (finite_subsets a) a_1) True) (Eq (element (skS.0 4 (finite_subsets a) a_1 a_2) (powerset a)) True) % 13.42/13.60 Clause #816 (by superposition #[805, 153]): ∀ (a a_1 a_2 : Iota), % 13.42/13.60 Or (Eq (subset (finite_subsets a) a_1) True) % 13.42/13.60 (Or (Eq True False) % 13.42/13.60 (Or (Eq (empty (powerset a)) True) (Eq (in (skS.0 4 (finite_subsets a) a_1 a_2) (powerset a)) True))) % 13.42/13.60 Clause #1686 (by clausification #[816]): ∀ (a a_1 a_2 : Iota), % 13.42/13.60 Or (Eq (subset (finite_subsets a) a_1) True) % 13.42/13.60 (Or (Eq (empty (powerset a)) True) (Eq (in (skS.0 4 (finite_subsets a) a_1 a_2) (powerset a)) True)) % 13.42/13.60 Clause #1687 (by forward demodulation #[1686, 48]): ∀ (a a_1 a_2 : Iota), % 13.42/13.60 Or (Eq (subset (finite_subsets a) a_1) True) % 13.42/13.60 (Or (Eq False True) (Eq (in (skS.0 4 (finite_subsets a) a_1 a_2) (powerset a)) True)) % 13.42/13.60 Clause #1688 (by clausification #[1687]): ∀ (a a_1 a_2 : Iota), % 13.42/13.60 Or (Eq (subset (finite_subsets a) a_1) True) (Eq (in (skS.0 4 (finite_subsets a) a_1 a_2) (powerset a)) True) % 13.42/13.60 Clause #1689 (by superposition #[1688, 98]): ∀ (a : Iota), % 13.42/13.60 Or (Eq (subset (finite_subsets a) (powerset a)) True) % 13.42/13.60 (Or (Eq (subset (finite_subsets a) (powerset a)) True) (Eq True False)) % 13.42/13.60 Clause #1700 (by clausification #[1689]): ∀ (a : Iota), Or (Eq (subset (finite_subsets a) (powerset a)) True) (Eq (subset (finite_subsets a) (powerset a)) True) % 13.42/13.60 Clause #1701 (by eliminate duplicate literals #[1700]): ∀ (a : Iota), Eq (subset (finite_subsets a) (powerset a)) True % 13.42/13.60 Clause #1702 (by superposition #[1701, 89]): Eq True False % 13.42/13.60 Clause #1731 (by clausification #[1702]): False % 13.42/13.60 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------