%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SWW530_5 : TPTP v9.2.0. Released v6.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.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 08:06:24 PM UTC 2025 % Result : Theorem 135.13s 135.30s % Output : Proof 135.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWW530_5 : TPTP v9.2.0. Released v6.0.0. % 0.11/0.14 % Command : duper %s % 0.13/0.35 % Computer : n010.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % 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 : Thu Oct 2 11:12:08 EDT 2025 % 0.13/0.35 % CPUTime : % 135.13/135.30 SZS status Theorem for theBenchmark.p % 135.13/135.30 SZS output start Proof for theBenchmark.p % 135.13/135.30 Clause #1 (by assumption #[]): Eq % 135.13/135.30 (∀ (A : Type) (A3 : A) (T : huffma1450048681e_tree A), % 135.13/135.30 ord_less_eq nat (huffma410068972_depth A T A3) (huffma945805758height A T)) % 135.13/135.30 True % 135.13/135.30 Clause #5 (by assumption #[]): Eq (∀ (A : Type), linorder A → ∀ (Y X : A), ord_less_eq A X (ord_max A X Y)) True % 135.13/135.30 Clause #6 (by assumption #[]): Eq (∀ (A : Type), linorder A → ∀ (X Y : A), ord_less_eq A Y (ord_max A X Y)) True % 135.13/135.30 Clause #38 (by assumption #[]): Eq (∀ (N M : nat), ord_less_eq nat M N → ord_less_eq nat N M → Eq M N) True % 135.13/135.30 Clause #103 (by assumption #[]): Eq (linorder nat) True % 135.13/135.30 Clause #116 (by assumption #[]): Eq (Eq (huffma410068972_depth a t_2 a1) (ord_max nat (huffma945805758height b t_1) (huffma945805758height a t_2))) True % 135.13/135.30 Clause #117 (by assumption #[]): Eq % 135.13/135.30 (Eq (huffma410068972_depth a t_2 a1) (huffma945805758height a t_2) → % 135.13/135.30 ord_less_eq nat (huffma945805758height b t_1) (huffma945805758height a t_2) → p) % 135.13/135.30 True % 135.13/135.30 Clause #118 (by assumption #[]): Eq (Not p) True % 135.13/135.30 Clause #119 (by clausification #[118]): Eq p False % 135.13/135.30 Clause #131 (by clausification #[1]): ∀ (a : Type), % 135.13/135.30 Eq % 135.13/135.30 (∀ (A3 : a) (T : huffma1450048681e_tree a), % 135.13/135.30 ord_less_eq nat (huffma410068972_depth a T A3) (huffma945805758height a T)) % 135.13/135.30 True % 135.13/135.30 Clause #132 (by clausification #[131]): ∀ (a : Type) (a_1 : a), % 135.13/135.30 Eq (∀ (T : huffma1450048681e_tree a), ord_less_eq nat (huffma410068972_depth a T a_1) (huffma945805758height a T)) % 135.13/135.30 True % 135.13/135.30 Clause #133 (by clausification #[132]): ∀ (a : Type) (a_1 : huffma1450048681e_tree a) (a_2 : a), % 135.13/135.30 Eq (ord_less_eq nat (huffma410068972_depth a a_1 a_2) (huffma945805758height a a_1)) True % 135.13/135.30 Clause #153 (by clausification #[117]): Or (Eq (Eq (huffma410068972_depth a t_2 a1) (huffma945805758height a t_2)) False) % 135.13/135.30 (Eq (ord_less_eq nat (huffma945805758height b t_1) (huffma945805758height a t_2) → p) True) % 135.13/135.30 Clause #154 (by clausification #[153]): Or (Eq (ord_less_eq nat (huffma945805758height b t_1) (huffma945805758height a t_2) → p) True) % 135.13/135.30 (Ne (huffma410068972_depth a t_2 a1) (huffma945805758height a t_2)) % 135.13/135.30 Clause #155 (by clausification #[154]): Or (Ne (huffma410068972_depth a t_2 a1) (huffma945805758height a t_2)) % 135.13/135.30 (Or (Eq (ord_less_eq nat (huffma945805758height b t_1) (huffma945805758height a t_2)) False) (Eq p True)) % 135.13/135.30 Clause #156 (by forward demodulation #[155, 119]): Or (Ne (huffma410068972_depth a t_2 a1) (huffma945805758height a t_2)) % 135.13/135.30 (Or (Eq (ord_less_eq nat (huffma945805758height b t_1) (huffma945805758height a t_2)) False) (Eq False True)) % 135.13/135.30 Clause #157 (by clausification #[156]): Or (Ne (huffma410068972_depth a t_2 a1) (huffma945805758height a t_2)) % 135.13/135.30 (Eq (ord_less_eq nat (huffma945805758height b t_1) (huffma945805758height a t_2)) False) % 135.13/135.30 Clause #168 (by clausification #[5]): ∀ (a : Type), Eq (linorder a → ∀ (Y X : a), ord_less_eq a X (ord_max a X Y)) True % 135.13/135.30 Clause #169 (by clausification #[168]): ∀ (a : Type), Or (Eq (linorder a) False) (Eq (∀ (Y X : a), ord_less_eq a X (ord_max a X Y)) True) % 