%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV258^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 08:03:00 PM UTC 2025 % Result : Theorem 4.59s 4.79s % Output : Proof 4.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SEV258^5 : TPTP v9.2.0. Released v4.0.0. % 0.12/0.14 % Command : duper %s % 0.13/0.35 % Computer : n020.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 : Fri Oct 3 01:22:38 EDT 2025 % 0.13/0.35 % CPUTime : % 4.59/4.79 SZS status Theorem for theBenchmark.p % 4.59/4.79 SZS output start Proof for theBenchmark.p % 4.59/4.79 Clause #0 (by assumption #[]): Eq % 4.59/4.79 (Not % 4.59/4.79 (And % 4.59/4.79 (And (And (∀ (R : a → Prop), (Eq R fun Xx => False) → True) (∀ (R : a → Prop), (Eq R fun Xx => Not False) → True)) % 4.59/4.79 (∀ (K : (a → Prop) → Prop) (R : a → Prop), % 4.59/4.79 And (∀ (Xx : a → Prop), K Xx → True) (Eq R fun Xx => Exists fun S => And (K S) (S Xx)) → True)) % 4.59/4.79 (∀ (Y Z S : a → Prop), And (And True True) (Eq S fun Xx => And (Y Xx) (Z Xx)) → True))) % 4.59/4.79 True % 4.59/4.79 Clause #1 (by clausification #[0]): Eq % 4.59/4.79 (And % 4.59/4.79 (And (And (∀ (R : a → Prop), (Eq R fun Xx => False) → True) (∀ (R : a → Prop), (Eq R fun Xx => Not False) → True)) % 4.59/4.79 (∀ (K : (a → Prop) → Prop) (R : a → Prop), % 4.59/4.79 And (∀ (Xx : a → Prop), K Xx → True) (Eq R fun Xx => Exists fun S => And (K S) (S Xx)) → True)) % 4.59/4.79 (∀ (Y Z S : a → Prop), And (And True True) (Eq S fun Xx => And (Y Xx) (Z Xx)) → True)) % 4.59/4.79 False % 4.59/4.79 Clause #2 (by clausification #[1]): Or % 4.59/4.79 (Eq % 4.59/4.79 (And (And (∀ (R : a → Prop), (Eq R fun Xx => False) → True) (∀ (R : a → Prop), (Eq R fun Xx => Not False) → True)) % 4.59/4.79 (∀ (K : (a → Prop) → Prop) (R : a → Prop), % 4.59/4.79 And (∀ (Xx : a → Prop), K Xx → True) (Eq R fun Xx => Exists fun S => And (K S) (S Xx)) → True)) % 4.59/4.79 False) % 4.59/4.79 (Eq (∀ (Y Z S : a → Prop), And (And True True) (Eq S fun Xx => And (Y Xx) (Z Xx)) → True) False) % 4.59/4.79 Clause #3 (by clausification #[2]): Or (Eq (∀ (Y Z S : a → Prop), And (And True True) (Eq S fun Xx => And (Y Xx) (Z Xx)) → True) False) % 4.59/4.79 (Or % 4.59/4.79 (Eq (And (∀ (R : a → Prop), (Eq R fun Xx => False) → True) (∀ (R : a → Prop), (Eq R fun Xx => Not False) → True)) % 4.59/4.79 False) % 4.59/4.79 (Eq % 4.59/4.79 (∀ (K : (a → Prop) → Prop) (R : a → Prop), % 4.59/4.79 And (∀ (Xx : a → Prop), K Xx → True) (Eq R fun Xx => Exists fun S => And (K S) (S Xx)) → True) % 4.59/4.79 False)) % 4.59/4.79 Clause #4 (by clausification #[3]): ∀ (a_1 : a → Prop), % 4.59/4.79 Or % 4.59/4.79 (Eq (And (∀ (R : a → Prop), (Eq R fun Xx => False) → True) (∀ (R : a → Prop), (Eq R fun Xx => Not False) → True)) % 4.59/4.79 False) % 4.59/4.79 (Or % 4.59/4.79 (Eq % 4.59/4.79 (∀ (K : (a → Prop) → Prop) (R : a → Prop), % 4.59/4.79 And (∀ (Xx : a → Prop), K Xx → True) (Eq R fun Xx => Exists fun S => And (K S) (S Xx)) → True) % 4.59/4.79 False) % 4.59/4.79 (Eq (Not (∀ (Z S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_1 Xx) (Z Xx)) → True)) True)) % 4.59/4.79 Clause #5 (by clausification #[4]): ∀ (a_1 : a → Prop), % 4.59/4.79 Or % 4.59/4.79 (Eq % 4.59/4.79 (∀ (K : (a → Prop) → Prop) (R : a → Prop), % 4.59/4.79 And (∀ (Xx : a → Prop), K Xx → True) (Eq R fun Xx => Exists fun S => And (K S) (S Xx)) → True) % 4.59/4.79 False) % 4.59/4.79 (Or (Eq (Not (∀ (Z S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_1 Xx) (Z Xx)) → True)) True) % 4.59/4.79 (Or (Eq (∀ (R : a → Prop), (Eq R fun Xx => False) → True) False) % 4.59/4.79 (Eq (∀ (R : a → Prop), (Eq R fun Xx => Not False) → True) False))) % 4.59/4.79 Clause #6 (by clausification #[5]): ∀ (a_1 : a → Prop) (a_2 : (a → Prop) → Prop), % 4.59/4.79 Or (Eq (Not (∀ (Z S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_1 Xx) (Z Xx)) → True)) True) % 4.59/4.79 (Or (Eq (∀ (R : a → Prop), (Eq R fun Xx => False) → True) False) % 4.59/4.79 (Or (Eq (∀ (R : a → Prop), (Eq R fun Xx => Not False) → True) False) % 4.59/4.79 (Eq % 4.59/4.79 (Not % 4.59/4.79 (∀ (R : a → Prop), % 4.59/4.79 And (∀ (Xx : a → Prop), skS.0 1 a_2 Xx → True) % 4.59/4.79 (Eq R fun Xx => Exists fun S => And (skS.0 1 a_2 S) (S Xx)) → % 4.59/4.79 True)) % 4.59/4.79 True))) % 4.59/4.79 Clause #7 (by clausification #[6]): ∀ (a_1 : (a → Prop) → Prop) (a_2 : a → Prop), % 4.59/4.79 Or (Eq (∀ (R : a → Prop), (Eq R fun Xx => False) → True) False) % 4.59/4.79 (Or (Eq (∀ (R : a → Prop), (Eq R fun Xx => Not False) → True) False) % 4.59/4.79 (Or % 4.59/4.79 (Eq % 4.59/4.79 (Not % 4.59/4.79 (∀ (R : a → Prop), % 4.59/4.79 And (∀ (Xx : a → Prop), skS.0 1 a_1 Xx → True) % 4.59/4.79 (Eq R fun Xx => Exists fun S => And (skS.0 1 a_1 S) (S Xx)) → % 4.59/4.79 True)) % 4.59/4.81 True) % 4.59/4.81 (Eq (∀ (Z S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_2 Xx) (Z Xx)) → True) False))) % 4.59/4.81 Clause #8 (by clausification #[7]): ∀ (a_1 : (a → Prop) → Prop) (a_2 a_3 : a → Prop), % 4.59/4.81 Or (Eq (∀ (R : a → Prop), (Eq R fun Xx => Not False) → True) False) % 4.59/4.81 (Or % 4.59/4.81 (Eq % 4.59/4.81 (Not % 4.59/4.81 (∀ (R : a → Prop), % 4.59/4.81 And (∀ (Xx : a → Prop), skS.0 1 a_1 Xx → True) (Eq R fun Xx => Exists fun S => And (skS.0 1 a_1 S) (S Xx)) → % 4.59/4.81 True)) % 4.59/4.81 True) % 4.59/4.81 (Or (Eq (∀ (Z S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_2 Xx) (Z Xx)) → True) False) % 4.59/4.81 (Eq (Not ((Eq (skS.0 2 a_3) fun Xx => False) → True)) True))) % 4.59/4.81 Clause #9 (by clausification #[8]): ∀ (a_1 : (a → Prop) → Prop) (a_2 a_3 a_4 : a → Prop), % 4.59/4.81 Or % 4.59/4.81 (Eq % 4.59/4.81 (Not % 4.59/4.81 (∀ (R : a → Prop), % 4.59/4.81 