%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SWX200+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 : Tue May 5 06:59:09 PM UTC 2026 % Result : Theorem 3.66s 3.87s % Output : Proof 3.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX200+1 : TPTP v9.3.0. Released v9.3.0. % 0.13/0.13 % Command : duper %s % 0.17/0.34 % Computer : n021.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue May 5 11:16:10 EDT 2026 % 0.17/0.34 % CPUTime : % 3.66/3.87 SZS status Theorem for theBenchmark.p % 3.66/3.87 SZS output start Proof for theBenchmark.p % 3.66/3.87 Clause #6 (by assumption #[]): Eq (∀ (Z : Iota), Not (leqNat (s Z) z)) True % 3.66/3.87 Clause #8 (by assumption #[]): Eq (∀ (Y : Iota), Eq (merge nil Y) Y) True % 3.66/3.87 Clause #12 (by assumption #[]): Eq (ord nil) True % 3.66/3.87 Clause #14 (by assumption #[]): Eq (∀ (Y Y2 Xs : Iota), Iff (ord (cons Y (cons Y2 Xs))) (And (leqNat Y Y2) (ord (cons Y2 Xs)))) True % 3.66/3.87 Clause #15 (by assumption #[]): Eq (Not (Exists fun Xs => Exists fun Ys => Not (ord Xs → Not (ord Ys) → ord (merge Xs Ys)))) True % 3.66/3.87 Clause #20 (by clausification #[6]): ∀ (a : Iota), Eq (Not (leqNat (s a) z)) True % 3.66/3.87 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (leqNat (s a) z) False % 3.66/3.87 Clause #27 (by clausification #[8]): ∀ (a : Iota), Eq (Eq (merge nil a) a) True % 3.66/3.87 Clause #28 (by clausification #[27]): ∀ (a : Iota), Eq (merge nil a) a % 3.66/3.87 Clause #66 (by clausification #[15]): Eq (Exists fun Xs => Exists fun Ys => Not (ord Xs → Not (ord Ys) → ord (merge Xs Ys))) False % 3.66/3.87 Clause #67 (by clausification #[66]): ∀ (a : Iota), Eq (Exists fun Ys => Not (ord a → Not (ord Ys) → ord (merge a Ys))) False % 3.66/3.87 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), Eq (Not (ord a → Not (ord a_1) → ord (merge a a_1))) False % 3.66/3.87 Clause #69 (by clausification #[68]): ∀ (a a_1 : Iota), Eq (ord a → Not (ord a_1) → ord (merge a a_1)) True % 3.66/3.87 Clause #70 (by clausification #[69]): ∀ (a a_1 : Iota), Or (Eq (ord a) False) (Eq (Not (ord a_1) → ord (merge a a_1)) True) % 3.66/3.87 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota), Or (Eq (ord a) False) (Or (Eq (Not (ord a_1)) False) (Eq (ord (merge a a_1)) True)) % 3.66/3.87 Clause #72 (by clausification #[71]): ∀ (a a_1 : Iota), Or (Eq (ord a) False) (Or (Eq (ord (merge a a_1)) True) (Eq (ord a_1) True)) % 3.66/3.87 Clause #73 (by superposition #[72, 12]): ∀ (a : Iota), Or (Eq (ord (merge nil a)) True) (Or (Eq (ord a) True) (Eq False True)) % 3.66/3.87 Clause #82 (by clausification #[73]): ∀ (a : Iota), Or (Eq (ord (merge nil a)) True) (Eq (ord a) True) % 3.66/3.87 Clause #83 (by forward demodulation #[82, 28]): ∀ (a : Iota), Or (Eq (ord a) True) (Eq (ord a) True) % 3.66/3.88 Clause #84 (by eliminate duplicate literals #[83]): ∀ (a : Iota), Eq (ord a) True % 3.66/3.88 Clause #96 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (Y2 Xs : Iota), Iff (ord (cons a (cons Y2 Xs))) (And (leqNat a Y2) (ord (cons Y2 Xs)))) True % 3.66/3.88 Clause #97 (by clausification #[96]): ∀ (a a_1 : Iota), Eq (∀ (Xs : Iota), Iff (ord (cons a (cons a_1 Xs))) (And (leqNat a a_1) (ord (cons a_1 Xs)))) True % 3.66/3.88 Clause #98 (by clausification #[97]): ∀ (a a_1 a_2 : Iota), Eq (Iff (ord (cons a (cons a_1 a_2))) (And (leqNat a a_1) (ord (cons a_1 a_2)))) True % 3.66/3.88 Clause #100 (by clausification #[98]): ∀ (a a_1 a_2 : Iota), Or (Eq (ord (cons a (cons a_1 a_2))) False) (Eq (And (leqNat a a_1) (ord (cons a_1 a_2))) True) % 3.66/3.88 Clause #105 (by clausification #[100]): ∀ (a a_1 a_2 : Iota), Or (Eq (ord (cons a (cons a_1 a_2))) False) (Eq (leqNat a a_1) True) % 3.66/3.88 Clause #107 (by superposition #[105, 84]): ∀ (a a_1 : Iota), Or (Eq (leqNat a a_1) True) (Eq False True) % 3.66/3.88 Clause #108 (by clausification #[107]): ∀ (a a_1 : Iota), Eq (leqNat a a_1) True % 3.66/3.88 Clause #113 (by superposition #[108, 21]): Eq True False % 3.66/3.88 Clause #114 (by clausification #[113]): False % 3.66/3.88 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------