135.13/135.30 Clause #170 (by clausification #[169]): ∀ (a : Type) (a_1 : a), Or (Eq (linorder a) False) (Eq (∀ (X : a), ord_less_eq a X (ord_max a X a_1)) True) % 135.13/135.30 Clause #171 (by clausification #[170]): ∀ (a : Type) (a_1 a_2 : a), Or (Eq (linorder a) False) (Eq (ord_less_eq a a_1 (ord_max a a_1 a_2)) True) % 135.13/135.30 Clause #173 (by superposition #[171, 103]): ∀ (a a_1 : nat), Or (Eq (ord_less_eq nat a (ord_max nat a a_1)) True) (Eq False True) % 135.13/135.30 Clause #196 (by clausification #[6]): ∀ (a : Type), Eq (linorder a → ∀ (X Y : a), ord_less_eq a Y (ord_max a X Y)) True % 135.13/135.30 Clause #197 (by clausification #[196]): ∀ (a : Type), Or (Eq (linorder a) False) (Eq (∀ (X Y : a), ord_less_eq a Y (ord_max a X Y)) True) % 135.13/135.30 Clause #198 (by clausification #[197]): ∀ (a : Type) (a_1 : a), Or (Eq (linorder a) False) (Eq (∀ (Y : a), ord_less_eq a Y (ord_max a a_1 Y)) True) % 135.13/135.30 Clause #199 (by clausification #[198]): ∀ (a : Type) (a_1 a_2 : a), Or (Eq (linorder a) False) (Eq (ord_less_eq a a_1 (ord_max a a_2 a_1)) True) % 135.13/135.30 Clause #201 (by superposition #[199, 103]): ∀ (a a_1 : nat), Or (Eq (ord_less_eq nat a (ord_max nat a_1 a)) True) (Eq False True) % 135.33/135.59 Clause #237 (by clausification #[38]): ∀ (a : nat), Eq (∀ (M : nat), ord_less_eq nat M a → ord_less_eq nat a M → Eq M a) True % 135.33/135.59 Clause #238 (by clausification #[237]): ∀ (a a_1 : nat), Eq (ord_less_eq nat a a_1 → ord_less_eq nat a_1 a → Eq a a_1) True % 135.33/135.59 Clause #239 (by clausification #[238]): ∀ (a a_1 : nat), Or (Eq (ord_less_eq nat a a_1) False) (Eq (ord_less_eq nat a_1 a → Eq a a_1) True) % 135.33/135.59 Clause #240 (by clausification #[239]): ∀ (a a_1 : nat), Or (Eq (ord_less_eq nat a a_1) False) (Or (Eq (ord_less_eq nat a_1 a) False) (Eq (Eq a a_1) True)) % 135.33/135.59 Clause #241 (by clausification #[240]): ∀ (a a_1 : nat), Or (Eq (ord_less_eq nat a a_1) False) (Or (Eq (ord_less_eq nat a_1 a) False) (Eq a a_1)) % 135.33/135.59 Clause #242 (by superposition #[241, 133]): ∀ (a : Type) (a_1 : huffma1450048681e_tree a) (a_2 : a), % 135.33/135.59 Or (Eq (ord_less_eq nat (huffma945805758height a a_1) (huffma410068972_depth a a_1 a_2)) False) % 135.33/135.59 (Or (Eq (huffma410068972_depth a a_1 a_2) (huffma945805758height a a_1)) (Eq False True)) % 135.33/135.59 Clause #307 (by clausification #[201]): ∀ (a a_1 : nat), Eq (ord_less_eq nat a (ord_max nat a_1 a)) True % 135.33/135.59 Clause #310 (by clausification #[173]): ∀ (a a_1 : nat), Eq (ord_less_eq nat a (ord_max nat a a_1)) True % 135.33/135.59 Clause #2668 (by clausification #[116]): Eq (huffma410068972_depth a t_2 a1) (ord_max nat (huffma945805758height b t_1) (huffma945805758height a t_2)) % 135.33/135.59 Clause #2670 (by superposition #[2668, 307]): Eq (ord_less_eq nat (huffma945805758height a t_2) (huffma410068972_depth a t_2 a1)) True % 135.33/135.59 Clause #2671 (by superposition #[2668, 310]): Eq (ord_less_eq nat (huffma945805758height b t_1) (huffma410068972_depth a t_2 a1)) True % 135.33/135.59 Clause #4073 (by clausification #[242]): ∀ (a : Type) (a_1 : huffma1450048681e_tree a) (a_2 : a), % 135.33/135.59 Or (Eq (ord_less_eq nat (huffma945805758height a a_1) (huffma410068972_depth a a_1 a_2)) False) % 135.33/135.59 (Eq (huffma410068972_depth a a_1 a_2) (huffma945805758height a a_1)) % 135.33/135.59 Clause #42312 (by superposition #[2670, 4073]): Or (Eq (huffma410068972_depth a t_2 a1) (huffma945805758height a t_2)) (Eq False True) % 135.33/135.59 Clause #42320 (by clausification #[42312]): Eq (huffma410068972_depth a t_2 a1) (huffma945805758height a t_2) % 135.33/135.59 Clause #42323 (by backward demodulation #[42320, 2671]): Eq (ord_less_eq nat (huffma945805758height b t_1) (huffma945805758height a t_2)) True % 135.33/135.59 Clause #42325 (by backward contextual literal cutting #[42320, 157]): Eq (ord_less_eq nat (huffma945805758height b t_1) (huffma945805758height a t_2)) False % 135.33/135.59 Clause #42352 (by superposition #[42323, 42325]): Eq False True % 135.33/135.59 Clause #42353 (by clausification #[42352]): False % 135.33/135.59 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------