%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU117+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.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 6.06s 6.27s % Output : Proof 6.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU117+1 : TPTP v9.2.0. Released v3.2.0. % 0.03/0.14 % Command : duper %s % 0.13/0.34 % Computer : n018.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 06:10:38 EDT 2025 % 0.13/0.35 % CPUTime : % 6.06/6.27 SZS status Theorem for theBenchmark.p % 6.06/6.27 SZS output start Proof for theBenchmark.p % 6.06/6.27 Clause #3 (by assumption #[]): Eq (∀ (A B : Iota), element A B → Or (empty B) (in A B)) True % 6.06/6.27 Clause #10 (by assumption #[]): Eq (∀ (A : Iota), preboolean (finite_subsets A)) True % 6.06/6.27 Clause #12 (by assumption #[]): Eq % 6.06/6.27 (∀ (A : Iota), % 6.06/6.27 And (And (And (Not (empty (finite_subsets A))) (cup_closed (finite_subsets A))) (diff_closed (finite_subsets A))) % 6.06/6.27 (preboolean (finite_subsets A))) % 6.06/6.27 True % 6.06/6.27 Clause #26 (by assumption #[]): Eq (∀ (A B : Iota), Iff (element A (powerset B)) (subset A B)) True % 6.06/6.27 Clause #29 (by assumption #[]): Eq (Not (∀ (A B : Iota), element B (finite_subsets A) → element B (powerset A))) True % 6.06/6.27 Clause #30 (by assumption #[]): Eq % 6.06/6.27 (∀ (A B : Iota), % 6.06/6.27 preboolean B → Iff (Eq B (finite_subsets A)) (∀ (C : Iota), Iff (in C B) (And (subset C A) (finite C)))) % 6.06/6.27 True % 6.06/6.27 Clause #38 (by clausification #[10]): ∀ (a : Iota), Eq (preboolean (finite_subsets a)) True % 6.06/6.27 Clause #39 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B : Iota), element a B → Or (empty B) (in a B)) True % 6.06/6.27 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (element a a_1 → Or (empty a_1) (in a a_1)) True % 6.06/6.27 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Or (Eq (element a a_1) False) (Eq (Or (empty a_1) (in a a_1)) True) % 6.06/6.27 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Or (Eq (element a a_1) False) (Or (Eq (empty a_1) True) (Eq (in a a_1) True)) % 6.06/6.27 Clause #108 (by clausification #[29]): Eq (∀ (A B : Iota), element B (finite_subsets A) → element B (powerset A)) False % 6.06/6.27 Clause #109 (by clausification #[108]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), element B (finite_subsets (skS.0 3 a)) → element B (powerset (skS.0 3 a)))) True % 6.06/6.27 Clause #110 (by clausification #[109]): ∀ (a : Iota), Eq (∀ (B : Iota), element B (finite_subsets (skS.0 3 a)) → element B (powerset (skS.0 3 a))) False % 6.06/6.27 Clause #111 (by clausification #[110]): ∀ (a a_1 : Iota), % 6.06/6.27 Eq (Not (element (skS.0 4 a a_1) (finite_subsets (skS.0 3 a)) → element (skS.0 4 a a_1) (powerset (skS.0 3 a)))) True % 6.06/6.27 Clause #112 (by clausification #[111]): ∀ (a a_1 : Iota), % 6.06/6.27 Eq (element (skS.0 4 a a_1) (finite_subsets (skS.0 3 a)) → element (skS.0 4 a a_1) (powerset (skS.0 3 a))) False % 6.06/6.27 Clause #113 (by clausification #[112]): ∀ (a a_1 : Iota), Eq (element (skS.0 4 a a_1) (finite_subsets (skS.0 3 a))) True % 6.06/6.27 Clause #114 (by clausification #[112]): ∀ (a a_1 : Iota), Eq (element (skS.0 4 a a_1) (powerset (skS.0 3 a))) False % 6.06/6.27 Clause #116 (by superposition #[113, 42]): ∀ (a a_1 : Iota), % 6.06/6.27 Or (Eq True False) % 6.06/6.27 (Or (Eq (empty (finite_subsets (skS.0 3 a))) True) (Eq (in (skS.0 4 a a_1) (finite_subsets (skS.0 3 a))) True)) % 6.06/6.27 Clause #138 (by clausification #[12]): ∀ (a : Iota), % 6.06/6.27 Eq % 6.06/6.27 (And (And (And (Not (empty (finite_subsets a))) (cup_closed (finite_subsets a))) (diff_closed (finite_subsets a))) % 6.06/6.27 (preboolean (finite_subsets a))) % 6.06/6.27 True % 6.06/6.27 Clause #139 (by clausification #[138]): ∀ (a : Iota), % 6.06/6.27 Eq (And (And (Not (empty (finite_subsets a))) (cup_closed (finite_subsets a))) (diff_closed (finite_subsets a))) True % 6.06/6.27 Clause #144 (by clausification #[26]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (element a (powerset B)) (subset a B)) True % 6.06/6.27 Clause #145 (by clausification #[144]): ∀ (a a_1 : Iota), Eq (Iff (element a (powerset a_1)) (subset a a_1)) True % 6.06/6.27 Clause #146 (by clausification #[145]): ∀ (a a_1 : Iota), Or (Eq (element a (powerset a_1)) True) (Eq (subset a a_1) False) % 6.06/6.27 Clause #217 (by clausification #[30]): ∀ (a : Iota), % 6.06/6.27 Eq % 6.06/6.27 (∀ (B : Iota), % 6.06/6.27 preboolean B → Iff (Eq B (finite_subsets a)) (∀ (C : Iota), Iff (in C B) (And (subset C a) (finite C)))) % 6.06/6.27 True % 6.06/6.27 Clause #218 (by clausification #[217]): ∀ (a a_1 : Iota), % 6.06/6.27 Eq (preboolean a → Iff (Eq a (finite_subsets a_1)) (∀ (C : Iota), Iff (in C a) (And (subset C a_1) (finite C)))) True % 6.06/6.27 Clause #219 (by clausification #[218]): ∀ (a a_1 : Iota), % 6.06/6.27 Or (Eq (preboolean a) False) % 6.06/6.27 (Eq (Iff (Eq a (finite_subsets a_1)) (∀ (C : Iota), Iff (in C a) (And (subset C a_1) (finite C)))) True) % 6.06/6.27 Clause #221 (by clausification #[219]): ∀ (a a_1 : Iota), % 6.06/6.29 Or (Eq (preboolean a) False) % 6.06/6.29 (Or (Eq (Eq a (finite_subsets a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (And (subset C a_1) (finite C))) True)) % 6.06/6.29 Clause #237 (by clausification #[139]): ∀ (a : Iota), Eq (And (Not (empty (finite_subsets a))) (cup_closed (finite_subsets a))) True % 6.06/6.29 Clause #238 (by clausification #[237]): ∀ (a : Iota), Eq (Not (empty (finite_subsets a))) True % 6.06/6.29 Clause #239 (by clausification #[238]): ∀ (a : Iota), Eq (empty (finite_subsets a)) False % 6.06/6.29 Clause #264 (by clausification #[116]): ∀ (a a_1 : Iota), % 6.06/6.29 Or (Eq (empty (finite_subsets (skS.0 3 a))) True) (Eq (in (skS.0 4 a a_1) (finite_subsets (skS.0 3 a))) True) % 6.06/6.29 Clause #265 (by forward demodulation #[264, 239]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (in (skS.0 4 a a_1) (finite_subsets (skS.0 3 a))) True) % 6.06/6.29 Clause #266 (by clausification #[265]): ∀ (a a_1 : Iota), Eq (in (skS.0 4 a a_1) (finite_subsets (skS.0 3 a))) True % 6.06/6.29 Clause #347 (by clausification #[221]): ∀ (a a_1 : Iota), % 6.06/6.29 Or (Eq (preboolean a) False) % 6.06/6.29 (Or (Eq (∀ (C : Iota), Iff (in C a) (And (subset C a_1) (finite C))) True) (Ne a (finite_subsets a_1))) % 6.06/6.29 Clause #348 (by clausification #[347]): ∀ (a a_1 a_2 : Iota), % 6.06/6.29 Or (Eq (preboolean a) False) % 6.06/6.29 (Or (Ne a (finite_subsets a_1)) (Eq (Iff (in a_2 a) (And (subset a_2 a_1) (finite a_2))) True)) % 6.06/6.29 Clause #350 (by clausification #[348]): ∀ (a a_1 a_2 : Iota), % 6.06/6.29 Or (Eq (preboolean a) False) % 6.06/6.29 (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))) % 6.06/6.29 Clause #421 (by clausification #[350]): ∀ (a a_1 a_2 : Iota), % 6.06/6.29 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))) % 6.06/6.29 Clause #426 (by destructive equality resolution #[421]): ∀ (a a_1 : Iota), % 6.06/6.29 Or (Eq (preboolean (finite_subsets a)) False) (Or (Eq (in a_1 (finite_subsets a)) False) (Eq (subset a_1 a) True)) % 6.06/6.29 Clause #427 (by forward demodulation #[426, 38]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (in a (finite_subsets a_1)) False) (Eq (subset a a_1) True)) % 6.06/6.29 Clause #428 (by clausification #[427]): ∀ (a a_1 : Iota), Or (Eq (in a (finite_subsets a_1)) False) (Eq (subset a a_1) True) % 6.06/6.29 Clause #429 (by superposition #[428, 266]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 4 a a_1) (skS.0 3 a)) True) (Eq False True) % 6.06/6.29 Clause #445 (by clausification #[429]): ∀ (a a_1 : Iota), Eq (subset (skS.0 4 a a_1) (skS.0 3 a)) True % 6.06/6.29 Clause #446 (by superposition #[445, 146]): ∀ (a a_1 : Iota), Or (Eq (element (skS.0 4 a a_1) (powerset (skS.0 3 a))) True) (Eq True False) % 6.06/6.29 Clause #495 (by clausification #[446]): ∀ (a a_1 : Iota), Eq (element (skS.0 4 a a_1) (powerset (skS.0 3 a))) True % 6.06/6.29 Clause #496 (by superposition #[495, 114]): Eq True False % 6.06/6.29 Clause #500 (by clausification #[496]): False % 6.06/6.29 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------