%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU172+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 08:01:02 PM UTC 2025 % Result : Theorem 5.85s 6.02s % Output : Proof 5.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU172+1 : TPTP v9.2.0. Released v3.3.0. % 0.11/0.13 % Command : duper %s % 0.14/0.33 % Computer : n020.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.33 % CPULimit : 300 % 0.14/0.33 % WCLimit : 300 % 0.14/0.33 % DateTime : Fri Oct 3 06:16:23 EDT 2025 % 0.14/0.34 % CPUTime : % 5.85/6.02 SZS status Theorem for theBenchmark.p % 5.85/6.02 SZS output start Proof for theBenchmark.p % 5.85/6.02 Clause #16 (by assumption #[]): Eq (∀ (A B : Iota), element B (powerset A) → Eq (subset_complement A B) (set_difference A B)) True % 5.85/6.02 Clause #17 (by assumption #[]): Eq (Not (∀ (A B C : Iota), element C (powerset A) → Not (And (in B (subset_complement A C)) (in B C)))) True % 5.85/6.02 Clause #18 (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 % 5.85/6.02 Clause #83 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (B : Iota), element B (powerset a) → Eq (subset_complement a B) (set_difference a B)) True % 5.85/6.02 Clause #84 (by clausification #[83]): ∀ (a a_1 : Iota), Eq (element a (powerset a_1) → Eq (subset_complement a_1 a) (set_difference a_1 a)) True % 5.85/6.02 Clause #85 (by clausification #[84]): ∀ (a a_1 : Iota), % 5.85/6.02 Or (Eq (element a (powerset a_1)) False) (Eq (Eq (subset_complement a_1 a) (set_difference a_1 a)) True) % 5.85/6.02 Clause #86 (by clausification #[85]): ∀ (a a_1 : Iota), Or (Eq (element a (powerset a_1)) False) (Eq (subset_complement a_1 a) (set_difference a_1 a)) % 5.85/6.02 Clause #97 (by clausification #[17]): Eq (∀ (A B C : Iota), element C (powerset A) → Not (And (in B (subset_complement A C)) (in B C))) False % 5.85/6.02 Clause #98 (by clausification #[97]): ∀ (a : Iota), % 5.85/6.02 Eq % 5.85/6.02 (Not % 5.85/6.02 (∀ (B C : Iota), element C (powerset (skS.0 5 a)) → Not (And (in B (subset_complement (skS.0 5 a) C)) (in B C)))) % 5.85/6.02 True % 5.85/6.02 Clause #99 (by clausification #[98]): ∀ (a : Iota), % 5.85/6.02 Eq (∀ (B C : Iota), element C (powerset (skS.0 5 a)) → Not (And (in B (subset_complement (skS.0 5 a) C)) (in B C))) % 5.85/6.02 False % 5.85/6.02 Clause #100 (by clausification #[99]): ∀ (a a_1 : Iota), % 5.85/6.02 Eq % 5.85/6.02 (Not % 5.85/6.02 (∀ (C : Iota), % 5.85/6.02 element C (powerset (skS.0 5 a)) → % 5.85/6.02 Not (And (in (skS.0 6 a a_1) (subset_complement (skS.0 5 a) C)) (in (skS.0 6 a a_1) C)))) % 5.85/6.02 True % 5.85/6.02 Clause #101 (by clausification #[100]): ∀ (a a_1 : Iota), % 5.85/6.02 Eq % 5.85/6.02 (∀ (C : Iota), % 5.85/6.02 element C (powerset (skS.0 5 a)) → % 5.85/6.02 Not (And (in (skS.0 6 a a_1) (subset_complement (skS.0 5 a) C)) (in (skS.0 6 a a_1) C))) % 5.85/6.02 False % 5.85/6.02 Clause #102 (by clausification #[101]): ∀ (a a_1 a_2 : Iota), % 5.85/6.02 Eq % 5.85/6.02 (Not % 5.85/6.02 (element (skS.0 7 a a_1 a_2) (powerset (skS.0 5 a)) → % 5.85/6.02 Not % 5.85/6.02 (And (in (skS.0 6 a a_1) (subset_complement (skS.0 5 a) (skS.0 7 a a_1 a_2))) % 5.85/6.02 (in (skS.0 6 a a_1) (skS.0 7 a a_1 a_2))))) % 5.85/6.02 True % 5.85/6.02 Clause #103 (by clausification #[102]): ∀ (a a_1 a_2 : Iota), % 5.85/6.02 Eq % 5.85/6.02 (element (skS.0 7 a a_1 a_2) (powerset (skS.0 5 a)) → % 5.85/6.02 Not % 5.85/6.02 (And (in (skS.0 6 a a_1) (subset_complement (skS.0 5 a) (skS.0 7 a a_1 a_2))) % 5.85/6.02 (in (skS.0 6 a a_1) (skS.0 7 a a_1 a_2)))) % 