%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU927^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n016.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 08:02:39 PM UTC 2025 % Result : Theorem 3.92s 4.09s % Output : Proof 3.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU927^5 : TPTP v9.2.0. Released v4.0.0. % 0.12/0.14 % Command : duper %s % 0.14/0.36 % Computer : n016.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Fri Oct 3 06:45:08 EDT 2025 % 0.14/0.36 % CPUTime : % 3.92/4.09 SZS status Theorem for theBenchmark.p % 3.92/4.09 SZS output start Proof for theBenchmark.p % 3.92/4.09 Clause #0 (by assumption #[]): Eq % 3.92/4.09 (Not % 3.92/4.09 (∀ (Xf : a → a) (Xp : (a → a) → Prop), % 3.92/4.09 And (Xp fun Xu => Xu) (∀ (Xj : a → a), Xp Xj → Xp fun Xx => Xf (Xj Xx)) → Xp fun Xx => Xf (Xf Xx))) % 3.92/4.09 True % 3.92/4.09 Clause #1 (by clausification #[0]): Eq % 3.92/4.09 (∀ (Xf : a → a) (Xp : (a → a) → Prop), % 3.92/4.09 And (Xp fun Xu => Xu) (∀ (Xj : a → a), Xp Xj → Xp fun Xx => Xf (Xj Xx)) → Xp fun Xx => Xf (Xf Xx)) % 3.92/4.09 False % 3.92/4.09 Clause #2 (by clausification #[1]): ∀ (a_1 : a → a), % 3.92/4.09 Eq % 3.92/4.09 (Not % 3.92/4.09 (∀ (Xp : (a → a) → Prop), % 3.92/4.09 And (Xp fun Xu => Xu) (∀ (Xj : a → a), Xp Xj → Xp fun Xx => skS.0 0 a_1 (Xj Xx)) → % 3.92/4.09 Xp fun Xx => skS.0 0 a_1 (skS.0 0 a_1 Xx))) % 3.92/4.09 True % 3.92/4.09 Clause #3 (by clausification #[2]): ∀ (a_1 : a → a), % 3.92/4.09 Eq % 3.92/4.09 (∀ (Xp : (a → a) → Prop), % 3.92/4.09 And (Xp fun Xu => Xu) (∀ (Xj : a → a), Xp Xj → Xp fun Xx => skS.0 0 a_1 (Xj Xx)) → % 3.92/4.09 Xp fun Xx => skS.0 0 a_1 (skS.0 0 a_1 Xx)) % 3.92/4.09 False % 3.92/4.09 Clause #4 (by clausification #[3]): ∀ (a_1 : a → a) (a_2 : (a → a) → Prop), % 3.92/4.09 Eq % 3.92/4.09 (Not % 3.92/4.09 (And (skS.0 1 a_1 a_2 fun Xu => Xu) % 3.92/4.09 (∀ (Xj : a → a), skS.0 1 a_1 a_2 Xj → skS.0 1 a_1 a_2 fun Xx => skS.0 0 a_1 (Xj Xx)) → % 3.92/4.09 skS.0 1 a_1 a_2 fun Xx => skS.0 0 a_1 (skS.0 0 a_1 Xx))) % 3.92/4.09 True % 3.92/4.09 Clause #5 (by clausification #[4]): ∀ (a_1 : a → a) (a_2 : (a → a) → Prop), % 3.92/4.09 Eq % 3.92/4.09 (And (skS.0 1 a_1 a_2 fun Xu => Xu) % 3.92/4.09 (∀ (Xj : a → a), skS.0 1 a_1 a_2 Xj → skS.0 1 a_1 a_2 fun Xx => skS.0 0 a_1 (Xj Xx)) → % 3.92/4.09 skS.0 1 a_1 a_2 fun Xx => skS.0 0 a_1 (skS.0 0 a_1 Xx)) % 3.92/4.09 False % 3.92/4.09 Clause #6 (by clausification #[5]): ∀ (a_1 : a → a) (a_2 : (a → a) → Prop), % 3.92/4.09 Eq % 3.92/4.09 (And (skS.0 1 a_1 a_2 fun Xu => Xu) % 3.92/4.09 (∀ (Xj : a → a), skS.0 1 a_1 a_2 Xj → skS.0 1 a_1 a_2 fun Xx => skS.0 0 a_1 (Xj Xx))) % 3.92/4.09 True % 3.92/4.09 Clause #7 (by clausification #[5]): ∀ (a_1 : a → a) (a_2 : (a → a) → Prop), Eq (skS.0 1 a_1 a_2 fun Xx => skS.0 0 a_1 (skS.0 0 a_1 Xx)) False % 3.92/4.09 Clause #8 (by clausification #[6]): ∀ (a_1 : a → a) (a_2 : (a → a) → Prop), % 3.92/4.09 Eq (∀ (Xj : a → a), skS.0 1 a_1 a_2 Xj → skS.0 1 a_1 a_2 fun Xx => skS.0 0 a_1 (Xj Xx)) True % 3.92/4.09 Clause #9 (by clausification #[6]): ∀ (a_1 : a → a) (a_2 : (a → a) → Prop), Eq (skS.0 1 a_1 a_2 fun Xu => Xu) True % 3.92/4.09 Clause #10 (by clausification #[8]): ∀ (a_1 : a → a) (a_2 : (a → a) → Prop) (a_3 : a → a), % 3.92/4.09 Eq (skS.0 1 a_1 a_2 a_3 → skS.0 1 a_1 a_2 fun Xx => skS.0 0 a_1 (a_3 Xx)) True % 3.92/4.09 Clause #11 (by clausification #[10]): ∀ (a_1 : a → a) (a_2 : (a → a) → Prop) (a_3 : a → a), % 3.92/4.09 Or (Eq (skS.0 1 a_1 a_2 a_3) False) (Eq (skS.0 1 a_1 a_2 fun Xx => skS.0 0 a_1 (a_3 Xx)) True) % 3.92/4.09 Clause #12 (by superposition #[9, 11]): ∀ (a_1 : a → a) (a_2 : (a → a) → Prop), % 3.92/4.09 Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) fun Xx => skS.0 0 (fun x => a_1 x) ((fun Xu => Xu) Xx)) True) % 3.92/4.09 (Eq False True) % 3.92/4.09 Clause #16 (by betaEtaReduce #[12]): ∀ (a_1 : a → a) (a_2 : (a → a) → Prop), Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True) (Eq False True) % 3.92/4.09 Clause #17 (by clausification #[16]): ∀ (a_1 : a → a) (a_2 : (a → a) → Prop), Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True % 3.92/4.09 Clause #18 (by superposition #[17, 11]): ∀ (a_1 : a → a) (a_2 : (a → a) → Prop), % 3.92/4.09 Or (Eq True False) (Eq (skS.0 1 a_1 a_2 fun Xx => skS.0 0 a_1 (skS.0 0 a_1 Xx)) True) % 3.92/4.09 Clause #22 (by clausification #[18]): ∀ (a_1 : a → a) (a_2 : (a → a) → Prop), Eq (skS.0 1 a_1 a_2 fun Xx => skS.0 0 a_1 (skS.0 0 a_1 Xx)) True % 3.92/4.09 Clause #23 (by superposition #[22, 7]): Eq True False % 3.92/4.09 Clause #37 (by clausification #[23]): False % 3.92/4.09 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------