And (∀ (Xx : a → Prop), skS.0 1 a_1 Xx → True) (Eq R fun Xx => Exists fun S => And (skS.0 1 a_1 S) (S Xx)) → % 4.59/4.81 True)) % 4.59/4.81 True) % 4.59/4.81 (Or (Eq (∀ (Z S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_2 Xx) (Z Xx)) → True) False) % 4.59/4.81 (Or (Eq (Not ((Eq (skS.0 2 a_3) fun Xx => False) → True)) True) % 4.59/4.81 (Eq (Not ((Eq (skS.0 3 a_4) fun Xx => Not False) → True)) True))) % 4.59/4.81 Clause #10 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : (a → Prop) → Prop), % 4.59/4.81 Or (Eq (∀ (Z S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_1 Xx) (Z Xx)) → True) False) % 4.59/4.81 (Or (Eq (Not ((Eq (skS.0 2 a_2) fun Xx => False) → True)) True) % 4.59/4.81 (Or (Eq (Not ((Eq (skS.0 3 a_3) fun Xx => Not False) → True)) True) % 4.59/4.81 (Eq % 4.59/4.81 (∀ (R : a → Prop), % 4.59/4.81 And (∀ (Xx : a → Prop), skS.0 1 a_4 Xx → True) (Eq R fun Xx => Exists fun S => And (skS.0 1 a_4 S) (S Xx)) → % 4.59/4.81 True) % 4.59/4.81 False))) % 4.59/4.81 Clause #11 (by clausification #[10]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 a_5 : a → Prop), % 4.59/4.81 Or (Eq (Not ((Eq (skS.0 2 a_1) fun Xx => False) → True)) True) % 4.59/4.81 (Or (Eq (Not ((Eq (skS.0 3 a_2) fun Xx => Not False) → True)) True) % 4.59/4.81 (Or % 4.59/4.81 (Eq % 4.59/4.81 (∀ (R : a → Prop), % 4.59/4.81 And (∀ (Xx : a → Prop), skS.0 1 a_3 Xx → True) (Eq R fun Xx => Exists fun S => And (skS.0 1 a_3 S) (S Xx)) → % 4.59/4.81 True) % 4.59/4.81 False) % 4.59/4.81 (Eq % 4.59/4.81 (Not % 4.59/4.81 (∀ (S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_4 Xx) (skS.0 4 a_4 a_5 Xx)) → True)) % 4.59/4.81 True))) % 4.59/4.81 Clause #12 (by clausification #[11]): ∀ (a_1 : a → Prop) (a_2 : (a → Prop) → Prop) (a_3 a_4 a_5 : a → Prop), % 4.59/4.81 Or (Eq (Not ((Eq (skS.0 3 a_1) fun Xx => Not False) → True)) True) % 4.59/4.81 (Or % 4.59/4.81 (Eq % 4.59/4.81 (∀ (R : a → Prop), % 4.59/4.81 And (∀ (Xx : a → Prop), skS.0 1 a_2 Xx → True) (Eq R fun Xx => Exists fun S => And (skS.0 1 a_2 S) (S Xx)) → % 4.59/4.81 True) % 4.59/4.81 False) % 4.59/4.81 (Or % 4.59/4.81 (Eq % 4.59/4.81 (Not % 4.59/4.81 (∀ (S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_3 Xx) (skS.0 4 a_3 a_4 Xx)) → True)) % 4.59/4.81 True) % 4.59/4.81 (Eq ((Eq (skS.0 2 a_5) fun Xx => False) → True) False))) % 4.59/4.81 Clause #13 (by clausification #[12]): ∀ (a_1 : (a → Prop) → Prop) (a_2 a_3 a_4 a_5 : a → Prop), % 4.59/4.81 Or % 4.59/4.81 (Eq % 4.59/4.81 (∀ (R : a → Prop), % 4.59/4.81 And (∀ (Xx : a → Prop), skS.0 1 a_1 Xx → True) (Eq R fun Xx => Exists fun S => And (skS.0 1 a_1 S) (S Xx)) → % 4.59/4.81 True) % 4.59/4.81 False) % 4.59/4.81 (Or % 4.59/4.81 (Eq % 4.59/4.81 (Not (∀ (S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_2 Xx) (skS.0 4 a_2 a_3 Xx)) → True)) % 4.59/4.81 True) % 4.59/4.81 (Or (Eq ((Eq (skS.0 2 a_4) fun Xx => False) → True) False) % 4.59/4.81 (Eq ((Eq (skS.0 3 a_5) fun Xx => Not False) → True) False))) % 4.59/4.81 Clause #14 (by clausification #[13]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : (a → Prop) → Prop) (a_6 : a → Prop), % 4.59/4.81 Or % 4.59/4.81 (Eq (Not (∀ (S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_1 Xx) (skS.0 4 a_1 a_2 Xx)) → True)) % 4.59/4.81 True) % 4.59/4.81 (Or (Eq ((Eq (skS.0 2 a_3) fun Xx => False) → True) False) % 4.59/4.84 (Or (Eq ((Eq (skS.0 3 a_4) fun Xx => Not False) → True) False) % 4.59/4.84 (Eq % 4.59/4.84 (Not % 4.59/4.84 (And (∀ (Xx : a → Prop), skS.0 1 a_5 Xx → True) % 4.59/4.84 (Eq (skS.0 5 a_5 a_6) fun Xx => Exists fun S => And (skS.0 1 a_5 S) (S Xx)) → % 4.59/4.84 True)) % 4.59/4.84 True))) % 4.59/4.84 Clause #15 (by clausification #[14]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 a_5 a_6 : a → Prop), % 4.59/4.84 Or (Eq ((Eq (skS.0 2 a_1) fun Xx => False) → True) False) % 4.59/4.84 (Or (Eq ((Eq (skS.0 3 a_2) fun Xx => Not False) → True) False) % 4.59/4.84 (Or % 4.59/4.84 (Eq % 4.59/4.84 (Not % 4.59/4.84 (And (∀ (Xx : a → Prop), skS.0 1 a_3 Xx → True) % 4.59/4.84 (Eq (skS.0 5 a_3 a_4) fun Xx => Exists fun S => And (skS.0 1 a_3 S) (S Xx)) → % 4.59/4.84 True)) % 4.59/4.84 True) % 4.59/4.84 (Eq (∀ (S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_5 Xx) (skS.0 4 a_5 a_6 Xx)) → True) % 4.59/4.84 False))) % 4.59/4.84 Clause #17 (by clausification #[15]): ∀ (a_1 : a → Prop) (a_2 : (a → Prop) → Prop) (a_3 a_4 a_5 : a → Prop), % 4.59/4.84 Or (Eq ((Eq (skS.0 3 a_1) fun Xx => Not False) → True) False) % 4.59/4.84 (Or % 4.59/4.84 (Eq % 4.59/4.84 (Not % 4.59/4.84 (And (∀ (Xx : a → Prop), skS.0 1 a_2 Xx → True) % 4.59/4.84 (Eq (skS.0 5 a_2 a_3) fun Xx => Exists fun S => And (skS.0 1 a_2 S) (S Xx)) → % 4.59/4.84 True)) % 4.59/4.84 True) % 4.59/4.84 (Or % 4.59/4.84 (Eq (∀ (S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_4 Xx) (skS.0 4 a_4 a_5 Xx)) → True) % 4.59/4.84 False) % 4.59/4.84 (Eq True False))) % 4.59/4.84 Clause #58 (by clausification #[17]): ∀ (a_1 : (a → Prop) → Prop) (a_2 a_3 a_4 : a → Prop), % 4.59/4.84 Or % 4.59/4.84 (Eq % 4.59/4.84 (Not % 4.59/4.84 (And (∀ (Xx : a → Prop), skS.0 1 a_1 Xx → True) % 4.59/4.84 (Eq (skS.0 5 a_1 a_2) fun Xx => Exists fun S => And (skS.0 1 a_1 S) (S Xx)) → % 4.59/4.84 True)) % 4.59/4.84 True) % 4.59/4.84 (Or % 4.59/4.84 (Eq (∀ (S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_3 Xx) (skS.0 4 a_3 a_4 Xx)) → True) % 4.59/4.84 False) % 4.59/4.84 (Or (Eq True False) (Eq True False))) % 4.59/4.84 Clause #125 (by clausification #[58]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 : a → Prop), % 4.59/4.84 Or % 4.59/4.84 (Eq (∀ (S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_1 Xx) (skS.0 4 a_1 a_2 Xx)) → True) False) % 