%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU814^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n014.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 08:02:30 PM UTC 2025 % Result : Theorem 3.61s 3.83s % Output : Proof 3.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.11 % Problem : SEU814^2 : TPTP v9.2.0. Released v3.7.0. % 0.02/0.13 % Command : duper %s % 0.12/0.33 % Computer : n014.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 06:32:53 EDT 2025 % 0.12/0.34 % CPUTime : % 3.61/3.83 SZS status Theorem for theBenchmark.p % 3.61/3.83 SZS output start Proof for theBenchmark.p % 3.61/3.83 Clause #0 (by assumption #[]): Eq (Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)) True % 3.61/3.83 Clause #1 (by assumption #[]): Eq (Eq transitiveset fun A => ∀ (X : Iota), in X A → subset X A) True % 3.61/3.83 Clause #3 (by assumption #[]): Eq (Not (subsetE → transitivesetOp1 → ∀ (X : Iota), transitiveset X → ∀ (A Xx : Iota), in A X → in Xx A → in Xx X)) True % 3.61/3.83 Clause #16 (by clausification #[1]): Eq transitiveset fun A => ∀ (X : Iota), in X A → subset X A % 3.61/3.83 Clause #17 (by argument congruence #[16]): ∀ (a : Iota), Eq (transitiveset a) ((fun A => ∀ (X : Iota), in X A → subset X A) a) % 3.61/3.83 Clause #18 (by clausification #[0]): Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) % 3.61/3.83 Clause #22 (by betaEtaReduce #[17]): ∀ (a : Iota), Eq (transitiveset a) (∀ (X : Iota), in X a → subset X a) % 3.61/3.83 Clause #24 (by clausify Prop equality #[22]): ∀ (a : Iota), Or (Eq (transitiveset a) False) (Eq (∀ (X : Iota), in X a → subset X a) True) % 3.61/3.83 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (transitiveset a) False) (Eq (in a_1 a → subset a_1 a) True) % 3.61/3.83 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq (transitiveset a) False) (Or (Eq (in a_1 a) False) (Eq (subset a_1 a) True)) % 3.61/3.83 Clause #38 (by clausification #[3]): Eq (subsetE → transitivesetOp1 → ∀ (X : Iota), transitiveset X → ∀ (A Xx : Iota), in A X → in Xx A → in Xx X) False % 3.61/3.83 Clause #39 (by clausification #[38]): Eq subsetE True % 3.61/3.83 Clause #40 (by clausification #[38]): Eq (transitivesetOp1 → ∀ (X : Iota), transitiveset X → ∀ (A Xx : Iota), in A X → in Xx A → in Xx X) False % 3.61/3.83 Clause #41 (by backward demodulation #[39, 18]): Eq True (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) % 3.61/3.83 Clause #43 (by clausification #[41]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), subset a B → in Xx a → in Xx B) True % 3.61/3.83 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), subset a a_1 → in Xx a → in Xx a_1) True % 3.61/3.83 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Eq (subset a a_1 → in a_2 a → in a_2 a_1) True % 3.61/3.83 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True) % 3.61/3.83 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 a_1) True)) % 3.61/3.83 Clause #49 (by clausification #[40]): Eq (∀ (X : Iota), transitiveset X → ∀ (A Xx : Iota), in A X → in Xx A → in Xx X) False % 3.61/3.83 Clause #53 (by clausification #[49]): ∀ (a : Iota), % 3.61/3.83 Eq (Not (transitiveset (skS.0 2 a) → ∀ (A Xx : Iota), in A (skS.0 2 a) → in Xx A → in Xx (skS.0 2 a))) True % 3.61/3.83 Clause #54 (by clausification #[53]): ∀ (a : Iota), Eq (transitiveset (skS.0 2 a) → ∀ (A Xx : Iota), in A (skS.0 2 a) → in Xx A → in Xx (skS.0 2 a)) False % 3.61/3.83 Clause #55 (by clausification #[54]): ∀ (a : Iota), Eq (transitiveset (skS.0 2 a)) True % 3.61/3.83 Clause #56 (by clausification #[54]): ∀ (a : Iota), Eq (∀ (A Xx : Iota), in A (skS.0 2 a) → in Xx A → in Xx (skS.0 2 a)) False % 3.61/3.83 Clause #57 (by superposition #[55, 27]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (in a (skS.0 2 a_1)) False) (Eq (subset a (skS.0 2 a_1)) True)) % 3.61/3.83 Clause #72 (by clausification #[56]): ∀ (a a_1 : Iota), % 3.61/3.83 Eq (Not (∀ (Xx : Iota), in (skS.0 7 a a_1) (skS.0 2 a) → in Xx (skS.0 7 a a_1) → in Xx (skS.0 2 a))) True % 3.61/3.83 Clause #73 (by clausification #[72]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in (skS.0 7 a a_1) (skS.0 2 a) → in Xx (skS.0 7 a a_1) → in Xx (skS.0 2 a)) False % 3.61/3.83 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), % 3.61/3.83 Eq % 3.61/3.83 (Not (in (skS.0 7 a a_1) (skS.0 2 a) → in (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) → in (skS.0 8 a a_1 a_2) (skS.0 2 a))) % 3.61/3.83 True % 3.61/3.83 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 : Iota), % 3.61/3.83 Eq (in (skS.0 7 a a_1) (skS.0 2 a) → in (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) → in (skS.0 8 a a_1 a_2) (skS.0 2 a)) % 3.61/3.83 False % 3.61/3.83 Clause #76 (by clausification #[75]): ∀ (a a_1 : Iota), Eq (in (skS.0 7 a a_1) (skS.0 2 a)) True % 3.68/3.84 Clause #77 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) → in (skS.0 8 a a_1 a_2) (skS.0 2 a)) False % 3.68/3.84 Clause #81 (by clausification #[77]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) True % 3.68/3.84 Clause #82 (by clausification #[77]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 8 a a_1 a_2) (skS.0 2 a)) False % 3.68/3.84 Clause #83 (by clausification #[57]): ∀ (a a_1 : Iota), Or (Eq (in a (skS.0 2 a_1)) False) (Eq (subset a (skS.0 2 a_1)) True) % 3.68/3.84 Clause #84 (by superposition #[83, 76]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 7 a a_1) (skS.0 2 a)) True) (Eq False True) % 3.68/3.84 Clause #86 (by clausification #[84]): ∀ (a a_1 : Iota), Eq (subset (skS.0 7 a a_1) (skS.0 2 a)) True % 3.68/3.84 Clause #87 (by superposition #[86, 47]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (in a (skS.0 7 a_1 a_2)) False) (Eq (in a (skS.0 2 a_1)) True)) % 3.68/3.84 Clause #91 (by clausification #[87]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 7 a_1 a_2)) False) (Eq (in a (skS.0 2 a_1)) True) % 3.68/3.84 Clause #92 (by superposition #[91, 81]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 8 a a_1 a_2) (skS.0 2 a)) True) (Eq False True) % 3.68/3.84 Clause #94 (by clausification #[92]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 8 a a_1 a_2) (skS.0 2 a)) True % 3.68/3.84 Clause #95 (by superposition #[94, 82]): Eq True False % 3.68/3.84 Clause #97 (by clausification #[95]): False % 3.68/3.84 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------