%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : DAT144^1 : TPTP v9.2.0. Released v7.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n024.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 07:47:13 PM UTC 2025 % Result : Theorem 4.34s 4.56s % Output : Proof 4.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : DAT144^1 : TPTP v9.2.0. Released v7.0.0. % 0.12/0.13 % Command : duper %s % 0.13/0.35 % Computer : n024.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 21:33:53 EDT 2025 % 0.13/0.35 % CPUTime : % 4.34/4.56 SZS status Theorem for theBenchmark.p % 4.34/4.56 SZS output start Proof for theBenchmark.p % 4.34/4.56 Clause #0 (by assumption #[]): Eq (∀ (A : Type) (P : A → Prop) (Q : A → A → Prop) (X : A), Eq (bNF_eq_onp A P) Q → Eq (P X) (Q X X)) True % 4.34/4.56 Clause #302 (by assumption #[]): Eq (p x) True % 4.34/4.56 Clause #303 (by assumption #[]): Eq (Not (bNF_eq_onp a p x x)) True % 4.34/4.56 Clause #304 (by clausification #[0]): ∀ (a : Type), Eq (∀ (P : a → Prop) (Q : a → a → Prop) (X : a), Eq (bNF_eq_onp a P) Q → Eq (P X) (Q X X)) True % 4.34/4.56 Clause #305 (by clausification #[304]): ∀ (a : Type) (a_1 : a → Prop), Eq (∀ (Q : a → a → Prop) (X : a), Eq (bNF_eq_onp a a_1) Q → Eq (a_1 X) (Q X X)) True % 4.34/4.56 Clause #306 (by clausification #[305]): ∀ (a : Type) (a_1 : a → Prop) (a_2 : a → a → Prop), % 4.34/4.56 Eq (∀ (X : a), Eq (bNF_eq_onp a a_1) a_2 → Eq (a_1 X) (a_2 X X)) True % 4.34/4.56 Clause #307 (by clausification #[306]): ∀ (a : Type) (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : a), % 4.34/4.56 Eq (Eq (bNF_eq_onp a a_1) a_2 → Eq (a_1 a_3) (a_2 a_3 a_3)) True % 4.34/4.56 Clause #308 (by clausification #[307]): ∀ (a : Type) (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : a), % 4.34/4.56 Or (Eq (Eq (bNF_eq_onp a a_1) a_2) False) (Eq (Eq (a_1 a_3) (a_2 a_3 a_3)) True) % 4.34/4.56 Clause #309 (by clausification #[308]): ∀ (a : Type) (a_1 : a → Prop) (a_2 : a) (a_3 : a → a → Prop), % 4.34/4.56 Or (Eq (Eq (a_1 a_2) (a_3 a_2 a_2)) True) (Ne (bNF_eq_onp a a_1) a_3) % 4.34/4.56 Clause #310 (by clausification #[309]): ∀ (a : Type) (a_1 : a → Prop) (a_2 : a → a → Prop) (a_3 : a), % 4.34/4.56 Or (Ne (bNF_eq_onp a a_1) a_2) (Eq (a_1 a_3) (a_2 a_3 a_3)) % 4.34/4.56 Clause #311 (by destructive equality resolution #[310]): ∀ (a : Type) (a_1 : a → Prop) (a_2 : a), Eq (a_1 a_2) (bNF_eq_onp a a_1 a_2 a_2) % 4.34/4.56 Clause #732 (by clausification #[303]): Eq (bNF_eq_onp a p x x) False % 4.34/4.56 Clause #733 (by superposition #[732, 311]): Eq (p x) False % 4.34/4.56 Clause #734 (by superposition #[733, 302]): Eq False True % 4.34/4.56 Clause #735 (by clausification #[734]): False % 4.34/4.56 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------