%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET580^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n023.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 08:00:10 PM UTC 2025 % Result : Theorem 5.67s 5.88s % Output : Proof 5.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SET580^5 : TPTP v9.2.0. Released v4.0.0. % 0.10/0.11 % Command : duper %s % 0.11/0.32 % Computer : n023.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Thu Oct 2 14:47:53 EDT 2025 % 0.11/0.32 % CPUTime : % 5.67/5.88 SZS status Theorem for theBenchmark.p % 5.67/5.88 SZS output start Proof for theBenchmark.p % 5.67/5.88 Clause #0 (by assumption #[]): Eq % 5.67/5.88 (Not % 5.67/5.88 (∀ (Xx : a) (X Y : a → Prop), % 5.67/5.88 Iff (Iff (Or (And (X Xx) (Not (Y Xx))) (And (Y Xx) (Not (X Xx)))) (X Xx)) (Not (Y Xx)))) % 5.67/5.88 True % 5.67/5.88 Clause #1 (by clausification #[0]): Eq (∀ (Xx : a) (X Y : a → Prop), Iff (Iff (Or (And (X Xx) (Not (Y Xx))) (And (Y Xx) (Not (X Xx)))) (X Xx)) (Not (Y Xx))) % 5.67/5.88 False % 5.67/5.88 Clause #2 (by clausification #[1]): ∀ (a_1 : a), % 5.67/5.88 Eq % 5.67/5.88 (Not % 5.67/5.88 (∀ (X Y : a → Prop), % 5.67/5.88 Iff % 5.67/5.88 (Iff (Or (And (X (skS.0 0 a_1)) (Not (Y (skS.0 0 a_1)))) (And (Y (skS.0 0 a_1)) (Not (X (skS.0 0 a_1))))) % 5.67/5.88 (X (skS.0 0 a_1))) % 5.67/5.88 (Not (Y (skS.0 0 a_1))))) % 5.67/5.88 True % 5.67/5.88 Clause #3 (by clausification #[2]): ∀ (a_1 : a), % 5.67/5.88 Eq % 5.67/5.88 (∀ (X Y : a → Prop), % 5.67/5.88 Iff % 5.67/5.88 (Iff (Or (And (X (skS.0 0 a_1)) (Not (Y (skS.0 0 a_1)))) (And (Y (skS.0 0 a_1)) (Not (X (skS.0 0 a_1))))) % 5.67/5.88 (X (skS.0 0 a_1))) % 5.67/5.88 (Not (Y (skS.0 0 a_1)))) % 5.67/5.88 False % 5.67/5.88 Clause #4 (by clausification #[3]): ∀ (a_1 : a) (a_2 : a → Prop), % 5.67/5.88 Eq % 5.67/5.88 (Not % 5.67/5.88 (∀ (Y : a → Prop), % 5.67/5.88 Iff % 5.67/5.88 (Iff % 5.67/5.88 (Or (And (skS.0 1 a_1 a_2 (skS.0 0 a_1)) (Not (Y (skS.0 0 a_1)))) % 5.67/5.88 (And (Y (skS.0 0 a_1)) (Not (skS.0 1 a_1 a_2 (skS.0 0 a_1))))) % 5.67/5.88 (skS.0 1 a_1 a_2 (skS.0 0 a_1))) % 5.67/5.88 (Not (Y (skS.0 0 a_1))))) % 5.67/5.88 True % 5.67/5.88 Clause #5 (by clausification #[4]): ∀ (a_1 : a) (a_2 : a → Prop), % 5.67/5.88 Eq % 5.67/5.88 (∀ (Y : a → Prop), % 5.67/5.88 Iff % 5.67/5.88 (Iff % 5.67/5.88 (Or (And (skS.0 1 a_1 a_2 (skS.0 0 a_1)) (Not (Y (skS.0 0 a_1)))) % 5.67/5.88 (And (Y (skS.0 0 a_1)) (Not (skS.0 1 a_1 a_2 (skS.0 0 a_1))))) % 5.67/5.88 (skS.0 1 a_1 a_2 (skS.0 0 a_1))) % 5.67/5.88 (Not (Y (skS.0 0 a_1)))) % 5.67/5.88 False % 5.67/5.88 Clause #6 (by clausification #[5]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.67/5.88 Eq % 5.67/5.88 (Not % 5.67/5.88 (Iff % 5.67/5.88 (Iff % 5.67/5.88 (Or (And (skS.0 1 a_1 a_2 (skS.0 0 a_1)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)))) % 5.67/5.88 (And (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) (Not (skS.0 1 a_1 a_2 (skS.0 0 a_1))))) % 5.67/5.88 (skS.0 1 a_1 a_2 (skS.0 0 a_1))) % 5.67/5.88 (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1))))) % 5.67/5.88 True % 5.67/5.88 Clause #7 (by clausification #[6]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.67/5.88 Eq % 5.67/5.88 (Iff % 5.67/5.88 (Iff % 5.67/5.88 (Or (And (skS.0 1 a_1 a_2 (skS.0 0 a_1)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)))) % 5.67/5.88 (And (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) (Not (skS.0 1 a_1 a_2 (skS.0 0 a_1))))) % 5.67/5.88 (skS.0 1 a_1 a_2 (skS.0 0 a_1))) % 5.67/5.88 (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)))) % 5.67/5.88 False % 5.67/5.88 Clause #8 (by clausification #[7]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.67/5.88 Or % 5.67/5.88 (Eq % 5.67/5.88 (Iff % 5.67/5.88 (Or (And (skS.0 1 a_1 a_2 (skS.0 0 a_1)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)))) % 5.67/5.88 (And (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) (Not (skS.0 1 a_1 a_2 (skS.0 0 a_1))))) % 5.67/5.88 (skS.0 1 a_1 a_2 (skS.0 0 a_1))) % 5.67/5.88 False) % 5.67/5.88 (Eq (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1))) False) % 5.67/5.88 