5.85/6.02 False % 5.85/6.02 Clause #104 (by clausification #[103]): ∀ (a a_1 a_2 : Iota), Eq (element (skS.0 7 a a_1 a_2) (powerset (skS.0 5 a))) True % 5.85/6.02 Clause #105 (by clausification #[103]): ∀ (a a_1 a_2 : Iota), % 5.85/6.02 Eq % 5.85/6.02 (Not % 5.85/6.02 (And (in (skS.0 6 a a_1) (subset_complement (skS.0 5 a) (skS.0 7 a a_1 a_2))) % 5.85/6.02 (in (skS.0 6 a a_1) (skS.0 7 a a_1 a_2)))) % 5.85/6.02 False % 5.85/6.02 Clause #108 (by superposition #[104, 86]): ∀ (a a_1 a_2 : Iota), % 5.85/6.02 Or (Eq True False) % 5.85/6.02 (Eq (subset_complement (skS.0 5 a) (skS.0 7 a a_1 a_2)) (set_difference (skS.0 5 a) (skS.0 7 a a_1 a_2))) % 5.85/6.02 Clause #116 (by clausification #[18]): ∀ (a : Iota), % 5.85/6.02 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 % 5.85/6.02 Clause #117 (by clausification #[116]): ∀ (a a_1 : Iota), % 5.85/6.02 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 % 5.85/6.02 Clause #118 (by clausification #[117]): ∀ (a a_1 a_2 : Iota), % 5.85/6.02 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 % 5.85/6.02 Clause #120 (by clausification #[118]): ∀ (a a_1 a_2 : Iota), % 5.85/6.02 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) % 5.85/6.02 Clause #155 (by clausification #[120]): ∀ (a a_1 a_2 : Iota), % 5.85/6.02 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)) % 5.85/6.03 Clause #156 (by clausification #[155]): ∀ (a a_1 a_2 a_3 : Iota), % 5.85/6.03 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) % 5.85/6.03 Clause #158 (by clausification #[156]): ∀ (a a_1 a_2 a_3 : Iota), % 5.85/6.03 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)) % 5.85/6.03 Clause #162 (by clausification #[158]): ∀ (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 (Not (in a_3 a_2)) True)) % 5.85/6.03 Clause #164 (by clausification #[162]): ∀ (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_2) False)) % 5.85/6.03 Clause #165 (by destructive equality resolution #[164]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (set_difference a_1 a_2)) False) (Eq (in a a_2) False) % 5.85/6.03 Clause #184 (by clausification #[105]): ∀ (a a_1 a_2 : Iota), % 5.85/6.03 Eq % 5.85/6.03 (And (in (skS.0 6 a a_1) (subset_complement (skS.0 5 a) (skS.0 7 a a_1 a_2))) % 5.85/6.03 (in (skS.0 6 a a_1) (skS.0 7 a a_1 a_2))) % 5.85/6.03 True % 5.85/6.03 Clause #185 (by clausification #[184]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 6 a a_1) (skS.0 7 a a_1 a_2)) True % 5.85/6.03 Clause #186 (by clausification #[184]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 6 a a_1) (subset_complement (skS.0 5 a) (skS.0 7 a a_1 a_2))) True % 5.85/6.03 Clause #220 (by clausification #[108]): ∀ (a a_1 a_2 : Iota), % 5.85/6.03 Eq (subset_complement (skS.0 5 a) (skS.0 7 a a_1 a_2)) (set_difference (skS.0 5 a) (skS.0 7 a a_1 a_2)) % 5.85/6.03 Clause #221 (by superposition #[220, 165]): ∀ (a a_1 a_2 a_3 : Iota), % 5.85/6.03 Or (Eq (in a (subset_complement (skS.0 5 a_1) (skS.0 7 a_1 a_2 a_3))) False) (Eq (in a (skS.0 7 a_1 a_2 a_3)) False) % 5.85/6.03 Clause #365 (by superposition #[221, 186]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 6 a a_1) (skS.0 7 a a_1 a_2)) False) (Eq False True) % 5.85/6.03 Clause #373 (by clausification #[365]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 6 a a_1) (skS.0 7 a a_1 a_2)) False % 5.85/6.03 Clause #374 (by superposition #[373, 185]): Eq False True % 5.85/6.03 Clause #375 (by clausification #[374]): False % 5.85/6.03 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------