%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN319+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 08:07:23 PM UTC 2025 % Result : Theorem 3.54s 3.71s % Output : Proof 3.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN319+1 : TPTP v9.2.0. Released v2.0.0. % 0.07/0.14 % Command : duper %s % 0.14/0.35 % Computer : n019.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Thu Oct 2 15:19:08 EDT 2025 % 0.14/0.35 % CPUTime : % 3.54/3.71 SZS status Theorem for theBenchmark.p % 3.54/3.71 SZS output start Proof for theBenchmark.p % 3.54/3.71 Clause #0 (by assumption #[]): Eq % 3.54/3.71 (Not % 3.54/3.71 (Exists fun X => % 3.54/3.71 Exists fun Y => % 3.54/3.71 ∀ (Z1 Z2 : Iota), % 3.54/3.71 ((big_f Y → big_g Z1) → And (big_g X) (Not (big_f Z1))) → % 3.54/3.71 (Or (big_f X) (big_g X) → big_h X) → And (big_h Z2) (big_h Y → Or (big_f Z2) (big_g Z2) → big_h Z2))) % 3.54/3.71 True % 3.54/3.71 Clause #1 (by clausification #[0]): Eq % 3.54/3.71 (Exists fun X => % 3.54/3.71 Exists fun Y => % 3.54/3.71 ∀ (Z1 Z2 : Iota), % 3.54/3.71 ((big_f Y → big_g Z1) → And (big_g X) (Not (big_f Z1))) → % 3.54/3.71 (Or (big_f X) (big_g X) → big_h X) → And (big_h Z2) (big_h Y → Or (big_f Z2) (big_g Z2) → big_h Z2)) % 3.54/3.71 False % 3.54/3.71 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 3.54/3.71 Eq % 3.54/3.71 (Exists fun Y => % 3.54/3.71 ∀ (Z1 Z2 : Iota), % 3.54/3.71 ((big_f Y → big_g Z1) → And (big_g a) (Not (big_f Z1))) → % 3.54/3.71 (Or (big_f a) (big_g a) → big_h a) → And (big_h Z2) (big_h Y → Or (big_f Z2) (big_g Z2) → big_h Z2)) % 3.54/3.71 False % 3.54/3.71 Clause #3 (by clausification #[2]): ∀ (a a_1 : Iota), % 3.55/3.71 Eq % 3.55/3.71 (∀ (Z1 Z2 : Iota), % 3.55/3.71 ((big_f a → big_g Z1) → And (big_g a_1) (Not (big_f Z1))) → % 3.55/3.71 (Or (big_f a_1) (big_g a_1) → big_h a_1) → And (big_h Z2) (big_h a → Or (big_f Z2) (big_g Z2) → big_h Z2)) % 3.55/3.71 False % 3.55/3.71 Clause #4 (by clausification #[3]): ∀ (a a_1 a_2 : Iota), % 3.55/3.71 Eq % 3.55/3.71 (Not % 3.55/3.71 (∀ (Z2 : Iota), % 3.55/3.71 ((big_f a → big_g (skS.0 0 a a_1 a_2)) → And (big_g a_1) (Not (big_f (skS.0 0 a a_1 a_2)))) → % 3.55/3.71 (Or (big_f a_1) (big_g a_1) → big_h a_1) → And (big_h Z2) (big_h a → Or (big_f Z2) (big_g Z2) → big_h Z2))) % 3.55/3.71 True % 3.55/3.71 Clause #5 (by clausification #[4]): ∀ (a a_1 a_2 : Iota), % 3.55/3.71 Eq % 3.55/3.71 (∀ (Z2 : Iota), % 3.55/3.71 ((big_f a → big_g (skS.0 0 a a_1 a_2)) → And (big_g a_1) (Not (big_f (skS.0 0 a a_1 a_2)))) → % 3.55/3.71 (Or (big_f a_1) (big_g a_1) → big_h a_1) → And (big_h Z2) (big_h a → Or (big_f Z2) (big_g Z2) → big_h Z2)) % 3.55/3.71 False % 3.55/3.71 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 a_3 : Iota), % 3.55/3.71 Eq % 3.55/3.71 (Not % 3.55/3.71 (((big_f a → big_g (skS.0 0 a a_1 a_2)) → And (big_g a_1) (Not (big_f (skS.0 0 a a_1 a_2)))) → % 3.55/3.71 (Or (big_f a_1) (big_g a_1) → big_h a_1) → % 3.55/3.71 And (big_h (skS.0 1 a a_1 a_2 a_3)) % 3.55/3.71 (big_h a → % 3.55/3.71 Or (big_f (skS.0 1 a a_1 a_2 a_3)) (big_g (skS.0 1 a a_1 a_2 a_3)) → big_h (skS.0 1 a a_1 a_2 a_3)))) % 3.55/3.71 True % 3.55/3.71 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 a_3 : Iota), % 3.55/3.71 Eq % 3.55/3.71 (((big_f a → big_g (skS.0 0 a a_1 a_2)) → And (big_g a_1) (Not (big_f (skS.0 0 a a_1 a_2)))) → % 3.55/3.71 (Or (big_f a_1) (big_g a_1) → big_h a_1) → % 3.55/3.71 And (big_h (skS.0 1 a a_1 a_2 a_3)) % 3.55/3.71 (big_h a → % 3.55/3.71 Or (big_f (skS.0 1 a a_1 a_2 a_3)) (big_g (skS.0 1 a a_1 a_2 a_3)) → big_h (skS.0 1 a a_1 a_2 a_3))) % 3.55/3.71 False % 3.55/3.71 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), % 