%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU610^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 08:02:02 PM UTC 2025 % Result : Theorem 9.37s 9.60s % Output : Proof 9.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU610^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.13 % Command : duper %s % 0.14/0.34 % Computer : n031.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 04:10:38 EDT 2025 % 0.14/0.34 % CPUTime : % 9.37/9.60 SZS status Theorem for theBenchmark.p % 9.37/9.60 SZS output start Proof for theBenchmark.p % 9.37/9.60 Clause #0 (by assumption #[]): Eq (Eq emptysetE (∀ (Xx : Iota), in Xx emptyset → ∀ (Xphi : Prop), Xphi)) True % 9.37/9.60 Clause #2 (by assumption #[]): Eq (Eq subsetI2 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)) True % 9.37/9.60 Clause #3 (by assumption #[]): Eq (Eq setminusI (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B))) True % 9.37/9.60 Clause #4 (by assumption #[]): Eq (Not (emptysetE → in__Cong → subsetI2 → setminusI → ∀ (A B : Iota), Eq (setminus A B) emptyset → subset A B)) True % 9.37/9.60 Clause #5 (by clausification #[0]): Eq emptysetE (∀ (Xx : Iota), in Xx emptyset → ∀ (Xphi : Prop), Xphi) % 9.37/9.60 Clause #24 (by clausification #[2]): Eq subsetI2 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 9.37/9.60 Clause #43 (by clausification #[3]): Eq setminusI (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B)) % 9.37/9.60 Clause #47 (by clausification #[4]): Eq (emptysetE → in__Cong → subsetI2 → setminusI → ∀ (A B : Iota), Eq (setminus A B) emptyset → subset A B) False % 9.37/9.60 Clause #48 (by clausification #[47]): Eq emptysetE True % 9.37/9.60 Clause #49 (by clausification #[47]): Eq (in__Cong → subsetI2 → setminusI → ∀ (A B : Iota), Eq (setminus A B) emptyset → subset A B) False % 9.37/9.60 Clause #50 (by backward demodulation #[48, 5]): Eq True (∀ (Xx : Iota), in Xx emptyset → ∀ (Xphi : Prop), Xphi) % 9.37/9.60 Clause #55 (by clausification #[50]): ∀ (a : Iota), Eq (in a emptyset → ∀ (Xphi : Prop), Xphi) True % 9.37/9.60 Clause #56 (by clausification #[55]): ∀ (a : Iota), Or (Eq (in a emptyset) False) (Eq (∀ (Xphi : Prop), Xphi) True) % 9.37/9.60 Clause #57 (by clausification #[56]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (in a emptyset) False) (Eq a_1 True) % 9.37/9.60 Clause #59 (by clausification #[49]): Eq (subsetI2 → setminusI → ∀ (A B : Iota), Eq (setminus A B) emptyset → subset A B) False % 9.37/9.60 Clause #61 (by clausification #[59]): Eq subsetI2 True % 9.37/9.60 Clause #62 (by clausification #[59]): Eq (setminusI → ∀ (A B : Iota), Eq (setminus A B) emptyset → subset A B) False % 9.37/9.60 Clause #63 (by backward demodulation #[61, 24]): Eq True (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 9.37/9.60 Clause #74 (by clausification #[63]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx a → in Xx B) → subset a B) True % 9.37/9.60 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → subset a a_1) True % 9.37/9.60 Clause #76 (by clausification #[75]): ∀ (a a_1 : Iota), Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (subset a a_1) True) % 9.37/9.60 Clause #77 (by clausification #[76]): ∀ (a a_1 a_2 : Iota), % 9.37/9.60 Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 7 a a_1 a_2) a → in (skS.0 7 a a_1 a_2) a_1)) True) % 9.37/9.60 Clause #78 (by clausification #[77]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 7 a a_1 a_2) a → in (skS.0 7 a a_1 a_2) a_1) False) % 9.37/9.60 Clause #79 (by clausification #[78]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 7 a a_1 a_2) a) True) % 9.37/9.60 Clause #80 (by clausification #[78]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 7 a a_1 a_2) a_1) False) % 9.37/9.60 Clause #82 (by clausification #[62]): Eq setminusI True % 9.37/9.60 Clause #83 (by clausification #[62]): Eq (∀ (A B : Iota), Eq (setminus A B) emptyset → subset A B) False % 9.37/9.60 Clause #84 (by backward demodulation #[82, 43]): Eq True (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B)) % 9.37/9.60 Clause #85 (by clausification #[83]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), Eq (setminus (skS.0 8 a) B) emptyset → subset (skS.0 8 a) B)) True % 9.37/9.60 Clause #86 (by clausification #[85]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (setminus (skS.0 8 a) B) emptyset → subset (skS.0 8 a) B) False % 9.37/9.60 Clause #87 (by clausification #[86]): ∀ (a a_1 : Iota), % 9.37/9.60 Eq (Not (Eq (setminus (skS.0 8 a) (skS.0 9 a a_1)) emptyset → subset (skS.0 8 a) (skS.0 9 a a_1))) True % 9.37/9.60 Clause #88 (by clausification #[87]): ∀ (a a_1 : Iota), Eq (Eq (setminus (skS.0 8 a) (skS.0 9 a a_1)) emptyset → subset (skS.0 8 a) (skS.0 9 a a_1)) False % 9.37/9.62 Clause #89 (by clausification #[88]): ∀ (a a_1 : Iota), Eq (Eq (setminus (skS.0 8 a) (skS.0 9 a a_1)) emptyset) True % 9.37/9.62 Clause #90 (by clausification #[88]): ∀ (a a_1 : Iota), Eq (subset (skS.0 8 a) (skS.0 9 a a_1)) False % 9.37/9.62 Clause #91 (by clausification #[89]): ∀ (a a_1 : Iota), Eq (setminus (skS.0 8 a) (skS.0 9 a a_1)) emptyset % 9.37/9.62 Clause #113 (by clausification #[84]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx a → Not (in Xx B) → in Xx (setminus a B)) True % 9.37/9.62 Clause #114 (by clausification #[113]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx a → Not (in Xx a_1) → in Xx (setminus a a_1)) True % 9.37/9.62 Clause #115 (by clausification #[114]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → Not (in a a_2) → in a (setminus a_1 a_2)) True % 9.37/9.62 Clause #116 (by clausification #[115]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (Not (in a a_2) → in a (setminus a_1 a_2)) True) % 9.37/9.62 Clause #117 (by clausification #[116]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Or (Eq (Not (in a a_2)) False) (Eq (in a (setminus a_1 a_2)) True)) % 9.37/9.62 Clause #118 (by clausification #[117]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Or (Eq (in a (setminus a_1 a_2)) True) (Eq (in a a_2) True)) % 9.37/9.62 Clause #119 (by superposition #[118, 79]): ∀ (a a_1 a_2 a_3 : Iota), % 9.37/9.62 Or (Eq (in (skS.0 7 a a_1 a_2) (setminus a a_3)) True) % 9.37/9.62 (Or (Eq (in (skS.0 7 a a_1 a_2) a_3) True) (Or (Eq (subset a a_1) True) (Eq False True))) % 9.37/9.62 Clause #169 (by clausification #[119]): ∀ (a a_1 a_2 a_3 : Iota), % 9.37/9.62 Or (Eq (in (skS.0 7 a a_1 a_2) (setminus a a_3)) True) % 9.37/9.62 (Or (Eq (in (skS.0 7 a a_1 a_2) a_3) True) (Eq (subset a a_1) True)) % 9.37/9.62 Clause #172 (by superposition #[169, 91]): ∀ (a a_1 a_2 a_3 : Iota), % 9.37/9.62 Or (Eq (in (skS.0 7 (skS.0 8 a) a_1 a_2) emptyset) True) % 9.37/9.62 (Or (Eq (in (skS.0 7 (skS.0 8 a) a_1 a_2) (skS.0 9 a a_3)) True) (Eq (subset (skS.0 8 a) a_1) True)) % 9.37/9.62 Clause #240 (by superposition #[172, 80]): ∀ (a a_1 a_2 : Iota), % 9.37/9.62 Or (Eq (in (skS.0 7 (skS.0 8 a) (skS.0 9 a a_1) a_2) emptyset) True) % 9.37/9.62 (Or (Eq (subset (skS.0 8 a) (skS.0 9 a a_1)) True) % 9.37/9.62 (Or (Eq (subset (skS.0 8 a) (skS.0 9 a a_1)) True) (Eq True False))) % 9.37/9.62 Clause #466 (by clausification #[240]): ∀ (a a_1 a_2 : Iota), % 9.37/9.62 Or (Eq (in (skS.0 7 (skS.0 8 a) (skS.0 9 a a_1) a_2) emptyset) True) % 9.37/9.62 (Or (Eq (subset (skS.0 8 a) (skS.0 9 a a_1)) True) (Eq (subset (skS.0 8 a) (skS.0 9 a a_1)) True)) % 9.37/9.62 Clause #467 (by eliminate duplicate literals #[466]): ∀ (a a_1 a_2 : Iota), % 9.37/9.62 Or (Eq (in (skS.0 7 (skS.0 8 a) (skS.0 9 a a_1) a_2) emptyset) True) (Eq (subset (skS.0 8 a) (skS.0 9 a a_1)) True) % 9.37/9.62 Clause #468 (by forward demodulation #[467, 90]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 7 (skS.0 8 a) (skS.0 9 a a_1) a_2) emptyset) True) (Eq False True) % 9.37/9.62 Clause #469 (by clausification #[468]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 7 (skS.0 8 a) (skS.0 9 a a_1) a_2) emptyset) True % 9.37/9.62 Clause #470 (by superposition #[469, 57]): ∀ (a : Prop), Or (Eq True False) (Eq a True) % 9.37/9.62 Clause #472 (by clausification #[470]): ∀ (a : Prop), Eq a True % 9.37/9.62 Clause #474 (by falseElim #[472]): False % 9.37/9.62 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------