4.59/4.84 (Or (Eq True False) % 4.59/4.84 (Or (Eq True False) % 4.59/4.84 (Eq % 4.59/4.84 (And (∀ (Xx : a → Prop), skS.0 1 a_3 Xx → True) % 4.59/4.84 (Eq (skS.0 5 a_3 a_4) fun Xx => Exists fun S => And (skS.0 1 a_3 S) (S Xx)) → % 4.59/4.84 True) % 4.59/4.84 False))) % 4.59/4.84 Clause #126 (by clausification #[125]): ∀ (a_1 : (a → Prop) → Prop) (a_2 a_3 a_4 a_5 : a → Prop), % 4.59/4.84 Or (Eq True False) % 4.59/4.84 (Or (Eq True False) % 4.59/4.84 (Or % 4.59/4.84 (Eq % 4.59/4.84 (And (∀ (Xx : a → Prop), skS.0 1 a_1 Xx → True) % 4.59/4.84 (Eq (skS.0 5 a_1 a_2) fun Xx => Exists fun S => And (skS.0 1 a_1 S) (S Xx)) → % 4.59/4.84 True) % 4.59/4.84 False) % 4.59/4.84 (Eq % 4.59/4.84 (Not % 4.59/4.84 (And (And True True) (Eq (skS.0 8 a_3 a_4 a_5) fun Xx => And (skS.0 0 a_3 Xx) (skS.0 4 a_3 a_4 Xx)) → True)) % 4.59/4.84 True))) % 4.59/4.84 Clause #127 (by clausification #[126]): ∀ (a_1 : (a → Prop) → Prop) (a_2 a_3 a_4 a_5 : a → Prop), % 4.59/4.84 Or (Eq True False) % 4.59/4.84 (Or % 4.59/4.84 (Eq % 4.59/4.84 (And (∀ (Xx : a → Prop), skS.0 1 a_1 Xx → True) % 4.59/4.84 (Eq (skS.0 5 a_1 a_2) fun Xx => Exists fun S => And (skS.0 1 a_1 S) (S Xx)) → % 4.59/4.84 True) % 4.59/4.84 False) % 4.59/4.84 (Eq % 4.59/4.84 (Not % 4.59/4.84 (And (And True True) (Eq (skS.0 8 a_3 a_4 a_5) fun Xx => And (skS.0 0 a_3 Xx) (skS.0 4 a_3 a_4 Xx)) → True)) % 4.59/4.84 True)) % 4.59/4.84 Clause #128 (by clausification #[127]): ∀ (a_1 : (a → Prop) → Prop) (a_2 a_3 a_4 a_5 : a → Prop), % 4.59/4.84 Or % 4.59/4.84 (Eq % 4.59/4.84 (And (∀ (Xx : a → Prop), skS.0 1 a_1 Xx → True) % 4.59/4.84 (Eq (skS.0 5 a_1 a_2) fun Xx => Exists fun S => And (skS.0 1 a_1 S) (S Xx)) → % 4.59/4.84 True) % 4.59/4.84 False) % 4.59/4.84 (Eq % 4.59/4.84 (Not (And (And True True) (Eq (skS.0 8 a_3 a_4 a_5) fun Xx => And (skS.0 0 a_3 Xx) (skS.0 4 a_3 a_4 Xx)) → True)) % 4.59/4.84 True) % 4.59/4.84 Clause #130 (by clausification #[128]): ∀ (a_1 a_2 a_3 : a → Prop), % 4.59/4.84 Or % 4.59/4.84 (Eq % 4.59/4.84 (Not (And (And True True) (Eq (skS.0 8 a_1 a_2 a_3) fun Xx => And (skS.0 0 a_1 Xx) (skS.0 4 a_1 a_2 Xx)) → True)) % 4.59/4.84 True) % 4.59/4.84 (Eq True False) % 4.59/4.84 Clause #211 (by clausification #[130]): ∀ (a_1 a_2 a_3 : a → Prop), % 4.59/4.84 Or (Eq True False) % 4.59/4.84 (Eq (And (And True True) (Eq (skS.0 8 a_1 a_2 a_3) fun Xx => And (skS.0 0 a_1 Xx) (skS.0 4 a_1 a_2 Xx)) → True) % 4.59/4.84 False) % 4.59/4.84 Clause #212 (by clausification #[211]): ∀ (a_1 a_2 a_3 : a → Prop), % 4.59/4.84 Eq (And (And True True) (Eq (skS.0 8 a_1 a_2 a_3) fun Xx => And (skS.0 0 a_1 Xx) (skS.0 4 a_1 a_2 Xx)) → True) False % 4.59/4.84 Clause #214 (by clausification #[212]): Eq True False % 4.59/4.84 Clause #257 (by clausification #[214]): False % 4.59/4.84 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------