3.55/3.71 Eq ((big_f a → big_g (skS.0 0 a a_1 a_2)) → And (big_g a_1) (Not (big_f (skS.0 0 a a_1 a_2)))) True % 3.55/3.71 Clause #9 (by clausification #[7]): ∀ (a a_1 a_2 a_3 : Iota), % 3.55/3.71 Eq % 3.55/3.71 ((Or (big_f a) (big_g a) → big_h a) → % 3.55/3.71 And (big_h (skS.0 1 a_1 a a_2 a_3)) % 3.55/3.71 (big_h a_1 → % 3.55/3.71 Or (big_f (skS.0 1 a_1 a a_2 a_3)) (big_g (skS.0 1 a_1 a a_2 a_3)) → big_h (skS.0 1 a_1 a a_2 a_3))) % 3.55/3.71 False % 3.55/3.71 Clause #10 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), % 3.55/3.71 Or (Eq (big_f a → big_g (skS.0 0 a a_1 a_2)) False) (Eq (And (big_g a_1) (Not (big_f (skS.0 0 a a_1 a_2)))) True) % 3.55/3.71 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (big_g a) (Not (big_f (skS.0 0 a_1 a a_2)))) True) (Eq (big_f a_1) True) % 3.55/3.71 Clause #14 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (big_f a) True) (Eq (big_g a_1) True) % 3.55/3.71 Clause #22 (by clausification #[9]): ∀ (a : Iota), Eq (Or (big_f a) (big_g a) → big_h a) True % 3.55/3.71 Clause #23 (by clausification #[9]): ∀ (a a_1 a_2 a_3 : Iota), % 3.55/3.71 Eq % 3.55/3.71 (And (big_h (skS.0 1 a a_1 a_2 a_3)) % 3.55/3.71 (big_h a → Or (big_f (skS.0 1 a a_1 a_2 a_3)) (big_g (skS.0 1 a a_1 a_2 a_3)) → big_h (skS.0 1 a a_1 a_2 a_3))) % 3.55/3.71 False % 3.55/3.71 Clause #24 (by clausification #[22]): ∀ (a : Iota), Or (Eq (Or (big_f a) (big_g a)) False) (Eq (big_h a) True) % 3.55/3.72 Clause #25 (by clausification #[24]): ∀ (a : Iota), Or (Eq (big_h a) True) (Eq (big_g a) False) % 3.55/3.72 Clause #26 (by clausification #[24]): ∀ (a : Iota), Or (Eq (big_h a) True) (Eq (big_f a) False) % 3.55/3.72 Clause #27 (by superposition #[25, 14]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Or (Eq (big_f a_1) True) (Eq False True)) % 3.55/3.72 Clause #30 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Eq (big_f a_1) True) % 3.55/3.72 Clause #32 (by superposition #[30, 26]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Or (Eq (big_h a_1) True) (Eq True False)) % 3.55/3.72 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq (big_h a) True) (Eq (big_h a_1) True) % 3.55/3.72 Clause #34 (by equality factoring #[33]): ∀ (a : Iota), Or (Ne True True) (Eq (big_h a) True) % 3.55/3.72 Clause #35 (by clausification #[34]): ∀ (a : Iota), Or (Eq (big_h a) True) (Or (Eq True False) (Eq True False)) % 3.55/3.72 Clause #37 (by clausification #[35]): ∀ (a : Iota), Or (Eq (big_h a) True) (Eq True False) % 3.55/3.72 Clause #38 (by clausification #[37]): ∀ (a : Iota), Eq (big_h a) True % 3.55/3.72 Clause #43 (by clausification #[23]): ∀ (a a_1 a_2 a_3 : Iota), % 3.55/3.72 Or (Eq (big_h (skS.0 1 a a_1 a_2 a_3)) False) % 3.55/3.72 (Eq (big_h a → Or (big_f (skS.0 1 a a_1 a_2 a_3)) (big_g (skS.0 1 a a_1 a_2 a_3)) → big_h (skS.0 1 a a_1 a_2 a_3)) % 3.55/3.72 False) % 3.55/3.72 Clause #45 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), % 3.55/3.72 Or (Eq (big_h (skS.0 1 a a_1 a_2 a_3)) False) % 3.55/3.72 (Eq (Or (big_f (skS.0 1 a a_1 a_2 a_3)) (big_g (skS.0 1 a a_1 a_2 a_3)) → big_h (skS.0 1 a a_1 a_2 a_3)) False) % 3.55/3.72 Clause #48 (by clausification #[45]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_h (skS.0 1 a a_1 a_2 a_3)) False) (Eq (big_h (skS.0 1 a a_1 a_2 a_3)) False) % 3.55/3.72 Clause #52 (by eliminate duplicate literals #[48]): ∀ (a a_1 a_2 a_3 : Iota), Eq (big_h (skS.0 1 a a_1 a_2 a_3)) False % 3.55/3.72 Clause #53 (by superposition #[52, 38]): Eq False True % 3.55/3.72 Clause #54 (by clausification #[53]): False % 3.55/3.72 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------