Clause #9 (by clausification #[7]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.67/5.88 Or % 5.67/5.88 (Eq % 5.67/5.88 (Iff % 5.67/5.88 (Or (And (skS.0 1 a_1 a_2 (skS.0 0 a_1)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)))) % 5.67/5.88 (And (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) (Not (skS.0 1 a_1 a_2 (skS.0 0 a_1))))) % 5.67/5.88 (skS.0 1 a_1 a_2 (skS.0 0 a_1))) % 5.67/5.88 True) % 5.67/5.88 (Eq (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1))) True) % 5.67/5.88 Clause #10 (by clausification #[8]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.67/5.88 Or (Eq (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1))) False) % 5.67/5.88 (Or % 5.67/5.88 (Eq % 5.67/5.88 (Or (And (skS.0 1 a_1 a_2 (skS.0 0 a_1)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)))) % 5.67/5.88 (And (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) (Not (skS.0 1 a_1 a_2 (skS.0 0 a_1))))) % 5.67/5.88 False) % 5.67/5.88 (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) False)) % 5.67/5.88 Clause #11 (by clausification #[8]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.67/5.88 Or (Eq (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1))) False) % 5.67/5.88 (Or % 5.67/5.88 (Eq % 5.67/5.88 (Or (And (skS.0 1 a_1 a_2 (skS.0 0 a_1)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)))) % 5.67/5.88 (And (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) (Not (skS.0 1 a_1 a_2 (skS.0 0 a_1))))) % 5.67/5.88 True) % 5.67/5.88 (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True)) % 5.76/5.95 Clause #12 (by clausification #[10]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.76/5.95 Or % 5.76/5.95 (Eq % 5.76/5.95 (Or (And (skS.0 1 a_1 a_2 (skS.0 0 a_1)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)))) % 5.76/5.95 (And (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) (Not (skS.0 1 a_1 a_2 (skS.0 0 a_1))))) % 5.76/5.95 False) % 5.76/5.95 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) True)) % 5.76/5.95 Clause #14 (by clausification #[12]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.76/5.95 Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) False) % 5.76/5.95 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) True) % 5.76/5.95 (Eq (And (skS.0 1 a_1 a_2 (skS.0 0 a_1)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)))) False)) % 5.76/5.95 Clause #17 (by clausification #[14]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.76/5.95 Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) False) % 5.76/5.95 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) True) % 5.76/5.95 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) False) (Eq (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1))) False))) % 5.76/5.95 Clause #18 (by clausification #[17]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.76/5.95 Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) False) % 5.76/5.95 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) True) % 5.76/5.95 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) True))) % 5.76/5.95 Clause #19 (by eliminate duplicate literals #[18]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.76/5.95 Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) True) % 5.76/5.95 Clause #20 (by clausification #[11]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.76/5.95 Or % 5.76/5.95 (Eq % 5.76/5.95 (Or (And (skS.0 1 a_1 a_2 (skS.0 0 a_1)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)))) % 5.76/5.95 (And (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) (Not (skS.0 1 a_1 a_2 (skS.0 0 a_1))))) % 5.76/5.95 True) % 5.76/5.95 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) True)) % 5.76/5.95 Clause #21 (by clausification #[20]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.76/5.95 Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True) % 5.76/5.95 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) True) % 5.76/5.95 (Or (Eq (And (skS.0 1 a_1 a_2 (skS.0 0 a_1)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)))) True) % 5.76/5.95 (Eq (And (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) (Not (skS.0 1 a_1 a_2 (skS.0 0 a_1)))) True))) % 5.76/5.95 Clause #23 (by clausification #[21]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.76/5.95 Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True) % 5.76/5.95 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) True) % 5.76/5.95 (Or (Eq (And (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) (Not (skS.0 1 a_1 a_2 (skS.0 0 a_1)))) True) % 5.76/5.95 (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True))) % 5.76/5.95 Clause #30 (by clausification #[23]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.76/5.95 Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True) % 5.76/5.95 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) True) % 5.76/5.95 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) True))) % 5.76/5.95 Clause #32 (by clausification #[9]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.76/5.95 Or (Eq (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1))) True) % 5.76/5.95 (Or % 5.76/5.95 (Eq % 5.76/5.95 (Or (And (skS.0 1 a_1 a_2 (skS.0 0 a_1)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)))) % 5.76/5.95 (And (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) (Not (skS.0 1 a_1 a_2 (skS.0 0 a_1))))) % 5.76/5.95 True) % 5.76/5.95 (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) False)) % 5.76/5.95 Clause #33 (by clausification #[9]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.76/5.95 Or (Eq (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1))) True) % 5.76/5.95 (Or % 5.76/5.95 (Eq % 5.76/5.95 (Or (And (skS.0 1 a_1 a_2 (skS.0 0 a_1)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)))) % 5.76/5.95 (And (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) (Not (skS.0 1 a_1 a_2 (skS.0 0 a_1))))) % 5.76/5.95 False) % 5.76/5.95 (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True)) % 5.76/5.95 Clause #34 (by clausification #[32]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.76/5.95 Or % 5.76/5.95 (Eq % 5.76/5.95 (Or (And (skS.0 1 a_1 a_2 (skS.0 0 a_1)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)))) % 5.76/5.95 (And (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) (Not (skS.0 1 a_1 a_2 (skS.0 0 a_1))))) % 5.76/5.95 True) % 5.76/5.95 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) False)) % 5.76/5.95 Clause #35 (by clausification #[34]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.76/5.95 Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) False) % 5.76/5.95 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) False) % 5.85/6.00 (Or (Eq (And (skS.0 1 a_1 a_2 (skS.0 0 a_1)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)))) True) % 5.85/6.00 (Eq (And (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) (Not (skS.0 1 a_1 a_2 (skS.0 0 a_1)))) True))) % 5.85/6.00 Clause #36 (by clausification #[35]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.85/6.00 Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) False) % 5.85/6.00 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) False) % 5.85/6.00 (Or (Eq (And (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) (Not (skS.0 1 a_1 a_2 (skS.0 0 a_1)))) True) % 5.85/6.00 (Eq (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1))) True))) % 5.85/6.00 Clause #38 (by clausification #[36]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.85/6.00 Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) False) % 5.85/6.00 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) False) % 5.85/6.00 (Or (Eq (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1))) True) (Eq (Not (skS.0 1 a_1 a_2 (skS.0 0 a_1))) True))) % 5.85/6.00 Clause #40 (by clausification #[38]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.85/6.00 Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) False) % 5.85/6.00 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) False) % 5.85/6.00 (Or (Eq (Not (skS.0 1 a_1 a_2 (skS.0 0 a_1))) True) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) False))) % 5.85/6.00 Clause #41 (by clausification #[40]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.85/6.00 Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) False) % 5.85/6.00 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) False) % 5.85/6.00 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) False) (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) False))) % 5.85/6.00 Clause #42 (by eliminate duplicate literals #[41]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.85/6.00 Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) False) % 5.85/6.00 Clause #43 (by eliminate duplicate literals #[30]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.85/6.00 Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) True) % 5.85/6.00 Clause #48 (by clausification #[33]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.85/6.00 Or % 5.85/6.00 (Eq % 5.85/6.00 (Or (And (skS.0 1 a_1 a_2 (skS.0 0 a_1)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)))) % 5.85/6.00 (And (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) (Not (skS.0 1 a_1 a_2 (skS.0 0 a_1))))) % 5.85/6.00 False) % 5.85/6.00 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) False)) % 5.85/6.00 Clause #49 (by clausification #[48]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.85/6.00 Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True) % 5.85/6.00 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) False) % 5.85/6.00 (Eq (And (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) (Not (skS.0 1 a_1 a_2 (skS.0 0 a_1)))) False)) % 5.85/6.00 Clause #51 (by clausification #[49]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.85/6.00 Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True) % 5.85/6.00 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) False) % 5.85/6.00 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) False) (Eq (Not (skS.0 1 a_1 a_2 (skS.0 0 a_1))) False))) % 5.85/6.00 Clause #52 (by clausification #[51]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.85/6.00 Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True) % 5.85/6.00 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) False) % 5.85/6.00 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) False) (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True))) % 5.85/6.00 Clause #53 (by eliminate duplicate literals #[52]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), % 5.85/6.00 Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) False) % 5.85/6.00 Clause #54 (by superposition #[53, 43]): ∀ (a_1 : a) (a_2 : a → Prop), % 5.85/6.00 Or (Eq (skS.0 1 a_1 (fun x => a_2 x) (skS.0 0 a_1)) True) % 5.85/6.00 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True) (Eq False True)) % 5.85/6.00 Clause #57 (by betaEtaReduce #[54]): ∀ (a_1 : a) (a_2 : a → Prop), % 5.85/6.00 Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True) (Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True) (Eq False True)) % 5.85/6.00 Clause #58 (by clausification #[57]): ∀ (a_1 : a) (a_2 : a → Prop), Or (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True) % 5.85/6.00 Clause #59 (by eliminate duplicate literals #[58]): ∀ (a_1 : a) (a_2 : a → Prop), Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1)) True % 5.85/6.00 Clause #60 (by backward demodulation #[59, 19]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), Or (Eq True False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) True) % 5.85/6.00 Clause #61 (by backward demodulation #[59, 42]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), Or (Eq True False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) False) % 5.85/6.01 Clause #64 (by clausification #[61]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) False % 5.85/6.01 Clause #65 (by clausification #[60]): ∀ (a_1 : a) (a_2 a_3 : a → Prop), Eq (skS.0 2 a_1 a_2 a_3 (skS.0 0 a_1)) True % 5.85/6.01 Clause #66 (by superposition #[65, 64]): Eq True False % 5.85/6.01 Clause #67 (by clausification #[66]): False % 5.85/6.01 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------